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


Learning problem is:

env: {
nat -> {s, z}  ;  natlist -> {cons, nil}
}
definition:
{
(length, F:
{() -> length([nil, z])
(length([ll, _xaa])) -> length([cons(x, ll), s(_xaa)])}
(length([_yaa, _aba]) /\ length([_yaa, _zaa])) -> eq_nat([_zaa, _aba])
)
}

properties:
{(length([l, _cba]) /\ length([cons(z, cons(z, l)), _bba])) -> eq_nat([_bba, s(s(_cba))])}


over-approximation: {length}
under-approximation: {}

Clause system for inference is:

{
() -> length([nil, z]) -> 0
(length([l, _cba]) /\ length([cons(z, cons(z, l)), _bba])) -> eq_nat([_bba, s(s(_cba))]) -> 0
(length([ll, _xaa])) -> length([cons(x, ll), s(_xaa)]) -> 0
}


Solving took 63.535443 seconds.
DontKnow. Stopped because: timeout
Working model:
|_
{
length -> 
{{{
Q={q_gen_7156, q_gen_7157, q_gen_7158, q_gen_7159, q_gen_7160, q_gen_7161, q_gen_7162, q_gen_7163, q_gen_7164, q_gen_7165, q_gen_7166, q_gen_7167, q_gen_7168, q_gen_7169, q_gen_7170, q_gen_7171, q_gen_7172, q_gen_7173, q_gen_7174, q_gen_7175, q_gen_7176, q_gen_7177, q_gen_7178, q_gen_7179, q_gen_7180, q_gen_7181, q_gen_7182, q_gen_7183, q_gen_7184, q_gen_7185, q_gen_7186, q_gen_7187, q_gen_7188, q_gen_7189, q_gen_7190, q_gen_7191, q_gen_7192, q_gen_7193, q_gen_7194, q_gen_7195, q_gen_7196, q_gen_7197, q_gen_7198, q_gen_7199, q_gen_7200, q_gen_7201, q_gen_7202, q_gen_7203, q_gen_7204, q_gen_7205, q_gen_7206, q_gen_7207, q_gen_7208, q_gen_7209, q_gen_7210, q_gen_7211, q_gen_7212, q_gen_7213, q_gen_7214, q_gen_7215, q_gen_7216, q_gen_7217, q_gen_7218, q_gen_7219, q_gen_7220, q_gen_7221, q_gen_7222, q_gen_7223, q_gen_7224, q_gen_7225, q_gen_7226, q_gen_7227, q_gen_7228, q_gen_7229, q_gen_7230, q_gen_7231, q_gen_7232, q_gen_7233, q_gen_7234, q_gen_7235, q_gen_7236, q_gen_7237, q_gen_7238, q_gen_7239, q_gen_7240, q_gen_7241, q_gen_7242, q_gen_7243, q_gen_7244, q_gen_7245, q_gen_7246, q_gen_7247, q_gen_7248, q_gen_7249, q_gen_7250, q_gen_7251, q_gen_7252, q_gen_7253, q_gen_7254, q_gen_7255, q_gen_7256, q_gen_7257, q_gen_7258, q_gen_7259, q_gen_7260, q_gen_7261, q_gen_7262, q_gen_7263, q_gen_7264, q_gen_7265, q_gen_7266, q_gen_7267, q_gen_7268, q_gen_7269, q_gen_7270, q_gen_7271, q_gen_7272, q_gen_7273, q_gen_7274, q_gen_7275, q_gen_7276, q_gen_7277, q_gen_7278, q_gen_7279, q_gen_7280, q_gen_7281, q_gen_7282, q_gen_7283, q_gen_7284, q_gen_7285, q_gen_7286, q_gen_7287, q_gen_7288, q_gen_7289, q_gen_7290, q_gen_7291, q_gen_7292, q_gen_7293, q_gen_7294, q_gen_7295, q_gen_7296, q_gen_7297, q_gen_7298, q_gen_7299, q_gen_7300, q_gen_7301, q_gen_7302, q_gen_7303, q_gen_7304, q_gen_7305, q_gen_7306, q_gen_7307, q_gen_7308, q_gen_7309, q_gen_7310, q_gen_7311, q_gen_7312, q_gen_7313, q_gen_7314, q_gen_7315, q_gen_7316, q_gen_7317, q_gen_7318, q_gen_7319, q_gen_7320, q_gen_7321, q_gen_7322, q_gen_7323, q_gen_7324, q_gen_7325, q_gen_7326, q_gen_7327, q_gen_7328, q_gen_7329, q_gen_7330, q_gen_7331, q_gen_7332, q_gen_7333, q_gen_7334, q_gen_7335, q_gen_7336, q_gen_7337, q_gen_7338, q_gen_7339, q_gen_7340, q_gen_7341},
Q_f={},
Delta=
{
<nil>() -> q_gen_7158
<z>() -> q_gen_7162
<s>(q_gen_7162) -> q_gen_7165
<cons>(q_gen_7162, q_gen_7158) -> q_gen_7167
<s>(q_gen_7165) -> q_gen_7175
<cons>(q_gen_7162, q_gen_7167) -> q_gen_7182
<cons>(q_gen_7162, q_gen_7186) -> q_gen_7185
<cons>(q_gen_7162, q_gen_7182) -> q_gen_7186
<cons>(q_gen_7165, q_gen_7182) -> q_gen_7192
<cons>(q_gen_7162, q_gen_7192) -> q_gen_7197
<s>(q_gen_7175) -> q_gen_7204
<s>(q_gen_7204) -> q_gen_7213
<cons>(q_gen_7162, q_gen_7185) -> q_gen_7218
<s>(q_gen_7213) -> q_gen_7230
<s>(q_gen_7243) -> q_gen_7242
<s>(q_gen_7230) -> q_gen_7243
<s>(q_gen_7256) -> q_gen_7255
<s>(q_gen_7257) -> q_gen_7256
<s>(q_gen_7258) -> q_gen_7257
<s>(q_gen_7259) -> q_gen_7258
<s>(q_gen_7260) -> q_gen_7259
<s>(q_gen_7242) -> q_gen_7260
<cons>(q_gen_7162, q_gen_7304) -> q_gen_7303
<cons>(q_gen_7162, q_gen_7218) -> q_gen_7304
<cons>(q_gen_7162, q_gen_7197) -> q_gen_7330
<nil, z>() -> q_gen_7156
<cons, s>(q_gen_7159, q_gen_7158) -> q_gen_7157
<z, z>() -> q_gen_7159
<cons, s>(q_gen_7161, q_gen_7158) -> q_gen_7160
<s, z>(q_gen_7162) -> q_gen_7161
<cons, s>(q_gen_7164, q_gen_7158) -> q_gen_7163
<s, z>(q_gen_7165) -> q_gen_7164
<cons, s>(q_gen_7168, q_gen_7167) -> q_gen_7166
<z, s>(q_gen_7162) -> q_gen_7168
<cons, s>(q_gen_7159, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7167) -> q_gen_7170
<z, s>(q_gen_7165) -> q_gen_7171
<cons, s>(q_gen_7168, q_gen_7158) -> q_gen_7172
<cons, s>(q_gen_7174, q_gen_7158) -> q_gen_7173
<s, z>(q_gen_7175) -> q_gen_7174
<cons, s>(q_gen_7177, q_gen_7167) -> q_gen_7176
<z, s>(q_gen_7175) -> q_gen_7177
<cons, s>(q_gen_7171, q_gen_7158) -> q_gen_7178
<cons, s>(q_gen_7180, q_gen_7167) -> q_gen_7179
<s, s>(q_gen_7159) -> q_gen_7180
<cons, s>(q_gen_7183, q_gen_7182) -> q_gen_7181
<s, s>(q_gen_7168) -> q_gen_7183
<cons, s>(q_gen_7168, q_gen_7185) -> q_gen_7184
<cons, s>(q_gen_7168, q_gen_7182) -> q_gen_7187
<cons, s>(q_gen_7168, q_gen_7186) -> q_gen_7188
<cons, s>(q_gen_7159, q_gen_7182) -> q_gen_7189
<cons, s>(q_gen_7159, q_gen_7186) -> q_gen_7190
<cons, s>(q_gen_7177, q_gen_7192) -> q_gen_7191
<cons, s>(q_gen_7171, q_gen_7185) -> q_gen_7193
<cons, s>(q_gen_7171, q_gen_7182) -> q_gen_7194
<cons, s>(q_gen_7168, q_gen_7192) -> q_gen_7195
<cons, s>(q_gen_7171, q_gen_7197) -> q_gen_7196
<cons, s>(q_gen_7177, q_gen_7182) -> q_gen_7198
<cons, s>(q_gen_7159, q_gen_7185) -> q_gen_7199
<cons, s>(q_gen_7177, q_gen_7186) -> q_gen_7200
<cons, s>(q_gen_7177, q_gen_7185) -> q_gen_7201
<cons, s>(q_gen_7203, q_gen_7158) -> q_gen_7202
<s, z>(q_gen_7204) -> q_gen_7203
<cons, s>(q_gen_7206, q_gen_7186) -> q_gen_7205
<z, s>(q_gen_7204) -> q_gen_7206
<cons, s>(q_gen_7208, q_gen_7186) -> q_gen_7207
<s, s>(q_gen_7183) -> q_gen_7208
<cons, s>(q_gen_7206, q_gen_7167) -> q_gen_7209
<cons, s>(q_gen_7177, q_gen_7158) -> q_gen_7210
<cons, s>(q_gen_7212, q_gen_7186) -> q_gen_7211
<z, s>(q_gen_7213) -> q_gen_7212
<cons, s>(q_gen_7215, q_gen_7185) -> q_gen_7214
<s, s>(q_gen_7216) -> q_gen_7215
<s, s>(q_gen_7171) -> q_gen_7216
<cons, s>(q_gen_7171, q_gen_7218) -> q_gen_7217
<cons, s>(q_gen_7206, q_gen_7158) -> q_gen_7219
<cons, s>(q_gen_7221, q_gen_7167) -> q_gen_7220
<s, s>(q_gen_7222) -> q_gen_7221
<s, s>(q_gen_7177) -> q_gen_7222
<cons, s>(q_gen_7206, q_gen_7182) -> q_gen_7223
<cons, s>(q_gen_7206, q_gen_7185) -> q_gen_7224
<cons, s>(q_gen_7212, q_gen_7218) -> q_gen_7225
<cons, s>(q_gen_7206, q_gen_7218) -> q_gen_7226
<cons, s>(q_gen_7212, q_gen_7167) -> q_gen_7227
<cons, s>(q_gen_7229, q_gen_7158) -> q_gen_7228
<s, z>(q_gen_7230) -> q_gen_7229
<cons, s>(q_gen_7232, q_gen_7167) -> q_gen_7231
<z, s>(q_gen_7230) -> q_gen_7232
<cons, s>(q_gen_7232, q_gen_7158) -> q_gen_7233
<cons, s>(q_gen_7235, q_gen_7167) -> q_gen_7234
<s, s>(q_gen_7236) -> q_gen_7235
<s, s>(q_gen_7212) -> q_gen_7236
<cons, s>(q_gen_7212, q_gen_7158) -> q_gen_7237
<cons, s>(q_gen_7216, q_gen_7186) -> q_gen_7238
<cons, s>(q_gen_7212, q_gen_7182) -> q_gen_7239
<cons, s>(q_gen_7241, q_gen_7185) -> q_gen_7240
<z, s>(q_gen_7242) -> q_gen_7241
<cons, s>(q_gen_7245, q_gen_7218) -> q_gen_7244
<s, s>(q_gen_7246) -> q_gen_7245
<s, s>(q_gen_7247) -> q_gen_7246
<s, s>(q_gen_7232) -> q_gen_7247
<cons, s>(q_gen_7232, q_gen_7218) -> q_gen_7248
<cons, s>(q_gen_7212, q_gen_7192) -> q_gen_7249
<cons, s>(q_gen_7236, q_gen_7197) -> q_gen_7250
<cons, s>(q_gen_7252, q_gen_7218) -> q_gen_7251
<z, s>(q_gen_7243) -> q_gen_7252
<cons, s>(q_gen_7254, q_gen_7182) -> q_gen_7253
<z, s>(q_gen_7255) -> q_gen_7254
<cons, s>(q_gen_7262, q_gen_7186) -> q_gen_7261
<s, s>(q_gen_7263) -> q_gen_7262
<s, s>(q_gen_7264) -> q_gen_7263
<s, s>(q_gen_7265) -> q_gen_7264
<s, s>(q_gen_7266) -> q_gen_7265
<s, s>(q_gen_7267) -> q_gen_7266
<s, s>(q_gen_7268) -> q_gen_7267
<s, s>(q_gen_7269) -> q_gen_7268
<s, s>(q_gen_7270) -> q_gen_7269
<s, s>(q_gen_7271) -> q_gen_7270
<s, s>(q_gen_7272) -> q_gen_7271
<s, s>(q_gen_7215) -> q_gen_7272
<cons, s>(q_gen_7252, q_gen_7186) -> q_gen_7273
<cons, s>(q_gen_7252, q_gen_7158) -> q_gen_7274
<cons, s>(q_gen_7276, q_gen_7167) -> q_gen_7275
<s, s>(q_gen_7277) -> q_gen_7276
<s, s>(q_gen_7278) -> q_gen_7277
<s, s>(q_gen_7279) -> q_gen_7278
<s, s>(q_gen_7280) -> q_gen_7279
<s, s>(q_gen_7208) -> q_gen_7280
<cons, s>(q_gen_7232, q_gen_7186) -> q_gen_7281
<cons, s>(q_gen_7252, q_gen_7167) -> q_gen_7282
<cons, s>(q_gen_7284, q_gen_7182) -> q_gen_7283
<s, s>(q_gen_7285) -> q_gen_7284
<s, s>(q_gen_7286) -> q_gen_7285
<s, s>(q_gen_7287) -> q_gen_7286
<s, s>(q_gen_7206) -> q_gen_7287
<cons, s>(q_gen_7277, q_gen_7167) -> q_gen_7288
<cons, s>(q_gen_7241, q_gen_7186) -> q_gen_7289
<cons, s>(q_gen_7291, q_gen_7185) -> q_gen_7290
<z, s>(q_gen_7256) -> q_gen_7291
<cons, s>(q_gen_7293, q_gen_7218) -> q_gen_7292
<s, s>(q_gen_7294) -> q_gen_7293
<s, s>(q_gen_7295) -> q_gen_7294
<s, s>(q_gen_7296) -> q_gen_7295
<s, s>(q_gen_7297) -> q_gen_7296
<s, s>(q_gen_7245) -> q_gen_7297
<cons, s>(q_gen_7212, q_gen_7185) -> q_gen_7298
<cons, s>(q_gen_7272, q_gen_7218) -> q_gen_7299
<cons, s>(q_gen_7241, q_gen_7182) -> q_gen_7300
<cons, s>(q_gen_7232, q_gen_7182) -> q_gen_7301
<cons, s>(q_gen_7177, q_gen_7303) -> q_gen_7302
<cons, s>(q_gen_7232, q_gen_7197) -> q_gen_7305
<cons, s>(q_gen_7232, q_gen_7185) -> q_gen_7306
<cons, s>(q_gen_7254, q_gen_7158) -> q_gen_7307
<cons, s>(q_gen_7309, q_gen_7167) -> q_gen_7308
<s, s>(q_gen_7310) -> q_gen_7309
<s, s>(q_gen_7311) -> q_gen_7310
<s, s>(q_gen_7312) -> q_gen_7311
<s, s>(q_gen_7313) -> q_gen_7312
<s, s>(q_gen_7314) -> q_gen_7313
<s, s>(q_gen_7315) -> q_gen_7314
<s, s>(q_gen_7316) -> q_gen_7315
<s, s>(q_gen_7235) -> q_gen_7316
<cons, s>(q_gen_7236, q_gen_7304) -> q_gen_7317
<cons, s>(q_gen_7232, q_gen_7304) -> q_gen_7318
<cons, s>(q_gen_7252, q_gen_7304) -> q_gen_7319
<cons, s>(q_gen_7321, q_gen_7192) -> q_gen_7320
<z, s>(q_gen_7257) -> q_gen_7321
<cons, s>(q_gen_7323, q_gen_7197) -> q_gen_7322
<s, s>(q_gen_7324) -> q_gen_7323
<s, s>(q_gen_7325) -> q_gen_7324
<s, s>(q_gen_7326) -> q_gen_7325
<s, s>(q_gen_7327) -> q_gen_7326
<s, s>(q_gen_7284) -> q_gen_7327
<cons, s>(q_gen_7252, q_gen_7185) -> q_gen_7328
<cons, s>(q_gen_7252, q_gen_7330) -> q_gen_7329
<cons, s>(q_gen_7159, q_gen_7218) -> q_gen_7331
<cons, s>(q_gen_7333, q_gen_7182) -> q_gen_7332
<z, s>(q_gen_7260) -> q_gen_7333
<cons, s>(q_gen_7335, q_gen_7186) -> q_gen_7334
<s, s>(q_gen_7336) -> q_gen_7335
<s, s>(q_gen_7337) -> q_gen_7336
<s, s>(q_gen_7252) -> q_gen_7337
<cons, s>(q_gen_7339, q_gen_7182) -> q_gen_7338
<z, s>(q_gen_7259) -> q_gen_7339
<cons, s>(q_gen_7341, q_gen_7186) -> q_gen_7340
<s, s>(q_gen_7335) -> q_gen_7341
}

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

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

-------------------
STEPS:
-------------------------------------------
Step 0, which took 0.006891 s (model generation: 0.006775,  model checking: 0.000116):

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

}

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

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

Teacher's answer:
New clause system:
{
() -> length([nil, z]) -> 3
(length([l, _cba]) /\ length([cons(z, cons(z, l)), _bba])) -> eq_nat([_bba, s(s(_cba))]) -> 1
(length([ll, _xaa])) -> length([cons(x, ll), s(_xaa)]) -> 1
}
Sat witness: Found: (() -> length([nil, z]), {

})

-------------------------------------------
Step 1, which took 0.006976 s (model generation: 0.006837,  model checking: 0.000139):

Model:
|_
{
length -> 
{{{
Q={q_gen_7156},
Q_f={q_gen_7156},
Delta=
{
<nil, z>() -> q_gen_7156
}

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

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

Teacher's answer:
New clause system:
{
() -> length([nil, z]) -> 3
(length([l, _cba]) /\ length([cons(z, cons(z, l)), _bba])) -> eq_nat([_bba, s(s(_cba))]) -> 1
(length([ll, _xaa])) -> length([cons(x, ll), s(_xaa)]) -> 4
}
Sat witness: Found: ((length([ll, _xaa])) -> length([cons(x, ll), s(_xaa)]), {
_xaa -> z  ;  ll -> nil  ;  x -> z
})

-------------------------------------------
Step 2, which took 0.009718 s (model generation: 0.008039,  model checking: 0.001679):

Model:
|_
{
length -> 
{{{
Q={q_gen_7156, q_gen_7158, q_gen_7159},
Q_f={q_gen_7156},
Delta=
{
<nil>() -> q_gen_7158
<cons, s>(q_gen_7159, q_gen_7158) -> q_gen_7156
<nil, z>() -> q_gen_7156
<z, z>() -> q_gen_7159
}

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

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

Teacher's answer:
New clause system:
{
() -> length([nil, z]) -> 4
(length([l, _cba]) /\ length([cons(z, cons(z, l)), _bba])) -> eq_nat([_bba, s(s(_cba))]) -> 2
(length([ll, _xaa])) -> length([cons(x, ll), s(_xaa)]) -> 7
}
Sat witness: Found: ((length([ll, _xaa])) -> length([cons(x, ll), s(_xaa)]), {
_xaa -> z  ;  ll -> nil  ;  x -> s(z)
})

-------------------------------------------
Step 3, which took 0.008227 s (model generation: 0.007830,  model checking: 0.000397):

Model:
|_
{
length -> 
{{{
Q={q_gen_7156, q_gen_7158, q_gen_7159, q_gen_7162},
Q_f={q_gen_7156},
Delta=
{
<nil>() -> q_gen_7158
<z>() -> q_gen_7162
<cons, s>(q_gen_7159, q_gen_7158) -> q_gen_7156
<nil, z>() -> q_gen_7156
<s, z>(q_gen_7162) -> q_gen_7159
<z, z>() -> q_gen_7159
}

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

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

Teacher's answer:
New clause system:
{
() -> length([nil, z]) -> 5
(length([l, _cba]) /\ length([cons(z, cons(z, l)), _bba])) -> eq_nat([_bba, s(s(_cba))]) -> 3
(length([ll, _xaa])) -> length([cons(x, ll), s(_xaa)]) -> 10
}
Sat witness: Found: ((length([ll, _xaa])) -> length([cons(x, ll), s(_xaa)]), {
_xaa -> z  ;  ll -> nil  ;  x -> s(s(z))
})

-------------------------------------------
Step 4, which took 0.009155 s (model generation: 0.008024,  model checking: 0.001131):

Model:
|_
{
length -> 
{{{
Q={q_gen_7156, q_gen_7158, q_gen_7159, q_gen_7162},
Q_f={q_gen_7156},
Delta=
{
<nil>() -> q_gen_7158
<s>(q_gen_7162) -> q_gen_7162
<z>() -> q_gen_7162
<cons, s>(q_gen_7159, q_gen_7158) -> q_gen_7156
<nil, z>() -> q_gen_7156
<s, z>(q_gen_7162) -> q_gen_7159
<z, z>() -> q_gen_7159
}

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

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

Teacher's answer:
New clause system:
{
() -> length([nil, z]) -> 6
(length([l, _cba]) /\ length([cons(z, cons(z, l)), _bba])) -> eq_nat([_bba, s(s(_cba))]) -> 4
(length([ll, _xaa])) -> length([cons(x, ll), s(_xaa)]) -> 13
}
Sat witness: Found: ((length([ll, _xaa])) -> length([cons(x, ll), s(_xaa)]), {
_xaa -> s(z)  ;  ll -> cons(z, nil)  ;  x -> z
})

-------------------------------------------
Step 5, which took 0.009395 s (model generation: 0.009220,  model checking: 0.000175):

Model:
|_
{
length -> 
{{{
Q={q_gen_7156, q_gen_7158, q_gen_7159, q_gen_7162},
Q_f={q_gen_7156},
Delta=
{
<cons>(q_gen_7162, q_gen_7158) -> q_gen_7158
<nil>() -> q_gen_7158
<s>(q_gen_7162) -> q_gen_7162
<z>() -> q_gen_7162
<cons, s>(q_gen_7159, q_gen_7158) -> q_gen_7156
<nil, z>() -> q_gen_7156
<s, z>(q_gen_7162) -> q_gen_7159
<z, s>(q_gen_7162) -> q_gen_7159
<z, z>() -> q_gen_7159
}

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

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

Teacher's answer:
New clause system:
{
() -> length([nil, z]) -> 6
(length([l, _cba]) /\ length([cons(z, cons(z, l)), _bba])) -> eq_nat([_bba, s(s(_cba))]) -> 7
(length([ll, _xaa])) -> length([cons(x, ll), s(_xaa)]) -> 13
}
Sat witness: Found: ((length([l, _cba]) /\ length([cons(z, cons(z, l)), _bba])) -> eq_nat([_bba, s(s(_cba))]), {
_bba -> s(z)  ;  _cba -> z  ;  l -> nil
})

-------------------------------------------
Step 6, which took 0.010507 s (model generation: 0.009493,  model checking: 0.001014):

Model:
|_
{
length -> 
{{{
Q={q_gen_7156, q_gen_7158, q_gen_7159, q_gen_7162, q_gen_7167, q_gen_7168, q_gen_7169},
Q_f={q_gen_7156},
Delta=
{
<nil>() -> q_gen_7158
<s>(q_gen_7162) -> q_gen_7162
<z>() -> q_gen_7162
<cons>(q_gen_7162, q_gen_7158) -> q_gen_7167
<cons, s>(q_gen_7159, q_gen_7158) -> q_gen_7156
<cons, s>(q_gen_7168, q_gen_7167) -> q_gen_7156
<nil, z>() -> q_gen_7156
<s, z>(q_gen_7162) -> q_gen_7159
<z, z>() -> q_gen_7159
<z, s>(q_gen_7162) -> q_gen_7168
<cons, s>(q_gen_7159, q_gen_7167) -> q_gen_7169
}

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

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

Teacher's answer:
New clause system:
{
() -> length([nil, z]) -> 7
(length([l, _cba]) /\ length([cons(z, cons(z, l)), _bba])) -> eq_nat([_bba, s(s(_cba))]) -> 10
(length([ll, _xaa])) -> length([cons(x, ll), s(_xaa)]) -> 13
}
Sat witness: Found: ((length([l, _cba]) /\ length([cons(z, cons(z, l)), _bba])) -> eq_nat([_bba, s(s(_cba))]), {
_bba -> s(s(s(z)))  ;  _cba -> z  ;  l -> nil
})

-------------------------------------------
Step 7, which took 0.015048 s (model generation: 0.013069,  model checking: 0.001979):

Model:
|_
{
length -> 
{{{
Q={q_gen_7156, q_gen_7158, q_gen_7159, q_gen_7161, q_gen_7162, q_gen_7165, q_gen_7167, q_gen_7169},
Q_f={q_gen_7156},
Delta=
{
<nil>() -> q_gen_7158
<z>() -> q_gen_7162
<s>(q_gen_7162) -> q_gen_7165
<cons>(q_gen_7162, q_gen_7158) -> q_gen_7167
<cons, s>(q_gen_7159, q_gen_7158) -> q_gen_7156
<cons, s>(q_gen_7161, q_gen_7158) -> q_gen_7156
<cons, s>(q_gen_7161, q_gen_7167) -> q_gen_7156
<nil, z>() -> q_gen_7156
<z, s>(q_gen_7165) -> q_gen_7159
<z, z>() -> q_gen_7159
<s, z>(q_gen_7162) -> q_gen_7161
<s, z>(q_gen_7165) -> q_gen_7161
<z, s>(q_gen_7162) -> q_gen_7161
<cons, s>(q_gen_7159, q_gen_7167) -> q_gen_7169
}

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

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

Teacher's answer:
New clause system:
{
() -> length([nil, z]) -> 8
(length([l, _cba]) /\ length([cons(z, cons(z, l)), _bba])) -> eq_nat([_bba, s(s(_cba))]) -> 11
(length([ll, _xaa])) -> length([cons(x, ll), s(_xaa)]) -> 16
}
Sat witness: Found: ((length([ll, _xaa])) -> length([cons(x, ll), s(_xaa)]), {
_xaa -> s(s(z))  ;  ll -> cons(z, nil)  ;  x -> z
})

-------------------------------------------
Step 8, which took 0.016192 s (model generation: 0.014623,  model checking: 0.001569):

Model:
|_
{
length -> 
{{{
Q={q_gen_7156, q_gen_7158, q_gen_7159, q_gen_7162, q_gen_7165, q_gen_7167, q_gen_7168, q_gen_7169},
Q_f={q_gen_7156},
Delta=
{
<nil>() -> q_gen_7158
<z>() -> q_gen_7162
<s>(q_gen_7162) -> q_gen_7165
<cons>(q_gen_7162, q_gen_7158) -> q_gen_7167
<cons, s>(q_gen_7159, q_gen_7158) -> q_gen_7156
<cons, s>(q_gen_7168, q_gen_7167) -> q_gen_7156
<nil, z>() -> q_gen_7156
<s, z>(q_gen_7162) -> q_gen_7159
<s, z>(q_gen_7165) -> q_gen_7159
<z, s>(q_gen_7165) -> q_gen_7159
<z, z>() -> q_gen_7159
<z, s>(q_gen_7162) -> q_gen_7168
<cons, s>(q_gen_7159, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7158) -> q_gen_7169
}

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

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

Teacher's answer:
New clause system:
{
() -> length([nil, z]) -> 9
(length([l, _cba]) /\ length([cons(z, cons(z, l)), _bba])) -> eq_nat([_bba, s(s(_cba))]) -> 12
(length([ll, _xaa])) -> length([cons(x, ll), s(_xaa)]) -> 19
}
Sat witness: Found: ((length([ll, _xaa])) -> length([cons(x, ll), s(_xaa)]), {
_xaa -> z  ;  ll -> nil  ;  x -> s(s(s(z)))
})

-------------------------------------------
Step 9, which took 0.014218 s (model generation: 0.013546,  model checking: 0.000672):

Model:
|_
{
length -> 
{{{
Q={q_gen_7156, q_gen_7158, q_gen_7159, q_gen_7162, q_gen_7165, q_gen_7167, q_gen_7168, q_gen_7169},
Q_f={q_gen_7156},
Delta=
{
<nil>() -> q_gen_7158
<s>(q_gen_7165) -> q_gen_7162
<z>() -> q_gen_7162
<s>(q_gen_7162) -> q_gen_7165
<cons>(q_gen_7162, q_gen_7158) -> q_gen_7167
<cons, s>(q_gen_7159, q_gen_7158) -> q_gen_7156
<cons, s>(q_gen_7168, q_gen_7167) -> q_gen_7156
<nil, z>() -> q_gen_7156
<s, z>(q_gen_7162) -> q_gen_7159
<s, z>(q_gen_7165) -> q_gen_7159
<z, s>(q_gen_7165) -> q_gen_7159
<z, z>() -> q_gen_7159
<z, s>(q_gen_7162) -> q_gen_7168
<cons, s>(q_gen_7159, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7158) -> q_gen_7169
}

