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


Learning problem is:

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

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


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

Clause system for inference is:

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


Solving took 64.432500 seconds.
DontKnow. Stopped because: timeout
Working model:
|_
{
drop -> 
{{{
Q={q_gen_6324, q_gen_6325, q_gen_6326, q_gen_6330, q_gen_6331, q_gen_6332, q_gen_6337, q_gen_6338, q_gen_6339, q_gen_6340, q_gen_6341, q_gen_6346, q_gen_6347, q_gen_6351, q_gen_6352, q_gen_6353, q_gen_6356, q_gen_6357, q_gen_6364, q_gen_6365, q_gen_6369, q_gen_6370, q_gen_6371, q_gen_6376, q_gen_6377, q_gen_6378, q_gen_6381, q_gen_6382, q_gen_6383, q_gen_6384, q_gen_6389, q_gen_6390, q_gen_6391, q_gen_6392, q_gen_6397, q_gen_6398, q_gen_6399, q_gen_6404, q_gen_6405, q_gen_6406, q_gen_6407, q_gen_6412, q_gen_6413, q_gen_6414, q_gen_6415, q_gen_6416, q_gen_6419, q_gen_6420, q_gen_6421, q_gen_6422, q_gen_6423, q_gen_6424, q_gen_6425, q_gen_6426, q_gen_6427, q_gen_6430, q_gen_6431, q_gen_6432, q_gen_6433, q_gen_6434, q_gen_6435, q_gen_6436, q_gen_6438, q_gen_6439, q_gen_6442, q_gen_6443, q_gen_6444, q_gen_6445, q_gen_6446, q_gen_6448, q_gen_6449, q_gen_6454, q_gen_6455, q_gen_6458, q_gen_6459, q_gen_6460, q_gen_6461, q_gen_6462, q_gen_6463, q_gen_6464, q_gen_6466, q_gen_6467, q_gen_6468, q_gen_6469, q_gen_6470, q_gen_6471, q_gen_6474, q_gen_6475, q_gen_6477, q_gen_6495, q_gen_6496, q_gen_6497, q_gen_6500, q_gen_6501, q_gen_6502, q_gen_6503, q_gen_6506, q_gen_6507},
Q_f={},
Delta=
{
<z>() -> q_gen_6326
<b>() -> q_gen_6332
<s>(q_gen_6326) -> q_gen_6341
<a>() -> q_gen_6347
<nil>() -> q_gen_6371
<cons>(q_gen_6332, q_gen_6371) -> q_gen_6422
<s>(q_gen_6341) -> q_gen_6449
<cons>(q_gen_6332, q_gen_6422) -> q_gen_6468
<z, nil>() -> q_gen_6331
<nil, nil>() -> q_gen_6338
<b, b>() -> q_gen_6339
<cons, cons>(q_gen_6353, q_gen_6338) -> q_gen_6352
<a, a>() -> q_gen_6353
<s, nil>(q_gen_6326) -> q_gen_6357
<s, cons>(q_gen_6347, q_gen_6331) -> q_gen_6365
<z, cons>(q_gen_6332, q_gen_6371) -> q_gen_6378
<b, a>() -> q_gen_6384
<a, b>() -> q_gen_6390
<s, cons>(q_gen_6332, q_gen_6331) -> q_gen_6392
<s, cons>(q_gen_6332, q_gen_6399) -> q_gen_6398
<s, nil>(q_gen_6341) -> q_gen_6399
<s, cons>(q_gen_6332, q_gen_6378) -> q_gen_6407
<cons, cons>(q_gen_6339, q_gen_6338) -> q_gen_6413
<cons, nil>(q_gen_6332, q_gen_6371) -> q_gen_6416
<cons, cons>(q_gen_6390, q_gen_6413) -> q_gen_6431
<cons, cons>(q_gen_6390, q_gen_6416) -> q_gen_6434
<z, cons>(q_gen_6332, q_gen_6422) -> q_gen_6439
<cons, cons>(q_gen_6339, q_gen_6416) -> q_gen_6460
<cons, nil>(q_gen_6332, q_gen_6422) -> q_gen_6464
<s, cons>(q_gen_6332, q_gen_6471) -> q_gen_6470
<s, cons>(q_gen_6332, q_gen_6357) -> q_gen_6471
<s, cons>(q_gen_6332, q_gen_6392) -> q_gen_6475
<z, nil, nil>() -> q_gen_6324
<s, nil, nil>(q_gen_6326) -> q_gen_6325
<s, cons, nil>(q_gen_6332, q_gen_6331) -> q_gen_6330
<z, cons, cons>(q_gen_6339, q_gen_6338) -> q_gen_6337
<s, nil, nil>(q_gen_6341) -> q_gen_6340
<s, cons, nil>(q_gen_6347, q_gen_6331) -> q_gen_6346
<z, cons, cons>(q_gen_6353, q_gen_6352) -> q_gen_6351
<s, cons, nil>(q_gen_6332, q_gen_6357) -> q_gen_6356
<s, cons, nil>(q_gen_6332, q_gen_6365) -> q_gen_6364
<s, cons, cons>(q_gen_6339, q_gen_6370) -> q_gen_6369
<z, cons, nil>(q_gen_6332, q_gen_6371) -> q_gen_6370
<s, cons, cons>(q_gen_6339, q_gen_6377) -> q_gen_6376
<s, cons, nil>(q_gen_6332, q_gen_6378) -> q_gen_6377
<s, cons, cons>(q_gen_6353, q_gen_6370) -> q_gen_6381
<s, cons, cons>(q_gen_6384, q_gen_6383) -> q_gen_6382
<s, cons, nil>(q_gen_6347, q_gen_6378) -> q_gen_6383
<s, cons, cons>(q_gen_6390, q_gen_6370) -> q_gen_6389
<s, cons, nil>(q_gen_6332, q_gen_6392) -> q_gen_6391
<s, cons, nil>(q_gen_6332, q_gen_6398) -> q_gen_6397
<s, cons, cons>(q_gen_6384, q_gen_6377) -> q_gen_6404
<s, cons, cons>(q_gen_6384, q_gen_6406) -> q_gen_6405
<s, cons, nil>(q_gen_6332, q_gen_6407) -> q_gen_6406
<z, cons, cons>(q_gen_6384, q_gen_6413) -> q_gen_6412
<s, cons, cons>(q_gen_6353, q_gen_6415) -> q_gen_6414
<z, cons, cons>(q_gen_6339, q_gen_6416) -> q_gen_6415
<s, cons, cons>(q_gen_6384, q_gen_6420) -> q_gen_6419
<s, cons, cons>(q_gen_6390, q_gen_6421) -> q_gen_6420
<z, cons, nil>(q_gen_6332, q_gen_6422) -> q_gen_6421
<s, cons, cons>(q_gen_6339, q_gen_6325) -> q_gen_6423
<s, cons, cons>(q_gen_6384, q_gen_6324) -> q_gen_6424
<s, cons, cons>(q_gen_6353, q_gen_6330) -> q_gen_6425
<z, cons, cons>(q_gen_6339, q_gen_6413) -> q_gen_6426
<s, cons, cons>(q_gen_6384, q_gen_6325) -> q_gen_6427
<z, cons, cons>(q_gen_6339, q_gen_6431) -> q_gen_6430
<s, cons, cons>(q_gen_6339, q_gen_6433) -> q_gen_6432
<z, cons, cons>(q_gen_6339, q_gen_6434) -> q_gen_6433
<s, cons, cons>(q_gen_6339, q_gen_6324) -> q_gen_6435
<z, cons, cons>(q_gen_6339, q_gen_6352) -> q_gen_6436
<s, cons, nil>(q_gen_6332, q_gen_6439) -> q_gen_6438
<s, cons, cons>(q_gen_6390, q_gen_6443) -> q_gen_6442
<s, cons, cons>(q_gen_6339, q_gen_6415) -> q_gen_6443
<s, cons, cons>(q_gen_6339, q_gen_6445) -> q_gen_6444
<s, cons, cons>(q_gen_6390, q_gen_6446) -> q_gen_6445
<s, cons, cons>(q_gen_6339, q_gen_6421) -> q_gen_6446
<s, nil, nil>(q_gen_6449) -> q_gen_6448
<s, cons, cons>(q_gen_6390, q_gen_6455) -> q_gen_6454
<s, cons, cons>(q_gen_6390, q_gen_6438) -> q_gen_6455
<s, cons, cons>(q_gen_6384, q_gen_6459) -> q_gen_6458
<z, cons, cons>(q_gen_6339, q_gen_6460) -> q_gen_6459
<s, cons, cons>(q_gen_6384, q_gen_6462) -> q_gen_6461
<s, cons, cons>(q_gen_6339, q_gen_6463) -> q_gen_6462
<z, cons, cons>(q_gen_6339, q_gen_6464) -> q_gen_6463
<s, cons, cons>(q_gen_6339, q_gen_6467) -> q_gen_6466
<z, cons, nil>(q_gen_6332, q_gen_6468) -> q_gen_6467
<s, cons, nil>(q_gen_6332, q_gen_6470) -> q_gen_6469
<s, cons, nil>(q_gen_6332, q_gen_6475) -> q_gen_6474
<s, cons, nil>(q_gen_6332, q_gen_6471) -> q_gen_6477
<s, cons, cons>(q_gen_6390, q_gen_6435) -> q_gen_6495
<s, cons, cons>(q_gen_6339, q_gen_6497) -> q_gen_6496
<s, cons, cons>(q_gen_6390, q_gen_6330) -> q_gen_6497
<s, cons, cons>(q_gen_6339, q_gen_6501) -> q_gen_6500
<s, cons, cons>(q_gen_6384, q_gen_6421) -> q_gen_6501
<s, cons, cons>(q_gen_6390, q_gen_6503) -> q_gen_6502
<s, cons, cons>(q_gen_6384, q_gen_6438) -> q_gen_6503
<s, cons, cons>(q_gen_6390, q_gen_6415) -> q_gen_6506
<s, cons, cons>(q_gen_6339, q_gen_6420) -> q_gen_6507
}

Datatype: <nat, eltlist, eltlist>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_6323, q_gen_6328, q_gen_6329, q_gen_6344, q_gen_6345, q_gen_6379, q_gen_6385, q_gen_6408, q_gen_6493, q_gen_6494},
Q_f={},
Delta=
{
<b>() -> q_gen_6329
<a>() -> q_gen_6345
<nil, z>() -> q_gen_6323
<cons, s>(q_gen_6329, q_gen_6323) -> q_gen_6328
<cons, s>(q_gen_6345, q_gen_6323) -> q_gen_6344
<cons, s>(q_gen_6329, q_gen_6328) -> q_gen_6379
<cons, s>(q_gen_6329, q_gen_6344) -> q_gen_6385
<cons, s>(q_gen_6329, q_gen_6379) -> q_gen_6408
<cons, s>(q_gen_6345, q_gen_6328) -> q_gen_6493
<cons, s>(q_gen_6329, q_gen_6493) -> q_gen_6494
}

Datatype: <eltlist, nat>
Convolution form: right
}}}
  ;  minus -> 
{{{
Q={q_gen_6320, q_gen_6321, q_gen_6322, q_gen_6327, q_gen_6333, q_gen_6334, q_gen_6335, q_gen_6336, q_gen_6342, q_gen_6343, q_gen_6348, q_gen_6349, q_gen_6350, q_gen_6354, q_gen_6355, q_gen_6358, q_gen_6359, q_gen_6360, q_gen_6361, q_gen_6362, q_gen_6363, q_gen_6366, q_gen_6367, q_gen_6368, q_gen_6372, q_gen_6373, q_gen_6374, q_gen_6375, q_gen_6380, q_gen_6386, q_gen_6387, q_gen_6388, q_gen_6393, q_gen_6394, q_gen_6395, q_gen_6396, q_gen_6400, q_gen_6401, q_gen_6402, q_gen_6403, q_gen_6409, q_gen_6410, q_gen_6411, q_gen_6417, q_gen_6418, q_gen_6428, q_gen_6429, q_gen_6437, q_gen_6440, q_gen_6441, q_gen_6447, q_gen_6450, q_gen_6451, q_gen_6452, q_gen_6453, q_gen_6456, q_gen_6457, q_gen_6465, q_gen_6472, q_gen_6473, q_gen_6476, q_gen_6478, q_gen_6479, q_gen_6480, q_gen_6481, q_gen_6482, q_gen_6483, q_gen_6484, q_gen_6485, q_gen_6486, q_gen_6487, q_gen_6488, q_gen_6489, q_gen_6490, q_gen_6491, q_gen_6492, q_gen_6498, q_gen_6499, q_gen_6504, q_gen_6505},
Q_f={},
Delta=
{
<z>() -> q_gen_6334
<s>(q_gen_6334) -> q_gen_6350
<s>(q_gen_6350) -> q_gen_6375
<z, z>() -> q_gen_6322
<s, s>(q_gen_6322) -> q_gen_6336
<z, s>(q_gen_6334) -> q_gen_6355
<z, s>(q_gen_6350) -> q_gen_6361
<s, z>(q_gen_6334) -> q_gen_6368
<s, s>(q_gen_6336) -> q_gen_6387
<s, s>(q_gen_6368) -> q_gen_6411
<z, s>(q_gen_6375) -> q_gen_6418
<s, z>(q_gen_6350) -> q_gen_6457
<s, s>(q_gen_6355) -> q_gen_6499
<s, s>(q_gen_6457) -> q_gen_6505
<z, z, z>() -> q_gen_6320
<s, z, s>(q_gen_6322) -> q_gen_6321
<s, s, z>(q_gen_6322) -> q_gen_6327
<z, s, z>(q_gen_6334) -> q_gen_6333
<s, z, s>(q_gen_6336) -> q_gen_6335
<s, s, s>(q_gen_6343) -> q_gen_6342
<s, z, z>(q_gen_6334) -> q_gen_6343
<s, s, s>(q_gen_6320) -> q_gen_6348
<z, s, z>(q_gen_6350) -> q_gen_6349
<s, s, z>(q_gen_6355) -> q_gen_6354
<s, z, s>(q_gen_6355) -> q_gen_6358
<s, s, s>(q_gen_6360) -> q_gen_6359
<s, z, s>(q_gen_6361) -> q_gen_6360
<s, s, s>(q_gen_6363) -> q_gen_6362
<s, s, s>(q_gen_6358) -> q_gen_6363
<s, s, s>(q_gen_6333) -> q_gen_6366
<s, s, z>(q_gen_6368) -> q_gen_6367
<s, s, s>(q_gen_6373) -> q_gen_6372
<s, z, s>(q_gen_6368) -> q_gen_6373
<z, s, z>(q_gen_6375) -> q_gen_6374
<s, s, s>(q_gen_6367) -> q_gen_6380
<s, z, s>(q_gen_6387) -> q_gen_6386
<s, s, z>(q_gen_6336) -> q_gen_6388
<s, s, s>(q_gen_6348) -> q_gen_6393
<s, s, s>(q_gen_6395) -> q_gen_6394
<s, s, s>(q_gen_6396) -> q_gen_6395
<s, z, z>(q_gen_6350) -> q_gen_6396
<s, s, s>(q_gen_6401) -> q_gen_6400
<s, s, z>(q_gen_6361) -> q_gen_6401
<s, s, s>(q_gen_6403) -> q_gen_6402
<s, s, s>(q_gen_6321) -> q_gen_6403
<s, s, s>(q_gen_6410) -> q_gen_6409
<s, s, z>(q_gen_6411) -> q_gen_6410
<s, z, s>(q_gen_6418) -> q_gen_6417
<s, s, s>(q_gen_6372) -> q_gen_6428
<s, s, s>(q_gen_6394) -> q_gen_6429
<s, s, s>(q_gen_6335) -> q_gen_6437
<s, s, s>(q_gen_6359) -> q_gen_6440
<s, s, s>(q_gen_6362) -> q_gen_6441
<s, s, s>(q_gen_6342) -> q_gen_6447
<s, s, s>(q_gen_6327) -> q_gen_6450
<s, s, s>(q_gen_6366) -> q_gen_6451
<s, s, s>(q_gen_6453) -> q_gen_6452
<s, s, s>(q_gen_6354) -> q_gen_6453
<s, s, z>(q_gen_6457) -> q_gen_6456
<s, s, s>(q_gen_6447) -> q_gen_6465
<s, s, s>(q_gen_6473) -> q_gen_6472
<s, s, s>(q_gen_6456) -> q_gen_6473
<s, s, s>(q_gen_6450) -> q_gen_6476
<s, s, s>(q_gen_6479) -> q_gen_6478
<s, s, s>(q_gen_6480) -> q_gen_6479
<s, s, s>(q_gen_6349) -> q_gen_6480
<s, s, s>(q_gen_6482) -> q_gen_6481
<s, s, s>(q_gen_6400) -> q_gen_6482
<s, s, s>(q_gen_6484) -> q_gen_6483
<s, s, s>(q_gen_6388) -> q_gen_6484
<s, s, s>(q_gen_6486) -> q_gen_6485
<s, s, s>(q_gen_6487) -> q_gen_6486
<s, s, z>(q_gen_6387) -> q_gen_6487
<s, s, s>(q_gen_6489) -> q_gen_6488
<s, z, s>(q_gen_6411) -> q_gen_6489
<s, s, s>(q_gen_6491) -> q_gen_6490
<s, s, s>(q_gen_6492) -> q_gen_6491
<s, z, s>(q_gen_6457) -> q_gen_6492
<s, s, z>(q_gen_6499) -> q_gen_6498
<s, s, z>(q_gen_6505) -> q_gen_6504
}

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

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

-------------------
STEPS:
-------------------------------------------
Step 0, which took 0.005903 s (model generation: 0.004487,  model checking: 0.001416):

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

}

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

}

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

}

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

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

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

-------------------------------------------
Step 1, which took 0.010803 s (model generation: 0.010597,  model checking: 0.000206):

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

}

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

}

Datatype: <eltlist, nat>
Convolution form: right
}}}
  ;  minus -> 
{{{
Q={q_gen_6320},
Q_f={q_gen_6320},
Delta=
{
<z, z, z>() -> q_gen_6320
}

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

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

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

-------------------------------------------
Step 2, which took 0.010631 s (model generation: 0.010520,  model checking: 0.000111):

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

}

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

}

Datatype: <eltlist, nat>
Convolution form: right
}}}
  ;  minus -> 
{{{
Q={q_gen_6320, q_gen_6322},
Q_f={q_gen_6320},
Delta=
{
<z, z>() -> q_gen_6322
<s, z, s>(q_gen_6322) -> q_gen_6320
<z, z, z>() -> q_gen_6320
}

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

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

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

})

-------------------------------------------
Step 3, which took 0.010681 s (model generation: 0.010302,  model checking: 0.000379):

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

}

Datatype: <nat, eltlist, eltlist>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_6323},
Q_f={q_gen_6323},
Delta=
{
<nil, z>() -> q_gen_6323
}

Datatype: <eltlist, nat>
Convolution form: right
}}}
  ;  minus -> 
{{{
Q={q_gen_6320, q_gen_6322},
Q_f={q_gen_6320},
Delta=
{
<z, z>() -> q_gen_6322
<s, z, s>(q_gen_6322) -> q_gen_6320
<z, z, z>() -> q_gen_6320
}

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

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

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

-------------------------------------------
Step 4, which took 0.010854 s (model generation: 0.010552,  model checking: 0.000302):

Model:
|_
{
drop -> 
{{{
Q={q_gen_6324},
Q_f={q_gen_6324},
Delta=
{
<z, nil, nil>() -> q_gen_6324
}

Datatype: <nat, eltlist, eltlist>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_6323},
Q_f={q_gen_6323},
Delta=
{
<nil, z>() -> q_gen_6323
}

Datatype: <eltlist, nat>
Convolution form: right
}}}
  ;  minus -> 
{{{
Q={q_gen_6320, q_gen_6322},
Q_f={q_gen_6320},
Delta=
{
<z, z>() -> q_gen_6322
<s, z, s>(q_gen_6322) -> q_gen_6320
<z, z, z>() -> q_gen_6320
}

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

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

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

-------------------------------------------
Step 5, which took 0.012199 s (model generation: 0.010657,  model checking: 0.001542):

Model:
|_
{
drop -> 
{{{
Q={q_gen_6324, q_gen_6326},
Q_f={q_gen_6324},
Delta=
{
<z>() -> q_gen_6326
<s, nil, nil>(q_gen_6326) -> q_gen_6324
<z, nil, nil>() -> q_gen_6324
}

Datatype: <nat, eltlist, eltlist>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_6323},
Q_f={q_gen_6323},
Delta=
{
<nil, z>() -> q_gen_6323
}

Datatype: <eltlist, nat>
Convolution form: right
}}}
  ;  minus -> 
{{{
Q={q_gen_6320, q_gen_6322},
Q_f={q_gen_6320},
Delta=
{
<z, z>() -> q_gen_6322
<s, z, s>(q_gen_6322) -> q_gen_6320
<z, z, z>() -> q_gen_6320
}

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

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

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

-------------------------------------------
Step 6, which took 0.010674 s (model generation: 0.010405,  model checking: 0.000269):

Model:
|_
{
drop -> 
{{{
Q={q_gen_6324, q_gen_6326},
Q_f={q_gen_6324},
Delta=
{
<z>() -> q_gen_6326
<s, nil, nil>(q_gen_6326) -> q_gen_6324
<z, nil, nil>() -> q_gen_6324
}

Datatype: <nat, eltlist, eltlist>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_6323},
Q_f={q_gen_6323},
Delta=
{
<nil, z>() -> q_gen_6323
}

Datatype: <eltlist, nat>
Convolution form: right
}}}
  ;  minus -> 
{{{
Q={q_gen_6320, q_gen_6322},
Q_f={q_gen_6320},
Delta=
{
<z, z>() -> q_gen_6322
<s, s, z>(q_gen_6322) -> q_gen_6320
<s, z, s>(q_gen_6322) -> q_gen_6320
<z, z, z>() -> q_gen_6320
}

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

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

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

-------------------------------------------
Step 7, which took 0.005225 s (model generation: 0.004715,  model checking: 0.000510):

Model:
|_
{
drop -> 
{{{
Q={q_gen_6324, q_gen_6326},
Q_f={q_gen_6324},
Delta=
{
<z>() -> q_gen_6326
<s, nil, nil>(q_gen_6326) -> q_gen_6324
<z, nil, nil>() -> q_gen_6324
}

Datatype: <nat, eltlist, eltlist>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_6323, q_gen_6329},
Q_f={q_gen_6323},
Delta=
{
<b>() -> q_gen_6329
<cons, s>(q_gen_6329, q_gen_6323) -> q_gen_6323
<nil, z>() -> q_gen_6323
}

Datatype: <eltlist, nat>
Convolution form: right
}}}
  ;  minus -> 
{{{
Q={q_gen_6320, q_gen_6322},
Q_f={q_gen_6320},
Delta=
{
<z, z>() -> q_gen_6322
<s, s, z>(q_gen_6322) -> q_gen_6320
<s, z, s>(q_gen_6322) -> q_gen_6320
<z, z, z>() -> q_gen_6320
}

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

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

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

-------------------------------------------
Step 8, which took 0.010427 s (model generation: 0.010105,  model checking: 0.000322):

Model:
|_
{
drop -> 
{{{
Q={q_gen_6324, q_gen_6326, q_gen_6331, q_gen_6332},
Q_f={q_gen_6324},
Delta=
{
<z>() -> q_gen_6326
<b>() -> q_gen_6332
<z, nil>() -> q_gen_6331
<s, cons, nil>(q_gen_6332, q_gen_6331) -> q_gen_6324
<s, nil, nil>(q_gen_6326) -> q_gen_6324
<z, nil, nil>() -> q_gen_6324
}

Datatype: <nat, eltlist, eltlist>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_6323, q_gen_6329},
Q_f={q_gen_6323},
Delta=
{
<b>() -> q_gen_6329
<cons, s>(q_gen_6329, q_gen_6323) -> q_gen_6323
<nil, z>() -> q_gen_6323
}

Datatype: <eltlist, nat>
Convolution form: right
}}}
  ;  minus -> 
{{{
Q={q_gen_6320, q_gen_6322},
Q_f={q_gen_6320},
Delta=
{
<z, z>() -> q_gen_6322
<s, s, z>(q_gen_6322) -> q_gen_6320
<s, z, s>(q_gen_6322) -> q_gen_6320
<z, z, z>() -> q_gen_6320
}

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

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

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

-------------------------------------------
Step 9, which took 0.014392 s (model generation: 0.014033,  model checking: 0.000359):

Model:
|_
{
drop -> 
{{{
Q={q_gen_6324, q_gen_6326, q_gen_6331, q_gen_6332},
Q_f={q_gen_6324},
Delta=
{
<z>() -> q_gen_6326
<b>() -> q_gen_6332
<z, nil>() -> q_gen_6331
<s, cons, nil>(q_gen_6332, q_gen_6331) -> q_gen_6324
<s, nil, nil>(q_gen_6326) -> q_gen_6324
<z, nil, nil>() -> q_gen_6324
}

Datatype: <nat, eltlist, eltlist>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_6323, q_gen_6329},
Q_f={q_gen_6323},
Delta=
{
<b>() -> q_gen_6329
<cons, s>(q_gen_6329, q_gen_6323) -> q_gen_6323
<nil, z>() -> q_gen_6323
}

Datatype: <eltlist, nat>
Convolution form: right
}}}
  ;  minus -> 
{{{
Q={q_gen_6320, q_gen_6322, q_gen_6334},
Q_f={q_gen_6320},
Delta=
{
<z>() -> q_gen_6334
<z, z>() -> q_gen_6322
<s, s, z>(q_gen_6322) -> q_gen_6320
<s, z, s>(q_gen_6322) -> q_gen_6320
<z, s, z>(q_gen_6334) -> q_gen_6320
<z, z, z>() -> q_gen_6320
}

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

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

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

-------------------------------------------
Step 10, which took 0.013322 s (model generation: 0.012545,  model checking: 0.000777):

Model:
|_
{
drop -> 
{{{
Q={q_gen_6324, q_gen_6326, q_gen_6331, q_gen_6332},
Q_f={q_gen_6324},
Delta=
{
<z>() -> q_gen_6326
<b>() -> q_gen_6332
<z, nil>() -> q_gen_6331
<s, cons, nil>(q_gen_6332, q_gen_6331) -> q_gen_6324
<s, nil, nil>(q_gen_6326) -> q_gen_6324
<z, nil, nil>() -> q_gen_6324
}

Datatype: <nat, eltlist, eltlist>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_6323, q_gen_6329},
Q_f={q_gen_6323},
Delta=
{
<b>() -> q_gen_6329
<cons, s>(q_gen_6329, q_gen_6323) -> q_gen_6323
<nil, z>() -> q_gen_6323
}

Datatype: <eltlist, nat>
Convolution form: right
}}}
  ;  minus -> 
{{{
Q={q_gen_6320, q_gen_6322, q_gen_6334},
Q_f={q_gen_6320},
Delta=
{
<z>() -> q_gen_6334
<s, s>(q_gen_6322) -> q_gen_6322
<z, z>() -> q_gen_6322
<s, s, z>(q_gen_6322) -> q_gen_6320
<s, z, s>(q_gen_6322) -> q_gen_6320
<z, s, z>(q_gen_6334) -> q_gen_6320
<z, z, z>() -> q_gen_6320
}

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

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

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

-------------------------------------------
Step 11, which took 0.015306 s (model generation: 0.012741,  model checking: 0.002565):

Model:
|_
{
drop -> 
{{{
Q={q_gen_6324, q_gen_6326, q_gen_6331, q_gen_6332, q_gen_6338, q_gen_6339},
Q_f={q_gen_6324},
Delta=
{
<z>() -> q_gen_6326
<b>() -> q_gen_6332
<z, nil>() -> q_gen_6331
<nil, nil>() -> q_gen_6338
<b, b>() -> q_gen_6339
<s, cons, nil>(q_gen_6332, q_gen_6331) -> q_gen_6324
<s, nil, nil>(q_gen_6326) -> q_gen_6324
<z, cons, cons>(q_gen_6339, q_gen_6338) -> q_gen_6324
<z, nil, nil>() -> q_gen_6324
}

Datatype: <nat, eltlist, eltlist>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_6323, q_gen_6329},
Q_f={q_gen_6323},
Delta=
{
<b>() -> q_gen_6329
<cons, s>(q_gen_6329, q_gen_6323) -> q_gen_6323
<nil, z>() -> q_gen_6323
}

Datatype: <eltlist, nat>
Convolution form: right
}}}
  ;  minus -> 
{{{
Q={q_gen_6320, q_gen_6322, q_gen_6334},
Q_f={q_gen_6320},
Delta=
{
<z>() -> q_gen_6334
<s, s>(q_gen_6322) -> q_gen_6322
<z, z>() -> q_gen_6322
<s, s, z>(q_gen_6322) -> q_gen_6320
<s, z, s>(q_gen_6322) -> q_gen_6320
<z, s, z>(q_gen_6334) -> q_gen_6320
<z, z, z>() -> q_gen_6320
}

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

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

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

-------------------------------------------
Step 12, which took 0.013536 s (model generation: 0.013119,  model checking: 0.000417):

Model:
|_
{
drop -> 
{{{
Q={q_gen_6324, q_gen_6326, q_gen_6331, q_gen_6332, q_gen_6338, q_gen_6339},
Q_f={q_gen_6324},
Delta=
{
<s>(q_gen_6326) -> q_gen_6326
<z>() -> q_gen_6326
<b>() -> q_gen_6332
<z, nil>() -> q_gen_6331
<nil, nil>() -> q_gen_6338
<b, b>() -> q_gen_6339
<s, cons, nil>(q_gen_6332, q_gen_6331) -> q_gen_6324
<s, nil, nil>(q_gen_6326) -> q_gen_6324
<z, cons, cons>(q_gen_6339, q_gen_6338) -> q_gen_6324
<z, nil, nil>() -> q_gen_6324
}

Datatype: <nat, eltlist, eltlist>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_6323, q_gen_6329},
Q_f={q_gen_6323},
Delta=
{
<b>() -> q_gen_6329
<cons, s>(q_gen_6329, q_gen_6323) -> q_gen_6323
<nil, z>() -> q_gen_6323
}

Datatype: <eltlist, nat>
Convolution form: right
}}}
  ;  minus -> 
{{{
Q={q_gen_6320, q_gen_6322, q_gen_6334},
Q_f={q_gen_6320},
Delta=
{
<z>() -> q_gen_6334
<s, s>(q_gen_6322) -> q_gen_6322
<z, z>() -> q_gen_6322
<s, s, z>(q_gen_6322) -> q_gen_6320
<s, z, s>(q_gen_6322) -> q_gen_6320
<z, s, z>(q_gen_6334) -> q_gen_6320
<z, z, z>() -> q_gen_6320
}

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

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

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

-------------------------------------------
Step 13, which took 0.015533 s (model generation: 0.013841,  model checking: 0.001692):

Model:
|_
{
drop -> 
{{{
Q={q_gen_6324, q_gen_6326, q_gen_6331, q_gen_6332, q_gen_6338, q_gen_6339},
Q_f={q_gen_6324},
Delta=
{
<s>(q_gen_6326) -> q_gen_6326
<z>() -> q_gen_6326
<b>() -> q_gen_6332
<z, nil>() -> q_gen_6331
<nil, nil>() -> q_gen_6338
<b, b>() -> q_gen_6339
<s, cons, nil>(q_gen_6332, q_gen_6331) -> q_gen_6324
<s, nil, nil>(q_gen_6326) -> q_gen_6324
<z, cons, cons>(q_gen_6339, q_gen_6338) -> q_gen_6324
<z, nil, nil>() -> q_gen_6324
}

Datatype: <nat, eltlist, eltlist>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_6323, q_gen_6329},
Q_f={q_gen_6323},
Delta=
{
<b>() -> q_gen_6329
<cons, s>(q_gen_6329, q_gen_6323) -> q_gen_6323
<nil, z>() -> q_gen_6323
}

Datatype: <eltlist, nat>
Convolution form: right
}}}
  ;  minus -> 
{{{
Q={q_gen_6320, q_gen_6322, q_gen_6334},
Q_f={q_gen_6320},
Delta=
{
<z>() -> q_gen_6334
<s, s>(q_gen_6322) -> q_gen_6322
<z, z>() -> q_gen_6322
<s, s, s>(q_gen_6320) -> q_gen_6320
<s, s, z>(q_gen_6322) -> q_gen_6320
<s, z, s>(q_gen_6322) -> q_gen_6320
<s, z, z>(q_gen_6334) -> q_gen_6320
<z, s, z>(q_gen_6334) -> q_gen_6320
<z, z, z>() -> q_gen_6320
}

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

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

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

-------------------------------------------
Step 14, which took 0.015192 s (model generation: 0.014268,  model checking: 0.000924):

Model:
|_
{
drop -> 
{{{
Q={q_gen_6324, q_gen_6326, q_gen_6331, q_gen_6332, q_gen_6338, q_gen_6339},
Q_f={q_gen_6324},
Delta=
{
<s>(q_gen_6326) -> q_gen_6326
<z>() -> q_gen_6326
<b>() -> q_gen_6332
<z, nil>() -> q_gen_6331
<nil, nil>() -> q_gen_6338
<b, b>() -> q_gen_6339
<s, cons, nil>(q_gen_6332, q_gen_6331) -> q_gen_6324
<s, nil, nil>(q_gen_6326) -> q_gen_6324
<z, cons, cons>(q_gen_6339, q_gen_6338) -> q_gen_6324
<z, nil, nil>() -> q_gen_6324
}

Datatype: <nat, eltlist, eltlist>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_6323, q_gen_6329},
Q_f={q_gen_6323},
Delta=
{
<a>() -> q_gen_6329
<b>() -> q_gen_6329
<cons, s>(q_gen_6329, q_gen_6323) -> q_gen_6323
<nil, z>() -> q_gen_6323
}

Datatype: <eltlist, nat>
Convolution form: right
}}}
  ;  minus -> 
{{{
Q={q_gen_6320, q_gen_6322, q_gen_6334},
Q_f={q_gen_6320},
Delta=
{
<z>() -> q_gen_6334
<s, s>(q_gen_6322) -> q_gen_6322
<z, z>() -> q_gen_6322
<s, s, s>(q_gen_6320) -> q_gen_6320
<s, s, z>(q_gen_6322) -> q_gen_6320
<s, z, s>(q_gen_6322) -> q_gen_6320
<s, z, z>(q_gen_6334) -> q_gen_6320
<z, s, z>(q_gen_6334) -> q_gen_6320
<z, z, z>() -> q_gen_6320
}

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

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

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

-------------------------------------------
Step 15, which took 0.015914 s (model generation: 0.015545,  model checking: 0.000369):

Model:
|_
{
drop -> 
{{{
Q={q_gen_6324, q_gen_6326, q_gen_6331, q_gen_6332, q_gen_6338, q_gen_6339},
Q_f={q_gen_6324},
Delta=
{
<s>(q_gen_6326) -> q_gen_6326
<z>() -> q_gen_6326
<a>() -> q_gen_6332
<b>() -> q_gen_6332
<z, nil>() -> q_gen_6331
<nil, nil>() -> q_gen_6338
<b, b>() -> q_gen_6339
<s, cons, nil>(q_gen_6332, q_gen_6331) -> q_gen_6324
<s, nil, nil>(q_gen_6326) -> q_gen_6324
<z, cons, cons>(q_gen_6339, q_gen_6338) -> q_gen_6324
<z, nil, nil>() -> q_gen_6324
}

Datatype: <nat, eltlist, eltlist>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_6323, q_gen_6329},
Q_f={q_gen_6323},
Delta=
{
<a>() -> q_gen_6329
<b>() -> q_gen_6329
<cons, s>(q_gen_6329, q_gen_6323) -> q_gen_6323
<nil, z>() -> q_gen_6323
}

Datatype: <eltlist, nat>
Convolution form: right
}}}
  ;  minus -> 
{{{
Q={q_gen_6320, q_gen_6322, q_gen_6334},
Q_f={q_gen_6320},
Delta=
{
<z>() -> q_gen_6334
<s, s>(q_gen_6322) -> q_gen_6322
<z, z>() -> q_gen_6322
<s, s, s>(q_gen_6320) -> q_gen_6320
<s, s, z>(q_gen_6322) -> q_gen_6320
<s, z, s>(q_gen_6322) -> q_gen_6320
<s, z, z>(q_gen_6334) -> q_gen_6320
<z, s, z>(q_gen_6334) -> q_gen_6320
<z, z, z>() -> q_gen_6320
}

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

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

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

-------------------------------------------
Step 16, which took 0.015863 s (model generation: 0.015496,  model checking: 0.000367):

Model:
|_
{
drop -> 
{{{
Q={q_gen_6324, q_gen_6326, q_gen_6331, q_gen_6332, q_gen_6338, q_gen_6339},
Q_f={q_gen_6324},
Delta=
{
<s>(q_gen_6326) -> q_gen_6326
<z>() -> q_gen_6326
<a>() -> q_gen_6332
<b>() -> q_gen_6332
<z, nil>() -> q_gen_6331
<nil, nil>() -> q_gen_6338
<b, b>() -> q_gen_6339
<s, cons, nil>(q_gen_6332, q_gen_6331) -> q_gen_6324
<s, nil, nil>(q_gen_6326) -> q_gen_6324
<z, cons, cons>(q_gen_6339, q_gen_6338) -> q_gen_6324
<z, nil, nil>() -> q_gen_6324
}

Datatype: <nat, eltlist, eltlist>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_6323, q_gen_6329},
Q_f={q_gen_6323},
Delta=
{
<a>() -> q_gen_6329
<b>() -> q_gen_6329
<cons, s>(q_gen_6329, q_gen_6323) -> q_gen_6323
<nil, z>() -> q_gen_6323
}

Datatype: <eltlist, nat>
Convolution form: right
}}}
  ;  minus -> 
{{{
Q={q_gen_6320, q_gen_6322, q_gen_6334, q_gen_6343},
Q_f={q_gen_6320},
Delta=
{
<z>() -> q_gen_6334
<s, s>(q_gen_6322) -> q_gen_6322
<z, z>() -> q_gen_6322
<s, s, s>(q_gen_6343) -> q_gen_6320
<s, s, z>(q_gen_6322) -> q_gen_6320
<s, z, s>(q_gen_6322) -> q_gen_6320
<z, s, z>(q_gen_6334) -> q_gen_6320
<z, z, z>() -> q_gen_6320
<s, s, s>(q_gen_6320) -> q_gen_6343
<s, z, z>(q_gen_6334) -> q_gen_6343
}

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

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

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

-------------------------------------------
Step 17, which took 0.018449 s (model generation: 0.017506,  model checking: 0.000943):

Model:
|_
{
drop -> 
{{{
Q={q_gen_6324, q_gen_6326, q_gen_6331, q_gen_6332, q_gen_6338, q_gen_6339},
Q_f={q_gen_6324},
Delta=
{
<s>(q_gen_6326) -> q_gen_6326
<z>() -> q_gen_6326
<a>() -> q_gen_6332
<b>() -> q_gen_6332
<z, nil>() -> q_gen_6331
<nil, nil>() -> q_gen_6338
<b, b>() -> q_gen_6339
<s, cons, nil>(q_gen_6332, q_gen_6331) -> q_gen_6324
<s, nil, nil>(q_gen_6326) -> q_gen_6324
<z, cons, cons>(q_gen_6339, q_gen_6338) -> q_gen_6324
<z, nil, nil>() -> q_gen_6324
}

Datatype: <nat, eltlist, eltlist>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_6323, q_gen_6329},
Q_f={q_gen_6323},
Delta=
{
<a>() -> q_gen_6329
<b>() -> q_gen_6329
<cons, s>(q_gen_6329, q_gen_6323) -> q_gen_6323
<nil, z>() -> q_gen_6323
}

Datatype: <eltlist, nat>
Convolution form: right
}}}
  ;  minus -> 
{{{
Q={q_gen_6320, q_gen_6322, q_gen_6334, q_gen_6343},
Q_f={q_gen_6320},
Delta=
{
<s>(q_gen_6334) -> q_gen_6334
<z>() -> q_gen_6334
<s, s>(q_gen_6322) -> q_gen_6322
<z, z>() -> q_gen_6322
<s, s, s>(q_gen_6343) -> q_gen_6320
<s, s, z>(q_gen_6322) -> q_gen_6320
<s, z, s>(q_gen_6322) -> q_gen_6320
<z, s, z>(q_gen_6334) -> q_gen_6320
<z, z, z>() -> q_gen_6320
<s, s, s>(q_gen_6320) -> q_gen_6343
<s, z, z>(q_gen_6334) -> q_gen_6343
}

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

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

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

-------------------------------------------
Step 18, which took 0.018979 s (model generation: 0.017906,  model checking: 0.001073):

Model:
|_
{
drop -> 
{{{
Q={q_gen_6324, q_gen_6326, q_gen_6331, q_gen_6332, q_gen_6338, q_gen_6339},
Q_f={q_gen_6324},
Delta=
{
<s>(q_gen_6326) -> q_gen_6326
<z>() -> q_gen_6326
<a>() -> q_gen_6332
<b>() -> q_gen_6332
<z, nil>() -> q_gen_6331
<cons, cons>(q_gen_6339, q_gen_6338) -> q_gen_6338
<nil, nil>() -> q_gen_6338
<a, a>() -> q_gen_6339
<b, b>() -> q_gen_6339
<s, cons, nil>(q_gen_6332, q_gen_6331) -> q_gen_6324
<s, nil, nil>(q_gen_6326) -> q_gen_6324
<z, cons, cons>(q_gen_6339, q_gen_6338) -> q_gen_6324
<z, nil, nil>() -> q_gen_6324
}

Datatype: <nat, eltlist, eltlist>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_6323, q_gen_6329},
Q_f={q_gen_6323},
Delta=
{
<a>() -> q_gen_6329
<b>() -> q_gen_6329
<cons, s>(q_gen_6329, q_gen_6323) -> q_gen_6323
<nil, z>() -> q_gen_6323
}

Datatype: <eltlist, nat>
Convolution form: right
}}}
  ;  minus -> 
{{{
Q={q_gen_6320, q_gen_6322, q_gen_6334, q_gen_6343},
Q_f={q_gen_6320},
Delta=
{
<s>(q_gen_6334) -> q_gen_6334
<z>() -> q_gen_6334
<s, s>(q_gen_6322) -> q_gen_6322
<z, z>() -> q_gen_6322
<s, s, s>(q_gen_6343) -> q_gen_6320
<s, s, z>(q_gen_6322) -> q_gen_6320
<s, z, s>(q_gen_6322) -> q_gen_6320
<z, s, z>(q_gen_6334) -> q_gen_6320
<z, z, z>() -> q_gen_6320
<s, s, s>(q_gen_6320) -> q_gen_6343
<s, z, z>(q_gen_6334) -> q_gen_6343
}

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

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

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

-------------------------------------------
Step 19, which took 0.019070 s (model generation: 0.018121,  model checking: 0.000949):

Model:
|_
{
drop -> 
{{{
Q={q_gen_6324, q_gen_6326, q_gen_6331, q_gen_6332, q_gen_6338, q_gen_6339},
Q_f={q_gen_6324},
Delta=
{
<s>(q_gen_6326) -> q_gen_6326
<z>() -> q_gen_6326
<a>() -> q_gen_6332
<b>() -> q_gen_6332
<z, nil>() -> q_gen_6331
<cons, cons>(q_gen_6339, q_gen_6338) -> q_gen_6338
<nil, nil>() -> q_gen_6338
<a, a>() -> q_gen_6339
<b, b>() -> q_gen_6339
<s, cons, nil>(q_gen_6332, q_gen_6331) -> q_gen_6324
<s, nil, nil>(q_gen_6326) -> q_gen_6324
<z, cons, cons>(q_gen_6339, q_gen_6338) -> q_gen_6324
<z, nil, nil>() -> q_gen_6324
}

Datatype: <nat, eltlist, eltlist>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_6323, q_gen_6329},
Q_f={q_gen_6323},
Delta=
{
<a>() -> q_gen_6329
<b>() -> q_gen_6329
<cons, s>(q_gen_6329, q_gen_6323) -> q_gen_6323
<nil, z>() -> q_gen_6323
}

Datatype: <eltlist, nat>
Convolution form: right
}}}
  ;  minus -> 
{{{
Q={q_gen_6320, q_gen_6322, q_gen_6334, q_gen_6343},
Q_f={q_gen_6320},
Delta=
{
<s>(q_gen_6334) -> q_gen_6334
<z>() -> q_gen_6334
<s, s>(q_gen_6322) -> q_gen_6322
<z, s>(q_gen_6334) -> q_gen_6322
<z, z>() -> q_gen_6322
<s, s, s>(q_gen_6343) -> q_gen_6320
<s, s, z>(q_gen_6322) -> q_gen_6320
<s, z, s>(q_gen_6322) -> q_gen_6320
<z, s, z>(q_gen_6334) -> q_gen_6320
<z, z, z>() -> q_gen_6320
<s, s, s>(q_gen_6320) -> q_gen_6343
<s, z, z>(q_gen_6334) -> q_gen_6343
}

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

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

Teacher's answer:
New clause system:
{
() -> drop([s(u), nil, nil]) -> 7
() -> drop([z, l, l]) -> 9
() -> length([nil, z]) -> 7
() -> minus([s(u), z, s(u)]) -> 7
() -> minus([z, y, z]) -> 9
(drop([n, l1, _sga]) /\ length([_sga, _tga]) /\ length([l1, _uga]) /\ minus([_uga, n, _vga])) -> eq_nat([_tga, _vga]) -> 7
(drop([u, x3, _ega])) -> drop([s(u), cons(x2, x3), _ega]) -> 10
(length([ll, _jga])) -> length([cons(x, ll), s(_jga)]) -> 8
(minus([u, x2, _nga])) -> minus([s(u), s(x2), _nga]) -> 10
}
Sat witness: Found: ((drop([u, x3, _ega])) -> drop([s(u), cons(x2, x3), _ega]), {
_ega -> nil  ;  u -> s(z)  ;  x2 -> b  ;  x3 -> nil
})

-------------------------------------------
Step 20, which took 0.019286 s (model generation: 0.018084,  model checking: 0.001202):

Model:
|_
{
drop -> 
{{{
Q={q_gen_6324, q_gen_6326, q_gen_6331, q_gen_6332, q_gen_6338, q_gen_6339},
Q_f={q_gen_6324},
Delta=
{
<s>(q_gen_6326) -> q_gen_6326
<z>() -> q_gen_6326
<a>() -> q_gen_6332
<b>() -> q_gen_6332
<s, nil>(q_gen_6326) -> q_gen_6331
<z, nil>() -> q_gen_6331
<cons, cons>(q_gen_6339, q_gen_6338) -> q_gen_6338
<nil, nil>() -> q_gen_6338
<a, a>() -> q_gen_6339
<b, b>() -> q_gen_6339
<s, cons, nil>(q_gen_6332, q_gen_6331) -> q_gen_6324
<s, nil, nil>(q_gen_6326) -> q_gen_6324
<z, cons, cons>(q_gen_6339, q_gen_6338) -> q_gen_6324
<z, nil, nil>() -> q_gen_6324
}

Datatype: <nat, eltlist, eltlist>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_6323, q_gen_6329},
Q_f={q_gen_6323},
Delta=
{
<a>() -> q_gen_6329
<b>() -> q_gen_6329
<cons, s>(q_gen_6329, q_gen_6323) -> q_gen_6323
<nil, z>() -> q_gen_6323
}

Datatype: <eltlist, nat>
Convolution form: right
}}}
  ;  minus -> 
{{{
Q={q_gen_6320, q_gen_6322, q_gen_6334, q_gen_6343},
Q_f={q_gen_6320},
Delta=
{
<s>(q_gen_6334) -> q_gen_6334
<z>() -> q_gen_6334
<s, s>(q_gen_6322) -> q_gen_6322
<z, s>(q_gen_6334) -> q_gen_6322
<z, z>() -> q_gen_6322
<s, s, s>(q_gen_6343) -> q_gen_6320
<s, s, z>(q_gen_6322) -> q_gen_6320
<s, z, s>(q_gen_6322) -> q_gen_6320
<z, s, z>(q_gen_6334) -> q_gen_6320
<z, z, z>() -> q_gen_6320
<s, s, s>(q_gen_6320) -> q_gen_6343
<s, z, z>(q_gen_6334) -> q_gen_6343
}

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

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

Teacher's answer:
New clause system:
{
() -> drop([s(u), nil, nil]) -> 7
() -> drop([z, l, l]) -> 9
() -> length([nil, z]) -> 7
() -> minus([s(u), z, s(u)]) -> 7
() -> minus([z, y, z]) -> 9
(drop([n, l1, _sga]) /\ length([_sga, _tga]) /\ length([l1, _uga]) /\ minus([_uga, n, _vga])) -> eq_nat([_tga, _vga]) -> 10
(drop([u, x3, _ega])) -> drop([s(u), cons(x2, x3), _ega]) -> 10
(length([ll, _jga])) -> length([cons(x, ll), s(_jga)]) -> 8
(minus([u, x2, _nga])) -> minus([s(u), s(x2), _nga]) -> 10
}
Sat witness: Found: ((drop([n, l1, _sga]) /\ length([_sga, _tga]) /\ length([l1, _uga]) /\ minus([_uga, n, _vga])) -> eq_nat([_tga, _vga]), {
_sga -> cons(b, nil)  ;  _tga -> s(z)  ;  _uga -> s(z)  ;  _vga -> s(s(z))  ;  l1 -> cons(b, nil)  ;  n -> z
})

-------------------------------------------
Step 21, which took 0.021471 s (model generation: 0.018638,  model checking: 0.002833):

