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


Learning problem is:

env: {
elt -> {a, b}  ;  eltlist -> {cons, nil}  ;  nat -> {s, z}
}
definition:
{
(leq, P:
{() -> leq([z, s(nn2)])
() -> leq([z, z])
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)])
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2])
(leq([s(nn1), z])) -> BOT}
)
(prefix, P:
{() -> prefix([nil, y])
(prefix([zs, ys])) -> prefix([cons(y2, zs), cons(y2, ys)])
(prefix([cons(y2, zs), cons(y2, ys)])) -> prefix([zs, ys])
(prefix([cons(z, zs), cons(y2, ys)]) /\ not eq_elt([z, y2])) -> BOT
(prefix([cons(z, zs), nil])) -> BOT}
)
(count, F:
{() -> count([x, nil, z])
(count([x, t1, _jy])) -> count([x, cons(x, t1), s(_jy)])
(count([x, t1, _ky]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ky])}
(count([_ly, _my, _ny]) /\ count([_ly, _my, _oy])) -> eq_nat([_ny, _oy])
)
}

properties:
{(count([x, l1, _py]) /\ count([x, l2, _qy]) /\ prefix([l1, l2])) -> leq([_py, _qy])}


over-approximation: {count, prefix}
under-approximation: {leq}

Clause system for inference is:

{
() -> count([x, nil, z]) -> 0
() -> leq([z, s(nn2)]) -> 0
() -> leq([z, z]) -> 0
() -> prefix([nil, y]) -> 0
(count([x, l1, _py]) /\ count([x, l2, _qy]) /\ prefix([l1, l2])) -> leq([_py, _qy]) -> 0
(count([x, t1, _jy])) -> count([x, cons(x, t1), s(_jy)]) -> 0
(count([x, t1, _ky]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ky]) -> 0
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 0
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 0
(leq([s(nn1), z])) -> BOT -> 0
(prefix([zs, ys])) -> prefix([cons(y2, zs), cons(y2, ys)]) -> 0
(prefix([cons(y2, zs), cons(y2, ys)])) -> prefix([zs, ys]) -> 0
(prefix([cons(z, zs), cons(y2, ys)]) /\ not eq_elt([z, y2])) -> BOT -> 0
(prefix([cons(z, zs), nil])) -> BOT -> 0
}


Solving took 62.528458 seconds.
DontKnow. Stopped because: timeout
Working model:
|_
{
count -> 
{{{
Q={q_gen_6386, q_gen_6390, q_gen_6391, q_gen_6392, q_gen_6393, q_gen_6394, q_gen_6400, q_gen_6403, q_gen_6404, q_gen_6405, q_gen_6406, q_gen_6407, q_gen_6411, q_gen_6412, q_gen_6413, q_gen_6414, q_gen_6415, q_gen_6416, q_gen_6419, q_gen_6420, q_gen_6421, q_gen_6422, q_gen_6423, q_gen_6424, q_gen_6425, q_gen_6426, q_gen_6427, q_gen_6428, q_gen_6429, q_gen_6431, q_gen_6432, q_gen_6433, q_gen_6435, q_gen_6436, q_gen_6437, q_gen_6438, q_gen_6441, q_gen_6442, q_gen_6443, q_gen_6444, q_gen_6445, q_gen_6448, q_gen_6449, q_gen_6450, q_gen_6451, q_gen_6452, q_gen_6455, q_gen_6456, q_gen_6457, q_gen_6458, q_gen_6459, q_gen_6460, q_gen_6461, q_gen_6462, q_gen_6465, q_gen_6467, q_gen_6468, q_gen_6469, q_gen_6472, q_gen_6473, q_gen_6474, q_gen_6475, q_gen_6476, q_gen_6477, q_gen_6478, q_gen_6479, q_gen_6480, q_gen_6481, q_gen_6483, q_gen_6484, q_gen_6485, q_gen_6486, q_gen_6487, q_gen_6488, q_gen_6489, q_gen_6490, q_gen_6498, q_gen_6499, q_gen_6500, q_gen_6501, q_gen_6502, q_gen_6503, q_gen_6504, q_gen_6505, q_gen_6511, q_gen_6512, q_gen_6513, q_gen_6514, q_gen_6515, q_gen_6516, q_gen_6519, q_gen_6520, q_gen_6521, q_gen_6522, q_gen_6523, q_gen_6525, q_gen_6526, q_gen_6527, q_gen_6529, q_gen_6530, q_gen_6531, q_gen_6532, q_gen_6533, q_gen_6534, q_gen_6535, q_gen_6536, q_gen_6539, q_gen_6540, q_gen_6541, q_gen_6542, q_gen_6546, q_gen_6547, q_gen_6548, q_gen_6549, q_gen_6550, q_gen_6553, q_gen_6554, q_gen_6555, q_gen_6556, q_gen_6557, q_gen_6558, q_gen_6559, q_gen_6560, q_gen_6561, q_gen_6562, q_gen_6565, q_gen_6566},
Q_f={},
Delta=
{
<nil>() -> q_gen_6391
<a>() -> q_gen_6392
<b>() -> q_gen_6404
<cons>(q_gen_6404, q_gen_6391) -> q_gen_6412
<z>() -> q_gen_6415
<cons>(q_gen_6392, q_gen_6391) -> q_gen_6420
<cons>(q_gen_6404, q_gen_6420) -> q_gen_6423
<s>(q_gen_6415) -> q_gen_6425
<cons>(q_gen_6404, q_gen_6412) -> q_gen_6436
<cons>(q_gen_6392, q_gen_6420) -> q_gen_6444
<cons>(q_gen_6392, q_gen_6412) -> q_gen_6449
<cons>(q_gen_6392, q_gen_6423) -> q_gen_6456
<cons>(q_gen_6392, q_gen_6456) -> q_gen_6459
<cons>(q_gen_6392, q_gen_6444) -> q_gen_6481
<cons>(q_gen_6404, q_gen_6444) -> q_gen_6484
<cons>(q_gen_6392, q_gen_6488) -> q_gen_6487
<cons>(q_gen_6392, q_gen_6489) -> q_gen_6488
<cons>(q_gen_6392, q_gen_6481) -> q_gen_6489
<cons>(q_gen_6392, q_gen_6436) -> q_gen_6499
<cons>(q_gen_6392, q_gen_6499) -> q_gen_6501
<cons>(q_gen_6404, q_gen_6459) -> q_gen_6504
<cons>(q_gen_6404, q_gen_6449) -> q_gen_6513
<cons>(q_gen_6404, q_gen_6456) -> q_gen_6522
<cons>(q_gen_6392, q_gen_6449) -> q_gen_6530
<cons>(q_gen_6404, q_gen_6530) -> q_gen_6532
<cons>(q_gen_6404, q_gen_6513) -> q_gen_6534
<cons>(q_gen_6404, q_gen_6423) -> q_gen_6549
<cons>(q_gen_6404, q_gen_6499) -> q_gen_6560
<b, z>() -> q_gen_6394
<a, z>() -> q_gen_6406
<b, s>(q_gen_6415) -> q_gen_6414
<b, s>(q_gen_6425) -> q_gen_6424
<a, s>(q_gen_6415) -> q_gen_6460
<a, s>(q_gen_6425) -> q_gen_6475
<b, nil, z>() -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6391) -> q_gen_6390
<b, cons, s>(q_gen_6394, q_gen_6391) -> q_gen_6393
<a, nil, z>() -> q_gen_6400
<a, cons, z>(q_gen_6404, q_gen_6391) -> q_gen_6403
<a, cons, s>(q_gen_6406, q_gen_6391) -> q_gen_6405
<a, cons, s>(q_gen_6394, q_gen_6391) -> q_gen_6407
<a, cons, z>(q_gen_6404, q_gen_6412) -> q_gen_6411
<b, cons, s>(q_gen_6414, q_gen_6412) -> q_gen_6413
<b, cons, z>(q_gen_6404, q_gen_6391) -> q_gen_6416
<b, cons, z>(q_gen_6392, q_gen_6420) -> q_gen_6419
<b, cons, s>(q_gen_6414, q_gen_6420) -> q_gen_6421
<b, cons, s>(q_gen_6424, q_gen_6423) -> q_gen_6422
<b, cons, s>(q_gen_6406, q_gen_6391) -> q_gen_6426
<b, cons, s>(q_gen_6406, q_gen_6412) -> q_gen_6427
<b, cons, s>(q_gen_6394, q_gen_6420) -> q_gen_6428
<a, cons, s>(q_gen_6414, q_gen_6391) -> q_gen_6429
<a, cons, s>(q_gen_6394, q_gen_6420) -> q_gen_6431
<a, cons, z>(q_gen_6404, q_gen_6420) -> q_gen_6432
<a, cons, s>(q_gen_6406, q_gen_6423) -> q_gen_6433
<a, cons, z>(q_gen_6404, q_gen_6436) -> q_gen_6435
<a, cons, s>(q_gen_6406, q_gen_6412) -> q_gen_6437
<b, cons, z>(q_gen_6392, q_gen_6423) -> q_gen_6438
<b, cons, s>(q_gen_6394, q_gen_6412) -> q_gen_6441
<b, cons, s>(q_gen_6406, q_gen_6436) -> q_gen_6442
<b, cons, s>(q_gen_6394, q_gen_6444) -> q_gen_6443
<b, cons, s>(q_gen_6414, q_gen_6391) -> q_gen_6445
<b, cons, s>(q_gen_6406, q_gen_6449) -> q_gen_6448
<b, cons, s>(q_gen_6406, q_gen_6420) -> q_gen_6450
<b, cons, s>(q_gen_6414, q_gen_6444) -> q_gen_6451
<a, cons, z>(q_gen_6404, q_gen_6444) -> q_gen_6452
<a, cons, s>(q_gen_6394, q_gen_6456) -> q_gen_6455
<a, cons, s>(q_gen_6406, q_gen_6456) -> q_gen_6457
<a, cons, s>(q_gen_6460, q_gen_6459) -> q_gen_6458
<b, cons, s>(q_gen_6460, q_gen_6391) -> q_gen_6461
<a, cons, s>(q_gen_6460, q_gen_6420) -> q_gen_6462
<b, cons, z>(q_gen_6392, q_gen_6436) -> q_gen_6465
<a, cons, s>(q_gen_6460, q_gen_6412) -> q_gen_6467
<a, cons, s>(q_gen_6414, q_gen_6449) -> q_gen_6468
<a, cons, z>(q_gen_6404, q_gen_6449) -> q_gen_6469
<b, cons, z>(q_gen_6392, q_gen_6444) -> q_gen_6472
<a, cons, s>(q_gen_6414, q_gen_6420) -> q_gen_6473
<a, cons, s>(q_gen_6475, q_gen_6423) -> q_gen_6474
<a, cons, s>(q_gen_6414, q_gen_6444) -> q_gen_6476
<a, cons, s>(q_gen_6460, q_gen_6449) -> q_gen_6477
<a, cons, s>(q_gen_6460, q_gen_6391) -> q_gen_6478
<a, cons, s>(q_gen_6460, q_gen_6444) -> q_gen_6479
<a, cons, s>(q_gen_6475, q_gen_6481) -> q_gen_6480
<a, cons, s>(q_gen_6414, q_gen_6484) -> q_gen_6483
<b, cons, s>(q_gen_6414, q_gen_6484) -> q_gen_6485
<b, cons, z>(q_gen_6392, q_gen_6487) -> q_gen_6486
<b, cons, s>(q_gen_6406, q_gen_6444) -> q_gen_6490
<b, cons, s>(q_gen_6406, q_gen_6499) -> q_gen_6498
<b, cons, s>(q_gen_6406, q_gen_6501) -> q_gen_6500
<a, cons, s>(q_gen_6475, q_gen_6444) -> q_gen_6502
<a, cons, z>(q_gen_6404, q_gen_6504) -> q_gen_6503
<a, cons, s>(q_gen_6394, q_gen_6484) -> q_gen_6505
<a, cons, s>(q_gen_6394, q_gen_6449) -> q_gen_6511
<a, cons, s>(q_gen_6394, q_gen_6513) -> q_gen_6512
<a, cons, s>(q_gen_6460, q_gen_6423) -> q_gen_6514
<b, cons, s>(q_gen_6406, q_gen_6481) -> q_gen_6515
<b, cons, z>(q_gen_6392, q_gen_6481) -> q_gen_6516
<b, cons, s>(q_gen_6394, q_gen_6481) -> q_gen_6519
<b, cons, s>(q_gen_6394, q_gen_6456) -> q_gen_6520
<b, cons, s>(q_gen_6406, q_gen_6522) -> q_gen_6521
<b, cons, s>(q_gen_6414, q_gen_6499) -> q_gen_6523
<b, cons, z>(q_gen_6392, q_gen_6456) -> q_gen_6525
<b, cons, z>(q_gen_6392, q_gen_6459) -> q_gen_6526
<b, cons, s>(q_gen_6414, q_gen_6481) -> q_gen_6527
<b, cons, s>(q_gen_6414, q_gen_6530) -> q_gen_6529
<b, cons, s>(q_gen_6424, q_gen_6532) -> q_gen_6531
<a, cons, s>(q_gen_6394, q_gen_6534) -> q_gen_6533
<a, cons, s>(q_gen_6475, q_gen_6484) -> q_gen_6535
<a, cons, s>(q_gen_6394, q_gen_6481) -> q_gen_6536
<a, cons, s>(q_gen_6394, q_gen_6423) -> q_gen_6539
<b, cons, s>(q_gen_6414, q_gen_6459) -> q_gen_6540
<b, cons, s>(q_gen_6424, q_gen_6504) -> q_gen_6541
<a, cons, z>(q_gen_6404, q_gen_6530) -> q_gen_6542
<b, cons, s>(q_gen_6460, q_gen_6436) -> q_gen_6546
<b, cons, s>(q_gen_6414, q_gen_6423) -> q_gen_6547
<b, cons, s>(q_gen_6460, q_gen_6549) -> q_gen_6548
<a, cons, s>(q_gen_6394, q_gen_6530) -> q_gen_6550
<a, cons, s>(q_gen_6406, q_gen_6436) -> q_gen_6553
<a, cons, z>(q_gen_6404, q_gen_6423) -> q_gen_6554
<a, cons, z>(q_gen_6404, q_gen_6549) -> q_gen_6555
<a, cons, s>(q_gen_6460, q_gen_6549) -> q_gen_6556
<b, cons, s>(q_gen_6460, q_gen_6444) -> q_gen_6557
<a, cons, s>(q_gen_6394, q_gen_6499) -> q_gen_6558
<a, cons, s>(q_gen_6394, q_gen_6560) -> q_gen_6559
<a, cons, s>(q_gen_6475, q_gen_6456) -> q_gen_6561
<a, cons, z>(q_gen_6404, q_gen_6499) -> q_gen_6562
<b, cons, s>(q_gen_6414, q_gen_6449) -> q_gen_6565
<b, cons, s>(q_gen_6460, q_gen_6513) -> q_gen_6566
}

Datatype: <elt, eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_6383, q_gen_6384, q_gen_6385, q_gen_6389, q_gen_6398, q_gen_6399, q_gen_6408, q_gen_6430, q_gen_6447, q_gen_6463, q_gen_6464},
Q_f={},
Delta=
{
<z>() -> q_gen_6385
<s>(q_gen_6385) -> q_gen_6399
<s>(q_gen_6399) -> q_gen_6464
<z, z>() -> q_gen_6383
<z, s>(q_gen_6385) -> q_gen_6384
<s, s>(q_gen_6383) -> q_gen_6389
<z, s>(q_gen_6399) -> q_gen_6398
<s, z>(q_gen_6385) -> q_gen_6408
<s, z>(q_gen_6399) -> q_gen_6430
<s, s>(q_gen_6408) -> q_gen_6447
<z, s>(q_gen_6464) -> q_gen_6463
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  prefix -> 
{{{
Q={q_gen_6382, q_gen_6387, q_gen_6388, q_gen_6395, q_gen_6396, q_gen_6397, q_gen_6401, q_gen_6402, q_gen_6409, q_gen_6410, q_gen_6417, q_gen_6418, q_gen_6434, q_gen_6439, q_gen_6440, q_gen_6446, q_gen_6453, q_gen_6454, q_gen_6466, q_gen_6470, q_gen_6471, q_gen_6482, q_gen_6491, q_gen_6492, q_gen_6493, q_gen_6494, q_gen_6495, q_gen_6496, q_gen_6497, q_gen_6506, q_gen_6507, q_gen_6508, q_gen_6509, q_gen_6510, q_gen_6517, q_gen_6518, q_gen_6524, q_gen_6528, q_gen_6537, q_gen_6538, q_gen_6543, q_gen_6544, q_gen_6545, q_gen_6551, q_gen_6552, q_gen_6563, q_gen_6564},
Q_f={},
Delta=
{
<nil>() -> q_gen_6396
<b>() -> q_gen_6397
<a>() -> q_gen_6410
<cons>(q_gen_6397, q_gen_6396) -> q_gen_6418
<cons>(q_gen_6410, q_gen_6496) -> q_gen_6495
<cons>(q_gen_6410, q_gen_6497) -> q_gen_6496
<cons>(q_gen_6410, q_gen_6396) -> q_gen_6497
<nil, nil>() -> q_gen_6382
<cons, cons>(q_gen_6388, q_gen_6382) -> q_gen_6387
<b, b>() -> q_gen_6388
<nil, cons>(q_gen_6397, q_gen_6396) -> q_gen_6395
<cons, cons>(q_gen_6402, q_gen_6382) -> q_gen_6401
<a, a>() -> q_gen_6402
<nil, cons>(q_gen_6410, q_gen_6396) -> q_gen_6409
<nil, cons>(q_gen_6397, q_gen_6418) -> q_gen_6417
<cons, cons>(q_gen_6388, q_gen_6401) -> q_gen_6434
<cons, cons>(q_gen_6402, q_gen_6440) -> q_gen_6439
<cons, cons>(q_gen_6388, q_gen_6409) -> q_gen_6440
<cons, cons>(q_gen_6388, q_gen_6395) -> q_gen_6446
<cons, cons>(q_gen_6388, q_gen_6454) -> q_gen_6453
<cons, cons>(q_gen_6402, q_gen_6409) -> q_gen_6454
<cons, cons>(q_gen_6402, q_gen_6446) -> q_gen_6466
<cons, cons>(q_gen_6388, q_gen_6471) -> q_gen_6470
<cons, cons>(q_gen_6402, q_gen_6395) -> q_gen_6471
<cons, cons>(q_gen_6402, q_gen_6401) -> q_gen_6482
<cons, cons>(q_gen_6402, q_gen_6492) -> q_gen_6491
<cons, cons>(q_gen_6402, q_gen_6493) -> q_gen_6492
<cons, cons>(q_gen_6402, q_gen_6494) -> q_gen_6493
<nil, cons>(q_gen_6410, q_gen_6495) -> q_gen_6494
<cons, cons>(q_gen_6388, q_gen_6507) -> q_gen_6506
<cons, cons>(q_gen_6388, q_gen_6508) -> q_gen_6507
<cons, cons>(q_gen_6402, q_gen_6509) -> q_gen_6508
<cons, cons>(q_gen_6402, q_gen_6510) -> q_gen_6509
<nil, cons>(q_gen_6397, q_gen_6497) -> q_gen_6510
<cons, cons>(q_gen_6402, q_gen_6518) -> q_gen_6517
<cons, cons>(q_gen_6402, q_gen_6482) -> q_gen_6518
<cons, cons>(q_gen_6388, q_gen_6482) -> q_gen_6524
<cons, cons>(q_gen_6388, q_gen_6518) -> q_gen_6528
<cons, cons>(q_gen_6388, q_gen_6538) -> q_gen_6537
<cons, cons>(q_gen_6402, q_gen_6454) -> q_gen_6538
<cons, cons>(q_gen_6388, q_gen_6544) -> q_gen_6543
<cons, cons>(q_gen_6402, q_gen_6545) -> q_gen_6544
<nil, cons>(q_gen_6410, q_gen_6418) -> q_gen_6545
<cons, cons>(q_gen_6388, q_gen_6552) -> q_gen_6551
<cons, cons>(q_gen_6402, q_gen_6471) -> q_gen_6552
<cons, cons>(q_gen_6388, q_gen_6564) -> q_gen_6563
<cons, cons>(q_gen_6402, q_gen_6417) -> q_gen_6564
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

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

-------------------
STEPS:
-------------------------------------------
Step 0, which took 0.010240 s (model generation: 0.009491,  model checking: 0.000749):

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

}

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

}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  prefix -> 
{{{
Q={},
Q_f={},
Delta=
{

}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 0
() -> leq([z, s(nn2)]) -> 0
() -> leq([z, z]) -> 0
() -> prefix([nil, y]) -> 3
(count([x, l1, _py]) /\ count([x, l2, _qy]) /\ prefix([l1, l2])) -> leq([_py, _qy]) -> 1
(count([x, t1, _jy])) -> count([x, cons(x, t1), s(_jy)]) -> 1
(count([x, t1, _ky]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ky]) -> 1
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 1
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 1
(leq([s(nn1), z])) -> BOT -> 1
(prefix([zs, ys])) -> prefix([cons(y2, zs), cons(y2, ys)]) -> 1
(prefix([cons(y2, zs), cons(y2, ys)])) -> prefix([zs, ys]) -> 1
(prefix([cons(z, zs), cons(y2, ys)]) /\ not eq_elt([z, y2])) -> BOT -> 1
(prefix([cons(z, zs), nil])) -> BOT -> 1
}
Sat witness: Found: (() -> prefix([nil, y]), {
y -> nil
})

-------------------------------------------
Step 1, which took 0.015922 s (model generation: 0.015862,  model checking: 0.000060):

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

}

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

}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  prefix -> 
{{{
Q={q_gen_6382},
Q_f={q_gen_6382},
Delta=
{
<nil, nil>() -> q_gen_6382
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 0
() -> leq([z, s(nn2)]) -> 0
() -> leq([z, z]) -> 3
() -> prefix([nil, y]) -> 3
(count([x, l1, _py]) /\ count([x, l2, _qy]) /\ prefix([l1, l2])) -> leq([_py, _qy]) -> 1
(count([x, t1, _jy])) -> count([x, cons(x, t1), s(_jy)]) -> 1
(count([x, t1, _ky]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ky]) -> 1
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 1
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 1
(leq([s(nn1), z])) -> BOT -> 1
(prefix([zs, ys])) -> prefix([cons(y2, zs), cons(y2, ys)]) -> 1
(prefix([cons(y2, zs), cons(y2, ys)])) -> prefix([zs, ys]) -> 1
(prefix([cons(z, zs), cons(y2, ys)]) /\ not eq_elt([z, y2])) -> BOT -> 1
(prefix([cons(z, zs), nil])) -> BOT -> 1
}
Sat witness: Found: (() -> leq([z, z]), {

})

-------------------------------------------
Step 2, which took 0.018690 s (model generation: 0.018552,  model checking: 0.000138):

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

}

Datatype: <elt, eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_6383},
Q_f={q_gen_6383},
Delta=
{
<z, z>() -> q_gen_6383
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  prefix -> 
{{{
Q={q_gen_6382},
Q_f={q_gen_6382},
Delta=
{
<nil, nil>() -> q_gen_6382
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 0
() -> leq([z, s(nn2)]) -> 3
() -> leq([z, z]) -> 3
() -> prefix([nil, y]) -> 3
(count([x, l1, _py]) /\ count([x, l2, _qy]) /\ prefix([l1, l2])) -> leq([_py, _qy]) -> 1
(count([x, t1, _jy])) -> count([x, cons(x, t1), s(_jy)]) -> 1
(count([x, t1, _ky]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ky]) -> 1
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 1
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 1
(leq([s(nn1), z])) -> BOT -> 1
(prefix([zs, ys])) -> prefix([cons(y2, zs), cons(y2, ys)]) -> 1
(prefix([cons(y2, zs), cons(y2, ys)])) -> prefix([zs, ys]) -> 1
(prefix([cons(z, zs), cons(y2, ys)]) /\ not eq_elt([z, y2])) -> BOT -> 1
(prefix([cons(z, zs), nil])) -> BOT -> 1
}
Sat witness: Found: (() -> leq([z, s(nn2)]), {
nn2 -> z
})

-------------------------------------------
Step 3, which took 0.018359 s (model generation: 0.018240,  model checking: 0.000119):

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

}

Datatype: <elt, eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_6383, q_gen_6385},
Q_f={q_gen_6383},
Delta=
{
<z>() -> q_gen_6385
<z, s>(q_gen_6385) -> q_gen_6383
<z, z>() -> q_gen_6383
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  prefix -> 
{{{
Q={q_gen_6382},
Q_f={q_gen_6382},
Delta=
{
<nil, nil>() -> q_gen_6382
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 3
() -> leq([z, s(nn2)]) -> 3
() -> leq([z, z]) -> 3
() -> prefix([nil, y]) -> 3
(count([x, l1, _py]) /\ count([x, l2, _qy]) /\ prefix([l1, l2])) -> leq([_py, _qy]) -> 1
(count([x, t1, _jy])) -> count([x, cons(x, t1), s(_jy)]) -> 1
(count([x, t1, _ky]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ky]) -> 1
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 1
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 1
(leq([s(nn1), z])) -> BOT -> 1
(prefix([zs, ys])) -> prefix([cons(y2, zs), cons(y2, ys)]) -> 1
(prefix([cons(y2, zs), cons(y2, ys)])) -> prefix([zs, ys]) -> 1
(prefix([cons(z, zs), cons(y2, ys)]) /\ not eq_elt([z, y2])) -> BOT -> 1
(prefix([cons(z, zs), nil])) -> BOT -> 1
}
Sat witness: Found: (() -> count([x, nil, z]), {
x -> b
})

-------------------------------------------
Step 4, which took 0.012491 s (model generation: 0.012291,  model checking: 0.000200):

Model:
|_
{
count -> 
{{{
Q={q_gen_6386},
Q_f={q_gen_6386},
Delta=
{
<b, nil, z>() -> q_gen_6386
}

Datatype: <elt, eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_6383, q_gen_6385},
Q_f={q_gen_6383},
Delta=
{
<z>() -> q_gen_6385
<z, s>(q_gen_6385) -> q_gen_6383
<z, z>() -> q_gen_6383
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  prefix -> 
{{{
Q={q_gen_6382},
Q_f={q_gen_6382},
Delta=
{
<nil, nil>() -> q_gen_6382
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 3
() -> leq([z, s(nn2)]) -> 3
() -> leq([z, z]) -> 3
() -> prefix([nil, y]) -> 3
(count([x, l1, _py]) /\ count([x, l2, _qy]) /\ prefix([l1, l2])) -> leq([_py, _qy]) -> 1
(count([x, t1, _jy])) -> count([x, cons(x, t1), s(_jy)]) -> 1
(count([x, t1, _ky]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ky]) -> 1
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 1
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 1
(leq([s(nn1), z])) -> BOT -> 1
(prefix([zs, ys])) -> prefix([cons(y2, zs), cons(y2, ys)]) -> 4
(prefix([cons(y2, zs), cons(y2, ys)])) -> prefix([zs, ys]) -> 2
(prefix([cons(z, zs), cons(y2, ys)]) /\ not eq_elt([z, y2])) -> BOT -> 2
(prefix([cons(z, zs), nil])) -> BOT -> 2
}
Sat witness: Found: ((prefix([zs, ys])) -> prefix([cons(y2, zs), cons(y2, ys)]), {
y2 -> b  ;  ys -> nil  ;  zs -> nil
})

-------------------------------------------
Step 5, which took 0.014732 s (model generation: 0.014583,  model checking: 0.000149):

Model:
|_
{
count -> 
{{{
Q={q_gen_6386},
Q_f={q_gen_6386},
Delta=
{
<b, nil, z>() -> q_gen_6386
}

Datatype: <elt, eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_6383, q_gen_6385},
Q_f={q_gen_6383},
Delta=
{
<z>() -> q_gen_6385
<z, s>(q_gen_6385) -> q_gen_6383
<z, z>() -> q_gen_6383
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  prefix -> 
{{{
Q={q_gen_6382, q_gen_6388},
Q_f={q_gen_6382},
Delta=
{
<cons, cons>(q_gen_6388, q_gen_6382) -> q_gen_6382
<nil, nil>() -> q_gen_6382
<b, b>() -> q_gen_6388
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 3
() -> leq([z, s(nn2)]) -> 3
() -> leq([z, z]) -> 3
() -> prefix([nil, y]) -> 3
(count([x, l1, _py]) /\ count([x, l2, _qy]) /\ prefix([l1, l2])) -> leq([_py, _qy]) -> 1
(count([x, t1, _jy])) -> count([x, cons(x, t1), s(_jy)]) -> 1
(count([x, t1, _ky]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ky]) -> 1
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 4
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 2
(leq([s(nn1), z])) -> BOT -> 2
(prefix([zs, ys])) -> prefix([cons(y2, zs), cons(y2, ys)]) -> 4
(prefix([cons(y2, zs), cons(y2, ys)])) -> prefix([zs, ys]) -> 2
(prefix([cons(z, zs), cons(y2, ys)]) /\ not eq_elt([z, y2])) -> BOT -> 2
(prefix([cons(z, zs), nil])) -> BOT -> 2
}
Sat witness: Found: ((leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]), {
nn1 -> z  ;  nn2 -> z
})

-------------------------------------------
Step 6, which took 0.020583 s (model generation: 0.020423,  model checking: 0.000160):

Model:
|_
{
count -> 
{{{
Q={q_gen_6386},
Q_f={q_gen_6386},
Delta=
{
<b, nil, z>() -> q_gen_6386
}

Datatype: <elt, eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_6383, q_gen_6385},
Q_f={q_gen_6383},
Delta=
{
<z>() -> q_gen_6385
<s, s>(q_gen_6383) -> q_gen_6383
<z, s>(q_gen_6385) -> q_gen_6383
<z, z>() -> q_gen_6383
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  prefix -> 
{{{
Q={q_gen_6382, q_gen_6388},
Q_f={q_gen_6382},
Delta=
{
<cons, cons>(q_gen_6388, q_gen_6382) -> q_gen_6382
<nil, nil>() -> q_gen_6382
<b, b>() -> q_gen_6388
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 3
() -> leq([z, s(nn2)]) -> 3
() -> leq([z, z]) -> 3
() -> prefix([nil, y]) -> 3
(count([x, l1, _py]) /\ count([x, l2, _qy]) /\ prefix([l1, l2])) -> leq([_py, _qy]) -> 1
(count([x, t1, _jy])) -> count([x, cons(x, t1), s(_jy)]) -> 1
(count([x, t1, _ky]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ky]) -> 4
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 4
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 2
(leq([s(nn1), z])) -> BOT -> 2
(prefix([zs, ys])) -> prefix([cons(y2, zs), cons(y2, ys)]) -> 4
(prefix([cons(y2, zs), cons(y2, ys)])) -> prefix([zs, ys]) -> 2
(prefix([cons(z, zs), cons(y2, ys)]) /\ not eq_elt([z, y2])) -> BOT -> 2
(prefix([cons(z, zs), nil])) -> BOT -> 2
}
Sat witness: Found: ((count([x, t1, _ky]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ky]), {
_ky -> z  ;  h1 -> a  ;  t1 -> nil  ;  x -> b
})

-------------------------------------------
Step 7, which took 0.016174 s (model generation: 0.015901,  model checking: 0.000273):

Model:
|_
{
count -> 
{{{
Q={q_gen_6386, q_gen_6391, q_gen_6392},
Q_f={q_gen_6386},
Delta=
{
<nil>() -> q_gen_6391
<a>() -> q_gen_6392
<b, cons, z>(q_gen_6392, q_gen_6391) -> q_gen_6386
<b, nil, z>() -> q_gen_6386
}

Datatype: <elt, eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_6383, q_gen_6385},
Q_f={q_gen_6383},
Delta=
{
<z>() -> q_gen_6385
<s, s>(q_gen_6383) -> q_gen_6383
<z, s>(q_gen_6385) -> q_gen_6383
<z, z>() -> q_gen_6383
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  prefix -> 
{{{
Q={q_gen_6382, q_gen_6388},
Q_f={q_gen_6382},
Delta=
{
<cons, cons>(q_gen_6388, q_gen_6382) -> q_gen_6382
<nil, nil>() -> q_gen_6382
<b, b>() -> q_gen_6388
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 3
() -> leq([z, s(nn2)]) -> 3
() -> leq([z, z]) -> 3
() -> prefix([nil, y]) -> 3
(count([x, l1, _py]) /\ count([x, l2, _qy]) /\ prefix([l1, l2])) -> leq([_py, _qy]) -> 1
(count([x, t1, _jy])) -> count([x, cons(x, t1), s(_jy)]) -> 4
(count([x, t1, _ky]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ky]) -> 4
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 4
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 2
(leq([s(nn1), z])) -> BOT -> 2
(prefix([zs, ys])) -> prefix([cons(y2, zs), cons(y2, ys)]) -> 4
(prefix([cons(y2, zs), cons(y2, ys)])) -> prefix([zs, ys]) -> 2
(prefix([cons(z, zs), cons(y2, ys)]) /\ not eq_elt([z, y2])) -> BOT -> 2
(prefix([cons(z, zs), nil])) -> BOT -> 2
}
Sat witness: Found: ((count([x, t1, _jy])) -> count([x, cons(x, t1), s(_jy)]), {
_jy -> z  ;  t1 -> nil  ;  x -> b
})

-------------------------------------------
Step 8, which took 0.022518 s (model generation: 0.020998,  model checking: 0.001520):

Model:
|_
{
count -> 
{{{
Q={q_gen_6386, q_gen_6391, q_gen_6392, q_gen_6394},
Q_f={q_gen_6386},
Delta=
{
<nil>() -> q_gen_6391
<a>() -> q_gen_6392
<b, z>() -> q_gen_6394
<b, cons, s>(q_gen_6394, q_gen_6391) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6391) -> q_gen_6386
<b, nil, z>() -> q_gen_6386
}

Datatype: <elt, eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_6383, q_gen_6385},
Q_f={q_gen_6383},
Delta=
{
<z>() -> q_gen_6385
<s, s>(q_gen_6383) -> q_gen_6383
<z, s>(q_gen_6385) -> q_gen_6383
<z, z>() -> q_gen_6383
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  prefix -> 
{{{
Q={q_gen_6382, q_gen_6388},
Q_f={q_gen_6382},
Delta=
{
<cons, cons>(q_gen_6388, q_gen_6382) -> q_gen_6382
<nil, nil>() -> q_gen_6382
<b, b>() -> q_gen_6388
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 3
() -> leq([z, s(nn2)]) -> 3
() -> leq([z, z]) -> 3
() -> prefix([nil, y]) -> 6
(count([x, l1, _py]) /\ count([x, l2, _qy]) /\ prefix([l1, l2])) -> leq([_py, _qy]) -> 2
(count([x, t1, _jy])) -> count([x, cons(x, t1), s(_jy)]) -> 4
(count([x, t1, _ky]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ky]) -> 4
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 4
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 3
(leq([s(nn1), z])) -> BOT -> 3
(prefix([zs, ys])) -> prefix([cons(y2, zs), cons(y2, ys)]) -> 4
(prefix([cons(y2, zs), cons(y2, ys)])) -> prefix([zs, ys]) -> 3
(prefix([cons(z, zs), cons(y2, ys)]) /\ not eq_elt([z, y2])) -> BOT -> 3
(prefix([cons(z, zs), nil])) -> BOT -> 3
}
Sat witness: Found: (() -> prefix([nil, y]), {
y -> cons(b, nil)
})

-------------------------------------------
Step 9, which took 0.021427 s (model generation: 0.019650,  model checking: 0.001777):

Model:
|_
{
count -> 
{{{
Q={q_gen_6386, q_gen_6391, q_gen_6392, q_gen_6394},
Q_f={q_gen_6386},
Delta=
{
<nil>() -> q_gen_6391
<a>() -> q_gen_6392
<b, z>() -> q_gen_6394
<b, cons, s>(q_gen_6394, q_gen_6391) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6391) -> q_gen_6386
<b, nil, z>() -> q_gen_6386
}

Datatype: <elt, eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_6383, q_gen_6385},
Q_f={q_gen_6383},
Delta=
{
<z>() -> q_gen_6385
<s, s>(q_gen_6383) -> q_gen_6383
<z, s>(q_gen_6385) -> q_gen_6383
<z, z>() -> q_gen_6383
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  prefix -> 
{{{
Q={q_gen_6382, q_gen_6388, q_gen_6396, q_gen_6397},
Q_f={q_gen_6382},
Delta=
{
<nil>() -> q_gen_6396
<b>() -> q_gen_6397
<cons, cons>(q_gen_6388, q_gen_6382) -> q_gen_6382
<nil, cons>(q_gen_6397, q_gen_6396) -> q_gen_6382
<nil, nil>() -> q_gen_6382
<b, b>() -> q_gen_6388
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 3
() -> leq([z, s(nn2)]) -> 6
() -> leq([z, z]) -> 4
() -> prefix([nil, y]) -> 6
(count([x, l1, _py]) /\ count([x, l2, _qy]) /\ prefix([l1, l2])) -> leq([_py, _qy]) -> 3
(count([x, t1, _jy])) -> count([x, cons(x, t1), s(_jy)]) -> 4
(count([x, t1, _ky]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ky]) -> 4
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 4
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 4
(leq([s(nn1), z])) -> BOT -> 4
(prefix([zs, ys])) -> prefix([cons(y2, zs), cons(y2, ys)]) -> 4
(prefix([cons(y2, zs), cons(y2, ys)])) -> prefix([zs, ys]) -> 4
(prefix([cons(z, zs), cons(y2, ys)]) /\ not eq_elt([z, y2])) -> BOT -> 4
(prefix([cons(z, zs), nil])) -> BOT -> 4
}
Sat witness: Found: (() -> leq([z, s(nn2)]), {
nn2 -> s(z)
})

-------------------------------------------
Step 10, which took 0.018295 s (model generation: 0.017933,  model checking: 0.000362):

Model:
|_
{
count -> 
{{{
Q={q_gen_6386, q_gen_6391, q_gen_6392, q_gen_6394},
Q_f={q_gen_6386},
Delta=
{
<nil>() -> q_gen_6391
<a>() -> q_gen_6392
<b, z>() -> q_gen_6394
<b, cons, s>(q_gen_6394, q_gen_6391) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6391) -> q_gen_6386
<b, nil, z>() -> q_gen_6386
}

Datatype: <elt, eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_6383, q_gen_6385},
Q_f={q_gen_6383},
Delta=
{
<s>(q_gen_6385) -> q_gen_6385
<z>() -> q_gen_6385
<s, s>(q_gen_6383) -> q_gen_6383
<z, s>(q_gen_6385) -> q_gen_6383
<z, z>() -> q_gen_6383
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  prefix -> 
{{{
Q={q_gen_6382, q_gen_6388, q_gen_6396, q_gen_6397},
Q_f={q_gen_6382},
Delta=
{
<nil>() -> q_gen_6396
<b>() -> q_gen_6397
<cons, cons>(q_gen_6388, q_gen_6382) -> q_gen_6382
<nil, cons>(q_gen_6397, q_gen_6396) -> q_gen_6382
<nil, nil>() -> q_gen_6382
<b, b>() -> q_gen_6388
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 6
() -> leq([z, s(nn2)]) -> 6
() -> leq([z, z]) -> 4
() -> prefix([nil, y]) -> 6
(count([x, l1, _py]) /\ count([x, l2, _qy]) /\ prefix([l1, l2])) -> leq([_py, _qy]) -> 4
(count([x, t1, _jy])) -> count([x, cons(x, t1), s(_jy)]) -> 4
(count([x, t1, _ky]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ky]) -> 4
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 4
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 4
(leq([s(nn1), z])) -> BOT -> 4
(prefix([zs, ys])) -> prefix([cons(y2, zs), cons(y2, ys)]) -> 4
(prefix([cons(y2, zs), cons(y2, ys)])) -> prefix([zs, ys]) -> 4
(prefix([cons(z, zs), cons(y2, ys)]) /\ not eq_elt([z, y2])) -> BOT -> 4
(prefix([cons(z, zs), nil])) -> BOT -> 4
}
Sat witness: Found: (() -> count([x, nil, z]), {
x -> a
})

-------------------------------------------
Step 11, which took 0.018368 s (model generation: 0.016302,  model checking: 0.002066):

Model:
|_
{
count -> 
{{{
Q={q_gen_6386, q_gen_6391, q_gen_6392, q_gen_6394},
Q_f={q_gen_6386},
Delta=
{
<nil>() -> q_gen_6391
<a>() -> q_gen_6392
<b, z>() -> q_gen_6394
<a, nil, z>() -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6391) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6391) -> q_gen_6386
<b, nil, z>() -> q_gen_6386
}

Datatype: <elt, eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_6383, q_gen_6385},
Q_f={q_gen_6383},
Delta=
{
<s>(q_gen_6385) -> q_gen_6385
<z>() -> q_gen_6385
<s, s>(q_gen_6383) -> q_gen_6383
<z, s>(q_gen_6385) -> q_gen_6383
<z, z>() -> q_gen_6383
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  prefix -> 
{{{
Q={q_gen_6382, q_gen_6388, q_gen_6396, q_gen_6397},
Q_f={q_gen_6382},
Delta=
{
<nil>() -> q_gen_6396
<b>() -> q_gen_6397
<cons, cons>(q_gen_6388, q_gen_6382) -> q_gen_6382
<nil, cons>(q_gen_6397, q_gen_6396) -> q_gen_6382
<nil, nil>() -> q_gen_6382
<b, b>() -> q_gen_6388
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 6
() -> leq([z, s(nn2)]) -> 6
() -> leq([z, z]) -> 4
() -> prefix([nil, y]) -> 6
(count([x, l1, _py]) /\ count([x, l2, _qy]) /\ prefix([l1, l2])) -> leq([_py, _qy]) -> 4
(count([x, t1, _jy])) -> count([x, cons(x, t1), s(_jy)]) -> 4
(count([x, t1, _ky]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ky]) -> 4
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 4
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 4
(leq([s(nn1), z])) -> BOT -> 4
(prefix([zs, ys])) -> prefix([cons(y2, zs), cons(y2, ys)]) -> 7
(prefix([cons(y2, zs), cons(y2, ys)])) -> prefix([zs, ys]) -> 5
(prefix([cons(z, zs), cons(y2, ys)]) /\ not eq_elt([z, y2])) -> BOT -> 5
(prefix([cons(z, zs), nil])) -> BOT -> 5
}
Sat witness: Found: ((prefix([zs, ys])) -> prefix([cons(y2, zs), cons(y2, ys)]), {
y2 -> a  ;  ys -> nil  ;  zs -> nil
})

-------------------------------------------
Step 12, which took 0.022094 s (model generation: 0.021543,  model checking: 0.000551):

Model:
|_
{
count -> 
{{{
Q={q_gen_6386, q_gen_6391, q_gen_6392, q_gen_6394},
Q_f={q_gen_6386},
Delta=
{
<nil>() -> q_gen_6391
<a>() -> q_gen_6392
<b, z>() -> q_gen_6394
<a, nil, z>() -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6391) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6391) -> q_gen_6386
<b, nil, z>() -> q_gen_6386
}

Datatype: <elt, eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_6383, q_gen_6385},
Q_f={q_gen_6383},
Delta=
{
<s>(q_gen_6385) -> q_gen_6385
<z>() -> q_gen_6385
<s, s>(q_gen_6383) -> q_gen_6383
<z, s>(q_gen_6385) -> q_gen_6383
<z, z>() -> q_gen_6383
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  prefix -> 
{{{
Q={q_gen_6382, q_gen_6388, q_gen_6396, q_gen_6397},
Q_f={q_gen_6382},
Delta=
{
<nil>() -> q_gen_6396
<b>() -> q_gen_6397
<cons, cons>(q_gen_6388, q_gen_6382) -> q_gen_6382
<nil, cons>(q_gen_6397, q_gen_6396) -> q_gen_6382
<nil, nil>() -> q_gen_6382
<a, a>() -> q_gen_6388
<b, b>() -> q_gen_6388
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 6
() -> leq([z, s(nn2)]) -> 6
() -> leq([z, z]) -> 4
() -> prefix([nil, y]) -> 6
(count([x, l1, _py]) /\ count([x, l2, _qy]) /\ prefix([l1, l2])) -> leq([_py, _qy]) -> 4
(count([x, t1, _jy])) -> count([x, cons(x, t1), s(_jy)]) -> 4
(count([x, t1, _ky]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ky]) -> 7
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 5
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 5
(leq([s(nn1), z])) -> BOT -> 5
(prefix([zs, ys])) -> prefix([cons(y2, zs), cons(y2, ys)]) -> 7
(prefix([cons(y2, zs), cons(y2, ys)])) -> prefix([zs, ys]) -> 5
(prefix([cons(z, zs), cons(y2, ys)]) /\ not eq_elt([z, y2])) -> BOT -> 5
(prefix([cons(z, zs), nil])) -> BOT -> 5
}
Sat witness: Found: ((count([x, t1, _ky]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ky]), {
_ky -> z  ;  h1 -> b  ;  t1 -> nil  ;  x -> a
})

-------------------------------------------
Step 13, which took 0.018592 s (model generation: 0.018171,  model checking: 0.000421):

Model:
|_
{
count -> 
{{{
Q={q_gen_6386, q_gen_6391, q_gen_6392, q_gen_6394},
Q_f={q_gen_6386},
Delta=
{
<nil>() -> q_gen_6391
<a>() -> q_gen_6392
<b>() -> q_gen_6392
<b, z>() -> q_gen_6394
<a, cons, z>(q_gen_6392, q_gen_6391) -> q_gen_6386
<a, nil, z>() -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6391) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6391) -> q_gen_6386
<b, nil, z>() -> q_gen_6386
}

Datatype: <elt, eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_6383, q_gen_6385},
Q_f={q_gen_6383},
Delta=
{
<s>(q_gen_6385) -> q_gen_6385
<z>() -> q_gen_6385
<s, s>(q_gen_6383) -> q_gen_6383
<z, s>(q_gen_6385) -> q_gen_6383
<z, z>() -> q_gen_6383
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  prefix -> 
{{{
Q={q_gen_6382, q_gen_6388, q_gen_6396, q_gen_6397},
Q_f={q_gen_6382},
Delta=
{
<nil>() -> q_gen_6396
<b>() -> q_gen_6397
<cons, cons>(q_gen_6388, q_gen_6382) -> q_gen_6382
<nil, cons>(q_gen_6397, q_gen_6396) -> q_gen_6382
<nil, nil>() -> q_gen_6382
<a, a>() -> q_gen_6388
<b, b>() -> q_gen_6388
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 6
() -> leq([z, s(nn2)]) -> 6
() -> leq([z, z]) -> 4
() -> prefix([nil, y]) -> 6
(count([x, l1, _py]) /\ count([x, l2, _qy]) /\ prefix([l1, l2])) -> leq([_py, _qy]) -> 4
(count([x, t1, _jy])) -> count([x, cons(x, t1), s(_jy)]) -> 7
(count([x, t1, _ky]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ky]) -> 7
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 5
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 5
(leq([s(nn1), z])) -> BOT -> 5
(prefix([zs, ys])) -> prefix([cons(y2, zs), cons(y2, ys)]) -> 7
(prefix([cons(y2, zs), cons(y2, ys)])) -> prefix([zs, ys]) -> 5
(prefix([cons(z, zs), cons(y2, ys)]) /\ not eq_elt([z, y2])) -> BOT -> 5
(prefix([cons(z, zs), nil])) -> BOT -> 5
}
Sat witness: Found: ((count([x, t1, _jy])) -> count([x, cons(x, t1), s(_jy)]), {
_jy -> z  ;  t1 -> nil  ;  x -> a
})

-------------------------------------------
Step 14, which took 0.019847 s (model generation: 0.019498,  model checking: 0.000349):

Model:
|_
{
count -> 
{{{
Q={q_gen_6386, q_gen_6391, q_gen_6392, q_gen_6394},
Q_f={q_gen_6386},
Delta=
{
<nil>() -> q_gen_6391
<a>() -> q_gen_6392
<b>() -> q_gen_6392
<a, z>() -> q_gen_6394
<b, z>() -> q_gen_6394
<a, cons, s>(q_gen_6394, q_gen_6391) -> q_gen_6386
<a, cons, z>(q_gen_6392, q_gen_6391) -> q_gen_6386
<a, nil, z>() -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6391) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6391) -> q_gen_6386
<b, nil, z>() -> q_gen_6386
}

Datatype: <elt, eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_6383, q_gen_6385},
Q_f={q_gen_6383},
Delta=
{
<s>(q_gen_6385) -> q_gen_6385
<z>() -> q_gen_6385
<s, s>(q_gen_6383) -> q_gen_6383
<z, s>(q_gen_6385) -> q_gen_6383
<z, z>() -> q_gen_6383
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  prefix -> 
{{{
Q={q_gen_6382, q_gen_6388, q_gen_6396, q_gen_6397},
Q_f={q_gen_6382},
Delta=
{
<nil>() -> q_gen_6396
<b>() -> q_gen_6397
<cons, cons>(q_gen_6388, q_gen_6382) -> q_gen_6382
<nil, cons>(q_gen_6397, q_gen_6396) -> q_gen_6382
<nil, nil>() -> q_gen_6382
<a, a>() -> q_gen_6388
<b, b>() -> q_gen_6388
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 6
() -> leq([z, s(nn2)]) -> 6
() -> leq([z, z]) -> 4
() -> prefix([nil, y]) -> 6
(count([x, l1, _py]) /\ count([x, l2, _qy]) /\ prefix([l1, l2])) -> leq([_py, _qy]) -> 7
(count([x, t1, _jy])) -> count([x, cons(x, t1), s(_jy)]) -> 7
(count([x, t1, _ky]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ky]) -> 7
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 5
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 5
(leq([s(nn1), z])) -> BOT -> 5
(prefix([zs, ys])) -> prefix([cons(y2, zs), cons(y2, ys)]) -> 7
(prefix([cons(y2, zs), cons(y2, ys)])) -> prefix([zs, ys]) -> 5
(prefix([cons(z, zs), cons(y2, ys)]) /\ not eq_elt([z, y2])) -> BOT -> 5
(prefix([cons(z, zs), nil])) -> BOT -> 5
}
Sat witness: Found: ((count([x, l1, _py]) /\ count([x, l2, _qy]) /\ prefix([l1, l2])) -> leq([_py, _qy]), {
_py -> s(z)  ;  _qy -> z  ;  l1 -> cons(b, nil)  ;  l2 -> cons(b, nil)  ;  x -> a
})

-------------------------------------------
Step 15, which took 0.019241 s (model generation: 0.017491,  model checking: 0.001750):

Model:
|_
{
count -> 
{{{
Q={q_gen_6386, q_gen_6391, q_gen_6392, q_gen_6394},
Q_f={q_gen_6386},
Delta=
{
<nil>() -> q_gen_6391
<a>() -> q_gen_6392
<b>() -> q_gen_6392
<a, z>() -> q_gen_6394
<b, z>() -> q_gen_6394
<a, cons, s>(q_gen_6394, q_gen_6391) -> q_gen_6386
<a, cons, z>(q_gen_6392, q_gen_6391) -> q_gen_6386
<a, nil, z>() -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6391) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6391) -> q_gen_6386
<b, nil, z>() -> q_gen_6386
}

Datatype: <elt, eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_6383, q_gen_6385},
Q_f={q_gen_6383},
Delta=
{
<s>(q_gen_6385) -> q_gen_6385
<z>() -> q_gen_6385
<s, s>(q_gen_6383) -> q_gen_6383
<s, z>(q_gen_6385) -> q_gen_6383
<z, s>(q_gen_6385) -> q_gen_6383
<z, z>() -> q_gen_6383
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  prefix -> 
{{{
Q={q_gen_6382, q_gen_6388, q_gen_6396, q_gen_6397},
Q_f={q_gen_6382},
Delta=
{
<nil>() -> q_gen_6396
<b>() -> q_gen_6397
<cons, cons>(q_gen_6388, q_gen_6382) -> q_gen_6382
<nil, cons>(q_gen_6397, q_gen_6396) -> q_gen_6382
<nil, nil>() -> q_gen_6382
<a, a>() -> q_gen_6388
<b, b>() -> q_gen_6388
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 6
() -> leq([z, s(nn2)]) -> 6
() -> leq([z, z]) -> 5
() -> prefix([nil, y]) -> 6
(count([x, l1, _py]) /\ count([x, l2, _qy]) /\ prefix([l1, l2])) -> leq([_py, _qy]) -> 7
(count([x, t1, _jy])) -> count([x, cons(x, t1), s(_jy)]) -> 7
(count([x, t1, _ky]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ky]) -> 7
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 5
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 5
(leq([s(nn1), z])) -> BOT -> 8
(prefix([zs, ys])) -> prefix([cons(y2, zs), cons(y2, ys)]) -> 7
(prefix([cons(y2, zs), cons(y2, ys)])) -> prefix([zs, ys]) -> 6
(prefix([cons(z, zs), cons(y2, ys)]) /\ not eq_elt([z, y2])) -> BOT -> 6
(prefix([cons(z, zs), nil])) -> BOT -> 6
}
Sat witness: Found: ((leq([s(nn1), z])) -> BOT, {
nn1 -> z
})

-------------------------------------------
Step 16, which took 0.020442 s (model generation: 0.018524,  model checking: 0.001918):

Model:
|_
{
count -> 
{{{
Q={q_gen_6386, q_gen_6391, q_gen_6392, q_gen_6394, q_gen_6406, q_gen_6407},
Q_f={q_gen_6386},
Delta=
{
<nil>() -> q_gen_6391
<a>() -> q_gen_6392
<b>() -> q_gen_6392
<b, z>() -> q_gen_6394
<a, z>() -> q_gen_6406
<a, cons, s>(q_gen_6406, q_gen_6391) -> q_gen_6386
<a, cons, z>(q_gen_6392, q_gen_6391) -> q_gen_6386
<a, nil, z>() -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6391) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6391) -> q_gen_6386
<b, nil, z>() -> q_gen_6386
<a, cons, s>(q_gen_6394, q_gen_6391) -> q_gen_6407
}

Datatype: <elt, eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_6383, q_gen_6385, q_gen_6408},
Q_f={q_gen_6383},
Delta=
{
<s>(q_gen_6385) -> q_gen_6385
<z>() -> q_gen_6385
<s, s>(q_gen_6383) -> q_gen_6383
<z, s>(q_gen_6385) -> q_gen_6383
<z, z>() -> q_gen_6383
<s, z>(q_gen_6385) -> q_gen_6408
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  prefix -> 
{{{
Q={q_gen_6382, q_gen_6388, q_gen_6396, q_gen_6397},
Q_f={q_gen_6382},
Delta=
{
<nil>() -> q_gen_6396
<b>() -> q_gen_6397
<cons, cons>(q_gen_6388, q_gen_6382) -> q_gen_6382
<nil, cons>(q_gen_6397, q_gen_6396) -> q_gen_6382
<nil, nil>() -> q_gen_6382
<a, a>() -> q_gen_6388
<b, b>() -> q_gen_6388
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 6
() -> leq([z, s(nn2)]) -> 6
() -> leq([z, z]) -> 6
() -> prefix([nil, y]) -> 9
(count([x, l1, _py]) /\ count([x, l2, _qy]) /\ prefix([l1, l2])) -> leq([_py, _qy]) -> 7
(count([x, t1, _jy])) -> count([x, cons(x, t1), s(_jy)]) -> 7
(count([x, t1, _ky]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ky]) -> 7
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 6
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 6
(leq([s(nn1), z])) -> BOT -> 8
(prefix([zs, ys])) -> prefix([cons(y2, zs), cons(y2, ys)]) -> 7
(prefix([cons(y2, zs), cons(y2, ys)])) -> prefix([zs, ys]) -> 7
(prefix([cons(z, zs), cons(y2, ys)]) /\ not eq_elt([z, y2])) -> BOT -> 7
(prefix([cons(z, zs), nil])) -> BOT -> 7
}
Sat witness: Found: (() -> prefix([nil, y]), {
y -> cons(a, nil)
})

-------------------------------------------
Step 17, which took 0.017303 s (model generation: 0.014920,  model checking: 0.002383):

Model:
|_
{
count -> 
{{{
Q={q_gen_6386, q_gen_6391, q_gen_6392, q_gen_6394, q_gen_6406, q_gen_6407},
Q_f={q_gen_6386},
Delta=
{
<nil>() -> q_gen_6391
<a>() -> q_gen_6392
<b>() -> q_gen_6392
<b, z>() -> q_gen_6394
<a, z>() -> q_gen_6406
<a, cons, s>(q_gen_6406, q_gen_6391) -> q_gen_6386
<a, cons, z>(q_gen_6392, q_gen_6391) -> q_gen_6386
<a, nil, z>() -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6391) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6391) -> q_gen_6386
<b, nil, z>() -> q_gen_6386
<a, cons, s>(q_gen_6394, q_gen_6391) -> q_gen_6407
}

Datatype: <elt, eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_6383, q_gen_6385, q_gen_6408},
Q_f={q_gen_6383},
Delta=
{
<s>(q_gen_6385) -> q_gen_6385
<z>() -> q_gen_6385
<s, s>(q_gen_6383) -> q_gen_6383
<z, s>(q_gen_6385) -> q_gen_6383
<z, z>() -> q_gen_6383
<s, z>(q_gen_6385) -> q_gen_6408
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  prefix -> 
{{{
Q={q_gen_6382, q_gen_6388, q_gen_6396, q_gen_6397},
Q_f={q_gen_6382},
Delta=
{
<nil>() -> q_gen_6396
<a>() -> q_gen_6397
<b>() -> q_gen_6397
<cons, cons>(q_gen_6388, q_gen_6382) -> q_gen_6382
<nil, cons>(q_gen_6397, q_gen_6396) -> q_gen_6382
<nil, nil>() -> q_gen_6382
<a, a>() -> q_gen_6388
<b, b>() -> q_gen_6388
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 7
() -> leq([z, s(nn2)]) -> 7
() -> leq([z, z]) -> 7
() -> prefix([nil, y]) -> 9
(count([x, l1, _py]) /\ count([x, l2, _qy]) /\ prefix([l1, l2])) -> leq([_py, _qy]) -> 7
(count([x, t1, _jy])) -> count([x, cons(x, t1), s(_jy)]) -> 7
(count([x, t1, _ky]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ky]) -> 10
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 7
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 7
(leq([s(nn1), z])) -> BOT -> 8
(prefix([zs, ys])) -> prefix([cons(y2, zs), cons(y2, ys)]) -> 8
(prefix([cons(y2, zs), cons(y2, ys)])) -> prefix([zs, ys]) -> 8
(prefix([cons(z, zs), cons(y2, ys)]) /\ not eq_elt([z, y2])) -> BOT -> 8
(prefix([cons(z, zs), nil])) -> BOT -> 8
}
Sat witness: Found: ((count([x, t1, _ky]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ky]), {
_ky -> z  ;  h1 -> b  ;  t1 -> cons(b, nil)  ;  x -> a
})

-------------------------------------------
Step 18, which took 0.026243 s (model generation: 0.025583,  model checking: 0.000660):

Model:
|_
{
count -> 
{{{
Q={q_gen_6386, q_gen_6391, q_gen_6392, q_gen_6394, q_gen_6406, q_gen_6407},
Q_f={q_gen_6386},
Delta=
{
<cons>(q_gen_6392, q_gen_6391) -> q_gen_6391
<nil>() -> q_gen_6391
<a>() -> q_gen_6392
<b>() -> q_gen_6392
<b, z>() -> q_gen_6394
<a, z>() -> q_gen_6406
<a, cons, s>(q_gen_6406, q_gen_6391) -> q_gen_6386
<a, cons, z>(q_gen_6392, q_gen_6391) -> q_gen_6386
<a, nil, z>() -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6391) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6391) -> q_gen_6386
<b, nil, z>() -> q_gen_6386
<a, cons, s>(q_gen_6394, q_gen_6391) -> q_gen_6407
}

Datatype: <elt, eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_6383, q_gen_6385, q_gen_6408},
Q_f={q_gen_6383},
Delta=
{
<s>(q_gen_6385) -> q_gen_6385
<z>() -> q_gen_6385
<s, s>(q_gen_6383) -> q_gen_6383
<z, s>(q_gen_6385) -> q_gen_6383
<z, z>() -> q_gen_6383
<s, z>(q_gen_6385) -> q_gen_6408
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  prefix -> 
{{{
Q={q_gen_6382, q_gen_6388, q_gen_6396, q_gen_6397},
Q_f={q_gen_6382},
Delta=
{
<nil>() -> q_gen_6396
<a>() -> q_gen_6397
<b>() -> q_gen_6397
<cons, cons>(q_gen_6388, q_gen_6382) -> q_gen_6382
<nil, cons>(q_gen_6397, q_gen_6396) -> q_gen_6382
<nil, nil>() -> q_gen_6382
<a, a>() -> q_gen_6388
<b, b>() -> q_gen_6388
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 7
() -> leq([z, s(nn2)]) -> 7
() -> leq([z, z]) -> 7
() -> prefix([nil, y]) -> 9
(count([x, l1, _py]) /\ count([x, l2, _qy]) /\ prefix([l1, l2])) -> leq([_py, _qy]) -> 7
(count([x, t1, _jy])) -> count([x, cons(x, t1), s(_jy)]) -> 10
(count([x, t1, _ky]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ky]) -> 10
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 8
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 8
(leq([s(nn1), z])) -> BOT -> 8
(prefix([zs, ys])) -> prefix([cons(y2, zs), cons(y2, ys)]) -> 8
(prefix([cons(y2, zs), cons(y2, ys)])) -> prefix([zs, ys]) -> 8
(prefix([cons(z, zs), cons(y2, ys)]) /\ not eq_elt([z, y2])) -> BOT -> 8
(prefix([cons(z, zs), nil])) -> BOT -> 8
}
Sat witness: Found: ((count([x, t1, _jy])) -> count([x, cons(x, t1), s(_jy)]), {
_jy -> s(z)  ;  t1 -> cons(b, nil)  ;  x -> b
})

-------------------------------------------
Step 19, which took 0.021609 s (model generation: 0.021316,  model checking: 0.000293):

Model:
|_
{
count -> 
{{{
Q={q_gen_6386, q_gen_6391, q_gen_6392, q_gen_6394, q_gen_6406, q_gen_6407, q_gen_6415},
Q_f={q_gen_6386},
Delta=
{
<cons>(q_gen_6392, q_gen_6391) -> q_gen_6391
<nil>() -> q_gen_6391
<a>() -> q_gen_6392
<b>() -> q_gen_6392
<z>() -> q_gen_6415
<b, s>(q_gen_6415) -> q_gen_6394
<b, z>() -> q_gen_6394
<a, z>() -> q_gen_6406
<a, cons, s>(q_gen_6406, q_gen_6391) -> q_gen_6386
<a, cons, z>(q_gen_6392, q_gen_6391) -> q_gen_6386
<a, nil, z>() -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6391) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6391) -> q_gen_6386
<b, nil, z>() -> q_gen_6386
<a, cons, s>(q_gen_6394, q_gen_6391) -> q_gen_6407
}

Datatype: <elt, eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_6383, q_gen_6385, q_gen_6408},
Q_f={q_gen_6383},
Delta=
{
<s>(q_gen_6385) -> q_gen_6385
<z>() -> q_gen_6385
<s, s>(q_gen_6383) -> q_gen_6383
<z, s>(q_gen_6385) -> q_gen_6383
<z, z>() -> q_gen_6383
<s, z>(q_gen_6385) -> q_gen_6408
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  prefix -> 
{{{
Q={q_gen_6382, q_gen_6388, q_gen_6396, q_gen_6397},
Q_f={q_gen_6382},
Delta=
{
<nil>() -> q_gen_6396
<a>() -> q_gen_6397
<b>() -> q_gen_6397
<cons, cons>(q_gen_6388, q_gen_6382) -> q_gen_6382
<nil, cons>(q_gen_6397, q_gen_6396) -> q_gen_6382
<nil, nil>() -> q_gen_6382
<a, a>() -> q_gen_6388
<b, b>() -> q_gen_6388
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 7
() -> leq([z, s(nn2)]) -> 7
() -> leq([z, z]) -> 7
() -> prefix([nil, y]) -> 9
(count([x, l1, _py]) /\ count([x, l2, _qy]) /\ prefix([l1, l2])) -> leq([_py, _qy]) -> 10
(count([x, t1, _jy])) -> count([x, cons(x, t1), s(_jy)]) -> 10
(count([x, t1, _ky]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ky]) -> 10
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 8
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 8
(leq([s(nn1), z])) -> BOT -> 8
(prefix([zs, ys])) -> prefix([cons(y2, zs), cons(y2, ys)]) -> 8
(prefix([cons(y2, zs), cons(y2, ys)])) -> prefix([zs, ys]) -> 8
(prefix([cons(z, zs), cons(y2, ys)]) /\ not eq_elt([z, y2])) -> BOT -> 8
(prefix([cons(z, zs), nil])) -> BOT -> 8
}
Sat witness: Found: ((count([x, l1, _py]) /\ count([x, l2, _qy]) /\ prefix([l1, l2])) -> leq([_py, _qy]), {
_py -> s(z)  ;  _qy -> z  ;  l1 -> cons(b, nil)  ;  l2 -> cons(b, nil)  ;  x -> b
})

-------------------------------------------
Step 20, which took 0.024777 s (model generation: 0.022471,  model checking: 0.002306):

Model:
|_
{
count -> 
{{{
Q={q_gen_6386, q_gen_6391, q_gen_6392, q_gen_6394, q_gen_6404, q_gen_6406, q_gen_6407, q_gen_6415},
Q_f={q_gen_6386},
Delta=
{
<cons>(q_gen_6404, q_gen_6391) -> q_gen_6391
<nil>() -> q_gen_6391
<a>() -> q_gen_6392
<b>() -> q_gen_6404
<z>() -> q_gen_6415
<b, s>(q_gen_6415) -> q_gen_6394
<b, z>() -> q_gen_6394
<a, z>() -> q_gen_6406
<a, cons, s>(q_gen_6406, q_gen_6391) -> q_gen_6386
<a, cons, z>(q_gen_6404, q_gen_6391) -> q_gen_6386
<a, nil, z>() -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6391) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6391) -> q_gen_6386
<b, nil, z>() -> q_gen_6386
<a, cons, s>(q_gen_6394, q_gen_6391) -> q_gen_6407
<b, cons, z>(q_gen_6404, q_gen_6391) -> q_gen_6407
}

