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:
{
(count, F:
{() -> count([x, nil, z])
(count([x, t1, _gn])) -> count([x, cons(x, t1), s(_gn)])
(count([x, t1, _hn]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _hn])}
(count([_in, _jn, _kn]) /\ count([_in, _jn, _ln])) -> eq_nat([_kn, _ln])
)
}

properties:
{(count([x, l1, _nn]) /\ count([x, cons(x, l1), _mn])) -> eq_nat([_mn, s(_nn)])}


over-approximation: {count}
under-approximation: {}

Clause system for inference is:

{
() -> count([x, nil, z]) -> 0
(count([x, l1, _nn]) /\ count([x, cons(x, l1), _mn])) -> eq_nat([_mn, s(_nn)]) -> 0
(count([x, t1, _gn])) -> count([x, cons(x, t1), s(_gn)]) -> 0
(count([x, t1, _hn]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _hn]) -> 0
}


Solving took 60.080156 seconds.
DontKnow. Stopped because: timeout
Working model:
|_
{
count -> 
{{{
Q={q_gen_3400, q_gen_3401, q_gen_3402, q_gen_3403, q_gen_3404, q_gen_3405, q_gen_3406, q_gen_3407, q_gen_3408, q_gen_3409, q_gen_3410, q_gen_3411, q_gen_3412, q_gen_3413, q_gen_3414, q_gen_3415, q_gen_3416, q_gen_3417, q_gen_3418, q_gen_3419, q_gen_3420, q_gen_3421, q_gen_3422, q_gen_3423, q_gen_3424, q_gen_3425, q_gen_3426, q_gen_3427, q_gen_3428, q_gen_3429, q_gen_3430, q_gen_3431, q_gen_3432, q_gen_3433, q_gen_3434, q_gen_3435, q_gen_3436, q_gen_3437, q_gen_3438, q_gen_3439, q_gen_3440, q_gen_3441, q_gen_3442, q_gen_3443, q_gen_3444, q_gen_3445, q_gen_3446, q_gen_3447, q_gen_3448, q_gen_3449, q_gen_3450, q_gen_3451, q_gen_3452, q_gen_3453, q_gen_3454, q_gen_3455, q_gen_3456, q_gen_3457, q_gen_3458, q_gen_3459, q_gen_3460, q_gen_3461, q_gen_3462, q_gen_3463, q_gen_3464, q_gen_3465, q_gen_3466, q_gen_3467, q_gen_3468, q_gen_3469, q_gen_3470, q_gen_3471, q_gen_3472, q_gen_3473, q_gen_3474, q_gen_3475, q_gen_3476, q_gen_3477, q_gen_3478, q_gen_3479, q_gen_3480, q_gen_3481, q_gen_3482, q_gen_3483, q_gen_3484, q_gen_3485, q_gen_3486, q_gen_3487, q_gen_3488, q_gen_3489, q_gen_3490, q_gen_3491, q_gen_3492, q_gen_3493, q_gen_3494, q_gen_3495, q_gen_3496, q_gen_3497, q_gen_3498, q_gen_3499, q_gen_3500, q_gen_3501, q_gen_3502, q_gen_3503, q_gen_3504, q_gen_3505, q_gen_3506, q_gen_3507, q_gen_3508, q_gen_3509, q_gen_3510, q_gen_3511, q_gen_3512, q_gen_3513, q_gen_3514, q_gen_3515, q_gen_3516, q_gen_3517, q_gen_3518, q_gen_3519, q_gen_3520, q_gen_3521, q_gen_3522, q_gen_3523, q_gen_3524, q_gen_3525, q_gen_3526, q_gen_3527, q_gen_3528, q_gen_3529, q_gen_3530, q_gen_3531, q_gen_3532, q_gen_3533, q_gen_3534, q_gen_3535, q_gen_3536, q_gen_3537, q_gen_3538, q_gen_3539, q_gen_3540, q_gen_3541, q_gen_3542, q_gen_3543, q_gen_3544, q_gen_3545, q_gen_3546, q_gen_3547, q_gen_3548, q_gen_3549, q_gen_3550, q_gen_3551, q_gen_3552, q_gen_3553, q_gen_3554},
Q_f={},
Delta=
{
<nil>() -> q_gen_3402
<a>() -> q_gen_3403
<b>() -> q_gen_3408
<cons>(q_gen_3408, q_gen_3402) -> q_gen_3413
<cons>(q_gen_3403, q_gen_3402) -> q_gen_3415
<cons>(q_gen_3408, q_gen_3413) -> q_gen_3422
<cons>(q_gen_3403, q_gen_3415) -> q_gen_3424
<z>() -> q_gen_3427
<cons>(q_gen_3408, q_gen_3422) -> q_gen_3430
<cons>(q_gen_3403, q_gen_3413) -> q_gen_3433
<s>(q_gen_3427) -> q_gen_3436
<cons>(q_gen_3408, q_gen_3415) -> q_gen_3446
<cons>(q_gen_3408, q_gen_3446) -> q_gen_3452
<cons>(q_gen_3403, q_gen_3446) -> q_gen_3455
<cons>(q_gen_3408, q_gen_3433) -> q_gen_3460
<cons>(q_gen_3403, q_gen_3433) -> q_gen_3465
<s>(q_gen_3436) -> q_gen_3476
<cons>(q_gen_3408, q_gen_3455) -> q_gen_3479
<cons>(q_gen_3408, q_gen_3479) -> q_gen_3481
<cons>(q_gen_3408, q_gen_3460) -> q_gen_3484
<cons>(q_gen_3408, q_gen_3484) -> q_gen_3486
<cons>(q_gen_3403, q_gen_3455) -> q_gen_3492
<cons>(q_gen_3408, q_gen_3424) -> q_gen_3496
<cons>(q_gen_3408, q_gen_3496) -> q_gen_3498
<cons>(q_gen_3403, q_gen_3430) -> q_gen_3505
<cons>(q_gen_3408, q_gen_3509) -> q_gen_3508
<cons>(q_gen_3408, q_gen_3510) -> q_gen_3509
<cons>(q_gen_3403, q_gen_3424) -> q_gen_3510
<cons>(q_gen_3403, q_gen_3508) -> q_gen_3512
<cons>(q_gen_3403, q_gen_3452) -> q_gen_3516
<cons>(q_gen_3403, q_gen_3422) -> q_gen_3518
<cons>(q_gen_3408, q_gen_3518) -> q_gen_3520
<cons>(q_gen_3408, q_gen_3492) -> q_gen_3524
<cons>(q_gen_3403, q_gen_3520) -> q_gen_3528
<cons>(q_gen_3403, q_gen_3551) -> q_gen_3550
<cons>(q_gen_3403, q_gen_3552) -> q_gen_3551
<cons>(q_gen_3403, q_gen_3496) -> q_gen_3552
<cons>(q_gen_3403, q_gen_3550) -> q_gen_3554
<b, z>() -> q_gen_3405
<a, z>() -> q_gen_3411
<b, s>(q_gen_3427) -> q_gen_3426
<b, s>(q_gen_3436) -> q_gen_3435
<a, s>(q_gen_3436) -> q_gen_3470
<b, s>(q_gen_3476) -> q_gen_3475
<a, s>(q_gen_3427) -> q_gen_3487
<b, nil, z>() -> q_gen_3400
<b, cons, z>(q_gen_3403, q_gen_3402) -> q_gen_3401
<b, cons, s>(q_gen_3405, q_gen_3402) -> q_gen_3404
<a, nil, z>() -> q_gen_3406
<a, cons, z>(q_gen_3408, q_gen_3402) -> q_gen_3407
<a, cons, z>(q_gen_3403, q_gen_3402) -> q_gen_3409
<a, cons, s>(q_gen_3411, q_gen_3402) -> q_gen_3410
<a, cons, z>(q_gen_3408, q_gen_3413) -> q_gen_3412
<b, cons, s>(q_gen_3405, q_gen_3415) -> q_gen_3414
<b, cons, s>(q_gen_3405, q_gen_3413) -> q_gen_3416
<b, cons, s>(q_gen_3411, q_gen_3413) -> q_gen_3417
<a, cons, s>(q_gen_3411, q_gen_3413) -> q_gen_3418
<a, cons, s>(q_gen_3411, q_gen_3415) -> q_gen_3419
<b, cons, z>(q_gen_3403, q_gen_3415) -> q_gen_3420
<a, cons, s>(q_gen_3411, q_gen_3422) -> q_gen_3421
<b, cons, z>(q_gen_3403, q_gen_3424) -> q_gen_3423
<b, cons, s>(q_gen_3426, q_gen_3413) -> q_gen_3425
<a, cons, s>(q_gen_3426, q_gen_3413) -> q_gen_3428
<b, cons, s>(q_gen_3426, q_gen_3430) -> q_gen_3429
<b, cons, s>(q_gen_3426, q_gen_3422) -> q_gen_3431
<b, cons, s>(q_gen_3411, q_gen_3433) -> q_gen_3432
<b, cons, s>(q_gen_3435, q_gen_3422) -> q_gen_3434
<b, cons, s>(q_gen_3435, q_gen_3402) -> q_gen_3437
<a, cons, z>(q_gen_3408, q_gen_3422) -> q_gen_3438
<b, cons, s>(q_gen_3411, q_gen_3402) -> q_gen_3439
<b, cons, s>(q_gen_3426, q_gen_3415) -> q_gen_3440
<a, cons, z>(q_gen_3408, q_gen_3430) -> q_gen_3441
<b, cons, s>(q_gen_3411, q_gen_3415) -> q_gen_3442
<b, cons, s>(q_gen_3426, q_gen_3424) -> q_gen_3443
<a, cons, z>(q_gen_3408, q_gen_3415) -> q_gen_3444
<a, cons, z>(q_gen_3408, q_gen_3446) -> q_gen_3445
<a, cons, s>(q_gen_3411, q_gen_3430) -> q_gen_3447
<b, cons, s>(q_gen_3405, q_gen_3446) -> q_gen_3448
<a, cons, s>(q_gen_3405, q_gen_3415) -> q_gen_3449
<b, cons, s>(q_gen_3426, q_gen_3446) -> q_gen_3450
<b, cons, s>(q_gen_3435, q_gen_3452) -> q_gen_3451
<b, cons, s>(q_gen_3411, q_gen_3446) -> q_gen_3453
<b, cons, s>(q_gen_3435, q_gen_3455) -> q_gen_3454
<a, cons, z>(q_gen_3408, q_gen_3452) -> q_gen_3456
<b, cons, s>(q_gen_3405, q_gen_3424) -> q_gen_3457
<b, cons, s>(q_gen_3426, q_gen_3433) -> q_gen_3458
<b, cons, s>(q_gen_3405, q_gen_3460) -> q_gen_3459
<a, cons, s>(q_gen_3411, q_gen_3455) -> q_gen_3461
<a, cons, s>(q_gen_3411, q_gen_3446) -> q_gen_3462
<b, cons, z>(q_gen_3403, q_gen_3433) -> q_gen_3463
<b, cons, z>(q_gen_3403, q_gen_3465) -> q_gen_3464
<b, cons, s>(q_gen_3426, q_gen_3455) -> q_gen_3466
<b, cons, s>(q_gen_3426, q_gen_3402) -> q_gen_3467
<b, cons, s>(q_gen_3435, q_gen_3415) -> q_gen_3468
<b, cons, s>(q_gen_3470, q_gen_3446) -> q_gen_3469
<a, cons, s>(q_gen_3470, q_gen_3413) -> q_gen_3471
<b, cons, s>(q_gen_3411, q_gen_3455) -> q_gen_3472
<b, cons, s>(q_gen_3470, q_gen_3402) -> q_gen_3473
<b, cons, s>(q_gen_3475, q_gen_3415) -> q_gen_3474
<b, cons, s>(q_gen_3435, q_gen_3413) -> q_gen_3477
<b, cons, s>(q_gen_3435, q_gen_3479) -> q_gen_3478
<b, cons, s>(q_gen_3470, q_gen_3481) -> q_gen_3480
<b, cons, s>(q_gen_3475, q_gen_3413) -> q_gen_3482
<b, cons, s>(q_gen_3426, q_gen_3484) -> q_gen_3483
<b, cons, s>(q_gen_3487, q_gen_3486) -> q_gen_3485
<a, cons, s>(q_gen_3487, q_gen_3433) -> q_gen_3488
<a, cons, s>(q_gen_3487, q_gen_3413) -> q_gen_3489
<a, cons, s>(q_gen_3487, q_gen_3455) -> q_gen_3490
<a, cons, s>(q_gen_3426, q_gen_3492) -> q_gen_3491
<b, cons, s>(q_gen_3405, q_gen_3465) -> q_gen_3493
<b, cons, s>(q_gen_3475, q_gen_3422) -> q_gen_3494
<b, cons, s>(q_gen_3426, q_gen_3496) -> q_gen_3495
<b, cons, s>(q_gen_3487, q_gen_3498) -> q_gen_3497
<b, cons, s>(q_gen_3435, q_gen_3484) -> q_gen_3499
<b, cons, s>(q_gen_3475, q_gen_3486) -> q_gen_3500
<a, cons, s>(q_gen_3426, q_gen_3402) -> q_gen_3501
<b, cons, s>(q_gen_3426, q_gen_3460) -> q_gen_3502
<b, cons, s>(q_gen_3470, q_gen_3430) -> q_gen_3503
<b, cons, s>(q_gen_3426, q_gen_3505) -> q_gen_3504
<b, cons, s>(q_gen_3487, q_gen_3422) -> q_gen_3506
<b, cons, s>(q_gen_3487, q_gen_3508) -> q_gen_3507
<b, cons, s>(q_gen_3435, q_gen_3512) -> q_gen_3511
<b, cons, s>(q_gen_3475, q_gen_3402) -> q_gen_3513
<b, cons, s>(q_gen_3487, q_gen_3452) -> q_gen_3514
<b, cons, s>(q_gen_3487, q_gen_3516) -> q_gen_3515
<b, cons, s>(q_gen_3435, q_gen_3518) -> q_gen_3517
<b, cons, s>(q_gen_3475, q_gen_3520) -> q_gen_3519
<a, cons, s>(q_gen_3487, q_gen_3422) -> q_gen_3521
<b, cons, s>(q_gen_3426, q_gen_3492) -> q_gen_3522
<b, cons, s>(q_gen_3487, q_gen_3524) -> q_gen_3523
<b, cons, s>(q_gen_3411, q_gen_3465) -> q_gen_3525
<a, cons, s>(q_gen_3487, q_gen_3520) -> q_gen_3526
<a, cons, s>(q_gen_3470, q_gen_3528) -> q_gen_3527
<b, cons, s>(q_gen_3435, q_gen_3424) -> q_gen_3529
<a, cons, s>(q_gen_3470, q_gen_3433) -> q_gen_3530
<a, cons, s>(q_gen_3435, q_gen_3465) -> q_gen_3531
<a, cons, s>(q_gen_3487, q_gen_3518) -> q_gen_3532
<a, cons, s>(q_gen_3470, q_gen_3520) -> q_gen_3533
<a, cons, z>(q_gen_3408, q_gen_3518) -> q_gen_3534
<a, cons, s>(q_gen_3475, q_gen_3422) -> q_gen_3535
<a, cons, s>(q_gen_3475, q_gen_3430) -> q_gen_3536
<b, cons, s>(q_gen_3475, q_gen_3430) -> q_gen_3537
<a, cons, s>(q_gen_3470, q_gen_3422) -> q_gen_3538
<b, cons, s>(q_gen_3487, q_gen_3479) -> q_gen_3539
<b, cons, s>(q_gen_3487, q_gen_3446) -> q_gen_3540
<a, cons, s>(q_gen_3487, q_gen_3430) -> q_gen_3541
<b, cons, s>(q_gen_3411, q_gen_3496) -> q_gen_3542
<a, cons, s>(q_gen_3470, q_gen_3430) -> q_gen_3543
<a, cons, z>(q_gen_3408, q_gen_3424) -> q_gen_3544
<a, cons, z>(q_gen_3408, q_gen_3496) -> q_gen_3545
<b, cons, s>(q_gen_3487, q_gen_3430) -> q_gen_3546
<b, cons, s>(q_gen_3435, q_gen_3505) -> q_gen_3547
<b, cons, s>(q_gen_3405, q_gen_3430) -> q_gen_3548
<a, cons, s>(q_gen_3487, q_gen_3550) -> q_gen_3549
<a, cons, s>(q_gen_3426, q_gen_3554) -> q_gen_3553
}

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

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

-------------------
STEPS:
-------------------------------------------
Step 0, which took 0.011715 s (model generation: 0.011406,  model checking: 0.000309):

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

}

Datatype: <elt, eltlist, nat>
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
(count([x, l1, _nn]) /\ count([x, cons(x, l1), _mn])) -> eq_nat([_mn, s(_nn)]) -> 1
(count([x, t1, _gn])) -> count([x, cons(x, t1), s(_gn)]) -> 1
(count([x, t1, _hn]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _hn]) -> 1
}
Sat witness: Found: (() -> count([x, nil, z]), {
x -> b
})

-------------------------------------------
Step 1, which took 0.009030 s (model generation: 0.008899,  model checking: 0.000131):

Model:
|_
{
count -> 
{{{
Q={q_gen_3400},
Q_f={q_gen_3400},
Delta=
{
<b, nil, z>() -> q_gen_3400
}

Datatype: <elt, eltlist, nat>
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
(count([x, l1, _nn]) /\ count([x, cons(x, l1), _mn])) -> eq_nat([_mn, s(_nn)]) -> 1
(count([x, t1, _gn])) -> count([x, cons(x, t1), s(_gn)]) -> 1
(count([x, t1, _hn]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _hn]) -> 4
}
Sat witness: Found: ((count([x, t1, _hn]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _hn]), {
_hn -> z  ;  h1 -> a  ;  t1 -> nil  ;  x -> b
})

-------------------------------------------
Step 2, which took 0.009690 s (model generation: 0.009507,  model checking: 0.000183):

Model:
|_
{
count -> 
{{{
Q={q_gen_3400, q_gen_3402, q_gen_3403},
Q_f={q_gen_3400},
Delta=
{
<nil>() -> q_gen_3402
<a>() -> q_gen_3403
<b, cons, z>(q_gen_3403, q_gen_3402) -> q_gen_3400
<b, nil, z>() -> q_gen_3400
}

Datatype: <elt, eltlist, nat>
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
(count([x, l1, _nn]) /\ count([x, cons(x, l1), _mn])) -> eq_nat([_mn, s(_nn)]) -> 1
(count([x, t1, _gn])) -> count([x, cons(x, t1), s(_gn)]) -> 4
(count([x, t1, _hn]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _hn]) -> 4
}
Sat witness: Found: ((count([x, t1, _gn])) -> count([x, cons(x, t1), s(_gn)]), {
_gn -> z  ;  t1 -> nil  ;  x -> b
})

-------------------------------------------
Step 3, which took 0.009760 s (model generation: 0.009259,  model checking: 0.000501):

Model:
|_
{
count -> 
{{{
Q={q_gen_3400, q_gen_3402, q_gen_3403, q_gen_3405},
Q_f={q_gen_3400},
Delta=
{
<nil>() -> q_gen_3402
<a>() -> q_gen_3403
<b, z>() -> q_gen_3405
<b, cons, s>(q_gen_3405, q_gen_3402) -> q_gen_3400
<b, cons, z>(q_gen_3403, q_gen_3402) -> q_gen_3400
<b, nil, z>() -> q_gen_3400
}

Datatype: <elt, eltlist, nat>
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
(count([x, l1, _nn]) /\ count([x, cons(x, l1), _mn])) -> eq_nat([_mn, s(_nn)]) -> 2
(count([x, t1, _gn])) -> count([x, cons(x, t1), s(_gn)]) -> 4
(count([x, t1, _hn]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _hn]) -> 4
}
Sat witness: Found: (() -> count([x, nil, z]), {
x -> a
})

-------------------------------------------
Step 4, which took 0.016022 s (model generation: 0.014169,  model checking: 0.001853):

Model:
|_
{
count -> 
{{{
Q={q_gen_3400, q_gen_3402, q_gen_3403, q_gen_3405},
Q_f={q_gen_3400},
Delta=
{
<nil>() -> q_gen_3402
<a>() -> q_gen_3403
<b, z>() -> q_gen_3405
<a, nil, z>() -> q_gen_3400
<b, cons, s>(q_gen_3405, q_gen_3402) -> q_gen_3400
<b, cons, z>(q_gen_3403, q_gen_3402) -> q_gen_3400
<b, nil, z>() -> q_gen_3400
}

Datatype: <elt, eltlist, nat>
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
(count([x, l1, _nn]) /\ count([x, cons(x, l1), _mn])) -> eq_nat([_mn, s(_nn)]) -> 3
(count([x, t1, _gn])) -> count([x, cons(x, t1), s(_gn)]) -> 4
(count([x, t1, _hn]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _hn]) -> 7
}
Sat witness: Found: ((count([x, t1, _hn]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _hn]), {
_hn -> z  ;  h1 -> b  ;  t1 -> nil  ;  x -> a
})

-------------------------------------------
Step 5, which took 0.012377 s (model generation: 0.012155,  model checking: 0.000222):

Model:
|_
{
count -> 
{{{
Q={q_gen_3400, q_gen_3402, q_gen_3403, q_gen_3405},
Q_f={q_gen_3400},
Delta=
{
<nil>() -> q_gen_3402
<a>() -> q_gen_3403
<b>() -> q_gen_3403
<b, z>() -> q_gen_3405
<a, cons, z>(q_gen_3403, q_gen_3402) -> q_gen_3400
<a, nil, z>() -> q_gen_3400
<b, cons, s>(q_gen_3405, q_gen_3402) -> q_gen_3400
<b, cons, z>(q_gen_3403, q_gen_3402) -> q_gen_3400
<b, nil, z>() -> q_gen_3400
}

Datatype: <elt, eltlist, nat>
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
(count([x, l1, _nn]) /\ count([x, cons(x, l1), _mn])) -> eq_nat([_mn, s(_nn)]) -> 6
(count([x, t1, _gn])) -> count([x, cons(x, t1), s(_gn)]) -> 4
(count([x, t1, _hn]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _hn]) -> 7
}
Sat witness: Found: ((count([x, l1, _nn]) /\ count([x, cons(x, l1), _mn])) -> eq_nat([_mn, s(_nn)]), {
_mn -> z  ;  _nn -> z  ;  l1 -> nil  ;  x -> a
})

-------------------------------------------
Step 6, which took 0.011047 s (model generation: 0.010154,  model checking: 0.000893):

Model:
|_
{
count -> 
{{{
Q={q_gen_3400, q_gen_3402, q_gen_3403, q_gen_3405, q_gen_3408, q_gen_3409},
Q_f={q_gen_3400},
Delta=
{
<nil>() -> q_gen_3402
<a>() -> q_gen_3403
<b>() -> q_gen_3408
<b, z>() -> q_gen_3405
<a, cons, z>(q_gen_3408, q_gen_3402) -> q_gen_3400
<a, nil, z>() -> q_gen_3400
<b, cons, s>(q_gen_3405, q_gen_3402) -> q_gen_3400
<b, cons, z>(q_gen_3403, q_gen_3402) -> q_gen_3400
<b, nil, z>() -> q_gen_3400
<a, cons, z>(q_gen_3403, q_gen_3402) -> q_gen_3409
}

Datatype: <elt, eltlist, nat>
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
(count([x, l1, _nn]) /\ count([x, cons(x, l1), _mn])) -> eq_nat([_mn, s(_nn)]) -> 6
(count([x, t1, _gn])) -> count([x, cons(x, t1), s(_gn)]) -> 7
(count([x, t1, _hn]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _hn]) -> 7
}
Sat witness: Found: ((count([x, t1, _gn])) -> count([x, cons(x, t1), s(_gn)]), {
_gn -> z  ;  t1 -> nil  ;  x -> a
})

-------------------------------------------
Step 7, which took 0.011250 s (model generation: 0.010115,  model checking: 0.001135):

Model:
|_
{
count -> 
{{{
Q={q_gen_3400, q_gen_3402, q_gen_3403, q_gen_3405, q_gen_3408, q_gen_3409},
Q_f={q_gen_3400},
Delta=
{
<nil>() -> q_gen_3402
<a>() -> q_gen_3403
<b>() -> q_gen_3408
<a, z>() -> q_gen_3405
<b, z>() -> q_gen_3405
<a, cons, s>(q_gen_3405, q_gen_3402) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3402) -> q_gen_3400
<a, nil, z>() -> q_gen_3400
<b, cons, s>(q_gen_3405, q_gen_3402) -> q_gen_3400
<b, cons, z>(q_gen_3403, q_gen_3402) -> q_gen_3400
<b, nil, z>() -> q_gen_3400
<a, cons, z>(q_gen_3403, q_gen_3402) -> q_gen_3409
}

Datatype: <elt, eltlist, nat>
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
(count([x, l1, _nn]) /\ count([x, cons(x, l1), _mn])) -> eq_nat([_mn, s(_nn)]) -> 7
(count([x, t1, _gn])) -> count([x, cons(x, t1), s(_gn)]) -> 7
(count([x, t1, _hn]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _hn]) -> 10
}
Sat witness: Found: ((count([x, t1, _hn]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _hn]), {
_hn -> z  ;  h1 -> b  ;  t1 -> cons(b, nil)  ;  x -> a
})

-------------------------------------------
Step 8, which took 0.012537 s (model generation: 0.011643,  model checking: 0.000894):

Model:
|_
{
count -> 
{{{
Q={q_gen_3400, q_gen_3402, q_gen_3403, q_gen_3405, q_gen_3408, q_gen_3409},
Q_f={q_gen_3400},
Delta=
{
<cons>(q_gen_3408, q_gen_3402) -> q_gen_3402
<nil>() -> q_gen_3402
<a>() -> q_gen_3403
<b>() -> q_gen_3408
<a, z>() -> q_gen_3405
<b, z>() -> q_gen_3405
<a, cons, s>(q_gen_3405, q_gen_3402) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3402) -> q_gen_3400
<a, nil, z>() -> q_gen_3400
<b, cons, s>(q_gen_3405, q_gen_3402) -> q_gen_3400
<b, cons, z>(q_gen_3403, q_gen_3402) -> q_gen_3400
<b, nil, z>() -> q_gen_3400
<a, cons, z>(q_gen_3403, q_gen_3402) -> q_gen_3409
}

Datatype: <elt, eltlist, nat>
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
(count([x, l1, _nn]) /\ count([x, cons(x, l1), _mn])) -> eq_nat([_mn, s(_nn)]) -> 7
(count([x, t1, _gn])) -> count([x, cons(x, t1), s(_gn)]) -> 10
(count([x, t1, _hn]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _hn]) -> 10
}
Sat witness: Found: ((count([x, t1, _gn])) -> count([x, cons(x, t1), s(_gn)]), {
_gn -> z  ;  t1 -> cons(a, nil)  ;  x -> b
})

-------------------------------------------
Step 9, which took 0.013717 s (model generation: 0.012784,  model checking: 0.000933):

Model:
|_
{
count -> 
{{{
Q={q_gen_3400, q_gen_3402, q_gen_3403, q_gen_3405, q_gen_3408, q_gen_3409},
Q_f={q_gen_3400},
Delta=
{
<cons>(q_gen_3403, q_gen_3402) -> q_gen_3402
<cons>(q_gen_3408, q_gen_3402) -> q_gen_3402
<nil>() -> q_gen_3402
<a>() -> q_gen_3403
<b>() -> q_gen_3408
<a, z>() -> q_gen_3405
<b, z>() -> q_gen_3405
<a, cons, s>(q_gen_3405, q_gen_3402) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3402) -> q_gen_3400
<a, nil, z>() -> q_gen_3400
<b, cons, s>(q_gen_3405, q_gen_3402) -> q_gen_3400
<b, cons, z>(q_gen_3403, q_gen_3402) -> q_gen_3400
<b, nil, z>() -> q_gen_3400
<a, cons, z>(q_gen_3403, q_gen_3402) -> q_gen_3409
}

Datatype: <elt, eltlist, nat>
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
(count([x, l1, _nn]) /\ count([x, cons(x, l1), _mn])) -> eq_nat([_mn, s(_nn)]) -> 10
(count([x, t1, _gn])) -> count([x, cons(x, t1), s(_gn)]) -> 10
(count([x, t1, _hn]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _hn]) -> 10
}
Sat witness: Found: ((count([x, l1, _nn]) /\ count([x, cons(x, l1), _mn])) -> eq_nat([_mn, s(_nn)]), {
_mn -> s(z)  ;  _nn -> s(z)  ;  l1 -> cons(b, nil)  ;  x -> b
})

-------------------------------------------
Step 10, which took 0.012465 s (model generation: 0.011566,  model checking: 0.000899):

Model:
|_
{
count -> 
{{{
Q={q_gen_3400, q_gen_3402, q_gen_3403, q_gen_3405, q_gen_3408, q_gen_3409, q_gen_3413},
Q_f={q_gen_3400},
Delta=
{
<cons>(q_gen_3403, q_gen_3402) -> q_gen_3402
<nil>() -> q_gen_3402
<a>() -> q_gen_3403
<b>() -> q_gen_3408
<cons>(q_gen_3408, q_gen_3402) -> q_gen_3413
<a, z>() -> q_gen_3405
<b, z>() -> q_gen_3405
<a, cons, s>(q_gen_3405, q_gen_3402) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3402) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3413) -> q_gen_3400
<a, nil, z>() -> q_gen_3400
<b, cons, s>(q_gen_3405, q_gen_3402) -> q_gen_3400
<b, cons, z>(q_gen_3403, q_gen_3402) -> q_gen_3400
<b, nil, z>() -> q_gen_3400
<a, cons, z>(q_gen_3403, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3405, q_gen_3413) -> q_gen_3409
}

Datatype: <elt, eltlist, nat>
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
(count([x, l1, _nn]) /\ count([x, cons(x, l1), _mn])) -> eq_nat([_mn, s(_nn)]) -> 10
(count([x, t1, _gn])) -> count([x, cons(x, t1), s(_gn)]) -> 10
(count([x, t1, _hn]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _hn]) -> 13
}
Sat witness: Found: ((count([x, t1, _hn]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _hn]), {
_hn -> s(z)  ;  h1 -> a  ;  t1 -> cons(b, nil)  ;  x -> b
})

-------------------------------------------
Step 11, which took 0.017131 s (model generation: 0.015002,  model checking: 0.002129):

Model:
|_
{
count -> 
{{{
Q={q_gen_3400, q_gen_3402, q_gen_3403, q_gen_3405, q_gen_3408, q_gen_3409, q_gen_3411, q_gen_3413},
Q_f={q_gen_3400},
Delta=
{
<cons>(q_gen_3403, q_gen_3402) -> q_gen_3402
<nil>() -> q_gen_3402
<a>() -> q_gen_3403
<b>() -> q_gen_3408
<cons>(q_gen_3408, q_gen_3402) -> q_gen_3413
<b, z>() -> q_gen_3405
<a, z>() -> q_gen_3411
<a, cons, s>(q_gen_3411, q_gen_3402) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3402) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3413) -> q_gen_3400
<a, nil, z>() -> q_gen_3400
<b, cons, s>(q_gen_3405, q_gen_3402) -> q_gen_3400
<b, cons, s>(q_gen_3411, q_gen_3413) -> q_gen_3400
<b, cons, z>(q_gen_3403, q_gen_3402) -> q_gen_3400
<b, nil, z>() -> q_gen_3400
<a, cons, z>(q_gen_3403, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3405, q_gen_3413) -> q_gen_3409
}

Datatype: <elt, eltlist, nat>
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
(count([x, l1, _nn]) /\ count([x, cons(x, l1), _mn])) -> eq_nat([_mn, s(_nn)]) -> 10
(count([x, t1, _gn])) -> count([x, cons(x, t1), s(_gn)]) -> 13
(count([x, t1, _hn]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _hn]) -> 13
}
Sat witness: Found: ((count([x, t1, _gn])) -> count([x, cons(x, t1), s(_gn)]), {
_gn -> z  ;  t1 -> cons(b, nil)  ;  x -> a
})

-------------------------------------------
Step 12, which took 0.017253 s (model generation: 0.015219,  model checking: 0.002034):

Model:
|_
{
count -> 
{{{
Q={q_gen_3400, q_gen_3402, q_gen_3403, q_gen_3405, q_gen_3408, q_gen_3409, q_gen_3411, q_gen_3413},
Q_f={q_gen_3400},
Delta=
{
<cons>(q_gen_3403, q_gen_3402) -> q_gen_3402
<nil>() -> q_gen_3402
<a>() -> q_gen_3403
<b>() -> q_gen_3408
<cons>(q_gen_3408, q_gen_3402) -> q_gen_3413
<b, z>() -> q_gen_3405
<a, z>() -> q_gen_3411
<a, cons, s>(q_gen_3411, q_gen_3402) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3413) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3402) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3413) -> q_gen_3400
<a, nil, z>() -> q_gen_3400
<b, cons, s>(q_gen_3405, q_gen_3402) -> q_gen_3400
<b, cons, s>(q_gen_3411, q_gen_3413) -> q_gen_3400
<b, cons, z>(q_gen_3403, q_gen_3402) -> q_gen_3400
<b, nil, z>() -> q_gen_3400
<a, cons, z>(q_gen_3403, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3405, q_gen_3413) -> q_gen_3409
}

Datatype: <elt, eltlist, nat>
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
(count([x, l1, _nn]) /\ count([x, cons(x, l1), _mn])) -> eq_nat([_mn, s(_nn)]) -> 13
(count([x, t1, _gn])) -> count([x, cons(x, t1), s(_gn)]) -> 13
(count([x, t1, _hn]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _hn]) -> 13
}
Sat witness: Found: ((count([x, l1, _nn]) /\ count([x, cons(x, l1), _mn])) -> eq_nat([_mn, s(_nn)]), {
_mn -> s(z)  ;  _nn -> s(z)  ;  l1 -> cons(a, nil)  ;  x -> a
})

-------------------------------------------
Step 13, which took 0.016488 s (model generation: 0.014053,  model checking: 0.002435):

Model:
|_
{
count -> 
{{{
Q={q_gen_3400, q_gen_3402, q_gen_3403, q_gen_3405, q_gen_3408, q_gen_3409, q_gen_3411, q_gen_3413, q_gen_3415},
Q_f={q_gen_3400},
Delta=
{
<nil>() -> q_gen_3402
<a>() -> q_gen_3403
<b>() -> q_gen_3408
<cons>(q_gen_3408, q_gen_3402) -> q_gen_3413
<cons>(q_gen_3403, q_gen_3402) -> q_gen_3415
<b, z>() -> q_gen_3405
<a, z>() -> q_gen_3411
<a, cons, s>(q_gen_3411, q_gen_3402) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3413) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3402) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3413) -> q_gen_3400
<a, nil, z>() -> q_gen_3400
<b, cons, s>(q_gen_3405, q_gen_3402) -> q_gen_3400
<b, cons, s>(q_gen_3405, q_gen_3415) -> q_gen_3400
<b, cons, s>(q_gen_3411, q_gen_3413) -> q_gen_3400
<b, cons, z>(q_gen_3403, q_gen_3402) -> q_gen_3400
<b, nil, z>() -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3415) -> q_gen_3409
<a, cons, z>(q_gen_3403, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3405, q_gen_3413) -> q_gen_3409
}

Datatype: <elt, eltlist, nat>
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
(count([x, l1, _nn]) /\ count([x, cons(x, l1), _mn])) -> eq_nat([_mn, s(_nn)]) -> 13
(count([x, t1, _gn])) -> count([x, cons(x, t1), s(_gn)]) -> 13
(count([x, t1, _hn]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _hn]) -> 16
}
Sat witness: Found: ((count([x, t1, _hn]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _hn]), {
_hn -> z  ;  h1 -> a  ;  t1 -> cons(a, nil)  ;  x -> b
})

-------------------------------------------
Step 14, which took 0.017717 s (model generation: 0.014285,  model checking: 0.003432):

Model:
|_
{
count -> 
{{{
Q={q_gen_3400, q_gen_3402, q_gen_3403, q_gen_3405, q_gen_3408, q_gen_3409, q_gen_3411, q_gen_3413, q_gen_3415},
Q_f={q_gen_3400},
Delta=
{
<nil>() -> q_gen_3402
<a>() -> q_gen_3403
<b>() -> q_gen_3408
<cons>(q_gen_3408, q_gen_3402) -> q_gen_3413
<cons>(q_gen_3403, q_gen_3402) -> q_gen_3415
<b, z>() -> q_gen_3405
<a, z>() -> q_gen_3411
<a, cons, s>(q_gen_3411, q_gen_3402) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3413) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3402) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3413) -> q_gen_3400
<a, nil, z>() -> q_gen_3400
<b, cons, s>(q_gen_3405, q_gen_3402) -> q_gen_3400
<b, cons, s>(q_gen_3405, q_gen_3415) -> q_gen_3400
<b, cons, s>(q_gen_3411, q_gen_3413) -> q_gen_3400
<b, cons, z>(q_gen_3403, q_gen_3402) -> q_gen_3400
<b, cons, z>(q_gen_3403, q_gen_3415) -> q_gen_3400
<b, nil, z>() -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3415) -> q_gen_3409
<a, cons, z>(q_gen_3403, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3405, q_gen_3413) -> q_gen_3409
}

Datatype: <elt, eltlist, nat>
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
(count([x, l1, _nn]) /\ count([x, cons(x, l1), _mn])) -> eq_nat([_mn, s(_nn)]) -> 13
(count([x, t1, _gn])) -> count([x, cons(x, t1), s(_gn)]) -> 16
(count([x, t1, _hn]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _hn]) -> 16
}
Sat witness: Found: ((count([x, t1, _gn])) -> count([x, cons(x, t1), s(_gn)]), {
_gn -> z  ;  t1 -> cons(b, cons(b, nil))  ;  x -> a
})

-------------------------------------------
Step 15, which took 0.020540 s (model generation: 0.014656,  model checking: 0.005884):

Model:
|_
{
count -> 
{{{
Q={q_gen_3400, q_gen_3402, q_gen_3403, q_gen_3405, q_gen_3408, q_gen_3409, q_gen_3411, q_gen_3413, q_gen_3415},
Q_f={q_gen_3400},
Delta=
{
<cons>(q_gen_3408, q_gen_3413) -> q_gen_3402
<nil>() -> q_gen_3402
<a>() -> q_gen_3403
<b>() -> q_gen_3408
<cons>(q_gen_3408, q_gen_3402) -> q_gen_3413
<cons>(q_gen_3403, q_gen_3402) -> q_gen_3415
<b, z>() -> q_gen_3405
<a, z>() -> q_gen_3411
<a, cons, s>(q_gen_3411, q_gen_3402) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3413) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3402) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3413) -> q_gen_3400
<a, nil, z>() -> q_gen_3400
<b, cons, s>(q_gen_3405, q_gen_3402) -> q_gen_3400
<b, cons, s>(q_gen_3405, q_gen_3415) -> q_gen_3400
<b, cons, s>(q_gen_3411, q_gen_3413) -> q_gen_3400
<b, cons, z>(q_gen_3403, q_gen_3402) -> q_gen_3400
<b, cons, z>(q_gen_3403, q_gen_3415) -> q_gen_3400
<b, nil, z>() -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3415) -> q_gen_3409
<a, cons, z>(q_gen_3403, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3405, q_gen_3413) -> q_gen_3409
}

Datatype: <elt, eltlist, nat>
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
(count([x, l1, _nn]) /\ count([x, cons(x, l1), _mn])) -> eq_nat([_mn, s(_nn)]) -> 14
(count([x, t1, _gn])) -> count([x, cons(x, t1), s(_gn)]) -> 16
(count([x, t1, _hn]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _hn]) -> 19
}
Sat witness: Found: ((count([x, t1, _hn]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _hn]), {
_hn -> z  ;  h1 -> a  ;  t1 -> cons(a, cons(a, nil))  ;  x -> b
})

-------------------------------------------
Step 16, which took 0.026145 s (model generation: 0.019038,  model checking: 0.007107):

Model:
|_
{
count -> 
{{{
Q={q_gen_3400, q_gen_3402, q_gen_3403, q_gen_3405, q_gen_3408, q_gen_3409, q_gen_3411, q_gen_3413, q_gen_3415},
Q_f={q_gen_3400},
Delta=
{
<cons>(q_gen_3408, q_gen_3413) -> q_gen_3402
<nil>() -> q_gen_3402
<a>() -> q_gen_3403
<b>() -> q_gen_3408
<cons>(q_gen_3408, q_gen_3402) -> q_gen_3413
<cons>(q_gen_3403, q_gen_3402) -> q_gen_3415
<cons>(q_gen_3403, q_gen_3415) -> q_gen_3415
<b, z>() -> q_gen_3405
<a, z>() -> q_gen_3411
<a, cons, s>(q_gen_3411, q_gen_3402) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3413) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3402) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3413) -> q_gen_3400
<a, nil, z>() -> q_gen_3400
<b, cons, s>(q_gen_3405, q_gen_3402) -> q_gen_3400
<b, cons, s>(q_gen_3405, q_gen_3415) -> q_gen_3400
<b, cons, s>(q_gen_3411, q_gen_3413) -> q_gen_3400
<b, cons, z>(q_gen_3403, q_gen_3402) -> q_gen_3400
<b, cons, z>(q_gen_3403, q_gen_3415) -> q_gen_3400
<b, nil, z>() -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3415) -> q_gen_3409
<a, cons, z>(q_gen_3403, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3405, q_gen_3413) -> q_gen_3409
}

Datatype: <elt, eltlist, nat>
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
(count([x, l1, _nn]) /\ count([x, cons(x, l1), _mn])) -> eq_nat([_mn, s(_nn)]) -> 15
(count([x, t1, _gn])) -> count([x, cons(x, t1), s(_gn)]) -> 19
(count([x, t1, _hn]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _hn]) -> 19
}
Sat witness: Found: ((count([x, t1, _gn])) -> count([x, cons(x, t1), s(_gn)]), {
_gn -> s(z)  ;  t1 -> cons(b, nil)  ;  x -> b
})

-------------------------------------------
Step 17, which took 0.020537 s (model generation: 0.017283,  model checking: 0.003254):

Model:
|_
{
count -> 
{{{
Q={q_gen_3400, q_gen_3402, q_gen_3403, q_gen_3405, q_gen_3408, q_gen_3409, q_gen_3411, q_gen_3413, q_gen_3415, q_gen_3427},
Q_f={q_gen_3400},
Delta=
{
<nil>() -> q_gen_3402
<a>() -> q_gen_3403
<b>() -> q_gen_3408
<cons>(q_gen_3408, q_gen_3402) -> q_gen_3413
<cons>(q_gen_3408, q_gen_3413) -> q_gen_3413
<cons>(q_gen_3403, q_gen_3402) -> q_gen_3415
<cons>(q_gen_3403, q_gen_3415) -> q_gen_3415
<z>() -> q_gen_3427
<b, z>() -> q_gen_3405
<a, z>() -> q_gen_3411
<b, s>(q_gen_3427) -> q_gen_3411
<a, cons, s>(q_gen_3411, q_gen_3402) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3413) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3402) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3413) -> q_gen_3400
<a, nil, z>() -> q_gen_3400
<b, cons, s>(q_gen_3405, q_gen_3402) -> q_gen_3400
<b, cons, s>(q_gen_3405, q_gen_3415) -> q_gen_3400
<b, cons, s>(q_gen_3411, q_gen_3413) -> q_gen_3400
<b, cons, z>(q_gen_3403, q_gen_3402) -> q_gen_3400
<b, cons, z>(q_gen_3403, q_gen_3415) -> q_gen_3400
<b, nil, z>() -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3415) -> q_gen_3409
<a, cons, z>(q_gen_3403, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3405, q_gen_3413) -> q_gen_3409
}

Datatype: <elt, eltlist, nat>
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
(count([x, l1, _nn]) /\ count([x, cons(x, l1), _mn])) -> eq_nat([_mn, s(_nn)]) -> 18
(count([x, t1, _gn])) -> count([x, cons(x, t1), s(_gn)]) -> 19
(count([x, t1, _hn]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _hn]) -> 19
}
Sat witness: Found: ((count([x, l1, _nn]) /\ count([x, cons(x, l1), _mn])) -> eq_nat([_mn, s(_nn)]), {
_mn -> s(z)  ;  _nn -> s(s(z))  ;  l1 -> cons(b, cons(b, nil))  ;  x -> a
})

-------------------------------------------
Step 18, which took 0.023622 s (model generation: 0.019759,  model checking: 0.003863):

Model:
|_
{
count -> 
{{{
Q={q_gen_3400, q_gen_3402, q_gen_3403, q_gen_3405, q_gen_3408, q_gen_3409, q_gen_3411, q_gen_3413, q_gen_3415, q_gen_3426, q_gen_3427},
Q_f={q_gen_3400},
Delta=
{
<nil>() -> q_gen_3402
<a>() -> q_gen_3403
<b>() -> q_gen_3408
<cons>(q_gen_3408, q_gen_3402) -> q_gen_3413
<cons>(q_gen_3408, q_gen_3413) -> q_gen_3413
<cons>(q_gen_3403, q_gen_3402) -> q_gen_3415
<cons>(q_gen_3403, q_gen_3415) -> q_gen_3415
<z>() -> q_gen_3427
<b, z>() -> q_gen_3405
<a, z>() -> q_gen_3411
<b, s>(q_gen_3427) -> q_gen_3426
<a, cons, s>(q_gen_3411, q_gen_3402) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3413) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3402) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3413) -> q_gen_3400
<a, nil, z>() -> q_gen_3400
<b, cons, s>(q_gen_3405, q_gen_3402) -> q_gen_3400
<b, cons, s>(q_gen_3405, q_gen_3415) -> q_gen_3400
<b, cons, s>(q_gen_3411, q_gen_3413) -> q_gen_3400
<b, cons, s>(q_gen_3426, q_gen_3413) -> q_gen_3400
<b, cons, z>(q_gen_3403, q_gen_3402) -> q_gen_3400
<b, cons, z>(q_gen_3403, q_gen_3415) -> q_gen_3400
<b, nil, z>() -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3415) -> q_gen_3409
<a, cons, s>(q_gen_3426, q_gen_3413) -> q_gen_3409
<a, cons, z>(q_gen_3403, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3405, q_gen_3413) -> q_gen_3409
}

Datatype: <elt, eltlist, nat>
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
(count([x, l1, _nn]) /\ count([x, cons(x, l1), _mn])) -> eq_nat([_mn, s(_nn)]) -> 21
(count([x, t1, _gn])) -> count([x, cons(x, t1), s(_gn)]) -> 19
(count([x, t1, _hn]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _hn]) -> 19
}
Sat witness: Found: ((count([x, l1, _nn]) /\ count([x, cons(x, l1), _mn])) -> eq_nat([_mn, s(_nn)]), {
_mn -> s(s(z))  ;  _nn -> s(s(z))  ;  l1 -> cons(b, cons(b, cons(b, nil)))  ;  x -> b
})

-------------------------------------------
Step 19, which took 0.028507 s (model generation: 0.021284,  model checking: 0.007223):

Model:
|_
{
count -> 
{{{
Q={q_gen_3400, q_gen_3402, q_gen_3403, q_gen_3405, q_gen_3408, q_gen_3409, q_gen_3411, q_gen_3413, q_gen_3415, q_gen_3426, q_gen_3427},
Q_f={q_gen_3400},
Delta=
{
<cons>(q_gen_3408, q_gen_3413) -> q_gen_3402
<nil>() -> q_gen_3402
<a>() -> q_gen_3403
<b>() -> q_gen_3408
<cons>(q_gen_3408, q_gen_3402) -> q_gen_3413
<cons>(q_gen_3403, q_gen_3402) -> q_gen_3415
<cons>(q_gen_3403, q_gen_3415) -> q_gen_3415
<z>() -> q_gen_3427
<b, z>() -> q_gen_3405
<a, z>() -> q_gen_3411
<b, s>(q_gen_3427) -> q_gen_3426
<a, cons, s>(q_gen_3411, q_gen_3402) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3413) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3402) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3413) -> q_gen_3400
<a, nil, z>() -> q_gen_3400
<b, cons, s>(q_gen_3405, q_gen_3402) -> q_gen_3400
<b, cons, s>(q_gen_3405, q_gen_3415) -> q_gen_3400
<b, cons, s>(q_gen_3411, q_gen_3413) -> q_gen_3400
<b, cons, s>(q_gen_3426, q_gen_3413) -> q_gen_3400
<b, cons, z>(q_gen_3403, q_gen_3402) -> q_gen_3400
<b, cons, z>(q_gen_3403, q_gen_3415) -> q_gen_3400
<b, nil, z>() -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3415) -> q_gen_3409
<a, cons, s>(q_gen_3426, q_gen_3413) -> q_gen_3409
<a, cons, z>(q_gen_3403, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3405, q_gen_3413) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3402) -> q_gen_3409
}