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

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

Teacher's answer:
New clause system:
{
() -> length([nil, z]) -> 10
(length([l, _cba]) /\ length([cons(z, cons(z, l)), _bba])) -> eq_nat([_bba, s(s(_cba))]) -> 15
(length([ll, _xaa])) -> length([cons(x, ll), s(_xaa)]) -> 19
}
Sat witness: Found: ((length([l, _cba]) /\ length([cons(z, cons(z, l)), _bba])) -> eq_nat([_bba, s(s(_cba))]), {
_bba -> s(s(s(s(z))))  ;  _cba -> z  ;  l -> nil
})

-------------------------------------------
Step 10, which took 0.016002 s (model generation: 0.014545,  model checking: 0.001457):

Model:
|_
{
length -> 
{{{
Q={q_gen_7156, q_gen_7158, q_gen_7159, q_gen_7162, q_gen_7165, q_gen_7167, q_gen_7168, q_gen_7169},
Q_f={q_gen_7156},
Delta=
{
<nil>() -> q_gen_7158
<z>() -> q_gen_7162
<s>(q_gen_7162) -> q_gen_7165
<s>(q_gen_7165) -> q_gen_7165
<cons>(q_gen_7162, q_gen_7158) -> q_gen_7167
<cons, s>(q_gen_7159, q_gen_7158) -> q_gen_7156
<cons, s>(q_gen_7168, q_gen_7167) -> q_gen_7156
<nil, z>() -> q_gen_7156
<s, z>(q_gen_7162) -> q_gen_7159
<s, z>(q_gen_7165) -> q_gen_7159
<z, s>(q_gen_7165) -> q_gen_7159
<z, z>() -> q_gen_7159
<z, s>(q_gen_7162) -> q_gen_7168
<cons, s>(q_gen_7159, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7158) -> q_gen_7169
}

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

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

Teacher's answer:
New clause system:
{
() -> length([nil, z]) -> 11
(length([l, _cba]) /\ length([cons(z, cons(z, l)), _bba])) -> eq_nat([_bba, s(s(_cba))]) -> 16
(length([ll, _xaa])) -> length([cons(x, ll), s(_xaa)]) -> 22
}
Sat witness: Found: ((length([ll, _xaa])) -> length([cons(x, ll), s(_xaa)]), {
_xaa -> s(s(s(z)))  ;  ll -> cons(z, nil)  ;  x -> z
})

-------------------------------------------
Step 11, which took 0.018063 s (model generation: 0.015803,  model checking: 0.002260):

Model:
|_
{
length -> 
{{{
Q={q_gen_7156, q_gen_7158, q_gen_7159, q_gen_7162, q_gen_7165, q_gen_7167, q_gen_7168, q_gen_7169, q_gen_7171},
Q_f={q_gen_7156},
Delta=
{
<nil>() -> q_gen_7158
<z>() -> q_gen_7162
<s>(q_gen_7162) -> q_gen_7165
<s>(q_gen_7165) -> q_gen_7165
<cons>(q_gen_7162, q_gen_7158) -> q_gen_7167
<cons, s>(q_gen_7159, q_gen_7158) -> q_gen_7156
<cons, s>(q_gen_7168, q_gen_7167) -> q_gen_7156
<nil, z>() -> q_gen_7156
<s, z>(q_gen_7162) -> q_gen_7159
<s, z>(q_gen_7165) -> q_gen_7159
<z, z>() -> q_gen_7159
<z, s>(q_gen_7162) -> q_gen_7168
<cons, s>(q_gen_7159, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7167) -> q_gen_7169
<z, s>(q_gen_7165) -> q_gen_7171
}

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

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

Teacher's answer:
New clause system:
{
() -> length([nil, z]) -> 12
(length([l, _cba]) /\ length([cons(z, cons(z, l)), _bba])) -> eq_nat([_bba, s(s(_cba))]) -> 17
(length([ll, _xaa])) -> length([cons(x, ll), s(_xaa)]) -> 25
}
Sat witness: Found: ((length([ll, _xaa])) -> length([cons(x, ll), s(_xaa)]), {
_xaa -> s(z)  ;  ll -> cons(z, nil)  ;  x -> s(z)
})

-------------------------------------------
Step 12, which took 0.019121 s (model generation: 0.016589,  model checking: 0.002532):

Model:
|_
{
length -> 
{{{
Q={q_gen_7156, q_gen_7158, q_gen_7159, q_gen_7162, q_gen_7165, q_gen_7167, q_gen_7168, q_gen_7169, q_gen_7171},
Q_f={q_gen_7156},
Delta=
{
<nil>() -> q_gen_7158
<z>() -> q_gen_7162
<s>(q_gen_7162) -> q_gen_7165
<s>(q_gen_7165) -> q_gen_7165
<cons>(q_gen_7162, q_gen_7158) -> q_gen_7167
<cons, s>(q_gen_7159, q_gen_7158) -> q_gen_7156
<cons, s>(q_gen_7168, q_gen_7167) -> q_gen_7156
<nil, z>() -> q_gen_7156
<s, z>(q_gen_7162) -> q_gen_7159
<s, z>(q_gen_7165) -> q_gen_7159
<z, z>() -> q_gen_7159
<s, s>(q_gen_7159) -> q_gen_7168
<z, s>(q_gen_7162) -> q_gen_7168
<cons, s>(q_gen_7159, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7167) -> q_gen_7169
<z, s>(q_gen_7165) -> q_gen_7171
}

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

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

Teacher's answer:
New clause system:
{
() -> length([nil, z]) -> 13
(length([l, _cba]) /\ length([cons(z, cons(z, l)), _bba])) -> eq_nat([_bba, s(s(_cba))]) -> 18
(length([ll, _xaa])) -> length([cons(x, ll), s(_xaa)]) -> 28
}
Sat witness: Found: ((length([ll, _xaa])) -> length([cons(x, ll), s(_xaa)]), {
_xaa -> s(s(z))  ;  ll -> cons(z, cons(z, nil))  ;  x -> s(z)
})

-------------------------------------------
Step 13, which took 0.021022 s (model generation: 0.019798,  model checking: 0.001224):

Model:
|_
{
length -> 
{{{
Q={q_gen_7156, q_gen_7158, q_gen_7159, q_gen_7162, q_gen_7165, q_gen_7167, q_gen_7168, q_gen_7169, q_gen_7171},
Q_f={q_gen_7156},
Delta=
{
<nil>() -> q_gen_7158
<z>() -> q_gen_7162
<s>(q_gen_7162) -> q_gen_7165
<s>(q_gen_7165) -> q_gen_7165
<cons>(q_gen_7162, q_gen_7158) -> q_gen_7167
<cons>(q_gen_7162, q_gen_7167) -> q_gen_7167
<cons, s>(q_gen_7159, q_gen_7158) -> q_gen_7156
<cons, s>(q_gen_7168, q_gen_7167) -> q_gen_7156
<nil, z>() -> q_gen_7156
<s, z>(q_gen_7162) -> q_gen_7159
<s, z>(q_gen_7165) -> q_gen_7159
<z, z>() -> q_gen_7159
<s, s>(q_gen_7159) -> q_gen_7168
<s, s>(q_gen_7168) -> q_gen_7168
<z, s>(q_gen_7162) -> q_gen_7168
<cons, s>(q_gen_7159, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7167) -> q_gen_7169
<z, s>(q_gen_7165) -> q_gen_7171
}

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

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

Teacher's answer:
New clause system:
{
() -> length([nil, z]) -> 14
(length([l, _cba]) /\ length([cons(z, cons(z, l)), _bba])) -> eq_nat([_bba, s(s(_cba))]) -> 21
(length([ll, _xaa])) -> length([cons(x, ll), s(_xaa)]) -> 28
}
Sat witness: Found: ((length([l, _cba]) /\ length([cons(z, cons(z, l)), _bba])) -> eq_nat([_bba, s(s(_cba))]), {
_bba -> s(s(z))  ;  _cba -> s(s(z))  ;  l -> cons(z, cons(z, cons(z, nil)))
})

-------------------------------------------
Step 14, which took 0.022785 s (model generation: 0.021843,  model checking: 0.000942):

Model:
|_
{
length -> 
{{{
Q={q_gen_7156, q_gen_7158, q_gen_7159, q_gen_7162, q_gen_7165, q_gen_7167, q_gen_7168, q_gen_7169, q_gen_7171},
Q_f={q_gen_7156},
Delta=
{
<cons>(q_gen_7162, q_gen_7167) -> q_gen_7158
<nil>() -> q_gen_7158
<z>() -> q_gen_7162
<s>(q_gen_7162) -> q_gen_7165
<s>(q_gen_7165) -> q_gen_7165
<cons>(q_gen_7162, q_gen_7158) -> q_gen_7167
<cons, s>(q_gen_7159, q_gen_7158) -> q_gen_7156
<cons, s>(q_gen_7168, q_gen_7167) -> q_gen_7156
<nil, z>() -> q_gen_7156
<s, s>(q_gen_7168) -> q_gen_7159
<s, z>(q_gen_7162) -> q_gen_7159
<s, z>(q_gen_7165) -> q_gen_7159
<z, z>() -> q_gen_7159
<s, s>(q_gen_7159) -> q_gen_7168
<z, s>(q_gen_7162) -> q_gen_7168
<cons, s>(q_gen_7159, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7167) -> q_gen_7169
<z, s>(q_gen_7165) -> q_gen_7171
}

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

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

Teacher's answer:
New clause system:
{
() -> length([nil, z]) -> 15
(length([l, _cba]) /\ length([cons(z, cons(z, l)), _bba])) -> eq_nat([_bba, s(s(_cba))]) -> 24
(length([ll, _xaa])) -> length([cons(x, ll), s(_xaa)]) -> 28
}
Sat witness: Found: ((length([l, _cba]) /\ length([cons(z, cons(z, l)), _bba])) -> eq_nat([_bba, s(s(_cba))]), {
_bba -> s(s(z))  ;  _cba -> s(s(z))  ;  l -> cons(z, cons(z, nil))
})

-------------------------------------------
Step 15, which took 0.025647 s (model generation: 0.024343,  model checking: 0.001304):

Model:
|_
{
length -> 
{{{
Q={q_gen_7156, q_gen_7158, q_gen_7159, q_gen_7162, q_gen_7165, q_gen_7167, q_gen_7168, q_gen_7169, q_gen_7171, q_gen_7182},
Q_f={q_gen_7156},
Delta=
{
<cons>(q_gen_7162, q_gen_7182) -> q_gen_7158
<nil>() -> q_gen_7158
<z>() -> q_gen_7162
<s>(q_gen_7162) -> q_gen_7165
<s>(q_gen_7165) -> q_gen_7165
<cons>(q_gen_7162, q_gen_7158) -> q_gen_7167
<cons>(q_gen_7162, q_gen_7167) -> q_gen_7182
<cons, s>(q_gen_7159, q_gen_7158) -> q_gen_7156
<cons, s>(q_gen_7159, q_gen_7182) -> q_gen_7156
<cons, s>(q_gen_7168, q_gen_7167) -> q_gen_7156
<nil, z>() -> q_gen_7156
<s, s>(q_gen_7168) -> q_gen_7159
<s, z>(q_gen_7162) -> q_gen_7159
<s, z>(q_gen_7165) -> q_gen_7159
<z, z>() -> q_gen_7159
<s, s>(q_gen_7159) -> q_gen_7168
<z, s>(q_gen_7162) -> q_gen_7168
<cons, s>(q_gen_7159, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7167) -> q_gen_7169
<z, s>(q_gen_7165) -> q_gen_7171
}

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

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

Teacher's answer:
New clause system:
{
() -> length([nil, z]) -> 16
(length([l, _cba]) /\ length([cons(z, cons(z, l)), _bba])) -> eq_nat([_bba, s(s(_cba))]) -> 27
(length([ll, _xaa])) -> length([cons(x, ll), s(_xaa)]) -> 28
}
Sat witness: Found: ((length([l, _cba]) /\ length([cons(z, cons(z, l)), _bba])) -> eq_nat([_bba, s(s(_cba))]), {
_bba -> s(z)  ;  _cba -> s(z)  ;  l -> cons(z, nil)
})

-------------------------------------------
Step 16, which took 0.028532 s (model generation: 0.027459,  model checking: 0.001073):

Model:
|_
{
length -> 
{{{
Q={q_gen_7156, q_gen_7158, q_gen_7159, q_gen_7162, q_gen_7165, q_gen_7167, q_gen_7168, q_gen_7169, q_gen_7171, q_gen_7182},
Q_f={q_gen_7156},
Delta=
{
<cons>(q_gen_7162, q_gen_7182) -> q_gen_7158
<nil>() -> q_gen_7158
<z>() -> q_gen_7162
<s>(q_gen_7162) -> q_gen_7165
<s>(q_gen_7165) -> q_gen_7165
<cons>(q_gen_7162, q_gen_7158) -> q_gen_7167
<cons>(q_gen_7162, q_gen_7167) -> q_gen_7182
<cons, s>(q_gen_7159, q_gen_7158) -> q_gen_7156
<cons, s>(q_gen_7168, q_gen_7167) -> q_gen_7156
<cons, s>(q_gen_7171, q_gen_7182) -> q_gen_7156
<nil, z>() -> q_gen_7156
<s, z>(q_gen_7162) -> q_gen_7159
<s, z>(q_gen_7165) -> q_gen_7159
<z, z>() -> q_gen_7159
<s, s>(q_gen_7159) -> q_gen_7168
<z, s>(q_gen_7162) -> q_gen_7168
<cons, s>(q_gen_7159, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7159, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7167) -> q_gen_7169
<s, s>(q_gen_7168) -> q_gen_7171
<z, s>(q_gen_7165) -> q_gen_7171
}

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

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

Teacher's answer:
New clause system:
{
() -> length([nil, z]) -> 17
(length([l, _cba]) /\ length([cons(z, cons(z, l)), _bba])) -> eq_nat([_bba, s(s(_cba))]) -> 30
(length([ll, _xaa])) -> length([cons(x, ll), s(_xaa)]) -> 28
}
Sat witness: Found: ((length([l, _cba]) /\ length([cons(z, cons(z, l)), _bba])) -> eq_nat([_bba, s(s(_cba))]), {
_bba -> s(z)  ;  _cba -> s(s(z))  ;  l -> cons(z, cons(z, nil))
})

-------------------------------------------
Step 17, which took 0.036062 s (model generation: 0.028317,  model checking: 0.007745):

Model:
|_
{
length -> 
{{{
Q={q_gen_7156, q_gen_7158, q_gen_7159, q_gen_7162, q_gen_7165, q_gen_7167, q_gen_7168, q_gen_7169, q_gen_7171, q_gen_7182},
Q_f={q_gen_7156},
Delta=
{
<nil>() -> q_gen_7158
<z>() -> q_gen_7162
<s>(q_gen_7162) -> q_gen_7165
<s>(q_gen_7165) -> q_gen_7165
<cons>(q_gen_7162, q_gen_7158) -> q_gen_7167
<cons>(q_gen_7162, q_gen_7167) -> q_gen_7182
<cons>(q_gen_7162, q_gen_7182) -> q_gen_7182
<cons, s>(q_gen_7159, q_gen_7158) -> q_gen_7156
<cons, s>(q_gen_7168, q_gen_7167) -> q_gen_7156
<cons, s>(q_gen_7171, q_gen_7182) -> q_gen_7156
<nil, z>() -> q_gen_7156
<s, z>(q_gen_7162) -> q_gen_7159
<s, z>(q_gen_7165) -> q_gen_7159
<z, z>() -> q_gen_7159
<s, s>(q_gen_7159) -> q_gen_7168
<z, s>(q_gen_7162) -> q_gen_7168
<cons, s>(q_gen_7159, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7159, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7167) -> q_gen_7169
<s, s>(q_gen_7168) -> q_gen_7171
<z, s>(q_gen_7165) -> q_gen_7171
}

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

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

Teacher's answer:
New clause system:
{
() -> length([nil, z]) -> 18
(length([l, _cba]) /\ length([cons(z, cons(z, l)), _bba])) -> eq_nat([_bba, s(s(_cba))]) -> 30
(length([ll, _xaa])) -> length([cons(x, ll), s(_xaa)]) -> 31
}
Sat witness: Found: ((length([ll, _xaa])) -> length([cons(x, ll), s(_xaa)]), {
_xaa -> s(s(s(z)))  ;  ll -> cons(s(z), cons(z, cons(z, nil)))  ;  x -> z
})

-------------------------------------------
Step 18, which took 0.033916 s (model generation: 0.031398,  model checking: 0.002518):

Model:
|_
{
length -> 
{{{
Q={q_gen_7156, q_gen_7158, q_gen_7159, q_gen_7162, q_gen_7165, q_gen_7167, q_gen_7168, q_gen_7169, q_gen_7171, q_gen_7182},
Q_f={q_gen_7156},
Delta=
{
<nil>() -> q_gen_7158
<z>() -> q_gen_7162
<s>(q_gen_7162) -> q_gen_7165
<s>(q_gen_7165) -> q_gen_7165
<cons>(q_gen_7162, q_gen_7158) -> q_gen_7167
<cons>(q_gen_7162, q_gen_7167) -> q_gen_7182
<cons>(q_gen_7162, q_gen_7182) -> q_gen_7182
<cons>(q_gen_7165, q_gen_7182) -> q_gen_7182
<cons, s>(q_gen_7159, q_gen_7158) -> q_gen_7156
<cons, s>(q_gen_7168, q_gen_7167) -> q_gen_7156
<cons, s>(q_gen_7171, q_gen_7182) -> q_gen_7156
<nil, z>() -> q_gen_7156
<s, z>(q_gen_7162) -> q_gen_7159
<s, z>(q_gen_7165) -> q_gen_7159
<z, z>() -> q_gen_7159
<s, s>(q_gen_7159) -> q_gen_7168
<z, s>(q_gen_7162) -> q_gen_7168
<cons, s>(q_gen_7159, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7159, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7167) -> q_gen_7169
<s, s>(q_gen_7168) -> q_gen_7171
<z, s>(q_gen_7165) -> q_gen_7171
}

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

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

Teacher's answer:
New clause system:
{
() -> length([nil, z]) -> 19
(length([l, _cba]) /\ length([cons(z, cons(z, l)), _bba])) -> eq_nat([_bba, s(s(_cba))]) -> 33
(length([ll, _xaa])) -> length([cons(x, ll), s(_xaa)]) -> 31
}
Sat witness: Found: ((length([l, _cba]) /\ length([cons(z, cons(z, l)), _bba])) -> eq_nat([_bba, s(s(_cba))]), {
_bba -> s(s(s(z)))  ;  _cba -> s(s(s(z)))  ;  l -> cons(z, cons(z, cons(z, nil)))
})

-------------------------------------------
Step 19, which took 0.042913 s (model generation: 0.036371,  model checking: 0.006542):

Model:
|_
{
length -> 
{{{
Q={q_gen_7156, q_gen_7158, q_gen_7159, q_gen_7162, q_gen_7165, q_gen_7167, q_gen_7168, q_gen_7169, q_gen_7171, q_gen_7182, q_gen_7185},
Q_f={q_gen_7156},
Delta=
{
<nil>() -> q_gen_7158
<z>() -> q_gen_7162
<s>(q_gen_7162) -> q_gen_7165
<s>(q_gen_7165) -> q_gen_7165
<cons>(q_gen_7162, q_gen_7158) -> q_gen_7167
<cons>(q_gen_7162, q_gen_7167) -> q_gen_7182
<cons>(q_gen_7165, q_gen_7182) -> q_gen_7182
<cons>(q_gen_7162, q_gen_7182) -> q_gen_7185
<cons>(q_gen_7162, q_gen_7185) -> q_gen_7185
<cons, s>(q_gen_7159, q_gen_7158) -> q_gen_7156
<cons, s>(q_gen_7168, q_gen_7167) -> q_gen_7156
<cons, s>(q_gen_7168, q_gen_7182) -> q_gen_7156
<cons, s>(q_gen_7171, q_gen_7182) -> q_gen_7156
<nil, z>() -> q_gen_7156
<s, z>(q_gen_7162) -> q_gen_7159
<s, z>(q_gen_7165) -> q_gen_7159
<z, z>() -> q_gen_7159
<s, s>(q_gen_7159) -> q_gen_7168
<s, s>(q_gen_7168) -> q_gen_7168
<z, s>(q_gen_7162) -> q_gen_7168
<cons, s>(q_gen_7159, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7159, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7159, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7185) -> q_gen_7169
<z, s>(q_gen_7165) -> q_gen_7171
}

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

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

Teacher's answer:
New clause system:
{
() -> length([nil, z]) -> 20
(length([l, _cba]) /\ length([cons(z, cons(z, l)), _bba])) -> eq_nat([_bba, s(s(_cba))]) -> 33
(length([ll, _xaa])) -> length([cons(x, ll), s(_xaa)]) -> 34
}
Sat witness: Found: ((length([ll, _xaa])) -> length([cons(x, ll), s(_xaa)]), {
_xaa -> s(s(z))  ;  ll -> cons(z, cons(s(z), cons(z, cons(z, nil))))  ;  x -> z
})

-------------------------------------------
Step 20, which took 0.043131 s (model generation: 0.040746,  model checking: 0.002385):

Model:
|_
{
length -> 
{{{
Q={q_gen_7156, q_gen_7158, q_gen_7159, q_gen_7162, q_gen_7165, q_gen_7167, q_gen_7168, q_gen_7169, q_gen_7171, q_gen_7182, q_gen_7185},
Q_f={q_gen_7156},
Delta=
{
<nil>() -> q_gen_7158
<z>() -> q_gen_7162
<s>(q_gen_7162) -> q_gen_7165
<s>(q_gen_7165) -> q_gen_7165
<cons>(q_gen_7162, q_gen_7158) -> q_gen_7167
<cons>(q_gen_7162, q_gen_7167) -> q_gen_7182
<cons>(q_gen_7165, q_gen_7182) -> q_gen_7182
<cons>(q_gen_7162, q_gen_7182) -> q_gen_7185
<cons>(q_gen_7162, q_gen_7185) -> q_gen_7185
<cons, s>(q_gen_7159, q_gen_7158) -> q_gen_7156
<cons, s>(q_gen_7168, q_gen_7167) -> q_gen_7156
<cons, s>(q_gen_7171, q_gen_7182) -> q_gen_7156
<nil, z>() -> q_gen_7156
<s, z>(q_gen_7162) -> q_gen_7159
<s, z>(q_gen_7165) -> q_gen_7159
<z, z>() -> q_gen_7159
<s, s>(q_gen_7159) -> q_gen_7168
<z, s>(q_gen_7162) -> q_gen_7168
<cons, s>(q_gen_7159, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7159, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7159, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7185) -> q_gen_7169
<s, s>(q_gen_7168) -> q_gen_7171
<z, s>(q_gen_7165) -> q_gen_7171
}

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

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

Teacher's answer:
New clause system:
{
() -> length([nil, z]) -> 21
(length([l, _cba]) /\ length([cons(z, cons(z, l)), _bba])) -> eq_nat([_bba, s(s(_cba))]) -> 36
(length([ll, _xaa])) -> length([cons(x, ll), s(_xaa)]) -> 34
}
Sat witness: Found: ((length([l, _cba]) /\ length([cons(z, cons(z, l)), _bba])) -> eq_nat([_bba, s(s(_cba))]), {
_bba -> s(s(s(s(z))))  ;  _cba -> s(z)  ;  l -> cons(z, nil)
})

-------------------------------------------
Step 21, which took 0.055518 s (model generation: 0.048948,  model checking: 0.006570):

Model:
|_
{
length -> 
{{{
Q={q_gen_7156, q_gen_7158, q_gen_7159, q_gen_7162, q_gen_7165, q_gen_7167, q_gen_7168, q_gen_7169, q_gen_7171, q_gen_7182, q_gen_7185},
Q_f={q_gen_7156},
Delta=
{
<nil>() -> q_gen_7158
<z>() -> q_gen_7162
<s>(q_gen_7162) -> q_gen_7165
<s>(q_gen_7165) -> q_gen_7165
<cons>(q_gen_7162, q_gen_7158) -> q_gen_7167
<cons>(q_gen_7162, q_gen_7167) -> q_gen_7182
<cons>(q_gen_7162, q_gen_7182) -> q_gen_7185
<cons>(q_gen_7162, q_gen_7185) -> q_gen_7185
<cons>(q_gen_7165, q_gen_7182) -> q_gen_7185
<cons, s>(q_gen_7159, q_gen_7158) -> q_gen_7156
<cons, s>(q_gen_7168, q_gen_7167) -> q_gen_7156
<cons, s>(q_gen_7168, q_gen_7182) -> q_gen_7156
<cons, s>(q_gen_7171, q_gen_7185) -> q_gen_7156
<nil, z>() -> q_gen_7156
<s, z>(q_gen_7162) -> q_gen_7159
<s, z>(q_gen_7165) -> q_gen_7159
<z, z>() -> q_gen_7159
<s, s>(q_gen_7159) -> q_gen_7168
<s, s>(q_gen_7168) -> q_gen_7168
<z, s>(q_gen_7162) -> q_gen_7168
<cons, s>(q_gen_7159, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7159, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7159, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7182) -> q_gen_7169
<z, s>(q_gen_7165) -> q_gen_7171
}

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

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

Teacher's answer:
New clause system:
{
() -> length([nil, z]) -> 22
(length([l, _cba]) /\ length([cons(z, cons(z, l)), _bba])) -> eq_nat([_bba, s(s(_cba))]) -> 36
(length([ll, _xaa])) -> length([cons(x, ll), s(_xaa)]) -> 37
}
Sat witness: Found: ((length([ll, _xaa])) -> length([cons(x, ll), s(_xaa)]), {
_xaa -> s(s(z))  ;  ll -> cons(z, cons(z, nil))  ;  x -> z
})

-------------------------------------------
Step 22, which took 0.050400 s (model generation: 0.044493,  model checking: 0.005907):

Model:
|_
{
length -> 
{{{
Q={q_gen_7156, q_gen_7158, q_gen_7159, q_gen_7162, q_gen_7165, q_gen_7167, q_gen_7168, q_gen_7169, q_gen_7171, q_gen_7175, q_gen_7182, q_gen_7186},
Q_f={q_gen_7156},
Delta=
{
<cons>(q_gen_7162, q_gen_7186) -> q_gen_7158
<cons>(q_gen_7165, q_gen_7182) -> q_gen_7158
<nil>() -> q_gen_7158
<z>() -> q_gen_7162
<s>(q_gen_7162) -> q_gen_7165
<cons>(q_gen_7162, q_gen_7158) -> q_gen_7167
<s>(q_gen_7165) -> q_gen_7175
<cons>(q_gen_7162, q_gen_7167) -> q_gen_7182
<cons>(q_gen_7162, q_gen_7182) -> q_gen_7186
<cons, s>(q_gen_7159, q_gen_7158) -> q_gen_7156
<cons, s>(q_gen_7168, q_gen_7167) -> q_gen_7156
<cons, s>(q_gen_7171, q_gen_7182) -> q_gen_7156
<nil, z>() -> q_gen_7156
<s, z>(q_gen_7162) -> q_gen_7159
<s, z>(q_gen_7165) -> q_gen_7159
<s, z>(q_gen_7175) -> q_gen_7159
<z, s>(q_gen_7175) -> q_gen_7159
<z, z>() -> q_gen_7159
<s, s>(q_gen_7159) -> q_gen_7168
<z, s>(q_gen_7162) -> q_gen_7168
<cons, s>(q_gen_7159, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7159, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7159, q_gen_7186) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7186) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7167) -> q_gen_7169
<s, s>(q_gen_7168) -> q_gen_7171
<z, s>(q_gen_7165) -> q_gen_7171
}

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

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

Teacher's answer:
New clause system:
{
() -> length([nil, z]) -> 23
(length([l, _cba]) /\ length([cons(z, cons(z, l)), _bba])) -> eq_nat([_bba, s(s(_cba))]) -> 39
(length([ll, _xaa])) -> length([cons(x, ll), s(_xaa)]) -> 37
}
Sat witness: Found: ((length([l, _cba]) /\ length([cons(z, cons(z, l)), _bba])) -> eq_nat([_bba, s(s(_cba))]), {
_bba -> s(z)  ;  _cba -> s(s(s(z)))  ;  l -> cons(z, cons(z, cons(z, nil)))
})

-------------------------------------------
Step 23, which took 0.054369 s (model generation: 0.047035,  model checking: 0.007334):

