Solving ../../benchmarks/true/isaplanner_prop19.smt2...

Inference procedure has parameters:
Ice fuel: 200
Timeout: 30s
Convolution: complete


Learning problem is:

env: {
elt -> {a, b}  ;  eltlist -> {cons, nil}  ;  nat -> {s, z}
}
definition:
{
(drop, F:
{() -> drop([s(u), nil, nil])
() -> drop([z, l, l])
(drop([u, x3, _ega])) -> drop([s(u), cons(x2, x3), _ega])}
(drop([_fga, _gga, _hga]) /\ drop([_fga, _gga, _iga])) -> eq_eltlist([_hga, _iga])
)
(length, F:
{() -> length([nil, z])
(length([ll, _jga])) -> length([cons(x, ll), s(_jga)])}
(length([_kga, _lga]) /\ length([_kga, _mga])) -> eq_nat([_lga, _mga])
)
(minus, F:
{() -> minus([s(u), z, s(u)])
() -> minus([z, y, z])
(minus([u, x2, _nga])) -> minus([s(u), s(x2), _nga])}
(minus([_oga, _pga, _qga]) /\ minus([_oga, _pga, _rga])) -> eq_nat([_qga, _rga])
)
}

properties:
{(drop([n, l1, _sga]) /\ length([_sga, _tga]) /\ length([l1, _uga]) /\ minus([_uga, n, _vga])) -> eq_nat([_tga, _vga])}


over-approximation: {drop, length, minus}
under-approximation: {}

Clause system for inference is:

{
() -> drop([s(u), nil, nil]) -> 0  ;  () -> drop([z, l, l]) -> 0  ;  () -> length([nil, z]) -> 0  ;  () -> minus([s(u), z, s(u)]) -> 0  ;  () -> minus([z, y, z]) -> 0  ;  (drop([n, l1, _sga]) /\ length([_sga, _tga]) /\ length([l1, _uga]) /\ minus([_uga, n, _vga])) -> eq_nat([_tga, _vga]) -> 0  ;  (drop([u, x3, _ega])) -> drop([s(u), cons(x2, x3), _ega]) -> 0  ;  (length([ll, _jga])) -> length([cons(x, ll), s(_jga)]) -> 0  ;  (minus([u, x2, _nga])) -> minus([s(u), s(x2), _nga]) -> 0
}


Solving took 30.007865 seconds.
DontKnow. Stopped because: timeout
Working model:
|_
{
drop -> 
{{{
Q={q_gen_1352, q_gen_1353, q_gen_1354, q_gen_1358, q_gen_1359, q_gen_1360, q_gen_1365, q_gen_1366, q_gen_1367, q_gen_1368, q_gen_1369, q_gen_1370, q_gen_1371, q_gen_1376, q_gen_1377, q_gen_1381, q_gen_1382, q_gen_1383, q_gen_1384, q_gen_1390, q_gen_1391, q_gen_1392, q_gen_1394, q_gen_1395, q_gen_1396, q_gen_1397, q_gen_1398, q_gen_1399, q_gen_1407, q_gen_1408, q_gen_1410, q_gen_1411, q_gen_1412, q_gen_1413, q_gen_1414, q_gen_1421, q_gen_1422, q_gen_1423, q_gen_1424, q_gen_1426, q_gen_1427, q_gen_1428, q_gen_1430, q_gen_1431, q_gen_1432, q_gen_1433, q_gen_1434, q_gen_1435, q_gen_1436, q_gen_1437, q_gen_1439, q_gen_1440, q_gen_1441, q_gen_1442, q_gen_1443, q_gen_1446, q_gen_1447, q_gen_1448, q_gen_1451, q_gen_1452, q_gen_1453, q_gen_1454, q_gen_1455, q_gen_1456, q_gen_1457, q_gen_1458, q_gen_1461, q_gen_1462, q_gen_1463, q_gen_1464, q_gen_1465, q_gen_1466, q_gen_1467, q_gen_1468, q_gen_1471, q_gen_1472, q_gen_1473, q_gen_1477, q_gen_1478, q_gen_1479, q_gen_1480, q_gen_1481, q_gen_1482, q_gen_1494, q_gen_1495, q_gen_1496, q_gen_1499, q_gen_1500, q_gen_1501, q_gen_1502, q_gen_1503, q_gen_1504, q_gen_1508, q_gen_1509, q_gen_1510, q_gen_1511, q_gen_1512, q_gen_1513, q_gen_1518, q_gen_1519, q_gen_1520, q_gen_1521, q_gen_1522, q_gen_1523, q_gen_1524, q_gen_1525, q_gen_1526, q_gen_1527, q_gen_1528, q_gen_1529, q_gen_1530, q_gen_1531, q_gen_1532, q_gen_1533, q_gen_1534, q_gen_1535, q_gen_1536, q_gen_1537, q_gen_1538, q_gen_1547, q_gen_1548, q_gen_1549, 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_f={},
Delta=
{
<z>() -> q_gen_1354
<s>(q_gen_1354) -> q_gen_1371
<nil>() -> q_gen_1397
<b>() -> q_gen_1398
<a>() -> q_gen_1413
<cons>(q_gen_1398, q_gen_1397) -> q_gen_1442
<s>(q_gen_1371) -> q_gen_1482
<cons>(q_gen_1413, q_gen_1442) -> q_gen_1532
<cons>(q_gen_1413, q_gen_1397) -> q_gen_1559
<z, nil>() -> q_gen_1359
<z, b>() -> q_gen_1360
<nil, nil>() -> q_gen_1366
<nil, b>() -> q_gen_1367
<b, nil>() -> q_gen_1368
<b, b>() -> q_gen_1369
<z, a>() -> q_gen_1377
<nil, a>() -> q_gen_1382
<a, nil>() -> q_gen_1383
<a, a>() -> q_gen_1384
<s, nil>(q_gen_1354) -> q_gen_1391
<s, b>(q_gen_1354) -> q_gen_1392
<cons, cons>(q_gen_1369, q_gen_1368, q_gen_1367, q_gen_1366) -> q_gen_1395
<cons, b>(q_gen_1398, q_gen_1397) -> q_gen_1396
<b, cons>(q_gen_1398, q_gen_1397) -> q_gen_1399
<s, a>(q_gen_1354) -> q_gen_1408
<cons, cons>(q_gen_1384, q_gen_1383, q_gen_1382, q_gen_1366) -> q_gen_1411
<cons, b>(q_gen_1413, q_gen_1397) -> q_gen_1412
<b, cons>(q_gen_1413, q_gen_1397) -> q_gen_1414
<s, cons>(q_gen_1377, q_gen_1359) -> q_gen_1422
<s, cons>(q_gen_1360, q_gen_1359) -> q_gen_1424
<cons, a>(q_gen_1398, q_gen_1397) -> q_gen_1427
<a, cons>(q_gen_1398, q_gen_1397) -> q_gen_1428
<s, cons>(q_gen_1408, q_gen_1391) -> q_gen_1436
<s, b>(q_gen_1371) -> q_gen_1437
<cons, cons>(q_gen_1369, q_gen_1399, q_gen_1396, q_gen_1395) -> q_gen_1440
<cons, b>(q_gen_1398, q_gen_1442) -> q_gen_1441
<b, cons>(q_gen_1398, q_gen_1442) -> q_gen_1443
<z, cons>(q_gen_1413, q_gen_1397) -> q_gen_1448
<z, cons>(q_gen_1398, q_gen_1397) -> q_gen_1458
<s, cons>(q_gen_1360, q_gen_1458) -> q_gen_1465
<s, a>(q_gen_1371) -> q_gen_1478
<s, cons>(q_gen_1437, q_gen_1436) -> q_gen_1480
<s, a>(q_gen_1482) -> q_gen_1481
<s, cons>(q_gen_1392, q_gen_1424) -> q_gen_1504
<cons, a>(q_gen_1398, q_gen_1442) -> q_gen_1524
<a, cons>(q_gen_1398, q_gen_1442) -> q_gen_1525
<cons, cons>(q_gen_1369, q_gen_1530, q_gen_1529, q_gen_1528) -> q_gen_1527
<cons, cons>(q_gen_1384, q_gen_1428, q_gen_1427, q_gen_1395) -> q_gen_1528
<cons, b>(q_gen_1413, q_gen_1442) -> q_gen_1529
<b, cons>(q_gen_1413, q_gen_1442) -> q_gen_1530
<cons, b>(q_gen_1398, q_gen_1532) -> q_gen_1531
<b, cons>(q_gen_1398, q_gen_1532) -> q_gen_1533
<z, cons>(q_gen_1398, q_gen_1442) -> q_gen_1535
<cons, nil>(q_gen_1398, q_gen_1397) -> q_gen_1551
<cons, a>(q_gen_1413, q_gen_1397) -> q_gen_1554
<a, cons>(q_gen_1413, q_gen_1397) -> q_gen_1555
<cons, cons>(q_gen_1384, q_gen_1555, q_gen_1554, q_gen_1411) -> q_gen_1557
<cons, b>(q_gen_1413, q_gen_1559) -> q_gen_1558
<b, cons>(q_gen_1413, q_gen_1559) -> q_gen_1560
<z, nil, nil>() -> q_gen_1352
<s, nil, nil>(q_gen_1354) -> q_gen_1353
<s, cons, nil>(q_gen_1360, q_gen_1359) -> q_gen_1358
<z, cons, cons>(q_gen_1369, q_gen_1368, q_gen_1367, q_gen_1366) -> q_gen_1365
<s, nil, nil>(q_gen_1371) -> q_gen_1370
<s, cons, nil>(q_gen_1377, q_gen_1359) -> q_gen_1376
<z, cons, cons>(q_gen_1384, q_gen_1383, q_gen_1382, q_gen_1366) -> q_gen_1381
<s, cons, nil>(q_gen_1392, q_gen_1391) -> q_gen_1390
<z, cons, cons>(q_gen_1369, q_gen_1399, q_gen_1396, q_gen_1395) -> q_gen_1394
<s, cons, nil>(q_gen_1408, q_gen_1391) -> q_gen_1407
<z, cons, cons>(q_gen_1369, q_gen_1414, q_gen_1412, q_gen_1411) -> q_gen_1410
<s, cons, nil>(q_gen_1392, q_gen_1422) -> q_gen_1421
<s, cons, nil>(q_gen_1408, q_gen_1424) -> q_gen_1423
<z, cons, cons>(q_gen_1384, q_gen_1428, q_gen_1427, q_gen_1395) -> q_gen_1426
<s, cons, cons>(q_gen_1434, q_gen_1433, q_gen_1432, q_gen_1431) -> q_gen_1430
<z, cons, nil>(q_gen_1398, q_gen_1397) -> q_gen_1431
<z, cons, b>(q_gen_1398, q_gen_1397) -> q_gen_1432
<z, b, nil>() -> q_gen_1433
<z, b, b>() -> q_gen_1434
<s, cons, nil>(q_gen_1437, q_gen_1436) -> q_gen_1435
<z, cons, cons>(q_gen_1369, q_gen_1443, q_gen_1441, q_gen_1440) -> q_gen_1439
<z, cons, nil>(q_gen_1413, q_gen_1397) -> q_gen_1446
<s, cons, nil>(q_gen_1360, q_gen_1448) -> q_gen_1447
<s, cons, cons>(q_gen_1434, q_gen_1433, q_gen_1452, q_gen_1446) -> q_gen_1451
<z, cons, b>(q_gen_1413, q_gen_1397) -> q_gen_1452
<s, cons, cons>(q_gen_1456, q_gen_1455, q_gen_1454, q_gen_1447) -> q_gen_1453
<s, cons, b>(q_gen_1360, q_gen_1448) -> q_gen_1454
<s, b, nil>(q_gen_1354) -> q_gen_1455
<s, b, b>(q_gen_1354) -> q_gen_1456
<s, cons, nil>(q_gen_1360, q_gen_1458) -> q_gen_1457
<s, cons, cons>(q_gen_1456, q_gen_1455, q_gen_1462, q_gen_1457) -> q_gen_1461
<s, cons, b>(q_gen_1360, q_gen_1458) -> q_gen_1462
<s, cons, cons>(q_gen_1468, q_gen_1467, q_gen_1466, q_gen_1464) -> q_gen_1463
<s, cons, nil>(q_gen_1392, q_gen_1465) -> q_gen_1464
<s, cons, b>(q_gen_1392, q_gen_1465) -> q_gen_1466
<s, b, nil>(q_gen_1371) -> q_gen_1467
<s, b, b>(q_gen_1371) -> q_gen_1468
<s, cons, nil>(q_gen_1392, q_gen_1424) -> q_gen_1471
<s, cons, nil>(q_gen_1377, q_gen_1458) -> q_gen_1472
<s, cons, nil>(q_gen_1408, q_gen_1422) -> q_gen_1473
<s, cons, nil>(q_gen_1478, q_gen_1436) -> q_gen_1477
<s, cons, nil>(q_gen_1481, q_gen_1480) -> q_gen_1479
<s, cons, cons>(q_gen_1496, q_gen_1495, q_gen_1454, q_gen_1447) -> q_gen_1494
<s, a, nil>(q_gen_1354) -> q_gen_1495
<s, a, b>(q_gen_1354) -> q_gen_1496
<s, cons, cons>(q_gen_1502, q_gen_1501, q_gen_1500, q_gen_1446) -> q_gen_1499
<z, cons, a>(q_gen_1413, q_gen_1397) -> q_gen_1500
<z, a, nil>() -> q_gen_1501
<z, a, a>() -> q_gen_1502
<s, cons, nil>(q_gen_1437, q_gen_1504) -> q_gen_1503
<s, cons, cons>(q_gen_1511, q_gen_1455, q_gen_1510, q_gen_1509) -> q_gen_1508
<s, cons, nil>(q_gen_1377, q_gen_1448) -> q_gen_1509
<s, cons, a>(q_gen_1377, q_gen_1448) -> q_gen_1510
<s, b, a>(q_gen_1354) -> q_gen_1511
<s, cons, cons>(q_gen_1502, q_gen_1501, q_gen_1513, q_gen_1431) -> q_gen_1512
<z, cons, a>(q_gen_1398, q_gen_1397) -> q_gen_1513
<s, cons, cons>(q_gen_1519, q_gen_1495, q_gen_1510, q_gen_1509) -> q_gen_1518
<s, a, a>(q_gen_1354) -> q_gen_1519
<s, cons, cons>(q_gen_1434, q_gen_1433, q_gen_1522, q_gen_1521) -> q_gen_1520
<z, cons, nil>(q_gen_1398, q_gen_1442) -> q_gen_1521
<z, cons, b>(q_gen_1398, q_gen_1442) -> q_gen_1522
<z, cons, cons>(q_gen_1384, q_gen_1525, q_gen_1524, q_gen_1440) -> q_gen_1523
<z, cons, cons>(q_gen_1369, q_gen_1533, q_gen_1531, q_gen_1527) -> q_gen_1526
<s, cons, nil>(q_gen_1360, q_gen_1535) -> q_gen_1534
<z, cons, nil>(q_gen_1413, q_gen_1442) -> q_gen_1536
<s, cons, cons>(q_gen_1538, q_gen_1433, q_gen_1500, q_gen_1446) -> q_gen_1537
<z, b, a>() -> q_gen_1538
<s, cons, cons>(q_gen_1548, q_gen_1501, q_gen_1432, q_gen_1431) -> q_gen_1547
<z, a, b>() -> q_gen_1548
<s, cons, cons>(q_gen_1434, q_gen_1552, q_gen_1522, q_gen_1550) -> q_gen_1549
<z, cons, cons>(q_gen_1369, q_gen_1368, q_gen_1396, q_gen_1551) -> q_gen_1550
<z, b, cons>(q_gen_1398, q_gen_1397) -> q_gen_1552
<z, cons, cons>(q_gen_1384, q_gen_1555, q_gen_1554, q_gen_1411) -> q_gen_1553
<z, cons, cons>(q_gen_1369, q_gen_1560, q_gen_1558, q_gen_1557) -> q_gen_1556
}

Datatype: <nat, eltlist, eltlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_1351, q_gen_1356, q_gen_1357, q_gen_1374, q_gen_1375, q_gen_1387, q_gen_1388, q_gen_1389, q_gen_1405, q_gen_1406, q_gen_1417, q_gen_1418, q_gen_1419, q_gen_1420, q_gen_1483, q_gen_1484},
Q_f={},
Delta=
{
<z>() -> q_gen_1389
<s>(q_gen_1389) -> q_gen_1420
<nil, z>() -> q_gen_1351
<cons, s>(q_gen_1357, q_gen_1351) -> q_gen_1356
<b, z>() -> q_gen_1357
<cons, s>(q_gen_1375, q_gen_1351) -> q_gen_1374
<a, z>() -> q_gen_1375
<cons, s>(q_gen_1388, q_gen_1374) -> q_gen_1387
<b, s>(q_gen_1389) -> q_gen_1388
<cons, s>(q_gen_1406, q_gen_1356) -> q_gen_1405
<a, s>(q_gen_1389) -> q_gen_1406
<cons, s>(q_gen_1388, q_gen_1356) -> q_gen_1417
<cons, s>(q_gen_1419, q_gen_1417) -> q_gen_1418
<b, s>(q_gen_1420) -> q_gen_1419
<cons, s>(q_gen_1484, q_gen_1387) -> q_gen_1483
<a, s>(q_gen_1420) -> q_gen_1484
}

Datatype: <eltlist, nat>
Convolution form: complete
}}}
  ;  minus -> 
{{{
Q={q_gen_1348, q_gen_1349, q_gen_1350, q_gen_1355, q_gen_1361, q_gen_1362, q_gen_1363, q_gen_1364, q_gen_1372, q_gen_1373, q_gen_1378, q_gen_1379, q_gen_1380, q_gen_1385, q_gen_1386, q_gen_1393, q_gen_1400, q_gen_1401, q_gen_1402, q_gen_1403, q_gen_1404, q_gen_1409, q_gen_1415, q_gen_1416, q_gen_1425, q_gen_1429, q_gen_1438, q_gen_1444, q_gen_1445, q_gen_1449, q_gen_1450, q_gen_1459, q_gen_1460, q_gen_1469, q_gen_1470, q_gen_1474, q_gen_1475, q_gen_1476, q_gen_1485, q_gen_1486, q_gen_1487, q_gen_1488, q_gen_1489, q_gen_1490, q_gen_1491, q_gen_1492, q_gen_1493, q_gen_1497, q_gen_1498, q_gen_1505, q_gen_1506, q_gen_1507, q_gen_1514, q_gen_1515, q_gen_1516, q_gen_1517, q_gen_1539, q_gen_1540, q_gen_1541, q_gen_1542, q_gen_1543, q_gen_1544, q_gen_1545, q_gen_1546},
Q_f={},
Delta=
{
<z>() -> q_gen_1362
<s>(q_gen_1362) -> q_gen_1380
<s>(q_gen_1380) -> q_gen_1540
<z, z>() -> q_gen_1350
<s, s>(q_gen_1350) -> q_gen_1364
<z, s>(q_gen_1362) -> q_gen_1386
<z, s>(q_gen_1380) -> q_gen_1402
<s, z>(q_gen_1362) -> q_gen_1416
<s, s>(q_gen_1386) -> q_gen_1460
<s, s>(q_gen_1364) -> q_gen_1488
<s, s>(q_gen_1416) -> q_gen_1491
<s, z>(q_gen_1380) -> q_gen_1517
<z, z, z>() -> q_gen_1348
<s, z, s>(q_gen_1350) -> q_gen_1349
<s, s, z>(q_gen_1350) -> q_gen_1355
<z, s, z>(q_gen_1362) -> q_gen_1361
<s, z, s>(q_gen_1364) -> q_gen_1363
<s, s, s>(q_gen_1373) -> q_gen_1372
<s, z, z>(q_gen_1362) -> q_gen_1373
<s, s, s>(q_gen_1348) -> q_gen_1378
<z, s, z>(q_gen_1380) -> q_gen_1379
<s, s, z>(q_gen_1386) -> q_gen_1385
<s, z, s>(q_gen_1386) -> q_gen_1393
<s, s, s>(q_gen_1401) -> q_gen_1400
<s, z, s>(q_gen_1402) -> q_gen_1401
<s, s, s>(q_gen_1404) -> q_gen_1403
<s, s, s>(q_gen_1393) -> q_gen_1404
<s, s, s>(q_gen_1361) -> q_gen_1409
<s, s, z>(q_gen_1416) -> q_gen_1415
<s, s, s>(q_gen_1378) -> q_gen_1425
<s, s, s>(q_gen_1415) -> q_gen_1429
<s, s, s>(q_gen_1385) -> q_gen_1438
<s, s, s>(q_gen_1445) -> q_gen_1444
<s, z, s>(q_gen_1416) -> q_gen_1445
<s, s, s>(q_gen_1349) -> q_gen_1449
<s, s, s>(q_gen_1372) -> q_gen_1450
<s, s, z>(q_gen_1460) -> q_gen_1459
<s, s, s>(q_gen_1355) -> q_gen_1469
<s, s, s>(q_gen_1469) -> q_gen_1470
<s, s, s>(q_gen_1475) -> q_gen_1474
<s, s, s>(q_gen_1476) -> q_gen_1475
<s, z, z>(q_gen_1380) -> q_gen_1476
<s, s, s>(q_gen_1486) -> q_gen_1485
<s, s, s>(q_gen_1409) -> q_gen_1486
<s, z, s>(q_gen_1488) -> q_gen_1487
<s, s, s>(q_gen_1490) -> q_gen_1489
<s, z, s>(q_gen_1491) -> q_gen_1490
<s, s, s>(q_gen_1493) -> q_gen_1492
<s, s, z>(q_gen_1491) -> q_gen_1493
<s, s, s>(q_gen_1363) -> q_gen_1497
<s, s, s>(q_gen_1444) -> q_gen_1498
<s, s, s>(q_gen_1506) -> q_gen_1505
<s, s, z>(q_gen_1364) -> q_gen_1506
<s, s, s>(q_gen_1474) -> q_gen_1507
<s, s, s>(q_gen_1515) -> q_gen_1514
<s, s, s>(q_gen_1516) -> q_gen_1515
<s, z, s>(q_gen_1517) -> q_gen_1516
<z, s, z>(q_gen_1540) -> q_gen_1539
<s, z, s>(q_gen_1460) -> q_gen_1541
<s, s, s>(q_gen_1543) -> q_gen_1542
<s, s, s>(q_gen_1379) -> q_gen_1543
<s, s, s>(q_gen_1545) -> q_gen_1544
<s, s, s>(q_gen_1546) -> q_gen_1545
<s, s, z>(q_gen_1402) -> q_gen_1546
}

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

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

-------------------
STEPS:
-------------------------------------------
Step 0, which took 0.005618 s (model generation: 0.005130,  model checking: 0.000488):

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

}

Datatype: <nat, eltlist, eltlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={},
Q_f={},
Delta=
{

}

Datatype: <eltlist, nat>
Convolution form: complete
}}}
  ;  minus -> 
{{{
Q={},
Q_f={},
Delta=
{

}

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

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

Teacher's answer:
New clause system:
{
() -> drop([s(u), nil, nil]) -> 0  ;  () -> drop([z, l, l]) -> 0  ;  () -> length([nil, z]) -> 0  ;  () -> minus([s(u), z, s(u)]) -> 0  ;  () -> minus([z, y, z]) -> 3  ;  (drop([n, l1, _sga]) /\ length([_sga, _tga]) /\ length([l1, _uga]) /\ minus([_uga, n, _vga])) -> eq_nat([_tga, _vga]) -> 1  ;  (drop([u, x3, _ega])) -> drop([s(u), cons(x2, x3), _ega]) -> 1  ;  (length([ll, _jga])) -> length([cons(x, ll), s(_jga)]) -> 1  ;  (minus([u, x2, _nga])) -> minus([s(u), s(x2), _nga]) -> 1
}
Sat witness: Yes: (() -> minus([z, y, z]), {
y -> z
})

-------------------------------------------
Step 1, which took 0.004147 s (model generation: 0.004029,  model checking: 0.000118):

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

}

Datatype: <nat, eltlist, eltlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={},
Q_f={},
Delta=
{

}

Datatype: <eltlist, nat>
Convolution form: complete
}}}
  ;  minus -> 
{{{
Q={q_gen_1348},
Q_f={q_gen_1348},
Delta=
{
<z, z, z>() -> q_gen_1348
}

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

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

Teacher's answer:
New clause system:
{
() -> drop([s(u), nil, nil]) -> 0  ;  () -> drop([z, l, l]) -> 0  ;  () -> length([nil, z]) -> 0  ;  () -> minus([s(u), z, s(u)]) -> 3  ;  () -> minus([z, y, z]) -> 3  ;  (drop([n, l1, _sga]) /\ length([_sga, _tga]) /\ length([l1, _uga]) /\ minus([_uga, n, _vga])) -> eq_nat([_tga, _vga]) -> 1  ;  (drop([u, x3, _ega])) -> drop([s(u), cons(x2, x3), _ega]) -> 1  ;  (length([ll, _jga])) -> length([cons(x, ll), s(_jga)]) -> 1  ;  (minus([u, x2, _nga])) -> minus([s(u), s(x2), _nga]) -> 1
}
Sat witness: Yes: (() -> minus([s(u), z, s(u)]), {
u -> z
})

-------------------------------------------
Step 2, which took 0.004204 s (model generation: 0.004143,  model checking: 0.000061):

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

}

Datatype: <nat, eltlist, eltlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={},
Q_f={},
Delta=
{

}

Datatype: <eltlist, nat>
Convolution form: complete
}}}
  ;  minus -> 
{{{
Q={q_gen_1348, q_gen_1350},
Q_f={q_gen_1348},
Delta=
{
<z, z>() -> q_gen_1350
<s, z, s>(q_gen_1350) -> q_gen_1348
<z, z, z>() -> q_gen_1348
}

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

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

Teacher's answer:
New clause system:
{
() -> drop([s(u), nil, nil]) -> 0  ;  () -> drop([z, l, l]) -> 0  ;  () -> length([nil, z]) -> 3  ;  () -> minus([s(u), z, s(u)]) -> 3  ;  () -> minus([z, y, z]) -> 3  ;  (drop([n, l1, _sga]) /\ length([_sga, _tga]) /\ length([l1, _uga]) /\ minus([_uga, n, _vga])) -> eq_nat([_tga, _vga]) -> 1  ;  (drop([u, x3, _ega])) -> drop([s(u), cons(x2, x3), _ega]) -> 1  ;  (length([ll, _jga])) -> length([cons(x, ll), s(_jga)]) -> 1  ;  (minus([u, x2, _nga])) -> minus([s(u), s(x2), _nga]) -> 1
}
Sat witness: Yes: (() -> length([nil, z]), {

})

-------------------------------------------
Step 3, which took 0.004363 s (model generation: 0.003902,  model checking: 0.000461):

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

}

Datatype: <nat, eltlist, eltlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_1351},
Q_f={q_gen_1351},
Delta=
{
<nil, z>() -> q_gen_1351
}

Datatype: <eltlist, nat>
Convolution form: complete
}}}
  ;  minus -> 
{{{
Q={q_gen_1348, q_gen_1350},
Q_f={q_gen_1348},
Delta=
{
<z, z>() -> q_gen_1350
<s, z, s>(q_gen_1350) -> q_gen_1348
<z, z, z>() -> q_gen_1348
}

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

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

Teacher's answer:
New clause system:
{
() -> drop([s(u), nil, nil]) -> 0  ;  () -> drop([z, l, l]) -> 3  ;  () -> length([nil, z]) -> 3  ;  () -> minus([s(u), z, s(u)]) -> 3  ;  () -> minus([z, y, z]) -> 3  ;  (drop([n, l1, _sga]) /\ length([_sga, _tga]) /\ length([l1, _uga]) /\ minus([_uga, n, _vga])) -> eq_nat([_tga, _vga]) -> 1  ;  (drop([u, x3, _ega])) -> drop([s(u), cons(x2, x3), _ega]) -> 1  ;  (length([ll, _jga])) -> length([cons(x, ll), s(_jga)]) -> 1  ;  (minus([u, x2, _nga])) -> minus([s(u), s(x2), _nga]) -> 1
}
Sat witness: Yes: (() -> drop([z, l, l]), {
l -> nil
})

-------------------------------------------
Step 4, which took 0.004092 s (model generation: 0.003802,  model checking: 0.000290):

Model:
|_
{
drop -> 
{{{
Q={q_gen_1352},
Q_f={q_gen_1352},
Delta=
{
<z, nil, nil>() -> q_gen_1352
}

Datatype: <nat, eltlist, eltlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_1351},
Q_f={q_gen_1351},
Delta=
{
<nil, z>() -> q_gen_1351
}

Datatype: <eltlist, nat>
Convolution form: complete
}}}
  ;  minus -> 
{{{
Q={q_gen_1348, q_gen_1350},
Q_f={q_gen_1348},
Delta=
{
<z, z>() -> q_gen_1350
<s, z, s>(q_gen_1350) -> q_gen_1348
<z, z, z>() -> q_gen_1348
}

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

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

Teacher's answer:
New clause system:
{
() -> drop([s(u), nil, nil]) -> 3  ;  () -> drop([z, l, l]) -> 3  ;  () -> length([nil, z]) -> 3  ;  () -> minus([s(u), z, s(u)]) -> 3  ;  () -> minus([z, y, z]) -> 3  ;  (drop([n, l1, _sga]) /\ length([_sga, _tga]) /\ length([l1, _uga]) /\ minus([_uga, n, _vga])) -> eq_nat([_tga, _vga]) -> 1  ;  (drop([u, x3, _ega])) -> drop([s(u), cons(x2, x3), _ega]) -> 1  ;  (length([ll, _jga])) -> length([cons(x, ll), s(_jga)]) -> 1  ;  (minus([u, x2, _nga])) -> minus([s(u), s(x2), _nga]) -> 1
}
Sat witness: Yes: (() -> drop([s(u), nil, nil]), {
u -> z
})

-------------------------------------------
Step 5, which took 0.003688 s (model generation: 0.003588,  model checking: 0.000100):

Model:
|_
{
drop -> 
{{{
Q={q_gen_1352, q_gen_1354},
Q_f={q_gen_1352},
Delta=
{
<z>() -> q_gen_1354
<s, nil, nil>(q_gen_1354) -> q_gen_1352
<z, nil, nil>() -> q_gen_1352
}

Datatype: <nat, eltlist, eltlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_1351},
Q_f={q_gen_1351},
Delta=
{
<nil, z>() -> q_gen_1351
}

Datatype: <eltlist, nat>
Convolution form: complete
}}}
  ;  minus -> 
{{{
Q={q_gen_1348, q_gen_1350},
Q_f={q_gen_1348},
Delta=
{
<z, z>() -> q_gen_1350
<s, z, s>(q_gen_1350) -> q_gen_1348
<z, z, z>() -> q_gen_1348
}

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

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

Teacher's answer:
New clause system:
{
() -> drop([s(u), nil, nil]) -> 3  ;  () -> drop([z, l, l]) -> 3  ;  () -> length([nil, z]) -> 3  ;  () -> minus([s(u), z, s(u)]) -> 3  ;  () -> minus([z, y, z]) -> 3  ;  (drop([n, l1, _sga]) /\ length([_sga, _tga]) /\ length([l1, _uga]) /\ minus([_uga, n, _vga])) -> eq_nat([_tga, _vga]) -> 1  ;  (drop([u, x3, _ega])) -> drop([s(u), cons(x2, x3), _ega]) -> 1  ;  (length([ll, _jga])) -> length([cons(x, ll), s(_jga)]) -> 1  ;  (minus([u, x2, _nga])) -> minus([s(u), s(x2), _nga]) -> 4
}
Sat witness: Yes: ((minus([u, x2, _nga])) -> minus([s(u), s(x2), _nga]), {
_nga -> z  ;  u -> z  ;  x2 -> z
})

-------------------------------------------
Step 6, which took 0.006010 s (model generation: 0.005870,  model checking: 0.000140):

Model:
|_
{
drop -> 
{{{
Q={q_gen_1352, q_gen_1354},
Q_f={q_gen_1352},
Delta=
{
<z>() -> q_gen_1354
<s, nil, nil>(q_gen_1354) -> q_gen_1352
<z, nil, nil>() -> q_gen_1352
}

Datatype: <nat, eltlist, eltlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_1351},
Q_f={q_gen_1351},
Delta=
{
<nil, z>() -> q_gen_1351
}

Datatype: <eltlist, nat>
Convolution form: complete
}}}
  ;  minus -> 
{{{
Q={q_gen_1348, q_gen_1350},
Q_f={q_gen_1348},
Delta=
{
<z, z>() -> q_gen_1350
<s, s, z>(q_gen_1350) -> q_gen_1348
<s, z, s>(q_gen_1350) -> q_gen_1348
<z, z, z>() -> q_gen_1348
}

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

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

Teacher's answer:
New clause system:
{
() -> drop([s(u), nil, nil]) -> 3  ;  () -> drop([z, l, l]) -> 3  ;  () -> length([nil, z]) -> 3  ;  () -> minus([s(u), z, s(u)]) -> 3  ;  () -> minus([z, y, z]) -> 3  ;  (drop([n, l1, _sga]) /\ length([_sga, _tga]) /\ length([l1, _uga]) /\ minus([_uga, n, _vga])) -> eq_nat([_tga, _vga]) -> 1  ;  (drop([u, x3, _ega])) -> drop([s(u), cons(x2, x3), _ega]) -> 1  ;  (length([ll, _jga])) -> length([cons(x, ll), s(_jga)]) -> 4  ;  (minus([u, x2, _nga])) -> minus([s(u), s(x2), _nga]) -> 4
}
Sat witness: Yes: ((length([ll, _jga])) -> length([cons(x, ll), s(_jga)]), {
_jga -> z  ;  ll -> nil  ;  x -> b
})

-------------------------------------------
Step 7, which took 0.005248 s (model generation: 0.004919,  model checking: 0.000329):

Model:
|_
{
drop -> 
{{{
Q={q_gen_1352, q_gen_1354},
Q_f={q_gen_1352},
Delta=
{
<z>() -> q_gen_1354
<s, nil, nil>(q_gen_1354) -> q_gen_1352
<z, nil, nil>() -> q_gen_1352
}

Datatype: <nat, eltlist, eltlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_1351, q_gen_1357},
Q_f={q_gen_1351},
Delta=
{
<cons, s>(q_gen_1357, q_gen_1351) -> q_gen_1351
<nil, z>() -> q_gen_1351
<b, z>() -> q_gen_1357
}

Datatype: <eltlist, nat>
Convolution form: complete
}}}
  ;  minus -> 
{{{
Q={q_gen_1348, q_gen_1350},
Q_f={q_gen_1348},
Delta=
{
<z, z>() -> q_gen_1350
<s, s, z>(q_gen_1350) -> q_gen_1348
<s, z, s>(q_gen_1350) -> q_gen_1348
<z, z, z>() -> q_gen_1348
}

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

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

Teacher's answer:
New clause system:
{
() -> drop([s(u), nil, nil]) -> 3  ;  () -> drop([z, l, l]) -> 3  ;  () -> length([nil, z]) -> 3  ;  () -> minus([s(u), z, s(u)]) -> 3  ;  () -> minus([z, y, z]) -> 3  ;  (drop([n, l1, _sga]) /\ length([_sga, _tga]) /\ length([l1, _uga]) /\ minus([_uga, n, _vga])) -> eq_nat([_tga, _vga]) -> 1  ;  (drop([u, x3, _ega])) -> drop([s(u), cons(x2, x3), _ega]) -> 4  ;  (length([ll, _jga])) -> length([cons(x, ll), s(_jga)]) -> 4  ;  (minus([u, x2, _nga])) -> minus([s(u), s(x2), _nga]) -> 4
}
Sat witness: Yes: ((drop([u, x3, _ega])) -> drop([s(u), cons(x2, x3), _ega]), {
_ega -> nil  ;  u -> z  ;  x2 -> b  ;  x3 -> nil
})

-------------------------------------------
Step 8, which took 0.004447 s (model generation: 0.004163,  model checking: 0.000284):

Model:
|_
{
drop -> 
{{{
Q={q_gen_1352, q_gen_1354, q_gen_1359, q_gen_1360},
Q_f={q_gen_1352},
Delta=
{
<z>() -> q_gen_1354
<z, nil>() -> q_gen_1359
<z, b>() -> q_gen_1360
<s, cons, nil>(q_gen_1360, q_gen_1359) -> q_gen_1352
<s, nil, nil>(q_gen_1354) -> q_gen_1352
<z, nil, nil>() -> q_gen_1352
}

Datatype: <nat, eltlist, eltlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_1351, q_gen_1357},
Q_f={q_gen_1351},
Delta=
{
<cons, s>(q_gen_1357, q_gen_1351) -> q_gen_1351
<nil, z>() -> q_gen_1351
<b, z>() -> q_gen_1357
}

Datatype: <eltlist, nat>
Convolution form: complete
}}}
  ;  minus -> 
{{{
Q={q_gen_1348, q_gen_1350},
Q_f={q_gen_1348},
Delta=
{
<z, z>() -> q_gen_1350
<s, s, z>(q_gen_1350) -> q_gen_1348
<s, z, s>(q_gen_1350) -> q_gen_1348
<z, z, z>() -> q_gen_1348
}

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

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

Teacher's answer:
New clause system:
{
() -> drop([s(u), nil, nil]) -> 3  ;  () -> drop([z, l, l]) -> 3  ;  () -> length([nil, z]) -> 3  ;  () -> minus([s(u), z, s(u)]) -> 3  ;  () -> minus([z, y, z]) -> 6  ;  (drop([n, l1, _sga]) /\ length([_sga, _tga]) /\ length([l1, _uga]) /\ minus([_uga, n, _vga])) -> eq_nat([_tga, _vga]) -> 2  ;  (drop([u, x3, _ega])) -> drop([s(u), cons(x2, x3), _ega]) -> 4  ;  (length([ll, _jga])) -> length([cons(x, ll), s(_jga)]) -> 4  ;  (minus([u, x2, _nga])) -> minus([s(u), s(x2), _nga]) -> 4
}
Sat witness: Yes: (() -> minus([z, y, z]), {
y -> s(z)
})

-------------------------------------------
Step 9, which took 0.004568 s (model generation: 0.004366,  model checking: 0.000202):

Model:
|_
{
drop -> 
{{{
Q={q_gen_1352, q_gen_1354, q_gen_1359, q_gen_1360},
Q_f={q_gen_1352},
Delta=
{
<z>() -> q_gen_1354
<z, nil>() -> q_gen_1359
<z, b>() -> q_gen_1360
<s, cons, nil>(q_gen_1360, q_gen_1359) -> q_gen_1352
<s, nil, nil>(q_gen_1354) -> q_gen_1352
<z, nil, nil>() -> q_gen_1352
}

Datatype: <nat, eltlist, eltlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_1351, q_gen_1357},
Q_f={q_gen_1351},
Delta=
{
<cons, s>(q_gen_1357, q_gen_1351) -> q_gen_1351
<nil, z>() -> q_gen_1351
<b, z>() -> q_gen_1357
}

Datatype: <eltlist, nat>
Convolution form: complete
}}}
  ;  minus -> 
{{{
Q={q_gen_1348, q_gen_1350, q_gen_1362},
Q_f={q_gen_1348},
Delta=
{
<z>() -> q_gen_1362
<z, z>() -> q_gen_1350
<s, s, z>(q_gen_1350) -> q_gen_1348
<s, z, s>(q_gen_1350) -> q_gen_1348
<z, s, z>(q_gen_1362) -> q_gen_1348
<z, z, z>() -> q_gen_1348
}

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

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

Teacher's answer:
New clause system:
{
() -> drop([s(u), nil, nil]) -> 3  ;  () -> drop([z, l, l]) -> 3  ;  () -> length([nil, z]) -> 3  ;  () -> minus([s(u), z, s(u)]) -> 6  ;  () -> minus([z, y, z]) -> 6  ;  (drop([n, l1, _sga]) /\ length([_sga, _tga]) /\ length([l1, _uga]) /\ minus([_uga, n, _vga])) -> eq_nat([_tga, _vga]) -> 3  ;  (drop([u, x3, _ega])) -> drop([s(u), cons(x2, x3), _ega]) -> 4  ;  (length([ll, _jga])) -> length([cons(x, ll), s(_jga)]) -> 4  ;  (minus([u, x2, _nga])) -> minus([s(u), s(x2), _nga]) -> 4
}
Sat witness: Yes: (() -> minus([s(u), z, s(u)]), {
u -> s(z)
})

-------------------------------------------
Step 10, which took 0.005386 s (model generation: 0.004818,  model checking: 0.000568):

Model:
|_
{
drop -> 
{{{
Q={q_gen_1352, q_gen_1354, q_gen_1359, q_gen_1360},
Q_f={q_gen_1352},
Delta=
{
<z>() -> q_gen_1354
<z, nil>() -> q_gen_1359
<z, b>() -> q_gen_1360
<s, cons, nil>(q_gen_1360, q_gen_1359) -> q_gen_1352
<s, nil, nil>(q_gen_1354) -> q_gen_1352
<z, nil, nil>() -> q_gen_1352
}

Datatype: <nat, eltlist, eltlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_1351, q_gen_1357},
Q_f={q_gen_1351},
Delta=
{
<cons, s>(q_gen_1357, q_gen_1351) -> q_gen_1351
<nil, z>() -> q_gen_1351
<b, z>() -> q_gen_1357
}

Datatype: <eltlist, nat>
Convolution form: complete
}}}
  ;  minus -> 
{{{
Q={q_gen_1348, q_gen_1350, q_gen_1362},
Q_f={q_gen_1348},
Delta=
{
<z>() -> q_gen_1362
<s, s>(q_gen_1350) -> q_gen_1350
<z, z>() -> q_gen_1350
<s, s, z>(q_gen_1350) -> q_gen_1348
<s, z, s>(q_gen_1350) -> q_gen_1348
<z, s, z>(q_gen_1362) -> q_gen_1348
<z, z, z>() -> q_gen_1348
}

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

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

Teacher's answer:
New clause system:
{
() -> drop([s(u), nil, nil]) -> 3  ;  () -> drop([z, l, l]) -> 6  ;  () -> length([nil, z]) -> 4  ;  () -> minus([s(u), z, s(u)]) -> 6  ;  () -> minus([z, y, z]) -> 6  ;  (drop([n, l1, _sga]) /\ length([_sga, _tga]) /\ length([l1, _uga]) /\ minus([_uga, n, _vga])) -> eq_nat([_tga, _vga]) -> 4  ;  (drop([u, x3, _ega])) -> drop([s(u), cons(x2, x3), _ega]) -> 4  ;  (length([ll, _jga])) -> length([cons(x, ll), s(_jga)]) -> 4  ;  (minus([u, x2, _nga])) -> minus([s(u), s(x2), _nga]) -> 4
}
Sat witness: Yes: (() -> drop([z, l, l]), {
l -> cons(b, nil)
})

-------------------------------------------
Step 11, which took 0.004931 s (model generation: 0.004442,  model checking: 0.000489):

Model:
|_
{
drop -> 
{{{
Q={q_gen_1352, q_gen_1354, q_gen_1359, q_gen_1360, q_gen_1366, q_gen_1367, q_gen_1368, q_gen_1369},
Q_f={q_gen_1352},
Delta=
{
<z>() -> q_gen_1354
<z, nil>() -> q_gen_1359
<z, b>() -> q_gen_1360
<nil, nil>() -> q_gen_1366
<nil, b>() -> q_gen_1367
<b, nil>() -> q_gen_1368
<b, b>() -> q_gen_1369
<s, cons, nil>(q_gen_1360, q_gen_1359) -> q_gen_1352
<s, nil, nil>(q_gen_1354) -> q_gen_1352
<z, cons, cons>(q_gen_1369, q_gen_1368, q_gen_1367, q_gen_1366) -> q_gen_1352
<z, nil, nil>() -> q_gen_1352
}

Datatype: <nat, eltlist, eltlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_1351, q_gen_1357},
Q_f={q_gen_1351},
Delta=
{
<cons, s>(q_gen_1357, q_gen_1351) -> q_gen_1351
<nil, z>() -> q_gen_1351
<b, z>() -> q_gen_1357
}

Datatype: <eltlist, nat>
Convolution form: complete
}}}
  ;  minus -> 
{{{
Q={q_gen_1348, q_gen_1350, q_gen_1362},
Q_f={q_gen_1348},
Delta=
{
<z>() -> q_gen_1362
<s, s>(q_gen_1350) -> q_gen_1350
<z, z>() -> q_gen_1350
<s, s, z>(q_gen_1350) -> q_gen_1348
<s, z, s>(q_gen_1350) -> q_gen_1348
<z, s, z>(q_gen_1362) -> q_gen_1348
<z, z, z>() -> q_gen_1348
}

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

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

Teacher's answer:
New clause system:
{
() -> drop([s(u), nil, nil]) -> 6  ;  () -> drop([z, l, l]) -> 6  ;  () -> length([nil, z]) -> 4  ;  () -> minus([s(u), z, s(u)]) -> 6  ;  () -> minus([z, y, z]) -> 6  ;  (drop([n, l1, _sga]) /\ length([_sga, _tga]) /\ length([l1, _uga]) /\ minus([_uga, n, _vga])) -> eq_nat([_tga, _vga]) -> 4  ;  (drop([u, x3, _ega])) -> drop([s(u), cons(x2, x3), _ega]) -> 4  ;  (length([ll, _jga])) -> length([cons(x, ll), s(_jga)]) -> 4  ;  (minus([u, x2, _nga])) -> minus([s(u), s(x2), _nga]) -> 4
}
Sat witness: Yes: (() -> drop([s(u), nil, nil]), {
u -> s(z)
})

-------------------------------------------
Step 12, which took 0.004581 s (model generation: 0.004459,  model checking: 0.000122):

Model:
|_
{
drop -> 
{{{
Q={q_gen_1352, q_gen_1354, q_gen_1359, q_gen_1360, q_gen_1366, q_gen_1367, q_gen_1368, q_gen_1369},
Q_f={q_gen_1352},
Delta=
{
<s>(q_gen_1354) -> q_gen_1354
<z>() -> q_gen_1354
<z, nil>() -> q_gen_1359
<z, b>() -> q_gen_1360
<nil, nil>() -> q_gen_1366
<nil, b>() -> q_gen_1367
<b, nil>() -> q_gen_1368
<b, b>() -> q_gen_1369
<s, cons, nil>(q_gen_1360, q_gen_1359) -> q_gen_1352
<s, nil, nil>(q_gen_1354) -> q_gen_1352
<z, cons, cons>(q_gen_1369, q_gen_1368, q_gen_1367, q_gen_1366) -> q_gen_1352
<z, nil, nil>() -> q_gen_1352
}

Datatype: <nat, eltlist, eltlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_1351, q_gen_1357},
Q_f={q_gen_1351},
Delta=
{
<cons, s>(q_gen_1357, q_gen_1351) -> q_gen_1351
<nil, z>() -> q_gen_1351
<b, z>() -> q_gen_1357
}

Datatype: <eltlist, nat>
Convolution form: complete
}}}
  ;  minus -> 
{{{
Q={q_gen_1348, q_gen_1350, q_gen_1362},
Q_f={q_gen_1348},
Delta=
{
<z>() -> q_gen_1362
<s, s>(q_gen_1350) -> q_gen_1350
<z, z>() -> q_gen_1350
<s, s, z>(q_gen_1350) -> q_gen_1348
<s, z, s>(q_gen_1350) -> q_gen_1348
<z, s, z>(q_gen_1362) -> q_gen_1348
<z, z, z>() -> q_gen_1348
}

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

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

Teacher's answer:
New clause system:
{
() -> drop([s(u), nil, nil]) -> 6  ;  () -> drop([z, l, l]) -> 6  ;  () -> length([nil, z]) -> 4  ;  () -> minus([s(u), z, s(u)]) -> 6  ;  () -> minus([z, y, z]) -> 6  ;  (drop([n, l1, _sga]) /\ length([_sga, _tga]) /\ length([l1, _uga]) /\ minus([_uga, n, _vga])) -> eq_nat([_tga, _vga]) -> 4  ;  (drop([u, x3, _ega])) -> drop([s(u), cons(x2, x3), _ega]) -> 4  ;  (length([ll, _jga])) -> length([cons(x, ll), s(_jga)]) -> 4  ;  (minus([u, x2, _nga])) -> minus([s(u), s(x2), _nga]) -> 7
}
Sat witness: Yes: ((minus([u, x2, _nga])) -> minus([s(u), s(x2), _nga]), {
_nga -> s(z)  ;  u -> s(z)  ;  x2 -> z
})

-------------------------------------------
Step 13, which took 0.005307 s (model generation: 0.005187,  model checking: 0.000120):

Model:
|_
{
drop -> 
{{{
Q={q_gen_1352, q_gen_1354, q_gen_1359, q_gen_1360, q_gen_1366, q_gen_1367, q_gen_1368, q_gen_1369},
Q_f={q_gen_1352},
Delta=
{
<s>(q_gen_1354) -> q_gen_1354
<z>() -> q_gen_1354
<z, nil>() -> q_gen_1359
<z, b>() -> q_gen_1360
<nil, nil>() -> q_gen_1366
<nil, b>() -> q_gen_1367
<b, nil>() -> q_gen_1368
<b, b>() -> q_gen_1369
<s, cons, nil>(q_gen_1360, q_gen_1359) -> q_gen_1352
<s, nil, nil>(q_gen_1354) -> q_gen_1352
<z, cons, cons>(q_gen_1369, q_gen_1368, q_gen_1367, q_gen_1366) -> q_gen_1352
<z, nil, nil>() -> q_gen_1352
}

Datatype: <nat, eltlist, eltlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_1351, q_gen_1357},
Q_f={q_gen_1351},
Delta=
{
<cons, s>(q_gen_1357, q_gen_1351) -> q_gen_1351
<nil, z>() -> q_gen_1351
<b, z>() -> q_gen_1357
}

Datatype: <eltlist, nat>
Convolution form: complete
}}}
  ;  minus -> 
{{{
Q={q_gen_1348, q_gen_1350, q_gen_1362},
Q_f={q_gen_1348},
Delta=
{
<z>() -> q_gen_1362
<s, s>(q_gen_1350) -> q_gen_1350
<z, z>() -> q_gen_1350
<s, s, s>(q_gen_1348) -> q_gen_1348
<s, s, z>(q_gen_1350) -> q_gen_1348
<s, z, s>(q_gen_1350) -> q_gen_1348
<s, z, z>(q_gen_1362) -> q_gen_1348
<z, s, z>(q_gen_1362) -> q_gen_1348
<z, z, z>() -> q_gen_1348
}

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

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

Teacher's answer:
New clause system:
{
() -> drop([s(u), nil, nil]) -> 6  ;  () -> drop([z, l, l]) -> 6  ;  () -> length([nil, z]) -> 4  ;  () -> minus([s(u), z, s(u)]) -> 6  ;  () -> minus([z, y, z]) -> 6  ;  (drop([n, l1, _sga]) /\ length([_sga, _tga]) /\ length([l1, _uga]) /\ minus([_uga, n, _vga])) -> eq_nat([_tga, _vga]) -> 4  ;  (drop([u, x3, _ega])) -> drop([s(u), cons(x2, x3), _ega]) -> 4  ;  (length([ll, _jga])) -> length([cons(x, ll), s(_jga)]) -> 7  ;  (minus([u, x2, _nga])) -> minus([s(u), s(x2), _nga]) -> 7
}
Sat witness: Yes: ((length([ll, _jga])) -> length([cons(x, ll), s(_jga)]), {
_jga -> z  ;  ll -> nil  ;  x -> a
})

-------------------------------------------
Step 14, which took 0.005261 s (model generation: 0.004637,  model checking: 0.000624):

Model:
|_
{
drop -> 
{{{
Q={q_gen_1352, q_gen_1354, q_gen_1359, q_gen_1360, q_gen_1366, q_gen_1367, q_gen_1368, q_gen_1369},
Q_f={q_gen_1352},
Delta=
{
<s>(q_gen_1354) -> q_gen_1354
<z>() -> q_gen_1354
<z, nil>() -> q_gen_1359
<z, b>() -> q_gen_1360
<nil, nil>() -> q_gen_1366
<nil, b>() -> q_gen_1367
<b, nil>() -> q_gen_1368
<b, b>() -> q_gen_1369
<s, cons, nil>(q_gen_1360, q_gen_1359) -> q_gen_1352
<s, nil, nil>(q_gen_1354) -> q_gen_1352
<z, cons, cons>(q_gen_1369, q_gen_1368, q_gen_1367, q_gen_1366) -> q_gen_1352
<z, nil, nil>() -> q_gen_1352
}

Datatype: <nat, eltlist, eltlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_1351, q_gen_1357},
Q_f={q_gen_1351},
Delta=
{
<cons, s>(q_gen_1357, q_gen_1351) -> q_gen_1351
<nil, z>() -> q_gen_1351
<a, z>() -> q_gen_1357
<b, z>() -> q_gen_1357
}

Datatype: <eltlist, nat>
Convolution form: complete
}}}
  ;  minus -> 
{{{
Q={q_gen_1348, q_gen_1350, q_gen_1362},
Q_f={q_gen_1348},
Delta=
{
<z>() -> q_gen_1362
<s, s>(q_gen_1350) -> q_gen_1350
<z, z>() -> q_gen_1350
<s, s, s>(q_gen_1348) -> q_gen_1348
<s, s, z>(q_gen_1350) -> q_gen_1348
<s, z, s>(q_gen_1350) -> q_gen_1348
<s, z, z>(q_gen_1362) -> q_gen_1348
<z, s, z>(q_gen_1362) -> q_gen_1348
<z, z, z>() -> q_gen_1348
}

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

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

Teacher's answer:
New clause system:
{
() -> drop([s(u), nil, nil]) -> 6  ;  () -> drop([z, l, l]) -> 6  ;  () -> length([nil, z]) -> 4  ;  () -> minus([s(u), z, s(u)]) -> 6  ;  () -> minus([z, y, z]) -> 6  ;  (drop([n, l1, _sga]) /\ length([_sga, _tga]) /\ length([l1, _uga]) /\ minus([_uga, n, _vga])) -> eq_nat([_tga, _vga]) -> 4  ;  (drop([u, x3, _ega])) -> drop([s(u), cons(x2, x3), _ega]) -> 7  ;  (length([ll, _jga])) -> length([cons(x, ll), s(_jga)]) -> 7  ;  (minus([u, x2, _nga])) -> minus([s(u), s(x2), _nga]) -> 7
}
Sat witness: Yes: ((drop([u, x3, _ega])) -> drop([s(u), cons(x2, x3), _ega]), {
_ega -> nil  ;  u -> z  ;  x2 -> a  ;  x3 -> nil
})

-------------------------------------------
Step 15, which took 0.005038 s (model generation: 0.004906,  model checking: 0.000132):

Model:
|_
{
drop -> 
{{{
Q={q_gen_1352, q_gen_1354, q_gen_1359, q_gen_1360, q_gen_1366, q_gen_1367, q_gen_1368, q_gen_1369},
Q_f={q_gen_1352},
Delta=
{
<s>(q_gen_1354) -> q_gen_1354
<z>() -> q_gen_1354
<z, nil>() -> q_gen_1359
<z, a>() -> q_gen_1360
<z, b>() -> q_gen_1360
<nil, nil>() -> q_gen_1366
<nil, b>() -> q_gen_1367
<b, nil>() -> q_gen_1368
<b, b>() -> q_gen_1369
<s, cons, nil>(q_gen_1360, q_gen_1359) -> q_gen_1352
<s, nil, nil>(q_gen_1354) -> q_gen_1352
<z, cons, cons>(q_gen_1369, q_gen_1368, q_gen_1367, q_gen_1366) -> q_gen_1352
<z, nil, nil>() -> q_gen_1352
}

Datatype: <nat, eltlist, eltlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_1351, q_gen_1357},
Q_f={q_gen_1351},
Delta=
{
<cons, s>(q_gen_1357, q_gen_1351) -> q_gen_1351
<nil, z>() -> q_gen_1351
<a, z>() -> q_gen_1357
<b, z>() -> q_gen_1357
}

Datatype: <eltlist, nat>
Convolution form: complete
}}}
  ;  minus -> 
{{{
Q={q_gen_1348, q_gen_1350, q_gen_1362},
Q_f={q_gen_1348},
Delta=
{
<z>() -> q_gen_1362
<s, s>(q_gen_1350) -> q_gen_1350
<z, z>() -> q_gen_1350
<s, s, s>(q_gen_1348) -> q_gen_1348
<s, s, z>(q_gen_1350) -> q_gen_1348
<s, z, s>(q_gen_1350) -> q_gen_1348
<s, z, z>(q_gen_1362) -> q_gen_1348
<z, s, z>(q_gen_1362) -> q_gen_1348
<z, z, z>() -> q_gen_1348
}

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

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

Teacher's answer:
New clause system:
{
() -> drop([s(u), nil, nil]) -> 6  ;  () -> drop([z, l, l]) -> 6  ;  () -> length([nil, z]) -> 4  ;  () -> minus([s(u), z, s(u)]) -> 6  ;  () -> minus([z, y, z]) -> 6  ;  (drop([n, l1, _sga]) /\ length([_sga, _tga]) /\ length([l1, _uga]) /\ minus([_uga, n, _vga])) -> eq_nat([_tga, _vga]) -> 7  ;  (drop([u, x3, _ega])) -> drop([s(u), cons(x2, x3), _ega]) -> 7  ;  (length([ll, _jga])) -> length([cons(x, ll), s(_jga)]) -> 7  ;  (minus([u, x2, _nga])) -> minus([s(u), s(x2), _nga]) -> 7
}
Sat witness: Yes: ((drop([n, l1, _sga]) /\ length([_sga, _tga]) /\ length([l1, _uga]) /\ minus([_uga, n, _vga])) -> eq_nat([_tga, _vga]), {
_sga -> nil  ;  _tga -> z  ;  _uga -> s(z)  ;  _vga -> s(z)  ;  l1 -> cons(b, nil)  ;  n -> s(z)
})

-------------------------------------------
Step 16, which took 0.005040 s (model generation: 0.004896,  model checking: 0.000144):

Model:
|_
{
drop -> 
{{{
Q={q_gen_1352, q_gen_1354, q_gen_1359, q_gen_1360, q_gen_1366, q_gen_1367, q_gen_1368, q_gen_1369},
Q_f={q_gen_1352},
Delta=
{
<s>(q_gen_1354) -> q_gen_1354
<z>() -> q_gen_1354
<z, nil>() -> q_gen_1359
<z, a>() -> q_gen_1360
<z, b>() -> q_gen_1360
<nil, nil>() -> q_gen_1366
<nil, b>() -> q_gen_1367
<b, nil>() -> q_gen_1368
<b, b>() -> q_gen_1369
<s, cons, nil>(q_gen_1360, q_gen_1359) -> q_gen_1352
<s, nil, nil>(q_gen_1354) -> q_gen_1352
<z, cons, cons>(q_gen_1369, q_gen_1368, q_gen_1367, q_gen_1366) -> q_gen_1352
<z, nil, nil>() -> q_gen_1352
}

Datatype: <nat, eltlist, eltlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_1351, q_gen_1357},
Q_f={q_gen_1351},
Delta=
{
<cons, s>(q_gen_1357, q_gen_1351) -> q_gen_1351
<nil, z>() -> q_gen_1351
<a, z>() -> q_gen_1357
<b, z>() -> q_gen_1357
}

Datatype: <eltlist, nat>
Convolution form: complete
}}}
  ;  minus -> 
{{{
Q={q_gen_1348, q_gen_1350, q_gen_1362, q_gen_1373},
Q_f={q_gen_1348},
Delta=
{
<z>() -> q_gen_1362
<s, s>(q_gen_1350) -> q_gen_1350
<z, z>() -> q_gen_1350
<s, s, s>(q_gen_1373) -> q_gen_1348
<s, s, z>(q_gen_1350) -> q_gen_1348
<s, z, s>(q_gen_1350) -> q_gen_1348
<z, s, z>(q_gen_1362) -> q_gen_1348
<z, z, z>() -> q_gen_1348
<s, s, s>(q_gen_1348) -> q_gen_1373
<s, z, z>(q_gen_1362) -> q_gen_1373
}

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

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

Teacher's answer:
New clause system:
{
() -> drop([s(u), nil, nil]) -> 6  ;  () -> drop([z, l, l]) -> 6  ;  () -> length([nil, z]) -> 5  ;  () -> minus([s(u), z, s(u)]) -> 6  ;  () -> minus([z, y, z]) -> 9  ;  (drop([n, l1, _sga]) /\ length([_sga, _tga]) /\ length([l1, _uga]) /\ minus([_uga, n, _vga])) -> eq_nat([_tga, _vga]) -> 7  ;  (drop([u, x3, _ega])) -> drop([s(u), cons(x2, x3), _ega]) -> 7  ;  (length([ll, _jga])) -> length([cons(x, ll), s(_jga)]) -> 7  ;  (minus([u, x2, _nga])) -> minus([s(u), s(x2), _nga]) -> 7
}
Sat witness: Yes: (() -> minus([z, y, z]), {
y -> s(s(z))
})

-------------------------------------------
Step 17, which took 0.006321 s (model generation: 0.005490,  model checking: 0.000831):

Model:
|_
{
drop -> 
{{{
Q={q_gen_1352, q_gen_1354, q_gen_1359, q_gen_1360, q_gen_1366, q_gen_1367, q_gen_1368, q_gen_1369},
Q_f={q_gen_1352},
Delta=
{
<s>(q_gen_1354) -> q_gen_1354
<z>() -> q_gen_1354
<z, nil>() -> q_gen_1359
<z, a>() -> q_gen_1360
<z, b>() -> q_gen_1360
<nil, nil>() -> q_gen_1366
<nil, b>() -> q_gen_1367
<b, nil>() -> q_gen_1368
<b, b>() -> q_gen_1369
<s, cons, nil>(q_gen_1360, q_gen_1359) -> q_gen_1352
<s, nil, nil>(q_gen_1354) -> q_gen_1352
<z, cons, cons>(q_gen_1369, q_gen_1368, q_gen_1367, q_gen_1366) -> q_gen_1352
<z, nil, nil>() -> q_gen_1352
}

Datatype: <nat, eltlist, eltlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_1351, q_gen_1357},
Q_f={q_gen_1351},
Delta=
{
<cons, s>(q_gen_1357, q_gen_1351) -> q_gen_1351
<nil, z>() -> q_gen_1351
<a, z>() -> q_gen_1357
<b, z>() -> q_gen_1357
}

Datatype: <eltlist, nat>
Convolution form: complete
}}}
  ;  minus -> 
{{{
Q={q_gen_1348, q_gen_1350, q_gen_1362, q_gen_1373},
Q_f={q_gen_1348},
Delta=
{
<s>(q_gen_1362) -> q_gen_1362
<z>() -> q_gen_1362
<s, s>(q_gen_1350) -> q_gen_1350
<z, z>() -> q_gen_1350
<s, s, s>(q_gen_1373) -> q_gen_1348
<s, s, z>(q_gen_1350) -> q_gen_1348
<s, z, s>(q_gen_1350) -> q_gen_1348
<z, s, z>(q_gen_1362) -> q_gen_1348
<z, z, z>() -> q_gen_1348
<s, s, s>(q_gen_1348) -> q_gen_1373
<s, z, z>(q_gen_1362) -> q_gen_1373
}

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

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

Teacher's answer:
New clause system:
{
() -> drop([s(u), nil, nil]) -> 6  ;  () -> drop([z, l, l]) -> 9  ;  () -> length([nil, z]) -> 6  ;  () -> minus([s(u), z, s(u)]) -> 7  ;  () -> minus([z, y, z]) -> 9  ;  (drop([n, l1, _sga]) /\ length([_sga, _tga]) /\ length([l1, _uga]) /\ minus([_uga, n, _vga])) -> eq_nat([_tga, _vga]) -> 7  ;  (drop([u, x3, _ega])) -> drop([s(u), cons(x2, x3), _ega]) -> 7  ;  (length([ll, _jga])) -> length([cons(x, ll), s(_jga)]) -> 7  ;  (minus([u, x2, _nga])) -> minus([s(u), s(x2), _nga]) -> 7
}
Sat witness: Yes: (() -> drop([z, l, l]), {
l -> cons(a, nil)
})

-------------------------------------------
Step 18, which took 0.006143 s (model generation: 0.005531,  model checking: 0.000612):

Model:
|_
{
drop -> 
{{{
Q={q_gen_1352, q_gen_1354, q_gen_1359, q_gen_1360, q_gen_1366, q_gen_1367, q_gen_1368, q_gen_1369},
Q_f={q_gen_1352},
Delta=
{
<s>(q_gen_1354) -> q_gen_1354
<z>() -> q_gen_1354
<z, nil>() -> q_gen_1359
<z, a>() -> q_gen_1360
<z, b>() -> q_gen_1360
<nil, nil>() -> q_gen_1366
<nil, a>() -> q_gen_1367
<nil, b>() -> q_gen_1367
<a, nil>() -> q_gen_1368
<b, nil>() -> q_gen_1368
<a, a>() -> q_gen_1369
<b, b>() -> q_gen_1369
<s, cons, nil>(q_gen_1360, q_gen_1359) -> q_gen_1352
<s, nil, nil>(q_gen_1354) -> q_gen_1352
<z, cons, cons>(q_gen_1369, q_gen_1368, q_gen_1367, q_gen_1366) -> q_gen_1352
<z, nil, nil>() -> q_gen_1352
}