Datatype: <elt, eltlist, nat>
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
(count([x, l1, _nn]) /\ count([x, cons(x, l1), _mn])) -> eq_nat([_mn, s(_nn)]) -> 21
(count([x, t1, _gn])) -> count([x, cons(x, t1), s(_gn)]) -> 19
(count([x, t1, _hn]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _hn]) -> 22
}
Sat witness: Found: ((count([x, t1, _hn]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _hn]), {
_hn -> s(z)  ;  h1 -> a  ;  t1 -> cons(a, cons(b, nil))  ;  x -> b
})

-------------------------------------------
Step 20, which took 0.035924 s (model generation: 0.024705,  model checking: 0.011219):

Model:
|_
{
count -> 
{{{
Q={q_gen_3400, q_gen_3402, q_gen_3403, q_gen_3405, q_gen_3408, q_gen_3409, q_gen_3411, q_gen_3413, q_gen_3415, q_gen_3426, q_gen_3427},
Q_f={q_gen_3400},
Delta=
{
<cons>(q_gen_3408, q_gen_3413) -> q_gen_3402
<nil>() -> q_gen_3402
<a>() -> q_gen_3403
<b>() -> q_gen_3408
<cons>(q_gen_3408, q_gen_3402) -> q_gen_3413
<cons>(q_gen_3403, q_gen_3402) -> q_gen_3415
<cons>(q_gen_3403, q_gen_3413) -> q_gen_3415
<cons>(q_gen_3403, q_gen_3415) -> q_gen_3415
<z>() -> q_gen_3427
<b, z>() -> q_gen_3405
<a, z>() -> q_gen_3411
<b, s>(q_gen_3427) -> q_gen_3426
<a, cons, s>(q_gen_3411, q_gen_3402) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3413) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3402) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3413) -> q_gen_3400
<a, nil, z>() -> q_gen_3400
<b, cons, s>(q_gen_3405, q_gen_3402) -> q_gen_3400
<b, cons, s>(q_gen_3405, q_gen_3415) -> q_gen_3400
<b, cons, s>(q_gen_3411, q_gen_3413) -> q_gen_3400
<b, cons, s>(q_gen_3411, q_gen_3415) -> q_gen_3400
<b, cons, s>(q_gen_3426, q_gen_3413) -> q_gen_3400
<b, cons, z>(q_gen_3403, q_gen_3402) -> q_gen_3400
<b, cons, z>(q_gen_3403, q_gen_3415) -> q_gen_3400
<b, nil, z>() -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3415) -> q_gen_3409
<a, cons, s>(q_gen_3426, q_gen_3413) -> q_gen_3409
<a, cons, z>(q_gen_3403, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3405, q_gen_3413) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3402) -> q_gen_3409
}

Datatype: <elt, eltlist, nat>
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
(count([x, l1, _nn]) /\ count([x, cons(x, l1), _mn])) -> eq_nat([_mn, s(_nn)]) -> 21
(count([x, t1, _gn])) -> count([x, cons(x, t1), s(_gn)]) -> 22
(count([x, t1, _hn]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _hn]) -> 22
}
Sat witness: Found: ((count([x, t1, _gn])) -> count([x, cons(x, t1), s(_gn)]), {
_gn -> s(s(z))  ;  t1 -> cons(b, cons(b, nil))  ;  x -> b
})

-------------------------------------------
Step 21, which took 0.028708 s (model generation: 0.025752,  model checking: 0.002956):

Model:
|_
{
count -> 
{{{
Q={q_gen_3400, q_gen_3402, q_gen_3403, q_gen_3405, q_gen_3408, q_gen_3409, q_gen_3411, q_gen_3413, q_gen_3415, q_gen_3426, q_gen_3427, q_gen_3436},
Q_f={q_gen_3400},
Delta=
{
<cons>(q_gen_3408, q_gen_3413) -> q_gen_3402
<nil>() -> q_gen_3402
<a>() -> q_gen_3403
<b>() -> q_gen_3408
<cons>(q_gen_3408, q_gen_3402) -> q_gen_3413
<cons>(q_gen_3403, q_gen_3402) -> q_gen_3415
<cons>(q_gen_3403, q_gen_3413) -> q_gen_3415
<cons>(q_gen_3403, q_gen_3415) -> q_gen_3415
<z>() -> q_gen_3427
<s>(q_gen_3427) -> q_gen_3436
<b, z>() -> q_gen_3405
<a, z>() -> q_gen_3411
<b, s>(q_gen_3436) -> q_gen_3411
<b, s>(q_gen_3427) -> q_gen_3426
<a, cons, s>(q_gen_3411, q_gen_3402) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3413) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3402) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3413) -> q_gen_3400
<a, nil, z>() -> q_gen_3400
<b, cons, s>(q_gen_3405, q_gen_3402) -> q_gen_3400
<b, cons, s>(q_gen_3405, q_gen_3415) -> q_gen_3400
<b, cons, s>(q_gen_3411, q_gen_3402) -> q_gen_3400
<b, cons, s>(q_gen_3411, q_gen_3413) -> q_gen_3400
<b, cons, s>(q_gen_3411, q_gen_3415) -> q_gen_3400
<b, cons, s>(q_gen_3426, q_gen_3413) -> q_gen_3400
<b, cons, z>(q_gen_3403, q_gen_3402) -> q_gen_3400
<b, cons, z>(q_gen_3403, q_gen_3415) -> q_gen_3400
<b, nil, z>() -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3415) -> q_gen_3409
<a, cons, s>(q_gen_3426, q_gen_3413) -> q_gen_3409
<a, cons, z>(q_gen_3403, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3405, q_gen_3413) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3402) -> q_gen_3409
}

Datatype: <elt, eltlist, nat>
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
(count([x, l1, _nn]) /\ count([x, cons(x, l1), _mn])) -> eq_nat([_mn, s(_nn)]) -> 24
(count([x, t1, _gn])) -> count([x, cons(x, t1), s(_gn)]) -> 22
(count([x, t1, _hn]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _hn]) -> 22
}
Sat witness: Found: ((count([x, l1, _nn]) /\ count([x, cons(x, l1), _mn])) -> eq_nat([_mn, s(_nn)]), {
_mn -> s(s(s(z)))  ;  _nn -> z  ;  l1 -> nil  ;  x -> b
})

-------------------------------------------
Step 22, which took 0.034162 s (model generation: 0.027559,  model checking: 0.006603):

Model:
|_
{
count -> 
{{{
Q={q_gen_3400, q_gen_3402, q_gen_3403, q_gen_3405, q_gen_3408, q_gen_3409, q_gen_3411, q_gen_3413, q_gen_3415, q_gen_3422, q_gen_3426, q_gen_3427},
Q_f={q_gen_3400},
Delta=
{
<nil>() -> q_gen_3402
<a>() -> q_gen_3403
<b>() -> q_gen_3408
<cons>(q_gen_3408, q_gen_3402) -> q_gen_3413
<cons>(q_gen_3403, q_gen_3402) -> q_gen_3415
<cons>(q_gen_3403, q_gen_3413) -> q_gen_3415
<cons>(q_gen_3403, q_gen_3415) -> q_gen_3415
<cons>(q_gen_3408, q_gen_3422) -> q_gen_3415
<cons>(q_gen_3408, q_gen_3413) -> q_gen_3422
<s>(q_gen_3427) -> q_gen_3427
<z>() -> q_gen_3427
<b, z>() -> q_gen_3405
<a, z>() -> q_gen_3411
<b, s>(q_gen_3427) -> q_gen_3426
<a, cons, s>(q_gen_3411, q_gen_3402) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3413) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3422) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3402) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3413) -> q_gen_3400
<a, nil, z>() -> q_gen_3400
<b, cons, s>(q_gen_3405, q_gen_3402) -> q_gen_3400
<b, cons, s>(q_gen_3405, q_gen_3415) -> q_gen_3400
<b, cons, s>(q_gen_3411, q_gen_3413) -> q_gen_3400
<b, cons, s>(q_gen_3411, q_gen_3415) -> q_gen_3400
<b, cons, s>(q_gen_3426, q_gen_3413) -> q_gen_3400
<b, cons, s>(q_gen_3426, q_gen_3422) -> q_gen_3400
<b, cons, z>(q_gen_3403, q_gen_3402) -> q_gen_3400
<b, cons, z>(q_gen_3403, q_gen_3415) -> q_gen_3400
<b, nil, z>() -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3415) -> q_gen_3409
<a, cons, s>(q_gen_3426, q_gen_3413) -> q_gen_3409
<a, cons, z>(q_gen_3403, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3405, q_gen_3413) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3415) -> q_gen_3409
}

Datatype: <elt, eltlist, nat>
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
(count([x, l1, _nn]) /\ count([x, cons(x, l1), _mn])) -> eq_nat([_mn, s(_nn)]) -> 24
(count([x, t1, _gn])) -> count([x, cons(x, t1), s(_gn)]) -> 22
(count([x, t1, _hn]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _hn]) -> 25
}
Sat witness: Found: ((count([x, t1, _hn]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _hn]), {
_hn -> z  ;  h1 -> b  ;  t1 -> cons(b, cons(b, nil))  ;  x -> a
})

-------------------------------------------
Step 23, which took 0.034650 s (model generation: 0.029083,  model checking: 0.005567):

Model:
|_
{
count -> 
{{{
Q={q_gen_3400, q_gen_3402, q_gen_3403, q_gen_3405, q_gen_3408, q_gen_3409, q_gen_3411, q_gen_3413, q_gen_3415, q_gen_3422, q_gen_3426, q_gen_3427},
Q_f={q_gen_3400},
Delta=
{
<cons>(q_gen_3403, q_gen_3413) -> q_gen_3402
<nil>() -> q_gen_3402
<a>() -> q_gen_3403
<b>() -> q_gen_3408
<cons>(q_gen_3408, q_gen_3402) -> q_gen_3413
<cons>(q_gen_3403, q_gen_3402) -> q_gen_3415
<cons>(q_gen_3403, q_gen_3415) -> q_gen_3415
<cons>(q_gen_3408, q_gen_3422) -> q_gen_3415
<cons>(q_gen_3408, q_gen_3413) -> q_gen_3422
<s>(q_gen_3427) -> q_gen_3427
<z>() -> q_gen_3427
<b, z>() -> q_gen_3405
<a, z>() -> q_gen_3411
<b, s>(q_gen_3427) -> q_gen_3426
<a, cons, s>(q_gen_3411, q_gen_3402) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3413) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3422) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3402) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3413) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3422) -> q_gen_3400
<a, nil, z>() -> q_gen_3400
<b, cons, s>(q_gen_3405, q_gen_3402) -> q_gen_3400
<b, cons, s>(q_gen_3405, q_gen_3415) -> q_gen_3400
<b, cons, s>(q_gen_3411, q_gen_3402) -> q_gen_3400
<b, cons, s>(q_gen_3411, q_gen_3413) -> q_gen_3400
<b, cons, s>(q_gen_3426, q_gen_3413) -> q_gen_3400
<b, cons, s>(q_gen_3426, q_gen_3422) -> q_gen_3400
<b, cons, z>(q_gen_3403, q_gen_3402) -> q_gen_3400
<b, cons, z>(q_gen_3403, q_gen_3415) -> q_gen_3400
<b, nil, z>() -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3415) -> q_gen_3409
<a, cons, s>(q_gen_3426, q_gen_3413) -> q_gen_3409
<a, cons, z>(q_gen_3403, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3405, q_gen_3413) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3415) -> q_gen_3409
}

Datatype: <elt, eltlist, nat>
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
(count([x, l1, _nn]) /\ count([x, cons(x, l1), _mn])) -> eq_nat([_mn, s(_nn)]) -> 24
(count([x, t1, _gn])) -> count([x, cons(x, t1), s(_gn)]) -> 25
(count([x, t1, _hn]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _hn]) -> 25
}
Sat witness: Found: ((count([x, t1, _gn])) -> count([x, cons(x, t1), s(_gn)]), {
_gn -> s(z)  ;  t1 -> cons(a, nil)  ;  x -> b
})

-------------------------------------------
Step 24, which took 0.039452 s (model generation: 0.034751,  model checking: 0.004701):

Model:
|_
{
count -> 
{{{
Q={q_gen_3400, q_gen_3402, q_gen_3403, q_gen_3405, q_gen_3408, q_gen_3409, q_gen_3411, q_gen_3413, q_gen_3415, q_gen_3422, q_gen_3426, q_gen_3427},
Q_f={q_gen_3400},
Delta=
{
<cons>(q_gen_3408, q_gen_3422) -> q_gen_3402
<nil>() -> q_gen_3402
<a>() -> q_gen_3403
<b>() -> q_gen_3408
<cons>(q_gen_3408, q_gen_3402) -> q_gen_3413
<cons>(q_gen_3403, q_gen_3402) -> q_gen_3415
<cons>(q_gen_3403, q_gen_3413) -> q_gen_3415
<cons>(q_gen_3403, q_gen_3415) -> q_gen_3415
<cons>(q_gen_3408, q_gen_3413) -> q_gen_3422
<s>(q_gen_3427) -> q_gen_3427
<z>() -> q_gen_3427
<b, z>() -> q_gen_3405
<a, z>() -> q_gen_3411
<b, s>(q_gen_3427) -> q_gen_3426
<a, cons, s>(q_gen_3411, q_gen_3402) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3413) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3422) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3402) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3413) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3422) -> q_gen_3400
<a, nil, z>() -> q_gen_3400
<b, cons, s>(q_gen_3405, q_gen_3402) -> q_gen_3400
<b, cons, s>(q_gen_3405, q_gen_3415) -> q_gen_3400
<b, cons, s>(q_gen_3411, q_gen_3413) -> q_gen_3400
<b, cons, s>(q_gen_3411, q_gen_3415) -> q_gen_3400
<b, cons, s>(q_gen_3426, q_gen_3413) -> q_gen_3400
<b, cons, s>(q_gen_3426, q_gen_3415) -> q_gen_3400
<b, cons, s>(q_gen_3426, q_gen_3422) -> q_gen_3400
<b, cons, z>(q_gen_3403, q_gen_3402) -> q_gen_3400
<b, cons, z>(q_gen_3403, q_gen_3415) -> q_gen_3400
<b, nil, z>() -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3415) -> q_gen_3409
<a, cons, s>(q_gen_3426, q_gen_3413) -> q_gen_3409
<a, cons, z>(q_gen_3403, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3405, q_gen_3413) -> q_gen_3409
<b, cons, s>(q_gen_3411, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3402) -> q_gen_3409
}

Datatype: <elt, eltlist, nat>
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
(count([x, l1, _nn]) /\ count([x, cons(x, l1), _mn])) -> eq_nat([_mn, s(_nn)]) -> 27
(count([x, t1, _gn])) -> count([x, cons(x, t1), s(_gn)]) -> 25
(count([x, t1, _hn]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _hn]) -> 25
}
Sat witness: Found: ((count([x, l1, _nn]) /\ count([x, cons(x, l1), _mn])) -> eq_nat([_mn, s(_nn)]), {
_mn -> s(s(z))  ;  _nn -> z  ;  l1 -> cons(a, nil)  ;  x -> b
})

-------------------------------------------
Step 25, which took 0.038999 s (model generation: 0.032323,  model checking: 0.006676):

Model:
|_
{
count -> 
{{{
Q={q_gen_3400, q_gen_3402, q_gen_3403, q_gen_3405, q_gen_3408, q_gen_3409, q_gen_3411, q_gen_3413, q_gen_3415, q_gen_3422, q_gen_3426, q_gen_3427},
Q_f={q_gen_3400},
Delta=
{
<nil>() -> q_gen_3402
<a>() -> q_gen_3403
<b>() -> q_gen_3408
<cons>(q_gen_3408, q_gen_3402) -> q_gen_3413
<cons>(q_gen_3403, q_gen_3402) -> q_gen_3415
<cons>(q_gen_3403, q_gen_3413) -> q_gen_3415
<cons>(q_gen_3403, q_gen_3415) -> q_gen_3415
<cons>(q_gen_3408, q_gen_3422) -> q_gen_3415
<cons>(q_gen_3408, q_gen_3413) -> q_gen_3422
<s>(q_gen_3427) -> q_gen_3427
<z>() -> q_gen_3427
<b, z>() -> q_gen_3405
<a, z>() -> q_gen_3411
<b, s>(q_gen_3427) -> q_gen_3426
<a, cons, s>(q_gen_3411, q_gen_3402) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3413) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3422) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3402) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3413) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3422) -> q_gen_3400
<a, nil, z>() -> q_gen_3400
<b, cons, s>(q_gen_3405, q_gen_3402) -> q_gen_3400
<b, cons, s>(q_gen_3405, q_gen_3415) -> q_gen_3400
<b, cons, s>(q_gen_3411, q_gen_3413) -> q_gen_3400
<b, cons, s>(q_gen_3411, q_gen_3415) -> q_gen_3400
<b, cons, s>(q_gen_3426, q_gen_3413) -> q_gen_3400
<b, cons, s>(q_gen_3426, q_gen_3422) -> q_gen_3400
<b, cons, z>(q_gen_3403, q_gen_3402) -> q_gen_3400
<b, cons, z>(q_gen_3403, q_gen_3415) -> q_gen_3400
<b, nil, z>() -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3415) -> q_gen_3409
<a, cons, s>(q_gen_3426, q_gen_3413) -> q_gen_3409
<a, cons, z>(q_gen_3403, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3405, q_gen_3413) -> q_gen_3409
<b, cons, s>(q_gen_3411, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3415) -> q_gen_3409
}

Datatype: <elt, eltlist, nat>
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
(count([x, l1, _nn]) /\ count([x, cons(x, l1), _mn])) -> eq_nat([_mn, s(_nn)]) -> 27
(count([x, t1, _gn])) -> count([x, cons(x, t1), s(_gn)]) -> 25
(count([x, t1, _hn]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _hn]) -> 28
}
Sat witness: Found: ((count([x, t1, _hn]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _hn]), {
_hn -> z  ;  h1 -> b  ;  t1 -> cons(b, cons(b, cons(b, nil)))  ;  x -> a
})

-------------------------------------------
Step 26, which took 0.038803 s (model generation: 0.035535,  model checking: 0.003268):

Model:
|_
{
count -> 
{{{
Q={q_gen_3400, q_gen_3402, q_gen_3403, q_gen_3405, q_gen_3408, q_gen_3409, q_gen_3411, q_gen_3413, q_gen_3415, q_gen_3422, q_gen_3426, q_gen_3427},
Q_f={q_gen_3400},
Delta=
{
<nil>() -> q_gen_3402
<a>() -> q_gen_3403
<b>() -> q_gen_3408
<cons>(q_gen_3408, q_gen_3402) -> q_gen_3413
<cons>(q_gen_3403, q_gen_3402) -> q_gen_3415
<cons>(q_gen_3403, q_gen_3413) -> q_gen_3415
<cons>(q_gen_3403, q_gen_3415) -> q_gen_3415
<cons>(q_gen_3408, q_gen_3422) -> q_gen_3415
<cons>(q_gen_3408, q_gen_3413) -> q_gen_3422
<s>(q_gen_3427) -> q_gen_3427
<z>() -> q_gen_3427
<b, z>() -> q_gen_3405
<a, z>() -> q_gen_3411
<b, s>(q_gen_3427) -> q_gen_3426
<a, cons, s>(q_gen_3411, q_gen_3402) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3413) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3422) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3402) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3413) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3415) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3422) -> q_gen_3400
<a, nil, z>() -> q_gen_3400
<b, cons, s>(q_gen_3405, q_gen_3402) -> q_gen_3400
<b, cons, s>(q_gen_3405, q_gen_3415) -> q_gen_3400
<b, cons, s>(q_gen_3411, q_gen_3413) -> q_gen_3400
<b, cons, s>(q_gen_3411, q_gen_3415) -> q_gen_3400
<b, cons, s>(q_gen_3426, q_gen_3413) -> q_gen_3400
<b, cons, s>(q_gen_3426, q_gen_3422) -> q_gen_3400
<b, cons, z>(q_gen_3403, q_gen_3402) -> q_gen_3400
<b, cons, z>(q_gen_3403, q_gen_3415) -> q_gen_3400
<b, nil, z>() -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3415) -> q_gen_3409
<a, cons, s>(q_gen_3426, q_gen_3413) -> q_gen_3409
<a, cons, z>(q_gen_3403, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3405, q_gen_3413) -> q_gen_3409
<b, cons, s>(q_gen_3411, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3415) -> q_gen_3409
}

Datatype: <elt, eltlist, nat>
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
(count([x, l1, _nn]) /\ count([x, cons(x, l1), _mn])) -> eq_nat([_mn, s(_nn)]) -> 27
(count([x, t1, _gn])) -> count([x, cons(x, t1), s(_gn)]) -> 28
(count([x, t1, _hn]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _hn]) -> 28
}
Sat witness: Found: ((count([x, t1, _gn])) -> count([x, cons(x, t1), s(_gn)]), {
_gn -> s(z)  ;  t1 -> cons(a, cons(a, nil))  ;  x -> b
})

-------------------------------------------
Step 27, which took 0.049076 s (model generation: 0.041982,  model checking: 0.007094):

Model:
|_
{
count -> 
{{{
Q={q_gen_3400, q_gen_3402, q_gen_3403, q_gen_3405, q_gen_3408, q_gen_3409, q_gen_3411, q_gen_3413, q_gen_3415, q_gen_3422, q_gen_3426, q_gen_3427},
Q_f={q_gen_3400},
Delta=
{
<nil>() -> q_gen_3402
<a>() -> q_gen_3403
<b>() -> q_gen_3408
<cons>(q_gen_3403, q_gen_3415) -> q_gen_3413
<cons>(q_gen_3408, q_gen_3402) -> q_gen_3413
<cons>(q_gen_3403, q_gen_3402) -> q_gen_3415
<cons>(q_gen_3408, q_gen_3422) -> q_gen_3415
<cons>(q_gen_3403, q_gen_3413) -> q_gen_3422
<cons>(q_gen_3408, q_gen_3413) -> q_gen_3422
<s>(q_gen_3427) -> q_gen_3427
<z>() -> q_gen_3427
<b, z>() -> q_gen_3405
<a, z>() -> q_gen_3411
<b, s>(q_gen_3427) -> q_gen_3426
<a, cons, s>(q_gen_3411, q_gen_3402) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3413) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3422) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3402) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3413) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3415) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3422) -> q_gen_3400
<a, nil, z>() -> q_gen_3400
<b, cons, s>(q_gen_3405, q_gen_3402) -> q_gen_3400
<b, cons, s>(q_gen_3405, q_gen_3415) -> q_gen_3400
<b, cons, s>(q_gen_3411, q_gen_3413) -> q_gen_3400
<b, cons, s>(q_gen_3411, q_gen_3415) -> q_gen_3400
<b, cons, s>(q_gen_3411, q_gen_3422) -> q_gen_3400
<b, cons, s>(q_gen_3426, q_gen_3413) -> q_gen_3400
<b, cons, s>(q_gen_3426, q_gen_3422) -> q_gen_3400
<b, cons, z>(q_gen_3403, q_gen_3402) -> q_gen_3400
<b, cons, z>(q_gen_3403, q_gen_3413) -> q_gen_3400
<b, cons, z>(q_gen_3403, q_gen_3415) -> q_gen_3400
<b, nil, z>() -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3415) -> q_gen_3409
<a, cons, s>(q_gen_3426, q_gen_3413) -> q_gen_3409
<a, cons, z>(q_gen_3403, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3405, q_gen_3413) -> q_gen_3409
<b, cons, s>(q_gen_3411, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3415) -> q_gen_3409
}

Datatype: <elt, eltlist, nat>
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
(count([x, l1, _nn]) /\ count([x, cons(x, l1), _mn])) -> eq_nat([_mn, s(_nn)]) -> 30
(count([x, t1, _gn])) -> count([x, cons(x, t1), s(_gn)]) -> 28
(count([x, t1, _hn]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _hn]) -> 28
}
Sat witness: Found: ((count([x, l1, _nn]) /\ count([x, cons(x, l1), _mn])) -> eq_nat([_mn, s(_nn)]), {
_mn -> s(s(z))  ;  _nn -> z  ;  l1 -> cons(a, cons(a, nil))  ;  x -> b
})

-------------------------------------------
Step 28, which took 0.046531 s (model generation: 0.039134,  model checking: 0.007397):

Model:
|_
{
count -> 
{{{
Q={q_gen_3400, q_gen_3402, q_gen_3403, q_gen_3405, q_gen_3408, q_gen_3409, q_gen_3411, q_gen_3413, q_gen_3415, q_gen_3422, q_gen_3426, q_gen_3427},
Q_f={q_gen_3400},
Delta=
{
<nil>() -> q_gen_3402
<a>() -> q_gen_3403
<b>() -> q_gen_3408
<cons>(q_gen_3403, q_gen_3413) -> q_gen_3413
<cons>(q_gen_3408, q_gen_3402) -> q_gen_3413
<cons>(q_gen_3403, q_gen_3402) -> q_gen_3415
<cons>(q_gen_3403, q_gen_3415) -> q_gen_3415
<cons>(q_gen_3408, q_gen_3422) -> q_gen_3415
<cons>(q_gen_3408, q_gen_3413) -> q_gen_3422
<s>(q_gen_3427) -> q_gen_3427
<z>() -> q_gen_3427
<b, z>() -> q_gen_3405
<a, z>() -> q_gen_3411
<b, s>(q_gen_3427) -> q_gen_3426
<a, cons, s>(q_gen_3411, q_gen_3402) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3413) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3422) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3402) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3413) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3415) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3422) -> q_gen_3400
<a, nil, z>() -> q_gen_3400
<b, cons, s>(q_gen_3405, q_gen_3402) -> q_gen_3400
<b, cons, s>(q_gen_3405, q_gen_3415) -> q_gen_3400
<b, cons, s>(q_gen_3411, q_gen_3413) -> q_gen_3400
<b, cons, s>(q_gen_3426, q_gen_3413) -> q_gen_3400
<b, cons, s>(q_gen_3426, q_gen_3422) -> q_gen_3400
<b, cons, z>(q_gen_3403, q_gen_3402) -> q_gen_3400
<b, cons, z>(q_gen_3403, q_gen_3415) -> q_gen_3400
<b, nil, z>() -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3415) -> q_gen_3409
<a, cons, s>(q_gen_3426, q_gen_3413) -> q_gen_3409
<a, cons, z>(q_gen_3403, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3405, q_gen_3413) -> q_gen_3409
<b, cons, s>(q_gen_3411, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3411, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3415) -> q_gen_3409
}

Datatype: <elt, eltlist, nat>
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
(count([x, l1, _nn]) /\ count([x, cons(x, l1), _mn])) -> eq_nat([_mn, s(_nn)]) -> 30
(count([x, t1, _gn])) -> count([x, cons(x, t1), s(_gn)]) -> 28
(count([x, t1, _hn]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _hn]) -> 31
}
Sat witness: Found: ((count([x, t1, _hn]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _hn]), {
_hn -> z  ;  h1 -> b  ;  t1 -> cons(b, cons(a, nil))  ;  x -> a
})

-------------------------------------------
Step 29, which took 0.050095 s (model generation: 0.046308,  model checking: 0.003787):

Model:
|_
{
count -> 
{{{
Q={q_gen_3400, q_gen_3402, q_gen_3403, q_gen_3405, q_gen_3408, q_gen_3409, q_gen_3411, q_gen_3413, q_gen_3415, q_gen_3422, q_gen_3426, q_gen_3427},
Q_f={q_gen_3400},
Delta=
{
<cons>(q_gen_3408, q_gen_3415) -> q_gen_3402
<nil>() -> q_gen_3402
<a>() -> q_gen_3403
<b>() -> q_gen_3408
<cons>(q_gen_3403, q_gen_3413) -> q_gen_3413
<cons>(q_gen_3408, q_gen_3402) -> q_gen_3413
<cons>(q_gen_3403, q_gen_3402) -> q_gen_3415
<cons>(q_gen_3403, q_gen_3415) -> q_gen_3415
<cons>(q_gen_3408, q_gen_3422) -> q_gen_3415
<cons>(q_gen_3408, q_gen_3413) -> q_gen_3422
<s>(q_gen_3427) -> q_gen_3427
<z>() -> q_gen_3427
<b, z>() -> q_gen_3405
<a, z>() -> q_gen_3411
<b, s>(q_gen_3427) -> q_gen_3426
<a, cons, s>(q_gen_3411, q_gen_3402) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3413) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3422) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3402) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3413) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3415) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3422) -> q_gen_3400
<a, nil, z>() -> q_gen_3400
<b, cons, s>(q_gen_3405, q_gen_3402) -> q_gen_3400
<b, cons, s>(q_gen_3405, q_gen_3415) -> q_gen_3400
<b, cons, s>(q_gen_3411, q_gen_3413) -> q_gen_3400
<b, cons, s>(q_gen_3426, q_gen_3413) -> q_gen_3400
<b, cons, s>(q_gen_3426, q_gen_3422) -> q_gen_3400
<b, cons, z>(q_gen_3403, q_gen_3402) -> q_gen_3400
<b, cons, z>(q_gen_3403, q_gen_3415) -> q_gen_3400
<b, nil, z>() -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3415) -> q_gen_3409
<a, cons, s>(q_gen_3426, q_gen_3413) -> q_gen_3409
<a, cons, z>(q_gen_3403, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3405, q_gen_3413) -> q_gen_3409
<b, cons, s>(q_gen_3411, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3411, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3415) -> q_gen_3409
}

Datatype: <elt, eltlist, nat>
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
(count([x, l1, _nn]) /\ count([x, cons(x, l1), _mn])) -> eq_nat([_mn, s(_nn)]) -> 30
(count([x, t1, _gn])) -> count([x, cons(x, t1), s(_gn)]) -> 31
(count([x, t1, _hn]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _hn]) -> 31
}
Sat witness: Found: ((count([x, t1, _gn])) -> count([x, cons(x, t1), s(_gn)]), {
_gn -> z  ;  t1 -> cons(b, cons(b, cons(b, nil)))  ;  x -> a
})

-------------------------------------------
Step 30, which took 0.057904 s (model generation: 0.047326,  model checking: 0.010578):

Model:
|_
{
count -> 
{{{
Q={q_gen_3400, q_gen_3402, q_gen_3403, q_gen_3405, q_gen_3408, q_gen_3409, q_gen_3411, q_gen_3413, q_gen_3415, q_gen_3422, q_gen_3426, q_gen_3427},
Q_f={q_gen_3400},
Delta=
{
<cons>(q_gen_3408, q_gen_3415) -> q_gen_3402
<cons>(q_gen_3408, q_gen_3422) -> q_gen_3402
<nil>() -> q_gen_3402
<a>() -> q_gen_3403
<b>() -> q_gen_3408
<cons>(q_gen_3403, q_gen_3413) -> q_gen_3413
<cons>(q_gen_3408, q_gen_3402) -> q_gen_3413
<cons>(q_gen_3403, q_gen_3402) -> q_gen_3415
<cons>(q_gen_3403, q_gen_3415) -> q_gen_3415
<cons>(q_gen_3408, q_gen_3413) -> q_gen_3422
<s>(q_gen_3427) -> q_gen_3427
<z>() -> q_gen_3427
<b, z>() -> q_gen_3405
<a, z>() -> q_gen_3411
<b, s>(q_gen_3427) -> q_gen_3426
<a, cons, s>(q_gen_3411, q_gen_3402) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3413) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3422) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3402) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3413) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3415) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3422) -> q_gen_3400
<a, nil, z>() -> q_gen_3400
<b, cons, s>(q_gen_3405, q_gen_3402) -> q_gen_3400
<b, cons, s>(q_gen_3405, q_gen_3415) -> q_gen_3400
<b, cons, s>(q_gen_3411, q_gen_3413) -> q_gen_3400
<b, cons, s>(q_gen_3426, q_gen_3413) -> q_gen_3400
<b, cons, s>(q_gen_3426, q_gen_3422) -> q_gen_3400
<b, cons, z>(q_gen_3403, q_gen_3402) -> q_gen_3400
<b, cons, z>(q_gen_3403, q_gen_3415) -> q_gen_3400
<b, nil, z>() -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3415) -> q_gen_3409
<a, cons, s>(q_gen_3426, q_gen_3413) -> q_gen_3409
<a, cons, z>(q_gen_3403, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3405, q_gen_3413) -> q_gen_3409
<b, cons, s>(q_gen_3411, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3411, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3415) -> q_gen_3409
}

Datatype: <elt, eltlist, nat>
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
(count([x, l1, _nn]) /\ count([x, cons(x, l1), _mn])) -> eq_nat([_mn, s(_nn)]) -> 33
(count([x, t1, _gn])) -> count([x, cons(x, t1), s(_gn)]) -> 31
(count([x, t1, _hn]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _hn]) -> 31
}
Sat witness: Found: ((count([x, l1, _nn]) /\ count([x, cons(x, l1), _mn])) -> eq_nat([_mn, s(_nn)]), {
_mn -> s(z)  ;  _nn -> s(z)  ;  l1 -> cons(b, cons(a, nil))  ;  x -> b
})

-------------------------------------------
Step 31, which took 0.062086 s (model generation: 0.051638,  model checking: 0.010448):

Model:
|_
{
count -> 
{{{
Q={q_gen_3400, q_gen_3402, q_gen_3403, q_gen_3405, q_gen_3408, q_gen_3409, q_gen_3411, q_gen_3413, q_gen_3415, q_gen_3422, q_gen_3426, q_gen_3427},
Q_f={q_gen_3400},
Delta=
{
<cons>(q_gen_3408, q_gen_3422) -> q_gen_3402
<nil>() -> q_gen_3402
<a>() -> q_gen_3403
<b>() -> q_gen_3408
<cons>(q_gen_3403, q_gen_3413) -> q_gen_3413
<cons>(q_gen_3408, q_gen_3402) -> q_gen_3413
<cons>(q_gen_3403, q_gen_3402) -> q_gen_3415
<cons>(q_gen_3403, q_gen_3415) -> q_gen_3415
<cons>(q_gen_3408, q_gen_3413) -> q_gen_3422
<cons>(q_gen_3408, q_gen_3415) -> q_gen_3422
<s>(q_gen_3427) -> q_gen_3427
<z>() -> q_gen_3427
<b, z>() -> q_gen_3405
<a, z>() -> q_gen_3411
<b, s>(q_gen_3427) -> q_gen_3426
<a, cons, s>(q_gen_3411, q_gen_3402) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3413) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3422) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3402) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3413) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3415) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3422) -> q_gen_3400
<a, nil, z>() -> q_gen_3400
<b, cons, s>(q_gen_3405, q_gen_3402) -> q_gen_3400
<b, cons, s>(q_gen_3405, q_gen_3415) -> q_gen_3400
<b, cons, s>(q_gen_3411, q_gen_3413) -> q_gen_3400
<b, cons, s>(q_gen_3426, q_gen_3413) -> q_gen_3400
<b, cons, s>(q_gen_3426, q_gen_3422) -> q_gen_3400
<b, cons, z>(q_gen_3403, q_gen_3402) -> q_gen_3400
<b, cons, z>(q_gen_3403, q_gen_3415) -> q_gen_3400
<b, nil, z>() -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3415) -> q_gen_3409
<a, cons, s>(q_gen_3426, q_gen_3413) -> q_gen_3409
<a, cons, z>(q_gen_3403, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3405, q_gen_3413) -> q_gen_3409
<b, cons, s>(q_gen_3405, q_gen_3422) -> q_gen_3409
<b, cons, s>(q_gen_3411, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3411, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3415) -> q_gen_3409
}

Datatype: <elt, eltlist, nat>
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
(count([x, l1, _nn]) /\ count([x, cons(x, l1), _mn])) -> eq_nat([_mn, s(_nn)]) -> 33
(count([x, t1, _gn])) -> count([x, cons(x, t1), s(_gn)]) -> 31
(count([x, t1, _hn]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _hn]) -> 34
}
Sat witness: Found: ((count([x, t1, _hn]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _hn]), {
_hn -> s(z)  ;  h1 -> b  ;  t1 -> cons(a, nil)  ;  x -> a
})

-------------------------------------------
Step 32, which took 0.069097 s (model generation: 0.063177,  model checking: 0.005920):

Model:
|_
{
count -> 
{{{
Q={q_gen_3400, q_gen_3402, q_gen_3403, q_gen_3405, q_gen_3408, q_gen_3409, q_gen_3411, q_gen_3413, q_gen_3415, q_gen_3422, q_gen_3426, q_gen_3427},
Q_f={q_gen_3400},
Delta=
{
<cons>(q_gen_3408, q_gen_3422) -> q_gen_3402
<nil>() -> q_gen_3402
<a>() -> q_gen_3403
<b>() -> q_gen_3408
<cons>(q_gen_3403, q_gen_3413) -> q_gen_3413
<cons>(q_gen_3408, q_gen_3402) -> q_gen_3413
<cons>(q_gen_3403, q_gen_3402) -> q_gen_3415
<cons>(q_gen_3403, q_gen_3415) -> q_gen_3415
<cons>(q_gen_3408, q_gen_3413) -> q_gen_3422
<cons>(q_gen_3408, q_gen_3415) -> q_gen_3422
<s>(q_gen_3427) -> q_gen_3427
<z>() -> q_gen_3427
<b, z>() -> q_gen_3405
<a, z>() -> q_gen_3411
<b, s>(q_gen_3427) -> q_gen_3426
<a, cons, s>(q_gen_3405, q_gen_3415) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3402) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3413) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3422) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3402) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3413) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3415) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3422) -> q_gen_3400
<a, nil, z>() -> q_gen_3400
<b, cons, s>(q_gen_3405, q_gen_3402) -> q_gen_3400
<b, cons, s>(q_gen_3405, q_gen_3415) -> q_gen_3400
<b, cons, s>(q_gen_3411, q_gen_3413) -> q_gen_3400
<b, cons, s>(q_gen_3426, q_gen_3413) -> q_gen_3400
<b, cons, s>(q_gen_3426, q_gen_3422) -> q_gen_3400
<b, cons, z>(q_gen_3403, q_gen_3402) -> q_gen_3400
<b, cons, z>(q_gen_3403, q_gen_3415) -> q_gen_3400
<b, nil, z>() -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3415) -> q_gen_3409
<a, cons, s>(q_gen_3426, q_gen_3413) -> q_gen_3409
<a, cons, z>(q_gen_3403, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3405, q_gen_3413) -> q_gen_3409
<b, cons, s>(q_gen_3405, q_gen_3422) -> q_gen_3409
<b, cons, s>(q_gen_3411, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3411, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3415) -> q_gen_3409
}

Datatype: <elt, eltlist, nat>
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
(count([x, l1, _nn]) /\ count([x, cons(x, l1), _mn])) -> eq_nat([_mn, s(_nn)]) -> 33
(count([x, t1, _gn])) -> count([x, cons(x, t1), s(_gn)]) -> 34
(count([x, t1, _hn]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _hn]) -> 34
}
Sat witness: Found: ((count([x, t1, _gn])) -> count([x, cons(x, t1), s(_gn)]), {
_gn -> s(s(z))  ;  t1 -> cons(b, cons(b, cons(a, nil)))  ;  x -> b
})

-------------------------------------------
Step 33, which took 0.072052 s (model generation: 0.061375,  model checking: 0.010677):

Model:
|_
{
count -> 
{{{
Q={q_gen_3400, q_gen_3402, q_gen_3403, q_gen_3405, q_gen_3408, q_gen_3409, q_gen_3411, q_gen_3413, q_gen_3415, q_gen_3422, q_gen_3426, q_gen_3427},
Q_f={q_gen_3400},
Delta=
{
<cons>(q_gen_3408, q_gen_3422) -> q_gen_3402
<nil>() -> q_gen_3402
<a>() -> q_gen_3403
<b>() -> q_gen_3408
<cons>(q_gen_3403, q_gen_3413) -> q_gen_3413
<cons>(q_gen_3408, q_gen_3402) -> q_gen_3413
<cons>(q_gen_3408, q_gen_3415) -> q_gen_3413
<cons>(q_gen_3403, q_gen_3402) -> q_gen_3415
<cons>(q_gen_3403, q_gen_3415) -> q_gen_3415
<cons>(q_gen_3408, q_gen_3413) -> q_gen_3422
<s>(q_gen_3427) -> q_gen_3427
<z>() -> q_gen_3427
<b, z>() -> q_gen_3405
<a, z>() -> q_gen_3411
<b, s>(q_gen_3427) -> q_gen_3426
<a, cons, s>(q_gen_3405, q_gen_3415) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3402) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3413) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3422) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3402) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3413) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3415) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3422) -> q_gen_3400
<a, nil, z>() -> q_gen_3400
<b, cons, s>(q_gen_3405, q_gen_3402) -> q_gen_3400
<b, cons, s>(q_gen_3405, q_gen_3415) -> q_gen_3400
<b, cons, s>(q_gen_3411, q_gen_3413) -> q_gen_3400
<b, cons, s>(q_gen_3426, q_gen_3413) -> q_gen_3400
<b, cons, s>(q_gen_3426, q_gen_3422) -> q_gen_3400
<b, cons, z>(q_gen_3403, q_gen_3402) -> q_gen_3400
<b, cons, z>(q_gen_3403, q_gen_3415) -> q_gen_3400
<b, nil, z>() -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3415) -> q_gen_3409
<a, cons, s>(q_gen_3426, q_gen_3413) -> q_gen_3409
<a, cons, z>(q_gen_3403, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3405, q_gen_3413) -> q_gen_3409
<b, cons, s>(q_gen_3411, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3411, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3415) -> q_gen_3409
}

Datatype: <elt, eltlist, nat>
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
(count([x, l1, _nn]) /\ count([x, cons(x, l1), _mn])) -> eq_nat([_mn, s(_nn)]) -> 36
(count([x, t1, _gn])) -> count([x, cons(x, t1), s(_gn)]) -> 34
(count([x, t1, _hn]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _hn]) -> 34
}
Sat witness: Found: ((count([x, l1, _nn]) /\ count([x, cons(x, l1), _mn])) -> eq_nat([_mn, s(_nn)]), {
_mn -> s(s(s(z)))  ;  _nn -> s(z)  ;  l1 -> cons(a, cons(b, cons(a, nil)))  ;  x -> b
})

-------------------------------------------
Step 34, which took 0.076043 s (model generation: 0.069394,  model checking: 0.006649):

Model:
|_
{
count -> 
{{{
Q={q_gen_3400, q_gen_3402, q_gen_3403, q_gen_3405, q_gen_3408, q_gen_3409, q_gen_3411, q_gen_3413, q_gen_3415, q_gen_3422, q_gen_3426, q_gen_3427, q_gen_3430},
Q_f={q_gen_3400},
Delta=
{
<cons>(q_gen_3403, q_gen_3430) -> q_gen_3402
<nil>() -> q_gen_3402
<a>() -> q_gen_3403
<b>() -> q_gen_3408
<cons>(q_gen_3403, q_gen_3413) -> q_gen_3413
<cons>(q_gen_3408, q_gen_3402) -> q_gen_3413
<cons>(q_gen_3403, q_gen_3402) -> q_gen_3415
<cons>(q_gen_3403, q_gen_3415) -> q_gen_3415
<cons>(q_gen_3408, q_gen_3430) -> q_gen_3415
<cons>(q_gen_3408, q_gen_3413) -> q_gen_3422
<s>(q_gen_3427) -> q_gen_3427
<z>() -> q_gen_3427
<cons>(q_gen_3408, q_gen_3415) -> q_gen_3430
<cons>(q_gen_3408, q_gen_3422) -> q_gen_3430
<b, z>() -> q_gen_3405
<a, z>() -> q_gen_3411
<b, s>(q_gen_3427) -> q_gen_3426
<a, cons, s>(q_gen_3405, q_gen_3415) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3402) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3413) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3422) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3430) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3402) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3413) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3422) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3430) -> q_gen_3400
<a, nil, z>() -> q_gen_3400
<b, cons, s>(q_gen_3405, q_gen_3402) -> q_gen_3400
<b, cons, s>(q_gen_3405, q_gen_3415) -> q_gen_3400
<b, cons, s>(q_gen_3411, q_gen_3413) -> q_gen_3400
<b, cons, s>(q_gen_3426, q_gen_3413) -> q_gen_3400
<b, cons, s>(q_gen_3426, q_gen_3422) -> q_gen_3400
<b, cons, z>(q_gen_3403, q_gen_3402) -> q_gen_3400
<b, cons, z>(q_gen_3403, q_gen_3415) -> q_gen_3400
<b, nil, z>() -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3415) -> q_gen_3409
<a, cons, s>(q_gen_3426, q_gen_3413) -> q_gen_3409
<a, cons, z>(q_gen_3403, q_gen_3402) -> q_gen_3409
<a, cons, z>(q_gen_3408, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3405, q_gen_3413) -> q_gen_3409
<b, cons, s>(q_gen_3405, q_gen_3430) -> q_gen_3409
<b, cons, s>(q_gen_3411, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3411, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3411, q_gen_3430) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3430) -> q_gen_3409
}

Datatype: <elt, eltlist, nat>
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
(count([x, l1, _nn]) /\ count([x, cons(x, l1), _mn])) -> eq_nat([_mn, s(_nn)]) -> 36
(count([x, t1, _gn])) -> count([x, cons(x, t1), s(_gn)]) -> 34
(count([x, t1, _hn]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _hn]) -> 37
}
Sat witness: Found: ((count([x, t1, _hn]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _hn]), {
_hn -> z  ;  h1 -> b  ;  t1 -> cons(b, cons(b, cons(a, nil)))  ;  x -> a
})

-------------------------------------------
Step 35, which took 0.077940 s (model generation: 0.074597,  model checking: 0.003343):

Model:
|_
{
count -> 
{{{
Q={q_gen_3400, q_gen_3402, q_gen_3403, q_gen_3405, q_gen_3408, q_gen_3409, q_gen_3411, q_gen_3413, q_gen_3415, q_gen_3422, q_gen_3424, q_gen_3426, q_gen_3427},
Q_f={q_gen_3400},
Delta=
{
<cons>(q_gen_3408, q_gen_3422) -> q_gen_3402
<cons>(q_gen_3408, q_gen_3424) -> q_gen_3402
<nil>() -> q_gen_3402
<a>() -> q_gen_3403
<b>() -> q_gen_3408
<cons>(q_gen_3403, q_gen_3413) -> q_gen_3413
<cons>(q_gen_3408, q_gen_3402) -> q_gen_3413
<cons>(q_gen_3403, q_gen_3402) -> q_gen_3415
<cons>(q_gen_3403, q_gen_3424) -> q_gen_3415
<cons>(q_gen_3408, q_gen_3413) -> q_gen_3422
<cons>(q_gen_3403, q_gen_3415) -> q_gen_3424
<cons>(q_gen_3408, q_gen_3415) -> q_gen_3424
<s>(q_gen_3427) -> q_gen_3427
<z>() -> q_gen_3427
<b, z>() -> q_gen_3405
<a, z>() -> q_gen_3411
<b, s>(q_gen_3427) -> q_gen_3426
<a, cons, s>(q_gen_3405, q_gen_3415) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3402) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3413) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3422) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3402) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3413) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3422) -> q_gen_3400
<a, nil, z>() -> q_gen_3400
<b, cons, s>(q_gen_3405, q_gen_3402) -> q_gen_3400
<b, cons, s>(q_gen_3405, q_gen_3415) -> q_gen_3400
<b, cons, s>(q_gen_3411, q_gen_3413) -> q_gen_3400
<b, cons, s>(q_gen_3426, q_gen_3413) -> q_gen_3400
<b, cons, s>(q_gen_3426, q_gen_3422) -> q_gen_3400
<b, cons, z>(q_gen_3403, q_gen_3402) -> q_gen_3400
<b, cons, z>(q_gen_3403, q_gen_3415) -> q_gen_3400
<b, cons, z>(q_gen_3403, q_gen_3424) -> q_gen_3400
<b, nil, z>() -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3415) -> q_gen_3409
<a, cons, s>(q_gen_3426, q_gen_3413) -> q_gen_3409
<a, cons, z>(q_gen_3403, q_gen_3402) -> q_gen_3409
<a, cons, z>(q_gen_3408, q_gen_3415) -> q_gen_3409
<a, cons, z>(q_gen_3408, q_gen_3424) -> q_gen_3409
<b, cons, s>(q_gen_3405, q_gen_3413) -> q_gen_3409
<b, cons, s>(q_gen_3405, q_gen_3424) -> q_gen_3409
<b, cons, s>(q_gen_3411, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3411, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3411, q_gen_3424) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3424) -> q_gen_3409
}