Model:
|_
{
length -> 
{{{
Q={q_gen_7156, q_gen_7158, q_gen_7159, q_gen_7162, q_gen_7165, q_gen_7167, q_gen_7168, q_gen_7169, q_gen_7171, q_gen_7175, q_gen_7182, q_gen_7185},
Q_f={q_gen_7156},
Delta=
{
<cons>(q_gen_7165, q_gen_7182) -> q_gen_7158
<nil>() -> q_gen_7158
<z>() -> q_gen_7162
<s>(q_gen_7162) -> q_gen_7165
<cons>(q_gen_7162, q_gen_7158) -> q_gen_7167
<s>(q_gen_7165) -> q_gen_7175
<cons>(q_gen_7162, q_gen_7167) -> q_gen_7182
<cons>(q_gen_7162, q_gen_7182) -> q_gen_7185
<cons>(q_gen_7162, q_gen_7185) -> q_gen_7185
<cons, s>(q_gen_7159, q_gen_7158) -> q_gen_7156
<cons, s>(q_gen_7168, q_gen_7167) -> q_gen_7156
<cons, s>(q_gen_7171, q_gen_7182) -> q_gen_7156
<nil, z>() -> q_gen_7156
<s, z>(q_gen_7162) -> q_gen_7159
<s, z>(q_gen_7165) -> q_gen_7159
<s, z>(q_gen_7175) -> q_gen_7159
<z, s>(q_gen_7175) -> q_gen_7159
<z, z>() -> q_gen_7159
<s, s>(q_gen_7159) -> q_gen_7168
<z, s>(q_gen_7162) -> q_gen_7168
<cons, s>(q_gen_7159, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7159, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7159, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7185) -> q_gen_7169
<s, s>(q_gen_7168) -> q_gen_7171
<z, s>(q_gen_7165) -> q_gen_7171
}

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

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

Teacher's answer:
New clause system:
{
() -> length([nil, z]) -> 24
(length([l, _cba]) /\ length([cons(z, cons(z, l)), _bba])) -> eq_nat([_bba, s(s(_cba))]) -> 39
(length([ll, _xaa])) -> length([cons(x, ll), s(_xaa)]) -> 40
}
Sat witness: Found: ((length([ll, _xaa])) -> length([cons(x, ll), s(_xaa)]), {
_xaa -> s(s(s(z)))  ;  ll -> cons(z, cons(z, cons(z, nil)))  ;  x -> z
})

-------------------------------------------
Step 24, which took 0.053055 s (model generation: 0.049902,  model checking: 0.003153):

Model:
|_
{
length -> 
{{{
Q={q_gen_7156, q_gen_7158, q_gen_7159, q_gen_7161, q_gen_7162, q_gen_7165, q_gen_7167, q_gen_7168, q_gen_7169, q_gen_7171, q_gen_7175, q_gen_7182, q_gen_7185},
Q_f={q_gen_7156},
Delta=
{
<cons>(q_gen_7165, q_gen_7182) -> q_gen_7158
<nil>() -> q_gen_7158
<z>() -> q_gen_7162
<s>(q_gen_7162) -> q_gen_7165
<cons>(q_gen_7162, q_gen_7158) -> q_gen_7167
<s>(q_gen_7165) -> q_gen_7175
<cons>(q_gen_7162, q_gen_7167) -> q_gen_7182
<cons>(q_gen_7162, q_gen_7182) -> q_gen_7185
<cons>(q_gen_7162, q_gen_7185) -> q_gen_7185
<cons, s>(q_gen_7159, q_gen_7158) -> q_gen_7156
<cons, s>(q_gen_7161, q_gen_7158) -> q_gen_7156
<cons, s>(q_gen_7161, q_gen_7185) -> q_gen_7156
<cons, s>(q_gen_7168, q_gen_7167) -> q_gen_7156
<cons, s>(q_gen_7171, q_gen_7182) -> q_gen_7156
<nil, z>() -> q_gen_7156
<z, z>() -> q_gen_7159
<s, z>(q_gen_7162) -> q_gen_7161
<s, z>(q_gen_7165) -> q_gen_7161
<s, z>(q_gen_7175) -> q_gen_7161
<z, s>(q_gen_7175) -> q_gen_7161
<s, s>(q_gen_7159) -> q_gen_7168
<z, s>(q_gen_7162) -> q_gen_7168
<cons, s>(q_gen_7159, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7159, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7159, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7161, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7161, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7185) -> q_gen_7169
<s, s>(q_gen_7168) -> q_gen_7171
<z, s>(q_gen_7165) -> q_gen_7171
}

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

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

Teacher's answer:
New clause system:
{
() -> length([nil, z]) -> 25
(length([l, _cba]) /\ length([cons(z, cons(z, l)), _bba])) -> eq_nat([_bba, s(s(_cba))]) -> 42
(length([ll, _xaa])) -> length([cons(x, ll), s(_xaa)]) -> 40
}
Sat witness: Found: ((length([l, _cba]) /\ length([cons(z, cons(z, l)), _bba])) -> eq_nat([_bba, s(s(_cba))]), {
_bba -> s(s(s(s(z))))  ;  _cba -> s(s(s(z)))  ;  l -> cons(z, cons(z, cons(z, nil)))
})

-------------------------------------------
Step 25, which took 0.065601 s (model generation: 0.053690,  model checking: 0.011911):

Model:
|_
{
length -> 
{{{
Q={q_gen_7156, q_gen_7158, q_gen_7159, q_gen_7162, q_gen_7164, q_gen_7165, q_gen_7167, q_gen_7168, q_gen_7169, q_gen_7171, q_gen_7175, q_gen_7182, q_gen_7186},
Q_f={q_gen_7156},
Delta=
{
<cons>(q_gen_7165, q_gen_7182) -> q_gen_7158
<nil>() -> q_gen_7158
<z>() -> q_gen_7162
<s>(q_gen_7162) -> q_gen_7165
<cons>(q_gen_7162, q_gen_7158) -> q_gen_7167
<cons>(q_gen_7162, q_gen_7186) -> q_gen_7167
<s>(q_gen_7165) -> q_gen_7175
<cons>(q_gen_7162, q_gen_7167) -> q_gen_7182
<cons>(q_gen_7162, q_gen_7182) -> q_gen_7186
<cons, s>(q_gen_7159, q_gen_7158) -> q_gen_7156
<cons, s>(q_gen_7164, q_gen_7158) -> q_gen_7156
<cons, s>(q_gen_7164, q_gen_7186) -> q_gen_7156
<cons, s>(q_gen_7168, q_gen_7167) -> q_gen_7156
<cons, s>(q_gen_7171, q_gen_7182) -> q_gen_7156
<nil, z>() -> q_gen_7156
<s, z>(q_gen_7162) -> q_gen_7159
<z, z>() -> q_gen_7159
<s, z>(q_gen_7165) -> q_gen_7164
<s, z>(q_gen_7175) -> q_gen_7164
<z, s>(q_gen_7175) -> q_gen_7164
<s, s>(q_gen_7159) -> q_gen_7168
<z, s>(q_gen_7162) -> q_gen_7168
<cons, s>(q_gen_7159, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7159, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7159, q_gen_7186) -> q_gen_7169
<cons, s>(q_gen_7164, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7164, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7186) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7167) -> q_gen_7169
<s, s>(q_gen_7168) -> q_gen_7171
<z, s>(q_gen_7165) -> q_gen_7171
}

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

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

Teacher's answer:
New clause system:
{
() -> length([nil, z]) -> 26
(length([l, _cba]) /\ length([cons(z, cons(z, l)), _bba])) -> eq_nat([_bba, s(s(_cba))]) -> 42
(length([ll, _xaa])) -> length([cons(x, ll), s(_xaa)]) -> 43
}
Sat witness: Found: ((length([ll, _xaa])) -> length([cons(x, ll), s(_xaa)]), {
_xaa -> z  ;  ll -> nil  ;  x -> s(s(s(s(z))))
})

-------------------------------------------
Step 26, which took 0.060067 s (model generation: 0.058034,  model checking: 0.002033):

Model:
|_
{
length -> 
{{{
Q={q_gen_7156, q_gen_7158, q_gen_7159, q_gen_7162, q_gen_7165, q_gen_7167, q_gen_7168, q_gen_7169, q_gen_7171, q_gen_7174, q_gen_7175, q_gen_7182, q_gen_7186},
Q_f={q_gen_7156},
Delta=
{
<cons>(q_gen_7165, q_gen_7182) -> q_gen_7158
<nil>() -> q_gen_7158
<z>() -> q_gen_7162
<s>(q_gen_7162) -> q_gen_7165
<cons>(q_gen_7162, q_gen_7158) -> q_gen_7167
<cons>(q_gen_7162, q_gen_7186) -> q_gen_7167
<s>(q_gen_7165) -> q_gen_7175
<s>(q_gen_7175) -> q_gen_7175
<cons>(q_gen_7162, q_gen_7167) -> q_gen_7182
<cons>(q_gen_7162, q_gen_7182) -> q_gen_7186
<cons, s>(q_gen_7159, q_gen_7158) -> q_gen_7156
<cons, s>(q_gen_7168, q_gen_7167) -> q_gen_7156
<cons, s>(q_gen_7171, q_gen_7182) -> q_gen_7156
<cons, s>(q_gen_7174, q_gen_7158) -> q_gen_7156
<cons, s>(q_gen_7174, q_gen_7186) -> q_gen_7156
<nil, z>() -> q_gen_7156
<s, z>(q_gen_7162) -> q_gen_7159
<s, z>(q_gen_7165) -> q_gen_7159
<z, z>() -> q_gen_7159
<s, s>(q_gen_7159) -> q_gen_7168
<z, s>(q_gen_7162) -> q_gen_7168
<cons, s>(q_gen_7159, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7159, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7159, q_gen_7186) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7186) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7174, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7174, q_gen_7182) -> q_gen_7169
<s, s>(q_gen_7168) -> q_gen_7171
<z, s>(q_gen_7165) -> q_gen_7171
<s, z>(q_gen_7175) -> q_gen_7174
<z, s>(q_gen_7175) -> q_gen_7174
}

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

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

Teacher's answer:
New clause system:
{
() -> length([nil, z]) -> 27
(length([l, _cba]) /\ length([cons(z, cons(z, l)), _bba])) -> eq_nat([_bba, s(s(_cba))]) -> 45
(length([ll, _xaa])) -> length([cons(x, ll), s(_xaa)]) -> 43
}
Sat witness: Found: ((length([l, _cba]) /\ length([cons(z, cons(z, l)), _bba])) -> eq_nat([_bba, s(s(_cba))]), {
_bba -> s(s(s(s(s(z)))))  ;  _cba -> s(s(z))  ;  l -> cons(z, cons(z, nil))
})

-------------------------------------------
Step 27, which took 0.083938 s (model generation: 0.062698,  model checking: 0.021240):

Model:
|_
{
length -> 
{{{
Q={q_gen_7156, q_gen_7158, q_gen_7159, q_gen_7162, q_gen_7165, q_gen_7167, q_gen_7168, q_gen_7169, q_gen_7171, q_gen_7174, q_gen_7175, q_gen_7182, q_gen_7186},
Q_f={q_gen_7156},
Delta=
{
<cons>(q_gen_7165, q_gen_7182) -> q_gen_7158
<nil>() -> q_gen_7158
<s>(q_gen_7175) -> q_gen_7162
<z>() -> q_gen_7162
<s>(q_gen_7162) -> q_gen_7165
<cons>(q_gen_7162, q_gen_7158) -> q_gen_7167
<cons>(q_gen_7162, q_gen_7186) -> q_gen_7167
<s>(q_gen_7165) -> q_gen_7175
<cons>(q_gen_7162, q_gen_7167) -> q_gen_7182
<cons>(q_gen_7162, q_gen_7182) -> q_gen_7186
<cons, s>(q_gen_7159, q_gen_7158) -> q_gen_7156
<cons, s>(q_gen_7168, q_gen_7167) -> q_gen_7156
<cons, s>(q_gen_7171, q_gen_7182) -> q_gen_7156
<cons, s>(q_gen_7174, q_gen_7158) -> q_gen_7156
<cons, s>(q_gen_7174, q_gen_7186) -> q_gen_7156
<nil, z>() -> q_gen_7156
<s, z>(q_gen_7162) -> q_gen_7159
<s, z>(q_gen_7165) -> q_gen_7159
<z, z>() -> q_gen_7159
<s, s>(q_gen_7159) -> q_gen_7168
<z, s>(q_gen_7162) -> q_gen_7168
<cons, s>(q_gen_7159, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7159, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7159, q_gen_7186) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7186) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7174, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7174, q_gen_7182) -> q_gen_7169
<s, s>(q_gen_7168) -> q_gen_7171
<z, s>(q_gen_7165) -> q_gen_7171
<s, z>(q_gen_7175) -> q_gen_7174
<z, s>(q_gen_7175) -> q_gen_7174
}

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

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

Teacher's answer:
New clause system:
{
() -> length([nil, z]) -> 28
(length([l, _cba]) /\ length([cons(z, cons(z, l)), _bba])) -> eq_nat([_bba, s(s(_cba))]) -> 45
(length([ll, _xaa])) -> length([cons(x, ll), s(_xaa)]) -> 46
}
Sat witness: Found: ((length([ll, _xaa])) -> length([cons(x, ll), s(_xaa)]), {
_xaa -> s(s(s(z)))  ;  ll -> cons(z, cons(z, cons(z, nil)))  ;  x -> s(s(z))
})

-------------------------------------------
Step 28, which took 0.067024 s (model generation: 0.065445,  model checking: 0.001579):

Model:
|_
{
length -> 
{{{
Q={q_gen_7156, q_gen_7158, q_gen_7159, q_gen_7162, q_gen_7165, q_gen_7167, q_gen_7168, q_gen_7169, q_gen_7171, q_gen_7174, q_gen_7175, q_gen_7182, q_gen_7186},
Q_f={q_gen_7156},
Delta=
{
<nil>() -> q_gen_7158
<s>(q_gen_7175) -> q_gen_7162
<z>() -> q_gen_7162
<s>(q_gen_7162) -> q_gen_7165
<cons>(q_gen_7162, q_gen_7158) -> q_gen_7167
<cons>(q_gen_7162, q_gen_7186) -> q_gen_7167
<s>(q_gen_7165) -> q_gen_7175
<cons>(q_gen_7162, q_gen_7167) -> q_gen_7182
<cons>(q_gen_7162, q_gen_7182) -> q_gen_7186
<cons>(q_gen_7165, q_gen_7182) -> q_gen_7186
<cons, s>(q_gen_7159, q_gen_7158) -> q_gen_7156
<cons, s>(q_gen_7168, q_gen_7167) -> q_gen_7156
<cons, s>(q_gen_7171, q_gen_7182) -> q_gen_7156
<cons, s>(q_gen_7174, q_gen_7158) -> q_gen_7156
<cons, s>(q_gen_7174, q_gen_7186) -> q_gen_7156
<nil, z>() -> q_gen_7156
<s, z>(q_gen_7162) -> q_gen_7159
<s, z>(q_gen_7165) -> q_gen_7159
<z, z>() -> q_gen_7159
<s, s>(q_gen_7159) -> q_gen_7168
<z, s>(q_gen_7162) -> q_gen_7168
<cons, s>(q_gen_7159, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7159, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7159, q_gen_7186) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7186) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7174, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7174, q_gen_7182) -> q_gen_7169
<s, s>(q_gen_7168) -> q_gen_7171
<z, s>(q_gen_7165) -> q_gen_7171
<s, s>(q_gen_7171) -> q_gen_7174
<s, z>(q_gen_7175) -> q_gen_7174
<z, s>(q_gen_7175) -> q_gen_7174
}

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

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

Teacher's answer:
New clause system:
{
() -> length([nil, z]) -> 29
(length([l, _cba]) /\ length([cons(z, cons(z, l)), _bba])) -> eq_nat([_bba, s(s(_cba))]) -> 48
(length([ll, _xaa])) -> length([cons(x, ll), s(_xaa)]) -> 46
}
Sat witness: Found: ((length([l, _cba]) /\ length([cons(z, cons(z, l)), _bba])) -> eq_nat([_bba, s(s(_cba))]), {
_bba -> s(s(s(s(s(z)))))  ;  _cba -> z  ;  l -> nil
})

-------------------------------------------
Step 29, which took 0.083892 s (model generation: 0.076683,  model checking: 0.007209):

Model:
|_
{
length -> 
{{{
Q={q_gen_7156, q_gen_7158, q_gen_7159, q_gen_7162, q_gen_7165, q_gen_7167, q_gen_7168, q_gen_7169, q_gen_7171, q_gen_7174, q_gen_7175, q_gen_7182, q_gen_7186},
Q_f={q_gen_7156},
Delta=
{
<nil>() -> q_gen_7158
<z>() -> q_gen_7162
<s>(q_gen_7162) -> q_gen_7165
<s>(q_gen_7175) -> q_gen_7165
<cons>(q_gen_7162, q_gen_7158) -> q_gen_7167
<cons>(q_gen_7162, q_gen_7186) -> q_gen_7167
<s>(q_gen_7165) -> q_gen_7175
<cons>(q_gen_7162, q_gen_7167) -> q_gen_7182
<cons>(q_gen_7162, q_gen_7182) -> q_gen_7186
<cons>(q_gen_7165, q_gen_7182) -> q_gen_7186
<cons, s>(q_gen_7159, q_gen_7158) -> q_gen_7156
<cons, s>(q_gen_7168, q_gen_7167) -> q_gen_7156
<cons, s>(q_gen_7171, q_gen_7182) -> q_gen_7156
<cons, s>(q_gen_7174, q_gen_7158) -> q_gen_7156
<cons, s>(q_gen_7174, q_gen_7186) -> q_gen_7156
<nil, z>() -> q_gen_7156
<s, z>(q_gen_7162) -> q_gen_7159
<s, z>(q_gen_7165) -> q_gen_7159
<z, z>() -> q_gen_7159
<s, s>(q_gen_7159) -> q_gen_7168
<z, s>(q_gen_7162) -> q_gen_7168
<cons, s>(q_gen_7159, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7159, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7159, q_gen_7186) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7186) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7186) -> q_gen_7169
<cons, s>(q_gen_7174, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7174, q_gen_7182) -> q_gen_7169
<s, s>(q_gen_7168) -> q_gen_7171
<z, s>(q_gen_7165) -> q_gen_7171
<s, s>(q_gen_7171) -> q_gen_7174
<s, z>(q_gen_7175) -> q_gen_7174
<z, s>(q_gen_7175) -> q_gen_7174
}

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

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

Teacher's answer:
New clause system:
{
() -> length([nil, z]) -> 30
(length([l, _cba]) /\ length([cons(z, cons(z, l)), _bba])) -> eq_nat([_bba, s(s(_cba))]) -> 48
(length([ll, _xaa])) -> length([cons(x, ll), s(_xaa)]) -> 49
}
Sat witness: Found: ((length([ll, _xaa])) -> length([cons(x, ll), s(_xaa)]), {
_xaa -> s(s(s(s(z))))  ;  ll -> cons(z, nil)  ;  x -> z
})

-------------------------------------------
Step 30, which took 0.077441 s (model generation: 0.074632,  model checking: 0.002809):

Model:
|_
{
length -> 
{{{
Q={q_gen_7156, q_gen_7158, q_gen_7159, q_gen_7162, q_gen_7165, q_gen_7167, q_gen_7168, q_gen_7169, q_gen_7171, q_gen_7175, q_gen_7177, q_gen_7182, q_gen_7186},
Q_f={q_gen_7156},
Delta=
{
<nil>() -> q_gen_7158
<z>() -> q_gen_7162
<s>(q_gen_7162) -> q_gen_7165
<s>(q_gen_7175) -> q_gen_7165
<cons>(q_gen_7162, q_gen_7158) -> q_gen_7167
<cons>(q_gen_7162, q_gen_7186) -> q_gen_7167
<s>(q_gen_7165) -> q_gen_7175
<cons>(q_gen_7162, q_gen_7167) -> q_gen_7182
<cons>(q_gen_7162, q_gen_7182) -> q_gen_7186
<cons>(q_gen_7165, q_gen_7182) -> q_gen_7186
<cons, s>(q_gen_7159, q_gen_7158) -> q_gen_7156
<cons, s>(q_gen_7168, q_gen_7167) -> q_gen_7156
<cons, s>(q_gen_7171, q_gen_7182) -> q_gen_7156
<cons, s>(q_gen_7177, q_gen_7186) -> q_gen_7156
<nil, z>() -> q_gen_7156
<s, z>(q_gen_7162) -> q_gen_7159
<s, z>(q_gen_7165) -> q_gen_7159
<s, z>(q_gen_7175) -> q_gen_7159
<z, z>() -> q_gen_7159
<s, s>(q_gen_7159) -> q_gen_7168
<z, s>(q_gen_7162) -> q_gen_7168
<cons, s>(q_gen_7159, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7159, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7159, q_gen_7186) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7186) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7186) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7182) -> q_gen_7169
<s, s>(q_gen_7168) -> q_gen_7171
<z, s>(q_gen_7165) -> q_gen_7171
<s, s>(q_gen_7171) -> q_gen_7177
<z, s>(q_gen_7175) -> q_gen_7177
}

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

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

Teacher's answer:
New clause system:
{
() -> length([nil, z]) -> 31
(length([l, _cba]) /\ length([cons(z, cons(z, l)), _bba])) -> eq_nat([_bba, s(s(_cba))]) -> 51
(length([ll, _xaa])) -> length([cons(x, ll), s(_xaa)]) -> 49
}
Sat witness: Found: ((length([l, _cba]) /\ length([cons(z, cons(z, l)), _bba])) -> eq_nat([_bba, s(s(_cba))]), {
_bba -> s(s(s(s(s(s(z))))))  ;  _cba -> s(s(z))  ;  l -> cons(z, cons(z, nil))
})

-------------------------------------------
Step 31, which took 0.092262 s (model generation: 0.080412,  model checking: 0.011850):

Model:
|_
{
length -> 
{{{
Q={q_gen_7156, q_gen_7158, q_gen_7159, q_gen_7162, q_gen_7165, q_gen_7167, q_gen_7168, q_gen_7169, q_gen_7171, q_gen_7175, q_gen_7177, q_gen_7182, q_gen_7186, q_gen_7204},
Q_f={q_gen_7156},
Delta=
{
<nil>() -> q_gen_7158
<s>(q_gen_7204) -> q_gen_7162
<z>() -> q_gen_7162
<s>(q_gen_7162) -> q_gen_7165
<cons>(q_gen_7162, q_gen_7158) -> q_gen_7167
<cons>(q_gen_7162, q_gen_7186) -> q_gen_7167
<s>(q_gen_7165) -> q_gen_7175
<cons>(q_gen_7162, q_gen_7167) -> q_gen_7182
<cons>(q_gen_7162, q_gen_7182) -> q_gen_7186
<cons>(q_gen_7165, q_gen_7182) -> q_gen_7186
<s>(q_gen_7175) -> q_gen_7204
<cons, s>(q_gen_7159, q_gen_7158) -> q_gen_7156
<cons, s>(q_gen_7168, q_gen_7167) -> q_gen_7156
<cons, s>(q_gen_7171, q_gen_7182) -> q_gen_7156
<cons, s>(q_gen_7171, q_gen_7186) -> q_gen_7156
<cons, s>(q_gen_7177, q_gen_7186) -> q_gen_7156
<nil, z>() -> q_gen_7156
<s, z>(q_gen_7162) -> q_gen_7159
<s, z>(q_gen_7165) -> q_gen_7159
<s, z>(q_gen_7175) -> q_gen_7159
<s, z>(q_gen_7204) -> q_gen_7159
<z, s>(q_gen_7204) -> q_gen_7159
<z, z>() -> q_gen_7159
<s, s>(q_gen_7159) -> q_gen_7168
<z, s>(q_gen_7162) -> q_gen_7168
<cons, s>(q_gen_7159, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7159, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7159, q_gen_7186) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7186) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7182) -> q_gen_7169
<s, s>(q_gen_7168) -> q_gen_7171
<s, s>(q_gen_7171) -> q_gen_7171
<z, s>(q_gen_7165) -> q_gen_7171
<z, s>(q_gen_7175) -> q_gen_7177
}

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

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

Teacher's answer:
New clause system:
{
() -> length([nil, z]) -> 32
(length([l, _cba]) /\ length([cons(z, cons(z, l)), _bba])) -> eq_nat([_bba, s(s(_cba))]) -> 51
(length([ll, _xaa])) -> length([cons(x, ll), s(_xaa)]) -> 52
}
Sat witness: Found: ((length([ll, _xaa])) -> length([cons(x, ll), s(_xaa)]), {
_xaa -> s(s(s(s(z))))  ;  ll -> cons(z, cons(z, cons(z, cons(z, nil))))  ;  x -> s(s(z))
})

-------------------------------------------
Step 32, which took 0.092185 s (model generation: 0.086796,  model checking: 0.005389):

Model:
|_
{
length -> 
{{{
Q={q_gen_7156, q_gen_7158, q_gen_7159, q_gen_7162, q_gen_7165, q_gen_7167, q_gen_7168, q_gen_7169, q_gen_7171, q_gen_7175, q_gen_7177, q_gen_7182, q_gen_7186, q_gen_7204},
Q_f={q_gen_7156},
Delta=
{
<nil>() -> q_gen_7158
<z>() -> q_gen_7162
<s>(q_gen_7162) -> q_gen_7165
<cons>(q_gen_7162, q_gen_7158) -> q_gen_7167
<cons>(q_gen_7162, q_gen_7186) -> q_gen_7167
<s>(q_gen_7165) -> q_gen_7175
<cons>(q_gen_7162, q_gen_7167) -> q_gen_7182
<cons>(q_gen_7162, q_gen_7182) -> q_gen_7186
<cons>(q_gen_7165, q_gen_7182) -> q_gen_7186
<s>(q_gen_7175) -> q_gen_7204
<s>(q_gen_7204) -> q_gen_7204
<cons, s>(q_gen_7159, q_gen_7158) -> q_gen_7156
<cons, s>(q_gen_7168, q_gen_7167) -> q_gen_7156
<cons, s>(q_gen_7171, q_gen_7182) -> q_gen_7156
<cons, s>(q_gen_7177, q_gen_7186) -> q_gen_7156
<nil, z>() -> q_gen_7156
<s, z>(q_gen_7162) -> q_gen_7159
<s, z>(q_gen_7165) -> q_gen_7159
<s, z>(q_gen_7175) -> q_gen_7159
<s, z>(q_gen_7204) -> q_gen_7159
<z, s>(q_gen_7204) -> q_gen_7159
<z, z>() -> q_gen_7159
<s, s>(q_gen_7159) -> q_gen_7168
<s, s>(q_gen_7177) -> q_gen_7168
<z, s>(q_gen_7162) -> q_gen_7168
<cons, s>(q_gen_7159, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7159, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7159, q_gen_7186) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7186) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7182) -> q_gen_7169
<s, s>(q_gen_7168) -> q_gen_7171
<z, s>(q_gen_7165) -> q_gen_7171
<s, s>(q_gen_7171) -> q_gen_7177
<z, s>(q_gen_7175) -> q_gen_7177
}

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

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

Teacher's answer:
New clause system:
{
() -> length([nil, z]) -> 33
(length([l, _cba]) /\ length([cons(z, cons(z, l)), _bba])) -> eq_nat([_bba, s(s(_cba))]) -> 54
(length([ll, _xaa])) -> length([cons(x, ll), s(_xaa)]) -> 52
}
Sat witness: Found: ((length([l, _cba]) /\ length([cons(z, cons(z, l)), _bba])) -> eq_nat([_bba, s(s(_cba))]), {
_bba -> s(s(s(z)))  ;  _cba -> s(s(s(s(z))))  ;  l -> cons(z, cons(z, cons(z, cons(z, nil))))
})

-------------------------------------------
Step 33, which took 0.107541 s (model generation: 0.097018,  model checking: 0.010523):

Model:
|_
{
length -> 
{{{
Q={q_gen_7156, q_gen_7158, q_gen_7159, q_gen_7162, q_gen_7165, q_gen_7167, q_gen_7168, q_gen_7169, q_gen_7171, q_gen_7175, q_gen_7177, q_gen_7182, q_gen_7185, q_gen_7186, q_gen_7204},
Q_f={q_gen_7156},
Delta=
{
<cons>(q_gen_7162, q_gen_7185) -> q_gen_7158
<nil>() -> q_gen_7158
<s>(q_gen_7204) -> q_gen_7162
<z>() -> q_gen_7162
<s>(q_gen_7162) -> q_gen_7165
<cons>(q_gen_7162, q_gen_7158) -> q_gen_7167
<s>(q_gen_7165) -> q_gen_7175
<cons>(q_gen_7162, q_gen_7167) -> q_gen_7182
<cons>(q_gen_7162, q_gen_7186) -> q_gen_7185
<cons>(q_gen_7162, q_gen_7182) -> q_gen_7186
<cons>(q_gen_7165, q_gen_7182) -> q_gen_7186
<s>(q_gen_7175) -> q_gen_7204
<cons, s>(q_gen_7159, q_gen_7158) -> q_gen_7156
<cons, s>(q_gen_7168, q_gen_7167) -> q_gen_7156
<cons, s>(q_gen_7168, q_gen_7185) -> q_gen_7156
<cons, s>(q_gen_7171, q_gen_7182) -> q_gen_7156
<cons, s>(q_gen_7177, q_gen_7186) -> q_gen_7156
<nil, z>() -> q_gen_7156
<s, z>(q_gen_7162) -> q_gen_7159
<s, z>(q_gen_7165) -> q_gen_7159
<s, z>(q_gen_7175) -> q_gen_7159
<s, z>(q_gen_7204) -> q_gen_7159
<z, s>(q_gen_7204) -> q_gen_7159
<z, z>() -> q_gen_7159
<s, s>(q_gen_7159) -> q_gen_7168
<s, s>(q_gen_7177) -> q_gen_7168
<z, s>(q_gen_7162) -> q_gen_7168
<cons, s>(q_gen_7159, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7159, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7159, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7159, q_gen_7186) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7186) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7185) -> q_gen_7169
<s, s>(q_gen_7168) -> q_gen_7171
<z, s>(q_gen_7165) -> q_gen_7171
<s, s>(q_gen_7171) -> q_gen_7177
<z, s>(q_gen_7175) -> q_gen_7177
}