Datatype: <nat, eltlist, eltlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_1351, q_gen_1357},
Q_f={q_gen_1351},
Delta=
{
<cons, s>(q_gen_1357, q_gen_1351) -> q_gen_1351
<nil, z>() -> q_gen_1351
<a, z>() -> q_gen_1357
<b, z>() -> q_gen_1357
}

Datatype: <eltlist, nat>
Convolution form: complete
}}}
  ;  minus -> 
{{{
Q={q_gen_1348, q_gen_1350, q_gen_1362, q_gen_1373},
Q_f={q_gen_1348},
Delta=
{
<s>(q_gen_1362) -> q_gen_1362
<z>() -> q_gen_1362
<s, s>(q_gen_1350) -> q_gen_1350
<z, z>() -> q_gen_1350
<s, s, s>(q_gen_1373) -> q_gen_1348
<s, s, z>(q_gen_1350) -> q_gen_1348
<s, z, s>(q_gen_1350) -> q_gen_1348
<z, s, z>(q_gen_1362) -> q_gen_1348
<z, z, z>() -> q_gen_1348
<s, s, s>(q_gen_1348) -> q_gen_1373
<s, z, z>(q_gen_1362) -> q_gen_1373
}

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

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

Teacher's answer:
New clause system:
{
() -> drop([s(u), nil, nil]) -> 7  ;  () -> drop([z, l, l]) -> 9  ;  () -> length([nil, z]) -> 7  ;  () -> minus([s(u), z, s(u)]) -> 7  ;  () -> minus([z, y, z]) -> 9  ;  (drop([n, l1, _sga]) /\ length([_sga, _tga]) /\ length([l1, _uga]) /\ minus([_uga, n, _vga])) -> eq_nat([_tga, _vga]) -> 7  ;  (drop([u, x3, _ega])) -> drop([s(u), cons(x2, x3), _ega]) -> 7  ;  (length([ll, _jga])) -> length([cons(x, ll), s(_jga)]) -> 7  ;  (minus([u, x2, _nga])) -> minus([s(u), s(x2), _nga]) -> 10
}
Sat witness: Yes: ((minus([u, x2, _nga])) -> minus([s(u), s(x2), _nga]), {
_nga -> z  ;  u -> z  ;  x2 -> s(z)
})

-------------------------------------------
Step 19, which took 0.007053 s (model generation: 0.006816,  model checking: 0.000237):

Model:
|_
{
drop -> 
{{{
Q={q_gen_1352, q_gen_1354, q_gen_1359, q_gen_1360, q_gen_1366, q_gen_1367, q_gen_1368, q_gen_1369},
Q_f={q_gen_1352},
Delta=
{
<s>(q_gen_1354) -> q_gen_1354
<z>() -> q_gen_1354
<z, nil>() -> q_gen_1359
<z, a>() -> q_gen_1360
<z, b>() -> q_gen_1360
<nil, nil>() -> q_gen_1366
<nil, a>() -> q_gen_1367
<nil, b>() -> q_gen_1367
<a, nil>() -> q_gen_1368
<b, nil>() -> q_gen_1368
<a, a>() -> q_gen_1369
<b, b>() -> q_gen_1369
<s, cons, nil>(q_gen_1360, q_gen_1359) -> q_gen_1352
<s, nil, nil>(q_gen_1354) -> q_gen_1352
<z, cons, cons>(q_gen_1369, q_gen_1368, q_gen_1367, q_gen_1366) -> q_gen_1352
<z, nil, nil>() -> q_gen_1352
}

Datatype: <nat, eltlist, eltlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_1351, q_gen_1357},
Q_f={q_gen_1351},
Delta=
{
<cons, s>(q_gen_1357, q_gen_1351) -> q_gen_1351
<nil, z>() -> q_gen_1351
<a, z>() -> q_gen_1357
<b, z>() -> q_gen_1357
}

Datatype: <eltlist, nat>
Convolution form: complete
}}}
  ;  minus -> 
{{{
Q={q_gen_1348, q_gen_1350, q_gen_1362, q_gen_1373},
Q_f={q_gen_1348},
Delta=
{
<s>(q_gen_1362) -> q_gen_1362
<z>() -> q_gen_1362
<s, s>(q_gen_1350) -> q_gen_1350
<z, s>(q_gen_1362) -> q_gen_1350
<z, z>() -> q_gen_1350
<s, s, s>(q_gen_1373) -> q_gen_1348
<s, s, z>(q_gen_1350) -> q_gen_1348
<s, z, s>(q_gen_1350) -> q_gen_1348
<z, s, z>(q_gen_1362) -> q_gen_1348
<z, z, z>() -> q_gen_1348
<s, s, s>(q_gen_1348) -> q_gen_1373
<s, z, z>(q_gen_1362) -> q_gen_1373
}

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

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

Teacher's answer:
New clause system:
{
() -> drop([s(u), nil, nil]) -> 7  ;  () -> drop([z, l, l]) -> 9  ;  () -> length([nil, z]) -> 7  ;  () -> minus([s(u), z, s(u)]) -> 7  ;  () -> minus([z, y, z]) -> 9  ;  (drop([n, l1, _sga]) /\ length([_sga, _tga]) /\ length([l1, _uga]) /\ minus([_uga, n, _vga])) -> eq_nat([_tga, _vga]) -> 7  ;  (drop([u, x3, _ega])) -> drop([s(u), cons(x2, x3), _ega]) -> 7  ;  (length([ll, _jga])) -> length([cons(x, ll), s(_jga)]) -> 10  ;  (minus([u, x2, _nga])) -> minus([s(u), s(x2), _nga]) -> 10
}
Sat witness: Yes: ((length([ll, _jga])) -> length([cons(x, ll), s(_jga)]), {
_jga -> s(z)  ;  ll -> cons(a, nil)  ;  x -> b
})

-------------------------------------------
Step 20, which took 0.007385 s (model generation: 0.006613,  model checking: 0.000772):

Model:
|_
{
drop -> 
{{{
Q={q_gen_1352, q_gen_1354, q_gen_1359, q_gen_1360, q_gen_1366, q_gen_1367, q_gen_1368, q_gen_1369},
Q_f={q_gen_1352},
Delta=
{
<s>(q_gen_1354) -> q_gen_1354
<z>() -> q_gen_1354
<z, nil>() -> q_gen_1359
<z, a>() -> q_gen_1360
<z, b>() -> q_gen_1360
<nil, nil>() -> q_gen_1366
<nil, a>() -> q_gen_1367
<nil, b>() -> q_gen_1367
<a, nil>() -> q_gen_1368
<b, nil>() -> q_gen_1368
<a, a>() -> q_gen_1369
<b, b>() -> q_gen_1369
<s, cons, nil>(q_gen_1360, q_gen_1359) -> q_gen_1352
<s, nil, nil>(q_gen_1354) -> q_gen_1352
<z, cons, cons>(q_gen_1369, q_gen_1368, q_gen_1367, q_gen_1366) -> q_gen_1352
<z, nil, nil>() -> q_gen_1352
}

Datatype: <nat, eltlist, eltlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_1351, q_gen_1357, q_gen_1389},
Q_f={q_gen_1351},
Delta=
{
<z>() -> q_gen_1389
<cons, s>(q_gen_1357, q_gen_1351) -> q_gen_1351
<nil, z>() -> q_gen_1351
<a, z>() -> q_gen_1357
<b, s>(q_gen_1389) -> q_gen_1357
<b, z>() -> q_gen_1357
}

Datatype: <eltlist, nat>
Convolution form: complete
}}}
  ;  minus -> 
{{{
Q={q_gen_1348, q_gen_1350, q_gen_1362, q_gen_1373},
Q_f={q_gen_1348},
Delta=
{
<s>(q_gen_1362) -> q_gen_1362
<z>() -> q_gen_1362
<s, s>(q_gen_1350) -> q_gen_1350
<z, s>(q_gen_1362) -> q_gen_1350
<z, z>() -> q_gen_1350
<s, s, s>(q_gen_1373) -> q_gen_1348
<s, s, z>(q_gen_1350) -> q_gen_1348
<s, z, s>(q_gen_1350) -> q_gen_1348
<z, s, z>(q_gen_1362) -> q_gen_1348
<z, z, z>() -> q_gen_1348
<s, s, s>(q_gen_1348) -> q_gen_1373
<s, z, z>(q_gen_1362) -> q_gen_1373
}

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

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

Teacher's answer:
New clause system:
{
() -> drop([s(u), nil, nil]) -> 7  ;  () -> drop([z, l, l]) -> 9  ;  () -> length([nil, z]) -> 7  ;  () -> minus([s(u), z, s(u)]) -> 7  ;  () -> minus([z, y, z]) -> 9  ;  (drop([n, l1, _sga]) /\ length([_sga, _tga]) /\ length([l1, _uga]) /\ minus([_uga, n, _vga])) -> eq_nat([_tga, _vga]) -> 7  ;  (drop([u, x3, _ega])) -> drop([s(u), cons(x2, x3), _ega]) -> 10  ;  (length([ll, _jga])) -> length([cons(x, ll), s(_jga)]) -> 10  ;  (minus([u, x2, _nga])) -> minus([s(u), s(x2), _nga]) -> 10
}
Sat witness: Yes: ((drop([u, x3, _ega])) -> drop([s(u), cons(x2, x3), _ega]), {
_ega -> nil  ;  u -> s(z)  ;  x2 -> b  ;  x3 -> nil
})

-------------------------------------------
Step 21, which took 0.007307 s (model generation: 0.007040,  model checking: 0.000267):

Model:
|_
{
drop -> 
{{{
Q={q_gen_1352, q_gen_1354, q_gen_1359, q_gen_1360, q_gen_1366, q_gen_1367, q_gen_1368, q_gen_1369},
Q_f={q_gen_1352},
Delta=
{
<s>(q_gen_1354) -> q_gen_1354
<z>() -> q_gen_1354
<s, nil>(q_gen_1354) -> q_gen_1359
<z, nil>() -> q_gen_1359
<s, b>(q_gen_1354) -> q_gen_1360
<z, a>() -> q_gen_1360
<z, b>() -> q_gen_1360
<nil, nil>() -> q_gen_1366
<nil, a>() -> q_gen_1367
<nil, b>() -> q_gen_1367
<a, nil>() -> q_gen_1368
<b, nil>() -> q_gen_1368
<a, a>() -> q_gen_1369
<b, b>() -> q_gen_1369
<s, cons, nil>(q_gen_1360, q_gen_1359) -> q_gen_1352
<s, nil, nil>(q_gen_1354) -> q_gen_1352
<z, cons, cons>(q_gen_1369, q_gen_1368, q_gen_1367, q_gen_1366) -> q_gen_1352
<z, nil, nil>() -> q_gen_1352
}

Datatype: <nat, eltlist, eltlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_1351, q_gen_1357, q_gen_1389},
Q_f={q_gen_1351},
Delta=
{
<z>() -> q_gen_1389
<cons, s>(q_gen_1357, q_gen_1351) -> q_gen_1351
<nil, z>() -> q_gen_1351
<a, z>() -> q_gen_1357
<b, s>(q_gen_1389) -> q_gen_1357
<b, z>() -> q_gen_1357
}

Datatype: <eltlist, nat>
Convolution form: complete
}}}
  ;  minus -> 
{{{
Q={q_gen_1348, q_gen_1350, q_gen_1362, q_gen_1373},
Q_f={q_gen_1348},
Delta=
{
<s>(q_gen_1362) -> q_gen_1362
<z>() -> q_gen_1362
<s, s>(q_gen_1350) -> q_gen_1350
<z, s>(q_gen_1362) -> q_gen_1350
<z, z>() -> q_gen_1350
<s, s, s>(q_gen_1373) -> q_gen_1348
<s, s, z>(q_gen_1350) -> q_gen_1348
<s, z, s>(q_gen_1350) -> q_gen_1348
<z, s, z>(q_gen_1362) -> q_gen_1348
<z, z, z>() -> q_gen_1348
<s, s, s>(q_gen_1348) -> q_gen_1373
<s, z, z>(q_gen_1362) -> q_gen_1373
}

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

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

Teacher's answer:
New clause system:
{
() -> drop([s(u), nil, nil]) -> 7  ;  () -> drop([z, l, l]) -> 9  ;  () -> length([nil, z]) -> 7  ;  () -> minus([s(u), z, s(u)]) -> 7  ;  () -> minus([z, y, z]) -> 9  ;  (drop([n, l1, _sga]) /\ length([_sga, _tga]) /\ length([l1, _uga]) /\ minus([_uga, n, _vga])) -> eq_nat([_tga, _vga]) -> 10  ;  (drop([u, x3, _ega])) -> drop([s(u), cons(x2, x3), _ega]) -> 10  ;  (length([ll, _jga])) -> length([cons(x, ll), s(_jga)]) -> 10  ;  (minus([u, x2, _nga])) -> minus([s(u), s(x2), _nga]) -> 10
}
Sat witness: Yes: ((drop([n, l1, _sga]) /\ length([_sga, _tga]) /\ length([l1, _uga]) /\ minus([_uga, n, _vga])) -> eq_nat([_tga, _vga]), {
_sga -> cons(a, nil)  ;  _tga -> s(z)  ;  _uga -> s(z)  ;  _vga -> s(s(z))  ;  l1 -> cons(a, nil)  ;  n -> z
})

-------------------------------------------
Step 22, which took 0.009120 s (model generation: 0.007037,  model checking: 0.002083):

Model:
|_
{
drop -> 
{{{
Q={q_gen_1352, q_gen_1354, q_gen_1359, q_gen_1360, q_gen_1366, q_gen_1367, q_gen_1368, q_gen_1369},
Q_f={q_gen_1352},
Delta=
{
<s>(q_gen_1354) -> q_gen_1354
<z>() -> q_gen_1354
<s, nil>(q_gen_1354) -> q_gen_1359
<z, nil>() -> q_gen_1359
<s, b>(q_gen_1354) -> q_gen_1360
<z, a>() -> q_gen_1360
<z, b>() -> q_gen_1360
<nil, nil>() -> q_gen_1366
<nil, a>() -> q_gen_1367
<nil, b>() -> q_gen_1367
<a, nil>() -> q_gen_1368
<b, nil>() -> q_gen_1368
<a, a>() -> q_gen_1369
<b, b>() -> q_gen_1369
<s, cons, nil>(q_gen_1360, q_gen_1359) -> q_gen_1352
<s, nil, nil>(q_gen_1354) -> q_gen_1352
<z, cons, cons>(q_gen_1369, q_gen_1368, q_gen_1367, q_gen_1366) -> q_gen_1352
<z, nil, nil>() -> q_gen_1352
}

Datatype: <nat, eltlist, eltlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_1351, q_gen_1357, q_gen_1389},
Q_f={q_gen_1351},
Delta=
{
<z>() -> q_gen_1389
<cons, s>(q_gen_1357, q_gen_1351) -> q_gen_1351
<nil, z>() -> q_gen_1351
<a, z>() -> q_gen_1357
<b, s>(q_gen_1389) -> q_gen_1357
<b, z>() -> q_gen_1357
}

Datatype: <eltlist, nat>
Convolution form: complete
}}}
  ;  minus -> 
{{{
Q={q_gen_1348, q_gen_1350, q_gen_1362, q_gen_1373, q_gen_1386},
Q_f={q_gen_1348},
Delta=
{
<s>(q_gen_1362) -> q_gen_1362
<z>() -> q_gen_1362
<s, s>(q_gen_1350) -> q_gen_1350
<z, z>() -> q_gen_1350
<z, s>(q_gen_1362) -> q_gen_1386
<s, s, s>(q_gen_1373) -> q_gen_1348
<s, s, z>(q_gen_1350) -> q_gen_1348
<s, s, z>(q_gen_1386) -> q_gen_1348
<s, z, s>(q_gen_1350) -> q_gen_1348
<z, s, z>(q_gen_1362) -> q_gen_1348
<z, z, z>() -> q_gen_1348
<s, s, s>(q_gen_1348) -> q_gen_1373
<s, z, s>(q_gen_1386) -> q_gen_1373
<s, z, z>(q_gen_1362) -> q_gen_1373
}

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

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

Teacher's answer:
New clause system:
{
() -> drop([s(u), nil, nil]) -> 8  ;  () -> drop([z, l, l]) -> 12  ;  () -> length([nil, z]) -> 8  ;  () -> minus([s(u), z, s(u)]) -> 8  ;  () -> minus([z, y, z]) -> 10  ;  (drop([n, l1, _sga]) /\ length([_sga, _tga]) /\ length([l1, _uga]) /\ minus([_uga, n, _vga])) -> eq_nat([_tga, _vga]) -> 10  ;  (drop([u, x3, _ega])) -> drop([s(u), cons(x2, x3), _ega]) -> 10  ;  (length([ll, _jga])) -> length([cons(x, ll), s(_jga)]) -> 10  ;  (minus([u, x2, _nga])) -> minus([s(u), s(x2), _nga]) -> 10
}
Sat witness: Yes: (() -> drop([z, l, l]), {
l -> cons(b, cons(b, nil))
})

-------------------------------------------
Step 23, which took 0.008177 s (model generation: 0.007331,  model checking: 0.000846):

Model:
|_
{
drop -> 
{{{
Q={q_gen_1352, q_gen_1354, q_gen_1359, q_gen_1360, q_gen_1366, q_gen_1367, q_gen_1368, q_gen_1369, q_gen_1397, q_gen_1398},
Q_f={q_gen_1352},
Delta=
{
<s>(q_gen_1354) -> q_gen_1354
<z>() -> q_gen_1354
<nil>() -> q_gen_1397
<b>() -> q_gen_1398
<s, nil>(q_gen_1354) -> q_gen_1359
<z, nil>() -> q_gen_1359
<s, b>(q_gen_1354) -> q_gen_1360
<z, a>() -> q_gen_1360
<z, b>() -> q_gen_1360
<cons, cons>(q_gen_1369, q_gen_1368, q_gen_1367, q_gen_1366) -> q_gen_1366
<nil, nil>() -> q_gen_1366
<cons, b>(q_gen_1398, q_gen_1397) -> q_gen_1367
<nil, a>() -> q_gen_1367
<nil, b>() -> q_gen_1367
<a, nil>() -> q_gen_1368
<b, cons>(q_gen_1398, q_gen_1397) -> q_gen_1368
<b, nil>() -> q_gen_1368
<a, a>() -> q_gen_1369
<b, b>() -> q_gen_1369
<s, cons, nil>(q_gen_1360, q_gen_1359) -> q_gen_1352
<s, nil, nil>(q_gen_1354) -> q_gen_1352
<z, cons, cons>(q_gen_1369, q_gen_1368, q_gen_1367, q_gen_1366) -> q_gen_1352
<z, nil, nil>() -> q_gen_1352
}

Datatype: <nat, eltlist, eltlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_1351, q_gen_1357, q_gen_1389},
Q_f={q_gen_1351},
Delta=
{
<z>() -> q_gen_1389
<cons, s>(q_gen_1357, q_gen_1351) -> q_gen_1351
<nil, z>() -> q_gen_1351
<a, z>() -> q_gen_1357
<b, s>(q_gen_1389) -> q_gen_1357
<b, z>() -> q_gen_1357
}

Datatype: <eltlist, nat>
Convolution form: complete
}}}
  ;  minus -> 
{{{
Q={q_gen_1348, q_gen_1350, q_gen_1362, q_gen_1373, q_gen_1386},
Q_f={q_gen_1348},
Delta=
{
<s>(q_gen_1362) -> q_gen_1362
<z>() -> q_gen_1362
<s, s>(q_gen_1350) -> q_gen_1350
<z, z>() -> q_gen_1350
<z, s>(q_gen_1362) -> q_gen_1386
<s, s, s>(q_gen_1373) -> q_gen_1348
<s, s, z>(q_gen_1350) -> q_gen_1348
<s, s, z>(q_gen_1386) -> q_gen_1348
<s, z, s>(q_gen_1350) -> q_gen_1348
<z, s, z>(q_gen_1362) -> q_gen_1348
<z, z, z>() -> q_gen_1348
<s, s, s>(q_gen_1348) -> q_gen_1373
<s, z, s>(q_gen_1386) -> q_gen_1373
<s, z, z>(q_gen_1362) -> q_gen_1373
}

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

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

Teacher's answer:
New clause system:
{
() -> drop([s(u), nil, nil]) -> 9  ;  () -> drop([z, l, l]) -> 12  ;  () -> length([nil, z]) -> 9  ;  () -> minus([s(u), z, s(u)]) -> 9  ;  () -> minus([z, y, z]) -> 10  ;  (drop([n, l1, _sga]) /\ length([_sga, _tga]) /\ length([l1, _uga]) /\ minus([_uga, n, _vga])) -> eq_nat([_tga, _vga]) -> 10  ;  (drop([u, x3, _ega])) -> drop([s(u), cons(x2, x3), _ega]) -> 10  ;  (length([ll, _jga])) -> length([cons(x, ll), s(_jga)]) -> 10  ;  (minus([u, x2, _nga])) -> minus([s(u), s(x2), _nga]) -> 13
}
Sat witness: Yes: ((minus([u, x2, _nga])) -> minus([s(u), s(x2), _nga]), {
_nga -> s(s(s(s(z))))  ;  u -> s(s(z))  ;  x2 -> s(z)
})

-------------------------------------------
Step 24, which took 0.009975 s (model generation: 0.008850,  model checking: 0.001125):

Model:
|_
{
drop -> 
{{{
Q={q_gen_1352, q_gen_1354, q_gen_1359, q_gen_1360, q_gen_1366, q_gen_1367, q_gen_1368, q_gen_1369, q_gen_1397, q_gen_1398},
Q_f={q_gen_1352},
Delta=
{
<s>(q_gen_1354) -> q_gen_1354
<z>() -> q_gen_1354
<nil>() -> q_gen_1397
<b>() -> q_gen_1398
<s, nil>(q_gen_1354) -> q_gen_1359
<z, nil>() -> q_gen_1359
<s, b>(q_gen_1354) -> q_gen_1360
<z, a>() -> q_gen_1360
<z, b>() -> q_gen_1360
<cons, cons>(q_gen_1369, q_gen_1368, q_gen_1367, q_gen_1366) -> q_gen_1366
<nil, nil>() -> q_gen_1366
<cons, b>(q_gen_1398, q_gen_1397) -> q_gen_1367
<nil, a>() -> q_gen_1367
<nil, b>() -> q_gen_1367
<a, nil>() -> q_gen_1368
<b, cons>(q_gen_1398, q_gen_1397) -> q_gen_1368
<b, nil>() -> q_gen_1368
<a, a>() -> q_gen_1369
<b, b>() -> q_gen_1369
<s, cons, nil>(q_gen_1360, q_gen_1359) -> q_gen_1352
<s, nil, nil>(q_gen_1354) -> q_gen_1352
<z, cons, cons>(q_gen_1369, q_gen_1368, q_gen_1367, q_gen_1366) -> q_gen_1352
<z, nil, nil>() -> q_gen_1352
}

Datatype: <nat, eltlist, eltlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_1351, q_gen_1357, q_gen_1389},
Q_f={q_gen_1351},
Delta=
{
<z>() -> q_gen_1389
<cons, s>(q_gen_1357, q_gen_1351) -> q_gen_1351
<nil, z>() -> q_gen_1351
<a, z>() -> q_gen_1357
<b, s>(q_gen_1389) -> q_gen_1357
<b, z>() -> q_gen_1357
}

Datatype: <eltlist, nat>
Convolution form: complete
}}}
  ;  minus -> 
{{{
Q={q_gen_1348, q_gen_1349, q_gen_1350, q_gen_1362, q_gen_1378, q_gen_1386},
Q_f={q_gen_1348, q_gen_1349},
Delta=
{
<s>(q_gen_1362) -> q_gen_1362
<z>() -> q_gen_1362
<s, s>(q_gen_1350) -> q_gen_1350
<z, z>() -> q_gen_1350
<z, s>(q_gen_1362) -> q_gen_1386
<s, s, z>(q_gen_1386) -> q_gen_1348
<z, z, z>() -> q_gen_1348
<s, s, s>(q_gen_1349) -> q_gen_1349
<s, s, z>(q_gen_1350) -> q_gen_1349
<s, z, s>(q_gen_1350) -> q_gen_1349
<s, z, z>(q_gen_1362) -> q_gen_1349
<z, s, z>(q_gen_1362) -> q_gen_1349
<s, s, s>(q_gen_1348) -> q_gen_1378
<s, s, s>(q_gen_1378) -> q_gen_1378
<s, z, s>(q_gen_1386) -> q_gen_1378
}

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

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

Teacher's answer:
New clause system:
{
() -> drop([s(u), nil, nil]) -> 10  ;  () -> drop([z, l, l]) -> 12  ;  () -> length([nil, z]) -> 10  ;  () -> minus([s(u), z, s(u)]) -> 10  ;  () -> minus([z, y, z]) -> 10  ;  (drop([n, l1, _sga]) /\ length([_sga, _tga]) /\ length([l1, _uga]) /\ minus([_uga, n, _vga])) -> eq_nat([_tga, _vga]) -> 10  ;  (drop([u, x3, _ega])) -> drop([s(u), cons(x2, x3), _ega]) -> 10  ;  (length([ll, _jga])) -> length([cons(x, ll), s(_jga)]) -> 13  ;  (minus([u, x2, _nga])) -> minus([s(u), s(x2), _nga]) -> 13
}
Sat witness: Yes: ((length([ll, _jga])) -> length([cons(x, ll), s(_jga)]), {
_jga -> s(z)  ;  ll -> cons(b, nil)  ;  x -> a
})

-------------------------------------------
Step 25, which took 0.013115 s (model generation: 0.012384,  model checking: 0.000731):

Model:
|_
{
drop -> 
{{{
Q={q_gen_1352, q_gen_1354, q_gen_1359, q_gen_1360, q_gen_1366, q_gen_1367, q_gen_1368, q_gen_1369, q_gen_1397, q_gen_1398},
Q_f={q_gen_1352},
Delta=
{
<s>(q_gen_1354) -> q_gen_1354
<z>() -> q_gen_1354
<nil>() -> q_gen_1397
<b>() -> q_gen_1398
<s, nil>(q_gen_1354) -> q_gen_1359
<z, nil>() -> q_gen_1359
<s, b>(q_gen_1354) -> q_gen_1360
<z, a>() -> q_gen_1360
<z, b>() -> q_gen_1360
<cons, cons>(q_gen_1369, q_gen_1368, q_gen_1367, q_gen_1366) -> q_gen_1366
<nil, nil>() -> q_gen_1366
<cons, b>(q_gen_1398, q_gen_1397) -> q_gen_1367
<nil, a>() -> q_gen_1367
<nil, b>() -> q_gen_1367
<a, nil>() -> q_gen_1368
<b, cons>(q_gen_1398, q_gen_1397) -> q_gen_1368
<b, nil>() -> q_gen_1368
<a, a>() -> q_gen_1369
<b, b>() -> q_gen_1369
<s, cons, nil>(q_gen_1360, q_gen_1359) -> q_gen_1352
<s, nil, nil>(q_gen_1354) -> q_gen_1352
<z, cons, cons>(q_gen_1369, q_gen_1368, q_gen_1367, q_gen_1366) -> q_gen_1352
<z, nil, nil>() -> q_gen_1352
}

Datatype: <nat, eltlist, eltlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_1351, q_gen_1357, q_gen_1389},
Q_f={q_gen_1351},
Delta=
{
<z>() -> q_gen_1389
<cons, s>(q_gen_1357, q_gen_1351) -> q_gen_1351
<nil, z>() -> q_gen_1351
<a, s>(q_gen_1389) -> q_gen_1357
<a, z>() -> q_gen_1357
<b, s>(q_gen_1389) -> q_gen_1357
<b, z>() -> q_gen_1357
}

Datatype: <eltlist, nat>
Convolution form: complete
}}}
  ;  minus -> 
{{{
Q={q_gen_1348, q_gen_1349, q_gen_1350, q_gen_1362, q_gen_1378, q_gen_1386},
Q_f={q_gen_1348, q_gen_1349},
Delta=
{
<s>(q_gen_1362) -> q_gen_1362
<z>() -> q_gen_1362
<s, s>(q_gen_1350) -> q_gen_1350
<z, z>() -> q_gen_1350
<z, s>(q_gen_1362) -> q_gen_1386
<s, s, z>(q_gen_1386) -> q_gen_1348
<z, z, z>() -> q_gen_1348
<s, s, s>(q_gen_1349) -> q_gen_1349
<s, s, z>(q_gen_1350) -> q_gen_1349
<s, z, s>(q_gen_1350) -> q_gen_1349
<s, z, z>(q_gen_1362) -> q_gen_1349
<z, s, z>(q_gen_1362) -> q_gen_1349
<s, s, s>(q_gen_1348) -> q_gen_1378
<s, s, s>(q_gen_1378) -> q_gen_1378
<s, z, s>(q_gen_1386) -> q_gen_1378
}

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

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

Teacher's answer:
New clause system:
{
() -> drop([s(u), nil, nil]) -> 10  ;  () -> drop([z, l, l]) -> 12  ;  () -> length([nil, z]) -> 10  ;  () -> minus([s(u), z, s(u)]) -> 10  ;  () -> minus([z, y, z]) -> 10  ;  (drop([n, l1, _sga]) /\ length([_sga, _tga]) /\ length([l1, _uga]) /\ minus([_uga, n, _vga])) -> eq_nat([_tga, _vga]) -> 10  ;  (drop([u, x3, _ega])) -> drop([s(u), cons(x2, x3), _ega]) -> 13  ;  (length([ll, _jga])) -> length([cons(x, ll), s(_jga)]) -> 13  ;  (minus([u, x2, _nga])) -> minus([s(u), s(x2), _nga]) -> 13
}
Sat witness: Yes: ((drop([u, x3, _ega])) -> drop([s(u), cons(x2, x3), _ega]), {
_ega -> nil  ;  u -> s(z)  ;  x2 -> a  ;  x3 -> nil
})

-------------------------------------------
Step 26, which took 0.009399 s (model generation: 0.009130,  model checking: 0.000269):

Model:
|_
{
drop -> 
{{{
Q={q_gen_1352, q_gen_1354, q_gen_1359, q_gen_1360, q_gen_1366, q_gen_1367, q_gen_1368, q_gen_1369, q_gen_1397, q_gen_1398},
Q_f={q_gen_1352},
Delta=
{
<s>(q_gen_1354) -> q_gen_1354
<z>() -> q_gen_1354
<nil>() -> q_gen_1397
<b>() -> q_gen_1398
<s, nil>(q_gen_1354) -> q_gen_1359
<z, nil>() -> q_gen_1359
<s, a>(q_gen_1354) -> q_gen_1360
<s, b>(q_gen_1354) -> q_gen_1360
<z, a>() -> q_gen_1360
<z, b>() -> q_gen_1360
<cons, cons>(q_gen_1369, q_gen_1368, q_gen_1367, q_gen_1366) -> q_gen_1366
<nil, nil>() -> q_gen_1366
<cons, b>(q_gen_1398, q_gen_1397) -> q_gen_1367
<nil, a>() -> q_gen_1367
<nil, b>() -> q_gen_1367
<a, nil>() -> q_gen_1368
<b, cons>(q_gen_1398, q_gen_1397) -> q_gen_1368
<b, nil>() -> q_gen_1368
<a, a>() -> q_gen_1369
<b, b>() -> q_gen_1369
<s, cons, nil>(q_gen_1360, q_gen_1359) -> q_gen_1352
<s, nil, nil>(q_gen_1354) -> q_gen_1352
<z, cons, cons>(q_gen_1369, q_gen_1368, q_gen_1367, q_gen_1366) -> q_gen_1352
<z, nil, nil>() -> q_gen_1352
}

Datatype: <nat, eltlist, eltlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_1351, q_gen_1357, q_gen_1389},
Q_f={q_gen_1351},
Delta=
{
<z>() -> q_gen_1389
<cons, s>(q_gen_1357, q_gen_1351) -> q_gen_1351
<nil, z>() -> q_gen_1351
<a, s>(q_gen_1389) -> q_gen_1357
<a, z>() -> q_gen_1357
<b, s>(q_gen_1389) -> q_gen_1357
<b, z>() -> q_gen_1357
}

Datatype: <eltlist, nat>
Convolution form: complete
}}}
  ;  minus -> 
{{{
Q={q_gen_1348, q_gen_1349, q_gen_1350, q_gen_1362, q_gen_1378, q_gen_1386},
Q_f={q_gen_1348, q_gen_1349},
Delta=
{
<s>(q_gen_1362) -> q_gen_1362
<z>() -> q_gen_1362
<s, s>(q_gen_1350) -> q_gen_1350
<z, z>() -> q_gen_1350
<z, s>(q_gen_1362) -> q_gen_1386
<s, s, z>(q_gen_1386) -> q_gen_1348
<z, z, z>() -> q_gen_1348
<s, s, s>(q_gen_1349) -> q_gen_1349
<s, s, z>(q_gen_1350) -> q_gen_1349
<s, z, s>(q_gen_1350) -> q_gen_1349
<s, z, z>(q_gen_1362) -> q_gen_1349
<z, s, z>(q_gen_1362) -> q_gen_1349
<s, s, s>(q_gen_1348) -> q_gen_1378
<s, s, s>(q_gen_1378) -> q_gen_1378
<s, z, s>(q_gen_1386) -> q_gen_1378
}

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

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

Teacher's answer:
New clause system:
{
() -> drop([s(u), nil, nil]) -> 10  ;  () -> drop([z, l, l]) -> 12  ;  () -> length([nil, z]) -> 10  ;  () -> minus([s(u), z, s(u)]) -> 10  ;  () -> minus([z, y, z]) -> 10  ;  (drop([n, l1, _sga]) /\ length([_sga, _tga]) /\ length([l1, _uga]) /\ minus([_uga, n, _vga])) -> eq_nat([_tga, _vga]) -> 13  ;  (drop([u, x3, _ega])) -> drop([s(u), cons(x2, x3), _ega]) -> 13  ;  (length([ll, _jga])) -> length([cons(x, ll), s(_jga)]) -> 13  ;  (minus([u, x2, _nga])) -> minus([s(u), s(x2), _nga]) -> 13
}
Sat witness: Yes: ((drop([n, l1, _sga]) /\ length([_sga, _tga]) /\ length([l1, _uga]) /\ minus([_uga, n, _vga])) -> eq_nat([_tga, _vga]), {
_sga -> nil  ;  _tga -> z  ;  _uga -> s(z)  ;  _vga -> s(z)  ;  l1 -> cons(a, nil)  ;  n -> s(s(z))
})

-------------------------------------------
Step 27, which took 0.020859 s (model generation: 0.010795,  model checking: 0.010064):

Model:
|_
{
drop -> 
{{{
Q={q_gen_1352, q_gen_1354, q_gen_1359, q_gen_1360, q_gen_1366, q_gen_1367, q_gen_1368, q_gen_1369, q_gen_1397, q_gen_1398},
Q_f={q_gen_1352},
Delta=
{
<s>(q_gen_1354) -> q_gen_1354
<z>() -> q_gen_1354
<nil>() -> q_gen_1397
<b>() -> q_gen_1398
<s, nil>(q_gen_1354) -> q_gen_1359
<z, nil>() -> q_gen_1359
<s, a>(q_gen_1354) -> q_gen_1360
<s, b>(q_gen_1354) -> q_gen_1360
<z, a>() -> q_gen_1360
<z, b>() -> q_gen_1360
<cons, cons>(q_gen_1369, q_gen_1368, q_gen_1367, q_gen_1366) -> q_gen_1366
<nil, nil>() -> q_gen_1366
<cons, b>(q_gen_1398, q_gen_1397) -> q_gen_1367
<nil, a>() -> q_gen_1367
<nil, b>() -> q_gen_1367
<a, nil>() -> q_gen_1368
<b, cons>(q_gen_1398, q_gen_1397) -> q_gen_1368
<b, nil>() -> q_gen_1368
<a, a>() -> q_gen_1369
<b, b>() -> q_gen_1369
<s, cons, nil>(q_gen_1360, q_gen_1359) -> q_gen_1352
<s, nil, nil>(q_gen_1354) -> q_gen_1352
<z, cons, cons>(q_gen_1369, q_gen_1368, q_gen_1367, q_gen_1366) -> q_gen_1352
<z, nil, nil>() -> q_gen_1352
}

Datatype: <nat, eltlist, eltlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_1351, q_gen_1357, q_gen_1389},
Q_f={q_gen_1351},
Delta=
{
<z>() -> q_gen_1389
<cons, s>(q_gen_1357, q_gen_1351) -> q_gen_1351
<nil, z>() -> q_gen_1351
<a, s>(q_gen_1389) -> q_gen_1357
<a, z>() -> q_gen_1357
<b, s>(q_gen_1389) -> q_gen_1357
<b, z>() -> q_gen_1357
}

Datatype: <eltlist, nat>
Convolution form: complete
}}}
  ;  minus -> 
{{{
Q={q_gen_1348, q_gen_1349, q_gen_1350, q_gen_1362, q_gen_1378, q_gen_1386},
Q_f={q_gen_1348, q_gen_1349},
Delta=
{
<s>(q_gen_1362) -> q_gen_1362
<z>() -> q_gen_1362
<s, s>(q_gen_1350) -> q_gen_1350
<z, z>() -> q_gen_1350
<z, s>(q_gen_1362) -> q_gen_1386
<s, s, z>(q_gen_1386) -> q_gen_1348
<z, s, z>(q_gen_1362) -> q_gen_1348
<z, z, z>() -> q_gen_1348
<s, s, s>(q_gen_1349) -> q_gen_1349
<s, s, z>(q_gen_1350) -> q_gen_1349
<s, z, s>(q_gen_1350) -> q_gen_1349
<s, z, z>(q_gen_1362) -> q_gen_1349
<s, s, s>(q_gen_1348) -> q_gen_1378
<s, s, s>(q_gen_1378) -> q_gen_1378
<s, z, s>(q_gen_1386) -> q_gen_1378
}

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

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

Teacher's answer:
New clause system:
{
() -> drop([s(u), nil, nil]) -> 11  ;  () -> drop([z, l, l]) -> 15  ;  () -> length([nil, z]) -> 11  ;  () -> minus([s(u), z, s(u)]) -> 11  ;  () -> minus([z, y, z]) -> 11  ;  (drop([n, l1, _sga]) /\ length([_sga, _tga]) /\ length([l1, _uga]) /\ minus([_uga, n, _vga])) -> eq_nat([_tga, _vga]) -> 13  ;  (drop([u, x3, _ega])) -> drop([s(u), cons(x2, x3), _ega]) -> 13  ;  (length([ll, _jga])) -> length([cons(x, ll), s(_jga)]) -> 13  ;  (minus([u, x2, _nga])) -> minus([s(u), s(x2), _nga]) -> 13
}
Sat witness: Yes: (() -> drop([z, l, l]), {
l -> cons(b, cons(a, nil))
})

-------------------------------------------
Step 28, which took 0.012078 s (model generation: 0.011106,  model checking: 0.000972):

Model:
|_
{
drop -> 
{{{
Q={q_gen_1352, q_gen_1354, q_gen_1359, q_gen_1360, q_gen_1366, q_gen_1367, q_gen_1368, q_gen_1369, q_gen_1397, q_gen_1398},
Q_f={q_gen_1352},
Delta=
{
<s>(q_gen_1354) -> q_gen_1354
<z>() -> q_gen_1354
<nil>() -> q_gen_1397
<a>() -> q_gen_1398
<b>() -> q_gen_1398
<s, nil>(q_gen_1354) -> q_gen_1359
<z, nil>() -> q_gen_1359
<s, a>(q_gen_1354) -> q_gen_1360
<s, b>(q_gen_1354) -> q_gen_1360
<z, a>() -> q_gen_1360
<z, b>() -> q_gen_1360
<cons, cons>(q_gen_1369, q_gen_1368, q_gen_1367, q_gen_1366) -> q_gen_1366
<nil, nil>() -> q_gen_1366
<cons, b>(q_gen_1398, q_gen_1397) -> q_gen_1367
<nil, a>() -> q_gen_1367
<nil, b>() -> q_gen_1367
<a, nil>() -> q_gen_1368
<b, cons>(q_gen_1398, q_gen_1397) -> q_gen_1368
<b, nil>() -> q_gen_1368
<a, a>() -> q_gen_1369
<b, b>() -> q_gen_1369
<s, cons, nil>(q_gen_1360, q_gen_1359) -> q_gen_1352
<s, nil, nil>(q_gen_1354) -> q_gen_1352
<z, cons, cons>(q_gen_1369, q_gen_1368, q_gen_1367, q_gen_1366) -> q_gen_1352
<z, nil, nil>() -> q_gen_1352
}

Datatype: <nat, eltlist, eltlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_1351, q_gen_1357, q_gen_1389},
Q_f={q_gen_1351},
Delta=
{
<z>() -> q_gen_1389
<cons, s>(q_gen_1357, q_gen_1351) -> q_gen_1351
<nil, z>() -> q_gen_1351
<a, s>(q_gen_1389) -> q_gen_1357
<a, z>() -> q_gen_1357
<b, s>(q_gen_1389) -> q_gen_1357
<b, z>() -> q_gen_1357
}

Datatype: <eltlist, nat>
Convolution form: complete
}}}
  ;  minus -> 
{{{
Q={q_gen_1348, q_gen_1349, q_gen_1350, q_gen_1362, q_gen_1378, q_gen_1386},
Q_f={q_gen_1348, q_gen_1349},
Delta=
{
<s>(q_gen_1362) -> q_gen_1362
<z>() -> q_gen_1362
<s, s>(q_gen_1350) -> q_gen_1350
<z, z>() -> q_gen_1350
<z, s>(q_gen_1362) -> q_gen_1386
<s, s, z>(q_gen_1386) -> q_gen_1348
<z, s, z>(q_gen_1362) -> q_gen_1348
<z, z, z>() -> q_gen_1348
<s, s, s>(q_gen_1349) -> q_gen_1349
<s, s, z>(q_gen_1350) -> q_gen_1349
<s, z, s>(q_gen_1350) -> q_gen_1349
<s, z, z>(q_gen_1362) -> q_gen_1349
<s, s, s>(q_gen_1348) -> q_gen_1378
<s, s, s>(q_gen_1378) -> q_gen_1378
<s, z, s>(q_gen_1386) -> q_gen_1378
}

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

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

Teacher's answer:
New clause system:
{
() -> drop([s(u), nil, nil]) -> 12  ;  () -> drop([z, l, l]) -> 15  ;  () -> length([nil, z]) -> 12  ;  () -> minus([s(u), z, s(u)]) -> 12  ;  () -> minus([z, y, z]) -> 12  ;  (drop([n, l1, _sga]) /\ length([_sga, _tga]) /\ length([l1, _uga]) /\ minus([_uga, n, _vga])) -> eq_nat([_tga, _vga]) -> 13  ;  (drop([u, x3, _ega])) -> drop([s(u), cons(x2, x3), _ega]) -> 13  ;  (length([ll, _jga])) -> length([cons(x, ll), s(_jga)]) -> 13  ;  (minus([u, x2, _nga])) -> minus([s(u), s(x2), _nga]) -> 16
}
Sat witness: Yes: ((minus([u, x2, _nga])) -> minus([s(u), s(x2), _nga]), {
_nga -> z  ;  u -> s(z)  ;  x2 -> z
})

-------------------------------------------
Step 29, which took 0.012671 s (model generation: 0.011335,  model checking: 0.001336):

Model:
|_
{
drop -> 
{{{
Q={q_gen_1352, q_gen_1354, q_gen_1359, q_gen_1360, q_gen_1366, q_gen_1367, q_gen_1368, q_gen_1369, q_gen_1397, q_gen_1398},
Q_f={q_gen_1352},
Delta=
{
<s>(q_gen_1354) -> q_gen_1354
<z>() -> q_gen_1354
<nil>() -> q_gen_1397
<a>() -> q_gen_1398
<b>() -> q_gen_1398
<s, nil>(q_gen_1354) -> q_gen_1359
<z, nil>() -> q_gen_1359
<s, a>(q_gen_1354) -> q_gen_1360
<s, b>(q_gen_1354) -> q_gen_1360
<z, a>() -> q_gen_1360
<z, b>() -> q_gen_1360
<cons, cons>(q_gen_1369, q_gen_1368, q_gen_1367, q_gen_1366) -> q_gen_1366
<nil, nil>() -> q_gen_1366
<cons, b>(q_gen_1398, q_gen_1397) -> q_gen_1367
<nil, a>() -> q_gen_1367
<nil, b>() -> q_gen_1367
<a, nil>() -> q_gen_1368
<b, cons>(q_gen_1398, q_gen_1397) -> q_gen_1368
<b, nil>() -> q_gen_1368
<a, a>() -> q_gen_1369
<b, b>() -> q_gen_1369
<s, cons, nil>(q_gen_1360, q_gen_1359) -> q_gen_1352
<s, nil, nil>(q_gen_1354) -> q_gen_1352
<z, cons, cons>(q_gen_1369, q_gen_1368, q_gen_1367, q_gen_1366) -> q_gen_1352
<z, nil, nil>() -> q_gen_1352
}

Datatype: <nat, eltlist, eltlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_1351, q_gen_1357, q_gen_1389},
Q_f={q_gen_1351},
Delta=
{
<z>() -> q_gen_1389
<cons, s>(q_gen_1357, q_gen_1351) -> q_gen_1351
<nil, z>() -> q_gen_1351
<a, s>(q_gen_1389) -> q_gen_1357
<a, z>() -> q_gen_1357
<b, s>(q_gen_1389) -> q_gen_1357
<b, z>() -> q_gen_1357
}

Datatype: <eltlist, nat>
Convolution form: complete
}}}
  ;  minus -> 
{{{
Q={q_gen_1348, q_gen_1350, q_gen_1362, q_gen_1372, q_gen_1378, q_gen_1386},
Q_f={q_gen_1348, q_gen_1372},
Delta=
{
<s>(q_gen_1362) -> q_gen_1362
<z>() -> q_gen_1362
<s, s>(q_gen_1350) -> q_gen_1350
<s, z>(q_gen_1362) -> q_gen_1350
<z, z>() -> q_gen_1350
<z, s>(q_gen_1362) -> q_gen_1386
<s, s, z>(q_gen_1350) -> q_gen_1348
<s, z, s>(q_gen_1350) -> q_gen_1348
<z, s, z>(q_gen_1362) -> q_gen_1348
<z, z, z>() -> q_gen_1348
<s, s, s>(q_gen_1372) -> q_gen_1372
<s, s, z>(q_gen_1386) -> q_gen_1372
<s, z, z>(q_gen_1362) -> q_gen_1372
<s, s, s>(q_gen_1348) -> q_gen_1378
<s, s, s>(q_gen_1378) -> q_gen_1378
<s, z, s>(q_gen_1386) -> q_gen_1378
}

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

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

Teacher's answer:
New clause system:
{
() -> drop([s(u), nil, nil]) -> 13  ;  () -> drop([z, l, l]) -> 15  ;  () -> length([nil, z]) -> 13  ;  () -> minus([s(u), z, s(u)]) -> 13  ;  () -> minus([z, y, z]) -> 13  ;  (drop([n, l1, _sga]) /\ length([_sga, _tga]) /\ length([l1, _uga]) /\ minus([_uga, n, _vga])) -> eq_nat([_tga, _vga]) -> 13  ;  (drop([u, x3, _ega])) -> drop([s(u), cons(x2, x3), _ega]) -> 13  ;  (length([ll, _jga])) -> length([cons(x, ll), s(_jga)]) -> 16  ;  (minus([u, x2, _nga])) -> minus([s(u), s(x2), _nga]) -> 16
}
Sat witness: Yes: ((length([ll, _jga])) -> length([cons(x, ll), s(_jga)]), {
_jga -> s(s(z))  ;  ll -> cons(b, cons(b, nil))  ;  x -> b
})

-------------------------------------------
Step 30, which took 0.013060 s (model generation: 0.012307,  model checking: 0.000753):

Model:
|_
{
drop -> 
{{{
Q={q_gen_1352, q_gen_1354, q_gen_1359, q_gen_1360, q_gen_1366, q_gen_1367, q_gen_1368, q_gen_1369, q_gen_1397, q_gen_1398},
Q_f={q_gen_1352},
Delta=
{
<s>(q_gen_1354) -> q_gen_1354
<z>() -> q_gen_1354
<nil>() -> q_gen_1397
<a>() -> q_gen_1398
<b>() -> q_gen_1398
<s, nil>(q_gen_1354) -> q_gen_1359
<z, nil>() -> q_gen_1359
<s, a>(q_gen_1354) -> q_gen_1360
<s, b>(q_gen_1354) -> q_gen_1360
<z, a>() -> q_gen_1360
<z, b>() -> q_gen_1360
<cons, cons>(q_gen_1369, q_gen_1368, q_gen_1367, q_gen_1366) -> q_gen_1366
<nil, nil>() -> q_gen_1366
<cons, b>(q_gen_1398, q_gen_1397) -> q_gen_1367
<nil, a>() -> q_gen_1367
<nil, b>() -> q_gen_1367
<a, nil>() -> q_gen_1368
<b, cons>(q_gen_1398, q_gen_1397) -> q_gen_1368
<b, nil>() -> q_gen_1368
<a, a>() -> q_gen_1369
<b, b>() -> q_gen_1369
<s, cons, nil>(q_gen_1360, q_gen_1359) -> q_gen_1352
<s, nil, nil>(q_gen_1354) -> q_gen_1352
<z, cons, cons>(q_gen_1369, q_gen_1368, q_gen_1367, q_gen_1366) -> q_gen_1352
<z, nil, nil>() -> q_gen_1352
}

Datatype: <nat, eltlist, eltlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_1351, q_gen_1357, q_gen_1389},
Q_f={q_gen_1351},
Delta=
{
<s>(q_gen_1389) -> q_gen_1389
<z>() -> q_gen_1389
<cons, s>(q_gen_1357, q_gen_1351) -> q_gen_1351
<nil, z>() -> q_gen_1351
<a, s>(q_gen_1389) -> q_gen_1357
<a, z>() -> q_gen_1357
<b, s>(q_gen_1389) -> q_gen_1357
<b, z>() -> q_gen_1357
}

Datatype: <eltlist, nat>
Convolution form: complete
}}}
  ;  minus -> 
{{{
Q={q_gen_1348, q_gen_1350, q_gen_1355, q_gen_1362, q_gen_1378, q_gen_1386},
Q_f={q_gen_1348, q_gen_1355},
Delta=
{
<s>(q_gen_1362) -> q_gen_1362
<z>() -> q_gen_1362
<s, s>(q_gen_1350) -> q_gen_1350
<s, z>(q_gen_1362) -> q_gen_1350
<z, z>() -> q_gen_1350
<z, s>(q_gen_1362) -> q_gen_1386
<s, z, s>(q_gen_1350) -> q_gen_1348
<z, s, z>(q_gen_1362) -> q_gen_1348
<z, z, z>() -> q_gen_1348
<s, s, s>(q_gen_1355) -> q_gen_1355
<s, s, z>(q_gen_1350) -> q_gen_1355
<s, s, z>(q_gen_1386) -> q_gen_1355
<s, z, z>(q_gen_1362) -> q_gen_1355
<s, s, s>(q_gen_1348) -> q_gen_1378
<s, s, s>(q_gen_1378) -> q_gen_1378
<s, z, s>(q_gen_1386) -> q_gen_1378
}

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

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

Teacher's answer:
New clause system:
{
() -> drop([s(u), nil, nil]) -> 13  ;  () -> drop([z, l, l]) -> 15  ;  () -> length([nil, z]) -> 13  ;  () -> minus([s(u), z, s(u)]) -> 13  ;  () -> minus([z, y, z]) -> 13  ;  (drop([n, l1, _sga]) /\ length([_sga, _tga]) /\ length([l1, _uga]) /\ minus([_uga, n, _vga])) -> eq_nat([_tga, _vga]) -> 13  ;  (drop([u, x3, _ega])) -> drop([s(u), cons(x2, x3), _ega]) -> 16  ;  (length([ll, _jga])) -> length([cons(x, ll), s(_jga)]) -> 16  ;  (minus([u, x2, _nga])) -> minus([s(u), s(x2), _nga]) -> 16
}
Sat witness: Yes: ((drop([u, x3, _ega])) -> drop([s(u), cons(x2, x3), _ega]), {
_ega -> nil  ;  u -> s(z)  ;  x2 -> b  ;  x3 -> cons(a, nil)
})

-------------------------------------------
Step 31, which took 0.012500 s (model generation: 0.012144,  model checking: 0.000356):

Model:
|_
{
drop -> 
{{{
Q={q_gen_1352, q_gen_1354, q_gen_1359, q_gen_1360, q_gen_1366, q_gen_1367, q_gen_1368, q_gen_1369, q_gen_1397, q_gen_1398},
Q_f={q_gen_1352},
Delta=
{
<s>(q_gen_1354) -> q_gen_1354
<z>() -> q_gen_1354
<nil>() -> q_gen_1397
<a>() -> q_gen_1398
<b>() -> q_gen_1398
<s, cons>(q_gen_1360, q_gen_1359) -> q_gen_1359
<s, nil>(q_gen_1354) -> q_gen_1359
<z, nil>() -> q_gen_1359
<s, a>(q_gen_1354) -> q_gen_1360
<s, b>(q_gen_1354) -> q_gen_1360
<z, a>() -> q_gen_1360
<z, b>() -> q_gen_1360
<cons, cons>(q_gen_1369, q_gen_1368, q_gen_1367, q_gen_1366) -> q_gen_1366
<nil, nil>() -> q_gen_1366
<cons, b>(q_gen_1398, q_gen_1397) -> q_gen_1367
<nil, a>() -> q_gen_1367
<nil, b>() -> q_gen_1367
<a, nil>() -> q_gen_1368
<b, cons>(q_gen_1398, q_gen_1397) -> q_gen_1368
<b, nil>() -> q_gen_1368
<a, a>() -> q_gen_1369
<b, b>() -> q_gen_1369
<s, cons, nil>(q_gen_1360, q_gen_1359) -> q_gen_1352
<s, nil, nil>(q_gen_1354) -> q_gen_1352
<z, cons, cons>(q_gen_1369, q_gen_1368, q_gen_1367, q_gen_1366) -> q_gen_1352
<z, nil, nil>() -> q_gen_1352
}

Datatype: <nat, eltlist, eltlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_1351, q_gen_1357, q_gen_1389},
Q_f={q_gen_1351},
Delta=
{
<s>(q_gen_1389) -> q_gen_1389
<z>() -> q_gen_1389
<cons, s>(q_gen_1357, q_gen_1351) -> q_gen_1351
<nil, z>() -> q_gen_1351
<a, s>(q_gen_1389) -> q_gen_1357
<a, z>() -> q_gen_1357
<b, s>(q_gen_1389) -> q_gen_1357
<b, z>() -> q_gen_1357
}

Datatype: <eltlist, nat>
Convolution form: complete
}}}
  ;  minus -> 
{{{
Q={q_gen_1348, q_gen_1350, q_gen_1362, q_gen_1373, q_gen_1386, q_gen_1393},
Q_f={q_gen_1348},
Delta=
{
<s>(q_gen_1362) -> q_gen_1362
<z>() -> q_gen_1362
<s, s>(q_gen_1350) -> q_gen_1350
<z, z>() -> q_gen_1350
<s, z>(q_gen_1362) -> q_gen_1386
<z, s>(q_gen_1362) -> q_gen_1386
<s, s, s>(q_gen_1373) -> q_gen_1348
<s, s, z>(q_gen_1350) -> q_gen_1348
<s, s, z>(q_gen_1386) -> q_gen_1348
<s, z, s>(q_gen_1350) -> q_gen_1348
<z, s, z>(q_gen_1362) -> q_gen_1348
<z, z, z>() -> q_gen_1348
<s, s, s>(q_gen_1348) -> q_gen_1373
<s, z, z>(q_gen_1362) -> q_gen_1373
<s, s, s>(q_gen_1393) -> q_gen_1393
<s, z, s>(q_gen_1386) -> q_gen_1393
}

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

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

Teacher's answer:
New clause system:
{
() -> drop([s(u), nil, nil]) -> 13  ;  () -> drop([z, l, l]) -> 15  ;  () -> length([nil, z]) -> 13  ;  () -> minus([s(u), z, s(u)]) -> 13  ;  () -> minus([z, y, z]) -> 13  ;  (drop([n, l1, _sga]) /\ length([_sga, _tga]) /\ length([l1, _uga]) /\ minus([_uga, n, _vga])) -> eq_nat([_tga, _vga]) -> 16  ;  (drop([u, x3, _ega])) -> drop([s(u), cons(x2, x3), _ega]) -> 16  ;  (length([ll, _jga])) -> length([cons(x, ll), s(_jga)]) -> 16  ;  (minus([u, x2, _nga])) -> minus([s(u), s(x2), _nga]) -> 16
}
Sat witness: Yes: ((drop([n, l1, _sga]) /\ length([_sga, _tga]) /\ length([l1, _uga]) /\ minus([_uga, n, _vga])) -> eq_nat([_tga, _vga]), {
_sga -> nil  ;  _tga -> z  ;  _uga -> s(s(z))  ;  _vga -> s(s(z))  ;  l1 -> cons(a, cons(b, nil))  ;  n -> s(s(z))
})

-------------------------------------------
Step 32, which took 0.016402 s (model generation: 0.013087,  model checking: 0.003315):

Model:
|_
{
drop -> 
{{{
Q={q_gen_1352, q_gen_1354, q_gen_1359, q_gen_1360, q_gen_1366, q_gen_1367, q_gen_1368, q_gen_1369, q_gen_1397, q_gen_1398},
Q_f={q_gen_1352},
Delta=
{
<s>(q_gen_1354) -> q_gen_1354
<z>() -> q_gen_1354
<nil>() -> q_gen_1397
<a>() -> q_gen_1398
<b>() -> q_gen_1398
<s, cons>(q_gen_1360, q_gen_1359) -> q_gen_1359
<s, nil>(q_gen_1354) -> q_gen_1359
<z, nil>() -> q_gen_1359
<s, a>(q_gen_1354) -> q_gen_1360
<s, b>(q_gen_1354) -> q_gen_1360
<z, a>() -> q_gen_1360
<z, b>() -> q_gen_1360
<cons, cons>(q_gen_1369, q_gen_1368, q_gen_1367, q_gen_1366) -> q_gen_1366
<nil, nil>() -> q_gen_1366
<cons, b>(q_gen_1398, q_gen_1397) -> q_gen_1367
<nil, a>() -> q_gen_1367
<nil, b>() -> q_gen_1367
<a, nil>() -> q_gen_1368
<b, cons>(q_gen_1398, q_gen_1397) -> q_gen_1368
<b, nil>() -> q_gen_1368
<a, a>() -> q_gen_1369
<b, b>() -> q_gen_1369
<s, cons, nil>(q_gen_1360, q_gen_1359) -> q_gen_1352
<s, nil, nil>(q_gen_1354) -> q_gen_1352
<z, cons, cons>(q_gen_1369, q_gen_1368, q_gen_1367, q_gen_1366) -> q_gen_1352
<z, nil, nil>() -> q_gen_1352
}

Datatype: <nat, eltlist, eltlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_1351, q_gen_1357, q_gen_1389},
Q_f={q_gen_1351},
Delta=
{
<s>(q_gen_1389) -> q_gen_1389
<z>() -> q_gen_1389
<cons, s>(q_gen_1357, q_gen_1351) -> q_gen_1351
<nil, z>() -> q_gen_1351
<a, s>(q_gen_1389) -> q_gen_1357
<a, z>() -> q_gen_1357
<b, s>(q_gen_1389) -> q_gen_1357
<b, z>() -> q_gen_1357
}

Datatype: <eltlist, nat>
Convolution form: complete
}}}
  ;  minus -> 
{{{
Q={q_gen_1348, q_gen_1350, q_gen_1362, q_gen_1372, q_gen_1378, q_gen_1386},
Q_f={q_gen_1348, q_gen_1372},
Delta=
{
<s>(q_gen_1362) -> q_gen_1362
<z>() -> q_gen_1362
<s, s>(q_gen_1350) -> q_gen_1350
<s, z>(q_gen_1362) -> q_gen_1350
<z, z>() -> q_gen_1350
<z, s>(q_gen_1362) -> q_gen_1386
<s, s, z>(q_gen_1350) -> q_gen_1348
<s, z, s>(q_gen_1350) -> q_gen_1348
<z, s, z>(q_gen_1362) -> q_gen_1348
<z, z, z>() -> q_gen_1348
<s, s, s>(q_gen_1372) -> q_gen_1372
<s, s, z>(q_gen_1386) -> q_gen_1372
<s, z, z>(q_gen_1362) -> q_gen_1372
<s, s, s>(q_gen_1348) -> q_gen_1378
<s, s, s>(q_gen_1378) -> q_gen_1378
<s, z, s>(q_gen_1386) -> q_gen_1378
}

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

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

Teacher's answer:
New clause system:
{
() -> drop([s(u), nil, nil]) -> 14  ;  () -> drop([z, l, l]) -> 18  ;  () -> length([nil, z]) -> 14  ;  () -> minus([s(u), z, s(u)]) -> 14  ;  () -> minus([z, y, z]) -> 14  ;  (drop([n, l1, _sga]) /\ length([_sga, _tga]) /\ length([l1, _uga]) /\ minus([_uga, n, _vga])) -> eq_nat([_tga, _vga]) -> 16  ;  (drop([u, x3, _ega])) -> drop([s(u), cons(x2, x3), _ega]) -> 16  ;  (length([ll, _jga])) -> length([cons(x, ll), s(_jga)]) -> 16  ;  (minus([u, x2, _nga])) -> minus([s(u), s(x2), _nga]) -> 16
}
Sat witness: Yes: (() -> drop([z, l, l]), {
l -> cons(a, cons(b, nil))
})

-------------------------------------------
Step 33, which took 0.015501 s (model generation: 0.014564,  model checking: 0.000937):

Model:
|_
{
drop -> 
{{{
Q={q_gen_1352, q_gen_1354, q_gen_1359, q_gen_1360, q_gen_1366, q_gen_1367, q_gen_1368, q_gen_1369, q_gen_1397, q_gen_1398},
Q_f={q_gen_1352},
Delta=
{
<s>(q_gen_1354) -> q_gen_1354
<z>() -> q_gen_1354
<nil>() -> q_gen_1397
<a>() -> q_gen_1398
<b>() -> q_gen_1398
<s, cons>(q_gen_1360, q_gen_1359) -> q_gen_1359
<s, nil>(q_gen_1354) -> q_gen_1359
<z, nil>() -> q_gen_1359
<s, a>(q_gen_1354) -> q_gen_1360
<s, b>(q_gen_1354) -> q_gen_1360
<z, a>() -> q_gen_1360
<z, b>() -> q_gen_1360
<cons, cons>(q_gen_1369, q_gen_1368, q_gen_1367, q_gen_1366) -> q_gen_1366
<nil, nil>() -> q_gen_1366
<cons, a>(q_gen_1398, q_gen_1397) -> q_gen_1367
<cons, b>(q_gen_1398, q_gen_1397) -> q_gen_1367
<nil, a>() -> q_gen_1367
<nil, b>() -> q_gen_1367
<a, cons>(q_gen_1398, q_gen_1397) -> q_gen_1368
<a, nil>() -> q_gen_1368
<b, cons>(q_gen_1398, q_gen_1397) -> q_gen_1368
<b, nil>() -> q_gen_1368
<a, a>() -> q_gen_1369
<b, b>() -> q_gen_1369
<s, cons, nil>(q_gen_1360, q_gen_1359) -> q_gen_1352
<s, nil, nil>(q_gen_1354) -> q_gen_1352
<z, cons, cons>(q_gen_1369, q_gen_1368, q_gen_1367, q_gen_1366) -> q_gen_1352
<z, nil, nil>() -> q_gen_1352
}

Datatype: <nat, eltlist, eltlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_1351, q_gen_1357, q_gen_1389},
Q_f={q_gen_1351},
Delta=
{
<s>(q_gen_1389) -> q_gen_1389
<z>() -> q_gen_1389
<cons, s>(q_gen_1357, q_gen_1351) -> q_gen_1351
<nil, z>() -> q_gen_1351
<a, s>(q_gen_1389) -> q_gen_1357
<a, z>() -> q_gen_1357
<b, s>(q_gen_1389) -> q_gen_1357
<b, z>() -> q_gen_1357
}