Datatype: <elt, eltlist, nat>
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
(count([x, l1, _nn]) /\ count([x, cons(x, l1), _mn])) -> eq_nat([_mn, s(_nn)]) -> 36
(count([x, t1, _gn])) -> count([x, cons(x, t1), s(_gn)]) -> 37
(count([x, t1, _hn]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _hn]) -> 37
}
Sat witness: Found: ((count([x, t1, _gn])) -> count([x, cons(x, t1), s(_gn)]), {
_gn -> z  ;  t1 -> cons(a, cons(a, nil))  ;  x -> b
})

-------------------------------------------
Step 36, which took 0.094651 s (model generation: 0.077608,  model checking: 0.017043):

Model:
|_
{
count -> 
{{{
Q={q_gen_3400, q_gen_3402, q_gen_3403, q_gen_3405, q_gen_3408, q_gen_3409, q_gen_3411, q_gen_3413, q_gen_3415, q_gen_3422, q_gen_3426, q_gen_3427, q_gen_3446},
Q_f={q_gen_3400},
Delta=
{
<cons>(q_gen_3408, q_gen_3422) -> q_gen_3402
<cons>(q_gen_3408, q_gen_3446) -> q_gen_3402
<nil>() -> q_gen_3402
<a>() -> q_gen_3403
<b>() -> q_gen_3408
<cons>(q_gen_3408, q_gen_3402) -> q_gen_3413
<cons>(q_gen_3403, q_gen_3402) -> q_gen_3415
<cons>(q_gen_3403, q_gen_3415) -> q_gen_3415
<cons>(q_gen_3403, q_gen_3446) -> q_gen_3415
<cons>(q_gen_3403, q_gen_3413) -> q_gen_3422
<cons>(q_gen_3408, q_gen_3413) -> q_gen_3422
<s>(q_gen_3427) -> q_gen_3427
<z>() -> q_gen_3427
<cons>(q_gen_3408, q_gen_3415) -> q_gen_3446
<b, z>() -> q_gen_3405
<a, z>() -> q_gen_3411
<b, s>(q_gen_3427) -> q_gen_3426
<a, cons, s>(q_gen_3405, q_gen_3415) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3402) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3413) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3422) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3402) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3413) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3422) -> q_gen_3400
<a, nil, z>() -> q_gen_3400
<b, cons, s>(q_gen_3405, q_gen_3402) -> q_gen_3400
<b, cons, s>(q_gen_3405, q_gen_3415) -> q_gen_3400
<b, cons, s>(q_gen_3411, q_gen_3413) -> q_gen_3400
<b, cons, s>(q_gen_3411, q_gen_3422) -> q_gen_3400
<b, cons, s>(q_gen_3426, q_gen_3413) -> q_gen_3400
<b, cons, s>(q_gen_3426, q_gen_3422) -> q_gen_3400
<b, cons, z>(q_gen_3403, q_gen_3402) -> q_gen_3400
<b, cons, z>(q_gen_3403, q_gen_3415) -> q_gen_3400
<b, nil, z>() -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3415) -> q_gen_3409
<a, cons, s>(q_gen_3426, q_gen_3413) -> q_gen_3409
<a, cons, z>(q_gen_3403, q_gen_3402) -> q_gen_3409
<a, cons, z>(q_gen_3408, q_gen_3415) -> q_gen_3409
<a, cons, z>(q_gen_3408, q_gen_3446) -> q_gen_3409
<b, cons, s>(q_gen_3405, q_gen_3413) -> q_gen_3409
<b, cons, s>(q_gen_3405, q_gen_3446) -> q_gen_3409
<b, cons, s>(q_gen_3411, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3411, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3411, q_gen_3446) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3446) -> q_gen_3409
}

Datatype: <elt, eltlist, nat>
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
(count([x, l1, _nn]) /\ count([x, cons(x, l1), _mn])) -> eq_nat([_mn, s(_nn)]) -> 39
(count([x, t1, _gn])) -> count([x, cons(x, t1), s(_gn)]) -> 37
(count([x, t1, _hn]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _hn]) -> 37
}
Sat witness: Found: ((count([x, l1, _nn]) /\ count([x, cons(x, l1), _mn])) -> eq_nat([_mn, s(_nn)]), {
_mn -> s(z)  ;  _nn -> s(s(z))  ;  l1 -> cons(b, cons(a, cons(b, nil)))  ;  x -> b
})

-------------------------------------------
Step 37, which took 0.103964 s (model generation: 0.098746,  model checking: 0.005218):

Model:
|_
{
count -> 
{{{
Q={q_gen_3400, q_gen_3402, q_gen_3403, q_gen_3405, q_gen_3408, q_gen_3409, q_gen_3411, q_gen_3413, q_gen_3415, q_gen_3422, q_gen_3426, q_gen_3427, q_gen_3430},
Q_f={q_gen_3400},
Delta=
{
<cons>(q_gen_3408, q_gen_3430) -> q_gen_3402
<nil>() -> q_gen_3402
<a>() -> q_gen_3403
<b>() -> q_gen_3408
<cons>(q_gen_3408, q_gen_3402) -> q_gen_3413
<cons>(q_gen_3403, q_gen_3402) -> q_gen_3415
<cons>(q_gen_3403, q_gen_3415) -> q_gen_3415
<cons>(q_gen_3403, q_gen_3430) -> q_gen_3415
<cons>(q_gen_3403, q_gen_3413) -> q_gen_3422
<cons>(q_gen_3408, q_gen_3413) -> q_gen_3422
<s>(q_gen_3427) -> q_gen_3427
<z>() -> q_gen_3427
<cons>(q_gen_3408, q_gen_3415) -> q_gen_3430
<cons>(q_gen_3408, q_gen_3422) -> q_gen_3430
<b, z>() -> q_gen_3405
<a, z>() -> q_gen_3411
<b, s>(q_gen_3427) -> q_gen_3426
<a, cons, s>(q_gen_3405, q_gen_3415) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3402) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3413) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3422) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3430) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3402) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3413) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3422) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3430) -> q_gen_3400
<a, nil, z>() -> q_gen_3400
<b, cons, s>(q_gen_3405, q_gen_3402) -> q_gen_3400
<b, cons, s>(q_gen_3405, q_gen_3415) -> q_gen_3400
<b, cons, s>(q_gen_3411, q_gen_3413) -> q_gen_3400
<b, cons, s>(q_gen_3411, q_gen_3422) -> q_gen_3400
<b, cons, s>(q_gen_3426, q_gen_3413) -> q_gen_3400
<b, cons, s>(q_gen_3426, q_gen_3422) -> q_gen_3400
<b, cons, z>(q_gen_3403, q_gen_3402) -> q_gen_3400
<b, cons, z>(q_gen_3403, q_gen_3415) -> q_gen_3400
<b, nil, z>() -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3415) -> q_gen_3409
<a, cons, s>(q_gen_3426, q_gen_3413) -> q_gen_3409
<a, cons, z>(q_gen_3403, q_gen_3402) -> q_gen_3409
<a, cons, z>(q_gen_3408, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3405, q_gen_3413) -> q_gen_3409
<b, cons, s>(q_gen_3405, q_gen_3430) -> q_gen_3409
<b, cons, s>(q_gen_3411, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3411, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3411, q_gen_3430) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3430) -> q_gen_3409
}

Datatype: <elt, eltlist, nat>
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
(count([x, l1, _nn]) /\ count([x, cons(x, l1), _mn])) -> eq_nat([_mn, s(_nn)]) -> 39
(count([x, t1, _gn])) -> count([x, cons(x, t1), s(_gn)]) -> 37
(count([x, t1, _hn]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _hn]) -> 40
}
Sat witness: Found: ((count([x, t1, _hn]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _hn]), {
_hn -> s(z)  ;  h1 -> a  ;  t1 -> cons(b, cons(a, nil))  ;  x -> b
})

-------------------------------------------
Step 38, which took 0.097474 s (model generation: 0.091594,  model checking: 0.005880):

Model:
|_
{
count -> 
{{{
Q={q_gen_3400, q_gen_3402, q_gen_3403, q_gen_3405, q_gen_3408, q_gen_3409, q_gen_3411, q_gen_3413, q_gen_3415, q_gen_3422, q_gen_3426, q_gen_3427, q_gen_3433},
Q_f={q_gen_3400},
Delta=
{
<cons>(q_gen_3403, q_gen_3433) -> q_gen_3402
<cons>(q_gen_3408, q_gen_3422) -> q_gen_3402
<nil>() -> q_gen_3402
<a>() -> q_gen_3403
<b>() -> q_gen_3408
<cons>(q_gen_3408, q_gen_3402) -> q_gen_3413
<cons>(q_gen_3403, q_gen_3402) -> q_gen_3415
<cons>(q_gen_3403, q_gen_3415) -> q_gen_3415
<cons>(q_gen_3408, q_gen_3413) -> q_gen_3422
<cons>(q_gen_3408, q_gen_3433) -> q_gen_3422
<s>(q_gen_3427) -> q_gen_3427
<z>() -> q_gen_3427
<cons>(q_gen_3403, q_gen_3413) -> q_gen_3433
<cons>(q_gen_3408, q_gen_3415) -> q_gen_3433
<b, z>() -> q_gen_3405
<a, z>() -> q_gen_3411
<b, s>(q_gen_3427) -> q_gen_3426
<a, cons, s>(q_gen_3405, q_gen_3415) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3402) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3413) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3422) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3402) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3413) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3422) -> q_gen_3400
<a, nil, z>() -> q_gen_3400
<b, cons, s>(q_gen_3405, q_gen_3402) -> q_gen_3400
<b, cons, s>(q_gen_3405, q_gen_3415) -> q_gen_3400
<b, cons, s>(q_gen_3411, q_gen_3413) -> q_gen_3400
<b, cons, s>(q_gen_3411, q_gen_3433) -> q_gen_3400
<b, cons, s>(q_gen_3426, q_gen_3413) -> q_gen_3400
<b, cons, s>(q_gen_3426, q_gen_3422) -> q_gen_3400
<b, cons, z>(q_gen_3403, q_gen_3402) -> q_gen_3400
<b, cons, z>(q_gen_3403, q_gen_3415) -> q_gen_3400
<b, nil, z>() -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3415) -> q_gen_3409
<a, cons, s>(q_gen_3426, q_gen_3413) -> q_gen_3409
<a, cons, z>(q_gen_3403, q_gen_3402) -> q_gen_3409
<a, cons, z>(q_gen_3408, q_gen_3415) -> q_gen_3409
<a, cons, z>(q_gen_3408, q_gen_3433) -> q_gen_3409
<b, cons, s>(q_gen_3405, q_gen_3413) -> q_gen_3409
<b, cons, s>(q_gen_3405, q_gen_3422) -> q_gen_3409
<b, cons, s>(q_gen_3405, q_gen_3433) -> q_gen_3409
<b, cons, s>(q_gen_3411, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3411, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3433) -> q_gen_3409
}

Datatype: <elt, eltlist, nat>
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
(count([x, l1, _nn]) /\ count([x, cons(x, l1), _mn])) -> eq_nat([_mn, s(_nn)]) -> 39
(count([x, t1, _gn])) -> count([x, cons(x, t1), s(_gn)]) -> 40
(count([x, t1, _hn]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _hn]) -> 40
}
Sat witness: Found: ((count([x, t1, _gn])) -> count([x, cons(x, t1), s(_gn)]), {
_gn -> s(z)  ;  t1 -> cons(b, cons(a, nil))  ;  x -> b
})

-------------------------------------------
Step 39, which took 0.112113 s (model generation: 0.090252,  model checking: 0.021861):

Model:
|_
{
count -> 
{{{
Q={q_gen_3400, q_gen_3402, q_gen_3403, q_gen_3405, q_gen_3408, q_gen_3409, q_gen_3411, q_gen_3413, q_gen_3415, q_gen_3422, q_gen_3424, q_gen_3426, q_gen_3427},
Q_f={q_gen_3400},
Delta=
{
<nil>() -> q_gen_3402
<a>() -> q_gen_3403
<b>() -> q_gen_3408
<cons>(q_gen_3408, q_gen_3402) -> q_gen_3413
<cons>(q_gen_3408, q_gen_3415) -> q_gen_3413
<cons>(q_gen_3408, q_gen_3424) -> q_gen_3413
<cons>(q_gen_3403, q_gen_3402) -> q_gen_3415
<cons>(q_gen_3408, q_gen_3413) -> q_gen_3422
<cons>(q_gen_3403, q_gen_3413) -> q_gen_3424
<cons>(q_gen_3403, q_gen_3415) -> q_gen_3424
<cons>(q_gen_3408, q_gen_3422) -> q_gen_3424
<s>(q_gen_3427) -> q_gen_3427
<z>() -> q_gen_3427
<b, z>() -> q_gen_3405
<a, z>() -> q_gen_3411
<b, s>(q_gen_3427) -> q_gen_3426
<a, cons, s>(q_gen_3405, q_gen_3415) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3402) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3413) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3422) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3424) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3402) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3413) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3415) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3422) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3424) -> q_gen_3400
<a, nil, z>() -> q_gen_3400
<b, cons, s>(q_gen_3405, q_gen_3402) -> q_gen_3400
<b, cons, s>(q_gen_3405, q_gen_3415) -> q_gen_3400
<b, cons, s>(q_gen_3405, q_gen_3424) -> q_gen_3400
<b, cons, s>(q_gen_3411, q_gen_3413) -> q_gen_3400
<b, cons, s>(q_gen_3411, q_gen_3424) -> q_gen_3400
<b, cons, s>(q_gen_3426, q_gen_3413) -> q_gen_3400
<b, cons, s>(q_gen_3426, q_gen_3422) -> q_gen_3400
<b, cons, z>(q_gen_3403, q_gen_3402) -> q_gen_3400
<b, cons, z>(q_gen_3403, q_gen_3415) -> q_gen_3400
<b, cons, z>(q_gen_3403, q_gen_3424) -> q_gen_3400
<b, nil, z>() -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3415) -> q_gen_3409
<a, cons, s>(q_gen_3426, q_gen_3413) -> q_gen_3409
<a, cons, z>(q_gen_3403, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3405, q_gen_3413) -> q_gen_3409
<b, cons, s>(q_gen_3411, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3411, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3424) -> q_gen_3409
}

Datatype: <elt, eltlist, nat>
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
(count([x, l1, _nn]) /\ count([x, cons(x, l1), _mn])) -> eq_nat([_mn, s(_nn)]) -> 42
(count([x, t1, _gn])) -> count([x, cons(x, t1), s(_gn)]) -> 40
(count([x, t1, _hn]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _hn]) -> 40
}
Sat witness: Found: ((count([x, l1, _nn]) /\ count([x, cons(x, l1), _mn])) -> eq_nat([_mn, s(_nn)]), {
_mn -> s(z)  ;  _nn -> s(z)  ;  l1 -> cons(a, cons(b, cons(a, nil)))  ;  x -> a
})

-------------------------------------------
Step 40, which took 0.114207 s (model generation: 0.100216,  model checking: 0.013991):

Model:
|_
{
count -> 
{{{
Q={q_gen_3400, q_gen_3402, q_gen_3403, q_gen_3405, q_gen_3408, q_gen_3409, q_gen_3411, q_gen_3413, q_gen_3415, q_gen_3422, q_gen_3424, q_gen_3426, q_gen_3427},
Q_f={q_gen_3400},
Delta=
{
<cons>(q_gen_3408, q_gen_3422) -> q_gen_3402
<nil>() -> q_gen_3402
<a>() -> q_gen_3403
<b>() -> q_gen_3408
<cons>(q_gen_3408, q_gen_3402) -> q_gen_3413
<cons>(q_gen_3408, q_gen_3415) -> q_gen_3413
<cons>(q_gen_3408, q_gen_3424) -> q_gen_3413
<cons>(q_gen_3403, q_gen_3402) -> q_gen_3415
<cons>(q_gen_3408, q_gen_3413) -> q_gen_3422
<cons>(q_gen_3403, q_gen_3413) -> q_gen_3424
<cons>(q_gen_3403, q_gen_3415) -> q_gen_3424
<s>(q_gen_3427) -> q_gen_3427
<z>() -> q_gen_3427
<b, z>() -> q_gen_3405
<a, z>() -> q_gen_3411
<b, s>(q_gen_3427) -> q_gen_3426
<a, cons, s>(q_gen_3405, q_gen_3415) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3402) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3413) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3422) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3402) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3413) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3415) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3422) -> q_gen_3400
<a, nil, z>() -> q_gen_3400
<b, cons, s>(q_gen_3405, q_gen_3402) -> q_gen_3400
<b, cons, s>(q_gen_3405, q_gen_3415) -> q_gen_3400
<b, cons, s>(q_gen_3405, q_gen_3424) -> q_gen_3400
<b, cons, s>(q_gen_3411, q_gen_3413) -> q_gen_3400
<b, cons, s>(q_gen_3411, q_gen_3424) -> q_gen_3400
<b, cons, s>(q_gen_3426, q_gen_3413) -> q_gen_3400
<b, cons, s>(q_gen_3426, q_gen_3422) -> q_gen_3400
<b, cons, z>(q_gen_3403, q_gen_3402) -> q_gen_3400
<b, cons, z>(q_gen_3403, q_gen_3415) -> q_gen_3400
<b, cons, z>(q_gen_3403, q_gen_3424) -> q_gen_3400
<b, nil, z>() -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3415) -> q_gen_3409
<a, cons, s>(q_gen_3411, q_gen_3424) -> q_gen_3409
<a, cons, s>(q_gen_3426, q_gen_3413) -> q_gen_3409
<a, cons, z>(q_gen_3403, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3405, q_gen_3413) -> q_gen_3409
<b, cons, s>(q_gen_3411, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3411, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3424) -> q_gen_3409
}

Datatype: <elt, eltlist, nat>
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
(count([x, l1, _nn]) /\ count([x, cons(x, l1), _mn])) -> eq_nat([_mn, s(_nn)]) -> 42
(count([x, t1, _gn])) -> count([x, cons(x, t1), s(_gn)]) -> 40
(count([x, t1, _hn]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _hn]) -> 43
}
Sat witness: Found: ((count([x, t1, _hn]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _hn]), {
_hn -> z  ;  h1 -> a  ;  t1 -> cons(a, cons(a, cons(b, nil)))  ;  x -> b
})

-------------------------------------------
Step 41, which took 0.121917 s (model generation: 0.115381,  model checking: 0.006536):

Model:
|_
{
count -> 
{{{
Q={q_gen_3400, q_gen_3402, q_gen_3403, q_gen_3405, q_gen_3408, q_gen_3409, q_gen_3411, q_gen_3413, q_gen_3415, q_gen_3422, q_gen_3426, q_gen_3427, q_gen_3433},
Q_f={q_gen_3400},
Delta=
{
<cons>(q_gen_3408, q_gen_3422) -> q_gen_3402
<nil>() -> q_gen_3402
<a>() -> q_gen_3403
<b>() -> q_gen_3408
<cons>(q_gen_3408, q_gen_3402) -> q_gen_3413
<cons>(q_gen_3403, q_gen_3402) -> q_gen_3415
<cons>(q_gen_3403, q_gen_3415) -> q_gen_3415
<cons>(q_gen_3403, q_gen_3433) -> q_gen_3415
<cons>(q_gen_3408, q_gen_3413) -> q_gen_3422
<s>(q_gen_3427) -> q_gen_3427
<z>() -> q_gen_3427
<cons>(q_gen_3403, q_gen_3413) -> q_gen_3433
<cons>(q_gen_3408, q_gen_3415) -> q_gen_3433
<cons>(q_gen_3408, q_gen_3433) -> q_gen_3433
<b, z>() -> q_gen_3405
<a, z>() -> q_gen_3411
<b, s>(q_gen_3427) -> q_gen_3426
<a, cons, s>(q_gen_3405, q_gen_3415) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3402) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3413) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3422) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3402) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3413) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3422) -> q_gen_3400
<a, nil, z>() -> q_gen_3400
<b, cons, s>(q_gen_3405, q_gen_3402) -> q_gen_3400
<b, cons, s>(q_gen_3405, q_gen_3415) -> q_gen_3400
<b, cons, s>(q_gen_3411, q_gen_3413) -> q_gen_3400
<b, cons, s>(q_gen_3411, q_gen_3433) -> q_gen_3400
<b, cons, s>(q_gen_3426, q_gen_3413) -> q_gen_3400
<b, cons, s>(q_gen_3426, q_gen_3422) -> q_gen_3400
<b, cons, s>(q_gen_3426, q_gen_3433) -> q_gen_3400
<b, cons, z>(q_gen_3403, q_gen_3402) -> q_gen_3400
<b, cons, z>(q_gen_3403, q_gen_3415) -> q_gen_3400
<b, nil, z>() -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3415) -> q_gen_3409
<a, cons, s>(q_gen_3411, q_gen_3433) -> q_gen_3409
<a, cons, s>(q_gen_3426, q_gen_3413) -> q_gen_3409
<a, cons, z>(q_gen_3403, q_gen_3402) -> q_gen_3409
<a, cons, z>(q_gen_3408, q_gen_3415) -> q_gen_3409
<a, cons, z>(q_gen_3408, q_gen_3433) -> q_gen_3409
<b, cons, s>(q_gen_3405, q_gen_3413) -> q_gen_3409
<b, cons, s>(q_gen_3405, q_gen_3433) -> q_gen_3409
<b, cons, s>(q_gen_3411, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3411, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3415) -> q_gen_3409
<b, cons, z>(q_gen_3403, q_gen_3433) -> q_gen_3409
}

Datatype: <elt, eltlist, nat>
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
(count([x, l1, _nn]) /\ count([x, cons(x, l1), _mn])) -> eq_nat([_mn, s(_nn)]) -> 42
(count([x, t1, _gn])) -> count([x, cons(x, t1), s(_gn)]) -> 43
(count([x, t1, _hn]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _hn]) -> 43
}
Sat witness: Found: ((count([x, t1, _gn])) -> count([x, cons(x, t1), s(_gn)]), {
_gn -> s(z)  ;  t1 -> cons(a, cons(b, cons(a, nil)))  ;  x -> b
})

-------------------------------------------
Step 42, which took 0.135105 s (model generation: 0.130118,  model checking: 0.004987):

Model:
|_
{
count -> 
{{{
Q={q_gen_3400, q_gen_3402, q_gen_3403, q_gen_3405, q_gen_3408, q_gen_3409, q_gen_3411, q_gen_3413, q_gen_3415, q_gen_3422, q_gen_3426, q_gen_3427, q_gen_3436, q_gen_3446},
Q_f={q_gen_3400},
Delta=
{
<cons>(q_gen_3403, q_gen_3446) -> q_gen_3402
<nil>() -> q_gen_3402
<a>() -> q_gen_3403
<b>() -> q_gen_3408
<cons>(q_gen_3408, q_gen_3402) -> q_gen_3413
<cons>(q_gen_3403, q_gen_3402) -> q_gen_3415
<cons>(q_gen_3403, q_gen_3415) -> q_gen_3415
<cons>(q_gen_3403, q_gen_3413) -> q_gen_3422
<cons>(q_gen_3408, q_gen_3413) -> q_gen_3422
<cons>(q_gen_3408, q_gen_3422) -> q_gen_3422
<z>() -> q_gen_3427
<s>(q_gen_3427) -> q_gen_3436
<cons>(q_gen_3403, q_gen_3422) -> q_gen_3446
<cons>(q_gen_3408, q_gen_3415) -> q_gen_3446
<cons>(q_gen_3408, q_gen_3446) -> q_gen_3446
<b, z>() -> q_gen_3405
<a, z>() -> q_gen_3411
<b, s>(q_gen_3436) -> q_gen_3411
<b, s>(q_gen_3427) -> q_gen_3426
<a, cons, s>(q_gen_3405, q_gen_3415) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3402) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3413) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3422) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3402) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3413) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3422) -> q_gen_3400
<a, nil, z>() -> q_gen_3400
<b, cons, s>(q_gen_3405, q_gen_3402) -> q_gen_3400
<b, cons, s>(q_gen_3405, q_gen_3415) -> q_gen_3400
<b, cons, s>(q_gen_3411, q_gen_3413) -> q_gen_3400
<b, cons, s>(q_gen_3411, q_gen_3422) -> q_gen_3400
<b, cons, s>(q_gen_3411, q_gen_3446) -> q_gen_3400
<b, cons, s>(q_gen_3426, q_gen_3402) -> q_gen_3400
<b, cons, s>(q_gen_3426, q_gen_3413) -> q_gen_3400
<b, cons, s>(q_gen_3426, q_gen_3446) -> q_gen_3400
<b, cons, z>(q_gen_3403, q_gen_3402) -> q_gen_3400
<b, cons, z>(q_gen_3403, q_gen_3415) -> q_gen_3400
<b, nil, z>() -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3415) -> q_gen_3409
<a, cons, s>(q_gen_3411, q_gen_3446) -> q_gen_3409
<a, cons, s>(q_gen_3426, q_gen_3413) -> q_gen_3409
<a, cons, z>(q_gen_3403, q_gen_3402) -> q_gen_3409
<a, cons, z>(q_gen_3408, q_gen_3415) -> q_gen_3409
<a, cons, z>(q_gen_3408, q_gen_3446) -> q_gen_3409
<b, cons, s>(q_gen_3405, q_gen_3413) -> q_gen_3409
<b, cons, s>(q_gen_3405, q_gen_3422) -> q_gen_3409
<b, cons, s>(q_gen_3405, q_gen_3446) -> q_gen_3409
<b, cons, s>(q_gen_3411, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3411, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3422) -> q_gen_3409
<b, cons, z>(q_gen_3403, q_gen_3422) -> q_gen_3409
<b, cons, z>(q_gen_3403, q_gen_3446) -> q_gen_3409
}

Datatype: <elt, eltlist, nat>
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
(count([x, l1, _nn]) /\ count([x, cons(x, l1), _mn])) -> eq_nat([_mn, s(_nn)]) -> 45
(count([x, t1, _gn])) -> count([x, cons(x, t1), s(_gn)]) -> 43
(count([x, t1, _hn]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _hn]) -> 43
}
Sat witness: Found: ((count([x, l1, _nn]) /\ count([x, cons(x, l1), _mn])) -> eq_nat([_mn, s(_nn)]), {
_mn -> s(s(z))  ;  _nn -> z  ;  l1 -> nil  ;  x -> b
})

-------------------------------------------
Step 43, which took 0.188974 s (model generation: 0.141294,  model checking: 0.047680):

Model:
|_
{
count -> 
{{{
Q={q_gen_3400, q_gen_3402, q_gen_3403, q_gen_3405, q_gen_3408, q_gen_3409, q_gen_3411, q_gen_3413, q_gen_3415, q_gen_3422, q_gen_3426, q_gen_3427, q_gen_3435, q_gen_3436, q_gen_3446},
Q_f={q_gen_3400},
Delta=
{
<nil>() -> q_gen_3402
<a>() -> q_gen_3403
<b>() -> q_gen_3408
<cons>(q_gen_3408, q_gen_3402) -> q_gen_3413
<cons>(q_gen_3403, q_gen_3402) -> q_gen_3415
<cons>(q_gen_3403, q_gen_3415) -> q_gen_3415
<cons>(q_gen_3408, q_gen_3446) -> q_gen_3415
<cons>(q_gen_3403, q_gen_3413) -> q_gen_3422
<cons>(q_gen_3408, q_gen_3413) -> q_gen_3422
<cons>(q_gen_3408, q_gen_3422) -> q_gen_3422
<z>() -> q_gen_3427
<s>(q_gen_3427) -> q_gen_3436
<cons>(q_gen_3403, q_gen_3422) -> q_gen_3446
<cons>(q_gen_3403, q_gen_3446) -> q_gen_3446
<cons>(q_gen_3408, q_gen_3415) -> q_gen_3446
<b, z>() -> q_gen_3405
<a, z>() -> q_gen_3411
<b, s>(q_gen_3427) -> q_gen_3426
<b, s>(q_gen_3436) -> q_gen_3435
<a, cons, s>(q_gen_3405, q_gen_3415) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3402) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3413) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3422) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3402) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3413) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3422) -> q_gen_3400
<a, nil, z>() -> q_gen_3400
<b, cons, s>(q_gen_3405, q_gen_3402) -> q_gen_3400
<b, cons, s>(q_gen_3405, q_gen_3415) -> q_gen_3400
<b, cons, s>(q_gen_3411, q_gen_3413) -> q_gen_3400
<b, cons, s>(q_gen_3411, q_gen_3422) -> q_gen_3400
<b, cons, s>(q_gen_3411, q_gen_3446) -> q_gen_3400
<b, cons, s>(q_gen_3426, q_gen_3413) -> q_gen_3400
<b, cons, s>(q_gen_3426, q_gen_3446) -> q_gen_3400
<b, cons, s>(q_gen_3435, q_gen_3415) -> q_gen_3400
<b, cons, s>(q_gen_3435, q_gen_3422) -> q_gen_3400
<b, cons, z>(q_gen_3403, q_gen_3402) -> q_gen_3400
<b, cons, z>(q_gen_3403, q_gen_3415) -> q_gen_3400
<b, nil, z>() -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3415) -> q_gen_3409
<a, cons, s>(q_gen_3411, q_gen_3446) -> q_gen_3409
<a, cons, s>(q_gen_3426, q_gen_3413) -> q_gen_3409
<a, cons, z>(q_gen_3403, q_gen_3402) -> q_gen_3409
<a, cons, z>(q_gen_3408, q_gen_3415) -> q_gen_3409
<a, cons, z>(q_gen_3408, q_gen_3446) -> q_gen_3409
<b, cons, s>(q_gen_3405, q_gen_3413) -> q_gen_3409
<b, cons, s>(q_gen_3405, q_gen_3422) -> q_gen_3409
<b, cons, s>(q_gen_3405, q_gen_3446) -> q_gen_3409
<b, cons, s>(q_gen_3411, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3411, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3422) -> q_gen_3409
<b, cons, s>(q_gen_3435, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3435, q_gen_3446) -> q_gen_3409
<b, cons, z>(q_gen_3403, q_gen_3422) -> q_gen_3409
<b, cons, z>(q_gen_3403, q_gen_3446) -> q_gen_3409
}

Datatype: <elt, eltlist, nat>
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
(count([x, l1, _nn]) /\ count([x, cons(x, l1), _mn])) -> eq_nat([_mn, s(_nn)]) -> 45
(count([x, t1, _gn])) -> count([x, cons(x, t1), s(_gn)]) -> 43
(count([x, t1, _hn]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _hn]) -> 46
}
Sat witness: Found: ((count([x, t1, _hn]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _hn]), {
_hn -> s(s(s(z)))  ;  h1 -> a  ;  t1 -> cons(b, cons(a, nil))  ;  x -> b
})

-------------------------------------------
Step 44, which took 0.156109 s (model generation: 0.139142,  model checking: 0.016967):

Model:
|_
{
count -> 
{{{
Q={q_gen_3400, q_gen_3402, q_gen_3403, q_gen_3405, q_gen_3408, q_gen_3409, q_gen_3411, q_gen_3413, q_gen_3415, q_gen_3422, q_gen_3426, q_gen_3427, q_gen_3436, q_gen_3446, q_gen_3455},
Q_f={q_gen_3400},
Delta=
{
<nil>() -> q_gen_3402
<a>() -> q_gen_3403
<b>() -> q_gen_3408
<cons>(q_gen_3408, q_gen_3402) -> q_gen_3413
<cons>(q_gen_3403, q_gen_3402) -> q_gen_3415
<cons>(q_gen_3403, q_gen_3415) -> q_gen_3415
<cons>(q_gen_3403, q_gen_3413) -> q_gen_3422
<cons>(q_gen_3408, q_gen_3413) -> q_gen_3422
<cons>(q_gen_3408, q_gen_3422) -> q_gen_3422
<z>() -> q_gen_3427
<s>(q_gen_3427) -> q_gen_3436
<cons>(q_gen_3408, q_gen_3415) -> q_gen_3446
<cons>(q_gen_3408, q_gen_3446) -> q_gen_3446
<cons>(q_gen_3403, q_gen_3422) -> q_gen_3455
<cons>(q_gen_3403, q_gen_3446) -> q_gen_3455
<a, s>(q_gen_3436) -> q_gen_3405
<b, z>() -> q_gen_3405
<a, z>() -> q_gen_3411
<b, s>(q_gen_3436) -> q_gen_3411
<b, s>(q_gen_3427) -> q_gen_3426
<a, cons, s>(q_gen_3405, q_gen_3415) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3402) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3413) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3422) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3402) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3413) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3422) -> q_gen_3400
<a, nil, z>() -> q_gen_3400
<b, cons, s>(q_gen_3405, q_gen_3402) -> q_gen_3400
<b, cons, s>(q_gen_3405, q_gen_3415) -> q_gen_3400
<b, cons, s>(q_gen_3411, q_gen_3413) -> q_gen_3400
<b, cons, s>(q_gen_3411, q_gen_3422) -> q_gen_3400
<b, cons, s>(q_gen_3411, q_gen_3446) -> q_gen_3400
<b, cons, s>(q_gen_3426, q_gen_3413) -> q_gen_3400
<b, cons, s>(q_gen_3426, q_gen_3446) -> q_gen_3400
<b, cons, s>(q_gen_3426, q_gen_3455) -> q_gen_3400
<b, cons, z>(q_gen_3403, q_gen_3402) -> q_gen_3400
<b, cons, z>(q_gen_3403, q_gen_3415) -> q_gen_3400
<b, nil, z>() -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3415) -> q_gen_3409
<a, cons, s>(q_gen_3411, q_gen_3446) -> q_gen_3409
<a, cons, s>(q_gen_3411, q_gen_3455) -> q_gen_3409
<a, cons, s>(q_gen_3426, q_gen_3413) -> q_gen_3409
<a, cons, z>(q_gen_3403, q_gen_3402) -> q_gen_3409
<a, cons, z>(q_gen_3408, q_gen_3415) -> q_gen_3409
<a, cons, z>(q_gen_3408, q_gen_3446) -> q_gen_3409
<b, cons, s>(q_gen_3405, q_gen_3413) -> q_gen_3409
<b, cons, s>(q_gen_3405, q_gen_3422) -> q_gen_3409
<b, cons, s>(q_gen_3405, q_gen_3446) -> q_gen_3409
<b, cons, s>(q_gen_3411, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3411, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3411, q_gen_3455) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3422) -> q_gen_3409
<b, cons, z>(q_gen_3403, q_gen_3422) -> q_gen_3409
<b, cons, z>(q_gen_3403, q_gen_3455) -> q_gen_3409
}

Datatype: <elt, eltlist, nat>
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
(count([x, l1, _nn]) /\ count([x, cons(x, l1), _mn])) -> eq_nat([_mn, s(_nn)]) -> 45
(count([x, t1, _gn])) -> count([x, cons(x, t1), s(_gn)]) -> 46
(count([x, t1, _hn]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _hn]) -> 46
}
Sat witness: Found: ((count([x, t1, _gn])) -> count([x, cons(x, t1), s(_gn)]), {
_gn -> s(z)  ;  t1 -> cons(a, cons(b, nil))  ;  x -> b
})

-------------------------------------------
Step 45, which took 0.155502 s (model generation: 0.148756,  model checking: 0.006746):

Model:
|_
{
count -> 
{{{
Q={q_gen_3400, q_gen_3402, q_gen_3403, q_gen_3405, q_gen_3408, q_gen_3409, q_gen_3411, q_gen_3413, q_gen_3415, q_gen_3422, q_gen_3426, q_gen_3427, q_gen_3433, q_gen_3436, q_gen_3455},
Q_f={q_gen_3400},
Delta=
{
<nil>() -> q_gen_3402
<a>() -> q_gen_3403
<b>() -> q_gen_3408
<cons>(q_gen_3408, q_gen_3402) -> q_gen_3413
<cons>(q_gen_3403, q_gen_3402) -> q_gen_3415
<cons>(q_gen_3403, q_gen_3415) -> q_gen_3415
<cons>(q_gen_3408, q_gen_3413) -> q_gen_3422
<cons>(q_gen_3408, q_gen_3422) -> q_gen_3422
<cons>(q_gen_3408, q_gen_3433) -> q_gen_3422
<z>() -> q_gen_3427
<cons>(q_gen_3403, q_gen_3413) -> q_gen_3433
<cons>(q_gen_3408, q_gen_3415) -> q_gen_3433
<s>(q_gen_3427) -> q_gen_3436
<cons>(q_gen_3403, q_gen_3433) -> q_gen_3455
<b, z>() -> q_gen_3405
<a, s>(q_gen_3436) -> q_gen_3411
<a, z>() -> q_gen_3411
<b, s>(q_gen_3436) -> q_gen_3411
<b, s>(q_gen_3427) -> q_gen_3426
<a, cons, s>(q_gen_3405, q_gen_3415) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3402) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3413) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3422) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3402) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3413) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3422) -> q_gen_3400
<a, nil, z>() -> q_gen_3400
<b, cons, s>(q_gen_3405, q_gen_3402) -> q_gen_3400
<b, cons, s>(q_gen_3405, q_gen_3415) -> q_gen_3400
<b, cons, s>(q_gen_3411, q_gen_3413) -> q_gen_3400
<b, cons, s>(q_gen_3411, q_gen_3422) -> q_gen_3400
<b, cons, s>(q_gen_3411, q_gen_3433) -> q_gen_3400
<b, cons, s>(q_gen_3426, q_gen_3413) -> q_gen_3400
<b, cons, s>(q_gen_3426, q_gen_3433) -> q_gen_3400
<b, cons, s>(q_gen_3426, q_gen_3455) -> q_gen_3400
<b, cons, z>(q_gen_3403, q_gen_3402) -> q_gen_3400
<b, cons, z>(q_gen_3403, q_gen_3415) -> q_gen_3400
<b, nil, z>() -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3415) -> q_gen_3409
<a, cons, s>(q_gen_3411, q_gen_3433) -> q_gen_3409
<a, cons, s>(q_gen_3411, q_gen_3455) -> q_gen_3409
<a, cons, s>(q_gen_3426, q_gen_3413) -> q_gen_3409
<a, cons, z>(q_gen_3403, q_gen_3402) -> q_gen_3409
<a, cons, z>(q_gen_3408, q_gen_3415) -> q_gen_3409
<a, cons, z>(q_gen_3408, q_gen_3433) -> q_gen_3409
<b, cons, s>(q_gen_3405, q_gen_3413) -> q_gen_3409
<b, cons, s>(q_gen_3405, q_gen_3422) -> q_gen_3409
<b, cons, s>(q_gen_3405, q_gen_3433) -> q_gen_3409
<b, cons, s>(q_gen_3411, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3411, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3411, q_gen_3455) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3422) -> q_gen_3409
<b, cons, z>(q_gen_3403, q_gen_3433) -> q_gen_3409
<b, cons, z>(q_gen_3403, q_gen_3455) -> q_gen_3409
}

Datatype: <elt, eltlist, nat>
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
(count([x, l1, _nn]) /\ count([x, cons(x, l1), _mn])) -> eq_nat([_mn, s(_nn)]) -> 48
(count([x, t1, _gn])) -> count([x, cons(x, t1), s(_gn)]) -> 46
(count([x, t1, _hn]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _hn]) -> 46
}
Sat witness: Found: ((count([x, l1, _nn]) /\ count([x, cons(x, l1), _mn])) -> eq_nat([_mn, s(_nn)]), {
_mn -> s(s(s(z)))  ;  _nn -> z  ;  l1 -> cons(b, nil)  ;  x -> a
})

-------------------------------------------
Step 46, which took 0.151850 s (model generation: 0.142555,  model checking: 0.009295):

Model:
|_
{
count -> 
{{{
Q={q_gen_3400, q_gen_3402, q_gen_3403, q_gen_3405, q_gen_3408, q_gen_3409, q_gen_3411, q_gen_3413, q_gen_3415, q_gen_3422, q_gen_3426, q_gen_3427, q_gen_3436, q_gen_3446, q_gen_3455},
Q_f={q_gen_3400},
Delta=
{
<nil>() -> q_gen_3402
<a>() -> q_gen_3403
<b>() -> q_gen_3408
<cons>(q_gen_3403, q_gen_3413) -> q_gen_3413
<cons>(q_gen_3408, q_gen_3402) -> q_gen_3413
<cons>(q_gen_3403, q_gen_3402) -> q_gen_3415
<cons>(q_gen_3403, q_gen_3415) -> q_gen_3415
<cons>(q_gen_3408, q_gen_3413) -> q_gen_3422
<cons>(q_gen_3408, q_gen_3422) -> q_gen_3422
<z>() -> q_gen_3427
<s>(q_gen_3427) -> q_gen_3436
<cons>(q_gen_3408, q_gen_3415) -> q_gen_3446
<cons>(q_gen_3408, q_gen_3446) -> q_gen_3446
<cons>(q_gen_3403, q_gen_3446) -> q_gen_3455
<a, s>(q_gen_3436) -> q_gen_3405
<b, z>() -> q_gen_3405
<a, z>() -> q_gen_3411
<b, s>(q_gen_3436) -> q_gen_3411
<b, s>(q_gen_3427) -> q_gen_3426
<a, cons, s>(q_gen_3405, q_gen_3415) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3402) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3413) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3422) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3402) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3413) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3422) -> q_gen_3400
<a, nil, z>() -> q_gen_3400
<b, cons, s>(q_gen_3405, q_gen_3402) -> q_gen_3400
<b, cons, s>(q_gen_3405, q_gen_3415) -> q_gen_3400
<b, cons, s>(q_gen_3411, q_gen_3413) -> q_gen_3400
<b, cons, s>(q_gen_3411, q_gen_3422) -> q_gen_3400
<b, cons, s>(q_gen_3411, q_gen_3446) -> q_gen_3400
<b, cons, s>(q_gen_3426, q_gen_3413) -> q_gen_3400
<b, cons, s>(q_gen_3426, q_gen_3446) -> q_gen_3400
<b, cons, s>(q_gen_3426, q_gen_3455) -> q_gen_3400
<b, cons, z>(q_gen_3403, q_gen_3402) -> q_gen_3400
<b, cons, z>(q_gen_3403, q_gen_3415) -> q_gen_3400
<b, nil, z>() -> q_gen_3400
<a, cons, s>(q_gen_3405, q_gen_3413) -> q_gen_3409
<a, cons, s>(q_gen_3411, q_gen_3415) -> q_gen_3409
<a, cons, s>(q_gen_3411, q_gen_3446) -> q_gen_3409
<a, cons, s>(q_gen_3411, q_gen_3455) -> q_gen_3409
<a, cons, s>(q_gen_3426, q_gen_3413) -> q_gen_3409
<a, cons, z>(q_gen_3403, q_gen_3402) -> q_gen_3409
<a, cons, z>(q_gen_3408, q_gen_3415) -> q_gen_3409
<a, cons, z>(q_gen_3408, q_gen_3446) -> q_gen_3409
<b, cons, s>(q_gen_3405, q_gen_3413) -> q_gen_3409
<b, cons, s>(q_gen_3405, q_gen_3422) -> q_gen_3409
<b, cons, s>(q_gen_3405, q_gen_3446) -> q_gen_3409
<b, cons, s>(q_gen_3411, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3411, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3411, q_gen_3455) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3422) -> q_gen_3409
<b, cons, z>(q_gen_3403, q_gen_3413) -> q_gen_3409
}

Datatype: <elt, eltlist, nat>
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
(count([x, l1, _nn]) /\ count([x, cons(x, l1), _mn])) -> eq_nat([_mn, s(_nn)]) -> 48
(count([x, t1, _gn])) -> count([x, cons(x, t1), s(_gn)]) -> 46
(count([x, t1, _hn]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _hn]) -> 49
}
Sat witness: Found: ((count([x, t1, _hn]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _hn]), {
_hn -> s(z)  ;  h1 -> a  ;  t1 -> cons(a, cons(b, cons(a, nil)))  ;  x -> b
})

-------------------------------------------
Step 47, which took 0.205240 s (model generation: 0.163847,  model checking: 0.041393):

Model:
|_
{
count -> 
{{{
Q={q_gen_3400, q_gen_3402, q_gen_3403, q_gen_3405, q_gen_3408, q_gen_3409, q_gen_3411, q_gen_3413, q_gen_3415, q_gen_3422, q_gen_3426, q_gen_3427, q_gen_3433, q_gen_3435, q_gen_3436},
Q_f={q_gen_3400},
Delta=
{
<nil>() -> q_gen_3402
<a>() -> q_gen_3403
<b>() -> q_gen_3408
<cons>(q_gen_3408, q_gen_3402) -> q_gen_3413
<cons>(q_gen_3408, q_gen_3433) -> q_gen_3413
<cons>(q_gen_3403, q_gen_3402) -> q_gen_3415
<cons>(q_gen_3403, q_gen_3415) -> q_gen_3415
<cons>(q_gen_3408, q_gen_3413) -> q_gen_3422
<cons>(q_gen_3408, q_gen_3422) -> q_gen_3422
<z>() -> q_gen_3427
<cons>(q_gen_3403, q_gen_3413) -> q_gen_3433
<cons>(q_gen_3403, q_gen_3433) -> q_gen_3433
<cons>(q_gen_3408, q_gen_3415) -> q_gen_3433
<s>(q_gen_3427) -> q_gen_3436
<a, s>(q_gen_3436) -> q_gen_3405
<b, z>() -> q_gen_3405
<a, z>() -> q_gen_3411
<b, s>(q_gen_3427) -> q_gen_3426
<b, s>(q_gen_3436) -> q_gen_3435
<a, cons, s>(q_gen_3405, q_gen_3415) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3402) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3413) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3422) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3402) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3413) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3422) -> q_gen_3400
<a, nil, z>() -> q_gen_3400
<b, cons, s>(q_gen_3405, q_gen_3402) -> q_gen_3400
<b, cons, s>(q_gen_3405, q_gen_3415) -> q_gen_3400
<b, cons, s>(q_gen_3411, q_gen_3413) -> q_gen_3400
<b, cons, s>(q_gen_3411, q_gen_3433) -> q_gen_3400
<b, cons, s>(q_gen_3426, q_gen_3413) -> q_gen_3400
<b, cons, s>(q_gen_3426, q_gen_3433) -> q_gen_3400
<b, cons, s>(q_gen_3435, q_gen_3413) -> q_gen_3400
<b, cons, s>(q_gen_3435, q_gen_3422) -> q_gen_3400
<b, cons, z>(q_gen_3403, q_gen_3402) -> q_gen_3400
<b, cons, z>(q_gen_3403, q_gen_3415) -> q_gen_3400
<b, nil, z>() -> q_gen_3400
<a, cons, s>(q_gen_3405, q_gen_3413) -> q_gen_3409
<a, cons, s>(q_gen_3411, q_gen_3415) -> q_gen_3409
<a, cons, s>(q_gen_3411, q_gen_3433) -> q_gen_3409
<a, cons, s>(q_gen_3426, q_gen_3413) -> q_gen_3409
<a, cons, z>(q_gen_3403, q_gen_3402) -> q_gen_3409
<a, cons, z>(q_gen_3408, q_gen_3415) -> q_gen_3409
<a, cons, z>(q_gen_3408, q_gen_3433) -> q_gen_3409
<b, cons, s>(q_gen_3405, q_gen_3413) -> q_gen_3409
<b, cons, s>(q_gen_3405, q_gen_3433) -> q_gen_3409
<b, cons, s>(q_gen_3411, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3411, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3422) -> q_gen_3409
<b, cons, s>(q_gen_3435, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3435, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3435, q_gen_3433) -> q_gen_3409
<b, cons, z>(q_gen_3403, q_gen_3433) -> q_gen_3409
}