Model:
|_
{
drop -> 
{{{
Q={q_gen_6324, q_gen_6326, q_gen_6331, q_gen_6332, q_gen_6338, q_gen_6339},
Q_f={q_gen_6324},
Delta=
{
<s>(q_gen_6326) -> q_gen_6326
<z>() -> q_gen_6326
<a>() -> q_gen_6332
<b>() -> q_gen_6332
<s, nil>(q_gen_6326) -> q_gen_6331
<z, nil>() -> q_gen_6331
<cons, cons>(q_gen_6339, q_gen_6338) -> q_gen_6338
<nil, nil>() -> q_gen_6338
<a, a>() -> q_gen_6339
<b, b>() -> q_gen_6339
<s, cons, nil>(q_gen_6332, q_gen_6331) -> q_gen_6324
<s, nil, nil>(q_gen_6326) -> q_gen_6324
<z, cons, cons>(q_gen_6339, q_gen_6338) -> q_gen_6324
<z, nil, nil>() -> q_gen_6324
}

Datatype: <nat, eltlist, eltlist>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_6323, q_gen_6329},
Q_f={q_gen_6323},
Delta=
{
<a>() -> q_gen_6329
<b>() -> q_gen_6329
<cons, s>(q_gen_6329, q_gen_6323) -> q_gen_6323
<nil, z>() -> q_gen_6323
}

Datatype: <eltlist, nat>
Convolution form: right
}}}
  ;  minus -> 
{{{
Q={q_gen_6320, q_gen_6322, q_gen_6334, q_gen_6343, q_gen_6355},
Q_f={q_gen_6320},
Delta=
{
<s>(q_gen_6334) -> q_gen_6334
<z>() -> q_gen_6334
<s, s>(q_gen_6322) -> q_gen_6322
<z, z>() -> q_gen_6322
<z, s>(q_gen_6334) -> q_gen_6355
<s, s, s>(q_gen_6343) -> q_gen_6320
<s, s, z>(q_gen_6322) -> q_gen_6320
<s, s, z>(q_gen_6355) -> q_gen_6320
<s, z, s>(q_gen_6322) -> q_gen_6320
<z, s, z>(q_gen_6334) -> q_gen_6320
<z, z, z>() -> q_gen_6320
<s, s, s>(q_gen_6320) -> q_gen_6343
<s, z, s>(q_gen_6355) -> q_gen_6343
<s, z, z>(q_gen_6334) -> q_gen_6343
}

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

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

Teacher's answer:
New clause system:
{
() -> drop([s(u), nil, nil]) -> 8
() -> drop([z, l, l]) -> 10
() -> length([nil, z]) -> 8
() -> minus([s(u), z, s(u)]) -> 8
() -> minus([z, y, z]) -> 10
(drop([n, l1, _sga]) /\ length([_sga, _tga]) /\ length([l1, _uga]) /\ minus([_uga, n, _vga])) -> eq_nat([_tga, _vga]) -> 10
(drop([u, x3, _ega])) -> drop([s(u), cons(x2, x3), _ega]) -> 10
(length([ll, _jga])) -> length([cons(x, ll), s(_jga)]) -> 9
(minus([u, x2, _nga])) -> minus([s(u), s(x2), _nga]) -> 13
}
Sat witness: Found: ((minus([u, x2, _nga])) -> minus([s(u), s(x2), _nga]), {
_nga -> s(s(s(s(z))))  ;  u -> s(s(z))  ;  x2 -> s(z)
})

-------------------------------------------
Step 22, which took 0.024959 s (model generation: 0.022662,  model checking: 0.002297):

Model:
|_
{
drop -> 
{{{
Q={q_gen_6324, q_gen_6326, q_gen_6331, q_gen_6332, q_gen_6338, q_gen_6339},
Q_f={q_gen_6324},
Delta=
{
<s>(q_gen_6326) -> q_gen_6326
<z>() -> q_gen_6326
<a>() -> q_gen_6332
<b>() -> q_gen_6332
<s, nil>(q_gen_6326) -> q_gen_6331
<z, nil>() -> q_gen_6331
<cons, cons>(q_gen_6339, q_gen_6338) -> q_gen_6338
<nil, nil>() -> q_gen_6338
<a, a>() -> q_gen_6339
<b, b>() -> q_gen_6339
<s, cons, nil>(q_gen_6332, q_gen_6331) -> q_gen_6324
<s, nil, nil>(q_gen_6326) -> q_gen_6324
<z, cons, cons>(q_gen_6339, q_gen_6338) -> q_gen_6324
<z, nil, nil>() -> q_gen_6324
}

Datatype: <nat, eltlist, eltlist>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_6323, q_gen_6329},
Q_f={q_gen_6323},
Delta=
{
<a>() -> q_gen_6329
<b>() -> q_gen_6329
<cons, s>(q_gen_6329, q_gen_6323) -> q_gen_6323
<nil, z>() -> q_gen_6323
}

Datatype: <eltlist, nat>
Convolution form: right
}}}
  ;  minus -> 
{{{
Q={q_gen_6320, q_gen_6321, q_gen_6322, q_gen_6334, q_gen_6348, q_gen_6355},
Q_f={q_gen_6320, q_gen_6321},
Delta=
{
<s>(q_gen_6334) -> q_gen_6334
<z>() -> q_gen_6334
<s, s>(q_gen_6322) -> q_gen_6322
<z, z>() -> q_gen_6322
<z, s>(q_gen_6334) -> q_gen_6355
<s, s, z>(q_gen_6355) -> q_gen_6320
<z, z, z>() -> q_gen_6320
<s, s, s>(q_gen_6321) -> q_gen_6321
<s, s, z>(q_gen_6322) -> q_gen_6321
<s, z, s>(q_gen_6322) -> q_gen_6321
<s, z, z>(q_gen_6334) -> q_gen_6321
<z, s, z>(q_gen_6334) -> q_gen_6321
<s, s, s>(q_gen_6320) -> q_gen_6348
<s, s, s>(q_gen_6348) -> q_gen_6348
<s, z, s>(q_gen_6355) -> q_gen_6348
}

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

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

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

-------------------------------------------
Step 23, which took 0.025200 s (model generation: 0.023759,  model checking: 0.001441):

Model:
|_
{
drop -> 
{{{
Q={q_gen_6324, q_gen_6326, q_gen_6331, q_gen_6332, q_gen_6338, q_gen_6339},
Q_f={q_gen_6324},
Delta=
{
<s>(q_gen_6326) -> q_gen_6326
<z>() -> q_gen_6326
<a>() -> q_gen_6332
<b>() -> q_gen_6332
<s, cons>(q_gen_6332, q_gen_6331) -> q_gen_6331
<s, nil>(q_gen_6326) -> q_gen_6331
<z, nil>() -> q_gen_6331
<cons, cons>(q_gen_6339, q_gen_6338) -> q_gen_6338
<nil, nil>() -> q_gen_6338
<a, a>() -> q_gen_6339
<b, b>() -> q_gen_6339
<s, cons, nil>(q_gen_6332, q_gen_6331) -> q_gen_6324
<s, nil, nil>(q_gen_6326) -> q_gen_6324
<z, cons, cons>(q_gen_6339, q_gen_6338) -> q_gen_6324
<z, nil, nil>() -> q_gen_6324
}

Datatype: <nat, eltlist, eltlist>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_6323, q_gen_6329},
Q_f={q_gen_6323},
Delta=
{
<a>() -> q_gen_6329
<b>() -> q_gen_6329
<cons, s>(q_gen_6329, q_gen_6323) -> q_gen_6323
<nil, z>() -> q_gen_6323
}

Datatype: <eltlist, nat>
Convolution form: right
}}}
  ;  minus -> 
{{{
Q={q_gen_6320, q_gen_6321, q_gen_6322, q_gen_6334, q_gen_6348, q_gen_6355},
Q_f={q_gen_6320, q_gen_6321},
Delta=
{
<s>(q_gen_6334) -> q_gen_6334
<z>() -> q_gen_6334
<s, s>(q_gen_6322) -> q_gen_6322
<z, z>() -> q_gen_6322
<z, s>(q_gen_6334) -> q_gen_6355
<s, s, z>(q_gen_6355) -> q_gen_6320
<z, z, z>() -> q_gen_6320
<s, s, s>(q_gen_6321) -> q_gen_6321
<s, s, z>(q_gen_6322) -> q_gen_6321
<s, z, s>(q_gen_6322) -> q_gen_6321
<s, z, z>(q_gen_6334) -> q_gen_6321
<z, s, z>(q_gen_6334) -> q_gen_6321
<s, s, s>(q_gen_6320) -> q_gen_6348
<s, s, s>(q_gen_6348) -> q_gen_6348
<s, z, s>(q_gen_6355) -> q_gen_6348
}

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

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

Teacher's answer:
New clause system:
{
() -> drop([s(u), nil, nil]) -> 10
() -> drop([z, l, l]) -> 10
() -> length([nil, z]) -> 10
() -> minus([s(u), z, s(u)]) -> 10
() -> minus([z, y, z]) -> 10
(drop([n, l1, _sga]) /\ length([_sga, _tga]) /\ length([l1, _uga]) /\ minus([_uga, n, _vga])) -> eq_nat([_tga, _vga]) -> 13
(drop([u, x3, _ega])) -> drop([s(u), cons(x2, x3), _ega]) -> 13
(length([ll, _jga])) -> length([cons(x, ll), s(_jga)]) -> 11
(minus([u, x2, _nga])) -> minus([s(u), s(x2), _nga]) -> 13
}
Sat witness: Found: ((drop([n, l1, _sga]) /\ length([_sga, _tga]) /\ length([l1, _uga]) /\ minus([_uga, n, _vga])) -> eq_nat([_tga, _vga]), {
_sga -> nil  ;  _tga -> z  ;  _uga -> s(z)  ;  _vga -> s(z)  ;  l1 -> cons(b, nil)  ;  n -> s(s(z))
})

-------------------------------------------
Step 24, which took 0.027025 s (model generation: 0.024300,  model checking: 0.002725):

Model:
|_
{
drop -> 
{{{
Q={q_gen_6324, q_gen_6326, q_gen_6331, q_gen_6332, q_gen_6338, q_gen_6339},
Q_f={q_gen_6324},
Delta=
{
<s>(q_gen_6326) -> q_gen_6326
<z>() -> q_gen_6326
<a>() -> q_gen_6332
<b>() -> q_gen_6332
<s, cons>(q_gen_6332, q_gen_6331) -> q_gen_6331
<s, nil>(q_gen_6326) -> q_gen_6331
<z, nil>() -> q_gen_6331
<cons, cons>(q_gen_6339, q_gen_6338) -> q_gen_6338
<nil, nil>() -> q_gen_6338
<a, a>() -> q_gen_6339
<b, b>() -> q_gen_6339
<s, cons, nil>(q_gen_6332, q_gen_6331) -> q_gen_6324
<s, nil, nil>(q_gen_6326) -> q_gen_6324
<z, cons, cons>(q_gen_6339, q_gen_6338) -> q_gen_6324
<z, nil, nil>() -> q_gen_6324
}

Datatype: <nat, eltlist, eltlist>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_6323, q_gen_6329},
Q_f={q_gen_6323},
Delta=
{
<a>() -> q_gen_6329
<b>() -> q_gen_6329
<cons, s>(q_gen_6329, q_gen_6323) -> q_gen_6323
<nil, z>() -> q_gen_6323
}

Datatype: <eltlist, nat>
Convolution form: right
}}}
  ;  minus -> 
{{{
Q={q_gen_6320, q_gen_6321, q_gen_6322, q_gen_6334, q_gen_6348, q_gen_6355},
Q_f={q_gen_6320, q_gen_6321},
Delta=
{
<s>(q_gen_6334) -> q_gen_6334
<z>() -> q_gen_6334
<s, s>(q_gen_6322) -> q_gen_6322
<z, z>() -> q_gen_6322
<z, s>(q_gen_6334) -> q_gen_6355
<s, s, z>(q_gen_6355) -> q_gen_6320
<z, s, z>(q_gen_6334) -> q_gen_6320
<z, z, z>() -> q_gen_6320
<s, s, s>(q_gen_6321) -> q_gen_6321
<s, s, z>(q_gen_6322) -> q_gen_6321
<s, z, s>(q_gen_6322) -> q_gen_6321
<s, z, z>(q_gen_6334) -> q_gen_6321
<s, s, s>(q_gen_6320) -> q_gen_6348
<s, s, s>(q_gen_6348) -> q_gen_6348
<s, z, s>(q_gen_6355) -> q_gen_6348
}

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

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

Teacher's answer:
New clause system:
{
() -> drop([s(u), nil, nil]) -> 11
() -> drop([z, l, l]) -> 11
() -> length([nil, z]) -> 11
() -> minus([s(u), z, s(u)]) -> 11
() -> minus([z, y, z]) -> 11
(drop([n, l1, _sga]) /\ length([_sga, _tga]) /\ length([l1, _uga]) /\ minus([_uga, n, _vga])) -> eq_nat([_tga, _vga]) -> 13
(drop([u, x3, _ega])) -> drop([s(u), cons(x2, x3), _ega]) -> 13
(length([ll, _jga])) -> length([cons(x, ll), s(_jga)]) -> 12
(minus([u, x2, _nga])) -> minus([s(u), s(x2), _nga]) -> 16
}
Sat witness: Found: ((minus([u, x2, _nga])) -> minus([s(u), s(x2), _nga]), {
_nga -> z  ;  u -> s(z)  ;  x2 -> z
})

-------------------------------------------
Step 25, which took 0.029770 s (model generation: 0.026546,  model checking: 0.003224):

Model:
|_
{
drop -> 
{{{
Q={q_gen_6324, q_gen_6326, q_gen_6331, q_gen_6332, q_gen_6338, q_gen_6339},
Q_f={q_gen_6324},
Delta=
{
<s>(q_gen_6326) -> q_gen_6326
<z>() -> q_gen_6326
<a>() -> q_gen_6332
<b>() -> q_gen_6332
<s, cons>(q_gen_6332, q_gen_6331) -> q_gen_6331
<s, nil>(q_gen_6326) -> q_gen_6331
<z, nil>() -> q_gen_6331
<cons, cons>(q_gen_6339, q_gen_6338) -> q_gen_6338
<nil, nil>() -> q_gen_6338
<a, a>() -> q_gen_6339
<b, b>() -> q_gen_6339
<s, cons, nil>(q_gen_6332, q_gen_6331) -> q_gen_6324
<s, nil, nil>(q_gen_6326) -> q_gen_6324
<z, cons, cons>(q_gen_6339, q_gen_6338) -> q_gen_6324
<z, nil, nil>() -> q_gen_6324
}

Datatype: <nat, eltlist, eltlist>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_6323, q_gen_6329},
Q_f={q_gen_6323},
Delta=
{
<a>() -> q_gen_6329
<b>() -> q_gen_6329
<cons, s>(q_gen_6329, q_gen_6323) -> q_gen_6323
<nil, z>() -> q_gen_6323
}

Datatype: <eltlist, nat>
Convolution form: right
}}}
  ;  minus -> 
{{{
Q={q_gen_6320, q_gen_6322, q_gen_6334, q_gen_6343, q_gen_6355, q_gen_6358},
Q_f={q_gen_6320},
Delta=
{
<s>(q_gen_6334) -> q_gen_6334
<z>() -> q_gen_6334
<s, s>(q_gen_6322) -> q_gen_6322
<s, z>(q_gen_6334) -> q_gen_6322
<z, z>() -> q_gen_6322
<z, s>(q_gen_6334) -> q_gen_6355
<s, s, s>(q_gen_6343) -> q_gen_6320
<s, s, z>(q_gen_6322) -> q_gen_6320
<s, s, z>(q_gen_6355) -> q_gen_6320
<s, z, s>(q_gen_6322) -> q_gen_6320
<z, s, z>(q_gen_6334) -> q_gen_6320
<z, z, z>() -> q_gen_6320
<s, s, s>(q_gen_6320) -> q_gen_6343
<s, z, z>(q_gen_6334) -> q_gen_6343
<s, s, s>(q_gen_6358) -> q_gen_6358
<s, z, s>(q_gen_6355) -> q_gen_6358
}

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

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

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

-------------------------------------------
Step 26, which took 0.031414 s (model generation: 0.028468,  model checking: 0.002946):

Model:
|_
{
drop -> 
{{{
Q={q_gen_6324, q_gen_6326, q_gen_6331, q_gen_6332, q_gen_6338, q_gen_6339, q_gen_6371},
Q_f={q_gen_6324},
Delta=
{
<s>(q_gen_6326) -> q_gen_6326
<z>() -> q_gen_6326
<a>() -> q_gen_6332
<b>() -> q_gen_6332
<nil>() -> q_gen_6371
<s, cons>(q_gen_6332, q_gen_6331) -> q_gen_6331
<s, nil>(q_gen_6326) -> q_gen_6331
<z, nil>() -> q_gen_6331
<cons, cons>(q_gen_6339, q_gen_6338) -> q_gen_6338
<nil, nil>() -> q_gen_6338
<a, a>() -> q_gen_6339
<b, b>() -> q_gen_6339
<s, cons, cons>(q_gen_6339, q_gen_6324) -> q_gen_6324
<s, cons, nil>(q_gen_6332, q_gen_6331) -> q_gen_6324
<s, nil, nil>(q_gen_6326) -> q_gen_6324
<z, cons, cons>(q_gen_6339, q_gen_6338) -> q_gen_6324
<z, cons, nil>(q_gen_6332, q_gen_6371) -> q_gen_6324
<z, nil, nil>() -> q_gen_6324
}

Datatype: <nat, eltlist, eltlist>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_6323, q_gen_6329},
Q_f={q_gen_6323},
Delta=
{
<a>() -> q_gen_6329
<b>() -> q_gen_6329
<cons, s>(q_gen_6329, q_gen_6323) -> q_gen_6323
<nil, z>() -> q_gen_6323
}

Datatype: <eltlist, nat>
Convolution form: right
}}}
  ;  minus -> 
{{{
Q={q_gen_6320, q_gen_6322, q_gen_6334, q_gen_6343, q_gen_6355, q_gen_6358},
Q_f={q_gen_6320},
Delta=
{
<s>(q_gen_6334) -> q_gen_6334
<z>() -> q_gen_6334
<s, s>(q_gen_6322) -> q_gen_6322
<s, z>(q_gen_6334) -> q_gen_6322
<z, z>() -> q_gen_6322
<z, s>(q_gen_6334) -> q_gen_6355
<s, s, s>(q_gen_6343) -> q_gen_6320
<s, s, z>(q_gen_6322) -> q_gen_6320
<s, s, z>(q_gen_6355) -> q_gen_6320
<s, z, s>(q_gen_6322) -> q_gen_6320
<z, s, z>(q_gen_6334) -> q_gen_6320
<z, z, z>() -> q_gen_6320
<s, s, s>(q_gen_6320) -> q_gen_6343
<s, z, z>(q_gen_6334) -> q_gen_6343
<s, s, s>(q_gen_6358) -> q_gen_6358
<s, z, s>(q_gen_6355) -> q_gen_6358
}

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

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

Teacher's answer:
New clause system:
{
() -> drop([s(u), nil, nil]) -> 13
() -> drop([z, l, l]) -> 13
() -> length([nil, z]) -> 13
() -> minus([s(u), z, s(u)]) -> 13
() -> minus([z, y, z]) -> 13
(drop([n, l1, _sga]) /\ length([_sga, _tga]) /\ length([l1, _uga]) /\ minus([_uga, n, _vga])) -> eq_nat([_tga, _vga]) -> 16
(drop([u, x3, _ega])) -> drop([s(u), cons(x2, x3), _ega]) -> 16
(length([ll, _jga])) -> length([cons(x, ll), s(_jga)]) -> 14
(minus([u, x2, _nga])) -> minus([s(u), s(x2), _nga]) -> 16
}
Sat witness: Found: ((drop([n, l1, _sga]) /\ length([_sga, _tga]) /\ length([l1, _uga]) /\ minus([_uga, n, _vga])) -> eq_nat([_tga, _vga]), {
_sga -> nil  ;  _tga -> z  ;  _uga -> s(z)  ;  _vga -> s(z)  ;  l1 -> cons(b, nil)  ;  n -> z
})

-------------------------------------------
Step 27, which took 0.030761 s (model generation: 0.028367,  model checking: 0.002394):

Model:
|_
{
drop -> 
{{{
Q={q_gen_6324, q_gen_6326, q_gen_6331, q_gen_6332, q_gen_6338, q_gen_6339, q_gen_6370, q_gen_6371},
Q_f={q_gen_6324},
Delta=
{
<s>(q_gen_6326) -> q_gen_6326
<z>() -> q_gen_6326
<a>() -> q_gen_6332
<b>() -> q_gen_6332
<nil>() -> q_gen_6371
<s, cons>(q_gen_6332, q_gen_6331) -> q_gen_6331
<s, nil>(q_gen_6326) -> q_gen_6331
<z, nil>() -> q_gen_6331
<cons, cons>(q_gen_6339, q_gen_6338) -> q_gen_6338
<nil, nil>() -> q_gen_6338
<a, a>() -> q_gen_6339
<b, b>() -> q_gen_6339
<s, cons, cons>(q_gen_6339, q_gen_6370) -> q_gen_6324
<s, cons, nil>(q_gen_6332, q_gen_6331) -> q_gen_6324
<s, nil, nil>(q_gen_6326) -> q_gen_6324
<z, cons, cons>(q_gen_6339, q_gen_6338) -> q_gen_6324
<z, nil, nil>() -> q_gen_6324
<z, cons, nil>(q_gen_6332, q_gen_6371) -> q_gen_6370
}

Datatype: <nat, eltlist, eltlist>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_6323, q_gen_6329},
Q_f={q_gen_6323},
Delta=
{
<a>() -> q_gen_6329
<b>() -> q_gen_6329
<cons, s>(q_gen_6329, q_gen_6323) -> q_gen_6323
<nil, z>() -> q_gen_6323
}

Datatype: <eltlist, nat>
Convolution form: right
}}}
  ;  minus -> 
{{{
Q={q_gen_6320, q_gen_6322, q_gen_6334, q_gen_6343, q_gen_6355, q_gen_6358},
Q_f={q_gen_6320},
Delta=
{
<s>(q_gen_6334) -> q_gen_6334
<z>() -> q_gen_6334
<s, s>(q_gen_6322) -> q_gen_6322
<s, z>(q_gen_6334) -> q_gen_6322
<z, z>() -> q_gen_6322
<z, s>(q_gen_6334) -> q_gen_6355
<s, s, s>(q_gen_6343) -> q_gen_6320
<s, s, z>(q_gen_6322) -> q_gen_6320
<s, s, z>(q_gen_6355) -> q_gen_6320
<s, z, s>(q_gen_6322) -> q_gen_6320
<z, s, z>(q_gen_6334) -> q_gen_6320
<z, z, z>() -> q_gen_6320
<s, s, s>(q_gen_6320) -> q_gen_6343
<s, z, z>(q_gen_6334) -> q_gen_6343
<s, s, s>(q_gen_6358) -> q_gen_6358
<s, z, s>(q_gen_6355) -> q_gen_6358
}

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

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

Teacher's answer:
New clause system:
{
() -> drop([s(u), nil, nil]) -> 14
() -> drop([z, l, l]) -> 14
() -> length([nil, z]) -> 14
() -> minus([s(u), z, s(u)]) -> 14
() -> minus([z, y, z]) -> 14
(drop([n, l1, _sga]) /\ length([_sga, _tga]) /\ length([l1, _uga]) /\ minus([_uga, n, _vga])) -> eq_nat([_tga, _vga]) -> 16
(drop([u, x3, _ega])) -> drop([s(u), cons(x2, x3), _ega]) -> 16
(length([ll, _jga])) -> length([cons(x, ll), s(_jga)]) -> 15
(minus([u, x2, _nga])) -> minus([s(u), s(x2), _nga]) -> 19
}
Sat witness: Found: ((minus([u, x2, _nga])) -> minus([s(u), s(x2), _nga]), {
_nga -> s(s(z))  ;  u -> s(s(z))  ;  x2 -> z
})

-------------------------------------------
Step 28, which took 0.030788 s (model generation: 0.030458,  model checking: 0.000330):

Model:
|_
{
drop -> 
{{{
Q={q_gen_6324, q_gen_6326, q_gen_6331, q_gen_6332, q_gen_6338, q_gen_6339, q_gen_6370, q_gen_6371},
Q_f={q_gen_6324},
Delta=
{
<s>(q_gen_6326) -> q_gen_6326
<z>() -> q_gen_6326
<a>() -> q_gen_6332
<b>() -> q_gen_6332
<nil>() -> q_gen_6371
<s, cons>(q_gen_6332, q_gen_6331) -> q_gen_6331
<s, nil>(q_gen_6326) -> q_gen_6331
<z, nil>() -> q_gen_6331
<cons, cons>(q_gen_6339, q_gen_6338) -> q_gen_6338
<nil, nil>() -> q_gen_6338
<a, a>() -> q_gen_6339
<b, b>() -> q_gen_6339
<s, cons, cons>(q_gen_6339, q_gen_6370) -> q_gen_6324
<s, cons, nil>(q_gen_6332, q_gen_6331) -> q_gen_6324
<s, nil, nil>(q_gen_6326) -> q_gen_6324
<z, cons, cons>(q_gen_6339, q_gen_6338) -> q_gen_6324
<z, nil, nil>() -> q_gen_6324
<z, cons, nil>(q_gen_6332, q_gen_6371) -> q_gen_6370
}

Datatype: <nat, eltlist, eltlist>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_6323, q_gen_6329},
Q_f={q_gen_6323},
Delta=
{
<a>() -> q_gen_6329
<b>() -> q_gen_6329
<cons, s>(q_gen_6329, q_gen_6323) -> q_gen_6323
<nil, z>() -> q_gen_6323
}

Datatype: <eltlist, nat>
Convolution form: right
}}}
  ;  minus -> 
{{{
Q={q_gen_6320, q_gen_6322, q_gen_6334, q_gen_6343, q_gen_6350, q_gen_6355},
Q_f={q_gen_6320},
Delta=
{
<z>() -> q_gen_6334
<s>(q_gen_6334) -> q_gen_6350
<s, s>(q_gen_6322) -> q_gen_6322
<z, s>(q_gen_6350) -> q_gen_6322
<z, z>() -> q_gen_6322
<s, z>(q_gen_6334) -> q_gen_6355
<z, s>(q_gen_6334) -> q_gen_6355
<s, s, s>(q_gen_6343) -> q_gen_6320
<s, s, z>(q_gen_6322) -> q_gen_6320
<s, s, z>(q_gen_6355) -> q_gen_6320
<s, z, s>(q_gen_6322) -> q_gen_6320
<z, s, z>(q_gen_6334) -> q_gen_6320
<z, s, z>(q_gen_6350) -> q_gen_6320
<z, z, z>() -> q_gen_6320
<s, s, s>(q_gen_6320) -> q_gen_6343
<s, z, s>(q_gen_6355) -> q_gen_6343
<s, z, z>(q_gen_6334) -> q_gen_6343
}

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

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

Teacher's answer:
New clause system:
{
() -> drop([s(u), nil, nil]) -> 14
() -> drop([z, l, l]) -> 14
() -> length([nil, z]) -> 14
() -> minus([s(u), z, s(u)]) -> 14
() -> minus([z, y, z]) -> 17
(drop([n, l1, _sga]) /\ length([_sga, _tga]) /\ length([l1, _uga]) /\ minus([_uga, n, _vga])) -> eq_nat([_tga, _vga]) -> 16
(drop([u, x3, _ega])) -> drop([s(u), cons(x2, x3), _ega]) -> 16
(length([ll, _jga])) -> length([cons(x, ll), s(_jga)]) -> 15
(minus([u, x2, _nga])) -> minus([s(u), s(x2), _nga]) -> 19
}
Sat witness: Found: (() -> minus([z, y, z]), {
y -> s(s(s(z)))
})

-------------------------------------------
Step 29, which took 0.036612 s (model generation: 0.032838,  model checking: 0.003774):

Model:
|_
{
drop -> 
{{{
Q={q_gen_6324, q_gen_6326, q_gen_6331, q_gen_6332, q_gen_6338, q_gen_6339, q_gen_6370, q_gen_6371},
Q_f={q_gen_6324},
Delta=
{
<s>(q_gen_6326) -> q_gen_6326
<z>() -> q_gen_6326
<a>() -> q_gen_6332
<b>() -> q_gen_6332
<nil>() -> q_gen_6371
<s, cons>(q_gen_6332, q_gen_6331) -> q_gen_6331
<s, nil>(q_gen_6326) -> q_gen_6331
<z, nil>() -> q_gen_6331
<cons, cons>(q_gen_6339, q_gen_6338) -> q_gen_6338
<nil, nil>() -> q_gen_6338
<a, a>() -> q_gen_6339
<b, b>() -> q_gen_6339
<s, cons, cons>(q_gen_6339, q_gen_6370) -> q_gen_6324
<s, cons, nil>(q_gen_6332, q_gen_6331) -> q_gen_6324
<s, nil, nil>(q_gen_6326) -> q_gen_6324
<z, cons, cons>(q_gen_6339, q_gen_6338) -> q_gen_6324
<z, nil, nil>() -> q_gen_6324
<z, cons, nil>(q_gen_6332, q_gen_6371) -> q_gen_6370
}

Datatype: <nat, eltlist, eltlist>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_6323, q_gen_6329},
Q_f={q_gen_6323},
Delta=
{
<a>() -> q_gen_6329
<b>() -> q_gen_6329
<cons, s>(q_gen_6329, q_gen_6323) -> q_gen_6323
<nil, z>() -> q_gen_6323
}

Datatype: <eltlist, nat>
Convolution form: right
}}}
  ;  minus -> 
{{{
Q={q_gen_6320, q_gen_6322, q_gen_6334, q_gen_6343, q_gen_6350, q_gen_6355},
Q_f={q_gen_6320},
Delta=
{
<z>() -> q_gen_6334
<s>(q_gen_6334) -> q_gen_6350
<s>(q_gen_6350) -> q_gen_6350
<s, s>(q_gen_6322) -> q_gen_6322
<z, s>(q_gen_6350) -> q_gen_6322
<z, z>() -> q_gen_6322
<s, z>(q_gen_6334) -> q_gen_6355
<z, s>(q_gen_6334) -> q_gen_6355
<s, s, s>(q_gen_6343) -> q_gen_6320
<s, s, z>(q_gen_6322) -> q_gen_6320
<s, s, z>(q_gen_6355) -> q_gen_6320
<s, z, s>(q_gen_6322) -> q_gen_6320
<z, s, z>(q_gen_6334) -> q_gen_6320
<z, s, z>(q_gen_6350) -> q_gen_6320
<z, z, z>() -> q_gen_6320
<s, s, s>(q_gen_6320) -> q_gen_6343
<s, z, s>(q_gen_6355) -> q_gen_6343
<s, z, z>(q_gen_6334) -> q_gen_6343
}

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

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

Teacher's answer:
New clause system:
{
() -> drop([s(u), nil, nil]) -> 15
() -> drop([z, l, l]) -> 15
() -> length([nil, z]) -> 15
() -> minus([s(u), z, s(u)]) -> 15
() -> minus([z, y, z]) -> 17
(drop([n, l1, _sga]) /\ length([_sga, _tga]) /\ length([l1, _uga]) /\ minus([_uga, n, _vga])) -> eq_nat([_tga, _vga]) -> 16
(drop([u, x3, _ega])) -> drop([s(u), cons(x2, x3), _ega]) -> 19
(length([ll, _jga])) -> length([cons(x, ll), s(_jga)]) -> 16
(minus([u, x2, _nga])) -> minus([s(u), s(x2), _nga]) -> 19
}
Sat witness: Found: ((drop([u, x3, _ega])) -> drop([s(u), cons(x2, x3), _ega]), {
_ega -> cons(b, nil)  ;  u -> s(z)  ;  x2 -> b  ;  x3 -> cons(b, cons(b, nil))
})

-------------------------------------------
Step 30, which took 0.038887 s (model generation: 0.035598,  model checking: 0.003289):

Model:
|_
{
drop -> 
{{{
Q={q_gen_6324, q_gen_6326, q_gen_6331, q_gen_6332, q_gen_6338, q_gen_6339, q_gen_6370, q_gen_6371},
Q_f={q_gen_6324},
Delta=
{
<s>(q_gen_6326) -> q_gen_6326
<z>() -> q_gen_6326
<a>() -> q_gen_6332
<b>() -> q_gen_6332
<nil>() -> q_gen_6371
<s, cons>(q_gen_6332, q_gen_6331) -> q_gen_6331
<s, nil>(q_gen_6326) -> q_gen_6331
<z, cons>(q_gen_6332, q_gen_6371) -> q_gen_6331
<z, nil>() -> q_gen_6331
<cons, cons>(q_gen_6339, q_gen_6338) -> q_gen_6338
<nil, nil>() -> q_gen_6338
<a, a>() -> q_gen_6339
<b, b>() -> q_gen_6339
<s, cons, cons>(q_gen_6339, q_gen_6324) -> q_gen_6324
<s, cons, cons>(q_gen_6339, q_gen_6370) -> q_gen_6324
<s, cons, nil>(q_gen_6332, q_gen_6331) -> q_gen_6324
<s, nil, nil>(q_gen_6326) -> q_gen_6324
<z, cons, cons>(q_gen_6339, q_gen_6338) -> q_gen_6324
<z, nil, nil>() -> q_gen_6324
<z, cons, nil>(q_gen_6332, q_gen_6371) -> q_gen_6370
}

Datatype: <nat, eltlist, eltlist>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_6323, q_gen_6329},
Q_f={q_gen_6323},
Delta=
{
<a>() -> q_gen_6329
<b>() -> q_gen_6329
<cons, s>(q_gen_6329, q_gen_6323) -> q_gen_6323
<nil, z>() -> q_gen_6323
}

Datatype: <eltlist, nat>
Convolution form: right
}}}
  ;  minus -> 
{{{
Q={q_gen_6320, q_gen_6322, q_gen_6334, q_gen_6343, q_gen_6350, q_gen_6355},
Q_f={q_gen_6320},
Delta=
{
<z>() -> q_gen_6334
<s>(q_gen_6334) -> q_gen_6350
<s>(q_gen_6350) -> q_gen_6350
<s, s>(q_gen_6322) -> q_gen_6322
<z, s>(q_gen_6350) -> q_gen_6322
<z, z>() -> q_gen_6322
<s, z>(q_gen_6334) -> q_gen_6355
<z, s>(q_gen_6334) -> q_gen_6355
<s, s, s>(q_gen_6343) -> q_gen_6320
<s, s, z>(q_gen_6322) -> q_gen_6320
<s, s, z>(q_gen_6355) -> q_gen_6320
<s, z, s>(q_gen_6322) -> q_gen_6320
<z, s, z>(q_gen_6334) -> q_gen_6320
<z, s, z>(q_gen_6350) -> q_gen_6320
<z, z, z>() -> q_gen_6320
<s, s, s>(q_gen_6320) -> q_gen_6343
<s, z, s>(q_gen_6355) -> q_gen_6343
<s, z, z>(q_gen_6334) -> q_gen_6343
}

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

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

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

-------------------------------------------
Step 31, which took 0.040061 s (model generation: 0.037045,  model checking: 0.003016):

Model:
|_
{
drop -> 
{{{
Q={q_gen_6324, q_gen_6326, q_gen_6331, q_gen_6332, q_gen_6338, q_gen_6339, q_gen_6370, q_gen_6371, q_gen_6378},
Q_f={q_gen_6324},
Delta=
{
<s>(q_gen_6326) -> q_gen_6326
<z>() -> q_gen_6326
<a>() -> q_gen_6332
<b>() -> q_gen_6332
<nil>() -> q_gen_6371
<s, cons>(q_gen_6332, q_gen_6331) -> q_gen_6331
<s, nil>(q_gen_6326) -> q_gen_6331
<z, nil>() -> q_gen_6331
<cons, cons>(q_gen_6339, q_gen_6338) -> q_gen_6338
<nil, nil>() -> q_gen_6338
<a, a>() -> q_gen_6339
<b, b>() -> q_gen_6339
<z, cons>(q_gen_6332, q_gen_6371) -> q_gen_6378
<s, cons, cons>(q_gen_6339, q_gen_6370) -> q_gen_6324
<s, cons, nil>(q_gen_6332, q_gen_6331) -> q_gen_6324
<s, nil, nil>(q_gen_6326) -> q_gen_6324
<z, cons, cons>(q_gen_6339, q_gen_6338) -> q_gen_6324
<z, nil, nil>() -> q_gen_6324
<s, cons, nil>(q_gen_6332, q_gen_6378) -> q_gen_6370
<z, cons, nil>(q_gen_6332, q_gen_6371) -> q_gen_6370
}

Datatype: <nat, eltlist, eltlist>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_6323, q_gen_6329},
Q_f={q_gen_6323},
Delta=
{
<a>() -> q_gen_6329
<b>() -> q_gen_6329
<cons, s>(q_gen_6329, q_gen_6323) -> q_gen_6323
<nil, z>() -> q_gen_6323
}

Datatype: <eltlist, nat>
Convolution form: right
}}}
  ;  minus -> 
{{{
Q={q_gen_6320, q_gen_6322, q_gen_6334, q_gen_6343, q_gen_6350, q_gen_6355},
Q_f={q_gen_6320},
Delta=
{
<z>() -> q_gen_6334
<s>(q_gen_6334) -> q_gen_6350
<s>(q_gen_6350) -> q_gen_6350
<s, s>(q_gen_6322) -> q_gen_6322
<z, s>(q_gen_6350) -> q_gen_6322
<z, z>() -> q_gen_6322
<s, z>(q_gen_6334) -> q_gen_6355
<z, s>(q_gen_6334) -> q_gen_6355
<s, s, s>(q_gen_6343) -> q_gen_6320
<s, s, z>(q_gen_6322) -> q_gen_6320
<s, s, z>(q_gen_6355) -> q_gen_6320
<s, z, s>(q_gen_6322) -> q_gen_6320
<z, s, z>(q_gen_6334) -> q_gen_6320
<z, s, z>(q_gen_6350) -> q_gen_6320
<z, z, z>() -> q_gen_6320
<s, s, s>(q_gen_6320) -> q_gen_6343
<s, z, s>(q_gen_6355) -> q_gen_6343
<s, z, z>(q_gen_6334) -> q_gen_6343
}

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

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

Teacher's answer:
New clause system:
{
() -> drop([s(u), nil, nil]) -> 17
() -> drop([z, l, l]) -> 17
() -> length([nil, z]) -> 17
() -> minus([s(u), z, s(u)]) -> 17
() -> minus([z, y, z]) -> 18
(drop([n, l1, _sga]) /\ length([_sga, _tga]) /\ length([l1, _uga]) /\ minus([_uga, n, _vga])) -> eq_nat([_tga, _vga]) -> 19
(drop([u, x3, _ega])) -> drop([s(u), cons(x2, x3), _ega]) -> 19
(length([ll, _jga])) -> length([cons(x, ll), s(_jga)]) -> 18
(minus([u, x2, _nga])) -> minus([s(u), s(x2), _nga]) -> 22
}
Sat witness: Found: ((minus([u, x2, _nga])) -> minus([s(u), s(x2), _nga]), {
_nga -> s(z)  ;  u -> s(s(z))  ;  x2 -> s(z)
})

-------------------------------------------
Step 32, which took 0.045288 s (model generation: 0.039951,  model checking: 0.005337):

Model:
|_
{
drop -> 
{{{
Q={q_gen_6324, q_gen_6326, q_gen_6331, q_gen_6332, q_gen_6338, q_gen_6339, q_gen_6370, q_gen_6371, q_gen_6378},
Q_f={q_gen_6324},
Delta=
{
<s>(q_gen_6326) -> q_gen_6326
<z>() -> q_gen_6326
<a>() -> q_gen_6332
<b>() -> q_gen_6332
<nil>() -> q_gen_6371
<s, cons>(q_gen_6332, q_gen_6331) -> q_gen_6331
<s, nil>(q_gen_6326) -> q_gen_6331
<z, nil>() -> q_gen_6331
<cons, cons>(q_gen_6339, q_gen_6338) -> q_gen_6338
<nil, nil>() -> q_gen_6338
<a, a>() -> q_gen_6339
<b, b>() -> q_gen_6339
<z, cons>(q_gen_6332, q_gen_6371) -> q_gen_6378
<s, cons, cons>(q_gen_6339, q_gen_6370) -> q_gen_6324
<s, cons, nil>(q_gen_6332, q_gen_6331) -> q_gen_6324
<s, nil, nil>(q_gen_6326) -> q_gen_6324
<z, cons, cons>(q_gen_6339, q_gen_6338) -> q_gen_6324
<z, nil, nil>() -> q_gen_6324
<s, cons, nil>(q_gen_6332, q_gen_6378) -> q_gen_6370
<z, cons, nil>(q_gen_6332, q_gen_6371) -> q_gen_6370
}

Datatype: <nat, eltlist, eltlist>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_6323, q_gen_6329},
Q_f={q_gen_6323},
Delta=
{
<a>() -> q_gen_6329
<b>() -> q_gen_6329
<cons, s>(q_gen_6329, q_gen_6323) -> q_gen_6323
<nil, z>() -> q_gen_6323
}

Datatype: <eltlist, nat>
Convolution form: right
}}}
  ;  minus -> 
{{{
Q={q_gen_6320, q_gen_6321, q_gen_6322, q_gen_6334, q_gen_6348, q_gen_6355},
Q_f={q_gen_6320, q_gen_6321},
Delta=
{
<s>(q_gen_6334) -> q_gen_6334
<z>() -> q_gen_6334
<s, s>(q_gen_6322) -> q_gen_6322
<s, z>(q_gen_6334) -> q_gen_6322
<z, z>() -> q_gen_6322
<z, s>(q_gen_6334) -> q_gen_6355
<s, s, s>(q_gen_6321) -> q_gen_6320
<z, s, z>(q_gen_6334) -> q_gen_6320
<z, z, z>() -> q_gen_6320
<s, s, z>(q_gen_6322) -> q_gen_6321
<s, s, z>(q_gen_6355) -> q_gen_6321
<s, z, s>(q_gen_6322) -> q_gen_6321
<s, z, z>(q_gen_6334) -> q_gen_6321
<s, s, s>(q_gen_6320) -> q_gen_6348
<s, s, s>(q_gen_6348) -> q_gen_6348
<s, z, s>(q_gen_6355) -> q_gen_6348
}

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

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

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

-------------------------------------------
Step 33, which took 0.046777 s (model generation: 0.043837,  model checking: 0.002940):

Model:
|_
{
drop -> 
{{{
Q={q_gen_6324, q_gen_6326, q_gen_6331, q_gen_6332, q_gen_6338, q_gen_6339, q_gen_6370, q_gen_6371, q_gen_6378},
Q_f={q_gen_6324},
Delta=
{
<s>(q_gen_6326) -> q_gen_6326
<z>() -> q_gen_6326
<a>() -> q_gen_6332
<b>() -> q_gen_6332
<nil>() -> q_gen_6371
<s, cons>(q_gen_6332, q_gen_6331) -> q_gen_6331
<s, nil>(q_gen_6326) -> q_gen_6331
<z, nil>() -> q_gen_6331
<cons, cons>(q_gen_6339, q_gen_6338) -> q_gen_6338
<nil, nil>() -> q_gen_6338
<a, a>() -> q_gen_6339
<b, a>() -> q_gen_6339
<b, b>() -> q_gen_6339
<z, cons>(q_gen_6332, q_gen_6371) -> q_gen_6378
<s, cons, cons>(q_gen_6339, q_gen_6370) -> q_gen_6324
<s, cons, nil>(q_gen_6332, q_gen_6331) -> q_gen_6324
<s, nil, nil>(q_gen_6326) -> q_gen_6324
<z, cons, cons>(q_gen_6339, q_gen_6338) -> q_gen_6324
<z, nil, nil>() -> q_gen_6324
<s, cons, nil>(q_gen_6332, q_gen_6378) -> q_gen_6370
<z, cons, nil>(q_gen_6332, q_gen_6371) -> q_gen_6370
}

Datatype: <nat, eltlist, eltlist>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_6323, q_gen_6329},
Q_f={q_gen_6323},
Delta=
{
<a>() -> q_gen_6329
<b>() -> q_gen_6329
<cons, s>(q_gen_6329, q_gen_6323) -> q_gen_6323
<nil, z>() -> q_gen_6323
}

Datatype: <eltlist, nat>
Convolution form: right
}}}
  ;  minus -> 
{{{
Q={q_gen_6320, q_gen_6322, q_gen_6327, q_gen_6334, q_gen_6348, q_gen_6355},
Q_f={q_gen_6320, q_gen_6327},
Delta=
{
<s>(q_gen_6334) -> q_gen_6334
<z>() -> q_gen_6334
<s, s>(q_gen_6322) -> q_gen_6322
<z, z>() -> q_gen_6322
<s, z>(q_gen_6334) -> q_gen_6355
<z, s>(q_gen_6334) -> q_gen_6355
<s, s, s>(q_gen_6327) -> q_gen_6320
<s, z, s>(q_gen_6322) -> q_gen_6320
<z, s, z>(q_gen_6334) -> q_gen_6320
<z, z, z>() -> q_gen_6320
<s, s, s>(q_gen_6348) -> q_gen_6327
<s, s, z>(q_gen_6322) -> q_gen_6327
<s, s, z>(q_gen_6355) -> q_gen_6327
<s, z, z>(q_gen_6334) -> q_gen_6327
<s, s, s>(q_gen_6320) -> q_gen_6348
<s, z, s>(q_gen_6355) -> q_gen_6348
}

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

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

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

-------------------------------------------
Step 34, which took 0.046057 s (model generation: 0.043510,  model checking: 0.002547):

Model:
|_
{
drop -> 
{{{
Q={q_gen_6324, q_gen_6326, q_gen_6331, q_gen_6332, q_gen_6338, q_gen_6339, q_gen_6370, q_gen_6371},
Q_f={q_gen_6324},
Delta=
{
<s>(q_gen_6326) -> q_gen_6326
<z>() -> q_gen_6326
<a>() -> q_gen_6332
<b>() -> q_gen_6332
<nil>() -> q_gen_6371
<s, cons>(q_gen_6332, q_gen_6331) -> q_gen_6331
<s, nil>(q_gen_6326) -> q_gen_6331
<z, cons>(q_gen_6332, q_gen_6371) -> q_gen_6331
<z, nil>() -> q_gen_6331
<cons, cons>(q_gen_6339, q_gen_6338) -> q_gen_6338
<nil, nil>() -> q_gen_6338
<a, a>() -> q_gen_6339
<b, a>() -> q_gen_6339
<b, b>() -> q_gen_6339
<s, cons, cons>(q_gen_6339, q_gen_6324) -> q_gen_6324
<s, cons, cons>(q_gen_6339, q_gen_6370) -> q_gen_6324
<s, cons, nil>(q_gen_6332, q_gen_6331) -> q_gen_6324
<s, nil, nil>(q_gen_6326) -> q_gen_6324
<z, cons, cons>(q_gen_6339, q_gen_6338) -> q_gen_6324
<z, nil, nil>() -> q_gen_6324
<z, cons, nil>(q_gen_6332, q_gen_6371) -> q_gen_6370
}

Datatype: <nat, eltlist, eltlist>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_6323, q_gen_6328, q_gen_6329, q_gen_6379},
Q_f={q_gen_6323, q_gen_6328},
Delta=
{
<a>() -> q_gen_6329
<b>() -> q_gen_6329
<nil, z>() -> q_gen_6323
<cons, s>(q_gen_6329, q_gen_6323) -> q_gen_6328
<cons, s>(q_gen_6329, q_gen_6328) -> q_gen_6379
}

Datatype: <eltlist, nat>
Convolution form: right
}}}
  ;  minus -> 
{{{
Q={q_gen_6320, q_gen_6322, q_gen_6334, q_gen_6342, q_gen_6348, q_gen_6355},
Q_f={q_gen_6320, q_gen_6342},
Delta=
{
<s>(q_gen_6334) -> q_gen_6334
<z>() -> q_gen_6334
<s, s>(q_gen_6322) -> q_gen_6322
<z, z>() -> q_gen_6322
<s, z>(q_gen_6334) -> q_gen_6355
<z, s>(q_gen_6334) -> q_gen_6355
<s, s, z>(q_gen_6322) -> q_gen_6320
<s, z, s>(q_gen_6322) -> q_gen_6320
<z, s, z>(q_gen_6334) -> q_gen_6320
<z, z, z>() -> q_gen_6320
<s, s, s>(q_gen_6342) -> q_gen_6342
<s, s, s>(q_gen_6348) -> q_gen_6342
<s, s, z>(q_gen_6355) -> q_gen_6342
<s, z, z>(q_gen_6334) -> q_gen_6342
<s, s, s>(q_gen_6320) -> q_gen_6348
<s, z, s>(q_gen_6355) -> q_gen_6348
}

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

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

Teacher's answer:
New clause system:
{
() -> drop([s(u), nil, nil]) -> 20
() -> drop([z, l, l]) -> 20
() -> length([nil, z]) -> 20
() -> minus([s(u), z, s(u)]) -> 20
() -> minus([z, y, z]) -> 20
(drop([n, l1, _sga]) /\ length([_sga, _tga]) /\ length([l1, _uga]) /\ minus([_uga, n, _vga])) -> eq_nat([_tga, _vga]) -> 22
(drop([u, x3, _ega])) -> drop([s(u), cons(x2, x3), _ega]) -> 22
(length([ll, _jga])) -> length([cons(x, ll), s(_jga)]) -> 23
(minus([u, x2, _nga])) -> minus([s(u), s(x2), _nga]) -> 22
}
Sat witness: Found: ((length([ll, _jga])) -> length([cons(x, ll), s(_jga)]), {
_jga -> s(z)  ;  ll -> cons(a, nil)  ;  x -> b
})

-------------------------------------------
Step 35, which took 0.044687 s (model generation: 0.044100,  model checking: 0.000587):

