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


Learning problem is:

env: {
elt -> {a, b}  ;  eltlist -> {cons, nil}  ;  nat -> {s, z}
}
definition:
{
(append, F:
{() -> append([nil, l2, l2])
(append([t1, l2, _qp])) -> append([cons(h1, t1), l2, cons(h1, _qp)])}
(append([_rp, _sp, _tp]) /\ append([_rp, _sp, _up])) -> eq_eltlist([_tp, _up])
)
(leq, P:
{() -> leq([z, s(nn2)])
() -> leq([z, z])
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)])
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2])
(leq([s(nn1), z])) -> BOT}
)
(length, F:
{() -> length([nil, z])
(length([ll, _vp])) -> length([cons(x, ll), s(_vp)])}
(length([_wp, _xp]) /\ length([_wp, _yp])) -> eq_nat([_xp, _yp])
)
}

properties:
{(append([l1, l2, _aq]) /\ length([_aq, _bq]) /\ length([l1, _zp])) -> leq([_zp, _bq]), (append([l1, l2, _dq]) /\ length([_dq, _eq]) /\ length([l2, _cq])) -> leq([_cq, _eq])}


over-approximation: {append, length}
under-approximation: {leq}

Clause system for inference is:

{
() -> append([nil, l2, l2]) -> 0
() -> length([nil, z]) -> 0
() -> leq([z, s(nn2)]) -> 0
() -> leq([z, z]) -> 0
(append([l1, l2, _aq]) /\ length([_aq, _bq]) /\ length([l1, _zp])) -> leq([_zp, _bq]) -> 0
(append([l1, l2, _dq]) /\ length([_dq, _eq]) /\ length([l2, _cq])) -> leq([_cq, _eq]) -> 0
(append([t1, l2, _qp])) -> append([cons(h1, t1), l2, cons(h1, _qp)]) -> 0
(length([ll, _vp])) -> length([cons(x, ll), s(_vp)]) -> 0
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 0
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 0
(leq([s(nn1), z])) -> BOT -> 0
}


Solving took 67.912675 seconds.
DontKnow. Stopped because: timeout
Working model:
|_
{
append -> 
{{{
Q={q_gen_4095, q_gen_4100, q_gen_4101, q_gen_4102, q_gen_4105, q_gen_4106, q_gen_4107, q_gen_4110, q_gen_4111, q_gen_4112, q_gen_4113, q_gen_4114, q_gen_4115, q_gen_4121, q_gen_4125, q_gen_4126, q_gen_4129, q_gen_4131, q_gen_4132, q_gen_4137, q_gen_4140, q_gen_4141, q_gen_4142, q_gen_4147, q_gen_4148, q_gen_4149, q_gen_4150, q_gen_4155, q_gen_4156, q_gen_4157, q_gen_4158, q_gen_4159, q_gen_4160, q_gen_4167, q_gen_4168, q_gen_4170, q_gen_4171, q_gen_4172, q_gen_4180, q_gen_4181, q_gen_4182, q_gen_4183, q_gen_4190, q_gen_4192, q_gen_4193, q_gen_4194, q_gen_4195, q_gen_4196, q_gen_4201, q_gen_4202, q_gen_4203, q_gen_4204, q_gen_4205, q_gen_4206, q_gen_4207, q_gen_4208, q_gen_4209, q_gen_4213, q_gen_4214, q_gen_4218, q_gen_4219, q_gen_4220, q_gen_4221, q_gen_4222, q_gen_4223, q_gen_4229, q_gen_4230, q_gen_4232, q_gen_4239, q_gen_4240, q_gen_4243, q_gen_4250, q_gen_4252, q_gen_4253, q_gen_4261, q_gen_4263, q_gen_4264, q_gen_4265, q_gen_4266, q_gen_4267, q_gen_4268, q_gen_4269, q_gen_4270, q_gen_4271, q_gen_4274, q_gen_4275, q_gen_4276, q_gen_4277, q_gen_4278, q_gen_4281, q_gen_4284, q_gen_4285, q_gen_4286},
Q_f={},
Delta=
{
<nil>() -> q_gen_4113
<b>() -> q_gen_4114
<a>() -> q_gen_4157
<cons>(q_gen_4114, q_gen_4113) -> q_gen_4182
<cons>(q_gen_4114, q_gen_4182) -> q_gen_4278
<nil, nil>() -> q_gen_4101
<b, b>() -> q_gen_4102
<cons, cons>(q_gen_4107, q_gen_4101) -> q_gen_4106
<a, a>() -> q_gen_4107
<nil, cons>(q_gen_4114, q_gen_4113) -> q_gen_4126
<cons, cons>(q_gen_4102, q_gen_4101) -> q_gen_4150
<cons, cons>(q_gen_4102, q_gen_4126) -> q_gen_4160
<cons, cons>(q_gen_4102, q_gen_4150) -> q_gen_4168
<b, a>() -> q_gen_4195
<cons, cons>(q_gen_4102, q_gen_4168) -> q_gen_4202
<nil, cons>(q_gen_4157, q_gen_4113) -> q_gen_4205
<cons, cons>(q_gen_4102, q_gen_4205) -> q_gen_4208
<a, b>() -> q_gen_4221
<cons, cons>(q_gen_4102, q_gen_4160) -> q_gen_4230
<cons, cons>(q_gen_4102, q_gen_4230) -> q_gen_4240
<nil, cons>(q_gen_4114, q_gen_4182) -> q_gen_4253
<cons, cons>(q_gen_4102, q_gen_4276) -> q_gen_4275
<cons, cons>(q_gen_4102, q_gen_4277) -> q_gen_4276
<nil, cons>(q_gen_4114, q_gen_4278) -> q_gen_4277
<cons, cons>(q_gen_4102, q_gen_4286) -> q_gen_4285
<cons, cons>(q_gen_4102, q_gen_4253) -> q_gen_4286
<nil, nil, nil>() -> q_gen_4095
<cons, nil, cons>(q_gen_4102, q_gen_4101) -> q_gen_4100
<nil, cons, cons>(q_gen_4107, q_gen_4106) -> q_gen_4105
<nil, cons, cons>(q_gen_4102, q_gen_4101) -> q_gen_4110
<cons, cons, cons>(q_gen_4115, q_gen_4112) -> q_gen_4111
<nil, nil, cons>(q_gen_4114, q_gen_4113) -> q_gen_4112
<b, b, b>() -> q_gen_4115
<cons, cons, cons>(q_gen_4115, q_gen_4095) -> q_gen_4121
<cons, nil, cons>(q_gen_4102, q_gen_4126) -> q_gen_4125
<nil, cons, cons>(q_gen_4107, q_gen_4101) -> q_gen_4129
<cons, cons, cons>(q_gen_4132, q_gen_4112) -> q_gen_4131
<a, b, a>() -> q_gen_4132
<cons, cons, cons>(q_gen_4115, q_gen_4100) -> q_gen_4137
<cons, cons, cons>(q_gen_4115, q_gen_4125) -> q_gen_4140
<cons, cons, cons>(q_gen_4115, q_gen_4142) -> q_gen_4141
<nil, cons, cons>(q_gen_4102, q_gen_4126) -> q_gen_4142
<cons, nil, cons>(q_gen_4107, q_gen_4101) -> q_gen_4147
<cons, nil, cons>(q_gen_4102, q_gen_4106) -> q_gen_4148
<nil, cons, cons>(q_gen_4102, q_gen_4150) -> q_gen_4149
<cons, cons, cons>(q_gen_4158, q_gen_4156) -> q_gen_4155
<nil, nil, cons>(q_gen_4157, q_gen_4113) -> q_gen_4156
<b, a, b>() -> q_gen_4158
<nil, cons, cons>(q_gen_4107, q_gen_4160) -> q_gen_4159
<cons, nil, cons>(q_gen_4102, q_gen_4168) -> q_gen_4167
<cons, cons, cons>(q_gen_4171, q_gen_4156) -> q_gen_4170
<a, a, a>() -> q_gen_4171
<nil, cons, cons>(q_gen_4102, q_gen_4160) -> q_gen_4172
<cons, cons, cons>(q_gen_4115, q_gen_4181) -> q_gen_4180
<nil, nil, cons>(q_gen_4114, q_gen_4182) -> q_gen_4181
<cons, cons, cons>(q_gen_4132, q_gen_4100) -> q_gen_4183
<cons, cons, cons>(q_gen_4132, q_gen_4125) -> q_gen_4190
<nil, cons, cons>(q_gen_4107, q_gen_4150) -> q_gen_4192
<cons, cons, cons>(q_gen_4171, q_gen_4194) -> q_gen_4193
<nil, cons, cons>(q_gen_4195, q_gen_4126) -> q_gen_4194
<cons, nil, cons>(q_gen_4102, q_gen_4150) -> q_gen_4196
<nil, cons, cons>(q_gen_4102, q_gen_4202) -> q_gen_4201
<cons, cons, cons>(q_gen_4115, q_gen_4204) -> q_gen_4203
<cons, nil, cons>(q_gen_4102, q_gen_4205) -> q_gen_4204
<cons, cons, cons>(q_gen_4132, q_gen_4207) -> q_gen_4206
<cons, nil, cons>(q_gen_4102, q_gen_4208) -> q_gen_4207
<cons, cons, cons>(q_gen_4115, q_gen_4149) -> q_gen_4209
<cons, cons, cons>(q_gen_4115, q_gen_4214) -> q_gen_4213
<cons, cons, cons>(q_gen_4115, q_gen_4180) -> q_gen_4214
<nil, cons, cons>(q_gen_4102, q_gen_4106) -> q_gen_4218
<cons, cons, cons>(q_gen_4132, q_gen_4220) -> q_gen_4219
<nil, cons, cons>(q_gen_4221, q_gen_4205) -> q_gen_4220
<cons, cons, cons>(q_gen_4115, q_gen_4223) -> q_gen_4222
<nil, cons, cons>(q_gen_4195, q_gen_4160) -> q_gen_4223
<cons, nil, cons>(q_gen_4102, q_gen_4230) -> q_gen_4229
<nil, cons, cons>(q_gen_4221, q_gen_4230) -> q_gen_4232
<nil, cons, cons>(q_gen_4102, q_gen_4240) -> q_gen_4239
<cons, nil, cons>(q_gen_4102, q_gen_4202) -> q_gen_4243
<cons, cons, cons>(q_gen_4158, q_gen_4142) -> q_gen_4250
<cons, nil, cons>(q_gen_4221, q_gen_4253) -> q_gen_4252
<cons, cons, cons>(q_gen_4171, q_gen_4180) -> q_gen_4261
<cons, cons, cons>(q_gen_4115, q_gen_4264) -> q_gen_4263
<cons, cons, cons>(q_gen_4171, q_gen_4265) -> q_gen_4264
<nil, cons, cons>(q_gen_4195, q_gen_4101) -> q_gen_4265
<cons, cons, cons>(q_gen_4115, q_gen_4267) -> q_gen_4266
<cons, cons, cons>(q_gen_4158, q_gen_4268) -> q_gen_4267
<cons, cons, cons>(q_gen_4132, q_gen_4156) -> q_gen_4268
<cons, cons, cons>(q_gen_4158, q_gen_4181) -> q_gen_4269
<cons, cons, cons>(q_gen_4115, q_gen_4271) -> q_gen_4270
<cons, cons, cons>(q_gen_4115, q_gen_4111) -> q_gen_4271
<cons, nil, cons>(q_gen_4102, q_gen_4275) -> q_gen_4274
<nil, cons, cons>(q_gen_4102, q_gen_4208) -> q_gen_4281
<cons, nil, cons>(q_gen_4195, q_gen_4285) -> q_gen_4284
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_4094, q_gen_4097, q_gen_4098, q_gen_4099, q_gen_4108, q_gen_4109, q_gen_4116, q_gen_4117, q_gen_4118, q_gen_4119, q_gen_4120, q_gen_4122, q_gen_4127, q_gen_4128, q_gen_4130, q_gen_4133, q_gen_4134, q_gen_4135, q_gen_4136, q_gen_4138, q_gen_4143, q_gen_4144, q_gen_4145, q_gen_4146, q_gen_4151, q_gen_4152, q_gen_4153, q_gen_4154, q_gen_4161, q_gen_4162, q_gen_4163, q_gen_4164, q_gen_4165, q_gen_4166, q_gen_4169, q_gen_4173, q_gen_4175, q_gen_4176, q_gen_4177, q_gen_4178, q_gen_4179, q_gen_4184, q_gen_4191, q_gen_4197, q_gen_4198, q_gen_4199, q_gen_4200, q_gen_4210, q_gen_4211, q_gen_4212, q_gen_4215, q_gen_4216, q_gen_4217, q_gen_4224, q_gen_4225, q_gen_4226, q_gen_4227, q_gen_4228, q_gen_4231, q_gen_4233, q_gen_4234, q_gen_4235, q_gen_4237, q_gen_4238, q_gen_4241, q_gen_4242, q_gen_4244, q_gen_4246, q_gen_4247, q_gen_4248, q_gen_4249, q_gen_4251, q_gen_4254, q_gen_4255, q_gen_4256, q_gen_4262, q_gen_4272, q_gen_4273, q_gen_4279, q_gen_4280, q_gen_4282, q_gen_4283, q_gen_4287, q_gen_4288, q_gen_4289, q_gen_4290, q_gen_4291},
Q_f={},
Delta=
{
<nil>() -> q_gen_4098
<cons>(q_gen_4118, q_gen_4098) -> q_gen_4117
<b>() -> q_gen_4118
<z>() -> q_gen_4120
<cons>(q_gen_4118, q_gen_4117) -> q_gen_4134
<s>(q_gen_4120) -> q_gen_4136
<cons>(q_gen_4146, q_gen_4098) -> q_gen_4145
<a>() -> q_gen_4146
<cons>(q_gen_4146, q_gen_4117) -> q_gen_4153
<cons>(q_gen_4146, q_gen_4153) -> q_gen_4164
<s>(q_gen_4136) -> q_gen_4166
<cons>(q_gen_4118, q_gen_4153) -> q_gen_4178
<s>(q_gen_4166) -> q_gen_4200
<cons>(q_gen_4118, q_gen_4178) -> q_gen_4212
<cons>(q_gen_4118, q_gen_4217) -> q_gen_4216
<cons>(q_gen_4118, q_gen_4134) -> q_gen_4217
<cons>(q_gen_4146, q_gen_4134) -> q_gen_4225
<cons>(q_gen_4146, q_gen_4212) -> q_gen_4228
<cons>(q_gen_4146, q_gen_4178) -> q_gen_4238
<cons>(q_gen_4118, q_gen_4145) -> q_gen_4247
<cons>(q_gen_4118, q_gen_4247) -> q_gen_4249
<s>(q_gen_4200) -> q_gen_4256
<cons>(q_gen_4118, q_gen_4216) -> q_gen_4280
<cons>(q_gen_4146, q_gen_4145) -> q_gen_4289
<cons>(q_gen_4118, q_gen_4289) -> q_gen_4291
<nil, z>() -> q_gen_4094
<cons, s>(q_gen_4099, q_gen_4098) -> q_gen_4097
<b, z>() -> q_gen_4099
<cons, s>(q_gen_4109, q_gen_4098) -> q_gen_4108
<a, z>() -> q_gen_4109
<cons, s>(q_gen_4119, q_gen_4117) -> q_gen_4116
<b, s>(q_gen_4120) -> q_gen_4119
<cons, s>(q_gen_4119, q_gen_4098) -> q_gen_4122
<cons, s>(q_gen_4128, q_gen_4117) -> q_gen_4127
<a, s>(q_gen_4120) -> q_gen_4128
<cons, s>(q_gen_4128, q_gen_4098) -> q_gen_4130
<cons, s>(q_gen_4135, q_gen_4134) -> q_gen_4133
<b, s>(q_gen_4136) -> q_gen_4135
<cons, s>(q_gen_4135, q_gen_4117) -> q_gen_4138
<cons, s>(q_gen_4099, q_gen_4134) -> q_gen_4143
<cons, s>(q_gen_4119, q_gen_4145) -> q_gen_4144
<cons, s>(q_gen_4135, q_gen_4098) -> q_gen_4151
<cons, s>(q_gen_4154, q_gen_4153) -> q_gen_4152
<a, s>(q_gen_4136) -> q_gen_4154
<cons, s>(q_gen_4128, q_gen_4134) -> q_gen_4161
<cons, s>(q_gen_4154, q_gen_4117) -> q_gen_4162
<cons, s>(q_gen_4165, q_gen_4164) -> q_gen_4163
<b, s>(q_gen_4166) -> q_gen_4165
<cons, s>(q_gen_4119, q_gen_4134) -> q_gen_4169
<cons, s>(q_gen_4165, q_gen_4117) -> q_gen_4173
<cons, s>(q_gen_4165, q_gen_4134) -> q_gen_4175
<cons, s>(q_gen_4135, q_gen_4153) -> q_gen_4176
<cons, s>(q_gen_4179, q_gen_4178) -> q_gen_4177
<a, s>(q_gen_4166) -> q_gen_4179
<cons, s>(q_gen_4165, q_gen_4098) -> q_gen_4184
<cons, s>(q_gen_4109, q_gen_4134) -> q_gen_4191
<cons, s>(q_gen_4179, q_gen_4098) -> q_gen_4197
<cons, s>(q_gen_4199, q_gen_4145) -> q_gen_4198
<b, s>(q_gen_4200) -> q_gen_4199
<cons, s>(q_gen_4099, q_gen_4178) -> q_gen_4210
<cons, s>(q_gen_4128, q_gen_4212) -> q_gen_4211
<cons, s>(q_gen_4119, q_gen_4216) -> q_gen_4215
<cons, s>(q_gen_4135, q_gen_4225) -> q_gen_4224
<cons, s>(q_gen_4179, q_gen_4212) -> q_gen_4226
<cons, s>(q_gen_4199, q_gen_4228) -> q_gen_4227
<cons, s>(q_gen_4119, q_gen_4217) -> q_gen_4231
<cons, s>(q_gen_4179, q_gen_4134) -> q_gen_4233
<cons, s>(q_gen_4135, q_gen_4217) -> q_gen_4234
<cons, s>(q_gen_4199, q_gen_4134) -> q_gen_4235
<cons, s>(q_gen_4199, q_gen_4238) -> q_gen_4237
<cons, s>(q_gen_4135, q_gen_4216) -> q_gen_4241
<cons, s>(q_gen_4165, q_gen_4217) -> q_gen_4242
<cons, s>(q_gen_4199, q_gen_4217) -> q_gen_4244
<cons, s>(q_gen_4119, q_gen_4247) -> q_gen_4246
<cons, s>(q_gen_4135, q_gen_4249) -> q_gen_4248
<cons, s>(q_gen_4179, q_gen_4117) -> q_gen_4251
<cons, s>(q_gen_4255, q_gen_4098) -> q_gen_4254
<a, s>(q_gen_4256) -> q_gen_4255
<cons, s>(q_gen_4179, q_gen_4217) -> q_gen_4262
<cons, s>(q_gen_4099, q_gen_4217) -> q_gen_4272
<cons, s>(q_gen_4154, q_gen_4247) -> q_gen_4273
<cons, s>(q_gen_4119, q_gen_4280) -> q_gen_4279
<cons, s>(q_gen_4135, q_gen_4247) -> q_gen_4282
<cons, s>(q_gen_4199, q_gen_4117) -> q_gen_4283
<cons, s>(q_gen_4154, q_gen_4216) -> q_gen_4287
<cons, s>(q_gen_4135, q_gen_4289) -> q_gen_4288
<cons, s>(q_gen_4165, q_gen_4291) -> q_gen_4290
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_4091, q_gen_4092, q_gen_4093, q_gen_4096, q_gen_4103, q_gen_4104, q_gen_4123, q_gen_4124, q_gen_4139, q_gen_4174, q_gen_4185, q_gen_4186, q_gen_4187, q_gen_4188, q_gen_4189, q_gen_4236, q_gen_4245, q_gen_4257, q_gen_4258, q_gen_4259, q_gen_4260},
Q_f={},
Delta=
{
<z>() -> q_gen_4093
<s>(q_gen_4093) -> q_gen_4104
<s>(q_gen_4104) -> q_gen_4189
<z, z>() -> q_gen_4091
<z, s>(q_gen_4093) -> q_gen_4092
<s, s>(q_gen_4091) -> q_gen_4096
<z, s>(q_gen_4104) -> q_gen_4103
<s, s>(q_gen_4124) -> q_gen_4123
<s, z>(q_gen_4093) -> q_gen_4124
<s, s>(q_gen_4123) -> q_gen_4139
<s, s>(q_gen_4139) -> q_gen_4174
<s, s>(q_gen_4186) -> q_gen_4185
<s, s>(q_gen_4187) -> q_gen_4186
<s, z>(q_gen_4104) -> q_gen_4187
<z, s>(q_gen_4189) -> q_gen_4188
<s, s>(q_gen_4185) -> q_gen_4236
<s, s>(q_gen_4174) -> q_gen_4245
<s, s>(q_gen_4258) -> q_gen_4257
<s, s>(q_gen_4259) -> q_gen_4258
<s, s>(q_gen_4260) -> q_gen_4259
<s, z>(q_gen_4189) -> q_gen_4260
}

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

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

-------------------
STEPS:
-------------------------------------------
Step 0, which took 0.016120 s (model generation: 0.015768,  model checking: 0.000352):

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

}

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

}

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

}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 0
() -> length([nil, z]) -> 0
() -> leq([z, s(nn2)]) -> 0
() -> leq([z, z]) -> 3
(append([l1, l2, _aq]) /\ length([_aq, _bq]) /\ length([l1, _zp])) -> leq([_zp, _bq]) -> 1
(append([l1, l2, _dq]) /\ length([_dq, _eq]) /\ length([l2, _cq])) -> leq([_cq, _eq]) -> 1
(append([t1, l2, _qp])) -> append([cons(h1, t1), l2, cons(h1, _qp)]) -> 1
(length([ll, _vp])) -> length([cons(x, ll), s(_vp)]) -> 1
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 1
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 1
(leq([s(nn1), z])) -> BOT -> 1
}
Sat witness: Found: (() -> leq([z, z]), {

})

-------------------------------------------
Step 1, which took 0.011317 s (model generation: 0.011237,  model checking: 0.000080):

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

}

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

}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_4091},
Q_f={q_gen_4091},
Delta=
{
<z, z>() -> q_gen_4091
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 0
() -> length([nil, z]) -> 0
() -> leq([z, s(nn2)]) -> 3
() -> leq([z, z]) -> 3
(append([l1, l2, _aq]) /\ length([_aq, _bq]) /\ length([l1, _zp])) -> leq([_zp, _bq]) -> 1
(append([l1, l2, _dq]) /\ length([_dq, _eq]) /\ length([l2, _cq])) -> leq([_cq, _eq]) -> 1
(append([t1, l2, _qp])) -> append([cons(h1, t1), l2, cons(h1, _qp)]) -> 1
(length([ll, _vp])) -> length([cons(x, ll), s(_vp)]) -> 1
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 1
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 1
(leq([s(nn1), z])) -> BOT -> 1
}
Sat witness: Found: (() -> leq([z, s(nn2)]), {
nn2 -> z
})

-------------------------------------------
Step 2, which took 0.008895 s (model generation: 0.008819,  model checking: 0.000076):

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

}

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

}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_4091, q_gen_4093},
Q_f={q_gen_4091},
Delta=
{
<z>() -> q_gen_4093
<z, s>(q_gen_4093) -> q_gen_4091
<z, z>() -> q_gen_4091
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 0
() -> length([nil, z]) -> 3
() -> leq([z, s(nn2)]) -> 3
() -> leq([z, z]) -> 3
(append([l1, l2, _aq]) /\ length([_aq, _bq]) /\ length([l1, _zp])) -> leq([_zp, _bq]) -> 1
(append([l1, l2, _dq]) /\ length([_dq, _eq]) /\ length([l2, _cq])) -> leq([_cq, _eq]) -> 1
(append([t1, l2, _qp])) -> append([cons(h1, t1), l2, cons(h1, _qp)]) -> 1
(length([ll, _vp])) -> length([cons(x, ll), s(_vp)]) -> 1
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 1
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 1
(leq([s(nn1), z])) -> BOT -> 1
}
Sat witness: Found: (() -> length([nil, z]), {

})

-------------------------------------------
Step 3, which took 0.012073 s (model generation: 0.011880,  model checking: 0.000193):

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

}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_4094},
Q_f={q_gen_4094},
Delta=
{
<nil, z>() -> q_gen_4094
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_4091, q_gen_4093},
Q_f={q_gen_4091},
Delta=
{
<z>() -> q_gen_4093
<z, s>(q_gen_4093) -> q_gen_4091
<z, z>() -> q_gen_4091
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 3
() -> length([nil, z]) -> 3
() -> leq([z, s(nn2)]) -> 3
() -> leq([z, z]) -> 3
(append([l1, l2, _aq]) /\ length([_aq, _bq]) /\ length([l1, _zp])) -> leq([_zp, _bq]) -> 1
(append([l1, l2, _dq]) /\ length([_dq, _eq]) /\ length([l2, _cq])) -> leq([_cq, _eq]) -> 1
(append([t1, l2, _qp])) -> append([cons(h1, t1), l2, cons(h1, _qp)]) -> 1
(length([ll, _vp])) -> length([cons(x, ll), s(_vp)]) -> 1
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 1
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 1
(leq([s(nn1), z])) -> BOT -> 1
}
Sat witness: Found: (() -> append([nil, l2, l2]), {
l2 -> nil
})

-------------------------------------------
Step 4, which took 0.010803 s (model generation: 0.008962,  model checking: 0.001841):

Model:
|_
{
append -> 
{{{
Q={q_gen_4095},
Q_f={q_gen_4095},
Delta=
{
<nil, nil, nil>() -> q_gen_4095
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_4094},
Q_f={q_gen_4094},
Delta=
{
<nil, z>() -> q_gen_4094
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_4091, q_gen_4093},
Q_f={q_gen_4091},
Delta=
{
<z>() -> q_gen_4093
<z, s>(q_gen_4093) -> q_gen_4091
<z, z>() -> q_gen_4091
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 3
() -> length([nil, z]) -> 3
() -> leq([z, s(nn2)]) -> 3
() -> leq([z, z]) -> 3
(append([l1, l2, _aq]) /\ length([_aq, _bq]) /\ length([l1, _zp])) -> leq([_zp, _bq]) -> 1
(append([l1, l2, _dq]) /\ length([_dq, _eq]) /\ length([l2, _cq])) -> leq([_cq, _eq]) -> 1
(append([t1, l2, _qp])) -> append([cons(h1, t1), l2, cons(h1, _qp)]) -> 1
(length([ll, _vp])) -> length([cons(x, ll), s(_vp)]) -> 1
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 4
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 2
(leq([s(nn1), z])) -> BOT -> 2
}
Sat witness: Found: ((leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]), {
nn1 -> z  ;  nn2 -> z
})

-------------------------------------------
Step 5, which took 0.009527 s (model generation: 0.009423,  model checking: 0.000104):

Model:
|_
{
append -> 
{{{
Q={q_gen_4095},
Q_f={q_gen_4095},
Delta=
{
<nil, nil, nil>() -> q_gen_4095
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_4094},
Q_f={q_gen_4094},
Delta=
{
<nil, z>() -> q_gen_4094
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_4091, q_gen_4093},
Q_f={q_gen_4091},
Delta=
{
<z>() -> q_gen_4093
<s, s>(q_gen_4091) -> q_gen_4091
<z, s>(q_gen_4093) -> q_gen_4091
<z, z>() -> q_gen_4091
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 3
() -> length([nil, z]) -> 3
() -> leq([z, s(nn2)]) -> 3
() -> leq([z, z]) -> 3
(append([l1, l2, _aq]) /\ length([_aq, _bq]) /\ length([l1, _zp])) -> leq([_zp, _bq]) -> 1
(append([l1, l2, _dq]) /\ length([_dq, _eq]) /\ length([l2, _cq])) -> leq([_cq, _eq]) -> 1
(append([t1, l2, _qp])) -> append([cons(h1, t1), l2, cons(h1, _qp)]) -> 1
(length([ll, _vp])) -> length([cons(x, ll), s(_vp)]) -> 4
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 4
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 2
(leq([s(nn1), z])) -> BOT -> 2
}
Sat witness: Found: ((length([ll, _vp])) -> length([cons(x, ll), s(_vp)]), {
_vp -> z  ;  ll -> nil  ;  x -> b
})

-------------------------------------------
Step 6, which took 0.009115 s (model generation: 0.008873,  model checking: 0.000242):

Model:
|_
{
append -> 
{{{
Q={q_gen_4095},
Q_f={q_gen_4095},
Delta=
{
<nil, nil, nil>() -> q_gen_4095
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_4094, q_gen_4098, q_gen_4099},
Q_f={q_gen_4094},
Delta=
{
<nil>() -> q_gen_4098
<cons, s>(q_gen_4099, q_gen_4098) -> q_gen_4094
<nil, z>() -> q_gen_4094
<b, z>() -> q_gen_4099
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_4091, q_gen_4093},
Q_f={q_gen_4091},
Delta=
{
<z>() -> q_gen_4093
<s, s>(q_gen_4091) -> q_gen_4091
<z, s>(q_gen_4093) -> q_gen_4091
<z, z>() -> q_gen_4091
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 3
() -> length([nil, z]) -> 3
() -> leq([z, s(nn2)]) -> 3
() -> leq([z, z]) -> 3
(append([l1, l2, _aq]) /\ length([_aq, _bq]) /\ length([l1, _zp])) -> leq([_zp, _bq]) -> 1
(append([l1, l2, _dq]) /\ length([_dq, _eq]) /\ length([l2, _cq])) -> leq([_cq, _eq]) -> 1
(append([t1, l2, _qp])) -> append([cons(h1, t1), l2, cons(h1, _qp)]) -> 4
(length([ll, _vp])) -> length([cons(x, ll), s(_vp)]) -> 4
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 4
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 2
(leq([s(nn1), z])) -> BOT -> 2
}
Sat witness: Found: ((append([t1, l2, _qp])) -> append([cons(h1, t1), l2, cons(h1, _qp)]), {
_qp -> nil  ;  h1 -> b  ;  l2 -> nil  ;  t1 -> nil
})

-------------------------------------------
Step 7, which took 0.010713 s (model generation: 0.009406,  model checking: 0.001307):

Model:
|_
{
append -> 
{{{
Q={q_gen_4095, q_gen_4101, q_gen_4102},
Q_f={q_gen_4095},
Delta=
{
<nil, nil>() -> q_gen_4101
<b, b>() -> q_gen_4102
<cons, nil, cons>(q_gen_4102, q_gen_4101) -> q_gen_4095
<nil, nil, nil>() -> q_gen_4095
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_4094, q_gen_4098, q_gen_4099},
Q_f={q_gen_4094},
Delta=
{
<nil>() -> q_gen_4098
<cons, s>(q_gen_4099, q_gen_4098) -> q_gen_4094
<nil, z>() -> q_gen_4094
<b, z>() -> q_gen_4099
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_4091, q_gen_4093},
Q_f={q_gen_4091},
Delta=
{
<z>() -> q_gen_4093
<s, s>(q_gen_4091) -> q_gen_4091
<z, s>(q_gen_4093) -> q_gen_4091
<z, z>() -> q_gen_4091
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 3
() -> length([nil, z]) -> 3
() -> leq([z, s(nn2)]) -> 6
() -> leq([z, z]) -> 4
(append([l1, l2, _aq]) /\ length([_aq, _bq]) /\ length([l1, _zp])) -> leq([_zp, _bq]) -> 2
(append([l1, l2, _dq]) /\ length([_dq, _eq]) /\ length([l2, _cq])) -> leq([_cq, _eq]) -> 2
(append([t1, l2, _qp])) -> append([cons(h1, t1), l2, cons(h1, _qp)]) -> 4
(length([ll, _vp])) -> length([cons(x, ll), s(_vp)]) -> 4
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 4
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 3
(leq([s(nn1), z])) -> BOT -> 3
}
Sat witness: Found: (() -> leq([z, s(nn2)]), {
nn2 -> s(z)
})

-------------------------------------------
Step 8, which took 0.011053 s (model generation: 0.010565,  model checking: 0.000488):

Model:
|_
{
append -> 
{{{
Q={q_gen_4095, q_gen_4101, q_gen_4102},
Q_f={q_gen_4095},
Delta=
{
<nil, nil>() -> q_gen_4101
<b, b>() -> q_gen_4102
<cons, nil, cons>(q_gen_4102, q_gen_4101) -> q_gen_4095
<nil, nil, nil>() -> q_gen_4095
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_4094, q_gen_4098, q_gen_4099},
Q_f={q_gen_4094},
Delta=
{
<nil>() -> q_gen_4098
<cons, s>(q_gen_4099, q_gen_4098) -> q_gen_4094
<nil, z>() -> q_gen_4094
<b, z>() -> q_gen_4099
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_4091, q_gen_4093},
Q_f={q_gen_4091},
Delta=
{
<s>(q_gen_4093) -> q_gen_4093
<z>() -> q_gen_4093
<s, s>(q_gen_4091) -> q_gen_4091
<z, s>(q_gen_4093) -> q_gen_4091
<z, z>() -> q_gen_4091
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 6
() -> length([nil, z]) -> 4
() -> leq([z, s(nn2)]) -> 6
() -> leq([z, z]) -> 4
(append([l1, l2, _aq]) /\ length([_aq, _bq]) /\ length([l1, _zp])) -> leq([_zp, _bq]) -> 3
(append([l1, l2, _dq]) /\ length([_dq, _eq]) /\ length([l2, _cq])) -> leq([_cq, _eq]) -> 3
(append([t1, l2, _qp])) -> append([cons(h1, t1), l2, cons(h1, _qp)]) -> 4
(length([ll, _vp])) -> length([cons(x, ll), s(_vp)]) -> 4
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 4
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 4
(leq([s(nn1), z])) -> BOT -> 4
}
Sat witness: Found: (() -> append([nil, l2, l2]), {
l2 -> cons(a, cons(a, nil))
})

-------------------------------------------
Step 9, which took 0.011656 s (model generation: 0.011200,  model checking: 0.000456):

Model:
|_
{
append -> 
{{{
Q={q_gen_4095, q_gen_4101, q_gen_4102},
Q_f={q_gen_4095},
Delta=
{
<cons, cons>(q_gen_4102, q_gen_4101) -> q_gen_4101
<nil, nil>() -> q_gen_4101
<a, a>() -> q_gen_4102
<b, b>() -> q_gen_4102
<cons, nil, cons>(q_gen_4102, q_gen_4101) -> q_gen_4095
<nil, cons, cons>(q_gen_4102, q_gen_4101) -> q_gen_4095
<nil, nil, nil>() -> q_gen_4095
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_4094, q_gen_4098, q_gen_4099},
Q_f={q_gen_4094},
Delta=
{
<nil>() -> q_gen_4098
<cons, s>(q_gen_4099, q_gen_4098) -> q_gen_4094
<nil, z>() -> q_gen_4094
<b, z>() -> q_gen_4099
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_4091, q_gen_4093},
Q_f={q_gen_4091},
Delta=
{
<s>(q_gen_4093) -> q_gen_4093
<z>() -> q_gen_4093
<s, s>(q_gen_4091) -> q_gen_4091
<z, s>(q_gen_4093) -> q_gen_4091
<z, z>() -> q_gen_4091
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 6
() -> length([nil, z]) -> 4
() -> leq([z, s(nn2)]) -> 6
() -> leq([z, z]) -> 4
(append([l1, l2, _aq]) /\ length([_aq, _bq]) /\ length([l1, _zp])) -> leq([_zp, _bq]) -> 4
(append([l1, l2, _dq]) /\ length([_dq, _eq]) /\ length([l2, _cq])) -> leq([_cq, _eq]) -> 4
(append([t1, l2, _qp])) -> append([cons(h1, t1), l2, cons(h1, _qp)]) -> 4
(length([ll, _vp])) -> length([cons(x, ll), s(_vp)]) -> 7
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 5
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 5
(leq([s(nn1), z])) -> BOT -> 5
}
Sat witness: Found: ((length([ll, _vp])) -> length([cons(x, ll), s(_vp)]), {
_vp -> z  ;  ll -> nil  ;  x -> a
})

-------------------------------------------
Step 10, which took 0.011564 s (model generation: 0.010294,  model checking: 0.001270):

Model:
|_
{
append -> 
{{{
Q={q_gen_4095, q_gen_4101, q_gen_4102},
Q_f={q_gen_4095},
Delta=
{
<cons, cons>(q_gen_4102, q_gen_4101) -> q_gen_4101
<nil, nil>() -> q_gen_4101
<a, a>() -> q_gen_4102
<b, b>() -> q_gen_4102
<cons, nil, cons>(q_gen_4102, q_gen_4101) -> q_gen_4095
<nil, cons, cons>(q_gen_4102, q_gen_4101) -> q_gen_4095
<nil, nil, nil>() -> q_gen_4095
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_4094, q_gen_4098, q_gen_4099},
Q_f={q_gen_4094},
Delta=
{
<nil>() -> q_gen_4098
<cons, s>(q_gen_4099, q_gen_4098) -> q_gen_4094
<nil, z>() -> q_gen_4094
<a, z>() -> q_gen_4099
<b, z>() -> q_gen_4099
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_4091, q_gen_4093},
Q_f={q_gen_4091},
Delta=
{
<s>(q_gen_4093) -> q_gen_4093
<z>() -> q_gen_4093
<s, s>(q_gen_4091) -> q_gen_4091
<z, s>(q_gen_4093) -> q_gen_4091
<z, z>() -> q_gen_4091
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 6
() -> length([nil, z]) -> 4
() -> leq([z, s(nn2)]) -> 6
() -> leq([z, z]) -> 4
(append([l1, l2, _aq]) /\ length([_aq, _bq]) /\ length([l1, _zp])) -> leq([_zp, _bq]) -> 4
(append([l1, l2, _dq]) /\ length([_dq, _eq]) /\ length([l2, _cq])) -> leq([_cq, _eq]) -> 4
(append([t1, l2, _qp])) -> append([cons(h1, t1), l2, cons(h1, _qp)]) -> 7
(length([ll, _vp])) -> length([cons(x, ll), s(_vp)]) -> 7
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 5
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 5
(leq([s(nn1), z])) -> BOT -> 5
}
Sat witness: Found: ((append([t1, l2, _qp])) -> append([cons(h1, t1), l2, cons(h1, _qp)]), {
_qp -> cons(b, nil)  ;  h1 -> b  ;  l2 -> cons(b, nil)  ;  t1 -> nil
})

-------------------------------------------
Step 11, which took 0.012638 s (model generation: 0.011572,  model checking: 0.001066):

Model:
|_
{
append -> 
{{{
Q={q_gen_4095, q_gen_4101, q_gen_4102, q_gen_4113, q_gen_4114, q_gen_4115},
Q_f={q_gen_4095},
Delta=
{
<nil>() -> q_gen_4113
<b>() -> q_gen_4114
<cons, cons>(q_gen_4102, q_gen_4101) -> q_gen_4101
<nil, nil>() -> q_gen_4101
<a, a>() -> q_gen_4102
<b, b>() -> q_gen_4102
<cons, cons, cons>(q_gen_4115, q_gen_4095) -> q_gen_4095
<cons, nil, cons>(q_gen_4102, q_gen_4101) -> q_gen_4095
<nil, cons, cons>(q_gen_4102, q_gen_4101) -> q_gen_4095
<nil, nil, cons>(q_gen_4114, q_gen_4113) -> q_gen_4095
<nil, nil, nil>() -> q_gen_4095
<b, b, b>() -> q_gen_4115
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_4094, q_gen_4098, q_gen_4099},
Q_f={q_gen_4094},
Delta=
{
<nil>() -> q_gen_4098
<cons, s>(q_gen_4099, q_gen_4098) -> q_gen_4094
<nil, z>() -> q_gen_4094
<a, z>() -> q_gen_4099
<b, z>() -> q_gen_4099
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_4091, q_gen_4093},
Q_f={q_gen_4091},
Delta=
{
<s>(q_gen_4093) -> q_gen_4093
<z>() -> q_gen_4093
<s, s>(q_gen_4091) -> q_gen_4091
<z, s>(q_gen_4093) -> q_gen_4091
<z, z>() -> q_gen_4091
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 7
() -> length([nil, z]) -> 5
() -> leq([z, s(nn2)]) -> 7
() -> leq([z, z]) -> 5
(append([l1, l2, _aq]) /\ length([_aq, _bq]) /\ length([l1, _zp])) -> leq([_zp, _bq]) -> 5
(append([l1, l2, _dq]) /\ length([_dq, _eq]) /\ length([l2, _cq])) -> leq([_cq, _eq]) -> 5
(append([t1, l2, _qp])) -> append([cons(h1, t1), l2, cons(h1, _qp)]) -> 7
(length([ll, _vp])) -> length([cons(x, ll), s(_vp)]) -> 10
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 6
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 6
(leq([s(nn1), z])) -> BOT -> 6
}
Sat witness: Found: ((length([ll, _vp])) -> length([cons(x, ll), s(_vp)]), {
_vp -> s(z)  ;  ll -> cons(b, nil)  ;  x -> b
})

-------------------------------------------
Step 12, which took 0.011629 s (model generation: 0.010913,  model checking: 0.000716):

Model:
|_
{
append -> 
{{{
Q={q_gen_4095, q_gen_4101, q_gen_4102, q_gen_4113, q_gen_4114, q_gen_4115},
Q_f={q_gen_4095},
Delta=
{
<nil>() -> q_gen_4113
<b>() -> q_gen_4114
<cons, cons>(q_gen_4102, q_gen_4101) -> q_gen_4101
<nil, nil>() -> q_gen_4101
<a, a>() -> q_gen_4102
<b, b>() -> q_gen_4102
<cons, cons, cons>(q_gen_4115, q_gen_4095) -> q_gen_4095
<cons, nil, cons>(q_gen_4102, q_gen_4101) -> q_gen_4095
<nil, cons, cons>(q_gen_4102, q_gen_4101) -> q_gen_4095
<nil, nil, cons>(q_gen_4114, q_gen_4113) -> q_gen_4095
<nil, nil, nil>() -> q_gen_4095
<b, b, b>() -> q_gen_4115
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_4094, q_gen_4098, q_gen_4099, q_gen_4118, q_gen_4120},
Q_f={q_gen_4094},
Delta=
{
<cons>(q_gen_4118, q_gen_4098) -> q_gen_4098
<nil>() -> q_gen_4098
<b>() -> q_gen_4118
<z>() -> q_gen_4120
<cons, s>(q_gen_4099, q_gen_4098) -> q_gen_4094
<nil, z>() -> q_gen_4094
<a, z>() -> q_gen_4099
<b, s>(q_gen_4120) -> q_gen_4099
<b, z>() -> q_gen_4099
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_4091, q_gen_4093},
Q_f={q_gen_4091},
Delta=
{
<s>(q_gen_4093) -> q_gen_4093
<z>() -> q_gen_4093
<s, s>(q_gen_4091) -> q_gen_4091
<z, s>(q_gen_4093) -> q_gen_4091
<z, z>() -> q_gen_4091
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 7
() -> length([nil, z]) -> 5
() -> leq([z, s(nn2)]) -> 7
() -> leq([z, z]) -> 5
(append([l1, l2, _aq]) /\ length([_aq, _bq]) /\ length([l1, _zp])) -> leq([_zp, _bq]) -> 5
(append([l1, l2, _dq]) /\ length([_dq, _eq]) /\ length([l2, _cq])) -> leq([_cq, _eq]) -> 8
(append([t1, l2, _qp])) -> append([cons(h1, t1), l2, cons(h1, _qp)]) -> 7
(length([ll, _vp])) -> length([cons(x, ll), s(_vp)]) -> 10
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 6
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 6
(leq([s(nn1), z])) -> BOT -> 6
}
Sat witness: Found: ((append([l1, l2, _dq]) /\ length([_dq, _eq]) /\ length([l2, _cq])) -> leq([_cq, _eq]), {
_cq -> s(s(z))  ;  _dq -> cons(b, nil)  ;  _eq -> s(z)  ;  l1 -> cons(b, nil)  ;  l2 -> cons(b, nil)
})

-------------------------------------------
Step 13, which took 0.019025 s (model generation: 0.018756,  model checking: 0.000269):

Model:
|_
{
append -> 
{{{
Q={q_gen_4095, q_gen_4101, q_gen_4102, q_gen_4113, q_gen_4114, q_gen_4115},
Q_f={q_gen_4095},
Delta=
{
<nil>() -> q_gen_4113
<b>() -> q_gen_4114
<cons, cons>(q_gen_4102, q_gen_4101) -> q_gen_4101
<nil, nil>() -> q_gen_4101
<a, a>() -> q_gen_4102
<b, b>() -> q_gen_4102
<cons, cons, cons>(q_gen_4115, q_gen_4095) -> q_gen_4095
<cons, nil, cons>(q_gen_4102, q_gen_4101) -> q_gen_4095
<nil, cons, cons>(q_gen_4102, q_gen_4101) -> q_gen_4095
<nil, nil, cons>(q_gen_4114, q_gen_4113) -> q_gen_4095
<nil, nil, nil>() -> q_gen_4095
<b, b, b>() -> q_gen_4115
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_4094, q_gen_4098, q_gen_4099, q_gen_4118, q_gen_4120},
Q_f={q_gen_4094},
Delta=
{
<cons>(q_gen_4118, q_gen_4098) -> q_gen_4098
<nil>() -> q_gen_4098
<b>() -> q_gen_4118
<z>() -> q_gen_4120
<cons, s>(q_gen_4099, q_gen_4098) -> q_gen_4094
<nil, z>() -> q_gen_4094
<a, z>() -> q_gen_4099
<b, s>(q_gen_4120) -> q_gen_4099
<b, z>() -> q_gen_4099
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_4091, q_gen_4093},
Q_f={q_gen_4091},
Delta=
{
<s>(q_gen_4093) -> q_gen_4093
<z>() -> q_gen_4093
<s, s>(q_gen_4091) -> q_gen_4091
<s, z>(q_gen_4093) -> q_gen_4091
<z, s>(q_gen_4093) -> q_gen_4091
<z, z>() -> q_gen_4091
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 7
() -> length([nil, z]) -> 6
() -> leq([z, s(nn2)]) -> 7
() -> leq([z, z]) -> 6
(append([l1, l2, _aq]) /\ length([_aq, _bq]) /\ length([l1, _zp])) -> leq([_zp, _bq]) -> 6
(append([l1, l2, _dq]) /\ length([_dq, _eq]) /\ length([l2, _cq])) -> leq([_cq, _eq]) -> 8
(append([t1, l2, _qp])) -> append([cons(h1, t1), l2, cons(h1, _qp)]) -> 7
(length([ll, _vp])) -> length([cons(x, ll), s(_vp)]) -> 10
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 6
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 6
(leq([s(nn1), z])) -> BOT -> 9
}
Sat witness: Found: ((leq([s(nn1), z])) -> BOT, {
nn1 -> z
})

-------------------------------------------
Step 14, which took 0.014597 s (model generation: 0.014500,  model checking: 0.000097):

