Inference procedure has parameters:
Ice fuel: 200
Timeout: 60s
Convolution: right


Learning problem is:

env: {
elt -> {a, b}  ;  eltlist -> {cons, nil}  ;  nat -> {s, z}
}
definition:
{
(delete_one, F:
{() -> delete_one([x, nil, nil])
() -> delete_one([y, cons(y, r), r])
(delete_one([x, r, _mg]) /\ not eq_elt([x, y])) -> delete_one([x, cons(y, r), cons(y, _mg)])}
(delete_one([_ng, _og, _pg]) /\ delete_one([_ng, _og, _qg])) -> eq_eltlist([_pg, _qg])
)
(delete_all, F:
{() -> delete_all([x, nil, nil])
(delete_all([x, r, _sg]) /\ not eq_elt([x, y])) -> delete_all([x, cons(y, r), cons(y, _sg)])
(delete_all([y, r, _rg])) -> delete_all([y, cons(y, r), _rg])}
(delete_all([_tg, _ug, _vg]) /\ delete_all([_tg, _ug, _wg])) -> eq_eltlist([_vg, _wg])
)
(leqnat, P:
{() -> leqnat([z, n2])
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)])
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2])
(leqnat([s(nn1), z])) -> BOT}
)
(count, F:
{() -> count([x, nil, z])
(count([x, r, _yg]) /\ not eq_elt([x, y])) -> count([x, cons(y, r), _yg])
(count([y, r, _xg])) -> count([y, cons(y, r), s(_xg)])}
(count([_zg, _ah, _bh]) /\ count([_zg, _ah, _ch])) -> eq_nat([_bh, _ch])
)
}

properties:
{(count([x, l, _fh]) /\ delete_all([x, l, _eh]) /\ delete_one([x, l, _eh])) -> leqnat([_fh, s(z)])}


over-approximation: {count, delete_all, delete_one}
under-approximation: {leqnat}

Clause system for inference is:

{
() -> count([x, nil, z]) -> 0
() -> delete_all([x, nil, nil]) -> 0
() -> delete_one([x, nil, nil]) -> 0
() -> delete_one([y, cons(y, r), r]) -> 0
() -> leqnat([z, n2]) -> 0
(count([x, l, _fh]) /\ delete_all([x, l, _eh]) /\ delete_one([x, l, _eh])) -> leqnat([_fh, s(z)]) -> 0
(count([x, r, _yg]) /\ not eq_elt([x, y])) -> count([x, cons(y, r), _yg]) -> 0
(count([y, r, _xg])) -> count([y, cons(y, r), s(_xg)]) -> 0
(delete_all([x, r, _sg]) /\ not eq_elt([x, y])) -> delete_all([x, cons(y, r), cons(y, _sg)]) -> 0
(delete_all([y, r, _rg])) -> delete_all([y, cons(y, r), _rg]) -> 0
(delete_one([x, r, _mg]) /\ not eq_elt([x, y])) -> delete_one([x, cons(y, r), cons(y, _mg)]) -> 0
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 0
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 0
(leqnat([s(nn1), z])) -> BOT -> 0
}


Solving took 63.874867 seconds.
DontKnow. Stopped because: timeout
Working model:
|_
{
count -> 
{{{
Q={q_gen_1378, q_gen_1389, q_gen_1390, q_gen_1391, q_gen_1392, q_gen_1393, q_gen_1394, q_gen_1403, q_gen_1410, q_gen_1411, q_gen_1420, q_gen_1421, q_gen_1422, q_gen_1423, q_gen_1432, q_gen_1433, q_gen_1434, q_gen_1435, q_gen_1441, q_gen_1442, q_gen_1447, q_gen_1448, q_gen_1449, q_gen_1450, q_gen_1451, q_gen_1452, q_gen_1453, q_gen_1454, q_gen_1455, q_gen_1460, q_gen_1461, q_gen_1462, q_gen_1463, q_gen_1469, q_gen_1470, q_gen_1478, q_gen_1479, q_gen_1482, q_gen_1489, q_gen_1490, q_gen_1496, q_gen_1497, q_gen_1498, q_gen_1501, q_gen_1508, q_gen_1512, q_gen_1513, q_gen_1527, q_gen_1528, q_gen_1534, q_gen_1535, q_gen_1536, q_gen_1537, q_gen_1538, q_gen_1545, q_gen_1546, q_gen_1547, q_gen_1548, q_gen_1561, q_gen_1562, q_gen_1563, q_gen_1564, q_gen_1572, q_gen_1573, q_gen_1574, q_gen_1575, q_gen_1576, q_gen_1577, q_gen_1578},
Q_f={},
Delta=
{
<b>() -> q_gen_1391
<nil>() -> q_gen_1393
<a>() -> q_gen_1394
<cons>(q_gen_1391, q_gen_1393) -> q_gen_1423
<cons>(q_gen_1394, q_gen_1393) -> q_gen_1442
<cons>(q_gen_1394, q_gen_1442) -> q_gen_1546
<cons>(q_gen_1391, q_gen_1442) -> q_gen_1575
<nil, z>() -> q_gen_1390
<cons, z>(q_gen_1391, q_gen_1393) -> q_gen_1421
<cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1434
<cons, z>(q_gen_1394, q_gen_1393) -> q_gen_1448
<cons, s>(q_gen_1394, q_gen_1390) -> q_gen_1451
<cons, s>(q_gen_1394, q_gen_1448) -> q_gen_1461
<cons, s>(q_gen_1394, q_gen_1451) -> q_gen_1463
<cons, z>(q_gen_1391, q_gen_1442) -> q_gen_1470
<cons, s>(q_gen_1391, q_gen_1434) -> q_gen_1479
<cons, s>(q_gen_1391, q_gen_1448) -> q_gen_1490
<cons, s>(q_gen_1391, q_gen_1498) -> q_gen_1497
<cons, z>(q_gen_1394, q_gen_1442) -> q_gen_1498
<cons, z>(q_gen_1394, q_gen_1423) -> q_gen_1513
<cons, s>(q_gen_1394, q_gen_1434) -> q_gen_1536
<cons, s>(q_gen_1391, q_gen_1451) -> q_gen_1538
<cons, s>(q_gen_1394, q_gen_1421) -> q_gen_1548
<cons, s>(q_gen_1391, q_gen_1563) -> q_gen_1562
<cons, z>(q_gen_1391, q_gen_1546) -> q_gen_1563
<cons, z>(q_gen_1391, q_gen_1575) -> q_gen_1574
<cons, s>(q_gen_1394, q_gen_1536) -> q_gen_1578
<b, nil, z>() -> q_gen_1378
<b, cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1389
<b, cons, z>(q_gen_1394, q_gen_1393) -> q_gen_1392
<a, nil, z>() -> q_gen_1403
<a, cons, s>(q_gen_1394, q_gen_1390) -> q_gen_1410
<a, cons, z>(q_gen_1391, q_gen_1393) -> q_gen_1411
<a, cons, s>(q_gen_1394, q_gen_1421) -> q_gen_1420
<a, cons, z>(q_gen_1391, q_gen_1423) -> q_gen_1422
<a, cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1432
<a, cons, s>(q_gen_1394, q_gen_1434) -> q_gen_1433
<a, cons, s>(q_gen_1391, q_gen_1434) -> q_gen_1435
<b, cons, z>(q_gen_1394, q_gen_1442) -> q_gen_1441
<b, cons, s>(q_gen_1391, q_gen_1448) -> q_gen_1447
<a, cons, s>(q_gen_1391, q_gen_1448) -> q_gen_1449
<a, cons, s>(q_gen_1394, q_gen_1451) -> q_gen_1450
<a, cons, s>(q_gen_1391, q_gen_1451) -> q_gen_1452
<b, cons, s>(q_gen_1394, q_gen_1421) -> q_gen_1453
<b, cons, s>(q_gen_1391, q_gen_1434) -> q_gen_1454
<b, cons, s>(q_gen_1391, q_gen_1451) -> q_gen_1455
<a, cons, s>(q_gen_1391, q_gen_1461) -> q_gen_1460
<a, cons, s>(q_gen_1394, q_gen_1463) -> q_gen_1462
<a, cons, s>(q_gen_1391, q_gen_1470) -> q_gen_1469
<b, cons, s>(q_gen_1391, q_gen_1479) -> q_gen_1478
<b, cons, s>(q_gen_1394, q_gen_1470) -> q_gen_1482
<b, cons, s>(q_gen_1391, q_gen_1490) -> q_gen_1489
<a, cons, s>(q_gen_1391, q_gen_1497) -> q_gen_1496
<a, cons, s>(q_gen_1391, q_gen_1490) -> q_gen_1501
<a, cons, s>(q_gen_1394, q_gen_1490) -> q_gen_1508
<a, cons, s>(q_gen_1391, q_gen_1513) -> q_gen_1512
<b, cons, s>(q_gen_1394, q_gen_1448) -> q_gen_1527
<b, cons, s>(q_gen_1394, q_gen_1498) -> q_gen_1528
<b, cons, s>(q_gen_1394, q_gen_1434) -> q_gen_1534
<b, cons, s>(q_gen_1391, q_gen_1536) -> q_gen_1535
<b, cons, s>(q_gen_1391, q_gen_1538) -> q_gen_1537
<b, cons, z>(q_gen_1394, q_gen_1546) -> q_gen_1545
<a, cons, s>(q_gen_1394, q_gen_1548) -> q_gen_1547
<a, cons, s>(q_gen_1391, q_gen_1562) -> q_gen_1561
<a, cons, s>(q_gen_1391, q_gen_1548) -> q_gen_1564
<b, cons, s>(q_gen_1391, q_gen_1470) -> q_gen_1572
<b, cons, s>(q_gen_1394, q_gen_1574) -> q_gen_1573
<a, cons, s>(q_gen_1394, q_gen_1536) -> q_gen_1576
<a, cons, s>(q_gen_1394, q_gen_1578) -> q_gen_1577
}

Datatype: <elt, eltlist, nat>
Convolution form: right
}}}
  ;  delete_all -> 
{{{
Q={q_gen_1377, q_gen_1383, q_gen_1384, q_gen_1385, q_gen_1386, q_gen_1387, q_gen_1388, q_gen_1402, q_gen_1406, q_gen_1407, q_gen_1408, q_gen_1409, q_gen_1416, q_gen_1417, q_gen_1418, q_gen_1419, q_gen_1427, q_gen_1428, q_gen_1429, q_gen_1430, q_gen_1431, q_gen_1436, q_gen_1445, q_gen_1446, q_gen_1456, q_gen_1457, q_gen_1464, q_gen_1466, q_gen_1467, q_gen_1468, q_gen_1476, q_gen_1477, q_gen_1480, q_gen_1487, q_gen_1488, q_gen_1491, q_gen_1492, q_gen_1493, q_gen_1494, q_gen_1495, q_gen_1499, q_gen_1500, q_gen_1502, q_gen_1503, q_gen_1505, q_gen_1506, q_gen_1507, q_gen_1511, q_gen_1514, q_gen_1515, q_gen_1517, q_gen_1518, q_gen_1519, q_gen_1520, q_gen_1521, q_gen_1525, q_gen_1539, q_gen_1540, q_gen_1544, q_gen_1550, q_gen_1551, q_gen_1552, q_gen_1553, q_gen_1554, q_gen_1555, q_gen_1556, q_gen_1557, q_gen_1558, q_gen_1559, q_gen_1560, q_gen_1565, q_gen_1567, q_gen_1568, q_gen_1569, q_gen_1570, q_gen_1571, q_gen_1579, q_gen_1581, q_gen_1582},
Q_f={},
Delta=
{
<nil>() -> q_gen_1384
<b>() -> q_gen_1385
<a>() -> q_gen_1407
<cons>(q_gen_1385, q_gen_1384) -> q_gen_1417
<cons>(q_gen_1407, q_gen_1384) -> q_gen_1495
<nil, nil>() -> q_gen_1387
<a, a>() -> q_gen_1388
<b, b>() -> q_gen_1409
<cons, nil>(q_gen_1407, q_gen_1384) -> q_gen_1419
<cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1428
<a, b>() -> q_gen_1429
<cons, cons>(q_gen_1409, q_gen_1387) -> q_gen_1431
<b, a>() -> q_gen_1446
<cons, cons>(q_gen_1429, q_gen_1387) -> q_gen_1457
<cons, cons>(q_gen_1429, q_gen_1428) -> q_gen_1468
<cons, nil>(q_gen_1407, q_gen_1495) -> q_gen_1494
<cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1500
<cons, cons>(q_gen_1446, q_gen_1457) -> q_gen_1503
<cons, cons>(q_gen_1409, q_gen_1419) -> q_gen_1507
<cons, cons>(q_gen_1446, q_gen_1387) -> q_gen_1515
<cons, nil>(q_gen_1385, q_gen_1495) -> q_gen_1518
<cons, cons>(q_gen_1388, q_gen_1507) -> q_gen_1521
<cons, cons>(q_gen_1446, q_gen_1419) -> q_gen_1540
<cons, cons>(q_gen_1409, q_gen_1553) -> q_gen_1552
<cons, cons>(q_gen_1388, q_gen_1419) -> q_gen_1553
<cons, cons>(q_gen_1409, q_gen_1556) -> q_gen_1555
<cons, cons>(q_gen_1446, q_gen_1494) -> q_gen_1556
<cons, cons>(q_gen_1446, q_gen_1500) -> q_gen_1558
<cons, cons>(q_gen_1388, q_gen_1558) -> q_gen_1560
<cons, cons>(q_gen_1429, q_gen_1419) -> q_gen_1571
<cons, nil>(q_gen_1407, q_gen_1417) -> q_gen_1582
<b, nil, nil>() -> q_gen_1377
<b, cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1383
<b, cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1386
<a, nil, nil>() -> q_gen_1402
<a, cons, nil>(q_gen_1407, q_gen_1384) -> q_gen_1406
<a, cons, cons>(q_gen_1409, q_gen_1387) -> q_gen_1408
<b, cons, nil>(q_gen_1385, q_gen_1417) -> q_gen_1416
<a, cons, cons>(q_gen_1409, q_gen_1419) -> q_gen_1418
<a, cons, cons>(q_gen_1429, q_gen_1428) -> q_gen_1427
<a, cons, cons>(q_gen_1409, q_gen_1431) -> q_gen_1430
<a, cons, cons>(q_gen_1409, q_gen_1428) -> q_gen_1436
<b, cons, cons>(q_gen_1446, q_gen_1419) -> q_gen_1445
<b, cons, cons>(q_gen_1409, q_gen_1457) -> q_gen_1456
<a, cons, cons>(q_gen_1429, q_gen_1457) -> q_gen_1464
<a, cons, cons>(q_gen_1429, q_gen_1431) -> q_gen_1466
<a, cons, cons>(q_gen_1429, q_gen_1468) -> q_gen_1467
<b, cons, cons>(q_gen_1429, q_gen_1387) -> q_gen_1476
<b, cons, cons>(q_gen_1388, q_gen_1457) -> q_gen_1477
<b, cons, cons>(q_gen_1409, q_gen_1419) -> q_gen_1480
<b, cons, nil>(q_gen_1407, q_gen_1384) -> q_gen_1487
<b, cons, cons>(q_gen_1388, q_gen_1419) -> q_gen_1488
<b, cons, cons>(q_gen_1409, q_gen_1428) -> q_gen_1491
<b, cons, cons>(q_gen_1429, q_gen_1419) -> q_gen_1492
<b, cons, cons>(q_gen_1409, q_gen_1494) -> q_gen_1493
<b, cons, cons>(q_gen_1388, q_gen_1500) -> q_gen_1499
<a, cons, cons>(q_gen_1409, q_gen_1503) -> q_gen_1502
<a, cons, cons>(q_gen_1409, q_gen_1457) -> q_gen_1505
<a, cons, cons>(q_gen_1429, q_gen_1507) -> q_gen_1506
<a, cons, cons>(q_gen_1409, q_gen_1507) -> q_gen_1511
<b, cons, cons>(q_gen_1446, q_gen_1515) -> q_gen_1514
<b, cons, cons>(q_gen_1409, q_gen_1518) -> q_gen_1517
<b, cons, cons>(q_gen_1388, q_gen_1507) -> q_gen_1519
<b, cons, cons>(q_gen_1388, q_gen_1521) -> q_gen_1520
<a, cons, cons>(q_gen_1388, q_gen_1457) -> q_gen_1525
<b, cons, cons>(q_gen_1446, q_gen_1540) -> q_gen_1539
<b, cons, cons>(q_gen_1446, q_gen_1518) -> q_gen_1544
<b, cons, cons>(q_gen_1388, q_gen_1428) -> q_gen_1550
<b, cons, cons>(q_gen_1446, q_gen_1552) -> q_gen_1551
<b, cons, cons>(q_gen_1446, q_gen_1555) -> q_gen_1554
<b, cons, cons>(q_gen_1388, q_gen_1558) -> q_gen_1557
<b, cons, cons>(q_gen_1388, q_gen_1560) -> q_gen_1559
<a, cons, cons>(q_gen_1409, q_gen_1468) -> q_gen_1565
<a, cons, cons>(q_gen_1429, q_gen_1500) -> q_gen_1567
<a, cons, cons>(q_gen_1429, q_gen_1553) -> q_gen_1568
<a, cons, cons>(q_gen_1429, q_gen_1419) -> q_gen_1569
<a, cons, cons>(q_gen_1409, q_gen_1571) -> q_gen_1570
<b, cons, cons>(q_gen_1388, q_gen_1431) -> q_gen_1579
<a, cons, cons>(q_gen_1429, q_gen_1582) -> q_gen_1581
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  delete_one -> 
{{{
Q={q_gen_1373, q_gen_1374, q_gen_1375, q_gen_1376, q_gen_1380, q_gen_1381, q_gen_1382, q_gen_1399, q_gen_1400, q_gen_1401, q_gen_1404, q_gen_1405, q_gen_1412, q_gen_1413, q_gen_1414, q_gen_1415, q_gen_1424, q_gen_1425, q_gen_1426, q_gen_1437, q_gen_1440, q_gen_1443, q_gen_1444, q_gen_1458, q_gen_1459, q_gen_1465, q_gen_1471, q_gen_1472, q_gen_1473, q_gen_1474, q_gen_1475, q_gen_1481, q_gen_1483, q_gen_1484, q_gen_1485, q_gen_1486, q_gen_1504, q_gen_1509, q_gen_1510, q_gen_1516, q_gen_1522, q_gen_1523, q_gen_1524, q_gen_1526, q_gen_1529, q_gen_1530, q_gen_1531, q_gen_1532, q_gen_1533, q_gen_1541, q_gen_1549, q_gen_1566, q_gen_1580, q_gen_1583},
Q_f={},
Delta=
{
<nil>() -> q_gen_1374
<b>() -> q_gen_1375
<a>() -> q_gen_1400
<nil, nil>() -> q_gen_1381
<a, a>() -> q_gen_1382
<b, b>() -> q_gen_1405
<cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1413
<cons, cons>(q_gen_1405, q_gen_1381) -> q_gen_1415
<cons, nil>(q_gen_1400, q_gen_1374) -> q_gen_1425
<b, a>() -> q_gen_1426
<a, b>() -> q_gen_1444
<cons, cons>(q_gen_1444, q_gen_1381) -> q_gen_1459
<cons, cons>(q_gen_1444, q_gen_1413) -> q_gen_1472
<cons, cons>(q_gen_1426, q_gen_1381) -> q_gen_1475
<cons, cons>(q_gen_1426, q_gen_1459) -> q_gen_1486
<cons, cons>(q_gen_1426, q_gen_1425) -> q_gen_1510
<cons, cons>(q_gen_1405, q_gen_1413) -> q_gen_1524
<cons, cons>(q_gen_1444, q_gen_1531) -> q_gen_1530
<cons, cons>(q_gen_1426, q_gen_1532) -> q_gen_1531
<cons, cons>(q_gen_1382, q_gen_1533) -> q_gen_1532
<cons, cons>(q_gen_1382, q_gen_1425) -> q_gen_1533
<b, cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1373
<b, nil, nil>() -> q_gen_1376
<b, cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1380
<a, cons, nil>(q_gen_1400, q_gen_1374) -> q_gen_1399
<a, nil, nil>() -> q_gen_1401
<a, cons, cons>(q_gen_1405, q_gen_1381) -> q_gen_1404
<b, cons, cons>(q_gen_1405, q_gen_1413) -> q_gen_1412
<a, cons, cons>(q_gen_1405, q_gen_1415) -> q_gen_1414
<b, cons, cons>(q_gen_1426, q_gen_1425) -> q_gen_1424
<a, cons, cons>(q_gen_1405, q_gen_1413) -> q_gen_1437
<a, cons, cons>(q_gen_1405, q_gen_1425) -> q_gen_1440
<a, cons, cons>(q_gen_1444, q_gen_1413) -> q_gen_1443
<b, cons, cons>(q_gen_1405, q_gen_1459) -> q_gen_1458
<a, cons, cons>(q_gen_1444, q_gen_1459) -> q_gen_1465
<b, cons, cons>(q_gen_1426, q_gen_1472) -> q_gen_1471
<b, cons, cons>(q_gen_1426, q_gen_1381) -> q_gen_1473
<b, cons, cons>(q_gen_1382, q_gen_1475) -> q_gen_1474
<b, cons, cons>(q_gen_1405, q_gen_1425) -> q_gen_1481
<a, cons, cons>(q_gen_1382, q_gen_1425) -> q_gen_1483
<b, cons, cons>(q_gen_1426, q_gen_1459) -> q_gen_1484
<b, cons, cons>(q_gen_1382, q_gen_1486) -> q_gen_1485
<a, cons, cons>(q_gen_1405, q_gen_1486) -> q_gen_1504
<a, cons, cons>(q_gen_1444, q_gen_1510) -> q_gen_1509
<b, cons, cons>(q_gen_1426, q_gen_1475) -> q_gen_1516
<b, cons, cons>(q_gen_1405, q_gen_1510) -> q_gen_1522
<a, cons, cons>(q_gen_1405, q_gen_1524) -> q_gen_1523
<a, cons, cons>(q_gen_1382, q_gen_1459) -> q_gen_1526
<a, cons, cons>(q_gen_1382, q_gen_1530) -> q_gen_1529
<b, cons, cons>(q_gen_1426, q_gen_1510) -> q_gen_1541
<a, cons, cons>(q_gen_1444, q_gen_1472) -> q_gen_1549
<a, cons, cons>(q_gen_1405, q_gen_1472) -> q_gen_1566
<b, cons, cons>(q_gen_1382, q_gen_1415) -> q_gen_1580
<b, cons, cons>(q_gen_1426, q_gen_1533) -> q_gen_1583
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  leqnat -> 
{{{
Q={q_gen_1372, q_gen_1379, q_gen_1395, q_gen_1396, q_gen_1397, q_gen_1398, q_gen_1438, q_gen_1439, q_gen_1542, q_gen_1543},
Q_f={},
Delta=
{
<z>() -> q_gen_1396
<s>(q_gen_1396) -> q_gen_1398
<z, z>() -> q_gen_1372
<s, s>(q_gen_1372) -> q_gen_1379
<z, s>(q_gen_1396) -> q_gen_1395
<z, s>(q_gen_1398) -> q_gen_1397
<s, s>(q_gen_1439) -> q_gen_1438
<s, z>(q_gen_1396) -> q_gen_1439
<s, s>(q_gen_1543) -> q_gen_1542
<s, z>(q_gen_1398) -> q_gen_1543
}

Datatype: <nat, nat>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist, eq_nat}
_|

-------------------
STEPS:
-------------------------------------------
Step 0, which took 0.005887 s (model generation: 0.005361,  model checking: 0.000526):

Model:
|_
{
count -> 
{{{
Q={},
Q_f={},
Delta=
{

}

Datatype: <elt, eltlist, nat>
Convolution form: right
}}}
  ;  delete_all -> 
{{{
Q={},
Q_f={},
Delta=
{

}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  delete_one -> 
{{{
Q={},
Q_f={},
Delta=
{

}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  leqnat -> 
{{{
Q={},
Q_f={},
Delta=
{

}

Datatype: <nat, nat>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist, eq_nat}
_|

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 0
() -> delete_all([x, nil, nil]) -> 0
() -> delete_one([x, nil, nil]) -> 0
() -> delete_one([y, cons(y, r), r]) -> 0
() -> leqnat([z, n2]) -> 3
(count([x, l, _fh]) /\ delete_all([x, l, _eh]) /\ delete_one([x, l, _eh])) -> leqnat([_fh, s(z)]) -> 1
(count([x, r, _yg]) /\ not eq_elt([x, y])) -> count([x, cons(y, r), _yg]) -> 1
(count([y, r, _xg])) -> count([y, cons(y, r), s(_xg)]) -> 1
(delete_all([x, r, _sg]) /\ not eq_elt([x, y])) -> delete_all([x, cons(y, r), cons(y, _sg)]) -> 1
(delete_all([y, r, _rg])) -> delete_all([y, cons(y, r), _rg]) -> 1
(delete_one([x, r, _mg]) /\ not eq_elt([x, y])) -> delete_one([x, cons(y, r), cons(y, _mg)]) -> 1
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 1
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 1
(leqnat([s(nn1), z])) -> BOT -> 1
}
Sat witness: Found: (() -> leqnat([z, n2]), {
n2 -> z
})

-------------------------------------------
Step 1, which took 0.007185 s (model generation: 0.005764,  model checking: 0.001421):

Model:
|_
{
count -> 
{{{
Q={},
Q_f={},
Delta=
{

}

Datatype: <elt, eltlist, nat>
Convolution form: right
}}}
  ;  delete_all -> 
{{{
Q={},
Q_f={},
Delta=
{

}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  delete_one -> 
{{{
Q={},
Q_f={},
Delta=
{

}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  leqnat -> 
{{{
Q={q_gen_1372},
Q_f={q_gen_1372},
Delta=
{
<z, z>() -> q_gen_1372
}

Datatype: <nat, nat>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist, eq_nat}
_|

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 0
() -> delete_all([x, nil, nil]) -> 0
() -> delete_one([x, nil, nil]) -> 0
() -> delete_one([y, cons(y, r), r]) -> 3
() -> leqnat([z, n2]) -> 3
(count([x, l, _fh]) /\ delete_all([x, l, _eh]) /\ delete_one([x, l, _eh])) -> leqnat([_fh, s(z)]) -> 1
(count([x, r, _yg]) /\ not eq_elt([x, y])) -> count([x, cons(y, r), _yg]) -> 1
(count([y, r, _xg])) -> count([y, cons(y, r), s(_xg)]) -> 1
(delete_all([x, r, _sg]) /\ not eq_elt([x, y])) -> delete_all([x, cons(y, r), cons(y, _sg)]) -> 1
(delete_all([y, r, _rg])) -> delete_all([y, cons(y, r), _rg]) -> 1
(delete_one([x, r, _mg]) /\ not eq_elt([x, y])) -> delete_one([x, cons(y, r), cons(y, _mg)]) -> 1
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 1
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 1
(leqnat([s(nn1), z])) -> BOT -> 1
}
Sat witness: Found: (() -> delete_one([y, cons(y, r), r]), {
r -> nil  ;  y -> b
})

-------------------------------------------
Step 2, which took 0.006165 s (model generation: 0.005997,  model checking: 0.000168):

Model:
|_
{
count -> 
{{{
Q={},
Q_f={},
Delta=
{

}

Datatype: <elt, eltlist, nat>
Convolution form: right
}}}
  ;  delete_all -> 
{{{
Q={},
Q_f={},
Delta=
{

}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  delete_one -> 
{{{
Q={q_gen_1373, q_gen_1374, q_gen_1375},
Q_f={q_gen_1373},
Delta=
{
<nil>() -> q_gen_1374
<b>() -> q_gen_1375
<b, cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1373
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  leqnat -> 
{{{
Q={q_gen_1372},
Q_f={q_gen_1372},
Delta=
{
<z, z>() -> q_gen_1372
}

Datatype: <nat, nat>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist, eq_nat}
_|

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 0
() -> delete_all([x, nil, nil]) -> 0
() -> delete_one([x, nil, nil]) -> 3
() -> delete_one([y, cons(y, r), r]) -> 3
() -> leqnat([z, n2]) -> 3
(count([x, l, _fh]) /\ delete_all([x, l, _eh]) /\ delete_one([x, l, _eh])) -> leqnat([_fh, s(z)]) -> 1
(count([x, r, _yg]) /\ not eq_elt([x, y])) -> count([x, cons(y, r), _yg]) -> 1
(count([y, r, _xg])) -> count([y, cons(y, r), s(_xg)]) -> 1
(delete_all([x, r, _sg]) /\ not eq_elt([x, y])) -> delete_all([x, cons(y, r), cons(y, _sg)]) -> 1
(delete_all([y, r, _rg])) -> delete_all([y, cons(y, r), _rg]) -> 1
(delete_one([x, r, _mg]) /\ not eq_elt([x, y])) -> delete_one([x, cons(y, r), cons(y, _mg)]) -> 1
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 1
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 1
(leqnat([s(nn1), z])) -> BOT -> 1
}
Sat witness: Found: (() -> delete_one([x, nil, nil]), {
x -> b
})

-------------------------------------------
Step 3, which took 0.006056 s (model generation: 0.005943,  model checking: 0.000113):

Model:
|_
{
count -> 
{{{
Q={},
Q_f={},
Delta=
{

}

Datatype: <elt, eltlist, nat>
Convolution form: right
}}}
  ;  delete_all -> 
{{{
Q={},
Q_f={},
Delta=
{

}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  delete_one -> 
{{{
Q={q_gen_1373, q_gen_1374, q_gen_1375},
Q_f={q_gen_1373},
Delta=
{
<nil>() -> q_gen_1374
<b>() -> q_gen_1375
<b, cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1373
<b, nil, nil>() -> q_gen_1373
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  leqnat -> 
{{{
Q={q_gen_1372},
Q_f={q_gen_1372},
Delta=
{
<z, z>() -> q_gen_1372
}

Datatype: <nat, nat>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist, eq_nat}
_|

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 0
() -> delete_all([x, nil, nil]) -> 3
() -> delete_one([x, nil, nil]) -> 3
() -> delete_one([y, cons(y, r), r]) -> 3
() -> leqnat([z, n2]) -> 3
(count([x, l, _fh]) /\ delete_all([x, l, _eh]) /\ delete_one([x, l, _eh])) -> leqnat([_fh, s(z)]) -> 1
(count([x, r, _yg]) /\ not eq_elt([x, y])) -> count([x, cons(y, r), _yg]) -> 1
(count([y, r, _xg])) -> count([y, cons(y, r), s(_xg)]) -> 1
(delete_all([x, r, _sg]) /\ not eq_elt([x, y])) -> delete_all([x, cons(y, r), cons(y, _sg)]) -> 1
(delete_all([y, r, _rg])) -> delete_all([y, cons(y, r), _rg]) -> 1
(delete_one([x, r, _mg]) /\ not eq_elt([x, y])) -> delete_one([x, cons(y, r), cons(y, _mg)]) -> 1
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 1
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 1
(leqnat([s(nn1), z])) -> BOT -> 1
}
Sat witness: Found: (() -> delete_all([x, nil, nil]), {
x -> b
})

-------------------------------------------
Step 4, which took 0.005847 s (model generation: 0.005695,  model checking: 0.000152):

Model:
|_
{
count -> 
{{{
Q={},
Q_f={},
Delta=
{

}

Datatype: <elt, eltlist, nat>
Convolution form: right
}}}
  ;  delete_all -> 
{{{
Q={q_gen_1377},
Q_f={q_gen_1377},
Delta=
{
<b, nil, nil>() -> q_gen_1377
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  delete_one -> 
{{{
Q={q_gen_1373, q_gen_1374, q_gen_1375},
Q_f={q_gen_1373},
Delta=
{
<nil>() -> q_gen_1374
<b>() -> q_gen_1375
<b, cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1373
<b, nil, nil>() -> q_gen_1373
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  leqnat -> 
{{{
Q={q_gen_1372},
Q_f={q_gen_1372},
Delta=
{
<z, z>() -> q_gen_1372
}

Datatype: <nat, nat>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist, eq_nat}
_|

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 3
() -> delete_all([x, nil, nil]) -> 3
() -> delete_one([x, nil, nil]) -> 3
() -> delete_one([y, cons(y, r), r]) -> 3
() -> leqnat([z, n2]) -> 3
(count([x, l, _fh]) /\ delete_all([x, l, _eh]) /\ delete_one([x, l, _eh])) -> leqnat([_fh, s(z)]) -> 1
(count([x, r, _yg]) /\ not eq_elt([x, y])) -> count([x, cons(y, r), _yg]) -> 1
(count([y, r, _xg])) -> count([y, cons(y, r), s(_xg)]) -> 1
(delete_all([x, r, _sg]) /\ not eq_elt([x, y])) -> delete_all([x, cons(y, r), cons(y, _sg)]) -> 1
(delete_all([y, r, _rg])) -> delete_all([y, cons(y, r), _rg]) -> 1
(delete_one([x, r, _mg]) /\ not eq_elt([x, y])) -> delete_one([x, cons(y, r), cons(y, _mg)]) -> 1
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 1
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 1
(leqnat([s(nn1), z])) -> BOT -> 1
}
Sat witness: Found: (() -> count([x, nil, z]), {
x -> b
})

-------------------------------------------
Step 5, which took 0.006495 s (model generation: 0.006396,  model checking: 0.000099):

Model:
|_
{
count -> 
{{{
Q={q_gen_1378},
Q_f={q_gen_1378},
Delta=
{
<b, nil, z>() -> q_gen_1378
}

Datatype: <elt, eltlist, nat>
Convolution form: right
}}}
  ;  delete_all -> 
{{{
Q={q_gen_1377},
Q_f={q_gen_1377},
Delta=
{
<b, nil, nil>() -> q_gen_1377
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  delete_one -> 
{{{
Q={q_gen_1373, q_gen_1374, q_gen_1375},
Q_f={q_gen_1373},
Delta=
{
<nil>() -> q_gen_1374
<b>() -> q_gen_1375
<b, cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1373
<b, nil, nil>() -> q_gen_1373
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  leqnat -> 
{{{
Q={q_gen_1372},
Q_f={q_gen_1372},
Delta=
{
<z, z>() -> q_gen_1372
}

Datatype: <nat, nat>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist, eq_nat}
_|

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 3
() -> delete_all([x, nil, nil]) -> 3
() -> delete_one([x, nil, nil]) -> 3
() -> delete_one([y, cons(y, r), r]) -> 3
() -> leqnat([z, n2]) -> 3
(count([x, l, _fh]) /\ delete_all([x, l, _eh]) /\ delete_one([x, l, _eh])) -> leqnat([_fh, s(z)]) -> 1
(count([x, r, _yg]) /\ not eq_elt([x, y])) -> count([x, cons(y, r), _yg]) -> 1
(count([y, r, _xg])) -> count([y, cons(y, r), s(_xg)]) -> 1
(delete_all([x, r, _sg]) /\ not eq_elt([x, y])) -> delete_all([x, cons(y, r), cons(y, _sg)]) -> 1
(delete_all([y, r, _rg])) -> delete_all([y, cons(y, r), _rg]) -> 1
(delete_one([x, r, _mg]) /\ not eq_elt([x, y])) -> delete_one([x, cons(y, r), cons(y, _mg)]) -> 1
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 4
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 2
(leqnat([s(nn1), z])) -> BOT -> 2
}
Sat witness: Found: ((leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]), {
nn1 -> z  ;  nn2 -> z
})

-------------------------------------------
Step 6, which took 0.007846 s (model generation: 0.005443,  model checking: 0.002403):

Model:
|_
{
count -> 
{{{
Q={q_gen_1378},
Q_f={q_gen_1378},
Delta=
{
<b, nil, z>() -> q_gen_1378
}

Datatype: <elt, eltlist, nat>
Convolution form: right
}}}
  ;  delete_all -> 
{{{
Q={q_gen_1377},
Q_f={q_gen_1377},
Delta=
{
<b, nil, nil>() -> q_gen_1377
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  delete_one -> 
{{{
Q={q_gen_1373, q_gen_1374, q_gen_1375},
Q_f={q_gen_1373},
Delta=
{
<nil>() -> q_gen_1374
<b>() -> q_gen_1375
<b, cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1373
<b, nil, nil>() -> q_gen_1373
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  leqnat -> 
{{{
Q={q_gen_1372},
Q_f={q_gen_1372},
Delta=
{
<s, s>(q_gen_1372) -> q_gen_1372
<z, z>() -> q_gen_1372
}

Datatype: <nat, nat>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist, eq_nat}
_|

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 3
() -> delete_all([x, nil, nil]) -> 3
() -> delete_one([x, nil, nil]) -> 3
() -> delete_one([y, cons(y, r), r]) -> 3
() -> leqnat([z, n2]) -> 3
(count([x, l, _fh]) /\ delete_all([x, l, _eh]) /\ delete_one([x, l, _eh])) -> leqnat([_fh, s(z)]) -> 1
(count([x, r, _yg]) /\ not eq_elt([x, y])) -> count([x, cons(y, r), _yg]) -> 1
(count([y, r, _xg])) -> count([y, cons(y, r), s(_xg)]) -> 1
(delete_all([x, r, _sg]) /\ not eq_elt([x, y])) -> delete_all([x, cons(y, r), cons(y, _sg)]) -> 1
(delete_all([y, r, _rg])) -> delete_all([y, cons(y, r), _rg]) -> 1
(delete_one([x, r, _mg]) /\ not eq_elt([x, y])) -> delete_one([x, cons(y, r), cons(y, _mg)]) -> 4
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 4
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 2
(leqnat([s(nn1), z])) -> BOT -> 2
}
Sat witness: Found: ((delete_one([x, r, _mg]) /\ not eq_elt([x, y])) -> delete_one([x, cons(y, r), cons(y, _mg)]), {
_mg -> nil  ;  r -> nil  ;  x -> b  ;  y -> a
})

-------------------------------------------
Step 7, which took 0.006691 s (model generation: 0.006499,  model checking: 0.000192):

Model:
|_
{
count -> 
{{{
Q={q_gen_1378},
Q_f={q_gen_1378},
Delta=
{
<b, nil, z>() -> q_gen_1378
}

Datatype: <elt, eltlist, nat>
Convolution form: right
}}}
  ;  delete_all -> 
{{{
Q={q_gen_1377},
Q_f={q_gen_1377},
Delta=
{
<b, nil, nil>() -> q_gen_1377
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  delete_one -> 
{{{
Q={q_gen_1373, q_gen_1374, q_gen_1375, q_gen_1381, q_gen_1382},
Q_f={q_gen_1373},
Delta=
{
<nil>() -> q_gen_1374
<b>() -> q_gen_1375
<nil, nil>() -> q_gen_1381
<a, a>() -> q_gen_1382
<b, cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1373
<b, cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1373
<b, nil, nil>() -> q_gen_1373
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  leqnat -> 
{{{
Q={q_gen_1372},
Q_f={q_gen_1372},
Delta=
{
<s, s>(q_gen_1372) -> q_gen_1372
<z, z>() -> q_gen_1372
}

Datatype: <nat, nat>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist, eq_nat}
_|

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 3
() -> delete_all([x, nil, nil]) -> 3
() -> delete_one([x, nil, nil]) -> 3
() -> delete_one([y, cons(y, r), r]) -> 3
() -> leqnat([z, n2]) -> 3
(count([x, l, _fh]) /\ delete_all([x, l, _eh]) /\ delete_one([x, l, _eh])) -> leqnat([_fh, s(z)]) -> 1
(count([x, r, _yg]) /\ not eq_elt([x, y])) -> count([x, cons(y, r), _yg]) -> 1
(count([y, r, _xg])) -> count([y, cons(y, r), s(_xg)]) -> 1
(delete_all([x, r, _sg]) /\ not eq_elt([x, y])) -> delete_all([x, cons(y, r), cons(y, _sg)]) -> 1
(delete_all([y, r, _rg])) -> delete_all([y, cons(y, r), _rg]) -> 4
(delete_one([x, r, _mg]) /\ not eq_elt([x, y])) -> delete_one([x, cons(y, r), cons(y, _mg)]) -> 4
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 4
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 2
(leqnat([s(nn1), z])) -> BOT -> 2
}
Sat witness: Found: ((delete_all([y, r, _rg])) -> delete_all([y, cons(y, r), _rg]), {
_rg -> nil  ;  r -> nil  ;  y -> b
})

-------------------------------------------
Step 8, which took 0.006631 s (model generation: 0.006357,  model checking: 0.000274):

Model:
|_
{
count -> 
{{{
Q={q_gen_1378},
Q_f={q_gen_1378},
Delta=
{
<b, nil, z>() -> q_gen_1378
}

Datatype: <elt, eltlist, nat>
Convolution form: right
}}}
  ;  delete_all -> 
{{{
Q={q_gen_1377, q_gen_1384, q_gen_1385},
Q_f={q_gen_1377},
Delta=
{
<nil>() -> q_gen_1384
<b>() -> q_gen_1385
<b, cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1377
<b, nil, nil>() -> q_gen_1377
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  delete_one -> 
{{{
Q={q_gen_1373, q_gen_1374, q_gen_1375, q_gen_1381, q_gen_1382},
Q_f={q_gen_1373},
Delta=
{
<nil>() -> q_gen_1374
<b>() -> q_gen_1375
<nil, nil>() -> q_gen_1381
<a, a>() -> q_gen_1382
<b, cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1373
<b, cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1373
<b, nil, nil>() -> q_gen_1373
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  leqnat -> 
{{{
Q={q_gen_1372},
Q_f={q_gen_1372},
Delta=
{
<s, s>(q_gen_1372) -> q_gen_1372
<z, z>() -> q_gen_1372
}

Datatype: <nat, nat>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist, eq_nat}
_|

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 3
() -> delete_all([x, nil, nil]) -> 3
() -> delete_one([x, nil, nil]) -> 3
() -> delete_one([y, cons(y, r), r]) -> 3
() -> leqnat([z, n2]) -> 3
(count([x, l, _fh]) /\ delete_all([x, l, _eh]) /\ delete_one([x, l, _eh])) -> leqnat([_fh, s(z)]) -> 1
(count([x, r, _yg]) /\ not eq_elt([x, y])) -> count([x, cons(y, r), _yg]) -> 1
(count([y, r, _xg])) -> count([y, cons(y, r), s(_xg)]) -> 1
(delete_all([x, r, _sg]) /\ not eq_elt([x, y])) -> delete_all([x, cons(y, r), cons(y, _sg)]) -> 4
(delete_all([y, r, _rg])) -> delete_all([y, cons(y, r), _rg]) -> 4
(delete_one([x, r, _mg]) /\ not eq_elt([x, y])) -> delete_one([x, cons(y, r), cons(y, _mg)]) -> 4
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 4
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 2
(leqnat([s(nn1), z])) -> BOT -> 2
}
Sat witness: Found: ((delete_all([x, r, _sg]) /\ not eq_elt([x, y])) -> delete_all([x, cons(y, r), cons(y, _sg)]), {
_sg -> nil  ;  r -> nil  ;  x -> b  ;  y -> a
})

-------------------------------------------
Step 9, which took 0.008906 s (model generation: 0.008797,  model checking: 0.000109):

Model:
|_
{
count -> 
{{{
Q={q_gen_1378},
Q_f={q_gen_1378},
Delta=
{
<b, nil, z>() -> q_gen_1378
}

Datatype: <elt, eltlist, nat>
Convolution form: right
}}}
  ;  delete_all -> 
{{{
Q={q_gen_1377, q_gen_1384, q_gen_1385, q_gen_1387, q_gen_1388},
Q_f={q_gen_1377},
Delta=
{
<nil>() -> q_gen_1384
<b>() -> q_gen_1385
<nil, nil>() -> q_gen_1387
<a, a>() -> q_gen_1388
<b, cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1377
<b, cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1377
<b, nil, nil>() -> q_gen_1377
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  delete_one -> 
{{{
Q={q_gen_1373, q_gen_1374, q_gen_1375, q_gen_1381, q_gen_1382},
Q_f={q_gen_1373},
Delta=
{
<nil>() -> q_gen_1374
<b>() -> q_gen_1375
<nil, nil>() -> q_gen_1381
<a, a>() -> q_gen_1382
<b, cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1373
<b, cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1373
<b, nil, nil>() -> q_gen_1373
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  leqnat -> 
{{{
Q={q_gen_1372},
Q_f={q_gen_1372},
Delta=
{
<s, s>(q_gen_1372) -> q_gen_1372
<z, z>() -> q_gen_1372
}

Datatype: <nat, nat>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist, eq_nat}
_|

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 3
() -> delete_all([x, nil, nil]) -> 3
() -> delete_one([x, nil, nil]) -> 3
() -> delete_one([y, cons(y, r), r]) -> 3
() -> leqnat([z, n2]) -> 3
(count([x, l, _fh]) /\ delete_all([x, l, _eh]) /\ delete_one([x, l, _eh])) -> leqnat([_fh, s(z)]) -> 1
(count([x, r, _yg]) /\ not eq_elt([x, y])) -> count([x, cons(y, r), _yg]) -> 1
(count([y, r, _xg])) -> count([y, cons(y, r), s(_xg)]) -> 4
(delete_all([x, r, _sg]) /\ not eq_elt([x, y])) -> delete_all([x, cons(y, r), cons(y, _sg)]) -> 4
(delete_all([y, r, _rg])) -> delete_all([y, cons(y, r), _rg]) -> 4
(delete_one([x, r, _mg]) /\ not eq_elt([x, y])) -> delete_one([x, cons(y, r), cons(y, _mg)]) -> 4
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 4
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 2
(leqnat([s(nn1), z])) -> BOT -> 2
}
Sat witness: Found: ((count([y, r, _xg])) -> count([y, cons(y, r), s(_xg)]), {
_xg -> z  ;  r -> nil  ;  y -> b
})

-------------------------------------------
Step 10, which took 0.006997 s (model generation: 0.006568,  model checking: 0.000429):

Model:
|_
{
count -> 
{{{
Q={q_gen_1378, q_gen_1390, q_gen_1391},
Q_f={q_gen_1378},
Delta=
{
<b>() -> q_gen_1391
<nil, z>() -> q_gen_1390
<b, cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1378
<b, nil, z>() -> q_gen_1378
}

Datatype: <elt, eltlist, nat>
Convolution form: right
}}}
  ;  delete_all -> 
{{{
Q={q_gen_1377, q_gen_1384, q_gen_1385, q_gen_1387, q_gen_1388},
Q_f={q_gen_1377},
Delta=
{
<nil>() -> q_gen_1384
<b>() -> q_gen_1385
<nil, nil>() -> q_gen_1387
<a, a>() -> q_gen_1388
<b, cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1377
<b, cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1377
<b, nil, nil>() -> q_gen_1377
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  delete_one -> 
{{{
Q={q_gen_1373, q_gen_1374, q_gen_1375, q_gen_1381, q_gen_1382},
Q_f={q_gen_1373},
Delta=
{
<nil>() -> q_gen_1374
<b>() -> q_gen_1375
<nil, nil>() -> q_gen_1381
<a, a>() -> q_gen_1382
<b, cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1373
<b, cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1373
<b, nil, nil>() -> q_gen_1373
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  leqnat -> 
{{{
Q={q_gen_1372},
Q_f={q_gen_1372},
Delta=
{
<s, s>(q_gen_1372) -> q_gen_1372
<z, z>() -> q_gen_1372
}

Datatype: <nat, nat>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist, eq_nat}
_|

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 3
() -> delete_all([x, nil, nil]) -> 3
() -> delete_one([x, nil, nil]) -> 3
() -> delete_one([y, cons(y, r), r]) -> 3
() -> leqnat([z, n2]) -> 3
(count([x, l, _fh]) /\ delete_all([x, l, _eh]) /\ delete_one([x, l, _eh])) -> leqnat([_fh, s(z)]) -> 1
(count([x, r, _yg]) /\ not eq_elt([x, y])) -> count([x, cons(y, r), _yg]) -> 4
(count([y, r, _xg])) -> count([y, cons(y, r), s(_xg)]) -> 4
(delete_all([x, r, _sg]) /\ not eq_elt([x, y])) -> delete_all([x, cons(y, r), cons(y, _sg)]) -> 4
(delete_all([y, r, _rg])) -> delete_all([y, cons(y, r), _rg]) -> 4
(delete_one([x, r, _mg]) /\ not eq_elt([x, y])) -> delete_one([x, cons(y, r), cons(y, _mg)]) -> 4
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 4
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 2
(leqnat([s(nn1), z])) -> BOT -> 2
}
Sat witness: Found: ((count([x, r, _yg]) /\ not eq_elt([x, y])) -> count([x, cons(y, r), _yg]), {
_yg -> z  ;  r -> nil  ;  x -> b  ;  y -> a
})

-------------------------------------------
Step 11, which took 0.007583 s (model generation: 0.006187,  model checking: 0.001396):

Model:
|_
{
count -> 
{{{
Q={q_gen_1378, q_gen_1390, q_gen_1391, q_gen_1393},
Q_f={q_gen_1378},
Delta=
{
<a>() -> q_gen_1391
<b>() -> q_gen_1391
<nil>() -> q_gen_1393
<nil, z>() -> q_gen_1390
<b, cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1378
<b, cons, z>(q_gen_1391, q_gen_1393) -> q_gen_1378
<b, nil, z>() -> q_gen_1378
}

Datatype: <elt, eltlist, nat>
Convolution form: right
}}}
  ;  delete_all -> 
{{{
Q={q_gen_1377, q_gen_1384, q_gen_1385, q_gen_1387, q_gen_1388},
Q_f={q_gen_1377},
Delta=
{
<nil>() -> q_gen_1384
<b>() -> q_gen_1385
<nil, nil>() -> q_gen_1387
<a, a>() -> q_gen_1388
<b, cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1377
<b, cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1377
<b, nil, nil>() -> q_gen_1377
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  delete_one -> 
{{{
Q={q_gen_1373, q_gen_1374, q_gen_1375, q_gen_1381, q_gen_1382},
Q_f={q_gen_1373},
Delta=
{
<nil>() -> q_gen_1374
<b>() -> q_gen_1375
<nil, nil>() -> q_gen_1381
<a, a>() -> q_gen_1382
<b, cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1373
<b, cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1373
<b, nil, nil>() -> q_gen_1373
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  leqnat -> 
{{{
Q={q_gen_1372},
Q_f={q_gen_1372},
Delta=
{
<s, s>(q_gen_1372) -> q_gen_1372
<z, z>() -> q_gen_1372
}

Datatype: <nat, nat>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist, eq_nat}
_|

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 3
() -> delete_all([x, nil, nil]) -> 3
() -> delete_one([x, nil, nil]) -> 3
() -> delete_one([y, cons(y, r), r]) -> 3
() -> leqnat([z, n2]) -> 3
(count([x, l, _fh]) /\ delete_all([x, l, _eh]) /\ delete_one([x, l, _eh])) -> leqnat([_fh, s(z)]) -> 4
(count([x, r, _yg]) /\ not eq_elt([x, y])) -> count([x, cons(y, r), _yg]) -> 4
(count([y, r, _xg])) -> count([y, cons(y, r), s(_xg)]) -> 4
(delete_all([x, r, _sg]) /\ not eq_elt([x, y])) -> delete_all([x, cons(y, r), cons(y, _sg)]) -> 4
(delete_all([y, r, _rg])) -> delete_all([y, cons(y, r), _rg]) -> 4
(delete_one([x, r, _mg]) /\ not eq_elt([x, y])) -> delete_one([x, cons(y, r), cons(y, _mg)]) -> 4
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 4
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 2
(leqnat([s(nn1), z])) -> BOT -> 2
}
Sat witness: Found: ((count([x, l, _fh]) /\ delete_all([x, l, _eh]) /\ delete_one([x, l, _eh])) -> leqnat([_fh, s(z)]), {
_eh -> nil  ;  _fh -> z  ;  l -> nil  ;  x -> b
})

-------------------------------------------
Step 12, which took 0.007572 s (model generation: 0.007353,  model checking: 0.000219):

Model:
|_
{
count -> 
{{{
Q={q_gen_1378, q_gen_1390, q_gen_1391, q_gen_1393},
Q_f={q_gen_1378},
Delta=
{
<a>() -> q_gen_1391
<b>() -> q_gen_1391
<nil>() -> q_gen_1393
<nil, z>() -> q_gen_1390
<b, cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1378
<b, cons, z>(q_gen_1391, q_gen_1393) -> q_gen_1378
<b, nil, z>() -> q_gen_1378
}

Datatype: <elt, eltlist, nat>
Convolution form: right
}}}
  ;  delete_all -> 
{{{
Q={q_gen_1377, q_gen_1384, q_gen_1385, q_gen_1387, q_gen_1388},
Q_f={q_gen_1377},
Delta=
{
<nil>() -> q_gen_1384
<b>() -> q_gen_1385
<nil, nil>() -> q_gen_1387
<a, a>() -> q_gen_1388
<b, cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1377
<b, cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1377
<b, nil, nil>() -> q_gen_1377
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  delete_one -> 
{{{
Q={q_gen_1373, q_gen_1374, q_gen_1375, q_gen_1381, q_gen_1382},
Q_f={q_gen_1373},
Delta=
{
<nil>() -> q_gen_1374
<b>() -> q_gen_1375
<nil, nil>() -> q_gen_1381
<a, a>() -> q_gen_1382
<b, cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1373
<b, cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1373
<b, nil, nil>() -> q_gen_1373
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  leqnat -> 
{{{
Q={q_gen_1372, q_gen_1396},
Q_f={q_gen_1372},
Delta=
{
<z>() -> q_gen_1396
<s, s>(q_gen_1372) -> q_gen_1372
<z, s>(q_gen_1396) -> q_gen_1372
<z, z>() -> q_gen_1372
}

Datatype: <nat, nat>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist, eq_nat}
_|

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 3
() -> delete_all([x, nil, nil]) -> 3
() -> delete_one([x, nil, nil]) -> 3
() -> delete_one([y, cons(y, r), r]) -> 3
() -> leqnat([z, n2]) -> 6
(count([x, l, _fh]) /\ delete_all([x, l, _eh]) /\ delete_one([x, l, _eh])) -> leqnat([_fh, s(z)]) -> 4
(count([x, r, _yg]) /\ not eq_elt([x, y])) -> count([x, cons(y, r), _yg]) -> 4
(count([y, r, _xg])) -> count([y, cons(y, r), s(_xg)]) -> 4
(delete_all([x, r, _sg]) /\ not eq_elt([x, y])) -> delete_all([x, cons(y, r), cons(y, _sg)]) -> 4
(delete_all([y, r, _rg])) -> delete_all([y, cons(y, r), _rg]) -> 4
(delete_one([x, r, _mg]) /\ not eq_elt([x, y])) -> delete_one([x, cons(y, r), cons(y, _mg)]) -> 4
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 4
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 3
(leqnat([s(nn1), z])) -> BOT -> 3
}
Sat witness: Found: (() -> leqnat([z, n2]), {
n2 -> s(s(z))
})

-------------------------------------------
Step 13, which took 0.007132 s (model generation: 0.005931,  model checking: 0.001201):

Model:
|_
{
count -> 
{{{
Q={q_gen_1378, q_gen_1390, q_gen_1391, q_gen_1393},
Q_f={q_gen_1378},
Delta=
{
<a>() -> q_gen_1391
<b>() -> q_gen_1391
<nil>() -> q_gen_1393
<nil, z>() -> q_gen_1390
<b, cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1378
<b, cons, z>(q_gen_1391, q_gen_1393) -> q_gen_1378
<b, nil, z>() -> q_gen_1378
}

Datatype: <elt, eltlist, nat>
Convolution form: right
}}}
  ;  delete_all -> 
{{{
Q={q_gen_1377, q_gen_1384, q_gen_1385, q_gen_1387, q_gen_1388},
Q_f={q_gen_1377},
Delta=
{
<nil>() -> q_gen_1384
<b>() -> q_gen_1385
<nil, nil>() -> q_gen_1387
<a, a>() -> q_gen_1388
<b, cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1377
<b, cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1377
<b, nil, nil>() -> q_gen_1377
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  delete_one -> 
{{{
Q={q_gen_1373, q_gen_1374, q_gen_1375, q_gen_1381, q_gen_1382},
Q_f={q_gen_1373},
Delta=
{
<nil>() -> q_gen_1374
<b>() -> q_gen_1375
<nil, nil>() -> q_gen_1381
<a, a>() -> q_gen_1382
<b, cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1373
<b, cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1373
<b, nil, nil>() -> q_gen_1373
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  leqnat -> 
{{{
Q={q_gen_1372, q_gen_1396},
Q_f={q_gen_1372},
Delta=
{
<s>(q_gen_1396) -> q_gen_1396
<z>() -> q_gen_1396
<s, s>(q_gen_1372) -> q_gen_1372
<z, s>(q_gen_1396) -> q_gen_1372
<z, z>() -> q_gen_1372
}

Datatype: <nat, nat>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist, eq_nat}
_|

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 3
() -> delete_all([x, nil, nil]) -> 3
() -> delete_one([x, nil, nil]) -> 3
() -> delete_one([y, cons(y, r), r]) -> 6
() -> leqnat([z, n2]) -> 6
(count([x, l, _fh]) /\ delete_all([x, l, _eh]) /\ delete_one([x, l, _eh])) -> leqnat([_fh, s(z)]) -> 4
(count([x, r, _yg]) /\ not eq_elt([x, y])) -> count([x, cons(y, r), _yg]) -> 4
(count([y, r, _xg])) -> count([y, cons(y, r), s(_xg)]) -> 4
(delete_all([x, r, _sg]) /\ not eq_elt([x, y])) -> delete_all([x, cons(y, r), cons(y, _sg)]) -> 4
(delete_all([y, r, _rg])) -> delete_all([y, cons(y, r), _rg]) -> 4
(delete_one([x, r, _mg]) /\ not eq_elt([x, y])) -> delete_one([x, cons(y, r), cons(y, _mg)]) -> 4
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 4
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 4
(leqnat([s(nn1), z])) -> BOT -> 4
}
Sat witness: Found: (() -> delete_one([y, cons(y, r), r]), {
r -> nil  ;  y -> a
})

-------------------------------------------
Step 14, which took 0.006291 s (model generation: 0.005802,  model checking: 0.000489):

Model:
|_
{
count -> 
{{{
Q={q_gen_1378, q_gen_1390, q_gen_1391, q_gen_1393},
Q_f={q_gen_1378},
Delta=
{
<a>() -> q_gen_1391
<b>() -> q_gen_1391
<nil>() -> q_gen_1393
<nil, z>() -> q_gen_1390
<b, cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1378
<b, cons, z>(q_gen_1391, q_gen_1393) -> q_gen_1378
<b, nil, z>() -> q_gen_1378
}

Datatype: <elt, eltlist, nat>
Convolution form: right
}}}
  ;  delete_all -> 
{{{
Q={q_gen_1377, q_gen_1384, q_gen_1385, q_gen_1387, q_gen_1388},
Q_f={q_gen_1377},
Delta=
{
<nil>() -> q_gen_1384
<b>() -> q_gen_1385
<nil, nil>() -> q_gen_1387
<a, a>() -> q_gen_1388
<b, cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1377
<b, cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1377
<b, nil, nil>() -> q_gen_1377
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  delete_one -> 
{{{
Q={q_gen_1373, q_gen_1374, q_gen_1375, q_gen_1381, q_gen_1382},
Q_f={q_gen_1373},
Delta=
{
<nil>() -> q_gen_1374
<a>() -> q_gen_1375
<b>() -> q_gen_1375
<nil, nil>() -> q_gen_1381
<a, a>() -> q_gen_1382
<a, cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1373
<b, cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1373
<b, cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1373
<b, nil, nil>() -> q_gen_1373
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  leqnat -> 
{{{
Q={q_gen_1372, q_gen_1396},
Q_f={q_gen_1372},
Delta=
{
<s>(q_gen_1396) -> q_gen_1396
<z>() -> q_gen_1396
<s, s>(q_gen_1372) -> q_gen_1372
<z, s>(q_gen_1396) -> q_gen_1372
<z, z>() -> q_gen_1372
}

Datatype: <nat, nat>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist, eq_nat}
_|

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 3
() -> delete_all([x, nil, nil]) -> 3
() -> delete_one([x, nil, nil]) -> 6
() -> delete_one([y, cons(y, r), r]) -> 6
() -> leqnat([z, n2]) -> 6
(count([x, l, _fh]) /\ delete_all([x, l, _eh]) /\ delete_one([x, l, _eh])) -> leqnat([_fh, s(z)]) -> 4
(count([x, r, _yg]) /\ not eq_elt([x, y])) -> count([x, cons(y, r), _yg]) -> 4
(count([y, r, _xg])) -> count([y, cons(y, r), s(_xg)]) -> 4
(delete_all([x, r, _sg]) /\ not eq_elt([x, y])) -> delete_all([x, cons(y, r), cons(y, _sg)]) -> 4
(delete_all([y, r, _rg])) -> delete_all([y, cons(y, r), _rg]) -> 4
(delete_one([x, r, _mg]) /\ not eq_elt([x, y])) -> delete_one([x, cons(y, r), cons(y, _mg)]) -> 4
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 4
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 4
(leqnat([s(nn1), z])) -> BOT -> 4
}
Sat witness: Found: (() -> delete_one([x, nil, nil]), {
x -> a
})

-------------------------------------------
Step 15, which took 0.007592 s (model generation: 0.006718,  model checking: 0.000874):

Model:
|_
{
count -> 
{{{
Q={q_gen_1378, q_gen_1390, q_gen_1391, q_gen_1393},
Q_f={q_gen_1378},
Delta=
{
<a>() -> q_gen_1391
<b>() -> q_gen_1391
<nil>() -> q_gen_1393
<nil, z>() -> q_gen_1390
<b, cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1378
<b, cons, z>(q_gen_1391, q_gen_1393) -> q_gen_1378
<b, nil, z>() -> q_gen_1378
}

Datatype: <elt, eltlist, nat>
Convolution form: right
}}}
  ;  delete_all -> 
{{{
Q={q_gen_1377, q_gen_1384, q_gen_1385, q_gen_1387, q_gen_1388},
Q_f={q_gen_1377},
Delta=
{
<nil>() -> q_gen_1384
<b>() -> q_gen_1385
<nil, nil>() -> q_gen_1387
<a, a>() -> q_gen_1388
<b, cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1377
<b, cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1377
<b, nil, nil>() -> q_gen_1377
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  delete_one -> 
{{{
Q={q_gen_1373, q_gen_1374, q_gen_1375, q_gen_1381, q_gen_1382},
Q_f={q_gen_1373},
Delta=
{
<nil>() -> q_gen_1374
<a>() -> q_gen_1375
<b>() -> q_gen_1375
<nil, nil>() -> q_gen_1381
<a, a>() -> q_gen_1382
<a, cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1373
<a, nil, nil>() -> q_gen_1373
<b, cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1373
<b, cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1373
<b, nil, nil>() -> q_gen_1373
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  leqnat -> 
{{{
Q={q_gen_1372, q_gen_1396},
Q_f={q_gen_1372},
Delta=
{
<s>(q_gen_1396) -> q_gen_1396
<z>() -> q_gen_1396
<s, s>(q_gen_1372) -> q_gen_1372
<z, s>(q_gen_1396) -> q_gen_1372
<z, z>() -> q_gen_1372
}

Datatype: <nat, nat>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist, eq_nat}
_|

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 3
() -> delete_all([x, nil, nil]) -> 6
() -> delete_one([x, nil, nil]) -> 6
() -> delete_one([y, cons(y, r), r]) -> 6
() -> leqnat([z, n2]) -> 6
(count([x, l, _fh]) /\ delete_all([x, l, _eh]) /\ delete_one([x, l, _eh])) -> leqnat([_fh, s(z)]) -> 4
(count([x, r, _yg]) /\ not eq_elt([x, y])) -> count([x, cons(y, r), _yg]) -> 4
(count([y, r, _xg])) -> count([y, cons(y, r), s(_xg)]) -> 4
(delete_all([x, r, _sg]) /\ not eq_elt([x, y])) -> delete_all([x, cons(y, r), cons(y, _sg)]) -> 4
(delete_all([y, r, _rg])) -> delete_all([y, cons(y, r), _rg]) -> 4
(delete_one([x, r, _mg]) /\ not eq_elt([x, y])) -> delete_one([x, cons(y, r), cons(y, _mg)]) -> 4
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 4
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 4
(leqnat([s(nn1), z])) -> BOT -> 4
}
Sat witness: Found: (() -> delete_all([x, nil, nil]), {
x -> a
})

-------------------------------------------
Step 16, which took 0.006344 s (model generation: 0.006107,  model checking: 0.000237):

Model:
|_
{
count -> 
{{{
Q={q_gen_1378, q_gen_1390, q_gen_1391, q_gen_1393},
Q_f={q_gen_1378},
Delta=
{
<a>() -> q_gen_1391
<b>() -> q_gen_1391
<nil>() -> q_gen_1393
<nil, z>() -> q_gen_1390
<b, cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1378
<b, cons, z>(q_gen_1391, q_gen_1393) -> q_gen_1378
<b, nil, z>() -> q_gen_1378
}

Datatype: <elt, eltlist, nat>
Convolution form: right
}}}
  ;  delete_all -> 
{{{
Q={q_gen_1377, q_gen_1384, q_gen_1385, q_gen_1387, q_gen_1388},
Q_f={q_gen_1377},
Delta=
{
<nil>() -> q_gen_1384
<b>() -> q_gen_1385
<nil, nil>() -> q_gen_1387
<a, a>() -> q_gen_1388
<a, nil, nil>() -> q_gen_1377
<b, cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1377
<b, cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1377
<b, nil, nil>() -> q_gen_1377
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  delete_one -> 
{{{
Q={q_gen_1373, q_gen_1374, q_gen_1375, q_gen_1381, q_gen_1382},
Q_f={q_gen_1373},
Delta=
{
<nil>() -> q_gen_1374
<a>() -> q_gen_1375
<b>() -> q_gen_1375
<nil, nil>() -> q_gen_1381
<a, a>() -> q_gen_1382
<a, cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1373
<a, nil, nil>() -> q_gen_1373
<b, cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1373
<b, cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1373
<b, nil, nil>() -> q_gen_1373
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  leqnat -> 
{{{
Q={q_gen_1372, q_gen_1396},
Q_f={q_gen_1372},
Delta=
{
<s>(q_gen_1396) -> q_gen_1396
<z>() -> q_gen_1396
<s, s>(q_gen_1372) -> q_gen_1372
<z, s>(q_gen_1396) -> q_gen_1372
<z, z>() -> q_gen_1372
}

Datatype: <nat, nat>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist, eq_nat}
_|

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 6
() -> delete_all([x, nil, nil]) -> 6
() -> delete_one([x, nil, nil]) -> 6
() -> delete_one([y, cons(y, r), r]) -> 6
() -> leqnat([z, n2]) -> 6
(count([x, l, _fh]) /\ delete_all([x, l, _eh]) /\ delete_one([x, l, _eh])) -> leqnat([_fh, s(z)]) -> 4
(count([x, r, _yg]) /\ not eq_elt([x, y])) -> count([x, cons(y, r), _yg]) -> 4
(count([y, r, _xg])) -> count([y, cons(y, r), s(_xg)]) -> 4
(delete_all([x, r, _sg]) /\ not eq_elt([x, y])) -> delete_all([x, cons(y, r), cons(y, _sg)]) -> 4
(delete_all([y, r, _rg])) -> delete_all([y, cons(y, r), _rg]) -> 4
(delete_one([x, r, _mg]) /\ not eq_elt([x, y])) -> delete_one([x, cons(y, r), cons(y, _mg)]) -> 4
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 4
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 4
(leqnat([s(nn1), z])) -> BOT -> 4
}
Sat witness: Found: (() -> count([x, nil, z]), {
x -> a
})

-------------------------------------------
Step 17, which took 0.008289 s (model generation: 0.007043,  model checking: 0.001246):

Model:
|_
{
count -> 
{{{
Q={q_gen_1378, q_gen_1390, q_gen_1391, q_gen_1393},
Q_f={q_gen_1378},
Delta=
{
<a>() -> q_gen_1391
<b>() -> q_gen_1391
<nil>() -> q_gen_1393
<nil, z>() -> q_gen_1390
<a, nil, z>() -> q_gen_1378
<b, cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1378
<b, cons, z>(q_gen_1391, q_gen_1393) -> q_gen_1378
<b, nil, z>() -> q_gen_1378
}

Datatype: <elt, eltlist, nat>
Convolution form: right
}}}
  ;  delete_all -> 
{{{
Q={q_gen_1377, q_gen_1384, q_gen_1385, q_gen_1387, q_gen_1388},
Q_f={q_gen_1377},
Delta=
{
<nil>() -> q_gen_1384
<b>() -> q_gen_1385
<nil, nil>() -> q_gen_1387
<a, a>() -> q_gen_1388
<a, nil, nil>() -> q_gen_1377
<b, cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1377
<b, cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1377
<b, nil, nil>() -> q_gen_1377
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  delete_one -> 
{{{
Q={q_gen_1373, q_gen_1374, q_gen_1375, q_gen_1381, q_gen_1382},
Q_f={q_gen_1373},
Delta=
{
<nil>() -> q_gen_1374
<a>() -> q_gen_1375
<b>() -> q_gen_1375
<nil, nil>() -> q_gen_1381
<a, a>() -> q_gen_1382
<a, cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1373
<a, nil, nil>() -> q_gen_1373
<b, cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1373
<b, cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1373
<b, nil, nil>() -> q_gen_1373
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  leqnat -> 
{{{
Q={q_gen_1372, q_gen_1396},
Q_f={q_gen_1372},
Delta=
{
<s>(q_gen_1396) -> q_gen_1396
<z>() -> q_gen_1396
<s, s>(q_gen_1372) -> q_gen_1372
<z, s>(q_gen_1396) -> q_gen_1372
<z, z>() -> q_gen_1372
}

Datatype: <nat, nat>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist, eq_nat}
_|