Model:
|_
{
drop -> 
{{{
Q={q_gen_6324, q_gen_6326, q_gen_6331, q_gen_6332, q_gen_6338, q_gen_6339, q_gen_6370, q_gen_6371, q_gen_6378},
Q_f={q_gen_6324},
Delta=
{
<s>(q_gen_6326) -> q_gen_6326
<z>() -> q_gen_6326
<a>() -> q_gen_6332
<b>() -> q_gen_6332
<nil>() -> q_gen_6371
<s, cons>(q_gen_6332, q_gen_6331) -> q_gen_6331
<s, nil>(q_gen_6326) -> q_gen_6331
<z, nil>() -> q_gen_6331
<cons, cons>(q_gen_6339, q_gen_6338) -> q_gen_6338
<nil, nil>() -> q_gen_6338
<a, a>() -> q_gen_6339
<b, a>() -> q_gen_6339
<b, b>() -> q_gen_6339
<z, cons>(q_gen_6332, q_gen_6371) -> q_gen_6378
<s, cons, cons>(q_gen_6339, q_gen_6370) -> q_gen_6324
<s, cons, nil>(q_gen_6332, q_gen_6331) -> q_gen_6324
<s, nil, nil>(q_gen_6326) -> q_gen_6324
<z, cons, cons>(q_gen_6339, q_gen_6338) -> q_gen_6324
<z, nil, nil>() -> q_gen_6324
<s, cons, nil>(q_gen_6332, q_gen_6378) -> q_gen_6370
<z, cons, nil>(q_gen_6332, q_gen_6371) -> q_gen_6370
}

Datatype: <nat, eltlist, eltlist>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_6323, q_gen_6329},
Q_f={q_gen_6323},
Delta=
{
<a>() -> q_gen_6329
<b>() -> q_gen_6329
<cons, s>(q_gen_6329, q_gen_6323) -> q_gen_6323
<nil, z>() -> q_gen_6323
}

Datatype: <eltlist, nat>
Convolution form: right
}}}
  ;  minus -> 
{{{
Q={q_gen_6320, q_gen_6322, q_gen_6327, q_gen_6334, q_gen_6336, q_gen_6343, q_gen_6355},
Q_f={q_gen_6320, q_gen_6327},
Delta=
{
<s>(q_gen_6334) -> q_gen_6334
<z>() -> q_gen_6334
<z, z>() -> q_gen_6322
<s, s>(q_gen_6322) -> q_gen_6336
<s, z>(q_gen_6334) -> q_gen_6336
<z, s>(q_gen_6334) -> q_gen_6355
<s, z, s>(q_gen_6322) -> q_gen_6320
<z, s, z>(q_gen_6334) -> q_gen_6320
<z, z, z>() -> q_gen_6320
<s, s, s>(q_gen_6327) -> q_gen_6327
<s, s, s>(q_gen_6343) -> q_gen_6327
<s, s, z>(q_gen_6322) -> q_gen_6327
<s, s, z>(q_gen_6355) -> q_gen_6327
<s, z, s>(q_gen_6336) -> q_gen_6327
<s, s, s>(q_gen_6320) -> q_gen_6343
<s, s, z>(q_gen_6336) -> q_gen_6343
<s, z, s>(q_gen_6355) -> q_gen_6343
<s, z, z>(q_gen_6334) -> q_gen_6343
}

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

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

Teacher's answer:
New clause system:
{
() -> drop([s(u), nil, nil]) -> 20
() -> drop([z, l, l]) -> 20
() -> length([nil, z]) -> 20
() -> minus([s(u), z, s(u)]) -> 23
() -> minus([z, y, z]) -> 21
(drop([n, l1, _sga]) /\ length([_sga, _tga]) /\ length([l1, _uga]) /\ minus([_uga, n, _vga])) -> eq_nat([_tga, _vga]) -> 22
(drop([u, x3, _ega])) -> drop([s(u), cons(x2, x3), _ega]) -> 22
(length([ll, _jga])) -> length([cons(x, ll), s(_jga)]) -> 23
(minus([u, x2, _nga])) -> minus([s(u), s(x2), _nga]) -> 22
}
Sat witness: Found: (() -> minus([s(u), z, s(u)]), {
u -> s(s(z))
})

-------------------------------------------
Step 36, which took 0.046515 s (model generation: 0.044728,  model checking: 0.001787):

Model:
|_
{
drop -> 
{{{
Q={q_gen_6324, q_gen_6326, q_gen_6331, q_gen_6332, q_gen_6338, q_gen_6339, q_gen_6370, q_gen_6371, q_gen_6378},
Q_f={q_gen_6324},
Delta=
{
<s>(q_gen_6326) -> q_gen_6326
<z>() -> q_gen_6326
<a>() -> q_gen_6332
<b>() -> q_gen_6332
<nil>() -> q_gen_6371
<s, cons>(q_gen_6332, q_gen_6331) -> q_gen_6331
<s, nil>(q_gen_6326) -> q_gen_6331
<z, nil>() -> q_gen_6331
<cons, cons>(q_gen_6339, q_gen_6338) -> q_gen_6338
<nil, nil>() -> q_gen_6338
<a, a>() -> q_gen_6339
<b, a>() -> q_gen_6339
<b, b>() -> q_gen_6339
<z, cons>(q_gen_6332, q_gen_6371) -> q_gen_6378
<s, cons, cons>(q_gen_6339, q_gen_6370) -> q_gen_6324
<s, cons, nil>(q_gen_6332, q_gen_6331) -> q_gen_6324
<s, nil, nil>(q_gen_6326) -> q_gen_6324
<z, cons, cons>(q_gen_6339, q_gen_6338) -> q_gen_6324
<z, nil, nil>() -> q_gen_6324
<s, cons, nil>(q_gen_6332, q_gen_6378) -> q_gen_6370
<z, cons, nil>(q_gen_6332, q_gen_6371) -> q_gen_6370
}

Datatype: <nat, eltlist, eltlist>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_6323, q_gen_6329},
Q_f={q_gen_6323},
Delta=
{
<a>() -> q_gen_6329
<b>() -> q_gen_6329
<cons, s>(q_gen_6329, q_gen_6323) -> q_gen_6323
<nil, z>() -> q_gen_6323
}

Datatype: <eltlist, nat>
Convolution form: right
}}}
  ;  minus -> 
{{{
Q={q_gen_6320, q_gen_6322, q_gen_6327, q_gen_6334, q_gen_6336, q_gen_6343, q_gen_6355},
Q_f={q_gen_6320, q_gen_6327},
Delta=
{
<s>(q_gen_6334) -> q_gen_6334
<z>() -> q_gen_6334
<s, s>(q_gen_6336) -> q_gen_6322
<z, z>() -> q_gen_6322
<s, s>(q_gen_6322) -> q_gen_6336
<s, z>(q_gen_6334) -> q_gen_6336
<z, s>(q_gen_6334) -> q_gen_6355
<s, z, s>(q_gen_6322) -> q_gen_6320
<z, s, z>(q_gen_6334) -> q_gen_6320
<z, z, z>() -> q_gen_6320
<s, s, s>(q_gen_6327) -> q_gen_6327
<s, s, s>(q_gen_6343) -> q_gen_6327
<s, s, z>(q_gen_6322) -> q_gen_6327
<s, s, z>(q_gen_6355) -> q_gen_6327
<s, z, s>(q_gen_6336) -> q_gen_6327
<s, s, s>(q_gen_6320) -> q_gen_6343
<s, s, z>(q_gen_6336) -> q_gen_6343
<s, z, s>(q_gen_6355) -> q_gen_6343
<s, z, z>(q_gen_6334) -> q_gen_6343
}

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

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

Teacher's answer:
New clause system:
{
() -> drop([s(u), nil, nil]) -> 21
() -> drop([z, l, l]) -> 21
() -> length([nil, z]) -> 21
() -> minus([s(u), z, s(u)]) -> 23
() -> minus([z, y, z]) -> 22
(drop([n, l1, _sga]) /\ length([_sga, _tga]) /\ length([l1, _uga]) /\ minus([_uga, n, _vga])) -> eq_nat([_tga, _vga]) -> 22
(drop([u, x3, _ega])) -> drop([s(u), cons(x2, x3), _ega]) -> 22
(length([ll, _jga])) -> length([cons(x, ll), s(_jga)]) -> 23
(minus([u, x2, _nga])) -> minus([s(u), s(x2), _nga]) -> 25
}
Sat witness: Found: ((minus([u, x2, _nga])) -> minus([s(u), s(x2), _nga]), {
_nga -> z  ;  u -> s(z)  ;  x2 -> s(z)
})

-------------------------------------------
Step 37, which took 0.051614 s (model generation: 0.046799,  model checking: 0.004815):

Model:
|_
{
drop -> 
{{{
Q={q_gen_6324, q_gen_6326, q_gen_6331, q_gen_6332, q_gen_6338, q_gen_6339, q_gen_6370, q_gen_6371, q_gen_6378},
Q_f={q_gen_6324},
Delta=
{
<s>(q_gen_6326) -> q_gen_6326
<z>() -> q_gen_6326
<a>() -> q_gen_6332
<b>() -> q_gen_6332
<nil>() -> q_gen_6371
<s, cons>(q_gen_6332, q_gen_6331) -> q_gen_6331
<s, nil>(q_gen_6326) -> q_gen_6331
<z, nil>() -> q_gen_6331
<cons, cons>(q_gen_6339, q_gen_6338) -> q_gen_6338
<nil, nil>() -> q_gen_6338
<a, a>() -> q_gen_6339
<b, a>() -> q_gen_6339
<b, b>() -> q_gen_6339
<z, cons>(q_gen_6332, q_gen_6371) -> q_gen_6378
<s, cons, cons>(q_gen_6339, q_gen_6370) -> q_gen_6324
<s, cons, nil>(q_gen_6332, q_gen_6331) -> q_gen_6324
<s, nil, nil>(q_gen_6326) -> q_gen_6324
<z, cons, cons>(q_gen_6339, q_gen_6338) -> q_gen_6324
<z, nil, nil>() -> q_gen_6324
<s, cons, nil>(q_gen_6332, q_gen_6378) -> q_gen_6370
<z, cons, nil>(q_gen_6332, q_gen_6371) -> q_gen_6370
}

Datatype: <nat, eltlist, eltlist>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_6323, q_gen_6329},
Q_f={q_gen_6323},
Delta=
{
<a>() -> q_gen_6329
<b>() -> q_gen_6329
<cons, s>(q_gen_6329, q_gen_6323) -> q_gen_6323
<nil, z>() -> q_gen_6323
}

Datatype: <eltlist, nat>
Convolution form: right
}}}
  ;  minus -> 
{{{
Q={q_gen_6320, q_gen_6322, q_gen_6334, q_gen_6343, q_gen_6350, q_gen_6355, q_gen_6368},
Q_f={q_gen_6320},
Delta=
{
<z>() -> q_gen_6334
<s>(q_gen_6334) -> q_gen_6350
<s>(q_gen_6350) -> q_gen_6350
<s, s>(q_gen_6322) -> q_gen_6322
<z, s>(q_gen_6350) -> q_gen_6322
<z, z>() -> q_gen_6322
<z, s>(q_gen_6334) -> q_gen_6355
<s, z>(q_gen_6334) -> q_gen_6368
<s, s, s>(q_gen_6343) -> q_gen_6320
<s, s, z>(q_gen_6322) -> q_gen_6320
<s, s, z>(q_gen_6355) -> q_gen_6320
<s, z, s>(q_gen_6322) -> q_gen_6320
<z, s, z>(q_gen_6334) -> q_gen_6320
<z, s, z>(q_gen_6350) -> q_gen_6320
<z, z, z>() -> q_gen_6320
<s, s, s>(q_gen_6320) -> q_gen_6343
<s, s, z>(q_gen_6368) -> q_gen_6343
<s, z, s>(q_gen_6355) -> q_gen_6343
<s, z, s>(q_gen_6368) -> q_gen_6343
<s, z, z>(q_gen_6334) -> q_gen_6343
}

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

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

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

-------------------------------------------
Step 38, which took 0.052227 s (model generation: 0.051430,  model checking: 0.000797):

Model:
|_
{
drop -> 
{{{
Q={q_gen_6324, q_gen_6326, q_gen_6331, q_gen_6332, q_gen_6338, q_gen_6339, q_gen_6370, q_gen_6371, q_gen_6378},
Q_f={q_gen_6324},
Delta=
{
<s>(q_gen_6326) -> q_gen_6326
<z>() -> q_gen_6326
<a>() -> q_gen_6332
<b>() -> q_gen_6332
<nil>() -> q_gen_6371
<s, cons>(q_gen_6332, q_gen_6331) -> q_gen_6331
<s, nil>(q_gen_6326) -> q_gen_6331
<z, nil>() -> q_gen_6331
<cons, cons>(q_gen_6339, q_gen_6338) -> q_gen_6338
<nil, nil>() -> q_gen_6338
<a, a>() -> q_gen_6339
<a, b>() -> q_gen_6339
<b, a>() -> q_gen_6339
<b, b>() -> q_gen_6339
<z, cons>(q_gen_6332, q_gen_6371) -> q_gen_6378
<s, cons, cons>(q_gen_6339, q_gen_6370) -> q_gen_6324
<s, cons, nil>(q_gen_6332, q_gen_6331) -> q_gen_6324
<s, nil, nil>(q_gen_6326) -> q_gen_6324
<z, cons, cons>(q_gen_6339, q_gen_6338) -> q_gen_6324
<z, nil, nil>() -> q_gen_6324
<s, cons, nil>(q_gen_6332, q_gen_6378) -> q_gen_6370
<z, cons, nil>(q_gen_6332, q_gen_6371) -> q_gen_6370
}

Datatype: <nat, eltlist, eltlist>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_6323, q_gen_6329},
Q_f={q_gen_6323},
Delta=
{
<a>() -> q_gen_6329
<b>() -> q_gen_6329
<cons, s>(q_gen_6329, q_gen_6323) -> q_gen_6323
<nil, z>() -> q_gen_6323
}

Datatype: <eltlist, nat>
Convolution form: right
}}}
  ;  minus -> 
{{{
Q={q_gen_6320, q_gen_6322, q_gen_6334, q_gen_6342, q_gen_6343, q_gen_6355, q_gen_6368},
Q_f={q_gen_6320, q_gen_6342},
Delta=
{
<s>(q_gen_6334) -> q_gen_6334
<z>() -> q_gen_6334
<s, s>(q_gen_6322) -> q_gen_6322
<z, z>() -> q_gen_6322
<z, s>(q_gen_6334) -> q_gen_6355
<s, z>(q_gen_6334) -> q_gen_6368
<s, s, s>(q_gen_6342) -> q_gen_6320
<s, s, z>(q_gen_6322) -> q_gen_6320
<s, s, z>(q_gen_6355) -> q_gen_6320
<s, z, s>(q_gen_6322) -> q_gen_6320
<z, s, z>(q_gen_6334) -> q_gen_6320
<z, z, z>() -> q_gen_6320
<s, s, s>(q_gen_6343) -> q_gen_6342
<s, z, s>(q_gen_6368) -> q_gen_6342
<s, s, s>(q_gen_6320) -> q_gen_6343
<s, s, z>(q_gen_6368) -> q_gen_6343
<s, z, s>(q_gen_6355) -> q_gen_6343
<s, z, z>(q_gen_6334) -> q_gen_6343
}

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

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

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

-------------------------------------------
Step 39, which took 0.062259 s (model generation: 0.059659,  model checking: 0.002600):

Model:
|_
{
drop -> 
{{{
Q={q_gen_6324, q_gen_6326, q_gen_6331, q_gen_6332, q_gen_6338, q_gen_6339, q_gen_6370, q_gen_6371, q_gen_6378},
Q_f={q_gen_6324},
Delta=
{
<s>(q_gen_6326) -> q_gen_6326
<z>() -> q_gen_6326
<a>() -> q_gen_6332
<b>() -> q_gen_6332
<nil>() -> q_gen_6371
<s, cons>(q_gen_6332, q_gen_6331) -> q_gen_6331
<s, nil>(q_gen_6326) -> q_gen_6331
<z, nil>() -> q_gen_6331
<cons, cons>(q_gen_6339, q_gen_6338) -> q_gen_6338
<nil, nil>() -> q_gen_6338
<a, a>() -> q_gen_6339
<a, b>() -> q_gen_6339
<b, a>() -> q_gen_6339
<b, b>() -> q_gen_6339
<z, cons>(q_gen_6332, q_gen_6371) -> q_gen_6378
<s, cons, cons>(q_gen_6339, q_gen_6370) -> q_gen_6324
<s, cons, nil>(q_gen_6332, q_gen_6331) -> q_gen_6324
<s, nil, nil>(q_gen_6326) -> q_gen_6324
<z, cons, cons>(q_gen_6339, q_gen_6338) -> q_gen_6324
<z, nil, nil>() -> q_gen_6324
<s, cons, nil>(q_gen_6332, q_gen_6378) -> q_gen_6370
<z, cons, nil>(q_gen_6332, q_gen_6371) -> q_gen_6370
}

Datatype: <nat, eltlist, eltlist>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_6323, q_gen_6329},
Q_f={q_gen_6323},
Delta=
{
<a>() -> q_gen_6329
<b>() -> q_gen_6329
<cons, s>(q_gen_6329, q_gen_6323) -> q_gen_6323
<nil, z>() -> q_gen_6323
}

Datatype: <eltlist, nat>
Convolution form: right
}}}
  ;  minus -> 
{{{
Q={q_gen_6320, q_gen_6322, q_gen_6334, q_gen_6343, q_gen_6348, q_gen_6355, q_gen_6368},
Q_f={q_gen_6320},
Delta=
{
<s>(q_gen_6334) -> q_gen_6334
<z>() -> q_gen_6334
<s, s>(q_gen_6322) -> q_gen_6322
<z, z>() -> q_gen_6322
<z, s>(q_gen_6334) -> q_gen_6355
<s, z>(q_gen_6334) -> q_gen_6368
<s, s, s>(q_gen_6343) -> q_gen_6320
<s, s, z>(q_gen_6322) -> q_gen_6320
<s, s, z>(q_gen_6355) -> q_gen_6320
<s, z, s>(q_gen_6322) -> q_gen_6320
<z, s, z>(q_gen_6334) -> q_gen_6320
<z, z, z>() -> q_gen_6320
<s, s, z>(q_gen_6368) -> q_gen_6343
<s, z, s>(q_gen_6368) -> q_gen_6343
<s, z, z>(q_gen_6334) -> q_gen_6343
<s, s, s>(q_gen_6320) -> q_gen_6348
<s, s, s>(q_gen_6348) -> q_gen_6348
<s, z, s>(q_gen_6355) -> q_gen_6348
}

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

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

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

-------------------------------------------
Step 40, which took 0.069399 s (model generation: 0.067873,  model checking: 0.001526):

Model:
|_
{
drop -> 
{{{
Q={q_gen_6324, q_gen_6326, q_gen_6331, q_gen_6332, q_gen_6338, q_gen_6339, q_gen_6370, q_gen_6371},
Q_f={q_gen_6324},
Delta=
{
<s>(q_gen_6326) -> q_gen_6326
<z>() -> q_gen_6326
<a>() -> q_gen_6332
<b>() -> q_gen_6332
<nil>() -> q_gen_6371
<s, cons>(q_gen_6332, q_gen_6331) -> q_gen_6331
<s, nil>(q_gen_6326) -> q_gen_6331
<z, cons>(q_gen_6332, q_gen_6371) -> q_gen_6331
<z, nil>() -> q_gen_6331
<cons, cons>(q_gen_6339, q_gen_6338) -> q_gen_6338
<nil, nil>() -> q_gen_6338
<a, a>() -> q_gen_6339
<a, b>() -> q_gen_6339
<b, a>() -> q_gen_6339
<b, b>() -> q_gen_6339
<s, cons, cons>(q_gen_6339, q_gen_6324) -> q_gen_6324
<s, cons, cons>(q_gen_6339, q_gen_6370) -> q_gen_6324
<s, cons, nil>(q_gen_6332, q_gen_6331) -> q_gen_6324
<s, nil, nil>(q_gen_6326) -> q_gen_6324
<z, cons, cons>(q_gen_6339, q_gen_6338) -> q_gen_6324
<z, nil, nil>() -> q_gen_6324
<z, cons, nil>(q_gen_6332, q_gen_6371) -> q_gen_6370
}

Datatype: <nat, eltlist, eltlist>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_6323, q_gen_6328, q_gen_6329, q_gen_6345, q_gen_6379},
Q_f={q_gen_6323, q_gen_6328},
Delta=
{
<b>() -> q_gen_6329
<a>() -> q_gen_6345
<cons, s>(q_gen_6345, q_gen_6323) -> q_gen_6323
<nil, z>() -> q_gen_6323
<cons, s>(q_gen_6329, q_gen_6323) -> q_gen_6328
<cons, s>(q_gen_6329, q_gen_6328) -> q_gen_6379
}

Datatype: <eltlist, nat>
Convolution form: right
}}}
  ;  minus -> 
{{{
Q={q_gen_6320, q_gen_6322, q_gen_6334, q_gen_6342, q_gen_6343, q_gen_6355},
Q_f={q_gen_6320, q_gen_6342},
Delta=
{
<s>(q_gen_6334) -> q_gen_6334
<z>() -> q_gen_6334
<s, s>(q_gen_6322) -> q_gen_6322
<z, z>() -> q_gen_6322
<s, z>(q_gen_6334) -> q_gen_6355
<z, s>(q_gen_6334) -> q_gen_6355
<s, s, s>(q_gen_6342) -> q_gen_6320
<s, s, z>(q_gen_6322) -> q_gen_6320
<s, z, s>(q_gen_6322) -> q_gen_6320
<z, s, z>(q_gen_6334) -> q_gen_6320
<z, z, z>() -> q_gen_6320
<s, s, s>(q_gen_6343) -> q_gen_6342
<s, s, z>(q_gen_6355) -> q_gen_6342
<s, s, s>(q_gen_6320) -> q_gen_6343
<s, z, s>(q_gen_6355) -> q_gen_6343
<s, z, z>(q_gen_6334) -> q_gen_6343
}

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

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

Teacher's answer:
New clause system:
{
() -> drop([s(u), nil, nil]) -> 24
() -> drop([z, l, l]) -> 24
() -> length([nil, z]) -> 24
() -> minus([s(u), z, s(u)]) -> 24
() -> minus([z, y, z]) -> 24
(drop([n, l1, _sga]) /\ length([_sga, _tga]) /\ length([l1, _uga]) /\ minus([_uga, n, _vga])) -> eq_nat([_tga, _vga]) -> 25
(drop([u, x3, _ega])) -> drop([s(u), cons(x2, x3), _ega]) -> 25
(length([ll, _jga])) -> length([cons(x, ll), s(_jga)]) -> 27
(minus([u, x2, _nga])) -> minus([s(u), s(x2), _nga]) -> 28
}
Sat witness: Found: ((length([ll, _jga])) -> length([cons(x, ll), s(_jga)]), {
_jga -> s(z)  ;  ll -> cons(b, nil)  ;  x -> b
})

-------------------------------------------
Step 41, which took 0.047691 s (model generation: 0.046609,  model checking: 0.001082):

Model:
|_
{
drop -> 
{{{
Q={q_gen_6324, q_gen_6326, q_gen_6331, q_gen_6332, q_gen_6338, q_gen_6339, q_gen_6347, q_gen_6370, q_gen_6371, q_gen_6378},
Q_f={q_gen_6324},
Delta=
{
<s>(q_gen_6326) -> q_gen_6326
<z>() -> q_gen_6326
<b>() -> q_gen_6332
<a>() -> q_gen_6347
<nil>() -> q_gen_6371
<s, cons>(q_gen_6347, q_gen_6331) -> q_gen_6331
<s, nil>(q_gen_6326) -> q_gen_6331
<z, nil>() -> q_gen_6331
<cons, cons>(q_gen_6339, q_gen_6338) -> q_gen_6338
<nil, nil>() -> q_gen_6338
<a, a>() -> q_gen_6339
<a, b>() -> q_gen_6339
<b, a>() -> q_gen_6339
<b, b>() -> q_gen_6339
<s, cons>(q_gen_6332, q_gen_6331) -> q_gen_6378
<z, cons>(q_gen_6332, q_gen_6371) -> q_gen_6378
<s, cons, cons>(q_gen_6339, q_gen_6370) -> q_gen_6324
<s, cons, nil>(q_gen_6332, q_gen_6331) -> q_gen_6324
<s, cons, nil>(q_gen_6347, q_gen_6331) -> q_gen_6324
<s, nil, nil>(q_gen_6326) -> q_gen_6324
<z, cons, cons>(q_gen_6339, q_gen_6338) -> q_gen_6324
<z, nil, nil>() -> q_gen_6324
<s, cons, nil>(q_gen_6332, q_gen_6378) -> q_gen_6370
<s, cons, nil>(q_gen_6347, q_gen_6378) -> q_gen_6370
<z, cons, nil>(q_gen_6332, q_gen_6371) -> q_gen_6370
}

Datatype: <nat, eltlist, eltlist>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_6323, q_gen_6329},
Q_f={q_gen_6323},
Delta=
{
<a>() -> q_gen_6329
<b>() -> q_gen_6329
<cons, s>(q_gen_6329, q_gen_6323) -> q_gen_6323
<nil, z>() -> q_gen_6323
}

Datatype: <eltlist, nat>
Convolution form: right
}}}
  ;  minus -> 
{{{
Q={q_gen_6320, q_gen_6322, q_gen_6334, q_gen_6342, q_gen_6343, q_gen_6355, q_gen_6368},
Q_f={q_gen_6320, q_gen_6342},
Delta=
{
<s>(q_gen_6334) -> q_gen_6334
<z>() -> q_gen_6334
<s, s>(q_gen_6322) -> q_gen_6322
<z, z>() -> q_gen_6322
<z, s>(q_gen_6334) -> q_gen_6355
<s, z>(q_gen_6334) -> q_gen_6368
<s, s, s>(q_gen_6342) -> q_gen_6320
<s, s, z>(q_gen_6322) -> q_gen_6320
<s, s, z>(q_gen_6355) -> q_gen_6320
<s, z, s>(q_gen_6322) -> q_gen_6320
<z, s, z>(q_gen_6334) -> q_gen_6320
<z, z, z>() -> q_gen_6320
<s, s, s>(q_gen_6343) -> q_gen_6342
<s, z, s>(q_gen_6368) -> q_gen_6342
<s, s, s>(q_gen_6320) -> q_gen_6343
<s, s, z>(q_gen_6368) -> q_gen_6343
<s, z, s>(q_gen_6355) -> q_gen_6343
<s, z, z>(q_gen_6334) -> q_gen_6343
}

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

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

Teacher's answer:
New clause system:
{
() -> drop([s(u), nil, nil]) -> 25
() -> drop([z, l, l]) -> 25
() -> length([nil, z]) -> 25
() -> minus([s(u), z, s(u)]) -> 25
() -> minus([z, y, z]) -> 25
(drop([n, l1, _sga]) /\ length([_sga, _tga]) /\ length([l1, _uga]) /\ minus([_uga, n, _vga])) -> eq_nat([_tga, _vga]) -> 25
(drop([u, x3, _ega])) -> drop([s(u), cons(x2, x3), _ega]) -> 28
(length([ll, _jga])) -> length([cons(x, ll), s(_jga)]) -> 27
(minus([u, x2, _nga])) -> minus([s(u), s(x2), _nga]) -> 28
}
Sat witness: Found: ((drop([u, x3, _ega])) -> drop([s(u), cons(x2, x3), _ega]), {
_ega -> nil  ;  u -> s(z)  ;  x2 -> b  ;  x3 -> cons(b, nil)
})

-------------------------------------------
Step 42, which took 0.050779 s (model generation: 0.049940,  model checking: 0.000839):

Model:
|_
{
drop -> 
{{{
Q={q_gen_6324, q_gen_6326, q_gen_6331, q_gen_6332, q_gen_6338, q_gen_6339, q_gen_6370, q_gen_6371, q_gen_6378},
Q_f={q_gen_6324},
Delta=
{
<s>(q_gen_6326) -> q_gen_6326
<z>() -> q_gen_6326
<a>() -> q_gen_6332
<b>() -> q_gen_6332
<nil>() -> q_gen_6371
<s, cons>(q_gen_6332, q_gen_6331) -> q_gen_6331
<s, nil>(q_gen_6326) -> q_gen_6331
<z, nil>() -> q_gen_6331
<cons, cons>(q_gen_6339, q_gen_6338) -> q_gen_6338
<nil, nil>() -> q_gen_6338
<a, a>() -> q_gen_6339
<a, b>() -> q_gen_6339
<b, a>() -> q_gen_6339
<b, b>() -> q_gen_6339
<z, cons>(q_gen_6332, q_gen_6371) -> q_gen_6378
<s, cons, cons>(q_gen_6339, q_gen_6370) -> q_gen_6324
<s, cons, nil>(q_gen_6332, q_gen_6331) -> q_gen_6324
<s, nil, nil>(q_gen_6326) -> q_gen_6324
<z, cons, cons>(q_gen_6339, q_gen_6338) -> q_gen_6324
<z, nil, nil>() -> q_gen_6324
<s, cons, nil>(q_gen_6332, q_gen_6378) -> q_gen_6370
<z, cons, nil>(q_gen_6332, q_gen_6371) -> q_gen_6370
}

Datatype: <nat, eltlist, eltlist>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_6323, q_gen_6329},
Q_f={q_gen_6323},
Delta=
{
<a>() -> q_gen_6329
<b>() -> q_gen_6329
<cons, s>(q_gen_6329, q_gen_6323) -> q_gen_6323
<nil, z>() -> q_gen_6323
}

Datatype: <eltlist, nat>
Convolution form: right
}}}
  ;  minus -> 
{{{
Q={q_gen_6320, q_gen_6322, q_gen_6334, q_gen_6343, q_gen_6348, q_gen_6350, q_gen_6355, q_gen_6361},
Q_f={q_gen_6320},
Delta=
{
<s>(q_gen_6350) -> q_gen_6334
<z>() -> q_gen_6334
<s>(q_gen_6334) -> q_gen_6350
<s, s>(q_gen_6322) -> q_gen_6322
<z, z>() -> q_gen_6322
<z, s>(q_gen_6334) -> q_gen_6355
<s, z>(q_gen_6334) -> q_gen_6361
<z, s>(q_gen_6350) -> q_gen_6361
<s, s, s>(q_gen_6343) -> q_gen_6320
<s, s, z>(q_gen_6322) -> q_gen_6320
<s, s, z>(q_gen_6355) -> q_gen_6320
<s, z, s>(q_gen_6322) -> q_gen_6320
<z, s, z>(q_gen_6334) -> q_gen_6320
<z, s, z>(q_gen_6350) -> q_gen_6320
<z, z, z>() -> q_gen_6320
<s, s, s>(q_gen_6348) -> q_gen_6343
<s, s, z>(q_gen_6361) -> q_gen_6343
<s, z, s>(q_gen_6361) -> q_gen_6343
<s, z, z>(q_gen_6334) -> q_gen_6343
<s, s, s>(q_gen_6320) -> q_gen_6348
<s, z, s>(q_gen_6355) -> q_gen_6348
<s, z, z>(q_gen_6350) -> q_gen_6348
}

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

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

Teacher's answer:
New clause system:
{
() -> drop([s(u), nil, nil]) -> 25
() -> drop([z, l, l]) -> 25
() -> length([nil, z]) -> 25
() -> minus([s(u), z, s(u)]) -> 25
() -> minus([z, y, z]) -> 25
(drop([n, l1, _sga]) /\ length([_sga, _tga]) /\ length([l1, _uga]) /\ minus([_uga, n, _vga])) -> eq_nat([_tga, _vga]) -> 28
(drop([u, x3, _ega])) -> drop([s(u), cons(x2, x3), _ega]) -> 28
(length([ll, _jga])) -> length([cons(x, ll), s(_jga)]) -> 27
(minus([u, x2, _nga])) -> minus([s(u), s(x2), _nga]) -> 28
}
Sat witness: Found: ((drop([n, l1, _sga]) /\ length([_sga, _tga]) /\ length([l1, _uga]) /\ minus([_uga, n, _vga])) -> eq_nat([_tga, _vga]), {
_sga -> nil  ;  _tga -> z  ;  _uga -> s(s(z))  ;  _vga -> s(z)  ;  l1 -> cons(b, cons(b, nil))  ;  n -> s(s(s(s(z))))
})

-------------------------------------------
Step 43, which took 0.067503 s (model generation: 0.065802,  model checking: 0.001701):

Model:
|_
{
drop -> 
{{{
Q={q_gen_6324, q_gen_6326, q_gen_6331, q_gen_6332, q_gen_6338, q_gen_6339, q_gen_6370, q_gen_6371, q_gen_6378},
Q_f={q_gen_6324},
Delta=
{
<s>(q_gen_6326) -> q_gen_6326
<z>() -> q_gen_6326
<a>() -> q_gen_6332
<b>() -> q_gen_6332
<nil>() -> q_gen_6371
<s, cons>(q_gen_6332, q_gen_6331) -> q_gen_6331
<s, nil>(q_gen_6326) -> q_gen_6331
<z, nil>() -> q_gen_6331
<cons, cons>(q_gen_6339, q_gen_6338) -> q_gen_6338
<nil, nil>() -> q_gen_6338
<a, a>() -> q_gen_6339
<a, b>() -> q_gen_6339
<b, a>() -> q_gen_6339
<b, b>() -> q_gen_6339
<z, cons>(q_gen_6332, q_gen_6371) -> q_gen_6378
<s, cons, cons>(q_gen_6339, q_gen_6370) -> q_gen_6324
<s, cons, nil>(q_gen_6332, q_gen_6331) -> q_gen_6324
<s, nil, nil>(q_gen_6326) -> q_gen_6324
<z, cons, cons>(q_gen_6339, q_gen_6338) -> q_gen_6324
<z, nil, nil>() -> q_gen_6324
<s, cons, nil>(q_gen_6332, q_gen_6378) -> q_gen_6370
<z, cons, nil>(q_gen_6332, q_gen_6371) -> q_gen_6370
}

Datatype: <nat, eltlist, eltlist>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_6323, q_gen_6329},
Q_f={q_gen_6323},
Delta=
{
<a>() -> q_gen_6329
<b>() -> q_gen_6329
<cons, s>(q_gen_6329, q_gen_6323) -> q_gen_6323
<nil, z>() -> q_gen_6323
}

Datatype: <eltlist, nat>
Convolution form: right
}}}
  ;  minus -> 
{{{
Q={q_gen_6320, q_gen_6322, q_gen_6334, q_gen_6342, q_gen_6343, q_gen_6348, q_gen_6355, q_gen_6368},
Q_f={q_gen_6320, q_gen_6342},
Delta=
{
<s>(q_gen_6334) -> q_gen_6334
<z>() -> q_gen_6334
<s, s>(q_gen_6322) -> q_gen_6322
<z, z>() -> q_gen_6322
<z, s>(q_gen_6334) -> q_gen_6355
<s, z>(q_gen_6334) -> q_gen_6368
<s, s, z>(q_gen_6322) -> q_gen_6320
<s, s, z>(q_gen_6355) -> q_gen_6320
<s, z, s>(q_gen_6322) -> q_gen_6320
<z, s, z>(q_gen_6334) -> q_gen_6320
<z, z, z>() -> q_gen_6320
<s, s, s>(q_gen_6342) -> q_gen_6342
<s, s, s>(q_gen_6343) -> q_gen_6342
<s, z, s>(q_gen_6368) -> q_gen_6342
<s, s, s>(q_gen_6348) -> q_gen_6343
<s, s, z>(q_gen_6368) -> q_gen_6343
<s, z, s>(q_gen_6355) -> q_gen_6343
<s, z, z>(q_gen_6334) -> q_gen_6343
<s, s, s>(q_gen_6320) -> q_gen_6348
}

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

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

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

-------------------------------------------
Step 44, which took 0.076781 s (model generation: 0.073215,  model checking: 0.003566):

Model:
|_
{
drop -> 
{{{
Q={q_gen_6324, q_gen_6326, q_gen_6331, q_gen_6332, q_gen_6338, q_gen_6339, q_gen_6370, q_gen_6371, q_gen_6378},
Q_f={q_gen_6324},
Delta=
{
<s>(q_gen_6326) -> q_gen_6326
<z>() -> q_gen_6326
<a>() -> q_gen_6332
<b>() -> q_gen_6332
<nil>() -> q_gen_6371
<s, cons>(q_gen_6332, q_gen_6331) -> q_gen_6331
<s, nil>(q_gen_6326) -> q_gen_6331
<z, nil>() -> q_gen_6331
<cons, cons>(q_gen_6339, q_gen_6338) -> q_gen_6338
<nil, nil>() -> q_gen_6338
<a, a>() -> q_gen_6339
<a, b>() -> q_gen_6339
<b, a>() -> q_gen_6339
<b, b>() -> q_gen_6339
<z, cons>(q_gen_6332, q_gen_6371) -> q_gen_6378
<s, cons, cons>(q_gen_6339, q_gen_6370) -> q_gen_6324
<s, cons, nil>(q_gen_6332, q_gen_6331) -> q_gen_6324
<s, nil, nil>(q_gen_6326) -> q_gen_6324
<z, cons, cons>(q_gen_6339, q_gen_6338) -> q_gen_6324
<z, nil, nil>() -> q_gen_6324
<s, cons, nil>(q_gen_6332, q_gen_6378) -> q_gen_6370
<z, cons, nil>(q_gen_6332, q_gen_6371) -> q_gen_6370
}

Datatype: <nat, eltlist, eltlist>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_6323, q_gen_6329},
Q_f={q_gen_6323},
Delta=
{
<a>() -> q_gen_6329
<b>() -> q_gen_6329
<cons, s>(q_gen_6329, q_gen_6323) -> q_gen_6323
<nil, z>() -> q_gen_6323
}

Datatype: <eltlist, nat>
Convolution form: right
}}}
  ;  minus -> 
{{{
Q={q_gen_6320, q_gen_6322, q_gen_6334, q_gen_6342, q_gen_6343, q_gen_6348, q_gen_6355, q_gen_6368},
Q_f={q_gen_6320, q_gen_6342},
Delta=
{
<s>(q_gen_6334) -> q_gen_6334
<z>() -> q_gen_6334
<s, s>(q_gen_6322) -> q_gen_6322
<z, z>() -> q_gen_6322
<z, s>(q_gen_6334) -> q_gen_6355
<s, z>(q_gen_6334) -> q_gen_6368
<s, s, s>(q_gen_6342) -> q_gen_6320
<s, s, z>(q_gen_6322) -> q_gen_6320
<s, s, z>(q_gen_6355) -> q_gen_6320
<s, z, s>(q_gen_6322) -> q_gen_6320
<z, s, z>(q_gen_6334) -> q_gen_6320
<z, z, z>() -> q_gen_6320
<s, s, s>(q_gen_6343) -> q_gen_6342
<s, z, s>(q_gen_6368) -> q_gen_6342
<s, s, s>(q_gen_6348) -> q_gen_6343
<s, s, z>(q_gen_6368) -> q_gen_6343
<s, z, z>(q_gen_6334) -> q_gen_6343
<s, s, s>(q_gen_6320) -> q_gen_6348
<s, z, s>(q_gen_6355) -> q_gen_6348
}

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

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

Teacher's answer:
New clause system:
{
() -> drop([s(u), nil, nil]) -> 27
() -> drop([z, l, l]) -> 27
() -> length([nil, z]) -> 27
() -> minus([s(u), z, s(u)]) -> 27
() -> minus([z, y, z]) -> 27
(drop([n, l1, _sga]) /\ length([_sga, _tga]) /\ length([l1, _uga]) /\ minus([_uga, n, _vga])) -> eq_nat([_tga, _vga]) -> 28
(drop([u, x3, _ega])) -> drop([s(u), cons(x2, x3), _ega]) -> 31
(length([ll, _jga])) -> length([cons(x, ll), s(_jga)]) -> 29
(minus([u, x2, _nga])) -> minus([s(u), s(x2), _nga]) -> 31
}
Sat witness: Found: ((drop([u, x3, _ega])) -> drop([s(u), cons(x2, x3), _ega]), {
_ega -> cons(a, nil)  ;  u -> s(s(z))  ;  x2 -> b  ;  x3 -> cons(b, cons(b, cons(b, nil)))
})

-------------------------------------------
Step 45, which took 0.080591 s (model generation: 0.079212,  model checking: 0.001379):

Model:
|_
{
drop -> 
{{{
Q={q_gen_6324, q_gen_6326, q_gen_6331, q_gen_6332, q_gen_6338, q_gen_6339, q_gen_6370, q_gen_6371, q_gen_6378},
Q_f={q_gen_6324},
Delta=
{
<s>(q_gen_6326) -> q_gen_6326
<z>() -> q_gen_6326
<a>() -> q_gen_6332
<b>() -> q_gen_6332
<nil>() -> q_gen_6371
<s, cons>(q_gen_6332, q_gen_6331) -> q_gen_6331
<s, cons>(q_gen_6332, q_gen_6378) -> q_gen_6331
<s, nil>(q_gen_6326) -> q_gen_6331
<z, nil>() -> q_gen_6331
<cons, cons>(q_gen_6339, q_gen_6338) -> q_gen_6338
<nil, nil>() -> q_gen_6338
<a, a>() -> q_gen_6339
<a, b>() -> q_gen_6339
<b, a>() -> q_gen_6339
<b, b>() -> q_gen_6339
<z, cons>(q_gen_6332, q_gen_6371) -> q_gen_6378
<s, cons, cons>(q_gen_6339, q_gen_6324) -> q_gen_6324
<s, cons, cons>(q_gen_6339, q_gen_6370) -> q_gen_6324
<s, cons, nil>(q_gen_6332, q_gen_6331) -> q_gen_6324
<s, nil, nil>(q_gen_6326) -> q_gen_6324
<z, cons, cons>(q_gen_6339, q_gen_6338) -> q_gen_6324
<z, nil, nil>() -> q_gen_6324
<s, cons, nil>(q_gen_6332, q_gen_6378) -> q_gen_6370
<z, cons, nil>(q_gen_6332, q_gen_6371) -> q_gen_6370
}

Datatype: <nat, eltlist, eltlist>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_6323, q_gen_6329},
Q_f={q_gen_6323},
Delta=
{
<a>() -> q_gen_6329
<b>() -> q_gen_6329
<cons, s>(q_gen_6329, q_gen_6323) -> q_gen_6323
<nil, z>() -> q_gen_6323
}

Datatype: <eltlist, nat>
Convolution form: right
}}}
  ;  minus -> 
{{{
Q={q_gen_6320, q_gen_6321, q_gen_6322, q_gen_6334, q_gen_6343, q_gen_6348, q_gen_6355, q_gen_6368},
Q_f={q_gen_6320, q_gen_6321},
Delta=
{
<s>(q_gen_6334) -> q_gen_6334
<z>() -> q_gen_6334
<s, s>(q_gen_6322) -> q_gen_6322
<z, z>() -> q_gen_6322
<z, s>(q_gen_6334) -> q_gen_6355
<s, z>(q_gen_6334) -> q_gen_6368
<s, s, s>(q_gen_6321) -> q_gen_6320
<s, s, z>(q_gen_6322) -> q_gen_6320
<s, s, z>(q_gen_6355) -> q_gen_6320
<z, s, z>(q_gen_6334) -> q_gen_6320
<z, z, z>() -> q_gen_6320
<s, s, s>(q_gen_6343) -> q_gen_6321
<s, z, s>(q_gen_6322) -> q_gen_6321
<s, s, s>(q_gen_6348) -> q_gen_6343
<s, s, z>(q_gen_6368) -> q_gen_6343
<s, z, s>(q_gen_6368) -> q_gen_6343
<s, z, z>(q_gen_6334) -> q_gen_6343
<s, s, s>(q_gen_6320) -> q_gen_6348
<s, z, s>(q_gen_6355) -> q_gen_6348
}

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

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

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

-------------------------------------------
Step 46, which took 0.075040 s (model generation: 0.073612,  model checking: 0.001428):

Model:
|_
{
drop -> 
{{{
Q={q_gen_6324, q_gen_6326, q_gen_6331, q_gen_6332, q_gen_6338, q_gen_6339, q_gen_6370, q_gen_6371, q_gen_6378},
Q_f={q_gen_6324},
Delta=
{
<s>(q_gen_6326) -> q_gen_6326
<z>() -> q_gen_6326
<a>() -> q_gen_6332
<b>() -> q_gen_6332
<nil>() -> q_gen_6371
<s, cons>(q_gen_6332, q_gen_6331) -> q_gen_6331
<s, nil>(q_gen_6326) -> q_gen_6331
<z, nil>() -> q_gen_6331
<cons, cons>(q_gen_6339, q_gen_6338) -> q_gen_6338
<nil, nil>() -> q_gen_6338
<a, a>() -> q_gen_6339
<a, b>() -> q_gen_6339
<b, a>() -> q_gen_6339
<b, b>() -> q_gen_6339
<s, cons>(q_gen_6332, q_gen_6378) -> q_gen_6378
<z, cons>(q_gen_6332, q_gen_6371) -> q_gen_6378
<s, cons, cons>(q_gen_6339, q_gen_6370) -> q_gen_6324
<s, cons, nil>(q_gen_6332, q_gen_6331) -> q_gen_6324
<s, nil, nil>(q_gen_6326) -> q_gen_6324
<z, cons, cons>(q_gen_6339, q_gen_6338) -> q_gen_6324
<z, nil, nil>() -> q_gen_6324
<s, cons, nil>(q_gen_6332, q_gen_6378) -> q_gen_6370
<z, cons, nil>(q_gen_6332, q_gen_6371) -> q_gen_6370
}

Datatype: <nat, eltlist, eltlist>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_6323, q_gen_6329},
Q_f={q_gen_6323},
Delta=
{
<a>() -> q_gen_6329
<b>() -> q_gen_6329
<cons, s>(q_gen_6329, q_gen_6323) -> q_gen_6323
<nil, z>() -> q_gen_6323
}

Datatype: <eltlist, nat>
Convolution form: right
}}}
  ;  minus -> 
{{{
Q={q_gen_6320, q_gen_6322, q_gen_6334, q_gen_6342, q_gen_6343, q_gen_6348, q_gen_6355, q_gen_6368},
Q_f={q_gen_6320, q_gen_6342},
Delta=
{
<s>(q_gen_6334) -> q_gen_6334
<z>() -> q_gen_6334
<s, s>(q_gen_6322) -> q_gen_6322
<z, z>() -> q_gen_6322
<z, s>(q_gen_6334) -> q_gen_6355
<s, z>(q_gen_6334) -> q_gen_6368
<s, s, s>(q_gen_6342) -> q_gen_6320
<s, s, z>(q_gen_6322) -> q_gen_6320
<s, s, z>(q_gen_6355) -> q_gen_6320
<s, z, s>(q_gen_6322) -> q_gen_6320
<z, s, z>(q_gen_6334) -> q_gen_6320
<z, z, z>() -> q_gen_6320
<s, s, s>(q_gen_6343) -> q_gen_6342
<s, z, s>(q_gen_6368) -> q_gen_6342
<s, s, z>(q_gen_6368) -> q_gen_6343
<s, z, z>(q_gen_6334) -> q_gen_6343
<s, s, s>(q_gen_6320) -> q_gen_6348
<s, s, s>(q_gen_6348) -> q_gen_6348
<s, z, s>(q_gen_6355) -> q_gen_6348
}

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

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

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

-------------------------------------------
Step 47, which took 0.082834 s (model generation: 0.080969,  model checking: 0.001865):

Model:
|_
{
drop -> 
{{{
Q={q_gen_6324, q_gen_6326, q_gen_6331, q_gen_6332, q_gen_6338, q_gen_6339, q_gen_6370, q_gen_6371, q_gen_6378},
Q_f={q_gen_6324},
Delta=
{
<s>(q_gen_6326) -> q_gen_6326
<z>() -> q_gen_6326
<a>() -> q_gen_6332
<b>() -> q_gen_6332
<nil>() -> q_gen_6371
<s, cons>(q_gen_6332, q_gen_6331) -> q_gen_6331
<s, nil>(q_gen_6326) -> q_gen_6331
<z, nil>() -> q_gen_6331
<cons, cons>(q_gen_6339, q_gen_6338) -> q_gen_6338
<nil, nil>() -> q_gen_6338
<a, a>() -> q_gen_6339
<a, b>() -> q_gen_6339
<b, a>() -> q_gen_6339
<b, b>() -> q_gen_6339
<s, cons>(q_gen_6332, q_gen_6378) -> q_gen_6378
<z, cons>(q_gen_6332, q_gen_6371) -> q_gen_6378
<s, cons, cons>(q_gen_6339, q_gen_6370) -> q_gen_6324
<s, cons, nil>(q_gen_6332, q_gen_6331) -> q_gen_6324
<s, nil, nil>(q_gen_6326) -> q_gen_6324
<z, cons, cons>(q_gen_6339, q_gen_6338) -> q_gen_6324
<z, nil, nil>() -> q_gen_6324
<s, cons, nil>(q_gen_6332, q_gen_6378) -> q_gen_6370
<z, cons, nil>(q_gen_6332, q_gen_6371) -> q_gen_6370
}

Datatype: <nat, eltlist, eltlist>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_6323, q_gen_6329},
Q_f={q_gen_6323},
Delta=
{
<a>() -> q_gen_6329
<b>() -> q_gen_6329
<cons, s>(q_gen_6329, q_gen_6323) -> q_gen_6323
<nil, z>() -> q_gen_6323
}

Datatype: <eltlist, nat>
Convolution form: right
}}}
  ;  minus -> 
{{{
Q={q_gen_6320, q_gen_6322, q_gen_6334, q_gen_6342, q_gen_6343, q_gen_6348, q_gen_6355, q_gen_6368},
Q_f={q_gen_6320, q_gen_6342},
Delta=
{
<s>(q_gen_6334) -> q_gen_6334
<z>() -> q_gen_6334
<s, s>(q_gen_6322) -> q_gen_6322
<z, z>() -> q_gen_6322
<z, s>(q_gen_6334) -> q_gen_6355
<s, s>(q_gen_6368) -> q_gen_6368
<s, z>(q_gen_6334) -> q_gen_6368
<s, s, s>(q_gen_6342) -> q_gen_6320
<s, s, z>(q_gen_6322) -> q_gen_6320
<s, s, z>(q_gen_6355) -> q_gen_6320
<s, z, s>(q_gen_6322) -> q_gen_6320
<z, s, z>(q_gen_6334) -> q_gen_6320
<z, z, z>() -> q_gen_6320
<s, s, s>(q_gen_6343) -> q_gen_6342
<s, s, s>(q_gen_6348) -> q_gen_6343
<s, s, z>(q_gen_6368) -> q_gen_6343
<s, z, s>(q_gen_6368) -> q_gen_6343
<s, z, z>(q_gen_6334) -> q_gen_6343
<s, s, s>(q_gen_6320) -> q_gen_6348
<s, z, s>(q_gen_6355) -> q_gen_6348
}