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

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

Teacher's answer:
New clause system:
{
() -> length([nil, z]) -> 34
(length([l, _cba]) /\ length([cons(z, cons(z, l)), _bba])) -> eq_nat([_bba, s(s(_cba))]) -> 54
(length([ll, _xaa])) -> length([cons(x, ll), s(_xaa)]) -> 55
}
Sat witness: Found: ((length([ll, _xaa])) -> length([cons(x, ll), s(_xaa)]), {
_xaa -> s(s(s(s(s(z)))))  ;  ll -> cons(z, nil)  ;  x -> s(s(z))
})

-------------------------------------------
Step 34, which took 0.115915 s (model generation: 0.109802,  model checking: 0.006113):

Model:
|_
{
length -> 
{{{
Q={q_gen_7156, q_gen_7158, q_gen_7159, q_gen_7162, q_gen_7165, q_gen_7167, q_gen_7168, q_gen_7169, q_gen_7171, q_gen_7175, q_gen_7177, q_gen_7182, q_gen_7185, q_gen_7186, q_gen_7204},
Q_f={q_gen_7156},
Delta=
{
<cons>(q_gen_7162, q_gen_7185) -> q_gen_7158
<nil>() -> q_gen_7158
<z>() -> q_gen_7162
<s>(q_gen_7162) -> q_gen_7165
<cons>(q_gen_7162, q_gen_7158) -> q_gen_7167
<s>(q_gen_7165) -> q_gen_7175
<cons>(q_gen_7162, q_gen_7167) -> q_gen_7182
<cons>(q_gen_7162, q_gen_7186) -> q_gen_7185
<cons>(q_gen_7162, q_gen_7182) -> q_gen_7186
<cons>(q_gen_7165, q_gen_7182) -> q_gen_7186
<s>(q_gen_7175) -> q_gen_7204
<s>(q_gen_7204) -> q_gen_7204
<cons, s>(q_gen_7159, q_gen_7158) -> q_gen_7156
<cons, s>(q_gen_7168, q_gen_7167) -> q_gen_7156
<cons, s>(q_gen_7168, q_gen_7185) -> q_gen_7156
<cons, s>(q_gen_7171, q_gen_7182) -> q_gen_7156
<cons, s>(q_gen_7177, q_gen_7186) -> q_gen_7156
<nil, z>() -> q_gen_7156
<s, z>(q_gen_7162) -> q_gen_7159
<s, z>(q_gen_7165) -> q_gen_7159
<s, z>(q_gen_7175) -> q_gen_7159
<s, z>(q_gen_7204) -> q_gen_7159
<z, z>() -> q_gen_7159
<s, s>(q_gen_7159) -> q_gen_7168
<s, s>(q_gen_7177) -> q_gen_7168
<z, s>(q_gen_7162) -> q_gen_7168
<cons, s>(q_gen_7159, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7159, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7159, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7159, q_gen_7186) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7186) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7186) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7185) -> q_gen_7169
<s, s>(q_gen_7168) -> q_gen_7171
<z, s>(q_gen_7165) -> q_gen_7171
<z, s>(q_gen_7204) -> q_gen_7171
<s, s>(q_gen_7171) -> q_gen_7177
<z, s>(q_gen_7175) -> q_gen_7177
}

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

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

Teacher's answer:
New clause system:
{
() -> length([nil, z]) -> 35
(length([l, _cba]) /\ length([cons(z, cons(z, l)), _bba])) -> eq_nat([_bba, s(s(_cba))]) -> 57
(length([ll, _xaa])) -> length([cons(x, ll), s(_xaa)]) -> 55
}
Sat witness: Found: ((length([l, _cba]) /\ length([cons(z, cons(z, l)), _bba])) -> eq_nat([_bba, s(s(_cba))]), {
_bba -> s(s(s(s(s(z)))))  ;  _cba -> s(z)  ;  l -> cons(z, nil)
})

-------------------------------------------
Step 35, which took 0.135953 s (model generation: 0.114523,  model checking: 0.021430):

Model:
|_
{
length -> 
{{{
Q={q_gen_7156, q_gen_7158, q_gen_7159, q_gen_7162, q_gen_7165, q_gen_7167, q_gen_7168, q_gen_7169, q_gen_7171, q_gen_7175, q_gen_7177, q_gen_7182, q_gen_7185, q_gen_7186, q_gen_7204, q_gen_7206},
Q_f={q_gen_7156},
Delta=
{
<cons>(q_gen_7162, q_gen_7185) -> q_gen_7158
<nil>() -> q_gen_7158
<z>() -> q_gen_7162
<s>(q_gen_7162) -> q_gen_7165
<cons>(q_gen_7162, q_gen_7158) -> q_gen_7167
<s>(q_gen_7165) -> q_gen_7175
<cons>(q_gen_7162, q_gen_7167) -> q_gen_7182
<cons>(q_gen_7162, q_gen_7186) -> q_gen_7185
<cons>(q_gen_7162, q_gen_7182) -> q_gen_7186
<cons>(q_gen_7165, q_gen_7182) -> q_gen_7186
<s>(q_gen_7175) -> q_gen_7204
<s>(q_gen_7204) -> q_gen_7204
<cons, s>(q_gen_7159, q_gen_7158) -> q_gen_7156
<cons, s>(q_gen_7168, q_gen_7167) -> q_gen_7156
<cons, s>(q_gen_7171, q_gen_7182) -> q_gen_7156
<cons, s>(q_gen_7177, q_gen_7186) -> q_gen_7156
<cons, s>(q_gen_7206, q_gen_7185) -> q_gen_7156
<nil, z>() -> q_gen_7156
<s, s>(q_gen_7206) -> q_gen_7159
<s, z>(q_gen_7162) -> q_gen_7159
<s, z>(q_gen_7165) -> q_gen_7159
<s, z>(q_gen_7175) -> q_gen_7159
<s, z>(q_gen_7204) -> q_gen_7159
<z, z>() -> q_gen_7159
<s, s>(q_gen_7159) -> q_gen_7168
<z, s>(q_gen_7162) -> q_gen_7168
<cons, s>(q_gen_7159, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7159, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7159, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7159, q_gen_7186) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7186) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7206, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7206, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7206, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7206, q_gen_7186) -> q_gen_7169
<s, s>(q_gen_7168) -> q_gen_7171
<z, s>(q_gen_7165) -> q_gen_7171
<s, s>(q_gen_7171) -> q_gen_7177
<z, s>(q_gen_7175) -> q_gen_7177
<s, s>(q_gen_7177) -> q_gen_7206
<z, s>(q_gen_7204) -> q_gen_7206
}

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

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

Teacher's answer:
New clause system:
{
() -> length([nil, z]) -> 36
(length([l, _cba]) /\ length([cons(z, cons(z, l)), _bba])) -> eq_nat([_bba, s(s(_cba))]) -> 57
(length([ll, _xaa])) -> length([cons(x, ll), s(_xaa)]) -> 58
}
Sat witness: Found: ((length([ll, _xaa])) -> length([cons(x, ll), s(_xaa)]), {
_xaa -> s(s(s(s(s(z)))))  ;  ll -> cons(z, cons(z, cons(z, cons(z, cons(z, nil)))))  ;  x -> z
})

-------------------------------------------
Step 36, which took 0.131713 s (model generation: 0.128316,  model checking: 0.003397):

Model:
|_
{
length -> 
{{{
Q={q_gen_7156, q_gen_7158, q_gen_7159, q_gen_7162, q_gen_7165, q_gen_7167, q_gen_7168, q_gen_7169, q_gen_7171, q_gen_7175, q_gen_7177, q_gen_7182, q_gen_7185, q_gen_7186, q_gen_7204, q_gen_7206},
Q_f={q_gen_7156},
Delta=
{
<nil>() -> q_gen_7158
<z>() -> q_gen_7162
<s>(q_gen_7162) -> q_gen_7165
<cons>(q_gen_7162, q_gen_7158) -> q_gen_7167
<s>(q_gen_7165) -> q_gen_7175
<cons>(q_gen_7162, q_gen_7167) -> q_gen_7182
<cons>(q_gen_7162, q_gen_7185) -> q_gen_7185
<cons>(q_gen_7162, q_gen_7186) -> q_gen_7185
<cons>(q_gen_7162, q_gen_7182) -> q_gen_7186
<cons>(q_gen_7165, q_gen_7182) -> q_gen_7186
<s>(q_gen_7175) -> q_gen_7204
<s>(q_gen_7204) -> q_gen_7204
<cons, s>(q_gen_7159, q_gen_7158) -> q_gen_7156
<cons, s>(q_gen_7168, q_gen_7167) -> q_gen_7156
<cons, s>(q_gen_7171, q_gen_7182) -> q_gen_7156
<cons, s>(q_gen_7177, q_gen_7186) -> q_gen_7156
<cons, s>(q_gen_7206, q_gen_7185) -> q_gen_7156
<nil, z>() -> q_gen_7156
<s, s>(q_gen_7206) -> q_gen_7159
<s, z>(q_gen_7162) -> q_gen_7159
<s, z>(q_gen_7165) -> q_gen_7159
<s, z>(q_gen_7175) -> q_gen_7159
<s, z>(q_gen_7204) -> q_gen_7159
<z, z>() -> q_gen_7159
<s, s>(q_gen_7159) -> q_gen_7168
<z, s>(q_gen_7162) -> q_gen_7168
<cons, s>(q_gen_7159, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7159, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7159, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7159, q_gen_7186) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7186) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7206, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7206, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7206, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7206, q_gen_7186) -> q_gen_7169
<s, s>(q_gen_7168) -> q_gen_7171
<z, s>(q_gen_7165) -> q_gen_7171
<s, s>(q_gen_7171) -> q_gen_7177
<z, s>(q_gen_7175) -> q_gen_7177
<s, s>(q_gen_7177) -> q_gen_7206
<z, s>(q_gen_7204) -> q_gen_7206
}

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

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

Teacher's answer:
New clause system:
{
() -> length([nil, z]) -> 37
(length([l, _cba]) /\ length([cons(z, cons(z, l)), _bba])) -> eq_nat([_bba, s(s(_cba))]) -> 60
(length([ll, _xaa])) -> length([cons(x, ll), s(_xaa)]) -> 58
}
Sat witness: Found: ((length([l, _cba]) /\ length([cons(z, cons(z, l)), _bba])) -> eq_nat([_bba, s(s(_cba))]), {
_bba -> s(s(s(s(s(z)))))  ;  _cba -> s(s(s(s(z))))  ;  l -> cons(z, cons(z, cons(z, cons(z, nil))))
})

-------------------------------------------
Step 37, which took 0.154350 s (model generation: 0.132650,  model checking: 0.021700):

Model:
|_
{
length -> 
{{{
Q={q_gen_7156, q_gen_7158, q_gen_7159, q_gen_7162, q_gen_7165, q_gen_7167, q_gen_7168, q_gen_7169, q_gen_7171, q_gen_7175, q_gen_7177, q_gen_7182, q_gen_7185, q_gen_7186, q_gen_7204, q_gen_7208},
Q_f={q_gen_7156},
Delta=
{
<nil>() -> q_gen_7158
<z>() -> q_gen_7162
<s>(q_gen_7162) -> q_gen_7165
<cons>(q_gen_7162, q_gen_7158) -> q_gen_7167
<s>(q_gen_7165) -> q_gen_7175
<cons>(q_gen_7162, q_gen_7167) -> q_gen_7182
<cons>(q_gen_7162, q_gen_7185) -> q_gen_7185
<cons>(q_gen_7162, q_gen_7186) -> q_gen_7185
<cons>(q_gen_7162, q_gen_7182) -> q_gen_7186
<cons>(q_gen_7165, q_gen_7182) -> q_gen_7186
<s>(q_gen_7175) -> q_gen_7204
<s>(q_gen_7204) -> q_gen_7204
<cons, s>(q_gen_7159, q_gen_7158) -> q_gen_7156
<cons, s>(q_gen_7168, q_gen_7167) -> q_gen_7156
<cons, s>(q_gen_7171, q_gen_7182) -> q_gen_7156
<cons, s>(q_gen_7177, q_gen_7186) -> q_gen_7156
<cons, s>(q_gen_7208, q_gen_7185) -> q_gen_7156
<cons, s>(q_gen_7208, q_gen_7186) -> q_gen_7156
<nil, z>() -> q_gen_7156
<s, s>(q_gen_7177) -> q_gen_7159
<s, z>(q_gen_7162) -> q_gen_7159
<s, z>(q_gen_7165) -> q_gen_7159
<s, z>(q_gen_7175) -> q_gen_7159
<s, z>(q_gen_7204) -> q_gen_7159
<z, s>(q_gen_7204) -> q_gen_7159
<z, z>() -> q_gen_7159
<s, s>(q_gen_7159) -> q_gen_7168
<z, s>(q_gen_7162) -> q_gen_7168
<cons, s>(q_gen_7159, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7159, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7159, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7159, q_gen_7186) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7186) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7185) -> q_gen_7169
<s, s>(q_gen_7168) -> q_gen_7171
<z, s>(q_gen_7165) -> q_gen_7171
<z, s>(q_gen_7175) -> q_gen_7177
<s, s>(q_gen_7171) -> q_gen_7208
<s, s>(q_gen_7208) -> q_gen_7208
}

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

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

Teacher's answer:
New clause system:
{
() -> length([nil, z]) -> 38
(length([l, _cba]) /\ length([cons(z, cons(z, l)), _bba])) -> eq_nat([_bba, s(s(_cba))]) -> 60
(length([ll, _xaa])) -> length([cons(x, ll), s(_xaa)]) -> 61
}
Sat witness: Found: ((length([ll, _xaa])) -> length([cons(x, ll), s(_xaa)]), {
_xaa -> s(s(s(s(z))))  ;  ll -> cons(z, cons(z, cons(z, cons(z, nil))))  ;  x -> z
})

-------------------------------------------
Step 38, which took 0.133498 s (model generation: 0.131615,  model checking: 0.001883):

Model:
|_
{
length -> 
{{{
Q={q_gen_7156, q_gen_7158, q_gen_7159, q_gen_7162, q_gen_7165, q_gen_7167, q_gen_7168, q_gen_7169, q_gen_7171, q_gen_7175, q_gen_7177, q_gen_7182, q_gen_7185, q_gen_7186, q_gen_7204, q_gen_7206},
Q_f={q_gen_7156},
Delta=
{
<nil>() -> q_gen_7158
<s>(q_gen_7204) -> q_gen_7162
<z>() -> q_gen_7162
<s>(q_gen_7162) -> q_gen_7165
<cons>(q_gen_7162, q_gen_7158) -> q_gen_7167
<cons>(q_gen_7162, q_gen_7185) -> q_gen_7167
<s>(q_gen_7165) -> q_gen_7175
<cons>(q_gen_7162, q_gen_7167) -> q_gen_7182
<cons>(q_gen_7162, q_gen_7186) -> q_gen_7185
<cons>(q_gen_7162, q_gen_7182) -> q_gen_7186
<cons>(q_gen_7165, q_gen_7182) -> q_gen_7186
<s>(q_gen_7175) -> q_gen_7204
<cons, s>(q_gen_7159, q_gen_7158) -> q_gen_7156
<cons, s>(q_gen_7168, q_gen_7167) -> q_gen_7156
<cons, s>(q_gen_7171, q_gen_7182) -> q_gen_7156
<cons, s>(q_gen_7177, q_gen_7186) -> q_gen_7156
<cons, s>(q_gen_7206, q_gen_7185) -> q_gen_7156
<nil, z>() -> q_gen_7156
<s, s>(q_gen_7206) -> q_gen_7159
<s, z>(q_gen_7162) -> q_gen_7159
<s, z>(q_gen_7165) -> q_gen_7159
<s, z>(q_gen_7175) -> q_gen_7159
<s, z>(q_gen_7204) -> q_gen_7159
<z, z>() -> q_gen_7159
<s, s>(q_gen_7159) -> q_gen_7168
<z, s>(q_gen_7162) -> q_gen_7168
<cons, s>(q_gen_7159, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7159, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7159, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7159, q_gen_7186) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7186) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7206, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7206, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7206, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7206, q_gen_7186) -> q_gen_7169
<s, s>(q_gen_7168) -> q_gen_7171
<z, s>(q_gen_7165) -> q_gen_7171
<s, s>(q_gen_7171) -> q_gen_7177
<z, s>(q_gen_7175) -> q_gen_7177
<s, s>(q_gen_7177) -> q_gen_7206
<z, s>(q_gen_7204) -> q_gen_7206
}

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

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

Teacher's answer:
New clause system:
{
() -> length([nil, z]) -> 39
(length([l, _cba]) /\ length([cons(z, cons(z, l)), _bba])) -> eq_nat([_bba, s(s(_cba))]) -> 63
(length([ll, _xaa])) -> length([cons(x, ll), s(_xaa)]) -> 61
}
Sat witness: Found: ((length([l, _cba]) /\ length([cons(z, cons(z, l)), _bba])) -> eq_nat([_bba, s(s(_cba))]), {
_bba -> s(s(s(s(s(s(z))))))  ;  _cba -> z  ;  l -> nil
})

-------------------------------------------
Step 39, which took 0.189086 s (model generation: 0.144679,  model checking: 0.044407):

Model:
|_
{
length -> 
{{{
Q={q_gen_7156, q_gen_7158, q_gen_7159, q_gen_7162, q_gen_7165, q_gen_7167, q_gen_7168, q_gen_7169, q_gen_7171, q_gen_7175, q_gen_7177, q_gen_7182, q_gen_7185, q_gen_7186, q_gen_7204, q_gen_7206, q_gen_7213},
Q_f={q_gen_7156},
Delta=
{
<cons>(q_gen_7162, q_gen_7185) -> q_gen_7158
<nil>() -> q_gen_7158
<z>() -> q_gen_7162
<s>(q_gen_7162) -> q_gen_7165
<cons>(q_gen_7162, q_gen_7158) -> q_gen_7167
<s>(q_gen_7165) -> q_gen_7175
<cons>(q_gen_7162, q_gen_7167) -> q_gen_7182
<cons>(q_gen_7162, q_gen_7186) -> q_gen_7185
<cons>(q_gen_7162, q_gen_7182) -> q_gen_7186
<cons>(q_gen_7165, q_gen_7182) -> q_gen_7186
<s>(q_gen_7175) -> q_gen_7204
<s>(q_gen_7204) -> q_gen_7213
<cons, s>(q_gen_7159, q_gen_7158) -> q_gen_7156
<cons, s>(q_gen_7168, q_gen_7167) -> q_gen_7156
<cons, s>(q_gen_7171, q_gen_7182) -> q_gen_7156
<cons, s>(q_gen_7177, q_gen_7186) -> q_gen_7156
<cons, s>(q_gen_7206, q_gen_7185) -> q_gen_7156
<nil, z>() -> q_gen_7156
<s, s>(q_gen_7206) -> q_gen_7159
<s, z>(q_gen_7162) -> q_gen_7159
<s, z>(q_gen_7165) -> q_gen_7159
<s, z>(q_gen_7175) -> q_gen_7159
<s, z>(q_gen_7204) -> q_gen_7159
<z, s>(q_gen_7213) -> q_gen_7159
<z, z>() -> q_gen_7159
<s, s>(q_gen_7159) -> q_gen_7168
<z, s>(q_gen_7162) -> q_gen_7168
<cons, s>(q_gen_7159, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7159, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7159, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7159, q_gen_7186) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7186) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7206, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7206, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7206, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7206, q_gen_7186) -> q_gen_7169
<s, s>(q_gen_7168) -> q_gen_7171
<z, s>(q_gen_7165) -> q_gen_7171
<s, s>(q_gen_7171) -> q_gen_7177
<z, s>(q_gen_7175) -> q_gen_7177
<s, s>(q_gen_7177) -> q_gen_7206
<z, s>(q_gen_7204) -> q_gen_7206
}

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

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

Teacher's answer:
New clause system:
{
() -> length([nil, z]) -> 40
(length([l, _cba]) /\ length([cons(z, cons(z, l)), _bba])) -> eq_nat([_bba, s(s(_cba))]) -> 63
(length([ll, _xaa])) -> length([cons(x, ll), s(_xaa)]) -> 64
}
Sat witness: Found: ((length([ll, _xaa])) -> length([cons(x, ll), s(_xaa)]), {
_xaa -> z  ;  ll -> nil  ;  x -> s(s(s(s(s(s(z))))))
})

-------------------------------------------
Step 40, which took 0.158011 s (model generation: 0.155940,  model checking: 0.002071):

Model:
|_
{
length -> 
{{{
Q={q_gen_7156, q_gen_7158, q_gen_7159, q_gen_7162, q_gen_7165, q_gen_7167, q_gen_7168, q_gen_7169, q_gen_7171, q_gen_7175, q_gen_7177, q_gen_7182, q_gen_7185, q_gen_7186, q_gen_7204, q_gen_7206, q_gen_7213},
Q_f={q_gen_7156},
Delta=
{
<cons>(q_gen_7162, q_gen_7185) -> q_gen_7158
<nil>() -> q_gen_7158
<s>(q_gen_7213) -> q_gen_7162
<z>() -> q_gen_7162
<s>(q_gen_7162) -> q_gen_7165
<cons>(q_gen_7162, q_gen_7158) -> q_gen_7167
<s>(q_gen_7165) -> q_gen_7175
<cons>(q_gen_7162, q_gen_7167) -> q_gen_7182
<cons>(q_gen_7162, q_gen_7186) -> q_gen_7185
<cons>(q_gen_7162, q_gen_7182) -> q_gen_7186
<cons>(q_gen_7165, q_gen_7182) -> q_gen_7186
<s>(q_gen_7175) -> q_gen_7204
<s>(q_gen_7204) -> q_gen_7213
<cons, s>(q_gen_7159, q_gen_7158) -> q_gen_7156
<cons, s>(q_gen_7168, q_gen_7167) -> q_gen_7156
<cons, s>(q_gen_7171, q_gen_7182) -> q_gen_7156
<cons, s>(q_gen_7177, q_gen_7186) -> q_gen_7156
<cons, s>(q_gen_7206, q_gen_7185) -> q_gen_7156
<nil, z>() -> q_gen_7156
<s, s>(q_gen_7206) -> q_gen_7159
<s, z>(q_gen_7162) -> q_gen_7159
<s, z>(q_gen_7165) -> q_gen_7159
<s, z>(q_gen_7175) -> q_gen_7159
<s, z>(q_gen_7204) -> q_gen_7159
<z, s>(q_gen_7213) -> q_gen_7159
<z, z>() -> q_gen_7159
<s, s>(q_gen_7159) -> q_gen_7168
<z, s>(q_gen_7162) -> q_gen_7168
<cons, s>(q_gen_7159, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7159, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7159, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7159, q_gen_7186) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7186) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7206, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7206, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7206, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7206, q_gen_7186) -> q_gen_7169
<s, s>(q_gen_7168) -> q_gen_7171
<z, s>(q_gen_7165) -> q_gen_7171
<s, s>(q_gen_7171) -> q_gen_7177
<z, s>(q_gen_7175) -> q_gen_7177
<s, s>(q_gen_7177) -> q_gen_7206
<z, s>(q_gen_7204) -> q_gen_7206
}

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

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

Teacher's answer:
New clause system:
{
() -> length([nil, z]) -> 41
(length([l, _cba]) /\ length([cons(z, cons(z, l)), _bba])) -> eq_nat([_bba, s(s(_cba))]) -> 66
(length([ll, _xaa])) -> length([cons(x, ll), s(_xaa)]) -> 64
}
Sat witness: Found: ((length([l, _cba]) /\ length([cons(z, cons(z, l)), _bba])) -> eq_nat([_bba, s(s(_cba))]), {
_bba -> s(s(s(s(s(s(s(z)))))))  ;  _cba -> z  ;  l -> nil
})

-------------------------------------------
Step 41, which took 0.176517 s (model generation: 0.159984,  model checking: 0.016533):

Model:
|_
{
length -> 
{{{
Q={q_gen_7156, q_gen_7158, q_gen_7159, q_gen_7162, q_gen_7165, q_gen_7167, q_gen_7168, q_gen_7169, q_gen_7171, q_gen_7175, q_gen_7177, q_gen_7182, q_gen_7185, q_gen_7186, q_gen_7204, q_gen_7206, q_gen_7213},
Q_f={q_gen_7156},
Delta=
{
<cons>(q_gen_7162, q_gen_7185) -> q_gen_7158
<nil>() -> q_gen_7158
<z>() -> q_gen_7162
<s>(q_gen_7162) -> q_gen_7165
<cons>(q_gen_7162, q_gen_7158) -> q_gen_7167
<s>(q_gen_7165) -> q_gen_7175
<cons>(q_gen_7162, q_gen_7167) -> q_gen_7182
<cons>(q_gen_7162, q_gen_7186) -> q_gen_7185
<cons>(q_gen_7162, q_gen_7182) -> q_gen_7186
<cons>(q_gen_7165, q_gen_7182) -> q_gen_7186
<s>(q_gen_7175) -> q_gen_7204
<s>(q_gen_7204) -> q_gen_7213
<s>(q_gen_7213) -> q_gen_7213
<cons, s>(q_gen_7159, q_gen_7158) -> q_gen_7156
<cons, s>(q_gen_7168, q_gen_7167) -> q_gen_7156
<cons, s>(q_gen_7171, q_gen_7182) -> q_gen_7156
<cons, s>(q_gen_7177, q_gen_7186) -> q_gen_7156
<cons, s>(q_gen_7206, q_gen_7185) -> q_gen_7156
<nil, z>() -> q_gen_7156
<s, s>(q_gen_7206) -> q_gen_7159
<s, z>(q_gen_7162) -> q_gen_7159
<s, z>(q_gen_7165) -> q_gen_7159
<s, z>(q_gen_7175) -> q_gen_7159
<s, z>(q_gen_7204) -> q_gen_7159
<s, z>(q_gen_7213) -> q_gen_7159
<z, s>(q_gen_7213) -> q_gen_7159
<z, z>() -> q_gen_7159
<s, s>(q_gen_7159) -> q_gen_7168
<z, s>(q_gen_7162) -> q_gen_7168
<cons, s>(q_gen_7159, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7159, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7159, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7159, q_gen_7186) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7186) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7206, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7206, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7206, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7206, q_gen_7186) -> q_gen_7169
<s, s>(q_gen_7168) -> q_gen_7171
<z, s>(q_gen_7165) -> q_gen_7171
<s, s>(q_gen_7171) -> q_gen_7177
<z, s>(q_gen_7175) -> q_gen_7177
<s, s>(q_gen_7177) -> q_gen_7206
<z, s>(q_gen_7204) -> q_gen_7206
}

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

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

Teacher's answer:
New clause system:
{
() -> length([nil, z]) -> 42
(length([l, _cba]) /\ length([cons(z, cons(z, l)), _bba])) -> eq_nat([_bba, s(s(_cba))]) -> 66
(length([ll, _xaa])) -> length([cons(x, ll), s(_xaa)]) -> 67
}
Sat witness: Found: ((length([ll, _xaa])) -> length([cons(x, ll), s(_xaa)]), {
_xaa -> s(s(s(s(s(s(s(z)))))))  ;  ll -> cons(z, nil)  ;  x -> s(s(z))
})

-------------------------------------------
Step 42, which took 0.188989 s (model generation: 0.179970,  model checking: 0.009019):

Model:
|_
{
length -> 
{{{
Q={q_gen_7156, q_gen_7158, q_gen_7159, q_gen_7162, q_gen_7165, q_gen_7167, q_gen_7168, q_gen_7169, q_gen_7171, q_gen_7175, q_gen_7177, q_gen_7182, q_gen_7185, q_gen_7186, q_gen_7204, q_gen_7206, q_gen_7213},
Q_f={q_gen_7156},
Delta=
{
<cons>(q_gen_7162, q_gen_7185) -> q_gen_7158
<nil>() -> q_gen_7158
<z>() -> q_gen_7162
<s>(q_gen_7162) -> q_gen_7165
<cons>(q_gen_7162, q_gen_7158) -> q_gen_7167
<s>(q_gen_7165) -> q_gen_7175
<cons>(q_gen_7162, q_gen_7167) -> q_gen_7182
<cons>(q_gen_7162, q_gen_7186) -> q_gen_7185
<cons>(q_gen_7162, q_gen_7182) -> q_gen_7186
<cons>(q_gen_7165, q_gen_7182) -> q_gen_7186
<s>(q_gen_7175) -> q_gen_7204
<s>(q_gen_7213) -> q_gen_7204
<s>(q_gen_7204) -> q_gen_7213
<cons, s>(q_gen_7159, q_gen_7158) -> q_gen_7156
<cons, s>(q_gen_7168, q_gen_7167) -> q_gen_7156
<cons, s>(q_gen_7171, q_gen_7182) -> q_gen_7156
<cons, s>(q_gen_7177, q_gen_7186) -> q_gen_7156
<cons, s>(q_gen_7206, q_gen_7185) -> q_gen_7156
<nil, z>() -> q_gen_7156
<s, z>(q_gen_7162) -> q_gen_7159
<s, z>(q_gen_7165) -> q_gen_7159
<s, z>(q_gen_7175) -> q_gen_7159
<s, z>(q_gen_7204) -> q_gen_7159
<z, s>(q_gen_7213) -> q_gen_7159
<z, z>() -> q_gen_7159
<s, s>(q_gen_7159) -> q_gen_7168
<z, s>(q_gen_7162) -> q_gen_7168
<cons, s>(q_gen_7159, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7159, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7159, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7159, q_gen_7186) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7186) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7206, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7206, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7206, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7206, q_gen_7186) -> q_gen_7169
<s, s>(q_gen_7168) -> q_gen_7171
<z, s>(q_gen_7165) -> q_gen_7171
<s, s>(q_gen_7171) -> q_gen_7177
<s, s>(q_gen_7206) -> q_gen_7177
<z, s>(q_gen_7175) -> q_gen_7177
<s, s>(q_gen_7177) -> q_gen_7206
<z, s>(q_gen_7204) -> q_gen_7206
}