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 6
() -> delete_all([x, nil, nil]) -> 6
() -> delete_one([x, nil, nil]) -> 6
() -> delete_one([y, cons(y, r), r]) -> 6
() -> leqnat([z, n2]) -> 6
(count([x, l, _fh]) /\ delete_all([x, l, _eh]) /\ delete_one([x, l, _eh])) -> leqnat([_fh, s(z)]) -> 4
(count([x, r, _yg]) /\ not eq_elt([x, y])) -> count([x, cons(y, r), _yg]) -> 4
(count([y, r, _xg])) -> count([y, cons(y, r), s(_xg)]) -> 4
(delete_all([x, r, _sg]) /\ not eq_elt([x, y])) -> delete_all([x, cons(y, r), cons(y, _sg)]) -> 4
(delete_all([y, r, _rg])) -> delete_all([y, cons(y, r), _rg]) -> 4
(delete_one([x, r, _mg]) /\ not eq_elt([x, y])) -> delete_one([x, cons(y, r), cons(y, _mg)]) -> 7
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 5
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 5
(leqnat([s(nn1), z])) -> BOT -> 5
}
Sat witness: Found: ((delete_one([x, r, _mg]) /\ not eq_elt([x, y])) -> delete_one([x, cons(y, r), cons(y, _mg)]), {
_mg -> nil  ;  r -> nil  ;  x -> a  ;  y -> b
})

-------------------------------------------
Step 18, which took 0.015272 s (model generation: 0.014429,  model checking: 0.000843):

Model:
|_
{
count -> 
{{{
Q={q_gen_1378, q_gen_1390, q_gen_1391, q_gen_1393},
Q_f={q_gen_1378},
Delta=
{
<a>() -> q_gen_1391
<b>() -> q_gen_1391
<nil>() -> q_gen_1393
<nil, z>() -> q_gen_1390
<a, nil, z>() -> q_gen_1378
<b, cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1378
<b, cons, z>(q_gen_1391, q_gen_1393) -> q_gen_1378
<b, nil, z>() -> q_gen_1378
}

Datatype: <elt, eltlist, nat>
Convolution form: right
}}}
  ;  delete_all -> 
{{{
Q={q_gen_1377, q_gen_1384, q_gen_1385, q_gen_1387, q_gen_1388},
Q_f={q_gen_1377},
Delta=
{
<nil>() -> q_gen_1384
<b>() -> q_gen_1385
<nil, nil>() -> q_gen_1387
<a, a>() -> q_gen_1388
<a, nil, nil>() -> q_gen_1377
<b, cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1377
<b, cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1377
<b, nil, nil>() -> q_gen_1377
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  delete_one -> 
{{{
Q={q_gen_1373, q_gen_1374, q_gen_1375, q_gen_1381, q_gen_1382},
Q_f={q_gen_1373},
Delta=
{
<nil>() -> q_gen_1374
<a>() -> q_gen_1375
<b>() -> q_gen_1375
<nil, nil>() -> q_gen_1381
<a, a>() -> q_gen_1382
<b, b>() -> q_gen_1382
<a, cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1373
<a, cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1373
<a, nil, nil>() -> q_gen_1373
<b, cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1373
<b, cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1373
<b, nil, nil>() -> q_gen_1373
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  leqnat -> 
{{{
Q={q_gen_1372, q_gen_1396},
Q_f={q_gen_1372},
Delta=
{
<s>(q_gen_1396) -> q_gen_1396
<z>() -> q_gen_1396
<s, s>(q_gen_1372) -> q_gen_1372
<z, s>(q_gen_1396) -> q_gen_1372
<z, z>() -> q_gen_1372
}

Datatype: <nat, nat>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist, eq_nat}
_|

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 6
() -> delete_all([x, nil, nil]) -> 6
() -> delete_one([x, nil, nil]) -> 6
() -> delete_one([y, cons(y, r), r]) -> 6
() -> leqnat([z, n2]) -> 6
(count([x, l, _fh]) /\ delete_all([x, l, _eh]) /\ delete_one([x, l, _eh])) -> leqnat([_fh, s(z)]) -> 4
(count([x, r, _yg]) /\ not eq_elt([x, y])) -> count([x, cons(y, r), _yg]) -> 4
(count([y, r, _xg])) -> count([y, cons(y, r), s(_xg)]) -> 4
(delete_all([x, r, _sg]) /\ not eq_elt([x, y])) -> delete_all([x, cons(y, r), cons(y, _sg)]) -> 4
(delete_all([y, r, _rg])) -> delete_all([y, cons(y, r), _rg]) -> 7
(delete_one([x, r, _mg]) /\ not eq_elt([x, y])) -> delete_one([x, cons(y, r), cons(y, _mg)]) -> 7
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 5
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 5
(leqnat([s(nn1), z])) -> BOT -> 5
}
Sat witness: Found: ((delete_all([y, r, _rg])) -> delete_all([y, cons(y, r), _rg]), {
_rg -> nil  ;  r -> nil  ;  y -> a
})

-------------------------------------------
Step 19, which took 0.009648 s (model generation: 0.008732,  model checking: 0.000916):

Model:
|_
{
count -> 
{{{
Q={q_gen_1378, q_gen_1390, q_gen_1391, q_gen_1393},
Q_f={q_gen_1378},
Delta=
{
<a>() -> q_gen_1391
<b>() -> q_gen_1391
<nil>() -> q_gen_1393
<nil, z>() -> q_gen_1390
<a, nil, z>() -> q_gen_1378
<b, cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1378
<b, cons, z>(q_gen_1391, q_gen_1393) -> q_gen_1378
<b, nil, z>() -> q_gen_1378
}

Datatype: <elt, eltlist, nat>
Convolution form: right
}}}
  ;  delete_all -> 
{{{
Q={q_gen_1377, q_gen_1384, q_gen_1385, q_gen_1387, q_gen_1388},
Q_f={q_gen_1377},
Delta=
{
<nil>() -> q_gen_1384
<a>() -> q_gen_1385
<b>() -> q_gen_1385
<nil, nil>() -> q_gen_1387
<a, a>() -> q_gen_1388
<a, cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1377
<a, nil, nil>() -> q_gen_1377
<b, cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1377
<b, cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1377
<b, nil, nil>() -> q_gen_1377
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  delete_one -> 
{{{
Q={q_gen_1373, q_gen_1374, q_gen_1375, q_gen_1381, q_gen_1382},
Q_f={q_gen_1373},
Delta=
{
<nil>() -> q_gen_1374
<a>() -> q_gen_1375
<b>() -> q_gen_1375
<nil, nil>() -> q_gen_1381
<a, a>() -> q_gen_1382
<b, b>() -> q_gen_1382
<a, cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1373
<a, cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1373
<a, nil, nil>() -> q_gen_1373
<b, cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1373
<b, cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1373
<b, nil, nil>() -> q_gen_1373
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  leqnat -> 
{{{
Q={q_gen_1372, q_gen_1396},
Q_f={q_gen_1372},
Delta=
{
<s>(q_gen_1396) -> q_gen_1396
<z>() -> q_gen_1396
<s, s>(q_gen_1372) -> q_gen_1372
<z, s>(q_gen_1396) -> q_gen_1372
<z, z>() -> q_gen_1372
}

Datatype: <nat, nat>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist, eq_nat}
_|

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 6
() -> delete_all([x, nil, nil]) -> 6
() -> delete_one([x, nil, nil]) -> 6
() -> delete_one([y, cons(y, r), r]) -> 6
() -> leqnat([z, n2]) -> 6
(count([x, l, _fh]) /\ delete_all([x, l, _eh]) /\ delete_one([x, l, _eh])) -> leqnat([_fh, s(z)]) -> 4
(count([x, r, _yg]) /\ not eq_elt([x, y])) -> count([x, cons(y, r), _yg]) -> 4
(count([y, r, _xg])) -> count([y, cons(y, r), s(_xg)]) -> 4
(delete_all([x, r, _sg]) /\ not eq_elt([x, y])) -> delete_all([x, cons(y, r), cons(y, _sg)]) -> 7
(delete_all([y, r, _rg])) -> delete_all([y, cons(y, r), _rg]) -> 7
(delete_one([x, r, _mg]) /\ not eq_elt([x, y])) -> delete_one([x, cons(y, r), cons(y, _mg)]) -> 7
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 5
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 5
(leqnat([s(nn1), z])) -> BOT -> 5
}
Sat witness: Found: ((delete_all([x, r, _sg]) /\ not eq_elt([x, y])) -> delete_all([x, cons(y, r), cons(y, _sg)]), {
_sg -> nil  ;  r -> nil  ;  x -> a  ;  y -> b
})

-------------------------------------------
Step 20, which took 0.008861 s (model generation: 0.008649,  model checking: 0.000212):

Model:
|_
{
count -> 
{{{
Q={q_gen_1378, q_gen_1390, q_gen_1391, q_gen_1393},
Q_f={q_gen_1378},
Delta=
{
<a>() -> q_gen_1391
<b>() -> q_gen_1391
<nil>() -> q_gen_1393
<nil, z>() -> q_gen_1390
<a, nil, z>() -> q_gen_1378
<b, cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1378
<b, cons, z>(q_gen_1391, q_gen_1393) -> q_gen_1378
<b, nil, z>() -> q_gen_1378
}

Datatype: <elt, eltlist, nat>
Convolution form: right
}}}
  ;  delete_all -> 
{{{
Q={q_gen_1377, q_gen_1384, q_gen_1385, q_gen_1387, q_gen_1388},
Q_f={q_gen_1377},
Delta=
{
<nil>() -> q_gen_1384
<a>() -> q_gen_1385
<b>() -> q_gen_1385
<nil, nil>() -> q_gen_1387
<a, a>() -> q_gen_1388
<b, b>() -> q_gen_1388
<a, cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1377
<a, cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1377
<a, nil, nil>() -> q_gen_1377
<b, cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1377
<b, cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1377
<b, nil, nil>() -> q_gen_1377
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  delete_one -> 
{{{
Q={q_gen_1373, q_gen_1374, q_gen_1375, q_gen_1381, q_gen_1382},
Q_f={q_gen_1373},
Delta=
{
<nil>() -> q_gen_1374
<a>() -> q_gen_1375
<b>() -> q_gen_1375
<nil, nil>() -> q_gen_1381
<a, a>() -> q_gen_1382
<b, b>() -> q_gen_1382
<a, cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1373
<a, cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1373
<a, nil, nil>() -> q_gen_1373
<b, cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1373
<b, cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1373
<b, nil, nil>() -> q_gen_1373
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  leqnat -> 
{{{
Q={q_gen_1372, q_gen_1396},
Q_f={q_gen_1372},
Delta=
{
<s>(q_gen_1396) -> q_gen_1396
<z>() -> q_gen_1396
<s, s>(q_gen_1372) -> q_gen_1372
<z, s>(q_gen_1396) -> q_gen_1372
<z, z>() -> q_gen_1372
}

Datatype: <nat, nat>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist, eq_nat}
_|

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 6
() -> delete_all([x, nil, nil]) -> 6
() -> delete_one([x, nil, nil]) -> 6
() -> delete_one([y, cons(y, r), r]) -> 6
() -> leqnat([z, n2]) -> 6
(count([x, l, _fh]) /\ delete_all([x, l, _eh]) /\ delete_one([x, l, _eh])) -> leqnat([_fh, s(z)]) -> 4
(count([x, r, _yg]) /\ not eq_elt([x, y])) -> count([x, cons(y, r), _yg]) -> 4
(count([y, r, _xg])) -> count([y, cons(y, r), s(_xg)]) -> 7
(delete_all([x, r, _sg]) /\ not eq_elt([x, y])) -> delete_all([x, cons(y, r), cons(y, _sg)]) -> 7
(delete_all([y, r, _rg])) -> delete_all([y, cons(y, r), _rg]) -> 7
(delete_one([x, r, _mg]) /\ not eq_elt([x, y])) -> delete_one([x, cons(y, r), cons(y, _mg)]) -> 7
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 5
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 5
(leqnat([s(nn1), z])) -> BOT -> 5
}
Sat witness: Found: ((count([y, r, _xg])) -> count([y, cons(y, r), s(_xg)]), {
_xg -> z  ;  r -> nil  ;  y -> a
})

-------------------------------------------
Step 21, which took 0.007694 s (model generation: 0.007462,  model checking: 0.000232):

Model:
|_
{
count -> 
{{{
Q={q_gen_1378, q_gen_1390, q_gen_1391, q_gen_1393},
Q_f={q_gen_1378},
Delta=
{
<a>() -> q_gen_1391
<b>() -> q_gen_1391
<nil>() -> q_gen_1393
<nil, z>() -> q_gen_1390
<a, cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1378
<a, nil, z>() -> q_gen_1378
<b, cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1378
<b, cons, z>(q_gen_1391, q_gen_1393) -> q_gen_1378
<b, nil, z>() -> q_gen_1378
}

Datatype: <elt, eltlist, nat>
Convolution form: right
}}}
  ;  delete_all -> 
{{{
Q={q_gen_1377, q_gen_1384, q_gen_1385, q_gen_1387, q_gen_1388},
Q_f={q_gen_1377},
Delta=
{
<nil>() -> q_gen_1384
<a>() -> q_gen_1385
<b>() -> q_gen_1385
<nil, nil>() -> q_gen_1387
<a, a>() -> q_gen_1388
<b, b>() -> q_gen_1388
<a, cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1377
<a, cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1377
<a, nil, nil>() -> q_gen_1377
<b, cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1377
<b, cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1377
<b, nil, nil>() -> q_gen_1377
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  delete_one -> 
{{{
Q={q_gen_1373, q_gen_1374, q_gen_1375, q_gen_1381, q_gen_1382},
Q_f={q_gen_1373},
Delta=
{
<nil>() -> q_gen_1374
<a>() -> q_gen_1375
<b>() -> q_gen_1375
<nil, nil>() -> q_gen_1381
<a, a>() -> q_gen_1382
<b, b>() -> q_gen_1382
<a, cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1373
<a, cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1373
<a, nil, nil>() -> q_gen_1373
<b, cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1373
<b, cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1373
<b, nil, nil>() -> q_gen_1373
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  leqnat -> 
{{{
Q={q_gen_1372, q_gen_1396},
Q_f={q_gen_1372},
Delta=
{
<s>(q_gen_1396) -> q_gen_1396
<z>() -> q_gen_1396
<s, s>(q_gen_1372) -> q_gen_1372
<z, s>(q_gen_1396) -> q_gen_1372
<z, z>() -> q_gen_1372
}

Datatype: <nat, nat>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist, eq_nat}
_|

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 6
() -> delete_all([x, nil, nil]) -> 6
() -> delete_one([x, nil, nil]) -> 6
() -> delete_one([y, cons(y, r), r]) -> 6
() -> leqnat([z, n2]) -> 6
(count([x, l, _fh]) /\ delete_all([x, l, _eh]) /\ delete_one([x, l, _eh])) -> leqnat([_fh, s(z)]) -> 4
(count([x, r, _yg]) /\ not eq_elt([x, y])) -> count([x, cons(y, r), _yg]) -> 7
(count([y, r, _xg])) -> count([y, cons(y, r), s(_xg)]) -> 7
(delete_all([x, r, _sg]) /\ not eq_elt([x, y])) -> delete_all([x, cons(y, r), cons(y, _sg)]) -> 7
(delete_all([y, r, _rg])) -> delete_all([y, cons(y, r), _rg]) -> 7
(delete_one([x, r, _mg]) /\ not eq_elt([x, y])) -> delete_one([x, cons(y, r), cons(y, _mg)]) -> 7
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 5
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 5
(leqnat([s(nn1), z])) -> BOT -> 5
}
Sat witness: Found: ((count([x, r, _yg]) /\ not eq_elt([x, y])) -> count([x, cons(y, r), _yg]), {
_yg -> z  ;  r -> nil  ;  x -> a  ;  y -> b
})

-------------------------------------------
Step 22, which took 0.009288 s (model generation: 0.007969,  model checking: 0.001319):

Model:
|_
{
count -> 
{{{
Q={q_gen_1378, q_gen_1390, q_gen_1391, q_gen_1393},
Q_f={q_gen_1378},
Delta=
{
<a>() -> q_gen_1391
<b>() -> q_gen_1391
<nil>() -> q_gen_1393
<nil, z>() -> q_gen_1390
<a, cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1378
<a, cons, z>(q_gen_1391, q_gen_1393) -> q_gen_1378
<a, nil, z>() -> q_gen_1378
<b, cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1378
<b, cons, z>(q_gen_1391, q_gen_1393) -> q_gen_1378
<b, nil, z>() -> q_gen_1378
}

Datatype: <elt, eltlist, nat>
Convolution form: right
}}}
  ;  delete_all -> 
{{{
Q={q_gen_1377, q_gen_1384, q_gen_1385, q_gen_1387, q_gen_1388},
Q_f={q_gen_1377},
Delta=
{
<nil>() -> q_gen_1384
<a>() -> q_gen_1385
<b>() -> q_gen_1385
<nil, nil>() -> q_gen_1387
<a, a>() -> q_gen_1388
<b, b>() -> q_gen_1388
<a, cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1377
<a, cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1377
<a, nil, nil>() -> q_gen_1377
<b, cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1377
<b, cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1377
<b, nil, nil>() -> q_gen_1377
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  delete_one -> 
{{{
Q={q_gen_1373, q_gen_1374, q_gen_1375, q_gen_1381, q_gen_1382},
Q_f={q_gen_1373},
Delta=
{
<nil>() -> q_gen_1374
<a>() -> q_gen_1375
<b>() -> q_gen_1375
<nil, nil>() -> q_gen_1381
<a, a>() -> q_gen_1382
<b, b>() -> q_gen_1382
<a, cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1373
<a, cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1373
<a, nil, nil>() -> q_gen_1373
<b, cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1373
<b, cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1373
<b, nil, nil>() -> q_gen_1373
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  leqnat -> 
{{{
Q={q_gen_1372, q_gen_1396},
Q_f={q_gen_1372},
Delta=
{
<s>(q_gen_1396) -> q_gen_1396
<z>() -> q_gen_1396
<s, s>(q_gen_1372) -> q_gen_1372
<z, s>(q_gen_1396) -> q_gen_1372
<z, z>() -> q_gen_1372
}

Datatype: <nat, nat>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist, eq_nat}
_|

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 6
() -> delete_all([x, nil, nil]) -> 6
() -> delete_one([x, nil, nil]) -> 6
() -> delete_one([y, cons(y, r), r]) -> 9
() -> leqnat([z, n2]) -> 7
(count([x, l, _fh]) /\ delete_all([x, l, _eh]) /\ delete_one([x, l, _eh])) -> leqnat([_fh, s(z)]) -> 5
(count([x, r, _yg]) /\ not eq_elt([x, y])) -> count([x, cons(y, r), _yg]) -> 7
(count([y, r, _xg])) -> count([y, cons(y, r), s(_xg)]) -> 7
(delete_all([x, r, _sg]) /\ not eq_elt([x, y])) -> delete_all([x, cons(y, r), cons(y, _sg)]) -> 7
(delete_all([y, r, _rg])) -> delete_all([y, cons(y, r), _rg]) -> 7
(delete_one([x, r, _mg]) /\ not eq_elt([x, y])) -> delete_one([x, cons(y, r), cons(y, _mg)]) -> 7
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 6
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 6
(leqnat([s(nn1), z])) -> BOT -> 6
}
Sat witness: Found: (() -> delete_one([y, cons(y, r), r]), {
r -> cons(b, nil)  ;  y -> b
})

-------------------------------------------
Step 23, which took 0.008135 s (model generation: 0.006619,  model checking: 0.001516):

Model:
|_
{
count -> 
{{{
Q={q_gen_1378, q_gen_1390, q_gen_1391, q_gen_1393},
Q_f={q_gen_1378},
Delta=
{
<a>() -> q_gen_1391
<b>() -> q_gen_1391
<nil>() -> q_gen_1393
<nil, z>() -> q_gen_1390
<a, cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1378
<a, cons, z>(q_gen_1391, q_gen_1393) -> q_gen_1378
<a, nil, z>() -> q_gen_1378
<b, cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1378
<b, cons, z>(q_gen_1391, q_gen_1393) -> q_gen_1378
<b, nil, z>() -> q_gen_1378
}

Datatype: <elt, eltlist, nat>
Convolution form: right
}}}
  ;  delete_all -> 
{{{
Q={q_gen_1377, q_gen_1384, q_gen_1385, q_gen_1387, q_gen_1388},
Q_f={q_gen_1377},
Delta=
{
<nil>() -> q_gen_1384
<a>() -> q_gen_1385
<b>() -> q_gen_1385
<nil, nil>() -> q_gen_1387
<a, a>() -> q_gen_1388
<b, b>() -> q_gen_1388
<a, cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1377
<a, cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1377
<a, nil, nil>() -> q_gen_1377
<b, cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1377
<b, cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1377
<b, nil, nil>() -> q_gen_1377
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  delete_one -> 
{{{
Q={q_gen_1373, q_gen_1374, q_gen_1375, q_gen_1381, q_gen_1382},
Q_f={q_gen_1373},
Delta=
{
<nil>() -> q_gen_1374
<a>() -> q_gen_1375
<b>() -> q_gen_1375
<cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1381
<nil, nil>() -> q_gen_1381
<a, a>() -> q_gen_1382
<b, b>() -> q_gen_1382
<a, cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1373
<a, cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1373
<a, nil, nil>() -> q_gen_1373
<b, cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1373
<b, cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1373
<b, nil, nil>() -> q_gen_1373
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  leqnat -> 
{{{
Q={q_gen_1372, q_gen_1396},
Q_f={q_gen_1372},
Delta=
{
<s>(q_gen_1396) -> q_gen_1396
<z>() -> q_gen_1396
<s, s>(q_gen_1372) -> q_gen_1372
<z, s>(q_gen_1396) -> q_gen_1372
<z, z>() -> q_gen_1372
}

Datatype: <nat, nat>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist, eq_nat}
_|

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 7
() -> delete_all([x, nil, nil]) -> 7
() -> delete_one([x, nil, nil]) -> 7
() -> delete_one([y, cons(y, r), r]) -> 9
() -> leqnat([z, n2]) -> 7
(count([x, l, _fh]) /\ delete_all([x, l, _eh]) /\ delete_one([x, l, _eh])) -> leqnat([_fh, s(z)]) -> 6
(count([x, r, _yg]) /\ not eq_elt([x, y])) -> count([x, cons(y, r), _yg]) -> 7
(count([y, r, _xg])) -> count([y, cons(y, r), s(_xg)]) -> 7
(delete_all([x, r, _sg]) /\ not eq_elt([x, y])) -> delete_all([x, cons(y, r), cons(y, _sg)]) -> 7
(delete_all([y, r, _rg])) -> delete_all([y, cons(y, r), _rg]) -> 7
(delete_one([x, r, _mg]) /\ not eq_elt([x, y])) -> delete_one([x, cons(y, r), cons(y, _mg)]) -> 10
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 7
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 7
(leqnat([s(nn1), z])) -> BOT -> 7
}
Sat witness: Found: ((delete_one([x, r, _mg]) /\ not eq_elt([x, y])) -> delete_one([x, cons(y, r), cons(y, _mg)]), {
_mg -> cons(b, nil)  ;  r -> cons(b, nil)  ;  x -> a  ;  y -> b
})

-------------------------------------------
Step 24, which took 0.009266 s (model generation: 0.008450,  model checking: 0.000816):

Model:
|_
{
count -> 
{{{
Q={q_gen_1378, q_gen_1390, q_gen_1391, q_gen_1393},
Q_f={q_gen_1378},
Delta=
{
<a>() -> q_gen_1391
<b>() -> q_gen_1391
<nil>() -> q_gen_1393
<nil, z>() -> q_gen_1390
<a, cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1378
<a, cons, z>(q_gen_1391, q_gen_1393) -> q_gen_1378
<a, nil, z>() -> q_gen_1378
<b, cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1378
<b, cons, z>(q_gen_1391, q_gen_1393) -> q_gen_1378
<b, nil, z>() -> q_gen_1378
}

Datatype: <elt, eltlist, nat>
Convolution form: right
}}}
  ;  delete_all -> 
{{{
Q={q_gen_1377, q_gen_1384, q_gen_1385, q_gen_1387, q_gen_1388},
Q_f={q_gen_1377},
Delta=
{
<nil>() -> q_gen_1384
<a>() -> q_gen_1385
<b>() -> q_gen_1385
<nil, nil>() -> q_gen_1387
<a, a>() -> q_gen_1388
<b, b>() -> q_gen_1388
<a, cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1377
<a, cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1377
<a, nil, nil>() -> q_gen_1377
<b, cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1377
<b, cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1377
<b, nil, nil>() -> q_gen_1377
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  delete_one -> 
{{{
Q={q_gen_1373, q_gen_1374, q_gen_1375, q_gen_1381, q_gen_1382},
Q_f={q_gen_1373},
Delta=
{
<nil>() -> q_gen_1374
<a>() -> q_gen_1375
<b>() -> q_gen_1375
<cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1381
<cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1381
<nil, nil>() -> q_gen_1381
<a, a>() -> q_gen_1382
<b, b>() -> q_gen_1382
<a, cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1373
<a, cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1373
<a, nil, nil>() -> q_gen_1373
<b, cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1373
<b, cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1373
<b, nil, nil>() -> q_gen_1373
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  leqnat -> 
{{{
Q={q_gen_1372, q_gen_1396},
Q_f={q_gen_1372},
Delta=
{
<s>(q_gen_1396) -> q_gen_1396
<z>() -> q_gen_1396
<s, s>(q_gen_1372) -> q_gen_1372
<z, s>(q_gen_1396) -> q_gen_1372
<z, z>() -> q_gen_1372
}

Datatype: <nat, nat>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist, eq_nat}
_|

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 7
() -> delete_all([x, nil, nil]) -> 7
() -> delete_one([x, nil, nil]) -> 7
() -> delete_one([y, cons(y, r), r]) -> 9
() -> leqnat([z, n2]) -> 7
(count([x, l, _fh]) /\ delete_all([x, l, _eh]) /\ delete_one([x, l, _eh])) -> leqnat([_fh, s(z)]) -> 7
(count([x, r, _yg]) /\ not eq_elt([x, y])) -> count([x, cons(y, r), _yg]) -> 7
(count([y, r, _xg])) -> count([y, cons(y, r), s(_xg)]) -> 7
(delete_all([x, r, _sg]) /\ not eq_elt([x, y])) -> delete_all([x, cons(y, r), cons(y, _sg)]) -> 7
(delete_all([y, r, _rg])) -> delete_all([y, cons(y, r), _rg]) -> 10
(delete_one([x, r, _mg]) /\ not eq_elt([x, y])) -> delete_one([x, cons(y, r), cons(y, _mg)]) -> 10
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 8
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 8
(leqnat([s(nn1), z])) -> BOT -> 8
}
Sat witness: Found: ((delete_all([y, r, _rg])) -> delete_all([y, cons(y, r), _rg]), {
_rg -> nil  ;  r -> cons(b, nil)  ;  y -> b
})

-------------------------------------------
Step 25, which took 0.014566 s (model generation: 0.012926,  model checking: 0.001640):

Model:
|_
{
count -> 
{{{
Q={q_gen_1378, q_gen_1390, q_gen_1391, q_gen_1393},
Q_f={q_gen_1378},
Delta=
{
<a>() -> q_gen_1391
<b>() -> q_gen_1391
<nil>() -> q_gen_1393
<nil, z>() -> q_gen_1390
<a, cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1378
<a, cons, z>(q_gen_1391, q_gen_1393) -> q_gen_1378
<a, nil, z>() -> q_gen_1378
<b, cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1378
<b, cons, z>(q_gen_1391, q_gen_1393) -> q_gen_1378
<b, nil, z>() -> q_gen_1378
}

Datatype: <elt, eltlist, nat>
Convolution form: right
}}}
  ;  delete_all -> 
{{{
Q={q_gen_1377, q_gen_1384, q_gen_1385, q_gen_1387, q_gen_1388},
Q_f={q_gen_1377},
Delta=
{
<cons>(q_gen_1385, q_gen_1384) -> q_gen_1384
<nil>() -> q_gen_1384
<a>() -> q_gen_1385
<b>() -> q_gen_1385
<nil, nil>() -> q_gen_1387
<a, a>() -> q_gen_1388
<b, b>() -> q_gen_1388
<a, cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1377
<a, cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1377
<a, nil, nil>() -> q_gen_1377
<b, cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1377
<b, cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1377
<b, nil, nil>() -> q_gen_1377
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  delete_one -> 
{{{
Q={q_gen_1373, q_gen_1374, q_gen_1375, q_gen_1381, q_gen_1382},
Q_f={q_gen_1373},
Delta=
{
<nil>() -> q_gen_1374
<a>() -> q_gen_1375
<b>() -> q_gen_1375
<cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1381
<cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1381
<nil, nil>() -> q_gen_1381
<a, a>() -> q_gen_1382
<b, b>() -> q_gen_1382
<a, cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1373
<a, cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1373
<a, nil, nil>() -> q_gen_1373
<b, cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1373
<b, cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1373
<b, nil, nil>() -> q_gen_1373
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  leqnat -> 
{{{
Q={q_gen_1372, q_gen_1396},
Q_f={q_gen_1372},
Delta=
{
<s>(q_gen_1396) -> q_gen_1396
<z>() -> q_gen_1396
<s, s>(q_gen_1372) -> q_gen_1372
<z, s>(q_gen_1396) -> q_gen_1372
<z, z>() -> q_gen_1372
}

Datatype: <nat, nat>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist, eq_nat}
_|

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 7
() -> delete_all([x, nil, nil]) -> 7
() -> delete_one([x, nil, nil]) -> 7
() -> delete_one([y, cons(y, r), r]) -> 9
() -> leqnat([z, n2]) -> 7
(count([x, l, _fh]) /\ delete_all([x, l, _eh]) /\ delete_one([x, l, _eh])) -> leqnat([_fh, s(z)]) -> 7
(count([x, r, _yg]) /\ not eq_elt([x, y])) -> count([x, cons(y, r), _yg]) -> 7
(count([y, r, _xg])) -> count([y, cons(y, r), s(_xg)]) -> 7
(delete_all([x, r, _sg]) /\ not eq_elt([x, y])) -> delete_all([x, cons(y, r), cons(y, _sg)]) -> 10
(delete_all([y, r, _rg])) -> delete_all([y, cons(y, r), _rg]) -> 10
(delete_one([x, r, _mg]) /\ not eq_elt([x, y])) -> delete_one([x, cons(y, r), cons(y, _mg)]) -> 10
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 8
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 8
(leqnat([s(nn1), z])) -> BOT -> 8
}
Sat witness: Found: ((delete_all([x, r, _sg]) /\ not eq_elt([x, y])) -> delete_all([x, cons(y, r), cons(y, _sg)]), {
_sg -> nil  ;  r -> cons(a, nil)  ;  x -> a  ;  y -> b
})

-------------------------------------------
Step 26, which took 0.020533 s (model generation: 0.019796,  model checking: 0.000737):

Model:
|_
{
count -> 
{{{
Q={q_gen_1378, q_gen_1390, q_gen_1391, q_gen_1393},
Q_f={q_gen_1378},
Delta=
{
<a>() -> q_gen_1391
<b>() -> q_gen_1391
<nil>() -> q_gen_1393
<nil, z>() -> q_gen_1390
<a, cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1378
<a, cons, z>(q_gen_1391, q_gen_1393) -> q_gen_1378
<a, nil, z>() -> q_gen_1378
<b, cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1378
<b, cons, z>(q_gen_1391, q_gen_1393) -> q_gen_1378
<b, nil, z>() -> q_gen_1378
}

Datatype: <elt, eltlist, nat>
Convolution form: right
}}}
  ;  delete_all -> 
{{{
Q={q_gen_1377, q_gen_1384, q_gen_1385, q_gen_1387, q_gen_1388},
Q_f={q_gen_1377},
Delta=
{
<cons>(q_gen_1385, q_gen_1384) -> q_gen_1384
<nil>() -> q_gen_1384
<a>() -> q_gen_1385
<b>() -> q_gen_1385
<cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1387
<nil, nil>() -> q_gen_1387
<a, a>() -> q_gen_1388
<b, b>() -> q_gen_1388
<a, cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1377
<a, cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1377
<a, nil, nil>() -> q_gen_1377
<b, cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1377
<b, cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1377
<b, nil, nil>() -> q_gen_1377
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  delete_one -> 
{{{
Q={q_gen_1373, q_gen_1374, q_gen_1375, q_gen_1381, q_gen_1382},
Q_f={q_gen_1373},
Delta=
{
<nil>() -> q_gen_1374
<a>() -> q_gen_1375
<b>() -> q_gen_1375
<cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1381
<cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1381
<nil, nil>() -> q_gen_1381
<a, a>() -> q_gen_1382
<b, b>() -> q_gen_1382
<a, cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1373
<a, cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1373
<a, nil, nil>() -> q_gen_1373
<b, cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1373
<b, cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1373
<b, nil, nil>() -> q_gen_1373
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  leqnat -> 
{{{
Q={q_gen_1372, q_gen_1396},
Q_f={q_gen_1372},
Delta=
{
<s>(q_gen_1396) -> q_gen_1396
<z>() -> q_gen_1396
<s, s>(q_gen_1372) -> q_gen_1372
<z, s>(q_gen_1396) -> q_gen_1372
<z, z>() -> q_gen_1372
}

Datatype: <nat, nat>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist, eq_nat}
_|

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 7
() -> delete_all([x, nil, nil]) -> 7
() -> delete_one([x, nil, nil]) -> 7
() -> delete_one([y, cons(y, r), r]) -> 9
() -> leqnat([z, n2]) -> 7
(count([x, l, _fh]) /\ delete_all([x, l, _eh]) /\ delete_one([x, l, _eh])) -> leqnat([_fh, s(z)]) -> 7
(count([x, r, _yg]) /\ not eq_elt([x, y])) -> count([x, cons(y, r), _yg]) -> 7
(count([y, r, _xg])) -> count([y, cons(y, r), s(_xg)]) -> 10
(delete_all([x, r, _sg]) /\ not eq_elt([x, y])) -> delete_all([x, cons(y, r), cons(y, _sg)]) -> 10
(delete_all([y, r, _rg])) -> delete_all([y, cons(y, r), _rg]) -> 10
(delete_one([x, r, _mg]) /\ not eq_elt([x, y])) -> delete_one([x, cons(y, r), cons(y, _mg)]) -> 10
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 8
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 8
(leqnat([s(nn1), z])) -> BOT -> 8
}
Sat witness: Found: ((count([y, r, _xg])) -> count([y, cons(y, r), s(_xg)]), {
_xg -> z  ;  r -> cons(b, nil)  ;  y -> a
})

-------------------------------------------
Step 27, which took 0.008465 s (model generation: 0.007837,  model checking: 0.000628):

Model:
|_
{
count -> 
{{{
Q={q_gen_1378, q_gen_1390, q_gen_1391, q_gen_1393},
Q_f={q_gen_1378},
Delta=
{
<a>() -> q_gen_1391
<b>() -> q_gen_1391
<nil>() -> q_gen_1393
<cons, z>(q_gen_1391, q_gen_1393) -> q_gen_1390
<nil, z>() -> q_gen_1390
<a, cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1378
<a, cons, z>(q_gen_1391, q_gen_1393) -> q_gen_1378
<a, nil, z>() -> q_gen_1378
<b, cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1378
<b, cons, z>(q_gen_1391, q_gen_1393) -> q_gen_1378
<b, nil, z>() -> q_gen_1378
}

Datatype: <elt, eltlist, nat>
Convolution form: right
}}}
  ;  delete_all -> 
{{{
Q={q_gen_1377, q_gen_1384, q_gen_1385, q_gen_1387, q_gen_1388},
Q_f={q_gen_1377},
Delta=
{
<cons>(q_gen_1385, q_gen_1384) -> q_gen_1384
<nil>() -> q_gen_1384
<a>() -> q_gen_1385
<b>() -> q_gen_1385
<cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1387
<nil, nil>() -> q_gen_1387
<a, a>() -> q_gen_1388
<b, b>() -> q_gen_1388
<a, cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1377
<a, cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1377
<a, nil, nil>() -> q_gen_1377
<b, cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1377
<b, cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1377
<b, nil, nil>() -> q_gen_1377
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  delete_one -> 
{{{
Q={q_gen_1373, q_gen_1374, q_gen_1375, q_gen_1381, q_gen_1382},
Q_f={q_gen_1373},
Delta=
{
<nil>() -> q_gen_1374
<a>() -> q_gen_1375
<b>() -> q_gen_1375
<cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1381
<cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1381
<nil, nil>() -> q_gen_1381
<a, a>() -> q_gen_1382
<b, b>() -> q_gen_1382
<a, cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1373
<a, cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1373
<a, nil, nil>() -> q_gen_1373
<b, cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1373
<b, cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1373
<b, nil, nil>() -> q_gen_1373
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  leqnat -> 
{{{
Q={q_gen_1372, q_gen_1396},
Q_f={q_gen_1372},
Delta=
{
<s>(q_gen_1396) -> q_gen_1396
<z>() -> q_gen_1396
<s, s>(q_gen_1372) -> q_gen_1372
<z, s>(q_gen_1396) -> q_gen_1372
<z, z>() -> q_gen_1372
}

Datatype: <nat, nat>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist, eq_nat}
_|

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 7
() -> delete_all([x, nil, nil]) -> 7
() -> delete_one([x, nil, nil]) -> 7
() -> delete_one([y, cons(y, r), r]) -> 9
() -> leqnat([z, n2]) -> 7
(count([x, l, _fh]) /\ delete_all([x, l, _eh]) /\ delete_one([x, l, _eh])) -> leqnat([_fh, s(z)]) -> 7
(count([x, r, _yg]) /\ not eq_elt([x, y])) -> count([x, cons(y, r), _yg]) -> 10
(count([y, r, _xg])) -> count([y, cons(y, r), s(_xg)]) -> 10
(delete_all([x, r, _sg]) /\ not eq_elt([x, y])) -> delete_all([x, cons(y, r), cons(y, _sg)]) -> 10
(delete_all([y, r, _rg])) -> delete_all([y, cons(y, r), _rg]) -> 10
(delete_one([x, r, _mg]) /\ not eq_elt([x, y])) -> delete_one([x, cons(y, r), cons(y, _mg)]) -> 10
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 8
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 8
(leqnat([s(nn1), z])) -> BOT -> 8
}
Sat witness: Found: ((count([x, r, _yg]) /\ not eq_elt([x, y])) -> count([x, cons(y, r), _yg]), {
_yg -> z  ;  r -> cons(b, nil)  ;  x -> a  ;  y -> b
})

-------------------------------------------
Step 28, which took 0.012597 s (model generation: 0.011478,  model checking: 0.001119):

Model:
|_
{
count -> 
{{{
Q={q_gen_1378, q_gen_1390, q_gen_1391, q_gen_1393},
Q_f={q_gen_1378},
Delta=
{
<a>() -> q_gen_1391
<b>() -> q_gen_1391
<cons>(q_gen_1391, q_gen_1393) -> q_gen_1393
<nil>() -> q_gen_1393
<cons, z>(q_gen_1391, q_gen_1393) -> q_gen_1390
<nil, z>() -> q_gen_1390
<a, cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1378
<a, cons, z>(q_gen_1391, q_gen_1393) -> q_gen_1378
<a, nil, z>() -> q_gen_1378
<b, cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1378
<b, cons, z>(q_gen_1391, q_gen_1393) -> q_gen_1378
<b, nil, z>() -> q_gen_1378
}

Datatype: <elt, eltlist, nat>
Convolution form: right
}}}
  ;  delete_all -> 
{{{
Q={q_gen_1377, q_gen_1384, q_gen_1385, q_gen_1387, q_gen_1388},
Q_f={q_gen_1377},
Delta=
{
<cons>(q_gen_1385, q_gen_1384) -> q_gen_1384
<nil>() -> q_gen_1384
<a>() -> q_gen_1385
<b>() -> q_gen_1385
<cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1387
<nil, nil>() -> q_gen_1387
<a, a>() -> q_gen_1388
<b, b>() -> q_gen_1388
<a, cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1377
<a, cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1377
<a, nil, nil>() -> q_gen_1377
<b, cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1377
<b, cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1377
<b, nil, nil>() -> q_gen_1377
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  delete_one -> 
{{{
Q={q_gen_1373, q_gen_1374, q_gen_1375, q_gen_1381, q_gen_1382},
Q_f={q_gen_1373},
Delta=
{
<nil>() -> q_gen_1374
<a>() -> q_gen_1375
<b>() -> q_gen_1375
<cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1381
<cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1381
<nil, nil>() -> q_gen_1381
<a, a>() -> q_gen_1382
<b, b>() -> q_gen_1382
<a, cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1373
<a, cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1373
<a, nil, nil>() -> q_gen_1373
<b, cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1373
<b, cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1373
<b, nil, nil>() -> q_gen_1373
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  leqnat -> 
{{{
Q={q_gen_1372, q_gen_1396},
Q_f={q_gen_1372},
Delta=
{
<s>(q_gen_1396) -> q_gen_1396
<z>() -> q_gen_1396
<s, s>(q_gen_1372) -> q_gen_1372
<z, s>(q_gen_1396) -> q_gen_1372
<z, z>() -> q_gen_1372
}

Datatype: <nat, nat>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist, eq_nat}
_|

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 8
() -> delete_all([x, nil, nil]) -> 8
() -> delete_one([x, nil, nil]) -> 8
() -> delete_one([y, cons(y, r), r]) -> 12
() -> leqnat([z, n2]) -> 8
(count([x, l, _fh]) /\ delete_all([x, l, _eh]) /\ delete_one([x, l, _eh])) -> leqnat([_fh, s(z)]) -> 8
(count([x, r, _yg]) /\ not eq_elt([x, y])) -> count([x, cons(y, r), _yg]) -> 10
(count([y, r, _xg])) -> count([y, cons(y, r), s(_xg)]) -> 10
(delete_all([x, r, _sg]) /\ not eq_elt([x, y])) -> delete_all([x, cons(y, r), cons(y, _sg)]) -> 10
(delete_all([y, r, _rg])) -> delete_all([y, cons(y, r), _rg]) -> 10
(delete_one([x, r, _mg]) /\ not eq_elt([x, y])) -> delete_one([x, cons(y, r), cons(y, _mg)]) -> 10
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 9
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 9
(leqnat([s(nn1), z])) -> BOT -> 9
}
Sat witness: Found: (() -> delete_one([y, cons(y, r), r]), {
r -> cons(a, nil)  ;  y -> b
})

-------------------------------------------
Step 29, which took 0.016713 s (model generation: 0.014706,  model checking: 0.002007):

Model:
|_
{
count -> 
{{{
Q={q_gen_1378, q_gen_1390, q_gen_1391, q_gen_1393},
Q_f={q_gen_1378},
Delta=
{
<a>() -> q_gen_1391
<b>() -> q_gen_1391
<cons>(q_gen_1391, q_gen_1393) -> q_gen_1393
<nil>() -> q_gen_1393
<cons, z>(q_gen_1391, q_gen_1393) -> q_gen_1390
<nil, z>() -> q_gen_1390
<a, cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1378
<a, cons, z>(q_gen_1391, q_gen_1393) -> q_gen_1378
<a, nil, z>() -> q_gen_1378
<b, cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1378
<b, cons, z>(q_gen_1391, q_gen_1393) -> q_gen_1378
<b, nil, z>() -> q_gen_1378
}

Datatype: <elt, eltlist, nat>
Convolution form: right
}}}
  ;  delete_all -> 
{{{
Q={q_gen_1377, q_gen_1384, q_gen_1385, q_gen_1387, q_gen_1388},
Q_f={q_gen_1377},
Delta=
{
<cons>(q_gen_1385, q_gen_1384) -> q_gen_1384
<nil>() -> q_gen_1384
<a>() -> q_gen_1385
<b>() -> q_gen_1385
<cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1387
<nil, nil>() -> q_gen_1387
<a, a>() -> q_gen_1388
<b, b>() -> q_gen_1388
<a, cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1377
<a, cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1377
<a, nil, nil>() -> q_gen_1377
<b, cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1377
<b, cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1377
<b, nil, nil>() -> q_gen_1377
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  delete_one -> 
{{{
Q={q_gen_1373, q_gen_1374, q_gen_1375, q_gen_1381, q_gen_1382},
Q_f={q_gen_1373},
Delta=
{
<nil>() -> q_gen_1374
<a>() -> q_gen_1375
<b>() -> q_gen_1375
<cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1381
<cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1381
<nil, nil>() -> q_gen_1381
<a, a>() -> q_gen_1382
<b, a>() -> q_gen_1382
<b, b>() -> q_gen_1382
<a, cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1373
<a, cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1373
<a, nil, nil>() -> q_gen_1373
<b, cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1373
<b, cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1373
<b, nil, nil>() -> q_gen_1373
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  leqnat -> 
{{{
Q={q_gen_1372, q_gen_1396},
Q_f={q_gen_1372},
Delta=
{
<s>(q_gen_1396) -> q_gen_1396
<z>() -> q_gen_1396
<s, s>(q_gen_1372) -> q_gen_1372
<z, s>(q_gen_1396) -> q_gen_1372
<z, z>() -> q_gen_1372
}

Datatype: <nat, nat>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist, eq_nat}
_|

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 9
() -> delete_all([x, nil, nil]) -> 9
() -> delete_one([x, nil, nil]) -> 9
() -> delete_one([y, cons(y, r), r]) -> 12
() -> leqnat([z, n2]) -> 9
(count([x, l, _fh]) /\ delete_all([x, l, _eh]) /\ delete_one([x, l, _eh])) -> leqnat([_fh, s(z)]) -> 9
(count([x, r, _yg]) /\ not eq_elt([x, y])) -> count([x, cons(y, r), _yg]) -> 10
(count([y, r, _xg])) -> count([y, cons(y, r), s(_xg)]) -> 10
(delete_all([x, r, _sg]) /\ not eq_elt([x, y])) -> delete_all([x, cons(y, r), cons(y, _sg)]) -> 10
(delete_all([y, r, _rg])) -> delete_all([y, cons(y, r), _rg]) -> 13
(delete_one([x, r, _mg]) /\ not eq_elt([x, y])) -> delete_one([x, cons(y, r), cons(y, _mg)]) -> 11
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 10
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 10
(leqnat([s(nn1), z])) -> BOT -> 10
}
Sat witness: Found: ((delete_all([y, r, _rg])) -> delete_all([y, cons(y, r), _rg]), {
_rg -> cons(b, nil)  ;  r -> cons(b, nil)  ;  y -> a
})

-------------------------------------------
Step 30, which took 0.016677 s (model generation: 0.015636,  model checking: 0.001041):

Model:
|_
{
count -> 
{{{
Q={q_gen_1378, q_gen_1390, q_gen_1391, q_gen_1393},
Q_f={q_gen_1378},
Delta=
{
<a>() -> q_gen_1391
<b>() -> q_gen_1391
<cons>(q_gen_1391, q_gen_1393) -> q_gen_1393
<nil>() -> q_gen_1393
<cons, z>(q_gen_1391, q_gen_1393) -> q_gen_1390
<nil, z>() -> q_gen_1390
<a, cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1378
<a, cons, z>(q_gen_1391, q_gen_1393) -> q_gen_1378
<a, nil, z>() -> q_gen_1378
<b, cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1378
<b, cons, z>(q_gen_1391, q_gen_1393) -> q_gen_1378
<b, nil, z>() -> q_gen_1378
}

Datatype: <elt, eltlist, nat>
Convolution form: right
}}}
  ;  delete_all -> 
{{{
Q={q_gen_1377, q_gen_1384, q_gen_1385, q_gen_1387, q_gen_1388},
Q_f={q_gen_1377},
Delta=
{
<cons>(q_gen_1385, q_gen_1384) -> q_gen_1384
<nil>() -> q_gen_1384
<a>() -> q_gen_1385
<b>() -> q_gen_1385
<cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1387
<nil, nil>() -> q_gen_1387
<a, a>() -> q_gen_1388
<a, b>() -> q_gen_1388
<b, b>() -> q_gen_1388
<a, cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1377
<a, cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1377
<a, nil, nil>() -> q_gen_1377
<b, cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1377
<b, cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1377
<b, nil, nil>() -> q_gen_1377
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  delete_one -> 
{{{
Q={q_gen_1373, q_gen_1374, q_gen_1375, q_gen_1381, q_gen_1382},
Q_f={q_gen_1373},
Delta=
{
<nil>() -> q_gen_1374
<a>() -> q_gen_1375
<b>() -> q_gen_1375
<cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1381
<cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1381
<nil, nil>() -> q_gen_1381
<a, a>() -> q_gen_1382
<b, a>() -> q_gen_1382
<b, b>() -> q_gen_1382
<a, cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1373
<a, cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1373
<a, nil, nil>() -> q_gen_1373
<b, cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1373
<b, cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1373
<b, nil, nil>() -> q_gen_1373
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  leqnat -> 
{{{
Q={q_gen_1372, q_gen_1396},
Q_f={q_gen_1372},
Delta=
{
<s>(q_gen_1396) -> q_gen_1396
<z>() -> q_gen_1396
<s, s>(q_gen_1372) -> q_gen_1372
<z, s>(q_gen_1396) -> q_gen_1372
<z, z>() -> q_gen_1372
}

Datatype: <nat, nat>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist, eq_nat}
_|

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 10
() -> delete_all([x, nil, nil]) -> 10
() -> delete_one([x, nil, nil]) -> 10
() -> delete_one([y, cons(y, r), r]) -> 12
() -> leqnat([z, n2]) -> 10
(count([x, l, _fh]) /\ delete_all([x, l, _eh]) /\ delete_one([x, l, _eh])) -> leqnat([_fh, s(z)]) -> 10
(count([x, r, _yg]) /\ not eq_elt([x, y])) -> count([x, cons(y, r), _yg]) -> 10
(count([y, r, _xg])) -> count([y, cons(y, r), s(_xg)]) -> 10
(delete_all([x, r, _sg]) /\ not eq_elt([x, y])) -> delete_all([x, cons(y, r), cons(y, _sg)]) -> 13
(delete_all([y, r, _rg])) -> delete_all([y, cons(y, r), _rg]) -> 13
(delete_one([x, r, _mg]) /\ not eq_elt([x, y])) -> delete_one([x, cons(y, r), cons(y, _mg)]) -> 11
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 11
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 11
(leqnat([s(nn1), z])) -> BOT -> 11
}
Sat witness: Found: ((delete_all([x, r, _sg]) /\ not eq_elt([x, y])) -> delete_all([x, cons(y, r), cons(y, _sg)]), {
_sg -> cons(b, nil)  ;  r -> cons(b, nil)  ;  x -> a  ;  y -> b
})

-------------------------------------------
Step 31, which took 0.014944 s (model generation: 0.013795,  model checking: 0.001149):

Model:
|_
{
count -> 
{{{
Q={q_gen_1378, q_gen_1390, q_gen_1391, q_gen_1393},
Q_f={q_gen_1378},
Delta=
{
<a>() -> q_gen_1391
<b>() -> q_gen_1391
<cons>(q_gen_1391, q_gen_1393) -> q_gen_1393
<nil>() -> q_gen_1393
<cons, z>(q_gen_1391, q_gen_1393) -> q_gen_1390
<nil, z>() -> q_gen_1390
<a, cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1378
<a, cons, z>(q_gen_1391, q_gen_1393) -> q_gen_1378
<a, nil, z>() -> q_gen_1378
<b, cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1378
<b, cons, z>(q_gen_1391, q_gen_1393) -> q_gen_1378
<b, nil, z>() -> q_gen_1378
}

Datatype: <elt, eltlist, nat>
Convolution form: right
}}}
  ;  delete_all -> 
{{{
Q={q_gen_1377, q_gen_1384, q_gen_1385, q_gen_1387, q_gen_1388},
Q_f={q_gen_1377},
Delta=
{
<cons>(q_gen_1385, q_gen_1384) -> q_gen_1384
<nil>() -> q_gen_1384
<a>() -> q_gen_1385
<b>() -> q_gen_1385
<cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1387
<cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1387
<nil, nil>() -> q_gen_1387
<a, a>() -> q_gen_1388
<a, b>() -> q_gen_1388
<b, b>() -> q_gen_1388
<a, cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1377
<a, cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1377
<a, nil, nil>() -> q_gen_1377
<b, cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1377
<b, cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1377
<b, nil, nil>() -> q_gen_1377
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  delete_one -> 
{{{
Q={q_gen_1373, q_gen_1374, q_gen_1375, q_gen_1381, q_gen_1382},
Q_f={q_gen_1373},
Delta=
{
<nil>() -> q_gen_1374
<a>() -> q_gen_1375
<b>() -> q_gen_1375
<cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1381
<cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1381
<nil, nil>() -> q_gen_1381
<a, a>() -> q_gen_1382
<b, a>() -> q_gen_1382
<b, b>() -> q_gen_1382
<a, cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1373
<a, cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1373
<a, nil, nil>() -> q_gen_1373
<b, cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1373
<b, cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1373
<b, nil, nil>() -> q_gen_1373
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  leqnat -> 
{{{
Q={q_gen_1372, q_gen_1396},
Q_f={q_gen_1372},
Delta=
{
<s>(q_gen_1396) -> q_gen_1396
<z>() -> q_gen_1396
<s, s>(q_gen_1372) -> q_gen_1372
<z, s>(q_gen_1396) -> q_gen_1372
<z, z>() -> q_gen_1372
}

Datatype: <nat, nat>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist, eq_nat}
_|

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 10
() -> delete_all([x, nil, nil]) -> 10
() -> delete_one([x, nil, nil]) -> 10
() -> delete_one([y, cons(y, r), r]) -> 12
() -> leqnat([z, n2]) -> 10
(count([x, l, _fh]) /\ delete_all([x, l, _eh]) /\ delete_one([x, l, _eh])) -> leqnat([_fh, s(z)]) -> 10
(count([x, r, _yg]) /\ not eq_elt([x, y])) -> count([x, cons(y, r), _yg]) -> 10
(count([y, r, _xg])) -> count([y, cons(y, r), s(_xg)]) -> 13
(delete_all([x, r, _sg]) /\ not eq_elt([x, y])) -> delete_all([x, cons(y, r), cons(y, _sg)]) -> 13
(delete_all([y, r, _rg])) -> delete_all([y, cons(y, r), _rg]) -> 13
(delete_one([x, r, _mg]) /\ not eq_elt([x, y])) -> delete_one([x, cons(y, r), cons(y, _mg)]) -> 11
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 11
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 11
(leqnat([s(nn1), z])) -> BOT -> 11
}
Sat witness: Found: ((count([y, r, _xg])) -> count([y, cons(y, r), s(_xg)]), {
_xg -> s(z)  ;  r -> cons(b, nil)  ;  y -> a
})

-------------------------------------------
Step 32, which took 0.027504 s (model generation: 0.026083,  model checking: 0.001421):

Model:
|_
{
count -> 
{{{
Q={q_gen_1378, q_gen_1390, q_gen_1391, q_gen_1393},
Q_f={q_gen_1378},
Delta=
{
<a>() -> q_gen_1391
<b>() -> q_gen_1391
<cons>(q_gen_1391, q_gen_1393) -> q_gen_1393
<nil>() -> q_gen_1393
<cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1390
<cons, z>(q_gen_1391, q_gen_1393) -> q_gen_1390
<nil, z>() -> q_gen_1390
<a, cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1378
<a, cons, z>(q_gen_1391, q_gen_1393) -> q_gen_1378
<a, nil, z>() -> q_gen_1378
<b, cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1378
<b, cons, z>(q_gen_1391, q_gen_1393) -> q_gen_1378
<b, nil, z>() -> q_gen_1378
}

Datatype: <elt, eltlist, nat>
Convolution form: right
}}}
  ;  delete_all -> 
{{{
Q={q_gen_1377, q_gen_1384, q_gen_1385, q_gen_1387, q_gen_1388},
Q_f={q_gen_1377},
Delta=
{
<cons>(q_gen_1385, q_gen_1384) -> q_gen_1384
<nil>() -> q_gen_1384
<a>() -> q_gen_1385
<b>() -> q_gen_1385
<cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1387
<cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1387
<nil, nil>() -> q_gen_1387
<a, a>() -> q_gen_1388
<a, b>() -> q_gen_1388
<b, b>() -> q_gen_1388
<a, cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1377
<a, cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1377
<a, nil, nil>() -> q_gen_1377
<b, cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1377
<b, cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1377
<b, nil, nil>() -> q_gen_1377
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  delete_one -> 
{{{
Q={q_gen_1373, q_gen_1374, q_gen_1375, q_gen_1381, q_gen_1382},
Q_f={q_gen_1373},
Delta=
{
<nil>() -> q_gen_1374
<a>() -> q_gen_1375
<b>() -> q_gen_1375
<cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1381
<cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1381
<nil, nil>() -> q_gen_1381
<a, a>() -> q_gen_1382
<b, a>() -> q_gen_1382
<b, b>() -> q_gen_1382
<a, cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1373
<a, cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1373
<a, nil, nil>() -> q_gen_1373
<b, cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1373
<b, cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1373
<b, nil, nil>() -> q_gen_1373
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  leqnat -> 
{{{
Q={q_gen_1372, q_gen_1396},
Q_f={q_gen_1372},
Delta=
{
<s>(q_gen_1396) -> q_gen_1396
<z>() -> q_gen_1396
<s, s>(q_gen_1372) -> q_gen_1372
<z, s>(q_gen_1396) -> q_gen_1372
<z, z>() -> q_gen_1372
}

Datatype: <nat, nat>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist, eq_nat}
_|

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 10
() -> delete_all([x, nil, nil]) -> 10
() -> delete_one([x, nil, nil]) -> 10
() -> delete_one([y, cons(y, r), r]) -> 12
() -> leqnat([z, n2]) -> 10
(count([x, l, _fh]) /\ delete_all([x, l, _eh]) /\ delete_one([x, l, _eh])) -> leqnat([_fh, s(z)]) -> 13
(count([x, r, _yg]) /\ not eq_elt([x, y])) -> count([x, cons(y, r), _yg]) -> 11
(count([y, r, _xg])) -> count([y, cons(y, r), s(_xg)]) -> 13
(delete_all([x, r, _sg]) /\ not eq_elt([x, y])) -> delete_all([x, cons(y, r), cons(y, _sg)]) -> 13
(delete_all([y, r, _rg])) -> delete_all([y, cons(y, r), _rg]) -> 13
(delete_one([x, r, _mg]) /\ not eq_elt([x, y])) -> delete_one([x, cons(y, r), cons(y, _mg)]) -> 11
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 11
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 11
(leqnat([s(nn1), z])) -> BOT -> 11
}
Sat witness: Found: ((count([x, l, _fh]) /\ delete_all([x, l, _eh]) /\ delete_one([x, l, _eh])) -> leqnat([_fh, s(z)]), {
_eh -> cons(b, nil)  ;  _fh -> s(s(z))  ;  l -> cons(b, cons(b, nil))  ;  x -> a
})

-------------------------------------------
Step 33, which took 0.033194 s (model generation: 0.032051,  model checking: 0.001143):

Model:
|_
{
count -> 
{{{
Q={q_gen_1378, q_gen_1390, q_gen_1391, q_gen_1393},
Q_f={q_gen_1378},
Delta=
{
<a>() -> q_gen_1391
<b>() -> q_gen_1391
<cons>(q_gen_1391, q_gen_1393) -> q_gen_1393
<nil>() -> q_gen_1393
<cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1390
<cons, z>(q_gen_1391, q_gen_1393) -> q_gen_1390
<nil, z>() -> q_gen_1390
<a, cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1378
<a, cons, z>(q_gen_1391, q_gen_1393) -> q_gen_1378
<a, nil, z>() -> q_gen_1378
<b, cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1378
<b, cons, z>(q_gen_1391, q_gen_1393) -> q_gen_1378
<b, nil, z>() -> q_gen_1378
}

Datatype: <elt, eltlist, nat>
Convolution form: right
}}}
  ;  delete_all -> 
{{{
Q={q_gen_1377, q_gen_1384, q_gen_1385, q_gen_1387, q_gen_1388},
Q_f={q_gen_1377},
Delta=
{
<cons>(q_gen_1385, q_gen_1384) -> q_gen_1384
<nil>() -> q_gen_1384
<a>() -> q_gen_1385
<b>() -> q_gen_1385
<cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1387
<cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1387
<nil, nil>() -> q_gen_1387
<a, a>() -> q_gen_1388
<a, b>() -> q_gen_1388
<b, b>() -> q_gen_1388
<a, cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1377
<a, cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1377
<a, nil, nil>() -> q_gen_1377
<b, cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1377
<b, cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1377
<b, nil, nil>() -> q_gen_1377
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  delete_one -> 
{{{
Q={q_gen_1373, q_gen_1374, q_gen_1375, q_gen_1381, q_gen_1382},
Q_f={q_gen_1373},
Delta=
{
<nil>() -> q_gen_1374
<a>() -> q_gen_1375
<b>() -> q_gen_1375
<cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1381
<cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1381
<nil, nil>() -> q_gen_1381
<a, a>() -> q_gen_1382
<b, a>() -> q_gen_1382
<b, b>() -> q_gen_1382
<a, cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1373
<a, cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1373
<a, nil, nil>() -> q_gen_1373
<b, cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1373
<b, cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1373
<b, nil, nil>() -> q_gen_1373
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  leqnat -> 
{{{
Q={q_gen_1372, q_gen_1396},
Q_f={q_gen_1372},
Delta=
{
<s>(q_gen_1396) -> q_gen_1396
<z>() -> q_gen_1396
<s, s>(q_gen_1372) -> q_gen_1372
<s, z>(q_gen_1396) -> q_gen_1372
<z, s>(q_gen_1396) -> q_gen_1372
<z, z>() -> q_gen_1372
}

Datatype: <nat, nat>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist, eq_nat}
_|

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 11
() -> delete_all([x, nil, nil]) -> 11
() -> delete_one([x, nil, nil]) -> 11
() -> delete_one([y, cons(y, r), r]) -> 12
() -> leqnat([z, n2]) -> 11
(count([x, l, _fh]) /\ delete_all([x, l, _eh]) /\ delete_one([x, l, _eh])) -> leqnat([_fh, s(z)]) -> 13
(count([x, r, _yg]) /\ not eq_elt([x, y])) -> count([x, cons(y, r), _yg]) -> 11
(count([y, r, _xg])) -> count([y, cons(y, r), s(_xg)]) -> 13
(delete_all([x, r, _sg]) /\ not eq_elt([x, y])) -> delete_all([x, cons(y, r), cons(y, _sg)]) -> 13
(delete_all([y, r, _rg])) -> delete_all([y, cons(y, r), _rg]) -> 13
(delete_one([x, r, _mg]) /\ not eq_elt([x, y])) -> delete_one([x, cons(y, r), cons(y, _mg)]) -> 11
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 11
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 11
(leqnat([s(nn1), z])) -> BOT -> 14
}
Sat witness: Found: ((leqnat([s(nn1), z])) -> BOT, {
nn1 -> z
})

-------------------------------------------
Step 34, which took 0.034525 s (model generation: 0.034298,  model checking: 0.000227):

Model:
|_
{
count -> 
{{{
Q={q_gen_1378, q_gen_1390, q_gen_1391, q_gen_1393},
Q_f={q_gen_1378},
Delta=
{
<a>() -> q_gen_1391
<b>() -> q_gen_1391
<cons>(q_gen_1391, q_gen_1393) -> q_gen_1393
<nil>() -> q_gen_1393
<cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1390
<cons, z>(q_gen_1391, q_gen_1393) -> q_gen_1390
<nil, z>() -> q_gen_1390
<a, cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1378
<a, cons, z>(q_gen_1391, q_gen_1393) -> q_gen_1378
<a, nil, z>() -> q_gen_1378
<b, cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1378
<b, cons, z>(q_gen_1391, q_gen_1393) -> q_gen_1378
<b, nil, z>() -> q_gen_1378
}

Datatype: <elt, eltlist, nat>
Convolution form: right
}}}
  ;  delete_all -> 
{{{
Q={q_gen_1377, q_gen_1384, q_gen_1385, q_gen_1387, q_gen_1388},
Q_f={q_gen_1377},
Delta=
{
<cons>(q_gen_1385, q_gen_1384) -> q_gen_1384
<nil>() -> q_gen_1384
<a>() -> q_gen_1385
<b>() -> q_gen_1385
<cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1387
<cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1387
<nil, nil>() -> q_gen_1387
<a, a>() -> q_gen_1388
<a, b>() -> q_gen_1388
<b, b>() -> q_gen_1388
<a, cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1377
<a, cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1377
<a, nil, nil>() -> q_gen_1377
<b, cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1377
<b, cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1377
<b, nil, nil>() -> q_gen_1377
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  delete_one -> 
{{{
Q={q_gen_1373, q_gen_1374, q_gen_1375, q_gen_1381, q_gen_1382},
Q_f={q_gen_1373},
Delta=
{
<nil>() -> q_gen_1374
<a>() -> q_gen_1375
<b>() -> q_gen_1375
<cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1381
<cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1381
<nil, nil>() -> q_gen_1381
<a, a>() -> q_gen_1382
<b, a>() -> q_gen_1382
<b, b>() -> q_gen_1382
<a, cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1373
<a, cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1373
<a, nil, nil>() -> q_gen_1373
<b, cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1373
<b, cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1373
<b, nil, nil>() -> q_gen_1373
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  leqnat -> 
{{{
Q={q_gen_1372, q_gen_1396, q_gen_1439},
Q_f={q_gen_1372},
Delta=
{
<s>(q_gen_1396) -> q_gen_1396
<z>() -> q_gen_1396
<s, s>(q_gen_1372) -> q_gen_1372
<s, s>(q_gen_1439) -> q_gen_1372
<z, s>(q_gen_1396) -> q_gen_1372
<z, z>() -> q_gen_1372
<s, z>(q_gen_1396) -> q_gen_1439
}

Datatype: <nat, nat>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist, eq_nat}
_|

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 11
() -> delete_all([x, nil, nil]) -> 11
() -> delete_one([x, nil, nil]) -> 11
() -> delete_one([y, cons(y, r), r]) -> 12
() -> leqnat([z, n2]) -> 11
(count([x, l, _fh]) /\ delete_all([x, l, _eh]) /\ delete_one([x, l, _eh])) -> leqnat([_fh, s(z)]) -> 13
(count([x, r, _yg]) /\ not eq_elt([x, y])) -> count([x, cons(y, r), _yg]) -> 11
(count([y, r, _xg])) -> count([y, cons(y, r), s(_xg)]) -> 13
(delete_all([x, r, _sg]) /\ not eq_elt([x, y])) -> delete_all([x, cons(y, r), cons(y, _sg)]) -> 13
(delete_all([y, r, _rg])) -> delete_all([y, cons(y, r), _rg]) -> 13
(delete_one([x, r, _mg]) /\ not eq_elt([x, y])) -> delete_one([x, cons(y, r), cons(y, _mg)]) -> 11
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 11
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 14
(leqnat([s(nn1), z])) -> BOT -> 14
}
Sat witness: Found: ((leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]), {
nn1 -> s(z)  ;  nn2 -> z
})

-------------------------------------------
Step 35, which took 0.034333 s (model generation: 0.032960,  model checking: 0.001373):

Model:
|_
{
count -> 
{{{
Q={q_gen_1378, q_gen_1390, q_gen_1391, q_gen_1393},
Q_f={q_gen_1378},
Delta=
{
<a>() -> q_gen_1391
<b>() -> q_gen_1391
<cons>(q_gen_1391, q_gen_1393) -> q_gen_1393
<nil>() -> q_gen_1393
<cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1390
<cons, z>(q_gen_1391, q_gen_1393) -> q_gen_1390
<nil, z>() -> q_gen_1390
<a, cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1378
<a, cons, z>(q_gen_1391, q_gen_1393) -> q_gen_1378
<a, nil, z>() -> q_gen_1378
<b, cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1378
<b, cons, z>(q_gen_1391, q_gen_1393) -> q_gen_1378
<b, nil, z>() -> q_gen_1378
}

Datatype: <elt, eltlist, nat>
Convolution form: right
}}}
  ;  delete_all -> 
{{{
Q={q_gen_1377, q_gen_1384, q_gen_1385, q_gen_1387, q_gen_1388},
Q_f={q_gen_1377},
Delta=
{
<cons>(q_gen_1385, q_gen_1384) -> q_gen_1384
<nil>() -> q_gen_1384
<a>() -> q_gen_1385
<b>() -> q_gen_1385
<cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1387
<cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1387
<nil, nil>() -> q_gen_1387
<a, a>() -> q_gen_1388
<a, b>() -> q_gen_1388
<b, b>() -> q_gen_1388
<a, cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1377
<a, cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1377
<a, nil, nil>() -> q_gen_1377
<b, cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1377
<b, cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1377
<b, nil, nil>() -> q_gen_1377
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  delete_one -> 
{{{
Q={q_gen_1373, q_gen_1374, q_gen_1375, q_gen_1381, q_gen_1382, q_gen_1413, q_gen_1437},
Q_f={q_gen_1373},
Delta=
{
<nil>() -> q_gen_1374
<a>() -> q_gen_1375
<b>() -> q_gen_1375
<cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1381
<nil, nil>() -> q_gen_1381
<a, a>() -> q_gen_1382
<b, a>() -> q_gen_1382
<b, b>() -> q_gen_1382
<cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1413
<a, cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1373
<a, cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1373
<a, nil, nil>() -> q_gen_1373
<b, cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1373
<b, cons, cons>(q_gen_1382, q_gen_1413) -> q_gen_1373
<b, cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1373
<b, nil, nil>() -> q_gen_1373
<a, cons, cons>(q_gen_1382, q_gen_1413) -> q_gen_1437
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  leqnat -> 
{{{
Q={q_gen_1372, q_gen_1396, q_gen_1438},
Q_f={q_gen_1372},
Delta=
{
<s>(q_gen_1396) -> q_gen_1396
<z>() -> q_gen_1396
<s, s>(q_gen_1372) -> q_gen_1372
<z, s>(q_gen_1396) -> q_gen_1372
<z, z>() -> q_gen_1372
<s, s>(q_gen_1438) -> q_gen_1438
<s, z>(q_gen_1396) -> q_gen_1438
}