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

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

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

-------------------------------------------
Step 48, which took 0.095214 s (model generation: 0.094179,  model checking: 0.001035):

Model:
|_
{
drop -> 
{{{
Q={q_gen_6324, q_gen_6326, q_gen_6331, q_gen_6332, q_gen_6338, q_gen_6339, q_gen_6370, q_gen_6371, q_gen_6378},
Q_f={q_gen_6324},
Delta=
{
<s>(q_gen_6326) -> q_gen_6326
<z>() -> q_gen_6326
<a>() -> q_gen_6332
<b>() -> q_gen_6332
<nil>() -> q_gen_6371
<s, cons>(q_gen_6332, q_gen_6331) -> q_gen_6331
<s, nil>(q_gen_6326) -> q_gen_6331
<z, nil>() -> q_gen_6331
<cons, cons>(q_gen_6339, q_gen_6338) -> q_gen_6338
<cons, nil>(q_gen_6332, q_gen_6371) -> q_gen_6338
<nil, nil>() -> q_gen_6338
<a, a>() -> q_gen_6339
<a, b>() -> q_gen_6339
<b, a>() -> q_gen_6339
<b, b>() -> q_gen_6339
<s, cons>(q_gen_6332, q_gen_6378) -> q_gen_6378
<z, cons>(q_gen_6332, q_gen_6371) -> q_gen_6378
<s, cons, cons>(q_gen_6339, q_gen_6324) -> q_gen_6324
<s, cons, cons>(q_gen_6339, q_gen_6370) -> q_gen_6324
<s, cons, nil>(q_gen_6332, q_gen_6331) -> q_gen_6324
<s, nil, nil>(q_gen_6326) -> q_gen_6324
<z, cons, cons>(q_gen_6339, q_gen_6338) -> q_gen_6324
<z, nil, nil>() -> q_gen_6324
<s, cons, nil>(q_gen_6332, q_gen_6378) -> q_gen_6370
<z, cons, nil>(q_gen_6332, q_gen_6371) -> q_gen_6370
}

Datatype: <nat, eltlist, eltlist>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_6323, q_gen_6329},
Q_f={q_gen_6323},
Delta=
{
<a>() -> q_gen_6329
<b>() -> q_gen_6329
<cons, s>(q_gen_6329, q_gen_6323) -> q_gen_6323
<nil, z>() -> q_gen_6323
}

Datatype: <eltlist, nat>
Convolution form: right
}}}
  ;  minus -> 
{{{
Q={q_gen_6320, q_gen_6321, q_gen_6322, q_gen_6334, q_gen_6343, q_gen_6348, q_gen_6355, q_gen_6368},
Q_f={q_gen_6320, q_gen_6321},
Delta=
{
<s>(q_gen_6334) -> q_gen_6334
<z>() -> q_gen_6334
<s, s>(q_gen_6322) -> q_gen_6322
<z, z>() -> q_gen_6322
<z, s>(q_gen_6334) -> q_gen_6355
<s, s>(q_gen_6368) -> q_gen_6368
<s, z>(q_gen_6334) -> q_gen_6368
<s, s, s>(q_gen_6321) -> q_gen_6320
<s, s, z>(q_gen_6355) -> q_gen_6320
<z, s, z>(q_gen_6334) -> q_gen_6320
<z, z, z>() -> q_gen_6320
<s, s, s>(q_gen_6343) -> q_gen_6321
<s, s, z>(q_gen_6322) -> q_gen_6321
<s, z, s>(q_gen_6322) -> q_gen_6321
<s, s, s>(q_gen_6348) -> q_gen_6343
<s, s, z>(q_gen_6368) -> q_gen_6343
<s, z, s>(q_gen_6368) -> q_gen_6343
<s, z, z>(q_gen_6334) -> q_gen_6343
<s, s, s>(q_gen_6320) -> q_gen_6348
<s, z, s>(q_gen_6355) -> q_gen_6348
}

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

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

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

-------------------------------------------
Step 49, which took 0.091411 s (model generation: 0.090425,  model checking: 0.000986):

Model:
|_
{
drop -> 
{{{
Q={q_gen_6324, q_gen_6326, q_gen_6331, q_gen_6332, q_gen_6338, q_gen_6339, q_gen_6370, q_gen_6371, q_gen_6378, q_gen_6416},
Q_f={q_gen_6324},
Delta=
{
<s>(q_gen_6326) -> q_gen_6326
<z>() -> q_gen_6326
<a>() -> q_gen_6332
<b>() -> q_gen_6332
<nil>() -> q_gen_6371
<s, cons>(q_gen_6332, q_gen_6331) -> q_gen_6331
<s, nil>(q_gen_6326) -> q_gen_6331
<z, nil>() -> q_gen_6331
<cons, cons>(q_gen_6339, q_gen_6338) -> q_gen_6338
<nil, nil>() -> q_gen_6338
<a, a>() -> q_gen_6339
<a, b>() -> q_gen_6339
<b, a>() -> q_gen_6339
<b, b>() -> q_gen_6339
<s, cons>(q_gen_6332, q_gen_6378) -> q_gen_6378
<z, cons>(q_gen_6332, q_gen_6371) -> q_gen_6378
<cons, nil>(q_gen_6332, q_gen_6371) -> q_gen_6416
<s, cons, cons>(q_gen_6339, q_gen_6370) -> q_gen_6324
<s, cons, nil>(q_gen_6332, q_gen_6331) -> q_gen_6324
<s, nil, nil>(q_gen_6326) -> q_gen_6324
<z, cons, cons>(q_gen_6339, q_gen_6338) -> q_gen_6324
<z, nil, nil>() -> q_gen_6324
<s, cons, nil>(q_gen_6332, q_gen_6378) -> q_gen_6370
<z, cons, cons>(q_gen_6339, q_gen_6416) -> q_gen_6370
<z, cons, nil>(q_gen_6332, q_gen_6371) -> q_gen_6370
}

Datatype: <nat, eltlist, eltlist>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_6323, q_gen_6329},
Q_f={q_gen_6323},
Delta=
{
<a>() -> q_gen_6329
<b>() -> q_gen_6329
<cons, s>(q_gen_6329, q_gen_6323) -> q_gen_6323
<nil, z>() -> q_gen_6323
}

Datatype: <eltlist, nat>
Convolution form: right
}}}
  ;  minus -> 
{{{
Q={q_gen_6320, q_gen_6322, q_gen_6334, q_gen_6343, q_gen_6348, q_gen_6350, q_gen_6355, q_gen_6368},
Q_f={q_gen_6320},
Delta=
{
<z>() -> q_gen_6334
<s>(q_gen_6334) -> q_gen_6350
<s>(q_gen_6350) -> q_gen_6350
<s, s>(q_gen_6322) -> q_gen_6322
<z, s>(q_gen_6350) -> q_gen_6322
<z, z>() -> q_gen_6322
<z, s>(q_gen_6334) -> q_gen_6355
<s, s>(q_gen_6368) -> q_gen_6368
<s, z>(q_gen_6334) -> q_gen_6368
<s, s, s>(q_gen_6343) -> q_gen_6320
<s, s, z>(q_gen_6322) -> q_gen_6320
<s, s, z>(q_gen_6355) -> q_gen_6320
<s, z, s>(q_gen_6322) -> q_gen_6320
<z, s, z>(q_gen_6334) -> q_gen_6320
<z, s, z>(q_gen_6350) -> q_gen_6320
<z, z, z>() -> q_gen_6320
<s, s, s>(q_gen_6348) -> q_gen_6343
<s, s, z>(q_gen_6368) -> q_gen_6343
<s, z, s>(q_gen_6368) -> q_gen_6343
<s, z, z>(q_gen_6334) -> q_gen_6343
<s, s, s>(q_gen_6320) -> q_gen_6348
<s, z, s>(q_gen_6355) -> q_gen_6348
<s, z, z>(q_gen_6350) -> q_gen_6348
}

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

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

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

-------------------------------------------
Step 50, which took 0.092454 s (model generation: 0.090245,  model checking: 0.002209):

Model:
|_
{
drop -> 
{{{
Q={q_gen_6324, q_gen_6326, q_gen_6331, q_gen_6332, q_gen_6338, q_gen_6339, q_gen_6370, q_gen_6371, q_gen_6378, q_gen_6416},
Q_f={q_gen_6324},
Delta=
{
<s>(q_gen_6326) -> q_gen_6326
<z>() -> q_gen_6326
<a>() -> q_gen_6332
<b>() -> q_gen_6332
<nil>() -> q_gen_6371
<s, cons>(q_gen_6332, q_gen_6331) -> q_gen_6331
<s, nil>(q_gen_6326) -> q_gen_6331
<z, nil>() -> q_gen_6331
<cons, cons>(q_gen_6339, q_gen_6338) -> q_gen_6338
<nil, nil>() -> q_gen_6338
<a, a>() -> q_gen_6339
<a, b>() -> q_gen_6339
<b, a>() -> q_gen_6339
<b, b>() -> q_gen_6339
<s, cons>(q_gen_6332, q_gen_6378) -> q_gen_6378
<z, cons>(q_gen_6332, q_gen_6371) -> q_gen_6378
<cons, nil>(q_gen_6332, q_gen_6371) -> q_gen_6416
<s, cons, cons>(q_gen_6339, q_gen_6370) -> q_gen_6324
<s, cons, nil>(q_gen_6332, q_gen_6331) -> q_gen_6324
<s, nil, nil>(q_gen_6326) -> q_gen_6324
<z, cons, cons>(q_gen_6339, q_gen_6338) -> q_gen_6324
<z, nil, nil>() -> q_gen_6324
<s, cons, nil>(q_gen_6332, q_gen_6378) -> q_gen_6370
<z, cons, cons>(q_gen_6339, q_gen_6416) -> q_gen_6370
<z, cons, nil>(q_gen_6332, q_gen_6371) -> q_gen_6370
}

Datatype: <nat, eltlist, eltlist>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_6323, q_gen_6329},
Q_f={q_gen_6323},
Delta=
{
<a>() -> q_gen_6329
<b>() -> q_gen_6329
<cons, s>(q_gen_6329, q_gen_6323) -> q_gen_6323
<nil, z>() -> q_gen_6323
}

Datatype: <eltlist, nat>
Convolution form: right
}}}
  ;  minus -> 
{{{
Q={q_gen_6320, q_gen_6321, q_gen_6322, q_gen_6334, q_gen_6343, q_gen_6348, q_gen_6355, q_gen_6368},
Q_f={q_gen_6320, q_gen_6321},
Delta=
{
<s>(q_gen_6334) -> q_gen_6334
<z>() -> q_gen_6334
<s, s>(q_gen_6322) -> q_gen_6322
<z, z>() -> q_gen_6322
<z, s>(q_gen_6334) -> q_gen_6355
<s, s>(q_gen_6368) -> q_gen_6368
<s, z>(q_gen_6334) -> q_gen_6368
<s, s, s>(q_gen_6321) -> q_gen_6320
<s, s, z>(q_gen_6355) -> q_gen_6320
<z, s, z>(q_gen_6334) -> q_gen_6320
<z, z, z>() -> q_gen_6320
<s, s, s>(q_gen_6343) -> q_gen_6321
<s, s, z>(q_gen_6322) -> q_gen_6321
<s, z, s>(q_gen_6322) -> q_gen_6321
<s, s, z>(q_gen_6368) -> q_gen_6343
<s, z, s>(q_gen_6368) -> q_gen_6343
<s, z, z>(q_gen_6334) -> q_gen_6343
<s, s, s>(q_gen_6320) -> q_gen_6348
<s, s, s>(q_gen_6348) -> q_gen_6348
<s, z, s>(q_gen_6355) -> q_gen_6348
}

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

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

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

-------------------------------------------
Step 51, which took 0.110422 s (model generation: 0.109438,  model checking: 0.000984):

Model:
|_
{
drop -> 
{{{
Q={q_gen_6324, q_gen_6326, q_gen_6331, q_gen_6332, q_gen_6338, q_gen_6339, q_gen_6370, q_gen_6371, q_gen_6378, q_gen_6416},
Q_f={q_gen_6324},
Delta=
{
<s>(q_gen_6326) -> q_gen_6326
<z>() -> q_gen_6326
<a>() -> q_gen_6332
<b>() -> q_gen_6332
<cons>(q_gen_6332, q_gen_6371) -> q_gen_6371
<nil>() -> q_gen_6371
<s, cons>(q_gen_6332, q_gen_6331) -> q_gen_6331
<s, nil>(q_gen_6326) -> q_gen_6331
<z, nil>() -> q_gen_6331
<cons, cons>(q_gen_6339, q_gen_6338) -> q_gen_6338
<nil, nil>() -> q_gen_6338
<a, a>() -> q_gen_6339
<a, b>() -> q_gen_6339
<b, a>() -> q_gen_6339
<b, b>() -> q_gen_6339
<s, cons>(q_gen_6332, q_gen_6378) -> q_gen_6378
<z, cons>(q_gen_6332, q_gen_6371) -> q_gen_6378
<cons, nil>(q_gen_6332, q_gen_6371) -> q_gen_6416
<s, cons, cons>(q_gen_6339, q_gen_6324) -> q_gen_6324
<s, cons, cons>(q_gen_6339, q_gen_6370) -> q_gen_6324
<s, cons, nil>(q_gen_6332, q_gen_6331) -> q_gen_6324
<s, nil, nil>(q_gen_6326) -> q_gen_6324
<z, cons, cons>(q_gen_6339, q_gen_6338) -> q_gen_6324
<z, nil, nil>() -> q_gen_6324
<s, cons, nil>(q_gen_6332, q_gen_6378) -> q_gen_6370
<z, cons, cons>(q_gen_6339, q_gen_6416) -> q_gen_6370
<z, cons, nil>(q_gen_6332, q_gen_6371) -> q_gen_6370
}

Datatype: <nat, eltlist, eltlist>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_6323, q_gen_6329},
Q_f={q_gen_6323},
Delta=
{
<a>() -> q_gen_6329
<b>() -> q_gen_6329
<cons, s>(q_gen_6329, q_gen_6323) -> q_gen_6323
<nil, z>() -> q_gen_6323
}

Datatype: <eltlist, nat>
Convolution form: right
}}}
  ;  minus -> 
{{{
Q={q_gen_6320, q_gen_6322, q_gen_6334, q_gen_6343, q_gen_6348, q_gen_6350, q_gen_6355, q_gen_6368},
Q_f={q_gen_6320},
Delta=
{
<s>(q_gen_6350) -> q_gen_6334
<z>() -> q_gen_6334
<s>(q_gen_6334) -> q_gen_6350
<s, s>(q_gen_6322) -> q_gen_6322
<z, s>(q_gen_6350) -> q_gen_6322
<z, z>() -> q_gen_6322
<z, s>(q_gen_6334) -> q_gen_6355
<s, s>(q_gen_6368) -> q_gen_6368
<s, z>(q_gen_6334) -> q_gen_6368
<s, s, s>(q_gen_6343) -> q_gen_6320
<s, s, z>(q_gen_6322) -> q_gen_6320
<s, s, z>(q_gen_6355) -> q_gen_6320
<s, z, s>(q_gen_6322) -> q_gen_6320
<z, s, z>(q_gen_6334) -> q_gen_6320
<z, s, z>(q_gen_6350) -> q_gen_6320
<z, z, z>() -> q_gen_6320
<s, s, s>(q_gen_6348) -> q_gen_6343
<s, s, z>(q_gen_6368) -> q_gen_6343
<s, z, s>(q_gen_6368) -> q_gen_6343
<s, z, z>(q_gen_6334) -> q_gen_6343
<s, s, s>(q_gen_6320) -> q_gen_6348
<s, z, s>(q_gen_6355) -> q_gen_6348
<s, z, z>(q_gen_6350) -> q_gen_6348
}

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

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

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

-------------------------------------------
Step 52, which took 0.097377 s (model generation: 0.096265,  model checking: 0.001112):

Model:
|_
{
drop -> 
{{{
Q={q_gen_6324, q_gen_6326, q_gen_6331, q_gen_6332, q_gen_6338, q_gen_6339, q_gen_6370, q_gen_6371, q_gen_6378, q_gen_6384, q_gen_6416},
Q_f={q_gen_6324},
Delta=
{
<s>(q_gen_6326) -> q_gen_6326
<z>() -> q_gen_6326
<a>() -> q_gen_6332
<b>() -> q_gen_6332
<cons>(q_gen_6332, q_gen_6371) -> q_gen_6371
<nil>() -> q_gen_6371
<s, cons>(q_gen_6332, q_gen_6331) -> q_gen_6331
<s, nil>(q_gen_6326) -> q_gen_6331
<z, nil>() -> q_gen_6331
<cons, cons>(q_gen_6339, q_gen_6338) -> q_gen_6338
<nil, nil>() -> q_gen_6338
<a, a>() -> q_gen_6339
<b, b>() -> q_gen_6339
<s, cons>(q_gen_6332, q_gen_6378) -> q_gen_6378
<z, cons>(q_gen_6332, q_gen_6371) -> q_gen_6378
<a, b>() -> q_gen_6384
<b, a>() -> q_gen_6384
<cons, nil>(q_gen_6332, q_gen_6371) -> q_gen_6416
<s, cons, cons>(q_gen_6339, q_gen_6370) -> q_gen_6324
<s, cons, cons>(q_gen_6384, q_gen_6324) -> q_gen_6324
<s, cons, cons>(q_gen_6384, q_gen_6370) -> q_gen_6324
<s, cons, nil>(q_gen_6332, q_gen_6331) -> q_gen_6324
<s, nil, nil>(q_gen_6326) -> q_gen_6324
<z, cons, cons>(q_gen_6339, q_gen_6338) -> q_gen_6324
<z, nil, nil>() -> q_gen_6324
<s, cons, cons>(q_gen_6339, q_gen_6324) -> q_gen_6370
<s, cons, nil>(q_gen_6332, q_gen_6378) -> q_gen_6370
<z, cons, cons>(q_gen_6339, q_gen_6416) -> q_gen_6370
<z, cons, cons>(q_gen_6384, q_gen_6338) -> q_gen_6370
<z, cons, nil>(q_gen_6332, q_gen_6371) -> q_gen_6370
}

Datatype: <nat, eltlist, eltlist>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_6323, q_gen_6329},
Q_f={q_gen_6323},
Delta=
{
<a>() -> q_gen_6329
<b>() -> q_gen_6329
<cons, s>(q_gen_6329, q_gen_6323) -> q_gen_6323
<nil, z>() -> q_gen_6323
}

Datatype: <eltlist, nat>
Convolution form: right
}}}
  ;  minus -> 
{{{
Q={q_gen_6320, q_gen_6322, q_gen_6334, q_gen_6343, q_gen_6348, q_gen_6350, q_gen_6355, q_gen_6368},
Q_f={q_gen_6320},
Delta=
{
<s>(q_gen_6350) -> q_gen_6334
<z>() -> q_gen_6334
<s>(q_gen_6334) -> q_gen_6350
<s, s>(q_gen_6322) -> q_gen_6322
<z, s>(q_gen_6350) -> q_gen_6322
<z, z>() -> q_gen_6322
<z, s>(q_gen_6334) -> q_gen_6355
<s, s>(q_gen_6368) -> q_gen_6368
<s, z>(q_gen_6334) -> q_gen_6368
<s, s, s>(q_gen_6343) -> q_gen_6320
<s, s, z>(q_gen_6322) -> q_gen_6320
<s, s, z>(q_gen_6355) -> q_gen_6320
<s, z, s>(q_gen_6322) -> q_gen_6320
<z, s, z>(q_gen_6334) -> q_gen_6320
<z, s, z>(q_gen_6350) -> q_gen_6320
<z, z, z>() -> q_gen_6320
<s, s, s>(q_gen_6348) -> q_gen_6343
<s, s, z>(q_gen_6368) -> q_gen_6343
<s, z, s>(q_gen_6368) -> q_gen_6343
<s, z, z>(q_gen_6334) -> q_gen_6343
<s, s, s>(q_gen_6320) -> q_gen_6348
<s, z, s>(q_gen_6355) -> q_gen_6348
<s, z, z>(q_gen_6350) -> q_gen_6348
}

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

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

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

-------------------------------------------
Step 53, which took 0.099086 s (model generation: 0.097188,  model checking: 0.001898):

Model:
|_
{
drop -> 
{{{
Q={q_gen_6324, q_gen_6326, q_gen_6331, q_gen_6332, q_gen_6338, q_gen_6339, q_gen_6370, q_gen_6371, q_gen_6378, q_gen_6384, q_gen_6416},
Q_f={q_gen_6324},
Delta=
{
<s>(q_gen_6326) -> q_gen_6326
<z>() -> q_gen_6326
<a>() -> q_gen_6332
<b>() -> q_gen_6332
<cons>(q_gen_6332, q_gen_6371) -> q_gen_6371
<nil>() -> q_gen_6371
<s, cons>(q_gen_6332, q_gen_6331) -> q_gen_6331
<s, nil>(q_gen_6326) -> q_gen_6331
<z, nil>() -> q_gen_6331
<cons, cons>(q_gen_6339, q_gen_6338) -> q_gen_6338
<nil, nil>() -> q_gen_6338
<a, a>() -> q_gen_6339
<b, b>() -> q_gen_6339
<s, cons>(q_gen_6332, q_gen_6378) -> q_gen_6378
<z, cons>(q_gen_6332, q_gen_6371) -> q_gen_6378
<a, b>() -> q_gen_6384
<b, a>() -> q_gen_6384
<cons, nil>(q_gen_6332, q_gen_6371) -> q_gen_6416
<s, cons, cons>(q_gen_6339, q_gen_6370) -> q_gen_6324
<s, cons, cons>(q_gen_6384, q_gen_6324) -> q_gen_6324
<s, cons, cons>(q_gen_6384, q_gen_6370) -> q_gen_6324
<s, cons, nil>(q_gen_6332, q_gen_6331) -> q_gen_6324
<s, nil, nil>(q_gen_6326) -> q_gen_6324
<z, cons, cons>(q_gen_6339, q_gen_6338) -> q_gen_6324
<z, nil, nil>() -> q_gen_6324
<s, cons, cons>(q_gen_6339, q_gen_6324) -> q_gen_6370
<s, cons, nil>(q_gen_6332, q_gen_6378) -> q_gen_6370
<z, cons, cons>(q_gen_6339, q_gen_6416) -> q_gen_6370
<z, cons, cons>(q_gen_6384, q_gen_6338) -> q_gen_6370
<z, cons, nil>(q_gen_6332, q_gen_6371) -> q_gen_6370
}

Datatype: <nat, eltlist, eltlist>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_6323, q_gen_6329},
Q_f={q_gen_6323},
Delta=
{
<a>() -> q_gen_6329
<b>() -> q_gen_6329
<cons, s>(q_gen_6329, q_gen_6323) -> q_gen_6323
<nil, z>() -> q_gen_6323
}

Datatype: <eltlist, nat>
Convolution form: right
}}}
  ;  minus -> 
{{{
Q={q_gen_6320, q_gen_6322, q_gen_6334, q_gen_6343, q_gen_6348, q_gen_6350, q_gen_6355, q_gen_6368},
Q_f={q_gen_6320},
Delta=
{
<s>(q_gen_6350) -> q_gen_6334
<z>() -> q_gen_6334
<s>(q_gen_6334) -> q_gen_6350
<s, s>(q_gen_6322) -> q_gen_6322
<z, z>() -> q_gen_6322
<z, s>(q_gen_6334) -> q_gen_6355
<z, s>(q_gen_6350) -> q_gen_6355
<s, s>(q_gen_6368) -> q_gen_6368
<s, z>(q_gen_6334) -> q_gen_6368
<s, s, s>(q_gen_6343) -> q_gen_6320
<s, s, z>(q_gen_6322) -> q_gen_6320
<s, s, z>(q_gen_6355) -> q_gen_6320
<s, z, s>(q_gen_6322) -> q_gen_6320
<z, s, z>(q_gen_6334) -> q_gen_6320
<z, s, z>(q_gen_6350) -> q_gen_6320
<z, z, z>() -> q_gen_6320
<s, s, s>(q_gen_6348) -> q_gen_6343
<s, s, z>(q_gen_6368) -> q_gen_6343
<s, z, s>(q_gen_6368) -> q_gen_6343
<s, z, z>(q_gen_6334) -> q_gen_6343
<s, s, s>(q_gen_6320) -> q_gen_6348
<s, z, s>(q_gen_6355) -> q_gen_6348
<s, z, z>(q_gen_6350) -> q_gen_6348
}

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

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

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

-------------------------------------------
Step 54, which took 0.118735 s (model generation: 0.118199,  model checking: 0.000536):

Model:
|_
{
drop -> 
{{{
Q={q_gen_6324, q_gen_6326, q_gen_6331, q_gen_6332, q_gen_6338, q_gen_6339, q_gen_6353, q_gen_6370, q_gen_6371, q_gen_6378, q_gen_6413},
Q_f={q_gen_6324},
Delta=
{
<s>(q_gen_6326) -> q_gen_6326
<z>() -> q_gen_6326
<a>() -> q_gen_6332
<b>() -> q_gen_6332
<cons>(q_gen_6332, q_gen_6371) -> q_gen_6371
<nil>() -> q_gen_6371
<s, cons>(q_gen_6332, q_gen_6331) -> q_gen_6331
<s, nil>(q_gen_6326) -> q_gen_6331
<z, nil>() -> q_gen_6331
<cons, cons>(q_gen_6353, q_gen_6338) -> q_gen_6338
<nil, nil>() -> q_gen_6338
<b, b>() -> q_gen_6339
<a, a>() -> q_gen_6353
<a, b>() -> q_gen_6353
<b, a>() -> q_gen_6353
<s, cons>(q_gen_6332, q_gen_6378) -> q_gen_6378
<z, cons>(q_gen_6332, q_gen_6371) -> q_gen_6378
<cons, cons>(q_gen_6339, q_gen_6338) -> q_gen_6413
<cons, nil>(q_gen_6332, q_gen_6371) -> q_gen_6413
<s, cons, cons>(q_gen_6339, q_gen_6370) -> q_gen_6324
<s, cons, cons>(q_gen_6353, q_gen_6324) -> q_gen_6324
<s, cons, cons>(q_gen_6353, q_gen_6370) -> q_gen_6324
<s, cons, nil>(q_gen_6332, q_gen_6331) -> q_gen_6324
<s, nil, nil>(q_gen_6326) -> q_gen_6324
<z, cons, cons>(q_gen_6339, q_gen_6338) -> q_gen_6324
<z, cons, cons>(q_gen_6353, q_gen_6338) -> q_gen_6324
<z, nil, nil>() -> q_gen_6324
<s, cons, cons>(q_gen_6339, q_gen_6324) -> q_gen_6370
<s, cons, nil>(q_gen_6332, q_gen_6378) -> q_gen_6370
<z, cons, cons>(q_gen_6339, q_gen_6413) -> q_gen_6370
<z, cons, cons>(q_gen_6353, q_gen_6413) -> q_gen_6370
<z, cons, nil>(q_gen_6332, q_gen_6371) -> q_gen_6370
}

Datatype: <nat, eltlist, eltlist>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_6323, q_gen_6329},
Q_f={q_gen_6323},
Delta=
{
<a>() -> q_gen_6329
<b>() -> q_gen_6329
<cons, s>(q_gen_6329, q_gen_6323) -> q_gen_6323
<nil, z>() -> q_gen_6323
}

Datatype: <eltlist, nat>
Convolution form: right
}}}
  ;  minus -> 
{{{
Q={q_gen_6320, q_gen_6322, q_gen_6334, q_gen_6343, q_gen_6348, q_gen_6350, q_gen_6355, q_gen_6368},
Q_f={q_gen_6320},
Delta=
{
<s>(q_gen_6350) -> q_gen_6334
<z>() -> q_gen_6334
<s>(q_gen_6334) -> q_gen_6350
<s, s>(q_gen_6322) -> q_gen_6322
<z, z>() -> q_gen_6322
<z, s>(q_gen_6334) -> q_gen_6355
<z, s>(q_gen_6350) -> q_gen_6355
<s, s>(q_gen_6368) -> q_gen_6368
<s, z>(q_gen_6334) -> q_gen_6368
<s, s, s>(q_gen_6343) -> q_gen_6320
<s, s, z>(q_gen_6322) -> q_gen_6320
<s, s, z>(q_gen_6355) -> q_gen_6320
<s, z, s>(q_gen_6322) -> q_gen_6320
<z, s, z>(q_gen_6334) -> q_gen_6320
<z, s, z>(q_gen_6350) -> q_gen_6320
<z, z, z>() -> q_gen_6320
<s, s, s>(q_gen_6348) -> q_gen_6343
<s, s, z>(q_gen_6368) -> q_gen_6343
<s, z, s>(q_gen_6368) -> q_gen_6343
<s, z, z>(q_gen_6334) -> q_gen_6343
<s, s, s>(q_gen_6320) -> q_gen_6348
<s, z, s>(q_gen_6355) -> q_gen_6348
<s, z, z>(q_gen_6350) -> q_gen_6348
}

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

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

Teacher's answer:
New clause system:
{
() -> drop([s(u), nil, nil]) -> 36
() -> drop([z, l, l]) -> 39
() -> length([nil, z]) -> 37
() -> minus([s(u), z, s(u)]) -> 37
() -> minus([z, y, z]) -> 37
(drop([n, l1, _sga]) /\ length([_sga, _tga]) /\ length([l1, _uga]) /\ minus([_uga, n, _vga])) -> eq_nat([_tga, _vga]) -> 37
(drop([u, x3, _ega])) -> drop([s(u), cons(x2, x3), _ega]) -> 40
(length([ll, _jga])) -> length([cons(x, ll), s(_jga)]) -> 37
(minus([u, x2, _nga])) -> minus([s(u), s(x2), _nga]) -> 40
}
Sat witness: Found: (() -> drop([z, l, l]), {
l -> cons(b, cons(b, nil))
})

-------------------------------------------
Step 55, which took 0.131145 s (model generation: 0.129142,  model checking: 0.002003):

Model:
|_
{
drop -> 
{{{
Q={q_gen_6324, q_gen_6326, q_gen_6331, q_gen_6332, q_gen_6338, q_gen_6339, q_gen_6353, q_gen_6370, q_gen_6371, q_gen_6378, q_gen_6416},
Q_f={q_gen_6324},
Delta=
{
<s>(q_gen_6326) -> q_gen_6326
<z>() -> q_gen_6326
<a>() -> q_gen_6332
<b>() -> q_gen_6332
<cons>(q_gen_6332, q_gen_6371) -> q_gen_6371
<nil>() -> q_gen_6371
<s, cons>(q_gen_6332, q_gen_6331) -> q_gen_6331
<s, nil>(q_gen_6326) -> q_gen_6331
<z, nil>() -> q_gen_6331
<cons, cons>(q_gen_6339, q_gen_6338) -> q_gen_6338
<cons, cons>(q_gen_6353, q_gen_6338) -> q_gen_6338
<nil, nil>() -> q_gen_6338
<b, b>() -> q_gen_6339
<a, a>() -> q_gen_6353
<a, b>() -> q_gen_6353
<b, a>() -> q_gen_6353
<s, cons>(q_gen_6332, q_gen_6378) -> q_gen_6378
<z, cons>(q_gen_6332, q_gen_6371) -> q_gen_6378
<cons, nil>(q_gen_6332, q_gen_6371) -> q_gen_6416
<s, cons, cons>(q_gen_6339, q_gen_6370) -> q_gen_6324
<s, cons, cons>(q_gen_6353, q_gen_6324) -> q_gen_6324
<s, cons, cons>(q_gen_6353, q_gen_6370) -> q_gen_6324
<s, cons, nil>(q_gen_6332, q_gen_6331) -> q_gen_6324
<s, nil, nil>(q_gen_6326) -> q_gen_6324
<z, cons, cons>(q_gen_6339, q_gen_6338) -> q_gen_6324
<z, cons, cons>(q_gen_6353, q_gen_6338) -> q_gen_6324
<z, nil, nil>() -> q_gen_6324
<s, cons, cons>(q_gen_6339, q_gen_6324) -> q_gen_6370
<s, cons, nil>(q_gen_6332, q_gen_6378) -> q_gen_6370
<z, cons, cons>(q_gen_6339, q_gen_6416) -> q_gen_6370
<z, cons, nil>(q_gen_6332, q_gen_6371) -> q_gen_6370
}

Datatype: <nat, eltlist, eltlist>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_6323, q_gen_6329},
Q_f={q_gen_6323},
Delta=
{
<a>() -> q_gen_6329
<b>() -> q_gen_6329
<cons, s>(q_gen_6329, q_gen_6323) -> q_gen_6323
<nil, z>() -> q_gen_6323
}

Datatype: <eltlist, nat>
Convolution form: right
}}}
  ;  minus -> 
{{{
Q={q_gen_6320, q_gen_6322, q_gen_6334, q_gen_6343, q_gen_6348, q_gen_6350, q_gen_6355, q_gen_6368},
Q_f={q_gen_6320},
Delta=
{
<s>(q_gen_6350) -> q_gen_6334
<z>() -> q_gen_6334
<s>(q_gen_6334) -> q_gen_6350
<s, s>(q_gen_6322) -> q_gen_6322
<z, z>() -> q_gen_6322
<z, s>(q_gen_6334) -> q_gen_6355
<z, s>(q_gen_6350) -> q_gen_6355
<s, s>(q_gen_6368) -> q_gen_6368
<s, z>(q_gen_6334) -> q_gen_6368
<s, s, s>(q_gen_6343) -> q_gen_6320
<s, s, z>(q_gen_6322) -> q_gen_6320
<s, s, z>(q_gen_6355) -> q_gen_6320
<s, z, s>(q_gen_6322) -> q_gen_6320
<z, s, z>(q_gen_6334) -> q_gen_6320
<z, s, z>(q_gen_6350) -> q_gen_6320
<z, z, z>() -> q_gen_6320
<s, s, s>(q_gen_6348) -> q_gen_6343
<s, s, z>(q_gen_6368) -> q_gen_6343
<s, z, s>(q_gen_6368) -> q_gen_6343
<s, z, z>(q_gen_6334) -> q_gen_6343
<s, s, s>(q_gen_6320) -> q_gen_6348
<s, z, s>(q_gen_6355) -> q_gen_6348
<s, z, z>(q_gen_6350) -> q_gen_6348
}

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

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

Teacher's answer:
New clause system:
{
() -> drop([s(u), nil, nil]) -> 37
() -> drop([z, l, l]) -> 39
() -> length([nil, z]) -> 37
() -> minus([s(u), z, s(u)]) -> 37
() -> minus([z, y, z]) -> 37
(drop([n, l1, _sga]) /\ length([_sga, _tga]) /\ length([l1, _uga]) /\ minus([_uga, n, _vga])) -> eq_nat([_tga, _vga]) -> 40
(drop([u, x3, _ega])) -> drop([s(u), cons(x2, x3), _ega]) -> 40
(length([ll, _jga])) -> length([cons(x, ll), s(_jga)]) -> 38
(minus([u, x2, _nga])) -> minus([s(u), s(x2), _nga]) -> 40
}
Sat witness: Found: ((drop([n, l1, _sga]) /\ length([_sga, _tga]) /\ length([l1, _uga]) /\ minus([_uga, n, _vga])) -> eq_nat([_tga, _vga]), {
_sga -> cons(a, nil)  ;  _tga -> s(z)  ;  _uga -> s(z)  ;  _vga -> z  ;  l1 -> cons(b, nil)  ;  n -> s(s(z))
})

-------------------------------------------
Step 56, which took 0.098773 s (model generation: 0.097366,  model checking: 0.001407):

Model:
|_
{
drop -> 
{{{
Q={q_gen_6324, q_gen_6325, q_gen_6326, q_gen_6331, q_gen_6332, q_gen_6338, q_gen_6339, q_gen_6370, q_gen_6371, q_gen_6378, q_gen_6416},
Q_f={q_gen_6324, q_gen_6325},
Delta=
{
<s>(q_gen_6326) -> q_gen_6326
<z>() -> q_gen_6326
<a>() -> q_gen_6332
<b>() -> q_gen_6332
<cons>(q_gen_6332, q_gen_6371) -> q_gen_6371
<nil>() -> q_gen_6371
<s, cons>(q_gen_6332, q_gen_6331) -> q_gen_6331
<s, nil>(q_gen_6326) -> q_gen_6331
<z, nil>() -> q_gen_6331
<cons, cons>(q_gen_6339, q_gen_6338) -> q_gen_6338
<nil, nil>() -> q_gen_6338
<a, a>() -> q_gen_6339
<a, b>() -> q_gen_6339
<b, a>() -> q_gen_6339
<b, b>() -> q_gen_6339
<s, cons>(q_gen_6332, q_gen_6378) -> q_gen_6378
<z, cons>(q_gen_6332, q_gen_6371) -> q_gen_6378
<cons, nil>(q_gen_6332, q_gen_6371) -> q_gen_6416
<s, cons, cons>(q_gen_6339, q_gen_6324) -> q_gen_6324
<s, cons, cons>(q_gen_6339, q_gen_6370) -> q_gen_6324
<s, cons, nil>(q_gen_6332, q_gen_6331) -> q_gen_6324
<z, nil, nil>() -> q_gen_6324
<s, nil, nil>(q_gen_6326) -> q_gen_6325
<z, cons, cons>(q_gen_6339, q_gen_6338) -> q_gen_6325
<s, cons, cons>(q_gen_6339, q_gen_6325) -> q_gen_6370
<s, cons, nil>(q_gen_6332, q_gen_6378) -> q_gen_6370
<z, cons, cons>(q_gen_6339, q_gen_6416) -> q_gen_6370
<z, cons, nil>(q_gen_6332, q_gen_6371) -> q_gen_6370
}

Datatype: <nat, eltlist, eltlist>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_6323, q_gen_6329},
Q_f={q_gen_6323},
Delta=
{
<a>() -> q_gen_6329
<b>() -> q_gen_6329
<cons, s>(q_gen_6329, q_gen_6323) -> q_gen_6323
<nil, z>() -> q_gen_6323
}

Datatype: <eltlist, nat>
Convolution form: right
}}}
  ;  minus -> 
{{{
Q={q_gen_6320, q_gen_6321, q_gen_6322, q_gen_6334, q_gen_6343, q_gen_6348, q_gen_6355, q_gen_6368},
Q_f={q_gen_6320, q_gen_6321},
Delta=
{
<s>(q_gen_6334) -> q_gen_6334
<z>() -> q_gen_6334
<s, s>(q_gen_6322) -> q_gen_6322
<z, z>() -> q_gen_6322
<z, s>(q_gen_6334) -> q_gen_6355
<s, s>(q_gen_6368) -> q_gen_6368
<s, z>(q_gen_6334) -> q_gen_6368
<s, s, s>(q_gen_6321) -> q_gen_6320
<s, s, z>(q_gen_6355) -> q_gen_6320
<z, s, z>(q_gen_6334) -> q_gen_6320
<z, z, z>() -> q_gen_6320
<s, s, s>(q_gen_6343) -> q_gen_6321
<s, s, z>(q_gen_6322) -> q_gen_6321
<s, z, s>(q_gen_6322) -> q_gen_6321
<s, s, z>(q_gen_6368) -> q_gen_6343
<s, z, s>(q_gen_6368) -> q_gen_6343
<s, z, z>(q_gen_6334) -> q_gen_6343
<s, s, s>(q_gen_6320) -> q_gen_6348
<s, s, s>(q_gen_6348) -> q_gen_6348
<s, z, s>(q_gen_6355) -> q_gen_6348
}

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

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

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

-------------------------------------------
Step 57, which took 0.109076 s (model generation: 0.107385,  model checking: 0.001691):

Model:
|_
{
drop -> 
{{{
Q={q_gen_6324, q_gen_6325, q_gen_6326, q_gen_6331, q_gen_6332, q_gen_6338, q_gen_6339, q_gen_6370, q_gen_6371, q_gen_6378, q_gen_6416},
Q_f={q_gen_6324, q_gen_6325},
Delta=
{
<s>(q_gen_6326) -> q_gen_6326
<z>() -> q_gen_6326
<a>() -> q_gen_6332
<b>() -> q_gen_6332
<cons>(q_gen_6332, q_gen_6371) -> q_gen_6371
<nil>() -> q_gen_6371
<s, cons>(q_gen_6332, q_gen_6331) -> q_gen_6331
<s, nil>(q_gen_6326) -> q_gen_6331
<z, nil>() -> q_gen_6331
<cons, cons>(q_gen_6339, q_gen_6338) -> q_gen_6338
<nil, nil>() -> q_gen_6338
<a, a>() -> q_gen_6339
<a, b>() -> q_gen_6339
<b, a>() -> q_gen_6339
<b, b>() -> q_gen_6339
<s, cons>(q_gen_6332, q_gen_6378) -> q_gen_6378
<z, cons>(q_gen_6332, q_gen_6371) -> q_gen_6378
<cons, nil>(q_gen_6332, q_gen_6371) -> q_gen_6416
<s, cons, cons>(q_gen_6339, q_gen_6324) -> q_gen_6324
<s, cons, cons>(q_gen_6339, q_gen_6370) -> q_gen_6324
<s, cons, nil>(q_gen_6332, q_gen_6331) -> q_gen_6324
<z, cons, cons>(q_gen_6339, q_gen_6338) -> q_gen_6324
<z, nil, nil>() -> q_gen_6324
<s, nil, nil>(q_gen_6326) -> q_gen_6325
<s, cons, cons>(q_gen_6339, q_gen_6325) -> q_gen_6370
<s, cons, nil>(q_gen_6332, q_gen_6378) -> q_gen_6370
<z, cons, cons>(q_gen_6339, q_gen_6416) -> q_gen_6370
<z, cons, nil>(q_gen_6332, q_gen_6371) -> q_gen_6370
}

Datatype: <nat, eltlist, eltlist>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_6323, q_gen_6329},
Q_f={q_gen_6323},
Delta=
{
<a>() -> q_gen_6329
<b>() -> q_gen_6329
<cons, s>(q_gen_6329, q_gen_6323) -> q_gen_6323
<nil, z>() -> q_gen_6323
}

Datatype: <eltlist, nat>
Convolution form: right
}}}
  ;  minus -> 
{{{
Q={q_gen_6320, q_gen_6321, q_gen_6322, q_gen_6334, q_gen_6343, q_gen_6348, q_gen_6355, q_gen_6368},
Q_f={q_gen_6320, q_gen_6321},
Delta=
{
<s>(q_gen_6334) -> q_gen_6334
<z>() -> q_gen_6334
<s, s>(q_gen_6322) -> q_gen_6322
<z, z>() -> q_gen_6322
<z, s>(q_gen_6334) -> q_gen_6355
<s, s>(q_gen_6368) -> q_gen_6368
<s, z>(q_gen_6334) -> q_gen_6368
<s, s, z>(q_gen_6355) -> q_gen_6320
<z, s, z>(q_gen_6334) -> q_gen_6320
<z, z, z>() -> q_gen_6320
<s, s, s>(q_gen_6321) -> q_gen_6321
<s, s, s>(q_gen_6343) -> q_gen_6321
<s, s, z>(q_gen_6322) -> q_gen_6321
<s, z, s>(q_gen_6322) -> q_gen_6321
<s, s, z>(q_gen_6368) -> q_gen_6343
<s, z, s>(q_gen_6368) -> q_gen_6343
<s, z, z>(q_gen_6334) -> q_gen_6343
<s, s, s>(q_gen_6320) -> q_gen_6348
<s, s, s>(q_gen_6348) -> q_gen_6348
<s, z, s>(q_gen_6355) -> q_gen_6348
}

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

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

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

-------------------------------------------
Step 58, which took 0.102943 s (model generation: 0.101570,  model checking: 0.001373):

Model:
|_
{
drop -> 
{{{
Q={q_gen_6324, q_gen_6325, q_gen_6326, q_gen_6331, q_gen_6332, q_gen_6338, q_gen_6339, q_gen_6370, q_gen_6371, q_gen_6378, q_gen_6416},
Q_f={q_gen_6324, q_gen_6325},
Delta=
{
<s>(q_gen_6326) -> q_gen_6326
<z>() -> q_gen_6326
<a>() -> q_gen_6332
<b>() -> q_gen_6332
<cons>(q_gen_6332, q_gen_6371) -> q_gen_6371
<nil>() -> q_gen_6371
<s, cons>(q_gen_6332, q_gen_6331) -> q_gen_6331
<s, nil>(q_gen_6326) -> q_gen_6331
<z, nil>() -> q_gen_6331
<cons, cons>(q_gen_6339, q_gen_6338) -> q_gen_6338
<nil, nil>() -> q_gen_6338
<a, a>() -> q_gen_6339
<a, b>() -> q_gen_6339
<b, a>() -> q_gen_6339
<b, b>() -> q_gen_6339
<s, cons>(q_gen_6332, q_gen_6378) -> q_gen_6378
<z, cons>(q_gen_6332, q_gen_6371) -> q_gen_6378
<cons, cons>(q_gen_6339, q_gen_6416) -> q_gen_6416
<cons, nil>(q_gen_6332, q_gen_6371) -> q_gen_6416
<s, cons, cons>(q_gen_6339, q_gen_6324) -> q_gen_6324
<s, cons, cons>(q_gen_6339, q_gen_6370) -> q_gen_6324
<s, cons, nil>(q_gen_6332, q_gen_6331) -> q_gen_6324
<z, cons, cons>(q_gen_6339, q_gen_6338) -> q_gen_6324
<z, nil, nil>() -> q_gen_6324
<s, nil, nil>(q_gen_6326) -> q_gen_6325
<s, cons, cons>(q_gen_6339, q_gen_6325) -> q_gen_6370
<s, cons, nil>(q_gen_6332, q_gen_6378) -> q_gen_6370
<z, cons, cons>(q_gen_6339, q_gen_6416) -> q_gen_6370
<z, cons, nil>(q_gen_6332, q_gen_6371) -> q_gen_6370
}

Datatype: <nat, eltlist, eltlist>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_6323, q_gen_6329},
Q_f={q_gen_6323},
Delta=
{
<a>() -> q_gen_6329
<b>() -> q_gen_6329
<cons, s>(q_gen_6329, q_gen_6323) -> q_gen_6323
<nil, z>() -> q_gen_6323
}

Datatype: <eltlist, nat>
Convolution form: right
}}}
  ;  minus -> 
{{{
Q={q_gen_6320, q_gen_6322, q_gen_6334, q_gen_6343, q_gen_6348, q_gen_6350, q_gen_6355, q_gen_6368},
Q_f={q_gen_6320},
Delta=
{
<s>(q_gen_6350) -> q_gen_6334
<z>() -> q_gen_6334
<s>(q_gen_6334) -> q_gen_6350
<s, s>(q_gen_6322) -> q_gen_6322
<z, z>() -> q_gen_6322
<z, s>(q_gen_6334) -> q_gen_6355
<z, s>(q_gen_6350) -> q_gen_6355
<s, s>(q_gen_6368) -> q_gen_6368
<s, z>(q_gen_6334) -> q_gen_6368
<s, s, s>(q_gen_6343) -> q_gen_6320
<s, s, z>(q_gen_6322) -> q_gen_6320
<s, s, z>(q_gen_6355) -> q_gen_6320
<s, z, s>(q_gen_6322) -> q_gen_6320
<z, s, z>(q_gen_6334) -> q_gen_6320
<z, s, z>(q_gen_6350) -> q_gen_6320
<z, z, z>() -> q_gen_6320
<s, s, s>(q_gen_6348) -> q_gen_6343
<s, s, z>(q_gen_6368) -> q_gen_6343
<s, z, s>(q_gen_6368) -> q_gen_6343
<s, z, z>(q_gen_6334) -> q_gen_6343
<s, s, s>(q_gen_6320) -> q_gen_6348
<s, z, s>(q_gen_6355) -> q_gen_6348
<s, z, z>(q_gen_6350) -> q_gen_6348
}

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

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

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

-------------------------------------------
Step 59, which took 0.149454 s (model generation: 0.148992,  model checking: 0.000462):

Model:
|_
{
drop -> 
{{{
Q={q_gen_6324, q_gen_6326, q_gen_6331, q_gen_6332, q_gen_6338, q_gen_6339, q_gen_6352, q_gen_6353, q_gen_6370, q_gen_6371, q_gen_6378},
Q_f={q_gen_6324},
Delta=
{
<s>(q_gen_6326) -> q_gen_6326
<z>() -> q_gen_6326
<a>() -> q_gen_6332
<b>() -> q_gen_6332
<cons>(q_gen_6332, q_gen_6371) -> q_gen_6371
<nil>() -> q_gen_6371
<s, cons>(q_gen_6332, q_gen_6331) -> q_gen_6331
<s, nil>(q_gen_6326) -> q_gen_6331
<z, nil>() -> q_gen_6331
<cons, cons>(q_gen_6339, q_gen_6338) -> q_gen_6338
<nil, nil>() -> q_gen_6338
<a, b>() -> q_gen_6339
<b, b>() -> q_gen_6339
<cons, cons>(q_gen_6339, q_gen_6352) -> q_gen_6352
<cons, cons>(q_gen_6353, q_gen_6338) -> q_gen_6352
<cons, nil>(q_gen_6332, q_gen_6371) -> q_gen_6352
<a, a>() -> q_gen_6353
<b, a>() -> q_gen_6353
<s, cons>(q_gen_6332, q_gen_6378) -> q_gen_6378
<z, cons>(q_gen_6332, q_gen_6371) -> q_gen_6378
<s, cons, cons>(q_gen_6339, q_gen_6370) -> q_gen_6324
<s, cons, nil>(q_gen_6332, q_gen_6331) -> q_gen_6324
<s, nil, nil>(q_gen_6326) -> q_gen_6324
<z, cons, cons>(q_gen_6339, q_gen_6338) -> q_gen_6324
<z, cons, cons>(q_gen_6353, q_gen_6352) -> q_gen_6324
<z, nil, nil>() -> q_gen_6324
<s, cons, cons>(q_gen_6339, q_gen_6324) -> q_gen_6370
<s, cons, cons>(q_gen_6353, q_gen_6324) -> q_gen_6370
<s, cons, cons>(q_gen_6353, q_gen_6370) -> q_gen_6370
<s, cons, nil>(q_gen_6332, q_gen_6378) -> q_gen_6370
<z, cons, cons>(q_gen_6339, q_gen_6352) -> q_gen_6370
<z, cons, cons>(q_gen_6353, q_gen_6338) -> q_gen_6370
<z, cons, nil>(q_gen_6332, q_gen_6371) -> q_gen_6370
}