Datatype: <eltlist, nat>
Convolution form: complete
}}}
  ;  minus -> 
{{{
Q={q_gen_1348, q_gen_1350, q_gen_1362, q_gen_1372, q_gen_1378, q_gen_1386},
Q_f={q_gen_1348, q_gen_1372},
Delta=
{
<s>(q_gen_1362) -> q_gen_1362
<z>() -> q_gen_1362
<s, s>(q_gen_1350) -> q_gen_1350
<s, z>(q_gen_1362) -> q_gen_1350
<z, z>() -> q_gen_1350
<z, s>(q_gen_1362) -> q_gen_1386
<s, s, z>(q_gen_1350) -> q_gen_1348
<s, z, s>(q_gen_1350) -> q_gen_1348
<z, s, z>(q_gen_1362) -> q_gen_1348
<z, z, z>() -> q_gen_1348
<s, s, s>(q_gen_1372) -> q_gen_1372
<s, s, z>(q_gen_1386) -> q_gen_1372
<s, z, z>(q_gen_1362) -> q_gen_1372
<s, s, s>(q_gen_1348) -> q_gen_1378
<s, s, s>(q_gen_1378) -> q_gen_1378
<s, z, s>(q_gen_1386) -> q_gen_1378
}

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

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

Teacher's answer:
New clause system:
{
() -> drop([s(u), nil, nil]) -> 15  ;  () -> drop([z, l, l]) -> 18  ;  () -> length([nil, z]) -> 15  ;  () -> minus([s(u), z, s(u)]) -> 15  ;  () -> minus([z, y, z]) -> 15  ;  (drop([n, l1, _sga]) /\ length([_sga, _tga]) /\ length([l1, _uga]) /\ minus([_uga, n, _vga])) -> eq_nat([_tga, _vga]) -> 16  ;  (drop([u, x3, _ega])) -> drop([s(u), cons(x2, x3), _ega]) -> 16  ;  (length([ll, _jga])) -> length([cons(x, ll), s(_jga)]) -> 16  ;  (minus([u, x2, _nga])) -> minus([s(u), s(x2), _nga]) -> 19
}
Sat witness: Yes: ((minus([u, x2, _nga])) -> minus([s(u), s(x2), _nga]), {
_nga -> s(z)  ;  u -> s(s(z))  ;  x2 -> s(z)
})

-------------------------------------------
Step 34, which took 0.027892 s (model generation: 0.016301,  model checking: 0.011591):

Model:
|_
{
drop -> 
{{{
Q={q_gen_1352, q_gen_1354, q_gen_1359, q_gen_1360, q_gen_1366, q_gen_1367, q_gen_1368, q_gen_1369, q_gen_1397, q_gen_1398},
Q_f={q_gen_1352},
Delta=
{
<s>(q_gen_1354) -> q_gen_1354
<z>() -> q_gen_1354
<nil>() -> q_gen_1397
<a>() -> q_gen_1398
<b>() -> q_gen_1398
<s, cons>(q_gen_1360, q_gen_1359) -> q_gen_1359
<s, nil>(q_gen_1354) -> q_gen_1359
<z, nil>() -> q_gen_1359
<s, a>(q_gen_1354) -> q_gen_1360
<s, b>(q_gen_1354) -> q_gen_1360
<z, a>() -> q_gen_1360
<z, b>() -> q_gen_1360
<cons, cons>(q_gen_1369, q_gen_1368, q_gen_1367, q_gen_1366) -> q_gen_1366
<nil, nil>() -> q_gen_1366
<cons, a>(q_gen_1398, q_gen_1397) -> q_gen_1367
<cons, b>(q_gen_1398, q_gen_1397) -> q_gen_1367
<nil, a>() -> q_gen_1367
<nil, b>() -> q_gen_1367
<a, cons>(q_gen_1398, q_gen_1397) -> q_gen_1368
<a, nil>() -> q_gen_1368
<b, cons>(q_gen_1398, q_gen_1397) -> q_gen_1368
<b, nil>() -> q_gen_1368
<a, a>() -> q_gen_1369
<b, b>() -> q_gen_1369
<s, cons, nil>(q_gen_1360, q_gen_1359) -> q_gen_1352
<s, nil, nil>(q_gen_1354) -> q_gen_1352
<z, cons, cons>(q_gen_1369, q_gen_1368, q_gen_1367, q_gen_1366) -> q_gen_1352
<z, nil, nil>() -> q_gen_1352
}

Datatype: <nat, eltlist, eltlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_1351, q_gen_1357, q_gen_1389},
Q_f={q_gen_1351},
Delta=
{
<s>(q_gen_1389) -> q_gen_1389
<z>() -> q_gen_1389
<cons, s>(q_gen_1357, q_gen_1351) -> q_gen_1351
<nil, z>() -> q_gen_1351
<a, s>(q_gen_1389) -> q_gen_1357
<a, z>() -> q_gen_1357
<b, s>(q_gen_1389) -> q_gen_1357
<b, z>() -> q_gen_1357
}

Datatype: <eltlist, nat>
Convolution form: complete
}}}
  ;  minus -> 
{{{
Q={q_gen_1348, q_gen_1350, q_gen_1355, q_gen_1362, q_gen_1378, q_gen_1386},
Q_f={q_gen_1348, q_gen_1355},
Delta=
{
<s>(q_gen_1362) -> q_gen_1362
<z>() -> q_gen_1362
<s, s>(q_gen_1350) -> q_gen_1350
<s, z>(q_gen_1362) -> q_gen_1350
<z, z>() -> q_gen_1350
<z, s>(q_gen_1362) -> q_gen_1386
<s, z, s>(q_gen_1350) -> q_gen_1348
<z, s, z>(q_gen_1362) -> q_gen_1348
<z, z, z>() -> q_gen_1348
<s, s, s>(q_gen_1355) -> q_gen_1355
<s, s, z>(q_gen_1350) -> q_gen_1355
<s, s, z>(q_gen_1386) -> q_gen_1355
<s, z, z>(q_gen_1362) -> q_gen_1355
<s, s, s>(q_gen_1348) -> q_gen_1378
<s, s, s>(q_gen_1378) -> q_gen_1378
<s, z, s>(q_gen_1386) -> q_gen_1378
}

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

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

Teacher's answer:
New clause system:
{
() -> drop([s(u), nil, nil]) -> 16  ;  () -> drop([z, l, l]) -> 18  ;  () -> length([nil, z]) -> 16  ;  () -> minus([s(u), z, s(u)]) -> 16  ;  () -> minus([z, y, z]) -> 16  ;  (drop([n, l1, _sga]) /\ length([_sga, _tga]) /\ length([l1, _uga]) /\ minus([_uga, n, _vga])) -> eq_nat([_tga, _vga]) -> 16  ;  (drop([u, x3, _ega])) -> drop([s(u), cons(x2, x3), _ega]) -> 19  ;  (length([ll, _jga])) -> length([cons(x, ll), s(_jga)]) -> 17  ;  (minus([u, x2, _nga])) -> minus([s(u), s(x2), _nga]) -> 19
}
Sat witness: Yes: ((drop([u, x3, _ega])) -> drop([s(u), cons(x2, x3), _ega]), {
_ega -> cons(b, nil)  ;  u -> z  ;  x2 -> b  ;  x3 -> cons(b, nil)
})

-------------------------------------------
Step 35, which took 0.016536 s (model generation: 0.016219,  model checking: 0.000317):

Model:
|_
{
drop -> 
{{{
Q={q_gen_1352, q_gen_1354, q_gen_1359, q_gen_1360, q_gen_1366, q_gen_1367, q_gen_1368, q_gen_1369, q_gen_1397, q_gen_1398, q_gen_1432, q_gen_1433, q_gen_1434},
Q_f={q_gen_1352},
Delta=
{
<s>(q_gen_1354) -> q_gen_1354
<z>() -> q_gen_1354
<nil>() -> q_gen_1397
<a>() -> q_gen_1398
<b>() -> q_gen_1398
<s, cons>(q_gen_1360, q_gen_1359) -> q_gen_1359
<s, nil>(q_gen_1354) -> q_gen_1359
<z, nil>() -> q_gen_1359
<s, a>(q_gen_1354) -> q_gen_1360
<s, b>(q_gen_1354) -> q_gen_1360
<z, a>() -> q_gen_1360
<z, b>() -> q_gen_1360
<cons, cons>(q_gen_1369, q_gen_1368, q_gen_1367, q_gen_1366) -> q_gen_1366
<nil, nil>() -> q_gen_1366
<cons, a>(q_gen_1398, q_gen_1397) -> q_gen_1367
<cons, b>(q_gen_1398, q_gen_1397) -> q_gen_1367
<nil, a>() -> q_gen_1367
<nil, b>() -> q_gen_1367
<a, cons>(q_gen_1398, q_gen_1397) -> q_gen_1368
<a, nil>() -> q_gen_1368
<b, cons>(q_gen_1398, q_gen_1397) -> q_gen_1368
<b, nil>() -> q_gen_1368
<a, a>() -> q_gen_1369
<b, b>() -> q_gen_1369
<s, cons, cons>(q_gen_1434, q_gen_1433, q_gen_1432, q_gen_1352) -> q_gen_1352
<s, cons, nil>(q_gen_1360, q_gen_1359) -> q_gen_1352
<s, nil, nil>(q_gen_1354) -> q_gen_1352
<z, cons, cons>(q_gen_1369, q_gen_1368, q_gen_1367, q_gen_1366) -> q_gen_1352
<z, cons, nil>(q_gen_1398, q_gen_1397) -> q_gen_1352
<z, nil, nil>() -> q_gen_1352
<z, cons, b>(q_gen_1398, q_gen_1397) -> q_gen_1432
<z, b, nil>() -> q_gen_1433
<z, b, b>() -> q_gen_1434
}

Datatype: <nat, eltlist, eltlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_1351, q_gen_1357, q_gen_1389},
Q_f={q_gen_1351},
Delta=
{
<s>(q_gen_1389) -> q_gen_1389
<z>() -> q_gen_1389
<cons, s>(q_gen_1357, q_gen_1351) -> q_gen_1351
<nil, z>() -> q_gen_1351
<a, s>(q_gen_1389) -> q_gen_1357
<a, z>() -> q_gen_1357
<b, s>(q_gen_1389) -> q_gen_1357
<b, z>() -> q_gen_1357
}

Datatype: <eltlist, nat>
Convolution form: complete
}}}
  ;  minus -> 
{{{
Q={q_gen_1348, q_gen_1350, q_gen_1362, q_gen_1372, q_gen_1378, q_gen_1386},
Q_f={q_gen_1348, q_gen_1372},
Delta=
{
<s>(q_gen_1362) -> q_gen_1362
<z>() -> q_gen_1362
<s, s>(q_gen_1350) -> q_gen_1350
<z, z>() -> q_gen_1350
<s, z>(q_gen_1362) -> q_gen_1386
<z, s>(q_gen_1362) -> q_gen_1386
<s, s, z>(q_gen_1350) -> q_gen_1348
<s, z, s>(q_gen_1350) -> q_gen_1348
<z, s, z>(q_gen_1362) -> q_gen_1348
<z, z, z>() -> q_gen_1348
<s, s, s>(q_gen_1372) -> q_gen_1372
<s, s, z>(q_gen_1386) -> q_gen_1372
<s, z, z>(q_gen_1362) -> q_gen_1372
<s, s, s>(q_gen_1348) -> q_gen_1378
<s, s, s>(q_gen_1378) -> q_gen_1378
<s, z, s>(q_gen_1386) -> q_gen_1378
}

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

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

Teacher's answer:
New clause system:
{
() -> drop([s(u), nil, nil]) -> 16  ;  () -> drop([z, l, l]) -> 18  ;  () -> length([nil, z]) -> 16  ;  () -> minus([s(u), z, s(u)]) -> 16  ;  () -> minus([z, y, z]) -> 16  ;  (drop([n, l1, _sga]) /\ length([_sga, _tga]) /\ length([l1, _uga]) /\ minus([_uga, n, _vga])) -> eq_nat([_tga, _vga]) -> 19  ;  (drop([u, x3, _ega])) -> drop([s(u), cons(x2, x3), _ega]) -> 19  ;  (length([ll, _jga])) -> length([cons(x, ll), s(_jga)]) -> 17  ;  (minus([u, x2, _nga])) -> minus([s(u), s(x2), _nga]) -> 19
}
Sat witness: Yes: ((drop([n, l1, _sga]) /\ length([_sga, _tga]) /\ length([l1, _uga]) /\ minus([_uga, n, _vga])) -> eq_nat([_tga, _vga]), {
_sga -> nil  ;  _tga -> z  ;  _uga -> s(s(z))  ;  _vga -> s(z)  ;  l1 -> cons(b, cons(a, nil))  ;  n -> s(s(s(z)))
})

-------------------------------------------
Step 36, which took 0.026527 s (model generation: 0.018908,  model checking: 0.007619):

Model:
|_
{
drop -> 
{{{
Q={q_gen_1352, q_gen_1354, q_gen_1359, q_gen_1360, q_gen_1366, q_gen_1367, q_gen_1368, q_gen_1369, q_gen_1397, q_gen_1398, q_gen_1432, q_gen_1433, q_gen_1434},
Q_f={q_gen_1352},
Delta=
{
<s>(q_gen_1354) -> q_gen_1354
<z>() -> q_gen_1354
<nil>() -> q_gen_1397
<a>() -> q_gen_1398
<b>() -> q_gen_1398
<s, cons>(q_gen_1360, q_gen_1359) -> q_gen_1359
<s, nil>(q_gen_1354) -> q_gen_1359
<z, nil>() -> q_gen_1359
<s, a>(q_gen_1354) -> q_gen_1360
<s, b>(q_gen_1354) -> q_gen_1360
<z, a>() -> q_gen_1360
<z, b>() -> q_gen_1360
<cons, cons>(q_gen_1369, q_gen_1368, q_gen_1367, q_gen_1366) -> q_gen_1366
<nil, nil>() -> q_gen_1366
<cons, a>(q_gen_1398, q_gen_1397) -> q_gen_1367
<cons, b>(q_gen_1398, q_gen_1397) -> q_gen_1367
<nil, a>() -> q_gen_1367
<nil, b>() -> q_gen_1367
<a, cons>(q_gen_1398, q_gen_1397) -> q_gen_1368
<a, nil>() -> q_gen_1368
<b, cons>(q_gen_1398, q_gen_1397) -> q_gen_1368
<b, nil>() -> q_gen_1368
<a, a>() -> q_gen_1369
<b, b>() -> q_gen_1369
<s, cons, cons>(q_gen_1434, q_gen_1433, q_gen_1432, q_gen_1352) -> q_gen_1352
<s, cons, nil>(q_gen_1360, q_gen_1359) -> q_gen_1352
<s, nil, nil>(q_gen_1354) -> q_gen_1352
<z, cons, cons>(q_gen_1369, q_gen_1368, q_gen_1367, q_gen_1366) -> q_gen_1352
<z, cons, nil>(q_gen_1398, q_gen_1397) -> q_gen_1352
<z, nil, nil>() -> q_gen_1352
<z, cons, b>(q_gen_1398, q_gen_1397) -> q_gen_1432
<z, b, nil>() -> q_gen_1433
<z, b, b>() -> q_gen_1434
}

Datatype: <nat, eltlist, eltlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_1351, q_gen_1357, q_gen_1389},
Q_f={q_gen_1351},
Delta=
{
<s>(q_gen_1389) -> q_gen_1389
<z>() -> q_gen_1389
<cons, s>(q_gen_1357, q_gen_1351) -> q_gen_1351
<nil, z>() -> q_gen_1351
<a, s>(q_gen_1389) -> q_gen_1357
<a, z>() -> q_gen_1357
<b, s>(q_gen_1389) -> q_gen_1357
<b, z>() -> q_gen_1357
}

Datatype: <eltlist, nat>
Convolution form: complete
}}}
  ;  minus -> 
{{{
Q={q_gen_1348, q_gen_1350, q_gen_1355, q_gen_1362, q_gen_1378, q_gen_1386},
Q_f={q_gen_1348, q_gen_1355},
Delta=
{
<s>(q_gen_1362) -> q_gen_1362
<z>() -> q_gen_1362
<s, s>(q_gen_1350) -> q_gen_1350
<s, z>(q_gen_1362) -> q_gen_1350
<z, z>() -> q_gen_1350
<z, s>(q_gen_1362) -> q_gen_1386
<s, s, s>(q_gen_1355) -> q_gen_1348
<s, s, z>(q_gen_1386) -> q_gen_1348
<s, z, s>(q_gen_1350) -> q_gen_1348
<z, s, z>(q_gen_1362) -> q_gen_1348
<z, z, z>() -> q_gen_1348
<s, s, z>(q_gen_1350) -> q_gen_1355
<s, z, z>(q_gen_1362) -> q_gen_1355
<s, s, s>(q_gen_1348) -> q_gen_1378
<s, s, s>(q_gen_1378) -> q_gen_1378
<s, z, s>(q_gen_1386) -> q_gen_1378
}

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

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

Teacher's answer:
New clause system:
{
() -> drop([s(u), nil, nil]) -> 17  ;  () -> drop([z, l, l]) -> 21  ;  () -> length([nil, z]) -> 17  ;  () -> minus([s(u), z, s(u)]) -> 17  ;  () -> minus([z, y, z]) -> 17  ;  (drop([n, l1, _sga]) /\ length([_sga, _tga]) /\ length([l1, _uga]) /\ minus([_uga, n, _vga])) -> eq_nat([_tga, _vga]) -> 19  ;  (drop([u, x3, _ega])) -> drop([s(u), cons(x2, x3), _ega]) -> 19  ;  (length([ll, _jga])) -> length([cons(x, ll), s(_jga)]) -> 18  ;  (minus([u, x2, _nga])) -> minus([s(u), s(x2), _nga]) -> 19
}
Sat witness: Yes: (() -> drop([z, l, l]), {
l -> cons(b, cons(b, cons(b, nil)))
})

-------------------------------------------
Step 37, which took 0.024626 s (model generation: 0.023711,  model checking: 0.000915):

Model:
|_
{
drop -> 
{{{
Q={q_gen_1352, q_gen_1354, q_gen_1359, q_gen_1360, q_gen_1366, q_gen_1367, q_gen_1368, q_gen_1369, q_gen_1397, q_gen_1398, q_gen_1432, q_gen_1433, q_gen_1434},
Q_f={q_gen_1352},
Delta=
{
<s>(q_gen_1354) -> q_gen_1354
<z>() -> q_gen_1354
<cons>(q_gen_1398, q_gen_1397) -> q_gen_1397
<nil>() -> q_gen_1397
<a>() -> q_gen_1398
<b>() -> q_gen_1398
<s, cons>(q_gen_1360, q_gen_1359) -> q_gen_1359
<s, nil>(q_gen_1354) -> q_gen_1359
<z, nil>() -> q_gen_1359
<s, a>(q_gen_1354) -> q_gen_1360
<s, b>(q_gen_1354) -> q_gen_1360
<z, a>() -> q_gen_1360
<z, b>() -> q_gen_1360
<cons, cons>(q_gen_1369, q_gen_1368, q_gen_1367, q_gen_1366) -> q_gen_1366
<nil, nil>() -> q_gen_1366
<cons, a>(q_gen_1398, q_gen_1397) -> q_gen_1367
<cons, b>(q_gen_1398, q_gen_1397) -> q_gen_1367
<nil, a>() -> q_gen_1367
<nil, b>() -> q_gen_1367
<a, cons>(q_gen_1398, q_gen_1397) -> q_gen_1368
<a, nil>() -> q_gen_1368
<b, cons>(q_gen_1398, q_gen_1397) -> q_gen_1368
<b, nil>() -> q_gen_1368
<a, a>() -> q_gen_1369
<b, b>() -> q_gen_1369
<s, cons, cons>(q_gen_1434, q_gen_1433, q_gen_1432, q_gen_1352) -> q_gen_1352
<s, cons, nil>(q_gen_1360, q_gen_1359) -> q_gen_1352
<s, nil, nil>(q_gen_1354) -> q_gen_1352
<z, cons, cons>(q_gen_1369, q_gen_1368, q_gen_1367, q_gen_1366) -> q_gen_1352
<z, cons, nil>(q_gen_1398, q_gen_1397) -> q_gen_1352
<z, nil, nil>() -> q_gen_1352
<z, cons, b>(q_gen_1398, q_gen_1397) -> q_gen_1432
<z, b, nil>() -> q_gen_1433
<z, b, b>() -> q_gen_1434
}

Datatype: <nat, eltlist, eltlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_1351, q_gen_1357, q_gen_1389},
Q_f={q_gen_1351},
Delta=
{
<s>(q_gen_1389) -> q_gen_1389
<z>() -> q_gen_1389
<cons, s>(q_gen_1357, q_gen_1351) -> q_gen_1351
<nil, z>() -> q_gen_1351
<a, s>(q_gen_1389) -> q_gen_1357
<a, z>() -> q_gen_1357
<b, s>(q_gen_1389) -> q_gen_1357
<b, z>() -> q_gen_1357
}

Datatype: <eltlist, nat>
Convolution form: complete
}}}
  ;  minus -> 
{{{
Q={q_gen_1348, q_gen_1350, q_gen_1355, q_gen_1362, q_gen_1378, q_gen_1386},
Q_f={q_gen_1348, q_gen_1355},
Delta=
{
<s>(q_gen_1362) -> q_gen_1362
<z>() -> q_gen_1362
<s, s>(q_gen_1350) -> q_gen_1350
<s, z>(q_gen_1362) -> q_gen_1350
<z, z>() -> q_gen_1350
<z, s>(q_gen_1362) -> q_gen_1386
<s, s, s>(q_gen_1355) -> q_gen_1348
<s, s, z>(q_gen_1386) -> q_gen_1348
<s, z, s>(q_gen_1350) -> q_gen_1348
<z, s, z>(q_gen_1362) -> q_gen_1348
<z, z, z>() -> q_gen_1348
<s, s, z>(q_gen_1350) -> q_gen_1355
<s, z, z>(q_gen_1362) -> q_gen_1355
<s, s, s>(q_gen_1348) -> q_gen_1378
<s, s, s>(q_gen_1378) -> q_gen_1378
<s, z, s>(q_gen_1386) -> q_gen_1378
}

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

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

Teacher's answer:
New clause system:
{
() -> drop([s(u), nil, nil]) -> 18  ;  () -> drop([z, l, l]) -> 21  ;  () -> length([nil, z]) -> 18  ;  () -> minus([s(u), z, s(u)]) -> 18  ;  () -> minus([z, y, z]) -> 18  ;  (drop([n, l1, _sga]) /\ length([_sga, _tga]) /\ length([l1, _uga]) /\ minus([_uga, n, _vga])) -> eq_nat([_tga, _vga]) -> 19  ;  (drop([u, x3, _ega])) -> drop([s(u), cons(x2, x3), _ega]) -> 19  ;  (length([ll, _jga])) -> length([cons(x, ll), s(_jga)]) -> 19  ;  (minus([u, x2, _nga])) -> minus([s(u), s(x2), _nga]) -> 22
}
Sat witness: Yes: ((minus([u, x2, _nga])) -> minus([s(u), s(x2), _nga]), {
_nga -> s(s(z))  ;  u -> s(s(z))  ;  x2 -> z
})

-------------------------------------------
Step 38, which took 0.020911 s (model generation: 0.019114,  model checking: 0.001797):

Model:
|_
{
drop -> 
{{{
Q={q_gen_1352, q_gen_1354, q_gen_1359, q_gen_1360, q_gen_1366, q_gen_1367, q_gen_1368, q_gen_1369, q_gen_1397, q_gen_1398, q_gen_1432, q_gen_1433, q_gen_1434},
Q_f={q_gen_1352},
Delta=
{
<s>(q_gen_1354) -> q_gen_1354
<z>() -> q_gen_1354
<cons>(q_gen_1398, q_gen_1397) -> q_gen_1397
<nil>() -> q_gen_1397
<a>() -> q_gen_1398
<b>() -> q_gen_1398
<s, cons>(q_gen_1360, q_gen_1359) -> q_gen_1359
<s, nil>(q_gen_1354) -> q_gen_1359
<z, nil>() -> q_gen_1359
<s, a>(q_gen_1354) -> q_gen_1360
<s, b>(q_gen_1354) -> q_gen_1360
<z, a>() -> q_gen_1360
<z, b>() -> q_gen_1360
<cons, cons>(q_gen_1369, q_gen_1368, q_gen_1367, q_gen_1366) -> q_gen_1366
<nil, nil>() -> q_gen_1366
<cons, a>(q_gen_1398, q_gen_1397) -> q_gen_1367
<cons, b>(q_gen_1398, q_gen_1397) -> q_gen_1367
<nil, a>() -> q_gen_1367
<nil, b>() -> q_gen_1367
<a, cons>(q_gen_1398, q_gen_1397) -> q_gen_1368
<a, nil>() -> q_gen_1368
<b, cons>(q_gen_1398, q_gen_1397) -> q_gen_1368
<b, nil>() -> q_gen_1368
<a, a>() -> q_gen_1369
<b, b>() -> q_gen_1369
<s, cons, cons>(q_gen_1434, q_gen_1433, q_gen_1432, q_gen_1352) -> q_gen_1352
<s, cons, nil>(q_gen_1360, q_gen_1359) -> q_gen_1352
<s, nil, nil>(q_gen_1354) -> q_gen_1352
<z, cons, cons>(q_gen_1369, q_gen_1368, q_gen_1367, q_gen_1366) -> q_gen_1352
<z, cons, nil>(q_gen_1398, q_gen_1397) -> q_gen_1352
<z, nil, nil>() -> q_gen_1352
<z, cons, b>(q_gen_1398, q_gen_1397) -> q_gen_1432
<z, b, nil>() -> q_gen_1433
<z, b, b>() -> q_gen_1434
}

Datatype: <nat, eltlist, eltlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_1351, q_gen_1357, q_gen_1389},
Q_f={q_gen_1351},
Delta=
{
<s>(q_gen_1389) -> q_gen_1389
<z>() -> q_gen_1389
<cons, s>(q_gen_1357, q_gen_1351) -> q_gen_1351
<nil, z>() -> q_gen_1351
<a, s>(q_gen_1389) -> q_gen_1357
<a, z>() -> q_gen_1357
<b, s>(q_gen_1389) -> q_gen_1357
<b, z>() -> q_gen_1357
}

Datatype: <eltlist, nat>
Convolution form: complete
}}}
  ;  minus -> 
{{{
Q={q_gen_1348, q_gen_1349, q_gen_1350, q_gen_1362, q_gen_1378, q_gen_1386},
Q_f={q_gen_1348, q_gen_1349},
Delta=
{
<s>(q_gen_1362) -> q_gen_1362
<z>() -> q_gen_1362
<s, s>(q_gen_1350) -> q_gen_1350
<s, z>(q_gen_1362) -> q_gen_1350
<z, z>() -> q_gen_1350
<z, s>(q_gen_1362) -> q_gen_1386
<s, s, s>(q_gen_1349) -> q_gen_1348
<s, s, z>(q_gen_1386) -> q_gen_1348
<z, s, z>(q_gen_1362) -> q_gen_1348
<z, z, z>() -> q_gen_1348
<s, s, z>(q_gen_1350) -> q_gen_1349
<s, z, s>(q_gen_1350) -> q_gen_1349
<s, z, z>(q_gen_1362) -> q_gen_1349
<s, s, s>(q_gen_1348) -> q_gen_1378
<s, s, s>(q_gen_1378) -> q_gen_1378
<s, z, s>(q_gen_1386) -> q_gen_1378
}

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

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

Teacher's answer:
New clause system:
{
() -> drop([s(u), nil, nil]) -> 19  ;  () -> drop([z, l, l]) -> 21  ;  () -> length([nil, z]) -> 19  ;  () -> minus([s(u), z, s(u)]) -> 19  ;  () -> minus([z, y, z]) -> 19  ;  (drop([n, l1, _sga]) /\ length([_sga, _tga]) /\ length([l1, _uga]) /\ minus([_uga, n, _vga])) -> eq_nat([_tga, _vga]) -> 19  ;  (drop([u, x3, _ega])) -> drop([s(u), cons(x2, x3), _ega]) -> 22  ;  (length([ll, _jga])) -> length([cons(x, ll), s(_jga)]) -> 20  ;  (minus([u, x2, _nga])) -> minus([s(u), s(x2), _nga]) -> 22
}
Sat witness: Yes: ((drop([u, x3, _ega])) -> drop([s(u), cons(x2, x3), _ega]), {
_ega -> nil  ;  u -> z  ;  x2 -> b  ;  x3 -> cons(a, nil)
})

-------------------------------------------
Step 39, which took 0.024043 s (model generation: 0.023672,  model checking: 0.000371):

Model:
|_
{
drop -> 
{{{
Q={q_gen_1352, q_gen_1354, q_gen_1359, q_gen_1360, q_gen_1366, q_gen_1367, q_gen_1368, q_gen_1369, q_gen_1397, q_gen_1398, q_gen_1432, q_gen_1433, q_gen_1434},
Q_f={q_gen_1352},
Delta=
{
<s>(q_gen_1354) -> q_gen_1354
<z>() -> q_gen_1354
<cons>(q_gen_1398, q_gen_1397) -> q_gen_1397
<nil>() -> q_gen_1397
<a>() -> q_gen_1398
<b>() -> q_gen_1398
<s, cons>(q_gen_1360, q_gen_1359) -> q_gen_1359
<s, nil>(q_gen_1354) -> q_gen_1359
<z, cons>(q_gen_1398, q_gen_1397) -> q_gen_1359
<z, nil>() -> q_gen_1359
<s, a>(q_gen_1354) -> q_gen_1360
<s, b>(q_gen_1354) -> q_gen_1360
<z, a>() -> q_gen_1360
<z, b>() -> q_gen_1360
<cons, cons>(q_gen_1369, q_gen_1368, q_gen_1367, q_gen_1366) -> q_gen_1366
<nil, nil>() -> q_gen_1366
<cons, a>(q_gen_1398, q_gen_1397) -> q_gen_1367
<cons, b>(q_gen_1398, q_gen_1397) -> q_gen_1367
<nil, a>() -> q_gen_1367
<nil, b>() -> q_gen_1367
<a, cons>(q_gen_1398, q_gen_1397) -> q_gen_1368
<a, nil>() -> q_gen_1368
<b, cons>(q_gen_1398, q_gen_1397) -> q_gen_1368
<b, nil>() -> q_gen_1368
<a, a>() -> q_gen_1369
<b, b>() -> q_gen_1369
<s, cons, cons>(q_gen_1434, q_gen_1433, q_gen_1432, q_gen_1352) -> q_gen_1352
<s, cons, nil>(q_gen_1360, q_gen_1359) -> q_gen_1352
<s, nil, nil>(q_gen_1354) -> q_gen_1352
<z, cons, cons>(q_gen_1369, q_gen_1368, q_gen_1367, q_gen_1366) -> q_gen_1352
<z, cons, nil>(q_gen_1398, q_gen_1397) -> q_gen_1352
<z, nil, nil>() -> q_gen_1352
<z, cons, b>(q_gen_1398, q_gen_1397) -> q_gen_1432
<z, b, nil>() -> q_gen_1433
<z, b, b>() -> q_gen_1434
}

Datatype: <nat, eltlist, eltlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_1351, q_gen_1357, q_gen_1389},
Q_f={q_gen_1351},
Delta=
{
<s>(q_gen_1389) -> q_gen_1389
<z>() -> q_gen_1389
<cons, s>(q_gen_1357, q_gen_1351) -> q_gen_1351
<nil, z>() -> q_gen_1351
<a, s>(q_gen_1389) -> q_gen_1357
<a, z>() -> q_gen_1357
<b, s>(q_gen_1389) -> q_gen_1357
<b, z>() -> q_gen_1357
}

Datatype: <eltlist, nat>
Convolution form: complete
}}}
  ;  minus -> 
{{{
Q={q_gen_1348, q_gen_1349, q_gen_1350, q_gen_1362, q_gen_1378, q_gen_1386},
Q_f={q_gen_1348, q_gen_1349},
Delta=
{
<s>(q_gen_1362) -> q_gen_1362
<z>() -> q_gen_1362
<s, s>(q_gen_1350) -> q_gen_1350
<s, z>(q_gen_1362) -> q_gen_1350
<z, z>() -> q_gen_1350
<z, s>(q_gen_1362) -> q_gen_1386
<s, s, z>(q_gen_1386) -> q_gen_1348
<z, s, z>(q_gen_1362) -> q_gen_1348
<z, z, z>() -> q_gen_1348
<s, s, s>(q_gen_1349) -> q_gen_1349
<s, s, z>(q_gen_1350) -> q_gen_1349
<s, z, s>(q_gen_1350) -> q_gen_1349
<s, z, z>(q_gen_1362) -> q_gen_1349
<s, s, s>(q_gen_1348) -> q_gen_1378
<s, s, s>(q_gen_1378) -> q_gen_1378
<s, z, s>(q_gen_1386) -> q_gen_1378
}

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

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

Teacher's answer:
New clause system:
{
() -> drop([s(u), nil, nil]) -> 19  ;  () -> drop([z, l, l]) -> 21  ;  () -> length([nil, z]) -> 19  ;  () -> minus([s(u), z, s(u)]) -> 19  ;  () -> minus([z, y, z]) -> 19  ;  (drop([n, l1, _sga]) /\ length([_sga, _tga]) /\ length([l1, _uga]) /\ minus([_uga, n, _vga])) -> eq_nat([_tga, _vga]) -> 22  ;  (drop([u, x3, _ega])) -> drop([s(u), cons(x2, x3), _ega]) -> 22  ;  (length([ll, _jga])) -> length([cons(x, ll), s(_jga)]) -> 20  ;  (minus([u, x2, _nga])) -> minus([s(u), s(x2), _nga]) -> 22
}
Sat witness: Yes: ((drop([n, l1, _sga]) /\ length([_sga, _tga]) /\ length([l1, _uga]) /\ minus([_uga, n, _vga])) -> eq_nat([_tga, _vga]), {
_sga -> nil  ;  _tga -> z  ;  _uga -> s(z)  ;  _vga -> s(z)  ;  l1 -> cons(b, nil)  ;  n -> z
})

-------------------------------------------
Step 40, which took 0.025427 s (model generation: 0.023816,  model checking: 0.001611):

Model:
|_
{
drop -> 
{{{
Q={q_gen_1352, q_gen_1354, q_gen_1359, q_gen_1360, q_gen_1366, q_gen_1367, q_gen_1368, q_gen_1369, q_gen_1397, q_gen_1398, q_gen_1431, q_gen_1432, q_gen_1433, q_gen_1434},
Q_f={q_gen_1352},
Delta=
{
<s>(q_gen_1354) -> q_gen_1354
<z>() -> q_gen_1354
<cons>(q_gen_1398, q_gen_1397) -> q_gen_1397
<nil>() -> q_gen_1397
<a>() -> q_gen_1398
<b>() -> q_gen_1398
<s, cons>(q_gen_1360, q_gen_1359) -> q_gen_1359
<s, nil>(q_gen_1354) -> q_gen_1359
<z, cons>(q_gen_1398, q_gen_1397) -> q_gen_1359
<z, nil>() -> q_gen_1359
<s, a>(q_gen_1354) -> q_gen_1360
<s, b>(q_gen_1354) -> q_gen_1360
<z, a>() -> q_gen_1360
<z, b>() -> q_gen_1360
<cons, cons>(q_gen_1369, q_gen_1368, q_gen_1367, q_gen_1366) -> q_gen_1366
<nil, nil>() -> q_gen_1366
<cons, a>(q_gen_1398, q_gen_1397) -> q_gen_1367
<cons, b>(q_gen_1398, q_gen_1397) -> q_gen_1367
<nil, a>() -> q_gen_1367
<nil, b>() -> q_gen_1367
<a, cons>(q_gen_1398, q_gen_1397) -> q_gen_1368
<a, nil>() -> q_gen_1368
<b, cons>(q_gen_1398, q_gen_1397) -> q_gen_1368
<b, nil>() -> q_gen_1368
<a, a>() -> q_gen_1369
<b, b>() -> q_gen_1369
<s, cons, cons>(q_gen_1434, q_gen_1433, q_gen_1432, q_gen_1431) -> q_gen_1352
<s, cons, nil>(q_gen_1360, q_gen_1359) -> q_gen_1352
<s, nil, nil>(q_gen_1354) -> q_gen_1352
<z, cons, cons>(q_gen_1369, q_gen_1368, q_gen_1367, q_gen_1366) -> q_gen_1352
<z, nil, nil>() -> q_gen_1352
<z, cons, nil>(q_gen_1398, q_gen_1397) -> q_gen_1431
<z, cons, b>(q_gen_1398, q_gen_1397) -> q_gen_1432
<z, b, nil>() -> q_gen_1433
<z, b, b>() -> q_gen_1434
}

Datatype: <nat, eltlist, eltlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_1351, q_gen_1357, q_gen_1389},
Q_f={q_gen_1351},
Delta=
{
<s>(q_gen_1389) -> q_gen_1389
<z>() -> q_gen_1389
<cons, s>(q_gen_1357, q_gen_1351) -> q_gen_1351
<nil, z>() -> q_gen_1351
<a, s>(q_gen_1389) -> q_gen_1357
<a, z>() -> q_gen_1357
<b, s>(q_gen_1389) -> q_gen_1357
<b, z>() -> q_gen_1357
}

Datatype: <eltlist, nat>
Convolution form: complete
}}}
  ;  minus -> 
{{{
Q={q_gen_1348, q_gen_1349, q_gen_1350, q_gen_1362, q_gen_1378, q_gen_1386},
Q_f={q_gen_1348, q_gen_1349},
Delta=
{
<s>(q_gen_1362) -> q_gen_1362
<z>() -> q_gen_1362
<s, s>(q_gen_1350) -> q_gen_1350
<s, z>(q_gen_1362) -> q_gen_1350
<z, z>() -> q_gen_1350
<z, s>(q_gen_1362) -> q_gen_1386
<s, s, s>(q_gen_1349) -> q_gen_1348
<s, s, z>(q_gen_1386) -> q_gen_1348
<z, s, z>(q_gen_1362) -> q_gen_1348
<z, z, z>() -> q_gen_1348
<s, s, z>(q_gen_1350) -> q_gen_1349
<s, z, s>(q_gen_1350) -> q_gen_1349
<s, z, z>(q_gen_1362) -> q_gen_1349
<s, s, s>(q_gen_1348) -> q_gen_1378
<s, s, s>(q_gen_1378) -> q_gen_1378
<s, z, s>(q_gen_1386) -> q_gen_1378
}

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

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

Teacher's answer:
New clause system:
{
() -> drop([s(u), nil, nil]) -> 20  ;  () -> drop([z, l, l]) -> 22  ;  () -> length([nil, z]) -> 20  ;  () -> minus([s(u), z, s(u)]) -> 20  ;  () -> minus([z, y, z]) -> 20  ;  (drop([n, l1, _sga]) /\ length([_sga, _tga]) /\ length([l1, _uga]) /\ minus([_uga, n, _vga])) -> eq_nat([_tga, _vga]) -> 22  ;  (drop([u, x3, _ega])) -> drop([s(u), cons(x2, x3), _ega]) -> 22  ;  (length([ll, _jga])) -> length([cons(x, ll), s(_jga)]) -> 21  ;  (minus([u, x2, _nga])) -> minus([s(u), s(x2), _nga]) -> 25
}
Sat witness: Yes: ((minus([u, x2, _nga])) -> minus([s(u), s(x2), _nga]), {
_nga -> s(s(z))  ;  u -> s(s(z))  ;  x2 -> s(z)
})

-------------------------------------------
Step 41, which took 0.027351 s (model generation: 0.025070,  model checking: 0.002281):

Model:
|_
{
drop -> 
{{{
Q={q_gen_1352, q_gen_1354, q_gen_1359, q_gen_1360, q_gen_1366, q_gen_1367, q_gen_1368, q_gen_1369, q_gen_1397, q_gen_1398, q_gen_1431, q_gen_1432, q_gen_1433, q_gen_1434},
Q_f={q_gen_1352},
Delta=
{
<s>(q_gen_1354) -> q_gen_1354
<z>() -> q_gen_1354
<cons>(q_gen_1398, q_gen_1397) -> q_gen_1397
<nil>() -> q_gen_1397
<a>() -> q_gen_1398
<b>() -> q_gen_1398
<s, cons>(q_gen_1360, q_gen_1359) -> q_gen_1359
<s, nil>(q_gen_1354) -> q_gen_1359
<z, cons>(q_gen_1398, q_gen_1397) -> q_gen_1359
<z, nil>() -> q_gen_1359
<s, a>(q_gen_1354) -> q_gen_1360
<s, b>(q_gen_1354) -> q_gen_1360
<z, a>() -> q_gen_1360
<z, b>() -> q_gen_1360
<cons, cons>(q_gen_1369, q_gen_1368, q_gen_1367, q_gen_1366) -> q_gen_1366
<nil, nil>() -> q_gen_1366
<cons, a>(q_gen_1398, q_gen_1397) -> q_gen_1367
<cons, b>(q_gen_1398, q_gen_1397) -> q_gen_1367
<nil, a>() -> q_gen_1367
<nil, b>() -> q_gen_1367
<a, cons>(q_gen_1398, q_gen_1397) -> q_gen_1368
<a, nil>() -> q_gen_1368
<b, cons>(q_gen_1398, q_gen_1397) -> q_gen_1368
<b, nil>() -> q_gen_1368
<a, a>() -> q_gen_1369
<b, b>() -> q_gen_1369
<s, cons, cons>(q_gen_1434, q_gen_1433, q_gen_1432, q_gen_1431) -> q_gen_1352
<s, cons, nil>(q_gen_1360, q_gen_1359) -> q_gen_1352
<s, nil, nil>(q_gen_1354) -> q_gen_1352
<z, cons, cons>(q_gen_1369, q_gen_1368, q_gen_1367, q_gen_1366) -> q_gen_1352
<z, nil, nil>() -> q_gen_1352
<z, cons, nil>(q_gen_1398, q_gen_1397) -> q_gen_1431
<z, cons, b>(q_gen_1398, q_gen_1397) -> q_gen_1432
<z, b, nil>() -> q_gen_1433
<z, b, b>() -> q_gen_1434
}

Datatype: <nat, eltlist, eltlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_1351, q_gen_1357, q_gen_1389},
Q_f={q_gen_1351},
Delta=
{
<s>(q_gen_1389) -> q_gen_1389
<z>() -> q_gen_1389
<cons, s>(q_gen_1357, q_gen_1351) -> q_gen_1351
<nil, z>() -> q_gen_1351
<a, s>(q_gen_1389) -> q_gen_1357
<a, z>() -> q_gen_1357
<b, s>(q_gen_1389) -> q_gen_1357
<b, z>() -> q_gen_1357
}

Datatype: <eltlist, nat>
Convolution form: complete
}}}
  ;  minus -> 
{{{
Q={q_gen_1348, q_gen_1349, q_gen_1350, q_gen_1362, q_gen_1378, q_gen_1386},
Q_f={q_gen_1348, q_gen_1349},
Delta=
{
<s>(q_gen_1362) -> q_gen_1362
<z>() -> q_gen_1362
<s, s>(q_gen_1350) -> q_gen_1350
<s, z>(q_gen_1362) -> q_gen_1350
<z, z>() -> q_gen_1350
<z, s>(q_gen_1362) -> q_gen_1386
<s, s, z>(q_gen_1386) -> q_gen_1348
<z, s, z>(q_gen_1362) -> q_gen_1348
<z, z, z>() -> q_gen_1348
<s, s, s>(q_gen_1349) -> q_gen_1349
<s, s, z>(q_gen_1350) -> q_gen_1349
<s, z, s>(q_gen_1350) -> q_gen_1349
<s, z, z>(q_gen_1362) -> q_gen_1349
<s, s, s>(q_gen_1348) -> q_gen_1378
<s, s, s>(q_gen_1378) -> q_gen_1378
<s, z, s>(q_gen_1386) -> q_gen_1378
}

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

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

Teacher's answer:
New clause system:
{
() -> drop([s(u), nil, nil]) -> 21  ;  () -> drop([z, l, l]) -> 22  ;  () -> length([nil, z]) -> 21  ;  () -> minus([s(u), z, s(u)]) -> 21  ;  () -> minus([z, y, z]) -> 21  ;  (drop([n, l1, _sga]) /\ length([_sga, _tga]) /\ length([l1, _uga]) /\ minus([_uga, n, _vga])) -> eq_nat([_tga, _vga]) -> 22  ;  (drop([u, x3, _ega])) -> drop([s(u), cons(x2, x3), _ega]) -> 25  ;  (length([ll, _jga])) -> length([cons(x, ll), s(_jga)]) -> 22  ;  (minus([u, x2, _nga])) -> minus([s(u), s(x2), _nga]) -> 25
}
Sat witness: Yes: ((drop([u, x3, _ega])) -> drop([s(u), cons(x2, x3), _ega]), {
_ega -> cons(b, nil)  ;  u -> s(z)  ;  x2 -> b  ;  x3 -> cons(b, cons(a, nil))
})

-------------------------------------------
Step 42, which took 0.026704 s (model generation: 0.025540,  model checking: 0.001164):

Model:
|_
{
drop -> 
{{{
Q={q_gen_1352, q_gen_1354, q_gen_1359, q_gen_1360, q_gen_1366, q_gen_1367, q_gen_1368, q_gen_1369, q_gen_1397, q_gen_1398, q_gen_1431, q_gen_1432, q_gen_1433, q_gen_1434},
Q_f={q_gen_1352},
Delta=
{
<s>(q_gen_1354) -> q_gen_1354
<z>() -> q_gen_1354
<cons>(q_gen_1398, q_gen_1397) -> q_gen_1397
<nil>() -> q_gen_1397
<a>() -> q_gen_1398
<b>() -> q_gen_1398
<s, cons>(q_gen_1360, q_gen_1359) -> q_gen_1359
<s, nil>(q_gen_1354) -> q_gen_1359
<z, cons>(q_gen_1398, q_gen_1397) -> q_gen_1359
<z, nil>() -> q_gen_1359
<s, a>(q_gen_1354) -> q_gen_1360
<s, b>(q_gen_1354) -> q_gen_1360
<z, a>() -> q_gen_1360
<z, b>() -> q_gen_1360
<cons, cons>(q_gen_1369, q_gen_1368, q_gen_1367, q_gen_1366) -> q_gen_1366
<nil, nil>() -> q_gen_1366
<cons, a>(q_gen_1398, q_gen_1397) -> q_gen_1367
<cons, b>(q_gen_1398, q_gen_1397) -> q_gen_1367
<nil, a>() -> q_gen_1367
<nil, b>() -> q_gen_1367
<a, cons>(q_gen_1398, q_gen_1397) -> q_gen_1368
<a, nil>() -> q_gen_1368
<b, cons>(q_gen_1398, q_gen_1397) -> q_gen_1368
<b, nil>() -> q_gen_1368
<a, a>() -> q_gen_1369
<b, b>() -> q_gen_1369
<s, cons, cons>(q_gen_1434, q_gen_1433, q_gen_1432, q_gen_1352) -> q_gen_1352
<s, cons, cons>(q_gen_1434, q_gen_1433, q_gen_1432, q_gen_1431) -> q_gen_1352
<s, cons, nil>(q_gen_1360, q_gen_1359) -> q_gen_1352
<s, nil, nil>(q_gen_1354) -> q_gen_1352
<z, cons, cons>(q_gen_1369, q_gen_1368, q_gen_1367, q_gen_1366) -> q_gen_1352
<z, nil, nil>() -> q_gen_1352
<z, cons, nil>(q_gen_1398, q_gen_1397) -> q_gen_1431
<s, cons, b>(q_gen_1360, q_gen_1359) -> q_gen_1432
<z, cons, b>(q_gen_1398, q_gen_1397) -> q_gen_1432
<s, b, nil>(q_gen_1354) -> q_gen_1433
<z, b, nil>() -> q_gen_1433
<s, b, b>(q_gen_1354) -> q_gen_1434
<z, b, b>() -> q_gen_1434
}

Datatype: <nat, eltlist, eltlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_1351, q_gen_1357, q_gen_1389},
Q_f={q_gen_1351},
Delta=
{
<s>(q_gen_1389) -> q_gen_1389
<z>() -> q_gen_1389
<cons, s>(q_gen_1357, q_gen_1351) -> q_gen_1351
<nil, z>() -> q_gen_1351
<a, s>(q_gen_1389) -> q_gen_1357
<a, z>() -> q_gen_1357
<b, s>(q_gen_1389) -> q_gen_1357
<b, z>() -> q_gen_1357
}

Datatype: <eltlist, nat>
Convolution form: complete
}}}
  ;  minus -> 
{{{
Q={q_gen_1348, q_gen_1349, q_gen_1350, q_gen_1362, q_gen_1378, q_gen_1386},
Q_f={q_gen_1348, q_gen_1349},
Delta=
{
<s>(q_gen_1362) -> q_gen_1362
<z>() -> q_gen_1362
<s, s>(q_gen_1350) -> q_gen_1350
<s, z>(q_gen_1362) -> q_gen_1350
<z, z>() -> q_gen_1350
<z, s>(q_gen_1362) -> q_gen_1386
<s, s, z>(q_gen_1386) -> q_gen_1348
<z, s, z>(q_gen_1362) -> q_gen_1348
<z, z, z>() -> q_gen_1348
<s, s, s>(q_gen_1349) -> q_gen_1349
<s, s, z>(q_gen_1350) -> q_gen_1349
<s, z, s>(q_gen_1350) -> q_gen_1349
<s, z, z>(q_gen_1362) -> q_gen_1349
<s, s, s>(q_gen_1348) -> q_gen_1378
<s, s, s>(q_gen_1378) -> q_gen_1378
<s, z, s>(q_gen_1386) -> q_gen_1378
}

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

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

Teacher's answer:
New clause system:
{
() -> drop([s(u), nil, nil]) -> 22  ;  () -> drop([z, l, l]) -> 22  ;  () -> length([nil, z]) -> 22  ;  () -> minus([s(u), z, s(u)]) -> 22  ;  () -> minus([z, y, z]) -> 22  ;  (drop([n, l1, _sga]) /\ length([_sga, _tga]) /\ length([l1, _uga]) /\ minus([_uga, n, _vga])) -> eq_nat([_tga, _vga]) -> 25  ;  (drop([u, x3, _ega])) -> drop([s(u), cons(x2, x3), _ega]) -> 25  ;  (length([ll, _jga])) -> length([cons(x, ll), s(_jga)]) -> 23  ;  (minus([u, x2, _nga])) -> minus([s(u), s(x2), _nga]) -> 25
}
Sat witness: Yes: ((drop([n, l1, _sga]) /\ length([_sga, _tga]) /\ length([l1, _uga]) /\ minus([_uga, n, _vga])) -> eq_nat([_tga, _vga]), {
_sga -> nil  ;  _tga -> z  ;  _uga -> s(s(z))  ;  _vga -> s(z)  ;  l1 -> cons(b, cons(b, nil))  ;  n -> s(z)
})

-------------------------------------------
Step 43, which took 0.026848 s (model generation: 0.025035,  model checking: 0.001813):

Model:
|_
{
drop -> 
{{{
Q={q_gen_1352, q_gen_1354, q_gen_1359, q_gen_1360, q_gen_1366, q_gen_1367, q_gen_1368, q_gen_1369, q_gen_1397, q_gen_1398, q_gen_1431, q_gen_1432, q_gen_1433, q_gen_1434, q_gen_1448},
Q_f={q_gen_1352},
Delta=
{
<s>(q_gen_1354) -> q_gen_1354
<z>() -> q_gen_1354
<cons>(q_gen_1398, q_gen_1397) -> q_gen_1397
<nil>() -> q_gen_1397
<a>() -> q_gen_1398
<b>() -> q_gen_1398
<s, cons>(q_gen_1360, q_gen_1359) -> q_gen_1359
<s, nil>(q_gen_1354) -> q_gen_1359
<z, nil>() -> q_gen_1359
<s, a>(q_gen_1354) -> q_gen_1360
<s, b>(q_gen_1354) -> q_gen_1360
<z, a>() -> q_gen_1360
<z, b>() -> q_gen_1360
<cons, cons>(q_gen_1369, q_gen_1368, q_gen_1367, q_gen_1366) -> q_gen_1366
<nil, nil>() -> q_gen_1366
<cons, a>(q_gen_1398, q_gen_1397) -> q_gen_1367
<cons, b>(q_gen_1398, q_gen_1397) -> q_gen_1367
<nil, a>() -> q_gen_1367
<nil, b>() -> q_gen_1367
<a, cons>(q_gen_1398, q_gen_1397) -> q_gen_1368
<a, nil>() -> q_gen_1368
<b, cons>(q_gen_1398, q_gen_1397) -> q_gen_1368
<b, nil>() -> q_gen_1368
<a, a>() -> q_gen_1369
<b, b>() -> q_gen_1369
<z, cons>(q_gen_1398, q_gen_1397) -> q_gen_1448
<s, cons, cons>(q_gen_1434, q_gen_1433, q_gen_1432, q_gen_1431) -> q_gen_1352
<s, cons, nil>(q_gen_1360, q_gen_1359) -> q_gen_1352
<s, nil, nil>(q_gen_1354) -> q_gen_1352
<z, cons, cons>(q_gen_1369, q_gen_1368, q_gen_1367, q_gen_1366) -> q_gen_1352
<z, nil, nil>() -> q_gen_1352
<s, cons, nil>(q_gen_1360, q_gen_1448) -> q_gen_1431
<z, cons, nil>(q_gen_1398, q_gen_1397) -> q_gen_1431
<s, cons, b>(q_gen_1360, q_gen_1448) -> q_gen_1432
<z, cons, b>(q_gen_1398, q_gen_1397) -> q_gen_1432
<s, b, nil>(q_gen_1354) -> q_gen_1433
<z, b, nil>() -> q_gen_1433
<s, b, b>(q_gen_1354) -> q_gen_1434
<z, b, b>() -> q_gen_1434
}

Datatype: <nat, eltlist, eltlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_1351, q_gen_1357, q_gen_1389},
Q_f={q_gen_1351},
Delta=
{
<s>(q_gen_1389) -> q_gen_1389
<z>() -> q_gen_1389
<cons, s>(q_gen_1357, q_gen_1351) -> q_gen_1351
<nil, z>() -> q_gen_1351
<a, s>(q_gen_1389) -> q_gen_1357
<a, z>() -> q_gen_1357
<b, s>(q_gen_1389) -> q_gen_1357
<b, z>() -> q_gen_1357
}

Datatype: <eltlist, nat>
Convolution form: complete
}}}
  ;  minus -> 
{{{
Q={q_gen_1348, q_gen_1349, q_gen_1350, q_gen_1362, q_gen_1378, q_gen_1386},
Q_f={q_gen_1348, q_gen_1349},
Delta=
{
<s>(q_gen_1362) -> q_gen_1362
<z>() -> q_gen_1362
<s, s>(q_gen_1350) -> q_gen_1350
<s, z>(q_gen_1362) -> q_gen_1350
<z, z>() -> q_gen_1350
<z, s>(q_gen_1362) -> q_gen_1386
<s, s, z>(q_gen_1386) -> q_gen_1348
<z, s, z>(q_gen_1362) -> q_gen_1348
<z, z, z>() -> q_gen_1348
<s, s, s>(q_gen_1349) -> q_gen_1349
<s, s, z>(q_gen_1350) -> q_gen_1349
<s, z, s>(q_gen_1350) -> q_gen_1349
<s, z, z>(q_gen_1362) -> q_gen_1349
<s, s, s>(q_gen_1348) -> q_gen_1378
<s, s, s>(q_gen_1378) -> q_gen_1378
<s, z, s>(q_gen_1386) -> q_gen_1378
}

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

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

Teacher's answer:
New clause system:
{
() -> drop([s(u), nil, nil]) -> 23  ;  () -> drop([z, l, l]) -> 23  ;  () -> length([nil, z]) -> 23  ;  () -> minus([s(u), z, s(u)]) -> 23  ;  () -> minus([z, y, z]) -> 23  ;  (drop([n, l1, _sga]) /\ length([_sga, _tga]) /\ length([l1, _uga]) /\ minus([_uga, n, _vga])) -> eq_nat([_tga, _vga]) -> 25  ;  (drop([u, x3, _ega])) -> drop([s(u), cons(x2, x3), _ega]) -> 25  ;  (length([ll, _jga])) -> length([cons(x, ll), s(_jga)]) -> 24  ;  (minus([u, x2, _nga])) -> minus([s(u), s(x2), _nga]) -> 28
}
Sat witness: Yes: ((minus([u, x2, _nga])) -> minus([s(u), s(x2), _nga]), {
_nga -> z  ;  u -> s(z)  ;  x2 -> s(s(z))
})

-------------------------------------------
Step 44, which took 0.036412 s (model generation: 0.030756,  model checking: 0.005656):

Model:
|_
{
drop -> 
{{{
Q={q_gen_1352, q_gen_1354, q_gen_1359, q_gen_1360, q_gen_1366, q_gen_1367, q_gen_1368, q_gen_1369, q_gen_1397, q_gen_1398, q_gen_1431, q_gen_1432, q_gen_1433, q_gen_1434, q_gen_1448},
Q_f={q_gen_1352},
Delta=
{
<s>(q_gen_1354) -> q_gen_1354
<z>() -> q_gen_1354
<cons>(q_gen_1398, q_gen_1397) -> q_gen_1397
<nil>() -> q_gen_1397
<a>() -> q_gen_1398
<b>() -> q_gen_1398
<s, cons>(q_gen_1360, q_gen_1359) -> q_gen_1359
<s, nil>(q_gen_1354) -> q_gen_1359
<z, nil>() -> q_gen_1359
<s, a>(q_gen_1354) -> q_gen_1360
<s, b>(q_gen_1354) -> q_gen_1360
<z, a>() -> q_gen_1360
<z, b>() -> q_gen_1360
<cons, cons>(q_gen_1369, q_gen_1368, q_gen_1367, q_gen_1366) -> q_gen_1366
<nil, nil>() -> q_gen_1366
<cons, a>(q_gen_1398, q_gen_1397) -> q_gen_1367
<cons, b>(q_gen_1398, q_gen_1397) -> q_gen_1367
<nil, a>() -> q_gen_1367
<nil, b>() -> q_gen_1367
<a, cons>(q_gen_1398, q_gen_1397) -> q_gen_1368
<a, nil>() -> q_gen_1368
<b, cons>(q_gen_1398, q_gen_1397) -> q_gen_1368
<b, nil>() -> q_gen_1368
<a, a>() -> q_gen_1369
<b, b>() -> q_gen_1369
<z, cons>(q_gen_1398, q_gen_1397) -> q_gen_1448
<s, cons, cons>(q_gen_1434, q_gen_1433, q_gen_1432, q_gen_1431) -> q_gen_1352
<s, cons, nil>(q_gen_1360, q_gen_1359) -> q_gen_1352
<s, nil, nil>(q_gen_1354) -> q_gen_1352
<z, cons, cons>(q_gen_1369, q_gen_1368, q_gen_1367, q_gen_1366) -> q_gen_1352
<z, nil, nil>() -> q_gen_1352
<s, cons, nil>(q_gen_1360, q_gen_1448) -> q_gen_1431
<z, cons, nil>(q_gen_1398, q_gen_1397) -> q_gen_1431
<s, cons, b>(q_gen_1360, q_gen_1448) -> q_gen_1432
<z, cons, b>(q_gen_1398, q_gen_1397) -> q_gen_1432
<s, b, nil>(q_gen_1354) -> q_gen_1433
<z, b, nil>() -> q_gen_1433
<s, b, b>(q_gen_1354) -> q_gen_1434
<z, b, b>() -> q_gen_1434
}

Datatype: <nat, eltlist, eltlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_1351, q_gen_1357, q_gen_1389},
Q_f={q_gen_1351},
Delta=
{
<s>(q_gen_1389) -> q_gen_1389
<z>() -> q_gen_1389
<cons, s>(q_gen_1357, q_gen_1351) -> q_gen_1351
<nil, z>() -> q_gen_1351
<a, s>(q_gen_1389) -> q_gen_1357
<a, z>() -> q_gen_1357
<b, s>(q_gen_1389) -> q_gen_1357
<b, z>() -> q_gen_1357
}

Datatype: <eltlist, nat>
Convolution form: complete
}}}
  ;  minus -> 
{{{
Q={q_gen_1348, q_gen_1349, q_gen_1350, q_gen_1362, q_gen_1378, q_gen_1386},
Q_f={q_gen_1348, q_gen_1349},
Delta=
{
<s>(q_gen_1362) -> q_gen_1362
<z>() -> q_gen_1362
<s, s>(q_gen_1350) -> q_gen_1350
<s, z>(q_gen_1362) -> q_gen_1350
<z, z>() -> q_gen_1350
<s, s>(q_gen_1386) -> q_gen_1386
<z, s>(q_gen_1362) -> q_gen_1386
<s, s, z>(q_gen_1386) -> q_gen_1348
<z, s, z>(q_gen_1362) -> q_gen_1348
<z, z, z>() -> q_gen_1348
<s, s, s>(q_gen_1349) -> q_gen_1349
<s, s, z>(q_gen_1350) -> q_gen_1349
<s, z, s>(q_gen_1350) -> q_gen_1349
<s, z, z>(q_gen_1362) -> q_gen_1349
<s, s, s>(q_gen_1348) -> q_gen_1378
<s, s, s>(q_gen_1378) -> q_gen_1378
<s, z, s>(q_gen_1386) -> q_gen_1378
}

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

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

Teacher's answer:
New clause system:
{
() -> drop([s(u), nil, nil]) -> 24  ;  () -> drop([z, l, l]) -> 24  ;  () -> length([nil, z]) -> 24  ;  () -> minus([s(u), z, s(u)]) -> 24  ;  () -> minus([z, y, z]) -> 24  ;  (drop([n, l1, _sga]) /\ length([_sga, _tga]) /\ length([l1, _uga]) /\ minus([_uga, n, _vga])) -> eq_nat([_tga, _vga]) -> 25  ;  (drop([u, x3, _ega])) -> drop([s(u), cons(x2, x3), _ega]) -> 28  ;  (length([ll, _jga])) -> length([cons(x, ll), s(_jga)]) -> 25  ;  (minus([u, x2, _nga])) -> minus([s(u), s(x2), _nga]) -> 28
}
Sat witness: Yes: ((drop([u, x3, _ega])) -> drop([s(u), cons(x2, x3), _ega]), {
_ega -> cons(b, nil)  ;  u -> s(s(z))  ;  x2 -> b  ;  x3 -> cons(b, cons(b, cons(b, nil)))
})

-------------------------------------------
Step 45, which took 0.089977 s (model generation: 0.088127,  model checking: 0.001850):

Model:
|_
{
drop -> 
{{{
Q={q_gen_1352, q_gen_1354, q_gen_1359, q_gen_1360, q_gen_1366, q_gen_1367, q_gen_1368, q_gen_1369, q_gen_1397, q_gen_1398, q_gen_1431, q_gen_1432, q_gen_1433, q_gen_1434, q_gen_1448},
Q_f={q_gen_1352},
Delta=
{
<s>(q_gen_1354) -> q_gen_1354
<z>() -> q_gen_1354
<cons>(q_gen_1398, q_gen_1397) -> q_gen_1397
<nil>() -> q_gen_1397
<a>() -> q_gen_1398
<b>() -> q_gen_1398
<s, cons>(q_gen_1360, q_gen_1359) -> q_gen_1359
<s, nil>(q_gen_1354) -> q_gen_1359
<z, nil>() -> q_gen_1359
<s, a>(q_gen_1354) -> q_gen_1360
<s, b>(q_gen_1354) -> q_gen_1360
<z, a>() -> q_gen_1360
<z, b>() -> q_gen_1360
<cons, cons>(q_gen_1369, q_gen_1368, q_gen_1367, q_gen_1366) -> q_gen_1366
<nil, nil>() -> q_gen_1366
<cons, a>(q_gen_1398, q_gen_1397) -> q_gen_1367
<cons, b>(q_gen_1398, q_gen_1397) -> q_gen_1367
<nil, a>() -> q_gen_1367
<nil, b>() -> q_gen_1367
<a, cons>(q_gen_1398, q_gen_1397) -> q_gen_1368
<a, nil>() -> q_gen_1368
<b, cons>(q_gen_1398, q_gen_1397) -> q_gen_1368
<b, nil>() -> q_gen_1368
<a, a>() -> q_gen_1369
<b, b>() -> q_gen_1369
<s, cons>(q_gen_1360, q_gen_1448) -> q_gen_1448
<z, cons>(q_gen_1398, q_gen_1397) -> q_gen_1448
<s, cons, cons>(q_gen_1434, q_gen_1433, q_gen_1432, q_gen_1431) -> q_gen_1352
<s, cons, nil>(q_gen_1360, q_gen_1359) -> q_gen_1352
<s, nil, nil>(q_gen_1354) -> q_gen_1352
<z, cons, cons>(q_gen_1369, q_gen_1368, q_gen_1367, q_gen_1366) -> q_gen_1352
<z, nil, nil>() -> q_gen_1352
<s, cons, nil>(q_gen_1360, q_gen_1448) -> q_gen_1431
<z, cons, nil>(q_gen_1398, q_gen_1397) -> q_gen_1431
<s, cons, b>(q_gen_1360, q_gen_1448) -> q_gen_1432
<z, cons, b>(q_gen_1398, q_gen_1397) -> q_gen_1432
<s, b, nil>(q_gen_1354) -> q_gen_1433
<z, b, nil>() -> q_gen_1433
<s, b, b>(q_gen_1354) -> q_gen_1434
<z, b, b>() -> q_gen_1434
}