Datatype: <nat, nat>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist, eq_nat}
_|

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 11
() -> delete_all([x, nil, nil]) -> 11
() -> delete_one([x, nil, nil]) -> 11
() -> delete_one([y, cons(y, r), r]) -> 12
() -> leqnat([z, n2]) -> 11
(count([x, l, _fh]) /\ delete_all([x, l, _eh]) /\ delete_one([x, l, _eh])) -> leqnat([_fh, s(z)]) -> 13
(count([x, r, _yg]) /\ not eq_elt([x, y])) -> count([x, cons(y, r), _yg]) -> 11
(count([y, r, _xg])) -> count([y, cons(y, r), s(_xg)]) -> 13
(delete_all([x, r, _sg]) /\ not eq_elt([x, y])) -> delete_all([x, cons(y, r), cons(y, _sg)]) -> 13
(delete_all([y, r, _rg])) -> delete_all([y, cons(y, r), _rg]) -> 13
(delete_one([x, r, _mg]) /\ not eq_elt([x, y])) -> delete_one([x, cons(y, r), cons(y, _mg)]) -> 14
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 12
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 14
(leqnat([s(nn1), z])) -> BOT -> 14
}
Sat witness: Found: ((delete_one([x, r, _mg]) /\ not eq_elt([x, y])) -> delete_one([x, cons(y, r), cons(y, _mg)]), {
_mg -> nil  ;  r -> cons(a, nil)  ;  x -> a  ;  y -> b
})

-------------------------------------------
Step 36, which took 0.035168 s (model generation: 0.033912,  model checking: 0.001256):

Model:
|_
{
count -> 
{{{
Q={q_gen_1378, q_gen_1390, q_gen_1391, q_gen_1393, q_gen_1394, q_gen_1432},
Q_f={q_gen_1378},
Delta=
{
<b>() -> q_gen_1391
<cons>(q_gen_1391, q_gen_1393) -> q_gen_1393
<nil>() -> q_gen_1393
<a>() -> q_gen_1394
<cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1390
<cons, z>(q_gen_1391, q_gen_1393) -> q_gen_1390
<nil, z>() -> q_gen_1390
<a, cons, s>(q_gen_1394, q_gen_1390) -> q_gen_1378
<a, cons, z>(q_gen_1391, q_gen_1393) -> q_gen_1378
<a, nil, z>() -> q_gen_1378
<b, cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1378
<b, cons, z>(q_gen_1394, q_gen_1393) -> q_gen_1378
<b, nil, z>() -> q_gen_1378
<a, cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1432
}

Datatype: <elt, eltlist, nat>
Convolution form: right
}}}
  ;  delete_all -> 
{{{
Q={q_gen_1377, q_gen_1384, q_gen_1385, q_gen_1387, q_gen_1388},
Q_f={q_gen_1377},
Delta=
{
<cons>(q_gen_1385, q_gen_1384) -> q_gen_1384
<nil>() -> q_gen_1384
<a>() -> q_gen_1385
<b>() -> q_gen_1385
<cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1387
<cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1387
<nil, nil>() -> q_gen_1387
<a, a>() -> q_gen_1388
<a, b>() -> q_gen_1388
<b, b>() -> q_gen_1388
<a, cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1377
<a, cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1377
<a, nil, nil>() -> q_gen_1377
<b, cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1377
<b, cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1377
<b, nil, nil>() -> q_gen_1377
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  delete_one -> 
{{{
Q={q_gen_1373, q_gen_1374, q_gen_1375, q_gen_1381, q_gen_1382},
Q_f={q_gen_1373},
Delta=
{
<nil>() -> q_gen_1374
<a>() -> q_gen_1375
<b>() -> q_gen_1375
<cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1381
<cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1381
<nil, nil>() -> q_gen_1381
<a, a>() -> q_gen_1382
<b, a>() -> q_gen_1382
<b, b>() -> q_gen_1382
<a, cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1373
<a, cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1373
<a, nil, nil>() -> q_gen_1373
<b, cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1373
<b, cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1373
<b, nil, nil>() -> q_gen_1373
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  leqnat -> 
{{{
Q={q_gen_1372, q_gen_1396, q_gen_1438},
Q_f={q_gen_1372},
Delta=
{
<s>(q_gen_1396) -> q_gen_1396
<z>() -> q_gen_1396
<s, s>(q_gen_1372) -> q_gen_1372
<z, s>(q_gen_1396) -> q_gen_1372
<z, z>() -> q_gen_1372
<s, s>(q_gen_1438) -> q_gen_1438
<s, z>(q_gen_1396) -> q_gen_1438
}

Datatype: <nat, nat>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist, eq_nat}
_|

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 11
() -> delete_all([x, nil, nil]) -> 11
() -> delete_one([x, nil, nil]) -> 11
() -> delete_one([y, cons(y, r), r]) -> 12
() -> leqnat([z, n2]) -> 11
(count([x, l, _fh]) /\ delete_all([x, l, _eh]) /\ delete_one([x, l, _eh])) -> leqnat([_fh, s(z)]) -> 13
(count([x, r, _yg]) /\ not eq_elt([x, y])) -> count([x, cons(y, r), _yg]) -> 14
(count([y, r, _xg])) -> count([y, cons(y, r), s(_xg)]) -> 13
(delete_all([x, r, _sg]) /\ not eq_elt([x, y])) -> delete_all([x, cons(y, r), cons(y, _sg)]) -> 13
(delete_all([y, r, _rg])) -> delete_all([y, cons(y, r), _rg]) -> 13
(delete_one([x, r, _mg]) /\ not eq_elt([x, y])) -> delete_one([x, cons(y, r), cons(y, _mg)]) -> 14
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 12
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 14
(leqnat([s(nn1), z])) -> BOT -> 14
}
Sat witness: Found: ((count([x, r, _yg]) /\ not eq_elt([x, y])) -> count([x, cons(y, r), _yg]), {
_yg -> z  ;  r -> cons(a, nil)  ;  x -> b  ;  y -> a
})

-------------------------------------------
Step 37, which took 0.035900 s (model generation: 0.033604,  model checking: 0.002296):

Model:
|_
{
count -> 
{{{
Q={q_gen_1378, q_gen_1390, q_gen_1391, q_gen_1393, q_gen_1394, q_gen_1432},
Q_f={q_gen_1378},
Delta=
{
<b>() -> q_gen_1391
<cons>(q_gen_1391, q_gen_1393) -> q_gen_1393
<cons>(q_gen_1394, q_gen_1393) -> q_gen_1393
<nil>() -> q_gen_1393
<a>() -> q_gen_1394
<cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1390
<cons, z>(q_gen_1391, q_gen_1393) -> q_gen_1390
<nil, z>() -> q_gen_1390
<a, cons, s>(q_gen_1394, q_gen_1390) -> q_gen_1378
<a, cons, z>(q_gen_1391, q_gen_1393) -> q_gen_1378
<a, nil, z>() -> q_gen_1378
<b, cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1378
<b, cons, z>(q_gen_1394, q_gen_1393) -> q_gen_1378
<b, nil, z>() -> q_gen_1378
<a, cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1432
}

Datatype: <elt, eltlist, nat>
Convolution form: right
}}}
  ;  delete_all -> 
{{{
Q={q_gen_1377, q_gen_1384, q_gen_1385, q_gen_1387, q_gen_1388},
Q_f={q_gen_1377},
Delta=
{
<cons>(q_gen_1385, q_gen_1384) -> q_gen_1384
<nil>() -> q_gen_1384
<a>() -> q_gen_1385
<b>() -> q_gen_1385
<cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1387
<cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1387
<nil, nil>() -> q_gen_1387
<a, a>() -> q_gen_1388
<a, b>() -> q_gen_1388
<b, b>() -> q_gen_1388
<a, cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1377
<a, cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1377
<a, nil, nil>() -> q_gen_1377
<b, cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1377
<b, cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1377
<b, nil, nil>() -> q_gen_1377
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  delete_one -> 
{{{
Q={q_gen_1373, q_gen_1374, q_gen_1375, q_gen_1381, q_gen_1382},
Q_f={q_gen_1373},
Delta=
{
<nil>() -> q_gen_1374
<a>() -> q_gen_1375
<b>() -> q_gen_1375
<cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1381
<cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1381
<nil, nil>() -> q_gen_1381
<a, a>() -> q_gen_1382
<b, a>() -> q_gen_1382
<b, b>() -> q_gen_1382
<a, cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1373
<a, cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1373
<a, nil, nil>() -> q_gen_1373
<b, cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1373
<b, cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1373
<b, nil, nil>() -> q_gen_1373
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  leqnat -> 
{{{
Q={q_gen_1372, q_gen_1396, q_gen_1438},
Q_f={q_gen_1372},
Delta=
{
<s>(q_gen_1396) -> q_gen_1396
<z>() -> q_gen_1396
<s, s>(q_gen_1372) -> q_gen_1372
<z, s>(q_gen_1396) -> q_gen_1372
<z, z>() -> q_gen_1372
<s, s>(q_gen_1438) -> q_gen_1438
<s, z>(q_gen_1396) -> q_gen_1438
}

Datatype: <nat, nat>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist, eq_nat}
_|

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 12
() -> delete_all([x, nil, nil]) -> 12
() -> delete_one([x, nil, nil]) -> 12
() -> delete_one([y, cons(y, r), r]) -> 15
() -> leqnat([z, n2]) -> 12
(count([x, l, _fh]) /\ delete_all([x, l, _eh]) /\ delete_one([x, l, _eh])) -> leqnat([_fh, s(z)]) -> 13
(count([x, r, _yg]) /\ not eq_elt([x, y])) -> count([x, cons(y, r), _yg]) -> 14
(count([y, r, _xg])) -> count([y, cons(y, r), s(_xg)]) -> 13
(delete_all([x, r, _sg]) /\ not eq_elt([x, y])) -> delete_all([x, cons(y, r), cons(y, _sg)]) -> 13
(delete_all([y, r, _rg])) -> delete_all([y, cons(y, r), _rg]) -> 13
(delete_one([x, r, _mg]) /\ not eq_elt([x, y])) -> delete_one([x, cons(y, r), cons(y, _mg)]) -> 14
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 13
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 14
(leqnat([s(nn1), z])) -> BOT -> 14
}
Sat witness: Found: (() -> delete_one([y, cons(y, r), r]), {
r -> cons(b, nil)  ;  y -> a
})

-------------------------------------------
Step 38, which took 0.036485 s (model generation: 0.033863,  model checking: 0.002622):

Model:
|_
{
count -> 
{{{
Q={q_gen_1378, q_gen_1390, q_gen_1391, q_gen_1393, q_gen_1394, q_gen_1432},
Q_f={q_gen_1378},
Delta=
{
<b>() -> q_gen_1391
<cons>(q_gen_1391, q_gen_1393) -> q_gen_1393
<cons>(q_gen_1394, q_gen_1393) -> q_gen_1393
<nil>() -> q_gen_1393
<a>() -> q_gen_1394
<cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1390
<cons, z>(q_gen_1391, q_gen_1393) -> q_gen_1390
<nil, z>() -> q_gen_1390
<a, cons, s>(q_gen_1394, q_gen_1390) -> q_gen_1378
<a, cons, z>(q_gen_1391, q_gen_1393) -> q_gen_1378
<a, nil, z>() -> q_gen_1378
<b, cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1378
<b, cons, z>(q_gen_1394, q_gen_1393) -> q_gen_1378
<b, nil, z>() -> q_gen_1378
<a, cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1432
}

Datatype: <elt, eltlist, nat>
Convolution form: right
}}}
  ;  delete_all -> 
{{{
Q={q_gen_1377, q_gen_1384, q_gen_1385, q_gen_1387, q_gen_1388},
Q_f={q_gen_1377},
Delta=
{
<cons>(q_gen_1385, q_gen_1384) -> q_gen_1384
<nil>() -> q_gen_1384
<a>() -> q_gen_1385
<b>() -> q_gen_1385
<cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1387
<cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1387
<nil, nil>() -> q_gen_1387
<a, a>() -> q_gen_1388
<a, b>() -> q_gen_1388
<b, b>() -> q_gen_1388
<a, cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1377
<a, cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1377
<a, nil, nil>() -> q_gen_1377
<b, cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1377
<b, cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1377
<b, nil, nil>() -> q_gen_1377
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  delete_one -> 
{{{
Q={q_gen_1373, q_gen_1374, q_gen_1375, q_gen_1381, q_gen_1382},
Q_f={q_gen_1373},
Delta=
{
<nil>() -> q_gen_1374
<a>() -> q_gen_1375
<b>() -> q_gen_1375
<cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1381
<cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1381
<nil, nil>() -> q_gen_1381
<a, a>() -> q_gen_1382
<a, b>() -> q_gen_1382
<b, a>() -> q_gen_1382
<b, b>() -> q_gen_1382
<a, cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1373
<a, cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1373
<a, nil, nil>() -> q_gen_1373
<b, cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1373
<b, cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1373
<b, nil, nil>() -> q_gen_1373
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  leqnat -> 
{{{
Q={q_gen_1372, q_gen_1396, q_gen_1438},
Q_f={q_gen_1372},
Delta=
{
<s>(q_gen_1396) -> q_gen_1396
<z>() -> q_gen_1396
<s, s>(q_gen_1372) -> q_gen_1372
<z, s>(q_gen_1396) -> q_gen_1372
<z, z>() -> q_gen_1372
<s, s>(q_gen_1438) -> q_gen_1438
<s, z>(q_gen_1396) -> q_gen_1438
}

Datatype: <nat, nat>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist, eq_nat}
_|

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 13
() -> delete_all([x, nil, nil]) -> 13
() -> delete_one([x, nil, nil]) -> 13
() -> delete_one([y, cons(y, r), r]) -> 15
() -> leqnat([z, n2]) -> 13
(count([x, l, _fh]) /\ delete_all([x, l, _eh]) /\ delete_one([x, l, _eh])) -> leqnat([_fh, s(z)]) -> 13
(count([x, r, _yg]) /\ not eq_elt([x, y])) -> count([x, cons(y, r), _yg]) -> 14
(count([y, r, _xg])) -> count([y, cons(y, r), s(_xg)]) -> 13
(delete_all([x, r, _sg]) /\ not eq_elt([x, y])) -> delete_all([x, cons(y, r), cons(y, _sg)]) -> 13
(delete_all([y, r, _rg])) -> delete_all([y, cons(y, r), _rg]) -> 16
(delete_one([x, r, _mg]) /\ not eq_elt([x, y])) -> delete_one([x, cons(y, r), cons(y, _mg)]) -> 14
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 14
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 14
(leqnat([s(nn1), z])) -> BOT -> 14
}
Sat witness: Found: ((delete_all([y, r, _rg])) -> delete_all([y, cons(y, r), _rg]), {
_rg -> cons(a, nil)  ;  r -> cons(a, nil)  ;  y -> b
})

-------------------------------------------
Step 39, which took 0.037018 s (model generation: 0.035197,  model checking: 0.001821):

Model:
|_
{
count -> 
{{{
Q={q_gen_1378, q_gen_1390, q_gen_1391, q_gen_1393, q_gen_1394, q_gen_1432},
Q_f={q_gen_1378},
Delta=
{
<b>() -> q_gen_1391
<cons>(q_gen_1391, q_gen_1393) -> q_gen_1393
<cons>(q_gen_1394, q_gen_1393) -> q_gen_1393
<nil>() -> q_gen_1393
<a>() -> q_gen_1394
<cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1390
<cons, z>(q_gen_1391, q_gen_1393) -> q_gen_1390
<nil, z>() -> q_gen_1390
<a, cons, s>(q_gen_1394, q_gen_1390) -> q_gen_1378
<a, cons, z>(q_gen_1391, q_gen_1393) -> q_gen_1378
<a, nil, z>() -> q_gen_1378
<b, cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1378
<b, cons, z>(q_gen_1394, q_gen_1393) -> q_gen_1378
<b, nil, z>() -> q_gen_1378
<a, cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1432
}

Datatype: <elt, eltlist, nat>
Convolution form: right
}}}
  ;  delete_all -> 
{{{
Q={q_gen_1377, q_gen_1384, q_gen_1385, q_gen_1387, q_gen_1388},
Q_f={q_gen_1377},
Delta=
{
<cons>(q_gen_1385, q_gen_1384) -> q_gen_1384
<nil>() -> q_gen_1384
<a>() -> q_gen_1385
<b>() -> q_gen_1385
<cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1387
<cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1387
<nil, nil>() -> q_gen_1387
<a, a>() -> q_gen_1388
<a, b>() -> q_gen_1388
<b, a>() -> q_gen_1388
<b, b>() -> q_gen_1388
<a, cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1377
<a, cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1377
<a, nil, nil>() -> q_gen_1377
<b, cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1377
<b, cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1377
<b, nil, nil>() -> q_gen_1377
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  delete_one -> 
{{{
Q={q_gen_1373, q_gen_1374, q_gen_1375, q_gen_1381, q_gen_1382},
Q_f={q_gen_1373},
Delta=
{
<nil>() -> q_gen_1374
<a>() -> q_gen_1375
<b>() -> q_gen_1375
<cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1381
<cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1381
<nil, nil>() -> q_gen_1381
<a, a>() -> q_gen_1382
<a, b>() -> q_gen_1382
<b, a>() -> q_gen_1382
<b, b>() -> q_gen_1382
<a, cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1373
<a, cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1373
<a, nil, nil>() -> q_gen_1373
<b, cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1373
<b, cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1373
<b, nil, nil>() -> q_gen_1373
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  leqnat -> 
{{{
Q={q_gen_1372, q_gen_1396, q_gen_1438},
Q_f={q_gen_1372},
Delta=
{
<s>(q_gen_1396) -> q_gen_1396
<z>() -> q_gen_1396
<s, s>(q_gen_1372) -> q_gen_1372
<z, s>(q_gen_1396) -> q_gen_1372
<z, z>() -> q_gen_1372
<s, s>(q_gen_1438) -> q_gen_1438
<s, z>(q_gen_1396) -> q_gen_1438
}

Datatype: <nat, nat>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist, eq_nat}
_|

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 13
() -> delete_all([x, nil, nil]) -> 13
() -> delete_one([x, nil, nil]) -> 13
() -> delete_one([y, cons(y, r), r]) -> 15
() -> leqnat([z, n2]) -> 13
(count([x, l, _fh]) /\ delete_all([x, l, _eh]) /\ delete_one([x, l, _eh])) -> leqnat([_fh, s(z)]) -> 13
(count([x, r, _yg]) /\ not eq_elt([x, y])) -> count([x, cons(y, r), _yg]) -> 14
(count([y, r, _xg])) -> count([y, cons(y, r), s(_xg)]) -> 16
(delete_all([x, r, _sg]) /\ not eq_elt([x, y])) -> delete_all([x, cons(y, r), cons(y, _sg)]) -> 14
(delete_all([y, r, _rg])) -> delete_all([y, cons(y, r), _rg]) -> 16
(delete_one([x, r, _mg]) /\ not eq_elt([x, y])) -> delete_one([x, cons(y, r), cons(y, _mg)]) -> 14
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 14
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 14
(leqnat([s(nn1), z])) -> BOT -> 14
}
Sat witness: Found: ((count([y, r, _xg])) -> count([y, cons(y, r), s(_xg)]), {
_xg -> z  ;  r -> cons(a, nil)  ;  y -> b
})

-------------------------------------------
Step 40, which took 0.036666 s (model generation: 0.035998,  model checking: 0.000668):

Model:
|_
{
count -> 
{{{
Q={q_gen_1378, q_gen_1390, q_gen_1391, q_gen_1393, q_gen_1394, q_gen_1432},
Q_f={q_gen_1378},
Delta=
{
<b>() -> q_gen_1391
<cons>(q_gen_1391, q_gen_1393) -> q_gen_1393
<cons>(q_gen_1394, q_gen_1393) -> q_gen_1393
<nil>() -> q_gen_1393
<a>() -> q_gen_1394
<cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1390
<cons, z>(q_gen_1391, q_gen_1393) -> q_gen_1390
<cons, z>(q_gen_1394, q_gen_1393) -> q_gen_1390
<nil, z>() -> q_gen_1390
<a, cons, s>(q_gen_1394, q_gen_1390) -> q_gen_1378
<a, cons, z>(q_gen_1391, q_gen_1393) -> q_gen_1378
<a, nil, z>() -> q_gen_1378
<b, cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1378
<b, cons, z>(q_gen_1394, q_gen_1393) -> q_gen_1378
<b, nil, z>() -> q_gen_1378
<a, cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1432
}

Datatype: <elt, eltlist, nat>
Convolution form: right
}}}
  ;  delete_all -> 
{{{
Q={q_gen_1377, q_gen_1384, q_gen_1385, q_gen_1387, q_gen_1388},
Q_f={q_gen_1377},
Delta=
{
<cons>(q_gen_1385, q_gen_1384) -> q_gen_1384
<nil>() -> q_gen_1384
<a>() -> q_gen_1385
<b>() -> q_gen_1385
<cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1387
<cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1387
<nil, nil>() -> q_gen_1387
<a, a>() -> q_gen_1388
<a, b>() -> q_gen_1388
<b, a>() -> q_gen_1388
<b, b>() -> q_gen_1388
<a, cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1377
<a, cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1377
<a, nil, nil>() -> q_gen_1377
<b, cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1377
<b, cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1377
<b, nil, nil>() -> q_gen_1377
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  delete_one -> 
{{{
Q={q_gen_1373, q_gen_1374, q_gen_1375, q_gen_1381, q_gen_1382},
Q_f={q_gen_1373},
Delta=
{
<nil>() -> q_gen_1374
<a>() -> q_gen_1375
<b>() -> q_gen_1375
<cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1381
<cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1381
<nil, nil>() -> q_gen_1381
<a, a>() -> q_gen_1382
<a, b>() -> q_gen_1382
<b, a>() -> q_gen_1382
<b, b>() -> q_gen_1382
<a, cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1373
<a, cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1373
<a, nil, nil>() -> q_gen_1373
<b, cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1373
<b, cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1373
<b, nil, nil>() -> q_gen_1373
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  leqnat -> 
{{{
Q={q_gen_1372, q_gen_1396, q_gen_1438},
Q_f={q_gen_1372},
Delta=
{
<s>(q_gen_1396) -> q_gen_1396
<z>() -> q_gen_1396
<s, s>(q_gen_1372) -> q_gen_1372
<z, s>(q_gen_1396) -> q_gen_1372
<z, z>() -> q_gen_1372
<s, s>(q_gen_1438) -> q_gen_1438
<s, z>(q_gen_1396) -> q_gen_1438
}

Datatype: <nat, nat>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist, eq_nat}
_|

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 13
() -> delete_all([x, nil, nil]) -> 13
() -> delete_one([x, nil, nil]) -> 13
() -> delete_one([y, cons(y, r), r]) -> 15
() -> leqnat([z, n2]) -> 13
(count([x, l, _fh]) /\ delete_all([x, l, _eh]) /\ delete_one([x, l, _eh])) -> leqnat([_fh, s(z)]) -> 16
(count([x, r, _yg]) /\ not eq_elt([x, y])) -> count([x, cons(y, r), _yg]) -> 14
(count([y, r, _xg])) -> count([y, cons(y, r), s(_xg)]) -> 16
(delete_all([x, r, _sg]) /\ not eq_elt([x, y])) -> delete_all([x, cons(y, r), cons(y, _sg)]) -> 14
(delete_all([y, r, _rg])) -> delete_all([y, cons(y, r), _rg]) -> 16
(delete_one([x, r, _mg]) /\ not eq_elt([x, y])) -> delete_one([x, cons(y, r), cons(y, _mg)]) -> 14
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 14
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 14
(leqnat([s(nn1), z])) -> BOT -> 14
}
Sat witness: Found: ((count([x, l, _fh]) /\ delete_all([x, l, _eh]) /\ delete_one([x, l, _eh])) -> leqnat([_fh, s(z)]), {
_eh -> cons(b, nil)  ;  _fh -> s(s(z))  ;  l -> cons(a, cons(b, nil))  ;  x -> a
})

-------------------------------------------
Step 41, which took 0.039923 s (model generation: 0.035764,  model checking: 0.004159):

Model:
|_
{
count -> 
{{{
Q={q_gen_1378, q_gen_1390, q_gen_1391, q_gen_1393, q_gen_1394, q_gen_1432, q_gen_1434},
Q_f={q_gen_1378},
Delta=
{
<b>() -> q_gen_1391
<cons>(q_gen_1391, q_gen_1393) -> q_gen_1393
<cons>(q_gen_1394, q_gen_1393) -> q_gen_1393
<nil>() -> q_gen_1393
<a>() -> q_gen_1394
<cons, z>(q_gen_1391, q_gen_1393) -> q_gen_1390
<nil, z>() -> q_gen_1390
<cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1434
<cons, z>(q_gen_1394, q_gen_1393) -> q_gen_1434
<a, cons, s>(q_gen_1394, q_gen_1390) -> q_gen_1378
<a, cons, z>(q_gen_1391, q_gen_1393) -> q_gen_1378
<a, nil, z>() -> q_gen_1378
<b, cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1378
<b, cons, s>(q_gen_1391, q_gen_1434) -> q_gen_1378
<b, cons, z>(q_gen_1394, q_gen_1393) -> q_gen_1378
<b, nil, z>() -> q_gen_1378
<a, cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1432
<a, cons, s>(q_gen_1391, q_gen_1434) -> q_gen_1432
<a, cons, s>(q_gen_1394, q_gen_1434) -> q_gen_1432
}

Datatype: <elt, eltlist, nat>
Convolution form: right
}}}
  ;  delete_all -> 
{{{
Q={q_gen_1377, q_gen_1384, q_gen_1385, q_gen_1387, q_gen_1388},
Q_f={q_gen_1377},
Delta=
{
<cons>(q_gen_1385, q_gen_1384) -> q_gen_1384
<nil>() -> q_gen_1384
<a>() -> q_gen_1385
<b>() -> q_gen_1385
<cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1387
<cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1387
<nil, nil>() -> q_gen_1387
<a, a>() -> q_gen_1388
<a, b>() -> q_gen_1388
<b, a>() -> q_gen_1388
<b, b>() -> q_gen_1388
<a, cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1377
<a, cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1377
<a, nil, nil>() -> q_gen_1377
<b, cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1377
<b, cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1377
<b, nil, nil>() -> q_gen_1377
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  delete_one -> 
{{{
Q={q_gen_1373, q_gen_1374, q_gen_1375, q_gen_1381, q_gen_1382},
Q_f={q_gen_1373},
Delta=
{
<nil>() -> q_gen_1374
<a>() -> q_gen_1375
<b>() -> q_gen_1375
<cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1381
<cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1381
<nil, nil>() -> q_gen_1381
<a, a>() -> q_gen_1382
<a, b>() -> q_gen_1382
<b, a>() -> q_gen_1382
<b, b>() -> q_gen_1382
<a, cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1373
<a, cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1373
<a, nil, nil>() -> q_gen_1373
<b, cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1373
<b, cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1373
<b, nil, nil>() -> q_gen_1373
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  leqnat -> 
{{{
Q={q_gen_1372, q_gen_1396, q_gen_1438},
Q_f={q_gen_1372},
Delta=
{
<s>(q_gen_1396) -> q_gen_1396
<z>() -> q_gen_1396
<s, s>(q_gen_1372) -> q_gen_1372
<z, s>(q_gen_1396) -> q_gen_1372
<z, z>() -> q_gen_1372
<s, s>(q_gen_1438) -> q_gen_1438
<s, z>(q_gen_1396) -> q_gen_1438
}

Datatype: <nat, nat>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist, eq_nat}
_|

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 14
() -> delete_all([x, nil, nil]) -> 14
() -> delete_one([x, nil, nil]) -> 14
() -> delete_one([y, cons(y, r), r]) -> 15
() -> leqnat([z, n2]) -> 14
(count([x, l, _fh]) /\ delete_all([x, l, _eh]) /\ delete_one([x, l, _eh])) -> leqnat([_fh, s(z)]) -> 16
(count([x, r, _yg]) /\ not eq_elt([x, y])) -> count([x, cons(y, r), _yg]) -> 17
(count([y, r, _xg])) -> count([y, cons(y, r), s(_xg)]) -> 16
(delete_all([x, r, _sg]) /\ not eq_elt([x, y])) -> delete_all([x, cons(y, r), cons(y, _sg)]) -> 15
(delete_all([y, r, _rg])) -> delete_all([y, cons(y, r), _rg]) -> 16
(delete_one([x, r, _mg]) /\ not eq_elt([x, y])) -> delete_one([x, cons(y, r), cons(y, _mg)]) -> 15
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 15
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 15
(leqnat([s(nn1), z])) -> BOT -> 15
}
Sat witness: Found: ((count([x, r, _yg]) /\ not eq_elt([x, y])) -> count([x, cons(y, r), _yg]), {
_yg -> s(z)  ;  r -> cons(a, nil)  ;  x -> a  ;  y -> b
})

-------------------------------------------
Step 42, which took 0.047182 s (model generation: 0.037731,  model checking: 0.009451):

Model:
|_
{
count -> 
{{{
Q={q_gen_1378, q_gen_1390, q_gen_1391, q_gen_1393, q_gen_1394, q_gen_1432, q_gen_1434, q_gen_1448},
Q_f={q_gen_1378},
Delta=
{
<b>() -> q_gen_1391
<cons>(q_gen_1391, q_gen_1393) -> q_gen_1393
<cons>(q_gen_1394, q_gen_1393) -> q_gen_1393
<nil>() -> q_gen_1393
<a>() -> q_gen_1394
<cons, z>(q_gen_1391, q_gen_1393) -> q_gen_1390
<nil, z>() -> q_gen_1390
<cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1434
<cons, z>(q_gen_1394, q_gen_1393) -> q_gen_1448
<a, cons, s>(q_gen_1391, q_gen_1448) -> q_gen_1378
<a, cons, s>(q_gen_1394, q_gen_1390) -> q_gen_1378
<a, cons, z>(q_gen_1391, q_gen_1393) -> q_gen_1378
<a, nil, z>() -> q_gen_1378
<b, cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1378
<b, cons, s>(q_gen_1391, q_gen_1448) -> q_gen_1378
<b, cons, z>(q_gen_1394, q_gen_1393) -> q_gen_1378
<b, nil, z>() -> q_gen_1378
<a, cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1432
<a, cons, s>(q_gen_1391, q_gen_1434) -> q_gen_1432
<a, cons, s>(q_gen_1394, q_gen_1434) -> q_gen_1432
}

Datatype: <elt, eltlist, nat>
Convolution form: right
}}}
  ;  delete_all -> 
{{{
Q={q_gen_1377, q_gen_1384, q_gen_1385, q_gen_1387, q_gen_1388},
Q_f={q_gen_1377},
Delta=
{
<cons>(q_gen_1385, q_gen_1384) -> q_gen_1384
<nil>() -> q_gen_1384
<a>() -> q_gen_1385
<b>() -> q_gen_1385
<cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1387
<cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1387
<nil, nil>() -> q_gen_1387
<a, a>() -> q_gen_1388
<a, b>() -> q_gen_1388
<b, a>() -> q_gen_1388
<b, b>() -> q_gen_1388
<a, cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1377
<a, cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1377
<a, nil, nil>() -> q_gen_1377
<b, cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1377
<b, cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1377
<b, nil, nil>() -> q_gen_1377
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  delete_one -> 
{{{
Q={q_gen_1373, q_gen_1374, q_gen_1375, q_gen_1381, q_gen_1382},
Q_f={q_gen_1373},
Delta=
{
<nil>() -> q_gen_1374
<a>() -> q_gen_1375
<b>() -> q_gen_1375
<cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1381
<cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1381
<nil, nil>() -> q_gen_1381
<a, a>() -> q_gen_1382
<a, b>() -> q_gen_1382
<b, a>() -> q_gen_1382
<b, b>() -> q_gen_1382
<a, cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1373
<a, cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1373
<a, nil, nil>() -> q_gen_1373
<b, cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1373
<b, cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1373
<b, nil, nil>() -> q_gen_1373
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  leqnat -> 
{{{
Q={q_gen_1372, q_gen_1396, q_gen_1438},
Q_f={q_gen_1372},
Delta=
{
<s>(q_gen_1396) -> q_gen_1396
<z>() -> q_gen_1396
<s, s>(q_gen_1372) -> q_gen_1372
<z, s>(q_gen_1396) -> q_gen_1372
<z, z>() -> q_gen_1372
<s, s>(q_gen_1438) -> q_gen_1438
<s, z>(q_gen_1396) -> q_gen_1438
}

Datatype: <nat, nat>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist, eq_nat}
_|

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 15
() -> delete_all([x, nil, nil]) -> 15
() -> delete_one([x, nil, nil]) -> 15
() -> delete_one([y, cons(y, r), r]) -> 16
() -> leqnat([z, n2]) -> 15
(count([x, l, _fh]) /\ delete_all([x, l, _eh]) /\ delete_one([x, l, _eh])) -> leqnat([_fh, s(z)]) -> 16
(count([x, r, _yg]) /\ not eq_elt([x, y])) -> count([x, cons(y, r), _yg]) -> 17
(count([y, r, _xg])) -> count([y, cons(y, r), s(_xg)]) -> 19
(delete_all([x, r, _sg]) /\ not eq_elt([x, y])) -> delete_all([x, cons(y, r), cons(y, _sg)]) -> 16
(delete_all([y, r, _rg])) -> delete_all([y, cons(y, r), _rg]) -> 17
(delete_one([x, r, _mg]) /\ not eq_elt([x, y])) -> delete_one([x, cons(y, r), cons(y, _mg)]) -> 16
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 16
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 16
(leqnat([s(nn1), z])) -> BOT -> 16
}
Sat witness: Found: ((count([y, r, _xg])) -> count([y, cons(y, r), s(_xg)]), {
_xg -> s(z)  ;  r -> cons(a, nil)  ;  y -> a
})

-------------------------------------------
Step 43, which took 0.044833 s (model generation: 0.040866,  model checking: 0.003967):

Model:
|_
{
count -> 
{{{
Q={q_gen_1378, q_gen_1390, q_gen_1391, q_gen_1393, q_gen_1394, q_gen_1421, q_gen_1432, q_gen_1434},
Q_f={q_gen_1378},
Delta=
{
<b>() -> q_gen_1391
<cons>(q_gen_1391, q_gen_1393) -> q_gen_1393
<cons>(q_gen_1394, q_gen_1393) -> q_gen_1393
<nil>() -> q_gen_1393
<a>() -> q_gen_1394
<nil, z>() -> q_gen_1390
<cons, s>(q_gen_1394, q_gen_1390) -> q_gen_1421
<cons, z>(q_gen_1391, q_gen_1393) -> q_gen_1421
<cons, z>(q_gen_1394, q_gen_1393) -> q_gen_1421
<cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1434
<a, cons, s>(q_gen_1391, q_gen_1421) -> q_gen_1378
<a, cons, s>(q_gen_1394, q_gen_1390) -> q_gen_1378
<a, cons, s>(q_gen_1394, q_gen_1421) -> q_gen_1378
<a, cons, z>(q_gen_1391, q_gen_1393) -> q_gen_1378
<a, nil, z>() -> q_gen_1378
<b, cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1378
<b, cons, s>(q_gen_1391, q_gen_1421) -> q_gen_1378
<b, cons, z>(q_gen_1394, q_gen_1393) -> q_gen_1378
<b, nil, z>() -> q_gen_1378
<a, cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1432
<a, cons, s>(q_gen_1391, q_gen_1434) -> q_gen_1432
<a, cons, s>(q_gen_1394, q_gen_1434) -> q_gen_1432
}

Datatype: <elt, eltlist, nat>
Convolution form: right
}}}
  ;  delete_all -> 
{{{
Q={q_gen_1377, q_gen_1384, q_gen_1385, q_gen_1387, q_gen_1388},
Q_f={q_gen_1377},
Delta=
{
<cons>(q_gen_1385, q_gen_1384) -> q_gen_1384
<nil>() -> q_gen_1384
<a>() -> q_gen_1385
<b>() -> q_gen_1385
<cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1387
<cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1387
<nil, nil>() -> q_gen_1387
<a, a>() -> q_gen_1388
<a, b>() -> q_gen_1388
<b, a>() -> q_gen_1388
<b, b>() -> q_gen_1388
<a, cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1377
<a, cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1377
<a, nil, nil>() -> q_gen_1377
<b, cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1377
<b, cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1377
<b, nil, nil>() -> q_gen_1377
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  delete_one -> 
{{{
Q={q_gen_1373, q_gen_1374, q_gen_1375, q_gen_1381, q_gen_1382},
Q_f={q_gen_1373},
Delta=
{
<nil>() -> q_gen_1374
<a>() -> q_gen_1375
<b>() -> q_gen_1375
<cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1381
<cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1381
<nil, nil>() -> q_gen_1381
<a, a>() -> q_gen_1382
<a, b>() -> q_gen_1382
<b, a>() -> q_gen_1382
<b, b>() -> q_gen_1382
<a, cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1373
<a, cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1373
<a, nil, nil>() -> q_gen_1373
<b, cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1373
<b, cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1373
<b, nil, nil>() -> q_gen_1373
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  leqnat -> 
{{{
Q={q_gen_1372, q_gen_1396, q_gen_1438},
Q_f={q_gen_1372},
Delta=
{
<s>(q_gen_1396) -> q_gen_1396
<z>() -> q_gen_1396
<s, s>(q_gen_1372) -> q_gen_1372
<z, s>(q_gen_1396) -> q_gen_1372
<z, z>() -> q_gen_1372
<s, s>(q_gen_1438) -> q_gen_1438
<s, z>(q_gen_1396) -> q_gen_1438
}

Datatype: <nat, nat>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist, eq_nat}
_|

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 16
() -> delete_all([x, nil, nil]) -> 16
() -> delete_one([x, nil, nil]) -> 16
() -> delete_one([y, cons(y, r), r]) -> 16
() -> leqnat([z, n2]) -> 16
(count([x, l, _fh]) /\ delete_all([x, l, _eh]) /\ delete_one([x, l, _eh])) -> leqnat([_fh, s(z)]) -> 19
(count([x, r, _yg]) /\ not eq_elt([x, y])) -> count([x, cons(y, r), _yg]) -> 17
(count([y, r, _xg])) -> count([y, cons(y, r), s(_xg)]) -> 19
(delete_all([x, r, _sg]) /\ not eq_elt([x, y])) -> delete_all([x, cons(y, r), cons(y, _sg)]) -> 17
(delete_all([y, r, _rg])) -> delete_all([y, cons(y, r), _rg]) -> 17
(delete_one([x, r, _mg]) /\ not eq_elt([x, y])) -> delete_one([x, cons(y, r), cons(y, _mg)]) -> 17
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 17
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 17
(leqnat([s(nn1), z])) -> BOT -> 17
}
Sat witness: Found: ((count([x, l, _fh]) /\ delete_all([x, l, _eh]) /\ delete_one([x, l, _eh])) -> leqnat([_fh, s(z)]), {
_eh -> cons(b, nil)  ;  _fh -> s(s(z))  ;  l -> cons(b, cons(a, nil))  ;  x -> a
})

-------------------------------------------
Step 44, which took 0.045748 s (model generation: 0.039438,  model checking: 0.006310):

Model:
|_
{
count -> 
{{{
Q={q_gen_1378, q_gen_1390, q_gen_1391, q_gen_1393, q_gen_1394, q_gen_1421, q_gen_1432, q_gen_1434},
Q_f={q_gen_1378},
Delta=
{
<b>() -> q_gen_1391
<cons>(q_gen_1391, q_gen_1393) -> q_gen_1393
<cons>(q_gen_1394, q_gen_1393) -> q_gen_1393
<nil>() -> q_gen_1393
<a>() -> q_gen_1394
<cons, s>(q_gen_1394, q_gen_1390) -> q_gen_1390
<nil, z>() -> q_gen_1390
<cons, z>(q_gen_1391, q_gen_1393) -> q_gen_1421
<cons, z>(q_gen_1394, q_gen_1393) -> q_gen_1421
<cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1434
<a, cons, s>(q_gen_1391, q_gen_1421) -> q_gen_1378
<a, cons, s>(q_gen_1394, q_gen_1390) -> q_gen_1378
<a, cons, s>(q_gen_1394, q_gen_1421) -> q_gen_1378
<a, cons, z>(q_gen_1391, q_gen_1393) -> q_gen_1378
<a, nil, z>() -> q_gen_1378
<b, cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1378
<b, cons, s>(q_gen_1391, q_gen_1421) -> q_gen_1378
<b, cons, z>(q_gen_1394, q_gen_1393) -> q_gen_1378
<b, nil, z>() -> q_gen_1378
<a, cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1432
<a, cons, s>(q_gen_1391, q_gen_1434) -> q_gen_1432
<a, cons, s>(q_gen_1394, q_gen_1434) -> q_gen_1432
}

Datatype: <elt, eltlist, nat>
Convolution form: right
}}}
  ;  delete_all -> 
{{{
Q={q_gen_1377, q_gen_1384, q_gen_1385, q_gen_1387, q_gen_1388},
Q_f={q_gen_1377},
Delta=
{
<cons>(q_gen_1385, q_gen_1384) -> q_gen_1384
<nil>() -> q_gen_1384
<a>() -> q_gen_1385
<b>() -> q_gen_1385
<cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1387
<cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1387
<nil, nil>() -> q_gen_1387
<a, a>() -> q_gen_1388
<a, b>() -> q_gen_1388
<b, a>() -> q_gen_1388
<b, b>() -> q_gen_1388
<a, cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1377
<a, cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1377
<a, nil, nil>() -> q_gen_1377
<b, cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1377
<b, cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1377
<b, nil, nil>() -> q_gen_1377
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  delete_one -> 
{{{
Q={q_gen_1373, q_gen_1374, q_gen_1375, q_gen_1381, q_gen_1382},
Q_f={q_gen_1373},
Delta=
{
<nil>() -> q_gen_1374
<a>() -> q_gen_1375
<b>() -> q_gen_1375
<cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1381
<cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1381
<nil, nil>() -> q_gen_1381
<a, a>() -> q_gen_1382
<a, b>() -> q_gen_1382
<b, a>() -> q_gen_1382
<b, b>() -> q_gen_1382
<a, cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1373
<a, cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1373
<a, nil, nil>() -> q_gen_1373
<b, cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1373
<b, cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1373
<b, nil, nil>() -> q_gen_1373
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  leqnat -> 
{{{
Q={q_gen_1372, q_gen_1396, q_gen_1438},
Q_f={q_gen_1372},
Delta=
{
<s>(q_gen_1396) -> q_gen_1396
<z>() -> q_gen_1396
<s, s>(q_gen_1372) -> q_gen_1372
<z, s>(q_gen_1396) -> q_gen_1372
<z, z>() -> q_gen_1372
<s, s>(q_gen_1438) -> q_gen_1438
<s, z>(q_gen_1396) -> q_gen_1438
}

Datatype: <nat, nat>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist, eq_nat}
_|

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 17
() -> delete_all([x, nil, nil]) -> 17
() -> delete_one([x, nil, nil]) -> 17
() -> delete_one([y, cons(y, r), r]) -> 17
() -> leqnat([z, n2]) -> 17
(count([x, l, _fh]) /\ delete_all([x, l, _eh]) /\ delete_one([x, l, _eh])) -> leqnat([_fh, s(z)]) -> 19
(count([x, r, _yg]) /\ not eq_elt([x, y])) -> count([x, cons(y, r), _yg]) -> 20
(count([y, r, _xg])) -> count([y, cons(y, r), s(_xg)]) -> 19
(delete_all([x, r, _sg]) /\ not eq_elt([x, y])) -> delete_all([x, cons(y, r), cons(y, _sg)]) -> 18
(delete_all([y, r, _rg])) -> delete_all([y, cons(y, r), _rg]) -> 18
(delete_one([x, r, _mg]) /\ not eq_elt([x, y])) -> delete_one([x, cons(y, r), cons(y, _mg)]) -> 18
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 18
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 18
(leqnat([s(nn1), z])) -> BOT -> 18
}
Sat witness: Found: ((count([x, r, _yg]) /\ not eq_elt([x, y])) -> count([x, cons(y, r), _yg]), {
_yg -> s(z)  ;  r -> cons(b, nil)  ;  x -> b  ;  y -> a
})

-------------------------------------------
Step 45, which took 0.047649 s (model generation: 0.041215,  model checking: 0.006434):

Model:
|_
{
count -> 
{{{
Q={q_gen_1378, q_gen_1390, q_gen_1391, q_gen_1393, q_gen_1394, q_gen_1421, q_gen_1432, q_gen_1434},
Q_f={q_gen_1378},
Delta=
{
<b>() -> q_gen_1391
<cons>(q_gen_1391, q_gen_1393) -> q_gen_1393
<cons>(q_gen_1394, q_gen_1393) -> q_gen_1393
<nil>() -> q_gen_1393
<a>() -> q_gen_1394
<cons, s>(q_gen_1394, q_gen_1390) -> q_gen_1390
<nil, z>() -> q_gen_1390
<cons, z>(q_gen_1391, q_gen_1393) -> q_gen_1421
<cons, z>(q_gen_1394, q_gen_1393) -> q_gen_1421
<cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1434
<a, cons, s>(q_gen_1391, q_gen_1421) -> q_gen_1378
<a, cons, s>(q_gen_1394, q_gen_1390) -> q_gen_1378
<a, cons, s>(q_gen_1394, q_gen_1421) -> q_gen_1378
<a, cons, z>(q_gen_1391, q_gen_1393) -> q_gen_1378
<a, nil, z>() -> q_gen_1378
<b, cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1378
<b, cons, s>(q_gen_1391, q_gen_1421) -> q_gen_1378
<b, cons, s>(q_gen_1394, q_gen_1421) -> q_gen_1378
<b, cons, z>(q_gen_1394, q_gen_1393) -> q_gen_1378
<b, nil, z>() -> q_gen_1378
<a, cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1432
<a, cons, s>(q_gen_1391, q_gen_1434) -> q_gen_1432
<a, cons, s>(q_gen_1394, q_gen_1434) -> q_gen_1432
}

Datatype: <elt, eltlist, nat>
Convolution form: right
}}}
  ;  delete_all -> 
{{{
Q={q_gen_1377, q_gen_1384, q_gen_1385, q_gen_1387, q_gen_1388},
Q_f={q_gen_1377},
Delta=
{
<cons>(q_gen_1385, q_gen_1384) -> q_gen_1384
<nil>() -> q_gen_1384
<a>() -> q_gen_1385
<b>() -> q_gen_1385
<cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1387
<cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1387
<nil, nil>() -> q_gen_1387
<a, a>() -> q_gen_1388
<a, b>() -> q_gen_1388
<b, a>() -> q_gen_1388
<b, b>() -> q_gen_1388
<a, cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1377
<a, cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1377
<a, nil, nil>() -> q_gen_1377
<b, cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1377
<b, cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1377
<b, nil, nil>() -> q_gen_1377
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  delete_one -> 
{{{
Q={q_gen_1373, q_gen_1374, q_gen_1375, q_gen_1381, q_gen_1382},
Q_f={q_gen_1373},
Delta=
{
<nil>() -> q_gen_1374
<a>() -> q_gen_1375
<b>() -> q_gen_1375
<cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1381
<cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1381
<nil, nil>() -> q_gen_1381
<a, a>() -> q_gen_1382
<a, b>() -> q_gen_1382
<b, a>() -> q_gen_1382
<b, b>() -> q_gen_1382
<a, cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1373
<a, cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1373
<a, nil, nil>() -> q_gen_1373
<b, cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1373
<b, cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1373
<b, nil, nil>() -> q_gen_1373
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  leqnat -> 
{{{
Q={q_gen_1372, q_gen_1396, q_gen_1438},
Q_f={q_gen_1372},
Delta=
{
<s>(q_gen_1396) -> q_gen_1396
<z>() -> q_gen_1396
<s, s>(q_gen_1372) -> q_gen_1372
<z, s>(q_gen_1396) -> q_gen_1372
<z, z>() -> q_gen_1372
<s, s>(q_gen_1438) -> q_gen_1438
<s, z>(q_gen_1396) -> q_gen_1438
}

Datatype: <nat, nat>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist, eq_nat}
_|

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 18
() -> delete_all([x, nil, nil]) -> 18
() -> delete_one([x, nil, nil]) -> 18
() -> delete_one([y, cons(y, r), r]) -> 18
() -> leqnat([z, n2]) -> 18
(count([x, l, _fh]) /\ delete_all([x, l, _eh]) /\ delete_one([x, l, _eh])) -> leqnat([_fh, s(z)]) -> 19
(count([x, r, _yg]) /\ not eq_elt([x, y])) -> count([x, cons(y, r), _yg]) -> 20
(count([y, r, _xg])) -> count([y, cons(y, r), s(_xg)]) -> 22
(delete_all([x, r, _sg]) /\ not eq_elt([x, y])) -> delete_all([x, cons(y, r), cons(y, _sg)]) -> 19
(delete_all([y, r, _rg])) -> delete_all([y, cons(y, r), _rg]) -> 19
(delete_one([x, r, _mg]) /\ not eq_elt([x, y])) -> delete_one([x, cons(y, r), cons(y, _mg)]) -> 19
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 19
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 19
(leqnat([s(nn1), z])) -> BOT -> 19
}
Sat witness: Found: ((count([y, r, _xg])) -> count([y, cons(y, r), s(_xg)]), {
_xg -> s(z)  ;  r -> cons(b, nil)  ;  y -> b
})

-------------------------------------------
Step 46, which took 0.047838 s (model generation: 0.042562,  model checking: 0.005276):

Model:
|_
{
count -> 
{{{
Q={q_gen_1378, q_gen_1390, q_gen_1391, q_gen_1393, q_gen_1394, q_gen_1432, q_gen_1434, q_gen_1448},
Q_f={q_gen_1378},
Delta=
{
<b>() -> q_gen_1391
<cons>(q_gen_1391, q_gen_1393) -> q_gen_1393
<cons>(q_gen_1394, q_gen_1393) -> q_gen_1393
<nil>() -> q_gen_1393
<a>() -> q_gen_1394
<cons, s>(q_gen_1394, q_gen_1390) -> q_gen_1390
<cons, z>(q_gen_1391, q_gen_1393) -> q_gen_1390
<nil, z>() -> q_gen_1390
<cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1434
<cons, z>(q_gen_1394, q_gen_1393) -> q_gen_1448
<a, cons, s>(q_gen_1391, q_gen_1448) -> q_gen_1378
<a, cons, s>(q_gen_1394, q_gen_1390) -> q_gen_1378
<a, cons, z>(q_gen_1391, q_gen_1393) -> q_gen_1378
<a, nil, z>() -> q_gen_1378
<b, cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1378
<b, cons, s>(q_gen_1391, q_gen_1434) -> q_gen_1378
<b, cons, s>(q_gen_1391, q_gen_1448) -> q_gen_1378
<b, cons, s>(q_gen_1394, q_gen_1390) -> q_gen_1378
<b, cons, z>(q_gen_1394, q_gen_1393) -> q_gen_1378
<b, nil, z>() -> q_gen_1378
<a, cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1432
<a, cons, s>(q_gen_1391, q_gen_1434) -> q_gen_1432
<a, cons, s>(q_gen_1394, q_gen_1434) -> q_gen_1432
}

Datatype: <elt, eltlist, nat>
Convolution form: right
}}}
  ;  delete_all -> 
{{{
Q={q_gen_1377, q_gen_1384, q_gen_1385, q_gen_1387, q_gen_1388},
Q_f={q_gen_1377},
Delta=
{
<cons>(q_gen_1385, q_gen_1384) -> q_gen_1384
<nil>() -> q_gen_1384
<a>() -> q_gen_1385
<b>() -> q_gen_1385
<cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1387
<cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1387
<nil, nil>() -> q_gen_1387
<a, a>() -> q_gen_1388
<a, b>() -> q_gen_1388
<b, a>() -> q_gen_1388
<b, b>() -> q_gen_1388
<a, cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1377
<a, cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1377
<a, nil, nil>() -> q_gen_1377
<b, cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1377
<b, cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1377
<b, nil, nil>() -> q_gen_1377
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  delete_one -> 
{{{
Q={q_gen_1373, q_gen_1374, q_gen_1375, q_gen_1381, q_gen_1382},
Q_f={q_gen_1373},
Delta=
{
<nil>() -> q_gen_1374
<a>() -> q_gen_1375
<b>() -> q_gen_1375
<cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1381
<cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1381
<nil, nil>() -> q_gen_1381
<a, a>() -> q_gen_1382
<a, b>() -> q_gen_1382
<b, a>() -> q_gen_1382
<b, b>() -> q_gen_1382
<a, cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1373
<a, cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1373
<a, nil, nil>() -> q_gen_1373
<b, cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1373
<b, cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1373
<b, nil, nil>() -> q_gen_1373
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  leqnat -> 
{{{
Q={q_gen_1372, q_gen_1396, q_gen_1438},
Q_f={q_gen_1372},
Delta=
{
<s>(q_gen_1396) -> q_gen_1396
<z>() -> q_gen_1396
<s, s>(q_gen_1372) -> q_gen_1372
<z, s>(q_gen_1396) -> q_gen_1372
<z, z>() -> q_gen_1372
<s, s>(q_gen_1438) -> q_gen_1438
<s, z>(q_gen_1396) -> q_gen_1438
}

Datatype: <nat, nat>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist, eq_nat}
_|

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 19
() -> delete_all([x, nil, nil]) -> 19
() -> delete_one([x, nil, nil]) -> 19
() -> delete_one([y, cons(y, r), r]) -> 19
() -> leqnat([z, n2]) -> 19
(count([x, l, _fh]) /\ delete_all([x, l, _eh]) /\ delete_one([x, l, _eh])) -> leqnat([_fh, s(z)]) -> 22
(count([x, r, _yg]) /\ not eq_elt([x, y])) -> count([x, cons(y, r), _yg]) -> 20
(count([y, r, _xg])) -> count([y, cons(y, r), s(_xg)]) -> 22
(delete_all([x, r, _sg]) /\ not eq_elt([x, y])) -> delete_all([x, cons(y, r), cons(y, _sg)]) -> 20
(delete_all([y, r, _rg])) -> delete_all([y, cons(y, r), _rg]) -> 20
(delete_one([x, r, _mg]) /\ not eq_elt([x, y])) -> delete_one([x, cons(y, r), cons(y, _mg)]) -> 20
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 20
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 20
(leqnat([s(nn1), z])) -> BOT -> 20
}
Sat witness: Found: ((count([x, l, _fh]) /\ delete_all([x, l, _eh]) /\ delete_one([x, l, _eh])) -> leqnat([_fh, s(z)]), {
_eh -> cons(b, cons(b, nil))  ;  _fh -> s(s(z))  ;  l -> cons(b, cons(a, nil))  ;  x -> b
})

-------------------------------------------
Step 47, which took 0.059271 s (model generation: 0.051242,  model checking: 0.008029):

Model:
|_
{
count -> 
{{{
Q={q_gen_1378, q_gen_1390, q_gen_1391, q_gen_1393, q_gen_1394, q_gen_1421, q_gen_1432, q_gen_1434, q_gen_1451},
Q_f={q_gen_1378},
Delta=
{
<b>() -> q_gen_1391
<cons>(q_gen_1391, q_gen_1393) -> q_gen_1393
<cons>(q_gen_1394, q_gen_1393) -> q_gen_1393
<nil>() -> q_gen_1393
<a>() -> q_gen_1394
<nil, z>() -> q_gen_1390
<cons, z>(q_gen_1391, q_gen_1393) -> q_gen_1421
<cons, z>(q_gen_1394, q_gen_1393) -> q_gen_1421
<cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1434
<cons, s>(q_gen_1394, q_gen_1390) -> q_gen_1451
<a, cons, s>(q_gen_1391, q_gen_1421) -> q_gen_1378
<a, cons, s>(q_gen_1394, q_gen_1390) -> q_gen_1378
<a, cons, s>(q_gen_1394, q_gen_1421) -> q_gen_1378
<a, cons, s>(q_gen_1394, q_gen_1451) -> q_gen_1378
<a, cons, z>(q_gen_1391, q_gen_1393) -> q_gen_1378
<a, nil, z>() -> q_gen_1378
<b, cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1378
<b, cons, s>(q_gen_1391, q_gen_1421) -> q_gen_1378
<b, cons, s>(q_gen_1391, q_gen_1434) -> q_gen_1378
<b, cons, s>(q_gen_1394, q_gen_1421) -> q_gen_1378
<b, cons, z>(q_gen_1394, q_gen_1393) -> q_gen_1378
<b, nil, z>() -> q_gen_1378
<a, cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1432
<a, cons, s>(q_gen_1391, q_gen_1434) -> q_gen_1432
<a, cons, s>(q_gen_1391, q_gen_1451) -> q_gen_1432
<a, cons, s>(q_gen_1394, q_gen_1434) -> q_gen_1432
<b, cons, s>(q_gen_1391, q_gen_1451) -> q_gen_1432
}

Datatype: <elt, eltlist, nat>
Convolution form: right
}}}
  ;  delete_all -> 
{{{
Q={q_gen_1377, q_gen_1384, q_gen_1385, q_gen_1387, q_gen_1388},
Q_f={q_gen_1377},
Delta=
{
<cons>(q_gen_1385, q_gen_1384) -> q_gen_1384
<nil>() -> q_gen_1384
<a>() -> q_gen_1385
<b>() -> q_gen_1385
<cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1387
<cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1387
<nil, nil>() -> q_gen_1387
<a, a>() -> q_gen_1388
<a, b>() -> q_gen_1388
<b, a>() -> q_gen_1388
<b, b>() -> q_gen_1388
<a, cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1377
<a, cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1377
<a, nil, nil>() -> q_gen_1377
<b, cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1377
<b, cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1377
<b, nil, nil>() -> q_gen_1377
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  delete_one -> 
{{{
Q={q_gen_1373, q_gen_1374, q_gen_1375, q_gen_1381, q_gen_1382},
Q_f={q_gen_1373},
Delta=
{
<nil>() -> q_gen_1374
<a>() -> q_gen_1375
<b>() -> q_gen_1375
<cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1381
<cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1381
<nil, nil>() -> q_gen_1381
<a, a>() -> q_gen_1382
<a, b>() -> q_gen_1382
<b, a>() -> q_gen_1382
<b, b>() -> q_gen_1382
<a, cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1373
<a, cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1373
<a, nil, nil>() -> q_gen_1373
<b, cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1373
<b, cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1373
<b, nil, nil>() -> q_gen_1373
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  leqnat -> 
{{{
Q={q_gen_1372, q_gen_1396, q_gen_1438},
Q_f={q_gen_1372},
Delta=
{
<s>(q_gen_1396) -> q_gen_1396
<z>() -> q_gen_1396
<s, s>(q_gen_1372) -> q_gen_1372
<z, s>(q_gen_1396) -> q_gen_1372
<z, z>() -> q_gen_1372
<s, s>(q_gen_1438) -> q_gen_1438
<s, z>(q_gen_1396) -> q_gen_1438
}

Datatype: <nat, nat>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist, eq_nat}
_|

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 20
() -> delete_all([x, nil, nil]) -> 20
() -> delete_one([x, nil, nil]) -> 20
() -> delete_one([y, cons(y, r), r]) -> 20
() -> leqnat([z, n2]) -> 20
(count([x, l, _fh]) /\ delete_all([x, l, _eh]) /\ delete_one([x, l, _eh])) -> leqnat([_fh, s(z)]) -> 22
(count([x, r, _yg]) /\ not eq_elt([x, y])) -> count([x, cons(y, r), _yg]) -> 23
(count([y, r, _xg])) -> count([y, cons(y, r), s(_xg)]) -> 22
(delete_all([x, r, _sg]) /\ not eq_elt([x, y])) -> delete_all([x, cons(y, r), cons(y, _sg)]) -> 21
(delete_all([y, r, _rg])) -> delete_all([y, cons(y, r), _rg]) -> 21
(delete_one([x, r, _mg]) /\ not eq_elt([x, y])) -> delete_one([x, cons(y, r), cons(y, _mg)]) -> 21
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 21
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 21
(leqnat([s(nn1), z])) -> BOT -> 21
}
Sat witness: Found: ((count([x, r, _yg]) /\ not eq_elt([x, y])) -> count([x, cons(y, r), _yg]), {
_yg -> s(s(z))  ;  r -> cons(a, cons(a, nil))  ;  x -> a  ;  y -> b
})

-------------------------------------------
Step 48, which took 0.059966 s (model generation: 0.052089,  model checking: 0.007877):

Model:
|_
{
count -> 
{{{
Q={q_gen_1378, q_gen_1390, q_gen_1391, q_gen_1393, q_gen_1394, q_gen_1421, q_gen_1432, q_gen_1434, q_gen_1451},
Q_f={q_gen_1378},
Delta=
{
<b>() -> q_gen_1391
<cons>(q_gen_1391, q_gen_1393) -> q_gen_1393
<cons>(q_gen_1394, q_gen_1393) -> q_gen_1393
<nil>() -> q_gen_1393
<a>() -> q_gen_1394
<nil, z>() -> q_gen_1390
<cons, s>(q_gen_1394, q_gen_1421) -> q_gen_1421
<cons, z>(q_gen_1391, q_gen_1393) -> q_gen_1421
<cons, z>(q_gen_1394, q_gen_1393) -> q_gen_1421
<cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1434
<cons, s>(q_gen_1394, q_gen_1390) -> q_gen_1451
<a, cons, s>(q_gen_1391, q_gen_1421) -> q_gen_1378
<a, cons, s>(q_gen_1394, q_gen_1390) -> q_gen_1378
<a, cons, s>(q_gen_1394, q_gen_1421) -> q_gen_1378
<a, cons, s>(q_gen_1394, q_gen_1451) -> q_gen_1378
<a, cons, z>(q_gen_1391, q_gen_1393) -> q_gen_1378
<a, nil, z>() -> q_gen_1378
<b, cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1378
<b, cons, s>(q_gen_1391, q_gen_1421) -> q_gen_1378
<b, cons, s>(q_gen_1391, q_gen_1434) -> q_gen_1378
<b, cons, s>(q_gen_1394, q_gen_1421) -> q_gen_1378
<b, cons, z>(q_gen_1394, q_gen_1393) -> q_gen_1378
<b, nil, z>() -> q_gen_1378
<a, cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1432
<a, cons, s>(q_gen_1391, q_gen_1434) -> q_gen_1432
<a, cons, s>(q_gen_1391, q_gen_1451) -> q_gen_1432
<a, cons, s>(q_gen_1394, q_gen_1434) -> q_gen_1432
<b, cons, s>(q_gen_1391, q_gen_1451) -> q_gen_1432
}

Datatype: <elt, eltlist, nat>
Convolution form: right
}}}
  ;  delete_all -> 
{{{
Q={q_gen_1377, q_gen_1384, q_gen_1385, q_gen_1387, q_gen_1388},
Q_f={q_gen_1377},
Delta=
{
<cons>(q_gen_1385, q_gen_1384) -> q_gen_1384
<nil>() -> q_gen_1384
<a>() -> q_gen_1385
<b>() -> q_gen_1385
<cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1387
<cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1387
<nil, nil>() -> q_gen_1387
<a, a>() -> q_gen_1388
<a, b>() -> q_gen_1388
<b, a>() -> q_gen_1388
<b, b>() -> q_gen_1388
<a, cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1377
<a, cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1377
<a, nil, nil>() -> q_gen_1377
<b, cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1377
<b, cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1377
<b, nil, nil>() -> q_gen_1377
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  delete_one -> 
{{{
Q={q_gen_1373, q_gen_1374, q_gen_1375, q_gen_1381, q_gen_1382},
Q_f={q_gen_1373},
Delta=
{
<nil>() -> q_gen_1374
<a>() -> q_gen_1375
<b>() -> q_gen_1375
<cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1381
<cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1381
<nil, nil>() -> q_gen_1381
<a, a>() -> q_gen_1382
<a, b>() -> q_gen_1382
<b, a>() -> q_gen_1382
<b, b>() -> q_gen_1382
<a, cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1373
<a, cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1373
<a, nil, nil>() -> q_gen_1373
<b, cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1373
<b, cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1373
<b, nil, nil>() -> q_gen_1373
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  leqnat -> 
{{{
Q={q_gen_1372, q_gen_1396, q_gen_1438},
Q_f={q_gen_1372},
Delta=
{
<s>(q_gen_1396) -> q_gen_1396
<z>() -> q_gen_1396
<s, s>(q_gen_1372) -> q_gen_1372
<z, s>(q_gen_1396) -> q_gen_1372
<z, z>() -> q_gen_1372
<s, s>(q_gen_1438) -> q_gen_1438
<s, z>(q_gen_1396) -> q_gen_1438
}

Datatype: <nat, nat>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist, eq_nat}
_|

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 21
() -> delete_all([x, nil, nil]) -> 21
() -> delete_one([x, nil, nil]) -> 21
() -> delete_one([y, cons(y, r), r]) -> 21
() -> leqnat([z, n2]) -> 21
(count([x, l, _fh]) /\ delete_all([x, l, _eh]) /\ delete_one([x, l, _eh])) -> leqnat([_fh, s(z)]) -> 22
(count([x, r, _yg]) /\ not eq_elt([x, y])) -> count([x, cons(y, r), _yg]) -> 23
(count([y, r, _xg])) -> count([y, cons(y, r), s(_xg)]) -> 25
(delete_all([x, r, _sg]) /\ not eq_elt([x, y])) -> delete_all([x, cons(y, r), cons(y, _sg)]) -> 22
(delete_all([y, r, _rg])) -> delete_all([y, cons(y, r), _rg]) -> 22
(delete_one([x, r, _mg]) /\ not eq_elt([x, y])) -> delete_one([x, cons(y, r), cons(y, _mg)]) -> 22
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 22
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 22
(leqnat([s(nn1), z])) -> BOT -> 22
}
Sat witness: Found: ((count([y, r, _xg])) -> count([y, cons(y, r), s(_xg)]), {
_xg -> s(s(z))  ;  r -> cons(a, cons(a, nil))  ;  y -> a
})

-------------------------------------------
Step 49, which took 0.062795 s (model generation: 0.056868,  model checking: 0.005927):

Model:
|_
{
count -> 
{{{
Q={q_gen_1378, q_gen_1390, q_gen_1391, q_gen_1393, q_gen_1394, q_gen_1432, q_gen_1434, q_gen_1448, q_gen_1451},
Q_f={q_gen_1378},
Delta=
{
<b>() -> q_gen_1391
<cons>(q_gen_1391, q_gen_1393) -> q_gen_1393
<cons>(q_gen_1394, q_gen_1393) -> q_gen_1393
<nil>() -> q_gen_1393
<a>() -> q_gen_1394
<cons, s>(q_gen_1394, q_gen_1451) -> q_gen_1390
<cons, z>(q_gen_1391, q_gen_1393) -> q_gen_1390
<nil, z>() -> q_gen_1390
<cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1434
<cons, s>(q_gen_1394, q_gen_1448) -> q_gen_1448
<cons, z>(q_gen_1394, q_gen_1393) -> q_gen_1448
<cons, s>(q_gen_1394, q_gen_1390) -> q_gen_1451
<a, cons, s>(q_gen_1391, q_gen_1448) -> q_gen_1378
<a, cons, s>(q_gen_1394, q_gen_1390) -> q_gen_1378
<a, cons, s>(q_gen_1394, q_gen_1451) -> q_gen_1378
<a, cons, z>(q_gen_1391, q_gen_1393) -> q_gen_1378
<a, nil, z>() -> q_gen_1378
<b, cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1378
<b, cons, s>(q_gen_1391, q_gen_1434) -> q_gen_1378
<b, cons, s>(q_gen_1391, q_gen_1448) -> q_gen_1378
<b, cons, s>(q_gen_1394, q_gen_1390) -> q_gen_1378
<b, cons, z>(q_gen_1394, q_gen_1393) -> q_gen_1378
<b, nil, z>() -> q_gen_1378
<a, cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1432
<a, cons, s>(q_gen_1391, q_gen_1434) -> q_gen_1432
<a, cons, s>(q_gen_1391, q_gen_1451) -> q_gen_1432
<a, cons, s>(q_gen_1394, q_gen_1434) -> q_gen_1432
<b, cons, s>(q_gen_1391, q_gen_1451) -> q_gen_1432
}

Datatype: <elt, eltlist, nat>
Convolution form: right
}}}
  ;  delete_all -> 
{{{
Q={q_gen_1377, q_gen_1384, q_gen_1385, q_gen_1387, q_gen_1388},
Q_f={q_gen_1377},
Delta=
{
<cons>(q_gen_1385, q_gen_1384) -> q_gen_1384
<nil>() -> q_gen_1384
<a>() -> q_gen_1385
<b>() -> q_gen_1385
<cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1387
<cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1387
<nil, nil>() -> q_gen_1387
<a, a>() -> q_gen_1388
<a, b>() -> q_gen_1388
<b, a>() -> q_gen_1388
<b, b>() -> q_gen_1388
<a, cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1377
<a, cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1377
<a, nil, nil>() -> q_gen_1377
<b, cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1377
<b, cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1377
<b, nil, nil>() -> q_gen_1377
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  delete_one -> 
{{{
Q={q_gen_1373, q_gen_1374, q_gen_1375, q_gen_1381, q_gen_1382},
Q_f={q_gen_1373},
Delta=
{
<nil>() -> q_gen_1374
<a>() -> q_gen_1375
<b>() -> q_gen_1375
<cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1381
<cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1381
<nil, nil>() -> q_gen_1381
<a, a>() -> q_gen_1382
<a, b>() -> q_gen_1382
<b, a>() -> q_gen_1382
<b, b>() -> q_gen_1382
<a, cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1373
<a, cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1373
<a, nil, nil>() -> q_gen_1373
<b, cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1373
<b, cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1373
<b, nil, nil>() -> q_gen_1373
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  leqnat -> 
{{{
Q={q_gen_1372, q_gen_1396, q_gen_1438},
Q_f={q_gen_1372},
Delta=
{
<s>(q_gen_1396) -> q_gen_1396
<z>() -> q_gen_1396
<s, s>(q_gen_1372) -> q_gen_1372
<z, s>(q_gen_1396) -> q_gen_1372
<z, z>() -> q_gen_1372
<s, s>(q_gen_1438) -> q_gen_1438
<s, z>(q_gen_1396) -> q_gen_1438
}

