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


Learning problem is:

env: {
nat -> {s, z}
}
definition:
{
(minus, F:
{() -> minus([s(u), z, s(u)])
() -> minus([z, y, z])
(minus([u, x2, _fq])) -> minus([s(u), s(x2), _fq])}
(minus([_gq, _hq, _iq]) /\ minus([_gq, _hq, _jq])) -> eq_nat([_iq, _jq])
)
(plus, F:
{() -> plus([n, z, n])
(plus([n, mm, _kq])) -> plus([n, s(mm), s(_kq)])}
(plus([_lq, _mq, _nq]) /\ plus([_lq, _mq, _oq])) -> eq_nat([_nq, _oq])
)
}

properties:
{(minus([_pq, n, _qq]) /\ plus([m, n, _pq])) -> eq_nat([_qq, m])}


over-approximation: {minus, plus}
under-approximation: {}

Clause system for inference is:

{
() -> minus([s(u), z, s(u)]) -> 0
() -> minus([z, y, z]) -> 0
() -> plus([n, z, n]) -> 0
(minus([_pq, n, _qq]) /\ plus([m, n, _pq])) -> eq_nat([_qq, m]) -> 0
(minus([u, x2, _fq])) -> minus([s(u), s(x2), _fq]) -> 0
(plus([n, mm, _kq])) -> plus([n, s(mm), s(_kq)]) -> 0
}


Solving took 65.647629 seconds.
DontKnow. Stopped because: timeout
Working model:
|_
{
minus -> 
{{{
Q={q_gen_4293, q_gen_4294, q_gen_4295, q_gen_4298, q_gen_4300, q_gen_4301, q_gen_4302, q_gen_4303, q_gen_4307, q_gen_4308, q_gen_4312, q_gen_4313, q_gen_4317, q_gen_4318, q_gen_4319, q_gen_4324, q_gen_4325, q_gen_4326, q_gen_4329, q_gen_4330, q_gen_4334, q_gen_4335, q_gen_4336, q_gen_4337, q_gen_4338, q_gen_4340, q_gen_4341, q_gen_4346, q_gen_4351, q_gen_4352, q_gen_4353, q_gen_4357, q_gen_4358, q_gen_4359, q_gen_4360, q_gen_4361, q_gen_4362, q_gen_4366, q_gen_4367, q_gen_4372, q_gen_4373, q_gen_4374, q_gen_4375, q_gen_4378, q_gen_4379, q_gen_4383, q_gen_4384, q_gen_4386, q_gen_4387, q_gen_4388, q_gen_4389, q_gen_4392, q_gen_4393, q_gen_4394, q_gen_4395, q_gen_4396, q_gen_4403, q_gen_4404, q_gen_4405, q_gen_4406, q_gen_4407, q_gen_4408, q_gen_4409, q_gen_4410, q_gen_4411, q_gen_4412, q_gen_4413, q_gen_4414, q_gen_4415, q_gen_4416, q_gen_4417, q_gen_4418, q_gen_4424, q_gen_4425, q_gen_4426, q_gen_4427, q_gen_4428, q_gen_4429, q_gen_4430, q_gen_4431, q_gen_4432, q_gen_4439, q_gen_4440, q_gen_4444, q_gen_4452},
Q_f={},
Delta=
{
<z>() -> q_gen_4301
<s>(q_gen_4301) -> q_gen_4313
<s>(q_gen_4313) -> q_gen_4353
<s>(q_gen_4353) -> q_gen_4431
<z, z>() -> q_gen_4295
<s, s>(q_gen_4295) -> q_gen_4303
<z, s>(q_gen_4301) -> q_gen_4318
<z, s>(q_gen_4313) -> q_gen_4336
<s, z>(q_gen_4301) -> q_gen_4341
<s, s>(q_gen_4303) -> q_gen_4358
<s, s>(q_gen_4318) -> q_gen_4360
<s, z>(q_gen_4313) -> q_gen_4373
<z, s>(q_gen_4353) -> q_gen_4384
<s, s>(q_gen_4358) -> q_gen_4389
<s, s>(q_gen_4341) -> q_gen_4396
<s, s>(q_gen_4373) -> q_gen_4427
<z, z, z>() -> q_gen_4293
<s, z, s>(q_gen_4295) -> q_gen_4294
<s, s, z>(q_gen_4295) -> q_gen_4298
<z, s, z>(q_gen_4301) -> q_gen_4300
<s, z, s>(q_gen_4303) -> q_gen_4302
<s, s, s>(q_gen_4308) -> q_gen_4307
<s, z, z>(q_gen_4301) -> q_gen_4308
<z, s, z>(q_gen_4313) -> q_gen_4312
<s, s, z>(q_gen_4318) -> q_gen_4317
<s, s, s>(q_gen_4293) -> q_gen_4319
<s, z, s>(q_gen_4318) -> q_gen_4324
<s, s, s>(q_gen_4294) -> q_gen_4325
<s, s, s>(q_gen_4298) -> q_gen_4326
<s, s, s>(q_gen_4300) -> q_gen_4329
<s, s, s>(q_gen_4317) -> q_gen_4330
<s, s, s>(q_gen_4335) -> q_gen_4334
<s, z, s>(q_gen_4336) -> q_gen_4335
<s, s, s>(q_gen_4338) -> q_gen_4337
<s, s, s>(q_gen_4324) -> q_gen_4338
<s, s, z>(q_gen_4341) -> q_gen_4340
<s, s, s>(q_gen_4307) -> q_gen_4346
<s, s, s>(q_gen_4340) -> q_gen_4351
<z, s, z>(q_gen_4353) -> q_gen_4352
<s, z, s>(q_gen_4358) -> q_gen_4357
<s, s, z>(q_gen_4360) -> q_gen_4359
<s, s, s>(q_gen_4362) -> q_gen_4361
<s, z, z>(q_gen_4313) -> q_gen_4362
<s, s, z>(q_gen_4336) -> q_gen_4366
<s, s, z>(q_gen_4303) -> q_gen_4367
<s, s, z>(q_gen_4373) -> q_gen_4372
<s, s, s>(q_gen_4375) -> q_gen_4374
<s, z, s>(q_gen_4341) -> q_gen_4375
<s, s, s>(q_gen_4361) -> q_gen_4378
<s, s, z>(q_gen_4358) -> q_gen_4379
<s, z, s>(q_gen_4384) -> q_gen_4383
<s, s, s>(q_gen_4387) -> q_gen_4386
<s, s, s>(q_gen_4372) -> q_gen_4387
<s, z, s>(q_gen_4389) -> q_gen_4388
<s, s, s>(q_gen_4393) -> q_gen_4392
<s, z, z>(q_gen_4353) -> q_gen_4393
<s, s, s>(q_gen_4395) -> q_gen_4394
<s, z, s>(q_gen_4396) -> q_gen_4395
<s, s, s>(q_gen_4319) -> q_gen_4403
<s, s, s>(q_gen_4405) -> q_gen_4404
<s, s, s>(q_gen_4406) -> q_gen_4405
<s, z, s>(q_gen_4373) -> q_gen_4406
<s, z, s>(q_gen_4360) -> q_gen_4407
<s, s, s>(q_gen_4409) -> q_gen_4408
<s, s, s>(q_gen_4383) -> q_gen_4409
<s, s, s>(q_gen_4411) -> q_gen_4410
<s, s, s>(q_gen_4334) -> q_gen_4411
<s, s, s>(q_gen_4413) -> q_gen_4412
<s, s, z>(q_gen_4396) -> q_gen_4413
<s, s, s>(q_gen_4325) -> q_gen_4414
<s, s, s>(q_gen_4414) -> q_gen_4415
<s, s, s>(q_gen_4403) -> q_gen_4416
<s, s, s>(q_gen_4418) -> q_gen_4417
<s, s, s>(q_gen_4392) -> q_gen_4418
<s, s, s>(q_gen_4425) -> q_gen_4424
<s, s, s>(q_gen_4426) -> q_gen_4425
<s, s, z>(q_gen_4427) -> q_gen_4426
<s, s, s>(q_gen_4404) -> q_gen_4428
<s, s, s>(q_gen_4417) -> q_gen_4429
<z, s, z>(q_gen_4431) -> q_gen_4430
<s, s, s>(q_gen_4337) -> q_gen_4432
<s, s, s>(q_gen_4312) -> q_gen_4439
<s, s, s>(q_gen_4366) -> q_gen_4440
<s, s, s>(q_gen_4394) -> q_gen_4444
<s, s, s>(q_gen_4374) -> q_gen_4452
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_4292, q_gen_4296, q_gen_4297, q_gen_4299, q_gen_4304, q_gen_4305, q_gen_4306, q_gen_4309, q_gen_4310, q_gen_4311, q_gen_4314, q_gen_4315, q_gen_4316, q_gen_4320, q_gen_4321, q_gen_4322, q_gen_4323, q_gen_4327, q_gen_4328, q_gen_4331, q_gen_4332, q_gen_4333, q_gen_4339, q_gen_4342, q_gen_4343, q_gen_4344, q_gen_4345, q_gen_4347, q_gen_4348, q_gen_4349, q_gen_4350, q_gen_4354, q_gen_4355, q_gen_4356, q_gen_4363, q_gen_4364, q_gen_4365, q_gen_4368, q_gen_4369, q_gen_4370, q_gen_4371, q_gen_4376, q_gen_4377, q_gen_4380, q_gen_4381, q_gen_4382, q_gen_4385, q_gen_4390, q_gen_4391, q_gen_4397, q_gen_4398, q_gen_4399, q_gen_4400, q_gen_4401, q_gen_4402, q_gen_4419, q_gen_4420, q_gen_4421, q_gen_4422, q_gen_4423, q_gen_4433, q_gen_4434, q_gen_4435, q_gen_4436, q_gen_4437, q_gen_4438, q_gen_4441, q_gen_4442, q_gen_4443, q_gen_4445, q_gen_4446, q_gen_4447, q_gen_4448, q_gen_4449, q_gen_4450, q_gen_4451, q_gen_4453, q_gen_4454},
Q_f={},
Delta=
{
<z>() -> q_gen_4306
<s>(q_gen_4306) -> q_gen_4323
<s>(q_gen_4323) -> q_gen_4371
<z, z>() -> q_gen_4297
<s, s>(q_gen_4297) -> q_gen_4311
<z, s>(q_gen_4306) -> q_gen_4316
<z, s>(q_gen_4323) -> q_gen_4343
<s, s>(q_gen_4311) -> q_gen_4345
<s, s>(q_gen_4316) -> q_gen_4365
<s, s>(q_gen_4343) -> q_gen_4402
<z, s>(q_gen_4371) -> q_gen_4438
<s, s>(q_gen_4345) -> q_gen_4454
<z, z, z>() -> q_gen_4292
<z, s, s>(q_gen_4297) -> q_gen_4296
<s, z, s>(q_gen_4297) -> q_gen_4299
<s, s, s>(q_gen_4305) -> q_gen_4304
<z, z, s>(q_gen_4306) -> q_gen_4305
<s, s, s>(q_gen_4292) -> q_gen_4309
<s, z, s>(q_gen_4311) -> q_gen_4310
<s, s, s>(q_gen_4315) -> q_gen_4314
<z, s, s>(q_gen_4316) -> q_gen_4315
<s, z, s>(q_gen_4316) -> q_gen_4320
<s, s, s>(q_gen_4322) -> q_gen_4321
<z, z, s>(q_gen_4323) -> q_gen_4322
<z, s, s>(q_gen_4311) -> q_gen_4327
<s, s, s>(q_gen_4320) -> q_gen_4328
<s, s, s>(q_gen_4309) -> q_gen_4331
<s, s, s>(q_gen_4333) -> q_gen_4332
<s, s, s>(q_gen_4296) -> q_gen_4333
<s, s, s>(q_gen_4321) -> q_gen_4339
<z, s, s>(q_gen_4343) -> q_gen_4342
<s, z, s>(q_gen_4345) -> q_gen_4344
<s, s, s>(q_gen_4348) -> q_gen_4347
<s, s, s>(q_gen_4299) -> q_gen_4348
<s, s, s>(q_gen_4350) -> q_gen_4349
<s, s, s>(q_gen_4304) -> q_gen_4350
<s, s, s>(q_gen_4327) -> q_gen_4354
<s, s, s>(q_gen_4356) -> q_gen_4355
<z, s, s>(q_gen_4345) -> q_gen_4356
<s, s, s>(q_gen_4364) -> q_gen_4363
<s, z, s>(q_gen_4365) -> q_gen_4364
<s, z, s>(q_gen_4343) -> q_gen_4368
<s, s, s>(q_gen_4370) -> q_gen_4369
<z, z, s>(q_gen_4371) -> q_gen_4370
<s, s, s>(q_gen_4310) -> q_gen_4376
<s, s, s>(q_gen_4328) -> q_gen_4377
<s, s, s>(q_gen_4331) -> q_gen_4380
<s, s, s>(q_gen_4382) -> q_gen_4381
<s, s, s>(q_gen_4342) -> q_gen_4382
<s, s, s>(q_gen_4339) -> q_gen_4385
<s, s, s>(q_gen_4391) -> q_gen_4390
<s, s, s>(q_gen_4368) -> q_gen_4391
<s, s, s>(q_gen_4398) -> q_gen_4397
<s, s, s>(q_gen_4369) -> q_gen_4398
<s, s, s>(q_gen_4400) -> q_gen_4399
<s, s, s>(q_gen_4401) -> q_gen_4400
<z, s, s>(q_gen_4402) -> q_gen_4401
<s, s, s>(q_gen_4420) -> q_gen_4419
<s, s, s>(q_gen_4347) -> q_gen_4420
<s, s, s>(q_gen_4422) -> q_gen_4421
<s, s, s>(q_gen_4349) -> q_gen_4422
<s, s, s>(q_gen_4381) -> q_gen_4423
<s, s, s>(q_gen_4314) -> q_gen_4433
<s, s, s>(q_gen_4435) -> q_gen_4434
<s, s, s>(q_gen_4436) -> q_gen_4435
<s, s, s>(q_gen_4437) -> q_gen_4436
<z, s, s>(q_gen_4438) -> q_gen_4437
<s, s, s>(q_gen_4380) -> q_gen_4441
<s, s, s>(q_gen_4443) -> q_gen_4442
<s, s, s>(q_gen_4332) -> q_gen_4443
<s, s, s>(q_gen_4446) -> q_gen_4445
<s, s, s>(q_gen_4447) -> q_gen_4446
<s, z, s>(q_gen_4402) -> q_gen_4447
<s, s, s>(q_gen_4449) -> q_gen_4448
<s, s, s>(q_gen_4450) -> q_gen_4449
<s, s, s>(q_gen_4451) -> q_gen_4450
<s, z, s>(q_gen_4438) -> q_gen_4451
<s, z, s>(q_gen_4454) -> q_gen_4453
}

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

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

-------------------
STEPS:
-------------------------------------------
Step 0, which took 0.025931 s (model generation: 0.025665,  model checking: 0.000266):

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

}

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

}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 0
() -> minus([z, y, z]) -> 0
() -> plus([n, z, n]) -> 3
(minus([_pq, n, _qq]) /\ plus([m, n, _pq])) -> eq_nat([_qq, m]) -> 1
(minus([u, x2, _fq])) -> minus([s(u), s(x2), _fq]) -> 1
(plus([n, mm, _kq])) -> plus([n, s(mm), s(_kq)]) -> 1
}
Sat witness: Found: (() -> plus([n, z, n]), {
n -> z
})

-------------------------------------------
Step 1, which took 0.012228 s (model generation: 0.011590,  model checking: 0.000638):

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

}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_4292},
Q_f={q_gen_4292},
Delta=
{
<z, z, z>() -> q_gen_4292
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 0
() -> minus([z, y, z]) -> 3
() -> plus([n, z, n]) -> 3
(minus([_pq, n, _qq]) /\ plus([m, n, _pq])) -> eq_nat([_qq, m]) -> 1
(minus([u, x2, _fq])) -> minus([s(u), s(x2), _fq]) -> 1
(plus([n, mm, _kq])) -> plus([n, s(mm), s(_kq)]) -> 1
}
Sat witness: Found: (() -> minus([z, y, z]), {
y -> z
})

-------------------------------------------
Step 2, which took 0.011807 s (model generation: 0.011671,  model checking: 0.000136):

Model:
|_
{
minus -> 
{{{
Q={q_gen_4293},
Q_f={q_gen_4293},
Delta=
{
<z, z, z>() -> q_gen_4293
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_4292},
Q_f={q_gen_4292},
Delta=
{
<z, z, z>() -> q_gen_4292
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 3
() -> minus([z, y, z]) -> 3
() -> plus([n, z, n]) -> 3
(minus([_pq, n, _qq]) /\ plus([m, n, _pq])) -> eq_nat([_qq, m]) -> 1
(minus([u, x2, _fq])) -> minus([s(u), s(x2), _fq]) -> 1
(plus([n, mm, _kq])) -> plus([n, s(mm), s(_kq)]) -> 1
}
Sat witness: Found: (() -> minus([s(u), z, s(u)]), {
u -> z
})

-------------------------------------------
Step 3, which took 0.014519 s (model generation: 0.014406,  model checking: 0.000113):

Model:
|_
{
minus -> 
{{{
Q={q_gen_4293, q_gen_4295},
Q_f={q_gen_4293},
Delta=
{
<z, z>() -> q_gen_4295
<s, z, s>(q_gen_4295) -> q_gen_4293
<z, z, z>() -> q_gen_4293
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_4292},
Q_f={q_gen_4292},
Delta=
{
<z, z, z>() -> q_gen_4292
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 3
() -> minus([z, y, z]) -> 3
() -> plus([n, z, n]) -> 3
(minus([_pq, n, _qq]) /\ plus([m, n, _pq])) -> eq_nat([_qq, m]) -> 1
(minus([u, x2, _fq])) -> minus([s(u), s(x2), _fq]) -> 1
(plus([n, mm, _kq])) -> plus([n, s(mm), s(_kq)]) -> 4
}
Sat witness: Found: ((plus([n, mm, _kq])) -> plus([n, s(mm), s(_kq)]), {
_kq -> z  ;  mm -> z  ;  n -> z
})

-------------------------------------------
Step 4, which took 0.014659 s (model generation: 0.014483,  model checking: 0.000176):

Model:
|_
{
minus -> 
{{{
Q={q_gen_4293, q_gen_4295},
Q_f={q_gen_4293},
Delta=
{
<z, z>() -> q_gen_4295
<s, z, s>(q_gen_4295) -> q_gen_4293
<z, z, z>() -> q_gen_4293
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_4292, q_gen_4297},
Q_f={q_gen_4292},
Delta=
{
<z, z>() -> q_gen_4297
<z, s, s>(q_gen_4297) -> q_gen_4292
<z, z, z>() -> q_gen_4292
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 3
() -> minus([z, y, z]) -> 3
() -> plus([n, z, n]) -> 3
(minus([_pq, n, _qq]) /\ plus([m, n, _pq])) -> eq_nat([_qq, m]) -> 1
(minus([u, x2, _fq])) -> minus([s(u), s(x2), _fq]) -> 4
(plus([n, mm, _kq])) -> plus([n, s(mm), s(_kq)]) -> 4
}
Sat witness: Found: ((minus([u, x2, _fq])) -> minus([s(u), s(x2), _fq]), {
_fq -> z  ;  u -> z  ;  x2 -> z
})

-------------------------------------------
Step 5, which took 0.011364 s (model generation: 0.011207,  model checking: 0.000157):

Model:
|_
{
minus -> 
{{{
Q={q_gen_4293, q_gen_4295},
Q_f={q_gen_4293},
Delta=
{
<z, z>() -> q_gen_4295
<s, s, z>(q_gen_4295) -> q_gen_4293
<s, z, s>(q_gen_4295) -> q_gen_4293
<z, z, z>() -> q_gen_4293
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_4292, q_gen_4297},
Q_f={q_gen_4292},
Delta=
{
<z, z>() -> q_gen_4297
<z, s, s>(q_gen_4297) -> q_gen_4292
<z, z, z>() -> q_gen_4292
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 3
() -> minus([z, y, z]) -> 3
() -> plus([n, z, n]) -> 6
(minus([_pq, n, _qq]) /\ plus([m, n, _pq])) -> eq_nat([_qq, m]) -> 2
(minus([u, x2, _fq])) -> minus([s(u), s(x2), _fq]) -> 4
(plus([n, mm, _kq])) -> plus([n, s(mm), s(_kq)]) -> 4
}
Sat witness: Found: (() -> plus([n, z, n]), {
n -> s(z)
})

-------------------------------------------
Step 6, which took 0.014801 s (model generation: 0.013301,  model checking: 0.001500):

Model:
|_
{
minus -> 
{{{
Q={q_gen_4293, q_gen_4295},
Q_f={q_gen_4293},
Delta=
{
<z, z>() -> q_gen_4295
<s, s, z>(q_gen_4295) -> q_gen_4293
<s, z, s>(q_gen_4295) -> q_gen_4293
<z, z, z>() -> q_gen_4293
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_4292, q_gen_4297},
Q_f={q_gen_4292},
Delta=
{
<z, z>() -> q_gen_4297
<s, z, s>(q_gen_4297) -> q_gen_4292
<z, s, s>(q_gen_4297) -> q_gen_4292
<z, z, z>() -> q_gen_4292
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 3
() -> minus([z, y, z]) -> 6
() -> plus([n, z, n]) -> 6
(minus([_pq, n, _qq]) /\ plus([m, n, _pq])) -> eq_nat([_qq, m]) -> 3
(minus([u, x2, _fq])) -> minus([s(u), s(x2), _fq]) -> 4
(plus([n, mm, _kq])) -> plus([n, s(mm), s(_kq)]) -> 4
}
Sat witness: Found: (() -> minus([z, y, z]), {
y -> s(z)
})

-------------------------------------------
Step 7, which took 0.010902 s (model generation: 0.010720,  model checking: 0.000182):

Model:
|_
{
minus -> 
{{{
Q={q_gen_4293, q_gen_4295, q_gen_4301},
Q_f={q_gen_4293},
Delta=
{
<z>() -> q_gen_4301
<z, z>() -> q_gen_4295
<s, s, z>(q_gen_4295) -> q_gen_4293
<s, z, s>(q_gen_4295) -> q_gen_4293
<z, s, z>(q_gen_4301) -> q_gen_4293
<z, z, z>() -> q_gen_4293
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_4292, q_gen_4297},
Q_f={q_gen_4292},
Delta=
{
<z, z>() -> q_gen_4297
<s, z, s>(q_gen_4297) -> q_gen_4292
<z, s, s>(q_gen_4297) -> q_gen_4292
<z, z, z>() -> q_gen_4292
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 6
() -> minus([z, y, z]) -> 6
() -> plus([n, z, n]) -> 6
(minus([_pq, n, _qq]) /\ plus([m, n, _pq])) -> eq_nat([_qq, m]) -> 4
(minus([u, x2, _fq])) -> minus([s(u), s(x2), _fq]) -> 4
(plus([n, mm, _kq])) -> plus([n, s(mm), s(_kq)]) -> 4
}
Sat witness: Found: (() -> minus([s(u), z, s(u)]), {
u -> s(z)
})

-------------------------------------------
Step 8, which took 0.011498 s (model generation: 0.011315,  model checking: 0.000183):

Model:
|_
{
minus -> 
{{{
Q={q_gen_4293, q_gen_4295, q_gen_4301},
Q_f={q_gen_4293},
Delta=
{
<z>() -> q_gen_4301
<s, s>(q_gen_4295) -> q_gen_4295
<z, z>() -> q_gen_4295
<s, s, z>(q_gen_4295) -> q_gen_4293
<s, z, s>(q_gen_4295) -> q_gen_4293
<z, s, z>(q_gen_4301) -> q_gen_4293
<z, z, z>() -> q_gen_4293
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_4292, q_gen_4297},
Q_f={q_gen_4292},
Delta=
{
<z, z>() -> q_gen_4297
<s, z, s>(q_gen_4297) -> q_gen_4292
<z, s, s>(q_gen_4297) -> q_gen_4292
<z, z, z>() -> q_gen_4292
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 6
() -> minus([z, y, z]) -> 6
() -> plus([n, z, n]) -> 6
(minus([_pq, n, _qq]) /\ plus([m, n, _pq])) -> eq_nat([_qq, m]) -> 4
(minus([u, x2, _fq])) -> minus([s(u), s(x2), _fq]) -> 4
(plus([n, mm, _kq])) -> plus([n, s(mm), s(_kq)]) -> 7
}
Sat witness: Found: ((plus([n, mm, _kq])) -> plus([n, s(mm), s(_kq)]), {
_kq -> s(z)  ;  mm -> z  ;  n -> s(z)
})

-------------------------------------------
Step 9, which took 0.010226 s (model generation: 0.010062,  model checking: 0.000164):

Model:
|_
{
minus -> 
{{{
Q={q_gen_4293, q_gen_4295, q_gen_4301},
Q_f={q_gen_4293},
Delta=
{
<z>() -> q_gen_4301
<s, s>(q_gen_4295) -> q_gen_4295
<z, z>() -> q_gen_4295
<s, s, z>(q_gen_4295) -> q_gen_4293
<s, z, s>(q_gen_4295) -> q_gen_4293
<z, s, z>(q_gen_4301) -> q_gen_4293
<z, z, z>() -> q_gen_4293
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_4292, q_gen_4297, q_gen_4306},
Q_f={q_gen_4292},
Delta=
{
<z>() -> q_gen_4306
<z, z>() -> q_gen_4297
<s, s, s>(q_gen_4292) -> q_gen_4292
<s, z, s>(q_gen_4297) -> q_gen_4292
<z, s, s>(q_gen_4297) -> q_gen_4292
<z, z, s>(q_gen_4306) -> q_gen_4292
<z, z, z>() -> q_gen_4292
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 6
() -> minus([z, y, z]) -> 6
() -> plus([n, z, n]) -> 6
(minus([_pq, n, _qq]) /\ plus([m, n, _pq])) -> eq_nat([_qq, m]) -> 4
(minus([u, x2, _fq])) -> minus([s(u), s(x2), _fq]) -> 7
(plus([n, mm, _kq])) -> plus([n, s(mm), s(_kq)]) -> 7
}
Sat witness: Found: ((minus([u, x2, _fq])) -> minus([s(u), s(x2), _fq]), {
_fq -> s(z)  ;  u -> s(z)  ;  x2 -> z
})

-------------------------------------------
Step 10, which took 0.011721 s (model generation: 0.011565,  model checking: 0.000156):

Model:
|_
{
minus -> 
{{{
Q={q_gen_4293, q_gen_4295, q_gen_4301},
Q_f={q_gen_4293},
Delta=
{
<z>() -> q_gen_4301
<s, s>(q_gen_4295) -> q_gen_4295
<z, z>() -> q_gen_4295
<s, s, s>(q_gen_4293) -> q_gen_4293
<s, s, z>(q_gen_4295) -> q_gen_4293
<s, z, s>(q_gen_4295) -> q_gen_4293
<s, z, z>(q_gen_4301) -> q_gen_4293
<z, s, z>(q_gen_4301) -> q_gen_4293
<z, z, z>() -> q_gen_4293
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_4292, q_gen_4297, q_gen_4306},
Q_f={q_gen_4292},
Delta=
{
<z>() -> q_gen_4306
<z, z>() -> q_gen_4297
<s, s, s>(q_gen_4292) -> q_gen_4292
<s, z, s>(q_gen_4297) -> q_gen_4292
<z, s, s>(q_gen_4297) -> q_gen_4292
<z, z, s>(q_gen_4306) -> q_gen_4292
<z, z, z>() -> q_gen_4292
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 6
() -> minus([z, y, z]) -> 6
() -> plus([n, z, n]) -> 6
(minus([_pq, n, _qq]) /\ plus([m, n, _pq])) -> eq_nat([_qq, m]) -> 7
(minus([u, x2, _fq])) -> minus([s(u), s(x2), _fq]) -> 7
(plus([n, mm, _kq])) -> plus([n, s(mm), s(_kq)]) -> 7
}
Sat witness: Found: ((minus([_pq, n, _qq]) /\ plus([m, n, _pq])) -> eq_nat([_qq, m]), {
_pq -> s(z)  ;  _qq -> z  ;  m -> s(z)  ;  n -> s(z)
})

-------------------------------------------
Step 11, which took 0.010729 s (model generation: 0.010566,  model checking: 0.000163):

Model:
|_
{
minus -> 
{{{
Q={q_gen_4293, q_gen_4295, q_gen_4301},
Q_f={q_gen_4293},
Delta=
{
<z>() -> q_gen_4301
<s, s>(q_gen_4295) -> q_gen_4295
<z, z>() -> q_gen_4295
<s, s, s>(q_gen_4293) -> q_gen_4293
<s, s, z>(q_gen_4295) -> q_gen_4293
<s, z, s>(q_gen_4295) -> q_gen_4293
<s, z, z>(q_gen_4301) -> q_gen_4293
<z, s, z>(q_gen_4301) -> q_gen_4293
<z, z, z>() -> q_gen_4293
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_4292, q_gen_4297, q_gen_4305, q_gen_4306},
Q_f={q_gen_4292},
Delta=
{
<z>() -> q_gen_4306
<z, z>() -> q_gen_4297
<s, s, s>(q_gen_4305) -> q_gen_4292
<s, z, s>(q_gen_4297) -> q_gen_4292
<z, s, s>(q_gen_4297) -> q_gen_4292
<z, z, z>() -> q_gen_4292
<s, s, s>(q_gen_4292) -> q_gen_4305
<z, z, s>(q_gen_4306) -> q_gen_4305
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 6
() -> minus([z, y, z]) -> 6
() -> plus([n, z, n]) -> 9
(minus([_pq, n, _qq]) /\ plus([m, n, _pq])) -> eq_nat([_qq, m]) -> 7
(minus([u, x2, _fq])) -> minus([s(u), s(x2), _fq]) -> 7
(plus([n, mm, _kq])) -> plus([n, s(mm), s(_kq)]) -> 7
}
Sat witness: Found: (() -> plus([n, z, n]), {
n -> s(s(z))
})

-------------------------------------------
Step 12, which took 0.011186 s (model generation: 0.011060,  model checking: 0.000126):

Model:
|_
{
minus -> 
{{{
Q={q_gen_4293, q_gen_4295, q_gen_4301},
Q_f={q_gen_4293},
Delta=
{
<z>() -> q_gen_4301
<s, s>(q_gen_4295) -> q_gen_4295
<z, z>() -> q_gen_4295
<s, s, s>(q_gen_4293) -> q_gen_4293
<s, s, z>(q_gen_4295) -> q_gen_4293
<s, z, s>(q_gen_4295) -> q_gen_4293
<s, z, z>(q_gen_4301) -> q_gen_4293
<z, s, z>(q_gen_4301) -> q_gen_4293
<z, z, z>() -> q_gen_4293
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_4292, q_gen_4297, q_gen_4305, q_gen_4306},
Q_f={q_gen_4292},
Delta=
{
<z>() -> q_gen_4306
<s, s>(q_gen_4297) -> q_gen_4297
<z, z>() -> q_gen_4297
<s, s, s>(q_gen_4305) -> q_gen_4292
<s, z, s>(q_gen_4297) -> q_gen_4292
<z, s, s>(q_gen_4297) -> q_gen_4292
<z, z, z>() -> q_gen_4292
<s, s, s>(q_gen_4292) -> q_gen_4305
<z, z, s>(q_gen_4306) -> q_gen_4305
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 6
() -> minus([z, y, z]) -> 9
() -> plus([n, z, n]) -> 9
(minus([_pq, n, _qq]) /\ plus([m, n, _pq])) -> eq_nat([_qq, m]) -> 7
(minus([u, x2, _fq])) -> minus([s(u), s(x2), _fq]) -> 7
(plus([n, mm, _kq])) -> plus([n, s(mm), s(_kq)]) -> 7
}
Sat witness: Found: (() -> minus([z, y, z]), {
y -> s(s(z))
})

-------------------------------------------
Step 13, which took 0.012542 s (model generation: 0.012165,  model checking: 0.000377):

Model:
|_
{
minus -> 
{{{
Q={q_gen_4293, q_gen_4295, q_gen_4301},
Q_f={q_gen_4293},
Delta=
{
<s>(q_gen_4301) -> q_gen_4301
<z>() -> q_gen_4301
<s, s>(q_gen_4295) -> q_gen_4295
<z, z>() -> q_gen_4295
<s, s, s>(q_gen_4293) -> q_gen_4293
<s, s, z>(q_gen_4295) -> q_gen_4293
<s, z, s>(q_gen_4295) -> q_gen_4293
<s, z, z>(q_gen_4301) -> q_gen_4293
<z, s, z>(q_gen_4301) -> q_gen_4293
<z, z, z>() -> q_gen_4293
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_4292, q_gen_4297, q_gen_4305, q_gen_4306},
Q_f={q_gen_4292},
Delta=
{
<z>() -> q_gen_4306
<s, s>(q_gen_4297) -> q_gen_4297
<z, z>() -> q_gen_4297
<s, s, s>(q_gen_4305) -> q_gen_4292
<s, z, s>(q_gen_4297) -> q_gen_4292
<z, s, s>(q_gen_4297) -> q_gen_4292
<z, z, z>() -> q_gen_4292
<s, s, s>(q_gen_4292) -> q_gen_4305
<z, z, s>(q_gen_4306) -> q_gen_4305
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 7
() -> minus([z, y, z]) -> 9
() -> plus([n, z, n]) -> 9
(minus([_pq, n, _qq]) /\ plus([m, n, _pq])) -> eq_nat([_qq, m]) -> 7
(minus([u, x2, _fq])) -> minus([s(u), s(x2), _fq]) -> 7
(plus([n, mm, _kq])) -> plus([n, s(mm), s(_kq)]) -> 10
}
Sat witness: Found: ((plus([n, mm, _kq])) -> plus([n, s(mm), s(_kq)]), {
_kq -> s(s(z))  ;  mm -> s(z)  ;  n -> s(z)
})

-------------------------------------------
Step 14, which took 0.013348 s (model generation: 0.012654,  model checking: 0.000694):

Model:
|_
{
minus -> 
{{{
Q={q_gen_4293, q_gen_4295, q_gen_4301},
Q_f={q_gen_4293},
Delta=
{
<s>(q_gen_4301) -> q_gen_4301
<z>() -> q_gen_4301
<s, s>(q_gen_4295) -> q_gen_4295
<z, z>() -> q_gen_4295
<s, s, s>(q_gen_4293) -> q_gen_4293
<s, s, z>(q_gen_4295) -> q_gen_4293
<s, z, s>(q_gen_4295) -> q_gen_4293
<s, z, z>(q_gen_4301) -> q_gen_4293
<z, s, z>(q_gen_4301) -> q_gen_4293
<z, z, z>() -> q_gen_4293
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_4292, q_gen_4296, q_gen_4297, q_gen_4306, q_gen_4309},
Q_f={q_gen_4292, q_gen_4296},
Delta=
{
<z>() -> q_gen_4306
<s, s>(q_gen_4297) -> q_gen_4297
<z, s>(q_gen_4306) -> q_gen_4297
<z, z>() -> q_gen_4297
<z, z, z>() -> q_gen_4292
<s, s, s>(q_gen_4296) -> q_gen_4296
<s, z, s>(q_gen_4297) -> q_gen_4296
<z, s, s>(q_gen_4297) -> q_gen_4296
<z, z, s>(q_gen_4306) -> q_gen_4296
<s, s, s>(q_gen_4292) -> q_gen_4309
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 7
() -> minus([z, y, z]) -> 9
() -> plus([n, z, n]) -> 9
(minus([_pq, n, _qq]) /\ plus([m, n, _pq])) -> eq_nat([_qq, m]) -> 7
(minus([u, x2, _fq])) -> minus([s(u), s(x2), _fq]) -> 10
(plus([n, mm, _kq])) -> plus([n, s(mm), s(_kq)]) -> 10
}
Sat witness: Found: ((minus([u, x2, _fq])) -> minus([s(u), s(x2), _fq]), {
_fq -> z  ;  u -> z  ;  x2 -> s(z)
})

-------------------------------------------
Step 15, which took 0.015557 s (model generation: 0.015379,  model checking: 0.000178):

Model:
|_
{
minus -> 
{{{
Q={q_gen_4293, q_gen_4295, q_gen_4301},
Q_f={q_gen_4293},
Delta=
{
<s>(q_gen_4301) -> q_gen_4301
<z>() -> q_gen_4301
<s, s>(q_gen_4295) -> q_gen_4295
<z, s>(q_gen_4301) -> q_gen_4295
<z, z>() -> q_gen_4295
<s, s, s>(q_gen_4293) -> q_gen_4293
<s, s, z>(q_gen_4295) -> q_gen_4293
<s, z, s>(q_gen_4295) -> q_gen_4293
<s, z, z>(q_gen_4301) -> q_gen_4293
<z, s, z>(q_gen_4301) -> q_gen_4293
<z, z, z>() -> q_gen_4293
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_4292, q_gen_4297, q_gen_4305, q_gen_4306, q_gen_4316},
Q_f={q_gen_4292},
Delta=
{
<z>() -> q_gen_4306
<s, s>(q_gen_4297) -> q_gen_4297
<z, z>() -> q_gen_4297
<z, s>(q_gen_4306) -> q_gen_4316
<s, s, s>(q_gen_4305) -> q_gen_4292
<s, z, s>(q_gen_4297) -> q_gen_4292
<z, s, s>(q_gen_4297) -> q_gen_4292
<z, z, z>() -> q_gen_4292
<s, s, s>(q_gen_4292) -> q_gen_4305
<z, s, s>(q_gen_4316) -> q_gen_4305
<z, z, s>(q_gen_4306) -> q_gen_4305
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 7
() -> minus([z, y, z]) -> 9
() -> plus([n, z, n]) -> 9
(minus([_pq, n, _qq]) /\ plus([m, n, _pq])) -> eq_nat([_qq, m]) -> 10
(minus([u, x2, _fq])) -> minus([s(u), s(x2), _fq]) -> 10
(plus([n, mm, _kq])) -> plus([n, s(mm), s(_kq)]) -> 10
}
Sat witness: Found: ((minus([_pq, n, _qq]) /\ plus([m, n, _pq])) -> eq_nat([_qq, m]), {
_pq -> s(z)  ;  _qq -> s(z)  ;  m -> z  ;  n -> s(z)
})

-------------------------------------------
Step 16, which took 0.018196 s (model generation: 0.015673,  model checking: 0.002523):

Model:
|_
{
minus -> 
{{{
Q={q_gen_4293, q_gen_4295, q_gen_4301, q_gen_4308},
Q_f={q_gen_4293},
Delta=
{
<s>(q_gen_4301) -> q_gen_4301
<z>() -> q_gen_4301
<s, s>(q_gen_4295) -> q_gen_4295
<z, s>(q_gen_4301) -> q_gen_4295
<z, z>() -> q_gen_4295
<s, s, s>(q_gen_4308) -> q_gen_4293
<s, s, z>(q_gen_4295) -> q_gen_4293
<s, z, s>(q_gen_4295) -> q_gen_4293
<z, s, z>(q_gen_4301) -> q_gen_4293
<z, z, z>() -> q_gen_4293
<s, s, s>(q_gen_4293) -> q_gen_4308
<s, z, z>(q_gen_4301) -> q_gen_4308
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_4292, q_gen_4296, q_gen_4297, q_gen_4306, q_gen_4309},
Q_f={q_gen_4292, q_gen_4296},
Delta=
{
<z>() -> q_gen_4306
<s, s>(q_gen_4297) -> q_gen_4297
<z, s>(q_gen_4306) -> q_gen_4297
<z, z>() -> q_gen_4297
<z, z, z>() -> q_gen_4292
<s, s, s>(q_gen_4296) -> q_gen_4296
<s, z, s>(q_gen_4297) -> q_gen_4296
<z, s, s>(q_gen_4297) -> q_gen_4296
<z, z, s>(q_gen_4306) -> q_gen_4296
<s, s, s>(q_gen_4292) -> q_gen_4309
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 8
() -> minus([z, y, z]) -> 10
() -> plus([n, z, n]) -> 10
(minus([_pq, n, _qq]) /\ plus([m, n, _pq])) -> eq_nat([_qq, m]) -> 10
(minus([u, x2, _fq])) -> minus([s(u), s(x2), _fq]) -> 10
(plus([n, mm, _kq])) -> plus([n, s(mm), s(_kq)]) -> 13
}
Sat witness: Found: ((plus([n, mm, _kq])) -> plus([n, s(mm), s(_kq)]), {
_kq -> s(s(z))  ;  mm -> z  ;  n -> s(z)
})

-------------------------------------------
Step 17, which took 0.021170 s (model generation: 0.020604,  model checking: 0.000566):

Model:
|_
{
minus -> 
{{{
Q={q_gen_4293, q_gen_4295, q_gen_4301, q_gen_4308},
Q_f={q_gen_4293},
Delta=
{
<s>(q_gen_4301) -> q_gen_4301
<z>() -> q_gen_4301
<s, s>(q_gen_4295) -> q_gen_4295
<z, s>(q_gen_4301) -> q_gen_4295
<z, z>() -> q_gen_4295
<s, s, s>(q_gen_4308) -> q_gen_4293
<s, s, z>(q_gen_4295) -> q_gen_4293
<s, z, s>(q_gen_4295) -> q_gen_4293
<z, s, z>(q_gen_4301) -> q_gen_4293
<z, z, z>() -> q_gen_4293
<s, s, s>(q_gen_4293) -> q_gen_4308
<s, z, z>(q_gen_4301) -> q_gen_4308
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_4292, q_gen_4296, q_gen_4297, q_gen_4306, q_gen_4309},
Q_f={q_gen_4292, q_gen_4296},
Delta=
{
<s>(q_gen_4306) -> q_gen_4306
<z>() -> q_gen_4306
<s, s>(q_gen_4297) -> q_gen_4297
<z, s>(q_gen_4306) -> q_gen_4297
<z, z>() -> q_gen_4297
<s, z, s>(q_gen_4297) -> q_gen_4292
<z, z, z>() -> q_gen_4292
<s, s, s>(q_gen_4296) -> q_gen_4296
<z, s, s>(q_gen_4297) -> q_gen_4296
<z, z, s>(q_gen_4306) -> q_gen_4296
<s, s, s>(q_gen_4292) -> q_gen_4309
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 9
() -> minus([z, y, z]) -> 10
() -> plus([n, z, n]) -> 10
(minus([_pq, n, _qq]) /\ plus([m, n, _pq])) -> eq_nat([_qq, m]) -> 10
(minus([u, x2, _fq])) -> minus([s(u), s(x2), _fq]) -> 13
(plus([n, mm, _kq])) -> plus([n, s(mm), s(_kq)]) -> 13
}
Sat witness: Found: ((minus([u, x2, _fq])) -> minus([s(u), s(x2), _fq]), {
_fq -> s(s(z))  ;  u -> s(z)  ;  x2 -> z
})

-------------------------------------------
Step 18, which took 0.018805 s (model generation: 0.018302,  model checking: 0.000503):