Datatype: <elt, eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_6383, q_gen_6385, q_gen_6408},
Q_f={q_gen_6383},
Delta=
{
<s>(q_gen_6385) -> q_gen_6385
<z>() -> q_gen_6385
<s, s>(q_gen_6383) -> q_gen_6383
<z, s>(q_gen_6385) -> q_gen_6383
<z, z>() -> q_gen_6383
<s, z>(q_gen_6385) -> q_gen_6408
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  prefix -> 
{{{
Q={q_gen_6382, q_gen_6388, q_gen_6396, q_gen_6397},
Q_f={q_gen_6382},
Delta=
{
<nil>() -> q_gen_6396
<a>() -> q_gen_6397
<b>() -> q_gen_6397
<cons, cons>(q_gen_6388, q_gen_6382) -> q_gen_6382
<nil, cons>(q_gen_6397, q_gen_6396) -> q_gen_6382
<nil, nil>() -> q_gen_6382
<a, a>() -> q_gen_6388
<b, b>() -> q_gen_6388
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 8
() -> leq([z, s(nn2)]) -> 8
() -> leq([z, z]) -> 8
() -> prefix([nil, y]) -> 12
(count([x, l1, _py]) /\ count([x, l2, _qy]) /\ prefix([l1, l2])) -> leq([_py, _qy]) -> 10
(count([x, t1, _jy])) -> count([x, cons(x, t1), s(_jy)]) -> 10
(count([x, t1, _ky]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ky]) -> 10
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 9
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 9
(leq([s(nn1), z])) -> BOT -> 9
(prefix([zs, ys])) -> prefix([cons(y2, zs), cons(y2, ys)]) -> 9
(prefix([cons(y2, zs), cons(y2, ys)])) -> prefix([zs, ys]) -> 9
(prefix([cons(z, zs), cons(y2, ys)]) /\ not eq_elt([z, y2])) -> BOT -> 9
(prefix([cons(z, zs), nil])) -> BOT -> 9
}
Sat witness: Found: (() -> prefix([nil, y]), {
y -> cons(b, cons(b, nil))
})

-------------------------------------------
Step 21, which took 0.022968 s (model generation: 0.020252,  model checking: 0.002716):

Model:
|_
{
count -> 
{{{
Q={q_gen_6386, q_gen_6391, q_gen_6392, q_gen_6394, q_gen_6404, q_gen_6406, q_gen_6407, q_gen_6415},
Q_f={q_gen_6386},
Delta=
{
<cons>(q_gen_6404, q_gen_6391) -> q_gen_6391
<nil>() -> q_gen_6391
<a>() -> q_gen_6392
<b>() -> q_gen_6404
<z>() -> q_gen_6415
<b, z>() -> q_gen_6394
<a, z>() -> q_gen_6406
<b, s>(q_gen_6415) -> q_gen_6406
<a, cons, s>(q_gen_6406, q_gen_6391) -> q_gen_6386
<a, cons, z>(q_gen_6404, q_gen_6391) -> q_gen_6386
<a, nil, z>() -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6391) -> q_gen_6386
<b, cons, s>(q_gen_6406, q_gen_6391) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6391) -> q_gen_6386
<b, nil, z>() -> q_gen_6386
<a, cons, s>(q_gen_6394, q_gen_6391) -> q_gen_6407
<b, cons, z>(q_gen_6404, q_gen_6391) -> q_gen_6407
}

Datatype: <elt, eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_6383, q_gen_6385, q_gen_6408},
Q_f={q_gen_6383},
Delta=
{
<s>(q_gen_6385) -> q_gen_6385
<z>() -> q_gen_6385
<s, s>(q_gen_6383) -> q_gen_6383
<z, s>(q_gen_6385) -> q_gen_6383
<z, z>() -> q_gen_6383
<s, z>(q_gen_6385) -> q_gen_6408
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  prefix -> 
{{{
Q={q_gen_6382, q_gen_6388, q_gen_6396, q_gen_6397},
Q_f={q_gen_6382},
Delta=
{
<cons>(q_gen_6397, q_gen_6396) -> q_gen_6396
<nil>() -> q_gen_6396
<a>() -> q_gen_6397
<b>() -> q_gen_6397
<cons, cons>(q_gen_6388, q_gen_6382) -> q_gen_6382
<nil, cons>(q_gen_6397, q_gen_6396) -> q_gen_6382
<nil, nil>() -> q_gen_6382
<a, a>() -> q_gen_6388
<b, b>() -> q_gen_6388
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 9
() -> leq([z, s(nn2)]) -> 9
() -> leq([z, z]) -> 9
() -> prefix([nil, y]) -> 12
(count([x, l1, _py]) /\ count([x, l2, _qy]) /\ prefix([l1, l2])) -> leq([_py, _qy]) -> 10
(count([x, t1, _jy])) -> count([x, cons(x, t1), s(_jy)]) -> 10
(count([x, t1, _ky]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ky]) -> 13
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 10
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 10
(leq([s(nn1), z])) -> BOT -> 10
(prefix([zs, ys])) -> prefix([cons(y2, zs), cons(y2, ys)]) -> 10
(prefix([cons(y2, zs), cons(y2, ys)])) -> prefix([zs, ys]) -> 10
(prefix([cons(z, zs), cons(y2, ys)]) /\ not eq_elt([z, y2])) -> BOT -> 10
(prefix([cons(z, zs), nil])) -> BOT -> 10
}
Sat witness: Found: ((count([x, t1, _ky]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ky]), {
_ky -> z  ;  h1 -> a  ;  t1 -> cons(a, nil)  ;  x -> b
})

-------------------------------------------
Step 22, which took 0.027065 s (model generation: 0.024507,  model checking: 0.002558):

Model:
|_
{
count -> 
{{{
Q={q_gen_6386, q_gen_6391, q_gen_6392, q_gen_6394, q_gen_6404, q_gen_6406, q_gen_6407, q_gen_6415},
Q_f={q_gen_6386},
Delta=
{
<cons>(q_gen_6392, q_gen_6391) -> q_gen_6391
<cons>(q_gen_6404, q_gen_6391) -> q_gen_6391
<nil>() -> q_gen_6391
<a>() -> q_gen_6392
<b>() -> q_gen_6404
<z>() -> q_gen_6415
<b, s>(q_gen_6415) -> q_gen_6394
<b, z>() -> q_gen_6394
<a, z>() -> q_gen_6406
<a, cons, s>(q_gen_6406, q_gen_6391) -> q_gen_6386
<a, cons, z>(q_gen_6404, q_gen_6391) -> q_gen_6386
<a, nil, z>() -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6391) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6391) -> q_gen_6386
<b, nil, z>() -> q_gen_6386
<a, cons, s>(q_gen_6394, q_gen_6391) -> q_gen_6407
<b, cons, z>(q_gen_6404, q_gen_6391) -> q_gen_6407
}

Datatype: <elt, eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_6383, q_gen_6385, q_gen_6408},
Q_f={q_gen_6383},
Delta=
{
<s>(q_gen_6385) -> q_gen_6385
<z>() -> q_gen_6385
<s, s>(q_gen_6383) -> q_gen_6383
<z, s>(q_gen_6385) -> q_gen_6383
<z, z>() -> q_gen_6383
<s, z>(q_gen_6385) -> q_gen_6408
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  prefix -> 
{{{
Q={q_gen_6382, q_gen_6388, q_gen_6396, q_gen_6397},
Q_f={q_gen_6382},
Delta=
{
<cons>(q_gen_6397, q_gen_6396) -> q_gen_6396
<nil>() -> q_gen_6396
<a>() -> q_gen_6397
<b>() -> q_gen_6397
<cons, cons>(q_gen_6388, q_gen_6382) -> q_gen_6382
<nil, cons>(q_gen_6397, q_gen_6396) -> q_gen_6382
<nil, nil>() -> q_gen_6382
<a, a>() -> q_gen_6388
<b, b>() -> q_gen_6388
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 10
() -> leq([z, s(nn2)]) -> 10
() -> leq([z, z]) -> 10
() -> prefix([nil, y]) -> 12
(count([x, l1, _py]) /\ count([x, l2, _qy]) /\ prefix([l1, l2])) -> leq([_py, _qy]) -> 10
(count([x, t1, _jy])) -> count([x, cons(x, t1), s(_jy)]) -> 13
(count([x, t1, _ky]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ky]) -> 13
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 11
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 11
(leq([s(nn1), z])) -> BOT -> 11
(prefix([zs, ys])) -> prefix([cons(y2, zs), cons(y2, ys)]) -> 11
(prefix([cons(y2, zs), cons(y2, ys)])) -> prefix([zs, ys]) -> 11
(prefix([cons(z, zs), cons(y2, ys)]) /\ not eq_elt([z, y2])) -> BOT -> 11
(prefix([cons(z, zs), nil])) -> BOT -> 11
}
Sat witness: Found: ((count([x, t1, _jy])) -> count([x, cons(x, t1), s(_jy)]), {
_jy -> s(s(z))  ;  t1 -> cons(b, cons(a, nil))  ;  x -> b
})

-------------------------------------------
Step 23, which took 0.023146 s (model generation: 0.022792,  model checking: 0.000354):

Model:
|_
{
count -> 
{{{
Q={q_gen_6386, q_gen_6391, q_gen_6392, q_gen_6394, q_gen_6404, q_gen_6406, q_gen_6407, q_gen_6415},
Q_f={q_gen_6386},
Delta=
{
<cons>(q_gen_6392, q_gen_6391) -> q_gen_6391
<cons>(q_gen_6404, q_gen_6391) -> q_gen_6391
<nil>() -> q_gen_6391
<a>() -> q_gen_6392
<b>() -> q_gen_6404
<s>(q_gen_6415) -> q_gen_6415
<z>() -> q_gen_6415
<b, z>() -> q_gen_6394
<a, z>() -> q_gen_6406
<b, s>(q_gen_6415) -> q_gen_6406
<a, cons, s>(q_gen_6406, q_gen_6391) -> q_gen_6386
<a, cons, z>(q_gen_6404, q_gen_6391) -> q_gen_6386
<a, nil, z>() -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6391) -> q_gen_6386
<b, cons, s>(q_gen_6406, q_gen_6391) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6391) -> q_gen_6386
<b, nil, z>() -> q_gen_6386
<a, cons, s>(q_gen_6394, q_gen_6391) -> q_gen_6407
<b, cons, z>(q_gen_6404, q_gen_6391) -> q_gen_6407
}

Datatype: <elt, eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_6383, q_gen_6385, q_gen_6408},
Q_f={q_gen_6383},
Delta=
{
<s>(q_gen_6385) -> q_gen_6385
<z>() -> q_gen_6385
<s, s>(q_gen_6383) -> q_gen_6383
<z, s>(q_gen_6385) -> q_gen_6383
<z, z>() -> q_gen_6383
<s, z>(q_gen_6385) -> q_gen_6408
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  prefix -> 
{{{
Q={q_gen_6382, q_gen_6388, q_gen_6396, q_gen_6397},
Q_f={q_gen_6382},
Delta=
{
<cons>(q_gen_6397, q_gen_6396) -> q_gen_6396
<nil>() -> q_gen_6396
<a>() -> q_gen_6397
<b>() -> q_gen_6397
<cons, cons>(q_gen_6388, q_gen_6382) -> q_gen_6382
<nil, cons>(q_gen_6397, q_gen_6396) -> q_gen_6382
<nil, nil>() -> q_gen_6382
<a, a>() -> q_gen_6388
<b, b>() -> q_gen_6388
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 10
() -> leq([z, s(nn2)]) -> 10
() -> leq([z, z]) -> 10
() -> prefix([nil, y]) -> 12
(count([x, l1, _py]) /\ count([x, l2, _qy]) /\ prefix([l1, l2])) -> leq([_py, _qy]) -> 13
(count([x, t1, _jy])) -> count([x, cons(x, t1), s(_jy)]) -> 13
(count([x, t1, _ky]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ky]) -> 13
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 11
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 11
(leq([s(nn1), z])) -> BOT -> 11
(prefix([zs, ys])) -> prefix([cons(y2, zs), cons(y2, ys)]) -> 11
(prefix([cons(y2, zs), cons(y2, ys)])) -> prefix([zs, ys]) -> 11
(prefix([cons(z, zs), cons(y2, ys)]) /\ not eq_elt([z, y2])) -> BOT -> 11
(prefix([cons(z, zs), nil])) -> BOT -> 11
}
Sat witness: Found: ((count([x, l1, _py]) /\ count([x, l2, _qy]) /\ prefix([l1, l2])) -> leq([_py, _qy]), {
_py -> s(z)  ;  _qy -> z  ;  l1 -> cons(a, nil)  ;  l2 -> cons(a, nil)  ;  x -> b
})

-------------------------------------------
Step 24, which took 0.032295 s (model generation: 0.029728,  model checking: 0.002567):

Model:
|_
{
count -> 
{{{
Q={q_gen_6386, q_gen_6391, q_gen_6392, q_gen_6394, q_gen_6404, q_gen_6406, q_gen_6407, q_gen_6415},
Q_f={q_gen_6386},
Delta=
{
<cons>(q_gen_6392, q_gen_6391) -> q_gen_6391
<cons>(q_gen_6404, q_gen_6391) -> q_gen_6391
<nil>() -> q_gen_6391
<a>() -> q_gen_6392
<b>() -> q_gen_6404
<s>(q_gen_6415) -> q_gen_6415
<z>() -> q_gen_6415
<b, s>(q_gen_6415) -> q_gen_6394
<b, z>() -> q_gen_6394
<a, z>() -> q_gen_6406
<a, cons, s>(q_gen_6406, q_gen_6391) -> q_gen_6386
<a, cons, z>(q_gen_6404, q_gen_6391) -> q_gen_6386
<a, nil, z>() -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6391) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6391) -> q_gen_6386
<b, nil, z>() -> q_gen_6386
<a, cons, s>(q_gen_6394, q_gen_6391) -> q_gen_6407
<b, cons, s>(q_gen_6406, q_gen_6391) -> q_gen_6407
<b, cons, z>(q_gen_6404, q_gen_6391) -> q_gen_6407
}

Datatype: <elt, eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_6383, q_gen_6385, q_gen_6408},
Q_f={q_gen_6383},
Delta=
{
<s>(q_gen_6385) -> q_gen_6385
<z>() -> q_gen_6385
<s, s>(q_gen_6383) -> q_gen_6383
<z, s>(q_gen_6385) -> q_gen_6383
<z, z>() -> q_gen_6383
<s, z>(q_gen_6385) -> q_gen_6408
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  prefix -> 
{{{
Q={q_gen_6382, q_gen_6388, q_gen_6396, q_gen_6397},
Q_f={q_gen_6382},
Delta=
{
<cons>(q_gen_6397, q_gen_6396) -> q_gen_6396
<nil>() -> q_gen_6396
<a>() -> q_gen_6397
<b>() -> q_gen_6397
<cons, cons>(q_gen_6388, q_gen_6382) -> q_gen_6382
<nil, cons>(q_gen_6397, q_gen_6396) -> q_gen_6382
<nil, nil>() -> q_gen_6382
<a, a>() -> q_gen_6388
<b, b>() -> q_gen_6388
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 11
() -> leq([z, s(nn2)]) -> 11
() -> leq([z, z]) -> 11
() -> prefix([nil, y]) -> 13
(count([x, l1, _py]) /\ count([x, l2, _qy]) /\ prefix([l1, l2])) -> leq([_py, _qy]) -> 13
(count([x, t1, _jy])) -> count([x, cons(x, t1), s(_jy)]) -> 13
(count([x, t1, _ky]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ky]) -> 16
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 12
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 12
(leq([s(nn1), z])) -> BOT -> 12
(prefix([zs, ys])) -> prefix([cons(y2, zs), cons(y2, ys)]) -> 12
(prefix([cons(y2, zs), cons(y2, ys)])) -> prefix([zs, ys]) -> 12
(prefix([cons(z, zs), cons(y2, ys)]) /\ not eq_elt([z, y2])) -> BOT -> 12
(prefix([cons(z, zs), nil])) -> BOT -> 12
}
Sat witness: Found: ((count([x, t1, _ky]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ky]), {
_ky -> s(z)  ;  h1 -> a  ;  t1 -> cons(b, nil)  ;  x -> b
})

-------------------------------------------
Step 25, which took 0.033600 s (model generation: 0.028555,  model checking: 0.005045):

Model:
|_
{
count -> 
{{{
Q={q_gen_6386, q_gen_6391, q_gen_6392, q_gen_6394, q_gen_6404, q_gen_6406, q_gen_6407, q_gen_6412, q_gen_6415},
Q_f={q_gen_6386},
Delta=
{
<nil>() -> q_gen_6391
<a>() -> q_gen_6392
<b>() -> q_gen_6404
<cons>(q_gen_6392, q_gen_6391) -> q_gen_6412
<cons>(q_gen_6404, q_gen_6391) -> q_gen_6412
<cons>(q_gen_6404, q_gen_6412) -> q_gen_6412
<s>(q_gen_6415) -> q_gen_6415
<z>() -> q_gen_6415
<b, z>() -> q_gen_6394
<a, z>() -> q_gen_6406
<b, s>(q_gen_6415) -> q_gen_6406
<a, cons, s>(q_gen_6406, q_gen_6391) -> q_gen_6386
<a, cons, z>(q_gen_6404, q_gen_6391) -> q_gen_6386
<a, cons, z>(q_gen_6404, q_gen_6412) -> q_gen_6386
<a, nil, z>() -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6391) -> q_gen_6386
<b, cons, s>(q_gen_6406, q_gen_6412) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6391) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6412) -> q_gen_6386
<b, nil, z>() -> q_gen_6386
<a, cons, s>(q_gen_6394, q_gen_6391) -> q_gen_6407
<b, cons, s>(q_gen_6406, q_gen_6391) -> q_gen_6407
<b, cons, z>(q_gen_6404, q_gen_6391) -> q_gen_6407
}

Datatype: <elt, eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_6383, q_gen_6385, q_gen_6408},
Q_f={q_gen_6383},
Delta=
{
<s>(q_gen_6385) -> q_gen_6385
<z>() -> q_gen_6385
<s, s>(q_gen_6383) -> q_gen_6383
<z, s>(q_gen_6385) -> q_gen_6383
<z, z>() -> q_gen_6383
<s, z>(q_gen_6385) -> q_gen_6408
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  prefix -> 
{{{
Q={q_gen_6382, q_gen_6388, q_gen_6396, q_gen_6397},
Q_f={q_gen_6382},
Delta=
{
<cons>(q_gen_6397, q_gen_6396) -> q_gen_6396
<nil>() -> q_gen_6396
<a>() -> q_gen_6397
<b>() -> q_gen_6397
<cons, cons>(q_gen_6388, q_gen_6382) -> q_gen_6382
<nil, cons>(q_gen_6397, q_gen_6396) -> q_gen_6382
<nil, nil>() -> q_gen_6382
<a, a>() -> q_gen_6388
<b, b>() -> q_gen_6388
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 12
() -> leq([z, s(nn2)]) -> 12
() -> leq([z, z]) -> 12
() -> prefix([nil, y]) -> 13
(count([x, l1, _py]) /\ count([x, l2, _qy]) /\ prefix([l1, l2])) -> leq([_py, _qy]) -> 13
(count([x, t1, _jy])) -> count([x, cons(x, t1), s(_jy)]) -> 16
(count([x, t1, _ky]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ky]) -> 16
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 13
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 13
(leq([s(nn1), z])) -> BOT -> 13
(prefix([zs, ys])) -> prefix([cons(y2, zs), cons(y2, ys)]) -> 13
(prefix([cons(y2, zs), cons(y2, ys)])) -> prefix([zs, ys]) -> 13
(prefix([cons(z, zs), cons(y2, ys)]) /\ not eq_elt([z, y2])) -> BOT -> 13
(prefix([cons(z, zs), nil])) -> BOT -> 13
}
Sat witness: Found: ((count([x, t1, _jy])) -> count([x, cons(x, t1), s(_jy)]), {
_jy -> z  ;  t1 -> cons(a, nil)  ;  x -> b
})

-------------------------------------------
Step 26, which took 0.031267 s (model generation: 0.029012,  model checking: 0.002255):

Model:
|_
{
count -> 
{{{
Q={q_gen_6386, q_gen_6391, q_gen_6392, q_gen_6394, q_gen_6404, q_gen_6406, q_gen_6407, q_gen_6412, q_gen_6415},
Q_f={q_gen_6386},
Delta=
{
<cons>(q_gen_6392, q_gen_6391) -> q_gen_6391
<nil>() -> q_gen_6391
<a>() -> q_gen_6392
<b>() -> q_gen_6404
<cons>(q_gen_6404, q_gen_6391) -> q_gen_6412
<s>(q_gen_6415) -> q_gen_6415
<z>() -> q_gen_6415
<b, z>() -> q_gen_6394
<a, z>() -> q_gen_6406
<b, s>(q_gen_6415) -> q_gen_6406
<a, cons, s>(q_gen_6406, q_gen_6391) -> q_gen_6386
<a, cons, z>(q_gen_6404, q_gen_6391) -> q_gen_6386
<a, cons, z>(q_gen_6404, q_gen_6412) -> q_gen_6386
<a, nil, z>() -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6391) -> q_gen_6386
<b, cons, s>(q_gen_6406, q_gen_6412) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6391) -> q_gen_6386
<b, nil, z>() -> q_gen_6386
<a, cons, s>(q_gen_6394, q_gen_6391) -> q_gen_6407
<b, cons, s>(q_gen_6406, q_gen_6391) -> q_gen_6407
<b, cons, z>(q_gen_6404, q_gen_6391) -> q_gen_6407
}

Datatype: <elt, eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_6383, q_gen_6385, q_gen_6408},
Q_f={q_gen_6383},
Delta=
{
<s>(q_gen_6385) -> q_gen_6385
<z>() -> q_gen_6385
<s, s>(q_gen_6383) -> q_gen_6383
<z, s>(q_gen_6385) -> q_gen_6383
<z, z>() -> q_gen_6383
<s, z>(q_gen_6385) -> q_gen_6408
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  prefix -> 
{{{
Q={q_gen_6382, q_gen_6388, q_gen_6396, q_gen_6397},
Q_f={q_gen_6382},
Delta=
{
<cons>(q_gen_6397, q_gen_6396) -> q_gen_6396
<nil>() -> q_gen_6396
<a>() -> q_gen_6397
<b>() -> q_gen_6397
<cons, cons>(q_gen_6388, q_gen_6382) -> q_gen_6382
<nil, cons>(q_gen_6397, q_gen_6396) -> q_gen_6382
<nil, nil>() -> q_gen_6382
<a, a>() -> q_gen_6388
<b, b>() -> q_gen_6388
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 13
() -> leq([z, s(nn2)]) -> 13
() -> leq([z, z]) -> 13
() -> prefix([nil, y]) -> 13
(count([x, l1, _py]) /\ count([x, l2, _qy]) /\ prefix([l1, l2])) -> leq([_py, _qy]) -> 16
(count([x, t1, _jy])) -> count([x, cons(x, t1), s(_jy)]) -> 16
(count([x, t1, _ky]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ky]) -> 16
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 14
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 14
(leq([s(nn1), z])) -> BOT -> 14
(prefix([zs, ys])) -> prefix([cons(y2, zs), cons(y2, ys)]) -> 14
(prefix([cons(y2, zs), cons(y2, ys)])) -> prefix([zs, ys]) -> 14
(prefix([cons(z, zs), cons(y2, ys)]) /\ not eq_elt([z, y2])) -> BOT -> 14
(prefix([cons(z, zs), nil])) -> BOT -> 14
}
Sat witness: Found: ((count([x, l1, _py]) /\ count([x, l2, _qy]) /\ prefix([l1, l2])) -> leq([_py, _qy]), {
_py -> s(s(z))  ;  _qy -> z  ;  l1 -> cons(b, nil)  ;  l2 -> cons(b, nil)  ;  x -> a
})

-------------------------------------------
Step 27, which took 0.030732 s (model generation: 0.028116,  model checking: 0.002616):

Model:
|_
{
count -> 
{{{
Q={q_gen_6386, q_gen_6391, q_gen_6392, q_gen_6394, q_gen_6404, q_gen_6406, q_gen_6407, q_gen_6412, q_gen_6415},
Q_f={q_gen_6386},
Delta=
{
<cons>(q_gen_6392, q_gen_6391) -> q_gen_6391
<nil>() -> q_gen_6391
<a>() -> q_gen_6392
<b>() -> q_gen_6404
<cons>(q_gen_6404, q_gen_6391) -> q_gen_6412
<s>(q_gen_6415) -> q_gen_6415
<z>() -> q_gen_6415
<b, s>(q_gen_6415) -> q_gen_6394
<b, z>() -> q_gen_6394
<a, z>() -> q_gen_6406
<a, cons, s>(q_gen_6406, q_gen_6391) -> q_gen_6386
<a, cons, z>(q_gen_6404, q_gen_6391) -> q_gen_6386
<a, cons, z>(q_gen_6404, q_gen_6412) -> q_gen_6386
<a, nil, z>() -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6391) -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6412) -> q_gen_6386
<b, cons, s>(q_gen_6406, q_gen_6412) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6391) -> q_gen_6386
<b, nil, z>() -> q_gen_6386
<a, cons, s>(q_gen_6394, q_gen_6391) -> q_gen_6407
<b, cons, s>(q_gen_6406, q_gen_6391) -> q_gen_6407
<b, cons, z>(q_gen_6404, q_gen_6391) -> q_gen_6407
}

Datatype: <elt, eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_6383, q_gen_6385, q_gen_6408},
Q_f={q_gen_6383},
Delta=
{
<s>(q_gen_6385) -> q_gen_6385
<z>() -> q_gen_6385
<s, s>(q_gen_6383) -> q_gen_6383
<z, s>(q_gen_6385) -> q_gen_6383
<z, z>() -> q_gen_6383
<s, z>(q_gen_6385) -> q_gen_6408
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  prefix -> 
{{{
Q={q_gen_6382, q_gen_6388, q_gen_6396, q_gen_6397},
Q_f={q_gen_6382},
Delta=
{
<cons>(q_gen_6397, q_gen_6396) -> q_gen_6396
<nil>() -> q_gen_6396
<a>() -> q_gen_6397
<b>() -> q_gen_6397
<cons, cons>(q_gen_6388, q_gen_6382) -> q_gen_6382
<nil, cons>(q_gen_6397, q_gen_6396) -> q_gen_6382
<nil, nil>() -> q_gen_6382
<a, a>() -> q_gen_6388
<b, b>() -> q_gen_6388
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 14
() -> leq([z, s(nn2)]) -> 14
() -> leq([z, z]) -> 14
() -> prefix([nil, y]) -> 14
(count([x, l1, _py]) /\ count([x, l2, _qy]) /\ prefix([l1, l2])) -> leq([_py, _qy]) -> 16
(count([x, t1, _jy])) -> count([x, cons(x, t1), s(_jy)]) -> 16
(count([x, t1, _ky]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ky]) -> 19
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 15
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 15
(leq([s(nn1), z])) -> BOT -> 15
(prefix([zs, ys])) -> prefix([cons(y2, zs), cons(y2, ys)]) -> 15
(prefix([cons(y2, zs), cons(y2, ys)])) -> prefix([zs, ys]) -> 15
(prefix([cons(z, zs), cons(y2, ys)]) /\ not eq_elt([z, y2])) -> BOT -> 15
(prefix([cons(z, zs), nil])) -> BOT -> 15
}
Sat witness: Found: ((count([x, t1, _ky]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ky]), {
_ky -> s(z)  ;  h1 -> b  ;  t1 -> cons(a, nil)  ;  x -> a
})

-------------------------------------------
Step 28, which took 0.035252 s (model generation: 0.031393,  model checking: 0.003859):

Model:
|_
{
count -> 
{{{
Q={q_gen_6386, q_gen_6391, q_gen_6392, q_gen_6394, q_gen_6404, q_gen_6406, q_gen_6407, q_gen_6412, q_gen_6415},
Q_f={q_gen_6386},
Delta=
{
<nil>() -> q_gen_6391
<a>() -> q_gen_6392
<b>() -> q_gen_6404
<cons>(q_gen_6392, q_gen_6391) -> q_gen_6412
<cons>(q_gen_6404, q_gen_6391) -> q_gen_6412
<cons>(q_gen_6404, q_gen_6412) -> q_gen_6412
<s>(q_gen_6415) -> q_gen_6415
<z>() -> q_gen_6415
<b, s>(q_gen_6415) -> q_gen_6394
<b, z>() -> q_gen_6394
<a, z>() -> q_gen_6406
<a, cons, s>(q_gen_6394, q_gen_6412) -> q_gen_6386
<a, cons, s>(q_gen_6406, q_gen_6391) -> q_gen_6386
<a, cons, z>(q_gen_6404, q_gen_6391) -> q_gen_6386
<a, cons, z>(q_gen_6404, q_gen_6412) -> q_gen_6386
<a, nil, z>() -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6391) -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6412) -> q_gen_6386
<b, cons, s>(q_gen_6406, q_gen_6412) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6391) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6412) -> q_gen_6386
<b, nil, z>() -> q_gen_6386
<a, cons, s>(q_gen_6394, q_gen_6391) -> q_gen_6407
<b, cons, s>(q_gen_6406, q_gen_6391) -> q_gen_6407
<b, cons, z>(q_gen_6404, q_gen_6391) -> q_gen_6407
}

Datatype: <elt, eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_6383, q_gen_6385, q_gen_6408},
Q_f={q_gen_6383},
Delta=
{
<s>(q_gen_6385) -> q_gen_6385
<z>() -> q_gen_6385
<s, s>(q_gen_6383) -> q_gen_6383
<z, s>(q_gen_6385) -> q_gen_6383
<z, z>() -> q_gen_6383
<s, z>(q_gen_6385) -> q_gen_6408
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  prefix -> 
{{{
Q={q_gen_6382, q_gen_6388, q_gen_6396, q_gen_6397},
Q_f={q_gen_6382},
Delta=
{
<cons>(q_gen_6397, q_gen_6396) -> q_gen_6396
<nil>() -> q_gen_6396
<a>() -> q_gen_6397
<b>() -> q_gen_6397
<cons, cons>(q_gen_6388, q_gen_6382) -> q_gen_6382
<nil, cons>(q_gen_6397, q_gen_6396) -> q_gen_6382
<nil, nil>() -> q_gen_6382
<a, a>() -> q_gen_6388
<b, b>() -> q_gen_6388
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 15
() -> leq([z, s(nn2)]) -> 15
() -> leq([z, z]) -> 15
() -> prefix([nil, y]) -> 15
(count([x, l1, _py]) /\ count([x, l2, _qy]) /\ prefix([l1, l2])) -> leq([_py, _qy]) -> 16
(count([x, t1, _jy])) -> count([x, cons(x, t1), s(_jy)]) -> 19
(count([x, t1, _ky]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ky]) -> 19
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 16
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 16
(leq([s(nn1), z])) -> BOT -> 16
(prefix([zs, ys])) -> prefix([cons(y2, zs), cons(y2, ys)]) -> 16
(prefix([cons(y2, zs), cons(y2, ys)])) -> prefix([zs, ys]) -> 16
(prefix([cons(z, zs), cons(y2, ys)]) /\ not eq_elt([z, y2])) -> BOT -> 16
(prefix([cons(z, zs), nil])) -> BOT -> 16
}
Sat witness: Found: ((count([x, t1, _jy])) -> count([x, cons(x, t1), s(_jy)]), {
_jy -> z  ;  t1 -> cons(b, cons(a, nil))  ;  x -> a
})

-------------------------------------------
Step 29, which took 0.043607 s (model generation: 0.040525,  model checking: 0.003082):

Model:
|_
{
count -> 
{{{
Q={q_gen_6386, q_gen_6391, q_gen_6392, q_gen_6394, q_gen_6404, q_gen_6406, q_gen_6407, q_gen_6412, q_gen_6415},
Q_f={q_gen_6386},
Delta=
{
<nil>() -> q_gen_6391
<a>() -> q_gen_6392
<b>() -> q_gen_6404
<cons>(q_gen_6392, q_gen_6391) -> q_gen_6412
<cons>(q_gen_6404, q_gen_6391) -> q_gen_6412
<cons>(q_gen_6404, q_gen_6412) -> q_gen_6412
<s>(q_gen_6415) -> q_gen_6415
<z>() -> q_gen_6415
<b, s>(q_gen_6415) -> q_gen_6394
<b, z>() -> q_gen_6394
<a, z>() -> q_gen_6406
<a, cons, s>(q_gen_6394, q_gen_6412) -> q_gen_6386
<a, cons, s>(q_gen_6406, q_gen_6391) -> q_gen_6386
<a, cons, s>(q_gen_6406, q_gen_6412) -> q_gen_6386
<a, cons, z>(q_gen_6404, q_gen_6391) -> q_gen_6386
<a, cons, z>(q_gen_6404, q_gen_6412) -> q_gen_6386
<a, nil, z>() -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6391) -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6412) -> q_gen_6386
<b, cons, s>(q_gen_6406, q_gen_6412) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6391) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6412) -> q_gen_6386
<b, nil, z>() -> q_gen_6386
<a, cons, s>(q_gen_6394, q_gen_6391) -> q_gen_6407
<b, cons, s>(q_gen_6406, q_gen_6391) -> q_gen_6407
<b, cons, z>(q_gen_6404, q_gen_6391) -> q_gen_6407
}

Datatype: <elt, eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_6383, q_gen_6385, q_gen_6408},
Q_f={q_gen_6383},
Delta=
{
<s>(q_gen_6385) -> q_gen_6385
<z>() -> q_gen_6385
<s, s>(q_gen_6383) -> q_gen_6383
<z, s>(q_gen_6385) -> q_gen_6383
<z, z>() -> q_gen_6383
<s, z>(q_gen_6385) -> q_gen_6408
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  prefix -> 
{{{
Q={q_gen_6382, q_gen_6388, q_gen_6396, q_gen_6397},
Q_f={q_gen_6382},
Delta=
{
<cons>(q_gen_6397, q_gen_6396) -> q_gen_6396
<nil>() -> q_gen_6396
<a>() -> q_gen_6397
<b>() -> q_gen_6397
<cons, cons>(q_gen_6388, q_gen_6382) -> q_gen_6382
<nil, cons>(q_gen_6397, q_gen_6396) -> q_gen_6382
<nil, nil>() -> q_gen_6382
<a, a>() -> q_gen_6388
<b, b>() -> q_gen_6388
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 16
() -> leq([z, s(nn2)]) -> 16
() -> leq([z, z]) -> 16
() -> prefix([nil, y]) -> 16
(count([x, l1, _py]) /\ count([x, l2, _qy]) /\ prefix([l1, l2])) -> leq([_py, _qy]) -> 19
(count([x, t1, _jy])) -> count([x, cons(x, t1), s(_jy)]) -> 19
(count([x, t1, _ky]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ky]) -> 19
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 17
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 17
(leq([s(nn1), z])) -> BOT -> 17
(prefix([zs, ys])) -> prefix([cons(y2, zs), cons(y2, ys)]) -> 17
(prefix([cons(y2, zs), cons(y2, ys)])) -> prefix([zs, ys]) -> 17
(prefix([cons(z, zs), cons(y2, ys)]) /\ not eq_elt([z, y2])) -> BOT -> 17
(prefix([cons(z, zs), nil])) -> BOT -> 17
}
Sat witness: Found: ((count([x, l1, _py]) /\ count([x, l2, _qy]) /\ prefix([l1, l2])) -> leq([_py, _qy]), {
_py -> s(z)  ;  _qy -> z  ;  l1 -> cons(b, cons(a, nil))  ;  l2 -> cons(b, cons(a, nil))  ;  x -> a
})

-------------------------------------------
Step 30, which took 0.040971 s (model generation: 0.036085,  model checking: 0.004886):

Model:
|_
{
count -> 
{{{
Q={q_gen_6386, q_gen_6391, q_gen_6392, q_gen_6394, q_gen_6404, q_gen_6406, q_gen_6407, q_gen_6412, q_gen_6415, q_gen_6420},
Q_f={q_gen_6386},
Delta=
{
<nil>() -> q_gen_6391
<a>() -> q_gen_6392
<b>() -> q_gen_6404
<cons>(q_gen_6404, q_gen_6391) -> q_gen_6412
<s>(q_gen_6415) -> q_gen_6415
<z>() -> q_gen_6415
<cons>(q_gen_6392, q_gen_6391) -> q_gen_6420
<cons>(q_gen_6404, q_gen_6420) -> q_gen_6420
<b, s>(q_gen_6415) -> q_gen_6394
<b, z>() -> q_gen_6394
<a, z>() -> q_gen_6406
<a, cons, s>(q_gen_6394, q_gen_6420) -> q_gen_6386
<a, cons, s>(q_gen_6406, q_gen_6391) -> q_gen_6386
<a, cons, z>(q_gen_6404, q_gen_6391) -> q_gen_6386
<a, cons, z>(q_gen_6404, q_gen_6412) -> q_gen_6386
<a, nil, z>() -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6391) -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6412) -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6420) -> q_gen_6386
<b, cons, s>(q_gen_6406, q_gen_6412) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6391) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6420) -> q_gen_6386
<b, nil, z>() -> q_gen_6386
<a, cons, s>(q_gen_6394, q_gen_6391) -> q_gen_6407
<a, cons, s>(q_gen_6406, q_gen_6420) -> q_gen_6407
<a, cons, z>(q_gen_6404, q_gen_6420) -> q_gen_6407
<b, cons, s>(q_gen_6406, q_gen_6391) -> q_gen_6407
<b, cons, z>(q_gen_6404, q_gen_6391) -> q_gen_6407
}

Datatype: <elt, eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_6383, q_gen_6385, q_gen_6408},
Q_f={q_gen_6383},
Delta=
{
<s>(q_gen_6385) -> q_gen_6385
<z>() -> q_gen_6385
<s, s>(q_gen_6383) -> q_gen_6383
<z, s>(q_gen_6385) -> q_gen_6383
<z, z>() -> q_gen_6383
<s, z>(q_gen_6385) -> q_gen_6408
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  prefix -> 
{{{
Q={q_gen_6382, q_gen_6388, q_gen_6396, q_gen_6397},
Q_f={q_gen_6382},
Delta=
{
<cons>(q_gen_6397, q_gen_6396) -> q_gen_6396
<nil>() -> q_gen_6396
<a>() -> q_gen_6397
<b>() -> q_gen_6397
<cons, cons>(q_gen_6388, q_gen_6382) -> q_gen_6382
<nil, cons>(q_gen_6397, q_gen_6396) -> q_gen_6382
<nil, nil>() -> q_gen_6382
<a, a>() -> q_gen_6388
<b, b>() -> q_gen_6388
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 17
() -> leq([z, s(nn2)]) -> 17
() -> leq([z, z]) -> 17
() -> prefix([nil, y]) -> 17
(count([x, l1, _py]) /\ count([x, l2, _qy]) /\ prefix([l1, l2])) -> leq([_py, _qy]) -> 19
(count([x, t1, _jy])) -> count([x, cons(x, t1), s(_jy)]) -> 19
(count([x, t1, _ky]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ky]) -> 22
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 18
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 18
(leq([s(nn1), z])) -> BOT -> 18
(prefix([zs, ys])) -> prefix([cons(y2, zs), cons(y2, ys)]) -> 18
(prefix([cons(y2, zs), cons(y2, ys)])) -> prefix([zs, ys]) -> 18
(prefix([cons(z, zs), cons(y2, ys)]) /\ not eq_elt([z, y2])) -> BOT -> 18
(prefix([cons(z, zs), nil])) -> BOT -> 18
}
Sat witness: Found: ((count([x, t1, _ky]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ky]), {
_ky -> z  ;  h1 -> b  ;  t1 -> cons(b, cons(b, nil))  ;  x -> a
})

-------------------------------------------
Step 31, which took 0.038033 s (model generation: 0.033265,  model checking: 0.004768):

Model:
|_
{
count -> 
{{{
Q={q_gen_6386, q_gen_6391, q_gen_6392, q_gen_6394, q_gen_6404, q_gen_6406, q_gen_6407, q_gen_6412, q_gen_6415, q_gen_6420},
Q_f={q_gen_6386},
Delta=
{
<cons>(q_gen_6404, q_gen_6412) -> q_gen_6391
<cons>(q_gen_6404, q_gen_6420) -> q_gen_6391
<nil>() -> q_gen_6391
<a>() -> q_gen_6392
<b>() -> q_gen_6404
<cons>(q_gen_6404, q_gen_6391) -> q_gen_6412
<s>(q_gen_6415) -> q_gen_6415
<z>() -> q_gen_6415
<cons>(q_gen_6392, q_gen_6391) -> q_gen_6420
<b, s>(q_gen_6415) -> q_gen_6394
<b, z>() -> q_gen_6394
<a, z>() -> q_gen_6406
<a, cons, s>(q_gen_6394, q_gen_6420) -> q_gen_6386
<a, cons, s>(q_gen_6406, q_gen_6391) -> q_gen_6386
<a, cons, z>(q_gen_6404, q_gen_6391) -> q_gen_6386
<a, cons, z>(q_gen_6404, q_gen_6412) -> q_gen_6386
<a, nil, z>() -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6391) -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6412) -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6420) -> q_gen_6386
<b, cons, s>(q_gen_6406, q_gen_6412) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6391) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6420) -> q_gen_6386
<b, nil, z>() -> q_gen_6386
<a, cons, s>(q_gen_6394, q_gen_6391) -> q_gen_6407
<a, cons, z>(q_gen_6404, q_gen_6420) -> q_gen_6407
<b, cons, s>(q_gen_6406, q_gen_6391) -> q_gen_6407
<b, cons, z>(q_gen_6404, q_gen_6391) -> q_gen_6407
}

Datatype: <elt, eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_6383, q_gen_6385, q_gen_6408},
Q_f={q_gen_6383},
Delta=
{
<s>(q_gen_6385) -> q_gen_6385
<z>() -> q_gen_6385
<s, s>(q_gen_6383) -> q_gen_6383
<z, s>(q_gen_6385) -> q_gen_6383
<z, z>() -> q_gen_6383
<s, z>(q_gen_6385) -> q_gen_6408
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  prefix -> 
{{{
Q={q_gen_6382, q_gen_6388, q_gen_6396, q_gen_6397},
Q_f={q_gen_6382},
Delta=
{
<cons>(q_gen_6397, q_gen_6396) -> q_gen_6396
<nil>() -> q_gen_6396
<a>() -> q_gen_6397
<b>() -> q_gen_6397
<cons, cons>(q_gen_6388, q_gen_6382) -> q_gen_6382
<nil, cons>(q_gen_6397, q_gen_6396) -> q_gen_6382
<nil, nil>() -> q_gen_6382
<a, a>() -> q_gen_6388
<b, b>() -> q_gen_6388
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 18
() -> leq([z, s(nn2)]) -> 18
() -> leq([z, z]) -> 18
() -> prefix([nil, y]) -> 18
(count([x, l1, _py]) /\ count([x, l2, _qy]) /\ prefix([l1, l2])) -> leq([_py, _qy]) -> 19
(count([x, t1, _jy])) -> count([x, cons(x, t1), s(_jy)]) -> 22
(count([x, t1, _ky]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ky]) -> 22
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 19
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 19
(leq([s(nn1), z])) -> BOT -> 19
(prefix([zs, ys])) -> prefix([cons(y2, zs), cons(y2, ys)]) -> 19
(prefix([cons(y2, zs), cons(y2, ys)])) -> prefix([zs, ys]) -> 19
(prefix([cons(z, zs), cons(y2, ys)]) /\ not eq_elt([z, y2])) -> BOT -> 19
(prefix([cons(z, zs), nil])) -> BOT -> 19
}
Sat witness: Found: ((count([x, t1, _jy])) -> count([x, cons(x, t1), s(_jy)]), {
_jy -> z  ;  t1 -> cons(b, nil)  ;  x -> a
})

-------------------------------------------
Step 32, which took 0.044115 s (model generation: 0.040951,  model checking: 0.003164):

Model:
|_
{
count -> 
{{{
Q={q_gen_6386, q_gen_6391, q_gen_6392, q_gen_6394, q_gen_6404, q_gen_6406, q_gen_6407, q_gen_6412, q_gen_6415, q_gen_6420},
Q_f={q_gen_6386},
Delta=
{
<cons>(q_gen_6404, q_gen_6412) -> q_gen_6391
<nil>() -> q_gen_6391
<a>() -> q_gen_6392
<b>() -> q_gen_6404
<cons>(q_gen_6404, q_gen_6391) -> q_gen_6412
<s>(q_gen_6415) -> q_gen_6415
<z>() -> q_gen_6415
<cons>(q_gen_6392, q_gen_6391) -> q_gen_6420
<cons>(q_gen_6404, q_gen_6420) -> q_gen_6420
<b, s>(q_gen_6415) -> q_gen_6394
<b, z>() -> q_gen_6394
<a, z>() -> q_gen_6406
<a, cons, s>(q_gen_6394, q_gen_6420) -> q_gen_6386
<a, cons, s>(q_gen_6406, q_gen_6391) -> q_gen_6386
<a, cons, s>(q_gen_6406, q_gen_6412) -> q_gen_6386
<a, cons, z>(q_gen_6404, q_gen_6391) -> q_gen_6386
<a, cons, z>(q_gen_6404, q_gen_6412) -> q_gen_6386
<a, nil, z>() -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6391) -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6412) -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6420) -> q_gen_6386
<b, cons, s>(q_gen_6406, q_gen_6412) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6391) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6420) -> q_gen_6386
<b, nil, z>() -> q_gen_6386
<a, cons, s>(q_gen_6394, q_gen_6391) -> q_gen_6407
<a, cons, s>(q_gen_6406, q_gen_6420) -> q_gen_6407
<a, cons, z>(q_gen_6404, q_gen_6420) -> q_gen_6407
<b, cons, s>(q_gen_6406, q_gen_6391) -> q_gen_6407
<b, cons, z>(q_gen_6404, q_gen_6391) -> q_gen_6407
}

Datatype: <elt, eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_6383, q_gen_6385, q_gen_6408},
Q_f={q_gen_6383},
Delta=
{
<s>(q_gen_6385) -> q_gen_6385
<z>() -> q_gen_6385
<s, s>(q_gen_6383) -> q_gen_6383
<z, s>(q_gen_6385) -> q_gen_6383
<z, z>() -> q_gen_6383
<s, z>(q_gen_6385) -> q_gen_6408
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  prefix -> 
{{{
Q={q_gen_6382, q_gen_6388, q_gen_6396, q_gen_6397},
Q_f={q_gen_6382},
Delta=
{
<cons>(q_gen_6397, q_gen_6396) -> q_gen_6396
<nil>() -> q_gen_6396
<a>() -> q_gen_6397
<b>() -> q_gen_6397
<cons, cons>(q_gen_6388, q_gen_6382) -> q_gen_6382
<nil, cons>(q_gen_6397, q_gen_6396) -> q_gen_6382
<nil, nil>() -> q_gen_6382
<a, a>() -> q_gen_6388
<b, b>() -> q_gen_6388
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 19
() -> leq([z, s(nn2)]) -> 19
() -> leq([z, z]) -> 19
() -> prefix([nil, y]) -> 19
(count([x, l1, _py]) /\ count([x, l2, _qy]) /\ prefix([l1, l2])) -> leq([_py, _qy]) -> 22
(count([x, t1, _jy])) -> count([x, cons(x, t1), s(_jy)]) -> 22
(count([x, t1, _ky]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ky]) -> 22
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 20
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 20
(leq([s(nn1), z])) -> BOT -> 20
(prefix([zs, ys])) -> prefix([cons(y2, zs), cons(y2, ys)]) -> 20
(prefix([cons(y2, zs), cons(y2, ys)])) -> prefix([zs, ys]) -> 20
(prefix([cons(z, zs), cons(y2, ys)]) /\ not eq_elt([z, y2])) -> BOT -> 20
(prefix([cons(z, zs), nil])) -> BOT -> 20
}
Sat witness: Found: ((count([x, l1, _py]) /\ count([x, l2, _qy]) /\ prefix([l1, l2])) -> leq([_py, _qy]), {
_py -> s(z)  ;  _qy -> z  ;  l1 -> cons(a, cons(b, nil))  ;  l2 -> cons(a, cons(b, cons(a, nil)))  ;  x -> b
})

-------------------------------------------
Step 33, which took 0.042779 s (model generation: 0.039480,  model checking: 0.003299):

Model:
|_
{
count -> 
{{{
Q={q_gen_6386, q_gen_6391, q_gen_6392, q_gen_6394, q_gen_6404, q_gen_6406, q_gen_6407, q_gen_6412, q_gen_6415, q_gen_6420},
Q_f={q_gen_6386},
Delta=
{
<cons>(q_gen_6404, q_gen_6412) -> q_gen_6391
<nil>() -> q_gen_6391
<a>() -> q_gen_6392
<b>() -> q_gen_6404
<cons>(q_gen_6404, q_gen_6391) -> q_gen_6412
<cons>(q_gen_6404, q_gen_6420) -> q_gen_6412
<s>(q_gen_6415) -> q_gen_6415
<z>() -> q_gen_6415
<cons>(q_gen_6392, q_gen_6391) -> q_gen_6420
<b, s>(q_gen_6415) -> q_gen_6394
<b, z>() -> q_gen_6394
<a, z>() -> q_gen_6406
<a, cons, s>(q_gen_6394, q_gen_6420) -> q_gen_6386
<a, cons, s>(q_gen_6406, q_gen_6391) -> q_gen_6386
<a, cons, s>(q_gen_6406, q_gen_6412) -> q_gen_6386
<a, cons, z>(q_gen_6404, q_gen_6391) -> q_gen_6386
<a, cons, z>(q_gen_6404, q_gen_6412) -> q_gen_6386
<a, nil, z>() -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6391) -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6412) -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6420) -> q_gen_6386
<b, cons, s>(q_gen_6406, q_gen_6412) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6391) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6420) -> q_gen_6386
<b, nil, z>() -> q_gen_6386
<a, cons, s>(q_gen_6394, q_gen_6391) -> q_gen_6407
<a, cons, z>(q_gen_6404, q_gen_6420) -> q_gen_6407
<b, cons, s>(q_gen_6406, q_gen_6391) -> q_gen_6407
<b, cons, z>(q_gen_6392, q_gen_6412) -> q_gen_6407
<b, cons, z>(q_gen_6404, q_gen_6391) -> q_gen_6407
}

Datatype: <elt, eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_6383, q_gen_6385, q_gen_6408},
Q_f={q_gen_6383},
Delta=
{
<s>(q_gen_6385) -> q_gen_6385
<z>() -> q_gen_6385
<s, s>(q_gen_6383) -> q_gen_6383
<z, s>(q_gen_6385) -> q_gen_6383
<z, z>() -> q_gen_6383
<s, z>(q_gen_6385) -> q_gen_6408
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  prefix -> 
{{{
Q={q_gen_6382, q_gen_6388, q_gen_6396, q_gen_6397},
Q_f={q_gen_6382},
Delta=
{
<cons>(q_gen_6397, q_gen_6396) -> q_gen_6396
<nil>() -> q_gen_6396
<a>() -> q_gen_6397
<b>() -> q_gen_6397
<cons, cons>(q_gen_6388, q_gen_6382) -> q_gen_6382
<nil, cons>(q_gen_6397, q_gen_6396) -> q_gen_6382
<nil, nil>() -> q_gen_6382
<a, a>() -> q_gen_6388
<b, b>() -> q_gen_6388
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 20
() -> leq([z, s(nn2)]) -> 20
() -> leq([z, z]) -> 20
() -> prefix([nil, y]) -> 20
(count([x, l1, _py]) /\ count([x, l2, _qy]) /\ prefix([l1, l2])) -> leq([_py, _qy]) -> 22
(count([x, t1, _jy])) -> count([x, cons(x, t1), s(_jy)]) -> 22
(count([x, t1, _ky]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ky]) -> 25
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 21
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 21
(leq([s(nn1), z])) -> BOT -> 21
(prefix([zs, ys])) -> prefix([cons(y2, zs), cons(y2, ys)]) -> 21
(prefix([cons(y2, zs), cons(y2, ys)])) -> prefix([zs, ys]) -> 21
(prefix([cons(z, zs), cons(y2, ys)]) /\ not eq_elt([z, y2])) -> BOT -> 21
(prefix([cons(z, zs), nil])) -> BOT -> 21
}
Sat witness: Found: ((count([x, t1, _ky]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ky]), {
_ky -> s(z)  ;  h1 -> a  ;  t1 -> cons(b, cons(b, nil))  ;  x -> b
})

-------------------------------------------
Step 34, which took 0.054031 s (model generation: 0.048261,  model checking: 0.005770):

Model:
|_
{
count -> 
{{{
Q={q_gen_6386, q_gen_6391, q_gen_6392, q_gen_6394, q_gen_6404, q_gen_6406, q_gen_6407, q_gen_6412, q_gen_6415, q_gen_6420},
Q_f={q_gen_6386},
Delta=
{
<nil>() -> q_gen_6391
<a>() -> q_gen_6392
<b>() -> q_gen_6404
<cons>(q_gen_6404, q_gen_6391) -> q_gen_6412
<cons>(q_gen_6404, q_gen_6412) -> q_gen_6412
<cons>(q_gen_6404, q_gen_6420) -> q_gen_6412
<s>(q_gen_6415) -> q_gen_6415
<z>() -> q_gen_6415
<cons>(q_gen_6392, q_gen_6391) -> q_gen_6420
<b, s>(q_gen_6415) -> q_gen_6394
<b, z>() -> q_gen_6394
<a, z>() -> q_gen_6406
<a, cons, s>(q_gen_6394, q_gen_6420) -> q_gen_6386
<a, cons, s>(q_gen_6406, q_gen_6391) -> q_gen_6386
<a, cons, s>(q_gen_6406, q_gen_6412) -> q_gen_6386
<a, cons, z>(q_gen_6404, q_gen_6391) -> q_gen_6386
<a, cons, z>(q_gen_6404, q_gen_6412) -> q_gen_6386
<a, nil, z>() -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6391) -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6412) -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6420) -> q_gen_6386
<b, cons, s>(q_gen_6406, q_gen_6412) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6391) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6420) -> q_gen_6386
<b, nil, z>() -> q_gen_6386
<a, cons, s>(q_gen_6394, q_gen_6391) -> q_gen_6407
<a, cons, z>(q_gen_6404, q_gen_6420) -> q_gen_6407
<b, cons, s>(q_gen_6406, q_gen_6391) -> q_gen_6407
<b, cons, z>(q_gen_6392, q_gen_6412) -> q_gen_6407
<b, cons, z>(q_gen_6404, q_gen_6391) -> q_gen_6407
}

Datatype: <elt, eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_6383, q_gen_6385, q_gen_6408},
Q_f={q_gen_6383},
Delta=
{
<s>(q_gen_6385) -> q_gen_6385
<z>() -> q_gen_6385
<s, s>(q_gen_6383) -> q_gen_6383
<z, s>(q_gen_6385) -> q_gen_6383
<z, z>() -> q_gen_6383
<s, z>(q_gen_6385) -> q_gen_6408
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  prefix -> 
{{{
Q={q_gen_6382, q_gen_6388, q_gen_6396, q_gen_6397},
Q_f={q_gen_6382},
Delta=
{
<cons>(q_gen_6397, q_gen_6396) -> q_gen_6396
<nil>() -> q_gen_6396
<a>() -> q_gen_6397
<b>() -> q_gen_6397
<cons, cons>(q_gen_6388, q_gen_6382) -> q_gen_6382
<nil, cons>(q_gen_6397, q_gen_6396) -> q_gen_6382
<nil, nil>() -> q_gen_6382
<a, a>() -> q_gen_6388
<b, b>() -> q_gen_6388
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 21
() -> leq([z, s(nn2)]) -> 21
() -> leq([z, z]) -> 21
() -> prefix([nil, y]) -> 21
(count([x, l1, _py]) /\ count([x, l2, _qy]) /\ prefix([l1, l2])) -> leq([_py, _qy]) -> 22
(count([x, t1, _jy])) -> count([x, cons(x, t1), s(_jy)]) -> 25
(count([x, t1, _ky]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ky]) -> 25
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 22
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 22
(leq([s(nn1), z])) -> BOT -> 22
(prefix([zs, ys])) -> prefix([cons(y2, zs), cons(y2, ys)]) -> 22
(prefix([cons(y2, zs), cons(y2, ys)])) -> prefix([zs, ys]) -> 22
(prefix([cons(z, zs), cons(y2, ys)]) /\ not eq_elt([z, y2])) -> BOT -> 22
(prefix([cons(z, zs), nil])) -> BOT -> 22
}
Sat witness: Found: ((count([x, t1, _jy])) -> count([x, cons(x, t1), s(_jy)]), {
_jy -> z  ;  t1 -> cons(a, cons(a, nil))  ;  x -> b
})

-------------------------------------------
Step 35, which took 0.053259 s (model generation: 0.048147,  model checking: 0.005112):

Model:
|_
{
count -> 
{{{
Q={q_gen_6386, q_gen_6391, q_gen_6392, q_gen_6394, q_gen_6404, q_gen_6406, q_gen_6407, q_gen_6412, q_gen_6415, q_gen_6420},
Q_f={q_gen_6386},
Delta=
{
<nil>() -> q_gen_6391
<a>() -> q_gen_6392
<b>() -> q_gen_6404
<cons>(q_gen_6404, q_gen_6391) -> q_gen_6412
<cons>(q_gen_6404, q_gen_6412) -> q_gen_6412
<cons>(q_gen_6404, q_gen_6420) -> q_gen_6412
<s>(q_gen_6415) -> q_gen_6415
<z>() -> q_gen_6415
<cons>(q_gen_6392, q_gen_6391) -> q_gen_6420
<cons>(q_gen_6392, q_gen_6420) -> q_gen_6420
<b, s>(q_gen_6415) -> q_gen_6394
<b, z>() -> q_gen_6394
<a, z>() -> q_gen_6406
<a, cons, s>(q_gen_6394, q_gen_6420) -> q_gen_6386
<a, cons, s>(q_gen_6406, q_gen_6391) -> q_gen_6386
<a, cons, s>(q_gen_6406, q_gen_6412) -> q_gen_6386
<a, cons, z>(q_gen_6404, q_gen_6391) -> q_gen_6386
<a, cons, z>(q_gen_6404, q_gen_6412) -> q_gen_6386
<a, nil, z>() -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6391) -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6412) -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6420) -> q_gen_6386
<b, cons, s>(q_gen_6406, q_gen_6412) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6391) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6420) -> q_gen_6386
<b, nil, z>() -> q_gen_6386
<a, cons, s>(q_gen_6394, q_gen_6391) -> q_gen_6407
<a, cons, z>(q_gen_6404, q_gen_6420) -> q_gen_6407
<b, cons, s>(q_gen_6406, q_gen_6391) -> q_gen_6407
<b, cons, z>(q_gen_6392, q_gen_6412) -> q_gen_6407
<b, cons, z>(q_gen_6404, q_gen_6391) -> q_gen_6407
}

Datatype: <elt, eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_6383, q_gen_6385, q_gen_6408},
Q_f={q_gen_6383},
Delta=
{
<s>(q_gen_6385) -> q_gen_6385
<z>() -> q_gen_6385
<s, s>(q_gen_6383) -> q_gen_6383
<z, s>(q_gen_6385) -> q_gen_6383
<z, z>() -> q_gen_6383
<s, z>(q_gen_6385) -> q_gen_6408
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  prefix -> 
{{{
Q={q_gen_6382, q_gen_6388, q_gen_6396, q_gen_6397},
Q_f={q_gen_6382},
Delta=
{
<cons>(q_gen_6397, q_gen_6396) -> q_gen_6396
<nil>() -> q_gen_6396
<a>() -> q_gen_6397
<b>() -> q_gen_6397
<cons, cons>(q_gen_6388, q_gen_6382) -> q_gen_6382
<nil, cons>(q_gen_6397, q_gen_6396) -> q_gen_6382
<nil, nil>() -> q_gen_6382
<a, a>() -> q_gen_6388
<b, b>() -> q_gen_6388
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 22
() -> leq([z, s(nn2)]) -> 22
() -> leq([z, z]) -> 22
() -> prefix([nil, y]) -> 22
(count([x, l1, _py]) /\ count([x, l2, _qy]) /\ prefix([l1, l2])) -> leq([_py, _qy]) -> 25
(count([x, t1, _jy])) -> count([x, cons(x, t1), s(_jy)]) -> 25
(count([x, t1, _ky]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ky]) -> 25
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 23
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 23
(leq([s(nn1), z])) -> BOT -> 23
(prefix([zs, ys])) -> prefix([cons(y2, zs), cons(y2, ys)]) -> 23
(prefix([cons(y2, zs), cons(y2, ys)])) -> prefix([zs, ys]) -> 23
(prefix([cons(z, zs), cons(y2, ys)]) /\ not eq_elt([z, y2])) -> BOT -> 23
(prefix([cons(z, zs), nil])) -> BOT -> 23
}
Sat witness: Found: ((count([x, l1, _py]) /\ count([x, l2, _qy]) /\ prefix([l1, l2])) -> leq([_py, _qy]), {
_py -> s(s(z))  ;  _qy -> s(z)  ;  l1 -> cons(b, nil)  ;  l2 -> cons(b, cons(b, nil))  ;  x -> b
})

-------------------------------------------
Step 36, which took 0.054608 s (model generation: 0.052482,  model checking: 0.002126):

Model:
|_
{
count -> 
{{{
Q={q_gen_6386, q_gen_6391, q_gen_6392, q_gen_6394, q_gen_6404, q_gen_6406, q_gen_6407, q_gen_6412, q_gen_6415, q_gen_6420},
Q_f={q_gen_6386},
Delta=
{
<nil>() -> q_gen_6391
<a>() -> q_gen_6392
<b>() -> q_gen_6404
<cons>(q_gen_6404, q_gen_6391) -> q_gen_6412
<cons>(q_gen_6404, q_gen_6412) -> q_gen_6412
<cons>(q_gen_6404, q_gen_6420) -> q_gen_6412
<s>(q_gen_6415) -> q_gen_6415
<z>() -> q_gen_6415
<cons>(q_gen_6392, q_gen_6391) -> q_gen_6420
<cons>(q_gen_6392, q_gen_6420) -> q_gen_6420
<b, s>(q_gen_6415) -> q_gen_6394
<b, z>() -> q_gen_6394
<a, z>() -> q_gen_6406
<a, cons, s>(q_gen_6394, q_gen_6420) -> q_gen_6386
<a, cons, s>(q_gen_6406, q_gen_6391) -> q_gen_6386
<a, cons, s>(q_gen_6406, q_gen_6412) -> q_gen_6386
<a, cons, z>(q_gen_6404, q_gen_6391) -> q_gen_6386
<a, cons, z>(q_gen_6404, q_gen_6412) -> q_gen_6386
<a, nil, z>() -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6391) -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6412) -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6420) -> q_gen_6386
<b, cons, s>(q_gen_6406, q_gen_6412) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6391) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6420) -> q_gen_6386
<b, nil, z>() -> q_gen_6386
<a, cons, s>(q_gen_6394, q_gen_6391) -> q_gen_6407
<a, cons, z>(q_gen_6404, q_gen_6420) -> q_gen_6407
<b, cons, s>(q_gen_6406, q_gen_6391) -> q_gen_6407
<b, cons, z>(q_gen_6392, q_gen_6412) -> q_gen_6407
<b, cons, z>(q_gen_6404, q_gen_6391) -> q_gen_6407
}

Datatype: <elt, eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_6383, q_gen_6385, q_gen_6408},
Q_f={q_gen_6383},
Delta=
{
<s>(q_gen_6385) -> q_gen_6385
<z>() -> q_gen_6385
<s, s>(q_gen_6383) -> q_gen_6383
<s, s>(q_gen_6408) -> q_gen_6383
<z, s>(q_gen_6385) -> q_gen_6383
<z, z>() -> q_gen_6383
<s, z>(q_gen_6385) -> q_gen_6408
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  prefix -> 
{{{
Q={q_gen_6382, q_gen_6388, q_gen_6396, q_gen_6397},
Q_f={q_gen_6382},
Delta=
{
<cons>(q_gen_6397, q_gen_6396) -> q_gen_6396
<nil>() -> q_gen_6396
<a>() -> q_gen_6397
<b>() -> q_gen_6397
<cons, cons>(q_gen_6388, q_gen_6382) -> q_gen_6382
<nil, cons>(q_gen_6397, q_gen_6396) -> q_gen_6382
<nil, nil>() -> q_gen_6382
<a, a>() -> q_gen_6388
<b, b>() -> q_gen_6388
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 23
() -> leq([z, s(nn2)]) -> 23
() -> leq([z, z]) -> 23
() -> prefix([nil, y]) -> 23
(count([x, l1, _py]) /\ count([x, l2, _qy]) /\ prefix([l1, l2])) -> leq([_py, _qy]) -> 25
(count([x, t1, _jy])) -> count([x, cons(x, t1), s(_jy)]) -> 25
(count([x, t1, _ky]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ky]) -> 25
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 23
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 26
(leq([s(nn1), z])) -> BOT -> 24
(prefix([zs, ys])) -> prefix([cons(y2, zs), cons(y2, ys)]) -> 24
(prefix([cons(y2, zs), cons(y2, ys)])) -> prefix([zs, ys]) -> 24
(prefix([cons(z, zs), cons(y2, ys)]) /\ not eq_elt([z, y2])) -> BOT -> 24
(prefix([cons(z, zs), nil])) -> BOT -> 24
}
Sat witness: Found: ((leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]), {
nn1 -> s(z)  ;  nn2 -> z
})

-------------------------------------------
Step 37, which took 0.059990 s (model generation: 0.058882,  model checking: 0.001108):