Datatype: <elt, eltlist, nat>
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
(count([x, l1, _nn]) /\ count([x, cons(x, l1), _mn])) -> eq_nat([_mn, s(_nn)]) -> 48
(count([x, t1, _gn])) -> count([x, cons(x, t1), s(_gn)]) -> 49
(count([x, t1, _hn]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _hn]) -> 49
}
Sat witness: Found: ((count([x, t1, _gn])) -> count([x, cons(x, t1), s(_gn)]), {
_gn -> s(s(s(z)))  ;  t1 -> cons(a, nil)  ;  x -> b
})

-------------------------------------------
Step 48, which took 0.196165 s (model generation: 0.179678,  model checking: 0.016487):

Model:
|_
{
count -> 
{{{
Q={q_gen_3400, q_gen_3402, q_gen_3403, q_gen_3405, q_gen_3408, q_gen_3409, q_gen_3411, q_gen_3413, q_gen_3415, q_gen_3422, q_gen_3426, q_gen_3427, q_gen_3433, q_gen_3435, q_gen_3436},
Q_f={q_gen_3400},
Delta=
{
<nil>() -> q_gen_3402
<a>() -> q_gen_3403
<b>() -> q_gen_3408
<cons>(q_gen_3408, q_gen_3402) -> q_gen_3413
<cons>(q_gen_3408, q_gen_3433) -> q_gen_3413
<cons>(q_gen_3403, q_gen_3402) -> q_gen_3415
<cons>(q_gen_3403, q_gen_3415) -> q_gen_3415
<cons>(q_gen_3408, q_gen_3413) -> q_gen_3422
<cons>(q_gen_3408, q_gen_3422) -> q_gen_3422
<z>() -> q_gen_3427
<cons>(q_gen_3403, q_gen_3413) -> q_gen_3433
<cons>(q_gen_3403, q_gen_3433) -> q_gen_3433
<cons>(q_gen_3408, q_gen_3415) -> q_gen_3433
<s>(q_gen_3427) -> q_gen_3436
<s>(q_gen_3436) -> q_gen_3436
<b, z>() -> q_gen_3405
<a, z>() -> q_gen_3411
<b, s>(q_gen_3427) -> q_gen_3426
<a, s>(q_gen_3436) -> q_gen_3435
<b, s>(q_gen_3436) -> q_gen_3435
<a, cons, s>(q_gen_3405, q_gen_3415) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3402) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3413) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3422) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3402) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3413) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3422) -> q_gen_3400
<a, nil, z>() -> q_gen_3400
<b, cons, s>(q_gen_3405, q_gen_3402) -> q_gen_3400
<b, cons, s>(q_gen_3405, q_gen_3415) -> q_gen_3400
<b, cons, s>(q_gen_3411, q_gen_3413) -> q_gen_3400
<b, cons, s>(q_gen_3411, q_gen_3433) -> q_gen_3400
<b, cons, s>(q_gen_3426, q_gen_3413) -> q_gen_3400
<b, cons, s>(q_gen_3426, q_gen_3433) -> q_gen_3400
<b, cons, s>(q_gen_3435, q_gen_3413) -> q_gen_3400
<b, cons, s>(q_gen_3435, q_gen_3422) -> q_gen_3400
<b, cons, z>(q_gen_3403, q_gen_3402) -> q_gen_3400
<b, cons, z>(q_gen_3403, q_gen_3415) -> q_gen_3400
<b, nil, z>() -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3415) -> q_gen_3409
<a, cons, s>(q_gen_3411, q_gen_3433) -> q_gen_3409
<a, cons, s>(q_gen_3426, q_gen_3413) -> q_gen_3409
<a, cons, s>(q_gen_3435, q_gen_3413) -> q_gen_3409
<a, cons, z>(q_gen_3403, q_gen_3402) -> q_gen_3409
<a, cons, z>(q_gen_3408, q_gen_3415) -> q_gen_3409
<a, cons, z>(q_gen_3408, q_gen_3433) -> q_gen_3409
<b, cons, s>(q_gen_3405, q_gen_3413) -> q_gen_3409
<b, cons, s>(q_gen_3405, q_gen_3433) -> q_gen_3409
<b, cons, s>(q_gen_3411, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3411, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3422) -> q_gen_3409
<b, cons, s>(q_gen_3435, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3435, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3435, q_gen_3433) -> q_gen_3409
<b, cons, z>(q_gen_3403, q_gen_3433) -> q_gen_3409
}

Datatype: <elt, eltlist, nat>
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
(count([x, l1, _nn]) /\ count([x, cons(x, l1), _mn])) -> eq_nat([_mn, s(_nn)]) -> 51
(count([x, t1, _gn])) -> count([x, cons(x, t1), s(_gn)]) -> 49
(count([x, t1, _hn]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _hn]) -> 49
}
Sat witness: Found: ((count([x, l1, _nn]) /\ count([x, cons(x, l1), _mn])) -> eq_nat([_mn, s(_nn)]), {
_mn -> s(s(s(z)))  ;  _nn -> s(z)  ;  l1 -> cons(b, nil)  ;  x -> b
})

-------------------------------------------
Step 49, which took 0.188181 s (model generation: 0.176207,  model checking: 0.011974):

Model:
|_
{
count -> 
{{{
Q={q_gen_3400, q_gen_3402, q_gen_3403, q_gen_3405, q_gen_3408, q_gen_3409, q_gen_3411, q_gen_3413, q_gen_3415, q_gen_3422, q_gen_3426, q_gen_3427, q_gen_3435, q_gen_3436, q_gen_3446},
Q_f={q_gen_3400},
Delta=
{
<cons>(q_gen_3408, q_gen_3422) -> q_gen_3402
<nil>() -> q_gen_3402
<a>() -> q_gen_3403
<b>() -> q_gen_3408
<cons>(q_gen_3403, q_gen_3413) -> q_gen_3413
<cons>(q_gen_3408, q_gen_3402) -> q_gen_3413
<cons>(q_gen_3403, q_gen_3402) -> q_gen_3415
<cons>(q_gen_3403, q_gen_3415) -> q_gen_3415
<cons>(q_gen_3408, q_gen_3413) -> q_gen_3422
<cons>(q_gen_3408, q_gen_3446) -> q_gen_3422
<s>(q_gen_3436) -> q_gen_3427
<z>() -> q_gen_3427
<s>(q_gen_3427) -> q_gen_3436
<cons>(q_gen_3403, q_gen_3446) -> q_gen_3446
<cons>(q_gen_3408, q_gen_3415) -> q_gen_3446
<b, z>() -> q_gen_3405
<a, z>() -> q_gen_3411
<b, s>(q_gen_3427) -> q_gen_3426
<a, s>(q_gen_3436) -> q_gen_3435
<b, s>(q_gen_3436) -> q_gen_3435
<a, cons, s>(q_gen_3405, q_gen_3415) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3402) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3413) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3422) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3402) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3413) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3422) -> q_gen_3400
<a, nil, z>() -> q_gen_3400
<b, cons, s>(q_gen_3405, q_gen_3402) -> q_gen_3400
<b, cons, s>(q_gen_3405, q_gen_3415) -> q_gen_3400
<b, cons, s>(q_gen_3411, q_gen_3413) -> q_gen_3400
<b, cons, s>(q_gen_3411, q_gen_3446) -> q_gen_3400
<b, cons, s>(q_gen_3426, q_gen_3413) -> q_gen_3400
<b, cons, s>(q_gen_3426, q_gen_3446) -> q_gen_3400
<b, cons, s>(q_gen_3435, q_gen_3422) -> q_gen_3400
<b, cons, z>(q_gen_3403, q_gen_3402) -> q_gen_3400
<b, cons, z>(q_gen_3403, q_gen_3415) -> q_gen_3400
<b, nil, z>() -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3415) -> q_gen_3409
<a, cons, s>(q_gen_3411, q_gen_3446) -> q_gen_3409
<a, cons, s>(q_gen_3426, q_gen_3413) -> q_gen_3409
<a, cons, s>(q_gen_3435, q_gen_3413) -> q_gen_3409
<a, cons, z>(q_gen_3403, q_gen_3402) -> q_gen_3409
<a, cons, z>(q_gen_3408, q_gen_3415) -> q_gen_3409
<a, cons, z>(q_gen_3408, q_gen_3446) -> q_gen_3409
<b, cons, s>(q_gen_3405, q_gen_3413) -> q_gen_3409
<b, cons, s>(q_gen_3405, q_gen_3422) -> q_gen_3409
<b, cons, s>(q_gen_3405, q_gen_3446) -> q_gen_3409
<b, cons, s>(q_gen_3411, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3411, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3422) -> q_gen_3409
<b, cons, s>(q_gen_3435, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3435, q_gen_3413) -> q_gen_3409
<b, cons, s>(q_gen_3435, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3435, q_gen_3446) -> q_gen_3409
<b, cons, z>(q_gen_3403, q_gen_3413) -> q_gen_3409
}

Datatype: <elt, eltlist, nat>
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
(count([x, l1, _nn]) /\ count([x, cons(x, l1), _mn])) -> eq_nat([_mn, s(_nn)]) -> 51
(count([x, t1, _gn])) -> count([x, cons(x, t1), s(_gn)]) -> 49
(count([x, t1, _hn]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _hn]) -> 52
}
Sat witness: Found: ((count([x, t1, _hn]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _hn]), {
_hn -> s(s(s(z)))  ;  h1 -> a  ;  t1 -> cons(b, cons(b, cons(a, cons(b, cons(a, nil)))))  ;  x -> b
})

-------------------------------------------
Step 50, which took 0.213523 s (model generation: 0.207682,  model checking: 0.005841):

Model:
|_
{
count -> 
{{{
Q={q_gen_3400, q_gen_3402, q_gen_3403, q_gen_3405, q_gen_3408, q_gen_3409, q_gen_3411, q_gen_3413, q_gen_3415, q_gen_3422, q_gen_3426, q_gen_3427, q_gen_3435, q_gen_3436, q_gen_3446},
Q_f={q_gen_3400},
Delta=
{
<nil>() -> q_gen_3402
<a>() -> q_gen_3403
<b>() -> q_gen_3408
<cons>(q_gen_3403, q_gen_3413) -> q_gen_3413
<cons>(q_gen_3403, q_gen_3446) -> q_gen_3413
<cons>(q_gen_3408, q_gen_3402) -> q_gen_3413
<cons>(q_gen_3408, q_gen_3422) -> q_gen_3413
<cons>(q_gen_3403, q_gen_3402) -> q_gen_3415
<cons>(q_gen_3403, q_gen_3415) -> q_gen_3415
<cons>(q_gen_3408, q_gen_3413) -> q_gen_3422
<cons>(q_gen_3408, q_gen_3446) -> q_gen_3422
<s>(q_gen_3436) -> q_gen_3427
<z>() -> q_gen_3427
<s>(q_gen_3427) -> q_gen_3436
<cons>(q_gen_3408, q_gen_3415) -> q_gen_3446
<b, z>() -> q_gen_3405
<a, z>() -> q_gen_3411
<a, s>(q_gen_3436) -> q_gen_3426
<b, s>(q_gen_3427) -> q_gen_3426
<b, s>(q_gen_3436) -> q_gen_3435
<a, cons, s>(q_gen_3405, q_gen_3415) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3402) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3413) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3422) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3402) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3413) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3415) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3422) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3446) -> q_gen_3400
<a, nil, z>() -> q_gen_3400
<b, cons, s>(q_gen_3405, q_gen_3402) -> q_gen_3400
<b, cons, s>(q_gen_3405, q_gen_3415) -> q_gen_3400
<b, cons, s>(q_gen_3411, q_gen_3413) -> q_gen_3400
<b, cons, s>(q_gen_3411, q_gen_3446) -> q_gen_3400
<b, cons, s>(q_gen_3426, q_gen_3413) -> q_gen_3400
<b, cons, s>(q_gen_3426, q_gen_3446) -> q_gen_3400
<b, cons, s>(q_gen_3435, q_gen_3422) -> q_gen_3400
<b, cons, z>(q_gen_3403, q_gen_3402) -> q_gen_3400
<b, cons, z>(q_gen_3403, q_gen_3415) -> q_gen_3400
<b, nil, z>() -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3415) -> q_gen_3409
<a, cons, s>(q_gen_3411, q_gen_3446) -> q_gen_3409
<a, cons, s>(q_gen_3426, q_gen_3413) -> q_gen_3409
<a, cons, z>(q_gen_3403, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3405, q_gen_3413) -> q_gen_3409
<b, cons, s>(q_gen_3405, q_gen_3422) -> q_gen_3409
<b, cons, s>(q_gen_3405, q_gen_3446) -> q_gen_3409
<b, cons, s>(q_gen_3411, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3411, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3422) -> q_gen_3409
<b, cons, s>(q_gen_3435, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3435, q_gen_3413) -> q_gen_3409
<b, cons, s>(q_gen_3435, q_gen_3415) -> q_gen_3409
<b, cons, z>(q_gen_3403, q_gen_3413) -> q_gen_3409
}

Datatype: <elt, eltlist, nat>
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
(count([x, l1, _nn]) /\ count([x, cons(x, l1), _mn])) -> eq_nat([_mn, s(_nn)]) -> 51
(count([x, t1, _gn])) -> count([x, cons(x, t1), s(_gn)]) -> 52
(count([x, t1, _hn]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _hn]) -> 52
}
Sat witness: Found: ((count([x, t1, _gn])) -> count([x, cons(x, t1), s(_gn)]), {
_gn -> z  ;  t1 -> cons(b, cons(a, nil))  ;  x -> a
})

-------------------------------------------
Step 51, which took 0.216689 s (model generation: 0.198561,  model checking: 0.018128):

Model:
|_
{
count -> 
{{{
Q={q_gen_3400, q_gen_3402, q_gen_3403, q_gen_3405, q_gen_3408, q_gen_3409, q_gen_3411, q_gen_3413, q_gen_3415, q_gen_3422, q_gen_3426, q_gen_3427, q_gen_3435, q_gen_3436, q_gen_3446},
Q_f={q_gen_3400},
Delta=
{
<nil>() -> q_gen_3402
<a>() -> q_gen_3403
<b>() -> q_gen_3408
<cons>(q_gen_3403, q_gen_3413) -> q_gen_3413
<cons>(q_gen_3403, q_gen_3446) -> q_gen_3413
<cons>(q_gen_3408, q_gen_3402) -> q_gen_3413
<cons>(q_gen_3408, q_gen_3422) -> q_gen_3413
<cons>(q_gen_3403, q_gen_3402) -> q_gen_3415
<cons>(q_gen_3403, q_gen_3415) -> q_gen_3415
<cons>(q_gen_3408, q_gen_3413) -> q_gen_3422
<cons>(q_gen_3408, q_gen_3446) -> q_gen_3422
<s>(q_gen_3436) -> q_gen_3427
<z>() -> q_gen_3427
<s>(q_gen_3427) -> q_gen_3436
<cons>(q_gen_3408, q_gen_3415) -> q_gen_3446
<b, z>() -> q_gen_3405
<a, z>() -> q_gen_3411
<a, s>(q_gen_3436) -> q_gen_3426
<b, s>(q_gen_3427) -> q_gen_3426
<b, s>(q_gen_3436) -> q_gen_3435
<a, cons, s>(q_gen_3405, q_gen_3415) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3402) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3413) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3422) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3402) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3413) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3422) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3446) -> q_gen_3400
<a, nil, z>() -> q_gen_3400
<b, cons, s>(q_gen_3405, q_gen_3402) -> q_gen_3400
<b, cons, s>(q_gen_3405, q_gen_3415) -> q_gen_3400
<b, cons, s>(q_gen_3411, q_gen_3413) -> q_gen_3400
<b, cons, s>(q_gen_3411, q_gen_3446) -> q_gen_3400
<b, cons, s>(q_gen_3426, q_gen_3413) -> q_gen_3400
<b, cons, s>(q_gen_3426, q_gen_3446) -> q_gen_3400
<b, cons, s>(q_gen_3435, q_gen_3422) -> q_gen_3400
<b, cons, z>(q_gen_3403, q_gen_3402) -> q_gen_3400
<b, cons, z>(q_gen_3403, q_gen_3415) -> q_gen_3400
<b, nil, z>() -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3415) -> q_gen_3409
<a, cons, s>(q_gen_3411, q_gen_3446) -> q_gen_3409
<a, cons, s>(q_gen_3426, q_gen_3413) -> q_gen_3409
<a, cons, z>(q_gen_3403, q_gen_3402) -> q_gen_3409
<a, cons, z>(q_gen_3408, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3405, q_gen_3413) -> q_gen_3409
<b, cons, s>(q_gen_3405, q_gen_3422) -> q_gen_3409
<b, cons, s>(q_gen_3405, q_gen_3446) -> q_gen_3409
<b, cons, s>(q_gen_3411, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3411, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3422) -> q_gen_3409
<b, cons, s>(q_gen_3435, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3435, q_gen_3413) -> q_gen_3409
<b, cons, s>(q_gen_3435, q_gen_3415) -> q_gen_3409
<b, cons, z>(q_gen_3403, q_gen_3413) -> q_gen_3409
}

Datatype: <elt, eltlist, nat>
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
(count([x, l1, _nn]) /\ count([x, cons(x, l1), _mn])) -> eq_nat([_mn, s(_nn)]) -> 54
(count([x, t1, _gn])) -> count([x, cons(x, t1), s(_gn)]) -> 52
(count([x, t1, _hn]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _hn]) -> 52
}
Sat witness: Found: ((count([x, l1, _nn]) /\ count([x, cons(x, l1), _mn])) -> eq_nat([_mn, s(_nn)]), {
_mn -> s(s(s(s(z))))  ;  _nn -> s(z)  ;  l1 -> cons(b, nil)  ;  x -> b
})

-------------------------------------------
Step 52, which took 0.267216 s (model generation: 0.215641,  model checking: 0.051575):

Model:
|_
{
count -> 
{{{
Q={q_gen_3400, q_gen_3402, q_gen_3403, q_gen_3405, q_gen_3408, q_gen_3409, q_gen_3411, q_gen_3413, q_gen_3415, q_gen_3422, q_gen_3426, q_gen_3427, q_gen_3435, q_gen_3436, q_gen_3446},
Q_f={q_gen_3400},
Delta=
{
<nil>() -> q_gen_3402
<a>() -> q_gen_3403
<b>() -> q_gen_3408
<cons>(q_gen_3403, q_gen_3413) -> q_gen_3413
<cons>(q_gen_3403, q_gen_3446) -> q_gen_3413
<cons>(q_gen_3408, q_gen_3402) -> q_gen_3413
<cons>(q_gen_3408, q_gen_3422) -> q_gen_3413
<cons>(q_gen_3403, q_gen_3402) -> q_gen_3415
<cons>(q_gen_3403, q_gen_3415) -> q_gen_3415
<cons>(q_gen_3408, q_gen_3413) -> q_gen_3422
<cons>(q_gen_3408, q_gen_3446) -> q_gen_3422
<z>() -> q_gen_3427
<s>(q_gen_3427) -> q_gen_3436
<s>(q_gen_3436) -> q_gen_3436
<cons>(q_gen_3408, q_gen_3415) -> q_gen_3446
<b, z>() -> q_gen_3405
<a, z>() -> q_gen_3411
<a, s>(q_gen_3436) -> q_gen_3426
<b, s>(q_gen_3427) -> q_gen_3426
<b, s>(q_gen_3436) -> q_gen_3435
<a, cons, s>(q_gen_3405, q_gen_3415) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3402) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3413) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3422) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3402) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3413) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3422) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3446) -> q_gen_3400
<a, nil, z>() -> q_gen_3400
<b, cons, s>(q_gen_3405, q_gen_3402) -> q_gen_3400
<b, cons, s>(q_gen_3405, q_gen_3415) -> q_gen_3400
<b, cons, s>(q_gen_3411, q_gen_3413) -> q_gen_3400
<b, cons, s>(q_gen_3411, q_gen_3446) -> q_gen_3400
<b, cons, s>(q_gen_3426, q_gen_3413) -> q_gen_3400
<b, cons, s>(q_gen_3426, q_gen_3446) -> q_gen_3400
<b, cons, s>(q_gen_3435, q_gen_3422) -> q_gen_3400
<b, cons, z>(q_gen_3403, q_gen_3402) -> q_gen_3400
<b, cons, z>(q_gen_3403, q_gen_3415) -> q_gen_3400
<b, nil, z>() -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3415) -> q_gen_3409
<a, cons, s>(q_gen_3411, q_gen_3446) -> q_gen_3409
<a, cons, s>(q_gen_3426, q_gen_3413) -> q_gen_3409
<a, cons, z>(q_gen_3403, q_gen_3402) -> q_gen_3409
<a, cons, z>(q_gen_3408, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3405, q_gen_3413) -> q_gen_3409
<b, cons, s>(q_gen_3405, q_gen_3422) -> q_gen_3409
<b, cons, s>(q_gen_3405, q_gen_3446) -> q_gen_3409
<b, cons, s>(q_gen_3411, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3411, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3422) -> q_gen_3409
<b, cons, s>(q_gen_3435, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3435, q_gen_3413) -> q_gen_3409
<b, cons, s>(q_gen_3435, q_gen_3415) -> q_gen_3409
<b, cons, z>(q_gen_3403, q_gen_3413) -> q_gen_3409
}

Datatype: <elt, eltlist, nat>
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
(count([x, l1, _nn]) /\ count([x, cons(x, l1), _mn])) -> eq_nat([_mn, s(_nn)]) -> 54
(count([x, t1, _gn])) -> count([x, cons(x, t1), s(_gn)]) -> 52
(count([x, t1, _hn]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _hn]) -> 55
}
Sat witness: Found: ((count([x, t1, _hn]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _hn]), {
_hn -> s(s(z))  ;  h1 -> a  ;  t1 -> cons(b, cons(b, cons(b, cons(a, cons(b, nil)))))  ;  x -> b
})

-------------------------------------------
Step 53, which took 0.250738 s (model generation: 0.239693,  model checking: 0.011045):

Model:
|_
{
count -> 
{{{
Q={q_gen_3400, q_gen_3402, q_gen_3403, q_gen_3405, q_gen_3408, q_gen_3409, q_gen_3411, q_gen_3413, q_gen_3415, q_gen_3422, q_gen_3426, q_gen_3427, q_gen_3433, q_gen_3435, q_gen_3436},
Q_f={q_gen_3400},
Delta=
{
<nil>() -> q_gen_3402
<a>() -> q_gen_3403
<b>() -> q_gen_3408
<cons>(q_gen_3408, q_gen_3402) -> q_gen_3413
<cons>(q_gen_3408, q_gen_3422) -> q_gen_3413
<cons>(q_gen_3403, q_gen_3402) -> q_gen_3415
<cons>(q_gen_3403, q_gen_3415) -> q_gen_3415
<cons>(q_gen_3408, q_gen_3413) -> q_gen_3422
<cons>(q_gen_3408, q_gen_3433) -> q_gen_3422
<z>() -> q_gen_3427
<cons>(q_gen_3403, q_gen_3413) -> q_gen_3433
<cons>(q_gen_3403, q_gen_3433) -> q_gen_3433
<cons>(q_gen_3408, q_gen_3415) -> q_gen_3433
<s>(q_gen_3427) -> q_gen_3436
<s>(q_gen_3436) -> q_gen_3436
<b, z>() -> q_gen_3405
<a, s>(q_gen_3427) -> q_gen_3411
<a, z>() -> q_gen_3411
<a, s>(q_gen_3436) -> q_gen_3426
<b, s>(q_gen_3427) -> q_gen_3426
<b, s>(q_gen_3436) -> q_gen_3435
<a, cons, s>(q_gen_3405, q_gen_3415) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3402) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3413) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3422) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3402) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3413) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3422) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3433) -> q_gen_3400
<a, nil, z>() -> q_gen_3400
<b, cons, s>(q_gen_3405, q_gen_3402) -> q_gen_3400
<b, cons, s>(q_gen_3405, q_gen_3415) -> q_gen_3400
<b, cons, s>(q_gen_3411, q_gen_3413) -> q_gen_3400
<b, cons, s>(q_gen_3411, q_gen_3422) -> q_gen_3400
<b, cons, s>(q_gen_3411, q_gen_3433) -> q_gen_3400
<b, cons, s>(q_gen_3426, q_gen_3413) -> q_gen_3400
<b, cons, s>(q_gen_3426, q_gen_3433) -> q_gen_3400
<b, cons, s>(q_gen_3435, q_gen_3422) -> q_gen_3400
<b, cons, z>(q_gen_3403, q_gen_3402) -> q_gen_3400
<b, cons, z>(q_gen_3403, q_gen_3415) -> q_gen_3400
<b, nil, z>() -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3415) -> q_gen_3409
<a, cons, s>(q_gen_3411, q_gen_3433) -> q_gen_3409
<a, cons, s>(q_gen_3426, q_gen_3413) -> q_gen_3409
<a, cons, z>(q_gen_3403, q_gen_3402) -> q_gen_3409
<a, cons, z>(q_gen_3408, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3405, q_gen_3413) -> q_gen_3409
<b, cons, s>(q_gen_3405, q_gen_3422) -> q_gen_3409
<b, cons, s>(q_gen_3405, q_gen_3433) -> q_gen_3409
<b, cons, s>(q_gen_3411, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3411, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3422) -> q_gen_3409
<b, cons, s>(q_gen_3435, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3435, q_gen_3413) -> q_gen_3409
<b, cons, s>(q_gen_3435, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3435, q_gen_3433) -> q_gen_3409
<b, cons, z>(q_gen_3403, q_gen_3433) -> q_gen_3409
}

Datatype: <elt, eltlist, nat>
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
(count([x, l1, _nn]) /\ count([x, cons(x, l1), _mn])) -> eq_nat([_mn, s(_nn)]) -> 54
(count([x, t1, _gn])) -> count([x, cons(x, t1), s(_gn)]) -> 55
(count([x, t1, _hn]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _hn]) -> 55
}
Sat witness: Found: ((count([x, t1, _gn])) -> count([x, cons(x, t1), s(_gn)]), {
_gn -> s(z)  ;  t1 -> cons(a, cons(b, nil))  ;  x -> a
})

-------------------------------------------
Step 54, which took 0.253073 s (model generation: 0.244768,  model checking: 0.008305):

Model:
|_
{
count -> 
{{{
Q={q_gen_3400, q_gen_3402, q_gen_3403, q_gen_3405, q_gen_3408, q_gen_3409, q_gen_3411, q_gen_3413, q_gen_3415, q_gen_3422, q_gen_3426, q_gen_3427, q_gen_3435, q_gen_3436, q_gen_3446},
Q_f={q_gen_3400},
Delta=
{
<cons>(q_gen_3408, q_gen_3422) -> q_gen_3402
<nil>() -> q_gen_3402
<a>() -> q_gen_3403
<b>() -> q_gen_3408
<cons>(q_gen_3403, q_gen_3413) -> q_gen_3413
<cons>(q_gen_3408, q_gen_3402) -> q_gen_3413
<cons>(q_gen_3403, q_gen_3402) -> q_gen_3415
<cons>(q_gen_3403, q_gen_3415) -> q_gen_3415
<cons>(q_gen_3408, q_gen_3446) -> q_gen_3415
<cons>(q_gen_3408, q_gen_3413) -> q_gen_3422
<z>() -> q_gen_3427
<s>(q_gen_3427) -> q_gen_3436
<s>(q_gen_3436) -> q_gen_3436
<cons>(q_gen_3403, q_gen_3446) -> q_gen_3446
<cons>(q_gen_3408, q_gen_3415) -> q_gen_3446
<a, s>(q_gen_3427) -> q_gen_3405
<b, z>() -> q_gen_3405
<a, z>() -> q_gen_3411
<a, s>(q_gen_3436) -> q_gen_3426
<b, s>(q_gen_3427) -> q_gen_3426
<b, s>(q_gen_3436) -> q_gen_3435
<a, cons, s>(q_gen_3405, q_gen_3413) -> q_gen_3400
<a, cons, s>(q_gen_3405, q_gen_3415) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3402) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3413) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3422) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3402) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3413) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3422) -> q_gen_3400
<a, nil, z>() -> q_gen_3400
<b, cons, s>(q_gen_3405, q_gen_3402) -> q_gen_3400
<b, cons, s>(q_gen_3405, q_gen_3415) -> q_gen_3400
<b, cons, s>(q_gen_3411, q_gen_3413) -> q_gen_3400
<b, cons, s>(q_gen_3411, q_gen_3446) -> q_gen_3400
<b, cons, s>(q_gen_3426, q_gen_3413) -> q_gen_3400
<b, cons, s>(q_gen_3426, q_gen_3422) -> q_gen_3400
<b, cons, s>(q_gen_3426, q_gen_3446) -> q_gen_3400
<b, cons, s>(q_gen_3435, q_gen_3415) -> q_gen_3400
<b, cons, s>(q_gen_3435, q_gen_3422) -> q_gen_3400
<b, cons, z>(q_gen_3403, q_gen_3402) -> q_gen_3400
<b, cons, z>(q_gen_3403, q_gen_3415) -> q_gen_3400
<b, nil, z>() -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3415) -> q_gen_3409
<a, cons, s>(q_gen_3411, q_gen_3446) -> q_gen_3409
<a, cons, s>(q_gen_3426, q_gen_3413) -> q_gen_3409
<a, cons, z>(q_gen_3403, q_gen_3402) -> q_gen_3409
<a, cons, z>(q_gen_3408, q_gen_3415) -> q_gen_3409
<a, cons, z>(q_gen_3408, q_gen_3446) -> q_gen_3409
<b, cons, s>(q_gen_3405, q_gen_3413) -> q_gen_3409
<b, cons, s>(q_gen_3405, q_gen_3422) -> q_gen_3409
<b, cons, s>(q_gen_3405, q_gen_3446) -> q_gen_3409
<b, cons, s>(q_gen_3411, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3411, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3435, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3435, q_gen_3413) -> q_gen_3409
<b, cons, s>(q_gen_3435, q_gen_3446) -> q_gen_3409
<b, cons, z>(q_gen_3403, q_gen_3413) -> q_gen_3409
}

Datatype: <elt, eltlist, nat>
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
(count([x, l1, _nn]) /\ count([x, cons(x, l1), _mn])) -> eq_nat([_mn, s(_nn)]) -> 57
(count([x, t1, _gn])) -> count([x, cons(x, t1), s(_gn)]) -> 55
(count([x, t1, _hn]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _hn]) -> 55
}
Sat witness: Found: ((count([x, l1, _nn]) /\ count([x, cons(x, l1), _mn])) -> eq_nat([_mn, s(_nn)]), {
_mn -> s(s(z))  ;  _nn -> z  ;  l1 -> cons(b, nil)  ;  x -> a
})

-------------------------------------------
Step 55, which took 0.298145 s (model generation: 0.283413,  model checking: 0.014732):

Model:
|_
{
count -> 
{{{
Q={q_gen_3400, q_gen_3402, q_gen_3403, q_gen_3405, q_gen_3408, q_gen_3409, q_gen_3411, q_gen_3413, q_gen_3415, q_gen_3422, q_gen_3426, q_gen_3427, q_gen_3433, q_gen_3435, q_gen_3436},
Q_f={q_gen_3400},
Delta=
{
<nil>() -> q_gen_3402
<a>() -> q_gen_3403
<b>() -> q_gen_3408
<cons>(q_gen_3403, q_gen_3433) -> q_gen_3413
<cons>(q_gen_3408, q_gen_3402) -> q_gen_3413
<cons>(q_gen_3408, q_gen_3415) -> q_gen_3413
<cons>(q_gen_3408, q_gen_3422) -> q_gen_3413
<cons>(q_gen_3403, q_gen_3402) -> q_gen_3415
<cons>(q_gen_3403, q_gen_3415) -> q_gen_3415
<cons>(q_gen_3408, q_gen_3413) -> q_gen_3422
<cons>(q_gen_3408, q_gen_3433) -> q_gen_3422
<z>() -> q_gen_3427
<cons>(q_gen_3403, q_gen_3413) -> q_gen_3433
<s>(q_gen_3427) -> q_gen_3436
<s>(q_gen_3436) -> q_gen_3436
<b, z>() -> q_gen_3405
<a, z>() -> q_gen_3411
<a, s>(q_gen_3436) -> q_gen_3426
<b, s>(q_gen_3427) -> q_gen_3426
<a, s>(q_gen_3427) -> q_gen_3435
<b, s>(q_gen_3436) -> q_gen_3435
<a, cons, s>(q_gen_3405, q_gen_3415) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3402) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3413) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3422) -> q_gen_3400
<a, cons, s>(q_gen_3435, q_gen_3433) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3402) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3413) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3422) -> q_gen_3400
<a, nil, z>() -> q_gen_3400
<b, cons, s>(q_gen_3405, q_gen_3402) -> q_gen_3400
<b, cons, s>(q_gen_3405, q_gen_3415) -> q_gen_3400
<b, cons, s>(q_gen_3411, q_gen_3413) -> q_gen_3400
<b, cons, s>(q_gen_3411, q_gen_3433) -> q_gen_3400
<b, cons, s>(q_gen_3426, q_gen_3413) -> q_gen_3400
<b, cons, s>(q_gen_3426, q_gen_3433) -> q_gen_3400
<b, cons, s>(q_gen_3435, q_gen_3415) -> q_gen_3400
<b, cons, s>(q_gen_3435, q_gen_3422) -> q_gen_3400
<b, cons, z>(q_gen_3403, q_gen_3402) -> q_gen_3400
<b, cons, z>(q_gen_3403, q_gen_3415) -> q_gen_3400
<b, nil, z>() -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3415) -> q_gen_3409
<a, cons, s>(q_gen_3411, q_gen_3433) -> q_gen_3409
<a, cons, s>(q_gen_3426, q_gen_3413) -> q_gen_3409
<a, cons, s>(q_gen_3435, q_gen_3413) -> q_gen_3409
<a, cons, z>(q_gen_3403, q_gen_3402) -> q_gen_3409
<a, cons, z>(q_gen_3408, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3405, q_gen_3413) -> q_gen_3409
<b, cons, s>(q_gen_3405, q_gen_3422) -> q_gen_3409
<b, cons, s>(q_gen_3411, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3411, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3422) -> q_gen_3409
<b, cons, s>(q_gen_3435, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3435, q_gen_3413) -> q_gen_3409
<b, cons, s>(q_gen_3435, q_gen_3433) -> q_gen_3409
<b, cons, z>(q_gen_3403, q_gen_3413) -> q_gen_3409
<b, cons, z>(q_gen_3403, q_gen_3433) -> q_gen_3409
}

Datatype: <elt, eltlist, nat>
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
(count([x, l1, _nn]) /\ count([x, cons(x, l1), _mn])) -> eq_nat([_mn, s(_nn)]) -> 57
(count([x, t1, _gn])) -> count([x, cons(x, t1), s(_gn)]) -> 55
(count([x, t1, _hn]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _hn]) -> 58
}
Sat witness: Found: ((count([x, t1, _hn]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _hn]), {
_hn -> s(s(z))  ;  h1 -> b  ;  t1 -> cons(a, cons(a, cons(b, cons(a, nil))))  ;  x -> a
})

-------------------------------------------
Step 56, which took 0.314305 s (model generation: 0.304393,  model checking: 0.009912):

Model:
|_
{
count -> 
{{{
Q={q_gen_3400, q_gen_3402, q_gen_3403, q_gen_3405, q_gen_3408, q_gen_3409, q_gen_3411, q_gen_3413, q_gen_3415, q_gen_3422, q_gen_3426, q_gen_3427, q_gen_3433, q_gen_3435, q_gen_3436},
Q_f={q_gen_3400},
Delta=
{
<nil>() -> q_gen_3402
<a>() -> q_gen_3403
<b>() -> q_gen_3408
<cons>(q_gen_3408, q_gen_3402) -> q_gen_3413
<cons>(q_gen_3403, q_gen_3402) -> q_gen_3415
<cons>(q_gen_3403, q_gen_3415) -> q_gen_3415
<cons>(q_gen_3408, q_gen_3413) -> q_gen_3422
<cons>(q_gen_3408, q_gen_3422) -> q_gen_3422
<cons>(q_gen_3408, q_gen_3433) -> q_gen_3422
<z>() -> q_gen_3427
<cons>(q_gen_3403, q_gen_3413) -> q_gen_3433
<cons>(q_gen_3403, q_gen_3433) -> q_gen_3433
<cons>(q_gen_3408, q_gen_3415) -> q_gen_3433
<s>(q_gen_3427) -> q_gen_3436
<s>(q_gen_3436) -> q_gen_3436
<a, s>(q_gen_3427) -> q_gen_3405
<b, z>() -> q_gen_3405
<a, z>() -> q_gen_3411
<b, s>(q_gen_3427) -> q_gen_3426
<a, s>(q_gen_3436) -> q_gen_3435
<b, s>(q_gen_3436) -> q_gen_3435
<a, cons, s>(q_gen_3405, q_gen_3415) -> q_gen_3400
<a, cons, s>(q_gen_3405, q_gen_3433) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3402) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3413) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3422) -> q_gen_3400
<a, cons, s>(q_gen_3426, q_gen_3433) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3402) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3413) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3422) -> q_gen_3400
<a, nil, z>() -> q_gen_3400
<b, cons, s>(q_gen_3405, q_gen_3402) -> q_gen_3400
<b, cons, s>(q_gen_3405, q_gen_3415) -> q_gen_3400
<b, cons, s>(q_gen_3411, q_gen_3413) -> q_gen_3400
<b, cons, s>(q_gen_3411, q_gen_3433) -> q_gen_3400
<b, cons, s>(q_gen_3426, q_gen_3413) -> q_gen_3400
<b, cons, s>(q_gen_3426, q_gen_3433) -> q_gen_3400
<b, cons, s>(q_gen_3435, q_gen_3422) -> q_gen_3400
<b, cons, z>(q_gen_3403, q_gen_3402) -> q_gen_3400
<b, cons, z>(q_gen_3403, q_gen_3415) -> q_gen_3400
<b, cons, z>(q_gen_3403, q_gen_3433) -> q_gen_3400
<b, nil, z>() -> q_gen_3400
<a, cons, s>(q_gen_3405, q_gen_3413) -> q_gen_3409
<a, cons, s>(q_gen_3411, q_gen_3415) -> q_gen_3409
<a, cons, s>(q_gen_3411, q_gen_3433) -> q_gen_3409
<a, cons, s>(q_gen_3426, q_gen_3413) -> q_gen_3409
<a, cons, s>(q_gen_3435, q_gen_3413) -> q_gen_3409
<a, cons, z>(q_gen_3403, q_gen_3402) -> q_gen_3409
<a, cons, z>(q_gen_3408, q_gen_3415) -> q_gen_3409
<a, cons, z>(q_gen_3408, q_gen_3433) -> q_gen_3409
<b, cons, s>(q_gen_3405, q_gen_3413) -> q_gen_3409
<b, cons, s>(q_gen_3405, q_gen_3422) -> q_gen_3409
<b, cons, s>(q_gen_3405, q_gen_3433) -> q_gen_3409
<b, cons, s>(q_gen_3411, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3411, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3422) -> q_gen_3409
<b, cons, s>(q_gen_3435, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3435, q_gen_3413) -> q_gen_3409
<b, cons, s>(q_gen_3435, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3435, q_gen_3433) -> q_gen_3409
}

Datatype: <elt, eltlist, nat>
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
(count([x, l1, _nn]) /\ count([x, cons(x, l1), _mn])) -> eq_nat([_mn, s(_nn)]) -> 57
(count([x, t1, _gn])) -> count([x, cons(x, t1), s(_gn)]) -> 58
(count([x, t1, _hn]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _hn]) -> 58
}
Sat witness: Found: ((count([x, t1, _gn])) -> count([x, cons(x, t1), s(_gn)]), {
_gn -> z  ;  t1 -> cons(a, cons(a, cons(b, nil)))  ;  x -> b
})

-------------------------------------------
Step 57, which took 0.345590 s (model generation: 0.315789,  model checking: 0.029801):

Model:
|_
{
count -> 
{{{
Q={q_gen_3400, q_gen_3402, q_gen_3403, q_gen_3405, q_gen_3408, q_gen_3409, q_gen_3411, q_gen_3413, q_gen_3415, q_gen_3422, q_gen_3426, q_gen_3427, q_gen_3433, q_gen_3435, q_gen_3436},
Q_f={q_gen_3400},
Delta=
{
<nil>() -> q_gen_3402
<a>() -> q_gen_3403
<b>() -> q_gen_3408
<cons>(q_gen_3408, q_gen_3402) -> q_gen_3413
<cons>(q_gen_3403, q_gen_3402) -> q_gen_3415
<cons>(q_gen_3403, q_gen_3415) -> q_gen_3415
<cons>(q_gen_3408, q_gen_3413) -> q_gen_3422
<cons>(q_gen_3408, q_gen_3422) -> q_gen_3422
<cons>(q_gen_3408, q_gen_3433) -> q_gen_3422
<z>() -> q_gen_3427
<cons>(q_gen_3403, q_gen_3413) -> q_gen_3433
<cons>(q_gen_3403, q_gen_3433) -> q_gen_3433
<cons>(q_gen_3408, q_gen_3415) -> q_gen_3433
<s>(q_gen_3427) -> q_gen_3436
<s>(q_gen_3436) -> q_gen_3436
<a, s>(q_gen_3427) -> q_gen_3405
<b, z>() -> q_gen_3405
<a, z>() -> q_gen_3411
<b, s>(q_gen_3427) -> q_gen_3426
<a, s>(q_gen_3436) -> q_gen_3435
<b, s>(q_gen_3436) -> q_gen_3435
<a, cons, s>(q_gen_3405, q_gen_3415) -> q_gen_3400
<a, cons, s>(q_gen_3405, q_gen_3433) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3402) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3413) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3422) -> q_gen_3400
<a, cons, s>(q_gen_3426, q_gen_3433) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3402) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3413) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3422) -> q_gen_3400
<a, nil, z>() -> q_gen_3400
<b, cons, s>(q_gen_3405, q_gen_3402) -> q_gen_3400
<b, cons, s>(q_gen_3405, q_gen_3415) -> q_gen_3400
<b, cons, s>(q_gen_3411, q_gen_3413) -> q_gen_3400
<b, cons, s>(q_gen_3411, q_gen_3433) -> q_gen_3400
<b, cons, s>(q_gen_3426, q_gen_3413) -> q_gen_3400
<b, cons, s>(q_gen_3426, q_gen_3433) -> q_gen_3400
<b, cons, s>(q_gen_3435, q_gen_3422) -> q_gen_3400
<b, cons, z>(q_gen_3403, q_gen_3402) -> q_gen_3400
<b, cons, z>(q_gen_3403, q_gen_3415) -> q_gen_3400
<b, nil, z>() -> q_gen_3400
<a, cons, s>(q_gen_3405, q_gen_3413) -> q_gen_3409
<a, cons, s>(q_gen_3411, q_gen_3415) -> q_gen_3409
<a, cons, s>(q_gen_3411, q_gen_3433) -> q_gen_3409
<a, cons, s>(q_gen_3426, q_gen_3413) -> q_gen_3409
<a, cons, s>(q_gen_3435, q_gen_3413) -> q_gen_3409
<a, cons, z>(q_gen_3403, q_gen_3402) -> q_gen_3409
<a, cons, z>(q_gen_3408, q_gen_3415) -> q_gen_3409
<a, cons, z>(q_gen_3408, q_gen_3433) -> q_gen_3409
<b, cons, s>(q_gen_3405, q_gen_3413) -> q_gen_3409
<b, cons, s>(q_gen_3405, q_gen_3422) -> q_gen_3409
<b, cons, s>(q_gen_3405, q_gen_3433) -> q_gen_3409
<b, cons, s>(q_gen_3411, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3411, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3422) -> q_gen_3409
<b, cons, s>(q_gen_3435, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3435, q_gen_3413) -> q_gen_3409
<b, cons, s>(q_gen_3435, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3435, q_gen_3433) -> q_gen_3409
<b, cons, z>(q_gen_3403, q_gen_3433) -> q_gen_3409
}

Datatype: <elt, eltlist, nat>
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
(count([x, l1, _nn]) /\ count([x, cons(x, l1), _mn])) -> eq_nat([_mn, s(_nn)]) -> 60
(count([x, t1, _gn])) -> count([x, cons(x, t1), s(_gn)]) -> 58
(count([x, t1, _hn]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _hn]) -> 58
}
Sat witness: Found: ((count([x, l1, _nn]) /\ count([x, cons(x, l1), _mn])) -> eq_nat([_mn, s(_nn)]), {
_mn -> s(s(s(s(z))))  ;  _nn -> s(s(z))  ;  l1 -> cons(b, cons(b, nil))  ;  x -> b
})

-------------------------------------------
Step 58, which took 0.328902 s (model generation: 0.317589,  model checking: 0.011313):

Model:
|_
{
count -> 
{{{
Q={q_gen_3400, q_gen_3402, q_gen_3403, q_gen_3405, q_gen_3408, q_gen_3409, q_gen_3411, q_gen_3413, q_gen_3415, q_gen_3422, q_gen_3426, q_gen_3427, q_gen_3433, q_gen_3435, q_gen_3436, q_gen_3476},
Q_f={q_gen_3400},
Delta=
{
<nil>() -> q_gen_3402
<a>() -> q_gen_3403
<b>() -> q_gen_3408
<cons>(q_gen_3408, q_gen_3402) -> q_gen_3413
<cons>(q_gen_3403, q_gen_3402) -> q_gen_3415
<cons>(q_gen_3403, q_gen_3415) -> q_gen_3415
<cons>(q_gen_3408, q_gen_3413) -> q_gen_3422
<cons>(q_gen_3408, q_gen_3422) -> q_gen_3422
<cons>(q_gen_3408, q_gen_3433) -> q_gen_3422
<z>() -> q_gen_3427
<cons>(q_gen_3403, q_gen_3413) -> q_gen_3433
<cons>(q_gen_3403, q_gen_3433) -> q_gen_3433
<cons>(q_gen_3408, q_gen_3415) -> q_gen_3433
<s>(q_gen_3427) -> q_gen_3436
<s>(q_gen_3436) -> q_gen_3476
<b, s>(q_gen_3476) -> q_gen_3405
<b, z>() -> q_gen_3405
<a, z>() -> q_gen_3411
<a, s>(q_gen_3427) -> q_gen_3426
<b, s>(q_gen_3427) -> q_gen_3426
<a, s>(q_gen_3436) -> q_gen_3435
<b, s>(q_gen_3436) -> q_gen_3435
<a, cons, s>(q_gen_3405, q_gen_3415) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3402) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3413) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3422) -> q_gen_3400
<a, cons, s>(q_gen_3426, q_gen_3433) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3402) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3413) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3422) -> q_gen_3400
<a, nil, z>() -> q_gen_3400
<b, cons, s>(q_gen_3405, q_gen_3402) -> q_gen_3400
<b, cons, s>(q_gen_3405, q_gen_3415) -> q_gen_3400
<b, cons, s>(q_gen_3411, q_gen_3413) -> q_gen_3400
<b, cons, s>(q_gen_3411, q_gen_3433) -> q_gen_3400
<b, cons, s>(q_gen_3426, q_gen_3413) -> q_gen_3400
<b, cons, s>(q_gen_3426, q_gen_3433) -> q_gen_3400
<b, cons, s>(q_gen_3435, q_gen_3422) -> q_gen_3400
<b, cons, z>(q_gen_3403, q_gen_3402) -> q_gen_3400
<b, cons, z>(q_gen_3403, q_gen_3415) -> q_gen_3400
<b, nil, z>() -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3415) -> q_gen_3409
<a, cons, s>(q_gen_3411, q_gen_3433) -> q_gen_3409
<a, cons, s>(q_gen_3426, q_gen_3413) -> q_gen_3409
<a, cons, s>(q_gen_3435, q_gen_3413) -> q_gen_3409
<a, cons, z>(q_gen_3403, q_gen_3402) -> q_gen_3409
<a, cons, z>(q_gen_3408, q_gen_3415) -> q_gen_3409
<a, cons, z>(q_gen_3408, q_gen_3433) -> q_gen_3409
<b, cons, s>(q_gen_3405, q_gen_3413) -> q_gen_3409
<b, cons, s>(q_gen_3405, q_gen_3422) -> q_gen_3409
<b, cons, s>(q_gen_3405, q_gen_3433) -> q_gen_3409
<b, cons, s>(q_gen_3411, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3411, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3422) -> q_gen_3409
<b, cons, s>(q_gen_3435, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3435, q_gen_3413) -> q_gen_3409
<b, cons, s>(q_gen_3435, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3435, q_gen_3433) -> q_gen_3409
<b, cons, z>(q_gen_3403, q_gen_3433) -> q_gen_3409
}