Datatype: <nat, eltlist, eltlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_1351, q_gen_1357, q_gen_1389},
Q_f={q_gen_1351},
Delta=
{
<s>(q_gen_1389) -> q_gen_1389
<z>() -> q_gen_1389
<cons, s>(q_gen_1357, q_gen_1351) -> q_gen_1351
<nil, z>() -> q_gen_1351
<a, s>(q_gen_1389) -> q_gen_1357
<a, z>() -> q_gen_1357
<b, s>(q_gen_1389) -> q_gen_1357
<b, z>() -> q_gen_1357
}

Datatype: <eltlist, nat>
Convolution form: complete
}}}
  ;  minus -> 
{{{
Q={q_gen_1348, q_gen_1349, q_gen_1350, q_gen_1362, q_gen_1378, q_gen_1386},
Q_f={q_gen_1348, q_gen_1349},
Delta=
{
<s>(q_gen_1362) -> q_gen_1362
<z>() -> q_gen_1362
<s, s>(q_gen_1350) -> q_gen_1350
<s, z>(q_gen_1362) -> q_gen_1350
<z, z>() -> q_gen_1350
<s, s>(q_gen_1386) -> q_gen_1386
<z, s>(q_gen_1362) -> q_gen_1386
<s, s, z>(q_gen_1386) -> q_gen_1348
<z, s, z>(q_gen_1362) -> q_gen_1348
<z, z, z>() -> q_gen_1348
<s, s, s>(q_gen_1349) -> q_gen_1349
<s, s, z>(q_gen_1350) -> q_gen_1349
<s, z, s>(q_gen_1350) -> q_gen_1349
<s, z, z>(q_gen_1362) -> q_gen_1349
<s, s, s>(q_gen_1348) -> q_gen_1378
<s, s, s>(q_gen_1378) -> q_gen_1378
<s, z, s>(q_gen_1386) -> q_gen_1378
}

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

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

Teacher's answer:
New clause system:
{
() -> drop([s(u), nil, nil]) -> 25  ;  () -> drop([z, l, l]) -> 25  ;  () -> length([nil, z]) -> 25  ;  () -> minus([s(u), z, s(u)]) -> 25  ;  () -> minus([z, y, z]) -> 25  ;  (drop([n, l1, _sga]) /\ length([_sga, _tga]) /\ length([l1, _uga]) /\ minus([_uga, n, _vga])) -> eq_nat([_tga, _vga]) -> 28  ;  (drop([u, x3, _ega])) -> drop([s(u), cons(x2, x3), _ega]) -> 28  ;  (length([ll, _jga])) -> length([cons(x, ll), s(_jga)]) -> 26  ;  (minus([u, x2, _nga])) -> minus([s(u), s(x2), _nga]) -> 28
}
Sat witness: Yes: ((drop([n, l1, _sga]) /\ length([_sga, _tga]) /\ length([l1, _uga]) /\ minus([_uga, n, _vga])) -> eq_nat([_tga, _vga]), {
_sga -> nil  ;  _tga -> z  ;  _uga -> s(s(z))  ;  _vga -> s(z)  ;  l1 -> cons(a, cons(b, nil))  ;  n -> s(s(z))
})

-------------------------------------------
Step 46, which took 0.491190 s (model generation: 0.489298,  model checking: 0.001892):

Model:
|_
{
drop -> 
{{{
Q={q_gen_1352, q_gen_1354, q_gen_1359, q_gen_1360, q_gen_1366, q_gen_1367, q_gen_1368, q_gen_1369, q_gen_1377, q_gen_1397, q_gen_1398, q_gen_1423, q_gen_1424, q_gen_1432, q_gen_1433, q_gen_1434},
Q_f={q_gen_1352},
Delta=
{
<s>(q_gen_1354) -> q_gen_1354
<z>() -> q_gen_1354
<cons>(q_gen_1398, q_gen_1397) -> q_gen_1397
<nil>() -> q_gen_1397
<a>() -> q_gen_1398
<b>() -> q_gen_1398
<s, cons>(q_gen_1360, q_gen_1424) -> q_gen_1359
<s, cons>(q_gen_1377, q_gen_1359) -> q_gen_1359
<s, nil>(q_gen_1354) -> q_gen_1359
<z, nil>() -> q_gen_1359
<z, b>() -> q_gen_1360
<cons, cons>(q_gen_1369, q_gen_1368, q_gen_1367, q_gen_1366) -> q_gen_1366
<nil, nil>() -> q_gen_1366
<cons, a>(q_gen_1398, q_gen_1397) -> q_gen_1367
<cons, b>(q_gen_1398, q_gen_1397) -> q_gen_1367
<nil, a>() -> q_gen_1367
<nil, b>() -> q_gen_1367
<a, cons>(q_gen_1398, q_gen_1397) -> q_gen_1368
<a, nil>() -> q_gen_1368
<b, cons>(q_gen_1398, q_gen_1397) -> q_gen_1368
<b, nil>() -> q_gen_1368
<a, a>() -> q_gen_1369
<b, b>() -> q_gen_1369
<s, a>(q_gen_1354) -> q_gen_1377
<s, b>(q_gen_1354) -> q_gen_1377
<z, a>() -> q_gen_1377
<s, cons>(q_gen_1360, q_gen_1359) -> q_gen_1424
<z, cons>(q_gen_1398, q_gen_1397) -> q_gen_1424
<s, cons, cons>(q_gen_1434, q_gen_1433, q_gen_1432, q_gen_1352) -> q_gen_1352
<s, cons, cons>(q_gen_1434, q_gen_1433, q_gen_1432, q_gen_1423) -> q_gen_1352
<s, cons, nil>(q_gen_1360, q_gen_1359) -> q_gen_1352
<s, cons, nil>(q_gen_1377, q_gen_1359) -> q_gen_1352
<s, nil, nil>(q_gen_1354) -> q_gen_1352
<z, cons, cons>(q_gen_1369, q_gen_1368, q_gen_1367, q_gen_1366) -> q_gen_1352
<z, nil, nil>() -> q_gen_1352
<s, cons, nil>(q_gen_1360, q_gen_1424) -> q_gen_1423
<s, cons, nil>(q_gen_1377, q_gen_1424) -> q_gen_1423
<z, cons, nil>(q_gen_1398, q_gen_1397) -> q_gen_1423
<s, cons, b>(q_gen_1360, q_gen_1424) -> q_gen_1432
<s, cons, b>(q_gen_1377, q_gen_1359) -> q_gen_1432
<z, cons, b>(q_gen_1398, q_gen_1397) -> q_gen_1432
<s, b, nil>(q_gen_1354) -> q_gen_1433
<z, b, nil>() -> q_gen_1433
<s, b, b>(q_gen_1354) -> q_gen_1434
<z, b, b>() -> q_gen_1434
}

Datatype: <nat, eltlist, eltlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_1351, q_gen_1357, q_gen_1389},
Q_f={q_gen_1351},
Delta=
{
<s>(q_gen_1389) -> q_gen_1389
<z>() -> q_gen_1389
<cons, s>(q_gen_1357, q_gen_1351) -> q_gen_1351
<nil, z>() -> q_gen_1351
<a, s>(q_gen_1389) -> q_gen_1357
<a, z>() -> q_gen_1357
<b, s>(q_gen_1389) -> q_gen_1357
<b, z>() -> q_gen_1357
}

Datatype: <eltlist, nat>
Convolution form: complete
}}}
  ;  minus -> 
{{{
Q={q_gen_1348, q_gen_1349, q_gen_1350, q_gen_1362, q_gen_1373, q_gen_1386},
Q_f={q_gen_1348, q_gen_1349},
Delta=
{
<s>(q_gen_1362) -> q_gen_1362
<z>() -> q_gen_1362
<s, s>(q_gen_1350) -> q_gen_1350
<s, s>(q_gen_1386) -> q_gen_1350
<s, z>(q_gen_1362) -> q_gen_1350
<z, z>() -> q_gen_1350
<z, s>(q_gen_1362) -> q_gen_1386
<s, s, s>(q_gen_1349) -> q_gen_1348
<s, s, z>(q_gen_1386) -> q_gen_1348
<z, s, z>(q_gen_1362) -> q_gen_1348
<z, z, z>() -> q_gen_1348
<s, s, s>(q_gen_1373) -> q_gen_1349
<s, s, z>(q_gen_1350) -> q_gen_1349
<s, z, s>(q_gen_1350) -> q_gen_1349
<s, s, s>(q_gen_1348) -> q_gen_1373
<s, z, s>(q_gen_1386) -> q_gen_1373
<s, z, z>(q_gen_1362) -> q_gen_1373
}

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

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

Teacher's answer:
New clause system:
{
() -> drop([s(u), nil, nil]) -> 26  ;  () -> drop([z, l, l]) -> 26  ;  () -> length([nil, z]) -> 26  ;  () -> minus([s(u), z, s(u)]) -> 26  ;  () -> minus([z, y, z]) -> 26  ;  (drop([n, l1, _sga]) /\ length([_sga, _tga]) /\ length([l1, _uga]) /\ minus([_uga, n, _vga])) -> eq_nat([_tga, _vga]) -> 28  ;  (drop([u, x3, _ega])) -> drop([s(u), cons(x2, x3), _ega]) -> 28  ;  (length([ll, _jga])) -> length([cons(x, ll), s(_jga)]) -> 27  ;  (minus([u, x2, _nga])) -> minus([s(u), s(x2), _nga]) -> 31
}
Sat witness: Yes: ((minus([u, x2, _nga])) -> minus([s(u), s(x2), _nga]), {
_nga -> s(s(z))  ;  u -> s(s(z))  ;  x2 -> s(s(z))
})

-------------------------------------------
Step 47, which took 0.080086 s (model generation: 0.077251,  model checking: 0.002835):

Model:
|_
{
drop -> 
{{{
Q={q_gen_1352, q_gen_1354, q_gen_1359, q_gen_1360, q_gen_1366, q_gen_1367, q_gen_1368, q_gen_1369, q_gen_1377, q_gen_1397, q_gen_1398, q_gen_1423, q_gen_1424, q_gen_1432, q_gen_1433, q_gen_1434},
Q_f={q_gen_1352},
Delta=
{
<s>(q_gen_1354) -> q_gen_1354
<z>() -> q_gen_1354
<cons>(q_gen_1398, q_gen_1397) -> q_gen_1397
<nil>() -> q_gen_1397
<a>() -> q_gen_1398
<b>() -> q_gen_1398
<s, cons>(q_gen_1377, q_gen_1359) -> q_gen_1359
<s, nil>(q_gen_1354) -> q_gen_1359
<z, nil>() -> q_gen_1359
<s, a>(q_gen_1354) -> q_gen_1360
<z, b>() -> q_gen_1360
<cons, cons>(q_gen_1369, q_gen_1368, q_gen_1367, q_gen_1366) -> q_gen_1366
<nil, nil>() -> q_gen_1366
<cons, a>(q_gen_1398, q_gen_1397) -> q_gen_1367
<cons, b>(q_gen_1398, q_gen_1397) -> q_gen_1367
<nil, a>() -> q_gen_1367
<nil, b>() -> q_gen_1367
<a, cons>(q_gen_1398, q_gen_1397) -> q_gen_1368
<a, nil>() -> q_gen_1368
<b, cons>(q_gen_1398, q_gen_1397) -> q_gen_1368
<b, nil>() -> q_gen_1368
<a, a>() -> q_gen_1369
<b, b>() -> q_gen_1369
<s, b>(q_gen_1354) -> q_gen_1377
<z, a>() -> q_gen_1377
<s, cons>(q_gen_1360, q_gen_1359) -> q_gen_1424
<s, cons>(q_gen_1360, q_gen_1424) -> q_gen_1424
<z, cons>(q_gen_1398, q_gen_1397) -> q_gen_1424
<s, cons, cons>(q_gen_1434, q_gen_1433, q_gen_1432, q_gen_1423) -> q_gen_1352
<s, cons, nil>(q_gen_1360, q_gen_1359) -> q_gen_1352
<s, cons, nil>(q_gen_1377, q_gen_1359) -> q_gen_1352
<s, nil, nil>(q_gen_1354) -> q_gen_1352
<z, cons, cons>(q_gen_1369, q_gen_1368, q_gen_1367, q_gen_1366) -> q_gen_1352
<z, nil, nil>() -> q_gen_1352
<s, cons, nil>(q_gen_1360, q_gen_1424) -> q_gen_1423
<s, cons, nil>(q_gen_1377, q_gen_1424) -> q_gen_1423
<z, cons, nil>(q_gen_1398, q_gen_1397) -> q_gen_1423
<s, cons, b>(q_gen_1360, q_gen_1424) -> q_gen_1432
<s, cons, b>(q_gen_1377, q_gen_1424) -> q_gen_1432
<z, cons, b>(q_gen_1398, q_gen_1397) -> q_gen_1432
<s, b, nil>(q_gen_1354) -> q_gen_1433
<z, b, nil>() -> q_gen_1433
<s, b, b>(q_gen_1354) -> q_gen_1434
<z, b, b>() -> q_gen_1434
}

Datatype: <nat, eltlist, eltlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_1351, q_gen_1357, q_gen_1389},
Q_f={q_gen_1351},
Delta=
{
<s>(q_gen_1389) -> q_gen_1389
<z>() -> q_gen_1389
<cons, s>(q_gen_1357, q_gen_1351) -> q_gen_1351
<nil, z>() -> q_gen_1351
<a, s>(q_gen_1389) -> q_gen_1357
<a, z>() -> q_gen_1357
<b, s>(q_gen_1389) -> q_gen_1357
<b, z>() -> q_gen_1357
}

Datatype: <eltlist, nat>
Convolution form: complete
}}}
  ;  minus -> 
{{{
Q={q_gen_1348, q_gen_1350, q_gen_1362, q_gen_1373, q_gen_1378, q_gen_1386},
Q_f={q_gen_1348, q_gen_1373},
Delta=
{
<s>(q_gen_1362) -> q_gen_1362
<z>() -> q_gen_1362
<s, s>(q_gen_1350) -> q_gen_1350
<s, s>(q_gen_1386) -> q_gen_1350
<z, z>() -> q_gen_1350
<s, z>(q_gen_1362) -> q_gen_1386
<z, s>(q_gen_1362) -> q_gen_1386
<s, s, s>(q_gen_1373) -> q_gen_1348
<s, s, z>(q_gen_1350) -> q_gen_1348
<s, z, s>(q_gen_1350) -> q_gen_1348
<z, s, z>(q_gen_1362) -> q_gen_1348
<z, z, z>() -> q_gen_1348
<s, s, s>(q_gen_1378) -> q_gen_1373
<s, s, z>(q_gen_1386) -> q_gen_1373
<s, z, z>(q_gen_1362) -> q_gen_1373
<s, s, s>(q_gen_1348) -> q_gen_1378
<s, z, s>(q_gen_1386) -> q_gen_1378
}

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

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

Teacher's answer:
New clause system:
{
() -> drop([s(u), nil, nil]) -> 27  ;  () -> drop([z, l, l]) -> 27  ;  () -> length([nil, z]) -> 27  ;  () -> minus([s(u), z, s(u)]) -> 27  ;  () -> minus([z, y, z]) -> 27  ;  (drop([n, l1, _sga]) /\ length([_sga, _tga]) /\ length([l1, _uga]) /\ minus([_uga, n, _vga])) -> eq_nat([_tga, _vga]) -> 28  ;  (drop([u, x3, _ega])) -> drop([s(u), cons(x2, x3), _ega]) -> 31  ;  (length([ll, _jga])) -> length([cons(x, ll), s(_jga)]) -> 28  ;  (minus([u, x2, _nga])) -> minus([s(u), s(x2), _nga]) -> 31
}
Sat witness: Yes: ((drop([u, x3, _ega])) -> drop([s(u), cons(x2, x3), _ega]), {
_ega -> nil  ;  u -> s(z)  ;  x2 -> b  ;  x3 -> cons(b, nil)
})

-------------------------------------------
Step 48, which took 0.112495 s (model generation: 0.110345,  model checking: 0.002150):

Model:
|_
{
drop -> 
{{{
Q={q_gen_1352, q_gen_1354, q_gen_1359, q_gen_1360, q_gen_1366, q_gen_1367, q_gen_1368, q_gen_1369, q_gen_1377, q_gen_1397, q_gen_1398, q_gen_1422, q_gen_1423, q_gen_1432, q_gen_1433, q_gen_1434},
Q_f={q_gen_1352},
Delta=
{
<s>(q_gen_1354) -> q_gen_1354
<z>() -> q_gen_1354
<cons>(q_gen_1398, q_gen_1397) -> q_gen_1397
<nil>() -> q_gen_1397
<a>() -> q_gen_1398
<b>() -> q_gen_1398
<s, nil>(q_gen_1354) -> q_gen_1359
<z, nil>() -> q_gen_1359
<s, a>(q_gen_1354) -> q_gen_1360
<z, b>() -> q_gen_1360
<cons, cons>(q_gen_1369, q_gen_1368, q_gen_1367, q_gen_1366) -> q_gen_1366
<nil, nil>() -> q_gen_1366
<cons, a>(q_gen_1398, q_gen_1397) -> q_gen_1367
<cons, b>(q_gen_1398, q_gen_1397) -> q_gen_1367
<nil, a>() -> q_gen_1367
<nil, b>() -> q_gen_1367
<a, cons>(q_gen_1398, q_gen_1397) -> q_gen_1368
<a, nil>() -> q_gen_1368
<b, cons>(q_gen_1398, q_gen_1397) -> q_gen_1368
<b, nil>() -> q_gen_1368
<a, a>() -> q_gen_1369
<b, b>() -> q_gen_1369
<s, b>(q_gen_1354) -> q_gen_1377
<z, a>() -> q_gen_1377
<s, cons>(q_gen_1360, q_gen_1359) -> q_gen_1422
<s, cons>(q_gen_1360, q_gen_1422) -> q_gen_1422
<s, cons>(q_gen_1377, q_gen_1359) -> q_gen_1422
<z, cons>(q_gen_1398, q_gen_1397) -> q_gen_1422
<s, cons, cons>(q_gen_1434, q_gen_1433, q_gen_1432, q_gen_1352) -> q_gen_1352
<s, cons, cons>(q_gen_1434, q_gen_1433, q_gen_1432, q_gen_1423) -> q_gen_1352
<s, cons, nil>(q_gen_1360, q_gen_1359) -> q_gen_1352
<s, cons, nil>(q_gen_1377, q_gen_1359) -> q_gen_1352
<s, cons, nil>(q_gen_1377, q_gen_1422) -> q_gen_1352
<s, nil, nil>(q_gen_1354) -> q_gen_1352
<z, cons, cons>(q_gen_1369, q_gen_1368, q_gen_1367, q_gen_1366) -> q_gen_1352
<z, nil, nil>() -> q_gen_1352
<s, cons, nil>(q_gen_1360, q_gen_1422) -> q_gen_1423
<z, cons, nil>(q_gen_1398, q_gen_1397) -> q_gen_1423
<s, cons, b>(q_gen_1360, q_gen_1422) -> q_gen_1432
<s, cons, b>(q_gen_1377, q_gen_1422) -> q_gen_1432
<z, cons, b>(q_gen_1398, q_gen_1397) -> q_gen_1432
<s, b, nil>(q_gen_1354) -> q_gen_1433
<z, b, nil>() -> q_gen_1433
<s, b, b>(q_gen_1354) -> q_gen_1434
<z, b, b>() -> q_gen_1434
}

Datatype: <nat, eltlist, eltlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_1351, q_gen_1357, q_gen_1389},
Q_f={q_gen_1351},
Delta=
{
<s>(q_gen_1389) -> q_gen_1389
<z>() -> q_gen_1389
<cons, s>(q_gen_1357, q_gen_1351) -> q_gen_1351
<nil, z>() -> q_gen_1351
<a, s>(q_gen_1389) -> q_gen_1357
<a, z>() -> q_gen_1357
<b, s>(q_gen_1389) -> q_gen_1357
<b, z>() -> q_gen_1357
}

Datatype: <eltlist, nat>
Convolution form: complete
}}}
  ;  minus -> 
{{{
Q={q_gen_1348, q_gen_1349, q_gen_1350, q_gen_1362, q_gen_1378, q_gen_1386},
Q_f={q_gen_1348, q_gen_1349},
Delta=
{
<s>(q_gen_1362) -> q_gen_1362
<z>() -> q_gen_1362
<s, s>(q_gen_1350) -> q_gen_1350
<s, z>(q_gen_1362) -> q_gen_1350
<z, z>() -> q_gen_1350
<s, s>(q_gen_1386) -> q_gen_1386
<z, s>(q_gen_1362) -> q_gen_1386
<s, s, z>(q_gen_1386) -> q_gen_1348
<z, s, z>(q_gen_1362) -> q_gen_1348
<z, z, z>() -> q_gen_1348
<s, s, s>(q_gen_1349) -> q_gen_1349
<s, s, z>(q_gen_1350) -> q_gen_1349
<s, z, s>(q_gen_1350) -> q_gen_1349
<s, z, z>(q_gen_1362) -> q_gen_1349
<s, s, s>(q_gen_1348) -> q_gen_1378
<s, s, s>(q_gen_1378) -> q_gen_1378
<s, z, s>(q_gen_1386) -> q_gen_1378
}

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

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

Teacher's answer:
New clause system:
{
() -> drop([s(u), nil, nil]) -> 28  ;  () -> drop([z, l, l]) -> 28  ;  () -> length([nil, z]) -> 28  ;  () -> minus([s(u), z, s(u)]) -> 28  ;  () -> minus([z, y, z]) -> 28  ;  (drop([n, l1, _sga]) /\ length([_sga, _tga]) /\ length([l1, _uga]) /\ minus([_uga, n, _vga])) -> eq_nat([_tga, _vga]) -> 31  ;  (drop([u, x3, _ega])) -> drop([s(u), cons(x2, x3), _ega]) -> 31  ;  (length([ll, _jga])) -> length([cons(x, ll), s(_jga)]) -> 29  ;  (minus([u, x2, _nga])) -> minus([s(u), s(x2), _nga]) -> 31
}
Sat witness: Yes: ((drop([n, l1, _sga]) /\ length([_sga, _tga]) /\ length([l1, _uga]) /\ minus([_uga, n, _vga])) -> eq_nat([_tga, _vga]), {
_sga -> nil  ;  _tga -> z  ;  _uga -> s(s(z))  ;  _vga -> s(z)  ;  l1 -> cons(a, cons(b, nil))  ;  n -> s(z)
})

-------------------------------------------
Step 49, which took 0.066737 s (model generation: 0.064053,  model checking: 0.002684):

Model:
|_
{
drop -> 
{{{
Q={q_gen_1352, q_gen_1354, q_gen_1359, q_gen_1360, q_gen_1366, q_gen_1367, q_gen_1368, q_gen_1369, q_gen_1392, q_gen_1397, q_gen_1398, q_gen_1422, q_gen_1423, q_gen_1432, q_gen_1433, q_gen_1434},
Q_f={q_gen_1352},
Delta=
{
<s>(q_gen_1354) -> q_gen_1354
<z>() -> q_gen_1354
<cons>(q_gen_1398, q_gen_1397) -> q_gen_1397
<nil>() -> q_gen_1397
<a>() -> q_gen_1398
<b>() -> q_gen_1398
<s, nil>(q_gen_1354) -> q_gen_1359
<z, nil>() -> q_gen_1359
<s, a>(q_gen_1354) -> q_gen_1360
<z, a>() -> q_gen_1360
<z, b>() -> q_gen_1360
<cons, cons>(q_gen_1369, q_gen_1368, q_gen_1367, q_gen_1366) -> q_gen_1366
<nil, nil>() -> q_gen_1366
<cons, a>(q_gen_1398, q_gen_1397) -> q_gen_1367
<cons, b>(q_gen_1398, q_gen_1397) -> q_gen_1367
<nil, a>() -> q_gen_1367
<nil, b>() -> q_gen_1367
<a, cons>(q_gen_1398, q_gen_1397) -> q_gen_1368
<a, nil>() -> q_gen_1368
<b, cons>(q_gen_1398, q_gen_1397) -> q_gen_1368
<b, nil>() -> q_gen_1368
<a, a>() -> q_gen_1369
<b, b>() -> q_gen_1369
<s, b>(q_gen_1354) -> q_gen_1392
<s, cons>(q_gen_1360, q_gen_1359) -> q_gen_1422
<s, cons>(q_gen_1360, q_gen_1422) -> q_gen_1422
<z, cons>(q_gen_1398, q_gen_1397) -> q_gen_1422
<s, cons, cons>(q_gen_1434, q_gen_1433, q_gen_1432, q_gen_1352) -> q_gen_1352
<s, cons, cons>(q_gen_1434, q_gen_1433, q_gen_1432, q_gen_1423) -> q_gen_1352
<s, cons, nil>(q_gen_1360, q_gen_1359) -> q_gen_1352
<s, cons, nil>(q_gen_1392, q_gen_1359) -> q_gen_1352
<s, cons, nil>(q_gen_1392, q_gen_1422) -> q_gen_1352
<s, nil, nil>(q_gen_1354) -> q_gen_1352
<z, cons, cons>(q_gen_1369, q_gen_1368, q_gen_1367, q_gen_1366) -> q_gen_1352
<z, nil, nil>() -> q_gen_1352
<s, cons, nil>(q_gen_1360, q_gen_1422) -> q_gen_1423
<z, cons, nil>(q_gen_1398, q_gen_1397) -> q_gen_1423
<s, cons, b>(q_gen_1360, q_gen_1422) -> q_gen_1432
<s, cons, b>(q_gen_1392, q_gen_1422) -> q_gen_1432
<z, cons, b>(q_gen_1398, q_gen_1397) -> q_gen_1432
<s, b, nil>(q_gen_1354) -> q_gen_1433
<z, b, nil>() -> q_gen_1433
<s, b, b>(q_gen_1354) -> q_gen_1434
<z, b, b>() -> q_gen_1434
}

Datatype: <nat, eltlist, eltlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_1351, q_gen_1357, q_gen_1389},
Q_f={q_gen_1351},
Delta=
{
<s>(q_gen_1389) -> q_gen_1389
<z>() -> q_gen_1389
<cons, s>(q_gen_1357, q_gen_1351) -> q_gen_1351
<nil, z>() -> q_gen_1351
<a, s>(q_gen_1389) -> q_gen_1357
<a, z>() -> q_gen_1357
<b, s>(q_gen_1389) -> q_gen_1357
<b, z>() -> q_gen_1357
}

Datatype: <eltlist, nat>
Convolution form: complete
}}}
  ;  minus -> 
{{{
Q={q_gen_1348, q_gen_1349, q_gen_1350, q_gen_1362, q_gen_1378, q_gen_1386},
Q_f={q_gen_1348, q_gen_1349},
Delta=
{
<s>(q_gen_1362) -> q_gen_1362
<z>() -> q_gen_1362
<s, s>(q_gen_1350) -> q_gen_1350
<s, z>(q_gen_1362) -> q_gen_1350
<z, z>() -> q_gen_1350
<s, s>(q_gen_1386) -> q_gen_1386
<z, s>(q_gen_1362) -> q_gen_1386
<s, s, z>(q_gen_1386) -> q_gen_1348
<z, s, z>(q_gen_1362) -> q_gen_1348
<z, z, z>() -> q_gen_1348
<s, s, s>(q_gen_1349) -> q_gen_1349
<s, s, z>(q_gen_1350) -> q_gen_1349
<s, z, s>(q_gen_1350) -> q_gen_1349
<s, z, z>(q_gen_1362) -> q_gen_1349
<s, s, s>(q_gen_1348) -> q_gen_1378
<s, s, s>(q_gen_1378) -> q_gen_1378
<s, z, s>(q_gen_1386) -> q_gen_1378
}

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

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

Teacher's answer:
New clause system:
{
() -> drop([s(u), nil, nil]) -> 29  ;  () -> drop([z, l, l]) -> 29  ;  () -> length([nil, z]) -> 29  ;  () -> minus([s(u), z, s(u)]) -> 29  ;  () -> minus([z, y, z]) -> 29  ;  (drop([n, l1, _sga]) /\ length([_sga, _tga]) /\ length([l1, _uga]) /\ minus([_uga, n, _vga])) -> eq_nat([_tga, _vga]) -> 31  ;  (drop([u, x3, _ega])) -> drop([s(u), cons(x2, x3), _ega]) -> 34  ;  (length([ll, _jga])) -> length([cons(x, ll), s(_jga)]) -> 30  ;  (minus([u, x2, _nga])) -> minus([s(u), s(x2), _nga]) -> 32
}
Sat witness: Yes: ((drop([u, x3, _ega])) -> drop([s(u), cons(x2, x3), _ega]), {
_ega -> nil  ;  u -> s(z)  ;  x2 -> a  ;  x3 -> cons(a, nil)
})

-------------------------------------------
Step 50, which took 0.138409 s (model generation: 0.136424,  model checking: 0.001985):

Model:
|_
{
drop -> 
{{{
Q={q_gen_1352, q_gen_1354, q_gen_1359, q_gen_1360, q_gen_1366, q_gen_1367, q_gen_1368, q_gen_1369, q_gen_1397, q_gen_1398, q_gen_1431, q_gen_1432, q_gen_1433, q_gen_1434, q_gen_1448},
Q_f={q_gen_1352},
Delta=
{
<s>(q_gen_1354) -> q_gen_1354
<z>() -> q_gen_1354
<cons>(q_gen_1398, q_gen_1397) -> q_gen_1397
<nil>() -> q_gen_1397
<a>() -> q_gen_1398
<b>() -> q_gen_1398
<s, cons>(q_gen_1360, q_gen_1359) -> q_gen_1359
<s, nil>(q_gen_1354) -> q_gen_1359
<z, nil>() -> q_gen_1359
<s, a>(q_gen_1354) -> q_gen_1360
<s, b>(q_gen_1354) -> q_gen_1360
<z, a>() -> q_gen_1360
<z, b>() -> q_gen_1360
<cons, cons>(q_gen_1369, q_gen_1368, q_gen_1367, q_gen_1366) -> q_gen_1366
<nil, nil>() -> q_gen_1366
<cons, a>(q_gen_1398, q_gen_1397) -> q_gen_1367
<cons, b>(q_gen_1398, q_gen_1397) -> q_gen_1367
<nil, a>() -> q_gen_1367
<nil, b>() -> q_gen_1367
<a, cons>(q_gen_1398, q_gen_1397) -> q_gen_1368
<a, nil>() -> q_gen_1368
<b, cons>(q_gen_1398, q_gen_1397) -> q_gen_1368
<b, nil>() -> q_gen_1368
<a, a>() -> q_gen_1369
<b, b>() -> q_gen_1369
<s, cons>(q_gen_1360, q_gen_1448) -> q_gen_1448
<z, cons>(q_gen_1398, q_gen_1397) -> q_gen_1448
<s, cons, cons>(q_gen_1434, q_gen_1433, q_gen_1432, q_gen_1431) -> q_gen_1352
<s, cons, nil>(q_gen_1360, q_gen_1359) -> q_gen_1352
<s, nil, nil>(q_gen_1354) -> q_gen_1352
<z, cons, cons>(q_gen_1369, q_gen_1368, q_gen_1367, q_gen_1366) -> q_gen_1352
<z, nil, nil>() -> q_gen_1352
<s, cons, nil>(q_gen_1360, q_gen_1448) -> q_gen_1431
<z, cons, nil>(q_gen_1398, q_gen_1397) -> q_gen_1431
<s, cons, b>(q_gen_1360, q_gen_1448) -> q_gen_1432
<z, cons, b>(q_gen_1398, q_gen_1397) -> q_gen_1432
<s, b, nil>(q_gen_1354) -> q_gen_1433
<z, b, nil>() -> q_gen_1433
<s, b, b>(q_gen_1354) -> q_gen_1434
<z, b, b>() -> q_gen_1434
}

Datatype: <nat, eltlist, eltlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_1351, q_gen_1357, q_gen_1389},
Q_f={q_gen_1351},
Delta=
{
<s>(q_gen_1389) -> q_gen_1389
<z>() -> q_gen_1389
<cons, s>(q_gen_1357, q_gen_1351) -> q_gen_1351
<nil, z>() -> q_gen_1351
<a, s>(q_gen_1389) -> q_gen_1357
<a, z>() -> q_gen_1357
<b, s>(q_gen_1389) -> q_gen_1357
<b, z>() -> q_gen_1357
}

Datatype: <eltlist, nat>
Convolution form: complete
}}}
  ;  minus -> 
{{{
Q={q_gen_1348, q_gen_1349, q_gen_1350, q_gen_1362, q_gen_1378, q_gen_1386, q_gen_1416},
Q_f={q_gen_1348, q_gen_1349},
Delta=
{
<s>(q_gen_1362) -> q_gen_1362
<z>() -> q_gen_1362
<s, s>(q_gen_1350) -> q_gen_1350
<z, z>() -> q_gen_1350
<s, s>(q_gen_1386) -> q_gen_1386
<z, s>(q_gen_1362) -> q_gen_1386
<s, z>(q_gen_1362) -> q_gen_1416
<s, s, z>(q_gen_1350) -> q_gen_1348
<s, s, z>(q_gen_1386) -> q_gen_1348
<z, s, z>(q_gen_1362) -> q_gen_1348
<z, z, z>() -> q_gen_1348
<s, s, s>(q_gen_1349) -> q_gen_1349
<s, s, z>(q_gen_1416) -> q_gen_1349
<s, z, s>(q_gen_1350) -> q_gen_1349
<s, z, s>(q_gen_1416) -> q_gen_1349
<s, z, z>(q_gen_1362) -> q_gen_1349
<s, s, s>(q_gen_1348) -> q_gen_1378
<s, s, s>(q_gen_1378) -> q_gen_1378
<s, z, s>(q_gen_1386) -> q_gen_1378
}

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

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

Teacher's answer:
New clause system:
{
() -> drop([s(u), nil, nil]) -> 30  ;  () -> drop([z, l, l]) -> 30  ;  () -> length([nil, z]) -> 30  ;  () -> minus([s(u), z, s(u)]) -> 30  ;  () -> minus([z, y, z]) -> 30  ;  (drop([n, l1, _sga]) /\ length([_sga, _tga]) /\ length([l1, _uga]) /\ minus([_uga, n, _vga])) -> eq_nat([_tga, _vga]) -> 34  ;  (drop([u, x3, _ega])) -> drop([s(u), cons(x2, x3), _ega]) -> 34  ;  (length([ll, _jga])) -> length([cons(x, ll), s(_jga)]) -> 31  ;  (minus([u, x2, _nga])) -> minus([s(u), s(x2), _nga]) -> 32
}
Sat witness: Yes: ((drop([n, l1, _sga]) /\ length([_sga, _tga]) /\ length([l1, _uga]) /\ minus([_uga, n, _vga])) -> eq_nat([_tga, _vga]), {
_sga -> cons(b, nil)  ;  _tga -> s(z)  ;  _uga -> s(z)  ;  _vga -> z  ;  l1 -> cons(b, nil)  ;  n -> z
})

-------------------------------------------
Step 51, which took 0.070544 s (model generation: 0.068758,  model checking: 0.001786):

Model:
|_
{
drop -> 
{{{
Q={q_gen_1352, q_gen_1354, q_gen_1359, q_gen_1360, q_gen_1366, q_gen_1367, q_gen_1368, q_gen_1369, q_gen_1397, q_gen_1398, q_gen_1431, q_gen_1432, q_gen_1433, q_gen_1434, q_gen_1448},
Q_f={q_gen_1352},
Delta=
{
<s>(q_gen_1354) -> q_gen_1354
<z>() -> q_gen_1354
<cons>(q_gen_1398, q_gen_1397) -> q_gen_1397
<nil>() -> q_gen_1397
<a>() -> q_gen_1398
<b>() -> q_gen_1398
<s, cons>(q_gen_1360, q_gen_1359) -> q_gen_1359
<s, nil>(q_gen_1354) -> q_gen_1359
<z, nil>() -> q_gen_1359
<s, a>(q_gen_1354) -> q_gen_1360
<s, b>(q_gen_1354) -> q_gen_1360
<z, a>() -> q_gen_1360
<z, b>() -> q_gen_1360
<cons, cons>(q_gen_1369, q_gen_1368, q_gen_1367, q_gen_1366) -> q_gen_1366
<nil, nil>() -> q_gen_1366
<cons, a>(q_gen_1398, q_gen_1397) -> q_gen_1367
<cons, b>(q_gen_1398, q_gen_1397) -> q_gen_1367
<nil, a>() -> q_gen_1367
<nil, b>() -> q_gen_1367
<a, cons>(q_gen_1398, q_gen_1397) -> q_gen_1368
<a, nil>() -> q_gen_1368
<b, cons>(q_gen_1398, q_gen_1397) -> q_gen_1368
<b, nil>() -> q_gen_1368
<a, a>() -> q_gen_1369
<b, b>() -> q_gen_1369
<s, cons>(q_gen_1360, q_gen_1448) -> q_gen_1448
<z, cons>(q_gen_1398, q_gen_1397) -> q_gen_1448
<s, cons, cons>(q_gen_1434, q_gen_1433, q_gen_1432, q_gen_1431) -> q_gen_1352
<s, cons, nil>(q_gen_1360, q_gen_1359) -> q_gen_1352
<s, nil, nil>(q_gen_1354) -> q_gen_1352
<z, cons, cons>(q_gen_1369, q_gen_1368, q_gen_1367, q_gen_1366) -> q_gen_1352
<z, nil, nil>() -> q_gen_1352
<s, cons, nil>(q_gen_1360, q_gen_1448) -> q_gen_1431
<z, cons, nil>(q_gen_1398, q_gen_1397) -> q_gen_1431
<s, cons, b>(q_gen_1360, q_gen_1448) -> q_gen_1432
<z, cons, b>(q_gen_1398, q_gen_1397) -> q_gen_1432
<s, b, nil>(q_gen_1354) -> q_gen_1433
<z, b, nil>() -> q_gen_1433
<s, b, b>(q_gen_1354) -> q_gen_1434
<z, b, b>() -> q_gen_1434
}

Datatype: <nat, eltlist, eltlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_1351, q_gen_1357, q_gen_1389},
Q_f={q_gen_1351},
Delta=
{
<s>(q_gen_1389) -> q_gen_1389
<z>() -> q_gen_1389
<cons, s>(q_gen_1357, q_gen_1351) -> q_gen_1351
<nil, z>() -> q_gen_1351
<a, s>(q_gen_1389) -> q_gen_1357
<a, z>() -> q_gen_1357
<b, s>(q_gen_1389) -> q_gen_1357
<b, z>() -> q_gen_1357
}

Datatype: <eltlist, nat>
Convolution form: complete
}}}
  ;  minus -> 
{{{
Q={q_gen_1348, q_gen_1350, q_gen_1362, q_gen_1373, q_gen_1378, q_gen_1386, q_gen_1416},
Q_f={q_gen_1348},
Delta=
{
<s>(q_gen_1362) -> q_gen_1362
<z>() -> q_gen_1362
<s, s>(q_gen_1350) -> q_gen_1350
<z, z>() -> q_gen_1350
<s, s>(q_gen_1386) -> q_gen_1386
<z, s>(q_gen_1362) -> q_gen_1386
<s, z>(q_gen_1362) -> q_gen_1416
<s, s, s>(q_gen_1373) -> q_gen_1348
<s, s, z>(q_gen_1350) -> q_gen_1348
<s, s, z>(q_gen_1386) -> q_gen_1348
<s, z, s>(q_gen_1350) -> q_gen_1348
<z, s, z>(q_gen_1362) -> q_gen_1348
<z, z, z>() -> q_gen_1348
<s, s, z>(q_gen_1416) -> q_gen_1373
<s, z, s>(q_gen_1416) -> q_gen_1373
<s, z, z>(q_gen_1362) -> q_gen_1373
<s, s, s>(q_gen_1348) -> q_gen_1378
<s, s, s>(q_gen_1378) -> q_gen_1378
<s, z, s>(q_gen_1386) -> q_gen_1378
}

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

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

Teacher's answer:
New clause system:
{
() -> drop([s(u), nil, nil]) -> 31  ;  () -> drop([z, l, l]) -> 31  ;  () -> length([nil, z]) -> 31  ;  () -> minus([s(u), z, s(u)]) -> 31  ;  () -> minus([z, y, z]) -> 31  ;  (drop([n, l1, _sga]) /\ length([_sga, _tga]) /\ length([l1, _uga]) /\ minus([_uga, n, _vga])) -> eq_nat([_tga, _vga]) -> 34  ;  (drop([u, x3, _ega])) -> drop([s(u), cons(x2, x3), _ega]) -> 34  ;  (length([ll, _jga])) -> length([cons(x, ll), s(_jga)]) -> 32  ;  (minus([u, x2, _nga])) -> minus([s(u), s(x2), _nga]) -> 35
}
Sat witness: Yes: ((minus([u, x2, _nga])) -> minus([s(u), s(x2), _nga]), {
_nga -> s(s(z))  ;  u -> s(s(s(z)))  ;  x2 -> s(z)
})

-------------------------------------------
Step 52, which took 0.085946 s (model generation: 0.083580,  model checking: 0.002366):

Model:
|_
{
drop -> 
{{{
Q={q_gen_1352, q_gen_1354, q_gen_1359, q_gen_1360, q_gen_1366, q_gen_1367, q_gen_1368, q_gen_1369, q_gen_1391, q_gen_1397, q_gen_1398, q_gen_1431, q_gen_1432, q_gen_1433, q_gen_1434, q_gen_1436},
Q_f={q_gen_1352},
Delta=
{
<s>(q_gen_1354) -> q_gen_1354
<z>() -> q_gen_1354
<cons>(q_gen_1398, q_gen_1397) -> q_gen_1397
<nil>() -> q_gen_1397
<a>() -> q_gen_1398
<b>() -> q_gen_1398
<z, nil>() -> q_gen_1359
<s, a>(q_gen_1354) -> q_gen_1360
<s, b>(q_gen_1354) -> q_gen_1360
<z, a>() -> q_gen_1360
<z, b>() -> q_gen_1360
<cons, cons>(q_gen_1369, q_gen_1368, q_gen_1367, q_gen_1366) -> q_gen_1366
<nil, nil>() -> q_gen_1366
<cons, a>(q_gen_1398, q_gen_1397) -> q_gen_1367
<cons, b>(q_gen_1398, q_gen_1397) -> q_gen_1367
<nil, a>() -> q_gen_1367
<nil, b>() -> q_gen_1367
<a, cons>(q_gen_1398, q_gen_1397) -> q_gen_1368
<a, nil>() -> q_gen_1368
<b, cons>(q_gen_1398, q_gen_1397) -> q_gen_1368
<b, nil>() -> q_gen_1368
<a, a>() -> q_gen_1369
<b, b>() -> q_gen_1369
<s, cons>(q_gen_1360, q_gen_1359) -> q_gen_1391
<s, cons>(q_gen_1360, q_gen_1436) -> q_gen_1391
<s, nil>(q_gen_1354) -> q_gen_1391
<s, cons>(q_gen_1360, q_gen_1391) -> q_gen_1436
<z, cons>(q_gen_1398, q_gen_1397) -> q_gen_1436
<s, cons, cons>(q_gen_1434, q_gen_1433, q_gen_1432, q_gen_1352) -> q_gen_1352
<s, cons, cons>(q_gen_1434, q_gen_1433, q_gen_1432, q_gen_1431) -> q_gen_1352
<s, cons, nil>(q_gen_1360, q_gen_1359) -> q_gen_1352
<s, cons, nil>(q_gen_1360, q_gen_1391) -> q_gen_1352
<s, nil, nil>(q_gen_1354) -> q_gen_1352
<z, cons, cons>(q_gen_1369, q_gen_1368, q_gen_1367, q_gen_1366) -> q_gen_1352
<z, nil, nil>() -> q_gen_1352
<s, cons, nil>(q_gen_1360, q_gen_1436) -> q_gen_1431
<z, cons, nil>(q_gen_1398, q_gen_1397) -> q_gen_1431
<s, cons, b>(q_gen_1360, q_gen_1391) -> q_gen_1432
<s, cons, b>(q_gen_1360, q_gen_1436) -> q_gen_1432
<z, cons, b>(q_gen_1398, q_gen_1397) -> q_gen_1432
<s, b, nil>(q_gen_1354) -> q_gen_1433
<z, b, nil>() -> q_gen_1433
<s, b, b>(q_gen_1354) -> q_gen_1434
<z, b, b>() -> q_gen_1434
}

Datatype: <nat, eltlist, eltlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_1351, q_gen_1357, q_gen_1389},
Q_f={q_gen_1351},
Delta=
{
<s>(q_gen_1389) -> q_gen_1389
<z>() -> q_gen_1389
<cons, s>(q_gen_1357, q_gen_1351) -> q_gen_1351
<nil, z>() -> q_gen_1351
<a, s>(q_gen_1389) -> q_gen_1357
<a, z>() -> q_gen_1357
<b, s>(q_gen_1389) -> q_gen_1357
<b, z>() -> q_gen_1357
}

Datatype: <eltlist, nat>
Convolution form: complete
}}}
  ;  minus -> 
{{{
Q={q_gen_1348, q_gen_1349, q_gen_1350, q_gen_1362, q_gen_1373, q_gen_1378, q_gen_1386},
Q_f={q_gen_1348, q_gen_1349},
Delta=
{
<s>(q_gen_1362) -> q_gen_1362
<z>() -> q_gen_1362
<s, s>(q_gen_1350) -> q_gen_1350
<s, s>(q_gen_1386) -> q_gen_1350
<z, z>() -> q_gen_1350
<s, z>(q_gen_1362) -> q_gen_1386
<z, s>(q_gen_1362) -> q_gen_1386
<s, s, s>(q_gen_1349) -> q_gen_1348
<s, s, z>(q_gen_1350) -> q_gen_1348
<z, s, z>(q_gen_1362) -> q_gen_1348
<z, z, z>() -> q_gen_1348
<s, s, s>(q_gen_1373) -> q_gen_1349
<s, s, z>(q_gen_1386) -> q_gen_1349
<s, z, s>(q_gen_1350) -> q_gen_1349
<s, z, s>(q_gen_1386) -> q_gen_1373
<s, z, z>(q_gen_1362) -> q_gen_1373
<s, s, s>(q_gen_1348) -> q_gen_1378
<s, s, s>(q_gen_1378) -> q_gen_1378
}

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

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

Teacher's answer:
New clause system:
{
() -> drop([s(u), nil, nil]) -> 32  ;  () -> drop([z, l, l]) -> 32  ;  () -> length([nil, z]) -> 32  ;  () -> minus([s(u), z, s(u)]) -> 32  ;  () -> minus([z, y, z]) -> 32  ;  (drop([n, l1, _sga]) /\ length([_sga, _tga]) /\ length([l1, _uga]) /\ minus([_uga, n, _vga])) -> eq_nat([_tga, _vga]) -> 34  ;  (drop([u, x3, _ega])) -> drop([s(u), cons(x2, x3), _ega]) -> 37  ;  (length([ll, _jga])) -> length([cons(x, ll), s(_jga)]) -> 33  ;  (minus([u, x2, _nga])) -> minus([s(u), s(x2), _nga]) -> 35
}
Sat witness: Yes: ((drop([u, x3, _ega])) -> drop([s(u), cons(x2, x3), _ega]), {
_ega -> nil  ;  u -> s(s(z))  ;  x2 -> a  ;  x3 -> cons(a, nil)
})

-------------------------------------------
Step 53, which took 0.097351 s (model generation: 0.095097,  model checking: 0.002254):

Model:
|_
{
drop -> 
{{{
Q={q_gen_1352, q_gen_1354, q_gen_1359, q_gen_1360, q_gen_1366, q_gen_1367, q_gen_1368, q_gen_1369, q_gen_1397, q_gen_1398, q_gen_1408, q_gen_1431, q_gen_1432, q_gen_1433, q_gen_1434, q_gen_1436},
Q_f={q_gen_1352},
Delta=
{
<s>(q_gen_1354) -> q_gen_1354
<z>() -> q_gen_1354
<cons>(q_gen_1398, q_gen_1397) -> q_gen_1397
<nil>() -> q_gen_1397
<a>() -> q_gen_1398
<b>() -> q_gen_1398
<s, cons>(q_gen_1360, q_gen_1359) -> q_gen_1359
<s, nil>(q_gen_1354) -> q_gen_1359
<z, nil>() -> q_gen_1359
<s, b>(q_gen_1354) -> q_gen_1360
<z, a>() -> q_gen_1360
<z, b>() -> q_gen_1360
<cons, cons>(q_gen_1369, q_gen_1368, q_gen_1367, q_gen_1366) -> q_gen_1366
<nil, nil>() -> q_gen_1366
<cons, a>(q_gen_1398, q_gen_1397) -> q_gen_1367
<cons, b>(q_gen_1398, q_gen_1397) -> q_gen_1367
<nil, a>() -> q_gen_1367
<nil, b>() -> q_gen_1367
<a, cons>(q_gen_1398, q_gen_1397) -> q_gen_1368
<a, nil>() -> q_gen_1368
<b, cons>(q_gen_1398, q_gen_1397) -> q_gen_1368
<b, nil>() -> q_gen_1368
<a, a>() -> q_gen_1369
<b, b>() -> q_gen_1369
<s, a>(q_gen_1354) -> q_gen_1408
<s, cons>(q_gen_1360, q_gen_1436) -> q_gen_1436
<s, cons>(q_gen_1408, q_gen_1359) -> q_gen_1436
<z, cons>(q_gen_1398, q_gen_1397) -> q_gen_1436
<s, cons, cons>(q_gen_1434, q_gen_1433, q_gen_1432, q_gen_1431) -> q_gen_1352
<s, cons, nil>(q_gen_1360, q_gen_1359) -> q_gen_1352
<s, cons, nil>(q_gen_1408, q_gen_1359) -> q_gen_1352
<s, cons, nil>(q_gen_1408, q_gen_1436) -> q_gen_1352
<s, nil, nil>(q_gen_1354) -> q_gen_1352
<z, cons, cons>(q_gen_1369, q_gen_1368, q_gen_1367, q_gen_1366) -> q_gen_1352
<z, nil, nil>() -> q_gen_1352
<s, cons, nil>(q_gen_1360, q_gen_1436) -> q_gen_1431
<z, cons, nil>(q_gen_1398, q_gen_1397) -> q_gen_1431
<s, cons, b>(q_gen_1360, q_gen_1436) -> q_gen_1432
<z, cons, b>(q_gen_1398, q_gen_1397) -> q_gen_1432
<s, b, nil>(q_gen_1354) -> q_gen_1433
<z, b, nil>() -> q_gen_1433
<s, b, b>(q_gen_1354) -> q_gen_1434
<z, b, b>() -> q_gen_1434
}

Datatype: <nat, eltlist, eltlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_1351, q_gen_1357, q_gen_1389},
Q_f={q_gen_1351},
Delta=
{
<s>(q_gen_1389) -> q_gen_1389
<z>() -> q_gen_1389
<cons, s>(q_gen_1357, q_gen_1351) -> q_gen_1351
<nil, z>() -> q_gen_1351
<a, s>(q_gen_1389) -> q_gen_1357
<a, z>() -> q_gen_1357
<b, s>(q_gen_1389) -> q_gen_1357
<b, z>() -> q_gen_1357
}

Datatype: <eltlist, nat>
Convolution form: complete
}}}
  ;  minus -> 
{{{
Q={q_gen_1348, q_gen_1349, q_gen_1350, q_gen_1362, q_gen_1373, q_gen_1378, q_gen_1386},
Q_f={q_gen_1348, q_gen_1349},
Delta=
{
<s>(q_gen_1362) -> q_gen_1362
<z>() -> q_gen_1362
<s, s>(q_gen_1350) -> q_gen_1350
<s, s>(q_gen_1386) -> q_gen_1350
<z, z>() -> q_gen_1350
<s, z>(q_gen_1362) -> q_gen_1386
<z, s>(q_gen_1362) -> q_gen_1386
<s, s, s>(q_gen_1349) -> q_gen_1348
<s, s, z>(q_gen_1350) -> q_gen_1348
<z, s, z>(q_gen_1362) -> q_gen_1348
<z, z, z>() -> q_gen_1348
<s, s, s>(q_gen_1373) -> q_gen_1349
<s, s, z>(q_gen_1386) -> q_gen_1349
<s, z, s>(q_gen_1350) -> q_gen_1349
<s, s, s>(q_gen_1378) -> q_gen_1373
<s, z, s>(q_gen_1386) -> q_gen_1373
<s, z, z>(q_gen_1362) -> q_gen_1373
<s, s, s>(q_gen_1348) -> q_gen_1378
}

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

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

Teacher's answer:
New clause system:
{
() -> drop([s(u), nil, nil]) -> 33  ;  () -> drop([z, l, l]) -> 33  ;  () -> length([nil, z]) -> 33  ;  () -> minus([s(u), z, s(u)]) -> 33  ;  () -> minus([z, y, z]) -> 33  ;  (drop([n, l1, _sga]) /\ length([_sga, _tga]) /\ length([l1, _uga]) /\ minus([_uga, n, _vga])) -> eq_nat([_tga, _vga]) -> 37  ;  (drop([u, x3, _ega])) -> drop([s(u), cons(x2, x3), _ega]) -> 37  ;  (length([ll, _jga])) -> length([cons(x, ll), s(_jga)]) -> 34  ;  (minus([u, x2, _nga])) -> minus([s(u), s(x2), _nga]) -> 35
}
Sat witness: Yes: ((drop([n, l1, _sga]) /\ length([_sga, _tga]) /\ length([l1, _uga]) /\ minus([_uga, n, _vga])) -> eq_nat([_tga, _vga]), {
_sga -> nil  ;  _tga -> z  ;  _uga -> s(s(s(z)))  ;  _vga -> s(s(s(z)))  ;  l1 -> cons(a, cons(b, cons(a, nil)))  ;  n -> s(s(s(s(z))))
})

-------------------------------------------
Step 54, which took 0.151190 s (model generation: 0.149351,  model checking: 0.001839):

Model:
|_
{
drop -> 
{{{
Q={q_gen_1352, q_gen_1354, q_gen_1359, q_gen_1360, q_gen_1366, q_gen_1367, q_gen_1368, q_gen_1369, q_gen_1397, q_gen_1398, q_gen_1431, q_gen_1432, q_gen_1433, q_gen_1434, q_gen_1448},
Q_f={q_gen_1352},
Delta=
{
<s>(q_gen_1354) -> q_gen_1354
<z>() -> q_gen_1354
<cons>(q_gen_1398, q_gen_1397) -> q_gen_1397
<nil>() -> q_gen_1397
<a>() -> q_gen_1398
<b>() -> q_gen_1398
<s, cons>(q_gen_1360, q_gen_1359) -> q_gen_1359
<s, nil>(q_gen_1354) -> q_gen_1359
<z, nil>() -> q_gen_1359
<s, a>(q_gen_1354) -> q_gen_1360
<s, b>(q_gen_1354) -> q_gen_1360
<z, a>() -> q_gen_1360
<z, b>() -> q_gen_1360
<cons, cons>(q_gen_1369, q_gen_1368, q_gen_1367, q_gen_1366) -> q_gen_1366
<nil, nil>() -> q_gen_1366
<cons, a>(q_gen_1398, q_gen_1397) -> q_gen_1367
<cons, b>(q_gen_1398, q_gen_1397) -> q_gen_1367
<nil, a>() -> q_gen_1367
<nil, b>() -> q_gen_1367
<a, cons>(q_gen_1398, q_gen_1397) -> q_gen_1368
<a, nil>() -> q_gen_1368
<b, cons>(q_gen_1398, q_gen_1397) -> q_gen_1368
<b, nil>() -> q_gen_1368
<a, a>() -> q_gen_1369
<b, b>() -> q_gen_1369
<s, cons>(q_gen_1360, q_gen_1448) -> q_gen_1448
<z, cons>(q_gen_1398, q_gen_1397) -> q_gen_1448
<s, cons, cons>(q_gen_1434, q_gen_1433, q_gen_1432, q_gen_1431) -> q_gen_1352
<s, cons, nil>(q_gen_1360, q_gen_1359) -> q_gen_1352
<s, nil, nil>(q_gen_1354) -> q_gen_1352
<z, cons, cons>(q_gen_1369, q_gen_1368, q_gen_1367, q_gen_1366) -> q_gen_1352
<z, nil, nil>() -> q_gen_1352
<s, cons, nil>(q_gen_1360, q_gen_1448) -> q_gen_1431
<z, cons, nil>(q_gen_1398, q_gen_1397) -> q_gen_1431
<s, cons, b>(q_gen_1360, q_gen_1448) -> q_gen_1432
<z, cons, b>(q_gen_1398, q_gen_1397) -> q_gen_1432
<s, b, nil>(q_gen_1354) -> q_gen_1433
<z, b, nil>() -> q_gen_1433
<s, b, b>(q_gen_1354) -> q_gen_1434
<z, b, b>() -> q_gen_1434
}

Datatype: <nat, eltlist, eltlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_1351, q_gen_1357, q_gen_1389},
Q_f={q_gen_1351},
Delta=
{
<s>(q_gen_1389) -> q_gen_1389
<z>() -> q_gen_1389
<cons, s>(q_gen_1357, q_gen_1351) -> q_gen_1351
<nil, z>() -> q_gen_1351
<a, s>(q_gen_1389) -> q_gen_1357
<a, z>() -> q_gen_1357
<b, s>(q_gen_1389) -> q_gen_1357
<b, z>() -> q_gen_1357
}

Datatype: <eltlist, nat>
Convolution form: complete
}}}
  ;  minus -> 
{{{
Q={q_gen_1348, q_gen_1349, q_gen_1350, q_gen_1362, q_gen_1373, q_gen_1378, q_gen_1386, q_gen_1416},
Q_f={q_gen_1348, q_gen_1349},
Delta=
{
<s>(q_gen_1362) -> q_gen_1362
<z>() -> q_gen_1362
<s, s>(q_gen_1350) -> q_gen_1350
<z, z>() -> q_gen_1350
<s, s>(q_gen_1386) -> q_gen_1386
<z, s>(q_gen_1362) -> q_gen_1386
<s, z>(q_gen_1362) -> q_gen_1416
<s, s, z>(q_gen_1350) -> q_gen_1348
<s, s, z>(q_gen_1386) -> q_gen_1348
<z, s, z>(q_gen_1362) -> q_gen_1348
<z, z, z>() -> q_gen_1348
<s, s, s>(q_gen_1349) -> q_gen_1349
<s, s, s>(q_gen_1373) -> q_gen_1349
<s, z, s>(q_gen_1350) -> q_gen_1349
<s, s, z>(q_gen_1416) -> q_gen_1373
<s, z, s>(q_gen_1416) -> q_gen_1373
<s, z, z>(q_gen_1362) -> q_gen_1373
<s, s, s>(q_gen_1348) -> q_gen_1378
<s, s, s>(q_gen_1378) -> q_gen_1378
<s, z, s>(q_gen_1386) -> q_gen_1378
}

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

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

Teacher's answer:
New clause system:
{
() -> drop([s(u), nil, nil]) -> 34  ;  () -> drop([z, l, l]) -> 34  ;  () -> length([nil, z]) -> 34  ;  () -> minus([s(u), z, s(u)]) -> 34  ;  () -> minus([z, y, z]) -> 34  ;  (drop([n, l1, _sga]) /\ length([_sga, _tga]) /\ length([l1, _uga]) /\ minus([_uga, n, _vga])) -> eq_nat([_tga, _vga]) -> 37  ;  (drop([u, x3, _ega])) -> drop([s(u), cons(x2, x3), _ega]) -> 37  ;  (length([ll, _jga])) -> length([cons(x, ll), s(_jga)]) -> 35  ;  (minus([u, x2, _nga])) -> minus([s(u), s(x2), _nga]) -> 38
}
Sat witness: Yes: ((minus([u, x2, _nga])) -> minus([s(u), s(x2), _nga]), {
_nga -> s(s(s(z)))  ;  u -> s(s(s(z)))  ;  x2 -> z
})

-------------------------------------------
Step 55, which took 0.151052 s (model generation: 0.148304,  model checking: 0.002748):

Model:
|_
{
drop -> 
{{{
Q={q_gen_1352, q_gen_1354, q_gen_1359, q_gen_1360, q_gen_1366, q_gen_1367, q_gen_1368, q_gen_1369, q_gen_1377, q_gen_1392, q_gen_1397, q_gen_1398, q_gen_1423, q_gen_1424, q_gen_1432, q_gen_1433, q_gen_1434},
Q_f={q_gen_1352},
Delta=
{
<s>(q_gen_1354) -> q_gen_1354
<z>() -> q_gen_1354
<cons>(q_gen_1398, q_gen_1397) -> q_gen_1397
<nil>() -> q_gen_1397
<a>() -> q_gen_1398
<b>() -> q_gen_1398
<s, cons>(q_gen_1360, q_gen_1424) -> q_gen_1359
<s, cons>(q_gen_1377, q_gen_1359) -> q_gen_1359
<s, nil>(q_gen_1354) -> q_gen_1359
<z, nil>() -> q_gen_1359
<z, b>() -> q_gen_1360
<cons, cons>(q_gen_1369, q_gen_1368, q_gen_1367, q_gen_1366) -> q_gen_1366
<nil, nil>() -> q_gen_1366
<cons, a>(q_gen_1398, q_gen_1397) -> q_gen_1367
<cons, b>(q_gen_1398, q_gen_1397) -> q_gen_1367
<nil, a>() -> q_gen_1367
<nil, b>() -> q_gen_1367
<a, cons>(q_gen_1398, q_gen_1397) -> q_gen_1368
<a, nil>() -> q_gen_1368
<b, cons>(q_gen_1398, q_gen_1397) -> q_gen_1368
<b, nil>() -> q_gen_1368
<a, a>() -> q_gen_1369
<b, b>() -> q_gen_1369
<s, a>(q_gen_1354) -> q_gen_1377
<z, a>() -> q_gen_1377
<s, b>(q_gen_1354) -> q_gen_1392
<s, cons>(q_gen_1360, q_gen_1359) -> q_gen_1424
<s, cons>(q_gen_1392, q_gen_1359) -> q_gen_1424
<z, cons>(q_gen_1398, q_gen_1397) -> q_gen_1424
<s, cons, cons>(q_gen_1434, q_gen_1433, q_gen_1432, q_gen_1352) -> q_gen_1352
<s, cons, cons>(q_gen_1434, q_gen_1433, q_gen_1432, q_gen_1423) -> q_gen_1352
<s, cons, nil>(q_gen_1360, q_gen_1359) -> q_gen_1352
<s, cons, nil>(q_gen_1377, q_gen_1359) -> q_gen_1352
<s, cons, nil>(q_gen_1392, q_gen_1359) -> q_gen_1352
<s, cons, nil>(q_gen_1392, q_gen_1424) -> q_gen_1352
<s, nil, nil>(q_gen_1354) -> q_gen_1352
<z, cons, cons>(q_gen_1369, q_gen_1368, q_gen_1367, q_gen_1366) -> q_gen_1352
<z, nil, nil>() -> q_gen_1352
<s, cons, nil>(q_gen_1360, q_gen_1424) -> q_gen_1423
<s, cons, nil>(q_gen_1377, q_gen_1424) -> q_gen_1423
<z, cons, nil>(q_gen_1398, q_gen_1397) -> q_gen_1423
<s, cons, b>(q_gen_1360, q_gen_1424) -> q_gen_1432
<s, cons, b>(q_gen_1392, q_gen_1359) -> q_gen_1432
<z, cons, b>(q_gen_1398, q_gen_1397) -> q_gen_1432
<s, b, nil>(q_gen_1354) -> q_gen_1433
<z, b, nil>() -> q_gen_1433
<s, b, b>(q_gen_1354) -> q_gen_1434
<z, b, b>() -> q_gen_1434
}

Datatype: <nat, eltlist, eltlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_1351, q_gen_1357, q_gen_1389},
Q_f={q_gen_1351},
Delta=
{
<s>(q_gen_1389) -> q_gen_1389
<z>() -> q_gen_1389
<cons, s>(q_gen_1357, q_gen_1351) -> q_gen_1351
<nil, z>() -> q_gen_1351
<a, s>(q_gen_1389) -> q_gen_1357
<a, z>() -> q_gen_1357
<b, s>(q_gen_1389) -> q_gen_1357
<b, z>() -> q_gen_1357
}

Datatype: <eltlist, nat>
Convolution form: complete
}}}
  ;  minus -> 
{{{
Q={q_gen_1348, q_gen_1349, q_gen_1350, q_gen_1362, q_gen_1373, q_gen_1386},
Q_f={q_gen_1348, q_gen_1349},
Delta=
{
<s>(q_gen_1362) -> q_gen_1362
<z>() -> q_gen_1362
<s, s>(q_gen_1350) -> q_gen_1350
<s, z>(q_gen_1362) -> q_gen_1350
<z, z>() -> q_gen_1350
<s, s>(q_gen_1386) -> q_gen_1386
<z, s>(q_gen_1362) -> q_gen_1386
<s, s, z>(q_gen_1386) -> q_gen_1348
<z, s, z>(q_gen_1362) -> q_gen_1348
<z, z, z>() -> q_gen_1348
<s, s, s>(q_gen_1349) -> q_gen_1349
<s, s, s>(q_gen_1373) -> q_gen_1349
<s, s, z>(q_gen_1350) -> q_gen_1349
<s, z, s>(q_gen_1350) -> q_gen_1349
<s, s, s>(q_gen_1348) -> q_gen_1373
<s, z, s>(q_gen_1386) -> q_gen_1373
<s, z, z>(q_gen_1362) -> q_gen_1373
}