Model:
|_
{
count -> 
{{{
Q={q_gen_6386, q_gen_6391, q_gen_6392, q_gen_6394, q_gen_6404, q_gen_6406, q_gen_6407, q_gen_6412, q_gen_6415},
Q_f={q_gen_6386},
Delta=
{
<nil>() -> q_gen_6391
<a>() -> q_gen_6392
<b>() -> q_gen_6404
<cons>(q_gen_6392, q_gen_6391) -> q_gen_6412
<cons>(q_gen_6392, q_gen_6412) -> q_gen_6412
<cons>(q_gen_6404, q_gen_6391) -> q_gen_6412
<cons>(q_gen_6404, q_gen_6412) -> q_gen_6412
<s>(q_gen_6415) -> q_gen_6415
<z>() -> q_gen_6415
<b, s>(q_gen_6415) -> q_gen_6394
<b, z>() -> q_gen_6394
<a, z>() -> q_gen_6406
<a, cons, s>(q_gen_6394, q_gen_6412) -> q_gen_6386
<a, cons, s>(q_gen_6406, q_gen_6391) -> q_gen_6386
<a, cons, s>(q_gen_6406, q_gen_6412) -> q_gen_6386
<a, cons, z>(q_gen_6404, q_gen_6391) -> q_gen_6386
<a, cons, z>(q_gen_6404, q_gen_6412) -> q_gen_6386
<a, nil, z>() -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6391) -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6412) -> q_gen_6386
<b, cons, s>(q_gen_6406, q_gen_6412) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6391) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6412) -> q_gen_6386
<b, nil, z>() -> q_gen_6386
<a, cons, s>(q_gen_6394, q_gen_6391) -> q_gen_6407
<b, cons, s>(q_gen_6406, q_gen_6391) -> q_gen_6407
<b, cons, z>(q_gen_6404, q_gen_6391) -> q_gen_6407
}

Datatype: <elt, eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_6383, q_gen_6385, q_gen_6408},
Q_f={q_gen_6383},
Delta=
{
<s>(q_gen_6385) -> q_gen_6385
<z>() -> q_gen_6385
<s, s>(q_gen_6383) -> q_gen_6383
<z, s>(q_gen_6385) -> q_gen_6383
<z, z>() -> q_gen_6383
<s, s>(q_gen_6408) -> q_gen_6408
<s, z>(q_gen_6385) -> q_gen_6408
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  prefix -> 
{{{
Q={q_gen_6382, q_gen_6387, q_gen_6388, q_gen_6396, q_gen_6397, q_gen_6434},
Q_f={q_gen_6382, q_gen_6387},
Delta=
{
<cons>(q_gen_6397, q_gen_6396) -> q_gen_6396
<nil>() -> q_gen_6396
<a>() -> q_gen_6397
<b>() -> q_gen_6397
<nil, nil>() -> q_gen_6382
<cons, cons>(q_gen_6388, q_gen_6382) -> q_gen_6387
<nil, cons>(q_gen_6397, q_gen_6396) -> q_gen_6387
<a, a>() -> q_gen_6388
<b, b>() -> q_gen_6388
<cons, cons>(q_gen_6388, q_gen_6387) -> q_gen_6434
<cons, cons>(q_gen_6388, q_gen_6434) -> q_gen_6434
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 24
() -> leq([z, s(nn2)]) -> 24
() -> leq([z, z]) -> 24
() -> prefix([nil, y]) -> 24
(count([x, l1, _py]) /\ count([x, l2, _qy]) /\ prefix([l1, l2])) -> leq([_py, _qy]) -> 25
(count([x, t1, _jy])) -> count([x, cons(x, t1), s(_jy)]) -> 25
(count([x, t1, _ky]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ky]) -> 25
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 24
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 26
(leq([s(nn1), z])) -> BOT -> 24
(prefix([zs, ys])) -> prefix([cons(y2, zs), cons(y2, ys)]) -> 27
(prefix([cons(y2, zs), cons(y2, ys)])) -> prefix([zs, ys]) -> 25
(prefix([cons(z, zs), cons(y2, ys)]) /\ not eq_elt([z, y2])) -> BOT -> 25
(prefix([cons(z, zs), nil])) -> BOT -> 25
}
Sat witness: Found: ((prefix([zs, ys])) -> prefix([cons(y2, zs), cons(y2, ys)]), {
y2 -> b  ;  ys -> cons(a, nil)  ;  zs -> nil
})

-------------------------------------------
Step 38, which took 0.070312 s (model generation: 0.059221,  model checking: 0.011091):

Model:
|_
{
count -> 
{{{
Q={q_gen_6386, q_gen_6391, q_gen_6392, q_gen_6394, q_gen_6404, q_gen_6406, q_gen_6407, q_gen_6412, q_gen_6414, q_gen_6415, q_gen_6420},
Q_f={q_gen_6386},
Delta=
{
<cons>(q_gen_6404, q_gen_6412) -> q_gen_6391
<nil>() -> q_gen_6391
<a>() -> q_gen_6392
<b>() -> q_gen_6404
<cons>(q_gen_6404, q_gen_6391) -> q_gen_6412
<cons>(q_gen_6404, q_gen_6420) -> q_gen_6412
<s>(q_gen_6415) -> q_gen_6415
<z>() -> q_gen_6415
<cons>(q_gen_6392, q_gen_6391) -> q_gen_6420
<cons>(q_gen_6392, q_gen_6420) -> q_gen_6420
<b, z>() -> q_gen_6394
<a, z>() -> q_gen_6406
<b, s>(q_gen_6415) -> q_gen_6414
<a, cons, s>(q_gen_6394, q_gen_6420) -> q_gen_6386
<a, cons, s>(q_gen_6406, q_gen_6391) -> q_gen_6386
<a, cons, s>(q_gen_6406, q_gen_6412) -> q_gen_6386
<a, cons, z>(q_gen_6404, q_gen_6391) -> q_gen_6386
<a, cons, z>(q_gen_6404, q_gen_6412) -> q_gen_6386
<a, nil, z>() -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6391) -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6420) -> q_gen_6386
<b, cons, s>(q_gen_6406, q_gen_6412) -> q_gen_6386
<b, cons, s>(q_gen_6414, q_gen_6391) -> q_gen_6386
<b, cons, s>(q_gen_6414, q_gen_6412) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6391) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6420) -> q_gen_6386
<b, nil, z>() -> q_gen_6386
<a, cons, s>(q_gen_6394, q_gen_6391) -> q_gen_6407
<a, cons, s>(q_gen_6414, q_gen_6391) -> q_gen_6407
<a, cons, z>(q_gen_6404, q_gen_6420) -> q_gen_6407
<b, cons, s>(q_gen_6394, q_gen_6412) -> q_gen_6407
<b, cons, s>(q_gen_6406, q_gen_6391) -> q_gen_6407
<b, cons, s>(q_gen_6414, q_gen_6420) -> q_gen_6407
<b, cons, z>(q_gen_6392, q_gen_6412) -> q_gen_6407
<b, cons, z>(q_gen_6404, q_gen_6391) -> q_gen_6407
}

Datatype: <elt, eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_6383, q_gen_6385, q_gen_6408},
Q_f={q_gen_6383},
Delta=
{
<s>(q_gen_6385) -> q_gen_6385
<z>() -> q_gen_6385
<s, s>(q_gen_6383) -> q_gen_6383
<z, s>(q_gen_6385) -> q_gen_6383
<z, z>() -> q_gen_6383
<s, s>(q_gen_6408) -> q_gen_6408
<s, z>(q_gen_6385) -> q_gen_6408
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  prefix -> 
{{{
Q={q_gen_6382, q_gen_6388, q_gen_6396, q_gen_6397},
Q_f={q_gen_6382},
Delta=
{
<cons>(q_gen_6397, q_gen_6396) -> q_gen_6396
<nil>() -> q_gen_6396
<a>() -> q_gen_6397
<b>() -> q_gen_6397
<cons, cons>(q_gen_6388, q_gen_6382) -> q_gen_6382
<nil, cons>(q_gen_6397, q_gen_6396) -> q_gen_6382
<nil, nil>() -> q_gen_6382
<a, a>() -> q_gen_6388
<b, b>() -> q_gen_6388
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 25
() -> leq([z, s(nn2)]) -> 25
() -> leq([z, z]) -> 25
() -> prefix([nil, y]) -> 25
(count([x, l1, _py]) /\ count([x, l2, _qy]) /\ prefix([l1, l2])) -> leq([_py, _qy]) -> 25
(count([x, t1, _jy])) -> count([x, cons(x, t1), s(_jy)]) -> 25
(count([x, t1, _ky]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ky]) -> 28
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 25
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 26
(leq([s(nn1), z])) -> BOT -> 25
(prefix([zs, ys])) -> prefix([cons(y2, zs), cons(y2, ys)]) -> 27
(prefix([cons(y2, zs), cons(y2, ys)])) -> prefix([zs, ys]) -> 26
(prefix([cons(z, zs), cons(y2, ys)]) /\ not eq_elt([z, y2])) -> BOT -> 26
(prefix([cons(z, zs), nil])) -> BOT -> 26
}
Sat witness: Found: ((count([x, t1, _ky]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ky]), {
_ky -> s(z)  ;  h1 -> a  ;  t1 -> cons(a, cons(b, nil))  ;  x -> b
})

-------------------------------------------
Step 39, which took 0.068099 s (model generation: 0.064797,  model checking: 0.003302):

Model:
|_
{
count -> 
{{{
Q={q_gen_6386, q_gen_6391, q_gen_6392, q_gen_6394, q_gen_6404, q_gen_6406, q_gen_6407, q_gen_6412, q_gen_6414, q_gen_6415, q_gen_6420},
Q_f={q_gen_6386},
Delta=
{
<cons>(q_gen_6404, q_gen_6412) -> q_gen_6391
<nil>() -> q_gen_6391
<a>() -> q_gen_6392
<b>() -> q_gen_6404
<cons>(q_gen_6404, q_gen_6391) -> q_gen_6412
<cons>(q_gen_6404, q_gen_6420) -> q_gen_6412
<s>(q_gen_6415) -> q_gen_6415
<z>() -> q_gen_6415
<cons>(q_gen_6392, q_gen_6391) -> q_gen_6420
<cons>(q_gen_6392, q_gen_6412) -> q_gen_6420
<cons>(q_gen_6392, q_gen_6420) -> q_gen_6420
<b, z>() -> q_gen_6394
<a, z>() -> q_gen_6406
<b, s>(q_gen_6415) -> q_gen_6414
<a, cons, s>(q_gen_6394, q_gen_6420) -> q_gen_6386
<a, cons, s>(q_gen_6406, q_gen_6391) -> q_gen_6386
<a, cons, s>(q_gen_6406, q_gen_6412) -> q_gen_6386
<a, cons, z>(q_gen_6404, q_gen_6391) -> q_gen_6386
<a, cons, z>(q_gen_6404, q_gen_6412) -> q_gen_6386
<a, nil, z>() -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6391) -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6420) -> q_gen_6386
<b, cons, s>(q_gen_6406, q_gen_6412) -> q_gen_6386
<b, cons, s>(q_gen_6406, q_gen_6420) -> q_gen_6386
<b, cons, s>(q_gen_6414, q_gen_6391) -> q_gen_6386
<b, cons, s>(q_gen_6414, q_gen_6412) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6391) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6420) -> q_gen_6386
<b, nil, z>() -> q_gen_6386
<a, cons, s>(q_gen_6394, q_gen_6391) -> q_gen_6407
<a, cons, s>(q_gen_6414, q_gen_6391) -> q_gen_6407
<a, cons, z>(q_gen_6404, q_gen_6420) -> q_gen_6407
<b, cons, s>(q_gen_6394, q_gen_6412) -> q_gen_6407
<b, cons, s>(q_gen_6406, q_gen_6391) -> q_gen_6407
<b, cons, s>(q_gen_6414, q_gen_6420) -> q_gen_6407
<b, cons, z>(q_gen_6392, q_gen_6412) -> q_gen_6407
<b, cons, z>(q_gen_6404, q_gen_6391) -> q_gen_6407
}

Datatype: <elt, eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_6383, q_gen_6385, q_gen_6408},
Q_f={q_gen_6383},
Delta=
{
<s>(q_gen_6385) -> q_gen_6385
<z>() -> q_gen_6385
<s, s>(q_gen_6383) -> q_gen_6383
<z, s>(q_gen_6385) -> q_gen_6383
<z, z>() -> q_gen_6383
<s, s>(q_gen_6408) -> q_gen_6408
<s, z>(q_gen_6385) -> q_gen_6408
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  prefix -> 
{{{
Q={q_gen_6382, q_gen_6388, q_gen_6396, q_gen_6397},
Q_f={q_gen_6382},
Delta=
{
<cons>(q_gen_6397, q_gen_6396) -> q_gen_6396
<nil>() -> q_gen_6396
<a>() -> q_gen_6397
<b>() -> q_gen_6397
<cons, cons>(q_gen_6388, q_gen_6382) -> q_gen_6382
<nil, cons>(q_gen_6397, q_gen_6396) -> q_gen_6382
<nil, nil>() -> q_gen_6382
<a, a>() -> q_gen_6388
<b, b>() -> q_gen_6388
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 25
() -> leq([z, s(nn2)]) -> 25
() -> leq([z, z]) -> 25
() -> prefix([nil, y]) -> 25
(count([x, l1, _py]) /\ count([x, l2, _qy]) /\ prefix([l1, l2])) -> leq([_py, _qy]) -> 25
(count([x, t1, _jy])) -> count([x, cons(x, t1), s(_jy)]) -> 28
(count([x, t1, _ky]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ky]) -> 28
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 26
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 26
(leq([s(nn1), z])) -> BOT -> 26
(prefix([zs, ys])) -> prefix([cons(y2, zs), cons(y2, ys)]) -> 27
(prefix([cons(y2, zs), cons(y2, ys)])) -> prefix([zs, ys]) -> 26
(prefix([cons(z, zs), cons(y2, ys)]) /\ not eq_elt([z, y2])) -> BOT -> 26
(prefix([cons(z, zs), nil])) -> BOT -> 26
}
Sat witness: Found: ((count([x, t1, _jy])) -> count([x, cons(x, t1), s(_jy)]), {
_jy -> s(z)  ;  t1 -> cons(a, cons(a, nil))  ;  x -> b
})

-------------------------------------------
Step 40, which took 0.071426 s (model generation: 0.068359,  model checking: 0.003067):

Model:
|_
{
count -> 
{{{
Q={q_gen_6386, q_gen_6391, q_gen_6392, q_gen_6394, q_gen_6404, q_gen_6406, q_gen_6407, q_gen_6412, q_gen_6415, q_gen_6420},
Q_f={q_gen_6386},
Delta=
{
<cons>(q_gen_6392, q_gen_6420) -> q_gen_6391
<nil>() -> q_gen_6391
<a>() -> q_gen_6392
<b>() -> q_gen_6404
<cons>(q_gen_6392, q_gen_6412) -> q_gen_6412
<cons>(q_gen_6404, q_gen_6391) -> q_gen_6412
<cons>(q_gen_6404, q_gen_6412) -> q_gen_6412
<cons>(q_gen_6404, q_gen_6420) -> q_gen_6412
<s>(q_gen_6415) -> q_gen_6415
<z>() -> q_gen_6415
<cons>(q_gen_6392, q_gen_6391) -> q_gen_6420
<b, z>() -> q_gen_6394
<a, z>() -> q_gen_6406
<b, s>(q_gen_6415) -> q_gen_6406
<a, cons, s>(q_gen_6394, q_gen_6420) -> q_gen_6386
<a, cons, s>(q_gen_6406, q_gen_6391) -> q_gen_6386
<a, cons, s>(q_gen_6406, q_gen_6412) -> q_gen_6386
<a, cons, z>(q_gen_6404, q_gen_6391) -> q_gen_6386
<a, cons, z>(q_gen_6404, q_gen_6412) -> q_gen_6386
<a, nil, z>() -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6391) -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6412) -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6420) -> q_gen_6386
<b, cons, s>(q_gen_6406, q_gen_6412) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6391) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6420) -> q_gen_6386
<b, nil, z>() -> q_gen_6386
<a, cons, s>(q_gen_6394, q_gen_6391) -> q_gen_6407
<a, cons, z>(q_gen_6404, q_gen_6420) -> q_gen_6407
<b, cons, s>(q_gen_6406, q_gen_6391) -> q_gen_6407
<b, cons, s>(q_gen_6406, q_gen_6420) -> q_gen_6407
<b, cons, z>(q_gen_6392, q_gen_6412) -> q_gen_6407
<b, cons, z>(q_gen_6404, q_gen_6391) -> q_gen_6407
}

Datatype: <elt, eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_6383, q_gen_6385, q_gen_6399, q_gen_6408},
Q_f={q_gen_6383},
Delta=
{
<z>() -> q_gen_6385
<s>(q_gen_6385) -> q_gen_6399
<s, s>(q_gen_6383) -> q_gen_6383
<s, z>(q_gen_6399) -> q_gen_6383
<z, s>(q_gen_6385) -> q_gen_6383
<z, s>(q_gen_6399) -> q_gen_6383
<z, z>() -> q_gen_6383
<s, s>(q_gen_6408) -> q_gen_6408
<s, z>(q_gen_6385) -> q_gen_6408
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  prefix -> 
{{{
Q={q_gen_6382, q_gen_6388, q_gen_6396, q_gen_6397},
Q_f={q_gen_6382},
Delta=
{
<cons>(q_gen_6397, q_gen_6396) -> q_gen_6396
<nil>() -> q_gen_6396
<a>() -> q_gen_6397
<b>() -> q_gen_6397
<cons, cons>(q_gen_6388, q_gen_6382) -> q_gen_6382
<nil, cons>(q_gen_6397, q_gen_6396) -> q_gen_6382
<nil, nil>() -> q_gen_6382
<a, a>() -> q_gen_6388
<b, b>() -> q_gen_6388
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 25
() -> leq([z, s(nn2)]) -> 25
() -> leq([z, z]) -> 25
() -> prefix([nil, y]) -> 25
(count([x, l1, _py]) /\ count([x, l2, _qy]) /\ prefix([l1, l2])) -> leq([_py, _qy]) -> 28
(count([x, t1, _jy])) -> count([x, cons(x, t1), s(_jy)]) -> 28
(count([x, t1, _ky]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ky]) -> 28
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 26
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 26
(leq([s(nn1), z])) -> BOT -> 26
(prefix([zs, ys])) -> prefix([cons(y2, zs), cons(y2, ys)]) -> 27
(prefix([cons(y2, zs), cons(y2, ys)])) -> prefix([zs, ys]) -> 26
(prefix([cons(z, zs), cons(y2, ys)]) /\ not eq_elt([z, y2])) -> BOT -> 26
(prefix([cons(z, zs), nil])) -> BOT -> 26
}
Sat witness: Found: ((count([x, l1, _py]) /\ count([x, l2, _qy]) /\ prefix([l1, l2])) -> leq([_py, _qy]), {
_py -> s(z)  ;  _qy -> z  ;  l1 -> cons(b, cons(a, nil))  ;  l2 -> cons(b, cons(a, cons(a, nil)))  ;  x -> a
})

-------------------------------------------
Step 41, which took 0.085847 s (model generation: 0.071383,  model checking: 0.014464):

Model:
|_
{
count -> 
{{{
Q={q_gen_6386, q_gen_6391, q_gen_6392, q_gen_6394, q_gen_6404, q_gen_6406, q_gen_6407, q_gen_6412, q_gen_6414, q_gen_6415, q_gen_6420},
Q_f={q_gen_6386},
Delta=
{
<cons>(q_gen_6404, q_gen_6412) -> q_gen_6391
<nil>() -> q_gen_6391
<a>() -> q_gen_6392
<b>() -> q_gen_6404
<cons>(q_gen_6392, q_gen_6412) -> q_gen_6412
<cons>(q_gen_6404, q_gen_6391) -> q_gen_6412
<cons>(q_gen_6404, q_gen_6420) -> q_gen_6412
<s>(q_gen_6415) -> q_gen_6415
<z>() -> q_gen_6415
<cons>(q_gen_6392, q_gen_6391) -> q_gen_6420
<cons>(q_gen_6392, q_gen_6420) -> q_gen_6420
<b, z>() -> q_gen_6394
<a, z>() -> q_gen_6406
<b, s>(q_gen_6415) -> q_gen_6414
<a, cons, s>(q_gen_6394, q_gen_6420) -> q_gen_6386
<a, cons, s>(q_gen_6406, q_gen_6391) -> q_gen_6386
<a, cons, s>(q_gen_6406, q_gen_6412) -> q_gen_6386
<a, cons, z>(q_gen_6404, q_gen_6391) -> q_gen_6386
<a, cons, z>(q_gen_6404, q_gen_6412) -> q_gen_6386
<a, nil, z>() -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6391) -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6420) -> q_gen_6386
<b, cons, s>(q_gen_6406, q_gen_6412) -> q_gen_6386
<b, cons, s>(q_gen_6414, q_gen_6412) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6391) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6420) -> q_gen_6386
<b, nil, z>() -> q_gen_6386
<a, cons, s>(q_gen_6394, q_gen_6391) -> q_gen_6407
<a, cons, s>(q_gen_6414, q_gen_6391) -> q_gen_6407
<a, cons, z>(q_gen_6404, q_gen_6420) -> q_gen_6407
<b, cons, s>(q_gen_6394, q_gen_6412) -> q_gen_6407
<b, cons, s>(q_gen_6406, q_gen_6391) -> q_gen_6407
<b, cons, s>(q_gen_6406, q_gen_6420) -> q_gen_6407
<b, cons, s>(q_gen_6414, q_gen_6391) -> q_gen_6407
<b, cons, s>(q_gen_6414, q_gen_6420) -> q_gen_6407
<b, cons, z>(q_gen_6392, q_gen_6412) -> q_gen_6407
<b, cons, z>(q_gen_6404, q_gen_6391) -> q_gen_6407
}

Datatype: <elt, eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_6383, q_gen_6385, q_gen_6408},
Q_f={q_gen_6383},
Delta=
{
<s>(q_gen_6385) -> q_gen_6385
<z>() -> q_gen_6385
<s, s>(q_gen_6383) -> q_gen_6383
<z, s>(q_gen_6385) -> q_gen_6383
<z, z>() -> q_gen_6383
<s, s>(q_gen_6408) -> q_gen_6408
<s, z>(q_gen_6385) -> q_gen_6408
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  prefix -> 
{{{
Q={q_gen_6382, q_gen_6388, q_gen_6396, q_gen_6397},
Q_f={q_gen_6382},
Delta=
{
<cons>(q_gen_6397, q_gen_6396) -> q_gen_6396
<nil>() -> q_gen_6396
<a>() -> q_gen_6397
<b>() -> q_gen_6397
<cons, cons>(q_gen_6388, q_gen_6382) -> q_gen_6382
<nil, cons>(q_gen_6397, q_gen_6396) -> q_gen_6382
<nil, nil>() -> q_gen_6382
<a, a>() -> q_gen_6388
<b, b>() -> q_gen_6388
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 26
() -> leq([z, s(nn2)]) -> 26
() -> leq([z, z]) -> 26
() -> prefix([nil, y]) -> 26
(count([x, l1, _py]) /\ count([x, l2, _qy]) /\ prefix([l1, l2])) -> leq([_py, _qy]) -> 28
(count([x, t1, _jy])) -> count([x, cons(x, t1), s(_jy)]) -> 28
(count([x, t1, _ky]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ky]) -> 31
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 27
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 27
(leq([s(nn1), z])) -> BOT -> 27
(prefix([zs, ys])) -> prefix([cons(y2, zs), cons(y2, ys)]) -> 28
(prefix([cons(y2, zs), cons(y2, ys)])) -> prefix([zs, ys]) -> 27
(prefix([cons(z, zs), cons(y2, ys)]) /\ not eq_elt([z, y2])) -> BOT -> 27
(prefix([cons(z, zs), nil])) -> BOT -> 27
}
Sat witness: Found: ((count([x, t1, _ky]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ky]), {
_ky -> s(z)  ;  h1 -> b  ;  t1 -> cons(a, cons(b, cons(a, nil)))  ;  x -> a
})

-------------------------------------------
Step 42, which took 0.098858 s (model generation: 0.083613,  model checking: 0.015245):

Model:
|_
{
count -> 
{{{
Q={q_gen_6386, q_gen_6391, q_gen_6392, q_gen_6394, q_gen_6404, q_gen_6406, q_gen_6407, q_gen_6412, q_gen_6414, q_gen_6415, q_gen_6420},
Q_f={q_gen_6386},
Delta=
{
<cons>(q_gen_6404, q_gen_6412) -> q_gen_6391
<nil>() -> q_gen_6391
<a>() -> q_gen_6392
<b>() -> q_gen_6404
<cons>(q_gen_6392, q_gen_6412) -> q_gen_6412
<cons>(q_gen_6404, q_gen_6391) -> q_gen_6412
<cons>(q_gen_6404, q_gen_6420) -> q_gen_6412
<s>(q_gen_6415) -> q_gen_6415
<z>() -> q_gen_6415
<cons>(q_gen_6392, q_gen_6391) -> q_gen_6420
<cons>(q_gen_6392, q_gen_6420) -> q_gen_6420
<b, z>() -> q_gen_6394
<a, z>() -> q_gen_6406
<b, s>(q_gen_6415) -> q_gen_6414
<a, cons, s>(q_gen_6394, q_gen_6412) -> q_gen_6386
<a, cons, s>(q_gen_6394, q_gen_6420) -> q_gen_6386
<a, cons, s>(q_gen_6406, q_gen_6391) -> q_gen_6386
<a, cons, s>(q_gen_6406, q_gen_6412) -> q_gen_6386
<a, cons, z>(q_gen_6404, q_gen_6391) -> q_gen_6386
<a, cons, z>(q_gen_6404, q_gen_6412) -> q_gen_6386
<a, nil, z>() -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6391) -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6420) -> q_gen_6386
<b, cons, s>(q_gen_6406, q_gen_6412) -> q_gen_6386
<b, cons, s>(q_gen_6414, q_gen_6391) -> q_gen_6386
<b, cons, s>(q_gen_6414, q_gen_6412) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6391) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6420) -> q_gen_6386
<b, nil, z>() -> q_gen_6386
<a, cons, s>(q_gen_6394, q_gen_6391) -> q_gen_6407
<a, cons, s>(q_gen_6414, q_gen_6391) -> q_gen_6407
<a, cons, z>(q_gen_6404, q_gen_6420) -> q_gen_6407
<b, cons, s>(q_gen_6394, q_gen_6412) -> q_gen_6407
<b, cons, s>(q_gen_6406, q_gen_6391) -> q_gen_6407
<b, cons, s>(q_gen_6406, q_gen_6420) -> q_gen_6407
<b, cons, s>(q_gen_6414, q_gen_6420) -> q_gen_6407
<b, cons, z>(q_gen_6392, q_gen_6412) -> q_gen_6407
<b, cons, z>(q_gen_6404, q_gen_6391) -> q_gen_6407
}

Datatype: <elt, eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_6383, q_gen_6385, q_gen_6408},
Q_f={q_gen_6383},
Delta=
{
<s>(q_gen_6385) -> q_gen_6385
<z>() -> q_gen_6385
<s, s>(q_gen_6383) -> q_gen_6383
<z, s>(q_gen_6385) -> q_gen_6383
<z, z>() -> q_gen_6383
<s, s>(q_gen_6408) -> q_gen_6408
<s, z>(q_gen_6385) -> q_gen_6408
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  prefix -> 
{{{
Q={q_gen_6382, q_gen_6388, q_gen_6396, q_gen_6397},
Q_f={q_gen_6382},
Delta=
{
<cons>(q_gen_6397, q_gen_6396) -> q_gen_6396
<nil>() -> q_gen_6396
<a>() -> q_gen_6397
<b>() -> q_gen_6397
<cons, cons>(q_gen_6388, q_gen_6382) -> q_gen_6382
<nil, cons>(q_gen_6397, q_gen_6396) -> q_gen_6382
<nil, nil>() -> q_gen_6382
<a, a>() -> q_gen_6388
<b, b>() -> q_gen_6388
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 27
() -> leq([z, s(nn2)]) -> 27
() -> leq([z, z]) -> 27
() -> prefix([nil, y]) -> 27
(count([x, l1, _py]) /\ count([x, l2, _qy]) /\ prefix([l1, l2])) -> leq([_py, _qy]) -> 28
(count([x, t1, _jy])) -> count([x, cons(x, t1), s(_jy)]) -> 31
(count([x, t1, _ky]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ky]) -> 31
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 28
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 28
(leq([s(nn1), z])) -> BOT -> 28
(prefix([zs, ys])) -> prefix([cons(y2, zs), cons(y2, ys)]) -> 29
(prefix([cons(y2, zs), cons(y2, ys)])) -> prefix([zs, ys]) -> 28
(prefix([cons(z, zs), cons(y2, ys)]) /\ not eq_elt([z, y2])) -> BOT -> 28
(prefix([cons(z, zs), nil])) -> BOT -> 28
}
Sat witness: Found: ((count([x, t1, _jy])) -> count([x, cons(x, t1), s(_jy)]), {
_jy -> s(z)  ;  t1 -> cons(a, cons(a, cons(b, cons(a, nil))))  ;  x -> a
})

-------------------------------------------
Step 43, which took 0.097333 s (model generation: 0.091562,  model checking: 0.005771):

Model:
|_
{
count -> 
{{{
Q={q_gen_6386, q_gen_6391, q_gen_6392, q_gen_6394, q_gen_6404, q_gen_6406, q_gen_6407, q_gen_6412, q_gen_6414, q_gen_6415, q_gen_6420},
Q_f={q_gen_6386},
Delta=
{
<cons>(q_gen_6404, q_gen_6412) -> q_gen_6391
<nil>() -> q_gen_6391
<a>() -> q_gen_6392
<b>() -> q_gen_6404
<cons>(q_gen_6404, q_gen_6391) -> q_gen_6412
<cons>(q_gen_6404, q_gen_6420) -> q_gen_6412
<s>(q_gen_6415) -> q_gen_6415
<z>() -> q_gen_6415
<cons>(q_gen_6392, q_gen_6391) -> q_gen_6420
<cons>(q_gen_6392, q_gen_6412) -> q_gen_6420
<cons>(q_gen_6392, q_gen_6420) -> q_gen_6420
<a, s>(q_gen_6415) -> q_gen_6394
<b, z>() -> q_gen_6394
<a, z>() -> q_gen_6406
<b, s>(q_gen_6415) -> q_gen_6414
<a, cons, s>(q_gen_6394, q_gen_6420) -> q_gen_6386
<a, cons, s>(q_gen_6406, q_gen_6391) -> q_gen_6386
<a, cons, s>(q_gen_6406, q_gen_6412) -> q_gen_6386
<a, cons, s>(q_gen_6406, q_gen_6420) -> q_gen_6386
<a, cons, z>(q_gen_6404, q_gen_6391) -> q_gen_6386
<a, cons, z>(q_gen_6404, q_gen_6412) -> q_gen_6386
<a, nil, z>() -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6391) -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6420) -> q_gen_6386
<b, cons, s>(q_gen_6406, q_gen_6412) -> q_gen_6386
<b, cons, s>(q_gen_6406, q_gen_6420) -> q_gen_6386
<b, cons, s>(q_gen_6414, q_gen_6391) -> q_gen_6386
<b, cons, s>(q_gen_6414, q_gen_6412) -> q_gen_6386
<b, cons, s>(q_gen_6414, q_gen_6420) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6391) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6420) -> q_gen_6386
<b, nil, z>() -> q_gen_6386
<a, cons, s>(q_gen_6394, q_gen_6391) -> q_gen_6407
<a, cons, s>(q_gen_6414, q_gen_6391) -> q_gen_6407
<a, cons, z>(q_gen_6404, q_gen_6420) -> q_gen_6407
<b, cons, s>(q_gen_6394, q_gen_6412) -> q_gen_6407
<b, cons, s>(q_gen_6406, q_gen_6391) -> q_gen_6407
<b, cons, z>(q_gen_6392, q_gen_6412) -> q_gen_6407
<b, cons, z>(q_gen_6404, q_gen_6391) -> q_gen_6407
}

Datatype: <elt, eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_6383, q_gen_6385, q_gen_6408},
Q_f={q_gen_6383},
Delta=
{
<s>(q_gen_6385) -> q_gen_6385
<z>() -> q_gen_6385
<s, s>(q_gen_6383) -> q_gen_6383
<z, s>(q_gen_6385) -> q_gen_6383
<z, z>() -> q_gen_6383
<s, s>(q_gen_6408) -> q_gen_6408
<s, z>(q_gen_6385) -> q_gen_6408
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  prefix -> 
{{{
Q={q_gen_6382, q_gen_6388, q_gen_6396, q_gen_6397},
Q_f={q_gen_6382},
Delta=
{
<cons>(q_gen_6397, q_gen_6396) -> q_gen_6396
<nil>() -> q_gen_6396
<a>() -> q_gen_6397
<b>() -> q_gen_6397
<cons, cons>(q_gen_6388, q_gen_6382) -> q_gen_6382
<nil, cons>(q_gen_6397, q_gen_6396) -> q_gen_6382
<nil, nil>() -> q_gen_6382
<a, a>() -> q_gen_6388
<b, b>() -> q_gen_6388
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 28
() -> leq([z, s(nn2)]) -> 28
() -> leq([z, z]) -> 28
() -> prefix([nil, y]) -> 28
(count([x, l1, _py]) /\ count([x, l2, _qy]) /\ prefix([l1, l2])) -> leq([_py, _qy]) -> 31
(count([x, t1, _jy])) -> count([x, cons(x, t1), s(_jy)]) -> 31
(count([x, t1, _ky]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ky]) -> 31
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 29
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 29
(leq([s(nn1), z])) -> BOT -> 29
(prefix([zs, ys])) -> prefix([cons(y2, zs), cons(y2, ys)]) -> 29
(prefix([cons(y2, zs), cons(y2, ys)])) -> prefix([zs, ys]) -> 29
(prefix([cons(z, zs), cons(y2, ys)]) /\ not eq_elt([z, y2])) -> BOT -> 29
(prefix([cons(z, zs), nil])) -> BOT -> 29
}
Sat witness: Found: ((count([x, l1, _py]) /\ count([x, l2, _qy]) /\ prefix([l1, l2])) -> leq([_py, _qy]), {
_py -> s(s(z))  ;  _qy -> z  ;  l1 -> cons(a, nil)  ;  l2 -> cons(a, nil)  ;  x -> b
})

-------------------------------------------
Step 44, which took 0.102615 s (model generation: 0.089233,  model checking: 0.013382):

Model:
|_
{
count -> 
{{{
Q={q_gen_6386, q_gen_6391, q_gen_6392, q_gen_6394, q_gen_6404, q_gen_6406, q_gen_6407, q_gen_6412, q_gen_6414, q_gen_6415, q_gen_6420},
Q_f={q_gen_6386},
Delta=
{
<nil>() -> q_gen_6391
<a>() -> q_gen_6392
<b>() -> q_gen_6404
<cons>(q_gen_6392, q_gen_6412) -> q_gen_6412
<cons>(q_gen_6404, q_gen_6391) -> q_gen_6412
<cons>(q_gen_6404, q_gen_6412) -> q_gen_6412
<cons>(q_gen_6404, q_gen_6420) -> q_gen_6412
<s>(q_gen_6415) -> q_gen_6415
<z>() -> q_gen_6415
<cons>(q_gen_6392, q_gen_6391) -> q_gen_6420
<cons>(q_gen_6392, q_gen_6420) -> q_gen_6420
<b, z>() -> q_gen_6394
<a, z>() -> q_gen_6406
<a, s>(q_gen_6415) -> q_gen_6414
<b, s>(q_gen_6415) -> q_gen_6414
<a, cons, s>(q_gen_6394, q_gen_6412) -> q_gen_6386
<a, cons, s>(q_gen_6394, q_gen_6420) -> q_gen_6386
<a, cons, s>(q_gen_6406, q_gen_6391) -> q_gen_6386
<a, cons, s>(q_gen_6406, q_gen_6412) -> q_gen_6386
<a, cons, s>(q_gen_6414, q_gen_6412) -> q_gen_6386
<a, cons, z>(q_gen_6404, q_gen_6391) -> q_gen_6386
<a, cons, z>(q_gen_6404, q_gen_6412) -> q_gen_6386
<a, nil, z>() -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6391) -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6412) -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6420) -> q_gen_6386
<b, cons, s>(q_gen_6406, q_gen_6412) -> q_gen_6386
<b, cons, s>(q_gen_6414, q_gen_6412) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6391) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6420) -> q_gen_6386
<b, nil, z>() -> q_gen_6386
<a, cons, s>(q_gen_6394, q_gen_6391) -> q_gen_6407
<a, cons, s>(q_gen_6414, q_gen_6391) -> q_gen_6407
<a, cons, z>(q_gen_6404, q_gen_6420) -> q_gen_6407
<b, cons, s>(q_gen_6406, q_gen_6391) -> q_gen_6407
<b, cons, s>(q_gen_6406, q_gen_6420) -> q_gen_6407
<b, cons, s>(q_gen_6414, q_gen_6391) -> q_gen_6407
<b, cons, s>(q_gen_6414, q_gen_6420) -> q_gen_6407
<b, cons, z>(q_gen_6392, q_gen_6412) -> q_gen_6407
<b, cons, z>(q_gen_6404, q_gen_6391) -> q_gen_6407
}

Datatype: <elt, eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_6383, q_gen_6385, q_gen_6408},
Q_f={q_gen_6383},
Delta=
{
<s>(q_gen_6385) -> q_gen_6385
<z>() -> q_gen_6385
<s, s>(q_gen_6383) -> q_gen_6383
<z, s>(q_gen_6385) -> q_gen_6383
<z, z>() -> q_gen_6383
<s, s>(q_gen_6408) -> q_gen_6408
<s, z>(q_gen_6385) -> q_gen_6408
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  prefix -> 
{{{
Q={q_gen_6382, q_gen_6388, q_gen_6396, q_gen_6397},
Q_f={q_gen_6382},
Delta=
{
<cons>(q_gen_6397, q_gen_6396) -> q_gen_6396
<nil>() -> q_gen_6396
<a>() -> q_gen_6397
<b>() -> q_gen_6397
<cons, cons>(q_gen_6388, q_gen_6382) -> q_gen_6382
<nil, cons>(q_gen_6397, q_gen_6396) -> q_gen_6382
<nil, nil>() -> q_gen_6382
<a, a>() -> q_gen_6388
<b, b>() -> q_gen_6388
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 29
() -> leq([z, s(nn2)]) -> 29
() -> leq([z, z]) -> 29
() -> prefix([nil, y]) -> 29
(count([x, l1, _py]) /\ count([x, l2, _qy]) /\ prefix([l1, l2])) -> leq([_py, _qy]) -> 31
(count([x, t1, _jy])) -> count([x, cons(x, t1), s(_jy)]) -> 34
(count([x, t1, _ky]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ky]) -> 32
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 30
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 30
(leq([s(nn1), z])) -> BOT -> 30
(prefix([zs, ys])) -> prefix([cons(y2, zs), cons(y2, ys)]) -> 30
(prefix([cons(y2, zs), cons(y2, ys)])) -> prefix([zs, ys]) -> 30
(prefix([cons(z, zs), cons(y2, ys)]) /\ not eq_elt([z, y2])) -> BOT -> 30
(prefix([cons(z, zs), nil])) -> BOT -> 30
}
Sat witness: Found: ((count([x, t1, _jy])) -> count([x, cons(x, t1), s(_jy)]), {
_jy -> s(z)  ;  t1 -> cons(a, nil)  ;  x -> a
})

-------------------------------------------
Step 45, which took 0.096154 s (model generation: 0.095898,  model checking: 0.000256):

Model:
|_
{
count -> 
{{{
Q={q_gen_6386, q_gen_6391, q_gen_6392, q_gen_6394, q_gen_6404, q_gen_6406, q_gen_6407, q_gen_6412, q_gen_6415, q_gen_6420},
Q_f={q_gen_6386},
Delta=
{
<cons>(q_gen_6404, q_gen_6412) -> q_gen_6391
<nil>() -> q_gen_6391
<a>() -> q_gen_6392
<b>() -> q_gen_6404
<cons>(q_gen_6404, q_gen_6391) -> q_gen_6412
<cons>(q_gen_6404, q_gen_6420) -> q_gen_6412
<s>(q_gen_6415) -> q_gen_6415
<z>() -> q_gen_6415
<cons>(q_gen_6392, q_gen_6391) -> q_gen_6420
<cons>(q_gen_6392, q_gen_6412) -> q_gen_6420
<cons>(q_gen_6392, q_gen_6420) -> q_gen_6420
<a, s>(q_gen_6415) -> q_gen_6394
<b, z>() -> q_gen_6394
<a, z>() -> q_gen_6406
<b, s>(q_gen_6415) -> q_gen_6406
<a, cons, s>(q_gen_6394, q_gen_6420) -> q_gen_6386
<a, cons, s>(q_gen_6406, q_gen_6391) -> q_gen_6386
<a, cons, s>(q_gen_6406, q_gen_6412) -> q_gen_6386
<a, cons, s>(q_gen_6406, q_gen_6420) -> q_gen_6386
<a, cons, z>(q_gen_6404, q_gen_6391) -> q_gen_6386
<a, cons, z>(q_gen_6404, q_gen_6412) -> q_gen_6386
<a, nil, z>() -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6391) -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6420) -> q_gen_6386
<b, cons, s>(q_gen_6406, q_gen_6412) -> q_gen_6386
<b, cons, s>(q_gen_6406, q_gen_6420) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6391) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6420) -> q_gen_6386
<b, nil, z>() -> q_gen_6386
<a, cons, s>(q_gen_6394, q_gen_6391) -> q_gen_6407
<a, cons, z>(q_gen_6404, q_gen_6420) -> q_gen_6407
<b, cons, s>(q_gen_6394, q_gen_6412) -> q_gen_6407
<b, cons, s>(q_gen_6406, q_gen_6391) -> q_gen_6407
<b, cons, z>(q_gen_6392, q_gen_6412) -> q_gen_6407
<b, cons, z>(q_gen_6404, q_gen_6391) -> q_gen_6407
}

Datatype: <elt, eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_6383, q_gen_6385, q_gen_6399, q_gen_6408},
Q_f={q_gen_6383},
Delta=
{
<z>() -> q_gen_6385
<s>(q_gen_6385) -> q_gen_6399
<s, s>(q_gen_6383) -> q_gen_6383
<s, z>(q_gen_6399) -> q_gen_6383
<z, s>(q_gen_6385) -> q_gen_6383
<z, s>(q_gen_6399) -> q_gen_6383
<z, z>() -> q_gen_6383
<s, s>(q_gen_6408) -> q_gen_6408
<s, z>(q_gen_6385) -> q_gen_6408
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  prefix -> 
{{{
Q={q_gen_6382, q_gen_6388, q_gen_6396, q_gen_6397},
Q_f={q_gen_6382},
Delta=
{
<cons>(q_gen_6397, q_gen_6396) -> q_gen_6396
<nil>() -> q_gen_6396
<a>() -> q_gen_6397
<b>() -> q_gen_6397
<cons, cons>(q_gen_6388, q_gen_6382) -> q_gen_6382
<nil, cons>(q_gen_6397, q_gen_6396) -> q_gen_6382
<nil, nil>() -> q_gen_6382
<a, a>() -> q_gen_6388
<b, b>() -> q_gen_6388
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 29
() -> leq([z, s(nn2)]) -> 32
() -> leq([z, z]) -> 30
() -> prefix([nil, y]) -> 30
(count([x, l1, _py]) /\ count([x, l2, _qy]) /\ prefix([l1, l2])) -> leq([_py, _qy]) -> 31
(count([x, t1, _jy])) -> count([x, cons(x, t1), s(_jy)]) -> 34
(count([x, t1, _ky]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ky]) -> 32
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 30
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 30
(leq([s(nn1), z])) -> BOT -> 30
(prefix([zs, ys])) -> prefix([cons(y2, zs), cons(y2, ys)]) -> 30
(prefix([cons(y2, zs), cons(y2, ys)])) -> prefix([zs, ys]) -> 30
(prefix([cons(z, zs), cons(y2, ys)]) /\ not eq_elt([z, y2])) -> BOT -> 30
(prefix([cons(z, zs), nil])) -> BOT -> 30
}
Sat witness: Found: (() -> leq([z, s(nn2)]), {
nn2 -> s(s(z))
})

-------------------------------------------
Step 46, which took 0.096525 s (model generation: 0.094502,  model checking: 0.002023):

Model:
|_
{
count -> 
{{{
Q={q_gen_6386, q_gen_6391, q_gen_6392, q_gen_6394, q_gen_6404, q_gen_6406, q_gen_6407, q_gen_6412, q_gen_6415, q_gen_6420},
Q_f={q_gen_6386},
Delta=
{
<cons>(q_gen_6404, q_gen_6412) -> q_gen_6391
<nil>() -> q_gen_6391
<a>() -> q_gen_6392
<b>() -> q_gen_6404
<cons>(q_gen_6404, q_gen_6391) -> q_gen_6412
<cons>(q_gen_6404, q_gen_6420) -> q_gen_6412
<s>(q_gen_6415) -> q_gen_6415
<z>() -> q_gen_6415
<cons>(q_gen_6392, q_gen_6391) -> q_gen_6420
<cons>(q_gen_6392, q_gen_6412) -> q_gen_6420
<cons>(q_gen_6392, q_gen_6420) -> q_gen_6420
<a, s>(q_gen_6415) -> q_gen_6394
<b, z>() -> q_gen_6394
<a, z>() -> q_gen_6406
<b, s>(q_gen_6415) -> q_gen_6406
<a, cons, s>(q_gen_6394, q_gen_6420) -> q_gen_6386
<a, cons, s>(q_gen_6406, q_gen_6391) -> q_gen_6386
<a, cons, s>(q_gen_6406, q_gen_6412) -> q_gen_6386
<a, cons, s>(q_gen_6406, q_gen_6420) -> q_gen_6386
<a, cons, z>(q_gen_6404, q_gen_6391) -> q_gen_6386
<a, cons, z>(q_gen_6404, q_gen_6412) -> q_gen_6386
<a, nil, z>() -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6391) -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6420) -> q_gen_6386
<b, cons, s>(q_gen_6406, q_gen_6412) -> q_gen_6386
<b, cons, s>(q_gen_6406, q_gen_6420) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6391) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6420) -> q_gen_6386
<b, nil, z>() -> q_gen_6386
<a, cons, s>(q_gen_6394, q_gen_6391) -> q_gen_6407
<a, cons, z>(q_gen_6404, q_gen_6420) -> q_gen_6407
<b, cons, s>(q_gen_6394, q_gen_6412) -> q_gen_6407
<b, cons, s>(q_gen_6406, q_gen_6391) -> q_gen_6407
<b, cons, z>(q_gen_6392, q_gen_6412) -> q_gen_6407
<b, cons, z>(q_gen_6404, q_gen_6391) -> q_gen_6407
}

Datatype: <elt, eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_6383, q_gen_6385, q_gen_6399, q_gen_6408},
Q_f={q_gen_6383},
Delta=
{
<s>(q_gen_6399) -> q_gen_6385
<z>() -> q_gen_6385
<s>(q_gen_6385) -> q_gen_6399
<s, s>(q_gen_6383) -> q_gen_6383
<s, z>(q_gen_6399) -> q_gen_6383
<z, s>(q_gen_6385) -> q_gen_6383
<z, s>(q_gen_6399) -> q_gen_6383
<z, z>() -> q_gen_6383
<s, s>(q_gen_6408) -> q_gen_6408
<s, z>(q_gen_6385) -> q_gen_6408
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  prefix -> 
{{{
Q={q_gen_6382, q_gen_6388, q_gen_6396, q_gen_6397},
Q_f={q_gen_6382},
Delta=
{
<cons>(q_gen_6397, q_gen_6396) -> q_gen_6396
<nil>() -> q_gen_6396
<a>() -> q_gen_6397
<b>() -> q_gen_6397
<cons, cons>(q_gen_6388, q_gen_6382) -> q_gen_6382
<nil, cons>(q_gen_6397, q_gen_6396) -> q_gen_6382
<nil, nil>() -> q_gen_6382
<a, a>() -> q_gen_6388
<b, b>() -> q_gen_6388
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 30
() -> leq([z, s(nn2)]) -> 32
() -> leq([z, z]) -> 30
() -> prefix([nil, y]) -> 30
(count([x, l1, _py]) /\ count([x, l2, _qy]) /\ prefix([l1, l2])) -> leq([_py, _qy]) -> 31
(count([x, t1, _jy])) -> count([x, cons(x, t1), s(_jy)]) -> 34
(count([x, t1, _ky]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ky]) -> 32
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 30
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 30
(leq([s(nn1), z])) -> BOT -> 33
(prefix([zs, ys])) -> prefix([cons(y2, zs), cons(y2, ys)]) -> 31
(prefix([cons(y2, zs), cons(y2, ys)])) -> prefix([zs, ys]) -> 31
(prefix([cons(z, zs), cons(y2, ys)]) /\ not eq_elt([z, y2])) -> BOT -> 31
(prefix([cons(z, zs), nil])) -> BOT -> 31
}
Sat witness: Found: ((leq([s(nn1), z])) -> BOT, {
nn1 -> s(z)
})

-------------------------------------------
Step 47, which took 0.106685 s (model generation: 0.099586,  model checking: 0.007099):

Model:
|_
{
count -> 
{{{
Q={q_gen_6386, q_gen_6391, q_gen_6392, q_gen_6394, q_gen_6404, q_gen_6406, q_gen_6407, q_gen_6412, q_gen_6414, q_gen_6415, q_gen_6420},
Q_f={q_gen_6386},
Delta=
{
<cons>(q_gen_6404, q_gen_6412) -> q_gen_6391
<nil>() -> q_gen_6391
<a>() -> q_gen_6392
<b>() -> q_gen_6404
<cons>(q_gen_6404, q_gen_6391) -> q_gen_6412
<cons>(q_gen_6404, q_gen_6420) -> q_gen_6412
<s>(q_gen_6415) -> q_gen_6415
<z>() -> q_gen_6415
<cons>(q_gen_6392, q_gen_6391) -> q_gen_6420
<cons>(q_gen_6392, q_gen_6412) -> q_gen_6420
<cons>(q_gen_6392, q_gen_6420) -> q_gen_6420
<b, z>() -> q_gen_6394
<a, s>(q_gen_6415) -> q_gen_6406
<a, z>() -> q_gen_6406
<b, s>(q_gen_6415) -> q_gen_6414
<a, cons, s>(q_gen_6394, q_gen_6420) -> q_gen_6386
<a, cons, s>(q_gen_6406, q_gen_6391) -> q_gen_6386
<a, cons, s>(q_gen_6406, q_gen_6412) -> q_gen_6386
<a, cons, s>(q_gen_6406, q_gen_6420) -> q_gen_6386
<a, cons, z>(q_gen_6404, q_gen_6391) -> q_gen_6386
<a, cons, z>(q_gen_6404, q_gen_6412) -> q_gen_6386
<a, nil, z>() -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6391) -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6420) -> q_gen_6386
<b, cons, s>(q_gen_6406, q_gen_6412) -> q_gen_6386
<b, cons, s>(q_gen_6406, q_gen_6420) -> q_gen_6386
<b, cons, s>(q_gen_6414, q_gen_6391) -> q_gen_6386
<b, cons, s>(q_gen_6414, q_gen_6412) -> q_gen_6386
<b, cons, s>(q_gen_6414, q_gen_6420) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6391) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6420) -> q_gen_6386
<b, nil, z>() -> q_gen_6386
<a, cons, s>(q_gen_6394, q_gen_6391) -> q_gen_6407
<a, cons, s>(q_gen_6414, q_gen_6391) -> q_gen_6407
<a, cons, z>(q_gen_6404, q_gen_6420) -> q_gen_6407
<b, cons, s>(q_gen_6394, q_gen_6412) -> q_gen_6407
<b, cons, s>(q_gen_6406, q_gen_6391) -> q_gen_6407
<b, cons, z>(q_gen_6392, q_gen_6412) -> q_gen_6407
<b, cons, z>(q_gen_6404, q_gen_6391) -> q_gen_6407
}

Datatype: <elt, eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_6383, q_gen_6385, q_gen_6408},
Q_f={q_gen_6383},
Delta=
{
<s>(q_gen_6385) -> q_gen_6385
<z>() -> q_gen_6385
<s, s>(q_gen_6383) -> q_gen_6383
<z, s>(q_gen_6385) -> q_gen_6383
<z, z>() -> q_gen_6383
<s, s>(q_gen_6408) -> q_gen_6408
<s, z>(q_gen_6385) -> q_gen_6408
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  prefix -> 
{{{
Q={q_gen_6382, q_gen_6388, q_gen_6396, q_gen_6397},
Q_f={q_gen_6382},
Delta=
{
<cons>(q_gen_6397, q_gen_6396) -> q_gen_6396
<nil>() -> q_gen_6396
<a>() -> q_gen_6397
<b>() -> q_gen_6397
<cons, cons>(q_gen_6388, q_gen_6382) -> q_gen_6382
<nil, cons>(q_gen_6397, q_gen_6396) -> q_gen_6382
<nil, nil>() -> q_gen_6382
<a, a>() -> q_gen_6388
<b, b>() -> q_gen_6388
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 31
() -> leq([z, s(nn2)]) -> 32
() -> leq([z, z]) -> 31
() -> prefix([nil, y]) -> 31
(count([x, l1, _py]) /\ count([x, l2, _qy]) /\ prefix([l1, l2])) -> leq([_py, _qy]) -> 34
(count([x, t1, _jy])) -> count([x, cons(x, t1), s(_jy)]) -> 34
(count([x, t1, _ky]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ky]) -> 32
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 31
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 31
(leq([s(nn1), z])) -> BOT -> 33
(prefix([zs, ys])) -> prefix([cons(y2, zs), cons(y2, ys)]) -> 32
(prefix([cons(y2, zs), cons(y2, ys)])) -> prefix([zs, ys]) -> 32
(prefix([cons(z, zs), cons(y2, ys)]) /\ not eq_elt([z, y2])) -> BOT -> 32
(prefix([cons(z, zs), nil])) -> BOT -> 32
}
Sat witness: Found: ((count([x, l1, _py]) /\ count([x, l2, _qy]) /\ prefix([l1, l2])) -> leq([_py, _qy]), {
_py -> s(z)  ;  _qy -> z  ;  l1 -> cons(a, cons(b, nil))  ;  l2 -> cons(a, cons(b, cons(b, nil)))  ;  x -> b
})

-------------------------------------------
Step 48, which took 0.105629 s (model generation: 0.098560,  model checking: 0.007069):

Model:
|_
{
count -> 
{{{
Q={q_gen_6386, q_gen_6391, q_gen_6392, q_gen_6394, q_gen_6404, q_gen_6406, q_gen_6407, q_gen_6412, q_gen_6414, q_gen_6415, q_gen_6420},
Q_f={q_gen_6386},
Delta=
{
<nil>() -> q_gen_6391
<a>() -> q_gen_6392
<b>() -> q_gen_6404
<cons>(q_gen_6392, q_gen_6412) -> q_gen_6412
<cons>(q_gen_6404, q_gen_6391) -> q_gen_6412
<cons>(q_gen_6404, q_gen_6412) -> q_gen_6412
<cons>(q_gen_6404, q_gen_6420) -> q_gen_6412
<s>(q_gen_6415) -> q_gen_6415
<z>() -> q_gen_6415
<cons>(q_gen_6392, q_gen_6391) -> q_gen_6420
<cons>(q_gen_6392, q_gen_6420) -> q_gen_6420
<b, z>() -> q_gen_6394
<a, s>(q_gen_6415) -> q_gen_6406
<a, z>() -> q_gen_6406
<b, s>(q_gen_6415) -> q_gen_6414
<a, cons, s>(q_gen_6394, q_gen_6412) -> q_gen_6386
<a, cons, s>(q_gen_6394, q_gen_6420) -> q_gen_6386
<a, cons, s>(q_gen_6406, q_gen_6391) -> q_gen_6386
<a, cons, s>(q_gen_6406, q_gen_6412) -> q_gen_6386
<a, cons, s>(q_gen_6406, q_gen_6420) -> q_gen_6386
<a, cons, z>(q_gen_6404, q_gen_6391) -> q_gen_6386
<a, cons, z>(q_gen_6404, q_gen_6412) -> q_gen_6386
<a, nil, z>() -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6391) -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6420) -> q_gen_6386
<b, cons, s>(q_gen_6406, q_gen_6412) -> q_gen_6386
<b, cons, s>(q_gen_6414, q_gen_6391) -> q_gen_6386
<b, cons, s>(q_gen_6414, q_gen_6412) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6391) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6420) -> q_gen_6386
<b, nil, z>() -> q_gen_6386
<a, cons, s>(q_gen_6394, q_gen_6391) -> q_gen_6407
<a, cons, s>(q_gen_6414, q_gen_6391) -> q_gen_6407
<a, cons, z>(q_gen_6404, q_gen_6420) -> q_gen_6407
<b, cons, s>(q_gen_6394, q_gen_6412) -> q_gen_6407
<b, cons, s>(q_gen_6406, q_gen_6391) -> q_gen_6407
<b, cons, s>(q_gen_6406, q_gen_6420) -> q_gen_6407
<b, cons, s>(q_gen_6414, q_gen_6420) -> q_gen_6407
<b, cons, z>(q_gen_6392, q_gen_6412) -> q_gen_6407
<b, cons, z>(q_gen_6404, q_gen_6391) -> q_gen_6407
}

Datatype: <elt, eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_6383, q_gen_6385, q_gen_6408},
Q_f={q_gen_6383},
Delta=
{
<s>(q_gen_6385) -> q_gen_6385
<z>() -> q_gen_6385
<s, s>(q_gen_6383) -> q_gen_6383
<z, s>(q_gen_6385) -> q_gen_6383
<z, z>() -> q_gen_6383
<s, s>(q_gen_6408) -> q_gen_6408
<s, z>(q_gen_6385) -> q_gen_6408
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  prefix -> 
{{{
Q={q_gen_6382, q_gen_6388, q_gen_6396, q_gen_6397},
Q_f={q_gen_6382},
Delta=
{
<cons>(q_gen_6397, q_gen_6396) -> q_gen_6396
<nil>() -> q_gen_6396
<a>() -> q_gen_6397
<b>() -> q_gen_6397
<cons, cons>(q_gen_6388, q_gen_6382) -> q_gen_6382
<nil, cons>(q_gen_6397, q_gen_6396) -> q_gen_6382
<nil, nil>() -> q_gen_6382
<a, a>() -> q_gen_6388
<b, b>() -> q_gen_6388
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 32
() -> leq([z, s(nn2)]) -> 32
() -> leq([z, z]) -> 32
() -> prefix([nil, y]) -> 32
(count([x, l1, _py]) /\ count([x, l2, _qy]) /\ prefix([l1, l2])) -> leq([_py, _qy]) -> 34
(count([x, t1, _jy])) -> count([x, cons(x, t1), s(_jy)]) -> 34
(count([x, t1, _ky]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ky]) -> 35
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 32
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 32
(leq([s(nn1), z])) -> BOT -> 33
(prefix([zs, ys])) -> prefix([cons(y2, zs), cons(y2, ys)]) -> 33
(prefix([cons(y2, zs), cons(y2, ys)])) -> prefix([zs, ys]) -> 33
(prefix([cons(z, zs), cons(y2, ys)]) /\ not eq_elt([z, y2])) -> BOT -> 33
(prefix([cons(z, zs), nil])) -> BOT -> 33
}
Sat witness: Found: ((count([x, t1, _ky]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ky]), {
_ky -> s(s(z))  ;  h1 -> b  ;  t1 -> cons(a, cons(b, nil))  ;  x -> a
})

-------------------------------------------
Step 49, which took 0.126762 s (model generation: 0.113446,  model checking: 0.013316):

Model:
|_
{
count -> 
{{{
Q={q_gen_6386, q_gen_6391, q_gen_6392, q_gen_6394, q_gen_6404, q_gen_6406, q_gen_6407, q_gen_6412, q_gen_6414, q_gen_6415, q_gen_6420},
Q_f={q_gen_6386},
Delta=
{
<nil>() -> q_gen_6391
<a>() -> q_gen_6392
<b>() -> q_gen_6404
<cons>(q_gen_6404, q_gen_6391) -> q_gen_6412
<cons>(q_gen_6404, q_gen_6412) -> q_gen_6412
<cons>(q_gen_6404, q_gen_6420) -> q_gen_6412
<s>(q_gen_6415) -> q_gen_6415
<z>() -> q_gen_6415
<cons>(q_gen_6392, q_gen_6391) -> q_gen_6420
<cons>(q_gen_6392, q_gen_6412) -> q_gen_6420
<cons>(q_gen_6392, q_gen_6420) -> q_gen_6420
<b, z>() -> q_gen_6394
<a, z>() -> q_gen_6406
<a, s>(q_gen_6415) -> q_gen_6414
<b, s>(q_gen_6415) -> q_gen_6414
<a, cons, s>(q_gen_6394, q_gen_6420) -> q_gen_6386
<a, cons, s>(q_gen_6406, q_gen_6391) -> q_gen_6386
<a, cons, s>(q_gen_6406, q_gen_6412) -> q_gen_6386
<a, cons, s>(q_gen_6414, q_gen_6412) -> q_gen_6386
<a, cons, s>(q_gen_6414, q_gen_6420) -> q_gen_6386
<a, cons, z>(q_gen_6404, q_gen_6391) -> q_gen_6386
<a, cons, z>(q_gen_6404, q_gen_6412) -> q_gen_6386
<a, nil, z>() -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6391) -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6412) -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6420) -> q_gen_6386
<b, cons, s>(q_gen_6406, q_gen_6412) -> q_gen_6386
<b, cons, s>(q_gen_6406, q_gen_6420) -> q_gen_6386
<b, cons, s>(q_gen_6414, q_gen_6412) -> q_gen_6386
<b, cons, s>(q_gen_6414, q_gen_6420) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6391) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6420) -> q_gen_6386
<b, nil, z>() -> q_gen_6386
<a, cons, s>(q_gen_6394, q_gen_6391) -> q_gen_6407
<a, cons, s>(q_gen_6406, q_gen_6420) -> q_gen_6407
<a, cons, s>(q_gen_6414, q_gen_6391) -> q_gen_6407
<a, cons, z>(q_gen_6404, q_gen_6420) -> q_gen_6407
<b, cons, s>(q_gen_6406, q_gen_6391) -> q_gen_6407
<b, cons, s>(q_gen_6414, q_gen_6391) -> q_gen_6407
<b, cons, z>(q_gen_6392, q_gen_6412) -> q_gen_6407
<b, cons, z>(q_gen_6404, q_gen_6391) -> q_gen_6407
}

Datatype: <elt, eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_6383, q_gen_6385, q_gen_6408},
Q_f={q_gen_6383},
Delta=
{
<s>(q_gen_6385) -> q_gen_6385
<z>() -> q_gen_6385
<s, s>(q_gen_6383) -> q_gen_6383
<z, s>(q_gen_6385) -> q_gen_6383
<z, z>() -> q_gen_6383
<s, s>(q_gen_6408) -> q_gen_6408
<s, z>(q_gen_6385) -> q_gen_6408
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  prefix -> 
{{{
Q={q_gen_6382, q_gen_6388, q_gen_6396, q_gen_6397},
Q_f={q_gen_6382},
Delta=
{
<cons>(q_gen_6397, q_gen_6396) -> q_gen_6396
<nil>() -> q_gen_6396
<a>() -> q_gen_6397
<b>() -> q_gen_6397
<cons, cons>(q_gen_6388, q_gen_6382) -> q_gen_6382
<nil, cons>(q_gen_6397, q_gen_6396) -> q_gen_6382
<nil, nil>() -> q_gen_6382
<a, a>() -> q_gen_6388
<b, b>() -> q_gen_6388
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 33
() -> leq([z, s(nn2)]) -> 33
() -> leq([z, z]) -> 33
() -> prefix([nil, y]) -> 33
(count([x, l1, _py]) /\ count([x, l2, _qy]) /\ prefix([l1, l2])) -> leq([_py, _qy]) -> 37
(count([x, t1, _jy])) -> count([x, cons(x, t1), s(_jy)]) -> 35
(count([x, t1, _ky]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ky]) -> 35
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 33
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 33
(leq([s(nn1), z])) -> BOT -> 34
(prefix([zs, ys])) -> prefix([cons(y2, zs), cons(y2, ys)]) -> 34
(prefix([cons(y2, zs), cons(y2, ys)])) -> prefix([zs, ys]) -> 34
(prefix([cons(z, zs), cons(y2, ys)]) /\ not eq_elt([z, y2])) -> BOT -> 34
(prefix([cons(z, zs), nil])) -> BOT -> 34
}
Sat witness: Found: ((count([x, l1, _py]) /\ count([x, l2, _qy]) /\ prefix([l1, l2])) -> leq([_py, _qy]), {
_py -> s(s(z))  ;  _qy -> s(z)  ;  l1 -> cons(b, cons(a, nil))  ;  l2 -> cons(b, cons(a, nil))  ;  x -> b
})

-------------------------------------------
Step 50, which took 0.123732 s (model generation: 0.107633,  model checking: 0.016099):