Datatype: <nat, nat>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist, eq_nat}
_|

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 22
() -> delete_all([x, nil, nil]) -> 22
() -> delete_one([x, nil, nil]) -> 22
() -> delete_one([y, cons(y, r), r]) -> 22
() -> leqnat([z, n2]) -> 22
(count([x, l, _fh]) /\ delete_all([x, l, _eh]) /\ delete_one([x, l, _eh])) -> leqnat([_fh, s(z)]) -> 25
(count([x, r, _yg]) /\ not eq_elt([x, y])) -> count([x, cons(y, r), _yg]) -> 23
(count([y, r, _xg])) -> count([y, cons(y, r), s(_xg)]) -> 25
(delete_all([x, r, _sg]) /\ not eq_elt([x, y])) -> delete_all([x, cons(y, r), cons(y, _sg)]) -> 23
(delete_all([y, r, _rg])) -> delete_all([y, cons(y, r), _rg]) -> 23
(delete_one([x, r, _mg]) /\ not eq_elt([x, y])) -> delete_one([x, cons(y, r), cons(y, _mg)]) -> 23
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 23
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 23
(leqnat([s(nn1), z])) -> BOT -> 23
}
Sat witness: Found: ((count([x, l, _fh]) /\ delete_all([x, l, _eh]) /\ delete_one([x, l, _eh])) -> leqnat([_fh, s(z)]), {
_eh -> cons(b, cons(b, nil))  ;  _fh -> s(s(z))  ;  l -> cons(a, cons(a, nil))  ;  x -> a
})

-------------------------------------------
Step 50, which took 0.075565 s (model generation: 0.072728,  model checking: 0.002837):

Model:
|_
{
count -> 
{{{
Q={q_gen_1378, q_gen_1390, q_gen_1391, q_gen_1393, q_gen_1394, q_gen_1432, q_gen_1434, q_gen_1448},
Q_f={q_gen_1378},
Delta=
{
<b>() -> q_gen_1391
<cons>(q_gen_1391, q_gen_1393) -> q_gen_1393
<cons>(q_gen_1394, q_gen_1393) -> q_gen_1393
<nil>() -> q_gen_1393
<a>() -> q_gen_1394
<cons, s>(q_gen_1394, q_gen_1390) -> q_gen_1390
<cons, z>(q_gen_1391, q_gen_1393) -> q_gen_1390
<nil, z>() -> q_gen_1390
<cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1434
<cons, s>(q_gen_1394, q_gen_1448) -> q_gen_1448
<cons, z>(q_gen_1394, q_gen_1393) -> q_gen_1448
<a, cons, s>(q_gen_1391, q_gen_1448) -> q_gen_1378
<a, cons, s>(q_gen_1394, q_gen_1390) -> q_gen_1378
<a, cons, z>(q_gen_1391, q_gen_1393) -> q_gen_1378
<a, nil, z>() -> q_gen_1378
<b, cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1378
<b, cons, s>(q_gen_1391, q_gen_1434) -> q_gen_1378
<b, cons, s>(q_gen_1391, q_gen_1448) -> q_gen_1378
<b, cons, s>(q_gen_1394, q_gen_1390) -> q_gen_1378
<b, cons, z>(q_gen_1394, q_gen_1393) -> q_gen_1378
<b, nil, z>() -> q_gen_1378
<a, cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1432
<a, cons, s>(q_gen_1391, q_gen_1434) -> q_gen_1432
<a, cons, s>(q_gen_1394, q_gen_1434) -> q_gen_1432
}

Datatype: <elt, eltlist, nat>
Convolution form: right
}}}
  ;  delete_all -> 
{{{
Q={q_gen_1377, q_gen_1384, q_gen_1385, q_gen_1387, q_gen_1388, q_gen_1429, q_gen_1456, q_gen_1457},
Q_f={q_gen_1377},
Delta=
{
<cons>(q_gen_1385, q_gen_1384) -> q_gen_1384
<nil>() -> q_gen_1384
<a>() -> q_gen_1385
<b>() -> q_gen_1385
<cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1387
<cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1387
<nil, nil>() -> q_gen_1387
<a, a>() -> q_gen_1388
<b, b>() -> q_gen_1388
<a, b>() -> q_gen_1429
<b, a>() -> q_gen_1429
<cons, cons>(q_gen_1429, q_gen_1387) -> q_gen_1457
<a, cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1377
<a, cons, cons>(q_gen_1429, q_gen_1387) -> q_gen_1377
<a, cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1377
<a, nil, nil>() -> q_gen_1377
<b, cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1377
<b, cons, cons>(q_gen_1429, q_gen_1387) -> q_gen_1377
<b, cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1377
<b, nil, nil>() -> q_gen_1377
<a, cons, cons>(q_gen_1429, q_gen_1457) -> q_gen_1456
<b, cons, cons>(q_gen_1388, q_gen_1457) -> q_gen_1456
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  delete_one -> 
{{{
Q={q_gen_1373, q_gen_1374, q_gen_1375, q_gen_1381, q_gen_1382},
Q_f={q_gen_1373},
Delta=
{
<nil>() -> q_gen_1374
<a>() -> q_gen_1375
<b>() -> q_gen_1375
<cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1381
<cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1381
<nil, nil>() -> q_gen_1381
<a, a>() -> q_gen_1382
<a, b>() -> q_gen_1382
<b, a>() -> q_gen_1382
<b, b>() -> q_gen_1382
<a, cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1373
<a, cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1373
<a, nil, nil>() -> q_gen_1373
<b, cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1373
<b, cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1373
<b, nil, nil>() -> q_gen_1373
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  leqnat -> 
{{{
Q={q_gen_1372, q_gen_1396, q_gen_1438},
Q_f={q_gen_1372},
Delta=
{
<s>(q_gen_1396) -> q_gen_1396
<z>() -> q_gen_1396
<s, s>(q_gen_1372) -> q_gen_1372
<z, s>(q_gen_1396) -> q_gen_1372
<z, z>() -> q_gen_1372
<s, s>(q_gen_1438) -> q_gen_1438
<s, z>(q_gen_1396) -> q_gen_1438
}

Datatype: <nat, nat>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist, eq_nat}
_|

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 23
() -> delete_all([x, nil, nil]) -> 23
() -> delete_one([x, nil, nil]) -> 23
() -> delete_one([y, cons(y, r), r]) -> 23
() -> leqnat([z, n2]) -> 23
(count([x, l, _fh]) /\ delete_all([x, l, _eh]) /\ delete_one([x, l, _eh])) -> leqnat([_fh, s(z)]) -> 25
(count([x, r, _yg]) /\ not eq_elt([x, y])) -> count([x, cons(y, r), _yg]) -> 23
(count([y, r, _xg])) -> count([y, cons(y, r), s(_xg)]) -> 25
(delete_all([x, r, _sg]) /\ not eq_elt([x, y])) -> delete_all([x, cons(y, r), cons(y, _sg)]) -> 23
(delete_all([y, r, _rg])) -> delete_all([y, cons(y, r), _rg]) -> 26
(delete_one([x, r, _mg]) /\ not eq_elt([x, y])) -> delete_one([x, cons(y, r), cons(y, _mg)]) -> 24
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 24
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 24
(leqnat([s(nn1), z])) -> BOT -> 24
}
Sat witness: Found: ((delete_all([y, r, _rg])) -> delete_all([y, cons(y, r), _rg]), {
_rg -> cons(b, cons(b, nil))  ;  r -> cons(a, cons(b, nil))  ;  y -> a
})

-------------------------------------------
Step 51, which took 0.071922 s (model generation: 0.070317,  model checking: 0.001605):

Model:
|_
{
count -> 
{{{
Q={q_gen_1378, q_gen_1390, q_gen_1391, q_gen_1393, q_gen_1394, q_gen_1432, q_gen_1434, q_gen_1448},
Q_f={q_gen_1378},
Delta=
{
<b>() -> q_gen_1391
<cons>(q_gen_1391, q_gen_1393) -> q_gen_1393
<cons>(q_gen_1394, q_gen_1393) -> q_gen_1393
<nil>() -> q_gen_1393
<a>() -> q_gen_1394
<cons, s>(q_gen_1394, q_gen_1390) -> q_gen_1390
<cons, z>(q_gen_1391, q_gen_1393) -> q_gen_1390
<nil, z>() -> q_gen_1390
<cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1434
<cons, s>(q_gen_1394, q_gen_1448) -> q_gen_1448
<cons, z>(q_gen_1394, q_gen_1393) -> q_gen_1448
<a, cons, s>(q_gen_1391, q_gen_1448) -> q_gen_1378
<a, cons, s>(q_gen_1394, q_gen_1390) -> q_gen_1378
<a, cons, z>(q_gen_1391, q_gen_1393) -> q_gen_1378
<a, nil, z>() -> q_gen_1378
<b, cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1378
<b, cons, s>(q_gen_1391, q_gen_1434) -> q_gen_1378
<b, cons, s>(q_gen_1391, q_gen_1448) -> q_gen_1378
<b, cons, s>(q_gen_1394, q_gen_1390) -> q_gen_1378
<b, cons, z>(q_gen_1394, q_gen_1393) -> q_gen_1378
<b, nil, z>() -> q_gen_1378
<a, cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1432
<a, cons, s>(q_gen_1391, q_gen_1434) -> q_gen_1432
<a, cons, s>(q_gen_1394, q_gen_1434) -> q_gen_1432
}

Datatype: <elt, eltlist, nat>
Convolution form: right
}}}
  ;  delete_all -> 
{{{
Q={q_gen_1377, q_gen_1384, q_gen_1385, q_gen_1387, q_gen_1388},
Q_f={q_gen_1377},
Delta=
{
<cons>(q_gen_1385, q_gen_1384) -> q_gen_1384
<nil>() -> q_gen_1384
<a>() -> q_gen_1385
<b>() -> q_gen_1385
<cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1387
<cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1387
<nil, nil>() -> q_gen_1387
<a, a>() -> q_gen_1388
<a, b>() -> q_gen_1388
<b, a>() -> q_gen_1388
<b, b>() -> q_gen_1388
<a, cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1377
<a, cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1377
<a, nil, nil>() -> q_gen_1377
<b, cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1377
<b, cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1377
<b, nil, nil>() -> q_gen_1377
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  delete_one -> 
{{{
Q={q_gen_1373, q_gen_1374, q_gen_1375, q_gen_1381, q_gen_1382, q_gen_1405, q_gen_1458, q_gen_1459},
Q_f={q_gen_1373},
Delta=
{
<nil>() -> q_gen_1374
<a>() -> q_gen_1375
<b>() -> q_gen_1375
<cons, cons>(q_gen_1405, q_gen_1381) -> q_gen_1381
<cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1381
<nil, nil>() -> q_gen_1381
<a, a>() -> q_gen_1382
<a, b>() -> q_gen_1382
<b, a>() -> q_gen_1405
<b, b>() -> q_gen_1405
<cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1459
<a, cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1373
<a, cons, cons>(q_gen_1405, q_gen_1381) -> q_gen_1373
<a, cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1373
<a, nil, nil>() -> q_gen_1373
<b, cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1373
<b, cons, cons>(q_gen_1405, q_gen_1381) -> q_gen_1373
<b, cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1373
<b, nil, nil>() -> q_gen_1373
<a, cons, cons>(q_gen_1382, q_gen_1459) -> q_gen_1458
<b, cons, cons>(q_gen_1405, q_gen_1459) -> q_gen_1458
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  leqnat -> 
{{{
Q={q_gen_1372, q_gen_1396, q_gen_1438},
Q_f={q_gen_1372},
Delta=
{
<s>(q_gen_1396) -> q_gen_1396
<z>() -> q_gen_1396
<s, s>(q_gen_1372) -> q_gen_1372
<z, s>(q_gen_1396) -> q_gen_1372
<z, z>() -> q_gen_1372
<s, s>(q_gen_1438) -> q_gen_1438
<s, z>(q_gen_1396) -> q_gen_1438
}

Datatype: <nat, nat>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist, eq_nat}
_|

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 23
() -> delete_all([x, nil, nil]) -> 23
() -> delete_one([x, nil, nil]) -> 23
() -> delete_one([y, cons(y, r), r]) -> 23
() -> leqnat([z, n2]) -> 23
(count([x, l, _fh]) /\ delete_all([x, l, _eh]) /\ delete_one([x, l, _eh])) -> leqnat([_fh, s(z)]) -> 25
(count([x, r, _yg]) /\ not eq_elt([x, y])) -> count([x, cons(y, r), _yg]) -> 26
(count([y, r, _xg])) -> count([y, cons(y, r), s(_xg)]) -> 25
(delete_all([x, r, _sg]) /\ not eq_elt([x, y])) -> delete_all([x, cons(y, r), cons(y, _sg)]) -> 24
(delete_all([y, r, _rg])) -> delete_all([y, cons(y, r), _rg]) -> 26
(delete_one([x, r, _mg]) /\ not eq_elt([x, y])) -> delete_one([x, cons(y, r), cons(y, _mg)]) -> 24
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 24
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 24
(leqnat([s(nn1), z])) -> BOT -> 24
}
Sat witness: Found: ((count([x, r, _yg]) /\ not eq_elt([x, y])) -> count([x, cons(y, r), _yg]), {
_yg -> s(z)  ;  r -> cons(b, cons(a, nil))  ;  x -> a  ;  y -> b
})

-------------------------------------------
Step 52, which took 0.083852 s (model generation: 0.083387,  model checking: 0.000465):

Model:
|_
{
count -> 
{{{
Q={q_gen_1378, q_gen_1390, q_gen_1391, q_gen_1393, q_gen_1394, q_gen_1421, q_gen_1432, q_gen_1434},
Q_f={q_gen_1378},
Delta=
{
<b>() -> q_gen_1391
<cons>(q_gen_1391, q_gen_1393) -> q_gen_1393
<cons>(q_gen_1394, q_gen_1393) -> q_gen_1393
<nil>() -> q_gen_1393
<a>() -> q_gen_1394
<cons, s>(q_gen_1394, q_gen_1390) -> q_gen_1390
<nil, z>() -> q_gen_1390
<cons, s>(q_gen_1394, q_gen_1421) -> q_gen_1421
<cons, z>(q_gen_1391, q_gen_1393) -> q_gen_1421
<cons, z>(q_gen_1394, q_gen_1393) -> q_gen_1421
<cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1434
<a, cons, s>(q_gen_1391, q_gen_1421) -> q_gen_1378
<a, cons, s>(q_gen_1394, q_gen_1390) -> q_gen_1378
<a, cons, s>(q_gen_1394, q_gen_1421) -> q_gen_1378
<a, cons, z>(q_gen_1391, q_gen_1393) -> q_gen_1378
<a, nil, z>() -> q_gen_1378
<b, cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1378
<b, cons, s>(q_gen_1391, q_gen_1421) -> q_gen_1378
<b, cons, s>(q_gen_1391, q_gen_1434) -> q_gen_1378
<b, cons, s>(q_gen_1394, q_gen_1421) -> q_gen_1378
<b, cons, z>(q_gen_1394, q_gen_1393) -> q_gen_1378
<b, nil, z>() -> q_gen_1378
<a, cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1432
<a, cons, s>(q_gen_1391, q_gen_1434) -> q_gen_1432
<a, cons, s>(q_gen_1394, q_gen_1434) -> q_gen_1432
}

Datatype: <elt, eltlist, nat>
Convolution form: right
}}}
  ;  delete_all -> 
{{{
Q={q_gen_1377, q_gen_1384, q_gen_1385, q_gen_1387, q_gen_1388},
Q_f={q_gen_1377},
Delta=
{
<cons>(q_gen_1385, q_gen_1384) -> q_gen_1384
<nil>() -> q_gen_1384
<a>() -> q_gen_1385
<b>() -> q_gen_1385
<cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1387
<cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1387
<nil, nil>() -> q_gen_1387
<a, a>() -> q_gen_1388
<a, b>() -> q_gen_1388
<b, a>() -> q_gen_1388
<b, b>() -> q_gen_1388
<a, cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1377
<a, cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1377
<a, nil, nil>() -> q_gen_1377
<b, cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1377
<b, cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1377
<b, nil, nil>() -> q_gen_1377
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  delete_one -> 
{{{
Q={q_gen_1373, q_gen_1374, q_gen_1375, q_gen_1381, q_gen_1382, q_gen_1444, q_gen_1458, q_gen_1459},
Q_f={q_gen_1373},
Delta=
{
<nil>() -> q_gen_1374
<a>() -> q_gen_1375
<b>() -> q_gen_1375
<cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1381
<cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1381
<nil, nil>() -> q_gen_1381
<a, a>() -> q_gen_1382
<b, a>() -> q_gen_1382
<b, b>() -> q_gen_1382
<a, b>() -> q_gen_1444
<cons, cons>(q_gen_1444, q_gen_1381) -> q_gen_1459
<a, cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1373
<a, cons, cons>(q_gen_1444, q_gen_1381) -> q_gen_1373
<a, cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1373
<a, nil, nil>() -> q_gen_1373
<b, cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1373
<b, cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1373
<b, nil, nil>() -> q_gen_1373
<a, cons, cons>(q_gen_1444, q_gen_1459) -> q_gen_1458
<b, cons, cons>(q_gen_1382, q_gen_1459) -> q_gen_1458
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  leqnat -> 
{{{
Q={q_gen_1372, q_gen_1396, q_gen_1438},
Q_f={q_gen_1372},
Delta=
{
<s>(q_gen_1396) -> q_gen_1396
<z>() -> q_gen_1396
<s, s>(q_gen_1372) -> q_gen_1372
<z, s>(q_gen_1396) -> q_gen_1372
<z, z>() -> q_gen_1372
<s, s>(q_gen_1438) -> q_gen_1438
<s, z>(q_gen_1396) -> q_gen_1438
}

Datatype: <nat, nat>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist, eq_nat}
_|

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 23
() -> delete_all([x, nil, nil]) -> 23
() -> delete_one([x, nil, nil]) -> 23
() -> delete_one([y, cons(y, r), r]) -> 26
() -> leqnat([z, n2]) -> 24
(count([x, l, _fh]) /\ delete_all([x, l, _eh]) /\ delete_one([x, l, _eh])) -> leqnat([_fh, s(z)]) -> 25
(count([x, r, _yg]) /\ not eq_elt([x, y])) -> count([x, cons(y, r), _yg]) -> 26
(count([y, r, _xg])) -> count([y, cons(y, r), s(_xg)]) -> 25
(delete_all([x, r, _sg]) /\ not eq_elt([x, y])) -> delete_all([x, cons(y, r), cons(y, _sg)]) -> 24
(delete_all([y, r, _rg])) -> delete_all([y, cons(y, r), _rg]) -> 26
(delete_one([x, r, _mg]) /\ not eq_elt([x, y])) -> delete_one([x, cons(y, r), cons(y, _mg)]) -> 24
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 24
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 24
(leqnat([s(nn1), z])) -> BOT -> 24
}
Sat witness: Found: (() -> delete_one([y, cons(y, r), r]), {
r -> cons(a, cons(b, nil))  ;  y -> b
})

-------------------------------------------
Step 53, which took 0.039966 s (model generation: 0.038471,  model checking: 0.001495):

Model:
|_
{
count -> 
{{{
Q={q_gen_1378, q_gen_1390, q_gen_1391, q_gen_1393, q_gen_1394, q_gen_1421, q_gen_1432, q_gen_1434},
Q_f={q_gen_1378},
Delta=
{
<b>() -> q_gen_1391
<cons>(q_gen_1391, q_gen_1393) -> q_gen_1393
<cons>(q_gen_1394, q_gen_1393) -> q_gen_1393
<nil>() -> q_gen_1393
<a>() -> q_gen_1394
<cons, s>(q_gen_1394, q_gen_1390) -> q_gen_1390
<nil, z>() -> q_gen_1390
<cons, s>(q_gen_1394, q_gen_1421) -> q_gen_1421
<cons, z>(q_gen_1391, q_gen_1393) -> q_gen_1421
<cons, z>(q_gen_1394, q_gen_1393) -> q_gen_1421
<cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1434
<a, cons, s>(q_gen_1391, q_gen_1421) -> q_gen_1378
<a, cons, s>(q_gen_1394, q_gen_1390) -> q_gen_1378
<a, cons, s>(q_gen_1394, q_gen_1421) -> q_gen_1378
<a, cons, z>(q_gen_1391, q_gen_1393) -> q_gen_1378
<a, nil, z>() -> q_gen_1378
<b, cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1378
<b, cons, s>(q_gen_1391, q_gen_1421) -> q_gen_1378
<b, cons, s>(q_gen_1391, q_gen_1434) -> q_gen_1378
<b, cons, s>(q_gen_1394, q_gen_1421) -> q_gen_1378
<b, cons, z>(q_gen_1394, q_gen_1393) -> q_gen_1378
<b, nil, z>() -> q_gen_1378
<a, cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1432
<a, cons, s>(q_gen_1391, q_gen_1434) -> q_gen_1432
<a, cons, s>(q_gen_1394, q_gen_1434) -> q_gen_1432
}

Datatype: <elt, eltlist, nat>
Convolution form: right
}}}
  ;  delete_all -> 
{{{
Q={q_gen_1377, q_gen_1384, q_gen_1385, q_gen_1387, q_gen_1388},
Q_f={q_gen_1377},
Delta=
{
<cons>(q_gen_1385, q_gen_1384) -> q_gen_1384
<nil>() -> q_gen_1384
<a>() -> q_gen_1385
<b>() -> q_gen_1385
<cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1387
<cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1387
<nil, nil>() -> q_gen_1387
<a, a>() -> q_gen_1388
<a, b>() -> q_gen_1388
<b, a>() -> q_gen_1388
<b, b>() -> q_gen_1388
<a, cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1377
<a, cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1377
<a, nil, nil>() -> q_gen_1377
<b, cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1377
<b, cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1377
<b, nil, nil>() -> q_gen_1377
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  delete_one -> 
{{{
Q={q_gen_1373, q_gen_1374, q_gen_1375, q_gen_1381, q_gen_1382, q_gen_1415, q_gen_1426, q_gen_1458},
Q_f={q_gen_1373},
Delta=
{
<nil>() -> q_gen_1374
<a>() -> q_gen_1375
<b>() -> q_gen_1375
<cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1381
<nil, nil>() -> q_gen_1381
<a, a>() -> q_gen_1382
<b, b>() -> q_gen_1382
<cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1415
<cons, cons>(q_gen_1426, q_gen_1381) -> q_gen_1415
<a, b>() -> q_gen_1426
<b, a>() -> q_gen_1426
<a, cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1373
<a, cons, cons>(q_gen_1382, q_gen_1415) -> q_gen_1373
<a, cons, cons>(q_gen_1426, q_gen_1381) -> q_gen_1373
<a, cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1373
<a, nil, nil>() -> q_gen_1373
<b, cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1373
<b, cons, cons>(q_gen_1426, q_gen_1381) -> q_gen_1373
<b, cons, cons>(q_gen_1426, q_gen_1415) -> q_gen_1373
<b, cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1373
<b, nil, nil>() -> q_gen_1373
<a, cons, cons>(q_gen_1426, q_gen_1415) -> q_gen_1458
<b, cons, cons>(q_gen_1382, q_gen_1415) -> q_gen_1458
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  leqnat -> 
{{{
Q={q_gen_1372, q_gen_1396, q_gen_1438},
Q_f={q_gen_1372},
Delta=
{
<s>(q_gen_1396) -> q_gen_1396
<z>() -> q_gen_1396
<s, s>(q_gen_1372) -> q_gen_1372
<z, s>(q_gen_1396) -> q_gen_1372
<z, z>() -> q_gen_1372
<s, s>(q_gen_1438) -> q_gen_1438
<s, z>(q_gen_1396) -> q_gen_1438
}

Datatype: <nat, nat>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist, eq_nat}
_|

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 24
() -> delete_all([x, nil, nil]) -> 24
() -> delete_one([x, nil, nil]) -> 24
() -> delete_one([y, cons(y, r), r]) -> 26
() -> leqnat([z, n2]) -> 24
(count([x, l, _fh]) /\ delete_all([x, l, _eh]) /\ delete_one([x, l, _eh])) -> leqnat([_fh, s(z)]) -> 25
(count([x, r, _yg]) /\ not eq_elt([x, y])) -> count([x, cons(y, r), _yg]) -> 26
(count([y, r, _xg])) -> count([y, cons(y, r), s(_xg)]) -> 25
(delete_all([x, r, _sg]) /\ not eq_elt([x, y])) -> delete_all([x, cons(y, r), cons(y, _sg)]) -> 24
(delete_all([y, r, _rg])) -> delete_all([y, cons(y, r), _rg]) -> 26
(delete_one([x, r, _mg]) /\ not eq_elt([x, y])) -> delete_one([x, cons(y, r), cons(y, _mg)]) -> 27
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 25
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 25
(leqnat([s(nn1), z])) -> BOT -> 25
}
Sat witness: Found: ((delete_one([x, r, _mg]) /\ not eq_elt([x, y])) -> delete_one([x, cons(y, r), cons(y, _mg)]), {
_mg -> cons(a, nil)  ;  r -> cons(b, nil)  ;  x -> b  ;  y -> a
})

-------------------------------------------
Step 54, which took 0.073655 s (model generation: 0.072672,  model checking: 0.000983):

Model:
|_
{
count -> 
{{{
Q={q_gen_1378, q_gen_1390, q_gen_1391, q_gen_1393, q_gen_1394, q_gen_1421, q_gen_1432, q_gen_1434},
Q_f={q_gen_1378},
Delta=
{
<b>() -> q_gen_1391
<cons>(q_gen_1391, q_gen_1393) -> q_gen_1393
<cons>(q_gen_1394, q_gen_1393) -> q_gen_1393
<nil>() -> q_gen_1393
<a>() -> q_gen_1394
<cons, s>(q_gen_1394, q_gen_1390) -> q_gen_1390
<nil, z>() -> q_gen_1390
<cons, s>(q_gen_1394, q_gen_1421) -> q_gen_1421
<cons, z>(q_gen_1391, q_gen_1393) -> q_gen_1421
<cons, z>(q_gen_1394, q_gen_1393) -> q_gen_1421
<cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1434
<a, cons, s>(q_gen_1391, q_gen_1421) -> q_gen_1378
<a, cons, s>(q_gen_1394, q_gen_1390) -> q_gen_1378
<a, cons, s>(q_gen_1394, q_gen_1421) -> q_gen_1378
<a, cons, z>(q_gen_1391, q_gen_1393) -> q_gen_1378
<a, nil, z>() -> q_gen_1378
<b, cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1378
<b, cons, s>(q_gen_1391, q_gen_1421) -> q_gen_1378
<b, cons, s>(q_gen_1391, q_gen_1434) -> q_gen_1378
<b, cons, s>(q_gen_1394, q_gen_1421) -> q_gen_1378
<b, cons, z>(q_gen_1394, q_gen_1393) -> q_gen_1378
<b, nil, z>() -> q_gen_1378
<a, cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1432
<a, cons, s>(q_gen_1391, q_gen_1434) -> q_gen_1432
<a, cons, s>(q_gen_1394, q_gen_1434) -> q_gen_1432
}

Datatype: <elt, eltlist, nat>
Convolution form: right
}}}
  ;  delete_all -> 
{{{
Q={q_gen_1377, q_gen_1384, q_gen_1385, q_gen_1387, q_gen_1388, q_gen_1429, q_gen_1431, q_gen_1456},
Q_f={q_gen_1377},
Delta=
{
<cons>(q_gen_1385, q_gen_1384) -> q_gen_1384
<nil>() -> q_gen_1384
<a>() -> q_gen_1385
<b>() -> q_gen_1385
<cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1387
<nil, nil>() -> q_gen_1387
<a, a>() -> q_gen_1388
<b, b>() -> q_gen_1388
<a, b>() -> q_gen_1429
<b, a>() -> q_gen_1429
<cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1431
<cons, cons>(q_gen_1429, q_gen_1387) -> q_gen_1431
<a, cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1377
<a, cons, cons>(q_gen_1388, q_gen_1431) -> q_gen_1377
<a, cons, cons>(q_gen_1429, q_gen_1387) -> q_gen_1377
<a, cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1377
<a, nil, nil>() -> q_gen_1377
<b, cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1377
<b, cons, cons>(q_gen_1429, q_gen_1387) -> q_gen_1377
<b, cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1377
<b, nil, nil>() -> q_gen_1377
<a, cons, cons>(q_gen_1429, q_gen_1431) -> q_gen_1456
<b, cons, cons>(q_gen_1388, q_gen_1431) -> q_gen_1456
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  delete_one -> 
{{{
Q={q_gen_1373, q_gen_1374, q_gen_1375, q_gen_1381, q_gen_1382},
Q_f={q_gen_1373},
Delta=
{
<nil>() -> q_gen_1374
<a>() -> q_gen_1375
<b>() -> q_gen_1375
<cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1381
<cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1381
<nil, nil>() -> q_gen_1381
<a, a>() -> q_gen_1382
<a, b>() -> q_gen_1382
<b, a>() -> q_gen_1382
<b, b>() -> q_gen_1382
<a, cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1373
<a, cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1373
<a, nil, nil>() -> q_gen_1373
<b, cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1373
<b, cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1373
<b, nil, nil>() -> q_gen_1373
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  leqnat -> 
{{{
Q={q_gen_1372, q_gen_1396, q_gen_1438},
Q_f={q_gen_1372},
Delta=
{
<s>(q_gen_1396) -> q_gen_1396
<z>() -> q_gen_1396
<s, s>(q_gen_1372) -> q_gen_1372
<z, s>(q_gen_1396) -> q_gen_1372
<z, z>() -> q_gen_1372
<s, s>(q_gen_1438) -> q_gen_1438
<s, z>(q_gen_1396) -> q_gen_1438
}

Datatype: <nat, nat>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist, eq_nat}
_|

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 24
() -> delete_all([x, nil, nil]) -> 24
() -> delete_one([x, nil, nil]) -> 24
() -> delete_one([y, cons(y, r), r]) -> 26
() -> leqnat([z, n2]) -> 24
(count([x, l, _fh]) /\ delete_all([x, l, _eh]) /\ delete_one([x, l, _eh])) -> leqnat([_fh, s(z)]) -> 25
(count([x, r, _yg]) /\ not eq_elt([x, y])) -> count([x, cons(y, r), _yg]) -> 26
(count([y, r, _xg])) -> count([y, cons(y, r), s(_xg)]) -> 25
(delete_all([x, r, _sg]) /\ not eq_elt([x, y])) -> delete_all([x, cons(y, r), cons(y, _sg)]) -> 27
(delete_all([y, r, _rg])) -> delete_all([y, cons(y, r), _rg]) -> 26
(delete_one([x, r, _mg]) /\ not eq_elt([x, y])) -> delete_one([x, cons(y, r), cons(y, _mg)]) -> 27
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 25
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 25
(leqnat([s(nn1), z])) -> BOT -> 25
}
Sat witness: Found: ((delete_all([x, r, _sg]) /\ not eq_elt([x, y])) -> delete_all([x, cons(y, r), cons(y, _sg)]), {
_sg -> cons(b, nil)  ;  r -> cons(a, nil)  ;  x -> b  ;  y -> a
})

-------------------------------------------
Step 55, which took 0.048964 s (model generation: 0.047364,  model checking: 0.001600):

Model:
|_
{
count -> 
{{{
Q={q_gen_1378, q_gen_1390, q_gen_1391, q_gen_1393, q_gen_1394, q_gen_1421, q_gen_1432, q_gen_1434},
Q_f={q_gen_1378},
Delta=
{
<b>() -> q_gen_1391
<cons>(q_gen_1391, q_gen_1393) -> q_gen_1393
<cons>(q_gen_1394, q_gen_1393) -> q_gen_1393
<nil>() -> q_gen_1393
<a>() -> q_gen_1394
<cons, s>(q_gen_1394, q_gen_1390) -> q_gen_1390
<nil, z>() -> q_gen_1390
<cons, s>(q_gen_1394, q_gen_1421) -> q_gen_1421
<cons, z>(q_gen_1391, q_gen_1393) -> q_gen_1421
<cons, z>(q_gen_1394, q_gen_1393) -> q_gen_1421
<cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1434
<a, cons, s>(q_gen_1391, q_gen_1421) -> q_gen_1378
<a, cons, s>(q_gen_1394, q_gen_1390) -> q_gen_1378
<a, cons, s>(q_gen_1394, q_gen_1421) -> q_gen_1378
<a, cons, z>(q_gen_1391, q_gen_1393) -> q_gen_1378
<a, nil, z>() -> q_gen_1378
<b, cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1378
<b, cons, s>(q_gen_1391, q_gen_1421) -> q_gen_1378
<b, cons, s>(q_gen_1391, q_gen_1434) -> q_gen_1378
<b, cons, s>(q_gen_1394, q_gen_1421) -> q_gen_1378
<b, cons, z>(q_gen_1394, q_gen_1393) -> q_gen_1378
<b, nil, z>() -> q_gen_1378
<a, cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1432
<a, cons, s>(q_gen_1391, q_gen_1434) -> q_gen_1432
<a, cons, s>(q_gen_1394, q_gen_1434) -> q_gen_1432
}

Datatype: <elt, eltlist, nat>
Convolution form: right
}}}
  ;  delete_all -> 
{{{
Q={q_gen_1377, q_gen_1384, q_gen_1385, q_gen_1387, q_gen_1388},
Q_f={q_gen_1377},
Delta=
{
<cons>(q_gen_1385, q_gen_1384) -> q_gen_1384
<nil>() -> q_gen_1384
<a>() -> q_gen_1385
<b>() -> q_gen_1385
<cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1387
<cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1387
<nil, nil>() -> q_gen_1387
<a, a>() -> q_gen_1388
<a, b>() -> q_gen_1388
<b, a>() -> q_gen_1388
<b, b>() -> q_gen_1388
<a, cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1377
<a, cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1377
<a, nil, nil>() -> q_gen_1377
<b, cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1377
<b, cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1377
<b, nil, nil>() -> q_gen_1377
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  delete_one -> 
{{{
Q={q_gen_1373, q_gen_1374, q_gen_1375, q_gen_1381, q_gen_1382, q_gen_1405, q_gen_1458, q_gen_1459},
Q_f={q_gen_1373},
Delta=
{
<nil>() -> q_gen_1374
<a>() -> q_gen_1375
<b>() -> q_gen_1375
<cons, cons>(q_gen_1405, q_gen_1381) -> q_gen_1381
<cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1381
<nil, nil>() -> q_gen_1381
<a, a>() -> q_gen_1382
<a, b>() -> q_gen_1382
<b, a>() -> q_gen_1382
<b, b>() -> q_gen_1405
<cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1459
<a, cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1373
<a, cons, cons>(q_gen_1405, q_gen_1381) -> q_gen_1373
<a, cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1373
<a, nil, nil>() -> q_gen_1373
<b, cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1373
<b, cons, cons>(q_gen_1382, q_gen_1459) -> q_gen_1373
<b, cons, cons>(q_gen_1405, q_gen_1381) -> q_gen_1373
<b, cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1373
<b, nil, nil>() -> q_gen_1373
<a, cons, cons>(q_gen_1382, q_gen_1459) -> q_gen_1458
<b, cons, cons>(q_gen_1405, q_gen_1459) -> q_gen_1458
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  leqnat -> 
{{{
Q={q_gen_1372, q_gen_1396, q_gen_1438},
Q_f={q_gen_1372},
Delta=
{
<s>(q_gen_1396) -> q_gen_1396
<z>() -> q_gen_1396
<s, s>(q_gen_1372) -> q_gen_1372
<z, s>(q_gen_1396) -> q_gen_1372
<z, z>() -> q_gen_1372
<s, s>(q_gen_1438) -> q_gen_1438
<s, z>(q_gen_1396) -> q_gen_1438
}

Datatype: <nat, nat>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist, eq_nat}
_|

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 25
() -> delete_all([x, nil, nil]) -> 25
() -> delete_one([x, nil, nil]) -> 25
() -> delete_one([y, cons(y, r), r]) -> 26
() -> leqnat([z, n2]) -> 25
(count([x, l, _fh]) /\ delete_all([x, l, _eh]) /\ delete_one([x, l, _eh])) -> leqnat([_fh, s(z)]) -> 25
(count([x, r, _yg]) /\ not eq_elt([x, y])) -> count([x, cons(y, r), _yg]) -> 26
(count([y, r, _xg])) -> count([y, cons(y, r), s(_xg)]) -> 28
(delete_all([x, r, _sg]) /\ not eq_elt([x, y])) -> delete_all([x, cons(y, r), cons(y, _sg)]) -> 27
(delete_all([y, r, _rg])) -> delete_all([y, cons(y, r), _rg]) -> 26
(delete_one([x, r, _mg]) /\ not eq_elt([x, y])) -> delete_one([x, cons(y, r), cons(y, _mg)]) -> 27
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 26
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 26
(leqnat([s(nn1), z])) -> BOT -> 26
}
Sat witness: Found: ((count([y, r, _xg])) -> count([y, cons(y, r), s(_xg)]), {
_xg -> s(s(z))  ;  r -> cons(b, cons(b, nil))  ;  y -> b
})

-------------------------------------------
Step 56, which took 0.074556 s (model generation: 0.072817,  model checking: 0.001739):

Model:
|_
{
count -> 
{{{
Q={q_gen_1378, q_gen_1390, q_gen_1391, q_gen_1393, q_gen_1394, q_gen_1421, q_gen_1432, q_gen_1434},
Q_f={q_gen_1378},
Delta=
{
<b>() -> q_gen_1391
<cons>(q_gen_1391, q_gen_1393) -> q_gen_1393
<cons>(q_gen_1394, q_gen_1393) -> q_gen_1393
<nil>() -> q_gen_1393
<a>() -> q_gen_1394
<cons, s>(q_gen_1394, q_gen_1390) -> q_gen_1390
<nil, z>() -> q_gen_1390
<cons, s>(q_gen_1394, q_gen_1421) -> q_gen_1421
<cons, z>(q_gen_1391, q_gen_1393) -> q_gen_1421
<cons, z>(q_gen_1394, q_gen_1393) -> q_gen_1421
<cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1434
<cons, s>(q_gen_1391, q_gen_1434) -> q_gen_1434
<a, cons, s>(q_gen_1391, q_gen_1421) -> q_gen_1378
<a, cons, s>(q_gen_1394, q_gen_1390) -> q_gen_1378
<a, cons, s>(q_gen_1394, q_gen_1421) -> q_gen_1378
<a, cons, z>(q_gen_1391, q_gen_1393) -> q_gen_1378
<a, nil, z>() -> q_gen_1378
<b, cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1378
<b, cons, s>(q_gen_1391, q_gen_1421) -> q_gen_1378
<b, cons, s>(q_gen_1391, q_gen_1434) -> q_gen_1378
<b, cons, s>(q_gen_1394, q_gen_1421) -> q_gen_1378
<b, cons, z>(q_gen_1394, q_gen_1393) -> q_gen_1378
<b, nil, z>() -> q_gen_1378
<a, cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1432
<a, cons, s>(q_gen_1391, q_gen_1434) -> q_gen_1432
<a, cons, s>(q_gen_1394, q_gen_1434) -> q_gen_1432
}

Datatype: <elt, eltlist, nat>
Convolution form: right
}}}
  ;  delete_all -> 
{{{
Q={q_gen_1377, q_gen_1384, q_gen_1385, q_gen_1387, q_gen_1388, q_gen_1409, q_gen_1431, q_gen_1456},
Q_f={q_gen_1377},
Delta=
{
<cons>(q_gen_1385, q_gen_1384) -> q_gen_1384
<nil>() -> q_gen_1384
<a>() -> q_gen_1385
<b>() -> q_gen_1385
<cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1387
<nil, nil>() -> q_gen_1387
<a, a>() -> q_gen_1388
<a, b>() -> q_gen_1388
<b, a>() -> q_gen_1409
<b, b>() -> q_gen_1409
<cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1431
<cons, cons>(q_gen_1409, q_gen_1387) -> q_gen_1431
<a, cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1377
<a, cons, cons>(q_gen_1409, q_gen_1387) -> q_gen_1377
<a, cons, cons>(q_gen_1409, q_gen_1431) -> q_gen_1377
<a, cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1377
<a, nil, nil>() -> q_gen_1377
<b, cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1377
<b, cons, cons>(q_gen_1388, q_gen_1431) -> q_gen_1377
<b, cons, cons>(q_gen_1409, q_gen_1387) -> q_gen_1377
<b, cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1377
<b, nil, nil>() -> q_gen_1377
<a, cons, cons>(q_gen_1388, q_gen_1431) -> q_gen_1456
<b, cons, cons>(q_gen_1409, q_gen_1431) -> q_gen_1456
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  delete_one -> 
{{{
Q={q_gen_1373, q_gen_1374, q_gen_1375, q_gen_1381, q_gen_1382},
Q_f={q_gen_1373},
Delta=
{
<nil>() -> q_gen_1374
<a>() -> q_gen_1375
<b>() -> q_gen_1375
<cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1381
<cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1381
<nil, nil>() -> q_gen_1381
<a, a>() -> q_gen_1382
<a, b>() -> q_gen_1382
<b, a>() -> q_gen_1382
<b, b>() -> q_gen_1382
<a, cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1373
<a, cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1373
<a, nil, nil>() -> q_gen_1373
<b, cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1373
<b, cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1373
<b, nil, nil>() -> q_gen_1373
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  leqnat -> 
{{{
Q={q_gen_1372, q_gen_1396, q_gen_1438},
Q_f={q_gen_1372},
Delta=
{
<s>(q_gen_1396) -> q_gen_1396
<z>() -> q_gen_1396
<s, s>(q_gen_1372) -> q_gen_1372
<z, s>(q_gen_1396) -> q_gen_1372
<z, z>() -> q_gen_1372
<s, s>(q_gen_1438) -> q_gen_1438
<s, z>(q_gen_1396) -> q_gen_1438
}

Datatype: <nat, nat>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist, eq_nat}
_|

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 25
() -> delete_all([x, nil, nil]) -> 25
() -> delete_one([x, nil, nil]) -> 25
() -> delete_one([y, cons(y, r), r]) -> 26
() -> leqnat([z, n2]) -> 25
(count([x, l, _fh]) /\ delete_all([x, l, _eh]) /\ delete_one([x, l, _eh])) -> leqnat([_fh, s(z)]) -> 28
(count([x, r, _yg]) /\ not eq_elt([x, y])) -> count([x, cons(y, r), _yg]) -> 26
(count([y, r, _xg])) -> count([y, cons(y, r), s(_xg)]) -> 28
(delete_all([x, r, _sg]) /\ not eq_elt([x, y])) -> delete_all([x, cons(y, r), cons(y, _sg)]) -> 27
(delete_all([y, r, _rg])) -> delete_all([y, cons(y, r), _rg]) -> 26
(delete_one([x, r, _mg]) /\ not eq_elt([x, y])) -> delete_one([x, cons(y, r), cons(y, _mg)]) -> 27
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 26
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 26
(leqnat([s(nn1), z])) -> BOT -> 26
}
Sat witness: Found: ((count([x, l, _fh]) /\ delete_all([x, l, _eh]) /\ delete_one([x, l, _eh])) -> leqnat([_fh, s(z)]), {
_eh -> cons(b, nil)  ;  _fh -> s(s(z))  ;  l -> cons(b, cons(a, nil))  ;  x -> b
})

-------------------------------------------
Step 57, which took 0.092944 s (model generation: 0.091969,  model checking: 0.000975):

Model:
|_
{
count -> 
{{{
Q={q_gen_1378, q_gen_1390, q_gen_1391, q_gen_1393, q_gen_1394, q_gen_1421, q_gen_1432, q_gen_1434},
Q_f={q_gen_1378},
Delta=
{
<b>() -> q_gen_1391
<cons>(q_gen_1391, q_gen_1393) -> q_gen_1393
<cons>(q_gen_1394, q_gen_1393) -> q_gen_1393
<nil>() -> q_gen_1393
<a>() -> q_gen_1394
<cons, s>(q_gen_1394, q_gen_1390) -> q_gen_1390
<nil, z>() -> q_gen_1390
<cons, s>(q_gen_1394, q_gen_1421) -> q_gen_1421
<cons, z>(q_gen_1391, q_gen_1393) -> q_gen_1421
<cons, z>(q_gen_1394, q_gen_1393) -> q_gen_1421
<cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1434
<cons, s>(q_gen_1391, q_gen_1434) -> q_gen_1434
<a, cons, s>(q_gen_1391, q_gen_1421) -> q_gen_1378
<a, cons, s>(q_gen_1394, q_gen_1390) -> q_gen_1378
<a, cons, s>(q_gen_1394, q_gen_1421) -> q_gen_1378
<a, cons, z>(q_gen_1391, q_gen_1393) -> q_gen_1378
<a, nil, z>() -> q_gen_1378
<b, cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1378
<b, cons, s>(q_gen_1391, q_gen_1421) -> q_gen_1378
<b, cons, s>(q_gen_1391, q_gen_1434) -> q_gen_1378
<b, cons, s>(q_gen_1394, q_gen_1421) -> q_gen_1378
<b, cons, z>(q_gen_1394, q_gen_1393) -> q_gen_1378
<b, nil, z>() -> q_gen_1378
<a, cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1432
<a, cons, s>(q_gen_1391, q_gen_1434) -> q_gen_1432
<a, cons, s>(q_gen_1394, q_gen_1434) -> q_gen_1432
}

Datatype: <elt, eltlist, nat>
Convolution form: right
}}}
  ;  delete_all -> 
{{{
Q={q_gen_1377, q_gen_1384, q_gen_1385, q_gen_1387, q_gen_1388, q_gen_1409, q_gen_1431, q_gen_1456},
Q_f={q_gen_1377},
Delta=
{
<cons>(q_gen_1385, q_gen_1384) -> q_gen_1384
<nil>() -> q_gen_1384
<a>() -> q_gen_1385
<b>() -> q_gen_1385
<cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1387
<nil, nil>() -> q_gen_1387
<a, a>() -> q_gen_1388
<a, b>() -> q_gen_1388
<b, a>() -> q_gen_1388
<b, b>() -> q_gen_1409
<cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1431
<cons, cons>(q_gen_1409, q_gen_1387) -> q_gen_1431
<a, cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1377
<a, cons, cons>(q_gen_1409, q_gen_1387) -> q_gen_1377
<a, cons, cons>(q_gen_1409, q_gen_1431) -> q_gen_1377
<a, cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1377
<a, nil, nil>() -> q_gen_1377
<b, cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1377
<b, cons, cons>(q_gen_1388, q_gen_1431) -> q_gen_1377
<b, cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1377
<b, nil, nil>() -> q_gen_1377
<a, cons, cons>(q_gen_1388, q_gen_1431) -> q_gen_1456
<b, cons, cons>(q_gen_1409, q_gen_1387) -> q_gen_1456
<b, cons, cons>(q_gen_1409, q_gen_1431) -> q_gen_1456
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  delete_one -> 
{{{
Q={q_gen_1373, q_gen_1374, q_gen_1375, q_gen_1381, q_gen_1382},
Q_f={q_gen_1373},
Delta=
{
<nil>() -> q_gen_1374
<a>() -> q_gen_1375
<b>() -> q_gen_1375
<cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1381
<cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1381
<nil, nil>() -> q_gen_1381
<a, a>() -> q_gen_1382
<a, b>() -> q_gen_1382
<b, a>() -> q_gen_1382
<b, b>() -> q_gen_1382
<a, cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1373
<a, cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1373
<a, nil, nil>() -> q_gen_1373
<b, cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1373
<b, cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1373
<b, nil, nil>() -> q_gen_1373
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  leqnat -> 
{{{
Q={q_gen_1372, q_gen_1396, q_gen_1438},
Q_f={q_gen_1372},
Delta=
{
<s>(q_gen_1396) -> q_gen_1396
<z>() -> q_gen_1396
<s, s>(q_gen_1372) -> q_gen_1372
<z, s>(q_gen_1396) -> q_gen_1372
<z, z>() -> q_gen_1372
<s, s>(q_gen_1438) -> q_gen_1438
<s, z>(q_gen_1396) -> q_gen_1438
}

Datatype: <nat, nat>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist, eq_nat}
_|

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 26
() -> delete_all([x, nil, nil]) -> 26
() -> delete_one([x, nil, nil]) -> 26
() -> delete_one([y, cons(y, r), r]) -> 26
() -> leqnat([z, n2]) -> 26
(count([x, l, _fh]) /\ delete_all([x, l, _eh]) /\ delete_one([x, l, _eh])) -> leqnat([_fh, s(z)]) -> 28
(count([x, r, _yg]) /\ not eq_elt([x, y])) -> count([x, cons(y, r), _yg]) -> 26
(count([y, r, _xg])) -> count([y, cons(y, r), s(_xg)]) -> 28
(delete_all([x, r, _sg]) /\ not eq_elt([x, y])) -> delete_all([x, cons(y, r), cons(y, _sg)]) -> 27
(delete_all([y, r, _rg])) -> delete_all([y, cons(y, r), _rg]) -> 29
(delete_one([x, r, _mg]) /\ not eq_elt([x, y])) -> delete_one([x, cons(y, r), cons(y, _mg)]) -> 27
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 27
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 27
(leqnat([s(nn1), z])) -> BOT -> 27
}
Sat witness: Found: ((delete_all([y, r, _rg])) -> delete_all([y, cons(y, r), _rg]), {
_rg -> cons(b, nil)  ;  r -> cons(a, nil)  ;  y -> b
})

-------------------------------------------
Step 58, which took 0.087070 s (model generation: 0.085239,  model checking: 0.001831):

Model:
|_
{
count -> 
{{{
Q={q_gen_1378, q_gen_1390, q_gen_1391, q_gen_1393, q_gen_1394, q_gen_1432, q_gen_1434, q_gen_1442},
Q_f={q_gen_1378},
Delta=
{
<b>() -> q_gen_1391
<cons>(q_gen_1391, q_gen_1393) -> q_gen_1393
<nil>() -> q_gen_1393
<a>() -> q_gen_1394
<cons>(q_gen_1394, q_gen_1393) -> q_gen_1442
<cons, s>(q_gen_1394, q_gen_1390) -> q_gen_1390
<cons, z>(q_gen_1391, q_gen_1393) -> q_gen_1390
<nil, z>() -> q_gen_1390
<cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1434
<cons, s>(q_gen_1391, q_gen_1434) -> q_gen_1434
<cons, s>(q_gen_1394, q_gen_1434) -> q_gen_1434
<cons, z>(q_gen_1391, q_gen_1442) -> q_gen_1434
<cons, z>(q_gen_1394, q_gen_1393) -> q_gen_1434
<a, cons, s>(q_gen_1391, q_gen_1434) -> q_gen_1378
<a, cons, s>(q_gen_1394, q_gen_1390) -> q_gen_1378
<a, cons, z>(q_gen_1391, q_gen_1393) -> q_gen_1378
<a, nil, z>() -> q_gen_1378
<b, cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1378
<b, cons, s>(q_gen_1391, q_gen_1434) -> q_gen_1378
<b, cons, s>(q_gen_1394, q_gen_1390) -> q_gen_1378
<b, cons, z>(q_gen_1394, q_gen_1393) -> q_gen_1378
<b, cons, z>(q_gen_1394, q_gen_1442) -> q_gen_1378
<b, nil, z>() -> q_gen_1378
<a, cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1432
<a, cons, s>(q_gen_1394, q_gen_1434) -> q_gen_1432
}

Datatype: <elt, eltlist, nat>
Convolution form: right
}}}
  ;  delete_all -> 
{{{
Q={q_gen_1377, q_gen_1384, q_gen_1385, q_gen_1387, q_gen_1388},
Q_f={q_gen_1377},
Delta=
{
<cons>(q_gen_1385, q_gen_1384) -> q_gen_1384
<nil>() -> q_gen_1384
<a>() -> q_gen_1385
<b>() -> q_gen_1385
<cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1387
<cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1387
<nil, nil>() -> q_gen_1387
<a, a>() -> q_gen_1388
<a, b>() -> q_gen_1388
<b, a>() -> q_gen_1388
<b, b>() -> q_gen_1388
<a, cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1377
<a, cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1377
<a, nil, nil>() -> q_gen_1377
<b, cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1377
<b, cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1377
<b, nil, nil>() -> q_gen_1377
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  delete_one -> 
{{{
Q={q_gen_1373, q_gen_1374, q_gen_1375, q_gen_1381, q_gen_1382, q_gen_1400, q_gen_1405, q_gen_1413, q_gen_1437},
Q_f={q_gen_1373},
Delta=
{
<nil>() -> q_gen_1374
<b>() -> q_gen_1375
<a>() -> q_gen_1400
<cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1381
<cons, cons>(q_gen_1405, q_gen_1381) -> q_gen_1381
<cons, nil>(q_gen_1400, q_gen_1374) -> q_gen_1381
<nil, nil>() -> q_gen_1381
<a, a>() -> q_gen_1382
<a, b>() -> q_gen_1382
<b, a>() -> q_gen_1382
<b, b>() -> q_gen_1405
<cons, cons>(q_gen_1382, q_gen_1413) -> q_gen_1413
<cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1413
<a, cons, cons>(q_gen_1382, q_gen_1413) -> q_gen_1373
<a, cons, cons>(q_gen_1405, q_gen_1381) -> q_gen_1373
<a, cons, nil>(q_gen_1400, q_gen_1374) -> q_gen_1373
<a, nil, nil>() -> q_gen_1373
<b, cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1373
<b, cons, cons>(q_gen_1382, q_gen_1413) -> q_gen_1373
<b, cons, cons>(q_gen_1405, q_gen_1413) -> q_gen_1373
<b, cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1373
<b, nil, nil>() -> q_gen_1373
<a, cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1437
<a, cons, cons>(q_gen_1405, q_gen_1413) -> q_gen_1437
<b, cons, cons>(q_gen_1405, q_gen_1381) -> q_gen_1437
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  leqnat -> 
{{{
Q={q_gen_1372, q_gen_1396, q_gen_1438},
Q_f={q_gen_1372},
Delta=
{
<s>(q_gen_1396) -> q_gen_1396
<z>() -> q_gen_1396
<s, s>(q_gen_1372) -> q_gen_1372
<z, s>(q_gen_1396) -> q_gen_1372
<z, z>() -> q_gen_1372
<s, s>(q_gen_1438) -> q_gen_1438
<s, z>(q_gen_1396) -> q_gen_1438
}

Datatype: <nat, nat>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist, eq_nat}
_|

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 26
() -> delete_all([x, nil, nil]) -> 26
() -> delete_one([x, nil, nil]) -> 26
() -> delete_one([y, cons(y, r), r]) -> 26
() -> leqnat([z, n2]) -> 26
(count([x, l, _fh]) /\ delete_all([x, l, _eh]) /\ delete_one([x, l, _eh])) -> leqnat([_fh, s(z)]) -> 28
(count([x, r, _yg]) /\ not eq_elt([x, y])) -> count([x, cons(y, r), _yg]) -> 29
(count([y, r, _xg])) -> count([y, cons(y, r), s(_xg)]) -> 28
(delete_all([x, r, _sg]) /\ not eq_elt([x, y])) -> delete_all([x, cons(y, r), cons(y, _sg)]) -> 27
(delete_all([y, r, _rg])) -> delete_all([y, cons(y, r), _rg]) -> 29
(delete_one([x, r, _mg]) /\ not eq_elt([x, y])) -> delete_one([x, cons(y, r), cons(y, _mg)]) -> 27
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 27
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 27
(leqnat([s(nn1), z])) -> BOT -> 27
}
Sat witness: Found: ((count([x, r, _yg]) /\ not eq_elt([x, y])) -> count([x, cons(y, r), _yg]), {
_yg -> s(z)  ;  r -> cons(b, cons(a, nil))  ;  x -> b  ;  y -> a
})

-------------------------------------------
Step 59, which took 0.047814 s (model generation: 0.047506,  model checking: 0.000308):

Model:
|_
{
count -> 
{{{
Q={q_gen_1378, q_gen_1390, q_gen_1391, q_gen_1393, q_gen_1394, q_gen_1421, q_gen_1432, q_gen_1434},
Q_f={q_gen_1378},
Delta=
{
<b>() -> q_gen_1391
<cons>(q_gen_1391, q_gen_1393) -> q_gen_1393
<cons>(q_gen_1394, q_gen_1393) -> q_gen_1393
<nil>() -> q_gen_1393
<a>() -> q_gen_1394
<cons, s>(q_gen_1394, q_gen_1390) -> q_gen_1390
<nil, z>() -> q_gen_1390
<cons, s>(q_gen_1394, q_gen_1421) -> q_gen_1421
<cons, z>(q_gen_1391, q_gen_1393) -> q_gen_1421
<cons, z>(q_gen_1394, q_gen_1393) -> q_gen_1421
<cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1434
<cons, s>(q_gen_1391, q_gen_1434) -> q_gen_1434
<a, cons, s>(q_gen_1391, q_gen_1421) -> q_gen_1378
<a, cons, s>(q_gen_1394, q_gen_1390) -> q_gen_1378
<a, cons, s>(q_gen_1394, q_gen_1421) -> q_gen_1378
<a, cons, z>(q_gen_1391, q_gen_1393) -> q_gen_1378
<a, nil, z>() -> q_gen_1378
<b, cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1378
<b, cons, s>(q_gen_1391, q_gen_1421) -> q_gen_1378
<b, cons, s>(q_gen_1391, q_gen_1434) -> q_gen_1378
<b, cons, s>(q_gen_1394, q_gen_1421) -> q_gen_1378
<b, cons, z>(q_gen_1394, q_gen_1393) -> q_gen_1378
<b, nil, z>() -> q_gen_1378
<a, cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1432
<a, cons, s>(q_gen_1391, q_gen_1434) -> q_gen_1432
<a, cons, s>(q_gen_1394, q_gen_1434) -> q_gen_1432
}

Datatype: <elt, eltlist, nat>
Convolution form: right
}}}
  ;  delete_all -> 
{{{
Q={q_gen_1377, q_gen_1384, q_gen_1385, q_gen_1387, q_gen_1388},
Q_f={q_gen_1377},
Delta=
{
<cons>(q_gen_1385, q_gen_1384) -> q_gen_1384
<nil>() -> q_gen_1384
<a>() -> q_gen_1385
<b>() -> q_gen_1385
<cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1387
<cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1387
<nil, nil>() -> q_gen_1387
<a, a>() -> q_gen_1388
<a, b>() -> q_gen_1388
<b, a>() -> q_gen_1388
<b, b>() -> q_gen_1388
<a, cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1377
<a, cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1377
<a, nil, nil>() -> q_gen_1377
<b, cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1377
<b, cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1377
<b, nil, nil>() -> q_gen_1377
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  delete_one -> 
{{{
Q={q_gen_1373, q_gen_1374, q_gen_1375, q_gen_1381, q_gen_1382, q_gen_1400, q_gen_1405, q_gen_1425, q_gen_1458},
Q_f={q_gen_1373},
Delta=
{
<nil>() -> q_gen_1374
<b>() -> q_gen_1375
<a>() -> q_gen_1400
<cons, cons>(q_gen_1405, q_gen_1381) -> q_gen_1381
<cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1381
<nil, nil>() -> q_gen_1381
<a, a>() -> q_gen_1382
<a, b>() -> q_gen_1382
<b, a>() -> q_gen_1382
<b, b>() -> q_gen_1405
<cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1425
<cons, nil>(q_gen_1400, q_gen_1374) -> q_gen_1425
<a, cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1373
<a, cons, cons>(q_gen_1405, q_gen_1381) -> q_gen_1373
<a, cons, cons>(q_gen_1405, q_gen_1425) -> q_gen_1373
<a, cons, nil>(q_gen_1400, q_gen_1374) -> q_gen_1373
<a, nil, nil>() -> q_gen_1373
<b, cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1373
<b, cons, cons>(q_gen_1382, q_gen_1425) -> q_gen_1373
<b, cons, cons>(q_gen_1405, q_gen_1381) -> q_gen_1373
<b, cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1373
<b, nil, nil>() -> q_gen_1373
<a, cons, cons>(q_gen_1382, q_gen_1425) -> q_gen_1458
<b, cons, cons>(q_gen_1405, q_gen_1425) -> q_gen_1458
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  leqnat -> 
{{{
Q={q_gen_1372, q_gen_1396, q_gen_1438},
Q_f={q_gen_1372},
Delta=
{
<s>(q_gen_1396) -> q_gen_1396
<z>() -> q_gen_1396
<s, s>(q_gen_1372) -> q_gen_1372
<z, s>(q_gen_1396) -> q_gen_1372
<z, z>() -> q_gen_1372
<s, s>(q_gen_1438) -> q_gen_1438
<s, z>(q_gen_1396) -> q_gen_1438
}

Datatype: <nat, nat>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist, eq_nat}
_|

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 26
() -> delete_all([x, nil, nil]) -> 26
() -> delete_one([x, nil, nil]) -> 26
() -> delete_one([y, cons(y, r), r]) -> 29
() -> leqnat([z, n2]) -> 27
(count([x, l, _fh]) /\ delete_all([x, l, _eh]) /\ delete_one([x, l, _eh])) -> leqnat([_fh, s(z)]) -> 28
(count([x, r, _yg]) /\ not eq_elt([x, y])) -> count([x, cons(y, r), _yg]) -> 29
(count([y, r, _xg])) -> count([y, cons(y, r), s(_xg)]) -> 28
(delete_all([x, r, _sg]) /\ not eq_elt([x, y])) -> delete_all([x, cons(y, r), cons(y, _sg)]) -> 27
(delete_all([y, r, _rg])) -> delete_all([y, cons(y, r), _rg]) -> 29
(delete_one([x, r, _mg]) /\ not eq_elt([x, y])) -> delete_one([x, cons(y, r), cons(y, _mg)]) -> 27
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 27
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 27
(leqnat([s(nn1), z])) -> BOT -> 27
}
Sat witness: Found: (() -> delete_one([y, cons(y, r), r]), {
r -> cons(a, nil)  ;  y -> a
})

-------------------------------------------
Step 60, which took 0.089037 s (model generation: 0.087410,  model checking: 0.001627):

Model:
|_
{
count -> 
{{{
Q={q_gen_1378, q_gen_1390, q_gen_1391, q_gen_1393, q_gen_1394, q_gen_1421, q_gen_1432, q_gen_1434},
Q_f={q_gen_1378},
Delta=
{
<b>() -> q_gen_1391
<cons>(q_gen_1391, q_gen_1393) -> q_gen_1393
<cons>(q_gen_1394, q_gen_1393) -> q_gen_1393
<nil>() -> q_gen_1393
<a>() -> q_gen_1394
<cons, s>(q_gen_1394, q_gen_1390) -> q_gen_1390
<nil, z>() -> q_gen_1390
<cons, s>(q_gen_1394, q_gen_1421) -> q_gen_1421
<cons, z>(q_gen_1391, q_gen_1393) -> q_gen_1421
<cons, z>(q_gen_1394, q_gen_1393) -> q_gen_1421
<cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1434
<cons, s>(q_gen_1391, q_gen_1434) -> q_gen_1434
<a, cons, s>(q_gen_1391, q_gen_1421) -> q_gen_1378
<a, cons, s>(q_gen_1394, q_gen_1390) -> q_gen_1378
<a, cons, s>(q_gen_1394, q_gen_1421) -> q_gen_1378
<a, cons, z>(q_gen_1391, q_gen_1393) -> q_gen_1378
<a, nil, z>() -> q_gen_1378
<b, cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1378
<b, cons, s>(q_gen_1391, q_gen_1421) -> q_gen_1378
<b, cons, s>(q_gen_1391, q_gen_1434) -> q_gen_1378
<b, cons, s>(q_gen_1394, q_gen_1421) -> q_gen_1378
<b, cons, z>(q_gen_1394, q_gen_1393) -> q_gen_1378
<b, nil, z>() -> q_gen_1378
<a, cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1432
<a, cons, s>(q_gen_1391, q_gen_1434) -> q_gen_1432
<a, cons, s>(q_gen_1394, q_gen_1434) -> q_gen_1432
}

Datatype: <elt, eltlist, nat>
Convolution form: right
}}}
  ;  delete_all -> 
{{{
Q={q_gen_1377, q_gen_1384, q_gen_1385, q_gen_1387, q_gen_1388},
Q_f={q_gen_1377},
Delta=
{
<cons>(q_gen_1385, q_gen_1384) -> q_gen_1384
<nil>() -> q_gen_1384
<a>() -> q_gen_1385
<b>() -> q_gen_1385
<cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1387
<cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1387
<nil, nil>() -> q_gen_1387
<a, a>() -> q_gen_1388
<a, b>() -> q_gen_1388
<b, a>() -> q_gen_1388
<b, b>() -> q_gen_1388
<a, cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1377
<a, cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1377
<a, nil, nil>() -> q_gen_1377
<b, cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1377
<b, cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1377
<b, nil, nil>() -> q_gen_1377
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  delete_one -> 
{{{
Q={q_gen_1373, q_gen_1374, q_gen_1375, q_gen_1381, q_gen_1382, q_gen_1400, q_gen_1425, q_gen_1426, q_gen_1458},
Q_f={q_gen_1373},
Delta=
{
<nil>() -> q_gen_1374
<b>() -> q_gen_1375
<a>() -> q_gen_1400
<cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1381
<cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1381
<nil, nil>() -> q_gen_1381
<a, a>() -> q_gen_1382
<b, b>() -> q_gen_1382
<cons, cons>(q_gen_1426, q_gen_1381) -> q_gen_1425
<cons, nil>(q_gen_1400, q_gen_1374) -> q_gen_1425
<a, b>() -> q_gen_1426
<b, a>() -> q_gen_1426
<a, cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1373
<a, cons, cons>(q_gen_1382, q_gen_1425) -> q_gen_1373
<a, cons, cons>(q_gen_1426, q_gen_1381) -> q_gen_1373
<a, cons, nil>(q_gen_1400, q_gen_1374) -> q_gen_1373
<a, nil, nil>() -> q_gen_1373
<b, cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1373
<b, cons, cons>(q_gen_1426, q_gen_1425) -> q_gen_1373
<b, cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1373
<b, nil, nil>() -> q_gen_1373
<a, cons, cons>(q_gen_1426, q_gen_1425) -> q_gen_1458
<b, cons, cons>(q_gen_1382, q_gen_1425) -> q_gen_1458
<b, cons, cons>(q_gen_1426, q_gen_1381) -> q_gen_1458
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  leqnat -> 
{{{
Q={q_gen_1372, q_gen_1396, q_gen_1438},
Q_f={q_gen_1372},
Delta=
{
<s>(q_gen_1396) -> q_gen_1396
<z>() -> q_gen_1396
<s, s>(q_gen_1372) -> q_gen_1372
<z, s>(q_gen_1396) -> q_gen_1372
<z, z>() -> q_gen_1372
<s, s>(q_gen_1438) -> q_gen_1438
<s, z>(q_gen_1396) -> q_gen_1438
}

Datatype: <nat, nat>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist, eq_nat}
_|

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 27
() -> delete_all([x, nil, nil]) -> 27
() -> delete_one([x, nil, nil]) -> 27
() -> delete_one([y, cons(y, r), r]) -> 29
() -> leqnat([z, n2]) -> 27
(count([x, l, _fh]) /\ delete_all([x, l, _eh]) /\ delete_one([x, l, _eh])) -> leqnat([_fh, s(z)]) -> 28
(count([x, r, _yg]) /\ not eq_elt([x, y])) -> count([x, cons(y, r), _yg]) -> 29
(count([y, r, _xg])) -> count([y, cons(y, r), s(_xg)]) -> 28
(delete_all([x, r, _sg]) /\ not eq_elt([x, y])) -> delete_all([x, cons(y, r), cons(y, _sg)]) -> 27
(delete_all([y, r, _rg])) -> delete_all([y, cons(y, r), _rg]) -> 29
(delete_one([x, r, _mg]) /\ not eq_elt([x, y])) -> delete_one([x, cons(y, r), cons(y, _mg)]) -> 30
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 28
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 28
(leqnat([s(nn1), z])) -> BOT -> 28
}
Sat witness: Found: ((delete_one([x, r, _mg]) /\ not eq_elt([x, y])) -> delete_one([x, cons(y, r), cons(y, _mg)]), {
_mg -> cons(a, cons(b, nil))  ;  r -> cons(b, cons(a, nil))  ;  x -> b  ;  y -> a
})

-------------------------------------------
Step 61, which took 0.044803 s (model generation: 0.044220,  model checking: 0.000583):

Model:
|_
{
count -> 
{{{
Q={q_gen_1378, q_gen_1390, q_gen_1391, q_gen_1393, q_gen_1394, q_gen_1421, q_gen_1432, q_gen_1434},
Q_f={q_gen_1378},
Delta=
{
<b>() -> q_gen_1391
<cons>(q_gen_1391, q_gen_1393) -> q_gen_1393
<cons>(q_gen_1394, q_gen_1393) -> q_gen_1393
<nil>() -> q_gen_1393
<a>() -> q_gen_1394
<cons, s>(q_gen_1394, q_gen_1390) -> q_gen_1390
<nil, z>() -> q_gen_1390
<cons, s>(q_gen_1394, q_gen_1421) -> q_gen_1421
<cons, z>(q_gen_1391, q_gen_1393) -> q_gen_1421
<cons, z>(q_gen_1394, q_gen_1393) -> q_gen_1421
<cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1434
<cons, s>(q_gen_1391, q_gen_1434) -> q_gen_1434
<a, cons, s>(q_gen_1391, q_gen_1421) -> q_gen_1378
<a, cons, s>(q_gen_1394, q_gen_1390) -> q_gen_1378
<a, cons, s>(q_gen_1394, q_gen_1421) -> q_gen_1378
<a, cons, z>(q_gen_1391, q_gen_1393) -> q_gen_1378
<a, nil, z>() -> q_gen_1378
<b, cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1378
<b, cons, s>(q_gen_1391, q_gen_1421) -> q_gen_1378
<b, cons, s>(q_gen_1391, q_gen_1434) -> q_gen_1378
<b, cons, s>(q_gen_1394, q_gen_1421) -> q_gen_1378
<b, cons, z>(q_gen_1394, q_gen_1393) -> q_gen_1378
<b, nil, z>() -> q_gen_1378
<a, cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1432
<a, cons, s>(q_gen_1391, q_gen_1434) -> q_gen_1432
<a, cons, s>(q_gen_1394, q_gen_1434) -> q_gen_1432
}