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

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

Teacher's answer:
New clause system:
{
() -> drop([s(u), nil, nil]) -> 35  ;  () -> drop([z, l, l]) -> 35  ;  () -> length([nil, z]) -> 35  ;  () -> minus([s(u), z, s(u)]) -> 35  ;  () -> minus([z, y, z]) -> 35  ;  (drop([n, l1, _sga]) /\ length([_sga, _tga]) /\ length([l1, _uga]) /\ minus([_uga, n, _vga])) -> eq_nat([_tga, _vga]) -> 37  ;  (drop([u, x3, _ega])) -> drop([s(u), cons(x2, x3), _ega]) -> 40  ;  (length([ll, _jga])) -> length([cons(x, ll), s(_jga)]) -> 36  ;  (minus([u, x2, _nga])) -> minus([s(u), s(x2), _nga]) -> 38
}
Sat witness: Yes: ((drop([u, x3, _ega])) -> drop([s(u), cons(x2, x3), _ega]), {
_ega -> nil  ;  u -> s(z)  ;  x2 -> a  ;  x3 -> cons(b, nil)
})

-------------------------------------------
Step 56, which took 0.142977 s (model generation: 0.142788,  model checking: 0.000189):

Model:
|_
{
drop -> 
{{{
Q={q_gen_1352, q_gen_1354, q_gen_1359, q_gen_1360, q_gen_1366, q_gen_1367, q_gen_1368, q_gen_1369, q_gen_1397, q_gen_1398, q_gen_1431, q_gen_1432, q_gen_1433, q_gen_1434, q_gen_1448},
Q_f={q_gen_1352},
Delta=
{
<s>(q_gen_1354) -> q_gen_1354
<z>() -> q_gen_1354
<cons>(q_gen_1398, q_gen_1397) -> q_gen_1397
<nil>() -> q_gen_1397
<a>() -> q_gen_1398
<b>() -> q_gen_1398
<s, cons>(q_gen_1360, q_gen_1359) -> q_gen_1359
<s, cons>(q_gen_1360, q_gen_1448) -> q_gen_1359
<s, nil>(q_gen_1354) -> q_gen_1359
<z, nil>() -> q_gen_1359
<s, a>(q_gen_1354) -> q_gen_1360
<s, b>(q_gen_1354) -> q_gen_1360
<z, a>() -> q_gen_1360
<z, b>() -> q_gen_1360
<cons, cons>(q_gen_1369, q_gen_1368, q_gen_1367, q_gen_1366) -> q_gen_1366
<nil, nil>() -> q_gen_1366
<cons, a>(q_gen_1398, q_gen_1397) -> q_gen_1367
<cons, b>(q_gen_1398, q_gen_1397) -> q_gen_1367
<nil, a>() -> q_gen_1367
<nil, b>() -> q_gen_1367
<a, cons>(q_gen_1398, q_gen_1397) -> q_gen_1368
<a, nil>() -> q_gen_1368
<b, cons>(q_gen_1398, q_gen_1397) -> q_gen_1368
<b, nil>() -> q_gen_1368
<a, a>() -> q_gen_1369
<b, b>() -> q_gen_1369
<z, cons>(q_gen_1398, q_gen_1397) -> q_gen_1448
<s, cons, cons>(q_gen_1434, q_gen_1433, q_gen_1432, q_gen_1352) -> q_gen_1352
<s, cons, cons>(q_gen_1434, q_gen_1433, q_gen_1432, q_gen_1431) -> q_gen_1352
<s, cons, nil>(q_gen_1360, q_gen_1359) -> q_gen_1352
<s, nil, nil>(q_gen_1354) -> q_gen_1352
<z, cons, cons>(q_gen_1369, q_gen_1368, q_gen_1367, q_gen_1366) -> q_gen_1352
<z, nil, nil>() -> q_gen_1352
<s, cons, nil>(q_gen_1360, q_gen_1448) -> q_gen_1431
<z, cons, nil>(q_gen_1398, q_gen_1397) -> q_gen_1431
<s, cons, b>(q_gen_1360, q_gen_1359) -> q_gen_1432
<s, cons, b>(q_gen_1360, q_gen_1448) -> q_gen_1432
<z, cons, b>(q_gen_1398, q_gen_1397) -> q_gen_1432
<s, b, nil>(q_gen_1354) -> q_gen_1433
<z, b, nil>() -> q_gen_1433
<s, b, b>(q_gen_1354) -> q_gen_1434
<z, b, b>() -> q_gen_1434
}

Datatype: <nat, eltlist, eltlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_1351, q_gen_1357, q_gen_1389},
Q_f={q_gen_1351},
Delta=
{
<s>(q_gen_1389) -> q_gen_1389
<z>() -> q_gen_1389
<cons, s>(q_gen_1357, q_gen_1351) -> q_gen_1351
<nil, z>() -> q_gen_1351
<a, s>(q_gen_1389) -> q_gen_1357
<a, z>() -> q_gen_1357
<b, s>(q_gen_1389) -> q_gen_1357
<b, z>() -> q_gen_1357
}

Datatype: <eltlist, nat>
Convolution form: complete
}}}
  ;  minus -> 
{{{
Q={q_gen_1348, q_gen_1349, q_gen_1350, q_gen_1362, q_gen_1364, q_gen_1373, q_gen_1378, q_gen_1386},
Q_f={q_gen_1348, q_gen_1349},
Delta=
{
<s>(q_gen_1362) -> q_gen_1362
<z>() -> q_gen_1362
<s, s>(q_gen_1386) -> q_gen_1350
<z, z>() -> q_gen_1350
<s, s>(q_gen_1350) -> q_gen_1364
<s, z>(q_gen_1362) -> q_gen_1364
<s, s>(q_gen_1364) -> q_gen_1386
<z, s>(q_gen_1362) -> q_gen_1386
<s, s, s>(q_gen_1349) -> q_gen_1348
<s, s, z>(q_gen_1350) -> q_gen_1348
<s, s, z>(q_gen_1386) -> q_gen_1348
<z, s, z>(q_gen_1362) -> q_gen_1348
<z, z, z>() -> q_gen_1348
<s, s, s>(q_gen_1373) -> q_gen_1349
<s, z, s>(q_gen_1350) -> q_gen_1349
<s, z, s>(q_gen_1364) -> q_gen_1349
<s, s, z>(q_gen_1364) -> q_gen_1373
<s, z, s>(q_gen_1386) -> q_gen_1373
<s, z, z>(q_gen_1362) -> q_gen_1373
<s, s, s>(q_gen_1348) -> q_gen_1378
<s, s, s>(q_gen_1378) -> q_gen_1378
}

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

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

Teacher's answer:
New clause system:
{
() -> drop([s(u), nil, nil]) -> 35  ;  () -> drop([z, l, l]) -> 35  ;  () -> length([nil, z]) -> 35  ;  () -> minus([s(u), z, s(u)]) -> 38  ;  () -> minus([z, y, z]) -> 36  ;  (drop([n, l1, _sga]) /\ length([_sga, _tga]) /\ length([l1, _uga]) /\ minus([_uga, n, _vga])) -> eq_nat([_tga, _vga]) -> 37  ;  (drop([u, x3, _ega])) -> drop([s(u), cons(x2, x3), _ega]) -> 40  ;  (length([ll, _jga])) -> length([cons(x, ll), s(_jga)]) -> 36  ;  (minus([u, x2, _nga])) -> minus([s(u), s(x2), _nga]) -> 38
}
Sat witness: Yes: (() -> minus([s(u), z, s(u)]), {
u -> s(s(z))
})

-------------------------------------------
Step 57, which took 0.185294 s (model generation: 0.183062,  model checking: 0.002232):

Model:
|_
{
drop -> 
{{{
Q={q_gen_1352, q_gen_1354, q_gen_1359, q_gen_1360, q_gen_1366, q_gen_1367, q_gen_1368, q_gen_1369, q_gen_1397, q_gen_1398, q_gen_1408, q_gen_1431, q_gen_1432, q_gen_1433, q_gen_1434, q_gen_1436},
Q_f={q_gen_1352},
Delta=
{
<s>(q_gen_1354) -> q_gen_1354
<z>() -> q_gen_1354
<cons>(q_gen_1398, q_gen_1397) -> q_gen_1397
<nil>() -> q_gen_1397
<a>() -> q_gen_1398
<b>() -> q_gen_1398
<s, cons>(q_gen_1360, q_gen_1359) -> q_gen_1359
<s, nil>(q_gen_1354) -> q_gen_1359
<z, nil>() -> q_gen_1359
<s, b>(q_gen_1354) -> q_gen_1360
<z, a>() -> q_gen_1360
<z, b>() -> q_gen_1360
<cons, cons>(q_gen_1369, q_gen_1368, q_gen_1367, q_gen_1366) -> q_gen_1366
<nil, nil>() -> q_gen_1366
<cons, a>(q_gen_1398, q_gen_1397) -> q_gen_1367
<cons, b>(q_gen_1398, q_gen_1397) -> q_gen_1367
<nil, a>() -> q_gen_1367
<nil, b>() -> q_gen_1367
<a, cons>(q_gen_1398, q_gen_1397) -> q_gen_1368
<a, nil>() -> q_gen_1368
<b, cons>(q_gen_1398, q_gen_1397) -> q_gen_1368
<b, nil>() -> q_gen_1368
<a, a>() -> q_gen_1369
<b, b>() -> q_gen_1369
<s, a>(q_gen_1354) -> q_gen_1408
<s, cons>(q_gen_1360, q_gen_1436) -> q_gen_1436
<s, cons>(q_gen_1408, q_gen_1359) -> q_gen_1436
<z, cons>(q_gen_1398, q_gen_1397) -> q_gen_1436
<s, cons, cons>(q_gen_1434, q_gen_1433, q_gen_1432, q_gen_1431) -> q_gen_1352
<s, cons, nil>(q_gen_1360, q_gen_1359) -> q_gen_1352
<s, cons, nil>(q_gen_1408, q_gen_1359) -> q_gen_1352
<s, cons, nil>(q_gen_1408, q_gen_1436) -> q_gen_1352
<s, nil, nil>(q_gen_1354) -> q_gen_1352
<z, cons, cons>(q_gen_1369, q_gen_1368, q_gen_1367, q_gen_1366) -> q_gen_1352
<z, nil, nil>() -> q_gen_1352
<s, cons, nil>(q_gen_1360, q_gen_1436) -> q_gen_1431
<z, cons, nil>(q_gen_1398, q_gen_1397) -> q_gen_1431
<s, cons, b>(q_gen_1360, q_gen_1436) -> q_gen_1432
<z, cons, b>(q_gen_1398, q_gen_1397) -> q_gen_1432
<s, b, nil>(q_gen_1354) -> q_gen_1433
<z, b, nil>() -> q_gen_1433
<s, b, b>(q_gen_1354) -> q_gen_1434
<z, b, b>() -> q_gen_1434
}

Datatype: <nat, eltlist, eltlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_1351, q_gen_1357, q_gen_1389},
Q_f={q_gen_1351},
Delta=
{
<s>(q_gen_1389) -> q_gen_1389
<z>() -> q_gen_1389
<cons, s>(q_gen_1357, q_gen_1351) -> q_gen_1351
<nil, z>() -> q_gen_1351
<a, s>(q_gen_1389) -> q_gen_1357
<a, z>() -> q_gen_1357
<b, s>(q_gen_1389) -> q_gen_1357
<b, z>() -> q_gen_1357
}

Datatype: <eltlist, nat>
Convolution form: complete
}}}
  ;  minus -> 
{{{
Q={q_gen_1348, q_gen_1349, q_gen_1350, q_gen_1362, q_gen_1373, q_gen_1378, q_gen_1386},
Q_f={q_gen_1348, q_gen_1349},
Delta=
{
<s>(q_gen_1362) -> q_gen_1362
<z>() -> q_gen_1362
<s, s>(q_gen_1350) -> q_gen_1350
<s, s>(q_gen_1386) -> q_gen_1350
<z, z>() -> q_gen_1350
<s, z>(q_gen_1362) -> q_gen_1386
<z, s>(q_gen_1362) -> q_gen_1386
<s, s, s>(q_gen_1349) -> q_gen_1348
<s, s, z>(q_gen_1350) -> q_gen_1348
<z, s, z>(q_gen_1362) -> q_gen_1348
<z, z, z>() -> q_gen_1348
<s, s, s>(q_gen_1373) -> q_gen_1349
<s, s, z>(q_gen_1386) -> q_gen_1349
<s, z, s>(q_gen_1350) -> q_gen_1349
<s, z, s>(q_gen_1386) -> q_gen_1373
<s, z, z>(q_gen_1362) -> q_gen_1373
<s, s, s>(q_gen_1348) -> q_gen_1378
<s, s, s>(q_gen_1378) -> q_gen_1378
}

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

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

Teacher's answer:
New clause system:
{
() -> drop([s(u), nil, nil]) -> 36  ;  () -> drop([z, l, l]) -> 36  ;  () -> length([nil, z]) -> 36  ;  () -> minus([s(u), z, s(u)]) -> 38  ;  () -> minus([z, y, z]) -> 37  ;  (drop([n, l1, _sga]) /\ length([_sga, _tga]) /\ length([l1, _uga]) /\ minus([_uga, n, _vga])) -> eq_nat([_tga, _vga]) -> 40  ;  (drop([u, x3, _ega])) -> drop([s(u), cons(x2, x3), _ega]) -> 40  ;  (length([ll, _jga])) -> length([cons(x, ll), s(_jga)]) -> 37  ;  (minus([u, x2, _nga])) -> minus([s(u), s(x2), _nga]) -> 38
}
Sat witness: Yes: ((drop([n, l1, _sga]) /\ length([_sga, _tga]) /\ length([l1, _uga]) /\ minus([_uga, n, _vga])) -> eq_nat([_tga, _vga]), {
_sga -> cons(b, nil)  ;  _tga -> s(z)  ;  _uga -> s(s(z))  ;  _vga -> s(s(s(z)))  ;  l1 -> cons(b, cons(b, nil))  ;  n -> s(z)
})

-------------------------------------------
Step 58, which took 0.100545 s (model generation: 0.098875,  model checking: 0.001670):

Model:
|_
{
drop -> 
{{{
Q={q_gen_1352, q_gen_1354, q_gen_1359, q_gen_1360, q_gen_1366, q_gen_1367, q_gen_1368, q_gen_1369, q_gen_1397, q_gen_1398, q_gen_1431, q_gen_1432, q_gen_1433, q_gen_1434, q_gen_1448},
Q_f={q_gen_1352},
Delta=
{
<s>(q_gen_1354) -> q_gen_1354
<z>() -> q_gen_1354
<cons>(q_gen_1398, q_gen_1397) -> q_gen_1397
<nil>() -> q_gen_1397
<a>() -> q_gen_1398
<b>() -> q_gen_1398
<s, cons>(q_gen_1360, q_gen_1359) -> q_gen_1359
<s, cons>(q_gen_1360, q_gen_1448) -> q_gen_1359
<s, nil>(q_gen_1354) -> q_gen_1359
<z, nil>() -> q_gen_1359
<s, a>(q_gen_1354) -> q_gen_1360
<s, b>(q_gen_1354) -> q_gen_1360
<z, a>() -> q_gen_1360
<z, b>() -> q_gen_1360
<cons, cons>(q_gen_1369, q_gen_1368, q_gen_1367, q_gen_1366) -> q_gen_1366
<nil, nil>() -> q_gen_1366
<cons, a>(q_gen_1398, q_gen_1397) -> q_gen_1367
<cons, b>(q_gen_1398, q_gen_1397) -> q_gen_1367
<nil, a>() -> q_gen_1367
<nil, b>() -> q_gen_1367
<a, cons>(q_gen_1398, q_gen_1397) -> q_gen_1368
<a, nil>() -> q_gen_1368
<b, cons>(q_gen_1398, q_gen_1397) -> q_gen_1368
<b, nil>() -> q_gen_1368
<a, a>() -> q_gen_1369
<b, b>() -> q_gen_1369
<z, cons>(q_gen_1398, q_gen_1397) -> q_gen_1448
<s, cons, cons>(q_gen_1434, q_gen_1433, q_gen_1432, q_gen_1352) -> q_gen_1352
<s, cons, cons>(q_gen_1434, q_gen_1433, q_gen_1432, q_gen_1431) -> q_gen_1352
<s, cons, nil>(q_gen_1360, q_gen_1359) -> q_gen_1352
<s, nil, nil>(q_gen_1354) -> q_gen_1352
<z, cons, cons>(q_gen_1369, q_gen_1368, q_gen_1367, q_gen_1366) -> q_gen_1352
<z, nil, nil>() -> q_gen_1352
<s, cons, nil>(q_gen_1360, q_gen_1448) -> q_gen_1431
<z, cons, nil>(q_gen_1398, q_gen_1397) -> q_gen_1431
<s, cons, b>(q_gen_1360, q_gen_1359) -> q_gen_1432
<s, cons, b>(q_gen_1360, q_gen_1448) -> q_gen_1432
<z, cons, b>(q_gen_1398, q_gen_1397) -> q_gen_1432
<s, b, nil>(q_gen_1354) -> q_gen_1433
<z, b, nil>() -> q_gen_1433
<s, b, b>(q_gen_1354) -> q_gen_1434
<z, b, b>() -> q_gen_1434
}

Datatype: <nat, eltlist, eltlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_1351, q_gen_1357, q_gen_1389},
Q_f={q_gen_1351},
Delta=
{
<s>(q_gen_1389) -> q_gen_1389
<z>() -> q_gen_1389
<cons, s>(q_gen_1357, q_gen_1351) -> q_gen_1351
<nil, z>() -> q_gen_1351
<a, s>(q_gen_1389) -> q_gen_1357
<a, z>() -> q_gen_1357
<b, s>(q_gen_1389) -> q_gen_1357
<b, z>() -> q_gen_1357
}

Datatype: <eltlist, nat>
Convolution form: complete
}}}
  ;  minus -> 
{{{
Q={q_gen_1348, q_gen_1349, q_gen_1350, q_gen_1362, q_gen_1373, q_gen_1378, q_gen_1386, q_gen_1416},
Q_f={q_gen_1348, q_gen_1349},
Delta=
{
<s>(q_gen_1362) -> q_gen_1362
<z>() -> q_gen_1362
<s, s>(q_gen_1350) -> q_gen_1350
<s, s>(q_gen_1416) -> q_gen_1350
<z, z>() -> q_gen_1350
<s, s>(q_gen_1386) -> q_gen_1386
<z, s>(q_gen_1362) -> q_gen_1386
<s, z>(q_gen_1362) -> q_gen_1416
<s, s, s>(q_gen_1349) -> q_gen_1348
<s, s, z>(q_gen_1350) -> q_gen_1348
<s, s, z>(q_gen_1386) -> q_gen_1348
<z, s, z>(q_gen_1362) -> q_gen_1348
<z, z, z>() -> q_gen_1348
<s, s, s>(q_gen_1373) -> q_gen_1349
<s, z, s>(q_gen_1350) -> q_gen_1349
<s, s, z>(q_gen_1416) -> q_gen_1373
<s, z, s>(q_gen_1416) -> q_gen_1373
<s, z, z>(q_gen_1362) -> q_gen_1373
<s, s, s>(q_gen_1348) -> q_gen_1378
<s, s, s>(q_gen_1378) -> q_gen_1378
<s, z, s>(q_gen_1386) -> q_gen_1378
}

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

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

Teacher's answer:
New clause system:
{
() -> drop([s(u), nil, nil]) -> 37  ;  () -> drop([z, l, l]) -> 37  ;  () -> length([nil, z]) -> 37  ;  () -> minus([s(u), z, s(u)]) -> 38  ;  () -> minus([z, y, z]) -> 38  ;  (drop([n, l1, _sga]) /\ length([_sga, _tga]) /\ length([l1, _uga]) /\ minus([_uga, n, _vga])) -> eq_nat([_tga, _vga]) -> 40  ;  (drop([u, x3, _ega])) -> drop([s(u), cons(x2, x3), _ega]) -> 40  ;  (length([ll, _jga])) -> length([cons(x, ll), s(_jga)]) -> 38  ;  (minus([u, x2, _nga])) -> minus([s(u), s(x2), _nga]) -> 41
}
Sat witness: Yes: ((minus([u, x2, _nga])) -> minus([s(u), s(x2), _nga]), {
_nga -> s(z)  ;  u -> s(s(s(z)))  ;  x2 -> s(s(z))
})

-------------------------------------------
Step 59, which took 0.334647 s (model generation: 0.330267,  model checking: 0.004380):

Model:
|_
{
drop -> 
{{{
Q={q_gen_1352, q_gen_1354, q_gen_1359, q_gen_1360, q_gen_1366, q_gen_1367, q_gen_1368, q_gen_1369, q_gen_1397, q_gen_1398, q_gen_1431, q_gen_1432, q_gen_1433, q_gen_1434, q_gen_1448},
Q_f={q_gen_1352},
Delta=
{
<s>(q_gen_1354) -> q_gen_1354
<z>() -> q_gen_1354
<cons>(q_gen_1398, q_gen_1397) -> q_gen_1397
<nil>() -> q_gen_1397
<a>() -> q_gen_1398
<b>() -> q_gen_1398
<s, cons>(q_gen_1360, q_gen_1359) -> q_gen_1359
<s, nil>(q_gen_1354) -> q_gen_1359
<z, nil>() -> q_gen_1359
<s, a>(q_gen_1354) -> q_gen_1360
<s, b>(q_gen_1354) -> q_gen_1360
<z, a>() -> q_gen_1360
<z, b>() -> q_gen_1360
<cons, cons>(q_gen_1369, q_gen_1368, q_gen_1367, q_gen_1366) -> q_gen_1366
<nil, nil>() -> q_gen_1366
<cons, a>(q_gen_1398, q_gen_1397) -> q_gen_1367
<cons, b>(q_gen_1398, q_gen_1397) -> q_gen_1367
<nil, a>() -> q_gen_1367
<nil, b>() -> q_gen_1367
<a, cons>(q_gen_1398, q_gen_1397) -> q_gen_1368
<a, nil>() -> q_gen_1368
<b, cons>(q_gen_1398, q_gen_1397) -> q_gen_1368
<b, nil>() -> q_gen_1368
<a, a>() -> q_gen_1369
<b, b>() -> q_gen_1369
<s, cons>(q_gen_1360, q_gen_1448) -> q_gen_1448
<z, cons>(q_gen_1398, q_gen_1397) -> q_gen_1448
<s, cons, cons>(q_gen_1434, q_gen_1433, q_gen_1432, q_gen_1431) -> q_gen_1352
<s, cons, nil>(q_gen_1360, q_gen_1359) -> q_gen_1352
<s, nil, nil>(q_gen_1354) -> q_gen_1352
<z, cons, cons>(q_gen_1369, q_gen_1368, q_gen_1367, q_gen_1366) -> q_gen_1352
<z, nil, nil>() -> q_gen_1352
<s, cons, nil>(q_gen_1360, q_gen_1448) -> q_gen_1431
<z, cons, nil>(q_gen_1398, q_gen_1397) -> q_gen_1431
<s, cons, b>(q_gen_1360, q_gen_1448) -> q_gen_1432
<z, cons, b>(q_gen_1398, q_gen_1397) -> q_gen_1432
<s, b, nil>(q_gen_1354) -> q_gen_1433
<z, b, nil>() -> q_gen_1433
<s, b, b>(q_gen_1354) -> q_gen_1434
<z, b, b>() -> q_gen_1434
}

Datatype: <nat, eltlist, eltlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_1351, q_gen_1357, q_gen_1389},
Q_f={q_gen_1351},
Delta=
{
<s>(q_gen_1389) -> q_gen_1389
<z>() -> q_gen_1389
<cons, s>(q_gen_1357, q_gen_1351) -> q_gen_1351
<nil, z>() -> q_gen_1351
<a, s>(q_gen_1389) -> q_gen_1357
<a, z>() -> q_gen_1357
<b, s>(q_gen_1389) -> q_gen_1357
<b, z>() -> q_gen_1357
}

Datatype: <eltlist, nat>
Convolution form: complete
}}}
  ;  minus -> 
{{{
Q={q_gen_1348, q_gen_1349, q_gen_1350, q_gen_1362, q_gen_1373, q_gen_1378, q_gen_1386, q_gen_1416},
Q_f={q_gen_1348, q_gen_1349},
Delta=
{
<s>(q_gen_1362) -> q_gen_1362
<z>() -> q_gen_1362
<s, s>(q_gen_1350) -> q_gen_1350
<s, s>(q_gen_1386) -> q_gen_1350
<z, z>() -> q_gen_1350
<z, s>(q_gen_1362) -> q_gen_1386
<s, s>(q_gen_1416) -> q_gen_1416
<s, z>(q_gen_1362) -> q_gen_1416
<s, s, z>(q_gen_1350) -> q_gen_1348
<s, s, z>(q_gen_1386) -> q_gen_1348
<z, s, z>(q_gen_1362) -> q_gen_1348
<z, z, z>() -> q_gen_1348
<s, s, s>(q_gen_1349) -> q_gen_1349
<s, s, s>(q_gen_1373) -> q_gen_1349
<s, z, s>(q_gen_1350) -> q_gen_1349
<s, s, z>(q_gen_1416) -> q_gen_1373
<s, z, s>(q_gen_1416) -> q_gen_1373
<s, z, z>(q_gen_1362) -> q_gen_1373
<s, s, s>(q_gen_1348) -> q_gen_1378
<s, s, s>(q_gen_1378) -> q_gen_1378
<s, z, s>(q_gen_1386) -> q_gen_1378
}

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

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

Teacher's answer:
New clause system:
{
() -> drop([s(u), nil, nil]) -> 38  ;  () -> drop([z, l, l]) -> 38  ;  () -> length([nil, z]) -> 38  ;  () -> minus([s(u), z, s(u)]) -> 39  ;  () -> minus([z, y, z]) -> 39  ;  (drop([n, l1, _sga]) /\ length([_sga, _tga]) /\ length([l1, _uga]) /\ minus([_uga, n, _vga])) -> eq_nat([_tga, _vga]) -> 40  ;  (drop([u, x3, _ega])) -> drop([s(u), cons(x2, x3), _ega]) -> 43  ;  (length([ll, _jga])) -> length([cons(x, ll), s(_jga)]) -> 39  ;  (minus([u, x2, _nga])) -> minus([s(u), s(x2), _nga]) -> 41
}
Sat witness: Yes: ((drop([u, x3, _ega])) -> drop([s(u), cons(x2, x3), _ega]), {
_ega -> cons(b, nil)  ;  u -> s(z)  ;  x2 -> a  ;  x3 -> cons(b, cons(a, nil))
})

-------------------------------------------
Step 60, which took 0.226434 s (model generation: 0.224527,  model checking: 0.001907):

Model:
|_
{
drop -> 
{{{
Q={q_gen_1352, q_gen_1354, q_gen_1359, q_gen_1360, q_gen_1366, q_gen_1367, q_gen_1368, q_gen_1369, q_gen_1397, q_gen_1398, q_gen_1431, q_gen_1432, q_gen_1433, q_gen_1434, q_gen_1448},
Q_f={q_gen_1352},
Delta=
{
<s>(q_gen_1354) -> q_gen_1354
<z>() -> q_gen_1354
<cons>(q_gen_1398, q_gen_1397) -> q_gen_1397
<nil>() -> q_gen_1397
<a>() -> q_gen_1398
<b>() -> q_gen_1398
<s, cons>(q_gen_1360, q_gen_1359) -> q_gen_1359
<s, cons>(q_gen_1360, q_gen_1448) -> q_gen_1359
<s, nil>(q_gen_1354) -> q_gen_1359
<z, nil>() -> q_gen_1359
<s, a>(q_gen_1354) -> q_gen_1360
<s, b>(q_gen_1354) -> q_gen_1360
<z, a>() -> q_gen_1360
<z, b>() -> q_gen_1360
<cons, cons>(q_gen_1369, q_gen_1368, q_gen_1367, q_gen_1366) -> q_gen_1366
<nil, nil>() -> q_gen_1366
<cons, a>(q_gen_1398, q_gen_1397) -> q_gen_1367
<cons, b>(q_gen_1398, q_gen_1397) -> q_gen_1367
<nil, a>() -> q_gen_1367
<nil, b>() -> q_gen_1367
<a, cons>(q_gen_1398, q_gen_1397) -> q_gen_1368
<a, nil>() -> q_gen_1368
<b, cons>(q_gen_1398, q_gen_1397) -> q_gen_1368
<b, nil>() -> q_gen_1368
<a, a>() -> q_gen_1369
<b, b>() -> q_gen_1369
<z, cons>(q_gen_1398, q_gen_1397) -> q_gen_1448
<s, cons, cons>(q_gen_1434, q_gen_1433, q_gen_1432, q_gen_1352) -> q_gen_1352
<s, cons, cons>(q_gen_1434, q_gen_1433, q_gen_1432, q_gen_1431) -> q_gen_1352
<s, cons, nil>(q_gen_1360, q_gen_1359) -> q_gen_1352
<s, nil, nil>(q_gen_1354) -> q_gen_1352
<z, cons, cons>(q_gen_1369, q_gen_1368, q_gen_1367, q_gen_1366) -> q_gen_1352
<z, nil, nil>() -> q_gen_1352
<s, cons, nil>(q_gen_1360, q_gen_1448) -> q_gen_1431
<z, cons, nil>(q_gen_1398, q_gen_1397) -> q_gen_1431
<s, cons, b>(q_gen_1360, q_gen_1359) -> q_gen_1432
<s, cons, b>(q_gen_1360, q_gen_1448) -> q_gen_1432
<z, cons, b>(q_gen_1398, q_gen_1397) -> q_gen_1432
<s, a, nil>(q_gen_1354) -> q_gen_1433
<s, b, nil>(q_gen_1354) -> q_gen_1433
<z, b, nil>() -> q_gen_1433
<s, a, b>(q_gen_1354) -> q_gen_1434
<s, b, b>(q_gen_1354) -> q_gen_1434
<z, b, b>() -> q_gen_1434
}

Datatype: <nat, eltlist, eltlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_1351, q_gen_1357, q_gen_1389},
Q_f={q_gen_1351},
Delta=
{
<s>(q_gen_1389) -> q_gen_1389
<z>() -> q_gen_1389
<cons, s>(q_gen_1357, q_gen_1351) -> q_gen_1351
<nil, z>() -> q_gen_1351
<a, s>(q_gen_1389) -> q_gen_1357
<a, z>() -> q_gen_1357
<b, s>(q_gen_1389) -> q_gen_1357
<b, z>() -> q_gen_1357
}

Datatype: <eltlist, nat>
Convolution form: complete
}}}
  ;  minus -> 
{{{
Q={q_gen_1348, q_gen_1349, q_gen_1350, q_gen_1362, q_gen_1364, q_gen_1373, q_gen_1378, q_gen_1386},
Q_f={q_gen_1348, q_gen_1349},
Delta=
{
<s>(q_gen_1362) -> q_gen_1362
<z>() -> q_gen_1362
<z, z>() -> q_gen_1350
<s, s>(q_gen_1350) -> q_gen_1364
<s, s>(q_gen_1364) -> q_gen_1364
<s, z>(q_gen_1362) -> q_gen_1364
<s, s>(q_gen_1386) -> q_gen_1386
<z, s>(q_gen_1362) -> q_gen_1386
<s, s, s>(q_gen_1349) -> q_gen_1348
<s, s, z>(q_gen_1350) -> q_gen_1348
<s, s, z>(q_gen_1386) -> q_gen_1348
<z, s, z>(q_gen_1362) -> q_gen_1348
<z, z, z>() -> q_gen_1348
<s, s, s>(q_gen_1373) -> q_gen_1349
<s, z, s>(q_gen_1350) -> q_gen_1349
<s, z, s>(q_gen_1364) -> q_gen_1349
<s, s, z>(q_gen_1364) -> q_gen_1373
<s, z, z>(q_gen_1362) -> q_gen_1373
<s, s, s>(q_gen_1348) -> q_gen_1378
<s, s, s>(q_gen_1378) -> q_gen_1378
<s, z, s>(q_gen_1386) -> q_gen_1378
}

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

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

Teacher's answer:
New clause system:
{
() -> drop([s(u), nil, nil]) -> 39  ;  () -> drop([z, l, l]) -> 39  ;  () -> length([nil, z]) -> 39  ;  () -> minus([s(u), z, s(u)]) -> 40  ;  () -> minus([z, y, z]) -> 40  ;  (drop([n, l1, _sga]) /\ length([_sga, _tga]) /\ length([l1, _uga]) /\ minus([_uga, n, _vga])) -> eq_nat([_tga, _vga]) -> 43  ;  (drop([u, x3, _ega])) -> drop([s(u), cons(x2, x3), _ega]) -> 43  ;  (length([ll, _jga])) -> length([cons(x, ll), s(_jga)]) -> 40  ;  (minus([u, x2, _nga])) -> minus([s(u), s(x2), _nga]) -> 41
}
Sat witness: Yes: ((drop([n, l1, _sga]) /\ length([_sga, _tga]) /\ length([l1, _uga]) /\ minus([_uga, n, _vga])) -> eq_nat([_tga, _vga]), {
_sga -> nil  ;  _tga -> z  ;  _uga -> s(s(s(z)))  ;  _vga -> s(z)  ;  l1 -> cons(b, cons(b, cons(b, nil)))  ;  n -> s(s(z))
})

-------------------------------------------
Step 61, which took 0.291398 s (model generation: 0.289435,  model checking: 0.001963):

Model:
|_
{
drop -> 
{{{
Q={q_gen_1352, q_gen_1354, q_gen_1359, q_gen_1360, q_gen_1366, q_gen_1367, q_gen_1368, q_gen_1369, q_gen_1397, q_gen_1398, q_gen_1431, q_gen_1432, q_gen_1433, q_gen_1434, q_gen_1448},
Q_f={q_gen_1352},
Delta=
{
<s>(q_gen_1354) -> q_gen_1354
<z>() -> q_gen_1354
<cons>(q_gen_1398, q_gen_1397) -> q_gen_1397
<nil>() -> q_gen_1397
<a>() -> q_gen_1398
<b>() -> q_gen_1398
<s, cons>(q_gen_1360, q_gen_1359) -> q_gen_1359
<s, nil>(q_gen_1354) -> q_gen_1359
<z, nil>() -> q_gen_1359
<s, a>(q_gen_1354) -> q_gen_1360
<s, b>(q_gen_1354) -> q_gen_1360
<z, a>() -> q_gen_1360
<z, b>() -> q_gen_1360
<cons, cons>(q_gen_1369, q_gen_1368, q_gen_1367, q_gen_1366) -> q_gen_1366
<nil, nil>() -> q_gen_1366
<cons, a>(q_gen_1398, q_gen_1397) -> q_gen_1367
<cons, b>(q_gen_1398, q_gen_1397) -> q_gen_1367
<nil, a>() -> q_gen_1367
<nil, b>() -> q_gen_1367
<a, cons>(q_gen_1398, q_gen_1397) -> q_gen_1368
<a, nil>() -> q_gen_1368
<b, cons>(q_gen_1398, q_gen_1397) -> q_gen_1368
<b, nil>() -> q_gen_1368
<a, a>() -> q_gen_1369
<b, b>() -> q_gen_1369
<s, cons>(q_gen_1360, q_gen_1448) -> q_gen_1448
<z, cons>(q_gen_1398, q_gen_1397) -> q_gen_1448
<s, cons, cons>(q_gen_1434, q_gen_1433, q_gen_1432, q_gen_1431) -> q_gen_1352
<s, cons, nil>(q_gen_1360, q_gen_1359) -> q_gen_1352
<s, nil, nil>(q_gen_1354) -> q_gen_1352
<z, cons, cons>(q_gen_1369, q_gen_1368, q_gen_1367, q_gen_1366) -> q_gen_1352
<z, nil, nil>() -> q_gen_1352
<s, cons, nil>(q_gen_1360, q_gen_1448) -> q_gen_1431
<z, cons, nil>(q_gen_1398, q_gen_1397) -> q_gen_1431
<s, cons, b>(q_gen_1360, q_gen_1448) -> q_gen_1432
<z, cons, b>(q_gen_1398, q_gen_1397) -> q_gen_1432
<s, a, nil>(q_gen_1354) -> q_gen_1433
<s, b, nil>(q_gen_1354) -> q_gen_1433
<z, b, nil>() -> q_gen_1433
<s, a, b>(q_gen_1354) -> q_gen_1434
<s, b, b>(q_gen_1354) -> q_gen_1434
<z, b, b>() -> q_gen_1434
}

Datatype: <nat, eltlist, eltlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_1351, q_gen_1357, q_gen_1389},
Q_f={q_gen_1351},
Delta=
{
<s>(q_gen_1389) -> q_gen_1389
<z>() -> q_gen_1389
<cons, s>(q_gen_1357, q_gen_1351) -> q_gen_1351
<nil, z>() -> q_gen_1351
<a, s>(q_gen_1389) -> q_gen_1357
<a, z>() -> q_gen_1357
<b, s>(q_gen_1389) -> q_gen_1357
<b, z>() -> q_gen_1357
}

Datatype: <eltlist, nat>
Convolution form: complete
}}}
  ;  minus -> 
{{{
Q={q_gen_1348, q_gen_1349, q_gen_1350, q_gen_1362, q_gen_1364, q_gen_1373, q_gen_1378, q_gen_1386},
Q_f={q_gen_1348, q_gen_1349},
Delta=
{
<s>(q_gen_1362) -> q_gen_1362
<z>() -> q_gen_1362
<z, z>() -> q_gen_1350
<s, s>(q_gen_1350) -> q_gen_1364
<s, s>(q_gen_1364) -> q_gen_1364
<s, z>(q_gen_1362) -> q_gen_1364
<s, s>(q_gen_1386) -> q_gen_1386
<z, s>(q_gen_1362) -> q_gen_1386
<s, s, s>(q_gen_1349) -> q_gen_1348
<s, s, z>(q_gen_1350) -> q_gen_1348
<s, s, z>(q_gen_1386) -> q_gen_1348
<z, s, z>(q_gen_1362) -> q_gen_1348
<z, z, z>() -> q_gen_1348
<s, s, s>(q_gen_1373) -> q_gen_1349
<s, z, s>(q_gen_1350) -> q_gen_1349
<s, z, s>(q_gen_1364) -> q_gen_1349
<s, s, z>(q_gen_1364) -> q_gen_1373
<s, z, z>(q_gen_1362) -> q_gen_1373
<s, s, s>(q_gen_1348) -> q_gen_1378
<s, s, s>(q_gen_1378) -> q_gen_1378
<s, z, s>(q_gen_1386) -> q_gen_1378
}

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

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

Teacher's answer:
New clause system:
{
() -> drop([s(u), nil, nil]) -> 40  ;  () -> drop([z, l, l]) -> 40  ;  () -> length([nil, z]) -> 40  ;  () -> minus([s(u), z, s(u)]) -> 41  ;  () -> minus([z, y, z]) -> 41  ;  (drop([n, l1, _sga]) /\ length([_sga, _tga]) /\ length([l1, _uga]) /\ minus([_uga, n, _vga])) -> eq_nat([_tga, _vga]) -> 43  ;  (drop([u, x3, _ega])) -> drop([s(u), cons(x2, x3), _ega]) -> 43  ;  (length([ll, _jga])) -> length([cons(x, ll), s(_jga)]) -> 41  ;  (minus([u, x2, _nga])) -> minus([s(u), s(x2), _nga]) -> 44
}
Sat witness: Yes: ((minus([u, x2, _nga])) -> minus([s(u), s(x2), _nga]), {
_nga -> s(s(s(z)))  ;  u -> s(s(s(z)))  ;  x2 -> s(z)
})

-------------------------------------------
Step 62, which took 0.178684 s (model generation: 0.174118,  model checking: 0.004566):

Model:
|_
{
drop -> 
{{{
Q={q_gen_1352, q_gen_1354, q_gen_1359, q_gen_1360, q_gen_1366, q_gen_1367, q_gen_1368, q_gen_1369, q_gen_1397, q_gen_1398, q_gen_1431, q_gen_1432, q_gen_1433, q_gen_1434, q_gen_1448},
Q_f={q_gen_1352},
Delta=
{
<s>(q_gen_1354) -> q_gen_1354
<z>() -> q_gen_1354
<cons>(q_gen_1398, q_gen_1397) -> q_gen_1397
<nil>() -> q_gen_1397
<a>() -> q_gen_1398
<b>() -> q_gen_1398
<s, cons>(q_gen_1360, q_gen_1359) -> q_gen_1359
<s, nil>(q_gen_1354) -> q_gen_1359
<z, nil>() -> q_gen_1359
<s, a>(q_gen_1354) -> q_gen_1360
<s, b>(q_gen_1354) -> q_gen_1360
<z, a>() -> q_gen_1360
<z, b>() -> q_gen_1360
<cons, cons>(q_gen_1369, q_gen_1368, q_gen_1367, q_gen_1366) -> q_gen_1366
<nil, nil>() -> q_gen_1366
<cons, a>(q_gen_1398, q_gen_1397) -> q_gen_1367
<cons, b>(q_gen_1398, q_gen_1397) -> q_gen_1367
<nil, a>() -> q_gen_1367
<nil, b>() -> q_gen_1367
<a, cons>(q_gen_1398, q_gen_1397) -> q_gen_1368
<a, nil>() -> q_gen_1368
<b, cons>(q_gen_1398, q_gen_1397) -> q_gen_1368
<b, nil>() -> q_gen_1368
<a, a>() -> q_gen_1369
<b, b>() -> q_gen_1369
<s, cons>(q_gen_1360, q_gen_1448) -> q_gen_1448
<z, cons>(q_gen_1398, q_gen_1397) -> q_gen_1448
<s, cons, cons>(q_gen_1434, q_gen_1433, q_gen_1432, q_gen_1431) -> q_gen_1352
<s, cons, nil>(q_gen_1360, q_gen_1359) -> q_gen_1352
<s, nil, nil>(q_gen_1354) -> q_gen_1352
<z, cons, cons>(q_gen_1369, q_gen_1368, q_gen_1367, q_gen_1366) -> q_gen_1352
<z, nil, nil>() -> q_gen_1352
<s, cons, nil>(q_gen_1360, q_gen_1448) -> q_gen_1431
<z, cons, nil>(q_gen_1398, q_gen_1397) -> q_gen_1431
<s, cons, b>(q_gen_1360, q_gen_1448) -> q_gen_1432
<z, cons, b>(q_gen_1398, q_gen_1397) -> q_gen_1432
<s, a, nil>(q_gen_1354) -> q_gen_1433
<s, b, nil>(q_gen_1354) -> q_gen_1433
<z, b, nil>() -> q_gen_1433
<s, a, b>(q_gen_1354) -> q_gen_1434
<s, b, b>(q_gen_1354) -> q_gen_1434
<z, b, b>() -> q_gen_1434
}

Datatype: <nat, eltlist, eltlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_1351, q_gen_1357, q_gen_1389},
Q_f={q_gen_1351},
Delta=
{
<s>(q_gen_1389) -> q_gen_1389
<z>() -> q_gen_1389
<cons, s>(q_gen_1357, q_gen_1351) -> q_gen_1351
<nil, z>() -> q_gen_1351
<a, s>(q_gen_1389) -> q_gen_1357
<a, z>() -> q_gen_1357
<b, s>(q_gen_1389) -> q_gen_1357
<b, z>() -> q_gen_1357
}

Datatype: <eltlist, nat>
Convolution form: complete
}}}
  ;  minus -> 
{{{
Q={q_gen_1348, q_gen_1349, q_gen_1350, q_gen_1362, q_gen_1364, q_gen_1373, q_gen_1378, q_gen_1386},
Q_f={q_gen_1348, q_gen_1349},
Delta=
{
<s>(q_gen_1362) -> q_gen_1362
<z>() -> q_gen_1362
<z, z>() -> q_gen_1350
<s, s>(q_gen_1350) -> q_gen_1364
<s, s>(q_gen_1364) -> q_gen_1364
<s, z>(q_gen_1362) -> q_gen_1364
<s, s>(q_gen_1386) -> q_gen_1386
<z, s>(q_gen_1362) -> q_gen_1386
<s, s, z>(q_gen_1350) -> q_gen_1348
<s, s, z>(q_gen_1386) -> q_gen_1348
<z, s, z>(q_gen_1362) -> q_gen_1348
<z, z, z>() -> q_gen_1348
<s, s, s>(q_gen_1349) -> q_gen_1349
<s, s, s>(q_gen_1373) -> q_gen_1349
<s, z, s>(q_gen_1350) -> q_gen_1349
<s, z, s>(q_gen_1364) -> q_gen_1349
<s, s, z>(q_gen_1364) -> q_gen_1373
<s, z, z>(q_gen_1362) -> q_gen_1373
<s, s, s>(q_gen_1348) -> q_gen_1378
<s, s, s>(q_gen_1378) -> q_gen_1378
<s, z, s>(q_gen_1386) -> q_gen_1378
}

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

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

Teacher's answer:
New clause system:
{
() -> drop([s(u), nil, nil]) -> 41  ;  () -> drop([z, l, l]) -> 41  ;  () -> length([nil, z]) -> 41  ;  () -> minus([s(u), z, s(u)]) -> 42  ;  () -> minus([z, y, z]) -> 42  ;  (drop([n, l1, _sga]) /\ length([_sga, _tga]) /\ length([l1, _uga]) /\ minus([_uga, n, _vga])) -> eq_nat([_tga, _vga]) -> 43  ;  (drop([u, x3, _ega])) -> drop([s(u), cons(x2, x3), _ega]) -> 46  ;  (length([ll, _jga])) -> length([cons(x, ll), s(_jga)]) -> 42  ;  (minus([u, x2, _nga])) -> minus([s(u), s(x2), _nga]) -> 44
}
Sat witness: Yes: ((drop([u, x3, _ega])) -> drop([s(u), cons(x2, x3), _ega]), {
_ega -> cons(a, nil)  ;  u -> z  ;  x2 -> a  ;  x3 -> cons(a, nil)
})

-------------------------------------------
Step 63, which took 0.200902 s (model generation: 0.198939,  model checking: 0.001963):

Model:
|_
{
drop -> 
{{{
Q={q_gen_1352, q_gen_1354, q_gen_1359, q_gen_1360, q_gen_1366, q_gen_1367, q_gen_1368, q_gen_1369, q_gen_1397, q_gen_1398, q_gen_1431, q_gen_1432, q_gen_1433, q_gen_1434, q_gen_1448},
Q_f={q_gen_1352},
Delta=
{
<s>(q_gen_1354) -> q_gen_1354
<z>() -> q_gen_1354
<cons>(q_gen_1398, q_gen_1397) -> q_gen_1397
<nil>() -> q_gen_1397
<a>() -> q_gen_1398
<b>() -> q_gen_1398
<s, cons>(q_gen_1360, q_gen_1359) -> q_gen_1359
<s, nil>(q_gen_1354) -> q_gen_1359
<z, nil>() -> q_gen_1359
<s, a>(q_gen_1354) -> q_gen_1360
<s, b>(q_gen_1354) -> q_gen_1360
<z, a>() -> q_gen_1360
<z, b>() -> q_gen_1360
<cons, cons>(q_gen_1369, q_gen_1368, q_gen_1367, q_gen_1366) -> q_gen_1366
<nil, nil>() -> q_gen_1366
<cons, a>(q_gen_1398, q_gen_1397) -> q_gen_1367
<cons, b>(q_gen_1398, q_gen_1397) -> q_gen_1367
<nil, a>() -> q_gen_1367
<nil, b>() -> q_gen_1367
<a, cons>(q_gen_1398, q_gen_1397) -> q_gen_1368
<a, nil>() -> q_gen_1368
<b, cons>(q_gen_1398, q_gen_1397) -> q_gen_1368
<b, nil>() -> q_gen_1368
<a, a>() -> q_gen_1369
<b, b>() -> q_gen_1369
<s, cons>(q_gen_1360, q_gen_1448) -> q_gen_1448
<z, cons>(q_gen_1398, q_gen_1397) -> q_gen_1448
<s, cons, cons>(q_gen_1434, q_gen_1433, q_gen_1432, q_gen_1431) -> q_gen_1352
<s, cons, nil>(q_gen_1360, q_gen_1359) -> q_gen_1352
<s, nil, nil>(q_gen_1354) -> q_gen_1352
<z, cons, cons>(q_gen_1369, q_gen_1368, q_gen_1367, q_gen_1366) -> q_gen_1352
<z, nil, nil>() -> q_gen_1352
<s, cons, nil>(q_gen_1360, q_gen_1448) -> q_gen_1431
<z, cons, nil>(q_gen_1398, q_gen_1397) -> q_gen_1431
<s, cons, b>(q_gen_1360, q_gen_1448) -> q_gen_1432
<z, cons, a>(q_gen_1398, q_gen_1397) -> q_gen_1432
<z, cons, b>(q_gen_1398, q_gen_1397) -> q_gen_1432
<s, a, nil>(q_gen_1354) -> q_gen_1433
<s, b, nil>(q_gen_1354) -> q_gen_1433
<z, a, nil>() -> q_gen_1433
<z, b, nil>() -> q_gen_1433
<s, a, b>(q_gen_1354) -> q_gen_1434
<s, b, b>(q_gen_1354) -> q_gen_1434
<z, a, a>() -> q_gen_1434
<z, b, b>() -> q_gen_1434
}

Datatype: <nat, eltlist, eltlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_1351, q_gen_1357, q_gen_1389},
Q_f={q_gen_1351},
Delta=
{
<s>(q_gen_1389) -> q_gen_1389
<z>() -> q_gen_1389
<cons, s>(q_gen_1357, q_gen_1351) -> q_gen_1351
<nil, z>() -> q_gen_1351
<a, s>(q_gen_1389) -> q_gen_1357
<a, z>() -> q_gen_1357
<b, s>(q_gen_1389) -> q_gen_1357
<b, z>() -> q_gen_1357
}

Datatype: <eltlist, nat>
Convolution form: complete
}}}
  ;  minus -> 
{{{
Q={q_gen_1348, q_gen_1349, q_gen_1350, q_gen_1362, q_gen_1364, q_gen_1373, q_gen_1378, q_gen_1386},
Q_f={q_gen_1348, q_gen_1349},
Delta=
{
<s>(q_gen_1362) -> q_gen_1362
<z>() -> q_gen_1362
<z, z>() -> q_gen_1350
<s, s>(q_gen_1350) -> q_gen_1364
<s, s>(q_gen_1364) -> q_gen_1364
<s, z>(q_gen_1362) -> q_gen_1364
<s, s>(q_gen_1386) -> q_gen_1386
<z, s>(q_gen_1362) -> q_gen_1386
<s, s, z>(q_gen_1350) -> q_gen_1348
<s, s, z>(q_gen_1386) -> q_gen_1348
<z, s, z>(q_gen_1362) -> q_gen_1348
<z, z, z>() -> q_gen_1348
<s, s, s>(q_gen_1349) -> q_gen_1349
<s, s, s>(q_gen_1373) -> q_gen_1349
<s, z, s>(q_gen_1350) -> q_gen_1349
<s, z, s>(q_gen_1364) -> q_gen_1349
<s, s, z>(q_gen_1364) -> q_gen_1373
<s, z, z>(q_gen_1362) -> q_gen_1373
<s, s, s>(q_gen_1348) -> q_gen_1378
<s, s, s>(q_gen_1378) -> q_gen_1378
<s, z, s>(q_gen_1386) -> q_gen_1378
}

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

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

Teacher's answer:
New clause system:
{
() -> drop([s(u), nil, nil]) -> 42  ;  () -> drop([z, l, l]) -> 42  ;  () -> length([nil, z]) -> 42  ;  () -> minus([s(u), z, s(u)]) -> 43  ;  () -> minus([z, y, z]) -> 43  ;  (drop([n, l1, _sga]) /\ length([_sga, _tga]) /\ length([l1, _uga]) /\ minus([_uga, n, _vga])) -> eq_nat([_tga, _vga]) -> 46  ;  (drop([u, x3, _ega])) -> drop([s(u), cons(x2, x3), _ega]) -> 46  ;  (length([ll, _jga])) -> length([cons(x, ll), s(_jga)]) -> 43  ;  (minus([u, x2, _nga])) -> minus([s(u), s(x2), _nga]) -> 44
}
Sat witness: Yes: ((drop([n, l1, _sga]) /\ length([_sga, _tga]) /\ length([l1, _uga]) /\ minus([_uga, n, _vga])) -> eq_nat([_tga, _vga]), {
_sga -> nil  ;  _tga -> z  ;  _uga -> s(s(s(z)))  ;  _vga -> s(z)  ;  l1 -> cons(b, cons(b, cons(b, nil)))  ;  n -> s(s(s(z)))
})

-------------------------------------------
Step 64, which took 0.304103 s (model generation: 0.302284,  model checking: 0.001819):

Model:
|_
{
drop -> 
{{{
Q={q_gen_1352, q_gen_1354, q_gen_1359, q_gen_1360, q_gen_1366, q_gen_1367, q_gen_1368, q_gen_1369, q_gen_1397, q_gen_1398, q_gen_1431, q_gen_1432, q_gen_1433, q_gen_1434, q_gen_1448},
Q_f={q_gen_1352},
Delta=
{
<s>(q_gen_1354) -> q_gen_1354
<z>() -> q_gen_1354
<cons>(q_gen_1398, q_gen_1397) -> q_gen_1397
<nil>() -> q_gen_1397
<a>() -> q_gen_1398
<b>() -> q_gen_1398
<s, cons>(q_gen_1360, q_gen_1359) -> q_gen_1359
<s, nil>(q_gen_1354) -> q_gen_1359
<z, nil>() -> q_gen_1359
<s, a>(q_gen_1354) -> q_gen_1360
<s, b>(q_gen_1354) -> q_gen_1360
<z, a>() -> q_gen_1360
<z, b>() -> q_gen_1360
<cons, cons>(q_gen_1369, q_gen_1368, q_gen_1367, q_gen_1366) -> q_gen_1366
<nil, nil>() -> q_gen_1366
<cons, a>(q_gen_1398, q_gen_1397) -> q_gen_1367
<cons, b>(q_gen_1398, q_gen_1397) -> q_gen_1367
<nil, a>() -> q_gen_1367
<nil, b>() -> q_gen_1367
<a, cons>(q_gen_1398, q_gen_1397) -> q_gen_1368
<a, nil>() -> q_gen_1368
<b, cons>(q_gen_1398, q_gen_1397) -> q_gen_1368
<b, nil>() -> q_gen_1368
<a, a>() -> q_gen_1369
<b, b>() -> q_gen_1369
<s, cons>(q_gen_1360, q_gen_1448) -> q_gen_1448
<z, cons>(q_gen_1398, q_gen_1397) -> q_gen_1448
<s, cons, cons>(q_gen_1434, q_gen_1433, q_gen_1432, q_gen_1431) -> q_gen_1352
<s, cons, nil>(q_gen_1360, q_gen_1359) -> q_gen_1352
<s, nil, nil>(q_gen_1354) -> q_gen_1352
<z, cons, cons>(q_gen_1369, q_gen_1368, q_gen_1367, q_gen_1366) -> q_gen_1352
<z, nil, nil>() -> q_gen_1352
<s, cons, nil>(q_gen_1360, q_gen_1448) -> q_gen_1431
<z, cons, nil>(q_gen_1398, q_gen_1397) -> q_gen_1431
<s, cons, b>(q_gen_1360, q_gen_1448) -> q_gen_1432
<z, cons, a>(q_gen_1398, q_gen_1397) -> q_gen_1432
<z, cons, b>(q_gen_1398, q_gen_1397) -> q_gen_1432
<s, a, nil>(q_gen_1354) -> q_gen_1433
<s, b, nil>(q_gen_1354) -> q_gen_1433
<z, a, nil>() -> q_gen_1433
<z, b, nil>() -> q_gen_1433
<s, a, b>(q_gen_1354) -> q_gen_1434
<s, b, b>(q_gen_1354) -> q_gen_1434
<z, a, a>() -> q_gen_1434
<z, b, b>() -> q_gen_1434
}

Datatype: <nat, eltlist, eltlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_1351, q_gen_1357, q_gen_1389},
Q_f={q_gen_1351},
Delta=
{
<s>(q_gen_1389) -> q_gen_1389
<z>() -> q_gen_1389
<cons, s>(q_gen_1357, q_gen_1351) -> q_gen_1351
<nil, z>() -> q_gen_1351
<a, s>(q_gen_1389) -> q_gen_1357
<a, z>() -> q_gen_1357
<b, s>(q_gen_1389) -> q_gen_1357
<b, z>() -> q_gen_1357
}

Datatype: <eltlist, nat>
Convolution form: complete
}}}
  ;  minus -> 
{{{
Q={q_gen_1348, q_gen_1349, q_gen_1350, q_gen_1362, q_gen_1373, q_gen_1378, q_gen_1386, q_gen_1416},
Q_f={q_gen_1348, q_gen_1349},
Delta=
{
<s>(q_gen_1362) -> q_gen_1362
<z>() -> q_gen_1362
<s, s>(q_gen_1350) -> q_gen_1350
<z, z>() -> q_gen_1350
<s, s>(q_gen_1386) -> q_gen_1386
<z, s>(q_gen_1362) -> q_gen_1386
<s, s>(q_gen_1416) -> q_gen_1416
<s, z>(q_gen_1362) -> q_gen_1416
<s, s, s>(q_gen_1349) -> q_gen_1348
<s, s, z>(q_gen_1350) -> q_gen_1348
<s, s, z>(q_gen_1386) -> q_gen_1348
<z, s, z>(q_gen_1362) -> q_gen_1348
<z, z, z>() -> q_gen_1348
<s, s, s>(q_gen_1373) -> q_gen_1349
<s, z, s>(q_gen_1350) -> q_gen_1349
<s, s, z>(q_gen_1416) -> q_gen_1373
<s, z, s>(q_gen_1416) -> q_gen_1373
<s, z, z>(q_gen_1362) -> q_gen_1373
<s, s, s>(q_gen_1348) -> q_gen_1378
<s, s, s>(q_gen_1378) -> q_gen_1378
<s, z, s>(q_gen_1386) -> q_gen_1378
}

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

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

Teacher's answer:
New clause system:
{
() -> drop([s(u), nil, nil]) -> 43  ;  () -> drop([z, l, l]) -> 43  ;  () -> length([nil, z]) -> 43  ;  () -> minus([s(u), z, s(u)]) -> 44  ;  () -> minus([z, y, z]) -> 44  ;  (drop([n, l1, _sga]) /\ length([_sga, _tga]) /\ length([l1, _uga]) /\ minus([_uga, n, _vga])) -> eq_nat([_tga, _vga]) -> 46  ;  (drop([u, x3, _ega])) -> drop([s(u), cons(x2, x3), _ega]) -> 46  ;  (length([ll, _jga])) -> length([cons(x, ll), s(_jga)]) -> 44  ;  (minus([u, x2, _nga])) -> minus([s(u), s(x2), _nga]) -> 47
}
Sat witness: Yes: ((minus([u, x2, _nga])) -> minus([s(u), s(x2), _nga]), {
_nga -> s(s(s(z)))  ;  u -> s(s(s(s(z))))  ;  x2 -> s(s(z))
})

-------------------------------------------
Step 65, which took 0.769412 s (model generation: 0.765245,  model checking: 0.004167):

Model:
|_
{
drop -> 
{{{
Q={q_gen_1352, q_gen_1354, q_gen_1359, q_gen_1360, q_gen_1366, q_gen_1367, q_gen_1368, q_gen_1369, q_gen_1397, q_gen_1398, q_gen_1431, q_gen_1432, q_gen_1433, q_gen_1434, q_gen_1448},
Q_f={q_gen_1352},
Delta=
{
<s>(q_gen_1354) -> q_gen_1354
<z>() -> q_gen_1354
<cons>(q_gen_1398, q_gen_1397) -> q_gen_1397
<nil>() -> q_gen_1397
<a>() -> q_gen_1398
<b>() -> q_gen_1398
<s, cons>(q_gen_1360, q_gen_1359) -> q_gen_1359
<s, nil>(q_gen_1354) -> q_gen_1359
<z, nil>() -> q_gen_1359
<s, a>(q_gen_1354) -> q_gen_1360
<s, b>(q_gen_1354) -> q_gen_1360
<z, a>() -> q_gen_1360
<z, b>() -> q_gen_1360
<cons, cons>(q_gen_1369, q_gen_1368, q_gen_1367, q_gen_1366) -> q_gen_1366
<nil, nil>() -> q_gen_1366
<cons, a>(q_gen_1398, q_gen_1397) -> q_gen_1367
<cons, b>(q_gen_1398, q_gen_1397) -> q_gen_1367
<nil, a>() -> q_gen_1367
<nil, b>() -> q_gen_1367
<a, cons>(q_gen_1398, q_gen_1397) -> q_gen_1368
<a, nil>() -> q_gen_1368
<b, cons>(q_gen_1398, q_gen_1397) -> q_gen_1368
<b, nil>() -> q_gen_1368
<a, a>() -> q_gen_1369
<b, b>() -> q_gen_1369
<s, cons>(q_gen_1360, q_gen_1448) -> q_gen_1448
<z, cons>(q_gen_1398, q_gen_1397) -> q_gen_1448
<s, cons, cons>(q_gen_1434, q_gen_1433, q_gen_1432, q_gen_1431) -> q_gen_1352
<s, cons, nil>(q_gen_1360, q_gen_1359) -> q_gen_1352
<s, nil, nil>(q_gen_1354) -> q_gen_1352
<z, cons, cons>(q_gen_1369, q_gen_1368, q_gen_1367, q_gen_1366) -> q_gen_1352
<z, nil, nil>() -> q_gen_1352
<s, cons, nil>(q_gen_1360, q_gen_1448) -> q_gen_1431
<z, cons, nil>(q_gen_1398, q_gen_1397) -> q_gen_1431
<s, cons, b>(q_gen_1360, q_gen_1448) -> q_gen_1432
<z, cons, a>(q_gen_1398, q_gen_1397) -> q_gen_1432
<z, cons, b>(q_gen_1398, q_gen_1397) -> q_gen_1432
<s, a, nil>(q_gen_1354) -> q_gen_1433
<s, b, nil>(q_gen_1354) -> q_gen_1433
<z, a, nil>() -> q_gen_1433
<z, b, nil>() -> q_gen_1433
<s, a, b>(q_gen_1354) -> q_gen_1434
<s, b, b>(q_gen_1354) -> q_gen_1434
<z, a, a>() -> q_gen_1434
<z, b, b>() -> q_gen_1434
}

Datatype: <nat, eltlist, eltlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_1351, q_gen_1357, q_gen_1389},
Q_f={q_gen_1351},
Delta=
{
<s>(q_gen_1389) -> q_gen_1389
<z>() -> q_gen_1389
<cons, s>(q_gen_1357, q_gen_1351) -> q_gen_1351
<nil, z>() -> q_gen_1351
<a, s>(q_gen_1389) -> q_gen_1357
<a, z>() -> q_gen_1357
<b, s>(q_gen_1389) -> q_gen_1357
<b, z>() -> q_gen_1357
}

Datatype: <eltlist, nat>
Convolution form: complete
}}}
  ;  minus -> 
{{{
Q={q_gen_1348, q_gen_1349, q_gen_1350, q_gen_1362, q_gen_1373, q_gen_1378, q_gen_1386, q_gen_1416},
Q_f={q_gen_1348, q_gen_1349},
Delta=
{
<s>(q_gen_1362) -> q_gen_1362
<z>() -> q_gen_1362
<s, s>(q_gen_1350) -> q_gen_1350
<z, z>() -> q_gen_1350
<s, s>(q_gen_1386) -> q_gen_1386
<z, s>(q_gen_1362) -> q_gen_1386
<s, s>(q_gen_1416) -> q_gen_1416
<s, z>(q_gen_1362) -> q_gen_1416
<s, s, z>(q_gen_1350) -> q_gen_1348
<s, s, z>(q_gen_1386) -> q_gen_1348
<z, s, z>(q_gen_1362) -> q_gen_1348
<z, z, z>() -> q_gen_1348
<s, s, s>(q_gen_1349) -> q_gen_1349
<s, s, s>(q_gen_1373) -> q_gen_1349
<s, z, s>(q_gen_1350) -> q_gen_1349
<s, s, z>(q_gen_1416) -> q_gen_1373
<s, z, s>(q_gen_1416) -> q_gen_1373
<s, z, z>(q_gen_1362) -> q_gen_1373
<s, s, s>(q_gen_1348) -> q_gen_1378
<s, s, s>(q_gen_1378) -> q_gen_1378
<s, z, s>(q_gen_1386) -> q_gen_1378
}