Model:
|_
{
minus -> 
{{{
Q={q_gen_4293, q_gen_4294, q_gen_4295, q_gen_4301, q_gen_4319},
Q_f={q_gen_4293, q_gen_4294},
Delta=
{
<s>(q_gen_4301) -> q_gen_4301
<z>() -> q_gen_4301
<s, s>(q_gen_4295) -> q_gen_4295
<z, s>(q_gen_4301) -> q_gen_4295
<z, z>() -> q_gen_4295
<z, z, z>() -> q_gen_4293
<s, s, s>(q_gen_4294) -> q_gen_4294
<s, s, z>(q_gen_4295) -> q_gen_4294
<s, z, s>(q_gen_4295) -> q_gen_4294
<s, z, z>(q_gen_4301) -> q_gen_4294
<z, s, z>(q_gen_4301) -> q_gen_4294
<s, s, s>(q_gen_4293) -> q_gen_4319
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_4292, q_gen_4296, q_gen_4297, q_gen_4306, q_gen_4309},
Q_f={q_gen_4292, q_gen_4296},
Delta=
{
<s>(q_gen_4306) -> q_gen_4306
<z>() -> q_gen_4306
<s, s>(q_gen_4297) -> q_gen_4297
<z, s>(q_gen_4306) -> q_gen_4297
<z, z>() -> q_gen_4297
<s, z, s>(q_gen_4297) -> q_gen_4292
<z, z, z>() -> q_gen_4292
<s, s, s>(q_gen_4296) -> q_gen_4296
<z, s, s>(q_gen_4297) -> q_gen_4296
<z, z, s>(q_gen_4306) -> q_gen_4296
<s, s, s>(q_gen_4292) -> q_gen_4309
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 10
() -> minus([z, y, z]) -> 10
() -> plus([n, z, n]) -> 10
(minus([_pq, n, _qq]) /\ plus([m, n, _pq])) -> eq_nat([_qq, m]) -> 13
(minus([u, x2, _fq])) -> minus([s(u), s(x2), _fq]) -> 13
(plus([n, mm, _kq])) -> plus([n, s(mm), s(_kq)]) -> 13
}
Sat witness: Found: ((minus([_pq, n, _qq]) /\ plus([m, n, _pq])) -> eq_nat([_qq, m]), {
_pq -> s(s(z))  ;  _qq -> s(z)  ;  m -> z  ;  n -> s(s(z))
})

-------------------------------------------
Step 19, which took 0.019027 s (model generation: 0.018363,  model checking: 0.000664):

Model:
|_
{
minus -> 
{{{
Q={q_gen_4293, q_gen_4294, q_gen_4295, q_gen_4301, q_gen_4319},
Q_f={q_gen_4293, q_gen_4294},
Delta=
{
<s>(q_gen_4301) -> q_gen_4301
<z>() -> q_gen_4301
<s, s>(q_gen_4295) -> q_gen_4295
<z, s>(q_gen_4301) -> q_gen_4295
<z, z>() -> q_gen_4295
<s, s, z>(q_gen_4295) -> q_gen_4293
<z, z, z>() -> q_gen_4293
<s, s, s>(q_gen_4294) -> q_gen_4294
<s, z, s>(q_gen_4295) -> q_gen_4294
<s, z, z>(q_gen_4301) -> q_gen_4294
<z, s, z>(q_gen_4301) -> q_gen_4294
<s, s, s>(q_gen_4293) -> q_gen_4319
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_4292, q_gen_4296, q_gen_4297, q_gen_4306, q_gen_4309},
Q_f={q_gen_4292, q_gen_4296},
Delta=
{
<s>(q_gen_4306) -> q_gen_4306
<z>() -> q_gen_4306
<s, s>(q_gen_4297) -> q_gen_4297
<z, s>(q_gen_4306) -> q_gen_4297
<z, z>() -> q_gen_4297
<s, z, s>(q_gen_4297) -> q_gen_4292
<z, z, z>() -> q_gen_4292
<s, s, s>(q_gen_4296) -> q_gen_4296
<z, s, s>(q_gen_4297) -> q_gen_4296
<z, z, s>(q_gen_4306) -> q_gen_4296
<s, s, s>(q_gen_4292) -> q_gen_4309
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 11
() -> minus([z, y, z]) -> 11
() -> plus([n, z, n]) -> 11
(minus([_pq, n, _qq]) /\ plus([m, n, _pq])) -> eq_nat([_qq, m]) -> 13
(minus([u, x2, _fq])) -> minus([s(u), s(x2), _fq]) -> 13
(plus([n, mm, _kq])) -> plus([n, s(mm), s(_kq)]) -> 16
}
Sat witness: Found: ((plus([n, mm, _kq])) -> plus([n, s(mm), s(_kq)]), {
_kq -> s(s(z))  ;  mm -> z  ;  n -> s(s(z))
})

-------------------------------------------
Step 20, which took 0.019608 s (model generation: 0.019182,  model checking: 0.000426):

Model:
|_
{
minus -> 
{{{
Q={q_gen_4293, q_gen_4294, q_gen_4295, q_gen_4301, q_gen_4319},
Q_f={q_gen_4293, q_gen_4294},
Delta=
{
<s>(q_gen_4301) -> q_gen_4301
<z>() -> q_gen_4301
<s, s>(q_gen_4295) -> q_gen_4295
<z, s>(q_gen_4301) -> q_gen_4295
<z, z>() -> q_gen_4295
<s, s, z>(q_gen_4295) -> q_gen_4293
<z, z, z>() -> q_gen_4293
<s, s, s>(q_gen_4294) -> q_gen_4294
<s, z, s>(q_gen_4295) -> q_gen_4294
<s, z, z>(q_gen_4301) -> q_gen_4294
<z, s, z>(q_gen_4301) -> q_gen_4294
<s, s, s>(q_gen_4293) -> q_gen_4319
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_4292, q_gen_4296, q_gen_4297, q_gen_4306, q_gen_4309},
Q_f={q_gen_4292, q_gen_4296},
Delta=
{
<s>(q_gen_4306) -> q_gen_4306
<z>() -> q_gen_4306
<s, s>(q_gen_4297) -> q_gen_4297
<z, s>(q_gen_4306) -> q_gen_4297
<z, z>() -> q_gen_4297
<z, z, z>() -> q_gen_4292
<s, s, s>(q_gen_4296) -> q_gen_4296
<s, z, s>(q_gen_4297) -> q_gen_4296
<z, s, s>(q_gen_4297) -> q_gen_4296
<z, z, s>(q_gen_4306) -> q_gen_4296
<s, s, s>(q_gen_4292) -> q_gen_4309
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 12
() -> minus([z, y, z]) -> 12
() -> plus([n, z, n]) -> 12
(minus([_pq, n, _qq]) /\ plus([m, n, _pq])) -> eq_nat([_qq, m]) -> 13
(minus([u, x2, _fq])) -> minus([s(u), s(x2), _fq]) -> 16
(plus([n, mm, _kq])) -> plus([n, s(mm), s(_kq)]) -> 16
}
Sat witness: Found: ((minus([u, x2, _fq])) -> minus([s(u), s(x2), _fq]), {
_fq -> s(z)  ;  u -> s(z)  ;  x2 -> s(s(z))
})

-------------------------------------------
Step 21, which took 0.022930 s (model generation: 0.022486,  model checking: 0.000444):

Model:
|_
{
minus -> 
{{{
Q={q_gen_4293, q_gen_4294, q_gen_4295, q_gen_4301, q_gen_4308},
Q_f={q_gen_4293, q_gen_4294},
Delta=
{
<s>(q_gen_4301) -> q_gen_4301
<z>() -> q_gen_4301
<s, s>(q_gen_4295) -> q_gen_4295
<z, s>(q_gen_4301) -> q_gen_4295
<z, z>() -> q_gen_4295
<s, s, s>(q_gen_4294) -> q_gen_4293
<s, s, z>(q_gen_4295) -> q_gen_4293
<z, s, z>(q_gen_4301) -> q_gen_4293
<z, z, z>() -> q_gen_4293
<s, s, s>(q_gen_4308) -> q_gen_4294
<s, z, s>(q_gen_4295) -> q_gen_4294
<s, s, s>(q_gen_4293) -> q_gen_4308
<s, z, z>(q_gen_4301) -> q_gen_4308
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_4292, q_gen_4296, q_gen_4297, q_gen_4306, q_gen_4309},
Q_f={q_gen_4292, q_gen_4296},
Delta=
{
<s>(q_gen_4306) -> q_gen_4306
<z>() -> q_gen_4306
<s, s>(q_gen_4297) -> q_gen_4297
<z, s>(q_gen_4306) -> q_gen_4297
<z, z>() -> q_gen_4297
<z, z, z>() -> q_gen_4292
<s, s, s>(q_gen_4296) -> q_gen_4296
<s, z, s>(q_gen_4297) -> q_gen_4296
<z, s, s>(q_gen_4297) -> q_gen_4296
<z, z, s>(q_gen_4306) -> q_gen_4296
<s, s, s>(q_gen_4292) -> q_gen_4309
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 13
() -> minus([z, y, z]) -> 13
() -> plus([n, z, n]) -> 13
(minus([_pq, n, _qq]) /\ plus([m, n, _pq])) -> eq_nat([_qq, m]) -> 16
(minus([u, x2, _fq])) -> minus([s(u), s(x2), _fq]) -> 16
(plus([n, mm, _kq])) -> plus([n, s(mm), s(_kq)]) -> 16
}
Sat witness: Found: ((minus([_pq, n, _qq]) /\ plus([m, n, _pq])) -> eq_nat([_qq, m]), {
_pq -> s(z)  ;  _qq -> s(z)  ;  m -> z  ;  n -> z
})

-------------------------------------------
Step 22, which took 0.021936 s (model generation: 0.021396,  model checking: 0.000540):

Model:
|_
{
minus -> 
{{{
Q={q_gen_4293, q_gen_4294, q_gen_4295, q_gen_4301, q_gen_4308},
Q_f={q_gen_4293, q_gen_4294},
Delta=
{
<s>(q_gen_4301) -> q_gen_4301
<z>() -> q_gen_4301
<s, s>(q_gen_4295) -> q_gen_4295
<z, s>(q_gen_4301) -> q_gen_4295
<z, z>() -> q_gen_4295
<s, s, s>(q_gen_4294) -> q_gen_4293
<s, s, z>(q_gen_4295) -> q_gen_4293
<z, s, z>(q_gen_4301) -> q_gen_4293
<z, z, z>() -> q_gen_4293
<s, s, s>(q_gen_4308) -> q_gen_4294
<s, z, s>(q_gen_4295) -> q_gen_4294
<s, s, s>(q_gen_4293) -> q_gen_4308
<s, z, z>(q_gen_4301) -> q_gen_4308
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_4292, q_gen_4296, q_gen_4297, q_gen_4305, q_gen_4306},
Q_f={q_gen_4292, q_gen_4296},
Delta=
{
<s>(q_gen_4306) -> q_gen_4306
<z>() -> q_gen_4306
<s, s>(q_gen_4297) -> q_gen_4297
<z, s>(q_gen_4306) -> q_gen_4297
<z, z>() -> q_gen_4297
<s, s, s>(q_gen_4296) -> q_gen_4292
<z, z, z>() -> q_gen_4292
<s, s, s>(q_gen_4305) -> q_gen_4296
<s, z, s>(q_gen_4297) -> q_gen_4296
<z, s, s>(q_gen_4297) -> q_gen_4296
<s, s, s>(q_gen_4292) -> q_gen_4305
<z, z, s>(q_gen_4306) -> q_gen_4305
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 14
() -> minus([z, y, z]) -> 14
() -> plus([n, z, n]) -> 14
(minus([_pq, n, _qq]) /\ plus([m, n, _pq])) -> eq_nat([_qq, m]) -> 16
(minus([u, x2, _fq])) -> minus([s(u), s(x2), _fq]) -> 16
(plus([n, mm, _kq])) -> plus([n, s(mm), s(_kq)]) -> 19
}
Sat witness: Found: ((plus([n, mm, _kq])) -> plus([n, s(mm), s(_kq)]), {
_kq -> s(s(z))  ;  mm -> s(s(z))  ;  n -> s(s(z))
})

-------------------------------------------
Step 23, which took 0.031008 s (model generation: 0.029559,  model checking: 0.001449):

Model:
|_
{
minus -> 
{{{
Q={q_gen_4293, q_gen_4295, q_gen_4301, q_gen_4308, q_gen_4318},
Q_f={q_gen_4293},
Delta=
{
<s>(q_gen_4301) -> q_gen_4301
<z>() -> q_gen_4301
<s, s>(q_gen_4295) -> q_gen_4295
<z, z>() -> q_gen_4295
<z, s>(q_gen_4301) -> q_gen_4318
<s, s, s>(q_gen_4308) -> q_gen_4293
<s, s, z>(q_gen_4295) -> q_gen_4293
<s, s, z>(q_gen_4318) -> q_gen_4293
<s, z, s>(q_gen_4295) -> q_gen_4293
<z, s, z>(q_gen_4301) -> q_gen_4293
<z, z, z>() -> q_gen_4293
<s, s, s>(q_gen_4293) -> q_gen_4308
<s, z, s>(q_gen_4318) -> q_gen_4308
<s, z, z>(q_gen_4301) -> q_gen_4308
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_4292, q_gen_4297, q_gen_4305, q_gen_4306, q_gen_4316},
Q_f={q_gen_4292},
Delta=
{
<s>(q_gen_4306) -> q_gen_4306
<z>() -> q_gen_4306
<s, s>(q_gen_4297) -> q_gen_4297
<z, z>() -> q_gen_4297
<z, s>(q_gen_4306) -> q_gen_4316
<s, s, s>(q_gen_4305) -> q_gen_4292
<s, z, s>(q_gen_4297) -> q_gen_4292
<z, s, s>(q_gen_4297) -> q_gen_4292
<z, z, z>() -> q_gen_4292
<s, s, s>(q_gen_4292) -> q_gen_4305
<s, z, s>(q_gen_4316) -> q_gen_4305
<z, s, s>(q_gen_4316) -> q_gen_4305
<z, z, s>(q_gen_4306) -> q_gen_4305
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 15
() -> minus([z, y, z]) -> 15
() -> plus([n, z, n]) -> 15
(minus([_pq, n, _qq]) /\ plus([m, n, _pq])) -> eq_nat([_qq, m]) -> 16
(minus([u, x2, _fq])) -> minus([s(u), s(x2), _fq]) -> 19
(plus([n, mm, _kq])) -> plus([n, s(mm), s(_kq)]) -> 19
}
Sat witness: Found: ((minus([u, x2, _fq])) -> minus([s(u), s(x2), _fq]), {
_fq -> s(s(s(s(z))))  ;  u -> s(s(z))  ;  x2 -> s(z)
})

-------------------------------------------
Step 24, which took 0.029631 s (model generation: 0.029127,  model checking: 0.000504):

Model:
|_
{
minus -> 
{{{
Q={q_gen_4293, q_gen_4294, q_gen_4295, q_gen_4301, q_gen_4319},
Q_f={q_gen_4293, q_gen_4294},
Delta=
{
<s>(q_gen_4301) -> q_gen_4301
<z>() -> q_gen_4301
<s, s>(q_gen_4295) -> q_gen_4295
<z, s>(q_gen_4301) -> q_gen_4295
<z, z>() -> q_gen_4295
<s, s, z>(q_gen_4295) -> q_gen_4293
<z, s, z>(q_gen_4301) -> q_gen_4293
<z, z, z>() -> q_gen_4293
<s, s, s>(q_gen_4294) -> q_gen_4294
<s, z, s>(q_gen_4295) -> q_gen_4294
<s, z, z>(q_gen_4301) -> q_gen_4294
<s, s, s>(q_gen_4293) -> q_gen_4319
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_4292, q_gen_4296, q_gen_4297, q_gen_4305, q_gen_4306},
Q_f={q_gen_4292, q_gen_4296},
Delta=
{
<s>(q_gen_4306) -> q_gen_4306
<z>() -> q_gen_4306
<s, s>(q_gen_4297) -> q_gen_4297
<z, s>(q_gen_4306) -> q_gen_4297
<z, z>() -> q_gen_4297
<s, s, s>(q_gen_4305) -> q_gen_4292
<z, z, z>() -> q_gen_4292
<s, s, s>(q_gen_4296) -> q_gen_4296
<s, z, s>(q_gen_4297) -> q_gen_4296
<z, s, s>(q_gen_4297) -> q_gen_4296
<s, s, s>(q_gen_4292) -> q_gen_4305
<z, z, s>(q_gen_4306) -> q_gen_4305
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 16
() -> minus([z, y, z]) -> 16
() -> plus([n, z, n]) -> 16
(minus([_pq, n, _qq]) /\ plus([m, n, _pq])) -> eq_nat([_qq, m]) -> 19
(minus([u, x2, _fq])) -> minus([s(u), s(x2), _fq]) -> 19
(plus([n, mm, _kq])) -> plus([n, s(mm), s(_kq)]) -> 19
}
Sat witness: Found: ((minus([_pq, n, _qq]) /\ plus([m, n, _pq])) -> eq_nat([_qq, m]), {
_pq -> s(s(z))  ;  _qq -> s(z)  ;  m -> z  ;  n -> s(z)
})

-------------------------------------------
Step 25, which took 0.029831 s (model generation: 0.029251,  model checking: 0.000580):

Model:
|_
{
minus -> 
{{{
Q={q_gen_4293, q_gen_4294, q_gen_4295, q_gen_4301, q_gen_4319},
Q_f={q_gen_4293, q_gen_4294},
Delta=
{
<s>(q_gen_4301) -> q_gen_4301
<z>() -> q_gen_4301
<s, s>(q_gen_4295) -> q_gen_4295
<z, s>(q_gen_4301) -> q_gen_4295
<z, z>() -> q_gen_4295
<s, s, z>(q_gen_4295) -> q_gen_4293
<z, s, z>(q_gen_4301) -> q_gen_4293
<z, z, z>() -> q_gen_4293
<s, s, s>(q_gen_4294) -> q_gen_4294
<s, z, s>(q_gen_4295) -> q_gen_4294
<s, z, z>(q_gen_4301) -> q_gen_4294
<s, s, s>(q_gen_4293) -> q_gen_4319
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_4292, q_gen_4297, q_gen_4305, q_gen_4306, q_gen_4316},
Q_f={q_gen_4292},
Delta=
{
<s>(q_gen_4306) -> q_gen_4306
<z>() -> q_gen_4306
<s, s>(q_gen_4297) -> q_gen_4297
<z, z>() -> q_gen_4297
<z, s>(q_gen_4306) -> q_gen_4316
<s, s, s>(q_gen_4305) -> q_gen_4292
<s, z, s>(q_gen_4297) -> q_gen_4292
<z, s, s>(q_gen_4297) -> q_gen_4292
<z, z, z>() -> q_gen_4292
<s, s, s>(q_gen_4292) -> q_gen_4305
<s, z, s>(q_gen_4316) -> q_gen_4305
<z, s, s>(q_gen_4316) -> q_gen_4305
<z, z, s>(q_gen_4306) -> q_gen_4305
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 17
() -> minus([z, y, z]) -> 17
() -> plus([n, z, n]) -> 17
(minus([_pq, n, _qq]) /\ plus([m, n, _pq])) -> eq_nat([_qq, m]) -> 19
(minus([u, x2, _fq])) -> minus([s(u), s(x2), _fq]) -> 19
(plus([n, mm, _kq])) -> plus([n, s(mm), s(_kq)]) -> 22
}
Sat witness: Found: ((plus([n, mm, _kq])) -> plus([n, s(mm), s(_kq)]), {
_kq -> s(s(s(z)))  ;  mm -> s(z)  ;  n -> s(s(z))
})

-------------------------------------------
Step 26, which took 0.030435 s (model generation: 0.029960,  model checking: 0.000475):

Model:
|_
{
minus -> 
{{{
Q={q_gen_4293, q_gen_4294, q_gen_4295, q_gen_4301, q_gen_4319},
Q_f={q_gen_4293, q_gen_4294},
Delta=
{
<s>(q_gen_4301) -> q_gen_4301
<z>() -> q_gen_4301
<s, s>(q_gen_4295) -> q_gen_4295
<z, s>(q_gen_4301) -> q_gen_4295
<z, z>() -> q_gen_4295
<s, s, z>(q_gen_4295) -> q_gen_4293
<z, s, z>(q_gen_4301) -> q_gen_4293
<z, z, z>() -> q_gen_4293
<s, s, s>(q_gen_4294) -> q_gen_4294
<s, z, s>(q_gen_4295) -> q_gen_4294
<s, z, z>(q_gen_4301) -> q_gen_4294
<s, s, s>(q_gen_4293) -> q_gen_4319
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_4292, q_gen_4296, q_gen_4297, q_gen_4305, q_gen_4306, q_gen_4316},
Q_f={q_gen_4292, q_gen_4296},
Delta=
{
<s>(q_gen_4306) -> q_gen_4306
<z>() -> q_gen_4306
<s, s>(q_gen_4297) -> q_gen_4297
<z, z>() -> q_gen_4297
<z, s>(q_gen_4306) -> q_gen_4316
<z, z, z>() -> q_gen_4292
<s, s, s>(q_gen_4296) -> q_gen_4296
<s, s, s>(q_gen_4305) -> q_gen_4296
<s, z, s>(q_gen_4297) -> q_gen_4296
<z, s, s>(q_gen_4297) -> q_gen_4296
<s, s, s>(q_gen_4292) -> q_gen_4305
<s, z, s>(q_gen_4316) -> q_gen_4305
<z, s, s>(q_gen_4316) -> q_gen_4305
<z, z, s>(q_gen_4306) -> q_gen_4305
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 18
() -> minus([z, y, z]) -> 18
() -> plus([n, z, n]) -> 18
(minus([_pq, n, _qq]) /\ plus([m, n, _pq])) -> eq_nat([_qq, m]) -> 19
(minus([u, x2, _fq])) -> minus([s(u), s(x2), _fq]) -> 22
(plus([n, mm, _kq])) -> plus([n, s(mm), s(_kq)]) -> 22
}
Sat witness: Found: ((minus([u, x2, _fq])) -> minus([s(u), s(x2), _fq]), {
_fq -> z  ;  u -> s(z)  ;  x2 -> z
})

-------------------------------------------
Step 27, which took 0.032524 s (model generation: 0.032060,  model checking: 0.000464):

Model:
|_
{
minus -> 
{{{
Q={q_gen_4293, q_gen_4294, q_gen_4295, q_gen_4301, q_gen_4319},
Q_f={q_gen_4293, q_gen_4294},
Delta=
{
<s>(q_gen_4301) -> q_gen_4301
<z>() -> q_gen_4301
<s, s>(q_gen_4295) -> q_gen_4295
<s, z>(q_gen_4301) -> q_gen_4295
<z, s>(q_gen_4301) -> q_gen_4295
<z, z>() -> q_gen_4295
<s, s, z>(q_gen_4295) -> q_gen_4293
<z, s, z>(q_gen_4301) -> q_gen_4293
<z, z, z>() -> q_gen_4293
<s, s, s>(q_gen_4294) -> q_gen_4294
<s, z, s>(q_gen_4295) -> q_gen_4294
<s, z, z>(q_gen_4301) -> q_gen_4294
<s, s, s>(q_gen_4293) -> q_gen_4319
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_4292, q_gen_4296, q_gen_4297, q_gen_4305, q_gen_4306, q_gen_4316},
Q_f={q_gen_4292, q_gen_4296},
Delta=
{
<s>(q_gen_4306) -> q_gen_4306
<z>() -> q_gen_4306
<s, s>(q_gen_4297) -> q_gen_4297
<z, z>() -> q_gen_4297
<z, s>(q_gen_4306) -> q_gen_4316
<z, z, z>() -> q_gen_4292
<s, s, s>(q_gen_4296) -> q_gen_4296
<s, s, s>(q_gen_4305) -> q_gen_4296
<s, z, s>(q_gen_4297) -> q_gen_4296
<z, s, s>(q_gen_4297) -> q_gen_4296
<s, s, s>(q_gen_4292) -> q_gen_4305
<s, z, s>(q_gen_4316) -> q_gen_4305
<z, s, s>(q_gen_4316) -> q_gen_4305
<z, z, s>(q_gen_4306) -> q_gen_4305
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 19
() -> minus([z, y, z]) -> 19
() -> plus([n, z, n]) -> 19
(minus([_pq, n, _qq]) /\ plus([m, n, _pq])) -> eq_nat([_qq, m]) -> 22
(minus([u, x2, _fq])) -> minus([s(u), s(x2), _fq]) -> 22
(plus([n, mm, _kq])) -> plus([n, s(mm), s(_kq)]) -> 22
}
Sat witness: Found: ((minus([_pq, n, _qq]) /\ plus([m, n, _pq])) -> eq_nat([_qq, m]), {
_pq -> s(z)  ;  _qq -> z  ;  m -> s(z)  ;  n -> z
})

-------------------------------------------
Step 28, which took 0.033337 s (model generation: 0.032503,  model checking: 0.000834):

Model:
|_
{
minus -> 
{{{
Q={q_gen_4293, q_gen_4294, q_gen_4295, q_gen_4301, q_gen_4308},
Q_f={q_gen_4293, q_gen_4294},
Delta=
{
<s>(q_gen_4301) -> q_gen_4301
<z>() -> q_gen_4301
<s, s>(q_gen_4295) -> q_gen_4295
<s, z>(q_gen_4301) -> q_gen_4295
<z, s>(q_gen_4301) -> q_gen_4295
<z, z>() -> q_gen_4295
<s, s, z>(q_gen_4295) -> q_gen_4293
<z, s, z>(q_gen_4301) -> q_gen_4293
<z, z, z>() -> q_gen_4293
<s, s, s>(q_gen_4294) -> q_gen_4294
<s, s, s>(q_gen_4308) -> q_gen_4294
<s, z, s>(q_gen_4295) -> q_gen_4294
<s, s, s>(q_gen_4293) -> q_gen_4308
<s, z, z>(q_gen_4301) -> q_gen_4308
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_4292, q_gen_4297, q_gen_4305, q_gen_4306, q_gen_4316, q_gen_4323},
Q_f={q_gen_4292},
Delta=
{
<z>() -> q_gen_4306
<s>(q_gen_4306) -> q_gen_4323
<s, s>(q_gen_4297) -> q_gen_4297
<z, z>() -> q_gen_4297
<z, s>(q_gen_4306) -> q_gen_4316
<s, s, s>(q_gen_4305) -> q_gen_4292
<s, z, s>(q_gen_4297) -> q_gen_4292
<z, s, s>(q_gen_4297) -> q_gen_4292
<z, z, s>(q_gen_4323) -> q_gen_4292
<z, z, z>() -> q_gen_4292
<s, s, s>(q_gen_4292) -> q_gen_4305
<s, z, s>(q_gen_4316) -> q_gen_4305
<z, s, s>(q_gen_4316) -> q_gen_4305
<z, z, s>(q_gen_4306) -> q_gen_4305
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 20
() -> minus([z, y, z]) -> 20
() -> plus([n, z, n]) -> 20
(minus([_pq, n, _qq]) /\ plus([m, n, _pq])) -> eq_nat([_qq, m]) -> 22
(minus([u, x2, _fq])) -> minus([s(u), s(x2), _fq]) -> 22
(plus([n, mm, _kq])) -> plus([n, s(mm), s(_kq)]) -> 25
}
Sat witness: Found: ((plus([n, mm, _kq])) -> plus([n, s(mm), s(_kq)]), {
_kq -> s(s(z))  ;  mm -> z  ;  n -> z
})

-------------------------------------------
Step 29, which took 0.032009 s (model generation: 0.031816,  model checking: 0.000193):

Model:
|_
{
minus -> 
{{{
Q={q_gen_4293, q_gen_4294, q_gen_4295, q_gen_4301, q_gen_4308},
Q_f={q_gen_4293, q_gen_4294},
Delta=
{
<s>(q_gen_4301) -> q_gen_4301
<z>() -> q_gen_4301
<s, s>(q_gen_4295) -> q_gen_4295
<s, z>(q_gen_4301) -> q_gen_4295
<z, s>(q_gen_4301) -> q_gen_4295
<z, z>() -> q_gen_4295
<s, s, z>(q_gen_4295) -> q_gen_4293
<z, s, z>(q_gen_4301) -> q_gen_4293
<z, z, z>() -> q_gen_4293
<s, s, s>(q_gen_4294) -> q_gen_4294
<s, s, s>(q_gen_4308) -> q_gen_4294
<s, z, s>(q_gen_4295) -> q_gen_4294
<s, s, s>(q_gen_4293) -> q_gen_4308
<s, z, z>(q_gen_4301) -> q_gen_4308
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_4292, q_gen_4296, q_gen_4297, q_gen_4305, q_gen_4306, q_gen_4311},
Q_f={q_gen_4292, q_gen_4296},
Delta=
{
<s>(q_gen_4306) -> q_gen_4306
<z>() -> q_gen_4306
<z, z>() -> q_gen_4297
<s, s>(q_gen_4297) -> q_gen_4311
<z, s>(q_gen_4306) -> q_gen_4311
<z, z, z>() -> q_gen_4292
<s, s, s>(q_gen_4296) -> q_gen_4296
<s, s, s>(q_gen_4305) -> q_gen_4296
<s, z, s>(q_gen_4297) -> q_gen_4296
<s, z, s>(q_gen_4311) -> q_gen_4296
<z, s, s>(q_gen_4297) -> q_gen_4296
<s, s, s>(q_gen_4292) -> q_gen_4305
<z, s, s>(q_gen_4311) -> q_gen_4305
<z, z, s>(q_gen_4306) -> q_gen_4305
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 20
() -> minus([z, y, z]) -> 20
() -> plus([n, z, n]) -> 23
(minus([_pq, n, _qq]) /\ plus([m, n, _pq])) -> eq_nat([_qq, m]) -> 22
(minus([u, x2, _fq])) -> minus([s(u), s(x2), _fq]) -> 22
(plus([n, mm, _kq])) -> plus([n, s(mm), s(_kq)]) -> 25
}
Sat witness: Found: (() -> plus([n, z, n]), {
n -> s(s(s(z)))
})

-------------------------------------------
Step 30, which took 0.033484 s (model generation: 0.033154,  model checking: 0.000330):

Model:
|_
{
minus -> 
{{{
Q={q_gen_4293, q_gen_4294, q_gen_4295, q_gen_4301, q_gen_4308},
Q_f={q_gen_4293, q_gen_4294},
Delta=
{
<s>(q_gen_4301) -> q_gen_4301
<z>() -> q_gen_4301
<s, s>(q_gen_4295) -> q_gen_4295
<s, z>(q_gen_4301) -> q_gen_4295
<z, s>(q_gen_4301) -> q_gen_4295
<z, z>() -> q_gen_4295
<s, s, s>(q_gen_4308) -> q_gen_4293
<s, s, z>(q_gen_4295) -> q_gen_4293
<z, s, z>(q_gen_4301) -> q_gen_4293
<z, z, z>() -> q_gen_4293
<s, s, s>(q_gen_4294) -> q_gen_4294
<s, z, s>(q_gen_4295) -> q_gen_4294
<s, s, s>(q_gen_4293) -> q_gen_4308
<s, z, z>(q_gen_4301) -> q_gen_4308
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_4292, q_gen_4297, q_gen_4299, q_gen_4305, q_gen_4306, q_gen_4316},
Q_f={q_gen_4292, q_gen_4299},
Delta=
{
<s>(q_gen_4306) -> q_gen_4306
<z>() -> q_gen_4306
<s, s>(q_gen_4297) -> q_gen_4297
<z, z>() -> q_gen_4297
<z, s>(q_gen_4306) -> q_gen_4316
<s, s, s>(q_gen_4299) -> q_gen_4292
<z, s, s>(q_gen_4297) -> q_gen_4292
<z, z, z>() -> q_gen_4292
<s, s, s>(q_gen_4305) -> q_gen_4299
<s, z, s>(q_gen_4297) -> q_gen_4299
<s, s, s>(q_gen_4292) -> q_gen_4305
<s, z, s>(q_gen_4316) -> q_gen_4305
<z, s, s>(q_gen_4316) -> q_gen_4305
<z, z, s>(q_gen_4306) -> q_gen_4305
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 21
() -> minus([z, y, z]) -> 21
() -> plus([n, z, n]) -> 23
(minus([_pq, n, _qq]) /\ plus([m, n, _pq])) -> eq_nat([_qq, m]) -> 22
(minus([u, x2, _fq])) -> minus([s(u), s(x2), _fq]) -> 25
(plus([n, mm, _kq])) -> plus([n, s(mm), s(_kq)]) -> 25
}
Sat witness: Found: ((minus([u, x2, _fq])) -> minus([s(u), s(x2), _fq]), {
_fq -> s(s(z))  ;  u -> s(s(z))  ;  x2 -> s(z)
})

-------------------------------------------
Step 31, which took 0.036365 s (model generation: 0.035948,  model checking: 0.000417):

Model:
|_
{
minus -> 
{{{
Q={q_gen_4293, q_gen_4294, q_gen_4295, q_gen_4301, q_gen_4308},
Q_f={q_gen_4293, q_gen_4294},
Delta=
{
<s>(q_gen_4301) -> q_gen_4301
<z>() -> q_gen_4301
<s, s>(q_gen_4295) -> q_gen_4295
<s, z>(q_gen_4301) -> q_gen_4295
<z, s>(q_gen_4301) -> q_gen_4295
<z, z>() -> q_gen_4295
<s, s, z>(q_gen_4295) -> q_gen_4293
<z, s, z>(q_gen_4301) -> q_gen_4293
<z, z, z>() -> q_gen_4293
<s, s, s>(q_gen_4294) -> q_gen_4294
<s, s, s>(q_gen_4308) -> q_gen_4294
<s, z, s>(q_gen_4295) -> q_gen_4294
<s, s, s>(q_gen_4293) -> q_gen_4308
<s, z, z>(q_gen_4301) -> q_gen_4308
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_4292, q_gen_4296, q_gen_4297, q_gen_4305, q_gen_4306, q_gen_4311},
Q_f={q_gen_4292, q_gen_4296},
Delta=
{
<s>(q_gen_4306) -> q_gen_4306
<z>() -> q_gen_4306
<z, z>() -> q_gen_4297
<s, s>(q_gen_4297) -> q_gen_4311
<s, s>(q_gen_4311) -> q_gen_4311
<z, s>(q_gen_4306) -> q_gen_4311
<z, z, z>() -> q_gen_4292
<s, s, s>(q_gen_4296) -> q_gen_4296
<s, s, s>(q_gen_4305) -> q_gen_4296
<s, z, s>(q_gen_4297) -> q_gen_4296
<s, z, s>(q_gen_4311) -> q_gen_4296
<z, s, s>(q_gen_4297) -> q_gen_4296
<s, s, s>(q_gen_4292) -> q_gen_4305
<z, s, s>(q_gen_4311) -> q_gen_4305
<z, z, s>(q_gen_4306) -> q_gen_4305
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 22
() -> minus([z, y, z]) -> 22
() -> plus([n, z, n]) -> 23
(minus([_pq, n, _qq]) /\ plus([m, n, _pq])) -> eq_nat([_qq, m]) -> 25
(minus([u, x2, _fq])) -> minus([s(u), s(x2), _fq]) -> 25
(plus([n, mm, _kq])) -> plus([n, s(mm), s(_kq)]) -> 25
}
Sat witness: Found: ((minus([_pq, n, _qq]) /\ plus([m, n, _pq])) -> eq_nat([_qq, m]), {
_pq -> s(z)  ;  _qq -> s(s(z))  ;  m -> s(z)  ;  n -> z
})

-------------------------------------------
Step 32, which took 0.041047 s (model generation: 0.040435,  model checking: 0.000612):

Model:
|_
{
minus -> 
{{{
Q={q_gen_4293, q_gen_4295, q_gen_4301, q_gen_4307, q_gen_4308, q_gen_4318},
Q_f={q_gen_4293, q_gen_4307},
Delta=
{
<s>(q_gen_4301) -> q_gen_4301
<z>() -> q_gen_4301
<s, s>(q_gen_4295) -> q_gen_4295
<s, z>(q_gen_4301) -> q_gen_4295
<z, z>() -> q_gen_4295
<z, s>(q_gen_4301) -> q_gen_4318
<s, s, s>(q_gen_4307) -> q_gen_4293
<s, s, z>(q_gen_4295) -> q_gen_4293
<s, s, z>(q_gen_4318) -> q_gen_4293
<s, z, s>(q_gen_4295) -> q_gen_4293
<z, s, z>(q_gen_4301) -> q_gen_4293
<z, z, z>() -> q_gen_4293
<s, s, s>(q_gen_4308) -> q_gen_4307
<s, s, s>(q_gen_4293) -> q_gen_4308
<s, z, s>(q_gen_4318) -> q_gen_4308
<s, z, z>(q_gen_4301) -> q_gen_4308
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_4292, q_gen_4297, q_gen_4304, q_gen_4305, q_gen_4306, q_gen_4311},
Q_f={q_gen_4292, q_gen_4304},
Delta=
{
<s>(q_gen_4306) -> q_gen_4306
<z>() -> q_gen_4306
<z, z>() -> q_gen_4297
<s, s>(q_gen_4297) -> q_gen_4311
<s, s>(q_gen_4311) -> q_gen_4311
<z, s>(q_gen_4306) -> q_gen_4311
<s, s, s>(q_gen_4304) -> q_gen_4292
<s, z, s>(q_gen_4297) -> q_gen_4292
<z, s, s>(q_gen_4297) -> q_gen_4292
<z, z, z>() -> q_gen_4292
<s, s, s>(q_gen_4305) -> q_gen_4304
<s, z, s>(q_gen_4311) -> q_gen_4304
<s, s, s>(q_gen_4292) -> q_gen_4305
<z, s, s>(q_gen_4311) -> q_gen_4305
<z, z, s>(q_gen_4306) -> q_gen_4305
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 23
() -> minus([z, y, z]) -> 23
() -> plus([n, z, n]) -> 24
(minus([_pq, n, _qq]) /\ plus([m, n, _pq])) -> eq_nat([_qq, m]) -> 25
(minus([u, x2, _fq])) -> minus([s(u), s(x2), _fq]) -> 25
(plus([n, mm, _kq])) -> plus([n, s(mm), s(_kq)]) -> 28
}
Sat witness: Found: ((plus([n, mm, _kq])) -> plus([n, s(mm), s(_kq)]), {
_kq -> s(s(s(z)))  ;  mm -> s(s(z))  ;  n -> s(s(s(z)))
})

-------------------------------------------
Step 33, which took 0.042897 s (model generation: 0.042316,  model checking: 0.000581):

Model:
|_
{
minus -> 
{{{
Q={q_gen_4293, q_gen_4295, q_gen_4301, q_gen_4307, q_gen_4308, q_gen_4318},
Q_f={q_gen_4293, q_gen_4307},
Delta=
{
<s>(q_gen_4301) -> q_gen_4301
<z>() -> q_gen_4301
<s, s>(q_gen_4295) -> q_gen_4295
<s, z>(q_gen_4301) -> q_gen_4295
<z, z>() -> q_gen_4295
<z, s>(q_gen_4301) -> q_gen_4318
<s, s, s>(q_gen_4307) -> q_gen_4293
<s, s, z>(q_gen_4295) -> q_gen_4293
<s, s, z>(q_gen_4318) -> q_gen_4293
<s, z, s>(q_gen_4295) -> q_gen_4293
<z, s, z>(q_gen_4301) -> q_gen_4293
<z, z, z>() -> q_gen_4293
<s, s, s>(q_gen_4308) -> q_gen_4307
<s, s, s>(q_gen_4293) -> q_gen_4308
<s, z, s>(q_gen_4318) -> q_gen_4308
<s, z, z>(q_gen_4301) -> q_gen_4308
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_4292, q_gen_4297, q_gen_4299, q_gen_4305, q_gen_4306, q_gen_4316},
Q_f={q_gen_4292, q_gen_4299},
Delta=
{
<s>(q_gen_4306) -> q_gen_4306
<z>() -> q_gen_4306
<s, s>(q_gen_4297) -> q_gen_4297
<z, z>() -> q_gen_4297
<z, s>(q_gen_4306) -> q_gen_4316
<s, s, s>(q_gen_4299) -> q_gen_4292
<z, s, s>(q_gen_4297) -> q_gen_4292
<z, z, z>() -> q_gen_4292
<s, s, s>(q_gen_4305) -> q_gen_4299
<s, z, s>(q_gen_4297) -> q_gen_4299
<s, s, s>(q_gen_4292) -> q_gen_4305
<s, z, s>(q_gen_4316) -> q_gen_4305
<z, s, s>(q_gen_4316) -> q_gen_4305
<z, z, s>(q_gen_4306) -> q_gen_4305
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 24
() -> minus([z, y, z]) -> 24
() -> plus([n, z, n]) -> 25
(minus([_pq, n, _qq]) /\ plus([m, n, _pq])) -> eq_nat([_qq, m]) -> 25
(minus([u, x2, _fq])) -> minus([s(u), s(x2), _fq]) -> 28
(plus([n, mm, _kq])) -> plus([n, s(mm), s(_kq)]) -> 28
}
Sat witness: Found: ((minus([u, x2, _fq])) -> minus([s(u), s(x2), _fq]), {
_fq -> s(z)  ;  u -> s(s(z))  ;  x2 -> s(z)
})

-------------------------------------------
Step 34, which took 0.043909 s (model generation: 0.043477,  model checking: 0.000432):

Model:
|_
{
minus -> 
{{{
Q={q_gen_4293, q_gen_4295, q_gen_4300, q_gen_4301, q_gen_4308, q_gen_4318},
Q_f={q_gen_4293, q_gen_4300},
Delta=
{
<s>(q_gen_4301) -> q_gen_4301
<z>() -> q_gen_4301
<s, s>(q_gen_4295) -> q_gen_4295
<z, z>() -> q_gen_4295
<s, z>(q_gen_4301) -> q_gen_4318
<z, s>(q_gen_4301) -> q_gen_4318
<s, s, z>(q_gen_4295) -> q_gen_4293
<s, z, s>(q_gen_4295) -> q_gen_4293
<z, z, z>() -> q_gen_4293
<s, s, s>(q_gen_4300) -> q_gen_4300
<s, s, s>(q_gen_4308) -> q_gen_4300
<s, s, z>(q_gen_4318) -> q_gen_4300
<z, s, z>(q_gen_4301) -> q_gen_4300
<s, s, s>(q_gen_4293) -> q_gen_4308
<s, z, s>(q_gen_4318) -> q_gen_4308
<s, z, z>(q_gen_4301) -> q_gen_4308
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_4292, q_gen_4297, q_gen_4299, q_gen_4305, q_gen_4306, q_gen_4316},
Q_f={q_gen_4292, q_gen_4299},
Delta=
{
<s>(q_gen_4306) -> q_gen_4306
<z>() -> q_gen_4306
<s, s>(q_gen_4297) -> q_gen_4297
<z, z>() -> q_gen_4297
<z, s>(q_gen_4306) -> q_gen_4316
<s, s, s>(q_gen_4299) -> q_gen_4292
<z, s, s>(q_gen_4297) -> q_gen_4292
<z, z, z>() -> q_gen_4292
<s, s, s>(q_gen_4305) -> q_gen_4299
<s, z, s>(q_gen_4297) -> q_gen_4299
<s, s, s>(q_gen_4292) -> q_gen_4305
<s, z, s>(q_gen_4316) -> q_gen_4305
<z, s, s>(q_gen_4316) -> q_gen_4305
<z, z, s>(q_gen_4306) -> q_gen_4305
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 25
() -> minus([z, y, z]) -> 25
() -> plus([n, z, n]) -> 25
(minus([_pq, n, _qq]) /\ plus([m, n, _pq])) -> eq_nat([_qq, m]) -> 28
(minus([u, x2, _fq])) -> minus([s(u), s(x2), _fq]) -> 28
(plus([n, mm, _kq])) -> plus([n, s(mm), s(_kq)]) -> 28
}
Sat witness: Found: ((minus([_pq, n, _qq]) /\ plus([m, n, _pq])) -> eq_nat([_qq, m]), {
_pq -> s(s(z))  ;  _qq -> z  ;  m -> s(z)  ;  n -> s(z)
})