Datatype: <elt, eltlist, nat>
Convolution form: right
}}}
  ;  delete_all -> 
{{{
Q={q_gen_1377, q_gen_1384, q_gen_1385, q_gen_1387, q_gen_1388, q_gen_1419, q_gen_1429, q_gen_1456, q_gen_1457},
Q_f={q_gen_1377},
Delta=
{
<cons>(q_gen_1385, q_gen_1384) -> q_gen_1384
<nil>() -> q_gen_1384
<a>() -> q_gen_1385
<b>() -> q_gen_1385
<nil, nil>() -> q_gen_1387
<a, a>() -> q_gen_1388
<b, b>() -> q_gen_1388
<cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1419
<cons, cons>(q_gen_1429, q_gen_1419) -> q_gen_1419
<cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1419
<a, b>() -> q_gen_1429
<b, a>() -> q_gen_1429
<cons, cons>(q_gen_1429, q_gen_1387) -> q_gen_1457
<a, cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1377
<a, cons, cons>(q_gen_1388, q_gen_1419) -> q_gen_1377
<a, cons, cons>(q_gen_1429, q_gen_1419) -> q_gen_1377
<a, cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1377
<a, nil, nil>() -> q_gen_1377
<b, cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1377
<b, cons, cons>(q_gen_1429, q_gen_1419) -> q_gen_1377
<b, cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1377
<b, nil, nil>() -> q_gen_1377
<a, cons, cons>(q_gen_1429, q_gen_1457) -> q_gen_1456
<b, cons, cons>(q_gen_1388, q_gen_1419) -> q_gen_1456
<b, cons, cons>(q_gen_1388, q_gen_1457) -> q_gen_1456
<b, cons, cons>(q_gen_1429, q_gen_1387) -> q_gen_1456
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  delete_one -> 
{{{
Q={q_gen_1373, q_gen_1374, q_gen_1375, q_gen_1381, q_gen_1382},
Q_f={q_gen_1373},
Delta=
{
<nil>() -> q_gen_1374
<a>() -> q_gen_1375
<b>() -> q_gen_1375
<cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1381
<cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1381
<nil, nil>() -> q_gen_1381
<a, a>() -> q_gen_1382
<a, b>() -> q_gen_1382
<b, a>() -> q_gen_1382
<b, b>() -> q_gen_1382
<a, cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1373
<a, cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1373
<a, nil, nil>() -> q_gen_1373
<b, cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1373
<b, cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1373
<b, nil, nil>() -> q_gen_1373
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  leqnat -> 
{{{
Q={q_gen_1372, q_gen_1396, q_gen_1438},
Q_f={q_gen_1372},
Delta=
{
<s>(q_gen_1396) -> q_gen_1396
<z>() -> q_gen_1396
<s, s>(q_gen_1372) -> q_gen_1372
<z, s>(q_gen_1396) -> q_gen_1372
<z, z>() -> q_gen_1372
<s, s>(q_gen_1438) -> q_gen_1438
<s, z>(q_gen_1396) -> q_gen_1438
}

Datatype: <nat, nat>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist, eq_nat}
_|

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 27
() -> delete_all([x, nil, nil]) -> 27
() -> delete_one([x, nil, nil]) -> 27
() -> delete_one([y, cons(y, r), r]) -> 29
() -> leqnat([z, n2]) -> 27
(count([x, l, _fh]) /\ delete_all([x, l, _eh]) /\ delete_one([x, l, _eh])) -> leqnat([_fh, s(z)]) -> 28
(count([x, r, _yg]) /\ not eq_elt([x, y])) -> count([x, cons(y, r), _yg]) -> 29
(count([y, r, _xg])) -> count([y, cons(y, r), s(_xg)]) -> 28
(delete_all([x, r, _sg]) /\ not eq_elt([x, y])) -> delete_all([x, cons(y, r), cons(y, _sg)]) -> 30
(delete_all([y, r, _rg])) -> delete_all([y, cons(y, r), _rg]) -> 29
(delete_one([x, r, _mg]) /\ not eq_elt([x, y])) -> delete_one([x, cons(y, r), cons(y, _mg)]) -> 30
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 28
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 28
(leqnat([s(nn1), z])) -> BOT -> 28
}
Sat witness: Found: ((delete_all([x, r, _sg]) /\ not eq_elt([x, y])) -> delete_all([x, cons(y, r), cons(y, _sg)]), {
_sg -> nil  ;  r -> cons(a, nil)  ;  x -> b  ;  y -> a
})

-------------------------------------------
Step 62, which took 0.151454 s (model generation: 0.147998,  model checking: 0.003456):

Model:
|_
{
count -> 
{{{
Q={q_gen_1378, q_gen_1390, q_gen_1391, q_gen_1393, q_gen_1394, q_gen_1421, q_gen_1432, q_gen_1434, q_gen_1451},
Q_f={q_gen_1378},
Delta=
{
<b>() -> q_gen_1391
<cons>(q_gen_1391, q_gen_1393) -> q_gen_1393
<cons>(q_gen_1394, q_gen_1393) -> q_gen_1393
<nil>() -> q_gen_1393
<a>() -> q_gen_1394
<cons, s>(q_gen_1394, q_gen_1451) -> q_gen_1390
<nil, z>() -> q_gen_1390
<cons, s>(q_gen_1394, q_gen_1421) -> q_gen_1421
<cons, z>(q_gen_1391, q_gen_1393) -> q_gen_1421
<cons, z>(q_gen_1394, q_gen_1393) -> q_gen_1421
<cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1434
<cons, s>(q_gen_1391, q_gen_1434) -> q_gen_1434
<cons, s>(q_gen_1394, q_gen_1390) -> q_gen_1451
<a, cons, s>(q_gen_1391, q_gen_1421) -> q_gen_1378
<a, cons, s>(q_gen_1394, q_gen_1390) -> q_gen_1378
<a, cons, s>(q_gen_1394, q_gen_1421) -> q_gen_1378
<a, cons, s>(q_gen_1394, q_gen_1451) -> q_gen_1378
<a, cons, z>(q_gen_1391, q_gen_1393) -> q_gen_1378
<a, nil, z>() -> q_gen_1378
<b, cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1378
<b, cons, s>(q_gen_1391, q_gen_1421) -> q_gen_1378
<b, cons, s>(q_gen_1391, q_gen_1434) -> q_gen_1378
<b, cons, s>(q_gen_1394, q_gen_1421) -> q_gen_1378
<b, cons, z>(q_gen_1394, q_gen_1393) -> q_gen_1378
<b, nil, z>() -> q_gen_1378
<a, cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1432
<a, cons, s>(q_gen_1391, q_gen_1434) -> q_gen_1432
<a, cons, s>(q_gen_1391, q_gen_1451) -> q_gen_1432
<a, cons, s>(q_gen_1394, q_gen_1434) -> q_gen_1432
<b, cons, s>(q_gen_1391, q_gen_1451) -> q_gen_1432
}

Datatype: <elt, eltlist, nat>
Convolution form: right
}}}
  ;  delete_all -> 
{{{
Q={q_gen_1377, q_gen_1384, q_gen_1385, q_gen_1387, q_gen_1388},
Q_f={q_gen_1377},
Delta=
{
<cons>(q_gen_1385, q_gen_1384) -> q_gen_1384
<nil>() -> q_gen_1384
<a>() -> q_gen_1385
<b>() -> q_gen_1385
<cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1387
<cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1387
<nil, nil>() -> q_gen_1387
<a, a>() -> q_gen_1388
<a, b>() -> q_gen_1388
<b, a>() -> q_gen_1388
<b, b>() -> q_gen_1388
<a, cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1377
<a, cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1377
<a, nil, nil>() -> q_gen_1377
<b, cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1377
<b, cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1377
<b, nil, nil>() -> q_gen_1377
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  delete_one -> 
{{{
Q={q_gen_1373, q_gen_1374, q_gen_1375, q_gen_1381, q_gen_1382, q_gen_1444, q_gen_1459, q_gen_1465},
Q_f={q_gen_1373},
Delta=
{
<nil>() -> q_gen_1374
<a>() -> q_gen_1375
<b>() -> q_gen_1375
<cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1381
<cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1381
<nil, nil>() -> q_gen_1381
<a, a>() -> q_gen_1382
<b, a>() -> q_gen_1382
<b, b>() -> q_gen_1382
<a, b>() -> q_gen_1444
<cons, cons>(q_gen_1382, q_gen_1459) -> q_gen_1459
<cons, cons>(q_gen_1444, q_gen_1381) -> q_gen_1459
<a, cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1373
<a, cons, cons>(q_gen_1444, q_gen_1381) -> q_gen_1373
<a, cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1373
<a, nil, nil>() -> q_gen_1373
<b, cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1373
<b, cons, cons>(q_gen_1382, q_gen_1459) -> q_gen_1373
<b, cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1373
<b, nil, nil>() -> q_gen_1373
<a, cons, cons>(q_gen_1444, q_gen_1459) -> q_gen_1465
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  leqnat -> 
{{{
Q={q_gen_1372, q_gen_1396, q_gen_1438},
Q_f={q_gen_1372},
Delta=
{
<s>(q_gen_1396) -> q_gen_1396
<z>() -> q_gen_1396
<s, s>(q_gen_1372) -> q_gen_1372
<z, s>(q_gen_1396) -> q_gen_1372
<z, z>() -> q_gen_1372
<s, s>(q_gen_1438) -> q_gen_1438
<s, z>(q_gen_1396) -> q_gen_1438
}

Datatype: <nat, nat>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist, eq_nat}
_|

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 28
() -> delete_all([x, nil, nil]) -> 28
() -> delete_one([x, nil, nil]) -> 28
() -> delete_one([y, cons(y, r), r]) -> 29
() -> leqnat([z, n2]) -> 28
(count([x, l, _fh]) /\ delete_all([x, l, _eh]) /\ delete_one([x, l, _eh])) -> leqnat([_fh, s(z)]) -> 28
(count([x, r, _yg]) /\ not eq_elt([x, y])) -> count([x, cons(y, r), _yg]) -> 29
(count([y, r, _xg])) -> count([y, cons(y, r), s(_xg)]) -> 31
(delete_all([x, r, _sg]) /\ not eq_elt([x, y])) -> delete_all([x, cons(y, r), cons(y, _sg)]) -> 30
(delete_all([y, r, _rg])) -> delete_all([y, cons(y, r), _rg]) -> 29
(delete_one([x, r, _mg]) /\ not eq_elt([x, y])) -> delete_one([x, cons(y, r), cons(y, _mg)]) -> 30
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 29
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 29
(leqnat([s(nn1), z])) -> BOT -> 29
}
Sat witness: Found: ((count([y, r, _xg])) -> count([y, cons(y, r), s(_xg)]), {
_xg -> s(z)  ;  r -> cons(b, cons(a, nil))  ;  y -> b
})

-------------------------------------------
Step 63, which took 0.167588 s (model generation: 0.166162,  model checking: 0.001426):

Model:
|_
{
count -> 
{{{
Q={q_gen_1378, q_gen_1390, q_gen_1391, q_gen_1393, q_gen_1394, q_gen_1421, q_gen_1432, q_gen_1434},
Q_f={q_gen_1378},
Delta=
{
<b>() -> q_gen_1391
<cons>(q_gen_1391, q_gen_1393) -> q_gen_1393
<cons>(q_gen_1394, q_gen_1393) -> q_gen_1393
<nil>() -> q_gen_1393
<a>() -> q_gen_1394
<cons, s>(q_gen_1394, q_gen_1390) -> q_gen_1390
<nil, z>() -> q_gen_1390
<cons, s>(q_gen_1394, q_gen_1421) -> q_gen_1421
<cons, z>(q_gen_1391, q_gen_1393) -> q_gen_1421
<cons, z>(q_gen_1394, q_gen_1393) -> q_gen_1421
<cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1434
<cons, s>(q_gen_1391, q_gen_1421) -> q_gen_1434
<cons, s>(q_gen_1391, q_gen_1434) -> q_gen_1434
<a, cons, s>(q_gen_1391, q_gen_1421) -> q_gen_1378
<a, cons, s>(q_gen_1394, q_gen_1390) -> q_gen_1378
<a, cons, s>(q_gen_1394, q_gen_1421) -> q_gen_1378
<a, cons, z>(q_gen_1391, q_gen_1393) -> q_gen_1378
<a, nil, z>() -> q_gen_1378
<b, cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1378
<b, cons, s>(q_gen_1391, q_gen_1421) -> q_gen_1378
<b, cons, s>(q_gen_1391, q_gen_1434) -> q_gen_1378
<b, cons, s>(q_gen_1394, q_gen_1421) -> q_gen_1378
<b, cons, z>(q_gen_1394, q_gen_1393) -> q_gen_1378
<b, nil, z>() -> q_gen_1378
<a, cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1432
<a, cons, s>(q_gen_1391, q_gen_1434) -> q_gen_1432
<a, cons, s>(q_gen_1394, q_gen_1434) -> q_gen_1432
}

Datatype: <elt, eltlist, nat>
Convolution form: right
}}}
  ;  delete_all -> 
{{{
Q={q_gen_1377, q_gen_1384, q_gen_1385, q_gen_1387, q_gen_1388},
Q_f={q_gen_1377},
Delta=
{
<cons>(q_gen_1385, q_gen_1384) -> q_gen_1384
<nil>() -> q_gen_1384
<a>() -> q_gen_1385
<b>() -> q_gen_1385
<cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1387
<cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1387
<nil, nil>() -> q_gen_1387
<a, a>() -> q_gen_1388
<a, b>() -> q_gen_1388
<b, a>() -> q_gen_1388
<b, b>() -> q_gen_1388
<a, cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1377
<a, cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1377
<a, nil, nil>() -> q_gen_1377
<b, cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1377
<b, cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1377
<b, nil, nil>() -> q_gen_1377
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  delete_one -> 
{{{
Q={q_gen_1373, q_gen_1374, q_gen_1375, q_gen_1381, q_gen_1382, q_gen_1400, q_gen_1415, q_gen_1426, q_gen_1458},
Q_f={q_gen_1373},
Delta=
{
<nil>() -> q_gen_1374
<b>() -> q_gen_1375
<a>() -> q_gen_1400
<cons, cons>(q_gen_1426, q_gen_1415) -> q_gen_1381
<cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1381
<nil, nil>() -> q_gen_1381
<a, a>() -> q_gen_1382
<b, b>() -> q_gen_1382
<cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1415
<cons, cons>(q_gen_1426, q_gen_1381) -> q_gen_1415
<cons, nil>(q_gen_1400, q_gen_1374) -> q_gen_1415
<a, b>() -> q_gen_1426
<b, a>() -> q_gen_1426
<a, cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1373
<a, cons, cons>(q_gen_1382, q_gen_1415) -> q_gen_1373
<a, cons, cons>(q_gen_1426, q_gen_1381) -> q_gen_1373
<a, cons, nil>(q_gen_1400, q_gen_1374) -> q_gen_1373
<a, nil, nil>() -> q_gen_1373
<b, cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1373
<b, cons, cons>(q_gen_1426, q_gen_1415) -> q_gen_1373
<b, cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1373
<b, nil, nil>() -> q_gen_1373
<a, cons, cons>(q_gen_1426, q_gen_1415) -> q_gen_1458
<b, cons, cons>(q_gen_1382, q_gen_1415) -> q_gen_1458
<b, cons, cons>(q_gen_1426, q_gen_1381) -> q_gen_1458
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  leqnat -> 
{{{
Q={q_gen_1372, q_gen_1396, q_gen_1438},
Q_f={q_gen_1372},
Delta=
{
<s>(q_gen_1396) -> q_gen_1396
<z>() -> q_gen_1396
<s, s>(q_gen_1372) -> q_gen_1372
<z, s>(q_gen_1396) -> q_gen_1372
<z, z>() -> q_gen_1372
<s, s>(q_gen_1438) -> q_gen_1438
<s, z>(q_gen_1396) -> q_gen_1438
}

Datatype: <nat, nat>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist, eq_nat}
_|

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 28
() -> delete_all([x, nil, nil]) -> 28
() -> delete_one([x, nil, nil]) -> 28
() -> delete_one([y, cons(y, r), r]) -> 29
() -> leqnat([z, n2]) -> 28
(count([x, l, _fh]) /\ delete_all([x, l, _eh]) /\ delete_one([x, l, _eh])) -> leqnat([_fh, s(z)]) -> 31
(count([x, r, _yg]) /\ not eq_elt([x, y])) -> count([x, cons(y, r), _yg]) -> 29
(count([y, r, _xg])) -> count([y, cons(y, r), s(_xg)]) -> 31
(delete_all([x, r, _sg]) /\ not eq_elt([x, y])) -> delete_all([x, cons(y, r), cons(y, _sg)]) -> 30
(delete_all([y, r, _rg])) -> delete_all([y, cons(y, r), _rg]) -> 29
(delete_one([x, r, _mg]) /\ not eq_elt([x, y])) -> delete_one([x, cons(y, r), cons(y, _mg)]) -> 30
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 29
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 29
(leqnat([s(nn1), z])) -> BOT -> 29
}
Sat witness: Found: ((count([x, l, _fh]) /\ delete_all([x, l, _eh]) /\ delete_one([x, l, _eh])) -> leqnat([_fh, s(z)]), {
_eh -> cons(b, nil)  ;  _fh -> s(s(z))  ;  l -> cons(b, cons(b, nil))  ;  x -> b
})

-------------------------------------------
Step 64, which took 0.128364 s (model generation: 0.127045,  model checking: 0.001319):

Model:
|_
{
count -> 
{{{
Q={q_gen_1378, q_gen_1390, q_gen_1391, q_gen_1393, q_gen_1394, q_gen_1421, q_gen_1432, q_gen_1434},
Q_f={q_gen_1378},
Delta=
{
<b>() -> q_gen_1391
<cons>(q_gen_1391, q_gen_1393) -> q_gen_1393
<cons>(q_gen_1394, q_gen_1393) -> q_gen_1393
<nil>() -> q_gen_1393
<a>() -> q_gen_1394
<cons, s>(q_gen_1394, q_gen_1390) -> q_gen_1390
<nil, z>() -> q_gen_1390
<cons, s>(q_gen_1394, q_gen_1421) -> q_gen_1421
<cons, z>(q_gen_1391, q_gen_1393) -> q_gen_1421
<cons, z>(q_gen_1394, q_gen_1393) -> q_gen_1421
<cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1434
<cons, s>(q_gen_1391, q_gen_1421) -> q_gen_1434
<cons, s>(q_gen_1391, q_gen_1434) -> q_gen_1434
<a, cons, s>(q_gen_1391, q_gen_1421) -> q_gen_1378
<a, cons, s>(q_gen_1394, q_gen_1390) -> q_gen_1378
<a, cons, s>(q_gen_1394, q_gen_1421) -> q_gen_1378
<a, cons, z>(q_gen_1391, q_gen_1393) -> q_gen_1378
<a, nil, z>() -> q_gen_1378
<b, cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1378
<b, cons, s>(q_gen_1391, q_gen_1421) -> q_gen_1378
<b, cons, s>(q_gen_1391, q_gen_1434) -> q_gen_1378
<b, cons, s>(q_gen_1394, q_gen_1421) -> q_gen_1378
<b, cons, z>(q_gen_1394, q_gen_1393) -> q_gen_1378
<b, nil, z>() -> q_gen_1378
<a, cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1432
<a, cons, s>(q_gen_1391, q_gen_1434) -> q_gen_1432
<a, cons, s>(q_gen_1394, q_gen_1434) -> q_gen_1432
}

Datatype: <elt, eltlist, nat>
Convolution form: right
}}}
  ;  delete_all -> 
{{{
Q={q_gen_1377, q_gen_1384, q_gen_1385, q_gen_1387, q_gen_1388, q_gen_1409, q_gen_1419, q_gen_1429, q_gen_1456},
Q_f={q_gen_1377},
Delta=
{
<cons>(q_gen_1385, q_gen_1384) -> q_gen_1384
<nil>() -> q_gen_1384
<a>() -> q_gen_1385
<b>() -> q_gen_1385
<cons, cons>(q_gen_1409, q_gen_1387) -> q_gen_1387
<cons, cons>(q_gen_1429, q_gen_1387) -> q_gen_1387
<cons, cons>(q_gen_1429, q_gen_1419) -> q_gen_1387
<nil, nil>() -> q_gen_1387
<a, a>() -> q_gen_1388
<b, b>() -> q_gen_1409
<cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1419
<a, b>() -> q_gen_1429
<b, a>() -> q_gen_1429
<a, cons, cons>(q_gen_1409, q_gen_1387) -> q_gen_1377
<a, cons, cons>(q_gen_1409, q_gen_1419) -> q_gen_1377
<a, cons, cons>(q_gen_1429, q_gen_1419) -> q_gen_1377
<a, cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1377
<a, nil, nil>() -> q_gen_1377
<b, cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1377
<b, cons, cons>(q_gen_1388, q_gen_1419) -> q_gen_1377
<b, cons, cons>(q_gen_1429, q_gen_1419) -> q_gen_1377
<b, cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1377
<b, nil, nil>() -> q_gen_1377
<a, cons, cons>(q_gen_1429, q_gen_1387) -> q_gen_1456
<b, cons, cons>(q_gen_1409, q_gen_1387) -> q_gen_1456
<b, cons, cons>(q_gen_1409, q_gen_1419) -> q_gen_1456
<b, cons, cons>(q_gen_1429, q_gen_1387) -> q_gen_1456
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  delete_one -> 
{{{
Q={q_gen_1373, q_gen_1374, q_gen_1375, q_gen_1381, q_gen_1382},
Q_f={q_gen_1373},
Delta=
{
<nil>() -> q_gen_1374
<a>() -> q_gen_1375
<b>() -> q_gen_1375
<cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1381
<cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1381
<nil, nil>() -> q_gen_1381
<a, a>() -> q_gen_1382
<a, b>() -> q_gen_1382
<b, a>() -> q_gen_1382
<b, b>() -> q_gen_1382
<a, cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1373
<a, cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1373
<a, nil, nil>() -> q_gen_1373
<b, cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1373
<b, cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1373
<b, nil, nil>() -> q_gen_1373
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  leqnat -> 
{{{
Q={q_gen_1372, q_gen_1396, q_gen_1438},
Q_f={q_gen_1372},
Delta=
{
<s>(q_gen_1396) -> q_gen_1396
<z>() -> q_gen_1396
<s, s>(q_gen_1372) -> q_gen_1372
<z, s>(q_gen_1396) -> q_gen_1372
<z, z>() -> q_gen_1372
<s, s>(q_gen_1438) -> q_gen_1438
<s, z>(q_gen_1396) -> q_gen_1438
}

Datatype: <nat, nat>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist, eq_nat}
_|

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 29
() -> delete_all([x, nil, nil]) -> 29
() -> delete_one([x, nil, nil]) -> 29
() -> delete_one([y, cons(y, r), r]) -> 29
() -> leqnat([z, n2]) -> 29
(count([x, l, _fh]) /\ delete_all([x, l, _eh]) /\ delete_one([x, l, _eh])) -> leqnat([_fh, s(z)]) -> 31
(count([x, r, _yg]) /\ not eq_elt([x, y])) -> count([x, cons(y, r), _yg]) -> 29
(count([y, r, _xg])) -> count([y, cons(y, r), s(_xg)]) -> 31
(delete_all([x, r, _sg]) /\ not eq_elt([x, y])) -> delete_all([x, cons(y, r), cons(y, _sg)]) -> 30
(delete_all([y, r, _rg])) -> delete_all([y, cons(y, r), _rg]) -> 32
(delete_one([x, r, _mg]) /\ not eq_elt([x, y])) -> delete_one([x, cons(y, r), cons(y, _mg)]) -> 30
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 30
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 30
(leqnat([s(nn1), z])) -> BOT -> 30
}
Sat witness: Found: ((delete_all([y, r, _rg])) -> delete_all([y, cons(y, r), _rg]), {
_rg -> cons(b, nil)  ;  r -> cons(a, cons(a, nil))  ;  y -> b
})

-------------------------------------------
Step 65, which took 0.114621 s (model generation: 0.113783,  model checking: 0.000838):

Model:
|_
{
count -> 
{{{
Q={q_gen_1378, q_gen_1390, q_gen_1391, q_gen_1393, q_gen_1394, q_gen_1421, q_gen_1432, q_gen_1434},
Q_f={q_gen_1378},
Delta=
{
<b>() -> q_gen_1391
<cons>(q_gen_1391, q_gen_1393) -> q_gen_1393
<cons>(q_gen_1394, q_gen_1393) -> q_gen_1393
<nil>() -> q_gen_1393
<a>() -> q_gen_1394
<cons, s>(q_gen_1394, q_gen_1390) -> q_gen_1390
<nil, z>() -> q_gen_1390
<cons, s>(q_gen_1394, q_gen_1421) -> q_gen_1421
<cons, z>(q_gen_1391, q_gen_1393) -> q_gen_1421
<cons, z>(q_gen_1394, q_gen_1393) -> q_gen_1421
<cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1434
<cons, s>(q_gen_1391, q_gen_1421) -> q_gen_1434
<cons, s>(q_gen_1391, q_gen_1434) -> q_gen_1434
<a, cons, s>(q_gen_1391, q_gen_1421) -> q_gen_1378
<a, cons, s>(q_gen_1394, q_gen_1390) -> q_gen_1378
<a, cons, s>(q_gen_1394, q_gen_1421) -> q_gen_1378
<a, cons, z>(q_gen_1391, q_gen_1393) -> q_gen_1378
<a, nil, z>() -> q_gen_1378
<b, cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1378
<b, cons, s>(q_gen_1391, q_gen_1421) -> q_gen_1378
<b, cons, s>(q_gen_1391, q_gen_1434) -> q_gen_1378
<b, cons, s>(q_gen_1394, q_gen_1421) -> q_gen_1378
<b, cons, z>(q_gen_1394, q_gen_1393) -> q_gen_1378
<b, nil, z>() -> q_gen_1378
<a, cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1432
<a, cons, s>(q_gen_1391, q_gen_1434) -> q_gen_1432
<a, cons, s>(q_gen_1394, q_gen_1434) -> q_gen_1432
}

Datatype: <elt, eltlist, nat>
Convolution form: right
}}}
  ;  delete_all -> 
{{{
Q={q_gen_1377, q_gen_1384, q_gen_1385, q_gen_1387, q_gen_1388, q_gen_1409, q_gen_1419, q_gen_1429, q_gen_1456},
Q_f={q_gen_1377},
Delta=
{
<cons>(q_gen_1385, q_gen_1384) -> q_gen_1384
<nil>() -> q_gen_1384
<a>() -> q_gen_1385
<b>() -> q_gen_1385
<cons, cons>(q_gen_1429, q_gen_1387) -> q_gen_1387
<nil, nil>() -> q_gen_1387
<a, a>() -> q_gen_1388
<b, a>() -> q_gen_1388
<b, b>() -> q_gen_1409
<cons, cons>(q_gen_1409, q_gen_1387) -> q_gen_1419
<cons, cons>(q_gen_1429, q_gen_1419) -> q_gen_1419
<cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1419
<a, b>() -> q_gen_1429
<a, cons, cons>(q_gen_1409, q_gen_1387) -> q_gen_1377
<a, cons, cons>(q_gen_1409, q_gen_1419) -> q_gen_1377
<a, cons, cons>(q_gen_1429, q_gen_1419) -> q_gen_1377
<a, cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1377
<a, nil, nil>() -> q_gen_1377
<b, cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1377
<b, cons, cons>(q_gen_1388, q_gen_1419) -> q_gen_1377
<b, cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1377
<b, nil, nil>() -> q_gen_1377
<a, cons, cons>(q_gen_1429, q_gen_1387) -> q_gen_1456
<b, cons, cons>(q_gen_1409, q_gen_1387) -> q_gen_1456
<b, cons, cons>(q_gen_1409, q_gen_1419) -> q_gen_1456
<b, cons, cons>(q_gen_1429, q_gen_1387) -> q_gen_1456
<b, cons, cons>(q_gen_1429, q_gen_1419) -> q_gen_1456
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  delete_one -> 
{{{
Q={q_gen_1373, q_gen_1374, q_gen_1375, q_gen_1381, q_gen_1382},
Q_f={q_gen_1373},
Delta=
{
<nil>() -> q_gen_1374
<a>() -> q_gen_1375
<b>() -> q_gen_1375
<cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1381
<cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1381
<nil, nil>() -> q_gen_1381
<a, a>() -> q_gen_1382
<a, b>() -> q_gen_1382
<b, a>() -> q_gen_1382
<b, b>() -> q_gen_1382
<a, cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1373
<a, cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1373
<a, nil, nil>() -> q_gen_1373
<b, cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1373
<b, cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1373
<b, nil, nil>() -> q_gen_1373
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  leqnat -> 
{{{
Q={q_gen_1372, q_gen_1396, q_gen_1438},
Q_f={q_gen_1372},
Delta=
{
<s>(q_gen_1396) -> q_gen_1396
<z>() -> q_gen_1396
<s, s>(q_gen_1372) -> q_gen_1372
<z, s>(q_gen_1396) -> q_gen_1372
<z, z>() -> q_gen_1372
<s, s>(q_gen_1438) -> q_gen_1438
<s, z>(q_gen_1396) -> q_gen_1438
}

Datatype: <nat, nat>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist, eq_nat}
_|

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 29
() -> delete_all([x, nil, nil]) -> 29
() -> delete_one([x, nil, nil]) -> 29
() -> delete_one([y, cons(y, r), r]) -> 29
() -> leqnat([z, n2]) -> 29
(count([x, l, _fh]) /\ delete_all([x, l, _eh]) /\ delete_one([x, l, _eh])) -> leqnat([_fh, s(z)]) -> 31
(count([x, r, _yg]) /\ not eq_elt([x, y])) -> count([x, cons(y, r), _yg]) -> 32
(count([y, r, _xg])) -> count([y, cons(y, r), s(_xg)]) -> 31
(delete_all([x, r, _sg]) /\ not eq_elt([x, y])) -> delete_all([x, cons(y, r), cons(y, _sg)]) -> 30
(delete_all([y, r, _rg])) -> delete_all([y, cons(y, r), _rg]) -> 32
(delete_one([x, r, _mg]) /\ not eq_elt([x, y])) -> delete_one([x, cons(y, r), cons(y, _mg)]) -> 30
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 30
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 30
(leqnat([s(nn1), z])) -> BOT -> 30
}
Sat witness: Found: ((count([x, r, _yg]) /\ not eq_elt([x, y])) -> count([x, cons(y, r), _yg]), {
_yg -> s(s(z))  ;  r -> cons(b, cons(a, cons(a, nil)))  ;  x -> a  ;  y -> b
})

-------------------------------------------
Step 66, which took 0.123137 s (model generation: 0.120086,  model checking: 0.003051):

Model:
|_
{
count -> 
{{{
Q={q_gen_1378, q_gen_1390, q_gen_1391, q_gen_1393, q_gen_1394, q_gen_1421, q_gen_1432, q_gen_1434},
Q_f={q_gen_1378},
Delta=
{
<b>() -> q_gen_1391
<cons>(q_gen_1391, q_gen_1393) -> q_gen_1393
<cons>(q_gen_1394, q_gen_1393) -> q_gen_1393
<nil>() -> q_gen_1393
<a>() -> q_gen_1394
<cons, s>(q_gen_1394, q_gen_1390) -> q_gen_1390
<nil, z>() -> q_gen_1390
<cons, s>(q_gen_1391, q_gen_1421) -> q_gen_1421
<cons, s>(q_gen_1394, q_gen_1421) -> q_gen_1421
<cons, z>(q_gen_1391, q_gen_1393) -> q_gen_1421
<cons, z>(q_gen_1394, q_gen_1393) -> q_gen_1421
<cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1434
<cons, s>(q_gen_1391, q_gen_1434) -> q_gen_1434
<a, cons, s>(q_gen_1391, q_gen_1421) -> q_gen_1378
<a, cons, s>(q_gen_1394, q_gen_1390) -> q_gen_1378
<a, cons, s>(q_gen_1394, q_gen_1421) -> q_gen_1378
<a, cons, z>(q_gen_1391, q_gen_1393) -> q_gen_1378
<a, nil, z>() -> q_gen_1378
<b, cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1378
<b, cons, s>(q_gen_1391, q_gen_1421) -> q_gen_1378
<b, cons, s>(q_gen_1391, q_gen_1434) -> q_gen_1378
<b, cons, s>(q_gen_1394, q_gen_1421) -> q_gen_1378
<b, cons, z>(q_gen_1394, q_gen_1393) -> q_gen_1378
<b, nil, z>() -> q_gen_1378
<a, cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1432
<a, cons, s>(q_gen_1391, q_gen_1434) -> q_gen_1432
<a, cons, s>(q_gen_1394, q_gen_1434) -> q_gen_1432
}

Datatype: <elt, eltlist, nat>
Convolution form: right
}}}
  ;  delete_all -> 
{{{
Q={q_gen_1377, q_gen_1384, q_gen_1385, q_gen_1387, q_gen_1388, q_gen_1409, q_gen_1419, q_gen_1429, q_gen_1456},
Q_f={q_gen_1377},
Delta=
{
<cons>(q_gen_1385, q_gen_1384) -> q_gen_1384
<nil>() -> q_gen_1384
<a>() -> q_gen_1385
<b>() -> q_gen_1385
<cons, cons>(q_gen_1409, q_gen_1387) -> q_gen_1387
<cons, cons>(q_gen_1429, q_gen_1387) -> q_gen_1387
<cons, cons>(q_gen_1429, q_gen_1419) -> q_gen_1387
<nil, nil>() -> q_gen_1387
<a, a>() -> q_gen_1388
<b, a>() -> q_gen_1388
<b, b>() -> q_gen_1409
<cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1419
<a, b>() -> q_gen_1429
<a, cons, cons>(q_gen_1409, q_gen_1387) -> q_gen_1377
<a, cons, cons>(q_gen_1409, q_gen_1419) -> q_gen_1377
<a, cons, cons>(q_gen_1429, q_gen_1419) -> q_gen_1377
<a, cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1377
<a, nil, nil>() -> q_gen_1377
<b, cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1377
<b, cons, cons>(q_gen_1388, q_gen_1419) -> q_gen_1377
<b, cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1377
<b, nil, nil>() -> q_gen_1377
<a, cons, cons>(q_gen_1429, q_gen_1387) -> q_gen_1456
<b, cons, cons>(q_gen_1409, q_gen_1387) -> q_gen_1456
<b, cons, cons>(q_gen_1409, q_gen_1419) -> q_gen_1456
<b, cons, cons>(q_gen_1429, q_gen_1387) -> q_gen_1456
<b, cons, cons>(q_gen_1429, q_gen_1419) -> q_gen_1456
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  delete_one -> 
{{{
Q={q_gen_1373, q_gen_1374, q_gen_1375, q_gen_1381, q_gen_1382},
Q_f={q_gen_1373},
Delta=
{
<nil>() -> q_gen_1374
<a>() -> q_gen_1375
<b>() -> q_gen_1375
<cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1381
<cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1381
<nil, nil>() -> q_gen_1381
<a, a>() -> q_gen_1382
<a, b>() -> q_gen_1382
<b, a>() -> q_gen_1382
<b, b>() -> q_gen_1382
<a, cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1373
<a, cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1373
<a, nil, nil>() -> q_gen_1373
<b, cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1373
<b, cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1373
<b, nil, nil>() -> q_gen_1373
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  leqnat -> 
{{{
Q={q_gen_1372, q_gen_1396, q_gen_1438},
Q_f={q_gen_1372},
Delta=
{
<s>(q_gen_1396) -> q_gen_1396
<z>() -> q_gen_1396
<s, s>(q_gen_1372) -> q_gen_1372
<z, s>(q_gen_1396) -> q_gen_1372
<z, z>() -> q_gen_1372
<s, s>(q_gen_1438) -> q_gen_1438
<s, z>(q_gen_1396) -> q_gen_1438
}

Datatype: <nat, nat>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist, eq_nat}
_|

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 30
() -> delete_all([x, nil, nil]) -> 30
() -> delete_one([x, nil, nil]) -> 30
() -> delete_one([y, cons(y, r), r]) -> 30
() -> leqnat([z, n2]) -> 30
(count([x, l, _fh]) /\ delete_all([x, l, _eh]) /\ delete_one([x, l, _eh])) -> leqnat([_fh, s(z)]) -> 31
(count([x, r, _yg]) /\ not eq_elt([x, y])) -> count([x, cons(y, r), _yg]) -> 32
(count([y, r, _xg])) -> count([y, cons(y, r), s(_xg)]) -> 31
(delete_all([x, r, _sg]) /\ not eq_elt([x, y])) -> delete_all([x, cons(y, r), cons(y, _sg)]) -> 33
(delete_all([y, r, _rg])) -> delete_all([y, cons(y, r), _rg]) -> 32
(delete_one([x, r, _mg]) /\ not eq_elt([x, y])) -> delete_one([x, cons(y, r), cons(y, _mg)]) -> 31
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 31
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 31
(leqnat([s(nn1), z])) -> BOT -> 31
}
Sat witness: Found: ((delete_all([x, r, _sg]) /\ not eq_elt([x, y])) -> delete_all([x, cons(y, r), cons(y, _sg)]), {
_sg -> cons(a, nil)  ;  r -> cons(a, nil)  ;  x -> b  ;  y -> a
})

-------------------------------------------
Step 67, which took 0.133286 s (model generation: 0.128849,  model checking: 0.004437):

Model:
|_
{
count -> 
{{{
Q={q_gen_1378, q_gen_1390, q_gen_1391, q_gen_1393, q_gen_1394, q_gen_1421, q_gen_1432, q_gen_1434},
Q_f={q_gen_1378},
Delta=
{
<b>() -> q_gen_1391
<cons>(q_gen_1391, q_gen_1393) -> q_gen_1393
<cons>(q_gen_1394, q_gen_1393) -> q_gen_1393
<nil>() -> q_gen_1393
<a>() -> q_gen_1394
<cons, s>(q_gen_1394, q_gen_1390) -> q_gen_1390
<nil, z>() -> q_gen_1390
<cons, s>(q_gen_1391, q_gen_1421) -> q_gen_1421
<cons, s>(q_gen_1394, q_gen_1421) -> q_gen_1421
<cons, z>(q_gen_1391, q_gen_1393) -> q_gen_1421
<cons, z>(q_gen_1394, q_gen_1393) -> q_gen_1421
<cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1434
<cons, s>(q_gen_1391, q_gen_1434) -> q_gen_1434
<a, cons, s>(q_gen_1391, q_gen_1421) -> q_gen_1378
<a, cons, s>(q_gen_1394, q_gen_1390) -> q_gen_1378
<a, cons, s>(q_gen_1394, q_gen_1421) -> q_gen_1378
<a, cons, z>(q_gen_1391, q_gen_1393) -> q_gen_1378
<a, nil, z>() -> q_gen_1378
<b, cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1378
<b, cons, s>(q_gen_1391, q_gen_1421) -> q_gen_1378
<b, cons, s>(q_gen_1391, q_gen_1434) -> q_gen_1378
<b, cons, s>(q_gen_1394, q_gen_1421) -> q_gen_1378
<b, cons, z>(q_gen_1394, q_gen_1393) -> q_gen_1378
<b, nil, z>() -> q_gen_1378
<a, cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1432
<a, cons, s>(q_gen_1391, q_gen_1434) -> q_gen_1432
<a, cons, s>(q_gen_1394, q_gen_1434) -> q_gen_1432
}

Datatype: <elt, eltlist, nat>
Convolution form: right
}}}
  ;  delete_all -> 
{{{
Q={q_gen_1377, q_gen_1384, q_gen_1385, q_gen_1387, q_gen_1388, q_gen_1409, q_gen_1419, q_gen_1429, q_gen_1456},
Q_f={q_gen_1377},
Delta=
{
<cons>(q_gen_1385, q_gen_1384) -> q_gen_1384
<nil>() -> q_gen_1384
<a>() -> q_gen_1385
<b>() -> q_gen_1385
<cons, cons>(q_gen_1409, q_gen_1387) -> q_gen_1387
<cons, cons>(q_gen_1429, q_gen_1387) -> q_gen_1387
<nil, nil>() -> q_gen_1387
<a, a>() -> q_gen_1388
<b, a>() -> q_gen_1388
<b, b>() -> q_gen_1409
<cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1419
<cons, cons>(q_gen_1429, q_gen_1419) -> q_gen_1419
<cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1419
<a, b>() -> q_gen_1429
<a, cons, cons>(q_gen_1409, q_gen_1387) -> q_gen_1377
<a, cons, cons>(q_gen_1409, q_gen_1419) -> q_gen_1377
<a, cons, cons>(q_gen_1429, q_gen_1419) -> q_gen_1377
<a, cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1377
<a, nil, nil>() -> q_gen_1377
<b, cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1377
<b, cons, cons>(q_gen_1388, q_gen_1419) -> q_gen_1377
<b, cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1377
<b, nil, nil>() -> q_gen_1377
<a, cons, cons>(q_gen_1429, q_gen_1387) -> q_gen_1456
<b, cons, cons>(q_gen_1409, q_gen_1387) -> q_gen_1456
<b, cons, cons>(q_gen_1409, q_gen_1419) -> q_gen_1456
<b, cons, cons>(q_gen_1429, q_gen_1387) -> q_gen_1456
<b, cons, cons>(q_gen_1429, q_gen_1419) -> q_gen_1456
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  delete_one -> 
{{{
Q={q_gen_1373, q_gen_1374, q_gen_1375, q_gen_1381, q_gen_1382},
Q_f={q_gen_1373},
Delta=
{
<nil>() -> q_gen_1374
<a>() -> q_gen_1375
<b>() -> q_gen_1375
<cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1381
<cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1381
<nil, nil>() -> q_gen_1381
<a, a>() -> q_gen_1382
<a, b>() -> q_gen_1382
<b, a>() -> q_gen_1382
<b, b>() -> q_gen_1382
<a, cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1373
<a, cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1373
<a, nil, nil>() -> q_gen_1373
<b, cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1373
<b, cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1373
<b, nil, nil>() -> q_gen_1373
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  leqnat -> 
{{{
Q={q_gen_1372, q_gen_1396, q_gen_1438},
Q_f={q_gen_1372},
Delta=
{
<s>(q_gen_1396) -> q_gen_1396
<z>() -> q_gen_1396
<s, s>(q_gen_1372) -> q_gen_1372
<z, s>(q_gen_1396) -> q_gen_1372
<z, z>() -> q_gen_1372
<s, s>(q_gen_1438) -> q_gen_1438
<s, z>(q_gen_1396) -> q_gen_1438
}

Datatype: <nat, nat>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist, eq_nat}
_|

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 31
() -> delete_all([x, nil, nil]) -> 31
() -> delete_one([x, nil, nil]) -> 31
() -> delete_one([y, cons(y, r), r]) -> 31
() -> leqnat([z, n2]) -> 31
(count([x, l, _fh]) /\ delete_all([x, l, _eh]) /\ delete_one([x, l, _eh])) -> leqnat([_fh, s(z)]) -> 34
(count([x, r, _yg]) /\ not eq_elt([x, y])) -> count([x, cons(y, r), _yg]) -> 32
(count([y, r, _xg])) -> count([y, cons(y, r), s(_xg)]) -> 32
(delete_all([x, r, _sg]) /\ not eq_elt([x, y])) -> delete_all([x, cons(y, r), cons(y, _sg)]) -> 33
(delete_all([y, r, _rg])) -> delete_all([y, cons(y, r), _rg]) -> 32
(delete_one([x, r, _mg]) /\ not eq_elt([x, y])) -> delete_one([x, cons(y, r), cons(y, _mg)]) -> 32
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 32
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 32
(leqnat([s(nn1), z])) -> BOT -> 32
}
Sat witness: Found: ((count([x, l, _fh]) /\ delete_all([x, l, _eh]) /\ delete_one([x, l, _eh])) -> leqnat([_fh, s(z)]), {
_eh -> cons(b, cons(a, cons(b, nil)))  ;  _fh -> s(s(z))  ;  l -> cons(b, cons(b, cons(a, nil)))  ;  x -> a
})

-------------------------------------------
Step 68, which took 0.140503 s (model generation: 0.135888,  model checking: 0.004615):

Model:
|_
{
count -> 
{{{
Q={q_gen_1378, q_gen_1390, q_gen_1391, q_gen_1393, q_gen_1394, q_gen_1421, q_gen_1423, q_gen_1432, q_gen_1434},
Q_f={q_gen_1378},
Delta=
{
<b>() -> q_gen_1391
<nil>() -> q_gen_1393
<a>() -> q_gen_1394
<cons>(q_gen_1391, q_gen_1393) -> q_gen_1423
<cons>(q_gen_1394, q_gen_1393) -> q_gen_1423
<cons, s>(q_gen_1394, q_gen_1390) -> q_gen_1390
<nil, z>() -> q_gen_1390
<cons, s>(q_gen_1391, q_gen_1434) -> q_gen_1421
<cons, s>(q_gen_1394, q_gen_1421) -> q_gen_1421
<cons, z>(q_gen_1391, q_gen_1393) -> q_gen_1421
<cons, z>(q_gen_1391, q_gen_1423) -> q_gen_1421
<cons, z>(q_gen_1394, q_gen_1393) -> q_gen_1421
<cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1434
<cons, s>(q_gen_1391, q_gen_1421) -> q_gen_1434
<cons, z>(q_gen_1394, q_gen_1423) -> q_gen_1434
<a, cons, s>(q_gen_1391, q_gen_1421) -> q_gen_1378
<a, cons, s>(q_gen_1394, q_gen_1390) -> q_gen_1378
<a, cons, s>(q_gen_1394, q_gen_1421) -> q_gen_1378
<a, cons, z>(q_gen_1391, q_gen_1393) -> q_gen_1378
<a, cons, z>(q_gen_1391, q_gen_1423) -> q_gen_1378
<a, nil, z>() -> q_gen_1378
<b, cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1378
<b, cons, s>(q_gen_1391, q_gen_1421) -> q_gen_1378
<b, cons, s>(q_gen_1391, q_gen_1434) -> q_gen_1378
<b, cons, s>(q_gen_1394, q_gen_1421) -> q_gen_1378
<b, cons, z>(q_gen_1394, q_gen_1393) -> q_gen_1378
<b, cons, z>(q_gen_1394, q_gen_1423) -> q_gen_1378
<b, nil, z>() -> q_gen_1378
<a, cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1432
<a, cons, s>(q_gen_1391, q_gen_1434) -> q_gen_1432
<a, cons, s>(q_gen_1394, q_gen_1434) -> q_gen_1432
}

Datatype: <elt, eltlist, nat>
Convolution form: right
}}}
  ;  delete_all -> 
{{{
Q={q_gen_1377, q_gen_1384, q_gen_1385, q_gen_1387, q_gen_1388, q_gen_1409, q_gen_1419, q_gen_1429, q_gen_1456},
Q_f={q_gen_1377},
Delta=
{
<cons>(q_gen_1385, q_gen_1384) -> q_gen_1384
<nil>() -> q_gen_1384
<a>() -> q_gen_1385
<b>() -> q_gen_1385
<cons, cons>(q_gen_1429, q_gen_1387) -> q_gen_1387
<nil, nil>() -> q_gen_1387
<a, a>() -> q_gen_1388
<b, a>() -> q_gen_1388
<b, b>() -> q_gen_1409
<cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1419
<cons, cons>(q_gen_1409, q_gen_1387) -> q_gen_1419
<cons, cons>(q_gen_1429, q_gen_1419) -> q_gen_1419
<cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1419
<a, b>() -> q_gen_1429
<a, cons, cons>(q_gen_1409, q_gen_1387) -> q_gen_1377
<a, cons, cons>(q_gen_1409, q_gen_1419) -> q_gen_1377
<a, cons, cons>(q_gen_1429, q_gen_1419) -> q_gen_1377
<a, cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1377
<a, nil, nil>() -> q_gen_1377
<b, cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1377
<b, cons, cons>(q_gen_1388, q_gen_1419) -> q_gen_1377
<b, cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1377
<b, nil, nil>() -> q_gen_1377
<a, cons, cons>(q_gen_1429, q_gen_1387) -> q_gen_1456
<b, cons, cons>(q_gen_1409, q_gen_1387) -> q_gen_1456
<b, cons, cons>(q_gen_1409, q_gen_1419) -> q_gen_1456
<b, cons, cons>(q_gen_1429, q_gen_1387) -> q_gen_1456
<b, cons, cons>(q_gen_1429, q_gen_1419) -> q_gen_1456
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  delete_one -> 
{{{
Q={q_gen_1373, q_gen_1374, q_gen_1375, q_gen_1381, q_gen_1382},
Q_f={q_gen_1373},
Delta=
{
<nil>() -> q_gen_1374
<a>() -> q_gen_1375
<b>() -> q_gen_1375
<cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1381
<cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1381
<nil, nil>() -> q_gen_1381
<a, a>() -> q_gen_1382
<a, b>() -> q_gen_1382
<b, a>() -> q_gen_1382
<b, b>() -> q_gen_1382
<a, cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1373
<a, cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1373
<a, nil, nil>() -> q_gen_1373
<b, cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1373
<b, cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1373
<b, nil, nil>() -> q_gen_1373
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  leqnat -> 
{{{
Q={q_gen_1372, q_gen_1396, q_gen_1438},
Q_f={q_gen_1372},
Delta=
{
<s>(q_gen_1396) -> q_gen_1396
<z>() -> q_gen_1396
<s, s>(q_gen_1372) -> q_gen_1372
<z, s>(q_gen_1396) -> q_gen_1372
<z, z>() -> q_gen_1372
<s, s>(q_gen_1438) -> q_gen_1438
<s, z>(q_gen_1396) -> q_gen_1438
}

Datatype: <nat, nat>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist, eq_nat}
_|

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 32
() -> delete_all([x, nil, nil]) -> 32
() -> delete_one([x, nil, nil]) -> 32
() -> delete_one([y, cons(y, r), r]) -> 32
() -> leqnat([z, n2]) -> 32
(count([x, l, _fh]) /\ delete_all([x, l, _eh]) /\ delete_one([x, l, _eh])) -> leqnat([_fh, s(z)]) -> 34
(count([x, r, _yg]) /\ not eq_elt([x, y])) -> count([x, cons(y, r), _yg]) -> 32
(count([y, r, _xg])) -> count([y, cons(y, r), s(_xg)]) -> 32
(delete_all([x, r, _sg]) /\ not eq_elt([x, y])) -> delete_all([x, cons(y, r), cons(y, _sg)]) -> 33
(delete_all([y, r, _rg])) -> delete_all([y, cons(y, r), _rg]) -> 35
(delete_one([x, r, _mg]) /\ not eq_elt([x, y])) -> delete_one([x, cons(y, r), cons(y, _mg)]) -> 33
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 33
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 33
(leqnat([s(nn1), z])) -> BOT -> 33
}
Sat witness: Found: ((delete_all([y, r, _rg])) -> delete_all([y, cons(y, r), _rg]), {
_rg -> cons(b, cons(b, nil))  ;  r -> cons(b, cons(a, nil))  ;  y -> a
})

-------------------------------------------
Step 69, which took 0.198587 s (model generation: 0.197277,  model checking: 0.001310):

Model:
|_
{
count -> 
{{{
Q={q_gen_1378, q_gen_1390, q_gen_1391, q_gen_1393, q_gen_1394, q_gen_1423, q_gen_1432, q_gen_1434, q_gen_1448},
Q_f={q_gen_1378},
Delta=
{
<b>() -> q_gen_1391
<nil>() -> q_gen_1393
<a>() -> q_gen_1394
<cons>(q_gen_1391, q_gen_1393) -> q_gen_1423
<cons>(q_gen_1394, q_gen_1393) -> q_gen_1423
<cons, s>(q_gen_1394, q_gen_1390) -> q_gen_1390
<cons, z>(q_gen_1391, q_gen_1393) -> q_gen_1390
<nil, z>() -> q_gen_1390
<cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1434
<cons, s>(q_gen_1391, q_gen_1448) -> q_gen_1434
<cons, z>(q_gen_1394, q_gen_1423) -> q_gen_1434
<cons, s>(q_gen_1391, q_gen_1434) -> q_gen_1448
<cons, s>(q_gen_1394, q_gen_1448) -> q_gen_1448
<cons, z>(q_gen_1391, q_gen_1423) -> q_gen_1448
<cons, z>(q_gen_1394, q_gen_1393) -> q_gen_1448
<a, cons, s>(q_gen_1391, q_gen_1448) -> q_gen_1378
<a, cons, s>(q_gen_1394, q_gen_1390) -> q_gen_1378
<a, cons, z>(q_gen_1391, q_gen_1393) -> q_gen_1378
<a, cons, z>(q_gen_1391, q_gen_1423) -> q_gen_1378
<a, nil, z>() -> q_gen_1378
<b, cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1378
<b, cons, s>(q_gen_1391, q_gen_1434) -> q_gen_1378
<b, cons, s>(q_gen_1391, q_gen_1448) -> q_gen_1378
<b, cons, s>(q_gen_1394, q_gen_1390) -> q_gen_1378
<b, cons, s>(q_gen_1394, q_gen_1448) -> q_gen_1378
<b, cons, z>(q_gen_1394, q_gen_1393) -> q_gen_1378
<b, cons, z>(q_gen_1394, q_gen_1423) -> q_gen_1378
<b, nil, z>() -> q_gen_1378
<a, cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1432
<a, cons, s>(q_gen_1391, q_gen_1434) -> q_gen_1432
<a, cons, s>(q_gen_1394, q_gen_1434) -> q_gen_1432
}

Datatype: <elt, eltlist, nat>
Convolution form: right
}}}
  ;  delete_all -> 
{{{
Q={q_gen_1377, q_gen_1384, q_gen_1385, q_gen_1387, q_gen_1388, q_gen_1409, q_gen_1419, q_gen_1429, q_gen_1456},
Q_f={q_gen_1377},
Delta=
{
<cons>(q_gen_1385, q_gen_1384) -> q_gen_1384
<nil>() -> q_gen_1384
<a>() -> q_gen_1385
<b>() -> q_gen_1385
<cons, cons>(q_gen_1429, q_gen_1387) -> q_gen_1387
<nil, nil>() -> q_gen_1387
<a, a>() -> q_gen_1388
<b, a>() -> q_gen_1388
<b, b>() -> q_gen_1409
<cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1419
<cons, cons>(q_gen_1409, q_gen_1387) -> q_gen_1419
<cons, cons>(q_gen_1409, q_gen_1419) -> q_gen_1419
<cons, cons>(q_gen_1429, q_gen_1419) -> q_gen_1419
<cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1419
<a, b>() -> q_gen_1429
<a, cons, cons>(q_gen_1409, q_gen_1387) -> q_gen_1377
<a, cons, cons>(q_gen_1409, q_gen_1419) -> q_gen_1377
<a, cons, cons>(q_gen_1429, q_gen_1419) -> q_gen_1377
<a, cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1377
<a, nil, nil>() -> q_gen_1377
<b, cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1377
<b, cons, cons>(q_gen_1388, q_gen_1419) -> q_gen_1377
<b, cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1377
<b, nil, nil>() -> q_gen_1377
<a, cons, cons>(q_gen_1429, q_gen_1387) -> q_gen_1456
<b, cons, cons>(q_gen_1409, q_gen_1387) -> q_gen_1456
<b, cons, cons>(q_gen_1409, q_gen_1419) -> q_gen_1456
<b, cons, cons>(q_gen_1429, q_gen_1387) -> q_gen_1456
<b, cons, cons>(q_gen_1429, q_gen_1419) -> q_gen_1456
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  delete_one -> 
{{{
Q={q_gen_1373, q_gen_1374, q_gen_1375, q_gen_1381, q_gen_1382},
Q_f={q_gen_1373},
Delta=
{
<nil>() -> q_gen_1374
<a>() -> q_gen_1375
<b>() -> q_gen_1375
<cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1381
<cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1381
<nil, nil>() -> q_gen_1381
<a, a>() -> q_gen_1382
<a, b>() -> q_gen_1382
<b, a>() -> q_gen_1382
<b, b>() -> q_gen_1382
<a, cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1373
<a, cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1373
<a, nil, nil>() -> q_gen_1373
<b, cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1373
<b, cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1373
<b, nil, nil>() -> q_gen_1373
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  leqnat -> 
{{{
Q={q_gen_1372, q_gen_1396, q_gen_1438},
Q_f={q_gen_1372},
Delta=
{
<s>(q_gen_1396) -> q_gen_1396
<z>() -> q_gen_1396
<s, s>(q_gen_1372) -> q_gen_1372
<z, s>(q_gen_1396) -> q_gen_1372
<z, z>() -> q_gen_1372
<s, s>(q_gen_1438) -> q_gen_1438
<s, z>(q_gen_1396) -> q_gen_1438
}

Datatype: <nat, nat>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist, eq_nat}
_|

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 32
() -> delete_all([x, nil, nil]) -> 32
() -> delete_one([x, nil, nil]) -> 32
() -> delete_one([y, cons(y, r), r]) -> 32
() -> leqnat([z, n2]) -> 32
(count([x, l, _fh]) /\ delete_all([x, l, _eh]) /\ delete_one([x, l, _eh])) -> leqnat([_fh, s(z)]) -> 34
(count([x, r, _yg]) /\ not eq_elt([x, y])) -> count([x, cons(y, r), _yg]) -> 32
(count([y, r, _xg])) -> count([y, cons(y, r), s(_xg)]) -> 35
(delete_all([x, r, _sg]) /\ not eq_elt([x, y])) -> delete_all([x, cons(y, r), cons(y, _sg)]) -> 33
(delete_all([y, r, _rg])) -> delete_all([y, cons(y, r), _rg]) -> 35
(delete_one([x, r, _mg]) /\ not eq_elt([x, y])) -> delete_one([x, cons(y, r), cons(y, _mg)]) -> 33
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 33
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 33
(leqnat([s(nn1), z])) -> BOT -> 33
}
Sat witness: Found: ((count([y, r, _xg])) -> count([y, cons(y, r), s(_xg)]), {
_xg -> s(z)  ;  r -> cons(b, cons(a, nil))  ;  y -> a
})

-------------------------------------------
Step 70, which took 0.276648 s (model generation: 0.274508,  model checking: 0.002140):

Model:
|_
{
count -> 
{{{
Q={q_gen_1378, q_gen_1390, q_gen_1391, q_gen_1393, q_gen_1394, q_gen_1421, q_gen_1432, q_gen_1434},
Q_f={q_gen_1378},
Delta=
{
<b>() -> q_gen_1391
<cons>(q_gen_1391, q_gen_1393) -> q_gen_1393
<cons>(q_gen_1394, q_gen_1393) -> q_gen_1393
<nil>() -> q_gen_1393
<a>() -> q_gen_1394
<cons, s>(q_gen_1394, q_gen_1390) -> q_gen_1390
<nil, z>() -> q_gen_1390
<cons, s>(q_gen_1391, q_gen_1421) -> q_gen_1421
<cons, s>(q_gen_1394, q_gen_1421) -> q_gen_1421
<cons, z>(q_gen_1391, q_gen_1393) -> q_gen_1421
<cons, z>(q_gen_1394, q_gen_1393) -> q_gen_1421
<cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1434
<cons, s>(q_gen_1391, q_gen_1434) -> q_gen_1434
<a, cons, s>(q_gen_1391, q_gen_1421) -> q_gen_1378
<a, cons, s>(q_gen_1394, q_gen_1390) -> q_gen_1378
<a, cons, s>(q_gen_1394, q_gen_1421) -> q_gen_1378
<a, cons, z>(q_gen_1391, q_gen_1393) -> q_gen_1378
<a, nil, z>() -> q_gen_1378
<b, cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1378
<b, cons, s>(q_gen_1391, q_gen_1421) -> q_gen_1378
<b, cons, s>(q_gen_1391, q_gen_1434) -> q_gen_1378
<b, cons, s>(q_gen_1394, q_gen_1421) -> q_gen_1378
<b, cons, z>(q_gen_1394, q_gen_1393) -> q_gen_1378
<b, nil, z>() -> q_gen_1378
<a, cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1432
<a, cons, s>(q_gen_1391, q_gen_1434) -> q_gen_1432
<a, cons, s>(q_gen_1394, q_gen_1434) -> q_gen_1432
}

Datatype: <elt, eltlist, nat>
Convolution form: right
}}}
  ;  delete_all -> 
{{{
Q={q_gen_1377, q_gen_1384, q_gen_1385, q_gen_1387, q_gen_1388, q_gen_1409, q_gen_1456},
Q_f={q_gen_1377},
Delta=
{
<cons>(q_gen_1385, q_gen_1384) -> q_gen_1384
<nil>() -> q_gen_1384
<a>() -> q_gen_1385
<b>() -> q_gen_1385
<cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1387
<cons, cons>(q_gen_1409, q_gen_1387) -> q_gen_1387
<cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1387
<nil, nil>() -> q_gen_1387
<a, a>() -> q_gen_1388
<b, a>() -> q_gen_1388
<a, b>() -> q_gen_1409
<b, b>() -> q_gen_1409
<a, cons, cons>(q_gen_1409, q_gen_1387) -> q_gen_1377
<a, cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1377
<a, nil, nil>() -> q_gen_1377
<b, cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1377
<b, cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1377
<b, nil, nil>() -> q_gen_1377
<b, cons, cons>(q_gen_1409, q_gen_1387) -> q_gen_1456
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  delete_one -> 
{{{
Q={q_gen_1373, q_gen_1374, q_gen_1375, q_gen_1381, q_gen_1382, q_gen_1405, q_gen_1458, q_gen_1459},
Q_f={q_gen_1373},
Delta=
{
<nil>() -> q_gen_1374
<a>() -> q_gen_1375
<b>() -> q_gen_1375
<cons, cons>(q_gen_1405, q_gen_1381) -> q_gen_1381
<cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1381
<nil, nil>() -> q_gen_1381
<a, a>() -> q_gen_1382
<a, b>() -> q_gen_1382
<b, a>() -> q_gen_1382
<b, b>() -> q_gen_1405
<cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1459
<cons, cons>(q_gen_1382, q_gen_1459) -> q_gen_1459
<a, cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1373
<a, cons, cons>(q_gen_1405, q_gen_1381) -> q_gen_1373
<a, cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1373
<a, nil, nil>() -> q_gen_1373
<b, cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1373
<b, cons, cons>(q_gen_1382, q_gen_1459) -> q_gen_1373
<b, cons, cons>(q_gen_1405, q_gen_1381) -> q_gen_1373
<b, cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1373
<b, nil, nil>() -> q_gen_1373
<a, cons, cons>(q_gen_1382, q_gen_1459) -> q_gen_1458
<a, cons, cons>(q_gen_1405, q_gen_1459) -> q_gen_1458
<b, cons, cons>(q_gen_1405, q_gen_1459) -> q_gen_1458
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  leqnat -> 
{{{
Q={q_gen_1372, q_gen_1396, q_gen_1438},
Q_f={q_gen_1372},
Delta=
{
<s>(q_gen_1396) -> q_gen_1396
<z>() -> q_gen_1396
<s, s>(q_gen_1372) -> q_gen_1372
<z, s>(q_gen_1396) -> q_gen_1372
<z, z>() -> q_gen_1372
<s, s>(q_gen_1438) -> q_gen_1438
<s, z>(q_gen_1396) -> q_gen_1438
}

Datatype: <nat, nat>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist, eq_nat}
_|

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 32
() -> delete_all([x, nil, nil]) -> 32
() -> delete_one([x, nil, nil]) -> 32
() -> delete_one([y, cons(y, r), r]) -> 35
() -> leqnat([z, n2]) -> 33
(count([x, l, _fh]) /\ delete_all([x, l, _eh]) /\ delete_one([x, l, _eh])) -> leqnat([_fh, s(z)]) -> 34
(count([x, r, _yg]) /\ not eq_elt([x, y])) -> count([x, cons(y, r), _yg]) -> 33
(count([y, r, _xg])) -> count([y, cons(y, r), s(_xg)]) -> 35
(delete_all([x, r, _sg]) /\ not eq_elt([x, y])) -> delete_all([x, cons(y, r), cons(y, _sg)]) -> 33
(delete_all([y, r, _rg])) -> delete_all([y, cons(y, r), _rg]) -> 35
(delete_one([x, r, _mg]) /\ not eq_elt([x, y])) -> delete_one([x, cons(y, r), cons(y, _mg)]) -> 33
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 33
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 33
(leqnat([s(nn1), z])) -> BOT -> 33
}
Sat witness: Found: (() -> delete_one([y, cons(y, r), r]), {
r -> cons(b, cons(a, nil))  ;  y -> a
})

-------------------------------------------
Step 71, which took 0.275231 s (model generation: 0.272944,  model checking: 0.002287):

Model:
|_
{
count -> 
{{{
Q={q_gen_1378, q_gen_1390, q_gen_1391, q_gen_1393, q_gen_1394, q_gen_1421, q_gen_1432, q_gen_1434},
Q_f={q_gen_1378},
Delta=
{
<b>() -> q_gen_1391
<cons>(q_gen_1391, q_gen_1393) -> q_gen_1393
<cons>(q_gen_1394, q_gen_1393) -> q_gen_1393
<nil>() -> q_gen_1393
<a>() -> q_gen_1394
<cons, s>(q_gen_1394, q_gen_1390) -> q_gen_1390
<nil, z>() -> q_gen_1390
<cons, s>(q_gen_1391, q_gen_1421) -> q_gen_1421
<cons, s>(q_gen_1394, q_gen_1421) -> q_gen_1421
<cons, z>(q_gen_1391, q_gen_1393) -> q_gen_1421
<cons, z>(q_gen_1394, q_gen_1393) -> q_gen_1421
<cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1434
<cons, s>(q_gen_1391, q_gen_1434) -> q_gen_1434
<a, cons, s>(q_gen_1391, q_gen_1421) -> q_gen_1378
<a, cons, s>(q_gen_1394, q_gen_1390) -> q_gen_1378
<a, cons, s>(q_gen_1394, q_gen_1421) -> q_gen_1378
<a, cons, z>(q_gen_1391, q_gen_1393) -> q_gen_1378
<a, nil, z>() -> q_gen_1378
<b, cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1378
<b, cons, s>(q_gen_1391, q_gen_1421) -> q_gen_1378
<b, cons, s>(q_gen_1391, q_gen_1434) -> q_gen_1378
<b, cons, s>(q_gen_1394, q_gen_1421) -> q_gen_1378
<b, cons, z>(q_gen_1394, q_gen_1393) -> q_gen_1378
<b, nil, z>() -> q_gen_1378
<a, cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1432
<a, cons, s>(q_gen_1391, q_gen_1434) -> q_gen_1432
<a, cons, s>(q_gen_1394, q_gen_1434) -> q_gen_1432
}

Datatype: <elt, eltlist, nat>
Convolution form: right
}}}
  ;  delete_all -> 
{{{
Q={q_gen_1377, q_gen_1384, q_gen_1385, q_gen_1387, q_gen_1388, q_gen_1409, q_gen_1419, q_gen_1429, q_gen_1456, q_gen_1457},
Q_f={q_gen_1377},
Delta=
{
<cons>(q_gen_1385, q_gen_1384) -> q_gen_1384
<nil>() -> q_gen_1384
<a>() -> q_gen_1385
<b>() -> q_gen_1385
<cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1387
<cons, cons>(q_gen_1409, q_gen_1387) -> q_gen_1387
<cons, cons>(q_gen_1429, q_gen_1419) -> q_gen_1387
<nil, nil>() -> q_gen_1387
<a, a>() -> q_gen_1388
<b, a>() -> q_gen_1388
<b, b>() -> q_gen_1409
<cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1419
<a, b>() -> q_gen_1429
<cons, cons>(q_gen_1388, q_gen_1457) -> q_gen_1457
<cons, cons>(q_gen_1409, q_gen_1419) -> q_gen_1457
<cons, cons>(q_gen_1429, q_gen_1387) -> q_gen_1457
<a, cons, cons>(q_gen_1409, q_gen_1387) -> q_gen_1377
<a, cons, cons>(q_gen_1409, q_gen_1419) -> q_gen_1377
<a, cons, cons>(q_gen_1429, q_gen_1419) -> q_gen_1377
<a, cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1377
<a, nil, nil>() -> q_gen_1377
<b, cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1377
<b, cons, cons>(q_gen_1388, q_gen_1419) -> q_gen_1377
<b, cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1377
<b, nil, nil>() -> q_gen_1377
<a, cons, cons>(q_gen_1409, q_gen_1457) -> q_gen_1456
<a, cons, cons>(q_gen_1429, q_gen_1387) -> q_gen_1456
<a, cons, cons>(q_gen_1429, q_gen_1457) -> q_gen_1456
<b, cons, cons>(q_gen_1388, q_gen_1457) -> q_gen_1456
<b, cons, cons>(q_gen_1409, q_gen_1419) -> q_gen_1456
<b, cons, cons>(q_gen_1409, q_gen_1457) -> q_gen_1456
<b, cons, cons>(q_gen_1429, q_gen_1387) -> q_gen_1456
<b, cons, cons>(q_gen_1429, q_gen_1419) -> q_gen_1456
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  delete_one -> 
{{{
Q={q_gen_1373, q_gen_1374, q_gen_1375, q_gen_1381, q_gen_1382},
Q_f={q_gen_1373},
Delta=
{
<nil>() -> q_gen_1374
<a>() -> q_gen_1375
<b>() -> q_gen_1375
<cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1381
<cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1381
<nil, nil>() -> q_gen_1381
<a, a>() -> q_gen_1382
<a, b>() -> q_gen_1382
<b, a>() -> q_gen_1382
<b, b>() -> q_gen_1382
<a, cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1373
<a, cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1373
<a, nil, nil>() -> q_gen_1373
<b, cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1373
<b, cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1373
<b, nil, nil>() -> q_gen_1373
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  leqnat -> 
{{{
Q={q_gen_1372, q_gen_1396, q_gen_1438},
Q_f={q_gen_1372},
Delta=
{
<s>(q_gen_1396) -> q_gen_1396
<z>() -> q_gen_1396
<s, s>(q_gen_1372) -> q_gen_1372
<z, s>(q_gen_1396) -> q_gen_1372
<z, z>() -> q_gen_1372
<s, s>(q_gen_1438) -> q_gen_1438
<s, z>(q_gen_1396) -> q_gen_1438
}