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

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

Teacher's answer:
New clause system:
{
() -> length([nil, z]) -> 43
(length([l, _cba]) /\ length([cons(z, cons(z, l)), _bba])) -> eq_nat([_bba, s(s(_cba))]) -> 69
(length([ll, _xaa])) -> length([cons(x, ll), s(_xaa)]) -> 67
}
Sat witness: Found: ((length([l, _cba]) /\ length([cons(z, cons(z, l)), _bba])) -> eq_nat([_bba, s(s(_cba))]), {
_bba -> s(s(s(z)))  ;  _cba -> s(s(s(s(s(s(z))))))  ;  l -> cons(z, nil)
})

-------------------------------------------
Step 43, which took 0.210149 s (model generation: 0.189505,  model checking: 0.020644):

Model:
|_
{
length -> 
{{{
Q={q_gen_7156, q_gen_7158, q_gen_7159, q_gen_7162, q_gen_7165, q_gen_7167, q_gen_7168, q_gen_7169, q_gen_7171, q_gen_7175, q_gen_7177, q_gen_7182, q_gen_7183, q_gen_7185, q_gen_7186, q_gen_7204, q_gen_7206, q_gen_7213, q_gen_7218},
Q_f={q_gen_7156},
Delta=
{
<nil>() -> q_gen_7158
<z>() -> q_gen_7162
<s>(q_gen_7162) -> q_gen_7165
<cons>(q_gen_7162, q_gen_7158) -> q_gen_7167
<s>(q_gen_7165) -> q_gen_7175
<s>(q_gen_7213) -> q_gen_7175
<cons>(q_gen_7162, q_gen_7167) -> q_gen_7182
<cons>(q_gen_7162, q_gen_7186) -> q_gen_7185
<cons>(q_gen_7162, q_gen_7182) -> q_gen_7186
<cons>(q_gen_7165, q_gen_7182) -> q_gen_7186
<s>(q_gen_7175) -> q_gen_7204
<s>(q_gen_7204) -> q_gen_7213
<cons>(q_gen_7162, q_gen_7185) -> q_gen_7218
<cons, s>(q_gen_7159, q_gen_7158) -> q_gen_7156
<cons, s>(q_gen_7168, q_gen_7167) -> q_gen_7156
<cons, s>(q_gen_7171, q_gen_7182) -> q_gen_7156
<cons, s>(q_gen_7177, q_gen_7186) -> q_gen_7156
<cons, s>(q_gen_7183, q_gen_7182) -> q_gen_7156
<cons, s>(q_gen_7183, q_gen_7185) -> q_gen_7156
<cons, s>(q_gen_7183, q_gen_7218) -> q_gen_7156
<cons, s>(q_gen_7206, q_gen_7185) -> q_gen_7156
<nil, z>() -> q_gen_7156
<s, s>(q_gen_7206) -> q_gen_7159
<s, z>(q_gen_7162) -> q_gen_7159
<s, z>(q_gen_7165) -> q_gen_7159
<s, z>(q_gen_7175) -> q_gen_7159
<s, z>(q_gen_7204) -> q_gen_7159
<z, z>() -> q_gen_7159
<s, s>(q_gen_7159) -> q_gen_7168
<s, s>(q_gen_7171) -> q_gen_7168
<z, s>(q_gen_7162) -> q_gen_7168
<cons, s>(q_gen_7159, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7159, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7159, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7159, q_gen_7186) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7186) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7218) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7183, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7183, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7183, q_gen_7186) -> q_gen_7169
<cons, s>(q_gen_7206, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7206, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7206, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7206, q_gen_7186) -> q_gen_7169
<cons, s>(q_gen_7206, q_gen_7218) -> q_gen_7169
<z, s>(q_gen_7165) -> q_gen_7171
<s, s>(q_gen_7183) -> q_gen_7177
<z, s>(q_gen_7175) -> q_gen_7177
<s, s>(q_gen_7168) -> q_gen_7183
<z, s>(q_gen_7213) -> q_gen_7183
<s, s>(q_gen_7177) -> q_gen_7206
<z, s>(q_gen_7204) -> q_gen_7206
}

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

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

Teacher's answer:
New clause system:
{
() -> length([nil, z]) -> 44
(length([l, _cba]) /\ length([cons(z, cons(z, l)), _bba])) -> eq_nat([_bba, s(s(_cba))]) -> 69
(length([ll, _xaa])) -> length([cons(x, ll), s(_xaa)]) -> 70
}
Sat witness: Found: ((length([ll, _xaa])) -> length([cons(x, ll), s(_xaa)]), {
_xaa -> s(s(s(z)))  ;  ll -> cons(z, cons(z, cons(z, nil)))  ;  x -> s(z)
})

-------------------------------------------
Step 44, which took 0.204061 s (model generation: 0.200595,  model checking: 0.003466):

Model:
|_
{
length -> 
{{{
Q={q_gen_7156, q_gen_7158, q_gen_7159, q_gen_7162, q_gen_7165, q_gen_7167, q_gen_7168, q_gen_7169, q_gen_7171, q_gen_7175, q_gen_7177, q_gen_7182, q_gen_7183, q_gen_7185, q_gen_7186, q_gen_7204, q_gen_7206, q_gen_7213, q_gen_7218},
Q_f={q_gen_7156},
Delta=
{
<nil>() -> q_gen_7158
<z>() -> q_gen_7162
<s>(q_gen_7162) -> q_gen_7165
<cons>(q_gen_7162, q_gen_7158) -> q_gen_7167
<s>(q_gen_7165) -> q_gen_7175
<cons>(q_gen_7162, q_gen_7167) -> q_gen_7182
<cons>(q_gen_7162, q_gen_7186) -> q_gen_7185
<cons>(q_gen_7162, q_gen_7182) -> q_gen_7186
<cons>(q_gen_7165, q_gen_7182) -> q_gen_7186
<s>(q_gen_7175) -> q_gen_7204
<s>(q_gen_7213) -> q_gen_7204
<s>(q_gen_7204) -> q_gen_7213
<cons>(q_gen_7162, q_gen_7185) -> q_gen_7218
<cons, s>(q_gen_7159, q_gen_7158) -> q_gen_7156
<cons, s>(q_gen_7168, q_gen_7167) -> q_gen_7156
<cons, s>(q_gen_7171, q_gen_7182) -> q_gen_7156
<cons, s>(q_gen_7177, q_gen_7186) -> q_gen_7156
<cons, s>(q_gen_7183, q_gen_7182) -> q_gen_7156
<cons, s>(q_gen_7183, q_gen_7218) -> q_gen_7156
<cons, s>(q_gen_7206, q_gen_7185) -> q_gen_7156
<nil, z>() -> q_gen_7156
<s, s>(q_gen_7206) -> q_gen_7159
<s, z>(q_gen_7162) -> q_gen_7159
<s, z>(q_gen_7165) -> q_gen_7159
<s, z>(q_gen_7175) -> q_gen_7159
<s, z>(q_gen_7204) -> q_gen_7159
<z, z>() -> q_gen_7159
<s, s>(q_gen_7159) -> q_gen_7168
<z, s>(q_gen_7162) -> q_gen_7168
<cons, s>(q_gen_7159, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7159, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7159, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7159, q_gen_7186) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7186) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7218) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7183, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7183, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7183, q_gen_7186) -> q_gen_7169
<cons, s>(q_gen_7206, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7206, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7206, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7206, q_gen_7186) -> q_gen_7169
<cons, s>(q_gen_7206, q_gen_7218) -> q_gen_7169
<z, s>(q_gen_7165) -> q_gen_7171
<s, s>(q_gen_7171) -> q_gen_7177
<s, s>(q_gen_7183) -> q_gen_7177
<z, s>(q_gen_7175) -> q_gen_7177
<s, s>(q_gen_7168) -> q_gen_7183
<z, s>(q_gen_7213) -> q_gen_7183
<s, s>(q_gen_7177) -> q_gen_7206
<z, s>(q_gen_7204) -> q_gen_7206
}

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

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

Teacher's answer:
New clause system:
{
() -> length([nil, z]) -> 45
(length([l, _cba]) /\ length([cons(z, cons(z, l)), _bba])) -> eq_nat([_bba, s(s(_cba))]) -> 72
(length([ll, _xaa])) -> length([cons(x, ll), s(_xaa)]) -> 70
}
Sat witness: Found: ((length([l, _cba]) /\ length([cons(z, cons(z, l)), _bba])) -> eq_nat([_bba, s(s(_cba))]), {
_bba -> s(s(s(s(s(s(z))))))  ;  _cba -> s(z)  ;  l -> cons(z, nil)
})

-------------------------------------------
Step 45, which took 0.230936 s (model generation: 0.207127,  model checking: 0.023809):

Model:
|_
{
length -> 
{{{
Q={q_gen_7156, q_gen_7158, q_gen_7159, q_gen_7162, q_gen_7165, q_gen_7167, q_gen_7168, q_gen_7169, q_gen_7171, q_gen_7175, q_gen_7177, q_gen_7182, q_gen_7185, q_gen_7186, q_gen_7204, q_gen_7206, q_gen_7212, q_gen_7213, q_gen_7218},
Q_f={q_gen_7156},
Delta=
{
<nil>() -> q_gen_7158
<z>() -> q_gen_7162
<s>(q_gen_7162) -> q_gen_7165
<cons>(q_gen_7162, q_gen_7158) -> q_gen_7167
<s>(q_gen_7165) -> q_gen_7175
<cons>(q_gen_7162, q_gen_7167) -> q_gen_7182
<cons>(q_gen_7162, q_gen_7186) -> q_gen_7185
<cons>(q_gen_7162, q_gen_7182) -> q_gen_7186
<cons>(q_gen_7165, q_gen_7182) -> q_gen_7186
<s>(q_gen_7175) -> q_gen_7204
<s>(q_gen_7213) -> q_gen_7204
<s>(q_gen_7204) -> q_gen_7213
<cons>(q_gen_7162, q_gen_7185) -> q_gen_7218
<cons, s>(q_gen_7159, q_gen_7158) -> q_gen_7156
<cons, s>(q_gen_7168, q_gen_7167) -> q_gen_7156
<cons, s>(q_gen_7171, q_gen_7182) -> q_gen_7156
<cons, s>(q_gen_7177, q_gen_7186) -> q_gen_7156
<cons, s>(q_gen_7206, q_gen_7185) -> q_gen_7156
<cons, s>(q_gen_7212, q_gen_7218) -> q_gen_7156
<nil, z>() -> q_gen_7156
<s, s>(q_gen_7206) -> q_gen_7159
<s, z>(q_gen_7162) -> q_gen_7159
<s, z>(q_gen_7165) -> q_gen_7159
<s, z>(q_gen_7175) -> q_gen_7159
<s, z>(q_gen_7204) -> q_gen_7159
<z, z>() -> q_gen_7159
<s, s>(q_gen_7159) -> q_gen_7168
<z, s>(q_gen_7162) -> q_gen_7168
<cons, s>(q_gen_7159, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7159, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7159, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7159, q_gen_7186) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7186) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7218) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7206, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7206, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7206, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7206, q_gen_7186) -> q_gen_7169
<cons, s>(q_gen_7206, q_gen_7218) -> q_gen_7169
<cons, s>(q_gen_7212, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7212, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7212, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7212, q_gen_7186) -> q_gen_7169
<s, s>(q_gen_7168) -> q_gen_7171
<z, s>(q_gen_7165) -> q_gen_7171
<s, s>(q_gen_7171) -> q_gen_7177
<z, s>(q_gen_7175) -> q_gen_7177
<s, s>(q_gen_7177) -> q_gen_7206
<z, s>(q_gen_7204) -> q_gen_7206
<s, s>(q_gen_7212) -> q_gen_7212
<z, s>(q_gen_7213) -> q_gen_7212
}

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

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

Teacher's answer:
New clause system:
{
() -> length([nil, z]) -> 46
(length([l, _cba]) /\ length([cons(z, cons(z, l)), _bba])) -> eq_nat([_bba, s(s(_cba))]) -> 72
(length([ll, _xaa])) -> length([cons(x, ll), s(_xaa)]) -> 73
}
Sat witness: Found: ((length([ll, _xaa])) -> length([cons(x, ll), s(_xaa)]), {
_xaa -> s(s(s(s(s(s(s(s(s(z)))))))))  ;  ll -> cons(z, cons(z, cons(z, cons(z, cons(z, nil)))))  ;  x -> s(s(s(z)))
})

-------------------------------------------
Step 46, which took 0.297014 s (model generation: 0.287866,  model checking: 0.009148):

Model:
|_
{
length -> 
{{{
Q={q_gen_7156, q_gen_7158, q_gen_7159, q_gen_7162, q_gen_7165, q_gen_7167, q_gen_7168, q_gen_7169, q_gen_7171, q_gen_7175, q_gen_7177, q_gen_7182, q_gen_7185, q_gen_7186, q_gen_7192, q_gen_7204, q_gen_7206, q_gen_7212, q_gen_7213},
Q_f={q_gen_7156},
Delta=
{
<nil>() -> q_gen_7158
<z>() -> q_gen_7162
<s>(q_gen_7162) -> q_gen_7165
<cons>(q_gen_7162, q_gen_7158) -> q_gen_7167
<s>(q_gen_7165) -> q_gen_7175
<cons>(q_gen_7162, q_gen_7167) -> q_gen_7182
<cons>(q_gen_7162, q_gen_7186) -> q_gen_7185
<cons>(q_gen_7162, q_gen_7192) -> q_gen_7185
<cons>(q_gen_7162, q_gen_7182) -> q_gen_7186
<cons>(q_gen_7162, q_gen_7185) -> q_gen_7192
<cons>(q_gen_7165, q_gen_7182) -> q_gen_7192
<s>(q_gen_7175) -> q_gen_7204
<s>(q_gen_7204) -> q_gen_7213
<s>(q_gen_7213) -> q_gen_7213
<cons, s>(q_gen_7159, q_gen_7158) -> q_gen_7156
<cons, s>(q_gen_7168, q_gen_7167) -> q_gen_7156
<cons, s>(q_gen_7171, q_gen_7182) -> q_gen_7156
<cons, s>(q_gen_7177, q_gen_7186) -> q_gen_7156
<cons, s>(q_gen_7177, q_gen_7192) -> q_gen_7156
<cons, s>(q_gen_7206, q_gen_7185) -> q_gen_7156
<cons, s>(q_gen_7212, q_gen_7192) -> q_gen_7156
<nil, z>() -> q_gen_7156
<s, z>(q_gen_7162) -> q_gen_7159
<s, z>(q_gen_7165) -> q_gen_7159
<s, z>(q_gen_7175) -> q_gen_7159
<s, z>(q_gen_7204) -> q_gen_7159
<s, z>(q_gen_7213) -> q_gen_7159
<z, z>() -> q_gen_7159
<s, s>(q_gen_7159) -> q_gen_7168
<s, s>(q_gen_7212) -> q_gen_7168
<z, s>(q_gen_7162) -> q_gen_7168
<cons, s>(q_gen_7159, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7159, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7159, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7159, q_gen_7186) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7186) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7192) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7192) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7206, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7206, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7206, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7206, q_gen_7186) -> q_gen_7169
<cons, s>(q_gen_7206, q_gen_7192) -> q_gen_7169
<cons, s>(q_gen_7212, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7212, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7212, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7212, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7212, q_gen_7186) -> q_gen_7169
<s, s>(q_gen_7168) -> q_gen_7171
<s, s>(q_gen_7206) -> q_gen_7171
<z, s>(q_gen_7165) -> q_gen_7171
<s, s>(q_gen_7171) -> q_gen_7177
<z, s>(q_gen_7175) -> q_gen_7177
<s, s>(q_gen_7177) -> q_gen_7206
<z, s>(q_gen_7204) -> q_gen_7206
<z, s>(q_gen_7213) -> q_gen_7212
}

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

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

Teacher's answer:
New clause system:
{
() -> length([nil, z]) -> 47
(length([l, _cba]) /\ length([cons(z, cons(z, l)), _bba])) -> eq_nat([_bba, s(s(_cba))]) -> 75
(length([ll, _xaa])) -> length([cons(x, ll), s(_xaa)]) -> 73
}
Sat witness: Found: ((length([l, _cba]) /\ length([cons(z, cons(z, l)), _bba])) -> eq_nat([_bba, s(s(_cba))]), {
_bba -> s(s(s(s(s(s(s(z)))))))  ;  _cba -> s(s(s(s(z))))  ;  l -> cons(z, cons(z, cons(z, cons(z, nil))))
})

-------------------------------------------
Step 47, which took 0.335021 s (model generation: 0.295308,  model checking: 0.039713):

Model:
|_
{
length -> 
{{{
Q={q_gen_7156, q_gen_7158, q_gen_7159, q_gen_7162, q_gen_7165, q_gen_7167, q_gen_7168, q_gen_7169, q_gen_7171, q_gen_7175, q_gen_7177, q_gen_7182, q_gen_7185, q_gen_7186, q_gen_7192, q_gen_7203, q_gen_7204, q_gen_7212, q_gen_7213},
Q_f={q_gen_7156},
Delta=
{
<nil>() -> q_gen_7158
<z>() -> q_gen_7162
<s>(q_gen_7162) -> q_gen_7165
<s>(q_gen_7213) -> q_gen_7165
<cons>(q_gen_7162, q_gen_7158) -> q_gen_7167
<s>(q_gen_7165) -> q_gen_7175
<cons>(q_gen_7162, q_gen_7167) -> q_gen_7182
<cons>(q_gen_7162, q_gen_7192) -> q_gen_7182
<cons>(q_gen_7162, q_gen_7186) -> q_gen_7185
<cons>(q_gen_7162, q_gen_7182) -> q_gen_7186
<cons>(q_gen_7162, q_gen_7185) -> q_gen_7192
<cons>(q_gen_7165, q_gen_7182) -> q_gen_7192
<s>(q_gen_7175) -> q_gen_7204
<s>(q_gen_7204) -> q_gen_7213
<cons, s>(q_gen_7159, q_gen_7158) -> q_gen_7156
<cons, s>(q_gen_7168, q_gen_7167) -> q_gen_7156
<cons, s>(q_gen_7168, q_gen_7192) -> q_gen_7156
<cons, s>(q_gen_7171, q_gen_7182) -> q_gen_7156
<cons, s>(q_gen_7177, q_gen_7186) -> q_gen_7156
<cons, s>(q_gen_7177, q_gen_7192) -> q_gen_7156
<cons, s>(q_gen_7203, q_gen_7158) -> q_gen_7156
<cons, s>(q_gen_7203, q_gen_7185) -> q_gen_7156
<cons, s>(q_gen_7212, q_gen_7185) -> q_gen_7156
<cons, s>(q_gen_7212, q_gen_7192) -> q_gen_7156
<nil, z>() -> q_gen_7156
<s, z>(q_gen_7162) -> q_gen_7159
<s, z>(q_gen_7165) -> q_gen_7159
<s, z>(q_gen_7175) -> q_gen_7159
<z, z>() -> q_gen_7159
<s, s>(q_gen_7159) -> q_gen_7168
<s, s>(q_gen_7212) -> q_gen_7168
<z, s>(q_gen_7162) -> q_gen_7168
<cons, s>(q_gen_7159, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7159, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7159, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7159, q_gen_7186) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7186) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7192) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7203, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7203, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7203, q_gen_7186) -> q_gen_7169
<cons, s>(q_gen_7203, q_gen_7192) -> q_gen_7169
<cons, s>(q_gen_7212, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7212, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7212, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7212, q_gen_7186) -> q_gen_7169
<s, s>(q_gen_7168) -> q_gen_7171
<z, s>(q_gen_7165) -> q_gen_7171
<s, s>(q_gen_7171) -> q_gen_7177
<z, s>(q_gen_7175) -> q_gen_7177
<s, z>(q_gen_7204) -> q_gen_7203
<z, s>(q_gen_7204) -> q_gen_7203
<s, s>(q_gen_7177) -> q_gen_7212
<z, s>(q_gen_7213) -> q_gen_7212
}

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

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

Teacher's answer:
New clause system:
{
() -> length([nil, z]) -> 48
(length([l, _cba]) /\ length([cons(z, cons(z, l)), _bba])) -> eq_nat([_bba, s(s(_cba))]) -> 75
(length([ll, _xaa])) -> length([cons(x, ll), s(_xaa)]) -> 76
}
Sat witness: Found: ((length([ll, _xaa])) -> length([cons(x, ll), s(_xaa)]), {
_xaa -> s(s(s(s(s(s(z))))))  ;  ll -> cons(z, cons(s(z), cons(z, cons(z, nil))))  ;  x -> s(z)
})

-------------------------------------------
Step 48, which took 0.369432 s (model generation: 0.354719,  model checking: 0.014713):

Model:
|_
{
length -> 
{{{
Q={q_gen_7156, q_gen_7158, q_gen_7159, q_gen_7162, q_gen_7165, q_gen_7167, q_gen_7168, q_gen_7169, q_gen_7171, q_gen_7175, q_gen_7177, q_gen_7182, q_gen_7185, q_gen_7186, q_gen_7192, q_gen_7204, q_gen_7206, q_gen_7212, q_gen_7213},
Q_f={q_gen_7156},
Delta=
{
<nil>() -> q_gen_7158
<z>() -> q_gen_7162
<s>(q_gen_7162) -> q_gen_7165
<cons>(q_gen_7162, q_gen_7158) -> q_gen_7167
<s>(q_gen_7165) -> q_gen_7175
<cons>(q_gen_7162, q_gen_7167) -> q_gen_7182
<cons>(q_gen_7162, q_gen_7186) -> q_gen_7185
<cons>(q_gen_7162, q_gen_7182) -> q_gen_7186
<cons>(q_gen_7162, q_gen_7192) -> q_gen_7186
<cons>(q_gen_7162, q_gen_7185) -> q_gen_7192
<cons>(q_gen_7165, q_gen_7182) -> q_gen_7192
<s>(q_gen_7175) -> q_gen_7204
<s>(q_gen_7213) -> q_gen_7204
<s>(q_gen_7204) -> q_gen_7213
<cons, s>(q_gen_7159, q_gen_7158) -> q_gen_7156
<cons, s>(q_gen_7168, q_gen_7167) -> q_gen_7156
<cons, s>(q_gen_7171, q_gen_7182) -> q_gen_7156
<cons, s>(q_gen_7177, q_gen_7186) -> q_gen_7156
<cons, s>(q_gen_7177, q_gen_7192) -> q_gen_7156
<cons, s>(q_gen_7206, q_gen_7185) -> q_gen_7156
<cons, s>(q_gen_7212, q_gen_7185) -> q_gen_7156
<cons, s>(q_gen_7212, q_gen_7192) -> q_gen_7156
<nil, z>() -> q_gen_7156
<s, z>(q_gen_7162) -> q_gen_7159
<s, z>(q_gen_7165) -> q_gen_7159
<s, z>(q_gen_7175) -> q_gen_7159
<s, z>(q_gen_7204) -> q_gen_7159
<z, z>() -> q_gen_7159
<s, s>(q_gen_7159) -> q_gen_7168
<s, s>(q_gen_7206) -> q_gen_7168
<z, s>(q_gen_7162) -> q_gen_7168
<cons, s>(q_gen_7159, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7159, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7159, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7159, q_gen_7186) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7186) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7192) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7186) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7192) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7206, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7206, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7206, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7206, q_gen_7186) -> q_gen_7169
<cons, s>(q_gen_7206, q_gen_7192) -> q_gen_7169
<cons, s>(q_gen_7212, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7212, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7212, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7212, q_gen_7186) -> q_gen_7169
<s, s>(q_gen_7168) -> q_gen_7171
<z, s>(q_gen_7165) -> q_gen_7171
<s, s>(q_gen_7171) -> q_gen_7177
<s, s>(q_gen_7212) -> q_gen_7177
<z, s>(q_gen_7175) -> q_gen_7177
<z, s>(q_gen_7204) -> q_gen_7206
<s, s>(q_gen_7177) -> q_gen_7212
<z, s>(q_gen_7213) -> q_gen_7212
}

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

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

Teacher's answer:
New clause system:
{
() -> length([nil, z]) -> 49
(length([l, _cba]) /\ length([cons(z, cons(z, l)), _bba])) -> eq_nat([_bba, s(s(_cba))]) -> 78
(length([ll, _xaa])) -> length([cons(x, ll), s(_xaa)]) -> 76
}
Sat witness: Found: ((length([l, _cba]) /\ length([cons(z, cons(z, l)), _bba])) -> eq_nat([_bba, s(s(_cba))]), {
_bba -> s(s(s(s(s(s(s(s(z))))))))  ;  _cba -> s(s(s(s(z))))  ;  l -> cons(z, cons(z, cons(z, cons(z, nil))))
})

-------------------------------------------
Step 49, which took 0.430191 s (model generation: 0.370060,  model checking: 0.060131):

Model:
|_
{
length -> 
{{{
Q={q_gen_7156, q_gen_7158, q_gen_7159, q_gen_7162, q_gen_7165, q_gen_7167, q_gen_7168, q_gen_7169, q_gen_7171, q_gen_7175, q_gen_7177, q_gen_7182, q_gen_7185, q_gen_7186, q_gen_7204, q_gen_7206, q_gen_7212, q_gen_7213, q_gen_7218},
Q_f={q_gen_7156},
Delta=
{
<nil>() -> q_gen_7158
<z>() -> q_gen_7162
<s>(q_gen_7162) -> q_gen_7165
<s>(q_gen_7213) -> q_gen_7165
<cons>(q_gen_7162, q_gen_7158) -> q_gen_7167
<s>(q_gen_7165) -> q_gen_7175
<cons>(q_gen_7162, q_gen_7167) -> q_gen_7182
<cons>(q_gen_7162, q_gen_7186) -> q_gen_7185
<cons>(q_gen_7162, q_gen_7182) -> q_gen_7186
<cons>(q_gen_7165, q_gen_7182) -> q_gen_7186
<s>(q_gen_7175) -> q_gen_7204
<s>(q_gen_7204) -> q_gen_7213
<cons>(q_gen_7162, q_gen_7185) -> q_gen_7218
<cons, s>(q_gen_7159, q_gen_7158) -> q_gen_7156
<cons, s>(q_gen_7159, q_gen_7218) -> q_gen_7156
<cons, s>(q_gen_7168, q_gen_7167) -> q_gen_7156
<cons, s>(q_gen_7171, q_gen_7182) -> q_gen_7156
<cons, s>(q_gen_7177, q_gen_7186) -> q_gen_7156
<cons, s>(q_gen_7206, q_gen_7185) -> q_gen_7156
<cons, s>(q_gen_7212, q_gen_7218) -> q_gen_7156
<nil, z>() -> q_gen_7156
<s, s>(q_gen_7206) -> q_gen_7159
<s, z>(q_gen_7162) -> q_gen_7159
<s, z>(q_gen_7165) -> q_gen_7159
<s, z>(q_gen_7175) -> q_gen_7159
<s, z>(q_gen_7204) -> q_gen_7159
<z, z>() -> q_gen_7159
<s, s>(q_gen_7159) -> q_gen_7168
<z, s>(q_gen_7162) -> q_gen_7168
<cons, s>(q_gen_7159, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7159, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7159, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7159, q_gen_7186) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7186) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7218) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7218) -> q_gen_7169
<cons, s>(q_gen_7206, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7206, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7206, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7206, q_gen_7186) -> q_gen_7169
<cons, s>(q_gen_7206, q_gen_7218) -> q_gen_7169
<cons, s>(q_gen_7212, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7212, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7212, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7212, q_gen_7186) -> q_gen_7169
<s, s>(q_gen_7168) -> q_gen_7171
<s, s>(q_gen_7212) -> q_gen_7171
<z, s>(q_gen_7165) -> q_gen_7171
<s, s>(q_gen_7171) -> q_gen_7177
<z, s>(q_gen_7175) -> q_gen_7177
<s, s>(q_gen_7177) -> q_gen_7206
<z, s>(q_gen_7204) -> q_gen_7206
<z, s>(q_gen_7213) -> q_gen_7212
}