-------------------------------------------
Step 35, which took 0.052265 s (model generation: 0.051867,  model checking: 0.000398):

Model:
|_
{
minus -> 
{{{
Q={q_gen_4293, q_gen_4295, q_gen_4301, q_gen_4308, q_gen_4313, q_gen_4318, q_gen_4336},
Q_f={q_gen_4293},
Delta=
{
<z>() -> q_gen_4301
<s>(q_gen_4301) -> q_gen_4313
<s, s>(q_gen_4295) -> q_gen_4295
<z, z>() -> q_gen_4295
<z, s>(q_gen_4301) -> q_gen_4318
<s, z>(q_gen_4301) -> q_gen_4336
<z, s>(q_gen_4313) -> q_gen_4336
<s, s, s>(q_gen_4308) -> q_gen_4293
<s, s, z>(q_gen_4295) -> q_gen_4293
<s, s, z>(q_gen_4318) -> q_gen_4293
<s, z, s>(q_gen_4295) -> q_gen_4293
<s, z, s>(q_gen_4336) -> q_gen_4293
<z, s, z>(q_gen_4301) -> q_gen_4293
<z, s, z>(q_gen_4313) -> q_gen_4293
<z, z, z>() -> q_gen_4293
<s, s, s>(q_gen_4293) -> q_gen_4308
<s, s, z>(q_gen_4336) -> q_gen_4308
<s, z, s>(q_gen_4318) -> q_gen_4308
<s, z, z>(q_gen_4301) -> q_gen_4308
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_4292, q_gen_4297, q_gen_4299, q_gen_4305, q_gen_4306, q_gen_4311},
Q_f={q_gen_4292, q_gen_4299},
Delta=
{
<s>(q_gen_4306) -> q_gen_4306
<z>() -> q_gen_4306
<z, z>() -> q_gen_4297
<s, s>(q_gen_4297) -> q_gen_4311
<s, s>(q_gen_4311) -> q_gen_4311
<z, s>(q_gen_4306) -> q_gen_4311
<s, s, s>(q_gen_4299) -> q_gen_4292
<z, s, s>(q_gen_4297) -> q_gen_4292
<z, z, z>() -> q_gen_4292
<s, s, s>(q_gen_4305) -> q_gen_4299
<s, z, s>(q_gen_4297) -> q_gen_4299
<s, z, s>(q_gen_4311) -> q_gen_4299
<s, s, s>(q_gen_4292) -> q_gen_4305
<z, s, s>(q_gen_4311) -> q_gen_4305
<z, z, s>(q_gen_4306) -> q_gen_4305
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 25
() -> minus([z, y, z]) -> 28
() -> plus([n, z, n]) -> 26
(minus([_pq, n, _qq]) /\ plus([m, n, _pq])) -> eq_nat([_qq, m]) -> 28
(minus([u, x2, _fq])) -> minus([s(u), s(x2), _fq]) -> 28
(plus([n, mm, _kq])) -> plus([n, s(mm), s(_kq)]) -> 28
}
Sat witness: Found: (() -> minus([z, y, z]), {
y -> s(s(s(z)))
})

-------------------------------------------
Step 36, which took 0.049260 s (model generation: 0.048709,  model checking: 0.000551):

Model:
|_
{
minus -> 
{{{
Q={q_gen_4293, q_gen_4295, q_gen_4301, q_gen_4308, q_gen_4318, q_gen_4319, q_gen_4341},
Q_f={q_gen_4293},
Delta=
{
<s>(q_gen_4301) -> q_gen_4301
<z>() -> q_gen_4301
<s, s>(q_gen_4295) -> q_gen_4295
<z, z>() -> q_gen_4295
<z, s>(q_gen_4301) -> q_gen_4318
<s, z>(q_gen_4301) -> q_gen_4341
<s, s, s>(q_gen_4308) -> q_gen_4293
<s, s, z>(q_gen_4295) -> q_gen_4293
<s, s, z>(q_gen_4318) -> q_gen_4293
<s, z, s>(q_gen_4295) -> q_gen_4293
<z, s, z>(q_gen_4301) -> q_gen_4293
<z, z, z>() -> q_gen_4293
<s, s, s>(q_gen_4319) -> q_gen_4308
<s, s, z>(q_gen_4341) -> q_gen_4308
<s, z, z>(q_gen_4301) -> q_gen_4308
<s, s, s>(q_gen_4293) -> q_gen_4319
<s, z, s>(q_gen_4318) -> q_gen_4319
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_4292, q_gen_4297, q_gen_4304, q_gen_4305, q_gen_4306, q_gen_4311},
Q_f={q_gen_4292, q_gen_4304},
Delta=
{
<s>(q_gen_4306) -> q_gen_4306
<z>() -> q_gen_4306
<s, s>(q_gen_4311) -> q_gen_4297
<z, z>() -> q_gen_4297
<s, s>(q_gen_4297) -> q_gen_4311
<z, s>(q_gen_4306) -> q_gen_4311
<s, z, s>(q_gen_4297) -> q_gen_4292
<z, s, s>(q_gen_4297) -> q_gen_4292
<z, z, z>() -> q_gen_4292
<s, s, s>(q_gen_4304) -> q_gen_4304
<s, s, s>(q_gen_4305) -> q_gen_4304
<s, z, s>(q_gen_4311) -> q_gen_4304
<s, s, s>(q_gen_4292) -> q_gen_4305
<z, s, s>(q_gen_4311) -> q_gen_4305
<z, z, s>(q_gen_4306) -> q_gen_4305
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 26
() -> minus([z, y, z]) -> 28
() -> plus([n, z, n]) -> 27
(minus([_pq, n, _qq]) /\ plus([m, n, _pq])) -> eq_nat([_qq, m]) -> 28
(minus([u, x2, _fq])) -> minus([s(u), s(x2), _fq]) -> 28
(plus([n, mm, _kq])) -> plus([n, s(mm), s(_kq)]) -> 31
}
Sat witness: Found: ((plus([n, mm, _kq])) -> plus([n, s(mm), s(_kq)]), {
_kq -> s(s(s(z)))  ;  mm -> s(s(s(z)))  ;  n -> s(z)
})

-------------------------------------------
Step 37, which took 0.052732 s (model generation: 0.052573,  model checking: 0.000159):

Model:
|_
{
minus -> 
{{{
Q={q_gen_4293, q_gen_4295, q_gen_4301, q_gen_4303, q_gen_4307, q_gen_4308, q_gen_4318},
Q_f={q_gen_4293, q_gen_4307},
Delta=
{
<s>(q_gen_4301) -> q_gen_4301
<z>() -> q_gen_4301
<z, z>() -> q_gen_4295
<s, s>(q_gen_4295) -> q_gen_4303
<s, z>(q_gen_4301) -> q_gen_4303
<z, s>(q_gen_4301) -> q_gen_4318
<s, s, z>(q_gen_4295) -> q_gen_4293
<s, s, z>(q_gen_4318) -> q_gen_4293
<s, z, s>(q_gen_4295) -> q_gen_4293
<s, z, s>(q_gen_4303) -> q_gen_4293
<z, s, z>(q_gen_4301) -> q_gen_4293
<z, z, z>() -> q_gen_4293
<s, s, s>(q_gen_4307) -> q_gen_4307
<s, s, s>(q_gen_4308) -> q_gen_4307
<s, s, s>(q_gen_4293) -> q_gen_4308
<s, s, z>(q_gen_4303) -> q_gen_4308
<s, z, s>(q_gen_4318) -> q_gen_4308
<s, z, z>(q_gen_4301) -> q_gen_4308
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_4292, q_gen_4297, q_gen_4299, q_gen_4305, q_gen_4306, q_gen_4316},
Q_f={q_gen_4292, q_gen_4299},
Delta=
{
<s>(q_gen_4306) -> q_gen_4306
<z>() -> q_gen_4306
<s, s>(q_gen_4297) -> q_gen_4297
<z, z>() -> q_gen_4297
<z, s>(q_gen_4306) -> q_gen_4316
<s, s, s>(q_gen_4299) -> q_gen_4292
<z, s, s>(q_gen_4297) -> q_gen_4292
<z, z, z>() -> q_gen_4292
<s, s, s>(q_gen_4305) -> q_gen_4299
<s, z, s>(q_gen_4297) -> q_gen_4299
<s, s, s>(q_gen_4292) -> q_gen_4305
<s, z, s>(q_gen_4316) -> q_gen_4305
<z, s, s>(q_gen_4316) -> q_gen_4305
<z, z, s>(q_gen_4306) -> q_gen_4305
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 29
() -> minus([z, y, z]) -> 28
() -> plus([n, z, n]) -> 27
(minus([_pq, n, _qq]) /\ plus([m, n, _pq])) -> eq_nat([_qq, m]) -> 28
(minus([u, x2, _fq])) -> minus([s(u), s(x2), _fq]) -> 28
(plus([n, mm, _kq])) -> plus([n, s(mm), s(_kq)]) -> 31
}
Sat witness: Found: (() -> minus([s(u), z, s(u)]), {
u -> s(s(z))
})

-------------------------------------------
Step 38, which took 0.053524 s (model generation: 0.052983,  model checking: 0.000541):

Model:
|_
{
minus -> 
{{{
Q={q_gen_4293, q_gen_4295, q_gen_4300, q_gen_4301, q_gen_4308, q_gen_4318, q_gen_4341},
Q_f={q_gen_4293, q_gen_4300},
Delta=
{
<s>(q_gen_4301) -> q_gen_4301
<z>() -> q_gen_4301
<s, s>(q_gen_4295) -> q_gen_4295
<z, z>() -> q_gen_4295
<z, s>(q_gen_4301) -> q_gen_4318
<s, z>(q_gen_4301) -> q_gen_4341
<s, s, z>(q_gen_4295) -> q_gen_4293
<s, z, s>(q_gen_4295) -> q_gen_4293
<z, z, z>() -> q_gen_4293
<s, s, s>(q_gen_4300) -> q_gen_4300
<s, s, s>(q_gen_4308) -> q_gen_4300
<s, s, z>(q_gen_4318) -> q_gen_4300
<z, s, z>(q_gen_4301) -> q_gen_4300
<s, s, s>(q_gen_4293) -> q_gen_4308
<s, s, z>(q_gen_4341) -> q_gen_4308
<s, z, s>(q_gen_4318) -> q_gen_4308
<s, z, z>(q_gen_4301) -> q_gen_4308
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_4292, q_gen_4297, q_gen_4299, q_gen_4305, q_gen_4306, q_gen_4316},
Q_f={q_gen_4292, q_gen_4299},
Delta=
{
<s>(q_gen_4306) -> q_gen_4306
<z>() -> q_gen_4306
<s, s>(q_gen_4297) -> q_gen_4297
<z, z>() -> q_gen_4297
<z, s>(q_gen_4306) -> q_gen_4316
<s, s, s>(q_gen_4299) -> q_gen_4292
<z, s, s>(q_gen_4297) -> q_gen_4292
<z, z, z>() -> q_gen_4292
<s, s, s>(q_gen_4305) -> q_gen_4299
<s, z, s>(q_gen_4297) -> q_gen_4299
<s, s, s>(q_gen_4292) -> q_gen_4305
<s, z, s>(q_gen_4316) -> q_gen_4305
<z, s, s>(q_gen_4316) -> q_gen_4305
<z, z, s>(q_gen_4306) -> q_gen_4305
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 29
() -> minus([z, y, z]) -> 28
() -> plus([n, z, n]) -> 28
(minus([_pq, n, _qq]) /\ plus([m, n, _pq])) -> eq_nat([_qq, m]) -> 28
(minus([u, x2, _fq])) -> minus([s(u), s(x2), _fq]) -> 31
(plus([n, mm, _kq])) -> plus([n, s(mm), s(_kq)]) -> 31
}
Sat witness: Found: ((minus([u, x2, _fq])) -> minus([s(u), s(x2), _fq]), {
_fq -> z  ;  u -> s(z)  ;  x2 -> s(s(z))
})

-------------------------------------------
Step 39, which took 0.055045 s (model generation: 0.054751,  model checking: 0.000294):

Model:
|_
{
minus -> 
{{{
Q={q_gen_4293, q_gen_4295, q_gen_4301, q_gen_4307, q_gen_4308, q_gen_4318, q_gen_4341},
Q_f={q_gen_4293, q_gen_4307},
Delta=
{
<s>(q_gen_4301) -> q_gen_4301
<z>() -> q_gen_4301
<s, s>(q_gen_4295) -> q_gen_4295
<z, z>() -> q_gen_4295
<s, s>(q_gen_4318) -> q_gen_4318
<z, s>(q_gen_4301) -> q_gen_4318
<s, z>(q_gen_4301) -> q_gen_4341
<s, s, z>(q_gen_4295) -> q_gen_4293
<s, s, z>(q_gen_4318) -> q_gen_4293
<s, z, s>(q_gen_4295) -> q_gen_4293
<z, s, z>(q_gen_4301) -> q_gen_4293
<z, z, z>() -> q_gen_4293
<s, s, s>(q_gen_4307) -> q_gen_4307
<s, s, s>(q_gen_4308) -> q_gen_4307
<s, s, s>(q_gen_4293) -> q_gen_4308
<s, s, z>(q_gen_4341) -> q_gen_4308
<s, z, s>(q_gen_4318) -> q_gen_4308
<s, z, z>(q_gen_4301) -> q_gen_4308
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_4292, q_gen_4297, q_gen_4299, q_gen_4305, q_gen_4306, q_gen_4316},
Q_f={q_gen_4292, q_gen_4299},
Delta=
{
<s>(q_gen_4306) -> q_gen_4306
<z>() -> q_gen_4306
<s, s>(q_gen_4297) -> q_gen_4297
<z, z>() -> q_gen_4297
<z, s>(q_gen_4306) -> q_gen_4316
<s, s, s>(q_gen_4299) -> q_gen_4292
<z, s, s>(q_gen_4297) -> q_gen_4292
<z, z, z>() -> q_gen_4292
<s, s, s>(q_gen_4305) -> q_gen_4299
<s, z, s>(q_gen_4297) -> q_gen_4299
<s, s, s>(q_gen_4292) -> q_gen_4305
<s, z, s>(q_gen_4316) -> q_gen_4305
<z, s, s>(q_gen_4316) -> q_gen_4305
<z, z, s>(q_gen_4306) -> q_gen_4305
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 29
() -> minus([z, y, z]) -> 28
() -> plus([n, z, n]) -> 28
(minus([_pq, n, _qq]) /\ plus([m, n, _pq])) -> eq_nat([_qq, m]) -> 31
(minus([u, x2, _fq])) -> minus([s(u), s(x2), _fq]) -> 31
(plus([n, mm, _kq])) -> plus([n, s(mm), s(_kq)]) -> 31
}
Sat witness: Found: ((minus([_pq, n, _qq]) /\ plus([m, n, _pq])) -> eq_nat([_qq, m]), {
_pq -> s(s(s(z)))  ;  _qq -> s(z)  ;  m -> s(s(z))  ;  n -> s(z)
})

-------------------------------------------
Step 40, which took 0.057015 s (model generation: 0.056117,  model checking: 0.000898):

Model:
|_
{
minus -> 
{{{
Q={q_gen_4293, q_gen_4295, q_gen_4301, q_gen_4308, q_gen_4313, q_gen_4318, q_gen_4341},
Q_f={q_gen_4293},
Delta=
{
<s>(q_gen_4313) -> q_gen_4301
<z>() -> q_gen_4301
<s>(q_gen_4301) -> q_gen_4313
<s, s>(q_gen_4295) -> q_gen_4295
<z, s>(q_gen_4313) -> q_gen_4295
<z, z>() -> q_gen_4295
<s, s>(q_gen_4318) -> q_gen_4318
<z, s>(q_gen_4301) -> q_gen_4318
<s, z>(q_gen_4301) -> q_gen_4341
<s, s, s>(q_gen_4308) -> q_gen_4293
<s, s, z>(q_gen_4295) -> q_gen_4293
<s, s, z>(q_gen_4318) -> q_gen_4293
<s, z, s>(q_gen_4295) -> q_gen_4293
<s, z, z>(q_gen_4313) -> q_gen_4293
<z, s, z>(q_gen_4301) -> q_gen_4293
<z, s, z>(q_gen_4313) -> q_gen_4293
<z, z, z>() -> q_gen_4293
<s, s, s>(q_gen_4293) -> q_gen_4308
<s, s, z>(q_gen_4341) -> q_gen_4308
<s, z, s>(q_gen_4318) -> q_gen_4308
<s, z, z>(q_gen_4301) -> q_gen_4308
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_4292, q_gen_4297, q_gen_4299, q_gen_4305, q_gen_4306, q_gen_4316},
Q_f={q_gen_4292, q_gen_4299},
Delta=
{
<s>(q_gen_4306) -> q_gen_4306
<z>() -> q_gen_4306
<s, s>(q_gen_4297) -> q_gen_4297
<z, z>() -> q_gen_4297
<z, s>(q_gen_4306) -> q_gen_4316
<s, s, s>(q_gen_4299) -> q_gen_4292
<z, s, s>(q_gen_4297) -> q_gen_4292
<z, z, z>() -> q_gen_4292
<s, s, s>(q_gen_4305) -> q_gen_4299
<s, z, s>(q_gen_4297) -> q_gen_4299
<s, s, s>(q_gen_4292) -> q_gen_4305
<s, z, s>(q_gen_4316) -> q_gen_4305
<z, s, s>(q_gen_4316) -> q_gen_4305
<z, z, s>(q_gen_4306) -> q_gen_4305
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 30
() -> minus([z, y, z]) -> 29
() -> plus([n, z, n]) -> 29
(minus([_pq, n, _qq]) /\ plus([m, n, _pq])) -> eq_nat([_qq, m]) -> 31
(minus([u, x2, _fq])) -> minus([s(u), s(x2), _fq]) -> 31
(plus([n, mm, _kq])) -> plus([n, s(mm), s(_kq)]) -> 34
}
Sat witness: Found: ((plus([n, mm, _kq])) -> plus([n, s(mm), s(_kq)]), {
_kq -> s(s(s(z)))  ;  mm -> z  ;  n -> s(s(s(z)))
})

-------------------------------------------
Step 41, which took 0.079645 s (model generation: 0.078842,  model checking: 0.000803):

Model:
|_
{
minus -> 
{{{
Q={q_gen_4293, q_gen_4295, q_gen_4301, q_gen_4308, q_gen_4313, q_gen_4318, q_gen_4336},
Q_f={q_gen_4293},
Delta=
{
<s>(q_gen_4313) -> q_gen_4301
<z>() -> q_gen_4301
<s>(q_gen_4301) -> q_gen_4313
<s, s>(q_gen_4295) -> q_gen_4295
<z, z>() -> q_gen_4295
<s, s>(q_gen_4318) -> q_gen_4318
<z, s>(q_gen_4301) -> q_gen_4318
<s, z>(q_gen_4301) -> q_gen_4336
<z, s>(q_gen_4313) -> q_gen_4336
<s, s, s>(q_gen_4308) -> q_gen_4293
<s, s, z>(q_gen_4295) -> q_gen_4293
<s, s, z>(q_gen_4318) -> q_gen_4293
<s, z, s>(q_gen_4295) -> q_gen_4293
<s, z, s>(q_gen_4336) -> q_gen_4293
<s, z, z>(q_gen_4313) -> q_gen_4293
<z, s, z>(q_gen_4301) -> q_gen_4293
<z, s, z>(q_gen_4313) -> q_gen_4293
<z, z, z>() -> q_gen_4293
<s, s, s>(q_gen_4293) -> q_gen_4308
<s, s, z>(q_gen_4336) -> q_gen_4308
<s, z, s>(q_gen_4318) -> q_gen_4308
<s, z, z>(q_gen_4301) -> q_gen_4308
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_4292, q_gen_4296, q_gen_4297, q_gen_4305, q_gen_4306, q_gen_4316},
Q_f={q_gen_4292, q_gen_4296},
Delta=
{
<s>(q_gen_4306) -> q_gen_4306
<z>() -> q_gen_4306
<s, s>(q_gen_4297) -> q_gen_4297
<z, z>() -> q_gen_4297
<s, s>(q_gen_4316) -> q_gen_4316
<z, s>(q_gen_4306) -> q_gen_4316
<z, z, z>() -> q_gen_4292
<s, s, s>(q_gen_4296) -> q_gen_4296
<s, s, s>(q_gen_4305) -> q_gen_4296
<s, z, s>(q_gen_4297) -> q_gen_4296
<z, s, s>(q_gen_4297) -> q_gen_4296
<s, s, s>(q_gen_4292) -> q_gen_4305
<s, z, s>(q_gen_4316) -> q_gen_4305
<z, s, s>(q_gen_4316) -> q_gen_4305
<z, z, s>(q_gen_4306) -> q_gen_4305
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 31
() -> minus([z, y, z]) -> 30
() -> plus([n, z, n]) -> 30
(minus([_pq, n, _qq]) /\ plus([m, n, _pq])) -> eq_nat([_qq, m]) -> 31
(minus([u, x2, _fq])) -> minus([s(u), s(x2), _fq]) -> 34
(plus([n, mm, _kq])) -> plus([n, s(mm), s(_kq)]) -> 34
}
Sat witness: Found: ((minus([u, x2, _fq])) -> minus([s(u), s(x2), _fq]), {
_fq -> z  ;  u -> z  ;  x2 -> s(s(z))
})

-------------------------------------------
Step 42, which took 0.079494 s (model generation: 0.078824,  model checking: 0.000670):

Model:
|_
{
minus -> 
{{{
Q={q_gen_4293, q_gen_4295, q_gen_4301, q_gen_4303, q_gen_4308, q_gen_4313, q_gen_4318},
Q_f={q_gen_4293},
Delta=
{
<s>(q_gen_4313) -> q_gen_4301
<z>() -> q_gen_4301
<s>(q_gen_4301) -> q_gen_4313
<z, s>(q_gen_4313) -> q_gen_4295
<z, z>() -> q_gen_4295
<s, s>(q_gen_4295) -> q_gen_4303
<s, s>(q_gen_4303) -> q_gen_4303
<s, z>(q_gen_4301) -> q_gen_4303
<s, s>(q_gen_4318) -> q_gen_4318
<z, s>(q_gen_4301) -> q_gen_4318
<s, s, s>(q_gen_4308) -> q_gen_4293
<s, s, z>(q_gen_4295) -> q_gen_4293
<s, s, z>(q_gen_4318) -> q_gen_4293
<s, z, s>(q_gen_4295) -> q_gen_4293
<s, z, s>(q_gen_4303) -> q_gen_4293
<s, z, z>(q_gen_4313) -> q_gen_4293
<z, s, z>(q_gen_4301) -> q_gen_4293
<z, s, z>(q_gen_4313) -> q_gen_4293
<z, z, z>() -> q_gen_4293
<s, s, s>(q_gen_4293) -> q_gen_4308
<s, s, z>(q_gen_4303) -> q_gen_4308
<s, z, s>(q_gen_4318) -> q_gen_4308
<s, z, z>(q_gen_4301) -> q_gen_4308
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_4292, q_gen_4296, q_gen_4297, q_gen_4305, q_gen_4306, q_gen_4311},
Q_f={q_gen_4292, q_gen_4296},
Delta=
{
<s>(q_gen_4306) -> q_gen_4306
<z>() -> q_gen_4306
<s, s>(q_gen_4311) -> q_gen_4297
<z, z>() -> q_gen_4297
<s, s>(q_gen_4297) -> q_gen_4311
<z, s>(q_gen_4306) -> q_gen_4311
<z, z, z>() -> q_gen_4292
<s, s, s>(q_gen_4296) -> q_gen_4296
<s, s, s>(q_gen_4305) -> q_gen_4296
<s, z, s>(q_gen_4297) -> q_gen_4296
<s, z, s>(q_gen_4311) -> q_gen_4296
<z, s, s>(q_gen_4297) -> q_gen_4296
<s, s, s>(q_gen_4292) -> q_gen_4305
<z, s, s>(q_gen_4311) -> q_gen_4305
<z, z, s>(q_gen_4306) -> q_gen_4305
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 31
() -> minus([z, y, z]) -> 31
() -> plus([n, z, n]) -> 31
(minus([_pq, n, _qq]) /\ plus([m, n, _pq])) -> eq_nat([_qq, m]) -> 34
(minus([u, x2, _fq])) -> minus([s(u), s(x2), _fq]) -> 34
(plus([n, mm, _kq])) -> plus([n, s(mm), s(_kq)]) -> 34
}
Sat witness: Found: ((minus([_pq, n, _qq]) /\ plus([m, n, _pq])) -> eq_nat([_qq, m]), {
_pq -> s(s(z))  ;  _qq -> z  ;  m -> s(z)  ;  n -> z
})

-------------------------------------------
Step 43, which took 0.079018 s (model generation: 0.077896,  model checking: 0.001122):

Model:
|_
{
minus -> 
{{{
Q={q_gen_4293, q_gen_4295, q_gen_4301, q_gen_4303, q_gen_4308, q_gen_4313, q_gen_4318},
Q_f={q_gen_4293},
Delta=
{
<s>(q_gen_4313) -> q_gen_4301
<z>() -> q_gen_4301
<s>(q_gen_4301) -> q_gen_4313
<z, s>(q_gen_4313) -> q_gen_4295
<z, z>() -> q_gen_4295
<s, s>(q_gen_4295) -> q_gen_4303
<s, s>(q_gen_4303) -> q_gen_4303
<s, z>(q_gen_4301) -> q_gen_4303
<s, s>(q_gen_4318) -> q_gen_4318
<z, s>(q_gen_4301) -> q_gen_4318
<s, s, s>(q_gen_4308) -> q_gen_4293
<s, s, z>(q_gen_4295) -> q_gen_4293
<s, s, z>(q_gen_4318) -> q_gen_4293
<s, z, s>(q_gen_4295) -> q_gen_4293
<s, z, s>(q_gen_4303) -> q_gen_4293
<s, z, z>(q_gen_4313) -> q_gen_4293
<z, s, z>(q_gen_4301) -> q_gen_4293
<z, s, z>(q_gen_4313) -> q_gen_4293
<z, z, z>() -> q_gen_4293
<s, s, s>(q_gen_4293) -> q_gen_4308
<s, s, z>(q_gen_4303) -> q_gen_4308
<s, z, s>(q_gen_4318) -> q_gen_4308
<s, z, z>(q_gen_4301) -> q_gen_4308
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_4292, q_gen_4296, q_gen_4297, q_gen_4305, q_gen_4306, q_gen_4316},
Q_f={q_gen_4292, q_gen_4296},
Delta=
{
<s>(q_gen_4306) -> q_gen_4306
<z>() -> q_gen_4306
<s, s>(q_gen_4297) -> q_gen_4297
<z, z>() -> q_gen_4297
<s, s>(q_gen_4316) -> q_gen_4316
<z, s>(q_gen_4306) -> q_gen_4316
<z, z, z>() -> q_gen_4292
<s, s, s>(q_gen_4296) -> q_gen_4296
<s, s, s>(q_gen_4305) -> q_gen_4296
<s, z, s>(q_gen_4297) -> q_gen_4296
<z, s, s>(q_gen_4297) -> q_gen_4296
<s, s, s>(q_gen_4292) -> q_gen_4305
<s, z, s>(q_gen_4316) -> q_gen_4305
<z, s, s>(q_gen_4316) -> q_gen_4305
<z, z, s>(q_gen_4306) -> q_gen_4305
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 32
() -> minus([z, y, z]) -> 32
() -> plus([n, z, n]) -> 32
(minus([_pq, n, _qq]) /\ plus([m, n, _pq])) -> eq_nat([_qq, m]) -> 34
(minus([u, x2, _fq])) -> minus([s(u), s(x2), _fq]) -> 37
(plus([n, mm, _kq])) -> plus([n, s(mm), s(_kq)]) -> 35
}
Sat witness: Found: ((minus([u, x2, _fq])) -> minus([s(u), s(x2), _fq]), {
_fq -> z  ;  u -> s(z)  ;  x2 -> s(z)
})

-------------------------------------------
Step 44, which took 0.077468 s (model generation: 0.076779,  model checking: 0.000689):

Model:
|_
{
minus -> 
{{{
Q={q_gen_4293, q_gen_4295, q_gen_4301, q_gen_4308, q_gen_4313, q_gen_4318, q_gen_4341},
Q_f={q_gen_4293},
Delta=
{
<s>(q_gen_4313) -> q_gen_4301
<z>() -> q_gen_4301
<s>(q_gen_4301) -> q_gen_4313
<s, s>(q_gen_4295) -> q_gen_4295
<z, s>(q_gen_4313) -> q_gen_4295
<z, z>() -> q_gen_4295
<s, s>(q_gen_4318) -> q_gen_4318
<z, s>(q_gen_4301) -> q_gen_4318
<s, z>(q_gen_4301) -> q_gen_4341
<s, s, s>(q_gen_4308) -> q_gen_4293
<s, s, z>(q_gen_4295) -> q_gen_4293
<s, s, z>(q_gen_4318) -> q_gen_4293
<s, z, s>(q_gen_4295) -> q_gen_4293
<s, z, z>(q_gen_4313) -> q_gen_4293
<z, s, z>(q_gen_4301) -> q_gen_4293
<z, s, z>(q_gen_4313) -> q_gen_4293
<z, z, z>() -> q_gen_4293
<s, s, s>(q_gen_4293) -> q_gen_4308
<s, s, z>(q_gen_4341) -> q_gen_4308
<s, z, s>(q_gen_4318) -> q_gen_4308
<s, z, z>(q_gen_4301) -> q_gen_4308
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_4292, q_gen_4296, q_gen_4297, q_gen_4305, q_gen_4306, q_gen_4316},
Q_f={q_gen_4292, q_gen_4296},
Delta=
{
<s>(q_gen_4306) -> q_gen_4306
<z>() -> q_gen_4306
<s, s>(q_gen_4297) -> q_gen_4297
<z, z>() -> q_gen_4297
<s, s>(q_gen_4316) -> q_gen_4316
<z, s>(q_gen_4306) -> q_gen_4316
<z, z, z>() -> q_gen_4292
<s, s, s>(q_gen_4296) -> q_gen_4296
<s, s, s>(q_gen_4305) -> q_gen_4296
<s, z, s>(q_gen_4297) -> q_gen_4296
<z, s, s>(q_gen_4297) -> q_gen_4296
<s, s, s>(q_gen_4292) -> q_gen_4305
<s, z, s>(q_gen_4316) -> q_gen_4305
<z, s, s>(q_gen_4316) -> q_gen_4305
<z, z, s>(q_gen_4306) -> q_gen_4305
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 33
() -> minus([z, y, z]) -> 33
() -> plus([n, z, n]) -> 33
(minus([_pq, n, _qq]) /\ plus([m, n, _pq])) -> eq_nat([_qq, m]) -> 37
(minus([u, x2, _fq])) -> minus([s(u), s(x2), _fq]) -> 37
(plus([n, mm, _kq])) -> plus([n, s(mm), s(_kq)]) -> 35
}
Sat witness: Found: ((minus([_pq, n, _qq]) /\ plus([m, n, _pq])) -> eq_nat([_qq, m]), {
_pq -> s(s(z))  ;  _qq -> z  ;  m -> s(z)  ;  n -> s(s(z))
})

-------------------------------------------
Step 45, which took 0.080541 s (model generation: 0.079253,  model checking: 0.001288):

Model:
|_
{
minus -> 
{{{
Q={q_gen_4293, q_gen_4295, q_gen_4301, q_gen_4308, q_gen_4313, q_gen_4318, q_gen_4341},
Q_f={q_gen_4293},
Delta=
{
<s>(q_gen_4313) -> q_gen_4301
<z>() -> q_gen_4301
<s>(q_gen_4301) -> q_gen_4313
<s, s>(q_gen_4295) -> q_gen_4295
<z, s>(q_gen_4313) -> q_gen_4295
<z, z>() -> q_gen_4295
<s, s>(q_gen_4318) -> q_gen_4318
<z, s>(q_gen_4301) -> q_gen_4318
<s, z>(q_gen_4301) -> q_gen_4341
<s, s, s>(q_gen_4308) -> q_gen_4293
<s, s, z>(q_gen_4295) -> q_gen_4293
<s, s, z>(q_gen_4318) -> q_gen_4293
<s, z, s>(q_gen_4295) -> q_gen_4293
<s, z, z>(q_gen_4313) -> q_gen_4293
<z, s, z>(q_gen_4301) -> q_gen_4293
<z, s, z>(q_gen_4313) -> q_gen_4293
<z, z, z>() -> q_gen_4293
<s, s, s>(q_gen_4293) -> q_gen_4308
<s, s, z>(q_gen_4341) -> q_gen_4308
<s, z, s>(q_gen_4318) -> q_gen_4308
<s, z, z>(q_gen_4301) -> q_gen_4308
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_4292, q_gen_4297, q_gen_4305, q_gen_4306, q_gen_4316, q_gen_4323},
Q_f={q_gen_4292},
Delta=
{
<z>() -> q_gen_4306
<s>(q_gen_4306) -> q_gen_4323
<s, s>(q_gen_4297) -> q_gen_4297
<z, s>(q_gen_4323) -> q_gen_4297
<z, z>() -> q_gen_4297
<s, s>(q_gen_4316) -> q_gen_4316
<z, s>(q_gen_4306) -> q_gen_4316
<s, s, s>(q_gen_4305) -> q_gen_4292
<s, z, s>(q_gen_4297) -> q_gen_4292
<z, s, s>(q_gen_4297) -> q_gen_4292
<z, z, s>(q_gen_4323) -> q_gen_4292
<z, z, z>() -> q_gen_4292
<s, s, s>(q_gen_4292) -> q_gen_4305
<s, z, s>(q_gen_4316) -> q_gen_4305
<z, s, s>(q_gen_4316) -> q_gen_4305
<z, z, s>(q_gen_4306) -> q_gen_4305
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 34
() -> minus([z, y, z]) -> 34
() -> plus([n, z, n]) -> 34
(minus([_pq, n, _qq]) /\ plus([m, n, _pq])) -> eq_nat([_qq, m]) -> 37
(minus([u, x2, _fq])) -> minus([s(u), s(x2), _fq]) -> 37
(plus([n, mm, _kq])) -> plus([n, s(mm), s(_kq)]) -> 38
}
Sat witness: Found: ((plus([n, mm, _kq])) -> plus([n, s(mm), s(_kq)]), {
_kq -> s(s(s(z)))  ;  mm -> z  ;  n -> s(z)
})

-------------------------------------------
Step 46, which took 0.104659 s (model generation: 0.103451,  model checking: 0.001208):

Model:
|_
{
minus -> 
{{{
Q={q_gen_4293, q_gen_4295, q_gen_4301, q_gen_4308, q_gen_4313, q_gen_4318, q_gen_4341},
Q_f={q_gen_4293},
Delta=
{
<s>(q_gen_4313) -> q_gen_4301
<z>() -> q_gen_4301
<s>(q_gen_4301) -> q_gen_4313
<s, s>(q_gen_4295) -> q_gen_4295
<z, s>(q_gen_4313) -> q_gen_4295
<z, z>() -> q_gen_4295
<s, s>(q_gen_4318) -> q_gen_4318
<z, s>(q_gen_4301) -> q_gen_4318
<s, z>(q_gen_4301) -> q_gen_4341
<s, s, s>(q_gen_4308) -> q_gen_4293
<s, s, z>(q_gen_4295) -> q_gen_4293
<s, s, z>(q_gen_4318) -> q_gen_4293
<s, z, s>(q_gen_4295) -> q_gen_4293
<s, z, z>(q_gen_4313) -> q_gen_4293
<z, s, z>(q_gen_4301) -> q_gen_4293
<z, s, z>(q_gen_4313) -> q_gen_4293
<z, z, z>() -> q_gen_4293
<s, s, s>(q_gen_4293) -> q_gen_4308
<s, s, z>(q_gen_4341) -> q_gen_4308
<s, z, s>(q_gen_4318) -> q_gen_4308
<s, z, z>(q_gen_4301) -> q_gen_4308
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_4292, q_gen_4297, q_gen_4305, q_gen_4306, q_gen_4316, q_gen_4323},
Q_f={q_gen_4292},
Delta=
{
<s>(q_gen_4323) -> q_gen_4306
<z>() -> q_gen_4306
<s>(q_gen_4306) -> q_gen_4323
<s, s>(q_gen_4297) -> q_gen_4297
<z, s>(q_gen_4323) -> q_gen_4297
<z, z>() -> q_gen_4297
<s, s>(q_gen_4316) -> q_gen_4316
<z, s>(q_gen_4306) -> q_gen_4316
<s, s, s>(q_gen_4305) -> q_gen_4292
<s, z, s>(q_gen_4297) -> q_gen_4292
<z, s, s>(q_gen_4297) -> q_gen_4292
<z, z, s>(q_gen_4323) -> q_gen_4292
<z, z, z>() -> q_gen_4292
<s, s, s>(q_gen_4292) -> q_gen_4305
<s, z, s>(q_gen_4316) -> q_gen_4305
<z, s, s>(q_gen_4316) -> q_gen_4305
<z, z, s>(q_gen_4306) -> q_gen_4305
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 35
() -> minus([z, y, z]) -> 35
() -> plus([n, z, n]) -> 35
(minus([_pq, n, _qq]) /\ plus([m, n, _pq])) -> eq_nat([_qq, m]) -> 37
(minus([u, x2, _fq])) -> minus([s(u), s(x2), _fq]) -> 40
(plus([n, mm, _kq])) -> plus([n, s(mm), s(_kq)]) -> 38
}
Sat witness: Found: ((minus([u, x2, _fq])) -> minus([s(u), s(x2), _fq]), {
_fq -> z  ;  u -> s(s(z))  ;  x2 -> z
})

-------------------------------------------
Step 47, which took 0.102807 s (model generation: 0.101617,  model checking: 0.001190):

Model:
|_
{
minus -> 
{{{
Q={q_gen_4293, q_gen_4295, q_gen_4301, q_gen_4308, q_gen_4313, q_gen_4318, q_gen_4341},
Q_f={q_gen_4293},
Delta=
{
<s>(q_gen_4313) -> q_gen_4301
<z>() -> q_gen_4301
<s>(q_gen_4301) -> q_gen_4313
<s, s>(q_gen_4295) -> q_gen_4295
<z, s>(q_gen_4313) -> q_gen_4295
<z, z>() -> q_gen_4295
<s, s>(q_gen_4318) -> q_gen_4318
<s, z>(q_gen_4313) -> q_gen_4318
<z, s>(q_gen_4301) -> q_gen_4318
<s, z>(q_gen_4301) -> q_gen_4341
<s, s, s>(q_gen_4308) -> q_gen_4293
<s, s, z>(q_gen_4295) -> q_gen_4293
<s, s, z>(q_gen_4318) -> q_gen_4293
<s, z, s>(q_gen_4295) -> q_gen_4293
<s, z, z>(q_gen_4313) -> q_gen_4293
<z, s, z>(q_gen_4301) -> q_gen_4293
<z, s, z>(q_gen_4313) -> q_gen_4293
<z, z, z>() -> q_gen_4293
<s, s, s>(q_gen_4293) -> q_gen_4308
<s, s, z>(q_gen_4341) -> q_gen_4308
<s, z, s>(q_gen_4318) -> q_gen_4308
<s, z, z>(q_gen_4301) -> q_gen_4308
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_4292, q_gen_4297, q_gen_4305, q_gen_4306, q_gen_4316, q_gen_4323},
Q_f={q_gen_4292},
Delta=
{
<s>(q_gen_4323) -> q_gen_4306
<z>() -> q_gen_4306
<s>(q_gen_4306) -> q_gen_4323
<s, s>(q_gen_4297) -> q_gen_4297
<z, s>(q_gen_4323) -> q_gen_4297
<z, z>() -> q_gen_4297
<s, s>(q_gen_4316) -> q_gen_4316
<z, s>(q_gen_4306) -> q_gen_4316
<s, s, s>(q_gen_4305) -> q_gen_4292
<s, z, s>(q_gen_4297) -> q_gen_4292
<z, s, s>(q_gen_4297) -> q_gen_4292
<z, z, s>(q_gen_4323) -> q_gen_4292
<z, z, z>() -> q_gen_4292
<s, s, s>(q_gen_4292) -> q_gen_4305
<s, z, s>(q_gen_4316) -> q_gen_4305
<z, s, s>(q_gen_4316) -> q_gen_4305
<z, z, s>(q_gen_4306) -> q_gen_4305
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 36
() -> minus([z, y, z]) -> 36
() -> plus([n, z, n]) -> 36
(minus([_pq, n, _qq]) /\ plus([m, n, _pq])) -> eq_nat([_qq, m]) -> 40
(minus([u, x2, _fq])) -> minus([s(u), s(x2), _fq]) -> 40
(plus([n, mm, _kq])) -> plus([n, s(mm), s(_kq)]) -> 38
}
Sat witness: Found: ((minus([_pq, n, _qq]) /\ plus([m, n, _pq])) -> eq_nat([_qq, m]), {
_pq -> s(s(s(z)))  ;  _qq -> z  ;  m -> s(s(z))  ;  n -> s(z)
})

-------------------------------------------
Step 48, which took 0.099834 s (model generation: 0.098004,  model checking: 0.001830):