Datatype: <nat, nat>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist, eq_nat}
_|

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 33
() -> delete_all([x, nil, nil]) -> 33
() -> delete_one([x, nil, nil]) -> 33
() -> delete_one([y, cons(y, r), r]) -> 35
() -> leqnat([z, n2]) -> 33
(count([x, l, _fh]) /\ delete_all([x, l, _eh]) /\ delete_one([x, l, _eh])) -> leqnat([_fh, s(z)]) -> 34
(count([x, r, _yg]) /\ not eq_elt([x, y])) -> count([x, cons(y, r), _yg]) -> 33
(count([y, r, _xg])) -> count([y, cons(y, r), s(_xg)]) -> 35
(delete_all([x, r, _sg]) /\ not eq_elt([x, y])) -> delete_all([x, cons(y, r), cons(y, _sg)]) -> 36
(delete_all([y, r, _rg])) -> delete_all([y, cons(y, r), _rg]) -> 35
(delete_one([x, r, _mg]) /\ not eq_elt([x, y])) -> delete_one([x, cons(y, r), cons(y, _mg)]) -> 34
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 34
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 34
(leqnat([s(nn1), z])) -> BOT -> 34
}
Sat witness: Found: ((delete_all([x, r, _sg]) /\ not eq_elt([x, y])) -> delete_all([x, cons(y, r), cons(y, _sg)]), {
_sg -> cons(b, nil)  ;  r -> cons(b, cons(a, nil))  ;  x -> a  ;  y -> b
})

-------------------------------------------
Step 72, which took 0.267670 s (model generation: 0.266479,  model checking: 0.001191):

Model:
|_
{
count -> 
{{{
Q={q_gen_1378, q_gen_1390, q_gen_1391, q_gen_1393, q_gen_1394, q_gen_1421, q_gen_1423, q_gen_1432, q_gen_1434},
Q_f={q_gen_1378},
Delta=
{
<b>() -> q_gen_1391
<nil>() -> q_gen_1393
<a>() -> q_gen_1394
<cons>(q_gen_1391, q_gen_1393) -> q_gen_1423
<cons>(q_gen_1394, q_gen_1393) -> q_gen_1423
<cons, s>(q_gen_1391, q_gen_1421) -> q_gen_1390
<cons, s>(q_gen_1394, q_gen_1390) -> q_gen_1390
<nil, z>() -> q_gen_1390
<cons, s>(q_gen_1391, q_gen_1434) -> q_gen_1421
<cons, s>(q_gen_1394, q_gen_1421) -> q_gen_1421
<cons, z>(q_gen_1391, q_gen_1393) -> q_gen_1421
<cons, z>(q_gen_1391, q_gen_1423) -> q_gen_1421
<cons, z>(q_gen_1394, q_gen_1393) -> q_gen_1421
<cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1434
<cons, z>(q_gen_1394, q_gen_1423) -> q_gen_1434
<a, cons, s>(q_gen_1391, q_gen_1421) -> q_gen_1378
<a, cons, s>(q_gen_1394, q_gen_1390) -> q_gen_1378
<a, cons, s>(q_gen_1394, q_gen_1421) -> q_gen_1378
<a, cons, z>(q_gen_1391, q_gen_1393) -> q_gen_1378
<a, cons, z>(q_gen_1391, q_gen_1423) -> q_gen_1378
<a, nil, z>() -> q_gen_1378
<b, cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1378
<b, cons, s>(q_gen_1391, q_gen_1421) -> q_gen_1378
<b, cons, s>(q_gen_1391, q_gen_1434) -> q_gen_1378
<b, cons, s>(q_gen_1394, q_gen_1421) -> q_gen_1378
<b, cons, z>(q_gen_1394, q_gen_1393) -> q_gen_1378
<b, cons, z>(q_gen_1394, q_gen_1423) -> q_gen_1378
<b, nil, z>() -> q_gen_1378
<a, cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1432
<a, cons, s>(q_gen_1391, q_gen_1434) -> q_gen_1432
<a, cons, s>(q_gen_1394, q_gen_1434) -> q_gen_1432
}

Datatype: <elt, eltlist, nat>
Convolution form: right
}}}
  ;  delete_all -> 
{{{
Q={q_gen_1377, q_gen_1384, q_gen_1385, q_gen_1387, q_gen_1388, q_gen_1409, q_gen_1419, q_gen_1429, q_gen_1456},
Q_f={q_gen_1377},
Delta=
{
<cons>(q_gen_1385, q_gen_1384) -> q_gen_1384
<nil>() -> q_gen_1384
<a>() -> q_gen_1385
<b>() -> q_gen_1385
<cons, cons>(q_gen_1429, q_gen_1387) -> q_gen_1387
<nil, nil>() -> q_gen_1387
<a, a>() -> q_gen_1388
<b, a>() -> q_gen_1388
<b, b>() -> q_gen_1409
<cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1419
<cons, cons>(q_gen_1409, q_gen_1387) -> q_gen_1419
<cons, cons>(q_gen_1409, q_gen_1419) -> q_gen_1419
<cons, cons>(q_gen_1429, q_gen_1419) -> q_gen_1419
<cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1419
<a, b>() -> q_gen_1429
<a, cons, cons>(q_gen_1409, q_gen_1387) -> q_gen_1377
<a, cons, cons>(q_gen_1409, q_gen_1419) -> q_gen_1377
<a, cons, cons>(q_gen_1429, q_gen_1419) -> q_gen_1377
<a, cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1377
<a, nil, nil>() -> q_gen_1377
<b, cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1377
<b, cons, cons>(q_gen_1388, q_gen_1419) -> q_gen_1377
<b, cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1377
<b, nil, nil>() -> q_gen_1377
<a, cons, cons>(q_gen_1429, q_gen_1387) -> q_gen_1456
<b, cons, cons>(q_gen_1409, q_gen_1387) -> q_gen_1456
<b, cons, cons>(q_gen_1409, q_gen_1419) -> q_gen_1456
<b, cons, cons>(q_gen_1429, q_gen_1387) -> q_gen_1456
<b, cons, cons>(q_gen_1429, q_gen_1419) -> q_gen_1456
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  delete_one -> 
{{{
Q={q_gen_1373, q_gen_1374, q_gen_1375, q_gen_1381, q_gen_1382},
Q_f={q_gen_1373},
Delta=
{
<nil>() -> q_gen_1374
<a>() -> q_gen_1375
<b>() -> q_gen_1375
<cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1381
<cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1381
<nil, nil>() -> q_gen_1381
<a, a>() -> q_gen_1382
<a, b>() -> q_gen_1382
<b, a>() -> q_gen_1382
<b, b>() -> q_gen_1382
<a, cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1373
<a, cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1373
<a, nil, nil>() -> q_gen_1373
<b, cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1373
<b, cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1373
<b, nil, nil>() -> q_gen_1373
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  leqnat -> 
{{{
Q={q_gen_1372, q_gen_1396, q_gen_1438},
Q_f={q_gen_1372},
Delta=
{
<s>(q_gen_1396) -> q_gen_1396
<z>() -> q_gen_1396
<s, s>(q_gen_1372) -> q_gen_1372
<z, s>(q_gen_1396) -> q_gen_1372
<z, z>() -> q_gen_1372
<s, s>(q_gen_1438) -> q_gen_1438
<s, z>(q_gen_1396) -> q_gen_1438
}

Datatype: <nat, nat>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist, eq_nat}
_|

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 33
() -> delete_all([x, nil, nil]) -> 33
() -> delete_one([x, nil, nil]) -> 33
() -> delete_one([y, cons(y, r), r]) -> 35
() -> leqnat([z, n2]) -> 33
(count([x, l, _fh]) /\ delete_all([x, l, _eh]) /\ delete_one([x, l, _eh])) -> leqnat([_fh, s(z)]) -> 34
(count([x, r, _yg]) /\ not eq_elt([x, y])) -> count([x, cons(y, r), _yg]) -> 36
(count([y, r, _xg])) -> count([y, cons(y, r), s(_xg)]) -> 35
(delete_all([x, r, _sg]) /\ not eq_elt([x, y])) -> delete_all([x, cons(y, r), cons(y, _sg)]) -> 36
(delete_all([y, r, _rg])) -> delete_all([y, cons(y, r), _rg]) -> 35
(delete_one([x, r, _mg]) /\ not eq_elt([x, y])) -> delete_one([x, cons(y, r), cons(y, _mg)]) -> 34
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 34
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 34
(leqnat([s(nn1), z])) -> BOT -> 34
}
Sat witness: Found: ((count([x, r, _yg]) /\ not eq_elt([x, y])) -> count([x, cons(y, r), _yg]), {
_yg -> s(z)  ;  r -> cons(a, cons(b, nil))  ;  x -> a  ;  y -> b
})

-------------------------------------------
Step 73, which took 0.330762 s (model generation: 0.328361,  model checking: 0.002401):

Model:
|_
{
count -> 
{{{
Q={q_gen_1378, q_gen_1390, q_gen_1391, q_gen_1393, q_gen_1394, q_gen_1432, q_gen_1434, q_gen_1442, q_gen_1448},
Q_f={q_gen_1378},
Delta=
{
<b>() -> q_gen_1391
<cons>(q_gen_1391, q_gen_1393) -> q_gen_1393
<nil>() -> q_gen_1393
<a>() -> q_gen_1394
<cons>(q_gen_1394, q_gen_1393) -> q_gen_1442
<cons, s>(q_gen_1391, q_gen_1448) -> q_gen_1390
<cons, s>(q_gen_1394, q_gen_1390) -> q_gen_1390
<cons, z>(q_gen_1391, q_gen_1393) -> q_gen_1390
<nil, z>() -> q_gen_1390
<cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1434
<cons, z>(q_gen_1394, q_gen_1442) -> q_gen_1434
<cons, s>(q_gen_1391, q_gen_1434) -> q_gen_1448
<cons, s>(q_gen_1394, q_gen_1448) -> q_gen_1448
<cons, z>(q_gen_1391, q_gen_1442) -> q_gen_1448
<cons, z>(q_gen_1394, q_gen_1393) -> q_gen_1448
<a, cons, s>(q_gen_1391, q_gen_1448) -> q_gen_1378
<a, cons, s>(q_gen_1394, q_gen_1390) -> q_gen_1378
<a, cons, z>(q_gen_1391, q_gen_1393) -> q_gen_1378
<a, nil, z>() -> q_gen_1378
<b, cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1378
<b, cons, s>(q_gen_1391, q_gen_1434) -> q_gen_1378
<b, cons, s>(q_gen_1391, q_gen_1448) -> q_gen_1378
<b, cons, s>(q_gen_1394, q_gen_1390) -> q_gen_1378
<b, cons, s>(q_gen_1394, q_gen_1448) -> q_gen_1378
<b, cons, z>(q_gen_1394, q_gen_1393) -> q_gen_1378
<b, cons, z>(q_gen_1394, q_gen_1442) -> q_gen_1378
<b, nil, z>() -> q_gen_1378
<a, cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1432
<a, cons, s>(q_gen_1391, q_gen_1434) -> q_gen_1432
<a, cons, s>(q_gen_1394, q_gen_1434) -> q_gen_1432
}

Datatype: <elt, eltlist, nat>
Convolution form: right
}}}
  ;  delete_all -> 
{{{
Q={q_gen_1377, q_gen_1384, q_gen_1385, q_gen_1387, q_gen_1388, q_gen_1409, q_gen_1419, q_gen_1429, q_gen_1456},
Q_f={q_gen_1377},
Delta=
{
<cons>(q_gen_1385, q_gen_1384) -> q_gen_1384
<nil>() -> q_gen_1384
<a>() -> q_gen_1385
<b>() -> q_gen_1385
<cons, cons>(q_gen_1429, q_gen_1387) -> q_gen_1387
<nil, nil>() -> q_gen_1387
<a, a>() -> q_gen_1388
<b, a>() -> q_gen_1388
<b, b>() -> q_gen_1409
<cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1419
<cons, cons>(q_gen_1409, q_gen_1387) -> q_gen_1419
<cons, cons>(q_gen_1409, q_gen_1419) -> q_gen_1419
<cons, cons>(q_gen_1429, q_gen_1419) -> q_gen_1419
<cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1419
<a, b>() -> q_gen_1429
<a, cons, cons>(q_gen_1409, q_gen_1387) -> q_gen_1377
<a, cons, cons>(q_gen_1409, q_gen_1419) -> q_gen_1377
<a, cons, cons>(q_gen_1429, q_gen_1419) -> q_gen_1377
<a, cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1377
<a, nil, nil>() -> q_gen_1377
<b, cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1377
<b, cons, cons>(q_gen_1388, q_gen_1419) -> q_gen_1377
<b, cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1377
<b, nil, nil>() -> q_gen_1377
<a, cons, cons>(q_gen_1429, q_gen_1387) -> q_gen_1456
<b, cons, cons>(q_gen_1409, q_gen_1387) -> q_gen_1456
<b, cons, cons>(q_gen_1409, q_gen_1419) -> q_gen_1456
<b, cons, cons>(q_gen_1429, q_gen_1387) -> q_gen_1456
<b, cons, cons>(q_gen_1429, q_gen_1419) -> q_gen_1456
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  delete_one -> 
{{{
Q={q_gen_1373, q_gen_1374, q_gen_1375, q_gen_1381, q_gen_1382},
Q_f={q_gen_1373},
Delta=
{
<nil>() -> q_gen_1374
<a>() -> q_gen_1375
<b>() -> q_gen_1375
<cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1381
<cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1381
<nil, nil>() -> q_gen_1381
<a, a>() -> q_gen_1382
<a, b>() -> q_gen_1382
<b, a>() -> q_gen_1382
<b, b>() -> q_gen_1382
<a, cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1373
<a, cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1373
<a, nil, nil>() -> q_gen_1373
<b, cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1373
<b, cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1373
<b, nil, nil>() -> q_gen_1373
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  leqnat -> 
{{{
Q={q_gen_1372, q_gen_1396, q_gen_1438},
Q_f={q_gen_1372},
Delta=
{
<s>(q_gen_1396) -> q_gen_1396
<z>() -> q_gen_1396
<s, s>(q_gen_1372) -> q_gen_1372
<z, s>(q_gen_1396) -> q_gen_1372
<z, z>() -> q_gen_1372
<s, s>(q_gen_1438) -> q_gen_1438
<s, z>(q_gen_1396) -> q_gen_1438
}

Datatype: <nat, nat>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist, eq_nat}
_|

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 34
() -> delete_all([x, nil, nil]) -> 34
() -> delete_one([x, nil, nil]) -> 34
() -> delete_one([y, cons(y, r), r]) -> 35
() -> leqnat([z, n2]) -> 34
(count([x, l, _fh]) /\ delete_all([x, l, _eh]) /\ delete_one([x, l, _eh])) -> leqnat([_fh, s(z)]) -> 37
(count([x, r, _yg]) /\ not eq_elt([x, y])) -> count([x, cons(y, r), _yg]) -> 36
(count([y, r, _xg])) -> count([y, cons(y, r), s(_xg)]) -> 35
(delete_all([x, r, _sg]) /\ not eq_elt([x, y])) -> delete_all([x, cons(y, r), cons(y, _sg)]) -> 36
(delete_all([y, r, _rg])) -> delete_all([y, cons(y, r), _rg]) -> 35
(delete_one([x, r, _mg]) /\ not eq_elt([x, y])) -> delete_one([x, cons(y, r), cons(y, _mg)]) -> 35
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 35
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 35
(leqnat([s(nn1), z])) -> BOT -> 35
}
Sat witness: Found: ((count([x, l, _fh]) /\ delete_all([x, l, _eh]) /\ delete_one([x, l, _eh])) -> leqnat([_fh, s(z)]), {
_eh -> cons(a, cons(a, nil))  ;  _fh -> s(s(z))  ;  l -> cons(b, cons(b, nil))  ;  x -> b
})

-------------------------------------------
Step 74, which took 0.493324 s (model generation: 0.491784,  model checking: 0.001540):

Model:
|_
{
count -> 
{{{
Q={q_gen_1378, q_gen_1390, q_gen_1391, q_gen_1393, q_gen_1394, q_gen_1421, q_gen_1432, q_gen_1434, q_gen_1442},
Q_f={q_gen_1378},
Delta=
{
<b>() -> q_gen_1391
<cons>(q_gen_1391, q_gen_1393) -> q_gen_1393
<nil>() -> q_gen_1393
<a>() -> q_gen_1394
<cons>(q_gen_1394, q_gen_1393) -> q_gen_1442
<cons, s>(q_gen_1391, q_gen_1434) -> q_gen_1390
<cons, s>(q_gen_1394, q_gen_1421) -> q_gen_1390
<cons, z>(q_gen_1394, q_gen_1442) -> q_gen_1390
<nil, z>() -> q_gen_1390
<cons, s>(q_gen_1394, q_gen_1390) -> q_gen_1421
<cons, z>(q_gen_1391, q_gen_1393) -> q_gen_1421
<cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1434
<cons, s>(q_gen_1394, q_gen_1434) -> q_gen_1434
<cons, z>(q_gen_1391, q_gen_1442) -> q_gen_1434
<cons, z>(q_gen_1394, q_gen_1393) -> q_gen_1434
<a, cons, s>(q_gen_1391, q_gen_1434) -> q_gen_1378
<a, cons, s>(q_gen_1394, q_gen_1390) -> q_gen_1378
<a, cons, s>(q_gen_1394, q_gen_1421) -> q_gen_1378
<a, cons, z>(q_gen_1391, q_gen_1393) -> q_gen_1378
<a, nil, z>() -> q_gen_1378
<b, cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1378
<b, cons, s>(q_gen_1391, q_gen_1434) -> q_gen_1378
<b, cons, s>(q_gen_1394, q_gen_1421) -> q_gen_1378
<b, cons, s>(q_gen_1394, q_gen_1434) -> q_gen_1378
<b, cons, z>(q_gen_1394, q_gen_1393) -> q_gen_1378
<b, cons, z>(q_gen_1394, q_gen_1442) -> q_gen_1378
<b, nil, z>() -> q_gen_1378
<a, cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1432
<a, cons, s>(q_gen_1391, q_gen_1421) -> q_gen_1432
<a, cons, s>(q_gen_1394, q_gen_1434) -> q_gen_1432
<b, cons, s>(q_gen_1391, q_gen_1421) -> q_gen_1432
}

Datatype: <elt, eltlist, nat>
Convolution form: right
}}}
  ;  delete_all -> 
{{{
Q={q_gen_1377, q_gen_1384, q_gen_1385, q_gen_1387, q_gen_1388, q_gen_1407, q_gen_1419, q_gen_1428, q_gen_1429, q_gen_1436},
Q_f={q_gen_1377},
Delta=
{
<cons>(q_gen_1385, q_gen_1384) -> q_gen_1384
<cons>(q_gen_1407, q_gen_1384) -> q_gen_1384
<nil>() -> q_gen_1384
<b>() -> q_gen_1385
<a>() -> q_gen_1407
<cons, cons>(q_gen_1429, q_gen_1387) -> q_gen_1387
<nil, nil>() -> q_gen_1387
<a, a>() -> q_gen_1388
<b, b>() -> q_gen_1388
<cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1419
<cons, cons>(q_gen_1388, q_gen_1419) -> q_gen_1419
<cons, cons>(q_gen_1429, q_gen_1428) -> q_gen_1419
<cons, nil>(q_gen_1407, q_gen_1384) -> q_gen_1419
<cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1428
<a, b>() -> q_gen_1429
<b, a>() -> q_gen_1429
<a, cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1377
<a, cons, cons>(q_gen_1388, q_gen_1419) -> q_gen_1377
<a, cons, cons>(q_gen_1429, q_gen_1419) -> q_gen_1377
<a, cons, cons>(q_gen_1429, q_gen_1428) -> q_gen_1377
<a, cons, nil>(q_gen_1407, q_gen_1384) -> q_gen_1377
<a, nil, nil>() -> q_gen_1377
<b, cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1377
<b, cons, cons>(q_gen_1388, q_gen_1419) -> q_gen_1377
<b, cons, cons>(q_gen_1429, q_gen_1419) -> q_gen_1377
<b, cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1377
<b, nil, nil>() -> q_gen_1377
<a, cons, cons>(q_gen_1388, q_gen_1428) -> q_gen_1436
<a, cons, cons>(q_gen_1429, q_gen_1387) -> q_gen_1436
<b, cons, cons>(q_gen_1388, q_gen_1428) -> q_gen_1436
<b, cons, cons>(q_gen_1429, q_gen_1387) -> q_gen_1436
<b, cons, nil>(q_gen_1407, q_gen_1384) -> q_gen_1436
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  delete_one -> 
{{{
Q={q_gen_1373, q_gen_1374, q_gen_1375, q_gen_1381, q_gen_1382},
Q_f={q_gen_1373},
Delta=
{
<nil>() -> q_gen_1374
<a>() -> q_gen_1375
<b>() -> q_gen_1375
<cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1381
<cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1381
<nil, nil>() -> q_gen_1381
<a, a>() -> q_gen_1382
<a, b>() -> q_gen_1382
<b, a>() -> q_gen_1382
<b, b>() -> q_gen_1382
<a, cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1373
<a, cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1373
<a, nil, nil>() -> q_gen_1373
<b, cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1373
<b, cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1373
<b, nil, nil>() -> q_gen_1373
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  leqnat -> 
{{{
Q={q_gen_1372, q_gen_1396, q_gen_1438},
Q_f={q_gen_1372},
Delta=
{
<s>(q_gen_1396) -> q_gen_1396
<z>() -> q_gen_1396
<s, s>(q_gen_1372) -> q_gen_1372
<z, s>(q_gen_1396) -> q_gen_1372
<z, z>() -> q_gen_1372
<s, s>(q_gen_1438) -> q_gen_1438
<s, z>(q_gen_1396) -> q_gen_1438
}

Datatype: <nat, nat>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist, eq_nat}
_|

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 35
() -> delete_all([x, nil, nil]) -> 35
() -> delete_one([x, nil, nil]) -> 35
() -> delete_one([y, cons(y, r), r]) -> 35
() -> leqnat([z, n2]) -> 35
(count([x, l, _fh]) /\ delete_all([x, l, _eh]) /\ delete_one([x, l, _eh])) -> leqnat([_fh, s(z)]) -> 37
(count([x, r, _yg]) /\ not eq_elt([x, y])) -> count([x, cons(y, r), _yg]) -> 36
(count([y, r, _xg])) -> count([y, cons(y, r), s(_xg)]) -> 35
(delete_all([x, r, _sg]) /\ not eq_elt([x, y])) -> delete_all([x, cons(y, r), cons(y, _sg)]) -> 36
(delete_all([y, r, _rg])) -> delete_all([y, cons(y, r), _rg]) -> 38
(delete_one([x, r, _mg]) /\ not eq_elt([x, y])) -> delete_one([x, cons(y, r), cons(y, _mg)]) -> 36
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 36
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 36
(leqnat([s(nn1), z])) -> BOT -> 36
}
Sat witness: Found: ((delete_all([y, r, _rg])) -> delete_all([y, cons(y, r), _rg]), {
_rg -> cons(b, nil)  ;  r -> cons(b, cons(a, nil))  ;  y -> b
})

-------------------------------------------
Step 75, which took 0.549337 s (model generation: 0.506864,  model checking: 0.042473):

Model:
|_
{
count -> 
{{{
Q={q_gen_1378, q_gen_1390, q_gen_1391, q_gen_1393, q_gen_1394, q_gen_1432, q_gen_1434, q_gen_1442, q_gen_1448},
Q_f={q_gen_1378},
Delta=
{
<b>() -> q_gen_1391
<cons>(q_gen_1391, q_gen_1393) -> q_gen_1393
<nil>() -> q_gen_1393
<a>() -> q_gen_1394
<cons>(q_gen_1394, q_gen_1393) -> q_gen_1442
<cons, s>(q_gen_1391, q_gen_1448) -> q_gen_1390
<cons, s>(q_gen_1394, q_gen_1390) -> q_gen_1390
<cons, z>(q_gen_1391, q_gen_1393) -> q_gen_1390
<nil, z>() -> q_gen_1390
<cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1434
<cons, z>(q_gen_1394, q_gen_1442) -> q_gen_1434
<cons, s>(q_gen_1391, q_gen_1434) -> q_gen_1448
<cons, s>(q_gen_1394, q_gen_1448) -> q_gen_1448
<cons, z>(q_gen_1391, q_gen_1442) -> q_gen_1448
<cons, z>(q_gen_1394, q_gen_1393) -> q_gen_1448
<a, cons, s>(q_gen_1391, q_gen_1448) -> q_gen_1378
<a, cons, s>(q_gen_1394, q_gen_1390) -> q_gen_1378
<a, cons, z>(q_gen_1391, q_gen_1393) -> q_gen_1378
<a, nil, z>() -> q_gen_1378
<b, cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1378
<b, cons, s>(q_gen_1391, q_gen_1434) -> q_gen_1378
<b, cons, s>(q_gen_1391, q_gen_1448) -> q_gen_1378
<b, cons, s>(q_gen_1394, q_gen_1390) -> q_gen_1378
<b, cons, s>(q_gen_1394, q_gen_1448) -> q_gen_1378
<b, cons, z>(q_gen_1394, q_gen_1393) -> q_gen_1378
<b, cons, z>(q_gen_1394, q_gen_1442) -> q_gen_1378
<b, nil, z>() -> q_gen_1378
<a, cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1432
<a, cons, s>(q_gen_1391, q_gen_1434) -> q_gen_1432
<a, cons, s>(q_gen_1394, q_gen_1434) -> q_gen_1432
}

Datatype: <elt, eltlist, nat>
Convolution form: right
}}}
  ;  delete_all -> 
{{{
Q={q_gen_1377, q_gen_1384, q_gen_1385, q_gen_1387, q_gen_1388, q_gen_1409, q_gen_1419, q_gen_1429, q_gen_1446, q_gen_1456},
Q_f={q_gen_1377},
Delta=
{
<cons>(q_gen_1385, q_gen_1384) -> q_gen_1384
<nil>() -> q_gen_1384
<a>() -> q_gen_1385
<b>() -> q_gen_1385
<cons, cons>(q_gen_1409, q_gen_1387) -> q_gen_1387
<cons, cons>(q_gen_1429, q_gen_1387) -> q_gen_1387
<cons, cons>(q_gen_1429, q_gen_1419) -> q_gen_1387
<cons, cons>(q_gen_1446, q_gen_1387) -> q_gen_1387
<nil, nil>() -> q_gen_1387
<a, a>() -> q_gen_1388
<b, b>() -> q_gen_1409
<cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1419
<cons, cons>(q_gen_1409, q_gen_1419) -> q_gen_1419
<cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1419
<a, b>() -> q_gen_1429
<b, a>() -> q_gen_1446
<a, cons, cons>(q_gen_1409, q_gen_1387) -> q_gen_1377
<a, cons, cons>(q_gen_1409, q_gen_1419) -> q_gen_1377
<a, cons, cons>(q_gen_1429, q_gen_1419) -> q_gen_1377
<a, cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1377
<a, nil, nil>() -> q_gen_1377
<b, cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1377
<b, cons, cons>(q_gen_1388, q_gen_1419) -> q_gen_1377
<b, cons, cons>(q_gen_1446, q_gen_1419) -> q_gen_1377
<b, cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1377
<b, nil, nil>() -> q_gen_1377
<a, cons, cons>(q_gen_1429, q_gen_1387) -> q_gen_1456
<b, cons, cons>(q_gen_1409, q_gen_1387) -> q_gen_1456
<b, cons, cons>(q_gen_1409, q_gen_1419) -> q_gen_1456
<b, cons, cons>(q_gen_1429, q_gen_1387) -> q_gen_1456
<b, cons, cons>(q_gen_1429, q_gen_1419) -> q_gen_1456
<b, cons, cons>(q_gen_1446, q_gen_1387) -> q_gen_1456
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  delete_one -> 
{{{
Q={q_gen_1373, q_gen_1374, q_gen_1375, q_gen_1381, q_gen_1382},
Q_f={q_gen_1373},
Delta=
{
<nil>() -> q_gen_1374
<a>() -> q_gen_1375
<b>() -> q_gen_1375
<cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1381
<cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1381
<nil, nil>() -> q_gen_1381
<a, a>() -> q_gen_1382
<a, b>() -> q_gen_1382
<b, a>() -> q_gen_1382
<b, b>() -> q_gen_1382
<a, cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1373
<a, cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1373
<a, nil, nil>() -> q_gen_1373
<b, cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1373
<b, cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1373
<b, nil, nil>() -> q_gen_1373
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  leqnat -> 
{{{
Q={q_gen_1372, q_gen_1396, q_gen_1438},
Q_f={q_gen_1372},
Delta=
{
<s>(q_gen_1396) -> q_gen_1396
<z>() -> q_gen_1396
<s, s>(q_gen_1372) -> q_gen_1372
<z, s>(q_gen_1396) -> q_gen_1372
<z, z>() -> q_gen_1372
<s, s>(q_gen_1438) -> q_gen_1438
<s, z>(q_gen_1396) -> q_gen_1438
}

Datatype: <nat, nat>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist, eq_nat}
_|

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 36
() -> delete_all([x, nil, nil]) -> 36
() -> delete_one([x, nil, nil]) -> 36
() -> delete_one([y, cons(y, r), r]) -> 36
() -> leqnat([z, n2]) -> 36
(count([x, l, _fh]) /\ delete_all([x, l, _eh]) /\ delete_one([x, l, _eh])) -> leqnat([_fh, s(z)]) -> 37
(count([x, r, _yg]) /\ not eq_elt([x, y])) -> count([x, cons(y, r), _yg]) -> 36
(count([y, r, _xg])) -> count([y, cons(y, r), s(_xg)]) -> 36
(delete_all([x, r, _sg]) /\ not eq_elt([x, y])) -> delete_all([x, cons(y, r), cons(y, _sg)]) -> 39
(delete_all([y, r, _rg])) -> delete_all([y, cons(y, r), _rg]) -> 38
(delete_one([x, r, _mg]) /\ not eq_elt([x, y])) -> delete_one([x, cons(y, r), cons(y, _mg)]) -> 37
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 37
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 37
(leqnat([s(nn1), z])) -> BOT -> 37
}
Sat witness: Found: ((delete_all([x, r, _sg]) /\ not eq_elt([x, y])) -> delete_all([x, cons(y, r), cons(y, _sg)]), {
_sg -> cons(a, cons(b, nil))  ;  r -> cons(a, cons(b, cons(a, nil)))  ;  x -> b  ;  y -> a
})

-------------------------------------------
Step 76, which took 0.772739 s (model generation: 0.768844,  model checking: 0.003895):

Model:
|_
{
count -> 
{{{
Q={q_gen_1378, q_gen_1390, q_gen_1391, q_gen_1393, q_gen_1394, q_gen_1421, q_gen_1432, q_gen_1434},
Q_f={q_gen_1378},
Delta=
{
<b>() -> q_gen_1391
<cons>(q_gen_1391, q_gen_1393) -> q_gen_1393
<cons>(q_gen_1394, q_gen_1393) -> q_gen_1393
<nil>() -> q_gen_1393
<a>() -> q_gen_1394
<cons, s>(q_gen_1394, q_gen_1390) -> q_gen_1390
<nil, z>() -> q_gen_1390
<cons, s>(q_gen_1391, q_gen_1421) -> q_gen_1421
<cons, s>(q_gen_1394, q_gen_1421) -> q_gen_1421
<cons, z>(q_gen_1391, q_gen_1393) -> q_gen_1421
<cons, z>(q_gen_1394, q_gen_1393) -> q_gen_1421
<cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1434
<cons, s>(q_gen_1391, q_gen_1434) -> q_gen_1434
<a, cons, s>(q_gen_1391, q_gen_1421) -> q_gen_1378
<a, cons, s>(q_gen_1394, q_gen_1390) -> q_gen_1378
<a, cons, s>(q_gen_1394, q_gen_1421) -> q_gen_1378
<a, cons, z>(q_gen_1391, q_gen_1393) -> q_gen_1378
<a, nil, z>() -> q_gen_1378
<b, cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1378
<b, cons, s>(q_gen_1391, q_gen_1421) -> q_gen_1378
<b, cons, s>(q_gen_1391, q_gen_1434) -> q_gen_1378
<b, cons, s>(q_gen_1394, q_gen_1421) -> q_gen_1378
<b, cons, z>(q_gen_1394, q_gen_1393) -> q_gen_1378
<b, nil, z>() -> q_gen_1378
<a, cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1432
<a, cons, s>(q_gen_1391, q_gen_1434) -> q_gen_1432
<a, cons, s>(q_gen_1394, q_gen_1434) -> q_gen_1432
}

Datatype: <elt, eltlist, nat>
Convolution form: right
}}}
  ;  delete_all -> 
{{{
Q={q_gen_1377, q_gen_1384, q_gen_1385, q_gen_1387, q_gen_1388, q_gen_1409, q_gen_1456},
Q_f={q_gen_1377},
Delta=
{
<cons>(q_gen_1385, q_gen_1384) -> q_gen_1384
<nil>() -> q_gen_1384
<a>() -> q_gen_1385
<b>() -> q_gen_1385
<cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1387
<cons, cons>(q_gen_1409, q_gen_1387) -> q_gen_1387
<cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1387
<nil, nil>() -> q_gen_1387
<a, a>() -> q_gen_1388
<b, a>() -> q_gen_1388
<a, b>() -> q_gen_1409
<b, b>() -> q_gen_1409
<a, cons, cons>(q_gen_1409, q_gen_1387) -> q_gen_1377
<a, cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1377
<a, nil, nil>() -> q_gen_1377
<b, cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1377
<b, cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1377
<b, nil, nil>() -> q_gen_1377
<b, cons, cons>(q_gen_1409, q_gen_1387) -> q_gen_1456
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  delete_one -> 
{{{
Q={q_gen_1373, q_gen_1374, q_gen_1375, q_gen_1381, q_gen_1382, q_gen_1405, q_gen_1415, q_gen_1459, q_gen_1465},
Q_f={q_gen_1373},
Delta=
{
<nil>() -> q_gen_1374
<a>() -> q_gen_1375
<b>() -> q_gen_1375
<cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1381
<nil, nil>() -> q_gen_1381
<a, a>() -> q_gen_1382
<a, b>() -> q_gen_1382
<b, a>() -> q_gen_1405
<b, b>() -> q_gen_1405
<cons, cons>(q_gen_1405, q_gen_1381) -> q_gen_1415
<cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1459
<cons, cons>(q_gen_1405, q_gen_1459) -> q_gen_1459
<a, cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1373
<a, cons, cons>(q_gen_1382, q_gen_1415) -> q_gen_1373
<a, cons, cons>(q_gen_1405, q_gen_1381) -> q_gen_1373
<a, cons, cons>(q_gen_1405, q_gen_1415) -> q_gen_1373
<a, cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1373
<a, nil, nil>() -> q_gen_1373
<b, cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1373
<b, cons, cons>(q_gen_1382, q_gen_1415) -> q_gen_1373
<b, cons, cons>(q_gen_1382, q_gen_1459) -> q_gen_1373
<b, cons, cons>(q_gen_1405, q_gen_1381) -> q_gen_1373
<b, cons, cons>(q_gen_1405, q_gen_1459) -> q_gen_1373
<b, cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1373
<b, nil, nil>() -> q_gen_1373
<a, cons, cons>(q_gen_1382, q_gen_1459) -> q_gen_1465
<a, cons, cons>(q_gen_1405, q_gen_1459) -> q_gen_1465
<b, cons, cons>(q_gen_1405, q_gen_1415) -> q_gen_1465
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  leqnat -> 
{{{
Q={q_gen_1372, q_gen_1396, q_gen_1438},
Q_f={q_gen_1372},
Delta=
{
<s>(q_gen_1396) -> q_gen_1396
<z>() -> q_gen_1396
<s, s>(q_gen_1372) -> q_gen_1372
<z, s>(q_gen_1396) -> q_gen_1372
<z, z>() -> q_gen_1372
<s, s>(q_gen_1438) -> q_gen_1438
<s, z>(q_gen_1396) -> q_gen_1438
}

Datatype: <nat, nat>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist, eq_nat}
_|

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 36
() -> delete_all([x, nil, nil]) -> 36
() -> delete_one([x, nil, nil]) -> 36
() -> delete_one([y, cons(y, r), r]) -> 39
() -> leqnat([z, n2]) -> 37
(count([x, l, _fh]) /\ delete_all([x, l, _eh]) /\ delete_one([x, l, _eh])) -> leqnat([_fh, s(z)]) -> 37
(count([x, r, _yg]) /\ not eq_elt([x, y])) -> count([x, cons(y, r), _yg]) -> 37
(count([y, r, _xg])) -> count([y, cons(y, r), s(_xg)]) -> 37
(delete_all([x, r, _sg]) /\ not eq_elt([x, y])) -> delete_all([x, cons(y, r), cons(y, _sg)]) -> 39
(delete_all([y, r, _rg])) -> delete_all([y, cons(y, r), _rg]) -> 38
(delete_one([x, r, _mg]) /\ not eq_elt([x, y])) -> delete_one([x, cons(y, r), cons(y, _mg)]) -> 37
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 37
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 37
(leqnat([s(nn1), z])) -> BOT -> 37
}
Sat witness: Found: (() -> delete_one([y, cons(y, r), r]), {
r -> cons(b, cons(a, nil))  ;  y -> b
})

-------------------------------------------
Step 77, which took 0.848020 s (model generation: 0.845452,  model checking: 0.002568):

Model:
|_
{
count -> 
{{{
Q={q_gen_1378, q_gen_1390, q_gen_1391, q_gen_1393, q_gen_1394, q_gen_1421, q_gen_1432, q_gen_1434},
Q_f={q_gen_1378},
Delta=
{
<b>() -> q_gen_1391
<cons>(q_gen_1391, q_gen_1393) -> q_gen_1393
<cons>(q_gen_1394, q_gen_1393) -> q_gen_1393
<nil>() -> q_gen_1393
<a>() -> q_gen_1394
<cons, s>(q_gen_1394, q_gen_1390) -> q_gen_1390
<nil, z>() -> q_gen_1390
<cons, s>(q_gen_1391, q_gen_1421) -> q_gen_1421
<cons, s>(q_gen_1394, q_gen_1421) -> q_gen_1421
<cons, z>(q_gen_1391, q_gen_1393) -> q_gen_1421
<cons, z>(q_gen_1394, q_gen_1393) -> q_gen_1421
<cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1434
<cons, s>(q_gen_1391, q_gen_1434) -> q_gen_1434
<a, cons, s>(q_gen_1391, q_gen_1421) -> q_gen_1378
<a, cons, s>(q_gen_1394, q_gen_1390) -> q_gen_1378
<a, cons, s>(q_gen_1394, q_gen_1421) -> q_gen_1378
<a, cons, z>(q_gen_1391, q_gen_1393) -> q_gen_1378
<a, nil, z>() -> q_gen_1378
<b, cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1378
<b, cons, s>(q_gen_1391, q_gen_1421) -> q_gen_1378
<b, cons, s>(q_gen_1391, q_gen_1434) -> q_gen_1378
<b, cons, s>(q_gen_1394, q_gen_1421) -> q_gen_1378
<b, cons, z>(q_gen_1394, q_gen_1393) -> q_gen_1378
<b, nil, z>() -> q_gen_1378
<a, cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1432
<a, cons, s>(q_gen_1391, q_gen_1434) -> q_gen_1432
<a, cons, s>(q_gen_1394, q_gen_1434) -> q_gen_1432
}

Datatype: <elt, eltlist, nat>
Convolution form: right
}}}
  ;  delete_all -> 
{{{
Q={q_gen_1377, q_gen_1384, q_gen_1385, q_gen_1387, q_gen_1388, q_gen_1409, q_gen_1456},
Q_f={q_gen_1377},
Delta=
{
<cons>(q_gen_1385, q_gen_1384) -> q_gen_1384
<nil>() -> q_gen_1384
<a>() -> q_gen_1385
<b>() -> q_gen_1385
<cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1387
<cons, cons>(q_gen_1409, q_gen_1387) -> q_gen_1387
<cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1387
<nil, nil>() -> q_gen_1387
<a, a>() -> q_gen_1388
<b, a>() -> q_gen_1388
<a, b>() -> q_gen_1409
<b, b>() -> q_gen_1409
<a, cons, cons>(q_gen_1409, q_gen_1387) -> q_gen_1377
<a, cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1377
<a, nil, nil>() -> q_gen_1377
<b, cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1377
<b, cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1377
<b, nil, nil>() -> q_gen_1377
<b, cons, cons>(q_gen_1409, q_gen_1387) -> q_gen_1456
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  delete_one -> 
{{{
Q={q_gen_1373, q_gen_1374, q_gen_1375, q_gen_1381, q_gen_1382, q_gen_1413, q_gen_1426, q_gen_1458, q_gen_1459},
Q_f={q_gen_1373},
Delta=
{
<nil>() -> q_gen_1374
<a>() -> q_gen_1375
<b>() -> q_gen_1375
<cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1381
<nil, nil>() -> q_gen_1381
<a, a>() -> q_gen_1382
<b, b>() -> q_gen_1382
<cons, cons>(q_gen_1426, q_gen_1413) -> q_gen_1413
<cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1413
<a, b>() -> q_gen_1426
<b, a>() -> q_gen_1426
<cons, cons>(q_gen_1426, q_gen_1381) -> q_gen_1459
<cons, cons>(q_gen_1426, q_gen_1459) -> q_gen_1459
<a, cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1373
<a, cons, cons>(q_gen_1382, q_gen_1413) -> q_gen_1373
<a, cons, cons>(q_gen_1426, q_gen_1413) -> q_gen_1373
<a, cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1373
<a, nil, nil>() -> q_gen_1373
<b, cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1373
<b, cons, cons>(q_gen_1382, q_gen_1413) -> q_gen_1373
<b, cons, cons>(q_gen_1426, q_gen_1413) -> q_gen_1373
<b, cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1373
<b, nil, nil>() -> q_gen_1373
<a, cons, cons>(q_gen_1382, q_gen_1459) -> q_gen_1458
<a, cons, cons>(q_gen_1426, q_gen_1459) -> q_gen_1458
<b, cons, cons>(q_gen_1382, q_gen_1459) -> q_gen_1458
<b, cons, cons>(q_gen_1426, q_gen_1381) -> q_gen_1458
<b, cons, cons>(q_gen_1426, q_gen_1459) -> q_gen_1458
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  leqnat -> 
{{{
Q={q_gen_1372, q_gen_1396, q_gen_1438},
Q_f={q_gen_1372},
Delta=
{
<s>(q_gen_1396) -> q_gen_1396
<z>() -> q_gen_1396
<s, s>(q_gen_1372) -> q_gen_1372
<z, s>(q_gen_1396) -> q_gen_1372
<z, z>() -> q_gen_1372
<s, s>(q_gen_1438) -> q_gen_1438
<s, z>(q_gen_1396) -> q_gen_1438
}

Datatype: <nat, nat>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist, eq_nat}
_|

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 37
() -> delete_all([x, nil, nil]) -> 37
() -> delete_one([x, nil, nil]) -> 37
() -> delete_one([y, cons(y, r), r]) -> 39
() -> leqnat([z, n2]) -> 37
(count([x, l, _fh]) /\ delete_all([x, l, _eh]) /\ delete_one([x, l, _eh])) -> leqnat([_fh, s(z)]) -> 37
(count([x, r, _yg]) /\ not eq_elt([x, y])) -> count([x, cons(y, r), _yg]) -> 37
(count([y, r, _xg])) -> count([y, cons(y, r), s(_xg)]) -> 37
(delete_all([x, r, _sg]) /\ not eq_elt([x, y])) -> delete_all([x, cons(y, r), cons(y, _sg)]) -> 39
(delete_all([y, r, _rg])) -> delete_all([y, cons(y, r), _rg]) -> 38
(delete_one([x, r, _mg]) /\ not eq_elt([x, y])) -> delete_one([x, cons(y, r), cons(y, _mg)]) -> 40
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 38
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 38
(leqnat([s(nn1), z])) -> BOT -> 38
}
Sat witness: Found: ((delete_one([x, r, _mg]) /\ not eq_elt([x, y])) -> delete_one([x, cons(y, r), cons(y, _mg)]), {
_mg -> cons(b, nil)  ;  r -> cons(b, cons(b, nil))  ;  x -> a  ;  y -> b
})

-------------------------------------------
Step 78, which took 0.664015 s (model generation: 0.659037,  model checking: 0.004978):

Model:
|_
{
count -> 
{{{
Q={q_gen_1378, q_gen_1390, q_gen_1391, q_gen_1393, q_gen_1394, q_gen_1421, q_gen_1432, q_gen_1434},
Q_f={q_gen_1378},
Delta=
{
<b>() -> q_gen_1391
<cons>(q_gen_1391, q_gen_1393) -> q_gen_1393
<cons>(q_gen_1394, q_gen_1393) -> q_gen_1393
<nil>() -> q_gen_1393
<a>() -> q_gen_1394
<cons, s>(q_gen_1394, q_gen_1390) -> q_gen_1390
<nil, z>() -> q_gen_1390
<cons, s>(q_gen_1391, q_gen_1421) -> q_gen_1421
<cons, s>(q_gen_1394, q_gen_1421) -> q_gen_1421
<cons, z>(q_gen_1391, q_gen_1393) -> q_gen_1421
<cons, z>(q_gen_1394, q_gen_1393) -> q_gen_1421
<cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1434
<cons, s>(q_gen_1391, q_gen_1434) -> q_gen_1434
<a, cons, s>(q_gen_1391, q_gen_1421) -> q_gen_1378
<a, cons, s>(q_gen_1394, q_gen_1390) -> q_gen_1378
<a, cons, s>(q_gen_1394, q_gen_1421) -> q_gen_1378
<a, cons, z>(q_gen_1391, q_gen_1393) -> q_gen_1378
<a, nil, z>() -> q_gen_1378
<b, cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1378
<b, cons, s>(q_gen_1391, q_gen_1421) -> q_gen_1378
<b, cons, s>(q_gen_1391, q_gen_1434) -> q_gen_1378
<b, cons, s>(q_gen_1394, q_gen_1421) -> q_gen_1378
<b, cons, z>(q_gen_1394, q_gen_1393) -> q_gen_1378
<b, nil, z>() -> q_gen_1378
<a, cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1432
<a, cons, s>(q_gen_1391, q_gen_1434) -> q_gen_1432
<a, cons, s>(q_gen_1394, q_gen_1434) -> q_gen_1432
}

Datatype: <elt, eltlist, nat>
Convolution form: right
}}}
  ;  delete_all -> 
{{{
Q={q_gen_1377, q_gen_1384, q_gen_1385, q_gen_1387, q_gen_1388, q_gen_1407, q_gen_1419, q_gen_1428, q_gen_1429, q_gen_1436, q_gen_1446},
Q_f={q_gen_1377},
Delta=
{
<cons>(q_gen_1385, q_gen_1384) -> q_gen_1384
<cons>(q_gen_1407, q_gen_1384) -> q_gen_1384
<nil>() -> q_gen_1384
<b>() -> q_gen_1385
<a>() -> q_gen_1407
<cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1387
<cons, cons>(q_gen_1388, q_gen_1419) -> q_gen_1387
<nil, nil>() -> q_gen_1387
<a, a>() -> q_gen_1388
<b, b>() -> q_gen_1388
<cons, cons>(q_gen_1429, q_gen_1387) -> q_gen_1419
<cons, nil>(q_gen_1407, q_gen_1384) -> q_gen_1419
<cons, cons>(q_gen_1429, q_gen_1428) -> q_gen_1428
<cons, cons>(q_gen_1446, q_gen_1387) -> q_gen_1428
<cons, cons>(q_gen_1446, q_gen_1419) -> q_gen_1428
<cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1428
<a, b>() -> q_gen_1429
<b, a>() -> q_gen_1446
<a, cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1377
<a, cons, cons>(q_gen_1388, q_gen_1419) -> q_gen_1377
<a, cons, cons>(q_gen_1429, q_gen_1387) -> q_gen_1377
<a, cons, cons>(q_gen_1429, q_gen_1428) -> q_gen_1377
<a, cons, nil>(q_gen_1407, q_gen_1384) -> q_gen_1377
<a, nil, nil>() -> q_gen_1377
<b, cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1377
<b, cons, cons>(q_gen_1446, q_gen_1419) -> q_gen_1377
<b, cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1377
<b, nil, nil>() -> q_gen_1377
<a, cons, cons>(q_gen_1388, q_gen_1428) -> q_gen_1436
<a, cons, cons>(q_gen_1429, q_gen_1419) -> q_gen_1436
<b, cons, cons>(q_gen_1388, q_gen_1419) -> q_gen_1436
<b, cons, cons>(q_gen_1388, q_gen_1428) -> q_gen_1436
<b, cons, cons>(q_gen_1429, q_gen_1387) -> q_gen_1436
<b, cons, cons>(q_gen_1429, q_gen_1419) -> q_gen_1436
<b, cons, cons>(q_gen_1446, q_gen_1428) -> q_gen_1436
<b, cons, nil>(q_gen_1407, q_gen_1384) -> q_gen_1436
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  delete_one -> 
{{{
Q={q_gen_1373, q_gen_1374, q_gen_1375, q_gen_1381, q_gen_1382},
Q_f={q_gen_1373},
Delta=
{
<nil>() -> q_gen_1374
<a>() -> q_gen_1375
<b>() -> q_gen_1375
<cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1381
<cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1381
<nil, nil>() -> q_gen_1381
<a, a>() -> q_gen_1382
<a, b>() -> q_gen_1382
<b, a>() -> q_gen_1382
<b, b>() -> q_gen_1382
<a, cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1373
<a, cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1373
<a, nil, nil>() -> q_gen_1373
<b, cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1373
<b, cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1373
<b, nil, nil>() -> q_gen_1373
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  leqnat -> 
{{{
Q={q_gen_1372, q_gen_1396, q_gen_1438},
Q_f={q_gen_1372},
Delta=
{
<s>(q_gen_1396) -> q_gen_1396
<z>() -> q_gen_1396
<s, s>(q_gen_1372) -> q_gen_1372
<z, s>(q_gen_1396) -> q_gen_1372
<z, z>() -> q_gen_1372
<s, s>(q_gen_1438) -> q_gen_1438
<s, z>(q_gen_1396) -> q_gen_1438
}

Datatype: <nat, nat>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist, eq_nat}
_|

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 37
() -> delete_all([x, nil, nil]) -> 37
() -> delete_one([x, nil, nil]) -> 37
() -> delete_one([y, cons(y, r), r]) -> 39
() -> leqnat([z, n2]) -> 37
(count([x, l, _fh]) /\ delete_all([x, l, _eh]) /\ delete_one([x, l, _eh])) -> leqnat([_fh, s(z)]) -> 40
(count([x, r, _yg]) /\ not eq_elt([x, y])) -> count([x, cons(y, r), _yg]) -> 38
(count([y, r, _xg])) -> count([y, cons(y, r), s(_xg)]) -> 38
(delete_all([x, r, _sg]) /\ not eq_elt([x, y])) -> delete_all([x, cons(y, r), cons(y, _sg)]) -> 39
(delete_all([y, r, _rg])) -> delete_all([y, cons(y, r), _rg]) -> 38
(delete_one([x, r, _mg]) /\ not eq_elt([x, y])) -> delete_one([x, cons(y, r), cons(y, _mg)]) -> 40
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 38
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 38
(leqnat([s(nn1), z])) -> BOT -> 38
}
Sat witness: Found: ((count([x, l, _fh]) /\ delete_all([x, l, _eh]) /\ delete_one([x, l, _eh])) -> leqnat([_fh, s(z)]), {
_eh -> cons(a, cons(b, nil))  ;  _fh -> s(s(z))  ;  l -> cons(a, cons(a, nil))  ;  x -> a
})

-------------------------------------------
Step 79, which took 1.418693 s (model generation: 1.368867,  model checking: 0.049826):

Model:
|_
{
count -> 
{{{
Q={q_gen_1378, q_gen_1390, q_gen_1391, q_gen_1393, q_gen_1394, q_gen_1432, q_gen_1434, q_gen_1442, q_gen_1448},
Q_f={q_gen_1378},
Delta=
{
<b>() -> q_gen_1391
<cons>(q_gen_1391, q_gen_1393) -> q_gen_1393
<nil>() -> q_gen_1393
<a>() -> q_gen_1394
<cons>(q_gen_1394, q_gen_1393) -> q_gen_1442
<cons, s>(q_gen_1391, q_gen_1448) -> q_gen_1390
<cons, s>(q_gen_1394, q_gen_1390) -> q_gen_1390
<cons, z>(q_gen_1391, q_gen_1393) -> q_gen_1390
<nil, z>() -> q_gen_1390
<cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1434
<cons, z>(q_gen_1394, q_gen_1442) -> q_gen_1434
<cons, s>(q_gen_1391, q_gen_1434) -> q_gen_1448
<cons, s>(q_gen_1394, q_gen_1448) -> q_gen_1448
<cons, z>(q_gen_1391, q_gen_1442) -> q_gen_1448
<cons, z>(q_gen_1394, q_gen_1393) -> q_gen_1448
<a, cons, s>(q_gen_1391, q_gen_1448) -> q_gen_1378
<a, cons, s>(q_gen_1394, q_gen_1390) -> q_gen_1378
<a, cons, z>(q_gen_1391, q_gen_1393) -> q_gen_1378
<a, nil, z>() -> q_gen_1378
<b, cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1378
<b, cons, s>(q_gen_1391, q_gen_1434) -> q_gen_1378
<b, cons, s>(q_gen_1391, q_gen_1448) -> q_gen_1378
<b, cons, s>(q_gen_1394, q_gen_1390) -> q_gen_1378
<b, cons, s>(q_gen_1394, q_gen_1448) -> q_gen_1378
<b, cons, z>(q_gen_1394, q_gen_1393) -> q_gen_1378
<b, cons, z>(q_gen_1394, q_gen_1442) -> q_gen_1378
<b, nil, z>() -> q_gen_1378
<a, cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1432
<a, cons, s>(q_gen_1391, q_gen_1434) -> q_gen_1432
<a, cons, s>(q_gen_1394, q_gen_1434) -> q_gen_1432
}

Datatype: <elt, eltlist, nat>
Convolution form: right
}}}
  ;  delete_all -> 
{{{
Q={q_gen_1377, q_gen_1384, q_gen_1385, q_gen_1387, q_gen_1388, q_gen_1409, q_gen_1456},
Q_f={q_gen_1377},
Delta=
{
<cons>(q_gen_1385, q_gen_1384) -> q_gen_1384
<nil>() -> q_gen_1384
<a>() -> q_gen_1385
<b>() -> q_gen_1385
<cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1387
<cons, cons>(q_gen_1409, q_gen_1387) -> q_gen_1387
<cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1387
<nil, nil>() -> q_gen_1387
<a, a>() -> q_gen_1388
<b, a>() -> q_gen_1388
<a, b>() -> q_gen_1409
<b, b>() -> q_gen_1409
<a, cons, cons>(q_gen_1409, q_gen_1387) -> q_gen_1377
<a, cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1377
<a, nil, nil>() -> q_gen_1377
<b, cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1377
<b, cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1377
<b, nil, nil>() -> q_gen_1377
<a, cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1456
<b, cons, cons>(q_gen_1409, q_gen_1387) -> q_gen_1456
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  delete_one -> 
{{{
Q={q_gen_1373, q_gen_1374, q_gen_1375, q_gen_1381, q_gen_1382, q_gen_1413, q_gen_1426, q_gen_1465},
Q_f={q_gen_1373},
Delta=
{
<nil>() -> q_gen_1374
<a>() -> q_gen_1375
<b>() -> q_gen_1375
<cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1381
<cons, cons>(q_gen_1382, q_gen_1413) -> q_gen_1381
<cons, cons>(q_gen_1426, q_gen_1381) -> q_gen_1381
<nil, nil>() -> q_gen_1381
<a, a>() -> q_gen_1382
<b, b>() -> q_gen_1382
<cons, cons>(q_gen_1426, q_gen_1413) -> q_gen_1413
<cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1413
<a, b>() -> q_gen_1426
<b, a>() -> q_gen_1426
<a, cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1373
<a, cons, cons>(q_gen_1382, q_gen_1413) -> q_gen_1373
<a, cons, cons>(q_gen_1426, q_gen_1413) -> q_gen_1373
<a, cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1373
<a, nil, nil>() -> q_gen_1373
<b, cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1373
<b, cons, cons>(q_gen_1382, q_gen_1413) -> q_gen_1373
<b, cons, cons>(q_gen_1426, q_gen_1413) -> q_gen_1373
<b, cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1373
<b, nil, nil>() -> q_gen_1373
<a, cons, cons>(q_gen_1426, q_gen_1381) -> q_gen_1465
<b, cons, cons>(q_gen_1426, q_gen_1381) -> q_gen_1465
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  leqnat -> 
{{{
Q={q_gen_1372, q_gen_1396, q_gen_1438},
Q_f={q_gen_1372},
Delta=
{
<s>(q_gen_1396) -> q_gen_1396
<z>() -> q_gen_1396
<s, s>(q_gen_1372) -> q_gen_1372
<z, s>(q_gen_1396) -> q_gen_1372
<z, z>() -> q_gen_1372
<s, s>(q_gen_1438) -> q_gen_1438
<s, z>(q_gen_1396) -> q_gen_1438
}

Datatype: <nat, nat>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist, eq_nat}
_|

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 38
() -> delete_all([x, nil, nil]) -> 38
() -> delete_one([x, nil, nil]) -> 38
() -> delete_one([y, cons(y, r), r]) -> 39
() -> leqnat([z, n2]) -> 38
(count([x, l, _fh]) /\ delete_all([x, l, _eh]) /\ delete_one([x, l, _eh])) -> leqnat([_fh, s(z)]) -> 40
(count([x, r, _yg]) /\ not eq_elt([x, y])) -> count([x, cons(y, r), _yg]) -> 41
(count([y, r, _xg])) -> count([y, cons(y, r), s(_xg)]) -> 39
(delete_all([x, r, _sg]) /\ not eq_elt([x, y])) -> delete_all([x, cons(y, r), cons(y, _sg)]) -> 39
(delete_all([y, r, _rg])) -> delete_all([y, cons(y, r), _rg]) -> 39
(delete_one([x, r, _mg]) /\ not eq_elt([x, y])) -> delete_one([x, cons(y, r), cons(y, _mg)]) -> 40
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 39
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 39
(leqnat([s(nn1), z])) -> BOT -> 39
}
Sat witness: Found: ((count([x, r, _yg]) /\ not eq_elt([x, y])) -> count([x, cons(y, r), _yg]), {
_yg -> s(z)  ;  r -> cons(a, cons(a, nil))  ;  x -> b  ;  y -> a
})

-------------------------------------------
Step 80, which took 1.602112 s (model generation: 1.596295,  model checking: 0.005817):

Model:
|_
{
count -> 
{{{
Q={q_gen_1378, q_gen_1390, q_gen_1391, q_gen_1393, q_gen_1394, q_gen_1421, q_gen_1432, q_gen_1434},
Q_f={q_gen_1378},
Delta=
{
<b>() -> q_gen_1391
<cons>(q_gen_1391, q_gen_1393) -> q_gen_1393
<cons>(q_gen_1394, q_gen_1393) -> q_gen_1393
<nil>() -> q_gen_1393
<a>() -> q_gen_1394
<cons, s>(q_gen_1394, q_gen_1390) -> q_gen_1390
<nil, z>() -> q_gen_1390
<cons, s>(q_gen_1391, q_gen_1421) -> q_gen_1421
<cons, s>(q_gen_1394, q_gen_1421) -> q_gen_1421
<cons, z>(q_gen_1391, q_gen_1393) -> q_gen_1421
<cons, z>(q_gen_1394, q_gen_1393) -> q_gen_1421
<cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1434
<cons, s>(q_gen_1391, q_gen_1434) -> q_gen_1434
<a, cons, s>(q_gen_1391, q_gen_1421) -> q_gen_1378
<a, cons, s>(q_gen_1394, q_gen_1390) -> q_gen_1378
<a, cons, s>(q_gen_1394, q_gen_1421) -> q_gen_1378
<a, cons, z>(q_gen_1391, q_gen_1393) -> q_gen_1378
<a, nil, z>() -> q_gen_1378
<b, cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1378
<b, cons, s>(q_gen_1391, q_gen_1421) -> q_gen_1378
<b, cons, s>(q_gen_1391, q_gen_1434) -> q_gen_1378
<b, cons, s>(q_gen_1394, q_gen_1421) -> q_gen_1378
<b, cons, z>(q_gen_1394, q_gen_1393) -> q_gen_1378
<b, nil, z>() -> q_gen_1378
<a, cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1432
<a, cons, s>(q_gen_1391, q_gen_1434) -> q_gen_1432
<a, cons, s>(q_gen_1394, q_gen_1434) -> q_gen_1432
}

Datatype: <elt, eltlist, nat>
Convolution form: right
}}}
  ;  delete_all -> 
{{{
Q={q_gen_1377, q_gen_1384, q_gen_1385, q_gen_1387, q_gen_1388, q_gen_1409, q_gen_1456},
Q_f={q_gen_1377},
Delta=
{
<cons>(q_gen_1385, q_gen_1384) -> q_gen_1384
<nil>() -> q_gen_1384
<a>() -> q_gen_1385
<b>() -> q_gen_1385
<cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1387
<cons, cons>(q_gen_1409, q_gen_1387) -> q_gen_1387
<cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1387
<nil, nil>() -> q_gen_1387
<a, a>() -> q_gen_1388
<b, a>() -> q_gen_1388
<a, b>() -> q_gen_1409
<b, b>() -> q_gen_1409
<a, cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1377
<a, cons, cons>(q_gen_1409, q_gen_1387) -> q_gen_1377
<a, cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1377
<a, nil, nil>() -> q_gen_1377
<b, cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1377
<b, cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1377
<b, nil, nil>() -> q_gen_1377
<b, cons, cons>(q_gen_1409, q_gen_1387) -> q_gen_1456
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  delete_one -> 
{{{
Q={q_gen_1373, q_gen_1374, q_gen_1375, q_gen_1381, q_gen_1382, q_gen_1413, q_gen_1426, q_gen_1459, q_gen_1465},
Q_f={q_gen_1373},
Delta=
{
<nil>() -> q_gen_1374
<a>() -> q_gen_1375
<b>() -> q_gen_1375
<cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1381
<cons, cons>(q_gen_1382, q_gen_1413) -> q_gen_1381
<nil, nil>() -> q_gen_1381
<a, a>() -> q_gen_1382
<b, b>() -> q_gen_1382
<cons, cons>(q_gen_1426, q_gen_1413) -> q_gen_1413
<cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1413
<a, b>() -> q_gen_1426
<b, a>() -> q_gen_1426
<cons, cons>(q_gen_1426, q_gen_1381) -> q_gen_1459
<cons, cons>(q_gen_1426, q_gen_1459) -> q_gen_1459
<a, cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1373
<a, cons, cons>(q_gen_1382, q_gen_1413) -> q_gen_1373
<a, cons, cons>(q_gen_1426, q_gen_1413) -> q_gen_1373
<a, cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1373
<a, nil, nil>() -> q_gen_1373
<b, cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1373
<b, cons, cons>(q_gen_1382, q_gen_1413) -> q_gen_1373
<b, cons, cons>(q_gen_1382, q_gen_1459) -> q_gen_1373
<b, cons, cons>(q_gen_1426, q_gen_1381) -> q_gen_1373
<b, cons, cons>(q_gen_1426, q_gen_1413) -> q_gen_1373
<b, cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1373
<b, nil, nil>() -> q_gen_1373
<a, cons, cons>(q_gen_1382, q_gen_1459) -> q_gen_1465
<a, cons, cons>(q_gen_1426, q_gen_1459) -> q_gen_1465
<b, cons, cons>(q_gen_1426, q_gen_1459) -> q_gen_1465
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  leqnat -> 
{{{
Q={q_gen_1372, q_gen_1396, q_gen_1438},
Q_f={q_gen_1372},
Delta=
{
<s>(q_gen_1396) -> q_gen_1396
<z>() -> q_gen_1396
<s, s>(q_gen_1372) -> q_gen_1372
<z, s>(q_gen_1396) -> q_gen_1372
<z, z>() -> q_gen_1372
<s, s>(q_gen_1438) -> q_gen_1438
<s, z>(q_gen_1396) -> q_gen_1438
}

Datatype: <nat, nat>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist, eq_nat}
_|

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 39
() -> delete_all([x, nil, nil]) -> 39
() -> delete_one([x, nil, nil]) -> 39
() -> delete_one([y, cons(y, r), r]) -> 42
() -> leqnat([z, n2]) -> 39
(count([x, l, _fh]) /\ delete_all([x, l, _eh]) /\ delete_one([x, l, _eh])) -> leqnat([_fh, s(z)]) -> 40
(count([x, r, _yg]) /\ not eq_elt([x, y])) -> count([x, cons(y, r), _yg]) -> 41
(count([y, r, _xg])) -> count([y, cons(y, r), s(_xg)]) -> 40
(delete_all([x, r, _sg]) /\ not eq_elt([x, y])) -> delete_all([x, cons(y, r), cons(y, _sg)]) -> 40
(delete_all([y, r, _rg])) -> delete_all([y, cons(y, r), _rg]) -> 40
(delete_one([x, r, _mg]) /\ not eq_elt([x, y])) -> delete_one([x, cons(y, r), cons(y, _mg)]) -> 40
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 40
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 40
(leqnat([s(nn1), z])) -> BOT -> 40
}
Sat witness: Found: (() -> delete_one([y, cons(y, r), r]), {
r -> cons(a, cons(b, cons(a, cons(a, cons(a, nil)))))  ;  y -> a
})

-------------------------------------------
Step 81, which took 1.729879 s (model generation: 1.714427,  model checking: 0.015452):

Model:
|_
{
count -> 
{{{
Q={q_gen_1378, q_gen_1390, q_gen_1391, q_gen_1393, q_gen_1394, q_gen_1432, q_gen_1434, q_gen_1442, q_gen_1448},
Q_f={q_gen_1378},
Delta=
{
<b>() -> q_gen_1391
<cons>(q_gen_1391, q_gen_1393) -> q_gen_1393
<nil>() -> q_gen_1393
<a>() -> q_gen_1394
<cons>(q_gen_1394, q_gen_1393) -> q_gen_1442
<cons, s>(q_gen_1391, q_gen_1448) -> q_gen_1390
<cons, s>(q_gen_1394, q_gen_1390) -> q_gen_1390
<cons, z>(q_gen_1391, q_gen_1393) -> q_gen_1390
<nil, z>() -> q_gen_1390
<cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1434
<cons, z>(q_gen_1394, q_gen_1442) -> q_gen_1434
<cons, s>(q_gen_1391, q_gen_1434) -> q_gen_1448
<cons, s>(q_gen_1394, q_gen_1448) -> q_gen_1448
<cons, z>(q_gen_1391, q_gen_1442) -> q_gen_1448
<cons, z>(q_gen_1394, q_gen_1393) -> q_gen_1448
<a, cons, s>(q_gen_1391, q_gen_1448) -> q_gen_1378
<a, cons, s>(q_gen_1394, q_gen_1390) -> q_gen_1378
<a, cons, z>(q_gen_1391, q_gen_1393) -> q_gen_1378
<a, nil, z>() -> q_gen_1378
<b, cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1378
<b, cons, s>(q_gen_1391, q_gen_1434) -> q_gen_1378
<b, cons, s>(q_gen_1391, q_gen_1448) -> q_gen_1378
<b, cons, s>(q_gen_1394, q_gen_1390) -> q_gen_1378
<b, cons, s>(q_gen_1394, q_gen_1434) -> q_gen_1378
<b, cons, s>(q_gen_1394, q_gen_1448) -> q_gen_1378
<b, cons, z>(q_gen_1394, q_gen_1393) -> q_gen_1378
<b, cons, z>(q_gen_1394, q_gen_1442) -> q_gen_1378
<b, nil, z>() -> q_gen_1378
<a, cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1432
<a, cons, s>(q_gen_1391, q_gen_1434) -> q_gen_1432
<a, cons, s>(q_gen_1394, q_gen_1434) -> q_gen_1432
}