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

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

Teacher's answer:
New clause system:
{
() -> length([nil, z]) -> 50
(length([l, _cba]) /\ length([cons(z, cons(z, l)), _bba])) -> eq_nat([_bba, s(s(_cba))]) -> 78
(length([ll, _xaa])) -> length([cons(x, ll), s(_xaa)]) -> 79
}
Sat witness: Found: ((length([ll, _xaa])) -> length([cons(x, ll), s(_xaa)]), {
_xaa -> s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(z)))))))))))))))  ;  ll -> cons(z, cons(z, cons(z, nil)))  ;  x -> s(s(s(s(s(s(s(s(s(s(s(s(s(z)))))))))))))
})

-------------------------------------------
Step 50, which took 0.487874 s (model generation: 0.484070,  model checking: 0.003804):

Model:
|_
{
length -> 
{{{
Q={q_gen_7156, q_gen_7158, q_gen_7159, q_gen_7161, q_gen_7162, q_gen_7165, q_gen_7167, q_gen_7168, q_gen_7169, q_gen_7171, q_gen_7175, q_gen_7177, q_gen_7182, q_gen_7185, q_gen_7186, q_gen_7204, q_gen_7212, q_gen_7213, q_gen_7218},
Q_f={q_gen_7156},
Delta=
{
<nil>() -> q_gen_7158
<z>() -> q_gen_7162
<s>(q_gen_7162) -> q_gen_7165
<s>(q_gen_7213) -> q_gen_7165
<cons>(q_gen_7162, q_gen_7158) -> q_gen_7167
<s>(q_gen_7165) -> q_gen_7175
<cons>(q_gen_7162, q_gen_7167) -> q_gen_7182
<cons>(q_gen_7162, q_gen_7186) -> q_gen_7185
<cons>(q_gen_7162, q_gen_7182) -> q_gen_7186
<cons>(q_gen_7165, q_gen_7182) -> q_gen_7186
<s>(q_gen_7175) -> q_gen_7204
<s>(q_gen_7204) -> q_gen_7213
<cons>(q_gen_7162, q_gen_7185) -> q_gen_7218
<cons, s>(q_gen_7159, q_gen_7158) -> q_gen_7156
<cons, s>(q_gen_7161, q_gen_7158) -> q_gen_7156
<cons, s>(q_gen_7161, q_gen_7185) -> q_gen_7156
<cons, s>(q_gen_7168, q_gen_7167) -> q_gen_7156
<cons, s>(q_gen_7168, q_gen_7218) -> q_gen_7156
<cons, s>(q_gen_7171, q_gen_7182) -> q_gen_7156
<cons, s>(q_gen_7177, q_gen_7186) -> q_gen_7156
<cons, s>(q_gen_7212, q_gen_7218) -> q_gen_7156
<nil, z>() -> q_gen_7156
<s, z>(q_gen_7204) -> q_gen_7159
<z, z>() -> q_gen_7159
<s, s>(q_gen_7177) -> q_gen_7161
<s, z>(q_gen_7162) -> q_gen_7161
<s, z>(q_gen_7165) -> q_gen_7161
<s, z>(q_gen_7175) -> q_gen_7161
<z, s>(q_gen_7204) -> q_gen_7161
<s, s>(q_gen_7159) -> q_gen_7168
<s, s>(q_gen_7161) -> q_gen_7168
<z, s>(q_gen_7162) -> q_gen_7168
<cons, s>(q_gen_7159, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7159, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7159, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7159, q_gen_7186) -> q_gen_7169
<cons, s>(q_gen_7161, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7161, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7161, q_gen_7186) -> q_gen_7169
<cons, s>(q_gen_7161, q_gen_7218) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7186) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7218) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7218) -> q_gen_7169
<cons, s>(q_gen_7212, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7212, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7212, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7212, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7212, q_gen_7186) -> q_gen_7169
<s, s>(q_gen_7168) -> q_gen_7171
<z, s>(q_gen_7165) -> q_gen_7171
<s, s>(q_gen_7171) -> q_gen_7177
<z, s>(q_gen_7175) -> q_gen_7177
<s, s>(q_gen_7212) -> q_gen_7212
<z, s>(q_gen_7213) -> q_gen_7212
}

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

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

Teacher's answer:
New clause system:
{
() -> length([nil, z]) -> 51
(length([l, _cba]) /\ length([cons(z, cons(z, l)), _bba])) -> eq_nat([_bba, s(s(_cba))]) -> 81
(length([ll, _xaa])) -> length([cons(x, ll), s(_xaa)]) -> 79
}
Sat witness: Found: ((length([l, _cba]) /\ length([cons(z, cons(z, l)), _bba])) -> eq_nat([_bba, s(s(_cba))]), {
_bba -> s(s(s(s(s(s(s(s(z))))))))  ;  _cba -> s(s(z))  ;  l -> cons(z, cons(z, nil))
})

-------------------------------------------
Step 51, which took 0.529044 s (model generation: 0.504633,  model checking: 0.024411):

Model:
|_
{
length -> 
{{{
Q={q_gen_7156, q_gen_7158, q_gen_7159, q_gen_7161, q_gen_7162, q_gen_7165, q_gen_7167, q_gen_7168, q_gen_7169, q_gen_7171, q_gen_7175, q_gen_7177, q_gen_7182, q_gen_7185, q_gen_7186, q_gen_7204, q_gen_7212, q_gen_7213, q_gen_7218},
Q_f={q_gen_7156},
Delta=
{
<nil>() -> q_gen_7158
<z>() -> q_gen_7162
<s>(q_gen_7162) -> q_gen_7165
<cons>(q_gen_7162, q_gen_7158) -> q_gen_7167
<s>(q_gen_7165) -> q_gen_7175
<s>(q_gen_7213) -> q_gen_7175
<cons>(q_gen_7162, q_gen_7167) -> q_gen_7182
<cons>(q_gen_7162, q_gen_7186) -> q_gen_7185
<cons>(q_gen_7162, q_gen_7182) -> q_gen_7186
<cons>(q_gen_7165, q_gen_7182) -> q_gen_7186
<s>(q_gen_7175) -> q_gen_7204
<s>(q_gen_7204) -> q_gen_7213
<cons>(q_gen_7162, q_gen_7185) -> q_gen_7218
<cons, s>(q_gen_7159, q_gen_7158) -> q_gen_7156
<cons, s>(q_gen_7161, q_gen_7158) -> q_gen_7156
<cons, s>(q_gen_7161, q_gen_7185) -> q_gen_7156
<cons, s>(q_gen_7168, q_gen_7167) -> q_gen_7156
<cons, s>(q_gen_7171, q_gen_7182) -> q_gen_7156
<cons, s>(q_gen_7177, q_gen_7186) -> q_gen_7156
<cons, s>(q_gen_7212, q_gen_7218) -> q_gen_7156
<nil, z>() -> q_gen_7156
<s, z>(q_gen_7204) -> q_gen_7159
<z, z>() -> q_gen_7159
<s, s>(q_gen_7177) -> q_gen_7161
<s, z>(q_gen_7162) -> q_gen_7161
<s, z>(q_gen_7165) -> q_gen_7161
<s, z>(q_gen_7175) -> q_gen_7161
<z, s>(q_gen_7204) -> q_gen_7161
<s, s>(q_gen_7159) -> q_gen_7168
<s, s>(q_gen_7161) -> q_gen_7168
<s, s>(q_gen_7212) -> q_gen_7168
<z, s>(q_gen_7162) -> q_gen_7168
<cons, s>(q_gen_7159, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7159, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7159, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7159, q_gen_7186) -> q_gen_7169
<cons, s>(q_gen_7161, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7161, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7161, q_gen_7186) -> q_gen_7169
<cons, s>(q_gen_7161, q_gen_7218) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7186) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7218) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7218) -> q_gen_7169
<cons, s>(q_gen_7212, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7212, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7212, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7212, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7212, q_gen_7186) -> q_gen_7169
<s, s>(q_gen_7168) -> q_gen_7171
<z, s>(q_gen_7165) -> q_gen_7171
<s, s>(q_gen_7171) -> q_gen_7177
<z, s>(q_gen_7175) -> q_gen_7177
<z, s>(q_gen_7213) -> q_gen_7212
}

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

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

Teacher's answer:
New clause system:
{
() -> length([nil, z]) -> 52
(length([l, _cba]) /\ length([cons(z, cons(z, l)), _bba])) -> eq_nat([_bba, s(s(_cba))]) -> 81
(length([ll, _xaa])) -> length([cons(x, ll), s(_xaa)]) -> 82
}
Sat witness: Found: ((length([ll, _xaa])) -> length([cons(x, ll), s(_xaa)]), {
_xaa -> s(s(s(s(s(s(s(s(z))))))))  ;  ll -> cons(z, nil)  ;  x -> s(s(s(s(s(s(s(z)))))))
})

-------------------------------------------
Step 52, which took 0.576557 s (model generation: 0.572281,  model checking: 0.004276):

Model:
|_
{
length -> 
{{{
Q={q_gen_7156, q_gen_7158, q_gen_7159, q_gen_7162, q_gen_7165, q_gen_7167, q_gen_7168, q_gen_7169, q_gen_7171, q_gen_7175, q_gen_7177, q_gen_7182, q_gen_7185, q_gen_7186, q_gen_7204, q_gen_7206, q_gen_7212, q_gen_7213, q_gen_7218},
Q_f={q_gen_7156},
Delta=
{
<nil>() -> q_gen_7158
<z>() -> q_gen_7162
<s>(q_gen_7162) -> q_gen_7165
<cons>(q_gen_7162, q_gen_7158) -> q_gen_7167
<s>(q_gen_7165) -> q_gen_7175
<s>(q_gen_7213) -> q_gen_7175
<cons>(q_gen_7162, q_gen_7167) -> q_gen_7182
<cons>(q_gen_7162, q_gen_7186) -> q_gen_7185
<cons>(q_gen_7162, q_gen_7182) -> q_gen_7186
<cons>(q_gen_7165, q_gen_7182) -> q_gen_7186
<s>(q_gen_7175) -> q_gen_7204
<s>(q_gen_7204) -> q_gen_7213
<cons>(q_gen_7162, q_gen_7185) -> q_gen_7218
<cons, s>(q_gen_7159, q_gen_7158) -> q_gen_7156
<cons, s>(q_gen_7168, q_gen_7167) -> q_gen_7156
<cons, s>(q_gen_7171, q_gen_7182) -> q_gen_7156
<cons, s>(q_gen_7177, q_gen_7186) -> q_gen_7156
<cons, s>(q_gen_7206, q_gen_7185) -> q_gen_7156
<cons, s>(q_gen_7212, q_gen_7218) -> q_gen_7156
<nil, z>() -> q_gen_7156
<s, s>(q_gen_7206) -> q_gen_7159
<s, z>(q_gen_7162) -> q_gen_7159
<s, z>(q_gen_7165) -> q_gen_7159
<s, z>(q_gen_7175) -> q_gen_7159
<s, z>(q_gen_7204) -> q_gen_7159
<z, z>() -> q_gen_7159
<s, s>(q_gen_7159) -> q_gen_7168
<z, s>(q_gen_7162) -> q_gen_7168
<cons, s>(q_gen_7159, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7159, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7159, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7159, q_gen_7186) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7186) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7218) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7218) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7218) -> q_gen_7169
<cons, s>(q_gen_7206, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7206, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7206, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7206, q_gen_7186) -> q_gen_7169
<cons, s>(q_gen_7206, q_gen_7218) -> q_gen_7169
<cons, s>(q_gen_7212, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7212, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7212, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7212, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7212, q_gen_7186) -> q_gen_7169
<s, s>(q_gen_7168) -> q_gen_7171
<z, s>(q_gen_7165) -> q_gen_7171
<s, s>(q_gen_7171) -> q_gen_7177
<z, s>(q_gen_7175) -> q_gen_7177
<s, s>(q_gen_7177) -> q_gen_7206
<z, s>(q_gen_7204) -> q_gen_7206
<s, s>(q_gen_7212) -> q_gen_7212
<z, s>(q_gen_7213) -> q_gen_7212
}

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

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

Teacher's answer:
New clause system:
{
() -> length([nil, z]) -> 53
(length([l, _cba]) /\ length([cons(z, cons(z, l)), _bba])) -> eq_nat([_bba, s(s(_cba))]) -> 84
(length([ll, _xaa])) -> length([cons(x, ll), s(_xaa)]) -> 82
}
Sat witness: Found: ((length([l, _cba]) /\ length([cons(z, cons(z, l)), _bba])) -> eq_nat([_bba, s(s(_cba))]), {
_bba -> s(s(s(s(s(s(s(z)))))))  ;  _cba -> s(s(z))  ;  l -> cons(z, cons(z, nil))
})

-------------------------------------------
Step 53, which took 0.827330 s (model generation: 0.776656,  model checking: 0.050674):

Model:
|_
{
length -> 
{{{
Q={q_gen_7156, q_gen_7158, q_gen_7159, q_gen_7162, q_gen_7165, q_gen_7167, q_gen_7168, q_gen_7169, q_gen_7171, q_gen_7175, q_gen_7177, q_gen_7182, q_gen_7185, q_gen_7186, q_gen_7204, q_gen_7206, q_gen_7212, q_gen_7213, q_gen_7218, q_gen_7230},
Q_f={q_gen_7156},
Delta=
{
<nil>() -> q_gen_7158
<s>(q_gen_7230) -> q_gen_7162
<z>() -> q_gen_7162
<s>(q_gen_7162) -> q_gen_7165
<cons>(q_gen_7162, q_gen_7158) -> q_gen_7167
<s>(q_gen_7165) -> q_gen_7175
<cons>(q_gen_7162, q_gen_7167) -> q_gen_7182
<cons>(q_gen_7162, q_gen_7186) -> q_gen_7185
<cons>(q_gen_7162, q_gen_7182) -> q_gen_7186
<cons>(q_gen_7165, q_gen_7182) -> q_gen_7186
<s>(q_gen_7175) -> q_gen_7204
<s>(q_gen_7204) -> q_gen_7213
<cons>(q_gen_7162, q_gen_7185) -> q_gen_7218
<s>(q_gen_7213) -> q_gen_7230
<cons, s>(q_gen_7159, q_gen_7158) -> q_gen_7156
<cons, s>(q_gen_7168, q_gen_7167) -> q_gen_7156
<cons, s>(q_gen_7171, q_gen_7182) -> q_gen_7156
<cons, s>(q_gen_7177, q_gen_7186) -> q_gen_7156
<cons, s>(q_gen_7206, q_gen_7185) -> q_gen_7156
<cons, s>(q_gen_7212, q_gen_7185) -> q_gen_7156
<cons, s>(q_gen_7212, q_gen_7218) -> q_gen_7156
<nil, z>() -> q_gen_7156
<s, s>(q_gen_7206) -> q_gen_7159
<s, z>(q_gen_7162) -> q_gen_7159
<s, z>(q_gen_7165) -> q_gen_7159
<s, z>(q_gen_7175) -> q_gen_7159
<s, z>(q_gen_7204) -> q_gen_7159
<s, z>(q_gen_7230) -> q_gen_7159
<z, z>() -> q_gen_7159
<s, s>(q_gen_7159) -> q_gen_7168
<z, s>(q_gen_7162) -> q_gen_7168
<cons, s>(q_gen_7159, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7159, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7159, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7159, q_gen_7186) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7186) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7218) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7218) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7206, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7206, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7206, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7206, q_gen_7186) -> q_gen_7169
<cons, s>(q_gen_7206, q_gen_7218) -> q_gen_7169
<cons, s>(q_gen_7212, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7212, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7212, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7212, q_gen_7186) -> q_gen_7169
<s, s>(q_gen_7168) -> q_gen_7171
<s, s>(q_gen_7212) -> q_gen_7171
<z, s>(q_gen_7165) -> q_gen_7171
<s, s>(q_gen_7171) -> q_gen_7177
<z, s>(q_gen_7175) -> q_gen_7177
<z, s>(q_gen_7204) -> q_gen_7206
<z, s>(q_gen_7230) -> q_gen_7206
<s, s>(q_gen_7177) -> q_gen_7212
<z, s>(q_gen_7213) -> q_gen_7212
}

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

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

Teacher's answer:
New clause system:
{
() -> length([nil, z]) -> 54
(length([l, _cba]) /\ length([cons(z, cons(z, l)), _bba])) -> eq_nat([_bba, s(s(_cba))]) -> 84
(length([ll, _xaa])) -> length([cons(x, ll), s(_xaa)]) -> 85
}
Sat witness: Found: ((length([ll, _xaa])) -> length([cons(x, ll), s(_xaa)]), {
_xaa -> s(s(s(s(s(s(s(s(z))))))))  ;  ll -> cons(z, cons(z, nil))  ;  x -> s(s(s(s(z))))
})

-------------------------------------------
Step 54, which took 0.792528 s (model generation: 0.789073,  model checking: 0.003455):

Model:
|_
{
length -> 
{{{
Q={q_gen_7156, q_gen_7158, q_gen_7159, q_gen_7161, q_gen_7162, q_gen_7165, q_gen_7167, q_gen_7168, q_gen_7169, q_gen_7171, q_gen_7175, q_gen_7177, q_gen_7182, q_gen_7185, q_gen_7186, q_gen_7204, q_gen_7212, q_gen_7213, q_gen_7218, q_gen_7230},
Q_f={q_gen_7156},
Delta=
{
<nil>() -> q_gen_7158
<s>(q_gen_7230) -> q_gen_7162
<z>() -> q_gen_7162
<s>(q_gen_7162) -> q_gen_7165
<cons>(q_gen_7162, q_gen_7158) -> q_gen_7167
<s>(q_gen_7165) -> q_gen_7175
<cons>(q_gen_7162, q_gen_7167) -> q_gen_7182
<cons>(q_gen_7162, q_gen_7186) -> q_gen_7185
<cons>(q_gen_7162, q_gen_7182) -> q_gen_7186
<cons>(q_gen_7165, q_gen_7182) -> q_gen_7186
<s>(q_gen_7175) -> q_gen_7204
<s>(q_gen_7204) -> q_gen_7213
<cons>(q_gen_7162, q_gen_7185) -> q_gen_7218
<s>(q_gen_7213) -> q_gen_7230
<cons, s>(q_gen_7159, q_gen_7158) -> q_gen_7156
<cons, s>(q_gen_7161, q_gen_7158) -> q_gen_7156
<cons, s>(q_gen_7161, q_gen_7185) -> q_gen_7156
<cons, s>(q_gen_7168, q_gen_7167) -> q_gen_7156
<cons, s>(q_gen_7171, q_gen_7182) -> q_gen_7156
<cons, s>(q_gen_7177, q_gen_7186) -> q_gen_7156
<cons, s>(q_gen_7212, q_gen_7185) -> q_gen_7156
<cons, s>(q_gen_7212, q_gen_7218) -> q_gen_7156
<nil, z>() -> q_gen_7156
<s, z>(q_gen_7204) -> q_gen_7159
<s, z>(q_gen_7230) -> q_gen_7159
<z, z>() -> q_gen_7159
<s, z>(q_gen_7162) -> q_gen_7161
<s, z>(q_gen_7165) -> q_gen_7161
<s, z>(q_gen_7175) -> q_gen_7161
<z, s>(q_gen_7204) -> q_gen_7161
<s, s>(q_gen_7159) -> q_gen_7168
<s, s>(q_gen_7212) -> q_gen_7168
<z, s>(q_gen_7162) -> q_gen_7168
<cons, s>(q_gen_7159, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7159, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7159, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7159, q_gen_7186) -> q_gen_7169
<cons, s>(q_gen_7161, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7161, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7161, q_gen_7186) -> q_gen_7169
<cons, s>(q_gen_7161, q_gen_7218) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7186) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7218) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7186) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7218) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7212, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7212, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7212, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7212, q_gen_7186) -> q_gen_7169
<s, s>(q_gen_7168) -> q_gen_7171
<z, s>(q_gen_7165) -> q_gen_7171
<z, s>(q_gen_7230) -> q_gen_7171
<s, s>(q_gen_7161) -> q_gen_7177
<s, s>(q_gen_7171) -> q_gen_7177
<z, s>(q_gen_7175) -> q_gen_7177
<s, s>(q_gen_7177) -> q_gen_7212
<z, s>(q_gen_7213) -> q_gen_7212
}

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

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

Teacher's answer:
New clause system:
{
() -> length([nil, z]) -> 55
(length([l, _cba]) /\ length([cons(z, cons(z, l)), _bba])) -> eq_nat([_bba, s(s(_cba))]) -> 87
(length([ll, _xaa])) -> length([cons(x, ll), s(_xaa)]) -> 85
}
Sat witness: Found: ((length([l, _cba]) /\ length([cons(z, cons(z, l)), _bba])) -> eq_nat([_bba, s(s(_cba))]), {
_bba -> s(s(s(s(s(s(s(s(z))))))))  ;  _cba -> z  ;  l -> nil
})

-------------------------------------------
Step 55, which took 0.803499 s (model generation: 0.777561,  model checking: 0.025938):

Model:
|_
{
length -> 
{{{
Q={q_gen_7156, q_gen_7158, q_gen_7159, q_gen_7161, q_gen_7162, q_gen_7165, q_gen_7167, q_gen_7168, q_gen_7169, q_gen_7171, q_gen_7175, q_gen_7177, q_gen_7182, q_gen_7185, q_gen_7186, q_gen_7204, q_gen_7212, q_gen_7213, q_gen_7218, q_gen_7230},
Q_f={q_gen_7156},
Delta=
{
<nil>() -> q_gen_7158
<z>() -> q_gen_7162
<s>(q_gen_7162) -> q_gen_7165
<s>(q_gen_7230) -> q_gen_7165
<cons>(q_gen_7162, q_gen_7158) -> q_gen_7167
<s>(q_gen_7165) -> q_gen_7175
<cons>(q_gen_7162, q_gen_7167) -> q_gen_7182
<cons>(q_gen_7162, q_gen_7186) -> q_gen_7185
<cons>(q_gen_7162, q_gen_7182) -> q_gen_7186
<cons>(q_gen_7165, q_gen_7182) -> q_gen_7186
<s>(q_gen_7175) -> q_gen_7204
<s>(q_gen_7204) -> q_gen_7213
<cons>(q_gen_7162, q_gen_7185) -> q_gen_7218
<s>(q_gen_7213) -> q_gen_7230
<cons, s>(q_gen_7159, q_gen_7158) -> q_gen_7156
<cons, s>(q_gen_7161, q_gen_7158) -> q_gen_7156
<cons, s>(q_gen_7161, q_gen_7185) -> q_gen_7156
<cons, s>(q_gen_7168, q_gen_7167) -> q_gen_7156
<cons, s>(q_gen_7171, q_gen_7182) -> q_gen_7156
<cons, s>(q_gen_7177, q_gen_7186) -> q_gen_7156
<cons, s>(q_gen_7212, q_gen_7218) -> q_gen_7156
<nil, z>() -> q_gen_7156
<s, s>(q_gen_7212) -> q_gen_7159
<s, z>(q_gen_7204) -> q_gen_7159
<s, z>(q_gen_7230) -> q_gen_7159
<z, z>() -> q_gen_7159
<s, s>(q_gen_7177) -> q_gen_7161
<s, z>(q_gen_7162) -> q_gen_7161
<s, z>(q_gen_7165) -> q_gen_7161
<s, z>(q_gen_7175) -> q_gen_7161
<z, s>(q_gen_7204) -> q_gen_7161
<z, s>(q_gen_7230) -> q_gen_7161
<s, s>(q_gen_7159) -> q_gen_7168
<s, s>(q_gen_7161) -> q_gen_7168
<z, s>(q_gen_7162) -> q_gen_7168
<cons, s>(q_gen_7159, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7159, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7159, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7159, q_gen_7186) -> q_gen_7169
<cons, s>(q_gen_7161, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7161, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7161, q_gen_7186) -> q_gen_7169
<cons, s>(q_gen_7161, q_gen_7218) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7186) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7186) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7218) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7218) -> q_gen_7169
<cons, s>(q_gen_7212, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7212, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7212, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7212, q_gen_7186) -> q_gen_7169
<s, s>(q_gen_7168) -> q_gen_7171
<z, s>(q_gen_7165) -> q_gen_7171
<s, s>(q_gen_7171) -> q_gen_7177
<z, s>(q_gen_7175) -> q_gen_7177
<z, s>(q_gen_7213) -> q_gen_7212
}

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

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

Teacher's answer:
New clause system:
{
() -> length([nil, z]) -> 56
(length([l, _cba]) /\ length([cons(z, cons(z, l)), _bba])) -> eq_nat([_bba, s(s(_cba))]) -> 87
(length([ll, _xaa])) -> length([cons(x, ll), s(_xaa)]) -> 88
}
Sat witness: Found: ((length([ll, _xaa])) -> length([cons(x, ll), s(_xaa)]), {
_xaa -> s(s(s(s(s(s(s(z)))))))  ;  ll -> cons(z, nil)  ;  x -> s(s(s(s(s(s(z))))))
})

-------------------------------------------
Step 56, which took 0.781063 s (model generation: 0.776630,  model checking: 0.004433):

Model:
|_
{
length -> 
{{{
Q={q_gen_7156, q_gen_7158, q_gen_7159, q_gen_7161, q_gen_7162, q_gen_7165, q_gen_7167, q_gen_7168, q_gen_7169, q_gen_7171, q_gen_7175, q_gen_7177, q_gen_7182, q_gen_7185, q_gen_7186, q_gen_7204, q_gen_7212, q_gen_7213, q_gen_7218, q_gen_7230},
Q_f={q_gen_7156},
Delta=
{
<nil>() -> q_gen_7158
<z>() -> q_gen_7162
<s>(q_gen_7162) -> q_gen_7165
<s>(q_gen_7230) -> q_gen_7165
<cons>(q_gen_7162, q_gen_7158) -> q_gen_7167
<s>(q_gen_7165) -> q_gen_7175
<cons>(q_gen_7162, q_gen_7167) -> q_gen_7182
<cons>(q_gen_7162, q_gen_7186) -> q_gen_7185
<cons>(q_gen_7162, q_gen_7182) -> q_gen_7186
<cons>(q_gen_7165, q_gen_7182) -> q_gen_7186
<s>(q_gen_7175) -> q_gen_7204
<s>(q_gen_7204) -> q_gen_7213
<cons>(q_gen_7162, q_gen_7185) -> q_gen_7218
<s>(q_gen_7213) -> q_gen_7230
<cons, s>(q_gen_7159, q_gen_7158) -> q_gen_7156
<cons, s>(q_gen_7161, q_gen_7158) -> q_gen_7156
<cons, s>(q_gen_7161, q_gen_7185) -> q_gen_7156
<cons, s>(q_gen_7168, q_gen_7167) -> q_gen_7156
<cons, s>(q_gen_7171, q_gen_7182) -> q_gen_7156
<cons, s>(q_gen_7177, q_gen_7186) -> q_gen_7156
<cons, s>(q_gen_7212, q_gen_7218) -> q_gen_7156
<nil, z>() -> q_gen_7156
<s, z>(q_gen_7165) -> q_gen_7159
<s, z>(q_gen_7175) -> q_gen_7159
<s, z>(q_gen_7204) -> q_gen_7159
<s, z>(q_gen_7230) -> q_gen_7159
<z, z>() -> q_gen_7159
<s, s>(q_gen_7177) -> q_gen_7161
<s, z>(q_gen_7162) -> q_gen_7161
<z, s>(q_gen_7204) -> q_gen_7161
<s, s>(q_gen_7159) -> q_gen_7168
<s, s>(q_gen_7161) -> q_gen_7168
<z, s>(q_gen_7162) -> q_gen_7168
<cons, s>(q_gen_7159, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7159, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7159, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7159, q_gen_7186) -> q_gen_7169
<cons, s>(q_gen_7161, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7161, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7161, q_gen_7186) -> q_gen_7169
<cons, s>(q_gen_7161, q_gen_7218) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7186) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7218) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7186) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7218) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7212, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7212, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7212, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7212, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7212, q_gen_7186) -> q_gen_7169
<s, s>(q_gen_7168) -> q_gen_7171
<z, s>(q_gen_7165) -> q_gen_7171
<z, s>(q_gen_7230) -> q_gen_7171
<s, s>(q_gen_7171) -> q_gen_7177
<z, s>(q_gen_7175) -> q_gen_7177
<s, s>(q_gen_7212) -> q_gen_7212
<z, s>(q_gen_7213) -> q_gen_7212
}

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

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

Teacher's answer:
New clause system:
{
() -> length([nil, z]) -> 57
(length([l, _cba]) /\ length([cons(z, cons(z, l)), _bba])) -> eq_nat([_bba, s(s(_cba))]) -> 90
(length([ll, _xaa])) -> length([cons(x, ll), s(_xaa)]) -> 88
}
Sat witness: Found: ((length([l, _cba]) /\ length([cons(z, cons(z, l)), _bba])) -> eq_nat([_bba, s(s(_cba))]), {
_bba -> s(s(s(s(s(s(s(s(s(z)))))))))  ;  _cba -> s(s(z))  ;  l -> cons(z, cons(z, nil))
})

-------------------------------------------
Step 57, which took 0.886272 s (model generation: 0.841446,  model checking: 0.044826):