Model:
|_
{
minus -> 
{{{
Q={q_gen_4293, q_gen_4295, q_gen_4301, q_gen_4308, q_gen_4313, q_gen_4318, q_gen_4341, q_gen_4361},
Q_f={q_gen_4293},
Delta=
{
<s>(q_gen_4313) -> q_gen_4301
<z>() -> q_gen_4301
<s>(q_gen_4301) -> q_gen_4313
<s, s>(q_gen_4295) -> q_gen_4295
<z, s>(q_gen_4313) -> q_gen_4295
<z, z>() -> q_gen_4295
<s, s>(q_gen_4318) -> q_gen_4318
<z, s>(q_gen_4301) -> q_gen_4318
<s, z>(q_gen_4301) -> q_gen_4341
<s, z>(q_gen_4313) -> q_gen_4341
<s, s, s>(q_gen_4308) -> q_gen_4293
<s, s, z>(q_gen_4295) -> q_gen_4293
<s, s, z>(q_gen_4318) -> q_gen_4293
<s, z, s>(q_gen_4295) -> q_gen_4293
<z, s, z>(q_gen_4301) -> q_gen_4293
<z, s, z>(q_gen_4313) -> q_gen_4293
<z, z, z>() -> q_gen_4293
<s, s, s>(q_gen_4293) -> q_gen_4308
<s, s, z>(q_gen_4341) -> q_gen_4308
<s, z, s>(q_gen_4318) -> q_gen_4308
<s, z, z>(q_gen_4301) -> q_gen_4308
<s, s, s>(q_gen_4361) -> q_gen_4361
<s, z, z>(q_gen_4313) -> q_gen_4361
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_4292, q_gen_4297, q_gen_4305, q_gen_4306, q_gen_4316, q_gen_4323},
Q_f={q_gen_4292},
Delta=
{
<s>(q_gen_4323) -> q_gen_4306
<z>() -> q_gen_4306
<s>(q_gen_4306) -> q_gen_4323
<s, s>(q_gen_4297) -> q_gen_4297
<z, s>(q_gen_4323) -> q_gen_4297
<z, z>() -> q_gen_4297
<s, s>(q_gen_4316) -> q_gen_4316
<z, s>(q_gen_4306) -> q_gen_4316
<s, s, s>(q_gen_4305) -> q_gen_4292
<s, z, s>(q_gen_4297) -> q_gen_4292
<z, s, s>(q_gen_4297) -> q_gen_4292
<z, z, s>(q_gen_4323) -> q_gen_4292
<z, z, z>() -> q_gen_4292
<s, s, s>(q_gen_4292) -> q_gen_4305
<s, z, s>(q_gen_4316) -> q_gen_4305
<z, s, s>(q_gen_4316) -> q_gen_4305
<z, z, s>(q_gen_4306) -> q_gen_4305
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 37
() -> minus([z, y, z]) -> 37
() -> plus([n, z, n]) -> 37
(minus([_pq, n, _qq]) /\ plus([m, n, _pq])) -> eq_nat([_qq, m]) -> 40
(minus([u, x2, _fq])) -> minus([s(u), s(x2), _fq]) -> 43
(plus([n, mm, _kq])) -> plus([n, s(mm), s(_kq)]) -> 39
}
Sat witness: Found: ((minus([u, x2, _fq])) -> minus([s(u), s(x2), _fq]), {
_fq -> s(s(z))  ;  u -> s(s(z))  ;  x2 -> z
})

-------------------------------------------
Step 49, which took 0.116755 s (model generation: 0.115913,  model checking: 0.000842):

Model:
|_
{
minus -> 
{{{
Q={q_gen_4293, q_gen_4295, q_gen_4301, q_gen_4308, q_gen_4313, q_gen_4318, q_gen_4324, q_gen_4341},
Q_f={q_gen_4293},
Delta=
{
<s>(q_gen_4313) -> q_gen_4301
<z>() -> q_gen_4301
<s>(q_gen_4301) -> q_gen_4313
<s, s>(q_gen_4295) -> q_gen_4295
<z, s>(q_gen_4313) -> q_gen_4295
<z, z>() -> q_gen_4295
<s, s>(q_gen_4318) -> q_gen_4318
<z, s>(q_gen_4301) -> q_gen_4318
<s, z>(q_gen_4301) -> q_gen_4341
<s, z>(q_gen_4313) -> q_gen_4341
<s, s, s>(q_gen_4308) -> q_gen_4293
<s, s, z>(q_gen_4295) -> q_gen_4293
<s, s, z>(q_gen_4318) -> q_gen_4293
<s, z, s>(q_gen_4295) -> q_gen_4293
<z, s, z>(q_gen_4301) -> q_gen_4293
<z, s, z>(q_gen_4313) -> q_gen_4293
<z, z, z>() -> q_gen_4293
<s, s, s>(q_gen_4293) -> q_gen_4308
<s, s, z>(q_gen_4341) -> q_gen_4308
<s, z, s>(q_gen_4341) -> q_gen_4308
<s, z, z>(q_gen_4301) -> q_gen_4308
<s, s, s>(q_gen_4324) -> q_gen_4324
<s, z, s>(q_gen_4318) -> q_gen_4324
<s, z, z>(q_gen_4313) -> q_gen_4324
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_4292, q_gen_4297, q_gen_4304, q_gen_4305, q_gen_4306, q_gen_4311},
Q_f={q_gen_4292, q_gen_4304},
Delta=
{
<s>(q_gen_4306) -> q_gen_4306
<z>() -> q_gen_4306
<z, z>() -> q_gen_4297
<s, s>(q_gen_4297) -> q_gen_4311
<s, s>(q_gen_4311) -> q_gen_4311
<z, s>(q_gen_4306) -> q_gen_4311
<s, z, s>(q_gen_4297) -> q_gen_4292
<z, s, s>(q_gen_4297) -> q_gen_4292
<z, z, z>() -> q_gen_4292
<s, s, s>(q_gen_4304) -> q_gen_4304
<s, s, s>(q_gen_4305) -> q_gen_4304
<s, z, s>(q_gen_4311) -> q_gen_4304
<s, s, s>(q_gen_4292) -> q_gen_4305
<z, s, s>(q_gen_4311) -> q_gen_4305
<z, z, s>(q_gen_4306) -> q_gen_4305
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 38
() -> minus([z, y, z]) -> 38
() -> plus([n, z, n]) -> 38
(minus([_pq, n, _qq]) /\ plus([m, n, _pq])) -> eq_nat([_qq, m]) -> 40
(minus([u, x2, _fq])) -> minus([s(u), s(x2), _fq]) -> 43
(plus([n, mm, _kq])) -> plus([n, s(mm), s(_kq)]) -> 42
}
Sat witness: Found: ((plus([n, mm, _kq])) -> plus([n, s(mm), s(_kq)]), {
_kq -> s(z)  ;  mm -> s(z)  ;  n -> z
})

-------------------------------------------
Step 50, which took 0.106329 s (model generation: 0.105482,  model checking: 0.000847):

Model:
|_
{
minus -> 
{{{
Q={q_gen_4293, q_gen_4295, q_gen_4301, q_gen_4308, q_gen_4313, q_gen_4318, q_gen_4324, q_gen_4341},
Q_f={q_gen_4293},
Delta=
{
<s>(q_gen_4313) -> q_gen_4301
<z>() -> q_gen_4301
<s>(q_gen_4301) -> q_gen_4313
<s, s>(q_gen_4295) -> q_gen_4295
<z, z>() -> q_gen_4295
<s, s>(q_gen_4318) -> q_gen_4318
<z, s>(q_gen_4301) -> q_gen_4318
<z, s>(q_gen_4313) -> q_gen_4318
<s, z>(q_gen_4301) -> q_gen_4341
<s, z>(q_gen_4313) -> q_gen_4341
<s, s, s>(q_gen_4308) -> q_gen_4293
<s, s, z>(q_gen_4295) -> q_gen_4293
<s, s, z>(q_gen_4318) -> q_gen_4293
<s, z, s>(q_gen_4295) -> q_gen_4293
<z, s, z>(q_gen_4301) -> q_gen_4293
<z, s, z>(q_gen_4313) -> q_gen_4293
<z, z, z>() -> q_gen_4293
<s, s, s>(q_gen_4293) -> q_gen_4308
<s, s, z>(q_gen_4341) -> q_gen_4308
<s, z, s>(q_gen_4341) -> q_gen_4308
<s, z, z>(q_gen_4301) -> q_gen_4308
<s, s, s>(q_gen_4324) -> q_gen_4324
<s, z, s>(q_gen_4318) -> q_gen_4324
<s, z, z>(q_gen_4313) -> q_gen_4324
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_4292, q_gen_4297, q_gen_4305, q_gen_4306, q_gen_4316, q_gen_4323},
Q_f={q_gen_4292},
Delta=
{
<s>(q_gen_4323) -> q_gen_4306
<z>() -> q_gen_4306
<s>(q_gen_4306) -> q_gen_4323
<s, s>(q_gen_4297) -> q_gen_4297
<z, s>(q_gen_4323) -> q_gen_4297
<z, z>() -> q_gen_4297
<s, s>(q_gen_4316) -> q_gen_4316
<z, s>(q_gen_4306) -> q_gen_4316
<s, s, s>(q_gen_4305) -> q_gen_4292
<s, z, s>(q_gen_4297) -> q_gen_4292
<z, s, s>(q_gen_4297) -> q_gen_4292
<z, z, s>(q_gen_4323) -> q_gen_4292
<z, z, z>() -> q_gen_4292
<s, s, s>(q_gen_4292) -> q_gen_4305
<s, z, s>(q_gen_4316) -> q_gen_4305
<z, s, s>(q_gen_4316) -> q_gen_4305
<z, z, s>(q_gen_4306) -> q_gen_4305
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 39
() -> minus([z, y, z]) -> 39
() -> plus([n, z, n]) -> 39
(minus([_pq, n, _qq]) /\ plus([m, n, _pq])) -> eq_nat([_qq, m]) -> 43
(minus([u, x2, _fq])) -> minus([s(u), s(x2), _fq]) -> 43
(plus([n, mm, _kq])) -> plus([n, s(mm), s(_kq)]) -> 42
}
Sat witness: Found: ((minus([_pq, n, _qq]) /\ plus([m, n, _pq])) -> eq_nat([_qq, m]), {
_pq -> s(s(z))  ;  _qq -> s(s(z))  ;  m -> z  ;  n -> z
})

-------------------------------------------
Step 51, which took 0.114581 s (model generation: 0.113388,  model checking: 0.001193):

Model:
|_
{
minus -> 
{{{
Q={q_gen_4293, q_gen_4295, q_gen_4301, q_gen_4308, q_gen_4313, q_gen_4318, q_gen_4324, q_gen_4341},
Q_f={q_gen_4293},
Delta=
{
<z>() -> q_gen_4301
<s>(q_gen_4301) -> q_gen_4313
<s>(q_gen_4313) -> q_gen_4313
<s, s>(q_gen_4295) -> q_gen_4295
<z, z>() -> q_gen_4295
<s, s>(q_gen_4318) -> q_gen_4318
<z, s>(q_gen_4301) -> q_gen_4318
<z, s>(q_gen_4313) -> q_gen_4318
<s, z>(q_gen_4301) -> q_gen_4341
<s, z>(q_gen_4313) -> q_gen_4341
<s, s, s>(q_gen_4308) -> q_gen_4293
<s, s, z>(q_gen_4295) -> q_gen_4293
<s, s, z>(q_gen_4318) -> q_gen_4293
<s, z, s>(q_gen_4295) -> q_gen_4293
<z, s, z>(q_gen_4301) -> q_gen_4293
<z, s, z>(q_gen_4313) -> q_gen_4293
<z, z, z>() -> q_gen_4293
<s, s, s>(q_gen_4293) -> q_gen_4308
<s, s, z>(q_gen_4341) -> q_gen_4308
<s, z, s>(q_gen_4341) -> q_gen_4308
<s, z, z>(q_gen_4301) -> q_gen_4308
<s, s, s>(q_gen_4324) -> q_gen_4324
<s, z, s>(q_gen_4318) -> q_gen_4324
<s, z, z>(q_gen_4313) -> q_gen_4324
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_4292, q_gen_4297, q_gen_4299, q_gen_4305, q_gen_4306, q_gen_4316},
Q_f={q_gen_4292, q_gen_4299},
Delta=
{
<s>(q_gen_4306) -> q_gen_4306
<z>() -> q_gen_4306
<s, s>(q_gen_4297) -> q_gen_4297
<z, z>() -> q_gen_4297
<s, s>(q_gen_4316) -> q_gen_4316
<z, s>(q_gen_4306) -> q_gen_4316
<s, s, s>(q_gen_4299) -> q_gen_4292
<z, s, s>(q_gen_4297) -> q_gen_4292
<z, z, z>() -> q_gen_4292
<s, s, s>(q_gen_4305) -> q_gen_4299
<s, z, s>(q_gen_4297) -> q_gen_4299
<s, z, s>(q_gen_4316) -> q_gen_4299
<s, s, s>(q_gen_4292) -> q_gen_4305
<z, s, s>(q_gen_4316) -> q_gen_4305
<z, z, s>(q_gen_4306) -> q_gen_4305
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 40
() -> minus([z, y, z]) -> 40
() -> plus([n, z, n]) -> 40
(minus([_pq, n, _qq]) /\ plus([m, n, _pq])) -> eq_nat([_qq, m]) -> 43
(minus([u, x2, _fq])) -> minus([s(u), s(x2), _fq]) -> 43
(plus([n, mm, _kq])) -> plus([n, s(mm), s(_kq)]) -> 45
}
Sat witness: Found: ((plus([n, mm, _kq])) -> plus([n, s(mm), s(_kq)]), {
_kq -> s(s(s(z)))  ;  mm -> s(z)  ;  n -> s(s(s(z)))
})

-------------------------------------------
Step 52, which took 0.122585 s (model generation: 0.121935,  model checking: 0.000650):

Model:
|_
{
minus -> 
{{{
Q={q_gen_4293, q_gen_4295, q_gen_4301, q_gen_4308, q_gen_4313, q_gen_4318, q_gen_4324, q_gen_4341},
Q_f={q_gen_4293},
Delta=
{
<z>() -> q_gen_4301
<s>(q_gen_4301) -> q_gen_4313
<s>(q_gen_4313) -> q_gen_4313
<s, s>(q_gen_4295) -> q_gen_4295
<z, z>() -> q_gen_4295
<s, s>(q_gen_4318) -> q_gen_4318
<z, s>(q_gen_4301) -> q_gen_4318
<z, s>(q_gen_4313) -> q_gen_4318
<s, z>(q_gen_4301) -> q_gen_4341
<s, z>(q_gen_4313) -> q_gen_4341
<s, s, s>(q_gen_4308) -> q_gen_4293
<s, s, z>(q_gen_4295) -> q_gen_4293
<s, s, z>(q_gen_4318) -> q_gen_4293
<s, z, s>(q_gen_4295) -> q_gen_4293
<z, s, z>(q_gen_4301) -> q_gen_4293
<z, s, z>(q_gen_4313) -> q_gen_4293
<z, z, z>() -> q_gen_4293
<s, s, s>(q_gen_4293) -> q_gen_4308
<s, s, z>(q_gen_4341) -> q_gen_4308
<s, z, s>(q_gen_4341) -> q_gen_4308
<s, z, z>(q_gen_4301) -> q_gen_4308
<s, s, s>(q_gen_4324) -> q_gen_4324
<s, z, s>(q_gen_4318) -> q_gen_4324
<s, z, z>(q_gen_4313) -> q_gen_4324
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_4292, q_gen_4297, q_gen_4304, q_gen_4305, q_gen_4306, q_gen_4316},
Q_f={q_gen_4292, q_gen_4304},
Delta=
{
<s>(q_gen_4306) -> q_gen_4306
<z>() -> q_gen_4306
<s, s>(q_gen_4297) -> q_gen_4297
<z, z>() -> q_gen_4297
<s, s>(q_gen_4316) -> q_gen_4316
<z, s>(q_gen_4306) -> q_gen_4316
<s, z, s>(q_gen_4297) -> q_gen_4292
<z, s, s>(q_gen_4297) -> q_gen_4292
<z, z, z>() -> q_gen_4292
<s, s, s>(q_gen_4304) -> q_gen_4304
<s, s, s>(q_gen_4305) -> q_gen_4304
<s, z, s>(q_gen_4316) -> q_gen_4304
<s, s, s>(q_gen_4292) -> q_gen_4305
<z, s, s>(q_gen_4316) -> q_gen_4305
<z, z, s>(q_gen_4306) -> q_gen_4305
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 41
() -> minus([z, y, z]) -> 41
() -> plus([n, z, n]) -> 41
(minus([_pq, n, _qq]) /\ plus([m, n, _pq])) -> eq_nat([_qq, m]) -> 43
(minus([u, x2, _fq])) -> minus([s(u), s(x2), _fq]) -> 46
(plus([n, mm, _kq])) -> plus([n, s(mm), s(_kq)]) -> 45
}
Sat witness: Found: ((minus([u, x2, _fq])) -> minus([s(u), s(x2), _fq]), {
_fq -> s(s(z))  ;  u -> s(s(s(z)))  ;  x2 -> s(z)
})

-------------------------------------------
Step 53, which took 0.128837 s (model generation: 0.128006,  model checking: 0.000831):

Model:
|_
{
minus -> 
{{{
Q={q_gen_4293, q_gen_4295, q_gen_4301, q_gen_4308, q_gen_4313, q_gen_4318, q_gen_4324, q_gen_4341},
Q_f={q_gen_4293},
Delta=
{
<s>(q_gen_4313) -> q_gen_4301
<z>() -> q_gen_4301
<s>(q_gen_4301) -> q_gen_4313
<s, s>(q_gen_4295) -> q_gen_4295
<z, z>() -> q_gen_4295
<s, s>(q_gen_4318) -> q_gen_4318
<z, s>(q_gen_4301) -> q_gen_4318
<z, s>(q_gen_4313) -> q_gen_4318
<s, z>(q_gen_4301) -> q_gen_4341
<s, z>(q_gen_4313) -> q_gen_4341
<s, s, s>(q_gen_4308) -> q_gen_4293
<s, s, z>(q_gen_4295) -> q_gen_4293
<s, s, z>(q_gen_4318) -> q_gen_4293
<s, z, s>(q_gen_4295) -> q_gen_4293
<z, s, z>(q_gen_4301) -> q_gen_4293
<z, s, z>(q_gen_4313) -> q_gen_4293
<z, z, z>() -> q_gen_4293
<s, s, s>(q_gen_4293) -> q_gen_4308
<s, s, s>(q_gen_4324) -> q_gen_4308
<s, s, z>(q_gen_4341) -> q_gen_4308
<s, z, s>(q_gen_4341) -> q_gen_4308
<s, z, z>(q_gen_4301) -> q_gen_4308
<s, z, s>(q_gen_4318) -> q_gen_4324
<s, z, z>(q_gen_4313) -> q_gen_4324
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_4292, q_gen_4297, q_gen_4304, q_gen_4305, q_gen_4306, q_gen_4316},
Q_f={q_gen_4292, q_gen_4304},
Delta=
{
<s>(q_gen_4306) -> q_gen_4306
<z>() -> q_gen_4306
<s, s>(q_gen_4297) -> q_gen_4297
<z, z>() -> q_gen_4297
<s, s>(q_gen_4316) -> q_gen_4316
<z, s>(q_gen_4306) -> q_gen_4316
<s, z, s>(q_gen_4297) -> q_gen_4292
<z, s, s>(q_gen_4297) -> q_gen_4292
<z, z, z>() -> q_gen_4292
<s, s, s>(q_gen_4304) -> q_gen_4304
<s, s, s>(q_gen_4305) -> q_gen_4304
<s, s, s>(q_gen_4292) -> q_gen_4305
<s, z, s>(q_gen_4316) -> q_gen_4305
<z, s, s>(q_gen_4316) -> q_gen_4305
<z, z, s>(q_gen_4306) -> q_gen_4305
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 42
() -> minus([z, y, z]) -> 42
() -> plus([n, z, n]) -> 42
(minus([_pq, n, _qq]) /\ plus([m, n, _pq])) -> eq_nat([_qq, m]) -> 46
(minus([u, x2, _fq])) -> minus([s(u), s(x2), _fq]) -> 46
(plus([n, mm, _kq])) -> plus([n, s(mm), s(_kq)]) -> 45
}
Sat witness: Found: ((minus([_pq, n, _qq]) /\ plus([m, n, _pq])) -> eq_nat([_qq, m]), {
_pq -> s(s(s(z)))  ;  _qq -> z  ;  m -> s(s(s(z)))  ;  n -> s(s(s(z)))
})

-------------------------------------------
Step 54, which took 0.162566 s (model generation: 0.161326,  model checking: 0.001240):

Model:
|_
{
minus -> 
{{{
Q={q_gen_4293, q_gen_4295, q_gen_4301, q_gen_4308, q_gen_4313, q_gen_4318, q_gen_4324, q_gen_4341},
Q_f={q_gen_4293},
Delta=
{
<z>() -> q_gen_4301
<s>(q_gen_4301) -> q_gen_4313
<s>(q_gen_4313) -> q_gen_4313
<s, s>(q_gen_4295) -> q_gen_4295
<z, s>(q_gen_4313) -> q_gen_4295
<z, z>() -> q_gen_4295
<s, s>(q_gen_4318) -> q_gen_4318
<z, s>(q_gen_4301) -> q_gen_4318
<s, z>(q_gen_4301) -> q_gen_4341
<s, z>(q_gen_4313) -> q_gen_4341
<s, s, s>(q_gen_4308) -> q_gen_4293
<s, s, z>(q_gen_4295) -> q_gen_4293
<s, s, z>(q_gen_4318) -> q_gen_4293
<s, z, s>(q_gen_4295) -> q_gen_4293
<z, s, z>(q_gen_4301) -> q_gen_4293
<z, s, z>(q_gen_4313) -> q_gen_4293
<z, z, z>() -> q_gen_4293
<s, s, s>(q_gen_4293) -> q_gen_4308
<s, s, s>(q_gen_4324) -> q_gen_4308
<s, s, z>(q_gen_4341) -> q_gen_4308
<s, z, s>(q_gen_4341) -> q_gen_4308
<s, z, z>(q_gen_4301) -> q_gen_4308
<s, z, s>(q_gen_4318) -> q_gen_4324
<s, z, z>(q_gen_4313) -> q_gen_4324
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_4292, q_gen_4297, q_gen_4305, q_gen_4306, q_gen_4316, q_gen_4322, q_gen_4323},
Q_f={q_gen_4292},
Delta=
{
<z>() -> q_gen_4306
<s>(q_gen_4306) -> q_gen_4323
<s>(q_gen_4323) -> q_gen_4323
<s, s>(q_gen_4297) -> q_gen_4297
<z, z>() -> q_gen_4297
<s, s>(q_gen_4316) -> q_gen_4316
<z, s>(q_gen_4306) -> q_gen_4316
<z, s>(q_gen_4323) -> q_gen_4316
<s, s, s>(q_gen_4305) -> q_gen_4292
<s, z, s>(q_gen_4297) -> q_gen_4292
<z, s, s>(q_gen_4297) -> q_gen_4292
<z, z, z>() -> q_gen_4292
<s, s, s>(q_gen_4292) -> q_gen_4305
<s, s, s>(q_gen_4322) -> q_gen_4305
<s, z, s>(q_gen_4316) -> q_gen_4305
<z, s, s>(q_gen_4316) -> q_gen_4305
<z, z, s>(q_gen_4306) -> q_gen_4305
<z, z, s>(q_gen_4323) -> q_gen_4322
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 43
() -> minus([z, y, z]) -> 43
() -> plus([n, z, n]) -> 43
(minus([_pq, n, _qq]) /\ plus([m, n, _pq])) -> eq_nat([_qq, m]) -> 46
(minus([u, x2, _fq])) -> minus([s(u), s(x2), _fq]) -> 46
(plus([n, mm, _kq])) -> plus([n, s(mm), s(_kq)]) -> 48
}
Sat witness: Found: ((plus([n, mm, _kq])) -> plus([n, s(mm), s(_kq)]), {
_kq -> s(s(s(s(z))))  ;  mm -> s(s(z))  ;  n -> s(s(z))
})

-------------------------------------------
Step 55, which took 0.194048 s (model generation: 0.192629,  model checking: 0.001419):

Model:
|_
{
minus -> 
{{{
Q={q_gen_4293, q_gen_4295, q_gen_4301, q_gen_4308, q_gen_4313, q_gen_4318, q_gen_4341, q_gen_4362},
Q_f={q_gen_4293},
Delta=
{
<z>() -> q_gen_4301
<s>(q_gen_4301) -> q_gen_4313
<s>(q_gen_4313) -> q_gen_4313
<s, s>(q_gen_4295) -> q_gen_4295
<z, s>(q_gen_4313) -> q_gen_4295
<z, z>() -> q_gen_4295
<s, s>(q_gen_4318) -> q_gen_4318
<z, s>(q_gen_4301) -> q_gen_4318
<s, z>(q_gen_4301) -> q_gen_4341
<s, z>(q_gen_4313) -> q_gen_4341
<s, s, s>(q_gen_4308) -> q_gen_4293
<s, s, z>(q_gen_4295) -> q_gen_4293
<s, s, z>(q_gen_4318) -> q_gen_4293
<s, z, s>(q_gen_4295) -> q_gen_4293
<z, s, z>(q_gen_4301) -> q_gen_4293
<z, s, z>(q_gen_4313) -> q_gen_4293
<z, z, z>() -> q_gen_4293
<s, s, s>(q_gen_4293) -> q_gen_4308
<s, s, s>(q_gen_4362) -> q_gen_4308
<s, s, z>(q_gen_4341) -> q_gen_4308
<s, z, s>(q_gen_4318) -> q_gen_4308
<s, z, s>(q_gen_4341) -> q_gen_4308
<s, z, z>(q_gen_4301) -> q_gen_4308
<s, z, z>(q_gen_4313) -> q_gen_4362
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_4292, q_gen_4297, q_gen_4299, q_gen_4305, q_gen_4306, q_gen_4309, q_gen_4316},
Q_f={q_gen_4292, q_gen_4299},
Delta=
{
<s>(q_gen_4306) -> q_gen_4306
<z>() -> q_gen_4306
<s, s>(q_gen_4297) -> q_gen_4297
<z, z>() -> q_gen_4297
<s, s>(q_gen_4316) -> q_gen_4316
<z, s>(q_gen_4306) -> q_gen_4316
<s, s, s>(q_gen_4299) -> q_gen_4292
<z, s, s>(q_gen_4297) -> q_gen_4292
<z, z, z>() -> q_gen_4292
<s, s, s>(q_gen_4305) -> q_gen_4299
<s, z, s>(q_gen_4297) -> q_gen_4299
<s, z, s>(q_gen_4316) -> q_gen_4305
<z, s, s>(q_gen_4316) -> q_gen_4305
<z, z, s>(q_gen_4306) -> q_gen_4305
<s, s, s>(q_gen_4292) -> q_gen_4309
<s, s, s>(q_gen_4309) -> q_gen_4309
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 44
() -> minus([z, y, z]) -> 44
() -> plus([n, z, n]) -> 44
(minus([_pq, n, _qq]) /\ plus([m, n, _pq])) -> eq_nat([_qq, m]) -> 46
(minus([u, x2, _fq])) -> minus([s(u), s(x2), _fq]) -> 49
(plus([n, mm, _kq])) -> plus([n, s(mm), s(_kq)]) -> 48
}
Sat witness: Found: ((minus([u, x2, _fq])) -> minus([s(u), s(x2), _fq]), {
_fq -> s(s(s(s(z))))  ;  u -> s(z)  ;  x2 -> z
})

-------------------------------------------
Step 56, which took 0.224706 s (model generation: 0.223400,  model checking: 0.001306):

Model:
|_
{
minus -> 
{{{
Q={q_gen_4293, q_gen_4295, q_gen_4301, q_gen_4308, q_gen_4313, q_gen_4318, q_gen_4324, q_gen_4341},
Q_f={q_gen_4293},
Delta=
{
<s>(q_gen_4313) -> q_gen_4301
<z>() -> q_gen_4301
<s>(q_gen_4301) -> q_gen_4313
<s, s>(q_gen_4295) -> q_gen_4295
<z, s>(q_gen_4313) -> q_gen_4295
<z, z>() -> q_gen_4295
<s, s>(q_gen_4318) -> q_gen_4318
<z, s>(q_gen_4301) -> q_gen_4318
<s, z>(q_gen_4301) -> q_gen_4341
<s, z>(q_gen_4313) -> q_gen_4341
<s, s, s>(q_gen_4308) -> q_gen_4293
<s, s, z>(q_gen_4295) -> q_gen_4293
<s, s, z>(q_gen_4318) -> q_gen_4293
<s, z, s>(q_gen_4295) -> q_gen_4293
<z, s, z>(q_gen_4301) -> q_gen_4293
<z, s, z>(q_gen_4313) -> q_gen_4293
<z, z, z>() -> q_gen_4293
<s, s, s>(q_gen_4293) -> q_gen_4308
<s, s, s>(q_gen_4324) -> q_gen_4308
<s, s, z>(q_gen_4341) -> q_gen_4308
<s, z, s>(q_gen_4341) -> q_gen_4308
<s, z, z>(q_gen_4301) -> q_gen_4308
<s, z, s>(q_gen_4318) -> q_gen_4324
<s, z, z>(q_gen_4313) -> q_gen_4324
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_4292, q_gen_4297, q_gen_4305, q_gen_4306, q_gen_4316, q_gen_4322, q_gen_4323},
Q_f={q_gen_4292},
Delta=
{
<s>(q_gen_4323) -> q_gen_4306
<z>() -> q_gen_4306
<s>(q_gen_4306) -> q_gen_4323
<s, s>(q_gen_4297) -> q_gen_4297
<z, s>(q_gen_4323) -> q_gen_4297
<z, z>() -> q_gen_4297
<s, s>(q_gen_4316) -> q_gen_4316
<z, s>(q_gen_4306) -> q_gen_4316
<s, s, s>(q_gen_4305) -> q_gen_4292
<s, z, s>(q_gen_4297) -> q_gen_4292
<z, s, s>(q_gen_4297) -> q_gen_4292
<z, z, z>() -> q_gen_4292
<s, s, s>(q_gen_4292) -> q_gen_4305
<s, s, s>(q_gen_4322) -> q_gen_4305
<s, z, s>(q_gen_4316) -> q_gen_4305
<z, s, s>(q_gen_4316) -> q_gen_4305
<z, z, s>(q_gen_4306) -> q_gen_4305
<z, z, s>(q_gen_4323) -> q_gen_4322
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 45
() -> minus([z, y, z]) -> 45
() -> plus([n, z, n]) -> 45
(minus([_pq, n, _qq]) /\ plus([m, n, _pq])) -> eq_nat([_qq, m]) -> 49
(minus([u, x2, _fq])) -> minus([s(u), s(x2), _fq]) -> 49
(plus([n, mm, _kq])) -> plus([n, s(mm), s(_kq)]) -> 48
}
Sat witness: Found: ((minus([_pq, n, _qq]) /\ plus([m, n, _pq])) -> eq_nat([_qq, m]), {
_pq -> s(s(s(z)))  ;  _qq -> s(s(z))  ;  m -> z  ;  n -> s(z)
})

-------------------------------------------
Step 57, which took 0.224659 s (model generation: 0.223375,  model checking: 0.001284):

Model:
|_
{
minus -> 
{{{
Q={q_gen_4293, q_gen_4295, q_gen_4301, q_gen_4308, q_gen_4313, q_gen_4318, q_gen_4341, q_gen_4362},
Q_f={q_gen_4293},
Delta=
{
<s>(q_gen_4313) -> q_gen_4301
<z>() -> q_gen_4301
<s>(q_gen_4301) -> q_gen_4313
<s, s>(q_gen_4295) -> q_gen_4295
<z, s>(q_gen_4313) -> q_gen_4295
<z, z>() -> q_gen_4295
<s, s>(q_gen_4318) -> q_gen_4318
<z, s>(q_gen_4301) -> q_gen_4318
<s, z>(q_gen_4301) -> q_gen_4341
<s, z>(q_gen_4313) -> q_gen_4341
<s, s, s>(q_gen_4308) -> q_gen_4293
<s, s, z>(q_gen_4295) -> q_gen_4293
<s, s, z>(q_gen_4318) -> q_gen_4293
<s, z, s>(q_gen_4295) -> q_gen_4293
<z, s, z>(q_gen_4301) -> q_gen_4293
<z, s, z>(q_gen_4313) -> q_gen_4293
<z, z, z>() -> q_gen_4293
<s, s, s>(q_gen_4293) -> q_gen_4308
<s, s, s>(q_gen_4362) -> q_gen_4308
<s, s, z>(q_gen_4341) -> q_gen_4308
<s, z, s>(q_gen_4318) -> q_gen_4308
<s, z, s>(q_gen_4341) -> q_gen_4308
<s, z, z>(q_gen_4301) -> q_gen_4308
<s, z, z>(q_gen_4313) -> q_gen_4362
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_4292, q_gen_4297, q_gen_4299, q_gen_4305, q_gen_4306, q_gen_4309, q_gen_4316},
Q_f={q_gen_4292, q_gen_4299},
Delta=
{
<s>(q_gen_4306) -> q_gen_4306
<z>() -> q_gen_4306
<s, s>(q_gen_4297) -> q_gen_4297
<z, z>() -> q_gen_4297
<s, s>(q_gen_4316) -> q_gen_4316
<z, s>(q_gen_4306) -> q_gen_4316
<s, s, s>(q_gen_4299) -> q_gen_4292
<z, s, s>(q_gen_4297) -> q_gen_4292
<z, z, z>() -> q_gen_4292
<s, s, s>(q_gen_4305) -> q_gen_4299
<s, z, s>(q_gen_4297) -> q_gen_4299
<s, z, s>(q_gen_4316) -> q_gen_4305
<z, s, s>(q_gen_4316) -> q_gen_4305
<z, z, s>(q_gen_4306) -> q_gen_4305
<s, s, s>(q_gen_4292) -> q_gen_4309
<s, s, s>(q_gen_4309) -> q_gen_4309
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 46
() -> minus([z, y, z]) -> 46
() -> plus([n, z, n]) -> 46
(minus([_pq, n, _qq]) /\ plus([m, n, _pq])) -> eq_nat([_qq, m]) -> 49
(minus([u, x2, _fq])) -> minus([s(u), s(x2), _fq]) -> 49
(plus([n, mm, _kq])) -> plus([n, s(mm), s(_kq)]) -> 51
}
Sat witness: Found: ((plus([n, mm, _kq])) -> plus([n, s(mm), s(_kq)]), {
_kq -> s(s(s(s(z))))  ;  mm -> s(s(z))  ;  n -> s(s(s(z)))
})

-------------------------------------------
Step 58, which took 0.211954 s (model generation: 0.210874,  model checking: 0.001080):

Model:
|_
{
minus -> 
{{{
Q={q_gen_4293, q_gen_4295, q_gen_4301, q_gen_4308, q_gen_4313, q_gen_4318, q_gen_4341, q_gen_4362},
Q_f={q_gen_4293},
Delta=
{
<s>(q_gen_4313) -> q_gen_4301
<z>() -> q_gen_4301
<s>(q_gen_4301) -> q_gen_4313
<s, s>(q_gen_4295) -> q_gen_4295
<z, s>(q_gen_4313) -> q_gen_4295
<z, z>() -> q_gen_4295
<s, s>(q_gen_4318) -> q_gen_4318
<z, s>(q_gen_4301) -> q_gen_4318
<s, z>(q_gen_4301) -> q_gen_4341
<s, z>(q_gen_4313) -> q_gen_4341
<s, s, s>(q_gen_4308) -> q_gen_4293
<s, s, z>(q_gen_4295) -> q_gen_4293
<s, s, z>(q_gen_4318) -> q_gen_4293
<s, z, s>(q_gen_4295) -> q_gen_4293
<z, s, z>(q_gen_4301) -> q_gen_4293
<z, s, z>(q_gen_4313) -> q_gen_4293
<z, z, z>() -> q_gen_4293
<s, s, s>(q_gen_4293) -> q_gen_4308
<s, s, s>(q_gen_4362) -> q_gen_4308
<s, s, z>(q_gen_4341) -> q_gen_4308
<s, z, s>(q_gen_4318) -> q_gen_4308
<s, z, s>(q_gen_4341) -> q_gen_4308
<s, z, z>(q_gen_4301) -> q_gen_4308
<s, z, z>(q_gen_4313) -> q_gen_4362
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_4292, q_gen_4297, q_gen_4299, q_gen_4305, q_gen_4306, q_gen_4309, q_gen_4316},
Q_f={q_gen_4292, q_gen_4299},
Delta=
{
<s>(q_gen_4306) -> q_gen_4306
<z>() -> q_gen_4306
<s, s>(q_gen_4297) -> q_gen_4297
<s, s>(q_gen_4316) -> q_gen_4297
<z, z>() -> q_gen_4297
<z, s>(q_gen_4306) -> q_gen_4316
<z, s, s>(q_gen_4297) -> q_gen_4292
<z, z, z>() -> q_gen_4292
<s, s, s>(q_gen_4299) -> q_gen_4299
<s, s, s>(q_gen_4305) -> q_gen_4299
<s, z, s>(q_gen_4297) -> q_gen_4299
<s, z, s>(q_gen_4316) -> q_gen_4305
<z, s, s>(q_gen_4316) -> q_gen_4305
<z, z, s>(q_gen_4306) -> q_gen_4305
<s, s, s>(q_gen_4292) -> q_gen_4309
<s, s, s>(q_gen_4309) -> q_gen_4309
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 47
() -> minus([z, y, z]) -> 47
() -> plus([n, z, n]) -> 47
(minus([_pq, n, _qq]) /\ plus([m, n, _pq])) -> eq_nat([_qq, m]) -> 49
(minus([u, x2, _fq])) -> minus([s(u), s(x2), _fq]) -> 52
(plus([n, mm, _kq])) -> plus([n, s(mm), s(_kq)]) -> 51
}
Sat witness: Found: ((minus([u, x2, _fq])) -> minus([s(u), s(x2), _fq]), {
_fq -> s(s(z))  ;  u -> s(s(s(s(z))))  ;  x2 -> s(s(z))
})

-------------------------------------------
Step 59, which took 0.231044 s (model generation: 0.230549,  model checking: 0.000495):

Model:
|_
{
minus -> 
{{{
Q={q_gen_4293, q_gen_4294, q_gen_4295, q_gen_4301, q_gen_4303, q_gen_4308, q_gen_4313, q_gen_4318, q_gen_4341, q_gen_4362},
Q_f={q_gen_4293, q_gen_4294},
Delta=
{
<s>(q_gen_4313) -> q_gen_4301
<z>() -> q_gen_4301
<s>(q_gen_4301) -> q_gen_4313
<z, s>(q_gen_4313) -> q_gen_4295
<z, z>() -> q_gen_4295
<s, s>(q_gen_4295) -> q_gen_4303
<s, s>(q_gen_4318) -> q_gen_4303
<z, s>(q_gen_4301) -> q_gen_4318
<s, s>(q_gen_4303) -> q_gen_4341
<s, z>(q_gen_4301) -> q_gen_4341
<s, z>(q_gen_4313) -> q_gen_4341
<s, s, s>(q_gen_4294) -> q_gen_4293
<s, s, z>(q_gen_4295) -> q_gen_4293
<s, s, z>(q_gen_4318) -> q_gen_4293
<s, z, s>(q_gen_4303) -> q_gen_4293
<z, s, z>(q_gen_4301) -> q_gen_4293
<z, s, z>(q_gen_4313) -> q_gen_4293
<z, z, z>() -> q_gen_4293
<s, s, s>(q_gen_4308) -> q_gen_4294
<s, s, z>(q_gen_4303) -> q_gen_4294
<s, z, s>(q_gen_4295) -> q_gen_4294
<s, z, s>(q_gen_4341) -> q_gen_4294
<s, s, s>(q_gen_4293) -> q_gen_4308
<s, s, s>(q_gen_4362) -> q_gen_4308
<s, s, z>(q_gen_4341) -> q_gen_4308
<s, z, s>(q_gen_4318) -> q_gen_4308
<s, z, z>(q_gen_4301) -> q_gen_4308
<s, z, z>(q_gen_4313) -> q_gen_4362
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_4292, q_gen_4297, q_gen_4299, q_gen_4305, q_gen_4306, q_gen_4316},
Q_f={q_gen_4292, q_gen_4299},
Delta=
{
<s>(q_gen_4306) -> q_gen_4306
<z>() -> q_gen_4306
<s, s>(q_gen_4297) -> q_gen_4297
<z, z>() -> q_gen_4297
<s, s>(q_gen_4316) -> q_gen_4316
<z, s>(q_gen_4306) -> q_gen_4316
<z, s, s>(q_gen_4297) -> q_gen_4292
<z, z, z>() -> q_gen_4292
<s, s, s>(q_gen_4299) -> q_gen_4299
<s, s, s>(q_gen_4305) -> q_gen_4299
<s, z, s>(q_gen_4297) -> q_gen_4299
<s, s, s>(q_gen_4292) -> q_gen_4305
<s, z, s>(q_gen_4316) -> q_gen_4305
<z, s, s>(q_gen_4316) -> q_gen_4305
<z, z, s>(q_gen_4306) -> q_gen_4305
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 50
() -> minus([z, y, z]) -> 48
() -> plus([n, z, n]) -> 48
(minus([_pq, n, _qq]) /\ plus([m, n, _pq])) -> eq_nat([_qq, m]) -> 49
(minus([u, x2, _fq])) -> minus([s(u), s(x2), _fq]) -> 52
(plus([n, mm, _kq])) -> plus([n, s(mm), s(_kq)]) -> 51
}
Sat witness: Found: (() -> minus([s(u), z, s(u)]), {
u -> s(s(s(z)))
})

-------------------------------------------
Step 60, which took 0.402933 s (model generation: 0.401767,  model checking: 0.001166):

Model:
|_
{
minus -> 
{{{
Q={q_gen_4293, q_gen_4294, q_gen_4295, q_gen_4301, q_gen_4303, q_gen_4308, q_gen_4313, q_gen_4318, q_gen_4341, q_gen_4362},
Q_f={q_gen_4293, q_gen_4294},
Delta=
{
<s>(q_gen_4313) -> q_gen_4301
<z>() -> q_gen_4301
<s>(q_gen_4301) -> q_gen_4313
<z, z>() -> q_gen_4295
<s, s>(q_gen_4295) -> q_gen_4303
<s, s>(q_gen_4341) -> q_gen_4303
<z, s>(q_gen_4313) -> q_gen_4303
<s, s>(q_gen_4318) -> q_gen_4318
<z, s>(q_gen_4301) -> q_gen_4318
<s, s>(q_gen_4303) -> q_gen_4341
<s, z>(q_gen_4301) -> q_gen_4341
<s, z>(q_gen_4313) -> q_gen_4341
<s, s, s>(q_gen_4294) -> q_gen_4293
<s, s, z>(q_gen_4295) -> q_gen_4293
<s, s, z>(q_gen_4303) -> q_gen_4293
<s, z, s>(q_gen_4303) -> q_gen_4293
<z, s, z>(q_gen_4313) -> q_gen_4293
<z, z, z>() -> q_gen_4293
<s, s, s>(q_gen_4308) -> q_gen_4294
<s, s, z>(q_gen_4318) -> q_gen_4294
<s, z, s>(q_gen_4295) -> q_gen_4294
<s, z, s>(q_gen_4341) -> q_gen_4294
<z, s, z>(q_gen_4301) -> q_gen_4294
<s, s, s>(q_gen_4293) -> q_gen_4308
<s, s, s>(q_gen_4362) -> q_gen_4308
<s, s, z>(q_gen_4341) -> q_gen_4308
<s, z, s>(q_gen_4318) -> q_gen_4308
<s, z, z>(q_gen_4301) -> q_gen_4308
<s, z, z>(q_gen_4313) -> q_gen_4362
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_4292, q_gen_4297, q_gen_4299, q_gen_4305, q_gen_4306, q_gen_4316},
Q_f={q_gen_4292, q_gen_4299},
Delta=
{
<s>(q_gen_4306) -> q_gen_4306
<z>() -> q_gen_4306
<s, s>(q_gen_4297) -> q_gen_4297
<z, z>() -> q_gen_4297
<s, s>(q_gen_4316) -> q_gen_4316
<z, s>(q_gen_4306) -> q_gen_4316
<z, s, s>(q_gen_4297) -> q_gen_4292
<z, z, z>() -> q_gen_4292
<s, s, s>(q_gen_4299) -> q_gen_4299
<s, s, s>(q_gen_4305) -> q_gen_4299
<s, z, s>(q_gen_4297) -> q_gen_4299
<s, s, s>(q_gen_4292) -> q_gen_4305
<s, z, s>(q_gen_4316) -> q_gen_4305
<z, s, s>(q_gen_4316) -> q_gen_4305
<z, z, s>(q_gen_4306) -> q_gen_4305
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 50
() -> minus([z, y, z]) -> 49
() -> plus([n, z, n]) -> 49
(minus([_pq, n, _qq]) /\ plus([m, n, _pq])) -> eq_nat([_qq, m]) -> 52
(minus([u, x2, _fq])) -> minus([s(u), s(x2), _fq]) -> 52
(plus([n, mm, _kq])) -> plus([n, s(mm), s(_kq)]) -> 51
}
Sat witness: Found: ((minus([_pq, n, _qq]) /\ plus([m, n, _pq])) -> eq_nat([_qq, m]), {
_pq -> s(s(z))  ;  _qq -> s(z)  ;  m -> s(s(z))  ;  n -> s(z)
})