Datatype: <nat, eltlist, eltlist>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_6323, q_gen_6329},
Q_f={q_gen_6323},
Delta=
{
<a>() -> q_gen_6329
<b>() -> q_gen_6329
<cons, s>(q_gen_6329, q_gen_6323) -> q_gen_6323
<nil, z>() -> q_gen_6323
}

Datatype: <eltlist, nat>
Convolution form: right
}}}
  ;  minus -> 
{{{
Q={q_gen_6320, q_gen_6321, q_gen_6322, q_gen_6334, q_gen_6343, q_gen_6348, q_gen_6355, q_gen_6368},
Q_f={q_gen_6320, q_gen_6321},
Delta=
{
<s>(q_gen_6334) -> q_gen_6334
<z>() -> q_gen_6334
<s, s>(q_gen_6322) -> q_gen_6322
<s, s>(q_gen_6368) -> q_gen_6322
<z, z>() -> q_gen_6322
<z, s>(q_gen_6334) -> q_gen_6355
<s, z>(q_gen_6334) -> q_gen_6368
<s, s, s>(q_gen_6321) -> q_gen_6320
<s, s, z>(q_gen_6355) -> q_gen_6320
<z, s, z>(q_gen_6334) -> q_gen_6320
<z, z, z>() -> q_gen_6320
<s, s, s>(q_gen_6343) -> q_gen_6321
<s, s, z>(q_gen_6322) -> q_gen_6321
<s, z, s>(q_gen_6322) -> q_gen_6321
<s, z, s>(q_gen_6368) -> q_gen_6321
<s, s, z>(q_gen_6368) -> q_gen_6343
<s, z, z>(q_gen_6334) -> q_gen_6343
<s, s, s>(q_gen_6320) -> q_gen_6348
<s, s, s>(q_gen_6348) -> q_gen_6348
<s, z, s>(q_gen_6355) -> q_gen_6348
}

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

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

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

-------------------------------------------
Step 60, which took 0.201821 s (model generation: 0.200408,  model checking: 0.001413):

Model:
|_
{
drop -> 
{{{
Q={q_gen_6324, q_gen_6326, q_gen_6331, q_gen_6332, q_gen_6338, q_gen_6339, q_gen_6370, q_gen_6371, q_gen_6378, q_gen_6416, q_gen_6422},
Q_f={q_gen_6324},
Delta=
{
<s>(q_gen_6326) -> q_gen_6326
<z>() -> q_gen_6326
<a>() -> q_gen_6332
<b>() -> q_gen_6332
<nil>() -> q_gen_6371
<cons>(q_gen_6332, q_gen_6371) -> q_gen_6422
<s, cons>(q_gen_6332, q_gen_6331) -> q_gen_6331
<s, nil>(q_gen_6326) -> q_gen_6331
<z, nil>() -> q_gen_6331
<cons, cons>(q_gen_6339, q_gen_6338) -> q_gen_6338
<nil, nil>() -> q_gen_6338
<a, a>() -> q_gen_6339
<a, b>() -> q_gen_6339
<b, a>() -> q_gen_6339
<b, b>() -> q_gen_6339
<s, cons>(q_gen_6332, q_gen_6378) -> q_gen_6378
<z, cons>(q_gen_6332, q_gen_6371) -> q_gen_6378
<cons, cons>(q_gen_6339, q_gen_6416) -> q_gen_6416
<cons, nil>(q_gen_6332, q_gen_6371) -> q_gen_6416
<s, cons, cons>(q_gen_6339, q_gen_6370) -> q_gen_6324
<s, cons, nil>(q_gen_6332, q_gen_6331) -> q_gen_6324
<s, nil, nil>(q_gen_6326) -> q_gen_6324
<z, cons, cons>(q_gen_6339, q_gen_6338) -> q_gen_6324
<z, cons, nil>(q_gen_6332, q_gen_6422) -> q_gen_6324
<z, nil, nil>() -> q_gen_6324
<s, cons, cons>(q_gen_6339, q_gen_6324) -> q_gen_6370
<s, cons, nil>(q_gen_6332, q_gen_6378) -> q_gen_6370
<z, cons, cons>(q_gen_6339, q_gen_6416) -> q_gen_6370
<z, cons, nil>(q_gen_6332, q_gen_6371) -> q_gen_6370
}

Datatype: <nat, eltlist, eltlist>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_6323, q_gen_6329},
Q_f={q_gen_6323},
Delta=
{
<a>() -> q_gen_6329
<b>() -> q_gen_6329
<cons, s>(q_gen_6329, q_gen_6323) -> q_gen_6323
<nil, z>() -> q_gen_6323
}

Datatype: <eltlist, nat>
Convolution form: right
}}}
  ;  minus -> 
{{{
Q={q_gen_6320, q_gen_6321, q_gen_6322, q_gen_6334, q_gen_6343, q_gen_6348, q_gen_6355, q_gen_6368},
Q_f={q_gen_6320, q_gen_6321},
Delta=
{
<s>(q_gen_6334) -> q_gen_6334
<z>() -> q_gen_6334
<s, s>(q_gen_6322) -> q_gen_6322
<z, z>() -> q_gen_6322
<z, s>(q_gen_6334) -> q_gen_6355
<s, s>(q_gen_6368) -> q_gen_6368
<s, z>(q_gen_6334) -> q_gen_6368
<s, s, s>(q_gen_6321) -> q_gen_6320
<s, s, z>(q_gen_6355) -> q_gen_6320
<z, s, z>(q_gen_6334) -> q_gen_6320
<z, z, z>() -> q_gen_6320
<s, s, s>(q_gen_6343) -> q_gen_6321
<s, s, z>(q_gen_6322) -> q_gen_6321
<s, z, s>(q_gen_6322) -> q_gen_6321
<s, z, s>(q_gen_6368) -> q_gen_6321
<s, s, z>(q_gen_6368) -> q_gen_6343
<s, z, z>(q_gen_6334) -> q_gen_6343
<s, s, s>(q_gen_6320) -> q_gen_6348
<s, s, s>(q_gen_6348) -> q_gen_6348
<s, z, s>(q_gen_6355) -> q_gen_6348
}

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

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

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

-------------------------------------------
Step 61, which took 0.149212 s (model generation: 0.147206,  model checking: 0.002006):

Model:
|_
{
drop -> 
{{{
Q={q_gen_6324, q_gen_6326, q_gen_6331, q_gen_6332, q_gen_6338, q_gen_6339, q_gen_6370, q_gen_6371, q_gen_6378, q_gen_6416, q_gen_6422},
Q_f={q_gen_6324},
Delta=
{
<s>(q_gen_6326) -> q_gen_6326
<z>() -> q_gen_6326
<a>() -> q_gen_6332
<b>() -> q_gen_6332
<nil>() -> q_gen_6371
<cons>(q_gen_6332, q_gen_6371) -> q_gen_6422
<s, cons>(q_gen_6332, q_gen_6331) -> q_gen_6331
<s, nil>(q_gen_6326) -> q_gen_6331
<z, nil>() -> q_gen_6331
<cons, cons>(q_gen_6339, q_gen_6338) -> q_gen_6338
<nil, nil>() -> q_gen_6338
<a, a>() -> q_gen_6339
<a, b>() -> q_gen_6339
<b, a>() -> q_gen_6339
<b, b>() -> q_gen_6339
<s, cons>(q_gen_6332, q_gen_6378) -> q_gen_6378
<z, cons>(q_gen_6332, q_gen_6371) -> q_gen_6378
<cons, cons>(q_gen_6339, q_gen_6416) -> q_gen_6416
<cons, nil>(q_gen_6332, q_gen_6371) -> q_gen_6416
<s, cons, cons>(q_gen_6339, q_gen_6370) -> q_gen_6324
<s, cons, nil>(q_gen_6332, q_gen_6331) -> q_gen_6324
<s, nil, nil>(q_gen_6326) -> q_gen_6324
<z, cons, cons>(q_gen_6339, q_gen_6338) -> q_gen_6324
<z, cons, nil>(q_gen_6332, q_gen_6422) -> q_gen_6324
<z, nil, nil>() -> q_gen_6324
<s, cons, cons>(q_gen_6339, q_gen_6324) -> q_gen_6370
<s, cons, nil>(q_gen_6332, q_gen_6378) -> q_gen_6370
<z, cons, cons>(q_gen_6339, q_gen_6416) -> q_gen_6370
<z, cons, nil>(q_gen_6332, q_gen_6371) -> q_gen_6370
}

Datatype: <nat, eltlist, eltlist>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_6323, q_gen_6329},
Q_f={q_gen_6323},
Delta=
{
<a>() -> q_gen_6329
<b>() -> q_gen_6329
<cons, s>(q_gen_6329, q_gen_6323) -> q_gen_6323
<nil, z>() -> q_gen_6323
}

Datatype: <eltlist, nat>
Convolution form: right
}}}
  ;  minus -> 
{{{
Q={q_gen_6320, q_gen_6322, q_gen_6334, q_gen_6343, q_gen_6348, q_gen_6350, q_gen_6355, q_gen_6368},
Q_f={q_gen_6320},
Delta=
{
<s>(q_gen_6350) -> q_gen_6334
<z>() -> q_gen_6334
<s>(q_gen_6334) -> q_gen_6350
<s, s>(q_gen_6322) -> q_gen_6322
<z, z>() -> q_gen_6322
<z, s>(q_gen_6334) -> q_gen_6355
<z, s>(q_gen_6350) -> q_gen_6355
<s, s>(q_gen_6368) -> q_gen_6368
<s, z>(q_gen_6334) -> q_gen_6368
<s, s, s>(q_gen_6343) -> q_gen_6320
<s, s, z>(q_gen_6322) -> q_gen_6320
<s, s, z>(q_gen_6355) -> q_gen_6320
<s, z, s>(q_gen_6322) -> q_gen_6320
<z, s, z>(q_gen_6334) -> q_gen_6320
<z, s, z>(q_gen_6350) -> q_gen_6320
<z, z, z>() -> q_gen_6320
<s, s, s>(q_gen_6348) -> q_gen_6343
<s, s, z>(q_gen_6368) -> q_gen_6343
<s, z, s>(q_gen_6368) -> q_gen_6343
<s, z, z>(q_gen_6334) -> q_gen_6343
<s, s, s>(q_gen_6320) -> q_gen_6348
<s, z, s>(q_gen_6355) -> q_gen_6348
<s, z, z>(q_gen_6350) -> q_gen_6348
}

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

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

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

-------------------------------------------
Step 62, which took 0.214086 s (model generation: 0.213388,  model checking: 0.000698):

Model:
|_
{
drop -> 
{{{
Q={q_gen_6324, q_gen_6326, q_gen_6331, q_gen_6332, q_gen_6338, q_gen_6339, q_gen_6370, q_gen_6371, q_gen_6378, q_gen_6416, q_gen_6422},
Q_f={q_gen_6324},
Delta=
{
<s>(q_gen_6326) -> q_gen_6326
<z>() -> q_gen_6326
<a>() -> q_gen_6332
<b>() -> q_gen_6332
<nil>() -> q_gen_6371
<cons>(q_gen_6332, q_gen_6371) -> q_gen_6422
<s, cons>(q_gen_6332, q_gen_6331) -> q_gen_6331
<s, nil>(q_gen_6326) -> q_gen_6331
<z, cons>(q_gen_6332, q_gen_6422) -> q_gen_6331
<z, nil>() -> q_gen_6331
<cons, cons>(q_gen_6339, q_gen_6338) -> q_gen_6338
<nil, nil>() -> q_gen_6338
<a, a>() -> q_gen_6339
<a, b>() -> q_gen_6339
<b, a>() -> q_gen_6339
<b, b>() -> q_gen_6339
<s, cons>(q_gen_6332, q_gen_6378) -> q_gen_6378
<z, cons>(q_gen_6332, q_gen_6371) -> q_gen_6378
<cons, cons>(q_gen_6339, q_gen_6416) -> q_gen_6416
<cons, nil>(q_gen_6332, q_gen_6371) -> q_gen_6416
<s, cons, cons>(q_gen_6339, q_gen_6370) -> q_gen_6324
<s, cons, nil>(q_gen_6332, q_gen_6331) -> q_gen_6324
<s, nil, nil>(q_gen_6326) -> q_gen_6324
<z, cons, cons>(q_gen_6339, q_gen_6338) -> q_gen_6324
<z, cons, nil>(q_gen_6332, q_gen_6422) -> q_gen_6324
<z, nil, nil>() -> q_gen_6324
<s, cons, cons>(q_gen_6339, q_gen_6324) -> q_gen_6370
<s, cons, nil>(q_gen_6332, q_gen_6378) -> q_gen_6370
<z, cons, cons>(q_gen_6339, q_gen_6416) -> q_gen_6370
<z, cons, nil>(q_gen_6332, q_gen_6371) -> q_gen_6370
}

Datatype: <nat, eltlist, eltlist>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_6323, q_gen_6329},
Q_f={q_gen_6323},
Delta=
{
<a>() -> q_gen_6329
<b>() -> q_gen_6329
<cons, s>(q_gen_6329, q_gen_6323) -> q_gen_6323
<nil, z>() -> q_gen_6323
}

Datatype: <eltlist, nat>
Convolution form: right
}}}
  ;  minus -> 
{{{
Q={q_gen_6320, q_gen_6322, q_gen_6334, q_gen_6343, q_gen_6348, q_gen_6350, q_gen_6355, q_gen_6368},
Q_f={q_gen_6320},
Delta=
{
<s>(q_gen_6350) -> q_gen_6334
<z>() -> q_gen_6334
<s>(q_gen_6334) -> q_gen_6350
<s, s>(q_gen_6322) -> q_gen_6322
<z, z>() -> q_gen_6322
<z, s>(q_gen_6334) -> q_gen_6355
<z, s>(q_gen_6350) -> q_gen_6355
<s, s>(q_gen_6368) -> q_gen_6368
<s, z>(q_gen_6334) -> q_gen_6368
<s, s, s>(q_gen_6343) -> q_gen_6320
<s, s, z>(q_gen_6322) -> q_gen_6320
<s, s, z>(q_gen_6355) -> q_gen_6320
<s, z, s>(q_gen_6322) -> q_gen_6320
<z, s, z>(q_gen_6334) -> q_gen_6320
<z, s, z>(q_gen_6350) -> q_gen_6320
<z, z, z>() -> q_gen_6320
<s, s, s>(q_gen_6348) -> q_gen_6343
<s, s, z>(q_gen_6368) -> q_gen_6343
<s, z, s>(q_gen_6368) -> q_gen_6343
<s, z, z>(q_gen_6334) -> q_gen_6343
<s, s, s>(q_gen_6320) -> q_gen_6348
<s, z, s>(q_gen_6355) -> q_gen_6348
<s, z, z>(q_gen_6350) -> q_gen_6348
}

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

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

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

-------------------------------------------
Step 63, which took 0.246397 s (model generation: 0.245329,  model checking: 0.001068):

Model:
|_
{
drop -> 
{{{
Q={q_gen_6324, q_gen_6326, q_gen_6331, q_gen_6332, q_gen_6338, q_gen_6339, q_gen_6369, q_gen_6370, q_gen_6371, q_gen_6378, q_gen_6416},
Q_f={q_gen_6324, q_gen_6369},
Delta=
{
<s>(q_gen_6326) -> q_gen_6326
<z>() -> q_gen_6326
<a>() -> q_gen_6332
<b>() -> q_gen_6332
<cons>(q_gen_6332, q_gen_6371) -> q_gen_6371
<nil>() -> q_gen_6371
<s, cons>(q_gen_6332, q_gen_6331) -> q_gen_6331
<s, nil>(q_gen_6326) -> q_gen_6331
<z, nil>() -> q_gen_6331
<cons, cons>(q_gen_6339, q_gen_6338) -> q_gen_6338
<nil, nil>() -> q_gen_6338
<a, a>() -> q_gen_6339
<a, b>() -> q_gen_6339
<b, a>() -> q_gen_6339
<b, b>() -> q_gen_6339
<s, cons>(q_gen_6332, q_gen_6378) -> q_gen_6378
<z, cons>(q_gen_6332, q_gen_6371) -> q_gen_6378
<cons, cons>(q_gen_6339, q_gen_6416) -> q_gen_6416
<cons, nil>(q_gen_6332, q_gen_6371) -> q_gen_6416
<s, cons, cons>(q_gen_6339, q_gen_6369) -> q_gen_6324
<s, cons, nil>(q_gen_6332, q_gen_6331) -> q_gen_6324
<s, nil, nil>(q_gen_6326) -> q_gen_6324
<z, cons, cons>(q_gen_6339, q_gen_6338) -> q_gen_6324
<z, nil, nil>() -> q_gen_6324
<s, cons, cons>(q_gen_6339, q_gen_6370) -> q_gen_6369
<s, cons, cons>(q_gen_6339, q_gen_6324) -> q_gen_6370
<s, cons, nil>(q_gen_6332, q_gen_6378) -> q_gen_6370
<z, cons, cons>(q_gen_6339, q_gen_6416) -> q_gen_6370
<z, cons, nil>(q_gen_6332, q_gen_6371) -> q_gen_6370
}

Datatype: <nat, eltlist, eltlist>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_6323, q_gen_6329},
Q_f={q_gen_6323},
Delta=
{
<a>() -> q_gen_6329
<b>() -> q_gen_6329
<cons, s>(q_gen_6329, q_gen_6323) -> q_gen_6323
<nil, z>() -> q_gen_6323
}

Datatype: <eltlist, nat>
Convolution form: right
}}}
  ;  minus -> 
{{{
Q={q_gen_6320, q_gen_6322, q_gen_6334, q_gen_6343, q_gen_6348, q_gen_6350, q_gen_6355, q_gen_6368},
Q_f={q_gen_6320},
Delta=
{
<s>(q_gen_6350) -> q_gen_6334
<z>() -> q_gen_6334
<s>(q_gen_6334) -> q_gen_6350
<s, s>(q_gen_6322) -> q_gen_6322
<z, z>() -> q_gen_6322
<z, s>(q_gen_6334) -> q_gen_6355
<z, s>(q_gen_6350) -> q_gen_6355
<s, s>(q_gen_6368) -> q_gen_6368
<s, z>(q_gen_6334) -> q_gen_6368
<s, s, s>(q_gen_6343) -> q_gen_6320
<s, s, z>(q_gen_6322) -> q_gen_6320
<s, s, z>(q_gen_6355) -> q_gen_6320
<s, z, s>(q_gen_6322) -> q_gen_6320
<z, s, z>(q_gen_6334) -> q_gen_6320
<z, s, z>(q_gen_6350) -> q_gen_6320
<z, z, z>() -> q_gen_6320
<s, s, s>(q_gen_6348) -> q_gen_6343
<s, s, z>(q_gen_6368) -> q_gen_6343
<s, z, s>(q_gen_6368) -> q_gen_6343
<s, z, z>(q_gen_6334) -> q_gen_6343
<s, s, s>(q_gen_6320) -> q_gen_6348
<s, z, s>(q_gen_6355) -> q_gen_6348
<s, z, z>(q_gen_6350) -> q_gen_6348
}

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

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

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

-------------------------------------------
Step 64, which took 0.273122 s (model generation: 0.268902,  model checking: 0.004220):

Model:
|_
{
drop -> 
{{{
Q={q_gen_6324, q_gen_6326, q_gen_6331, q_gen_6332, q_gen_6337, q_gen_6338, q_gen_6339, q_gen_6370, q_gen_6371, q_gen_6378, q_gen_6416},
Q_f={q_gen_6324, q_gen_6337},
Delta=
{
<s>(q_gen_6326) -> q_gen_6326
<z>() -> q_gen_6326
<a>() -> q_gen_6332
<b>() -> q_gen_6332
<cons>(q_gen_6332, q_gen_6371) -> q_gen_6371
<nil>() -> q_gen_6371
<s, cons>(q_gen_6332, q_gen_6331) -> q_gen_6331
<s, nil>(q_gen_6326) -> q_gen_6331
<z, nil>() -> q_gen_6331
<cons, cons>(q_gen_6339, q_gen_6338) -> q_gen_6338
<nil, nil>() -> q_gen_6338
<a, a>() -> q_gen_6339
<a, b>() -> q_gen_6339
<b, a>() -> q_gen_6339
<b, b>() -> q_gen_6339
<s, cons>(q_gen_6332, q_gen_6378) -> q_gen_6378
<z, cons>(q_gen_6332, q_gen_6371) -> q_gen_6378
<cons, cons>(q_gen_6339, q_gen_6416) -> q_gen_6416
<cons, nil>(q_gen_6332, q_gen_6371) -> q_gen_6416
<s, cons, cons>(q_gen_6339, q_gen_6337) -> q_gen_6324
<s, cons, nil>(q_gen_6332, q_gen_6331) -> q_gen_6324
<s, nil, nil>(q_gen_6326) -> q_gen_6324
<z, nil, nil>() -> q_gen_6324
<s, cons, cons>(q_gen_6339, q_gen_6370) -> q_gen_6337
<z, cons, cons>(q_gen_6339, q_gen_6338) -> q_gen_6337
<s, cons, cons>(q_gen_6339, q_gen_6324) -> q_gen_6370
<s, cons, nil>(q_gen_6332, q_gen_6378) -> q_gen_6370
<z, cons, cons>(q_gen_6339, q_gen_6416) -> q_gen_6370
<z, cons, nil>(q_gen_6332, q_gen_6371) -> q_gen_6370
}

Datatype: <nat, eltlist, eltlist>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_6323, q_gen_6329},
Q_f={q_gen_6323},
Delta=
{
<a>() -> q_gen_6329
<b>() -> q_gen_6329
<cons, s>(q_gen_6329, q_gen_6323) -> q_gen_6323
<nil, z>() -> q_gen_6323
}

Datatype: <eltlist, nat>
Convolution form: right
}}}
  ;  minus -> 
{{{
Q={q_gen_6320, q_gen_6321, q_gen_6322, q_gen_6334, q_gen_6343, q_gen_6348, q_gen_6355, q_gen_6368},
Q_f={q_gen_6320, q_gen_6321},
Delta=
{
<s>(q_gen_6334) -> q_gen_6334
<z>() -> q_gen_6334
<s, s>(q_gen_6322) -> q_gen_6322
<z, z>() -> q_gen_6322
<z, s>(q_gen_6334) -> q_gen_6355
<s, s>(q_gen_6368) -> q_gen_6368
<s, z>(q_gen_6334) -> q_gen_6368
<s, s, z>(q_gen_6355) -> q_gen_6320
<z, s, z>(q_gen_6334) -> q_gen_6320
<z, z, z>() -> q_gen_6320
<s, s, s>(q_gen_6321) -> q_gen_6321
<s, s, s>(q_gen_6343) -> q_gen_6321
<s, s, z>(q_gen_6322) -> q_gen_6321
<s, z, s>(q_gen_6322) -> q_gen_6321
<s, s, z>(q_gen_6368) -> q_gen_6343
<s, z, s>(q_gen_6368) -> q_gen_6343
<s, z, z>(q_gen_6334) -> q_gen_6343
<s, s, s>(q_gen_6320) -> q_gen_6348
<s, s, s>(q_gen_6348) -> q_gen_6348
<s, z, s>(q_gen_6355) -> q_gen_6348
}

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

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

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

-------------------------------------------
Step 65, which took 0.267942 s (model generation: 0.266722,  model checking: 0.001220):

Model:
|_
{
drop -> 
{{{
Q={q_gen_6324, q_gen_6326, q_gen_6331, q_gen_6332, q_gen_6337, q_gen_6338, q_gen_6339, q_gen_6370, q_gen_6371, q_gen_6378, q_gen_6416},
Q_f={q_gen_6324, q_gen_6337},
Delta=
{
<s>(q_gen_6326) -> q_gen_6326
<z>() -> q_gen_6326
<a>() -> q_gen_6332
<b>() -> q_gen_6332
<cons>(q_gen_6332, q_gen_6371) -> q_gen_6371
<nil>() -> q_gen_6371
<s, cons>(q_gen_6332, q_gen_6331) -> q_gen_6331
<s, nil>(q_gen_6326) -> q_gen_6331
<z, nil>() -> q_gen_6331
<cons, cons>(q_gen_6339, q_gen_6338) -> q_gen_6338
<nil, nil>() -> q_gen_6338
<a, a>() -> q_gen_6339
<a, b>() -> q_gen_6339
<b, a>() -> q_gen_6339
<b, b>() -> q_gen_6339
<s, cons>(q_gen_6332, q_gen_6378) -> q_gen_6378
<z, cons>(q_gen_6332, q_gen_6371) -> q_gen_6378
<cons, cons>(q_gen_6339, q_gen_6416) -> q_gen_6416
<cons, nil>(q_gen_6332, q_gen_6371) -> q_gen_6416
<s, cons, nil>(q_gen_6332, q_gen_6331) -> q_gen_6324
<s, nil, nil>(q_gen_6326) -> q_gen_6324
<z, nil, nil>() -> q_gen_6324
<s, cons, cons>(q_gen_6339, q_gen_6337) -> q_gen_6337
<s, cons, cons>(q_gen_6339, q_gen_6370) -> q_gen_6337
<z, cons, cons>(q_gen_6339, q_gen_6338) -> q_gen_6337
<s, cons, cons>(q_gen_6339, q_gen_6324) -> q_gen_6370
<s, cons, nil>(q_gen_6332, q_gen_6378) -> q_gen_6370
<z, cons, cons>(q_gen_6339, q_gen_6416) -> q_gen_6370
<z, cons, nil>(q_gen_6332, q_gen_6371) -> q_gen_6370
}

Datatype: <nat, eltlist, eltlist>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_6323, q_gen_6329},
Q_f={q_gen_6323},
Delta=
{
<a>() -> q_gen_6329
<b>() -> q_gen_6329
<cons, s>(q_gen_6329, q_gen_6323) -> q_gen_6323
<nil, z>() -> q_gen_6323
}

Datatype: <eltlist, nat>
Convolution form: right
}}}
  ;  minus -> 
{{{
Q={q_gen_6320, q_gen_6321, q_gen_6322, q_gen_6334, q_gen_6343, q_gen_6348, q_gen_6355, q_gen_6368},
Q_f={q_gen_6320, q_gen_6321},
Delta=
{
<s>(q_gen_6334) -> q_gen_6334
<z>() -> q_gen_6334
<s, s>(q_gen_6322) -> q_gen_6322
<z, z>() -> q_gen_6322
<z, s>(q_gen_6334) -> q_gen_6355
<s, s>(q_gen_6368) -> q_gen_6368
<s, z>(q_gen_6334) -> q_gen_6368
<s, s, z>(q_gen_6355) -> q_gen_6320
<z, s, z>(q_gen_6334) -> q_gen_6320
<z, z, z>() -> q_gen_6320
<s, s, s>(q_gen_6321) -> q_gen_6321
<s, s, s>(q_gen_6343) -> q_gen_6321
<s, s, z>(q_gen_6322) -> q_gen_6321
<s, z, s>(q_gen_6322) -> q_gen_6321
<s, s, z>(q_gen_6368) -> q_gen_6343
<s, z, s>(q_gen_6368) -> q_gen_6343
<s, z, z>(q_gen_6334) -> q_gen_6343
<s, s, s>(q_gen_6320) -> q_gen_6348
<s, s, s>(q_gen_6348) -> q_gen_6348
<s, z, s>(q_gen_6355) -> q_gen_6348
}

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

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

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

-------------------------------------------
Step 66, which took 0.280253 s (model generation: 0.279251,  model checking: 0.001002):

Model:
|_
{
drop -> 
{{{
Q={q_gen_6324, q_gen_6326, q_gen_6331, q_gen_6332, q_gen_6338, q_gen_6339, q_gen_6340, q_gen_6341, q_gen_6370, q_gen_6371, q_gen_6378, q_gen_6416},
Q_f={q_gen_6324, q_gen_6340},
Delta=
{
<z>() -> q_gen_6326
<a>() -> q_gen_6332
<b>() -> q_gen_6332
<s>(q_gen_6326) -> q_gen_6341
<cons>(q_gen_6332, q_gen_6371) -> q_gen_6371
<nil>() -> q_gen_6371
<s, cons>(q_gen_6332, q_gen_6331) -> q_gen_6331
<s, nil>(q_gen_6326) -> q_gen_6331
<z, nil>() -> q_gen_6331
<cons, cons>(q_gen_6339, q_gen_6338) -> q_gen_6338
<nil, nil>() -> q_gen_6338
<a, a>() -> q_gen_6339
<a, b>() -> q_gen_6339
<b, a>() -> q_gen_6339
<b, b>() -> q_gen_6339
<s, cons>(q_gen_6332, q_gen_6378) -> q_gen_6378
<s, nil>(q_gen_6341) -> q_gen_6378
<z, cons>(q_gen_6332, q_gen_6371) -> q_gen_6378
<cons, cons>(q_gen_6339, q_gen_6416) -> q_gen_6416
<cons, nil>(q_gen_6332, q_gen_6371) -> q_gen_6416
<s, cons, nil>(q_gen_6332, q_gen_6331) -> q_gen_6324
<s, nil, nil>(q_gen_6326) -> q_gen_6324
<z, cons, cons>(q_gen_6339, q_gen_6338) -> q_gen_6324
<z, nil, nil>() -> q_gen_6324
<s, cons, cons>(q_gen_6339, q_gen_6340) -> q_gen_6340
<s, cons, cons>(q_gen_6339, q_gen_6370) -> q_gen_6340
<s, nil, nil>(q_gen_6341) -> q_gen_6340
<s, cons, cons>(q_gen_6339, q_gen_6324) -> q_gen_6370
<s, cons, nil>(q_gen_6332, q_gen_6378) -> q_gen_6370
<z, cons, cons>(q_gen_6339, q_gen_6416) -> q_gen_6370
<z, cons, nil>(q_gen_6332, q_gen_6371) -> q_gen_6370
}

Datatype: <nat, eltlist, eltlist>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_6323, q_gen_6329},
Q_f={q_gen_6323},
Delta=
{
<a>() -> q_gen_6329
<b>() -> q_gen_6329
<cons, s>(q_gen_6329, q_gen_6323) -> q_gen_6323
<nil, z>() -> q_gen_6323
}

Datatype: <eltlist, nat>
Convolution form: right
}}}
  ;  minus -> 
{{{
Q={q_gen_6320, q_gen_6322, q_gen_6334, q_gen_6343, q_gen_6348, q_gen_6350, q_gen_6355, q_gen_6361},
Q_f={q_gen_6320},
Delta=
{
<s>(q_gen_6350) -> q_gen_6334
<z>() -> q_gen_6334
<s>(q_gen_6334) -> q_gen_6350
<s, s>(q_gen_6322) -> q_gen_6322
<z, z>() -> q_gen_6322
<z, s>(q_gen_6334) -> q_gen_6355
<s, s>(q_gen_6361) -> q_gen_6361
<s, z>(q_gen_6334) -> q_gen_6361
<z, s>(q_gen_6350) -> q_gen_6361
<s, s, s>(q_gen_6343) -> q_gen_6320
<s, s, z>(q_gen_6322) -> q_gen_6320
<s, s, z>(q_gen_6355) -> q_gen_6320
<s, z, s>(q_gen_6322) -> q_gen_6320
<z, s, z>(q_gen_6334) -> q_gen_6320
<z, s, z>(q_gen_6350) -> q_gen_6320
<z, z, z>() -> q_gen_6320
<s, s, s>(q_gen_6348) -> q_gen_6343
<s, s, z>(q_gen_6361) -> q_gen_6343
<s, z, s>(q_gen_6361) -> q_gen_6343
<s, z, z>(q_gen_6334) -> q_gen_6343
<s, s, s>(q_gen_6320) -> q_gen_6348
<s, z, s>(q_gen_6355) -> q_gen_6348
<s, z, z>(q_gen_6350) -> q_gen_6348
}

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

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

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

-------------------------------------------
Step 67, which took 0.344116 s (model generation: 0.343056,  model checking: 0.001060):

Model:
|_
{
drop -> 
{{{
Q={q_gen_6324, q_gen_6326, q_gen_6331, q_gen_6332, q_gen_6338, q_gen_6339, q_gen_6356, q_gen_6357, q_gen_6370, q_gen_6371, q_gen_6378, q_gen_6416},
Q_f={q_gen_6324, q_gen_6356},
Delta=
{
<s>(q_gen_6326) -> q_gen_6326
<z>() -> q_gen_6326
<a>() -> q_gen_6332
<b>() -> q_gen_6332
<cons>(q_gen_6332, q_gen_6371) -> q_gen_6371
<nil>() -> q_gen_6371
<z, nil>() -> q_gen_6331
<cons, cons>(q_gen_6339, q_gen_6338) -> q_gen_6338
<nil, nil>() -> q_gen_6338
<a, a>() -> q_gen_6339
<a, b>() -> q_gen_6339
<b, a>() -> q_gen_6339
<b, b>() -> q_gen_6339
<s, cons>(q_gen_6332, q_gen_6331) -> q_gen_6357
<s, nil>(q_gen_6326) -> q_gen_6357
<s, cons>(q_gen_6332, q_gen_6357) -> q_gen_6378
<s, cons>(q_gen_6332, q_gen_6378) -> q_gen_6378
<z, cons>(q_gen_6332, q_gen_6371) -> q_gen_6378
<cons, cons>(q_gen_6339, q_gen_6416) -> q_gen_6416
<cons, nil>(q_gen_6332, q_gen_6371) -> q_gen_6416
<s, cons, nil>(q_gen_6332, q_gen_6331) -> q_gen_6324
<s, nil, nil>(q_gen_6326) -> q_gen_6324
<z, cons, cons>(q_gen_6339, q_gen_6338) -> q_gen_6324
<z, nil, nil>() -> q_gen_6324
<s, cons, cons>(q_gen_6339, q_gen_6356) -> q_gen_6356
<s, cons, cons>(q_gen_6339, q_gen_6370) -> q_gen_6356
<s, cons, nil>(q_gen_6332, q_gen_6357) -> q_gen_6356
<s, cons, cons>(q_gen_6339, q_gen_6324) -> q_gen_6370
<s, cons, nil>(q_gen_6332, q_gen_6378) -> q_gen_6370
<z, cons, cons>(q_gen_6339, q_gen_6416) -> q_gen_6370
<z, cons, nil>(q_gen_6332, q_gen_6371) -> q_gen_6370
}

Datatype: <nat, eltlist, eltlist>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_6323, q_gen_6329},
Q_f={q_gen_6323},
Delta=
{
<a>() -> q_gen_6329
<b>() -> q_gen_6329
<cons, s>(q_gen_6329, q_gen_6323) -> q_gen_6323
<nil, z>() -> q_gen_6323
}

Datatype: <eltlist, nat>
Convolution form: right
}}}
  ;  minus -> 
{{{
Q={q_gen_6320, q_gen_6322, q_gen_6334, q_gen_6343, q_gen_6348, q_gen_6350, q_gen_6355, q_gen_6361},
Q_f={q_gen_6320},
Delta=
{
<s>(q_gen_6350) -> q_gen_6334
<z>() -> q_gen_6334
<s>(q_gen_6334) -> q_gen_6350
<s, s>(q_gen_6322) -> q_gen_6322
<z, z>() -> q_gen_6322
<z, s>(q_gen_6334) -> q_gen_6355
<s, s>(q_gen_6361) -> q_gen_6361
<s, z>(q_gen_6334) -> q_gen_6361
<z, s>(q_gen_6350) -> q_gen_6361
<s, s, s>(q_gen_6343) -> q_gen_6320
<s, s, z>(q_gen_6322) -> q_gen_6320
<s, s, z>(q_gen_6355) -> q_gen_6320
<s, z, s>(q_gen_6322) -> q_gen_6320
<z, s, z>(q_gen_6334) -> q_gen_6320
<z, s, z>(q_gen_6350) -> q_gen_6320
<z, z, z>() -> q_gen_6320
<s, s, s>(q_gen_6348) -> q_gen_6343
<s, s, z>(q_gen_6361) -> q_gen_6343
<s, z, s>(q_gen_6361) -> q_gen_6343
<s, z, z>(q_gen_6334) -> q_gen_6343
<s, s, s>(q_gen_6320) -> q_gen_6348
<s, z, s>(q_gen_6355) -> q_gen_6348
<s, z, z>(q_gen_6350) -> q_gen_6348
}

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

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

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

-------------------------------------------
Step 68, which took 0.230901 s (model generation: 0.228396,  model checking: 0.002505):

Model:
|_
{
drop -> 
{{{
Q={q_gen_6324, q_gen_6326, q_gen_6330, q_gen_6331, q_gen_6332, q_gen_6338, q_gen_6339, q_gen_6370, q_gen_6371, q_gen_6378, q_gen_6416},
Q_f={q_gen_6324, q_gen_6330},
Delta=
{
<s>(q_gen_6326) -> q_gen_6326
<z>() -> q_gen_6326
<a>() -> q_gen_6332
<b>() -> q_gen_6332
<cons>(q_gen_6332, q_gen_6371) -> q_gen_6371
<nil>() -> q_gen_6371
<s, cons>(q_gen_6332, q_gen_6331) -> q_gen_6331
<s, nil>(q_gen_6326) -> q_gen_6331
<z, nil>() -> q_gen_6331
<cons, cons>(q_gen_6339, q_gen_6338) -> q_gen_6338
<nil, nil>() -> q_gen_6338
<a, a>() -> q_gen_6339
<a, b>() -> q_gen_6339
<b, a>() -> q_gen_6339
<b, b>() -> q_gen_6339
<s, cons>(q_gen_6332, q_gen_6378) -> q_gen_6378
<z, cons>(q_gen_6332, q_gen_6371) -> q_gen_6378
<cons, cons>(q_gen_6339, q_gen_6416) -> q_gen_6416
<cons, nil>(q_gen_6332, q_gen_6371) -> q_gen_6416
<s, nil, nil>(q_gen_6326) -> q_gen_6324
<z, cons, cons>(q_gen_6339, q_gen_6338) -> q_gen_6324
<z, nil, nil>() -> q_gen_6324
<s, cons, cons>(q_gen_6339, q_gen_6330) -> q_gen_6330
<s, cons, cons>(q_gen_6339, q_gen_6370) -> q_gen_6330
<s, cons, nil>(q_gen_6332, q_gen_6331) -> q_gen_6330
<s, cons, cons>(q_gen_6339, q_gen_6324) -> q_gen_6370
<s, cons, nil>(q_gen_6332, q_gen_6378) -> q_gen_6370
<z, cons, cons>(q_gen_6339, q_gen_6416) -> q_gen_6370
<z, cons, nil>(q_gen_6332, q_gen_6371) -> q_gen_6370
}

Datatype: <nat, eltlist, eltlist>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_6323, q_gen_6329},
Q_f={q_gen_6323},
Delta=
{
<a>() -> q_gen_6329
<b>() -> q_gen_6329
<cons, s>(q_gen_6329, q_gen_6323) -> q_gen_6323
<nil, z>() -> q_gen_6323
}

Datatype: <eltlist, nat>
Convolution form: right
}}}
  ;  minus -> 
{{{
Q={q_gen_6320, q_gen_6321, q_gen_6322, q_gen_6334, q_gen_6343, q_gen_6348, q_gen_6350, q_gen_6355, q_gen_6368},
Q_f={q_gen_6320, q_gen_6321},
Delta=
{
<s>(q_gen_6350) -> q_gen_6334
<z>() -> q_gen_6334
<s>(q_gen_6334) -> q_gen_6350
<s, s>(q_gen_6322) -> q_gen_6322
<z, z>() -> q_gen_6322
<z, s>(q_gen_6334) -> q_gen_6355
<z, s>(q_gen_6350) -> q_gen_6355
<s, s>(q_gen_6368) -> q_gen_6368
<s, z>(q_gen_6334) -> q_gen_6368
<s, s, s>(q_gen_6343) -> q_gen_6320
<s, s, z>(q_gen_6355) -> q_gen_6320
<z, s, z>(q_gen_6334) -> q_gen_6320
<z, s, z>(q_gen_6350) -> q_gen_6320
<z, z, z>() -> q_gen_6320
<s, s, s>(q_gen_6321) -> q_gen_6321
<s, s, z>(q_gen_6322) -> q_gen_6321
<s, z, s>(q_gen_6322) -> q_gen_6321
<s, z, s>(q_gen_6368) -> q_gen_6321
<s, z, z>(q_gen_6350) -> q_gen_6321
<s, s, z>(q_gen_6368) -> q_gen_6343
<s, z, z>(q_gen_6334) -> q_gen_6343
<s, s, s>(q_gen_6320) -> q_gen_6348
<s, s, s>(q_gen_6348) -> q_gen_6348
<s, z, s>(q_gen_6355) -> q_gen_6348
}

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

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

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

-------------------------------------------
Step 69, which took 0.341884 s (model generation: 0.338739,  model checking: 0.003145):

Model:
|_
{
drop -> 
{{{
Q={q_gen_6324, q_gen_6326, q_gen_6331, q_gen_6332, q_gen_6338, q_gen_6339, q_gen_6369, q_gen_6370, q_gen_6371, q_gen_6378, q_gen_6416},
Q_f={q_gen_6324, q_gen_6369},
Delta=
{
<s>(q_gen_6326) -> q_gen_6326
<z>() -> q_gen_6326
<a>() -> q_gen_6332
<b>() -> q_gen_6332
<cons>(q_gen_6332, q_gen_6371) -> q_gen_6371
<nil>() -> q_gen_6371
<s, cons>(q_gen_6332, q_gen_6331) -> q_gen_6331
<s, nil>(q_gen_6326) -> q_gen_6331
<z, nil>() -> q_gen_6331
<cons, cons>(q_gen_6339, q_gen_6338) -> q_gen_6338
<nil, nil>() -> q_gen_6338
<a, a>() -> q_gen_6339
<a, b>() -> q_gen_6339
<b, a>() -> q_gen_6339
<b, b>() -> q_gen_6339
<s, cons>(q_gen_6332, q_gen_6378) -> q_gen_6378
<z, cons>(q_gen_6332, q_gen_6371) -> q_gen_6378
<cons, cons>(q_gen_6339, q_gen_6416) -> q_gen_6416
<cons, nil>(q_gen_6332, q_gen_6371) -> q_gen_6416
<s, cons, nil>(q_gen_6332, q_gen_6331) -> q_gen_6324
<s, nil, nil>(q_gen_6326) -> q_gen_6324
<z, cons, cons>(q_gen_6339, q_gen_6338) -> q_gen_6324
<z, nil, nil>() -> q_gen_6324
<s, cons, cons>(q_gen_6339, q_gen_6369) -> q_gen_6369
<s, cons, cons>(q_gen_6339, q_gen_6370) -> q_gen_6369
<s, cons, cons>(q_gen_6339, q_gen_6324) -> q_gen_6370
<s, cons, nil>(q_gen_6332, q_gen_6378) -> q_gen_6370
<z, cons, cons>(q_gen_6339, q_gen_6416) -> q_gen_6370
<z, cons, nil>(q_gen_6332, q_gen_6371) -> q_gen_6370
}

Datatype: <nat, eltlist, eltlist>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_6323, q_gen_6329},
Q_f={q_gen_6323},
Delta=
{
<a>() -> q_gen_6329
<b>() -> q_gen_6329
<cons, s>(q_gen_6329, q_gen_6323) -> q_gen_6323
<nil, z>() -> q_gen_6323
}

Datatype: <eltlist, nat>
Convolution form: right
}}}
  ;  minus -> 
{{{
Q={q_gen_6320, q_gen_6321, q_gen_6322, q_gen_6334, q_gen_6343, q_gen_6348, q_gen_6350, q_gen_6355, q_gen_6368},
Q_f={q_gen_6320, q_gen_6321},
Delta=
{
<s>(q_gen_6350) -> q_gen_6334
<z>() -> q_gen_6334
<s>(q_gen_6334) -> q_gen_6350
<s, s>(q_gen_6322) -> q_gen_6322
<z, z>() -> q_gen_6322
<z, s>(q_gen_6334) -> q_gen_6355
<z, s>(q_gen_6350) -> q_gen_6355
<s, s>(q_gen_6368) -> q_gen_6368
<s, z>(q_gen_6334) -> q_gen_6368
<s, s, z>(q_gen_6355) -> q_gen_6320
<z, s, z>(q_gen_6350) -> q_gen_6320
<z, z, z>() -> q_gen_6320
<s, s, s>(q_gen_6343) -> q_gen_6321
<s, s, z>(q_gen_6322) -> q_gen_6321
<s, z, s>(q_gen_6322) -> q_gen_6321
<s, z, z>(q_gen_6350) -> q_gen_6321
<z, s, z>(q_gen_6334) -> q_gen_6321
<s, s, s>(q_gen_6321) -> q_gen_6343
<s, s, z>(q_gen_6368) -> q_gen_6343
<s, z, s>(q_gen_6368) -> q_gen_6343
<s, z, z>(q_gen_6334) -> q_gen_6343
<s, s, s>(q_gen_6320) -> q_gen_6348
<s, s, s>(q_gen_6348) -> q_gen_6348
<s, z, s>(q_gen_6355) -> q_gen_6348
}

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

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

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

-------------------------------------------
Step 70, which took 0.318442 s (model generation: 0.315137,  model checking: 0.003305):

Model:
|_
{
drop -> 
{{{
Q={q_gen_6324, q_gen_6326, q_gen_6331, q_gen_6332, q_gen_6338, q_gen_6339, q_gen_6369, q_gen_6370, q_gen_6371, q_gen_6378, q_gen_6416},
Q_f={q_gen_6324, q_gen_6369},
Delta=
{
<s>(q_gen_6326) -> q_gen_6326
<z>() -> q_gen_6326
<a>() -> q_gen_6332
<b>() -> q_gen_6332
<cons>(q_gen_6332, q_gen_6371) -> q_gen_6371
<nil>() -> q_gen_6371
<s, cons>(q_gen_6332, q_gen_6331) -> q_gen_6331
<s, nil>(q_gen_6326) -> q_gen_6331
<z, nil>() -> q_gen_6331
<cons, cons>(q_gen_6339, q_gen_6338) -> q_gen_6338
<nil, nil>() -> q_gen_6338
<a, a>() -> q_gen_6339
<a, b>() -> q_gen_6339
<b, a>() -> q_gen_6339
<b, b>() -> q_gen_6339
<s, cons>(q_gen_6332, q_gen_6378) -> q_gen_6378
<z, cons>(q_gen_6332, q_gen_6371) -> q_gen_6378
<cons, cons>(q_gen_6339, q_gen_6416) -> q_gen_6416
<cons, nil>(q_gen_6332, q_gen_6371) -> q_gen_6416
<s, cons, nil>(q_gen_6332, q_gen_6331) -> q_gen_6324
<s, nil, nil>(q_gen_6326) -> q_gen_6324
<z, cons, cons>(q_gen_6339, q_gen_6338) -> q_gen_6324
<z, nil, nil>() -> q_gen_6324
<s, cons, cons>(q_gen_6339, q_gen_6369) -> q_gen_6369
<s, cons, cons>(q_gen_6339, q_gen_6370) -> q_gen_6369
<s, cons, cons>(q_gen_6339, q_gen_6324) -> q_gen_6370
<s, cons, nil>(q_gen_6332, q_gen_6378) -> q_gen_6370
<z, cons, cons>(q_gen_6339, q_gen_6416) -> q_gen_6370
<z, cons, nil>(q_gen_6332, q_gen_6371) -> q_gen_6370
}

Datatype: <nat, eltlist, eltlist>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_6323, q_gen_6329},
Q_f={q_gen_6323},
Delta=
{
<a>() -> q_gen_6329
<b>() -> q_gen_6329
<cons, s>(q_gen_6329, q_gen_6323) -> q_gen_6323
<nil, z>() -> q_gen_6323
}

Datatype: <eltlist, nat>
Convolution form: right
}}}
  ;  minus -> 
{{{
Q={q_gen_6320, q_gen_6322, q_gen_6334, q_gen_6343, q_gen_6348, q_gen_6350, q_gen_6355, q_gen_6368, q_gen_6372},
Q_f={q_gen_6320, q_gen_6372},
Delta=
{
<s>(q_gen_6350) -> q_gen_6334
<z>() -> q_gen_6334
<s>(q_gen_6334) -> q_gen_6350
<s, s>(q_gen_6322) -> q_gen_6322
<z, z>() -> q_gen_6322
<z, s>(q_gen_6334) -> q_gen_6355
<z, s>(q_gen_6350) -> q_gen_6355
<s, s>(q_gen_6368) -> q_gen_6368
<s, z>(q_gen_6334) -> q_gen_6368
<s, s, s>(q_gen_6343) -> q_gen_6320
<s, s, z>(q_gen_6322) -> q_gen_6320
<s, s, z>(q_gen_6355) -> q_gen_6320
<s, z, s>(q_gen_6322) -> q_gen_6320
<z, s, z>(q_gen_6334) -> q_gen_6320
<z, s, z>(q_gen_6350) -> q_gen_6320
<z, z, z>() -> q_gen_6320
<s, s, z>(q_gen_6368) -> q_gen_6343
<s, z, z>(q_gen_6334) -> q_gen_6343
<s, s, s>(q_gen_6320) -> q_gen_6348
<s, s, s>(q_gen_6348) -> q_gen_6348
<s, z, s>(q_gen_6355) -> q_gen_6348
<s, s, s>(q_gen_6372) -> q_gen_6372
<s, z, s>(q_gen_6368) -> q_gen_6372
<s, z, z>(q_gen_6350) -> q_gen_6372
}