Model:
|_
{
count -> 
{{{
Q={q_gen_6386, q_gen_6391, q_gen_6392, q_gen_6394, q_gen_6404, q_gen_6406, q_gen_6407, q_gen_6412, q_gen_6414, q_gen_6415, q_gen_6420},
Q_f={q_gen_6386},
Delta=
{
<nil>() -> q_gen_6391
<a>() -> q_gen_6392
<b>() -> q_gen_6404
<cons>(q_gen_6392, q_gen_6412) -> q_gen_6412
<cons>(q_gen_6404, q_gen_6391) -> q_gen_6412
<cons>(q_gen_6404, q_gen_6412) -> q_gen_6412
<cons>(q_gen_6404, q_gen_6420) -> q_gen_6412
<s>(q_gen_6415) -> q_gen_6415
<z>() -> q_gen_6415
<cons>(q_gen_6392, q_gen_6391) -> q_gen_6420
<cons>(q_gen_6392, q_gen_6420) -> q_gen_6420
<b, z>() -> q_gen_6394
<a, z>() -> q_gen_6406
<a, s>(q_gen_6415) -> q_gen_6414
<b, s>(q_gen_6415) -> q_gen_6414
<a, cons, s>(q_gen_6394, q_gen_6412) -> q_gen_6386
<a, cons, s>(q_gen_6394, q_gen_6420) -> q_gen_6386
<a, cons, s>(q_gen_6406, q_gen_6391) -> q_gen_6386
<a, cons, s>(q_gen_6406, q_gen_6412) -> q_gen_6386
<a, cons, s>(q_gen_6414, q_gen_6412) -> q_gen_6386
<a, cons, s>(q_gen_6414, q_gen_6420) -> q_gen_6386
<a, cons, z>(q_gen_6404, q_gen_6391) -> q_gen_6386
<a, cons, z>(q_gen_6404, q_gen_6412) -> q_gen_6386
<a, nil, z>() -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6391) -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6420) -> q_gen_6386
<b, cons, s>(q_gen_6406, q_gen_6412) -> q_gen_6386
<b, cons, s>(q_gen_6414, q_gen_6412) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6391) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6420) -> q_gen_6386
<b, nil, z>() -> q_gen_6386
<a, cons, s>(q_gen_6394, q_gen_6391) -> q_gen_6407
<a, cons, s>(q_gen_6414, q_gen_6391) -> q_gen_6407
<a, cons, z>(q_gen_6404, q_gen_6420) -> q_gen_6407
<b, cons, s>(q_gen_6394, q_gen_6412) -> q_gen_6407
<b, cons, s>(q_gen_6406, q_gen_6391) -> q_gen_6407
<b, cons, s>(q_gen_6406, q_gen_6420) -> q_gen_6407
<b, cons, s>(q_gen_6414, q_gen_6391) -> q_gen_6407
<b, cons, s>(q_gen_6414, q_gen_6420) -> q_gen_6407
<b, cons, z>(q_gen_6392, q_gen_6412) -> q_gen_6407
<b, cons, z>(q_gen_6404, q_gen_6391) -> q_gen_6407
}

Datatype: <elt, eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_6383, q_gen_6385, q_gen_6408},
Q_f={q_gen_6383},
Delta=
{
<s>(q_gen_6385) -> q_gen_6385
<z>() -> q_gen_6385
<s, s>(q_gen_6383) -> q_gen_6383
<z, s>(q_gen_6385) -> q_gen_6383
<z, z>() -> q_gen_6383
<s, s>(q_gen_6408) -> q_gen_6408
<s, z>(q_gen_6385) -> q_gen_6408
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  prefix -> 
{{{
Q={q_gen_6382, q_gen_6388, q_gen_6396, q_gen_6397},
Q_f={q_gen_6382},
Delta=
{
<cons>(q_gen_6397, q_gen_6396) -> q_gen_6396
<nil>() -> q_gen_6396
<a>() -> q_gen_6397
<b>() -> q_gen_6397
<cons, cons>(q_gen_6388, q_gen_6382) -> q_gen_6382
<nil, cons>(q_gen_6397, q_gen_6396) -> q_gen_6382
<nil, nil>() -> q_gen_6382
<a, a>() -> q_gen_6388
<b, b>() -> q_gen_6388
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 34
() -> leq([z, s(nn2)]) -> 34
() -> leq([z, z]) -> 34
() -> prefix([nil, y]) -> 34
(count([x, l1, _py]) /\ count([x, l2, _qy]) /\ prefix([l1, l2])) -> leq([_py, _qy]) -> 40
(count([x, t1, _jy])) -> count([x, cons(x, t1), s(_jy)]) -> 36
(count([x, t1, _ky]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ky]) -> 36
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 34
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 34
(leq([s(nn1), z])) -> BOT -> 35
(prefix([zs, ys])) -> prefix([cons(y2, zs), cons(y2, ys)]) -> 35
(prefix([cons(y2, zs), cons(y2, ys)])) -> prefix([zs, ys]) -> 35
(prefix([cons(z, zs), cons(y2, ys)]) /\ not eq_elt([z, y2])) -> BOT -> 35
(prefix([cons(z, zs), nil])) -> BOT -> 35
}
Sat witness: Found: ((count([x, l1, _py]) /\ count([x, l2, _qy]) /\ prefix([l1, l2])) -> leq([_py, _qy]), {
_py -> s(z)  ;  _qy -> z  ;  l1 -> cons(b, cons(a, nil))  ;  l2 -> cons(b, cons(a, cons(b, nil)))  ;  x -> a
})

-------------------------------------------
Step 51, which took 0.132859 s (model generation: 0.127165,  model checking: 0.005694):

Model:
|_
{
count -> 
{{{
Q={q_gen_6386, q_gen_6391, q_gen_6392, q_gen_6394, q_gen_6404, q_gen_6406, q_gen_6407, q_gen_6412, q_gen_6414, q_gen_6415, q_gen_6420, q_gen_6423},
Q_f={q_gen_6386},
Delta=
{
<nil>() -> q_gen_6391
<a>() -> q_gen_6392
<b>() -> q_gen_6404
<cons>(q_gen_6404, q_gen_6391) -> q_gen_6412
<cons>(q_gen_6404, q_gen_6412) -> q_gen_6412
<s>(q_gen_6415) -> q_gen_6415
<z>() -> q_gen_6415
<cons>(q_gen_6392, q_gen_6391) -> q_gen_6420
<cons>(q_gen_6392, q_gen_6423) -> q_gen_6420
<cons>(q_gen_6392, q_gen_6412) -> q_gen_6423
<cons>(q_gen_6392, q_gen_6420) -> q_gen_6423
<cons>(q_gen_6404, q_gen_6420) -> q_gen_6423
<b, z>() -> q_gen_6394
<a, z>() -> q_gen_6406
<a, s>(q_gen_6415) -> q_gen_6414
<b, s>(q_gen_6415) -> q_gen_6414
<a, cons, s>(q_gen_6394, q_gen_6420) -> q_gen_6386
<a, cons, s>(q_gen_6406, q_gen_6391) -> q_gen_6386
<a, cons, s>(q_gen_6406, q_gen_6412) -> q_gen_6386
<a, cons, s>(q_gen_6406, q_gen_6423) -> q_gen_6386
<a, cons, s>(q_gen_6414, q_gen_6420) -> q_gen_6386
<a, cons, z>(q_gen_6404, q_gen_6391) -> q_gen_6386
<a, cons, z>(q_gen_6404, q_gen_6412) -> q_gen_6386
<a, nil, z>() -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6391) -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6420) -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6423) -> q_gen_6386
<b, cons, s>(q_gen_6406, q_gen_6412) -> q_gen_6386
<b, cons, s>(q_gen_6406, q_gen_6420) -> q_gen_6386
<b, cons, s>(q_gen_6406, q_gen_6423) -> q_gen_6386
<b, cons, s>(q_gen_6414, q_gen_6412) -> q_gen_6386
<b, cons, s>(q_gen_6414, q_gen_6423) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6391) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6420) -> q_gen_6386
<b, nil, z>() -> q_gen_6386
<a, cons, s>(q_gen_6394, q_gen_6391) -> q_gen_6407
<a, cons, s>(q_gen_6406, q_gen_6420) -> q_gen_6407
<a, cons, s>(q_gen_6414, q_gen_6391) -> q_gen_6407
<a, cons, s>(q_gen_6414, q_gen_6412) -> q_gen_6407
<a, cons, s>(q_gen_6414, q_gen_6423) -> q_gen_6407
<a, cons, z>(q_gen_6404, q_gen_6420) -> q_gen_6407
<a, cons, z>(q_gen_6404, q_gen_6423) -> q_gen_6407
<b, cons, s>(q_gen_6394, q_gen_6412) -> q_gen_6407
<b, cons, s>(q_gen_6406, q_gen_6391) -> q_gen_6407
<b, cons, s>(q_gen_6414, q_gen_6391) -> q_gen_6407
<b, cons, s>(q_gen_6414, q_gen_6420) -> q_gen_6407
<b, cons, z>(q_gen_6392, q_gen_6412) -> q_gen_6407
<b, cons, z>(q_gen_6392, q_gen_6423) -> q_gen_6407
<b, cons, z>(q_gen_6404, q_gen_6391) -> q_gen_6407
}

Datatype: <elt, eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_6383, q_gen_6385, q_gen_6408},
Q_f={q_gen_6383},
Delta=
{
<s>(q_gen_6385) -> q_gen_6385
<z>() -> q_gen_6385
<s, s>(q_gen_6383) -> q_gen_6383
<z, s>(q_gen_6385) -> q_gen_6383
<z, z>() -> q_gen_6383
<s, s>(q_gen_6408) -> q_gen_6408
<s, z>(q_gen_6385) -> q_gen_6408
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  prefix -> 
{{{
Q={q_gen_6382, q_gen_6388, q_gen_6396, q_gen_6397},
Q_f={q_gen_6382},
Delta=
{
<cons>(q_gen_6397, q_gen_6396) -> q_gen_6396
<nil>() -> q_gen_6396
<a>() -> q_gen_6397
<b>() -> q_gen_6397
<cons, cons>(q_gen_6388, q_gen_6382) -> q_gen_6382
<nil, cons>(q_gen_6397, q_gen_6396) -> q_gen_6382
<nil, nil>() -> q_gen_6382
<a, a>() -> q_gen_6388
<b, b>() -> q_gen_6388
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 35
() -> leq([z, s(nn2)]) -> 35
() -> leq([z, z]) -> 35
() -> prefix([nil, y]) -> 35
(count([x, l1, _py]) /\ count([x, l2, _qy]) /\ prefix([l1, l2])) -> leq([_py, _qy]) -> 40
(count([x, t1, _jy])) -> count([x, cons(x, t1), s(_jy)]) -> 36
(count([x, t1, _ky]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ky]) -> 39
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 35
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 35
(leq([s(nn1), z])) -> BOT -> 36
(prefix([zs, ys])) -> prefix([cons(y2, zs), cons(y2, ys)]) -> 36
(prefix([cons(y2, zs), cons(y2, ys)])) -> prefix([zs, ys]) -> 36
(prefix([cons(z, zs), cons(y2, ys)]) /\ not eq_elt([z, y2])) -> BOT -> 36
(prefix([cons(z, zs), nil])) -> BOT -> 36
}
Sat witness: Found: ((count([x, t1, _ky]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ky]), {
_ky -> z  ;  h1 -> a  ;  t1 -> cons(a, cons(a, nil))  ;  x -> b
})

-------------------------------------------
Step 52, which took 0.131790 s (model generation: 0.125128,  model checking: 0.006662):

Model:
|_
{
count -> 
{{{
Q={q_gen_6386, q_gen_6391, q_gen_6392, q_gen_6394, q_gen_6404, q_gen_6406, q_gen_6407, q_gen_6412, q_gen_6414, q_gen_6415, q_gen_6420, q_gen_6449},
Q_f={q_gen_6386},
Delta=
{
<nil>() -> q_gen_6391
<a>() -> q_gen_6392
<b>() -> q_gen_6404
<cons>(q_gen_6404, q_gen_6391) -> q_gen_6412
<cons>(q_gen_6404, q_gen_6412) -> q_gen_6412
<cons>(q_gen_6404, q_gen_6420) -> q_gen_6412
<s>(q_gen_6415) -> q_gen_6415
<z>() -> q_gen_6415
<cons>(q_gen_6392, q_gen_6391) -> q_gen_6420
<cons>(q_gen_6392, q_gen_6420) -> q_gen_6420
<cons>(q_gen_6392, q_gen_6412) -> q_gen_6449
<cons>(q_gen_6392, q_gen_6449) -> q_gen_6449
<b, z>() -> q_gen_6394
<a, z>() -> q_gen_6406
<a, s>(q_gen_6415) -> q_gen_6414
<b, s>(q_gen_6415) -> q_gen_6414
<a, cons, s>(q_gen_6394, q_gen_6420) -> q_gen_6386
<a, cons, s>(q_gen_6394, q_gen_6449) -> q_gen_6386
<a, cons, s>(q_gen_6406, q_gen_6391) -> q_gen_6386
<a, cons, s>(q_gen_6406, q_gen_6412) -> q_gen_6386
<a, cons, s>(q_gen_6414, q_gen_6420) -> q_gen_6386
<a, cons, z>(q_gen_6404, q_gen_6391) -> q_gen_6386
<a, cons, z>(q_gen_6404, q_gen_6412) -> q_gen_6386
<a, nil, z>() -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6391) -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6420) -> q_gen_6386
<b, cons, s>(q_gen_6406, q_gen_6412) -> q_gen_6386
<b, cons, s>(q_gen_6406, q_gen_6449) -> q_gen_6386
<b, cons, s>(q_gen_6414, q_gen_6412) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6391) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6420) -> q_gen_6386
<b, nil, z>() -> q_gen_6386
<a, cons, s>(q_gen_6394, q_gen_6391) -> q_gen_6407
<a, cons, s>(q_gen_6406, q_gen_6449) -> q_gen_6407
<a, cons, s>(q_gen_6414, q_gen_6391) -> q_gen_6407
<a, cons, s>(q_gen_6414, q_gen_6412) -> q_gen_6407
<a, cons, s>(q_gen_6414, q_gen_6449) -> q_gen_6407
<a, cons, z>(q_gen_6404, q_gen_6420) -> q_gen_6407
<a, cons, z>(q_gen_6404, q_gen_6449) -> q_gen_6407
<b, cons, s>(q_gen_6394, q_gen_6412) -> q_gen_6407
<b, cons, s>(q_gen_6406, q_gen_6391) -> q_gen_6407
<b, cons, s>(q_gen_6406, q_gen_6420) -> q_gen_6407
<b, cons, s>(q_gen_6414, q_gen_6391) -> q_gen_6407
<b, cons, s>(q_gen_6414, q_gen_6420) -> q_gen_6407
<b, cons, z>(q_gen_6392, q_gen_6412) -> q_gen_6407
<b, cons, z>(q_gen_6404, q_gen_6391) -> q_gen_6407
}

Datatype: <elt, eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_6383, q_gen_6385, q_gen_6408},
Q_f={q_gen_6383},
Delta=
{
<s>(q_gen_6385) -> q_gen_6385
<z>() -> q_gen_6385
<s, s>(q_gen_6383) -> q_gen_6383
<z, s>(q_gen_6385) -> q_gen_6383
<z, z>() -> q_gen_6383
<s, s>(q_gen_6408) -> q_gen_6408
<s, z>(q_gen_6385) -> q_gen_6408
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  prefix -> 
{{{
Q={q_gen_6382, q_gen_6388, q_gen_6396, q_gen_6397},
Q_f={q_gen_6382},
Delta=
{
<cons>(q_gen_6397, q_gen_6396) -> q_gen_6396
<nil>() -> q_gen_6396
<a>() -> q_gen_6397
<b>() -> q_gen_6397
<cons, cons>(q_gen_6388, q_gen_6382) -> q_gen_6382
<nil, cons>(q_gen_6397, q_gen_6396) -> q_gen_6382
<nil, nil>() -> q_gen_6382
<a, a>() -> q_gen_6388
<b, b>() -> q_gen_6388
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 36
() -> leq([z, s(nn2)]) -> 36
() -> leq([z, z]) -> 36
() -> prefix([nil, y]) -> 36
(count([x, l1, _py]) /\ count([x, l2, _qy]) /\ prefix([l1, l2])) -> leq([_py, _qy]) -> 40
(count([x, t1, _jy])) -> count([x, cons(x, t1), s(_jy)]) -> 39
(count([x, t1, _ky]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ky]) -> 39
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 36
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 36
(leq([s(nn1), z])) -> BOT -> 37
(prefix([zs, ys])) -> prefix([cons(y2, zs), cons(y2, ys)]) -> 37
(prefix([cons(y2, zs), cons(y2, ys)])) -> prefix([zs, ys]) -> 37
(prefix([cons(z, zs), cons(y2, ys)]) /\ not eq_elt([z, y2])) -> BOT -> 37
(prefix([cons(z, zs), nil])) -> BOT -> 37
}
Sat witness: Found: ((count([x, t1, _jy])) -> count([x, cons(x, t1), s(_jy)]), {
_jy -> s(s(z))  ;  t1 -> cons(b, cons(a, nil))  ;  x -> a
})

-------------------------------------------
Step 53, which took 0.153096 s (model generation: 0.146197,  model checking: 0.006899):

Model:
|_
{
count -> 
{{{
Q={q_gen_6386, q_gen_6391, q_gen_6392, q_gen_6394, q_gen_6404, q_gen_6406, q_gen_6407, q_gen_6412, q_gen_6414, q_gen_6415, q_gen_6420, q_gen_6423},
Q_f={q_gen_6386},
Delta=
{
<nil>() -> q_gen_6391
<a>() -> q_gen_6392
<b>() -> q_gen_6404
<cons>(q_gen_6404, q_gen_6391) -> q_gen_6412
<cons>(q_gen_6404, q_gen_6412) -> q_gen_6412
<s>(q_gen_6415) -> q_gen_6415
<z>() -> q_gen_6415
<cons>(q_gen_6392, q_gen_6391) -> q_gen_6420
<cons>(q_gen_6392, q_gen_6420) -> q_gen_6420
<cons>(q_gen_6392, q_gen_6412) -> q_gen_6423
<cons>(q_gen_6392, q_gen_6423) -> q_gen_6423
<cons>(q_gen_6404, q_gen_6420) -> q_gen_6423
<b, z>() -> q_gen_6394
<a, s>(q_gen_6415) -> q_gen_6406
<a, z>() -> q_gen_6406
<b, s>(q_gen_6415) -> q_gen_6414
<a, cons, s>(q_gen_6394, q_gen_6420) -> q_gen_6386
<a, cons, s>(q_gen_6394, q_gen_6423) -> q_gen_6386
<a, cons, s>(q_gen_6406, q_gen_6391) -> q_gen_6386
<a, cons, s>(q_gen_6406, q_gen_6412) -> q_gen_6386
<a, cons, s>(q_gen_6406, q_gen_6420) -> q_gen_6386
<a, cons, s>(q_gen_6414, q_gen_6423) -> q_gen_6386
<a, cons, z>(q_gen_6404, q_gen_6391) -> q_gen_6386
<a, cons, z>(q_gen_6404, q_gen_6412) -> q_gen_6386
<a, nil, z>() -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6391) -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6420) -> q_gen_6386
<b, cons, s>(q_gen_6406, q_gen_6412) -> q_gen_6386
<b, cons, s>(q_gen_6406, q_gen_6423) -> q_gen_6386
<b, cons, s>(q_gen_6414, q_gen_6391) -> q_gen_6386
<b, cons, s>(q_gen_6414, q_gen_6412) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6391) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6420) -> q_gen_6386
<b, nil, z>() -> q_gen_6386
<a, cons, s>(q_gen_6394, q_gen_6391) -> q_gen_6407
<a, cons, s>(q_gen_6406, q_gen_6423) -> q_gen_6407
<a, cons, s>(q_gen_6414, q_gen_6391) -> q_gen_6407
<a, cons, s>(q_gen_6414, q_gen_6420) -> q_gen_6407
<a, cons, z>(q_gen_6404, q_gen_6420) -> q_gen_6407
<a, cons, z>(q_gen_6404, q_gen_6423) -> q_gen_6407
<b, cons, s>(q_gen_6394, q_gen_6412) -> q_gen_6407
<b, cons, s>(q_gen_6406, q_gen_6391) -> q_gen_6407
<b, cons, s>(q_gen_6406, q_gen_6420) -> q_gen_6407
<b, cons, s>(q_gen_6414, q_gen_6420) -> q_gen_6407
<b, cons, s>(q_gen_6414, q_gen_6423) -> q_gen_6407
<b, cons, z>(q_gen_6392, q_gen_6412) -> q_gen_6407
<b, cons, z>(q_gen_6392, q_gen_6423) -> q_gen_6407
<b, cons, z>(q_gen_6404, q_gen_6391) -> q_gen_6407
}

Datatype: <elt, eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_6383, q_gen_6385, q_gen_6408},
Q_f={q_gen_6383},
Delta=
{
<s>(q_gen_6385) -> q_gen_6385
<z>() -> q_gen_6385
<s, s>(q_gen_6383) -> q_gen_6383
<z, s>(q_gen_6385) -> q_gen_6383
<z, z>() -> q_gen_6383
<s, s>(q_gen_6408) -> q_gen_6408
<s, z>(q_gen_6385) -> q_gen_6408
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  prefix -> 
{{{
Q={q_gen_6382, q_gen_6388, q_gen_6396, q_gen_6397},
Q_f={q_gen_6382},
Delta=
{
<cons>(q_gen_6397, q_gen_6396) -> q_gen_6396
<nil>() -> q_gen_6396
<a>() -> q_gen_6397
<b>() -> q_gen_6397
<cons, cons>(q_gen_6388, q_gen_6382) -> q_gen_6382
<nil, cons>(q_gen_6397, q_gen_6396) -> q_gen_6382
<nil, nil>() -> q_gen_6382
<a, a>() -> q_gen_6388
<b, b>() -> q_gen_6388
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 37
() -> leq([z, s(nn2)]) -> 37
() -> leq([z, z]) -> 37
() -> prefix([nil, y]) -> 37
(count([x, l1, _py]) /\ count([x, l2, _qy]) /\ prefix([l1, l2])) -> leq([_py, _qy]) -> 40
(count([x, t1, _jy])) -> count([x, cons(x, t1), s(_jy)]) -> 39
(count([x, t1, _ky]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ky]) -> 42
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 37
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 37
(leq([s(nn1), z])) -> BOT -> 38
(prefix([zs, ys])) -> prefix([cons(y2, zs), cons(y2, ys)]) -> 38
(prefix([cons(y2, zs), cons(y2, ys)])) -> prefix([zs, ys]) -> 38
(prefix([cons(z, zs), cons(y2, ys)]) /\ not eq_elt([z, y2])) -> BOT -> 38
(prefix([cons(z, zs), nil])) -> BOT -> 38
}
Sat witness: Found: ((count([x, t1, _ky]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ky]), {
_ky -> s(s(z))  ;  h1 -> b  ;  t1 -> cons(a, cons(a, nil))  ;  x -> a
})

-------------------------------------------
Step 54, which took 0.144521 s (model generation: 0.143466,  model checking: 0.001055):

Model:
|_
{
count -> 
{{{
Q={q_gen_6386, q_gen_6391, q_gen_6392, q_gen_6394, q_gen_6404, q_gen_6406, q_gen_6407, q_gen_6412, q_gen_6414, q_gen_6415},
Q_f={q_gen_6386},
Delta=
{
<nil>() -> q_gen_6391
<a>() -> q_gen_6392
<b>() -> q_gen_6404
<cons>(q_gen_6392, q_gen_6391) -> q_gen_6412
<cons>(q_gen_6392, q_gen_6412) -> q_gen_6412
<cons>(q_gen_6404, q_gen_6391) -> q_gen_6412
<cons>(q_gen_6404, q_gen_6412) -> q_gen_6412
<s>(q_gen_6415) -> q_gen_6415
<z>() -> q_gen_6415
<b, z>() -> q_gen_6394
<a, z>() -> q_gen_6406
<a, s>(q_gen_6415) -> q_gen_6414
<b, s>(q_gen_6415) -> q_gen_6414
<a, cons, s>(q_gen_6394, q_gen_6412) -> q_gen_6386
<a, cons, s>(q_gen_6406, q_gen_6391) -> q_gen_6386
<a, cons, s>(q_gen_6406, q_gen_6412) -> q_gen_6386
<a, cons, s>(q_gen_6414, q_gen_6412) -> q_gen_6386
<a, cons, z>(q_gen_6404, q_gen_6391) -> q_gen_6386
<a, cons, z>(q_gen_6404, q_gen_6412) -> q_gen_6386
<a, nil, z>() -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6391) -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6412) -> q_gen_6386
<b, cons, s>(q_gen_6406, q_gen_6412) -> q_gen_6386
<b, cons, s>(q_gen_6414, q_gen_6412) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6391) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6412) -> q_gen_6386
<b, nil, z>() -> q_gen_6386
<a, cons, s>(q_gen_6394, q_gen_6391) -> q_gen_6407
<a, cons, s>(q_gen_6414, q_gen_6391) -> q_gen_6407
<b, cons, s>(q_gen_6406, q_gen_6391) -> q_gen_6407
<b, cons, s>(q_gen_6414, q_gen_6391) -> q_gen_6407
<b, cons, z>(q_gen_6404, q_gen_6391) -> q_gen_6407
}

Datatype: <elt, eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_6383, q_gen_6385, q_gen_6408},
Q_f={q_gen_6383},
Delta=
{
<s>(q_gen_6385) -> q_gen_6385
<z>() -> q_gen_6385
<s, s>(q_gen_6383) -> q_gen_6383
<z, s>(q_gen_6385) -> q_gen_6383
<z, z>() -> q_gen_6383
<s, s>(q_gen_6408) -> q_gen_6408
<s, z>(q_gen_6385) -> q_gen_6408
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  prefix -> 
{{{
Q={q_gen_6382, q_gen_6387, q_gen_6388, q_gen_6396, q_gen_6397, q_gen_6434},
Q_f={q_gen_6382, q_gen_6387},
Delta=
{
<cons>(q_gen_6397, q_gen_6396) -> q_gen_6396
<nil>() -> q_gen_6396
<a>() -> q_gen_6397
<b>() -> q_gen_6397
<nil, cons>(q_gen_6397, q_gen_6396) -> q_gen_6382
<nil, nil>() -> q_gen_6382
<cons, cons>(q_gen_6388, q_gen_6382) -> q_gen_6387
<a, a>() -> q_gen_6388
<b, b>() -> q_gen_6388
<cons, cons>(q_gen_6388, q_gen_6387) -> q_gen_6434
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 38
() -> leq([z, s(nn2)]) -> 38
() -> leq([z, z]) -> 38
() -> prefix([nil, y]) -> 38
(count([x, l1, _py]) /\ count([x, l2, _qy]) /\ prefix([l1, l2])) -> leq([_py, _qy]) -> 40
(count([x, t1, _jy])) -> count([x, cons(x, t1), s(_jy)]) -> 39
(count([x, t1, _ky]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ky]) -> 42
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 38
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 38
(leq([s(nn1), z])) -> BOT -> 38
(prefix([zs, ys])) -> prefix([cons(y2, zs), cons(y2, ys)]) -> 41
(prefix([cons(y2, zs), cons(y2, ys)])) -> prefix([zs, ys]) -> 39
(prefix([cons(z, zs), cons(y2, ys)]) /\ not eq_elt([z, y2])) -> BOT -> 39
(prefix([cons(z, zs), nil])) -> BOT -> 39
}
Sat witness: Found: ((prefix([zs, ys])) -> prefix([cons(y2, zs), cons(y2, ys)]), {
y2 -> b  ;  ys -> cons(a, nil)  ;  zs -> cons(a, nil)
})

-------------------------------------------
Step 55, which took 0.129538 s (model generation: 0.119635,  model checking: 0.009903):

Model:
|_
{
count -> 
{{{
Q={q_gen_6386, q_gen_6391, q_gen_6392, q_gen_6394, q_gen_6404, q_gen_6406, q_gen_6407, q_gen_6412, q_gen_6414, q_gen_6415, q_gen_6420, q_gen_6449},
Q_f={q_gen_6386},
Delta=
{
<nil>() -> q_gen_6391
<a>() -> q_gen_6392
<b>() -> q_gen_6404
<cons>(q_gen_6404, q_gen_6391) -> q_gen_6412
<cons>(q_gen_6404, q_gen_6412) -> q_gen_6412
<cons>(q_gen_6404, q_gen_6420) -> q_gen_6412
<s>(q_gen_6415) -> q_gen_6415
<z>() -> q_gen_6415
<cons>(q_gen_6392, q_gen_6391) -> q_gen_6420
<cons>(q_gen_6392, q_gen_6420) -> q_gen_6420
<cons>(q_gen_6392, q_gen_6412) -> q_gen_6449
<cons>(q_gen_6392, q_gen_6449) -> q_gen_6449
<b, z>() -> q_gen_6394
<a, s>(q_gen_6415) -> q_gen_6406
<a, z>() -> q_gen_6406
<b, s>(q_gen_6415) -> q_gen_6414
<a, cons, s>(q_gen_6394, q_gen_6420) -> q_gen_6386
<a, cons, s>(q_gen_6394, q_gen_6449) -> q_gen_6386
<a, cons, s>(q_gen_6406, q_gen_6391) -> q_gen_6386
<a, cons, s>(q_gen_6406, q_gen_6412) -> q_gen_6386
<a, cons, s>(q_gen_6406, q_gen_6420) -> q_gen_6386
<a, cons, s>(q_gen_6414, q_gen_6420) -> q_gen_6386
<a, cons, s>(q_gen_6414, q_gen_6449) -> q_gen_6386
<a, cons, z>(q_gen_6404, q_gen_6391) -> q_gen_6386
<a, cons, z>(q_gen_6404, q_gen_6412) -> q_gen_6386
<a, nil, z>() -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6391) -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6420) -> q_gen_6386
<b, cons, s>(q_gen_6406, q_gen_6412) -> q_gen_6386
<b, cons, s>(q_gen_6406, q_gen_6449) -> q_gen_6386
<b, cons, s>(q_gen_6414, q_gen_6412) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6391) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6420) -> q_gen_6386
<b, nil, z>() -> q_gen_6386
<a, cons, s>(q_gen_6394, q_gen_6391) -> q_gen_6407
<a, cons, s>(q_gen_6406, q_gen_6449) -> q_gen_6407
<a, cons, s>(q_gen_6414, q_gen_6391) -> q_gen_6407
<a, cons, z>(q_gen_6404, q_gen_6420) -> q_gen_6407
<a, cons, z>(q_gen_6404, q_gen_6449) -> q_gen_6407
<b, cons, s>(q_gen_6394, q_gen_6412) -> q_gen_6407
<b, cons, s>(q_gen_6406, q_gen_6391) -> q_gen_6407
<b, cons, s>(q_gen_6406, q_gen_6420) -> q_gen_6407
<b, cons, s>(q_gen_6414, q_gen_6391) -> q_gen_6407
<b, cons, s>(q_gen_6414, q_gen_6420) -> q_gen_6407
<b, cons, z>(q_gen_6392, q_gen_6412) -> q_gen_6407
<b, cons, z>(q_gen_6404, q_gen_6391) -> q_gen_6407
}

Datatype: <elt, eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_6383, q_gen_6385, q_gen_6408},
Q_f={q_gen_6383},
Delta=
{
<s>(q_gen_6385) -> q_gen_6385
<z>() -> q_gen_6385
<s, s>(q_gen_6383) -> q_gen_6383
<z, s>(q_gen_6385) -> q_gen_6383
<z, z>() -> q_gen_6383
<s, s>(q_gen_6408) -> q_gen_6408
<s, z>(q_gen_6385) -> q_gen_6408
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  prefix -> 
{{{
Q={q_gen_6382, q_gen_6388, q_gen_6396, q_gen_6397},
Q_f={q_gen_6382},
Delta=
{
<cons>(q_gen_6397, q_gen_6396) -> q_gen_6396
<nil>() -> q_gen_6396
<a>() -> q_gen_6397
<b>() -> q_gen_6397
<cons, cons>(q_gen_6388, q_gen_6382) -> q_gen_6382
<nil, cons>(q_gen_6397, q_gen_6396) -> q_gen_6382
<nil, nil>() -> q_gen_6382
<a, a>() -> q_gen_6388
<b, b>() -> q_gen_6388
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 39
() -> leq([z, s(nn2)]) -> 39
() -> leq([z, z]) -> 39
() -> prefix([nil, y]) -> 39
(count([x, l1, _py]) /\ count([x, l2, _qy]) /\ prefix([l1, l2])) -> leq([_py, _qy]) -> 40
(count([x, t1, _jy])) -> count([x, cons(x, t1), s(_jy)]) -> 42
(count([x, t1, _ky]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ky]) -> 42
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 39
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 39
(leq([s(nn1), z])) -> BOT -> 39
(prefix([zs, ys])) -> prefix([cons(y2, zs), cons(y2, ys)]) -> 41
(prefix([cons(y2, zs), cons(y2, ys)])) -> prefix([zs, ys]) -> 40
(prefix([cons(z, zs), cons(y2, ys)]) /\ not eq_elt([z, y2])) -> BOT -> 40
(prefix([cons(z, zs), nil])) -> BOT -> 40
}
Sat witness: Found: ((count([x, t1, _jy])) -> count([x, cons(x, t1), s(_jy)]), {
_jy -> s(z)  ;  t1 -> cons(a, cons(b, nil))  ;  x -> a
})

-------------------------------------------
Step 56, which took 0.152101 s (model generation: 0.144000,  model checking: 0.008101):

Model:
|_
{
count -> 
{{{
Q={q_gen_6386, q_gen_6391, q_gen_6392, q_gen_6394, q_gen_6404, q_gen_6406, q_gen_6407, q_gen_6412, q_gen_6414, q_gen_6415, q_gen_6420, q_gen_6423},
Q_f={q_gen_6386},
Delta=
{
<nil>() -> q_gen_6391
<a>() -> q_gen_6392
<b>() -> q_gen_6404
<cons>(q_gen_6404, q_gen_6391) -> q_gen_6412
<cons>(q_gen_6404, q_gen_6412) -> q_gen_6412
<s>(q_gen_6415) -> q_gen_6415
<z>() -> q_gen_6415
<cons>(q_gen_6392, q_gen_6391) -> q_gen_6420
<cons>(q_gen_6392, q_gen_6420) -> q_gen_6420
<cons>(q_gen_6392, q_gen_6412) -> q_gen_6423
<cons>(q_gen_6392, q_gen_6423) -> q_gen_6423
<cons>(q_gen_6404, q_gen_6420) -> q_gen_6423
<b, z>() -> q_gen_6394
<a, z>() -> q_gen_6406
<a, s>(q_gen_6415) -> q_gen_6414
<b, s>(q_gen_6415) -> q_gen_6414
<a, cons, s>(q_gen_6394, q_gen_6420) -> q_gen_6386
<a, cons, s>(q_gen_6406, q_gen_6391) -> q_gen_6386
<a, cons, s>(q_gen_6406, q_gen_6412) -> q_gen_6386
<a, cons, s>(q_gen_6414, q_gen_6420) -> q_gen_6386
<a, cons, s>(q_gen_6414, q_gen_6423) -> q_gen_6386
<a, cons, z>(q_gen_6404, q_gen_6391) -> q_gen_6386
<a, cons, z>(q_gen_6404, q_gen_6412) -> q_gen_6386
<a, nil, z>() -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6391) -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6420) -> q_gen_6386
<b, cons, s>(q_gen_6406, q_gen_6412) -> q_gen_6386
<b, cons, s>(q_gen_6406, q_gen_6423) -> q_gen_6386
<b, cons, s>(q_gen_6414, q_gen_6412) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6391) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6420) -> q_gen_6386
<b, nil, z>() -> q_gen_6386
<a, cons, s>(q_gen_6394, q_gen_6391) -> q_gen_6407
<a, cons, s>(q_gen_6394, q_gen_6423) -> q_gen_6407
<a, cons, s>(q_gen_6406, q_gen_6423) -> q_gen_6407
<a, cons, s>(q_gen_6414, q_gen_6391) -> q_gen_6407
<a, cons, s>(q_gen_6414, q_gen_6412) -> q_gen_6407
<a, cons, z>(q_gen_6404, q_gen_6420) -> q_gen_6407
<a, cons, z>(q_gen_6404, q_gen_6423) -> q_gen_6407
<b, cons, s>(q_gen_6394, q_gen_6412) -> q_gen_6407
<b, cons, s>(q_gen_6406, q_gen_6391) -> q_gen_6407
<b, cons, s>(q_gen_6406, q_gen_6420) -> q_gen_6407
<b, cons, s>(q_gen_6414, q_gen_6391) -> q_gen_6407
<b, cons, s>(q_gen_6414, q_gen_6420) -> q_gen_6407
<b, cons, s>(q_gen_6414, q_gen_6423) -> q_gen_6407
<b, cons, z>(q_gen_6392, q_gen_6412) -> q_gen_6407
<b, cons, z>(q_gen_6392, q_gen_6423) -> q_gen_6407
<b, cons, z>(q_gen_6404, q_gen_6391) -> q_gen_6407
}

Datatype: <elt, eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_6383, q_gen_6385, q_gen_6408},
Q_f={q_gen_6383},
Delta=
{
<s>(q_gen_6385) -> q_gen_6385
<z>() -> q_gen_6385
<s, s>(q_gen_6383) -> q_gen_6383
<z, s>(q_gen_6385) -> q_gen_6383
<z, z>() -> q_gen_6383
<s, s>(q_gen_6408) -> q_gen_6408
<s, z>(q_gen_6385) -> q_gen_6408
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  prefix -> 
{{{
Q={q_gen_6382, q_gen_6388, q_gen_6396, q_gen_6397},
Q_f={q_gen_6382},
Delta=
{
<cons>(q_gen_6397, q_gen_6396) -> q_gen_6396
<nil>() -> q_gen_6396
<a>() -> q_gen_6397
<b>() -> q_gen_6397
<cons, cons>(q_gen_6388, q_gen_6382) -> q_gen_6382
<nil, cons>(q_gen_6397, q_gen_6396) -> q_gen_6382
<nil, nil>() -> q_gen_6382
<a, a>() -> q_gen_6388
<b, b>() -> q_gen_6388
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 40
() -> leq([z, s(nn2)]) -> 40
() -> leq([z, z]) -> 40
() -> prefix([nil, y]) -> 40
(count([x, l1, _py]) /\ count([x, l2, _qy]) /\ prefix([l1, l2])) -> leq([_py, _qy]) -> 43
(count([x, t1, _jy])) -> count([x, cons(x, t1), s(_jy)]) -> 42
(count([x, t1, _ky]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ky]) -> 42
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 40
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 40
(leq([s(nn1), z])) -> BOT -> 40
(prefix([zs, ys])) -> prefix([cons(y2, zs), cons(y2, ys)]) -> 41
(prefix([cons(y2, zs), cons(y2, ys)])) -> prefix([zs, ys]) -> 41
(prefix([cons(z, zs), cons(y2, ys)]) /\ not eq_elt([z, y2])) -> BOT -> 41
(prefix([cons(z, zs), nil])) -> BOT -> 41
}
Sat witness: Found: ((count([x, l1, _py]) /\ count([x, l2, _qy]) /\ prefix([l1, l2])) -> leq([_py, _qy]), {
_py -> s(s(z))  ;  _qy -> s(z)  ;  l1 -> cons(b, cons(a, nil))  ;  l2 -> cons(b, cons(a, nil))  ;  x -> a
})

-------------------------------------------
Step 57, which took 0.179638 s (model generation: 0.168248,  model checking: 0.011390):

Model:
|_
{
count -> 
{{{
Q={q_gen_6386, q_gen_6391, q_gen_6392, q_gen_6394, q_gen_6404, q_gen_6406, q_gen_6407, q_gen_6412, q_gen_6414, q_gen_6415, q_gen_6420, q_gen_6444},
Q_f={q_gen_6386},
Delta=
{
<cons>(q_gen_6392, q_gen_6444) -> q_gen_6391
<nil>() -> q_gen_6391
<a>() -> q_gen_6392
<b>() -> q_gen_6404
<cons>(q_gen_6404, q_gen_6391) -> q_gen_6412
<cons>(q_gen_6404, q_gen_6412) -> q_gen_6412
<cons>(q_gen_6404, q_gen_6420) -> q_gen_6412
<s>(q_gen_6415) -> q_gen_6415
<z>() -> q_gen_6415
<cons>(q_gen_6392, q_gen_6391) -> q_gen_6420
<cons>(q_gen_6392, q_gen_6412) -> q_gen_6444
<cons>(q_gen_6392, q_gen_6420) -> q_gen_6444
<b, z>() -> q_gen_6394
<a, s>(q_gen_6415) -> q_gen_6406
<a, z>() -> q_gen_6406
<b, s>(q_gen_6415) -> q_gen_6414
<a, cons, s>(q_gen_6394, q_gen_6420) -> q_gen_6386
<a, cons, s>(q_gen_6394, q_gen_6444) -> q_gen_6386
<a, cons, s>(q_gen_6406, q_gen_6391) -> q_gen_6386
<a, cons, s>(q_gen_6406, q_gen_6412) -> q_gen_6386
<a, cons, s>(q_gen_6406, q_gen_6420) -> q_gen_6386
<a, cons, s>(q_gen_6406, q_gen_6444) -> q_gen_6386
<a, cons, s>(q_gen_6414, q_gen_6444) -> q_gen_6386
<a, cons, z>(q_gen_6404, q_gen_6391) -> q_gen_6386
<a, cons, z>(q_gen_6404, q_gen_6412) -> q_gen_6386
<a, nil, z>() -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6391) -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6420) -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6444) -> q_gen_6386
<b, cons, s>(q_gen_6406, q_gen_6412) -> q_gen_6386
<b, cons, s>(q_gen_6406, q_gen_6444) -> q_gen_6386
<b, cons, s>(q_gen_6414, q_gen_6412) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6391) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6420) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6444) -> q_gen_6386
<b, nil, z>() -> q_gen_6386
<a, cons, s>(q_gen_6394, q_gen_6391) -> q_gen_6407
<a, cons, s>(q_gen_6414, q_gen_6391) -> q_gen_6407
<a, cons, s>(q_gen_6414, q_gen_6420) -> q_gen_6407
<a, cons, z>(q_gen_6404, q_gen_6420) -> q_gen_6407
<a, cons, z>(q_gen_6404, q_gen_6444) -> q_gen_6407
<b, cons, s>(q_gen_6394, q_gen_6412) -> q_gen_6407
<b, cons, s>(q_gen_6406, q_gen_6391) -> q_gen_6407
<b, cons, s>(q_gen_6406, q_gen_6420) -> q_gen_6407
<b, cons, s>(q_gen_6414, q_gen_6391) -> q_gen_6407
<b, cons, s>(q_gen_6414, q_gen_6420) -> q_gen_6407
<b, cons, s>(q_gen_6414, q_gen_6444) -> q_gen_6407
<b, cons, z>(q_gen_6392, q_gen_6412) -> q_gen_6407
<b, cons, z>(q_gen_6404, q_gen_6391) -> q_gen_6407
}

Datatype: <elt, eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_6383, q_gen_6385, q_gen_6408},
Q_f={q_gen_6383},
Delta=
{
<s>(q_gen_6385) -> q_gen_6385
<z>() -> q_gen_6385
<s, s>(q_gen_6383) -> q_gen_6383
<z, s>(q_gen_6385) -> q_gen_6383
<z, z>() -> q_gen_6383
<s, s>(q_gen_6408) -> q_gen_6408
<s, z>(q_gen_6385) -> q_gen_6408
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  prefix -> 
{{{
Q={q_gen_6382, q_gen_6388, q_gen_6396, q_gen_6397},
Q_f={q_gen_6382},
Delta=
{
<cons>(q_gen_6397, q_gen_6396) -> q_gen_6396
<nil>() -> q_gen_6396
<a>() -> q_gen_6397
<b>() -> q_gen_6397
<cons, cons>(q_gen_6388, q_gen_6382) -> q_gen_6382
<nil, cons>(q_gen_6397, q_gen_6396) -> q_gen_6382
<nil, nil>() -> q_gen_6382
<a, a>() -> q_gen_6388
<b, b>() -> q_gen_6388
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 41
() -> leq([z, s(nn2)]) -> 41
() -> leq([z, z]) -> 41
() -> prefix([nil, y]) -> 41
(count([x, l1, _py]) /\ count([x, l2, _qy]) /\ prefix([l1, l2])) -> leq([_py, _qy]) -> 43
(count([x, t1, _jy])) -> count([x, cons(x, t1), s(_jy)]) -> 42
(count([x, t1, _ky]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ky]) -> 45
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 41
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 41
(leq([s(nn1), z])) -> BOT -> 41
(prefix([zs, ys])) -> prefix([cons(y2, zs), cons(y2, ys)]) -> 42
(prefix([cons(y2, zs), cons(y2, ys)])) -> prefix([zs, ys]) -> 42
(prefix([cons(z, zs), cons(y2, ys)]) /\ not eq_elt([z, y2])) -> BOT -> 42
(prefix([cons(z, zs), nil])) -> BOT -> 42
}
Sat witness: Found: ((count([x, t1, _ky]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ky]), {
_ky -> s(s(z))  ;  h1 -> b  ;  t1 -> cons(a, nil)  ;  x -> a
})

-------------------------------------------
Step 58, which took 0.178669 s (model generation: 0.171320,  model checking: 0.007349):

Model:
|_
{
count -> 
{{{
Q={q_gen_6386, q_gen_6391, q_gen_6392, q_gen_6394, q_gen_6404, q_gen_6406, q_gen_6407, q_gen_6412, q_gen_6414, q_gen_6415, q_gen_6420, q_gen_6444, q_gen_6460},
Q_f={q_gen_6386},
Delta=
{
<cons>(q_gen_6392, q_gen_6444) -> q_gen_6391
<nil>() -> q_gen_6391
<a>() -> q_gen_6392
<b>() -> q_gen_6404
<cons>(q_gen_6404, q_gen_6391) -> q_gen_6412
<cons>(q_gen_6404, q_gen_6412) -> q_gen_6412
<cons>(q_gen_6404, q_gen_6420) -> q_gen_6412
<s>(q_gen_6415) -> q_gen_6415
<z>() -> q_gen_6415
<cons>(q_gen_6392, q_gen_6391) -> q_gen_6420
<cons>(q_gen_6392, q_gen_6412) -> q_gen_6444
<cons>(q_gen_6392, q_gen_6420) -> q_gen_6444
<b, z>() -> q_gen_6394
<a, z>() -> q_gen_6406
<b, s>(q_gen_6415) -> q_gen_6414
<a, s>(q_gen_6415) -> q_gen_6460
<a, cons, s>(q_gen_6394, q_gen_6420) -> q_gen_6386
<a, cons, s>(q_gen_6394, q_gen_6444) -> q_gen_6386
<a, cons, s>(q_gen_6406, q_gen_6391) -> q_gen_6386
<a, cons, s>(q_gen_6406, q_gen_6412) -> q_gen_6386
<a, cons, s>(q_gen_6414, q_gen_6444) -> q_gen_6386
<a, cons, s>(q_gen_6460, q_gen_6420) -> q_gen_6386
<a, cons, s>(q_gen_6460, q_gen_6444) -> q_gen_6386
<a, cons, z>(q_gen_6404, q_gen_6391) -> q_gen_6386
<a, cons, z>(q_gen_6404, q_gen_6412) -> q_gen_6386
<a, nil, z>() -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6391) -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6420) -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6444) -> q_gen_6386
<b, cons, s>(q_gen_6406, q_gen_6412) -> q_gen_6386
<b, cons, s>(q_gen_6406, q_gen_6444) -> q_gen_6386
<b, cons, s>(q_gen_6414, q_gen_6412) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6391) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6420) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6444) -> q_gen_6386
<b, nil, z>() -> q_gen_6386
<a, cons, s>(q_gen_6394, q_gen_6391) -> q_gen_6407
<a, cons, s>(q_gen_6406, q_gen_6444) -> q_gen_6407
<a, cons, s>(q_gen_6414, q_gen_6391) -> q_gen_6407
<a, cons, s>(q_gen_6414, q_gen_6420) -> q_gen_6407
<a, cons, s>(q_gen_6460, q_gen_6391) -> q_gen_6407
<a, cons, s>(q_gen_6460, q_gen_6412) -> q_gen_6407
<a, cons, z>(q_gen_6404, q_gen_6420) -> q_gen_6407
<a, cons, z>(q_gen_6404, q_gen_6444) -> q_gen_6407
<b, cons, s>(q_gen_6394, q_gen_6412) -> q_gen_6407
<b, cons, s>(q_gen_6406, q_gen_6391) -> q_gen_6407
<b, cons, s>(q_gen_6406, q_gen_6420) -> q_gen_6407
<b, cons, s>(q_gen_6414, q_gen_6391) -> q_gen_6407
<b, cons, s>(q_gen_6414, q_gen_6420) -> q_gen_6407
<b, cons, s>(q_gen_6414, q_gen_6444) -> q_gen_6407
<b, cons, s>(q_gen_6460, q_gen_6391) -> q_gen_6407
<b, cons, z>(q_gen_6392, q_gen_6412) -> q_gen_6407
<b, cons, z>(q_gen_6404, q_gen_6391) -> q_gen_6407
}

Datatype: <elt, eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_6383, q_gen_6385, q_gen_6408},
Q_f={q_gen_6383},
Delta=
{
<s>(q_gen_6385) -> q_gen_6385
<z>() -> q_gen_6385
<s, s>(q_gen_6383) -> q_gen_6383
<z, s>(q_gen_6385) -> q_gen_6383
<z, z>() -> q_gen_6383
<s, s>(q_gen_6408) -> q_gen_6408
<s, z>(q_gen_6385) -> q_gen_6408
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  prefix -> 
{{{
Q={q_gen_6382, q_gen_6388, q_gen_6396, q_gen_6397},
Q_f={q_gen_6382},
Delta=
{
<cons>(q_gen_6397, q_gen_6396) -> q_gen_6396
<nil>() -> q_gen_6396
<a>() -> q_gen_6397
<b>() -> q_gen_6397
<cons, cons>(q_gen_6388, q_gen_6382) -> q_gen_6382
<nil, cons>(q_gen_6397, q_gen_6396) -> q_gen_6382
<nil, nil>() -> q_gen_6382
<a, a>() -> q_gen_6388
<b, b>() -> q_gen_6388
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 42
() -> leq([z, s(nn2)]) -> 42
() -> leq([z, z]) -> 42
() -> prefix([nil, y]) -> 42
(count([x, l1, _py]) /\ count([x, l2, _qy]) /\ prefix([l1, l2])) -> leq([_py, _qy]) -> 43
(count([x, t1, _jy])) -> count([x, cons(x, t1), s(_jy)]) -> 45
(count([x, t1, _ky]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ky]) -> 45
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 42
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 42
(leq([s(nn1), z])) -> BOT -> 42
(prefix([zs, ys])) -> prefix([cons(y2, zs), cons(y2, ys)]) -> 43
(prefix([cons(y2, zs), cons(y2, ys)])) -> prefix([zs, ys]) -> 43
(prefix([cons(z, zs), cons(y2, ys)]) /\ not eq_elt([z, y2])) -> BOT -> 43
(prefix([cons(z, zs), nil])) -> BOT -> 43
}
Sat witness: Found: ((count([x, t1, _jy])) -> count([x, cons(x, t1), s(_jy)]), {
_jy -> s(s(z))  ;  t1 -> cons(a, cons(a, cons(a, nil)))  ;  x -> a
})

-------------------------------------------
Step 59, which took 0.212805 s (model generation: 0.200318,  model checking: 0.012487):

Model:
|_
{
count -> 
{{{
Q={q_gen_6386, q_gen_6391, q_gen_6392, q_gen_6394, q_gen_6404, q_gen_6406, q_gen_6407, q_gen_6412, q_gen_6414, q_gen_6415, q_gen_6420, q_gen_6444, q_gen_6460},
Q_f={q_gen_6386},
Delta=
{
<nil>() -> q_gen_6391
<a>() -> q_gen_6392
<b>() -> q_gen_6404
<cons>(q_gen_6392, q_gen_6444) -> q_gen_6412
<cons>(q_gen_6404, q_gen_6391) -> q_gen_6412
<cons>(q_gen_6404, q_gen_6412) -> q_gen_6412
<cons>(q_gen_6404, q_gen_6420) -> q_gen_6412
<s>(q_gen_6415) -> q_gen_6415
<z>() -> q_gen_6415
<cons>(q_gen_6392, q_gen_6391) -> q_gen_6420
<cons>(q_gen_6392, q_gen_6412) -> q_gen_6420
<cons>(q_gen_6392, q_gen_6420) -> q_gen_6444
<b, z>() -> q_gen_6394
<a, z>() -> q_gen_6406
<b, s>(q_gen_6415) -> q_gen_6414
<a, s>(q_gen_6415) -> q_gen_6460
<a, cons, s>(q_gen_6394, q_gen_6420) -> q_gen_6386
<a, cons, s>(q_gen_6406, q_gen_6391) -> q_gen_6386
<a, cons, s>(q_gen_6406, q_gen_6412) -> q_gen_6386
<a, cons, s>(q_gen_6414, q_gen_6444) -> q_gen_6386
<a, cons, s>(q_gen_6460, q_gen_6420) -> q_gen_6386
<a, cons, z>(q_gen_6404, q_gen_6391) -> q_gen_6386
<a, cons, z>(q_gen_6404, q_gen_6412) -> q_gen_6386
<a, nil, z>() -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6391) -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6420) -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6444) -> q_gen_6386
<b, cons, s>(q_gen_6406, q_gen_6412) -> q_gen_6386
<b, cons, s>(q_gen_6406, q_gen_6420) -> q_gen_6386
<b, cons, s>(q_gen_6414, q_gen_6412) -> q_gen_6386
<b, cons, s>(q_gen_6414, q_gen_6444) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6391) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6420) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6444) -> q_gen_6386
<b, nil, z>() -> q_gen_6386
<a, cons, s>(q_gen_6394, q_gen_6391) -> q_gen_6407
<a, cons, s>(q_gen_6406, q_gen_6420) -> q_gen_6407
<a, cons, s>(q_gen_6414, q_gen_6391) -> q_gen_6407
<a, cons, s>(q_gen_6414, q_gen_6420) -> q_gen_6407
<a, cons, s>(q_gen_6460, q_gen_6391) -> q_gen_6407
<a, cons, s>(q_gen_6460, q_gen_6412) -> q_gen_6407
<a, cons, s>(q_gen_6460, q_gen_6444) -> q_gen_6407
<a, cons, z>(q_gen_6404, q_gen_6420) -> q_gen_6407
<a, cons, z>(q_gen_6404, q_gen_6444) -> q_gen_6407
<b, cons, s>(q_gen_6394, q_gen_6412) -> q_gen_6407
<b, cons, s>(q_gen_6406, q_gen_6391) -> q_gen_6407
<b, cons, s>(q_gen_6414, q_gen_6391) -> q_gen_6407
<b, cons, s>(q_gen_6414, q_gen_6420) -> q_gen_6407
<b, cons, s>(q_gen_6460, q_gen_6391) -> q_gen_6407
<b, cons, z>(q_gen_6392, q_gen_6412) -> q_gen_6407
<b, cons, z>(q_gen_6404, q_gen_6391) -> q_gen_6407
}

Datatype: <elt, eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_6383, q_gen_6385, q_gen_6408},
Q_f={q_gen_6383},
Delta=
{
<s>(q_gen_6385) -> q_gen_6385
<z>() -> q_gen_6385
<s, s>(q_gen_6383) -> q_gen_6383
<z, s>(q_gen_6385) -> q_gen_6383
<z, z>() -> q_gen_6383
<s, s>(q_gen_6408) -> q_gen_6408
<s, z>(q_gen_6385) -> q_gen_6408
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  prefix -> 
{{{
Q={q_gen_6382, q_gen_6388, q_gen_6396, q_gen_6397},
Q_f={q_gen_6382},
Delta=
{
<cons>(q_gen_6397, q_gen_6396) -> q_gen_6396
<nil>() -> q_gen_6396
<a>() -> q_gen_6397
<b>() -> q_gen_6397
<cons, cons>(q_gen_6388, q_gen_6382) -> q_gen_6382
<nil, cons>(q_gen_6397, q_gen_6396) -> q_gen_6382
<nil, nil>() -> q_gen_6382
<a, a>() -> q_gen_6388
<b, b>() -> q_gen_6388
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 43
() -> leq([z, s(nn2)]) -> 43
() -> leq([z, z]) -> 43
() -> prefix([nil, y]) -> 43
(count([x, l1, _py]) /\ count([x, l2, _qy]) /\ prefix([l1, l2])) -> leq([_py, _qy]) -> 46
(count([x, t1, _jy])) -> count([x, cons(x, t1), s(_jy)]) -> 45
(count([x, t1, _ky]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ky]) -> 45
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 43
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 43
(leq([s(nn1), z])) -> BOT -> 43
(prefix([zs, ys])) -> prefix([cons(y2, zs), cons(y2, ys)]) -> 44
(prefix([cons(y2, zs), cons(y2, ys)])) -> prefix([zs, ys]) -> 44
(prefix([cons(z, zs), cons(y2, ys)]) /\ not eq_elt([z, y2])) -> BOT -> 44
(prefix([cons(z, zs), nil])) -> BOT -> 44
}
Sat witness: Found: ((count([x, l1, _py]) /\ count([x, l2, _qy]) /\ prefix([l1, l2])) -> leq([_py, _qy]), {
_py -> s(z)  ;  _qy -> z  ;  l1 -> cons(a, cons(a, nil))  ;  l2 -> cons(a, cons(a, nil))  ;  x -> b
})

-------------------------------------------
Step 60, which took 0.262278 s (model generation: 0.239408,  model checking: 0.022870):

Model:
|_
{
count -> 
{{{
Q={q_gen_6386, q_gen_6391, q_gen_6392, q_gen_6394, q_gen_6404, q_gen_6406, q_gen_6407, q_gen_6412, q_gen_6414, q_gen_6415, q_gen_6420, q_gen_6444, q_gen_6460},
Q_f={q_gen_6386},
Delta=
{
<nil>() -> q_gen_6391
<a>() -> q_gen_6392
<b>() -> q_gen_6404
<cons>(q_gen_6404, q_gen_6391) -> q_gen_6412
<cons>(q_gen_6404, q_gen_6412) -> q_gen_6412
<cons>(q_gen_6404, q_gen_6420) -> q_gen_6412
<s>(q_gen_6415) -> q_gen_6415
<z>() -> q_gen_6415
<cons>(q_gen_6392, q_gen_6391) -> q_gen_6420
<cons>(q_gen_6392, q_gen_6412) -> q_gen_6444
<cons>(q_gen_6392, q_gen_6420) -> q_gen_6444
<cons>(q_gen_6392, q_gen_6444) -> q_gen_6444
<b, z>() -> q_gen_6394
<a, z>() -> q_gen_6406
<b, s>(q_gen_6415) -> q_gen_6414
<a, s>(q_gen_6415) -> q_gen_6460
<a, cons, s>(q_gen_6394, q_gen_6420) -> q_gen_6386
<a, cons, s>(q_gen_6394, q_gen_6444) -> q_gen_6386
<a, cons, s>(q_gen_6406, q_gen_6391) -> q_gen_6386
<a, cons, s>(q_gen_6406, q_gen_6412) -> q_gen_6386
<a, cons, s>(q_gen_6414, q_gen_6444) -> q_gen_6386
<a, cons, s>(q_gen_6460, q_gen_6420) -> q_gen_6386
<a, cons, s>(q_gen_6460, q_gen_6444) -> q_gen_6386
<a, cons, z>(q_gen_6404, q_gen_6391) -> q_gen_6386
<a, cons, z>(q_gen_6404, q_gen_6412) -> q_gen_6386
<a, nil, z>() -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6391) -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6420) -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6444) -> q_gen_6386
<b, cons, s>(q_gen_6406, q_gen_6412) -> q_gen_6386
<b, cons, s>(q_gen_6406, q_gen_6444) -> q_gen_6386
<b, cons, s>(q_gen_6414, q_gen_6412) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6391) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6420) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6444) -> q_gen_6386
<b, nil, z>() -> q_gen_6386
<a, cons, s>(q_gen_6394, q_gen_6391) -> q_gen_6407
<a, cons, s>(q_gen_6406, q_gen_6444) -> q_gen_6407
<a, cons, s>(q_gen_6414, q_gen_6391) -> q_gen_6407
<a, cons, s>(q_gen_6414, q_gen_6420) -> q_gen_6407
<a, cons, s>(q_gen_6460, q_gen_6391) -> q_gen_6407
<a, cons, s>(q_gen_6460, q_gen_6412) -> q_gen_6407
<a, cons, z>(q_gen_6404, q_gen_6420) -> q_gen_6407
<a, cons, z>(q_gen_6404, q_gen_6444) -> q_gen_6407
<b, cons, s>(q_gen_6394, q_gen_6412) -> q_gen_6407
<b, cons, s>(q_gen_6406, q_gen_6391) -> q_gen_6407
<b, cons, s>(q_gen_6406, q_gen_6420) -> q_gen_6407
<b, cons, s>(q_gen_6414, q_gen_6391) -> q_gen_6407
<b, cons, s>(q_gen_6414, q_gen_6420) -> q_gen_6407
<b, cons, s>(q_gen_6414, q_gen_6444) -> q_gen_6407
<b, cons, s>(q_gen_6460, q_gen_6391) -> q_gen_6407
<b, cons, z>(q_gen_6392, q_gen_6412) -> q_gen_6407
<b, cons, z>(q_gen_6404, q_gen_6391) -> q_gen_6407
}

Datatype: <elt, eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_6383, q_gen_6385, q_gen_6408},
Q_f={q_gen_6383},
Delta=
{
<s>(q_gen_6385) -> q_gen_6385
<z>() -> q_gen_6385
<s, s>(q_gen_6383) -> q_gen_6383
<z, s>(q_gen_6385) -> q_gen_6383
<z, z>() -> q_gen_6383
<s, s>(q_gen_6408) -> q_gen_6408
<s, z>(q_gen_6385) -> q_gen_6408
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  prefix -> 
{{{
Q={q_gen_6382, q_gen_6388, q_gen_6396, q_gen_6397},
Q_f={q_gen_6382},
Delta=
{
<cons>(q_gen_6397, q_gen_6396) -> q_gen_6396
<nil>() -> q_gen_6396
<a>() -> q_gen_6397
<b>() -> q_gen_6397
<cons, cons>(q_gen_6388, q_gen_6382) -> q_gen_6382
<nil, cons>(q_gen_6397, q_gen_6396) -> q_gen_6382
<nil, nil>() -> q_gen_6382
<a, a>() -> q_gen_6388
<b, b>() -> q_gen_6388
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 44
() -> leq([z, s(nn2)]) -> 44
() -> leq([z, z]) -> 44
() -> prefix([nil, y]) -> 44
(count([x, l1, _py]) /\ count([x, l2, _qy]) /\ prefix([l1, l2])) -> leq([_py, _qy]) -> 46
(count([x, t1, _jy])) -> count([x, cons(x, t1), s(_jy)]) -> 45
(count([x, t1, _ky]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ky]) -> 48
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 44
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 44
(leq([s(nn1), z])) -> BOT -> 44
(prefix([zs, ys])) -> prefix([cons(y2, zs), cons(y2, ys)]) -> 45
(prefix([cons(y2, zs), cons(y2, ys)])) -> prefix([zs, ys]) -> 45
(prefix([cons(z, zs), cons(y2, ys)]) /\ not eq_elt([z, y2])) -> BOT -> 45
(prefix([cons(z, zs), nil])) -> BOT -> 45
}
Sat witness: Found: ((count([x, t1, _ky]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ky]), {
_ky -> s(s(z))  ;  h1 -> b  ;  t1 -> cons(b, cons(a, cons(a, nil)))  ;  x -> a
})

-------------------------------------------
Step 61, which took 0.191751 s (model generation: 0.181437,  model checking: 0.010314):

Model:
|_
{
count -> 
{{{
Q={q_gen_6386, q_gen_6391, q_gen_6392, q_gen_6394, q_gen_6404, q_gen_6406, q_gen_6407, q_gen_6412, q_gen_6414, q_gen_6415, q_gen_6420, q_gen_6444, q_gen_6460},
Q_f={q_gen_6386},
Delta=
{
<nil>() -> q_gen_6391
<a>() -> q_gen_6392
<b>() -> q_gen_6404
<cons>(q_gen_6404, q_gen_6391) -> q_gen_6412
<cons>(q_gen_6404, q_gen_6412) -> q_gen_6412
<cons>(q_gen_6404, q_gen_6420) -> q_gen_6412
<s>(q_gen_6415) -> q_gen_6415
<z>() -> q_gen_6415
<cons>(q_gen_6392, q_gen_6391) -> q_gen_6420
<cons>(q_gen_6392, q_gen_6444) -> q_gen_6420
<cons>(q_gen_6392, q_gen_6412) -> q_gen_6444
<cons>(q_gen_6392, q_gen_6420) -> q_gen_6444
<cons>(q_gen_6404, q_gen_6444) -> q_gen_6444
<b, z>() -> q_gen_6394
<a, z>() -> q_gen_6406
<b, s>(q_gen_6415) -> q_gen_6414
<a, s>(q_gen_6415) -> q_gen_6460
<a, cons, s>(q_gen_6394, q_gen_6420) -> q_gen_6386
<a, cons, s>(q_gen_6394, q_gen_6444) -> q_gen_6386
<a, cons, s>(q_gen_6406, q_gen_6391) -> q_gen_6386
<a, cons, s>(q_gen_6406, q_gen_6412) -> q_gen_6386
<a, cons, s>(q_gen_6414, q_gen_6444) -> q_gen_6386
<a, cons, s>(q_gen_6460, q_gen_6420) -> q_gen_6386
<a, cons, s>(q_gen_6460, q_gen_6444) -> q_gen_6386
<a, cons, z>(q_gen_6404, q_gen_6391) -> q_gen_6386
<a, cons, z>(q_gen_6404, q_gen_6412) -> q_gen_6386
<a, nil, z>() -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6391) -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6420) -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6444) -> q_gen_6386
<b, cons, s>(q_gen_6406, q_gen_6412) -> q_gen_6386
<b, cons, s>(q_gen_6406, q_gen_6444) -> q_gen_6386
<b, cons, s>(q_gen_6414, q_gen_6412) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6391) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6420) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6444) -> q_gen_6386
<b, nil, z>() -> q_gen_6386
<a, cons, s>(q_gen_6394, q_gen_6391) -> q_gen_6407
<a, cons, s>(q_gen_6406, q_gen_6444) -> q_gen_6407
<a, cons, s>(q_gen_6414, q_gen_6391) -> q_gen_6407
<a, cons, s>(q_gen_6414, q_gen_6420) -> q_gen_6407
<a, cons, s>(q_gen_6460, q_gen_6391) -> q_gen_6407
<a, cons, s>(q_gen_6460, q_gen_6412) -> q_gen_6407
<a, cons, z>(q_gen_6404, q_gen_6420) -> q_gen_6407
<a, cons, z>(q_gen_6404, q_gen_6444) -> q_gen_6407
<b, cons, s>(q_gen_6394, q_gen_6412) -> q_gen_6407
<b, cons, s>(q_gen_6406, q_gen_6391) -> q_gen_6407
<b, cons, s>(q_gen_6406, q_gen_6420) -> q_gen_6407
<b, cons, s>(q_gen_6414, q_gen_6391) -> q_gen_6407
<b, cons, s>(q_gen_6414, q_gen_6420) -> q_gen_6407
<b, cons, s>(q_gen_6414, q_gen_6444) -> q_gen_6407
<b, cons, s>(q_gen_6460, q_gen_6391) -> q_gen_6407
<b, cons, z>(q_gen_6392, q_gen_6412) -> q_gen_6407
<b, cons, z>(q_gen_6404, q_gen_6391) -> q_gen_6407
}