Model:
|_
{
append -> 
{{{
Q={q_gen_4095, q_gen_4101, q_gen_4102, q_gen_4113, q_gen_4114, q_gen_4115},
Q_f={q_gen_4095},
Delta=
{
<nil>() -> q_gen_4113
<b>() -> q_gen_4114
<cons, cons>(q_gen_4102, q_gen_4101) -> q_gen_4101
<nil, nil>() -> q_gen_4101
<a, a>() -> q_gen_4102
<b, b>() -> q_gen_4102
<cons, cons, cons>(q_gen_4115, q_gen_4095) -> q_gen_4095
<cons, nil, cons>(q_gen_4102, q_gen_4101) -> q_gen_4095
<nil, cons, cons>(q_gen_4102, q_gen_4101) -> q_gen_4095
<nil, nil, cons>(q_gen_4114, q_gen_4113) -> q_gen_4095
<nil, nil, nil>() -> q_gen_4095
<b, b, b>() -> q_gen_4115
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_4094, q_gen_4098, q_gen_4099, q_gen_4118, q_gen_4120},
Q_f={q_gen_4094},
Delta=
{
<cons>(q_gen_4118, q_gen_4098) -> q_gen_4098
<nil>() -> q_gen_4098
<b>() -> q_gen_4118
<z>() -> q_gen_4120
<cons, s>(q_gen_4099, q_gen_4098) -> q_gen_4094
<nil, z>() -> q_gen_4094
<a, z>() -> q_gen_4099
<b, s>(q_gen_4120) -> q_gen_4099
<b, z>() -> q_gen_4099
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_4091, q_gen_4093, q_gen_4124},
Q_f={q_gen_4091},
Delta=
{
<s>(q_gen_4093) -> q_gen_4093
<z>() -> q_gen_4093
<s, s>(q_gen_4091) -> q_gen_4091
<s, s>(q_gen_4124) -> q_gen_4091
<z, s>(q_gen_4093) -> q_gen_4091
<z, z>() -> q_gen_4091
<s, z>(q_gen_4093) -> q_gen_4124
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 7
() -> length([nil, z]) -> 6
() -> leq([z, s(nn2)]) -> 7
() -> leq([z, z]) -> 6
(append([l1, l2, _aq]) /\ length([_aq, _bq]) /\ length([l1, _zp])) -> leq([_zp, _bq]) -> 6
(append([l1, l2, _dq]) /\ length([_dq, _eq]) /\ length([l2, _cq])) -> leq([_cq, _eq]) -> 8
(append([t1, l2, _qp])) -> append([cons(h1, t1), l2, cons(h1, _qp)]) -> 7
(length([ll, _vp])) -> length([cons(x, ll), s(_vp)]) -> 10
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 6
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 9
(leq([s(nn1), z])) -> BOT -> 9
}
Sat witness: Found: ((leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]), {
nn1 -> s(z)  ;  nn2 -> z
})

-------------------------------------------
Step 15, which took 0.013777 s (model generation: 0.013389,  model checking: 0.000388):

Model:
|_
{
append -> 
{{{
Q={q_gen_4095, q_gen_4101, q_gen_4102, q_gen_4112, q_gen_4113, q_gen_4114, q_gen_4115},
Q_f={q_gen_4095},
Delta=
{
<nil>() -> q_gen_4113
<b>() -> q_gen_4114
<cons, cons>(q_gen_4102, q_gen_4101) -> q_gen_4101
<nil, nil>() -> q_gen_4101
<a, a>() -> q_gen_4102
<b, b>() -> q_gen_4102
<cons, cons, cons>(q_gen_4115, q_gen_4112) -> q_gen_4095
<cons, nil, cons>(q_gen_4102, q_gen_4101) -> q_gen_4095
<nil, cons, cons>(q_gen_4102, q_gen_4101) -> q_gen_4095
<nil, nil, nil>() -> q_gen_4095
<cons, cons, cons>(q_gen_4115, q_gen_4095) -> q_gen_4112
<nil, nil, cons>(q_gen_4114, q_gen_4113) -> q_gen_4112
<b, b, b>() -> q_gen_4115
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_4094, q_gen_4098, q_gen_4099, q_gen_4118, q_gen_4120},
Q_f={q_gen_4094},
Delta=
{
<cons>(q_gen_4118, q_gen_4098) -> q_gen_4098
<nil>() -> q_gen_4098
<b>() -> q_gen_4118
<z>() -> q_gen_4120
<cons, s>(q_gen_4099, q_gen_4098) -> q_gen_4094
<nil, z>() -> q_gen_4094
<a, z>() -> q_gen_4099
<b, s>(q_gen_4120) -> q_gen_4099
<b, z>() -> q_gen_4099
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_4091, q_gen_4093, q_gen_4123},
Q_f={q_gen_4091},
Delta=
{
<s>(q_gen_4093) -> q_gen_4093
<z>() -> q_gen_4093
<s, s>(q_gen_4091) -> q_gen_4091
<z, s>(q_gen_4093) -> q_gen_4091
<z, z>() -> q_gen_4091
<s, s>(q_gen_4123) -> q_gen_4123
<s, z>(q_gen_4093) -> q_gen_4123
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 7
() -> length([nil, z]) -> 6
() -> leq([z, s(nn2)]) -> 7
() -> leq([z, z]) -> 6
(append([l1, l2, _aq]) /\ length([_aq, _bq]) /\ length([l1, _zp])) -> leq([_zp, _bq]) -> 9
(append([l1, l2, _dq]) /\ length([_dq, _eq]) /\ length([l2, _cq])) -> leq([_cq, _eq]) -> 8
(append([t1, l2, _qp])) -> append([cons(h1, t1), l2, cons(h1, _qp)]) -> 7
(length([ll, _vp])) -> length([cons(x, ll), s(_vp)]) -> 10
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 7
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 9
(leq([s(nn1), z])) -> BOT -> 9
}
Sat witness: Found: ((append([l1, l2, _aq]) /\ length([_aq, _bq]) /\ length([l1, _zp])) -> leq([_zp, _bq]), {
_aq -> cons(b, nil)  ;  _bq -> s(z)  ;  _zp -> s(s(z))  ;  l1 -> cons(b, nil)  ;  l2 -> nil
})

-------------------------------------------
Step 16, which took 0.017882 s (model generation: 0.016675,  model checking: 0.001207):

Model:
|_
{
append -> 
{{{
Q={q_gen_4095, q_gen_4101, q_gen_4102, q_gen_4113, q_gen_4114, q_gen_4115},
Q_f={q_gen_4095},
Delta=
{
<nil>() -> q_gen_4113
<b>() -> q_gen_4114
<cons, cons>(q_gen_4102, q_gen_4101) -> q_gen_4101
<nil, nil>() -> q_gen_4101
<a, a>() -> q_gen_4102
<b, b>() -> q_gen_4102
<cons, cons, cons>(q_gen_4115, q_gen_4095) -> q_gen_4095
<cons, nil, cons>(q_gen_4102, q_gen_4101) -> q_gen_4095
<nil, cons, cons>(q_gen_4102, q_gen_4101) -> q_gen_4095
<nil, nil, cons>(q_gen_4114, q_gen_4113) -> q_gen_4095
<nil, nil, nil>() -> q_gen_4095
<b, b, b>() -> q_gen_4115
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_4094, q_gen_4098, q_gen_4099, q_gen_4117, q_gen_4118, q_gen_4119, q_gen_4120, q_gen_4122},
Q_f={q_gen_4094},
Delta=
{
<nil>() -> q_gen_4098
<cons>(q_gen_4118, q_gen_4098) -> q_gen_4117
<b>() -> q_gen_4118
<z>() -> q_gen_4120
<cons, s>(q_gen_4099, q_gen_4098) -> q_gen_4094
<cons, s>(q_gen_4119, q_gen_4117) -> q_gen_4094
<nil, z>() -> q_gen_4094
<a, z>() -> q_gen_4099
<b, z>() -> q_gen_4099
<b, s>(q_gen_4120) -> q_gen_4119
<cons, s>(q_gen_4119, q_gen_4098) -> q_gen_4122
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_4091, q_gen_4093, q_gen_4123},
Q_f={q_gen_4091},
Delta=
{
<s>(q_gen_4093) -> q_gen_4093
<z>() -> q_gen_4093
<s, s>(q_gen_4091) -> q_gen_4091
<z, s>(q_gen_4093) -> q_gen_4091
<z, z>() -> q_gen_4091
<s, s>(q_gen_4123) -> q_gen_4123
<s, z>(q_gen_4093) -> q_gen_4123
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 7
() -> length([nil, z]) -> 7
() -> leq([z, s(nn2)]) -> 7
() -> leq([z, z]) -> 7
(append([l1, l2, _aq]) /\ length([_aq, _bq]) /\ length([l1, _zp])) -> leq([_zp, _bq]) -> 9
(append([l1, l2, _dq]) /\ length([_dq, _eq]) /\ length([l2, _cq])) -> leq([_cq, _eq]) -> 8
(append([t1, l2, _qp])) -> append([cons(h1, t1), l2, cons(h1, _qp)]) -> 10
(length([ll, _vp])) -> length([cons(x, ll), s(_vp)]) -> 10
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 8
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 9
(leq([s(nn1), z])) -> BOT -> 9
}
Sat witness: Found: ((append([t1, l2, _qp])) -> append([cons(h1, t1), l2, cons(h1, _qp)]), {
_qp -> cons(b, nil)  ;  h1 -> b  ;  l2 -> nil  ;  t1 -> nil
})

-------------------------------------------
Step 17, which took 0.015688 s (model generation: 0.012564,  model checking: 0.003124):

Model:
|_
{
append -> 
{{{
Q={q_gen_4095, q_gen_4101, q_gen_4102, q_gen_4113, q_gen_4114, q_gen_4115},
Q_f={q_gen_4095},
Delta=
{
<nil>() -> q_gen_4113
<b>() -> q_gen_4114
<cons, cons>(q_gen_4102, q_gen_4101) -> q_gen_4101
<nil, cons>(q_gen_4114, q_gen_4113) -> q_gen_4101
<nil, nil>() -> q_gen_4101
<a, a>() -> q_gen_4102
<b, b>() -> q_gen_4102
<cons, cons, cons>(q_gen_4115, q_gen_4095) -> q_gen_4095
<cons, nil, cons>(q_gen_4102, q_gen_4101) -> q_gen_4095
<nil, cons, cons>(q_gen_4102, q_gen_4101) -> q_gen_4095
<nil, nil, cons>(q_gen_4114, q_gen_4113) -> q_gen_4095
<nil, nil, nil>() -> q_gen_4095
<b, b, b>() -> q_gen_4115
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_4094, q_gen_4098, q_gen_4099, q_gen_4117, q_gen_4118, q_gen_4119, q_gen_4120, q_gen_4122},
Q_f={q_gen_4094},
Delta=
{
<nil>() -> q_gen_4098
<cons>(q_gen_4118, q_gen_4098) -> q_gen_4117
<b>() -> q_gen_4118
<z>() -> q_gen_4120
<cons, s>(q_gen_4099, q_gen_4098) -> q_gen_4094
<cons, s>(q_gen_4119, q_gen_4117) -> q_gen_4094
<nil, z>() -> q_gen_4094
<a, z>() -> q_gen_4099
<b, z>() -> q_gen_4099
<b, s>(q_gen_4120) -> q_gen_4119
<cons, s>(q_gen_4119, q_gen_4098) -> q_gen_4122
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_4091, q_gen_4093, q_gen_4123},
Q_f={q_gen_4091},
Delta=
{
<s>(q_gen_4093) -> q_gen_4093
<z>() -> q_gen_4093
<s, s>(q_gen_4091) -> q_gen_4091
<z, s>(q_gen_4093) -> q_gen_4091
<z, z>() -> q_gen_4091
<s, s>(q_gen_4123) -> q_gen_4123
<s, z>(q_gen_4093) -> q_gen_4123
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 8
() -> length([nil, z]) -> 8
() -> leq([z, s(nn2)]) -> 8
() -> leq([z, z]) -> 8
(append([l1, l2, _aq]) /\ length([_aq, _bq]) /\ length([l1, _zp])) -> leq([_zp, _bq]) -> 10
(append([l1, l2, _dq]) /\ length([_dq, _eq]) /\ length([l2, _cq])) -> leq([_cq, _eq]) -> 9
(append([t1, l2, _qp])) -> append([cons(h1, t1), l2, cons(h1, _qp)]) -> 10
(length([ll, _vp])) -> length([cons(x, ll), s(_vp)]) -> 13
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 9
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 10
(leq([s(nn1), z])) -> BOT -> 10
}
Sat witness: Found: ((length([ll, _vp])) -> length([cons(x, ll), s(_vp)]), {
_vp -> s(z)  ;  ll -> cons(b, nil)  ;  x -> a
})

-------------------------------------------
Step 18, which took 0.017196 s (model generation: 0.015354,  model checking: 0.001842):

Model:
|_
{
append -> 
{{{
Q={q_gen_4095, q_gen_4101, q_gen_4102, q_gen_4113, q_gen_4114, q_gen_4115},
Q_f={q_gen_4095},
Delta=
{
<nil>() -> q_gen_4113
<b>() -> q_gen_4114
<cons, cons>(q_gen_4102, q_gen_4101) -> q_gen_4101
<nil, cons>(q_gen_4114, q_gen_4113) -> q_gen_4101
<nil, nil>() -> q_gen_4101
<a, a>() -> q_gen_4102
<b, b>() -> q_gen_4102
<cons, cons, cons>(q_gen_4115, q_gen_4095) -> q_gen_4095
<cons, nil, cons>(q_gen_4102, q_gen_4101) -> q_gen_4095
<nil, cons, cons>(q_gen_4102, q_gen_4101) -> q_gen_4095
<nil, nil, cons>(q_gen_4114, q_gen_4113) -> q_gen_4095
<nil, nil, nil>() -> q_gen_4095
<b, b, b>() -> q_gen_4115
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_4094, q_gen_4098, q_gen_4099, q_gen_4117, q_gen_4118, q_gen_4119, q_gen_4120, q_gen_4122},
Q_f={q_gen_4094},
Delta=
{
<nil>() -> q_gen_4098
<cons>(q_gen_4118, q_gen_4098) -> q_gen_4117
<b>() -> q_gen_4118
<z>() -> q_gen_4120
<cons, s>(q_gen_4099, q_gen_4098) -> q_gen_4094
<cons, s>(q_gen_4099, q_gen_4117) -> q_gen_4094
<cons, s>(q_gen_4119, q_gen_4117) -> q_gen_4094
<nil, z>() -> q_gen_4094
<a, s>(q_gen_4120) -> q_gen_4099
<a, z>() -> q_gen_4099
<b, z>() -> q_gen_4099
<b, s>(q_gen_4120) -> q_gen_4119
<cons, s>(q_gen_4119, q_gen_4098) -> q_gen_4122
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_4091, q_gen_4093, q_gen_4123},
Q_f={q_gen_4091},
Delta=
{
<s>(q_gen_4093) -> q_gen_4093
<z>() -> q_gen_4093
<s, s>(q_gen_4091) -> q_gen_4091
<z, s>(q_gen_4093) -> q_gen_4091
<z, z>() -> q_gen_4091
<s, s>(q_gen_4123) -> q_gen_4123
<s, z>(q_gen_4093) -> q_gen_4123
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 9
() -> length([nil, z]) -> 9
() -> leq([z, s(nn2)]) -> 9
() -> leq([z, z]) -> 9
(append([l1, l2, _aq]) /\ length([_aq, _bq]) /\ length([l1, _zp])) -> leq([_zp, _bq]) -> 10
(append([l1, l2, _dq]) /\ length([_dq, _eq]) /\ length([l2, _cq])) -> leq([_cq, _eq]) -> 12
(append([t1, l2, _qp])) -> append([cons(h1, t1), l2, cons(h1, _qp)]) -> 10
(length([ll, _vp])) -> length([cons(x, ll), s(_vp)]) -> 13
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 10
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 10
(leq([s(nn1), z])) -> BOT -> 10
}
Sat witness: Found: ((append([l1, l2, _dq]) /\ length([_dq, _eq]) /\ length([l2, _cq])) -> leq([_cq, _eq]), {
_cq -> s(s(z))  ;  _dq -> cons(a, nil)  ;  _eq -> s(z)  ;  l1 -> nil  ;  l2 -> cons(a, nil)
})

-------------------------------------------
Step 19, which took 0.016786 s (model generation: 0.014766,  model checking: 0.002020):

Model:
|_
{
append -> 
{{{
Q={q_gen_4095, q_gen_4101, q_gen_4102, q_gen_4113, q_gen_4114, q_gen_4115},
Q_f={q_gen_4095},
Delta=
{
<nil>() -> q_gen_4113
<b>() -> q_gen_4114
<cons, cons>(q_gen_4102, q_gen_4101) -> q_gen_4101
<nil, cons>(q_gen_4114, q_gen_4113) -> q_gen_4101
<nil, nil>() -> q_gen_4101
<a, a>() -> q_gen_4102
<b, b>() -> q_gen_4102
<cons, cons, cons>(q_gen_4115, q_gen_4095) -> q_gen_4095
<cons, nil, cons>(q_gen_4102, q_gen_4101) -> q_gen_4095
<nil, cons, cons>(q_gen_4102, q_gen_4101) -> q_gen_4095
<nil, nil, cons>(q_gen_4114, q_gen_4113) -> q_gen_4095
<nil, nil, nil>() -> q_gen_4095
<b, b, b>() -> q_gen_4115
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_4094, q_gen_4098, q_gen_4099, q_gen_4117, q_gen_4118, q_gen_4119, q_gen_4120, q_gen_4122},
Q_f={q_gen_4094},
Delta=
{
<nil>() -> q_gen_4098
<cons>(q_gen_4118, q_gen_4098) -> q_gen_4117
<b>() -> q_gen_4118
<z>() -> q_gen_4120
<cons, s>(q_gen_4099, q_gen_4098) -> q_gen_4094
<cons, s>(q_gen_4119, q_gen_4117) -> q_gen_4094
<nil, z>() -> q_gen_4094
<a, z>() -> q_gen_4099
<b, z>() -> q_gen_4099
<a, s>(q_gen_4120) -> q_gen_4119
<b, s>(q_gen_4120) -> q_gen_4119
<cons, s>(q_gen_4119, q_gen_4098) -> q_gen_4122
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_4091, q_gen_4093, q_gen_4123},
Q_f={q_gen_4091},
Delta=
{
<s>(q_gen_4093) -> q_gen_4093
<z>() -> q_gen_4093
<s, s>(q_gen_4091) -> q_gen_4091
<z, s>(q_gen_4093) -> q_gen_4091
<z, z>() -> q_gen_4091
<s, s>(q_gen_4123) -> q_gen_4123
<s, z>(q_gen_4093) -> q_gen_4123
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 10
() -> length([nil, z]) -> 10
() -> leq([z, s(nn2)]) -> 10
() -> leq([z, z]) -> 10
(append([l1, l2, _aq]) /\ length([_aq, _bq]) /\ length([l1, _zp])) -> leq([_zp, _bq]) -> 10
(append([l1, l2, _dq]) /\ length([_dq, _eq]) /\ length([l2, _cq])) -> leq([_cq, _eq]) -> 12
(append([t1, l2, _qp])) -> append([cons(h1, t1), l2, cons(h1, _qp)]) -> 13
(length([ll, _vp])) -> length([cons(x, ll), s(_vp)]) -> 13
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 11
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 11
(leq([s(nn1), z])) -> BOT -> 11
}
Sat witness: Found: ((append([t1, l2, _qp])) -> append([cons(h1, t1), l2, cons(h1, _qp)]), {
_qp -> cons(b, nil)  ;  h1 -> a  ;  l2 -> cons(b, nil)  ;  t1 -> nil
})

-------------------------------------------
Step 20, which took 0.019716 s (model generation: 0.016462,  model checking: 0.003254):

Model:
|_
{
append -> 
{{{
Q={q_gen_4095, q_gen_4101, q_gen_4102, q_gen_4113, q_gen_4114, q_gen_4115},
Q_f={q_gen_4095},
Delta=
{
<nil>() -> q_gen_4113
<b>() -> q_gen_4114
<cons, cons>(q_gen_4102, q_gen_4101) -> q_gen_4101
<nil, cons>(q_gen_4114, q_gen_4113) -> q_gen_4101
<nil, nil>() -> q_gen_4101
<a, a>() -> q_gen_4102
<b, b>() -> q_gen_4102
<cons, cons, cons>(q_gen_4115, q_gen_4095) -> q_gen_4095
<cons, nil, cons>(q_gen_4102, q_gen_4101) -> q_gen_4095
<nil, cons, cons>(q_gen_4102, q_gen_4101) -> q_gen_4095
<nil, nil, cons>(q_gen_4114, q_gen_4113) -> q_gen_4095
<nil, nil, nil>() -> q_gen_4095
<a, b, a>() -> q_gen_4115
<b, b, b>() -> q_gen_4115
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_4094, q_gen_4098, q_gen_4099, q_gen_4117, q_gen_4118, q_gen_4119, q_gen_4120, q_gen_4122},
Q_f={q_gen_4094},
Delta=
{
<nil>() -> q_gen_4098
<cons>(q_gen_4118, q_gen_4098) -> q_gen_4117
<b>() -> q_gen_4118
<z>() -> q_gen_4120
<cons, s>(q_gen_4099, q_gen_4098) -> q_gen_4094
<cons, s>(q_gen_4119, q_gen_4117) -> q_gen_4094
<nil, z>() -> q_gen_4094
<a, z>() -> q_gen_4099
<b, z>() -> q_gen_4099
<a, s>(q_gen_4120) -> q_gen_4119
<b, s>(q_gen_4120) -> q_gen_4119
<cons, s>(q_gen_4119, q_gen_4098) -> q_gen_4122
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_4091, q_gen_4093, q_gen_4123},
Q_f={q_gen_4091},
Delta=
{
<s>(q_gen_4093) -> q_gen_4093
<z>() -> q_gen_4093
<s, s>(q_gen_4091) -> q_gen_4091
<z, s>(q_gen_4093) -> q_gen_4091
<z, z>() -> q_gen_4091
<s, s>(q_gen_4123) -> q_gen_4123
<s, z>(q_gen_4093) -> q_gen_4123
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 11
() -> length([nil, z]) -> 11
() -> leq([z, s(nn2)]) -> 11
() -> leq([z, z]) -> 11
(append([l1, l2, _aq]) /\ length([_aq, _bq]) /\ length([l1, _zp])) -> leq([_zp, _bq]) -> 11
(append([l1, l2, _dq]) /\ length([_dq, _eq]) /\ length([l2, _cq])) -> leq([_cq, _eq]) -> 13
(append([t1, l2, _qp])) -> append([cons(h1, t1), l2, cons(h1, _qp)]) -> 13
(length([ll, _vp])) -> length([cons(x, ll), s(_vp)]) -> 16
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 12
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 12
(leq([s(nn1), z])) -> BOT -> 12
}
Sat witness: Found: ((length([ll, _vp])) -> length([cons(x, ll), s(_vp)]), {
_vp -> s(s(z))  ;  ll -> cons(b, cons(b, nil))  ;  x -> b
})

-------------------------------------------
Step 21, which took 0.018508 s (model generation: 0.017006,  model checking: 0.001502):

Model:
|_
{
append -> 
{{{
Q={q_gen_4095, q_gen_4101, q_gen_4102, q_gen_4113, q_gen_4114, q_gen_4115},
Q_f={q_gen_4095},
Delta=
{
<nil>() -> q_gen_4113
<b>() -> q_gen_4114
<cons, cons>(q_gen_4102, q_gen_4101) -> q_gen_4101
<nil, cons>(q_gen_4114, q_gen_4113) -> q_gen_4101
<nil, nil>() -> q_gen_4101
<a, a>() -> q_gen_4102
<b, b>() -> q_gen_4102
<cons, cons, cons>(q_gen_4115, q_gen_4095) -> q_gen_4095
<cons, nil, cons>(q_gen_4102, q_gen_4101) -> q_gen_4095
<nil, cons, cons>(q_gen_4102, q_gen_4101) -> q_gen_4095
<nil, nil, cons>(q_gen_4114, q_gen_4113) -> q_gen_4095
<nil, nil, nil>() -> q_gen_4095
<a, b, a>() -> q_gen_4115
<b, b, b>() -> q_gen_4115
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_4094, q_gen_4098, q_gen_4099, q_gen_4117, q_gen_4118, q_gen_4119, q_gen_4120, q_gen_4122},
Q_f={q_gen_4094},
Delta=
{
<nil>() -> q_gen_4098
<cons>(q_gen_4118, q_gen_4098) -> q_gen_4117
<cons>(q_gen_4118, q_gen_4117) -> q_gen_4117
<b>() -> q_gen_4118
<s>(q_gen_4120) -> q_gen_4120
<z>() -> q_gen_4120
<cons, s>(q_gen_4099, q_gen_4098) -> q_gen_4094
<cons, s>(q_gen_4119, q_gen_4117) -> q_gen_4094
<nil, z>() -> q_gen_4094
<a, z>() -> q_gen_4099
<b, z>() -> q_gen_4099
<a, s>(q_gen_4120) -> q_gen_4119
<b, s>(q_gen_4120) -> q_gen_4119
<cons, s>(q_gen_4119, q_gen_4098) -> q_gen_4122
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_4091, q_gen_4093, q_gen_4123},
Q_f={q_gen_4091},
Delta=
{
<s>(q_gen_4093) -> q_gen_4093
<z>() -> q_gen_4093
<s, s>(q_gen_4091) -> q_gen_4091
<z, s>(q_gen_4093) -> q_gen_4091
<z, z>() -> q_gen_4091
<s, s>(q_gen_4123) -> q_gen_4123
<s, z>(q_gen_4093) -> q_gen_4123
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 11
() -> length([nil, z]) -> 11
() -> leq([z, s(nn2)]) -> 11
() -> leq([z, z]) -> 11
(append([l1, l2, _aq]) /\ length([_aq, _bq]) /\ length([l1, _zp])) -> leq([_zp, _bq]) -> 14
(append([l1, l2, _dq]) /\ length([_dq, _eq]) /\ length([l2, _cq])) -> leq([_cq, _eq]) -> 13
(append([t1, l2, _qp])) -> append([cons(h1, t1), l2, cons(h1, _qp)]) -> 13
(length([ll, _vp])) -> length([cons(x, ll), s(_vp)]) -> 16
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 12
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 12
(leq([s(nn1), z])) -> BOT -> 12
}
Sat witness: Found: ((append([l1, l2, _aq]) /\ length([_aq, _bq]) /\ length([l1, _zp])) -> leq([_zp, _bq]), {
_aq -> cons(b, cons(b, nil))  ;  _bq -> s(s(z))  ;  _zp -> s(s(s(z)))  ;  l1 -> cons(b, cons(b, nil))  ;  l2 -> cons(b, nil)
})

-------------------------------------------
Step 22, which took 0.020536 s (model generation: 0.018977,  model checking: 0.001559):

Model:
|_
{
append -> 
{{{
Q={q_gen_4095, q_gen_4101, q_gen_4102, q_gen_4112, q_gen_4113, q_gen_4114, q_gen_4115},
Q_f={q_gen_4095},
Delta=
{
<nil>() -> q_gen_4113
<b>() -> q_gen_4114
<cons, cons>(q_gen_4102, q_gen_4101) -> q_gen_4101
<nil, cons>(q_gen_4114, q_gen_4113) -> q_gen_4101
<nil, nil>() -> q_gen_4101
<a, a>() -> q_gen_4102
<b, b>() -> q_gen_4102
<cons, cons, cons>(q_gen_4115, q_gen_4112) -> q_gen_4095
<cons, nil, cons>(q_gen_4102, q_gen_4101) -> q_gen_4095
<nil, cons, cons>(q_gen_4102, q_gen_4101) -> q_gen_4095
<nil, nil, nil>() -> q_gen_4095
<cons, cons, cons>(q_gen_4115, q_gen_4095) -> q_gen_4112
<nil, nil, cons>(q_gen_4114, q_gen_4113) -> q_gen_4112
<a, b, a>() -> q_gen_4115
<b, b, b>() -> q_gen_4115
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_4094, q_gen_4098, q_gen_4099, q_gen_4117, q_gen_4118, q_gen_4119, q_gen_4120, q_gen_4122},
Q_f={q_gen_4094},
Delta=
{
<nil>() -> q_gen_4098
<cons>(q_gen_4118, q_gen_4098) -> q_gen_4117
<cons>(q_gen_4118, q_gen_4117) -> q_gen_4117
<b>() -> q_gen_4118
<s>(q_gen_4120) -> q_gen_4120
<z>() -> q_gen_4120
<cons, s>(q_gen_4099, q_gen_4098) -> q_gen_4094
<cons, s>(q_gen_4119, q_gen_4117) -> q_gen_4094
<nil, z>() -> q_gen_4094
<a, z>() -> q_gen_4099
<b, z>() -> q_gen_4099
<a, s>(q_gen_4120) -> q_gen_4119
<b, s>(q_gen_4120) -> q_gen_4119
<cons, s>(q_gen_4119, q_gen_4098) -> q_gen_4122
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_4091, q_gen_4093, q_gen_4123},
Q_f={q_gen_4091},
Delta=
{
<s>(q_gen_4093) -> q_gen_4093
<z>() -> q_gen_4093
<s, s>(q_gen_4091) -> q_gen_4091
<z, s>(q_gen_4093) -> q_gen_4091
<z, z>() -> q_gen_4091
<s, s>(q_gen_4123) -> q_gen_4123
<s, z>(q_gen_4093) -> q_gen_4123
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 12
() -> length([nil, z]) -> 12
() -> leq([z, s(nn2)]) -> 12
() -> leq([z, z]) -> 12
(append([l1, l2, _aq]) /\ length([_aq, _bq]) /\ length([l1, _zp])) -> leq([_zp, _bq]) -> 14
(append([l1, l2, _dq]) /\ length([_dq, _eq]) /\ length([l2, _cq])) -> leq([_cq, _eq]) -> 13
(append([t1, l2, _qp])) -> append([cons(h1, t1), l2, cons(h1, _qp)]) -> 16
(length([ll, _vp])) -> length([cons(x, ll), s(_vp)]) -> 16
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 13
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 13
(leq([s(nn1), z])) -> BOT -> 13
}
Sat witness: Found: ((append([t1, l2, _qp])) -> append([cons(h1, t1), l2, cons(h1, _qp)]), {
_qp -> cons(b, cons(b, nil))  ;  h1 -> b  ;  l2 -> cons(b, nil)  ;  t1 -> cons(b, nil)
})

-------------------------------------------
Step 23, which took 0.020351 s (model generation: 0.019348,  model checking: 0.001003):

Model:
|_
{
append -> 
{{{
Q={q_gen_4095, q_gen_4101, q_gen_4102, q_gen_4113, q_gen_4114, q_gen_4115},
Q_f={q_gen_4095},
Delta=
{
<nil>() -> q_gen_4113
<b>() -> q_gen_4114
<cons, cons>(q_gen_4102, q_gen_4101) -> q_gen_4101
<nil, cons>(q_gen_4114, q_gen_4113) -> q_gen_4101
<nil, nil>() -> q_gen_4101
<a, a>() -> q_gen_4102
<b, b>() -> q_gen_4102
<cons, cons, cons>(q_gen_4115, q_gen_4095) -> q_gen_4095
<cons, nil, cons>(q_gen_4102, q_gen_4101) -> q_gen_4095
<nil, cons, cons>(q_gen_4102, q_gen_4101) -> q_gen_4095
<nil, nil, cons>(q_gen_4114, q_gen_4113) -> q_gen_4095
<nil, nil, nil>() -> q_gen_4095
<a, b, a>() -> q_gen_4115
<b, b, b>() -> q_gen_4115
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_4094, q_gen_4098, q_gen_4099, q_gen_4117, q_gen_4118, q_gen_4119, q_gen_4120, q_gen_4122},
Q_f={q_gen_4094},
Delta=
{
<nil>() -> q_gen_4098
<cons>(q_gen_4118, q_gen_4098) -> q_gen_4117
<cons>(q_gen_4118, q_gen_4117) -> q_gen_4117
<b>() -> q_gen_4118
<s>(q_gen_4120) -> q_gen_4120
<z>() -> q_gen_4120
<cons, s>(q_gen_4099, q_gen_4098) -> q_gen_4094
<cons, s>(q_gen_4119, q_gen_4117) -> q_gen_4094
<nil, z>() -> q_gen_4094
<a, z>() -> q_gen_4099
<b, z>() -> q_gen_4099
<a, s>(q_gen_4120) -> q_gen_4119
<b, s>(q_gen_4120) -> q_gen_4119
<cons, s>(q_gen_4119, q_gen_4098) -> q_gen_4122
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_4091, q_gen_4093, q_gen_4123, q_gen_4124},
Q_f={q_gen_4091},
Delta=
{
<s>(q_gen_4093) -> q_gen_4093
<z>() -> q_gen_4093
<s, s>(q_gen_4091) -> q_gen_4091
<s, s>(q_gen_4123) -> q_gen_4091
<z, s>(q_gen_4093) -> q_gen_4091
<z, z>() -> q_gen_4091
<s, s>(q_gen_4124) -> q_gen_4123
<s, z>(q_gen_4093) -> q_gen_4124
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 13
() -> length([nil, z]) -> 13
() -> leq([z, s(nn2)]) -> 13
() -> leq([z, z]) -> 13
(append([l1, l2, _aq]) /\ length([_aq, _bq]) /\ length([l1, _zp])) -> leq([_zp, _bq]) -> 14
(append([l1, l2, _dq]) /\ length([_dq, _eq]) /\ length([l2, _cq])) -> leq([_cq, _eq]) -> 13
(append([t1, l2, _qp])) -> append([cons(h1, t1), l2, cons(h1, _qp)]) -> 16
(length([ll, _vp])) -> length([cons(x, ll), s(_vp)]) -> 16
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 13
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 16
(leq([s(nn1), z])) -> BOT -> 14
}
Sat witness: Found: ((leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]), {
nn1 -> s(s(z))  ;  nn2 -> s(z)
})

-------------------------------------------
Step 24, which took 0.022162 s (model generation: 0.020691,  model checking: 0.001471):

Model:
|_
{
append -> 
{{{
Q={q_gen_4095, q_gen_4101, q_gen_4102, q_gen_4113, q_gen_4114, q_gen_4115},
Q_f={q_gen_4095},
Delta=
{
<nil>() -> q_gen_4113
<b>() -> q_gen_4114
<cons, cons>(q_gen_4102, q_gen_4101) -> q_gen_4101
<nil, cons>(q_gen_4114, q_gen_4113) -> q_gen_4101
<nil, nil>() -> q_gen_4101
<a, a>() -> q_gen_4102
<b, b>() -> q_gen_4102
<cons, cons, cons>(q_gen_4115, q_gen_4095) -> q_gen_4095
<cons, nil, cons>(q_gen_4102, q_gen_4101) -> q_gen_4095
<nil, cons, cons>(q_gen_4102, q_gen_4101) -> q_gen_4095
<nil, nil, cons>(q_gen_4114, q_gen_4113) -> q_gen_4095
<nil, nil, nil>() -> q_gen_4095
<a, b, a>() -> q_gen_4115
<b, b, b>() -> q_gen_4115
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_4094, q_gen_4098, q_gen_4099, q_gen_4117, q_gen_4118, q_gen_4119, q_gen_4120, q_gen_4122, q_gen_4136},
Q_f={q_gen_4094},
Delta=
{
<cons>(q_gen_4118, q_gen_4117) -> q_gen_4098
<nil>() -> q_gen_4098
<cons>(q_gen_4118, q_gen_4098) -> q_gen_4117
<b>() -> q_gen_4118
<z>() -> q_gen_4120
<s>(q_gen_4120) -> q_gen_4136
<cons, s>(q_gen_4099, q_gen_4098) -> q_gen_4094
<cons, s>(q_gen_4119, q_gen_4117) -> q_gen_4094
<nil, z>() -> q_gen_4094
<a, z>() -> q_gen_4099
<b, s>(q_gen_4136) -> q_gen_4099
<b, z>() -> q_gen_4099
<a, s>(q_gen_4120) -> q_gen_4119
<b, s>(q_gen_4120) -> q_gen_4119
<cons, s>(q_gen_4099, q_gen_4117) -> q_gen_4122
<cons, s>(q_gen_4119, q_gen_4098) -> q_gen_4122
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_4091, q_gen_4093, q_gen_4123},
Q_f={q_gen_4091},
Delta=
{
<s>(q_gen_4093) -> q_gen_4093
<z>() -> q_gen_4093
<s, s>(q_gen_4091) -> q_gen_4091
<z, s>(q_gen_4093) -> q_gen_4091
<z, z>() -> q_gen_4091
<s, s>(q_gen_4123) -> q_gen_4123
<s, z>(q_gen_4093) -> q_gen_4123
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 13
() -> length([nil, z]) -> 13
() -> leq([z, s(nn2)]) -> 13
() -> leq([z, z]) -> 13
(append([l1, l2, _aq]) /\ length([_aq, _bq]) /\ length([l1, _zp])) -> leq([_zp, _bq]) -> 14
(append([l1, l2, _dq]) /\ length([_dq, _eq]) /\ length([l2, _cq])) -> leq([_cq, _eq]) -> 16
(append([t1, l2, _qp])) -> append([cons(h1, t1), l2, cons(h1, _qp)]) -> 16
(length([ll, _vp])) -> length([cons(x, ll), s(_vp)]) -> 16
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 14
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 16
(leq([s(nn1), z])) -> BOT -> 14
}
Sat witness: Found: ((append([l1, l2, _dq]) /\ length([_dq, _eq]) /\ length([l2, _cq])) -> leq([_cq, _eq]), {
_cq -> s(s(z))  ;  _dq -> cons(b, cons(b, cons(b, nil)))  ;  _eq -> s(z)  ;  l1 -> cons(b, nil)  ;  l2 -> cons(b, cons(b, nil))
})

-------------------------------------------
Step 25, which took 0.023366 s (model generation: 0.022695,  model checking: 0.000671):

Model:
|_
{
append -> 
{{{
Q={q_gen_4095, q_gen_4101, q_gen_4102, q_gen_4107, q_gen_4110, q_gen_4113, q_gen_4114, q_gen_4115},
Q_f={q_gen_4095},
Delta=
{
<nil>() -> q_gen_4113
<b>() -> q_gen_4114
<cons, cons>(q_gen_4107, q_gen_4101) -> q_gen_4101
<nil, cons>(q_gen_4114, q_gen_4113) -> q_gen_4101
<nil, nil>() -> q_gen_4101
<b, b>() -> q_gen_4102
<a, a>() -> q_gen_4107
<cons, nil, cons>(q_gen_4102, q_gen_4101) -> q_gen_4095
<nil, cons, cons>(q_gen_4107, q_gen_4101) -> q_gen_4095
<nil, nil, nil>() -> q_gen_4095
<cons, cons, cons>(q_gen_4115, q_gen_4095) -> q_gen_4110
<cons, cons, cons>(q_gen_4115, q_gen_4110) -> q_gen_4110
<nil, cons, cons>(q_gen_4102, q_gen_4101) -> q_gen_4110
<nil, nil, cons>(q_gen_4114, q_gen_4113) -> q_gen_4110
<a, b, a>() -> q_gen_4115
<b, b, b>() -> q_gen_4115
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_4094, q_gen_4098, q_gen_4099, q_gen_4117, q_gen_4118, q_gen_4119, q_gen_4120, q_gen_4122},
Q_f={q_gen_4094},
Delta=
{
<nil>() -> q_gen_4098
<cons>(q_gen_4118, q_gen_4098) -> q_gen_4117
<cons>(q_gen_4118, q_gen_4117) -> q_gen_4117
<b>() -> q_gen_4118
<s>(q_gen_4120) -> q_gen_4120
<z>() -> q_gen_4120
<cons, s>(q_gen_4099, q_gen_4098) -> q_gen_4094
<cons, s>(q_gen_4119, q_gen_4117) -> q_gen_4094
<nil, z>() -> q_gen_4094
<a, z>() -> q_gen_4099
<b, z>() -> q_gen_4099
<a, s>(q_gen_4120) -> q_gen_4119
<b, s>(q_gen_4120) -> q_gen_4119
<cons, s>(q_gen_4099, q_gen_4117) -> q_gen_4122
<cons, s>(q_gen_4119, q_gen_4098) -> q_gen_4122
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_4091, q_gen_4093, q_gen_4123},
Q_f={q_gen_4091},
Delta=
{
<s>(q_gen_4093) -> q_gen_4093
<z>() -> q_gen_4093
<s, s>(q_gen_4091) -> q_gen_4091
<z, s>(q_gen_4093) -> q_gen_4091
<z, z>() -> q_gen_4091
<s, s>(q_gen_4123) -> q_gen_4123
<s, z>(q_gen_4093) -> q_gen_4123
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 16
() -> length([nil, z]) -> 14
() -> leq([z, s(nn2)]) -> 14
() -> leq([z, z]) -> 14
(append([l1, l2, _aq]) /\ length([_aq, _bq]) /\ length([l1, _zp])) -> leq([_zp, _bq]) -> 14
(append([l1, l2, _dq]) /\ length([_dq, _eq]) /\ length([l2, _cq])) -> leq([_cq, _eq]) -> 16
(append([t1, l2, _qp])) -> append([cons(h1, t1), l2, cons(h1, _qp)]) -> 16
(length([ll, _vp])) -> length([cons(x, ll), s(_vp)]) -> 16
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 14
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 16
(leq([s(nn1), z])) -> BOT -> 14
}
Sat witness: Found: (() -> append([nil, l2, l2]), {
l2 -> cons(b, nil)
})

-------------------------------------------
Step 26, which took 0.030865 s (model generation: 0.028705,  model checking: 0.002160):

Model:
|_
{
append -> 
{{{
Q={q_gen_4095, q_gen_4101, q_gen_4102, q_gen_4106, q_gen_4112, q_gen_4113, q_gen_4114, q_gen_4115},
Q_f={q_gen_4095},
Delta=
{
<nil>() -> q_gen_4113
<b>() -> q_gen_4114
<nil, nil>() -> q_gen_4101
<a, a>() -> q_gen_4102
<b, b>() -> q_gen_4102
<cons, cons>(q_gen_4102, q_gen_4101) -> q_gen_4106
<nil, cons>(q_gen_4114, q_gen_4113) -> q_gen_4106
<cons, cons, cons>(q_gen_4115, q_gen_4112) -> q_gen_4095
<cons, nil, cons>(q_gen_4102, q_gen_4101) -> q_gen_4095
<nil, cons, cons>(q_gen_4102, q_gen_4101) -> q_gen_4095
<nil, cons, cons>(q_gen_4102, q_gen_4106) -> q_gen_4095
<nil, nil, nil>() -> q_gen_4095
<cons, cons, cons>(q_gen_4115, q_gen_4095) -> q_gen_4112
<cons, nil, cons>(q_gen_4102, q_gen_4106) -> q_gen_4112
<nil, nil, cons>(q_gen_4114, q_gen_4113) -> q_gen_4112
<a, b, a>() -> q_gen_4115
<b, b, b>() -> q_gen_4115
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_4094, q_gen_4098, q_gen_4099, q_gen_4117, q_gen_4118, q_gen_4119, q_gen_4120, q_gen_4122},
Q_f={q_gen_4094},
Delta=
{
<nil>() -> q_gen_4098
<cons>(q_gen_4118, q_gen_4098) -> q_gen_4117
<cons>(q_gen_4118, q_gen_4117) -> q_gen_4117
<b>() -> q_gen_4118
<s>(q_gen_4120) -> q_gen_4120
<z>() -> q_gen_4120
<cons, s>(q_gen_4099, q_gen_4098) -> q_gen_4094
<cons, s>(q_gen_4099, q_gen_4117) -> q_gen_4094
<cons, s>(q_gen_4119, q_gen_4117) -> q_gen_4094
<nil, z>() -> q_gen_4094
<a, z>() -> q_gen_4099
<b, z>() -> q_gen_4099
<a, s>(q_gen_4120) -> q_gen_4119
<b, s>(q_gen_4120) -> q_gen_4119
<cons, s>(q_gen_4119, q_gen_4098) -> q_gen_4122
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_4091, q_gen_4093, q_gen_4123},
Q_f={q_gen_4091},
Delta=
{
<s>(q_gen_4093) -> q_gen_4093
<z>() -> q_gen_4093
<s, s>(q_gen_4091) -> q_gen_4091
<z, s>(q_gen_4093) -> q_gen_4091
<z, z>() -> q_gen_4091
<s, s>(q_gen_4123) -> q_gen_4123
<s, z>(q_gen_4093) -> q_gen_4123
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 16
() -> length([nil, z]) -> 14
() -> leq([z, s(nn2)]) -> 14
() -> leq([z, z]) -> 14
(append([l1, l2, _aq]) /\ length([_aq, _bq]) /\ length([l1, _zp])) -> leq([_zp, _bq]) -> 17
(append([l1, l2, _dq]) /\ length([_dq, _eq]) /\ length([l2, _cq])) -> leq([_cq, _eq]) -> 16
(append([t1, l2, _qp])) -> append([cons(h1, t1), l2, cons(h1, _qp)]) -> 16
(length([ll, _vp])) -> length([cons(x, ll), s(_vp)]) -> 16
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 15
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 16
(leq([s(nn1), z])) -> BOT -> 15
}
Sat witness: Found: ((append([l1, l2, _aq]) /\ length([_aq, _bq]) /\ length([l1, _zp])) -> leq([_zp, _bq]), {
_aq -> cons(b, cons(b, cons(b, nil)))  ;  _bq -> s(z)  ;  _zp -> s(s(z))  ;  l1 -> cons(b, cons(b, nil))  ;  l2 -> cons(b, nil)
})

-------------------------------------------
Step 27, which took 0.026291 s (model generation: 0.024199,  model checking: 0.002092):