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

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

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

-------------------------------------------
Step 71, which took 0.314928 s (model generation: 0.312396,  model checking: 0.002532):

Model:
|_
{
drop -> 
{{{
Q={q_gen_6324, q_gen_6326, q_gen_6331, q_gen_6332, q_gen_6338, q_gen_6339, q_gen_6370, q_gen_6371, q_gen_6378, q_gen_6416, q_gen_6421, q_gen_6422},
Q_f={q_gen_6324},
Delta=
{
<s>(q_gen_6326) -> q_gen_6326
<z>() -> q_gen_6326
<a>() -> q_gen_6332
<b>() -> q_gen_6332
<nil>() -> q_gen_6371
<cons>(q_gen_6332, q_gen_6371) -> q_gen_6422
<s, cons>(q_gen_6332, q_gen_6331) -> q_gen_6331
<s, nil>(q_gen_6326) -> q_gen_6331
<z, nil>() -> q_gen_6331
<cons, cons>(q_gen_6339, q_gen_6338) -> q_gen_6338
<nil, nil>() -> q_gen_6338
<a, a>() -> q_gen_6339
<a, b>() -> q_gen_6339
<b, a>() -> q_gen_6339
<b, b>() -> q_gen_6339
<s, cons>(q_gen_6332, q_gen_6378) -> q_gen_6378
<z, cons>(q_gen_6332, q_gen_6371) -> q_gen_6378
<z, cons>(q_gen_6332, q_gen_6422) -> q_gen_6378
<cons, cons>(q_gen_6339, q_gen_6416) -> q_gen_6416
<cons, nil>(q_gen_6332, q_gen_6371) -> q_gen_6416
<s, cons, cons>(q_gen_6339, q_gen_6370) -> q_gen_6324
<s, cons, nil>(q_gen_6332, q_gen_6331) -> q_gen_6324
<s, nil, nil>(q_gen_6326) -> q_gen_6324
<z, cons, cons>(q_gen_6339, q_gen_6338) -> q_gen_6324
<z, nil, nil>() -> q_gen_6324
<s, cons, cons>(q_gen_6339, q_gen_6421) -> q_gen_6370
<s, cons, nil>(q_gen_6332, q_gen_6378) -> q_gen_6370
<z, cons, cons>(q_gen_6339, q_gen_6416) -> q_gen_6370
<z, cons, nil>(q_gen_6332, q_gen_6371) -> q_gen_6370
<s, cons, cons>(q_gen_6339, q_gen_6324) -> q_gen_6421
<z, cons, nil>(q_gen_6332, q_gen_6422) -> q_gen_6421
}

Datatype: <nat, eltlist, eltlist>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_6323, q_gen_6329},
Q_f={q_gen_6323},
Delta=
{
<a>() -> q_gen_6329
<b>() -> q_gen_6329
<cons, s>(q_gen_6329, q_gen_6323) -> q_gen_6323
<nil, z>() -> q_gen_6323
}

Datatype: <eltlist, nat>
Convolution form: right
}}}
  ;  minus -> 
{{{
Q={q_gen_6320, q_gen_6321, q_gen_6322, q_gen_6334, q_gen_6343, q_gen_6348, q_gen_6350, q_gen_6355, q_gen_6368},
Q_f={q_gen_6320, q_gen_6321},
Delta=
{
<s>(q_gen_6350) -> q_gen_6334
<z>() -> q_gen_6334
<s>(q_gen_6334) -> q_gen_6350
<s, s>(q_gen_6322) -> q_gen_6322
<z, z>() -> q_gen_6322
<z, s>(q_gen_6334) -> q_gen_6355
<z, s>(q_gen_6350) -> q_gen_6355
<s, s>(q_gen_6368) -> q_gen_6368
<s, z>(q_gen_6334) -> q_gen_6368
<s, s, s>(q_gen_6343) -> q_gen_6320
<s, s, z>(q_gen_6322) -> q_gen_6320
<z, s, z>(q_gen_6350) -> q_gen_6320
<z, z, z>() -> q_gen_6320
<s, s, z>(q_gen_6355) -> q_gen_6321
<s, z, s>(q_gen_6322) -> q_gen_6321
<s, z, z>(q_gen_6350) -> q_gen_6321
<z, s, z>(q_gen_6334) -> q_gen_6321
<s, s, s>(q_gen_6321) -> q_gen_6343
<s, s, z>(q_gen_6368) -> q_gen_6343
<s, z, s>(q_gen_6368) -> q_gen_6343
<s, z, z>(q_gen_6334) -> q_gen_6343
<s, s, s>(q_gen_6320) -> q_gen_6348
<s, s, s>(q_gen_6348) -> q_gen_6348
<s, z, s>(q_gen_6355) -> q_gen_6348
}

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

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

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

-------------------------------------------
Step 72, which took 0.265751 s (model generation: 0.264266,  model checking: 0.001485):

Model:
|_
{
drop -> 
{{{
Q={q_gen_6324, q_gen_6326, q_gen_6331, q_gen_6332, q_gen_6338, q_gen_6339, q_gen_6370, q_gen_6371, q_gen_6378, q_gen_6416, q_gen_6421, q_gen_6422},
Q_f={q_gen_6324},
Delta=
{
<s>(q_gen_6326) -> q_gen_6326
<z>() -> q_gen_6326
<a>() -> q_gen_6332
<b>() -> q_gen_6332
<nil>() -> q_gen_6371
<cons>(q_gen_6332, q_gen_6371) -> q_gen_6422
<s, cons>(q_gen_6332, q_gen_6331) -> q_gen_6331
<s, nil>(q_gen_6326) -> q_gen_6331
<z, cons>(q_gen_6332, q_gen_6422) -> q_gen_6331
<z, nil>() -> q_gen_6331
<cons, cons>(q_gen_6339, q_gen_6338) -> q_gen_6338
<nil, nil>() -> q_gen_6338
<a, a>() -> q_gen_6339
<a, b>() -> q_gen_6339
<b, a>() -> q_gen_6339
<b, b>() -> q_gen_6339
<s, cons>(q_gen_6332, q_gen_6378) -> q_gen_6378
<z, cons>(q_gen_6332, q_gen_6371) -> q_gen_6378
<cons, cons>(q_gen_6339, q_gen_6416) -> q_gen_6416
<cons, nil>(q_gen_6332, q_gen_6371) -> q_gen_6416
<s, cons, cons>(q_gen_6339, q_gen_6370) -> q_gen_6324
<s, cons, nil>(q_gen_6332, q_gen_6331) -> q_gen_6324
<s, nil, nil>(q_gen_6326) -> q_gen_6324
<z, cons, cons>(q_gen_6339, q_gen_6338) -> q_gen_6324
<z, nil, nil>() -> q_gen_6324
<s, cons, cons>(q_gen_6339, q_gen_6324) -> q_gen_6370
<s, cons, cons>(q_gen_6339, q_gen_6421) -> q_gen_6370
<s, cons, nil>(q_gen_6332, q_gen_6378) -> q_gen_6370
<z, cons, cons>(q_gen_6339, q_gen_6416) -> q_gen_6370
<z, cons, nil>(q_gen_6332, q_gen_6371) -> q_gen_6370
<z, cons, nil>(q_gen_6332, q_gen_6422) -> q_gen_6421
}

Datatype: <nat, eltlist, eltlist>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_6323, q_gen_6329},
Q_f={q_gen_6323},
Delta=
{
<a>() -> q_gen_6329
<b>() -> q_gen_6329
<cons, s>(q_gen_6329, q_gen_6323) -> q_gen_6323
<nil, z>() -> q_gen_6323
}

Datatype: <eltlist, nat>
Convolution form: right
}}}
  ;  minus -> 
{{{
Q={q_gen_6320, q_gen_6321, q_gen_6322, q_gen_6334, q_gen_6343, q_gen_6348, q_gen_6350, q_gen_6355, q_gen_6368},
Q_f={q_gen_6320, q_gen_6321},
Delta=
{
<s>(q_gen_6350) -> q_gen_6334
<z>() -> q_gen_6334
<s>(q_gen_6334) -> q_gen_6350
<s, s>(q_gen_6322) -> q_gen_6322
<z, z>() -> q_gen_6322
<z, s>(q_gen_6334) -> q_gen_6355
<z, s>(q_gen_6350) -> q_gen_6355
<s, s>(q_gen_6368) -> q_gen_6368
<s, z>(q_gen_6334) -> q_gen_6368
<s, s, z>(q_gen_6322) -> q_gen_6320
<s, s, z>(q_gen_6355) -> q_gen_6320
<z, s, z>(q_gen_6334) -> q_gen_6320
<z, s, z>(q_gen_6350) -> q_gen_6320
<z, z, z>() -> q_gen_6320
<s, s, s>(q_gen_6343) -> q_gen_6321
<s, z, s>(q_gen_6322) -> q_gen_6321
<s, z, z>(q_gen_6350) -> q_gen_6321
<s, s, s>(q_gen_6321) -> q_gen_6343
<s, s, z>(q_gen_6368) -> q_gen_6343
<s, z, s>(q_gen_6368) -> q_gen_6343
<s, z, z>(q_gen_6334) -> q_gen_6343
<s, s, s>(q_gen_6320) -> q_gen_6348
<s, s, s>(q_gen_6348) -> q_gen_6348
<s, z, s>(q_gen_6355) -> q_gen_6348
}

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

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

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

-------------------------------------------
Step 73, which took 0.269551 s (model generation: 0.265071,  model checking: 0.004480):

Model:
|_
{
drop -> 
{{{
Q={q_gen_6324, q_gen_6326, q_gen_6331, q_gen_6332, q_gen_6338, q_gen_6339, q_gen_6370, q_gen_6371, q_gen_6378, q_gen_6416, q_gen_6421, q_gen_6422},
Q_f={q_gen_6324},
Delta=
{
<s>(q_gen_6326) -> q_gen_6326
<z>() -> q_gen_6326
<a>() -> q_gen_6332
<b>() -> q_gen_6332
<nil>() -> q_gen_6371
<cons>(q_gen_6332, q_gen_6371) -> q_gen_6422
<s, cons>(q_gen_6332, q_gen_6331) -> q_gen_6331
<s, nil>(q_gen_6326) -> q_gen_6331
<z, cons>(q_gen_6332, q_gen_6422) -> q_gen_6331
<z, nil>() -> q_gen_6331
<cons, cons>(q_gen_6339, q_gen_6338) -> q_gen_6338
<nil, nil>() -> q_gen_6338
<a, a>() -> q_gen_6339
<a, b>() -> q_gen_6339
<b, a>() -> q_gen_6339
<b, b>() -> q_gen_6339
<s, cons>(q_gen_6332, q_gen_6378) -> q_gen_6378
<z, cons>(q_gen_6332, q_gen_6371) -> q_gen_6378
<cons, cons>(q_gen_6339, q_gen_6416) -> q_gen_6416
<cons, nil>(q_gen_6332, q_gen_6371) -> q_gen_6416
<s, cons, cons>(q_gen_6339, q_gen_6370) -> q_gen_6324
<s, cons, nil>(q_gen_6332, q_gen_6331) -> q_gen_6324
<s, nil, nil>(q_gen_6326) -> q_gen_6324
<z, cons, cons>(q_gen_6339, q_gen_6338) -> q_gen_6324
<z, nil, nil>() -> q_gen_6324
<s, cons, cons>(q_gen_6339, q_gen_6324) -> q_gen_6370
<s, cons, cons>(q_gen_6339, q_gen_6421) -> q_gen_6370
<s, cons, nil>(q_gen_6332, q_gen_6378) -> q_gen_6370
<z, cons, cons>(q_gen_6339, q_gen_6416) -> q_gen_6370
<z, cons, nil>(q_gen_6332, q_gen_6371) -> q_gen_6370
<z, cons, nil>(q_gen_6332, q_gen_6422) -> q_gen_6421
}

Datatype: <nat, eltlist, eltlist>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_6323, q_gen_6329},
Q_f={q_gen_6323},
Delta=
{
<a>() -> q_gen_6329
<b>() -> q_gen_6329
<cons, s>(q_gen_6329, q_gen_6323) -> q_gen_6323
<nil, z>() -> q_gen_6323
}

Datatype: <eltlist, nat>
Convolution form: right
}}}
  ;  minus -> 
{{{
Q={q_gen_6320, q_gen_6322, q_gen_6334, q_gen_6343, q_gen_6348, q_gen_6350, q_gen_6355, q_gen_6368, q_gen_6372},
Q_f={q_gen_6320, q_gen_6372},
Delta=
{
<s>(q_gen_6350) -> q_gen_6334
<z>() -> q_gen_6334
<s>(q_gen_6334) -> q_gen_6350
<s, s>(q_gen_6322) -> q_gen_6322
<z, z>() -> q_gen_6322
<s, z>(q_gen_6350) -> q_gen_6355
<z, s>(q_gen_6334) -> q_gen_6355
<z, s>(q_gen_6350) -> q_gen_6355
<s, s>(q_gen_6368) -> q_gen_6368
<s, z>(q_gen_6334) -> q_gen_6368
<s, s, s>(q_gen_6343) -> q_gen_6320
<s, s, z>(q_gen_6322) -> q_gen_6320
<s, s, z>(q_gen_6355) -> q_gen_6320
<s, z, s>(q_gen_6322) -> q_gen_6320
<z, s, z>(q_gen_6334) -> q_gen_6320
<z, s, z>(q_gen_6350) -> q_gen_6320
<z, z, z>() -> q_gen_6320
<s, s, z>(q_gen_6368) -> q_gen_6343
<s, z, z>(q_gen_6334) -> q_gen_6343
<s, s, s>(q_gen_6320) -> q_gen_6348
<s, s, s>(q_gen_6348) -> q_gen_6348
<s, z, s>(q_gen_6355) -> q_gen_6348
<s, s, s>(q_gen_6372) -> q_gen_6372
<s, z, s>(q_gen_6368) -> q_gen_6372
<s, z, z>(q_gen_6350) -> q_gen_6372
}

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

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

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

-------------------------------------------
Step 74, which took 0.386340 s (model generation: 0.383462,  model checking: 0.002878):

Model:
|_
{
drop -> 
{{{
Q={q_gen_6324, q_gen_6326, q_gen_6331, q_gen_6332, q_gen_6338, q_gen_6339, q_gen_6370, q_gen_6371, q_gen_6378, q_gen_6416, q_gen_6421, q_gen_6422},
Q_f={q_gen_6324},
Delta=
{
<s>(q_gen_6326) -> q_gen_6326
<z>() -> q_gen_6326
<a>() -> q_gen_6332
<b>() -> q_gen_6332
<nil>() -> q_gen_6371
<cons>(q_gen_6332, q_gen_6371) -> q_gen_6422
<s, cons>(q_gen_6332, q_gen_6331) -> q_gen_6331
<s, nil>(q_gen_6326) -> q_gen_6331
<z, cons>(q_gen_6332, q_gen_6422) -> q_gen_6331
<z, nil>() -> q_gen_6331
<cons, cons>(q_gen_6339, q_gen_6338) -> q_gen_6338
<cons, nil>(q_gen_6332, q_gen_6422) -> q_gen_6338
<nil, nil>() -> q_gen_6338
<a, a>() -> q_gen_6339
<a, b>() -> q_gen_6339
<b, a>() -> q_gen_6339
<b, b>() -> q_gen_6339
<s, cons>(q_gen_6332, q_gen_6378) -> q_gen_6378
<z, cons>(q_gen_6332, q_gen_6371) -> q_gen_6378
<cons, cons>(q_gen_6339, q_gen_6416) -> q_gen_6416
<cons, nil>(q_gen_6332, q_gen_6371) -> q_gen_6416
<s, cons, cons>(q_gen_6339, q_gen_6370) -> q_gen_6324
<s, cons, nil>(q_gen_6332, q_gen_6331) -> q_gen_6324
<s, nil, nil>(q_gen_6326) -> q_gen_6324
<z, cons, cons>(q_gen_6339, q_gen_6338) -> q_gen_6324
<z, nil, nil>() -> q_gen_6324
<s, cons, cons>(q_gen_6339, q_gen_6324) -> q_gen_6370
<s, cons, cons>(q_gen_6339, q_gen_6421) -> q_gen_6370
<s, cons, nil>(q_gen_6332, q_gen_6378) -> q_gen_6370
<z, cons, cons>(q_gen_6339, q_gen_6416) -> q_gen_6370
<z, cons, nil>(q_gen_6332, q_gen_6371) -> q_gen_6370
<z, cons, nil>(q_gen_6332, q_gen_6422) -> q_gen_6421
}

Datatype: <nat, eltlist, eltlist>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_6323, q_gen_6329},
Q_f={q_gen_6323},
Delta=
{
<a>() -> q_gen_6329
<b>() -> q_gen_6329
<cons, s>(q_gen_6329, q_gen_6323) -> q_gen_6323
<nil, z>() -> q_gen_6323
}

Datatype: <eltlist, nat>
Convolution form: right
}}}
  ;  minus -> 
{{{
Q={q_gen_6320, q_gen_6321, q_gen_6322, q_gen_6334, q_gen_6343, q_gen_6348, q_gen_6350, q_gen_6355, q_gen_6368},
Q_f={q_gen_6320, q_gen_6321},
Delta=
{
<s>(q_gen_6350) -> q_gen_6334
<z>() -> q_gen_6334
<s>(q_gen_6334) -> q_gen_6350
<s, s>(q_gen_6322) -> q_gen_6322
<z, s>(q_gen_6350) -> q_gen_6322
<z, z>() -> q_gen_6322
<s, z>(q_gen_6350) -> q_gen_6355
<z, s>(q_gen_6334) -> q_gen_6355
<s, s>(q_gen_6368) -> q_gen_6368
<s, z>(q_gen_6334) -> q_gen_6368
<s, s, z>(q_gen_6355) -> q_gen_6320
<z, s, z>(q_gen_6334) -> q_gen_6320
<z, s, z>(q_gen_6350) -> q_gen_6320
<z, z, z>() -> q_gen_6320
<s, s, s>(q_gen_6343) -> q_gen_6321
<s, s, z>(q_gen_6322) -> q_gen_6321
<s, z, s>(q_gen_6322) -> q_gen_6321
<s, z, z>(q_gen_6350) -> q_gen_6321
<s, s, s>(q_gen_6321) -> q_gen_6343
<s, s, z>(q_gen_6368) -> q_gen_6343
<s, z, s>(q_gen_6355) -> q_gen_6343
<s, z, s>(q_gen_6368) -> q_gen_6343
<s, z, z>(q_gen_6334) -> q_gen_6343
<s, s, s>(q_gen_6320) -> q_gen_6348
<s, s, s>(q_gen_6348) -> q_gen_6348
}

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

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

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

-------------------------------------------
Step 75, which took 0.411501 s (model generation: 0.410261,  model checking: 0.001240):

Model:
|_
{
drop -> 
{{{
Q={q_gen_6324, q_gen_6326, q_gen_6331, q_gen_6332, q_gen_6338, q_gen_6339, q_gen_6370, q_gen_6371, q_gen_6378, q_gen_6416, q_gen_6421, q_gen_6422},
Q_f={q_gen_6324},
Delta=
{
<s>(q_gen_6326) -> q_gen_6326
<z>() -> q_gen_6326
<a>() -> q_gen_6332
<b>() -> q_gen_6332
<nil>() -> q_gen_6371
<cons>(q_gen_6332, q_gen_6371) -> q_gen_6422
<s, cons>(q_gen_6332, q_gen_6331) -> q_gen_6331
<s, nil>(q_gen_6326) -> q_gen_6331
<z, cons>(q_gen_6332, q_gen_6422) -> q_gen_6331
<z, nil>() -> q_gen_6331
<cons, cons>(q_gen_6339, q_gen_6338) -> q_gen_6338
<cons, nil>(q_gen_6332, q_gen_6422) -> q_gen_6338
<nil, nil>() -> q_gen_6338
<a, a>() -> q_gen_6339
<a, b>() -> q_gen_6339
<b, a>() -> q_gen_6339
<b, b>() -> q_gen_6339
<s, cons>(q_gen_6332, q_gen_6378) -> q_gen_6378
<z, cons>(q_gen_6332, q_gen_6371) -> q_gen_6378
<cons, cons>(q_gen_6339, q_gen_6416) -> q_gen_6416
<cons, nil>(q_gen_6332, q_gen_6371) -> q_gen_6416
<s, cons, cons>(q_gen_6339, q_gen_6370) -> q_gen_6324
<s, cons, nil>(q_gen_6332, q_gen_6331) -> q_gen_6324
<s, nil, nil>(q_gen_6326) -> q_gen_6324
<z, cons, cons>(q_gen_6339, q_gen_6338) -> q_gen_6324
<z, nil, nil>() -> q_gen_6324
<s, cons, cons>(q_gen_6339, q_gen_6324) -> q_gen_6370
<s, cons, cons>(q_gen_6339, q_gen_6421) -> q_gen_6370
<s, cons, nil>(q_gen_6332, q_gen_6378) -> q_gen_6370
<z, cons, cons>(q_gen_6339, q_gen_6416) -> q_gen_6370
<z, cons, nil>(q_gen_6332, q_gen_6371) -> q_gen_6370
<z, cons, nil>(q_gen_6332, q_gen_6422) -> q_gen_6421
}

Datatype: <nat, eltlist, eltlist>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_6323, q_gen_6329},
Q_f={q_gen_6323},
Delta=
{
<a>() -> q_gen_6329
<b>() -> q_gen_6329
<cons, s>(q_gen_6329, q_gen_6323) -> q_gen_6323
<nil, z>() -> q_gen_6323
}

Datatype: <eltlist, nat>
Convolution form: right
}}}
  ;  minus -> 
{{{
Q={q_gen_6320, q_gen_6321, q_gen_6322, q_gen_6334, q_gen_6343, q_gen_6348, q_gen_6350, q_gen_6355, q_gen_6368},
Q_f={q_gen_6320, q_gen_6321},
Delta=
{
<s>(q_gen_6350) -> q_gen_6334
<z>() -> q_gen_6334
<s>(q_gen_6334) -> q_gen_6350
<s, s>(q_gen_6322) -> q_gen_6322
<z, z>() -> q_gen_6322
<s, z>(q_gen_6350) -> q_gen_6355
<z, s>(q_gen_6334) -> q_gen_6355
<z, s>(q_gen_6350) -> q_gen_6355
<s, s>(q_gen_6368) -> q_gen_6368
<s, z>(q_gen_6334) -> q_gen_6368
<s, s, s>(q_gen_6343) -> q_gen_6320
<s, s, z>(q_gen_6322) -> q_gen_6320
<s, s, z>(q_gen_6355) -> q_gen_6320
<z, s, z>(q_gen_6334) -> q_gen_6320
<z, s, z>(q_gen_6350) -> q_gen_6320
<z, z, z>() -> q_gen_6320
<s, z, s>(q_gen_6322) -> q_gen_6321
<s, z, z>(q_gen_6350) -> q_gen_6321
<s, s, s>(q_gen_6321) -> q_gen_6343
<s, s, z>(q_gen_6368) -> q_gen_6343
<s, z, s>(q_gen_6368) -> q_gen_6343
<s, z, z>(q_gen_6334) -> q_gen_6343
<s, s, s>(q_gen_6320) -> q_gen_6348
<s, s, s>(q_gen_6348) -> q_gen_6348
<s, z, s>(q_gen_6355) -> q_gen_6348
}

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

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

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

-------------------------------------------
Step 76, which took 0.437457 s (model generation: 0.433996,  model checking: 0.003461):

Model:
|_
{
drop -> 
{{{
Q={q_gen_6324, q_gen_6326, q_gen_6331, q_gen_6332, q_gen_6338, q_gen_6339, q_gen_6370, q_gen_6371, q_gen_6378, q_gen_6416, q_gen_6421, q_gen_6422},
Q_f={q_gen_6324},
Delta=
{
<s>(q_gen_6326) -> q_gen_6326
<z>() -> q_gen_6326
<a>() -> q_gen_6332
<b>() -> q_gen_6332
<nil>() -> q_gen_6371
<cons>(q_gen_6332, q_gen_6371) -> q_gen_6422
<s, cons>(q_gen_6332, q_gen_6331) -> q_gen_6331
<s, nil>(q_gen_6326) -> q_gen_6331
<z, cons>(q_gen_6332, q_gen_6422) -> q_gen_6331
<z, nil>() -> q_gen_6331
<cons, cons>(q_gen_6339, q_gen_6338) -> q_gen_6338
<cons, nil>(q_gen_6332, q_gen_6422) -> q_gen_6338
<nil, nil>() -> q_gen_6338
<a, a>() -> q_gen_6339
<a, b>() -> q_gen_6339
<b, a>() -> q_gen_6339
<b, b>() -> q_gen_6339
<s, cons>(q_gen_6332, q_gen_6378) -> q_gen_6378
<z, cons>(q_gen_6332, q_gen_6371) -> q_gen_6378
<cons, cons>(q_gen_6339, q_gen_6416) -> q_gen_6416
<cons, nil>(q_gen_6332, q_gen_6371) -> q_gen_6416
<s, cons, cons>(q_gen_6339, q_gen_6370) -> q_gen_6324
<s, cons, nil>(q_gen_6332, q_gen_6331) -> q_gen_6324
<s, nil, nil>(q_gen_6326) -> q_gen_6324
<z, cons, cons>(q_gen_6339, q_gen_6338) -> q_gen_6324
<z, nil, nil>() -> q_gen_6324
<s, cons, cons>(q_gen_6339, q_gen_6324) -> q_gen_6370
<s, cons, cons>(q_gen_6339, q_gen_6421) -> q_gen_6370
<s, cons, nil>(q_gen_6332, q_gen_6378) -> q_gen_6370
<z, cons, cons>(q_gen_6339, q_gen_6416) -> q_gen_6370
<z, cons, nil>(q_gen_6332, q_gen_6371) -> q_gen_6370
<z, cons, nil>(q_gen_6332, q_gen_6422) -> q_gen_6421
}

Datatype: <nat, eltlist, eltlist>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_6323, q_gen_6329},
Q_f={q_gen_6323},
Delta=
{
<a>() -> q_gen_6329
<b>() -> q_gen_6329
<cons, s>(q_gen_6329, q_gen_6323) -> q_gen_6323
<nil, z>() -> q_gen_6323
}

Datatype: <eltlist, nat>
Convolution form: right
}}}
  ;  minus -> 
{{{
Q={q_gen_6320, q_gen_6322, q_gen_6334, q_gen_6343, q_gen_6348, q_gen_6350, q_gen_6355, q_gen_6368, q_gen_6394},
Q_f={q_gen_6320, q_gen_6394},
Delta=
{
<s>(q_gen_6350) -> q_gen_6334
<z>() -> q_gen_6334
<s>(q_gen_6334) -> q_gen_6350
<s, s>(q_gen_6322) -> q_gen_6322
<z, z>() -> q_gen_6322
<s, z>(q_gen_6350) -> q_gen_6355
<z, s>(q_gen_6334) -> q_gen_6355
<z, s>(q_gen_6350) -> q_gen_6355
<s, s>(q_gen_6368) -> q_gen_6368
<s, z>(q_gen_6334) -> q_gen_6368
<s, s, s>(q_gen_6343) -> q_gen_6320
<s, s, z>(q_gen_6322) -> q_gen_6320
<s, s, z>(q_gen_6355) -> q_gen_6320
<s, z, s>(q_gen_6322) -> q_gen_6320
<z, s, z>(q_gen_6334) -> q_gen_6320
<z, s, z>(q_gen_6350) -> q_gen_6320
<z, z, z>() -> q_gen_6320
<s, s, z>(q_gen_6368) -> q_gen_6343
<s, z, s>(q_gen_6368) -> q_gen_6343
<s, z, z>(q_gen_6334) -> q_gen_6343
<s, s, s>(q_gen_6320) -> q_gen_6348
<s, s, s>(q_gen_6348) -> q_gen_6348
<s, z, s>(q_gen_6355) -> q_gen_6348
<s, s, s>(q_gen_6394) -> q_gen_6394
<s, z, z>(q_gen_6350) -> q_gen_6394
}

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

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

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

-------------------------------------------
Step 77, which took 0.382174 s (model generation: 0.381045,  model checking: 0.001129):

Model:
|_
{
drop -> 
{{{
Q={q_gen_6324, q_gen_6326, q_gen_6331, q_gen_6332, q_gen_6338, q_gen_6339, q_gen_6370, q_gen_6371, q_gen_6378, q_gen_6416, q_gen_6421, q_gen_6422},
Q_f={q_gen_6324},
Delta=
{
<s>(q_gen_6326) -> q_gen_6326
<z>() -> q_gen_6326
<a>() -> q_gen_6332
<b>() -> q_gen_6332
<cons>(q_gen_6332, q_gen_6422) -> q_gen_6371
<nil>() -> q_gen_6371
<cons>(q_gen_6332, q_gen_6371) -> q_gen_6422
<s, cons>(q_gen_6332, q_gen_6331) -> q_gen_6331
<s, nil>(q_gen_6326) -> q_gen_6331
<z, cons>(q_gen_6332, q_gen_6422) -> q_gen_6331
<z, nil>() -> q_gen_6331
<cons, cons>(q_gen_6339, q_gen_6338) -> q_gen_6338
<cons, nil>(q_gen_6332, q_gen_6422) -> q_gen_6338
<nil, nil>() -> q_gen_6338
<a, a>() -> q_gen_6339
<a, b>() -> q_gen_6339
<b, a>() -> q_gen_6339
<b, b>() -> q_gen_6339
<s, cons>(q_gen_6332, q_gen_6378) -> q_gen_6378
<z, cons>(q_gen_6332, q_gen_6371) -> q_gen_6378
<cons, cons>(q_gen_6339, q_gen_6416) -> q_gen_6416
<cons, nil>(q_gen_6332, q_gen_6371) -> q_gen_6416
<s, cons, cons>(q_gen_6339, q_gen_6370) -> q_gen_6324
<s, cons, nil>(q_gen_6332, q_gen_6331) -> q_gen_6324
<s, nil, nil>(q_gen_6326) -> q_gen_6324
<z, cons, cons>(q_gen_6339, q_gen_6338) -> q_gen_6324
<z, nil, nil>() -> q_gen_6324
<s, cons, cons>(q_gen_6339, q_gen_6324) -> q_gen_6370
<s, cons, cons>(q_gen_6339, q_gen_6421) -> q_gen_6370
<s, cons, nil>(q_gen_6332, q_gen_6378) -> q_gen_6370
<z, cons, cons>(q_gen_6339, q_gen_6416) -> q_gen_6370
<z, cons, nil>(q_gen_6332, q_gen_6371) -> q_gen_6370
<z, cons, nil>(q_gen_6332, q_gen_6422) -> q_gen_6421
}

Datatype: <nat, eltlist, eltlist>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_6323, q_gen_6329},
Q_f={q_gen_6323},
Delta=
{
<a>() -> q_gen_6329
<b>() -> q_gen_6329
<cons, s>(q_gen_6329, q_gen_6323) -> q_gen_6323
<nil, z>() -> q_gen_6323
}

Datatype: <eltlist, nat>
Convolution form: right
}}}
  ;  minus -> 
{{{
Q={q_gen_6320, q_gen_6321, q_gen_6322, q_gen_6334, q_gen_6343, q_gen_6348, q_gen_6350, q_gen_6355, q_gen_6368},
Q_f={q_gen_6320, q_gen_6321},
Delta=
{
<s>(q_gen_6350) -> q_gen_6334
<z>() -> q_gen_6334
<s>(q_gen_6334) -> q_gen_6350
<s, s>(q_gen_6322) -> q_gen_6322
<z, z>() -> q_gen_6322
<s, z>(q_gen_6350) -> q_gen_6355
<z, s>(q_gen_6334) -> q_gen_6355
<z, s>(q_gen_6350) -> q_gen_6355
<s, s>(q_gen_6368) -> q_gen_6368
<s, z>(q_gen_6334) -> q_gen_6368
<z, s, z>(q_gen_6334) -> q_gen_6320
<z, s, z>(q_gen_6350) -> q_gen_6320
<z, z, z>() -> q_gen_6320
<s, s, s>(q_gen_6343) -> q_gen_6321
<s, s, z>(q_gen_6322) -> q_gen_6321
<s, s, z>(q_gen_6355) -> q_gen_6321
<s, z, s>(q_gen_6322) -> q_gen_6321
<s, z, z>(q_gen_6350) -> q_gen_6321
<s, s, s>(q_gen_6321) -> q_gen_6343
<s, s, z>(q_gen_6368) -> q_gen_6343
<s, z, s>(q_gen_6368) -> q_gen_6343
<s, z, z>(q_gen_6334) -> q_gen_6343
<s, s, s>(q_gen_6320) -> q_gen_6348
<s, s, s>(q_gen_6348) -> q_gen_6348
<s, z, s>(q_gen_6355) -> q_gen_6348
}

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

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

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

-------------------------------------------
Step 78, which took 0.500437 s (model generation: 0.499370,  model checking: 0.001067):

Model:
|_
{
drop -> 
{{{
Q={q_gen_6324, q_gen_6326, q_gen_6331, q_gen_6332, q_gen_6338, q_gen_6339, q_gen_6370, q_gen_6371, q_gen_6378, q_gen_6416, q_gen_6421, q_gen_6422},
Q_f={q_gen_6324},
Delta=
{
<s>(q_gen_6326) -> q_gen_6326
<z>() -> q_gen_6326
<a>() -> q_gen_6332
<b>() -> q_gen_6332
<cons>(q_gen_6332, q_gen_6422) -> q_gen_6371
<nil>() -> q_gen_6371
<cons>(q_gen_6332, q_gen_6371) -> q_gen_6422
<s, cons>(q_gen_6332, q_gen_6331) -> q_gen_6331
<s, nil>(q_gen_6326) -> q_gen_6331
<z, cons>(q_gen_6332, q_gen_6422) -> q_gen_6331
<z, nil>() -> q_gen_6331
<cons, cons>(q_gen_6339, q_gen_6338) -> q_gen_6338
<cons, nil>(q_gen_6332, q_gen_6422) -> q_gen_6338
<nil, nil>() -> q_gen_6338
<a, a>() -> q_gen_6339
<a, b>() -> q_gen_6339
<b, a>() -> q_gen_6339
<b, b>() -> q_gen_6339
<s, cons>(q_gen_6332, q_gen_6378) -> q_gen_6378
<z, cons>(q_gen_6332, q_gen_6371) -> q_gen_6378
<cons, cons>(q_gen_6339, q_gen_6416) -> q_gen_6416
<cons, nil>(q_gen_6332, q_gen_6371) -> q_gen_6416
<s, cons, cons>(q_gen_6339, q_gen_6370) -> q_gen_6324
<s, cons, nil>(q_gen_6332, q_gen_6331) -> q_gen_6324
<s, nil, nil>(q_gen_6326) -> q_gen_6324
<z, cons, cons>(q_gen_6339, q_gen_6338) -> q_gen_6324
<z, nil, nil>() -> q_gen_6324
<s, cons, cons>(q_gen_6339, q_gen_6324) -> q_gen_6370
<s, cons, cons>(q_gen_6339, q_gen_6421) -> q_gen_6370
<s, cons, nil>(q_gen_6332, q_gen_6378) -> q_gen_6370
<z, cons, cons>(q_gen_6339, q_gen_6416) -> q_gen_6370
<z, cons, nil>(q_gen_6332, q_gen_6371) -> q_gen_6370
<z, cons, nil>(q_gen_6332, q_gen_6422) -> q_gen_6421
}

Datatype: <nat, eltlist, eltlist>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_6323, q_gen_6329},
Q_f={q_gen_6323},
Delta=
{
<a>() -> q_gen_6329
<b>() -> q_gen_6329
<cons, s>(q_gen_6329, q_gen_6323) -> q_gen_6323
<nil, z>() -> q_gen_6323
}

Datatype: <eltlist, nat>
Convolution form: right
}}}
  ;  minus -> 
{{{
Q={q_gen_6320, q_gen_6321, q_gen_6322, q_gen_6334, q_gen_6343, q_gen_6348, q_gen_6350, q_gen_6355, q_gen_6368},
Q_f={q_gen_6320, q_gen_6321},
Delta=
{
<s>(q_gen_6350) -> q_gen_6334
<z>() -> q_gen_6334
<s>(q_gen_6334) -> q_gen_6350
<s, s>(q_gen_6322) -> q_gen_6322
<z, z>() -> q_gen_6322
<s, z>(q_gen_6350) -> q_gen_6355
<z, s>(q_gen_6334) -> q_gen_6355
<z, s>(q_gen_6350) -> q_gen_6355
<s, s>(q_gen_6368) -> q_gen_6368
<s, z>(q_gen_6334) -> q_gen_6368
<s, s, z>(q_gen_6355) -> q_gen_6320
<z, s, z>(q_gen_6334) -> q_gen_6320
<z, s, z>(q_gen_6350) -> q_gen_6320
<z, z, z>() -> q_gen_6320
<s, s, s>(q_gen_6343) -> q_gen_6321
<s, s, z>(q_gen_6322) -> q_gen_6321
<s, z, s>(q_gen_6322) -> q_gen_6321
<s, z, z>(q_gen_6350) -> q_gen_6321
<s, s, s>(q_gen_6321) -> q_gen_6343
<s, s, z>(q_gen_6368) -> q_gen_6343
<s, z, s>(q_gen_6368) -> q_gen_6343
<s, z, z>(q_gen_6334) -> q_gen_6343
<s, s, s>(q_gen_6320) -> q_gen_6348
<s, s, s>(q_gen_6348) -> q_gen_6348
<s, z, s>(q_gen_6355) -> q_gen_6348
}

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

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

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

-------------------------------------------
Step 79, which took 0.492589 s (model generation: 0.488444,  model checking: 0.004145):

Model:
|_
{
drop -> 
{{{
Q={q_gen_6324, q_gen_6326, q_gen_6331, q_gen_6332, q_gen_6338, q_gen_6339, q_gen_6370, q_gen_6371, q_gen_6378, q_gen_6416, q_gen_6421, q_gen_6422},
Q_f={q_gen_6324},
Delta=
{
<s>(q_gen_6326) -> q_gen_6326
<z>() -> q_gen_6326
<a>() -> q_gen_6332
<b>() -> q_gen_6332
<cons>(q_gen_6332, q_gen_6422) -> q_gen_6371
<nil>() -> q_gen_6371
<cons>(q_gen_6332, q_gen_6371) -> q_gen_6422
<s, cons>(q_gen_6332, q_gen_6331) -> q_gen_6331
<s, nil>(q_gen_6326) -> q_gen_6331
<z, cons>(q_gen_6332, q_gen_6422) -> q_gen_6331
<z, nil>() -> q_gen_6331
<cons, cons>(q_gen_6339, q_gen_6338) -> q_gen_6338
<cons, nil>(q_gen_6332, q_gen_6422) -> q_gen_6338
<nil, nil>() -> q_gen_6338
<a, a>() -> q_gen_6339
<a, b>() -> q_gen_6339
<b, a>() -> q_gen_6339
<b, b>() -> q_gen_6339
<s, cons>(q_gen_6332, q_gen_6378) -> q_gen_6378
<z, cons>(q_gen_6332, q_gen_6371) -> q_gen_6378
<cons, cons>(q_gen_6339, q_gen_6416) -> q_gen_6416
<cons, nil>(q_gen_6332, q_gen_6371) -> q_gen_6416
<s, cons, cons>(q_gen_6339, q_gen_6370) -> q_gen_6324
<s, cons, nil>(q_gen_6332, q_gen_6331) -> q_gen_6324
<s, nil, nil>(q_gen_6326) -> q_gen_6324
<z, cons, cons>(q_gen_6339, q_gen_6338) -> q_gen_6324
<z, nil, nil>() -> q_gen_6324
<s, cons, cons>(q_gen_6339, q_gen_6324) -> q_gen_6370
<s, cons, cons>(q_gen_6339, q_gen_6421) -> q_gen_6370
<s, cons, nil>(q_gen_6332, q_gen_6378) -> q_gen_6370
<z, cons, cons>(q_gen_6339, q_gen_6416) -> q_gen_6370
<z, cons, nil>(q_gen_6332, q_gen_6371) -> q_gen_6370
<z, cons, nil>(q_gen_6332, q_gen_6422) -> q_gen_6421
}

Datatype: <nat, eltlist, eltlist>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_6323, q_gen_6329},
Q_f={q_gen_6323},
Delta=
{
<a>() -> q_gen_6329
<b>() -> q_gen_6329
<cons, s>(q_gen_6329, q_gen_6323) -> q_gen_6323
<nil, z>() -> q_gen_6323
}

Datatype: <eltlist, nat>
Convolution form: right
}}}
  ;  minus -> 
{{{
Q={q_gen_6320, q_gen_6321, q_gen_6322, q_gen_6334, q_gen_6343, q_gen_6348, q_gen_6350, q_gen_6355, q_gen_6368},
Q_f={q_gen_6320, q_gen_6321},
Delta=
{
<s>(q_gen_6350) -> q_gen_6334
<z>() -> q_gen_6334
<s>(q_gen_6334) -> q_gen_6350
<s, s>(q_gen_6322) -> q_gen_6322
<s, z>(q_gen_6350) -> q_gen_6322
<z, z>() -> q_gen_6322
<z, s>(q_gen_6334) -> q_gen_6355
<z, s>(q_gen_6350) -> q_gen_6355
<s, s>(q_gen_6368) -> q_gen_6368
<s, z>(q_gen_6334) -> q_gen_6368
<s, s, z>(q_gen_6355) -> q_gen_6320
<z, s, z>(q_gen_6334) -> q_gen_6320
<z, s, z>(q_gen_6350) -> q_gen_6320
<z, z, z>() -> q_gen_6320
<s, s, s>(q_gen_6343) -> q_gen_6321
<s, s, z>(q_gen_6322) -> q_gen_6321
<s, z, s>(q_gen_6322) -> q_gen_6321
<s, z, z>(q_gen_6350) -> q_gen_6321
<s, s, s>(q_gen_6321) -> q_gen_6343
<s, s, z>(q_gen_6368) -> q_gen_6343
<s, z, s>(q_gen_6368) -> q_gen_6343
<s, z, z>(q_gen_6334) -> q_gen_6343
<s, s, s>(q_gen_6320) -> q_gen_6348
<s, s, s>(q_gen_6348) -> q_gen_6348
<s, z, s>(q_gen_6355) -> q_gen_6348
}

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

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

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

-------------------------------------------
Step 80, which took 0.658230 s (model generation: 0.656950,  model checking: 0.001280):

Model:
|_
{
drop -> 
{{{
Q={q_gen_6324, q_gen_6326, q_gen_6331, q_gen_6332, q_gen_6338, q_gen_6339, q_gen_6357, q_gen_6370, q_gen_6371, q_gen_6378, q_gen_6416, q_gen_6421, q_gen_6422},
Q_f={q_gen_6324},
Delta=
{
<s>(q_gen_6326) -> q_gen_6326
<z>() -> q_gen_6326
<a>() -> q_gen_6332
<b>() -> q_gen_6332
<cons>(q_gen_6332, q_gen_6422) -> q_gen_6371
<nil>() -> q_gen_6371
<cons>(q_gen_6332, q_gen_6371) -> q_gen_6422
<z, cons>(q_gen_6332, q_gen_6422) -> q_gen_6331
<z, nil>() -> q_gen_6331
<cons, cons>(q_gen_6339, q_gen_6338) -> q_gen_6338
<cons, nil>(q_gen_6332, q_gen_6422) -> q_gen_6338
<nil, nil>() -> q_gen_6338
<a, a>() -> q_gen_6339
<a, b>() -> q_gen_6339
<b, a>() -> q_gen_6339
<b, b>() -> q_gen_6339
<s, cons>(q_gen_6332, q_gen_6331) -> q_gen_6357
<s, nil>(q_gen_6326) -> q_gen_6357
<s, cons>(q_gen_6332, q_gen_6357) -> q_gen_6378
<s, cons>(q_gen_6332, q_gen_6378) -> q_gen_6378
<z, cons>(q_gen_6332, q_gen_6371) -> q_gen_6378
<cons, cons>(q_gen_6339, q_gen_6416) -> q_gen_6416
<cons, nil>(q_gen_6332, q_gen_6371) -> q_gen_6416
<s, cons, cons>(q_gen_6339, q_gen_6370) -> q_gen_6324
<s, cons, nil>(q_gen_6332, q_gen_6331) -> q_gen_6324
<s, cons, nil>(q_gen_6332, q_gen_6357) -> q_gen_6324
<s, nil, nil>(q_gen_6326) -> q_gen_6324
<z, cons, cons>(q_gen_6339, q_gen_6338) -> q_gen_6324
<z, nil, nil>() -> q_gen_6324
<s, cons, cons>(q_gen_6339, q_gen_6324) -> q_gen_6370
<s, cons, cons>(q_gen_6339, q_gen_6421) -> q_gen_6370
<s, cons, nil>(q_gen_6332, q_gen_6378) -> q_gen_6370
<z, cons, cons>(q_gen_6339, q_gen_6416) -> q_gen_6370
<z, cons, nil>(q_gen_6332, q_gen_6371) -> q_gen_6370
<z, cons, nil>(q_gen_6332, q_gen_6422) -> q_gen_6421
}

Datatype: <nat, eltlist, eltlist>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_6323, q_gen_6329},
Q_f={q_gen_6323},
Delta=
{
<a>() -> q_gen_6329
<b>() -> q_gen_6329
<cons, s>(q_gen_6329, q_gen_6323) -> q_gen_6323
<nil, z>() -> q_gen_6323
}

Datatype: <eltlist, nat>
Convolution form: right
}}}
  ;  minus -> 
{{{
Q={q_gen_6320, q_gen_6321, q_gen_6322, q_gen_6334, q_gen_6343, q_gen_6348, q_gen_6350, q_gen_6355, q_gen_6368},
Q_f={q_gen_6320, q_gen_6321},
Delta=
{
<s>(q_gen_6350) -> q_gen_6334
<z>() -> q_gen_6334
<s>(q_gen_6334) -> q_gen_6350
<s, s>(q_gen_6322) -> q_gen_6322
<s, z>(q_gen_6350) -> q_gen_6322
<z, z>() -> q_gen_6322
<z, s>(q_gen_6334) -> q_gen_6355
<z, s>(q_gen_6350) -> q_gen_6355
<s, s>(q_gen_6368) -> q_gen_6368
<s, z>(q_gen_6334) -> q_gen_6368
<s, s, z>(q_gen_6355) -> q_gen_6320
<z, s, z>(q_gen_6334) -> q_gen_6320
<z, s, z>(q_gen_6350) -> q_gen_6320
<z, z, z>() -> q_gen_6320
<s, s, s>(q_gen_6343) -> q_gen_6321
<s, s, z>(q_gen_6322) -> q_gen_6321
<s, z, s>(q_gen_6322) -> q_gen_6321
<s, z, z>(q_gen_6350) -> q_gen_6321
<s, s, s>(q_gen_6321) -> q_gen_6343
<s, s, z>(q_gen_6368) -> q_gen_6343
<s, z, s>(q_gen_6368) -> q_gen_6343
<s, z, z>(q_gen_6334) -> q_gen_6343
<s, s, s>(q_gen_6320) -> q_gen_6348
<s, s, s>(q_gen_6348) -> q_gen_6348
<s, z, s>(q_gen_6355) -> q_gen_6348
}

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

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

Teacher's answer:
New clause system:
{
() -> drop([s(u), nil, nil]) -> 61
() -> drop([z, l, l]) -> 61
() -> length([nil, z]) -> 61
() -> minus([s(u), z, s(u)]) -> 61
() -> minus([z, y, z]) -> 61
(drop([n, l1, _sga]) /\ length([_sga, _tga]) /\ length([l1, _uga]) /\ minus([_uga, n, _vga])) -> eq_nat([_tga, _vga]) -> 64
(drop([u, x3, _ega])) -> drop([s(u), cons(x2, x3), _ega]) -> 65
(length([ll, _jga])) -> length([cons(x, ll), s(_jga)]) -> 61
(minus([u, x2, _nga])) -> minus([s(u), s(x2), _nga]) -> 64
}
Sat witness: Found: ((drop([u, x3, _ega])) -> drop([s(u), cons(x2, x3), _ega]), {
_ega -> nil  ;  u -> s(s(z))  ;  x2 -> b  ;  x3 -> cons(b, nil)
})

-------------------------------------------
Step 81, which took 0.899545 s (model generation: 0.898007,  model checking: 0.001538):

Model:
|_
{
drop -> 
{{{
Q={q_gen_6324, q_gen_6326, q_gen_6331, q_gen_6332, q_gen_6338, q_gen_6339, q_gen_6370, q_gen_6371, q_gen_6378, q_gen_6416, q_gen_6421, q_gen_6422},
Q_f={q_gen_6324},
Delta=
{
<s>(q_gen_6326) -> q_gen_6326
<z>() -> q_gen_6326
<a>() -> q_gen_6332
<b>() -> q_gen_6332
<cons>(q_gen_6332, q_gen_6422) -> q_gen_6371
<nil>() -> q_gen_6371
<cons>(q_gen_6332, q_gen_6371) -> q_gen_6422
<s, cons>(q_gen_6332, q_gen_6331) -> q_gen_6331
<s, nil>(q_gen_6326) -> q_gen_6331
<z, cons>(q_gen_6332, q_gen_6422) -> q_gen_6331
<z, nil>() -> q_gen_6331
<cons, cons>(q_gen_6339, q_gen_6338) -> q_gen_6338
<cons, nil>(q_gen_6332, q_gen_6422) -> q_gen_6338
<nil, nil>() -> q_gen_6338
<a, a>() -> q_gen_6339
<a, b>() -> q_gen_6339
<b, a>() -> q_gen_6339
<b, b>() -> q_gen_6339
<s, cons>(q_gen_6332, q_gen_6378) -> q_gen_6378
<z, cons>(q_gen_6332, q_gen_6371) -> q_gen_6378
<cons, cons>(q_gen_6339, q_gen_6416) -> q_gen_6416
<cons, nil>(q_gen_6332, q_gen_6371) -> q_gen_6416
<s, cons, cons>(q_gen_6339, q_gen_6370) -> q_gen_6324
<s, cons, nil>(q_gen_6332, q_gen_6331) -> q_gen_6324
<s, nil, nil>(q_gen_6326) -> q_gen_6324
<z, cons, cons>(q_gen_6339, q_gen_6338) -> q_gen_6324
<z, nil, nil>() -> q_gen_6324
<s, cons, cons>(q_gen_6339, q_gen_6324) -> q_gen_6370
<s, cons, cons>(q_gen_6339, q_gen_6421) -> q_gen_6370
<s, cons, nil>(q_gen_6332, q_gen_6378) -> q_gen_6370
<z, cons, cons>(q_gen_6339, q_gen_6416) -> q_gen_6370
<z, cons, nil>(q_gen_6332, q_gen_6371) -> q_gen_6370
<z, cons, nil>(q_gen_6332, q_gen_6422) -> q_gen_6421
}