Datatype: <elt, eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_6383, q_gen_6385, q_gen_6408},
Q_f={q_gen_6383},
Delta=
{
<s>(q_gen_6385) -> q_gen_6385
<z>() -> q_gen_6385
<s, s>(q_gen_6383) -> q_gen_6383
<z, s>(q_gen_6385) -> q_gen_6383
<z, z>() -> q_gen_6383
<s, s>(q_gen_6408) -> q_gen_6408
<s, z>(q_gen_6385) -> q_gen_6408
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  prefix -> 
{{{
Q={q_gen_6382, q_gen_6388, q_gen_6396, q_gen_6397},
Q_f={q_gen_6382},
Delta=
{
<cons>(q_gen_6397, q_gen_6396) -> q_gen_6396
<nil>() -> q_gen_6396
<a>() -> q_gen_6397
<b>() -> q_gen_6397
<cons, cons>(q_gen_6388, q_gen_6382) -> q_gen_6382
<nil, cons>(q_gen_6397, q_gen_6396) -> q_gen_6382
<nil, nil>() -> q_gen_6382
<a, a>() -> q_gen_6388
<b, b>() -> q_gen_6388
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 45
() -> leq([z, s(nn2)]) -> 45
() -> leq([z, z]) -> 45
() -> prefix([nil, y]) -> 45
(count([x, l1, _py]) /\ count([x, l2, _qy]) /\ prefix([l1, l2])) -> leq([_py, _qy]) -> 46
(count([x, t1, _jy])) -> count([x, cons(x, t1), s(_jy)]) -> 48
(count([x, t1, _ky]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ky]) -> 48
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 45
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 45
(leq([s(nn1), z])) -> BOT -> 45
(prefix([zs, ys])) -> prefix([cons(y2, zs), cons(y2, ys)]) -> 46
(prefix([cons(y2, zs), cons(y2, ys)])) -> prefix([zs, ys]) -> 46
(prefix([cons(z, zs), cons(y2, ys)]) /\ not eq_elt([z, y2])) -> BOT -> 46
(prefix([cons(z, zs), nil])) -> BOT -> 46
}
Sat witness: Found: ((count([x, t1, _jy])) -> count([x, cons(x, t1), s(_jy)]), {
_jy -> s(z)  ;  t1 -> cons(b, cons(a, cons(a, nil)))  ;  x -> b
})

-------------------------------------------
Step 62, which took 0.205619 s (model generation: 0.193714,  model checking: 0.011905):

Model:
|_
{
count -> 
{{{
Q={q_gen_6386, q_gen_6391, q_gen_6392, q_gen_6394, q_gen_6404, q_gen_6406, q_gen_6407, q_gen_6412, q_gen_6414, q_gen_6415, q_gen_6420, q_gen_6444, q_gen_6460},
Q_f={q_gen_6386},
Delta=
{
<nil>() -> q_gen_6391
<a>() -> q_gen_6392
<b>() -> q_gen_6404
<cons>(q_gen_6392, q_gen_6444) -> q_gen_6412
<cons>(q_gen_6404, q_gen_6391) -> q_gen_6412
<cons>(q_gen_6404, q_gen_6412) -> q_gen_6412
<cons>(q_gen_6404, q_gen_6420) -> q_gen_6412
<s>(q_gen_6415) -> q_gen_6415
<z>() -> q_gen_6415
<cons>(q_gen_6392, q_gen_6391) -> q_gen_6420
<cons>(q_gen_6392, q_gen_6412) -> q_gen_6444
<cons>(q_gen_6392, q_gen_6420) -> q_gen_6444
<cons>(q_gen_6404, q_gen_6444) -> q_gen_6444
<b, z>() -> q_gen_6394
<a, z>() -> q_gen_6406
<b, s>(q_gen_6415) -> q_gen_6414
<a, s>(q_gen_6415) -> q_gen_6460
<a, cons, s>(q_gen_6394, q_gen_6420) -> q_gen_6386
<a, cons, s>(q_gen_6394, q_gen_6444) -> q_gen_6386
<a, cons, s>(q_gen_6406, q_gen_6391) -> q_gen_6386
<a, cons, s>(q_gen_6406, q_gen_6412) -> q_gen_6386
<a, cons, s>(q_gen_6414, q_gen_6444) -> q_gen_6386
<a, cons, s>(q_gen_6460, q_gen_6412) -> q_gen_6386
<a, cons, s>(q_gen_6460, q_gen_6420) -> q_gen_6386
<a, cons, s>(q_gen_6460, q_gen_6444) -> q_gen_6386
<a, cons, z>(q_gen_6404, q_gen_6391) -> q_gen_6386
<a, cons, z>(q_gen_6404, q_gen_6412) -> q_gen_6386
<a, nil, z>() -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6391) -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6420) -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6444) -> q_gen_6386
<b, cons, s>(q_gen_6406, q_gen_6412) -> q_gen_6386
<b, cons, s>(q_gen_6406, q_gen_6444) -> q_gen_6386
<b, cons, s>(q_gen_6414, q_gen_6412) -> q_gen_6386
<b, cons, s>(q_gen_6414, q_gen_6444) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6391) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6420) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6444) -> q_gen_6386
<b, nil, z>() -> q_gen_6386
<a, cons, s>(q_gen_6394, q_gen_6391) -> q_gen_6407
<a, cons, s>(q_gen_6406, q_gen_6444) -> q_gen_6407
<a, cons, s>(q_gen_6414, q_gen_6391) -> q_gen_6407
<a, cons, s>(q_gen_6414, q_gen_6420) -> q_gen_6407
<a, cons, s>(q_gen_6460, q_gen_6391) -> q_gen_6407
<a, cons, z>(q_gen_6404, q_gen_6420) -> q_gen_6407
<a, cons, z>(q_gen_6404, q_gen_6444) -> q_gen_6407
<b, cons, s>(q_gen_6394, q_gen_6412) -> q_gen_6407
<b, cons, s>(q_gen_6406, q_gen_6391) -> q_gen_6407
<b, cons, s>(q_gen_6406, q_gen_6420) -> q_gen_6407
<b, cons, s>(q_gen_6414, q_gen_6391) -> q_gen_6407
<b, cons, s>(q_gen_6414, q_gen_6420) -> q_gen_6407
<b, cons, s>(q_gen_6460, q_gen_6391) -> q_gen_6407
<b, cons, z>(q_gen_6392, q_gen_6412) -> q_gen_6407
<b, cons, z>(q_gen_6404, q_gen_6391) -> q_gen_6407
}

Datatype: <elt, eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_6383, q_gen_6385, q_gen_6408},
Q_f={q_gen_6383},
Delta=
{
<s>(q_gen_6385) -> q_gen_6385
<z>() -> q_gen_6385
<s, s>(q_gen_6383) -> q_gen_6383
<z, s>(q_gen_6385) -> q_gen_6383
<z, z>() -> q_gen_6383
<s, s>(q_gen_6408) -> q_gen_6408
<s, z>(q_gen_6385) -> q_gen_6408
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  prefix -> 
{{{
Q={q_gen_6382, q_gen_6388, q_gen_6396, q_gen_6397},
Q_f={q_gen_6382},
Delta=
{
<cons>(q_gen_6397, q_gen_6396) -> q_gen_6396
<nil>() -> q_gen_6396
<a>() -> q_gen_6397
<b>() -> q_gen_6397
<cons, cons>(q_gen_6388, q_gen_6382) -> q_gen_6382
<nil, cons>(q_gen_6397, q_gen_6396) -> q_gen_6382
<nil, nil>() -> q_gen_6382
<a, a>() -> q_gen_6388
<b, b>() -> q_gen_6388
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 46
() -> leq([z, s(nn2)]) -> 46
() -> leq([z, z]) -> 46
() -> prefix([nil, y]) -> 46
(count([x, l1, _py]) /\ count([x, l2, _qy]) /\ prefix([l1, l2])) -> leq([_py, _qy]) -> 49
(count([x, t1, _jy])) -> count([x, cons(x, t1), s(_jy)]) -> 48
(count([x, t1, _ky]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ky]) -> 48
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 46
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 46
(leq([s(nn1), z])) -> BOT -> 46
(prefix([zs, ys])) -> prefix([cons(y2, zs), cons(y2, ys)]) -> 47
(prefix([cons(y2, zs), cons(y2, ys)])) -> prefix([zs, ys]) -> 47
(prefix([cons(z, zs), cons(y2, ys)]) /\ not eq_elt([z, y2])) -> BOT -> 47
(prefix([cons(z, zs), nil])) -> BOT -> 47
}
Sat witness: Found: ((count([x, l1, _py]) /\ count([x, l2, _qy]) /\ prefix([l1, l2])) -> leq([_py, _qy]), {
_py -> s(z)  ;  _qy -> z  ;  l1 -> cons(a, cons(a, cons(a, nil)))  ;  l2 -> cons(a, cons(a, cons(a, cons(a, cons(a, cons(a, cons(a, nil)))))))  ;  x -> b
})

-------------------------------------------
Step 63, which took 0.296067 s (model generation: 0.277196,  model checking: 0.018871):

Model:
|_
{
count -> 
{{{
Q={q_gen_6386, q_gen_6391, q_gen_6392, q_gen_6394, q_gen_6404, q_gen_6406, q_gen_6407, q_gen_6412, q_gen_6414, q_gen_6415, q_gen_6420, q_gen_6444, q_gen_6449, q_gen_6460},
Q_f={q_gen_6386},
Delta=
{
<nil>() -> q_gen_6391
<a>() -> q_gen_6392
<b>() -> q_gen_6404
<cons>(q_gen_6404, q_gen_6391) -> q_gen_6412
<cons>(q_gen_6404, q_gen_6412) -> q_gen_6412
<cons>(q_gen_6404, q_gen_6420) -> q_gen_6412
<s>(q_gen_6415) -> q_gen_6415
<z>() -> q_gen_6415
<cons>(q_gen_6392, q_gen_6391) -> q_gen_6420
<cons>(q_gen_6392, q_gen_6444) -> q_gen_6420
<cons>(q_gen_6392, q_gen_6449) -> q_gen_6420
<cons>(q_gen_6392, q_gen_6420) -> q_gen_6444
<cons>(q_gen_6392, q_gen_6412) -> q_gen_6449
<cons>(q_gen_6404, q_gen_6444) -> q_gen_6449
<b, z>() -> q_gen_6394
<a, z>() -> q_gen_6406
<b, s>(q_gen_6415) -> q_gen_6414
<a, s>(q_gen_6415) -> q_gen_6460
<a, cons, s>(q_gen_6394, q_gen_6420) -> q_gen_6386
<a, cons, s>(q_gen_6394, q_gen_6449) -> q_gen_6386
<a, cons, s>(q_gen_6406, q_gen_6391) -> q_gen_6386
<a, cons, s>(q_gen_6406, q_gen_6412) -> q_gen_6386
<a, cons, s>(q_gen_6414, q_gen_6444) -> q_gen_6386
<a, cons, s>(q_gen_6414, q_gen_6449) -> q_gen_6386
<a, cons, s>(q_gen_6460, q_gen_6420) -> q_gen_6386
<a, cons, s>(q_gen_6460, q_gen_6449) -> q_gen_6386
<a, cons, z>(q_gen_6404, q_gen_6391) -> q_gen_6386
<a, cons, z>(q_gen_6404, q_gen_6412) -> q_gen_6386
<a, nil, z>() -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6391) -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6420) -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6444) -> q_gen_6386
<b, cons, s>(q_gen_6406, q_gen_6412) -> q_gen_6386
<b, cons, s>(q_gen_6406, q_gen_6449) -> q_gen_6386
<b, cons, s>(q_gen_6414, q_gen_6412) -> q_gen_6386
<b, cons, s>(q_gen_6414, q_gen_6449) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6391) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6420) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6444) -> q_gen_6386
<b, nil, z>() -> q_gen_6386
<a, cons, s>(q_gen_6394, q_gen_6391) -> q_gen_6407
<a, cons, s>(q_gen_6406, q_gen_6449) -> q_gen_6407
<a, cons, s>(q_gen_6414, q_gen_6391) -> q_gen_6407
<a, cons, s>(q_gen_6414, q_gen_6420) -> q_gen_6407
<a, cons, s>(q_gen_6460, q_gen_6391) -> q_gen_6407
<a, cons, s>(q_gen_6460, q_gen_6412) -> q_gen_6407
<a, cons, s>(q_gen_6460, q_gen_6444) -> q_gen_6407
<a, cons, z>(q_gen_6404, q_gen_6420) -> q_gen_6407
<a, cons, z>(q_gen_6404, q_gen_6444) -> q_gen_6407
<a, cons, z>(q_gen_6404, q_gen_6449) -> q_gen_6407
<b, cons, s>(q_gen_6394, q_gen_6412) -> q_gen_6407
<b, cons, s>(q_gen_6406, q_gen_6391) -> q_gen_6407
<b, cons, s>(q_gen_6406, q_gen_6420) -> q_gen_6407
<b, cons, s>(q_gen_6406, q_gen_6444) -> q_gen_6407
<b, cons, s>(q_gen_6414, q_gen_6391) -> q_gen_6407
<b, cons, s>(q_gen_6414, q_gen_6420) -> q_gen_6407
<b, cons, s>(q_gen_6414, q_gen_6444) -> q_gen_6407
<b, cons, s>(q_gen_6460, q_gen_6391) -> q_gen_6407
<b, cons, z>(q_gen_6392, q_gen_6412) -> q_gen_6407
<b, cons, z>(q_gen_6404, q_gen_6391) -> q_gen_6407
}

Datatype: <elt, eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_6383, q_gen_6385, q_gen_6408},
Q_f={q_gen_6383},
Delta=
{
<s>(q_gen_6385) -> q_gen_6385
<z>() -> q_gen_6385
<s, s>(q_gen_6383) -> q_gen_6383
<z, s>(q_gen_6385) -> q_gen_6383
<z, z>() -> q_gen_6383
<s, s>(q_gen_6408) -> q_gen_6408
<s, z>(q_gen_6385) -> q_gen_6408
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  prefix -> 
{{{
Q={q_gen_6382, q_gen_6388, q_gen_6396, q_gen_6397},
Q_f={q_gen_6382},
Delta=
{
<cons>(q_gen_6397, q_gen_6396) -> q_gen_6396
<nil>() -> q_gen_6396
<a>() -> q_gen_6397
<b>() -> q_gen_6397
<cons, cons>(q_gen_6388, q_gen_6382) -> q_gen_6382
<nil, cons>(q_gen_6397, q_gen_6396) -> q_gen_6382
<nil, nil>() -> q_gen_6382
<a, a>() -> q_gen_6388
<b, b>() -> q_gen_6388
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 47
() -> leq([z, s(nn2)]) -> 47
() -> leq([z, z]) -> 47
() -> prefix([nil, y]) -> 47
(count([x, l1, _py]) /\ count([x, l2, _qy]) /\ prefix([l1, l2])) -> leq([_py, _qy]) -> 49
(count([x, t1, _jy])) -> count([x, cons(x, t1), s(_jy)]) -> 48
(count([x, t1, _ky]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ky]) -> 51
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 47
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 47
(leq([s(nn1), z])) -> BOT -> 47
(prefix([zs, ys])) -> prefix([cons(y2, zs), cons(y2, ys)]) -> 48
(prefix([cons(y2, zs), cons(y2, ys)])) -> prefix([zs, ys]) -> 48
(prefix([cons(z, zs), cons(y2, ys)]) /\ not eq_elt([z, y2])) -> BOT -> 48
(prefix([cons(z, zs), nil])) -> BOT -> 48
}
Sat witness: Found: ((count([x, t1, _ky]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ky]), {
_ky -> s(z)  ;  h1 -> a  ;  t1 -> cons(a, cons(a, cons(b, cons(b, nil))))  ;  x -> b
})

-------------------------------------------
Step 64, which took 0.364108 s (model generation: 0.339266,  model checking: 0.024842):

Model:
|_
{
count -> 
{{{
Q={q_gen_6386, q_gen_6391, q_gen_6392, q_gen_6394, q_gen_6404, q_gen_6406, q_gen_6407, q_gen_6412, q_gen_6414, q_gen_6415, q_gen_6420, q_gen_6444, q_gen_6449, q_gen_6460},
Q_f={q_gen_6386},
Delta=
{
<nil>() -> q_gen_6391
<a>() -> q_gen_6392
<b>() -> q_gen_6404
<cons>(q_gen_6392, q_gen_6449) -> q_gen_6412
<cons>(q_gen_6404, q_gen_6391) -> q_gen_6412
<cons>(q_gen_6404, q_gen_6412) -> q_gen_6412
<cons>(q_gen_6404, q_gen_6420) -> q_gen_6412
<cons>(q_gen_6404, q_gen_6444) -> q_gen_6412
<s>(q_gen_6415) -> q_gen_6415
<z>() -> q_gen_6415
<cons>(q_gen_6392, q_gen_6391) -> q_gen_6420
<cons>(q_gen_6392, q_gen_6420) -> q_gen_6444
<cons>(q_gen_6392, q_gen_6412) -> q_gen_6449
<cons>(q_gen_6392, q_gen_6444) -> q_gen_6449
<b, z>() -> q_gen_6394
<a, z>() -> q_gen_6406
<b, s>(q_gen_6415) -> q_gen_6414
<a, s>(q_gen_6415) -> q_gen_6460
<a, cons, s>(q_gen_6394, q_gen_6420) -> q_gen_6386
<a, cons, s>(q_gen_6394, q_gen_6449) -> q_gen_6386
<a, cons, s>(q_gen_6406, q_gen_6391) -> q_gen_6386
<a, cons, s>(q_gen_6406, q_gen_6412) -> q_gen_6386
<a, cons, s>(q_gen_6406, q_gen_6449) -> q_gen_6386
<a, cons, s>(q_gen_6414, q_gen_6412) -> q_gen_6386
<a, cons, s>(q_gen_6414, q_gen_6444) -> q_gen_6386
<a, cons, s>(q_gen_6414, q_gen_6449) -> q_gen_6386
<a, cons, s>(q_gen_6460, q_gen_6412) -> q_gen_6386
<a, cons, s>(q_gen_6460, q_gen_6420) -> q_gen_6386
<a, cons, s>(q_gen_6460, q_gen_6449) -> q_gen_6386
<a, cons, z>(q_gen_6404, q_gen_6391) -> q_gen_6386
<a, cons, z>(q_gen_6404, q_gen_6412) -> q_gen_6386
<a, nil, z>() -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6391) -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6412) -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6420) -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6444) -> q_gen_6386
<b, cons, s>(q_gen_6406, q_gen_6412) -> q_gen_6386
<b, cons, s>(q_gen_6406, q_gen_6444) -> q_gen_6386
<b, cons, s>(q_gen_6406, q_gen_6449) -> q_gen_6386
<b, cons, s>(q_gen_6414, q_gen_6412) -> q_gen_6386
<b, cons, s>(q_gen_6414, q_gen_6444) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6391) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6420) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6444) -> q_gen_6386
<b, nil, z>() -> q_gen_6386
<a, cons, s>(q_gen_6394, q_gen_6391) -> q_gen_6407
<a, cons, s>(q_gen_6414, q_gen_6391) -> q_gen_6407
<a, cons, s>(q_gen_6414, q_gen_6420) -> q_gen_6407
<a, cons, s>(q_gen_6460, q_gen_6391) -> q_gen_6407
<a, cons, s>(q_gen_6460, q_gen_6444) -> q_gen_6407
<a, cons, z>(q_gen_6404, q_gen_6420) -> q_gen_6407
<a, cons, z>(q_gen_6404, q_gen_6444) -> q_gen_6407
<a, cons, z>(q_gen_6404, q_gen_6449) -> q_gen_6407
<b, cons, s>(q_gen_6406, q_gen_6391) -> q_gen_6407
<b, cons, s>(q_gen_6406, q_gen_6420) -> q_gen_6407
<b, cons, s>(q_gen_6414, q_gen_6391) -> q_gen_6407
<b, cons, s>(q_gen_6414, q_gen_6420) -> q_gen_6407
<b, cons, s>(q_gen_6460, q_gen_6391) -> q_gen_6407
<b, cons, z>(q_gen_6392, q_gen_6412) -> q_gen_6407
<b, cons, z>(q_gen_6404, q_gen_6391) -> q_gen_6407
}

Datatype: <elt, eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_6383, q_gen_6385, q_gen_6408},
Q_f={q_gen_6383},
Delta=
{
<s>(q_gen_6385) -> q_gen_6385
<z>() -> q_gen_6385
<s, s>(q_gen_6383) -> q_gen_6383
<z, s>(q_gen_6385) -> q_gen_6383
<z, z>() -> q_gen_6383
<s, s>(q_gen_6408) -> q_gen_6408
<s, z>(q_gen_6385) -> q_gen_6408
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  prefix -> 
{{{
Q={q_gen_6382, q_gen_6388, q_gen_6396, q_gen_6397},
Q_f={q_gen_6382},
Delta=
{
<cons>(q_gen_6397, q_gen_6396) -> q_gen_6396
<nil>() -> q_gen_6396
<a>() -> q_gen_6397
<b>() -> q_gen_6397
<cons, cons>(q_gen_6388, q_gen_6382) -> q_gen_6382
<nil, cons>(q_gen_6397, q_gen_6396) -> q_gen_6382
<nil, nil>() -> q_gen_6382
<a, a>() -> q_gen_6388
<b, b>() -> q_gen_6388
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 48
() -> leq([z, s(nn2)]) -> 48
() -> leq([z, z]) -> 48
() -> prefix([nil, y]) -> 48
(count([x, l1, _py]) /\ count([x, l2, _qy]) /\ prefix([l1, l2])) -> leq([_py, _qy]) -> 49
(count([x, t1, _jy])) -> count([x, cons(x, t1), s(_jy)]) -> 51
(count([x, t1, _ky]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ky]) -> 51
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 48
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 48
(leq([s(nn1), z])) -> BOT -> 48
(prefix([zs, ys])) -> prefix([cons(y2, zs), cons(y2, ys)]) -> 49
(prefix([cons(y2, zs), cons(y2, ys)])) -> prefix([zs, ys]) -> 49
(prefix([cons(z, zs), cons(y2, ys)]) /\ not eq_elt([z, y2])) -> BOT -> 49
(prefix([cons(z, zs), nil])) -> BOT -> 49
}
Sat witness: Found: ((count([x, t1, _jy])) -> count([x, cons(x, t1), s(_jy)]), {
_jy -> s(s(z))  ;  t1 -> cons(a, cons(a, nil))  ;  x -> a
})

-------------------------------------------
Step 65, which took 0.396507 s (model generation: 0.371906,  model checking: 0.024601):

Model:
|_
{
count -> 
{{{
Q={q_gen_6386, q_gen_6391, q_gen_6392, q_gen_6394, q_gen_6404, q_gen_6406, q_gen_6407, q_gen_6412, q_gen_6414, q_gen_6415, q_gen_6420, q_gen_6444, q_gen_6449, q_gen_6460},
Q_f={q_gen_6386},
Delta=
{
<nil>() -> q_gen_6391
<a>() -> q_gen_6392
<b>() -> q_gen_6404
<cons>(q_gen_6392, q_gen_6449) -> q_gen_6412
<cons>(q_gen_6404, q_gen_6391) -> q_gen_6412
<cons>(q_gen_6404, q_gen_6412) -> q_gen_6412
<cons>(q_gen_6404, q_gen_6420) -> q_gen_6412
<s>(q_gen_6415) -> q_gen_6415
<z>() -> q_gen_6415
<cons>(q_gen_6392, q_gen_6391) -> q_gen_6420
<cons>(q_gen_6392, q_gen_6444) -> q_gen_6420
<cons>(q_gen_6392, q_gen_6420) -> q_gen_6444
<cons>(q_gen_6392, q_gen_6412) -> q_gen_6449
<cons>(q_gen_6404, q_gen_6444) -> q_gen_6449
<b, z>() -> q_gen_6394
<a, z>() -> q_gen_6406
<b, s>(q_gen_6415) -> q_gen_6414
<a, s>(q_gen_6415) -> q_gen_6460
<a, cons, s>(q_gen_6394, q_gen_6420) -> q_gen_6386
<a, cons, s>(q_gen_6394, q_gen_6449) -> q_gen_6386
<a, cons, s>(q_gen_6406, q_gen_6391) -> q_gen_6386
<a, cons, s>(q_gen_6406, q_gen_6412) -> q_gen_6386
<a, cons, s>(q_gen_6406, q_gen_6449) -> q_gen_6386
<a, cons, s>(q_gen_6414, q_gen_6444) -> q_gen_6386
<a, cons, s>(q_gen_6414, q_gen_6449) -> q_gen_6386
<a, cons, s>(q_gen_6460, q_gen_6412) -> q_gen_6386
<a, cons, s>(q_gen_6460, q_gen_6420) -> q_gen_6386
<a, cons, s>(q_gen_6460, q_gen_6444) -> q_gen_6386
<a, cons, s>(q_gen_6460, q_gen_6449) -> q_gen_6386
<a, cons, z>(q_gen_6404, q_gen_6391) -> q_gen_6386
<a, cons, z>(q_gen_6404, q_gen_6412) -> q_gen_6386
<a, nil, z>() -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6391) -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6412) -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6420) -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6444) -> q_gen_6386
<b, cons, s>(q_gen_6406, q_gen_6412) -> q_gen_6386
<b, cons, s>(q_gen_6406, q_gen_6449) -> q_gen_6386
<b, cons, s>(q_gen_6414, q_gen_6412) -> q_gen_6386
<b, cons, s>(q_gen_6414, q_gen_6444) -> q_gen_6386
<b, cons, s>(q_gen_6414, q_gen_6449) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6391) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6420) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6444) -> q_gen_6386
<b, nil, z>() -> q_gen_6386
<a, cons, s>(q_gen_6394, q_gen_6391) -> q_gen_6407
<a, cons, s>(q_gen_6414, q_gen_6391) -> q_gen_6407
<a, cons, s>(q_gen_6414, q_gen_6420) -> q_gen_6407
<a, cons, s>(q_gen_6460, q_gen_6391) -> q_gen_6407
<a, cons, z>(q_gen_6404, q_gen_6420) -> q_gen_6407
<a, cons, z>(q_gen_6404, q_gen_6444) -> q_gen_6407
<a, cons, z>(q_gen_6404, q_gen_6449) -> q_gen_6407
<b, cons, s>(q_gen_6406, q_gen_6391) -> q_gen_6407
<b, cons, s>(q_gen_6406, q_gen_6420) -> q_gen_6407
<b, cons, s>(q_gen_6406, q_gen_6444) -> q_gen_6407
<b, cons, s>(q_gen_6414, q_gen_6391) -> q_gen_6407
<b, cons, s>(q_gen_6414, q_gen_6420) -> q_gen_6407
<b, cons, s>(q_gen_6460, q_gen_6391) -> q_gen_6407
<b, cons, z>(q_gen_6392, q_gen_6412) -> q_gen_6407
<b, cons, z>(q_gen_6404, q_gen_6391) -> q_gen_6407
}

Datatype: <elt, eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_6383, q_gen_6385, q_gen_6408},
Q_f={q_gen_6383},
Delta=
{
<s>(q_gen_6385) -> q_gen_6385
<z>() -> q_gen_6385
<s, s>(q_gen_6383) -> q_gen_6383
<z, s>(q_gen_6385) -> q_gen_6383
<z, z>() -> q_gen_6383
<s, s>(q_gen_6408) -> q_gen_6408
<s, z>(q_gen_6385) -> q_gen_6408
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  prefix -> 
{{{
Q={q_gen_6382, q_gen_6388, q_gen_6396, q_gen_6397},
Q_f={q_gen_6382},
Delta=
{
<cons>(q_gen_6397, q_gen_6396) -> q_gen_6396
<nil>() -> q_gen_6396
<a>() -> q_gen_6397
<b>() -> q_gen_6397
<cons, cons>(q_gen_6388, q_gen_6382) -> q_gen_6382
<nil, cons>(q_gen_6397, q_gen_6396) -> q_gen_6382
<nil, nil>() -> q_gen_6382
<a, a>() -> q_gen_6388
<b, b>() -> q_gen_6388
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 49
() -> leq([z, s(nn2)]) -> 49
() -> leq([z, z]) -> 49
() -> prefix([nil, y]) -> 49
(count([x, l1, _py]) /\ count([x, l2, _qy]) /\ prefix([l1, l2])) -> leq([_py, _qy]) -> 52
(count([x, t1, _jy])) -> count([x, cons(x, t1), s(_jy)]) -> 51
(count([x, t1, _ky]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ky]) -> 51
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 49
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 49
(leq([s(nn1), z])) -> BOT -> 49
(prefix([zs, ys])) -> prefix([cons(y2, zs), cons(y2, ys)]) -> 50
(prefix([cons(y2, zs), cons(y2, ys)])) -> prefix([zs, ys]) -> 50
(prefix([cons(z, zs), cons(y2, ys)]) /\ not eq_elt([z, y2])) -> BOT -> 50
(prefix([cons(z, zs), nil])) -> BOT -> 50
}
Sat witness: Found: ((count([x, l1, _py]) /\ count([x, l2, _qy]) /\ prefix([l1, l2])) -> leq([_py, _qy]), {
_py -> s(z)  ;  _qy -> z  ;  l1 -> cons(b, cons(b, cons(a, cons(a, nil))))  ;  l2 -> cons(b, cons(b, cons(a, cons(a, cons(b, cons(a, nil))))))  ;  x -> a
})

-------------------------------------------
Step 66, which took 0.603238 s (model generation: 0.575317,  model checking: 0.027921):

Model:
|_
{
count -> 
{{{
Q={q_gen_6386, q_gen_6391, q_gen_6392, q_gen_6394, q_gen_6404, q_gen_6406, q_gen_6407, q_gen_6412, q_gen_6414, q_gen_6415, q_gen_6420, q_gen_6444, q_gen_6449, q_gen_6460},
Q_f={q_gen_6386},
Delta=
{
<nil>() -> q_gen_6391
<a>() -> q_gen_6392
<b>() -> q_gen_6404
<cons>(q_gen_6392, q_gen_6444) -> q_gen_6412
<cons>(q_gen_6404, q_gen_6391) -> q_gen_6412
<cons>(q_gen_6404, q_gen_6412) -> q_gen_6412
<cons>(q_gen_6404, q_gen_6420) -> q_gen_6412
<cons>(q_gen_6404, q_gen_6444) -> q_gen_6412
<cons>(q_gen_6404, q_gen_6449) -> q_gen_6412
<s>(q_gen_6415) -> q_gen_6415
<z>() -> q_gen_6415
<cons>(q_gen_6392, q_gen_6391) -> q_gen_6420
<cons>(q_gen_6392, q_gen_6420) -> q_gen_6444
<cons>(q_gen_6392, q_gen_6412) -> q_gen_6449
<cons>(q_gen_6392, q_gen_6449) -> q_gen_6449
<b, z>() -> q_gen_6394
<a, z>() -> q_gen_6406
<b, s>(q_gen_6415) -> q_gen_6414
<a, s>(q_gen_6415) -> q_gen_6460
<a, cons, s>(q_gen_6394, q_gen_6420) -> q_gen_6386
<a, cons, s>(q_gen_6394, q_gen_6449) -> q_gen_6386
<a, cons, s>(q_gen_6406, q_gen_6391) -> q_gen_6386
<a, cons, s>(q_gen_6406, q_gen_6412) -> q_gen_6386
<a, cons, s>(q_gen_6406, q_gen_6449) -> q_gen_6386
<a, cons, s>(q_gen_6414, q_gen_6412) -> q_gen_6386
<a, cons, s>(q_gen_6414, q_gen_6444) -> q_gen_6386
<a, cons, s>(q_gen_6414, q_gen_6449) -> q_gen_6386
<a, cons, s>(q_gen_6460, q_gen_6412) -> q_gen_6386
<a, cons, s>(q_gen_6460, q_gen_6420) -> q_gen_6386
<a, cons, s>(q_gen_6460, q_gen_6444) -> q_gen_6386
<a, cons, s>(q_gen_6460, q_gen_6449) -> q_gen_6386
<a, cons, z>(q_gen_6404, q_gen_6391) -> q_gen_6386
<a, cons, z>(q_gen_6404, q_gen_6412) -> q_gen_6386
<a, nil, z>() -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6391) -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6412) -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6420) -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6444) -> q_gen_6386
<b, cons, s>(q_gen_6406, q_gen_6412) -> q_gen_6386
<b, cons, s>(q_gen_6406, q_gen_6444) -> q_gen_6386
<b, cons, s>(q_gen_6406, q_gen_6449) -> q_gen_6386
<b, cons, s>(q_gen_6414, q_gen_6412) -> q_gen_6386
<b, cons, s>(q_gen_6414, q_gen_6444) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6391) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6420) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6444) -> q_gen_6386
<b, nil, z>() -> q_gen_6386
<a, cons, s>(q_gen_6394, q_gen_6391) -> q_gen_6407
<a, cons, s>(q_gen_6394, q_gen_6412) -> q_gen_6407
<a, cons, s>(q_gen_6414, q_gen_6391) -> q_gen_6407
<a, cons, s>(q_gen_6414, q_gen_6420) -> q_gen_6407
<a, cons, s>(q_gen_6460, q_gen_6391) -> q_gen_6407
<a, cons, z>(q_gen_6404, q_gen_6420) -> q_gen_6407
<a, cons, z>(q_gen_6404, q_gen_6444) -> q_gen_6407
<a, cons, z>(q_gen_6404, q_gen_6449) -> q_gen_6407
<b, cons, s>(q_gen_6406, q_gen_6391) -> q_gen_6407
<b, cons, s>(q_gen_6406, q_gen_6420) -> q_gen_6407
<b, cons, s>(q_gen_6414, q_gen_6391) -> q_gen_6407
<b, cons, s>(q_gen_6414, q_gen_6420) -> q_gen_6407
<b, cons, s>(q_gen_6460, q_gen_6391) -> q_gen_6407
<b, cons, z>(q_gen_6392, q_gen_6412) -> q_gen_6407
<b, cons, z>(q_gen_6392, q_gen_6449) -> q_gen_6407
<b, cons, z>(q_gen_6404, q_gen_6391) -> q_gen_6407
}

Datatype: <elt, eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_6383, q_gen_6385, q_gen_6408},
Q_f={q_gen_6383},
Delta=
{
<s>(q_gen_6385) -> q_gen_6385
<z>() -> q_gen_6385
<s, s>(q_gen_6383) -> q_gen_6383
<z, s>(q_gen_6385) -> q_gen_6383
<z, z>() -> q_gen_6383
<s, s>(q_gen_6408) -> q_gen_6408
<s, z>(q_gen_6385) -> q_gen_6408
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  prefix -> 
{{{
Q={q_gen_6382, q_gen_6388, q_gen_6396, q_gen_6397},
Q_f={q_gen_6382},
Delta=
{
<cons>(q_gen_6397, q_gen_6396) -> q_gen_6396
<nil>() -> q_gen_6396
<a>() -> q_gen_6397
<b>() -> q_gen_6397
<cons, cons>(q_gen_6388, q_gen_6382) -> q_gen_6382
<nil, cons>(q_gen_6397, q_gen_6396) -> q_gen_6382
<nil, nil>() -> q_gen_6382
<a, a>() -> q_gen_6388
<b, b>() -> q_gen_6388
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 50
() -> leq([z, s(nn2)]) -> 50
() -> leq([z, z]) -> 50
() -> prefix([nil, y]) -> 50
(count([x, l1, _py]) /\ count([x, l2, _qy]) /\ prefix([l1, l2])) -> leq([_py, _qy]) -> 52
(count([x, t1, _jy])) -> count([x, cons(x, t1), s(_jy)]) -> 51
(count([x, t1, _ky]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ky]) -> 54
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 50
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 50
(leq([s(nn1), z])) -> BOT -> 50
(prefix([zs, ys])) -> prefix([cons(y2, zs), cons(y2, ys)]) -> 51
(prefix([cons(y2, zs), cons(y2, ys)])) -> prefix([zs, ys]) -> 51
(prefix([cons(z, zs), cons(y2, ys)]) /\ not eq_elt([z, y2])) -> BOT -> 51
(prefix([cons(z, zs), nil])) -> BOT -> 51
}
Sat witness: Found: ((count([x, t1, _ky]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ky]), {
_ky -> s(z)  ;  h1 -> b  ;  t1 -> cons(b, cons(a, cons(b, nil)))  ;  x -> a
})

-------------------------------------------
Step 67, which took 0.562047 s (model generation: 0.538438,  model checking: 0.023609):

Model:
|_
{
count -> 
{{{
Q={q_gen_6386, q_gen_6391, q_gen_6392, q_gen_6394, q_gen_6404, q_gen_6406, q_gen_6407, q_gen_6412, q_gen_6414, q_gen_6415, q_gen_6420, q_gen_6444, q_gen_6449, q_gen_6460},
Q_f={q_gen_6386},
Delta=
{
<nil>() -> q_gen_6391
<a>() -> q_gen_6392
<b>() -> q_gen_6404
<cons>(q_gen_6404, q_gen_6391) -> q_gen_6412
<cons>(q_gen_6404, q_gen_6412) -> q_gen_6412
<cons>(q_gen_6404, q_gen_6420) -> q_gen_6412
<cons>(q_gen_6404, q_gen_6444) -> q_gen_6412
<s>(q_gen_6415) -> q_gen_6415
<z>() -> q_gen_6415
<cons>(q_gen_6392, q_gen_6391) -> q_gen_6420
<cons>(q_gen_6404, q_gen_6449) -> q_gen_6420
<cons>(q_gen_6392, q_gen_6420) -> q_gen_6444
<cons>(q_gen_6392, q_gen_6412) -> q_gen_6449
<cons>(q_gen_6392, q_gen_6444) -> q_gen_6449
<cons>(q_gen_6392, q_gen_6449) -> q_gen_6449
<b, z>() -> q_gen_6394
<a, z>() -> q_gen_6406
<b, s>(q_gen_6415) -> q_gen_6414
<a, s>(q_gen_6415) -> q_gen_6460
<a, cons, s>(q_gen_6394, q_gen_6420) -> q_gen_6386
<a, cons, s>(q_gen_6394, q_gen_6449) -> q_gen_6386
<a, cons, s>(q_gen_6406, q_gen_6391) -> q_gen_6386
<a, cons, s>(q_gen_6406, q_gen_6412) -> q_gen_6386
<a, cons, s>(q_gen_6406, q_gen_6449) -> q_gen_6386
<a, cons, s>(q_gen_6414, q_gen_6412) -> q_gen_6386
<a, cons, s>(q_gen_6414, q_gen_6444) -> q_gen_6386
<a, cons, s>(q_gen_6460, q_gen_6420) -> q_gen_6386
<a, cons, s>(q_gen_6460, q_gen_6444) -> q_gen_6386
<a, cons, s>(q_gen_6460, q_gen_6449) -> q_gen_6386
<a, cons, z>(q_gen_6404, q_gen_6391) -> q_gen_6386
<a, cons, z>(q_gen_6404, q_gen_6412) -> q_gen_6386
<a, nil, z>() -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6391) -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6412) -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6420) -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6444) -> q_gen_6386
<b, cons, s>(q_gen_6406, q_gen_6412) -> q_gen_6386
<b, cons, s>(q_gen_6406, q_gen_6444) -> q_gen_6386
<b, cons, s>(q_gen_6406, q_gen_6449) -> q_gen_6386
<b, cons, s>(q_gen_6414, q_gen_6412) -> q_gen_6386
<b, cons, s>(q_gen_6414, q_gen_6444) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6391) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6420) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6444) -> q_gen_6386
<b, nil, z>() -> q_gen_6386
<a, cons, s>(q_gen_6394, q_gen_6391) -> q_gen_6407
<a, cons, s>(q_gen_6394, q_gen_6412) -> q_gen_6407
<a, cons, s>(q_gen_6414, q_gen_6391) -> q_gen_6407
<a, cons, s>(q_gen_6414, q_gen_6420) -> q_gen_6407
<a, cons, s>(q_gen_6414, q_gen_6449) -> q_gen_6407
<a, cons, s>(q_gen_6460, q_gen_6391) -> q_gen_6407
<a, cons, s>(q_gen_6460, q_gen_6412) -> q_gen_6407
<a, cons, z>(q_gen_6404, q_gen_6420) -> q_gen_6407
<a, cons, z>(q_gen_6404, q_gen_6444) -> q_gen_6407
<a, cons, z>(q_gen_6404, q_gen_6449) -> q_gen_6407
<b, cons, s>(q_gen_6406, q_gen_6391) -> q_gen_6407
<b, cons, s>(q_gen_6406, q_gen_6420) -> q_gen_6407
<b, cons, s>(q_gen_6414, q_gen_6391) -> q_gen_6407
<b, cons, s>(q_gen_6414, q_gen_6420) -> q_gen_6407
<b, cons, s>(q_gen_6460, q_gen_6391) -> q_gen_6407
<b, cons, z>(q_gen_6392, q_gen_6412) -> q_gen_6407
<b, cons, z>(q_gen_6392, q_gen_6449) -> q_gen_6407
<b, cons, z>(q_gen_6404, q_gen_6391) -> q_gen_6407
}

Datatype: <elt, eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_6383, q_gen_6385, q_gen_6408},
Q_f={q_gen_6383},
Delta=
{
<s>(q_gen_6385) -> q_gen_6385
<z>() -> q_gen_6385
<s, s>(q_gen_6383) -> q_gen_6383
<z, s>(q_gen_6385) -> q_gen_6383
<z, z>() -> q_gen_6383
<s, s>(q_gen_6408) -> q_gen_6408
<s, z>(q_gen_6385) -> q_gen_6408
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  prefix -> 
{{{
Q={q_gen_6382, q_gen_6388, q_gen_6396, q_gen_6397},
Q_f={q_gen_6382},
Delta=
{
<cons>(q_gen_6397, q_gen_6396) -> q_gen_6396
<nil>() -> q_gen_6396
<a>() -> q_gen_6397
<b>() -> q_gen_6397
<cons, cons>(q_gen_6388, q_gen_6382) -> q_gen_6382
<nil, cons>(q_gen_6397, q_gen_6396) -> q_gen_6382
<nil, nil>() -> q_gen_6382
<a, a>() -> q_gen_6388
<b, b>() -> q_gen_6388
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 51
() -> leq([z, s(nn2)]) -> 51
() -> leq([z, z]) -> 51
() -> prefix([nil, y]) -> 51
(count([x, l1, _py]) /\ count([x, l2, _qy]) /\ prefix([l1, l2])) -> leq([_py, _qy]) -> 52
(count([x, t1, _jy])) -> count([x, cons(x, t1), s(_jy)]) -> 54
(count([x, t1, _ky]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ky]) -> 54
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 51
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 51
(leq([s(nn1), z])) -> BOT -> 51
(prefix([zs, ys])) -> prefix([cons(y2, zs), cons(y2, ys)]) -> 52
(prefix([cons(y2, zs), cons(y2, ys)])) -> prefix([zs, ys]) -> 52
(prefix([cons(z, zs), cons(y2, ys)]) /\ not eq_elt([z, y2])) -> BOT -> 52
(prefix([cons(z, zs), nil])) -> BOT -> 52
}
Sat witness: Found: ((count([x, t1, _jy])) -> count([x, cons(x, t1), s(_jy)]), {
_jy -> s(z)  ;  t1 -> cons(b, cons(a, nil))  ;  x -> a
})

-------------------------------------------
Step 68, which took 0.687931 s (model generation: 0.665856,  model checking: 0.022075):

Model:
|_
{
count -> 
{{{
Q={q_gen_6386, q_gen_6391, q_gen_6392, q_gen_6394, q_gen_6404, q_gen_6406, q_gen_6407, q_gen_6412, q_gen_6414, q_gen_6415, q_gen_6420, q_gen_6444, q_gen_6449, q_gen_6460},
Q_f={q_gen_6386},
Delta=
{
<nil>() -> q_gen_6391
<a>() -> q_gen_6392
<b>() -> q_gen_6404
<cons>(q_gen_6404, q_gen_6391) -> q_gen_6412
<cons>(q_gen_6404, q_gen_6412) -> q_gen_6412
<cons>(q_gen_6404, q_gen_6420) -> q_gen_6412
<s>(q_gen_6415) -> q_gen_6415
<z>() -> q_gen_6415
<cons>(q_gen_6392, q_gen_6391) -> q_gen_6420
<cons>(q_gen_6404, q_gen_6449) -> q_gen_6420
<cons>(q_gen_6392, q_gen_6420) -> q_gen_6444
<cons>(q_gen_6392, q_gen_6412) -> q_gen_6449
<cons>(q_gen_6392, q_gen_6444) -> q_gen_6449
<cons>(q_gen_6392, q_gen_6449) -> q_gen_6449
<cons>(q_gen_6404, q_gen_6444) -> q_gen_6449
<b, z>() -> q_gen_6394
<a, z>() -> q_gen_6406
<b, s>(q_gen_6415) -> q_gen_6414
<a, s>(q_gen_6415) -> q_gen_6460
<a, cons, s>(q_gen_6394, q_gen_6420) -> q_gen_6386
<a, cons, s>(q_gen_6394, q_gen_6449) -> q_gen_6386
<a, cons, s>(q_gen_6406, q_gen_6391) -> q_gen_6386
<a, cons, s>(q_gen_6406, q_gen_6412) -> q_gen_6386
<a, cons, s>(q_gen_6406, q_gen_6449) -> q_gen_6386
<a, cons, s>(q_gen_6414, q_gen_6444) -> q_gen_6386
<a, cons, s>(q_gen_6414, q_gen_6449) -> q_gen_6386
<a, cons, s>(q_gen_6460, q_gen_6412) -> q_gen_6386
<a, cons, s>(q_gen_6460, q_gen_6420) -> q_gen_6386
<a, cons, s>(q_gen_6460, q_gen_6444) -> q_gen_6386
<a, cons, s>(q_gen_6460, q_gen_6449) -> q_gen_6386
<a, cons, z>(q_gen_6404, q_gen_6391) -> q_gen_6386
<a, cons, z>(q_gen_6404, q_gen_6412) -> q_gen_6386
<a, nil, z>() -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6391) -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6412) -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6420) -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6444) -> q_gen_6386
<b, cons, s>(q_gen_6406, q_gen_6412) -> q_gen_6386
<b, cons, s>(q_gen_6406, q_gen_6449) -> q_gen_6386
<b, cons, s>(q_gen_6414, q_gen_6412) -> q_gen_6386
<b, cons, s>(q_gen_6414, q_gen_6444) -> q_gen_6386
<b, cons, s>(q_gen_6414, q_gen_6449) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6391) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6420) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6444) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6449) -> q_gen_6386
<b, nil, z>() -> q_gen_6386
<a, cons, s>(q_gen_6394, q_gen_6391) -> q_gen_6407
<a, cons, s>(q_gen_6414, q_gen_6391) -> q_gen_6407
<a, cons, s>(q_gen_6414, q_gen_6420) -> q_gen_6407
<a, cons, s>(q_gen_6460, q_gen_6391) -> q_gen_6407
<a, cons, z>(q_gen_6404, q_gen_6420) -> q_gen_6407
<a, cons, z>(q_gen_6404, q_gen_6444) -> q_gen_6407
<a, cons, z>(q_gen_6404, q_gen_6449) -> q_gen_6407
<b, cons, s>(q_gen_6406, q_gen_6391) -> q_gen_6407
<b, cons, s>(q_gen_6406, q_gen_6420) -> q_gen_6407
<b, cons, s>(q_gen_6406, q_gen_6444) -> q_gen_6407
<b, cons, s>(q_gen_6414, q_gen_6391) -> q_gen_6407
<b, cons, s>(q_gen_6414, q_gen_6420) -> q_gen_6407
<b, cons, s>(q_gen_6460, q_gen_6391) -> q_gen_6407
<b, cons, z>(q_gen_6392, q_gen_6412) -> q_gen_6407
<b, cons, z>(q_gen_6404, q_gen_6391) -> q_gen_6407
}

Datatype: <elt, eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_6383, q_gen_6385, q_gen_6408},
Q_f={q_gen_6383},
Delta=
{
<s>(q_gen_6385) -> q_gen_6385
<z>() -> q_gen_6385
<s, s>(q_gen_6383) -> q_gen_6383
<z, s>(q_gen_6385) -> q_gen_6383
<z, z>() -> q_gen_6383
<s, s>(q_gen_6408) -> q_gen_6408
<s, z>(q_gen_6385) -> q_gen_6408
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  prefix -> 
{{{
Q={q_gen_6382, q_gen_6388, q_gen_6396, q_gen_6397},
Q_f={q_gen_6382},
Delta=
{
<cons>(q_gen_6397, q_gen_6396) -> q_gen_6396
<nil>() -> q_gen_6396
<a>() -> q_gen_6397
<b>() -> q_gen_6397
<cons, cons>(q_gen_6388, q_gen_6382) -> q_gen_6382
<nil, cons>(q_gen_6397, q_gen_6396) -> q_gen_6382
<nil, nil>() -> q_gen_6382
<a, a>() -> q_gen_6388
<b, b>() -> q_gen_6388
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 52
() -> leq([z, s(nn2)]) -> 52
() -> leq([z, z]) -> 52
() -> prefix([nil, y]) -> 52
(count([x, l1, _py]) /\ count([x, l2, _qy]) /\ prefix([l1, l2])) -> leq([_py, _qy]) -> 55
(count([x, t1, _jy])) -> count([x, cons(x, t1), s(_jy)]) -> 54
(count([x, t1, _ky]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ky]) -> 54
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 52
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 52
(leq([s(nn1), z])) -> BOT -> 52
(prefix([zs, ys])) -> prefix([cons(y2, zs), cons(y2, ys)]) -> 53
(prefix([cons(y2, zs), cons(y2, ys)])) -> prefix([zs, ys]) -> 53
(prefix([cons(z, zs), cons(y2, ys)]) /\ not eq_elt([z, y2])) -> BOT -> 53
(prefix([cons(z, zs), nil])) -> BOT -> 53
}
Sat witness: Found: ((count([x, l1, _py]) /\ count([x, l2, _qy]) /\ prefix([l1, l2])) -> leq([_py, _qy]), {
_py -> s(z)  ;  _qy -> z  ;  l1 -> cons(a, cons(a, cons(a, cons(a, nil))))  ;  l2 -> cons(a, cons(a, cons(a, cons(a, nil))))  ;  x -> b
})

-------------------------------------------
Step 69, which took 0.588241 s (model generation: 0.565750,  model checking: 0.022491):

Model:
|_
{
count -> 
{{{
Q={q_gen_6386, q_gen_6391, q_gen_6392, q_gen_6394, q_gen_6404, q_gen_6406, q_gen_6407, q_gen_6412, q_gen_6414, q_gen_6415, q_gen_6420, q_gen_6423, q_gen_6444, q_gen_6460},
Q_f={q_gen_6386},
Delta=
{
<nil>() -> q_gen_6391
<a>() -> q_gen_6392
<b>() -> q_gen_6404
<cons>(q_gen_6392, q_gen_6423) -> q_gen_6412
<cons>(q_gen_6404, q_gen_6391) -> q_gen_6412
<cons>(q_gen_6404, q_gen_6412) -> q_gen_6412
<s>(q_gen_6415) -> q_gen_6415
<z>() -> q_gen_6415
<cons>(q_gen_6392, q_gen_6391) -> q_gen_6420
<cons>(q_gen_6392, q_gen_6444) -> q_gen_6420
<cons>(q_gen_6404, q_gen_6423) -> q_gen_6420
<cons>(q_gen_6392, q_gen_6412) -> q_gen_6423
<cons>(q_gen_6404, q_gen_6420) -> q_gen_6423
<cons>(q_gen_6392, q_gen_6420) -> q_gen_6444
<cons>(q_gen_6404, q_gen_6444) -> q_gen_6444
<b, z>() -> q_gen_6394
<a, z>() -> q_gen_6406
<b, s>(q_gen_6415) -> q_gen_6414
<a, s>(q_gen_6415) -> q_gen_6460
<a, cons, s>(q_gen_6394, q_gen_6412) -> q_gen_6386
<a, cons, s>(q_gen_6394, q_gen_6420) -> q_gen_6386
<a, cons, s>(q_gen_6406, q_gen_6391) -> q_gen_6386
<a, cons, s>(q_gen_6406, q_gen_6412) -> q_gen_6386
<a, cons, s>(q_gen_6406, q_gen_6423) -> q_gen_6386
<a, cons, s>(q_gen_6414, q_gen_6423) -> q_gen_6386
<a, cons, s>(q_gen_6414, q_gen_6444) -> q_gen_6386
<a, cons, s>(q_gen_6460, q_gen_6412) -> q_gen_6386
<a, cons, s>(q_gen_6460, q_gen_6420) -> q_gen_6386
<a, cons, s>(q_gen_6460, q_gen_6423) -> q_gen_6386
<a, cons, s>(q_gen_6460, q_gen_6444) -> q_gen_6386
<a, cons, z>(q_gen_6404, q_gen_6391) -> q_gen_6386
<a, cons, z>(q_gen_6404, q_gen_6412) -> q_gen_6386
<a, nil, z>() -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6391) -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6420) -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6444) -> q_gen_6386
<b, cons, s>(q_gen_6406, q_gen_6412) -> q_gen_6386
<b, cons, s>(q_gen_6406, q_gen_6423) -> q_gen_6386
<b, cons, s>(q_gen_6414, q_gen_6412) -> q_gen_6386
<b, cons, s>(q_gen_6414, q_gen_6444) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6391) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6420) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6444) -> q_gen_6386
<b, nil, z>() -> q_gen_6386
<a, cons, s>(q_gen_6394, q_gen_6391) -> q_gen_6407
<a, cons, s>(q_gen_6394, q_gen_6423) -> q_gen_6407
<a, cons, s>(q_gen_6394, q_gen_6444) -> q_gen_6407
<a, cons, s>(q_gen_6414, q_gen_6391) -> q_gen_6407
<a, cons, s>(q_gen_6414, q_gen_6420) -> q_gen_6407
<a, cons, s>(q_gen_6460, q_gen_6391) -> q_gen_6407
<a, cons, z>(q_gen_6404, q_gen_6420) -> q_gen_6407
<a, cons, z>(q_gen_6404, q_gen_6423) -> q_gen_6407
<a, cons, z>(q_gen_6404, q_gen_6444) -> q_gen_6407
<b, cons, s>(q_gen_6394, q_gen_6412) -> q_gen_6407
<b, cons, s>(q_gen_6406, q_gen_6391) -> q_gen_6407
<b, cons, s>(q_gen_6406, q_gen_6420) -> q_gen_6407
<b, cons, s>(q_gen_6406, q_gen_6444) -> q_gen_6407
<b, cons, s>(q_gen_6414, q_gen_6391) -> q_gen_6407
<b, cons, s>(q_gen_6414, q_gen_6420) -> q_gen_6407
<b, cons, s>(q_gen_6414, q_gen_6423) -> q_gen_6407
<b, cons, s>(q_gen_6460, q_gen_6391) -> q_gen_6407
<b, cons, z>(q_gen_6392, q_gen_6412) -> q_gen_6407
<b, cons, z>(q_gen_6392, q_gen_6423) -> q_gen_6407
<b, cons, z>(q_gen_6404, q_gen_6391) -> q_gen_6407
}

Datatype: <elt, eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_6383, q_gen_6385, q_gen_6408},
Q_f={q_gen_6383},
Delta=
{
<s>(q_gen_6385) -> q_gen_6385
<z>() -> q_gen_6385
<s, s>(q_gen_6383) -> q_gen_6383
<z, s>(q_gen_6385) -> q_gen_6383
<z, z>() -> q_gen_6383
<s, s>(q_gen_6408) -> q_gen_6408
<s, z>(q_gen_6385) -> q_gen_6408
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  prefix -> 
{{{
Q={q_gen_6382, q_gen_6388, q_gen_6396, q_gen_6397},
Q_f={q_gen_6382},
Delta=
{
<cons>(q_gen_6397, q_gen_6396) -> q_gen_6396
<nil>() -> q_gen_6396
<a>() -> q_gen_6397
<b>() -> q_gen_6397
<cons, cons>(q_gen_6388, q_gen_6382) -> q_gen_6382
<nil, cons>(q_gen_6397, q_gen_6396) -> q_gen_6382
<nil, nil>() -> q_gen_6382
<a, a>() -> q_gen_6388
<b, b>() -> q_gen_6388
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 53
() -> leq([z, s(nn2)]) -> 53
() -> leq([z, z]) -> 53
() -> prefix([nil, y]) -> 53
(count([x, l1, _py]) /\ count([x, l2, _qy]) /\ prefix([l1, l2])) -> leq([_py, _qy]) -> 55
(count([x, t1, _jy])) -> count([x, cons(x, t1), s(_jy)]) -> 54
(count([x, t1, _ky]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ky]) -> 57
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 53
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 53
(leq([s(nn1), z])) -> BOT -> 53
(prefix([zs, ys])) -> prefix([cons(y2, zs), cons(y2, ys)]) -> 54
(prefix([cons(y2, zs), cons(y2, ys)])) -> prefix([zs, ys]) -> 54
(prefix([cons(z, zs), cons(y2, ys)]) /\ not eq_elt([z, y2])) -> BOT -> 54
(prefix([cons(z, zs), nil])) -> BOT -> 54
}
Sat witness: Found: ((count([x, t1, _ky]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ky]), {
_ky -> s(z)  ;  h1 -> b  ;  t1 -> cons(a, cons(b, nil))  ;  x -> a
})

-------------------------------------------
Step 70, which took 0.601164 s (model generation: 0.559981,  model checking: 0.041183):

Model:
|_
{
count -> 
{{{
Q={q_gen_6386, q_gen_6391, q_gen_6392, q_gen_6394, q_gen_6404, q_gen_6406, q_gen_6407, q_gen_6412, q_gen_6414, q_gen_6415, q_gen_6420, q_gen_6444, q_gen_6449, q_gen_6460},
Q_f={q_gen_6386},
Delta=
{
<nil>() -> q_gen_6391
<a>() -> q_gen_6392
<b>() -> q_gen_6404
<cons>(q_gen_6404, q_gen_6391) -> q_gen_6412
<cons>(q_gen_6404, q_gen_6412) -> q_gen_6412
<cons>(q_gen_6404, q_gen_6420) -> q_gen_6412
<s>(q_gen_6415) -> q_gen_6415
<z>() -> q_gen_6415
<cons>(q_gen_6392, q_gen_6391) -> q_gen_6420
<cons>(q_gen_6404, q_gen_6449) -> q_gen_6420
<cons>(q_gen_6392, q_gen_6420) -> q_gen_6444
<cons>(q_gen_6404, q_gen_6444) -> q_gen_6444
<cons>(q_gen_6392, q_gen_6412) -> q_gen_6449
<cons>(q_gen_6392, q_gen_6444) -> q_gen_6449
<cons>(q_gen_6392, q_gen_6449) -> q_gen_6449
<b, z>() -> q_gen_6394
<a, z>() -> q_gen_6406
<b, s>(q_gen_6415) -> q_gen_6414
<a, s>(q_gen_6415) -> q_gen_6460
<a, cons, s>(q_gen_6394, q_gen_6420) -> q_gen_6386
<a, cons, s>(q_gen_6394, q_gen_6449) -> q_gen_6386
<a, cons, s>(q_gen_6406, q_gen_6391) -> q_gen_6386
<a, cons, s>(q_gen_6406, q_gen_6412) -> q_gen_6386
<a, cons, s>(q_gen_6406, q_gen_6449) -> q_gen_6386
<a, cons, s>(q_gen_6414, q_gen_6444) -> q_gen_6386
<a, cons, s>(q_gen_6414, q_gen_6449) -> q_gen_6386
<a, cons, s>(q_gen_6460, q_gen_6412) -> q_gen_6386
<a, cons, s>(q_gen_6460, q_gen_6420) -> q_gen_6386
<a, cons, s>(q_gen_6460, q_gen_6444) -> q_gen_6386
<a, cons, s>(q_gen_6460, q_gen_6449) -> q_gen_6386
<a, cons, z>(q_gen_6404, q_gen_6391) -> q_gen_6386
<a, cons, z>(q_gen_6404, q_gen_6412) -> q_gen_6386
<a, nil, z>() -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6391) -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6412) -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6420) -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6444) -> q_gen_6386
<b, cons, s>(q_gen_6406, q_gen_6412) -> q_gen_6386
<b, cons, s>(q_gen_6406, q_gen_6444) -> q_gen_6386
<b, cons, s>(q_gen_6406, q_gen_6449) -> q_gen_6386
<b, cons, s>(q_gen_6414, q_gen_6412) -> q_gen_6386
<b, cons, s>(q_gen_6414, q_gen_6444) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6391) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6420) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6444) -> q_gen_6386
<b, nil, z>() -> q_gen_6386
<a, cons, s>(q_gen_6394, q_gen_6391) -> q_gen_6407
<a, cons, s>(q_gen_6394, q_gen_6444) -> q_gen_6407
<a, cons, s>(q_gen_6414, q_gen_6391) -> q_gen_6407
<a, cons, s>(q_gen_6414, q_gen_6420) -> q_gen_6407
<a, cons, s>(q_gen_6460, q_gen_6391) -> q_gen_6407
<a, cons, z>(q_gen_6404, q_gen_6420) -> q_gen_6407
<a, cons, z>(q_gen_6404, q_gen_6444) -> q_gen_6407
<a, cons, z>(q_gen_6404, q_gen_6449) -> q_gen_6407
<b, cons, s>(q_gen_6406, q_gen_6391) -> q_gen_6407
<b, cons, s>(q_gen_6406, q_gen_6420) -> q_gen_6407
<b, cons, s>(q_gen_6414, q_gen_6391) -> q_gen_6407
<b, cons, s>(q_gen_6414, q_gen_6420) -> q_gen_6407
<b, cons, s>(q_gen_6460, q_gen_6391) -> q_gen_6407
<b, cons, z>(q_gen_6392, q_gen_6412) -> q_gen_6407
<b, cons, z>(q_gen_6392, q_gen_6449) -> q_gen_6407
<b, cons, z>(q_gen_6404, q_gen_6391) -> q_gen_6407
}

Datatype: <elt, eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_6383, q_gen_6385, q_gen_6408},
Q_f={q_gen_6383},
Delta=
{
<s>(q_gen_6385) -> q_gen_6385
<z>() -> q_gen_6385
<s, s>(q_gen_6383) -> q_gen_6383
<z, s>(q_gen_6385) -> q_gen_6383
<z, z>() -> q_gen_6383
<s, s>(q_gen_6408) -> q_gen_6408
<s, z>(q_gen_6385) -> q_gen_6408
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  prefix -> 
{{{
Q={q_gen_6382, q_gen_6388, q_gen_6396, q_gen_6397},
Q_f={q_gen_6382},
Delta=
{
<cons>(q_gen_6397, q_gen_6396) -> q_gen_6396
<nil>() -> q_gen_6396
<a>() -> q_gen_6397
<b>() -> q_gen_6397
<cons, cons>(q_gen_6388, q_gen_6382) -> q_gen_6382
<nil, cons>(q_gen_6397, q_gen_6396) -> q_gen_6382
<nil, nil>() -> q_gen_6382
<a, a>() -> q_gen_6388
<b, b>() -> q_gen_6388
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 54
() -> leq([z, s(nn2)]) -> 54
() -> leq([z, z]) -> 54
() -> prefix([nil, y]) -> 54
(count([x, l1, _py]) /\ count([x, l2, _qy]) /\ prefix([l1, l2])) -> leq([_py, _qy]) -> 55
(count([x, t1, _jy])) -> count([x, cons(x, t1), s(_jy)]) -> 57
(count([x, t1, _ky]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ky]) -> 57
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 54
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 54
(leq([s(nn1), z])) -> BOT -> 54
(prefix([zs, ys])) -> prefix([cons(y2, zs), cons(y2, ys)]) -> 55
(prefix([cons(y2, zs), cons(y2, ys)])) -> prefix([zs, ys]) -> 55
(prefix([cons(z, zs), cons(y2, ys)]) /\ not eq_elt([z, y2])) -> BOT -> 55
(prefix([cons(z, zs), nil])) -> BOT -> 55
}
Sat witness: Found: ((count([x, t1, _jy])) -> count([x, cons(x, t1), s(_jy)]), {
_jy -> z  ;  t1 -> cons(a, cons(a, cons(a, nil)))  ;  x -> b
})

-------------------------------------------
Step 71, which took 0.606250 s (model generation: 0.580578,  model checking: 0.025672):