Datatype: <elt, eltlist, nat>
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
(count([x, l1, _nn]) /\ count([x, cons(x, l1), _mn])) -> eq_nat([_mn, s(_nn)]) -> 60
(count([x, t1, _gn])) -> count([x, cons(x, t1), s(_gn)]) -> 58
(count([x, t1, _hn]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _hn]) -> 61
}
Sat witness: Found: ((count([x, t1, _hn]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _hn]), {
_hn -> s(s(z))  ;  h1 -> a  ;  t1 -> cons(b, cons(b, cons(a, cons(a, nil))))  ;  x -> b
})

-------------------------------------------
Step 59, which took 0.392012 s (model generation: 0.372001,  model checking: 0.020011):

Model:
|_
{
count -> 
{{{
Q={q_gen_3400, q_gen_3402, q_gen_3403, q_gen_3405, q_gen_3408, q_gen_3409, q_gen_3411, q_gen_3413, q_gen_3415, q_gen_3422, q_gen_3426, q_gen_3427, q_gen_3433, q_gen_3435, q_gen_3436, q_gen_3476},
Q_f={q_gen_3400},
Delta=
{
<nil>() -> q_gen_3402
<a>() -> q_gen_3403
<b>() -> q_gen_3408
<cons>(q_gen_3408, q_gen_3402) -> q_gen_3413
<cons>(q_gen_3408, q_gen_3415) -> q_gen_3413
<cons>(q_gen_3408, q_gen_3422) -> q_gen_3413
<cons>(q_gen_3408, q_gen_3433) -> q_gen_3413
<cons>(q_gen_3403, q_gen_3402) -> q_gen_3415
<cons>(q_gen_3403, q_gen_3415) -> q_gen_3415
<cons>(q_gen_3403, q_gen_3433) -> q_gen_3415
<cons>(q_gen_3408, q_gen_3413) -> q_gen_3422
<z>() -> q_gen_3427
<cons>(q_gen_3403, q_gen_3413) -> q_gen_3433
<s>(q_gen_3427) -> q_gen_3436
<s>(q_gen_3436) -> q_gen_3476
<b, s>(q_gen_3476) -> q_gen_3405
<b, z>() -> q_gen_3405
<a, z>() -> q_gen_3411
<a, s>(q_gen_3436) -> q_gen_3426
<b, s>(q_gen_3427) -> q_gen_3426
<a, s>(q_gen_3427) -> q_gen_3435
<b, s>(q_gen_3436) -> q_gen_3435
<a, cons, s>(q_gen_3405, q_gen_3415) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3402) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3413) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3422) -> q_gen_3400
<a, cons, s>(q_gen_3426, q_gen_3415) -> q_gen_3400
<a, cons, s>(q_gen_3435, q_gen_3433) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3402) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3413) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3422) -> q_gen_3400
<a, nil, z>() -> q_gen_3400
<b, cons, s>(q_gen_3405, q_gen_3402) -> q_gen_3400
<b, cons, s>(q_gen_3405, q_gen_3415) -> q_gen_3400
<b, cons, s>(q_gen_3411, q_gen_3413) -> q_gen_3400
<b, cons, s>(q_gen_3411, q_gen_3433) -> q_gen_3400
<b, cons, s>(q_gen_3426, q_gen_3413) -> q_gen_3400
<b, cons, s>(q_gen_3426, q_gen_3433) -> q_gen_3400
<b, cons, s>(q_gen_3435, q_gen_3422) -> q_gen_3400
<b, cons, z>(q_gen_3403, q_gen_3402) -> q_gen_3400
<b, cons, z>(q_gen_3403, q_gen_3415) -> q_gen_3400
<b, cons, z>(q_gen_3403, q_gen_3433) -> q_gen_3400
<b, nil, z>() -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3415) -> q_gen_3409
<a, cons, s>(q_gen_3411, q_gen_3433) -> q_gen_3409
<a, cons, s>(q_gen_3426, q_gen_3413) -> q_gen_3409
<a, cons, s>(q_gen_3435, q_gen_3413) -> q_gen_3409
<a, cons, z>(q_gen_3403, q_gen_3402) -> q_gen_3409
<a, cons, z>(q_gen_3408, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3405, q_gen_3413) -> q_gen_3409
<b, cons, s>(q_gen_3405, q_gen_3422) -> q_gen_3409
<b, cons, s>(q_gen_3411, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3411, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3422) -> q_gen_3409
<b, cons, s>(q_gen_3435, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3435, q_gen_3413) -> q_gen_3409
<b, cons, s>(q_gen_3435, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3435, q_gen_3433) -> q_gen_3409
}

Datatype: <elt, eltlist, nat>
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
(count([x, l1, _nn]) /\ count([x, cons(x, l1), _mn])) -> eq_nat([_mn, s(_nn)]) -> 60
(count([x, t1, _gn])) -> count([x, cons(x, t1), s(_gn)]) -> 61
(count([x, t1, _hn]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _hn]) -> 61
}
Sat witness: Found: ((count([x, t1, _gn])) -> count([x, cons(x, t1), s(_gn)]), {
_gn -> s(s(s(z)))  ;  t1 -> cons(b, cons(b, cons(b, cons(a, cons(b, nil)))))  ;  x -> b
})

-------------------------------------------
Step 60, which took 0.494559 s (model generation: 0.487525,  model checking: 0.007034):

Model:
|_
{
count -> 
{{{
Q={q_gen_3400, q_gen_3402, q_gen_3403, q_gen_3405, q_gen_3408, q_gen_3409, q_gen_3411, q_gen_3413, q_gen_3415, q_gen_3422, q_gen_3426, q_gen_3427, q_gen_3433, q_gen_3435, q_gen_3436, q_gen_3476},
Q_f={q_gen_3400},
Delta=
{
<cons>(q_gen_3408, q_gen_3422) -> q_gen_3402
<nil>() -> q_gen_3402
<a>() -> q_gen_3403
<b>() -> q_gen_3408
<cons>(q_gen_3403, q_gen_3433) -> q_gen_3413
<cons>(q_gen_3408, q_gen_3402) -> q_gen_3413
<cons>(q_gen_3403, q_gen_3402) -> q_gen_3415
<cons>(q_gen_3403, q_gen_3415) -> q_gen_3415
<cons>(q_gen_3408, q_gen_3413) -> q_gen_3422
<cons>(q_gen_3408, q_gen_3433) -> q_gen_3422
<z>() -> q_gen_3427
<cons>(q_gen_3403, q_gen_3413) -> q_gen_3433
<cons>(q_gen_3408, q_gen_3415) -> q_gen_3433
<s>(q_gen_3427) -> q_gen_3436
<s>(q_gen_3436) -> q_gen_3476
<a, s>(q_gen_3436) -> q_gen_3405
<b, s>(q_gen_3476) -> q_gen_3405
<b, z>() -> q_gen_3405
<a, z>() -> q_gen_3411
<b, s>(q_gen_3427) -> q_gen_3426
<a, s>(q_gen_3427) -> q_gen_3435
<b, s>(q_gen_3436) -> q_gen_3435
<a, cons, s>(q_gen_3405, q_gen_3415) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3402) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3413) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3422) -> q_gen_3400
<a, cons, s>(q_gen_3435, q_gen_3433) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3402) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3413) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3422) -> q_gen_3400
<a, nil, z>() -> q_gen_3400
<b, cons, s>(q_gen_3405, q_gen_3402) -> q_gen_3400
<b, cons, s>(q_gen_3405, q_gen_3415) -> q_gen_3400
<b, cons, s>(q_gen_3411, q_gen_3413) -> q_gen_3400
<b, cons, s>(q_gen_3411, q_gen_3433) -> q_gen_3400
<b, cons, s>(q_gen_3426, q_gen_3413) -> q_gen_3400
<b, cons, s>(q_gen_3426, q_gen_3433) -> q_gen_3400
<b, cons, s>(q_gen_3435, q_gen_3422) -> q_gen_3400
<b, cons, z>(q_gen_3403, q_gen_3402) -> q_gen_3400
<b, cons, z>(q_gen_3403, q_gen_3415) -> q_gen_3400
<b, nil, z>() -> q_gen_3400
<a, cons, s>(q_gen_3405, q_gen_3413) -> q_gen_3409
<a, cons, s>(q_gen_3411, q_gen_3415) -> q_gen_3409
<a, cons, s>(q_gen_3411, q_gen_3433) -> q_gen_3409
<a, cons, s>(q_gen_3426, q_gen_3413) -> q_gen_3409
<a, cons, s>(q_gen_3426, q_gen_3433) -> q_gen_3409
<a, cons, s>(q_gen_3435, q_gen_3413) -> q_gen_3409
<a, cons, z>(q_gen_3403, q_gen_3402) -> q_gen_3409
<a, cons, z>(q_gen_3408, q_gen_3415) -> q_gen_3409
<a, cons, z>(q_gen_3408, q_gen_3433) -> q_gen_3409
<b, cons, s>(q_gen_3405, q_gen_3413) -> q_gen_3409
<b, cons, s>(q_gen_3405, q_gen_3422) -> q_gen_3409
<b, cons, s>(q_gen_3405, q_gen_3433) -> q_gen_3409
<b, cons, s>(q_gen_3411, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3411, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3422) -> q_gen_3409
<b, cons, s>(q_gen_3435, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3435, q_gen_3413) -> q_gen_3409
<b, cons, s>(q_gen_3435, q_gen_3415) -> q_gen_3409
<b, cons, z>(q_gen_3403, q_gen_3413) -> q_gen_3409
<b, cons, z>(q_gen_3403, q_gen_3433) -> q_gen_3409
}

Datatype: <elt, eltlist, nat>
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
(count([x, l1, _nn]) /\ count([x, cons(x, l1), _mn])) -> eq_nat([_mn, s(_nn)]) -> 63
(count([x, t1, _gn])) -> count([x, cons(x, t1), s(_gn)]) -> 61
(count([x, t1, _hn]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _hn]) -> 61
}
Sat witness: Found: ((count([x, l1, _nn]) /\ count([x, cons(x, l1), _mn])) -> eq_nat([_mn, s(_nn)]), {
_mn -> s(s(s(s(z))))  ;  _nn -> z  ;  l1 -> cons(a, nil)  ;  x -> b
})

-------------------------------------------
Step 61, which took 0.535351 s (model generation: 0.514911,  model checking: 0.020440):

Model:
|_
{
count -> 
{{{
Q={q_gen_3400, q_gen_3402, q_gen_3403, q_gen_3405, q_gen_3408, q_gen_3409, q_gen_3411, q_gen_3413, q_gen_3415, q_gen_3422, q_gen_3426, q_gen_3427, q_gen_3433, q_gen_3435, q_gen_3436, q_gen_3470, q_gen_3476},
Q_f={q_gen_3400},
Delta=
{
<cons>(q_gen_3403, q_gen_3433) -> q_gen_3402
<nil>() -> q_gen_3402
<a>() -> q_gen_3403
<b>() -> q_gen_3408
<cons>(q_gen_3408, q_gen_3402) -> q_gen_3413
<cons>(q_gen_3408, q_gen_3415) -> q_gen_3413
<cons>(q_gen_3403, q_gen_3402) -> q_gen_3415
<cons>(q_gen_3403, q_gen_3415) -> q_gen_3422
<cons>(q_gen_3408, q_gen_3413) -> q_gen_3422
<cons>(q_gen_3408, q_gen_3422) -> q_gen_3422
<z>() -> q_gen_3427
<cons>(q_gen_3403, q_gen_3413) -> q_gen_3433
<cons>(q_gen_3408, q_gen_3433) -> q_gen_3433
<s>(q_gen_3427) -> q_gen_3436
<s>(q_gen_3436) -> q_gen_3476
<b, z>() -> q_gen_3405
<a, z>() -> q_gen_3411
<b, s>(q_gen_3427) -> q_gen_3426
<b, s>(q_gen_3436) -> q_gen_3435
<a, s>(q_gen_3427) -> q_gen_3470
<a, s>(q_gen_3436) -> q_gen_3470
<b, s>(q_gen_3476) -> q_gen_3470
<a, cons, s>(q_gen_3405, q_gen_3415) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3402) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3413) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3422) -> q_gen_3400
<a, cons, s>(q_gen_3426, q_gen_3402) -> q_gen_3400
<a, cons, s>(q_gen_3470, q_gen_3433) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3402) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3413) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3422) -> q_gen_3400
<a, nil, z>() -> q_gen_3400
<b, cons, s>(q_gen_3405, q_gen_3402) -> q_gen_3400
<b, cons, s>(q_gen_3405, q_gen_3415) -> q_gen_3400
<b, cons, s>(q_gen_3405, q_gen_3422) -> q_gen_3400
<b, cons, s>(q_gen_3411, q_gen_3413) -> q_gen_3400
<b, cons, s>(q_gen_3411, q_gen_3433) -> q_gen_3400
<b, cons, s>(q_gen_3426, q_gen_3413) -> q_gen_3400
<b, cons, s>(q_gen_3426, q_gen_3433) -> q_gen_3400
<b, cons, s>(q_gen_3435, q_gen_3422) -> q_gen_3400
<b, cons, s>(q_gen_3470, q_gen_3433) -> q_gen_3400
<b, cons, z>(q_gen_3403, q_gen_3402) -> q_gen_3400
<b, cons, z>(q_gen_3403, q_gen_3415) -> q_gen_3400
<b, cons, z>(q_gen_3403, q_gen_3422) -> q_gen_3400
<b, nil, z>() -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3415) -> q_gen_3409
<a, cons, s>(q_gen_3411, q_gen_3433) -> q_gen_3409
<a, cons, s>(q_gen_3426, q_gen_3413) -> q_gen_3409
<a, cons, s>(q_gen_3470, q_gen_3413) -> q_gen_3409
<a, cons, z>(q_gen_3403, q_gen_3402) -> q_gen_3409
<a, cons, z>(q_gen_3408, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3405, q_gen_3413) -> q_gen_3409
<b, cons, s>(q_gen_3405, q_gen_3433) -> q_gen_3409
<b, cons, s>(q_gen_3411, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3411, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3422) -> q_gen_3409
<b, cons, s>(q_gen_3435, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3435, q_gen_3413) -> q_gen_3409
<b, cons, s>(q_gen_3435, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3435, q_gen_3433) -> q_gen_3409
<b, cons, s>(q_gen_3470, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3470, q_gen_3413) -> q_gen_3409
<b, cons, s>(q_gen_3470, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3470, q_gen_3422) -> q_gen_3409
<b, cons, z>(q_gen_3403, q_gen_3433) -> q_gen_3409
}

Datatype: <elt, eltlist, nat>
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
(count([x, l1, _nn]) /\ count([x, cons(x, l1), _mn])) -> eq_nat([_mn, s(_nn)]) -> 63
(count([x, t1, _gn])) -> count([x, cons(x, t1), s(_gn)]) -> 61
(count([x, t1, _hn]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _hn]) -> 64
}
Sat witness: Found: ((count([x, t1, _hn]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _hn]), {
_hn -> s(s(z))  ;  h1 -> b  ;  t1 -> cons(b, nil)  ;  x -> a
})

-------------------------------------------
Step 62, which took 0.654966 s (model generation: 0.635728,  model checking: 0.019238):

Model:
|_
{
count -> 
{{{
Q={q_gen_3400, q_gen_3402, q_gen_3403, q_gen_3405, q_gen_3408, q_gen_3409, q_gen_3411, q_gen_3413, q_gen_3415, q_gen_3422, q_gen_3426, q_gen_3427, q_gen_3433, q_gen_3435, q_gen_3436, q_gen_3470, q_gen_3476},
Q_f={q_gen_3400},
Delta=
{
<cons>(q_gen_3403, q_gen_3415) -> q_gen_3402
<cons>(q_gen_3408, q_gen_3422) -> q_gen_3402
<nil>() -> q_gen_3402
<a>() -> q_gen_3403
<b>() -> q_gen_3408
<cons>(q_gen_3408, q_gen_3402) -> q_gen_3413
<cons>(q_gen_3408, q_gen_3415) -> q_gen_3413
<cons>(q_gen_3403, q_gen_3402) -> q_gen_3415
<cons>(q_gen_3403, q_gen_3433) -> q_gen_3422
<cons>(q_gen_3408, q_gen_3413) -> q_gen_3422
<z>() -> q_gen_3427
<cons>(q_gen_3403, q_gen_3413) -> q_gen_3433
<cons>(q_gen_3408, q_gen_3433) -> q_gen_3433
<s>(q_gen_3427) -> q_gen_3436
<s>(q_gen_3436) -> q_gen_3476
<b, z>() -> q_gen_3405
<a, z>() -> q_gen_3411
<a, s>(q_gen_3427) -> q_gen_3426
<b, s>(q_gen_3427) -> q_gen_3426
<b, s>(q_gen_3436) -> q_gen_3435
<a, s>(q_gen_3436) -> q_gen_3470
<b, s>(q_gen_3476) -> q_gen_3470
<a, cons, s>(q_gen_3405, q_gen_3415) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3402) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3413) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3422) -> q_gen_3400
<a, cons, s>(q_gen_3426, q_gen_3422) -> q_gen_3400
<a, cons, s>(q_gen_3426, q_gen_3433) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3402) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3413) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3422) -> q_gen_3400
<a, nil, z>() -> q_gen_3400
<b, cons, s>(q_gen_3405, q_gen_3402) -> q_gen_3400
<b, cons, s>(q_gen_3405, q_gen_3415) -> q_gen_3400
<b, cons, s>(q_gen_3411, q_gen_3413) -> q_gen_3400
<b, cons, s>(q_gen_3411, q_gen_3433) -> q_gen_3400
<b, cons, s>(q_gen_3426, q_gen_3413) -> q_gen_3400
<b, cons, s>(q_gen_3426, q_gen_3422) -> q_gen_3400
<b, cons, s>(q_gen_3426, q_gen_3433) -> q_gen_3400
<b, cons, s>(q_gen_3435, q_gen_3422) -> q_gen_3400
<b, cons, z>(q_gen_3403, q_gen_3402) -> q_gen_3400
<b, cons, z>(q_gen_3403, q_gen_3415) -> q_gen_3400
<b, cons, z>(q_gen_3403, q_gen_3422) -> q_gen_3400
<b, nil, z>() -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3415) -> q_gen_3409
<a, cons, s>(q_gen_3411, q_gen_3433) -> q_gen_3409
<a, cons, s>(q_gen_3426, q_gen_3402) -> q_gen_3409
<a, cons, s>(q_gen_3426, q_gen_3413) -> q_gen_3409
<a, cons, s>(q_gen_3470, q_gen_3413) -> q_gen_3409
<a, cons, z>(q_gen_3403, q_gen_3402) -> q_gen_3409
<a, cons, z>(q_gen_3408, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3405, q_gen_3413) -> q_gen_3409
<b, cons, s>(q_gen_3405, q_gen_3422) -> q_gen_3409
<b, cons, s>(q_gen_3405, q_gen_3433) -> q_gen_3409
<b, cons, s>(q_gen_3411, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3411, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3435, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3435, q_gen_3413) -> q_gen_3409
<b, cons, s>(q_gen_3435, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3435, q_gen_3433) -> q_gen_3409
<b, cons, s>(q_gen_3470, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3470, q_gen_3413) -> q_gen_3409
<b, cons, s>(q_gen_3470, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3470, q_gen_3422) -> q_gen_3409
<b, cons, s>(q_gen_3470, q_gen_3433) -> q_gen_3409
<b, cons, z>(q_gen_3403, q_gen_3433) -> q_gen_3409
}

Datatype: <elt, eltlist, nat>
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
(count([x, l1, _nn]) /\ count([x, cons(x, l1), _mn])) -> eq_nat([_mn, s(_nn)]) -> 63
(count([x, t1, _gn])) -> count([x, cons(x, t1), s(_gn)]) -> 64
(count([x, t1, _hn]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _hn]) -> 64
}
Sat witness: Found: ((count([x, t1, _gn])) -> count([x, cons(x, t1), s(_gn)]), {
_gn -> s(s(z))  ;  t1 -> cons(b, cons(b, cons(a, cons(b, nil))))  ;  x -> b
})

-------------------------------------------
Step 63, which took 0.780315 s (model generation: 0.761811,  model checking: 0.018504):

Model:
|_
{
count -> 
{{{
Q={q_gen_3400, q_gen_3402, q_gen_3403, q_gen_3405, q_gen_3408, q_gen_3409, q_gen_3411, q_gen_3413, q_gen_3415, q_gen_3422, q_gen_3426, q_gen_3427, q_gen_3433, q_gen_3435, q_gen_3436, q_gen_3475, q_gen_3476},
Q_f={q_gen_3400},
Delta=
{
<cons>(q_gen_3403, q_gen_3415) -> q_gen_3402
<nil>() -> q_gen_3402
<a>() -> q_gen_3403
<b>() -> q_gen_3408
<cons>(q_gen_3408, q_gen_3402) -> q_gen_3413
<cons>(q_gen_3408, q_gen_3422) -> q_gen_3413
<cons>(q_gen_3403, q_gen_3402) -> q_gen_3415
<cons>(q_gen_3408, q_gen_3413) -> q_gen_3422
<cons>(q_gen_3408, q_gen_3433) -> q_gen_3422
<z>() -> q_gen_3427
<cons>(q_gen_3403, q_gen_3413) -> q_gen_3433
<cons>(q_gen_3403, q_gen_3433) -> q_gen_3433
<cons>(q_gen_3408, q_gen_3415) -> q_gen_3433
<s>(q_gen_3427) -> q_gen_3436
<s>(q_gen_3436) -> q_gen_3476
<b, z>() -> q_gen_3405
<a, z>() -> q_gen_3411
<a, s>(q_gen_3436) -> q_gen_3426
<b, s>(q_gen_3427) -> q_gen_3426
<a, s>(q_gen_3427) -> q_gen_3435
<b, s>(q_gen_3436) -> q_gen_3435
<b, s>(q_gen_3476) -> q_gen_3475
<a, cons, s>(q_gen_3405, q_gen_3415) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3402) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3413) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3422) -> q_gen_3400
<a, cons, s>(q_gen_3426, q_gen_3433) -> q_gen_3400
<a, cons, s>(q_gen_3435, q_gen_3433) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3402) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3413) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3422) -> q_gen_3400
<a, nil, z>() -> q_gen_3400
<b, cons, s>(q_gen_3405, q_gen_3402) -> q_gen_3400
<b, cons, s>(q_gen_3405, q_gen_3415) -> q_gen_3400
<b, cons, s>(q_gen_3411, q_gen_3413) -> q_gen_3400
<b, cons, s>(q_gen_3411, q_gen_3433) -> q_gen_3400
<b, cons, s>(q_gen_3426, q_gen_3413) -> q_gen_3400
<b, cons, s>(q_gen_3426, q_gen_3433) -> q_gen_3400
<b, cons, s>(q_gen_3435, q_gen_3422) -> q_gen_3400
<b, cons, z>(q_gen_3403, q_gen_3402) -> q_gen_3400
<b, cons, z>(q_gen_3403, q_gen_3415) -> q_gen_3400
<b, nil, z>() -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3415) -> q_gen_3409
<a, cons, s>(q_gen_3411, q_gen_3433) -> q_gen_3409
<a, cons, s>(q_gen_3426, q_gen_3402) -> q_gen_3409
<a, cons, s>(q_gen_3426, q_gen_3413) -> q_gen_3409
<a, cons, s>(q_gen_3435, q_gen_3413) -> q_gen_3409
<a, cons, z>(q_gen_3403, q_gen_3402) -> q_gen_3409
<a, cons, z>(q_gen_3408, q_gen_3415) -> q_gen_3409
<a, cons, z>(q_gen_3408, q_gen_3433) -> q_gen_3409
<b, cons, s>(q_gen_3405, q_gen_3413) -> q_gen_3409
<b, cons, s>(q_gen_3405, q_gen_3422) -> q_gen_3409
<b, cons, s>(q_gen_3405, q_gen_3433) -> q_gen_3409
<b, cons, s>(q_gen_3411, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3411, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3422) -> q_gen_3409
<b, cons, s>(q_gen_3435, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3435, q_gen_3413) -> q_gen_3409
<b, cons, s>(q_gen_3435, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3435, q_gen_3433) -> q_gen_3409
<b, cons, s>(q_gen_3475, q_gen_3413) -> q_gen_3409
<b, cons, s>(q_gen_3475, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3475, q_gen_3422) -> q_gen_3409
<b, cons, z>(q_gen_3403, q_gen_3433) -> q_gen_3409
}

Datatype: <elt, eltlist, nat>
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
(count([x, l1, _nn]) /\ count([x, cons(x, l1), _mn])) -> eq_nat([_mn, s(_nn)]) -> 66
(count([x, t1, _gn])) -> count([x, cons(x, t1), s(_gn)]) -> 64
(count([x, t1, _hn]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _hn]) -> 64
}
Sat witness: Found: ((count([x, l1, _nn]) /\ count([x, cons(x, l1), _mn])) -> eq_nat([_mn, s(_nn)]), {
_mn -> s(s(z))  ;  _nn -> s(s(s(z)))  ;  l1 -> cons(a, cons(b, cons(b, cons(b, nil))))  ;  x -> b
})

-------------------------------------------
Step 64, which took 0.602234 s (model generation: 0.573252,  model checking: 0.028982):

Model:
|_
{
count -> 
{{{
Q={q_gen_3400, q_gen_3402, q_gen_3403, q_gen_3405, q_gen_3408, q_gen_3409, q_gen_3411, q_gen_3413, q_gen_3415, q_gen_3422, q_gen_3426, q_gen_3427, q_gen_3433, q_gen_3435, q_gen_3436, q_gen_3475, q_gen_3476},
Q_f={q_gen_3400},
Delta=
{
<cons>(q_gen_3408, q_gen_3422) -> q_gen_3402
<nil>() -> q_gen_3402
<a>() -> q_gen_3403
<b>() -> q_gen_3408
<cons>(q_gen_3408, q_gen_3402) -> q_gen_3413
<cons>(q_gen_3408, q_gen_3415) -> q_gen_3413
<cons>(q_gen_3408, q_gen_3433) -> q_gen_3413
<cons>(q_gen_3403, q_gen_3402) -> q_gen_3415
<cons>(q_gen_3403, q_gen_3415) -> q_gen_3422
<cons>(q_gen_3408, q_gen_3413) -> q_gen_3422
<z>() -> q_gen_3427
<cons>(q_gen_3403, q_gen_3413) -> q_gen_3433
<cons>(q_gen_3403, q_gen_3433) -> q_gen_3433
<s>(q_gen_3427) -> q_gen_3436
<s>(q_gen_3436) -> q_gen_3476
<b, z>() -> q_gen_3405
<a, z>() -> q_gen_3411
<a, s>(q_gen_3427) -> q_gen_3426
<b, s>(q_gen_3427) -> q_gen_3426
<a, s>(q_gen_3436) -> q_gen_3435
<b, s>(q_gen_3436) -> q_gen_3435
<b, s>(q_gen_3476) -> q_gen_3475
<a, cons, s>(q_gen_3405, q_gen_3415) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3402) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3413) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3422) -> q_gen_3400
<a, cons, s>(q_gen_3426, q_gen_3433) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3402) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3413) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3422) -> q_gen_3400
<a, nil, z>() -> q_gen_3400
<b, cons, s>(q_gen_3405, q_gen_3402) -> q_gen_3400
<b, cons, s>(q_gen_3405, q_gen_3415) -> q_gen_3400
<b, cons, s>(q_gen_3405, q_gen_3422) -> q_gen_3400
<b, cons, s>(q_gen_3411, q_gen_3413) -> q_gen_3400
<b, cons, s>(q_gen_3411, q_gen_3433) -> q_gen_3400
<b, cons, s>(q_gen_3426, q_gen_3413) -> q_gen_3400
<b, cons, s>(q_gen_3426, q_gen_3433) -> q_gen_3400
<b, cons, s>(q_gen_3435, q_gen_3422) -> q_gen_3400
<b, cons, s>(q_gen_3475, q_gen_3402) -> q_gen_3400
<b, cons, z>(q_gen_3403, q_gen_3402) -> q_gen_3400
<b, cons, z>(q_gen_3403, q_gen_3415) -> q_gen_3400
<b, cons, z>(q_gen_3403, q_gen_3422) -> q_gen_3400
<b, nil, z>() -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3415) -> q_gen_3409
<a, cons, s>(q_gen_3411, q_gen_3433) -> q_gen_3409
<a, cons, s>(q_gen_3426, q_gen_3402) -> q_gen_3409
<a, cons, s>(q_gen_3426, q_gen_3413) -> q_gen_3409
<a, cons, s>(q_gen_3435, q_gen_3413) -> q_gen_3409
<a, cons, z>(q_gen_3403, q_gen_3402) -> q_gen_3409
<a, cons, z>(q_gen_3408, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3405, q_gen_3413) -> q_gen_3409
<b, cons, s>(q_gen_3405, q_gen_3433) -> q_gen_3409
<b, cons, s>(q_gen_3411, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3411, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3422) -> q_gen_3409
<b, cons, s>(q_gen_3435, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3435, q_gen_3413) -> q_gen_3409
<b, cons, s>(q_gen_3435, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3435, q_gen_3433) -> q_gen_3409
<b, cons, s>(q_gen_3475, q_gen_3413) -> q_gen_3409
<b, cons, s>(q_gen_3475, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3475, q_gen_3422) -> q_gen_3409
<b, cons, z>(q_gen_3403, q_gen_3433) -> q_gen_3409
}

Datatype: <elt, eltlist, nat>
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
(count([x, l1, _nn]) /\ count([x, cons(x, l1), _mn])) -> eq_nat([_mn, s(_nn)]) -> 66
(count([x, t1, _gn])) -> count([x, cons(x, t1), s(_gn)]) -> 64
(count([x, t1, _hn]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _hn]) -> 67
}
Sat witness: Found: ((count([x, t1, _hn]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _hn]), {
_hn -> s(s(z))  ;  h1 -> a  ;  t1 -> cons(b, cons(b, nil))  ;  x -> b
})

-------------------------------------------
Step 65, which took 0.637854 s (model generation: 0.625309,  model checking: 0.012545):

Model:
|_
{
count -> 
{{{
Q={q_gen_3400, q_gen_3402, q_gen_3403, q_gen_3405, q_gen_3408, q_gen_3409, q_gen_3411, q_gen_3413, q_gen_3415, q_gen_3422, q_gen_3426, q_gen_3427, q_gen_3433, q_gen_3435, q_gen_3436, q_gen_3475, q_gen_3476},
Q_f={q_gen_3400},
Delta=
{
<nil>() -> q_gen_3402
<a>() -> q_gen_3403
<b>() -> q_gen_3408
<cons>(q_gen_3403, q_gen_3433) -> q_gen_3413
<cons>(q_gen_3408, q_gen_3402) -> q_gen_3413
<cons>(q_gen_3403, q_gen_3402) -> q_gen_3415
<cons>(q_gen_3403, q_gen_3422) -> q_gen_3415
<cons>(q_gen_3403, q_gen_3415) -> q_gen_3422
<cons>(q_gen_3408, q_gen_3413) -> q_gen_3422
<cons>(q_gen_3408, q_gen_3422) -> q_gen_3422
<z>() -> q_gen_3427
<cons>(q_gen_3403, q_gen_3413) -> q_gen_3433
<cons>(q_gen_3408, q_gen_3415) -> q_gen_3433
<cons>(q_gen_3408, q_gen_3433) -> q_gen_3433
<s>(q_gen_3427) -> q_gen_3436
<s>(q_gen_3436) -> q_gen_3476
<b, z>() -> q_gen_3405
<a, z>() -> q_gen_3411
<b, s>(q_gen_3427) -> q_gen_3426
<a, s>(q_gen_3427) -> q_gen_3435
<a, s>(q_gen_3436) -> q_gen_3435
<b, s>(q_gen_3436) -> q_gen_3435
<b, s>(q_gen_3476) -> q_gen_3475
<a, cons, s>(q_gen_3405, q_gen_3415) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3402) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3413) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3422) -> q_gen_3400
<a, cons, s>(q_gen_3435, q_gen_3433) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3402) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3413) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3422) -> q_gen_3400
<a, nil, z>() -> q_gen_3400
<b, cons, s>(q_gen_3405, q_gen_3402) -> q_gen_3400
<b, cons, s>(q_gen_3405, q_gen_3415) -> q_gen_3400
<b, cons, s>(q_gen_3405, q_gen_3422) -> q_gen_3400
<b, cons, s>(q_gen_3411, q_gen_3413) -> q_gen_3400
<b, cons, s>(q_gen_3411, q_gen_3433) -> q_gen_3400
<b, cons, s>(q_gen_3426, q_gen_3413) -> q_gen_3400
<b, cons, s>(q_gen_3426, q_gen_3433) -> q_gen_3400
<b, cons, s>(q_gen_3435, q_gen_3422) -> q_gen_3400
<b, cons, s>(q_gen_3435, q_gen_3433) -> q_gen_3400
<b, cons, s>(q_gen_3475, q_gen_3433) -> q_gen_3400
<b, cons, z>(q_gen_3403, q_gen_3402) -> q_gen_3400
<b, cons, z>(q_gen_3403, q_gen_3415) -> q_gen_3400
<b, cons, z>(q_gen_3403, q_gen_3422) -> q_gen_3400
<b, nil, z>() -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3415) -> q_gen_3409
<a, cons, s>(q_gen_3411, q_gen_3433) -> q_gen_3409
<a, cons, s>(q_gen_3426, q_gen_3402) -> q_gen_3409
<a, cons, s>(q_gen_3426, q_gen_3413) -> q_gen_3409
<a, cons, s>(q_gen_3426, q_gen_3433) -> q_gen_3409
<a, cons, s>(q_gen_3435, q_gen_3413) -> q_gen_3409
<a, cons, z>(q_gen_3403, q_gen_3402) -> q_gen_3409
<a, cons, z>(q_gen_3408, q_gen_3415) -> q_gen_3409
<a, cons, z>(q_gen_3408, q_gen_3433) -> q_gen_3409
<b, cons, s>(q_gen_3405, q_gen_3413) -> q_gen_3409
<b, cons, s>(q_gen_3405, q_gen_3433) -> q_gen_3409
<b, cons, s>(q_gen_3411, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3411, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3422) -> q_gen_3409
<b, cons, s>(q_gen_3435, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3435, q_gen_3413) -> q_gen_3409
<b, cons, s>(q_gen_3435, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3475, q_gen_3413) -> q_gen_3409
<b, cons, s>(q_gen_3475, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3475, q_gen_3422) -> q_gen_3409
<b, cons, z>(q_gen_3403, q_gen_3413) -> q_gen_3409
<b, cons, z>(q_gen_3403, q_gen_3433) -> q_gen_3409
}

Datatype: <elt, eltlist, nat>
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
(count([x, l1, _nn]) /\ count([x, cons(x, l1), _mn])) -> eq_nat([_mn, s(_nn)]) -> 66
(count([x, t1, _gn])) -> count([x, cons(x, t1), s(_gn)]) -> 67
(count([x, t1, _hn]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _hn]) -> 67
}
Sat witness: Found: ((count([x, t1, _gn])) -> count([x, cons(x, t1), s(_gn)]), {
_gn -> s(s(z))  ;  t1 -> cons(a, cons(b, cons(b, cons(a, cons(a, cons(a, nil))))))  ;  x -> b
})

-------------------------------------------
Step 66, which took 0.876289 s (model generation: 0.867427,  model checking: 0.008862):

Model:
|_
{
count -> 
{{{
Q={q_gen_3400, q_gen_3402, q_gen_3403, q_gen_3405, q_gen_3408, q_gen_3409, q_gen_3411, q_gen_3413, q_gen_3415, q_gen_3422, q_gen_3426, q_gen_3427, q_gen_3433, q_gen_3435, q_gen_3436, q_gen_3475, q_gen_3476},
Q_f={q_gen_3400},
Delta=
{
<cons>(q_gen_3408, q_gen_3422) -> q_gen_3402
<nil>() -> q_gen_3402
<a>() -> q_gen_3403
<b>() -> q_gen_3408
<cons>(q_gen_3403, q_gen_3422) -> q_gen_3413
<cons>(q_gen_3408, q_gen_3402) -> q_gen_3413
<cons>(q_gen_3408, q_gen_3415) -> q_gen_3413
<cons>(q_gen_3408, q_gen_3433) -> q_gen_3413
<cons>(q_gen_3403, q_gen_3402) -> q_gen_3415
<cons>(q_gen_3403, q_gen_3415) -> q_gen_3422
<cons>(q_gen_3408, q_gen_3413) -> q_gen_3422
<z>() -> q_gen_3427
<cons>(q_gen_3403, q_gen_3413) -> q_gen_3433
<cons>(q_gen_3403, q_gen_3433) -> q_gen_3433
<s>(q_gen_3427) -> q_gen_3436
<s>(q_gen_3436) -> q_gen_3476
<b, z>() -> q_gen_3405
<a, z>() -> q_gen_3411
<a, s>(q_gen_3436) -> q_gen_3426
<b, s>(q_gen_3427) -> q_gen_3426
<a, s>(q_gen_3427) -> q_gen_3435
<b, s>(q_gen_3436) -> q_gen_3435
<b, s>(q_gen_3476) -> q_gen_3475
<a, cons, s>(q_gen_3405, q_gen_3415) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3402) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3413) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3422) -> q_gen_3400
<a, cons, s>(q_gen_3426, q_gen_3433) -> q_gen_3400
<a, cons, s>(q_gen_3435, q_gen_3433) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3402) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3413) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3422) -> q_gen_3400
<a, nil, z>() -> q_gen_3400
<b, cons, s>(q_gen_3405, q_gen_3402) -> q_gen_3400
<b, cons, s>(q_gen_3405, q_gen_3415) -> q_gen_3400
<b, cons, s>(q_gen_3405, q_gen_3422) -> q_gen_3400
<b, cons, s>(q_gen_3411, q_gen_3413) -> q_gen_3400
<b, cons, s>(q_gen_3411, q_gen_3433) -> q_gen_3400
<b, cons, s>(q_gen_3426, q_gen_3413) -> q_gen_3400
<b, cons, s>(q_gen_3426, q_gen_3433) -> q_gen_3400
<b, cons, s>(q_gen_3435, q_gen_3422) -> q_gen_3400
<b, cons, s>(q_gen_3475, q_gen_3402) -> q_gen_3400
<b, cons, z>(q_gen_3403, q_gen_3402) -> q_gen_3400
<b, cons, z>(q_gen_3403, q_gen_3415) -> q_gen_3400
<b, cons, z>(q_gen_3403, q_gen_3422) -> q_gen_3400
<b, nil, z>() -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3415) -> q_gen_3409
<a, cons, s>(q_gen_3411, q_gen_3433) -> q_gen_3409
<a, cons, s>(q_gen_3426, q_gen_3402) -> q_gen_3409
<a, cons, s>(q_gen_3426, q_gen_3413) -> q_gen_3409
<a, cons, s>(q_gen_3435, q_gen_3413) -> q_gen_3409
<a, cons, z>(q_gen_3403, q_gen_3402) -> q_gen_3409
<a, cons, z>(q_gen_3408, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3405, q_gen_3413) -> q_gen_3409
<b, cons, s>(q_gen_3405, q_gen_3433) -> q_gen_3409
<b, cons, s>(q_gen_3411, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3411, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3422) -> q_gen_3409
<b, cons, s>(q_gen_3435, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3435, q_gen_3413) -> q_gen_3409
<b, cons, s>(q_gen_3435, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3435, q_gen_3433) -> q_gen_3409
<b, cons, s>(q_gen_3475, q_gen_3413) -> q_gen_3409
<b, cons, s>(q_gen_3475, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3475, q_gen_3422) -> q_gen_3409
<b, cons, z>(q_gen_3403, q_gen_3433) -> q_gen_3409
}

Datatype: <elt, eltlist, nat>
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
(count([x, l1, _nn]) /\ count([x, cons(x, l1), _mn])) -> eq_nat([_mn, s(_nn)]) -> 69
(count([x, t1, _gn])) -> count([x, cons(x, t1), s(_gn)]) -> 67
(count([x, t1, _hn]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _hn]) -> 67
}
Sat witness: Found: ((count([x, l1, _nn]) /\ count([x, cons(x, l1), _mn])) -> eq_nat([_mn, s(_nn)]), {
_mn -> s(s(s(s(z))))  ;  _nn -> z  ;  l1 -> nil  ;  x -> b
})

-------------------------------------------
Step 67, which took 0.710496 s (model generation: 0.691303,  model checking: 0.019193):

Model:
|_
{
count -> 
{{{
Q={q_gen_3400, q_gen_3402, q_gen_3403, q_gen_3405, q_gen_3408, q_gen_3409, q_gen_3411, q_gen_3413, q_gen_3415, q_gen_3422, q_gen_3426, q_gen_3427, q_gen_3433, q_gen_3435, q_gen_3436, q_gen_3475, q_gen_3476},
Q_f={q_gen_3400},
Delta=
{
<nil>() -> q_gen_3402
<a>() -> q_gen_3403
<b>() -> q_gen_3408
<cons>(q_gen_3403, q_gen_3433) -> q_gen_3413
<cons>(q_gen_3408, q_gen_3402) -> q_gen_3413
<cons>(q_gen_3403, q_gen_3402) -> q_gen_3415
<cons>(q_gen_3403, q_gen_3415) -> q_gen_3422
<cons>(q_gen_3403, q_gen_3422) -> q_gen_3422
<cons>(q_gen_3408, q_gen_3413) -> q_gen_3422
<cons>(q_gen_3408, q_gen_3422) -> q_gen_3422
<z>() -> q_gen_3427
<cons>(q_gen_3403, q_gen_3413) -> q_gen_3433
<cons>(q_gen_3408, q_gen_3415) -> q_gen_3433
<cons>(q_gen_3408, q_gen_3433) -> q_gen_3433
<s>(q_gen_3427) -> q_gen_3436
<s>(q_gen_3436) -> q_gen_3476
<b, z>() -> q_gen_3405
<a, z>() -> q_gen_3411
<b, s>(q_gen_3427) -> q_gen_3426
<a, s>(q_gen_3427) -> q_gen_3435
<a, s>(q_gen_3436) -> q_gen_3435
<b, s>(q_gen_3436) -> q_gen_3435
<b, s>(q_gen_3476) -> q_gen_3475
<a, cons, s>(q_gen_3405, q_gen_3415) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3402) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3413) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3422) -> q_gen_3400
<a, cons, s>(q_gen_3435, q_gen_3433) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3402) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3413) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3422) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3433) -> q_gen_3400
<a, nil, z>() -> q_gen_3400
<b, cons, s>(q_gen_3405, q_gen_3402) -> q_gen_3400
<b, cons, s>(q_gen_3405, q_gen_3415) -> q_gen_3400
<b, cons, s>(q_gen_3405, q_gen_3422) -> q_gen_3400
<b, cons, s>(q_gen_3411, q_gen_3413) -> q_gen_3400
<b, cons, s>(q_gen_3411, q_gen_3433) -> q_gen_3400
<b, cons, s>(q_gen_3426, q_gen_3413) -> q_gen_3400
<b, cons, s>(q_gen_3426, q_gen_3433) -> q_gen_3400
<b, cons, s>(q_gen_3435, q_gen_3415) -> q_gen_3400
<b, cons, s>(q_gen_3435, q_gen_3422) -> q_gen_3400
<b, cons, s>(q_gen_3435, q_gen_3433) -> q_gen_3400
<b, cons, s>(q_gen_3475, q_gen_3433) -> q_gen_3400
<b, cons, z>(q_gen_3403, q_gen_3402) -> q_gen_3400
<b, cons, z>(q_gen_3403, q_gen_3415) -> q_gen_3400
<b, cons, z>(q_gen_3403, q_gen_3422) -> q_gen_3400
<b, nil, z>() -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3415) -> q_gen_3409
<a, cons, s>(q_gen_3411, q_gen_3433) -> q_gen_3409
<a, cons, s>(q_gen_3426, q_gen_3402) -> q_gen_3409
<a, cons, s>(q_gen_3426, q_gen_3413) -> q_gen_3409
<a, cons, s>(q_gen_3426, q_gen_3433) -> q_gen_3409
<a, cons, s>(q_gen_3435, q_gen_3413) -> q_gen_3409
<a, cons, z>(q_gen_3403, q_gen_3402) -> q_gen_3409
<a, cons, z>(q_gen_3408, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3405, q_gen_3413) -> q_gen_3409
<b, cons, s>(q_gen_3405, q_gen_3433) -> q_gen_3409
<b, cons, s>(q_gen_3411, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3411, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3422) -> q_gen_3409
<b, cons, s>(q_gen_3435, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3435, q_gen_3413) -> q_gen_3409
<b, cons, s>(q_gen_3475, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3475, q_gen_3413) -> q_gen_3409
<b, cons, s>(q_gen_3475, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3475, q_gen_3422) -> q_gen_3409
<b, cons, z>(q_gen_3403, q_gen_3413) -> q_gen_3409
<b, cons, z>(q_gen_3403, q_gen_3433) -> q_gen_3409
}

Datatype: <elt, eltlist, nat>
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
(count([x, l1, _nn]) /\ count([x, cons(x, l1), _mn])) -> eq_nat([_mn, s(_nn)]) -> 69
(count([x, t1, _gn])) -> count([x, cons(x, t1), s(_gn)]) -> 67
(count([x, t1, _hn]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _hn]) -> 70
}
Sat witness: Found: ((count([x, t1, _hn]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _hn]), {
_hn -> s(s(z))  ;  h1 -> a  ;  t1 -> cons(a, cons(b, cons(b, cons(a, nil))))  ;  x -> b
})

-------------------------------------------
Step 68, which took 1.339726 s (model generation: 1.321288,  model checking: 0.018438):