Datatype: <nat, eltlist, eltlist>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_6323, q_gen_6329},
Q_f={q_gen_6323},
Delta=
{
<a>() -> q_gen_6329
<b>() -> q_gen_6329
<cons, s>(q_gen_6329, q_gen_6323) -> q_gen_6323
<nil, z>() -> q_gen_6323
}

Datatype: <eltlist, nat>
Convolution form: right
}}}
  ;  minus -> 
{{{
Q={q_gen_6320, q_gen_6321, q_gen_6322, q_gen_6334, q_gen_6343, q_gen_6348, q_gen_6350, q_gen_6355, q_gen_6361, q_gen_6368},
Q_f={q_gen_6320, q_gen_6321},
Delta=
{
<s>(q_gen_6350) -> q_gen_6334
<z>() -> q_gen_6334
<s>(q_gen_6334) -> q_gen_6350
<s, s>(q_gen_6322) -> q_gen_6322
<z, z>() -> q_gen_6322
<z, s>(q_gen_6334) -> q_gen_6355
<s, z>(q_gen_6350) -> q_gen_6361
<z, s>(q_gen_6350) -> q_gen_6361
<s, s>(q_gen_6368) -> q_gen_6368
<s, z>(q_gen_6334) -> q_gen_6368
<s, s, z>(q_gen_6322) -> q_gen_6320
<s, s, z>(q_gen_6355) -> q_gen_6320
<z, s, z>(q_gen_6334) -> q_gen_6320
<z, s, z>(q_gen_6350) -> q_gen_6320
<z, z, z>() -> q_gen_6320
<s, s, s>(q_gen_6343) -> q_gen_6321
<s, s, z>(q_gen_6361) -> q_gen_6321
<s, z, s>(q_gen_6322) -> q_gen_6321
<s, s, s>(q_gen_6321) -> q_gen_6343
<s, s, s>(q_gen_6348) -> q_gen_6343
<s, s, z>(q_gen_6368) -> q_gen_6343
<s, z, s>(q_gen_6355) -> q_gen_6343
<s, z, s>(q_gen_6368) -> q_gen_6343
<s, z, z>(q_gen_6334) -> q_gen_6343
<s, s, s>(q_gen_6320) -> q_gen_6348
<s, z, s>(q_gen_6361) -> q_gen_6348
<s, z, z>(q_gen_6350) -> q_gen_6348
}

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

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

Teacher's answer:
New clause system:
{
() -> drop([s(u), nil, nil]) -> 62
() -> drop([z, l, l]) -> 62
() -> length([nil, z]) -> 62
() -> minus([s(u), z, s(u)]) -> 62
() -> minus([z, y, z]) -> 62
(drop([n, l1, _sga]) /\ length([_sga, _tga]) /\ length([l1, _uga]) /\ minus([_uga, n, _vga])) -> eq_nat([_tga, _vga]) -> 64
(drop([u, x3, _ega])) -> drop([s(u), cons(x2, x3), _ega]) -> 65
(length([ll, _jga])) -> length([cons(x, ll), s(_jga)]) -> 62
(minus([u, x2, _nga])) -> minus([s(u), s(x2), _nga]) -> 67
}
Sat witness: Found: ((minus([u, x2, _nga])) -> minus([s(u), s(x2), _nga]), {
_nga -> s(s(s(z)))  ;  u -> s(s(s(z)))  ;  x2 -> s(s(s(s(s(z)))))
})

-------------------------------------------
Step 82, which took 0.732430 s (model generation: 0.730855,  model checking: 0.001575):

Model:
|_
{
drop -> 
{{{
Q={q_gen_6324, q_gen_6326, q_gen_6331, q_gen_6332, q_gen_6338, q_gen_6339, q_gen_6365, q_gen_6370, q_gen_6371, q_gen_6378, q_gen_6416, q_gen_6421, q_gen_6422},
Q_f={q_gen_6324},
Delta=
{
<s>(q_gen_6326) -> q_gen_6326
<z>() -> q_gen_6326
<a>() -> q_gen_6332
<b>() -> q_gen_6332
<cons>(q_gen_6332, q_gen_6422) -> q_gen_6371
<nil>() -> q_gen_6371
<cons>(q_gen_6332, q_gen_6371) -> q_gen_6422
<s, nil>(q_gen_6326) -> q_gen_6331
<z, nil>() -> q_gen_6331
<cons, cons>(q_gen_6339, q_gen_6338) -> q_gen_6338
<cons, nil>(q_gen_6332, q_gen_6422) -> q_gen_6338
<nil, nil>() -> q_gen_6338
<a, a>() -> q_gen_6339
<a, b>() -> q_gen_6339
<b, a>() -> q_gen_6339
<b, b>() -> q_gen_6339
<s, cons>(q_gen_6332, q_gen_6331) -> q_gen_6365
<z, cons>(q_gen_6332, q_gen_6422) -> q_gen_6365
<s, cons>(q_gen_6332, q_gen_6365) -> q_gen_6378
<s, cons>(q_gen_6332, q_gen_6378) -> q_gen_6378
<z, cons>(q_gen_6332, q_gen_6371) -> q_gen_6378
<cons, cons>(q_gen_6339, q_gen_6416) -> q_gen_6416
<cons, nil>(q_gen_6332, q_gen_6371) -> q_gen_6416
<s, cons, cons>(q_gen_6339, q_gen_6370) -> q_gen_6324
<s, cons, nil>(q_gen_6332, q_gen_6331) -> q_gen_6324
<s, cons, nil>(q_gen_6332, q_gen_6365) -> q_gen_6324
<s, nil, nil>(q_gen_6326) -> q_gen_6324
<z, cons, cons>(q_gen_6339, q_gen_6338) -> q_gen_6324
<z, nil, nil>() -> q_gen_6324
<s, cons, cons>(q_gen_6339, q_gen_6324) -> q_gen_6370
<s, cons, cons>(q_gen_6339, q_gen_6421) -> q_gen_6370
<s, cons, nil>(q_gen_6332, q_gen_6378) -> q_gen_6370
<z, cons, cons>(q_gen_6339, q_gen_6416) -> q_gen_6370
<z, cons, nil>(q_gen_6332, q_gen_6371) -> q_gen_6370
<z, cons, nil>(q_gen_6332, q_gen_6422) -> q_gen_6421
}

Datatype: <nat, eltlist, eltlist>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_6323, q_gen_6329},
Q_f={q_gen_6323},
Delta=
{
<a>() -> q_gen_6329
<b>() -> q_gen_6329
<cons, s>(q_gen_6329, q_gen_6323) -> q_gen_6323
<nil, z>() -> q_gen_6323
}

Datatype: <eltlist, nat>
Convolution form: right
}}}
  ;  minus -> 
{{{
Q={q_gen_6320, q_gen_6321, q_gen_6322, q_gen_6334, q_gen_6343, q_gen_6348, q_gen_6350, q_gen_6355, q_gen_6368},
Q_f={q_gen_6320, q_gen_6321},
Delta=
{
<s>(q_gen_6350) -> q_gen_6334
<z>() -> q_gen_6334
<s>(q_gen_6334) -> q_gen_6350
<s, s>(q_gen_6322) -> q_gen_6322
<z, z>() -> q_gen_6322
<s, z>(q_gen_6350) -> q_gen_6355
<z, s>(q_gen_6334) -> q_gen_6355
<z, s>(q_gen_6350) -> q_gen_6355
<s, s>(q_gen_6368) -> q_gen_6368
<s, z>(q_gen_6334) -> q_gen_6368
<s, s, z>(q_gen_6322) -> q_gen_6320
<z, s, z>(q_gen_6334) -> q_gen_6320
<z, z, z>() -> q_gen_6320
<s, s, s>(q_gen_6343) -> q_gen_6321
<s, s, z>(q_gen_6355) -> q_gen_6321
<s, z, s>(q_gen_6322) -> q_gen_6321
<s, z, z>(q_gen_6350) -> q_gen_6321
<z, s, z>(q_gen_6350) -> q_gen_6321
<s, s, s>(q_gen_6321) -> q_gen_6343
<s, s, z>(q_gen_6368) -> q_gen_6343
<s, z, s>(q_gen_6368) -> q_gen_6343
<s, z, z>(q_gen_6334) -> q_gen_6343
<s, s, s>(q_gen_6320) -> q_gen_6348
<s, s, s>(q_gen_6348) -> q_gen_6348
<s, z, s>(q_gen_6355) -> q_gen_6348
}

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

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

Teacher's answer:
New clause system:
{
() -> drop([s(u), nil, nil]) -> 63
() -> drop([z, l, l]) -> 63
() -> length([nil, z]) -> 63
() -> minus([s(u), z, s(u)]) -> 63
() -> minus([z, y, z]) -> 63
(drop([n, l1, _sga]) /\ length([_sga, _tga]) /\ length([l1, _uga]) /\ minus([_uga, n, _vga])) -> eq_nat([_tga, _vga]) -> 67
(drop([u, x3, _ega])) -> drop([s(u), cons(x2, x3), _ega]) -> 65
(length([ll, _jga])) -> length([cons(x, ll), s(_jga)]) -> 63
(minus([u, x2, _nga])) -> minus([s(u), s(x2), _nga]) -> 67
}
Sat witness: Found: ((drop([n, l1, _sga]) /\ length([_sga, _tga]) /\ length([l1, _uga]) /\ minus([_uga, n, _vga])) -> eq_nat([_tga, _vga]), {
_sga -> nil  ;  _tga -> z  ;  _uga -> s(s(z))  ;  _vga -> s(s(z))  ;  l1 -> cons(b, cons(b, nil))  ;  n -> s(s(s(s(z))))
})

-------------------------------------------
Step 83, which took 2.265367 s (model generation: 2.261075,  model checking: 0.004292):

Model:
|_
{
drop -> 
{{{
Q={q_gen_6324, q_gen_6326, q_gen_6331, q_gen_6332, q_gen_6338, q_gen_6339, q_gen_6370, q_gen_6371, q_gen_6378, q_gen_6416, q_gen_6421, q_gen_6422},
Q_f={q_gen_6324},
Delta=
{
<s>(q_gen_6326) -> q_gen_6326
<z>() -> q_gen_6326
<a>() -> q_gen_6332
<b>() -> q_gen_6332
<cons>(q_gen_6332, q_gen_6422) -> q_gen_6371
<nil>() -> q_gen_6371
<cons>(q_gen_6332, q_gen_6371) -> q_gen_6422
<s, cons>(q_gen_6332, q_gen_6331) -> q_gen_6331
<s, nil>(q_gen_6326) -> q_gen_6331
<z, cons>(q_gen_6332, q_gen_6422) -> q_gen_6331
<z, nil>() -> q_gen_6331
<cons, cons>(q_gen_6339, q_gen_6338) -> q_gen_6338
<cons, nil>(q_gen_6332, q_gen_6422) -> q_gen_6338
<nil, nil>() -> q_gen_6338
<a, a>() -> q_gen_6339
<a, b>() -> q_gen_6339
<b, a>() -> q_gen_6339
<b, b>() -> q_gen_6339
<s, cons>(q_gen_6332, q_gen_6378) -> q_gen_6378
<z, cons>(q_gen_6332, q_gen_6371) -> q_gen_6378
<cons, cons>(q_gen_6339, q_gen_6416) -> q_gen_6416
<cons, nil>(q_gen_6332, q_gen_6371) -> q_gen_6416
<s, cons, cons>(q_gen_6339, q_gen_6370) -> q_gen_6324
<s, cons, nil>(q_gen_6332, q_gen_6331) -> q_gen_6324
<s, nil, nil>(q_gen_6326) -> q_gen_6324
<z, cons, cons>(q_gen_6339, q_gen_6338) -> q_gen_6324
<z, nil, nil>() -> q_gen_6324
<s, cons, cons>(q_gen_6339, q_gen_6324) -> q_gen_6370
<s, cons, cons>(q_gen_6339, q_gen_6421) -> q_gen_6370
<s, cons, nil>(q_gen_6332, q_gen_6378) -> q_gen_6370
<z, cons, cons>(q_gen_6339, q_gen_6416) -> q_gen_6370
<z, cons, nil>(q_gen_6332, q_gen_6371) -> q_gen_6370
<z, cons, nil>(q_gen_6332, q_gen_6422) -> q_gen_6421
}

Datatype: <nat, eltlist, eltlist>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_6323, q_gen_6329},
Q_f={q_gen_6323},
Delta=
{
<a>() -> q_gen_6329
<b>() -> q_gen_6329
<cons, s>(q_gen_6329, q_gen_6323) -> q_gen_6323
<nil, z>() -> q_gen_6323
}

Datatype: <eltlist, nat>
Convolution form: right
}}}
  ;  minus -> 
{{{
Q={q_gen_6320, q_gen_6322, q_gen_6334, q_gen_6336, q_gen_6342, q_gen_6343, q_gen_6348, q_gen_6350, q_gen_6355, q_gen_6368},
Q_f={q_gen_6320, q_gen_6342},
Delta=
{
<s>(q_gen_6350) -> q_gen_6334
<z>() -> q_gen_6334
<s>(q_gen_6334) -> q_gen_6350
<s, s>(q_gen_6336) -> q_gen_6322
<z, z>() -> q_gen_6322
<s, s>(q_gen_6322) -> q_gen_6336
<s, z>(q_gen_6350) -> q_gen_6336
<z, s>(q_gen_6334) -> q_gen_6355
<z, s>(q_gen_6350) -> q_gen_6355
<s, s>(q_gen_6368) -> q_gen_6368
<s, z>(q_gen_6334) -> q_gen_6368
<s, s, z>(q_gen_6322) -> q_gen_6320
<s, s, z>(q_gen_6355) -> q_gen_6320
<s, z, s>(q_gen_6322) -> q_gen_6320
<s, z, s>(q_gen_6336) -> q_gen_6320
<z, s, z>(q_gen_6334) -> q_gen_6320
<z, s, z>(q_gen_6350) -> q_gen_6320
<z, z, z>() -> q_gen_6320
<s, s, s>(q_gen_6343) -> q_gen_6342
<s, s, z>(q_gen_6336) -> q_gen_6342
<s, z, z>(q_gen_6350) -> q_gen_6342
<s, s, s>(q_gen_6342) -> q_gen_6343
<s, s, z>(q_gen_6368) -> q_gen_6343
<s, z, s>(q_gen_6368) -> q_gen_6343
<s, z, z>(q_gen_6334) -> q_gen_6343
<s, s, s>(q_gen_6320) -> q_gen_6348
<s, s, s>(q_gen_6348) -> q_gen_6348
<s, z, s>(q_gen_6355) -> q_gen_6348
}

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

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

Teacher's answer:
New clause system:
{
() -> drop([s(u), nil, nil]) -> 64
() -> drop([z, l, l]) -> 64
() -> length([nil, z]) -> 64
() -> minus([s(u), z, s(u)]) -> 64
() -> minus([z, y, z]) -> 64
(drop([n, l1, _sga]) /\ length([_sga, _tga]) /\ length([l1, _uga]) /\ minus([_uga, n, _vga])) -> eq_nat([_tga, _vga]) -> 67
(drop([u, x3, _ega])) -> drop([s(u), cons(x2, x3), _ega]) -> 66
(length([ll, _jga])) -> length([cons(x, ll), s(_jga)]) -> 64
(minus([u, x2, _nga])) -> minus([s(u), s(x2), _nga]) -> 70
}
Sat witness: Found: ((minus([u, x2, _nga])) -> minus([s(u), s(x2), _nga]), {
_nga -> s(s(z))  ;  u -> s(s(s(s(z))))  ;  x2 -> s(s(s(s(z))))
})

-------------------------------------------
Step 84, which took 1.257396 s (model generation: 1.255089,  model checking: 0.002307):

Model:
|_
{
drop -> 
{{{
Q={q_gen_6324, q_gen_6326, q_gen_6331, q_gen_6332, q_gen_6338, q_gen_6339, q_gen_6365, q_gen_6370, q_gen_6371, q_gen_6378, q_gen_6416, q_gen_6421, q_gen_6422},
Q_f={q_gen_6324},
Delta=
{
<s>(q_gen_6326) -> q_gen_6326
<z>() -> q_gen_6326
<a>() -> q_gen_6332
<b>() -> q_gen_6332
<cons>(q_gen_6332, q_gen_6422) -> q_gen_6371
<nil>() -> q_gen_6371
<cons>(q_gen_6332, q_gen_6371) -> q_gen_6422
<s, nil>(q_gen_6326) -> q_gen_6331
<z, nil>() -> q_gen_6331
<cons, cons>(q_gen_6339, q_gen_6338) -> q_gen_6338
<cons, nil>(q_gen_6332, q_gen_6422) -> q_gen_6338
<nil, nil>() -> q_gen_6338
<a, a>() -> q_gen_6339
<a, b>() -> q_gen_6339
<b, a>() -> q_gen_6339
<b, b>() -> q_gen_6339
<s, cons>(q_gen_6332, q_gen_6331) -> q_gen_6365
<z, cons>(q_gen_6332, q_gen_6422) -> q_gen_6365
<s, cons>(q_gen_6332, q_gen_6365) -> q_gen_6378
<s, cons>(q_gen_6332, q_gen_6378) -> q_gen_6378
<z, cons>(q_gen_6332, q_gen_6371) -> q_gen_6378
<cons, cons>(q_gen_6339, q_gen_6416) -> q_gen_6416
<cons, nil>(q_gen_6332, q_gen_6371) -> q_gen_6416
<s, cons, cons>(q_gen_6339, q_gen_6370) -> q_gen_6324
<s, cons, nil>(q_gen_6332, q_gen_6331) -> q_gen_6324
<s, cons, nil>(q_gen_6332, q_gen_6365) -> q_gen_6324
<s, nil, nil>(q_gen_6326) -> q_gen_6324
<z, cons, cons>(q_gen_6339, q_gen_6338) -> q_gen_6324
<z, nil, nil>() -> q_gen_6324
<s, cons, cons>(q_gen_6339, q_gen_6324) -> q_gen_6370
<s, cons, cons>(q_gen_6339, q_gen_6421) -> q_gen_6370
<s, cons, nil>(q_gen_6332, q_gen_6378) -> q_gen_6370
<z, cons, cons>(q_gen_6339, q_gen_6416) -> q_gen_6370
<z, cons, nil>(q_gen_6332, q_gen_6371) -> q_gen_6370
<z, cons, nil>(q_gen_6332, q_gen_6422) -> q_gen_6421
}

Datatype: <nat, eltlist, eltlist>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_6323, q_gen_6329},
Q_f={q_gen_6323},
Delta=
{
<a>() -> q_gen_6329
<b>() -> q_gen_6329
<cons, s>(q_gen_6329, q_gen_6323) -> q_gen_6323
<nil, z>() -> q_gen_6323
}

Datatype: <eltlist, nat>
Convolution form: right
}}}
  ;  minus -> 
{{{
Q={q_gen_6320, q_gen_6321, q_gen_6322, q_gen_6334, q_gen_6343, q_gen_6348, q_gen_6350, q_gen_6355, q_gen_6368},
Q_f={q_gen_6320, q_gen_6321},
Delta=
{
<s>(q_gen_6350) -> q_gen_6334
<z>() -> q_gen_6334
<s>(q_gen_6334) -> q_gen_6350
<s, s>(q_gen_6322) -> q_gen_6322
<s, z>(q_gen_6350) -> q_gen_6322
<z, z>() -> q_gen_6322
<z, s>(q_gen_6334) -> q_gen_6355
<z, s>(q_gen_6350) -> q_gen_6355
<s, s>(q_gen_6368) -> q_gen_6368
<s, z>(q_gen_6334) -> q_gen_6368
<s, s, z>(q_gen_6355) -> q_gen_6320
<z, s, z>(q_gen_6334) -> q_gen_6320
<z, s, z>(q_gen_6350) -> q_gen_6320
<z, z, z>() -> q_gen_6320
<s, s, s>(q_gen_6343) -> q_gen_6321
<s, s, z>(q_gen_6322) -> q_gen_6321
<s, z, s>(q_gen_6322) -> q_gen_6321
<s, z, z>(q_gen_6350) -> q_gen_6321
<s, s, s>(q_gen_6321) -> q_gen_6343
<s, s, z>(q_gen_6368) -> q_gen_6343
<s, z, s>(q_gen_6368) -> q_gen_6343
<s, z, z>(q_gen_6334) -> q_gen_6343
<s, s, s>(q_gen_6320) -> q_gen_6348
<s, s, s>(q_gen_6348) -> q_gen_6348
<s, z, s>(q_gen_6355) -> q_gen_6348
}

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

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

Teacher's answer:
New clause system:
{
() -> drop([s(u), nil, nil]) -> 65
() -> drop([z, l, l]) -> 65
() -> length([nil, z]) -> 65
() -> minus([s(u), z, s(u)]) -> 65
() -> minus([z, y, z]) -> 65
(drop([n, l1, _sga]) /\ length([_sga, _tga]) /\ length([l1, _uga]) /\ minus([_uga, n, _vga])) -> eq_nat([_tga, _vga]) -> 67
(drop([u, x3, _ega])) -> drop([s(u), cons(x2, x3), _ega]) -> 69
(length([ll, _jga])) -> length([cons(x, ll), s(_jga)]) -> 65
(minus([u, x2, _nga])) -> minus([s(u), s(x2), _nga]) -> 70
}
Sat witness: Found: ((drop([u, x3, _ega])) -> drop([s(u), cons(x2, x3), _ega]), {
_ega -> nil  ;  u -> s(s(z))  ;  x2 -> b  ;  x3 -> cons(b, cons(b, nil))
})

-------------------------------------------
Step 85, which took 1.474691 s (model generation: 1.473558,  model checking: 0.001133):

Model:
|_
{
drop -> 
{{{
Q={q_gen_6324, q_gen_6326, q_gen_6331, q_gen_6332, q_gen_6338, q_gen_6339, q_gen_6370, q_gen_6371, q_gen_6378, q_gen_6416, q_gen_6421, q_gen_6422},
Q_f={q_gen_6324},
Delta=
{
<s>(q_gen_6326) -> q_gen_6326
<z>() -> q_gen_6326
<a>() -> q_gen_6332
<b>() -> q_gen_6332
<cons>(q_gen_6332, q_gen_6422) -> q_gen_6371
<nil>() -> q_gen_6371
<cons>(q_gen_6332, q_gen_6371) -> q_gen_6422
<s, cons>(q_gen_6332, q_gen_6331) -> q_gen_6331
<s, nil>(q_gen_6326) -> q_gen_6331
<z, cons>(q_gen_6332, q_gen_6422) -> q_gen_6331
<z, nil>() -> q_gen_6331
<cons, cons>(q_gen_6339, q_gen_6338) -> q_gen_6338
<cons, nil>(q_gen_6332, q_gen_6422) -> q_gen_6338
<nil, nil>() -> q_gen_6338
<a, a>() -> q_gen_6339
<a, b>() -> q_gen_6339
<b, a>() -> q_gen_6339
<b, b>() -> q_gen_6339
<s, cons>(q_gen_6332, q_gen_6378) -> q_gen_6378
<z, cons>(q_gen_6332, q_gen_6371) -> q_gen_6378
<cons, cons>(q_gen_6339, q_gen_6416) -> q_gen_6416
<cons, nil>(q_gen_6332, q_gen_6371) -> q_gen_6416
<s, cons, cons>(q_gen_6339, q_gen_6370) -> q_gen_6324
<s, cons, nil>(q_gen_6332, q_gen_6331) -> q_gen_6324
<s, nil, nil>(q_gen_6326) -> q_gen_6324
<z, cons, cons>(q_gen_6339, q_gen_6338) -> q_gen_6324
<z, nil, nil>() -> q_gen_6324
<s, cons, cons>(q_gen_6339, q_gen_6324) -> q_gen_6370
<s, cons, cons>(q_gen_6339, q_gen_6421) -> q_gen_6370
<s, cons, nil>(q_gen_6332, q_gen_6378) -> q_gen_6370
<z, cons, cons>(q_gen_6339, q_gen_6416) -> q_gen_6370
<z, cons, nil>(q_gen_6332, q_gen_6371) -> q_gen_6370
<z, cons, nil>(q_gen_6332, q_gen_6422) -> q_gen_6421
}

Datatype: <nat, eltlist, eltlist>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_6323, q_gen_6329},
Q_f={q_gen_6323},
Delta=
{
<a>() -> q_gen_6329
<b>() -> q_gen_6329
<cons, s>(q_gen_6329, q_gen_6323) -> q_gen_6323
<nil, z>() -> q_gen_6323
}

Datatype: <eltlist, nat>
Convolution form: right
}}}
  ;  minus -> 
{{{
Q={q_gen_6320, q_gen_6322, q_gen_6334, q_gen_6343, q_gen_6348, q_gen_6349, q_gen_6350, q_gen_6355, q_gen_6367, q_gen_6368},
Q_f={q_gen_6320, q_gen_6349},
Delta=
{
<z>() -> q_gen_6334
<s>(q_gen_6334) -> q_gen_6350
<s>(q_gen_6350) -> q_gen_6350
<s, s>(q_gen_6322) -> q_gen_6322
<z, z>() -> q_gen_6322
<z, s>(q_gen_6334) -> q_gen_6355
<z, s>(q_gen_6350) -> q_gen_6355
<s, s>(q_gen_6368) -> q_gen_6368
<s, z>(q_gen_6334) -> q_gen_6368
<s, z>(q_gen_6350) -> q_gen_6368
<s, s, s>(q_gen_6343) -> q_gen_6320
<s, s, s>(q_gen_6349) -> q_gen_6320
<s, s, z>(q_gen_6322) -> q_gen_6320
<s, s, z>(q_gen_6355) -> q_gen_6320
<s, z, s>(q_gen_6322) -> q_gen_6320
<z, s, z>(q_gen_6334) -> q_gen_6320
<z, z, z>() -> q_gen_6320
<s, z, s>(q_gen_6368) -> q_gen_6343
<s, z, z>(q_gen_6334) -> q_gen_6343
<s, s, s>(q_gen_6320) -> q_gen_6348
<s, s, s>(q_gen_6348) -> q_gen_6348
<s, z, s>(q_gen_6355) -> q_gen_6348
<s, s, s>(q_gen_6367) -> q_gen_6349
<z, s, z>(q_gen_6350) -> q_gen_6349
<s, s, z>(q_gen_6368) -> q_gen_6367
<s, z, z>(q_gen_6350) -> q_gen_6367
}

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

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

Teacher's answer:
New clause system:
{
() -> drop([s(u), nil, nil]) -> 66
() -> drop([z, l, l]) -> 66
() -> length([nil, z]) -> 66
() -> minus([s(u), z, s(u)]) -> 66
() -> minus([z, y, z]) -> 66
(drop([n, l1, _sga]) /\ length([_sga, _tga]) /\ length([l1, _uga]) /\ minus([_uga, n, _vga])) -> eq_nat([_tga, _vga]) -> 70
(drop([u, x3, _ega])) -> drop([s(u), cons(x2, x3), _ega]) -> 69
(length([ll, _jga])) -> length([cons(x, ll), s(_jga)]) -> 66
(minus([u, x2, _nga])) -> minus([s(u), s(x2), _nga]) -> 70
}
Sat witness: Found: ((drop([n, l1, _sga]) /\ length([_sga, _tga]) /\ length([l1, _uga]) /\ minus([_uga, n, _vga])) -> eq_nat([_tga, _vga]), {
_sga -> nil  ;  _tga -> z  ;  _uga -> s(s(s(z)))  ;  _vga -> s(z)  ;  l1 -> cons(b, cons(b, cons(b, nil)))  ;  n -> s(z)
})

-------------------------------------------
Step 86, which took 1.280517 s (model generation: 1.276156,  model checking: 0.004361):

Model:
|_
{
drop -> 
{{{
Q={q_gen_6324, q_gen_6326, q_gen_6331, q_gen_6332, q_gen_6338, q_gen_6339, q_gen_6370, q_gen_6371, q_gen_6378, q_gen_6416, q_gen_6421, q_gen_6422},
Q_f={q_gen_6324},
Delta=
{
<s>(q_gen_6326) -> q_gen_6326
<z>() -> q_gen_6326
<a>() -> q_gen_6332
<b>() -> q_gen_6332
<cons>(q_gen_6332, q_gen_6422) -> q_gen_6371
<nil>() -> q_gen_6371
<cons>(q_gen_6332, q_gen_6371) -> q_gen_6422
<s, cons>(q_gen_6332, q_gen_6331) -> q_gen_6331
<s, nil>(q_gen_6326) -> q_gen_6331
<z, cons>(q_gen_6332, q_gen_6422) -> q_gen_6331
<z, nil>() -> q_gen_6331
<cons, cons>(q_gen_6339, q_gen_6338) -> q_gen_6338
<cons, nil>(q_gen_6332, q_gen_6422) -> q_gen_6338
<nil, nil>() -> q_gen_6338
<a, a>() -> q_gen_6339
<a, b>() -> q_gen_6339
<b, a>() -> q_gen_6339
<b, b>() -> q_gen_6339
<s, cons>(q_gen_6332, q_gen_6378) -> q_gen_6378
<z, cons>(q_gen_6332, q_gen_6371) -> q_gen_6378
<cons, cons>(q_gen_6339, q_gen_6416) -> q_gen_6416
<cons, nil>(q_gen_6332, q_gen_6371) -> q_gen_6416
<s, cons, cons>(q_gen_6339, q_gen_6370) -> q_gen_6324
<s, cons, nil>(q_gen_6332, q_gen_6331) -> q_gen_6324
<s, nil, nil>(q_gen_6326) -> q_gen_6324
<z, cons, cons>(q_gen_6339, q_gen_6338) -> q_gen_6324
<z, nil, nil>() -> q_gen_6324
<s, cons, cons>(q_gen_6339, q_gen_6324) -> q_gen_6370
<s, cons, cons>(q_gen_6339, q_gen_6421) -> q_gen_6370
<s, cons, nil>(q_gen_6332, q_gen_6378) -> q_gen_6370
<z, cons, cons>(q_gen_6339, q_gen_6416) -> q_gen_6370
<z, cons, nil>(q_gen_6332, q_gen_6371) -> q_gen_6370
<z, cons, nil>(q_gen_6332, q_gen_6422) -> q_gen_6421
}

Datatype: <nat, eltlist, eltlist>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_6323, q_gen_6329},
Q_f={q_gen_6323},
Delta=
{
<a>() -> q_gen_6329
<b>() -> q_gen_6329
<cons, s>(q_gen_6329, q_gen_6323) -> q_gen_6323
<nil, z>() -> q_gen_6323
}

Datatype: <eltlist, nat>
Convolution form: right
}}}
  ;  minus -> 
{{{
Q={q_gen_6320, q_gen_6321, q_gen_6322, q_gen_6334, q_gen_6343, q_gen_6348, q_gen_6350, q_gen_6355, q_gen_6361, q_gen_6368},
Q_f={q_gen_6320, q_gen_6321},
Delta=
{
<z>() -> q_gen_6334
<s>(q_gen_6334) -> q_gen_6350
<s>(q_gen_6350) -> q_gen_6350
<s, s>(q_gen_6322) -> q_gen_6322
<z, z>() -> q_gen_6322
<z, s>(q_gen_6334) -> q_gen_6355
<s, z>(q_gen_6350) -> q_gen_6361
<z, s>(q_gen_6350) -> q_gen_6361
<s, s>(q_gen_6368) -> q_gen_6368
<s, z>(q_gen_6334) -> q_gen_6368
<s, s, z>(q_gen_6322) -> q_gen_6320
<s, s, z>(q_gen_6355) -> q_gen_6320
<z, s, z>(q_gen_6334) -> q_gen_6320
<z, s, z>(q_gen_6350) -> q_gen_6320
<z, z, z>() -> q_gen_6320
<s, s, s>(q_gen_6343) -> q_gen_6321
<s, s, z>(q_gen_6361) -> q_gen_6321
<s, z, s>(q_gen_6322) -> q_gen_6321
<s, z, z>(q_gen_6350) -> q_gen_6321
<s, s, s>(q_gen_6321) -> q_gen_6343
<s, s, z>(q_gen_6368) -> q_gen_6343
<s, z, s>(q_gen_6368) -> q_gen_6343
<s, z, z>(q_gen_6334) -> q_gen_6343
<s, s, s>(q_gen_6320) -> q_gen_6348
<s, s, s>(q_gen_6348) -> q_gen_6348
<s, z, s>(q_gen_6355) -> q_gen_6348
<s, z, s>(q_gen_6361) -> q_gen_6348
}

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

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

Teacher's answer:
New clause system:
{
() -> drop([s(u), nil, nil]) -> 67
() -> drop([z, l, l]) -> 67
() -> length([nil, z]) -> 67
() -> minus([s(u), z, s(u)]) -> 67
() -> minus([z, y, z]) -> 67
(drop([n, l1, _sga]) /\ length([_sga, _tga]) /\ length([l1, _uga]) /\ minus([_uga, n, _vga])) -> eq_nat([_tga, _vga]) -> 70
(drop([u, x3, _ega])) -> drop([s(u), cons(x2, x3), _ega]) -> 70
(length([ll, _jga])) -> length([cons(x, ll), s(_jga)]) -> 67
(minus([u, x2, _nga])) -> minus([s(u), s(x2), _nga]) -> 73
}
Sat witness: Found: ((minus([u, x2, _nga])) -> minus([s(u), s(x2), _nga]), {
_nga -> s(s(s(z)))  ;  u -> s(s(s(s(z))))  ;  x2 -> s(z)
})

-------------------------------------------
Step 87, which took 1.406636 s (model generation: 1.399856,  model checking: 0.006780):

Model:
|_
{
drop -> 
{{{
Q={q_gen_6324, q_gen_6326, q_gen_6331, q_gen_6332, q_gen_6338, q_gen_6339, q_gen_6370, q_gen_6371, q_gen_6378, q_gen_6416, q_gen_6421, q_gen_6422},
Q_f={q_gen_6324},
Delta=
{
<s>(q_gen_6326) -> q_gen_6326
<z>() -> q_gen_6326
<a>() -> q_gen_6332
<b>() -> q_gen_6332
<cons>(q_gen_6332, q_gen_6422) -> q_gen_6371
<nil>() -> q_gen_6371
<cons>(q_gen_6332, q_gen_6371) -> q_gen_6422
<s, cons>(q_gen_6332, q_gen_6331) -> q_gen_6331
<s, nil>(q_gen_6326) -> q_gen_6331
<z, cons>(q_gen_6332, q_gen_6422) -> q_gen_6331
<z, nil>() -> q_gen_6331
<cons, cons>(q_gen_6339, q_gen_6338) -> q_gen_6338
<cons, nil>(q_gen_6332, q_gen_6422) -> q_gen_6338
<nil, nil>() -> q_gen_6338
<a, a>() -> q_gen_6339
<a, b>() -> q_gen_6339
<b, a>() -> q_gen_6339
<b, b>() -> q_gen_6339
<s, cons>(q_gen_6332, q_gen_6378) -> q_gen_6378
<z, cons>(q_gen_6332, q_gen_6371) -> q_gen_6378
<cons, cons>(q_gen_6339, q_gen_6416) -> q_gen_6416
<cons, nil>(q_gen_6332, q_gen_6371) -> q_gen_6416
<s, cons, cons>(q_gen_6339, q_gen_6370) -> q_gen_6324
<s, cons, nil>(q_gen_6332, q_gen_6331) -> q_gen_6324
<s, nil, nil>(q_gen_6326) -> q_gen_6324
<z, cons, cons>(q_gen_6339, q_gen_6338) -> q_gen_6324
<z, nil, nil>() -> q_gen_6324
<s, cons, cons>(q_gen_6339, q_gen_6324) -> q_gen_6370
<s, cons, cons>(q_gen_6339, q_gen_6421) -> q_gen_6370
<s, cons, nil>(q_gen_6332, q_gen_6378) -> q_gen_6370
<z, cons, cons>(q_gen_6339, q_gen_6416) -> q_gen_6370
<z, cons, nil>(q_gen_6332, q_gen_6371) -> q_gen_6370
<z, cons, nil>(q_gen_6332, q_gen_6422) -> q_gen_6421
}

Datatype: <nat, eltlist, eltlist>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_6323, q_gen_6329},
Q_f={q_gen_6323},
Delta=
{
<a>() -> q_gen_6329
<b>() -> q_gen_6329
<cons, s>(q_gen_6329, q_gen_6323) -> q_gen_6323
<nil, z>() -> q_gen_6323
}

Datatype: <eltlist, nat>
Convolution form: right
}}}
  ;  minus -> 
{{{
Q={q_gen_6320, q_gen_6321, q_gen_6322, q_gen_6334, q_gen_6336, q_gen_6343, q_gen_6348, q_gen_6350, q_gen_6355, q_gen_6368},
Q_f={q_gen_6320, q_gen_6321},
Delta=
{
<s>(q_gen_6350) -> q_gen_6334
<z>() -> q_gen_6334
<s>(q_gen_6334) -> q_gen_6350
<z, z>() -> q_gen_6322
<s, s>(q_gen_6322) -> q_gen_6336
<s, s>(q_gen_6336) -> q_gen_6336
<s, z>(q_gen_6350) -> q_gen_6336
<z, s>(q_gen_6334) -> q_gen_6355
<z, s>(q_gen_6350) -> q_gen_6355
<s, s>(q_gen_6368) -> q_gen_6368
<s, z>(q_gen_6334) -> q_gen_6368
<s, s, z>(q_gen_6322) -> q_gen_6320
<s, s, z>(q_gen_6355) -> q_gen_6320
<z, s, z>(q_gen_6334) -> q_gen_6320
<z, s, z>(q_gen_6350) -> q_gen_6320
<z, z, z>() -> q_gen_6320
<s, s, s>(q_gen_6343) -> q_gen_6321
<s, s, z>(q_gen_6336) -> q_gen_6321
<s, z, s>(q_gen_6322) -> q_gen_6321
<s, z, s>(q_gen_6336) -> q_gen_6321
<s, z, z>(q_gen_6350) -> q_gen_6321
<s, s, s>(q_gen_6321) -> q_gen_6343
<s, s, z>(q_gen_6368) -> q_gen_6343
<s, z, s>(q_gen_6368) -> q_gen_6343
<s, z, z>(q_gen_6334) -> q_gen_6343
<s, s, s>(q_gen_6320) -> q_gen_6348
<s, s, s>(q_gen_6348) -> q_gen_6348
<s, z, s>(q_gen_6355) -> q_gen_6348
}

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

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

Teacher's answer:
New clause system:
{
() -> drop([s(u), nil, nil]) -> 68
() -> drop([z, l, l]) -> 68
() -> length([nil, z]) -> 68
() -> minus([s(u), z, s(u)]) -> 68
() -> minus([z, y, z]) -> 68
(drop([n, l1, _sga]) /\ length([_sga, _tga]) /\ length([l1, _uga]) /\ minus([_uga, n, _vga])) -> eq_nat([_tga, _vga]) -> 73
(drop([u, x3, _ega])) -> drop([s(u), cons(x2, x3), _ega]) -> 71
(length([ll, _jga])) -> length([cons(x, ll), s(_jga)]) -> 68
(minus([u, x2, _nga])) -> minus([s(u), s(x2), _nga]) -> 73
}
Sat witness: Found: ((drop([n, l1, _sga]) /\ length([_sga, _tga]) /\ length([l1, _uga]) /\ minus([_uga, n, _vga])) -> eq_nat([_tga, _vga]), {
_sga -> nil  ;  _tga -> z  ;  _uga -> s(s(s(z)))  ;  _vga -> s(s(z))  ;  l1 -> cons(b, cons(b, cons(b, nil)))  ;  n -> s(z)
})

-------------------------------------------
Step 88, which took 3.808266 s (model generation: 3.808108,  model checking: 0.000158):

Model:
|_
{
drop -> 
{{{
Q={q_gen_6324, q_gen_6326, q_gen_6330, q_gen_6331, q_gen_6332, q_gen_6338, q_gen_6339, q_gen_6370, q_gen_6371, q_gen_6378, q_gen_6416},
Q_f={q_gen_6324, q_gen_6330},
Delta=
{
<s>(q_gen_6326) -> q_gen_6326
<z>() -> q_gen_6326
<a>() -> q_gen_6332
<b>() -> q_gen_6332
<cons>(q_gen_6332, q_gen_6371) -> q_gen_6371
<nil>() -> q_gen_6371
<s, cons>(q_gen_6332, q_gen_6331) -> q_gen_6331
<s, nil>(q_gen_6326) -> q_gen_6331
<z, nil>() -> q_gen_6331
<cons, cons>(q_gen_6339, q_gen_6338) -> q_gen_6338
<nil, nil>() -> q_gen_6338
<a, a>() -> q_gen_6339
<a, b>() -> q_gen_6339
<b, a>() -> q_gen_6339
<b, b>() -> q_gen_6339
<s, cons>(q_gen_6332, q_gen_6378) -> q_gen_6378
<z, cons>(q_gen_6332, q_gen_6371) -> q_gen_6378
<cons, cons>(q_gen_6339, q_gen_6416) -> q_gen_6416
<cons, nil>(q_gen_6332, q_gen_6371) -> q_gen_6416
<s, nil, nil>(q_gen_6326) -> q_gen_6324
<z, cons, cons>(q_gen_6339, q_gen_6338) -> q_gen_6324
<z, nil, nil>() -> q_gen_6324
<s, cons, cons>(q_gen_6339, q_gen_6330) -> q_gen_6330
<s, cons, cons>(q_gen_6339, q_gen_6370) -> q_gen_6330
<s, cons, nil>(q_gen_6332, q_gen_6331) -> q_gen_6330
<s, cons, cons>(q_gen_6339, q_gen_6324) -> q_gen_6370
<s, cons, nil>(q_gen_6332, q_gen_6378) -> q_gen_6370
<z, cons, cons>(q_gen_6339, q_gen_6416) -> q_gen_6370
<z, cons, nil>(q_gen_6332, q_gen_6371) -> q_gen_6370
}

Datatype: <nat, eltlist, eltlist>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_6323, q_gen_6328, q_gen_6329, q_gen_6379, q_gen_6408},
Q_f={q_gen_6323, q_gen_6328, q_gen_6379},
Delta=
{
<a>() -> q_gen_6329
<b>() -> q_gen_6329
<nil, z>() -> q_gen_6323
<cons, s>(q_gen_6329, q_gen_6323) -> q_gen_6328
<cons, s>(q_gen_6329, q_gen_6328) -> q_gen_6379
<cons, s>(q_gen_6329, q_gen_6379) -> q_gen_6408
}

Datatype: <eltlist, nat>
Convolution form: right
}}}
  ;  minus -> 
{{{
Q={q_gen_6320, q_gen_6321, q_gen_6322, q_gen_6334, q_gen_6343, q_gen_6348, q_gen_6355, q_gen_6368},
Q_f={q_gen_6320, q_gen_6321},
Delta=
{
<s>(q_gen_6334) -> q_gen_6334
<z>() -> q_gen_6334
<s, s>(q_gen_6322) -> q_gen_6322
<z, z>() -> q_gen_6322
<z, s>(q_gen_6334) -> q_gen_6355
<s, s>(q_gen_6368) -> q_gen_6368
<s, z>(q_gen_6334) -> q_gen_6368
<s, s, z>(q_gen_6322) -> q_gen_6320
<s, s, z>(q_gen_6355) -> q_gen_6320
<z, s, z>(q_gen_6334) -> q_gen_6320
<z, z, z>() -> q_gen_6320
<s, s, s>(q_gen_6321) -> q_gen_6321
<s, s, s>(q_gen_6343) -> q_gen_6321
<s, z, s>(q_gen_6322) -> q_gen_6321
<s, z, s>(q_gen_6368) -> q_gen_6321
<s, s, z>(q_gen_6368) -> q_gen_6343
<s, z, z>(q_gen_6334) -> q_gen_6343
<s, s, s>(q_gen_6320) -> q_gen_6348
<s, s, s>(q_gen_6348) -> q_gen_6348
<s, z, s>(q_gen_6355) -> q_gen_6348
}

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

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

Teacher's answer:
New clause system:
{
() -> drop([s(u), nil, nil]) -> 68
() -> drop([z, l, l]) -> 68
() -> length([nil, z]) -> 68
() -> minus([s(u), z, s(u)]) -> 68
() -> minus([z, y, z]) -> 68
(drop([n, l1, _sga]) /\ length([_sga, _tga]) /\ length([l1, _uga]) /\ minus([_uga, n, _vga])) -> eq_nat([_tga, _vga]) -> 73
(drop([u, x3, _ega])) -> drop([s(u), cons(x2, x3), _ega]) -> 71
(length([ll, _jga])) -> length([cons(x, ll), s(_jga)]) -> 71
(minus([u, x2, _nga])) -> minus([s(u), s(x2), _nga]) -> 73
}
Sat witness: Found: ((length([ll, _jga])) -> length([cons(x, ll), s(_jga)]), {
_jga -> s(s(z))  ;  ll -> cons(a, cons(b, nil))  ;  x -> b
})

-------------------------------------------
Step 89, which took 3.052054 s (model generation: 3.049071,  model checking: 0.002983):

Model:
|_
{
drop -> 
{{{
Q={q_gen_6324, q_gen_6326, q_gen_6331, q_gen_6332, q_gen_6338, q_gen_6339, q_gen_6353, q_gen_6370, q_gen_6371, q_gen_6378, q_gen_6416, q_gen_6421, q_gen_6422},
Q_f={q_gen_6324},
Delta=
{
<s>(q_gen_6326) -> q_gen_6326
<z>() -> q_gen_6326
<a>() -> q_gen_6332
<b>() -> q_gen_6332
<cons>(q_gen_6332, q_gen_6422) -> q_gen_6371
<nil>() -> q_gen_6371
<cons>(q_gen_6332, q_gen_6371) -> q_gen_6422
<s, cons>(q_gen_6332, q_gen_6331) -> q_gen_6331
<s, nil>(q_gen_6326) -> q_gen_6331
<z, nil>() -> q_gen_6331
<cons, cons>(q_gen_6339, q_gen_6338) -> q_gen_6338
<cons, cons>(q_gen_6353, q_gen_6338) -> q_gen_6338
<cons, nil>(q_gen_6332, q_gen_6422) -> q_gen_6338
<nil, nil>() -> q_gen_6338
<b, b>() -> q_gen_6339
<a, a>() -> q_gen_6353
<a, b>() -> q_gen_6353
<b, a>() -> q_gen_6353
<s, cons>(q_gen_6332, q_gen_6378) -> q_gen_6378
<z, cons>(q_gen_6332, q_gen_6371) -> q_gen_6378
<z, cons>(q_gen_6332, q_gen_6422) -> q_gen_6378
<cons, cons>(q_gen_6339, q_gen_6416) -> q_gen_6416
<cons, cons>(q_gen_6353, q_gen_6416) -> q_gen_6416
<cons, nil>(q_gen_6332, q_gen_6371) -> q_gen_6416
<s, cons, cons>(q_gen_6339, q_gen_6370) -> q_gen_6324
<s, cons, cons>(q_gen_6353, q_gen_6370) -> q_gen_6324
<s, cons, nil>(q_gen_6332, q_gen_6331) -> q_gen_6324
<s, nil, nil>(q_gen_6326) -> q_gen_6324
<z, cons, cons>(q_gen_6339, q_gen_6338) -> q_gen_6324
<z, cons, cons>(q_gen_6353, q_gen_6338) -> q_gen_6324
<z, nil, nil>() -> q_gen_6324
<s, cons, cons>(q_gen_6339, q_gen_6324) -> q_gen_6370
<s, cons, cons>(q_gen_6353, q_gen_6421) -> q_gen_6370
<s, cons, nil>(q_gen_6332, q_gen_6378) -> q_gen_6370
<z, cons, cons>(q_gen_6339, q_gen_6416) -> q_gen_6370
<z, cons, nil>(q_gen_6332, q_gen_6371) -> q_gen_6370
<s, cons, cons>(q_gen_6339, q_gen_6421) -> q_gen_6421
<s, cons, cons>(q_gen_6353, q_gen_6324) -> q_gen_6421
<z, cons, nil>(q_gen_6332, q_gen_6422) -> q_gen_6421
}

Datatype: <nat, eltlist, eltlist>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_6323, q_gen_6329},
Q_f={q_gen_6323},
Delta=
{
<a>() -> q_gen_6329
<b>() -> q_gen_6329
<cons, s>(q_gen_6329, q_gen_6323) -> q_gen_6323
<nil, z>() -> q_gen_6323
}