Model:
|_
{
length -> 
{{{
Q={q_gen_7156, q_gen_7158, q_gen_7159, q_gen_7162, q_gen_7165, q_gen_7167, q_gen_7168, q_gen_7169, q_gen_7171, q_gen_7175, q_gen_7177, q_gen_7182, q_gen_7185, q_gen_7186, q_gen_7204, q_gen_7206, q_gen_7212, q_gen_7213, q_gen_7218, q_gen_7230},
Q_f={q_gen_7156},
Delta=
{
<nil>() -> q_gen_7158
<z>() -> q_gen_7162
<s>(q_gen_7162) -> q_gen_7165
<cons>(q_gen_7162, q_gen_7158) -> q_gen_7167
<s>(q_gen_7165) -> q_gen_7175
<cons>(q_gen_7162, q_gen_7167) -> q_gen_7182
<cons>(q_gen_7162, q_gen_7186) -> q_gen_7185
<cons>(q_gen_7162, q_gen_7182) -> q_gen_7186
<cons>(q_gen_7165, q_gen_7182) -> q_gen_7186
<s>(q_gen_7175) -> q_gen_7204
<s>(q_gen_7230) -> q_gen_7204
<s>(q_gen_7204) -> q_gen_7213
<cons>(q_gen_7162, q_gen_7185) -> q_gen_7218
<s>(q_gen_7213) -> q_gen_7230
<cons, s>(q_gen_7159, q_gen_7158) -> q_gen_7156
<cons, s>(q_gen_7168, q_gen_7167) -> q_gen_7156
<cons, s>(q_gen_7171, q_gen_7182) -> q_gen_7156
<cons, s>(q_gen_7177, q_gen_7186) -> q_gen_7156
<cons, s>(q_gen_7206, q_gen_7185) -> q_gen_7156
<cons, s>(q_gen_7212, q_gen_7218) -> q_gen_7156
<nil, z>() -> q_gen_7156
<s, s>(q_gen_7206) -> q_gen_7159
<s, z>(q_gen_7162) -> q_gen_7159
<s, z>(q_gen_7165) -> q_gen_7159
<s, z>(q_gen_7175) -> q_gen_7159
<s, z>(q_gen_7204) -> q_gen_7159
<s, z>(q_gen_7230) -> q_gen_7159
<z, z>() -> q_gen_7159
<s, s>(q_gen_7159) -> q_gen_7168
<z, s>(q_gen_7162) -> q_gen_7168
<cons, s>(q_gen_7159, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7159, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7159, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7159, q_gen_7186) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7186) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7218) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7206, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7206, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7206, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7206, q_gen_7186) -> q_gen_7169
<cons, s>(q_gen_7206, q_gen_7218) -> q_gen_7169
<cons, s>(q_gen_7212, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7212, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7212, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7212, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7212, q_gen_7186) -> q_gen_7169
<s, s>(q_gen_7168) -> q_gen_7171
<z, s>(q_gen_7165) -> q_gen_7171
<s, s>(q_gen_7171) -> q_gen_7177
<s, s>(q_gen_7212) -> q_gen_7177
<z, s>(q_gen_7175) -> q_gen_7177
<s, s>(q_gen_7177) -> q_gen_7206
<z, s>(q_gen_7204) -> q_gen_7206
<z, s>(q_gen_7230) -> q_gen_7206
<z, s>(q_gen_7213) -> q_gen_7212
}

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

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

Teacher's answer:
New clause system:
{
() -> length([nil, z]) -> 58
(length([l, _cba]) /\ length([cons(z, cons(z, l)), _bba])) -> eq_nat([_bba, s(s(_cba))]) -> 90
(length([ll, _xaa])) -> length([cons(x, ll), s(_xaa)]) -> 91
}
Sat witness: Found: ((length([ll, _xaa])) -> length([cons(x, ll), s(_xaa)]), {
_xaa -> s(s(s(s(s(s(s(s(s(s(s(s(s(s(z))))))))))))))  ;  ll -> cons(z, cons(z, cons(z, cons(z, cons(z, nil)))))  ;  x -> s(s(s(s(s(s(s(s(z))))))))
})

-------------------------------------------
Step 58, which took 1.282938 s (model generation: 1.273175,  model checking: 0.009763):

Model:
|_
{
length -> 
{{{
Q={q_gen_7156, q_gen_7158, q_gen_7159, q_gen_7161, q_gen_7162, q_gen_7165, q_gen_7167, q_gen_7168, q_gen_7169, q_gen_7171, q_gen_7175, q_gen_7177, q_gen_7182, q_gen_7185, q_gen_7186, q_gen_7204, q_gen_7212, q_gen_7213, q_gen_7218, q_gen_7230},
Q_f={q_gen_7156},
Delta=
{
<nil>() -> q_gen_7158
<z>() -> q_gen_7162
<s>(q_gen_7162) -> q_gen_7165
<cons>(q_gen_7162, q_gen_7158) -> q_gen_7167
<s>(q_gen_7165) -> q_gen_7175
<cons>(q_gen_7162, q_gen_7167) -> q_gen_7182
<cons>(q_gen_7162, q_gen_7186) -> q_gen_7185
<cons>(q_gen_7162, q_gen_7182) -> q_gen_7186
<cons>(q_gen_7165, q_gen_7182) -> q_gen_7186
<s>(q_gen_7175) -> q_gen_7204
<s>(q_gen_7204) -> q_gen_7213
<cons>(q_gen_7162, q_gen_7185) -> q_gen_7218
<s>(q_gen_7213) -> q_gen_7230
<s>(q_gen_7230) -> q_gen_7230
<cons, s>(q_gen_7159, q_gen_7158) -> q_gen_7156
<cons, s>(q_gen_7161, q_gen_7158) -> q_gen_7156
<cons, s>(q_gen_7161, q_gen_7185) -> q_gen_7156
<cons, s>(q_gen_7168, q_gen_7167) -> q_gen_7156
<cons, s>(q_gen_7168, q_gen_7218) -> q_gen_7156
<cons, s>(q_gen_7171, q_gen_7182) -> q_gen_7156
<cons, s>(q_gen_7177, q_gen_7186) -> q_gen_7156
<cons, s>(q_gen_7212, q_gen_7185) -> q_gen_7156
<cons, s>(q_gen_7212, q_gen_7218) -> q_gen_7156
<nil, z>() -> q_gen_7156
<s, z>(q_gen_7165) -> q_gen_7159
<s, z>(q_gen_7175) -> q_gen_7159
<s, z>(q_gen_7204) -> q_gen_7159
<z, z>() -> q_gen_7159
<s, s>(q_gen_7161) -> q_gen_7161
<s, z>(q_gen_7162) -> q_gen_7161
<s, z>(q_gen_7230) -> q_gen_7161
<z, s>(q_gen_7204) -> q_gen_7161
<s, s>(q_gen_7159) -> q_gen_7168
<s, s>(q_gen_7212) -> q_gen_7168
<z, s>(q_gen_7162) -> q_gen_7168
<cons, s>(q_gen_7159, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7159, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7159, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7159, q_gen_7186) -> q_gen_7169
<cons, s>(q_gen_7161, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7161, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7161, q_gen_7186) -> q_gen_7169
<cons, s>(q_gen_7161, q_gen_7218) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7186) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7186) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7218) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7212, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7212, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7212, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7212, q_gen_7186) -> q_gen_7169
<s, s>(q_gen_7168) -> q_gen_7171
<z, s>(q_gen_7165) -> q_gen_7171
<z, s>(q_gen_7230) -> q_gen_7171
<s, s>(q_gen_7171) -> q_gen_7177
<z, s>(q_gen_7175) -> q_gen_7177
<s, s>(q_gen_7177) -> q_gen_7212
<z, s>(q_gen_7213) -> q_gen_7212
}

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

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

Teacher's answer:
New clause system:
{
() -> length([nil, z]) -> 59
(length([l, _cba]) /\ length([cons(z, cons(z, l)), _bba])) -> eq_nat([_bba, s(s(_cba))]) -> 93
(length([ll, _xaa])) -> length([cons(x, ll), s(_xaa)]) -> 91
}
Sat witness: Found: ((length([l, _cba]) /\ length([cons(z, cons(z, l)), _bba])) -> eq_nat([_bba, s(s(_cba))]), {
_bba -> s(s(s(s(s(s(z))))))  ;  _cba -> s(s(s(z)))  ;  l -> cons(z, cons(z, cons(z, nil)))
})

-------------------------------------------
Step 59, which took 1.380814 s (model generation: 1.358588,  model checking: 0.022226):

Model:
|_
{
length -> 
{{{
Q={q_gen_7156, q_gen_7158, q_gen_7159, q_gen_7162, q_gen_7165, q_gen_7167, q_gen_7168, q_gen_7169, q_gen_7171, q_gen_7175, q_gen_7177, q_gen_7182, q_gen_7185, q_gen_7186, q_gen_7192, q_gen_7204, q_gen_7206, q_gen_7212, q_gen_7213, q_gen_7230},
Q_f={q_gen_7156},
Delta=
{
<nil>() -> q_gen_7158
<z>() -> q_gen_7162
<s>(q_gen_7162) -> q_gen_7165
<cons>(q_gen_7162, q_gen_7158) -> q_gen_7167
<s>(q_gen_7165) -> q_gen_7175
<cons>(q_gen_7162, q_gen_7167) -> q_gen_7182
<cons>(q_gen_7162, q_gen_7186) -> q_gen_7185
<cons>(q_gen_7162, q_gen_7182) -> q_gen_7186
<cons>(q_gen_7162, q_gen_7185) -> q_gen_7192
<cons>(q_gen_7162, q_gen_7192) -> q_gen_7192
<cons>(q_gen_7165, q_gen_7182) -> q_gen_7192
<s>(q_gen_7175) -> q_gen_7204
<s>(q_gen_7204) -> q_gen_7213
<s>(q_gen_7213) -> q_gen_7230
<s>(q_gen_7230) -> q_gen_7230
<cons, s>(q_gen_7159, q_gen_7158) -> q_gen_7156
<cons, s>(q_gen_7168, q_gen_7167) -> q_gen_7156
<cons, s>(q_gen_7171, q_gen_7182) -> q_gen_7156
<cons, s>(q_gen_7177, q_gen_7186) -> q_gen_7156
<cons, s>(q_gen_7177, q_gen_7192) -> q_gen_7156
<cons, s>(q_gen_7206, q_gen_7185) -> q_gen_7156
<cons, s>(q_gen_7212, q_gen_7192) -> q_gen_7156
<nil, z>() -> q_gen_7156
<s, z>(q_gen_7162) -> q_gen_7159
<s, z>(q_gen_7165) -> q_gen_7159
<s, z>(q_gen_7175) -> q_gen_7159
<s, z>(q_gen_7204) -> q_gen_7159
<s, z>(q_gen_7230) -> q_gen_7159
<z, z>() -> q_gen_7159
<s, s>(q_gen_7159) -> q_gen_7168
<s, s>(q_gen_7206) -> q_gen_7168
<z, s>(q_gen_7162) -> q_gen_7168
<cons, s>(q_gen_7159, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7159, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7159, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7159, q_gen_7186) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7186) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7192) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7186) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7192) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7206, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7206, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7206, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7206, q_gen_7186) -> q_gen_7169
<cons, s>(q_gen_7206, q_gen_7192) -> q_gen_7169
<cons, s>(q_gen_7212, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7212, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7212, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7212, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7212, q_gen_7186) -> q_gen_7169
<s, s>(q_gen_7168) -> q_gen_7171
<z, s>(q_gen_7165) -> q_gen_7171
<z, s>(q_gen_7230) -> q_gen_7171
<s, s>(q_gen_7171) -> q_gen_7177
<s, s>(q_gen_7212) -> q_gen_7177
<z, s>(q_gen_7175) -> q_gen_7177
<s, s>(q_gen_7177) -> q_gen_7206
<z, s>(q_gen_7204) -> q_gen_7206
<z, s>(q_gen_7213) -> q_gen_7212
}

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

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

Teacher's answer:
New clause system:
{
() -> length([nil, z]) -> 60
(length([l, _cba]) /\ length([cons(z, cons(z, l)), _bba])) -> eq_nat([_bba, s(s(_cba))]) -> 93
(length([ll, _xaa])) -> length([cons(x, ll), s(_xaa)]) -> 94
}
Sat witness: Found: ((length([ll, _xaa])) -> length([cons(x, ll), s(_xaa)]), {
_xaa -> s(s(s(s(s(z)))))  ;  ll -> cons(z, cons(z, cons(z, cons(z, cons(z, nil)))))  ;  x -> s(s(s(z)))
})

-------------------------------------------
Step 60, which took 1.173771 s (model generation: 1.166511,  model checking: 0.007260):

Model:
|_
{
length -> 
{{{
Q={q_gen_7156, q_gen_7158, q_gen_7159, q_gen_7161, q_gen_7162, q_gen_7165, q_gen_7167, q_gen_7168, q_gen_7169, q_gen_7171, q_gen_7175, q_gen_7177, q_gen_7182, q_gen_7185, q_gen_7186, q_gen_7204, q_gen_7212, q_gen_7213, q_gen_7218, q_gen_7230},
Q_f={q_gen_7156},
Delta=
{
<nil>() -> q_gen_7158
<z>() -> q_gen_7162
<s>(q_gen_7162) -> q_gen_7165
<cons>(q_gen_7162, q_gen_7158) -> q_gen_7167
<s>(q_gen_7165) -> q_gen_7175
<cons>(q_gen_7162, q_gen_7167) -> q_gen_7182
<cons>(q_gen_7162, q_gen_7186) -> q_gen_7185
<cons>(q_gen_7162, q_gen_7182) -> q_gen_7186
<cons>(q_gen_7165, q_gen_7182) -> q_gen_7186
<s>(q_gen_7175) -> q_gen_7204
<s>(q_gen_7204) -> q_gen_7213
<cons>(q_gen_7162, q_gen_7185) -> q_gen_7218
<s>(q_gen_7213) -> q_gen_7230
<s>(q_gen_7230) -> q_gen_7230
<cons, s>(q_gen_7159, q_gen_7158) -> q_gen_7156
<cons, s>(q_gen_7161, q_gen_7158) -> q_gen_7156
<cons, s>(q_gen_7161, q_gen_7185) -> q_gen_7156
<cons, s>(q_gen_7168, q_gen_7167) -> q_gen_7156
<cons, s>(q_gen_7168, q_gen_7218) -> q_gen_7156
<cons, s>(q_gen_7171, q_gen_7182) -> q_gen_7156
<cons, s>(q_gen_7177, q_gen_7186) -> q_gen_7156
<cons, s>(q_gen_7212, q_gen_7218) -> q_gen_7156
<nil, z>() -> q_gen_7156
<s, z>(q_gen_7165) -> q_gen_7159
<s, z>(q_gen_7175) -> q_gen_7159
<s, z>(q_gen_7230) -> q_gen_7159
<z, z>() -> q_gen_7159
<s, s>(q_gen_7177) -> q_gen_7161
<s, z>(q_gen_7162) -> q_gen_7161
<s, z>(q_gen_7204) -> q_gen_7161
<z, s>(q_gen_7204) -> q_gen_7161
<s, s>(q_gen_7159) -> q_gen_7168
<s, s>(q_gen_7161) -> q_gen_7168
<z, s>(q_gen_7162) -> q_gen_7168
<cons, s>(q_gen_7159, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7159, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7159, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7159, q_gen_7186) -> q_gen_7169
<cons, s>(q_gen_7161, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7161, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7161, q_gen_7186) -> q_gen_7169
<cons, s>(q_gen_7161, q_gen_7218) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7186) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7186) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7218) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7212, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7212, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7212, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7212, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7212, q_gen_7186) -> q_gen_7169
<s, s>(q_gen_7168) -> q_gen_7171
<z, s>(q_gen_7165) -> q_gen_7171
<z, s>(q_gen_7230) -> q_gen_7171
<s, s>(q_gen_7171) -> q_gen_7177
<z, s>(q_gen_7175) -> q_gen_7177
<s, s>(q_gen_7212) -> q_gen_7212
<z, s>(q_gen_7213) -> q_gen_7212
}

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

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

Teacher's answer:
New clause system:
{
() -> length([nil, z]) -> 61
(length([l, _cba]) /\ length([cons(z, cons(z, l)), _bba])) -> eq_nat([_bba, s(s(_cba))]) -> 96
(length([ll, _xaa])) -> length([cons(x, ll), s(_xaa)]) -> 94
}
Sat witness: Found: ((length([l, _cba]) /\ length([cons(z, cons(z, l)), _bba])) -> eq_nat([_bba, s(s(_cba))]), {
_bba -> s(s(s(s(s(s(s(s(s(z)))))))))  ;  _cba -> s(s(s(s(s(z)))))  ;  l -> cons(z, nil)
})

-------------------------------------------
Step 61, which took 1.535465 s (model generation: 1.463242,  model checking: 0.072223):

Model:
|_
{
length -> 
{{{
Q={q_gen_7156, q_gen_7158, q_gen_7159, q_gen_7162, q_gen_7165, q_gen_7167, q_gen_7168, q_gen_7169, q_gen_7171, q_gen_7175, q_gen_7177, q_gen_7182, q_gen_7185, q_gen_7186, q_gen_7192, q_gen_7204, q_gen_7206, q_gen_7212, q_gen_7213, q_gen_7230},
Q_f={q_gen_7156},
Delta=
{
<nil>() -> q_gen_7158
<z>() -> q_gen_7162
<s>(q_gen_7162) -> q_gen_7165
<cons>(q_gen_7162, q_gen_7158) -> q_gen_7167
<s>(q_gen_7165) -> q_gen_7175
<cons>(q_gen_7162, q_gen_7167) -> q_gen_7182
<cons>(q_gen_7162, q_gen_7192) -> q_gen_7182
<cons>(q_gen_7162, q_gen_7186) -> q_gen_7185
<cons>(q_gen_7162, q_gen_7182) -> q_gen_7186
<cons>(q_gen_7162, q_gen_7185) -> q_gen_7192
<cons>(q_gen_7165, q_gen_7182) -> q_gen_7192
<s>(q_gen_7175) -> q_gen_7204
<s>(q_gen_7204) -> q_gen_7213
<s>(q_gen_7213) -> q_gen_7230
<s>(q_gen_7230) -> q_gen_7230
<cons, s>(q_gen_7159, q_gen_7158) -> q_gen_7156
<cons, s>(q_gen_7168, q_gen_7167) -> q_gen_7156
<cons, s>(q_gen_7168, q_gen_7192) -> q_gen_7156
<cons, s>(q_gen_7171, q_gen_7182) -> q_gen_7156
<cons, s>(q_gen_7177, q_gen_7186) -> q_gen_7156
<cons, s>(q_gen_7177, q_gen_7192) -> q_gen_7156
<cons, s>(q_gen_7206, q_gen_7185) -> q_gen_7156
<cons, s>(q_gen_7212, q_gen_7192) -> q_gen_7156
<nil, z>() -> q_gen_7156
<s, z>(q_gen_7162) -> q_gen_7159
<s, z>(q_gen_7165) -> q_gen_7159
<s, z>(q_gen_7175) -> q_gen_7159
<s, z>(q_gen_7204) -> q_gen_7159
<s, z>(q_gen_7230) -> q_gen_7159
<z, z>() -> q_gen_7159
<s, s>(q_gen_7159) -> q_gen_7168
<s, s>(q_gen_7206) -> q_gen_7168
<z, s>(q_gen_7162) -> q_gen_7168
<cons, s>(q_gen_7159, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7159, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7159, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7159, q_gen_7186) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7186) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7186) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7192) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7206, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7206, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7206, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7206, q_gen_7186) -> q_gen_7169
<cons, s>(q_gen_7206, q_gen_7192) -> q_gen_7169
<cons, s>(q_gen_7212, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7212, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7212, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7212, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7212, q_gen_7186) -> q_gen_7169
<s, s>(q_gen_7168) -> q_gen_7171
<s, s>(q_gen_7212) -> q_gen_7171
<z, s>(q_gen_7165) -> q_gen_7171
<z, s>(q_gen_7230) -> q_gen_7171
<s, s>(q_gen_7171) -> q_gen_7177
<z, s>(q_gen_7175) -> q_gen_7177
<s, s>(q_gen_7177) -> q_gen_7206
<z, s>(q_gen_7204) -> q_gen_7206
<z, s>(q_gen_7213) -> q_gen_7212
}

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

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

Teacher's answer:
New clause system:
{
() -> length([nil, z]) -> 62
(length([l, _cba]) /\ length([cons(z, cons(z, l)), _bba])) -> eq_nat([_bba, s(s(_cba))]) -> 96
(length([ll, _xaa])) -> length([cons(x, ll), s(_xaa)]) -> 97
}
Sat witness: Found: ((length([ll, _xaa])) -> length([cons(x, ll), s(_xaa)]), {
_xaa -> s(s(s(s(s(s(s(z)))))))  ;  ll -> cons(z, cons(z, cons(z, nil)))  ;  x -> z
})

-------------------------------------------
Step 62, which took 1.512174 s (model generation: 1.502949,  model checking: 0.009225):

Model:
|_
{
length -> 
{{{
Q={q_gen_7156, q_gen_7158, q_gen_7159, q_gen_7162, q_gen_7165, q_gen_7167, q_gen_7168, q_gen_7169, q_gen_7171, q_gen_7175, q_gen_7177, q_gen_7182, q_gen_7185, q_gen_7186, q_gen_7192, q_gen_7204, q_gen_7206, q_gen_7212, q_gen_7213, q_gen_7230},
Q_f={q_gen_7156},
Delta=
{
<nil>() -> q_gen_7158
<z>() -> q_gen_7162
<s>(q_gen_7162) -> q_gen_7165
<cons>(q_gen_7162, q_gen_7158) -> q_gen_7167
<s>(q_gen_7165) -> q_gen_7175
<cons>(q_gen_7162, q_gen_7167) -> q_gen_7182
<cons>(q_gen_7162, q_gen_7186) -> q_gen_7185
<cons>(q_gen_7162, q_gen_7182) -> q_gen_7186
<cons>(q_gen_7162, q_gen_7185) -> q_gen_7192
<cons>(q_gen_7162, q_gen_7192) -> q_gen_7192
<cons>(q_gen_7165, q_gen_7182) -> q_gen_7192
<s>(q_gen_7175) -> q_gen_7204
<s>(q_gen_7204) -> q_gen_7213
<s>(q_gen_7213) -> q_gen_7230
<s>(q_gen_7230) -> q_gen_7230
<cons, s>(q_gen_7159, q_gen_7158) -> q_gen_7156
<cons, s>(q_gen_7168, q_gen_7167) -> q_gen_7156
<cons, s>(q_gen_7171, q_gen_7182) -> q_gen_7156
<cons, s>(q_gen_7177, q_gen_7186) -> q_gen_7156
<cons, s>(q_gen_7177, q_gen_7192) -> q_gen_7156
<cons, s>(q_gen_7206, q_gen_7185) -> q_gen_7156
<cons, s>(q_gen_7212, q_gen_7192) -> q_gen_7156
<nil, z>() -> q_gen_7156
<s, z>(q_gen_7162) -> q_gen_7159
<s, z>(q_gen_7165) -> q_gen_7159
<s, z>(q_gen_7175) -> q_gen_7159
<s, z>(q_gen_7204) -> q_gen_7159
<s, z>(q_gen_7230) -> q_gen_7159
<z, z>() -> q_gen_7159
<s, s>(q_gen_7159) -> q_gen_7168
<z, s>(q_gen_7162) -> q_gen_7168
<cons, s>(q_gen_7159, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7159, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7159, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7159, q_gen_7186) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7186) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7192) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7192) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7206, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7206, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7206, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7206, q_gen_7186) -> q_gen_7169
<cons, s>(q_gen_7206, q_gen_7192) -> q_gen_7169
<cons, s>(q_gen_7212, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7212, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7212, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7212, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7212, q_gen_7186) -> q_gen_7169
<s, s>(q_gen_7168) -> q_gen_7171
<z, s>(q_gen_7165) -> q_gen_7171
<s, s>(q_gen_7171) -> q_gen_7177
<z, s>(q_gen_7175) -> q_gen_7177
<s, s>(q_gen_7177) -> q_gen_7206
<z, s>(q_gen_7204) -> q_gen_7206
<z, s>(q_gen_7230) -> q_gen_7206
<s, s>(q_gen_7206) -> q_gen_7212
<s, s>(q_gen_7212) -> q_gen_7212
<z, s>(q_gen_7213) -> q_gen_7212
}

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

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

Teacher's answer:
New clause system:
{
() -> length([nil, z]) -> 63
(length([l, _cba]) /\ length([cons(z, cons(z, l)), _bba])) -> eq_nat([_bba, s(s(_cba))]) -> 99
(length([ll, _xaa])) -> length([cons(x, ll), s(_xaa)]) -> 97
}
Sat witness: Found: ((length([l, _cba]) /\ length([cons(z, cons(z, l)), _bba])) -> eq_nat([_bba, s(s(_cba))]), {
_bba -> s(s(s(s(z))))  ;  _cba -> s(s(s(s(s(s(z))))))  ;  l -> cons(z, cons(z, cons(z, cons(z, cons(z, cons(z, nil))))))
})

-------------------------------------------
Step 63, which took 1.571703 s (model generation: 1.515064,  model checking: 0.056639):

Model:
|_
{
length -> 
{{{
Q={q_gen_7156, q_gen_7158, q_gen_7159, q_gen_7162, q_gen_7165, q_gen_7167, q_gen_7168, q_gen_7169, q_gen_7171, q_gen_7175, q_gen_7177, q_gen_7182, q_gen_7185, q_gen_7186, q_gen_7192, q_gen_7204, q_gen_7206, q_gen_7212, q_gen_7213, q_gen_7230},
Q_f={q_gen_7156},
Delta=
{
<nil>() -> q_gen_7158
<z>() -> q_gen_7162
<s>(q_gen_7162) -> q_gen_7165
<cons>(q_gen_7162, q_gen_7158) -> q_gen_7167
<s>(q_gen_7165) -> q_gen_7175
<cons>(q_gen_7162, q_gen_7167) -> q_gen_7182
<cons>(q_gen_7162, q_gen_7186) -> q_gen_7185
<cons>(q_gen_7162, q_gen_7182) -> q_gen_7186
<cons>(q_gen_7162, q_gen_7192) -> q_gen_7186
<cons>(q_gen_7162, q_gen_7185) -> q_gen_7192
<cons>(q_gen_7165, q_gen_7182) -> q_gen_7192
<s>(q_gen_7175) -> q_gen_7204
<s>(q_gen_7230) -> q_gen_7204
<s>(q_gen_7204) -> q_gen_7213
<s>(q_gen_7213) -> q_gen_7230
<cons, s>(q_gen_7159, q_gen_7158) -> q_gen_7156
<cons, s>(q_gen_7168, q_gen_7167) -> q_gen_7156
<cons, s>(q_gen_7171, q_gen_7182) -> q_gen_7156
<cons, s>(q_gen_7177, q_gen_7186) -> q_gen_7156
<cons, s>(q_gen_7177, q_gen_7192) -> q_gen_7156
<cons, s>(q_gen_7206, q_gen_7185) -> q_gen_7156
<cons, s>(q_gen_7212, q_gen_7192) -> q_gen_7156
<nil, z>() -> q_gen_7156
<s, z>(q_gen_7162) -> q_gen_7159
<s, z>(q_gen_7165) -> q_gen_7159
<s, z>(q_gen_7175) -> q_gen_7159
<s, z>(q_gen_7204) -> q_gen_7159
<s, z>(q_gen_7230) -> q_gen_7159
<z, z>() -> q_gen_7159
<s, s>(q_gen_7159) -> q_gen_7168
<z, s>(q_gen_7162) -> q_gen_7168
<cons, s>(q_gen_7159, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7159, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7159, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7159, q_gen_7186) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7186) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7192) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7186) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7192) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7206, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7206, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7206, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7206, q_gen_7186) -> q_gen_7169
<cons, s>(q_gen_7206, q_gen_7192) -> q_gen_7169
<cons, s>(q_gen_7212, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7212, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7212, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7212, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7212, q_gen_7186) -> q_gen_7169
<s, s>(q_gen_7168) -> q_gen_7171
<z, s>(q_gen_7165) -> q_gen_7171
<s, s>(q_gen_7171) -> q_gen_7177
<s, s>(q_gen_7212) -> q_gen_7177
<z, s>(q_gen_7175) -> q_gen_7177
<s, s>(q_gen_7177) -> q_gen_7206
<z, s>(q_gen_7204) -> q_gen_7206
<z, s>(q_gen_7230) -> q_gen_7206
<s, s>(q_gen_7206) -> q_gen_7212
<z, s>(q_gen_7213) -> q_gen_7212
}

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

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

Teacher's answer:
New clause system:
{
() -> length([nil, z]) -> 64
(length([l, _cba]) /\ length([cons(z, cons(z, l)), _bba])) -> eq_nat([_bba, s(s(_cba))]) -> 99
(length([ll, _xaa])) -> length([cons(x, ll), s(_xaa)]) -> 100
}
Sat witness: Found: ((length([ll, _xaa])) -> length([cons(x, ll), s(_xaa)]), {
_xaa -> s(s(s(s(s(s(z))))))  ;  ll -> cons(z, cons(s(z), cons(z, cons(z, nil))))  ;  x -> z
})