Model:
|_
{
count -> 
{{{
Q={q_gen_3400, q_gen_3402, q_gen_3403, q_gen_3405, q_gen_3408, q_gen_3409, q_gen_3411, q_gen_3413, q_gen_3415, q_gen_3422, q_gen_3426, q_gen_3427, q_gen_3433, q_gen_3435, q_gen_3436, q_gen_3455, q_gen_3470, q_gen_3476},
Q_f={q_gen_3400},
Delta=
{
<cons>(q_gen_3403, q_gen_3415) -> q_gen_3402
<cons>(q_gen_3408, q_gen_3422) -> q_gen_3402
<nil>() -> q_gen_3402
<a>() -> q_gen_3403
<b>() -> q_gen_3408
<cons>(q_gen_3408, q_gen_3402) -> q_gen_3413
<cons>(q_gen_3403, q_gen_3402) -> q_gen_3415
<cons>(q_gen_3403, q_gen_3455) -> q_gen_3415
<cons>(q_gen_3403, q_gen_3422) -> q_gen_3422
<cons>(q_gen_3408, q_gen_3413) -> q_gen_3422
<cons>(q_gen_3408, q_gen_3433) -> q_gen_3422
<z>() -> q_gen_3427
<cons>(q_gen_3403, q_gen_3413) -> q_gen_3433
<cons>(q_gen_3408, q_gen_3415) -> q_gen_3433
<s>(q_gen_3427) -> q_gen_3436
<cons>(q_gen_3403, q_gen_3433) -> q_gen_3455
<cons>(q_gen_3408, q_gen_3455) -> q_gen_3455
<s>(q_gen_3436) -> q_gen_3476
<b, z>() -> q_gen_3405
<a, z>() -> q_gen_3411
<b, s>(q_gen_3427) -> q_gen_3426
<a, s>(q_gen_3427) -> q_gen_3435
<b, s>(q_gen_3436) -> q_gen_3435
<a, s>(q_gen_3436) -> q_gen_3470
<b, s>(q_gen_3476) -> q_gen_3470
<a, cons, s>(q_gen_3405, q_gen_3415) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3402) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3413) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3422) -> q_gen_3400
<a, cons, s>(q_gen_3435, q_gen_3433) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3402) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3413) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3422) -> q_gen_3400
<a, nil, z>() -> q_gen_3400
<b, cons, s>(q_gen_3405, q_gen_3402) -> q_gen_3400
<b, cons, s>(q_gen_3405, q_gen_3415) -> q_gen_3400
<b, cons, s>(q_gen_3411, q_gen_3413) -> q_gen_3400
<b, cons, s>(q_gen_3411, q_gen_3433) -> q_gen_3400
<b, cons, s>(q_gen_3411, q_gen_3455) -> q_gen_3400
<b, cons, s>(q_gen_3426, q_gen_3413) -> q_gen_3400
<b, cons, s>(q_gen_3426, q_gen_3433) -> q_gen_3400
<b, cons, s>(q_gen_3426, q_gen_3455) -> q_gen_3400
<b, cons, s>(q_gen_3435, q_gen_3415) -> q_gen_3400
<b, cons, s>(q_gen_3435, q_gen_3422) -> q_gen_3400
<b, cons, s>(q_gen_3470, q_gen_3433) -> q_gen_3400
<b, cons, s>(q_gen_3470, q_gen_3455) -> q_gen_3400
<b, cons, z>(q_gen_3403, q_gen_3402) -> q_gen_3400
<b, cons, z>(q_gen_3403, q_gen_3415) -> q_gen_3400
<b, nil, z>() -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3415) -> q_gen_3409
<a, cons, s>(q_gen_3411, q_gen_3433) -> q_gen_3409
<a, cons, s>(q_gen_3411, q_gen_3455) -> q_gen_3409
<a, cons, s>(q_gen_3426, q_gen_3402) -> q_gen_3409
<a, cons, s>(q_gen_3426, q_gen_3413) -> q_gen_3409
<a, cons, s>(q_gen_3426, q_gen_3415) -> q_gen_3409
<a, cons, s>(q_gen_3435, q_gen_3413) -> q_gen_3409
<a, cons, s>(q_gen_3435, q_gen_3455) -> q_gen_3409
<a, cons, s>(q_gen_3470, q_gen_3413) -> q_gen_3409
<a, cons, z>(q_gen_3403, q_gen_3402) -> q_gen_3409
<a, cons, z>(q_gen_3408, q_gen_3415) -> q_gen_3409
<a, cons, z>(q_gen_3408, q_gen_3433) -> q_gen_3409
<b, cons, s>(q_gen_3405, q_gen_3413) -> q_gen_3409
<b, cons, s>(q_gen_3405, q_gen_3422) -> q_gen_3409
<b, cons, s>(q_gen_3405, q_gen_3433) -> q_gen_3409
<b, cons, s>(q_gen_3405, q_gen_3455) -> q_gen_3409
<b, cons, s>(q_gen_3411, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3411, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3422) -> q_gen_3409
<b, cons, s>(q_gen_3435, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3435, q_gen_3413) -> q_gen_3409
<b, cons, s>(q_gen_3435, q_gen_3455) -> q_gen_3409
<b, cons, s>(q_gen_3470, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3470, q_gen_3413) -> q_gen_3409
<b, cons, s>(q_gen_3470, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3470, q_gen_3422) -> q_gen_3409
<b, cons, z>(q_gen_3403, q_gen_3433) -> q_gen_3409
<b, cons, z>(q_gen_3403, q_gen_3455) -> q_gen_3409
}

Datatype: <elt, eltlist, nat>
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
(count([x, l1, _nn]) /\ count([x, cons(x, l1), _mn])) -> eq_nat([_mn, s(_nn)]) -> 69
(count([x, t1, _gn])) -> count([x, cons(x, t1), s(_gn)]) -> 70
(count([x, t1, _hn]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _hn]) -> 70
}
Sat witness: Found: ((count([x, t1, _gn])) -> count([x, cons(x, t1), s(_gn)]), {
_gn -> s(s(s(z)))  ;  t1 -> cons(b, cons(a, cons(b, cons(b, nil))))  ;  x -> b
})

-------------------------------------------
Step 69, which took 1.578503 s (model generation: 1.563793,  model checking: 0.014710):

Model:
|_
{
count -> 
{{{
Q={q_gen_3400, q_gen_3402, q_gen_3403, q_gen_3405, q_gen_3408, q_gen_3409, q_gen_3411, q_gen_3413, q_gen_3415, q_gen_3422, q_gen_3426, q_gen_3427, q_gen_3430, q_gen_3435, q_gen_3436, q_gen_3455, q_gen_3470, q_gen_3476},
Q_f={q_gen_3400},
Delta=
{
<cons>(q_gen_3403, q_gen_3415) -> q_gen_3402
<nil>() -> q_gen_3402
<a>() -> q_gen_3403
<b>() -> q_gen_3408
<cons>(q_gen_3408, q_gen_3402) -> q_gen_3413
<cons>(q_gen_3403, q_gen_3402) -> q_gen_3415
<cons>(q_gen_3403, q_gen_3455) -> q_gen_3415
<cons>(q_gen_3408, q_gen_3430) -> q_gen_3415
<cons>(q_gen_3408, q_gen_3455) -> q_gen_3415
<cons>(q_gen_3403, q_gen_3413) -> q_gen_3422
<cons>(q_gen_3403, q_gen_3430) -> q_gen_3422
<cons>(q_gen_3408, q_gen_3413) -> q_gen_3422
<cons>(q_gen_3408, q_gen_3415) -> q_gen_3422
<z>() -> q_gen_3427
<cons>(q_gen_3408, q_gen_3422) -> q_gen_3430
<s>(q_gen_3427) -> q_gen_3436
<cons>(q_gen_3403, q_gen_3422) -> q_gen_3455
<s>(q_gen_3436) -> q_gen_3476
<b, z>() -> q_gen_3405
<a, z>() -> q_gen_3411
<b, s>(q_gen_3427) -> q_gen_3426
<a, s>(q_gen_3427) -> q_gen_3435
<b, s>(q_gen_3436) -> q_gen_3435
<a, s>(q_gen_3436) -> q_gen_3470
<b, s>(q_gen_3476) -> q_gen_3470
<a, cons, s>(q_gen_3405, q_gen_3415) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3402) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3413) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3422) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3430) -> q_gen_3400
<a, cons, s>(q_gen_3426, q_gen_3415) -> q_gen_3400
<a, cons, s>(q_gen_3435, q_gen_3422) -> q_gen_3400
<a, cons, s>(q_gen_3435, q_gen_3455) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3402) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3413) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3422) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3430) -> q_gen_3400
<a, nil, z>() -> q_gen_3400
<b, cons, s>(q_gen_3405, q_gen_3402) -> q_gen_3400
<b, cons, s>(q_gen_3405, q_gen_3415) -> q_gen_3400
<b, cons, s>(q_gen_3411, q_gen_3413) -> q_gen_3400
<b, cons, s>(q_gen_3411, q_gen_3422) -> q_gen_3400
<b, cons, s>(q_gen_3411, q_gen_3455) -> q_gen_3400
<b, cons, s>(q_gen_3426, q_gen_3413) -> q_gen_3400
<b, cons, s>(q_gen_3426, q_gen_3422) -> q_gen_3400
<b, cons, s>(q_gen_3426, q_gen_3455) -> q_gen_3400
<b, cons, s>(q_gen_3435, q_gen_3422) -> q_gen_3400
<b, cons, s>(q_gen_3435, q_gen_3430) -> q_gen_3400
<b, cons, z>(q_gen_3403, q_gen_3402) -> q_gen_3400
<b, cons, z>(q_gen_3403, q_gen_3415) -> q_gen_3400
<b, nil, z>() -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3415) -> q_gen_3409
<a, cons, s>(q_gen_3411, q_gen_3455) -> q_gen_3409
<a, cons, s>(q_gen_3426, q_gen_3402) -> q_gen_3409
<a, cons, s>(q_gen_3426, q_gen_3413) -> q_gen_3409
<a, cons, s>(q_gen_3435, q_gen_3413) -> q_gen_3409
<a, cons, s>(q_gen_3470, q_gen_3413) -> q_gen_3409
<a, cons, z>(q_gen_3403, q_gen_3402) -> q_gen_3409
<a, cons, z>(q_gen_3408, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3405, q_gen_3413) -> q_gen_3409
<b, cons, s>(q_gen_3405, q_gen_3422) -> q_gen_3409
<b, cons, s>(q_gen_3405, q_gen_3430) -> q_gen_3409
<b, cons, s>(q_gen_3405, q_gen_3455) -> q_gen_3409
<b, cons, s>(q_gen_3411, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3411, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3430) -> q_gen_3409
<b, cons, s>(q_gen_3435, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3435, q_gen_3413) -> q_gen_3409
<b, cons, s>(q_gen_3435, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3435, q_gen_3455) -> q_gen_3409
<b, cons, s>(q_gen_3470, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3470, q_gen_3413) -> q_gen_3409
<b, cons, s>(q_gen_3470, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3470, q_gen_3422) -> q_gen_3409
<b, cons, s>(q_gen_3470, q_gen_3430) -> q_gen_3409
<b, cons, z>(q_gen_3403, q_gen_3422) -> q_gen_3409
<b, cons, z>(q_gen_3403, q_gen_3455) -> q_gen_3409
}

Datatype: <elt, eltlist, nat>
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
(count([x, l1, _nn]) /\ count([x, cons(x, l1), _mn])) -> eq_nat([_mn, s(_nn)]) -> 72
(count([x, t1, _gn])) -> count([x, cons(x, t1), s(_gn)]) -> 70
(count([x, t1, _hn]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _hn]) -> 70
}
Sat witness: Found: ((count([x, l1, _nn]) /\ count([x, cons(x, l1), _mn])) -> eq_nat([_mn, s(_nn)]), {
_mn -> s(s(z))  ;  _nn -> z  ;  l1 -> cons(b, cons(b, nil))  ;  x -> a
})

-------------------------------------------
Step 70, which took 1.144799 s (model generation: 1.115610,  model checking: 0.029189):

Model:
|_
{
count -> 
{{{
Q={q_gen_3400, q_gen_3402, q_gen_3403, q_gen_3405, q_gen_3408, q_gen_3409, q_gen_3411, q_gen_3413, q_gen_3415, q_gen_3422, q_gen_3426, q_gen_3427, q_gen_3430, q_gen_3433, q_gen_3435, q_gen_3436, q_gen_3470, q_gen_3476},
Q_f={q_gen_3400},
Delta=
{
<nil>() -> q_gen_3402
<a>() -> q_gen_3403
<b>() -> q_gen_3408
<cons>(q_gen_3408, q_gen_3402) -> q_gen_3413
<cons>(q_gen_3408, q_gen_3415) -> q_gen_3413
<cons>(q_gen_3408, q_gen_3430) -> q_gen_3413
<cons>(q_gen_3403, q_gen_3402) -> q_gen_3415
<cons>(q_gen_3403, q_gen_3415) -> q_gen_3415
<cons>(q_gen_3403, q_gen_3430) -> q_gen_3415
<cons>(q_gen_3403, q_gen_3422) -> q_gen_3422
<cons>(q_gen_3408, q_gen_3413) -> q_gen_3422
<z>() -> q_gen_3427
<cons>(q_gen_3408, q_gen_3422) -> q_gen_3430
<cons>(q_gen_3408, q_gen_3433) -> q_gen_3430
<cons>(q_gen_3403, q_gen_3413) -> q_gen_3433
<cons>(q_gen_3403, q_gen_3433) -> q_gen_3433
<s>(q_gen_3427) -> q_gen_3436
<s>(q_gen_3436) -> q_gen_3476
<b, z>() -> q_gen_3405
<a, z>() -> q_gen_3411
<b, s>(q_gen_3427) -> q_gen_3426
<a, s>(q_gen_3427) -> q_gen_3435
<b, s>(q_gen_3436) -> q_gen_3435
<a, s>(q_gen_3436) -> q_gen_3470
<b, s>(q_gen_3476) -> q_gen_3470
<a, cons, s>(q_gen_3405, q_gen_3415) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3402) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3413) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3422) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3430) -> q_gen_3400
<a, cons, s>(q_gen_3426, q_gen_3433) -> q_gen_3400
<a, cons, s>(q_gen_3435, q_gen_3433) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3402) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3413) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3422) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3430) -> q_gen_3400
<a, nil, z>() -> q_gen_3400
<b, cons, s>(q_gen_3405, q_gen_3402) -> q_gen_3400
<b, cons, s>(q_gen_3405, q_gen_3415) -> q_gen_3400
<b, cons, s>(q_gen_3411, q_gen_3413) -> q_gen_3400
<b, cons, s>(q_gen_3411, q_gen_3433) -> q_gen_3400
<b, cons, s>(q_gen_3426, q_gen_3413) -> q_gen_3400
<b, cons, s>(q_gen_3426, q_gen_3433) -> q_gen_3400
<b, cons, s>(q_gen_3435, q_gen_3422) -> q_gen_3400
<b, cons, s>(q_gen_3470, q_gen_3430) -> q_gen_3400
<b, cons, z>(q_gen_3403, q_gen_3402) -> q_gen_3400
<b, cons, z>(q_gen_3403, q_gen_3415) -> q_gen_3400
<b, nil, z>() -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3415) -> q_gen_3409
<a, cons, s>(q_gen_3411, q_gen_3433) -> q_gen_3409
<a, cons, s>(q_gen_3426, q_gen_3402) -> q_gen_3409
<a, cons, s>(q_gen_3426, q_gen_3413) -> q_gen_3409
<a, cons, s>(q_gen_3435, q_gen_3413) -> q_gen_3409
<a, cons, s>(q_gen_3435, q_gen_3422) -> q_gen_3409
<a, cons, s>(q_gen_3470, q_gen_3413) -> q_gen_3409
<a, cons, z>(q_gen_3403, q_gen_3402) -> q_gen_3409
<a, cons, z>(q_gen_3408, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3405, q_gen_3413) -> q_gen_3409
<b, cons, s>(q_gen_3405, q_gen_3430) -> q_gen_3409
<b, cons, s>(q_gen_3405, q_gen_3433) -> q_gen_3409
<b, cons, s>(q_gen_3411, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3411, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3422) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3430) -> q_gen_3409
<b, cons, s>(q_gen_3435, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3435, q_gen_3413) -> q_gen_3409
<b, cons, s>(q_gen_3435, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3435, q_gen_3430) -> q_gen_3409
<b, cons, s>(q_gen_3435, q_gen_3433) -> q_gen_3409
<b, cons, s>(q_gen_3470, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3470, q_gen_3413) -> q_gen_3409
<b, cons, s>(q_gen_3470, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3470, q_gen_3422) -> q_gen_3409
<b, cons, z>(q_gen_3403, q_gen_3433) -> q_gen_3409
}

Datatype: <elt, eltlist, nat>
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
(count([x, l1, _nn]) /\ count([x, cons(x, l1), _mn])) -> eq_nat([_mn, s(_nn)]) -> 72
(count([x, t1, _gn])) -> count([x, cons(x, t1), s(_gn)]) -> 70
(count([x, t1, _hn]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _hn]) -> 73
}
Sat witness: Found: ((count([x, t1, _hn]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _hn]), {
_hn -> s(s(z))  ;  h1 -> a  ;  t1 -> cons(b, cons(a, cons(a, cons(b, cons(a, nil)))))  ;  x -> b
})

-------------------------------------------
Step 71, which took 1.110917 s (model generation: 1.081866,  model checking: 0.029051):

Model:
|_
{
count -> 
{{{
Q={q_gen_3400, q_gen_3402, q_gen_3403, q_gen_3405, q_gen_3408, q_gen_3409, q_gen_3411, q_gen_3413, q_gen_3415, q_gen_3422, q_gen_3426, q_gen_3427, q_gen_3433, q_gen_3435, q_gen_3436, q_gen_3446, q_gen_3475, q_gen_3476},
Q_f={q_gen_3400},
Delta=
{
<cons>(q_gen_3403, q_gen_3415) -> q_gen_3402
<nil>() -> q_gen_3402
<a>() -> q_gen_3403
<b>() -> q_gen_3408
<cons>(q_gen_3408, q_gen_3402) -> q_gen_3413
<cons>(q_gen_3408, q_gen_3422) -> q_gen_3413
<cons>(q_gen_3403, q_gen_3402) -> q_gen_3415
<cons>(q_gen_3403, q_gen_3422) -> q_gen_3415
<cons>(q_gen_3408, q_gen_3413) -> q_gen_3422
<cons>(q_gen_3408, q_gen_3433) -> q_gen_3422
<z>() -> q_gen_3427
<cons>(q_gen_3403, q_gen_3413) -> q_gen_3433
<cons>(q_gen_3403, q_gen_3433) -> q_gen_3433
<cons>(q_gen_3408, q_gen_3446) -> q_gen_3433
<s>(q_gen_3427) -> q_gen_3436
<cons>(q_gen_3403, q_gen_3446) -> q_gen_3446
<cons>(q_gen_3408, q_gen_3415) -> q_gen_3446
<s>(q_gen_3436) -> q_gen_3476
<b, z>() -> q_gen_3405
<a, z>() -> q_gen_3411
<b, s>(q_gen_3427) -> q_gen_3426
<a, s>(q_gen_3427) -> q_gen_3435
<a, s>(q_gen_3436) -> q_gen_3435
<b, s>(q_gen_3436) -> q_gen_3435
<b, s>(q_gen_3476) -> q_gen_3475
<a, cons, s>(q_gen_3405, q_gen_3415) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3402) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3413) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3422) -> q_gen_3400
<a, cons, s>(q_gen_3435, q_gen_3433) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3402) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3413) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3422) -> q_gen_3400
<a, nil, z>() -> q_gen_3400
<b, cons, s>(q_gen_3405, q_gen_3402) -> q_gen_3400
<b, cons, s>(q_gen_3405, q_gen_3415) -> q_gen_3400
<b, cons, s>(q_gen_3411, q_gen_3413) -> q_gen_3400
<b, cons, s>(q_gen_3411, q_gen_3433) -> q_gen_3400
<b, cons, s>(q_gen_3411, q_gen_3446) -> q_gen_3400
<b, cons, s>(q_gen_3426, q_gen_3413) -> q_gen_3400
<b, cons, s>(q_gen_3426, q_gen_3433) -> q_gen_3400
<b, cons, s>(q_gen_3426, q_gen_3446) -> q_gen_3400
<b, cons, s>(q_gen_3435, q_gen_3422) -> q_gen_3400
<b, cons, s>(q_gen_3435, q_gen_3433) -> q_gen_3400
<b, cons, s>(q_gen_3475, q_gen_3446) -> q_gen_3400
<b, cons, z>(q_gen_3403, q_gen_3402) -> q_gen_3400
<b, cons, z>(q_gen_3403, q_gen_3415) -> q_gen_3400
<b, nil, z>() -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3415) -> q_gen_3409
<a, cons, s>(q_gen_3411, q_gen_3446) -> q_gen_3409
<a, cons, s>(q_gen_3426, q_gen_3402) -> q_gen_3409
<a, cons, s>(q_gen_3426, q_gen_3413) -> q_gen_3409
<a, cons, s>(q_gen_3426, q_gen_3446) -> q_gen_3409
<a, cons, s>(q_gen_3435, q_gen_3413) -> q_gen_3409
<a, cons, s>(q_gen_3435, q_gen_3422) -> q_gen_3409
<a, cons, s>(q_gen_3435, q_gen_3446) -> q_gen_3409
<a, cons, z>(q_gen_3403, q_gen_3402) -> q_gen_3409
<a, cons, z>(q_gen_3408, q_gen_3415) -> q_gen_3409
<a, cons, z>(q_gen_3408, q_gen_3433) -> q_gen_3409
<a, cons, z>(q_gen_3408, q_gen_3446) -> q_gen_3409
<b, cons, s>(q_gen_3405, q_gen_3413) -> q_gen_3409
<b, cons, s>(q_gen_3405, q_gen_3422) -> q_gen_3409
<b, cons, s>(q_gen_3405, q_gen_3433) -> q_gen_3409
<b, cons, s>(q_gen_3405, q_gen_3446) -> q_gen_3409
<b, cons, s>(q_gen_3411, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3411, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3422) -> q_gen_3409
<b, cons, s>(q_gen_3435, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3435, q_gen_3413) -> q_gen_3409
<b, cons, s>(q_gen_3435, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3435, q_gen_3446) -> q_gen_3409
<b, cons, s>(q_gen_3475, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3475, q_gen_3413) -> q_gen_3409
<b, cons, s>(q_gen_3475, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3475, q_gen_3422) -> q_gen_3409
<b, cons, z>(q_gen_3403, q_gen_3433) -> q_gen_3409
}

Datatype: <elt, eltlist, nat>
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
(count([x, l1, _nn]) /\ count([x, cons(x, l1), _mn])) -> eq_nat([_mn, s(_nn)]) -> 72
(count([x, t1, _gn])) -> count([x, cons(x, t1), s(_gn)]) -> 73
(count([x, t1, _hn]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _hn]) -> 73
}
Sat witness: Found: ((count([x, t1, _gn])) -> count([x, cons(x, t1), s(_gn)]), {
_gn -> s(s(z))  ;  t1 -> cons(a, cons(b, cons(b, nil)))  ;  x -> b
})

-------------------------------------------
Step 72, which took 1.148517 s (model generation: 1.127246,  model checking: 0.021271):

Model:
|_
{
count -> 
{{{
Q={q_gen_3400, q_gen_3402, q_gen_3403, q_gen_3405, q_gen_3408, q_gen_3409, q_gen_3411, q_gen_3413, q_gen_3415, q_gen_3422, q_gen_3424, q_gen_3426, q_gen_3427, q_gen_3433, q_gen_3435, q_gen_3436, q_gen_3475, q_gen_3476},
Q_f={q_gen_3400},
Delta=
{
<nil>() -> q_gen_3402
<a>() -> q_gen_3403
<b>() -> q_gen_3408
<cons>(q_gen_3403, q_gen_3433) -> q_gen_3413
<cons>(q_gen_3408, q_gen_3402) -> q_gen_3413
<cons>(q_gen_3403, q_gen_3402) -> q_gen_3415
<cons>(q_gen_3403, q_gen_3422) -> q_gen_3415
<cons>(q_gen_3408, q_gen_3413) -> q_gen_3422
<cons>(q_gen_3403, q_gen_3415) -> q_gen_3424
<cons>(q_gen_3403, q_gen_3424) -> q_gen_3424
<cons>(q_gen_3408, q_gen_3422) -> q_gen_3424
<cons>(q_gen_3408, q_gen_3424) -> q_gen_3424
<z>() -> q_gen_3427
<cons>(q_gen_3403, q_gen_3413) -> q_gen_3433
<cons>(q_gen_3408, q_gen_3415) -> q_gen_3433
<cons>(q_gen_3408, q_gen_3433) -> q_gen_3433
<s>(q_gen_3427) -> q_gen_3436
<s>(q_gen_3436) -> q_gen_3476
<b, z>() -> q_gen_3405
<a, z>() -> q_gen_3411
<a, s>(q_gen_3427) -> q_gen_3426
<b, s>(q_gen_3427) -> q_gen_3426
<a, s>(q_gen_3436) -> q_gen_3435
<b, s>(q_gen_3436) -> q_gen_3435
<b, s>(q_gen_3476) -> q_gen_3475
<a, cons, s>(q_gen_3405, q_gen_3415) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3402) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3413) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3422) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3424) -> q_gen_3400
<a, cons, s>(q_gen_3426, q_gen_3433) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3402) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3413) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3422) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3424) -> q_gen_3400
<a, nil, z>() -> q_gen_3400
<b, cons, s>(q_gen_3405, q_gen_3402) -> q_gen_3400
<b, cons, s>(q_gen_3405, q_gen_3415) -> q_gen_3400
<b, cons, s>(q_gen_3405, q_gen_3424) -> q_gen_3400
<b, cons, s>(q_gen_3411, q_gen_3413) -> q_gen_3400
<b, cons, s>(q_gen_3411, q_gen_3433) -> q_gen_3400
<b, cons, s>(q_gen_3426, q_gen_3413) -> q_gen_3400
<b, cons, s>(q_gen_3426, q_gen_3422) -> q_gen_3400
<b, cons, s>(q_gen_3426, q_gen_3433) -> q_gen_3400
<b, cons, s>(q_gen_3435, q_gen_3415) -> q_gen_3400
<b, cons, s>(q_gen_3435, q_gen_3422) -> q_gen_3400
<b, cons, s>(q_gen_3435, q_gen_3424) -> q_gen_3400
<b, cons, s>(q_gen_3435, q_gen_3433) -> q_gen_3400
<b, cons, s>(q_gen_3475, q_gen_3433) -> q_gen_3400
<b, cons, z>(q_gen_3403, q_gen_3402) -> q_gen_3400
<b, cons, z>(q_gen_3403, q_gen_3415) -> q_gen_3400
<b, cons, z>(q_gen_3403, q_gen_3424) -> q_gen_3400
<b, nil, z>() -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3415) -> q_gen_3409
<a, cons, s>(q_gen_3411, q_gen_3433) -> q_gen_3409
<a, cons, s>(q_gen_3426, q_gen_3402) -> q_gen_3409
<a, cons, s>(q_gen_3426, q_gen_3413) -> q_gen_3409
<a, cons, s>(q_gen_3426, q_gen_3422) -> q_gen_3409
<a, cons, s>(q_gen_3435, q_gen_3413) -> q_gen_3409
<a, cons, z>(q_gen_3403, q_gen_3402) -> q_gen_3409
<a, cons, z>(q_gen_3408, q_gen_3415) -> q_gen_3409
<a, cons, z>(q_gen_3408, q_gen_3433) -> q_gen_3409
<b, cons, s>(q_gen_3405, q_gen_3413) -> q_gen_3409
<b, cons, s>(q_gen_3405, q_gen_3433) -> q_gen_3409
<b, cons, s>(q_gen_3411, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3411, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3424) -> q_gen_3409
<b, cons, s>(q_gen_3435, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3435, q_gen_3413) -> q_gen_3409
<b, cons, s>(q_gen_3475, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3475, q_gen_3413) -> q_gen_3409
<b, cons, s>(q_gen_3475, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3475, q_gen_3422) -> q_gen_3409
<b, cons, z>(q_gen_3403, q_gen_3413) -> q_gen_3409
<b, cons, z>(q_gen_3403, q_gen_3433) -> q_gen_3409
}

Datatype: <elt, eltlist, nat>
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
(count([x, l1, _nn]) /\ count([x, cons(x, l1), _mn])) -> eq_nat([_mn, s(_nn)]) -> 75
(count([x, t1, _gn])) -> count([x, cons(x, t1), s(_gn)]) -> 73
(count([x, t1, _hn]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _hn]) -> 73
}
Sat witness: Found: ((count([x, l1, _nn]) /\ count([x, cons(x, l1), _mn])) -> eq_nat([_mn, s(_nn)]), {
_mn -> s(s(s(z)))  ;  _nn -> z  ;  l1 -> cons(a, nil)  ;  x -> b
})

-------------------------------------------
Step 73, which took 1.423881 s (model generation: 1.396999,  model checking: 0.026882):

Model:
|_
{
count -> 
{{{
Q={q_gen_3400, q_gen_3402, q_gen_3403, q_gen_3405, q_gen_3408, q_gen_3409, q_gen_3411, q_gen_3413, q_gen_3415, q_gen_3422, q_gen_3424, q_gen_3426, q_gen_3427, q_gen_3433, q_gen_3435, q_gen_3436, q_gen_3475, q_gen_3476},
Q_f={q_gen_3400},
Delta=
{
<cons>(q_gen_3408, q_gen_3424) -> q_gen_3402
<nil>() -> q_gen_3402
<a>() -> q_gen_3403
<b>() -> q_gen_3408
<cons>(q_gen_3403, q_gen_3424) -> q_gen_3413
<cons>(q_gen_3408, q_gen_3402) -> q_gen_3413
<cons>(q_gen_3408, q_gen_3415) -> q_gen_3413
<cons>(q_gen_3408, q_gen_3433) -> q_gen_3413
<cons>(q_gen_3403, q_gen_3402) -> q_gen_3415
<cons>(q_gen_3403, q_gen_3433) -> q_gen_3415
<cons>(q_gen_3403, q_gen_3422) -> q_gen_3422
<cons>(q_gen_3408, q_gen_3413) -> q_gen_3422
<cons>(q_gen_3403, q_gen_3415) -> q_gen_3424
<cons>(q_gen_3408, q_gen_3422) -> q_gen_3424
<z>() -> q_gen_3427
<cons>(q_gen_3403, q_gen_3413) -> q_gen_3433
<s>(q_gen_3427) -> q_gen_3436
<s>(q_gen_3436) -> q_gen_3476
<b, z>() -> q_gen_3405
<a, z>() -> q_gen_3411
<b, s>(q_gen_3427) -> q_gen_3426
<a, s>(q_gen_3427) -> q_gen_3435
<a, s>(q_gen_3436) -> q_gen_3435
<b, s>(q_gen_3436) -> q_gen_3435
<b, s>(q_gen_3476) -> q_gen_3475
<a, cons, s>(q_gen_3405, q_gen_3415) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3402) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3413) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3422) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3424) -> q_gen_3400
<a, cons, s>(q_gen_3426, q_gen_3415) -> q_gen_3400
<a, cons, s>(q_gen_3435, q_gen_3433) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3402) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3413) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3422) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3424) -> q_gen_3400
<a, nil, z>() -> q_gen_3400
<b, cons, s>(q_gen_3405, q_gen_3402) -> q_gen_3400
<b, cons, s>(q_gen_3405, q_gen_3415) -> q_gen_3400
<b, cons, s>(q_gen_3405, q_gen_3424) -> q_gen_3400
<b, cons, s>(q_gen_3411, q_gen_3413) -> q_gen_3400
<b, cons, s>(q_gen_3411, q_gen_3433) -> q_gen_3400
<b, cons, s>(q_gen_3426, q_gen_3413) -> q_gen_3400
<b, cons, s>(q_gen_3426, q_gen_3433) -> q_gen_3400
<b, cons, s>(q_gen_3435, q_gen_3422) -> q_gen_3400
<b, cons, s>(q_gen_3475, q_gen_3424) -> q_gen_3400
<b, cons, z>(q_gen_3403, q_gen_3402) -> q_gen_3400
<b, cons, z>(q_gen_3403, q_gen_3415) -> q_gen_3400
<b, cons, z>(q_gen_3403, q_gen_3424) -> q_gen_3400
<b, nil, z>() -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3415) -> q_gen_3409
<a, cons, s>(q_gen_3411, q_gen_3433) -> q_gen_3409
<a, cons, s>(q_gen_3426, q_gen_3402) -> q_gen_3409
<a, cons, s>(q_gen_3426, q_gen_3413) -> q_gen_3409
<a, cons, s>(q_gen_3435, q_gen_3413) -> q_gen_3409
<a, cons, s>(q_gen_3435, q_gen_3422) -> q_gen_3409
<a, cons, z>(q_gen_3403, q_gen_3402) -> q_gen_3409
<a, cons, z>(q_gen_3408, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3405, q_gen_3413) -> q_gen_3409
<b, cons, s>(q_gen_3411, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3411, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3422) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3424) -> q_gen_3409
<b, cons, s>(q_gen_3435, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3435, q_gen_3413) -> q_gen_3409
<b, cons, s>(q_gen_3435, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3435, q_gen_3424) -> q_gen_3409
<b, cons, s>(q_gen_3435, q_gen_3433) -> q_gen_3409
<b, cons, s>(q_gen_3475, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3475, q_gen_3413) -> q_gen_3409
<b, cons, s>(q_gen_3475, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3475, q_gen_3422) -> q_gen_3409
<b, cons, z>(q_gen_3403, q_gen_3433) -> q_gen_3409
}

Datatype: <elt, eltlist, nat>
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
(count([x, l1, _nn]) /\ count([x, cons(x, l1), _mn])) -> eq_nat([_mn, s(_nn)]) -> 75
(count([x, t1, _gn])) -> count([x, cons(x, t1), s(_gn)]) -> 73
(count([x, t1, _hn]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _hn]) -> 76
}
Sat witness: Found: ((count([x, t1, _hn]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _hn]), {
_hn -> s(z)  ;  h1 -> a  ;  t1 -> cons(a, cons(a, cons(b, nil)))  ;  x -> b
})

-------------------------------------------
Step 74, which took 1.453191 s (model generation: 1.414385,  model checking: 0.038806):

Model:
|_
{
count -> 
{{{
Q={q_gen_3400, q_gen_3402, q_gen_3403, q_gen_3405, q_gen_3408, q_gen_3409, q_gen_3411, q_gen_3413, q_gen_3415, q_gen_3422, q_gen_3426, q_gen_3427, q_gen_3430, q_gen_3435, q_gen_3436, q_gen_3455, q_gen_3475, q_gen_3476},
Q_f={q_gen_3400},
Delta=
{
<cons>(q_gen_3403, q_gen_3415) -> q_gen_3402
<nil>() -> q_gen_3402
<a>() -> q_gen_3403
<b>() -> q_gen_3408
<cons>(q_gen_3403, q_gen_3455) -> q_gen_3413
<cons>(q_gen_3408, q_gen_3402) -> q_gen_3413
<cons>(q_gen_3403, q_gen_3402) -> q_gen_3415
<cons>(q_gen_3408, q_gen_3455) -> q_gen_3415
<cons>(q_gen_3403, q_gen_3422) -> q_gen_3422
<cons>(q_gen_3408, q_gen_3413) -> q_gen_3422
<cons>(q_gen_3408, q_gen_3430) -> q_gen_3422
<z>() -> q_gen_3427
<cons>(q_gen_3403, q_gen_3413) -> q_gen_3430
<cons>(q_gen_3408, q_gen_3415) -> q_gen_3430
<cons>(q_gen_3408, q_gen_3422) -> q_gen_3430
<s>(q_gen_3427) -> q_gen_3436
<cons>(q_gen_3403, q_gen_3430) -> q_gen_3455
<s>(q_gen_3436) -> q_gen_3476
<b, z>() -> q_gen_3405
<a, z>() -> q_gen_3411
<b, s>(q_gen_3427) -> q_gen_3426
<a, s>(q_gen_3427) -> q_gen_3435
<a, s>(q_gen_3436) -> q_gen_3435
<b, s>(q_gen_3436) -> q_gen_3435
<b, s>(q_gen_3476) -> q_gen_3475
<a, cons, s>(q_gen_3405, q_gen_3415) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3402) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3413) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3422) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3430) -> q_gen_3400
<a, cons, s>(q_gen_3435, q_gen_3430) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3402) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3413) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3422) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3430) -> q_gen_3400
<a, nil, z>() -> q_gen_3400
<b, cons, s>(q_gen_3405, q_gen_3402) -> q_gen_3400
<b, cons, s>(q_gen_3405, q_gen_3415) -> q_gen_3400
<b, cons, s>(q_gen_3411, q_gen_3413) -> q_gen_3400
<b, cons, s>(q_gen_3411, q_gen_3430) -> q_gen_3400
<b, cons, s>(q_gen_3411, q_gen_3455) -> q_gen_3400
<b, cons, s>(q_gen_3426, q_gen_3413) -> q_gen_3400
<b, cons, s>(q_gen_3426, q_gen_3430) -> q_gen_3400
<b, cons, s>(q_gen_3426, q_gen_3455) -> q_gen_3400
<b, cons, s>(q_gen_3435, q_gen_3422) -> q_gen_3400
<b, cons, s>(q_gen_3475, q_gen_3430) -> q_gen_3400
<b, cons, z>(q_gen_3403, q_gen_3402) -> q_gen_3400
<b, cons, z>(q_gen_3403, q_gen_3415) -> q_gen_3400
<b, nil, z>() -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3415) -> q_gen_3409
<a, cons, s>(q_gen_3411, q_gen_3455) -> q_gen_3409
<a, cons, s>(q_gen_3426, q_gen_3402) -> q_gen_3409
<a, cons, s>(q_gen_3426, q_gen_3413) -> q_gen_3409
<a, cons, s>(q_gen_3435, q_gen_3413) -> q_gen_3409
<a, cons, s>(q_gen_3435, q_gen_3422) -> q_gen_3409
<a, cons, s>(q_gen_3435, q_gen_3455) -> q_gen_3409
<a, cons, z>(q_gen_3403, q_gen_3402) -> q_gen_3409
<a, cons, z>(q_gen_3408, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3405, q_gen_3413) -> q_gen_3409
<b, cons, s>(q_gen_3405, q_gen_3422) -> q_gen_3409
<b, cons, s>(q_gen_3405, q_gen_3430) -> q_gen_3409
<b, cons, s>(q_gen_3405, q_gen_3455) -> q_gen_3409
<b, cons, s>(q_gen_3411, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3411, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3422) -> q_gen_3409
<b, cons, s>(q_gen_3435, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3435, q_gen_3413) -> q_gen_3409
<b, cons, s>(q_gen_3435, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3435, q_gen_3430) -> q_gen_3409
<b, cons, s>(q_gen_3435, q_gen_3455) -> q_gen_3409
<b, cons, s>(q_gen_3475, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3475, q_gen_3413) -> q_gen_3409
<b, cons, s>(q_gen_3475, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3475, q_gen_3422) -> q_gen_3409
<b, cons, z>(q_gen_3403, q_gen_3430) -> q_gen_3409
<b, cons, z>(q_gen_3403, q_gen_3455) -> q_gen_3409
}

Datatype: <elt, eltlist, nat>
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
(count([x, l1, _nn]) /\ count([x, cons(x, l1), _mn])) -> eq_nat([_mn, s(_nn)]) -> 75
(count([x, t1, _gn])) -> count([x, cons(x, t1), s(_gn)]) -> 76
(count([x, t1, _hn]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _hn]) -> 76
}
Sat witness: Found: ((count([x, t1, _gn])) -> count([x, cons(x, t1), s(_gn)]), {
_gn -> s(s(z))  ;  t1 -> cons(a, cons(b, cons(a, cons(b, cons(b, nil)))))  ;  x -> a
})

-------------------------------------------
Step 75, which took 1.215716 s (model generation: 1.201053,  model checking: 0.014663):

Model:
|_
{
count -> 
{{{
Q={q_gen_3400, q_gen_3402, q_gen_3403, q_gen_3405, q_gen_3408, q_gen_3409, q_gen_3411, q_gen_3413, q_gen_3415, q_gen_3422, q_gen_3426, q_gen_3427, q_gen_3430, q_gen_3433, q_gen_3435, q_gen_3436, q_gen_3475, q_gen_3476},
Q_f={q_gen_3400},
Delta=
{
<nil>() -> q_gen_3402
<a>() -> q_gen_3403
<b>() -> q_gen_3408
<cons>(q_gen_3408, q_gen_3402) -> q_gen_3413
<cons>(q_gen_3408, q_gen_3430) -> q_gen_3413
<cons>(q_gen_3403, q_gen_3402) -> q_gen_3415
<cons>(q_gen_3403, q_gen_3415) -> q_gen_3422
<cons>(q_gen_3403, q_gen_3422) -> q_gen_3422
<cons>(q_gen_3408, q_gen_3413) -> q_gen_3422
<z>() -> q_gen_3427
<cons>(q_gen_3403, q_gen_3430) -> q_gen_3430
<cons>(q_gen_3408, q_gen_3422) -> q_gen_3430
<cons>(q_gen_3408, q_gen_3433) -> q_gen_3430
<cons>(q_gen_3403, q_gen_3413) -> q_gen_3433
<cons>(q_gen_3403, q_gen_3433) -> q_gen_3433
<cons>(q_gen_3408, q_gen_3415) -> q_gen_3433
<s>(q_gen_3427) -> q_gen_3436
<s>(q_gen_3436) -> q_gen_3476
<b, z>() -> q_gen_3405
<a, z>() -> q_gen_3411
<a, s>(q_gen_3436) -> q_gen_3426
<b, s>(q_gen_3427) -> q_gen_3426
<a, s>(q_gen_3427) -> q_gen_3435
<b, s>(q_gen_3436) -> q_gen_3435
<b, s>(q_gen_3476) -> q_gen_3475
<a, cons, s>(q_gen_3405, q_gen_3415) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3402) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3413) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3422) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3430) -> q_gen_3400
<a, cons, s>(q_gen_3426, q_gen_3433) -> q_gen_3400
<a, cons, s>(q_gen_3435, q_gen_3433) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3402) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3413) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3422) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3430) -> q_gen_3400
<a, nil, z>() -> q_gen_3400
<b, cons, s>(q_gen_3405, q_gen_3402) -> q_gen_3400
<b, cons, s>(q_gen_3405, q_gen_3415) -> q_gen_3400
<b, cons, s>(q_gen_3405, q_gen_3422) -> q_gen_3400
<b, cons, s>(q_gen_3411, q_gen_3413) -> q_gen_3400
<b, cons, s>(q_gen_3411, q_gen_3433) -> q_gen_3400
<b, cons, s>(q_gen_3426, q_gen_3413) -> q_gen_3400
<b, cons, s>(q_gen_3426, q_gen_3433) -> q_gen_3400
<b, cons, s>(q_gen_3435, q_gen_3422) -> q_gen_3400
<b, cons, s>(q_gen_3435, q_gen_3430) -> q_gen_3400
<b, cons, s>(q_gen_3475, q_gen_3430) -> q_gen_3400
<b, cons, z>(q_gen_3403, q_gen_3402) -> q_gen_3400
<b, cons, z>(q_gen_3403, q_gen_3415) -> q_gen_3400
<b, cons, z>(q_gen_3403, q_gen_3422) -> q_gen_3400
<b, nil, z>() -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3415) -> q_gen_3409
<a, cons, s>(q_gen_3411, q_gen_3433) -> q_gen_3409
<a, cons, s>(q_gen_3426, q_gen_3402) -> q_gen_3409
<a, cons, s>(q_gen_3426, q_gen_3413) -> q_gen_3409
<a, cons, s>(q_gen_3426, q_gen_3430) -> q_gen_3409
<a, cons, s>(q_gen_3435, q_gen_3413) -> q_gen_3409
<a, cons, s>(q_gen_3435, q_gen_3422) -> q_gen_3409
<a, cons, s>(q_gen_3435, q_gen_3430) -> q_gen_3409
<a, cons, z>(q_gen_3403, q_gen_3402) -> q_gen_3409
<a, cons, z>(q_gen_3408, q_gen_3415) -> q_gen_3409
<a, cons, z>(q_gen_3408, q_gen_3433) -> q_gen_3409
<b, cons, s>(q_gen_3405, q_gen_3413) -> q_gen_3409
<b, cons, s>(q_gen_3405, q_gen_3430) -> q_gen_3409
<b, cons, s>(q_gen_3405, q_gen_3433) -> q_gen_3409
<b, cons, s>(q_gen_3411, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3411, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3422) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3430) -> q_gen_3409
<b, cons, s>(q_gen_3435, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3435, q_gen_3413) -> q_gen_3409
<b, cons, s>(q_gen_3435, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3435, q_gen_3433) -> q_gen_3409
<b, cons, s>(q_gen_3475, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3475, q_gen_3413) -> q_gen_3409
<b, cons, s>(q_gen_3475, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3475, q_gen_3422) -> q_gen_3409
<b, cons, z>(q_gen_3403, q_gen_3433) -> q_gen_3409
}

Datatype: <elt, eltlist, nat>
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
(count([x, l1, _nn]) /\ count([x, cons(x, l1), _mn])) -> eq_nat([_mn, s(_nn)]) -> 78
(count([x, t1, _gn])) -> count([x, cons(x, t1), s(_gn)]) -> 76
(count([x, t1, _hn]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _hn]) -> 76
}
Sat witness: Found: ((count([x, l1, _nn]) /\ count([x, cons(x, l1), _mn])) -> eq_nat([_mn, s(_nn)]), {
_mn -> s(s(s(z)))  ;  _nn -> z  ;  l1 -> cons(a, cons(a, nil))  ;  x -> b
})

-------------------------------------------
Step 76, which took 1.446280 s (model generation: 1.410451,  model checking: 0.035829):

Model:
|_
{
count -> 
{{{
Q={q_gen_3400, q_gen_3402, q_gen_3403, q_gen_3405, q_gen_3408, q_gen_3409, q_gen_3411, q_gen_3413, q_gen_3415, q_gen_3422, q_gen_3424, q_gen_3426, q_gen_3427, q_gen_3433, q_gen_3435, q_gen_3436, q_gen_3475, q_gen_3476},
Q_f={q_gen_3400},
Delta=
{
<nil>() -> q_gen_3402
<a>() -> q_gen_3403
<b>() -> q_gen_3408
<cons>(q_gen_3403, q_gen_3424) -> q_gen_3413
<cons>(q_gen_3408, q_gen_3402) -> q_gen_3413
<cons>(q_gen_3408, q_gen_3415) -> q_gen_3413
<cons>(q_gen_3408, q_gen_3433) -> q_gen_3413
<cons>(q_gen_3403, q_gen_3402) -> q_gen_3415
<cons>(q_gen_3403, q_gen_3422) -> q_gen_3422
<cons>(q_gen_3408, q_gen_3413) -> q_gen_3422
<cons>(q_gen_3408, q_gen_3424) -> q_gen_3422
<cons>(q_gen_3403, q_gen_3415) -> q_gen_3424
<cons>(q_gen_3403, q_gen_3433) -> q_gen_3424
<cons>(q_gen_3408, q_gen_3422) -> q_gen_3424
<z>() -> q_gen_3427
<cons>(q_gen_3403, q_gen_3413) -> q_gen_3433
<s>(q_gen_3427) -> q_gen_3436
<s>(q_gen_3436) -> q_gen_3476
<b, z>() -> q_gen_3405
<a, z>() -> q_gen_3411
<b, s>(q_gen_3427) -> q_gen_3426
<a, s>(q_gen_3427) -> q_gen_3435
<a, s>(q_gen_3436) -> q_gen_3435
<b, s>(q_gen_3436) -> q_gen_3435
<b, s>(q_gen_3476) -> q_gen_3475
<a, cons, s>(q_gen_3405, q_gen_3415) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3402) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3413) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3422) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3424) -> q_gen_3400
<a, cons, s>(q_gen_3426, q_gen_3424) -> q_gen_3400
<a, cons, s>(q_gen_3435, q_gen_3433) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3402) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3413) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3422) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3424) -> q_gen_3400
<a, nil, z>() -> q_gen_3400
<b, cons, s>(q_gen_3405, q_gen_3402) -> q_gen_3400
<b, cons, s>(q_gen_3405, q_gen_3415) -> q_gen_3400
<b, cons, s>(q_gen_3405, q_gen_3424) -> q_gen_3400
<b, cons, s>(q_gen_3411, q_gen_3413) -> q_gen_3400
<b, cons, s>(q_gen_3411, q_gen_3424) -> q_gen_3400
<b, cons, s>(q_gen_3411, q_gen_3433) -> q_gen_3400
<b, cons, s>(q_gen_3426, q_gen_3413) -> q_gen_3400
<b, cons, s>(q_gen_3426, q_gen_3433) -> q_gen_3400
<b, cons, s>(q_gen_3435, q_gen_3422) -> q_gen_3400
<b, cons, s>(q_gen_3475, q_gen_3424) -> q_gen_3400
<b, cons, z>(q_gen_3403, q_gen_3402) -> q_gen_3400
<b, cons, z>(q_gen_3403, q_gen_3415) -> q_gen_3400
<b, cons, z>(q_gen_3403, q_gen_3424) -> q_gen_3400
<b, nil, z>() -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3415) -> q_gen_3409
<a, cons, s>(q_gen_3411, q_gen_3433) -> q_gen_3409
<a, cons, s>(q_gen_3426, q_gen_3402) -> q_gen_3409
<a, cons, s>(q_gen_3426, q_gen_3413) -> q_gen_3409
<a, cons, s>(q_gen_3435, q_gen_3413) -> q_gen_3409
<a, cons, s>(q_gen_3435, q_gen_3422) -> q_gen_3409
<a, cons, s>(q_gen_3435, q_gen_3424) -> q_gen_3409
<a, cons, z>(q_gen_3403, q_gen_3402) -> q_gen_3409
<a, cons, z>(q_gen_3408, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3405, q_gen_3413) -> q_gen_3409
<b, cons, s>(q_gen_3411, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3411, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3422) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3424) -> q_gen_3409
<b, cons, s>(q_gen_3435, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3435, q_gen_3413) -> q_gen_3409
<b, cons, s>(q_gen_3435, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3435, q_gen_3424) -> q_gen_3409
<b, cons, s>(q_gen_3435, q_gen_3433) -> q_gen_3409
<b, cons, s>(q_gen_3475, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3475, q_gen_3413) -> q_gen_3409
<b, cons, s>(q_gen_3475, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3475, q_gen_3422) -> q_gen_3409
<b, cons, z>(q_gen_3403, q_gen_3433) -> q_gen_3409
}