Datatype: <eltlist, nat>
Convolution form: right
}}}
  ;  minus -> 
{{{
Q={q_gen_6320, q_gen_6321, q_gen_6322, q_gen_6334, q_gen_6336, q_gen_6343, q_gen_6348, q_gen_6350, q_gen_6355, q_gen_6368},
Q_f={q_gen_6320, q_gen_6321},
Delta=
{
<s>(q_gen_6350) -> q_gen_6334
<z>() -> q_gen_6334
<s>(q_gen_6334) -> q_gen_6350
<z, z>() -> q_gen_6322
<s, s>(q_gen_6322) -> q_gen_6336
<s, s>(q_gen_6336) -> q_gen_6336
<s, z>(q_gen_6350) -> q_gen_6336
<z, s>(q_gen_6334) -> q_gen_6355
<z, s>(q_gen_6350) -> q_gen_6355
<s, s>(q_gen_6368) -> q_gen_6368
<s, z>(q_gen_6334) -> q_gen_6368
<s, s, z>(q_gen_6322) -> q_gen_6320
<s, s, z>(q_gen_6355) -> q_gen_6320
<z, s, z>(q_gen_6334) -> q_gen_6320
<z, s, z>(q_gen_6350) -> q_gen_6320
<z, z, z>() -> q_gen_6320
<s, s, s>(q_gen_6343) -> q_gen_6321
<s, s, z>(q_gen_6336) -> q_gen_6321
<s, z, s>(q_gen_6322) -> q_gen_6321
<s, z, s>(q_gen_6336) -> q_gen_6321
<s, z, z>(q_gen_6350) -> q_gen_6321
<s, s, s>(q_gen_6321) -> q_gen_6343
<s, s, z>(q_gen_6368) -> q_gen_6343
<s, z, s>(q_gen_6368) -> q_gen_6343
<s, z, z>(q_gen_6334) -> q_gen_6343
<s, s, s>(q_gen_6320) -> q_gen_6348
<s, s, s>(q_gen_6348) -> q_gen_6348
<s, z, s>(q_gen_6355) -> q_gen_6348
}

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

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

Teacher's answer:
New clause system:
{
() -> drop([s(u), nil, nil]) -> 69
() -> drop([z, l, l]) -> 69
() -> length([nil, z]) -> 69
() -> minus([s(u), z, s(u)]) -> 69
() -> minus([z, y, z]) -> 69
(drop([n, l1, _sga]) /\ length([_sga, _tga]) /\ length([l1, _uga]) /\ minus([_uga, n, _vga])) -> eq_nat([_tga, _vga]) -> 73
(drop([u, x3, _ega])) -> drop([s(u), cons(x2, x3), _ega]) -> 74
(length([ll, _jga])) -> length([cons(x, ll), s(_jga)]) -> 72
(minus([u, x2, _nga])) -> minus([s(u), s(x2), _nga]) -> 73
}
Sat witness: Found: ((drop([u, x3, _ega])) -> drop([s(u), cons(x2, x3), _ega]), {
_ega -> cons(b, cons(b, nil))  ;  u -> s(s(z))  ;  x2 -> b  ;  x3 -> cons(a, cons(b, nil))
})

-------------------------------------------
Step 90, which took 5.715888 s (model generation: 5.713907,  model checking: 0.001981):

Model:
|_
{
drop -> 
{{{
Q={q_gen_6324, q_gen_6326, q_gen_6331, q_gen_6332, q_gen_6338, q_gen_6339, q_gen_6353, q_gen_6370, q_gen_6371, q_gen_6378, q_gen_6416, q_gen_6421, q_gen_6422},
Q_f={q_gen_6324},
Delta=
{
<s>(q_gen_6326) -> q_gen_6326
<z>() -> q_gen_6326
<a>() -> q_gen_6332
<b>() -> q_gen_6332
<cons>(q_gen_6332, q_gen_6422) -> q_gen_6371
<nil>() -> q_gen_6371
<cons>(q_gen_6332, q_gen_6371) -> q_gen_6422
<s, cons>(q_gen_6332, q_gen_6331) -> q_gen_6331
<s, nil>(q_gen_6326) -> q_gen_6331
<z, nil>() -> q_gen_6331
<cons, cons>(q_gen_6339, q_gen_6338) -> q_gen_6338
<cons, cons>(q_gen_6339, q_gen_6416) -> q_gen_6338
<cons, cons>(q_gen_6353, q_gen_6338) -> q_gen_6338
<nil, nil>() -> q_gen_6338
<b, a>() -> q_gen_6339
<b, b>() -> q_gen_6339
<a, a>() -> q_gen_6353
<a, b>() -> q_gen_6353
<s, cons>(q_gen_6332, q_gen_6378) -> q_gen_6378
<z, cons>(q_gen_6332, q_gen_6371) -> q_gen_6378
<z, cons>(q_gen_6332, q_gen_6422) -> q_gen_6378
<cons, cons>(q_gen_6353, q_gen_6416) -> q_gen_6416
<cons, nil>(q_gen_6332, q_gen_6371) -> q_gen_6416
<cons, nil>(q_gen_6332, q_gen_6422) -> q_gen_6416
<s, cons, cons>(q_gen_6339, q_gen_6370) -> q_gen_6324
<s, cons, cons>(q_gen_6353, q_gen_6370) -> q_gen_6324
<s, cons, nil>(q_gen_6332, q_gen_6331) -> q_gen_6324
<s, nil, nil>(q_gen_6326) -> q_gen_6324
<z, cons, cons>(q_gen_6339, q_gen_6338) -> q_gen_6324
<z, cons, cons>(q_gen_6353, q_gen_6338) -> q_gen_6324
<z, nil, nil>() -> q_gen_6324
<s, cons, cons>(q_gen_6353, q_gen_6421) -> q_gen_6370
<s, cons, nil>(q_gen_6332, q_gen_6378) -> q_gen_6370
<z, cons, cons>(q_gen_6339, q_gen_6416) -> q_gen_6370
<z, cons, nil>(q_gen_6332, q_gen_6371) -> q_gen_6370
<s, cons, cons>(q_gen_6339, q_gen_6324) -> q_gen_6421
<s, cons, cons>(q_gen_6339, q_gen_6421) -> q_gen_6421
<s, cons, cons>(q_gen_6353, q_gen_6324) -> q_gen_6421
<z, cons, nil>(q_gen_6332, q_gen_6422) -> q_gen_6421
}

Datatype: <nat, eltlist, eltlist>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_6323, q_gen_6329},
Q_f={q_gen_6323},
Delta=
{
<a>() -> q_gen_6329
<b>() -> q_gen_6329
<cons, s>(q_gen_6329, q_gen_6323) -> q_gen_6323
<nil, z>() -> q_gen_6323
}

Datatype: <eltlist, nat>
Convolution form: right
}}}
  ;  minus -> 
{{{
Q={q_gen_6320, q_gen_6321, q_gen_6322, q_gen_6334, q_gen_6336, q_gen_6343, q_gen_6348, q_gen_6350, q_gen_6355, q_gen_6368},
Q_f={q_gen_6320, q_gen_6321},
Delta=
{
<s>(q_gen_6350) -> q_gen_6334
<z>() -> q_gen_6334
<s>(q_gen_6334) -> q_gen_6350
<z, z>() -> q_gen_6322
<s, s>(q_gen_6322) -> q_gen_6336
<s, s>(q_gen_6336) -> q_gen_6336
<s, z>(q_gen_6350) -> q_gen_6336
<z, s>(q_gen_6334) -> q_gen_6355
<z, s>(q_gen_6350) -> q_gen_6355
<s, s>(q_gen_6368) -> q_gen_6368
<s, z>(q_gen_6334) -> q_gen_6368
<s, s, z>(q_gen_6322) -> q_gen_6320
<s, s, z>(q_gen_6355) -> q_gen_6320
<z, s, z>(q_gen_6334) -> q_gen_6320
<z, s, z>(q_gen_6350) -> q_gen_6320
<z, z, z>() -> q_gen_6320
<s, s, s>(q_gen_6343) -> q_gen_6321
<s, s, z>(q_gen_6336) -> q_gen_6321
<s, z, s>(q_gen_6322) -> q_gen_6321
<s, z, s>(q_gen_6336) -> q_gen_6321
<s, z, z>(q_gen_6350) -> q_gen_6321
<s, s, s>(q_gen_6321) -> q_gen_6343
<s, s, z>(q_gen_6368) -> q_gen_6343
<s, z, s>(q_gen_6368) -> q_gen_6343
<s, z, z>(q_gen_6334) -> q_gen_6343
<s, s, s>(q_gen_6320) -> q_gen_6348
<s, s, s>(q_gen_6348) -> q_gen_6348
<s, z, s>(q_gen_6355) -> q_gen_6348
}

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

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

Teacher's answer:
New clause system:
{
() -> drop([s(u), nil, nil]) -> 70
() -> drop([z, l, l]) -> 70
() -> length([nil, z]) -> 70
() -> minus([s(u), z, s(u)]) -> 70
() -> minus([z, y, z]) -> 70
(drop([n, l1, _sga]) /\ length([_sga, _tga]) /\ length([l1, _uga]) /\ minus([_uga, n, _vga])) -> eq_nat([_tga, _vga]) -> 73
(drop([u, x3, _ega])) -> drop([s(u), cons(x2, x3), _ega]) -> 74
(length([ll, _jga])) -> length([cons(x, ll), s(_jga)]) -> 73
(minus([u, x2, _nga])) -> minus([s(u), s(x2), _nga]) -> 76
}
Sat witness: Found: ((minus([u, x2, _nga])) -> minus([s(u), s(x2), _nga]), {
_nga -> z  ;  u -> s(z)  ;  x2 -> s(s(z))
})

-------------------------------------------
Step 91, which took 6.971252 s (model generation: 6.969171,  model checking: 0.002081):

Model:
|_
{
drop -> 
{{{
Q={q_gen_6324, q_gen_6326, q_gen_6331, q_gen_6332, q_gen_6338, q_gen_6339, q_gen_6370, q_gen_6371, q_gen_6378, q_gen_6384, q_gen_6416, q_gen_6421, q_gen_6422},
Q_f={q_gen_6324},
Delta=
{
<s>(q_gen_6326) -> q_gen_6326
<z>() -> q_gen_6326
<a>() -> q_gen_6332
<b>() -> q_gen_6332
<cons>(q_gen_6332, q_gen_6422) -> q_gen_6371
<nil>() -> q_gen_6371
<cons>(q_gen_6332, q_gen_6371) -> q_gen_6422
<s, cons>(q_gen_6332, q_gen_6331) -> q_gen_6331
<s, nil>(q_gen_6326) -> q_gen_6331
<z, nil>() -> q_gen_6331
<cons, cons>(q_gen_6339, q_gen_6338) -> q_gen_6338
<cons, cons>(q_gen_6339, q_gen_6416) -> q_gen_6338
<cons, cons>(q_gen_6384, q_gen_6338) -> q_gen_6338
<cons, nil>(q_gen_6332, q_gen_6422) -> q_gen_6338
<nil, nil>() -> q_gen_6338
<a, a>() -> q_gen_6339
<b, b>() -> q_gen_6339
<s, cons>(q_gen_6332, q_gen_6378) -> q_gen_6378
<z, cons>(q_gen_6332, q_gen_6371) -> q_gen_6378
<z, cons>(q_gen_6332, q_gen_6422) -> q_gen_6378
<a, b>() -> q_gen_6384
<b, a>() -> q_gen_6384
<cons, cons>(q_gen_6384, q_gen_6416) -> q_gen_6416
<cons, nil>(q_gen_6332, q_gen_6371) -> q_gen_6416
<s, cons, cons>(q_gen_6339, q_gen_6370) -> q_gen_6324
<s, cons, cons>(q_gen_6384, q_gen_6370) -> q_gen_6324
<s, cons, nil>(q_gen_6332, q_gen_6331) -> q_gen_6324
<s, nil, nil>(q_gen_6326) -> q_gen_6324
<z, cons, cons>(q_gen_6339, q_gen_6338) -> q_gen_6324
<z, nil, nil>() -> q_gen_6324
<s, cons, cons>(q_gen_6384, q_gen_6324) -> q_gen_6370
<s, cons, cons>(q_gen_6384, q_gen_6421) -> q_gen_6370
<s, cons, nil>(q_gen_6332, q_gen_6378) -> q_gen_6370
<z, cons, cons>(q_gen_6339, q_gen_6416) -> q_gen_6370
<z, cons, cons>(q_gen_6384, q_gen_6338) -> q_gen_6370
<z, cons, nil>(q_gen_6332, q_gen_6371) -> q_gen_6370
<s, cons, cons>(q_gen_6339, q_gen_6324) -> q_gen_6421
<s, cons, cons>(q_gen_6339, q_gen_6421) -> q_gen_6421
<z, cons, nil>(q_gen_6332, q_gen_6422) -> q_gen_6421
}

Datatype: <nat, eltlist, eltlist>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_6323, q_gen_6329},
Q_f={q_gen_6323},
Delta=
{
<a>() -> q_gen_6329
<b>() -> q_gen_6329
<cons, s>(q_gen_6329, q_gen_6323) -> q_gen_6323
<nil, z>() -> q_gen_6323
}

Datatype: <eltlist, nat>
Convolution form: right
}}}
  ;  minus -> 
{{{
Q={q_gen_6320, q_gen_6322, q_gen_6334, q_gen_6343, q_gen_6348, q_gen_6350, q_gen_6355, q_gen_6361, q_gen_6368, q_gen_6457},
Q_f={q_gen_6320},
Delta=
{
<s>(q_gen_6350) -> q_gen_6334
<z>() -> q_gen_6334
<s>(q_gen_6334) -> q_gen_6350
<s, s>(q_gen_6322) -> q_gen_6322
<s, s>(q_gen_6355) -> q_gen_6322
<z, z>() -> q_gen_6322
<z, s>(q_gen_6334) -> q_gen_6355
<z, s>(q_gen_6350) -> q_gen_6361
<s, s>(q_gen_6368) -> q_gen_6368
<s, z>(q_gen_6334) -> q_gen_6368
<s, z>(q_gen_6350) -> q_gen_6457
<s, s, s>(q_gen_6343) -> q_gen_6320
<s, s, z>(q_gen_6322) -> q_gen_6320
<s, s, z>(q_gen_6355) -> q_gen_6320
<s, s, z>(q_gen_6361) -> q_gen_6320
<s, z, s>(q_gen_6322) -> q_gen_6320
<z, s, z>(q_gen_6334) -> q_gen_6320
<z, s, z>(q_gen_6350) -> q_gen_6320
<z, z, z>() -> q_gen_6320
<s, s, s>(q_gen_6348) -> q_gen_6343
<s, s, z>(q_gen_6368) -> q_gen_6343
<s, z, s>(q_gen_6361) -> q_gen_6343
<s, z, s>(q_gen_6368) -> q_gen_6343
<s, z, z>(q_gen_6334) -> q_gen_6343
<s, s, s>(q_gen_6320) -> q_gen_6348
<s, s, z>(q_gen_6457) -> q_gen_6348
<s, z, s>(q_gen_6355) -> q_gen_6348
<s, z, s>(q_gen_6457) -> q_gen_6348
<s, z, z>(q_gen_6350) -> q_gen_6348
}

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

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

Teacher's answer:
New clause system:
{
() -> drop([s(u), nil, nil]) -> 71
() -> drop([z, l, l]) -> 71
() -> length([nil, z]) -> 71
() -> minus([s(u), z, s(u)]) -> 71
() -> minus([z, y, z]) -> 71
(drop([n, l1, _sga]) /\ length([_sga, _tga]) /\ length([l1, _uga]) /\ minus([_uga, n, _vga])) -> eq_nat([_tga, _vga]) -> 76
(drop([u, x3, _ega])) -> drop([s(u), cons(x2, x3), _ega]) -> 74
(length([ll, _jga])) -> length([cons(x, ll), s(_jga)]) -> 74
(minus([u, x2, _nga])) -> minus([s(u), s(x2), _nga]) -> 76
}
Sat witness: Found: ((drop([n, l1, _sga]) /\ length([_sga, _tga]) /\ length([l1, _uga]) /\ minus([_uga, n, _vga])) -> eq_nat([_tga, _vga]), {
_sga -> cons(b, nil)  ;  _tga -> s(z)  ;  _uga -> s(s(z))  ;  _vga -> s(s(s(s(z))))  ;  l1 -> cons(b, cons(b, nil))  ;  n -> s(z)
})

-------------------------------------------
Step 92, which took 2.678815 s (model generation: 2.673191,  model checking: 0.005624):

Model:
|_
{
drop -> 
{{{
Q={q_gen_6324, q_gen_6326, q_gen_6331, q_gen_6332, q_gen_6338, q_gen_6339, q_gen_6353, q_gen_6370, q_gen_6371, q_gen_6378, q_gen_6416, q_gen_6421, q_gen_6422},
Q_f={q_gen_6324},
Delta=
{
<s>(q_gen_6326) -> q_gen_6326
<z>() -> q_gen_6326
<a>() -> q_gen_6332
<b>() -> q_gen_6332
<cons>(q_gen_6332, q_gen_6422) -> q_gen_6371
<nil>() -> q_gen_6371
<cons>(q_gen_6332, q_gen_6371) -> q_gen_6422
<s, cons>(q_gen_6332, q_gen_6331) -> q_gen_6331
<s, nil>(q_gen_6326) -> q_gen_6331
<z, nil>() -> q_gen_6331
<cons, cons>(q_gen_6339, q_gen_6338) -> q_gen_6338
<cons, cons>(q_gen_6339, q_gen_6416) -> q_gen_6338
<cons, cons>(q_gen_6353, q_gen_6338) -> q_gen_6338
<cons, nil>(q_gen_6332, q_gen_6422) -> q_gen_6338
<nil, nil>() -> q_gen_6338
<b, b>() -> q_gen_6339
<a, a>() -> q_gen_6353
<a, b>() -> q_gen_6353
<b, a>() -> q_gen_6353
<s, cons>(q_gen_6332, q_gen_6378) -> q_gen_6378
<z, cons>(q_gen_6332, q_gen_6371) -> q_gen_6378
<z, cons>(q_gen_6332, q_gen_6422) -> q_gen_6378
<cons, cons>(q_gen_6353, q_gen_6416) -> q_gen_6416
<cons, nil>(q_gen_6332, q_gen_6371) -> q_gen_6416
<s, cons, cons>(q_gen_6339, q_gen_6370) -> q_gen_6324
<s, cons, cons>(q_gen_6353, q_gen_6370) -> q_gen_6324
<s, cons, nil>(q_gen_6332, q_gen_6331) -> q_gen_6324
<s, nil, nil>(q_gen_6326) -> q_gen_6324
<z, cons, cons>(q_gen_6339, q_gen_6338) -> q_gen_6324
<z, cons, cons>(q_gen_6353, q_gen_6338) -> q_gen_6324
<z, nil, nil>() -> q_gen_6324
<s, cons, cons>(q_gen_6353, q_gen_6421) -> q_gen_6370
<s, cons, nil>(q_gen_6332, q_gen_6378) -> q_gen_6370
<z, cons, cons>(q_gen_6339, q_gen_6416) -> q_gen_6370
<z, cons, nil>(q_gen_6332, q_gen_6371) -> q_gen_6370
<s, cons, cons>(q_gen_6339, q_gen_6324) -> q_gen_6421
<s, cons, cons>(q_gen_6339, q_gen_6421) -> q_gen_6421
<s, cons, cons>(q_gen_6353, q_gen_6324) -> q_gen_6421
<z, cons, nil>(q_gen_6332, q_gen_6422) -> q_gen_6421
}

Datatype: <nat, eltlist, eltlist>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_6323, q_gen_6329},
Q_f={q_gen_6323},
Delta=
{
<a>() -> q_gen_6329
<b>() -> q_gen_6329
<cons, s>(q_gen_6329, q_gen_6323) -> q_gen_6323
<nil, z>() -> q_gen_6323
}

Datatype: <eltlist, nat>
Convolution form: right
}}}
  ;  minus -> 
{{{
Q={q_gen_6320, q_gen_6322, q_gen_6334, q_gen_6336, q_gen_6343, q_gen_6348, q_gen_6350, q_gen_6355, q_gen_6368, q_gen_6388},
Q_f={q_gen_6320, q_gen_6388},
Delta=
{
<s>(q_gen_6350) -> q_gen_6334
<z>() -> q_gen_6334
<s>(q_gen_6334) -> q_gen_6350
<s, s>(q_gen_6355) -> q_gen_6322
<z, z>() -> q_gen_6322
<s, s>(q_gen_6322) -> q_gen_6336
<s, s>(q_gen_6336) -> q_gen_6336
<s, s>(q_gen_6368) -> q_gen_6336
<s, z>(q_gen_6350) -> q_gen_6336
<z, s>(q_gen_6334) -> q_gen_6355
<z, s>(q_gen_6350) -> q_gen_6355
<s, z>(q_gen_6334) -> q_gen_6368
<s, s, s>(q_gen_6343) -> q_gen_6320
<s, s, z>(q_gen_6322) -> q_gen_6320
<s, s, z>(q_gen_6355) -> q_gen_6320
<s, z, s>(q_gen_6322) -> q_gen_6320
<s, z, s>(q_gen_6336) -> q_gen_6320
<z, s, z>(q_gen_6334) -> q_gen_6320
<z, s, z>(q_gen_6350) -> q_gen_6320
<z, z, z>() -> q_gen_6320
<s, s, z>(q_gen_6368) -> q_gen_6343
<s, z, s>(q_gen_6368) -> q_gen_6343
<s, z, z>(q_gen_6334) -> q_gen_6343
<s, s, s>(q_gen_6320) -> q_gen_6348
<s, s, s>(q_gen_6348) -> q_gen_6348
<s, z, s>(q_gen_6355) -> q_gen_6348
<s, s, s>(q_gen_6388) -> q_gen_6388
<s, s, z>(q_gen_6336) -> q_gen_6388
<s, z, z>(q_gen_6350) -> q_gen_6388
}

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

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

Teacher's answer:
New clause system:
{
() -> drop([s(u), nil, nil]) -> 72
() -> drop([z, l, l]) -> 72
() -> length([nil, z]) -> 72
() -> minus([s(u), z, s(u)]) -> 72
() -> minus([z, y, z]) -> 72
(drop([n, l1, _sga]) /\ length([_sga, _tga]) /\ length([l1, _uga]) /\ minus([_uga, n, _vga])) -> eq_nat([_tga, _vga]) -> 76
(drop([u, x3, _ega])) -> drop([s(u), cons(x2, x3), _ega]) -> 77
(length([ll, _jga])) -> length([cons(x, ll), s(_jga)]) -> 75
(minus([u, x2, _nga])) -> minus([s(u), s(x2), _nga]) -> 76
}
Sat witness: Found: ((drop([u, x3, _ega])) -> drop([s(u), cons(x2, x3), _ega]), {
_ega -> cons(b, cons(a, nil))  ;  u -> s(s(z))  ;  x2 -> a  ;  x3 -> cons(b, cons(b, cons(b, cons(b, nil))))
})

-------------------------------------------
Step 93, which took 7.288322 s (model generation: 7.287286,  model checking: 0.001036):

Model:
|_
{
drop -> 
{{{
Q={q_gen_6324, q_gen_6326, q_gen_6331, q_gen_6332, q_gen_6338, q_gen_6339, q_gen_6353, q_gen_6370, q_gen_6371, q_gen_6378, q_gen_6416, q_gen_6421, q_gen_6422},
Q_f={q_gen_6324},
Delta=
{
<s>(q_gen_6326) -> q_gen_6326
<z>() -> q_gen_6326
<a>() -> q_gen_6332
<b>() -> q_gen_6332
<cons>(q_gen_6332, q_gen_6422) -> q_gen_6371
<nil>() -> q_gen_6371
<cons>(q_gen_6332, q_gen_6371) -> q_gen_6422
<s, cons>(q_gen_6332, q_gen_6331) -> q_gen_6331
<s, nil>(q_gen_6326) -> q_gen_6331
<z, nil>() -> q_gen_6331
<cons, cons>(q_gen_6339, q_gen_6338) -> q_gen_6338
<cons, cons>(q_gen_6339, q_gen_6416) -> q_gen_6338
<cons, cons>(q_gen_6353, q_gen_6338) -> q_gen_6338
<nil, nil>() -> q_gen_6338
<b, a>() -> q_gen_6339
<b, b>() -> q_gen_6339
<a, a>() -> q_gen_6353
<a, b>() -> q_gen_6353
<s, cons>(q_gen_6332, q_gen_6378) -> q_gen_6378
<z, cons>(q_gen_6332, q_gen_6371) -> q_gen_6378
<z, cons>(q_gen_6332, q_gen_6422) -> q_gen_6378
<cons, cons>(q_gen_6353, q_gen_6416) -> q_gen_6416
<cons, nil>(q_gen_6332, q_gen_6371) -> q_gen_6416
<cons, nil>(q_gen_6332, q_gen_6422) -> q_gen_6416
<s, cons, cons>(q_gen_6339, q_gen_6370) -> q_gen_6324
<s, cons, cons>(q_gen_6353, q_gen_6370) -> q_gen_6324
<s, cons, nil>(q_gen_6332, q_gen_6331) -> q_gen_6324
<s, nil, nil>(q_gen_6326) -> q_gen_6324
<z, cons, cons>(q_gen_6339, q_gen_6338) -> q_gen_6324
<z, cons, cons>(q_gen_6353, q_gen_6338) -> q_gen_6324
<z, nil, nil>() -> q_gen_6324
<s, cons, cons>(q_gen_6353, q_gen_6421) -> q_gen_6370
<s, cons, nil>(q_gen_6332, q_gen_6378) -> q_gen_6370
<z, cons, cons>(q_gen_6339, q_gen_6416) -> q_gen_6370
<z, cons, nil>(q_gen_6332, q_gen_6371) -> q_gen_6370
<s, cons, cons>(q_gen_6339, q_gen_6324) -> q_gen_6421
<s, cons, cons>(q_gen_6339, q_gen_6421) -> q_gen_6421
<s, cons, cons>(q_gen_6353, q_gen_6324) -> q_gen_6421
<z, cons, nil>(q_gen_6332, q_gen_6422) -> q_gen_6421
}

Datatype: <nat, eltlist, eltlist>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_6323, q_gen_6329},
Q_f={q_gen_6323},
Delta=
{
<a>() -> q_gen_6329
<b>() -> q_gen_6329
<cons, s>(q_gen_6329, q_gen_6323) -> q_gen_6323
<nil, z>() -> q_gen_6323
}

Datatype: <eltlist, nat>
Convolution form: right
}}}
  ;  minus -> 
{{{
Q={q_gen_6320, q_gen_6322, q_gen_6334, q_gen_6343, q_gen_6348, q_gen_6350, q_gen_6355, q_gen_6368, q_gen_6396, q_gen_6457},
Q_f={q_gen_6320, q_gen_6396},
Delta=
{
<s>(q_gen_6350) -> q_gen_6334
<z>() -> q_gen_6334
<s>(q_gen_6334) -> q_gen_6350
<s, s>(q_gen_6322) -> q_gen_6322
<s, s>(q_gen_6355) -> q_gen_6322
<z, z>() -> q_gen_6322
<z, s>(q_gen_6334) -> q_gen_6355
<z, s>(q_gen_6350) -> q_gen_6355
<s, s>(q_gen_6368) -> q_gen_6368
<s, z>(q_gen_6334) -> q_gen_6368
<s, z>(q_gen_6350) -> q_gen_6457
<s, s, s>(q_gen_6343) -> q_gen_6320
<s, s, z>(q_gen_6322) -> q_gen_6320
<s, s, z>(q_gen_6355) -> q_gen_6320
<s, z, s>(q_gen_6322) -> q_gen_6320
<z, s, z>(q_gen_6334) -> q_gen_6320
<z, s, z>(q_gen_6350) -> q_gen_6320
<z, z, z>() -> q_gen_6320
<s, s, s>(q_gen_6396) -> q_gen_6343
<s, s, z>(q_gen_6368) -> q_gen_6343
<s, z, s>(q_gen_6368) -> q_gen_6343
<s, z, z>(q_gen_6334) -> q_gen_6343
<s, s, s>(q_gen_6320) -> q_gen_6348
<s, s, s>(q_gen_6348) -> q_gen_6348
<s, z, s>(q_gen_6355) -> q_gen_6348
<s, s, z>(q_gen_6457) -> q_gen_6396
<s, z, s>(q_gen_6457) -> q_gen_6396
<s, z, z>(q_gen_6350) -> q_gen_6396
}

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

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

Teacher's answer:
New clause system:
{
() -> drop([s(u), nil, nil]) -> 73
() -> drop([z, l, l]) -> 73
() -> length([nil, z]) -> 73
() -> minus([s(u), z, s(u)]) -> 73
() -> minus([z, y, z]) -> 73
(drop([n, l1, _sga]) /\ length([_sga, _tga]) /\ length([l1, _uga]) /\ minus([_uga, n, _vga])) -> eq_nat([_tga, _vga]) -> 76
(drop([u, x3, _ega])) -> drop([s(u), cons(x2, x3), _ega]) -> 77
(length([ll, _jga])) -> length([cons(x, ll), s(_jga)]) -> 76
(minus([u, x2, _nga])) -> minus([s(u), s(x2), _nga]) -> 79
}
Sat witness: Found: ((minus([u, x2, _nga])) -> minus([s(u), s(x2), _nga]), {
_nga -> z  ;  u -> s(s(s(z)))  ;  x2 -> s(z)
})

-------------------------------------------
Step 94, which took 3.234080 s (model generation: 3.231977,  model checking: 0.002103):

Model:
|_
{
drop -> 
{{{
Q={q_gen_6324, q_gen_6326, q_gen_6331, q_gen_6332, q_gen_6338, q_gen_6339, q_gen_6353, q_gen_6370, q_gen_6371, q_gen_6378, q_gen_6416, q_gen_6421, q_gen_6422},
Q_f={q_gen_6324},
Delta=
{
<s>(q_gen_6326) -> q_gen_6326
<z>() -> q_gen_6326
<a>() -> q_gen_6332
<b>() -> q_gen_6332
<cons>(q_gen_6332, q_gen_6422) -> q_gen_6371
<nil>() -> q_gen_6371
<cons>(q_gen_6332, q_gen_6371) -> q_gen_6422
<s, cons>(q_gen_6332, q_gen_6331) -> q_gen_6331
<s, nil>(q_gen_6326) -> q_gen_6331
<z, nil>() -> q_gen_6331
<cons, cons>(q_gen_6339, q_gen_6338) -> q_gen_6338
<cons, cons>(q_gen_6339, q_gen_6416) -> q_gen_6338
<cons, cons>(q_gen_6353, q_gen_6338) -> q_gen_6338
<nil, nil>() -> q_gen_6338
<b, a>() -> q_gen_6339
<b, b>() -> q_gen_6339
<a, a>() -> q_gen_6353
<a, b>() -> q_gen_6353
<s, cons>(q_gen_6332, q_gen_6378) -> q_gen_6378
<z, cons>(q_gen_6332, q_gen_6371) -> q_gen_6378
<z, cons>(q_gen_6332, q_gen_6422) -> q_gen_6378
<cons, cons>(q_gen_6353, q_gen_6416) -> q_gen_6416
<cons, nil>(q_gen_6332, q_gen_6371) -> q_gen_6416
<cons, nil>(q_gen_6332, q_gen_6422) -> q_gen_6416
<s, cons, cons>(q_gen_6339, q_gen_6370) -> q_gen_6324
<s, cons, cons>(q_gen_6353, q_gen_6370) -> q_gen_6324
<s, cons, nil>(q_gen_6332, q_gen_6331) -> q_gen_6324
<s, nil, nil>(q_gen_6326) -> q_gen_6324
<z, cons, cons>(q_gen_6339, q_gen_6338) -> q_gen_6324
<z, cons, cons>(q_gen_6353, q_gen_6338) -> q_gen_6324
<z, nil, nil>() -> q_gen_6324
<s, cons, cons>(q_gen_6353, q_gen_6324) -> q_gen_6370
<s, cons, cons>(q_gen_6353, q_gen_6421) -> q_gen_6370
<s, cons, nil>(q_gen_6332, q_gen_6378) -> q_gen_6370
<z, cons, cons>(q_gen_6339, q_gen_6416) -> q_gen_6370
<z, cons, nil>(q_gen_6332, q_gen_6371) -> q_gen_6370
<s, cons, cons>(q_gen_6339, q_gen_6324) -> q_gen_6421
<s, cons, cons>(q_gen_6339, q_gen_6421) -> q_gen_6421
<z, cons, nil>(q_gen_6332, q_gen_6422) -> q_gen_6421
}

Datatype: <nat, eltlist, eltlist>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_6323, q_gen_6329},
Q_f={q_gen_6323},
Delta=
{
<a>() -> q_gen_6329
<b>() -> q_gen_6329
<cons, s>(q_gen_6329, q_gen_6323) -> q_gen_6323
<nil, z>() -> q_gen_6323
}

Datatype: <eltlist, nat>
Convolution form: right
}}}
  ;  minus -> 
{{{
Q={q_gen_6320, q_gen_6321, q_gen_6322, q_gen_6334, q_gen_6343, q_gen_6348, q_gen_6350, q_gen_6355, q_gen_6368, q_gen_6457},
Q_f={q_gen_6320, q_gen_6321},
Delta=
{
<z>() -> q_gen_6334
<s>(q_gen_6334) -> q_gen_6350
<s>(q_gen_6350) -> q_gen_6350
<s, s>(q_gen_6322) -> q_gen_6322
<z, z>() -> q_gen_6322
<s, s>(q_gen_6355) -> q_gen_6355
<s, s>(q_gen_6457) -> q_gen_6355
<z, s>(q_gen_6334) -> q_gen_6355
<z, s>(q_gen_6350) -> q_gen_6355
<s, s>(q_gen_6368) -> q_gen_6368
<s, z>(q_gen_6334) -> q_gen_6368
<s, z>(q_gen_6350) -> q_gen_6457
<s, s, z>(q_gen_6322) -> q_gen_6320
<s, s, z>(q_gen_6355) -> q_gen_6320
<z, s, z>(q_gen_6334) -> q_gen_6320
<z, s, z>(q_gen_6350) -> q_gen_6320
<z, z, z>() -> q_gen_6320
<s, s, s>(q_gen_6343) -> q_gen_6321
<s, s, z>(q_gen_6457) -> q_gen_6321
<s, z, s>(q_gen_6322) -> q_gen_6321
<s, z, s>(q_gen_6457) -> q_gen_6321
<s, z, z>(q_gen_6350) -> q_gen_6321
<s, s, s>(q_gen_6321) -> q_gen_6343
<s, s, z>(q_gen_6368) -> q_gen_6343
<s, z, s>(q_gen_6368) -> q_gen_6343
<s, z, z>(q_gen_6334) -> q_gen_6343
<s, s, s>(q_gen_6320) -> q_gen_6348
<s, s, s>(q_gen_6348) -> q_gen_6348
<s, z, s>(q_gen_6355) -> q_gen_6348
}

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

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

Teacher's answer:
New clause system:
{
() -> drop([s(u), nil, nil]) -> 74
() -> drop([z, l, l]) -> 74
() -> length([nil, z]) -> 74
() -> minus([s(u), z, s(u)]) -> 74
() -> minus([z, y, z]) -> 74
(drop([n, l1, _sga]) /\ length([_sga, _tga]) /\ length([l1, _uga]) /\ minus([_uga, n, _vga])) -> eq_nat([_tga, _vga]) -> 79
(drop([u, x3, _ega])) -> drop([s(u), cons(x2, x3), _ega]) -> 77
(length([ll, _jga])) -> length([cons(x, ll), s(_jga)]) -> 77
(minus([u, x2, _nga])) -> minus([s(u), s(x2), _nga]) -> 79
}
Sat witness: Found: ((drop([n, l1, _sga]) /\ length([_sga, _tga]) /\ length([l1, _uga]) /\ minus([_uga, n, _vga])) -> eq_nat([_tga, _vga]), {
_sga -> cons(b, nil)  ;  _tga -> s(z)  ;  _uga -> s(s(s(z)))  ;  _vga -> s(s(s(z)))  ;  l1 -> cons(b, cons(b, cons(b, nil)))  ;  n -> s(s(z))
})

-------------------------------------------
Step 95, which took 4.911898 s (model generation: 4.910406,  model checking: 0.001492):

Model:
|_
{
drop -> 
{{{
Q={q_gen_6324, q_gen_6326, q_gen_6331, q_gen_6332, q_gen_6338, q_gen_6339, q_gen_6353, q_gen_6370, q_gen_6371, q_gen_6378, q_gen_6416, q_gen_6420, q_gen_6422},
Q_f={q_gen_6324},
Delta=
{
<s>(q_gen_6326) -> q_gen_6326
<z>() -> q_gen_6326
<a>() -> q_gen_6332
<b>() -> q_gen_6332
<cons>(q_gen_6332, q_gen_6422) -> q_gen_6371
<nil>() -> q_gen_6371
<cons>(q_gen_6332, q_gen_6371) -> q_gen_6422
<s, cons>(q_gen_6332, q_gen_6331) -> q_gen_6331
<s, nil>(q_gen_6326) -> q_gen_6331
<z, nil>() -> q_gen_6331
<cons, cons>(q_gen_6339, q_gen_6338) -> q_gen_6338
<cons, cons>(q_gen_6353, q_gen_6338) -> q_gen_6338
<cons, nil>(q_gen_6332, q_gen_6422) -> q_gen_6338
<nil, nil>() -> q_gen_6338
<a, b>() -> q_gen_6339
<b, b>() -> q_gen_6339
<a, a>() -> q_gen_6353
<b, a>() -> q_gen_6353
<s, cons>(q_gen_6332, q_gen_6378) -> q_gen_6378
<z, cons>(q_gen_6332, q_gen_6371) -> q_gen_6378
<z, cons>(q_gen_6332, q_gen_6422) -> q_gen_6378
<cons, cons>(q_gen_6339, q_gen_6416) -> q_gen_6416
<cons, nil>(q_gen_6332, q_gen_6371) -> q_gen_6416
<s, cons, cons>(q_gen_6339, q_gen_6370) -> q_gen_6324
<s, cons, cons>(q_gen_6353, q_gen_6370) -> q_gen_6324
<s, cons, cons>(q_gen_6353, q_gen_6420) -> q_gen_6324
<s, cons, nil>(q_gen_6332, q_gen_6331) -> q_gen_6324
<s, nil, nil>(q_gen_6326) -> q_gen_6324
<z, cons, cons>(q_gen_6339, q_gen_6338) -> q_gen_6324
<z, cons, cons>(q_gen_6353, q_gen_6338) -> q_gen_6324
<z, nil, nil>() -> q_gen_6324
<s, cons, cons>(q_gen_6339, q_gen_6324) -> q_gen_6370
<s, cons, cons>(q_gen_6353, q_gen_6324) -> q_gen_6370
<s, cons, nil>(q_gen_6332, q_gen_6378) -> q_gen_6370
<z, cons, cons>(q_gen_6339, q_gen_6416) -> q_gen_6370
<z, cons, nil>(q_gen_6332, q_gen_6371) -> q_gen_6370
<s, cons, cons>(q_gen_6339, q_gen_6420) -> q_gen_6420
<z, cons, nil>(q_gen_6332, q_gen_6422) -> q_gen_6420
}

Datatype: <nat, eltlist, eltlist>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_6323, q_gen_6329},
Q_f={q_gen_6323},
Delta=
{
<a>() -> q_gen_6329
<b>() -> q_gen_6329
<cons, s>(q_gen_6329, q_gen_6323) -> q_gen_6323
<nil, z>() -> q_gen_6323
}

Datatype: <eltlist, nat>
Convolution form: right
}}}
  ;  minus -> 
{{{
Q={q_gen_6320, q_gen_6322, q_gen_6334, q_gen_6343, q_gen_6348, q_gen_6349, q_gen_6350, q_gen_6355, q_gen_6359, q_gen_6368},
Q_f={q_gen_6320, q_gen_6349},
Delta=
{
<z>() -> q_gen_6334
<s>(q_gen_6334) -> q_gen_6350
<s>(q_gen_6350) -> q_gen_6350
<s, s>(q_gen_6322) -> q_gen_6322
<s, s>(q_gen_6355) -> q_gen_6322
<z, z>() -> q_gen_6322
<z, s>(q_gen_6334) -> q_gen_6355
<z, s>(q_gen_6350) -> q_gen_6355
<s, s>(q_gen_6368) -> q_gen_6368
<s, z>(q_gen_6334) -> q_gen_6368
<s, z>(q_gen_6350) -> q_gen_6368
<s, s, s>(q_gen_6343) -> q_gen_6320
<s, s, s>(q_gen_6349) -> q_gen_6320
<s, s, z>(q_gen_6322) -> q_gen_6320
<s, s, z>(q_gen_6355) -> q_gen_6320
<s, z, s>(q_gen_6322) -> q_gen_6320
<z, s, z>(q_gen_6334) -> q_gen_6320
<z, z, z>() -> q_gen_6320
<s, z, z>(q_gen_6334) -> q_gen_6343
<s, s, s>(q_gen_6320) -> q_gen_6348
<s, z, s>(q_gen_6355) -> q_gen_6348
<s, z, z>(q_gen_6350) -> q_gen_6348
<s, s, s>(q_gen_6359) -> q_gen_6349
<z, s, z>(q_gen_6350) -> q_gen_6349
<s, s, s>(q_gen_6348) -> q_gen_6359
<s, s, z>(q_gen_6368) -> q_gen_6359
<s, z, s>(q_gen_6368) -> q_gen_6359
}

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

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

Teacher's answer:
New clause system:
{
() -> drop([s(u), nil, nil]) -> 75
() -> drop([z, l, l]) -> 75
() -> length([nil, z]) -> 75
() -> minus([s(u), z, s(u)]) -> 75
() -> minus([z, y, z]) -> 75
(drop([n, l1, _sga]) /\ length([_sga, _tga]) /\ length([l1, _uga]) /\ minus([_uga, n, _vga])) -> eq_nat([_tga, _vga]) -> 79
(drop([u, x3, _ega])) -> drop([s(u), cons(x2, x3), _ega]) -> 80
(length([ll, _jga])) -> length([cons(x, ll), s(_jga)]) -> 78
(minus([u, x2, _nga])) -> minus([s(u), s(x2), _nga]) -> 79
}
Sat witness: Found: ((drop([u, x3, _ega])) -> drop([s(u), cons(x2, x3), _ega]), {
_ega -> cons(b, cons(b, nil))  ;  u -> s(z)  ;  x2 -> b  ;  x3 -> cons(a, cons(b, cons(b, nil)))
})

-------------------------------------------
Step 96, which took 3.014090 s (model generation: 3.012789,  model checking: 0.001301):

Model:
|_
{
drop -> 
{{{
Q={q_gen_6324, q_gen_6325, q_gen_6326, q_gen_6331, q_gen_6332, q_gen_6338, q_gen_6339, q_gen_6353, q_gen_6370, q_gen_6371, q_gen_6378, q_gen_6381, q_gen_6416, q_gen_6422, q_gen_6434},
Q_f={q_gen_6324, q_gen_6325},
Delta=
{
<s>(q_gen_6326) -> q_gen_6326
<z>() -> q_gen_6326
<a>() -> q_gen_6332
<b>() -> q_gen_6332
<cons>(q_gen_6332, q_gen_6422) -> q_gen_6371
<nil>() -> q_gen_6371
<cons>(q_gen_6332, q_gen_6371) -> q_gen_6422
<s, cons>(q_gen_6332, q_gen_6331) -> q_gen_6331
<s, nil>(q_gen_6326) -> q_gen_6331
<z, nil>() -> q_gen_6331
<cons, cons>(q_gen_6339, q_gen_6338) -> q_gen_6338
<cons, cons>(q_gen_6353, q_gen_6338) -> q_gen_6338
<nil, nil>() -> q_gen_6338
<a, b>() -> q_gen_6339
<b, b>() -> q_gen_6339
<a, a>() -> q_gen_6353
<b, a>() -> q_gen_6353
<s, cons>(q_gen_6332, q_gen_6378) -> q_gen_6378
<z, cons>(q_gen_6332, q_gen_6371) -> q_gen_6378
<z, cons>(q_gen_6332, q_gen_6422) -> q_gen_6378
<cons, nil>(q_gen_6332, q_gen_6371) -> q_gen_6416
<cons, nil>(q_gen_6332, q_gen_6422) -> q_gen_6416
<cons, cons>(q_gen_6339, q_gen_6416) -> q_gen_6434
<s, cons, cons>(q_gen_6339, q_gen_6370) -> q_gen_6324
<s, cons, nil>(q_gen_6332, q_gen_6331) -> q_gen_6324
<z, cons, cons>(q_gen_6339, q_gen_6338) -> q_gen_6324
<z, nil, nil>() -> q_gen_6324
<s, cons, cons>(q_gen_6353, q_gen_6324) -> q_gen_6325
<s, cons, cons>(q_gen_6353, q_gen_6381) -> q_gen_6325
<s, nil, nil>(q_gen_6326) -> q_gen_6325
<z, cons, cons>(q_gen_6353, q_gen_6338) -> q_gen_6325
<s, cons, cons>(q_gen_6339, q_gen_6324) -> q_gen_6370
<s, cons, cons>(q_gen_6339, q_gen_6325) -> q_gen_6370
<s, cons, cons>(q_gen_6353, q_gen_6325) -> q_gen_6370
<s, cons, nil>(q_gen_6332, q_gen_6378) -> q_gen_6370
<z, cons, cons>(q_gen_6339, q_gen_6434) -> q_gen_6370
<z, cons, nil>(q_gen_6332, q_gen_6371) -> q_gen_6370
<s, cons, cons>(q_gen_6339, q_gen_6381) -> q_gen_6381
<s, cons, cons>(q_gen_6353, q_gen_6370) -> q_gen_6381
<z, cons, cons>(q_gen_6339, q_gen_6416) -> q_gen_6381
<z, cons, nil>(q_gen_6332, q_gen_6422) -> q_gen_6381
}

Datatype: <nat, eltlist, eltlist>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_6323, q_gen_6328, q_gen_6329, q_gen_6379},
Q_f={q_gen_6323, q_gen_6328, q_gen_6379},
Delta=
{
<a>() -> q_gen_6329
<b>() -> q_gen_6329
<cons, s>(q_gen_6329, q_gen_6379) -> q_gen_6323
<nil, z>() -> q_gen_6323
<cons, s>(q_gen_6329, q_gen_6323) -> q_gen_6328
<cons, s>(q_gen_6329, q_gen_6328) -> q_gen_6379
}

Datatype: <eltlist, nat>
Convolution form: right
}}}
  ;  minus -> 
{{{
Q={q_gen_6320, q_gen_6321, q_gen_6322, q_gen_6334, q_gen_6343, q_gen_6348, q_gen_6349, q_gen_6350, q_gen_6354, q_gen_6355, q_gen_6359, q_gen_6361, q_gen_6368, q_gen_6372, q_gen_6394, q_gen_6395, q_gen_6400, q_gen_6401},
Q_f={q_gen_6320, q_gen_6321, q_gen_6349, q_gen_6354, q_gen_6372, q_gen_6394, q_gen_6395, q_gen_6401},
Delta=
{
<s>(q_gen_6350) -> q_gen_6334
<z>() -> q_gen_6334
<s>(q_gen_6334) -> q_gen_6350
<s, s>(q_gen_6322) -> q_gen_6322
<z, z>() -> q_gen_6322
<s, s>(q_gen_6355) -> q_gen_6355
<s, s>(q_gen_6368) -> q_gen_6355
<z, s>(q_gen_6334) -> q_gen_6355
<s, s>(q_gen_6361) -> q_gen_6361
<s, z>(q_gen_6350) -> q_gen_6361
<z, s>(q_gen_6350) -> q_gen_6361
<s, z>(q_gen_6334) -> q_gen_6368
<s, s, z>(q_gen_6322) -> q_gen_6320
<z, s, z>(q_gen_6334) -> q_gen_6320
<z, z, z>() -> q_gen_6320
<s, s, s>(q_gen_6343) -> q_gen_6321
<s, s, s>(q_gen_6354) -> q_gen_6321
<s, z, s>(q_gen_6322) -> q_gen_6321
<s, s, s>(q_gen_6348) -> q_gen_6343
<s, s, s>(q_gen_6372) -> q_gen_6343
<s, s, z>(q_gen_6368) -> q_gen_6343
<s, z, z>(q_gen_6334) -> q_gen_6343
<s, s, s>(q_gen_6320) -> q_gen_6348
<s, s, s>(q_gen_6321) -> q_gen_6348
<s, z, s>(q_gen_6355) -> q_gen_6348
<s, z, s>(q_gen_6368) -> q_gen_6349
<z, s, z>(q_gen_6350) -> q_gen_6349
<s, s, z>(q_gen_6355) -> q_gen_6354
<s, s, s>(q_gen_6359) -> q_gen_6359
<s, z, s>(q_gen_6361) -> q_gen_6359
<s, s, s>(q_gen_6349) -> q_gen_6372
<s, s, s>(q_gen_6395) -> q_gen_6394
<s, s, s>(q_gen_6400) -> q_gen_6394
<s, z, z>(q_gen_6350) -> q_gen_6394
<s, s, s>(q_gen_6394) -> q_gen_6395
<s, s, s>(q_gen_6401) -> q_gen_6400
<s, s, z>(q_gen_6361) -> q_gen_6401
}

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

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

Teacher's answer:
New clause system:
{
() -> drop([s(u), nil, nil]) -> 76
() -> drop([z, l, l]) -> 76
() -> length([nil, z]) -> 76
() -> minus([s(u), z, s(u)]) -> 76
() -> minus([z, y, z]) -> 76
(drop([n, l1, _sga]) /\ length([_sga, _tga]) /\ length([l1, _uga]) /\ minus([_uga, n, _vga])) -> eq_nat([_tga, _vga]) -> 79
(drop([u, x3, _ega])) -> drop([s(u), cons(x2, x3), _ega]) -> 80
(length([ll, _jga])) -> length([cons(x, ll), s(_jga)]) -> 79
(minus([u, x2, _nga])) -> minus([s(u), s(x2), _nga]) -> 82
}
Sat witness: Found: ((minus([u, x2, _nga])) -> minus([s(u), s(x2), _nga]), {
_nga -> s(z)  ;  u -> s(s(s(z)))  ;  x2 -> s(z)
})

Total time: 64.432500
Reason for stopping: DontKnow. Stopped because: timeout