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

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

Teacher's answer:
New clause system:
{
() -> drop([s(u), nil, nil]) -> 44  ;  () -> drop([z, l, l]) -> 44  ;  () -> length([nil, z]) -> 44  ;  () -> minus([s(u), z, s(u)]) -> 45  ;  () -> minus([z, y, z]) -> 45  ;  (drop([n, l1, _sga]) /\ length([_sga, _tga]) /\ length([l1, _uga]) /\ minus([_uga, n, _vga])) -> eq_nat([_tga, _vga]) -> 46  ;  (drop([u, x3, _ega])) -> drop([s(u), cons(x2, x3), _ega]) -> 49  ;  (length([ll, _jga])) -> length([cons(x, ll), s(_jga)]) -> 45  ;  (minus([u, x2, _nga])) -> minus([s(u), s(x2), _nga]) -> 47
}
Sat witness: Yes: ((drop([u, x3, _ega])) -> drop([s(u), cons(x2, x3), _ega]), {
_ega -> cons(a, nil)  ;  u -> s(z)  ;  x2 -> b  ;  x3 -> cons(a, cons(a, nil))
})

-------------------------------------------
Step 66, which took 0.158500 s (model generation: 0.156190,  model checking: 0.002310):

Model:
|_
{
drop -> 
{{{
Q={q_gen_1352, q_gen_1354, q_gen_1359, q_gen_1360, q_gen_1366, q_gen_1367, q_gen_1368, q_gen_1369, q_gen_1397, q_gen_1398, q_gen_1431, q_gen_1432, q_gen_1433, q_gen_1434, q_gen_1448},
Q_f={q_gen_1352},
Delta=
{
<s>(q_gen_1354) -> q_gen_1354
<z>() -> q_gen_1354
<cons>(q_gen_1398, q_gen_1397) -> q_gen_1397
<nil>() -> q_gen_1397
<a>() -> q_gen_1398
<b>() -> q_gen_1398
<s, cons>(q_gen_1360, q_gen_1359) -> q_gen_1359
<s, nil>(q_gen_1354) -> q_gen_1359
<z, nil>() -> q_gen_1359
<s, a>(q_gen_1354) -> q_gen_1360
<s, b>(q_gen_1354) -> q_gen_1360
<z, a>() -> q_gen_1360
<z, b>() -> q_gen_1360
<cons, cons>(q_gen_1369, q_gen_1368, q_gen_1367, q_gen_1366) -> q_gen_1366
<nil, nil>() -> q_gen_1366
<cons, a>(q_gen_1398, q_gen_1397) -> q_gen_1367
<cons, b>(q_gen_1398, q_gen_1397) -> q_gen_1367
<nil, a>() -> q_gen_1367
<nil, b>() -> q_gen_1367
<a, cons>(q_gen_1398, q_gen_1397) -> q_gen_1368
<a, nil>() -> q_gen_1368
<b, cons>(q_gen_1398, q_gen_1397) -> q_gen_1368
<b, nil>() -> q_gen_1368
<a, a>() -> q_gen_1369
<b, b>() -> q_gen_1369
<s, cons>(q_gen_1360, q_gen_1448) -> q_gen_1448
<z, cons>(q_gen_1398, q_gen_1397) -> q_gen_1448
<s, cons, cons>(q_gen_1434, q_gen_1433, q_gen_1432, q_gen_1431) -> q_gen_1352
<s, cons, nil>(q_gen_1360, q_gen_1359) -> q_gen_1352
<s, nil, nil>(q_gen_1354) -> q_gen_1352
<z, cons, cons>(q_gen_1369, q_gen_1368, q_gen_1367, q_gen_1366) -> q_gen_1352
<z, nil, nil>() -> q_gen_1352
<s, cons, nil>(q_gen_1360, q_gen_1448) -> q_gen_1431
<z, cons, nil>(q_gen_1398, q_gen_1397) -> q_gen_1431
<s, cons, a>(q_gen_1360, q_gen_1448) -> q_gen_1432
<s, cons, b>(q_gen_1360, q_gen_1448) -> q_gen_1432
<z, cons, a>(q_gen_1398, q_gen_1397) -> q_gen_1432
<z, cons, b>(q_gen_1398, q_gen_1397) -> q_gen_1432
<s, a, nil>(q_gen_1354) -> q_gen_1433
<s, b, nil>(q_gen_1354) -> q_gen_1433
<z, a, nil>() -> q_gen_1433
<z, b, nil>() -> q_gen_1433
<s, a, b>(q_gen_1354) -> q_gen_1434
<s, b, a>(q_gen_1354) -> q_gen_1434
<s, b, b>(q_gen_1354) -> q_gen_1434
<z, a, a>() -> q_gen_1434
<z, b, b>() -> q_gen_1434
}

Datatype: <nat, eltlist, eltlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_1351, q_gen_1357, q_gen_1389},
Q_f={q_gen_1351},
Delta=
{
<s>(q_gen_1389) -> q_gen_1389
<z>() -> q_gen_1389
<cons, s>(q_gen_1357, q_gen_1351) -> q_gen_1351
<nil, z>() -> q_gen_1351
<a, s>(q_gen_1389) -> q_gen_1357
<a, z>() -> q_gen_1357
<b, s>(q_gen_1389) -> q_gen_1357
<b, z>() -> q_gen_1357
}

Datatype: <eltlist, nat>
Convolution form: complete
}}}
  ;  minus -> 
{{{
Q={q_gen_1348, q_gen_1349, q_gen_1350, q_gen_1362, q_gen_1373, q_gen_1378, q_gen_1386, q_gen_1416},
Q_f={q_gen_1348, q_gen_1349},
Delta=
{
<s>(q_gen_1362) -> q_gen_1362
<z>() -> q_gen_1362
<s, s>(q_gen_1350) -> q_gen_1350
<z, z>() -> q_gen_1350
<s, s>(q_gen_1386) -> q_gen_1386
<z, s>(q_gen_1362) -> q_gen_1386
<s, s>(q_gen_1416) -> q_gen_1416
<s, z>(q_gen_1362) -> q_gen_1416
<s, s, z>(q_gen_1350) -> q_gen_1348
<s, s, z>(q_gen_1386) -> q_gen_1348
<z, s, z>(q_gen_1362) -> q_gen_1348
<z, z, z>() -> q_gen_1348
<s, s, s>(q_gen_1349) -> q_gen_1349
<s, s, s>(q_gen_1373) -> q_gen_1349
<s, z, s>(q_gen_1350) -> q_gen_1349
<s, s, z>(q_gen_1416) -> q_gen_1373
<s, z, s>(q_gen_1416) -> q_gen_1373
<s, z, z>(q_gen_1362) -> q_gen_1373
<s, s, s>(q_gen_1348) -> q_gen_1378
<s, s, s>(q_gen_1378) -> q_gen_1378
<s, z, s>(q_gen_1386) -> q_gen_1378
}

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

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

Teacher's answer:
New clause system:
{
() -> drop([s(u), nil, nil]) -> 45  ;  () -> drop([z, l, l]) -> 45  ;  () -> length([nil, z]) -> 45  ;  () -> minus([s(u), z, s(u)]) -> 46  ;  () -> minus([z, y, z]) -> 46  ;  (drop([n, l1, _sga]) /\ length([_sga, _tga]) /\ length([l1, _uga]) /\ minus([_uga, n, _vga])) -> eq_nat([_tga, _vga]) -> 49  ;  (drop([u, x3, _ega])) -> drop([s(u), cons(x2, x3), _ega]) -> 49  ;  (length([ll, _jga])) -> length([cons(x, ll), s(_jga)]) -> 46  ;  (minus([u, x2, _nga])) -> minus([s(u), s(x2), _nga]) -> 47
}
Sat witness: Yes: ((drop([n, l1, _sga]) /\ length([_sga, _tga]) /\ length([l1, _uga]) /\ minus([_uga, n, _vga])) -> eq_nat([_tga, _vga]), {
_sga -> cons(a, nil)  ;  _tga -> s(z)  ;  _uga -> s(s(z))  ;  _vga -> s(s(z))  ;  l1 -> cons(a, cons(b, nil))  ;  n -> s(z)
})

-------------------------------------------
Step 67, which took 0.278853 s (model generation: 0.277014,  model checking: 0.001839):

Model:
|_
{
drop -> 
{{{
Q={q_gen_1352, q_gen_1354, q_gen_1359, q_gen_1360, q_gen_1366, q_gen_1367, q_gen_1368, q_gen_1369, q_gen_1397, q_gen_1398, q_gen_1431, q_gen_1432, q_gen_1433, q_gen_1434, q_gen_1448},
Q_f={q_gen_1352},
Delta=
{
<s>(q_gen_1354) -> q_gen_1354
<z>() -> q_gen_1354
<cons>(q_gen_1398, q_gen_1397) -> q_gen_1397
<nil>() -> q_gen_1397
<a>() -> q_gen_1398
<b>() -> q_gen_1398
<s, cons>(q_gen_1360, q_gen_1359) -> q_gen_1359
<s, nil>(q_gen_1354) -> q_gen_1359
<z, nil>() -> q_gen_1359
<s, a>(q_gen_1354) -> q_gen_1360
<s, b>(q_gen_1354) -> q_gen_1360
<z, a>() -> q_gen_1360
<z, b>() -> q_gen_1360
<cons, cons>(q_gen_1369, q_gen_1368, q_gen_1367, q_gen_1366) -> q_gen_1366
<nil, nil>() -> q_gen_1366
<cons, a>(q_gen_1398, q_gen_1397) -> q_gen_1367
<cons, b>(q_gen_1398, q_gen_1397) -> q_gen_1367
<nil, a>() -> q_gen_1367
<nil, b>() -> q_gen_1367
<a, cons>(q_gen_1398, q_gen_1397) -> q_gen_1368
<a, nil>() -> q_gen_1368
<b, cons>(q_gen_1398, q_gen_1397) -> q_gen_1368
<b, nil>() -> q_gen_1368
<a, a>() -> q_gen_1369
<b, b>() -> q_gen_1369
<s, cons>(q_gen_1360, q_gen_1448) -> q_gen_1448
<z, cons>(q_gen_1398, q_gen_1397) -> q_gen_1448
<s, cons, cons>(q_gen_1434, q_gen_1433, q_gen_1432, q_gen_1431) -> q_gen_1352
<s, cons, nil>(q_gen_1360, q_gen_1359) -> q_gen_1352
<s, nil, nil>(q_gen_1354) -> q_gen_1352
<z, cons, cons>(q_gen_1369, q_gen_1368, q_gen_1367, q_gen_1366) -> q_gen_1352
<z, nil, nil>() -> q_gen_1352
<s, cons, nil>(q_gen_1360, q_gen_1448) -> q_gen_1431
<z, cons, nil>(q_gen_1398, q_gen_1397) -> q_gen_1431
<s, cons, a>(q_gen_1360, q_gen_1448) -> q_gen_1432
<s, cons, b>(q_gen_1360, q_gen_1448) -> q_gen_1432
<z, cons, a>(q_gen_1398, q_gen_1397) -> q_gen_1432
<z, cons, b>(q_gen_1398, q_gen_1397) -> q_gen_1432
<s, a, nil>(q_gen_1354) -> q_gen_1433
<s, b, nil>(q_gen_1354) -> q_gen_1433
<z, a, nil>() -> q_gen_1433
<z, b, nil>() -> q_gen_1433
<s, a, b>(q_gen_1354) -> q_gen_1434
<s, b, a>(q_gen_1354) -> q_gen_1434
<s, b, b>(q_gen_1354) -> q_gen_1434
<z, a, a>() -> q_gen_1434
<z, b, b>() -> q_gen_1434
}

Datatype: <nat, eltlist, eltlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_1351, q_gen_1357, q_gen_1389},
Q_f={q_gen_1351},
Delta=
{
<s>(q_gen_1389) -> q_gen_1389
<z>() -> q_gen_1389
<cons, s>(q_gen_1357, q_gen_1351) -> q_gen_1351
<nil, z>() -> q_gen_1351
<a, s>(q_gen_1389) -> q_gen_1357
<a, z>() -> q_gen_1357
<b, s>(q_gen_1389) -> q_gen_1357
<b, z>() -> q_gen_1357
}

Datatype: <eltlist, nat>
Convolution form: complete
}}}
  ;  minus -> 
{{{
Q={q_gen_1348, q_gen_1350, q_gen_1362, q_gen_1372, q_gen_1373, q_gen_1378, q_gen_1386, q_gen_1416},
Q_f={q_gen_1348, q_gen_1372},
Delta=
{
<s>(q_gen_1362) -> q_gen_1362
<z>() -> q_gen_1362
<s, s>(q_gen_1350) -> q_gen_1350
<z, z>() -> q_gen_1350
<s, s>(q_gen_1386) -> q_gen_1386
<z, s>(q_gen_1362) -> q_gen_1386
<s, s>(q_gen_1416) -> q_gen_1416
<s, z>(q_gen_1362) -> q_gen_1416
<s, s, s>(q_gen_1372) -> q_gen_1348
<s, s, z>(q_gen_1350) -> q_gen_1348
<s, s, z>(q_gen_1386) -> q_gen_1348
<s, z, s>(q_gen_1350) -> q_gen_1348
<z, s, z>(q_gen_1362) -> q_gen_1348
<z, z, z>() -> q_gen_1348
<s, s, s>(q_gen_1373) -> q_gen_1372
<s, z, s>(q_gen_1416) -> q_gen_1372
<s, s, z>(q_gen_1416) -> q_gen_1373
<s, z, z>(q_gen_1362) -> q_gen_1373
<s, s, s>(q_gen_1348) -> q_gen_1378
<s, s, s>(q_gen_1378) -> q_gen_1378
<s, z, s>(q_gen_1386) -> q_gen_1378
}

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

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

Teacher's answer:
New clause system:
{
() -> drop([s(u), nil, nil]) -> 46  ;  () -> drop([z, l, l]) -> 46  ;  () -> length([nil, z]) -> 46  ;  () -> minus([s(u), z, s(u)]) -> 47  ;  () -> minus([z, y, z]) -> 47  ;  (drop([n, l1, _sga]) /\ length([_sga, _tga]) /\ length([l1, _uga]) /\ minus([_uga, n, _vga])) -> eq_nat([_tga, _vga]) -> 49  ;  (drop([u, x3, _ega])) -> drop([s(u), cons(x2, x3), _ega]) -> 49  ;  (length([ll, _jga])) -> length([cons(x, ll), s(_jga)]) -> 47  ;  (minus([u, x2, _nga])) -> minus([s(u), s(x2), _nga]) -> 50
}
Sat witness: Yes: ((minus([u, x2, _nga])) -> minus([s(u), s(x2), _nga]), {
_nga -> s(s(s(z)))  ;  u -> s(s(s(s(z))))  ;  x2 -> s(z)
})

-------------------------------------------
Step 68, which took 0.277529 s (model generation: 0.273191,  model checking: 0.004338):

Model:
|_
{
drop -> 
{{{
Q={q_gen_1352, q_gen_1354, q_gen_1359, q_gen_1360, q_gen_1366, q_gen_1367, q_gen_1368, q_gen_1369, q_gen_1397, q_gen_1398, q_gen_1431, q_gen_1432, q_gen_1433, q_gen_1434, q_gen_1448},
Q_f={q_gen_1352},
Delta=
{
<s>(q_gen_1354) -> q_gen_1354
<z>() -> q_gen_1354
<cons>(q_gen_1398, q_gen_1397) -> q_gen_1397
<nil>() -> q_gen_1397
<a>() -> q_gen_1398
<b>() -> q_gen_1398
<s, cons>(q_gen_1360, q_gen_1359) -> q_gen_1359
<s, nil>(q_gen_1354) -> q_gen_1359
<z, nil>() -> q_gen_1359
<s, a>(q_gen_1354) -> q_gen_1360
<s, b>(q_gen_1354) -> q_gen_1360
<z, a>() -> q_gen_1360
<z, b>() -> q_gen_1360
<cons, cons>(q_gen_1369, q_gen_1368, q_gen_1367, q_gen_1366) -> q_gen_1366
<nil, nil>() -> q_gen_1366
<cons, a>(q_gen_1398, q_gen_1397) -> q_gen_1367
<cons, b>(q_gen_1398, q_gen_1397) -> q_gen_1367
<nil, a>() -> q_gen_1367
<nil, b>() -> q_gen_1367
<a, cons>(q_gen_1398, q_gen_1397) -> q_gen_1368
<a, nil>() -> q_gen_1368
<b, cons>(q_gen_1398, q_gen_1397) -> q_gen_1368
<b, nil>() -> q_gen_1368
<a, a>() -> q_gen_1369
<b, b>() -> q_gen_1369
<s, cons>(q_gen_1360, q_gen_1448) -> q_gen_1448
<z, cons>(q_gen_1398, q_gen_1397) -> q_gen_1448
<s, cons, cons>(q_gen_1434, q_gen_1433, q_gen_1432, q_gen_1431) -> q_gen_1352
<s, cons, nil>(q_gen_1360, q_gen_1359) -> q_gen_1352
<s, nil, nil>(q_gen_1354) -> q_gen_1352
<z, cons, cons>(q_gen_1369, q_gen_1368, q_gen_1367, q_gen_1366) -> q_gen_1352
<z, nil, nil>() -> q_gen_1352
<s, cons, nil>(q_gen_1360, q_gen_1448) -> q_gen_1431
<z, cons, nil>(q_gen_1398, q_gen_1397) -> q_gen_1431
<s, cons, a>(q_gen_1360, q_gen_1448) -> q_gen_1432
<s, cons, b>(q_gen_1360, q_gen_1448) -> q_gen_1432
<z, cons, a>(q_gen_1398, q_gen_1397) -> q_gen_1432
<z, cons, b>(q_gen_1398, q_gen_1397) -> q_gen_1432
<s, a, nil>(q_gen_1354) -> q_gen_1433
<s, b, nil>(q_gen_1354) -> q_gen_1433
<z, a, nil>() -> q_gen_1433
<z, b, nil>() -> q_gen_1433
<s, a, b>(q_gen_1354) -> q_gen_1434
<s, b, a>(q_gen_1354) -> q_gen_1434
<s, b, b>(q_gen_1354) -> q_gen_1434
<z, a, a>() -> q_gen_1434
<z, b, b>() -> q_gen_1434
}

Datatype: <nat, eltlist, eltlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_1351, q_gen_1357, q_gen_1389},
Q_f={q_gen_1351},
Delta=
{
<s>(q_gen_1389) -> q_gen_1389
<z>() -> q_gen_1389
<cons, s>(q_gen_1357, q_gen_1351) -> q_gen_1351
<nil, z>() -> q_gen_1351
<a, s>(q_gen_1389) -> q_gen_1357
<a, z>() -> q_gen_1357
<b, s>(q_gen_1389) -> q_gen_1357
<b, z>() -> q_gen_1357
}

Datatype: <eltlist, nat>
Convolution form: complete
}}}
  ;  minus -> 
{{{
Q={q_gen_1348, q_gen_1350, q_gen_1362, q_gen_1372, q_gen_1373, q_gen_1378, q_gen_1386, q_gen_1416},
Q_f={q_gen_1348, q_gen_1372},
Delta=
{
<s>(q_gen_1362) -> q_gen_1362
<z>() -> q_gen_1362
<s, s>(q_gen_1350) -> q_gen_1350
<z, z>() -> q_gen_1350
<s, s>(q_gen_1386) -> q_gen_1386
<z, s>(q_gen_1362) -> q_gen_1386
<s, s>(q_gen_1416) -> q_gen_1416
<s, z>(q_gen_1362) -> q_gen_1416
<s, s, z>(q_gen_1350) -> q_gen_1348
<s, s, z>(q_gen_1386) -> q_gen_1348
<s, z, s>(q_gen_1350) -> q_gen_1348
<z, s, z>(q_gen_1362) -> q_gen_1348
<z, z, z>() -> q_gen_1348
<s, s, s>(q_gen_1372) -> q_gen_1372
<s, s, s>(q_gen_1373) -> q_gen_1372
<s, z, s>(q_gen_1416) -> q_gen_1372
<s, s, z>(q_gen_1416) -> q_gen_1373
<s, z, z>(q_gen_1362) -> q_gen_1373
<s, s, s>(q_gen_1348) -> q_gen_1378
<s, s, s>(q_gen_1378) -> q_gen_1378
<s, z, s>(q_gen_1386) -> q_gen_1378
}

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

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

Teacher's answer:
New clause system:
{
() -> drop([s(u), nil, nil]) -> 47  ;  () -> drop([z, l, l]) -> 47  ;  () -> length([nil, z]) -> 47  ;  () -> minus([s(u), z, s(u)]) -> 48  ;  () -> minus([z, y, z]) -> 48  ;  (drop([n, l1, _sga]) /\ length([_sga, _tga]) /\ length([l1, _uga]) /\ minus([_uga, n, _vga])) -> eq_nat([_tga, _vga]) -> 49  ;  (drop([u, x3, _ega])) -> drop([s(u), cons(x2, x3), _ega]) -> 52  ;  (length([ll, _jga])) -> length([cons(x, ll), s(_jga)]) -> 48  ;  (minus([u, x2, _nga])) -> minus([s(u), s(x2), _nga]) -> 50
}
Sat witness: Yes: ((drop([u, x3, _ega])) -> drop([s(u), cons(x2, x3), _ega]), {
_ega -> cons(a, nil)  ;  u -> s(z)  ;  x2 -> a  ;  x3 -> cons(a, cons(a, nil))
})

-------------------------------------------
Step 69, which took 0.255079 s (model generation: 0.252428,  model checking: 0.002651):

Model:
|_
{
drop -> 
{{{
Q={q_gen_1352, q_gen_1354, q_gen_1359, q_gen_1360, q_gen_1366, q_gen_1367, q_gen_1368, q_gen_1369, q_gen_1397, q_gen_1398, q_gen_1431, q_gen_1432, q_gen_1433, q_gen_1434, q_gen_1448},
Q_f={q_gen_1352},
Delta=
{
<s>(q_gen_1354) -> q_gen_1354
<z>() -> q_gen_1354
<cons>(q_gen_1398, q_gen_1397) -> q_gen_1397
<nil>() -> q_gen_1397
<a>() -> q_gen_1398
<b>() -> q_gen_1398
<s, cons>(q_gen_1360, q_gen_1359) -> q_gen_1359
<s, nil>(q_gen_1354) -> q_gen_1359
<z, nil>() -> q_gen_1359
<s, a>(q_gen_1354) -> q_gen_1360
<s, b>(q_gen_1354) -> q_gen_1360
<z, a>() -> q_gen_1360
<z, b>() -> q_gen_1360
<cons, cons>(q_gen_1369, q_gen_1368, q_gen_1367, q_gen_1366) -> q_gen_1366
<nil, nil>() -> q_gen_1366
<cons, a>(q_gen_1398, q_gen_1397) -> q_gen_1367
<cons, b>(q_gen_1398, q_gen_1397) -> q_gen_1367
<nil, a>() -> q_gen_1367
<nil, b>() -> q_gen_1367
<a, cons>(q_gen_1398, q_gen_1397) -> q_gen_1368
<a, nil>() -> q_gen_1368
<b, cons>(q_gen_1398, q_gen_1397) -> q_gen_1368
<b, nil>() -> q_gen_1368
<a, a>() -> q_gen_1369
<b, b>() -> q_gen_1369
<s, cons>(q_gen_1360, q_gen_1448) -> q_gen_1448
<z, cons>(q_gen_1398, q_gen_1397) -> q_gen_1448
<s, cons, cons>(q_gen_1434, q_gen_1433, q_gen_1432, q_gen_1431) -> q_gen_1352
<s, cons, nil>(q_gen_1360, q_gen_1359) -> q_gen_1352
<s, nil, nil>(q_gen_1354) -> q_gen_1352
<z, cons, cons>(q_gen_1369, q_gen_1368, q_gen_1367, q_gen_1366) -> q_gen_1352
<z, nil, nil>() -> q_gen_1352
<s, cons, nil>(q_gen_1360, q_gen_1448) -> q_gen_1431
<z, cons, nil>(q_gen_1398, q_gen_1397) -> q_gen_1431
<s, cons, a>(q_gen_1360, q_gen_1448) -> q_gen_1432
<s, cons, b>(q_gen_1360, q_gen_1448) -> q_gen_1432
<z, cons, a>(q_gen_1398, q_gen_1397) -> q_gen_1432
<z, cons, b>(q_gen_1398, q_gen_1397) -> q_gen_1432
<s, a, nil>(q_gen_1354) -> q_gen_1433
<s, b, nil>(q_gen_1354) -> q_gen_1433
<z, a, nil>() -> q_gen_1433
<z, b, nil>() -> q_gen_1433
<s, a, a>(q_gen_1354) -> q_gen_1434
<s, a, b>(q_gen_1354) -> q_gen_1434
<s, b, a>(q_gen_1354) -> q_gen_1434
<s, b, b>(q_gen_1354) -> q_gen_1434
<z, a, a>() -> q_gen_1434
<z, b, b>() -> q_gen_1434
}

Datatype: <nat, eltlist, eltlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_1351, q_gen_1357, q_gen_1389},
Q_f={q_gen_1351},
Delta=
{
<s>(q_gen_1389) -> q_gen_1389
<z>() -> q_gen_1389
<cons, s>(q_gen_1357, q_gen_1351) -> q_gen_1351
<nil, z>() -> q_gen_1351
<a, s>(q_gen_1389) -> q_gen_1357
<a, z>() -> q_gen_1357
<b, s>(q_gen_1389) -> q_gen_1357
<b, z>() -> q_gen_1357
}

Datatype: <eltlist, nat>
Convolution form: complete
}}}
  ;  minus -> 
{{{
Q={q_gen_1348, q_gen_1350, q_gen_1362, q_gen_1372, q_gen_1373, q_gen_1378, q_gen_1386, q_gen_1416},
Q_f={q_gen_1348, q_gen_1372},
Delta=
{
<s>(q_gen_1362) -> q_gen_1362
<z>() -> q_gen_1362
<s, s>(q_gen_1350) -> q_gen_1350
<z, z>() -> q_gen_1350
<s, s>(q_gen_1386) -> q_gen_1386
<z, s>(q_gen_1362) -> q_gen_1386
<s, s>(q_gen_1416) -> q_gen_1416
<s, z>(q_gen_1362) -> q_gen_1416
<s, s, z>(q_gen_1350) -> q_gen_1348
<s, s, z>(q_gen_1386) -> q_gen_1348
<s, z, s>(q_gen_1350) -> q_gen_1348
<z, s, z>(q_gen_1362) -> q_gen_1348
<z, z, z>() -> q_gen_1348
<s, s, s>(q_gen_1372) -> q_gen_1372
<s, s, s>(q_gen_1373) -> q_gen_1372
<s, z, s>(q_gen_1416) -> q_gen_1372
<s, s, z>(q_gen_1416) -> q_gen_1373
<s, z, z>(q_gen_1362) -> q_gen_1373
<s, s, s>(q_gen_1348) -> q_gen_1378
<s, s, s>(q_gen_1378) -> q_gen_1378
<s, z, s>(q_gen_1386) -> q_gen_1378
}

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

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

Teacher's answer:
New clause system:
{
() -> drop([s(u), nil, nil]) -> 48  ;  () -> drop([z, l, l]) -> 48  ;  () -> length([nil, z]) -> 48  ;  () -> minus([s(u), z, s(u)]) -> 49  ;  () -> minus([z, y, z]) -> 49  ;  (drop([n, l1, _sga]) /\ length([_sga, _tga]) /\ length([l1, _uga]) /\ minus([_uga, n, _vga])) -> eq_nat([_tga, _vga]) -> 52  ;  (drop([u, x3, _ega])) -> drop([s(u), cons(x2, x3), _ega]) -> 52  ;  (length([ll, _jga])) -> length([cons(x, ll), s(_jga)]) -> 49  ;  (minus([u, x2, _nga])) -> minus([s(u), s(x2), _nga]) -> 50
}
Sat witness: Yes: ((drop([n, l1, _sga]) /\ length([_sga, _tga]) /\ length([l1, _uga]) /\ minus([_uga, n, _vga])) -> eq_nat([_tga, _vga]), {
_sga -> cons(b, nil)  ;  _tga -> s(z)  ;  _uga -> s(s(s(z)))  ;  _vga -> s(s(z))  ;  l1 -> cons(b, cons(b, cons(b, nil)))  ;  n -> s(z)
})

-------------------------------------------
Step 70, which took 0.569689 s (model generation: 0.525095,  model checking: 0.044594):

Model:
|_
{
drop -> 
{{{
Q={q_gen_1352, q_gen_1354, q_gen_1359, q_gen_1360, q_gen_1366, q_gen_1367, q_gen_1368, q_gen_1369, q_gen_1397, q_gen_1398, q_gen_1431, q_gen_1432, q_gen_1433, q_gen_1434, q_gen_1442, q_gen_1448},
Q_f={q_gen_1352},
Delta=
{
<s>(q_gen_1354) -> q_gen_1354
<z>() -> q_gen_1354
<nil>() -> q_gen_1397
<a>() -> q_gen_1398
<b>() -> q_gen_1398
<cons>(q_gen_1398, q_gen_1397) -> q_gen_1442
<s, cons>(q_gen_1360, q_gen_1359) -> q_gen_1359
<s, nil>(q_gen_1354) -> q_gen_1359
<z, nil>() -> q_gen_1359
<s, a>(q_gen_1354) -> q_gen_1360
<s, b>(q_gen_1354) -> q_gen_1360
<z, a>() -> q_gen_1360
<z, b>() -> q_gen_1360
<cons, cons>(q_gen_1369, q_gen_1368, q_gen_1367, q_gen_1366) -> q_gen_1366
<nil, nil>() -> q_gen_1366
<cons, a>(q_gen_1398, q_gen_1397) -> q_gen_1367
<cons, b>(q_gen_1398, q_gen_1397) -> q_gen_1367
<cons, b>(q_gen_1398, q_gen_1442) -> q_gen_1367
<nil, a>() -> q_gen_1367
<nil, b>() -> q_gen_1367
<a, cons>(q_gen_1398, q_gen_1397) -> q_gen_1368
<a, nil>() -> q_gen_1368
<b, cons>(q_gen_1398, q_gen_1397) -> q_gen_1368
<b, cons>(q_gen_1398, q_gen_1442) -> q_gen_1368
<b, nil>() -> q_gen_1368
<a, a>() -> q_gen_1369
<b, b>() -> q_gen_1369
<s, cons>(q_gen_1360, q_gen_1448) -> q_gen_1448
<z, cons>(q_gen_1398, q_gen_1397) -> q_gen_1448
<s, cons, cons>(q_gen_1434, q_gen_1433, q_gen_1432, q_gen_1431) -> q_gen_1352
<s, cons, nil>(q_gen_1360, q_gen_1359) -> q_gen_1352
<s, nil, nil>(q_gen_1354) -> q_gen_1352
<z, cons, cons>(q_gen_1369, q_gen_1368, q_gen_1367, q_gen_1366) -> q_gen_1352
<z, cons, nil>(q_gen_1398, q_gen_1442) -> q_gen_1352
<z, nil, nil>() -> q_gen_1352
<s, cons, cons>(q_gen_1434, q_gen_1433, q_gen_1432, q_gen_1352) -> q_gen_1431
<s, cons, nil>(q_gen_1360, q_gen_1448) -> q_gen_1431
<z, cons, nil>(q_gen_1398, q_gen_1397) -> q_gen_1431
<s, cons, a>(q_gen_1360, q_gen_1448) -> q_gen_1432
<s, cons, b>(q_gen_1360, q_gen_1448) -> q_gen_1432
<z, cons, a>(q_gen_1398, q_gen_1397) -> q_gen_1432
<z, cons, b>(q_gen_1398, q_gen_1397) -> q_gen_1432
<z, cons, b>(q_gen_1398, q_gen_1442) -> q_gen_1432
<s, a, nil>(q_gen_1354) -> q_gen_1433
<s, b, nil>(q_gen_1354) -> q_gen_1433
<z, a, nil>() -> q_gen_1433
<z, b, nil>() -> q_gen_1433
<s, a, a>(q_gen_1354) -> q_gen_1434
<s, a, b>(q_gen_1354) -> q_gen_1434
<s, b, a>(q_gen_1354) -> q_gen_1434
<s, b, b>(q_gen_1354) -> q_gen_1434
<z, a, a>() -> q_gen_1434
<z, b, b>() -> q_gen_1434
}

Datatype: <nat, eltlist, eltlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_1351, q_gen_1357, q_gen_1389},
Q_f={q_gen_1351},
Delta=
{
<s>(q_gen_1389) -> q_gen_1389
<z>() -> q_gen_1389
<cons, s>(q_gen_1357, q_gen_1351) -> q_gen_1351
<nil, z>() -> q_gen_1351
<a, s>(q_gen_1389) -> q_gen_1357
<a, z>() -> q_gen_1357
<b, s>(q_gen_1389) -> q_gen_1357
<b, z>() -> q_gen_1357
}

Datatype: <eltlist, nat>
Convolution form: complete
}}}
  ;  minus -> 
{{{
Q={q_gen_1348, q_gen_1350, q_gen_1362, q_gen_1372, q_gen_1373, q_gen_1378, q_gen_1386, q_gen_1416},
Q_f={q_gen_1348, q_gen_1372},
Delta=
{
<s>(q_gen_1362) -> q_gen_1362
<z>() -> q_gen_1362
<s, s>(q_gen_1350) -> q_gen_1350
<z, z>() -> q_gen_1350
<s, s>(q_gen_1386) -> q_gen_1386
<z, s>(q_gen_1362) -> q_gen_1386
<s, s>(q_gen_1416) -> q_gen_1416
<s, z>(q_gen_1362) -> q_gen_1416
<s, s, z>(q_gen_1350) -> q_gen_1348
<s, s, z>(q_gen_1386) -> q_gen_1348
<s, z, s>(q_gen_1350) -> q_gen_1348
<z, s, z>(q_gen_1362) -> q_gen_1348
<z, z, z>() -> q_gen_1348
<s, s, s>(q_gen_1372) -> q_gen_1372
<s, s, s>(q_gen_1373) -> q_gen_1372
<s, z, s>(q_gen_1416) -> q_gen_1372
<s, s, z>(q_gen_1416) -> q_gen_1373
<s, z, z>(q_gen_1362) -> q_gen_1373
<s, s, s>(q_gen_1348) -> q_gen_1378
<s, s, s>(q_gen_1378) -> q_gen_1378
<s, z, s>(q_gen_1386) -> q_gen_1378
}

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

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

Teacher's answer:
New clause system:
{
() -> drop([s(u), nil, nil]) -> 48  ;  () -> drop([z, l, l]) -> 51  ;  () -> length([nil, z]) -> 49  ;  () -> minus([s(u), z, s(u)]) -> 49  ;  () -> minus([z, y, z]) -> 49  ;  (drop([n, l1, _sga]) /\ length([_sga, _tga]) /\ length([l1, _uga]) /\ minus([_uga, n, _vga])) -> eq_nat([_tga, _vga]) -> 52  ;  (drop([u, x3, _ega])) -> drop([s(u), cons(x2, x3), _ega]) -> 52  ;  (length([ll, _jga])) -> length([cons(x, ll), s(_jga)]) -> 49  ;  (minus([u, x2, _nga])) -> minus([s(u), s(x2), _nga]) -> 50
}
Sat witness: Yes: (() -> drop([z, l, l]), {
l -> cons(a, cons(b, cons(b, nil)))
})

-------------------------------------------
Step 71, which took 0.320567 s (model generation: 0.255701,  model checking: 0.064866):

Model:
|_
{
drop -> 
{{{
Q={q_gen_1352, q_gen_1354, q_gen_1359, q_gen_1360, q_gen_1366, q_gen_1367, q_gen_1368, q_gen_1369, q_gen_1397, q_gen_1398, q_gen_1431, q_gen_1432, q_gen_1433, q_gen_1434, q_gen_1442, q_gen_1448},
Q_f={q_gen_1352},
Delta=
{
<s>(q_gen_1354) -> q_gen_1354
<z>() -> q_gen_1354
<nil>() -> q_gen_1397
<a>() -> q_gen_1398
<b>() -> q_gen_1398
<cons>(q_gen_1398, q_gen_1397) -> q_gen_1442
<s, cons>(q_gen_1360, q_gen_1359) -> q_gen_1359
<s, nil>(q_gen_1354) -> q_gen_1359
<z, nil>() -> q_gen_1359
<s, a>(q_gen_1354) -> q_gen_1360
<s, b>(q_gen_1354) -> q_gen_1360
<z, a>() -> q_gen_1360
<z, b>() -> q_gen_1360
<cons, cons>(q_gen_1369, q_gen_1368, q_gen_1367, q_gen_1366) -> q_gen_1366
<nil, nil>() -> q_gen_1366
<cons, a>(q_gen_1398, q_gen_1397) -> q_gen_1367
<cons, a>(q_gen_1398, q_gen_1442) -> q_gen_1367
<cons, b>(q_gen_1398, q_gen_1397) -> q_gen_1367
<cons, b>(q_gen_1398, q_gen_1442) -> q_gen_1367
<nil, a>() -> q_gen_1367
<nil, b>() -> q_gen_1367
<a, cons>(q_gen_1398, q_gen_1397) -> q_gen_1368
<a, cons>(q_gen_1398, q_gen_1442) -> q_gen_1368
<a, nil>() -> q_gen_1368
<b, cons>(q_gen_1398, q_gen_1397) -> q_gen_1368
<b, cons>(q_gen_1398, q_gen_1442) -> q_gen_1368
<b, nil>() -> q_gen_1368
<a, a>() -> q_gen_1369
<b, b>() -> q_gen_1369
<s, cons>(q_gen_1360, q_gen_1448) -> q_gen_1448
<z, cons>(q_gen_1398, q_gen_1397) -> q_gen_1448
<s, cons, cons>(q_gen_1434, q_gen_1433, q_gen_1432, q_gen_1431) -> q_gen_1352
<s, cons, nil>(q_gen_1360, q_gen_1359) -> q_gen_1352
<s, nil, nil>(q_gen_1354) -> q_gen_1352
<z, cons, cons>(q_gen_1369, q_gen_1368, q_gen_1367, q_gen_1366) -> q_gen_1352
<z, cons, nil>(q_gen_1398, q_gen_1442) -> q_gen_1352
<z, nil, nil>() -> q_gen_1352
<s, cons, cons>(q_gen_1434, q_gen_1433, q_gen_1432, q_gen_1352) -> q_gen_1431
<s, cons, nil>(q_gen_1360, q_gen_1448) -> q_gen_1431
<z, cons, nil>(q_gen_1398, q_gen_1397) -> q_gen_1431
<s, cons, a>(q_gen_1360, q_gen_1448) -> q_gen_1432
<s, cons, b>(q_gen_1360, q_gen_1448) -> q_gen_1432
<z, cons, a>(q_gen_1398, q_gen_1397) -> q_gen_1432
<z, cons, b>(q_gen_1398, q_gen_1397) -> q_gen_1432
<z, cons, b>(q_gen_1398, q_gen_1442) -> q_gen_1432
<s, a, nil>(q_gen_1354) -> q_gen_1433
<s, b, nil>(q_gen_1354) -> q_gen_1433
<z, a, nil>() -> q_gen_1433
<z, b, nil>() -> q_gen_1433
<s, a, a>(q_gen_1354) -> q_gen_1434
<s, a, b>(q_gen_1354) -> q_gen_1434
<s, b, a>(q_gen_1354) -> q_gen_1434
<s, b, b>(q_gen_1354) -> q_gen_1434
<z, a, a>() -> q_gen_1434
<z, b, b>() -> q_gen_1434
}

Datatype: <nat, eltlist, eltlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_1351, q_gen_1357, q_gen_1389},
Q_f={q_gen_1351},
Delta=
{
<s>(q_gen_1389) -> q_gen_1389
<z>() -> q_gen_1389
<cons, s>(q_gen_1357, q_gen_1351) -> q_gen_1351
<nil, z>() -> q_gen_1351
<a, s>(q_gen_1389) -> q_gen_1357
<a, z>() -> q_gen_1357
<b, s>(q_gen_1389) -> q_gen_1357
<b, z>() -> q_gen_1357
}

Datatype: <eltlist, nat>
Convolution form: complete
}}}
  ;  minus -> 
{{{
Q={q_gen_1348, q_gen_1350, q_gen_1362, q_gen_1372, q_gen_1373, q_gen_1378, q_gen_1386, q_gen_1416},
Q_f={q_gen_1348, q_gen_1372},
Delta=
{
<s>(q_gen_1362) -> q_gen_1362
<z>() -> q_gen_1362
<s, s>(q_gen_1350) -> q_gen_1350
<z, z>() -> q_gen_1350
<s, s>(q_gen_1386) -> q_gen_1386
<z, s>(q_gen_1362) -> q_gen_1386
<s, s>(q_gen_1416) -> q_gen_1416
<s, z>(q_gen_1362) -> q_gen_1416
<s, s, z>(q_gen_1350) -> q_gen_1348
<s, s, z>(q_gen_1386) -> q_gen_1348
<s, z, s>(q_gen_1350) -> q_gen_1348
<z, s, z>(q_gen_1362) -> q_gen_1348
<z, z, z>() -> q_gen_1348
<s, s, s>(q_gen_1372) -> q_gen_1372
<s, s, s>(q_gen_1373) -> q_gen_1372
<s, z, s>(q_gen_1416) -> q_gen_1372
<s, s, z>(q_gen_1416) -> q_gen_1373
<s, z, z>(q_gen_1362) -> q_gen_1373
<s, s, s>(q_gen_1348) -> q_gen_1378
<s, s, s>(q_gen_1378) -> q_gen_1378
<s, z, s>(q_gen_1386) -> q_gen_1378
}

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

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

Teacher's answer:
New clause system:
{
() -> drop([s(u), nil, nil]) -> 49  ;  () -> drop([z, l, l]) -> 54  ;  () -> length([nil, z]) -> 50  ;  () -> minus([s(u), z, s(u)]) -> 50  ;  () -> minus([z, y, z]) -> 50  ;  (drop([n, l1, _sga]) /\ length([_sga, _tga]) /\ length([l1, _uga]) /\ minus([_uga, n, _vga])) -> eq_nat([_tga, _vga]) -> 52  ;  (drop([u, x3, _ega])) -> drop([s(u), cons(x2, x3), _ega]) -> 52  ;  (length([ll, _jga])) -> length([cons(x, ll), s(_jga)]) -> 50  ;  (minus([u, x2, _nga])) -> minus([s(u), s(x2), _nga]) -> 51
}
Sat witness: Yes: (() -> drop([z, l, l]), {
l -> cons(b, cons(b, cons(a, cons(b, nil))))
})

-------------------------------------------
Step 72, which took 0.380063 s (model generation: 0.376019,  model checking: 0.004044):

Model:
|_
{
drop -> 
{{{
Q={q_gen_1352, q_gen_1354, q_gen_1359, q_gen_1360, q_gen_1366, q_gen_1367, q_gen_1368, q_gen_1369, q_gen_1397, q_gen_1398, q_gen_1431, q_gen_1432, q_gen_1433, q_gen_1434, q_gen_1442, q_gen_1448},
Q_f={q_gen_1352},
Delta=
{
<s>(q_gen_1354) -> q_gen_1354
<z>() -> q_gen_1354
<nil>() -> q_gen_1397
<a>() -> q_gen_1398
<b>() -> q_gen_1398
<cons>(q_gen_1398, q_gen_1397) -> q_gen_1442
<cons>(q_gen_1398, q_gen_1442) -> q_gen_1442
<s, cons>(q_gen_1360, q_gen_1359) -> q_gen_1359
<s, nil>(q_gen_1354) -> q_gen_1359
<z, nil>() -> q_gen_1359
<s, a>(q_gen_1354) -> q_gen_1360
<s, b>(q_gen_1354) -> q_gen_1360
<z, a>() -> q_gen_1360
<z, b>() -> q_gen_1360
<cons, cons>(q_gen_1369, q_gen_1368, q_gen_1367, q_gen_1366) -> q_gen_1366
<nil, nil>() -> q_gen_1366
<cons, a>(q_gen_1398, q_gen_1397) -> q_gen_1367
<cons, a>(q_gen_1398, q_gen_1442) -> q_gen_1367
<cons, b>(q_gen_1398, q_gen_1397) -> q_gen_1367
<cons, b>(q_gen_1398, q_gen_1442) -> q_gen_1367
<nil, a>() -> q_gen_1367
<nil, b>() -> q_gen_1367
<a, cons>(q_gen_1398, q_gen_1397) -> q_gen_1368
<a, cons>(q_gen_1398, q_gen_1442) -> q_gen_1368
<a, nil>() -> q_gen_1368
<b, cons>(q_gen_1398, q_gen_1397) -> q_gen_1368
<b, cons>(q_gen_1398, q_gen_1442) -> q_gen_1368
<b, nil>() -> q_gen_1368
<a, a>() -> q_gen_1369
<b, b>() -> q_gen_1369
<s, cons>(q_gen_1360, q_gen_1448) -> q_gen_1448
<z, cons>(q_gen_1398, q_gen_1397) -> q_gen_1448
<s, cons, cons>(q_gen_1434, q_gen_1433, q_gen_1432, q_gen_1431) -> q_gen_1352
<s, cons, nil>(q_gen_1360, q_gen_1359) -> q_gen_1352
<s, nil, nil>(q_gen_1354) -> q_gen_1352
<z, cons, cons>(q_gen_1369, q_gen_1368, q_gen_1367, q_gen_1366) -> q_gen_1352
<z, cons, nil>(q_gen_1398, q_gen_1442) -> q_gen_1352
<z, nil, nil>() -> q_gen_1352
<s, cons, cons>(q_gen_1434, q_gen_1433, q_gen_1432, q_gen_1352) -> q_gen_1431
<s, cons, nil>(q_gen_1360, q_gen_1448) -> q_gen_1431
<z, cons, nil>(q_gen_1398, q_gen_1397) -> q_gen_1431
<s, cons, a>(q_gen_1360, q_gen_1448) -> q_gen_1432
<s, cons, b>(q_gen_1360, q_gen_1448) -> q_gen_1432
<z, cons, a>(q_gen_1398, q_gen_1397) -> q_gen_1432
<z, cons, b>(q_gen_1398, q_gen_1397) -> q_gen_1432
<z, cons, b>(q_gen_1398, q_gen_1442) -> q_gen_1432
<s, a, nil>(q_gen_1354) -> q_gen_1433
<s, b, nil>(q_gen_1354) -> q_gen_1433
<z, a, nil>() -> q_gen_1433
<z, b, nil>() -> q_gen_1433
<s, a, a>(q_gen_1354) -> q_gen_1434
<s, a, b>(q_gen_1354) -> q_gen_1434
<s, b, a>(q_gen_1354) -> q_gen_1434
<s, b, b>(q_gen_1354) -> q_gen_1434
<z, a, a>() -> q_gen_1434
<z, b, b>() -> q_gen_1434
}

Datatype: <nat, eltlist, eltlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_1351, q_gen_1357, q_gen_1389},
Q_f={q_gen_1351},
Delta=
{
<s>(q_gen_1389) -> q_gen_1389
<z>() -> q_gen_1389
<cons, s>(q_gen_1357, q_gen_1351) -> q_gen_1351
<nil, z>() -> q_gen_1351
<a, s>(q_gen_1389) -> q_gen_1357
<a, z>() -> q_gen_1357
<b, s>(q_gen_1389) -> q_gen_1357
<b, z>() -> q_gen_1357
}

Datatype: <eltlist, nat>
Convolution form: complete
}}}
  ;  minus -> 
{{{
Q={q_gen_1348, q_gen_1350, q_gen_1362, q_gen_1372, q_gen_1373, q_gen_1378, q_gen_1386, q_gen_1416},
Q_f={q_gen_1348, q_gen_1372},
Delta=
{
<s>(q_gen_1362) -> q_gen_1362
<z>() -> q_gen_1362
<s, s>(q_gen_1350) -> q_gen_1350
<z, z>() -> q_gen_1350
<s, s>(q_gen_1386) -> q_gen_1386
<z, s>(q_gen_1362) -> q_gen_1386
<s, s>(q_gen_1416) -> q_gen_1416
<s, z>(q_gen_1362) -> q_gen_1416
<s, s, z>(q_gen_1350) -> q_gen_1348
<s, s, z>(q_gen_1386) -> q_gen_1348
<s, z, s>(q_gen_1350) -> q_gen_1348
<z, s, z>(q_gen_1362) -> q_gen_1348
<z, z, z>() -> q_gen_1348
<s, s, s>(q_gen_1372) -> q_gen_1372
<s, s, s>(q_gen_1373) -> q_gen_1372
<s, z, s>(q_gen_1416) -> q_gen_1372
<s, s, z>(q_gen_1416) -> q_gen_1373
<s, z, z>(q_gen_1362) -> q_gen_1373
<s, s, s>(q_gen_1348) -> q_gen_1378
<s, s, s>(q_gen_1378) -> q_gen_1378
<s, z, s>(q_gen_1386) -> q_gen_1378
}

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

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

Teacher's answer:
New clause system:
{
() -> drop([s(u), nil, nil]) -> 50  ;  () -> drop([z, l, l]) -> 54  ;  () -> length([nil, z]) -> 51  ;  () -> minus([s(u), z, s(u)]) -> 51  ;  () -> minus([z, y, z]) -> 51  ;  (drop([n, l1, _sga]) /\ length([_sga, _tga]) /\ length([l1, _uga]) /\ minus([_uga, n, _vga])) -> eq_nat([_tga, _vga]) -> 52  ;  (drop([u, x3, _ega])) -> drop([s(u), cons(x2, x3), _ega]) -> 55  ;  (length([ll, _jga])) -> length([cons(x, ll), s(_jga)]) -> 51  ;  (minus([u, x2, _nga])) -> minus([s(u), s(x2), _nga]) -> 52
}
Sat witness: Yes: ((drop([u, x3, _ega])) -> drop([s(u), cons(x2, x3), _ega]), {
_ega -> nil  ;  u -> z  ;  x2 -> b  ;  x3 -> cons(b, cons(b, nil))
})

-------------------------------------------
Step 73, which took 0.428245 s (model generation: 0.426535,  model checking: 0.001710):

Model:
|_
{
drop -> 
{{{
Q={q_gen_1352, q_gen_1354, q_gen_1359, q_gen_1360, q_gen_1366, q_gen_1367, q_gen_1368, q_gen_1369, q_gen_1397, q_gen_1398, q_gen_1431, q_gen_1432, q_gen_1433, q_gen_1434, q_gen_1442, q_gen_1448},
Q_f={q_gen_1352},
Delta=
{
<s>(q_gen_1354) -> q_gen_1354
<z>() -> q_gen_1354
<nil>() -> q_gen_1397
<a>() -> q_gen_1398
<b>() -> q_gen_1398
<cons>(q_gen_1398, q_gen_1397) -> q_gen_1442
<cons>(q_gen_1398, q_gen_1442) -> q_gen_1442
<s, cons>(q_gen_1360, q_gen_1359) -> q_gen_1359
<s, nil>(q_gen_1354) -> q_gen_1359
<z, cons>(q_gen_1398, q_gen_1442) -> q_gen_1359
<z, nil>() -> q_gen_1359
<s, a>(q_gen_1354) -> q_gen_1360
<s, b>(q_gen_1354) -> q_gen_1360
<z, a>() -> q_gen_1360
<z, b>() -> q_gen_1360
<cons, cons>(q_gen_1369, q_gen_1368, q_gen_1367, q_gen_1366) -> q_gen_1366
<nil, nil>() -> q_gen_1366
<cons, a>(q_gen_1398, q_gen_1397) -> q_gen_1367
<cons, a>(q_gen_1398, q_gen_1442) -> q_gen_1367
<cons, b>(q_gen_1398, q_gen_1397) -> q_gen_1367
<cons, b>(q_gen_1398, q_gen_1442) -> q_gen_1367
<nil, a>() -> q_gen_1367
<nil, b>() -> q_gen_1367
<a, cons>(q_gen_1398, q_gen_1397) -> q_gen_1368
<a, cons>(q_gen_1398, q_gen_1442) -> q_gen_1368
<a, nil>() -> q_gen_1368
<b, cons>(q_gen_1398, q_gen_1397) -> q_gen_1368
<b, cons>(q_gen_1398, q_gen_1442) -> q_gen_1368
<b, nil>() -> q_gen_1368
<a, a>() -> q_gen_1369
<b, b>() -> q_gen_1369
<s, cons>(q_gen_1360, q_gen_1448) -> q_gen_1448
<z, cons>(q_gen_1398, q_gen_1397) -> q_gen_1448
<s, cons, cons>(q_gen_1434, q_gen_1433, q_gen_1432, q_gen_1431) -> q_gen_1352
<s, cons, nil>(q_gen_1360, q_gen_1359) -> q_gen_1352
<s, nil, nil>(q_gen_1354) -> q_gen_1352
<z, cons, cons>(q_gen_1369, q_gen_1368, q_gen_1367, q_gen_1366) -> q_gen_1352
<z, cons, nil>(q_gen_1398, q_gen_1442) -> q_gen_1352
<z, nil, nil>() -> q_gen_1352
<s, cons, cons>(q_gen_1434, q_gen_1433, q_gen_1432, q_gen_1352) -> q_gen_1431
<s, cons, nil>(q_gen_1360, q_gen_1448) -> q_gen_1431
<z, cons, nil>(q_gen_1398, q_gen_1397) -> q_gen_1431
<s, cons, a>(q_gen_1360, q_gen_1448) -> q_gen_1432
<s, cons, b>(q_gen_1360, q_gen_1448) -> q_gen_1432
<z, cons, a>(q_gen_1398, q_gen_1397) -> q_gen_1432
<z, cons, b>(q_gen_1398, q_gen_1397) -> q_gen_1432
<z, cons, b>(q_gen_1398, q_gen_1442) -> q_gen_1432
<s, a, nil>(q_gen_1354) -> q_gen_1433
<s, b, nil>(q_gen_1354) -> q_gen_1433
<z, a, nil>() -> q_gen_1433
<z, b, nil>() -> q_gen_1433
<s, a, a>(q_gen_1354) -> q_gen_1434
<s, a, b>(q_gen_1354) -> q_gen_1434
<s, b, a>(q_gen_1354) -> q_gen_1434
<s, b, b>(q_gen_1354) -> q_gen_1434
<z, a, a>() -> q_gen_1434
<z, b, b>() -> q_gen_1434
}

Datatype: <nat, eltlist, eltlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_1351, q_gen_1357, q_gen_1389},
Q_f={q_gen_1351},
Delta=
{
<s>(q_gen_1389) -> q_gen_1389
<z>() -> q_gen_1389
<cons, s>(q_gen_1357, q_gen_1351) -> q_gen_1351
<nil, z>() -> q_gen_1351
<a, s>(q_gen_1389) -> q_gen_1357
<a, z>() -> q_gen_1357
<b, s>(q_gen_1389) -> q_gen_1357
<b, z>() -> q_gen_1357
}

Datatype: <eltlist, nat>
Convolution form: complete
}}}
  ;  minus -> 
{{{
Q={q_gen_1348, q_gen_1350, q_gen_1362, q_gen_1372, q_gen_1373, q_gen_1378, q_gen_1386, q_gen_1416},
Q_f={q_gen_1348, q_gen_1372},
Delta=
{
<s>(q_gen_1362) -> q_gen_1362
<z>() -> q_gen_1362
<s, s>(q_gen_1350) -> q_gen_1350
<z, z>() -> q_gen_1350
<s, s>(q_gen_1386) -> q_gen_1386
<z, s>(q_gen_1362) -> q_gen_1386
<s, s>(q_gen_1416) -> q_gen_1416
<s, z>(q_gen_1362) -> q_gen_1416
<s, s, z>(q_gen_1350) -> q_gen_1348
<s, s, z>(q_gen_1386) -> q_gen_1348
<s, z, s>(q_gen_1350) -> q_gen_1348
<z, s, z>(q_gen_1362) -> q_gen_1348
<z, z, z>() -> q_gen_1348
<s, s, s>(q_gen_1372) -> q_gen_1372
<s, s, s>(q_gen_1373) -> q_gen_1372
<s, z, s>(q_gen_1416) -> q_gen_1372
<s, s, z>(q_gen_1416) -> q_gen_1373
<s, z, z>(q_gen_1362) -> q_gen_1373
<s, s, s>(q_gen_1348) -> q_gen_1378
<s, s, s>(q_gen_1378) -> q_gen_1378
<s, z, s>(q_gen_1386) -> q_gen_1378
}

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

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

Teacher's answer:
New clause system:
{
() -> drop([s(u), nil, nil]) -> 51  ;  () -> drop([z, l, l]) -> 54  ;  () -> length([nil, z]) -> 52  ;  () -> minus([s(u), z, s(u)]) -> 52  ;  () -> minus([z, y, z]) -> 52  ;  (drop([n, l1, _sga]) /\ length([_sga, _tga]) /\ length([l1, _uga]) /\ minus([_uga, n, _vga])) -> eq_nat([_tga, _vga]) -> 55  ;  (drop([u, x3, _ega])) -> drop([s(u), cons(x2, x3), _ega]) -> 55  ;  (length([ll, _jga])) -> length([cons(x, ll), s(_jga)]) -> 52  ;  (minus([u, x2, _nga])) -> minus([s(u), s(x2), _nga]) -> 53
}
Sat witness: Yes: ((drop([n, l1, _sga]) /\ length([_sga, _tga]) /\ length([l1, _uga]) /\ minus([_uga, n, _vga])) -> eq_nat([_tga, _vga]), {
_sga -> nil  ;  _tga -> z  ;  _uga -> s(s(z))  ;  _vga -> s(z)  ;  l1 -> cons(a, cons(b, nil))  ;  n -> z
})

-------------------------------------------
Step 74, which took 0.791779 s (model generation: 0.780081,  model checking: 0.011698):

Model:
|_
{
drop -> 
{{{
Q={q_gen_1352, q_gen_1354, q_gen_1359, q_gen_1360, q_gen_1366, q_gen_1367, q_gen_1368, q_gen_1369, q_gen_1397, q_gen_1398, q_gen_1431, q_gen_1432, q_gen_1433, q_gen_1434, q_gen_1442, q_gen_1448},
Q_f={q_gen_1352},
Delta=
{
<s>(q_gen_1354) -> q_gen_1354
<z>() -> q_gen_1354
<nil>() -> q_gen_1397
<a>() -> q_gen_1398
<b>() -> q_gen_1398
<cons>(q_gen_1398, q_gen_1397) -> q_gen_1442
<cons>(q_gen_1398, q_gen_1442) -> q_gen_1442
<s, cons>(q_gen_1360, q_gen_1359) -> q_gen_1359
<s, nil>(q_gen_1354) -> q_gen_1359
<z, cons>(q_gen_1398, q_gen_1442) -> q_gen_1359
<z, nil>() -> q_gen_1359
<s, a>(q_gen_1354) -> q_gen_1360
<s, b>(q_gen_1354) -> q_gen_1360
<z, a>() -> q_gen_1360
<z, b>() -> q_gen_1360
<cons, cons>(q_gen_1369, q_gen_1368, q_gen_1367, q_gen_1366) -> q_gen_1366
<nil, nil>() -> q_gen_1366
<cons, a>(q_gen_1398, q_gen_1397) -> q_gen_1367
<cons, a>(q_gen_1398, q_gen_1442) -> q_gen_1367
<cons, b>(q_gen_1398, q_gen_1397) -> q_gen_1367
<cons, b>(q_gen_1398, q_gen_1442) -> q_gen_1367
<nil, a>() -> q_gen_1367
<nil, b>() -> q_gen_1367
<a, cons>(q_gen_1398, q_gen_1397) -> q_gen_1368
<a, cons>(q_gen_1398, q_gen_1442) -> q_gen_1368
<a, nil>() -> q_gen_1368
<b, cons>(q_gen_1398, q_gen_1397) -> q_gen_1368
<b, cons>(q_gen_1398, q_gen_1442) -> q_gen_1368
<b, nil>() -> q_gen_1368
<a, a>() -> q_gen_1369
<b, b>() -> q_gen_1369
<s, cons>(q_gen_1360, q_gen_1448) -> q_gen_1448
<z, cons>(q_gen_1398, q_gen_1397) -> q_gen_1448
<s, cons, cons>(q_gen_1434, q_gen_1433, q_gen_1432, q_gen_1431) -> q_gen_1352
<s, cons, nil>(q_gen_1360, q_gen_1359) -> q_gen_1352
<s, nil, nil>(q_gen_1354) -> q_gen_1352
<z, cons, cons>(q_gen_1369, q_gen_1368, q_gen_1367, q_gen_1366) -> q_gen_1352
<z, cons, nil>(q_gen_1398, q_gen_1442) -> q_gen_1352
<z, nil, nil>() -> q_gen_1352
<s, cons, cons>(q_gen_1434, q_gen_1433, q_gen_1432, q_gen_1352) -> q_gen_1431
<s, cons, nil>(q_gen_1360, q_gen_1448) -> q_gen_1431
<z, cons, nil>(q_gen_1398, q_gen_1397) -> q_gen_1431
<s, cons, a>(q_gen_1360, q_gen_1448) -> q_gen_1432
<s, cons, b>(q_gen_1360, q_gen_1448) -> q_gen_1432
<z, cons, a>(q_gen_1398, q_gen_1397) -> q_gen_1432
<z, cons, b>(q_gen_1398, q_gen_1397) -> q_gen_1432
<z, cons, b>(q_gen_1398, q_gen_1442) -> q_gen_1432
<s, a, nil>(q_gen_1354) -> q_gen_1433
<s, b, nil>(q_gen_1354) -> q_gen_1433
<z, a, nil>() -> q_gen_1433
<z, b, nil>() -> q_gen_1433
<s, a, a>(q_gen_1354) -> q_gen_1434
<s, a, b>(q_gen_1354) -> q_gen_1434
<s, b, a>(q_gen_1354) -> q_gen_1434
<s, b, b>(q_gen_1354) -> q_gen_1434
<z, a, a>() -> q_gen_1434
<z, b, b>() -> q_gen_1434
}

Datatype: <nat, eltlist, eltlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_1351, q_gen_1357, q_gen_1389},
Q_f={q_gen_1351},
Delta=
{
<s>(q_gen_1389) -> q_gen_1389
<z>() -> q_gen_1389
<cons, s>(q_gen_1357, q_gen_1351) -> q_gen_1351
<nil, z>() -> q_gen_1351
<a, s>(q_gen_1389) -> q_gen_1357
<a, z>() -> q_gen_1357
<b, s>(q_gen_1389) -> q_gen_1357
<b, z>() -> q_gen_1357
}

Datatype: <eltlist, nat>
Convolution form: complete
}}}
  ;  minus -> 
{{{
Q={q_gen_1348, q_gen_1350, q_gen_1362, q_gen_1372, q_gen_1373, q_gen_1378, q_gen_1386, q_gen_1416},
Q_f={q_gen_1348, q_gen_1372},
Delta=
{
<s>(q_gen_1362) -> q_gen_1362
<z>() -> q_gen_1362
<s, s>(q_gen_1350) -> q_gen_1350
<z, z>() -> q_gen_1350
<s, s>(q_gen_1386) -> q_gen_1386
<z, s>(q_gen_1362) -> q_gen_1386
<s, s>(q_gen_1416) -> q_gen_1416
<s, z>(q_gen_1362) -> q_gen_1416
<s, s, z>(q_gen_1350) -> q_gen_1348
<s, s, z>(q_gen_1386) -> q_gen_1348
<s, z, s>(q_gen_1350) -> q_gen_1348
<z, s, z>(q_gen_1362) -> q_gen_1348
<z, z, z>() -> q_gen_1348
<s, s, s>(q_gen_1372) -> q_gen_1372
<s, s, s>(q_gen_1373) -> q_gen_1372
<s, s, z>(q_gen_1416) -> q_gen_1373
<s, z, s>(q_gen_1416) -> q_gen_1373
<s, z, z>(q_gen_1362) -> q_gen_1373
<s, s, s>(q_gen_1348) -> q_gen_1378
<s, s, s>(q_gen_1378) -> q_gen_1378
<s, z, s>(q_gen_1386) -> q_gen_1378
}

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

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

Teacher's answer:
New clause system:
{
() -> drop([s(u), nil, nil]) -> 52  ;  () -> drop([z, l, l]) -> 55  ;  () -> length([nil, z]) -> 53  ;  () -> minus([s(u), z, s(u)]) -> 53  ;  () -> minus([z, y, z]) -> 53  ;  (drop([n, l1, _sga]) /\ length([_sga, _tga]) /\ length([l1, _uga]) /\ minus([_uga, n, _vga])) -> eq_nat([_tga, _vga]) -> 55  ;  (drop([u, x3, _ega])) -> drop([s(u), cons(x2, x3), _ega]) -> 58  ;  (length([ll, _jga])) -> length([cons(x, ll), s(_jga)]) -> 53  ;  (minus([u, x2, _nga])) -> minus([s(u), s(x2), _nga]) -> 54
}
Sat witness: Yes: ((drop([u, x3, _ega])) -> drop([s(u), cons(x2, x3), _ega]), {
_ega -> cons(a, nil)  ;  u -> z  ;  x2 -> b  ;  x3 -> cons(a, nil)
})

-------------------------------------------
Step 75, which took 0.349948 s (model generation: 0.348367,  model checking: 0.001581):