Datatype: <elt, eltlist, nat>
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
(count([x, l1, _nn]) /\ count([x, cons(x, l1), _mn])) -> eq_nat([_mn, s(_nn)]) -> 78
(count([x, t1, _gn])) -> count([x, cons(x, t1), s(_gn)]) -> 76
(count([x, t1, _hn]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _hn]) -> 79
}
Sat witness: Found: ((count([x, t1, _hn]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _hn]), {
_hn -> s(s(s(z)))  ;  h1 -> b  ;  t1 -> cons(a, cons(a, cons(b, nil)))  ;  x -> a
})

-------------------------------------------
Step 77, which took 1.449969 s (model generation: 1.433583,  model checking: 0.016386):

Model:
|_
{
count -> 
{{{
Q={q_gen_3400, q_gen_3402, q_gen_3403, q_gen_3405, q_gen_3408, q_gen_3409, q_gen_3411, q_gen_3413, q_gen_3415, q_gen_3422, q_gen_3426, q_gen_3427, q_gen_3433, q_gen_3435, q_gen_3436, q_gen_3452, q_gen_3475, q_gen_3476},
Q_f={q_gen_3400},
Delta=
{
<nil>() -> q_gen_3402
<a>() -> q_gen_3403
<b>() -> q_gen_3408
<cons>(q_gen_3408, q_gen_3402) -> q_gen_3413
<cons>(q_gen_3408, q_gen_3422) -> q_gen_3413
<cons>(q_gen_3403, q_gen_3402) -> q_gen_3415
<cons>(q_gen_3403, q_gen_3415) -> q_gen_3415
<cons>(q_gen_3403, q_gen_3452) -> q_gen_3422
<cons>(q_gen_3408, q_gen_3413) -> q_gen_3422
<z>() -> q_gen_3427
<cons>(q_gen_3403, q_gen_3413) -> q_gen_3433
<cons>(q_gen_3403, q_gen_3433) -> q_gen_3433
<cons>(q_gen_3408, q_gen_3415) -> q_gen_3433
<s>(q_gen_3427) -> q_gen_3436
<cons>(q_gen_3403, q_gen_3422) -> q_gen_3452
<cons>(q_gen_3408, q_gen_3433) -> q_gen_3452
<cons>(q_gen_3408, q_gen_3452) -> q_gen_3452
<s>(q_gen_3436) -> q_gen_3476
<b, z>() -> q_gen_3405
<a, z>() -> q_gen_3411
<b, s>(q_gen_3427) -> q_gen_3426
<a, s>(q_gen_3427) -> q_gen_3435
<a, s>(q_gen_3436) -> q_gen_3435
<b, s>(q_gen_3436) -> q_gen_3435
<b, s>(q_gen_3476) -> q_gen_3475
<a, cons, s>(q_gen_3405, q_gen_3415) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3402) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3413) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3422) -> q_gen_3400
<a, cons, s>(q_gen_3426, q_gen_3433) -> q_gen_3400
<a, cons, s>(q_gen_3435, q_gen_3433) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3402) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3413) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3422) -> q_gen_3400
<a, nil, z>() -> q_gen_3400
<b, cons, s>(q_gen_3405, q_gen_3402) -> q_gen_3400
<b, cons, s>(q_gen_3405, q_gen_3415) -> q_gen_3400
<b, cons, s>(q_gen_3411, q_gen_3413) -> q_gen_3400
<b, cons, s>(q_gen_3411, q_gen_3433) -> q_gen_3400
<b, cons, s>(q_gen_3426, q_gen_3413) -> q_gen_3400
<b, cons, s>(q_gen_3426, q_gen_3433) -> q_gen_3400
<b, cons, s>(q_gen_3435, q_gen_3422) -> q_gen_3400
<b, cons, s>(q_gen_3435, q_gen_3452) -> q_gen_3400
<b, cons, s>(q_gen_3475, q_gen_3452) -> q_gen_3400
<b, cons, z>(q_gen_3403, q_gen_3402) -> q_gen_3400
<b, cons, z>(q_gen_3403, q_gen_3415) -> q_gen_3400
<b, nil, z>() -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3415) -> q_gen_3409
<a, cons, s>(q_gen_3411, q_gen_3433) -> q_gen_3409
<a, cons, s>(q_gen_3426, q_gen_3402) -> q_gen_3409
<a, cons, s>(q_gen_3426, q_gen_3413) -> q_gen_3409
<a, cons, s>(q_gen_3435, q_gen_3413) -> q_gen_3409
<a, cons, s>(q_gen_3435, q_gen_3422) -> q_gen_3409
<a, cons, s>(q_gen_3435, q_gen_3452) -> q_gen_3409
<a, cons, z>(q_gen_3403, q_gen_3402) -> q_gen_3409
<a, cons, z>(q_gen_3408, q_gen_3415) -> q_gen_3409
<a, cons, z>(q_gen_3408, q_gen_3433) -> q_gen_3409
<a, cons, z>(q_gen_3408, q_gen_3452) -> q_gen_3409
<b, cons, s>(q_gen_3405, q_gen_3413) -> q_gen_3409
<b, cons, s>(q_gen_3405, q_gen_3433) -> q_gen_3409
<b, cons, s>(q_gen_3405, q_gen_3452) -> q_gen_3409
<b, cons, s>(q_gen_3411, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3411, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3422) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3452) -> q_gen_3409
<b, cons, s>(q_gen_3435, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3435, q_gen_3413) -> q_gen_3409
<b, cons, s>(q_gen_3435, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3435, q_gen_3433) -> q_gen_3409
<b, cons, s>(q_gen_3475, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3475, q_gen_3413) -> q_gen_3409
<b, cons, s>(q_gen_3475, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3475, q_gen_3422) -> q_gen_3409
<b, cons, z>(q_gen_3403, q_gen_3433) -> q_gen_3409
}

Datatype: <elt, eltlist, nat>
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
(count([x, l1, _nn]) /\ count([x, cons(x, l1), _mn])) -> eq_nat([_mn, s(_nn)]) -> 78
(count([x, t1, _gn])) -> count([x, cons(x, t1), s(_gn)]) -> 79
(count([x, t1, _hn]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _hn]) -> 79
}
Sat witness: Found: ((count([x, t1, _gn])) -> count([x, cons(x, t1), s(_gn)]), {
_gn -> s(z)  ;  t1 -> cons(a, cons(b, cons(b, nil)))  ;  x -> a
})

-------------------------------------------
Step 78, which took 2.091219 s (model generation: 2.076015,  model checking: 0.015204):

Model:
|_
{
count -> 
{{{
Q={q_gen_3400, q_gen_3402, q_gen_3403, q_gen_3405, q_gen_3408, q_gen_3409, q_gen_3411, q_gen_3413, q_gen_3415, q_gen_3422, q_gen_3426, q_gen_3427, q_gen_3433, q_gen_3435, q_gen_3436, q_gen_3452, q_gen_3475, q_gen_3476},
Q_f={q_gen_3400},
Delta=
{
<cons>(q_gen_3403, q_gen_3415) -> q_gen_3402
<cons>(q_gen_3408, q_gen_3422) -> q_gen_3402
<nil>() -> q_gen_3402
<a>() -> q_gen_3403
<b>() -> q_gen_3408
<cons>(q_gen_3408, q_gen_3402) -> q_gen_3413
<cons>(q_gen_3403, q_gen_3402) -> q_gen_3415
<cons>(q_gen_3403, q_gen_3452) -> q_gen_3422
<cons>(q_gen_3408, q_gen_3413) -> q_gen_3422
<z>() -> q_gen_3427
<cons>(q_gen_3403, q_gen_3413) -> q_gen_3433
<cons>(q_gen_3403, q_gen_3433) -> q_gen_3433
<cons>(q_gen_3408, q_gen_3415) -> q_gen_3433
<cons>(q_gen_3408, q_gen_3452) -> q_gen_3433
<s>(q_gen_3427) -> q_gen_3436
<cons>(q_gen_3403, q_gen_3422) -> q_gen_3452
<cons>(q_gen_3408, q_gen_3433) -> q_gen_3452
<s>(q_gen_3436) -> q_gen_3476
<b, z>() -> q_gen_3405
<a, z>() -> q_gen_3411
<a, s>(q_gen_3436) -> q_gen_3426
<b, s>(q_gen_3427) -> q_gen_3426
<a, s>(q_gen_3427) -> q_gen_3435
<b, s>(q_gen_3436) -> q_gen_3435
<b, s>(q_gen_3476) -> q_gen_3475
<a, cons, s>(q_gen_3405, q_gen_3415) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3402) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3413) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3422) -> q_gen_3400
<a, cons, s>(q_gen_3426, q_gen_3433) -> q_gen_3400
<a, cons, s>(q_gen_3435, q_gen_3433) -> q_gen_3400
<a, cons, s>(q_gen_3435, q_gen_3452) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3402) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3413) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3422) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3452) -> q_gen_3400
<a, nil, z>() -> q_gen_3400
<b, cons, s>(q_gen_3405, q_gen_3402) -> q_gen_3400
<b, cons, s>(q_gen_3405, q_gen_3415) -> q_gen_3400
<b, cons, s>(q_gen_3411, q_gen_3413) -> q_gen_3400
<b, cons, s>(q_gen_3411, q_gen_3433) -> q_gen_3400
<b, cons, s>(q_gen_3426, q_gen_3413) -> q_gen_3400
<b, cons, s>(q_gen_3426, q_gen_3433) -> q_gen_3400
<b, cons, s>(q_gen_3435, q_gen_3422) -> q_gen_3400
<b, cons, s>(q_gen_3435, q_gen_3452) -> q_gen_3400
<b, cons, s>(q_gen_3475, q_gen_3433) -> q_gen_3400
<b, cons, s>(q_gen_3475, q_gen_3452) -> q_gen_3400
<b, cons, z>(q_gen_3403, q_gen_3402) -> q_gen_3400
<b, cons, z>(q_gen_3403, q_gen_3415) -> q_gen_3400
<b, nil, z>() -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3415) -> q_gen_3409
<a, cons, s>(q_gen_3411, q_gen_3433) -> q_gen_3409
<a, cons, s>(q_gen_3426, q_gen_3402) -> q_gen_3409
<a, cons, s>(q_gen_3426, q_gen_3413) -> q_gen_3409
<a, cons, s>(q_gen_3435, q_gen_3413) -> q_gen_3409
<a, cons, s>(q_gen_3435, q_gen_3422) -> q_gen_3409
<a, cons, z>(q_gen_3403, q_gen_3402) -> q_gen_3409
<a, cons, z>(q_gen_3408, q_gen_3415) -> q_gen_3409
<a, cons, z>(q_gen_3408, q_gen_3433) -> q_gen_3409
<b, cons, s>(q_gen_3405, q_gen_3413) -> q_gen_3409
<b, cons, s>(q_gen_3405, q_gen_3433) -> q_gen_3409
<b, cons, s>(q_gen_3405, q_gen_3452) -> q_gen_3409
<b, cons, s>(q_gen_3411, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3411, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3422) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3452) -> q_gen_3409
<b, cons, s>(q_gen_3435, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3435, q_gen_3413) -> q_gen_3409
<b, cons, s>(q_gen_3435, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3435, q_gen_3433) -> q_gen_3409
<b, cons, s>(q_gen_3475, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3475, q_gen_3413) -> q_gen_3409
<b, cons, s>(q_gen_3475, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3475, q_gen_3422) -> q_gen_3409
<b, cons, z>(q_gen_3403, q_gen_3433) -> q_gen_3409
}

Datatype: <elt, eltlist, nat>
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
(count([x, l1, _nn]) /\ count([x, cons(x, l1), _mn])) -> eq_nat([_mn, s(_nn)]) -> 81
(count([x, t1, _gn])) -> count([x, cons(x, t1), s(_gn)]) -> 79
(count([x, t1, _hn]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _hn]) -> 79
}
Sat witness: Found: ((count([x, l1, _nn]) /\ count([x, cons(x, l1), _mn])) -> eq_nat([_mn, s(_nn)]), {
_mn -> s(s(s(z)))  ;  _nn -> z  ;  l1 -> cons(b, cons(a, cons(b, cons(b, nil))))  ;  x -> a
})

-------------------------------------------
Step 79, which took 1.771413 s (model generation: 1.716427,  model checking: 0.054986):

Model:
|_
{
count -> 
{{{
Q={q_gen_3400, q_gen_3402, q_gen_3403, q_gen_3405, q_gen_3408, q_gen_3409, q_gen_3411, q_gen_3413, q_gen_3415, q_gen_3422, q_gen_3426, q_gen_3427, q_gen_3433, q_gen_3435, q_gen_3436, q_gen_3452, q_gen_3470, q_gen_3476},
Q_f={q_gen_3400},
Delta=
{
<nil>() -> q_gen_3402
<a>() -> q_gen_3403
<b>() -> q_gen_3408
<cons>(q_gen_3408, q_gen_3402) -> q_gen_3413
<cons>(q_gen_3408, q_gen_3422) -> q_gen_3413
<cons>(q_gen_3403, q_gen_3402) -> q_gen_3415
<cons>(q_gen_3403, q_gen_3415) -> q_gen_3415
<cons>(q_gen_3403, q_gen_3452) -> q_gen_3422
<cons>(q_gen_3408, q_gen_3413) -> q_gen_3422
<z>() -> q_gen_3427
<cons>(q_gen_3403, q_gen_3413) -> q_gen_3433
<cons>(q_gen_3403, q_gen_3433) -> q_gen_3433
<cons>(q_gen_3408, q_gen_3415) -> q_gen_3433
<s>(q_gen_3427) -> q_gen_3436
<cons>(q_gen_3403, q_gen_3422) -> q_gen_3452
<cons>(q_gen_3408, q_gen_3433) -> q_gen_3452
<cons>(q_gen_3408, q_gen_3452) -> q_gen_3452
<s>(q_gen_3436) -> q_gen_3476
<b, z>() -> q_gen_3405
<a, z>() -> q_gen_3411
<b, s>(q_gen_3427) -> q_gen_3426
<a, s>(q_gen_3427) -> q_gen_3435
<b, s>(q_gen_3436) -> q_gen_3435
<a, s>(q_gen_3436) -> q_gen_3470
<b, s>(q_gen_3476) -> q_gen_3470
<a, cons, s>(q_gen_3405, q_gen_3415) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3402) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3413) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3422) -> q_gen_3400
<a, cons, s>(q_gen_3426, q_gen_3433) -> q_gen_3400
<a, cons, s>(q_gen_3435, q_gen_3433) -> q_gen_3400
<a, cons, s>(q_gen_3435, q_gen_3452) -> q_gen_3400
<a, cons, s>(q_gen_3470, q_gen_3422) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3402) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3413) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3422) -> q_gen_3400
<a, nil, z>() -> q_gen_3400
<b, cons, s>(q_gen_3405, q_gen_3402) -> q_gen_3400
<b, cons, s>(q_gen_3405, q_gen_3415) -> q_gen_3400
<b, cons, s>(q_gen_3411, q_gen_3413) -> q_gen_3400
<b, cons, s>(q_gen_3411, q_gen_3433) -> q_gen_3400
<b, cons, s>(q_gen_3426, q_gen_3413) -> q_gen_3400
<b, cons, s>(q_gen_3426, q_gen_3433) -> q_gen_3400
<b, cons, s>(q_gen_3426, q_gen_3452) -> q_gen_3400
<b, cons, s>(q_gen_3435, q_gen_3422) -> q_gen_3400
<b, cons, s>(q_gen_3435, q_gen_3452) -> q_gen_3400
<b, cons, s>(q_gen_3470, q_gen_3433) -> q_gen_3400
<b, cons, s>(q_gen_3470, q_gen_3452) -> q_gen_3400
<b, cons, z>(q_gen_3403, q_gen_3402) -> q_gen_3400
<b, cons, z>(q_gen_3403, q_gen_3415) -> q_gen_3400
<b, nil, z>() -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3415) -> q_gen_3409
<a, cons, s>(q_gen_3411, q_gen_3433) -> q_gen_3409
<a, cons, s>(q_gen_3426, q_gen_3402) -> q_gen_3409
<a, cons, s>(q_gen_3426, q_gen_3413) -> q_gen_3409
<a, cons, s>(q_gen_3435, q_gen_3413) -> q_gen_3409
<a, cons, s>(q_gen_3435, q_gen_3422) -> q_gen_3409
<a, cons, s>(q_gen_3470, q_gen_3413) -> q_gen_3409
<a, cons, s>(q_gen_3470, q_gen_3433) -> q_gen_3409
<a, cons, s>(q_gen_3470, q_gen_3452) -> q_gen_3409
<a, cons, z>(q_gen_3403, q_gen_3402) -> q_gen_3409
<a, cons, z>(q_gen_3408, q_gen_3415) -> q_gen_3409
<a, cons, z>(q_gen_3408, q_gen_3433) -> q_gen_3409
<a, cons, z>(q_gen_3408, q_gen_3452) -> q_gen_3409
<b, cons, s>(q_gen_3405, q_gen_3413) -> q_gen_3409
<b, cons, s>(q_gen_3405, q_gen_3433) -> q_gen_3409
<b, cons, s>(q_gen_3405, q_gen_3452) -> q_gen_3409
<b, cons, s>(q_gen_3411, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3411, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3422) -> q_gen_3409
<b, cons, s>(q_gen_3435, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3435, q_gen_3413) -> q_gen_3409
<b, cons, s>(q_gen_3435, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3435, q_gen_3433) -> q_gen_3409
<b, cons, s>(q_gen_3470, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3470, q_gen_3413) -> q_gen_3409
<b, cons, s>(q_gen_3470, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3470, q_gen_3422) -> q_gen_3409
<b, cons, z>(q_gen_3403, q_gen_3433) -> q_gen_3409
}

Datatype: <elt, eltlist, nat>
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
(count([x, l1, _nn]) /\ count([x, cons(x, l1), _mn])) -> eq_nat([_mn, s(_nn)]) -> 81
(count([x, t1, _gn])) -> count([x, cons(x, t1), s(_gn)]) -> 79
(count([x, t1, _hn]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _hn]) -> 82
}
Sat witness: Found: ((count([x, t1, _hn]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _hn]), {
_hn -> s(s(s(s(z))))  ;  h1 -> b  ;  t1 -> cons(b, cons(b, cons(b, nil)))  ;  x -> a
})

-------------------------------------------
Step 80, which took 1.955235 s (model generation: 1.879945,  model checking: 0.075290):

Model:
|_
{
count -> 
{{{
Q={q_gen_3400, q_gen_3402, q_gen_3403, q_gen_3405, q_gen_3408, q_gen_3409, q_gen_3411, q_gen_3413, q_gen_3415, q_gen_3422, q_gen_3426, q_gen_3427, q_gen_3433, q_gen_3435, q_gen_3436, q_gen_3452, q_gen_3475, q_gen_3476},
Q_f={q_gen_3400},
Delta=
{
<cons>(q_gen_3403, q_gen_3415) -> q_gen_3402
<nil>() -> q_gen_3402
<a>() -> q_gen_3403
<b>() -> q_gen_3408
<cons>(q_gen_3408, q_gen_3402) -> q_gen_3413
<cons>(q_gen_3403, q_gen_3402) -> q_gen_3415
<cons>(q_gen_3408, q_gen_3413) -> q_gen_3422
<cons>(q_gen_3408, q_gen_3422) -> q_gen_3422
<z>() -> q_gen_3427
<cons>(q_gen_3403, q_gen_3413) -> q_gen_3433
<cons>(q_gen_3403, q_gen_3433) -> q_gen_3433
<cons>(q_gen_3408, q_gen_3415) -> q_gen_3433
<cons>(q_gen_3408, q_gen_3452) -> q_gen_3433
<s>(q_gen_3427) -> q_gen_3436
<cons>(q_gen_3403, q_gen_3422) -> q_gen_3452
<cons>(q_gen_3403, q_gen_3452) -> q_gen_3452
<cons>(q_gen_3408, q_gen_3433) -> q_gen_3452
<s>(q_gen_3436) -> q_gen_3476
<b, z>() -> q_gen_3405
<a, z>() -> q_gen_3411
<a, s>(q_gen_3436) -> q_gen_3426
<b, s>(q_gen_3427) -> q_gen_3426
<a, s>(q_gen_3427) -> q_gen_3435
<b, s>(q_gen_3436) -> q_gen_3435
<b, s>(q_gen_3476) -> q_gen_3475
<a, cons, s>(q_gen_3405, q_gen_3415) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3402) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3413) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3422) -> q_gen_3400
<a, cons, s>(q_gen_3426, q_gen_3433) -> q_gen_3400
<a, cons, s>(q_gen_3435, q_gen_3433) -> q_gen_3400
<a, cons, s>(q_gen_3435, q_gen_3452) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3402) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3413) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3422) -> q_gen_3400
<a, nil, z>() -> q_gen_3400
<b, cons, s>(q_gen_3405, q_gen_3402) -> q_gen_3400
<b, cons, s>(q_gen_3405, q_gen_3415) -> q_gen_3400
<b, cons, s>(q_gen_3411, q_gen_3413) -> q_gen_3400
<b, cons, s>(q_gen_3411, q_gen_3433) -> q_gen_3400
<b, cons, s>(q_gen_3426, q_gen_3413) -> q_gen_3400
<b, cons, s>(q_gen_3426, q_gen_3433) -> q_gen_3400
<b, cons, s>(q_gen_3435, q_gen_3422) -> q_gen_3400
<b, cons, s>(q_gen_3435, q_gen_3452) -> q_gen_3400
<b, cons, s>(q_gen_3475, q_gen_3433) -> q_gen_3400
<b, cons, s>(q_gen_3475, q_gen_3452) -> q_gen_3400
<b, cons, z>(q_gen_3403, q_gen_3402) -> q_gen_3400
<b, cons, z>(q_gen_3403, q_gen_3415) -> q_gen_3400
<b, nil, z>() -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3415) -> q_gen_3409
<a, cons, s>(q_gen_3411, q_gen_3433) -> q_gen_3409
<a, cons, s>(q_gen_3426, q_gen_3402) -> q_gen_3409
<a, cons, s>(q_gen_3426, q_gen_3413) -> q_gen_3409
<a, cons, s>(q_gen_3435, q_gen_3413) -> q_gen_3409
<a, cons, s>(q_gen_3435, q_gen_3422) -> q_gen_3409
<a, cons, s>(q_gen_3475, q_gen_3422) -> q_gen_3409
<a, cons, z>(q_gen_3403, q_gen_3402) -> q_gen_3409
<a, cons, z>(q_gen_3408, q_gen_3415) -> q_gen_3409
<a, cons, z>(q_gen_3408, q_gen_3433) -> q_gen_3409
<a, cons, z>(q_gen_3408, q_gen_3452) -> q_gen_3409
<b, cons, s>(q_gen_3405, q_gen_3413) -> q_gen_3409
<b, cons, s>(q_gen_3405, q_gen_3433) -> q_gen_3409
<b, cons, s>(q_gen_3405, q_gen_3452) -> q_gen_3409
<b, cons, s>(q_gen_3411, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3411, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3422) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3452) -> q_gen_3409
<b, cons, s>(q_gen_3435, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3435, q_gen_3413) -> q_gen_3409
<b, cons, s>(q_gen_3435, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3435, q_gen_3433) -> q_gen_3409
<b, cons, s>(q_gen_3475, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3475, q_gen_3413) -> q_gen_3409
<b, cons, s>(q_gen_3475, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3475, q_gen_3422) -> q_gen_3409
<b, cons, z>(q_gen_3403, q_gen_3433) -> q_gen_3409
}

Datatype: <elt, eltlist, nat>
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
(count([x, l1, _nn]) /\ count([x, cons(x, l1), _mn])) -> eq_nat([_mn, s(_nn)]) -> 81
(count([x, t1, _gn])) -> count([x, cons(x, t1), s(_gn)]) -> 82
(count([x, t1, _hn]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _hn]) -> 82
}
Sat witness: Found: ((count([x, t1, _gn])) -> count([x, cons(x, t1), s(_gn)]), {
_gn -> s(s(s(z)))  ;  t1 -> cons(b, cons(b, cons(b, nil)))  ;  x -> b
})

-------------------------------------------
Step 81, which took 1.852205 s (model generation: 1.833946,  model checking: 0.018259):

Model:
|_
{
count -> 
{{{
Q={q_gen_3400, q_gen_3402, q_gen_3403, q_gen_3405, q_gen_3408, q_gen_3409, q_gen_3411, q_gen_3413, q_gen_3415, q_gen_3422, q_gen_3426, q_gen_3427, q_gen_3430, q_gen_3433, q_gen_3435, q_gen_3436, q_gen_3475, q_gen_3476},
Q_f={q_gen_3400},
Delta=
{
<nil>() -> q_gen_3402
<a>() -> q_gen_3403
<b>() -> q_gen_3408
<cons>(q_gen_3403, q_gen_3433) -> q_gen_3413
<cons>(q_gen_3408, q_gen_3402) -> q_gen_3413
<cons>(q_gen_3403, q_gen_3402) -> q_gen_3415
<cons>(q_gen_3403, q_gen_3415) -> q_gen_3415
<cons>(q_gen_3403, q_gen_3430) -> q_gen_3422
<cons>(q_gen_3408, q_gen_3413) -> q_gen_3422
<cons>(q_gen_3408, q_gen_3430) -> q_gen_3422
<z>() -> q_gen_3427
<cons>(q_gen_3408, q_gen_3422) -> q_gen_3430
<cons>(q_gen_3408, q_gen_3433) -> q_gen_3430
<cons>(q_gen_3403, q_gen_3413) -> q_gen_3433
<cons>(q_gen_3403, q_gen_3422) -> q_gen_3433
<cons>(q_gen_3408, q_gen_3415) -> q_gen_3433
<s>(q_gen_3427) -> q_gen_3436
<s>(q_gen_3436) -> q_gen_3476
<b, z>() -> q_gen_3405
<a, z>() -> q_gen_3411
<a, s>(q_gen_3436) -> q_gen_3426
<b, s>(q_gen_3427) -> q_gen_3426
<a, s>(q_gen_3427) -> q_gen_3435
<b, s>(q_gen_3436) -> q_gen_3435
<b, s>(q_gen_3476) -> q_gen_3475
<a, cons, s>(q_gen_3405, q_gen_3415) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3402) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3413) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3422) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3430) -> q_gen_3400
<a, cons, s>(q_gen_3426, q_gen_3422) -> q_gen_3400
<a, cons, s>(q_gen_3426, q_gen_3430) -> q_gen_3400
<a, cons, s>(q_gen_3435, q_gen_3430) -> q_gen_3400
<a, cons, s>(q_gen_3435, q_gen_3433) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3402) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3413) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3422) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3430) -> q_gen_3400
<a, nil, z>() -> q_gen_3400
<b, cons, s>(q_gen_3405, q_gen_3402) -> q_gen_3400
<b, cons, s>(q_gen_3405, q_gen_3415) -> q_gen_3400
<b, cons, s>(q_gen_3411, q_gen_3413) -> q_gen_3400
<b, cons, s>(q_gen_3411, q_gen_3433) -> q_gen_3400
<b, cons, s>(q_gen_3426, q_gen_3413) -> q_gen_3400
<b, cons, s>(q_gen_3426, q_gen_3430) -> q_gen_3400
<b, cons, s>(q_gen_3426, q_gen_3433) -> q_gen_3400
<b, cons, s>(q_gen_3435, q_gen_3422) -> q_gen_3400
<b, cons, s>(q_gen_3435, q_gen_3430) -> q_gen_3400
<b, cons, s>(q_gen_3435, q_gen_3433) -> q_gen_3400
<b, cons, s>(q_gen_3475, q_gen_3430) -> q_gen_3400
<b, cons, z>(q_gen_3403, q_gen_3402) -> q_gen_3400
<b, cons, z>(q_gen_3403, q_gen_3415) -> q_gen_3400
<b, nil, z>() -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3415) -> q_gen_3409
<a, cons, s>(q_gen_3411, q_gen_3433) -> q_gen_3409
<a, cons, s>(q_gen_3426, q_gen_3402) -> q_gen_3409
<a, cons, s>(q_gen_3426, q_gen_3413) -> q_gen_3409
<a, cons, s>(q_gen_3426, q_gen_3433) -> q_gen_3409
<a, cons, s>(q_gen_3435, q_gen_3413) -> q_gen_3409
<a, cons, s>(q_gen_3435, q_gen_3422) -> q_gen_3409
<a, cons, s>(q_gen_3475, q_gen_3422) -> q_gen_3409
<a, cons, s>(q_gen_3475, q_gen_3430) -> q_gen_3409
<a, cons, z>(q_gen_3403, q_gen_3402) -> q_gen_3409
<a, cons, z>(q_gen_3408, q_gen_3415) -> q_gen_3409
<a, cons, z>(q_gen_3408, q_gen_3433) -> q_gen_3409
<b, cons, s>(q_gen_3405, q_gen_3413) -> q_gen_3409
<b, cons, s>(q_gen_3405, q_gen_3430) -> q_gen_3409
<b, cons, s>(q_gen_3405, q_gen_3433) -> q_gen_3409
<b, cons, s>(q_gen_3411, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3411, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3422) -> q_gen_3409
<b, cons, s>(q_gen_3435, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3435, q_gen_3413) -> q_gen_3409
<b, cons, s>(q_gen_3435, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3475, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3475, q_gen_3413) -> q_gen_3409
<b, cons, s>(q_gen_3475, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3475, q_gen_3422) -> q_gen_3409
<b, cons, z>(q_gen_3403, q_gen_3413) -> q_gen_3409
<b, cons, z>(q_gen_3403, q_gen_3433) -> q_gen_3409
}

Datatype: <elt, eltlist, nat>
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
(count([x, l1, _nn]) /\ count([x, cons(x, l1), _mn])) -> eq_nat([_mn, s(_nn)]) -> 84
(count([x, t1, _gn])) -> count([x, cons(x, t1), s(_gn)]) -> 82
(count([x, t1, _hn]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _hn]) -> 82
}
Sat witness: Found: ((count([x, l1, _nn]) /\ count([x, cons(x, l1), _mn])) -> eq_nat([_mn, s(_nn)]), {
_mn -> s(s(s(z)))  ;  _nn -> z  ;  l1 -> cons(b, cons(b, nil))  ;  x -> a
})

-------------------------------------------
Step 82, which took 1.615543 s (model generation: 1.569243,  model checking: 0.046300):

Model:
|_
{
count -> 
{{{
Q={q_gen_3400, q_gen_3402, q_gen_3403, q_gen_3405, q_gen_3408, q_gen_3409, q_gen_3411, q_gen_3413, q_gen_3415, q_gen_3422, q_gen_3426, q_gen_3427, q_gen_3430, q_gen_3433, q_gen_3435, q_gen_3436, q_gen_3475, q_gen_3476},
Q_f={q_gen_3400},
Delta=
{
<cons>(q_gen_3403, q_gen_3415) -> q_gen_3402
<nil>() -> q_gen_3402
<a>() -> q_gen_3403
<b>() -> q_gen_3408
<cons>(q_gen_3408, q_gen_3402) -> q_gen_3413
<cons>(q_gen_3408, q_gen_3415) -> q_gen_3413
<cons>(q_gen_3408, q_gen_3433) -> q_gen_3413
<cons>(q_gen_3403, q_gen_3402) -> q_gen_3415
<cons>(q_gen_3403, q_gen_3430) -> q_gen_3415
<cons>(q_gen_3408, q_gen_3413) -> q_gen_3422
<z>() -> q_gen_3427
<cons>(q_gen_3403, q_gen_3422) -> q_gen_3430
<cons>(q_gen_3403, q_gen_3433) -> q_gen_3430
<cons>(q_gen_3408, q_gen_3422) -> q_gen_3430
<cons>(q_gen_3403, q_gen_3413) -> q_gen_3433
<cons>(q_gen_3408, q_gen_3430) -> q_gen_3433
<s>(q_gen_3427) -> q_gen_3436
<s>(q_gen_3436) -> q_gen_3476
<b, z>() -> q_gen_3405
<a, z>() -> q_gen_3411
<a, s>(q_gen_3436) -> q_gen_3426
<b, s>(q_gen_3427) -> q_gen_3426
<a, s>(q_gen_3427) -> q_gen_3435
<b, s>(q_gen_3436) -> q_gen_3435
<b, s>(q_gen_3476) -> q_gen_3475
<a, cons, s>(q_gen_3405, q_gen_3415) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3402) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3413) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3422) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3430) -> q_gen_3400
<a, cons, s>(q_gen_3426, q_gen_3430) -> q_gen_3400
<a, cons, s>(q_gen_3435, q_gen_3430) -> q_gen_3400
<a, cons, s>(q_gen_3435, q_gen_3433) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3402) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3413) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3422) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3430) -> q_gen_3400
<a, nil, z>() -> q_gen_3400
<b, cons, s>(q_gen_3405, q_gen_3402) -> q_gen_3400
<b, cons, s>(q_gen_3405, q_gen_3415) -> q_gen_3400
<b, cons, s>(q_gen_3411, q_gen_3413) -> q_gen_3400
<b, cons, s>(q_gen_3411, q_gen_3430) -> q_gen_3400
<b, cons, s>(q_gen_3411, q_gen_3433) -> q_gen_3400
<b, cons, s>(q_gen_3426, q_gen_3413) -> q_gen_3400
<b, cons, s>(q_gen_3426, q_gen_3433) -> q_gen_3400
<b, cons, s>(q_gen_3435, q_gen_3422) -> q_gen_3400
<b, cons, s>(q_gen_3435, q_gen_3430) -> q_gen_3400
<b, cons, s>(q_gen_3475, q_gen_3430) -> q_gen_3400
<b, cons, s>(q_gen_3475, q_gen_3433) -> q_gen_3400
<b, cons, z>(q_gen_3403, q_gen_3402) -> q_gen_3400
<b, cons, z>(q_gen_3403, q_gen_3415) -> q_gen_3400
<b, nil, z>() -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3415) -> q_gen_3409
<a, cons, s>(q_gen_3411, q_gen_3433) -> q_gen_3409
<a, cons, s>(q_gen_3426, q_gen_3402) -> q_gen_3409
<a, cons, s>(q_gen_3426, q_gen_3413) -> q_gen_3409
<a, cons, s>(q_gen_3426, q_gen_3422) -> q_gen_3409
<a, cons, s>(q_gen_3426, q_gen_3433) -> q_gen_3409
<a, cons, s>(q_gen_3435, q_gen_3413) -> q_gen_3409
<a, cons, s>(q_gen_3435, q_gen_3422) -> q_gen_3409
<a, cons, s>(q_gen_3475, q_gen_3422) -> q_gen_3409
<a, cons, s>(q_gen_3475, q_gen_3430) -> q_gen_3409
<a, cons, z>(q_gen_3403, q_gen_3402) -> q_gen_3409
<a, cons, z>(q_gen_3408, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3405, q_gen_3413) -> q_gen_3409
<b, cons, s>(q_gen_3405, q_gen_3430) -> q_gen_3409
<b, cons, s>(q_gen_3411, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3411, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3422) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3430) -> q_gen_3409
<b, cons, s>(q_gen_3435, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3435, q_gen_3413) -> q_gen_3409
<b, cons, s>(q_gen_3435, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3435, q_gen_3433) -> q_gen_3409
<b, cons, s>(q_gen_3475, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3475, q_gen_3413) -> q_gen_3409
<b, cons, s>(q_gen_3475, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3475, q_gen_3422) -> q_gen_3409
<b, cons, z>(q_gen_3403, q_gen_3430) -> q_gen_3409
<b, cons, z>(q_gen_3403, q_gen_3433) -> q_gen_3409
}

Datatype: <elt, eltlist, nat>
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
(count([x, l1, _nn]) /\ count([x, cons(x, l1), _mn])) -> eq_nat([_mn, s(_nn)]) -> 84
(count([x, t1, _gn])) -> count([x, cons(x, t1), s(_gn)]) -> 82
(count([x, t1, _hn]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _hn]) -> 85
}
Sat witness: Found: ((count([x, t1, _hn]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _hn]), {
_hn -> s(s(z))  ;  h1 -> a  ;  t1 -> cons(b, cons(a, cons(b, cons(a, nil))))  ;  x -> b
})

-------------------------------------------
Step 83, which took 1.603690 s (model generation: 1.568838,  model checking: 0.034852):

Model:
|_
{
count -> 
{{{
Q={q_gen_3400, q_gen_3402, q_gen_3403, q_gen_3405, q_gen_3408, q_gen_3409, q_gen_3411, q_gen_3413, q_gen_3415, q_gen_3422, q_gen_3426, q_gen_3427, q_gen_3430, q_gen_3433, q_gen_3435, q_gen_3436, q_gen_3475, q_gen_3476},
Q_f={q_gen_3400},
Delta=
{
<nil>() -> q_gen_3402
<a>() -> q_gen_3403
<b>() -> q_gen_3408
<cons>(q_gen_3403, q_gen_3433) -> q_gen_3413
<cons>(q_gen_3408, q_gen_3402) -> q_gen_3413
<cons>(q_gen_3403, q_gen_3402) -> q_gen_3415
<cons>(q_gen_3403, q_gen_3415) -> q_gen_3415
<cons>(q_gen_3403, q_gen_3430) -> q_gen_3422
<cons>(q_gen_3408, q_gen_3413) -> q_gen_3422
<cons>(q_gen_3408, q_gen_3430) -> q_gen_3422
<z>() -> q_gen_3427
<cons>(q_gen_3408, q_gen_3422) -> q_gen_3430
<cons>(q_gen_3408, q_gen_3433) -> q_gen_3430
<cons>(q_gen_3403, q_gen_3413) -> q_gen_3433
<cons>(q_gen_3403, q_gen_3422) -> q_gen_3433
<cons>(q_gen_3408, q_gen_3415) -> q_gen_3433
<s>(q_gen_3427) -> q_gen_3436
<s>(q_gen_3436) -> q_gen_3476
<b, z>() -> q_gen_3405
<a, z>() -> q_gen_3411
<a, s>(q_gen_3436) -> q_gen_3426
<b, s>(q_gen_3427) -> q_gen_3426
<a, s>(q_gen_3427) -> q_gen_3435
<b, s>(q_gen_3436) -> q_gen_3435
<b, s>(q_gen_3476) -> q_gen_3475
<a, cons, s>(q_gen_3405, q_gen_3415) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3402) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3413) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3422) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3430) -> q_gen_3400
<a, cons, s>(q_gen_3435, q_gen_3433) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3402) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3413) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3422) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3430) -> q_gen_3400
<a, nil, z>() -> q_gen_3400
<b, cons, s>(q_gen_3405, q_gen_3402) -> q_gen_3400
<b, cons, s>(q_gen_3405, q_gen_3415) -> q_gen_3400
<b, cons, s>(q_gen_3411, q_gen_3413) -> q_gen_3400
<b, cons, s>(q_gen_3411, q_gen_3433) -> q_gen_3400
<b, cons, s>(q_gen_3426, q_gen_3413) -> q_gen_3400
<b, cons, s>(q_gen_3426, q_gen_3430) -> q_gen_3400
<b, cons, s>(q_gen_3426, q_gen_3433) -> q_gen_3400
<b, cons, s>(q_gen_3435, q_gen_3422) -> q_gen_3400
<b, cons, s>(q_gen_3435, q_gen_3430) -> q_gen_3400
<b, cons, s>(q_gen_3435, q_gen_3433) -> q_gen_3400
<b, cons, s>(q_gen_3475, q_gen_3430) -> q_gen_3400
<b, cons, z>(q_gen_3403, q_gen_3402) -> q_gen_3400
<b, cons, z>(q_gen_3403, q_gen_3415) -> q_gen_3400
<b, nil, z>() -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3415) -> q_gen_3409
<a, cons, s>(q_gen_3411, q_gen_3433) -> q_gen_3409
<a, cons, s>(q_gen_3426, q_gen_3402) -> q_gen_3409
<a, cons, s>(q_gen_3426, q_gen_3413) -> q_gen_3409
<a, cons, s>(q_gen_3426, q_gen_3422) -> q_gen_3409
<a, cons, s>(q_gen_3426, q_gen_3430) -> q_gen_3409
<a, cons, s>(q_gen_3426, q_gen_3433) -> q_gen_3409
<a, cons, s>(q_gen_3435, q_gen_3413) -> q_gen_3409
<a, cons, s>(q_gen_3435, q_gen_3422) -> q_gen_3409
<a, cons, s>(q_gen_3435, q_gen_3430) -> q_gen_3409
<a, cons, s>(q_gen_3475, q_gen_3422) -> q_gen_3409
<a, cons, s>(q_gen_3475, q_gen_3430) -> q_gen_3409
<a, cons, z>(q_gen_3403, q_gen_3402) -> q_gen_3409
<a, cons, z>(q_gen_3408, q_gen_3415) -> q_gen_3409
<a, cons, z>(q_gen_3408, q_gen_3433) -> q_gen_3409
<b, cons, s>(q_gen_3405, q_gen_3413) -> q_gen_3409
<b, cons, s>(q_gen_3405, q_gen_3430) -> q_gen_3409
<b, cons, s>(q_gen_3405, q_gen_3433) -> q_gen_3409
<b, cons, s>(q_gen_3411, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3411, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3422) -> q_gen_3409
<b, cons, s>(q_gen_3435, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3435, q_gen_3413) -> q_gen_3409
<b, cons, s>(q_gen_3435, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3475, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3475, q_gen_3413) -> q_gen_3409
<b, cons, s>(q_gen_3475, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3475, q_gen_3422) -> q_gen_3409
<b, cons, z>(q_gen_3403, q_gen_3413) -> q_gen_3409
<b, cons, z>(q_gen_3403, q_gen_3433) -> q_gen_3409
}

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

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 81
(count([x, l1, _nn]) /\ count([x, cons(x, l1), _mn])) -> eq_nat([_mn, s(_nn)]) -> 84
(count([x, t1, _gn])) -> count([x, cons(x, t1), s(_gn)]) -> 85
(count([x, t1, _hn]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _hn]) -> 85
}
Sat witness: Found: ((count([x, t1, _gn])) -> count([x, cons(x, t1), s(_gn)]), {
_gn -> s(s(z))  ;  t1 -> cons(a, cons(b, cons(a, nil)))  ;  x -> b
})

-------------------------------------------
Step 84, which took 2.626076 s (model generation: 2.611311,  model checking: 0.014765):

Model:
|_
{
count -> 
{{{
Q={q_gen_3400, q_gen_3402, q_gen_3403, q_gen_3405, q_gen_3408, q_gen_3409, q_gen_3411, q_gen_3413, q_gen_3415, q_gen_3422, q_gen_3426, q_gen_3427, q_gen_3430, q_gen_3433, q_gen_3435, q_gen_3436, q_gen_3475, q_gen_3476},
Q_f={q_gen_3400},
Delta=
{
<cons>(q_gen_3403, q_gen_3415) -> q_gen_3402
<nil>() -> q_gen_3402
<a>() -> q_gen_3403
<b>() -> q_gen_3408
<cons>(q_gen_3403, q_gen_3433) -> q_gen_3413
<cons>(q_gen_3408, q_gen_3402) -> q_gen_3413
<cons>(q_gen_3403, q_gen_3402) -> q_gen_3415
<cons>(q_gen_3403, q_gen_3430) -> q_gen_3415
<cons>(q_gen_3408, q_gen_3413) -> q_gen_3422
<cons>(q_gen_3408, q_gen_3433) -> q_gen_3422
<z>() -> q_gen_3427
<cons>(q_gen_3403, q_gen_3422) -> q_gen_3430
<cons>(q_gen_3408, q_gen_3422) -> q_gen_3430
<cons>(q_gen_3408, q_gen_3430) -> q_gen_3430
<cons>(q_gen_3403, q_gen_3413) -> q_gen_3433
<cons>(q_gen_3408, q_gen_3415) -> q_gen_3433
<s>(q_gen_3427) -> q_gen_3436
<s>(q_gen_3436) -> q_gen_3476
<b, z>() -> q_gen_3405
<a, z>() -> q_gen_3411
<a, s>(q_gen_3436) -> q_gen_3426
<b, s>(q_gen_3427) -> q_gen_3426
<a, s>(q_gen_3427) -> q_gen_3435
<b, s>(q_gen_3436) -> q_gen_3435
<b, s>(q_gen_3476) -> q_gen_3475
<a, cons, s>(q_gen_3405, q_gen_3415) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3402) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3413) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3422) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3430) -> q_gen_3400
<a, cons, s>(q_gen_3426, q_gen_3415) -> q_gen_3400
<a, cons, s>(q_gen_3435, q_gen_3430) -> q_gen_3400
<a, cons, s>(q_gen_3435, q_gen_3433) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3402) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3413) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3422) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3430) -> q_gen_3400
<a, nil, z>() -> q_gen_3400
<b, cons, s>(q_gen_3405, q_gen_3402) -> q_gen_3400
<b, cons, s>(q_gen_3405, q_gen_3415) -> q_gen_3400
<b, cons, s>(q_gen_3411, q_gen_3413) -> q_gen_3400
<b, cons, s>(q_gen_3411, q_gen_3433) -> q_gen_3400
<b, cons, s>(q_gen_3426, q_gen_3413) -> q_gen_3400
<b, cons, s>(q_gen_3426, q_gen_3430) -> q_gen_3400
<b, cons, s>(q_gen_3426, q_gen_3433) -> q_gen_3400
<b, cons, s>(q_gen_3435, q_gen_3422) -> q_gen_3400
<b, cons, s>(q_gen_3435, q_gen_3430) -> q_gen_3400
<b, cons, s>(q_gen_3475, q_gen_3430) -> q_gen_3400
<b, cons, z>(q_gen_3403, q_gen_3402) -> q_gen_3400
<b, cons, z>(q_gen_3403, q_gen_3415) -> q_gen_3400
<b, nil, z>() -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3415) -> q_gen_3409
<a, cons, s>(q_gen_3411, q_gen_3433) -> q_gen_3409
<a, cons, s>(q_gen_3426, q_gen_3402) -> q_gen_3409
<a, cons, s>(q_gen_3426, q_gen_3413) -> q_gen_3409
<a, cons, s>(q_gen_3426, q_gen_3422) -> q_gen_3409
<a, cons, s>(q_gen_3426, q_gen_3430) -> q_gen_3409
<a, cons, s>(q_gen_3426, q_gen_3433) -> q_gen_3409
<a, cons, s>(q_gen_3435, q_gen_3413) -> q_gen_3409
<a, cons, s>(q_gen_3435, q_gen_3422) -> q_gen_3409
<a, cons, s>(q_gen_3475, q_gen_3422) -> q_gen_3409
<a, cons, s>(q_gen_3475, q_gen_3430) -> q_gen_3409
<a, cons, z>(q_gen_3403, q_gen_3402) -> q_gen_3409
<a, cons, z>(q_gen_3408, q_gen_3415) -> q_gen_3409
<a, cons, z>(q_gen_3408, q_gen_3433) -> q_gen_3409
<b, cons, s>(q_gen_3405, q_gen_3413) -> q_gen_3409
<b, cons, s>(q_gen_3405, q_gen_3422) -> q_gen_3409
<b, cons, s>(q_gen_3405, q_gen_3433) -> q_gen_3409
<b, cons, s>(q_gen_3411, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3411, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3422) -> q_gen_3409
<b, cons, s>(q_gen_3435, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3435, q_gen_3413) -> q_gen_3409
<b, cons, s>(q_gen_3435, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3435, q_gen_3433) -> q_gen_3409
<b, cons, s>(q_gen_3475, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3475, q_gen_3413) -> q_gen_3409
<b, cons, s>(q_gen_3475, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3475, q_gen_3422) -> q_gen_3409
<b, cons, z>(q_gen_3403, q_gen_3413) -> q_gen_3409
<b, cons, z>(q_gen_3403, q_gen_3433) -> q_gen_3409
}

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

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 82
(count([x, l1, _nn]) /\ count([x, cons(x, l1), _mn])) -> eq_nat([_mn, s(_nn)]) -> 87
(count([x, t1, _gn])) -> count([x, cons(x, t1), s(_gn)]) -> 85
(count([x, t1, _hn]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _hn]) -> 85
}
Sat witness: Found: ((count([x, l1, _nn]) /\ count([x, cons(x, l1), _mn])) -> eq_nat([_mn, s(_nn)]), {
_mn -> s(s(z))  ;  _nn -> z  ;  l1 -> cons(b, cons(b, cons(b, nil)))  ;  x -> a
})