Datatype: <elt, eltlist, nat>
Convolution form: right
}}}
  ;  delete_all -> 
{{{
Q={q_gen_1377, q_gen_1384, q_gen_1385, q_gen_1387, q_gen_1388, q_gen_1409, q_gen_1456},
Q_f={q_gen_1377},
Delta=
{
<cons>(q_gen_1385, q_gen_1384) -> q_gen_1384
<nil>() -> q_gen_1384
<a>() -> q_gen_1385
<b>() -> q_gen_1385
<cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1387
<cons, cons>(q_gen_1409, q_gen_1387) -> q_gen_1387
<cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1387
<nil, nil>() -> q_gen_1387
<a, a>() -> q_gen_1388
<b, a>() -> q_gen_1388
<a, b>() -> q_gen_1409
<b, b>() -> q_gen_1409
<a, cons, cons>(q_gen_1409, q_gen_1387) -> q_gen_1377
<a, cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1377
<a, nil, nil>() -> q_gen_1377
<b, cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1377
<b, cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1377
<b, nil, nil>() -> q_gen_1377
<a, cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1456
<b, cons, cons>(q_gen_1409, q_gen_1387) -> q_gen_1456
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  delete_one -> 
{{{
Q={q_gen_1373, q_gen_1374, q_gen_1375, q_gen_1381, q_gen_1382, q_gen_1413, q_gen_1426, q_gen_1465},
Q_f={q_gen_1373},
Delta=
{
<nil>() -> q_gen_1374
<a>() -> q_gen_1375
<b>() -> q_gen_1375
<cons, cons>(q_gen_1426, q_gen_1381) -> q_gen_1381
<nil, nil>() -> q_gen_1381
<a, a>() -> q_gen_1382
<b, b>() -> q_gen_1382
<cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1413
<cons, cons>(q_gen_1382, q_gen_1413) -> q_gen_1413
<cons, cons>(q_gen_1426, q_gen_1413) -> q_gen_1413
<cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1413
<a, b>() -> q_gen_1426
<b, a>() -> q_gen_1426
<a, cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1373
<a, cons, cons>(q_gen_1382, q_gen_1413) -> q_gen_1373
<a, cons, cons>(q_gen_1426, q_gen_1413) -> q_gen_1373
<a, cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1373
<a, nil, nil>() -> q_gen_1373
<b, cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1373
<b, cons, cons>(q_gen_1382, q_gen_1413) -> q_gen_1373
<b, cons, cons>(q_gen_1426, q_gen_1413) -> q_gen_1373
<b, cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1373
<b, nil, nil>() -> q_gen_1373
<a, cons, cons>(q_gen_1426, q_gen_1381) -> q_gen_1465
<b, cons, cons>(q_gen_1426, q_gen_1381) -> q_gen_1465
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  leqnat -> 
{{{
Q={q_gen_1372, q_gen_1396, q_gen_1438},
Q_f={q_gen_1372},
Delta=
{
<s>(q_gen_1396) -> q_gen_1396
<z>() -> q_gen_1396
<s, s>(q_gen_1372) -> q_gen_1372
<z, s>(q_gen_1396) -> q_gen_1372
<z, z>() -> q_gen_1372
<s, s>(q_gen_1438) -> q_gen_1438
<s, z>(q_gen_1396) -> q_gen_1438
}

Datatype: <nat, nat>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist, eq_nat}
_|

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 40
() -> delete_all([x, nil, nil]) -> 40
() -> delete_one([x, nil, nil]) -> 40
() -> delete_one([y, cons(y, r), r]) -> 42
() -> leqnat([z, n2]) -> 40
(count([x, l, _fh]) /\ delete_all([x, l, _eh]) /\ delete_one([x, l, _eh])) -> leqnat([_fh, s(z)]) -> 40
(count([x, r, _yg]) /\ not eq_elt([x, y])) -> count([x, cons(y, r), _yg]) -> 41
(count([y, r, _xg])) -> count([y, cons(y, r), s(_xg)]) -> 43
(delete_all([x, r, _sg]) /\ not eq_elt([x, y])) -> delete_all([x, cons(y, r), cons(y, _sg)]) -> 41
(delete_all([y, r, _rg])) -> delete_all([y, cons(y, r), _rg]) -> 41
(delete_one([x, r, _mg]) /\ not eq_elt([x, y])) -> delete_one([x, cons(y, r), cons(y, _mg)]) -> 41
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 41
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 41
(leqnat([s(nn1), z])) -> BOT -> 41
}
Sat witness: Found: ((count([y, r, _xg])) -> count([y, cons(y, r), s(_xg)]), {
_xg -> s(s(z))  ;  r -> cons(a, cons(b, nil))  ;  y -> b
})

-------------------------------------------
Step 82, which took 2.389199 s (model generation: 2.387442,  model checking: 0.001757):

Model:
|_
{
count -> 
{{{
Q={q_gen_1378, q_gen_1390, q_gen_1391, q_gen_1393, q_gen_1394, q_gen_1421, q_gen_1432, q_gen_1434},
Q_f={q_gen_1378},
Delta=
{
<b>() -> q_gen_1391
<cons>(q_gen_1391, q_gen_1393) -> q_gen_1393
<cons>(q_gen_1394, q_gen_1393) -> q_gen_1393
<nil>() -> q_gen_1393
<a>() -> q_gen_1394
<cons, s>(q_gen_1394, q_gen_1390) -> q_gen_1390
<nil, z>() -> q_gen_1390
<cons, s>(q_gen_1391, q_gen_1421) -> q_gen_1421
<cons, s>(q_gen_1394, q_gen_1421) -> q_gen_1421
<cons, z>(q_gen_1391, q_gen_1393) -> q_gen_1421
<cons, z>(q_gen_1394, q_gen_1393) -> q_gen_1421
<cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1434
<cons, s>(q_gen_1391, q_gen_1434) -> q_gen_1434
<cons, s>(q_gen_1394, q_gen_1434) -> q_gen_1434
<a, cons, s>(q_gen_1391, q_gen_1421) -> q_gen_1378
<a, cons, s>(q_gen_1394, q_gen_1390) -> q_gen_1378
<a, cons, s>(q_gen_1394, q_gen_1421) -> q_gen_1378
<a, cons, z>(q_gen_1391, q_gen_1393) -> q_gen_1378
<a, nil, z>() -> q_gen_1378
<b, cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1378
<b, cons, s>(q_gen_1391, q_gen_1421) -> q_gen_1378
<b, cons, s>(q_gen_1391, q_gen_1434) -> q_gen_1378
<b, cons, s>(q_gen_1394, q_gen_1421) -> q_gen_1378
<b, cons, z>(q_gen_1394, q_gen_1393) -> q_gen_1378
<b, nil, z>() -> q_gen_1378
<a, cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1432
<a, cons, s>(q_gen_1391, q_gen_1434) -> q_gen_1432
<a, cons, s>(q_gen_1394, q_gen_1434) -> q_gen_1432
<b, cons, s>(q_gen_1394, q_gen_1434) -> q_gen_1432
}

Datatype: <elt, eltlist, nat>
Convolution form: right
}}}
  ;  delete_all -> 
{{{
Q={q_gen_1377, q_gen_1384, q_gen_1385, q_gen_1387, q_gen_1388, q_gen_1409, q_gen_1456},
Q_f={q_gen_1377},
Delta=
{
<cons>(q_gen_1385, q_gen_1384) -> q_gen_1384
<nil>() -> q_gen_1384
<a>() -> q_gen_1385
<b>() -> q_gen_1385
<cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1387
<cons, cons>(q_gen_1409, q_gen_1387) -> q_gen_1387
<cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1387
<nil, nil>() -> q_gen_1387
<a, a>() -> q_gen_1388
<b, a>() -> q_gen_1388
<a, b>() -> q_gen_1409
<b, b>() -> q_gen_1409
<a, cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1377
<a, cons, cons>(q_gen_1409, q_gen_1387) -> q_gen_1377
<a, cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1377
<a, nil, nil>() -> q_gen_1377
<b, cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1377
<b, cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1377
<b, nil, nil>() -> q_gen_1377
<b, cons, cons>(q_gen_1409, q_gen_1387) -> q_gen_1456
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  delete_one -> 
{{{
Q={q_gen_1373, q_gen_1374, q_gen_1375, q_gen_1381, q_gen_1382, q_gen_1413, q_gen_1426, q_gen_1458, q_gen_1459},
Q_f={q_gen_1373},
Delta=
{
<nil>() -> q_gen_1374
<a>() -> q_gen_1375
<b>() -> q_gen_1375
<cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1381
<nil, nil>() -> q_gen_1381
<a, a>() -> q_gen_1382
<b, b>() -> q_gen_1382
<cons, cons>(q_gen_1382, q_gen_1413) -> q_gen_1413
<cons, cons>(q_gen_1426, q_gen_1413) -> q_gen_1413
<cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1413
<a, b>() -> q_gen_1426
<b, a>() -> q_gen_1426
<cons, cons>(q_gen_1426, q_gen_1381) -> q_gen_1459
<cons, cons>(q_gen_1426, q_gen_1459) -> q_gen_1459
<a, cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1373
<a, cons, cons>(q_gen_1382, q_gen_1413) -> q_gen_1373
<a, cons, cons>(q_gen_1426, q_gen_1413) -> q_gen_1373
<a, cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1373
<a, nil, nil>() -> q_gen_1373
<b, cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1373
<b, cons, cons>(q_gen_1382, q_gen_1413) -> q_gen_1373
<b, cons, cons>(q_gen_1426, q_gen_1413) -> q_gen_1373
<b, cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1373
<b, nil, nil>() -> q_gen_1373
<a, cons, cons>(q_gen_1382, q_gen_1459) -> q_gen_1458
<a, cons, cons>(q_gen_1426, q_gen_1459) -> q_gen_1458
<b, cons, cons>(q_gen_1382, q_gen_1459) -> q_gen_1458
<b, cons, cons>(q_gen_1426, q_gen_1381) -> q_gen_1458
<b, cons, cons>(q_gen_1426, q_gen_1459) -> q_gen_1458
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  leqnat -> 
{{{
Q={q_gen_1372, q_gen_1396, q_gen_1438},
Q_f={q_gen_1372},
Delta=
{
<s>(q_gen_1396) -> q_gen_1396
<z>() -> q_gen_1396
<s, s>(q_gen_1372) -> q_gen_1372
<z, s>(q_gen_1396) -> q_gen_1372
<z, z>() -> q_gen_1372
<s, s>(q_gen_1438) -> q_gen_1438
<s, z>(q_gen_1396) -> q_gen_1438
}

Datatype: <nat, nat>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist, eq_nat}
_|

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 40
() -> delete_all([x, nil, nil]) -> 40
() -> delete_one([x, nil, nil]) -> 40
() -> delete_one([y, cons(y, r), r]) -> 42
() -> leqnat([z, n2]) -> 40
(count([x, l, _fh]) /\ delete_all([x, l, _eh]) /\ delete_one([x, l, _eh])) -> leqnat([_fh, s(z)]) -> 43
(count([x, r, _yg]) /\ not eq_elt([x, y])) -> count([x, cons(y, r), _yg]) -> 41
(count([y, r, _xg])) -> count([y, cons(y, r), s(_xg)]) -> 43
(delete_all([x, r, _sg]) /\ not eq_elt([x, y])) -> delete_all([x, cons(y, r), cons(y, _sg)]) -> 41
(delete_all([y, r, _rg])) -> delete_all([y, cons(y, r), _rg]) -> 41
(delete_one([x, r, _mg]) /\ not eq_elt([x, y])) -> delete_one([x, cons(y, r), cons(y, _mg)]) -> 41
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 41
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 41
(leqnat([s(nn1), z])) -> BOT -> 41
}
Sat witness: Found: ((count([x, l, _fh]) /\ delete_all([x, l, _eh]) /\ delete_one([x, l, _eh])) -> leqnat([_fh, s(z)]), {
_eh -> cons(a, cons(a, nil))  ;  _fh -> s(s(s(z)))  ;  l -> cons(b, cons(b, cons(a, nil)))  ;  x -> b
})

-------------------------------------------
Step 83, which took 2.237621 s (model generation: 2.235597,  model checking: 0.002024):

Model:
|_
{
count -> 
{{{
Q={q_gen_1378, q_gen_1390, q_gen_1391, q_gen_1393, q_gen_1394, q_gen_1421, q_gen_1432, q_gen_1434},
Q_f={q_gen_1378},
Delta=
{
<b>() -> q_gen_1391
<cons>(q_gen_1391, q_gen_1393) -> q_gen_1393
<cons>(q_gen_1394, q_gen_1393) -> q_gen_1393
<nil>() -> q_gen_1393
<a>() -> q_gen_1394
<cons, s>(q_gen_1394, q_gen_1390) -> q_gen_1390
<cons, s>(q_gen_1394, q_gen_1434) -> q_gen_1390
<nil, z>() -> q_gen_1390
<cons, s>(q_gen_1391, q_gen_1421) -> q_gen_1421
<cons, s>(q_gen_1394, q_gen_1421) -> q_gen_1421
<cons, z>(q_gen_1391, q_gen_1393) -> q_gen_1421
<cons, z>(q_gen_1394, q_gen_1393) -> q_gen_1421
<cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1434
<cons, s>(q_gen_1391, q_gen_1434) -> q_gen_1434
<a, cons, s>(q_gen_1391, q_gen_1421) -> q_gen_1378
<a, cons, s>(q_gen_1394, q_gen_1390) -> q_gen_1378
<a, cons, s>(q_gen_1394, q_gen_1421) -> q_gen_1378
<a, cons, z>(q_gen_1391, q_gen_1393) -> q_gen_1378
<a, nil, z>() -> q_gen_1378
<b, cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1378
<b, cons, s>(q_gen_1391, q_gen_1421) -> q_gen_1378
<b, cons, s>(q_gen_1391, q_gen_1434) -> q_gen_1378
<b, cons, s>(q_gen_1394, q_gen_1421) -> q_gen_1378
<b, cons, z>(q_gen_1394, q_gen_1393) -> q_gen_1378
<b, nil, z>() -> q_gen_1378
<a, cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1432
<a, cons, s>(q_gen_1391, q_gen_1434) -> q_gen_1432
<a, cons, s>(q_gen_1394, q_gen_1434) -> q_gen_1432
<b, cons, s>(q_gen_1394, q_gen_1434) -> q_gen_1432
}

Datatype: <elt, eltlist, nat>
Convolution form: right
}}}
  ;  delete_all -> 
{{{
Q={q_gen_1377, q_gen_1384, q_gen_1385, q_gen_1387, q_gen_1388, q_gen_1407, q_gen_1417, q_gen_1419, q_gen_1429, q_gen_1456, q_gen_1457},
Q_f={q_gen_1377},
Delta=
{
<nil>() -> q_gen_1384
<b>() -> q_gen_1385
<a>() -> q_gen_1407
<cons>(q_gen_1385, q_gen_1384) -> q_gen_1417
<cons>(q_gen_1407, q_gen_1384) -> q_gen_1417
<cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1387
<cons, cons>(q_gen_1429, q_gen_1419) -> q_gen_1387
<cons, nil>(q_gen_1385, q_gen_1417) -> q_gen_1387
<cons, nil>(q_gen_1407, q_gen_1417) -> q_gen_1387
<nil, nil>() -> q_gen_1387
<a, a>() -> q_gen_1388
<b, b>() -> q_gen_1388
<cons, cons>(q_gen_1388, q_gen_1419) -> q_gen_1419
<cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1419
<cons, nil>(q_gen_1407, q_gen_1384) -> q_gen_1419
<a, b>() -> q_gen_1429
<b, a>() -> q_gen_1429
<cons, cons>(q_gen_1429, q_gen_1387) -> q_gen_1457
<cons, cons>(q_gen_1429, q_gen_1457) -> q_gen_1457
<a, cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1377
<a, cons, cons>(q_gen_1388, q_gen_1419) -> q_gen_1377
<a, cons, cons>(q_gen_1429, q_gen_1419) -> q_gen_1377
<a, cons, nil>(q_gen_1407, q_gen_1384) -> q_gen_1377
<a, nil, nil>() -> q_gen_1377
<b, cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1377
<b, cons, cons>(q_gen_1429, q_gen_1419) -> q_gen_1377
<b, cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1377
<b, cons, nil>(q_gen_1385, q_gen_1417) -> q_gen_1377
<b, nil, nil>() -> q_gen_1377
<a, cons, cons>(q_gen_1388, q_gen_1457) -> q_gen_1456
<a, cons, cons>(q_gen_1429, q_gen_1387) -> q_gen_1456
<a, cons, cons>(q_gen_1429, q_gen_1457) -> q_gen_1456
<b, cons, cons>(q_gen_1388, q_gen_1419) -> q_gen_1456
<b, cons, cons>(q_gen_1388, q_gen_1457) -> q_gen_1456
<b, cons, cons>(q_gen_1429, q_gen_1387) -> q_gen_1456
<b, cons, cons>(q_gen_1429, q_gen_1457) -> q_gen_1456
<b, cons, nil>(q_gen_1407, q_gen_1384) -> q_gen_1456
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  delete_one -> 
{{{
Q={q_gen_1373, q_gen_1374, q_gen_1375, q_gen_1381, q_gen_1382},
Q_f={q_gen_1373},
Delta=
{
<nil>() -> q_gen_1374
<a>() -> q_gen_1375
<b>() -> q_gen_1375
<cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1381
<cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1381
<nil, nil>() -> q_gen_1381
<a, a>() -> q_gen_1382
<a, b>() -> q_gen_1382
<b, a>() -> q_gen_1382
<b, b>() -> q_gen_1382
<a, cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1373
<a, cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1373
<a, nil, nil>() -> q_gen_1373
<b, cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1373
<b, cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1373
<b, nil, nil>() -> q_gen_1373
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  leqnat -> 
{{{
Q={q_gen_1372, q_gen_1396, q_gen_1438},
Q_f={q_gen_1372},
Delta=
{
<s>(q_gen_1396) -> q_gen_1396
<z>() -> q_gen_1396
<s, s>(q_gen_1372) -> q_gen_1372
<z, s>(q_gen_1396) -> q_gen_1372
<z, z>() -> q_gen_1372
<s, s>(q_gen_1438) -> q_gen_1438
<s, z>(q_gen_1396) -> q_gen_1438
}

Datatype: <nat, nat>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist, eq_nat}
_|

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 41
() -> delete_all([x, nil, nil]) -> 41
() -> delete_one([x, nil, nil]) -> 41
() -> delete_one([y, cons(y, r), r]) -> 42
() -> leqnat([z, n2]) -> 41
(count([x, l, _fh]) /\ delete_all([x, l, _eh]) /\ delete_one([x, l, _eh])) -> leqnat([_fh, s(z)]) -> 43
(count([x, r, _yg]) /\ not eq_elt([x, y])) -> count([x, cons(y, r), _yg]) -> 41
(count([y, r, _xg])) -> count([y, cons(y, r), s(_xg)]) -> 43
(delete_all([x, r, _sg]) /\ not eq_elt([x, y])) -> delete_all([x, cons(y, r), cons(y, _sg)]) -> 41
(delete_all([y, r, _rg])) -> delete_all([y, cons(y, r), _rg]) -> 44
(delete_one([x, r, _mg]) /\ not eq_elt([x, y])) -> delete_one([x, cons(y, r), cons(y, _mg)]) -> 42
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 42
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 42
(leqnat([s(nn1), z])) -> BOT -> 42
}
Sat witness: Found: ((delete_all([y, r, _rg])) -> delete_all([y, cons(y, r), _rg]), {
_rg -> cons(a, nil)  ;  r -> cons(b, cons(a, nil))  ;  y -> b
})

-------------------------------------------
Step 84, which took 2.629327 s (model generation: 2.405775,  model checking: 0.223552):

Model:
|_
{
count -> 
{{{
Q={q_gen_1378, q_gen_1390, q_gen_1391, q_gen_1393, q_gen_1394, q_gen_1432, q_gen_1434, q_gen_1442, q_gen_1448},
Q_f={q_gen_1378},
Delta=
{
<b>() -> q_gen_1391
<cons>(q_gen_1391, q_gen_1393) -> q_gen_1393
<nil>() -> q_gen_1393
<a>() -> q_gen_1394
<cons>(q_gen_1394, q_gen_1393) -> q_gen_1442
<cons, s>(q_gen_1391, q_gen_1448) -> q_gen_1390
<cons, s>(q_gen_1394, q_gen_1390) -> q_gen_1390
<cons, z>(q_gen_1391, q_gen_1393) -> q_gen_1390
<nil, z>() -> q_gen_1390
<cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1434
<cons, s>(q_gen_1394, q_gen_1434) -> q_gen_1434
<cons, z>(q_gen_1394, q_gen_1442) -> q_gen_1434
<cons, s>(q_gen_1391, q_gen_1434) -> q_gen_1448
<cons, s>(q_gen_1394, q_gen_1448) -> q_gen_1448
<cons, z>(q_gen_1391, q_gen_1442) -> q_gen_1448
<cons, z>(q_gen_1394, q_gen_1393) -> q_gen_1448
<a, cons, s>(q_gen_1391, q_gen_1448) -> q_gen_1378
<a, cons, s>(q_gen_1394, q_gen_1390) -> q_gen_1378
<a, cons, z>(q_gen_1391, q_gen_1393) -> q_gen_1378
<a, nil, z>() -> q_gen_1378
<b, cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1378
<b, cons, s>(q_gen_1391, q_gen_1434) -> q_gen_1378
<b, cons, s>(q_gen_1391, q_gen_1448) -> q_gen_1378
<b, cons, s>(q_gen_1394, q_gen_1390) -> q_gen_1378
<b, cons, s>(q_gen_1394, q_gen_1434) -> q_gen_1378
<b, cons, s>(q_gen_1394, q_gen_1448) -> q_gen_1378
<b, cons, z>(q_gen_1394, q_gen_1393) -> q_gen_1378
<b, cons, z>(q_gen_1394, q_gen_1442) -> q_gen_1378
<b, nil, z>() -> q_gen_1378
<a, cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1432
<a, cons, s>(q_gen_1391, q_gen_1434) -> q_gen_1432
<a, cons, s>(q_gen_1394, q_gen_1434) -> q_gen_1432
}

Datatype: <elt, eltlist, nat>
Convolution form: right
}}}
  ;  delete_all -> 
{{{
Q={q_gen_1377, q_gen_1384, q_gen_1385, q_gen_1387, q_gen_1388, q_gen_1409, q_gen_1419, q_gen_1429, q_gen_1446, q_gen_1456},
Q_f={q_gen_1377},
Delta=
{
<cons>(q_gen_1385, q_gen_1384) -> q_gen_1384
<nil>() -> q_gen_1384
<a>() -> q_gen_1385
<b>() -> q_gen_1385
<cons, cons>(q_gen_1388, q_gen_1419) -> q_gen_1387
<cons, cons>(q_gen_1429, q_gen_1387) -> q_gen_1387
<cons, cons>(q_gen_1446, q_gen_1387) -> q_gen_1387
<cons, cons>(q_gen_1446, q_gen_1419) -> q_gen_1387
<nil, nil>() -> q_gen_1387
<a, a>() -> q_gen_1388
<b, b>() -> q_gen_1409
<cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1419
<cons, cons>(q_gen_1409, q_gen_1387) -> q_gen_1419
<cons, cons>(q_gen_1409, q_gen_1419) -> q_gen_1419
<cons, cons>(q_gen_1429, q_gen_1419) -> q_gen_1419
<cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1419
<a, b>() -> q_gen_1429
<b, a>() -> q_gen_1446
<a, cons, cons>(q_gen_1409, q_gen_1387) -> q_gen_1377
<a, cons, cons>(q_gen_1409, q_gen_1419) -> q_gen_1377
<a, cons, cons>(q_gen_1429, q_gen_1419) -> q_gen_1377
<a, cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1377
<a, nil, nil>() -> q_gen_1377
<b, cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1377
<b, cons, cons>(q_gen_1388, q_gen_1419) -> q_gen_1377
<b, cons, cons>(q_gen_1446, q_gen_1419) -> q_gen_1377
<b, cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1377
<b, nil, nil>() -> q_gen_1377
<a, cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1456
<a, cons, cons>(q_gen_1429, q_gen_1387) -> q_gen_1456
<b, cons, cons>(q_gen_1409, q_gen_1387) -> q_gen_1456
<b, cons, cons>(q_gen_1409, q_gen_1419) -> q_gen_1456
<b, cons, cons>(q_gen_1429, q_gen_1387) -> q_gen_1456
<b, cons, cons>(q_gen_1429, q_gen_1419) -> q_gen_1456
<b, cons, cons>(q_gen_1446, q_gen_1387) -> q_gen_1456
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  delete_one -> 
{{{
Q={q_gen_1373, q_gen_1374, q_gen_1375, q_gen_1381, q_gen_1382},
Q_f={q_gen_1373},
Delta=
{
<nil>() -> q_gen_1374
<a>() -> q_gen_1375
<b>() -> q_gen_1375
<cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1381
<cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1381
<nil, nil>() -> q_gen_1381
<a, a>() -> q_gen_1382
<a, b>() -> q_gen_1382
<b, a>() -> q_gen_1382
<b, b>() -> q_gen_1382
<a, cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1373
<a, cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1373
<a, nil, nil>() -> q_gen_1373
<b, cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1373
<b, cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1373
<b, nil, nil>() -> q_gen_1373
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  leqnat -> 
{{{
Q={q_gen_1372, q_gen_1396, q_gen_1438},
Q_f={q_gen_1372},
Delta=
{
<s>(q_gen_1396) -> q_gen_1396
<z>() -> q_gen_1396
<s, s>(q_gen_1372) -> q_gen_1372
<z, s>(q_gen_1396) -> q_gen_1372
<z, z>() -> q_gen_1372
<s, s>(q_gen_1438) -> q_gen_1438
<s, z>(q_gen_1396) -> q_gen_1438
}

Datatype: <nat, nat>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist, eq_nat}
_|

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 41
() -> delete_all([x, nil, nil]) -> 41
() -> delete_one([x, nil, nil]) -> 41
() -> delete_one([y, cons(y, r), r]) -> 42
() -> leqnat([z, n2]) -> 41
(count([x, l, _fh]) /\ delete_all([x, l, _eh]) /\ delete_one([x, l, _eh])) -> leqnat([_fh, s(z)]) -> 43
(count([x, r, _yg]) /\ not eq_elt([x, y])) -> count([x, cons(y, r), _yg]) -> 44
(count([y, r, _xg])) -> count([y, cons(y, r), s(_xg)]) -> 43
(delete_all([x, r, _sg]) /\ not eq_elt([x, y])) -> delete_all([x, cons(y, r), cons(y, _sg)]) -> 42
(delete_all([y, r, _rg])) -> delete_all([y, cons(y, r), _rg]) -> 44
(delete_one([x, r, _mg]) /\ not eq_elt([x, y])) -> delete_one([x, cons(y, r), cons(y, _mg)]) -> 42
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 42
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 42
(leqnat([s(nn1), z])) -> BOT -> 42
}
Sat witness: Found: ((count([x, r, _yg]) /\ not eq_elt([x, y])) -> count([x, cons(y, r), _yg]), {
_yg -> z  ;  r -> cons(a, cons(a, nil))  ;  x -> b  ;  y -> a
})

-------------------------------------------
Step 85, which took 3.161202 s (model generation: 3.046628,  model checking: 0.114574):

Model:
|_
{
count -> 
{{{
Q={q_gen_1378, q_gen_1390, q_gen_1391, q_gen_1393, q_gen_1394, q_gen_1432, q_gen_1434, q_gen_1442, q_gen_1448},
Q_f={q_gen_1378},
Delta=
{
<b>() -> q_gen_1391
<cons>(q_gen_1391, q_gen_1393) -> q_gen_1393
<nil>() -> q_gen_1393
<a>() -> q_gen_1394
<cons>(q_gen_1394, q_gen_1393) -> q_gen_1442
<cons>(q_gen_1394, q_gen_1442) -> q_gen_1442
<cons, s>(q_gen_1391, q_gen_1448) -> q_gen_1390
<cons, s>(q_gen_1394, q_gen_1390) -> q_gen_1390
<cons, s>(q_gen_1394, q_gen_1434) -> q_gen_1390
<cons, z>(q_gen_1391, q_gen_1393) -> q_gen_1390
<nil, z>() -> q_gen_1390
<cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1434
<cons, z>(q_gen_1394, q_gen_1442) -> q_gen_1434
<cons, s>(q_gen_1391, q_gen_1434) -> q_gen_1448
<cons, s>(q_gen_1394, q_gen_1448) -> q_gen_1448
<cons, z>(q_gen_1391, q_gen_1442) -> q_gen_1448
<cons, z>(q_gen_1394, q_gen_1393) -> q_gen_1448
<a, cons, s>(q_gen_1391, q_gen_1448) -> q_gen_1378
<a, cons, s>(q_gen_1394, q_gen_1390) -> q_gen_1378
<a, cons, z>(q_gen_1391, q_gen_1393) -> q_gen_1378
<a, nil, z>() -> q_gen_1378
<b, cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1378
<b, cons, s>(q_gen_1391, q_gen_1434) -> q_gen_1378
<b, cons, s>(q_gen_1391, q_gen_1448) -> q_gen_1378
<b, cons, s>(q_gen_1394, q_gen_1390) -> q_gen_1378
<b, cons, s>(q_gen_1394, q_gen_1434) -> q_gen_1378
<b, cons, s>(q_gen_1394, q_gen_1448) -> q_gen_1378
<b, cons, z>(q_gen_1394, q_gen_1393) -> q_gen_1378
<b, cons, z>(q_gen_1394, q_gen_1442) -> q_gen_1378
<b, nil, z>() -> q_gen_1378
<a, cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1432
<a, cons, s>(q_gen_1391, q_gen_1434) -> q_gen_1432
<a, cons, s>(q_gen_1394, q_gen_1434) -> q_gen_1432
}

Datatype: <elt, eltlist, nat>
Convolution form: right
}}}
  ;  delete_all -> 
{{{
Q={q_gen_1377, q_gen_1384, q_gen_1385, q_gen_1387, q_gen_1388, q_gen_1409, q_gen_1419, q_gen_1429, q_gen_1446, q_gen_1456},
Q_f={q_gen_1377},
Delta=
{
<cons>(q_gen_1385, q_gen_1384) -> q_gen_1384
<nil>() -> q_gen_1384
<a>() -> q_gen_1385
<b>() -> q_gen_1385
<cons, cons>(q_gen_1409, q_gen_1387) -> q_gen_1387
<cons, cons>(q_gen_1429, q_gen_1387) -> q_gen_1387
<cons, cons>(q_gen_1446, q_gen_1387) -> q_gen_1387
<cons, cons>(q_gen_1446, q_gen_1419) -> q_gen_1387
<nil, nil>() -> q_gen_1387
<a, a>() -> q_gen_1388
<b, b>() -> q_gen_1409
<cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1419
<cons, cons>(q_gen_1388, q_gen_1419) -> q_gen_1419
<cons, cons>(q_gen_1409, q_gen_1419) -> q_gen_1419
<cons, cons>(q_gen_1429, q_gen_1419) -> q_gen_1419
<cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1419
<a, b>() -> q_gen_1429
<b, a>() -> q_gen_1446
<a, cons, cons>(q_gen_1409, q_gen_1387) -> q_gen_1377
<a, cons, cons>(q_gen_1409, q_gen_1419) -> q_gen_1377
<a, cons, cons>(q_gen_1429, q_gen_1419) -> q_gen_1377
<a, cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1377
<a, nil, nil>() -> q_gen_1377
<b, cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1377
<b, cons, cons>(q_gen_1388, q_gen_1419) -> q_gen_1377
<b, cons, cons>(q_gen_1446, q_gen_1419) -> q_gen_1377
<b, cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1377
<b, nil, nil>() -> q_gen_1377
<a, cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1456
<a, cons, cons>(q_gen_1429, q_gen_1387) -> q_gen_1456
<b, cons, cons>(q_gen_1409, q_gen_1387) -> q_gen_1456
<b, cons, cons>(q_gen_1409, q_gen_1419) -> q_gen_1456
<b, cons, cons>(q_gen_1429, q_gen_1387) -> q_gen_1456
<b, cons, cons>(q_gen_1429, q_gen_1419) -> q_gen_1456
<b, cons, cons>(q_gen_1446, q_gen_1387) -> q_gen_1456
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  delete_one -> 
{{{
Q={q_gen_1373, q_gen_1374, q_gen_1375, q_gen_1381, q_gen_1382},
Q_f={q_gen_1373},
Delta=
{
<nil>() -> q_gen_1374
<a>() -> q_gen_1375
<b>() -> q_gen_1375
<cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1381
<cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1381
<nil, nil>() -> q_gen_1381
<a, a>() -> q_gen_1382
<a, b>() -> q_gen_1382
<b, a>() -> q_gen_1382
<b, b>() -> q_gen_1382
<a, cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1373
<a, cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1373
<a, nil, nil>() -> q_gen_1373
<b, cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1373
<b, cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1373
<b, nil, nil>() -> q_gen_1373
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  leqnat -> 
{{{
Q={q_gen_1372, q_gen_1396, q_gen_1438},
Q_f={q_gen_1372},
Delta=
{
<s>(q_gen_1396) -> q_gen_1396
<z>() -> q_gen_1396
<s, s>(q_gen_1372) -> q_gen_1372
<z, s>(q_gen_1396) -> q_gen_1372
<z, z>() -> q_gen_1372
<s, s>(q_gen_1438) -> q_gen_1438
<s, z>(q_gen_1396) -> q_gen_1438
}

Datatype: <nat, nat>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist, eq_nat}
_|

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 42
() -> delete_all([x, nil, nil]) -> 42
() -> delete_one([x, nil, nil]) -> 42
() -> delete_one([y, cons(y, r), r]) -> 43
() -> leqnat([z, n2]) -> 42
(count([x, l, _fh]) /\ delete_all([x, l, _eh]) /\ delete_one([x, l, _eh])) -> leqnat([_fh, s(z)]) -> 46
(count([x, r, _yg]) /\ not eq_elt([x, y])) -> count([x, cons(y, r), _yg]) -> 44
(count([y, r, _xg])) -> count([y, cons(y, r), s(_xg)]) -> 44
(delete_all([x, r, _sg]) /\ not eq_elt([x, y])) -> delete_all([x, cons(y, r), cons(y, _sg)]) -> 43
(delete_all([y, r, _rg])) -> delete_all([y, cons(y, r), _rg]) -> 44
(delete_one([x, r, _mg]) /\ not eq_elt([x, y])) -> delete_one([x, cons(y, r), cons(y, _mg)]) -> 43
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 43
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 43
(leqnat([s(nn1), z])) -> BOT -> 43
}
Sat witness: Found: ((count([x, l, _fh]) /\ delete_all([x, l, _eh]) /\ delete_one([x, l, _eh])) -> leqnat([_fh, s(z)]), {
_eh -> cons(b, cons(b, nil))  ;  _fh -> s(s(z))  ;  l -> cons(a, cons(a, cons(b, nil)))  ;  x -> a
})

-------------------------------------------
Step 86, which took 2.558229 s (model generation: 2.556057,  model checking: 0.002172):

Model:
|_
{
count -> 
{{{
Q={q_gen_1378, q_gen_1390, q_gen_1391, q_gen_1393, q_gen_1394, q_gen_1421, q_gen_1432, q_gen_1434},
Q_f={q_gen_1378},
Delta=
{
<b>() -> q_gen_1391
<cons>(q_gen_1391, q_gen_1393) -> q_gen_1393
<cons>(q_gen_1394, q_gen_1393) -> q_gen_1393
<nil>() -> q_gen_1393
<a>() -> q_gen_1394
<cons, s>(q_gen_1394, q_gen_1390) -> q_gen_1390
<nil, z>() -> q_gen_1390
<cons, s>(q_gen_1391, q_gen_1421) -> q_gen_1421
<cons, s>(q_gen_1391, q_gen_1434) -> q_gen_1421
<cons, s>(q_gen_1394, q_gen_1421) -> q_gen_1421
<cons, z>(q_gen_1391, q_gen_1393) -> q_gen_1421
<cons, z>(q_gen_1394, q_gen_1393) -> q_gen_1421
<cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1434
<cons, s>(q_gen_1394, q_gen_1434) -> q_gen_1434
<a, cons, s>(q_gen_1391, q_gen_1421) -> q_gen_1378
<a, cons, s>(q_gen_1394, q_gen_1390) -> q_gen_1378
<a, cons, s>(q_gen_1394, q_gen_1421) -> q_gen_1378
<a, cons, z>(q_gen_1391, q_gen_1393) -> q_gen_1378
<a, nil, z>() -> q_gen_1378
<b, cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1378
<b, cons, s>(q_gen_1391, q_gen_1421) -> q_gen_1378
<b, cons, s>(q_gen_1391, q_gen_1434) -> q_gen_1378
<b, cons, s>(q_gen_1394, q_gen_1421) -> q_gen_1378
<b, cons, z>(q_gen_1394, q_gen_1393) -> q_gen_1378
<b, nil, z>() -> q_gen_1378
<a, cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1432
<a, cons, s>(q_gen_1391, q_gen_1434) -> q_gen_1432
<a, cons, s>(q_gen_1394, q_gen_1434) -> q_gen_1432
<b, cons, s>(q_gen_1394, q_gen_1434) -> q_gen_1432
}

Datatype: <elt, eltlist, nat>
Convolution form: right
}}}
  ;  delete_all -> 
{{{
Q={q_gen_1377, q_gen_1384, q_gen_1385, q_gen_1387, q_gen_1388, q_gen_1407, q_gen_1417, q_gen_1419, q_gen_1429, q_gen_1456, q_gen_1457},
Q_f={q_gen_1377},
Delta=
{
<nil>() -> q_gen_1384
<b>() -> q_gen_1385
<a>() -> q_gen_1407
<cons>(q_gen_1385, q_gen_1384) -> q_gen_1417
<cons>(q_gen_1407, q_gen_1384) -> q_gen_1417
<cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1387
<cons, cons>(q_gen_1388, q_gen_1419) -> q_gen_1387
<cons, nil>(q_gen_1407, q_gen_1417) -> q_gen_1387
<nil, nil>() -> q_gen_1387
<a, a>() -> q_gen_1388
<b, b>() -> q_gen_1388
<cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1419
<cons, nil>(q_gen_1385, q_gen_1417) -> q_gen_1419
<cons, nil>(q_gen_1407, q_gen_1384) -> q_gen_1419
<a, b>() -> q_gen_1429
<b, a>() -> q_gen_1429
<cons, cons>(q_gen_1429, q_gen_1387) -> q_gen_1457
<cons, cons>(q_gen_1429, q_gen_1419) -> q_gen_1457
<cons, cons>(q_gen_1429, q_gen_1457) -> q_gen_1457
<a, cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1377
<a, cons, cons>(q_gen_1388, q_gen_1419) -> q_gen_1377
<a, cons, cons>(q_gen_1429, q_gen_1419) -> q_gen_1377
<a, cons, nil>(q_gen_1407, q_gen_1384) -> q_gen_1377
<a, nil, nil>() -> q_gen_1377
<b, cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1377
<b, cons, cons>(q_gen_1429, q_gen_1419) -> q_gen_1377
<b, cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1377
<b, cons, nil>(q_gen_1385, q_gen_1417) -> q_gen_1377
<b, nil, nil>() -> q_gen_1377
<a, cons, cons>(q_gen_1388, q_gen_1457) -> q_gen_1456
<a, cons, cons>(q_gen_1429, q_gen_1387) -> q_gen_1456
<a, cons, cons>(q_gen_1429, q_gen_1457) -> q_gen_1456
<b, cons, cons>(q_gen_1388, q_gen_1419) -> q_gen_1456
<b, cons, cons>(q_gen_1388, q_gen_1457) -> q_gen_1456
<b, cons, cons>(q_gen_1429, q_gen_1387) -> q_gen_1456
<b, cons, cons>(q_gen_1429, q_gen_1457) -> q_gen_1456
<b, cons, nil>(q_gen_1407, q_gen_1384) -> q_gen_1456
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  delete_one -> 
{{{
Q={q_gen_1373, q_gen_1374, q_gen_1375, q_gen_1381, q_gen_1382},
Q_f={q_gen_1373},
Delta=
{
<nil>() -> q_gen_1374
<a>() -> q_gen_1375
<b>() -> q_gen_1375
<cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1381
<cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1381
<nil, nil>() -> q_gen_1381
<a, a>() -> q_gen_1382
<a, b>() -> q_gen_1382
<b, a>() -> q_gen_1382
<b, b>() -> q_gen_1382
<a, cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1373
<a, cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1373
<a, nil, nil>() -> q_gen_1373
<b, cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1373
<b, cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1373
<b, nil, nil>() -> q_gen_1373
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  leqnat -> 
{{{
Q={q_gen_1372, q_gen_1396, q_gen_1438},
Q_f={q_gen_1372},
Delta=
{
<s>(q_gen_1396) -> q_gen_1396
<z>() -> q_gen_1396
<s, s>(q_gen_1372) -> q_gen_1372
<z, s>(q_gen_1396) -> q_gen_1372
<z, z>() -> q_gen_1372
<s, s>(q_gen_1438) -> q_gen_1438
<s, z>(q_gen_1396) -> q_gen_1438
}

Datatype: <nat, nat>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist, eq_nat}
_|

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 43
() -> delete_all([x, nil, nil]) -> 43
() -> delete_one([x, nil, nil]) -> 43
() -> delete_one([y, cons(y, r), r]) -> 43
() -> leqnat([z, n2]) -> 43
(count([x, l, _fh]) /\ delete_all([x, l, _eh]) /\ delete_one([x, l, _eh])) -> leqnat([_fh, s(z)]) -> 46
(count([x, r, _yg]) /\ not eq_elt([x, y])) -> count([x, cons(y, r), _yg]) -> 44
(count([y, r, _xg])) -> count([y, cons(y, r), s(_xg)]) -> 44
(delete_all([x, r, _sg]) /\ not eq_elt([x, y])) -> delete_all([x, cons(y, r), cons(y, _sg)]) -> 46
(delete_all([y, r, _rg])) -> delete_all([y, cons(y, r), _rg]) -> 44
(delete_one([x, r, _mg]) /\ not eq_elt([x, y])) -> delete_one([x, cons(y, r), cons(y, _mg)]) -> 44
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 44
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 44
(leqnat([s(nn1), z])) -> BOT -> 44
}
Sat witness: Found: ((delete_all([x, r, _sg]) /\ not eq_elt([x, y])) -> delete_all([x, cons(y, r), cons(y, _sg)]), {
_sg -> nil  ;  r -> cons(b, nil)  ;  x -> b  ;  y -> a
})

-------------------------------------------
Step 87, which took 1.292546 s (model generation: 1.285221,  model checking: 0.007325):

Model:
|_
{
count -> 
{{{
Q={q_gen_1378, q_gen_1390, q_gen_1391, q_gen_1393, q_gen_1394, q_gen_1421, q_gen_1432, q_gen_1434, q_gen_1442},
Q_f={q_gen_1378},
Delta=
{
<b>() -> q_gen_1391
<cons>(q_gen_1391, q_gen_1393) -> q_gen_1393
<nil>() -> q_gen_1393
<a>() -> q_gen_1394
<cons>(q_gen_1394, q_gen_1393) -> q_gen_1442
<cons>(q_gen_1394, q_gen_1442) -> q_gen_1442
<cons, s>(q_gen_1391, q_gen_1421) -> q_gen_1390
<cons, s>(q_gen_1394, q_gen_1390) -> q_gen_1390
<nil, z>() -> q_gen_1390
<cons, s>(q_gen_1391, q_gen_1434) -> q_gen_1421
<cons, s>(q_gen_1394, q_gen_1421) -> q_gen_1421
<cons, z>(q_gen_1391, q_gen_1393) -> q_gen_1421
<cons, z>(q_gen_1391, q_gen_1442) -> q_gen_1421
<cons, z>(q_gen_1394, q_gen_1393) -> q_gen_1421
<cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1434
<cons, s>(q_gen_1394, q_gen_1434) -> q_gen_1434
<cons, z>(q_gen_1394, q_gen_1442) -> q_gen_1434
<a, cons, s>(q_gen_1391, q_gen_1421) -> q_gen_1378
<a, cons, s>(q_gen_1394, q_gen_1390) -> q_gen_1378
<a, cons, s>(q_gen_1394, q_gen_1421) -> q_gen_1378
<a, cons, z>(q_gen_1391, q_gen_1393) -> q_gen_1378
<a, nil, z>() -> q_gen_1378
<b, cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1378
<b, cons, s>(q_gen_1391, q_gen_1421) -> q_gen_1378
<b, cons, s>(q_gen_1391, q_gen_1434) -> q_gen_1378
<b, cons, s>(q_gen_1394, q_gen_1421) -> q_gen_1378
<b, cons, s>(q_gen_1394, q_gen_1434) -> q_gen_1378
<b, cons, z>(q_gen_1394, q_gen_1393) -> q_gen_1378
<b, cons, z>(q_gen_1394, q_gen_1442) -> q_gen_1378
<b, nil, z>() -> q_gen_1378
<a, cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1432
<a, cons, s>(q_gen_1391, q_gen_1434) -> q_gen_1432
<a, cons, s>(q_gen_1394, q_gen_1434) -> q_gen_1432
}

Datatype: <elt, eltlist, nat>
Convolution form: right
}}}
  ;  delete_all -> 
{{{
Q={q_gen_1377, q_gen_1384, q_gen_1385, q_gen_1387, q_gen_1388, q_gen_1409, q_gen_1419, q_gen_1429, q_gen_1446, q_gen_1456},
Q_f={q_gen_1377},
Delta=
{
<cons>(q_gen_1385, q_gen_1384) -> q_gen_1384
<nil>() -> q_gen_1384
<a>() -> q_gen_1385
<b>() -> q_gen_1385
<cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1387
<cons, cons>(q_gen_1409, q_gen_1387) -> q_gen_1387
<cons, cons>(q_gen_1429, q_gen_1387) -> q_gen_1387
<cons, cons>(q_gen_1429, q_gen_1419) -> q_gen_1387
<cons, cons>(q_gen_1446, q_gen_1387) -> q_gen_1387
<cons, cons>(q_gen_1446, q_gen_1419) -> q_gen_1387
<nil, nil>() -> q_gen_1387
<a, a>() -> q_gen_1388
<b, b>() -> q_gen_1409
<cons, cons>(q_gen_1388, q_gen_1419) -> q_gen_1419
<cons, cons>(q_gen_1409, q_gen_1419) -> q_gen_1419
<cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1419
<a, b>() -> q_gen_1429
<b, a>() -> q_gen_1446
<a, cons, cons>(q_gen_1409, q_gen_1387) -> q_gen_1377
<a, cons, cons>(q_gen_1409, q_gen_1419) -> q_gen_1377
<a, cons, cons>(q_gen_1429, q_gen_1419) -> q_gen_1377
<a, cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1377
<a, nil, nil>() -> q_gen_1377
<b, cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1377
<b, cons, cons>(q_gen_1388, q_gen_1419) -> q_gen_1377
<b, cons, cons>(q_gen_1446, q_gen_1419) -> q_gen_1377
<b, cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1377
<b, nil, nil>() -> q_gen_1377
<a, cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1456
<a, cons, cons>(q_gen_1429, q_gen_1387) -> q_gen_1456
<b, cons, cons>(q_gen_1409, q_gen_1387) -> q_gen_1456
<b, cons, cons>(q_gen_1409, q_gen_1419) -> q_gen_1456
<b, cons, cons>(q_gen_1429, q_gen_1387) -> q_gen_1456
<b, cons, cons>(q_gen_1429, q_gen_1419) -> q_gen_1456
<b, cons, cons>(q_gen_1446, q_gen_1387) -> q_gen_1456
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  delete_one -> 
{{{
Q={q_gen_1373, q_gen_1374, q_gen_1375, q_gen_1381, q_gen_1382},
Q_f={q_gen_1373},
Delta=
{
<nil>() -> q_gen_1374
<a>() -> q_gen_1375
<b>() -> q_gen_1375
<cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1381
<cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1381
<nil, nil>() -> q_gen_1381
<a, a>() -> q_gen_1382
<a, b>() -> q_gen_1382
<b, a>() -> q_gen_1382
<b, b>() -> q_gen_1382
<a, cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1373
<a, cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1373
<a, nil, nil>() -> q_gen_1373
<b, cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1373
<b, cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1373
<b, nil, nil>() -> q_gen_1373
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  leqnat -> 
{{{
Q={q_gen_1372, q_gen_1396, q_gen_1438},
Q_f={q_gen_1372},
Delta=
{
<s>(q_gen_1396) -> q_gen_1396
<z>() -> q_gen_1396
<s, s>(q_gen_1372) -> q_gen_1372
<z, s>(q_gen_1396) -> q_gen_1372
<z, z>() -> q_gen_1372
<s, s>(q_gen_1438) -> q_gen_1438
<s, z>(q_gen_1396) -> q_gen_1438
}

Datatype: <nat, nat>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist, eq_nat}
_|

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 44
() -> delete_all([x, nil, nil]) -> 44
() -> delete_one([x, nil, nil]) -> 44
() -> delete_one([y, cons(y, r), r]) -> 44
() -> leqnat([z, n2]) -> 44
(count([x, l, _fh]) /\ delete_all([x, l, _eh]) /\ delete_one([x, l, _eh])) -> leqnat([_fh, s(z)]) -> 46
(count([x, r, _yg]) /\ not eq_elt([x, y])) -> count([x, cons(y, r), _yg]) -> 44
(count([y, r, _xg])) -> count([y, cons(y, r), s(_xg)]) -> 44
(delete_all([x, r, _sg]) /\ not eq_elt([x, y])) -> delete_all([x, cons(y, r), cons(y, _sg)]) -> 46
(delete_all([y, r, _rg])) -> delete_all([y, cons(y, r), _rg]) -> 47
(delete_one([x, r, _mg]) /\ not eq_elt([x, y])) -> delete_one([x, cons(y, r), cons(y, _mg)]) -> 45
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 45
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 45
(leqnat([s(nn1), z])) -> BOT -> 45
}
Sat witness: Found: ((delete_all([y, r, _rg])) -> delete_all([y, cons(y, r), _rg]), {
_rg -> cons(a, cons(b, cons(a, nil)))  ;  r -> cons(b, cons(b, cons(a, cons(a, nil))))  ;  y -> b
})

-------------------------------------------
Step 88, which took 1.052598 s (model generation: 1.036923,  model checking: 0.015675):

Model:
|_
{
count -> 
{{{
Q={q_gen_1378, q_gen_1390, q_gen_1391, q_gen_1393, q_gen_1394, q_gen_1421, q_gen_1432, q_gen_1434},
Q_f={q_gen_1378},
Delta=
{
<b>() -> q_gen_1391
<cons>(q_gen_1391, q_gen_1393) -> q_gen_1393
<cons>(q_gen_1394, q_gen_1393) -> q_gen_1393
<nil>() -> q_gen_1393
<a>() -> q_gen_1394
<cons, s>(q_gen_1391, q_gen_1434) -> q_gen_1390
<cons, s>(q_gen_1394, q_gen_1390) -> q_gen_1390
<cons, s>(q_gen_1394, q_gen_1434) -> q_gen_1390
<nil, z>() -> q_gen_1390
<cons, s>(q_gen_1391, q_gen_1421) -> q_gen_1421
<cons, s>(q_gen_1394, q_gen_1421) -> q_gen_1421
<cons, z>(q_gen_1391, q_gen_1393) -> q_gen_1421
<cons, z>(q_gen_1394, q_gen_1393) -> q_gen_1421
<cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1434
<a, cons, s>(q_gen_1391, q_gen_1421) -> q_gen_1378
<a, cons, s>(q_gen_1394, q_gen_1390) -> q_gen_1378
<a, cons, s>(q_gen_1394, q_gen_1421) -> q_gen_1378
<a, cons, z>(q_gen_1391, q_gen_1393) -> q_gen_1378
<a, nil, z>() -> q_gen_1378
<b, cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1378
<b, cons, s>(q_gen_1391, q_gen_1421) -> q_gen_1378
<b, cons, s>(q_gen_1391, q_gen_1434) -> q_gen_1378
<b, cons, s>(q_gen_1394, q_gen_1421) -> q_gen_1378
<b, cons, z>(q_gen_1394, q_gen_1393) -> q_gen_1378
<b, nil, z>() -> q_gen_1378
<a, cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1432
<a, cons, s>(q_gen_1391, q_gen_1434) -> q_gen_1432
<a, cons, s>(q_gen_1394, q_gen_1434) -> q_gen_1432
<b, cons, s>(q_gen_1394, q_gen_1434) -> q_gen_1432
}

Datatype: <elt, eltlist, nat>
Convolution form: right
}}}
  ;  delete_all -> 
{{{
Q={q_gen_1377, q_gen_1384, q_gen_1385, q_gen_1387, q_gen_1388, q_gen_1409, q_gen_1419, q_gen_1429, q_gen_1446, q_gen_1456, q_gen_1457},
Q_f={q_gen_1377},
Delta=
{
<cons>(q_gen_1385, q_gen_1384) -> q_gen_1384
<nil>() -> q_gen_1384
<a>() -> q_gen_1385
<b>() -> q_gen_1385
<cons, cons>(q_gen_1409, q_gen_1387) -> q_gen_1387
<cons, cons>(q_gen_1409, q_gen_1419) -> q_gen_1387
<cons, cons>(q_gen_1429, q_gen_1419) -> q_gen_1387
<cons, cons>(q_gen_1446, q_gen_1387) -> q_gen_1387
<nil, nil>() -> q_gen_1387
<a, a>() -> q_gen_1388
<b, b>() -> q_gen_1409
<cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1419
<cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1419
<a, b>() -> q_gen_1429
<b, a>() -> q_gen_1446
<cons, cons>(q_gen_1388, q_gen_1419) -> q_gen_1457
<cons, cons>(q_gen_1409, q_gen_1457) -> q_gen_1457
<cons, cons>(q_gen_1429, q_gen_1387) -> q_gen_1457
<cons, cons>(q_gen_1446, q_gen_1419) -> q_gen_1457
<cons, cons>(q_gen_1446, q_gen_1457) -> q_gen_1457
<a, cons, cons>(q_gen_1409, q_gen_1387) -> q_gen_1377
<a, cons, cons>(q_gen_1409, q_gen_1419) -> q_gen_1377
<a, cons, cons>(q_gen_1429, q_gen_1419) -> q_gen_1377
<a, cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1377
<a, nil, nil>() -> q_gen_1377
<b, cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1377
<b, cons, cons>(q_gen_1388, q_gen_1419) -> q_gen_1377
<b, cons, cons>(q_gen_1388, q_gen_1457) -> q_gen_1377
<b, cons, cons>(q_gen_1446, q_gen_1419) -> q_gen_1377
<b, cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1377
<b, nil, nil>() -> q_gen_1377
<a, cons, cons>(q_gen_1388, q_gen_1457) -> q_gen_1456
<a, cons, cons>(q_gen_1409, q_gen_1457) -> q_gen_1456
<a, cons, cons>(q_gen_1429, q_gen_1387) -> q_gen_1456
<a, cons, cons>(q_gen_1429, q_gen_1457) -> q_gen_1456
<b, cons, cons>(q_gen_1409, q_gen_1419) -> q_gen_1456
<b, cons, cons>(q_gen_1409, q_gen_1457) -> q_gen_1456
<b, cons, cons>(q_gen_1429, q_gen_1387) -> q_gen_1456
<b, cons, cons>(q_gen_1429, q_gen_1419) -> q_gen_1456
<b, cons, cons>(q_gen_1446, q_gen_1387) -> q_gen_1456
<b, cons, cons>(q_gen_1446, q_gen_1457) -> q_gen_1456
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  delete_one -> 
{{{
Q={q_gen_1373, q_gen_1374, q_gen_1375, q_gen_1381, q_gen_1382},
Q_f={q_gen_1373},
Delta=
{
<nil>() -> q_gen_1374
<a>() -> q_gen_1375
<b>() -> q_gen_1375
<cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1381
<cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1381
<nil, nil>() -> q_gen_1381
<a, a>() -> q_gen_1382
<a, b>() -> q_gen_1382
<b, a>() -> q_gen_1382
<b, b>() -> q_gen_1382
<a, cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1373
<a, cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1373
<a, nil, nil>() -> q_gen_1373
<b, cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1373
<b, cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1373
<b, nil, nil>() -> q_gen_1373
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  leqnat -> 
{{{
Q={q_gen_1372, q_gen_1396, q_gen_1438},
Q_f={q_gen_1372},
Delta=
{
<s>(q_gen_1396) -> q_gen_1396
<z>() -> q_gen_1396
<s, s>(q_gen_1372) -> q_gen_1372
<z, s>(q_gen_1396) -> q_gen_1372
<z, z>() -> q_gen_1372
<s, s>(q_gen_1438) -> q_gen_1438
<s, z>(q_gen_1396) -> q_gen_1438
}

Datatype: <nat, nat>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist, eq_nat}
_|

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 45
() -> delete_all([x, nil, nil]) -> 45
() -> delete_one([x, nil, nil]) -> 45
() -> delete_one([y, cons(y, r), r]) -> 45
() -> leqnat([z, n2]) -> 45
(count([x, l, _fh]) /\ delete_all([x, l, _eh]) /\ delete_one([x, l, _eh])) -> leqnat([_fh, s(z)]) -> 46
(count([x, r, _yg]) /\ not eq_elt([x, y])) -> count([x, cons(y, r), _yg]) -> 45
(count([y, r, _xg])) -> count([y, cons(y, r), s(_xg)]) -> 45
(delete_all([x, r, _sg]) /\ not eq_elt([x, y])) -> delete_all([x, cons(y, r), cons(y, _sg)]) -> 49
(delete_all([y, r, _rg])) -> delete_all([y, cons(y, r), _rg]) -> 47
(delete_one([x, r, _mg]) /\ not eq_elt([x, y])) -> delete_one([x, cons(y, r), cons(y, _mg)]) -> 46
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 46
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 46
(leqnat([s(nn1), z])) -> BOT -> 46
}
Sat witness: Found: ((delete_all([x, r, _sg]) /\ not eq_elt([x, y])) -> delete_all([x, cons(y, r), cons(y, _sg)]), {
_sg -> cons(a, cons(a, cons(a, nil)))  ;  r -> cons(a, cons(b, cons(a, nil)))  ;  x -> b  ;  y -> a
})

-------------------------------------------
Step 89, which took 1.889891 s (model generation: 0.850483,  model checking: 1.039408):

Model:
|_
{
count -> 
{{{
Q={q_gen_1378, q_gen_1390, q_gen_1391, q_gen_1393, q_gen_1394, q_gen_1432, q_gen_1434, q_gen_1442, q_gen_1448},
Q_f={q_gen_1378},
Delta=
{
<b>() -> q_gen_1391
<cons>(q_gen_1391, q_gen_1393) -> q_gen_1393
<cons>(q_gen_1394, q_gen_1442) -> q_gen_1393
<nil>() -> q_gen_1393
<a>() -> q_gen_1394
<cons>(q_gen_1394, q_gen_1393) -> q_gen_1442
<cons, s>(q_gen_1391, q_gen_1448) -> q_gen_1390
<cons, s>(q_gen_1394, q_gen_1390) -> q_gen_1390
<cons, z>(q_gen_1391, q_gen_1393) -> q_gen_1390
<nil, z>() -> q_gen_1390
<cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1434
<cons, s>(q_gen_1394, q_gen_1434) -> q_gen_1434
<cons, z>(q_gen_1394, q_gen_1442) -> q_gen_1434
<cons, s>(q_gen_1391, q_gen_1434) -> q_gen_1448
<cons, s>(q_gen_1394, q_gen_1448) -> q_gen_1448
<cons, z>(q_gen_1391, q_gen_1442) -> q_gen_1448
<cons, z>(q_gen_1394, q_gen_1393) -> q_gen_1448
<a, cons, s>(q_gen_1391, q_gen_1448) -> q_gen_1378
<a, cons, s>(q_gen_1394, q_gen_1390) -> q_gen_1378
<a, cons, z>(q_gen_1391, q_gen_1393) -> q_gen_1378
<a, nil, z>() -> q_gen_1378
<b, cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1378
<b, cons, s>(q_gen_1391, q_gen_1434) -> q_gen_1378
<b, cons, s>(q_gen_1391, q_gen_1448) -> q_gen_1378
<b, cons, s>(q_gen_1394, q_gen_1390) -> q_gen_1378
<b, cons, s>(q_gen_1394, q_gen_1434) -> q_gen_1378
<b, cons, s>(q_gen_1394, q_gen_1448) -> q_gen_1378
<b, cons, z>(q_gen_1394, q_gen_1393) -> q_gen_1378
<b, cons, z>(q_gen_1394, q_gen_1442) -> q_gen_1378
<b, nil, z>() -> q_gen_1378
<a, cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1432
<a, cons, s>(q_gen_1391, q_gen_1434) -> q_gen_1432
<a, cons, s>(q_gen_1394, q_gen_1434) -> q_gen_1432
}

Datatype: <elt, eltlist, nat>
Convolution form: right
}}}
  ;  delete_all -> 
{{{
Q={q_gen_1377, q_gen_1384, q_gen_1385, q_gen_1387, q_gen_1388, q_gen_1409, q_gen_1419, q_gen_1429, q_gen_1446, q_gen_1456},
Q_f={q_gen_1377},
Delta=
{
<cons>(q_gen_1385, q_gen_1384) -> q_gen_1384
<nil>() -> q_gen_1384
<a>() -> q_gen_1385
<b>() -> q_gen_1385
<cons, cons>(q_gen_1388, q_gen_1419) -> q_gen_1387
<cons, cons>(q_gen_1409, q_gen_1387) -> q_gen_1387
<cons, cons>(q_gen_1429, q_gen_1387) -> q_gen_1387
<cons, cons>(q_gen_1429, q_gen_1419) -> q_gen_1387
<cons, cons>(q_gen_1446, q_gen_1387) -> q_gen_1387
<cons, cons>(q_gen_1446, q_gen_1419) -> q_gen_1387
<nil, nil>() -> q_gen_1387
<a, a>() -> q_gen_1388
<b, b>() -> q_gen_1409
<cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1419
<cons, cons>(q_gen_1409, q_gen_1419) -> q_gen_1419
<cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1419
<a, b>() -> q_gen_1429
<b, a>() -> q_gen_1446
<a, cons, cons>(q_gen_1409, q_gen_1387) -> q_gen_1377
<a, cons, cons>(q_gen_1409, q_gen_1419) -> q_gen_1377
<a, cons, cons>(q_gen_1429, q_gen_1419) -> q_gen_1377
<a, cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1377
<a, nil, nil>() -> q_gen_1377
<b, cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1377
<b, cons, cons>(q_gen_1388, q_gen_1419) -> q_gen_1377
<b, cons, cons>(q_gen_1446, q_gen_1419) -> q_gen_1377
<b, cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1377
<b, nil, nil>() -> q_gen_1377
<a, cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1456
<a, cons, cons>(q_gen_1429, q_gen_1387) -> q_gen_1456
<b, cons, cons>(q_gen_1409, q_gen_1387) -> q_gen_1456
<b, cons, cons>(q_gen_1409, q_gen_1419) -> q_gen_1456
<b, cons, cons>(q_gen_1429, q_gen_1387) -> q_gen_1456
<b, cons, cons>(q_gen_1429, q_gen_1419) -> q_gen_1456
<b, cons, cons>(q_gen_1446, q_gen_1387) -> q_gen_1456
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  delete_one -> 
{{{
Q={q_gen_1373, q_gen_1374, q_gen_1375, q_gen_1381, q_gen_1382},
Q_f={q_gen_1373},
Delta=
{
<nil>() -> q_gen_1374
<a>() -> q_gen_1375
<b>() -> q_gen_1375
<cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1381
<cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1381
<nil, nil>() -> q_gen_1381
<a, a>() -> q_gen_1382
<a, b>() -> q_gen_1382
<b, a>() -> q_gen_1382
<b, b>() -> q_gen_1382
<a, cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1373
<a, cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1373
<a, nil, nil>() -> q_gen_1373
<b, cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1373
<b, cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1373
<b, nil, nil>() -> q_gen_1373
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  leqnat -> 
{{{
Q={q_gen_1372, q_gen_1396, q_gen_1438},
Q_f={q_gen_1372},
Delta=
{
<s>(q_gen_1396) -> q_gen_1396
<z>() -> q_gen_1396
<s, s>(q_gen_1372) -> q_gen_1372
<z, s>(q_gen_1396) -> q_gen_1372
<z, z>() -> q_gen_1372
<s, s>(q_gen_1438) -> q_gen_1438
<s, z>(q_gen_1396) -> q_gen_1438
}

Datatype: <nat, nat>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist, eq_nat}
_|

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 45
() -> delete_all([x, nil, nil]) -> 45
() -> delete_one([x, nil, nil]) -> 45
() -> delete_one([y, cons(y, r), r]) -> 45
() -> leqnat([z, n2]) -> 45
(count([x, l, _fh]) /\ delete_all([x, l, _eh]) /\ delete_one([x, l, _eh])) -> leqnat([_fh, s(z)]) -> 46
(count([x, r, _yg]) /\ not eq_elt([x, y])) -> count([x, cons(y, r), _yg]) -> 48
(count([y, r, _xg])) -> count([y, cons(y, r), s(_xg)]) -> 46
(delete_all([x, r, _sg]) /\ not eq_elt([x, y])) -> delete_all([x, cons(y, r), cons(y, _sg)]) -> 49
(delete_all([y, r, _rg])) -> delete_all([y, cons(y, r), _rg]) -> 47
(delete_one([x, r, _mg]) /\ not eq_elt([x, y])) -> delete_one([x, cons(y, r), cons(y, _mg)]) -> 46
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 46
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 46
(leqnat([s(nn1), z])) -> BOT -> 46
}
Sat witness: Found: ((count([x, r, _yg]) /\ not eq_elt([x, y])) -> count([x, cons(y, r), _yg]), {
_yg -> s(s(z))  ;  r -> cons(b, cons(b, cons(a, cons(a, nil))))  ;  x -> a  ;  y -> b
})

-------------------------------------------
Step 90, which took 1.586095 s (model generation: 1.578515,  model checking: 0.007580):

Model:
|_
{
count -> 
{{{
Q={q_gen_1378, q_gen_1390, q_gen_1391, q_gen_1393, q_gen_1394, q_gen_1421, q_gen_1432, q_gen_1434},
Q_f={q_gen_1378},
Delta=
{
<b>() -> q_gen_1391
<cons>(q_gen_1391, q_gen_1393) -> q_gen_1393
<cons>(q_gen_1394, q_gen_1393) -> q_gen_1393
<nil>() -> q_gen_1393
<a>() -> q_gen_1394
<cons, s>(q_gen_1391, q_gen_1434) -> q_gen_1390
<cons, s>(q_gen_1394, q_gen_1390) -> q_gen_1390
<nil, z>() -> q_gen_1390
<cons, s>(q_gen_1391, q_gen_1421) -> q_gen_1421
<cons, s>(q_gen_1394, q_gen_1421) -> q_gen_1421
<cons, z>(q_gen_1391, q_gen_1393) -> q_gen_1421
<cons, z>(q_gen_1394, q_gen_1393) -> q_gen_1421
<cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1434
<cons, s>(q_gen_1394, q_gen_1434) -> q_gen_1434
<a, cons, s>(q_gen_1391, q_gen_1421) -> q_gen_1378
<a, cons, s>(q_gen_1394, q_gen_1390) -> q_gen_1378
<a, cons, s>(q_gen_1394, q_gen_1421) -> q_gen_1378
<a, cons, z>(q_gen_1391, q_gen_1393) -> q_gen_1378
<a, nil, z>() -> q_gen_1378
<b, cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1378
<b, cons, s>(q_gen_1391, q_gen_1421) -> q_gen_1378
<b, cons, s>(q_gen_1391, q_gen_1434) -> q_gen_1378
<b, cons, s>(q_gen_1394, q_gen_1421) -> q_gen_1378
<b, cons, z>(q_gen_1394, q_gen_1393) -> q_gen_1378
<b, nil, z>() -> q_gen_1378
<a, cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1432
<a, cons, s>(q_gen_1391, q_gen_1434) -> q_gen_1432
<a, cons, s>(q_gen_1394, q_gen_1434) -> q_gen_1432
<b, cons, s>(q_gen_1394, q_gen_1434) -> q_gen_1432
}

Datatype: <elt, eltlist, nat>
Convolution form: right
}}}
  ;  delete_all -> 
{{{
Q={q_gen_1377, q_gen_1384, q_gen_1385, q_gen_1387, q_gen_1388, q_gen_1409, q_gen_1419, q_gen_1429, q_gen_1446, q_gen_1456, q_gen_1500},
Q_f={q_gen_1377},
Delta=
{
<cons>(q_gen_1385, q_gen_1384) -> q_gen_1384
<nil>() -> q_gen_1384
<a>() -> q_gen_1385
<b>() -> q_gen_1385
<cons, cons>(q_gen_1409, q_gen_1387) -> q_gen_1387
<cons, cons>(q_gen_1429, q_gen_1387) -> q_gen_1387
<cons, cons>(q_gen_1429, q_gen_1419) -> q_gen_1387
<cons, cons>(q_gen_1446, q_gen_1419) -> q_gen_1387
<nil, nil>() -> q_gen_1387
<a, a>() -> q_gen_1388
<b, b>() -> q_gen_1409
<cons, cons>(q_gen_1409, q_gen_1419) -> q_gen_1419
<cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1419
<a, b>() -> q_gen_1429
<b, a>() -> q_gen_1446
<cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1500
<cons, cons>(q_gen_1388, q_gen_1419) -> q_gen_1500
<cons, cons>(q_gen_1388, q_gen_1500) -> q_gen_1500
<cons, cons>(q_gen_1409, q_gen_1500) -> q_gen_1500
<cons, cons>(q_gen_1446, q_gen_1387) -> q_gen_1500
<cons, cons>(q_gen_1446, q_gen_1500) -> q_gen_1500
<a, cons, cons>(q_gen_1409, q_gen_1387) -> q_gen_1377
<a, cons, cons>(q_gen_1409, q_gen_1419) -> q_gen_1377
<a, cons, cons>(q_gen_1429, q_gen_1419) -> q_gen_1377
<a, cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1377
<a, nil, nil>() -> q_gen_1377
<b, cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1377
<b, cons, cons>(q_gen_1388, q_gen_1419) -> q_gen_1377
<b, cons, cons>(q_gen_1388, q_gen_1500) -> q_gen_1377
<b, cons, cons>(q_gen_1446, q_gen_1419) -> q_gen_1377
<b, cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1377
<b, nil, nil>() -> q_gen_1377
<a, cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1456
<a, cons, cons>(q_gen_1409, q_gen_1500) -> q_gen_1456
<a, cons, cons>(q_gen_1429, q_gen_1387) -> q_gen_1456
<b, cons, cons>(q_gen_1409, q_gen_1387) -> q_gen_1456
<b, cons, cons>(q_gen_1409, q_gen_1419) -> q_gen_1456
<b, cons, cons>(q_gen_1429, q_gen_1387) -> q_gen_1456
<b, cons, cons>(q_gen_1429, q_gen_1419) -> q_gen_1456
<b, cons, cons>(q_gen_1446, q_gen_1387) -> q_gen_1456
<b, cons, cons>(q_gen_1446, q_gen_1500) -> q_gen_1456
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  delete_one -> 
{{{
Q={q_gen_1373, q_gen_1374, q_gen_1375, q_gen_1381, q_gen_1382},
Q_f={q_gen_1373},
Delta=
{
<nil>() -> q_gen_1374
<a>() -> q_gen_1375
<b>() -> q_gen_1375
<cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1381
<cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1381
<nil, nil>() -> q_gen_1381
<a, a>() -> q_gen_1382
<a, b>() -> q_gen_1382
<b, a>() -> q_gen_1382
<b, b>() -> q_gen_1382
<a, cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1373
<a, cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1373
<a, nil, nil>() -> q_gen_1373
<b, cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1373
<b, cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1373
<b, nil, nil>() -> q_gen_1373
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  leqnat -> 
{{{
Q={q_gen_1372, q_gen_1396, q_gen_1438},
Q_f={q_gen_1372},
Delta=
{
<s>(q_gen_1396) -> q_gen_1396
<z>() -> q_gen_1396
<s, s>(q_gen_1372) -> q_gen_1372
<z, s>(q_gen_1396) -> q_gen_1372
<z, z>() -> q_gen_1372
<s, s>(q_gen_1438) -> q_gen_1438
<s, z>(q_gen_1396) -> q_gen_1438
}