Model:
|_
{
drop -> 
{{{
Q={q_gen_1352, q_gen_1354, q_gen_1359, q_gen_1360, q_gen_1366, q_gen_1367, q_gen_1368, q_gen_1369, q_gen_1397, q_gen_1398, q_gen_1431, q_gen_1432, q_gen_1433, q_gen_1434, q_gen_1442, q_gen_1448},
Q_f={q_gen_1352},
Delta=
{
<s>(q_gen_1354) -> q_gen_1354
<z>() -> q_gen_1354
<nil>() -> q_gen_1397
<a>() -> q_gen_1398
<b>() -> q_gen_1398
<cons>(q_gen_1398, q_gen_1397) -> q_gen_1442
<cons>(q_gen_1398, q_gen_1442) -> q_gen_1442
<s, cons>(q_gen_1360, q_gen_1359) -> q_gen_1359
<s, nil>(q_gen_1354) -> q_gen_1359
<z, cons>(q_gen_1398, q_gen_1442) -> q_gen_1359
<z, nil>() -> q_gen_1359
<s, a>(q_gen_1354) -> q_gen_1360
<s, b>(q_gen_1354) -> q_gen_1360
<z, a>() -> q_gen_1360
<z, b>() -> q_gen_1360
<cons, cons>(q_gen_1369, q_gen_1368, q_gen_1367, q_gen_1366) -> q_gen_1366
<nil, nil>() -> q_gen_1366
<cons, a>(q_gen_1398, q_gen_1397) -> q_gen_1367
<cons, a>(q_gen_1398, q_gen_1442) -> q_gen_1367
<cons, b>(q_gen_1398, q_gen_1397) -> q_gen_1367
<cons, b>(q_gen_1398, q_gen_1442) -> q_gen_1367
<nil, a>() -> q_gen_1367
<nil, b>() -> q_gen_1367
<a, cons>(q_gen_1398, q_gen_1397) -> q_gen_1368
<a, cons>(q_gen_1398, q_gen_1442) -> q_gen_1368
<a, nil>() -> q_gen_1368
<b, cons>(q_gen_1398, q_gen_1397) -> q_gen_1368
<b, cons>(q_gen_1398, q_gen_1442) -> q_gen_1368
<b, nil>() -> q_gen_1368
<a, a>() -> q_gen_1369
<b, b>() -> q_gen_1369
<s, cons>(q_gen_1360, q_gen_1448) -> q_gen_1448
<z, cons>(q_gen_1398, q_gen_1397) -> q_gen_1448
<s, cons, cons>(q_gen_1434, q_gen_1433, q_gen_1432, q_gen_1431) -> q_gen_1352
<s, cons, nil>(q_gen_1360, q_gen_1359) -> q_gen_1352
<s, nil, nil>(q_gen_1354) -> q_gen_1352
<z, cons, cons>(q_gen_1369, q_gen_1368, q_gen_1367, q_gen_1366) -> q_gen_1352
<z, cons, nil>(q_gen_1398, q_gen_1442) -> q_gen_1352
<z, nil, nil>() -> q_gen_1352
<s, cons, cons>(q_gen_1434, q_gen_1433, q_gen_1432, q_gen_1352) -> q_gen_1431
<s, cons, nil>(q_gen_1360, q_gen_1448) -> q_gen_1431
<z, cons, nil>(q_gen_1398, q_gen_1397) -> q_gen_1431
<s, cons, a>(q_gen_1360, q_gen_1448) -> q_gen_1432
<s, cons, b>(q_gen_1360, q_gen_1448) -> q_gen_1432
<z, cons, a>(q_gen_1398, q_gen_1397) -> q_gen_1432
<z, cons, b>(q_gen_1398, q_gen_1397) -> q_gen_1432
<z, cons, b>(q_gen_1398, q_gen_1442) -> q_gen_1432
<s, a, nil>(q_gen_1354) -> q_gen_1433
<s, b, nil>(q_gen_1354) -> q_gen_1433
<z, a, nil>() -> q_gen_1433
<z, b, nil>() -> q_gen_1433
<s, a, a>(q_gen_1354) -> q_gen_1434
<s, a, b>(q_gen_1354) -> q_gen_1434
<s, b, a>(q_gen_1354) -> q_gen_1434
<s, b, b>(q_gen_1354) -> q_gen_1434
<z, a, a>() -> q_gen_1434
<z, b, a>() -> q_gen_1434
<z, b, b>() -> q_gen_1434
}

Datatype: <nat, eltlist, eltlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_1351, q_gen_1357, q_gen_1389},
Q_f={q_gen_1351},
Delta=
{
<s>(q_gen_1389) -> q_gen_1389
<z>() -> q_gen_1389
<cons, s>(q_gen_1357, q_gen_1351) -> q_gen_1351
<nil, z>() -> q_gen_1351
<a, s>(q_gen_1389) -> q_gen_1357
<a, z>() -> q_gen_1357
<b, s>(q_gen_1389) -> q_gen_1357
<b, z>() -> q_gen_1357
}

Datatype: <eltlist, nat>
Convolution form: complete
}}}
  ;  minus -> 
{{{
Q={q_gen_1348, q_gen_1350, q_gen_1362, q_gen_1372, q_gen_1373, q_gen_1378, q_gen_1386, q_gen_1416},
Q_f={q_gen_1348, q_gen_1372},
Delta=
{
<s>(q_gen_1362) -> q_gen_1362
<z>() -> q_gen_1362
<s, s>(q_gen_1350) -> q_gen_1350
<z, z>() -> q_gen_1350
<s, s>(q_gen_1386) -> q_gen_1386
<z, s>(q_gen_1362) -> q_gen_1386
<s, s>(q_gen_1416) -> q_gen_1416
<s, z>(q_gen_1362) -> q_gen_1416
<s, s, z>(q_gen_1350) -> q_gen_1348
<s, s, z>(q_gen_1386) -> q_gen_1348
<s, z, s>(q_gen_1350) -> q_gen_1348
<z, s, z>(q_gen_1362) -> q_gen_1348
<z, z, z>() -> q_gen_1348
<s, s, s>(q_gen_1372) -> q_gen_1372
<s, s, s>(q_gen_1373) -> q_gen_1372
<s, s, z>(q_gen_1416) -> q_gen_1373
<s, z, s>(q_gen_1416) -> q_gen_1373
<s, z, z>(q_gen_1362) -> q_gen_1373
<s, s, s>(q_gen_1348) -> q_gen_1378
<s, s, s>(q_gen_1378) -> q_gen_1378
<s, z, s>(q_gen_1386) -> q_gen_1378
}

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

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

Teacher's answer:
New clause system:
{
() -> drop([s(u), nil, nil]) -> 53  ;  () -> drop([z, l, l]) -> 55  ;  () -> length([nil, z]) -> 54  ;  () -> minus([s(u), z, s(u)]) -> 54  ;  () -> minus([z, y, z]) -> 54  ;  (drop([n, l1, _sga]) /\ length([_sga, _tga]) /\ length([l1, _uga]) /\ minus([_uga, n, _vga])) -> eq_nat([_tga, _vga]) -> 58  ;  (drop([u, x3, _ega])) -> drop([s(u), cons(x2, x3), _ega]) -> 58  ;  (length([ll, _jga])) -> length([cons(x, ll), s(_jga)]) -> 54  ;  (minus([u, x2, _nga])) -> minus([s(u), s(x2), _nga]) -> 55
}
Sat witness: Yes: ((drop([n, l1, _sga]) /\ length([_sga, _tga]) /\ length([l1, _uga]) /\ minus([_uga, n, _vga])) -> eq_nat([_tga, _vga]), {
_sga -> nil  ;  _tga -> z  ;  _uga -> s(s(s(z)))  ;  _vga -> s(z)  ;  l1 -> cons(b, cons(b, cons(b, nil)))  ;  n -> s(z)
})

-------------------------------------------
Step 76, which took 0.360394 s (model generation: 0.359526,  model checking: 0.000868):

Model:
|_
{
drop -> 
{{{
Q={q_gen_1352, q_gen_1354, q_gen_1359, q_gen_1360, q_gen_1366, q_gen_1367, q_gen_1368, q_gen_1369, q_gen_1397, q_gen_1398, q_gen_1431, q_gen_1432, q_gen_1433, q_gen_1434, q_gen_1442, q_gen_1448},
Q_f={q_gen_1352},
Delta=
{
<s>(q_gen_1354) -> q_gen_1354
<z>() -> q_gen_1354
<nil>() -> q_gen_1397
<a>() -> q_gen_1398
<b>() -> q_gen_1398
<cons>(q_gen_1398, q_gen_1397) -> q_gen_1442
<cons>(q_gen_1398, q_gen_1442) -> q_gen_1442
<s, cons>(q_gen_1360, q_gen_1359) -> q_gen_1359
<s, nil>(q_gen_1354) -> q_gen_1359
<z, cons>(q_gen_1398, q_gen_1442) -> q_gen_1359
<z, nil>() -> q_gen_1359
<s, a>(q_gen_1354) -> q_gen_1360
<s, b>(q_gen_1354) -> q_gen_1360
<z, a>() -> q_gen_1360
<z, b>() -> q_gen_1360
<cons, cons>(q_gen_1369, q_gen_1368, q_gen_1367, q_gen_1366) -> q_gen_1366
<nil, nil>() -> q_gen_1366
<cons, a>(q_gen_1398, q_gen_1397) -> q_gen_1367
<cons, a>(q_gen_1398, q_gen_1442) -> q_gen_1367
<cons, b>(q_gen_1398, q_gen_1397) -> q_gen_1367
<cons, b>(q_gen_1398, q_gen_1442) -> q_gen_1367
<nil, a>() -> q_gen_1367
<nil, b>() -> q_gen_1367
<a, cons>(q_gen_1398, q_gen_1397) -> q_gen_1368
<a, cons>(q_gen_1398, q_gen_1442) -> q_gen_1368
<a, nil>() -> q_gen_1368
<b, cons>(q_gen_1398, q_gen_1397) -> q_gen_1368
<b, cons>(q_gen_1398, q_gen_1442) -> q_gen_1368
<b, nil>() -> q_gen_1368
<a, a>() -> q_gen_1369
<b, b>() -> q_gen_1369
<s, cons>(q_gen_1360, q_gen_1448) -> q_gen_1448
<z, cons>(q_gen_1398, q_gen_1397) -> q_gen_1448
<s, cons, cons>(q_gen_1434, q_gen_1433, q_gen_1432, q_gen_1431) -> q_gen_1352
<s, cons, nil>(q_gen_1360, q_gen_1359) -> q_gen_1352
<s, nil, nil>(q_gen_1354) -> q_gen_1352
<z, cons, cons>(q_gen_1369, q_gen_1368, q_gen_1367, q_gen_1366) -> q_gen_1352
<z, cons, nil>(q_gen_1398, q_gen_1442) -> q_gen_1352
<z, nil, nil>() -> q_gen_1352
<s, cons, cons>(q_gen_1434, q_gen_1433, q_gen_1432, q_gen_1352) -> q_gen_1431
<s, cons, nil>(q_gen_1360, q_gen_1448) -> q_gen_1431
<z, cons, nil>(q_gen_1398, q_gen_1397) -> q_gen_1431
<s, cons, a>(q_gen_1360, q_gen_1448) -> q_gen_1432
<s, cons, b>(q_gen_1360, q_gen_1448) -> q_gen_1432
<z, cons, a>(q_gen_1398, q_gen_1397) -> q_gen_1432
<z, cons, b>(q_gen_1398, q_gen_1397) -> q_gen_1432
<z, cons, b>(q_gen_1398, q_gen_1442) -> q_gen_1432
<s, a, nil>(q_gen_1354) -> q_gen_1433
<s, b, nil>(q_gen_1354) -> q_gen_1433
<z, a, nil>() -> q_gen_1433
<z, b, nil>() -> q_gen_1433
<s, a, a>(q_gen_1354) -> q_gen_1434
<s, a, b>(q_gen_1354) -> q_gen_1434
<s, b, a>(q_gen_1354) -> q_gen_1434
<s, b, b>(q_gen_1354) -> q_gen_1434
<z, a, a>() -> q_gen_1434
<z, b, a>() -> q_gen_1434
<z, b, b>() -> q_gen_1434
}

Datatype: <nat, eltlist, eltlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_1351, q_gen_1357, q_gen_1389},
Q_f={q_gen_1351},
Delta=
{
<s>(q_gen_1389) -> q_gen_1389
<z>() -> q_gen_1389
<cons, s>(q_gen_1357, q_gen_1351) -> q_gen_1351
<nil, z>() -> q_gen_1351
<a, s>(q_gen_1389) -> q_gen_1357
<a, z>() -> q_gen_1357
<b, s>(q_gen_1389) -> q_gen_1357
<b, z>() -> q_gen_1357
}

Datatype: <eltlist, nat>
Convolution form: complete
}}}
  ;  minus -> 
{{{
Q={q_gen_1348, q_gen_1349, q_gen_1350, q_gen_1362, q_gen_1373, q_gen_1378, q_gen_1380, q_gen_1386, q_gen_1416},
Q_f={q_gen_1348, q_gen_1349},
Delta=
{
<z>() -> q_gen_1362
<s>(q_gen_1362) -> q_gen_1380
<s, s>(q_gen_1350) -> q_gen_1350
<s, z>(q_gen_1380) -> q_gen_1350
<z, z>() -> q_gen_1350
<s, s>(q_gen_1386) -> q_gen_1386
<z, s>(q_gen_1362) -> q_gen_1386
<z, s>(q_gen_1380) -> q_gen_1386
<s, s>(q_gen_1416) -> q_gen_1416
<s, z>(q_gen_1362) -> q_gen_1416
<s, s, s>(q_gen_1373) -> q_gen_1348
<s, s, z>(q_gen_1350) -> q_gen_1348
<s, s, z>(q_gen_1386) -> q_gen_1348
<z, s, z>(q_gen_1362) -> q_gen_1348
<z, s, z>(q_gen_1380) -> q_gen_1348
<z, z, z>() -> q_gen_1348
<s, z, s>(q_gen_1350) -> q_gen_1349
<s, z, z>(q_gen_1380) -> q_gen_1349
<s, s, s>(q_gen_1349) -> q_gen_1373
<s, s, z>(q_gen_1416) -> q_gen_1373
<s, z, s>(q_gen_1416) -> q_gen_1373
<s, z, z>(q_gen_1362) -> q_gen_1373
<s, s, s>(q_gen_1348) -> q_gen_1378
<s, s, s>(q_gen_1378) -> q_gen_1378
<s, z, s>(q_gen_1386) -> q_gen_1378
}

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

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

Teacher's answer:
New clause system:
{
() -> drop([s(u), nil, nil]) -> 54  ;  () -> drop([z, l, l]) -> 55  ;  () -> length([nil, z]) -> 54  ;  () -> minus([s(u), z, s(u)]) -> 54  ;  () -> minus([z, y, z]) -> 57  ;  (drop([n, l1, _sga]) /\ length([_sga, _tga]) /\ length([l1, _uga]) /\ minus([_uga, n, _vga])) -> eq_nat([_tga, _vga]) -> 58  ;  (drop([u, x3, _ega])) -> drop([s(u), cons(x2, x3), _ega]) -> 58  ;  (length([ll, _jga])) -> length([cons(x, ll), s(_jga)]) -> 55  ;  (minus([u, x2, _nga])) -> minus([s(u), s(x2), _nga]) -> 55
}
Sat witness: Yes: (() -> minus([z, y, z]), {
y -> s(s(s(z)))
})

-------------------------------------------
Step 77, which took 0.771818 s (model generation: 0.770628,  model checking: 0.001190):

Model:
|_
{
drop -> 
{{{
Q={q_gen_1352, q_gen_1354, q_gen_1359, q_gen_1360, q_gen_1366, q_gen_1367, q_gen_1368, q_gen_1369, q_gen_1392, q_gen_1397, q_gen_1398, q_gen_1431, q_gen_1432, q_gen_1433, q_gen_1434, q_gen_1442, q_gen_1448},
Q_f={q_gen_1352},
Delta=
{
<s>(q_gen_1354) -> q_gen_1354
<z>() -> q_gen_1354
<nil>() -> q_gen_1397
<a>() -> q_gen_1398
<b>() -> q_gen_1398
<cons>(q_gen_1398, q_gen_1397) -> q_gen_1442
<cons>(q_gen_1398, q_gen_1442) -> q_gen_1442
<s, cons>(q_gen_1360, q_gen_1359) -> q_gen_1359
<s, nil>(q_gen_1354) -> q_gen_1359
<z, cons>(q_gen_1398, q_gen_1442) -> q_gen_1359
<z, nil>() -> q_gen_1359
<s, a>(q_gen_1354) -> q_gen_1360
<z, a>() -> q_gen_1360
<z, b>() -> q_gen_1360
<cons, cons>(q_gen_1369, q_gen_1368, q_gen_1367, q_gen_1366) -> q_gen_1366
<nil, nil>() -> q_gen_1366
<cons, a>(q_gen_1398, q_gen_1397) -> q_gen_1367
<cons, a>(q_gen_1398, q_gen_1442) -> q_gen_1367
<cons, b>(q_gen_1398, q_gen_1397) -> q_gen_1367
<cons, b>(q_gen_1398, q_gen_1442) -> q_gen_1367
<nil, a>() -> q_gen_1367
<nil, b>() -> q_gen_1367
<a, cons>(q_gen_1398, q_gen_1397) -> q_gen_1368
<a, cons>(q_gen_1398, q_gen_1442) -> q_gen_1368
<a, nil>() -> q_gen_1368
<b, cons>(q_gen_1398, q_gen_1397) -> q_gen_1368
<b, cons>(q_gen_1398, q_gen_1442) -> q_gen_1368
<b, nil>() -> q_gen_1368
<a, a>() -> q_gen_1369
<b, b>() -> q_gen_1369
<s, b>(q_gen_1354) -> q_gen_1392
<s, cons>(q_gen_1360, q_gen_1448) -> q_gen_1448
<s, cons>(q_gen_1392, q_gen_1359) -> q_gen_1448
<z, cons>(q_gen_1398, q_gen_1397) -> q_gen_1448
<s, cons, cons>(q_gen_1434, q_gen_1433, q_gen_1432, q_gen_1431) -> q_gen_1352
<s, cons, nil>(q_gen_1360, q_gen_1359) -> q_gen_1352
<s, cons, nil>(q_gen_1392, q_gen_1359) -> q_gen_1352
<s, nil, nil>(q_gen_1354) -> q_gen_1352
<z, cons, cons>(q_gen_1369, q_gen_1368, q_gen_1367, q_gen_1366) -> q_gen_1352
<z, cons, nil>(q_gen_1398, q_gen_1442) -> q_gen_1352
<z, nil, nil>() -> q_gen_1352
<s, cons, cons>(q_gen_1434, q_gen_1433, q_gen_1432, q_gen_1352) -> q_gen_1431
<s, cons, nil>(q_gen_1360, q_gen_1448) -> q_gen_1431
<s, cons, nil>(q_gen_1392, q_gen_1448) -> q_gen_1431
<z, cons, nil>(q_gen_1398, q_gen_1397) -> q_gen_1431
<s, cons, a>(q_gen_1360, q_gen_1448) -> q_gen_1432
<s, cons, b>(q_gen_1360, q_gen_1448) -> q_gen_1432
<s, cons, b>(q_gen_1392, q_gen_1448) -> q_gen_1432
<z, cons, a>(q_gen_1398, q_gen_1397) -> q_gen_1432
<z, cons, b>(q_gen_1398, q_gen_1397) -> q_gen_1432
<z, cons, b>(q_gen_1398, q_gen_1442) -> q_gen_1432
<s, a, nil>(q_gen_1354) -> q_gen_1433
<s, b, nil>(q_gen_1354) -> q_gen_1433
<z, a, nil>() -> q_gen_1433
<z, b, nil>() -> q_gen_1433
<s, a, a>(q_gen_1354) -> q_gen_1434
<s, a, b>(q_gen_1354) -> q_gen_1434
<s, b, a>(q_gen_1354) -> q_gen_1434
<s, b, b>(q_gen_1354) -> q_gen_1434
<z, a, a>() -> q_gen_1434
<z, b, a>() -> q_gen_1434
<z, b, b>() -> q_gen_1434
}

Datatype: <nat, eltlist, eltlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_1351, q_gen_1357, q_gen_1389},
Q_f={q_gen_1351},
Delta=
{
<s>(q_gen_1389) -> q_gen_1389
<z>() -> q_gen_1389
<cons, s>(q_gen_1357, q_gen_1351) -> q_gen_1351
<nil, z>() -> q_gen_1351
<a, s>(q_gen_1389) -> q_gen_1357
<a, z>() -> q_gen_1357
<b, s>(q_gen_1389) -> q_gen_1357
<b, z>() -> q_gen_1357
}

Datatype: <eltlist, nat>
Convolution form: complete
}}}
  ;  minus -> 
{{{
Q={q_gen_1348, q_gen_1350, q_gen_1362, q_gen_1373, q_gen_1378, q_gen_1380, q_gen_1386, q_gen_1416},
Q_f={q_gen_1348},
Delta=
{
<z>() -> q_gen_1362
<s>(q_gen_1362) -> q_gen_1380
<s>(q_gen_1380) -> q_gen_1380
<s, s>(q_gen_1350) -> q_gen_1350
<s, s>(q_gen_1386) -> q_gen_1350
<z, z>() -> q_gen_1350
<s, z>(q_gen_1380) -> q_gen_1386
<z, s>(q_gen_1362) -> q_gen_1386
<z, s>(q_gen_1380) -> q_gen_1386
<s, s>(q_gen_1416) -> q_gen_1416
<s, z>(q_gen_1362) -> q_gen_1416
<s, s, s>(q_gen_1373) -> q_gen_1348
<s, s, z>(q_gen_1350) -> q_gen_1348
<s, s, z>(q_gen_1386) -> q_gen_1348
<s, z, s>(q_gen_1350) -> q_gen_1348
<z, s, z>(q_gen_1362) -> q_gen_1348
<z, s, z>(q_gen_1380) -> q_gen_1348
<z, z, z>() -> q_gen_1348
<s, s, s>(q_gen_1378) -> q_gen_1373
<s, s, z>(q_gen_1416) -> q_gen_1373
<s, z, s>(q_gen_1416) -> q_gen_1373
<s, z, z>(q_gen_1362) -> q_gen_1373
<s, s, s>(q_gen_1348) -> q_gen_1378
<s, z, s>(q_gen_1386) -> q_gen_1378
<s, z, z>(q_gen_1380) -> q_gen_1378
}

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

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

Teacher's answer:
New clause system:
{
() -> drop([s(u), nil, nil]) -> 55  ;  () -> drop([z, l, l]) -> 55  ;  () -> length([nil, z]) -> 55  ;  () -> minus([s(u), z, s(u)]) -> 55  ;  () -> minus([z, y, z]) -> 57  ;  (drop([n, l1, _sga]) /\ length([_sga, _tga]) /\ length([l1, _uga]) /\ minus([_uga, n, _vga])) -> eq_nat([_tga, _vga]) -> 58  ;  (drop([u, x3, _ega])) -> drop([s(u), cons(x2, x3), _ega]) -> 58  ;  (length([ll, _jga])) -> length([cons(x, ll), s(_jga)]) -> 55  ;  (minus([u, x2, _nga])) -> minus([s(u), s(x2), _nga]) -> 58
}
Sat witness: Yes: ((minus([u, x2, _nga])) -> minus([s(u), s(x2), _nga]), {
_nga -> s(s(s(z)))  ;  u -> s(s(z))  ;  x2 -> z
})

-------------------------------------------
Step 78, which took 0.413227 s (model generation: 0.410992,  model checking: 0.002235):

Model:
|_
{
drop -> 
{{{
Q={q_gen_1352, q_gen_1354, q_gen_1359, q_gen_1360, q_gen_1366, q_gen_1367, q_gen_1368, q_gen_1369, q_gen_1397, q_gen_1398, q_gen_1431, q_gen_1432, q_gen_1433, q_gen_1434, q_gen_1442, q_gen_1448},
Q_f={q_gen_1352},
Delta=
{
<s>(q_gen_1354) -> q_gen_1354
<z>() -> q_gen_1354
<nil>() -> q_gen_1397
<a>() -> q_gen_1398
<b>() -> q_gen_1398
<cons>(q_gen_1398, q_gen_1397) -> q_gen_1442
<cons>(q_gen_1398, q_gen_1442) -> q_gen_1442
<s, cons>(q_gen_1360, q_gen_1359) -> q_gen_1359
<s, nil>(q_gen_1354) -> q_gen_1359
<z, cons>(q_gen_1398, q_gen_1442) -> q_gen_1359
<z, nil>() -> q_gen_1359
<s, a>(q_gen_1354) -> q_gen_1360
<s, b>(q_gen_1354) -> q_gen_1360
<z, a>() -> q_gen_1360
<z, b>() -> q_gen_1360
<cons, cons>(q_gen_1369, q_gen_1368, q_gen_1367, q_gen_1366) -> q_gen_1366
<nil, nil>() -> q_gen_1366
<cons, a>(q_gen_1398, q_gen_1397) -> q_gen_1367
<cons, a>(q_gen_1398, q_gen_1442) -> q_gen_1367
<cons, b>(q_gen_1398, q_gen_1397) -> q_gen_1367
<cons, b>(q_gen_1398, q_gen_1442) -> q_gen_1367
<nil, a>() -> q_gen_1367
<nil, b>() -> q_gen_1367
<a, cons>(q_gen_1398, q_gen_1397) -> q_gen_1368
<a, cons>(q_gen_1398, q_gen_1442) -> q_gen_1368
<a, nil>() -> q_gen_1368
<b, cons>(q_gen_1398, q_gen_1397) -> q_gen_1368
<b, cons>(q_gen_1398, q_gen_1442) -> q_gen_1368
<b, nil>() -> q_gen_1368
<a, a>() -> q_gen_1369
<b, b>() -> q_gen_1369
<s, cons>(q_gen_1360, q_gen_1448) -> q_gen_1448
<z, cons>(q_gen_1398, q_gen_1397) -> q_gen_1448
<s, cons, cons>(q_gen_1434, q_gen_1433, q_gen_1432, q_gen_1431) -> q_gen_1352
<s, cons, nil>(q_gen_1360, q_gen_1359) -> q_gen_1352
<s, nil, nil>(q_gen_1354) -> q_gen_1352
<z, cons, cons>(q_gen_1369, q_gen_1368, q_gen_1367, q_gen_1366) -> q_gen_1352
<z, cons, nil>(q_gen_1398, q_gen_1442) -> q_gen_1352
<z, nil, nil>() -> q_gen_1352
<s, cons, cons>(q_gen_1434, q_gen_1433, q_gen_1432, q_gen_1352) -> q_gen_1431
<s, cons, nil>(q_gen_1360, q_gen_1448) -> q_gen_1431
<z, cons, nil>(q_gen_1398, q_gen_1397) -> q_gen_1431
<s, cons, a>(q_gen_1360, q_gen_1448) -> q_gen_1432
<s, cons, b>(q_gen_1360, q_gen_1448) -> q_gen_1432
<z, cons, a>(q_gen_1398, q_gen_1397) -> q_gen_1432
<z, cons, b>(q_gen_1398, q_gen_1397) -> q_gen_1432
<z, cons, b>(q_gen_1398, q_gen_1442) -> q_gen_1432
<s, a, nil>(q_gen_1354) -> q_gen_1433
<s, b, nil>(q_gen_1354) -> q_gen_1433
<z, a, nil>() -> q_gen_1433
<z, b, nil>() -> q_gen_1433
<s, a, a>(q_gen_1354) -> q_gen_1434
<s, a, b>(q_gen_1354) -> q_gen_1434
<s, b, a>(q_gen_1354) -> q_gen_1434
<s, b, b>(q_gen_1354) -> q_gen_1434
<z, a, a>() -> q_gen_1434
<z, b, a>() -> q_gen_1434
<z, b, b>() -> q_gen_1434
}

Datatype: <nat, eltlist, eltlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_1351, q_gen_1357, q_gen_1389},
Q_f={q_gen_1351},
Delta=
{
<s>(q_gen_1389) -> q_gen_1389
<z>() -> q_gen_1389
<cons, s>(q_gen_1357, q_gen_1351) -> q_gen_1351
<nil, z>() -> q_gen_1351
<a, s>(q_gen_1389) -> q_gen_1357
<a, z>() -> q_gen_1357
<b, s>(q_gen_1389) -> q_gen_1357
<b, z>() -> q_gen_1357
}

Datatype: <eltlist, nat>
Convolution form: complete
}}}
  ;  minus -> 
{{{
Q={q_gen_1348, q_gen_1349, q_gen_1350, q_gen_1362, q_gen_1373, q_gen_1378, q_gen_1380, q_gen_1386, q_gen_1416},
Q_f={q_gen_1348, q_gen_1349},
Delta=
{
<z>() -> q_gen_1362
<s>(q_gen_1362) -> q_gen_1380
<s>(q_gen_1380) -> q_gen_1380
<s, s>(q_gen_1350) -> q_gen_1350
<s, z>(q_gen_1380) -> q_gen_1350
<z, z>() -> q_gen_1350
<s, s>(q_gen_1386) -> q_gen_1386
<z, s>(q_gen_1362) -> q_gen_1386
<z, s>(q_gen_1380) -> q_gen_1386
<s, s>(q_gen_1416) -> q_gen_1416
<s, z>(q_gen_1362) -> q_gen_1416
<s, s, z>(q_gen_1350) -> q_gen_1348
<s, s, z>(q_gen_1386) -> q_gen_1348
<z, s, z>(q_gen_1362) -> q_gen_1348
<z, z, z>() -> q_gen_1348
<s, s, s>(q_gen_1373) -> q_gen_1349
<s, z, s>(q_gen_1350) -> q_gen_1349
<s, z, z>(q_gen_1380) -> q_gen_1349
<z, s, z>(q_gen_1380) -> q_gen_1349
<s, s, s>(q_gen_1349) -> q_gen_1373
<s, s, z>(q_gen_1416) -> q_gen_1373
<s, z, s>(q_gen_1416) -> q_gen_1373
<s, z, z>(q_gen_1362) -> q_gen_1373
<s, s, s>(q_gen_1348) -> q_gen_1378
<s, s, s>(q_gen_1378) -> q_gen_1378
<s, z, s>(q_gen_1386) -> q_gen_1378
}

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

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

Teacher's answer:
New clause system:
{
() -> drop([s(u), nil, nil]) -> 56  ;  () -> drop([z, l, l]) -> 56  ;  () -> length([nil, z]) -> 56  ;  () -> minus([s(u), z, s(u)]) -> 56  ;  () -> minus([z, y, z]) -> 58  ;  (drop([n, l1, _sga]) /\ length([_sga, _tga]) /\ length([l1, _uga]) /\ minus([_uga, n, _vga])) -> eq_nat([_tga, _vga]) -> 58  ;  (drop([u, x3, _ega])) -> drop([s(u), cons(x2, x3), _ega]) -> 58  ;  (length([ll, _jga])) -> length([cons(x, ll), s(_jga)]) -> 56  ;  (minus([u, x2, _nga])) -> minus([s(u), s(x2), _nga]) -> 61
}
Sat witness: Yes: ((minus([u, x2, _nga])) -> minus([s(u), s(x2), _nga]), {
_nga -> s(s(z))  ;  u -> s(s(z))  ;  x2 -> s(s(s(s(z))))
})

-------------------------------------------
Step 79, which took 0.546636 s (model generation: 0.538695,  model checking: 0.007941):

Model:
|_
{
drop -> 
{{{
Q={q_gen_1352, q_gen_1354, q_gen_1359, q_gen_1360, q_gen_1366, q_gen_1367, q_gen_1368, q_gen_1369, q_gen_1397, q_gen_1398, q_gen_1431, q_gen_1432, q_gen_1433, q_gen_1434, q_gen_1442, q_gen_1448},
Q_f={q_gen_1352},
Delta=
{
<s>(q_gen_1354) -> q_gen_1354
<z>() -> q_gen_1354
<cons>(q_gen_1398, q_gen_1442) -> q_gen_1397
<nil>() -> q_gen_1397
<a>() -> q_gen_1398
<b>() -> q_gen_1398
<cons>(q_gen_1398, q_gen_1397) -> q_gen_1442
<s, cons>(q_gen_1360, q_gen_1359) -> q_gen_1359
<s, nil>(q_gen_1354) -> q_gen_1359
<z, cons>(q_gen_1398, q_gen_1442) -> q_gen_1359
<z, nil>() -> q_gen_1359
<s, a>(q_gen_1354) -> q_gen_1360
<s, b>(q_gen_1354) -> q_gen_1360
<z, a>() -> q_gen_1360
<z, b>() -> q_gen_1360
<cons, cons>(q_gen_1369, q_gen_1368, q_gen_1367, q_gen_1366) -> q_gen_1366
<nil, nil>() -> q_gen_1366
<cons, a>(q_gen_1398, q_gen_1397) -> q_gen_1367
<cons, a>(q_gen_1398, q_gen_1442) -> q_gen_1367
<cons, b>(q_gen_1398, q_gen_1397) -> q_gen_1367
<cons, b>(q_gen_1398, q_gen_1442) -> q_gen_1367
<nil, a>() -> q_gen_1367
<nil, b>() -> q_gen_1367
<a, cons>(q_gen_1398, q_gen_1397) -> q_gen_1368
<a, cons>(q_gen_1398, q_gen_1442) -> q_gen_1368
<a, nil>() -> q_gen_1368
<b, cons>(q_gen_1398, q_gen_1397) -> q_gen_1368
<b, cons>(q_gen_1398, q_gen_1442) -> q_gen_1368
<b, nil>() -> q_gen_1368
<a, a>() -> q_gen_1369
<b, b>() -> q_gen_1369
<s, cons>(q_gen_1360, q_gen_1448) -> q_gen_1448
<z, cons>(q_gen_1398, q_gen_1397) -> q_gen_1448
<s, cons, cons>(q_gen_1434, q_gen_1433, q_gen_1432, q_gen_1431) -> q_gen_1352
<s, cons, nil>(q_gen_1360, q_gen_1359) -> q_gen_1352
<s, nil, nil>(q_gen_1354) -> q_gen_1352
<z, cons, cons>(q_gen_1369, q_gen_1368, q_gen_1367, q_gen_1366) -> q_gen_1352
<z, cons, nil>(q_gen_1398, q_gen_1442) -> q_gen_1352
<z, nil, nil>() -> q_gen_1352
<s, cons, cons>(q_gen_1434, q_gen_1433, q_gen_1432, q_gen_1352) -> q_gen_1431
<s, cons, nil>(q_gen_1360, q_gen_1448) -> q_gen_1431
<z, cons, nil>(q_gen_1398, q_gen_1397) -> q_gen_1431
<s, cons, a>(q_gen_1360, q_gen_1448) -> q_gen_1432
<s, cons, b>(q_gen_1360, q_gen_1448) -> q_gen_1432
<z, cons, a>(q_gen_1398, q_gen_1397) -> q_gen_1432
<z, cons, b>(q_gen_1398, q_gen_1397) -> q_gen_1432
<z, cons, b>(q_gen_1398, q_gen_1442) -> q_gen_1432
<s, a, nil>(q_gen_1354) -> q_gen_1433
<s, b, nil>(q_gen_1354) -> q_gen_1433
<z, a, nil>() -> q_gen_1433
<z, b, nil>() -> q_gen_1433
<s, a, a>(q_gen_1354) -> q_gen_1434
<s, a, b>(q_gen_1354) -> q_gen_1434
<s, b, a>(q_gen_1354) -> q_gen_1434
<s, b, b>(q_gen_1354) -> q_gen_1434
<z, a, a>() -> q_gen_1434
<z, b, a>() -> q_gen_1434
<z, b, b>() -> q_gen_1434
}

Datatype: <nat, eltlist, eltlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_1351, q_gen_1357, q_gen_1389},
Q_f={q_gen_1351},
Delta=
{
<s>(q_gen_1389) -> q_gen_1389
<z>() -> q_gen_1389
<cons, s>(q_gen_1357, q_gen_1351) -> q_gen_1351
<nil, z>() -> q_gen_1351
<a, s>(q_gen_1389) -> q_gen_1357
<a, z>() -> q_gen_1357
<b, s>(q_gen_1389) -> q_gen_1357
<b, z>() -> q_gen_1357
}

Datatype: <eltlist, nat>
Convolution form: complete
}}}
  ;  minus -> 
{{{
Q={q_gen_1348, q_gen_1349, q_gen_1350, q_gen_1362, q_gen_1373, q_gen_1378, q_gen_1380, q_gen_1386, q_gen_1416},
Q_f={q_gen_1348, q_gen_1349},
Delta=
{
<z>() -> q_gen_1362
<s>(q_gen_1362) -> q_gen_1380
<s>(q_gen_1380) -> q_gen_1380
<s, s>(q_gen_1350) -> q_gen_1350
<s, z>(q_gen_1380) -> q_gen_1350
<z, s>(q_gen_1380) -> q_gen_1350
<z, z>() -> q_gen_1350
<s, s>(q_gen_1386) -> q_gen_1386
<z, s>(q_gen_1362) -> q_gen_1386
<s, s>(q_gen_1416) -> q_gen_1416
<s, z>(q_gen_1362) -> q_gen_1416
<s, s, z>(q_gen_1386) -> q_gen_1348
<z, s, z>(q_gen_1362) -> q_gen_1348
<z, z, z>() -> q_gen_1348
<s, s, s>(q_gen_1373) -> q_gen_1349
<s, s, z>(q_gen_1350) -> q_gen_1349
<s, z, s>(q_gen_1350) -> q_gen_1349
<s, z, z>(q_gen_1380) -> q_gen_1349
<z, s, z>(q_gen_1380) -> q_gen_1349
<s, s, s>(q_gen_1349) -> q_gen_1373
<s, s, z>(q_gen_1416) -> q_gen_1373
<s, z, s>(q_gen_1416) -> q_gen_1373
<s, z, z>(q_gen_1362) -> q_gen_1373
<s, s, s>(q_gen_1348) -> q_gen_1378
<s, s, s>(q_gen_1378) -> q_gen_1378
<s, z, s>(q_gen_1386) -> q_gen_1378
}

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

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

Teacher's answer:
New clause system:
{
() -> drop([s(u), nil, nil]) -> 57  ;  () -> drop([z, l, l]) -> 57  ;  () -> length([nil, z]) -> 57  ;  () -> minus([s(u), z, s(u)]) -> 57  ;  () -> minus([z, y, z]) -> 58  ;  (drop([n, l1, _sga]) /\ length([_sga, _tga]) /\ length([l1, _uga]) /\ minus([_uga, n, _vga])) -> eq_nat([_tga, _vga]) -> 58  ;  (drop([u, x3, _ega])) -> drop([s(u), cons(x2, x3), _ega]) -> 61  ;  (length([ll, _jga])) -> length([cons(x, ll), s(_jga)]) -> 57  ;  (minus([u, x2, _nga])) -> minus([s(u), s(x2), _nga]) -> 61
}
Sat witness: Yes: ((drop([u, x3, _ega])) -> drop([s(u), cons(x2, x3), _ega]), {
_ega -> cons(b, nil)  ;  u -> z  ;  x2 -> a  ;  x3 -> cons(b, nil)
})

-------------------------------------------
Step 80, which took 0.646945 s (model generation: 0.644761,  model checking: 0.002184):

Model:
|_
{
drop -> 
{{{
Q={q_gen_1352, q_gen_1354, q_gen_1359, q_gen_1360, q_gen_1366, q_gen_1367, q_gen_1368, q_gen_1369, q_gen_1397, q_gen_1398, q_gen_1431, q_gen_1432, q_gen_1433, q_gen_1434, q_gen_1442, q_gen_1448},
Q_f={q_gen_1352},
Delta=
{
<s>(q_gen_1354) -> q_gen_1354
<z>() -> q_gen_1354
<cons>(q_gen_1398, q_gen_1442) -> q_gen_1397
<nil>() -> q_gen_1397
<a>() -> q_gen_1398
<b>() -> q_gen_1398
<cons>(q_gen_1398, q_gen_1397) -> q_gen_1442
<s, cons>(q_gen_1360, q_gen_1359) -> q_gen_1359
<s, nil>(q_gen_1354) -> q_gen_1359
<z, cons>(q_gen_1398, q_gen_1442) -> q_gen_1359
<z, nil>() -> q_gen_1359
<s, a>(q_gen_1354) -> q_gen_1360
<s, b>(q_gen_1354) -> q_gen_1360
<z, a>() -> q_gen_1360
<z, b>() -> q_gen_1360
<cons, cons>(q_gen_1369, q_gen_1368, q_gen_1367, q_gen_1366) -> q_gen_1366
<nil, nil>() -> q_gen_1366
<cons, a>(q_gen_1398, q_gen_1397) -> q_gen_1367
<cons, a>(q_gen_1398, q_gen_1442) -> q_gen_1367
<cons, b>(q_gen_1398, q_gen_1397) -> q_gen_1367
<cons, b>(q_gen_1398, q_gen_1442) -> q_gen_1367
<nil, a>() -> q_gen_1367
<nil, b>() -> q_gen_1367
<a, cons>(q_gen_1398, q_gen_1397) -> q_gen_1368
<a, cons>(q_gen_1398, q_gen_1442) -> q_gen_1368
<a, nil>() -> q_gen_1368
<b, cons>(q_gen_1398, q_gen_1397) -> q_gen_1368
<b, cons>(q_gen_1398, q_gen_1442) -> q_gen_1368
<b, nil>() -> q_gen_1368
<a, a>() -> q_gen_1369
<b, b>() -> q_gen_1369
<s, cons>(q_gen_1360, q_gen_1448) -> q_gen_1448
<z, cons>(q_gen_1398, q_gen_1397) -> q_gen_1448
<s, cons, cons>(q_gen_1434, q_gen_1433, q_gen_1432, q_gen_1431) -> q_gen_1352
<s, cons, nil>(q_gen_1360, q_gen_1359) -> q_gen_1352
<s, nil, nil>(q_gen_1354) -> q_gen_1352
<z, cons, cons>(q_gen_1369, q_gen_1368, q_gen_1367, q_gen_1366) -> q_gen_1352
<z, cons, nil>(q_gen_1398, q_gen_1442) -> q_gen_1352
<z, nil, nil>() -> q_gen_1352
<s, cons, cons>(q_gen_1434, q_gen_1433, q_gen_1432, q_gen_1352) -> q_gen_1431
<s, cons, nil>(q_gen_1360, q_gen_1448) -> q_gen_1431
<z, cons, nil>(q_gen_1398, q_gen_1397) -> q_gen_1431
<s, cons, a>(q_gen_1360, q_gen_1448) -> q_gen_1432
<s, cons, b>(q_gen_1360, q_gen_1448) -> q_gen_1432
<z, cons, a>(q_gen_1398, q_gen_1397) -> q_gen_1432
<z, cons, b>(q_gen_1398, q_gen_1397) -> q_gen_1432
<z, cons, b>(q_gen_1398, q_gen_1442) -> q_gen_1432
<s, a, nil>(q_gen_1354) -> q_gen_1433
<s, b, nil>(q_gen_1354) -> q_gen_1433
<z, a, nil>() -> q_gen_1433
<z, b, nil>() -> q_gen_1433
<s, a, a>(q_gen_1354) -> q_gen_1434
<s, a, b>(q_gen_1354) -> q_gen_1434
<s, b, a>(q_gen_1354) -> q_gen_1434
<s, b, b>(q_gen_1354) -> q_gen_1434
<z, a, a>() -> q_gen_1434
<z, a, b>() -> q_gen_1434
<z, b, a>() -> q_gen_1434
<z, b, b>() -> q_gen_1434
}

Datatype: <nat, eltlist, eltlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_1351, q_gen_1357, q_gen_1389},
Q_f={q_gen_1351},
Delta=
{
<s>(q_gen_1389) -> q_gen_1389
<z>() -> q_gen_1389
<cons, s>(q_gen_1357, q_gen_1351) -> q_gen_1351
<nil, z>() -> q_gen_1351
<a, s>(q_gen_1389) -> q_gen_1357
<a, z>() -> q_gen_1357
<b, s>(q_gen_1389) -> q_gen_1357
<b, z>() -> q_gen_1357
}

Datatype: <eltlist, nat>
Convolution form: complete
}}}
  ;  minus -> 
{{{
Q={q_gen_1348, q_gen_1349, q_gen_1350, q_gen_1362, q_gen_1373, q_gen_1378, q_gen_1380, q_gen_1386, q_gen_1416},
Q_f={q_gen_1348, q_gen_1349},
Delta=
{
<s>(q_gen_1380) -> q_gen_1362
<z>() -> q_gen_1362
<s>(q_gen_1362) -> q_gen_1380
<s, s>(q_gen_1350) -> q_gen_1350
<s, z>(q_gen_1380) -> q_gen_1350
<z, s>(q_gen_1380) -> q_gen_1350
<z, z>() -> q_gen_1350
<s, s>(q_gen_1386) -> q_gen_1386
<z, s>(q_gen_1362) -> q_gen_1386
<s, s>(q_gen_1416) -> q_gen_1416
<s, z>(q_gen_1362) -> q_gen_1416
<s, s, s>(q_gen_1373) -> q_gen_1348
<s, s, z>(q_gen_1386) -> q_gen_1348
<z, s, z>(q_gen_1362) -> q_gen_1348
<z, z, z>() -> q_gen_1348
<s, s, z>(q_gen_1350) -> q_gen_1349
<s, z, s>(q_gen_1350) -> q_gen_1349
<s, z, z>(q_gen_1380) -> q_gen_1349
<z, s, z>(q_gen_1380) -> q_gen_1349
<s, s, s>(q_gen_1349) -> q_gen_1373
<s, s, z>(q_gen_1416) -> q_gen_1373
<s, z, s>(q_gen_1416) -> q_gen_1373
<s, z, z>(q_gen_1362) -> q_gen_1373
<s, s, s>(q_gen_1348) -> q_gen_1378
<s, s, s>(q_gen_1378) -> q_gen_1378
<s, z, s>(q_gen_1386) -> q_gen_1378
}

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

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

Teacher's answer:
New clause system:
{
() -> drop([s(u), nil, nil]) -> 58  ;  () -> drop([z, l, l]) -> 58  ;  () -> length([nil, z]) -> 58  ;  () -> minus([s(u), z, s(u)]) -> 58  ;  () -> minus([z, y, z]) -> 58  ;  (drop([n, l1, _sga]) /\ length([_sga, _tga]) /\ length([l1, _uga]) /\ minus([_uga, n, _vga])) -> eq_nat([_tga, _vga]) -> 61  ;  (drop([u, x3, _ega])) -> drop([s(u), cons(x2, x3), _ega]) -> 61  ;  (length([ll, _jga])) -> length([cons(x, ll), s(_jga)]) -> 58  ;  (minus([u, x2, _nga])) -> minus([s(u), s(x2), _nga]) -> 61
}
Sat witness: Yes: ((drop([n, l1, _sga]) /\ length([_sga, _tga]) /\ length([l1, _uga]) /\ minus([_uga, n, _vga])) -> eq_nat([_tga, _vga]), {
_sga -> nil  ;  _tga -> z  ;  _uga -> s(s(z))  ;  _vga -> s(s(z))  ;  l1 -> cons(b, cons(b, nil))  ;  n -> z
})

-------------------------------------------
Step 81, which took 1.304890 s (model generation: 1.246654,  model checking: 0.058236):

Model:
|_
{
drop -> 
{{{
Q={q_gen_1352, q_gen_1354, q_gen_1359, q_gen_1360, q_gen_1366, q_gen_1367, q_gen_1368, q_gen_1369, q_gen_1397, q_gen_1398, q_gen_1431, q_gen_1432, q_gen_1433, q_gen_1434, q_gen_1442, q_gen_1448, q_gen_1522},
Q_f={q_gen_1352},
Delta=
{
<s>(q_gen_1354) -> q_gen_1354
<z>() -> q_gen_1354
<cons>(q_gen_1398, q_gen_1442) -> q_gen_1397
<nil>() -> q_gen_1397
<a>() -> q_gen_1398
<b>() -> q_gen_1398
<cons>(q_gen_1398, q_gen_1397) -> q_gen_1442
<s, cons>(q_gen_1360, q_gen_1359) -> q_gen_1359
<s, nil>(q_gen_1354) -> q_gen_1359
<z, nil>() -> q_gen_1359
<s, a>(q_gen_1354) -> q_gen_1360
<s, b>(q_gen_1354) -> q_gen_1360
<z, a>() -> q_gen_1360
<z, b>() -> q_gen_1360
<cons, cons>(q_gen_1369, q_gen_1368, q_gen_1367, q_gen_1366) -> q_gen_1366
<nil, nil>() -> q_gen_1366
<cons, a>(q_gen_1398, q_gen_1397) -> q_gen_1367
<cons, a>(q_gen_1398, q_gen_1442) -> q_gen_1367
<cons, b>(q_gen_1398, q_gen_1397) -> q_gen_1367
<cons, b>(q_gen_1398, q_gen_1442) -> q_gen_1367
<nil, a>() -> q_gen_1367
<nil, b>() -> q_gen_1367
<a, cons>(q_gen_1398, q_gen_1397) -> q_gen_1368
<a, cons>(q_gen_1398, q_gen_1442) -> q_gen_1368
<a, nil>() -> q_gen_1368
<b, cons>(q_gen_1398, q_gen_1397) -> q_gen_1368
<b, cons>(q_gen_1398, q_gen_1442) -> q_gen_1368
<b, nil>() -> q_gen_1368
<a, a>() -> q_gen_1369
<b, b>() -> q_gen_1369
<s, cons>(q_gen_1360, q_gen_1448) -> q_gen_1448
<z, cons>(q_gen_1398, q_gen_1397) -> q_gen_1448
<z, cons>(q_gen_1398, q_gen_1442) -> q_gen_1448
<s, cons, cons>(q_gen_1434, q_gen_1433, q_gen_1432, q_gen_1431) -> q_gen_1352
<s, cons, nil>(q_gen_1360, q_gen_1359) -> q_gen_1352
<s, nil, nil>(q_gen_1354) -> q_gen_1352
<z, cons, cons>(q_gen_1369, q_gen_1368, q_gen_1367, q_gen_1366) -> q_gen_1352
<z, nil, nil>() -> q_gen_1352
<s, cons, cons>(q_gen_1434, q_gen_1433, q_gen_1522, q_gen_1431) -> q_gen_1431
<s, cons, nil>(q_gen_1360, q_gen_1448) -> q_gen_1431
<z, cons, nil>(q_gen_1398, q_gen_1397) -> q_gen_1431
<z, cons, nil>(q_gen_1398, q_gen_1442) -> q_gen_1431
<s, cons, a>(q_gen_1360, q_gen_1448) -> q_gen_1432
<s, cons, b>(q_gen_1360, q_gen_1448) -> q_gen_1432
<z, cons, a>(q_gen_1398, q_gen_1397) -> q_gen_1432
<z, cons, b>(q_gen_1398, q_gen_1397) -> q_gen_1432
<s, a, nil>(q_gen_1354) -> q_gen_1433
<s, b, nil>(q_gen_1354) -> q_gen_1433
<z, a, nil>() -> q_gen_1433
<z, b, nil>() -> q_gen_1433
<s, a, a>(q_gen_1354) -> q_gen_1434
<s, a, b>(q_gen_1354) -> q_gen_1434
<s, b, a>(q_gen_1354) -> q_gen_1434
<s, b, b>(q_gen_1354) -> q_gen_1434
<z, a, a>() -> q_gen_1434
<z, a, b>() -> q_gen_1434
<z, b, a>() -> q_gen_1434
<z, b, b>() -> q_gen_1434
<z, cons, b>(q_gen_1398, q_gen_1442) -> q_gen_1522
}

Datatype: <nat, eltlist, eltlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_1351, q_gen_1357, q_gen_1389},
Q_f={q_gen_1351},
Delta=
{
<s>(q_gen_1389) -> q_gen_1389
<z>() -> q_gen_1389
<cons, s>(q_gen_1357, q_gen_1351) -> q_gen_1351
<nil, z>() -> q_gen_1351
<a, s>(q_gen_1389) -> q_gen_1357
<a, z>() -> q_gen_1357
<b, s>(q_gen_1389) -> q_gen_1357
<b, z>() -> q_gen_1357
}

Datatype: <eltlist, nat>
Convolution form: complete
}}}
  ;  minus -> 
{{{
Q={q_gen_1348, q_gen_1350, q_gen_1362, q_gen_1372, q_gen_1373, q_gen_1378, q_gen_1386, q_gen_1416},
Q_f={q_gen_1348, q_gen_1372},
Delta=
{
<s>(q_gen_1362) -> q_gen_1362
<z>() -> q_gen_1362
<s, s>(q_gen_1350) -> q_gen_1350
<z, z>() -> q_gen_1350
<s, s>(q_gen_1386) -> q_gen_1386
<z, s>(q_gen_1362) -> q_gen_1386
<s, s>(q_gen_1416) -> q_gen_1416
<s, z>(q_gen_1362) -> q_gen_1416
<s, s, z>(q_gen_1350) -> q_gen_1348
<s, s, z>(q_gen_1386) -> q_gen_1348
<s, z, s>(q_gen_1350) -> q_gen_1348
<z, s, z>(q_gen_1362) -> q_gen_1348
<z, z, z>() -> q_gen_1348
<s, s, s>(q_gen_1372) -> q_gen_1372
<s, s, s>(q_gen_1373) -> q_gen_1372
<s, z, s>(q_gen_1416) -> q_gen_1372
<s, s, z>(q_gen_1416) -> q_gen_1373
<s, z, z>(q_gen_1362) -> q_gen_1373
<s, s, s>(q_gen_1348) -> q_gen_1378
<s, s, s>(q_gen_1378) -> q_gen_1378
<s, z, s>(q_gen_1386) -> q_gen_1378
}

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

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

Teacher's answer:
New clause system:
{
() -> drop([s(u), nil, nil]) -> 59  ;  () -> drop([z, l, l]) -> 59  ;  () -> length([nil, z]) -> 59  ;  () -> minus([s(u), z, s(u)]) -> 59  ;  () -> minus([z, y, z]) -> 59  ;  (drop([n, l1, _sga]) /\ length([_sga, _tga]) /\ length([l1, _uga]) /\ minus([_uga, n, _vga])) -> eq_nat([_tga, _vga]) -> 61  ;  (drop([u, x3, _ega])) -> drop([s(u), cons(x2, x3), _ega]) -> 64  ;  (length([ll, _jga])) -> length([cons(x, ll), s(_jga)]) -> 59  ;  (minus([u, x2, _nga])) -> minus([s(u), s(x2), _nga]) -> 62
}
Sat witness: Yes: ((drop([u, x3, _ega])) -> drop([s(u), cons(x2, x3), _ega]), {
_ega -> cons(b, cons(b, nil))  ;  u -> z  ;  x2 -> b  ;  x3 -> cons(b, cons(b, nil))
})

-------------------------------------------
Step 82, which took 1.346607 s (model generation: 1.342486,  model checking: 0.004121):

Model:
|_
{
drop -> 
{{{
Q={q_gen_1352, q_gen_1354, q_gen_1359, q_gen_1360, q_gen_1366, q_gen_1367, q_gen_1368, q_gen_1369, q_gen_1397, q_gen_1398, q_gen_1431, q_gen_1432, q_gen_1433, q_gen_1434, q_gen_1442, q_gen_1448, q_gen_1522},
Q_f={q_gen_1352},
Delta=
{
<s>(q_gen_1354) -> q_gen_1354
<z>() -> q_gen_1354
<nil>() -> q_gen_1397
<a>() -> q_gen_1398
<b>() -> q_gen_1398
<cons>(q_gen_1398, q_gen_1397) -> q_gen_1442
<cons>(q_gen_1398, q_gen_1442) -> q_gen_1442
<s, cons>(q_gen_1360, q_gen_1359) -> q_gen_1359
<s, nil>(q_gen_1354) -> q_gen_1359
<z, nil>() -> q_gen_1359
<s, a>(q_gen_1354) -> q_gen_1360
<s, b>(q_gen_1354) -> q_gen_1360
<z, a>() -> q_gen_1360
<z, b>() -> q_gen_1360
<cons, cons>(q_gen_1369, q_gen_1368, q_gen_1367, q_gen_1366) -> q_gen_1366
<cons, nil>(q_gen_1398, q_gen_1397) -> q_gen_1366
<nil, nil>() -> q_gen_1366
<cons, a>(q_gen_1398, q_gen_1397) -> q_gen_1367
<cons, a>(q_gen_1398, q_gen_1442) -> q_gen_1367
<cons, b>(q_gen_1398, q_gen_1397) -> q_gen_1367
<cons, b>(q_gen_1398, q_gen_1442) -> q_gen_1367
<nil, a>() -> q_gen_1367
<nil, b>() -> q_gen_1367
<a, cons>(q_gen_1398, q_gen_1397) -> q_gen_1368
<a, cons>(q_gen_1398, q_gen_1442) -> q_gen_1368
<a, nil>() -> q_gen_1368
<b, cons>(q_gen_1398, q_gen_1397) -> q_gen_1368
<b, cons>(q_gen_1398, q_gen_1442) -> q_gen_1368
<b, nil>() -> q_gen_1368
<a, a>() -> q_gen_1369
<b, b>() -> q_gen_1369
<s, cons>(q_gen_1360, q_gen_1448) -> q_gen_1448
<z, cons>(q_gen_1398, q_gen_1397) -> q_gen_1448
<z, cons>(q_gen_1398, q_gen_1442) -> q_gen_1448
<s, cons, cons>(q_gen_1434, q_gen_1433, q_gen_1432, q_gen_1431) -> q_gen_1352
<s, cons, cons>(q_gen_1434, q_gen_1433, q_gen_1522, q_gen_1352) -> q_gen_1352
<s, cons, nil>(q_gen_1360, q_gen_1359) -> q_gen_1352
<s, nil, nil>(q_gen_1354) -> q_gen_1352
<z, cons, cons>(q_gen_1369, q_gen_1368, q_gen_1367, q_gen_1366) -> q_gen_1352
<z, nil, nil>() -> q_gen_1352
<s, cons, cons>(q_gen_1434, q_gen_1433, q_gen_1522, q_gen_1431) -> q_gen_1431
<s, cons, nil>(q_gen_1360, q_gen_1448) -> q_gen_1431
<z, cons, nil>(q_gen_1398, q_gen_1397) -> q_gen_1431
<z, cons, nil>(q_gen_1398, q_gen_1442) -> q_gen_1431
<s, cons, a>(q_gen_1360, q_gen_1448) -> q_gen_1432
<s, cons, b>(q_gen_1360, q_gen_1448) -> q_gen_1432
<z, cons, a>(q_gen_1398, q_gen_1397) -> q_gen_1432
<z, cons, b>(q_gen_1398, q_gen_1397) -> q_gen_1432
<s, a, nil>(q_gen_1354) -> q_gen_1433
<s, b, nil>(q_gen_1354) -> q_gen_1433
<z, a, nil>() -> q_gen_1433
<z, b, cons>(q_gen_1398, q_gen_1397) -> q_gen_1433
<z, b, nil>() -> q_gen_1433
<s, a, a>(q_gen_1354) -> q_gen_1434
<s, a, b>(q_gen_1354) -> q_gen_1434
<s, b, a>(q_gen_1354) -> q_gen_1434
<s, b, b>(q_gen_1354) -> q_gen_1434
<z, a, a>() -> q_gen_1434
<z, a, b>() -> q_gen_1434
<z, b, a>() -> q_gen_1434
<z, b, b>() -> q_gen_1434
<z, cons, b>(q_gen_1398, q_gen_1442) -> q_gen_1522
}

Datatype: <nat, eltlist, eltlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_1351, q_gen_1357, q_gen_1389},
Q_f={q_gen_1351},
Delta=
{
<s>(q_gen_1389) -> q_gen_1389
<z>() -> q_gen_1389
<cons, s>(q_gen_1357, q_gen_1351) -> q_gen_1351
<nil, z>() -> q_gen_1351
<a, s>(q_gen_1389) -> q_gen_1357
<a, z>() -> q_gen_1357
<b, s>(q_gen_1389) -> q_gen_1357
<b, z>() -> q_gen_1357
}

Datatype: <eltlist, nat>
Convolution form: complete
}}}
  ;  minus -> 
{{{
Q={q_gen_1348, q_gen_1350, q_gen_1362, q_gen_1372, q_gen_1373, q_gen_1378, q_gen_1386, q_gen_1416},
Q_f={q_gen_1348, q_gen_1372},
Delta=
{
<s>(q_gen_1362) -> q_gen_1362
<z>() -> q_gen_1362
<s, s>(q_gen_1350) -> q_gen_1350
<z, z>() -> q_gen_1350
<s, s>(q_gen_1386) -> q_gen_1386
<z, s>(q_gen_1362) -> q_gen_1386
<s, s>(q_gen_1416) -> q_gen_1416
<s, z>(q_gen_1362) -> q_gen_1416
<s, s, z>(q_gen_1350) -> q_gen_1348
<s, s, z>(q_gen_1386) -> q_gen_1348
<s, z, s>(q_gen_1350) -> q_gen_1348
<z, s, z>(q_gen_1362) -> q_gen_1348
<z, z, z>() -> q_gen_1348
<s, s, s>(q_gen_1372) -> q_gen_1372
<s, s, s>(q_gen_1373) -> q_gen_1372
<s, z, s>(q_gen_1416) -> q_gen_1372
<s, s, z>(q_gen_1416) -> q_gen_1373
<s, z, z>(q_gen_1362) -> q_gen_1373
<s, s, s>(q_gen_1348) -> q_gen_1378
<s, s, s>(q_gen_1378) -> q_gen_1378
<s, z, s>(q_gen_1386) -> q_gen_1378
}

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

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

Teacher's answer:
New clause system:
{
() -> drop([s(u), nil, nil]) -> 60  ;  () -> drop([z, l, l]) -> 60  ;  () -> length([nil, z]) -> 60  ;  () -> minus([s(u), z, s(u)]) -> 60  ;  () -> minus([z, y, z]) -> 60  ;  (drop([n, l1, _sga]) /\ length([_sga, _tga]) /\ length([l1, _uga]) /\ minus([_uga, n, _vga])) -> eq_nat([_tga, _vga]) -> 64  ;  (drop([u, x3, _ega])) -> drop([s(u), cons(x2, x3), _ega]) -> 64  ;  (length([ll, _jga])) -> length([cons(x, ll), s(_jga)]) -> 60  ;  (minus([u, x2, _nga])) -> minus([s(u), s(x2), _nga]) -> 62
}
Sat witness: Yes: ((drop([n, l1, _sga]) /\ length([_sga, _tga]) /\ length([l1, _uga]) /\ minus([_uga, n, _vga])) -> eq_nat([_tga, _vga]), {
_sga -> cons(b, nil)  ;  _tga -> s(z)  ;  _uga -> s(s(s(z)))  ;  _vga -> s(s(z))  ;  l1 -> cons(b, cons(b, cons(b, nil)))  ;  n -> s(s(z))
})

-------------------------------------------
Step 83, which took 2.210024 s (model generation: 2.188945,  model checking: 0.021079):