Model:
|_
{
count -> 
{{{
Q={q_gen_6386, q_gen_6391, q_gen_6392, q_gen_6394, q_gen_6404, q_gen_6406, q_gen_6407, q_gen_6412, q_gen_6414, q_gen_6415, q_gen_6420, q_gen_6444, q_gen_6449, q_gen_6460},
Q_f={q_gen_6386},
Delta=
{
<nil>() -> q_gen_6391
<a>() -> q_gen_6392
<b>() -> q_gen_6404
<cons>(q_gen_6392, q_gen_6449) -> q_gen_6412
<cons>(q_gen_6404, q_gen_6391) -> q_gen_6412
<cons>(q_gen_6404, q_gen_6412) -> q_gen_6412
<cons>(q_gen_6404, q_gen_6420) -> q_gen_6412
<cons>(q_gen_6404, q_gen_6444) -> q_gen_6412
<s>(q_gen_6415) -> q_gen_6415
<z>() -> q_gen_6415
<cons>(q_gen_6392, q_gen_6391) -> q_gen_6420
<cons>(q_gen_6404, q_gen_6449) -> q_gen_6420
<cons>(q_gen_6392, q_gen_6420) -> q_gen_6444
<cons>(q_gen_6392, q_gen_6412) -> q_gen_6449
<cons>(q_gen_6392, q_gen_6444) -> q_gen_6449
<b, z>() -> q_gen_6394
<a, z>() -> q_gen_6406
<b, s>(q_gen_6415) -> q_gen_6414
<a, s>(q_gen_6415) -> q_gen_6460
<a, cons, s>(q_gen_6394, q_gen_6420) -> q_gen_6386
<a, cons, s>(q_gen_6394, q_gen_6449) -> q_gen_6386
<a, cons, s>(q_gen_6406, q_gen_6391) -> q_gen_6386
<a, cons, s>(q_gen_6406, q_gen_6412) -> q_gen_6386
<a, cons, s>(q_gen_6406, q_gen_6449) -> q_gen_6386
<a, cons, s>(q_gen_6414, q_gen_6412) -> q_gen_6386
<a, cons, s>(q_gen_6414, q_gen_6444) -> q_gen_6386
<a, cons, s>(q_gen_6414, q_gen_6449) -> q_gen_6386
<a, cons, s>(q_gen_6460, q_gen_6412) -> q_gen_6386
<a, cons, s>(q_gen_6460, q_gen_6420) -> q_gen_6386
<a, cons, s>(q_gen_6460, q_gen_6444) -> q_gen_6386
<a, cons, s>(q_gen_6460, q_gen_6449) -> q_gen_6386
<a, cons, z>(q_gen_6404, q_gen_6391) -> q_gen_6386
<a, cons, z>(q_gen_6404, q_gen_6412) -> q_gen_6386
<a, nil, z>() -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6391) -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6412) -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6420) -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6444) -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6449) -> q_gen_6386
<b, cons, s>(q_gen_6406, q_gen_6412) -> q_gen_6386
<b, cons, s>(q_gen_6406, q_gen_6444) -> q_gen_6386
<b, cons, s>(q_gen_6406, q_gen_6449) -> q_gen_6386
<b, cons, s>(q_gen_6414, q_gen_6412) -> q_gen_6386
<b, cons, s>(q_gen_6414, q_gen_6444) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6391) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6420) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6444) -> q_gen_6386
<b, nil, z>() -> q_gen_6386
<a, cons, s>(q_gen_6394, q_gen_6391) -> q_gen_6407
<a, cons, s>(q_gen_6394, q_gen_6412) -> q_gen_6407
<a, cons, s>(q_gen_6414, q_gen_6391) -> q_gen_6407
<a, cons, s>(q_gen_6414, q_gen_6420) -> q_gen_6407
<a, cons, s>(q_gen_6460, q_gen_6391) -> q_gen_6407
<a, cons, z>(q_gen_6404, q_gen_6420) -> q_gen_6407
<a, cons, z>(q_gen_6404, q_gen_6444) -> q_gen_6407
<a, cons, z>(q_gen_6404, q_gen_6449) -> q_gen_6407
<b, cons, s>(q_gen_6406, q_gen_6391) -> q_gen_6407
<b, cons, s>(q_gen_6406, q_gen_6420) -> q_gen_6407
<b, cons, s>(q_gen_6414, q_gen_6391) -> q_gen_6407
<b, cons, s>(q_gen_6414, q_gen_6420) -> q_gen_6407
<b, cons, s>(q_gen_6460, q_gen_6391) -> q_gen_6407
<b, cons, z>(q_gen_6392, q_gen_6412) -> q_gen_6407
<b, cons, z>(q_gen_6392, q_gen_6449) -> q_gen_6407
<b, cons, z>(q_gen_6404, q_gen_6391) -> q_gen_6407
}

Datatype: <elt, eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_6383, q_gen_6385, q_gen_6408},
Q_f={q_gen_6383},
Delta=
{
<s>(q_gen_6385) -> q_gen_6385
<z>() -> q_gen_6385
<s, s>(q_gen_6383) -> q_gen_6383
<z, s>(q_gen_6385) -> q_gen_6383
<z, z>() -> q_gen_6383
<s, s>(q_gen_6408) -> q_gen_6408
<s, z>(q_gen_6385) -> q_gen_6408
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  prefix -> 
{{{
Q={q_gen_6382, q_gen_6388, q_gen_6396, q_gen_6397},
Q_f={q_gen_6382},
Delta=
{
<cons>(q_gen_6397, q_gen_6396) -> q_gen_6396
<nil>() -> q_gen_6396
<a>() -> q_gen_6397
<b>() -> q_gen_6397
<cons, cons>(q_gen_6388, q_gen_6382) -> q_gen_6382
<nil, cons>(q_gen_6397, q_gen_6396) -> q_gen_6382
<nil, nil>() -> q_gen_6382
<a, a>() -> q_gen_6388
<b, b>() -> q_gen_6388
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 55
() -> leq([z, s(nn2)]) -> 55
() -> leq([z, z]) -> 55
() -> prefix([nil, y]) -> 55
(count([x, l1, _py]) /\ count([x, l2, _qy]) /\ prefix([l1, l2])) -> leq([_py, _qy]) -> 58
(count([x, t1, _jy])) -> count([x, cons(x, t1), s(_jy)]) -> 57
(count([x, t1, _ky]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ky]) -> 57
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 55
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 55
(leq([s(nn1), z])) -> BOT -> 55
(prefix([zs, ys])) -> prefix([cons(y2, zs), cons(y2, ys)]) -> 56
(prefix([cons(y2, zs), cons(y2, ys)])) -> prefix([zs, ys]) -> 56
(prefix([cons(z, zs), cons(y2, ys)]) /\ not eq_elt([z, y2])) -> BOT -> 56
(prefix([cons(z, zs), nil])) -> BOT -> 56
}
Sat witness: Found: ((count([x, l1, _py]) /\ count([x, l2, _qy]) /\ prefix([l1, l2])) -> leq([_py, _qy]), {
_py -> s(z)  ;  _qy -> z  ;  l1 -> cons(a, cons(a, cons(a, nil)))  ;  l2 -> cons(a, cons(a, cons(a, nil)))  ;  x -> b
})

-------------------------------------------
Step 72, which took 0.768135 s (model generation: 0.753490,  model checking: 0.014645):

Model:
|_
{
count -> 
{{{
Q={q_gen_6386, q_gen_6391, q_gen_6392, q_gen_6394, q_gen_6404, q_gen_6406, q_gen_6407, q_gen_6412, q_gen_6414, q_gen_6415, q_gen_6420, q_gen_6444, q_gen_6449, q_gen_6460},
Q_f={q_gen_6386},
Delta=
{
<nil>() -> q_gen_6391
<a>() -> q_gen_6392
<b>() -> q_gen_6404
<cons>(q_gen_6404, q_gen_6391) -> q_gen_6412
<cons>(q_gen_6404, q_gen_6412) -> q_gen_6412
<cons>(q_gen_6404, q_gen_6420) -> q_gen_6412
<cons>(q_gen_6404, q_gen_6444) -> q_gen_6412
<s>(q_gen_6415) -> q_gen_6415
<z>() -> q_gen_6415
<cons>(q_gen_6392, q_gen_6391) -> q_gen_6420
<cons>(q_gen_6404, q_gen_6449) -> q_gen_6420
<cons>(q_gen_6392, q_gen_6420) -> q_gen_6444
<cons>(q_gen_6392, q_gen_6412) -> q_gen_6449
<cons>(q_gen_6392, q_gen_6444) -> q_gen_6449
<cons>(q_gen_6392, q_gen_6449) -> q_gen_6449
<b, z>() -> q_gen_6394
<a, z>() -> q_gen_6406
<b, s>(q_gen_6415) -> q_gen_6414
<a, s>(q_gen_6415) -> q_gen_6460
<a, cons, s>(q_gen_6394, q_gen_6420) -> q_gen_6386
<a, cons, s>(q_gen_6394, q_gen_6449) -> q_gen_6386
<a, cons, s>(q_gen_6406, q_gen_6391) -> q_gen_6386
<a, cons, s>(q_gen_6406, q_gen_6412) -> q_gen_6386
<a, cons, s>(q_gen_6406, q_gen_6449) -> q_gen_6386
<a, cons, s>(q_gen_6414, q_gen_6412) -> q_gen_6386
<a, cons, s>(q_gen_6414, q_gen_6444) -> q_gen_6386
<a, cons, s>(q_gen_6414, q_gen_6449) -> q_gen_6386
<a, cons, s>(q_gen_6460, q_gen_6412) -> q_gen_6386
<a, cons, s>(q_gen_6460, q_gen_6420) -> q_gen_6386
<a, cons, s>(q_gen_6460, q_gen_6444) -> q_gen_6386
<a, cons, s>(q_gen_6460, q_gen_6449) -> q_gen_6386
<a, cons, z>(q_gen_6404, q_gen_6391) -> q_gen_6386
<a, cons, z>(q_gen_6404, q_gen_6412) -> q_gen_6386
<a, nil, z>() -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6391) -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6412) -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6420) -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6444) -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6449) -> q_gen_6386
<b, cons, s>(q_gen_6406, q_gen_6412) -> q_gen_6386
<b, cons, s>(q_gen_6406, q_gen_6449) -> q_gen_6386
<b, cons, s>(q_gen_6414, q_gen_6412) -> q_gen_6386
<b, cons, s>(q_gen_6414, q_gen_6444) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6391) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6420) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6444) -> q_gen_6386
<b, nil, z>() -> q_gen_6386
<a, cons, s>(q_gen_6394, q_gen_6391) -> q_gen_6407
<a, cons, s>(q_gen_6394, q_gen_6412) -> q_gen_6407
<a, cons, s>(q_gen_6414, q_gen_6391) -> q_gen_6407
<a, cons, s>(q_gen_6414, q_gen_6420) -> q_gen_6407
<a, cons, s>(q_gen_6460, q_gen_6391) -> q_gen_6407
<a, cons, z>(q_gen_6404, q_gen_6420) -> q_gen_6407
<a, cons, z>(q_gen_6404, q_gen_6444) -> q_gen_6407
<a, cons, z>(q_gen_6404, q_gen_6449) -> q_gen_6407
<b, cons, s>(q_gen_6406, q_gen_6391) -> q_gen_6407
<b, cons, s>(q_gen_6406, q_gen_6420) -> q_gen_6407
<b, cons, s>(q_gen_6406, q_gen_6444) -> q_gen_6407
<b, cons, s>(q_gen_6414, q_gen_6391) -> q_gen_6407
<b, cons, s>(q_gen_6414, q_gen_6420) -> q_gen_6407
<b, cons, s>(q_gen_6460, q_gen_6391) -> q_gen_6407
<b, cons, z>(q_gen_6392, q_gen_6412) -> q_gen_6407
<b, cons, z>(q_gen_6392, q_gen_6449) -> q_gen_6407
<b, cons, z>(q_gen_6404, q_gen_6391) -> q_gen_6407
}

Datatype: <elt, eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_6383, q_gen_6385, q_gen_6408},
Q_f={q_gen_6383},
Delta=
{
<s>(q_gen_6385) -> q_gen_6385
<z>() -> q_gen_6385
<s, s>(q_gen_6383) -> q_gen_6383
<z, s>(q_gen_6385) -> q_gen_6383
<z, z>() -> q_gen_6383
<s, s>(q_gen_6408) -> q_gen_6408
<s, z>(q_gen_6385) -> q_gen_6408
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  prefix -> 
{{{
Q={q_gen_6382, q_gen_6388, q_gen_6396, q_gen_6397},
Q_f={q_gen_6382},
Delta=
{
<cons>(q_gen_6397, q_gen_6396) -> q_gen_6396
<nil>() -> q_gen_6396
<a>() -> q_gen_6397
<b>() -> q_gen_6397
<cons, cons>(q_gen_6388, q_gen_6382) -> q_gen_6382
<nil, cons>(q_gen_6397, q_gen_6396) -> q_gen_6382
<nil, nil>() -> q_gen_6382
<a, a>() -> q_gen_6388
<b, b>() -> q_gen_6388
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 56
() -> leq([z, s(nn2)]) -> 56
() -> leq([z, z]) -> 56
() -> prefix([nil, y]) -> 56
(count([x, l1, _py]) /\ count([x, l2, _qy]) /\ prefix([l1, l2])) -> leq([_py, _qy]) -> 58
(count([x, t1, _jy])) -> count([x, cons(x, t1), s(_jy)]) -> 57
(count([x, t1, _ky]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ky]) -> 60
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 56
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 56
(leq([s(nn1), z])) -> BOT -> 56
(prefix([zs, ys])) -> prefix([cons(y2, zs), cons(y2, ys)]) -> 57
(prefix([cons(y2, zs), cons(y2, ys)])) -> prefix([zs, ys]) -> 57
(prefix([cons(z, zs), cons(y2, ys)]) /\ not eq_elt([z, y2])) -> BOT -> 57
(prefix([cons(z, zs), nil])) -> BOT -> 57
}
Sat witness: Found: ((count([x, t1, _ky]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ky]), {
_ky -> s(z)  ;  h1 -> a  ;  t1 -> cons(b, cons(a, cons(b, cons(a, nil))))  ;  x -> b
})

-------------------------------------------
Step 73, which took 0.897366 s (model generation: 0.848647,  model checking: 0.048719):

Model:
|_
{
count -> 
{{{
Q={q_gen_6386, q_gen_6391, q_gen_6392, q_gen_6394, q_gen_6404, q_gen_6406, q_gen_6407, q_gen_6412, q_gen_6414, q_gen_6415, q_gen_6420, q_gen_6444, q_gen_6449, q_gen_6460},
Q_f={q_gen_6386},
Delta=
{
<nil>() -> q_gen_6391
<a>() -> q_gen_6392
<b>() -> q_gen_6404
<cons>(q_gen_6392, q_gen_6449) -> q_gen_6412
<cons>(q_gen_6404, q_gen_6391) -> q_gen_6412
<cons>(q_gen_6404, q_gen_6412) -> q_gen_6412
<cons>(q_gen_6404, q_gen_6420) -> q_gen_6412
<cons>(q_gen_6404, q_gen_6444) -> q_gen_6412
<s>(q_gen_6415) -> q_gen_6415
<z>() -> q_gen_6415
<cons>(q_gen_6392, q_gen_6391) -> q_gen_6420
<cons>(q_gen_6392, q_gen_6420) -> q_gen_6444
<cons>(q_gen_6392, q_gen_6412) -> q_gen_6449
<cons>(q_gen_6392, q_gen_6444) -> q_gen_6449
<cons>(q_gen_6404, q_gen_6449) -> q_gen_6449
<b, z>() -> q_gen_6394
<a, z>() -> q_gen_6406
<b, s>(q_gen_6415) -> q_gen_6414
<a, s>(q_gen_6415) -> q_gen_6460
<a, cons, s>(q_gen_6394, q_gen_6420) -> q_gen_6386
<a, cons, s>(q_gen_6394, q_gen_6449) -> q_gen_6386
<a, cons, s>(q_gen_6406, q_gen_6391) -> q_gen_6386
<a, cons, s>(q_gen_6406, q_gen_6412) -> q_gen_6386
<a, cons, s>(q_gen_6406, q_gen_6449) -> q_gen_6386
<a, cons, s>(q_gen_6414, q_gen_6412) -> q_gen_6386
<a, cons, s>(q_gen_6414, q_gen_6444) -> q_gen_6386
<a, cons, s>(q_gen_6414, q_gen_6449) -> q_gen_6386
<a, cons, s>(q_gen_6460, q_gen_6412) -> q_gen_6386
<a, cons, s>(q_gen_6460, q_gen_6420) -> q_gen_6386
<a, cons, s>(q_gen_6460, q_gen_6444) -> q_gen_6386
<a, cons, s>(q_gen_6460, q_gen_6449) -> q_gen_6386
<a, cons, z>(q_gen_6404, q_gen_6391) -> q_gen_6386
<a, cons, z>(q_gen_6404, q_gen_6412) -> q_gen_6386
<a, nil, z>() -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6391) -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6412) -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6420) -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6444) -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6449) -> q_gen_6386
<b, cons, s>(q_gen_6406, q_gen_6412) -> q_gen_6386
<b, cons, s>(q_gen_6406, q_gen_6449) -> q_gen_6386
<b, cons, s>(q_gen_6414, q_gen_6412) -> q_gen_6386
<b, cons, s>(q_gen_6414, q_gen_6444) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6391) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6420) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6444) -> q_gen_6386
<b, nil, z>() -> q_gen_6386
<a, cons, s>(q_gen_6394, q_gen_6391) -> q_gen_6407
<a, cons, s>(q_gen_6394, q_gen_6412) -> q_gen_6407
<a, cons, s>(q_gen_6414, q_gen_6391) -> q_gen_6407
<a, cons, s>(q_gen_6414, q_gen_6420) -> q_gen_6407
<a, cons, s>(q_gen_6460, q_gen_6391) -> q_gen_6407
<a, cons, z>(q_gen_6404, q_gen_6420) -> q_gen_6407
<a, cons, z>(q_gen_6404, q_gen_6444) -> q_gen_6407
<a, cons, z>(q_gen_6404, q_gen_6449) -> q_gen_6407
<b, cons, s>(q_gen_6406, q_gen_6391) -> q_gen_6407
<b, cons, s>(q_gen_6406, q_gen_6420) -> q_gen_6407
<b, cons, s>(q_gen_6406, q_gen_6444) -> q_gen_6407
<b, cons, s>(q_gen_6414, q_gen_6391) -> q_gen_6407
<b, cons, s>(q_gen_6414, q_gen_6420) -> q_gen_6407
<b, cons, s>(q_gen_6460, q_gen_6391) -> q_gen_6407
<b, cons, z>(q_gen_6392, q_gen_6412) -> q_gen_6407
<b, cons, z>(q_gen_6392, q_gen_6449) -> q_gen_6407
<b, cons, z>(q_gen_6404, q_gen_6391) -> q_gen_6407
}

Datatype: <elt, eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_6383, q_gen_6385, q_gen_6408},
Q_f={q_gen_6383},
Delta=
{
<s>(q_gen_6385) -> q_gen_6385
<z>() -> q_gen_6385
<s, s>(q_gen_6383) -> q_gen_6383
<z, s>(q_gen_6385) -> q_gen_6383
<z, z>() -> q_gen_6383
<s, s>(q_gen_6408) -> q_gen_6408
<s, z>(q_gen_6385) -> q_gen_6408
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  prefix -> 
{{{
Q={q_gen_6382, q_gen_6388, q_gen_6396, q_gen_6397},
Q_f={q_gen_6382},
Delta=
{
<cons>(q_gen_6397, q_gen_6396) -> q_gen_6396
<nil>() -> q_gen_6396
<a>() -> q_gen_6397
<b>() -> q_gen_6397
<cons, cons>(q_gen_6388, q_gen_6382) -> q_gen_6382
<nil, cons>(q_gen_6397, q_gen_6396) -> q_gen_6382
<nil, nil>() -> q_gen_6382
<a, a>() -> q_gen_6388
<b, b>() -> q_gen_6388
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 57
() -> leq([z, s(nn2)]) -> 57
() -> leq([z, z]) -> 57
() -> prefix([nil, y]) -> 57
(count([x, l1, _py]) /\ count([x, l2, _qy]) /\ prefix([l1, l2])) -> leq([_py, _qy]) -> 58
(count([x, t1, _jy])) -> count([x, cons(x, t1), s(_jy)]) -> 60
(count([x, t1, _ky]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ky]) -> 60
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 57
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 57
(leq([s(nn1), z])) -> BOT -> 57
(prefix([zs, ys])) -> prefix([cons(y2, zs), cons(y2, ys)]) -> 58
(prefix([cons(y2, zs), cons(y2, ys)])) -> prefix([zs, ys]) -> 58
(prefix([cons(z, zs), cons(y2, ys)]) /\ not eq_elt([z, y2])) -> BOT -> 58
(prefix([cons(z, zs), nil])) -> BOT -> 58
}
Sat witness: Found: ((count([x, t1, _jy])) -> count([x, cons(x, t1), s(_jy)]), {
_jy -> s(z)  ;  t1 -> cons(a, cons(b, cons(b, nil)))  ;  x -> b
})

-------------------------------------------
Step 74, which took 0.975558 s (model generation: 0.939507,  model checking: 0.036051):

Model:
|_
{
count -> 
{{{
Q={q_gen_6386, q_gen_6391, q_gen_6392, q_gen_6394, q_gen_6404, q_gen_6406, q_gen_6407, q_gen_6412, q_gen_6414, q_gen_6415, q_gen_6420, q_gen_6444, q_gen_6449, q_gen_6460},
Q_f={q_gen_6386},
Delta=
{
<nil>() -> q_gen_6391
<a>() -> q_gen_6392
<b>() -> q_gen_6404
<cons>(q_gen_6404, q_gen_6391) -> q_gen_6412
<cons>(q_gen_6404, q_gen_6412) -> q_gen_6412
<cons>(q_gen_6404, q_gen_6420) -> q_gen_6412
<cons>(q_gen_6404, q_gen_6444) -> q_gen_6412
<s>(q_gen_6415) -> q_gen_6415
<z>() -> q_gen_6415
<cons>(q_gen_6392, q_gen_6391) -> q_gen_6420
<cons>(q_gen_6392, q_gen_6420) -> q_gen_6444
<cons>(q_gen_6392, q_gen_6412) -> q_gen_6449
<cons>(q_gen_6392, q_gen_6444) -> q_gen_6449
<cons>(q_gen_6392, q_gen_6449) -> q_gen_6449
<cons>(q_gen_6404, q_gen_6449) -> q_gen_6449
<b, z>() -> q_gen_6394
<a, z>() -> q_gen_6406
<b, s>(q_gen_6415) -> q_gen_6414
<a, s>(q_gen_6415) -> q_gen_6460
<a, cons, s>(q_gen_6394, q_gen_6420) -> q_gen_6386
<a, cons, s>(q_gen_6394, q_gen_6449) -> q_gen_6386
<a, cons, s>(q_gen_6406, q_gen_6391) -> q_gen_6386
<a, cons, s>(q_gen_6406, q_gen_6412) -> q_gen_6386
<a, cons, s>(q_gen_6406, q_gen_6449) -> q_gen_6386
<a, cons, s>(q_gen_6414, q_gen_6412) -> q_gen_6386
<a, cons, s>(q_gen_6414, q_gen_6444) -> q_gen_6386
<a, cons, s>(q_gen_6414, q_gen_6449) -> q_gen_6386
<a, cons, s>(q_gen_6460, q_gen_6412) -> q_gen_6386
<a, cons, s>(q_gen_6460, q_gen_6420) -> q_gen_6386
<a, cons, s>(q_gen_6460, q_gen_6444) -> q_gen_6386
<a, cons, s>(q_gen_6460, q_gen_6449) -> q_gen_6386
<a, cons, z>(q_gen_6404, q_gen_6391) -> q_gen_6386
<a, cons, z>(q_gen_6404, q_gen_6412) -> q_gen_6386
<a, nil, z>() -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6391) -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6412) -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6420) -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6444) -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6449) -> q_gen_6386
<b, cons, s>(q_gen_6406, q_gen_6412) -> q_gen_6386
<b, cons, s>(q_gen_6406, q_gen_6449) -> q_gen_6386
<b, cons, s>(q_gen_6414, q_gen_6412) -> q_gen_6386
<b, cons, s>(q_gen_6414, q_gen_6444) -> q_gen_6386
<b, cons, s>(q_gen_6414, q_gen_6449) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6391) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6420) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6444) -> q_gen_6386
<b, nil, z>() -> q_gen_6386
<a, cons, s>(q_gen_6394, q_gen_6391) -> q_gen_6407
<a, cons, s>(q_gen_6394, q_gen_6412) -> q_gen_6407
<a, cons, s>(q_gen_6414, q_gen_6391) -> q_gen_6407
<a, cons, s>(q_gen_6414, q_gen_6420) -> q_gen_6407
<a, cons, s>(q_gen_6460, q_gen_6391) -> q_gen_6407
<a, cons, z>(q_gen_6404, q_gen_6420) -> q_gen_6407
<a, cons, z>(q_gen_6404, q_gen_6444) -> q_gen_6407
<a, cons, z>(q_gen_6404, q_gen_6449) -> q_gen_6407
<b, cons, s>(q_gen_6406, q_gen_6391) -> q_gen_6407
<b, cons, s>(q_gen_6406, q_gen_6420) -> q_gen_6407
<b, cons, s>(q_gen_6406, q_gen_6444) -> q_gen_6407
<b, cons, s>(q_gen_6414, q_gen_6391) -> q_gen_6407
<b, cons, s>(q_gen_6414, q_gen_6420) -> q_gen_6407
<b, cons, s>(q_gen_6460, q_gen_6391) -> q_gen_6407
<b, cons, z>(q_gen_6392, q_gen_6412) -> q_gen_6407
<b, cons, z>(q_gen_6392, q_gen_6449) -> q_gen_6407
<b, cons, z>(q_gen_6404, q_gen_6391) -> q_gen_6407
}

Datatype: <elt, eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_6383, q_gen_6385, q_gen_6408},
Q_f={q_gen_6383},
Delta=
{
<s>(q_gen_6385) -> q_gen_6385
<z>() -> q_gen_6385
<s, s>(q_gen_6383) -> q_gen_6383
<z, s>(q_gen_6385) -> q_gen_6383
<z, z>() -> q_gen_6383
<s, s>(q_gen_6408) -> q_gen_6408
<s, z>(q_gen_6385) -> q_gen_6408
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  prefix -> 
{{{
Q={q_gen_6382, q_gen_6388, q_gen_6396, q_gen_6397},
Q_f={q_gen_6382},
Delta=
{
<cons>(q_gen_6397, q_gen_6396) -> q_gen_6396
<nil>() -> q_gen_6396
<a>() -> q_gen_6397
<b>() -> q_gen_6397
<cons, cons>(q_gen_6388, q_gen_6382) -> q_gen_6382
<nil, cons>(q_gen_6397, q_gen_6396) -> q_gen_6382
<nil, nil>() -> q_gen_6382
<a, a>() -> q_gen_6388
<b, b>() -> q_gen_6388
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 58
() -> leq([z, s(nn2)]) -> 58
() -> leq([z, z]) -> 58
() -> prefix([nil, y]) -> 58
(count([x, l1, _py]) /\ count([x, l2, _qy]) /\ prefix([l1, l2])) -> leq([_py, _qy]) -> 61
(count([x, t1, _jy])) -> count([x, cons(x, t1), s(_jy)]) -> 60
(count([x, t1, _ky]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ky]) -> 60
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 58
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 58
(leq([s(nn1), z])) -> BOT -> 58
(prefix([zs, ys])) -> prefix([cons(y2, zs), cons(y2, ys)]) -> 59
(prefix([cons(y2, zs), cons(y2, ys)])) -> prefix([zs, ys]) -> 59
(prefix([cons(z, zs), cons(y2, ys)]) /\ not eq_elt([z, y2])) -> BOT -> 59
(prefix([cons(z, zs), nil])) -> BOT -> 59
}
Sat witness: Found: ((count([x, l1, _py]) /\ count([x, l2, _qy]) /\ prefix([l1, l2])) -> leq([_py, _qy]), {
_py -> s(s(z))  ;  _qy -> s(z)  ;  l1 -> cons(b, cons(a, cons(a, nil)))  ;  l2 -> cons(b, cons(a, cons(a, nil)))  ;  x -> b
})

-------------------------------------------
Step 75, which took 0.836984 s (model generation: 0.816449,  model checking: 0.020535):

Model:
|_
{
count -> 
{{{
Q={q_gen_6386, q_gen_6391, q_gen_6392, q_gen_6394, q_gen_6404, q_gen_6406, q_gen_6407, q_gen_6412, q_gen_6414, q_gen_6415, q_gen_6420, q_gen_6444, q_gen_6449, q_gen_6460},
Q_f={q_gen_6386},
Delta=
{
<nil>() -> q_gen_6391
<a>() -> q_gen_6392
<b>() -> q_gen_6404
<cons>(q_gen_6392, q_gen_6444) -> q_gen_6412
<cons>(q_gen_6392, q_gen_6449) -> q_gen_6412
<cons>(q_gen_6404, q_gen_6391) -> q_gen_6412
<cons>(q_gen_6404, q_gen_6412) -> q_gen_6412
<cons>(q_gen_6404, q_gen_6420) -> q_gen_6412
<cons>(q_gen_6404, q_gen_6444) -> q_gen_6412
<s>(q_gen_6415) -> q_gen_6415
<z>() -> q_gen_6415
<cons>(q_gen_6392, q_gen_6391) -> q_gen_6420
<cons>(q_gen_6392, q_gen_6420) -> q_gen_6444
<cons>(q_gen_6404, q_gen_6449) -> q_gen_6444
<cons>(q_gen_6392, q_gen_6412) -> q_gen_6449
<b, z>() -> q_gen_6394
<a, z>() -> q_gen_6406
<b, s>(q_gen_6415) -> q_gen_6414
<a, s>(q_gen_6415) -> q_gen_6460
<a, cons, s>(q_gen_6394, q_gen_6420) -> q_gen_6386
<a, cons, s>(q_gen_6394, q_gen_6444) -> q_gen_6386
<a, cons, s>(q_gen_6394, q_gen_6449) -> q_gen_6386
<a, cons, s>(q_gen_6406, q_gen_6391) -> q_gen_6386
<a, cons, s>(q_gen_6406, q_gen_6412) -> q_gen_6386
<a, cons, s>(q_gen_6406, q_gen_6449) -> q_gen_6386
<a, cons, s>(q_gen_6414, q_gen_6412) -> q_gen_6386
<a, cons, s>(q_gen_6414, q_gen_6444) -> q_gen_6386
<a, cons, s>(q_gen_6414, q_gen_6449) -> q_gen_6386
<a, cons, s>(q_gen_6460, q_gen_6412) -> q_gen_6386
<a, cons, s>(q_gen_6460, q_gen_6420) -> q_gen_6386
<a, cons, s>(q_gen_6460, q_gen_6444) -> q_gen_6386
<a, cons, s>(q_gen_6460, q_gen_6449) -> q_gen_6386
<a, cons, z>(q_gen_6404, q_gen_6391) -> q_gen_6386
<a, cons, z>(q_gen_6404, q_gen_6412) -> q_gen_6386
<a, nil, z>() -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6391) -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6412) -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6420) -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6444) -> q_gen_6386
<b, cons, s>(q_gen_6406, q_gen_6412) -> q_gen_6386
<b, cons, s>(q_gen_6406, q_gen_6449) -> q_gen_6386
<b, cons, s>(q_gen_6414, q_gen_6412) -> q_gen_6386
<b, cons, s>(q_gen_6414, q_gen_6449) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6391) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6420) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6444) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6449) -> q_gen_6386
<b, nil, z>() -> q_gen_6386
<a, cons, s>(q_gen_6394, q_gen_6391) -> q_gen_6407
<a, cons, s>(q_gen_6394, q_gen_6412) -> q_gen_6407
<a, cons, s>(q_gen_6414, q_gen_6391) -> q_gen_6407
<a, cons, s>(q_gen_6414, q_gen_6420) -> q_gen_6407
<a, cons, s>(q_gen_6460, q_gen_6391) -> q_gen_6407
<a, cons, z>(q_gen_6404, q_gen_6420) -> q_gen_6407
<a, cons, z>(q_gen_6404, q_gen_6444) -> q_gen_6407
<a, cons, z>(q_gen_6404, q_gen_6449) -> q_gen_6407
<b, cons, s>(q_gen_6394, q_gen_6449) -> q_gen_6407
<b, cons, s>(q_gen_6406, q_gen_6391) -> q_gen_6407
<b, cons, s>(q_gen_6406, q_gen_6420) -> q_gen_6407
<b, cons, s>(q_gen_6406, q_gen_6444) -> q_gen_6407
<b, cons, s>(q_gen_6414, q_gen_6391) -> q_gen_6407
<b, cons, s>(q_gen_6414, q_gen_6420) -> q_gen_6407
<b, cons, s>(q_gen_6414, q_gen_6444) -> q_gen_6407
<b, cons, s>(q_gen_6460, q_gen_6391) -> q_gen_6407
<b, cons, z>(q_gen_6392, q_gen_6412) -> q_gen_6407
<b, cons, z>(q_gen_6404, q_gen_6391) -> q_gen_6407
}

Datatype: <elt, eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_6383, q_gen_6385, q_gen_6408},
Q_f={q_gen_6383},
Delta=
{
<s>(q_gen_6385) -> q_gen_6385
<z>() -> q_gen_6385
<s, s>(q_gen_6383) -> q_gen_6383
<z, s>(q_gen_6385) -> q_gen_6383
<z, z>() -> q_gen_6383
<s, s>(q_gen_6408) -> q_gen_6408
<s, z>(q_gen_6385) -> q_gen_6408
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  prefix -> 
{{{
Q={q_gen_6382, q_gen_6388, q_gen_6396, q_gen_6397},
Q_f={q_gen_6382},
Delta=
{
<cons>(q_gen_6397, q_gen_6396) -> q_gen_6396
<nil>() -> q_gen_6396
<a>() -> q_gen_6397
<b>() -> q_gen_6397
<cons, cons>(q_gen_6388, q_gen_6382) -> q_gen_6382
<nil, cons>(q_gen_6397, q_gen_6396) -> q_gen_6382
<nil, nil>() -> q_gen_6382
<a, a>() -> q_gen_6388
<b, b>() -> q_gen_6388
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 59
() -> leq([z, s(nn2)]) -> 59
() -> leq([z, z]) -> 59
() -> prefix([nil, y]) -> 59
(count([x, l1, _py]) /\ count([x, l2, _qy]) /\ prefix([l1, l2])) -> leq([_py, _qy]) -> 61
(count([x, t1, _jy])) -> count([x, cons(x, t1), s(_jy)]) -> 60
(count([x, t1, _ky]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ky]) -> 63
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 59
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 59
(leq([s(nn1), z])) -> BOT -> 59
(prefix([zs, ys])) -> prefix([cons(y2, zs), cons(y2, ys)]) -> 60
(prefix([cons(y2, zs), cons(y2, ys)])) -> prefix([zs, ys]) -> 60
(prefix([cons(z, zs), cons(y2, ys)]) /\ not eq_elt([z, y2])) -> BOT -> 60
(prefix([cons(z, zs), nil])) -> BOT -> 60
}
Sat witness: Found: ((count([x, t1, _ky]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ky]), {
_ky -> z  ;  h1 -> a  ;  t1 -> cons(a, cons(a, cons(b, cons(a, nil))))  ;  x -> b
})

-------------------------------------------
Step 76, which took 0.939947 s (model generation: 0.860060,  model checking: 0.079887):

Model:
|_
{
count -> 
{{{
Q={q_gen_6386, q_gen_6391, q_gen_6392, q_gen_6394, q_gen_6404, q_gen_6406, q_gen_6407, q_gen_6412, q_gen_6414, q_gen_6415, q_gen_6420, q_gen_6444, q_gen_6449, q_gen_6460},
Q_f={q_gen_6386},
Delta=
{
<nil>() -> q_gen_6391
<a>() -> q_gen_6392
<b>() -> q_gen_6404
<cons>(q_gen_6404, q_gen_6391) -> q_gen_6412
<cons>(q_gen_6404, q_gen_6412) -> q_gen_6412
<cons>(q_gen_6404, q_gen_6420) -> q_gen_6412
<cons>(q_gen_6404, q_gen_6444) -> q_gen_6412
<s>(q_gen_6415) -> q_gen_6415
<z>() -> q_gen_6415
<cons>(q_gen_6392, q_gen_6391) -> q_gen_6420
<cons>(q_gen_6392, q_gen_6420) -> q_gen_6444
<cons>(q_gen_6392, q_gen_6412) -> q_gen_6449
<cons>(q_gen_6392, q_gen_6444) -> q_gen_6449
<cons>(q_gen_6392, q_gen_6449) -> q_gen_6449
<cons>(q_gen_6404, q_gen_6449) -> q_gen_6449
<b, z>() -> q_gen_6394
<a, z>() -> q_gen_6406
<b, s>(q_gen_6415) -> q_gen_6414
<a, s>(q_gen_6415) -> q_gen_6460
<a, cons, s>(q_gen_6394, q_gen_6420) -> q_gen_6386
<a, cons, s>(q_gen_6394, q_gen_6449) -> q_gen_6386
<a, cons, s>(q_gen_6406, q_gen_6391) -> q_gen_6386
<a, cons, s>(q_gen_6406, q_gen_6412) -> q_gen_6386
<a, cons, s>(q_gen_6406, q_gen_6449) -> q_gen_6386
<a, cons, s>(q_gen_6414, q_gen_6412) -> q_gen_6386
<a, cons, s>(q_gen_6414, q_gen_6444) -> q_gen_6386
<a, cons, s>(q_gen_6414, q_gen_6449) -> q_gen_6386
<a, cons, s>(q_gen_6460, q_gen_6412) -> q_gen_6386
<a, cons, s>(q_gen_6460, q_gen_6420) -> q_gen_6386
<a, cons, s>(q_gen_6460, q_gen_6444) -> q_gen_6386
<a, cons, s>(q_gen_6460, q_gen_6449) -> q_gen_6386
<a, cons, z>(q_gen_6404, q_gen_6391) -> q_gen_6386
<a, cons, z>(q_gen_6404, q_gen_6412) -> q_gen_6386
<a, nil, z>() -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6391) -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6412) -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6420) -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6444) -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6449) -> q_gen_6386
<b, cons, s>(q_gen_6406, q_gen_6412) -> q_gen_6386
<b, cons, s>(q_gen_6406, q_gen_6449) -> q_gen_6386
<b, cons, s>(q_gen_6414, q_gen_6412) -> q_gen_6386
<b, cons, s>(q_gen_6414, q_gen_6449) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6391) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6420) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6444) -> q_gen_6386
<b, nil, z>() -> q_gen_6386
<a, cons, s>(q_gen_6394, q_gen_6391) -> q_gen_6407
<a, cons, s>(q_gen_6394, q_gen_6412) -> q_gen_6407
<a, cons, s>(q_gen_6414, q_gen_6391) -> q_gen_6407
<a, cons, s>(q_gen_6414, q_gen_6420) -> q_gen_6407
<a, cons, s>(q_gen_6460, q_gen_6391) -> q_gen_6407
<a, cons, z>(q_gen_6404, q_gen_6420) -> q_gen_6407
<a, cons, z>(q_gen_6404, q_gen_6444) -> q_gen_6407
<a, cons, z>(q_gen_6404, q_gen_6449) -> q_gen_6407
<b, cons, s>(q_gen_6406, q_gen_6391) -> q_gen_6407
<b, cons, s>(q_gen_6406, q_gen_6420) -> q_gen_6407
<b, cons, s>(q_gen_6406, q_gen_6444) -> q_gen_6407
<b, cons, s>(q_gen_6414, q_gen_6391) -> q_gen_6407
<b, cons, s>(q_gen_6414, q_gen_6420) -> q_gen_6407
<b, cons, s>(q_gen_6414, q_gen_6444) -> q_gen_6407
<b, cons, s>(q_gen_6460, q_gen_6391) -> q_gen_6407
<b, cons, z>(q_gen_6392, q_gen_6412) -> q_gen_6407
<b, cons, z>(q_gen_6392, q_gen_6449) -> q_gen_6407
<b, cons, z>(q_gen_6404, q_gen_6391) -> q_gen_6407
}

Datatype: <elt, eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_6383, q_gen_6385, q_gen_6408},
Q_f={q_gen_6383},
Delta=
{
<s>(q_gen_6385) -> q_gen_6385
<z>() -> q_gen_6385
<s, s>(q_gen_6383) -> q_gen_6383
<z, s>(q_gen_6385) -> q_gen_6383
<z, z>() -> q_gen_6383
<s, s>(q_gen_6408) -> q_gen_6408
<s, z>(q_gen_6385) -> q_gen_6408
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  prefix -> 
{{{
Q={q_gen_6382, q_gen_6388, q_gen_6396, q_gen_6397},
Q_f={q_gen_6382},
Delta=
{
<cons>(q_gen_6397, q_gen_6396) -> q_gen_6396
<nil>() -> q_gen_6396
<a>() -> q_gen_6397
<b>() -> q_gen_6397
<cons, cons>(q_gen_6388, q_gen_6382) -> q_gen_6382
<nil, cons>(q_gen_6397, q_gen_6396) -> q_gen_6382
<nil, nil>() -> q_gen_6382
<a, a>() -> q_gen_6388
<b, b>() -> q_gen_6388
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 60
() -> leq([z, s(nn2)]) -> 60
() -> leq([z, z]) -> 60
() -> prefix([nil, y]) -> 60
(count([x, l1, _py]) /\ count([x, l2, _qy]) /\ prefix([l1, l2])) -> leq([_py, _qy]) -> 64
(count([x, t1, _jy])) -> count([x, cons(x, t1), s(_jy)]) -> 61
(count([x, t1, _ky]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ky]) -> 63
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 60
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 60
(leq([s(nn1), z])) -> BOT -> 60
(prefix([zs, ys])) -> prefix([cons(y2, zs), cons(y2, ys)]) -> 61
(prefix([cons(y2, zs), cons(y2, ys)])) -> prefix([zs, ys]) -> 61
(prefix([cons(z, zs), cons(y2, ys)]) /\ not eq_elt([z, y2])) -> BOT -> 61
(prefix([cons(z, zs), nil])) -> BOT -> 61
}
Sat witness: Found: ((count([x, l1, _py]) /\ count([x, l2, _qy]) /\ prefix([l1, l2])) -> leq([_py, _qy]), {
_py -> s(s(z))  ;  _qy -> s(z)  ;  l1 -> cons(b, cons(a, cons(a, cons(a, nil))))  ;  l2 -> cons(b, cons(a, cons(a, cons(a, nil))))  ;  x -> b
})

-------------------------------------------
Step 77, which took 1.038016 s (model generation: 1.009509,  model checking: 0.028507):

Model:
|_
{
count -> 
{{{
Q={q_gen_6386, q_gen_6391, q_gen_6392, q_gen_6394, q_gen_6404, q_gen_6406, q_gen_6407, q_gen_6412, q_gen_6414, q_gen_6415, q_gen_6420, q_gen_6444, q_gen_6449, q_gen_6460},
Q_f={q_gen_6386},
Delta=
{
<nil>() -> q_gen_6391
<a>() -> q_gen_6392
<b>() -> q_gen_6404
<cons>(q_gen_6404, q_gen_6391) -> q_gen_6412
<cons>(q_gen_6404, q_gen_6412) -> q_gen_6412
<cons>(q_gen_6404, q_gen_6420) -> q_gen_6412
<cons>(q_gen_6404, q_gen_6444) -> q_gen_6412
<s>(q_gen_6415) -> q_gen_6415
<z>() -> q_gen_6415
<cons>(q_gen_6392, q_gen_6391) -> q_gen_6420
<cons>(q_gen_6404, q_gen_6449) -> q_gen_6420
<cons>(q_gen_6392, q_gen_6420) -> q_gen_6444
<cons>(q_gen_6392, q_gen_6444) -> q_gen_6444
<cons>(q_gen_6392, q_gen_6412) -> q_gen_6449
<cons>(q_gen_6392, q_gen_6449) -> q_gen_6449
<b, z>() -> q_gen_6394
<a, z>() -> q_gen_6406
<b, s>(q_gen_6415) -> q_gen_6414
<a, s>(q_gen_6415) -> q_gen_6460
<a, cons, s>(q_gen_6394, q_gen_6420) -> q_gen_6386
<a, cons, s>(q_gen_6394, q_gen_6449) -> q_gen_6386
<a, cons, s>(q_gen_6406, q_gen_6391) -> q_gen_6386
<a, cons, s>(q_gen_6406, q_gen_6412) -> q_gen_6386
<a, cons, s>(q_gen_6414, q_gen_6412) -> q_gen_6386
<a, cons, s>(q_gen_6414, q_gen_6444) -> q_gen_6386
<a, cons, s>(q_gen_6414, q_gen_6449) -> q_gen_6386
<a, cons, s>(q_gen_6460, q_gen_6412) -> q_gen_6386
<a, cons, s>(q_gen_6460, q_gen_6420) -> q_gen_6386
<a, cons, s>(q_gen_6460, q_gen_6444) -> q_gen_6386
<a, cons, s>(q_gen_6460, q_gen_6449) -> q_gen_6386
<a, cons, z>(q_gen_6404, q_gen_6391) -> q_gen_6386
<a, cons, z>(q_gen_6404, q_gen_6412) -> q_gen_6386
<a, nil, z>() -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6391) -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6412) -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6420) -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6444) -> q_gen_6386
<b, cons, s>(q_gen_6406, q_gen_6412) -> q_gen_6386
<b, cons, s>(q_gen_6406, q_gen_6449) -> q_gen_6386
<b, cons, s>(q_gen_6414, q_gen_6412) -> q_gen_6386
<b, cons, s>(q_gen_6414, q_gen_6449) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6391) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6420) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6444) -> q_gen_6386
<b, nil, z>() -> q_gen_6386
<a, cons, s>(q_gen_6394, q_gen_6391) -> q_gen_6407
<a, cons, s>(q_gen_6394, q_gen_6412) -> q_gen_6407
<a, cons, s>(q_gen_6406, q_gen_6449) -> q_gen_6407
<a, cons, s>(q_gen_6414, q_gen_6391) -> q_gen_6407
<a, cons, s>(q_gen_6414, q_gen_6420) -> q_gen_6407
<a, cons, s>(q_gen_6460, q_gen_6391) -> q_gen_6407
<a, cons, z>(q_gen_6404, q_gen_6420) -> q_gen_6407
<a, cons, z>(q_gen_6404, q_gen_6444) -> q_gen_6407
<a, cons, z>(q_gen_6404, q_gen_6449) -> q_gen_6407
<b, cons, s>(q_gen_6394, q_gen_6449) -> q_gen_6407
<b, cons, s>(q_gen_6406, q_gen_6391) -> q_gen_6407
<b, cons, s>(q_gen_6406, q_gen_6420) -> q_gen_6407
<b, cons, s>(q_gen_6406, q_gen_6444) -> q_gen_6407
<b, cons, s>(q_gen_6414, q_gen_6391) -> q_gen_6407
<b, cons, s>(q_gen_6414, q_gen_6420) -> q_gen_6407
<b, cons, s>(q_gen_6414, q_gen_6444) -> q_gen_6407
<b, cons, s>(q_gen_6460, q_gen_6391) -> q_gen_6407
<b, cons, z>(q_gen_6392, q_gen_6412) -> q_gen_6407
<b, cons, z>(q_gen_6392, q_gen_6449) -> q_gen_6407
<b, cons, z>(q_gen_6404, q_gen_6391) -> q_gen_6407
}

Datatype: <elt, eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_6383, q_gen_6385, q_gen_6408},
Q_f={q_gen_6383},
Delta=
{
<s>(q_gen_6385) -> q_gen_6385
<z>() -> q_gen_6385
<s, s>(q_gen_6383) -> q_gen_6383
<z, s>(q_gen_6385) -> q_gen_6383
<z, z>() -> q_gen_6383
<s, s>(q_gen_6408) -> q_gen_6408
<s, z>(q_gen_6385) -> q_gen_6408
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  prefix -> 
{{{
Q={q_gen_6382, q_gen_6388, q_gen_6396, q_gen_6397},
Q_f={q_gen_6382},
Delta=
{
<cons>(q_gen_6397, q_gen_6396) -> q_gen_6396
<nil>() -> q_gen_6396
<a>() -> q_gen_6397
<b>() -> q_gen_6397
<cons, cons>(q_gen_6388, q_gen_6382) -> q_gen_6382
<nil, cons>(q_gen_6397, q_gen_6396) -> q_gen_6382
<nil, nil>() -> q_gen_6382
<a, a>() -> q_gen_6388
<b, b>() -> q_gen_6388
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 61
() -> leq([z, s(nn2)]) -> 61
() -> leq([z, z]) -> 61
() -> prefix([nil, y]) -> 61
(count([x, l1, _py]) /\ count([x, l2, _qy]) /\ prefix([l1, l2])) -> leq([_py, _qy]) -> 64
(count([x, t1, _jy])) -> count([x, cons(x, t1), s(_jy)]) -> 64
(count([x, t1, _ky]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ky]) -> 63
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 61
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 61
(leq([s(nn1), z])) -> BOT -> 61
(prefix([zs, ys])) -> prefix([cons(y2, zs), cons(y2, ys)]) -> 62
(prefix([cons(y2, zs), cons(y2, ys)])) -> prefix([zs, ys]) -> 62
(prefix([cons(z, zs), cons(y2, ys)]) /\ not eq_elt([z, y2])) -> BOT -> 62
(prefix([cons(z, zs), nil])) -> BOT -> 62
}
Sat witness: Found: ((count([x, t1, _jy])) -> count([x, cons(x, t1), s(_jy)]), {
_jy -> s(s(z))  ;  t1 -> cons(b, cons(a, cons(a, cons(b, nil))))  ;  x -> b
})

-------------------------------------------
Step 78, which took 1.303337 s (model generation: 1.276300,  model checking: 0.027037):

Model:
|_
{
count -> 
{{{
Q={q_gen_6386, q_gen_6391, q_gen_6392, q_gen_6394, q_gen_6404, q_gen_6406, q_gen_6407, q_gen_6412, q_gen_6414, q_gen_6415, q_gen_6420, q_gen_6444, q_gen_6449, q_gen_6460},
Q_f={q_gen_6386},
Delta=
{
<nil>() -> q_gen_6391
<a>() -> q_gen_6392
<b>() -> q_gen_6404
<cons>(q_gen_6392, q_gen_6449) -> q_gen_6412
<cons>(q_gen_6404, q_gen_6391) -> q_gen_6412
<cons>(q_gen_6404, q_gen_6412) -> q_gen_6412
<cons>(q_gen_6404, q_gen_6420) -> q_gen_6412
<cons>(q_gen_6404, q_gen_6444) -> q_gen_6412
<s>(q_gen_6415) -> q_gen_6415
<z>() -> q_gen_6415
<cons>(q_gen_6392, q_gen_6391) -> q_gen_6420
<cons>(q_gen_6392, q_gen_6444) -> q_gen_6420
<cons>(q_gen_6392, q_gen_6420) -> q_gen_6444
<cons>(q_gen_6404, q_gen_6449) -> q_gen_6444
<cons>(q_gen_6392, q_gen_6412) -> q_gen_6449
<b, z>() -> q_gen_6394
<a, z>() -> q_gen_6406
<b, s>(q_gen_6415) -> q_gen_6414
<a, s>(q_gen_6415) -> q_gen_6460
<a, cons, s>(q_gen_6394, q_gen_6420) -> q_gen_6386
<a, cons, s>(q_gen_6394, q_gen_6444) -> q_gen_6386
<a, cons, s>(q_gen_6394, q_gen_6449) -> q_gen_6386
<a, cons, s>(q_gen_6406, q_gen_6391) -> q_gen_6386
<a, cons, s>(q_gen_6406, q_gen_6412) -> q_gen_6386
<a, cons, s>(q_gen_6414, q_gen_6412) -> q_gen_6386
<a, cons, s>(q_gen_6414, q_gen_6444) -> q_gen_6386
<a, cons, s>(q_gen_6414, q_gen_6449) -> q_gen_6386
<a, cons, s>(q_gen_6460, q_gen_6412) -> q_gen_6386
<a, cons, s>(q_gen_6460, q_gen_6420) -> q_gen_6386
<a, cons, s>(q_gen_6460, q_gen_6444) -> q_gen_6386
<a, cons, s>(q_gen_6460, q_gen_6449) -> q_gen_6386
<a, cons, z>(q_gen_6404, q_gen_6391) -> q_gen_6386
<a, cons, z>(q_gen_6404, q_gen_6412) -> q_gen_6386
<a, nil, z>() -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6391) -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6412) -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6420) -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6444) -> q_gen_6386
<b, cons, s>(q_gen_6406, q_gen_6412) -> q_gen_6386
<b, cons, s>(q_gen_6406, q_gen_6449) -> q_gen_6386
<b, cons, s>(q_gen_6414, q_gen_6412) -> q_gen_6386
<b, cons, s>(q_gen_6414, q_gen_6449) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6391) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6420) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6444) -> q_gen_6386
<b, nil, z>() -> q_gen_6386
<a, cons, s>(q_gen_6394, q_gen_6391) -> q_gen_6407
<a, cons, s>(q_gen_6394, q_gen_6412) -> q_gen_6407
<a, cons, s>(q_gen_6406, q_gen_6449) -> q_gen_6407
<a, cons, s>(q_gen_6414, q_gen_6391) -> q_gen_6407
<a, cons, s>(q_gen_6414, q_gen_6420) -> q_gen_6407
<a, cons, s>(q_gen_6460, q_gen_6391) -> q_gen_6407
<a, cons, z>(q_gen_6404, q_gen_6420) -> q_gen_6407
<a, cons, z>(q_gen_6404, q_gen_6444) -> q_gen_6407
<a, cons, z>(q_gen_6404, q_gen_6449) -> q_gen_6407
<b, cons, s>(q_gen_6394, q_gen_6449) -> q_gen_6407
<b, cons, s>(q_gen_6406, q_gen_6391) -> q_gen_6407
<b, cons, s>(q_gen_6406, q_gen_6420) -> q_gen_6407
<b, cons, s>(q_gen_6406, q_gen_6444) -> q_gen_6407
<b, cons, s>(q_gen_6414, q_gen_6391) -> q_gen_6407
<b, cons, s>(q_gen_6414, q_gen_6420) -> q_gen_6407
<b, cons, s>(q_gen_6414, q_gen_6444) -> q_gen_6407
<b, cons, s>(q_gen_6460, q_gen_6391) -> q_gen_6407
<b, cons, z>(q_gen_6392, q_gen_6412) -> q_gen_6407
<b, cons, z>(q_gen_6392, q_gen_6449) -> q_gen_6407
<b, cons, z>(q_gen_6404, q_gen_6391) -> q_gen_6407
}

Datatype: <elt, eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_6383, q_gen_6385, q_gen_6408},
Q_f={q_gen_6383},
Delta=
{
<s>(q_gen_6385) -> q_gen_6385
<z>() -> q_gen_6385
<s, s>(q_gen_6383) -> q_gen_6383
<z, s>(q_gen_6385) -> q_gen_6383
<z, z>() -> q_gen_6383
<s, s>(q_gen_6408) -> q_gen_6408
<s, z>(q_gen_6385) -> q_gen_6408
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  prefix -> 
{{{
Q={q_gen_6382, q_gen_6388, q_gen_6396, q_gen_6397},
Q_f={q_gen_6382},
Delta=
{
<cons>(q_gen_6397, q_gen_6396) -> q_gen_6396
<nil>() -> q_gen_6396
<a>() -> q_gen_6397
<b>() -> q_gen_6397
<cons, cons>(q_gen_6388, q_gen_6382) -> q_gen_6382
<nil, cons>(q_gen_6397, q_gen_6396) -> q_gen_6382
<nil, nil>() -> q_gen_6382
<a, a>() -> q_gen_6388
<b, b>() -> q_gen_6388
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 62
() -> leq([z, s(nn2)]) -> 62
() -> leq([z, z]) -> 62
() -> prefix([nil, y]) -> 62
(count([x, l1, _py]) /\ count([x, l2, _qy]) /\ prefix([l1, l2])) -> leq([_py, _qy]) -> 64
(count([x, t1, _jy])) -> count([x, cons(x, t1), s(_jy)]) -> 64
(count([x, t1, _ky]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ky]) -> 66
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 62
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 62
(leq([s(nn1), z])) -> BOT -> 62
(prefix([zs, ys])) -> prefix([cons(y2, zs), cons(y2, ys)]) -> 63
(prefix([cons(y2, zs), cons(y2, ys)])) -> prefix([zs, ys]) -> 63
(prefix([cons(z, zs), cons(y2, ys)]) /\ not eq_elt([z, y2])) -> BOT -> 63
(prefix([cons(z, zs), nil])) -> BOT -> 63
}
Sat witness: Found: ((count([x, t1, _ky]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ky]), {
_ky -> s(z)  ;  h1 -> b  ;  t1 -> cons(b, cons(b, cons(a, cons(b, nil))))  ;  x -> a
})

-------------------------------------------
Step 79, which took 1.089872 s (model generation: 1.069701,  model checking: 0.020171):

Model:
|_
{
count -> 
{{{
Q={q_gen_6386, q_gen_6391, q_gen_6392, q_gen_6394, q_gen_6404, q_gen_6406, q_gen_6407, q_gen_6412, q_gen_6414, q_gen_6415, q_gen_6420, q_gen_6423, q_gen_6444, q_gen_6460},
Q_f={q_gen_6386},
Delta=
{
<nil>() -> q_gen_6391
<a>() -> q_gen_6392
<b>() -> q_gen_6404
<cons>(q_gen_6404, q_gen_6391) -> q_gen_6412
<cons>(q_gen_6404, q_gen_6412) -> q_gen_6412
<cons>(q_gen_6404, q_gen_6444) -> q_gen_6412
<s>(q_gen_6415) -> q_gen_6415
<z>() -> q_gen_6415
<cons>(q_gen_6392, q_gen_6391) -> q_gen_6420
<cons>(q_gen_6392, q_gen_6444) -> q_gen_6420
<cons>(q_gen_6392, q_gen_6412) -> q_gen_6423
<cons>(q_gen_6392, q_gen_6423) -> q_gen_6423
<cons>(q_gen_6404, q_gen_6420) -> q_gen_6423
<cons>(q_gen_6404, q_gen_6423) -> q_gen_6423
<cons>(q_gen_6392, q_gen_6420) -> q_gen_6444
<b, z>() -> q_gen_6394
<a, z>() -> q_gen_6406
<b, s>(q_gen_6415) -> q_gen_6414
<a, s>(q_gen_6415) -> q_gen_6460
<a, cons, s>(q_gen_6394, q_gen_6420) -> q_gen_6386
<a, cons, s>(q_gen_6394, q_gen_6423) -> q_gen_6386
<a, cons, s>(q_gen_6406, q_gen_6391) -> q_gen_6386
<a, cons, s>(q_gen_6406, q_gen_6412) -> q_gen_6386
<a, cons, s>(q_gen_6414, q_gen_6412) -> q_gen_6386
<a, cons, s>(q_gen_6414, q_gen_6444) -> q_gen_6386
<a, cons, s>(q_gen_6460, q_gen_6420) -> q_gen_6386
<a, cons, s>(q_gen_6460, q_gen_6423) -> q_gen_6386
<a, cons, s>(q_gen_6460, q_gen_6444) -> q_gen_6386
<a, cons, z>(q_gen_6404, q_gen_6391) -> q_gen_6386
<a, cons, z>(q_gen_6404, q_gen_6412) -> q_gen_6386
<a, nil, z>() -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6391) -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6420) -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6444) -> q_gen_6386
<b, cons, s>(q_gen_6406, q_gen_6412) -> q_gen_6386
<b, cons, s>(q_gen_6406, q_gen_6423) -> q_gen_6386
<b, cons, s>(q_gen_6414, q_gen_6412) -> q_gen_6386
<b, cons, s>(q_gen_6414, q_gen_6423) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6391) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6420) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6444) -> q_gen_6386
<b, nil, z>() -> q_gen_6386
<a, cons, s>(q_gen_6394, q_gen_6391) -> q_gen_6407
<a, cons, s>(q_gen_6394, q_gen_6412) -> q_gen_6407
<a, cons, s>(q_gen_6406, q_gen_6423) -> q_gen_6407
<a, cons, s>(q_gen_6414, q_gen_6391) -> q_gen_6407
<a, cons, s>(q_gen_6414, q_gen_6420) -> q_gen_6407
<a, cons, s>(q_gen_6414, q_gen_6423) -> q_gen_6407
<a, cons, s>(q_gen_6460, q_gen_6391) -> q_gen_6407
<a, cons, s>(q_gen_6460, q_gen_6412) -> q_gen_6407
<a, cons, z>(q_gen_6404, q_gen_6420) -> q_gen_6407
<a, cons, z>(q_gen_6404, q_gen_6423) -> q_gen_6407
<a, cons, z>(q_gen_6404, q_gen_6444) -> q_gen_6407
<b, cons, s>(q_gen_6394, q_gen_6412) -> q_gen_6407
<b, cons, s>(q_gen_6394, q_gen_6423) -> q_gen_6407
<b, cons, s>(q_gen_6406, q_gen_6391) -> q_gen_6407
<b, cons, s>(q_gen_6406, q_gen_6420) -> q_gen_6407
<b, cons, s>(q_gen_6406, q_gen_6444) -> q_gen_6407
<b, cons, s>(q_gen_6414, q_gen_6391) -> q_gen_6407
<b, cons, s>(q_gen_6414, q_gen_6420) -> q_gen_6407
<b, cons, s>(q_gen_6414, q_gen_6444) -> q_gen_6407
<b, cons, s>(q_gen_6460, q_gen_6391) -> q_gen_6407
<b, cons, z>(q_gen_6392, q_gen_6412) -> q_gen_6407
<b, cons, z>(q_gen_6392, q_gen_6423) -> q_gen_6407
<b, cons, z>(q_gen_6404, q_gen_6391) -> q_gen_6407
}

Datatype: <elt, eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_6383, q_gen_6385, q_gen_6408},
Q_f={q_gen_6383},
Delta=
{
<s>(q_gen_6385) -> q_gen_6385
<z>() -> q_gen_6385
<s, s>(q_gen_6383) -> q_gen_6383
<z, s>(q_gen_6385) -> q_gen_6383
<z, z>() -> q_gen_6383
<s, s>(q_gen_6408) -> q_gen_6408
<s, z>(q_gen_6385) -> q_gen_6408
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  prefix -> 
{{{
Q={q_gen_6382, q_gen_6388, q_gen_6396, q_gen_6397},
Q_f={q_gen_6382},
Delta=
{
<cons>(q_gen_6397, q_gen_6396) -> q_gen_6396
<nil>() -> q_gen_6396
<a>() -> q_gen_6397
<b>() -> q_gen_6397
<cons, cons>(q_gen_6388, q_gen_6382) -> q_gen_6382
<nil, cons>(q_gen_6397, q_gen_6396) -> q_gen_6382
<nil, nil>() -> q_gen_6382
<a, a>() -> q_gen_6388
<b, b>() -> q_gen_6388
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 63
() -> leq([z, s(nn2)]) -> 63
() -> leq([z, z]) -> 63
() -> prefix([nil, y]) -> 63
(count([x, l1, _py]) /\ count([x, l2, _qy]) /\ prefix([l1, l2])) -> leq([_py, _qy]) -> 64
(count([x, t1, _jy])) -> count([x, cons(x, t1), s(_jy)]) -> 67
(count([x, t1, _ky]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ky]) -> 66
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 63
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 63
(leq([s(nn1), z])) -> BOT -> 63
(prefix([zs, ys])) -> prefix([cons(y2, zs), cons(y2, ys)]) -> 64
(prefix([cons(y2, zs), cons(y2, ys)])) -> prefix([zs, ys]) -> 64
(prefix([cons(z, zs), cons(y2, ys)]) /\ not eq_elt([z, y2])) -> BOT -> 64
(prefix([cons(z, zs), nil])) -> BOT -> 64
}
Sat witness: Found: ((count([x, t1, _jy])) -> count([x, cons(x, t1), s(_jy)]), {
_jy -> s(s(z))  ;  t1 -> cons(b, cons(a, cons(a, nil)))  ;  x -> a
})

-------------------------------------------
Step 80, which took 1.078068 s (model generation: 1.060424,  model checking: 0.017644):