-------------------------------------------
Step 61, which took 0.499171 s (model generation: 0.497494,  model checking: 0.001677):

Model:
|_
{
minus -> 
{{{
Q={q_gen_4293, q_gen_4294, q_gen_4295, q_gen_4301, q_gen_4303, q_gen_4308, q_gen_4313, q_gen_4318, q_gen_4324, q_gen_4341},
Q_f={q_gen_4293, q_gen_4294},
Delta=
{
<z>() -> q_gen_4301
<s>(q_gen_4301) -> q_gen_4313
<s>(q_gen_4313) -> q_gen_4313
<z, z>() -> q_gen_4295
<s, s>(q_gen_4295) -> q_gen_4303
<s, s>(q_gen_4318) -> q_gen_4303
<z, s>(q_gen_4301) -> q_gen_4318
<z, s>(q_gen_4313) -> q_gen_4318
<s, s>(q_gen_4303) -> q_gen_4341
<s, s>(q_gen_4341) -> q_gen_4341
<s, z>(q_gen_4301) -> q_gen_4341
<s, z>(q_gen_4313) -> q_gen_4341
<s, s, s>(q_gen_4294) -> q_gen_4293
<s, s, z>(q_gen_4295) -> q_gen_4293
<s, s, z>(q_gen_4318) -> q_gen_4293
<z, s, z>(q_gen_4301) -> q_gen_4293
<z, z, z>() -> q_gen_4293
<s, s, s>(q_gen_4308) -> q_gen_4294
<s, s, z>(q_gen_4303) -> q_gen_4294
<s, z, s>(q_gen_4295) -> q_gen_4294
<s, z, s>(q_gen_4303) -> q_gen_4294
<s, z, s>(q_gen_4341) -> q_gen_4294
<z, s, z>(q_gen_4313) -> q_gen_4294
<s, s, s>(q_gen_4293) -> q_gen_4308
<s, s, s>(q_gen_4324) -> q_gen_4308
<s, s, z>(q_gen_4341) -> q_gen_4308
<s, z, z>(q_gen_4301) -> q_gen_4308
<s, z, s>(q_gen_4318) -> q_gen_4324
<s, z, z>(q_gen_4313) -> q_gen_4324
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_4292, q_gen_4297, q_gen_4304, q_gen_4305, q_gen_4306, q_gen_4316},
Q_f={q_gen_4292, q_gen_4304},
Delta=
{
<s>(q_gen_4306) -> q_gen_4306
<z>() -> q_gen_4306
<s, s>(q_gen_4297) -> q_gen_4297
<z, z>() -> q_gen_4297
<s, s>(q_gen_4316) -> q_gen_4316
<z, s>(q_gen_4306) -> q_gen_4316
<s, z, s>(q_gen_4297) -> q_gen_4292
<z, s, s>(q_gen_4297) -> q_gen_4292
<z, z, z>() -> q_gen_4292
<s, s, s>(q_gen_4304) -> q_gen_4304
<s, s, s>(q_gen_4305) -> q_gen_4304
<s, s, s>(q_gen_4292) -> q_gen_4305
<s, z, s>(q_gen_4316) -> q_gen_4305
<z, s, s>(q_gen_4316) -> q_gen_4305
<z, z, s>(q_gen_4306) -> q_gen_4305
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 51
() -> minus([z, y, z]) -> 50
() -> plus([n, z, n]) -> 50
(minus([_pq, n, _qq]) /\ plus([m, n, _pq])) -> eq_nat([_qq, m]) -> 52
(minus([u, x2, _fq])) -> minus([s(u), s(x2), _fq]) -> 55
(plus([n, mm, _kq])) -> plus([n, s(mm), s(_kq)]) -> 52
}
Sat witness: Found: ((minus([u, x2, _fq])) -> minus([s(u), s(x2), _fq]), {
_fq -> s(z)  ;  u -> s(s(z))  ;  x2 -> z
})

-------------------------------------------
Step 62, which took 0.350048 s (model generation: 0.349079,  model checking: 0.000969):

Model:
|_
{
minus -> 
{{{
Q={q_gen_4293, q_gen_4294, q_gen_4295, q_gen_4301, q_gen_4308, q_gen_4313, q_gen_4318, q_gen_4324, q_gen_4341},
Q_f={q_gen_4293, q_gen_4294},
Delta=
{
<s>(q_gen_4313) -> q_gen_4301
<z>() -> q_gen_4301
<s>(q_gen_4301) -> q_gen_4313
<s, s>(q_gen_4295) -> q_gen_4295
<z, z>() -> q_gen_4295
<s, s>(q_gen_4318) -> q_gen_4318
<z, s>(q_gen_4301) -> q_gen_4318
<z, s>(q_gen_4313) -> q_gen_4318
<s, z>(q_gen_4301) -> q_gen_4341
<s, z>(q_gen_4313) -> q_gen_4341
<s, s, z>(q_gen_4295) -> q_gen_4293
<s, s, z>(q_gen_4318) -> q_gen_4293
<z, s, z>(q_gen_4301) -> q_gen_4293
<z, z, z>() -> q_gen_4293
<s, s, s>(q_gen_4294) -> q_gen_4294
<s, s, s>(q_gen_4308) -> q_gen_4294
<s, z, s>(q_gen_4295) -> q_gen_4294
<z, s, z>(q_gen_4313) -> q_gen_4294
<s, s, s>(q_gen_4293) -> q_gen_4308
<s, s, s>(q_gen_4324) -> q_gen_4308
<s, s, z>(q_gen_4341) -> q_gen_4308
<s, z, s>(q_gen_4341) -> q_gen_4308
<s, z, z>(q_gen_4301) -> q_gen_4308
<s, z, s>(q_gen_4318) -> q_gen_4324
<s, z, z>(q_gen_4313) -> q_gen_4324
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_4292, q_gen_4297, q_gen_4304, q_gen_4305, q_gen_4306, q_gen_4309, q_gen_4316},
Q_f={q_gen_4292, q_gen_4304},
Delta=
{
<s>(q_gen_4306) -> q_gen_4306
<z>() -> q_gen_4306
<s, s>(q_gen_4297) -> q_gen_4297
<z, z>() -> q_gen_4297
<s, s>(q_gen_4316) -> q_gen_4316
<z, s>(q_gen_4306) -> q_gen_4316
<s, s, s>(q_gen_4304) -> q_gen_4292
<s, z, s>(q_gen_4297) -> q_gen_4292
<z, s, s>(q_gen_4297) -> q_gen_4292
<z, z, z>() -> q_gen_4292
<s, s, s>(q_gen_4305) -> q_gen_4304
<s, z, s>(q_gen_4316) -> q_gen_4304
<z, s, s>(q_gen_4316) -> q_gen_4305
<z, z, s>(q_gen_4306) -> q_gen_4305
<s, s, s>(q_gen_4292) -> q_gen_4309
<s, s, s>(q_gen_4309) -> q_gen_4309
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 52
() -> minus([z, y, z]) -> 51
() -> plus([n, z, n]) -> 51
(minus([_pq, n, _qq]) /\ plus([m, n, _pq])) -> eq_nat([_qq, m]) -> 52
(minus([u, x2, _fq])) -> minus([s(u), s(x2), _fq]) -> 55
(plus([n, mm, _kq])) -> plus([n, s(mm), s(_kq)]) -> 55
}
Sat witness: Found: ((plus([n, mm, _kq])) -> plus([n, s(mm), s(_kq)]), {
_kq -> s(s(s(s(z))))  ;  mm -> s(z)  ;  n -> s(s(s(z)))
})

-------------------------------------------
Step 63, which took 0.301825 s (model generation: 0.300705,  model checking: 0.001120):

Model:
|_
{
minus -> 
{{{
Q={q_gen_4293, q_gen_4294, q_gen_4295, q_gen_4301, q_gen_4308, q_gen_4313, q_gen_4318, q_gen_4341, q_gen_4362},
Q_f={q_gen_4293, q_gen_4294},
Delta=
{
<s>(q_gen_4313) -> q_gen_4301
<z>() -> q_gen_4301
<s>(q_gen_4301) -> q_gen_4313
<s, s>(q_gen_4295) -> q_gen_4295
<s, s>(q_gen_4318) -> q_gen_4295
<z, s>(q_gen_4313) -> q_gen_4295
<z, z>() -> q_gen_4295
<z, s>(q_gen_4301) -> q_gen_4318
<s, z>(q_gen_4301) -> q_gen_4341
<s, z>(q_gen_4313) -> q_gen_4341
<s, s, s>(q_gen_4294) -> q_gen_4293
<s, s, z>(q_gen_4295) -> q_gen_4293
<z, s, z>(q_gen_4313) -> q_gen_4293
<z, z, z>() -> q_gen_4293
<s, s, s>(q_gen_4308) -> q_gen_4294
<s, s, z>(q_gen_4318) -> q_gen_4294
<s, z, s>(q_gen_4295) -> q_gen_4294
<z, s, z>(q_gen_4301) -> q_gen_4294
<s, s, s>(q_gen_4293) -> q_gen_4308
<s, s, s>(q_gen_4362) -> q_gen_4308
<s, s, z>(q_gen_4341) -> q_gen_4308
<s, z, s>(q_gen_4318) -> q_gen_4308
<s, z, s>(q_gen_4341) -> q_gen_4308
<s, z, z>(q_gen_4301) -> q_gen_4308
<s, z, z>(q_gen_4313) -> q_gen_4362
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_4292, q_gen_4297, q_gen_4304, q_gen_4305, q_gen_4306, q_gen_4309, q_gen_4316},
Q_f={q_gen_4292, q_gen_4304},
Delta=
{
<s>(q_gen_4306) -> q_gen_4306
<z>() -> q_gen_4306
<s, s>(q_gen_4297) -> q_gen_4297
<z, z>() -> q_gen_4297
<s, s>(q_gen_4316) -> q_gen_4316
<z, s>(q_gen_4306) -> q_gen_4316
<s, z, s>(q_gen_4297) -> q_gen_4292
<z, s, s>(q_gen_4297) -> q_gen_4292
<z, z, z>() -> q_gen_4292
<s, s, s>(q_gen_4304) -> q_gen_4304
<s, s, s>(q_gen_4305) -> q_gen_4304
<s, z, s>(q_gen_4316) -> q_gen_4305
<z, s, s>(q_gen_4316) -> q_gen_4305
<z, z, s>(q_gen_4306) -> q_gen_4305
<s, s, s>(q_gen_4292) -> q_gen_4309
<s, s, s>(q_gen_4309) -> q_gen_4309
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 52
() -> minus([z, y, z]) -> 52
() -> plus([n, z, n]) -> 52
(minus([_pq, n, _qq]) /\ plus([m, n, _pq])) -> eq_nat([_qq, m]) -> 55
(minus([u, x2, _fq])) -> minus([s(u), s(x2), _fq]) -> 55
(plus([n, mm, _kq])) -> plus([n, s(mm), s(_kq)]) -> 55
}
Sat witness: Found: ((minus([_pq, n, _qq]) /\ plus([m, n, _pq])) -> eq_nat([_qq, m]), {
_pq -> s(s(z))  ;  _qq -> s(s(s(z)))  ;  m -> s(z)  ;  n -> s(z)
})

-------------------------------------------
Step 64, which took 0.327977 s (model generation: 0.326253,  model checking: 0.001724):

Model:
|_
{
minus -> 
{{{
Q={q_gen_4293, q_gen_4295, q_gen_4301, q_gen_4303, q_gen_4308, q_gen_4313, q_gen_4318, q_gen_4324, q_gen_4341, q_gen_4358},
Q_f={q_gen_4293},
Delta=
{
<s>(q_gen_4313) -> q_gen_4301
<z>() -> q_gen_4301
<s>(q_gen_4301) -> q_gen_4313
<z, z>() -> q_gen_4295
<s, s>(q_gen_4295) -> q_gen_4303
<s, s>(q_gen_4358) -> q_gen_4303
<z, s>(q_gen_4313) -> q_gen_4303
<s, s>(q_gen_4318) -> q_gen_4318
<z, s>(q_gen_4301) -> q_gen_4318
<s, z>(q_gen_4301) -> q_gen_4341
<s, s>(q_gen_4303) -> q_gen_4358
<s, z>(q_gen_4313) -> q_gen_4358
<s, s, s>(q_gen_4308) -> q_gen_4293
<s, s, z>(q_gen_4295) -> q_gen_4293
<s, s, z>(q_gen_4303) -> q_gen_4293
<s, s, z>(q_gen_4318) -> q_gen_4293
<s, z, s>(q_gen_4295) -> q_gen_4293
<s, z, s>(q_gen_4303) -> q_gen_4293
<s, z, s>(q_gen_4358) -> q_gen_4293
<z, s, z>(q_gen_4301) -> q_gen_4293
<z, s, z>(q_gen_4313) -> q_gen_4293
<z, z, z>() -> q_gen_4293
<s, s, s>(q_gen_4293) -> q_gen_4308
<s, s, s>(q_gen_4324) -> q_gen_4308
<s, s, z>(q_gen_4341) -> q_gen_4308
<s, z, s>(q_gen_4341) -> q_gen_4308
<s, z, z>(q_gen_4301) -> q_gen_4308
<s, s, z>(q_gen_4358) -> q_gen_4324
<s, z, s>(q_gen_4318) -> q_gen_4324
<s, z, z>(q_gen_4313) -> q_gen_4324
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_4292, q_gen_4297, q_gen_4304, q_gen_4305, q_gen_4306, q_gen_4316},
Q_f={q_gen_4292, q_gen_4304},
Delta=
{
<s>(q_gen_4306) -> q_gen_4306
<z>() -> q_gen_4306
<s, s>(q_gen_4297) -> q_gen_4297
<z, z>() -> q_gen_4297
<s, s>(q_gen_4316) -> q_gen_4316
<z, s>(q_gen_4306) -> q_gen_4316
<s, z, s>(q_gen_4297) -> q_gen_4292
<z, s, s>(q_gen_4297) -> q_gen_4292
<z, z, z>() -> q_gen_4292
<s, s, s>(q_gen_4304) -> q_gen_4304
<s, s, s>(q_gen_4305) -> q_gen_4304
<s, s, s>(q_gen_4292) -> q_gen_4305
<s, z, s>(q_gen_4316) -> q_gen_4305
<z, s, s>(q_gen_4316) -> q_gen_4305
<z, z, s>(q_gen_4306) -> q_gen_4305
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 53
() -> minus([z, y, z]) -> 53
() -> plus([n, z, n]) -> 53
(minus([_pq, n, _qq]) /\ plus([m, n, _pq])) -> eq_nat([_qq, m]) -> 55
(minus([u, x2, _fq])) -> minus([s(u), s(x2), _fq]) -> 58
(plus([n, mm, _kq])) -> plus([n, s(mm), s(_kq)]) -> 56
}
Sat witness: Found: ((minus([u, x2, _fq])) -> minus([s(u), s(x2), _fq]), {
_fq -> z  ;  u -> s(s(z))  ;  x2 -> s(s(z))
})

-------------------------------------------
Step 65, which took 0.347237 s (model generation: 0.346427,  model checking: 0.000810):

Model:
|_
{
minus -> 
{{{
Q={q_gen_4293, q_gen_4294, q_gen_4295, q_gen_4301, q_gen_4308, q_gen_4313, q_gen_4318, q_gen_4324, q_gen_4341},
Q_f={q_gen_4293, q_gen_4294},
Delta=
{
<s>(q_gen_4313) -> q_gen_4301
<z>() -> q_gen_4301
<s>(q_gen_4301) -> q_gen_4313
<s, s>(q_gen_4295) -> q_gen_4295
<z, z>() -> q_gen_4295
<s, s>(q_gen_4318) -> q_gen_4318
<z, s>(q_gen_4301) -> q_gen_4318
<z, s>(q_gen_4313) -> q_gen_4318
<s, z>(q_gen_4301) -> q_gen_4341
<s, z>(q_gen_4313) -> q_gen_4341
<s, s, s>(q_gen_4294) -> q_gen_4293
<s, s, z>(q_gen_4295) -> q_gen_4293
<z, s, z>(q_gen_4301) -> q_gen_4293
<z, z, z>() -> q_gen_4293
<s, s, s>(q_gen_4308) -> q_gen_4294
<s, s, z>(q_gen_4318) -> q_gen_4294
<s, z, s>(q_gen_4295) -> q_gen_4294
<z, s, z>(q_gen_4313) -> q_gen_4294
<s, s, s>(q_gen_4293) -> q_gen_4308
<s, s, s>(q_gen_4324) -> q_gen_4308
<s, s, z>(q_gen_4341) -> q_gen_4308
<s, z, s>(q_gen_4341) -> q_gen_4308
<s, z, z>(q_gen_4301) -> q_gen_4308
<s, z, s>(q_gen_4318) -> q_gen_4324
<s, z, z>(q_gen_4313) -> q_gen_4324
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_4292, q_gen_4297, q_gen_4304, q_gen_4305, q_gen_4306, q_gen_4309, q_gen_4316},
Q_f={q_gen_4292, q_gen_4304},
Delta=
{
<s>(q_gen_4306) -> q_gen_4306
<z>() -> q_gen_4306
<s, s>(q_gen_4297) -> q_gen_4297
<z, z>() -> q_gen_4297
<s, s>(q_gen_4316) -> q_gen_4316
<z, s>(q_gen_4306) -> q_gen_4316
<s, s, s>(q_gen_4309) -> q_gen_4292
<s, z, s>(q_gen_4297) -> q_gen_4292
<z, s, s>(q_gen_4297) -> q_gen_4292
<z, z, z>() -> q_gen_4292
<s, s, s>(q_gen_4304) -> q_gen_4304
<s, s, s>(q_gen_4305) -> q_gen_4304
<s, z, s>(q_gen_4316) -> q_gen_4305
<z, s, s>(q_gen_4316) -> q_gen_4305
<z, z, s>(q_gen_4306) -> q_gen_4305
<s, s, s>(q_gen_4292) -> q_gen_4309
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 54
() -> minus([z, y, z]) -> 54
() -> plus([n, z, n]) -> 54
(minus([_pq, n, _qq]) /\ plus([m, n, _pq])) -> eq_nat([_qq, m]) -> 58
(minus([u, x2, _fq])) -> minus([s(u), s(x2), _fq]) -> 58
(plus([n, mm, _kq])) -> plus([n, s(mm), s(_kq)]) -> 56
}
Sat witness: Found: ((minus([_pq, n, _qq]) /\ plus([m, n, _pq])) -> eq_nat([_qq, m]), {
_pq -> s(s(s(s(z))))  ;  _qq -> s(z)  ;  m -> s(s(z))  ;  n -> s(z)
})

-------------------------------------------
Step 66, which took 0.290421 s (model generation: 0.288536,  model checking: 0.001885):

Model:
|_
{
minus -> 
{{{
Q={q_gen_4293, q_gen_4294, q_gen_4295, q_gen_4301, q_gen_4308, q_gen_4313, q_gen_4318, q_gen_4324, q_gen_4341},
Q_f={q_gen_4293, q_gen_4294},
Delta=
{
<z>() -> q_gen_4301
<s>(q_gen_4301) -> q_gen_4313
<s>(q_gen_4313) -> q_gen_4313
<s, s>(q_gen_4295) -> q_gen_4295
<z, z>() -> q_gen_4295
<s, s>(q_gen_4318) -> q_gen_4318
<z, s>(q_gen_4301) -> q_gen_4318
<z, s>(q_gen_4313) -> q_gen_4318
<s, z>(q_gen_4301) -> q_gen_4341
<s, z>(q_gen_4313) -> q_gen_4341
<s, s, s>(q_gen_4294) -> q_gen_4293
<s, s, z>(q_gen_4295) -> q_gen_4293
<s, s, z>(q_gen_4318) -> q_gen_4293
<z, s, z>(q_gen_4301) -> q_gen_4293
<z, z, z>() -> q_gen_4293
<s, s, s>(q_gen_4308) -> q_gen_4294
<s, z, s>(q_gen_4295) -> q_gen_4294
<z, s, z>(q_gen_4313) -> q_gen_4294
<s, s, s>(q_gen_4293) -> q_gen_4308
<s, s, s>(q_gen_4324) -> q_gen_4308
<s, s, z>(q_gen_4341) -> q_gen_4308
<s, z, s>(q_gen_4341) -> q_gen_4308
<s, z, z>(q_gen_4301) -> q_gen_4308
<s, z, s>(q_gen_4318) -> q_gen_4324
<s, z, z>(q_gen_4313) -> q_gen_4324
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_4292, q_gen_4297, q_gen_4304, q_gen_4305, q_gen_4306, q_gen_4309, q_gen_4316},
Q_f={q_gen_4292, q_gen_4304},
Delta=
{
<s>(q_gen_4306) -> q_gen_4306
<z>() -> q_gen_4306
<s, s>(q_gen_4297) -> q_gen_4297
<z, z>() -> q_gen_4297
<s, s>(q_gen_4316) -> q_gen_4316
<z, s>(q_gen_4306) -> q_gen_4316
<s, z, s>(q_gen_4297) -> q_gen_4292
<z, s, s>(q_gen_4297) -> q_gen_4292
<z, z, z>() -> q_gen_4292
<s, s, s>(q_gen_4304) -> q_gen_4304
<s, s, s>(q_gen_4305) -> q_gen_4304
<s, z, s>(q_gen_4316) -> q_gen_4305
<z, s, s>(q_gen_4316) -> q_gen_4305
<z, z, s>(q_gen_4306) -> q_gen_4305
<s, s, s>(q_gen_4292) -> q_gen_4309
<s, s, s>(q_gen_4309) -> q_gen_4309
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 55
() -> minus([z, y, z]) -> 55
() -> plus([n, z, n]) -> 55
(minus([_pq, n, _qq]) /\ plus([m, n, _pq])) -> eq_nat([_qq, m]) -> 58
(minus([u, x2, _fq])) -> minus([s(u), s(x2), _fq]) -> 61
(plus([n, mm, _kq])) -> plus([n, s(mm), s(_kq)]) -> 57
}
Sat witness: Found: ((minus([u, x2, _fq])) -> minus([s(u), s(x2), _fq]), {
_fq -> s(s(s(z)))  ;  u -> s(s(s(z)))  ;  x2 -> z
})

-------------------------------------------
Step 67, which took 0.857349 s (model generation: 0.855726,  model checking: 0.001623):

Model:
|_
{
minus -> 
{{{
Q={q_gen_4293, q_gen_4294, q_gen_4295, q_gen_4301, q_gen_4308, q_gen_4313, q_gen_4318, q_gen_4324, q_gen_4341},
Q_f={q_gen_4293, q_gen_4294},
Delta=
{
<z>() -> q_gen_4301
<s>(q_gen_4301) -> q_gen_4313
<s>(q_gen_4313) -> q_gen_4313
<s, s>(q_gen_4295) -> q_gen_4295
<s, s>(q_gen_4318) -> q_gen_4295
<z, z>() -> q_gen_4295
<z, s>(q_gen_4301) -> q_gen_4318
<z, s>(q_gen_4313) -> q_gen_4318
<s, s>(q_gen_4341) -> q_gen_4341
<s, z>(q_gen_4301) -> q_gen_4341
<s, z>(q_gen_4313) -> q_gen_4341
<s, s, s>(q_gen_4294) -> q_gen_4293
<s, s, z>(q_gen_4295) -> q_gen_4293
<s, s, z>(q_gen_4318) -> q_gen_4293
<z, s, z>(q_gen_4301) -> q_gen_4293
<z, z, z>() -> q_gen_4293
<s, s, s>(q_gen_4308) -> q_gen_4294
<s, z, s>(q_gen_4295) -> q_gen_4294
<z, s, z>(q_gen_4313) -> q_gen_4294
<s, s, s>(q_gen_4293) -> q_gen_4308
<s, s, s>(q_gen_4324) -> q_gen_4308
<s, s, z>(q_gen_4341) -> q_gen_4308
<s, z, s>(q_gen_4341) -> q_gen_4308
<s, z, z>(q_gen_4301) -> q_gen_4308
<s, z, s>(q_gen_4318) -> q_gen_4324
<s, z, z>(q_gen_4313) -> q_gen_4324
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_4292, q_gen_4297, q_gen_4304, q_gen_4305, q_gen_4306, q_gen_4309, q_gen_4316},
Q_f={q_gen_4292, q_gen_4304},
Delta=
{
<s>(q_gen_4306) -> q_gen_4306
<z>() -> q_gen_4306
<s, s>(q_gen_4297) -> q_gen_4297
<z, z>() -> q_gen_4297
<s, s>(q_gen_4316) -> q_gen_4316
<z, s>(q_gen_4306) -> q_gen_4316
<s, z, s>(q_gen_4297) -> q_gen_4292
<z, s, s>(q_gen_4297) -> q_gen_4292
<z, z, z>() -> q_gen_4292
<s, s, s>(q_gen_4304) -> q_gen_4304
<s, s, s>(q_gen_4305) -> q_gen_4304
<s, z, s>(q_gen_4316) -> q_gen_4305
<z, s, s>(q_gen_4316) -> q_gen_4305
<z, z, s>(q_gen_4306) -> q_gen_4305
<s, s, s>(q_gen_4292) -> q_gen_4309
<s, s, s>(q_gen_4309) -> q_gen_4309
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 56
() -> minus([z, y, z]) -> 56
() -> plus([n, z, n]) -> 56
(minus([_pq, n, _qq]) /\ plus([m, n, _pq])) -> eq_nat([_qq, m]) -> 61
(minus([u, x2, _fq])) -> minus([s(u), s(x2), _fq]) -> 61
(plus([n, mm, _kq])) -> plus([n, s(mm), s(_kq)]) -> 58
}
Sat witness: Found: ((minus([_pq, n, _qq]) /\ plus([m, n, _pq])) -> eq_nat([_qq, m]), {
_pq -> s(s(s(z)))  ;  _qq -> s(s(z))  ;  m -> s(z)  ;  n -> s(z)
})

-------------------------------------------
Step 68, which took 0.461136 s (model generation: 0.459729,  model checking: 0.001407):

Model:
|_
{
minus -> 
{{{
Q={q_gen_4293, q_gen_4294, q_gen_4295, q_gen_4301, q_gen_4308, q_gen_4313, q_gen_4318, q_gen_4324, q_gen_4341},
Q_f={q_gen_4293, q_gen_4294},
Delta=
{
<s>(q_gen_4313) -> q_gen_4301
<z>() -> q_gen_4301
<s>(q_gen_4301) -> q_gen_4313
<s, s>(q_gen_4295) -> q_gen_4295
<s, s>(q_gen_4318) -> q_gen_4295
<z, z>() -> q_gen_4295
<z, s>(q_gen_4301) -> q_gen_4318
<z, s>(q_gen_4313) -> q_gen_4318
<s, s>(q_gen_4341) -> q_gen_4341
<s, z>(q_gen_4301) -> q_gen_4341
<s, z>(q_gen_4313) -> q_gen_4341
<s, s, s>(q_gen_4294) -> q_gen_4293
<s, s, z>(q_gen_4295) -> q_gen_4293
<z, s, z>(q_gen_4301) -> q_gen_4293
<z, s, z>(q_gen_4313) -> q_gen_4293
<z, z, z>() -> q_gen_4293
<s, s, s>(q_gen_4308) -> q_gen_4294
<s, s, z>(q_gen_4318) -> q_gen_4294
<s, z, s>(q_gen_4295) -> q_gen_4294
<s, s, s>(q_gen_4293) -> q_gen_4308
<s, s, s>(q_gen_4324) -> q_gen_4308
<s, s, z>(q_gen_4341) -> q_gen_4308
<s, z, s>(q_gen_4341) -> q_gen_4308
<s, z, z>(q_gen_4301) -> q_gen_4308
<s, z, s>(q_gen_4318) -> q_gen_4324
<s, z, z>(q_gen_4313) -> q_gen_4324
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_4292, q_gen_4297, q_gen_4305, q_gen_4306, q_gen_4316, q_gen_4322, q_gen_4323, q_gen_4343},
Q_f={q_gen_4292},
Delta=
{
<z>() -> q_gen_4306
<s>(q_gen_4306) -> q_gen_4323
<s>(q_gen_4323) -> q_gen_4323
<s, s>(q_gen_4297) -> q_gen_4297
<z, z>() -> q_gen_4297
<s, s>(q_gen_4316) -> q_gen_4316
<z, s>(q_gen_4306) -> q_gen_4316
<z, s>(q_gen_4323) -> q_gen_4343
<s, s, s>(q_gen_4305) -> q_gen_4292
<s, z, s>(q_gen_4297) -> q_gen_4292
<z, s, s>(q_gen_4297) -> q_gen_4292
<z, z, z>() -> q_gen_4292
<s, s, s>(q_gen_4292) -> q_gen_4305
<s, s, s>(q_gen_4322) -> q_gen_4305
<s, z, s>(q_gen_4316) -> q_gen_4305
<z, s, s>(q_gen_4316) -> q_gen_4305
<z, z, s>(q_gen_4306) -> q_gen_4305
<s, z, s>(q_gen_4343) -> q_gen_4322
<z, s, s>(q_gen_4343) -> q_gen_4322
<z, z, s>(q_gen_4323) -> q_gen_4322
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 57
() -> minus([z, y, z]) -> 57
() -> plus([n, z, n]) -> 57
(minus([_pq, n, _qq]) /\ plus([m, n, _pq])) -> eq_nat([_qq, m]) -> 61
(minus([u, x2, _fq])) -> minus([s(u), s(x2), _fq]) -> 61
(plus([n, mm, _kq])) -> plus([n, s(mm), s(_kq)]) -> 61
}
Sat witness: Found: ((plus([n, mm, _kq])) -> plus([n, s(mm), s(_kq)]), {
_kq -> s(s(s(s(s(z)))))  ;  mm -> s(s(z))  ;  n -> s(s(s(z)))
})

-------------------------------------------
Step 69, which took 0.301193 s (model generation: 0.299581,  model checking: 0.001612):

Model:
|_
{
minus -> 
{{{
Q={q_gen_4293, q_gen_4294, q_gen_4295, q_gen_4301, q_gen_4308, q_gen_4313, q_gen_4318, q_gen_4324, q_gen_4341},
Q_f={q_gen_4293, q_gen_4294},
Delta=
{
<z>() -> q_gen_4301
<s>(q_gen_4301) -> q_gen_4313
<s>(q_gen_4313) -> q_gen_4313
<s, s>(q_gen_4295) -> q_gen_4295
<s, s>(q_gen_4341) -> q_gen_4295
<z, z>() -> q_gen_4295
<s, s>(q_gen_4318) -> q_gen_4318
<z, s>(q_gen_4301) -> q_gen_4318
<z, s>(q_gen_4313) -> q_gen_4318
<s, z>(q_gen_4301) -> q_gen_4341
<s, z>(q_gen_4313) -> q_gen_4341
<s, s, s>(q_gen_4294) -> q_gen_4293
<s, s, z>(q_gen_4295) -> q_gen_4293
<z, s, z>(q_gen_4301) -> q_gen_4293
<z, s, z>(q_gen_4313) -> q_gen_4293
<z, z, z>() -> q_gen_4293
<s, s, s>(q_gen_4308) -> q_gen_4294
<s, s, z>(q_gen_4318) -> q_gen_4294
<s, z, s>(q_gen_4295) -> q_gen_4294
<s, s, s>(q_gen_4293) -> q_gen_4308
<s, s, s>(q_gen_4324) -> q_gen_4308
<s, s, z>(q_gen_4341) -> q_gen_4308
<s, z, s>(q_gen_4341) -> q_gen_4308
<s, z, z>(q_gen_4301) -> q_gen_4308
<s, z, s>(q_gen_4318) -> q_gen_4324
<s, z, z>(q_gen_4313) -> q_gen_4324
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_4292, q_gen_4297, q_gen_4305, q_gen_4306, q_gen_4316, q_gen_4322, q_gen_4323, q_gen_4343},
Q_f={q_gen_4292},
Delta=
{
<s>(q_gen_4323) -> q_gen_4306
<z>() -> q_gen_4306
<s>(q_gen_4306) -> q_gen_4323
<s, s>(q_gen_4297) -> q_gen_4297
<z, z>() -> q_gen_4297
<s, s>(q_gen_4316) -> q_gen_4316
<z, s>(q_gen_4306) -> q_gen_4316
<z, s>(q_gen_4323) -> q_gen_4343
<s, s, s>(q_gen_4305) -> q_gen_4292
<s, z, s>(q_gen_4297) -> q_gen_4292
<z, s, s>(q_gen_4297) -> q_gen_4292
<z, z, z>() -> q_gen_4292
<s, s, s>(q_gen_4292) -> q_gen_4305
<s, s, s>(q_gen_4322) -> q_gen_4305
<s, z, s>(q_gen_4316) -> q_gen_4305
<z, s, s>(q_gen_4316) -> q_gen_4305
<z, z, s>(q_gen_4306) -> q_gen_4305
<s, z, s>(q_gen_4343) -> q_gen_4322
<z, s, s>(q_gen_4343) -> q_gen_4322
<z, z, s>(q_gen_4323) -> q_gen_4322
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 58
() -> minus([z, y, z]) -> 58
() -> plus([n, z, n]) -> 58
(minus([_pq, n, _qq]) /\ plus([m, n, _pq])) -> eq_nat([_qq, m]) -> 61
(minus([u, x2, _fq])) -> minus([s(u), s(x2), _fq]) -> 61
(plus([n, mm, _kq])) -> plus([n, s(mm), s(_kq)]) -> 64
}
Sat witness: Found: ((plus([n, mm, _kq])) -> plus([n, s(mm), s(_kq)]), {
_kq -> s(s(s(s(s(z)))))  ;  mm -> s(s(s(z)))  ;  n -> s(s(z))
})

-------------------------------------------
Step 70, which took 0.387290 s (model generation: 0.386445,  model checking: 0.000845):

Model:
|_
{
minus -> 
{{{
Q={q_gen_4293, q_gen_4294, q_gen_4295, q_gen_4301, q_gen_4308, q_gen_4313, q_gen_4318, q_gen_4324, q_gen_4341},
Q_f={q_gen_4293, q_gen_4294},
Delta=
{
<z>() -> q_gen_4301
<s>(q_gen_4301) -> q_gen_4313
<s>(q_gen_4313) -> q_gen_4313
<s, s>(q_gen_4295) -> q_gen_4295
<s, s>(q_gen_4341) -> q_gen_4295
<z, s>(q_gen_4313) -> q_gen_4295
<z, z>() -> q_gen_4295
<s, s>(q_gen_4318) -> q_gen_4318
<z, s>(q_gen_4301) -> q_gen_4318
<s, z>(q_gen_4301) -> q_gen_4341
<s, z>(q_gen_4313) -> q_gen_4341
<s, s, s>(q_gen_4294) -> q_gen_4293
<s, s, z>(q_gen_4295) -> q_gen_4293
<s, s, z>(q_gen_4318) -> q_gen_4293
<z, s, z>(q_gen_4301) -> q_gen_4293
<z, s, z>(q_gen_4313) -> q_gen_4293
<z, z, z>() -> q_gen_4293
<s, s, s>(q_gen_4308) -> q_gen_4294
<s, z, s>(q_gen_4295) -> q_gen_4294
<s, s, s>(q_gen_4293) -> q_gen_4308
<s, s, s>(q_gen_4324) -> q_gen_4308
<s, s, z>(q_gen_4341) -> q_gen_4308
<s, z, s>(q_gen_4341) -> q_gen_4308
<s, z, z>(q_gen_4301) -> q_gen_4308
<s, z, s>(q_gen_4318) -> q_gen_4324
<s, z, z>(q_gen_4313) -> q_gen_4324
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_4292, q_gen_4297, q_gen_4305, q_gen_4306, q_gen_4316, q_gen_4322, q_gen_4323, q_gen_4343},
Q_f={q_gen_4292},
Delta=
{
<s>(q_gen_4323) -> q_gen_4306
<z>() -> q_gen_4306
<s>(q_gen_4306) -> q_gen_4323
<s, s>(q_gen_4297) -> q_gen_4297
<s, s>(q_gen_4343) -> q_gen_4297
<z, z>() -> q_gen_4297
<s, s>(q_gen_4316) -> q_gen_4316
<z, s>(q_gen_4306) -> q_gen_4316
<z, s>(q_gen_4323) -> q_gen_4343
<s, s, s>(q_gen_4305) -> q_gen_4292
<s, z, s>(q_gen_4297) -> q_gen_4292
<z, s, s>(q_gen_4297) -> q_gen_4292
<z, z, z>() -> q_gen_4292
<s, s, s>(q_gen_4292) -> q_gen_4305
<s, s, s>(q_gen_4322) -> q_gen_4305
<s, z, s>(q_gen_4316) -> q_gen_4305
<z, s, s>(q_gen_4316) -> q_gen_4305
<z, z, s>(q_gen_4306) -> q_gen_4305
<s, z, s>(q_gen_4343) -> q_gen_4322
<z, s, s>(q_gen_4343) -> q_gen_4322
<z, z, s>(q_gen_4323) -> q_gen_4322
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 59
() -> minus([z, y, z]) -> 59
() -> plus([n, z, n]) -> 59
(minus([_pq, n, _qq]) /\ plus([m, n, _pq])) -> eq_nat([_qq, m]) -> 61
(minus([u, x2, _fq])) -> minus([s(u), s(x2), _fq]) -> 64
(plus([n, mm, _kq])) -> plus([n, s(mm), s(_kq)]) -> 64
}
Sat witness: Found: ((minus([u, x2, _fq])) -> minus([s(u), s(x2), _fq]), {
_fq -> s(s(s(z)))  ;  u -> s(z)  ;  x2 -> z
})

-------------------------------------------
Step 71, which took 0.426811 s (model generation: 0.425963,  model checking: 0.000848):

Model:
|_
{
minus -> 
{{{
Q={q_gen_4293, q_gen_4294, q_gen_4295, q_gen_4301, q_gen_4308, q_gen_4313, q_gen_4318, q_gen_4324, q_gen_4341},
Q_f={q_gen_4293, q_gen_4294},
Delta=
{
<z>() -> q_gen_4301
<s>(q_gen_4301) -> q_gen_4313
<s>(q_gen_4313) -> q_gen_4313
<s, s>(q_gen_4295) -> q_gen_4295
<s, s>(q_gen_4341) -> q_gen_4295
<z, z>() -> q_gen_4295
<s, s>(q_gen_4318) -> q_gen_4318
<z, s>(q_gen_4301) -> q_gen_4318
<z, s>(q_gen_4313) -> q_gen_4318
<s, z>(q_gen_4301) -> q_gen_4341
<s, z>(q_gen_4313) -> q_gen_4341
<s, s, s>(q_gen_4294) -> q_gen_4293
<s, s, z>(q_gen_4295) -> q_gen_4293
<s, s, z>(q_gen_4318) -> q_gen_4293
<z, s, z>(q_gen_4301) -> q_gen_4293
<z, s, z>(q_gen_4313) -> q_gen_4293
<z, z, z>() -> q_gen_4293
<s, s, s>(q_gen_4308) -> q_gen_4294
<s, z, s>(q_gen_4295) -> q_gen_4294
<s, s, s>(q_gen_4293) -> q_gen_4308
<s, s, s>(q_gen_4324) -> q_gen_4308
<s, s, z>(q_gen_4341) -> q_gen_4308
<s, z, s>(q_gen_4341) -> q_gen_4308
<s, z, z>(q_gen_4301) -> q_gen_4308
<s, z, s>(q_gen_4318) -> q_gen_4324
<s, z, z>(q_gen_4313) -> q_gen_4324
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_4292, q_gen_4297, q_gen_4305, q_gen_4306, q_gen_4316, q_gen_4322, q_gen_4323, q_gen_4343},
Q_f={q_gen_4292},
Delta=
{
<s>(q_gen_4323) -> q_gen_4306
<z>() -> q_gen_4306
<s>(q_gen_4306) -> q_gen_4323
<s, s>(q_gen_4297) -> q_gen_4297
<z, z>() -> q_gen_4297
<s, s>(q_gen_4316) -> q_gen_4316
<z, s>(q_gen_4306) -> q_gen_4316
<s, s>(q_gen_4343) -> q_gen_4343
<z, s>(q_gen_4323) -> q_gen_4343
<s, s, s>(q_gen_4305) -> q_gen_4292
<s, z, s>(q_gen_4297) -> q_gen_4292
<z, s, s>(q_gen_4297) -> q_gen_4292
<z, z, z>() -> q_gen_4292
<s, s, s>(q_gen_4292) -> q_gen_4305
<s, s, s>(q_gen_4322) -> q_gen_4305
<s, z, s>(q_gen_4316) -> q_gen_4305
<z, s, s>(q_gen_4316) -> q_gen_4305
<z, z, s>(q_gen_4306) -> q_gen_4305
<s, z, s>(q_gen_4343) -> q_gen_4322
<z, s, s>(q_gen_4343) -> q_gen_4322
<z, z, s>(q_gen_4323) -> q_gen_4322
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 60
() -> minus([z, y, z]) -> 60
() -> plus([n, z, n]) -> 60
(minus([_pq, n, _qq]) /\ plus([m, n, _pq])) -> eq_nat([_qq, m]) -> 64
(minus([u, x2, _fq])) -> minus([s(u), s(x2), _fq]) -> 64
(plus([n, mm, _kq])) -> plus([n, s(mm), s(_kq)]) -> 64
}
Sat witness: Found: ((minus([_pq, n, _qq]) /\ plus([m, n, _pq])) -> eq_nat([_qq, m]), {
_pq -> s(s(z))  ;  _qq -> s(s(z))  ;  m -> z  ;  n -> s(s(z))
})

-------------------------------------------
Step 72, which took 0.299490 s (model generation: 0.297504,  model checking: 0.001986):