Model:
|_
{
drop -> 
{{{
Q={q_gen_1352, q_gen_1354, q_gen_1359, q_gen_1360, q_gen_1366, q_gen_1367, q_gen_1368, q_gen_1369, q_gen_1397, q_gen_1398, q_gen_1413, q_gen_1431, q_gen_1432, q_gen_1433, q_gen_1434, q_gen_1442, q_gen_1452, q_gen_1458},
Q_f={q_gen_1352},
Delta=
{
<s>(q_gen_1354) -> q_gen_1354
<z>() -> q_gen_1354
<nil>() -> q_gen_1397
<b>() -> q_gen_1398
<a>() -> q_gen_1413
<cons>(q_gen_1398, q_gen_1397) -> q_gen_1442
<cons>(q_gen_1413, q_gen_1442) -> q_gen_1442
<s, cons>(q_gen_1360, q_gen_1359) -> q_gen_1359
<s, nil>(q_gen_1354) -> q_gen_1359
<z, cons>(q_gen_1413, q_gen_1397) -> q_gen_1359
<z, nil>() -> q_gen_1359
<s, a>(q_gen_1354) -> q_gen_1360
<s, b>(q_gen_1354) -> q_gen_1360
<z, a>() -> q_gen_1360
<z, b>() -> q_gen_1360
<cons, cons>(q_gen_1369, q_gen_1368, q_gen_1367, q_gen_1366) -> q_gen_1366
<cons, nil>(q_gen_1398, q_gen_1397) -> q_gen_1366
<nil, nil>() -> q_gen_1366
<cons, a>(q_gen_1398, q_gen_1397) -> q_gen_1367
<cons, a>(q_gen_1398, q_gen_1442) -> q_gen_1367
<cons, b>(q_gen_1398, q_gen_1397) -> q_gen_1367
<cons, b>(q_gen_1398, q_gen_1442) -> q_gen_1367
<cons, b>(q_gen_1413, q_gen_1397) -> q_gen_1367
<cons, b>(q_gen_1413, q_gen_1442) -> q_gen_1367
<nil, a>() -> q_gen_1367
<nil, b>() -> q_gen_1367
<a, cons>(q_gen_1398, q_gen_1397) -> q_gen_1368
<a, cons>(q_gen_1398, q_gen_1442) -> q_gen_1368
<a, nil>() -> q_gen_1368
<b, cons>(q_gen_1398, q_gen_1397) -> q_gen_1368
<b, cons>(q_gen_1398, q_gen_1442) -> q_gen_1368
<b, cons>(q_gen_1413, q_gen_1397) -> q_gen_1368
<b, cons>(q_gen_1413, q_gen_1442) -> q_gen_1368
<b, nil>() -> q_gen_1368
<a, a>() -> q_gen_1369
<b, b>() -> q_gen_1369
<s, cons>(q_gen_1360, q_gen_1458) -> q_gen_1458
<z, cons>(q_gen_1398, q_gen_1397) -> q_gen_1458
<z, cons>(q_gen_1398, q_gen_1442) -> q_gen_1458
<s, cons, cons>(q_gen_1434, q_gen_1433, q_gen_1432, q_gen_1352) -> q_gen_1352
<s, cons, cons>(q_gen_1434, q_gen_1433, q_gen_1432, q_gen_1431) -> q_gen_1352
<s, cons, cons>(q_gen_1434, q_gen_1433, q_gen_1452, q_gen_1352) -> q_gen_1352
<s, cons, nil>(q_gen_1360, q_gen_1359) -> q_gen_1352
<s, nil, nil>(q_gen_1354) -> q_gen_1352
<z, cons, cons>(q_gen_1369, q_gen_1368, q_gen_1367, q_gen_1366) -> q_gen_1352
<z, cons, nil>(q_gen_1413, q_gen_1397) -> q_gen_1352
<z, cons, nil>(q_gen_1413, q_gen_1442) -> q_gen_1352
<z, nil, nil>() -> q_gen_1352
<s, cons, cons>(q_gen_1434, q_gen_1433, q_gen_1452, q_gen_1431) -> q_gen_1431
<s, cons, nil>(q_gen_1360, q_gen_1458) -> q_gen_1431
<z, cons, nil>(q_gen_1398, q_gen_1397) -> q_gen_1431
<z, cons, nil>(q_gen_1398, q_gen_1442) -> q_gen_1431
<z, cons, a>(q_gen_1413, q_gen_1397) -> q_gen_1432
<z, cons, b>(q_gen_1398, q_gen_1397) -> q_gen_1432
<s, a, nil>(q_gen_1354) -> q_gen_1433
<s, b, nil>(q_gen_1354) -> q_gen_1433
<z, a, nil>() -> q_gen_1433
<z, b, cons>(q_gen_1398, q_gen_1397) -> q_gen_1433
<z, b, nil>() -> q_gen_1433
<s, a, a>(q_gen_1354) -> q_gen_1434
<s, a, b>(q_gen_1354) -> q_gen_1434
<s, b, a>(q_gen_1354) -> q_gen_1434
<s, b, b>(q_gen_1354) -> q_gen_1434
<z, a, a>() -> q_gen_1434
<z, a, b>() -> q_gen_1434
<z, b, a>() -> q_gen_1434
<z, b, b>() -> q_gen_1434
<s, cons, a>(q_gen_1360, q_gen_1359) -> q_gen_1452
<s, cons, b>(q_gen_1360, q_gen_1359) -> q_gen_1452
<s, cons, b>(q_gen_1360, q_gen_1458) -> q_gen_1452
<z, cons, a>(q_gen_1398, q_gen_1397) -> q_gen_1452
<z, cons, b>(q_gen_1398, q_gen_1442) -> q_gen_1452
<z, cons, b>(q_gen_1413, q_gen_1397) -> q_gen_1452
}

Datatype: <nat, eltlist, eltlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_1351, q_gen_1357, q_gen_1389},
Q_f={q_gen_1351},
Delta=
{
<s>(q_gen_1389) -> q_gen_1389
<z>() -> q_gen_1389
<cons, s>(q_gen_1357, q_gen_1351) -> q_gen_1351
<nil, z>() -> q_gen_1351
<a, s>(q_gen_1389) -> q_gen_1357
<a, z>() -> q_gen_1357
<b, s>(q_gen_1389) -> q_gen_1357
<b, z>() -> q_gen_1357
}

Datatype: <eltlist, nat>
Convolution form: complete
}}}
  ;  minus -> 
{{{
Q={q_gen_1348, q_gen_1349, q_gen_1350, q_gen_1362, q_gen_1373, q_gen_1378, q_gen_1386, q_gen_1416},
Q_f={q_gen_1348, q_gen_1349},
Delta=
{
<s>(q_gen_1362) -> q_gen_1362
<z>() -> q_gen_1362
<s, s>(q_gen_1350) -> q_gen_1350
<z, z>() -> q_gen_1350
<s, s>(q_gen_1386) -> q_gen_1386
<z, s>(q_gen_1362) -> q_gen_1386
<s, s>(q_gen_1416) -> q_gen_1416
<s, z>(q_gen_1362) -> q_gen_1416
<s, s, z>(q_gen_1350) -> q_gen_1348
<s, s, z>(q_gen_1386) -> q_gen_1348
<z, s, z>(q_gen_1362) -> q_gen_1348
<z, z, z>() -> q_gen_1348
<s, s, s>(q_gen_1349) -> q_gen_1349
<s, s, s>(q_gen_1373) -> q_gen_1349
<s, z, s>(q_gen_1350) -> q_gen_1349
<s, s, z>(q_gen_1416) -> q_gen_1373
<s, z, s>(q_gen_1416) -> q_gen_1373
<s, z, z>(q_gen_1362) -> q_gen_1373
<s, s, s>(q_gen_1348) -> q_gen_1378
<s, s, s>(q_gen_1378) -> q_gen_1378
<s, z, s>(q_gen_1386) -> q_gen_1378
}

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

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

Teacher's answer:
New clause system:
{
() -> drop([s(u), nil, nil]) -> 60  ;  () -> drop([z, l, l]) -> 63  ;  () -> length([nil, z]) -> 61  ;  () -> minus([s(u), z, s(u)]) -> 61  ;  () -> minus([z, y, z]) -> 61  ;  (drop([n, l1, _sga]) /\ length([_sga, _tga]) /\ length([l1, _uga]) /\ minus([_uga, n, _vga])) -> eq_nat([_tga, _vga]) -> 64  ;  (drop([u, x3, _ega])) -> drop([s(u), cons(x2, x3), _ega]) -> 64  ;  (length([ll, _jga])) -> length([cons(x, ll), s(_jga)]) -> 61  ;  (minus([u, x2, _nga])) -> minus([s(u), s(x2), _nga]) -> 62
}
Sat witness: Yes: (() -> drop([z, l, l]), {
l -> cons(a, cons(a, nil))
})

-------------------------------------------
Step 84, which took 2.464472 s (model generation: 1.756095,  model checking: 0.708377):

Model:
|_
{
drop -> 
{{{
Q={q_gen_1352, q_gen_1354, q_gen_1359, q_gen_1360, q_gen_1366, q_gen_1367, q_gen_1368, q_gen_1369, q_gen_1397, q_gen_1398, q_gen_1413, q_gen_1431, q_gen_1432, q_gen_1433, q_gen_1434, q_gen_1442, q_gen_1448, q_gen_1452},
Q_f={q_gen_1352},
Delta=
{
<s>(q_gen_1354) -> q_gen_1354
<z>() -> q_gen_1354
<nil>() -> q_gen_1397
<b>() -> q_gen_1398
<a>() -> q_gen_1413
<cons>(q_gen_1398, q_gen_1397) -> q_gen_1442
<cons>(q_gen_1413, q_gen_1442) -> q_gen_1442
<s, cons>(q_gen_1360, q_gen_1359) -> q_gen_1359
<s, nil>(q_gen_1354) -> q_gen_1359
<z, nil>() -> q_gen_1359
<s, a>(q_gen_1354) -> q_gen_1360
<s, b>(q_gen_1354) -> q_gen_1360
<z, a>() -> q_gen_1360
<z, b>() -> q_gen_1360
<cons, cons>(q_gen_1369, q_gen_1368, q_gen_1367, q_gen_1366) -> q_gen_1366
<cons, nil>(q_gen_1398, q_gen_1397) -> q_gen_1366
<nil, nil>() -> q_gen_1366
<cons, a>(q_gen_1398, q_gen_1397) -> q_gen_1367
<cons, a>(q_gen_1398, q_gen_1442) -> q_gen_1367
<cons, a>(q_gen_1413, q_gen_1397) -> q_gen_1367
<cons, b>(q_gen_1398, q_gen_1397) -> q_gen_1367
<cons, b>(q_gen_1398, q_gen_1442) -> q_gen_1367
<cons, b>(q_gen_1413, q_gen_1397) -> q_gen_1367
<cons, b>(q_gen_1413, q_gen_1442) -> q_gen_1367
<nil, a>() -> q_gen_1367
<nil, b>() -> q_gen_1367
<a, cons>(q_gen_1398, q_gen_1397) -> q_gen_1368
<a, cons>(q_gen_1398, q_gen_1442) -> q_gen_1368
<a, cons>(q_gen_1413, q_gen_1397) -> q_gen_1368
<a, nil>() -> q_gen_1368
<b, cons>(q_gen_1398, q_gen_1397) -> q_gen_1368
<b, cons>(q_gen_1398, q_gen_1442) -> q_gen_1368
<b, cons>(q_gen_1413, q_gen_1397) -> q_gen_1368
<b, cons>(q_gen_1413, q_gen_1442) -> q_gen_1368
<b, nil>() -> q_gen_1368
<a, a>() -> q_gen_1369
<b, b>() -> q_gen_1369
<s, cons>(q_gen_1360, q_gen_1448) -> q_gen_1448
<z, cons>(q_gen_1398, q_gen_1397) -> q_gen_1448
<z, cons>(q_gen_1398, q_gen_1442) -> q_gen_1448
<z, cons>(q_gen_1413, q_gen_1397) -> q_gen_1448
<s, cons, cons>(q_gen_1434, q_gen_1433, q_gen_1432, q_gen_1431) -> q_gen_1352
<s, cons, cons>(q_gen_1434, q_gen_1433, q_gen_1452, q_gen_1352) -> q_gen_1352
<s, cons, nil>(q_gen_1360, q_gen_1359) -> q_gen_1352
<s, nil, nil>(q_gen_1354) -> q_gen_1352
<z, cons, cons>(q_gen_1369, q_gen_1368, q_gen_1367, q_gen_1366) -> q_gen_1352
<z, cons, nil>(q_gen_1413, q_gen_1442) -> q_gen_1352
<z, nil, nil>() -> q_gen_1352
<s, cons, cons>(q_gen_1434, q_gen_1433, q_gen_1452, q_gen_1431) -> q_gen_1431
<s, cons, nil>(q_gen_1360, q_gen_1448) -> q_gen_1431
<z, cons, nil>(q_gen_1398, q_gen_1397) -> q_gen_1431
<z, cons, nil>(q_gen_1398, q_gen_1442) -> q_gen_1431
<z, cons, nil>(q_gen_1413, q_gen_1397) -> q_gen_1431
<s, cons, a>(q_gen_1360, q_gen_1448) -> q_gen_1432
<z, cons, a>(q_gen_1413, q_gen_1397) -> q_gen_1432
<z, cons, b>(q_gen_1398, q_gen_1397) -> q_gen_1432
<s, a, nil>(q_gen_1354) -> q_gen_1433
<s, b, nil>(q_gen_1354) -> q_gen_1433
<z, a, nil>() -> q_gen_1433
<z, b, cons>(q_gen_1398, q_gen_1397) -> q_gen_1433
<z, b, nil>() -> q_gen_1433
<s, a, a>(q_gen_1354) -> q_gen_1434
<s, a, b>(q_gen_1354) -> q_gen_1434
<s, b, a>(q_gen_1354) -> q_gen_1434
<s, b, b>(q_gen_1354) -> q_gen_1434
<z, a, a>() -> q_gen_1434
<z, a, b>() -> q_gen_1434
<z, b, a>() -> q_gen_1434
<z, b, b>() -> q_gen_1434
<s, cons, b>(q_gen_1360, q_gen_1448) -> q_gen_1452
<z, cons, a>(q_gen_1398, q_gen_1397) -> q_gen_1452
<z, cons, b>(q_gen_1398, q_gen_1442) -> q_gen_1452
<z, cons, b>(q_gen_1413, q_gen_1397) -> q_gen_1452
}

Datatype: <nat, eltlist, eltlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_1351, q_gen_1357, q_gen_1389},
Q_f={q_gen_1351},
Delta=
{
<s>(q_gen_1389) -> q_gen_1389
<z>() -> q_gen_1389
<cons, s>(q_gen_1357, q_gen_1351) -> q_gen_1351
<nil, z>() -> q_gen_1351
<a, s>(q_gen_1389) -> q_gen_1357
<a, z>() -> q_gen_1357
<b, s>(q_gen_1389) -> q_gen_1357
<b, z>() -> q_gen_1357
}

Datatype: <eltlist, nat>
Convolution form: complete
}}}
  ;  minus -> 
{{{
Q={q_gen_1348, q_gen_1349, q_gen_1350, q_gen_1362, q_gen_1373, q_gen_1378, q_gen_1386, q_gen_1416},
Q_f={q_gen_1348, q_gen_1349},
Delta=
{
<s>(q_gen_1362) -> q_gen_1362
<z>() -> q_gen_1362
<s, s>(q_gen_1350) -> q_gen_1350
<s, s>(q_gen_1386) -> q_gen_1350
<z, z>() -> q_gen_1350
<z, s>(q_gen_1362) -> q_gen_1386
<s, s>(q_gen_1416) -> q_gen_1416
<s, z>(q_gen_1362) -> q_gen_1416
<s, s, z>(q_gen_1350) -> q_gen_1348
<s, s, z>(q_gen_1386) -> q_gen_1348
<z, s, z>(q_gen_1362) -> q_gen_1348
<z, z, z>() -> q_gen_1348
<s, s, s>(q_gen_1349) -> q_gen_1349
<s, s, s>(q_gen_1373) -> q_gen_1349
<s, z, s>(q_gen_1350) -> q_gen_1349
<s, s, z>(q_gen_1416) -> q_gen_1373
<s, z, s>(q_gen_1416) -> q_gen_1373
<s, z, z>(q_gen_1362) -> q_gen_1373
<s, s, s>(q_gen_1348) -> q_gen_1378
<s, s, s>(q_gen_1378) -> q_gen_1378
<s, z, s>(q_gen_1386) -> q_gen_1378
}

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

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

Teacher's answer:
New clause system:
{
() -> drop([s(u), nil, nil]) -> 61  ;  () -> drop([z, l, l]) -> 66  ;  () -> length([nil, z]) -> 62  ;  () -> minus([s(u), z, s(u)]) -> 62  ;  () -> minus([z, y, z]) -> 62  ;  (drop([n, l1, _sga]) /\ length([_sga, _tga]) /\ length([l1, _uga]) /\ minus([_uga, n, _vga])) -> eq_nat([_tga, _vga]) -> 64  ;  (drop([u, x3, _ega])) -> drop([s(u), cons(x2, x3), _ega]) -> 64  ;  (length([ll, _jga])) -> length([cons(x, ll), s(_jga)]) -> 62  ;  (minus([u, x2, _nga])) -> minus([s(u), s(x2), _nga]) -> 63
}
Sat witness: Yes: (() -> drop([z, l, l]), {
l -> cons(b, cons(a, cons(a, nil)))
})

-------------------------------------------
Step 85, which took 1.573006 s (model generation: 1.568853,  model checking: 0.004153):

Model:
|_
{
drop -> 
{{{
Q={q_gen_1352, q_gen_1354, q_gen_1359, q_gen_1360, q_gen_1366, q_gen_1367, q_gen_1368, q_gen_1369, q_gen_1397, q_gen_1398, q_gen_1413, q_gen_1431, q_gen_1432, q_gen_1433, q_gen_1434, q_gen_1442, q_gen_1448, q_gen_1452},
Q_f={q_gen_1352},
Delta=
{
<s>(q_gen_1354) -> q_gen_1354
<z>() -> q_gen_1354
<cons>(q_gen_1413, q_gen_1397) -> q_gen_1397
<cons>(q_gen_1413, q_gen_1442) -> q_gen_1397
<nil>() -> q_gen_1397
<b>() -> q_gen_1398
<a>() -> q_gen_1413
<cons>(q_gen_1398, q_gen_1397) -> q_gen_1442
<s, cons>(q_gen_1360, q_gen_1359) -> q_gen_1359
<s, nil>(q_gen_1354) -> q_gen_1359
<z, nil>() -> q_gen_1359
<s, a>(q_gen_1354) -> q_gen_1360
<s, b>(q_gen_1354) -> q_gen_1360
<z, a>() -> q_gen_1360
<z, b>() -> q_gen_1360
<cons, cons>(q_gen_1369, q_gen_1368, q_gen_1367, q_gen_1366) -> q_gen_1366
<cons, nil>(q_gen_1398, q_gen_1397) -> q_gen_1366
<nil, nil>() -> q_gen_1366
<cons, a>(q_gen_1398, q_gen_1397) -> q_gen_1367
<cons, a>(q_gen_1398, q_gen_1442) -> q_gen_1367
<cons, a>(q_gen_1413, q_gen_1397) -> q_gen_1367
<cons, b>(q_gen_1398, q_gen_1397) -> q_gen_1367
<cons, b>(q_gen_1398, q_gen_1442) -> q_gen_1367
<cons, b>(q_gen_1413, q_gen_1397) -> q_gen_1367
<cons, b>(q_gen_1413, q_gen_1442) -> q_gen_1367
<nil, a>() -> q_gen_1367
<nil, b>() -> q_gen_1367
<a, cons>(q_gen_1398, q_gen_1397) -> q_gen_1368
<a, cons>(q_gen_1398, q_gen_1442) -> q_gen_1368
<a, cons>(q_gen_1413, q_gen_1397) -> q_gen_1368
<a, nil>() -> q_gen_1368
<b, cons>(q_gen_1398, q_gen_1397) -> q_gen_1368
<b, cons>(q_gen_1398, q_gen_1442) -> q_gen_1368
<b, cons>(q_gen_1413, q_gen_1397) -> q_gen_1368
<b, cons>(q_gen_1413, q_gen_1442) -> q_gen_1368
<b, nil>() -> q_gen_1368
<a, a>() -> q_gen_1369
<b, b>() -> q_gen_1369
<s, cons>(q_gen_1360, q_gen_1448) -> q_gen_1448
<z, cons>(q_gen_1398, q_gen_1397) -> q_gen_1448
<z, cons>(q_gen_1398, q_gen_1442) -> q_gen_1448
<z, cons>(q_gen_1413, q_gen_1397) -> q_gen_1448
<s, cons, cons>(q_gen_1434, q_gen_1433, q_gen_1432, q_gen_1431) -> q_gen_1352
<s, cons, cons>(q_gen_1434, q_gen_1433, q_gen_1452, q_gen_1352) -> q_gen_1352
<s, cons, nil>(q_gen_1360, q_gen_1359) -> q_gen_1352
<s, nil, nil>(q_gen_1354) -> q_gen_1352
<z, cons, cons>(q_gen_1369, q_gen_1368, q_gen_1367, q_gen_1366) -> q_gen_1352
<z, nil, nil>() -> q_gen_1352
<s, cons, cons>(q_gen_1434, q_gen_1433, q_gen_1452, q_gen_1431) -> q_gen_1431
<s, cons, nil>(q_gen_1360, q_gen_1448) -> q_gen_1431
<z, cons, nil>(q_gen_1398, q_gen_1397) -> q_gen_1431
<z, cons, nil>(q_gen_1398, q_gen_1442) -> q_gen_1431
<z, cons, nil>(q_gen_1413, q_gen_1397) -> q_gen_1431
<z, cons, nil>(q_gen_1413, q_gen_1442) -> q_gen_1431
<s, cons, a>(q_gen_1360, q_gen_1448) -> q_gen_1432
<z, cons, a>(q_gen_1413, q_gen_1397) -> q_gen_1432
<z, cons, b>(q_gen_1398, q_gen_1397) -> q_gen_1432
<s, a, nil>(q_gen_1354) -> q_gen_1433
<s, b, nil>(q_gen_1354) -> q_gen_1433
<z, a, nil>() -> q_gen_1433
<z, b, cons>(q_gen_1398, q_gen_1397) -> q_gen_1433
<z, b, nil>() -> q_gen_1433
<s, a, a>(q_gen_1354) -> q_gen_1434
<s, a, b>(q_gen_1354) -> q_gen_1434
<s, b, a>(q_gen_1354) -> q_gen_1434
<s, b, b>(q_gen_1354) -> q_gen_1434
<z, a, a>() -> q_gen_1434
<z, a, b>() -> q_gen_1434
<z, b, a>() -> q_gen_1434
<z, b, b>() -> q_gen_1434
<s, cons, b>(q_gen_1360, q_gen_1448) -> q_gen_1452
<z, cons, a>(q_gen_1398, q_gen_1397) -> q_gen_1452
<z, cons, b>(q_gen_1398, q_gen_1442) -> q_gen_1452
<z, cons, b>(q_gen_1413, q_gen_1397) -> q_gen_1452
}

Datatype: <nat, eltlist, eltlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_1351, q_gen_1357, q_gen_1389},
Q_f={q_gen_1351},
Delta=
{
<s>(q_gen_1389) -> q_gen_1389
<z>() -> q_gen_1389
<cons, s>(q_gen_1357, q_gen_1351) -> q_gen_1351
<nil, z>() -> q_gen_1351
<a, s>(q_gen_1389) -> q_gen_1357
<a, z>() -> q_gen_1357
<b, s>(q_gen_1389) -> q_gen_1357
<b, z>() -> q_gen_1357
}

Datatype: <eltlist, nat>
Convolution form: complete
}}}
  ;  minus -> 
{{{
Q={q_gen_1348, q_gen_1349, q_gen_1350, q_gen_1362, q_gen_1373, q_gen_1378, q_gen_1386, q_gen_1416},
Q_f={q_gen_1348, q_gen_1349},
Delta=
{
<s>(q_gen_1362) -> q_gen_1362
<z>() -> q_gen_1362
<s, s>(q_gen_1350) -> q_gen_1350
<z, z>() -> q_gen_1350
<s, s>(q_gen_1386) -> q_gen_1386
<z, s>(q_gen_1362) -> q_gen_1386
<s, s>(q_gen_1416) -> q_gen_1416
<s, z>(q_gen_1362) -> q_gen_1416
<s, s, z>(q_gen_1350) -> q_gen_1348
<s, s, z>(q_gen_1386) -> q_gen_1348
<z, s, z>(q_gen_1362) -> q_gen_1348
<z, z, z>() -> q_gen_1348
<s, s, s>(q_gen_1349) -> q_gen_1349
<s, s, s>(q_gen_1373) -> q_gen_1349
<s, z, s>(q_gen_1350) -> q_gen_1349
<s, s, z>(q_gen_1416) -> q_gen_1373
<s, z, s>(q_gen_1416) -> q_gen_1373
<s, z, z>(q_gen_1362) -> q_gen_1373
<s, s, s>(q_gen_1348) -> q_gen_1378
<s, s, s>(q_gen_1378) -> q_gen_1378
<s, z, s>(q_gen_1386) -> q_gen_1378
}

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

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

Teacher's answer:
New clause system:
{
() -> drop([s(u), nil, nil]) -> 62  ;  () -> drop([z, l, l]) -> 66  ;  () -> length([nil, z]) -> 63  ;  () -> minus([s(u), z, s(u)]) -> 63  ;  () -> minus([z, y, z]) -> 63  ;  (drop([n, l1, _sga]) /\ length([_sga, _tga]) /\ length([l1, _uga]) /\ minus([_uga, n, _vga])) -> eq_nat([_tga, _vga]) -> 64  ;  (drop([u, x3, _ega])) -> drop([s(u), cons(x2, x3), _ega]) -> 67  ;  (length([ll, _jga])) -> length([cons(x, ll), s(_jga)]) -> 63  ;  (minus([u, x2, _nga])) -> minus([s(u), s(x2), _nga]) -> 64
}
Sat witness: Yes: ((drop([u, x3, _ega])) -> drop([s(u), cons(x2, x3), _ega]), {
_ega -> cons(b, nil)  ;  u -> s(z)  ;  x2 -> b  ;  x3 -> cons(b, cons(b, nil))
})

-------------------------------------------
Step 86, which took 1.401420 s (model generation: 1.400228,  model checking: 0.001192):

Model:
|_
{
drop -> 
{{{
Q={q_gen_1352, q_gen_1354, q_gen_1359, q_gen_1360, q_gen_1366, q_gen_1367, q_gen_1368, q_gen_1369, q_gen_1397, q_gen_1398, q_gen_1431, q_gen_1432, q_gen_1433, q_gen_1434, q_gen_1442, q_gen_1448, q_gen_1521},
Q_f={q_gen_1352},
Delta=
{
<s>(q_gen_1354) -> q_gen_1354
<z>() -> q_gen_1354
<nil>() -> q_gen_1397
<a>() -> q_gen_1398
<b>() -> q_gen_1398
<cons>(q_gen_1398, q_gen_1397) -> q_gen_1442
<cons>(q_gen_1398, q_gen_1442) -> q_gen_1442
<s, cons>(q_gen_1360, q_gen_1359) -> q_gen_1359
<s, nil>(q_gen_1354) -> q_gen_1359
<z, nil>() -> q_gen_1359
<s, a>(q_gen_1354) -> q_gen_1360
<s, b>(q_gen_1354) -> q_gen_1360
<z, a>() -> q_gen_1360
<z, b>() -> q_gen_1360
<cons, cons>(q_gen_1369, q_gen_1368, q_gen_1367, q_gen_1366) -> q_gen_1366
<cons, nil>(q_gen_1398, q_gen_1397) -> q_gen_1366
<nil, nil>() -> q_gen_1366
<cons, a>(q_gen_1398, q_gen_1397) -> q_gen_1367
<cons, a>(q_gen_1398, q_gen_1442) -> q_gen_1367
<cons, b>(q_gen_1398, q_gen_1397) -> q_gen_1367
<cons, b>(q_gen_1398, q_gen_1442) -> q_gen_1367
<nil, a>() -> q_gen_1367
<nil, b>() -> q_gen_1367
<a, cons>(q_gen_1398, q_gen_1397) -> q_gen_1368
<a, cons>(q_gen_1398, q_gen_1442) -> q_gen_1368
<a, nil>() -> q_gen_1368
<b, cons>(q_gen_1398, q_gen_1397) -> q_gen_1368
<b, cons>(q_gen_1398, q_gen_1442) -> q_gen_1368
<b, nil>() -> q_gen_1368
<a, a>() -> q_gen_1369
<b, b>() -> q_gen_1369
<s, cons>(q_gen_1360, q_gen_1448) -> q_gen_1448
<z, cons>(q_gen_1398, q_gen_1397) -> q_gen_1448
<z, cons>(q_gen_1398, q_gen_1442) -> q_gen_1448
<s, cons, cons>(q_gen_1434, q_gen_1433, q_gen_1432, q_gen_1352) -> q_gen_1352
<s, cons, cons>(q_gen_1434, q_gen_1433, q_gen_1432, q_gen_1431) -> q_gen_1352
<s, cons, nil>(q_gen_1360, q_gen_1359) -> q_gen_1352
<s, nil, nil>(q_gen_1354) -> q_gen_1352
<z, cons, cons>(q_gen_1369, q_gen_1368, q_gen_1367, q_gen_1366) -> q_gen_1352
<z, nil, nil>() -> q_gen_1352
<s, cons, cons>(q_gen_1434, q_gen_1433, q_gen_1432, q_gen_1521) -> q_gen_1431
<s, cons, nil>(q_gen_1360, q_gen_1448) -> q_gen_1431
<z, cons, nil>(q_gen_1398, q_gen_1397) -> q_gen_1431
<s, cons, a>(q_gen_1360, q_gen_1448) -> q_gen_1432
<s, cons, b>(q_gen_1360, q_gen_1448) -> q_gen_1432
<z, cons, a>(q_gen_1398, q_gen_1397) -> q_gen_1432
<z, cons, b>(q_gen_1398, q_gen_1397) -> q_gen_1432
<z, cons, b>(q_gen_1398, q_gen_1442) -> q_gen_1432
<s, a, nil>(q_gen_1354) -> q_gen_1433
<s, b, nil>(q_gen_1354) -> q_gen_1433
<z, a, nil>() -> q_gen_1433
<z, b, cons>(q_gen_1398, q_gen_1397) -> q_gen_1433
<z, b, nil>() -> q_gen_1433
<s, a, a>(q_gen_1354) -> q_gen_1434
<s, a, b>(q_gen_1354) -> q_gen_1434
<s, b, a>(q_gen_1354) -> q_gen_1434
<s, b, b>(q_gen_1354) -> q_gen_1434
<z, a, a>() -> q_gen_1434
<z, a, b>() -> q_gen_1434
<z, b, a>() -> q_gen_1434
<z, b, b>() -> q_gen_1434
<z, cons, nil>(q_gen_1398, q_gen_1442) -> q_gen_1521
}

Datatype: <nat, eltlist, eltlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_1351, q_gen_1357, q_gen_1389},
Q_f={q_gen_1351},
Delta=
{
<s>(q_gen_1389) -> q_gen_1389
<z>() -> q_gen_1389
<cons, s>(q_gen_1357, q_gen_1351) -> q_gen_1351
<nil, z>() -> q_gen_1351
<a, s>(q_gen_1389) -> q_gen_1357
<a, z>() -> q_gen_1357
<b, s>(q_gen_1389) -> q_gen_1357
<b, z>() -> q_gen_1357
}

Datatype: <eltlist, nat>
Convolution form: complete
}}}
  ;  minus -> 
{{{
Q={q_gen_1348, q_gen_1349, q_gen_1350, q_gen_1362, q_gen_1373, q_gen_1378, q_gen_1380, q_gen_1386, q_gen_1416},
Q_f={q_gen_1348, q_gen_1349},
Delta=
{
<z>() -> q_gen_1362
<s>(q_gen_1362) -> q_gen_1380
<s>(q_gen_1380) -> q_gen_1380
<s, s>(q_gen_1350) -> q_gen_1350
<s, z>(q_gen_1380) -> q_gen_1350
<z, s>(q_gen_1380) -> q_gen_1350
<z, z>() -> q_gen_1350
<s, s>(q_gen_1386) -> q_gen_1386
<z, s>(q_gen_1362) -> q_gen_1386
<s, s>(q_gen_1416) -> q_gen_1416
<s, z>(q_gen_1362) -> q_gen_1416
<s, s, s>(q_gen_1373) -> q_gen_1348
<s, s, z>(q_gen_1386) -> q_gen_1348
<z, s, z>(q_gen_1362) -> q_gen_1348
<z, s, z>(q_gen_1380) -> q_gen_1348
<z, z, z>() -> q_gen_1348
<s, s, z>(q_gen_1350) -> q_gen_1349
<s, z, s>(q_gen_1350) -> q_gen_1349
<s, z, z>(q_gen_1380) -> q_gen_1349
<s, s, s>(q_gen_1349) -> q_gen_1373
<s, s, z>(q_gen_1416) -> q_gen_1373
<s, z, s>(q_gen_1416) -> q_gen_1373
<s, z, z>(q_gen_1362) -> q_gen_1373
<s, s, s>(q_gen_1348) -> q_gen_1378
<s, s, s>(q_gen_1378) -> q_gen_1378
<s, z, s>(q_gen_1386) -> q_gen_1378
}

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

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

Teacher's answer:
New clause system:
{
() -> drop([s(u), nil, nil]) -> 63  ;  () -> drop([z, l, l]) -> 66  ;  () -> length([nil, z]) -> 64  ;  () -> minus([s(u), z, s(u)]) -> 64  ;  () -> minus([z, y, z]) -> 64  ;  (drop([n, l1, _sga]) /\ length([_sga, _tga]) /\ length([l1, _uga]) /\ minus([_uga, n, _vga])) -> eq_nat([_tga, _vga]) -> 64  ;  (drop([u, x3, _ega])) -> drop([s(u), cons(x2, x3), _ega]) -> 67  ;  (length([ll, _jga])) -> length([cons(x, ll), s(_jga)]) -> 64  ;  (minus([u, x2, _nga])) -> minus([s(u), s(x2), _nga]) -> 67
}
Sat witness: Yes: ((minus([u, x2, _nga])) -> minus([s(u), s(x2), _nga]), {
_nga -> s(s(s(z)))  ;  u -> s(z)  ;  x2 -> z
})

-------------------------------------------
Step 87, which took 1.348390 s (model generation: 1.346827,  model checking: 0.001563):

Model:
|_
{
drop -> 
{{{
Q={q_gen_1352, q_gen_1354, q_gen_1359, q_gen_1360, q_gen_1366, q_gen_1367, q_gen_1368, q_gen_1369, q_gen_1397, q_gen_1398, q_gen_1431, q_gen_1432, q_gen_1433, q_gen_1434, q_gen_1442, q_gen_1448, q_gen_1522},
Q_f={q_gen_1352},
Delta=
{
<s>(q_gen_1354) -> q_gen_1354
<z>() -> q_gen_1354
<nil>() -> q_gen_1397
<a>() -> q_gen_1398
<b>() -> q_gen_1398
<cons>(q_gen_1398, q_gen_1397) -> q_gen_1442
<cons>(q_gen_1398, q_gen_1442) -> q_gen_1442
<s, cons>(q_gen_1360, q_gen_1359) -> q_gen_1359
<s, nil>(q_gen_1354) -> q_gen_1359
<z, cons>(q_gen_1398, q_gen_1442) -> q_gen_1359
<z, nil>() -> q_gen_1359
<s, a>(q_gen_1354) -> q_gen_1360
<s, b>(q_gen_1354) -> q_gen_1360
<z, a>() -> q_gen_1360
<z, b>() -> q_gen_1360
<cons, cons>(q_gen_1369, q_gen_1368, q_gen_1367, q_gen_1366) -> q_gen_1366
<cons, nil>(q_gen_1398, q_gen_1397) -> q_gen_1366
<nil, nil>() -> q_gen_1366
<cons, a>(q_gen_1398, q_gen_1397) -> q_gen_1367
<cons, a>(q_gen_1398, q_gen_1442) -> q_gen_1367
<cons, b>(q_gen_1398, q_gen_1397) -> q_gen_1367
<cons, b>(q_gen_1398, q_gen_1442) -> q_gen_1367
<nil, a>() -> q_gen_1367
<nil, b>() -> q_gen_1367
<a, cons>(q_gen_1398, q_gen_1397) -> q_gen_1368
<a, cons>(q_gen_1398, q_gen_1442) -> q_gen_1368
<a, nil>() -> q_gen_1368
<b, cons>(q_gen_1398, q_gen_1397) -> q_gen_1368
<b, cons>(q_gen_1398, q_gen_1442) -> q_gen_1368
<b, nil>() -> q_gen_1368
<a, a>() -> q_gen_1369
<b, b>() -> q_gen_1369
<s, cons>(q_gen_1360, q_gen_1448) -> q_gen_1448
<z, cons>(q_gen_1398, q_gen_1397) -> q_gen_1448
<s, cons, cons>(q_gen_1434, q_gen_1433, q_gen_1432, q_gen_1431) -> q_gen_1352
<s, cons, cons>(q_gen_1434, q_gen_1433, q_gen_1522, q_gen_1352) -> q_gen_1352
<s, cons, nil>(q_gen_1360, q_gen_1359) -> q_gen_1352
<s, nil, nil>(q_gen_1354) -> q_gen_1352
<z, cons, cons>(q_gen_1369, q_gen_1368, q_gen_1367, q_gen_1366) -> q_gen_1352
<z, nil, nil>() -> q_gen_1352
<s, cons, cons>(q_gen_1434, q_gen_1433, q_gen_1522, q_gen_1431) -> q_gen_1431
<s, cons, nil>(q_gen_1360, q_gen_1448) -> q_gen_1431
<z, cons, nil>(q_gen_1398, q_gen_1397) -> q_gen_1431
<z, cons, nil>(q_gen_1398, q_gen_1442) -> q_gen_1431
<s, cons, a>(q_gen_1360, q_gen_1448) -> q_gen_1432
<s, cons, b>(q_gen_1360, q_gen_1448) -> q_gen_1432
<z, cons, a>(q_gen_1398, q_gen_1397) -> q_gen_1432
<z, cons, b>(q_gen_1398, q_gen_1397) -> q_gen_1432
<s, a, nil>(q_gen_1354) -> q_gen_1433
<s, b, nil>(q_gen_1354) -> q_gen_1433
<z, a, nil>() -> q_gen_1433
<z, b, cons>(q_gen_1398, q_gen_1397) -> q_gen_1433
<z, b, nil>() -> q_gen_1433
<s, a, a>(q_gen_1354) -> q_gen_1434
<s, a, b>(q_gen_1354) -> q_gen_1434
<s, b, a>(q_gen_1354) -> q_gen_1434
<s, b, b>(q_gen_1354) -> q_gen_1434
<z, a, a>() -> q_gen_1434
<z, a, b>() -> q_gen_1434
<z, b, a>() -> q_gen_1434
<z, b, b>() -> q_gen_1434
<z, cons, b>(q_gen_1398, q_gen_1442) -> q_gen_1522
}

Datatype: <nat, eltlist, eltlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_1351, q_gen_1357, q_gen_1389},
Q_f={q_gen_1351},
Delta=
{
<s>(q_gen_1389) -> q_gen_1389
<z>() -> q_gen_1389
<cons, s>(q_gen_1357, q_gen_1351) -> q_gen_1351
<nil, z>() -> q_gen_1351
<a, s>(q_gen_1389) -> q_gen_1357
<a, z>() -> q_gen_1357
<b, s>(q_gen_1389) -> q_gen_1357
<b, z>() -> q_gen_1357
}

Datatype: <eltlist, nat>
Convolution form: complete
}}}
  ;  minus -> 
{{{
Q={q_gen_1348, q_gen_1349, q_gen_1350, q_gen_1362, q_gen_1373, q_gen_1378, q_gen_1380, q_gen_1386, q_gen_1416},
Q_f={q_gen_1348, q_gen_1349},
Delta=
{
<s>(q_gen_1380) -> q_gen_1362
<z>() -> q_gen_1362
<s>(q_gen_1362) -> q_gen_1380
<s, s>(q_gen_1350) -> q_gen_1350
<s, z>(q_gen_1380) -> q_gen_1350
<z, z>() -> q_gen_1350
<s, s>(q_gen_1386) -> q_gen_1386
<z, s>(q_gen_1362) -> q_gen_1386
<z, s>(q_gen_1380) -> q_gen_1386
<s, s>(q_gen_1416) -> q_gen_1416
<s, z>(q_gen_1362) -> q_gen_1416
<s, s, s>(q_gen_1373) -> q_gen_1348
<s, s, z>(q_gen_1350) -> q_gen_1348
<z, s, z>(q_gen_1380) -> q_gen_1348
<z, z, z>() -> q_gen_1348
<s, s, z>(q_gen_1386) -> q_gen_1349
<s, z, s>(q_gen_1350) -> q_gen_1349
<s, z, z>(q_gen_1380) -> q_gen_1349
<z, s, z>(q_gen_1362) -> q_gen_1349
<s, s, s>(q_gen_1349) -> q_gen_1373
<s, s, z>(q_gen_1416) -> q_gen_1373
<s, z, s>(q_gen_1416) -> q_gen_1373
<s, z, z>(q_gen_1362) -> q_gen_1373
<s, s, s>(q_gen_1348) -> q_gen_1378
<s, s, s>(q_gen_1378) -> q_gen_1378
<s, z, s>(q_gen_1386) -> q_gen_1378
}

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

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

Teacher's answer:
New clause system:
{
() -> drop([s(u), nil, nil]) -> 64  ;  () -> drop([z, l, l]) -> 66  ;  () -> length([nil, z]) -> 64  ;  () -> minus([s(u), z, s(u)]) -> 64  ;  () -> minus([z, y, z]) -> 64  ;  (drop([n, l1, _sga]) /\ length([_sga, _tga]) /\ length([l1, _uga]) /\ minus([_uga, n, _vga])) -> eq_nat([_tga, _vga]) -> 67  ;  (drop([u, x3, _ega])) -> drop([s(u), cons(x2, x3), _ega]) -> 67  ;  (length([ll, _jga])) -> length([cons(x, ll), s(_jga)]) -> 65  ;  (minus([u, x2, _nga])) -> minus([s(u), s(x2), _nga]) -> 67
}
Sat witness: Yes: ((drop([n, l1, _sga]) /\ length([_sga, _tga]) /\ length([l1, _uga]) /\ minus([_uga, n, _vga])) -> eq_nat([_tga, _vga]), {
_sga -> cons(b, nil)  ;  _tga -> s(z)  ;  _uga -> s(s(z))  ;  _vga -> z  ;  l1 -> cons(b, cons(b, nil))  ;  n -> z
})

-------------------------------------------
Step 88, which took 2.079566 s (model generation: 2.076682,  model checking: 0.002884):

Model:
|_
{
drop -> 
{{{
Q={q_gen_1352, q_gen_1354, q_gen_1359, q_gen_1360, q_gen_1366, q_gen_1367, q_gen_1368, q_gen_1369, q_gen_1392, q_gen_1397, q_gen_1398, q_gen_1431, q_gen_1432, q_gen_1433, q_gen_1434, q_gen_1442, q_gen_1448, q_gen_1520},
Q_f={q_gen_1352},
Delta=
{
<s>(q_gen_1354) -> q_gen_1354
<z>() -> q_gen_1354
<nil>() -> q_gen_1397
<a>() -> q_gen_1398
<b>() -> q_gen_1398
<cons>(q_gen_1398, q_gen_1397) -> q_gen_1442
<cons>(q_gen_1398, q_gen_1442) -> q_gen_1442
<s, cons>(q_gen_1360, q_gen_1359) -> q_gen_1359
<s, nil>(q_gen_1354) -> q_gen_1359
<z, cons>(q_gen_1398, q_gen_1442) -> q_gen_1359
<z, nil>() -> q_gen_1359
<s, a>(q_gen_1354) -> q_gen_1360
<z, a>() -> q_gen_1360
<z, b>() -> q_gen_1360
<cons, cons>(q_gen_1369, q_gen_1368, q_gen_1367, q_gen_1366) -> q_gen_1366
<cons, nil>(q_gen_1398, q_gen_1397) -> q_gen_1366
<nil, nil>() -> q_gen_1366
<cons, a>(q_gen_1398, q_gen_1397) -> q_gen_1367
<cons, a>(q_gen_1398, q_gen_1442) -> q_gen_1367
<cons, b>(q_gen_1398, q_gen_1397) -> q_gen_1367
<cons, b>(q_gen_1398, q_gen_1442) -> q_gen_1367
<nil, a>() -> q_gen_1367
<nil, b>() -> q_gen_1367
<a, cons>(q_gen_1398, q_gen_1397) -> q_gen_1368
<a, cons>(q_gen_1398, q_gen_1442) -> q_gen_1368
<a, nil>() -> q_gen_1368
<b, cons>(q_gen_1398, q_gen_1397) -> q_gen_1368
<b, cons>(q_gen_1398, q_gen_1442) -> q_gen_1368
<b, nil>() -> q_gen_1368
<a, a>() -> q_gen_1369
<b, b>() -> q_gen_1369
<s, b>(q_gen_1354) -> q_gen_1392
<s, cons>(q_gen_1360, q_gen_1448) -> q_gen_1448
<s, cons>(q_gen_1392, q_gen_1359) -> q_gen_1448
<z, cons>(q_gen_1398, q_gen_1397) -> q_gen_1448
<s, cons, cons>(q_gen_1434, q_gen_1433, q_gen_1432, q_gen_1352) -> q_gen_1352
<s, cons, cons>(q_gen_1434, q_gen_1433, q_gen_1432, q_gen_1431) -> q_gen_1352
<s, cons, nil>(q_gen_1360, q_gen_1359) -> q_gen_1352
<s, cons, nil>(q_gen_1392, q_gen_1359) -> q_gen_1352
<s, nil, nil>(q_gen_1354) -> q_gen_1352
<z, cons, cons>(q_gen_1369, q_gen_1368, q_gen_1367, q_gen_1366) -> q_gen_1352
<z, nil, nil>() -> q_gen_1352
<s, cons, nil>(q_gen_1360, q_gen_1448) -> q_gen_1431
<s, cons, nil>(q_gen_1392, q_gen_1448) -> q_gen_1431
<z, cons, nil>(q_gen_1398, q_gen_1397) -> q_gen_1431
<s, cons, a>(q_gen_1360, q_gen_1448) -> q_gen_1432
<s, cons, b>(q_gen_1360, q_gen_1448) -> q_gen_1432
<s, cons, b>(q_gen_1392, q_gen_1448) -> q_gen_1432
<z, cons, a>(q_gen_1398, q_gen_1397) -> q_gen_1432
<z, cons, b>(q_gen_1398, q_gen_1397) -> q_gen_1432
<z, cons, b>(q_gen_1398, q_gen_1442) -> q_gen_1432
<s, a, nil>(q_gen_1354) -> q_gen_1433
<s, b, nil>(q_gen_1354) -> q_gen_1433
<z, a, nil>() -> q_gen_1433
<z, b, cons>(q_gen_1398, q_gen_1397) -> q_gen_1433
<z, b, nil>() -> q_gen_1433
<s, a, a>(q_gen_1354) -> q_gen_1434
<s, a, b>(q_gen_1354) -> q_gen_1434
<s, b, a>(q_gen_1354) -> q_gen_1434
<s, b, b>(q_gen_1354) -> q_gen_1434
<z, a, a>() -> q_gen_1434
<z, a, b>() -> q_gen_1434
<z, b, a>() -> q_gen_1434
<z, b, b>() -> q_gen_1434
<s, cons, cons>(q_gen_1434, q_gen_1433, q_gen_1432, q_gen_1520) -> q_gen_1520
<z, cons, nil>(q_gen_1398, q_gen_1442) -> q_gen_1520
}

Datatype: <nat, eltlist, eltlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_1351, q_gen_1357, q_gen_1389},
Q_f={q_gen_1351},
Delta=
{
<s>(q_gen_1389) -> q_gen_1389
<z>() -> q_gen_1389
<cons, s>(q_gen_1357, q_gen_1351) -> q_gen_1351
<nil, z>() -> q_gen_1351
<a, s>(q_gen_1389) -> q_gen_1357
<a, z>() -> q_gen_1357
<b, s>(q_gen_1389) -> q_gen_1357
<b, z>() -> q_gen_1357
}

Datatype: <eltlist, nat>
Convolution form: complete
}}}
  ;  minus -> 
{{{
Q={q_gen_1348, q_gen_1350, q_gen_1362, q_gen_1373, q_gen_1378, q_gen_1380, q_gen_1386, q_gen_1402},
Q_f={q_gen_1348},
Delta=
{
<s>(q_gen_1380) -> q_gen_1362
<z>() -> q_gen_1362
<s>(q_gen_1362) -> q_gen_1380
<s, s>(q_gen_1350) -> q_gen_1350
<z, z>() -> q_gen_1350
<s, s>(q_gen_1386) -> q_gen_1386
<s, z>(q_gen_1380) -> q_gen_1386
<z, s>(q_gen_1362) -> q_gen_1386
<s, s>(q_gen_1402) -> q_gen_1402
<s, z>(q_gen_1362) -> q_gen_1402
<z, s>(q_gen_1380) -> q_gen_1402
<s, s, s>(q_gen_1373) -> q_gen_1348
<s, s, z>(q_gen_1350) -> q_gen_1348
<s, s, z>(q_gen_1386) -> q_gen_1348
<s, z, s>(q_gen_1350) -> q_gen_1348
<z, s, z>(q_gen_1362) -> q_gen_1348
<z, s, z>(q_gen_1380) -> q_gen_1348
<z, z, z>() -> q_gen_1348
<s, s, s>(q_gen_1378) -> q_gen_1373
<s, s, z>(q_gen_1402) -> q_gen_1373
<s, z, s>(q_gen_1402) -> q_gen_1373
<s, z, z>(q_gen_1362) -> q_gen_1373
<s, s, s>(q_gen_1348) -> q_gen_1378
<s, z, s>(q_gen_1386) -> q_gen_1378
<s, z, z>(q_gen_1380) -> q_gen_1378
}

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

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

Teacher's answer:
New clause system:
{
() -> drop([s(u), nil, nil]) -> 65  ;  () -> drop([z, l, l]) -> 67  ;  () -> length([nil, z]) -> 65  ;  () -> minus([s(u), z, s(u)]) -> 65  ;  () -> minus([z, y, z]) -> 65  ;  (drop([n, l1, _sga]) /\ length([_sga, _tga]) /\ length([l1, _uga]) /\ minus([_uga, n, _vga])) -> eq_nat([_tga, _vga]) -> 67  ;  (drop([u, x3, _ega])) -> drop([s(u), cons(x2, x3), _ega]) -> 67  ;  (length([ll, _jga])) -> length([cons(x, ll), s(_jga)]) -> 66  ;  (minus([u, x2, _nga])) -> minus([s(u), s(x2), _nga]) -> 70
}
Sat witness: Yes: ((minus([u, x2, _nga])) -> minus([s(u), s(x2), _nga]), {
_nga -> z  ;  u -> z  ;  x2 -> s(s(z))
})

-------------------------------------------
Step 89, which took 1.031945 s (model generation: 1.029877,  model checking: 0.002068):

Model:
|_
{
drop -> 
{{{
Q={q_gen_1352, q_gen_1354, q_gen_1359, q_gen_1360, q_gen_1366, q_gen_1367, q_gen_1368, q_gen_1369, q_gen_1397, q_gen_1398, q_gen_1431, q_gen_1432, q_gen_1433, q_gen_1434, q_gen_1442, q_gen_1448, q_gen_1520},
Q_f={q_gen_1352},
Delta=
{
<s>(q_gen_1354) -> q_gen_1354
<z>() -> q_gen_1354
<cons>(q_gen_1398, q_gen_1442) -> q_gen_1397
<nil>() -> q_gen_1397
<a>() -> q_gen_1398
<b>() -> q_gen_1398
<cons>(q_gen_1398, q_gen_1397) -> q_gen_1442
<s, cons>(q_gen_1360, q_gen_1359) -> q_gen_1359
<s, nil>(q_gen_1354) -> q_gen_1359
<z, nil>() -> q_gen_1359
<s, a>(q_gen_1354) -> q_gen_1360
<s, b>(q_gen_1354) -> q_gen_1360
<z, a>() -> q_gen_1360
<z, b>() -> q_gen_1360
<cons, cons>(q_gen_1369, q_gen_1368, q_gen_1367, q_gen_1366) -> q_gen_1366
<cons, nil>(q_gen_1398, q_gen_1397) -> q_gen_1366
<nil, nil>() -> q_gen_1366
<cons, a>(q_gen_1398, q_gen_1397) -> q_gen_1367
<cons, a>(q_gen_1398, q_gen_1442) -> q_gen_1367
<cons, b>(q_gen_1398, q_gen_1397) -> q_gen_1367
<cons, b>(q_gen_1398, q_gen_1442) -> q_gen_1367
<nil, a>() -> q_gen_1367
<nil, b>() -> q_gen_1367
<a, cons>(q_gen_1398, q_gen_1397) -> q_gen_1368
<a, cons>(q_gen_1398, q_gen_1442) -> q_gen_1368
<a, nil>() -> q_gen_1368
<b, cons>(q_gen_1398, q_gen_1397) -> q_gen_1368
<b, cons>(q_gen_1398, q_gen_1442) -> q_gen_1368
<b, nil>() -> q_gen_1368
<a, a>() -> q_gen_1369
<b, b>() -> q_gen_1369
<s, cons>(q_gen_1360, q_gen_1448) -> q_gen_1448
<z, cons>(q_gen_1398, q_gen_1397) -> q_gen_1448
<z, cons>(q_gen_1398, q_gen_1442) -> q_gen_1448
<s, cons, cons>(q_gen_1434, q_gen_1433, q_gen_1432, q_gen_1352) -> q_gen_1352
<s, cons, cons>(q_gen_1434, q_gen_1433, q_gen_1432, q_gen_1431) -> q_gen_1352
<s, cons, nil>(q_gen_1360, q_gen_1359) -> q_gen_1352
<s, nil, nil>(q_gen_1354) -> q_gen_1352
<z, cons, cons>(q_gen_1369, q_gen_1368, q_gen_1367, q_gen_1366) -> q_gen_1352
<z, nil, nil>() -> q_gen_1352
<s, cons, nil>(q_gen_1360, q_gen_1448) -> q_gen_1431
<z, cons, nil>(q_gen_1398, q_gen_1397) -> q_gen_1431
<s, cons, a>(q_gen_1360, q_gen_1448) -> q_gen_1432
<s, cons, b>(q_gen_1360, q_gen_1448) -> q_gen_1432
<z, cons, a>(q_gen_1398, q_gen_1397) -> q_gen_1432
<z, cons, b>(q_gen_1398, q_gen_1397) -> q_gen_1432
<z, cons, b>(q_gen_1398, q_gen_1442) -> q_gen_1432
<s, a, nil>(q_gen_1354) -> q_gen_1433
<s, b, nil>(q_gen_1354) -> q_gen_1433
<z, a, nil>() -> q_gen_1433
<z, b, cons>(q_gen_1398, q_gen_1397) -> q_gen_1433
<z, b, nil>() -> q_gen_1433
<s, a, a>(q_gen_1354) -> q_gen_1434
<s, a, b>(q_gen_1354) -> q_gen_1434
<s, b, a>(q_gen_1354) -> q_gen_1434
<s, b, b>(q_gen_1354) -> q_gen_1434
<z, a, a>() -> q_gen_1434
<z, a, b>() -> q_gen_1434
<z, b, a>() -> q_gen_1434
<z, b, b>() -> q_gen_1434
<s, cons, cons>(q_gen_1434, q_gen_1433, q_gen_1432, q_gen_1520) -> q_gen_1520
<z, cons, nil>(q_gen_1398, q_gen_1442) -> q_gen_1520
}

Datatype: <nat, eltlist, eltlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_1351, q_gen_1357, q_gen_1389},
Q_f={q_gen_1351},
Delta=
{
<s>(q_gen_1389) -> q_gen_1389
<z>() -> q_gen_1389
<cons, s>(q_gen_1357, q_gen_1351) -> q_gen_1351
<nil, z>() -> q_gen_1351
<a, s>(q_gen_1389) -> q_gen_1357
<a, z>() -> q_gen_1357
<b, s>(q_gen_1389) -> q_gen_1357
<b, z>() -> q_gen_1357
}

Datatype: <eltlist, nat>
Convolution form: complete
}}}
  ;  minus -> 
{{{
Q={q_gen_1348, q_gen_1349, q_gen_1350, q_gen_1362, q_gen_1373, q_gen_1378, q_gen_1380, q_gen_1386, q_gen_1416},
Q_f={q_gen_1348, q_gen_1349},
Delta=
{
<s>(q_gen_1380) -> q_gen_1362
<z>() -> q_gen_1362
<s>(q_gen_1362) -> q_gen_1380
<s, s>(q_gen_1350) -> q_gen_1350
<s, z>(q_gen_1380) -> q_gen_1350
<z, z>() -> q_gen_1350
<s, s>(q_gen_1386) -> q_gen_1386
<z, s>(q_gen_1362) -> q_gen_1386
<z, s>(q_gen_1380) -> q_gen_1386
<s, s>(q_gen_1416) -> q_gen_1416
<s, z>(q_gen_1362) -> q_gen_1416
<s, s, s>(q_gen_1373) -> q_gen_1348
<s, s, z>(q_gen_1386) -> q_gen_1348
<z, s, z>(q_gen_1380) -> q_gen_1348
<z, z, z>() -> q_gen_1348
<s, s, z>(q_gen_1350) -> q_gen_1349
<s, z, s>(q_gen_1350) -> q_gen_1349
<z, s, z>(q_gen_1362) -> q_gen_1349
<s, s, s>(q_gen_1349) -> q_gen_1373
<s, s, s>(q_gen_1378) -> q_gen_1373
<s, s, z>(q_gen_1416) -> q_gen_1373
<s, z, s>(q_gen_1416) -> q_gen_1373
<s, z, z>(q_gen_1362) -> q_gen_1373
<s, s, s>(q_gen_1348) -> q_gen_1378
<s, z, s>(q_gen_1386) -> q_gen_1378
<s, z, z>(q_gen_1380) -> q_gen_1378
}

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

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

Teacher's answer:
New clause system:
{
() -> drop([s(u), nil, nil]) -> 66  ;  () -> drop([z, l, l]) -> 67  ;  () -> length([nil, z]) -> 66  ;  () -> minus([s(u), z, s(u)]) -> 66  ;  () -> minus([z, y, z]) -> 66  ;  (drop([n, l1, _sga]) /\ length([_sga, _tga]) /\ length([l1, _uga]) /\ minus([_uga, n, _vga])) -> eq_nat([_tga, _vga]) -> 67  ;  (drop([u, x3, _ega])) -> drop([s(u), cons(x2, x3), _ega]) -> 70  ;  (length([ll, _jga])) -> length([cons(x, ll), s(_jga)]) -> 67  ;  (minus([u, x2, _nga])) -> minus([s(u), s(x2), _nga]) -> 70
}
Sat witness: Yes: ((drop([u, x3, _ega])) -> drop([s(u), cons(x2, x3), _ega]), {
_ega -> cons(b, nil)  ;  u -> z  ;  x2 -> b  ;  x3 -> cons(b, cons(b, nil))
})

-------------------------------------------
Step 90, which took 1.860920 s (model generation: 1.859883,  model checking: 0.001037):

Model:
|_
{
drop -> 
{{{
Q={q_gen_1352, q_gen_1354, q_gen_1359, q_gen_1360, q_gen_1366, q_gen_1367, q_gen_1368, q_gen_1369, q_gen_1397, q_gen_1398, q_gen_1431, q_gen_1432, q_gen_1433, q_gen_1434, q_gen_1448},
Q_f={q_gen_1352},
Delta=
{
<s>(q_gen_1354) -> q_gen_1354
<z>() -> q_gen_1354
<cons>(q_gen_1398, q_gen_1397) -> q_gen_1397
<nil>() -> q_gen_1397
<a>() -> q_gen_1398
<b>() -> q_gen_1398
<s, cons>(q_gen_1360, q_gen_1359) -> q_gen_1359
<s, cons>(q_gen_1360, q_gen_1448) -> q_gen_1359
<s, nil>(q_gen_1354) -> q_gen_1359
<z, nil>() -> q_gen_1359
<s, a>(q_gen_1354) -> q_gen_1360
<s, b>(q_gen_1354) -> q_gen_1360
<z, a>() -> q_gen_1360
<z, b>() -> q_gen_1360
<cons, cons>(q_gen_1369, q_gen_1368, q_gen_1367, q_gen_1366) -> q_gen_1366
<cons, nil>(q_gen_1398, q_gen_1397) -> q_gen_1366
<nil, nil>() -> q_gen_1366
<cons, a>(q_gen_1398, q_gen_1397) -> q_gen_1367
<cons, b>(q_gen_1398, q_gen_1397) -> q_gen_1367
<nil, a>() -> q_gen_1367
<nil, b>() -> q_gen_1367
<a, cons>(q_gen_1398, q_gen_1397) -> q_gen_1368
<a, nil>() -> q_gen_1368
<b, cons>(q_gen_1398, q_gen_1397) -> q_gen_1368
<b, nil>() -> q_gen_1368
<a, a>() -> q_gen_1369
<b, b>() -> q_gen_1369
<z, cons>(q_gen_1398, q_gen_1397) -> q_gen_1448
<s, cons, cons>(q_gen_1434, q_gen_1433, q_gen_1432, q_gen_1352) -> q_gen_1352
<s, cons, cons>(q_gen_1434, q_gen_1433, q_gen_1432, q_gen_1431) -> q_gen_1352
<s, cons, nil>(q_gen_1360, q_gen_1359) -> q_gen_1352
<s, nil, nil>(q_gen_1354) -> q_gen_1352
<z, cons, cons>(q_gen_1369, q_gen_1368, q_gen_1367, q_gen_1366) -> q_gen_1352
<z, nil, nil>() -> q_gen_1352
<s, cons, nil>(q_gen_1360, q_gen_1448) -> q_gen_1431
<z, cons, nil>(q_gen_1398, q_gen_1397) -> q_gen_1431
<s, cons, a>(q_gen_1360, q_gen_1448) -> q_gen_1432
<s, cons, b>(q_gen_1360, q_gen_1359) -> q_gen_1432
<s, cons, b>(q_gen_1360, q_gen_1448) -> q_gen_1432
<z, cons, a>(q_gen_1398, q_gen_1397) -> q_gen_1432
<z, cons, b>(q_gen_1398, q_gen_1397) -> q_gen_1432
<s, a, nil>(q_gen_1354) -> q_gen_1433
<s, b, nil>(q_gen_1354) -> q_gen_1433
<z, a, nil>() -> q_gen_1433
<z, b, cons>(q_gen_1398, q_gen_1397) -> q_gen_1433
<z, b, nil>() -> q_gen_1433
<s, a, a>(q_gen_1354) -> q_gen_1434
<s, a, b>(q_gen_1354) -> q_gen_1434
<s, b, a>(q_gen_1354) -> q_gen_1434
<s, b, b>(q_gen_1354) -> q_gen_1434
<z, a, a>() -> q_gen_1434
<z, a, b>() -> q_gen_1434
<z, b, a>() -> q_gen_1434
<z, b, b>() -> q_gen_1434
}

Datatype: <nat, eltlist, eltlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_1351, q_gen_1356, q_gen_1357, q_gen_1375, q_gen_1389, q_gen_1417},
Q_f={q_gen_1351, q_gen_1356},
Delta=
{
<s>(q_gen_1389) -> q_gen_1389
<z>() -> q_gen_1389
<cons, s>(q_gen_1375, q_gen_1351) -> q_gen_1351
<nil, z>() -> q_gen_1351
<cons, s>(q_gen_1357, q_gen_1351) -> q_gen_1356
<cons, s>(q_gen_1357, q_gen_1356) -> q_gen_1356
<a, s>(q_gen_1389) -> q_gen_1357
<b, z>() -> q_gen_1357
<a, z>() -> q_gen_1375
<b, s>(q_gen_1389) -> q_gen_1375
<cons, s>(q_gen_1375, q_gen_1356) -> q_gen_1417
<cons, s>(q_gen_1375, q_gen_1417) -> q_gen_1417
}

Datatype: <eltlist, nat>
Convolution form: complete
}}}
  ;  minus -> 
{{{
Q={q_gen_1348, q_gen_1350, q_gen_1362, q_gen_1363, q_gen_1364, q_gen_1373, q_gen_1378, q_gen_1386},
Q_f={q_gen_1348, q_gen_1363},
Delta=
{
<s>(q_gen_1362) -> q_gen_1362
<z>() -> q_gen_1362
<z, z>() -> q_gen_1350
<s, s>(q_gen_1350) -> q_gen_1364
<s, s>(q_gen_1364) -> q_gen_1364
<s, z>(q_gen_1362) -> q_gen_1364
<s, s>(q_gen_1386) -> q_gen_1386
<z, s>(q_gen_1362) -> q_gen_1386
<s, s, z>(q_gen_1350) -> q_gen_1348
<s, s, z>(q_gen_1386) -> q_gen_1348
<s, z, s>(q_gen_1350) -> q_gen_1348
<z, s, z>(q_gen_1362) -> q_gen_1348
<z, z, z>() -> q_gen_1348
<s, s, s>(q_gen_1363) -> q_gen_1363
<s, s, s>(q_gen_1373) -> q_gen_1363
<s, z, s>(q_gen_1364) -> q_gen_1363
<s, s, z>(q_gen_1364) -> q_gen_1373
<s, z, z>(q_gen_1362) -> q_gen_1373
<s, s, s>(q_gen_1348) -> q_gen_1378
<s, s, s>(q_gen_1378) -> q_gen_1378
<s, z, s>(q_gen_1386) -> q_gen_1378
}

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

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

Teacher's answer:
New clause system:
{
() -> drop([s(u), nil, nil]) -> 67  ;  () -> drop([z, l, l]) -> 67  ;  () -> length([nil, z]) -> 67  ;  () -> minus([s(u), z, s(u)]) -> 67  ;  () -> minus([z, y, z]) -> 67  ;  (drop([n, l1, _sga]) /\ length([_sga, _tga]) /\ length([l1, _uga]) /\ minus([_uga, n, _vga])) -> eq_nat([_tga, _vga]) -> 67  ;  (drop([u, x3, _ega])) -> drop([s(u), cons(x2, x3), _ega]) -> 70  ;  (length([ll, _jga])) -> length([cons(x, ll), s(_jga)]) -> 70  ;  (minus([u, x2, _nga])) -> minus([s(u), s(x2), _nga]) -> 70
}
Sat witness: Yes: ((length([ll, _jga])) -> length([cons(x, ll), s(_jga)]), {
_jga -> s(z)  ;  ll -> cons(b, nil)  ;  x -> b
})

Total time: 30.007865
Reason for stopping: DontKnow. Stopped because: timeout