Datatype: <nat, nat>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist, eq_nat}
_|

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 46
() -> delete_all([x, nil, nil]) -> 46
() -> delete_one([x, nil, nil]) -> 46
() -> delete_one([y, cons(y, r), r]) -> 46
() -> leqnat([z, n2]) -> 46
(count([x, l, _fh]) /\ delete_all([x, l, _eh]) /\ delete_one([x, l, _eh])) -> leqnat([_fh, s(z)]) -> 49
(count([x, r, _yg]) /\ not eq_elt([x, y])) -> count([x, cons(y, r), _yg]) -> 48
(count([y, r, _xg])) -> count([y, cons(y, r), s(_xg)]) -> 47
(delete_all([x, r, _sg]) /\ not eq_elt([x, y])) -> delete_all([x, cons(y, r), cons(y, _sg)]) -> 49
(delete_all([y, r, _rg])) -> delete_all([y, cons(y, r), _rg]) -> 47
(delete_one([x, r, _mg]) /\ not eq_elt([x, y])) -> delete_one([x, cons(y, r), cons(y, _mg)]) -> 47
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 47
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 47
(leqnat([s(nn1), z])) -> BOT -> 47
}
Sat witness: Found: ((count([x, l, _fh]) /\ delete_all([x, l, _eh]) /\ delete_one([x, l, _eh])) -> leqnat([_fh, s(z)]), {
_eh -> cons(b, cons(b, nil))  ;  _fh -> s(s(z))  ;  l -> cons(b, cons(a, cons(b, nil)))  ;  x -> a
})

-------------------------------------------
Step 91, which took 2.061555 s (model generation: 2.056765,  model checking: 0.004790):

Model:
|_
{
count -> 
{{{
Q={q_gen_1378, q_gen_1390, q_gen_1391, q_gen_1393, q_gen_1394, q_gen_1421, q_gen_1432, q_gen_1434},
Q_f={q_gen_1378},
Delta=
{
<b>() -> q_gen_1391
<cons>(q_gen_1391, q_gen_1393) -> q_gen_1393
<cons>(q_gen_1394, q_gen_1393) -> q_gen_1393
<nil>() -> q_gen_1393
<a>() -> q_gen_1394
<cons, s>(q_gen_1394, q_gen_1390) -> q_gen_1390
<cons, s>(q_gen_1394, q_gen_1434) -> q_gen_1390
<nil, z>() -> q_gen_1390
<cons, s>(q_gen_1391, q_gen_1421) -> q_gen_1421
<cons, s>(q_gen_1391, q_gen_1434) -> q_gen_1421
<cons, s>(q_gen_1394, q_gen_1421) -> q_gen_1421
<cons, z>(q_gen_1391, q_gen_1393) -> q_gen_1421
<cons, z>(q_gen_1394, q_gen_1393) -> q_gen_1421
<cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1434
<a, cons, s>(q_gen_1391, q_gen_1421) -> q_gen_1378
<a, cons, s>(q_gen_1394, q_gen_1390) -> q_gen_1378
<a, cons, s>(q_gen_1394, q_gen_1421) -> q_gen_1378
<a, cons, z>(q_gen_1391, q_gen_1393) -> q_gen_1378
<a, nil, z>() -> q_gen_1378
<b, cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1378
<b, cons, s>(q_gen_1391, q_gen_1421) -> q_gen_1378
<b, cons, s>(q_gen_1391, q_gen_1434) -> q_gen_1378
<b, cons, s>(q_gen_1394, q_gen_1421) -> q_gen_1378
<b, cons, z>(q_gen_1394, q_gen_1393) -> q_gen_1378
<b, nil, z>() -> q_gen_1378
<a, cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1432
<a, cons, s>(q_gen_1391, q_gen_1434) -> q_gen_1432
<a, cons, s>(q_gen_1394, q_gen_1434) -> q_gen_1432
<b, cons, s>(q_gen_1394, q_gen_1434) -> q_gen_1432
}

Datatype: <elt, eltlist, nat>
Convolution form: right
}}}
  ;  delete_all -> 
{{{
Q={q_gen_1377, q_gen_1384, q_gen_1385, q_gen_1387, q_gen_1388, q_gen_1409, q_gen_1419, q_gen_1429, q_gen_1446, q_gen_1456, q_gen_1457},
Q_f={q_gen_1377},
Delta=
{
<cons>(q_gen_1385, q_gen_1384) -> q_gen_1384
<nil>() -> q_gen_1384
<a>() -> q_gen_1385
<b>() -> q_gen_1385
<cons, cons>(q_gen_1409, q_gen_1387) -> q_gen_1387
<cons, cons>(q_gen_1409, q_gen_1457) -> q_gen_1387
<cons, cons>(q_gen_1446, q_gen_1387) -> q_gen_1387
<cons, cons>(q_gen_1446, q_gen_1419) -> q_gen_1387
<nil, nil>() -> q_gen_1387
<a, a>() -> q_gen_1388
<b, b>() -> q_gen_1409
<cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1419
<cons, cons>(q_gen_1409, q_gen_1419) -> q_gen_1419
<cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1419
<a, b>() -> q_gen_1429
<b, a>() -> q_gen_1446
<cons, cons>(q_gen_1388, q_gen_1419) -> q_gen_1457
<cons, cons>(q_gen_1429, q_gen_1387) -> q_gen_1457
<cons, cons>(q_gen_1429, q_gen_1419) -> q_gen_1457
<cons, cons>(q_gen_1446, q_gen_1457) -> q_gen_1457
<a, cons, cons>(q_gen_1409, q_gen_1387) -> q_gen_1377
<a, cons, cons>(q_gen_1409, q_gen_1419) -> q_gen_1377
<a, cons, cons>(q_gen_1429, q_gen_1419) -> q_gen_1377
<a, cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1377
<a, nil, nil>() -> q_gen_1377
<b, cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1377
<b, cons, cons>(q_gen_1388, q_gen_1419) -> q_gen_1377
<b, cons, cons>(q_gen_1388, q_gen_1457) -> q_gen_1377
<b, cons, cons>(q_gen_1446, q_gen_1419) -> q_gen_1377
<b, cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1377
<b, nil, nil>() -> q_gen_1377
<a, cons, cons>(q_gen_1388, q_gen_1457) -> q_gen_1456
<a, cons, cons>(q_gen_1409, q_gen_1457) -> q_gen_1456
<a, cons, cons>(q_gen_1429, q_gen_1387) -> q_gen_1456
<a, cons, cons>(q_gen_1429, q_gen_1457) -> q_gen_1456
<b, cons, cons>(q_gen_1409, q_gen_1419) -> q_gen_1456
<b, cons, cons>(q_gen_1409, q_gen_1457) -> q_gen_1456
<b, cons, cons>(q_gen_1429, q_gen_1387) -> q_gen_1456
<b, cons, cons>(q_gen_1429, q_gen_1419) -> q_gen_1456
<b, cons, cons>(q_gen_1446, q_gen_1387) -> q_gen_1456
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  delete_one -> 
{{{
Q={q_gen_1373, q_gen_1374, q_gen_1375, q_gen_1381, q_gen_1382},
Q_f={q_gen_1373},
Delta=
{
<nil>() -> q_gen_1374
<a>() -> q_gen_1375
<b>() -> q_gen_1375
<cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1381
<cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1381
<nil, nil>() -> q_gen_1381
<a, a>() -> q_gen_1382
<a, b>() -> q_gen_1382
<b, a>() -> q_gen_1382
<b, b>() -> q_gen_1382
<a, cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1373
<a, cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1373
<a, nil, nil>() -> q_gen_1373
<b, cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1373
<b, cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1373
<b, nil, nil>() -> q_gen_1373
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  leqnat -> 
{{{
Q={q_gen_1372, q_gen_1396, q_gen_1438},
Q_f={q_gen_1372},
Delta=
{
<s>(q_gen_1396) -> q_gen_1396
<z>() -> q_gen_1396
<s, s>(q_gen_1372) -> q_gen_1372
<z, s>(q_gen_1396) -> q_gen_1372
<z, z>() -> q_gen_1372
<s, s>(q_gen_1438) -> q_gen_1438
<s, z>(q_gen_1396) -> q_gen_1438
}

Datatype: <nat, nat>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist, eq_nat}
_|

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 47
() -> delete_all([x, nil, nil]) -> 47
() -> delete_one([x, nil, nil]) -> 47
() -> delete_one([y, cons(y, r), r]) -> 47
() -> leqnat([z, n2]) -> 47
(count([x, l, _fh]) /\ delete_all([x, l, _eh]) /\ delete_one([x, l, _eh])) -> leqnat([_fh, s(z)]) -> 49
(count([x, r, _yg]) /\ not eq_elt([x, y])) -> count([x, cons(y, r), _yg]) -> 48
(count([y, r, _xg])) -> count([y, cons(y, r), s(_xg)]) -> 47
(delete_all([x, r, _sg]) /\ not eq_elt([x, y])) -> delete_all([x, cons(y, r), cons(y, _sg)]) -> 49
(delete_all([y, r, _rg])) -> delete_all([y, cons(y, r), _rg]) -> 50
(delete_one([x, r, _mg]) /\ not eq_elt([x, y])) -> delete_one([x, cons(y, r), cons(y, _mg)]) -> 48
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 48
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 48
(leqnat([s(nn1), z])) -> BOT -> 48
}
Sat witness: Found: ((delete_all([y, r, _rg])) -> delete_all([y, cons(y, r), _rg]), {
_rg -> cons(b, cons(a, nil))  ;  r -> cons(a, cons(a, nil))  ;  y -> a
})

-------------------------------------------
Step 92, which took 2.988947 s (model generation: 2.980361,  model checking: 0.008586):

Model:
|_
{
count -> 
{{{
Q={q_gen_1378, q_gen_1390, q_gen_1391, q_gen_1393, q_gen_1394, q_gen_1421, q_gen_1432, q_gen_1434},
Q_f={q_gen_1378},
Delta=
{
<b>() -> q_gen_1391
<cons>(q_gen_1391, q_gen_1393) -> q_gen_1393
<cons>(q_gen_1394, q_gen_1393) -> q_gen_1393
<nil>() -> q_gen_1393
<a>() -> q_gen_1394
<cons, s>(q_gen_1394, q_gen_1390) -> q_gen_1390
<nil, z>() -> q_gen_1390
<cons, s>(q_gen_1391, q_gen_1421) -> q_gen_1421
<cons, s>(q_gen_1394, q_gen_1421) -> q_gen_1421
<cons, z>(q_gen_1391, q_gen_1393) -> q_gen_1421
<cons, z>(q_gen_1394, q_gen_1393) -> q_gen_1421
<cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1434
<cons, s>(q_gen_1391, q_gen_1434) -> q_gen_1434
<cons, s>(q_gen_1394, q_gen_1434) -> q_gen_1434
<a, cons, s>(q_gen_1391, q_gen_1421) -> q_gen_1378
<a, cons, s>(q_gen_1394, q_gen_1390) -> q_gen_1378
<a, cons, s>(q_gen_1394, q_gen_1421) -> q_gen_1378
<a, cons, z>(q_gen_1391, q_gen_1393) -> q_gen_1378
<a, nil, z>() -> q_gen_1378
<b, cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1378
<b, cons, s>(q_gen_1391, q_gen_1421) -> q_gen_1378
<b, cons, s>(q_gen_1391, q_gen_1434) -> q_gen_1378
<b, cons, s>(q_gen_1394, q_gen_1421) -> q_gen_1378
<b, cons, z>(q_gen_1394, q_gen_1393) -> q_gen_1378
<b, nil, z>() -> q_gen_1378
<a, cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1432
<a, cons, s>(q_gen_1391, q_gen_1434) -> q_gen_1432
<a, cons, s>(q_gen_1394, q_gen_1434) -> q_gen_1432
<b, cons, s>(q_gen_1394, q_gen_1434) -> q_gen_1432
}

Datatype: <elt, eltlist, nat>
Convolution form: right
}}}
  ;  delete_all -> 
{{{
Q={q_gen_1377, q_gen_1384, q_gen_1385, q_gen_1387, q_gen_1388, q_gen_1409, q_gen_1419, q_gen_1429, q_gen_1446, q_gen_1456, q_gen_1468},
Q_f={q_gen_1377},
Delta=
{
<cons>(q_gen_1385, q_gen_1384) -> q_gen_1384
<nil>() -> q_gen_1384
<a>() -> q_gen_1385
<b>() -> q_gen_1385
<cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1387
<cons, cons>(q_gen_1388, q_gen_1419) -> q_gen_1387
<cons, cons>(q_gen_1409, q_gen_1387) -> q_gen_1387
<cons, cons>(q_gen_1429, q_gen_1387) -> q_gen_1387
<cons, cons>(q_gen_1446, q_gen_1419) -> q_gen_1387
<nil, nil>() -> q_gen_1387
<a, a>() -> q_gen_1388
<b, b>() -> q_gen_1409
<cons, cons>(q_gen_1409, q_gen_1419) -> q_gen_1419
<cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1419
<a, b>() -> q_gen_1429
<b, a>() -> q_gen_1446
<cons, cons>(q_gen_1388, q_gen_1468) -> q_gen_1468
<cons, cons>(q_gen_1429, q_gen_1419) -> q_gen_1468
<cons, cons>(q_gen_1446, q_gen_1387) -> q_gen_1468
<a, cons, cons>(q_gen_1409, q_gen_1387) -> q_gen_1377
<a, cons, cons>(q_gen_1409, q_gen_1419) -> q_gen_1377
<a, cons, cons>(q_gen_1429, q_gen_1419) -> q_gen_1377
<a, cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1377
<a, nil, nil>() -> q_gen_1377
<b, cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1377
<b, cons, cons>(q_gen_1388, q_gen_1419) -> q_gen_1377
<b, cons, cons>(q_gen_1446, q_gen_1419) -> q_gen_1377
<b, cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1377
<b, nil, nil>() -> q_gen_1377
<a, cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1456
<a, cons, cons>(q_gen_1409, q_gen_1468) -> q_gen_1456
<a, cons, cons>(q_gen_1429, q_gen_1387) -> q_gen_1456
<a, cons, cons>(q_gen_1429, q_gen_1468) -> q_gen_1456
<b, cons, cons>(q_gen_1388, q_gen_1468) -> q_gen_1456
<b, cons, cons>(q_gen_1409, q_gen_1387) -> q_gen_1456
<b, cons, cons>(q_gen_1409, q_gen_1419) -> q_gen_1456
<b, cons, cons>(q_gen_1429, q_gen_1387) -> q_gen_1456
<b, cons, cons>(q_gen_1429, q_gen_1419) -> q_gen_1456
<b, cons, cons>(q_gen_1446, q_gen_1387) -> q_gen_1456
<b, cons, cons>(q_gen_1446, q_gen_1468) -> q_gen_1456
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  delete_one -> 
{{{
Q={q_gen_1373, q_gen_1374, q_gen_1375, q_gen_1381, q_gen_1382},
Q_f={q_gen_1373},
Delta=
{
<nil>() -> q_gen_1374
<a>() -> q_gen_1375
<b>() -> q_gen_1375
<cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1381
<cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1381
<nil, nil>() -> q_gen_1381
<a, a>() -> q_gen_1382
<a, b>() -> q_gen_1382
<b, a>() -> q_gen_1382
<b, b>() -> q_gen_1382
<a, cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1373
<a, cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1373
<a, nil, nil>() -> q_gen_1373
<b, cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1373
<b, cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1373
<b, nil, nil>() -> q_gen_1373
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  leqnat -> 
{{{
Q={q_gen_1372, q_gen_1396, q_gen_1438},
Q_f={q_gen_1372},
Delta=
{
<s>(q_gen_1396) -> q_gen_1396
<z>() -> q_gen_1396
<s, s>(q_gen_1372) -> q_gen_1372
<z, s>(q_gen_1396) -> q_gen_1372
<z, z>() -> q_gen_1372
<s, s>(q_gen_1438) -> q_gen_1438
<s, z>(q_gen_1396) -> q_gen_1438
}

Datatype: <nat, nat>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist, eq_nat}
_|

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 48
() -> delete_all([x, nil, nil]) -> 48
() -> delete_one([x, nil, nil]) -> 48
() -> delete_one([y, cons(y, r), r]) -> 48
() -> leqnat([z, n2]) -> 48
(count([x, l, _fh]) /\ delete_all([x, l, _eh]) /\ delete_one([x, l, _eh])) -> leqnat([_fh, s(z)]) -> 49
(count([x, r, _yg]) /\ not eq_elt([x, y])) -> count([x, cons(y, r), _yg]) -> 49
(count([y, r, _xg])) -> count([y, cons(y, r), s(_xg)]) -> 48
(delete_all([x, r, _sg]) /\ not eq_elt([x, y])) -> delete_all([x, cons(y, r), cons(y, _sg)]) -> 52
(delete_all([y, r, _rg])) -> delete_all([y, cons(y, r), _rg]) -> 50
(delete_one([x, r, _mg]) /\ not eq_elt([x, y])) -> delete_one([x, cons(y, r), cons(y, _mg)]) -> 49
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 49
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 49
(leqnat([s(nn1), z])) -> BOT -> 49
}
Sat witness: Found: ((delete_all([x, r, _sg]) /\ not eq_elt([x, y])) -> delete_all([x, cons(y, r), cons(y, _sg)]), {
_sg -> cons(b, nil)  ;  r -> cons(a, cons(a, nil))  ;  x -> a  ;  y -> b
})

-------------------------------------------
Step 93, which took 2.831722 s (model generation: 2.812189,  model checking: 0.019533):

Model:
|_
{
count -> 
{{{
Q={q_gen_1378, q_gen_1390, q_gen_1391, q_gen_1393, q_gen_1394, q_gen_1432, q_gen_1434, q_gen_1442},
Q_f={q_gen_1378},
Delta=
{
<b>() -> q_gen_1391
<cons>(q_gen_1391, q_gen_1393) -> q_gen_1393
<cons>(q_gen_1394, q_gen_1442) -> q_gen_1393
<nil>() -> q_gen_1393
<a>() -> q_gen_1394
<cons>(q_gen_1394, q_gen_1393) -> q_gen_1442
<cons, s>(q_gen_1391, q_gen_1434) -> q_gen_1390
<cons, s>(q_gen_1394, q_gen_1390) -> q_gen_1390
<cons, z>(q_gen_1391, q_gen_1393) -> q_gen_1390
<cons, z>(q_gen_1394, q_gen_1442) -> q_gen_1390
<nil, z>() -> q_gen_1390
<cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1434
<cons, s>(q_gen_1394, q_gen_1434) -> q_gen_1434
<cons, z>(q_gen_1391, q_gen_1442) -> q_gen_1434
<cons, z>(q_gen_1394, q_gen_1393) -> q_gen_1434
<a, cons, s>(q_gen_1391, q_gen_1434) -> q_gen_1378
<a, cons, s>(q_gen_1394, q_gen_1390) -> q_gen_1378
<a, cons, z>(q_gen_1391, q_gen_1393) -> q_gen_1378
<a, nil, z>() -> q_gen_1378
<b, cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1378
<b, cons, s>(q_gen_1391, q_gen_1434) -> q_gen_1378
<b, cons, s>(q_gen_1394, q_gen_1390) -> q_gen_1378
<b, cons, s>(q_gen_1394, q_gen_1434) -> q_gen_1378
<b, cons, z>(q_gen_1394, q_gen_1393) -> q_gen_1378
<b, cons, z>(q_gen_1394, q_gen_1442) -> q_gen_1378
<b, nil, z>() -> q_gen_1378
<a, cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1432
<a, cons, s>(q_gen_1394, q_gen_1434) -> q_gen_1432
}

Datatype: <elt, eltlist, nat>
Convolution form: right
}}}
  ;  delete_all -> 
{{{
Q={q_gen_1377, q_gen_1384, q_gen_1385, q_gen_1387, q_gen_1388, q_gen_1407, q_gen_1409, q_gen_1419, q_gen_1428, q_gen_1429, q_gen_1436, q_gen_1446},
Q_f={q_gen_1377},
Delta=
{
<cons>(q_gen_1385, q_gen_1384) -> q_gen_1384
<cons>(q_gen_1407, q_gen_1384) -> q_gen_1384
<nil>() -> q_gen_1384
<b>() -> q_gen_1385
<a>() -> q_gen_1407
<cons, cons>(q_gen_1388, q_gen_1428) -> q_gen_1387
<cons, cons>(q_gen_1409, q_gen_1419) -> q_gen_1387
<cons, cons>(q_gen_1409, q_gen_1428) -> q_gen_1387
<cons, cons>(q_gen_1446, q_gen_1387) -> q_gen_1387
<cons, cons>(q_gen_1446, q_gen_1419) -> q_gen_1387
<nil, nil>() -> q_gen_1387
<a, a>() -> q_gen_1388
<b, b>() -> q_gen_1409
<cons, cons>(q_gen_1409, q_gen_1387) -> q_gen_1419
<cons, cons>(q_gen_1429, q_gen_1387) -> q_gen_1419
<cons, cons>(q_gen_1429, q_gen_1428) -> q_gen_1419
<cons, nil>(q_gen_1407, q_gen_1384) -> q_gen_1419
<cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1428
<cons, cons>(q_gen_1388, q_gen_1419) -> q_gen_1428
<cons, cons>(q_gen_1429, q_gen_1419) -> q_gen_1428
<cons, cons>(q_gen_1446, q_gen_1428) -> q_gen_1428
<cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1428
<a, b>() -> q_gen_1429
<b, a>() -> q_gen_1446
<a, cons, cons>(q_gen_1409, q_gen_1387) -> q_gen_1377
<a, cons, cons>(q_gen_1409, q_gen_1419) -> q_gen_1377
<a, cons, cons>(q_gen_1429, q_gen_1387) -> q_gen_1377
<a, cons, cons>(q_gen_1429, q_gen_1428) -> q_gen_1377
<a, cons, nil>(q_gen_1407, q_gen_1384) -> q_gen_1377
<a, nil, nil>() -> q_gen_1377
<b, cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1377
<b, cons, cons>(q_gen_1388, q_gen_1428) -> q_gen_1377
<b, cons, cons>(q_gen_1446, q_gen_1419) -> q_gen_1377
<b, cons, cons>(q_gen_1446, q_gen_1428) -> q_gen_1377
<b, cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1377
<b, nil, nil>() -> q_gen_1377
<a, cons, cons>(q_gen_1388, q_gen_1419) -> q_gen_1436
<a, cons, cons>(q_gen_1409, q_gen_1428) -> q_gen_1436
<a, cons, cons>(q_gen_1429, q_gen_1419) -> q_gen_1436
<b, cons, cons>(q_gen_1388, q_gen_1419) -> q_gen_1436
<b, cons, cons>(q_gen_1409, q_gen_1419) -> q_gen_1436
<b, cons, cons>(q_gen_1409, q_gen_1428) -> q_gen_1436
<b, cons, cons>(q_gen_1429, q_gen_1387) -> q_gen_1436
<b, cons, cons>(q_gen_1429, q_gen_1419) -> q_gen_1436
<b, cons, cons>(q_gen_1446, q_gen_1387) -> q_gen_1436
<b, cons, nil>(q_gen_1407, q_gen_1384) -> q_gen_1436
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  delete_one -> 
{{{
Q={q_gen_1373, q_gen_1374, q_gen_1375, q_gen_1381, q_gen_1382},
Q_f={q_gen_1373},
Delta=
{
<nil>() -> q_gen_1374
<a>() -> q_gen_1375
<b>() -> q_gen_1375
<cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1381
<cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1381
<nil, nil>() -> q_gen_1381
<a, a>() -> q_gen_1382
<a, b>() -> q_gen_1382
<b, a>() -> q_gen_1382
<b, b>() -> q_gen_1382
<a, cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1373
<a, cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1373
<a, nil, nil>() -> q_gen_1373
<b, cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1373
<b, cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1373
<b, nil, nil>() -> q_gen_1373
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  leqnat -> 
{{{
Q={q_gen_1372, q_gen_1396, q_gen_1438},
Q_f={q_gen_1372},
Delta=
{
<s>(q_gen_1396) -> q_gen_1396
<z>() -> q_gen_1396
<s, s>(q_gen_1372) -> q_gen_1372
<z, s>(q_gen_1396) -> q_gen_1372
<z, z>() -> q_gen_1372
<s, s>(q_gen_1438) -> q_gen_1438
<s, z>(q_gen_1396) -> q_gen_1438
}

Datatype: <nat, nat>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist, eq_nat}
_|

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 49
() -> delete_all([x, nil, nil]) -> 49
() -> delete_one([x, nil, nil]) -> 49
() -> delete_one([y, cons(y, r), r]) -> 49
() -> leqnat([z, n2]) -> 49
(count([x, l, _fh]) /\ delete_all([x, l, _eh]) /\ delete_one([x, l, _eh])) -> leqnat([_fh, s(z)]) -> 49
(count([x, r, _yg]) /\ not eq_elt([x, y])) -> count([x, cons(y, r), _yg]) -> 52
(count([y, r, _xg])) -> count([y, cons(y, r), s(_xg)]) -> 49
(delete_all([x, r, _sg]) /\ not eq_elt([x, y])) -> delete_all([x, cons(y, r), cons(y, _sg)]) -> 52
(delete_all([y, r, _rg])) -> delete_all([y, cons(y, r), _rg]) -> 50
(delete_one([x, r, _mg]) /\ not eq_elt([x, y])) -> delete_one([x, cons(y, r), cons(y, _mg)]) -> 50
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 50
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 50
(leqnat([s(nn1), z])) -> BOT -> 50
}
Sat witness: Found: ((count([x, r, _yg]) /\ not eq_elt([x, y])) -> count([x, cons(y, r), _yg]), {
_yg -> s(z)  ;  r -> cons(b, cons(b, cons(a, nil)))  ;  x -> b  ;  y -> a
})

-------------------------------------------
Step 94, which took 3.677471 s (model generation: 3.675183,  model checking: 0.002288):

Model:
|_
{
count -> 
{{{
Q={q_gen_1378, q_gen_1390, q_gen_1391, q_gen_1393, q_gen_1394, q_gen_1421, q_gen_1423, q_gen_1432, q_gen_1434, q_gen_1448},
Q_f={q_gen_1378},
Delta=
{
<b>() -> q_gen_1391
<cons>(q_gen_1391, q_gen_1423) -> q_gen_1393
<cons>(q_gen_1394, q_gen_1423) -> q_gen_1393
<nil>() -> q_gen_1393
<a>() -> q_gen_1394
<cons>(q_gen_1391, q_gen_1393) -> q_gen_1423
<cons>(q_gen_1394, q_gen_1393) -> q_gen_1423
<cons, s>(q_gen_1391, q_gen_1448) -> q_gen_1390
<cons, s>(q_gen_1394, q_gen_1390) -> q_gen_1390
<nil, z>() -> q_gen_1390
<cons, s>(q_gen_1394, q_gen_1434) -> q_gen_1421
<cons, z>(q_gen_1391, q_gen_1393) -> q_gen_1421
<cons, z>(q_gen_1394, q_gen_1423) -> q_gen_1421
<cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1434
<cons, s>(q_gen_1391, q_gen_1434) -> q_gen_1434
<cons, s>(q_gen_1394, q_gen_1421) -> q_gen_1434
<cons, s>(q_gen_1391, q_gen_1421) -> q_gen_1448
<cons, s>(q_gen_1394, q_gen_1448) -> q_gen_1448
<cons, z>(q_gen_1391, q_gen_1423) -> q_gen_1448
<cons, z>(q_gen_1394, q_gen_1393) -> q_gen_1448
<a, cons, s>(q_gen_1391, q_gen_1421) -> q_gen_1378
<a, cons, s>(q_gen_1391, q_gen_1448) -> q_gen_1378
<a, cons, s>(q_gen_1394, q_gen_1390) -> q_gen_1378
<a, cons, s>(q_gen_1394, q_gen_1421) -> q_gen_1378
<a, cons, z>(q_gen_1391, q_gen_1393) -> q_gen_1378
<a, cons, z>(q_gen_1391, q_gen_1423) -> q_gen_1378
<a, nil, z>() -> q_gen_1378
<b, cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1378
<b, cons, s>(q_gen_1391, q_gen_1434) -> q_gen_1378
<b, cons, s>(q_gen_1391, q_gen_1448) -> q_gen_1378
<b, cons, s>(q_gen_1394, q_gen_1421) -> q_gen_1378
<b, cons, s>(q_gen_1394, q_gen_1448) -> q_gen_1378
<b, cons, z>(q_gen_1394, q_gen_1393) -> q_gen_1378
<b, cons, z>(q_gen_1394, q_gen_1423) -> q_gen_1378
<b, nil, z>() -> q_gen_1378
<a, cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1432
<a, cons, s>(q_gen_1391, q_gen_1434) -> q_gen_1432
<a, cons, s>(q_gen_1394, q_gen_1434) -> q_gen_1432
<b, cons, s>(q_gen_1391, q_gen_1421) -> q_gen_1432
<b, cons, s>(q_gen_1394, q_gen_1434) -> q_gen_1432
}

Datatype: <elt, eltlist, nat>
Convolution form: right
}}}
  ;  delete_all -> 
{{{
Q={q_gen_1377, q_gen_1384, q_gen_1385, q_gen_1387, q_gen_1388, q_gen_1409, q_gen_1419, q_gen_1429, q_gen_1446, q_gen_1456},
Q_f={q_gen_1377},
Delta=
{
<cons>(q_gen_1385, q_gen_1384) -> q_gen_1384
<nil>() -> q_gen_1384
<a>() -> q_gen_1385
<b>() -> q_gen_1385
<cons, cons>(q_gen_1429, q_gen_1387) -> q_gen_1387
<cons, cons>(q_gen_1446, q_gen_1387) -> q_gen_1387
<cons, cons>(q_gen_1446, q_gen_1419) -> q_gen_1387
<nil, nil>() -> q_gen_1387
<a, a>() -> q_gen_1388
<b, b>() -> q_gen_1409
<cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1419
<cons, cons>(q_gen_1388, q_gen_1419) -> q_gen_1419
<cons, cons>(q_gen_1409, q_gen_1387) -> q_gen_1419
<cons, cons>(q_gen_1409, q_gen_1419) -> q_gen_1419
<cons, cons>(q_gen_1429, q_gen_1419) -> q_gen_1419
<cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1419
<a, b>() -> q_gen_1429
<b, a>() -> q_gen_1446
<a, cons, cons>(q_gen_1409, q_gen_1387) -> q_gen_1377
<a, cons, cons>(q_gen_1409, q_gen_1419) -> q_gen_1377
<a, cons, cons>(q_gen_1429, q_gen_1419) -> q_gen_1377
<a, cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1377
<a, nil, nil>() -> q_gen_1377
<b, cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1377
<b, cons, cons>(q_gen_1388, q_gen_1419) -> q_gen_1377
<b, cons, cons>(q_gen_1446, q_gen_1419) -> q_gen_1377
<b, cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1377
<b, nil, nil>() -> q_gen_1377
<a, cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1456
<a, cons, cons>(q_gen_1429, q_gen_1387) -> q_gen_1456
<b, cons, cons>(q_gen_1409, q_gen_1387) -> q_gen_1456
<b, cons, cons>(q_gen_1409, q_gen_1419) -> q_gen_1456
<b, cons, cons>(q_gen_1429, q_gen_1387) -> q_gen_1456
<b, cons, cons>(q_gen_1429, q_gen_1419) -> q_gen_1456
<b, cons, cons>(q_gen_1446, q_gen_1387) -> q_gen_1456
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  delete_one -> 
{{{
Q={q_gen_1373, q_gen_1374, q_gen_1375, q_gen_1381, q_gen_1382},
Q_f={q_gen_1373},
Delta=
{
<nil>() -> q_gen_1374
<a>() -> q_gen_1375
<b>() -> q_gen_1375
<cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1381
<cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1381
<nil, nil>() -> q_gen_1381
<a, a>() -> q_gen_1382
<a, b>() -> q_gen_1382
<b, a>() -> q_gen_1382
<b, b>() -> q_gen_1382
<a, cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1373
<a, cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1373
<a, nil, nil>() -> q_gen_1373
<b, cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1373
<b, cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1373
<b, nil, nil>() -> q_gen_1373
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  leqnat -> 
{{{
Q={q_gen_1372, q_gen_1396, q_gen_1438},
Q_f={q_gen_1372},
Delta=
{
<s>(q_gen_1396) -> q_gen_1396
<z>() -> q_gen_1396
<s, s>(q_gen_1372) -> q_gen_1372
<z, s>(q_gen_1396) -> q_gen_1372
<z, z>() -> q_gen_1372
<s, s>(q_gen_1438) -> q_gen_1438
<s, z>(q_gen_1396) -> q_gen_1438
}

Datatype: <nat, nat>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist, eq_nat}
_|

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 49
() -> delete_all([x, nil, nil]) -> 49
() -> delete_one([x, nil, nil]) -> 49
() -> delete_one([y, cons(y, r), r]) -> 49
() -> leqnat([z, n2]) -> 49
(count([x, l, _fh]) /\ delete_all([x, l, _eh]) /\ delete_one([x, l, _eh])) -> leqnat([_fh, s(z)]) -> 49
(count([x, r, _yg]) /\ not eq_elt([x, y])) -> count([x, cons(y, r), _yg]) -> 52
(count([y, r, _xg])) -> count([y, cons(y, r), s(_xg)]) -> 52
(delete_all([x, r, _sg]) /\ not eq_elt([x, y])) -> delete_all([x, cons(y, r), cons(y, _sg)]) -> 52
(delete_all([y, r, _rg])) -> delete_all([y, cons(y, r), _rg]) -> 50
(delete_one([x, r, _mg]) /\ not eq_elt([x, y])) -> delete_one([x, cons(y, r), cons(y, _mg)]) -> 50
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 50
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 50
(leqnat([s(nn1), z])) -> BOT -> 50
}
Sat witness: Found: ((count([y, r, _xg])) -> count([y, cons(y, r), s(_xg)]), {
_xg -> s(s(s(z)))  ;  r -> cons(a, cons(a, cons(b, nil)))  ;  y -> a
})

-------------------------------------------
Step 95, which took 3.282284 s (model generation: 3.279432,  model checking: 0.002852):

Model:
|_
{
count -> 
{{{
Q={q_gen_1378, q_gen_1390, q_gen_1391, q_gen_1393, q_gen_1394, q_gen_1421, q_gen_1432, q_gen_1434},
Q_f={q_gen_1378},
Delta=
{
<b>() -> q_gen_1391
<cons>(q_gen_1391, q_gen_1393) -> q_gen_1393
<cons>(q_gen_1394, q_gen_1393) -> q_gen_1393
<nil>() -> q_gen_1393
<a>() -> q_gen_1394
<cons, s>(q_gen_1391, q_gen_1434) -> q_gen_1390
<cons, s>(q_gen_1394, q_gen_1390) -> q_gen_1390
<nil, z>() -> q_gen_1390
<cons, s>(q_gen_1391, q_gen_1421) -> q_gen_1421
<cons, s>(q_gen_1394, q_gen_1421) -> q_gen_1421
<cons, z>(q_gen_1391, q_gen_1393) -> q_gen_1421
<cons, z>(q_gen_1394, q_gen_1393) -> q_gen_1421
<cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1434
<cons, s>(q_gen_1394, q_gen_1434) -> q_gen_1434
<a, cons, s>(q_gen_1391, q_gen_1421) -> q_gen_1378
<a, cons, s>(q_gen_1394, q_gen_1390) -> q_gen_1378
<a, cons, s>(q_gen_1394, q_gen_1421) -> q_gen_1378
<a, cons, z>(q_gen_1391, q_gen_1393) -> q_gen_1378
<a, nil, z>() -> q_gen_1378
<b, cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1378
<b, cons, s>(q_gen_1391, q_gen_1421) -> q_gen_1378
<b, cons, s>(q_gen_1391, q_gen_1434) -> q_gen_1378
<b, cons, s>(q_gen_1394, q_gen_1421) -> q_gen_1378
<b, cons, s>(q_gen_1394, q_gen_1434) -> q_gen_1378
<b, cons, z>(q_gen_1394, q_gen_1393) -> q_gen_1378
<b, nil, z>() -> q_gen_1378
<a, cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1432
<a, cons, s>(q_gen_1391, q_gen_1434) -> q_gen_1432
<a, cons, s>(q_gen_1394, q_gen_1434) -> q_gen_1432
}

Datatype: <elt, eltlist, nat>
Convolution form: right
}}}
  ;  delete_all -> 
{{{
Q={q_gen_1377, q_gen_1384, q_gen_1385, q_gen_1387, q_gen_1388, q_gen_1409, q_gen_1456},
Q_f={q_gen_1377},
Delta=
{
<cons>(q_gen_1385, q_gen_1384) -> q_gen_1384
<nil>() -> q_gen_1384
<a>() -> q_gen_1385
<b>() -> q_gen_1385
<cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1387
<cons, cons>(q_gen_1409, q_gen_1387) -> q_gen_1387
<cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1387
<nil, nil>() -> q_gen_1387
<a, a>() -> q_gen_1388
<b, a>() -> q_gen_1388
<a, b>() -> q_gen_1409
<b, b>() -> q_gen_1409
<a, cons, cons>(q_gen_1409, q_gen_1387) -> q_gen_1377
<a, cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1377
<a, nil, nil>() -> q_gen_1377
<b, cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1377
<b, cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1377
<b, nil, nil>() -> q_gen_1377
<a, cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1456
<b, cons, cons>(q_gen_1409, q_gen_1387) -> q_gen_1456
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  delete_one -> 
{{{
Q={q_gen_1373, q_gen_1374, q_gen_1375, q_gen_1381, q_gen_1382, q_gen_1405, q_gen_1426, q_gen_1458, q_gen_1459, q_gen_1475},
Q_f={q_gen_1373},
Delta=
{
<nil>() -> q_gen_1374
<a>() -> q_gen_1375
<b>() -> q_gen_1375
<cons, cons>(q_gen_1405, q_gen_1381) -> q_gen_1381
<cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1381
<nil, nil>() -> q_gen_1381
<a, a>() -> q_gen_1382
<a, b>() -> q_gen_1382
<b, b>() -> q_gen_1405
<b, a>() -> q_gen_1426
<cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1459
<cons, cons>(q_gen_1426, q_gen_1475) -> q_gen_1459
<cons, cons>(q_gen_1382, q_gen_1459) -> q_gen_1475
<cons, cons>(q_gen_1426, q_gen_1381) -> q_gen_1475
<cons, cons>(q_gen_1426, q_gen_1459) -> q_gen_1475
<a, cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1373
<a, cons, cons>(q_gen_1382, q_gen_1475) -> q_gen_1373
<a, cons, cons>(q_gen_1405, q_gen_1381) -> q_gen_1373
<a, cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1373
<a, nil, nil>() -> q_gen_1373
<b, cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1373
<b, cons, cons>(q_gen_1382, q_gen_1475) -> q_gen_1373
<b, cons, cons>(q_gen_1405, q_gen_1381) -> q_gen_1373
<b, cons, cons>(q_gen_1405, q_gen_1475) -> q_gen_1373
<b, cons, cons>(q_gen_1426, q_gen_1381) -> q_gen_1373
<b, cons, cons>(q_gen_1426, q_gen_1459) -> q_gen_1373
<b, cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1373
<b, nil, nil>() -> q_gen_1373
<a, cons, cons>(q_gen_1382, q_gen_1459) -> q_gen_1458
<a, cons, cons>(q_gen_1405, q_gen_1459) -> q_gen_1458
<a, cons, cons>(q_gen_1405, q_gen_1475) -> q_gen_1458
<b, cons, cons>(q_gen_1405, q_gen_1459) -> q_gen_1458
<b, cons, cons>(q_gen_1426, q_gen_1475) -> q_gen_1458
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  leqnat -> 
{{{
Q={q_gen_1372, q_gen_1396, q_gen_1438},
Q_f={q_gen_1372},
Delta=
{
<s>(q_gen_1396) -> q_gen_1396
<z>() -> q_gen_1396
<s, s>(q_gen_1372) -> q_gen_1372
<z, s>(q_gen_1396) -> q_gen_1372
<z, z>() -> q_gen_1372
<s, s>(q_gen_1438) -> q_gen_1438
<s, z>(q_gen_1396) -> q_gen_1438
}

Datatype: <nat, nat>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist, eq_nat}
_|

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 49
() -> delete_all([x, nil, nil]) -> 49
() -> delete_one([x, nil, nil]) -> 49
() -> delete_one([y, cons(y, r), r]) -> 49
() -> leqnat([z, n2]) -> 49
(count([x, l, _fh]) /\ delete_all([x, l, _eh]) /\ delete_one([x, l, _eh])) -> leqnat([_fh, s(z)]) -> 52
(count([x, r, _yg]) /\ not eq_elt([x, y])) -> count([x, cons(y, r), _yg]) -> 52
(count([y, r, _xg])) -> count([y, cons(y, r), s(_xg)]) -> 52
(delete_all([x, r, _sg]) /\ not eq_elt([x, y])) -> delete_all([x, cons(y, r), cons(y, _sg)]) -> 52
(delete_all([y, r, _rg])) -> delete_all([y, cons(y, r), _rg]) -> 50
(delete_one([x, r, _mg]) /\ not eq_elt([x, y])) -> delete_one([x, cons(y, r), cons(y, _mg)]) -> 50
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 50
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 50
(leqnat([s(nn1), z])) -> BOT -> 50
}
Sat witness: Found: ((count([x, l, _fh]) /\ delete_all([x, l, _eh]) /\ delete_one([x, l, _eh])) -> leqnat([_fh, s(z)]), {
_eh -> cons(a, cons(b, nil))  ;  _fh -> s(s(z))  ;  l -> cons(a, cons(b, nil))  ;  x -> b
})

-------------------------------------------
Step 96, which took 6.120586 s (model generation: 6.116886,  model checking: 0.003700):

Model:
|_
{
count -> 
{{{
Q={q_gen_1378, q_gen_1390, q_gen_1391, q_gen_1393, q_gen_1394, q_gen_1421, q_gen_1432, q_gen_1434},
Q_f={q_gen_1378},
Delta=
{
<b>() -> q_gen_1391
<cons>(q_gen_1391, q_gen_1393) -> q_gen_1393
<cons>(q_gen_1394, q_gen_1393) -> q_gen_1393
<nil>() -> q_gen_1393
<a>() -> q_gen_1394
<cons, s>(q_gen_1394, q_gen_1390) -> q_gen_1390
<cons, s>(q_gen_1394, q_gen_1434) -> q_gen_1390
<nil, z>() -> q_gen_1390
<cons, s>(q_gen_1391, q_gen_1421) -> q_gen_1421
<cons, s>(q_gen_1394, q_gen_1421) -> q_gen_1421
<cons, z>(q_gen_1391, q_gen_1393) -> q_gen_1421
<cons, z>(q_gen_1394, q_gen_1393) -> q_gen_1421
<cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1434
<cons, s>(q_gen_1391, q_gen_1434) -> q_gen_1434
<a, cons, s>(q_gen_1391, q_gen_1421) -> q_gen_1378
<a, cons, s>(q_gen_1394, q_gen_1390) -> q_gen_1378
<a, cons, s>(q_gen_1394, q_gen_1421) -> q_gen_1378
<a, cons, z>(q_gen_1391, q_gen_1393) -> q_gen_1378
<a, nil, z>() -> q_gen_1378
<b, cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1378
<b, cons, s>(q_gen_1391, q_gen_1421) -> q_gen_1378
<b, cons, s>(q_gen_1391, q_gen_1434) -> q_gen_1378
<b, cons, s>(q_gen_1394, q_gen_1421) -> q_gen_1378
<b, cons, z>(q_gen_1394, q_gen_1393) -> q_gen_1378
<b, nil, z>() -> q_gen_1378
<a, cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1432
<a, cons, s>(q_gen_1391, q_gen_1434) -> q_gen_1432
<a, cons, s>(q_gen_1394, q_gen_1434) -> q_gen_1432
<b, cons, s>(q_gen_1394, q_gen_1434) -> q_gen_1432
}

Datatype: <elt, eltlist, nat>
Convolution form: right
}}}
  ;  delete_all -> 
{{{
Q={q_gen_1377, q_gen_1384, q_gen_1385, q_gen_1387, q_gen_1388, q_gen_1407, q_gen_1409, q_gen_1428, q_gen_1429, q_gen_1446, q_gen_1456, q_gen_1457},
Q_f={q_gen_1377},
Delta=
{
<cons>(q_gen_1385, q_gen_1384) -> q_gen_1384
<cons>(q_gen_1407, q_gen_1384) -> q_gen_1384
<nil>() -> q_gen_1384
<b>() -> q_gen_1385
<a>() -> q_gen_1407
<cons, cons>(q_gen_1388, q_gen_1457) -> q_gen_1387
<cons, cons>(q_gen_1409, q_gen_1387) -> q_gen_1387
<cons, cons>(q_gen_1409, q_gen_1457) -> q_gen_1387
<cons, nil>(q_gen_1407, q_gen_1384) -> q_gen_1387
<nil, nil>() -> q_gen_1387
<a, a>() -> q_gen_1388
<b, b>() -> q_gen_1409
<cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1428
<cons, cons>(q_gen_1409, q_gen_1428) -> q_gen_1428
<cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1428
<a, b>() -> q_gen_1429
<b, a>() -> q_gen_1446
<cons, cons>(q_gen_1429, q_gen_1387) -> q_gen_1457
<cons, cons>(q_gen_1429, q_gen_1428) -> q_gen_1457
<cons, cons>(q_gen_1446, q_gen_1387) -> q_gen_1457
<cons, cons>(q_gen_1446, q_gen_1428) -> q_gen_1457
<cons, cons>(q_gen_1446, q_gen_1457) -> q_gen_1457
<a, cons, cons>(q_gen_1409, q_gen_1387) -> q_gen_1377
<a, cons, cons>(q_gen_1409, q_gen_1428) -> q_gen_1377
<a, cons, cons>(q_gen_1429, q_gen_1428) -> q_gen_1377
<a, cons, nil>(q_gen_1407, q_gen_1384) -> q_gen_1377
<a, nil, nil>() -> q_gen_1377
<b, cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1377
<b, cons, cons>(q_gen_1388, q_gen_1428) -> q_gen_1377
<b, cons, cons>(q_gen_1388, q_gen_1457) -> q_gen_1377
<b, cons, cons>(q_gen_1446, q_gen_1387) -> q_gen_1377
<b, cons, cons>(q_gen_1446, q_gen_1428) -> q_gen_1377
<b, cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1377
<b, nil, nil>() -> q_gen_1377
<a, cons, cons>(q_gen_1388, q_gen_1457) -> q_gen_1456
<a, cons, cons>(q_gen_1409, q_gen_1457) -> q_gen_1456
<a, cons, cons>(q_gen_1429, q_gen_1387) -> q_gen_1456
<a, cons, cons>(q_gen_1429, q_gen_1457) -> q_gen_1456
<b, cons, cons>(q_gen_1409, q_gen_1387) -> q_gen_1456
<b, cons, cons>(q_gen_1409, q_gen_1428) -> q_gen_1456
<b, cons, cons>(q_gen_1409, q_gen_1457) -> q_gen_1456
<b, cons, cons>(q_gen_1429, q_gen_1387) -> q_gen_1456
<b, cons, cons>(q_gen_1446, q_gen_1457) -> q_gen_1456
<b, cons, nil>(q_gen_1407, q_gen_1384) -> q_gen_1456
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  delete_one -> 
{{{
Q={q_gen_1373, q_gen_1374, q_gen_1375, q_gen_1381, q_gen_1382},
Q_f={q_gen_1373},
Delta=
{
<nil>() -> q_gen_1374
<a>() -> q_gen_1375
<b>() -> q_gen_1375
<cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1381
<cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1381
<nil, nil>() -> q_gen_1381
<a, a>() -> q_gen_1382
<a, b>() -> q_gen_1382
<b, a>() -> q_gen_1382
<b, b>() -> q_gen_1382
<a, cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1373
<a, cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1373
<a, nil, nil>() -> q_gen_1373
<b, cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1373
<b, cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1373
<b, nil, nil>() -> q_gen_1373
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  leqnat -> 
{{{
Q={q_gen_1372, q_gen_1396, q_gen_1438},
Q_f={q_gen_1372},
Delta=
{
<s>(q_gen_1396) -> q_gen_1396
<z>() -> q_gen_1396
<s, s>(q_gen_1372) -> q_gen_1372
<z, s>(q_gen_1396) -> q_gen_1372
<z, z>() -> q_gen_1372
<s, s>(q_gen_1438) -> q_gen_1438
<s, z>(q_gen_1396) -> q_gen_1438
}

Datatype: <nat, nat>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist, eq_nat}
_|

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 50
() -> delete_all([x, nil, nil]) -> 50
() -> delete_one([x, nil, nil]) -> 50
() -> delete_one([y, cons(y, r), r]) -> 50
() -> leqnat([z, n2]) -> 50
(count([x, l, _fh]) /\ delete_all([x, l, _eh]) /\ delete_one([x, l, _eh])) -> leqnat([_fh, s(z)]) -> 52
(count([x, r, _yg]) /\ not eq_elt([x, y])) -> count([x, cons(y, r), _yg]) -> 52
(count([y, r, _xg])) -> count([y, cons(y, r), s(_xg)]) -> 52
(delete_all([x, r, _sg]) /\ not eq_elt([x, y])) -> delete_all([x, cons(y, r), cons(y, _sg)]) -> 52
(delete_all([y, r, _rg])) -> delete_all([y, cons(y, r), _rg]) -> 53
(delete_one([x, r, _mg]) /\ not eq_elt([x, y])) -> delete_one([x, cons(y, r), cons(y, _mg)]) -> 51
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 51
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 51
(leqnat([s(nn1), z])) -> BOT -> 51
}
Sat witness: Found: ((delete_all([y, r, _rg])) -> delete_all([y, cons(y, r), _rg]), {
_rg -> cons(b, nil)  ;  r -> cons(a, cons(b, nil))  ;  y -> a
})

-------------------------------------------
Step 97, which took 4.271840 s (model generation: 4.192624,  model checking: 0.079216):

Model:
|_
{
count -> 
{{{
Q={q_gen_1378, q_gen_1390, q_gen_1391, q_gen_1393, q_gen_1394, q_gen_1421, q_gen_1423, q_gen_1432, q_gen_1434, q_gen_1448},
Q_f={q_gen_1378},
Delta=
{
<b>() -> q_gen_1391
<cons>(q_gen_1394, q_gen_1423) -> q_gen_1393
<nil>() -> q_gen_1393
<a>() -> q_gen_1394
<cons>(q_gen_1391, q_gen_1393) -> q_gen_1423
<cons>(q_gen_1391, q_gen_1423) -> q_gen_1423
<cons>(q_gen_1394, q_gen_1393) -> q_gen_1423
<cons, s>(q_gen_1391, q_gen_1448) -> q_gen_1390
<cons, s>(q_gen_1394, q_gen_1390) -> q_gen_1390
<nil, z>() -> q_gen_1390
<cons, s>(q_gen_1391, q_gen_1421) -> q_gen_1421
<cons, z>(q_gen_1391, q_gen_1393) -> q_gen_1421
<cons, z>(q_gen_1394, q_gen_1423) -> q_gen_1421
<cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1434
<cons, s>(q_gen_1391, q_gen_1434) -> q_gen_1434
<cons, s>(q_gen_1394, q_gen_1421) -> q_gen_1434
<cons, s>(q_gen_1394, q_gen_1434) -> q_gen_1448
<cons, s>(q_gen_1394, q_gen_1448) -> q_gen_1448
<cons, z>(q_gen_1391, q_gen_1423) -> q_gen_1448
<cons, z>(q_gen_1394, q_gen_1393) -> q_gen_1448
<a, cons, s>(q_gen_1391, q_gen_1421) -> q_gen_1378
<a, cons, s>(q_gen_1391, q_gen_1448) -> q_gen_1378
<a, cons, s>(q_gen_1394, q_gen_1390) -> q_gen_1378
<a, cons, s>(q_gen_1394, q_gen_1421) -> q_gen_1378
<a, cons, z>(q_gen_1391, q_gen_1393) -> q_gen_1378
<a, cons, z>(q_gen_1391, q_gen_1423) -> q_gen_1378
<a, nil, z>() -> q_gen_1378
<b, cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1378
<b, cons, s>(q_gen_1391, q_gen_1434) -> q_gen_1378
<b, cons, s>(q_gen_1391, q_gen_1448) -> q_gen_1378
<b, cons, s>(q_gen_1394, q_gen_1421) -> q_gen_1378
<b, cons, s>(q_gen_1394, q_gen_1448) -> q_gen_1378
<b, cons, z>(q_gen_1394, q_gen_1393) -> q_gen_1378
<b, cons, z>(q_gen_1394, q_gen_1423) -> q_gen_1378
<b, nil, z>() -> q_gen_1378
<a, cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1432
<a, cons, s>(q_gen_1391, q_gen_1434) -> q_gen_1432
<a, cons, s>(q_gen_1394, q_gen_1434) -> q_gen_1432
<a, cons, s>(q_gen_1394, q_gen_1448) -> q_gen_1432
<b, cons, s>(q_gen_1394, q_gen_1434) -> q_gen_1432
}

Datatype: <elt, eltlist, nat>
Convolution form: right
}}}
  ;  delete_all -> 
{{{
Q={q_gen_1377, q_gen_1384, q_gen_1385, q_gen_1387, q_gen_1388, q_gen_1409, q_gen_1419, q_gen_1429, q_gen_1446, q_gen_1456},
Q_f={q_gen_1377},
Delta=
{
<cons>(q_gen_1385, q_gen_1384) -> q_gen_1384
<nil>() -> q_gen_1384
<a>() -> q_gen_1385
<b>() -> q_gen_1385
<cons, cons>(q_gen_1429, q_gen_1387) -> q_gen_1387
<cons, cons>(q_gen_1446, q_gen_1387) -> q_gen_1387
<cons, cons>(q_gen_1446, q_gen_1419) -> q_gen_1387
<nil, nil>() -> q_gen_1387
<a, a>() -> q_gen_1388
<b, b>() -> q_gen_1409
<cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1419
<cons, cons>(q_gen_1388, q_gen_1419) -> q_gen_1419
<cons, cons>(q_gen_1409, q_gen_1387) -> q_gen_1419
<cons, cons>(q_gen_1409, q_gen_1419) -> q_gen_1419
<cons, cons>(q_gen_1429, q_gen_1419) -> q_gen_1419
<cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1419
<a, b>() -> q_gen_1429
<b, a>() -> q_gen_1446
<a, cons, cons>(q_gen_1409, q_gen_1387) -> q_gen_1377
<a, cons, cons>(q_gen_1409, q_gen_1419) -> q_gen_1377
<a, cons, cons>(q_gen_1429, q_gen_1419) -> q_gen_1377
<a, cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1377
<a, nil, nil>() -> q_gen_1377
<b, cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1377
<b, cons, cons>(q_gen_1388, q_gen_1419) -> q_gen_1377
<b, cons, cons>(q_gen_1446, q_gen_1419) -> q_gen_1377
<b, cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1377
<b, nil, nil>() -> q_gen_1377
<a, cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1456
<a, cons, cons>(q_gen_1429, q_gen_1387) -> q_gen_1456
<b, cons, cons>(q_gen_1409, q_gen_1387) -> q_gen_1456
<b, cons, cons>(q_gen_1409, q_gen_1419) -> q_gen_1456
<b, cons, cons>(q_gen_1429, q_gen_1387) -> q_gen_1456
<b, cons, cons>(q_gen_1429, q_gen_1419) -> q_gen_1456
<b, cons, cons>(q_gen_1446, q_gen_1387) -> q_gen_1456
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  delete_one -> 
{{{
Q={q_gen_1373, q_gen_1374, q_gen_1375, q_gen_1381, q_gen_1382},
Q_f={q_gen_1373},
Delta=
{
<nil>() -> q_gen_1374
<a>() -> q_gen_1375
<b>() -> q_gen_1375
<cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1381
<cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1381
<nil, nil>() -> q_gen_1381
<a, a>() -> q_gen_1382
<a, b>() -> q_gen_1382
<b, a>() -> q_gen_1382
<b, b>() -> q_gen_1382
<a, cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1373
<a, cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1373
<a, nil, nil>() -> q_gen_1373
<b, cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1373
<b, cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1373
<b, nil, nil>() -> q_gen_1373
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  leqnat -> 
{{{
Q={q_gen_1372, q_gen_1396, q_gen_1438},
Q_f={q_gen_1372},
Delta=
{
<s>(q_gen_1396) -> q_gen_1396
<z>() -> q_gen_1396
<s, s>(q_gen_1372) -> q_gen_1372
<z, s>(q_gen_1396) -> q_gen_1372
<z, z>() -> q_gen_1372
<s, s>(q_gen_1438) -> q_gen_1438
<s, z>(q_gen_1396) -> q_gen_1438
}

Datatype: <nat, nat>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist, eq_nat}
_|

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 51
() -> delete_all([x, nil, nil]) -> 51
() -> delete_one([x, nil, nil]) -> 51
() -> delete_one([y, cons(y, r), r]) -> 51
() -> leqnat([z, n2]) -> 51
(count([x, l, _fh]) /\ delete_all([x, l, _eh]) /\ delete_one([x, l, _eh])) -> leqnat([_fh, s(z)]) -> 52
(count([x, r, _yg]) /\ not eq_elt([x, y])) -> count([x, cons(y, r), _yg]) -> 52
(count([y, r, _xg])) -> count([y, cons(y, r), s(_xg)]) -> 55
(delete_all([x, r, _sg]) /\ not eq_elt([x, y])) -> delete_all([x, cons(y, r), cons(y, _sg)]) -> 53
(delete_all([y, r, _rg])) -> delete_all([y, cons(y, r), _rg]) -> 53
(delete_one([x, r, _mg]) /\ not eq_elt([x, y])) -> delete_one([x, cons(y, r), cons(y, _mg)]) -> 52
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 52
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 52
(leqnat([s(nn1), z])) -> BOT -> 52
}
Sat witness: Found: ((count([y, r, _xg])) -> count([y, cons(y, r), s(_xg)]), {
_xg -> s(z)  ;  r -> cons(a, cons(b, nil))  ;  y -> a
})

-------------------------------------------
Step 98, which took 3.012155 s (model generation: 3.011853,  model checking: 0.000302):

Model:
|_
{
count -> 
{{{
Q={q_gen_1378, q_gen_1389, q_gen_1390, q_gen_1391, q_gen_1393, q_gen_1394, q_gen_1421, q_gen_1423, q_gen_1432, q_gen_1434, q_gen_1448, q_gen_1482, q_gen_1497, q_gen_1508, q_gen_1535},
Q_f={q_gen_1378, q_gen_1389, q_gen_1482, q_gen_1508},
Delta=
{
<b>() -> q_gen_1391
<nil>() -> q_gen_1393
<a>() -> q_gen_1394
<cons>(q_gen_1391, q_gen_1393) -> q_gen_1423
<cons>(q_gen_1391, q_gen_1423) -> q_gen_1423
<cons>(q_gen_1394, q_gen_1393) -> q_gen_1423
<cons>(q_gen_1394, q_gen_1423) -> q_gen_1423
<cons, s>(q_gen_1394, q_gen_1421) -> q_gen_1390
<nil, z>() -> q_gen_1390
<cons, s>(q_gen_1391, q_gen_1421) -> q_gen_1421
<cons, s>(q_gen_1394, q_gen_1390) -> q_gen_1421
<cons, z>(q_gen_1391, q_gen_1393) -> q_gen_1421
<cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1434
<cons, s>(q_gen_1391, q_gen_1434) -> q_gen_1434
<cons, s>(q_gen_1391, q_gen_1448) -> q_gen_1448
<cons, s>(q_gen_1394, q_gen_1448) -> q_gen_1448
<cons, s>(q_gen_1394, q_gen_1497) -> q_gen_1448
<cons, z>(q_gen_1391, q_gen_1423) -> q_gen_1448
<cons, z>(q_gen_1394, q_gen_1393) -> q_gen_1448
<cons, s>(q_gen_1391, q_gen_1497) -> q_gen_1497
<cons, s>(q_gen_1394, q_gen_1434) -> q_gen_1497
<cons, z>(q_gen_1394, q_gen_1423) -> q_gen_1497
<a, cons, s>(q_gen_1391, q_gen_1448) -> q_gen_1378
<a, cons, s>(q_gen_1394, q_gen_1390) -> q_gen_1378
<a, cons, s>(q_gen_1394, q_gen_1421) -> q_gen_1378
<a, cons, s>(q_gen_1394, q_gen_1497) -> q_gen_1378
<a, cons, z>(q_gen_1391, q_gen_1423) -> q_gen_1378
<b, cons, s>(q_gen_1391, q_gen_1434) -> q_gen_1378
<b, cons, s>(q_gen_1391, q_gen_1448) -> q_gen_1378
<b, cons, s>(q_gen_1394, q_gen_1421) -> q_gen_1378
<b, cons, z>(q_gen_1394, q_gen_1423) -> q_gen_1378
<b, nil, z>() -> q_gen_1378
<a, cons, s>(q_gen_1391, q_gen_1497) -> q_gen_1389
<a, cons, z>(q_gen_1391, q_gen_1393) -> q_gen_1389
<a, nil, z>() -> q_gen_1389
<b, cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1389
<b, cons, z>(q_gen_1394, q_gen_1393) -> q_gen_1389
<a, cons, s>(q_gen_1391, q_gen_1390) -> q_gen_1432
<a, cons, s>(q_gen_1391, q_gen_1421) -> q_gen_1432
<a, cons, s>(q_gen_1391, q_gen_1434) -> q_gen_1432
<a, cons, s>(q_gen_1394, q_gen_1434) -> q_gen_1432
<b, cons, s>(q_gen_1391, q_gen_1421) -> q_gen_1432
<b, cons, s>(q_gen_1394, q_gen_1434) -> q_gen_1432
<b, cons, s>(q_gen_1394, q_gen_1448) -> q_gen_1482
<a, cons, s>(q_gen_1394, q_gen_1448) -> q_gen_1508
<b, cons, s>(q_gen_1394, q_gen_1497) -> q_gen_1508
<b, cons, s>(q_gen_1391, q_gen_1497) -> q_gen_1535
}

Datatype: <elt, eltlist, nat>
Convolution form: right
}}}
  ;  delete_all -> 
{{{
Q={q_gen_1377, q_gen_1383, q_gen_1384, q_gen_1385, q_gen_1387, q_gen_1388, q_gen_1409, q_gen_1419, q_gen_1427, q_gen_1429, q_gen_1464, q_gen_1500},
Q_f={q_gen_1377, q_gen_1383, q_gen_1427},
Delta=
{
<cons>(q_gen_1385, q_gen_1384) -> q_gen_1384
<nil>() -> q_gen_1384
<a>() -> q_gen_1385
<b>() -> q_gen_1385
<cons, cons>(q_gen_1409, q_gen_1387) -> q_gen_1387
<cons, cons>(q_gen_1429, q_gen_1387) -> q_gen_1387
<cons, cons>(q_gen_1429, q_gen_1419) -> q_gen_1387
<nil, nil>() -> q_gen_1387
<a, a>() -> q_gen_1388
<b, a>() -> q_gen_1388
<b, b>() -> q_gen_1409
<cons, cons>(q_gen_1388, q_gen_1500) -> q_gen_1419
<cons, cons>(q_gen_1409, q_gen_1419) -> q_gen_1419
<cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1419
<a, b>() -> q_gen_1429
<cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1500
<cons, cons>(q_gen_1388, q_gen_1419) -> q_gen_1500
<cons, cons>(q_gen_1409, q_gen_1500) -> q_gen_1500
<a, cons, cons>(q_gen_1409, q_gen_1387) -> q_gen_1377
<a, cons, cons>(q_gen_1429, q_gen_1500) -> q_gen_1377
<b, cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1377
<b, nil, nil>() -> q_gen_1377
<a, cons, cons>(q_gen_1409, q_gen_1419) -> q_gen_1383
<a, cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1383
<a, nil, nil>() -> q_gen_1383
<b, cons, cons>(q_gen_1388, q_gen_1500) -> q_gen_1383
<b, cons, nil>(q_gen_1385, q_gen_1384) -> q_gen_1383
<a, cons, cons>(q_gen_1429, q_gen_1419) -> q_gen_1427
<b, cons, cons>(q_gen_1388, q_gen_1419) -> q_gen_1427
<b, cons, cons>(q_gen_1409, q_gen_1387) -> q_gen_1427
<a, cons, cons>(q_gen_1388, q_gen_1387) -> q_gen_1464
<a, cons, cons>(q_gen_1409, q_gen_1500) -> q_gen_1464
<a, cons, cons>(q_gen_1429, q_gen_1387) -> q_gen_1464
<b, cons, cons>(q_gen_1409, q_gen_1419) -> q_gen_1464
<b, cons, cons>(q_gen_1429, q_gen_1387) -> q_gen_1464
<b, cons, cons>(q_gen_1429, q_gen_1419) -> q_gen_1464
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  delete_one -> 
{{{
Q={q_gen_1373, q_gen_1374, q_gen_1375, q_gen_1376, q_gen_1381, q_gen_1382, q_gen_1413, q_gen_1426, q_gen_1443, q_gen_1473},
Q_f={q_gen_1373, q_gen_1376, q_gen_1443},
Delta=
{
<nil>() -> q_gen_1374
<a>() -> q_gen_1375
<b>() -> q_gen_1375
<cons, cons>(q_gen_1382, q_gen_1413) -> q_gen_1381
<cons, cons>(q_gen_1426, q_gen_1381) -> q_gen_1381
<nil, nil>() -> q_gen_1381
<a, a>() -> q_gen_1382
<b, b>() -> q_gen_1382
<cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1413
<cons, cons>(q_gen_1426, q_gen_1413) -> q_gen_1413
<cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1413
<a, b>() -> q_gen_1426
<b, a>() -> q_gen_1426
<a, cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1373
<a, cons, cons>(q_gen_1382, q_gen_1413) -> q_gen_1373
<b, cons, cons>(q_gen_1382, q_gen_1381) -> q_gen_1373
<b, cons, cons>(q_gen_1382, q_gen_1413) -> q_gen_1373
<b, cons, cons>(q_gen_1426, q_gen_1413) -> q_gen_1373
<b, cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1373
<a, cons, nil>(q_gen_1375, q_gen_1374) -> q_gen_1376
<a, nil, nil>() -> q_gen_1376
<b, nil, nil>() -> q_gen_1376
<a, cons, cons>(q_gen_1426, q_gen_1381) -> q_gen_1443
<a, cons, cons>(q_gen_1426, q_gen_1413) -> q_gen_1443
<b, cons, cons>(q_gen_1426, q_gen_1381) -> q_gen_1473
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  leqnat -> 
{{{
Q={q_gen_1372, q_gen_1396, q_gen_1438},
Q_f={q_gen_1372},
Delta=
{
<s>(q_gen_1396) -> q_gen_1396
<z>() -> q_gen_1396
<s, s>(q_gen_1372) -> q_gen_1372
<z, s>(q_gen_1396) -> q_gen_1372
<z, z>() -> q_gen_1372
<s, s>(q_gen_1438) -> q_gen_1438
<s, z>(q_gen_1396) -> q_gen_1438
}

Datatype: <nat, nat>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist, eq_nat}
_|

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 51
() -> delete_all([x, nil, nil]) -> 51
() -> delete_one([x, nil, nil]) -> 51
() -> delete_one([y, cons(y, r), r]) -> 54
() -> leqnat([z, n2]) -> 52
(count([x, l, _fh]) /\ delete_all([x, l, _eh]) /\ delete_one([x, l, _eh])) -> leqnat([_fh, s(z)]) -> 52
(count([x, r, _yg]) /\ not eq_elt([x, y])) -> count([x, cons(y, r), _yg]) -> 52
(count([y, r, _xg])) -> count([y, cons(y, r), s(_xg)]) -> 55
(delete_all([x, r, _sg]) /\ not eq_elt([x, y])) -> delete_all([x, cons(y, r), cons(y, _sg)]) -> 53
(delete_all([y, r, _rg])) -> delete_all([y, cons(y, r), _rg]) -> 53
(delete_one([x, r, _mg]) /\ not eq_elt([x, y])) -> delete_one([x, cons(y, r), cons(y, _mg)]) -> 52
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 52
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 52
(leqnat([s(nn1), z])) -> BOT -> 52
}
Sat witness: Found: (() -> delete_one([y, cons(y, r), r]), {
r -> cons(a, cons(a, nil))  ;  y -> b
})

Total time: 63.874867
Reason for stopping: DontKnow. Stopped because: timeout