-------------------------------------------
Step 85, which took 1.842943 s (model generation: 1.786995,  model checking: 0.055948):

Model:
|_
{
count -> 
{{{
Q={q_gen_3400, q_gen_3402, q_gen_3403, q_gen_3405, q_gen_3408, q_gen_3409, q_gen_3411, q_gen_3413, q_gen_3415, q_gen_3422, q_gen_3424, q_gen_3426, q_gen_3427, q_gen_3433, q_gen_3435, q_gen_3436, q_gen_3452, q_gen_3475, q_gen_3476},
Q_f={q_gen_3400},
Delta=
{
<cons>(q_gen_3408, q_gen_3424) -> q_gen_3402
<nil>() -> q_gen_3402
<a>() -> q_gen_3403
<b>() -> q_gen_3408
<cons>(q_gen_3408, q_gen_3402) -> q_gen_3413
<cons>(q_gen_3403, q_gen_3402) -> q_gen_3415
<cons>(q_gen_3408, q_gen_3413) -> q_gen_3422
<cons>(q_gen_3403, q_gen_3415) -> q_gen_3424
<cons>(q_gen_3403, q_gen_3424) -> q_gen_3424
<cons>(q_gen_3408, q_gen_3422) -> q_gen_3424
<z>() -> q_gen_3427
<cons>(q_gen_3403, q_gen_3413) -> q_gen_3433
<cons>(q_gen_3403, q_gen_3433) -> q_gen_3433
<cons>(q_gen_3408, q_gen_3415) -> q_gen_3433
<s>(q_gen_3427) -> q_gen_3436
<cons>(q_gen_3403, q_gen_3422) -> q_gen_3452
<cons>(q_gen_3403, q_gen_3452) -> q_gen_3452
<cons>(q_gen_3408, q_gen_3433) -> q_gen_3452
<cons>(q_gen_3408, q_gen_3452) -> q_gen_3452
<s>(q_gen_3436) -> q_gen_3476
<b, z>() -> q_gen_3405
<a, z>() -> q_gen_3411
<b, s>(q_gen_3427) -> q_gen_3426
<a, s>(q_gen_3427) -> q_gen_3435
<a, s>(q_gen_3436) -> q_gen_3435
<b, s>(q_gen_3436) -> q_gen_3435
<b, s>(q_gen_3476) -> q_gen_3475
<a, cons, s>(q_gen_3405, q_gen_3415) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3402) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3413) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3422) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3424) -> q_gen_3400
<a, cons, s>(q_gen_3426, q_gen_3433) -> q_gen_3400
<a, cons, s>(q_gen_3435, q_gen_3433) -> q_gen_3400
<a, cons, s>(q_gen_3435, q_gen_3452) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3402) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3413) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3422) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3424) -> q_gen_3400
<a, nil, z>() -> q_gen_3400
<b, cons, s>(q_gen_3405, q_gen_3402) -> q_gen_3400
<b, cons, s>(q_gen_3405, q_gen_3415) -> q_gen_3400
<b, cons, s>(q_gen_3405, q_gen_3424) -> q_gen_3400
<b, cons, s>(q_gen_3411, q_gen_3413) -> q_gen_3400
<b, cons, s>(q_gen_3411, q_gen_3433) -> q_gen_3400
<b, cons, s>(q_gen_3426, q_gen_3413) -> q_gen_3400
<b, cons, s>(q_gen_3426, q_gen_3433) -> q_gen_3400
<b, cons, s>(q_gen_3426, q_gen_3452) -> q_gen_3400
<b, cons, s>(q_gen_3435, q_gen_3422) -> q_gen_3400
<b, cons, s>(q_gen_3435, q_gen_3452) -> q_gen_3400
<b, cons, s>(q_gen_3475, q_gen_3424) -> q_gen_3400
<b, cons, s>(q_gen_3475, q_gen_3452) -> q_gen_3400
<b, cons, z>(q_gen_3403, q_gen_3402) -> q_gen_3400
<b, cons, z>(q_gen_3403, q_gen_3415) -> q_gen_3400
<b, cons, z>(q_gen_3403, q_gen_3424) -> q_gen_3400
<b, nil, z>() -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3415) -> q_gen_3409
<a, cons, s>(q_gen_3411, q_gen_3433) -> q_gen_3409
<a, cons, s>(q_gen_3426, q_gen_3402) -> q_gen_3409
<a, cons, s>(q_gen_3426, q_gen_3413) -> q_gen_3409
<a, cons, s>(q_gen_3435, q_gen_3413) -> q_gen_3409
<a, cons, s>(q_gen_3435, q_gen_3422) -> q_gen_3409
<a, cons, s>(q_gen_3435, q_gen_3424) -> q_gen_3409
<a, cons, s>(q_gen_3475, q_gen_3422) -> q_gen_3409
<a, cons, s>(q_gen_3475, q_gen_3424) -> q_gen_3409
<a, cons, z>(q_gen_3403, q_gen_3402) -> q_gen_3409
<a, cons, z>(q_gen_3408, q_gen_3415) -> q_gen_3409
<a, cons, z>(q_gen_3408, q_gen_3433) -> q_gen_3409
<a, cons, z>(q_gen_3408, q_gen_3452) -> q_gen_3409
<b, cons, s>(q_gen_3405, q_gen_3413) -> q_gen_3409
<b, cons, s>(q_gen_3405, q_gen_3433) -> q_gen_3409
<b, cons, s>(q_gen_3405, q_gen_3452) -> q_gen_3409
<b, cons, s>(q_gen_3411, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3411, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3422) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3424) -> q_gen_3409
<b, cons, s>(q_gen_3435, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3435, q_gen_3413) -> q_gen_3409
<b, cons, s>(q_gen_3435, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3435, q_gen_3424) -> q_gen_3409
<b, cons, s>(q_gen_3435, q_gen_3433) -> q_gen_3409
<b, cons, s>(q_gen_3475, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3475, q_gen_3413) -> q_gen_3409
<b, cons, s>(q_gen_3475, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3475, q_gen_3422) -> q_gen_3409
<b, cons, z>(q_gen_3403, q_gen_3433) -> q_gen_3409
}

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

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 83
(count([x, l1, _nn]) /\ count([x, cons(x, l1), _mn])) -> eq_nat([_mn, s(_nn)]) -> 87
(count([x, t1, _gn])) -> count([x, cons(x, t1), s(_gn)]) -> 85
(count([x, t1, _hn]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _hn]) -> 88
}
Sat witness: Found: ((count([x, t1, _hn]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _hn]), {
_hn -> s(z)  ;  h1 -> a  ;  t1 -> cons(b, cons(a, cons(a, nil)))  ;  x -> b
})

-------------------------------------------
Step 86, which took 2.689147 s (model generation: 2.648128,  model checking: 0.041019):

Model:
|_
{
count -> 
{{{
Q={q_gen_3400, q_gen_3402, q_gen_3403, q_gen_3405, q_gen_3408, q_gen_3409, q_gen_3411, q_gen_3413, q_gen_3415, q_gen_3422, q_gen_3424, q_gen_3426, q_gen_3427, q_gen_3433, q_gen_3435, q_gen_3436, q_gen_3446, q_gen_3470, q_gen_3476},
Q_f={q_gen_3400},
Delta=
{
<nil>() -> q_gen_3402
<a>() -> q_gen_3403
<b>() -> q_gen_3408
<cons>(q_gen_3408, q_gen_3402) -> q_gen_3413
<cons>(q_gen_3403, q_gen_3402) -> q_gen_3415
<cons>(q_gen_3408, q_gen_3413) -> q_gen_3422
<cons>(q_gen_3408, q_gen_3424) -> q_gen_3422
<cons>(q_gen_3403, q_gen_3415) -> q_gen_3424
<cons>(q_gen_3403, q_gen_3424) -> q_gen_3424
<cons>(q_gen_3408, q_gen_3422) -> q_gen_3424
<z>() -> q_gen_3427
<cons>(q_gen_3403, q_gen_3413) -> q_gen_3433
<cons>(q_gen_3403, q_gen_3422) -> q_gen_3433
<cons>(q_gen_3403, q_gen_3433) -> q_gen_3433
<cons>(q_gen_3408, q_gen_3433) -> q_gen_3433
<cons>(q_gen_3408, q_gen_3446) -> q_gen_3433
<s>(q_gen_3427) -> q_gen_3436
<cons>(q_gen_3403, q_gen_3446) -> q_gen_3446
<cons>(q_gen_3408, q_gen_3415) -> q_gen_3446
<s>(q_gen_3436) -> q_gen_3476
<b, z>() -> q_gen_3405
<a, z>() -> q_gen_3411
<b, s>(q_gen_3427) -> q_gen_3426
<a, s>(q_gen_3427) -> q_gen_3435
<b, s>(q_gen_3436) -> q_gen_3435
<a, s>(q_gen_3436) -> q_gen_3470
<b, s>(q_gen_3476) -> q_gen_3470
<a, cons, s>(q_gen_3405, q_gen_3415) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3402) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3413) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3422) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3424) -> q_gen_3400
<a, cons, s>(q_gen_3435, q_gen_3433) -> q_gen_3400
<a, cons, s>(q_gen_3470, q_gen_3433) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3402) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3413) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3422) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3424) -> q_gen_3400
<a, nil, z>() -> q_gen_3400
<b, cons, s>(q_gen_3405, q_gen_3402) -> q_gen_3400
<b, cons, s>(q_gen_3405, q_gen_3415) -> q_gen_3400
<b, cons, s>(q_gen_3405, q_gen_3424) -> q_gen_3400
<b, cons, s>(q_gen_3411, q_gen_3413) -> q_gen_3400
<b, cons, s>(q_gen_3411, q_gen_3422) -> q_gen_3400
<b, cons, s>(q_gen_3411, q_gen_3433) -> q_gen_3400
<b, cons, s>(q_gen_3411, q_gen_3446) -> q_gen_3400
<b, cons, s>(q_gen_3426, q_gen_3413) -> q_gen_3400
<b, cons, s>(q_gen_3426, q_gen_3433) -> q_gen_3400
<b, cons, s>(q_gen_3426, q_gen_3446) -> q_gen_3400
<b, cons, s>(q_gen_3435, q_gen_3422) -> q_gen_3400
<b, cons, s>(q_gen_3435, q_gen_3433) -> q_gen_3400
<b, cons, s>(q_gen_3470, q_gen_3424) -> q_gen_3400
<b, cons, s>(q_gen_3470, q_gen_3433) -> q_gen_3400
<b, cons, z>(q_gen_3403, q_gen_3402) -> q_gen_3400
<b, cons, z>(q_gen_3403, q_gen_3415) -> q_gen_3400
<b, cons, z>(q_gen_3403, q_gen_3424) -> q_gen_3400
<b, nil, z>() -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3415) -> q_gen_3409
<a, cons, s>(q_gen_3411, q_gen_3446) -> q_gen_3409
<a, cons, s>(q_gen_3426, q_gen_3402) -> q_gen_3409
<a, cons, s>(q_gen_3426, q_gen_3413) -> q_gen_3409
<a, cons, s>(q_gen_3426, q_gen_3446) -> q_gen_3409
<a, cons, s>(q_gen_3435, q_gen_3413) -> q_gen_3409
<a, cons, s>(q_gen_3435, q_gen_3422) -> q_gen_3409
<a, cons, s>(q_gen_3435, q_gen_3424) -> q_gen_3409
<a, cons, s>(q_gen_3435, q_gen_3446) -> q_gen_3409
<a, cons, s>(q_gen_3470, q_gen_3413) -> q_gen_3409
<a, cons, s>(q_gen_3470, q_gen_3422) -> q_gen_3409
<a, cons, s>(q_gen_3470, q_gen_3424) -> q_gen_3409
<a, cons, z>(q_gen_3403, q_gen_3402) -> q_gen_3409
<a, cons, z>(q_gen_3408, q_gen_3415) -> q_gen_3409
<a, cons, z>(q_gen_3408, q_gen_3433) -> q_gen_3409
<a, cons, z>(q_gen_3408, q_gen_3446) -> q_gen_3409
<b, cons, s>(q_gen_3405, q_gen_3413) -> q_gen_3409
<b, cons, s>(q_gen_3405, q_gen_3433) -> q_gen_3409
<b, cons, s>(q_gen_3405, q_gen_3446) -> q_gen_3409
<b, cons, s>(q_gen_3411, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3411, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3422) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3424) -> q_gen_3409
<b, cons, s>(q_gen_3435, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3435, q_gen_3413) -> q_gen_3409
<b, cons, s>(q_gen_3435, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3435, q_gen_3424) -> q_gen_3409
<b, cons, s>(q_gen_3435, q_gen_3446) -> q_gen_3409
<b, cons, s>(q_gen_3470, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3470, q_gen_3413) -> q_gen_3409
<b, cons, s>(q_gen_3470, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3470, q_gen_3422) -> q_gen_3409
<b, cons, s>(q_gen_3470, q_gen_3446) -> q_gen_3409
<b, cons, z>(q_gen_3403, q_gen_3433) -> q_gen_3409
}

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

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 84
(count([x, l1, _nn]) /\ count([x, cons(x, l1), _mn])) -> eq_nat([_mn, s(_nn)]) -> 87
(count([x, t1, _gn])) -> count([x, cons(x, t1), s(_gn)]) -> 88
(count([x, t1, _hn]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _hn]) -> 88
}
Sat witness: Found: ((count([x, t1, _gn])) -> count([x, cons(x, t1), s(_gn)]), {
_gn -> s(z)  ;  t1 -> cons(b, cons(a, cons(a, nil)))  ;  x -> b
})

-------------------------------------------
Step 87, which took 2.658599 s (model generation: 2.638094,  model checking: 0.020505):

Model:
|_
{
count -> 
{{{
Q={q_gen_3400, q_gen_3402, q_gen_3403, q_gen_3405, q_gen_3408, q_gen_3409, q_gen_3411, q_gen_3413, q_gen_3415, q_gen_3422, q_gen_3426, q_gen_3427, q_gen_3430, q_gen_3433, q_gen_3435, q_gen_3436, q_gen_3455, q_gen_3475, q_gen_3476},
Q_f={q_gen_3400},
Delta=
{
<cons>(q_gen_3403, q_gen_3415) -> q_gen_3402
<cons>(q_gen_3403, q_gen_3430) -> q_gen_3402
<nil>() -> q_gen_3402
<a>() -> q_gen_3403
<b>() -> q_gen_3408
<cons>(q_gen_3403, q_gen_3455) -> q_gen_3413
<cons>(q_gen_3408, q_gen_3402) -> q_gen_3413
<cons>(q_gen_3403, q_gen_3402) -> q_gen_3415
<cons>(q_gen_3408, q_gen_3430) -> q_gen_3415
<cons>(q_gen_3408, q_gen_3455) -> q_gen_3415
<cons>(q_gen_3408, q_gen_3413) -> q_gen_3422
<z>() -> q_gen_3427
<cons>(q_gen_3408, q_gen_3422) -> q_gen_3430
<cons>(q_gen_3408, q_gen_3433) -> q_gen_3430
<cons>(q_gen_3403, q_gen_3413) -> q_gen_3433
<cons>(q_gen_3403, q_gen_3422) -> q_gen_3433
<cons>(q_gen_3408, q_gen_3415) -> q_gen_3433
<s>(q_gen_3427) -> q_gen_3436
<cons>(q_gen_3403, q_gen_3433) -> q_gen_3455
<s>(q_gen_3436) -> q_gen_3476
<a, s>(q_gen_3427) -> q_gen_3405
<b, z>() -> q_gen_3405
<a, z>() -> q_gen_3411
<b, s>(q_gen_3427) -> q_gen_3426
<a, s>(q_gen_3436) -> q_gen_3435
<b, s>(q_gen_3436) -> q_gen_3435
<b, s>(q_gen_3476) -> q_gen_3475
<a, cons, s>(q_gen_3405, q_gen_3415) -> q_gen_3400
<a, cons, s>(q_gen_3405, q_gen_3433) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3402) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3413) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3422) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3430) -> q_gen_3400
<a, cons, s>(q_gen_3435, q_gen_3430) -> q_gen_3400
<a, cons, s>(q_gen_3435, q_gen_3455) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3402) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3413) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3422) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3430) -> q_gen_3400
<a, nil, z>() -> q_gen_3400
<b, cons, s>(q_gen_3405, q_gen_3402) -> q_gen_3400
<b, cons, s>(q_gen_3405, q_gen_3415) -> q_gen_3400
<b, cons, s>(q_gen_3405, q_gen_3422) -> q_gen_3400
<b, cons, s>(q_gen_3405, q_gen_3455) -> q_gen_3400
<b, cons, s>(q_gen_3411, q_gen_3413) -> q_gen_3400
<b, cons, s>(q_gen_3411, q_gen_3433) -> q_gen_3400
<b, cons, s>(q_gen_3411, q_gen_3455) -> q_gen_3400
<b, cons, s>(q_gen_3426, q_gen_3413) -> q_gen_3400
<b, cons, s>(q_gen_3426, q_gen_3433) -> q_gen_3400
<b, cons, s>(q_gen_3426, q_gen_3455) -> q_gen_3400
<b, cons, s>(q_gen_3435, q_gen_3422) -> q_gen_3400
<b, cons, s>(q_gen_3435, q_gen_3430) -> q_gen_3400
<b, cons, s>(q_gen_3435, q_gen_3433) -> q_gen_3400
<b, cons, s>(q_gen_3475, q_gen_3430) -> q_gen_3400
<b, cons, s>(q_gen_3475, q_gen_3433) -> q_gen_3400
<b, cons, z>(q_gen_3403, q_gen_3402) -> q_gen_3400
<b, cons, z>(q_gen_3403, q_gen_3415) -> q_gen_3400
<b, nil, z>() -> q_gen_3400
<a, cons, s>(q_gen_3405, q_gen_3413) -> q_gen_3409
<a, cons, s>(q_gen_3405, q_gen_3422) -> q_gen_3409
<a, cons, s>(q_gen_3405, q_gen_3430) -> q_gen_3409
<a, cons, s>(q_gen_3405, q_gen_3455) -> q_gen_3409
<a, cons, s>(q_gen_3411, q_gen_3415) -> q_gen_3409
<a, cons, s>(q_gen_3411, q_gen_3433) -> q_gen_3409
<a, cons, s>(q_gen_3411, q_gen_3455) -> q_gen_3409
<a, cons, s>(q_gen_3426, q_gen_3402) -> q_gen_3409
<a, cons, s>(q_gen_3426, q_gen_3413) -> q_gen_3409
<a, cons, s>(q_gen_3435, q_gen_3402) -> q_gen_3409
<a, cons, s>(q_gen_3435, q_gen_3413) -> q_gen_3409
<a, cons, s>(q_gen_3435, q_gen_3422) -> q_gen_3409
<a, cons, s>(q_gen_3435, q_gen_3433) -> q_gen_3409
<a, cons, s>(q_gen_3475, q_gen_3422) -> q_gen_3409
<a, cons, s>(q_gen_3475, q_gen_3430) -> q_gen_3409
<a, cons, z>(q_gen_3403, q_gen_3402) -> q_gen_3409
<a, cons, z>(q_gen_3408, q_gen_3415) -> q_gen_3409
<a, cons, z>(q_gen_3408, q_gen_3433) -> q_gen_3409
<b, cons, s>(q_gen_3405, q_gen_3413) -> q_gen_3409
<b, cons, s>(q_gen_3405, q_gen_3430) -> q_gen_3409
<b, cons, s>(q_gen_3405, q_gen_3433) -> q_gen_3409
<b, cons, s>(q_gen_3411, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3411, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3422) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3430) -> q_gen_3409
<b, cons, s>(q_gen_3435, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3435, q_gen_3413) -> q_gen_3409
<b, cons, s>(q_gen_3435, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3435, q_gen_3455) -> q_gen_3409
<b, cons, s>(q_gen_3475, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3475, q_gen_3413) -> q_gen_3409
<b, cons, s>(q_gen_3475, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3475, q_gen_3422) -> q_gen_3409
<b, cons, z>(q_gen_3403, q_gen_3433) -> q_gen_3409
<b, cons, z>(q_gen_3403, q_gen_3455) -> q_gen_3409
}

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

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 85
(count([x, l1, _nn]) /\ count([x, cons(x, l1), _mn])) -> eq_nat([_mn, s(_nn)]) -> 90
(count([x, t1, _gn])) -> count([x, cons(x, t1), s(_gn)]) -> 88
(count([x, t1, _hn]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _hn]) -> 88
}
Sat witness: Found: ((count([x, l1, _nn]) /\ count([x, cons(x, l1), _mn])) -> eq_nat([_mn, s(_nn)]), {
_mn -> s(s(s(z)))  ;  _nn -> z  ;  l1 -> cons(b, cons(b, cons(b, nil)))  ;  x -> a
})

-------------------------------------------
Step 88, which took 2.151076 s (model generation: 2.131633,  model checking: 0.019443):

Model:
|_
{
count -> 
{{{
Q={q_gen_3400, q_gen_3402, q_gen_3403, q_gen_3405, q_gen_3408, q_gen_3409, q_gen_3411, q_gen_3413, q_gen_3415, q_gen_3422, q_gen_3424, q_gen_3426, q_gen_3427, q_gen_3433, q_gen_3435, q_gen_3436, q_gen_3452, q_gen_3475, q_gen_3476},
Q_f={q_gen_3400},
Delta=
{
<nil>() -> q_gen_3402
<a>() -> q_gen_3403
<b>() -> q_gen_3408
<cons>(q_gen_3403, q_gen_3424) -> q_gen_3413
<cons>(q_gen_3408, q_gen_3402) -> q_gen_3413
<cons>(q_gen_3403, q_gen_3402) -> q_gen_3415
<cons>(q_gen_3408, q_gen_3413) -> q_gen_3422
<cons>(q_gen_3403, q_gen_3415) -> q_gen_3424
<cons>(q_gen_3408, q_gen_3422) -> q_gen_3424
<z>() -> q_gen_3427
<cons>(q_gen_3403, q_gen_3413) -> q_gen_3433
<cons>(q_gen_3403, q_gen_3433) -> q_gen_3433
<cons>(q_gen_3408, q_gen_3415) -> q_gen_3433
<cons>(q_gen_3408, q_gen_3424) -> q_gen_3433
<s>(q_gen_3427) -> q_gen_3436
<cons>(q_gen_3403, q_gen_3422) -> q_gen_3452
<cons>(q_gen_3403, q_gen_3452) -> q_gen_3452
<cons>(q_gen_3408, q_gen_3433) -> q_gen_3452
<cons>(q_gen_3408, q_gen_3452) -> q_gen_3452
<s>(q_gen_3436) -> q_gen_3476
<b, z>() -> q_gen_3405
<a, z>() -> q_gen_3411
<b, s>(q_gen_3427) -> q_gen_3426
<a, s>(q_gen_3427) -> q_gen_3435
<a, s>(q_gen_3436) -> q_gen_3435
<b, s>(q_gen_3436) -> q_gen_3435
<b, s>(q_gen_3476) -> q_gen_3475
<a, cons, s>(q_gen_3405, q_gen_3415) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3402) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3413) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3422) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3424) -> q_gen_3400
<a, cons, s>(q_gen_3426, q_gen_3433) -> q_gen_3400
<a, cons, s>(q_gen_3435, q_gen_3433) -> q_gen_3400
<a, cons, s>(q_gen_3435, q_gen_3452) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3402) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3413) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3422) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3424) -> q_gen_3400
<a, nil, z>() -> q_gen_3400
<b, cons, s>(q_gen_3405, q_gen_3402) -> q_gen_3400
<b, cons, s>(q_gen_3405, q_gen_3415) -> q_gen_3400
<b, cons, s>(q_gen_3405, q_gen_3424) -> q_gen_3400
<b, cons, s>(q_gen_3411, q_gen_3413) -> q_gen_3400
<b, cons, s>(q_gen_3411, q_gen_3433) -> q_gen_3400
<b, cons, s>(q_gen_3426, q_gen_3413) -> q_gen_3400
<b, cons, s>(q_gen_3426, q_gen_3433) -> q_gen_3400
<b, cons, s>(q_gen_3435, q_gen_3422) -> q_gen_3400
<b, cons, s>(q_gen_3435, q_gen_3452) -> q_gen_3400
<b, cons, s>(q_gen_3475, q_gen_3424) -> q_gen_3400
<b, cons, s>(q_gen_3475, q_gen_3452) -> q_gen_3400
<b, cons, z>(q_gen_3403, q_gen_3402) -> q_gen_3400
<b, cons, z>(q_gen_3403, q_gen_3415) -> q_gen_3400
<b, cons, z>(q_gen_3403, q_gen_3424) -> q_gen_3400
<b, nil, z>() -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3415) -> q_gen_3409
<a, cons, s>(q_gen_3411, q_gen_3433) -> q_gen_3409
<a, cons, s>(q_gen_3426, q_gen_3402) -> q_gen_3409
<a, cons, s>(q_gen_3426, q_gen_3413) -> q_gen_3409
<a, cons, s>(q_gen_3435, q_gen_3413) -> q_gen_3409
<a, cons, s>(q_gen_3435, q_gen_3422) -> q_gen_3409
<a, cons, s>(q_gen_3435, q_gen_3424) -> q_gen_3409
<a, cons, s>(q_gen_3475, q_gen_3422) -> q_gen_3409
<a, cons, s>(q_gen_3475, q_gen_3424) -> q_gen_3409
<a, cons, z>(q_gen_3403, q_gen_3402) -> q_gen_3409
<a, cons, z>(q_gen_3408, q_gen_3415) -> q_gen_3409
<a, cons, z>(q_gen_3408, q_gen_3433) -> q_gen_3409
<a, cons, z>(q_gen_3408, q_gen_3452) -> q_gen_3409
<b, cons, s>(q_gen_3405, q_gen_3413) -> q_gen_3409
<b, cons, s>(q_gen_3405, q_gen_3433) -> q_gen_3409
<b, cons, s>(q_gen_3405, q_gen_3452) -> q_gen_3409
<b, cons, s>(q_gen_3411, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3411, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3422) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3424) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3452) -> q_gen_3409
<b, cons, s>(q_gen_3435, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3435, q_gen_3413) -> q_gen_3409
<b, cons, s>(q_gen_3435, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3435, q_gen_3424) -> q_gen_3409
<b, cons, s>(q_gen_3435, q_gen_3433) -> q_gen_3409
<b, cons, s>(q_gen_3475, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3475, q_gen_3413) -> q_gen_3409
<b, cons, s>(q_gen_3475, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3475, q_gen_3422) -> q_gen_3409
<b, cons, z>(q_gen_3403, q_gen_3433) -> q_gen_3409
}

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

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 86
(count([x, l1, _nn]) /\ count([x, cons(x, l1), _mn])) -> eq_nat([_mn, s(_nn)]) -> 90
(count([x, t1, _gn])) -> count([x, cons(x, t1), s(_gn)]) -> 88
(count([x, t1, _hn]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _hn]) -> 91
}
Sat witness: Found: ((count([x, t1, _hn]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _hn]), {
_hn -> z  ;  h1 -> b  ;  t1 -> cons(b, cons(a, cons(a, nil)))  ;  x -> a
})

-------------------------------------------
Step 89, which took 2.880795 s (model generation: 2.853816,  model checking: 0.026979):

Model:
|_
{
count -> 
{{{
Q={q_gen_3400, q_gen_3402, q_gen_3403, q_gen_3405, q_gen_3408, q_gen_3409, q_gen_3411, q_gen_3413, q_gen_3415, q_gen_3422, q_gen_3426, q_gen_3427, q_gen_3430, q_gen_3433, q_gen_3435, q_gen_3436, q_gen_3446, q_gen_3475, q_gen_3476},
Q_f={q_gen_3400},
Delta=
{
<cons>(q_gen_3403, q_gen_3415) -> q_gen_3402
<cons>(q_gen_3408, q_gen_3430) -> q_gen_3402
<nil>() -> q_gen_3402
<a>() -> q_gen_3403
<b>() -> q_gen_3408
<cons>(q_gen_3408, q_gen_3402) -> q_gen_3413
<cons>(q_gen_3408, q_gen_3433) -> q_gen_3413
<cons>(q_gen_3403, q_gen_3402) -> q_gen_3415
<cons>(q_gen_3408, q_gen_3413) -> q_gen_3422
<z>() -> q_gen_3427
<cons>(q_gen_3403, q_gen_3430) -> q_gen_3430
<cons>(q_gen_3403, q_gen_3446) -> q_gen_3430
<cons>(q_gen_3408, q_gen_3422) -> q_gen_3430
<cons>(q_gen_3403, q_gen_3413) -> q_gen_3433
<cons>(q_gen_3403, q_gen_3433) -> q_gen_3433
<cons>(q_gen_3408, q_gen_3446) -> q_gen_3433
<s>(q_gen_3427) -> q_gen_3436
<cons>(q_gen_3403, q_gen_3422) -> q_gen_3446
<cons>(q_gen_3408, q_gen_3415) -> q_gen_3446
<s>(q_gen_3436) -> q_gen_3476
<a, s>(q_gen_3427) -> q_gen_3405
<b, z>() -> q_gen_3405
<a, z>() -> q_gen_3411
<b, s>(q_gen_3427) -> q_gen_3426
<a, s>(q_gen_3436) -> q_gen_3435
<b, s>(q_gen_3436) -> q_gen_3435
<b, s>(q_gen_3476) -> q_gen_3475
<a, cons, s>(q_gen_3405, q_gen_3415) -> q_gen_3400
<a, cons, s>(q_gen_3405, q_gen_3433) -> q_gen_3400
<a, cons, s>(q_gen_3405, q_gen_3446) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3402) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3413) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3422) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3430) -> q_gen_3400
<a, cons, s>(q_gen_3435, q_gen_3433) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3402) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3413) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3422) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3430) -> q_gen_3400
<a, nil, z>() -> q_gen_3400
<b, cons, s>(q_gen_3405, q_gen_3402) -> q_gen_3400
<b, cons, s>(q_gen_3405, q_gen_3415) -> q_gen_3400
<b, cons, s>(q_gen_3405, q_gen_3422) -> q_gen_3400
<b, cons, s>(q_gen_3405, q_gen_3430) -> q_gen_3400
<b, cons, s>(q_gen_3411, q_gen_3413) -> q_gen_3400
<b, cons, s>(q_gen_3411, q_gen_3430) -> q_gen_3400
<b, cons, s>(q_gen_3411, q_gen_3433) -> q_gen_3400
<b, cons, s>(q_gen_3411, q_gen_3446) -> q_gen_3400
<b, cons, s>(q_gen_3426, q_gen_3413) -> q_gen_3400
<b, cons, s>(q_gen_3426, q_gen_3430) -> q_gen_3400
<b, cons, s>(q_gen_3426, q_gen_3433) -> q_gen_3400
<b, cons, s>(q_gen_3426, q_gen_3446) -> q_gen_3400
<b, cons, s>(q_gen_3435, q_gen_3422) -> q_gen_3400
<b, cons, s>(q_gen_3435, q_gen_3433) -> q_gen_3400
<b, cons, s>(q_gen_3435, q_gen_3446) -> q_gen_3400
<b, cons, s>(q_gen_3475, q_gen_3430) -> q_gen_3400
<b, cons, s>(q_gen_3475, q_gen_3433) -> q_gen_3400
<b, cons, z>(q_gen_3403, q_gen_3402) -> q_gen_3400
<b, cons, z>(q_gen_3403, q_gen_3415) -> q_gen_3400
<b, nil, z>() -> q_gen_3400
<a, cons, s>(q_gen_3405, q_gen_3413) -> q_gen_3409
<a, cons, s>(q_gen_3405, q_gen_3422) -> q_gen_3409
<a, cons, s>(q_gen_3405, q_gen_3430) -> q_gen_3409
<a, cons, s>(q_gen_3411, q_gen_3415) -> q_gen_3409
<a, cons, s>(q_gen_3411, q_gen_3446) -> q_gen_3409
<a, cons, s>(q_gen_3426, q_gen_3402) -> q_gen_3409
<a, cons, s>(q_gen_3426, q_gen_3413) -> q_gen_3409
<a, cons, s>(q_gen_3426, q_gen_3430) -> q_gen_3409
<a, cons, s>(q_gen_3435, q_gen_3413) -> q_gen_3409
<a, cons, s>(q_gen_3435, q_gen_3422) -> q_gen_3409
<a, cons, s>(q_gen_3435, q_gen_3430) -> q_gen_3409
<a, cons, s>(q_gen_3475, q_gen_3422) -> q_gen_3409
<a, cons, s>(q_gen_3475, q_gen_3430) -> q_gen_3409
<a, cons, z>(q_gen_3403, q_gen_3402) -> q_gen_3409
<a, cons, z>(q_gen_3408, q_gen_3415) -> q_gen_3409
<a, cons, z>(q_gen_3408, q_gen_3433) -> q_gen_3409
<a, cons, z>(q_gen_3408, q_gen_3446) -> q_gen_3409
<b, cons, s>(q_gen_3405, q_gen_3413) -> q_gen_3409
<b, cons, s>(q_gen_3405, q_gen_3433) -> q_gen_3409
<b, cons, s>(q_gen_3405, q_gen_3446) -> q_gen_3409
<b, cons, s>(q_gen_3411, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3411, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3422) -> q_gen_3409
<b, cons, s>(q_gen_3435, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3435, q_gen_3413) -> q_gen_3409
<b, cons, s>(q_gen_3435, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3435, q_gen_3430) -> q_gen_3409
<b, cons, s>(q_gen_3475, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3475, q_gen_3413) -> q_gen_3409
<b, cons, s>(q_gen_3475, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3475, q_gen_3422) -> q_gen_3409
<b, cons, z>(q_gen_3403, q_gen_3433) -> q_gen_3409
}

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

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 87
(count([x, l1, _nn]) /\ count([x, cons(x, l1), _mn])) -> eq_nat([_mn, s(_nn)]) -> 90
(count([x, t1, _gn])) -> count([x, cons(x, t1), s(_gn)]) -> 91
(count([x, t1, _hn]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _hn]) -> 91
}
Sat witness: Found: ((count([x, t1, _gn])) -> count([x, cons(x, t1), s(_gn)]), {
_gn -> s(s(z))  ;  t1 -> cons(a, cons(b, cons(b, cons(b, nil))))  ;  x -> b
})

-------------------------------------------
Step 90, which took 3.282752 s (model generation: 3.233266,  model checking: 0.049486):

Model:
|_
{
count -> 
{{{
Q={q_gen_3400, q_gen_3402, q_gen_3403, q_gen_3405, q_gen_3408, q_gen_3409, q_gen_3411, q_gen_3413, q_gen_3415, q_gen_3422, q_gen_3426, q_gen_3427, q_gen_3430, q_gen_3433, q_gen_3435, q_gen_3436, q_gen_3452, q_gen_3475, q_gen_3476},
Q_f={q_gen_3400},
Delta=
{
<cons>(q_gen_3403, q_gen_3415) -> q_gen_3402
<cons>(q_gen_3408, q_gen_3430) -> q_gen_3402
<nil>() -> q_gen_3402
<a>() -> q_gen_3403
<b>() -> q_gen_3408
<cons>(q_gen_3408, q_gen_3402) -> q_gen_3413
<cons>(q_gen_3403, q_gen_3402) -> q_gen_3415
<cons>(q_gen_3408, q_gen_3413) -> q_gen_3422
<z>() -> q_gen_3427
<cons>(q_gen_3403, q_gen_3433) -> q_gen_3430
<cons>(q_gen_3408, q_gen_3422) -> q_gen_3430
<cons>(q_gen_3403, q_gen_3413) -> q_gen_3433
<cons>(q_gen_3403, q_gen_3422) -> q_gen_3433
<cons>(q_gen_3403, q_gen_3452) -> q_gen_3433
<cons>(q_gen_3408, q_gen_3415) -> q_gen_3433
<s>(q_gen_3427) -> q_gen_3436
<cons>(q_gen_3403, q_gen_3430) -> q_gen_3452
<cons>(q_gen_3408, q_gen_3433) -> q_gen_3452
<cons>(q_gen_3408, q_gen_3452) -> q_gen_3452
<s>(q_gen_3436) -> q_gen_3476
<a, s>(q_gen_3427) -> q_gen_3405
<b, z>() -> q_gen_3405
<a, z>() -> q_gen_3411
<b, s>(q_gen_3427) -> q_gen_3426
<a, s>(q_gen_3436) -> q_gen_3435
<b, s>(q_gen_3436) -> q_gen_3435
<b, s>(q_gen_3476) -> q_gen_3475
<a, cons, s>(q_gen_3405, q_gen_3415) -> q_gen_3400
<a, cons, s>(q_gen_3405, q_gen_3433) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3402) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3413) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3422) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3430) -> q_gen_3400
<a, cons, s>(q_gen_3426, q_gen_3452) -> q_gen_3400
<a, cons, s>(q_gen_3435, q_gen_3452) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3402) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3413) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3422) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3430) -> q_gen_3400
<a, nil, z>() -> q_gen_3400
<b, cons, s>(q_gen_3405, q_gen_3402) -> q_gen_3400
<b, cons, s>(q_gen_3405, q_gen_3415) -> q_gen_3400
<b, cons, s>(q_gen_3405, q_gen_3422) -> q_gen_3400
<b, cons, s>(q_gen_3405, q_gen_3430) -> q_gen_3400
<b, cons, s>(q_gen_3411, q_gen_3413) -> q_gen_3400
<b, cons, s>(q_gen_3411, q_gen_3430) -> q_gen_3400
<b, cons, s>(q_gen_3411, q_gen_3433) -> q_gen_3400
<b, cons, s>(q_gen_3426, q_gen_3413) -> q_gen_3400
<b, cons, s>(q_gen_3426, q_gen_3430) -> q_gen_3400
<b, cons, s>(q_gen_3426, q_gen_3433) -> q_gen_3400
<b, cons, s>(q_gen_3435, q_gen_3422) -> q_gen_3400
<b, cons, s>(q_gen_3435, q_gen_3433) -> q_gen_3400
<b, cons, s>(q_gen_3435, q_gen_3452) -> q_gen_3400
<b, cons, s>(q_gen_3475, q_gen_3430) -> q_gen_3400
<b, cons, s>(q_gen_3475, q_gen_3452) -> q_gen_3400
<b, cons, z>(q_gen_3403, q_gen_3402) -> q_gen_3400
<b, cons, z>(q_gen_3403, q_gen_3415) -> q_gen_3400
<b, nil, z>() -> q_gen_3400
<a, cons, s>(q_gen_3405, q_gen_3413) -> q_gen_3409
<a, cons, s>(q_gen_3405, q_gen_3422) -> q_gen_3409
<a, cons, s>(q_gen_3405, q_gen_3430) -> q_gen_3409
<a, cons, s>(q_gen_3405, q_gen_3452) -> q_gen_3409
<a, cons, s>(q_gen_3411, q_gen_3415) -> q_gen_3409
<a, cons, s>(q_gen_3411, q_gen_3433) -> q_gen_3409
<a, cons, s>(q_gen_3426, q_gen_3402) -> q_gen_3409
<a, cons, s>(q_gen_3426, q_gen_3413) -> q_gen_3409
<a, cons, s>(q_gen_3435, q_gen_3413) -> q_gen_3409
<a, cons, s>(q_gen_3435, q_gen_3422) -> q_gen_3409
<a, cons, s>(q_gen_3435, q_gen_3430) -> q_gen_3409
<a, cons, s>(q_gen_3435, q_gen_3433) -> q_gen_3409
<a, cons, s>(q_gen_3475, q_gen_3422) -> q_gen_3409
<a, cons, s>(q_gen_3475, q_gen_3430) -> q_gen_3409
<a, cons, z>(q_gen_3403, q_gen_3402) -> q_gen_3409
<a, cons, z>(q_gen_3408, q_gen_3415) -> q_gen_3409
<a, cons, z>(q_gen_3408, q_gen_3433) -> q_gen_3409
<a, cons, z>(q_gen_3408, q_gen_3452) -> q_gen_3409
<b, cons, s>(q_gen_3405, q_gen_3413) -> q_gen_3409
<b, cons, s>(q_gen_3405, q_gen_3433) -> q_gen_3409
<b, cons, s>(q_gen_3405, q_gen_3452) -> q_gen_3409
<b, cons, s>(q_gen_3411, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3411, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3422) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3452) -> q_gen_3409
<b, cons, s>(q_gen_3435, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3435, q_gen_3413) -> q_gen_3409
<b, cons, s>(q_gen_3435, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3435, q_gen_3430) -> q_gen_3409
<b, cons, s>(q_gen_3475, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3475, q_gen_3413) -> q_gen_3409
<b, cons, s>(q_gen_3475, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3475, q_gen_3422) -> q_gen_3409
<b, cons, z>(q_gen_3403, q_gen_3430) -> q_gen_3409
<b, cons, z>(q_gen_3403, q_gen_3433) -> q_gen_3409
}

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

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 88
(count([x, l1, _nn]) /\ count([x, cons(x, l1), _mn])) -> eq_nat([_mn, s(_nn)]) -> 93
(count([x, t1, _gn])) -> count([x, cons(x, t1), s(_gn)]) -> 91
(count([x, t1, _hn]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _hn]) -> 91
}
Sat witness: Found: ((count([x, l1, _nn]) /\ count([x, cons(x, l1), _mn])) -> eq_nat([_mn, s(_nn)]), {
_mn -> s(z)  ;  _nn -> s(s(s(z)))  ;  l1 -> cons(b, cons(b, cons(b, nil)))  ;  x -> b
})

-------------------------------------------
Step 91, which took 2.256315 s (model generation: 2.201075,  model checking: 0.055240):

Model:
|_
{
count -> 
{{{
Q={q_gen_3400, q_gen_3402, q_gen_3403, q_gen_3405, q_gen_3408, q_gen_3409, q_gen_3411, q_gen_3413, q_gen_3415, q_gen_3422, q_gen_3426, q_gen_3427, q_gen_3430, q_gen_3433, q_gen_3435, q_gen_3436, q_gen_3446, q_gen_3475, q_gen_3476},
Q_f={q_gen_3400},
Delta=
{
<nil>() -> q_gen_3402
<a>() -> q_gen_3403
<b>() -> q_gen_3408
<cons>(q_gen_3403, q_gen_3446) -> q_gen_3413
<cons>(q_gen_3408, q_gen_3402) -> q_gen_3413
<cons>(q_gen_3403, q_gen_3402) -> q_gen_3415
<cons>(q_gen_3403, q_gen_3415) -> q_gen_3415
<cons>(q_gen_3403, q_gen_3430) -> q_gen_3422
<cons>(q_gen_3408, q_gen_3413) -> q_gen_3422
<cons>(q_gen_3408, q_gen_3430) -> q_gen_3422
<cons>(q_gen_3408, q_gen_3446) -> q_gen_3422
<z>() -> q_gen_3427
<cons>(q_gen_3408, q_gen_3422) -> q_gen_3430
<cons>(q_gen_3408, q_gen_3433) -> q_gen_3430
<cons>(q_gen_3403, q_gen_3413) -> q_gen_3433
<cons>(q_gen_3403, q_gen_3422) -> q_gen_3433
<cons>(q_gen_3403, q_gen_3433) -> q_gen_3433
<s>(q_gen_3427) -> q_gen_3436
<cons>(q_gen_3408, q_gen_3415) -> q_gen_3446
<s>(q_gen_3436) -> q_gen_3476
<b, z>() -> q_gen_3405
<a, z>() -> q_gen_3411
<b, s>(q_gen_3427) -> q_gen_3426
<a, s>(q_gen_3427) -> q_gen_3435
<a, s>(q_gen_3436) -> q_gen_3435
<b, s>(q_gen_3436) -> q_gen_3435
<b, s>(q_gen_3476) -> q_gen_3475
<a, cons, s>(q_gen_3405, q_gen_3415) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3402) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3413) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3422) -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3430) -> q_gen_3400
<a, cons, s>(q_gen_3435, q_gen_3433) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3402) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3413) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3422) -> q_gen_3400
<a, cons, z>(q_gen_3408, q_gen_3430) -> q_gen_3400
<a, nil, z>() -> q_gen_3400
<b, cons, s>(q_gen_3405, q_gen_3402) -> q_gen_3400
<b, cons, s>(q_gen_3405, q_gen_3415) -> q_gen_3400
<b, cons, s>(q_gen_3411, q_gen_3413) -> q_gen_3400
<b, cons, s>(q_gen_3411, q_gen_3433) -> q_gen_3400
<b, cons, s>(q_gen_3411, q_gen_3446) -> q_gen_3400
<b, cons, s>(q_gen_3426, q_gen_3413) -> q_gen_3400
<b, cons, s>(q_gen_3426, q_gen_3430) -> q_gen_3400
<b, cons, s>(q_gen_3426, q_gen_3433) -> q_gen_3400
<b, cons, s>(q_gen_3426, q_gen_3446) -> q_gen_3400
<b, cons, s>(q_gen_3435, q_gen_3422) -> q_gen_3400
<b, cons, s>(q_gen_3435, q_gen_3430) -> q_gen_3400
<b, cons, s>(q_gen_3435, q_gen_3433) -> q_gen_3400
<b, cons, s>(q_gen_3475, q_gen_3430) -> q_gen_3400
<b, cons, z>(q_gen_3403, q_gen_3402) -> q_gen_3400
<b, cons, z>(q_gen_3403, q_gen_3415) -> q_gen_3400
<b, nil, z>() -> q_gen_3400
<a, cons, s>(q_gen_3411, q_gen_3415) -> q_gen_3409
<a, cons, s>(q_gen_3411, q_gen_3446) -> q_gen_3409
<a, cons, s>(q_gen_3426, q_gen_3402) -> q_gen_3409
<a, cons, s>(q_gen_3426, q_gen_3413) -> q_gen_3409
<a, cons, s>(q_gen_3426, q_gen_3433) -> q_gen_3409
<a, cons, s>(q_gen_3435, q_gen_3413) -> q_gen_3409
<a, cons, s>(q_gen_3435, q_gen_3422) -> q_gen_3409
<a, cons, s>(q_gen_3435, q_gen_3430) -> q_gen_3409
<a, cons, s>(q_gen_3475, q_gen_3422) -> q_gen_3409
<a, cons, s>(q_gen_3475, q_gen_3430) -> q_gen_3409
<a, cons, z>(q_gen_3403, q_gen_3402) -> q_gen_3409
<a, cons, z>(q_gen_3408, q_gen_3415) -> q_gen_3409
<a, cons, z>(q_gen_3408, q_gen_3433) -> q_gen_3409
<a, cons, z>(q_gen_3408, q_gen_3446) -> q_gen_3409
<b, cons, s>(q_gen_3405, q_gen_3413) -> q_gen_3409
<b, cons, s>(q_gen_3405, q_gen_3430) -> q_gen_3409
<b, cons, s>(q_gen_3405, q_gen_3433) -> q_gen_3409
<b, cons, s>(q_gen_3405, q_gen_3446) -> q_gen_3409
<b, cons, s>(q_gen_3411, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3411, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3426, q_gen_3422) -> q_gen_3409
<b, cons, s>(q_gen_3435, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3435, q_gen_3413) -> q_gen_3409
<b, cons, s>(q_gen_3435, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3435, q_gen_3446) -> q_gen_3409
<b, cons, s>(q_gen_3475, q_gen_3402) -> q_gen_3409
<b, cons, s>(q_gen_3475, q_gen_3413) -> q_gen_3409
<b, cons, s>(q_gen_3475, q_gen_3415) -> q_gen_3409
<b, cons, s>(q_gen_3475, q_gen_3422) -> q_gen_3409
<b, cons, z>(q_gen_3403, q_gen_3433) -> q_gen_3409
}

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

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 89
(count([x, l1, _nn]) /\ count([x, cons(x, l1), _mn])) -> eq_nat([_mn, s(_nn)]) -> 93
(count([x, t1, _gn])) -> count([x, cons(x, t1), s(_gn)]) -> 91
(count([x, t1, _hn]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _hn]) -> 94
}
Sat witness: Found: ((count([x, t1, _hn]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _hn]), {
_hn -> s(s(z))  ;  h1 -> b  ;  t1 -> cons(a, cons(a, cons(a, cons(a, cons(b, cons(a, cons(a, nil)))))))  ;  x -> a
})

Total time: 60.080156
Reason for stopping: DontKnow. Stopped because: timeout