Model:
|_
{
minus -> 
{{{
Q={q_gen_4293, q_gen_4295, q_gen_4301, q_gen_4308, q_gen_4313, q_gen_4318, q_gen_4319, q_gen_4341, q_gen_4373},
Q_f={q_gen_4293},
Delta=
{
<z>() -> q_gen_4301
<s>(q_gen_4301) -> q_gen_4313
<s>(q_gen_4313) -> q_gen_4313
<s, s>(q_gen_4295) -> q_gen_4295
<z, z>() -> q_gen_4295
<s, s>(q_gen_4318) -> q_gen_4318
<z, s>(q_gen_4301) -> q_gen_4318
<z, s>(q_gen_4313) -> q_gen_4318
<s, z>(q_gen_4301) -> q_gen_4341
<s, s>(q_gen_4341) -> q_gen_4373
<s, z>(q_gen_4313) -> q_gen_4373
<s, s, s>(q_gen_4308) -> q_gen_4293
<s, s, z>(q_gen_4295) -> q_gen_4293
<s, s, z>(q_gen_4318) -> q_gen_4293
<s, z, s>(q_gen_4295) -> q_gen_4293
<z, s, z>(q_gen_4301) -> q_gen_4293
<z, s, z>(q_gen_4313) -> q_gen_4293
<z, z, z>() -> q_gen_4293
<s, s, s>(q_gen_4319) -> q_gen_4308
<s, s, z>(q_gen_4341) -> q_gen_4308
<s, z, s>(q_gen_4341) -> q_gen_4308
<s, z, s>(q_gen_4373) -> q_gen_4308
<s, z, z>(q_gen_4301) -> q_gen_4308
<s, s, s>(q_gen_4293) -> q_gen_4319
<s, s, z>(q_gen_4373) -> q_gen_4319
<s, z, s>(q_gen_4318) -> q_gen_4319
<s, z, z>(q_gen_4313) -> q_gen_4319
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_4292, q_gen_4297, q_gen_4305, q_gen_4306, q_gen_4316, q_gen_4322, q_gen_4323, q_gen_4343},
Q_f={q_gen_4292},
Delta=
{
<s>(q_gen_4323) -> q_gen_4306
<z>() -> q_gen_4306
<s>(q_gen_4306) -> q_gen_4323
<s, s>(q_gen_4297) -> q_gen_4297
<s, s>(q_gen_4343) -> q_gen_4297
<z, z>() -> q_gen_4297
<s, s>(q_gen_4316) -> q_gen_4316
<z, s>(q_gen_4306) -> q_gen_4316
<z, s>(q_gen_4323) -> q_gen_4343
<s, s, s>(q_gen_4305) -> q_gen_4292
<s, z, s>(q_gen_4297) -> q_gen_4292
<z, s, s>(q_gen_4297) -> q_gen_4292
<z, z, z>() -> q_gen_4292
<s, s, s>(q_gen_4292) -> q_gen_4305
<s, s, s>(q_gen_4322) -> q_gen_4305
<s, z, s>(q_gen_4316) -> q_gen_4305
<z, s, s>(q_gen_4316) -> q_gen_4305
<z, z, s>(q_gen_4306) -> q_gen_4305
<s, z, s>(q_gen_4343) -> q_gen_4322
<z, s, s>(q_gen_4343) -> q_gen_4322
<z, z, s>(q_gen_4323) -> q_gen_4322
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 61
() -> minus([z, y, z]) -> 61
() -> plus([n, z, n]) -> 61
(minus([_pq, n, _qq]) /\ plus([m, n, _pq])) -> eq_nat([_qq, m]) -> 64
(minus([u, x2, _fq])) -> minus([s(u), s(x2), _fq]) -> 67
(plus([n, mm, _kq])) -> plus([n, s(mm), s(_kq)]) -> 65
}
Sat witness: Found: ((minus([u, x2, _fq])) -> minus([s(u), s(x2), _fq]), {
_fq -> s(s(s(z)))  ;  u -> s(s(s(s(z))))  ;  x2 -> s(z)
})

-------------------------------------------
Step 73, which took 0.471585 s (model generation: 0.470791,  model checking: 0.000794):

Model:
|_
{
minus -> 
{{{
Q={q_gen_4293, q_gen_4294, q_gen_4295, q_gen_4301, q_gen_4308, q_gen_4313, q_gen_4318, q_gen_4319, q_gen_4341},
Q_f={q_gen_4293, q_gen_4294},
Delta=
{
<z>() -> q_gen_4301
<s>(q_gen_4301) -> q_gen_4313
<s>(q_gen_4313) -> q_gen_4313
<s, s>(q_gen_4295) -> q_gen_4295
<s, s>(q_gen_4318) -> q_gen_4295
<s, s>(q_gen_4341) -> q_gen_4295
<z, z>() -> q_gen_4295
<z, s>(q_gen_4301) -> q_gen_4318
<z, s>(q_gen_4313) -> q_gen_4318
<s, z>(q_gen_4301) -> q_gen_4341
<s, z>(q_gen_4313) -> q_gen_4341
<s, s, s>(q_gen_4294) -> q_gen_4293
<s, s, z>(q_gen_4295) -> q_gen_4293
<z, s, z>(q_gen_4301) -> q_gen_4293
<z, s, z>(q_gen_4313) -> q_gen_4293
<z, z, z>() -> q_gen_4293
<s, s, s>(q_gen_4308) -> q_gen_4294
<s, s, z>(q_gen_4318) -> q_gen_4294
<s, z, s>(q_gen_4295) -> q_gen_4294
<s, s, s>(q_gen_4319) -> q_gen_4308
<s, s, z>(q_gen_4341) -> q_gen_4308
<s, z, s>(q_gen_4341) -> q_gen_4308
<s, z, z>(q_gen_4301) -> q_gen_4308
<s, s, s>(q_gen_4293) -> q_gen_4319
<s, z, s>(q_gen_4318) -> q_gen_4319
<s, z, z>(q_gen_4313) -> q_gen_4319
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_4292, q_gen_4297, q_gen_4305, q_gen_4306, q_gen_4316, q_gen_4322, q_gen_4323, q_gen_4343},
Q_f={q_gen_4292},
Delta=
{
<s>(q_gen_4323) -> q_gen_4306
<z>() -> q_gen_4306
<s>(q_gen_4306) -> q_gen_4323
<s, s>(q_gen_4297) -> q_gen_4297
<z, z>() -> q_gen_4297
<s, s>(q_gen_4316) -> q_gen_4316
<z, s>(q_gen_4306) -> q_gen_4316
<s, s>(q_gen_4343) -> q_gen_4343
<z, s>(q_gen_4323) -> q_gen_4343
<s, s, s>(q_gen_4305) -> q_gen_4292
<s, z, s>(q_gen_4297) -> q_gen_4292
<z, s, s>(q_gen_4297) -> q_gen_4292
<z, z, z>() -> q_gen_4292
<s, s, s>(q_gen_4292) -> q_gen_4305
<s, s, s>(q_gen_4322) -> q_gen_4305
<s, z, s>(q_gen_4316) -> q_gen_4305
<z, s, s>(q_gen_4316) -> q_gen_4305
<z, z, s>(q_gen_4306) -> q_gen_4305
<s, z, s>(q_gen_4343) -> q_gen_4322
<z, s, s>(q_gen_4343) -> q_gen_4322
<z, z, s>(q_gen_4323) -> q_gen_4322
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 62
() -> minus([z, y, z]) -> 62
() -> plus([n, z, n]) -> 62
(minus([_pq, n, _qq]) /\ plus([m, n, _pq])) -> eq_nat([_qq, m]) -> 67
(minus([u, x2, _fq])) -> minus([s(u), s(x2), _fq]) -> 67
(plus([n, mm, _kq])) -> plus([n, s(mm), s(_kq)]) -> 65
}
Sat witness: Found: ((minus([_pq, n, _qq]) /\ plus([m, n, _pq])) -> eq_nat([_qq, m]), {
_pq -> s(s(z))  ;  _qq -> s(s(s(z)))  ;  m -> s(s(z))  ;  n -> z
})

-------------------------------------------
Step 74, which took 0.467455 s (model generation: 0.465338,  model checking: 0.002117):

Model:
|_
{
minus -> 
{{{
Q={q_gen_4293, q_gen_4295, q_gen_4301, q_gen_4308, q_gen_4313, q_gen_4318, q_gen_4319, q_gen_4341, q_gen_4373},
Q_f={q_gen_4293},
Delta=
{
<s>(q_gen_4313) -> q_gen_4301
<z>() -> q_gen_4301
<s>(q_gen_4301) -> q_gen_4313
<s, s>(q_gen_4295) -> q_gen_4295
<z, z>() -> q_gen_4295
<s, s>(q_gen_4318) -> q_gen_4318
<z, s>(q_gen_4301) -> q_gen_4318
<z, s>(q_gen_4313) -> q_gen_4318
<s, s>(q_gen_4341) -> q_gen_4341
<s, z>(q_gen_4301) -> q_gen_4341
<s, z>(q_gen_4313) -> q_gen_4373
<s, s, s>(q_gen_4308) -> q_gen_4293
<s, s, z>(q_gen_4295) -> q_gen_4293
<s, s, z>(q_gen_4318) -> q_gen_4293
<s, z, s>(q_gen_4295) -> q_gen_4293
<z, s, z>(q_gen_4301) -> q_gen_4293
<z, s, z>(q_gen_4313) -> q_gen_4293
<z, z, z>() -> q_gen_4293
<s, s, s>(q_gen_4319) -> q_gen_4308
<s, s, z>(q_gen_4341) -> q_gen_4308
<s, z, s>(q_gen_4341) -> q_gen_4308
<s, z, z>(q_gen_4301) -> q_gen_4308
<s, s, s>(q_gen_4293) -> q_gen_4319
<s, s, z>(q_gen_4373) -> q_gen_4319
<s, z, s>(q_gen_4318) -> q_gen_4319
<s, z, s>(q_gen_4373) -> q_gen_4319
<s, z, z>(q_gen_4313) -> q_gen_4319
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_4292, q_gen_4297, q_gen_4305, q_gen_4306, q_gen_4316, q_gen_4322, q_gen_4323, q_gen_4343},
Q_f={q_gen_4292},
Delta=
{
<s>(q_gen_4323) -> q_gen_4306
<z>() -> q_gen_4306
<s>(q_gen_4306) -> q_gen_4323
<s, s>(q_gen_4297) -> q_gen_4297
<s, s>(q_gen_4343) -> q_gen_4297
<z, z>() -> q_gen_4297
<s, s>(q_gen_4316) -> q_gen_4316
<z, s>(q_gen_4306) -> q_gen_4316
<z, s>(q_gen_4323) -> q_gen_4343
<s, s, s>(q_gen_4305) -> q_gen_4292
<s, z, s>(q_gen_4297) -> q_gen_4292
<s, z, s>(q_gen_4343) -> q_gen_4292
<z, s, s>(q_gen_4297) -> q_gen_4292
<z, z, z>() -> q_gen_4292
<s, s, s>(q_gen_4292) -> q_gen_4305
<s, s, s>(q_gen_4322) -> q_gen_4305
<s, z, s>(q_gen_4316) -> q_gen_4305
<z, s, s>(q_gen_4316) -> q_gen_4305
<z, z, s>(q_gen_4306) -> q_gen_4305
<z, s, s>(q_gen_4343) -> q_gen_4322
<z, z, s>(q_gen_4323) -> q_gen_4322
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 63
() -> minus([z, y, z]) -> 63
() -> plus([n, z, n]) -> 63
(minus([_pq, n, _qq]) /\ plus([m, n, _pq])) -> eq_nat([_qq, m]) -> 67
(minus([u, x2, _fq])) -> minus([s(u), s(x2), _fq]) -> 70
(plus([n, mm, _kq])) -> plus([n, s(mm), s(_kq)]) -> 66
}
Sat witness: Found: ((minus([u, x2, _fq])) -> minus([s(u), s(x2), _fq]), {
_fq -> s(s(s(s(s(s(z))))))  ;  u -> s(s(s(z)))  ;  x2 -> s(s(z))
})

-------------------------------------------
Step 75, which took 0.518577 s (model generation: 0.516420,  model checking: 0.002157):

Model:
|_
{
minus -> 
{{{
Q={q_gen_4293, q_gen_4294, q_gen_4295, q_gen_4301, q_gen_4308, q_gen_4313, q_gen_4318, q_gen_4319, q_gen_4341},
Q_f={q_gen_4293, q_gen_4294},
Delta=
{
<z>() -> q_gen_4301
<s>(q_gen_4301) -> q_gen_4313
<s>(q_gen_4313) -> q_gen_4313
<s, s>(q_gen_4295) -> q_gen_4295
<s, s>(q_gen_4341) -> q_gen_4295
<z, z>() -> q_gen_4295
<s, s>(q_gen_4318) -> q_gen_4318
<z, s>(q_gen_4301) -> q_gen_4318
<z, s>(q_gen_4313) -> q_gen_4318
<s, z>(q_gen_4301) -> q_gen_4341
<s, z>(q_gen_4313) -> q_gen_4341
<s, s, s>(q_gen_4294) -> q_gen_4293
<s, s, z>(q_gen_4295) -> q_gen_4293
<z, s, z>(q_gen_4301) -> q_gen_4293
<z, s, z>(q_gen_4313) -> q_gen_4293
<z, z, z>() -> q_gen_4293
<s, s, s>(q_gen_4308) -> q_gen_4294
<s, s, z>(q_gen_4318) -> q_gen_4294
<s, z, s>(q_gen_4295) -> q_gen_4294
<s, s, s>(q_gen_4319) -> q_gen_4308
<s, s, z>(q_gen_4341) -> q_gen_4308
<s, z, s>(q_gen_4341) -> q_gen_4308
<s, z, z>(q_gen_4301) -> q_gen_4308
<s, s, s>(q_gen_4293) -> q_gen_4319
<s, z, s>(q_gen_4318) -> q_gen_4319
<s, z, z>(q_gen_4313) -> q_gen_4319
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_4292, q_gen_4297, q_gen_4305, q_gen_4306, q_gen_4316, q_gen_4322, q_gen_4323, q_gen_4343},
Q_f={q_gen_4292},
Delta=
{
<s>(q_gen_4323) -> q_gen_4306
<z>() -> q_gen_4306
<s>(q_gen_4306) -> q_gen_4323
<s, s>(q_gen_4297) -> q_gen_4297
<s, s>(q_gen_4343) -> q_gen_4297
<z, z>() -> q_gen_4297
<s, s>(q_gen_4316) -> q_gen_4316
<z, s>(q_gen_4306) -> q_gen_4316
<z, s>(q_gen_4323) -> q_gen_4343
<s, s, s>(q_gen_4305) -> q_gen_4292
<s, z, s>(q_gen_4297) -> q_gen_4292
<z, s, s>(q_gen_4297) -> q_gen_4292
<z, z, z>() -> q_gen_4292
<s, s, s>(q_gen_4292) -> q_gen_4305
<s, s, s>(q_gen_4322) -> q_gen_4305
<s, z, s>(q_gen_4316) -> q_gen_4305
<z, s, s>(q_gen_4316) -> q_gen_4305
<z, z, s>(q_gen_4306) -> q_gen_4305
<s, z, s>(q_gen_4343) -> q_gen_4322
<z, s, s>(q_gen_4343) -> q_gen_4322
<z, z, s>(q_gen_4323) -> q_gen_4322
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 64
() -> minus([z, y, z]) -> 64
() -> plus([n, z, n]) -> 64
(minus([_pq, n, _qq]) /\ plus([m, n, _pq])) -> eq_nat([_qq, m]) -> 70
(minus([u, x2, _fq])) -> minus([s(u), s(x2), _fq]) -> 70
(plus([n, mm, _kq])) -> plus([n, s(mm), s(_kq)]) -> 67
}
Sat witness: Found: ((minus([_pq, n, _qq]) /\ plus([m, n, _pq])) -> eq_nat([_qq, m]), {
_pq -> s(s(s(s(z))))  ;  _qq -> s(z)  ;  m -> z  ;  n -> s(s(z))
})

-------------------------------------------
Step 76, which took 0.772969 s (model generation: 0.771375,  model checking: 0.001594):

Model:
|_
{
minus -> 
{{{
Q={q_gen_4293, q_gen_4294, q_gen_4295, q_gen_4301, q_gen_4308, q_gen_4313, q_gen_4318, q_gen_4319, q_gen_4341},
Q_f={q_gen_4293, q_gen_4294},
Delta=
{
<z>() -> q_gen_4301
<s>(q_gen_4301) -> q_gen_4313
<s>(q_gen_4313) -> q_gen_4313
<s, s>(q_gen_4295) -> q_gen_4295
<s, s>(q_gen_4341) -> q_gen_4295
<z, z>() -> q_gen_4295
<s, s>(q_gen_4318) -> q_gen_4318
<z, s>(q_gen_4301) -> q_gen_4318
<z, s>(q_gen_4313) -> q_gen_4318
<s, z>(q_gen_4301) -> q_gen_4341
<s, z>(q_gen_4313) -> q_gen_4341
<s, s, s>(q_gen_4294) -> q_gen_4293
<s, s, z>(q_gen_4295) -> q_gen_4293
<z, s, z>(q_gen_4301) -> q_gen_4293
<z, s, z>(q_gen_4313) -> q_gen_4293
<z, z, z>() -> q_gen_4293
<s, s, s>(q_gen_4308) -> q_gen_4294
<s, s, z>(q_gen_4318) -> q_gen_4294
<s, z, s>(q_gen_4295) -> q_gen_4294
<s, s, s>(q_gen_4319) -> q_gen_4308
<s, s, z>(q_gen_4341) -> q_gen_4308
<s, z, s>(q_gen_4341) -> q_gen_4308
<s, z, z>(q_gen_4301) -> q_gen_4308
<s, s, s>(q_gen_4293) -> q_gen_4319
<s, z, s>(q_gen_4318) -> q_gen_4319
<s, z, z>(q_gen_4313) -> q_gen_4319
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_4292, q_gen_4297, q_gen_4305, q_gen_4306, q_gen_4316, q_gen_4322, q_gen_4323, q_gen_4343},
Q_f={q_gen_4292},
Delta=
{
<s>(q_gen_4323) -> q_gen_4306
<z>() -> q_gen_4306
<s>(q_gen_4306) -> q_gen_4323
<s, s>(q_gen_4297) -> q_gen_4297
<z, z>() -> q_gen_4297
<s, s>(q_gen_4316) -> q_gen_4316
<z, s>(q_gen_4306) -> q_gen_4316
<s, s>(q_gen_4343) -> q_gen_4343
<z, s>(q_gen_4323) -> q_gen_4343
<s, s, s>(q_gen_4305) -> q_gen_4292
<s, z, s>(q_gen_4297) -> q_gen_4292
<s, z, s>(q_gen_4343) -> q_gen_4292
<z, s, s>(q_gen_4297) -> q_gen_4292
<z, z, z>() -> q_gen_4292
<s, s, s>(q_gen_4292) -> q_gen_4305
<s, s, s>(q_gen_4322) -> q_gen_4305
<s, z, s>(q_gen_4316) -> q_gen_4305
<z, s, s>(q_gen_4316) -> q_gen_4305
<z, z, s>(q_gen_4306) -> q_gen_4305
<z, s, s>(q_gen_4343) -> q_gen_4322
<z, z, s>(q_gen_4323) -> q_gen_4322
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 65
() -> minus([z, y, z]) -> 65
() -> plus([n, z, n]) -> 65
(minus([_pq, n, _qq]) /\ plus([m, n, _pq])) -> eq_nat([_qq, m]) -> 70
(minus([u, x2, _fq])) -> minus([s(u), s(x2), _fq]) -> 73
(plus([n, mm, _kq])) -> plus([n, s(mm), s(_kq)]) -> 68
}
Sat witness: Found: ((minus([u, x2, _fq])) -> minus([s(u), s(x2), _fq]), {
_fq -> s(z)  ;  u -> s(s(s(z)))  ;  x2 -> s(s(z))
})

-------------------------------------------
Step 77, which took 0.524129 s (model generation: 0.522262,  model checking: 0.001867):

Model:
|_
{
minus -> 
{{{
Q={q_gen_4293, q_gen_4294, q_gen_4295, q_gen_4301, q_gen_4308, q_gen_4313, q_gen_4318, q_gen_4319, q_gen_4341},
Q_f={q_gen_4293, q_gen_4294},
Delta=
{
<s>(q_gen_4313) -> q_gen_4301
<z>() -> q_gen_4301
<s>(q_gen_4301) -> q_gen_4313
<s, s>(q_gen_4295) -> q_gen_4295
<z, z>() -> q_gen_4295
<s, s>(q_gen_4318) -> q_gen_4318
<z, s>(q_gen_4301) -> q_gen_4318
<z, s>(q_gen_4313) -> q_gen_4318
<s, s>(q_gen_4341) -> q_gen_4341
<s, z>(q_gen_4301) -> q_gen_4341
<s, z>(q_gen_4313) -> q_gen_4341
<s, s, z>(q_gen_4295) -> q_gen_4293
<z, s, z>(q_gen_4301) -> q_gen_4293
<z, s, z>(q_gen_4313) -> q_gen_4293
<z, z, z>() -> q_gen_4293
<s, s, s>(q_gen_4294) -> q_gen_4294
<s, s, s>(q_gen_4308) -> q_gen_4294
<s, s, z>(q_gen_4318) -> q_gen_4294
<s, z, s>(q_gen_4295) -> q_gen_4294
<s, s, s>(q_gen_4319) -> q_gen_4308
<s, s, z>(q_gen_4341) -> q_gen_4308
<s, z, s>(q_gen_4341) -> q_gen_4308
<s, z, z>(q_gen_4301) -> q_gen_4308
<s, s, s>(q_gen_4293) -> q_gen_4319
<s, z, s>(q_gen_4318) -> q_gen_4319
<s, z, z>(q_gen_4313) -> q_gen_4319
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_4292, q_gen_4297, q_gen_4305, q_gen_4306, q_gen_4316, q_gen_4322, q_gen_4323, q_gen_4343},
Q_f={q_gen_4292},
Delta=
{
<s>(q_gen_4323) -> q_gen_4306
<z>() -> q_gen_4306
<s>(q_gen_4306) -> q_gen_4323
<s, s>(q_gen_4297) -> q_gen_4297
<z, z>() -> q_gen_4297
<s, s>(q_gen_4316) -> q_gen_4316
<z, s>(q_gen_4306) -> q_gen_4316
<s, s>(q_gen_4343) -> q_gen_4343
<z, s>(q_gen_4323) -> q_gen_4343
<s, s, s>(q_gen_4305) -> q_gen_4292
<s, z, s>(q_gen_4297) -> q_gen_4292
<z, s, s>(q_gen_4297) -> q_gen_4292
<z, z, z>() -> q_gen_4292
<s, s, s>(q_gen_4292) -> q_gen_4305
<s, s, s>(q_gen_4322) -> q_gen_4305
<s, z, s>(q_gen_4316) -> q_gen_4305
<z, s, s>(q_gen_4316) -> q_gen_4305
<z, z, s>(q_gen_4306) -> q_gen_4305
<s, z, s>(q_gen_4343) -> q_gen_4322
<z, s, s>(q_gen_4343) -> q_gen_4322
<z, z, s>(q_gen_4323) -> q_gen_4322
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 66
() -> minus([z, y, z]) -> 66
() -> plus([n, z, n]) -> 66
(minus([_pq, n, _qq]) /\ plus([m, n, _pq])) -> eq_nat([_qq, m]) -> 73
(minus([u, x2, _fq])) -> minus([s(u), s(x2), _fq]) -> 73
(plus([n, mm, _kq])) -> plus([n, s(mm), s(_kq)]) -> 69
}
Sat witness: Found: ((minus([_pq, n, _qq]) /\ plus([m, n, _pq])) -> eq_nat([_qq, m]), {
_pq -> s(s(s(z)))  ;  _qq -> s(s(s(z)))  ;  m -> s(z)  ;  n -> s(s(z))
})

-------------------------------------------
Step 78, which took 0.616804 s (model generation: 0.614875,  model checking: 0.001929):

Model:
|_
{
minus -> 
{{{
Q={q_gen_4293, q_gen_4294, q_gen_4295, q_gen_4301, q_gen_4308, q_gen_4313, q_gen_4318, q_gen_4319, q_gen_4341},
Q_f={q_gen_4293, q_gen_4294},
Delta=
{
<s>(q_gen_4313) -> q_gen_4301
<z>() -> q_gen_4301
<s>(q_gen_4301) -> q_gen_4313
<s, s>(q_gen_4295) -> q_gen_4295
<z, z>() -> q_gen_4295
<s, s>(q_gen_4318) -> q_gen_4318
<z, s>(q_gen_4301) -> q_gen_4318
<z, s>(q_gen_4313) -> q_gen_4318
<s, s>(q_gen_4341) -> q_gen_4341
<s, z>(q_gen_4301) -> q_gen_4341
<s, z>(q_gen_4313) -> q_gen_4341
<s, s, s>(q_gen_4294) -> q_gen_4293
<s, s, z>(q_gen_4295) -> q_gen_4293
<s, s, z>(q_gen_4318) -> q_gen_4293
<z, s, z>(q_gen_4301) -> q_gen_4293
<z, s, z>(q_gen_4313) -> q_gen_4293
<z, z, z>() -> q_gen_4293
<s, s, s>(q_gen_4308) -> q_gen_4294
<s, z, s>(q_gen_4295) -> q_gen_4294
<s, s, s>(q_gen_4319) -> q_gen_4308
<s, s, z>(q_gen_4341) -> q_gen_4308
<s, z, s>(q_gen_4341) -> q_gen_4308
<s, z, z>(q_gen_4301) -> q_gen_4308
<s, s, s>(q_gen_4293) -> q_gen_4319
<s, z, s>(q_gen_4318) -> q_gen_4319
<s, z, z>(q_gen_4313) -> q_gen_4319
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_4292, q_gen_4297, q_gen_4305, q_gen_4306, q_gen_4316, q_gen_4322, q_gen_4323, q_gen_4343},
Q_f={q_gen_4292},
Delta=
{
<s>(q_gen_4323) -> q_gen_4306
<z>() -> q_gen_4306
<s>(q_gen_4306) -> q_gen_4323
<s, s>(q_gen_4297) -> q_gen_4297
<z, z>() -> q_gen_4297
<s, s>(q_gen_4316) -> q_gen_4316
<z, s>(q_gen_4306) -> q_gen_4316
<s, s>(q_gen_4343) -> q_gen_4343
<z, s>(q_gen_4323) -> q_gen_4343
<s, s, s>(q_gen_4305) -> q_gen_4292
<s, z, s>(q_gen_4297) -> q_gen_4292
<z, s, s>(q_gen_4297) -> q_gen_4292
<z, z, z>() -> q_gen_4292
<s, s, s>(q_gen_4292) -> q_gen_4305
<s, s, s>(q_gen_4322) -> q_gen_4305
<s, z, s>(q_gen_4316) -> q_gen_4305
<z, s, s>(q_gen_4316) -> q_gen_4305
<z, z, s>(q_gen_4306) -> q_gen_4305
<s, z, s>(q_gen_4343) -> q_gen_4322
<z, s, s>(q_gen_4343) -> q_gen_4322
<z, z, s>(q_gen_4323) -> q_gen_4322
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 67
() -> minus([z, y, z]) -> 67
() -> plus([n, z, n]) -> 67
(minus([_pq, n, _qq]) /\ plus([m, n, _pq])) -> eq_nat([_qq, m]) -> 73
(minus([u, x2, _fq])) -> minus([s(u), s(x2), _fq]) -> 76
(plus([n, mm, _kq])) -> plus([n, s(mm), s(_kq)]) -> 70
}
Sat witness: Found: ((minus([u, x2, _fq])) -> minus([s(u), s(x2), _fq]), {
_fq -> s(s(s(s(z))))  ;  u -> s(s(s(z)))  ;  x2 -> s(s(z))
})

-------------------------------------------
Step 79, which took 0.669603 s (model generation: 0.667637,  model checking: 0.001966):

Model:
|_
{
minus -> 
{{{
Q={q_gen_4293, q_gen_4295, q_gen_4301, q_gen_4307, q_gen_4308, q_gen_4313, q_gen_4318, q_gen_4319, q_gen_4341},
Q_f={q_gen_4293, q_gen_4307},
Delta=
{
<s>(q_gen_4313) -> q_gen_4301
<z>() -> q_gen_4301
<s>(q_gen_4301) -> q_gen_4313
<s, s>(q_gen_4295) -> q_gen_4295
<z, z>() -> q_gen_4295
<s, s>(q_gen_4318) -> q_gen_4318
<z, s>(q_gen_4301) -> q_gen_4318
<z, s>(q_gen_4313) -> q_gen_4318
<s, s>(q_gen_4341) -> q_gen_4341
<s, z>(q_gen_4301) -> q_gen_4341
<s, z>(q_gen_4313) -> q_gen_4341
<s, s, s>(q_gen_4307) -> q_gen_4293
<s, s, z>(q_gen_4295) -> q_gen_4293
<s, z, s>(q_gen_4295) -> q_gen_4293
<z, s, z>(q_gen_4301) -> q_gen_4293
<z, s, z>(q_gen_4313) -> q_gen_4293
<z, z, z>() -> q_gen_4293
<s, s, s>(q_gen_4308) -> q_gen_4307
<s, s, z>(q_gen_4318) -> q_gen_4307
<s, s, s>(q_gen_4319) -> q_gen_4308
<s, s, z>(q_gen_4341) -> q_gen_4308
<s, z, s>(q_gen_4341) -> q_gen_4308
<s, z, z>(q_gen_4301) -> q_gen_4308
<s, s, s>(q_gen_4293) -> q_gen_4319
<s, z, s>(q_gen_4318) -> q_gen_4319
<s, z, z>(q_gen_4313) -> q_gen_4319
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_4292, q_gen_4297, q_gen_4305, q_gen_4306, q_gen_4316, q_gen_4322, q_gen_4323, q_gen_4343},
Q_f={q_gen_4292},
Delta=
{
<s>(q_gen_4323) -> q_gen_4306
<z>() -> q_gen_4306
<s>(q_gen_4306) -> q_gen_4323
<s, s>(q_gen_4297) -> q_gen_4297
<z, z>() -> q_gen_4297
<s, s>(q_gen_4316) -> q_gen_4316
<z, s>(q_gen_4306) -> q_gen_4316
<s, s>(q_gen_4343) -> q_gen_4343
<z, s>(q_gen_4323) -> q_gen_4343
<s, s, s>(q_gen_4305) -> q_gen_4292
<s, z, s>(q_gen_4297) -> q_gen_4292
<s, z, s>(q_gen_4343) -> q_gen_4292
<z, s, s>(q_gen_4297) -> q_gen_4292
<z, z, z>() -> q_gen_4292
<s, s, s>(q_gen_4292) -> q_gen_4305
<s, s, s>(q_gen_4322) -> q_gen_4305
<s, z, s>(q_gen_4316) -> q_gen_4305
<z, s, s>(q_gen_4316) -> q_gen_4305
<z, z, s>(q_gen_4306) -> q_gen_4305
<z, s, s>(q_gen_4343) -> q_gen_4322
<z, z, s>(q_gen_4323) -> q_gen_4322
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 68
() -> minus([z, y, z]) -> 68
() -> plus([n, z, n]) -> 68
(minus([_pq, n, _qq]) /\ plus([m, n, _pq])) -> eq_nat([_qq, m]) -> 76
(minus([u, x2, _fq])) -> minus([s(u), s(x2), _fq]) -> 76
(plus([n, mm, _kq])) -> plus([n, s(mm), s(_kq)]) -> 71
}
Sat witness: Found: ((minus([_pq, n, _qq]) /\ plus([m, n, _pq])) -> eq_nat([_qq, m]), {
_pq -> s(s(s(z)))  ;  _qq -> s(s(s(z)))  ;  m -> s(s(z))  ;  n -> s(s(s(z)))
})

-------------------------------------------
Step 80, which took 0.847932 s (model generation: 0.845794,  model checking: 0.002138):

Model:
|_
{
minus -> 
{{{
Q={q_gen_4293, q_gen_4295, q_gen_4301, q_gen_4308, q_gen_4313, q_gen_4318, q_gen_4319, q_gen_4341, q_gen_4362, q_gen_4373},
Q_f={q_gen_4293},
Delta=
{
<s>(q_gen_4313) -> q_gen_4301
<z>() -> q_gen_4301
<s>(q_gen_4301) -> q_gen_4313
<s, s>(q_gen_4295) -> q_gen_4295
<z, z>() -> q_gen_4295
<s, s>(q_gen_4318) -> q_gen_4318
<z, s>(q_gen_4301) -> q_gen_4318
<z, s>(q_gen_4313) -> q_gen_4318
<s, s>(q_gen_4341) -> q_gen_4341
<s, z>(q_gen_4301) -> q_gen_4341
<s, z>(q_gen_4313) -> q_gen_4373
<s, s, s>(q_gen_4308) -> q_gen_4293
<s, s, z>(q_gen_4295) -> q_gen_4293
<s, s, z>(q_gen_4318) -> q_gen_4293
<s, z, s>(q_gen_4295) -> q_gen_4293
<z, s, z>(q_gen_4301) -> q_gen_4293
<z, s, z>(q_gen_4313) -> q_gen_4293
<z, z, z>() -> q_gen_4293
<s, s, s>(q_gen_4362) -> q_gen_4308
<s, s, z>(q_gen_4341) -> q_gen_4308
<s, z, s>(q_gen_4341) -> q_gen_4308
<s, z, z>(q_gen_4301) -> q_gen_4308
<s, s, s>(q_gen_4293) -> q_gen_4319
<s, s, s>(q_gen_4319) -> q_gen_4319
<s, z, s>(q_gen_4318) -> q_gen_4319
<s, s, z>(q_gen_4373) -> q_gen_4362
<s, z, s>(q_gen_4373) -> q_gen_4362
<s, z, z>(q_gen_4313) -> q_gen_4362
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_4292, q_gen_4297, q_gen_4305, q_gen_4306, q_gen_4316, q_gen_4322, q_gen_4323, q_gen_4343},
Q_f={q_gen_4292},
Delta=
{
<s>(q_gen_4323) -> q_gen_4306
<z>() -> q_gen_4306
<s>(q_gen_4306) -> q_gen_4323
<s, s>(q_gen_4297) -> q_gen_4297
<z, z>() -> q_gen_4297
<s, s>(q_gen_4316) -> q_gen_4316
<z, s>(q_gen_4306) -> q_gen_4316
<s, s>(q_gen_4343) -> q_gen_4343
<z, s>(q_gen_4323) -> q_gen_4343
<s, s, s>(q_gen_4305) -> q_gen_4292
<s, z, s>(q_gen_4297) -> q_gen_4292
<z, s, s>(q_gen_4297) -> q_gen_4292
<z, z, z>() -> q_gen_4292
<s, s, s>(q_gen_4292) -> q_gen_4305
<s, s, s>(q_gen_4322) -> q_gen_4305
<s, z, s>(q_gen_4316) -> q_gen_4305
<z, s, s>(q_gen_4316) -> q_gen_4305
<z, z, s>(q_gen_4306) -> q_gen_4305
<s, z, s>(q_gen_4343) -> q_gen_4322
<z, s, s>(q_gen_4343) -> q_gen_4322
<z, z, s>(q_gen_4323) -> q_gen_4322
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 69
() -> minus([z, y, z]) -> 69
() -> plus([n, z, n]) -> 69
(minus([_pq, n, _qq]) /\ plus([m, n, _pq])) -> eq_nat([_qq, m]) -> 76
(minus([u, x2, _fq])) -> minus([s(u), s(x2), _fq]) -> 79
(plus([n, mm, _kq])) -> plus([n, s(mm), s(_kq)]) -> 72
}
Sat witness: Found: ((minus([u, x2, _fq])) -> minus([s(u), s(x2), _fq]), {
_fq -> s(s(s(z)))  ;  u -> s(s(s(s(s(z)))))  ;  x2 -> s(s(z))
})

-------------------------------------------
Step 81, which took 1.153612 s (model generation: 1.152573,  model checking: 0.001039):

Model:
|_
{
minus -> 
{{{
Q={q_gen_4293, q_gen_4295, q_gen_4301, q_gen_4307, q_gen_4308, q_gen_4313, q_gen_4318, q_gen_4319, q_gen_4341},
Q_f={q_gen_4293, q_gen_4307},
Delta=
{
<z>() -> q_gen_4301
<s>(q_gen_4301) -> q_gen_4313
<s>(q_gen_4313) -> q_gen_4313
<s, s>(q_gen_4295) -> q_gen_4295
<z, z>() -> q_gen_4295
<s, s>(q_gen_4318) -> q_gen_4318
<z, s>(q_gen_4301) -> q_gen_4318
<z, s>(q_gen_4313) -> q_gen_4318
<s, s>(q_gen_4341) -> q_gen_4341
<s, z>(q_gen_4301) -> q_gen_4341
<s, z>(q_gen_4313) -> q_gen_4341
<s, s, z>(q_gen_4295) -> q_gen_4293
<s, s, z>(q_gen_4318) -> q_gen_4293
<s, z, s>(q_gen_4295) -> q_gen_4293
<z, s, z>(q_gen_4301) -> q_gen_4293
<z, s, z>(q_gen_4313) -> q_gen_4293
<z, z, z>() -> q_gen_4293
<s, s, s>(q_gen_4307) -> q_gen_4307
<s, s, s>(q_gen_4308) -> q_gen_4307
<s, s, s>(q_gen_4319) -> q_gen_4308
<s, s, z>(q_gen_4341) -> q_gen_4308
<s, z, s>(q_gen_4341) -> q_gen_4308
<s, z, z>(q_gen_4301) -> q_gen_4308
<s, s, s>(q_gen_4293) -> q_gen_4319
<s, z, s>(q_gen_4318) -> q_gen_4319
<s, z, z>(q_gen_4313) -> q_gen_4319
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_4292, q_gen_4297, q_gen_4304, q_gen_4305, q_gen_4306, q_gen_4309, q_gen_4316, q_gen_4322, q_gen_4323},
Q_f={q_gen_4292, q_gen_4304},
Delta=
{
<z>() -> q_gen_4306
<s>(q_gen_4306) -> q_gen_4323
<s>(q_gen_4323) -> q_gen_4323
<s, s>(q_gen_4297) -> q_gen_4297
<z, z>() -> q_gen_4297
<s, s>(q_gen_4316) -> q_gen_4316
<z, s>(q_gen_4306) -> q_gen_4316
<z, s>(q_gen_4323) -> q_gen_4316
<s, s, s>(q_gen_4304) -> q_gen_4292
<s, z, s>(q_gen_4297) -> q_gen_4292
<z, s, s>(q_gen_4297) -> q_gen_4292
<z, z, z>() -> q_gen_4292
<s, s, s>(q_gen_4305) -> q_gen_4304
<s, s, s>(q_gen_4322) -> q_gen_4305
<s, z, s>(q_gen_4316) -> q_gen_4305
<z, s, s>(q_gen_4316) -> q_gen_4305
<z, z, s>(q_gen_4306) -> q_gen_4305
<s, s, s>(q_gen_4292) -> q_gen_4309
<s, s, s>(q_gen_4309) -> q_gen_4322
<z, z, s>(q_gen_4323) -> q_gen_4322
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 70
() -> minus([z, y, z]) -> 70
() -> plus([n, z, n]) -> 70
(minus([_pq, n, _qq]) /\ plus([m, n, _pq])) -> eq_nat([_qq, m]) -> 76
(minus([u, x2, _fq])) -> minus([s(u), s(x2), _fq]) -> 79
(plus([n, mm, _kq])) -> plus([n, s(mm), s(_kq)]) -> 75
}
Sat witness: Found: ((plus([n, mm, _kq])) -> plus([n, s(mm), s(_kq)]), {
_kq -> s(s(s(s(s(z)))))  ;  mm -> s(s(s(s(z))))  ;  n -> s(s(s(s(s(z)))))
})

-------------------------------------------
Step 82, which took 1.146914 s (model generation: 1.145668,  model checking: 0.001246):

Model:
|_
{
minus -> 
{{{
Q={q_gen_4293, q_gen_4295, q_gen_4301, q_gen_4307, q_gen_4308, q_gen_4313, q_gen_4318, q_gen_4319, q_gen_4341},
Q_f={q_gen_4293, q_gen_4307},
Delta=
{
<z>() -> q_gen_4301
<s>(q_gen_4301) -> q_gen_4313
<s>(q_gen_4313) -> q_gen_4313
<s, s>(q_gen_4295) -> q_gen_4295
<z, z>() -> q_gen_4295
<s, s>(q_gen_4318) -> q_gen_4318
<z, s>(q_gen_4301) -> q_gen_4318
<z, s>(q_gen_4313) -> q_gen_4318
<s, s>(q_gen_4341) -> q_gen_4341
<s, z>(q_gen_4301) -> q_gen_4341
<s, z>(q_gen_4313) -> q_gen_4341
<s, s, s>(q_gen_4307) -> q_gen_4293
<s, s, z>(q_gen_4295) -> q_gen_4293
<s, s, z>(q_gen_4318) -> q_gen_4293
<s, z, s>(q_gen_4295) -> q_gen_4293
<z, s, z>(q_gen_4301) -> q_gen_4293
<z, s, z>(q_gen_4313) -> q_gen_4293
<z, z, z>() -> q_gen_4293
<s, s, s>(q_gen_4308) -> q_gen_4307
<s, s, s>(q_gen_4319) -> q_gen_4308
<s, s, z>(q_gen_4341) -> q_gen_4308
<s, z, s>(q_gen_4341) -> q_gen_4308
<s, z, z>(q_gen_4301) -> q_gen_4308
<s, s, s>(q_gen_4293) -> q_gen_4319
<s, z, s>(q_gen_4318) -> q_gen_4319
<s, z, z>(q_gen_4313) -> q_gen_4319
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_4292, q_gen_4297, q_gen_4304, q_gen_4305, q_gen_4306, q_gen_4309, q_gen_4316, q_gen_4322, q_gen_4323},
Q_f={q_gen_4292, q_gen_4304},
Delta=
{
<z>() -> q_gen_4306
<s>(q_gen_4306) -> q_gen_4323
<s>(q_gen_4323) -> q_gen_4323
<s, s>(q_gen_4297) -> q_gen_4297
<z, z>() -> q_gen_4297
<s, s>(q_gen_4316) -> q_gen_4316
<z, s>(q_gen_4306) -> q_gen_4316
<z, s>(q_gen_4323) -> q_gen_4316
<s, s, s>(q_gen_4304) -> q_gen_4292
<s, z, s>(q_gen_4297) -> q_gen_4292
<z, s, s>(q_gen_4297) -> q_gen_4292
<z, z, z>() -> q_gen_4292
<s, s, s>(q_gen_4305) -> q_gen_4304
<s, s, s>(q_gen_4322) -> q_gen_4305
<s, z, s>(q_gen_4316) -> q_gen_4305
<z, s, s>(q_gen_4316) -> q_gen_4305
<z, z, s>(q_gen_4306) -> q_gen_4305
<s, s, s>(q_gen_4292) -> q_gen_4309
<s, s, s>(q_gen_4309) -> q_gen_4309
<z, z, s>(q_gen_4323) -> q_gen_4322
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 71
() -> minus([z, y, z]) -> 71
() -> plus([n, z, n]) -> 71
(minus([_pq, n, _qq]) /\ plus([m, n, _pq])) -> eq_nat([_qq, m]) -> 76
(minus([u, x2, _fq])) -> minus([s(u), s(x2), _fq]) -> 79
(plus([n, mm, _kq])) -> plus([n, s(mm), s(_kq)]) -> 78
}
Sat witness: Found: ((plus([n, mm, _kq])) -> plus([n, s(mm), s(_kq)]), {
_kq -> s(s(s(s(s(z)))))  ;  mm -> s(s(s(z)))  ;  n -> s(s(s(z)))
})