Model:
|_
{
append -> 
{{{
Q={q_gen_4095, q_gen_4101, q_gen_4102, q_gen_4112, q_gen_4113, q_gen_4114, q_gen_4115, q_gen_4126},
Q_f={q_gen_4095},
Delta=
{
<nil>() -> q_gen_4113
<b>() -> q_gen_4114
<cons, cons>(q_gen_4102, q_gen_4101) -> q_gen_4101
<nil, nil>() -> q_gen_4101
<a, a>() -> q_gen_4102
<b, b>() -> q_gen_4102
<nil, cons>(q_gen_4114, q_gen_4113) -> q_gen_4126
<cons, cons, cons>(q_gen_4115, q_gen_4112) -> q_gen_4095
<cons, nil, cons>(q_gen_4102, q_gen_4101) -> q_gen_4095
<nil, cons, cons>(q_gen_4102, q_gen_4101) -> q_gen_4095
<nil, cons, cons>(q_gen_4102, q_gen_4126) -> q_gen_4095
<nil, nil, nil>() -> q_gen_4095
<cons, cons, cons>(q_gen_4115, q_gen_4095) -> q_gen_4112
<cons, nil, cons>(q_gen_4102, q_gen_4126) -> q_gen_4112
<nil, nil, cons>(q_gen_4114, q_gen_4113) -> q_gen_4112
<a, b, a>() -> q_gen_4115
<b, b, b>() -> q_gen_4115
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_4094, q_gen_4098, q_gen_4099, q_gen_4117, q_gen_4118, q_gen_4119, q_gen_4120, q_gen_4122},
Q_f={q_gen_4094},
Delta=
{
<nil>() -> q_gen_4098
<cons>(q_gen_4118, q_gen_4098) -> q_gen_4117
<cons>(q_gen_4118, q_gen_4117) -> q_gen_4117
<b>() -> q_gen_4118
<s>(q_gen_4120) -> q_gen_4120
<z>() -> q_gen_4120
<cons, s>(q_gen_4099, q_gen_4098) -> q_gen_4094
<cons, s>(q_gen_4119, q_gen_4117) -> q_gen_4094
<nil, z>() -> q_gen_4094
<a, z>() -> q_gen_4099
<b, z>() -> q_gen_4099
<a, s>(q_gen_4120) -> q_gen_4119
<b, s>(q_gen_4120) -> q_gen_4119
<cons, s>(q_gen_4099, q_gen_4117) -> q_gen_4122
<cons, s>(q_gen_4119, q_gen_4098) -> q_gen_4122
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_4091, q_gen_4093, q_gen_4123},
Q_f={q_gen_4091},
Delta=
{
<s>(q_gen_4093) -> q_gen_4093
<z>() -> q_gen_4093
<s, s>(q_gen_4091) -> q_gen_4091
<z, s>(q_gen_4093) -> q_gen_4091
<z, z>() -> q_gen_4091
<s, s>(q_gen_4123) -> q_gen_4123
<s, z>(q_gen_4093) -> q_gen_4123
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 16
() -> length([nil, z]) -> 15
() -> leq([z, s(nn2)]) -> 15
() -> leq([z, z]) -> 15
(append([l1, l2, _aq]) /\ length([_aq, _bq]) /\ length([l1, _zp])) -> leq([_zp, _bq]) -> 17
(append([l1, l2, _dq]) /\ length([_dq, _eq]) /\ length([l2, _cq])) -> leq([_cq, _eq]) -> 16
(append([t1, l2, _qp])) -> append([cons(h1, t1), l2, cons(h1, _qp)]) -> 16
(length([ll, _vp])) -> length([cons(x, ll), s(_vp)]) -> 19
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 16
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 17
(leq([s(nn1), z])) -> BOT -> 16
}
Sat witness: Found: ((length([ll, _vp])) -> length([cons(x, ll), s(_vp)]), {
_vp -> s(z)  ;  ll -> cons(a, nil)  ;  x -> b
})

-------------------------------------------
Step 28, which took 0.025100 s (model generation: 0.024181,  model checking: 0.000919):

Model:
|_
{
append -> 
{{{
Q={q_gen_4095, q_gen_4101, q_gen_4102, q_gen_4106, q_gen_4112, q_gen_4113, q_gen_4114, q_gen_4115},
Q_f={q_gen_4095},
Delta=
{
<nil>() -> q_gen_4113
<b>() -> q_gen_4114
<nil, nil>() -> q_gen_4101
<a, a>() -> q_gen_4102
<b, b>() -> q_gen_4102
<cons, cons>(q_gen_4102, q_gen_4101) -> q_gen_4106
<nil, cons>(q_gen_4114, q_gen_4113) -> q_gen_4106
<cons, cons, cons>(q_gen_4115, q_gen_4112) -> q_gen_4095
<cons, nil, cons>(q_gen_4102, q_gen_4101) -> q_gen_4095
<nil, cons, cons>(q_gen_4102, q_gen_4101) -> q_gen_4095
<nil, cons, cons>(q_gen_4102, q_gen_4106) -> q_gen_4095
<nil, nil, nil>() -> q_gen_4095
<cons, cons, cons>(q_gen_4115, q_gen_4095) -> q_gen_4112
<cons, nil, cons>(q_gen_4102, q_gen_4106) -> q_gen_4112
<nil, nil, cons>(q_gen_4114, q_gen_4113) -> q_gen_4112
<a, b, a>() -> q_gen_4115
<b, b, b>() -> q_gen_4115
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_4094, q_gen_4098, q_gen_4099, q_gen_4117, q_gen_4118, q_gen_4119, q_gen_4120, q_gen_4122},
Q_f={q_gen_4094},
Delta=
{
<nil>() -> q_gen_4098
<cons>(q_gen_4118, q_gen_4098) -> q_gen_4117
<cons>(q_gen_4118, q_gen_4117) -> q_gen_4117
<a>() -> q_gen_4118
<b>() -> q_gen_4118
<s>(q_gen_4120) -> q_gen_4120
<z>() -> q_gen_4120
<cons, s>(q_gen_4099, q_gen_4098) -> q_gen_4094
<cons, s>(q_gen_4119, q_gen_4117) -> q_gen_4094
<nil, z>() -> q_gen_4094
<a, z>() -> q_gen_4099
<b, z>() -> q_gen_4099
<a, s>(q_gen_4120) -> q_gen_4119
<b, s>(q_gen_4120) -> q_gen_4119
<cons, s>(q_gen_4099, q_gen_4117) -> q_gen_4122
<cons, s>(q_gen_4119, q_gen_4098) -> q_gen_4122
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_4091, q_gen_4093, q_gen_4123},
Q_f={q_gen_4091},
Delta=
{
<s>(q_gen_4093) -> q_gen_4093
<z>() -> q_gen_4093
<s, s>(q_gen_4091) -> q_gen_4091
<z, s>(q_gen_4093) -> q_gen_4091
<z, z>() -> q_gen_4091
<s, s>(q_gen_4123) -> q_gen_4123
<s, z>(q_gen_4093) -> q_gen_4123
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 16
() -> length([nil, z]) -> 16
() -> leq([z, s(nn2)]) -> 16
() -> leq([z, z]) -> 16
(append([l1, l2, _aq]) /\ length([_aq, _bq]) /\ length([l1, _zp])) -> leq([_zp, _bq]) -> 17
(append([l1, l2, _dq]) /\ length([_dq, _eq]) /\ length([l2, _cq])) -> leq([_cq, _eq]) -> 16
(append([t1, l2, _qp])) -> append([cons(h1, t1), l2, cons(h1, _qp)]) -> 19
(length([ll, _vp])) -> length([cons(x, ll), s(_vp)]) -> 19
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 17
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 17
(leq([s(nn1), z])) -> BOT -> 17
}
Sat witness: Found: ((append([t1, l2, _qp])) -> append([cons(h1, t1), l2, cons(h1, _qp)]), {
_qp -> cons(a, nil)  ;  h1 -> b  ;  l2 -> nil  ;  t1 -> cons(a, nil)
})

-------------------------------------------
Step 29, which took 0.026635 s (model generation: 0.025530,  model checking: 0.001105):

Model:
|_
{
append -> 
{{{
Q={q_gen_4095, q_gen_4101, q_gen_4102, q_gen_4112, q_gen_4113, q_gen_4114, q_gen_4115, q_gen_4126},
Q_f={q_gen_4095},
Delta=
{
<nil>() -> q_gen_4113
<b>() -> q_gen_4114
<cons, cons>(q_gen_4102, q_gen_4101) -> q_gen_4101
<nil, nil>() -> q_gen_4101
<a, a>() -> q_gen_4102
<b, b>() -> q_gen_4102
<nil, cons>(q_gen_4114, q_gen_4113) -> q_gen_4126
<cons, cons, cons>(q_gen_4115, q_gen_4112) -> q_gen_4095
<cons, nil, cons>(q_gen_4102, q_gen_4101) -> q_gen_4095
<nil, cons, cons>(q_gen_4102, q_gen_4101) -> q_gen_4095
<nil, nil, nil>() -> q_gen_4095
<cons, cons, cons>(q_gen_4115, q_gen_4095) -> q_gen_4112
<cons, nil, cons>(q_gen_4102, q_gen_4126) -> q_gen_4112
<nil, cons, cons>(q_gen_4102, q_gen_4126) -> q_gen_4112
<nil, nil, cons>(q_gen_4114, q_gen_4113) -> q_gen_4112
<a, b, a>() -> q_gen_4115
<b, b, b>() -> q_gen_4115
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_4094, q_gen_4098, q_gen_4099, q_gen_4117, q_gen_4118, q_gen_4119, q_gen_4120, q_gen_4122},
Q_f={q_gen_4094},
Delta=
{
<nil>() -> q_gen_4098
<cons>(q_gen_4118, q_gen_4098) -> q_gen_4117
<cons>(q_gen_4118, q_gen_4117) -> q_gen_4117
<a>() -> q_gen_4118
<b>() -> q_gen_4118
<s>(q_gen_4120) -> q_gen_4120
<z>() -> q_gen_4120
<cons, s>(q_gen_4099, q_gen_4098) -> q_gen_4094
<cons, s>(q_gen_4119, q_gen_4117) -> q_gen_4094
<nil, z>() -> q_gen_4094
<a, z>() -> q_gen_4099
<b, z>() -> q_gen_4099
<a, s>(q_gen_4120) -> q_gen_4119
<b, s>(q_gen_4120) -> q_gen_4119
<cons, s>(q_gen_4099, q_gen_4117) -> q_gen_4122
<cons, s>(q_gen_4119, q_gen_4098) -> q_gen_4122
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_4091, q_gen_4093, q_gen_4123},
Q_f={q_gen_4091},
Delta=
{
<s>(q_gen_4093) -> q_gen_4093
<z>() -> q_gen_4093
<s, s>(q_gen_4091) -> q_gen_4091
<z, s>(q_gen_4093) -> q_gen_4091
<z, z>() -> q_gen_4091
<s, s>(q_gen_4123) -> q_gen_4123
<s, z>(q_gen_4093) -> q_gen_4123
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 16
() -> length([nil, z]) -> 16
() -> leq([z, s(nn2)]) -> 16
() -> leq([z, z]) -> 16
(append([l1, l2, _aq]) /\ length([_aq, _bq]) /\ length([l1, _zp])) -> leq([_zp, _bq]) -> 17
(append([l1, l2, _dq]) /\ length([_dq, _eq]) /\ length([l2, _cq])) -> leq([_cq, _eq]) -> 19
(append([t1, l2, _qp])) -> append([cons(h1, t1), l2, cons(h1, _qp)]) -> 19
(length([ll, _vp])) -> length([cons(x, ll), s(_vp)]) -> 19
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 17
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 17
(leq([s(nn1), z])) -> BOT -> 17
}
Sat witness: Found: ((append([l1, l2, _dq]) /\ length([_dq, _eq]) /\ length([l2, _cq])) -> leq([_cq, _eq]), {
_cq -> s(s(s(z)))  ;  _dq -> cons(b, cons(b, nil))  ;  _eq -> s(s(z))  ;  l1 -> nil  ;  l2 -> cons(b, cons(b, nil))
})

-------------------------------------------
Step 30, which took 0.028525 s (model generation: 0.027790,  model checking: 0.000735):

Model:
|_
{
append -> 
{{{
Q={q_gen_4095, q_gen_4101, q_gen_4102, q_gen_4107, q_gen_4112, q_gen_4113, q_gen_4114, q_gen_4115, q_gen_4126},
Q_f={q_gen_4095},
Delta=
{
<nil>() -> q_gen_4113
<b>() -> q_gen_4114
<cons, cons>(q_gen_4107, q_gen_4101) -> q_gen_4101
<nil, nil>() -> q_gen_4101
<b, b>() -> q_gen_4102
<a, a>() -> q_gen_4107
<cons, cons>(q_gen_4102, q_gen_4101) -> q_gen_4126
<nil, cons>(q_gen_4114, q_gen_4113) -> q_gen_4126
<cons, cons, cons>(q_gen_4115, q_gen_4112) -> q_gen_4095
<cons, nil, cons>(q_gen_4102, q_gen_4101) -> q_gen_4095
<nil, cons, cons>(q_gen_4102, q_gen_4101) -> q_gen_4095
<nil, cons, cons>(q_gen_4107, q_gen_4101) -> q_gen_4095
<nil, nil, nil>() -> q_gen_4095
<cons, cons, cons>(q_gen_4115, q_gen_4095) -> q_gen_4112
<cons, nil, cons>(q_gen_4102, q_gen_4126) -> q_gen_4112
<cons, nil, cons>(q_gen_4107, q_gen_4101) -> q_gen_4112
<nil, cons, cons>(q_gen_4102, q_gen_4126) -> q_gen_4112
<nil, nil, cons>(q_gen_4114, q_gen_4113) -> q_gen_4112
<a, b, a>() -> q_gen_4115
<b, b, b>() -> q_gen_4115
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_4094, q_gen_4098, q_gen_4099, q_gen_4117, q_gen_4118, q_gen_4119, q_gen_4120, q_gen_4122},
Q_f={q_gen_4094},
Delta=
{
<nil>() -> q_gen_4098
<cons>(q_gen_4118, q_gen_4098) -> q_gen_4117
<cons>(q_gen_4118, q_gen_4117) -> q_gen_4117
<a>() -> q_gen_4118
<b>() -> q_gen_4118
<s>(q_gen_4120) -> q_gen_4120
<z>() -> q_gen_4120
<cons, s>(q_gen_4099, q_gen_4098) -> q_gen_4094
<cons, s>(q_gen_4119, q_gen_4117) -> q_gen_4094
<nil, z>() -> q_gen_4094
<a, z>() -> q_gen_4099
<b, z>() -> q_gen_4099
<a, s>(q_gen_4120) -> q_gen_4119
<b, s>(q_gen_4120) -> q_gen_4119
<cons, s>(q_gen_4099, q_gen_4117) -> q_gen_4122
<cons, s>(q_gen_4119, q_gen_4098) -> q_gen_4122
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_4091, q_gen_4093, q_gen_4123},
Q_f={q_gen_4091},
Delta=
{
<s>(q_gen_4093) -> q_gen_4093
<z>() -> q_gen_4093
<s, s>(q_gen_4091) -> q_gen_4091
<z, s>(q_gen_4093) -> q_gen_4091
<z, z>() -> q_gen_4091
<s, s>(q_gen_4123) -> q_gen_4123
<s, z>(q_gen_4093) -> q_gen_4123
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 19
() -> length([nil, z]) -> 17
() -> leq([z, s(nn2)]) -> 17
() -> leq([z, z]) -> 17
(append([l1, l2, _aq]) /\ length([_aq, _bq]) /\ length([l1, _zp])) -> leq([_zp, _bq]) -> 17
(append([l1, l2, _dq]) /\ length([_dq, _eq]) /\ length([l2, _cq])) -> leq([_cq, _eq]) -> 19
(append([t1, l2, _qp])) -> append([cons(h1, t1), l2, cons(h1, _qp)]) -> 19
(length([ll, _vp])) -> length([cons(x, ll), s(_vp)]) -> 19
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 17
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 17
(leq([s(nn1), z])) -> BOT -> 17
}
Sat witness: Found: (() -> append([nil, l2, l2]), {
l2 -> cons(b, cons(b, nil))
})

-------------------------------------------
Step 31, which took 0.030150 s (model generation: 0.027809,  model checking: 0.002341):

Model:
|_
{
append -> 
{{{
Q={q_gen_4095, q_gen_4101, q_gen_4102, q_gen_4113, q_gen_4114, q_gen_4115},
Q_f={q_gen_4095},
Delta=
{
<nil>() -> q_gen_4113
<b>() -> q_gen_4114
<cons, cons>(q_gen_4102, q_gen_4101) -> q_gen_4101
<nil, cons>(q_gen_4114, q_gen_4113) -> q_gen_4101
<nil, nil>() -> q_gen_4101
<a, a>() -> q_gen_4102
<b, b>() -> q_gen_4102
<cons, cons, cons>(q_gen_4115, q_gen_4095) -> q_gen_4095
<cons, nil, cons>(q_gen_4102, q_gen_4101) -> q_gen_4095
<nil, cons, cons>(q_gen_4102, q_gen_4101) -> q_gen_4095
<nil, nil, cons>(q_gen_4114, q_gen_4113) -> q_gen_4095
<nil, nil, nil>() -> q_gen_4095
<a, b, a>() -> q_gen_4115
<b, b, b>() -> q_gen_4115
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_4094, q_gen_4098, q_gen_4099, q_gen_4109, q_gen_4117, q_gen_4118, q_gen_4119, q_gen_4120, q_gen_4122, q_gen_4134, q_gen_4136},
Q_f={q_gen_4094},
Delta=
{
<nil>() -> q_gen_4098
<cons>(q_gen_4118, q_gen_4098) -> q_gen_4117
<a>() -> q_gen_4118
<b>() -> q_gen_4118
<z>() -> q_gen_4120
<cons>(q_gen_4118, q_gen_4117) -> q_gen_4134
<s>(q_gen_4120) -> q_gen_4136
<cons, s>(q_gen_4099, q_gen_4098) -> q_gen_4094
<cons, s>(q_gen_4109, q_gen_4098) -> q_gen_4094
<cons, s>(q_gen_4109, q_gen_4134) -> q_gen_4094
<cons, s>(q_gen_4119, q_gen_4117) -> q_gen_4094
<nil, z>() -> q_gen_4094
<b, z>() -> q_gen_4099
<a, z>() -> q_gen_4109
<b, s>(q_gen_4136) -> q_gen_4109
<a, s>(q_gen_4120) -> q_gen_4119
<b, s>(q_gen_4120) -> q_gen_4119
<cons, s>(q_gen_4099, q_gen_4134) -> q_gen_4122
<cons, s>(q_gen_4109, q_gen_4117) -> q_gen_4122
<cons, s>(q_gen_4119, q_gen_4098) -> q_gen_4122
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_4091, q_gen_4093, q_gen_4123},
Q_f={q_gen_4091},
Delta=
{
<s>(q_gen_4093) -> q_gen_4093
<z>() -> q_gen_4093
<s, s>(q_gen_4091) -> q_gen_4091
<z, s>(q_gen_4093) -> q_gen_4091
<z, z>() -> q_gen_4091
<s, s>(q_gen_4123) -> q_gen_4123
<s, z>(q_gen_4093) -> q_gen_4123
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 19
() -> length([nil, z]) -> 17
() -> leq([z, s(nn2)]) -> 17
() -> leq([z, z]) -> 17
(append([l1, l2, _aq]) /\ length([_aq, _bq]) /\ length([l1, _zp])) -> leq([_zp, _bq]) -> 20
(append([l1, l2, _dq]) /\ length([_dq, _eq]) /\ length([l2, _cq])) -> leq([_cq, _eq]) -> 19
(append([t1, l2, _qp])) -> append([cons(h1, t1), l2, cons(h1, _qp)]) -> 19
(length([ll, _vp])) -> length([cons(x, ll), s(_vp)]) -> 19
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 18
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 18
(leq([s(nn1), z])) -> BOT -> 18
}
Sat witness: Found: ((append([l1, l2, _aq]) /\ length([_aq, _bq]) /\ length([l1, _zp])) -> leq([_zp, _bq]), {
_aq -> cons(b, cons(b, nil))  ;  _bq -> s(s(z))  ;  _zp -> s(s(s(z)))  ;  l1 -> cons(b, nil)  ;  l2 -> nil
})

-------------------------------------------
Step 32, which took 0.032251 s (model generation: 0.028087,  model checking: 0.004164):

Model:
|_
{
append -> 
{{{
Q={q_gen_4095, q_gen_4101, q_gen_4102, q_gen_4113, q_gen_4114, q_gen_4115},
Q_f={q_gen_4095},
Delta=
{
<nil>() -> q_gen_4113
<b>() -> q_gen_4114
<cons, cons>(q_gen_4102, q_gen_4101) -> q_gen_4101
<nil, cons>(q_gen_4114, q_gen_4113) -> q_gen_4101
<nil, nil>() -> q_gen_4101
<a, a>() -> q_gen_4102
<b, b>() -> q_gen_4102
<cons, cons, cons>(q_gen_4115, q_gen_4095) -> q_gen_4095
<cons, nil, cons>(q_gen_4102, q_gen_4101) -> q_gen_4095
<nil, cons, cons>(q_gen_4102, q_gen_4101) -> q_gen_4095
<nil, nil, cons>(q_gen_4114, q_gen_4113) -> q_gen_4095
<nil, nil, nil>() -> q_gen_4095
<a, b, a>() -> q_gen_4115
<b, b, b>() -> q_gen_4115
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_4094, q_gen_4098, q_gen_4099, q_gen_4117, q_gen_4118, q_gen_4119, q_gen_4120, q_gen_4122, q_gen_4134, q_gen_4135, q_gen_4136},
Q_f={q_gen_4094},
Delta=
{
<nil>() -> q_gen_4098
<cons>(q_gen_4118, q_gen_4098) -> q_gen_4117
<a>() -> q_gen_4118
<b>() -> q_gen_4118
<z>() -> q_gen_4120
<cons>(q_gen_4118, q_gen_4117) -> q_gen_4134
<s>(q_gen_4120) -> q_gen_4136
<cons, s>(q_gen_4099, q_gen_4098) -> q_gen_4094
<cons, s>(q_gen_4119, q_gen_4117) -> q_gen_4094
<cons, s>(q_gen_4135, q_gen_4134) -> q_gen_4094
<nil, z>() -> q_gen_4094
<a, z>() -> q_gen_4099
<b, z>() -> q_gen_4099
<a, s>(q_gen_4120) -> q_gen_4119
<b, s>(q_gen_4120) -> q_gen_4119
<cons, s>(q_gen_4099, q_gen_4134) -> q_gen_4122
<cons, s>(q_gen_4119, q_gen_4098) -> q_gen_4122
<cons, s>(q_gen_4135, q_gen_4098) -> q_gen_4122
<cons, s>(q_gen_4135, q_gen_4117) -> q_gen_4122
<b, s>(q_gen_4136) -> q_gen_4135
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_4091, q_gen_4093, q_gen_4123},
Q_f={q_gen_4091},
Delta=
{
<s>(q_gen_4093) -> q_gen_4093
<z>() -> q_gen_4093
<s, s>(q_gen_4091) -> q_gen_4091
<z, s>(q_gen_4093) -> q_gen_4091
<z, z>() -> q_gen_4091
<s, s>(q_gen_4123) -> q_gen_4123
<s, z>(q_gen_4093) -> q_gen_4123
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 19
() -> length([nil, z]) -> 18
() -> leq([z, s(nn2)]) -> 18
() -> leq([z, z]) -> 18
(append([l1, l2, _aq]) /\ length([_aq, _bq]) /\ length([l1, _zp])) -> leq([_zp, _bq]) -> 20
(append([l1, l2, _dq]) /\ length([_dq, _eq]) /\ length([l2, _cq])) -> leq([_cq, _eq]) -> 19
(append([t1, l2, _qp])) -> append([cons(h1, t1), l2, cons(h1, _qp)]) -> 19
(length([ll, _vp])) -> length([cons(x, ll), s(_vp)]) -> 22
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 19
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 19
(leq([s(nn1), z])) -> BOT -> 19
}
Sat witness: Found: ((length([ll, _vp])) -> length([cons(x, ll), s(_vp)]), {
_vp -> s(s(z))  ;  ll -> cons(a, cons(b, nil))  ;  x -> a
})

-------------------------------------------
Step 33, which took 0.031864 s (model generation: 0.029988,  model checking: 0.001876):

Model:
|_
{
append -> 
{{{
Q={q_gen_4095, q_gen_4101, q_gen_4102, q_gen_4113, q_gen_4114, q_gen_4115},
Q_f={q_gen_4095},
Delta=
{
<nil>() -> q_gen_4113
<b>() -> q_gen_4114
<cons, cons>(q_gen_4102, q_gen_4101) -> q_gen_4101
<nil, cons>(q_gen_4114, q_gen_4113) -> q_gen_4101
<nil, nil>() -> q_gen_4101
<a, a>() -> q_gen_4102
<b, b>() -> q_gen_4102
<cons, cons, cons>(q_gen_4115, q_gen_4095) -> q_gen_4095
<cons, nil, cons>(q_gen_4102, q_gen_4101) -> q_gen_4095
<nil, cons, cons>(q_gen_4102, q_gen_4101) -> q_gen_4095
<nil, nil, cons>(q_gen_4114, q_gen_4113) -> q_gen_4095
<nil, nil, nil>() -> q_gen_4095
<a, b, a>() -> q_gen_4115
<b, b, b>() -> q_gen_4115
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_4094, q_gen_4098, q_gen_4099, q_gen_4117, q_gen_4118, q_gen_4119, q_gen_4120, q_gen_4122, q_gen_4134, q_gen_4135, q_gen_4136},
Q_f={q_gen_4094},
Delta=
{
<nil>() -> q_gen_4098
<cons>(q_gen_4118, q_gen_4098) -> q_gen_4117
<a>() -> q_gen_4118
<b>() -> q_gen_4118
<z>() -> q_gen_4120
<cons>(q_gen_4118, q_gen_4117) -> q_gen_4134
<s>(q_gen_4120) -> q_gen_4136
<cons, s>(q_gen_4099, q_gen_4098) -> q_gen_4094
<cons, s>(q_gen_4119, q_gen_4117) -> q_gen_4094
<cons, s>(q_gen_4119, q_gen_4134) -> q_gen_4094
<cons, s>(q_gen_4135, q_gen_4134) -> q_gen_4094
<nil, z>() -> q_gen_4094
<a, z>() -> q_gen_4099
<b, z>() -> q_gen_4099
<a, s>(q_gen_4120) -> q_gen_4119
<a, s>(q_gen_4136) -> q_gen_4119
<b, s>(q_gen_4120) -> q_gen_4119
<cons, s>(q_gen_4099, q_gen_4134) -> q_gen_4122
<cons, s>(q_gen_4119, q_gen_4098) -> q_gen_4122
<cons, s>(q_gen_4135, q_gen_4098) -> q_gen_4122
<cons, s>(q_gen_4135, q_gen_4117) -> q_gen_4122
<b, s>(q_gen_4136) -> q_gen_4135
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_4091, q_gen_4093, q_gen_4123},
Q_f={q_gen_4091},
Delta=
{
<s>(q_gen_4093) -> q_gen_4093
<z>() -> q_gen_4093
<s, s>(q_gen_4091) -> q_gen_4091
<z, s>(q_gen_4093) -> q_gen_4091
<z, z>() -> q_gen_4091
<s, s>(q_gen_4123) -> q_gen_4123
<s, z>(q_gen_4093) -> q_gen_4123
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 19
() -> length([nil, z]) -> 19
() -> leq([z, s(nn2)]) -> 19
() -> leq([z, z]) -> 19
(append([l1, l2, _aq]) /\ length([_aq, _bq]) /\ length([l1, _zp])) -> leq([_zp, _bq]) -> 20
(append([l1, l2, _dq]) /\ length([_dq, _eq]) /\ length([l2, _cq])) -> leq([_cq, _eq]) -> 19
(append([t1, l2, _qp])) -> append([cons(h1, t1), l2, cons(h1, _qp)]) -> 22
(length([ll, _vp])) -> length([cons(x, ll), s(_vp)]) -> 22
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 20
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 20
(leq([s(nn1), z])) -> BOT -> 20
}
Sat witness: Found: ((append([t1, l2, _qp])) -> append([cons(h1, t1), l2, cons(h1, _qp)]), {
_qp -> cons(a, nil)  ;  h1 -> b  ;  l2 -> cons(a, nil)  ;  t1 -> nil
})

-------------------------------------------
Step 34, which took 0.035111 s (model generation: 0.032705,  model checking: 0.002406):

Model:
|_
{
append -> 
{{{
Q={q_gen_4095, q_gen_4101, q_gen_4102, q_gen_4113, q_gen_4114, q_gen_4115},
Q_f={q_gen_4095},
Delta=
{
<nil>() -> q_gen_4113
<a>() -> q_gen_4114
<b>() -> q_gen_4114
<cons, cons>(q_gen_4102, q_gen_4101) -> q_gen_4101
<nil, cons>(q_gen_4114, q_gen_4113) -> q_gen_4101
<nil, nil>() -> q_gen_4101
<a, a>() -> q_gen_4102
<b, b>() -> q_gen_4102
<cons, cons, cons>(q_gen_4115, q_gen_4095) -> q_gen_4095
<cons, nil, cons>(q_gen_4102, q_gen_4101) -> q_gen_4095
<nil, cons, cons>(q_gen_4102, q_gen_4101) -> q_gen_4095
<nil, nil, cons>(q_gen_4114, q_gen_4113) -> q_gen_4095
<nil, nil, nil>() -> q_gen_4095
<a, b, a>() -> q_gen_4115
<b, a, b>() -> q_gen_4115
<b, b, b>() -> q_gen_4115
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_4094, q_gen_4098, q_gen_4099, q_gen_4117, q_gen_4118, q_gen_4119, q_gen_4120, q_gen_4122, q_gen_4134, q_gen_4135, q_gen_4136},
Q_f={q_gen_4094},
Delta=
{
<nil>() -> q_gen_4098
<cons>(q_gen_4118, q_gen_4098) -> q_gen_4117
<a>() -> q_gen_4118
<b>() -> q_gen_4118
<z>() -> q_gen_4120
<cons>(q_gen_4118, q_gen_4117) -> q_gen_4134
<s>(q_gen_4120) -> q_gen_4136
<cons, s>(q_gen_4099, q_gen_4098) -> q_gen_4094
<cons, s>(q_gen_4119, q_gen_4117) -> q_gen_4094
<cons, s>(q_gen_4119, q_gen_4134) -> q_gen_4094
<cons, s>(q_gen_4135, q_gen_4134) -> q_gen_4094
<nil, z>() -> q_gen_4094
<a, z>() -> q_gen_4099
<b, z>() -> q_gen_4099
<a, s>(q_gen_4120) -> q_gen_4119
<a, s>(q_gen_4136) -> q_gen_4119
<b, s>(q_gen_4120) -> q_gen_4119
<cons, s>(q_gen_4099, q_gen_4134) -> q_gen_4122
<cons, s>(q_gen_4119, q_gen_4098) -> q_gen_4122
<cons, s>(q_gen_4135, q_gen_4098) -> q_gen_4122
<cons, s>(q_gen_4135, q_gen_4117) -> q_gen_4122
<b, s>(q_gen_4136) -> q_gen_4135
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_4091, q_gen_4093, q_gen_4123},
Q_f={q_gen_4091},
Delta=
{
<s>(q_gen_4093) -> q_gen_4093
<z>() -> q_gen_4093
<s, s>(q_gen_4091) -> q_gen_4091
<z, s>(q_gen_4093) -> q_gen_4091
<z, z>() -> q_gen_4091
<s, s>(q_gen_4123) -> q_gen_4123
<s, z>(q_gen_4093) -> q_gen_4123
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 19
() -> length([nil, z]) -> 19
() -> leq([z, s(nn2)]) -> 19
() -> leq([z, z]) -> 19
(append([l1, l2, _aq]) /\ length([_aq, _bq]) /\ length([l1, _zp])) -> leq([_zp, _bq]) -> 20
(append([l1, l2, _dq]) /\ length([_dq, _eq]) /\ length([l2, _cq])) -> leq([_cq, _eq]) -> 22
(append([t1, l2, _qp])) -> append([cons(h1, t1), l2, cons(h1, _qp)]) -> 22
(length([ll, _vp])) -> length([cons(x, ll), s(_vp)]) -> 22
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 20
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 20
(leq([s(nn1), z])) -> BOT -> 20
}
Sat witness: Found: ((append([l1, l2, _dq]) /\ length([_dq, _eq]) /\ length([l2, _cq])) -> leq([_cq, _eq]), {
_cq -> s(s(s(z)))  ;  _dq -> cons(a, cons(b, cons(b, nil)))  ;  _eq -> s(s(z))  ;  l1 -> nil  ;  l2 -> cons(a, cons(b, nil))
})

-------------------------------------------
Step 35, which took 0.043913 s (model generation: 0.037945,  model checking: 0.005968):

Model:
|_
{
append -> 
{{{
Q={q_gen_4095, q_gen_4101, q_gen_4102, q_gen_4113, q_gen_4114, q_gen_4115},
Q_f={q_gen_4095},
Delta=
{
<nil>() -> q_gen_4113
<a>() -> q_gen_4114
<b>() -> q_gen_4114
<cons, cons>(q_gen_4102, q_gen_4101) -> q_gen_4101
<nil, cons>(q_gen_4114, q_gen_4113) -> q_gen_4101
<nil, nil>() -> q_gen_4101
<a, a>() -> q_gen_4102
<b, b>() -> q_gen_4102
<cons, cons, cons>(q_gen_4115, q_gen_4095) -> q_gen_4095
<cons, nil, cons>(q_gen_4102, q_gen_4101) -> q_gen_4095
<nil, cons, cons>(q_gen_4102, q_gen_4101) -> q_gen_4095
<nil, nil, cons>(q_gen_4114, q_gen_4113) -> q_gen_4095
<nil, nil, nil>() -> q_gen_4095
<a, b, a>() -> q_gen_4115
<b, a, b>() -> q_gen_4115
<b, b, b>() -> q_gen_4115
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_4094, q_gen_4098, q_gen_4099, q_gen_4117, q_gen_4118, q_gen_4119, q_gen_4120, q_gen_4122, q_gen_4134, q_gen_4135, q_gen_4136},
Q_f={q_gen_4094},
Delta=
{
<nil>() -> q_gen_4098
<cons>(q_gen_4118, q_gen_4098) -> q_gen_4117
<a>() -> q_gen_4118
<b>() -> q_gen_4118
<z>() -> q_gen_4120
<cons>(q_gen_4118, q_gen_4117) -> q_gen_4134
<s>(q_gen_4120) -> q_gen_4136
<cons, s>(q_gen_4099, q_gen_4098) -> q_gen_4094
<cons, s>(q_gen_4119, q_gen_4117) -> q_gen_4094
<cons, s>(q_gen_4135, q_gen_4134) -> q_gen_4094
<nil, z>() -> q_gen_4094
<a, z>() -> q_gen_4099
<b, z>() -> q_gen_4099
<a, s>(q_gen_4120) -> q_gen_4119
<b, s>(q_gen_4120) -> q_gen_4119
<cons, s>(q_gen_4099, q_gen_4134) -> q_gen_4122
<cons, s>(q_gen_4119, q_gen_4098) -> q_gen_4122
<cons, s>(q_gen_4119, q_gen_4134) -> q_gen_4122
<cons, s>(q_gen_4135, q_gen_4098) -> q_gen_4122
<cons, s>(q_gen_4135, q_gen_4117) -> q_gen_4122
<a, s>(q_gen_4136) -> q_gen_4135
<b, s>(q_gen_4136) -> q_gen_4135
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_4091, q_gen_4093, q_gen_4123},
Q_f={q_gen_4091},
Delta=
{
<s>(q_gen_4093) -> q_gen_4093
<z>() -> q_gen_4093
<s, s>(q_gen_4091) -> q_gen_4091
<z, s>(q_gen_4093) -> q_gen_4091
<z, z>() -> q_gen_4091
<s, s>(q_gen_4123) -> q_gen_4123
<s, z>(q_gen_4093) -> q_gen_4123
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 20
() -> length([nil, z]) -> 20
() -> leq([z, s(nn2)]) -> 20
() -> leq([z, z]) -> 20
(append([l1, l2, _aq]) /\ length([_aq, _bq]) /\ length([l1, _zp])) -> leq([_zp, _bq]) -> 21
(append([l1, l2, _dq]) /\ length([_dq, _eq]) /\ length([l2, _cq])) -> leq([_cq, _eq]) -> 22
(append([t1, l2, _qp])) -> append([cons(h1, t1), l2, cons(h1, _qp)]) -> 22
(length([ll, _vp])) -> length([cons(x, ll), s(_vp)]) -> 25
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 21
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 21
(leq([s(nn1), z])) -> BOT -> 21
}
Sat witness: Found: ((length([ll, _vp])) -> length([cons(x, ll), s(_vp)]), {
_vp -> s(s(s(z)))  ;  ll -> cons(a, cons(a, cons(b, nil)))  ;  x -> b
})

-------------------------------------------
Step 36, which took 0.045108 s (model generation: 0.041570,  model checking: 0.003538):

Model:
|_
{
append -> 
{{{
Q={q_gen_4095, q_gen_4101, q_gen_4102, q_gen_4113, q_gen_4114, q_gen_4115},
Q_f={q_gen_4095},
Delta=
{
<nil>() -> q_gen_4113
<a>() -> q_gen_4114
<b>() -> q_gen_4114
<cons, cons>(q_gen_4102, q_gen_4101) -> q_gen_4101
<nil, cons>(q_gen_4114, q_gen_4113) -> q_gen_4101
<nil, nil>() -> q_gen_4101
<a, a>() -> q_gen_4102
<b, b>() -> q_gen_4102
<cons, cons, cons>(q_gen_4115, q_gen_4095) -> q_gen_4095
<cons, nil, cons>(q_gen_4102, q_gen_4101) -> q_gen_4095
<nil, cons, cons>(q_gen_4102, q_gen_4101) -> q_gen_4095
<nil, nil, cons>(q_gen_4114, q_gen_4113) -> q_gen_4095
<nil, nil, nil>() -> q_gen_4095
<a, b, a>() -> q_gen_4115
<b, a, b>() -> q_gen_4115
<b, b, b>() -> q_gen_4115
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_4094, q_gen_4098, q_gen_4099, q_gen_4117, q_gen_4118, q_gen_4119, q_gen_4120, q_gen_4122, q_gen_4134, q_gen_4135, q_gen_4136},
Q_f={q_gen_4094},
Delta=
{
<nil>() -> q_gen_4098
<cons>(q_gen_4118, q_gen_4098) -> q_gen_4117
<a>() -> q_gen_4118
<b>() -> q_gen_4118
<z>() -> q_gen_4120
<cons>(q_gen_4118, q_gen_4117) -> q_gen_4134
<cons>(q_gen_4118, q_gen_4134) -> q_gen_4134
<s>(q_gen_4120) -> q_gen_4136
<s>(q_gen_4136) -> q_gen_4136
<cons, s>(q_gen_4099, q_gen_4098) -> q_gen_4094
<cons, s>(q_gen_4119, q_gen_4117) -> q_gen_4094
<cons, s>(q_gen_4119, q_gen_4134) -> q_gen_4094
<cons, s>(q_gen_4135, q_gen_4134) -> q_gen_4094
<nil, z>() -> q_gen_4094
<a, z>() -> q_gen_4099
<b, z>() -> q_gen_4099
<a, s>(q_gen_4120) -> q_gen_4119
<b, s>(q_gen_4120) -> q_gen_4119
<cons, s>(q_gen_4099, q_gen_4134) -> q_gen_4122
<cons, s>(q_gen_4119, q_gen_4098) -> q_gen_4122
<cons, s>(q_gen_4135, q_gen_4098) -> q_gen_4122
<cons, s>(q_gen_4135, q_gen_4117) -> q_gen_4122
<a, s>(q_gen_4136) -> q_gen_4135
<b, s>(q_gen_4136) -> q_gen_4135
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_4091, q_gen_4093, q_gen_4123},
Q_f={q_gen_4091},
Delta=
{
<s>(q_gen_4093) -> q_gen_4093
<z>() -> q_gen_4093
<s, s>(q_gen_4091) -> q_gen_4091
<z, s>(q_gen_4093) -> q_gen_4091
<z, z>() -> q_gen_4091
<s, s>(q_gen_4123) -> q_gen_4123
<s, z>(q_gen_4093) -> q_gen_4123
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 21
() -> length([nil, z]) -> 21
() -> leq([z, s(nn2)]) -> 21
() -> leq([z, z]) -> 21
(append([l1, l2, _aq]) /\ length([_aq, _bq]) /\ length([l1, _zp])) -> leq([_zp, _bq]) -> 24
(append([l1, l2, _dq]) /\ length([_dq, _eq]) /\ length([l2, _cq])) -> leq([_cq, _eq]) -> 22
(append([t1, l2, _qp])) -> append([cons(h1, t1), l2, cons(h1, _qp)]) -> 22
(length([ll, _vp])) -> length([cons(x, ll), s(_vp)]) -> 25
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 22
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 22
(leq([s(nn1), z])) -> BOT -> 22
}
Sat witness: Found: ((append([l1, l2, _aq]) /\ length([_aq, _bq]) /\ length([l1, _zp])) -> leq([_zp, _bq]), {
_aq -> cons(b, cons(b, cons(b, nil)))  ;  _bq -> s(s(z))  ;  _zp -> s(s(s(z)))  ;  l1 -> cons(b, cons(b, cons(b, nil)))  ;  l2 -> nil
})

-------------------------------------------
Step 37, which took 0.049689 s (model generation: 0.048206,  model checking: 0.001483):

Model:
|_
{
append -> 
{{{
Q={q_gen_4095, q_gen_4101, q_gen_4102, q_gen_4113, q_gen_4114, q_gen_4115},
Q_f={q_gen_4095},
Delta=
{
<nil>() -> q_gen_4113
<a>() -> q_gen_4114
<b>() -> q_gen_4114
<cons, cons>(q_gen_4102, q_gen_4101) -> q_gen_4101
<nil, cons>(q_gen_4114, q_gen_4113) -> q_gen_4101
<nil, nil>() -> q_gen_4101
<a, a>() -> q_gen_4102
<b, b>() -> q_gen_4102
<cons, cons, cons>(q_gen_4115, q_gen_4095) -> q_gen_4095
<cons, nil, cons>(q_gen_4102, q_gen_4101) -> q_gen_4095
<nil, cons, cons>(q_gen_4102, q_gen_4101) -> q_gen_4095
<nil, nil, cons>(q_gen_4114, q_gen_4113) -> q_gen_4095
<nil, nil, nil>() -> q_gen_4095
<a, b, a>() -> q_gen_4115
<b, a, b>() -> q_gen_4115
<b, b, b>() -> q_gen_4115
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_4094, q_gen_4098, q_gen_4099, q_gen_4117, q_gen_4118, q_gen_4119, q_gen_4120, q_gen_4122, q_gen_4134, q_gen_4135, q_gen_4136},
Q_f={q_gen_4094},
Delta=
{
<nil>() -> q_gen_4098
<cons>(q_gen_4118, q_gen_4098) -> q_gen_4117
<a>() -> q_gen_4118
<b>() -> q_gen_4118
<z>() -> q_gen_4120
<cons>(q_gen_4118, q_gen_4117) -> q_gen_4134
<cons>(q_gen_4118, q_gen_4134) -> q_gen_4134
<s>(q_gen_4120) -> q_gen_4136
<s>(q_gen_4136) -> q_gen_4136
<cons, s>(q_gen_4099, q_gen_4098) -> q_gen_4094
<cons, s>(q_gen_4119, q_gen_4117) -> q_gen_4094
<cons, s>(q_gen_4135, q_gen_4134) -> q_gen_4094
<nil, z>() -> q_gen_4094
<a, z>() -> q_gen_4099
<b, z>() -> q_gen_4099
<a, s>(q_gen_4120) -> q_gen_4119
<b, s>(q_gen_4120) -> q_gen_4119
<cons, s>(q_gen_4099, q_gen_4134) -> q_gen_4122
<cons, s>(q_gen_4119, q_gen_4098) -> q_gen_4122
<cons, s>(q_gen_4119, q_gen_4134) -> q_gen_4122
<cons, s>(q_gen_4135, q_gen_4098) -> q_gen_4122
<cons, s>(q_gen_4135, q_gen_4117) -> q_gen_4122
<a, s>(q_gen_4136) -> q_gen_4135
<b, s>(q_gen_4136) -> q_gen_4135
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_4091, q_gen_4093, q_gen_4123},
Q_f={q_gen_4091},
Delta=
{
<s>(q_gen_4093) -> q_gen_4093
<z>() -> q_gen_4093
<s, s>(q_gen_4091) -> q_gen_4091
<z, s>(q_gen_4093) -> q_gen_4091
<z, z>() -> q_gen_4091
<s, s>(q_gen_4123) -> q_gen_4123
<s, z>(q_gen_4093) -> q_gen_4123
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 22
() -> length([nil, z]) -> 22
() -> leq([z, s(nn2)]) -> 22
() -> leq([z, z]) -> 22
(append([l1, l2, _aq]) /\ length([_aq, _bq]) /\ length([l1, _zp])) -> leq([_zp, _bq]) -> 24
(append([l1, l2, _dq]) /\ length([_dq, _eq]) /\ length([l2, _cq])) -> leq([_cq, _eq]) -> 22
(append([t1, l2, _qp])) -> append([cons(h1, t1), l2, cons(h1, _qp)]) -> 25
(length([ll, _vp])) -> length([cons(x, ll), s(_vp)]) -> 25
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 23
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 23
(leq([s(nn1), z])) -> BOT -> 23
}
Sat witness: Found: ((append([t1, l2, _qp])) -> append([cons(h1, t1), l2, cons(h1, _qp)]), {
_qp -> cons(a, nil)  ;  h1 -> a  ;  l2 -> cons(a, nil)  ;  t1 -> nil
})

-------------------------------------------
Step 38, which took 0.049104 s (model generation: 0.046595,  model checking: 0.002509):

Model:
|_
{
append -> 
{{{
Q={q_gen_4095, q_gen_4101, q_gen_4102, q_gen_4113, q_gen_4114, q_gen_4115},
Q_f={q_gen_4095},
Delta=
{
<nil>() -> q_gen_4113
<a>() -> q_gen_4114
<b>() -> q_gen_4114
<cons, cons>(q_gen_4102, q_gen_4101) -> q_gen_4101
<nil, cons>(q_gen_4114, q_gen_4113) -> q_gen_4101
<nil, nil>() -> q_gen_4101
<a, a>() -> q_gen_4102
<b, b>() -> q_gen_4102
<cons, cons, cons>(q_gen_4115, q_gen_4095) -> q_gen_4095
<cons, nil, cons>(q_gen_4102, q_gen_4101) -> q_gen_4095
<nil, cons, cons>(q_gen_4102, q_gen_4101) -> q_gen_4095
<nil, nil, cons>(q_gen_4114, q_gen_4113) -> q_gen_4095
<nil, nil, nil>() -> q_gen_4095
<a, a, a>() -> q_gen_4115
<a, b, a>() -> q_gen_4115
<b, a, b>() -> q_gen_4115
<b, b, b>() -> q_gen_4115
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_4094, q_gen_4098, q_gen_4099, q_gen_4117, q_gen_4118, q_gen_4119, q_gen_4120, q_gen_4122, q_gen_4134, q_gen_4135, q_gen_4136},
Q_f={q_gen_4094},
Delta=
{
<nil>() -> q_gen_4098
<cons>(q_gen_4118, q_gen_4098) -> q_gen_4117
<cons>(q_gen_4118, q_gen_4134) -> q_gen_4117
<a>() -> q_gen_4118
<b>() -> q_gen_4118
<s>(q_gen_4136) -> q_gen_4120
<z>() -> q_gen_4120
<cons>(q_gen_4118, q_gen_4117) -> q_gen_4134
<s>(q_gen_4120) -> q_gen_4136
<cons, s>(q_gen_4099, q_gen_4098) -> q_gen_4094
<cons, s>(q_gen_4119, q_gen_4117) -> q_gen_4094
<cons, s>(q_gen_4135, q_gen_4134) -> q_gen_4094
<nil, z>() -> q_gen_4094
<a, z>() -> q_gen_4099
<b, z>() -> q_gen_4099
<a, s>(q_gen_4120) -> q_gen_4119
<b, s>(q_gen_4120) -> q_gen_4119
<cons, s>(q_gen_4099, q_gen_4134) -> q_gen_4122
<cons, s>(q_gen_4119, q_gen_4098) -> q_gen_4122
<cons, s>(q_gen_4119, q_gen_4134) -> q_gen_4122
<cons, s>(q_gen_4135, q_gen_4098) -> q_gen_4122
<cons, s>(q_gen_4135, q_gen_4117) -> q_gen_4122
<a, s>(q_gen_4136) -> q_gen_4135
<b, s>(q_gen_4136) -> q_gen_4135
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_4091, q_gen_4093, q_gen_4123},
Q_f={q_gen_4091},
Delta=
{
<s>(q_gen_4093) -> q_gen_4093
<z>() -> q_gen_4093
<s, s>(q_gen_4091) -> q_gen_4091
<z, s>(q_gen_4093) -> q_gen_4091
<z, z>() -> q_gen_4091
<s, s>(q_gen_4123) -> q_gen_4123
<s, z>(q_gen_4093) -> q_gen_4123
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 22
() -> length([nil, z]) -> 22
() -> leq([z, s(nn2)]) -> 22
() -> leq([z, z]) -> 22
(append([l1, l2, _aq]) /\ length([_aq, _bq]) /\ length([l1, _zp])) -> leq([_zp, _bq]) -> 24
(append([l1, l2, _dq]) /\ length([_dq, _eq]) /\ length([l2, _cq])) -> leq([_cq, _eq]) -> 25
(append([t1, l2, _qp])) -> append([cons(h1, t1), l2, cons(h1, _qp)]) -> 25
(length([ll, _vp])) -> length([cons(x, ll), s(_vp)]) -> 25
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 23
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 23
(leq([s(nn1), z])) -> BOT -> 23
}
Sat witness: Found: ((append([l1, l2, _dq]) /\ length([_dq, _eq]) /\ length([l2, _cq])) -> leq([_cq, _eq]), {
_cq -> s(s(s(s(z))))  ;  _dq -> cons(b, cons(b, cons(b, nil)))  ;  _eq -> s(s(s(z)))  ;  l1 -> nil  ;  l2 -> cons(b, cons(b, nil))
})