Model:
|_
{
count -> 
{{{
Q={q_gen_6386, q_gen_6391, q_gen_6392, q_gen_6394, q_gen_6404, q_gen_6406, q_gen_6407, q_gen_6412, q_gen_6414, q_gen_6415, q_gen_6420, q_gen_6423, q_gen_6444, q_gen_6460},
Q_f={q_gen_6386},
Delta=
{
<nil>() -> q_gen_6391
<a>() -> q_gen_6392
<b>() -> q_gen_6404
<cons>(q_gen_6404, q_gen_6391) -> q_gen_6412
<cons>(q_gen_6404, q_gen_6412) -> q_gen_6412
<s>(q_gen_6415) -> q_gen_6415
<z>() -> q_gen_6415
<cons>(q_gen_6392, q_gen_6391) -> q_gen_6420
<cons>(q_gen_6392, q_gen_6444) -> q_gen_6420
<cons>(q_gen_6392, q_gen_6412) -> q_gen_6423
<cons>(q_gen_6392, q_gen_6423) -> q_gen_6423
<cons>(q_gen_6404, q_gen_6420) -> q_gen_6423
<cons>(q_gen_6404, q_gen_6423) -> q_gen_6423
<cons>(q_gen_6404, q_gen_6444) -> q_gen_6423
<cons>(q_gen_6392, q_gen_6420) -> q_gen_6444
<b, z>() -> q_gen_6394
<a, z>() -> q_gen_6406
<b, s>(q_gen_6415) -> q_gen_6414
<a, s>(q_gen_6415) -> q_gen_6460
<a, cons, s>(q_gen_6394, q_gen_6420) -> q_gen_6386
<a, cons, s>(q_gen_6394, q_gen_6423) -> q_gen_6386
<a, cons, s>(q_gen_6406, q_gen_6391) -> q_gen_6386
<a, cons, s>(q_gen_6406, q_gen_6412) -> q_gen_6386
<a, cons, s>(q_gen_6414, q_gen_6423) -> q_gen_6386
<a, cons, s>(q_gen_6414, q_gen_6444) -> q_gen_6386
<a, cons, s>(q_gen_6460, q_gen_6420) -> q_gen_6386
<a, cons, s>(q_gen_6460, q_gen_6423) -> q_gen_6386
<a, cons, s>(q_gen_6460, q_gen_6444) -> q_gen_6386
<a, cons, z>(q_gen_6404, q_gen_6391) -> q_gen_6386
<a, cons, z>(q_gen_6404, q_gen_6412) -> q_gen_6386
<a, nil, z>() -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6391) -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6420) -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6444) -> q_gen_6386
<b, cons, s>(q_gen_6406, q_gen_6412) -> q_gen_6386
<b, cons, s>(q_gen_6406, q_gen_6423) -> q_gen_6386
<b, cons, s>(q_gen_6414, q_gen_6412) -> q_gen_6386
<b, cons, s>(q_gen_6414, q_gen_6423) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6391) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6420) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6444) -> q_gen_6386
<b, nil, z>() -> q_gen_6386
<a, cons, s>(q_gen_6394, q_gen_6391) -> q_gen_6407
<a, cons, s>(q_gen_6406, q_gen_6423) -> q_gen_6407
<a, cons, s>(q_gen_6414, q_gen_6391) -> q_gen_6407
<a, cons, s>(q_gen_6414, q_gen_6420) -> q_gen_6407
<a, cons, s>(q_gen_6460, q_gen_6391) -> q_gen_6407
<a, cons, s>(q_gen_6460, q_gen_6412) -> q_gen_6407
<a, cons, z>(q_gen_6404, q_gen_6420) -> q_gen_6407
<a, cons, z>(q_gen_6404, q_gen_6423) -> q_gen_6407
<a, cons, z>(q_gen_6404, q_gen_6444) -> q_gen_6407
<b, cons, s>(q_gen_6394, q_gen_6412) -> q_gen_6407
<b, cons, s>(q_gen_6394, q_gen_6423) -> q_gen_6407
<b, cons, s>(q_gen_6406, q_gen_6391) -> q_gen_6407
<b, cons, s>(q_gen_6406, q_gen_6420) -> q_gen_6407
<b, cons, s>(q_gen_6406, q_gen_6444) -> q_gen_6407
<b, cons, s>(q_gen_6414, q_gen_6391) -> q_gen_6407
<b, cons, s>(q_gen_6414, q_gen_6420) -> q_gen_6407
<b, cons, s>(q_gen_6414, q_gen_6444) -> q_gen_6407
<b, cons, s>(q_gen_6460, q_gen_6391) -> q_gen_6407
<b, cons, z>(q_gen_6392, q_gen_6412) -> q_gen_6407
<b, cons, z>(q_gen_6392, q_gen_6423) -> q_gen_6407
<b, cons, z>(q_gen_6404, q_gen_6391) -> q_gen_6407
}

Datatype: <elt, eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_6383, q_gen_6385, q_gen_6408},
Q_f={q_gen_6383},
Delta=
{
<s>(q_gen_6385) -> q_gen_6385
<z>() -> q_gen_6385
<s, s>(q_gen_6383) -> q_gen_6383
<z, s>(q_gen_6385) -> q_gen_6383
<z, z>() -> q_gen_6383
<s, s>(q_gen_6408) -> q_gen_6408
<s, z>(q_gen_6385) -> q_gen_6408
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  prefix -> 
{{{
Q={q_gen_6382, q_gen_6388, q_gen_6396, q_gen_6397},
Q_f={q_gen_6382},
Delta=
{
<cons>(q_gen_6397, q_gen_6396) -> q_gen_6396
<nil>() -> q_gen_6396
<a>() -> q_gen_6397
<b>() -> q_gen_6397
<cons, cons>(q_gen_6388, q_gen_6382) -> q_gen_6382
<nil, cons>(q_gen_6397, q_gen_6396) -> q_gen_6382
<nil, nil>() -> q_gen_6382
<a, a>() -> q_gen_6388
<b, b>() -> q_gen_6388
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 64
() -> leq([z, s(nn2)]) -> 64
() -> leq([z, z]) -> 64
() -> prefix([nil, y]) -> 64
(count([x, l1, _py]) /\ count([x, l2, _qy]) /\ prefix([l1, l2])) -> leq([_py, _qy]) -> 67
(count([x, t1, _jy])) -> count([x, cons(x, t1), s(_jy)]) -> 67
(count([x, t1, _ky]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ky]) -> 66
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 64
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 64
(leq([s(nn1), z])) -> BOT -> 64
(prefix([zs, ys])) -> prefix([cons(y2, zs), cons(y2, ys)]) -> 65
(prefix([cons(y2, zs), cons(y2, ys)])) -> prefix([zs, ys]) -> 65
(prefix([cons(z, zs), cons(y2, ys)]) /\ not eq_elt([z, y2])) -> BOT -> 65
(prefix([cons(z, zs), nil])) -> BOT -> 65
}
Sat witness: Found: ((count([x, l1, _py]) /\ count([x, l2, _qy]) /\ prefix([l1, l2])) -> leq([_py, _qy]), {
_py -> s(s(z))  ;  _qy -> s(z)  ;  l1 -> cons(b, cons(a, cons(a, nil)))  ;  l2 -> cons(b, cons(a, cons(a, cons(a, nil))))  ;  x -> a
})

-------------------------------------------
Step 81, which took 1.425465 s (model generation: 1.403274,  model checking: 0.022191):

Model:
|_
{
count -> 
{{{
Q={q_gen_6386, q_gen_6391, q_gen_6392, q_gen_6394, q_gen_6404, q_gen_6406, q_gen_6407, q_gen_6412, q_gen_6414, q_gen_6415, q_gen_6420, q_gen_6444, q_gen_6449, q_gen_6460},
Q_f={q_gen_6386},
Delta=
{
<nil>() -> q_gen_6391
<a>() -> q_gen_6392
<b>() -> q_gen_6404
<cons>(q_gen_6392, q_gen_6449) -> q_gen_6412
<cons>(q_gen_6404, q_gen_6391) -> q_gen_6412
<cons>(q_gen_6404, q_gen_6412) -> q_gen_6412
<cons>(q_gen_6404, q_gen_6420) -> q_gen_6412
<cons>(q_gen_6404, q_gen_6444) -> q_gen_6412
<s>(q_gen_6415) -> q_gen_6415
<z>() -> q_gen_6415
<cons>(q_gen_6392, q_gen_6391) -> q_gen_6420
<cons>(q_gen_6392, q_gen_6420) -> q_gen_6444
<cons>(q_gen_6392, q_gen_6444) -> q_gen_6444
<cons>(q_gen_6392, q_gen_6412) -> q_gen_6449
<cons>(q_gen_6404, q_gen_6449) -> q_gen_6449
<b, z>() -> q_gen_6394
<a, z>() -> q_gen_6406
<b, s>(q_gen_6415) -> q_gen_6414
<a, s>(q_gen_6415) -> q_gen_6460
<a, cons, s>(q_gen_6394, q_gen_6420) -> q_gen_6386
<a, cons, s>(q_gen_6394, q_gen_6449) -> q_gen_6386
<a, cons, s>(q_gen_6406, q_gen_6391) -> q_gen_6386
<a, cons, s>(q_gen_6406, q_gen_6412) -> q_gen_6386
<a, cons, s>(q_gen_6414, q_gen_6412) -> q_gen_6386
<a, cons, s>(q_gen_6414, q_gen_6444) -> q_gen_6386
<a, cons, s>(q_gen_6414, q_gen_6449) -> q_gen_6386
<a, cons, s>(q_gen_6460, q_gen_6412) -> q_gen_6386
<a, cons, s>(q_gen_6460, q_gen_6420) -> q_gen_6386
<a, cons, s>(q_gen_6460, q_gen_6444) -> q_gen_6386
<a, cons, s>(q_gen_6460, q_gen_6449) -> q_gen_6386
<a, cons, z>(q_gen_6404, q_gen_6391) -> q_gen_6386
<a, cons, z>(q_gen_6404, q_gen_6412) -> q_gen_6386
<a, nil, z>() -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6391) -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6412) -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6420) -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6444) -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6449) -> q_gen_6386
<b, cons, s>(q_gen_6406, q_gen_6412) -> q_gen_6386
<b, cons, s>(q_gen_6406, q_gen_6449) -> q_gen_6386
<b, cons, s>(q_gen_6414, q_gen_6412) -> q_gen_6386
<b, cons, s>(q_gen_6414, q_gen_6449) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6391) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6420) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6444) -> q_gen_6386
<b, nil, z>() -> q_gen_6386
<a, cons, s>(q_gen_6394, q_gen_6391) -> q_gen_6407
<a, cons, s>(q_gen_6394, q_gen_6412) -> q_gen_6407
<a, cons, s>(q_gen_6394, q_gen_6444) -> q_gen_6407
<a, cons, s>(q_gen_6406, q_gen_6449) -> q_gen_6407
<a, cons, s>(q_gen_6414, q_gen_6391) -> q_gen_6407
<a, cons, s>(q_gen_6414, q_gen_6420) -> q_gen_6407
<a, cons, s>(q_gen_6460, q_gen_6391) -> q_gen_6407
<a, cons, z>(q_gen_6404, q_gen_6420) -> q_gen_6407
<a, cons, z>(q_gen_6404, q_gen_6444) -> q_gen_6407
<a, cons, z>(q_gen_6404, q_gen_6449) -> q_gen_6407
<b, cons, s>(q_gen_6406, q_gen_6391) -> q_gen_6407
<b, cons, s>(q_gen_6406, q_gen_6420) -> q_gen_6407
<b, cons, s>(q_gen_6406, q_gen_6444) -> q_gen_6407
<b, cons, s>(q_gen_6414, q_gen_6391) -> q_gen_6407
<b, cons, s>(q_gen_6414, q_gen_6420) -> q_gen_6407
<b, cons, s>(q_gen_6414, q_gen_6444) -> q_gen_6407
<b, cons, s>(q_gen_6460, q_gen_6391) -> q_gen_6407
<b, cons, z>(q_gen_6392, q_gen_6412) -> q_gen_6407
<b, cons, z>(q_gen_6392, q_gen_6449) -> q_gen_6407
<b, cons, z>(q_gen_6404, q_gen_6391) -> q_gen_6407
}

Datatype: <elt, eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_6383, q_gen_6385, q_gen_6408},
Q_f={q_gen_6383},
Delta=
{
<s>(q_gen_6385) -> q_gen_6385
<z>() -> q_gen_6385
<s, s>(q_gen_6383) -> q_gen_6383
<z, s>(q_gen_6385) -> q_gen_6383
<z, z>() -> q_gen_6383
<s, s>(q_gen_6408) -> q_gen_6408
<s, z>(q_gen_6385) -> q_gen_6408
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  prefix -> 
{{{
Q={q_gen_6382, q_gen_6388, q_gen_6396, q_gen_6397},
Q_f={q_gen_6382},
Delta=
{
<cons>(q_gen_6397, q_gen_6396) -> q_gen_6396
<nil>() -> q_gen_6396
<a>() -> q_gen_6397
<b>() -> q_gen_6397
<cons, cons>(q_gen_6388, q_gen_6382) -> q_gen_6382
<nil, cons>(q_gen_6397, q_gen_6396) -> q_gen_6382
<nil, nil>() -> q_gen_6382
<a, a>() -> q_gen_6388
<b, b>() -> q_gen_6388
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 65
() -> leq([z, s(nn2)]) -> 65
() -> leq([z, z]) -> 65
() -> prefix([nil, y]) -> 65
(count([x, l1, _py]) /\ count([x, l2, _qy]) /\ prefix([l1, l2])) -> leq([_py, _qy]) -> 67
(count([x, t1, _jy])) -> count([x, cons(x, t1), s(_jy)]) -> 67
(count([x, t1, _ky]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ky]) -> 69
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 65
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 65
(leq([s(nn1), z])) -> BOT -> 65
(prefix([zs, ys])) -> prefix([cons(y2, zs), cons(y2, ys)]) -> 66
(prefix([cons(y2, zs), cons(y2, ys)])) -> prefix([zs, ys]) -> 66
(prefix([cons(z, zs), cons(y2, ys)]) /\ not eq_elt([z, y2])) -> BOT -> 66
(prefix([cons(z, zs), nil])) -> BOT -> 66
}
Sat witness: Found: ((count([x, t1, _ky]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ky]), {
_ky -> s(z)  ;  h1 -> b  ;  t1 -> cons(b, cons(a, nil))  ;  x -> a
})

-------------------------------------------
Step 82, which took 1.347376 s (model generation: 1.318008,  model checking: 0.029368):

Model:
|_
{
count -> 
{{{
Q={q_gen_6386, q_gen_6391, q_gen_6392, q_gen_6394, q_gen_6404, q_gen_6406, q_gen_6407, q_gen_6412, q_gen_6414, q_gen_6415, q_gen_6420, q_gen_6423, q_gen_6444, q_gen_6460},
Q_f={q_gen_6386},
Delta=
{
<nil>() -> q_gen_6391
<a>() -> q_gen_6392
<b>() -> q_gen_6404
<cons>(q_gen_6392, q_gen_6423) -> q_gen_6412
<cons>(q_gen_6404, q_gen_6391) -> q_gen_6412
<cons>(q_gen_6404, q_gen_6412) -> q_gen_6412
<cons>(q_gen_6404, q_gen_6444) -> q_gen_6412
<s>(q_gen_6415) -> q_gen_6415
<z>() -> q_gen_6415
<cons>(q_gen_6392, q_gen_6391) -> q_gen_6420
<cons>(q_gen_6404, q_gen_6423) -> q_gen_6420
<cons>(q_gen_6392, q_gen_6412) -> q_gen_6423
<cons>(q_gen_6404, q_gen_6420) -> q_gen_6423
<cons>(q_gen_6392, q_gen_6420) -> q_gen_6444
<cons>(q_gen_6392, q_gen_6444) -> q_gen_6444
<b, z>() -> q_gen_6394
<a, z>() -> q_gen_6406
<b, s>(q_gen_6415) -> q_gen_6414
<a, s>(q_gen_6415) -> q_gen_6460
<a, cons, s>(q_gen_6394, q_gen_6420) -> q_gen_6386
<a, cons, s>(q_gen_6394, q_gen_6423) -> q_gen_6386
<a, cons, s>(q_gen_6406, q_gen_6391) -> q_gen_6386
<a, cons, s>(q_gen_6406, q_gen_6412) -> q_gen_6386
<a, cons, s>(q_gen_6414, q_gen_6412) -> q_gen_6386
<a, cons, s>(q_gen_6414, q_gen_6423) -> q_gen_6386
<a, cons, s>(q_gen_6414, q_gen_6444) -> q_gen_6386
<a, cons, s>(q_gen_6460, q_gen_6412) -> q_gen_6386
<a, cons, s>(q_gen_6460, q_gen_6420) -> q_gen_6386
<a, cons, s>(q_gen_6460, q_gen_6423) -> q_gen_6386
<a, cons, s>(q_gen_6460, q_gen_6444) -> q_gen_6386
<a, cons, z>(q_gen_6404, q_gen_6391) -> q_gen_6386
<a, cons, z>(q_gen_6404, q_gen_6412) -> q_gen_6386
<a, nil, z>() -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6391) -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6412) -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6420) -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6444) -> q_gen_6386
<b, cons, s>(q_gen_6406, q_gen_6412) -> q_gen_6386
<b, cons, s>(q_gen_6406, q_gen_6423) -> q_gen_6386
<b, cons, s>(q_gen_6414, q_gen_6412) -> q_gen_6386
<b, cons, s>(q_gen_6414, q_gen_6423) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6391) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6420) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6444) -> q_gen_6386
<b, nil, z>() -> q_gen_6386
<a, cons, s>(q_gen_6394, q_gen_6391) -> q_gen_6407
<a, cons, s>(q_gen_6394, q_gen_6412) -> q_gen_6407
<a, cons, s>(q_gen_6394, q_gen_6444) -> q_gen_6407
<a, cons, s>(q_gen_6406, q_gen_6423) -> q_gen_6407
<a, cons, s>(q_gen_6414, q_gen_6391) -> q_gen_6407
<a, cons, s>(q_gen_6414, q_gen_6420) -> q_gen_6407
<a, cons, s>(q_gen_6460, q_gen_6391) -> q_gen_6407
<a, cons, z>(q_gen_6404, q_gen_6420) -> q_gen_6407
<a, cons, z>(q_gen_6404, q_gen_6423) -> q_gen_6407
<a, cons, z>(q_gen_6404, q_gen_6444) -> q_gen_6407
<b, cons, s>(q_gen_6406, q_gen_6391) -> q_gen_6407
<b, cons, s>(q_gen_6406, q_gen_6420) -> q_gen_6407
<b, cons, s>(q_gen_6406, q_gen_6444) -> q_gen_6407
<b, cons, s>(q_gen_6414, q_gen_6391) -> q_gen_6407
<b, cons, s>(q_gen_6414, q_gen_6420) -> q_gen_6407
<b, cons, s>(q_gen_6414, q_gen_6444) -> q_gen_6407
<b, cons, s>(q_gen_6460, q_gen_6391) -> q_gen_6407
<b, cons, z>(q_gen_6392, q_gen_6412) -> q_gen_6407
<b, cons, z>(q_gen_6392, q_gen_6423) -> q_gen_6407
<b, cons, z>(q_gen_6404, q_gen_6391) -> q_gen_6407
}

Datatype: <elt, eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_6383, q_gen_6385, q_gen_6408},
Q_f={q_gen_6383},
Delta=
{
<s>(q_gen_6385) -> q_gen_6385
<z>() -> q_gen_6385
<s, s>(q_gen_6383) -> q_gen_6383
<z, s>(q_gen_6385) -> q_gen_6383
<z, z>() -> q_gen_6383
<s, s>(q_gen_6408) -> q_gen_6408
<s, z>(q_gen_6385) -> q_gen_6408
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  prefix -> 
{{{
Q={q_gen_6382, q_gen_6388, q_gen_6396, q_gen_6397},
Q_f={q_gen_6382},
Delta=
{
<cons>(q_gen_6397, q_gen_6396) -> q_gen_6396
<nil>() -> q_gen_6396
<a>() -> q_gen_6397
<b>() -> q_gen_6397
<cons, cons>(q_gen_6388, q_gen_6382) -> q_gen_6382
<nil, cons>(q_gen_6397, q_gen_6396) -> q_gen_6382
<nil, nil>() -> q_gen_6382
<a, a>() -> q_gen_6388
<b, b>() -> q_gen_6388
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 66
() -> leq([z, s(nn2)]) -> 66
() -> leq([z, z]) -> 66
() -> prefix([nil, y]) -> 66
(count([x, l1, _py]) /\ count([x, l2, _qy]) /\ prefix([l1, l2])) -> leq([_py, _qy]) -> 67
(count([x, t1, _jy])) -> count([x, cons(x, t1), s(_jy)]) -> 70
(count([x, t1, _ky]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ky]) -> 69
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 66
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 66
(leq([s(nn1), z])) -> BOT -> 66
(prefix([zs, ys])) -> prefix([cons(y2, zs), cons(y2, ys)]) -> 67
(prefix([cons(y2, zs), cons(y2, ys)])) -> prefix([zs, ys]) -> 67
(prefix([cons(z, zs), cons(y2, ys)]) /\ not eq_elt([z, y2])) -> BOT -> 67
(prefix([cons(z, zs), nil])) -> BOT -> 67
}
Sat witness: Found: ((count([x, t1, _jy])) -> count([x, cons(x, t1), s(_jy)]), {
_jy -> s(s(z))  ;  t1 -> cons(b, cons(a, cons(a, cons(b, cons(a, nil)))))  ;  x -> b
})

-------------------------------------------
Step 83, which took 1.564078 s (model generation: 1.547367,  model checking: 0.016711):

Model:
|_
{
count -> 
{{{
Q={q_gen_6386, q_gen_6391, q_gen_6392, q_gen_6394, q_gen_6404, q_gen_6406, q_gen_6407, q_gen_6412, q_gen_6414, q_gen_6415, q_gen_6420, q_gen_6423, q_gen_6444, q_gen_6460},
Q_f={q_gen_6386},
Delta=
{
<nil>() -> q_gen_6391
<a>() -> q_gen_6392
<b>() -> q_gen_6404
<cons>(q_gen_6392, q_gen_6423) -> q_gen_6412
<cons>(q_gen_6404, q_gen_6391) -> q_gen_6412
<cons>(q_gen_6404, q_gen_6412) -> q_gen_6412
<cons>(q_gen_6404, q_gen_6444) -> q_gen_6412
<s>(q_gen_6415) -> q_gen_6415
<z>() -> q_gen_6415
<cons>(q_gen_6392, q_gen_6391) -> q_gen_6420
<cons>(q_gen_6392, q_gen_6412) -> q_gen_6423
<cons>(q_gen_6404, q_gen_6420) -> q_gen_6423
<cons>(q_gen_6404, q_gen_6423) -> q_gen_6423
<cons>(q_gen_6392, q_gen_6420) -> q_gen_6444
<cons>(q_gen_6392, q_gen_6444) -> q_gen_6444
<b, z>() -> q_gen_6394
<a, z>() -> q_gen_6406
<b, s>(q_gen_6415) -> q_gen_6414
<a, s>(q_gen_6415) -> q_gen_6460
<a, cons, s>(q_gen_6394, q_gen_6420) -> q_gen_6386
<a, cons, s>(q_gen_6394, q_gen_6423) -> q_gen_6386
<a, cons, s>(q_gen_6406, q_gen_6391) -> q_gen_6386
<a, cons, s>(q_gen_6406, q_gen_6412) -> q_gen_6386
<a, cons, s>(q_gen_6414, q_gen_6412) -> q_gen_6386
<a, cons, s>(q_gen_6414, q_gen_6423) -> q_gen_6386
<a, cons, s>(q_gen_6414, q_gen_6444) -> q_gen_6386
<a, cons, s>(q_gen_6460, q_gen_6412) -> q_gen_6386
<a, cons, s>(q_gen_6460, q_gen_6420) -> q_gen_6386
<a, cons, s>(q_gen_6460, q_gen_6423) -> q_gen_6386
<a, cons, s>(q_gen_6460, q_gen_6444) -> q_gen_6386
<a, cons, z>(q_gen_6404, q_gen_6391) -> q_gen_6386
<a, cons, z>(q_gen_6404, q_gen_6412) -> q_gen_6386
<a, nil, z>() -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6391) -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6420) -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6444) -> q_gen_6386
<b, cons, s>(q_gen_6406, q_gen_6412) -> q_gen_6386
<b, cons, s>(q_gen_6406, q_gen_6423) -> q_gen_6386
<b, cons, s>(q_gen_6414, q_gen_6412) -> q_gen_6386
<b, cons, s>(q_gen_6414, q_gen_6423) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6391) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6420) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6444) -> q_gen_6386
<b, nil, z>() -> q_gen_6386
<a, cons, s>(q_gen_6394, q_gen_6391) -> q_gen_6407
<a, cons, s>(q_gen_6394, q_gen_6412) -> q_gen_6407
<a, cons, s>(q_gen_6394, q_gen_6444) -> q_gen_6407
<a, cons, s>(q_gen_6406, q_gen_6423) -> q_gen_6407
<a, cons, s>(q_gen_6414, q_gen_6391) -> q_gen_6407
<a, cons, s>(q_gen_6414, q_gen_6420) -> q_gen_6407
<a, cons, s>(q_gen_6460, q_gen_6391) -> q_gen_6407
<a, cons, z>(q_gen_6404, q_gen_6420) -> q_gen_6407
<a, cons, z>(q_gen_6404, q_gen_6423) -> q_gen_6407
<a, cons, z>(q_gen_6404, q_gen_6444) -> q_gen_6407
<b, cons, s>(q_gen_6394, q_gen_6412) -> q_gen_6407
<b, cons, s>(q_gen_6406, q_gen_6391) -> q_gen_6407
<b, cons, s>(q_gen_6406, q_gen_6420) -> q_gen_6407
<b, cons, s>(q_gen_6406, q_gen_6444) -> q_gen_6407
<b, cons, s>(q_gen_6414, q_gen_6391) -> q_gen_6407
<b, cons, s>(q_gen_6414, q_gen_6420) -> q_gen_6407
<b, cons, s>(q_gen_6414, q_gen_6444) -> q_gen_6407
<b, cons, s>(q_gen_6460, q_gen_6391) -> q_gen_6407
<b, cons, z>(q_gen_6392, q_gen_6412) -> q_gen_6407
<b, cons, z>(q_gen_6392, q_gen_6423) -> q_gen_6407
<b, cons, z>(q_gen_6404, q_gen_6391) -> q_gen_6407
}

Datatype: <elt, eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_6383, q_gen_6385, q_gen_6408},
Q_f={q_gen_6383},
Delta=
{
<s>(q_gen_6385) -> q_gen_6385
<z>() -> q_gen_6385
<s, s>(q_gen_6383) -> q_gen_6383
<z, s>(q_gen_6385) -> q_gen_6383
<z, z>() -> q_gen_6383
<s, s>(q_gen_6408) -> q_gen_6408
<s, z>(q_gen_6385) -> q_gen_6408
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  prefix -> 
{{{
Q={q_gen_6382, q_gen_6388, q_gen_6396, q_gen_6397},
Q_f={q_gen_6382},
Delta=
{
<cons>(q_gen_6397, q_gen_6396) -> q_gen_6396
<nil>() -> q_gen_6396
<a>() -> q_gen_6397
<b>() -> q_gen_6397
<cons, cons>(q_gen_6388, q_gen_6382) -> q_gen_6382
<nil, cons>(q_gen_6397, q_gen_6396) -> q_gen_6382
<nil, nil>() -> q_gen_6382
<a, a>() -> q_gen_6388
<b, b>() -> q_gen_6388
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 67
() -> leq([z, s(nn2)]) -> 67
() -> leq([z, z]) -> 67
() -> prefix([nil, y]) -> 67
(count([x, l1, _py]) /\ count([x, l2, _qy]) /\ prefix([l1, l2])) -> leq([_py, _qy]) -> 70
(count([x, t1, _jy])) -> count([x, cons(x, t1), s(_jy)]) -> 70
(count([x, t1, _ky]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ky]) -> 69
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 67
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 67
(leq([s(nn1), z])) -> BOT -> 67
(prefix([zs, ys])) -> prefix([cons(y2, zs), cons(y2, ys)]) -> 68
(prefix([cons(y2, zs), cons(y2, ys)])) -> prefix([zs, ys]) -> 68
(prefix([cons(z, zs), cons(y2, ys)]) /\ not eq_elt([z, y2])) -> BOT -> 68
(prefix([cons(z, zs), nil])) -> BOT -> 68
}
Sat witness: Found: ((count([x, l1, _py]) /\ count([x, l2, _qy]) /\ prefix([l1, l2])) -> leq([_py, _qy]), {
_py -> s(z)  ;  _qy -> z  ;  l1 -> cons(b, cons(a, nil))  ;  l2 -> cons(b, cons(a, cons(a, cons(b, nil))))  ;  x -> a
})

-------------------------------------------
Step 84, which took 2.578155 s (model generation: 2.539318,  model checking: 0.038837):

Model:
|_
{
count -> 
{{{
Q={q_gen_6386, q_gen_6391, q_gen_6392, q_gen_6394, q_gen_6404, q_gen_6406, q_gen_6407, q_gen_6412, q_gen_6414, q_gen_6415, q_gen_6420, q_gen_6423, q_gen_6444, q_gen_6460},
Q_f={q_gen_6386},
Delta=
{
<nil>() -> q_gen_6391
<a>() -> q_gen_6392
<b>() -> q_gen_6404
<cons>(q_gen_6404, q_gen_6391) -> q_gen_6412
<cons>(q_gen_6404, q_gen_6412) -> q_gen_6412
<s>(q_gen_6415) -> q_gen_6415
<z>() -> q_gen_6415
<cons>(q_gen_6392, q_gen_6391) -> q_gen_6420
<cons>(q_gen_6392, q_gen_6412) -> q_gen_6423
<cons>(q_gen_6392, q_gen_6423) -> q_gen_6423
<cons>(q_gen_6404, q_gen_6420) -> q_gen_6423
<cons>(q_gen_6404, q_gen_6423) -> q_gen_6423
<cons>(q_gen_6404, q_gen_6444) -> q_gen_6423
<cons>(q_gen_6392, q_gen_6420) -> q_gen_6444
<cons>(q_gen_6392, q_gen_6444) -> q_gen_6444
<b, z>() -> q_gen_6394
<a, z>() -> q_gen_6406
<b, s>(q_gen_6415) -> q_gen_6414
<a, s>(q_gen_6415) -> q_gen_6460
<a, cons, s>(q_gen_6394, q_gen_6420) -> q_gen_6386
<a, cons, s>(q_gen_6394, q_gen_6423) -> q_gen_6386
<a, cons, s>(q_gen_6406, q_gen_6391) -> q_gen_6386
<a, cons, s>(q_gen_6406, q_gen_6412) -> q_gen_6386
<a, cons, s>(q_gen_6414, q_gen_6423) -> q_gen_6386
<a, cons, s>(q_gen_6414, q_gen_6444) -> q_gen_6386
<a, cons, s>(q_gen_6460, q_gen_6420) -> q_gen_6386
<a, cons, s>(q_gen_6460, q_gen_6423) -> q_gen_6386
<a, cons, s>(q_gen_6460, q_gen_6444) -> q_gen_6386
<a, cons, z>(q_gen_6404, q_gen_6391) -> q_gen_6386
<a, cons, z>(q_gen_6404, q_gen_6412) -> q_gen_6386
<a, nil, z>() -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6391) -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6412) -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6420) -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6444) -> q_gen_6386
<b, cons, s>(q_gen_6406, q_gen_6412) -> q_gen_6386
<b, cons, s>(q_gen_6406, q_gen_6423) -> q_gen_6386
<b, cons, s>(q_gen_6414, q_gen_6412) -> q_gen_6386
<b, cons, s>(q_gen_6414, q_gen_6423) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6391) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6420) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6444) -> q_gen_6386
<b, nil, z>() -> q_gen_6386
<a, cons, s>(q_gen_6394, q_gen_6391) -> q_gen_6407
<a, cons, s>(q_gen_6394, q_gen_6444) -> q_gen_6407
<a, cons, s>(q_gen_6406, q_gen_6423) -> q_gen_6407
<a, cons, s>(q_gen_6414, q_gen_6391) -> q_gen_6407
<a, cons, s>(q_gen_6414, q_gen_6420) -> q_gen_6407
<a, cons, s>(q_gen_6460, q_gen_6391) -> q_gen_6407
<a, cons, s>(q_gen_6460, q_gen_6412) -> q_gen_6407
<a, cons, z>(q_gen_6404, q_gen_6420) -> q_gen_6407
<a, cons, z>(q_gen_6404, q_gen_6423) -> q_gen_6407
<a, cons, z>(q_gen_6404, q_gen_6444) -> q_gen_6407
<b, cons, s>(q_gen_6394, q_gen_6423) -> q_gen_6407
<b, cons, s>(q_gen_6406, q_gen_6391) -> q_gen_6407
<b, cons, s>(q_gen_6406, q_gen_6420) -> q_gen_6407
<b, cons, s>(q_gen_6406, q_gen_6444) -> q_gen_6407
<b, cons, s>(q_gen_6414, q_gen_6391) -> q_gen_6407
<b, cons, s>(q_gen_6414, q_gen_6420) -> q_gen_6407
<b, cons, s>(q_gen_6414, q_gen_6444) -> q_gen_6407
<b, cons, s>(q_gen_6460, q_gen_6391) -> q_gen_6407
<b, cons, z>(q_gen_6392, q_gen_6412) -> q_gen_6407
<b, cons, z>(q_gen_6392, q_gen_6423) -> q_gen_6407
<b, cons, z>(q_gen_6404, q_gen_6391) -> q_gen_6407
}

Datatype: <elt, eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_6383, q_gen_6385, q_gen_6408},
Q_f={q_gen_6383},
Delta=
{
<s>(q_gen_6385) -> q_gen_6385
<z>() -> q_gen_6385
<s, s>(q_gen_6383) -> q_gen_6383
<z, s>(q_gen_6385) -> q_gen_6383
<z, z>() -> q_gen_6383
<s, s>(q_gen_6408) -> q_gen_6408
<s, z>(q_gen_6385) -> q_gen_6408
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  prefix -> 
{{{
Q={q_gen_6382, q_gen_6388, q_gen_6396, q_gen_6397},
Q_f={q_gen_6382},
Delta=
{
<cons>(q_gen_6397, q_gen_6396) -> q_gen_6396
<nil>() -> q_gen_6396
<a>() -> q_gen_6397
<b>() -> q_gen_6397
<cons, cons>(q_gen_6388, q_gen_6382) -> q_gen_6382
<nil, cons>(q_gen_6397, q_gen_6396) -> q_gen_6382
<nil, nil>() -> q_gen_6382
<a, a>() -> q_gen_6388
<b, b>() -> q_gen_6388
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 68
() -> leq([z, s(nn2)]) -> 68
() -> leq([z, z]) -> 68
() -> prefix([nil, y]) -> 68
(count([x, l1, _py]) /\ count([x, l2, _qy]) /\ prefix([l1, l2])) -> leq([_py, _qy]) -> 70
(count([x, t1, _jy])) -> count([x, cons(x, t1), s(_jy)]) -> 70
(count([x, t1, _ky]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ky]) -> 72
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 68
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 68
(leq([s(nn1), z])) -> BOT -> 68
(prefix([zs, ys])) -> prefix([cons(y2, zs), cons(y2, ys)]) -> 69
(prefix([cons(y2, zs), cons(y2, ys)])) -> prefix([zs, ys]) -> 69
(prefix([cons(z, zs), cons(y2, ys)]) /\ not eq_elt([z, y2])) -> BOT -> 69
(prefix([cons(z, zs), nil])) -> BOT -> 69
}
Sat witness: Found: ((count([x, t1, _ky]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ky]), {
_ky -> s(s(z))  ;  h1 -> a  ;  t1 -> cons(b, cons(b, nil))  ;  x -> b
})

-------------------------------------------
Step 85, which took 2.644495 s (model generation: 2.585852,  model checking: 0.058643):

Model:
|_
{
count -> 
{{{
Q={q_gen_6386, q_gen_6391, q_gen_6392, q_gen_6394, q_gen_6404, q_gen_6406, q_gen_6407, q_gen_6412, q_gen_6414, q_gen_6415, q_gen_6420, q_gen_6423, q_gen_6444, q_gen_6460},
Q_f={q_gen_6386},
Delta=
{
<nil>() -> q_gen_6391
<a>() -> q_gen_6392
<b>() -> q_gen_6404
<cons>(q_gen_6404, q_gen_6391) -> q_gen_6412
<cons>(q_gen_6404, q_gen_6412) -> q_gen_6412
<s>(q_gen_6415) -> q_gen_6415
<z>() -> q_gen_6415
<cons>(q_gen_6392, q_gen_6391) -> q_gen_6420
<cons>(q_gen_6392, q_gen_6412) -> q_gen_6423
<cons>(q_gen_6392, q_gen_6423) -> q_gen_6423
<cons>(q_gen_6404, q_gen_6420) -> q_gen_6423
<cons>(q_gen_6404, q_gen_6423) -> q_gen_6423
<cons>(q_gen_6404, q_gen_6444) -> q_gen_6423
<cons>(q_gen_6392, q_gen_6420) -> q_gen_6444
<cons>(q_gen_6392, q_gen_6444) -> q_gen_6444
<b, z>() -> q_gen_6394
<a, z>() -> q_gen_6406
<b, s>(q_gen_6415) -> q_gen_6414
<a, s>(q_gen_6415) -> q_gen_6460
<a, cons, s>(q_gen_6394, q_gen_6420) -> q_gen_6386
<a, cons, s>(q_gen_6394, q_gen_6423) -> q_gen_6386
<a, cons, s>(q_gen_6406, q_gen_6391) -> q_gen_6386
<a, cons, s>(q_gen_6406, q_gen_6412) -> q_gen_6386
<a, cons, s>(q_gen_6414, q_gen_6423) -> q_gen_6386
<a, cons, s>(q_gen_6414, q_gen_6444) -> q_gen_6386
<a, cons, s>(q_gen_6460, q_gen_6420) -> q_gen_6386
<a, cons, s>(q_gen_6460, q_gen_6423) -> q_gen_6386
<a, cons, s>(q_gen_6460, q_gen_6444) -> q_gen_6386
<a, cons, z>(q_gen_6404, q_gen_6391) -> q_gen_6386
<a, cons, z>(q_gen_6404, q_gen_6412) -> q_gen_6386
<a, nil, z>() -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6391) -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6420) -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6444) -> q_gen_6386
<b, cons, s>(q_gen_6406, q_gen_6412) -> q_gen_6386
<b, cons, s>(q_gen_6406, q_gen_6423) -> q_gen_6386
<b, cons, s>(q_gen_6414, q_gen_6391) -> q_gen_6386
<b, cons, s>(q_gen_6414, q_gen_6412) -> q_gen_6386
<b, cons, s>(q_gen_6414, q_gen_6423) -> q_gen_6386
<b, cons, s>(q_gen_6460, q_gen_6412) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6391) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6420) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6444) -> q_gen_6386
<b, nil, z>() -> q_gen_6386
<a, cons, s>(q_gen_6394, q_gen_6391) -> q_gen_6407
<a, cons, s>(q_gen_6394, q_gen_6444) -> q_gen_6407
<a, cons, s>(q_gen_6406, q_gen_6423) -> q_gen_6407
<a, cons, s>(q_gen_6414, q_gen_6391) -> q_gen_6407
<a, cons, s>(q_gen_6414, q_gen_6420) -> q_gen_6407
<a, cons, s>(q_gen_6460, q_gen_6391) -> q_gen_6407
<a, cons, s>(q_gen_6460, q_gen_6412) -> q_gen_6407
<a, cons, z>(q_gen_6404, q_gen_6420) -> q_gen_6407
<a, cons, z>(q_gen_6404, q_gen_6423) -> q_gen_6407
<a, cons, z>(q_gen_6404, q_gen_6444) -> q_gen_6407
<b, cons, s>(q_gen_6394, q_gen_6412) -> q_gen_6407
<b, cons, s>(q_gen_6394, q_gen_6423) -> q_gen_6407
<b, cons, s>(q_gen_6406, q_gen_6391) -> q_gen_6407
<b, cons, s>(q_gen_6406, q_gen_6420) -> q_gen_6407
<b, cons, s>(q_gen_6406, q_gen_6444) -> q_gen_6407
<b, cons, s>(q_gen_6414, q_gen_6420) -> q_gen_6407
<b, cons, s>(q_gen_6414, q_gen_6444) -> q_gen_6407
<b, cons, s>(q_gen_6460, q_gen_6391) -> q_gen_6407
<b, cons, z>(q_gen_6392, q_gen_6412) -> q_gen_6407
<b, cons, z>(q_gen_6392, q_gen_6423) -> q_gen_6407
<b, cons, z>(q_gen_6404, q_gen_6391) -> q_gen_6407
}

Datatype: <elt, eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_6383, q_gen_6385, q_gen_6408},
Q_f={q_gen_6383},
Delta=
{
<s>(q_gen_6385) -> q_gen_6385
<z>() -> q_gen_6385
<s, s>(q_gen_6383) -> q_gen_6383
<z, s>(q_gen_6385) -> q_gen_6383
<z, z>() -> q_gen_6383
<s, s>(q_gen_6408) -> q_gen_6408
<s, z>(q_gen_6385) -> q_gen_6408
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  prefix -> 
{{{
Q={q_gen_6382, q_gen_6388, q_gen_6396, q_gen_6397},
Q_f={q_gen_6382},
Delta=
{
<cons>(q_gen_6397, q_gen_6396) -> q_gen_6396
<nil>() -> q_gen_6396
<a>() -> q_gen_6397
<b>() -> q_gen_6397
<cons, cons>(q_gen_6388, q_gen_6382) -> q_gen_6382
<nil, cons>(q_gen_6397, q_gen_6396) -> q_gen_6382
<nil, nil>() -> q_gen_6382
<a, a>() -> q_gen_6388
<b, b>() -> q_gen_6388
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 69
() -> leq([z, s(nn2)]) -> 69
() -> leq([z, z]) -> 69
() -> prefix([nil, y]) -> 69
(count([x, l1, _py]) /\ count([x, l2, _qy]) /\ prefix([l1, l2])) -> leq([_py, _qy]) -> 73
(count([x, t1, _jy])) -> count([x, cons(x, t1), s(_jy)]) -> 71
(count([x, t1, _ky]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ky]) -> 72
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 69
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 69
(leq([s(nn1), z])) -> BOT -> 69
(prefix([zs, ys])) -> prefix([cons(y2, zs), cons(y2, ys)]) -> 70
(prefix([cons(y2, zs), cons(y2, ys)])) -> prefix([zs, ys]) -> 70
(prefix([cons(z, zs), cons(y2, ys)]) /\ not eq_elt([z, y2])) -> BOT -> 70
(prefix([cons(z, zs), nil])) -> BOT -> 70
}
Sat witness: Found: ((count([x, l1, _py]) /\ count([x, l2, _qy]) /\ prefix([l1, l2])) -> leq([_py, _qy]), {
_py -> s(s(z))  ;  _qy -> s(z)  ;  l1 -> cons(b, nil)  ;  l2 -> cons(b, nil)  ;  x -> b
})

-------------------------------------------
Step 86, which took 2.586726 s (model generation: 2.506378,  model checking: 0.080348):

Model:
|_
{
count -> 
{{{
Q={q_gen_6386, q_gen_6391, q_gen_6392, q_gen_6394, q_gen_6404, q_gen_6406, q_gen_6407, q_gen_6412, q_gen_6414, q_gen_6415, q_gen_6420, q_gen_6423, q_gen_6444, q_gen_6460},
Q_f={q_gen_6386},
Delta=
{
<nil>() -> q_gen_6391
<a>() -> q_gen_6392
<b>() -> q_gen_6404
<cons>(q_gen_6404, q_gen_6391) -> q_gen_6412
<cons>(q_gen_6404, q_gen_6412) -> q_gen_6412
<s>(q_gen_6415) -> q_gen_6415
<z>() -> q_gen_6415
<cons>(q_gen_6392, q_gen_6391) -> q_gen_6420
<cons>(q_gen_6392, q_gen_6412) -> q_gen_6423
<cons>(q_gen_6392, q_gen_6423) -> q_gen_6423
<cons>(q_gen_6404, q_gen_6420) -> q_gen_6423
<cons>(q_gen_6404, q_gen_6423) -> q_gen_6423
<cons>(q_gen_6404, q_gen_6444) -> q_gen_6423
<cons>(q_gen_6392, q_gen_6420) -> q_gen_6444
<cons>(q_gen_6392, q_gen_6444) -> q_gen_6444
<b, z>() -> q_gen_6394
<a, z>() -> q_gen_6406
<b, s>(q_gen_6415) -> q_gen_6414
<a, s>(q_gen_6415) -> q_gen_6460
<a, cons, s>(q_gen_6394, q_gen_6420) -> q_gen_6386
<a, cons, s>(q_gen_6394, q_gen_6423) -> q_gen_6386
<a, cons, s>(q_gen_6406, q_gen_6391) -> q_gen_6386
<a, cons, s>(q_gen_6406, q_gen_6412) -> q_gen_6386
<a, cons, s>(q_gen_6414, q_gen_6423) -> q_gen_6386
<a, cons, s>(q_gen_6414, q_gen_6444) -> q_gen_6386
<a, cons, s>(q_gen_6460, q_gen_6420) -> q_gen_6386
<a, cons, s>(q_gen_6460, q_gen_6423) -> q_gen_6386
<a, cons, s>(q_gen_6460, q_gen_6444) -> q_gen_6386
<a, cons, z>(q_gen_6404, q_gen_6391) -> q_gen_6386
<a, cons, z>(q_gen_6404, q_gen_6412) -> q_gen_6386
<a, nil, z>() -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6391) -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6420) -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6444) -> q_gen_6386
<b, cons, s>(q_gen_6406, q_gen_6412) -> q_gen_6386
<b, cons, s>(q_gen_6406, q_gen_6423) -> q_gen_6386
<b, cons, s>(q_gen_6414, q_gen_6412) -> q_gen_6386
<b, cons, s>(q_gen_6414, q_gen_6423) -> q_gen_6386
<b, cons, s>(q_gen_6460, q_gen_6412) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6391) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6420) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6444) -> q_gen_6386
<b, nil, z>() -> q_gen_6386
<a, cons, s>(q_gen_6394, q_gen_6391) -> q_gen_6407
<a, cons, s>(q_gen_6394, q_gen_6444) -> q_gen_6407
<a, cons, s>(q_gen_6406, q_gen_6423) -> q_gen_6407
<a, cons, s>(q_gen_6414, q_gen_6391) -> q_gen_6407
<a, cons, s>(q_gen_6414, q_gen_6420) -> q_gen_6407
<a, cons, s>(q_gen_6460, q_gen_6391) -> q_gen_6407
<a, cons, s>(q_gen_6460, q_gen_6412) -> q_gen_6407
<a, cons, z>(q_gen_6404, q_gen_6420) -> q_gen_6407
<a, cons, z>(q_gen_6404, q_gen_6423) -> q_gen_6407
<a, cons, z>(q_gen_6404, q_gen_6444) -> q_gen_6407
<b, cons, s>(q_gen_6394, q_gen_6412) -> q_gen_6407
<b, cons, s>(q_gen_6394, q_gen_6423) -> q_gen_6407
<b, cons, s>(q_gen_6406, q_gen_6391) -> q_gen_6407
<b, cons, s>(q_gen_6406, q_gen_6420) -> q_gen_6407
<b, cons, s>(q_gen_6406, q_gen_6444) -> q_gen_6407
<b, cons, s>(q_gen_6414, q_gen_6391) -> q_gen_6407
<b, cons, s>(q_gen_6414, q_gen_6420) -> q_gen_6407
<b, cons, s>(q_gen_6414, q_gen_6444) -> q_gen_6407
<b, cons, s>(q_gen_6460, q_gen_6391) -> q_gen_6407
<b, cons, z>(q_gen_6392, q_gen_6412) -> q_gen_6407
<b, cons, z>(q_gen_6392, q_gen_6423) -> q_gen_6407
<b, cons, z>(q_gen_6404, q_gen_6391) -> q_gen_6407
}

Datatype: <elt, eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_6383, q_gen_6385, q_gen_6408},
Q_f={q_gen_6383},
Delta=
{
<s>(q_gen_6385) -> q_gen_6385
<z>() -> q_gen_6385
<s, s>(q_gen_6383) -> q_gen_6383
<z, s>(q_gen_6385) -> q_gen_6383
<z, z>() -> q_gen_6383
<s, s>(q_gen_6408) -> q_gen_6408
<s, z>(q_gen_6385) -> q_gen_6408
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  prefix -> 
{{{
Q={q_gen_6382, q_gen_6388, q_gen_6396, q_gen_6397},
Q_f={q_gen_6382},
Delta=
{
<cons>(q_gen_6397, q_gen_6396) -> q_gen_6396
<nil>() -> q_gen_6396
<a>() -> q_gen_6397
<b>() -> q_gen_6397
<cons, cons>(q_gen_6388, q_gen_6382) -> q_gen_6382
<nil, cons>(q_gen_6397, q_gen_6396) -> q_gen_6382
<nil, nil>() -> q_gen_6382
<a, a>() -> q_gen_6388
<b, b>() -> q_gen_6388
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 70
() -> leq([z, s(nn2)]) -> 70
() -> leq([z, z]) -> 70
() -> prefix([nil, y]) -> 70
(count([x, l1, _py]) /\ count([x, l2, _qy]) /\ prefix([l1, l2])) -> leq([_py, _qy]) -> 73
(count([x, t1, _jy])) -> count([x, cons(x, t1), s(_jy)]) -> 72
(count([x, t1, _ky]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ky]) -> 75
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 70
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 70
(leq([s(nn1), z])) -> BOT -> 70
(prefix([zs, ys])) -> prefix([cons(y2, zs), cons(y2, ys)]) -> 71
(prefix([cons(y2, zs), cons(y2, ys)])) -> prefix([zs, ys]) -> 71
(prefix([cons(z, zs), cons(y2, ys)]) /\ not eq_elt([z, y2])) -> BOT -> 71
(prefix([cons(z, zs), nil])) -> BOT -> 71
}
Sat witness: Found: ((count([x, t1, _ky]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ky]), {
_ky -> s(s(z))  ;  h1 -> a  ;  t1 -> cons(b, cons(b, cons(a, nil)))  ;  x -> b
})

-------------------------------------------
Step 87, which took 2.371729 s (model generation: 2.310407,  model checking: 0.061322):

Model:
|_
{
count -> 
{{{
Q={q_gen_6386, q_gen_6391, q_gen_6392, q_gen_6394, q_gen_6404, q_gen_6406, q_gen_6407, q_gen_6412, q_gen_6414, q_gen_6415, q_gen_6420, q_gen_6423, q_gen_6444, q_gen_6460},
Q_f={q_gen_6386},
Delta=
{
<nil>() -> q_gen_6391
<a>() -> q_gen_6392
<b>() -> q_gen_6404
<cons>(q_gen_6404, q_gen_6391) -> q_gen_6412
<cons>(q_gen_6404, q_gen_6412) -> q_gen_6412
<s>(q_gen_6415) -> q_gen_6415
<z>() -> q_gen_6415
<cons>(q_gen_6392, q_gen_6391) -> q_gen_6420
<cons>(q_gen_6392, q_gen_6412) -> q_gen_6423
<cons>(q_gen_6392, q_gen_6423) -> q_gen_6423
<cons>(q_gen_6404, q_gen_6420) -> q_gen_6423
<cons>(q_gen_6404, q_gen_6423) -> q_gen_6423
<cons>(q_gen_6404, q_gen_6444) -> q_gen_6423
<cons>(q_gen_6392, q_gen_6420) -> q_gen_6444
<cons>(q_gen_6392, q_gen_6444) -> q_gen_6444
<b, z>() -> q_gen_6394
<a, z>() -> q_gen_6406
<b, s>(q_gen_6415) -> q_gen_6414
<a, s>(q_gen_6415) -> q_gen_6460
<a, cons, s>(q_gen_6394, q_gen_6420) -> q_gen_6386
<a, cons, s>(q_gen_6394, q_gen_6423) -> q_gen_6386
<a, cons, s>(q_gen_6406, q_gen_6391) -> q_gen_6386
<a, cons, s>(q_gen_6406, q_gen_6412) -> q_gen_6386
<a, cons, s>(q_gen_6414, q_gen_6423) -> q_gen_6386
<a, cons, s>(q_gen_6414, q_gen_6444) -> q_gen_6386
<a, cons, s>(q_gen_6460, q_gen_6420) -> q_gen_6386
<a, cons, s>(q_gen_6460, q_gen_6423) -> q_gen_6386
<a, cons, s>(q_gen_6460, q_gen_6444) -> q_gen_6386
<a, cons, z>(q_gen_6404, q_gen_6391) -> q_gen_6386
<a, cons, z>(q_gen_6404, q_gen_6412) -> q_gen_6386
<a, nil, z>() -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6391) -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6412) -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6420) -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6444) -> q_gen_6386
<b, cons, s>(q_gen_6406, q_gen_6412) -> q_gen_6386
<b, cons, s>(q_gen_6406, q_gen_6423) -> q_gen_6386
<b, cons, s>(q_gen_6414, q_gen_6412) -> q_gen_6386
<b, cons, s>(q_gen_6414, q_gen_6423) -> q_gen_6386
<b, cons, s>(q_gen_6460, q_gen_6412) -> q_gen_6386
<b, cons, s>(q_gen_6460, q_gen_6423) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6391) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6420) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6444) -> q_gen_6386
<b, nil, z>() -> q_gen_6386
<a, cons, s>(q_gen_6394, q_gen_6391) -> q_gen_6407
<a, cons, s>(q_gen_6394, q_gen_6444) -> q_gen_6407
<a, cons, s>(q_gen_6406, q_gen_6423) -> q_gen_6407
<a, cons, s>(q_gen_6414, q_gen_6391) -> q_gen_6407
<a, cons, s>(q_gen_6414, q_gen_6420) -> q_gen_6407
<a, cons, s>(q_gen_6460, q_gen_6391) -> q_gen_6407
<a, cons, s>(q_gen_6460, q_gen_6412) -> q_gen_6407
<a, cons, z>(q_gen_6404, q_gen_6420) -> q_gen_6407
<a, cons, z>(q_gen_6404, q_gen_6423) -> q_gen_6407
<a, cons, z>(q_gen_6404, q_gen_6444) -> q_gen_6407
<b, cons, s>(q_gen_6394, q_gen_6423) -> q_gen_6407
<b, cons, s>(q_gen_6406, q_gen_6391) -> q_gen_6407
<b, cons, s>(q_gen_6406, q_gen_6420) -> q_gen_6407
<b, cons, s>(q_gen_6406, q_gen_6444) -> q_gen_6407
<b, cons, s>(q_gen_6414, q_gen_6391) -> q_gen_6407
<b, cons, s>(q_gen_6414, q_gen_6420) -> q_gen_6407
<b, cons, s>(q_gen_6414, q_gen_6444) -> q_gen_6407
<b, cons, s>(q_gen_6460, q_gen_6391) -> q_gen_6407
<b, cons, z>(q_gen_6392, q_gen_6412) -> q_gen_6407
<b, cons, z>(q_gen_6392, q_gen_6423) -> q_gen_6407
<b, cons, z>(q_gen_6404, q_gen_6391) -> q_gen_6407
}

Datatype: <elt, eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_6383, q_gen_6385, q_gen_6408},
Q_f={q_gen_6383},
Delta=
{
<s>(q_gen_6385) -> q_gen_6385
<z>() -> q_gen_6385
<s, s>(q_gen_6383) -> q_gen_6383
<z, s>(q_gen_6385) -> q_gen_6383
<z, z>() -> q_gen_6383
<s, s>(q_gen_6408) -> q_gen_6408
<s, z>(q_gen_6385) -> q_gen_6408
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  prefix -> 
{{{
Q={q_gen_6382, q_gen_6388, q_gen_6396, q_gen_6397},
Q_f={q_gen_6382},
Delta=
{
<cons>(q_gen_6397, q_gen_6396) -> q_gen_6396
<nil>() -> q_gen_6396
<a>() -> q_gen_6397
<b>() -> q_gen_6397
<cons, cons>(q_gen_6388, q_gen_6382) -> q_gen_6382
<nil, cons>(q_gen_6397, q_gen_6396) -> q_gen_6382
<nil, nil>() -> q_gen_6382
<a, a>() -> q_gen_6388
<b, b>() -> q_gen_6388
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 71
() -> leq([z, s(nn2)]) -> 71
() -> leq([z, z]) -> 71
() -> prefix([nil, y]) -> 71
(count([x, l1, _py]) /\ count([x, l2, _qy]) /\ prefix([l1, l2])) -> leq([_py, _qy]) -> 76
(count([x, t1, _jy])) -> count([x, cons(x, t1), s(_jy)]) -> 73
(count([x, t1, _ky]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ky]) -> 75
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 71
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 71
(leq([s(nn1), z])) -> BOT -> 71
(prefix([zs, ys])) -> prefix([cons(y2, zs), cons(y2, ys)]) -> 72
(prefix([cons(y2, zs), cons(y2, ys)])) -> prefix([zs, ys]) -> 72
(prefix([cons(z, zs), cons(y2, ys)]) /\ not eq_elt([z, y2])) -> BOT -> 72
(prefix([cons(z, zs), nil])) -> BOT -> 72
}
Sat witness: Found: ((count([x, l1, _py]) /\ count([x, l2, _qy]) /\ prefix([l1, l2])) -> leq([_py, _qy]), {
_py -> s(s(z))  ;  _qy -> s(z)  ;  l1 -> cons(b, cons(a, cons(a, nil)))  ;  l2 -> cons(b, cons(a, cons(a, cons(b, nil))))  ;  x -> a
})

-------------------------------------------
Step 88, which took 2.169903 s (model generation: 2.164320,  model checking: 0.005583):

Model:
|_
{
count -> 
{{{
Q={q_gen_6386, q_gen_6391, q_gen_6392, q_gen_6394, q_gen_6404, q_gen_6406, q_gen_6407, q_gen_6412, q_gen_6414, q_gen_6415, q_gen_6420, q_gen_6460},
Q_f={q_gen_6386},
Delta=
{
<nil>() -> q_gen_6391
<a>() -> q_gen_6392
<b>() -> q_gen_6404
<cons>(q_gen_6392, q_gen_6412) -> q_gen_6412
<cons>(q_gen_6392, q_gen_6420) -> q_gen_6412
<cons>(q_gen_6404, q_gen_6391) -> q_gen_6412
<cons>(q_gen_6404, q_gen_6412) -> q_gen_6412
<s>(q_gen_6415) -> q_gen_6415
<z>() -> q_gen_6415
<cons>(q_gen_6392, q_gen_6391) -> q_gen_6420
<cons>(q_gen_6404, q_gen_6420) -> q_gen_6420
<b, z>() -> q_gen_6394
<a, z>() -> q_gen_6406
<b, s>(q_gen_6415) -> q_gen_6414
<a, s>(q_gen_6415) -> q_gen_6460
<a, cons, s>(q_gen_6394, q_gen_6412) -> q_gen_6386
<a, cons, s>(q_gen_6394, q_gen_6420) -> q_gen_6386
<a, cons, s>(q_gen_6406, q_gen_6391) -> q_gen_6386
<a, cons, s>(q_gen_6406, q_gen_6412) -> q_gen_6386
<a, cons, s>(q_gen_6414, q_gen_6412) -> q_gen_6386
<a, cons, s>(q_gen_6460, q_gen_6412) -> q_gen_6386
<a, cons, s>(q_gen_6460, q_gen_6420) -> q_gen_6386
<a, cons, z>(q_gen_6404, q_gen_6391) -> q_gen_6386
<a, cons, z>(q_gen_6404, q_gen_6412) -> q_gen_6386
<a, nil, z>() -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6391) -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6412) -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6420) -> q_gen_6386
<b, cons, s>(q_gen_6406, q_gen_6412) -> q_gen_6386
<b, cons, s>(q_gen_6414, q_gen_6412) -> q_gen_6386
<b, cons, s>(q_gen_6460, q_gen_6412) -> q_gen_6386
<b, cons, s>(q_gen_6460, q_gen_6420) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6391) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6412) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6420) -> q_gen_6386
<b, nil, z>() -> q_gen_6386
<a, cons, s>(q_gen_6394, q_gen_6391) -> q_gen_6407
<a, cons, s>(q_gen_6406, q_gen_6420) -> q_gen_6407
<a, cons, s>(q_gen_6414, q_gen_6391) -> q_gen_6407
<a, cons, s>(q_gen_6414, q_gen_6420) -> q_gen_6407
<a, cons, s>(q_gen_6460, q_gen_6391) -> q_gen_6407
<a, cons, z>(q_gen_6404, q_gen_6420) -> q_gen_6407
<b, cons, s>(q_gen_6406, q_gen_6391) -> q_gen_6407
<b, cons, s>(q_gen_6406, q_gen_6420) -> q_gen_6407
<b, cons, s>(q_gen_6414, q_gen_6391) -> q_gen_6407
<b, cons, s>(q_gen_6414, q_gen_6420) -> q_gen_6407
<b, cons, s>(q_gen_6460, q_gen_6391) -> q_gen_6407
<b, cons, z>(q_gen_6404, q_gen_6391) -> q_gen_6407
}

Datatype: <elt, eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_6383, q_gen_6385, q_gen_6408},
Q_f={q_gen_6383},
Delta=
{
<s>(q_gen_6385) -> q_gen_6385
<z>() -> q_gen_6385
<s, s>(q_gen_6383) -> q_gen_6383
<z, s>(q_gen_6385) -> q_gen_6383
<z, z>() -> q_gen_6383
<s, s>(q_gen_6408) -> q_gen_6408
<s, z>(q_gen_6385) -> q_gen_6408
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  prefix -> 
{{{
Q={q_gen_6382, q_gen_6387, q_gen_6388, q_gen_6396, q_gen_6397, q_gen_6402, q_gen_6439},
Q_f={q_gen_6382, q_gen_6387},
Delta=
{
<cons>(q_gen_6397, q_gen_6396) -> q_gen_6396
<nil>() -> q_gen_6396
<a>() -> q_gen_6397
<b>() -> q_gen_6397
<nil, nil>() -> q_gen_6382
<cons, cons>(q_gen_6388, q_gen_6382) -> q_gen_6387
<cons, cons>(q_gen_6388, q_gen_6387) -> q_gen_6387
<cons, cons>(q_gen_6402, q_gen_6382) -> q_gen_6387
<nil, cons>(q_gen_6397, q_gen_6396) -> q_gen_6387
<b, b>() -> q_gen_6388
<a, a>() -> q_gen_6402
<cons, cons>(q_gen_6388, q_gen_6439) -> q_gen_6439
<cons, cons>(q_gen_6402, q_gen_6387) -> q_gen_6439
<cons, cons>(q_gen_6402, q_gen_6439) -> q_gen_6439
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 72
() -> leq([z, s(nn2)]) -> 72
() -> leq([z, z]) -> 72
() -> prefix([nil, y]) -> 72
(count([x, l1, _py]) /\ count([x, l2, _qy]) /\ prefix([l1, l2])) -> leq([_py, _qy]) -> 76
(count([x, t1, _jy])) -> count([x, cons(x, t1), s(_jy)]) -> 73
(count([x, t1, _ky]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ky]) -> 75
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 72
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 72
(leq([s(nn1), z])) -> BOT -> 72
(prefix([zs, ys])) -> prefix([cons(y2, zs), cons(y2, ys)]) -> 75
(prefix([cons(y2, zs), cons(y2, ys)])) -> prefix([zs, ys]) -> 73
(prefix([cons(z, zs), cons(y2, ys)]) /\ not eq_elt([z, y2])) -> BOT -> 73
(prefix([cons(z, zs), nil])) -> BOT -> 73
}
Sat witness: Found: ((prefix([zs, ys])) -> prefix([cons(y2, zs), cons(y2, ys)]), {
y2 -> a  ;  ys -> cons(a, nil)  ;  zs -> nil
})

-------------------------------------------
Step 89, which took 2.755521 s (model generation: 2.744780,  model checking: 0.010741):

Model:
|_
{
count -> 
{{{
Q={q_gen_6386, q_gen_6391, q_gen_6392, q_gen_6394, q_gen_6404, q_gen_6406, q_gen_6407, q_gen_6412, q_gen_6414, q_gen_6415, q_gen_6420, q_gen_6423, q_gen_6444, q_gen_6449, q_gen_6460},
Q_f={q_gen_6386},
Delta=
{
<cons>(q_gen_6392, q_gen_6423) -> q_gen_6391
<nil>() -> q_gen_6391
<a>() -> q_gen_6392
<b>() -> q_gen_6404
<cons>(q_gen_6404, q_gen_6391) -> q_gen_6412
<cons>(q_gen_6404, q_gen_6444) -> q_gen_6412
<s>(q_gen_6415) -> q_gen_6415
<z>() -> q_gen_6415
<cons>(q_gen_6392, q_gen_6391) -> q_gen_6420
<cons>(q_gen_6404, q_gen_6423) -> q_gen_6420
<cons>(q_gen_6404, q_gen_6449) -> q_gen_6420
<cons>(q_gen_6404, q_gen_6412) -> q_gen_6423
<cons>(q_gen_6404, q_gen_6420) -> q_gen_6423
<cons>(q_gen_6392, q_gen_6420) -> q_gen_6444
<cons>(q_gen_6392, q_gen_6444) -> q_gen_6444
<cons>(q_gen_6392, q_gen_6449) -> q_gen_6444
<cons>(q_gen_6392, q_gen_6412) -> q_gen_6449
<b, z>() -> q_gen_6394
<a, z>() -> q_gen_6406
<b, s>(q_gen_6415) -> q_gen_6414
<a, s>(q_gen_6415) -> q_gen_6460
<a, cons, s>(q_gen_6394, q_gen_6420) -> q_gen_6386
<a, cons, s>(q_gen_6394, q_gen_6423) -> q_gen_6386
<a, cons, s>(q_gen_6394, q_gen_6449) -> q_gen_6386
<a, cons, s>(q_gen_6406, q_gen_6391) -> q_gen_6386
<a, cons, s>(q_gen_6406, q_gen_6412) -> q_gen_6386
<a, cons, s>(q_gen_6414, q_gen_6412) -> q_gen_6386
<a, cons, s>(q_gen_6414, q_gen_6444) -> q_gen_6386
<a, cons, s>(q_gen_6414, q_gen_6449) -> q_gen_6386
<a, cons, s>(q_gen_6460, q_gen_6412) -> q_gen_6386
<a, cons, s>(q_gen_6460, q_gen_6420) -> q_gen_6386
<a, cons, s>(q_gen_6460, q_gen_6423) -> q_gen_6386
<a, cons, s>(q_gen_6460, q_gen_6444) -> q_gen_6386
<a, cons, s>(q_gen_6460, q_gen_6449) -> q_gen_6386
<a, cons, z>(q_gen_6404, q_gen_6391) -> q_gen_6386
<a, cons, z>(q_gen_6404, q_gen_6412) -> q_gen_6386
<a, cons, z>(q_gen_6404, q_gen_6423) -> q_gen_6386
<a, nil, z>() -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6391) -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6420) -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6444) -> q_gen_6386
<b, cons, s>(q_gen_6406, q_gen_6412) -> q_gen_6386
<b, cons, s>(q_gen_6406, q_gen_6449) -> q_gen_6386
<b, cons, s>(q_gen_6414, q_gen_6412) -> q_gen_6386
<b, cons, s>(q_gen_6414, q_gen_6423) -> q_gen_6386
<b, cons, s>(q_gen_6460, q_gen_6420) -> q_gen_6386
<b, cons, s>(q_gen_6460, q_gen_6423) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6391) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6420) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6444) -> q_gen_6386
<b, nil, z>() -> q_gen_6386
<a, cons, s>(q_gen_6394, q_gen_6391) -> q_gen_6407
<a, cons, s>(q_gen_6394, q_gen_6412) -> q_gen_6407
<a, cons, s>(q_gen_6394, q_gen_6444) -> q_gen_6407
<a, cons, s>(q_gen_6406, q_gen_6423) -> q_gen_6407
<a, cons, s>(q_gen_6414, q_gen_6391) -> q_gen_6407
<a, cons, s>(q_gen_6414, q_gen_6420) -> q_gen_6407
<a, cons, s>(q_gen_6460, q_gen_6391) -> q_gen_6407
<a, cons, z>(q_gen_6404, q_gen_6420) -> q_gen_6407
<a, cons, z>(q_gen_6404, q_gen_6444) -> q_gen_6407
<a, cons, z>(q_gen_6404, q_gen_6449) -> q_gen_6407
<b, cons, s>(q_gen_6394, q_gen_6412) -> q_gen_6407
<b, cons, s>(q_gen_6406, q_gen_6391) -> q_gen_6407
<b, cons, s>(q_gen_6406, q_gen_6420) -> q_gen_6407
<b, cons, s>(q_gen_6406, q_gen_6423) -> q_gen_6407
<b, cons, s>(q_gen_6406, q_gen_6444) -> q_gen_6407
<b, cons, s>(q_gen_6414, q_gen_6391) -> q_gen_6407
<b, cons, s>(q_gen_6414, q_gen_6420) -> q_gen_6407
<b, cons, s>(q_gen_6414, q_gen_6444) -> q_gen_6407
<b, cons, s>(q_gen_6460, q_gen_6391) -> q_gen_6407
<b, cons, z>(q_gen_6392, q_gen_6423) -> q_gen_6407
<b, cons, z>(q_gen_6404, q_gen_6391) -> q_gen_6407
}