-------------------------------------------
Step 83, which took 1.470651 s (model generation: 1.469430,  model checking: 0.001221):

Model:
|_
{
minus -> 
{{{
Q={q_gen_4293, q_gen_4294, q_gen_4295, q_gen_4301, q_gen_4308, q_gen_4313, q_gen_4318, q_gen_4319, q_gen_4341, q_gen_4362},
Q_f={q_gen_4293, q_gen_4294},
Delta=
{
<z>() -> q_gen_4301
<s>(q_gen_4301) -> q_gen_4313
<s>(q_gen_4313) -> q_gen_4313
<s, s>(q_gen_4295) -> q_gen_4295
<z, z>() -> q_gen_4295
<s, s>(q_gen_4318) -> q_gen_4318
<z, s>(q_gen_4301) -> q_gen_4318
<z, s>(q_gen_4313) -> q_gen_4318
<s, s>(q_gen_4341) -> q_gen_4341
<s, z>(q_gen_4301) -> q_gen_4341
<s, z>(q_gen_4313) -> q_gen_4341
<s, s, s>(q_gen_4294) -> q_gen_4293
<s, s, z>(q_gen_4295) -> q_gen_4293
<z, s, z>(q_gen_4301) -> q_gen_4293
<z, s, z>(q_gen_4313) -> q_gen_4293
<z, z, z>() -> q_gen_4293
<s, s, s>(q_gen_4308) -> q_gen_4294
<s, s, z>(q_gen_4318) -> q_gen_4294
<s, z, s>(q_gen_4295) -> q_gen_4294
<s, s, s>(q_gen_4362) -> q_gen_4308
<s, s, z>(q_gen_4341) -> q_gen_4308
<s, z, s>(q_gen_4341) -> q_gen_4308
<s, z, z>(q_gen_4301) -> q_gen_4308
<s, s, s>(q_gen_4293) -> q_gen_4319
<s, s, s>(q_gen_4319) -> q_gen_4319
<s, z, s>(q_gen_4318) -> q_gen_4319
<s, z, z>(q_gen_4313) -> q_gen_4362
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_4292, q_gen_4297, q_gen_4305, q_gen_4306, q_gen_4316, q_gen_4322, q_gen_4323, q_gen_4343},
Q_f={q_gen_4292},
Delta=
{
<s>(q_gen_4323) -> q_gen_4306
<z>() -> q_gen_4306
<s>(q_gen_4306) -> q_gen_4323
<s, s>(q_gen_4297) -> q_gen_4297
<z, z>() -> q_gen_4297
<s, s>(q_gen_4316) -> q_gen_4316
<z, s>(q_gen_4306) -> q_gen_4316
<s, s>(q_gen_4343) -> q_gen_4343
<z, s>(q_gen_4323) -> q_gen_4343
<s, s, s>(q_gen_4305) -> q_gen_4292
<s, z, s>(q_gen_4297) -> q_gen_4292
<z, s, s>(q_gen_4297) -> q_gen_4292
<z, z, z>() -> q_gen_4292
<s, s, s>(q_gen_4292) -> q_gen_4305
<s, s, s>(q_gen_4322) -> q_gen_4305
<s, z, s>(q_gen_4316) -> q_gen_4305
<z, s, s>(q_gen_4316) -> q_gen_4305
<z, z, s>(q_gen_4306) -> q_gen_4305
<s, z, s>(q_gen_4343) -> q_gen_4322
<z, s, s>(q_gen_4343) -> q_gen_4322
<z, z, s>(q_gen_4323) -> q_gen_4322
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 72
() -> minus([z, y, z]) -> 72
() -> plus([n, z, n]) -> 72
(minus([_pq, n, _qq]) /\ plus([m, n, _pq])) -> eq_nat([_qq, m]) -> 79
(minus([u, x2, _fq])) -> minus([s(u), s(x2), _fq]) -> 79
(plus([n, mm, _kq])) -> plus([n, s(mm), s(_kq)]) -> 78
}
Sat witness: Found: ((minus([_pq, n, _qq]) /\ plus([m, n, _pq])) -> eq_nat([_qq, m]), {
_pq -> s(s(s(s(z))))  ;  _qq -> s(z)  ;  m -> s(s(z))  ;  n -> s(s(z))
})

-------------------------------------------
Step 84, which took 0.830108 s (model generation: 0.827727,  model checking: 0.002381):

Model:
|_
{
minus -> 
{{{
Q={q_gen_4293, q_gen_4294, q_gen_4295, q_gen_4301, q_gen_4308, q_gen_4313, q_gen_4318, q_gen_4319, q_gen_4341, q_gen_4362, q_gen_4373},
Q_f={q_gen_4293, q_gen_4294},
Delta=
{
<z>() -> q_gen_4301
<s>(q_gen_4301) -> q_gen_4313
<s>(q_gen_4313) -> q_gen_4313
<s, s>(q_gen_4295) -> q_gen_4295
<z, z>() -> q_gen_4295
<s, s>(q_gen_4318) -> q_gen_4318
<z, s>(q_gen_4301) -> q_gen_4318
<z, s>(q_gen_4313) -> q_gen_4318
<s, s>(q_gen_4341) -> q_gen_4341
<s, z>(q_gen_4301) -> q_gen_4341
<s, z>(q_gen_4313) -> q_gen_4373
<s, s, s>(q_gen_4294) -> q_gen_4293
<s, s, z>(q_gen_4295) -> q_gen_4293
<s, s, z>(q_gen_4318) -> q_gen_4293
<z, s, z>(q_gen_4301) -> q_gen_4293
<z, s, z>(q_gen_4313) -> q_gen_4293
<z, z, z>() -> q_gen_4293
<s, s, s>(q_gen_4308) -> q_gen_4294
<s, z, s>(q_gen_4295) -> q_gen_4294
<s, s, s>(q_gen_4362) -> q_gen_4308
<s, s, z>(q_gen_4341) -> q_gen_4308
<s, z, s>(q_gen_4341) -> q_gen_4308
<s, z, s>(q_gen_4373) -> q_gen_4308
<s, z, z>(q_gen_4301) -> q_gen_4308
<s, s, s>(q_gen_4293) -> q_gen_4319
<s, s, s>(q_gen_4319) -> q_gen_4319
<s, z, s>(q_gen_4318) -> q_gen_4319
<s, s, z>(q_gen_4373) -> q_gen_4362
<s, z, z>(q_gen_4313) -> q_gen_4362
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_4292, q_gen_4297, q_gen_4305, q_gen_4306, q_gen_4316, q_gen_4322, q_gen_4323, q_gen_4343},
Q_f={q_gen_4292},
Delta=
{
<s>(q_gen_4323) -> q_gen_4306
<z>() -> q_gen_4306
<s>(q_gen_4306) -> q_gen_4323
<s, s>(q_gen_4297) -> q_gen_4297
<z, z>() -> q_gen_4297
<s, s>(q_gen_4316) -> q_gen_4316
<z, s>(q_gen_4306) -> q_gen_4316
<s, s>(q_gen_4343) -> q_gen_4343
<z, s>(q_gen_4323) -> q_gen_4343
<s, s, s>(q_gen_4305) -> q_gen_4292
<s, z, s>(q_gen_4297) -> q_gen_4292
<z, s, s>(q_gen_4297) -> q_gen_4292
<z, z, z>() -> q_gen_4292
<s, s, s>(q_gen_4292) -> q_gen_4305
<s, s, s>(q_gen_4322) -> q_gen_4305
<s, z, s>(q_gen_4316) -> q_gen_4305
<z, s, s>(q_gen_4316) -> q_gen_4305
<z, z, s>(q_gen_4306) -> q_gen_4305
<s, z, s>(q_gen_4343) -> q_gen_4322
<z, s, s>(q_gen_4343) -> q_gen_4322
<z, z, s>(q_gen_4323) -> q_gen_4322
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 73
() -> minus([z, y, z]) -> 73
() -> plus([n, z, n]) -> 73
(minus([_pq, n, _qq]) /\ plus([m, n, _pq])) -> eq_nat([_qq, m]) -> 79
(minus([u, x2, _fq])) -> minus([s(u), s(x2), _fq]) -> 82
(plus([n, mm, _kq])) -> plus([n, s(mm), s(_kq)]) -> 79
}
Sat witness: Found: ((minus([u, x2, _fq])) -> minus([s(u), s(x2), _fq]), {
_fq -> s(s(z))  ;  u -> s(s(s(s(s(z)))))  ;  x2 -> s(s(s(z)))
})

-------------------------------------------
Step 85, which took 1.534033 s (model generation: 1.531625,  model checking: 0.002408):

Model:
|_
{
minus -> 
{{{
Q={q_gen_4293, q_gen_4294, q_gen_4295, q_gen_4301, q_gen_4308, q_gen_4313, q_gen_4318, q_gen_4319, q_gen_4341, q_gen_4362, q_gen_4373},
Q_f={q_gen_4293, q_gen_4294},
Delta=
{
<z>() -> q_gen_4301
<s>(q_gen_4301) -> q_gen_4313
<s>(q_gen_4313) -> q_gen_4313
<s, s>(q_gen_4295) -> q_gen_4295
<z, z>() -> q_gen_4295
<s, s>(q_gen_4318) -> q_gen_4318
<z, s>(q_gen_4301) -> q_gen_4318
<z, s>(q_gen_4313) -> q_gen_4318
<s, s>(q_gen_4341) -> q_gen_4341
<s, s>(q_gen_4373) -> q_gen_4341
<s, z>(q_gen_4301) -> q_gen_4341
<s, z>(q_gen_4313) -> q_gen_4373
<s, s, s>(q_gen_4294) -> q_gen_4293
<s, s, z>(q_gen_4295) -> q_gen_4293
<s, s, z>(q_gen_4318) -> q_gen_4293
<z, s, z>(q_gen_4301) -> q_gen_4293
<z, s, z>(q_gen_4313) -> q_gen_4293
<z, z, z>() -> q_gen_4293
<s, s, s>(q_gen_4308) -> q_gen_4294
<s, z, s>(q_gen_4295) -> q_gen_4294
<s, s, s>(q_gen_4362) -> q_gen_4308
<s, s, z>(q_gen_4341) -> q_gen_4308
<s, z, s>(q_gen_4341) -> q_gen_4308
<s, z, s>(q_gen_4373) -> q_gen_4308
<s, z, z>(q_gen_4301) -> q_gen_4308
<s, s, s>(q_gen_4293) -> q_gen_4319
<s, s, s>(q_gen_4319) -> q_gen_4319
<s, z, s>(q_gen_4318) -> q_gen_4319
<s, s, z>(q_gen_4373) -> q_gen_4362
<s, z, z>(q_gen_4313) -> q_gen_4362
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_4292, q_gen_4297, q_gen_4305, q_gen_4306, q_gen_4316, q_gen_4322, q_gen_4323, q_gen_4343},
Q_f={q_gen_4292},
Delta=
{
<s>(q_gen_4323) -> q_gen_4306
<z>() -> q_gen_4306
<s>(q_gen_4306) -> q_gen_4323
<s, s>(q_gen_4297) -> q_gen_4297
<z, z>() -> q_gen_4297
<s, s>(q_gen_4316) -> q_gen_4316
<z, s>(q_gen_4306) -> q_gen_4316
<s, s>(q_gen_4343) -> q_gen_4343
<z, s>(q_gen_4323) -> q_gen_4343
<s, s, s>(q_gen_4305) -> q_gen_4292
<s, z, s>(q_gen_4297) -> q_gen_4292
<z, s, s>(q_gen_4297) -> q_gen_4292
<z, z, z>() -> q_gen_4292
<s, s, s>(q_gen_4292) -> q_gen_4305
<s, s, s>(q_gen_4322) -> q_gen_4305
<s, z, s>(q_gen_4316) -> q_gen_4305
<z, s, s>(q_gen_4316) -> q_gen_4305
<z, z, s>(q_gen_4306) -> q_gen_4305
<s, z, s>(q_gen_4343) -> q_gen_4322
<z, s, s>(q_gen_4343) -> q_gen_4322
<z, z, s>(q_gen_4323) -> q_gen_4322
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 74
() -> minus([z, y, z]) -> 74
() -> plus([n, z, n]) -> 74
(minus([_pq, n, _qq]) /\ plus([m, n, _pq])) -> eq_nat([_qq, m]) -> 82
(minus([u, x2, _fq])) -> minus([s(u), s(x2), _fq]) -> 82
(plus([n, mm, _kq])) -> plus([n, s(mm), s(_kq)]) -> 80
}
Sat witness: Found: ((minus([_pq, n, _qq]) /\ plus([m, n, _pq])) -> eq_nat([_qq, m]), {
_pq -> s(s(s(s(s(z)))))  ;  _qq -> s(z)  ;  m -> s(s(z))  ;  n -> s(s(s(z)))
})

-------------------------------------------
Step 86, which took 0.976201 s (model generation: 0.972841,  model checking: 0.003360):

Model:
|_
{
minus -> 
{{{
Q={q_gen_4293, q_gen_4294, q_gen_4295, q_gen_4301, q_gen_4308, q_gen_4313, q_gen_4318, q_gen_4319, q_gen_4341, q_gen_4362, q_gen_4373},
Q_f={q_gen_4293, q_gen_4294},
Delta=
{
<z>() -> q_gen_4301
<s>(q_gen_4301) -> q_gen_4313
<s>(q_gen_4313) -> q_gen_4313
<s, s>(q_gen_4295) -> q_gen_4295
<z, z>() -> q_gen_4295
<s, s>(q_gen_4318) -> q_gen_4318
<z, s>(q_gen_4301) -> q_gen_4318
<z, s>(q_gen_4313) -> q_gen_4318
<s, s>(q_gen_4341) -> q_gen_4341
<s, z>(q_gen_4301) -> q_gen_4341
<s, s>(q_gen_4373) -> q_gen_4373
<s, z>(q_gen_4313) -> q_gen_4373
<s, s, s>(q_gen_4294) -> q_gen_4293
<s, s, z>(q_gen_4295) -> q_gen_4293
<s, s, z>(q_gen_4318) -> q_gen_4293
<z, s, z>(q_gen_4301) -> q_gen_4293
<z, s, z>(q_gen_4313) -> q_gen_4293
<z, z, z>() -> q_gen_4293
<s, s, s>(q_gen_4308) -> q_gen_4294
<s, z, s>(q_gen_4295) -> q_gen_4294
<s, s, s>(q_gen_4362) -> q_gen_4308
<s, s, z>(q_gen_4341) -> q_gen_4308
<s, z, s>(q_gen_4341) -> q_gen_4308
<s, z, z>(q_gen_4301) -> q_gen_4308
<s, s, s>(q_gen_4293) -> q_gen_4319
<s, s, s>(q_gen_4319) -> q_gen_4319
<s, z, s>(q_gen_4318) -> q_gen_4319
<s, s, z>(q_gen_4373) -> q_gen_4362
<s, z, s>(q_gen_4373) -> q_gen_4362
<s, z, z>(q_gen_4313) -> q_gen_4362
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_4292, q_gen_4297, q_gen_4305, q_gen_4306, q_gen_4316, q_gen_4322, q_gen_4323, q_gen_4343},
Q_f={q_gen_4292},
Delta=
{
<s>(q_gen_4323) -> q_gen_4306
<z>() -> q_gen_4306
<s>(q_gen_4306) -> q_gen_4323
<s, s>(q_gen_4297) -> q_gen_4297
<z, z>() -> q_gen_4297
<s, s>(q_gen_4316) -> q_gen_4316
<z, s>(q_gen_4306) -> q_gen_4316
<s, s>(q_gen_4343) -> q_gen_4343
<z, s>(q_gen_4323) -> q_gen_4343
<s, s, s>(q_gen_4305) -> q_gen_4292
<s, z, s>(q_gen_4297) -> q_gen_4292
<z, s, s>(q_gen_4297) -> q_gen_4292
<z, z, z>() -> q_gen_4292
<s, s, s>(q_gen_4292) -> q_gen_4305
<s, s, s>(q_gen_4322) -> q_gen_4305
<s, z, s>(q_gen_4316) -> q_gen_4305
<z, s, s>(q_gen_4316) -> q_gen_4305
<z, z, s>(q_gen_4306) -> q_gen_4305
<s, z, s>(q_gen_4343) -> q_gen_4322
<z, s, s>(q_gen_4343) -> q_gen_4322
<z, z, s>(q_gen_4323) -> q_gen_4322
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 75
() -> minus([z, y, z]) -> 75
() -> plus([n, z, n]) -> 75
(minus([_pq, n, _qq]) /\ plus([m, n, _pq])) -> eq_nat([_qq, m]) -> 82
(minus([u, x2, _fq])) -> minus([s(u), s(x2), _fq]) -> 85
(plus([n, mm, _kq])) -> plus([n, s(mm), s(_kq)]) -> 81
}
Sat witness: Found: ((minus([u, x2, _fq])) -> minus([s(u), s(x2), _fq]), {
_fq -> s(s(s(s(z))))  ;  u -> s(s(s(s(s(s(z))))))  ;  x2 -> s(s(s(z)))
})

-------------------------------------------
Step 87, which took 1.206158 s (model generation: 1.201764,  model checking: 0.004394):

Model:
|_
{
minus -> 
{{{
Q={q_gen_4293, q_gen_4294, q_gen_4295, q_gen_4301, q_gen_4308, q_gen_4313, q_gen_4318, q_gen_4319, q_gen_4341, q_gen_4362, q_gen_4373},
Q_f={q_gen_4293, q_gen_4294},
Delta=
{
<z>() -> q_gen_4301
<s>(q_gen_4301) -> q_gen_4313
<s>(q_gen_4313) -> q_gen_4313
<s, s>(q_gen_4295) -> q_gen_4295
<z, z>() -> q_gen_4295
<s, s>(q_gen_4318) -> q_gen_4318
<z, s>(q_gen_4301) -> q_gen_4318
<z, s>(q_gen_4313) -> q_gen_4318
<s, s>(q_gen_4341) -> q_gen_4341
<s, z>(q_gen_4301) -> q_gen_4341
<s, s>(q_gen_4373) -> q_gen_4373
<s, z>(q_gen_4313) -> q_gen_4373
<s, s, s>(q_gen_4294) -> q_gen_4293
<s, s, z>(q_gen_4295) -> q_gen_4293
<z, s, z>(q_gen_4313) -> q_gen_4293
<z, z, z>() -> q_gen_4293
<s, s, s>(q_gen_4308) -> q_gen_4294
<s, s, z>(q_gen_4318) -> q_gen_4294
<s, z, s>(q_gen_4295) -> q_gen_4294
<z, s, z>(q_gen_4301) -> q_gen_4294
<s, s, s>(q_gen_4362) -> q_gen_4308
<s, s, z>(q_gen_4341) -> q_gen_4308
<s, z, s>(q_gen_4341) -> q_gen_4308
<s, z, s>(q_gen_4373) -> q_gen_4308
<s, z, z>(q_gen_4301) -> q_gen_4308
<s, s, s>(q_gen_4293) -> q_gen_4319
<s, s, s>(q_gen_4319) -> q_gen_4319
<s, z, s>(q_gen_4318) -> q_gen_4319
<s, s, z>(q_gen_4373) -> q_gen_4362
<s, z, z>(q_gen_4313) -> q_gen_4362
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_4292, q_gen_4297, q_gen_4305, q_gen_4306, q_gen_4316, q_gen_4322, q_gen_4323, q_gen_4343},
Q_f={q_gen_4292},
Delta=
{
<s>(q_gen_4323) -> q_gen_4306
<z>() -> q_gen_4306
<s>(q_gen_4306) -> q_gen_4323
<s, s>(q_gen_4297) -> q_gen_4297
<s, s>(q_gen_4343) -> q_gen_4297
<z, z>() -> q_gen_4297
<s, s>(q_gen_4316) -> q_gen_4316
<z, s>(q_gen_4306) -> q_gen_4316
<z, s>(q_gen_4323) -> q_gen_4343
<s, s, s>(q_gen_4305) -> q_gen_4292
<s, z, s>(q_gen_4297) -> q_gen_4292
<s, z, s>(q_gen_4343) -> q_gen_4292
<z, s, s>(q_gen_4297) -> q_gen_4292
<z, z, z>() -> q_gen_4292
<s, s, s>(q_gen_4292) -> q_gen_4305
<s, s, s>(q_gen_4322) -> q_gen_4305
<s, z, s>(q_gen_4316) -> q_gen_4305
<z, s, s>(q_gen_4316) -> q_gen_4305
<z, z, s>(q_gen_4306) -> q_gen_4305
<z, s, s>(q_gen_4343) -> q_gen_4322
<z, z, s>(q_gen_4323) -> q_gen_4322
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 76
() -> minus([z, y, z]) -> 76
() -> plus([n, z, n]) -> 76
(minus([_pq, n, _qq]) /\ plus([m, n, _pq])) -> eq_nat([_qq, m]) -> 85
(minus([u, x2, _fq])) -> minus([s(u), s(x2), _fq]) -> 85
(plus([n, mm, _kq])) -> plus([n, s(mm), s(_kq)]) -> 82
}
Sat witness: Found: ((minus([_pq, n, _qq]) /\ plus([m, n, _pq])) -> eq_nat([_qq, m]), {
_pq -> s(s(s(s(z))))  ;  _qq -> s(z)  ;  m -> s(s(s(z)))  ;  n -> s(s(s(z)))
})

-------------------------------------------
Step 88, which took 1.524323 s (model generation: 1.523506,  model checking: 0.000817):

Model:
|_
{
minus -> 
{{{
Q={q_gen_4293, q_gen_4295, q_gen_4301, q_gen_4308, q_gen_4313, q_gen_4318, q_gen_4319, q_gen_4341, q_gen_4353, q_gen_4373},
Q_f={q_gen_4293},
Delta=
{
<z>() -> q_gen_4301
<s>(q_gen_4301) -> q_gen_4313
<s>(q_gen_4313) -> q_gen_4353
<s, s>(q_gen_4295) -> q_gen_4295
<z, z>() -> q_gen_4295
<s, s>(q_gen_4318) -> q_gen_4318
<z, s>(q_gen_4301) -> q_gen_4318
<z, s>(q_gen_4313) -> q_gen_4318
<s, s>(q_gen_4341) -> q_gen_4341
<s, z>(q_gen_4301) -> q_gen_4341
<z, s>(q_gen_4353) -> q_gen_4341
<s, s>(q_gen_4373) -> q_gen_4373
<s, z>(q_gen_4313) -> q_gen_4373
<s, s, s>(q_gen_4308) -> q_gen_4293
<s, s, z>(q_gen_4295) -> q_gen_4293
<s, s, z>(q_gen_4318) -> q_gen_4293
<s, z, s>(q_gen_4295) -> q_gen_4293
<s, z, z>(q_gen_4353) -> q_gen_4293
<z, s, z>(q_gen_4301) -> q_gen_4293
<z, s, z>(q_gen_4313) -> q_gen_4293
<z, s, z>(q_gen_4353) -> q_gen_4293
<z, z, z>() -> q_gen_4293
<s, s, s>(q_gen_4319) -> q_gen_4308
<s, s, z>(q_gen_4341) -> q_gen_4308
<s, z, s>(q_gen_4341) -> q_gen_4308
<s, z, z>(q_gen_4301) -> q_gen_4308
<s, s, s>(q_gen_4293) -> q_gen_4319
<s, s, z>(q_gen_4373) -> q_gen_4319
<s, z, s>(q_gen_4318) -> q_gen_4319
<s, z, s>(q_gen_4373) -> q_gen_4319
<s, z, z>(q_gen_4313) -> q_gen_4319
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_4292, q_gen_4297, q_gen_4305, q_gen_4306, q_gen_4309, q_gen_4316, q_gen_4322, q_gen_4323, q_gen_4343, q_gen_4371},
Q_f={q_gen_4292},
Delta=
{
<z>() -> q_gen_4306
<s>(q_gen_4306) -> q_gen_4323
<s>(q_gen_4323) -> q_gen_4371
<s, s>(q_gen_4297) -> q_gen_4297
<z, z>() -> q_gen_4297
<s, s>(q_gen_4316) -> q_gen_4316
<z, s>(q_gen_4306) -> q_gen_4316
<s, s>(q_gen_4343) -> q_gen_4343
<z, s>(q_gen_4323) -> q_gen_4343
<s, s, s>(q_gen_4305) -> q_gen_4292
<s, z, s>(q_gen_4297) -> q_gen_4292
<z, s, s>(q_gen_4297) -> q_gen_4292
<z, z, z>() -> q_gen_4292
<s, s, s>(q_gen_4322) -> q_gen_4305
<s, z, s>(q_gen_4316) -> q_gen_4305
<z, s, s>(q_gen_4316) -> q_gen_4305
<z, z, s>(q_gen_4306) -> q_gen_4305
<s, s, s>(q_gen_4292) -> q_gen_4309
<z, z, s>(q_gen_4371) -> q_gen_4309
<s, s, s>(q_gen_4309) -> q_gen_4322
<s, z, s>(q_gen_4343) -> q_gen_4322
<z, s, s>(q_gen_4343) -> q_gen_4322
<z, z, s>(q_gen_4323) -> q_gen_4322
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 76
() -> minus([z, y, z]) -> 79
() -> plus([n, z, n]) -> 77
(minus([_pq, n, _qq]) /\ plus([m, n, _pq])) -> eq_nat([_qq, m]) -> 85
(minus([u, x2, _fq])) -> minus([s(u), s(x2), _fq]) -> 85
(plus([n, mm, _kq])) -> plus([n, s(mm), s(_kq)]) -> 82
}
Sat witness: Found: (() -> minus([z, y, z]), {
y -> s(s(s(s(z))))
})

-------------------------------------------
Step 89, which took 1.431570 s (model generation: 1.429044,  model checking: 0.002526):

Model:
|_
{
minus -> 
{{{
Q={q_gen_4293, q_gen_4295, q_gen_4301, q_gen_4308, q_gen_4313, q_gen_4318, q_gen_4319, q_gen_4341, q_gen_4353, q_gen_4373},
Q_f={q_gen_4293},
Delta=
{
<z>() -> q_gen_4301
<s>(q_gen_4301) -> q_gen_4313
<s>(q_gen_4353) -> q_gen_4313
<s>(q_gen_4313) -> q_gen_4353
<s, s>(q_gen_4295) -> q_gen_4295
<z, z>() -> q_gen_4295
<s, s>(q_gen_4318) -> q_gen_4318
<z, s>(q_gen_4301) -> q_gen_4318
<z, s>(q_gen_4313) -> q_gen_4318
<s, s>(q_gen_4341) -> q_gen_4341
<s, z>(q_gen_4301) -> q_gen_4341
<z, s>(q_gen_4353) -> q_gen_4341
<s, s>(q_gen_4373) -> q_gen_4373
<s, z>(q_gen_4313) -> q_gen_4373
<s, s, s>(q_gen_4308) -> q_gen_4293
<s, s, z>(q_gen_4295) -> q_gen_4293
<s, s, z>(q_gen_4318) -> q_gen_4293
<s, z, s>(q_gen_4295) -> q_gen_4293
<s, z, z>(q_gen_4353) -> q_gen_4293
<z, s, z>(q_gen_4301) -> q_gen_4293
<z, s, z>(q_gen_4313) -> q_gen_4293
<z, s, z>(q_gen_4353) -> q_gen_4293
<z, z, z>() -> q_gen_4293
<s, s, s>(q_gen_4319) -> q_gen_4308
<s, s, z>(q_gen_4341) -> q_gen_4308
<s, z, s>(q_gen_4341) -> q_gen_4308
<s, z, z>(q_gen_4301) -> q_gen_4308
<s, s, s>(q_gen_4293) -> q_gen_4319
<s, s, z>(q_gen_4373) -> q_gen_4319
<s, z, s>(q_gen_4318) -> q_gen_4319
<s, z, s>(q_gen_4373) -> q_gen_4319
<s, z, z>(q_gen_4313) -> q_gen_4319
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_4292, q_gen_4297, q_gen_4305, q_gen_4306, q_gen_4309, q_gen_4314, q_gen_4315, q_gen_4316, q_gen_4322, q_gen_4323},
Q_f={q_gen_4292, q_gen_4314},
Delta=
{
<z>() -> q_gen_4306
<s>(q_gen_4306) -> q_gen_4323
<s>(q_gen_4323) -> q_gen_4323
<s, s>(q_gen_4297) -> q_gen_4297
<z, z>() -> q_gen_4297
<s, s>(q_gen_4316) -> q_gen_4316
<z, s>(q_gen_4306) -> q_gen_4316
<z, s>(q_gen_4323) -> q_gen_4316
<s, s, s>(q_gen_4305) -> q_gen_4292
<s, z, s>(q_gen_4297) -> q_gen_4292
<z, s, s>(q_gen_4297) -> q_gen_4292
<z, z, z>() -> q_gen_4292
<z, z, s>(q_gen_4306) -> q_gen_4305
<s, s, s>(q_gen_4292) -> q_gen_4309
<s, s, s>(q_gen_4314) -> q_gen_4314
<s, s, s>(q_gen_4315) -> q_gen_4314
<s, s, s>(q_gen_4322) -> q_gen_4315
<s, z, s>(q_gen_4316) -> q_gen_4315
<z, s, s>(q_gen_4316) -> q_gen_4315
<s, s, s>(q_gen_4309) -> q_gen_4322
<z, z, s>(q_gen_4323) -> q_gen_4322
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 77
() -> minus([z, y, z]) -> 80
() -> plus([n, z, n]) -> 78
(minus([_pq, n, _qq]) /\ plus([m, n, _pq])) -> eq_nat([_qq, m]) -> 85
(minus([u, x2, _fq])) -> minus([s(u), s(x2), _fq]) -> 88
(plus([n, mm, _kq])) -> plus([n, s(mm), s(_kq)]) -> 83
}
Sat witness: Found: ((minus([u, x2, _fq])) -> minus([s(u), s(x2), _fq]), {
_fq -> s(s(s(s(s(z)))))  ;  u -> s(s(s(z)))  ;  x2 -> s(s(z))
})

-------------------------------------------
Step 90, which took 1.545023 s (model generation: 1.542127,  model checking: 0.002896):

Model:
|_
{
minus -> 
{{{
Q={q_gen_4293, q_gen_4295, q_gen_4301, q_gen_4307, q_gen_4308, q_gen_4313, q_gen_4318, q_gen_4319, q_gen_4341, q_gen_4373},
Q_f={q_gen_4293, q_gen_4307},
Delta=
{
<z>() -> q_gen_4301
<s>(q_gen_4301) -> q_gen_4313
<s>(q_gen_4313) -> q_gen_4313
<s, s>(q_gen_4295) -> q_gen_4295
<z, z>() -> q_gen_4295
<s, s>(q_gen_4318) -> q_gen_4318
<z, s>(q_gen_4301) -> q_gen_4318
<z, s>(q_gen_4313) -> q_gen_4318
<s, s>(q_gen_4341) -> q_gen_4341
<s, z>(q_gen_4301) -> q_gen_4341
<s, s>(q_gen_4373) -> q_gen_4373
<s, z>(q_gen_4313) -> q_gen_4373
<s, s, s>(q_gen_4307) -> q_gen_4293
<s, s, z>(q_gen_4295) -> q_gen_4293
<s, z, s>(q_gen_4295) -> q_gen_4293
<z, s, z>(q_gen_4301) -> q_gen_4293
<z, s, z>(q_gen_4313) -> q_gen_4293
<z, z, z>() -> q_gen_4293
<s, s, s>(q_gen_4308) -> q_gen_4307
<s, s, z>(q_gen_4318) -> q_gen_4307
<s, s, s>(q_gen_4319) -> q_gen_4308
<s, s, z>(q_gen_4341) -> q_gen_4308
<s, z, s>(q_gen_4341) -> q_gen_4308
<s, z, s>(q_gen_4373) -> q_gen_4308
<s, z, z>(q_gen_4301) -> q_gen_4308
<s, s, s>(q_gen_4293) -> q_gen_4319
<s, s, z>(q_gen_4373) -> q_gen_4319
<s, z, s>(q_gen_4318) -> q_gen_4319
<s, z, z>(q_gen_4313) -> q_gen_4319
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_4292, q_gen_4297, q_gen_4305, q_gen_4306, q_gen_4309, q_gen_4314, q_gen_4315, q_gen_4316, q_gen_4322, q_gen_4323},
Q_f={q_gen_4292, q_gen_4314},
Delta=
{
<z>() -> q_gen_4306
<s>(q_gen_4306) -> q_gen_4323
<s>(q_gen_4323) -> q_gen_4323
<s, s>(q_gen_4297) -> q_gen_4297
<z, z>() -> q_gen_4297
<s, s>(q_gen_4316) -> q_gen_4316
<z, s>(q_gen_4306) -> q_gen_4316
<z, s>(q_gen_4323) -> q_gen_4316
<s, s, s>(q_gen_4305) -> q_gen_4292
<s, z, s>(q_gen_4297) -> q_gen_4292
<z, s, s>(q_gen_4297) -> q_gen_4292
<z, z, z>() -> q_gen_4292
<z, z, s>(q_gen_4306) -> q_gen_4305
<s, s, s>(q_gen_4292) -> q_gen_4309
<s, s, s>(q_gen_4314) -> q_gen_4314
<s, s, s>(q_gen_4315) -> q_gen_4314
<s, s, s>(q_gen_4322) -> q_gen_4315
<s, z, s>(q_gen_4316) -> q_gen_4315
<z, s, s>(q_gen_4316) -> q_gen_4315
<s, s, s>(q_gen_4309) -> q_gen_4322
<z, z, s>(q_gen_4323) -> q_gen_4322
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 78
() -> minus([z, y, z]) -> 81
() -> plus([n, z, n]) -> 79
(minus([_pq, n, _qq]) /\ plus([m, n, _pq])) -> eq_nat([_qq, m]) -> 88
(minus([u, x2, _fq])) -> minus([s(u), s(x2), _fq]) -> 88
(plus([n, mm, _kq])) -> plus([n, s(mm), s(_kq)]) -> 84
}
Sat witness: Found: ((minus([_pq, n, _qq]) /\ plus([m, n, _pq])) -> eq_nat([_qq, m]), {
_pq -> s(s(s(s(z))))  ;  _qq -> s(z)  ;  m -> s(s(z))  ;  n -> s(s(s(z)))
})

-------------------------------------------
Step 91, which took 1.382585 s (model generation: 1.380164,  model checking: 0.002421):

Model:
|_
{
minus -> 
{{{
Q={q_gen_4293, q_gen_4295, q_gen_4300, q_gen_4301, q_gen_4308, q_gen_4313, q_gen_4318, q_gen_4319, q_gen_4341, q_gen_4373},
Q_f={q_gen_4293, q_gen_4300},
Delta=
{
<s>(q_gen_4313) -> q_gen_4301
<z>() -> q_gen_4301
<s>(q_gen_4301) -> q_gen_4313
<s, s>(q_gen_4295) -> q_gen_4295
<z, z>() -> q_gen_4295
<s, s>(q_gen_4318) -> q_gen_4318
<z, s>(q_gen_4301) -> q_gen_4318
<z, s>(q_gen_4313) -> q_gen_4318
<s, s>(q_gen_4341) -> q_gen_4341
<s, z>(q_gen_4301) -> q_gen_4341
<s, s>(q_gen_4373) -> q_gen_4373
<s, z>(q_gen_4313) -> q_gen_4373
<s, s, z>(q_gen_4295) -> q_gen_4293
<s, z, s>(q_gen_4295) -> q_gen_4293
<z, s, z>(q_gen_4313) -> q_gen_4293
<z, z, z>() -> q_gen_4293
<s, s, s>(q_gen_4300) -> q_gen_4300
<s, s, s>(q_gen_4308) -> q_gen_4300
<s, s, z>(q_gen_4318) -> q_gen_4300
<z, s, z>(q_gen_4301) -> q_gen_4300
<s, s, s>(q_gen_4319) -> q_gen_4308
<s, s, z>(q_gen_4341) -> q_gen_4308
<s, z, s>(q_gen_4341) -> q_gen_4308
<s, z, z>(q_gen_4301) -> q_gen_4308
<s, s, s>(q_gen_4293) -> q_gen_4319
<s, s, z>(q_gen_4373) -> q_gen_4319
<s, z, s>(q_gen_4318) -> q_gen_4319
<s, z, s>(q_gen_4373) -> q_gen_4319
<s, z, z>(q_gen_4313) -> q_gen_4319
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_4292, q_gen_4297, q_gen_4305, q_gen_4306, q_gen_4309, q_gen_4316, q_gen_4322, q_gen_4323, q_gen_4343, q_gen_4371},
Q_f={q_gen_4292},
Delta=
{
<z>() -> q_gen_4306
<s>(q_gen_4306) -> q_gen_4323
<s>(q_gen_4323) -> q_gen_4371
<s, s>(q_gen_4297) -> q_gen_4297
<z, z>() -> q_gen_4297
<s, s>(q_gen_4316) -> q_gen_4316
<z, s>(q_gen_4306) -> q_gen_4316
<s, s>(q_gen_4343) -> q_gen_4343
<z, s>(q_gen_4323) -> q_gen_4343
<s, s, s>(q_gen_4305) -> q_gen_4292
<s, z, s>(q_gen_4297) -> q_gen_4292
<z, s, s>(q_gen_4297) -> q_gen_4292
<z, z, z>() -> q_gen_4292
<s, s, s>(q_gen_4322) -> q_gen_4305
<s, z, s>(q_gen_4316) -> q_gen_4305
<z, s, s>(q_gen_4316) -> q_gen_4305
<z, z, s>(q_gen_4306) -> q_gen_4305
<s, s, s>(q_gen_4292) -> q_gen_4309
<z, z, s>(q_gen_4371) -> q_gen_4309
<s, s, s>(q_gen_4309) -> q_gen_4322
<s, z, s>(q_gen_4343) -> q_gen_4322
<z, s, s>(q_gen_4343) -> q_gen_4322
<z, z, s>(q_gen_4323) -> q_gen_4322
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 79
() -> minus([z, y, z]) -> 82
() -> plus([n, z, n]) -> 80
(minus([_pq, n, _qq]) /\ plus([m, n, _pq])) -> eq_nat([_qq, m]) -> 88
(minus([u, x2, _fq])) -> minus([s(u), s(x2), _fq]) -> 88
(plus([n, mm, _kq])) -> plus([n, s(mm), s(_kq)]) -> 87
}
Sat witness: Found: ((plus([n, mm, _kq])) -> plus([n, s(mm), s(_kq)]), {
_kq -> s(s(s(s(s(s(z))))))  ;  mm -> s(s(s(z)))  ;  n -> s(s(s(z)))
})

-------------------------------------------
Step 92, which took 2.037935 s (model generation: 2.035993,  model checking: 0.001942):

Model:
|_
{
minus -> 
{{{
Q={q_gen_4293, q_gen_4295, q_gen_4300, q_gen_4301, q_gen_4308, q_gen_4313, q_gen_4318, q_gen_4319, q_gen_4341, q_gen_4373},
Q_f={q_gen_4293, q_gen_4300},
Delta=
{
<s>(q_gen_4313) -> q_gen_4301
<z>() -> q_gen_4301
<s>(q_gen_4301) -> q_gen_4313
<s, s>(q_gen_4295) -> q_gen_4295
<z, z>() -> q_gen_4295
<s, s>(q_gen_4318) -> q_gen_4318
<z, s>(q_gen_4301) -> q_gen_4318
<z, s>(q_gen_4313) -> q_gen_4318
<s, s>(q_gen_4341) -> q_gen_4341
<s, z>(q_gen_4301) -> q_gen_4341
<s, s>(q_gen_4373) -> q_gen_4373
<s, z>(q_gen_4313) -> q_gen_4373
<s, s, z>(q_gen_4295) -> q_gen_4293
<s, z, s>(q_gen_4295) -> q_gen_4293
<z, s, z>(q_gen_4313) -> q_gen_4293
<z, z, z>() -> q_gen_4293
<s, s, s>(q_gen_4300) -> q_gen_4300
<s, s, s>(q_gen_4308) -> q_gen_4300
<s, s, z>(q_gen_4318) -> q_gen_4300
<z, s, z>(q_gen_4301) -> q_gen_4300
<s, s, s>(q_gen_4319) -> q_gen_4308
<s, s, z>(q_gen_4341) -> q_gen_4308
<s, z, s>(q_gen_4341) -> q_gen_4308
<s, z, z>(q_gen_4301) -> q_gen_4308
<s, s, s>(q_gen_4293) -> q_gen_4319
<s, s, z>(q_gen_4373) -> q_gen_4319
<s, z, s>(q_gen_4318) -> q_gen_4319
<s, z, s>(q_gen_4373) -> q_gen_4319
<s, z, z>(q_gen_4313) -> q_gen_4319
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_4292, q_gen_4297, q_gen_4304, q_gen_4305, q_gen_4306, q_gen_4309, q_gen_4315, q_gen_4316, q_gen_4322, q_gen_4323, q_gen_4343},
Q_f={q_gen_4292, q_gen_4304},
Delta=
{
<z>() -> q_gen_4306
<s>(q_gen_4306) -> q_gen_4323
<s>(q_gen_4323) -> q_gen_4323
<s, s>(q_gen_4297) -> q_gen_4297
<z, z>() -> q_gen_4297
<s, s>(q_gen_4316) -> q_gen_4316
<z, s>(q_gen_4306) -> q_gen_4316
<s, s>(q_gen_4343) -> q_gen_4343
<z, s>(q_gen_4323) -> q_gen_4343
<s, s, s>(q_gen_4304) -> q_gen_4292
<s, s, s>(q_gen_4315) -> q_gen_4292
<s, z, s>(q_gen_4297) -> q_gen_4292
<z, s, s>(q_gen_4297) -> q_gen_4292
<z, z, z>() -> q_gen_4292
<s, s, s>(q_gen_4305) -> q_gen_4304
<s, s, s>(q_gen_4322) -> q_gen_4305
<z, z, s>(q_gen_4306) -> q_gen_4305
<s, s, s>(q_gen_4292) -> q_gen_4309
<s, s, s>(q_gen_4309) -> q_gen_4309
<s, z, s>(q_gen_4316) -> q_gen_4315
<z, s, s>(q_gen_4316) -> q_gen_4315
<s, z, s>(q_gen_4343) -> q_gen_4322
<z, s, s>(q_gen_4343) -> q_gen_4322
<z, z, s>(q_gen_4323) -> q_gen_4322
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 80
() -> minus([z, y, z]) -> 83
() -> plus([n, z, n]) -> 81
(minus([_pq, n, _qq]) /\ plus([m, n, _pq])) -> eq_nat([_qq, m]) -> 88
(minus([u, x2, _fq])) -> minus([s(u), s(x2), _fq]) -> 88
(plus([n, mm, _kq])) -> plus([n, s(mm), s(_kq)]) -> 90
}
Sat witness: Found: ((plus([n, mm, _kq])) -> plus([n, s(mm), s(_kq)]), {
_kq -> s(s(s(z)))  ;  mm -> s(s(z))  ;  n -> s(s(z))
})