-------------------------------------------
Step 39, which took 0.055065 s (model generation: 0.052015,  model checking: 0.003050):

Model:
|_
{
append -> 
{{{
Q={q_gen_4095, q_gen_4101, q_gen_4102, q_gen_4113, q_gen_4114, q_gen_4115},
Q_f={q_gen_4095},
Delta=
{
<nil>() -> q_gen_4113
<a>() -> q_gen_4114
<b>() -> q_gen_4114
<cons, cons>(q_gen_4102, q_gen_4101) -> q_gen_4101
<nil, cons>(q_gen_4114, q_gen_4113) -> q_gen_4101
<nil, nil>() -> q_gen_4101
<a, a>() -> q_gen_4102
<b, b>() -> q_gen_4102
<cons, cons, cons>(q_gen_4115, q_gen_4095) -> q_gen_4095
<cons, nil, cons>(q_gen_4102, q_gen_4101) -> q_gen_4095
<nil, cons, cons>(q_gen_4102, q_gen_4101) -> q_gen_4095
<nil, nil, cons>(q_gen_4114, q_gen_4113) -> q_gen_4095
<nil, nil, nil>() -> q_gen_4095
<a, a, a>() -> q_gen_4115
<a, b, a>() -> q_gen_4115
<b, a, b>() -> q_gen_4115
<b, b, b>() -> q_gen_4115
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_4094, q_gen_4098, q_gen_4099, q_gen_4117, q_gen_4118, q_gen_4119, q_gen_4120, q_gen_4122, q_gen_4134, q_gen_4135, q_gen_4136},
Q_f={q_gen_4094},
Delta=
{
<nil>() -> q_gen_4098
<cons>(q_gen_4118, q_gen_4098) -> q_gen_4117
<a>() -> q_gen_4118
<b>() -> q_gen_4118
<z>() -> q_gen_4120
<cons>(q_gen_4118, q_gen_4117) -> q_gen_4134
<cons>(q_gen_4118, q_gen_4134) -> q_gen_4134
<s>(q_gen_4120) -> q_gen_4136
<s>(q_gen_4136) -> q_gen_4136
<cons, s>(q_gen_4099, q_gen_4098) -> q_gen_4094
<cons, s>(q_gen_4119, q_gen_4117) -> q_gen_4094
<cons, s>(q_gen_4135, q_gen_4134) -> q_gen_4094
<nil, z>() -> q_gen_4094
<a, z>() -> q_gen_4099
<b, z>() -> q_gen_4099
<a, s>(q_gen_4120) -> q_gen_4119
<b, s>(q_gen_4120) -> q_gen_4119
<cons, s>(q_gen_4099, q_gen_4134) -> q_gen_4122
<cons, s>(q_gen_4119, q_gen_4098) -> q_gen_4122
<cons, s>(q_gen_4119, q_gen_4134) -> q_gen_4122
<cons, s>(q_gen_4135, q_gen_4098) -> q_gen_4122
<cons, s>(q_gen_4135, q_gen_4117) -> q_gen_4122
<a, s>(q_gen_4136) -> q_gen_4135
<b, s>(q_gen_4136) -> q_gen_4135
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_4091, q_gen_4093, q_gen_4123},
Q_f={q_gen_4091},
Delta=
{
<s>(q_gen_4093) -> q_gen_4093
<z>() -> q_gen_4093
<s, s>(q_gen_4091) -> q_gen_4091
<z, s>(q_gen_4093) -> q_gen_4091
<z, z>() -> q_gen_4091
<s, s>(q_gen_4123) -> q_gen_4123
<s, z>(q_gen_4093) -> q_gen_4123
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 23
() -> length([nil, z]) -> 23
() -> leq([z, s(nn2)]) -> 23
() -> leq([z, z]) -> 23
(append([l1, l2, _aq]) /\ length([_aq, _bq]) /\ length([l1, _zp])) -> leq([_zp, _bq]) -> 27
(append([l1, l2, _dq]) /\ length([_dq, _eq]) /\ length([l2, _cq])) -> leq([_cq, _eq]) -> 25
(append([t1, l2, _qp])) -> append([cons(h1, t1), l2, cons(h1, _qp)]) -> 25
(length([ll, _vp])) -> length([cons(x, ll), s(_vp)]) -> 25
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 24
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 24
(leq([s(nn1), z])) -> BOT -> 24
}
Sat witness: Found: ((append([l1, l2, _aq]) /\ length([_aq, _bq]) /\ length([l1, _zp])) -> leq([_zp, _bq]), {
_aq -> cons(b, cons(b, cons(b, nil)))  ;  _bq -> s(s(s(z)))  ;  _zp -> s(s(s(s(z))))  ;  l1 -> cons(b, cons(b, cons(b, nil)))  ;  l2 -> nil
})

-------------------------------------------
Step 40, which took 0.059986 s (model generation: 0.056471,  model checking: 0.003515):

Model:
|_
{
append -> 
{{{
Q={q_gen_4095, q_gen_4101, q_gen_4102, q_gen_4113, q_gen_4114, q_gen_4115},
Q_f={q_gen_4095},
Delta=
{
<nil>() -> q_gen_4113
<a>() -> q_gen_4114
<b>() -> q_gen_4114
<cons, cons>(q_gen_4102, q_gen_4101) -> q_gen_4101
<nil, cons>(q_gen_4114, q_gen_4113) -> q_gen_4101
<nil, nil>() -> q_gen_4101
<a, a>() -> q_gen_4102
<b, b>() -> q_gen_4102
<cons, cons, cons>(q_gen_4115, q_gen_4095) -> q_gen_4095
<cons, nil, cons>(q_gen_4102, q_gen_4101) -> q_gen_4095
<nil, cons, cons>(q_gen_4102, q_gen_4101) -> q_gen_4095
<nil, nil, cons>(q_gen_4114, q_gen_4113) -> q_gen_4095
<nil, nil, nil>() -> q_gen_4095
<a, a, a>() -> q_gen_4115
<a, b, a>() -> q_gen_4115
<b, a, b>() -> q_gen_4115
<b, b, b>() -> q_gen_4115
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_4094, q_gen_4098, q_gen_4099, q_gen_4117, q_gen_4118, q_gen_4119, q_gen_4120, q_gen_4122, q_gen_4134, q_gen_4135, q_gen_4136, q_gen_4166},
Q_f={q_gen_4094},
Delta=
{
<cons>(q_gen_4118, q_gen_4134) -> q_gen_4098
<nil>() -> q_gen_4098
<cons>(q_gen_4118, q_gen_4098) -> q_gen_4117
<a>() -> q_gen_4118
<b>() -> q_gen_4118
<z>() -> q_gen_4120
<cons>(q_gen_4118, q_gen_4117) -> q_gen_4134
<s>(q_gen_4120) -> q_gen_4136
<s>(q_gen_4136) -> q_gen_4166
<cons, s>(q_gen_4099, q_gen_4098) -> q_gen_4094
<cons, s>(q_gen_4119, q_gen_4117) -> q_gen_4094
<cons, s>(q_gen_4135, q_gen_4134) -> q_gen_4094
<nil, z>() -> q_gen_4094
<a, z>() -> q_gen_4099
<b, s>(q_gen_4166) -> q_gen_4099
<b, z>() -> q_gen_4099
<a, s>(q_gen_4120) -> q_gen_4119
<b, s>(q_gen_4120) -> q_gen_4119
<cons, s>(q_gen_4099, q_gen_4117) -> q_gen_4122
<cons, s>(q_gen_4099, q_gen_4134) -> q_gen_4122
<cons, s>(q_gen_4119, q_gen_4098) -> q_gen_4122
<cons, s>(q_gen_4119, q_gen_4134) -> q_gen_4122
<cons, s>(q_gen_4135, q_gen_4098) -> q_gen_4122
<cons, s>(q_gen_4135, q_gen_4117) -> q_gen_4122
<a, s>(q_gen_4136) -> q_gen_4135
<b, s>(q_gen_4136) -> q_gen_4135
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_4091, q_gen_4093, q_gen_4123},
Q_f={q_gen_4091},
Delta=
{
<s>(q_gen_4093) -> q_gen_4093
<z>() -> q_gen_4093
<s, s>(q_gen_4091) -> q_gen_4091
<z, s>(q_gen_4093) -> q_gen_4091
<z, z>() -> q_gen_4091
<s, s>(q_gen_4123) -> q_gen_4123
<s, z>(q_gen_4093) -> q_gen_4123
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 24
() -> length([nil, z]) -> 24
() -> leq([z, s(nn2)]) -> 24
() -> leq([z, z]) -> 24
(append([l1, l2, _aq]) /\ length([_aq, _bq]) /\ length([l1, _zp])) -> leq([_zp, _bq]) -> 27
(append([l1, l2, _dq]) /\ length([_dq, _eq]) /\ length([l2, _cq])) -> leq([_cq, _eq]) -> 25
(append([t1, l2, _qp])) -> append([cons(h1, t1), l2, cons(h1, _qp)]) -> 25
(length([ll, _vp])) -> length([cons(x, ll), s(_vp)]) -> 28
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 25
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 25
(leq([s(nn1), z])) -> BOT -> 25
}
Sat witness: Found: ((length([ll, _vp])) -> length([cons(x, ll), s(_vp)]), {
_vp -> s(s(s(z)))  ;  ll -> cons(b, cons(a, cons(b, nil)))  ;  x -> a
})

-------------------------------------------
Step 41, which took 0.065198 s (model generation: 0.063299,  model checking: 0.001899):

Model:
|_
{
append -> 
{{{
Q={q_gen_4095, q_gen_4101, q_gen_4102, q_gen_4113, q_gen_4114, q_gen_4115},
Q_f={q_gen_4095},
Delta=
{
<nil>() -> q_gen_4113
<a>() -> q_gen_4114
<b>() -> q_gen_4114
<cons, cons>(q_gen_4102, q_gen_4101) -> q_gen_4101
<nil, cons>(q_gen_4114, q_gen_4113) -> q_gen_4101
<nil, nil>() -> q_gen_4101
<a, a>() -> q_gen_4102
<b, b>() -> q_gen_4102
<cons, cons, cons>(q_gen_4115, q_gen_4095) -> q_gen_4095
<cons, nil, cons>(q_gen_4102, q_gen_4101) -> q_gen_4095
<nil, cons, cons>(q_gen_4102, q_gen_4101) -> q_gen_4095
<nil, nil, cons>(q_gen_4114, q_gen_4113) -> q_gen_4095
<nil, nil, nil>() -> q_gen_4095
<a, a, a>() -> q_gen_4115
<a, b, a>() -> q_gen_4115
<b, a, b>() -> q_gen_4115
<b, b, b>() -> q_gen_4115
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_4094, q_gen_4098, q_gen_4099, q_gen_4117, q_gen_4118, q_gen_4119, q_gen_4120, q_gen_4122, q_gen_4134, q_gen_4135, q_gen_4136, q_gen_4166},
Q_f={q_gen_4094},
Delta=
{
<cons>(q_gen_4118, q_gen_4134) -> q_gen_4098
<nil>() -> q_gen_4098
<cons>(q_gen_4118, q_gen_4098) -> q_gen_4117
<a>() -> q_gen_4118
<b>() -> q_gen_4118
<z>() -> q_gen_4120
<cons>(q_gen_4118, q_gen_4117) -> q_gen_4134
<s>(q_gen_4120) -> q_gen_4136
<s>(q_gen_4136) -> q_gen_4166
<cons, s>(q_gen_4099, q_gen_4098) -> q_gen_4094
<cons, s>(q_gen_4119, q_gen_4117) -> q_gen_4094
<cons, s>(q_gen_4135, q_gen_4134) -> q_gen_4094
<nil, z>() -> q_gen_4094
<a, s>(q_gen_4166) -> q_gen_4099
<a, z>() -> q_gen_4099
<b, s>(q_gen_4166) -> q_gen_4099
<b, z>() -> q_gen_4099
<a, s>(q_gen_4120) -> q_gen_4119
<b, s>(q_gen_4120) -> q_gen_4119
<cons, s>(q_gen_4099, q_gen_4117) -> q_gen_4122
<cons, s>(q_gen_4099, q_gen_4134) -> q_gen_4122
<cons, s>(q_gen_4119, q_gen_4098) -> q_gen_4122
<cons, s>(q_gen_4119, q_gen_4134) -> q_gen_4122
<cons, s>(q_gen_4135, q_gen_4098) -> q_gen_4122
<cons, s>(q_gen_4135, q_gen_4117) -> q_gen_4122
<a, s>(q_gen_4136) -> q_gen_4135
<b, s>(q_gen_4136) -> q_gen_4135
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_4091, q_gen_4093, q_gen_4123},
Q_f={q_gen_4091},
Delta=
{
<s>(q_gen_4093) -> q_gen_4093
<z>() -> q_gen_4093
<s, s>(q_gen_4091) -> q_gen_4091
<z, s>(q_gen_4093) -> q_gen_4091
<z, z>() -> q_gen_4091
<s, s>(q_gen_4123) -> q_gen_4123
<s, z>(q_gen_4093) -> q_gen_4123
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 25
() -> length([nil, z]) -> 25
() -> leq([z, s(nn2)]) -> 25
() -> leq([z, z]) -> 25
(append([l1, l2, _aq]) /\ length([_aq, _bq]) /\ length([l1, _zp])) -> leq([_zp, _bq]) -> 27
(append([l1, l2, _dq]) /\ length([_dq, _eq]) /\ length([l2, _cq])) -> leq([_cq, _eq]) -> 25
(append([t1, l2, _qp])) -> append([cons(h1, t1), l2, cons(h1, _qp)]) -> 28
(length([ll, _vp])) -> length([cons(x, ll), s(_vp)]) -> 28
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 26
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 26
(leq([s(nn1), z])) -> BOT -> 26
}
Sat witness: Found: ((append([t1, l2, _qp])) -> append([cons(h1, t1), l2, cons(h1, _qp)]), {
_qp -> cons(b, cons(b, nil))  ;  h1 -> b  ;  l2 -> cons(b, nil)  ;  t1 -> nil
})

-------------------------------------------
Step 42, which took 0.067279 s (model generation: 0.065516,  model checking: 0.001763):

Model:
|_
{
append -> 
{{{
Q={q_gen_4095, q_gen_4101, q_gen_4102, q_gen_4113, q_gen_4114, q_gen_4115},
Q_f={q_gen_4095},
Delta=
{
<cons>(q_gen_4114, q_gen_4113) -> q_gen_4113
<nil>() -> q_gen_4113
<a>() -> q_gen_4114
<b>() -> q_gen_4114
<cons, cons>(q_gen_4102, q_gen_4101) -> q_gen_4101
<nil, cons>(q_gen_4114, q_gen_4113) -> q_gen_4101
<nil, nil>() -> q_gen_4101
<a, a>() -> q_gen_4102
<b, b>() -> q_gen_4102
<cons, cons, cons>(q_gen_4115, q_gen_4095) -> q_gen_4095
<cons, nil, cons>(q_gen_4102, q_gen_4101) -> q_gen_4095
<nil, cons, cons>(q_gen_4102, q_gen_4101) -> q_gen_4095
<nil, nil, cons>(q_gen_4114, q_gen_4113) -> q_gen_4095
<nil, nil, nil>() -> q_gen_4095
<a, a, a>() -> q_gen_4115
<a, b, a>() -> q_gen_4115
<b, a, b>() -> q_gen_4115
<b, b, b>() -> q_gen_4115
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_4094, q_gen_4098, q_gen_4099, q_gen_4117, q_gen_4118, q_gen_4119, q_gen_4120, q_gen_4122, q_gen_4134, q_gen_4135, q_gen_4136, q_gen_4166},
Q_f={q_gen_4094},
Delta=
{
<cons>(q_gen_4118, q_gen_4134) -> q_gen_4098
<nil>() -> q_gen_4098
<cons>(q_gen_4118, q_gen_4098) -> q_gen_4117
<a>() -> q_gen_4118
<b>() -> q_gen_4118
<z>() -> q_gen_4120
<cons>(q_gen_4118, q_gen_4117) -> q_gen_4134
<s>(q_gen_4120) -> q_gen_4136
<s>(q_gen_4136) -> q_gen_4166
<cons, s>(q_gen_4099, q_gen_4098) -> q_gen_4094
<cons, s>(q_gen_4119, q_gen_4117) -> q_gen_4094
<cons, s>(q_gen_4135, q_gen_4134) -> q_gen_4094
<nil, z>() -> q_gen_4094
<a, s>(q_gen_4166) -> q_gen_4099
<a, z>() -> q_gen_4099
<b, s>(q_gen_4166) -> q_gen_4099
<b, z>() -> q_gen_4099
<a, s>(q_gen_4120) -> q_gen_4119
<b, s>(q_gen_4120) -> q_gen_4119
<cons, s>(q_gen_4099, q_gen_4117) -> q_gen_4122
<cons, s>(q_gen_4099, q_gen_4134) -> q_gen_4122
<cons, s>(q_gen_4119, q_gen_4098) -> q_gen_4122
<cons, s>(q_gen_4119, q_gen_4134) -> q_gen_4122
<cons, s>(q_gen_4135, q_gen_4098) -> q_gen_4122
<cons, s>(q_gen_4135, q_gen_4117) -> q_gen_4122
<a, s>(q_gen_4136) -> q_gen_4135
<b, s>(q_gen_4136) -> q_gen_4135
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_4091, q_gen_4093, q_gen_4123},
Q_f={q_gen_4091},
Delta=
{
<s>(q_gen_4093) -> q_gen_4093
<z>() -> q_gen_4093
<s, s>(q_gen_4091) -> q_gen_4091
<z, s>(q_gen_4093) -> q_gen_4091
<z, z>() -> q_gen_4091
<s, s>(q_gen_4123) -> q_gen_4123
<s, z>(q_gen_4093) -> q_gen_4123
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 25
() -> length([nil, z]) -> 25
() -> leq([z, s(nn2)]) -> 25
() -> leq([z, z]) -> 25
(append([l1, l2, _aq]) /\ length([_aq, _bq]) /\ length([l1, _zp])) -> leq([_zp, _bq]) -> 27
(append([l1, l2, _dq]) /\ length([_dq, _eq]) /\ length([l2, _cq])) -> leq([_cq, _eq]) -> 28
(append([t1, l2, _qp])) -> append([cons(h1, t1), l2, cons(h1, _qp)]) -> 28
(length([ll, _vp])) -> length([cons(x, ll), s(_vp)]) -> 28
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 26
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 26
(leq([s(nn1), z])) -> BOT -> 26
}
Sat witness: Found: ((append([l1, l2, _dq]) /\ length([_dq, _eq]) /\ length([l2, _cq])) -> leq([_cq, _eq]), {
_cq -> s(s(s(s(z))))  ;  _dq -> cons(a, cons(b, nil))  ;  _eq -> s(s(z))  ;  l1 -> cons(a, cons(b, nil))  ;  l2 -> cons(b, nil)
})

-------------------------------------------
Step 43, which took 0.074138 s (model generation: 0.073467,  model checking: 0.000671):

Model:
|_
{
append -> 
{{{
Q={q_gen_4095, q_gen_4101, q_gen_4102, q_gen_4113, q_gen_4114, q_gen_4115},
Q_f={q_gen_4095},
Delta=
{
<cons>(q_gen_4114, q_gen_4113) -> q_gen_4113
<nil>() -> q_gen_4113
<a>() -> q_gen_4114
<b>() -> q_gen_4114
<cons, cons>(q_gen_4102, q_gen_4101) -> q_gen_4101
<nil, cons>(q_gen_4114, q_gen_4113) -> q_gen_4101
<nil, nil>() -> q_gen_4101
<a, a>() -> q_gen_4102
<b, b>() -> q_gen_4102
<cons, cons, cons>(q_gen_4115, q_gen_4095) -> q_gen_4095
<cons, nil, cons>(q_gen_4102, q_gen_4101) -> q_gen_4095
<nil, cons, cons>(q_gen_4102, q_gen_4101) -> q_gen_4095
<nil, nil, cons>(q_gen_4114, q_gen_4113) -> q_gen_4095
<nil, nil, nil>() -> q_gen_4095
<a, a, a>() -> q_gen_4115
<a, b, a>() -> q_gen_4115
<b, a, b>() -> q_gen_4115
<b, b, b>() -> q_gen_4115
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_4094, q_gen_4098, q_gen_4099, q_gen_4117, q_gen_4118, q_gen_4119, q_gen_4120, q_gen_4122, q_gen_4134, q_gen_4135, q_gen_4136},
Q_f={q_gen_4094},
Delta=
{
<nil>() -> q_gen_4098
<cons>(q_gen_4118, q_gen_4098) -> q_gen_4117
<cons>(q_gen_4118, q_gen_4134) -> q_gen_4117
<a>() -> q_gen_4118
<b>() -> q_gen_4118
<s>(q_gen_4136) -> q_gen_4120
<z>() -> q_gen_4120
<cons>(q_gen_4118, q_gen_4117) -> q_gen_4134
<s>(q_gen_4120) -> q_gen_4136
<cons, s>(q_gen_4099, q_gen_4098) -> q_gen_4094
<cons, s>(q_gen_4119, q_gen_4117) -> q_gen_4094
<cons, s>(q_gen_4135, q_gen_4134) -> q_gen_4094
<nil, z>() -> q_gen_4094
<a, z>() -> q_gen_4099
<b, z>() -> q_gen_4099
<a, s>(q_gen_4120) -> q_gen_4119
<b, s>(q_gen_4120) -> q_gen_4119
<cons, s>(q_gen_4099, q_gen_4134) -> q_gen_4122
<cons, s>(q_gen_4119, q_gen_4098) -> q_gen_4122
<cons, s>(q_gen_4119, q_gen_4134) -> q_gen_4122
<cons, s>(q_gen_4135, q_gen_4098) -> q_gen_4122
<cons, s>(q_gen_4135, q_gen_4117) -> q_gen_4122
<a, s>(q_gen_4136) -> q_gen_4135
<b, s>(q_gen_4136) -> q_gen_4135
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_4091, q_gen_4093, q_gen_4123, q_gen_4124, q_gen_4139},
Q_f={q_gen_4091},
Delta=
{
<s>(q_gen_4093) -> q_gen_4093
<z>() -> q_gen_4093
<s, s>(q_gen_4091) -> q_gen_4091
<s, s>(q_gen_4139) -> q_gen_4091
<z, s>(q_gen_4093) -> q_gen_4091
<z, z>() -> q_gen_4091
<s, s>(q_gen_4124) -> q_gen_4123
<s, z>(q_gen_4093) -> q_gen_4124
<s, s>(q_gen_4123) -> q_gen_4139
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 26
() -> length([nil, z]) -> 26
() -> leq([z, s(nn2)]) -> 26
() -> leq([z, z]) -> 26
(append([l1, l2, _aq]) /\ length([_aq, _bq]) /\ length([l1, _zp])) -> leq([_zp, _bq]) -> 27
(append([l1, l2, _dq]) /\ length([_dq, _eq]) /\ length([l2, _cq])) -> leq([_cq, _eq]) -> 28
(append([t1, l2, _qp])) -> append([cons(h1, t1), l2, cons(h1, _qp)]) -> 28
(length([ll, _vp])) -> length([cons(x, ll), s(_vp)]) -> 28
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 26
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 29
(leq([s(nn1), z])) -> BOT -> 27
}
Sat witness: Found: ((leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]), {
nn1 -> s(s(s(z)))  ;  nn2 -> s(s(z))
})

-------------------------------------------
Step 44, which took 0.072322 s (model generation: 0.071967,  model checking: 0.000355):

Model:
|_
{
append -> 
{{{
Q={q_gen_4095, q_gen_4101, q_gen_4102, q_gen_4113, q_gen_4114, q_gen_4115},
Q_f={q_gen_4095},
Delta=
{
<cons>(q_gen_4114, q_gen_4113) -> q_gen_4113
<nil>() -> q_gen_4113
<a>() -> q_gen_4114
<b>() -> q_gen_4114
<cons, cons>(q_gen_4102, q_gen_4101) -> q_gen_4101
<nil, cons>(q_gen_4114, q_gen_4113) -> q_gen_4101
<nil, nil>() -> q_gen_4101
<a, a>() -> q_gen_4102
<b, b>() -> q_gen_4102
<cons, cons, cons>(q_gen_4115, q_gen_4095) -> q_gen_4095
<cons, nil, cons>(q_gen_4102, q_gen_4101) -> q_gen_4095
<nil, cons, cons>(q_gen_4102, q_gen_4101) -> q_gen_4095
<nil, nil, cons>(q_gen_4114, q_gen_4113) -> q_gen_4095
<nil, nil, nil>() -> q_gen_4095
<a, a, a>() -> q_gen_4115
<a, b, a>() -> q_gen_4115
<b, a, b>() -> q_gen_4115
<b, b, b>() -> q_gen_4115
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_4094, q_gen_4098, q_gen_4099, q_gen_4117, q_gen_4118, q_gen_4119, q_gen_4120, q_gen_4122, q_gen_4134, q_gen_4135, q_gen_4136, q_gen_4166},
Q_f={q_gen_4094},
Delta=
{
<cons>(q_gen_4118, q_gen_4134) -> q_gen_4098
<nil>() -> q_gen_4098
<cons>(q_gen_4118, q_gen_4098) -> q_gen_4117
<a>() -> q_gen_4118
<b>() -> q_gen_4118
<z>() -> q_gen_4120
<cons>(q_gen_4118, q_gen_4117) -> q_gen_4134
<s>(q_gen_4120) -> q_gen_4136
<s>(q_gen_4136) -> q_gen_4166
<cons, s>(q_gen_4099, q_gen_4098) -> q_gen_4094
<cons, s>(q_gen_4119, q_gen_4117) -> q_gen_4094
<cons, s>(q_gen_4135, q_gen_4134) -> q_gen_4094
<nil, z>() -> q_gen_4094
<a, s>(q_gen_4166) -> q_gen_4099
<a, z>() -> q_gen_4099
<b, s>(q_gen_4166) -> q_gen_4099
<b, z>() -> q_gen_4099
<a, s>(q_gen_4120) -> q_gen_4119
<b, s>(q_gen_4120) -> q_gen_4119
<cons, s>(q_gen_4099, q_gen_4117) -> q_gen_4122
<cons, s>(q_gen_4099, q_gen_4134) -> q_gen_4122
<cons, s>(q_gen_4119, q_gen_4098) -> q_gen_4122
<cons, s>(q_gen_4119, q_gen_4134) -> q_gen_4122
<cons, s>(q_gen_4135, q_gen_4098) -> q_gen_4122
<cons, s>(q_gen_4135, q_gen_4117) -> q_gen_4122
<a, s>(q_gen_4136) -> q_gen_4135
<b, s>(q_gen_4136) -> q_gen_4135
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_4091, q_gen_4093, q_gen_4104, q_gen_4123},
Q_f={q_gen_4091},
Delta=
{
<z>() -> q_gen_4093
<s>(q_gen_4093) -> q_gen_4104
<s, s>(q_gen_4091) -> q_gen_4091
<s, z>(q_gen_4104) -> q_gen_4091
<z, s>(q_gen_4093) -> q_gen_4091
<z, s>(q_gen_4104) -> q_gen_4091
<z, z>() -> q_gen_4091
<s, s>(q_gen_4123) -> q_gen_4123
<s, z>(q_gen_4093) -> q_gen_4123
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 26
() -> length([nil, z]) -> 26
() -> leq([z, s(nn2)]) -> 29
() -> leq([z, z]) -> 27
(append([l1, l2, _aq]) /\ length([_aq, _bq]) /\ length([l1, _zp])) -> leq([_zp, _bq]) -> 27
(append([l1, l2, _dq]) /\ length([_dq, _eq]) /\ length([l2, _cq])) -> leq([_cq, _eq]) -> 28
(append([t1, l2, _qp])) -> append([cons(h1, t1), l2, cons(h1, _qp)]) -> 28
(length([ll, _vp])) -> length([cons(x, ll), s(_vp)]) -> 28
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 27
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 29
(leq([s(nn1), z])) -> BOT -> 27
}
Sat witness: Found: (() -> leq([z, s(nn2)]), {
nn2 -> s(s(z))
})

-------------------------------------------
Step 45, which took 0.072754 s (model generation: 0.072191,  model checking: 0.000563):

Model:
|_
{
append -> 
{{{
Q={q_gen_4095, q_gen_4101, q_gen_4102, q_gen_4113, q_gen_4114, q_gen_4115},
Q_f={q_gen_4095},
Delta=
{
<cons>(q_gen_4114, q_gen_4113) -> q_gen_4113
<nil>() -> q_gen_4113
<a>() -> q_gen_4114
<b>() -> q_gen_4114
<cons, cons>(q_gen_4102, q_gen_4101) -> q_gen_4101
<nil, cons>(q_gen_4114, q_gen_4113) -> q_gen_4101
<nil, nil>() -> q_gen_4101
<a, a>() -> q_gen_4102
<b, b>() -> q_gen_4102
<cons, cons, cons>(q_gen_4115, q_gen_4095) -> q_gen_4095
<cons, nil, cons>(q_gen_4102, q_gen_4101) -> q_gen_4095
<nil, cons, cons>(q_gen_4102, q_gen_4101) -> q_gen_4095
<nil, nil, cons>(q_gen_4114, q_gen_4113) -> q_gen_4095
<nil, nil, nil>() -> q_gen_4095
<a, a, a>() -> q_gen_4115
<a, b, a>() -> q_gen_4115
<b, a, b>() -> q_gen_4115
<b, b, b>() -> q_gen_4115
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_4094, q_gen_4098, q_gen_4099, q_gen_4117, q_gen_4118, q_gen_4119, q_gen_4120, q_gen_4122, q_gen_4134, q_gen_4135, q_gen_4136, q_gen_4166},
Q_f={q_gen_4094},
Delta=
{
<cons>(q_gen_4118, q_gen_4134) -> q_gen_4098
<nil>() -> q_gen_4098
<cons>(q_gen_4118, q_gen_4098) -> q_gen_4117
<a>() -> q_gen_4118
<b>() -> q_gen_4118
<z>() -> q_gen_4120
<cons>(q_gen_4118, q_gen_4117) -> q_gen_4134
<s>(q_gen_4120) -> q_gen_4136
<s>(q_gen_4136) -> q_gen_4166
<cons, s>(q_gen_4099, q_gen_4098) -> q_gen_4094
<cons, s>(q_gen_4119, q_gen_4117) -> q_gen_4094
<cons, s>(q_gen_4135, q_gen_4134) -> q_gen_4094
<nil, z>() -> q_gen_4094
<a, s>(q_gen_4166) -> q_gen_4099
<a, z>() -> q_gen_4099
<b, s>(q_gen_4166) -> q_gen_4099
<b, z>() -> q_gen_4099
<a, s>(q_gen_4120) -> q_gen_4119
<b, s>(q_gen_4120) -> q_gen_4119
<cons, s>(q_gen_4099, q_gen_4117) -> q_gen_4122
<cons, s>(q_gen_4099, q_gen_4134) -> q_gen_4122
<cons, s>(q_gen_4119, q_gen_4098) -> q_gen_4122
<cons, s>(q_gen_4119, q_gen_4134) -> q_gen_4122
<cons, s>(q_gen_4135, q_gen_4098) -> q_gen_4122
<cons, s>(q_gen_4135, q_gen_4117) -> q_gen_4122
<a, s>(q_gen_4136) -> q_gen_4135
<b, s>(q_gen_4136) -> q_gen_4135
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_4091, q_gen_4093, q_gen_4104, q_gen_4123},
Q_f={q_gen_4091},
Delta=
{
<z>() -> q_gen_4093
<s>(q_gen_4093) -> q_gen_4104
<s>(q_gen_4104) -> q_gen_4104
<s, s>(q_gen_4091) -> q_gen_4091
<s, z>(q_gen_4104) -> q_gen_4091
<z, s>(q_gen_4093) -> q_gen_4091
<z, s>(q_gen_4104) -> q_gen_4091
<z, z>() -> q_gen_4091
<s, s>(q_gen_4123) -> q_gen_4123
<s, z>(q_gen_4093) -> q_gen_4123
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 27
() -> length([nil, z]) -> 27
() -> leq([z, s(nn2)]) -> 29
() -> leq([z, z]) -> 27
(append([l1, l2, _aq]) /\ length([_aq, _bq]) /\ length([l1, _zp])) -> leq([_zp, _bq]) -> 27
(append([l1, l2, _dq]) /\ length([_dq, _eq]) /\ length([l2, _cq])) -> leq([_cq, _eq]) -> 28
(append([t1, l2, _qp])) -> append([cons(h1, t1), l2, cons(h1, _qp)]) -> 28
(length([ll, _vp])) -> length([cons(x, ll), s(_vp)]) -> 28
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 27
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 29
(leq([s(nn1), z])) -> BOT -> 30
}
Sat witness: Found: ((leq([s(nn1), z])) -> BOT, {
nn1 -> s(z)
})

-------------------------------------------
Step 46, which took 0.080586 s (model generation: 0.075047,  model checking: 0.005539):

Model:
|_
{
append -> 
{{{
Q={q_gen_4095, q_gen_4101, q_gen_4102, q_gen_4112, q_gen_4113, q_gen_4114, q_gen_4115, q_gen_4126},
Q_f={q_gen_4095},
Delta=
{
<cons>(q_gen_4114, q_gen_4113) -> q_gen_4113
<nil>() -> q_gen_4113
<a>() -> q_gen_4114
<b>() -> q_gen_4114
<cons, cons>(q_gen_4102, q_gen_4101) -> q_gen_4101
<nil, nil>() -> q_gen_4101
<a, a>() -> q_gen_4102
<b, b>() -> q_gen_4102
<cons, cons>(q_gen_4102, q_gen_4126) -> q_gen_4126
<nil, cons>(q_gen_4114, q_gen_4113) -> q_gen_4126
<cons, cons, cons>(q_gen_4115, q_gen_4095) -> q_gen_4095
<cons, cons, cons>(q_gen_4115, q_gen_4112) -> q_gen_4095
<cons, nil, cons>(q_gen_4102, q_gen_4101) -> q_gen_4095
<nil, cons, cons>(q_gen_4102, q_gen_4101) -> q_gen_4095
<nil, nil, nil>() -> q_gen_4095
<cons, nil, cons>(q_gen_4102, q_gen_4126) -> q_gen_4112
<nil, cons, cons>(q_gen_4102, q_gen_4126) -> q_gen_4112
<nil, nil, cons>(q_gen_4114, q_gen_4113) -> q_gen_4112
<a, a, a>() -> q_gen_4115
<a, b, a>() -> q_gen_4115
<b, a, b>() -> q_gen_4115
<b, b, b>() -> q_gen_4115
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_4094, q_gen_4098, q_gen_4099, q_gen_4109, q_gen_4117, q_gen_4118, q_gen_4119, q_gen_4120, q_gen_4122, q_gen_4134, q_gen_4136},
Q_f={q_gen_4094},
Delta=
{
<nil>() -> q_gen_4098
<cons>(q_gen_4118, q_gen_4098) -> q_gen_4117
<cons>(q_gen_4118, q_gen_4134) -> q_gen_4117
<a>() -> q_gen_4118
<b>() -> q_gen_4118
<s>(q_gen_4136) -> q_gen_4120
<z>() -> q_gen_4120
<cons>(q_gen_4118, q_gen_4117) -> q_gen_4134
<s>(q_gen_4120) -> q_gen_4136
<cons, s>(q_gen_4099, q_gen_4098) -> q_gen_4094
<cons, s>(q_gen_4109, q_gen_4098) -> q_gen_4094
<cons, s>(q_gen_4109, q_gen_4134) -> q_gen_4094
<cons, s>(q_gen_4119, q_gen_4117) -> q_gen_4094
<nil, z>() -> q_gen_4094
<b, z>() -> q_gen_4099
<a, s>(q_gen_4136) -> q_gen_4109
<a, z>() -> q_gen_4109
<b, s>(q_gen_4136) -> q_gen_4109
<a, s>(q_gen_4120) -> q_gen_4119
<b, s>(q_gen_4120) -> q_gen_4119
<cons, s>(q_gen_4099, q_gen_4134) -> q_gen_4122
<cons, s>(q_gen_4109, q_gen_4117) -> q_gen_4122
<cons, s>(q_gen_4119, q_gen_4098) -> q_gen_4122
<cons, s>(q_gen_4119, q_gen_4134) -> q_gen_4122
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_4091, q_gen_4093, q_gen_4123},
Q_f={q_gen_4091},
Delta=
{
<s>(q_gen_4093) -> q_gen_4093
<z>() -> q_gen_4093
<s, s>(q_gen_4091) -> q_gen_4091
<z, s>(q_gen_4093) -> q_gen_4091
<z, z>() -> q_gen_4091
<s, s>(q_gen_4123) -> q_gen_4123
<s, z>(q_gen_4093) -> q_gen_4123
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 27
() -> length([nil, z]) -> 27
() -> leq([z, s(nn2)]) -> 29
() -> leq([z, z]) -> 27
(append([l1, l2, _aq]) /\ length([_aq, _bq]) /\ length([l1, _zp])) -> leq([_zp, _bq]) -> 30
(append([l1, l2, _dq]) /\ length([_dq, _eq]) /\ length([l2, _cq])) -> leq([_cq, _eq]) -> 28
(append([t1, l2, _qp])) -> append([cons(h1, t1), l2, cons(h1, _qp)]) -> 28
(length([ll, _vp])) -> length([cons(x, ll), s(_vp)]) -> 28
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 28
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 29
(leq([s(nn1), z])) -> BOT -> 30
}
Sat witness: Found: ((append([l1, l2, _aq]) /\ length([_aq, _bq]) /\ length([l1, _zp])) -> leq([_zp, _bq]), {
_aq -> cons(a, cons(b, cons(b, nil)))  ;  _bq -> s(z)  ;  _zp -> s(s(z))  ;  l1 -> cons(a, cons(b, nil))  ;  l2 -> cons(b, nil)
})

-------------------------------------------
Step 47, which took 0.176751 s (model generation: 0.080337,  model checking: 0.096414):

Model:
|_
{
append -> 
{{{
Q={q_gen_4095, q_gen_4101, q_gen_4102, q_gen_4112, q_gen_4113, q_gen_4114, q_gen_4115, q_gen_4126},
Q_f={q_gen_4095},
Delta=
{
<cons>(q_gen_4114, q_gen_4113) -> q_gen_4113
<nil>() -> q_gen_4113
<a>() -> q_gen_4114
<b>() -> q_gen_4114
<cons, cons>(q_gen_4102, q_gen_4101) -> q_gen_4101
<nil, nil>() -> q_gen_4101
<a, a>() -> q_gen_4102
<b, b>() -> q_gen_4102
<cons, cons>(q_gen_4102, q_gen_4126) -> q_gen_4126
<nil, cons>(q_gen_4114, q_gen_4113) -> q_gen_4126
<cons, cons, cons>(q_gen_4115, q_gen_4095) -> q_gen_4095
<cons, cons, cons>(q_gen_4115, q_gen_4112) -> q_gen_4095
<cons, nil, cons>(q_gen_4102, q_gen_4101) -> q_gen_4095
<nil, cons, cons>(q_gen_4102, q_gen_4101) -> q_gen_4095
<nil, nil, nil>() -> q_gen_4095
<cons, nil, cons>(q_gen_4102, q_gen_4126) -> q_gen_4112
<nil, cons, cons>(q_gen_4102, q_gen_4126) -> q_gen_4112
<nil, nil, cons>(q_gen_4114, q_gen_4113) -> q_gen_4112
<a, a, a>() -> q_gen_4115
<a, b, a>() -> q_gen_4115
<b, a, b>() -> q_gen_4115
<b, b, b>() -> q_gen_4115
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_4094, q_gen_4098, q_gen_4099, q_gen_4117, q_gen_4118, q_gen_4119, q_gen_4120, q_gen_4122, q_gen_4134, q_gen_4135, q_gen_4136},
Q_f={q_gen_4094},
Delta=
{
<nil>() -> q_gen_4098
<cons>(q_gen_4118, q_gen_4098) -> q_gen_4117
<cons>(q_gen_4118, q_gen_4134) -> q_gen_4117
<a>() -> q_gen_4118
<b>() -> q_gen_4118
<s>(q_gen_4136) -> q_gen_4120
<z>() -> q_gen_4120
<cons>(q_gen_4118, q_gen_4117) -> q_gen_4134
<s>(q_gen_4120) -> q_gen_4136
<cons, s>(q_gen_4099, q_gen_4098) -> q_gen_4094
<cons, s>(q_gen_4119, q_gen_4117) -> q_gen_4094
<cons, s>(q_gen_4135, q_gen_4098) -> q_gen_4094
<cons, s>(q_gen_4135, q_gen_4134) -> q_gen_4094
<nil, z>() -> q_gen_4094
<a, z>() -> q_gen_4099
<b, z>() -> q_gen_4099
<a, s>(q_gen_4120) -> q_gen_4119
<b, s>(q_gen_4120) -> q_gen_4119
<cons, s>(q_gen_4099, q_gen_4134) -> q_gen_4122
<cons, s>(q_gen_4119, q_gen_4098) -> q_gen_4122
<cons, s>(q_gen_4119, q_gen_4134) -> q_gen_4122
<cons, s>(q_gen_4135, q_gen_4117) -> q_gen_4122
<a, s>(q_gen_4136) -> q_gen_4135
<b, s>(q_gen_4136) -> q_gen_4135
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_4091, q_gen_4093, q_gen_4123},
Q_f={q_gen_4091},
Delta=
{
<s>(q_gen_4093) -> q_gen_4093
<z>() -> q_gen_4093
<s, s>(q_gen_4091) -> q_gen_4091
<z, s>(q_gen_4093) -> q_gen_4091
<z, z>() -> q_gen_4091
<s, s>(q_gen_4123) -> q_gen_4123
<s, z>(q_gen_4093) -> q_gen_4123
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 28
() -> length([nil, z]) -> 28
() -> leq([z, s(nn2)]) -> 29
() -> leq([z, z]) -> 28
(append([l1, l2, _aq]) /\ length([_aq, _bq]) /\ length([l1, _zp])) -> leq([_zp, _bq]) -> 30
(append([l1, l2, _dq]) /\ length([_dq, _eq]) /\ length([l2, _cq])) -> leq([_cq, _eq]) -> 28
(append([t1, l2, _qp])) -> append([cons(h1, t1), l2, cons(h1, _qp)]) -> 31
(length([ll, _vp])) -> length([cons(x, ll), s(_vp)]) -> 29
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 29
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 29
(leq([s(nn1), z])) -> BOT -> 30
}
Sat witness: Found: ((append([t1, l2, _qp])) -> append([cons(h1, t1), l2, cons(h1, _qp)]), {
_qp -> cons(a, cons(b, nil))  ;  h1 -> a  ;  l2 -> cons(a, cons(b, nil))  ;  t1 -> nil
})

-------------------------------------------
Step 48, which took 0.095312 s (model generation: 0.092536,  model checking: 0.002776):

Model:
|_
{
append -> 
{{{
Q={q_gen_4095, q_gen_4101, q_gen_4102, q_gen_4112, q_gen_4113, q_gen_4114, q_gen_4115, q_gen_4126},
Q_f={q_gen_4095},
Delta=
{
<cons>(q_gen_4114, q_gen_4113) -> q_gen_4113
<nil>() -> q_gen_4113
<a>() -> q_gen_4114
<b>() -> q_gen_4114
<cons, cons>(q_gen_4102, q_gen_4101) -> q_gen_4101
<nil, nil>() -> q_gen_4101
<a, a>() -> q_gen_4102
<b, a>() -> q_gen_4102
<b, b>() -> q_gen_4102
<cons, cons>(q_gen_4102, q_gen_4126) -> q_gen_4126
<nil, cons>(q_gen_4114, q_gen_4113) -> q_gen_4126
<cons, cons, cons>(q_gen_4115, q_gen_4112) -> q_gen_4095
<cons, nil, cons>(q_gen_4102, q_gen_4101) -> q_gen_4095
<nil, cons, cons>(q_gen_4102, q_gen_4101) -> q_gen_4095
<nil, nil, nil>() -> q_gen_4095
<cons, cons, cons>(q_gen_4115, q_gen_4095) -> q_gen_4112
<cons, nil, cons>(q_gen_4102, q_gen_4126) -> q_gen_4112
<nil, cons, cons>(q_gen_4102, q_gen_4126) -> q_gen_4112
<nil, nil, cons>(q_gen_4114, q_gen_4113) -> q_gen_4112
<a, a, a>() -> q_gen_4115
<a, b, a>() -> q_gen_4115
<b, a, b>() -> q_gen_4115
<b, b, b>() -> q_gen_4115
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_4094, q_gen_4098, q_gen_4099, q_gen_4117, q_gen_4118, q_gen_4119, q_gen_4120, q_gen_4122, q_gen_4134, q_gen_4135, q_gen_4136},
Q_f={q_gen_4094},
Delta=
{
<nil>() -> q_gen_4098
<cons>(q_gen_4118, q_gen_4098) -> q_gen_4117
<cons>(q_gen_4118, q_gen_4134) -> q_gen_4117
<a>() -> q_gen_4118
<b>() -> q_gen_4118
<s>(q_gen_4136) -> q_gen_4120
<z>() -> q_gen_4120
<cons>(q_gen_4118, q_gen_4117) -> q_gen_4134
<s>(q_gen_4120) -> q_gen_4136
<cons, s>(q_gen_4099, q_gen_4098) -> q_gen_4094
<cons, s>(q_gen_4119, q_gen_4117) -> q_gen_4094
<cons, s>(q_gen_4135, q_gen_4098) -> q_gen_4094
<cons, s>(q_gen_4135, q_gen_4134) -> q_gen_4094
<nil, z>() -> q_gen_4094
<a, z>() -> q_gen_4099
<b, z>() -> q_gen_4099
<a, s>(q_gen_4120) -> q_gen_4119
<b, s>(q_gen_4120) -> q_gen_4119
<cons, s>(q_gen_4099, q_gen_4134) -> q_gen_4122
<cons, s>(q_gen_4119, q_gen_4098) -> q_gen_4122
<cons, s>(q_gen_4119, q_gen_4134) -> q_gen_4122
<cons, s>(q_gen_4135, q_gen_4117) -> q_gen_4122
<a, s>(q_gen_4136) -> q_gen_4135
<b, s>(q_gen_4136) -> q_gen_4135
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_4091, q_gen_4093, q_gen_4123},
Q_f={q_gen_4091},
Delta=
{
<s>(q_gen_4093) -> q_gen_4093
<z>() -> q_gen_4093
<s, s>(q_gen_4091) -> q_gen_4091
<z, s>(q_gen_4093) -> q_gen_4091
<z, z>() -> q_gen_4091
<s, s>(q_gen_4123) -> q_gen_4123
<s, z>(q_gen_4093) -> q_gen_4123
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 28
() -> length([nil, z]) -> 28
() -> leq([z, s(nn2)]) -> 29
() -> leq([z, z]) -> 28
(append([l1, l2, _aq]) /\ length([_aq, _bq]) /\ length([l1, _zp])) -> leq([_zp, _bq]) -> 30
(append([l1, l2, _dq]) /\ length([_dq, _eq]) /\ length([l2, _cq])) -> leq([_cq, _eq]) -> 31
(append([t1, l2, _qp])) -> append([cons(h1, t1), l2, cons(h1, _qp)]) -> 31
(length([ll, _vp])) -> length([cons(x, ll), s(_vp)]) -> 29
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 29
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 29
(leq([s(nn1), z])) -> BOT -> 30
}
Sat witness: Found: ((append([l1, l2, _dq]) /\ length([_dq, _eq]) /\ length([l2, _cq])) -> leq([_cq, _eq]), {
_cq -> s(s(s(z)))  ;  _dq -> cons(b, cons(b, nil))  ;  _eq -> s(s(z))  ;  l1 -> cons(b, nil)  ;  l2 -> cons(b, nil)
})