Datatype: <elt, eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_6383, q_gen_6385, q_gen_6408},
Q_f={q_gen_6383},
Delta=
{
<s>(q_gen_6385) -> q_gen_6385
<z>() -> q_gen_6385
<s, s>(q_gen_6383) -> q_gen_6383
<z, s>(q_gen_6385) -> q_gen_6383
<z, z>() -> q_gen_6383
<s, s>(q_gen_6408) -> q_gen_6408
<s, z>(q_gen_6385) -> q_gen_6408
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  prefix -> 
{{{
Q={q_gen_6382, q_gen_6388, q_gen_6396, q_gen_6397},
Q_f={q_gen_6382},
Delta=
{
<cons>(q_gen_6397, q_gen_6396) -> q_gen_6396
<nil>() -> q_gen_6396
<a>() -> q_gen_6397
<b>() -> q_gen_6397
<cons, cons>(q_gen_6388, q_gen_6382) -> q_gen_6382
<nil, cons>(q_gen_6397, q_gen_6396) -> q_gen_6382
<nil, nil>() -> q_gen_6382
<a, a>() -> q_gen_6388
<b, b>() -> q_gen_6388
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 73
() -> leq([z, s(nn2)]) -> 73
() -> leq([z, z]) -> 73
() -> prefix([nil, y]) -> 73
(count([x, l1, _py]) /\ count([x, l2, _qy]) /\ prefix([l1, l2])) -> leq([_py, _qy]) -> 76
(count([x, t1, _jy])) -> count([x, cons(x, t1), s(_jy)]) -> 76
(count([x, t1, _ky]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ky]) -> 75
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 73
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 73
(leq([s(nn1), z])) -> BOT -> 73
(prefix([zs, ys])) -> prefix([cons(y2, zs), cons(y2, ys)]) -> 75
(prefix([cons(y2, zs), cons(y2, ys)])) -> prefix([zs, ys]) -> 74
(prefix([cons(z, zs), cons(y2, ys)]) /\ not eq_elt([z, y2])) -> BOT -> 74
(prefix([cons(z, zs), nil])) -> BOT -> 74
}
Sat witness: Found: ((count([x, t1, _jy])) -> count([x, cons(x, t1), s(_jy)]), {
_jy -> z  ;  t1 -> cons(b, cons(b, nil))  ;  x -> a
})

-------------------------------------------
Step 90, which took 2.395783 s (model generation: 2.393567,  model checking: 0.002216):

Model:
|_
{
count -> 
{{{
Q={q_gen_6386, q_gen_6391, q_gen_6392, q_gen_6394, q_gen_6404, q_gen_6406, q_gen_6407, q_gen_6412, q_gen_6414, q_gen_6415, q_gen_6420, q_gen_6460},
Q_f={q_gen_6386},
Delta=
{
<nil>() -> q_gen_6391
<a>() -> q_gen_6392
<b>() -> q_gen_6404
<cons>(q_gen_6392, q_gen_6412) -> q_gen_6412
<cons>(q_gen_6392, q_gen_6420) -> q_gen_6412
<cons>(q_gen_6404, q_gen_6391) -> q_gen_6412
<cons>(q_gen_6404, q_gen_6412) -> q_gen_6412
<cons>(q_gen_6404, q_gen_6420) -> q_gen_6412
<s>(q_gen_6415) -> q_gen_6415
<z>() -> q_gen_6415
<cons>(q_gen_6392, q_gen_6391) -> q_gen_6420
<b, z>() -> q_gen_6394
<a, z>() -> q_gen_6406
<b, s>(q_gen_6415) -> q_gen_6414
<a, s>(q_gen_6415) -> q_gen_6460
<a, cons, s>(q_gen_6394, q_gen_6412) -> q_gen_6386
<a, cons, s>(q_gen_6394, q_gen_6420) -> q_gen_6386
<a, cons, s>(q_gen_6406, q_gen_6391) -> q_gen_6386
<a, cons, s>(q_gen_6406, q_gen_6412) -> q_gen_6386
<a, cons, s>(q_gen_6414, q_gen_6412) -> q_gen_6386
<a, cons, s>(q_gen_6460, q_gen_6412) -> q_gen_6386
<a, cons, s>(q_gen_6460, q_gen_6420) -> q_gen_6386
<a, cons, z>(q_gen_6404, q_gen_6391) -> q_gen_6386
<a, cons, z>(q_gen_6404, q_gen_6412) -> q_gen_6386
<a, nil, z>() -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6391) -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6412) -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6420) -> q_gen_6386
<b, cons, s>(q_gen_6406, q_gen_6412) -> q_gen_6386
<b, cons, s>(q_gen_6414, q_gen_6412) -> q_gen_6386
<b, cons, s>(q_gen_6460, q_gen_6412) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6391) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6412) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6420) -> q_gen_6386
<b, nil, z>() -> q_gen_6386
<a, cons, s>(q_gen_6394, q_gen_6391) -> q_gen_6407
<a, cons, s>(q_gen_6414, q_gen_6391) -> q_gen_6407
<a, cons, s>(q_gen_6414, q_gen_6420) -> q_gen_6407
<a, cons, s>(q_gen_6460, q_gen_6391) -> q_gen_6407
<a, cons, z>(q_gen_6404, q_gen_6420) -> q_gen_6407
<b, cons, s>(q_gen_6406, q_gen_6391) -> q_gen_6407
<b, cons, s>(q_gen_6406, q_gen_6420) -> q_gen_6407
<b, cons, s>(q_gen_6414, q_gen_6391) -> q_gen_6407
<b, cons, s>(q_gen_6414, q_gen_6420) -> q_gen_6407
<b, cons, s>(q_gen_6460, q_gen_6391) -> q_gen_6407
<b, cons, z>(q_gen_6404, q_gen_6391) -> q_gen_6407
}

Datatype: <elt, eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_6383, q_gen_6385, q_gen_6408},
Q_f={q_gen_6383},
Delta=
{
<s>(q_gen_6385) -> q_gen_6385
<z>() -> q_gen_6385
<s, s>(q_gen_6383) -> q_gen_6383
<z, s>(q_gen_6385) -> q_gen_6383
<z, z>() -> q_gen_6383
<s, s>(q_gen_6408) -> q_gen_6408
<s, z>(q_gen_6385) -> q_gen_6408
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  prefix -> 
{{{
Q={q_gen_6382, q_gen_6387, q_gen_6388, q_gen_6396, q_gen_6397, q_gen_6434, q_gen_6439},
Q_f={q_gen_6382, q_gen_6387, q_gen_6434},
Delta=
{
<cons>(q_gen_6397, q_gen_6396) -> q_gen_6396
<nil>() -> q_gen_6396
<a>() -> q_gen_6397
<b>() -> q_gen_6397
<nil, nil>() -> q_gen_6382
<cons, cons>(q_gen_6388, q_gen_6382) -> q_gen_6387
<nil, cons>(q_gen_6397, q_gen_6396) -> q_gen_6387
<a, a>() -> q_gen_6388
<b, b>() -> q_gen_6388
<cons, cons>(q_gen_6388, q_gen_6387) -> q_gen_6434
<cons, cons>(q_gen_6388, q_gen_6434) -> q_gen_6439
<cons, cons>(q_gen_6388, q_gen_6439) -> q_gen_6439
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 74
() -> leq([z, s(nn2)]) -> 74
() -> leq([z, z]) -> 74
() -> prefix([nil, y]) -> 74
(count([x, l1, _py]) /\ count([x, l2, _qy]) /\ prefix([l1, l2])) -> leq([_py, _qy]) -> 76
(count([x, t1, _jy])) -> count([x, cons(x, t1), s(_jy)]) -> 76
(count([x, t1, _ky]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ky]) -> 75
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 74
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 74
(leq([s(nn1), z])) -> BOT -> 74
(prefix([zs, ys])) -> prefix([cons(y2, zs), cons(y2, ys)]) -> 78
(prefix([cons(y2, zs), cons(y2, ys)])) -> prefix([zs, ys]) -> 75
(prefix([cons(z, zs), cons(y2, ys)]) /\ not eq_elt([z, y2])) -> BOT -> 75
(prefix([cons(z, zs), nil])) -> BOT -> 75
}
Sat witness: Found: ((prefix([zs, ys])) -> prefix([cons(y2, zs), cons(y2, ys)]), {
y2 -> b  ;  ys -> cons(a, cons(a, nil))  ;  zs -> cons(a, nil)
})

-------------------------------------------
Step 91, which took 2.010497 s (model generation: 1.988995,  model checking: 0.021502):

Model:
|_
{
count -> 
{{{
Q={q_gen_6386, q_gen_6391, q_gen_6392, q_gen_6394, q_gen_6404, q_gen_6406, q_gen_6407, q_gen_6412, q_gen_6414, q_gen_6415, q_gen_6420, q_gen_6423, q_gen_6444, q_gen_6449, q_gen_6460},
Q_f={q_gen_6386},
Delta=
{
<nil>() -> q_gen_6391
<a>() -> q_gen_6392
<b>() -> q_gen_6404
<cons>(q_gen_6404, q_gen_6391) -> q_gen_6412
<s>(q_gen_6415) -> q_gen_6415
<z>() -> q_gen_6415
<cons>(q_gen_6392, q_gen_6391) -> q_gen_6420
<cons>(q_gen_6404, q_gen_6449) -> q_gen_6420
<cons>(q_gen_6392, q_gen_6423) -> q_gen_6423
<cons>(q_gen_6404, q_gen_6412) -> q_gen_6423
<cons>(q_gen_6404, q_gen_6420) -> q_gen_6423
<cons>(q_gen_6404, q_gen_6444) -> q_gen_6423
<cons>(q_gen_6392, q_gen_6420) -> q_gen_6444
<cons>(q_gen_6392, q_gen_6444) -> q_gen_6444
<cons>(q_gen_6392, q_gen_6449) -> q_gen_6444
<cons>(q_gen_6392, q_gen_6412) -> q_gen_6449
<cons>(q_gen_6404, q_gen_6423) -> q_gen_6449
<b, z>() -> q_gen_6394
<a, z>() -> q_gen_6406
<b, s>(q_gen_6415) -> q_gen_6414
<a, s>(q_gen_6415) -> q_gen_6460
<a, cons, s>(q_gen_6394, q_gen_6420) -> q_gen_6386
<a, cons, s>(q_gen_6394, q_gen_6423) -> q_gen_6386
<a, cons, s>(q_gen_6394, q_gen_6449) -> q_gen_6386
<a, cons, s>(q_gen_6406, q_gen_6391) -> q_gen_6386
<a, cons, s>(q_gen_6406, q_gen_6412) -> q_gen_6386
<a, cons, s>(q_gen_6406, q_gen_6423) -> q_gen_6386
<a, cons, s>(q_gen_6414, q_gen_6423) -> q_gen_6386
<a, cons, s>(q_gen_6414, q_gen_6444) -> q_gen_6386
<a, cons, s>(q_gen_6460, q_gen_6420) -> q_gen_6386
<a, cons, s>(q_gen_6460, q_gen_6423) -> q_gen_6386
<a, cons, s>(q_gen_6460, q_gen_6444) -> q_gen_6386
<a, cons, s>(q_gen_6460, q_gen_6449) -> q_gen_6386
<a, cons, z>(q_gen_6404, q_gen_6391) -> q_gen_6386
<a, cons, z>(q_gen_6404, q_gen_6412) -> q_gen_6386
<a, cons, z>(q_gen_6404, q_gen_6423) -> q_gen_6386
<a, nil, z>() -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6391) -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6420) -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6444) -> q_gen_6386
<b, cons, s>(q_gen_6406, q_gen_6412) -> q_gen_6386
<b, cons, s>(q_gen_6406, q_gen_6423) -> q_gen_6386
<b, cons, s>(q_gen_6406, q_gen_6449) -> q_gen_6386
<b, cons, s>(q_gen_6414, q_gen_6412) -> q_gen_6386
<b, cons, s>(q_gen_6414, q_gen_6423) -> q_gen_6386
<b, cons, s>(q_gen_6414, q_gen_6449) -> q_gen_6386
<b, cons, s>(q_gen_6460, q_gen_6423) -> q_gen_6386
<b, cons, s>(q_gen_6460, q_gen_6449) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6391) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6420) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6444) -> q_gen_6386
<b, nil, z>() -> q_gen_6386
<a, cons, s>(q_gen_6394, q_gen_6391) -> q_gen_6407
<a, cons, s>(q_gen_6394, q_gen_6444) -> q_gen_6407
<a, cons, s>(q_gen_6414, q_gen_6391) -> q_gen_6407
<a, cons, s>(q_gen_6414, q_gen_6420) -> q_gen_6407
<a, cons, s>(q_gen_6414, q_gen_6449) -> q_gen_6407
<a, cons, s>(q_gen_6460, q_gen_6391) -> q_gen_6407
<a, cons, s>(q_gen_6460, q_gen_6412) -> q_gen_6407
<a, cons, z>(q_gen_6404, q_gen_6420) -> q_gen_6407
<a, cons, z>(q_gen_6404, q_gen_6444) -> q_gen_6407
<a, cons, z>(q_gen_6404, q_gen_6449) -> q_gen_6407
<b, cons, s>(q_gen_6394, q_gen_6412) -> q_gen_6407
<b, cons, s>(q_gen_6394, q_gen_6423) -> q_gen_6407
<b, cons, s>(q_gen_6406, q_gen_6391) -> q_gen_6407
<b, cons, s>(q_gen_6406, q_gen_6420) -> q_gen_6407
<b, cons, s>(q_gen_6406, q_gen_6444) -> q_gen_6407
<b, cons, s>(q_gen_6414, q_gen_6391) -> q_gen_6407
<b, cons, s>(q_gen_6414, q_gen_6420) -> q_gen_6407
<b, cons, s>(q_gen_6414, q_gen_6444) -> q_gen_6407
<b, cons, s>(q_gen_6460, q_gen_6391) -> q_gen_6407
<b, cons, z>(q_gen_6392, q_gen_6423) -> q_gen_6407
<b, cons, z>(q_gen_6404, q_gen_6391) -> q_gen_6407
}

Datatype: <elt, eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_6383, q_gen_6385, q_gen_6408},
Q_f={q_gen_6383},
Delta=
{
<s>(q_gen_6385) -> q_gen_6385
<z>() -> q_gen_6385
<s, s>(q_gen_6383) -> q_gen_6383
<z, s>(q_gen_6385) -> q_gen_6383
<z, z>() -> q_gen_6383
<s, s>(q_gen_6408) -> q_gen_6408
<s, z>(q_gen_6385) -> q_gen_6408
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  prefix -> 
{{{
Q={q_gen_6382, q_gen_6388, q_gen_6396, q_gen_6397},
Q_f={q_gen_6382},
Delta=
{
<cons>(q_gen_6397, q_gen_6396) -> q_gen_6396
<nil>() -> q_gen_6396
<a>() -> q_gen_6397
<b>() -> q_gen_6397
<cons, cons>(q_gen_6388, q_gen_6382) -> q_gen_6382
<nil, cons>(q_gen_6397, q_gen_6396) -> q_gen_6382
<nil, nil>() -> q_gen_6382
<a, a>() -> q_gen_6388
<b, b>() -> q_gen_6388
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 75
() -> leq([z, s(nn2)]) -> 75
() -> leq([z, z]) -> 75
() -> prefix([nil, y]) -> 75
(count([x, l1, _py]) /\ count([x, l2, _qy]) /\ prefix([l1, l2])) -> leq([_py, _qy]) -> 76
(count([x, t1, _jy])) -> count([x, cons(x, t1), s(_jy)]) -> 76
(count([x, t1, _ky]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ky]) -> 78
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 75
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 75
(leq([s(nn1), z])) -> BOT -> 75
(prefix([zs, ys])) -> prefix([cons(y2, zs), cons(y2, ys)]) -> 78
(prefix([cons(y2, zs), cons(y2, ys)])) -> prefix([zs, ys]) -> 76
(prefix([cons(z, zs), cons(y2, ys)]) /\ not eq_elt([z, y2])) -> BOT -> 76
(prefix([cons(z, zs), nil])) -> BOT -> 76
}
Sat witness: Found: ((count([x, t1, _ky]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ky]), {
_ky -> z  ;  h1 -> b  ;  t1 -> cons(b, cons(b, cons(a, nil)))  ;  x -> a
})

-------------------------------------------
Step 92, which took 2.376848 s (model generation: 2.358806,  model checking: 0.018042):

Model:
|_
{
count -> 
{{{
Q={q_gen_6386, q_gen_6391, q_gen_6392, q_gen_6394, q_gen_6404, q_gen_6406, q_gen_6407, q_gen_6412, q_gen_6414, q_gen_6415, q_gen_6420, q_gen_6423, q_gen_6444, q_gen_6449, q_gen_6460},
Q_f={q_gen_6386},
Delta=
{
<cons>(q_gen_6404, q_gen_6423) -> q_gen_6391
<nil>() -> q_gen_6391
<a>() -> q_gen_6392
<b>() -> q_gen_6404
<cons>(q_gen_6404, q_gen_6391) -> q_gen_6412
<cons>(q_gen_6404, q_gen_6444) -> q_gen_6412
<s>(q_gen_6415) -> q_gen_6415
<z>() -> q_gen_6415
<cons>(q_gen_6392, q_gen_6391) -> q_gen_6420
<cons>(q_gen_6404, q_gen_6449) -> q_gen_6420
<cons>(q_gen_6392, q_gen_6423) -> q_gen_6423
<cons>(q_gen_6404, q_gen_6412) -> q_gen_6423
<cons>(q_gen_6404, q_gen_6420) -> q_gen_6423
<cons>(q_gen_6392, q_gen_6420) -> q_gen_6444
<cons>(q_gen_6392, q_gen_6444) -> q_gen_6444
<cons>(q_gen_6392, q_gen_6449) -> q_gen_6444
<cons>(q_gen_6392, q_gen_6412) -> q_gen_6449
<b, z>() -> q_gen_6394
<a, z>() -> q_gen_6406
<b, s>(q_gen_6415) -> q_gen_6414
<a, s>(q_gen_6415) -> q_gen_6460
<a, cons, s>(q_gen_6394, q_gen_6420) -> q_gen_6386
<a, cons, s>(q_gen_6394, q_gen_6423) -> q_gen_6386
<a, cons, s>(q_gen_6394, q_gen_6449) -> q_gen_6386
<a, cons, s>(q_gen_6406, q_gen_6391) -> q_gen_6386
<a, cons, s>(q_gen_6406, q_gen_6412) -> q_gen_6386
<a, cons, s>(q_gen_6406, q_gen_6423) -> q_gen_6386
<a, cons, s>(q_gen_6414, q_gen_6412) -> q_gen_6386
<a, cons, s>(q_gen_6414, q_gen_6444) -> q_gen_6386
<a, cons, s>(q_gen_6414, q_gen_6449) -> q_gen_6386
<a, cons, s>(q_gen_6460, q_gen_6412) -> q_gen_6386
<a, cons, s>(q_gen_6460, q_gen_6420) -> q_gen_6386
<a, cons, s>(q_gen_6460, q_gen_6423) -> q_gen_6386
<a, cons, s>(q_gen_6460, q_gen_6444) -> q_gen_6386
<a, cons, s>(q_gen_6460, q_gen_6449) -> q_gen_6386
<a, cons, z>(q_gen_6404, q_gen_6391) -> q_gen_6386
<a, cons, z>(q_gen_6404, q_gen_6412) -> q_gen_6386
<a, cons, z>(q_gen_6404, q_gen_6423) -> q_gen_6386
<a, nil, z>() -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6391) -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6420) -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6444) -> q_gen_6386
<b, cons, s>(q_gen_6406, q_gen_6412) -> q_gen_6386
<b, cons, s>(q_gen_6406, q_gen_6449) -> q_gen_6386
<b, cons, s>(q_gen_6414, q_gen_6412) -> q_gen_6386
<b, cons, s>(q_gen_6460, q_gen_6423) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6391) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6420) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6444) -> q_gen_6386
<b, nil, z>() -> q_gen_6386
<a, cons, s>(q_gen_6394, q_gen_6391) -> q_gen_6407
<a, cons, s>(q_gen_6394, q_gen_6412) -> q_gen_6407
<a, cons, s>(q_gen_6394, q_gen_6444) -> q_gen_6407
<a, cons, s>(q_gen_6414, q_gen_6391) -> q_gen_6407
<a, cons, s>(q_gen_6414, q_gen_6420) -> q_gen_6407
<a, cons, s>(q_gen_6460, q_gen_6391) -> q_gen_6407
<a, cons, z>(q_gen_6404, q_gen_6420) -> q_gen_6407
<a, cons, z>(q_gen_6404, q_gen_6444) -> q_gen_6407
<a, cons, z>(q_gen_6404, q_gen_6449) -> q_gen_6407
<b, cons, s>(q_gen_6394, q_gen_6412) -> q_gen_6407
<b, cons, s>(q_gen_6394, q_gen_6423) -> q_gen_6407
<b, cons, s>(q_gen_6406, q_gen_6391) -> q_gen_6407
<b, cons, s>(q_gen_6406, q_gen_6420) -> q_gen_6407
<b, cons, s>(q_gen_6406, q_gen_6423) -> q_gen_6407
<b, cons, s>(q_gen_6406, q_gen_6444) -> q_gen_6407
<b, cons, s>(q_gen_6414, q_gen_6391) -> q_gen_6407
<b, cons, s>(q_gen_6414, q_gen_6420) -> q_gen_6407
<b, cons, s>(q_gen_6414, q_gen_6423) -> q_gen_6407
<b, cons, s>(q_gen_6414, q_gen_6444) -> q_gen_6407
<b, cons, s>(q_gen_6460, q_gen_6391) -> q_gen_6407
<b, cons, z>(q_gen_6392, q_gen_6423) -> q_gen_6407
<b, cons, z>(q_gen_6404, q_gen_6391) -> q_gen_6407
}

Datatype: <elt, eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_6383, q_gen_6385, q_gen_6408},
Q_f={q_gen_6383},
Delta=
{
<s>(q_gen_6385) -> q_gen_6385
<z>() -> q_gen_6385
<s, s>(q_gen_6383) -> q_gen_6383
<z, s>(q_gen_6385) -> q_gen_6383
<z, z>() -> q_gen_6383
<s, s>(q_gen_6408) -> q_gen_6408
<s, z>(q_gen_6385) -> q_gen_6408
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  prefix -> 
{{{
Q={q_gen_6382, q_gen_6388, q_gen_6396, q_gen_6397},
Q_f={q_gen_6382},
Delta=
{
<cons>(q_gen_6397, q_gen_6396) -> q_gen_6396
<nil>() -> q_gen_6396
<a>() -> q_gen_6397
<b>() -> q_gen_6397
<cons, cons>(q_gen_6388, q_gen_6382) -> q_gen_6382
<nil, cons>(q_gen_6397, q_gen_6396) -> q_gen_6382
<nil, nil>() -> q_gen_6382
<a, a>() -> q_gen_6388
<b, b>() -> q_gen_6388
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 76
() -> leq([z, s(nn2)]) -> 76
() -> leq([z, z]) -> 76
() -> prefix([nil, y]) -> 76
(count([x, l1, _py]) /\ count([x, l2, _qy]) /\ prefix([l1, l2])) -> leq([_py, _qy]) -> 76
(count([x, t1, _jy])) -> count([x, cons(x, t1), s(_jy)]) -> 79
(count([x, t1, _ky]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ky]) -> 78
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 76
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 76
(leq([s(nn1), z])) -> BOT -> 76
(prefix([zs, ys])) -> prefix([cons(y2, zs), cons(y2, ys)]) -> 78
(prefix([cons(y2, zs), cons(y2, ys)])) -> prefix([zs, ys]) -> 77
(prefix([cons(z, zs), cons(y2, ys)]) /\ not eq_elt([z, y2])) -> BOT -> 77
(prefix([cons(z, zs), nil])) -> BOT -> 77
}
Sat witness: Found: ((count([x, t1, _jy])) -> count([x, cons(x, t1), s(_jy)]), {
_jy -> s(z)  ;  t1 -> cons(b, cons(b, cons(a, nil)))  ;  x -> a
})

-------------------------------------------
Step 93, which took 3.571734 s (model generation: 3.550481,  model checking: 0.021253):

Model:
|_
{
count -> 
{{{
Q={q_gen_6386, q_gen_6391, q_gen_6392, q_gen_6394, q_gen_6404, q_gen_6406, q_gen_6407, q_gen_6412, q_gen_6414, q_gen_6415, q_gen_6420, q_gen_6423, q_gen_6444, q_gen_6456, q_gen_6460},
Q_f={q_gen_6386},
Delta=
{
<nil>() -> q_gen_6391
<a>() -> q_gen_6392
<b>() -> q_gen_6404
<cons>(q_gen_6404, q_gen_6391) -> q_gen_6412
<cons>(q_gen_6404, q_gen_6412) -> q_gen_6412
<s>(q_gen_6415) -> q_gen_6415
<z>() -> q_gen_6415
<cons>(q_gen_6392, q_gen_6391) -> q_gen_6420
<cons>(q_gen_6392, q_gen_6412) -> q_gen_6423
<cons>(q_gen_6404, q_gen_6420) -> q_gen_6423
<cons>(q_gen_6404, q_gen_6444) -> q_gen_6423
<cons>(q_gen_6392, q_gen_6420) -> q_gen_6444
<cons>(q_gen_6392, q_gen_6456) -> q_gen_6444
<cons>(q_gen_6404, q_gen_6423) -> q_gen_6444
<cons>(q_gen_6392, q_gen_6423) -> q_gen_6456
<cons>(q_gen_6392, q_gen_6444) -> q_gen_6456
<cons>(q_gen_6404, q_gen_6456) -> q_gen_6456
<b, z>() -> q_gen_6394
<a, z>() -> q_gen_6406
<b, s>(q_gen_6415) -> q_gen_6414
<a, s>(q_gen_6415) -> q_gen_6460
<a, cons, s>(q_gen_6394, q_gen_6420) -> q_gen_6386
<a, cons, s>(q_gen_6394, q_gen_6423) -> q_gen_6386
<a, cons, s>(q_gen_6394, q_gen_6444) -> q_gen_6386
<a, cons, s>(q_gen_6406, q_gen_6391) -> q_gen_6386
<a, cons, s>(q_gen_6406, q_gen_6412) -> q_gen_6386
<a, cons, s>(q_gen_6414, q_gen_6423) -> q_gen_6386
<a, cons, s>(q_gen_6414, q_gen_6444) -> q_gen_6386
<a, cons, s>(q_gen_6460, q_gen_6420) -> q_gen_6386
<a, cons, s>(q_gen_6460, q_gen_6423) -> q_gen_6386
<a, cons, s>(q_gen_6460, q_gen_6444) -> q_gen_6386
<a, cons, s>(q_gen_6460, q_gen_6456) -> q_gen_6386
<a, cons, z>(q_gen_6404, q_gen_6391) -> q_gen_6386
<a, cons, z>(q_gen_6404, q_gen_6412) -> q_gen_6386
<a, nil, z>() -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6391) -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6420) -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6444) -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6456) -> q_gen_6386
<b, cons, s>(q_gen_6406, q_gen_6412) -> q_gen_6386
<b, cons, s>(q_gen_6406, q_gen_6423) -> q_gen_6386
<b, cons, s>(q_gen_6406, q_gen_6456) -> q_gen_6386
<b, cons, s>(q_gen_6414, q_gen_6412) -> q_gen_6386
<b, cons, s>(q_gen_6414, q_gen_6423) -> q_gen_6386
<b, cons, s>(q_gen_6460, q_gen_6412) -> q_gen_6386
<b, cons, s>(q_gen_6460, q_gen_6444) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6391) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6420) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6444) -> q_gen_6386
<b, nil, z>() -> q_gen_6386
<a, cons, s>(q_gen_6394, q_gen_6391) -> q_gen_6407
<a, cons, s>(q_gen_6394, q_gen_6456) -> q_gen_6407
<a, cons, s>(q_gen_6406, q_gen_6423) -> q_gen_6407
<a, cons, s>(q_gen_6406, q_gen_6456) -> q_gen_6407
<a, cons, s>(q_gen_6414, q_gen_6391) -> q_gen_6407
<a, cons, s>(q_gen_6414, q_gen_6420) -> q_gen_6407
<a, cons, s>(q_gen_6460, q_gen_6391) -> q_gen_6407
<a, cons, s>(q_gen_6460, q_gen_6412) -> q_gen_6407
<a, cons, z>(q_gen_6404, q_gen_6420) -> q_gen_6407
<a, cons, z>(q_gen_6404, q_gen_6423) -> q_gen_6407
<a, cons, z>(q_gen_6404, q_gen_6444) -> q_gen_6407
<a, cons, z>(q_gen_6404, q_gen_6456) -> q_gen_6407
<b, cons, s>(q_gen_6394, q_gen_6412) -> q_gen_6407
<b, cons, s>(q_gen_6406, q_gen_6391) -> q_gen_6407
<b, cons, s>(q_gen_6406, q_gen_6420) -> q_gen_6407
<b, cons, s>(q_gen_6406, q_gen_6444) -> q_gen_6407
<b, cons, s>(q_gen_6414, q_gen_6391) -> q_gen_6407
<b, cons, s>(q_gen_6414, q_gen_6420) -> q_gen_6407
<b, cons, s>(q_gen_6414, q_gen_6444) -> q_gen_6407
<b, cons, s>(q_gen_6414, q_gen_6456) -> q_gen_6407
<b, cons, s>(q_gen_6460, q_gen_6391) -> q_gen_6407
<b, cons, z>(q_gen_6392, q_gen_6412) -> q_gen_6407
<b, cons, z>(q_gen_6392, q_gen_6423) -> q_gen_6407
<b, cons, z>(q_gen_6392, q_gen_6456) -> q_gen_6407
<b, cons, z>(q_gen_6404, q_gen_6391) -> q_gen_6407
}

Datatype: <elt, eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_6383, q_gen_6385, q_gen_6408},
Q_f={q_gen_6383},
Delta=
{
<s>(q_gen_6385) -> q_gen_6385
<z>() -> q_gen_6385
<s, s>(q_gen_6383) -> q_gen_6383
<z, s>(q_gen_6385) -> q_gen_6383
<z, z>() -> q_gen_6383
<s, s>(q_gen_6408) -> q_gen_6408
<s, z>(q_gen_6385) -> q_gen_6408
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  prefix -> 
{{{
Q={q_gen_6382, q_gen_6388, q_gen_6396, q_gen_6397},
Q_f={q_gen_6382},
Delta=
{
<cons>(q_gen_6397, q_gen_6396) -> q_gen_6396
<nil>() -> q_gen_6396
<a>() -> q_gen_6397
<b>() -> q_gen_6397
<cons, cons>(q_gen_6388, q_gen_6382) -> q_gen_6382
<nil, cons>(q_gen_6397, q_gen_6396) -> q_gen_6382
<nil, nil>() -> q_gen_6382
<a, a>() -> q_gen_6388
<b, b>() -> q_gen_6388
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 76
() -> leq([z, s(nn2)]) -> 76
() -> leq([z, z]) -> 76
() -> prefix([nil, y]) -> 76
(count([x, l1, _py]) /\ count([x, l2, _qy]) /\ prefix([l1, l2])) -> leq([_py, _qy]) -> 79
(count([x, t1, _jy])) -> count([x, cons(x, t1), s(_jy)]) -> 79
(count([x, t1, _ky]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ky]) -> 78
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 77
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 77
(leq([s(nn1), z])) -> BOT -> 77
(prefix([zs, ys])) -> prefix([cons(y2, zs), cons(y2, ys)]) -> 78
(prefix([cons(y2, zs), cons(y2, ys)])) -> prefix([zs, ys]) -> 77
(prefix([cons(z, zs), cons(y2, ys)]) /\ not eq_elt([z, y2])) -> BOT -> 77
(prefix([cons(z, zs), nil])) -> BOT -> 77
}
Sat witness: Found: ((count([x, l1, _py]) /\ count([x, l2, _qy]) /\ prefix([l1, l2])) -> leq([_py, _qy]), {
_py -> s(s(z))  ;  _qy -> z  ;  l1 -> cons(a, cons(a, cons(a, nil)))  ;  l2 -> cons(a, cons(a, cons(a, nil)))  ;  x -> b
})

-------------------------------------------
Step 94, which took 3.448089 s (model generation: 3.431616,  model checking: 0.016473):

Model:
|_
{
count -> 
{{{
Q={q_gen_6386, q_gen_6391, q_gen_6392, q_gen_6394, q_gen_6404, q_gen_6406, q_gen_6407, q_gen_6412, q_gen_6414, q_gen_6415, q_gen_6420, q_gen_6423, q_gen_6444, q_gen_6449, q_gen_6460},
Q_f={q_gen_6386},
Delta=
{
<nil>() -> q_gen_6391
<a>() -> q_gen_6392
<b>() -> q_gen_6404
<cons>(q_gen_6404, q_gen_6391) -> q_gen_6412
<cons>(q_gen_6404, q_gen_6423) -> q_gen_6412
<cons>(q_gen_6404, q_gen_6444) -> q_gen_6412
<s>(q_gen_6415) -> q_gen_6415
<z>() -> q_gen_6415
<cons>(q_gen_6392, q_gen_6391) -> q_gen_6420
<cons>(q_gen_6404, q_gen_6449) -> q_gen_6420
<cons>(q_gen_6392, q_gen_6423) -> q_gen_6423
<cons>(q_gen_6404, q_gen_6412) -> q_gen_6423
<cons>(q_gen_6404, q_gen_6420) -> q_gen_6423
<cons>(q_gen_6392, q_gen_6420) -> q_gen_6444
<cons>(q_gen_6392, q_gen_6444) -> q_gen_6444
<cons>(q_gen_6392, q_gen_6449) -> q_gen_6444
<cons>(q_gen_6392, q_gen_6412) -> q_gen_6449
<b, z>() -> q_gen_6394
<a, z>() -> q_gen_6406
<b, s>(q_gen_6415) -> q_gen_6414
<a, s>(q_gen_6415) -> q_gen_6460
<a, cons, s>(q_gen_6394, q_gen_6420) -> q_gen_6386
<a, cons, s>(q_gen_6394, q_gen_6423) -> q_gen_6386
<a, cons, s>(q_gen_6394, q_gen_6449) -> q_gen_6386
<a, cons, s>(q_gen_6406, q_gen_6391) -> q_gen_6386
<a, cons, s>(q_gen_6406, q_gen_6412) -> q_gen_6386
<a, cons, s>(q_gen_6406, q_gen_6423) -> q_gen_6386
<a, cons, s>(q_gen_6414, q_gen_6412) -> q_gen_6386
<a, cons, s>(q_gen_6414, q_gen_6444) -> q_gen_6386
<a, cons, s>(q_gen_6414, q_gen_6449) -> q_gen_6386
<a, cons, s>(q_gen_6460, q_gen_6412) -> q_gen_6386
<a, cons, s>(q_gen_6460, q_gen_6420) -> q_gen_6386
<a, cons, s>(q_gen_6460, q_gen_6423) -> q_gen_6386
<a, cons, s>(q_gen_6460, q_gen_6444) -> q_gen_6386
<a, cons, s>(q_gen_6460, q_gen_6449) -> q_gen_6386
<a, cons, z>(q_gen_6404, q_gen_6391) -> q_gen_6386
<a, cons, z>(q_gen_6404, q_gen_6412) -> q_gen_6386
<a, cons, z>(q_gen_6404, q_gen_6423) -> q_gen_6386
<a, nil, z>() -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6391) -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6420) -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6444) -> q_gen_6386
<b, cons, s>(q_gen_6406, q_gen_6412) -> q_gen_6386
<b, cons, s>(q_gen_6406, q_gen_6423) -> q_gen_6386
<b, cons, s>(q_gen_6406, q_gen_6449) -> q_gen_6386
<b, cons, s>(q_gen_6414, q_gen_6412) -> q_gen_6386
<b, cons, s>(q_gen_6414, q_gen_6423) -> q_gen_6386
<b, cons, s>(q_gen_6460, q_gen_6412) -> q_gen_6386
<b, cons, s>(q_gen_6460, q_gen_6423) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6391) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6420) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6444) -> q_gen_6386
<b, nil, z>() -> q_gen_6386
<a, cons, s>(q_gen_6394, q_gen_6391) -> q_gen_6407
<a, cons, s>(q_gen_6394, q_gen_6412) -> q_gen_6407
<a, cons, s>(q_gen_6394, q_gen_6444) -> q_gen_6407
<a, cons, s>(q_gen_6414, q_gen_6391) -> q_gen_6407
<a, cons, s>(q_gen_6414, q_gen_6420) -> q_gen_6407
<a, cons, s>(q_gen_6460, q_gen_6391) -> q_gen_6407
<a, cons, z>(q_gen_6404, q_gen_6420) -> q_gen_6407
<a, cons, z>(q_gen_6404, q_gen_6444) -> q_gen_6407
<a, cons, z>(q_gen_6404, q_gen_6449) -> q_gen_6407
<b, cons, s>(q_gen_6394, q_gen_6412) -> q_gen_6407
<b, cons, s>(q_gen_6394, q_gen_6423) -> q_gen_6407
<b, cons, s>(q_gen_6406, q_gen_6391) -> q_gen_6407
<b, cons, s>(q_gen_6406, q_gen_6420) -> q_gen_6407
<b, cons, s>(q_gen_6406, q_gen_6444) -> q_gen_6407
<b, cons, s>(q_gen_6414, q_gen_6391) -> q_gen_6407
<b, cons, s>(q_gen_6414, q_gen_6420) -> q_gen_6407
<b, cons, s>(q_gen_6414, q_gen_6444) -> q_gen_6407
<b, cons, s>(q_gen_6460, q_gen_6391) -> q_gen_6407
<b, cons, s>(q_gen_6460, q_gen_6444) -> q_gen_6407
<b, cons, z>(q_gen_6392, q_gen_6423) -> q_gen_6407
<b, cons, z>(q_gen_6404, q_gen_6391) -> q_gen_6407
}

Datatype: <elt, eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_6383, q_gen_6385, q_gen_6408},
Q_f={q_gen_6383},
Delta=
{
<s>(q_gen_6385) -> q_gen_6385
<z>() -> q_gen_6385
<s, s>(q_gen_6383) -> q_gen_6383
<z, s>(q_gen_6385) -> q_gen_6383
<z, z>() -> q_gen_6383
<s, s>(q_gen_6408) -> q_gen_6408
<s, z>(q_gen_6385) -> q_gen_6408
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  prefix -> 
{{{
Q={q_gen_6382, q_gen_6388, q_gen_6396, q_gen_6397},
Q_f={q_gen_6382},
Delta=
{
<cons>(q_gen_6397, q_gen_6396) -> q_gen_6396
<nil>() -> q_gen_6396
<a>() -> q_gen_6397
<b>() -> q_gen_6397
<cons, cons>(q_gen_6388, q_gen_6382) -> q_gen_6382
<nil, cons>(q_gen_6397, q_gen_6396) -> q_gen_6382
<nil, nil>() -> q_gen_6382
<a, a>() -> q_gen_6388
<b, b>() -> q_gen_6388
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 77
() -> leq([z, s(nn2)]) -> 77
() -> leq([z, z]) -> 77
() -> prefix([nil, y]) -> 77
(count([x, l1, _py]) /\ count([x, l2, _qy]) /\ prefix([l1, l2])) -> leq([_py, _qy]) -> 79
(count([x, t1, _jy])) -> count([x, cons(x, t1), s(_jy)]) -> 79
(count([x, t1, _ky]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ky]) -> 81
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 78
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 78
(leq([s(nn1), z])) -> BOT -> 78
(prefix([zs, ys])) -> prefix([cons(y2, zs), cons(y2, ys)]) -> 79
(prefix([cons(y2, zs), cons(y2, ys)])) -> prefix([zs, ys]) -> 78
(prefix([cons(z, zs), cons(y2, ys)]) /\ not eq_elt([z, y2])) -> BOT -> 78
(prefix([cons(z, zs), nil])) -> BOT -> 78
}
Sat witness: Found: ((count([x, t1, _ky]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ky]), {
_ky -> s(z)  ;  h1 -> b  ;  t1 -> cons(b, cons(a, cons(b, cons(b, nil))))  ;  x -> a
})

-------------------------------------------
Step 95, which took 2.126544 s (model generation: 2.113721,  model checking: 0.012823):

Model:
|_
{
count -> 
{{{
Q={q_gen_6386, q_gen_6391, q_gen_6392, q_gen_6394, q_gen_6404, q_gen_6406, q_gen_6407, q_gen_6412, q_gen_6414, q_gen_6415, q_gen_6420, q_gen_6423, q_gen_6444, q_gen_6449, q_gen_6460},
Q_f={q_gen_6386},
Delta=
{
<nil>() -> q_gen_6391
<a>() -> q_gen_6392
<b>() -> q_gen_6404
<cons>(q_gen_6392, q_gen_6423) -> q_gen_6412
<cons>(q_gen_6404, q_gen_6391) -> q_gen_6412
<s>(q_gen_6415) -> q_gen_6415
<z>() -> q_gen_6415
<cons>(q_gen_6392, q_gen_6391) -> q_gen_6420
<cons>(q_gen_6404, q_gen_6412) -> q_gen_6423
<cons>(q_gen_6404, q_gen_6420) -> q_gen_6423
<cons>(q_gen_6404, q_gen_6423) -> q_gen_6423
<cons>(q_gen_6392, q_gen_6420) -> q_gen_6444
<cons>(q_gen_6392, q_gen_6444) -> q_gen_6444
<cons>(q_gen_6392, q_gen_6449) -> q_gen_6444
<cons>(q_gen_6392, q_gen_6412) -> q_gen_6449
<cons>(q_gen_6404, q_gen_6444) -> q_gen_6449
<cons>(q_gen_6404, q_gen_6449) -> q_gen_6449
<b, z>() -> q_gen_6394
<a, z>() -> q_gen_6406
<b, s>(q_gen_6415) -> q_gen_6414
<a, s>(q_gen_6415) -> q_gen_6460
<a, cons, s>(q_gen_6394, q_gen_6412) -> q_gen_6386
<a, cons, s>(q_gen_6394, q_gen_6420) -> q_gen_6386
<a, cons, s>(q_gen_6394, q_gen_6423) -> q_gen_6386
<a, cons, s>(q_gen_6394, q_gen_6449) -> q_gen_6386
<a, cons, s>(q_gen_6406, q_gen_6391) -> q_gen_6386
<a, cons, s>(q_gen_6406, q_gen_6412) -> q_gen_6386
<a, cons, s>(q_gen_6406, q_gen_6423) -> q_gen_6386
<a, cons, s>(q_gen_6414, q_gen_6444) -> q_gen_6386
<a, cons, s>(q_gen_6414, q_gen_6449) -> q_gen_6386
<a, cons, s>(q_gen_6460, q_gen_6420) -> q_gen_6386
<a, cons, s>(q_gen_6460, q_gen_6423) -> q_gen_6386
<a, cons, s>(q_gen_6460, q_gen_6444) -> q_gen_6386
<a, cons, s>(q_gen_6460, q_gen_6449) -> q_gen_6386
<a, cons, z>(q_gen_6404, q_gen_6391) -> q_gen_6386
<a, cons, z>(q_gen_6404, q_gen_6412) -> q_gen_6386
<a, cons, z>(q_gen_6404, q_gen_6423) -> q_gen_6386
<a, nil, z>() -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6391) -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6420) -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6444) -> q_gen_6386
<b, cons, s>(q_gen_6406, q_gen_6412) -> q_gen_6386
<b, cons, s>(q_gen_6406, q_gen_6423) -> q_gen_6386
<b, cons, s>(q_gen_6406, q_gen_6449) -> q_gen_6386
<b, cons, s>(q_gen_6414, q_gen_6412) -> q_gen_6386
<b, cons, s>(q_gen_6414, q_gen_6449) -> q_gen_6386
<b, cons, s>(q_gen_6460, q_gen_6423) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6391) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6420) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6444) -> q_gen_6386
<b, nil, z>() -> q_gen_6386
<a, cons, s>(q_gen_6394, q_gen_6391) -> q_gen_6407
<a, cons, s>(q_gen_6394, q_gen_6444) -> q_gen_6407
<a, cons, s>(q_gen_6414, q_gen_6391) -> q_gen_6407
<a, cons, s>(q_gen_6414, q_gen_6420) -> q_gen_6407
<a, cons, s>(q_gen_6460, q_gen_6391) -> q_gen_6407
<a, cons, s>(q_gen_6460, q_gen_6412) -> q_gen_6407
<a, cons, z>(q_gen_6404, q_gen_6420) -> q_gen_6407
<a, cons, z>(q_gen_6404, q_gen_6444) -> q_gen_6407
<a, cons, z>(q_gen_6404, q_gen_6449) -> q_gen_6407
<b, cons, s>(q_gen_6394, q_gen_6412) -> q_gen_6407
<b, cons, s>(q_gen_6406, q_gen_6391) -> q_gen_6407
<b, cons, s>(q_gen_6406, q_gen_6420) -> q_gen_6407
<b, cons, s>(q_gen_6406, q_gen_6444) -> q_gen_6407
<b, cons, s>(q_gen_6414, q_gen_6391) -> q_gen_6407
<b, cons, s>(q_gen_6414, q_gen_6420) -> q_gen_6407
<b, cons, s>(q_gen_6414, q_gen_6423) -> q_gen_6407
<b, cons, s>(q_gen_6414, q_gen_6444) -> q_gen_6407
<b, cons, s>(q_gen_6460, q_gen_6391) -> q_gen_6407
<b, cons, s>(q_gen_6460, q_gen_6444) -> q_gen_6407
<b, cons, z>(q_gen_6392, q_gen_6412) -> q_gen_6407
<b, cons, z>(q_gen_6392, q_gen_6423) -> q_gen_6407
<b, cons, z>(q_gen_6392, q_gen_6449) -> q_gen_6407
<b, cons, z>(q_gen_6404, q_gen_6391) -> q_gen_6407
}

Datatype: <elt, eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_6383, q_gen_6385, q_gen_6408},
Q_f={q_gen_6383},
Delta=
{
<s>(q_gen_6385) -> q_gen_6385
<z>() -> q_gen_6385
<s, s>(q_gen_6383) -> q_gen_6383
<z, s>(q_gen_6385) -> q_gen_6383
<z, z>() -> q_gen_6383
<s, s>(q_gen_6408) -> q_gen_6408
<s, z>(q_gen_6385) -> q_gen_6408
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  prefix -> 
{{{
Q={q_gen_6382, q_gen_6388, q_gen_6396, q_gen_6397},
Q_f={q_gen_6382},
Delta=
{
<cons>(q_gen_6397, q_gen_6396) -> q_gen_6396
<nil>() -> q_gen_6396
<a>() -> q_gen_6397
<b>() -> q_gen_6397
<cons, cons>(q_gen_6388, q_gen_6382) -> q_gen_6382
<nil, cons>(q_gen_6397, q_gen_6396) -> q_gen_6382
<nil, nil>() -> q_gen_6382
<a, a>() -> q_gen_6388
<b, b>() -> q_gen_6388
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 78
() -> leq([z, s(nn2)]) -> 78
() -> leq([z, z]) -> 78
() -> prefix([nil, y]) -> 78
(count([x, l1, _py]) /\ count([x, l2, _qy]) /\ prefix([l1, l2])) -> leq([_py, _qy]) -> 79
(count([x, t1, _jy])) -> count([x, cons(x, t1), s(_jy)]) -> 82
(count([x, t1, _ky]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ky]) -> 81
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 79
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 79
(leq([s(nn1), z])) -> BOT -> 79
(prefix([zs, ys])) -> prefix([cons(y2, zs), cons(y2, ys)]) -> 80
(prefix([cons(y2, zs), cons(y2, ys)])) -> prefix([zs, ys]) -> 79
(prefix([cons(z, zs), cons(y2, ys)]) /\ not eq_elt([z, y2])) -> BOT -> 79
(prefix([cons(z, zs), nil])) -> BOT -> 79
}
Sat witness: Found: ((count([x, t1, _jy])) -> count([x, cons(x, t1), s(_jy)]), {
_jy -> s(s(z))  ;  t1 -> cons(a, cons(b, cons(a, nil)))  ;  x -> a
})

-------------------------------------------
Step 96, which took 3.158777 s (model generation: 3.134554,  model checking: 0.024223):

Model:
|_
{
count -> 
{{{
Q={q_gen_6386, q_gen_6391, q_gen_6392, q_gen_6394, q_gen_6404, q_gen_6406, q_gen_6407, q_gen_6412, q_gen_6414, q_gen_6415, q_gen_6420, q_gen_6423, q_gen_6444, q_gen_6449, q_gen_6460},
Q_f={q_gen_6386},
Delta=
{
<nil>() -> q_gen_6391
<a>() -> q_gen_6392
<b>() -> q_gen_6404
<cons>(q_gen_6392, q_gen_6423) -> q_gen_6412
<cons>(q_gen_6404, q_gen_6391) -> q_gen_6412
<s>(q_gen_6415) -> q_gen_6415
<z>() -> q_gen_6415
<cons>(q_gen_6392, q_gen_6391) -> q_gen_6420
<cons>(q_gen_6404, q_gen_6412) -> q_gen_6423
<cons>(q_gen_6404, q_gen_6420) -> q_gen_6423
<cons>(q_gen_6404, q_gen_6423) -> q_gen_6423
<cons>(q_gen_6392, q_gen_6420) -> q_gen_6444
<cons>(q_gen_6392, q_gen_6444) -> q_gen_6444
<cons>(q_gen_6392, q_gen_6449) -> q_gen_6444
<cons>(q_gen_6392, q_gen_6412) -> q_gen_6449
<cons>(q_gen_6404, q_gen_6444) -> q_gen_6449
<cons>(q_gen_6404, q_gen_6449) -> q_gen_6449
<b, z>() -> q_gen_6394
<a, z>() -> q_gen_6406
<b, s>(q_gen_6415) -> q_gen_6414
<a, s>(q_gen_6415) -> q_gen_6460
<a, cons, s>(q_gen_6394, q_gen_6412) -> q_gen_6386
<a, cons, s>(q_gen_6394, q_gen_6420) -> q_gen_6386
<a, cons, s>(q_gen_6394, q_gen_6423) -> q_gen_6386
<a, cons, s>(q_gen_6394, q_gen_6449) -> q_gen_6386
<a, cons, s>(q_gen_6406, q_gen_6391) -> q_gen_6386
<a, cons, s>(q_gen_6406, q_gen_6412) -> q_gen_6386
<a, cons, s>(q_gen_6406, q_gen_6423) -> q_gen_6386
<a, cons, s>(q_gen_6414, q_gen_6444) -> q_gen_6386
<a, cons, s>(q_gen_6414, q_gen_6449) -> q_gen_6386
<a, cons, s>(q_gen_6460, q_gen_6412) -> q_gen_6386
<a, cons, s>(q_gen_6460, q_gen_6420) -> q_gen_6386
<a, cons, s>(q_gen_6460, q_gen_6423) -> q_gen_6386
<a, cons, s>(q_gen_6460, q_gen_6444) -> q_gen_6386
<a, cons, s>(q_gen_6460, q_gen_6449) -> q_gen_6386
<a, cons, z>(q_gen_6404, q_gen_6391) -> q_gen_6386
<a, cons, z>(q_gen_6404, q_gen_6412) -> q_gen_6386
<a, cons, z>(q_gen_6404, q_gen_6423) -> q_gen_6386
<a, nil, z>() -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6391) -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6420) -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6444) -> q_gen_6386
<b, cons, s>(q_gen_6406, q_gen_6412) -> q_gen_6386
<b, cons, s>(q_gen_6406, q_gen_6423) -> q_gen_6386
<b, cons, s>(q_gen_6406, q_gen_6449) -> q_gen_6386
<b, cons, s>(q_gen_6414, q_gen_6412) -> q_gen_6386
<b, cons, s>(q_gen_6414, q_gen_6449) -> q_gen_6386
<b, cons, s>(q_gen_6460, q_gen_6423) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6391) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6420) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6444) -> q_gen_6386
<b, nil, z>() -> q_gen_6386
<a, cons, s>(q_gen_6394, q_gen_6391) -> q_gen_6407
<a, cons, s>(q_gen_6394, q_gen_6444) -> q_gen_6407
<a, cons, s>(q_gen_6414, q_gen_6391) -> q_gen_6407
<a, cons, s>(q_gen_6414, q_gen_6420) -> q_gen_6407
<a, cons, s>(q_gen_6460, q_gen_6391) -> q_gen_6407
<a, cons, z>(q_gen_6404, q_gen_6420) -> q_gen_6407
<a, cons, z>(q_gen_6404, q_gen_6444) -> q_gen_6407
<a, cons, z>(q_gen_6404, q_gen_6449) -> q_gen_6407
<b, cons, s>(q_gen_6394, q_gen_6412) -> q_gen_6407
<b, cons, s>(q_gen_6406, q_gen_6391) -> q_gen_6407
<b, cons, s>(q_gen_6406, q_gen_6420) -> q_gen_6407
<b, cons, s>(q_gen_6406, q_gen_6444) -> q_gen_6407
<b, cons, s>(q_gen_6414, q_gen_6391) -> q_gen_6407
<b, cons, s>(q_gen_6414, q_gen_6420) -> q_gen_6407
<b, cons, s>(q_gen_6414, q_gen_6423) -> q_gen_6407
<b, cons, s>(q_gen_6414, q_gen_6444) -> q_gen_6407
<b, cons, s>(q_gen_6460, q_gen_6391) -> q_gen_6407
<b, cons, s>(q_gen_6460, q_gen_6444) -> q_gen_6407
<b, cons, z>(q_gen_6392, q_gen_6412) -> q_gen_6407
<b, cons, z>(q_gen_6392, q_gen_6423) -> q_gen_6407
<b, cons, z>(q_gen_6392, q_gen_6449) -> q_gen_6407
<b, cons, z>(q_gen_6404, q_gen_6391) -> q_gen_6407
}

Datatype: <elt, eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_6383, q_gen_6385, q_gen_6408},
Q_f={q_gen_6383},
Delta=
{
<s>(q_gen_6385) -> q_gen_6385
<z>() -> q_gen_6385
<s, s>(q_gen_6383) -> q_gen_6383
<z, s>(q_gen_6385) -> q_gen_6383
<z, z>() -> q_gen_6383
<s, s>(q_gen_6408) -> q_gen_6408
<s, z>(q_gen_6385) -> q_gen_6408
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  prefix -> 
{{{
Q={q_gen_6382, q_gen_6388, q_gen_6396, q_gen_6397},
Q_f={q_gen_6382},
Delta=
{
<cons>(q_gen_6397, q_gen_6396) -> q_gen_6396
<nil>() -> q_gen_6396
<a>() -> q_gen_6397
<b>() -> q_gen_6397
<cons, cons>(q_gen_6388, q_gen_6382) -> q_gen_6382
<nil, cons>(q_gen_6397, q_gen_6396) -> q_gen_6382
<nil, nil>() -> q_gen_6382
<a, a>() -> q_gen_6388
<b, b>() -> q_gen_6388
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 79
() -> leq([z, s(nn2)]) -> 79
() -> leq([z, z]) -> 79
() -> prefix([nil, y]) -> 79
(count([x, l1, _py]) /\ count([x, l2, _qy]) /\ prefix([l1, l2])) -> leq([_py, _qy]) -> 82
(count([x, t1, _jy])) -> count([x, cons(x, t1), s(_jy)]) -> 82
(count([x, t1, _ky]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ky]) -> 81
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 80
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 80
(leq([s(nn1), z])) -> BOT -> 80
(prefix([zs, ys])) -> prefix([cons(y2, zs), cons(y2, ys)]) -> 80
(prefix([cons(y2, zs), cons(y2, ys)])) -> prefix([zs, ys]) -> 80
(prefix([cons(z, zs), cons(y2, ys)]) /\ not eq_elt([z, y2])) -> BOT -> 80
(prefix([cons(z, zs), nil])) -> BOT -> 80
}
Sat witness: Found: ((count([x, l1, _py]) /\ count([x, l2, _qy]) /\ prefix([l1, l2])) -> leq([_py, _qy]), {
_py -> s(z)  ;  _qy -> z  ;  l1 -> cons(b, cons(a, nil))  ;  l2 -> cons(b, cons(a, cons(b, cons(b, nil))))  ;  x -> a
})

-------------------------------------------
Step 97, which took 2.634097 s (model generation: 2.585150,  model checking: 0.048947):

Model:
|_
{
count -> 
{{{
Q={q_gen_6386, q_gen_6391, q_gen_6392, q_gen_6394, q_gen_6404, q_gen_6406, q_gen_6407, q_gen_6412, q_gen_6414, q_gen_6415, q_gen_6420, q_gen_6444, q_gen_6449, q_gen_6459, q_gen_6460},
Q_f={q_gen_6386},
Delta=
{
<nil>() -> q_gen_6391
<a>() -> q_gen_6392
<b>() -> q_gen_6404
<cons>(q_gen_6392, q_gen_6459) -> q_gen_6412
<cons>(q_gen_6404, q_gen_6391) -> q_gen_6412
<cons>(q_gen_6404, q_gen_6412) -> q_gen_6412
<cons>(q_gen_6404, q_gen_6420) -> q_gen_6412
<s>(q_gen_6415) -> q_gen_6415
<z>() -> q_gen_6415
<cons>(q_gen_6392, q_gen_6391) -> q_gen_6420
<cons>(q_gen_6392, q_gen_6420) -> q_gen_6444
<cons>(q_gen_6404, q_gen_6449) -> q_gen_6444
<cons>(q_gen_6392, q_gen_6412) -> q_gen_6449
<cons>(q_gen_6404, q_gen_6444) -> q_gen_6449
<cons>(q_gen_6404, q_gen_6459) -> q_gen_6449
<cons>(q_gen_6392, q_gen_6444) -> q_gen_6459
<cons>(q_gen_6392, q_gen_6449) -> q_gen_6459
<b, z>() -> q_gen_6394
<a, z>() -> q_gen_6406
<b, s>(q_gen_6415) -> q_gen_6414
<a, s>(q_gen_6415) -> q_gen_6460
<a, cons, s>(q_gen_6394, q_gen_6412) -> q_gen_6386
<a, cons, s>(q_gen_6394, q_gen_6420) -> q_gen_6386
<a, cons, s>(q_gen_6394, q_gen_6444) -> q_gen_6386
<a, cons, s>(q_gen_6394, q_gen_6449) -> q_gen_6386
<a, cons, s>(q_gen_6406, q_gen_6391) -> q_gen_6386
<a, cons, s>(q_gen_6406, q_gen_6412) -> q_gen_6386
<a, cons, s>(q_gen_6406, q_gen_6449) -> q_gen_6386
<a, cons, s>(q_gen_6414, q_gen_6444) -> q_gen_6386
<a, cons, s>(q_gen_6414, q_gen_6449) -> q_gen_6386
<a, cons, s>(q_gen_6460, q_gen_6412) -> q_gen_6386
<a, cons, s>(q_gen_6460, q_gen_6420) -> q_gen_6386
<a, cons, s>(q_gen_6460, q_gen_6444) -> q_gen_6386
<a, cons, s>(q_gen_6460, q_gen_6449) -> q_gen_6386
<a, cons, s>(q_gen_6460, q_gen_6459) -> q_gen_6386
<a, cons, z>(q_gen_6404, q_gen_6391) -> q_gen_6386
<a, cons, z>(q_gen_6404, q_gen_6412) -> q_gen_6386
<a, nil, z>() -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6391) -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6420) -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6444) -> q_gen_6386
<b, cons, s>(q_gen_6394, q_gen_6459) -> q_gen_6386
<b, cons, s>(q_gen_6406, q_gen_6412) -> q_gen_6386
<b, cons, s>(q_gen_6406, q_gen_6449) -> q_gen_6386
<b, cons, s>(q_gen_6406, q_gen_6459) -> q_gen_6386
<b, cons, s>(q_gen_6414, q_gen_6412) -> q_gen_6386
<b, cons, s>(q_gen_6414, q_gen_6449) -> q_gen_6386
<b, cons, s>(q_gen_6460, q_gen_6412) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6391) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6420) -> q_gen_6386
<b, cons, z>(q_gen_6392, q_gen_6444) -> q_gen_6386
<b, nil, z>() -> q_gen_6386
<a, cons, s>(q_gen_6394, q_gen_6391) -> q_gen_6407
<a, cons, s>(q_gen_6394, q_gen_6459) -> q_gen_6407
<a, cons, s>(q_gen_6414, q_gen_6391) -> q_gen_6407
<a, cons, s>(q_gen_6414, q_gen_6420) -> q_gen_6407
<a, cons, s>(q_gen_6460, q_gen_6391) -> q_gen_6407
<a, cons, z>(q_gen_6404, q_gen_6420) -> q_gen_6407
<a, cons, z>(q_gen_6404, q_gen_6444) -> q_gen_6407
<a, cons, z>(q_gen_6404, q_gen_6449) -> q_gen_6407
<a, cons, z>(q_gen_6404, q_gen_6459) -> q_gen_6407
<b, cons, s>(q_gen_6394, q_gen_6412) -> q_gen_6407
<b, cons, s>(q_gen_6394, q_gen_6449) -> q_gen_6407
<b, cons, s>(q_gen_6406, q_gen_6391) -> q_gen_6407
<b, cons, s>(q_gen_6406, q_gen_6420) -> q_gen_6407
<b, cons, s>(q_gen_6406, q_gen_6444) -> q_gen_6407
<b, cons, s>(q_gen_6414, q_gen_6391) -> q_gen_6407
<b, cons, s>(q_gen_6414, q_gen_6420) -> q_gen_6407
<b, cons, s>(q_gen_6414, q_gen_6444) -> q_gen_6407
<b, cons, s>(q_gen_6414, q_gen_6459) -> q_gen_6407
<b, cons, s>(q_gen_6460, q_gen_6391) -> q_gen_6407
<b, cons, s>(q_gen_6460, q_gen_6444) -> q_gen_6407
<b, cons, z>(q_gen_6392, q_gen_6412) -> q_gen_6407
<b, cons, z>(q_gen_6392, q_gen_6449) -> q_gen_6407
<b, cons, z>(q_gen_6392, q_gen_6459) -> q_gen_6407
<b, cons, z>(q_gen_6404, q_gen_6391) -> q_gen_6407
}

Datatype: <elt, eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_6383, q_gen_6385, q_gen_6408},
Q_f={q_gen_6383},
Delta=
{
<s>(q_gen_6385) -> q_gen_6385
<z>() -> q_gen_6385
<s, s>(q_gen_6383) -> q_gen_6383
<z, s>(q_gen_6385) -> q_gen_6383
<z, z>() -> q_gen_6383
<s, s>(q_gen_6408) -> q_gen_6408
<s, z>(q_gen_6385) -> q_gen_6408
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  prefix -> 
{{{
Q={q_gen_6382, q_gen_6388, q_gen_6396, q_gen_6397},
Q_f={q_gen_6382},
Delta=
{
<cons>(q_gen_6397, q_gen_6396) -> q_gen_6396
<nil>() -> q_gen_6396
<a>() -> q_gen_6397
<b>() -> q_gen_6397
<cons, cons>(q_gen_6388, q_gen_6382) -> q_gen_6382
<nil, cons>(q_gen_6397, q_gen_6396) -> q_gen_6382
<nil, nil>() -> q_gen_6382
<a, a>() -> q_gen_6388
<b, b>() -> q_gen_6388
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 80
() -> leq([z, s(nn2)]) -> 80
() -> leq([z, z]) -> 80
() -> prefix([nil, y]) -> 80
(count([x, l1, _py]) /\ count([x, l2, _qy]) /\ prefix([l1, l2])) -> leq([_py, _qy]) -> 82
(count([x, t1, _jy])) -> count([x, cons(x, t1), s(_jy)]) -> 82
(count([x, t1, _ky]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ky]) -> 84
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 81
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 81
(leq([s(nn1), z])) -> BOT -> 81
(prefix([zs, ys])) -> prefix([cons(y2, zs), cons(y2, ys)]) -> 81
(prefix([cons(y2, zs), cons(y2, ys)])) -> prefix([zs, ys]) -> 81
(prefix([cons(z, zs), cons(y2, ys)]) /\ not eq_elt([z, y2])) -> BOT -> 81
(prefix([cons(z, zs), nil])) -> BOT -> 81
}
Sat witness: Found: ((count([x, t1, _ky]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _ky]), {
_ky -> s(s(z))  ;  h1 -> a  ;  t1 -> cons(b, cons(a, cons(b, nil)))  ;  x -> b
})

Total time: 62.528458
Reason for stopping: DontKnow. Stopped because: timeout