-------------------------------------------
Step 93, which took 1.635472 s (model generation: 1.634643,  model checking: 0.000829):

Model:
|_
{
minus -> 
{{{
Q={q_gen_4293, q_gen_4295, q_gen_4301, q_gen_4307, q_gen_4308, q_gen_4313, q_gen_4318, q_gen_4319, q_gen_4341, q_gen_4373},
Q_f={q_gen_4293, q_gen_4307},
Delta=
{
<s>(q_gen_4313) -> q_gen_4301
<z>() -> q_gen_4301
<s>(q_gen_4301) -> q_gen_4313
<s, s>(q_gen_4295) -> q_gen_4295
<z, z>() -> q_gen_4295
<s, s>(q_gen_4318) -> q_gen_4318
<z, s>(q_gen_4301) -> q_gen_4318
<z, s>(q_gen_4313) -> q_gen_4318
<s, s>(q_gen_4341) -> q_gen_4341
<s, z>(q_gen_4301) -> q_gen_4341
<s, s>(q_gen_4373) -> q_gen_4373
<s, z>(q_gen_4313) -> q_gen_4373
<s, s, z>(q_gen_4295) -> q_gen_4293
<s, s, z>(q_gen_4318) -> q_gen_4293
<s, z, s>(q_gen_4295) -> q_gen_4293
<z, s, z>(q_gen_4301) -> q_gen_4293
<z, z, z>() -> q_gen_4293
<s, s, s>(q_gen_4307) -> q_gen_4307
<s, s, s>(q_gen_4308) -> q_gen_4307
<z, s, z>(q_gen_4313) -> q_gen_4307
<s, s, s>(q_gen_4319) -> q_gen_4308
<s, s, z>(q_gen_4341) -> q_gen_4308
<s, z, s>(q_gen_4341) -> q_gen_4308
<s, z, z>(q_gen_4301) -> q_gen_4308
<s, s, s>(q_gen_4293) -> q_gen_4319
<s, s, z>(q_gen_4373) -> q_gen_4319
<s, z, s>(q_gen_4318) -> q_gen_4319
<s, z, s>(q_gen_4373) -> q_gen_4319
<s, z, z>(q_gen_4313) -> q_gen_4319
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_4292, q_gen_4297, q_gen_4305, q_gen_4306, q_gen_4309, q_gen_4316, q_gen_4322, q_gen_4323, q_gen_4343, q_gen_4365, q_gen_4371},
Q_f={q_gen_4292},
Delta=
{
<z>() -> q_gen_4306
<s>(q_gen_4306) -> q_gen_4323
<s>(q_gen_4323) -> q_gen_4371
<s, s>(q_gen_4297) -> q_gen_4297
<z, z>() -> q_gen_4297
<z, s>(q_gen_4306) -> q_gen_4316
<s, s>(q_gen_4343) -> q_gen_4343
<z, s>(q_gen_4323) -> q_gen_4343
<s, s>(q_gen_4316) -> q_gen_4365
<z, s>(q_gen_4371) -> q_gen_4365
<s, s, s>(q_gen_4305) -> q_gen_4292
<s, z, s>(q_gen_4297) -> q_gen_4292
<z, s, s>(q_gen_4297) -> q_gen_4292
<z, z, z>() -> q_gen_4292
<s, s, s>(q_gen_4322) -> q_gen_4305
<s, z, s>(q_gen_4316) -> q_gen_4305
<s, z, s>(q_gen_4365) -> q_gen_4305
<z, s, s>(q_gen_4316) -> q_gen_4305
<z, z, s>(q_gen_4306) -> q_gen_4305
<s, s, s>(q_gen_4292) -> q_gen_4309
<z, s, s>(q_gen_4365) -> q_gen_4309
<z, z, s>(q_gen_4371) -> q_gen_4309
<s, s, s>(q_gen_4309) -> q_gen_4322
<s, z, s>(q_gen_4343) -> q_gen_4322
<z, s, s>(q_gen_4343) -> q_gen_4322
<z, z, s>(q_gen_4323) -> q_gen_4322
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 81
() -> minus([z, y, z]) -> 84
() -> plus([n, z, n]) -> 82
(minus([_pq, n, _qq]) /\ plus([m, n, _pq])) -> eq_nat([_qq, m]) -> 88
(minus([u, x2, _fq])) -> minus([s(u), s(x2), _fq]) -> 91
(plus([n, mm, _kq])) -> plus([n, s(mm), s(_kq)]) -> 90
}
Sat witness: Found: ((minus([u, x2, _fq])) -> minus([s(u), s(x2), _fq]), {
_fq -> s(z)  ;  u -> s(z)  ;  x2 -> s(s(s(z)))
})

-------------------------------------------
Step 94, which took 2.150864 s (model generation: 2.149546,  model checking: 0.001318):

Model:
|_
{
minus -> 
{{{
Q={q_gen_4293, q_gen_4295, q_gen_4301, q_gen_4307, q_gen_4308, q_gen_4313, q_gen_4318, q_gen_4319, q_gen_4341, q_gen_4373},
Q_f={q_gen_4293, q_gen_4307},
Delta=
{
<z>() -> q_gen_4301
<s>(q_gen_4301) -> q_gen_4313
<s>(q_gen_4313) -> q_gen_4313
<s, s>(q_gen_4295) -> q_gen_4295
<z, z>() -> q_gen_4295
<s, s>(q_gen_4318) -> q_gen_4318
<z, s>(q_gen_4301) -> q_gen_4318
<z, s>(q_gen_4313) -> q_gen_4318
<s, s>(q_gen_4341) -> q_gen_4341
<s, z>(q_gen_4301) -> q_gen_4341
<s, s>(q_gen_4373) -> q_gen_4373
<s, z>(q_gen_4313) -> q_gen_4373
<s, s, s>(q_gen_4307) -> q_gen_4293
<s, s, z>(q_gen_4295) -> q_gen_4293
<s, z, s>(q_gen_4295) -> q_gen_4293
<z, s, z>(q_gen_4301) -> q_gen_4293
<z, z, z>() -> q_gen_4293
<s, s, s>(q_gen_4308) -> q_gen_4307
<s, s, z>(q_gen_4318) -> q_gen_4307
<z, s, z>(q_gen_4313) -> q_gen_4307
<s, s, s>(q_gen_4319) -> q_gen_4308
<s, s, z>(q_gen_4341) -> q_gen_4308
<s, z, s>(q_gen_4341) -> q_gen_4308
<s, z, s>(q_gen_4373) -> q_gen_4308
<s, z, z>(q_gen_4301) -> q_gen_4308
<s, s, s>(q_gen_4293) -> q_gen_4319
<s, s, z>(q_gen_4373) -> q_gen_4319
<s, z, s>(q_gen_4318) -> q_gen_4319
<s, z, z>(q_gen_4313) -> q_gen_4319
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_4292, q_gen_4296, q_gen_4297, q_gen_4305, q_gen_4306, q_gen_4309, q_gen_4316, q_gen_4322, q_gen_4323, q_gen_4343, q_gen_4371},
Q_f={q_gen_4292, q_gen_4296},
Delta=
{
<z>() -> q_gen_4306
<s>(q_gen_4306) -> q_gen_4323
<s>(q_gen_4323) -> q_gen_4371
<s, s>(q_gen_4297) -> q_gen_4297
<z, s>(q_gen_4371) -> q_gen_4297
<z, z>() -> q_gen_4297
<s, s>(q_gen_4316) -> q_gen_4316
<z, s>(q_gen_4306) -> q_gen_4316
<s, s>(q_gen_4343) -> q_gen_4343
<z, s>(q_gen_4323) -> q_gen_4343
<z, z, z>() -> q_gen_4292
<s, s, s>(q_gen_4305) -> q_gen_4296
<s, z, s>(q_gen_4297) -> q_gen_4296
<z, s, s>(q_gen_4297) -> q_gen_4296
<s, s, s>(q_gen_4322) -> q_gen_4305
<s, z, s>(q_gen_4316) -> q_gen_4305
<z, s, s>(q_gen_4316) -> q_gen_4305
<z, z, s>(q_gen_4306) -> q_gen_4305
<s, s, s>(q_gen_4292) -> q_gen_4309
<z, z, s>(q_gen_4371) -> q_gen_4309
<s, s, s>(q_gen_4296) -> q_gen_4322
<s, s, s>(q_gen_4309) -> q_gen_4322
<s, z, s>(q_gen_4343) -> q_gen_4322
<z, s, s>(q_gen_4343) -> q_gen_4322
<z, z, s>(q_gen_4323) -> q_gen_4322
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 82
() -> minus([z, y, z]) -> 85
() -> plus([n, z, n]) -> 83
(minus([_pq, n, _qq]) /\ plus([m, n, _pq])) -> eq_nat([_qq, m]) -> 91
(minus([u, x2, _fq])) -> minus([s(u), s(x2), _fq]) -> 91
(plus([n, mm, _kq])) -> plus([n, s(mm), s(_kq)]) -> 90
}
Sat witness: Found: ((minus([_pq, n, _qq]) /\ plus([m, n, _pq])) -> eq_nat([_qq, m]), {
_pq -> s(s(s(z)))  ;  _qq -> s(s(s(s(z))))  ;  m -> s(z)  ;  n -> s(s(z))
})

-------------------------------------------
Step 95, which took 3.161749 s (model generation: 3.160223,  model checking: 0.001526):

Model:
|_
{
minus -> 
{{{
Q={q_gen_4293, q_gen_4294, q_gen_4295, q_gen_4301, q_gen_4308, q_gen_4313, q_gen_4318, q_gen_4319, q_gen_4341, q_gen_4362, q_gen_4373},
Q_f={q_gen_4293, q_gen_4294},
Delta=
{
<z>() -> q_gen_4301
<s>(q_gen_4301) -> q_gen_4313
<s>(q_gen_4313) -> q_gen_4313
<s, s>(q_gen_4295) -> q_gen_4295
<z, z>() -> q_gen_4295
<s, s>(q_gen_4318) -> q_gen_4318
<z, s>(q_gen_4301) -> q_gen_4318
<z, s>(q_gen_4313) -> q_gen_4318
<s, s>(q_gen_4341) -> q_gen_4341
<s, z>(q_gen_4301) -> q_gen_4341
<s, s>(q_gen_4373) -> q_gen_4373
<s, z>(q_gen_4313) -> q_gen_4373
<s, s, s>(q_gen_4294) -> q_gen_4293
<s, s, z>(q_gen_4295) -> q_gen_4293
<s, s, z>(q_gen_4318) -> q_gen_4293
<z, s, z>(q_gen_4301) -> q_gen_4293
<z, s, z>(q_gen_4313) -> q_gen_4293
<z, z, z>() -> q_gen_4293
<s, s, s>(q_gen_4308) -> q_gen_4294
<s, z, s>(q_gen_4295) -> q_gen_4294
<s, s, s>(q_gen_4362) -> q_gen_4308
<s, s, z>(q_gen_4341) -> q_gen_4308
<s, z, s>(q_gen_4341) -> q_gen_4308
<s, z, s>(q_gen_4373) -> q_gen_4308
<s, z, z>(q_gen_4301) -> q_gen_4308
<s, s, s>(q_gen_4293) -> q_gen_4319
<s, s, s>(q_gen_4319) -> q_gen_4319
<s, z, s>(q_gen_4318) -> q_gen_4319
<s, s, z>(q_gen_4373) -> q_gen_4362
<s, z, z>(q_gen_4313) -> q_gen_4362
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_4292, q_gen_4296, q_gen_4297, q_gen_4305, q_gen_4306, q_gen_4309, q_gen_4316, q_gen_4322, q_gen_4323, q_gen_4343, q_gen_4371},
Q_f={q_gen_4292, q_gen_4296},
Delta=
{
<z>() -> q_gen_4306
<s>(q_gen_4306) -> q_gen_4323
<s>(q_gen_4323) -> q_gen_4371
<s, s>(q_gen_4297) -> q_gen_4297
<z, s>(q_gen_4371) -> q_gen_4297
<z, z>() -> q_gen_4297
<s, s>(q_gen_4316) -> q_gen_4316
<z, s>(q_gen_4306) -> q_gen_4316
<s, s>(q_gen_4343) -> q_gen_4343
<z, s>(q_gen_4323) -> q_gen_4343
<s, s, s>(q_gen_4305) -> q_gen_4292
<s, z, s>(q_gen_4297) -> q_gen_4292
<z, z, z>() -> q_gen_4292
<z, s, s>(q_gen_4297) -> q_gen_4296
<s, s, s>(q_gen_4322) -> q_gen_4305
<s, z, s>(q_gen_4316) -> q_gen_4305
<z, s, s>(q_gen_4316) -> q_gen_4305
<z, z, s>(q_gen_4306) -> q_gen_4305
<s, s, s>(q_gen_4292) -> q_gen_4309
<z, z, s>(q_gen_4371) -> q_gen_4309
<s, s, s>(q_gen_4296) -> q_gen_4322
<s, s, s>(q_gen_4309) -> q_gen_4322
<s, z, s>(q_gen_4343) -> q_gen_4322
<z, s, s>(q_gen_4343) -> q_gen_4322
<z, z, s>(q_gen_4323) -> q_gen_4322
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 83
() -> minus([z, y, z]) -> 86
() -> plus([n, z, n]) -> 84
(minus([_pq, n, _qq]) /\ plus([m, n, _pq])) -> eq_nat([_qq, m]) -> 91
(minus([u, x2, _fq])) -> minus([s(u), s(x2), _fq]) -> 91
(plus([n, mm, _kq])) -> plus([n, s(mm), s(_kq)]) -> 93
}
Sat witness: Found: ((plus([n, mm, _kq])) -> plus([n, s(mm), s(_kq)]), {
_kq -> s(s(s(s(z))))  ;  mm -> s(s(s(s(z))))  ;  n -> s(s(s(s(z))))
})

-------------------------------------------
Step 96, which took 3.236836 s (model generation: 3.235051,  model checking: 0.001785):

Model:
|_
{
minus -> 
{{{
Q={q_gen_4293, q_gen_4294, q_gen_4295, q_gen_4301, q_gen_4308, q_gen_4313, q_gen_4318, q_gen_4319, q_gen_4341, q_gen_4362, q_gen_4373},
Q_f={q_gen_4293, q_gen_4294},
Delta=
{
<z>() -> q_gen_4301
<s>(q_gen_4301) -> q_gen_4313
<s>(q_gen_4313) -> q_gen_4313
<s, s>(q_gen_4295) -> q_gen_4295
<z, z>() -> q_gen_4295
<s, s>(q_gen_4318) -> q_gen_4318
<z, s>(q_gen_4301) -> q_gen_4318
<z, s>(q_gen_4313) -> q_gen_4318
<s, s>(q_gen_4341) -> q_gen_4341
<s, z>(q_gen_4301) -> q_gen_4341
<s, s>(q_gen_4373) -> q_gen_4373
<s, z>(q_gen_4313) -> q_gen_4373
<s, s, s>(q_gen_4294) -> q_gen_4293
<s, s, z>(q_gen_4295) -> q_gen_4293
<s, s, z>(q_gen_4318) -> q_gen_4293
<z, s, z>(q_gen_4301) -> q_gen_4293
<z, s, z>(q_gen_4313) -> q_gen_4293
<z, z, z>() -> q_gen_4293
<s, s, s>(q_gen_4308) -> q_gen_4294
<s, z, s>(q_gen_4295) -> q_gen_4294
<s, s, s>(q_gen_4362) -> q_gen_4308
<s, s, z>(q_gen_4341) -> q_gen_4308
<s, z, s>(q_gen_4341) -> q_gen_4308
<s, z, s>(q_gen_4373) -> q_gen_4308
<s, z, z>(q_gen_4301) -> q_gen_4308
<s, s, s>(q_gen_4293) -> q_gen_4319
<s, s, s>(q_gen_4319) -> q_gen_4319
<s, z, s>(q_gen_4318) -> q_gen_4319
<s, s, z>(q_gen_4373) -> q_gen_4362
<s, z, z>(q_gen_4313) -> q_gen_4362
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_4292, q_gen_4296, q_gen_4297, q_gen_4305, q_gen_4306, q_gen_4309, q_gen_4316, q_gen_4322, q_gen_4323, q_gen_4343, q_gen_4371},
Q_f={q_gen_4292, q_gen_4296},
Delta=
{
<z>() -> q_gen_4306
<s>(q_gen_4306) -> q_gen_4323
<s>(q_gen_4323) -> q_gen_4371
<s, s>(q_gen_4297) -> q_gen_4297
<z, s>(q_gen_4371) -> q_gen_4297
<z, z>() -> q_gen_4297
<s, s>(q_gen_4316) -> q_gen_4316
<z, s>(q_gen_4306) -> q_gen_4316
<s, s>(q_gen_4343) -> q_gen_4343
<z, s>(q_gen_4323) -> q_gen_4343
<s, s, s>(q_gen_4305) -> q_gen_4292
<z, z, z>() -> q_gen_4292
<s, z, s>(q_gen_4297) -> q_gen_4296
<z, s, s>(q_gen_4297) -> q_gen_4296
<z, z, s>(q_gen_4371) -> q_gen_4296
<s, s, s>(q_gen_4322) -> q_gen_4305
<s, z, s>(q_gen_4316) -> q_gen_4305
<z, s, s>(q_gen_4316) -> q_gen_4305
<z, z, s>(q_gen_4306) -> q_gen_4305
<s, s, s>(q_gen_4292) -> q_gen_4309
<s, s, s>(q_gen_4309) -> q_gen_4309
<s, s, s>(q_gen_4296) -> q_gen_4322
<s, z, s>(q_gen_4343) -> q_gen_4322
<z, s, s>(q_gen_4343) -> q_gen_4322
<z, z, s>(q_gen_4323) -> q_gen_4322
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 84
() -> minus([z, y, z]) -> 87
() -> plus([n, z, n]) -> 85
(minus([_pq, n, _qq]) /\ plus([m, n, _pq])) -> eq_nat([_qq, m]) -> 91
(minus([u, x2, _fq])) -> minus([s(u), s(x2), _fq]) -> 94
(plus([n, mm, _kq])) -> plus([n, s(mm), s(_kq)]) -> 93
}
Sat witness: Found: ((minus([u, x2, _fq])) -> minus([s(u), s(x2), _fq]), {
_fq -> s(s(s(s(z))))  ;  u -> s(s(s(s(s(z)))))  ;  x2 -> s(s(z))
})

-------------------------------------------
Step 97, which took 3.473744 s (model generation: 3.472945,  model checking: 0.000799):

Model:
|_
{
minus -> 
{{{
Q={q_gen_4293, q_gen_4295, q_gen_4301, q_gen_4307, q_gen_4308, q_gen_4313, q_gen_4318, q_gen_4319, q_gen_4341, q_gen_4362, q_gen_4373},
Q_f={q_gen_4293, q_gen_4307},
Delta=
{
<s>(q_gen_4313) -> q_gen_4301
<z>() -> q_gen_4301
<s>(q_gen_4301) -> q_gen_4313
<s, s>(q_gen_4295) -> q_gen_4295
<z, z>() -> q_gen_4295
<s, s>(q_gen_4318) -> q_gen_4318
<z, s>(q_gen_4301) -> q_gen_4318
<z, s>(q_gen_4313) -> q_gen_4318
<s, s>(q_gen_4341) -> q_gen_4341
<s, z>(q_gen_4301) -> q_gen_4341
<s, s>(q_gen_4373) -> q_gen_4373
<s, z>(q_gen_4313) -> q_gen_4373
<s, s, z>(q_gen_4295) -> q_gen_4293
<s, s, z>(q_gen_4318) -> q_gen_4293
<s, z, s>(q_gen_4295) -> q_gen_4293
<z, s, z>(q_gen_4301) -> q_gen_4293
<z, z, z>() -> q_gen_4293
<s, s, s>(q_gen_4308) -> q_gen_4307
<s, z, s>(q_gen_4373) -> q_gen_4307
<z, s, z>(q_gen_4313) -> q_gen_4307
<s, s, s>(q_gen_4307) -> q_gen_4308
<s, s, s>(q_gen_4362) -> q_gen_4308
<s, s, z>(q_gen_4341) -> q_gen_4308
<s, z, s>(q_gen_4341) -> q_gen_4308
<s, z, z>(q_gen_4301) -> q_gen_4308
<s, s, s>(q_gen_4293) -> q_gen_4319
<s, s, s>(q_gen_4319) -> q_gen_4319
<s, z, s>(q_gen_4318) -> q_gen_4319
<s, s, z>(q_gen_4373) -> q_gen_4362
<s, z, z>(q_gen_4313) -> q_gen_4362
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_4292, q_gen_4296, q_gen_4297, q_gen_4305, q_gen_4306, q_gen_4309, q_gen_4316, q_gen_4322, q_gen_4323, q_gen_4343, q_gen_4371},
Q_f={q_gen_4292, q_gen_4296},
Delta=
{
<z>() -> q_gen_4306
<s>(q_gen_4306) -> q_gen_4323
<s>(q_gen_4323) -> q_gen_4371
<s, s>(q_gen_4297) -> q_gen_4297
<z, s>(q_gen_4371) -> q_gen_4297
<z, z>() -> q_gen_4297
<s, s>(q_gen_4316) -> q_gen_4316
<z, s>(q_gen_4306) -> q_gen_4316
<s, s>(q_gen_4343) -> q_gen_4343
<z, s>(q_gen_4323) -> q_gen_4343
<s, z, s>(q_gen_4297) -> q_gen_4292
<z, z, z>() -> q_gen_4292
<s, s, s>(q_gen_4305) -> q_gen_4296
<z, s, s>(q_gen_4297) -> q_gen_4296
<z, z, s>(q_gen_4371) -> q_gen_4296
<s, s, s>(q_gen_4322) -> q_gen_4305
<s, z, s>(q_gen_4316) -> q_gen_4305
<z, s, s>(q_gen_4316) -> q_gen_4305
<z, z, s>(q_gen_4306) -> q_gen_4305
<s, s, s>(q_gen_4292) -> q_gen_4309
<s, s, s>(q_gen_4309) -> q_gen_4309
<s, s, s>(q_gen_4296) -> q_gen_4322
<s, z, s>(q_gen_4343) -> q_gen_4322
<z, s, s>(q_gen_4343) -> q_gen_4322
<z, z, s>(q_gen_4323) -> q_gen_4322
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 85
() -> minus([z, y, z]) -> 88
() -> plus([n, z, n]) -> 86
(minus([_pq, n, _qq]) /\ plus([m, n, _pq])) -> eq_nat([_qq, m]) -> 94
(minus([u, x2, _fq])) -> minus([s(u), s(x2), _fq]) -> 94
(plus([n, mm, _kq])) -> plus([n, s(mm), s(_kq)]) -> 93
}
Sat witness: Found: ((minus([_pq, n, _qq]) /\ plus([m, n, _pq])) -> eq_nat([_qq, m]), {
_pq -> s(s(s(z)))  ;  _qq -> s(z)  ;  m -> z  ;  n -> z
})

-------------------------------------------
Step 98, which took 3.456640 s (model generation: 3.455302,  model checking: 0.001338):

Model:
|_
{
minus -> 
{{{
Q={q_gen_4293, q_gen_4295, q_gen_4301, q_gen_4307, q_gen_4308, q_gen_4313, q_gen_4318, q_gen_4319, q_gen_4341, q_gen_4362, q_gen_4373},
Q_f={q_gen_4293, q_gen_4307},
Delta=
{
<z>() -> q_gen_4301
<s>(q_gen_4301) -> q_gen_4313
<s>(q_gen_4313) -> q_gen_4313
<s, s>(q_gen_4295) -> q_gen_4295
<z, z>() -> q_gen_4295
<s, s>(q_gen_4318) -> q_gen_4318
<z, s>(q_gen_4301) -> q_gen_4318
<z, s>(q_gen_4313) -> q_gen_4318
<s, s>(q_gen_4341) -> q_gen_4341
<s, z>(q_gen_4301) -> q_gen_4341
<s, s>(q_gen_4373) -> q_gen_4373
<s, z>(q_gen_4313) -> q_gen_4373
<s, s, z>(q_gen_4295) -> q_gen_4293
<s, s, z>(q_gen_4318) -> q_gen_4293
<s, z, s>(q_gen_4295) -> q_gen_4293
<z, s, z>(q_gen_4301) -> q_gen_4293
<z, s, z>(q_gen_4313) -> q_gen_4293
<z, z, z>() -> q_gen_4293
<s, s, s>(q_gen_4307) -> q_gen_4307
<s, s, s>(q_gen_4308) -> q_gen_4307
<s, s, s>(q_gen_4362) -> q_gen_4308
<s, s, z>(q_gen_4341) -> q_gen_4308
<s, z, s>(q_gen_4341) -> q_gen_4308
<s, z, z>(q_gen_4301) -> q_gen_4308
<s, s, s>(q_gen_4293) -> q_gen_4319
<s, s, s>(q_gen_4319) -> q_gen_4319
<s, z, s>(q_gen_4318) -> q_gen_4319
<s, s, z>(q_gen_4373) -> q_gen_4362
<s, z, s>(q_gen_4373) -> q_gen_4362
<s, z, z>(q_gen_4313) -> q_gen_4362
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_4292, q_gen_4296, q_gen_4297, q_gen_4305, q_gen_4306, q_gen_4309, q_gen_4316, q_gen_4322, q_gen_4323, q_gen_4343, q_gen_4371},
Q_f={q_gen_4292, q_gen_4296},
Delta=
{
<z>() -> q_gen_4306
<s>(q_gen_4306) -> q_gen_4323
<s>(q_gen_4323) -> q_gen_4371
<s, s>(q_gen_4297) -> q_gen_4297
<z, s>(q_gen_4371) -> q_gen_4297
<z, z>() -> q_gen_4297
<s, s>(q_gen_4316) -> q_gen_4316
<z, s>(q_gen_4306) -> q_gen_4316
<s, s>(q_gen_4343) -> q_gen_4343
<z, s>(q_gen_4323) -> q_gen_4343
<s, z, s>(q_gen_4297) -> q_gen_4292
<z, z, z>() -> q_gen_4292
<s, s, s>(q_gen_4305) -> q_gen_4296
<z, s, s>(q_gen_4297) -> q_gen_4296
<z, z, s>(q_gen_4371) -> q_gen_4296
<s, s, s>(q_gen_4322) -> q_gen_4305
<s, z, s>(q_gen_4316) -> q_gen_4305
<z, s, s>(q_gen_4316) -> q_gen_4305
<z, z, s>(q_gen_4306) -> q_gen_4305
<s, s, s>(q_gen_4292) -> q_gen_4309
<s, s, s>(q_gen_4309) -> q_gen_4309
<s, s, s>(q_gen_4296) -> q_gen_4322
<s, z, s>(q_gen_4343) -> q_gen_4322
<z, s, s>(q_gen_4343) -> q_gen_4322
<z, z, s>(q_gen_4323) -> q_gen_4322
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 86
() -> minus([z, y, z]) -> 89
() -> plus([n, z, n]) -> 87
(minus([_pq, n, _qq]) /\ plus([m, n, _pq])) -> eq_nat([_qq, m]) -> 94
(minus([u, x2, _fq])) -> minus([s(u), s(x2), _fq]) -> 94
(plus([n, mm, _kq])) -> plus([n, s(mm), s(_kq)]) -> 96
}
Sat witness: Found: ((plus([n, mm, _kq])) -> plus([n, s(mm), s(_kq)]), {
_kq -> s(s(s(s(s(s(z))))))  ;  mm -> s(s(z))  ;  n -> s(s(s(s(z))))
})

-------------------------------------------
Step 99, which took 4.262291 s (model generation: 4.259881,  model checking: 0.002410):

Model:
|_
{
minus -> 
{{{
Q={q_gen_4293, q_gen_4295, q_gen_4301, q_gen_4307, q_gen_4308, q_gen_4313, q_gen_4318, q_gen_4319, q_gen_4341, q_gen_4362, q_gen_4373},
Q_f={q_gen_4293, q_gen_4307},
Delta=
{
<s>(q_gen_4313) -> q_gen_4301
<z>() -> q_gen_4301
<s>(q_gen_4301) -> q_gen_4313
<s, s>(q_gen_4295) -> q_gen_4295
<z, z>() -> q_gen_4295
<s, s>(q_gen_4318) -> q_gen_4318
<z, s>(q_gen_4301) -> q_gen_4318
<z, s>(q_gen_4313) -> q_gen_4318
<s, s>(q_gen_4341) -> q_gen_4341
<s, z>(q_gen_4301) -> q_gen_4341
<s, s>(q_gen_4373) -> q_gen_4373
<s, z>(q_gen_4313) -> q_gen_4373
<s, s, z>(q_gen_4295) -> q_gen_4293
<s, s, z>(q_gen_4318) -> q_gen_4293
<s, z, s>(q_gen_4295) -> q_gen_4293
<z, s, z>(q_gen_4301) -> q_gen_4293
<z, s, z>(q_gen_4313) -> q_gen_4293
<z, z, z>() -> q_gen_4293
<s, s, s>(q_gen_4308) -> q_gen_4307
<s, s, s>(q_gen_4307) -> q_gen_4308
<s, s, s>(q_gen_4362) -> q_gen_4308
<s, s, z>(q_gen_4341) -> q_gen_4308
<s, z, s>(q_gen_4341) -> q_gen_4308
<s, z, z>(q_gen_4301) -> q_gen_4308
<s, s, s>(q_gen_4293) -> q_gen_4319
<s, s, s>(q_gen_4319) -> q_gen_4319
<s, z, s>(q_gen_4318) -> q_gen_4319
<s, s, z>(q_gen_4373) -> q_gen_4362
<s, z, s>(q_gen_4373) -> q_gen_4362
<s, z, z>(q_gen_4313) -> q_gen_4362
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_4292, q_gen_4296, q_gen_4297, q_gen_4305, q_gen_4306, q_gen_4309, q_gen_4316, q_gen_4322, q_gen_4323, q_gen_4343, q_gen_4371},
Q_f={q_gen_4292, q_gen_4296},
Delta=
{
<z>() -> q_gen_4306
<s>(q_gen_4306) -> q_gen_4323
<s>(q_gen_4323) -> q_gen_4371
<s, s>(q_gen_4297) -> q_gen_4297
<z, s>(q_gen_4371) -> q_gen_4297
<z, z>() -> q_gen_4297
<s, s>(q_gen_4316) -> q_gen_4316
<z, s>(q_gen_4306) -> q_gen_4316
<s, s>(q_gen_4343) -> q_gen_4343
<z, s>(q_gen_4323) -> q_gen_4343
<z, z, z>() -> q_gen_4292
<s, s, s>(q_gen_4305) -> q_gen_4296
<s, z, s>(q_gen_4297) -> q_gen_4296
<z, s, s>(q_gen_4297) -> q_gen_4296
<z, z, s>(q_gen_4371) -> q_gen_4296
<s, s, s>(q_gen_4322) -> q_gen_4305
<s, z, s>(q_gen_4316) -> q_gen_4305
<z, s, s>(q_gen_4316) -> q_gen_4305
<z, z, s>(q_gen_4306) -> q_gen_4305
<s, s, s>(q_gen_4292) -> q_gen_4309
<s, s, s>(q_gen_4309) -> q_gen_4309
<s, s, s>(q_gen_4296) -> q_gen_4322
<s, z, s>(q_gen_4343) -> q_gen_4322
<z, s, s>(q_gen_4343) -> q_gen_4322
<z, z, s>(q_gen_4323) -> q_gen_4322
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 87
() -> minus([z, y, z]) -> 90
() -> plus([n, z, n]) -> 88
(minus([_pq, n, _qq]) /\ plus([m, n, _pq])) -> eq_nat([_qq, m]) -> 97
(minus([u, x2, _fq])) -> minus([s(u), s(x2), _fq]) -> 95
(plus([n, mm, _kq])) -> plus([n, s(mm), s(_kq)]) -> 96
}
Sat witness: Found: ((minus([_pq, n, _qq]) /\ plus([m, n, _pq])) -> eq_nat([_qq, m]), {
_pq -> s(s(s(s(z))))  ;  _qq -> s(z)  ;  m -> s(s(s(z)))  ;  n -> s(z)
})

-------------------------------------------
Step 100, which took 6.274656 s (model generation: 6.270421,  model checking: 0.004235):

Model:
|_
{
minus -> 
{{{
Q={q_gen_4293, q_gen_4295, q_gen_4301, q_gen_4307, q_gen_4308, q_gen_4313, q_gen_4318, q_gen_4319, q_gen_4341, q_gen_4362, q_gen_4373},
Q_f={q_gen_4293, q_gen_4307},
Delta=
{
<z>() -> q_gen_4301
<s>(q_gen_4301) -> q_gen_4313
<s>(q_gen_4313) -> q_gen_4313
<s, s>(q_gen_4295) -> q_gen_4295
<z, z>() -> q_gen_4295
<s, s>(q_gen_4318) -> q_gen_4318
<z, s>(q_gen_4301) -> q_gen_4318
<z, s>(q_gen_4313) -> q_gen_4318
<s, s>(q_gen_4341) -> q_gen_4341
<s, z>(q_gen_4301) -> q_gen_4341
<s, s>(q_gen_4373) -> q_gen_4373
<s, z>(q_gen_4313) -> q_gen_4373
<s, s, z>(q_gen_4295) -> q_gen_4293
<s, z, s>(q_gen_4295) -> q_gen_4293
<z, s, z>(q_gen_4301) -> q_gen_4293
<z, s, z>(q_gen_4313) -> q_gen_4293
<z, z, z>() -> q_gen_4293
<s, s, s>(q_gen_4307) -> q_gen_4307
<s, s, s>(q_gen_4308) -> q_gen_4307
<s, s, z>(q_gen_4318) -> q_gen_4307
<s, s, s>(q_gen_4362) -> q_gen_4308
<s, s, z>(q_gen_4341) -> q_gen_4308
<s, z, s>(q_gen_4341) -> q_gen_4308
<s, z, s>(q_gen_4373) -> q_gen_4308
<s, z, z>(q_gen_4301) -> q_gen_4308
<s, s, s>(q_gen_4293) -> q_gen_4319
<s, s, s>(q_gen_4319) -> q_gen_4319
<s, z, s>(q_gen_4318) -> q_gen_4319
<s, s, z>(q_gen_4373) -> q_gen_4362
<s, z, z>(q_gen_4313) -> q_gen_4362
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_4292, q_gen_4297, q_gen_4305, q_gen_4306, q_gen_4309, q_gen_4316, q_gen_4321, q_gen_4322, q_gen_4323, q_gen_4339, q_gen_4343},
Q_f={q_gen_4292, q_gen_4339},
Delta=
{
<z>() -> q_gen_4306
<s>(q_gen_4306) -> q_gen_4323
<s>(q_gen_4323) -> q_gen_4323
<s, s>(q_gen_4297) -> q_gen_4297
<z, z>() -> q_gen_4297
<s, s>(q_gen_4316) -> q_gen_4316
<z, s>(q_gen_4306) -> q_gen_4316
<s, s>(q_gen_4343) -> q_gen_4343
<z, s>(q_gen_4323) -> q_gen_4343
<s, s, s>(q_gen_4305) -> q_gen_4292
<s, z, s>(q_gen_4297) -> q_gen_4292
<z, s, s>(q_gen_4297) -> q_gen_4292
<z, z, z>() -> q_gen_4292
<s, z, s>(q_gen_4316) -> q_gen_4305
<z, s, s>(q_gen_4316) -> q_gen_4305
<z, z, s>(q_gen_4306) -> q_gen_4305
<s, s, s>(q_gen_4292) -> q_gen_4309
<s, s, s>(q_gen_4322) -> q_gen_4321
<s, z, s>(q_gen_4343) -> q_gen_4321
<s, s, s>(q_gen_4309) -> q_gen_4322
<z, s, s>(q_gen_4343) -> q_gen_4322
<z, z, s>(q_gen_4323) -> q_gen_4322
<s, s, s>(q_gen_4321) -> q_gen_4339
<s, s, s>(q_gen_4339) -> q_gen_4339
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 88
() -> minus([z, y, z]) -> 91
() -> plus([n, z, n]) -> 89
(minus([_pq, n, _qq]) /\ plus([m, n, _pq])) -> eq_nat([_qq, m]) -> 100
(minus([u, x2, _fq])) -> minus([s(u), s(x2), _fq]) -> 96
(plus([n, mm, _kq])) -> plus([n, s(mm), s(_kq)]) -> 97
}
Sat witness: Found: ((minus([_pq, n, _qq]) /\ plus([m, n, _pq])) -> eq_nat([_qq, m]), {
_pq -> s(s(s(s(z))))  ;  _qq -> s(s(s(z)))  ;  m -> s(s(z))  ;  n -> s(s(z))
})

-------------------------------------------
Step 101, which took 2.022297 s (model generation: 2.021711,  model checking: 0.000586):

Model:
|_
{
minus -> 
{{{
Q={q_gen_4293, q_gen_4294, q_gen_4295, q_gen_4301, q_gen_4308, q_gen_4312, q_gen_4313, q_gen_4318, q_gen_4319, q_gen_4335, q_gen_4336, q_gen_4340, q_gen_4341, q_gen_4373, q_gen_4405},
Q_f={q_gen_4293, q_gen_4294, q_gen_4312},
Delta=
{
<z>() -> q_gen_4301
<s>(q_gen_4301) -> q_gen_4313
<s>(q_gen_4313) -> q_gen_4313
<s, s>(q_gen_4295) -> q_gen_4295
<z, z>() -> q_gen_4295
<s, s>(q_gen_4318) -> q_gen_4318
<z, s>(q_gen_4301) -> q_gen_4318
<z, s>(q_gen_4313) -> q_gen_4336
<s, s>(q_gen_4341) -> q_gen_4341
<s, z>(q_gen_4301) -> q_gen_4341
<s, s>(q_gen_4373) -> q_gen_4373
<s, z>(q_gen_4313) -> q_gen_4373
<s, s, s>(q_gen_4294) -> q_gen_4293
<s, s, s>(q_gen_4340) -> q_gen_4293
<s, s, z>(q_gen_4295) -> q_gen_4293
<s, s, z>(q_gen_4318) -> q_gen_4293
<s, s, z>(q_gen_4336) -> q_gen_4293
<z, s, z>(q_gen_4301) -> q_gen_4293
<z, z, z>() -> q_gen_4293
<s, s, s>(q_gen_4308) -> q_gen_4294
<s, z, s>(q_gen_4295) -> q_gen_4294
<s, s, s>(q_gen_4335) -> q_gen_4308
<s, z, z>(q_gen_4301) -> q_gen_4308
<s, s, s>(q_gen_4405) -> q_gen_4312
<s, z, s>(q_gen_4373) -> q_gen_4312
<z, s, z>(q_gen_4313) -> q_gen_4312
<s, s, s>(q_gen_4293) -> q_gen_4319
<s, z, s>(q_gen_4318) -> q_gen_4319
<s, s, s>(q_gen_4319) -> q_gen_4335
<s, s, z>(q_gen_4373) -> q_gen_4335
<s, z, s>(q_gen_4336) -> q_gen_4335
<s, z, z>(q_gen_4313) -> q_gen_4335
<s, s, z>(q_gen_4341) -> q_gen_4340
<s, z, s>(q_gen_4341) -> q_gen_4340
<s, s, s>(q_gen_4312) -> q_gen_4405
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_4292, q_gen_4296, q_gen_4297, q_gen_4305, q_gen_4306, q_gen_4309, q_gen_4310, q_gen_4311, q_gen_4314, q_gen_4315, q_gen_4316, q_gen_4320, q_gen_4321, q_gen_4322, q_gen_4323, q_gen_4327, q_gen_4328, q_gen_4331, q_gen_4339, q_gen_4343, q_gen_4345, q_gen_4355, q_gen_4356, q_gen_4364, q_gen_4377},
Q_f={q_gen_4292, q_gen_4296, q_gen_4310, q_gen_4314, q_gen_4327, q_gen_4328, q_gen_4339, q_gen_4377},
Delta=
{
<z>() -> q_gen_4306
<s>(q_gen_4306) -> q_gen_4323
<s>(q_gen_4323) -> q_gen_4323
<z, z>() -> q_gen_4297
<s, s>(q_gen_4297) -> q_gen_4311
<z, s>(q_gen_4306) -> q_gen_4316
<s, s>(q_gen_4316) -> q_gen_4343
<z, s>(q_gen_4323) -> q_gen_4343
<s, s>(q_gen_4311) -> q_gen_4345
<s, s>(q_gen_4343) -> q_gen_4345
<s, s, s>(q_gen_4305) -> q_gen_4292
<s, z, s>(q_gen_4297) -> q_gen_4292
<z, z, z>() -> q_gen_4292
<s, s, s>(q_gen_4339) -> q_gen_4296
<s, s, s>(q_gen_4355) -> q_gen_4296
<z, s, s>(q_gen_4297) -> q_gen_4296
<s, s, s>(q_gen_4314) -> q_gen_4305
<s, s, s>(q_gen_4327) -> q_gen_4305
<z, z, s>(q_gen_4306) -> q_gen_4305
<s, s, s>(q_gen_4292) -> q_gen_4309
<s, s, s>(q_gen_4331) -> q_gen_4309
<s, z, s>(q_gen_4311) -> q_gen_4310
<s, s, s>(q_gen_4315) -> q_gen_4314
<z, s, s>(q_gen_4316) -> q_gen_4315
<s, s, s>(q_gen_4296) -> q_gen_4320
<s, z, s>(q_gen_4316) -> q_gen_4320
<z, s, s>(q_gen_4343) -> q_gen_4320
<s, s, s>(q_gen_4322) -> q_gen_4321
<z, z, s>(q_gen_4323) -> q_gen_4322
<z, s, s>(q_gen_4311) -> q_gen_4327
<s, s, s>(q_gen_4320) -> q_gen_4328
<s, s, s>(q_gen_4309) -> q_gen_4331
<s, s, s>(q_gen_4321) -> q_gen_4339
<s, s, s>(q_gen_4364) -> q_gen_4339
<s, s, s>(q_gen_4377) -> q_gen_4339
<s, z, s>(q_gen_4345) -> q_gen_4339
<s, s, s>(q_gen_4356) -> q_gen_4355
<z, s, s>(q_gen_4345) -> q_gen_4356
<s, s, s>(q_gen_4310) -> q_gen_4364
<s, z, s>(q_gen_4343) -> q_gen_4364
<s, s, s>(q_gen_4328) -> q_gen_4377
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 89
() -> minus([z, y, z]) -> 91
() -> plus([n, z, n]) -> 92
(minus([_pq, n, _qq]) /\ plus([m, n, _pq])) -> eq_nat([_qq, m]) -> 100
(minus([u, x2, _fq])) -> minus([s(u), s(x2), _fq]) -> 96
(plus([n, mm, _kq])) -> plus([n, s(mm), s(_kq)]) -> 97
}
Sat witness: Found: (() -> plus([n, z, n]), {
n -> s(s(s(s(z))))
})

Total time: 65.647629
Reason for stopping: DontKnow. Stopped because: timeout