-------------------------------------------
Step 49, which took 0.094426 s (model generation: 0.088894,  model checking: 0.005532):

Model:
|_
{
append -> 
{{{
Q={q_gen_4095, q_gen_4101, q_gen_4102, q_gen_4112, q_gen_4113, q_gen_4114, q_gen_4115, q_gen_4126},
Q_f={q_gen_4095},
Delta=
{
<cons>(q_gen_4114, q_gen_4113) -> q_gen_4113
<nil>() -> q_gen_4113
<a>() -> q_gen_4114
<b>() -> q_gen_4114
<cons, cons>(q_gen_4102, q_gen_4101) -> q_gen_4101
<nil, nil>() -> q_gen_4101
<a, a>() -> q_gen_4102
<b, a>() -> q_gen_4102
<b, b>() -> q_gen_4102
<cons, cons>(q_gen_4102, q_gen_4126) -> q_gen_4126
<nil, cons>(q_gen_4114, q_gen_4113) -> q_gen_4126
<cons, cons, cons>(q_gen_4115, q_gen_4112) -> q_gen_4095
<cons, nil, cons>(q_gen_4102, q_gen_4101) -> q_gen_4095
<nil, cons, cons>(q_gen_4102, q_gen_4101) -> q_gen_4095
<nil, nil, nil>() -> q_gen_4095
<cons, cons, cons>(q_gen_4115, q_gen_4095) -> q_gen_4112
<cons, nil, cons>(q_gen_4102, q_gen_4126) -> q_gen_4112
<nil, cons, cons>(q_gen_4102, q_gen_4126) -> q_gen_4112
<nil, nil, cons>(q_gen_4114, q_gen_4113) -> q_gen_4112
<a, a, a>() -> q_gen_4115
<a, b, a>() -> q_gen_4115
<b, a, b>() -> q_gen_4115
<b, b, b>() -> q_gen_4115
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_4094, q_gen_4098, q_gen_4099, q_gen_4117, q_gen_4118, q_gen_4119, q_gen_4120, q_gen_4122, q_gen_4134, q_gen_4135, q_gen_4136},
Q_f={q_gen_4094},
Delta=
{
<nil>() -> q_gen_4098
<cons>(q_gen_4118, q_gen_4098) -> q_gen_4117
<cons>(q_gen_4118, q_gen_4134) -> q_gen_4117
<a>() -> q_gen_4118
<b>() -> q_gen_4118
<s>(q_gen_4136) -> q_gen_4120
<z>() -> q_gen_4120
<cons>(q_gen_4118, q_gen_4117) -> q_gen_4134
<s>(q_gen_4120) -> q_gen_4136
<cons, s>(q_gen_4099, q_gen_4098) -> q_gen_4094
<cons, s>(q_gen_4119, q_gen_4117) -> q_gen_4094
<cons, s>(q_gen_4135, q_gen_4134) -> q_gen_4094
<nil, z>() -> q_gen_4094
<a, z>() -> q_gen_4099
<b, z>() -> q_gen_4099
<a, s>(q_gen_4120) -> q_gen_4119
<b, s>(q_gen_4120) -> q_gen_4119
<cons, s>(q_gen_4099, q_gen_4134) -> q_gen_4122
<cons, s>(q_gen_4119, q_gen_4098) -> q_gen_4122
<cons, s>(q_gen_4119, q_gen_4134) -> q_gen_4122
<cons, s>(q_gen_4135, q_gen_4098) -> q_gen_4122
<cons, s>(q_gen_4135, q_gen_4117) -> q_gen_4122
<a, s>(q_gen_4136) -> q_gen_4135
<b, s>(q_gen_4136) -> q_gen_4135
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_4091, q_gen_4093, q_gen_4123},
Q_f={q_gen_4091},
Delta=
{
<s>(q_gen_4093) -> q_gen_4093
<z>() -> q_gen_4093
<s, s>(q_gen_4091) -> q_gen_4091
<z, s>(q_gen_4093) -> q_gen_4091
<z, z>() -> q_gen_4091
<s, s>(q_gen_4123) -> q_gen_4123
<s, z>(q_gen_4093) -> q_gen_4123
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 29
() -> length([nil, z]) -> 29
() -> leq([z, s(nn2)]) -> 30
() -> leq([z, z]) -> 29
(append([l1, l2, _aq]) /\ length([_aq, _bq]) /\ length([l1, _zp])) -> leq([_zp, _bq]) -> 33
(append([l1, l2, _dq]) /\ length([_dq, _eq]) /\ length([l2, _cq])) -> leq([_cq, _eq]) -> 31
(append([t1, l2, _qp])) -> append([cons(h1, t1), l2, cons(h1, _qp)]) -> 31
(length([ll, _vp])) -> length([cons(x, ll), s(_vp)]) -> 30
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 30
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 30
(leq([s(nn1), z])) -> BOT -> 31
}
Sat witness: Found: ((append([l1, l2, _aq]) /\ length([_aq, _bq]) /\ length([l1, _zp])) -> leq([_zp, _bq]), {
_aq -> cons(b, cons(b, nil))  ;  _bq -> s(s(z))  ;  _zp -> s(s(s(s(z))))  ;  l1 -> cons(b, cons(b, nil))  ;  l2 -> nil
})

-------------------------------------------
Step 50, which took 0.105391 s (model generation: 0.098574,  model checking: 0.006817):

Model:
|_
{
append -> 
{{{
Q={q_gen_4095, q_gen_4101, q_gen_4102, q_gen_4113, q_gen_4114, q_gen_4115},
Q_f={q_gen_4095},
Delta=
{
<cons>(q_gen_4114, q_gen_4113) -> q_gen_4113
<nil>() -> q_gen_4113
<a>() -> q_gen_4114
<b>() -> q_gen_4114
<cons, cons>(q_gen_4102, q_gen_4101) -> q_gen_4101
<nil, cons>(q_gen_4114, q_gen_4113) -> q_gen_4101
<nil, nil>() -> q_gen_4101
<a, a>() -> q_gen_4102
<b, a>() -> q_gen_4102
<b, b>() -> q_gen_4102
<cons, cons, cons>(q_gen_4115, q_gen_4095) -> q_gen_4095
<cons, nil, cons>(q_gen_4102, q_gen_4101) -> q_gen_4095
<nil, cons, cons>(q_gen_4102, q_gen_4101) -> q_gen_4095
<nil, nil, cons>(q_gen_4114, q_gen_4113) -> q_gen_4095
<nil, nil, nil>() -> q_gen_4095
<a, a, a>() -> q_gen_4115
<a, b, a>() -> q_gen_4115
<b, a, b>() -> q_gen_4115
<b, b, b>() -> q_gen_4115
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_4094, q_gen_4098, q_gen_4099, q_gen_4117, q_gen_4118, q_gen_4119, q_gen_4120, q_gen_4122, q_gen_4134, q_gen_4135, q_gen_4136, q_gen_4164, q_gen_4165, q_gen_4166},
Q_f={q_gen_4094},
Delta=
{
<nil>() -> q_gen_4098
<cons>(q_gen_4118, q_gen_4098) -> q_gen_4117
<a>() -> q_gen_4118
<b>() -> q_gen_4118
<z>() -> q_gen_4120
<cons>(q_gen_4118, q_gen_4117) -> q_gen_4134
<s>(q_gen_4120) -> q_gen_4136
<cons>(q_gen_4118, q_gen_4134) -> q_gen_4164
<s>(q_gen_4136) -> q_gen_4166
<cons, s>(q_gen_4099, q_gen_4098) -> q_gen_4094
<cons, s>(q_gen_4099, q_gen_4164) -> q_gen_4094
<cons, s>(q_gen_4119, q_gen_4117) -> q_gen_4094
<cons, s>(q_gen_4135, q_gen_4134) -> q_gen_4094
<cons, s>(q_gen_4165, q_gen_4164) -> q_gen_4094
<nil, z>() -> q_gen_4094
<a, s>(q_gen_4166) -> q_gen_4099
<a, z>() -> q_gen_4099
<b, z>() -> q_gen_4099
<a, s>(q_gen_4120) -> q_gen_4119
<b, s>(q_gen_4120) -> q_gen_4119
<cons, s>(q_gen_4099, q_gen_4134) -> q_gen_4122
<cons, s>(q_gen_4119, q_gen_4098) -> q_gen_4122
<cons, s>(q_gen_4119, q_gen_4134) -> q_gen_4122
<cons, s>(q_gen_4135, q_gen_4098) -> q_gen_4122
<cons, s>(q_gen_4135, q_gen_4117) -> q_gen_4122
<cons, s>(q_gen_4165, q_gen_4098) -> q_gen_4122
<cons, s>(q_gen_4165, q_gen_4117) -> q_gen_4122
<cons, s>(q_gen_4165, q_gen_4134) -> q_gen_4122
<a, s>(q_gen_4136) -> q_gen_4135
<b, s>(q_gen_4136) -> q_gen_4135
<b, s>(q_gen_4166) -> q_gen_4165
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_4091, q_gen_4093, q_gen_4123},
Q_f={q_gen_4091},
Delta=
{
<s>(q_gen_4093) -> q_gen_4093
<z>() -> q_gen_4093
<s, s>(q_gen_4091) -> q_gen_4091
<z, s>(q_gen_4093) -> q_gen_4091
<z, z>() -> q_gen_4091
<s, s>(q_gen_4123) -> q_gen_4123
<s, z>(q_gen_4093) -> q_gen_4123
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 30
() -> length([nil, z]) -> 30
() -> leq([z, s(nn2)]) -> 30
() -> leq([z, z]) -> 30
(append([l1, l2, _aq]) /\ length([_aq, _bq]) /\ length([l1, _zp])) -> leq([_zp, _bq]) -> 33
(append([l1, l2, _dq]) /\ length([_dq, _eq]) /\ length([l2, _cq])) -> leq([_cq, _eq]) -> 31
(append([t1, l2, _qp])) -> append([cons(h1, t1), l2, cons(h1, _qp)]) -> 31
(length([ll, _vp])) -> length([cons(x, ll), s(_vp)]) -> 33
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 31
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 31
(leq([s(nn1), z])) -> BOT -> 31
}
Sat witness: Found: ((length([ll, _vp])) -> length([cons(x, ll), s(_vp)]), {
_vp -> s(s(s(s(z))))  ;  ll -> cons(a, nil)  ;  x -> b
})

-------------------------------------------
Step 51, which took 0.128145 s (model generation: 0.127509,  model checking: 0.000636):

Model:
|_
{
append -> 
{{{
Q={q_gen_4095, q_gen_4101, q_gen_4102, q_gen_4106, q_gen_4113, q_gen_4114, q_gen_4115, q_gen_4160, q_gen_4167},
Q_f={q_gen_4095},
Delta=
{
<cons>(q_gen_4114, q_gen_4113) -> q_gen_4113
<nil>() -> q_gen_4113
<a>() -> q_gen_4114
<b>() -> q_gen_4114
<nil, nil>() -> q_gen_4101
<a, a>() -> q_gen_4102
<b, a>() -> q_gen_4102
<b, b>() -> q_gen_4102
<cons, cons>(q_gen_4102, q_gen_4101) -> q_gen_4106
<nil, cons>(q_gen_4114, q_gen_4113) -> q_gen_4106
<cons, cons>(q_gen_4102, q_gen_4106) -> q_gen_4160
<cons, cons, cons>(q_gen_4115, q_gen_4095) -> q_gen_4095
<cons, nil, cons>(q_gen_4102, q_gen_4101) -> q_gen_4095
<cons, nil, cons>(q_gen_4102, q_gen_4106) -> q_gen_4095
<nil, cons, cons>(q_gen_4102, q_gen_4101) -> q_gen_4095
<nil, cons, cons>(q_gen_4102, q_gen_4106) -> q_gen_4095
<nil, cons, cons>(q_gen_4102, q_gen_4160) -> q_gen_4095
<nil, nil, cons>(q_gen_4114, q_gen_4113) -> q_gen_4095
<nil, nil, nil>() -> q_gen_4095
<a, a, a>() -> q_gen_4115
<a, b, a>() -> q_gen_4115
<b, a, b>() -> q_gen_4115
<b, b, b>() -> q_gen_4115
<cons, nil, cons>(q_gen_4102, q_gen_4160) -> q_gen_4167
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_4094, q_gen_4098, q_gen_4099, q_gen_4117, q_gen_4118, q_gen_4119, q_gen_4120, q_gen_4122, q_gen_4134, q_gen_4135, q_gen_4136},
Q_f={q_gen_4094},
Delta=
{
<nil>() -> q_gen_4098
<cons>(q_gen_4118, q_gen_4098) -> q_gen_4117
<a>() -> q_gen_4118
<b>() -> q_gen_4118
<z>() -> q_gen_4120
<cons>(q_gen_4118, q_gen_4117) -> q_gen_4134
<cons>(q_gen_4118, q_gen_4134) -> q_gen_4134
<s>(q_gen_4120) -> q_gen_4136
<s>(q_gen_4136) -> q_gen_4136
<cons, s>(q_gen_4099, q_gen_4098) -> q_gen_4094
<cons, s>(q_gen_4119, q_gen_4117) -> q_gen_4094
<cons, s>(q_gen_4135, q_gen_4134) -> q_gen_4094
<nil, z>() -> q_gen_4094
<a, z>() -> q_gen_4099
<b, z>() -> q_gen_4099
<a, s>(q_gen_4120) -> q_gen_4119
<b, s>(q_gen_4120) -> q_gen_4119
<cons, s>(q_gen_4099, q_gen_4134) -> q_gen_4122
<cons, s>(q_gen_4119, q_gen_4098) -> q_gen_4122
<cons, s>(q_gen_4119, q_gen_4134) -> q_gen_4122
<cons, s>(q_gen_4135, q_gen_4098) -> q_gen_4122
<cons, s>(q_gen_4135, q_gen_4117) -> q_gen_4122
<a, s>(q_gen_4136) -> q_gen_4135
<b, s>(q_gen_4136) -> q_gen_4135
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_4091, q_gen_4093, q_gen_4123},
Q_f={q_gen_4091},
Delta=
{
<s>(q_gen_4093) -> q_gen_4093
<z>() -> q_gen_4093
<s, s>(q_gen_4091) -> q_gen_4091
<z, s>(q_gen_4093) -> q_gen_4091
<z, z>() -> q_gen_4091
<s, s>(q_gen_4123) -> q_gen_4123
<s, z>(q_gen_4093) -> q_gen_4123
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 33
() -> length([nil, z]) -> 31
() -> leq([z, s(nn2)]) -> 31
() -> leq([z, z]) -> 31
(append([l1, l2, _aq]) /\ length([_aq, _bq]) /\ length([l1, _zp])) -> leq([_zp, _bq]) -> 33
(append([l1, l2, _dq]) /\ length([_dq, _eq]) /\ length([l2, _cq])) -> leq([_cq, _eq]) -> 31
(append([t1, l2, _qp])) -> append([cons(h1, t1), l2, cons(h1, _qp)]) -> 31
(length([ll, _vp])) -> length([cons(x, ll), s(_vp)]) -> 33
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 31
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 31
(leq([s(nn1), z])) -> BOT -> 31
}
Sat witness: Found: (() -> append([nil, l2, l2]), {
l2 -> cons(b, cons(b, cons(b, cons(b, nil))))
})

-------------------------------------------
Step 52, which took 0.127314 s (model generation: 0.125562,  model checking: 0.001752):

Model:
|_
{
append -> 
{{{
Q={q_gen_4095, q_gen_4101, q_gen_4102, q_gen_4112, q_gen_4113, q_gen_4114, q_gen_4115, q_gen_4126},
Q_f={q_gen_4095},
Delta=
{
<cons>(q_gen_4114, q_gen_4113) -> q_gen_4113
<nil>() -> q_gen_4113
<a>() -> q_gen_4114
<b>() -> q_gen_4114
<cons, cons>(q_gen_4102, q_gen_4101) -> q_gen_4101
<cons, cons>(q_gen_4102, q_gen_4126) -> q_gen_4101
<nil, nil>() -> q_gen_4101
<a, a>() -> q_gen_4102
<b, a>() -> q_gen_4102
<b, b>() -> q_gen_4102
<nil, cons>(q_gen_4114, q_gen_4113) -> q_gen_4126
<cons, cons, cons>(q_gen_4115, q_gen_4112) -> q_gen_4095
<cons, nil, cons>(q_gen_4102, q_gen_4101) -> q_gen_4095
<nil, cons, cons>(q_gen_4102, q_gen_4101) -> q_gen_4095
<nil, nil, nil>() -> q_gen_4095
<cons, cons, cons>(q_gen_4115, q_gen_4095) -> q_gen_4112
<cons, nil, cons>(q_gen_4102, q_gen_4126) -> q_gen_4112
<nil, cons, cons>(q_gen_4102, q_gen_4126) -> q_gen_4112
<nil, nil, cons>(q_gen_4114, q_gen_4113) -> q_gen_4112
<a, a, a>() -> q_gen_4115
<a, b, a>() -> q_gen_4115
<b, a, b>() -> q_gen_4115
<b, b, b>() -> q_gen_4115
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_4094, q_gen_4098, q_gen_4099, q_gen_4117, q_gen_4118, q_gen_4119, q_gen_4120, q_gen_4122, q_gen_4134, q_gen_4135, q_gen_4136, q_gen_4166},
Q_f={q_gen_4094},
Delta=
{
<cons>(q_gen_4118, q_gen_4134) -> q_gen_4098
<nil>() -> q_gen_4098
<cons>(q_gen_4118, q_gen_4098) -> q_gen_4117
<a>() -> q_gen_4118
<b>() -> q_gen_4118
<s>(q_gen_4166) -> q_gen_4120
<z>() -> q_gen_4120
<cons>(q_gen_4118, q_gen_4117) -> q_gen_4134
<s>(q_gen_4120) -> q_gen_4136
<s>(q_gen_4136) -> q_gen_4166
<cons, s>(q_gen_4099, q_gen_4098) -> q_gen_4094
<cons, s>(q_gen_4119, q_gen_4117) -> q_gen_4094
<cons, s>(q_gen_4135, q_gen_4134) -> q_gen_4094
<nil, z>() -> q_gen_4094
<a, s>(q_gen_4166) -> q_gen_4099
<a, z>() -> q_gen_4099
<b, s>(q_gen_4166) -> q_gen_4099
<b, z>() -> q_gen_4099
<a, s>(q_gen_4120) -> q_gen_4119
<b, s>(q_gen_4120) -> q_gen_4119
<cons, s>(q_gen_4099, q_gen_4117) -> q_gen_4122
<cons, s>(q_gen_4099, q_gen_4134) -> q_gen_4122
<cons, s>(q_gen_4119, q_gen_4098) -> q_gen_4122
<cons, s>(q_gen_4119, q_gen_4134) -> q_gen_4122
<cons, s>(q_gen_4135, q_gen_4098) -> q_gen_4122
<cons, s>(q_gen_4135, q_gen_4117) -> q_gen_4122
<a, s>(q_gen_4136) -> q_gen_4135
<b, s>(q_gen_4136) -> q_gen_4135
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_4091, q_gen_4093, q_gen_4123},
Q_f={q_gen_4091},
Delta=
{
<s>(q_gen_4093) -> q_gen_4093
<z>() -> q_gen_4093
<s, s>(q_gen_4091) -> q_gen_4091
<z, s>(q_gen_4093) -> q_gen_4091
<z, z>() -> q_gen_4091
<s, s>(q_gen_4123) -> q_gen_4123
<s, z>(q_gen_4093) -> q_gen_4123
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 33
() -> length([nil, z]) -> 31
() -> leq([z, s(nn2)]) -> 31
() -> leq([z, z]) -> 31
(append([l1, l2, _aq]) /\ length([_aq, _bq]) /\ length([l1, _zp])) -> leq([_zp, _bq]) -> 33
(append([l1, l2, _dq]) /\ length([_dq, _eq]) /\ length([l2, _cq])) -> leq([_cq, _eq]) -> 31
(append([t1, l2, _qp])) -> append([cons(h1, t1), l2, cons(h1, _qp)]) -> 34
(length([ll, _vp])) -> length([cons(x, ll), s(_vp)]) -> 33
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 32
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 32
(leq([s(nn1), z])) -> BOT -> 32
}
Sat witness: Found: ((append([t1, l2, _qp])) -> append([cons(h1, t1), l2, cons(h1, _qp)]), {
_qp -> cons(b, cons(b, cons(a, nil)))  ;  h1 -> a  ;  l2 -> cons(b, nil)  ;  t1 -> cons(b, cons(b, nil))
})

-------------------------------------------
Step 53, which took 0.208665 s (model generation: 0.202048,  model checking: 0.006617):

Model:
|_
{
append -> 
{{{
Q={q_gen_4095, q_gen_4101, q_gen_4102, q_gen_4106, q_gen_4107, q_gen_4113, q_gen_4114, q_gen_4115, q_gen_4147},
Q_f={q_gen_4095},
Delta=
{
<cons>(q_gen_4114, q_gen_4113) -> q_gen_4113
<nil>() -> q_gen_4113
<a>() -> q_gen_4114
<b>() -> q_gen_4114
<nil, cons>(q_gen_4114, q_gen_4113) -> q_gen_4101
<nil, nil>() -> q_gen_4101
<b, b>() -> q_gen_4102
<cons, cons>(q_gen_4102, q_gen_4101) -> q_gen_4106
<cons, cons>(q_gen_4102, q_gen_4106) -> q_gen_4106
<cons, cons>(q_gen_4107, q_gen_4101) -> q_gen_4106
<a, a>() -> q_gen_4107
<b, a>() -> q_gen_4107
<cons, cons, cons>(q_gen_4115, q_gen_4095) -> q_gen_4095
<cons, cons, cons>(q_gen_4115, q_gen_4147) -> q_gen_4095
<cons, nil, cons>(q_gen_4102, q_gen_4101) -> q_gen_4095
<nil, cons, cons>(q_gen_4102, q_gen_4101) -> q_gen_4095
<nil, cons, cons>(q_gen_4102, q_gen_4106) -> q_gen_4095
<nil, cons, cons>(q_gen_4107, q_gen_4101) -> q_gen_4095
<nil, cons, cons>(q_gen_4107, q_gen_4106) -> q_gen_4095
<nil, nil, cons>(q_gen_4114, q_gen_4113) -> q_gen_4095
<nil, nil, nil>() -> q_gen_4095
<a, a, a>() -> q_gen_4115
<a, b, a>() -> q_gen_4115
<b, a, b>() -> q_gen_4115
<b, b, b>() -> q_gen_4115
<cons, nil, cons>(q_gen_4102, q_gen_4106) -> q_gen_4147
<cons, nil, cons>(q_gen_4107, q_gen_4101) -> q_gen_4147
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_4094, q_gen_4098, q_gen_4099, q_gen_4117, q_gen_4118, q_gen_4119, q_gen_4120, q_gen_4122, q_gen_4134, q_gen_4135, q_gen_4136},
Q_f={q_gen_4094},
Delta=
{
<nil>() -> q_gen_4098
<cons>(q_gen_4118, q_gen_4098) -> q_gen_4117
<a>() -> q_gen_4118
<b>() -> q_gen_4118
<z>() -> q_gen_4120
<cons>(q_gen_4118, q_gen_4117) -> q_gen_4134
<cons>(q_gen_4118, q_gen_4134) -> q_gen_4134
<s>(q_gen_4120) -> q_gen_4136
<s>(q_gen_4136) -> q_gen_4136
<cons, s>(q_gen_4099, q_gen_4098) -> q_gen_4094
<cons, s>(q_gen_4119, q_gen_4117) -> q_gen_4094
<cons, s>(q_gen_4135, q_gen_4134) -> q_gen_4094
<nil, z>() -> q_gen_4094
<a, z>() -> q_gen_4099
<b, z>() -> q_gen_4099
<a, s>(q_gen_4120) -> q_gen_4119
<b, s>(q_gen_4120) -> q_gen_4119
<cons, s>(q_gen_4099, q_gen_4134) -> q_gen_4122
<cons, s>(q_gen_4119, q_gen_4098) -> q_gen_4122
<cons, s>(q_gen_4119, q_gen_4134) -> q_gen_4122
<cons, s>(q_gen_4135, q_gen_4098) -> q_gen_4122
<cons, s>(q_gen_4135, q_gen_4117) -> q_gen_4122
<a, s>(q_gen_4136) -> q_gen_4135
<b, s>(q_gen_4136) -> q_gen_4135
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_4091, q_gen_4093, q_gen_4123},
Q_f={q_gen_4091},
Delta=
{
<s>(q_gen_4093) -> q_gen_4093
<z>() -> q_gen_4093
<s, s>(q_gen_4091) -> q_gen_4091
<z, s>(q_gen_4093) -> q_gen_4091
<z, z>() -> q_gen_4091
<s, s>(q_gen_4123) -> q_gen_4123
<s, z>(q_gen_4093) -> q_gen_4123
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 33
() -> length([nil, z]) -> 31
() -> leq([z, s(nn2)]) -> 31
() -> leq([z, z]) -> 31
(append([l1, l2, _aq]) /\ length([_aq, _bq]) /\ length([l1, _zp])) -> leq([_zp, _bq]) -> 33
(append([l1, l2, _dq]) /\ length([_dq, _eq]) /\ length([l2, _cq])) -> leq([_cq, _eq]) -> 34
(append([t1, l2, _qp])) -> append([cons(h1, t1), l2, cons(h1, _qp)]) -> 34
(length([ll, _vp])) -> length([cons(x, ll), s(_vp)]) -> 33
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 32
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 32
(leq([s(nn1), z])) -> BOT -> 32
}
Sat witness: Found: ((append([l1, l2, _dq]) /\ length([_dq, _eq]) /\ length([l2, _cq])) -> leq([_cq, _eq]), {
_cq -> s(s(s(s(z))))  ;  _dq -> cons(b, cons(b, cons(b, nil)))  ;  _eq -> s(s(s(z)))  ;  l1 -> cons(b, nil)  ;  l2 -> cons(b, cons(b, cons(b, nil)))
})

-------------------------------------------
Step 54, which took 0.181290 s (model generation: 0.172885,  model checking: 0.008405):

Model:
|_
{
append -> 
{{{
Q={q_gen_4095, q_gen_4101, q_gen_4102, q_gen_4113, q_gen_4114, q_gen_4115},
Q_f={q_gen_4095},
Delta=
{
<cons>(q_gen_4114, q_gen_4113) -> q_gen_4113
<nil>() -> q_gen_4113
<a>() -> q_gen_4114
<b>() -> q_gen_4114
<cons, cons>(q_gen_4102, q_gen_4101) -> q_gen_4101
<nil, cons>(q_gen_4114, q_gen_4113) -> q_gen_4101
<nil, nil>() -> q_gen_4101
<a, a>() -> q_gen_4102
<b, a>() -> q_gen_4102
<b, b>() -> q_gen_4102
<cons, cons, cons>(q_gen_4115, q_gen_4095) -> q_gen_4095
<cons, nil, cons>(q_gen_4102, q_gen_4101) -> q_gen_4095
<nil, cons, cons>(q_gen_4102, q_gen_4101) -> q_gen_4095
<nil, nil, cons>(q_gen_4114, q_gen_4113) -> q_gen_4095
<nil, nil, nil>() -> q_gen_4095
<a, a, a>() -> q_gen_4115
<a, b, a>() -> q_gen_4115
<b, a, b>() -> q_gen_4115
<b, b, b>() -> q_gen_4115
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_4094, q_gen_4098, q_gen_4099, q_gen_4117, q_gen_4118, q_gen_4119, q_gen_4120, q_gen_4122, q_gen_4134, q_gen_4135, q_gen_4136, q_gen_4164, q_gen_4165, q_gen_4166},
Q_f={q_gen_4094},
Delta=
{
<nil>() -> q_gen_4098
<cons>(q_gen_4118, q_gen_4098) -> q_gen_4117
<a>() -> q_gen_4118
<b>() -> q_gen_4118
<s>(q_gen_4166) -> q_gen_4120
<z>() -> q_gen_4120
<cons>(q_gen_4118, q_gen_4117) -> q_gen_4134
<s>(q_gen_4120) -> q_gen_4136
<cons>(q_gen_4118, q_gen_4134) -> q_gen_4164
<s>(q_gen_4136) -> q_gen_4166
<cons, s>(q_gen_4099, q_gen_4098) -> q_gen_4094
<cons, s>(q_gen_4099, q_gen_4164) -> q_gen_4094
<cons, s>(q_gen_4119, q_gen_4117) -> q_gen_4094
<cons, s>(q_gen_4135, q_gen_4134) -> q_gen_4094
<cons, s>(q_gen_4165, q_gen_4164) -> q_gen_4094
<nil, z>() -> q_gen_4094
<a, s>(q_gen_4166) -> q_gen_4099
<a, z>() -> q_gen_4099
<b, z>() -> q_gen_4099
<a, s>(q_gen_4120) -> q_gen_4119
<b, s>(q_gen_4120) -> q_gen_4119
<cons, s>(q_gen_4099, q_gen_4134) -> q_gen_4122
<cons, s>(q_gen_4119, q_gen_4098) -> q_gen_4122
<cons, s>(q_gen_4119, q_gen_4134) -> q_gen_4122
<cons, s>(q_gen_4135, q_gen_4098) -> q_gen_4122
<cons, s>(q_gen_4135, q_gen_4117) -> q_gen_4122
<cons, s>(q_gen_4165, q_gen_4098) -> q_gen_4122
<cons, s>(q_gen_4165, q_gen_4117) -> q_gen_4122
<cons, s>(q_gen_4165, q_gen_4134) -> q_gen_4122
<a, s>(q_gen_4136) -> q_gen_4135
<b, s>(q_gen_4136) -> q_gen_4135
<b, s>(q_gen_4166) -> q_gen_4165
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_4091, q_gen_4093, q_gen_4123},
Q_f={q_gen_4091},
Delta=
{
<s>(q_gen_4093) -> q_gen_4093
<z>() -> q_gen_4093
<s, s>(q_gen_4091) -> q_gen_4091
<z, s>(q_gen_4093) -> q_gen_4091
<z, z>() -> q_gen_4091
<s, s>(q_gen_4123) -> q_gen_4123
<s, z>(q_gen_4093) -> q_gen_4123
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 33
() -> length([nil, z]) -> 32
() -> leq([z, s(nn2)]) -> 32
() -> leq([z, z]) -> 32
(append([l1, l2, _aq]) /\ length([_aq, _bq]) /\ length([l1, _zp])) -> leq([_zp, _bq]) -> 33
(append([l1, l2, _dq]) /\ length([_dq, _eq]) /\ length([l2, _cq])) -> leq([_cq, _eq]) -> 34
(append([t1, l2, _qp])) -> append([cons(h1, t1), l2, cons(h1, _qp)]) -> 34
(length([ll, _vp])) -> length([cons(x, ll), s(_vp)]) -> 36
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 33
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 33
(leq([s(nn1), z])) -> BOT -> 33
}
Sat witness: Found: ((length([ll, _vp])) -> length([cons(x, ll), s(_vp)]), {
_vp -> s(z)  ;  ll -> cons(b, cons(b, cons(a, cons(b, nil))))  ;  x -> a
})

-------------------------------------------
Step 55, which took 0.190139 s (model generation: 0.187440,  model checking: 0.002699):

Model:
|_
{
append -> 
{{{
Q={q_gen_4095, q_gen_4101, q_gen_4102, q_gen_4112, q_gen_4113, q_gen_4114, q_gen_4115, q_gen_4126},
Q_f={q_gen_4095},
Delta=
{
<cons>(q_gen_4114, q_gen_4113) -> q_gen_4113
<nil>() -> q_gen_4113
<a>() -> q_gen_4114
<b>() -> q_gen_4114
<cons, cons>(q_gen_4102, q_gen_4101) -> q_gen_4101
<nil, nil>() -> q_gen_4101
<a, a>() -> q_gen_4102
<b, a>() -> q_gen_4102
<b, b>() -> q_gen_4102
<cons, cons>(q_gen_4102, q_gen_4126) -> q_gen_4126
<nil, cons>(q_gen_4114, q_gen_4113) -> q_gen_4126
<cons, cons, cons>(q_gen_4115, q_gen_4112) -> q_gen_4095
<cons, nil, cons>(q_gen_4102, q_gen_4101) -> q_gen_4095
<nil, cons, cons>(q_gen_4102, q_gen_4101) -> q_gen_4095
<nil, nil, nil>() -> q_gen_4095
<cons, cons, cons>(q_gen_4115, q_gen_4095) -> q_gen_4112
<cons, nil, cons>(q_gen_4102, q_gen_4126) -> q_gen_4112
<nil, cons, cons>(q_gen_4102, q_gen_4126) -> q_gen_4112
<nil, nil, cons>(q_gen_4114, q_gen_4113) -> q_gen_4112
<a, a, a>() -> q_gen_4115
<a, b, a>() -> q_gen_4115
<b, a, b>() -> q_gen_4115
<b, b, b>() -> q_gen_4115
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_4094, q_gen_4098, q_gen_4099, q_gen_4117, q_gen_4118, q_gen_4119, q_gen_4120, q_gen_4122, q_gen_4134, q_gen_4135, q_gen_4136, q_gen_4166},
Q_f={q_gen_4094},
Delta=
{
<cons>(q_gen_4118, q_gen_4134) -> q_gen_4098
<nil>() -> q_gen_4098
<cons>(q_gen_4118, q_gen_4098) -> q_gen_4117
<a>() -> q_gen_4118
<b>() -> q_gen_4118
<s>(q_gen_4166) -> q_gen_4120
<z>() -> q_gen_4120
<cons>(q_gen_4118, q_gen_4117) -> q_gen_4134
<s>(q_gen_4120) -> q_gen_4136
<s>(q_gen_4136) -> q_gen_4166
<cons, s>(q_gen_4099, q_gen_4098) -> q_gen_4094
<cons, s>(q_gen_4119, q_gen_4117) -> q_gen_4094
<cons, s>(q_gen_4135, q_gen_4134) -> q_gen_4094
<nil, z>() -> q_gen_4094
<a, s>(q_gen_4166) -> q_gen_4099
<a, z>() -> q_gen_4099
<b, s>(q_gen_4166) -> q_gen_4099
<b, z>() -> q_gen_4099
<a, s>(q_gen_4120) -> q_gen_4119
<b, s>(q_gen_4120) -> q_gen_4119
<cons, s>(q_gen_4099, q_gen_4117) -> q_gen_4122
<cons, s>(q_gen_4099, q_gen_4134) -> q_gen_4122
<cons, s>(q_gen_4119, q_gen_4098) -> q_gen_4122
<cons, s>(q_gen_4119, q_gen_4134) -> q_gen_4122
<cons, s>(q_gen_4135, q_gen_4098) -> q_gen_4122
<cons, s>(q_gen_4135, q_gen_4117) -> q_gen_4122
<a, s>(q_gen_4136) -> q_gen_4135
<b, s>(q_gen_4136) -> q_gen_4135
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_4091, q_gen_4093, q_gen_4123},
Q_f={q_gen_4091},
Delta=
{
<s>(q_gen_4093) -> q_gen_4093
<z>() -> q_gen_4093
<s, s>(q_gen_4091) -> q_gen_4091
<z, s>(q_gen_4093) -> q_gen_4091
<z, z>() -> q_gen_4091
<s, s>(q_gen_4123) -> q_gen_4123
<s, z>(q_gen_4093) -> q_gen_4123
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 33
() -> length([nil, z]) -> 33
() -> leq([z, s(nn2)]) -> 33
() -> leq([z, z]) -> 33
(append([l1, l2, _aq]) /\ length([_aq, _bq]) /\ length([l1, _zp])) -> leq([_zp, _bq]) -> 36
(append([l1, l2, _dq]) /\ length([_dq, _eq]) /\ length([l2, _cq])) -> leq([_cq, _eq]) -> 34
(append([t1, l2, _qp])) -> append([cons(h1, t1), l2, cons(h1, _qp)]) -> 34
(length([ll, _vp])) -> length([cons(x, ll), s(_vp)]) -> 36
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 34
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 34
(leq([s(nn1), z])) -> BOT -> 34
}
Sat witness: Found: ((append([l1, l2, _aq]) /\ length([_aq, _bq]) /\ length([l1, _zp])) -> leq([_zp, _bq]), {
_aq -> cons(b, cons(b, cons(b, cons(b, cons(b, nil)))))  ;  _bq -> s(s(z))  ;  _zp -> s(s(s(z)))  ;  l1 -> cons(b, cons(b, cons(b, nil)))  ;  l2 -> cons(b, cons(b, cons(b, nil)))
})

-------------------------------------------
Step 56, which took 0.250465 s (model generation: 0.245622,  model checking: 0.004843):

Model:
|_
{
append -> 
{{{
Q={q_gen_4095, q_gen_4101, q_gen_4102, q_gen_4113, q_gen_4114, q_gen_4115},
Q_f={q_gen_4095},
Delta=
{
<cons>(q_gen_4114, q_gen_4113) -> q_gen_4113
<nil>() -> q_gen_4113
<a>() -> q_gen_4114
<b>() -> q_gen_4114
<cons, cons>(q_gen_4102, q_gen_4101) -> q_gen_4101
<nil, cons>(q_gen_4114, q_gen_4113) -> q_gen_4101
<nil, nil>() -> q_gen_4101
<a, a>() -> q_gen_4102
<b, a>() -> q_gen_4102
<b, b>() -> q_gen_4102
<cons, cons, cons>(q_gen_4115, q_gen_4095) -> q_gen_4095
<cons, nil, cons>(q_gen_4102, q_gen_4101) -> q_gen_4095
<nil, cons, cons>(q_gen_4102, q_gen_4101) -> q_gen_4095
<nil, nil, cons>(q_gen_4114, q_gen_4113) -> q_gen_4095
<nil, nil, nil>() -> q_gen_4095
<a, a, a>() -> q_gen_4115
<a, b, a>() -> q_gen_4115
<b, a, b>() -> q_gen_4115
<b, b, b>() -> q_gen_4115
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_4094, q_gen_4098, q_gen_4099, q_gen_4117, q_gen_4118, q_gen_4119, q_gen_4120, q_gen_4122, q_gen_4134, q_gen_4135, q_gen_4136, q_gen_4164, q_gen_4165, q_gen_4166},
Q_f={q_gen_4094},
Delta=
{
<cons>(q_gen_4118, q_gen_4164) -> q_gen_4098
<nil>() -> q_gen_4098
<cons>(q_gen_4118, q_gen_4098) -> q_gen_4117
<a>() -> q_gen_4118
<b>() -> q_gen_4118
<z>() -> q_gen_4120
<cons>(q_gen_4118, q_gen_4117) -> q_gen_4134
<s>(q_gen_4120) -> q_gen_4136
<s>(q_gen_4166) -> q_gen_4136
<cons>(q_gen_4118, q_gen_4134) -> q_gen_4164
<s>(q_gen_4136) -> q_gen_4166
<cons, s>(q_gen_4099, q_gen_4098) -> q_gen_4094
<cons, s>(q_gen_4119, q_gen_4117) -> q_gen_4094
<cons, s>(q_gen_4135, q_gen_4134) -> q_gen_4094
<cons, s>(q_gen_4165, q_gen_4164) -> q_gen_4094
<nil, z>() -> q_gen_4094
<a, z>() -> q_gen_4099
<b, z>() -> q_gen_4099
<a, s>(q_gen_4120) -> q_gen_4119
<b, s>(q_gen_4120) -> q_gen_4119
<cons, s>(q_gen_4099, q_gen_4134) -> q_gen_4122
<cons, s>(q_gen_4099, q_gen_4164) -> q_gen_4122
<cons, s>(q_gen_4119, q_gen_4098) -> q_gen_4122
<cons, s>(q_gen_4119, q_gen_4134) -> q_gen_4122
<cons, s>(q_gen_4135, q_gen_4098) -> q_gen_4122
<cons, s>(q_gen_4135, q_gen_4117) -> q_gen_4122
<cons, s>(q_gen_4165, q_gen_4098) -> q_gen_4122
<cons, s>(q_gen_4165, q_gen_4117) -> q_gen_4122
<cons, s>(q_gen_4165, q_gen_4134) -> q_gen_4122
<a, s>(q_gen_4136) -> q_gen_4135
<b, s>(q_gen_4136) -> q_gen_4135
<a, s>(q_gen_4166) -> q_gen_4165
<b, s>(q_gen_4166) -> q_gen_4165
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_4091, q_gen_4093, q_gen_4123},
Q_f={q_gen_4091},
Delta=
{
<s>(q_gen_4093) -> q_gen_4093
<z>() -> q_gen_4093
<s, s>(q_gen_4091) -> q_gen_4091
<z, s>(q_gen_4093) -> q_gen_4091
<z, z>() -> q_gen_4091
<s, s>(q_gen_4123) -> q_gen_4123
<s, z>(q_gen_4093) -> q_gen_4123
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 34
() -> length([nil, z]) -> 34
() -> leq([z, s(nn2)]) -> 34
() -> leq([z, z]) -> 34
(append([l1, l2, _aq]) /\ length([_aq, _bq]) /\ length([l1, _zp])) -> leq([_zp, _bq]) -> 36
(append([l1, l2, _dq]) /\ length([_dq, _eq]) /\ length([l2, _cq])) -> leq([_cq, _eq]) -> 34
(append([t1, l2, _qp])) -> append([cons(h1, t1), l2, cons(h1, _qp)]) -> 37
(length([ll, _vp])) -> length([cons(x, ll), s(_vp)]) -> 36
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 35
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 35
(leq([s(nn1), z])) -> BOT -> 35
}
Sat witness: Found: ((append([t1, l2, _qp])) -> append([cons(h1, t1), l2, cons(h1, _qp)]), {
_qp -> cons(b, cons(a, nil))  ;  h1 -> a  ;  l2 -> cons(b, cons(a, nil))  ;  t1 -> nil
})

-------------------------------------------
Step 57, which took 0.226146 s (model generation: 0.221342,  model checking: 0.004804):

Model:
|_
{
append -> 
{{{
Q={q_gen_4095, q_gen_4101, q_gen_4102, q_gen_4107, q_gen_4112, q_gen_4113, q_gen_4114, q_gen_4115, q_gen_4126},
Q_f={q_gen_4095},
Delta=
{
<cons>(q_gen_4114, q_gen_4113) -> q_gen_4113
<nil>() -> q_gen_4113
<a>() -> q_gen_4114
<b>() -> q_gen_4114
<cons, cons>(q_gen_4107, q_gen_4101) -> q_gen_4101
<nil, nil>() -> q_gen_4101
<b, b>() -> q_gen_4102
<a, a>() -> q_gen_4107
<a, b>() -> q_gen_4107
<b, a>() -> q_gen_4107
<cons, cons>(q_gen_4102, q_gen_4101) -> q_gen_4126
<cons, cons>(q_gen_4102, q_gen_4126) -> q_gen_4126
<nil, cons>(q_gen_4114, q_gen_4113) -> q_gen_4126
<cons, cons, cons>(q_gen_4115, q_gen_4112) -> q_gen_4095
<cons, nil, cons>(q_gen_4102, q_gen_4101) -> q_gen_4095
<nil, cons, cons>(q_gen_4102, q_gen_4101) -> q_gen_4095
<nil, cons, cons>(q_gen_4102, q_gen_4126) -> q_gen_4095
<nil, cons, cons>(q_gen_4107, q_gen_4101) -> q_gen_4095
<nil, nil, nil>() -> q_gen_4095
<cons, cons, cons>(q_gen_4115, q_gen_4095) -> q_gen_4112
<cons, nil, cons>(q_gen_4102, q_gen_4126) -> q_gen_4112
<cons, nil, cons>(q_gen_4107, q_gen_4101) -> q_gen_4112
<nil, cons, cons>(q_gen_4107, q_gen_4126) -> q_gen_4112
<nil, nil, cons>(q_gen_4114, q_gen_4113) -> q_gen_4112
<a, a, a>() -> q_gen_4115
<a, b, a>() -> q_gen_4115
<b, a, b>() -> q_gen_4115
<b, b, b>() -> q_gen_4115
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_4094, q_gen_4098, q_gen_4099, q_gen_4117, q_gen_4118, q_gen_4119, q_gen_4120, q_gen_4122, q_gen_4134, q_gen_4135, q_gen_4136},
Q_f={q_gen_4094},
Delta=
{
<nil>() -> q_gen_4098
<cons>(q_gen_4118, q_gen_4098) -> q_gen_4117
<a>() -> q_gen_4118
<b>() -> q_gen_4118
<z>() -> q_gen_4120
<cons>(q_gen_4118, q_gen_4117) -> q_gen_4134
<cons>(q_gen_4118, q_gen_4134) -> q_gen_4134
<s>(q_gen_4120) -> q_gen_4136
<s>(q_gen_4136) -> q_gen_4136
<cons, s>(q_gen_4099, q_gen_4098) -> q_gen_4094
<cons, s>(q_gen_4119, q_gen_4117) -> q_gen_4094
<cons, s>(q_gen_4135, q_gen_4134) -> q_gen_4094
<nil, z>() -> q_gen_4094
<a, z>() -> q_gen_4099
<b, z>() -> q_gen_4099
<a, s>(q_gen_4120) -> q_gen_4119
<b, s>(q_gen_4120) -> q_gen_4119
<cons, s>(q_gen_4099, q_gen_4134) -> q_gen_4122
<cons, s>(q_gen_4119, q_gen_4098) -> q_gen_4122
<cons, s>(q_gen_4119, q_gen_4134) -> q_gen_4122
<cons, s>(q_gen_4135, q_gen_4098) -> q_gen_4122
<cons, s>(q_gen_4135, q_gen_4117) -> q_gen_4122
<a, s>(q_gen_4136) -> q_gen_4135
<b, s>(q_gen_4136) -> q_gen_4135
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_4091, q_gen_4093, q_gen_4123},
Q_f={q_gen_4091},
Delta=
{
<s>(q_gen_4093) -> q_gen_4093
<z>() -> q_gen_4093
<s, s>(q_gen_4091) -> q_gen_4091
<z, s>(q_gen_4093) -> q_gen_4091
<z, z>() -> q_gen_4091
<s, s>(q_gen_4123) -> q_gen_4123
<s, z>(q_gen_4093) -> q_gen_4123
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 34
() -> length([nil, z]) -> 34
() -> leq([z, s(nn2)]) -> 34
() -> leq([z, z]) -> 34
(append([l1, l2, _aq]) /\ length([_aq, _bq]) /\ length([l1, _zp])) -> leq([_zp, _bq]) -> 36
(append([l1, l2, _dq]) /\ length([_dq, _eq]) /\ length([l2, _cq])) -> leq([_cq, _eq]) -> 37
(append([t1, l2, _qp])) -> append([cons(h1, t1), l2, cons(h1, _qp)]) -> 37
(length([ll, _vp])) -> length([cons(x, ll), s(_vp)]) -> 36
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 35
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 35
(leq([s(nn1), z])) -> BOT -> 35
}
Sat witness: Found: ((append([l1, l2, _dq]) /\ length([_dq, _eq]) /\ length([l2, _cq])) -> leq([_cq, _eq]), {
_cq -> s(s(s(s(z))))  ;  _dq -> cons(b, cons(a, cons(b, cons(b, nil))))  ;  _eq -> s(s(s(z)))  ;  l1 -> cons(b, nil)  ;  l2 -> cons(b, cons(b, cons(b, nil)))
})

-------------------------------------------
Step 58, which took 0.363943 s (model generation: 0.358935,  model checking: 0.005008):

Model:
|_
{
append -> 
{{{
Q={q_gen_4095, q_gen_4101, q_gen_4102, q_gen_4113, q_gen_4114, q_gen_4115},
Q_f={q_gen_4095},
Delta=
{
<cons>(q_gen_4114, q_gen_4113) -> q_gen_4113
<nil>() -> q_gen_4113
<a>() -> q_gen_4114
<b>() -> q_gen_4114
<cons, cons>(q_gen_4102, q_gen_4101) -> q_gen_4101
<nil, cons>(q_gen_4114, q_gen_4113) -> q_gen_4101
<nil, nil>() -> q_gen_4101
<a, a>() -> q_gen_4102
<a, b>() -> q_gen_4102
<b, a>() -> q_gen_4102
<b, b>() -> q_gen_4102
<cons, cons, cons>(q_gen_4115, q_gen_4095) -> q_gen_4095
<cons, nil, cons>(q_gen_4102, q_gen_4101) -> q_gen_4095
<nil, cons, cons>(q_gen_4102, q_gen_4101) -> q_gen_4095
<nil, nil, cons>(q_gen_4114, q_gen_4113) -> q_gen_4095
<nil, nil, nil>() -> q_gen_4095
<a, a, a>() -> q_gen_4115
<a, b, a>() -> q_gen_4115
<b, a, b>() -> q_gen_4115
<b, b, b>() -> q_gen_4115
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_4094, q_gen_4098, q_gen_4099, q_gen_4117, q_gen_4118, q_gen_4119, q_gen_4120, q_gen_4122, q_gen_4134, q_gen_4135, q_gen_4136, q_gen_4164, q_gen_4165, q_gen_4166},
Q_f={q_gen_4094},
Delta=
{
<nil>() -> q_gen_4098
<cons>(q_gen_4118, q_gen_4098) -> q_gen_4117
<a>() -> q_gen_4118
<b>() -> q_gen_4118
<z>() -> q_gen_4120
<cons>(q_gen_4118, q_gen_4117) -> q_gen_4134
<s>(q_gen_4120) -> q_gen_4136
<s>(q_gen_4166) -> q_gen_4136
<cons>(q_gen_4118, q_gen_4134) -> q_gen_4164
<cons>(q_gen_4118, q_gen_4164) -> q_gen_4164
<s>(q_gen_4136) -> q_gen_4166
<cons, s>(q_gen_4099, q_gen_4098) -> q_gen_4094
<cons, s>(q_gen_4119, q_gen_4117) -> q_gen_4094
<cons, s>(q_gen_4135, q_gen_4134) -> q_gen_4094
<cons, s>(q_gen_4165, q_gen_4164) -> q_gen_4094
<nil, z>() -> q_gen_4094
<a, z>() -> q_gen_4099
<b, z>() -> q_gen_4099
<a, s>(q_gen_4120) -> q_gen_4119
<b, s>(q_gen_4120) -> q_gen_4119
<cons, s>(q_gen_4099, q_gen_4134) -> q_gen_4122
<cons, s>(q_gen_4099, q_gen_4164) -> q_gen_4122
<cons, s>(q_gen_4119, q_gen_4098) -> q_gen_4122
<cons, s>(q_gen_4119, q_gen_4134) -> q_gen_4122
<cons, s>(q_gen_4119, q_gen_4164) -> q_gen_4122
<cons, s>(q_gen_4135, q_gen_4098) -> q_gen_4122
<cons, s>(q_gen_4135, q_gen_4117) -> q_gen_4122
<cons, s>(q_gen_4135, q_gen_4164) -> q_gen_4122
<cons, s>(q_gen_4165, q_gen_4098) -> q_gen_4122
<cons, s>(q_gen_4165, q_gen_4117) -> q_gen_4122
<cons, s>(q_gen_4165, q_gen_4134) -> q_gen_4122
<a, s>(q_gen_4136) -> q_gen_4135
<b, s>(q_gen_4136) -> q_gen_4135
<a, s>(q_gen_4166) -> q_gen_4165
<b, s>(q_gen_4166) -> q_gen_4165
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_4091, q_gen_4093, q_gen_4123},
Q_f={q_gen_4091},
Delta=
{
<s>(q_gen_4093) -> q_gen_4093
<z>() -> q_gen_4093
<s, s>(q_gen_4091) -> q_gen_4091
<z, s>(q_gen_4093) -> q_gen_4091
<z, z>() -> q_gen_4091
<s, s>(q_gen_4123) -> q_gen_4123
<s, z>(q_gen_4093) -> q_gen_4123
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 35
() -> length([nil, z]) -> 35
() -> leq([z, s(nn2)]) -> 35
() -> leq([z, z]) -> 35
(append([l1, l2, _aq]) /\ length([_aq, _bq]) /\ length([l1, _zp])) -> leq([_zp, _bq]) -> 36
(append([l1, l2, _dq]) /\ length([_dq, _eq]) /\ length([l2, _cq])) -> leq([_cq, _eq]) -> 37
(append([t1, l2, _qp])) -> append([cons(h1, t1), l2, cons(h1, _qp)]) -> 37
(length([ll, _vp])) -> length([cons(x, ll), s(_vp)]) -> 39
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 36
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 36
(leq([s(nn1), z])) -> BOT -> 36
}
Sat witness: Found: ((length([ll, _vp])) -> length([cons(x, ll), s(_vp)]), {
_vp -> s(s(s(s(z))))  ;  ll -> cons(a, cons(b, cons(b, cons(a, cons(b, nil)))))  ;  x -> b
})

-------------------------------------------
Step 59, which took 0.345479 s (model generation: 0.344949,  model checking: 0.000530):

Model:
|_
{
append -> 
{{{
Q={q_gen_4095, q_gen_4101, q_gen_4102, q_gen_4107, q_gen_4112, q_gen_4113, q_gen_4114, q_gen_4115, q_gen_4126},
Q_f={q_gen_4095},
Delta=
{
<cons>(q_gen_4114, q_gen_4113) -> q_gen_4113
<nil>() -> q_gen_4113
<a>() -> q_gen_4114
<b>() -> q_gen_4114
<cons, cons>(q_gen_4107, q_gen_4101) -> q_gen_4101
<nil, nil>() -> q_gen_4101
<b, a>() -> q_gen_4102
<b, b>() -> q_gen_4102
<a, a>() -> q_gen_4107
<a, b>() -> q_gen_4107
<cons, cons>(q_gen_4102, q_gen_4101) -> q_gen_4126
<cons, cons>(q_gen_4102, q_gen_4126) -> q_gen_4126
<nil, cons>(q_gen_4114, q_gen_4113) -> q_gen_4126
<cons, cons, cons>(q_gen_4115, q_gen_4112) -> q_gen_4095
<cons, nil, cons>(q_gen_4102, q_gen_4101) -> q_gen_4095
<nil, cons, cons>(q_gen_4102, q_gen_4101) -> q_gen_4095
<nil, cons, cons>(q_gen_4102, q_gen_4126) -> q_gen_4095
<nil, cons, cons>(q_gen_4107, q_gen_4101) -> q_gen_4095
<nil, nil, nil>() -> q_gen_4095
<cons, cons, cons>(q_gen_4115, q_gen_4095) -> q_gen_4112
<cons, nil, cons>(q_gen_4102, q_gen_4126) -> q_gen_4112
<cons, nil, cons>(q_gen_4107, q_gen_4101) -> q_gen_4112
<nil, cons, cons>(q_gen_4107, q_gen_4126) -> q_gen_4112
<nil, nil, cons>(q_gen_4114, q_gen_4113) -> q_gen_4112
<a, a, a>() -> q_gen_4115
<a, b, a>() -> q_gen_4115
<b, a, b>() -> q_gen_4115
<b, b, b>() -> q_gen_4115
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_4094, q_gen_4098, q_gen_4099, q_gen_4117, q_gen_4118, q_gen_4119, q_gen_4120, q_gen_4122, q_gen_4134, q_gen_4135, q_gen_4136},
Q_f={q_gen_4094},
Delta=
{
<nil>() -> q_gen_4098
<cons>(q_gen_4118, q_gen_4098) -> q_gen_4117
<a>() -> q_gen_4118
<b>() -> q_gen_4118
<z>() -> q_gen_4120
<cons>(q_gen_4118, q_gen_4117) -> q_gen_4134
<cons>(q_gen_4118, q_gen_4134) -> q_gen_4134
<s>(q_gen_4120) -> q_gen_4136
<s>(q_gen_4136) -> q_gen_4136
<cons, s>(q_gen_4099, q_gen_4098) -> q_gen_4094
<cons, s>(q_gen_4119, q_gen_4117) -> q_gen_4094
<cons, s>(q_gen_4135, q_gen_4134) -> q_gen_4094
<nil, z>() -> q_gen_4094
<a, z>() -> q_gen_4099
<b, z>() -> q_gen_4099
<a, s>(q_gen_4120) -> q_gen_4119
<b, s>(q_gen_4120) -> q_gen_4119
<cons, s>(q_gen_4099, q_gen_4134) -> q_gen_4122
<cons, s>(q_gen_4119, q_gen_4098) -> q_gen_4122
<cons, s>(q_gen_4119, q_gen_4134) -> q_gen_4122
<cons, s>(q_gen_4135, q_gen_4098) -> q_gen_4122
<cons, s>(q_gen_4135, q_gen_4117) -> q_gen_4122
<a, s>(q_gen_4136) -> q_gen_4135
<b, s>(q_gen_4136) -> q_gen_4135
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_4091, q_gen_4093, q_gen_4123},
Q_f={q_gen_4091},
Delta=
{
<s>(q_gen_4093) -> q_gen_4093
<z>() -> q_gen_4093
<s, s>(q_gen_4091) -> q_gen_4091
<z, s>(q_gen_4093) -> q_gen_4091
<z, z>() -> q_gen_4091
<s, s>(q_gen_4123) -> q_gen_4123
<s, z>(q_gen_4093) -> q_gen_4123
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 38
() -> length([nil, z]) -> 36
() -> leq([z, s(nn2)]) -> 36
() -> leq([z, z]) -> 36
(append([l1, l2, _aq]) /\ length([_aq, _bq]) /\ length([l1, _zp])) -> leq([_zp, _bq]) -> 36
(append([l1, l2, _dq]) /\ length([_dq, _eq]) /\ length([l2, _cq])) -> leq([_cq, _eq]) -> 37
(append([t1, l2, _qp])) -> append([cons(h1, t1), l2, cons(h1, _qp)]) -> 37
(length([ll, _vp])) -> length([cons(x, ll), s(_vp)]) -> 39
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 36
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 36
(leq([s(nn1), z])) -> BOT -> 36
}
Sat witness: Found: (() -> append([nil, l2, l2]), {
l2 -> cons(a, cons(b, nil))
})

-------------------------------------------
Step 60, which took 0.389825 s (model generation: 0.384023,  model checking: 0.005802):

Model:
|_
{
append -> 
{{{
Q={q_gen_4095, q_gen_4101, q_gen_4102, q_gen_4113, q_gen_4114, q_gen_4115},
Q_f={q_gen_4095},
Delta=
{
<cons>(q_gen_4114, q_gen_4113) -> q_gen_4113
<nil>() -> q_gen_4113
<a>() -> q_gen_4114
<b>() -> q_gen_4114
<cons, cons>(q_gen_4102, q_gen_4101) -> q_gen_4101
<nil, cons>(q_gen_4114, q_gen_4113) -> q_gen_4101
<nil, nil>() -> q_gen_4101
<a, a>() -> q_gen_4102
<a, b>() -> q_gen_4102
<b, a>() -> q_gen_4102
<b, b>() -> q_gen_4102
<cons, cons, cons>(q_gen_4115, q_gen_4095) -> q_gen_4095
<cons, nil, cons>(q_gen_4102, q_gen_4101) -> q_gen_4095
<nil, cons, cons>(q_gen_4102, q_gen_4101) -> q_gen_4095
<nil, nil, cons>(q_gen_4114, q_gen_4113) -> q_gen_4095
<nil, nil, nil>() -> q_gen_4095
<a, a, a>() -> q_gen_4115
<a, b, a>() -> q_gen_4115
<b, a, b>() -> q_gen_4115
<b, b, b>() -> q_gen_4115
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_4094, q_gen_4098, q_gen_4099, q_gen_4117, q_gen_4118, q_gen_4119, q_gen_4120, q_gen_4122, q_gen_4134, q_gen_4135, q_gen_4136, q_gen_4164, q_gen_4165, q_gen_4166},
Q_f={q_gen_4094},
Delta=
{
<nil>() -> q_gen_4098
<cons>(q_gen_4118, q_gen_4098) -> q_gen_4117
<a>() -> q_gen_4118
<b>() -> q_gen_4118
<z>() -> q_gen_4120
<cons>(q_gen_4118, q_gen_4117) -> q_gen_4134
<cons>(q_gen_4118, q_gen_4164) -> q_gen_4134
<s>(q_gen_4120) -> q_gen_4136
<s>(q_gen_4166) -> q_gen_4136
<cons>(q_gen_4118, q_gen_4134) -> q_gen_4164
<s>(q_gen_4136) -> q_gen_4166
<cons, s>(q_gen_4099, q_gen_4098) -> q_gen_4094
<cons, s>(q_gen_4119, q_gen_4117) -> q_gen_4094
<cons, s>(q_gen_4119, q_gen_4164) -> q_gen_4094
<cons, s>(q_gen_4135, q_gen_4134) -> q_gen_4094
<cons, s>(q_gen_4165, q_gen_4164) -> q_gen_4094
<nil, z>() -> q_gen_4094
<a, z>() -> q_gen_4099
<b, z>() -> q_gen_4099
<a, s>(q_gen_4120) -> q_gen_4119
<a, s>(q_gen_4166) -> q_gen_4119
<b, s>(q_gen_4120) -> q_gen_4119
<cons, s>(q_gen_4099, q_gen_4134) -> q_gen_4122
<cons, s>(q_gen_4099, q_gen_4164) -> q_gen_4122
<cons, s>(q_gen_4119, q_gen_4098) -> q_gen_4122
<cons, s>(q_gen_4119, q_gen_4134) -> q_gen_4122
<cons, s>(q_gen_4135, q_gen_4098) -> q_gen_4122
<cons, s>(q_gen_4135, q_gen_4117) -> q_gen_4122
<cons, s>(q_gen_4135, q_gen_4164) -> q_gen_4122
<cons, s>(q_gen_4165, q_gen_4098) -> q_gen_4122
<cons, s>(q_gen_4165, q_gen_4117) -> q_gen_4122
<cons, s>(q_gen_4165, q_gen_4134) -> q_gen_4122
<a, s>(q_gen_4136) -> q_gen_4135
<b, s>(q_gen_4136) -> q_gen_4135
<b, s>(q_gen_4166) -> q_gen_4165
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_4091, q_gen_4093, q_gen_4123},
Q_f={q_gen_4091},
Delta=
{
<s>(q_gen_4093) -> q_gen_4093
<z>() -> q_gen_4093
<s, s>(q_gen_4091) -> q_gen_4091
<z, s>(q_gen_4093) -> q_gen_4091
<z, z>() -> q_gen_4091
<s, s>(q_gen_4123) -> q_gen_4123
<s, z>(q_gen_4093) -> q_gen_4123
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 38
() -> length([nil, z]) -> 36
() -> leq([z, s(nn2)]) -> 36
() -> leq([z, z]) -> 36
(append([l1, l2, _aq]) /\ length([_aq, _bq]) /\ length([l1, _zp])) -> leq([_zp, _bq]) -> 39
(append([l1, l2, _dq]) /\ length([_dq, _eq]) /\ length([l2, _cq])) -> leq([_cq, _eq]) -> 37
(append([t1, l2, _qp])) -> append([cons(h1, t1), l2, cons(h1, _qp)]) -> 37
(length([ll, _vp])) -> length([cons(x, ll), s(_vp)]) -> 39
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 37
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 37
(leq([s(nn1), z])) -> BOT -> 37
}
Sat witness: Found: ((append([l1, l2, _aq]) /\ length([_aq, _bq]) /\ length([l1, _zp])) -> leq([_zp, _bq]), {
_aq -> cons(b, cons(b, cons(b, cons(b, nil))))  ;  _bq -> s(s(z))  ;  _zp -> s(s(s(z)))  ;  l1 -> cons(b, cons(b, cons(b, nil)))  ;  l2 -> nil
})

-------------------------------------------
Step 61, which took 0.412720 s (model generation: 0.401806,  model checking: 0.010914):

Model:
|_
{
append -> 
{{{
Q={q_gen_4095, q_gen_4101, q_gen_4102, q_gen_4113, q_gen_4114, q_gen_4115},
Q_f={q_gen_4095},
Delta=
{
<cons>(q_gen_4114, q_gen_4113) -> q_gen_4113
<nil>() -> q_gen_4113
<a>() -> q_gen_4114
<b>() -> q_gen_4114
<cons, cons>(q_gen_4102, q_gen_4101) -> q_gen_4101
<nil, cons>(q_gen_4114, q_gen_4113) -> q_gen_4101
<nil, nil>() -> q_gen_4101
<a, a>() -> q_gen_4102
<a, b>() -> q_gen_4102
<b, a>() -> q_gen_4102
<b, b>() -> q_gen_4102
<cons, cons, cons>(q_gen_4115, q_gen_4095) -> q_gen_4095
<cons, nil, cons>(q_gen_4102, q_gen_4101) -> q_gen_4095
<nil, cons, cons>(q_gen_4102, q_gen_4101) -> q_gen_4095
<nil, nil, cons>(q_gen_4114, q_gen_4113) -> q_gen_4095
<nil, nil, nil>() -> q_gen_4095
<a, a, a>() -> q_gen_4115
<a, b, a>() -> q_gen_4115
<b, a, b>() -> q_gen_4115
<b, b, b>() -> q_gen_4115
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_4094, q_gen_4098, q_gen_4099, q_gen_4117, q_gen_4118, q_gen_4119, q_gen_4120, q_gen_4122, q_gen_4134, q_gen_4135, q_gen_4136, q_gen_4164, q_gen_4165, q_gen_4166},
Q_f={q_gen_4094},
Delta=
{
<nil>() -> q_gen_4098
<cons>(q_gen_4118, q_gen_4098) -> q_gen_4117
<a>() -> q_gen_4118
<b>() -> q_gen_4118
<z>() -> q_gen_4120
<cons>(q_gen_4118, q_gen_4117) -> q_gen_4134
<s>(q_gen_4120) -> q_gen_4136
<cons>(q_gen_4118, q_gen_4134) -> q_gen_4164
<cons>(q_gen_4118, q_gen_4164) -> q_gen_4164
<s>(q_gen_4136) -> q_gen_4166
<s>(q_gen_4166) -> q_gen_4166
<cons, s>(q_gen_4099, q_gen_4098) -> q_gen_4094
<cons, s>(q_gen_4119, q_gen_4117) -> q_gen_4094
<cons, s>(q_gen_4135, q_gen_4134) -> q_gen_4094
<cons, s>(q_gen_4135, q_gen_4164) -> q_gen_4094
<cons, s>(q_gen_4165, q_gen_4164) -> q_gen_4094
<nil, z>() -> q_gen_4094
<a, z>() -> q_gen_4099
<b, z>() -> q_gen_4099
<a, s>(q_gen_4120) -> q_gen_4119
<b, s>(q_gen_4120) -> q_gen_4119
<cons, s>(q_gen_4099, q_gen_4134) -> q_gen_4122
<cons, s>(q_gen_4099, q_gen_4164) -> q_gen_4122
<cons, s>(q_gen_4119, q_gen_4098) -> q_gen_4122
<cons, s>(q_gen_4119, q_gen_4134) -> q_gen_4122
<cons, s>(q_gen_4119, q_gen_4164) -> q_gen_4122
<cons, s>(q_gen_4135, q_gen_4098) -> q_gen_4122
<cons, s>(q_gen_4135, q_gen_4117) -> q_gen_4122
<cons, s>(q_gen_4165, q_gen_4098) -> q_gen_4122
<cons, s>(q_gen_4165, q_gen_4117) -> q_gen_4122
<cons, s>(q_gen_4165, q_gen_4134) -> q_gen_4122
<a, s>(q_gen_4136) -> q_gen_4135
<a, s>(q_gen_4166) -> q_gen_4135
<b, s>(q_gen_4136) -> q_gen_4135
<b, s>(q_gen_4166) -> q_gen_4165
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_4091, q_gen_4093, q_gen_4123},
Q_f={q_gen_4091},
Delta=
{
<s>(q_gen_4093) -> q_gen_4093
<z>() -> q_gen_4093
<s, s>(q_gen_4091) -> q_gen_4091
<z, s>(q_gen_4093) -> q_gen_4091
<z, z>() -> q_gen_4091
<s, s>(q_gen_4123) -> q_gen_4123
<s, z>(q_gen_4093) -> q_gen_4123
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 38
() -> length([nil, z]) -> 37
() -> leq([z, s(nn2)]) -> 37
() -> leq([z, z]) -> 37
(append([l1, l2, _aq]) /\ length([_aq, _bq]) /\ length([l1, _zp])) -> leq([_zp, _bq]) -> 39
(append([l1, l2, _dq]) /\ length([_dq, _eq]) /\ length([l2, _cq])) -> leq([_cq, _eq]) -> 40
(append([t1, l2, _qp])) -> append([cons(h1, t1), l2, cons(h1, _qp)]) -> 38
(length([ll, _vp])) -> length([cons(x, ll), s(_vp)]) -> 39
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 38
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 38
(leq([s(nn1), z])) -> BOT -> 38
}
Sat witness: Found: ((append([l1, l2, _dq]) /\ length([_dq, _eq]) /\ length([l2, _cq])) -> leq([_cq, _eq]), {
_cq -> s(s(s(s(z))))  ;  _dq -> cons(b, cons(b, cons(b, cons(b, nil))))  ;  _eq -> s(s(s(z)))  ;  l1 -> nil  ;  l2 -> cons(a, cons(b, cons(b, nil)))
})

-------------------------------------------
Step 62, which took 0.564069 s (model generation: 0.549146,  model checking: 0.014923):

Model:
|_
{
append -> 
{{{
Q={q_gen_4095, q_gen_4101, q_gen_4102, q_gen_4113, q_gen_4114, q_gen_4115},
Q_f={q_gen_4095},
Delta=
{
<cons>(q_gen_4114, q_gen_4113) -> q_gen_4113
<nil>() -> q_gen_4113
<a>() -> q_gen_4114
<b>() -> q_gen_4114
<cons, cons>(q_gen_4102, q_gen_4101) -> q_gen_4101
<nil, cons>(q_gen_4114, q_gen_4113) -> q_gen_4101
<nil, nil>() -> q_gen_4101
<a, a>() -> q_gen_4102
<a, b>() -> q_gen_4102
<b, a>() -> q_gen_4102
<b, b>() -> q_gen_4102
<cons, cons, cons>(q_gen_4115, q_gen_4095) -> q_gen_4095
<cons, nil, cons>(q_gen_4102, q_gen_4101) -> q_gen_4095
<nil, cons, cons>(q_gen_4102, q_gen_4101) -> q_gen_4095
<nil, nil, cons>(q_gen_4114, q_gen_4113) -> q_gen_4095
<nil, nil, nil>() -> q_gen_4095
<a, a, a>() -> q_gen_4115
<a, b, a>() -> q_gen_4115
<b, a, b>() -> q_gen_4115
<b, b, b>() -> q_gen_4115
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_4094, q_gen_4098, q_gen_4099, q_gen_4117, q_gen_4118, q_gen_4119, q_gen_4120, q_gen_4122, q_gen_4134, q_gen_4135, q_gen_4136, q_gen_4164, q_gen_4165, q_gen_4166},
Q_f={q_gen_4094},
Delta=
{
<nil>() -> q_gen_4098
<cons>(q_gen_4118, q_gen_4098) -> q_gen_4117
<a>() -> q_gen_4118
<b>() -> q_gen_4118
<z>() -> q_gen_4120
<cons>(q_gen_4118, q_gen_4117) -> q_gen_4134
<cons>(q_gen_4118, q_gen_4164) -> q_gen_4134
<s>(q_gen_4120) -> q_gen_4136
<s>(q_gen_4166) -> q_gen_4136
<cons>(q_gen_4118, q_gen_4134) -> q_gen_4164
<s>(q_gen_4136) -> q_gen_4166
<cons, s>(q_gen_4099, q_gen_4098) -> q_gen_4094
<cons, s>(q_gen_4119, q_gen_4117) -> q_gen_4094
<cons, s>(q_gen_4135, q_gen_4134) -> q_gen_4094
<cons, s>(q_gen_4165, q_gen_4164) -> q_gen_4094
<nil, z>() -> q_gen_4094
<a, z>() -> q_gen_4099
<b, z>() -> q_gen_4099
<a, s>(q_gen_4120) -> q_gen_4119
<b, s>(q_gen_4120) -> q_gen_4119
<cons, s>(q_gen_4099, q_gen_4134) -> q_gen_4122
<cons, s>(q_gen_4099, q_gen_4164) -> q_gen_4122
<cons, s>(q_gen_4119, q_gen_4098) -> q_gen_4122
<cons, s>(q_gen_4119, q_gen_4134) -> q_gen_4122
<cons, s>(q_gen_4119, q_gen_4164) -> q_gen_4122
<cons, s>(q_gen_4135, q_gen_4098) -> q_gen_4122
<cons, s>(q_gen_4135, q_gen_4117) -> q_gen_4122
<cons, s>(q_gen_4135, q_gen_4164) -> q_gen_4122
<cons, s>(q_gen_4165, q_gen_4098) -> q_gen_4122
<cons, s>(q_gen_4165, q_gen_4117) -> q_gen_4122
<cons, s>(q_gen_4165, q_gen_4134) -> q_gen_4122
<a, s>(q_gen_4136) -> q_gen_4135
<b, s>(q_gen_4136) -> q_gen_4135
<a, s>(q_gen_4166) -> q_gen_4165
<b, s>(q_gen_4166) -> q_gen_4165
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_4091, q_gen_4093, q_gen_4123},
Q_f={q_gen_4091},
Delta=
{
<s>(q_gen_4093) -> q_gen_4093
<z>() -> q_gen_4093
<s, s>(q_gen_4091) -> q_gen_4091
<z, s>(q_gen_4093) -> q_gen_4091
<z, z>() -> q_gen_4091
<s, s>(q_gen_4123) -> q_gen_4123
<s, z>(q_gen_4093) -> q_gen_4123
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 39
() -> length([nil, z]) -> 38
() -> leq([z, s(nn2)]) -> 38
() -> leq([z, z]) -> 38
(append([l1, l2, _aq]) /\ length([_aq, _bq]) /\ length([l1, _zp])) -> leq([_zp, _bq]) -> 42
(append([l1, l2, _dq]) /\ length([_dq, _eq]) /\ length([l2, _cq])) -> leq([_cq, _eq]) -> 40
(append([t1, l2, _qp])) -> append([cons(h1, t1), l2, cons(h1, _qp)]) -> 39
(length([ll, _vp])) -> length([cons(x, ll), s(_vp)]) -> 40
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 39
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 39
(leq([s(nn1), z])) -> BOT -> 39
}
Sat witness: Found: ((append([l1, l2, _aq]) /\ length([_aq, _bq]) /\ length([l1, _zp])) -> leq([_zp, _bq]), {
_aq -> cons(b, cons(b, cons(b, nil)))  ;  _bq -> s(s(s(z)))  ;  _zp -> s(s(s(s(s(z)))))  ;  l1 -> cons(b, cons(b, cons(b, nil)))  ;  l2 -> nil
})

-------------------------------------------
Step 63, which took 0.466454 s (model generation: 0.456590,  model checking: 0.009864):

Model:
|_
{
append -> 
{{{
Q={q_gen_4095, q_gen_4101, q_gen_4102, q_gen_4113, q_gen_4114, q_gen_4115},
Q_f={q_gen_4095},
Delta=
{
<cons>(q_gen_4114, q_gen_4113) -> q_gen_4113
<nil>() -> q_gen_4113
<a>() -> q_gen_4114
<b>() -> q_gen_4114
<cons, cons>(q_gen_4102, q_gen_4101) -> q_gen_4101
<nil, cons>(q_gen_4114, q_gen_4113) -> q_gen_4101
<nil, nil>() -> q_gen_4101
<a, a>() -> q_gen_4102
<a, b>() -> q_gen_4102
<b, a>() -> q_gen_4102
<b, b>() -> q_gen_4102
<cons, cons, cons>(q_gen_4115, q_gen_4095) -> q_gen_4095
<cons, nil, cons>(q_gen_4102, q_gen_4101) -> q_gen_4095
<nil, cons, cons>(q_gen_4102, q_gen_4101) -> q_gen_4095
<nil, nil, cons>(q_gen_4114, q_gen_4113) -> q_gen_4095
<nil, nil, nil>() -> q_gen_4095
<a, a, a>() -> q_gen_4115
<a, b, a>() -> q_gen_4115
<b, a, b>() -> q_gen_4115
<b, b, b>() -> q_gen_4115
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_4094, q_gen_4098, q_gen_4099, q_gen_4117, q_gen_4118, q_gen_4119, q_gen_4120, q_gen_4122, q_gen_4134, q_gen_4135, q_gen_4136, q_gen_4164, q_gen_4165, q_gen_4166},
Q_f={q_gen_4094},
Delta=
{
<nil>() -> q_gen_4098
<cons>(q_gen_4118, q_gen_4098) -> q_gen_4117
<a>() -> q_gen_4118
<b>() -> q_gen_4118
<s>(q_gen_4166) -> q_gen_4120
<z>() -> q_gen_4120
<cons>(q_gen_4118, q_gen_4117) -> q_gen_4134
<cons>(q_gen_4118, q_gen_4164) -> q_gen_4134
<s>(q_gen_4120) -> q_gen_4136
<cons>(q_gen_4118, q_gen_4134) -> q_gen_4164
<s>(q_gen_4136) -> q_gen_4166
<cons, s>(q_gen_4099, q_gen_4098) -> q_gen_4094
<cons, s>(q_gen_4119, q_gen_4117) -> q_gen_4094
<cons, s>(q_gen_4135, q_gen_4134) -> q_gen_4094
<cons, s>(q_gen_4165, q_gen_4164) -> q_gen_4094
<nil, z>() -> q_gen_4094
<a, z>() -> q_gen_4099
<b, z>() -> q_gen_4099
<a, s>(q_gen_4120) -> q_gen_4119
<b, s>(q_gen_4120) -> q_gen_4119
<cons, s>(q_gen_4099, q_gen_4134) -> q_gen_4122
<cons, s>(q_gen_4099, q_gen_4164) -> q_gen_4122
<cons, s>(q_gen_4119, q_gen_4098) -> q_gen_4122
<cons, s>(q_gen_4119, q_gen_4134) -> q_gen_4122
<cons, s>(q_gen_4119, q_gen_4164) -> q_gen_4122
<cons, s>(q_gen_4135, q_gen_4098) -> q_gen_4122
<cons, s>(q_gen_4135, q_gen_4117) -> q_gen_4122
<cons, s>(q_gen_4135, q_gen_4164) -> q_gen_4122
<cons, s>(q_gen_4165, q_gen_4098) -> q_gen_4122
<cons, s>(q_gen_4165, q_gen_4117) -> q_gen_4122
<cons, s>(q_gen_4165, q_gen_4134) -> q_gen_4122
<a, s>(q_gen_4136) -> q_gen_4135
<b, s>(q_gen_4136) -> q_gen_4135
<a, s>(q_gen_4166) -> q_gen_4165
<b, s>(q_gen_4166) -> q_gen_4165
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_4091, q_gen_4093, q_gen_4123},
Q_f={q_gen_4091},
Delta=
{
<s>(q_gen_4093) -> q_gen_4093
<z>() -> q_gen_4093
<s, s>(q_gen_4091) -> q_gen_4091
<z, s>(q_gen_4093) -> q_gen_4091
<z, z>() -> q_gen_4091
<s, s>(q_gen_4123) -> q_gen_4123
<s, z>(q_gen_4093) -> q_gen_4123
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 40
() -> length([nil, z]) -> 39
() -> leq([z, s(nn2)]) -> 39
() -> leq([z, z]) -> 39
(append([l1, l2, _aq]) /\ length([_aq, _bq]) /\ length([l1, _zp])) -> leq([_zp, _bq]) -> 42
(append([l1, l2, _dq]) /\ length([_dq, _eq]) /\ length([l2, _cq])) -> leq([_cq, _eq]) -> 40
(append([t1, l2, _qp])) -> append([cons(h1, t1), l2, cons(h1, _qp)]) -> 40
(length([ll, _vp])) -> length([cons(x, ll), s(_vp)]) -> 43
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 40
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 40
(leq([s(nn1), z])) -> BOT -> 40
}
Sat witness: Found: ((length([ll, _vp])) -> length([cons(x, ll), s(_vp)]), {
_vp -> s(s(s(s(z))))  ;  ll -> cons(a, cons(b, cons(a, cons(b, nil))))  ;  x -> b
})

-------------------------------------------
Step 64, which took 0.521945 s (model generation: 0.509119,  model checking: 0.012826):

Model:
|_
{
append -> 
{{{
Q={q_gen_4095, q_gen_4101, q_gen_4102, q_gen_4113, q_gen_4114, q_gen_4115},
Q_f={q_gen_4095},
Delta=
{
<cons>(q_gen_4114, q_gen_4113) -> q_gen_4113
<nil>() -> q_gen_4113
<a>() -> q_gen_4114
<b>() -> q_gen_4114
<cons, cons>(q_gen_4102, q_gen_4101) -> q_gen_4101
<nil, cons>(q_gen_4114, q_gen_4113) -> q_gen_4101
<nil, nil>() -> q_gen_4101
<a, a>() -> q_gen_4102
<a, b>() -> q_gen_4102
<b, a>() -> q_gen_4102
<b, b>() -> q_gen_4102
<cons, cons, cons>(q_gen_4115, q_gen_4095) -> q_gen_4095
<cons, nil, cons>(q_gen_4102, q_gen_4101) -> q_gen_4095
<nil, cons, cons>(q_gen_4102, q_gen_4101) -> q_gen_4095
<nil, nil, cons>(q_gen_4114, q_gen_4113) -> q_gen_4095
<nil, nil, nil>() -> q_gen_4095
<a, a, a>() -> q_gen_4115
<a, b, a>() -> q_gen_4115
<b, a, b>() -> q_gen_4115
<b, b, b>() -> q_gen_4115
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_4094, q_gen_4098, q_gen_4099, q_gen_4117, q_gen_4118, q_gen_4119, q_gen_4120, q_gen_4122, q_gen_4134, q_gen_4135, q_gen_4136, q_gen_4164, q_gen_4165, q_gen_4166},
Q_f={q_gen_4094},
Delta=
{
<nil>() -> q_gen_4098
<cons>(q_gen_4118, q_gen_4098) -> q_gen_4117
<a>() -> q_gen_4118
<b>() -> q_gen_4118
<z>() -> q_gen_4120
<cons>(q_gen_4118, q_gen_4117) -> q_gen_4134
<s>(q_gen_4120) -> q_gen_4136
<cons>(q_gen_4118, q_gen_4134) -> q_gen_4164
<cons>(q_gen_4118, q_gen_4164) -> q_gen_4164
<s>(q_gen_4136) -> q_gen_4166
<s>(q_gen_4166) -> q_gen_4166
<cons, s>(q_gen_4099, q_gen_4098) -> q_gen_4094
<cons, s>(q_gen_4119, q_gen_4117) -> q_gen_4094
<cons, s>(q_gen_4135, q_gen_4134) -> q_gen_4094
<cons, s>(q_gen_4135, q_gen_4164) -> q_gen_4094
<cons, s>(q_gen_4165, q_gen_4164) -> q_gen_4094
<nil, z>() -> q_gen_4094
<a, z>() -> q_gen_4099
<b, z>() -> q_gen_4099
<a, s>(q_gen_4120) -> q_gen_4119
<b, s>(q_gen_4120) -> q_gen_4119
<cons, s>(q_gen_4099, q_gen_4134) -> q_gen_4122
<cons, s>(q_gen_4099, q_gen_4164) -> q_gen_4122
<cons, s>(q_gen_4119, q_gen_4098) -> q_gen_4122
<cons, s>(q_gen_4119, q_gen_4134) -> q_gen_4122
<cons, s>(q_gen_4119, q_gen_4164) -> q_gen_4122
<cons, s>(q_gen_4135, q_gen_4098) -> q_gen_4122
<cons, s>(q_gen_4135, q_gen_4117) -> q_gen_4122
<cons, s>(q_gen_4165, q_gen_4098) -> q_gen_4122
<cons, s>(q_gen_4165, q_gen_4117) -> q_gen_4122
<cons, s>(q_gen_4165, q_gen_4134) -> q_gen_4122
<a, s>(q_gen_4136) -> q_gen_4135
<b, s>(q_gen_4136) -> q_gen_4135
<a, s>(q_gen_4166) -> q_gen_4165
<b, s>(q_gen_4166) -> q_gen_4165
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_4091, q_gen_4093, q_gen_4123},
Q_f={q_gen_4091},
Delta=
{
<s>(q_gen_4093) -> q_gen_4093
<z>() -> q_gen_4093
<s, s>(q_gen_4091) -> q_gen_4091
<z, s>(q_gen_4093) -> q_gen_4091
<z, z>() -> q_gen_4091
<s, s>(q_gen_4123) -> q_gen_4123
<s, z>(q_gen_4093) -> q_gen_4123
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 40
() -> length([nil, z]) -> 40
() -> leq([z, s(nn2)]) -> 40
() -> leq([z, z]) -> 40
(append([l1, l2, _aq]) /\ length([_aq, _bq]) /\ length([l1, _zp])) -> leq([_zp, _bq]) -> 42
(append([l1, l2, _dq]) /\ length([_dq, _eq]) /\ length([l2, _cq])) -> leq([_cq, _eq]) -> 43
(append([t1, l2, _qp])) -> append([cons(h1, t1), l2, cons(h1, _qp)]) -> 41
(length([ll, _vp])) -> length([cons(x, ll), s(_vp)]) -> 43
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 41
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 41
(leq([s(nn1), z])) -> BOT -> 41
}
Sat witness: Found: ((append([l1, l2, _dq]) /\ length([_dq, _eq]) /\ length([l2, _cq])) -> leq([_cq, _eq]), {
_cq -> s(s(s(s(z))))  ;  _dq -> cons(b, cons(b, cons(b, cons(b, cons(b, nil)))))  ;  _eq -> s(s(s(z)))  ;  l1 -> nil  ;  l2 -> cons(b, cons(b, cons(b, cons(b, nil))))
})

-------------------------------------------
Step 65, which took 0.440922 s (model generation: 0.428372,  model checking: 0.012550):

Model:
|_
{
append -> 
{{{
Q={q_gen_4095, q_gen_4101, q_gen_4102, q_gen_4113, q_gen_4114, q_gen_4115},
Q_f={q_gen_4095},
Delta=
{
<cons>(q_gen_4114, q_gen_4113) -> q_gen_4113
<nil>() -> q_gen_4113
<a>() -> q_gen_4114
<b>() -> q_gen_4114
<cons, cons>(q_gen_4102, q_gen_4101) -> q_gen_4101
<nil, cons>(q_gen_4114, q_gen_4113) -> q_gen_4101
<nil, nil>() -> q_gen_4101
<a, a>() -> q_gen_4102
<a, b>() -> q_gen_4102
<b, a>() -> q_gen_4102
<b, b>() -> q_gen_4102
<cons, cons, cons>(q_gen_4115, q_gen_4095) -> q_gen_4095
<cons, nil, cons>(q_gen_4102, q_gen_4101) -> q_gen_4095
<nil, cons, cons>(q_gen_4102, q_gen_4101) -> q_gen_4095
<nil, nil, cons>(q_gen_4114, q_gen_4113) -> q_gen_4095
<nil, nil, nil>() -> q_gen_4095
<a, a, a>() -> q_gen_4115
<a, b, a>() -> q_gen_4115
<b, a, b>() -> q_gen_4115
<b, b, b>() -> q_gen_4115
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_4094, q_gen_4098, q_gen_4099, q_gen_4117, q_gen_4118, q_gen_4119, q_gen_4120, q_gen_4122, q_gen_4134, q_gen_4135, q_gen_4136, q_gen_4164, q_gen_4165, q_gen_4166},
Q_f={q_gen_4094},
Delta=
{
<nil>() -> q_gen_4098
<cons>(q_gen_4118, q_gen_4098) -> q_gen_4117
<a>() -> q_gen_4118
<b>() -> q_gen_4118
<z>() -> q_gen_4120
<cons>(q_gen_4118, q_gen_4117) -> q_gen_4134
<s>(q_gen_4120) -> q_gen_4136
<cons>(q_gen_4118, q_gen_4134) -> q_gen_4164
<cons>(q_gen_4118, q_gen_4164) -> q_gen_4164
<s>(q_gen_4136) -> q_gen_4166
<s>(q_gen_4166) -> q_gen_4166
<cons, s>(q_gen_4099, q_gen_4098) -> q_gen_4094
<cons, s>(q_gen_4119, q_gen_4117) -> q_gen_4094
<cons, s>(q_gen_4135, q_gen_4134) -> q_gen_4094
<cons, s>(q_gen_4165, q_gen_4164) -> q_gen_4094
<nil, z>() -> q_gen_4094
<a, z>() -> q_gen_4099
<b, z>() -> q_gen_4099
<a, s>(q_gen_4120) -> q_gen_4119
<b, s>(q_gen_4120) -> q_gen_4119
<cons, s>(q_gen_4099, q_gen_4134) -> q_gen_4122
<cons, s>(q_gen_4099, q_gen_4164) -> q_gen_4122
<cons, s>(q_gen_4119, q_gen_4098) -> q_gen_4122
<cons, s>(q_gen_4119, q_gen_4134) -> q_gen_4122
<cons, s>(q_gen_4119, q_gen_4164) -> q_gen_4122
<cons, s>(q_gen_4135, q_gen_4098) -> q_gen_4122
<cons, s>(q_gen_4135, q_gen_4117) -> q_gen_4122
<cons, s>(q_gen_4135, q_gen_4164) -> q_gen_4122
<cons, s>(q_gen_4165, q_gen_4098) -> q_gen_4122
<cons, s>(q_gen_4165, q_gen_4117) -> q_gen_4122
<cons, s>(q_gen_4165, q_gen_4134) -> q_gen_4122
<a, s>(q_gen_4136) -> q_gen_4135
<b, s>(q_gen_4136) -> q_gen_4135
<a, s>(q_gen_4166) -> q_gen_4165
<b, s>(q_gen_4166) -> q_gen_4165
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_4091, q_gen_4093, q_gen_4123},
Q_f={q_gen_4091},
Delta=
{
<s>(q_gen_4093) -> q_gen_4093
<z>() -> q_gen_4093
<s, s>(q_gen_4091) -> q_gen_4091
<z, s>(q_gen_4093) -> q_gen_4091
<z, z>() -> q_gen_4091
<s, s>(q_gen_4123) -> q_gen_4123
<s, z>(q_gen_4093) -> q_gen_4123
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 41
() -> length([nil, z]) -> 41
() -> leq([z, s(nn2)]) -> 41
() -> leq([z, z]) -> 41
(append([l1, l2, _aq]) /\ length([_aq, _bq]) /\ length([l1, _zp])) -> leq([_zp, _bq]) -> 45
(append([l1, l2, _dq]) /\ length([_dq, _eq]) /\ length([l2, _cq])) -> leq([_cq, _eq]) -> 43
(append([t1, l2, _qp])) -> append([cons(h1, t1), l2, cons(h1, _qp)]) -> 42
(length([ll, _vp])) -> length([cons(x, ll), s(_vp)]) -> 43
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 42
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 42
(leq([s(nn1), z])) -> BOT -> 42
}
Sat witness: Found: ((append([l1, l2, _aq]) /\ length([_aq, _bq]) /\ length([l1, _zp])) -> leq([_zp, _bq]), {
_aq -> cons(b, cons(b, cons(b, cons(b, nil))))  ;  _bq -> s(s(s(s(z))))  ;  _zp -> s(s(s(s(s(z)))))  ;  l1 -> cons(b, cons(b, cons(b, cons(b, nil))))  ;  l2 -> nil
})

-------------------------------------------
Step 66, which took 0.653136 s (model generation: 0.639296,  model checking: 0.013840):

Model:
|_
{
append -> 
{{{
Q={q_gen_4095, q_gen_4101, q_gen_4102, q_gen_4113, q_gen_4114, q_gen_4115},
Q_f={q_gen_4095},
Delta=
{
<cons>(q_gen_4114, q_gen_4113) -> q_gen_4113
<nil>() -> q_gen_4113
<a>() -> q_gen_4114
<b>() -> q_gen_4114
<cons, cons>(q_gen_4102, q_gen_4101) -> q_gen_4101
<nil, cons>(q_gen_4114, q_gen_4113) -> q_gen_4101
<nil, nil>() -> q_gen_4101
<a, a>() -> q_gen_4102
<a, b>() -> q_gen_4102
<b, a>() -> q_gen_4102
<b, b>() -> q_gen_4102
<cons, cons, cons>(q_gen_4115, q_gen_4095) -> q_gen_4095
<cons, nil, cons>(q_gen_4102, q_gen_4101) -> q_gen_4095
<nil, cons, cons>(q_gen_4102, q_gen_4101) -> q_gen_4095
<nil, nil, cons>(q_gen_4114, q_gen_4113) -> q_gen_4095
<nil, nil, nil>() -> q_gen_4095
<a, a, a>() -> q_gen_4115
<a, b, a>() -> q_gen_4115
<b, a, b>() -> q_gen_4115
<b, b, b>() -> q_gen_4115
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_4094, q_gen_4098, q_gen_4099, q_gen_4117, q_gen_4118, q_gen_4119, q_gen_4120, q_gen_4122, q_gen_4134, q_gen_4135, q_gen_4136, q_gen_4145, q_gen_4146, q_gen_4165, q_gen_4166},
Q_f={q_gen_4094},
Delta=
{
<cons>(q_gen_4146, q_gen_4134) -> q_gen_4098
<nil>() -> q_gen_4098
<cons>(q_gen_4118, q_gen_4098) -> q_gen_4117
<b>() -> q_gen_4118
<z>() -> q_gen_4120
<cons>(q_gen_4118, q_gen_4117) -> q_gen_4134
<cons>(q_gen_4118, q_gen_4134) -> q_gen_4134
<s>(q_gen_4120) -> q_gen_4136
<cons>(q_gen_4118, q_gen_4145) -> q_gen_4145
<cons>(q_gen_4146, q_gen_4098) -> q_gen_4145
<cons>(q_gen_4146, q_gen_4117) -> q_gen_4145
<cons>(q_gen_4146, q_gen_4145) -> q_gen_4145
<a>() -> q_gen_4146
<s>(q_gen_4136) -> q_gen_4166
<s>(q_gen_4166) -> q_gen_4166
<cons, s>(q_gen_4099, q_gen_4098) -> q_gen_4094
<cons, s>(q_gen_4119, q_gen_4117) -> q_gen_4094
<cons, s>(q_gen_4119, q_gen_4145) -> q_gen_4094
<cons, s>(q_gen_4135, q_gen_4134) -> q_gen_4094
<cons, s>(q_gen_4165, q_gen_4145) -> q_gen_4094
<nil, z>() -> q_gen_4094
<a, z>() -> q_gen_4099
<b, z>() -> q_gen_4099
<a, s>(q_gen_4120) -> q_gen_4119
<a, s>(q_gen_4136) -> q_gen_4119
<a, s>(q_gen_4166) -> q_gen_4119
<b, s>(q_gen_4120) -> q_gen_4119
<cons, s>(q_gen_4099, q_gen_4134) -> q_gen_4122
<cons, s>(q_gen_4099, q_gen_4145) -> q_gen_4122
<cons, s>(q_gen_4119, q_gen_4098) -> q_gen_4122
<cons, s>(q_gen_4119, q_gen_4134) -> q_gen_4122
<cons, s>(q_gen_4135, q_gen_4098) -> q_gen_4122
<cons, s>(q_gen_4135, q_gen_4117) -> q_gen_4122
<cons, s>(q_gen_4135, q_gen_4145) -> q_gen_4122
<cons, s>(q_gen_4165, q_gen_4098) -> q_gen_4122
<cons, s>(q_gen_4165, q_gen_4117) -> q_gen_4122
<cons, s>(q_gen_4165, q_gen_4134) -> q_gen_4122
<b, s>(q_gen_4136) -> q_gen_4135
<b, s>(q_gen_4166) -> q_gen_4165
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_4091, q_gen_4093, q_gen_4123},
Q_f={q_gen_4091},
Delta=
{
<s>(q_gen_4093) -> q_gen_4093
<z>() -> q_gen_4093
<s, s>(q_gen_4091) -> q_gen_4091
<z, s>(q_gen_4093) -> q_gen_4091
<z, z>() -> q_gen_4091
<s, s>(q_gen_4123) -> q_gen_4123
<s, z>(q_gen_4093) -> q_gen_4123
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 42
() -> length([nil, z]) -> 42
() -> leq([z, s(nn2)]) -> 42
() -> leq([z, z]) -> 42
(append([l1, l2, _aq]) /\ length([_aq, _bq]) /\ length([l1, _zp])) -> leq([_zp, _bq]) -> 45
(append([l1, l2, _dq]) /\ length([_dq, _eq]) /\ length([l2, _cq])) -> leq([_cq, _eq]) -> 43
(append([t1, l2, _qp])) -> append([cons(h1, t1), l2, cons(h1, _qp)]) -> 43
(length([ll, _vp])) -> length([cons(x, ll), s(_vp)]) -> 46
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 43
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 43
(leq([s(nn1), z])) -> BOT -> 43
}
Sat witness: Found: ((length([ll, _vp])) -> length([cons(x, ll), s(_vp)]), {
_vp -> s(s(z))  ;  ll -> cons(b, cons(b, cons(a, nil)))  ;  x -> b
})

-------------------------------------------
Step 67, which took 0.575399 s (model generation: 0.559158,  model checking: 0.016241):

Model:
|_
{
append -> 
{{{
Q={q_gen_4095, q_gen_4101, q_gen_4102, q_gen_4113, q_gen_4114, q_gen_4115},
Q_f={q_gen_4095},
Delta=
{
<cons>(q_gen_4114, q_gen_4113) -> q_gen_4113
<nil>() -> q_gen_4113
<a>() -> q_gen_4114
<b>() -> q_gen_4114
<cons, cons>(q_gen_4102, q_gen_4101) -> q_gen_4101
<nil, cons>(q_gen_4114, q_gen_4113) -> q_gen_4101
<nil, nil>() -> q_gen_4101
<a, a>() -> q_gen_4102
<a, b>() -> q_gen_4102
<b, a>() -> q_gen_4102
<b, b>() -> q_gen_4102
<cons, cons, cons>(q_gen_4115, q_gen_4095) -> q_gen_4095
<cons, nil, cons>(q_gen_4102, q_gen_4101) -> q_gen_4095
<nil, cons, cons>(q_gen_4102, q_gen_4101) -> q_gen_4095
<nil, nil, cons>(q_gen_4114, q_gen_4113) -> q_gen_4095
<nil, nil, nil>() -> q_gen_4095
<a, a, a>() -> q_gen_4115
<a, b, a>() -> q_gen_4115
<b, a, b>() -> q_gen_4115
<b, b, b>() -> q_gen_4115
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_4094, q_gen_4098, q_gen_4099, q_gen_4117, q_gen_4118, q_gen_4119, q_gen_4120, q_gen_4122, q_gen_4134, q_gen_4135, q_gen_4136, q_gen_4145, q_gen_4146, q_gen_4154, q_gen_4166},
Q_f={q_gen_4094},
Delta=
{
<nil>() -> q_gen_4098
<cons>(q_gen_4118, q_gen_4098) -> q_gen_4117
<b>() -> q_gen_4118
<z>() -> q_gen_4120
<cons>(q_gen_4118, q_gen_4117) -> q_gen_4134
<cons>(q_gen_4118, q_gen_4134) -> q_gen_4134
<cons>(q_gen_4118, q_gen_4145) -> q_gen_4134
<s>(q_gen_4120) -> q_gen_4136
<cons>(q_gen_4146, q_gen_4098) -> q_gen_4145
<cons>(q_gen_4146, q_gen_4117) -> q_gen_4145
<cons>(q_gen_4146, q_gen_4134) -> q_gen_4145
<cons>(q_gen_4146, q_gen_4145) -> q_gen_4145
<a>() -> q_gen_4146
<s>(q_gen_4136) -> q_gen_4166
<s>(q_gen_4166) -> q_gen_4166
<cons, s>(q_gen_4099, q_gen_4098) -> q_gen_4094
<cons, s>(q_gen_4119, q_gen_4117) -> q_gen_4094
<cons, s>(q_gen_4119, q_gen_4145) -> q_gen_4094
<cons, s>(q_gen_4135, q_gen_4134) -> q_gen_4094
<cons, s>(q_gen_4154, q_gen_4145) -> q_gen_4094
<nil, z>() -> q_gen_4094
<a, z>() -> q_gen_4099
<b, z>() -> q_gen_4099
<a, s>(q_gen_4120) -> q_gen_4119
<a, s>(q_gen_4166) -> q_gen_4119
<b, s>(q_gen_4120) -> q_gen_4119
<cons, s>(q_gen_4099, q_gen_4134) -> q_gen_4122
<cons, s>(q_gen_4119, q_gen_4098) -> q_gen_4122
<cons, s>(q_gen_4119, q_gen_4134) -> q_gen_4122
<cons, s>(q_gen_4135, q_gen_4098) -> q_gen_4122
<cons, s>(q_gen_4135, q_gen_4117) -> q_gen_4122
<cons, s>(q_gen_4135, q_gen_4145) -> q_gen_4122
<cons, s>(q_gen_4154, q_gen_4098) -> q_gen_4122
<cons, s>(q_gen_4154, q_gen_4117) -> q_gen_4122
<cons, s>(q_gen_4154, q_gen_4134) -> q_gen_4122
<b, s>(q_gen_4136) -> q_gen_4135
<a, s>(q_gen_4136) -> q_gen_4154
<b, s>(q_gen_4166) -> q_gen_4154
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_4091, q_gen_4093, q_gen_4123},
Q_f={q_gen_4091},
Delta=
{
<s>(q_gen_4093) -> q_gen_4093
<z>() -> q_gen_4093
<s, s>(q_gen_4091) -> q_gen_4091
<z, s>(q_gen_4093) -> q_gen_4091
<z, z>() -> q_gen_4091
<s, s>(q_gen_4123) -> q_gen_4123
<s, z>(q_gen_4093) -> q_gen_4123
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 43
() -> length([nil, z]) -> 43
() -> leq([z, s(nn2)]) -> 43
() -> leq([z, z]) -> 43
(append([l1, l2, _aq]) /\ length([_aq, _bq]) /\ length([l1, _zp])) -> leq([_zp, _bq]) -> 45
(append([l1, l2, _dq]) /\ length([_dq, _eq]) /\ length([l2, _cq])) -> leq([_cq, _eq]) -> 46
(append([t1, l2, _qp])) -> append([cons(h1, t1), l2, cons(h1, _qp)]) -> 44
(length([ll, _vp])) -> length([cons(x, ll), s(_vp)]) -> 46
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 44
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 44
(leq([s(nn1), z])) -> BOT -> 44
}
Sat witness: Found: ((append([l1, l2, _dq]) /\ length([_dq, _eq]) /\ length([l2, _cq])) -> leq([_cq, _eq]), {
_cq -> s(s(s(s(z))))  ;  _dq -> cons(b, cons(b, cons(b, nil)))  ;  _eq -> s(s(s(z)))  ;  l1 -> cons(b, nil)  ;  l2 -> cons(a, cons(b, nil))
})

-------------------------------------------
Step 68, which took 0.714622 s (model generation: 0.697984,  model checking: 0.016638):

Model:
|_
{
append -> 
{{{
Q={q_gen_4095, q_gen_4101, q_gen_4102, q_gen_4113, q_gen_4114, q_gen_4115},
Q_f={q_gen_4095},
Delta=
{
<cons>(q_gen_4114, q_gen_4113) -> q_gen_4113
<nil>() -> q_gen_4113
<a>() -> q_gen_4114
<b>() -> q_gen_4114
<cons, cons>(q_gen_4102, q_gen_4101) -> q_gen_4101
<nil, cons>(q_gen_4114, q_gen_4113) -> q_gen_4101
<nil, nil>() -> q_gen_4101
<a, a>() -> q_gen_4102
<a, b>() -> q_gen_4102
<b, a>() -> q_gen_4102
<b, b>() -> q_gen_4102
<cons, cons, cons>(q_gen_4115, q_gen_4095) -> q_gen_4095
<cons, nil, cons>(q_gen_4102, q_gen_4101) -> q_gen_4095
<nil, cons, cons>(q_gen_4102, q_gen_4101) -> q_gen_4095
<nil, nil, cons>(q_gen_4114, q_gen_4113) -> q_gen_4095
<nil, nil, nil>() -> q_gen_4095
<a, a, a>() -> q_gen_4115
<a, b, a>() -> q_gen_4115
<b, a, b>() -> q_gen_4115
<b, b, b>() -> q_gen_4115
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_4094, q_gen_4098, q_gen_4099, q_gen_4117, q_gen_4118, q_gen_4119, q_gen_4120, q_gen_4122, q_gen_4134, q_gen_4135, q_gen_4136, q_gen_4145, q_gen_4146, q_gen_4165, q_gen_4166},
Q_f={q_gen_4094},
Delta=
{
<nil>() -> q_gen_4098
<cons>(q_gen_4118, q_gen_4098) -> q_gen_4117
<b>() -> q_gen_4118
<s>(q_gen_4166) -> q_gen_4120
<z>() -> q_gen_4120
<cons>(q_gen_4118, q_gen_4117) -> q_gen_4134
<cons>(q_gen_4118, q_gen_4134) -> q_gen_4134
<s>(q_gen_4120) -> q_gen_4136
<cons>(q_gen_4118, q_gen_4145) -> q_gen_4145
<cons>(q_gen_4146, q_gen_4098) -> q_gen_4145
<cons>(q_gen_4146, q_gen_4117) -> q_gen_4145
<cons>(q_gen_4146, q_gen_4134) -> q_gen_4145
<cons>(q_gen_4146, q_gen_4145) -> q_gen_4145
<a>() -> q_gen_4146
<s>(q_gen_4136) -> q_gen_4166
<cons, s>(q_gen_4099, q_gen_4098) -> q_gen_4094
<cons, s>(q_gen_4099, q_gen_4117) -> q_gen_4094
<cons, s>(q_gen_4099, q_gen_4145) -> q_gen_4094
<cons, s>(q_gen_4119, q_gen_4117) -> q_gen_4094
<cons, s>(q_gen_4119, q_gen_4145) -> q_gen_4094
<cons, s>(q_gen_4135, q_gen_4134) -> q_gen_4094
<cons, s>(q_gen_4135, q_gen_4145) -> q_gen_4094
<cons, s>(q_gen_4165, q_gen_4145) -> q_gen_4094
<nil, z>() -> q_gen_4094
<a, s>(q_gen_4136) -> q_gen_4099
<a, z>() -> q_gen_4099
<b, z>() -> q_gen_4099
<a, s>(q_gen_4120) -> q_gen_4119
<b, s>(q_gen_4120) -> q_gen_4119
<cons, s>(q_gen_4099, q_gen_4134) -> q_gen_4122
<cons, s>(q_gen_4119, q_gen_4098) -> q_gen_4122
<cons, s>(q_gen_4119, q_gen_4134) -> q_gen_4122
<cons, s>(q_gen_4135, q_gen_4098) -> q_gen_4122
<cons, s>(q_gen_4135, q_gen_4117) -> q_gen_4122
<cons, s>(q_gen_4165, q_gen_4098) -> q_gen_4122
<cons, s>(q_gen_4165, q_gen_4117) -> q_gen_4122
<cons, s>(q_gen_4165, q_gen_4134) -> q_gen_4122
<b, s>(q_gen_4136) -> q_gen_4135
<a, s>(q_gen_4166) -> q_gen_4165
<b, s>(q_gen_4166) -> q_gen_4165
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_4091, q_gen_4093, q_gen_4123},
Q_f={q_gen_4091},
Delta=
{
<s>(q_gen_4093) -> q_gen_4093
<z>() -> q_gen_4093
<s, s>(q_gen_4091) -> q_gen_4091
<z, s>(q_gen_4093) -> q_gen_4091
<z, z>() -> q_gen_4091
<s, s>(q_gen_4123) -> q_gen_4123
<s, z>(q_gen_4093) -> q_gen_4123
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 44
() -> length([nil, z]) -> 44
() -> leq([z, s(nn2)]) -> 44
() -> leq([z, z]) -> 44
(append([l1, l2, _aq]) /\ length([_aq, _bq]) /\ length([l1, _zp])) -> leq([_zp, _bq]) -> 48
(append([l1, l2, _dq]) /\ length([_dq, _eq]) /\ length([l2, _cq])) -> leq([_cq, _eq]) -> 46
(append([t1, l2, _qp])) -> append([cons(h1, t1), l2, cons(h1, _qp)]) -> 45
(length([ll, _vp])) -> length([cons(x, ll), s(_vp)]) -> 46
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 45
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 45
(leq([s(nn1), z])) -> BOT -> 45
}
Sat witness: Found: ((append([l1, l2, _aq]) /\ length([_aq, _bq]) /\ length([l1, _zp])) -> leq([_zp, _bq]), {
_aq -> cons(b, cons(b, cons(b, nil)))  ;  _bq -> s(s(s(z)))  ;  _zp -> s(s(s(s(s(s(z))))))  ;  l1 -> cons(a, nil)  ;  l2 -> nil
})

-------------------------------------------
Step 69, which took 1.632003 s (model generation: 1.628548,  model checking: 0.003455):

Model:
|_
{
append -> 
{{{
Q={q_gen_4095, q_gen_4101, q_gen_4102, q_gen_4105, q_gen_4106, q_gen_4113, q_gen_4114, q_gen_4115, q_gen_4121},
Q_f={q_gen_4095, q_gen_4105},
Delta=
{
<cons>(q_gen_4114, q_gen_4113) -> q_gen_4113
<nil>() -> q_gen_4113
<a>() -> q_gen_4114
<b>() -> q_gen_4114
<nil, nil>() -> q_gen_4101
<a, a>() -> q_gen_4102
<a, b>() -> q_gen_4102
<b, a>() -> q_gen_4102
<b, b>() -> q_gen_4102
<cons, cons>(q_gen_4102, q_gen_4101) -> q_gen_4106
<cons, cons>(q_gen_4102, q_gen_4106) -> q_gen_4106
<nil, cons>(q_gen_4114, q_gen_4113) -> q_gen_4106
<cons, cons, cons>(q_gen_4115, q_gen_4105) -> q_gen_4095
<cons, nil, cons>(q_gen_4102, q_gen_4101) -> q_gen_4095
<nil, cons, cons>(q_gen_4102, q_gen_4101) -> q_gen_4095
<nil, nil, nil>() -> q_gen_4095
<cons, nil, cons>(q_gen_4102, q_gen_4106) -> q_gen_4105
<nil, cons, cons>(q_gen_4102, q_gen_4106) -> q_gen_4105
<nil, nil, cons>(q_gen_4114, q_gen_4113) -> q_gen_4105
<a, a, a>() -> q_gen_4115
<a, b, a>() -> q_gen_4115
<b, a, b>() -> q_gen_4115
<b, b, b>() -> q_gen_4115
<cons, cons, cons>(q_gen_4115, q_gen_4095) -> q_gen_4121
<cons, cons, cons>(q_gen_4115, q_gen_4121) -> q_gen_4121
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_4094, q_gen_4098, q_gen_4099, q_gen_4117, q_gen_4118, q_gen_4119, q_gen_4120, q_gen_4122, q_gen_4134, q_gen_4135, q_gen_4136, q_gen_4166},
Q_f={q_gen_4094},
Delta=
{
<cons>(q_gen_4118, q_gen_4134) -> q_gen_4098
<nil>() -> q_gen_4098
<cons>(q_gen_4118, q_gen_4098) -> q_gen_4117
<a>() -> q_gen_4118
<b>() -> q_gen_4118
<s>(q_gen_4166) -> q_gen_4120
<z>() -> q_gen_4120
<cons>(q_gen_4118, q_gen_4117) -> q_gen_4134
<s>(q_gen_4120) -> q_gen_4136
<s>(q_gen_4136) -> q_gen_4166
<cons, s>(q_gen_4099, q_gen_4098) -> q_gen_4094
<cons, s>(q_gen_4119, q_gen_4117) -> q_gen_4094
<cons, s>(q_gen_4135, q_gen_4134) -> q_gen_4094
<nil, z>() -> q_gen_4094
<a, s>(q_gen_4166) -> q_gen_4099
<a, z>() -> q_gen_4099
<b, s>(q_gen_4166) -> q_gen_4099
<b, z>() -> q_gen_4099
<a, s>(q_gen_4120) -> q_gen_4119
<b, s>(q_gen_4120) -> q_gen_4119
<cons, s>(q_gen_4099, q_gen_4117) -> q_gen_4122
<cons, s>(q_gen_4099, q_gen_4134) -> q_gen_4122
<cons, s>(q_gen_4119, q_gen_4098) -> q_gen_4122
<cons, s>(q_gen_4119, q_gen_4134) -> q_gen_4122
<cons, s>(q_gen_4135, q_gen_4098) -> q_gen_4122
<cons, s>(q_gen_4135, q_gen_4117) -> q_gen_4122
<a, s>(q_gen_4136) -> q_gen_4135
<b, s>(q_gen_4136) -> q_gen_4135
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_4091, q_gen_4093, q_gen_4123},
Q_f={q_gen_4091},
Delta=
{
<s>(q_gen_4093) -> q_gen_4093
<z>() -> q_gen_4093
<s, s>(q_gen_4091) -> q_gen_4091
<z, s>(q_gen_4093) -> q_gen_4091
<z, z>() -> q_gen_4091
<s, s>(q_gen_4123) -> q_gen_4123
<s, z>(q_gen_4093) -> q_gen_4123
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 45
() -> length([nil, z]) -> 45
() -> leq([z, s(nn2)]) -> 45
() -> leq([z, z]) -> 45
(append([l1, l2, _aq]) /\ length([_aq, _bq]) /\ length([l1, _zp])) -> leq([_zp, _bq]) -> 48
(append([l1, l2, _dq]) /\ length([_dq, _eq]) /\ length([l2, _cq])) -> leq([_cq, _eq]) -> 46
(append([t1, l2, _qp])) -> append([cons(h1, t1), l2, cons(h1, _qp)]) -> 48
(length([ll, _vp])) -> length([cons(x, ll), s(_vp)]) -> 46
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 46
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 46
(leq([s(nn1), z])) -> BOT -> 46
}
Sat witness: Found: ((append([t1, l2, _qp])) -> append([cons(h1, t1), l2, cons(h1, _qp)]), {
_qp -> cons(b, cons(b, cons(b, nil)))  ;  h1 -> a  ;  l2 -> cons(a, cons(b, nil))  ;  t1 -> cons(b, nil)
})

-------------------------------------------
Step 70, which took 2.015641 s (model generation: 2.010575,  model checking: 0.005066):

Model:
|_
{
append -> 
{{{
Q={q_gen_4095, q_gen_4100, q_gen_4101, q_gen_4102, q_gen_4112, q_gen_4113, q_gen_4114, q_gen_4115, q_gen_4126},
Q_f={q_gen_4095, q_gen_4100},
Delta=
{
<cons>(q_gen_4114, q_gen_4113) -> q_gen_4113
<nil>() -> q_gen_4113
<a>() -> q_gen_4114
<b>() -> q_gen_4114
<cons, cons>(q_gen_4102, q_gen_4101) -> q_gen_4101
<nil, nil>() -> q_gen_4101
<a, a>() -> q_gen_4102
<a, b>() -> q_gen_4102
<b, a>() -> q_gen_4102
<b, b>() -> q_gen_4102
<cons, cons>(q_gen_4102, q_gen_4126) -> q_gen_4126
<nil, cons>(q_gen_4114, q_gen_4113) -> q_gen_4126
<cons, cons, cons>(q_gen_4115, q_gen_4112) -> q_gen_4095
<cons, nil, cons>(q_gen_4102, q_gen_4126) -> q_gen_4095
<nil, cons, cons>(q_gen_4102, q_gen_4101) -> q_gen_4095
<nil, cons, cons>(q_gen_4102, q_gen_4126) -> q_gen_4095
<nil, nil, nil>() -> q_gen_4095
<cons, cons, cons>(q_gen_4115, q_gen_4095) -> q_gen_4100
<cons, nil, cons>(q_gen_4102, q_gen_4101) -> q_gen_4100
<cons, cons, cons>(q_gen_4115, q_gen_4100) -> q_gen_4112
<nil, nil, cons>(q_gen_4114, q_gen_4113) -> q_gen_4112
<a, a, a>() -> q_gen_4115
<a, b, a>() -> q_gen_4115
<b, a, b>() -> q_gen_4115
<b, b, b>() -> q_gen_4115
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_4094, q_gen_4098, q_gen_4099, q_gen_4117, q_gen_4118, q_gen_4119, q_gen_4120, q_gen_4122, q_gen_4134, q_gen_4135, q_gen_4136, q_gen_4166},
Q_f={q_gen_4094},
Delta=
{
<cons>(q_gen_4118, q_gen_4134) -> q_gen_4098
<nil>() -> q_gen_4098
<cons>(q_gen_4118, q_gen_4098) -> q_gen_4117
<a>() -> q_gen_4118
<b>() -> q_gen_4118
<s>(q_gen_4166) -> q_gen_4120
<z>() -> q_gen_4120
<cons>(q_gen_4118, q_gen_4117) -> q_gen_4134
<s>(q_gen_4120) -> q_gen_4136
<s>(q_gen_4136) -> q_gen_4166
<cons, s>(q_gen_4099, q_gen_4098) -> q_gen_4094
<cons, s>(q_gen_4119, q_gen_4117) -> q_gen_4094
<cons, s>(q_gen_4135, q_gen_4134) -> q_gen_4094
<nil, z>() -> q_gen_4094
<a, s>(q_gen_4166) -> q_gen_4099
<a, z>() -> q_gen_4099
<b, s>(q_gen_4166) -> q_gen_4099
<b, z>() -> q_gen_4099
<a, s>(q_gen_4120) -> q_gen_4119
<b, s>(q_gen_4120) -> q_gen_4119
<cons, s>(q_gen_4099, q_gen_4117) -> q_gen_4122
<cons, s>(q_gen_4099, q_gen_4134) -> q_gen_4122
<cons, s>(q_gen_4119, q_gen_4098) -> q_gen_4122
<cons, s>(q_gen_4119, q_gen_4134) -> q_gen_4122
<cons, s>(q_gen_4135, q_gen_4098) -> q_gen_4122
<cons, s>(q_gen_4135, q_gen_4117) -> q_gen_4122
<a, s>(q_gen_4136) -> q_gen_4135
<b, s>(q_gen_4136) -> q_gen_4135
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_4091, q_gen_4093, q_gen_4123},
Q_f={q_gen_4091},
Delta=
{
<s>(q_gen_4093) -> q_gen_4093
<z>() -> q_gen_4093
<s, s>(q_gen_4091) -> q_gen_4091
<z, s>(q_gen_4093) -> q_gen_4091
<z, z>() -> q_gen_4091
<s, s>(q_gen_4123) -> q_gen_4123
<s, z>(q_gen_4093) -> q_gen_4123
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 46
() -> length([nil, z]) -> 46
() -> leq([z, s(nn2)]) -> 46
() -> leq([z, z]) -> 46
(append([l1, l2, _aq]) /\ length([_aq, _bq]) /\ length([l1, _zp])) -> leq([_zp, _bq]) -> 48
(append([l1, l2, _dq]) /\ length([_dq, _eq]) /\ length([l2, _cq])) -> leq([_cq, _eq]) -> 49
(append([t1, l2, _qp])) -> append([cons(h1, t1), l2, cons(h1, _qp)]) -> 48
(length([ll, _vp])) -> length([cons(x, ll), s(_vp)]) -> 47
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 47
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 47
(leq([s(nn1), z])) -> BOT -> 47
}
Sat witness: Found: ((append([l1, l2, _dq]) /\ length([_dq, _eq]) /\ length([l2, _cq])) -> leq([_cq, _eq]), {
_cq -> s(s(s(s(z))))  ;  _dq -> cons(b, nil)  ;  _eq -> s(z)  ;  l1 -> cons(b, nil)  ;  l2 -> cons(b, nil)
})

-------------------------------------------
Step 71, which took 1.869855 s (model generation: 1.866582,  model checking: 0.003273):

Model:
|_
{
append -> 
{{{
Q={q_gen_4095, q_gen_4101, q_gen_4102, q_gen_4113, q_gen_4114, q_gen_4115},
Q_f={q_gen_4095},
Delta=
{
<cons>(q_gen_4114, q_gen_4113) -> q_gen_4113
<nil>() -> q_gen_4113
<a>() -> q_gen_4114
<b>() -> q_gen_4114
<cons, cons>(q_gen_4102, q_gen_4101) -> q_gen_4101
<nil, cons>(q_gen_4114, q_gen_4113) -> q_gen_4101
<nil, nil>() -> q_gen_4101
<a, a>() -> q_gen_4102
<a, b>() -> q_gen_4102
<b, a>() -> q_gen_4102
<b, b>() -> q_gen_4102
<cons, cons, cons>(q_gen_4115, q_gen_4095) -> q_gen_4095
<cons, nil, cons>(q_gen_4102, q_gen_4101) -> q_gen_4095
<nil, cons, cons>(q_gen_4102, q_gen_4101) -> q_gen_4095
<nil, nil, cons>(q_gen_4114, q_gen_4113) -> q_gen_4095
<nil, nil, nil>() -> q_gen_4095
<a, a, a>() -> q_gen_4115
<a, b, a>() -> q_gen_4115
<b, a, b>() -> q_gen_4115
<b, b, b>() -> q_gen_4115
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_4094, q_gen_4098, q_gen_4099, q_gen_4117, q_gen_4118, q_gen_4119, q_gen_4120, q_gen_4122, q_gen_4134, q_gen_4135, q_gen_4136, q_gen_4145, q_gen_4146, q_gen_4154, q_gen_4166},
Q_f={q_gen_4094},
Delta=
{
<cons>(q_gen_4118, q_gen_4145) -> q_gen_4098
<nil>() -> q_gen_4098
<cons>(q_gen_4118, q_gen_4098) -> q_gen_4117
<cons>(q_gen_4146, q_gen_4134) -> q_gen_4117
<b>() -> q_gen_4118
<s>(q_gen_4166) -> q_gen_4120
<z>() -> q_gen_4120
<cons>(q_gen_4118, q_gen_4117) -> q_gen_4134
<cons>(q_gen_4118, q_gen_4134) -> q_gen_4134
<s>(q_gen_4120) -> q_gen_4136
<cons>(q_gen_4146, q_gen_4098) -> q_gen_4145
<cons>(q_gen_4146, q_gen_4117) -> q_gen_4145
<cons>(q_gen_4146, q_gen_4145) -> q_gen_4145
<a>() -> q_gen_4146
<s>(q_gen_4136) -> q_gen_4166
<cons, s>(q_gen_4099, q_gen_4098) -> q_gen_4094
<cons, s>(q_gen_4119, q_gen_4117) -> q_gen_4094
<cons, s>(q_gen_4119, q_gen_4145) -> q_gen_4094
<cons, s>(q_gen_4135, q_gen_4134) -> q_gen_4094
<cons, s>(q_gen_4154, q_gen_4145) -> q_gen_4094
<nil, z>() -> q_gen_4094
<a, s>(q_gen_4166) -> q_gen_4099
<a, z>() -> q_gen_4099
<b, z>() -> q_gen_4099
<a, s>(q_gen_4120) -> q_gen_4119
<b, s>(q_gen_4120) -> q_gen_4119
<cons, s>(q_gen_4099, q_gen_4117) -> q_gen_4122
<cons, s>(q_gen_4099, q_gen_4134) -> q_gen_4122
<cons, s>(q_gen_4119, q_gen_4098) -> q_gen_4122
<cons, s>(q_gen_4119, q_gen_4134) -> q_gen_4122
<cons, s>(q_gen_4135, q_gen_4098) -> q_gen_4122
<cons, s>(q_gen_4135, q_gen_4117) -> q_gen_4122
<cons, s>(q_gen_4135, q_gen_4145) -> q_gen_4122
<cons, s>(q_gen_4154, q_gen_4098) -> q_gen_4122
<cons, s>(q_gen_4154, q_gen_4117) -> q_gen_4122
<cons, s>(q_gen_4154, q_gen_4134) -> q_gen_4122
<b, s>(q_gen_4136) -> q_gen_4135
<a, s>(q_gen_4136) -> q_gen_4154
<b, s>(q_gen_4166) -> q_gen_4154
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_4091, q_gen_4093, q_gen_4123},
Q_f={q_gen_4091},
Delta=
{
<s>(q_gen_4093) -> q_gen_4093
<z>() -> q_gen_4093
<s, s>(q_gen_4091) -> q_gen_4091
<z, s>(q_gen_4093) -> q_gen_4091
<z, z>() -> q_gen_4091
<s, s>(q_gen_4123) -> q_gen_4123
<s, z>(q_gen_4093) -> q_gen_4123
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 47
() -> length([nil, z]) -> 47
() -> leq([z, s(nn2)]) -> 47
() -> leq([z, z]) -> 47
(append([l1, l2, _aq]) /\ length([_aq, _bq]) /\ length([l1, _zp])) -> leq([_zp, _bq]) -> 48
(append([l1, l2, _dq]) /\ length([_dq, _eq]) /\ length([l2, _cq])) -> leq([_cq, _eq]) -> 49
(append([t1, l2, _qp])) -> append([cons(h1, t1), l2, cons(h1, _qp)]) -> 48
(length([ll, _vp])) -> length([cons(x, ll), s(_vp)]) -> 50
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 48
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 48
(leq([s(nn1), z])) -> BOT -> 48
}
Sat witness: Found: ((length([ll, _vp])) -> length([cons(x, ll), s(_vp)]), {
_vp -> s(s(s(z)))  ;  ll -> cons(b, cons(b, cons(b, nil)))  ;  x -> a
})

-------------------------------------------
Step 72, which took 1.733174 s (model generation: 1.730752,  model checking: 0.002422):

Model:
|_
{
append -> 
{{{
Q={q_gen_4095, q_gen_4101, q_gen_4102, q_gen_4111, q_gen_4112, q_gen_4113, q_gen_4114, q_gen_4115, q_gen_4126},
Q_f={q_gen_4095, q_gen_4111},
Delta=
{
<cons>(q_gen_4114, q_gen_4113) -> q_gen_4113
<nil>() -> q_gen_4113
<a>() -> q_gen_4114
<b>() -> q_gen_4114
<cons, cons>(q_gen_4102, q_gen_4101) -> q_gen_4101
<nil, nil>() -> q_gen_4101
<a, a>() -> q_gen_4102
<a, b>() -> q_gen_4102
<b, a>() -> q_gen_4102
<b, b>() -> q_gen_4102
<cons, cons>(q_gen_4102, q_gen_4126) -> q_gen_4126
<nil, cons>(q_gen_4114, q_gen_4113) -> q_gen_4126
<cons, cons, cons>(q_gen_4115, q_gen_4111) -> q_gen_4095
<cons, nil, cons>(q_gen_4102, q_gen_4101) -> q_gen_4095
<nil, cons, cons>(q_gen_4102, q_gen_4101) -> q_gen_4095
<nil, nil, nil>() -> q_gen_4095
<cons, cons, cons>(q_gen_4115, q_gen_4112) -> q_gen_4111
<cons, nil, cons>(q_gen_4102, q_gen_4126) -> q_gen_4111
<cons, cons, cons>(q_gen_4115, q_gen_4095) -> q_gen_4112
<nil, cons, cons>(q_gen_4102, q_gen_4126) -> q_gen_4112
<nil, nil, cons>(q_gen_4114, q_gen_4113) -> q_gen_4112
<a, a, a>() -> q_gen_4115
<a, b, a>() -> q_gen_4115
<b, a, b>() -> q_gen_4115
<b, b, b>() -> q_gen_4115
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_4094, q_gen_4098, q_gen_4099, q_gen_4117, q_gen_4118, q_gen_4119, q_gen_4120, q_gen_4122, q_gen_4134, q_gen_4135, q_gen_4136, q_gen_4166},
Q_f={q_gen_4094},
Delta=
{
<cons>(q_gen_4118, q_gen_4134) -> q_gen_4098
<nil>() -> q_gen_4098
<cons>(q_gen_4118, q_gen_4098) -> q_gen_4117
<a>() -> q_gen_4118
<b>() -> q_gen_4118
<s>(q_gen_4166) -> q_gen_4120
<z>() -> q_gen_4120
<cons>(q_gen_4118, q_gen_4117) -> q_gen_4134
<s>(q_gen_4120) -> q_gen_4136
<s>(q_gen_4136) -> q_gen_4166
<cons, s>(q_gen_4099, q_gen_4098) -> q_gen_4094
<cons, s>(q_gen_4119, q_gen_4117) -> q_gen_4094
<cons, s>(q_gen_4135, q_gen_4134) -> q_gen_4094
<nil, z>() -> q_gen_4094
<a, s>(q_gen_4166) -> q_gen_4099
<a, z>() -> q_gen_4099
<b, s>(q_gen_4166) -> q_gen_4099
<b, z>() -> q_gen_4099
<a, s>(q_gen_4120) -> q_gen_4119
<b, s>(q_gen_4120) -> q_gen_4119
<cons, s>(q_gen_4099, q_gen_4117) -> q_gen_4122
<cons, s>(q_gen_4099, q_gen_4134) -> q_gen_4122
<cons, s>(q_gen_4119, q_gen_4098) -> q_gen_4122
<cons, s>(q_gen_4119, q_gen_4134) -> q_gen_4122
<cons, s>(q_gen_4135, q_gen_4098) -> q_gen_4122
<cons, s>(q_gen_4135, q_gen_4117) -> q_gen_4122
<a, s>(q_gen_4136) -> q_gen_4135
<b, s>(q_gen_4136) -> q_gen_4135
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_4091, q_gen_4093, q_gen_4123},
Q_f={q_gen_4091},
Delta=
{
<s>(q_gen_4093) -> q_gen_4093
<z>() -> q_gen_4093
<s, s>(q_gen_4091) -> q_gen_4091
<z, s>(q_gen_4093) -> q_gen_4091
<z, z>() -> q_gen_4091
<s, s>(q_gen_4123) -> q_gen_4123
<s, z>(q_gen_4093) -> q_gen_4123
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 48
() -> length([nil, z]) -> 48
() -> leq([z, s(nn2)]) -> 48
() -> leq([z, z]) -> 48
(append([l1, l2, _aq]) /\ length([_aq, _bq]) /\ length([l1, _zp])) -> leq([_zp, _bq]) -> 48
(append([l1, l2, _dq]) /\ length([_dq, _eq]) /\ length([l2, _cq])) -> leq([_cq, _eq]) -> 49
(append([t1, l2, _qp])) -> append([cons(h1, t1), l2, cons(h1, _qp)]) -> 51
(length([ll, _vp])) -> length([cons(x, ll), s(_vp)]) -> 50
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 49
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 49
(leq([s(nn1), z])) -> BOT -> 49
}
Sat witness: Found: ((append([t1, l2, _qp])) -> append([cons(h1, t1), l2, cons(h1, _qp)]), {
_qp -> cons(b, cons(a, cons(a, nil)))  ;  h1 -> b  ;  l2 -> cons(b, cons(a, cons(b, nil)))  ;  t1 -> cons(b, cons(a, nil))
})

-------------------------------------------
Step 73, which took 2.519025 s (model generation: 2.516366,  model checking: 0.002659):

Model:
|_
{
append -> 
{{{
Q={q_gen_4095, q_gen_4101, q_gen_4102, q_gen_4105, q_gen_4106, q_gen_4112, q_gen_4113, q_gen_4114, q_gen_4115},
Q_f={q_gen_4095, q_gen_4105},
Delta=
{
<cons>(q_gen_4114, q_gen_4113) -> q_gen_4113
<nil>() -> q_gen_4113
<a>() -> q_gen_4114
<b>() -> q_gen_4114
<nil, nil>() -> q_gen_4101
<a, a>() -> q_gen_4102
<a, b>() -> q_gen_4102
<b, a>() -> q_gen_4102
<b, b>() -> q_gen_4102
<cons, cons>(q_gen_4102, q_gen_4101) -> q_gen_4106
<cons, cons>(q_gen_4102, q_gen_4106) -> q_gen_4106
<nil, cons>(q_gen_4114, q_gen_4113) -> q_gen_4106
<cons, cons, cons>(q_gen_4115, q_gen_4105) -> q_gen_4095
<cons, nil, cons>(q_gen_4102, q_gen_4101) -> q_gen_4095
<nil, nil, nil>() -> q_gen_4095
<cons, cons, cons>(q_gen_4115, q_gen_4112) -> q_gen_4105
<cons, nil, cons>(q_gen_4102, q_gen_4106) -> q_gen_4105
<nil, cons, cons>(q_gen_4102, q_gen_4101) -> q_gen_4105
<nil, cons, cons>(q_gen_4102, q_gen_4106) -> q_gen_4105
<cons, cons, cons>(q_gen_4115, q_gen_4095) -> q_gen_4112
<nil, nil, cons>(q_gen_4114, q_gen_4113) -> q_gen_4112
<a, a, a>() -> q_gen_4115
<a, b, a>() -> q_gen_4115
<b, a, b>() -> q_gen_4115
<b, b, b>() -> q_gen_4115
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_4094, q_gen_4098, q_gen_4099, q_gen_4117, q_gen_4118, q_gen_4119, q_gen_4120, q_gen_4122, q_gen_4134, q_gen_4135, q_gen_4136, q_gen_4166},
Q_f={q_gen_4094},
Delta=
{
<cons>(q_gen_4118, q_gen_4134) -> q_gen_4098
<nil>() -> q_gen_4098
<cons>(q_gen_4118, q_gen_4098) -> q_gen_4117
<a>() -> q_gen_4118
<b>() -> q_gen_4118
<s>(q_gen_4166) -> q_gen_4120
<z>() -> q_gen_4120
<cons>(q_gen_4118, q_gen_4117) -> q_gen_4134
<s>(q_gen_4120) -> q_gen_4136
<s>(q_gen_4136) -> q_gen_4166
<cons, s>(q_gen_4099, q_gen_4098) -> q_gen_4094
<cons, s>(q_gen_4119, q_gen_4117) -> q_gen_4094
<cons, s>(q_gen_4135, q_gen_4134) -> q_gen_4094
<nil, z>() -> q_gen_4094
<a, s>(q_gen_4166) -> q_gen_4099
<a, z>() -> q_gen_4099
<b, s>(q_gen_4166) -> q_gen_4099
<b, z>() -> q_gen_4099
<a, s>(q_gen_4120) -> q_gen_4119
<b, s>(q_gen_4120) -> q_gen_4119
<cons, s>(q_gen_4099, q_gen_4117) -> q_gen_4122
<cons, s>(q_gen_4099, q_gen_4134) -> q_gen_4122
<cons, s>(q_gen_4119, q_gen_4098) -> q_gen_4122
<cons, s>(q_gen_4119, q_gen_4134) -> q_gen_4122
<cons, s>(q_gen_4135, q_gen_4098) -> q_gen_4122
<cons, s>(q_gen_4135, q_gen_4117) -> q_gen_4122
<a, s>(q_gen_4136) -> q_gen_4135
<b, s>(q_gen_4136) -> q_gen_4135
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_4091, q_gen_4093, q_gen_4123},
Q_f={q_gen_4091},
Delta=
{
<s>(q_gen_4093) -> q_gen_4093
<z>() -> q_gen_4093
<s, s>(q_gen_4091) -> q_gen_4091
<z, s>(q_gen_4093) -> q_gen_4091
<z, z>() -> q_gen_4091
<s, s>(q_gen_4123) -> q_gen_4123
<s, z>(q_gen_4093) -> q_gen_4123
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 48
() -> length([nil, z]) -> 48
() -> leq([z, s(nn2)]) -> 48
() -> leq([z, z]) -> 48
(append([l1, l2, _aq]) /\ length([_aq, _bq]) /\ length([l1, _zp])) -> leq([_zp, _bq]) -> 51
(append([l1, l2, _dq]) /\ length([_dq, _eq]) /\ length([l2, _cq])) -> leq([_cq, _eq]) -> 49
(append([t1, l2, _qp])) -> append([cons(h1, t1), l2, cons(h1, _qp)]) -> 51
(length([ll, _vp])) -> length([cons(x, ll), s(_vp)]) -> 50
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 49
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 49
(leq([s(nn1), z])) -> BOT -> 49
}
Sat witness: Found: ((append([l1, l2, _aq]) /\ length([_aq, _bq]) /\ length([l1, _zp])) -> leq([_zp, _bq]), {
_aq -> cons(b, cons(b, cons(b, nil)))  ;  _bq -> s(s(s(z)))  ;  _zp -> s(s(s(s(z))))  ;  l1 -> cons(b, nil)  ;  l2 -> cons(a, nil)
})

-------------------------------------------
Step 74, which took 5.374545 s (model generation: 5.369506,  model checking: 0.005039):

Model:
|_
{
append -> 
{{{
Q={q_gen_4095, q_gen_4101, q_gen_4102, q_gen_4112, q_gen_4113, q_gen_4114, q_gen_4115, q_gen_4126, q_gen_4182},
Q_f={q_gen_4095},
Delta=
{
<nil>() -> q_gen_4113
<a>() -> q_gen_4114
<b>() -> q_gen_4114
<cons>(q_gen_4114, q_gen_4113) -> q_gen_4182
<cons, cons>(q_gen_4102, q_gen_4101) -> q_gen_4101
<nil, nil>() -> q_gen_4101
<a, a>() -> q_gen_4102
<a, b>() -> q_gen_4102
<b, a>() -> q_gen_4102
<b, b>() -> q_gen_4102
<cons, cons>(q_gen_4102, q_gen_4126) -> q_gen_4126
<nil, cons>(q_gen_4114, q_gen_4113) -> q_gen_4126
<nil, cons>(q_gen_4114, q_gen_4182) -> q_gen_4126
<cons, cons, cons>(q_gen_4115, q_gen_4112) -> q_gen_4095
<cons, nil, cons>(q_gen_4102, q_gen_4101) -> q_gen_4095
<nil, cons, cons>(q_gen_4102, q_gen_4101) -> q_gen_4095
<nil, nil, cons>(q_gen_4114, q_gen_4182) -> q_gen_4095
<nil, nil, nil>() -> q_gen_4095
<cons, cons, cons>(q_gen_4115, q_gen_4095) -> q_gen_4112
<cons, nil, cons>(q_gen_4102, q_gen_4126) -> q_gen_4112
<nil, cons, cons>(q_gen_4102, q_gen_4126) -> q_gen_4112
<nil, nil, cons>(q_gen_4114, q_gen_4113) -> q_gen_4112
<a, a, a>() -> q_gen_4115
<a, b, a>() -> q_gen_4115
<b, a, b>() -> q_gen_4115
<b, b, b>() -> q_gen_4115
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_4094, q_gen_4098, q_gen_4099, q_gen_4117, q_gen_4118, q_gen_4119, q_gen_4120, q_gen_4122, q_gen_4134, q_gen_4135, q_gen_4136, q_gen_4166},
Q_f={q_gen_4094},
Delta=
{
<cons>(q_gen_4118, q_gen_4134) -> q_gen_4098
<nil>() -> q_gen_4098
<cons>(q_gen_4118, q_gen_4098) -> q_gen_4117
<a>() -> q_gen_4118
<b>() -> q_gen_4118
<s>(q_gen_4166) -> q_gen_4120
<z>() -> q_gen_4120
<cons>(q_gen_4118, q_gen_4117) -> q_gen_4134
<s>(q_gen_4120) -> q_gen_4136
<s>(q_gen_4136) -> q_gen_4166
<cons, s>(q_gen_4099, q_gen_4098) -> q_gen_4094
<cons, s>(q_gen_4119, q_gen_4117) -> q_gen_4094
<cons, s>(q_gen_4135, q_gen_4134) -> q_gen_4094
<nil, z>() -> q_gen_4094
<a, s>(q_gen_4166) -> q_gen_4099
<a, z>() -> q_gen_4099
<b, s>(q_gen_4166) -> q_gen_4099
<b, z>() -> q_gen_4099
<a, s>(q_gen_4120) -> q_gen_4119
<b, s>(q_gen_4120) -> q_gen_4119
<cons, s>(q_gen_4099, q_gen_4117) -> q_gen_4122
<cons, s>(q_gen_4099, q_gen_4134) -> q_gen_4122
<cons, s>(q_gen_4119, q_gen_4098) -> q_gen_4122
<cons, s>(q_gen_4119, q_gen_4134) -> q_gen_4122
<cons, s>(q_gen_4135, q_gen_4098) -> q_gen_4122
<cons, s>(q_gen_4135, q_gen_4117) -> q_gen_4122
<a, s>(q_gen_4136) -> q_gen_4135
<b, s>(q_gen_4136) -> q_gen_4135
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_4091, q_gen_4093, q_gen_4123},
Q_f={q_gen_4091},
Delta=
{
<s>(q_gen_4093) -> q_gen_4093
<z>() -> q_gen_4093
<s, s>(q_gen_4091) -> q_gen_4091
<z, s>(q_gen_4093) -> q_gen_4091
<z, z>() -> q_gen_4091
<s, s>(q_gen_4123) -> q_gen_4123
<s, z>(q_gen_4093) -> q_gen_4123
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 49
() -> length([nil, z]) -> 49
() -> leq([z, s(nn2)]) -> 49
() -> leq([z, z]) -> 49
(append([l1, l2, _aq]) /\ length([_aq, _bq]) /\ length([l1, _zp])) -> leq([_zp, _bq]) -> 51
(append([l1, l2, _dq]) /\ length([_dq, _eq]) /\ length([l2, _cq])) -> leq([_cq, _eq]) -> 52
(append([t1, l2, _qp])) -> append([cons(h1, t1), l2, cons(h1, _qp)]) -> 51
(length([ll, _vp])) -> length([cons(x, ll), s(_vp)]) -> 50
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 50
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 50
(leq([s(nn1), z])) -> BOT -> 50
}
Sat witness: Found: ((append([l1, l2, _dq]) /\ length([_dq, _eq]) /\ length([l2, _cq])) -> leq([_cq, _eq]), {
_cq -> s(s(s(z)))  ;  _dq -> cons(b, cons(b, cons(b, cons(b, nil))))  ;  _eq -> s(z)  ;  l1 -> cons(b, cons(b, cons(b, nil)))  ;  l2 -> cons(b, cons(b, cons(b, nil)))
})

-------------------------------------------
Step 75, which took 5.159296 s (model generation: 5.149529,  model checking: 0.009767):

Model:
|_
{
append -> 
{{{
Q={q_gen_4095, q_gen_4101, q_gen_4102, q_gen_4113, q_gen_4114, q_gen_4115},
Q_f={q_gen_4095},
Delta=
{
<cons>(q_gen_4114, q_gen_4113) -> q_gen_4113
<nil>() -> q_gen_4113
<a>() -> q_gen_4114
<b>() -> q_gen_4114
<cons, cons>(q_gen_4102, q_gen_4101) -> q_gen_4101
<nil, cons>(q_gen_4114, q_gen_4113) -> q_gen_4101
<nil, nil>() -> q_gen_4101
<a, a>() -> q_gen_4102
<a, b>() -> q_gen_4102
<b, a>() -> q_gen_4102
<b, b>() -> q_gen_4102
<cons, cons, cons>(q_gen_4115, q_gen_4095) -> q_gen_4095
<cons, nil, cons>(q_gen_4102, q_gen_4101) -> q_gen_4095
<nil, cons, cons>(q_gen_4102, q_gen_4101) -> q_gen_4095
<nil, nil, cons>(q_gen_4114, q_gen_4113) -> q_gen_4095
<nil, nil, nil>() -> q_gen_4095
<a, a, a>() -> q_gen_4115
<a, b, a>() -> q_gen_4115
<b, a, b>() -> q_gen_4115
<b, b, b>() -> q_gen_4115
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_4094, q_gen_4098, q_gen_4099, q_gen_4117, q_gen_4118, q_gen_4119, q_gen_4120, q_gen_4122, q_gen_4134, q_gen_4135, q_gen_4136, q_gen_4146, q_gen_4153, q_gen_4154, q_gen_4166},
Q_f={q_gen_4094},
Delta=
{
<cons>(q_gen_4118, q_gen_4153) -> q_gen_4098
<nil>() -> q_gen_4098
<cons>(q_gen_4118, q_gen_4098) -> q_gen_4117
<cons>(q_gen_4146, q_gen_4098) -> q_gen_4117
<cons>(q_gen_4146, q_gen_4134) -> q_gen_4117
<b>() -> q_gen_4118
<s>(q_gen_4166) -> q_gen_4120
<z>() -> q_gen_4120
<cons>(q_gen_4118, q_gen_4117) -> q_gen_4134
<s>(q_gen_4120) -> q_gen_4136
<a>() -> q_gen_4146
<cons>(q_gen_4118, q_gen_4134) -> q_gen_4153
<cons>(q_gen_4146, q_gen_4117) -> q_gen_4153
<cons>(q_gen_4146, q_gen_4153) -> q_gen_4153
<s>(q_gen_4136) -> q_gen_4166
<cons, s>(q_gen_4099, q_gen_4098) -> q_gen_4094
<cons, s>(q_gen_4119, q_gen_4117) -> q_gen_4094
<cons, s>(q_gen_4135, q_gen_4134) -> q_gen_4094
<cons, s>(q_gen_4154, q_gen_4153) -> q_gen_4094
<nil, z>() -> q_gen_4094
<a, z>() -> q_gen_4099
<b, z>() -> q_gen_4099
<a, s>(q_gen_4120) -> q_gen_4119
<b, s>(q_gen_4120) -> q_gen_4119
<cons, s>(q_gen_4099, q_gen_4134) -> q_gen_4122
<cons, s>(q_gen_4099, q_gen_4153) -> q_gen_4122
<cons, s>(q_gen_4119, q_gen_4098) -> q_gen_4122
<cons, s>(q_gen_4119, q_gen_4134) -> q_gen_4122
<cons, s>(q_gen_4119, q_gen_4153) -> q_gen_4122
<cons, s>(q_gen_4135, q_gen_4098) -> q_gen_4122
<cons, s>(q_gen_4135, q_gen_4117) -> q_gen_4122
<cons, s>(q_gen_4135, q_gen_4153) -> q_gen_4122
<cons, s>(q_gen_4154, q_gen_4098) -> q_gen_4122
<cons, s>(q_gen_4154, q_gen_4117) -> q_gen_4122
<cons, s>(q_gen_4154, q_gen_4134) -> q_gen_4122
<b, s>(q_gen_4136) -> q_gen_4135
<a, s>(q_gen_4136) -> q_gen_4154
<a, s>(q_gen_4166) -> q_gen_4154
<b, s>(q_gen_4166) -> q_gen_4154
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_4091, q_gen_4093, q_gen_4123},
Q_f={q_gen_4091},
Delta=
{
<s>(q_gen_4093) -> q_gen_4093
<z>() -> q_gen_4093
<s, s>(q_gen_4091) -> q_gen_4091
<z, s>(q_gen_4093) -> q_gen_4091
<z, z>() -> q_gen_4091
<s, s>(q_gen_4123) -> q_gen_4123
<s, z>(q_gen_4093) -> q_gen_4123
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 50
() -> length([nil, z]) -> 50
() -> leq([z, s(nn2)]) -> 50
() -> leq([z, z]) -> 50
(append([l1, l2, _aq]) /\ length([_aq, _bq]) /\ length([l1, _zp])) -> leq([_zp, _bq]) -> 51
(append([l1, l2, _dq]) /\ length([_dq, _eq]) /\ length([l2, _cq])) -> leq([_cq, _eq]) -> 52
(append([t1, l2, _qp])) -> append([cons(h1, t1), l2, cons(h1, _qp)]) -> 51
(length([ll, _vp])) -> length([cons(x, ll), s(_vp)]) -> 53
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 51
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 51
(leq([s(nn1), z])) -> BOT -> 51
}
Sat witness: Found: ((length([ll, _vp])) -> length([cons(x, ll), s(_vp)]), {
_vp -> s(s(z))  ;  ll -> cons(b, cons(a, nil))  ;  x -> a
})

-------------------------------------------
Step 76, which took 3.279743 s (model generation: 3.266406,  model checking: 0.013337):

Model:
|_
{
append -> 
{{{
Q={q_gen_4095, q_gen_4101, q_gen_4102, q_gen_4113, q_gen_4114, q_gen_4115},
Q_f={q_gen_4095},
Delta=
{
<cons>(q_gen_4114, q_gen_4113) -> q_gen_4113
<nil>() -> q_gen_4113
<a>() -> q_gen_4114
<b>() -> q_gen_4114
<cons, cons>(q_gen_4102, q_gen_4101) -> q_gen_4101
<nil, cons>(q_gen_4114, q_gen_4113) -> q_gen_4101
<nil, nil>() -> q_gen_4101
<a, a>() -> q_gen_4102
<a, b>() -> q_gen_4102
<b, a>() -> q_gen_4102
<b, b>() -> q_gen_4102
<cons, cons, cons>(q_gen_4115, q_gen_4095) -> q_gen_4095
<cons, nil, cons>(q_gen_4102, q_gen_4101) -> q_gen_4095
<nil, cons, cons>(q_gen_4102, q_gen_4101) -> q_gen_4095
<nil, nil, cons>(q_gen_4114, q_gen_4113) -> q_gen_4095
<nil, nil, nil>() -> q_gen_4095
<a, a, a>() -> q_gen_4115
<a, b, a>() -> q_gen_4115
<b, a, b>() -> q_gen_4115
<b, b, b>() -> q_gen_4115
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_4094, q_gen_4098, q_gen_4099, q_gen_4117, q_gen_4118, q_gen_4119, q_gen_4120, q_gen_4122, q_gen_4134, q_gen_4135, q_gen_4136, q_gen_4146, q_gen_4164, q_gen_4165, q_gen_4166},
Q_f={q_gen_4094},
Delta=
{
<cons>(q_gen_4118, q_gen_4164) -> q_gen_4098
<nil>() -> q_gen_4098
<cons>(q_gen_4118, q_gen_4098) -> q_gen_4117
<cons>(q_gen_4146, q_gen_4098) -> q_gen_4117
<cons>(q_gen_4146, q_gen_4164) -> q_gen_4117
<b>() -> q_gen_4118
<s>(q_gen_4166) -> q_gen_4120
<z>() -> q_gen_4120
<cons>(q_gen_4118, q_gen_4117) -> q_gen_4134
<cons>(q_gen_4146, q_gen_4117) -> q_gen_4134
<s>(q_gen_4120) -> q_gen_4136
<a>() -> q_gen_4146
<cons>(q_gen_4118, q_gen_4134) -> q_gen_4164
<cons>(q_gen_4146, q_gen_4134) -> q_gen_4164
<s>(q_gen_4136) -> q_gen_4166
<cons, s>(q_gen_4099, q_gen_4098) -> q_gen_4094
<cons, s>(q_gen_4119, q_gen_4117) -> q_gen_4094
<cons, s>(q_gen_4135, q_gen_4134) -> q_gen_4094
<cons, s>(q_gen_4135, q_gen_4164) -> q_gen_4094
<cons, s>(q_gen_4165, q_gen_4164) -> q_gen_4094
<nil, z>() -> q_gen_4094
<a, z>() -> q_gen_4099
<b, z>() -> q_gen_4099
<a, s>(q_gen_4120) -> q_gen_4119
<b, s>(q_gen_4120) -> q_gen_4119
<cons, s>(q_gen_4099, q_gen_4134) -> q_gen_4122
<cons, s>(q_gen_4099, q_gen_4164) -> q_gen_4122
<cons, s>(q_gen_4119, q_gen_4098) -> q_gen_4122
<cons, s>(q_gen_4119, q_gen_4134) -> q_gen_4122
<cons, s>(q_gen_4119, q_gen_4164) -> q_gen_4122
<cons, s>(q_gen_4135, q_gen_4098) -> q_gen_4122
<cons, s>(q_gen_4135, q_gen_4117) -> q_gen_4122
<cons, s>(q_gen_4165, q_gen_4098) -> q_gen_4122
<cons, s>(q_gen_4165, q_gen_4117) -> q_gen_4122
<cons, s>(q_gen_4165, q_gen_4134) -> q_gen_4122
<a, s>(q_gen_4136) -> q_gen_4135
<b, s>(q_gen_4136) -> q_gen_4135
<a, s>(q_gen_4166) -> q_gen_4165
<b, s>(q_gen_4166) -> q_gen_4165
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_4091, q_gen_4093, q_gen_4123},
Q_f={q_gen_4091},
Delta=
{
<s>(q_gen_4093) -> q_gen_4093
<z>() -> q_gen_4093
<s, s>(q_gen_4091) -> q_gen_4091
<z, s>(q_gen_4093) -> q_gen_4091
<z, z>() -> q_gen_4091
<s, s>(q_gen_4123) -> q_gen_4123
<s, z>(q_gen_4093) -> q_gen_4123
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 51
() -> length([nil, z]) -> 51
() -> leq([z, s(nn2)]) -> 51
() -> leq([z, z]) -> 51
(append([l1, l2, _aq]) /\ length([_aq, _bq]) /\ length([l1, _zp])) -> leq([_zp, _bq]) -> 54
(append([l1, l2, _dq]) /\ length([_dq, _eq]) /\ length([l2, _cq])) -> leq([_cq, _eq]) -> 52
(append([t1, l2, _qp])) -> append([cons(h1, t1), l2, cons(h1, _qp)]) -> 52
(length([ll, _vp])) -> length([cons(x, ll), s(_vp)]) -> 53
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 52
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 52
(leq([s(nn1), z])) -> BOT -> 52
}
Sat witness: Found: ((append([l1, l2, _aq]) /\ length([_aq, _bq]) /\ length([l1, _zp])) -> leq([_zp, _bq]), {
_aq -> cons(b, cons(b, cons(b, cons(b, cons(b, cons(b, nil))))))  ;  _bq -> s(s(z))  ;  _zp -> s(s(s(z)))  ;  l1 -> cons(b, cons(b, cons(b, nil)))  ;  l2 -> nil
})

-------------------------------------------
Step 77, which took 4.185334 s (model generation: 4.173806,  model checking: 0.011528):

Model:
|_
{
append -> 
{{{
Q={q_gen_4095, q_gen_4101, q_gen_4102, q_gen_4113, q_gen_4114, q_gen_4115},
Q_f={q_gen_4095},
Delta=
{
<cons>(q_gen_4114, q_gen_4113) -> q_gen_4113
<nil>() -> q_gen_4113
<a>() -> q_gen_4114
<b>() -> q_gen_4114
<cons, cons>(q_gen_4102, q_gen_4101) -> q_gen_4101
<nil, cons>(q_gen_4114, q_gen_4113) -> q_gen_4101
<nil, nil>() -> q_gen_4101
<a, a>() -> q_gen_4102
<a, b>() -> q_gen_4102
<b, a>() -> q_gen_4102
<b, b>() -> q_gen_4102
<cons, cons, cons>(q_gen_4115, q_gen_4095) -> q_gen_4095
<cons, nil, cons>(q_gen_4102, q_gen_4101) -> q_gen_4095
<nil, cons, cons>(q_gen_4102, q_gen_4101) -> q_gen_4095
<nil, nil, cons>(q_gen_4114, q_gen_4113) -> q_gen_4095
<nil, nil, nil>() -> q_gen_4095
<a, a, a>() -> q_gen_4115
<a, b, a>() -> q_gen_4115
<b, a, b>() -> q_gen_4115
<b, b, b>() -> q_gen_4115
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_4094, q_gen_4098, q_gen_4099, q_gen_4117, q_gen_4118, q_gen_4119, q_gen_4120, q_gen_4122, q_gen_4134, q_gen_4135, q_gen_4136, q_gen_4146, q_gen_4164, q_gen_4165, q_gen_4166},
Q_f={q_gen_4094},
Delta=
{
<nil>() -> q_gen_4098
<cons>(q_gen_4118, q_gen_4098) -> q_gen_4117
<cons>(q_gen_4146, q_gen_4098) -> q_gen_4117
<cons>(q_gen_4146, q_gen_4164) -> q_gen_4117
<b>() -> q_gen_4118
<s>(q_gen_4166) -> q_gen_4120
<z>() -> q_gen_4120
<cons>(q_gen_4118, q_gen_4117) -> q_gen_4134
<cons>(q_gen_4146, q_gen_4117) -> q_gen_4134
<s>(q_gen_4120) -> q_gen_4136
<a>() -> q_gen_4146
<cons>(q_gen_4118, q_gen_4134) -> q_gen_4164
<cons>(q_gen_4118, q_gen_4164) -> q_gen_4164
<cons>(q_gen_4146, q_gen_4134) -> q_gen_4164
<s>(q_gen_4136) -> q_gen_4166
<cons, s>(q_gen_4099, q_gen_4098) -> q_gen_4094
<cons, s>(q_gen_4119, q_gen_4117) -> q_gen_4094
<cons, s>(q_gen_4135, q_gen_4134) -> q_gen_4094
<cons, s>(q_gen_4165, q_gen_4164) -> q_gen_4094
<nil, z>() -> q_gen_4094
<a, z>() -> q_gen_4099
<b, z>() -> q_gen_4099
<a, s>(q_gen_4120) -> q_gen_4119
<b, s>(q_gen_4120) -> q_gen_4119
<cons, s>(q_gen_4099, q_gen_4134) -> q_gen_4122
<cons, s>(q_gen_4099, q_gen_4164) -> q_gen_4122
<cons, s>(q_gen_4119, q_gen_4098) -> q_gen_4122
<cons, s>(q_gen_4119, q_gen_4134) -> q_gen_4122
<cons, s>(q_gen_4119, q_gen_4164) -> q_gen_4122
<cons, s>(q_gen_4135, q_gen_4098) -> q_gen_4122
<cons, s>(q_gen_4135, q_gen_4117) -> q_gen_4122
<cons, s>(q_gen_4135, q_gen_4164) -> q_gen_4122
<cons, s>(q_gen_4165, q_gen_4098) -> q_gen_4122
<cons, s>(q_gen_4165, q_gen_4117) -> q_gen_4122
<cons, s>(q_gen_4165, q_gen_4134) -> q_gen_4122
<a, s>(q_gen_4136) -> q_gen_4135
<b, s>(q_gen_4136) -> q_gen_4135
<a, s>(q_gen_4166) -> q_gen_4165
<b, s>(q_gen_4166) -> q_gen_4165
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_4091, q_gen_4093, q_gen_4123},
Q_f={q_gen_4091},
Delta=
{
<s>(q_gen_4093) -> q_gen_4093
<z>() -> q_gen_4093
<s, s>(q_gen_4091) -> q_gen_4091
<z, s>(q_gen_4093) -> q_gen_4091
<z, z>() -> q_gen_4091
<s, s>(q_gen_4123) -> q_gen_4123
<s, z>(q_gen_4093) -> q_gen_4123
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 52
() -> length([nil, z]) -> 52
() -> leq([z, s(nn2)]) -> 52
() -> leq([z, z]) -> 52
(append([l1, l2, _aq]) /\ length([_aq, _bq]) /\ length([l1, _zp])) -> leq([_zp, _bq]) -> 54
(append([l1, l2, _dq]) /\ length([_dq, _eq]) /\ length([l2, _cq])) -> leq([_cq, _eq]) -> 55
(append([t1, l2, _qp])) -> append([cons(h1, t1), l2, cons(h1, _qp)]) -> 53
(length([ll, _vp])) -> length([cons(x, ll), s(_vp)]) -> 53
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 53
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 53
(leq([s(nn1), z])) -> BOT -> 53
}
Sat witness: Found: ((append([l1, l2, _dq]) /\ length([_dq, _eq]) /\ length([l2, _cq])) -> leq([_cq, _eq]), {
_cq -> s(s(s(s(s(z)))))  ;  _dq -> cons(b, cons(b, cons(a, nil)))  ;  _eq -> s(s(s(z)))  ;  l1 -> nil  ;  l2 -> cons(b, cons(b, nil))
})

-------------------------------------------
Step 78, which took 9.846437 s (model generation: 9.845785,  model checking: 0.000652):

Model:
|_
{
append -> 
{{{
Q={q_gen_4095, q_gen_4101, q_gen_4102, q_gen_4106, q_gen_4107, q_gen_4112, q_gen_4113, q_gen_4114, q_gen_4115, q_gen_4150, q_gen_4158},
Q_f={q_gen_4095},
Delta=
{
<cons>(q_gen_4114, q_gen_4113) -> q_gen_4113
<nil>() -> q_gen_4113
<a>() -> q_gen_4114
<b>() -> q_gen_4114
<nil, nil>() -> q_gen_4101
<a, b>() -> q_gen_4102
<b, b>() -> q_gen_4102
<cons, cons>(q_gen_4102, q_gen_4106) -> q_gen_4106
<cons, cons>(q_gen_4107, q_gen_4101) -> q_gen_4106
<nil, cons>(q_gen_4114, q_gen_4113) -> q_gen_4106
<a, a>() -> q_gen_4107
<b, a>() -> q_gen_4107
<cons, cons>(q_gen_4102, q_gen_4101) -> q_gen_4150
<cons, cons>(q_gen_4102, q_gen_4150) -> q_gen_4150
<cons, cons, cons>(q_gen_4115, q_gen_4112) -> q_gen_4095
<cons, cons, cons>(q_gen_4158, q_gen_4095) -> q_gen_4095
<cons, cons, cons>(q_gen_4158, q_gen_4112) -> q_gen_4095
<cons, nil, cons>(q_gen_4102, q_gen_4101) -> q_gen_4095
<nil, cons, cons>(q_gen_4102, q_gen_4101) -> q_gen_4095
<nil, cons, cons>(q_gen_4102, q_gen_4150) -> q_gen_4095
<nil, cons, cons>(q_gen_4107, q_gen_4101) -> q_gen_4095
<nil, cons, cons>(q_gen_4107, q_gen_4106) -> q_gen_4095
<nil, cons, cons>(q_gen_4107, q_gen_4150) -> q_gen_4095
<nil, nil, nil>() -> q_gen_4095
<cons, cons, cons>(q_gen_4115, q_gen_4095) -> q_gen_4112
<cons, nil, cons>(q_gen_4102, q_gen_4106) -> q_gen_4112
<cons, nil, cons>(q_gen_4102, q_gen_4150) -> q_gen_4112
<cons, nil, cons>(q_gen_4107, q_gen_4101) -> q_gen_4112
<nil, cons, cons>(q_gen_4102, q_gen_4106) -> q_gen_4112
<nil, nil, cons>(q_gen_4114, q_gen_4113) -> q_gen_4112
<a, b, a>() -> q_gen_4115
<b, b, b>() -> q_gen_4115
<a, a, a>() -> q_gen_4158
<b, a, b>() -> q_gen_4158
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_4094, q_gen_4098, q_gen_4099, q_gen_4117, q_gen_4118, q_gen_4119, q_gen_4120, q_gen_4122, q_gen_4134, q_gen_4135, q_gen_4136},
Q_f={q_gen_4094},
Delta=
{
<nil>() -> q_gen_4098
<cons>(q_gen_4118, q_gen_4098) -> q_gen_4117
<a>() -> q_gen_4118
<b>() -> q_gen_4118
<z>() -> q_gen_4120
<cons>(q_gen_4118, q_gen_4117) -> q_gen_4134
<cons>(q_gen_4118, q_gen_4134) -> q_gen_4134
<s>(q_gen_4120) -> q_gen_4136
<s>(q_gen_4136) -> q_gen_4136
<cons, s>(q_gen_4099, q_gen_4098) -> q_gen_4094
<cons, s>(q_gen_4119, q_gen_4117) -> q_gen_4094
<cons, s>(q_gen_4135, q_gen_4134) -> q_gen_4094
<nil, z>() -> q_gen_4094
<a, z>() -> q_gen_4099
<b, z>() -> q_gen_4099
<a, s>(q_gen_4120) -> q_gen_4119
<b, s>(q_gen_4120) -> q_gen_4119
<cons, s>(q_gen_4099, q_gen_4134) -> q_gen_4122
<cons, s>(q_gen_4119, q_gen_4098) -> q_gen_4122
<cons, s>(q_gen_4119, q_gen_4134) -> q_gen_4122
<cons, s>(q_gen_4135, q_gen_4098) -> q_gen_4122
<cons, s>(q_gen_4135, q_gen_4117) -> q_gen_4122
<a, s>(q_gen_4136) -> q_gen_4135
<b, s>(q_gen_4136) -> q_gen_4135
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_4091, q_gen_4093, q_gen_4123},
Q_f={q_gen_4091},
Delta=
{
<s>(q_gen_4093) -> q_gen_4093
<z>() -> q_gen_4093
<s, s>(q_gen_4091) -> q_gen_4091
<z, s>(q_gen_4093) -> q_gen_4091
<z, z>() -> q_gen_4091
<s, s>(q_gen_4123) -> q_gen_4123
<s, z>(q_gen_4093) -> q_gen_4123
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 55
() -> length([nil, z]) -> 53
() -> leq([z, s(nn2)]) -> 53
() -> leq([z, z]) -> 53
(append([l1, l2, _aq]) /\ length([_aq, _bq]) /\ length([l1, _zp])) -> leq([_zp, _bq]) -> 54
(append([l1, l2, _dq]) /\ length([_dq, _eq]) /\ length([l2, _cq])) -> leq([_cq, _eq]) -> 55
(append([t1, l2, _qp])) -> append([cons(h1, t1), l2, cons(h1, _qp)]) -> 53
(length([ll, _vp])) -> length([cons(x, ll), s(_vp)]) -> 53
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 53
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 53
(leq([s(nn1), z])) -> BOT -> 53
}
Sat witness: Found: (() -> append([nil, l2, l2]), {
l2 -> cons(b, cons(a, nil))
})

-------------------------------------------
Step 79, which took 4.010861 s (model generation: 4.005366,  model checking: 0.005495):

Model:
|_
{
append -> 
{{{
Q={q_gen_4095, q_gen_4100, q_gen_4101, q_gen_4102, q_gen_4106, q_gen_4107, q_gen_4112, q_gen_4113, q_gen_4114, q_gen_4115, q_gen_4160},
Q_f={q_gen_4095, q_gen_4100},
Delta=
{
<cons>(q_gen_4114, q_gen_4113) -> q_gen_4113
<nil>() -> q_gen_4113
<a>() -> q_gen_4114
<b>() -> q_gen_4114
<nil, nil>() -> q_gen_4101
<b, b>() -> q_gen_4102
<cons, cons>(q_gen_4102, q_gen_4101) -> q_gen_4106
<cons, cons>(q_gen_4102, q_gen_4160) -> q_gen_4106
<cons, cons>(q_gen_4107, q_gen_4101) -> q_gen_4106
<nil, cons>(q_gen_4114, q_gen_4113) -> q_gen_4106
<a, a>() -> q_gen_4107
<a, b>() -> q_gen_4107
<b, a>() -> q_gen_4107
<cons, cons>(q_gen_4102, q_gen_4106) -> q_gen_4160
<cons, cons, cons>(q_gen_4115, q_gen_4112) -> q_gen_4095
<nil, cons, cons>(q_gen_4102, q_gen_4101) -> q_gen_4095
<nil, cons, cons>(q_gen_4107, q_gen_4101) -> q_gen_4095
<nil, cons, cons>(q_gen_4107, q_gen_4106) -> q_gen_4095
<nil, nil, nil>() -> q_gen_4095
<cons, cons, cons>(q_gen_4115, q_gen_4095) -> q_gen_4100
<cons, nil, cons>(q_gen_4102, q_gen_4101) -> q_gen_4100
<cons, nil, cons>(q_gen_4107, q_gen_4106) -> q_gen_4100
<nil, cons, cons>(q_gen_4102, q_gen_4106) -> q_gen_4100
<cons, cons, cons>(q_gen_4115, q_gen_4100) -> q_gen_4112
<cons, nil, cons>(q_gen_4102, q_gen_4106) -> q_gen_4112
<cons, nil, cons>(q_gen_4102, q_gen_4160) -> q_gen_4112
<cons, nil, cons>(q_gen_4107, q_gen_4101) -> q_gen_4112
<nil, cons, cons>(q_gen_4102, q_gen_4160) -> q_gen_4112
<nil, cons, cons>(q_gen_4107, q_gen_4160) -> q_gen_4112
<nil, nil, cons>(q_gen_4114, q_gen_4113) -> q_gen_4112
<a, a, a>() -> q_gen_4115
<a, b, a>() -> q_gen_4115
<b, a, b>() -> q_gen_4115
<b, b, b>() -> q_gen_4115
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_4094, q_gen_4098, q_gen_4099, q_gen_4117, q_gen_4118, q_gen_4119, q_gen_4120, q_gen_4122, q_gen_4134, q_gen_4135, q_gen_4136},
Q_f={q_gen_4094},
Delta=
{
<nil>() -> q_gen_4098
<cons>(q_gen_4118, q_gen_4098) -> q_gen_4117
<cons>(q_gen_4118, q_gen_4134) -> q_gen_4117
<a>() -> q_gen_4118
<b>() -> q_gen_4118
<s>(q_gen_4136) -> q_gen_4120
<z>() -> q_gen_4120
<cons>(q_gen_4118, q_gen_4117) -> q_gen_4134
<s>(q_gen_4120) -> q_gen_4136
<cons, s>(q_gen_4099, q_gen_4098) -> q_gen_4094
<cons, s>(q_gen_4119, q_gen_4117) -> q_gen_4094
<cons, s>(q_gen_4135, q_gen_4134) -> q_gen_4094
<nil, z>() -> q_gen_4094
<a, z>() -> q_gen_4099
<b, z>() -> q_gen_4099
<a, s>(q_gen_4120) -> q_gen_4119
<b, s>(q_gen_4120) -> q_gen_4119
<cons, s>(q_gen_4099, q_gen_4117) -> q_gen_4122
<cons, s>(q_gen_4099, q_gen_4134) -> q_gen_4122
<cons, s>(q_gen_4119, q_gen_4098) -> q_gen_4122
<cons, s>(q_gen_4119, q_gen_4134) -> q_gen_4122
<cons, s>(q_gen_4135, q_gen_4098) -> q_gen_4122
<cons, s>(q_gen_4135, q_gen_4117) -> q_gen_4122
<a, s>(q_gen_4136) -> q_gen_4135
<b, s>(q_gen_4136) -> q_gen_4135
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_4091, q_gen_4093, q_gen_4123},
Q_f={q_gen_4091},
Delta=
{
<s>(q_gen_4093) -> q_gen_4093
<z>() -> q_gen_4093
<s, s>(q_gen_4091) -> q_gen_4091
<z, s>(q_gen_4093) -> q_gen_4091
<z, z>() -> q_gen_4091
<s, s>(q_gen_4123) -> q_gen_4123
<s, z>(q_gen_4093) -> q_gen_4123
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 55
() -> length([nil, z]) -> 53
() -> leq([z, s(nn2)]) -> 53
() -> leq([z, z]) -> 53
(append([l1, l2, _aq]) /\ length([_aq, _bq]) /\ length([l1, _zp])) -> leq([_zp, _bq]) -> 54
(append([l1, l2, _dq]) /\ length([_dq, _eq]) /\ length([l2, _cq])) -> leq([_cq, _eq]) -> 55
(append([t1, l2, _qp])) -> append([cons(h1, t1), l2, cons(h1, _qp)]) -> 56
(length([ll, _vp])) -> length([cons(x, ll), s(_vp)]) -> 54
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 54
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 54
(leq([s(nn1), z])) -> BOT -> 54
}
Sat witness: Found: ((append([t1, l2, _qp])) -> append([cons(h1, t1), l2, cons(h1, _qp)]), {
_qp -> cons(b, nil)  ;  h1 -> b  ;  l2 -> nil  ;  t1 -> cons(b, nil)
})

-------------------------------------------
Step 80, which took 5.065876 s (model generation: 5.056998,  model checking: 0.008878):

Model:
|_
{
append -> 
{{{
Q={q_gen_4095, q_gen_4101, q_gen_4102, q_gen_4106, q_gen_4107, q_gen_4112, q_gen_4113, q_gen_4114, q_gen_4115, q_gen_4126, q_gen_4160},
Q_f={q_gen_4095},
Delta=
{
<cons>(q_gen_4114, q_gen_4113) -> q_gen_4113
<nil>() -> q_gen_4113
<a>() -> q_gen_4114
<b>() -> q_gen_4114
<nil, nil>() -> q_gen_4101
<b, b>() -> q_gen_4102
<cons, cons>(q_gen_4102, q_gen_4101) -> q_gen_4106
<cons, cons>(q_gen_4107, q_gen_4101) -> q_gen_4106
<a, a>() -> q_gen_4107
<a, b>() -> q_gen_4107
<b, a>() -> q_gen_4107
<cons, cons>(q_gen_4102, q_gen_4160) -> q_gen_4126
<nil, cons>(q_gen_4114, q_gen_4113) -> q_gen_4126
<cons, cons>(q_gen_4102, q_gen_4106) -> q_gen_4160
<cons, cons>(q_gen_4102, q_gen_4126) -> q_gen_4160
<cons, cons, cons>(q_gen_4115, q_gen_4112) -> q_gen_4095
<cons, nil, cons>(q_gen_4102, q_gen_4101) -> q_gen_4095
<cons, nil, cons>(q_gen_4102, q_gen_4106) -> q_gen_4095
<cons, nil, cons>(q_gen_4107, q_gen_4101) -> q_gen_4095
<cons, nil, cons>(q_gen_4107, q_gen_4126) -> q_gen_4095
<nil, cons, cons>(q_gen_4102, q_gen_4101) -> q_gen_4095
<nil, cons, cons>(q_gen_4102, q_gen_4106) -> q_gen_4095
<nil, cons, cons>(q_gen_4102, q_gen_4126) -> q_gen_4095
<nil, cons, cons>(q_gen_4107, q_gen_4106) -> q_gen_4095
<nil, cons, cons>(q_gen_4107, q_gen_4160) -> q_gen_4095
<nil, nil, nil>() -> q_gen_4095
<cons, cons, cons>(q_gen_4115, q_gen_4095) -> q_gen_4112
<cons, nil, cons>(q_gen_4102, q_gen_4126) -> q_gen_4112
<cons, nil, cons>(q_gen_4102, q_gen_4160) -> q_gen_4112
<nil, cons, cons>(q_gen_4102, q_gen_4160) -> q_gen_4112
<nil, cons, cons>(q_gen_4107, q_gen_4101) -> q_gen_4112
<nil, cons, cons>(q_gen_4107, q_gen_4126) -> q_gen_4112
<nil, nil, cons>(q_gen_4114, q_gen_4113) -> q_gen_4112
<a, a, a>() -> q_gen_4115
<a, b, a>() -> q_gen_4115
<b, a, b>() -> q_gen_4115
<b, b, b>() -> q_gen_4115
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_4094, q_gen_4098, q_gen_4099, q_gen_4117, q_gen_4118, q_gen_4119, q_gen_4120, q_gen_4122, q_gen_4134, q_gen_4135, q_gen_4136},
Q_f={q_gen_4094},
Delta=
{
<nil>() -> q_gen_4098
<cons>(q_gen_4118, q_gen_4098) -> q_gen_4117
<a>() -> q_gen_4118
<b>() -> q_gen_4118
<z>() -> q_gen_4120
<cons>(q_gen_4118, q_gen_4117) -> q_gen_4134
<cons>(q_gen_4118, q_gen_4134) -> q_gen_4134
<s>(q_gen_4120) -> q_gen_4136
<s>(q_gen_4136) -> q_gen_4136
<cons, s>(q_gen_4099, q_gen_4098) -> q_gen_4094
<cons, s>(q_gen_4119, q_gen_4117) -> q_gen_4094
<cons, s>(q_gen_4135, q_gen_4134) -> q_gen_4094
<nil, z>() -> q_gen_4094
<a, z>() -> q_gen_4099
<b, z>() -> q_gen_4099
<a, s>(q_gen_4120) -> q_gen_4119
<b, s>(q_gen_4120) -> q_gen_4119
<cons, s>(q_gen_4099, q_gen_4134) -> q_gen_4122
<cons, s>(q_gen_4119, q_gen_4098) -> q_gen_4122
<cons, s>(q_gen_4119, q_gen_4134) -> q_gen_4122
<cons, s>(q_gen_4135, q_gen_4098) -> q_gen_4122
<cons, s>(q_gen_4135, q_gen_4117) -> q_gen_4122
<a, s>(q_gen_4136) -> q_gen_4135
<b, s>(q_gen_4136) -> q_gen_4135
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_4091, q_gen_4093, q_gen_4123},
Q_f={q_gen_4091},
Delta=
{
<s>(q_gen_4093) -> q_gen_4093
<z>() -> q_gen_4093
<s, s>(q_gen_4091) -> q_gen_4091
<z, s>(q_gen_4093) -> q_gen_4091
<z, z>() -> q_gen_4091
<s, s>(q_gen_4123) -> q_gen_4123
<s, z>(q_gen_4093) -> q_gen_4123
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 55
() -> length([nil, z]) -> 54
() -> leq([z, s(nn2)]) -> 54
() -> leq([z, z]) -> 54
(append([l1, l2, _aq]) /\ length([_aq, _bq]) /\ length([l1, _zp])) -> leq([_zp, _bq]) -> 57
(append([l1, l2, _dq]) /\ length([_dq, _eq]) /\ length([l2, _cq])) -> leq([_cq, _eq]) -> 55
(append([t1, l2, _qp])) -> append([cons(h1, t1), l2, cons(h1, _qp)]) -> 56
(length([ll, _vp])) -> length([cons(x, ll), s(_vp)]) -> 55
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 55
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 55
(leq([s(nn1), z])) -> BOT -> 55
}
Sat witness: Found: ((append([l1, l2, _aq]) /\ length([_aq, _bq]) /\ length([l1, _zp])) -> leq([_zp, _bq]), {
_aq -> cons(a, cons(b, cons(b, cons(b, cons(b, nil)))))  ;  _bq -> s(s(s(z)))  ;  _zp -> s(s(s(s(z))))  ;  l1 -> cons(b, cons(b, cons(b, nil)))  ;  l2 -> nil
})

-------------------------------------------
Step 81, which took 4.039602 s (model generation: 4.035440,  model checking: 0.004162):

Model:
|_
{
append -> 
{{{
Q={q_gen_4095, q_gen_4100, q_gen_4101, q_gen_4102, q_gen_4106, q_gen_4107, q_gen_4113, q_gen_4114, q_gen_4115, q_gen_4126, q_gen_4129, q_gen_4132, q_gen_4142, q_gen_4150, q_gen_4157, q_gen_4159, q_gen_4190, q_gen_4204, q_gen_4205, q_gen_4264, q_gen_4266},
Q_f={q_gen_4095, q_gen_4100, q_gen_4142, q_gen_4159, q_gen_4204},
Delta=
{
<cons>(q_gen_4114, q_gen_4113) -> q_gen_4113
<nil>() -> q_gen_4113
<b>() -> q_gen_4114
<a>() -> q_gen_4157
<cons, cons>(q_gen_4102, q_gen_4106) -> q_gen_4101
<nil, nil>() -> q_gen_4101
<a, b>() -> q_gen_4102
<b, b>() -> q_gen_4102
<cons, cons>(q_gen_4102, q_gen_4150) -> q_gen_4106
<cons, cons>(q_gen_4107, q_gen_4101) -> q_gen_4106
<a, a>() -> q_gen_4107
<b, a>() -> q_gen_4107
<nil, cons>(q_gen_4114, q_gen_4113) -> q_gen_4126
<cons, cons>(q_gen_4102, q_gen_4101) -> q_gen_4150
<cons, cons>(q_gen_4102, q_gen_4126) -> q_gen_4150
<cons, cons>(q_gen_4102, q_gen_4205) -> q_gen_4205
<nil, cons>(q_gen_4157, q_gen_4113) -> q_gen_4205
<cons, cons, cons>(q_gen_4115, q_gen_4095) -> q_gen_4095
<cons, cons, cons>(q_gen_4132, q_gen_4100) -> q_gen_4095
<cons, cons, cons>(q_gen_4132, q_gen_4190) -> q_gen_4095
<cons, nil, cons>(q_gen_4102, q_gen_4126) -> q_gen_4095
<cons, nil, cons>(q_gen_4102, q_gen_4150) -> q_gen_4095
<nil, cons, cons>(q_gen_4102, q_gen_4101) -> q_gen_4095
<nil, nil, nil>() -> q_gen_4095
<cons, cons, cons>(q_gen_4115, q_gen_4100) -> q_gen_4100
<cons, nil, cons>(q_gen_4102, q_gen_4101) -> q_gen_4100
<nil, cons, cons>(q_gen_4107, q_gen_4106) -> q_gen_4100
<nil, nil, cons>(q_gen_4114, q_gen_4113) -> q_gen_4100
<nil, nil, cons>(q_gen_4157, q_gen_4113) -> q_gen_4100
<b, b, b>() -> q_gen_4115
<cons, cons, cons>(q_gen_4115, q_gen_4142) -> q_gen_4129
<cons, cons, cons>(q_gen_4132, q_gen_4142) -> q_gen_4129
<cons, nil, cons>(q_gen_4102, q_gen_4106) -> q_gen_4129
<cons, nil, cons>(q_gen_4107, q_gen_4101) -> q_gen_4129
<nil, cons, cons>(q_gen_4107, q_gen_4101) -> q_gen_4129
<a, a, a>() -> q_gen_4132
<a, b, a>() -> q_gen_4132
<b, a, b>() -> q_gen_4132
<nil, cons, cons>(q_gen_4102, q_gen_4126) -> q_gen_4142
<nil, cons, cons>(q_gen_4102, q_gen_4150) -> q_gen_4142
<nil, cons, cons>(q_gen_4107, q_gen_4150) -> q_gen_4159
<cons, cons, cons>(q_gen_4115, q_gen_4159) -> q_gen_4190
<cons, cons, cons>(q_gen_4115, q_gen_4204) -> q_gen_4190
<cons, cons, cons>(q_gen_4115, q_gen_4264) -> q_gen_4190
<cons, cons, cons>(q_gen_4132, q_gen_4095) -> q_gen_4190
<nil, cons, cons>(q_gen_4102, q_gen_4205) -> q_gen_4190
<nil, cons, cons>(q_gen_4107, q_gen_4126) -> q_gen_4190
<cons, cons, cons>(q_gen_4132, q_gen_4204) -> q_gen_4204
<cons, nil, cons>(q_gen_4102, q_gen_4205) -> q_gen_4204
<nil, cons, cons>(q_gen_4102, q_gen_4106) -> q_gen_4204
<cons, cons, cons>(q_gen_4132, q_gen_4129) -> q_gen_4264
<cons, cons, cons>(q_gen_4115, q_gen_4190) -> q_gen_4266
<cons, nil, cons>(q_gen_4107, q_gen_4106) -> q_gen_4266
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_4094, q_gen_4098, q_gen_4099, q_gen_4117, q_gen_4118, q_gen_4119, q_gen_4120, q_gen_4122, q_gen_4134, q_gen_4135, q_gen_4136, q_gen_4146, q_gen_4166, q_gen_4178, q_gen_4234},
Q_f={q_gen_4094},
Delta=
{
<nil>() -> q_gen_4098
<cons>(q_gen_4118, q_gen_4098) -> q_gen_4117
<cons>(q_gen_4146, q_gen_4098) -> q_gen_4117
<cons>(q_gen_4146, q_gen_4178) -> q_gen_4117
<b>() -> q_gen_4118
<s>(q_gen_4166) -> q_gen_4120
<z>() -> q_gen_4120
<cons>(q_gen_4118, q_gen_4117) -> q_gen_4134
<cons>(q_gen_4118, q_gen_4178) -> q_gen_4134
<cons>(q_gen_4146, q_gen_4117) -> q_gen_4134
<cons>(q_gen_4146, q_gen_4134) -> q_gen_4134
<s>(q_gen_4120) -> q_gen_4136
<a>() -> q_gen_4146
<s>(q_gen_4136) -> q_gen_4166
<cons>(q_gen_4118, q_gen_4134) -> q_gen_4178
<cons, s>(q_gen_4099, q_gen_4098) -> q_gen_4094
<cons, s>(q_gen_4119, q_gen_4117) -> q_gen_4094
<cons, s>(q_gen_4119, q_gen_4178) -> q_gen_4094
<cons, s>(q_gen_4135, q_gen_4134) -> q_gen_4094
<nil, z>() -> q_gen_4094
<a, z>() -> q_gen_4099
<b, z>() -> q_gen_4099
<a, s>(q_gen_4120) -> q_gen_4119
<a, s>(q_gen_4166) -> q_gen_4119
<b, s>(q_gen_4120) -> q_gen_4119
<cons, s>(q_gen_4099, q_gen_4134) -> q_gen_4122
<cons, s>(q_gen_4099, q_gen_4178) -> q_gen_4122
<cons, s>(q_gen_4119, q_gen_4098) -> q_gen_4122
<cons, s>(q_gen_4119, q_gen_4134) -> q_gen_4122
<cons, s>(q_gen_4135, q_gen_4098) -> q_gen_4122
<cons, s>(q_gen_4135, q_gen_4117) -> q_gen_4122
<a, s>(q_gen_4136) -> q_gen_4135
<b, s>(q_gen_4136) -> q_gen_4135
<b, s>(q_gen_4166) -> q_gen_4135
<cons, s>(q_gen_4135, q_gen_4178) -> q_gen_4234
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_4091, q_gen_4093, q_gen_4123, q_gen_4124},
Q_f={q_gen_4091},
Delta=
{
<s>(q_gen_4093) -> q_gen_4093
<z>() -> q_gen_4093
<s, s>(q_gen_4091) -> q_gen_4091
<z, s>(q_gen_4093) -> q_gen_4091
<z, z>() -> q_gen_4091
<s, s>(q_gen_4124) -> q_gen_4123
<s, s>(q_gen_4123) -> q_gen_4124
<s, z>(q_gen_4093) -> q_gen_4124
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 55
() -> length([nil, z]) -> 55
() -> leq([z, s(nn2)]) -> 55
() -> leq([z, z]) -> 55
(append([l1, l2, _aq]) /\ length([_aq, _bq]) /\ length([l1, _zp])) -> leq([_zp, _bq]) -> 57
(append([l1, l2, _dq]) /\ length([_dq, _eq]) /\ length([l2, _cq])) -> leq([_cq, _eq]) -> 55
(append([t1, l2, _qp])) -> append([cons(h1, t1), l2, cons(h1, _qp)]) -> 56
(length([ll, _vp])) -> length([cons(x, ll), s(_vp)]) -> 58
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 56
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 56
(leq([s(nn1), z])) -> BOT -> 56
}
Sat witness: Found: ((length([ll, _vp])) -> length([cons(x, ll), s(_vp)]), {
_vp -> s(s(s(z)))  ;  ll -> cons(b, cons(a, cons(a, nil)))  ;  x -> b
})

Total time: 67.912675
Reason for stopping: DontKnow. Stopped because: timeout