-------------------------------------------
Step 64, which took 1.533728 s (model generation: 1.525928,  model checking: 0.007800):

Model:
|_
{
length -> 
{{{
Q={q_gen_7156, q_gen_7158, q_gen_7159, q_gen_7162, q_gen_7165, q_gen_7167, q_gen_7168, q_gen_7169, q_gen_7171, q_gen_7175, q_gen_7177, q_gen_7182, q_gen_7185, q_gen_7186, q_gen_7204, q_gen_7206, q_gen_7212, q_gen_7213, q_gen_7218, q_gen_7230},
Q_f={q_gen_7156},
Delta=
{
<cons>(q_gen_7162, q_gen_7218) -> q_gen_7158
<nil>() -> q_gen_7158
<z>() -> q_gen_7162
<s>(q_gen_7162) -> q_gen_7165
<cons>(q_gen_7162, q_gen_7158) -> q_gen_7167
<s>(q_gen_7165) -> q_gen_7175
<cons>(q_gen_7162, q_gen_7167) -> q_gen_7182
<cons>(q_gen_7162, q_gen_7186) -> q_gen_7185
<cons>(q_gen_7162, q_gen_7182) -> q_gen_7186
<cons>(q_gen_7165, q_gen_7182) -> q_gen_7186
<s>(q_gen_7175) -> q_gen_7204
<s>(q_gen_7204) -> q_gen_7213
<cons>(q_gen_7162, q_gen_7185) -> q_gen_7218
<s>(q_gen_7213) -> q_gen_7230
<s>(q_gen_7230) -> q_gen_7230
<cons, s>(q_gen_7159, q_gen_7158) -> q_gen_7156
<cons, s>(q_gen_7168, q_gen_7167) -> q_gen_7156
<cons, s>(q_gen_7171, q_gen_7182) -> q_gen_7156
<cons, s>(q_gen_7177, q_gen_7186) -> q_gen_7156
<cons, s>(q_gen_7206, q_gen_7185) -> q_gen_7156
<cons, s>(q_gen_7212, q_gen_7218) -> q_gen_7156
<nil, z>() -> q_gen_7156
<s, z>(q_gen_7162) -> q_gen_7159
<s, z>(q_gen_7165) -> q_gen_7159
<s, z>(q_gen_7175) -> q_gen_7159
<s, z>(q_gen_7204) -> q_gen_7159
<s, z>(q_gen_7230) -> q_gen_7159
<z, z>() -> q_gen_7159
<s, s>(q_gen_7159) -> q_gen_7168
<z, s>(q_gen_7162) -> q_gen_7168
<cons, s>(q_gen_7159, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7159, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7159, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7159, q_gen_7186) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7186) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7218) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7206, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7206, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7206, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7206, q_gen_7186) -> q_gen_7169
<cons, s>(q_gen_7206, q_gen_7218) -> q_gen_7169
<cons, s>(q_gen_7212, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7212, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7212, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7212, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7212, q_gen_7186) -> q_gen_7169
<s, s>(q_gen_7168) -> q_gen_7171
<z, s>(q_gen_7165) -> q_gen_7171
<s, s>(q_gen_7171) -> q_gen_7177
<z, s>(q_gen_7175) -> q_gen_7177
<s, s>(q_gen_7177) -> q_gen_7206
<z, s>(q_gen_7204) -> q_gen_7206
<z, s>(q_gen_7230) -> q_gen_7206
<s, s>(q_gen_7206) -> q_gen_7212
<s, s>(q_gen_7212) -> q_gen_7212
<z, s>(q_gen_7213) -> q_gen_7212
}

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

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

Teacher's answer:
New clause system:
{
() -> length([nil, z]) -> 65
(length([l, _cba]) /\ length([cons(z, cons(z, l)), _bba])) -> eq_nat([_bba, s(s(_cba))]) -> 102
(length([ll, _xaa])) -> length([cons(x, ll), s(_xaa)]) -> 100
}
Sat witness: Found: ((length([l, _cba]) /\ length([cons(z, cons(z, l)), _bba])) -> eq_nat([_bba, s(s(_cba))]), {
_bba -> s(s(s(s(s(s(s(z)))))))  ;  _cba -> s(s(s(z)))  ;  l -> cons(z, cons(z, cons(z, nil)))
})

-------------------------------------------
Step 65, which took 1.628721 s (model generation: 1.586922,  model checking: 0.041799):

Model:
|_
{
length -> 
{{{
Q={q_gen_7156, q_gen_7158, q_gen_7159, q_gen_7162, q_gen_7165, q_gen_7167, q_gen_7168, q_gen_7169, q_gen_7171, q_gen_7175, q_gen_7177, q_gen_7182, q_gen_7185, q_gen_7186, q_gen_7192, q_gen_7204, q_gen_7206, q_gen_7212, q_gen_7213, q_gen_7230, q_gen_7243},
Q_f={q_gen_7156},
Delta=
{
<cons>(q_gen_7162, q_gen_7192) -> q_gen_7158
<nil>() -> q_gen_7158
<z>() -> q_gen_7162
<s>(q_gen_7162) -> q_gen_7165
<cons>(q_gen_7162, q_gen_7158) -> q_gen_7167
<s>(q_gen_7165) -> q_gen_7175
<cons>(q_gen_7162, q_gen_7167) -> q_gen_7182
<cons>(q_gen_7162, q_gen_7186) -> q_gen_7185
<cons>(q_gen_7162, q_gen_7182) -> q_gen_7186
<cons>(q_gen_7162, q_gen_7185) -> q_gen_7192
<cons>(q_gen_7165, q_gen_7182) -> q_gen_7192
<s>(q_gen_7175) -> q_gen_7204
<s>(q_gen_7243) -> q_gen_7204
<s>(q_gen_7204) -> q_gen_7213
<s>(q_gen_7213) -> q_gen_7230
<s>(q_gen_7230) -> q_gen_7243
<cons, s>(q_gen_7159, q_gen_7158) -> q_gen_7156
<cons, s>(q_gen_7168, q_gen_7167) -> q_gen_7156
<cons, s>(q_gen_7171, q_gen_7182) -> q_gen_7156
<cons, s>(q_gen_7177, q_gen_7186) -> q_gen_7156
<cons, s>(q_gen_7177, q_gen_7192) -> q_gen_7156
<cons, s>(q_gen_7206, q_gen_7185) -> q_gen_7156
<cons, s>(q_gen_7212, q_gen_7192) -> q_gen_7156
<nil, z>() -> q_gen_7156
<s, s>(q_gen_7212) -> q_gen_7159
<s, z>(q_gen_7162) -> q_gen_7159
<s, z>(q_gen_7165) -> q_gen_7159
<s, z>(q_gen_7175) -> q_gen_7159
<s, z>(q_gen_7204) -> q_gen_7159
<s, z>(q_gen_7230) -> q_gen_7159
<z, s>(q_gen_7230) -> q_gen_7159
<z, z>() -> q_gen_7159
<s, s>(q_gen_7159) -> q_gen_7168
<z, s>(q_gen_7162) -> q_gen_7168
<cons, s>(q_gen_7159, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7159, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7159, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7159, q_gen_7186) -> q_gen_7169
<cons, s>(q_gen_7159, q_gen_7192) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7186) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7192) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7192) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7206, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7206, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7206, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7206, q_gen_7186) -> q_gen_7169
<cons, s>(q_gen_7206, q_gen_7192) -> q_gen_7169
<cons, s>(q_gen_7212, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7212, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7212, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7212, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7212, q_gen_7186) -> q_gen_7169
<s, s>(q_gen_7168) -> q_gen_7171
<z, s>(q_gen_7165) -> q_gen_7171
<s, s>(q_gen_7171) -> q_gen_7177
<z, s>(q_gen_7175) -> q_gen_7177
<s, s>(q_gen_7177) -> q_gen_7206
<z, s>(q_gen_7204) -> q_gen_7206
<z, s>(q_gen_7243) -> q_gen_7206
<s, s>(q_gen_7206) -> q_gen_7212
<z, s>(q_gen_7213) -> q_gen_7212
}

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

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

Teacher's answer:
New clause system:
{
() -> length([nil, z]) -> 66
(length([l, _cba]) /\ length([cons(z, cons(z, l)), _bba])) -> eq_nat([_bba, s(s(_cba))]) -> 102
(length([ll, _xaa])) -> length([cons(x, ll), s(_xaa)]) -> 103
}
Sat witness: Found: ((length([ll, _xaa])) -> length([cons(x, ll), s(_xaa)]), {
_xaa -> s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(z)))))))))))))))  ;  ll -> cons(z, nil)  ;  x -> s(s(s(s(s(s(s(s(s(s(z))))))))))
})

-------------------------------------------
Step 66, which took 2.145091 s (model generation: 2.125537,  model checking: 0.019554):

Model:
|_
{
length -> 
{{{
Q={q_gen_7156, q_gen_7158, q_gen_7159, q_gen_7162, q_gen_7165, q_gen_7167, q_gen_7168, q_gen_7169, q_gen_7171, q_gen_7175, q_gen_7177, q_gen_7182, q_gen_7185, q_gen_7186, q_gen_7192, q_gen_7203, q_gen_7204, q_gen_7206, q_gen_7212, q_gen_7213, q_gen_7230},
Q_f={q_gen_7156},
Delta=
{
<cons>(q_gen_7162, q_gen_7192) -> q_gen_7158
<nil>() -> q_gen_7158
<z>() -> q_gen_7162
<s>(q_gen_7162) -> q_gen_7165
<cons>(q_gen_7162, q_gen_7158) -> q_gen_7167
<s>(q_gen_7165) -> q_gen_7175
<cons>(q_gen_7162, q_gen_7167) -> q_gen_7182
<cons>(q_gen_7162, q_gen_7186) -> q_gen_7185
<cons>(q_gen_7162, q_gen_7182) -> q_gen_7186
<cons>(q_gen_7162, q_gen_7185) -> q_gen_7192
<cons>(q_gen_7165, q_gen_7182) -> q_gen_7192
<s>(q_gen_7175) -> q_gen_7204
<s>(q_gen_7204) -> q_gen_7213
<s>(q_gen_7213) -> q_gen_7230
<s>(q_gen_7230) -> q_gen_7230
<cons, s>(q_gen_7159, q_gen_7158) -> q_gen_7156
<cons, s>(q_gen_7168, q_gen_7167) -> q_gen_7156
<cons, s>(q_gen_7171, q_gen_7182) -> q_gen_7156
<cons, s>(q_gen_7177, q_gen_7186) -> q_gen_7156
<cons, s>(q_gen_7177, q_gen_7192) -> q_gen_7156
<cons, s>(q_gen_7203, q_gen_7158) -> q_gen_7156
<cons, s>(q_gen_7203, q_gen_7167) -> q_gen_7156
<cons, s>(q_gen_7203, q_gen_7185) -> q_gen_7156
<cons, s>(q_gen_7203, q_gen_7186) -> q_gen_7156
<cons, s>(q_gen_7203, q_gen_7192) -> q_gen_7156
<cons, s>(q_gen_7206, q_gen_7185) -> q_gen_7156
<cons, s>(q_gen_7212, q_gen_7192) -> q_gen_7156
<nil, z>() -> q_gen_7156
<s, s>(q_gen_7212) -> q_gen_7159
<s, z>(q_gen_7162) -> q_gen_7159
<s, z>(q_gen_7165) -> q_gen_7159
<s, z>(q_gen_7175) -> q_gen_7159
<z, s>(q_gen_7230) -> q_gen_7159
<z, z>() -> q_gen_7159
<s, s>(q_gen_7159) -> q_gen_7168
<s, s>(q_gen_7177) -> q_gen_7168
<z, s>(q_gen_7162) -> q_gen_7168
<cons, s>(q_gen_7159, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7159, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7159, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7159, q_gen_7186) -> q_gen_7169
<cons, s>(q_gen_7159, q_gen_7192) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7186) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7192) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7192) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7203, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7206, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7206, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7206, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7206, q_gen_7186) -> q_gen_7169
<cons, s>(q_gen_7206, q_gen_7192) -> q_gen_7169
<cons, s>(q_gen_7212, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7212, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7212, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7212, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7212, q_gen_7186) -> q_gen_7169
<s, s>(q_gen_7168) -> q_gen_7171
<s, s>(q_gen_7206) -> q_gen_7171
<z, s>(q_gen_7165) -> q_gen_7171
<z, s>(q_gen_7175) -> q_gen_7177
<s, s>(q_gen_7171) -> q_gen_7203
<s, s>(q_gen_7203) -> q_gen_7203
<s, z>(q_gen_7204) -> q_gen_7203
<s, z>(q_gen_7230) -> q_gen_7203
<z, s>(q_gen_7204) -> q_gen_7206
<z, s>(q_gen_7213) -> q_gen_7212
}

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

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

Teacher's answer:
New clause system:
{
() -> length([nil, z]) -> 67
(length([l, _cba]) /\ length([cons(z, cons(z, l)), _bba])) -> eq_nat([_bba, s(s(_cba))]) -> 105
(length([ll, _xaa])) -> length([cons(x, ll), s(_xaa)]) -> 103
}
Sat witness: Found: ((length([l, _cba]) /\ length([cons(z, cons(z, l)), _bba])) -> eq_nat([_bba, s(s(_cba))]), {
_bba -> s(s(s(z)))  ;  _cba -> s(s(s(s(s(s(s(z)))))))  ;  l -> cons(z, nil)
})

-------------------------------------------
Step 67, which took 3.700707 s (model generation: 3.672915,  model checking: 0.027792):

Model:
|_
{
length -> 
{{{
Q={q_gen_7156, q_gen_7158, q_gen_7159, q_gen_7161, q_gen_7162, q_gen_7165, q_gen_7167, q_gen_7168, q_gen_7169, q_gen_7171, q_gen_7175, q_gen_7177, q_gen_7182, q_gen_7185, q_gen_7186, q_gen_7204, q_gen_7212, q_gen_7213, q_gen_7218, q_gen_7230, q_gen_7232},
Q_f={q_gen_7156},
Delta=
{
<nil>() -> q_gen_7158
<z>() -> q_gen_7162
<s>(q_gen_7162) -> q_gen_7165
<cons>(q_gen_7162, q_gen_7158) -> q_gen_7167
<cons>(q_gen_7162, q_gen_7218) -> q_gen_7167
<s>(q_gen_7165) -> q_gen_7175
<cons>(q_gen_7162, q_gen_7167) -> q_gen_7182
<cons>(q_gen_7162, q_gen_7186) -> q_gen_7185
<cons>(q_gen_7162, q_gen_7182) -> q_gen_7186
<cons>(q_gen_7165, q_gen_7182) -> q_gen_7186
<s>(q_gen_7175) -> q_gen_7204
<s>(q_gen_7204) -> q_gen_7213
<cons>(q_gen_7162, q_gen_7185) -> q_gen_7218
<s>(q_gen_7213) -> q_gen_7230
<s>(q_gen_7230) -> q_gen_7230
<cons, s>(q_gen_7159, q_gen_7158) -> q_gen_7156
<cons, s>(q_gen_7161, q_gen_7158) -> q_gen_7156
<cons, s>(q_gen_7161, q_gen_7185) -> q_gen_7156
<cons, s>(q_gen_7168, q_gen_7167) -> q_gen_7156
<cons, s>(q_gen_7168, q_gen_7218) -> q_gen_7156
<cons, s>(q_gen_7171, q_gen_7182) -> q_gen_7156
<cons, s>(q_gen_7177, q_gen_7186) -> q_gen_7156
<cons, s>(q_gen_7212, q_gen_7218) -> q_gen_7156
<nil, z>() -> q_gen_7156
<s, z>(q_gen_7204) -> q_gen_7159
<s, z>(q_gen_7230) -> q_gen_7159
<z, z>() -> q_gen_7159
<s, s>(q_gen_7177) -> q_gen_7161
<s, s>(q_gen_7232) -> q_gen_7161
<s, z>(q_gen_7162) -> q_gen_7161
<s, z>(q_gen_7165) -> q_gen_7161
<s, z>(q_gen_7175) -> q_gen_7161
<z, s>(q_gen_7204) -> q_gen_7161
<s, s>(q_gen_7159) -> q_gen_7168
<s, s>(q_gen_7161) -> q_gen_7168
<z, s>(q_gen_7162) -> q_gen_7168
<cons, s>(q_gen_7159, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7159, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7159, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7159, q_gen_7186) -> q_gen_7169
<cons, s>(q_gen_7161, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7161, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7161, q_gen_7186) -> q_gen_7169
<cons, s>(q_gen_7161, q_gen_7218) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7186) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7218) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7218) -> q_gen_7169
<cons, s>(q_gen_7212, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7212, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7212, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7212, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7212, q_gen_7186) -> q_gen_7169
<cons, s>(q_gen_7232, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7232, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7232, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7232, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7232, q_gen_7186) -> q_gen_7169
<cons, s>(q_gen_7232, q_gen_7218) -> q_gen_7169
<s, s>(q_gen_7168) -> q_gen_7171
<z, s>(q_gen_7165) -> q_gen_7171
<s, s>(q_gen_7171) -> q_gen_7177
<z, s>(q_gen_7175) -> q_gen_7177
<s, s>(q_gen_7212) -> q_gen_7212
<z, s>(q_gen_7213) -> q_gen_7212
<z, s>(q_gen_7230) -> q_gen_7232
}

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

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

Teacher's answer:
New clause system:
{
() -> length([nil, z]) -> 68
(length([l, _cba]) /\ length([cons(z, cons(z, l)), _bba])) -> eq_nat([_bba, s(s(_cba))]) -> 105
(length([ll, _xaa])) -> length([cons(x, ll), s(_xaa)]) -> 106
}
Sat witness: Found: ((length([ll, _xaa])) -> length([cons(x, ll), s(_xaa)]), {
_xaa -> s(s(s(s(s(s(z))))))  ;  ll -> cons(z, cons(z, cons(z, cons(z, cons(z, cons(z, nil))))))  ;  x -> s(z)
})

-------------------------------------------
Step 68, which took 1.629994 s (model generation: 1.625708,  model checking: 0.004286):

Model:
|_
{
length -> 
{{{
Q={q_gen_7156, q_gen_7158, q_gen_7159, q_gen_7161, q_gen_7162, q_gen_7165, q_gen_7167, q_gen_7168, q_gen_7169, q_gen_7171, q_gen_7175, q_gen_7177, q_gen_7182, q_gen_7185, q_gen_7186, q_gen_7204, q_gen_7212, q_gen_7213, q_gen_7218, q_gen_7230, q_gen_7232},
Q_f={q_gen_7156},
Delta=
{
<nil>() -> q_gen_7158
<z>() -> q_gen_7162
<s>(q_gen_7162) -> q_gen_7165
<cons>(q_gen_7162, q_gen_7158) -> q_gen_7167
<s>(q_gen_7165) -> q_gen_7175
<cons>(q_gen_7162, q_gen_7167) -> q_gen_7182
<cons>(q_gen_7162, q_gen_7186) -> q_gen_7185
<cons>(q_gen_7162, q_gen_7182) -> q_gen_7186
<cons>(q_gen_7165, q_gen_7182) -> q_gen_7186
<s>(q_gen_7175) -> q_gen_7204
<s>(q_gen_7204) -> q_gen_7213
<cons>(q_gen_7162, q_gen_7185) -> q_gen_7218
<cons>(q_gen_7162, q_gen_7218) -> q_gen_7218
<s>(q_gen_7213) -> q_gen_7230
<s>(q_gen_7230) -> q_gen_7230
<cons, s>(q_gen_7159, q_gen_7158) -> q_gen_7156
<cons, s>(q_gen_7161, q_gen_7158) -> q_gen_7156
<cons, s>(q_gen_7161, q_gen_7185) -> q_gen_7156
<cons, s>(q_gen_7168, q_gen_7167) -> q_gen_7156
<cons, s>(q_gen_7168, q_gen_7218) -> q_gen_7156
<cons, s>(q_gen_7171, q_gen_7182) -> q_gen_7156
<cons, s>(q_gen_7177, q_gen_7186) -> q_gen_7156
<cons, s>(q_gen_7212, q_gen_7218) -> q_gen_7156
<nil, z>() -> q_gen_7156
<s, z>(q_gen_7230) -> q_gen_7159
<z, z>() -> q_gen_7159
<s, s>(q_gen_7177) -> q_gen_7161
<s, z>(q_gen_7162) -> q_gen_7161
<s, z>(q_gen_7165) -> q_gen_7161
<s, z>(q_gen_7175) -> q_gen_7161
<s, z>(q_gen_7204) -> q_gen_7161
<z, s>(q_gen_7204) -> q_gen_7161
<s, s>(q_gen_7159) -> q_gen_7168
<s, s>(q_gen_7161) -> q_gen_7168
<z, s>(q_gen_7162) -> q_gen_7168
<cons, s>(q_gen_7159, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7159, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7159, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7159, q_gen_7186) -> q_gen_7169
<cons, s>(q_gen_7161, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7161, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7161, q_gen_7186) -> q_gen_7169
<cons, s>(q_gen_7161, q_gen_7218) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7186) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7218) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7218) -> q_gen_7169
<cons, s>(q_gen_7212, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7212, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7212, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7212, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7212, q_gen_7186) -> q_gen_7169
<cons, s>(q_gen_7232, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7232, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7232, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7232, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7232, q_gen_7186) -> q_gen_7169
<cons, s>(q_gen_7232, q_gen_7218) -> q_gen_7169
<s, s>(q_gen_7168) -> q_gen_7171
<s, s>(q_gen_7232) -> q_gen_7171
<z, s>(q_gen_7165) -> q_gen_7171
<s, s>(q_gen_7171) -> q_gen_7177
<z, s>(q_gen_7175) -> q_gen_7177
<s, s>(q_gen_7212) -> q_gen_7212
<z, s>(q_gen_7213) -> q_gen_7212
<z, s>(q_gen_7230) -> q_gen_7232
}

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

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

Teacher's answer:
New clause system:
{
() -> length([nil, z]) -> 69
(length([l, _cba]) /\ length([cons(z, cons(z, l)), _bba])) -> eq_nat([_bba, s(s(_cba))]) -> 108
(length([ll, _xaa])) -> length([cons(x, ll), s(_xaa)]) -> 106
}
Sat witness: Found: ((length([l, _cba]) /\ length([cons(z, cons(z, l)), _bba])) -> eq_nat([_bba, s(s(_cba))]), {
_bba -> s(s(s(z)))  ;  _cba -> s(s(s(s(s(z)))))  ;  l -> cons(z, nil)
})

-------------------------------------------
Step 69, which took 2.010965 s (model generation: 1.949007,  model checking: 0.061958):

Model:
|_
{
length -> 
{{{
Q={q_gen_7156, q_gen_7158, q_gen_7159, q_gen_7162, q_gen_7165, q_gen_7167, q_gen_7168, q_gen_7169, q_gen_7171, q_gen_7175, q_gen_7177, q_gen_7182, q_gen_7185, q_gen_7186, q_gen_7204, q_gen_7206, q_gen_7212, q_gen_7213, q_gen_7218, q_gen_7230, q_gen_7232},
Q_f={q_gen_7156},
Delta=
{
<cons>(q_gen_7162, q_gen_7218) -> q_gen_7158
<nil>() -> q_gen_7158
<z>() -> q_gen_7162
<s>(q_gen_7162) -> q_gen_7165
<cons>(q_gen_7162, q_gen_7158) -> q_gen_7167
<s>(q_gen_7165) -> q_gen_7175
<cons>(q_gen_7162, q_gen_7167) -> q_gen_7182
<cons>(q_gen_7162, q_gen_7186) -> q_gen_7185
<cons>(q_gen_7162, q_gen_7182) -> q_gen_7186
<cons>(q_gen_7165, q_gen_7182) -> q_gen_7186
<s>(q_gen_7175) -> q_gen_7204
<s>(q_gen_7204) -> q_gen_7213
<cons>(q_gen_7162, q_gen_7185) -> q_gen_7218
<s>(q_gen_7213) -> q_gen_7230
<s>(q_gen_7230) -> q_gen_7230
<cons, s>(q_gen_7159, q_gen_7158) -> q_gen_7156
<cons, s>(q_gen_7159, q_gen_7218) -> q_gen_7156
<cons, s>(q_gen_7168, q_gen_7167) -> q_gen_7156
<cons, s>(q_gen_7171, q_gen_7182) -> q_gen_7156
<cons, s>(q_gen_7177, q_gen_7186) -> q_gen_7156
<cons, s>(q_gen_7206, q_gen_7185) -> q_gen_7156
<cons, s>(q_gen_7212, q_gen_7218) -> q_gen_7156
<nil, z>() -> q_gen_7156
<s, s>(q_gen_7212) -> q_gen_7159
<s, z>(q_gen_7162) -> q_gen_7159
<s, z>(q_gen_7165) -> q_gen_7159
<s, z>(q_gen_7175) -> q_gen_7159
<s, z>(q_gen_7204) -> q_gen_7159
<s, z>(q_gen_7230) -> q_gen_7159
<z, z>() -> q_gen_7159
<s, s>(q_gen_7159) -> q_gen_7168
<z, s>(q_gen_7162) -> q_gen_7168
<cons, s>(q_gen_7159, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7159, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7159, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7159, q_gen_7186) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7186) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7218) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7218) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7206, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7206, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7206, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7206, q_gen_7186) -> q_gen_7169
<cons, s>(q_gen_7206, q_gen_7218) -> q_gen_7169
<cons, s>(q_gen_7212, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7212, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7212, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7212, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7212, q_gen_7186) -> q_gen_7169
<cons, s>(q_gen_7232, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7232, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7232, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7232, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7232, q_gen_7186) -> q_gen_7169
<cons, s>(q_gen_7232, q_gen_7218) -> q_gen_7169
<s, s>(q_gen_7168) -> q_gen_7171
<z, s>(q_gen_7165) -> q_gen_7171
<s, s>(q_gen_7171) -> q_gen_7177
<z, s>(q_gen_7175) -> q_gen_7177
<s, s>(q_gen_7177) -> q_gen_7206
<z, s>(q_gen_7204) -> q_gen_7206
<s, s>(q_gen_7206) -> q_gen_7212
<s, s>(q_gen_7232) -> q_gen_7212
<z, s>(q_gen_7213) -> q_gen_7212
<z, s>(q_gen_7230) -> q_gen_7232
}

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

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

Teacher's answer:
New clause system:
{
() -> length([nil, z]) -> 70
(length([l, _cba]) /\ length([cons(z, cons(z, l)), _bba])) -> eq_nat([_bba, s(s(_cba))]) -> 108
(length([ll, _xaa])) -> length([cons(x, ll), s(_xaa)]) -> 109
}
Sat witness: Found: ((length([ll, _xaa])) -> length([cons(x, ll), s(_xaa)]), {
_xaa -> s(s(s(s(s(s(z))))))  ;  ll -> cons(z, cons(z, cons(z, cons(z, cons(z, cons(z, nil))))))  ;  x -> z
})

-------------------------------------------
Step 70, which took 2.107839 s (model generation: 2.094622,  model checking: 0.013217):

Model:
|_
{
length -> 
{{{
Q={q_gen_7156, q_gen_7158, q_gen_7159, q_gen_7162, q_gen_7165, q_gen_7167, q_gen_7168, q_gen_7169, q_gen_7171, q_gen_7175, q_gen_7177, q_gen_7182, q_gen_7185, q_gen_7186, q_gen_7192, q_gen_7204, q_gen_7206, q_gen_7212, q_gen_7213, q_gen_7218, q_gen_7230, q_gen_7232},
Q_f={q_gen_7156},
Delta=
{
<nil>() -> q_gen_7158
<z>() -> q_gen_7162
<s>(q_gen_7162) -> q_gen_7165
<cons>(q_gen_7162, q_gen_7158) -> q_gen_7167
<s>(q_gen_7165) -> q_gen_7175
<cons>(q_gen_7162, q_gen_7167) -> q_gen_7182
<cons>(q_gen_7162, q_gen_7186) -> q_gen_7185
<cons>(q_gen_7162, q_gen_7192) -> q_gen_7185
<cons>(q_gen_7162, q_gen_7182) -> q_gen_7186
<cons>(q_gen_7162, q_gen_7218) -> q_gen_7192
<cons>(q_gen_7165, q_gen_7182) -> q_gen_7192
<s>(q_gen_7175) -> q_gen_7204
<s>(q_gen_7204) -> q_gen_7213
<cons>(q_gen_7162, q_gen_7185) -> q_gen_7218
<s>(q_gen_7213) -> q_gen_7230
<s>(q_gen_7230) -> q_gen_7230
<cons, s>(q_gen_7159, q_gen_7158) -> q_gen_7156
<cons, s>(q_gen_7159, q_gen_7218) -> q_gen_7156
<cons, s>(q_gen_7168, q_gen_7167) -> q_gen_7156
<cons, s>(q_gen_7171, q_gen_7182) -> q_gen_7156
<cons, s>(q_gen_7177, q_gen_7186) -> q_gen_7156
<cons, s>(q_gen_7177, q_gen_7192) -> q_gen_7156
<cons, s>(q_gen_7206, q_gen_7185) -> q_gen_7156
<cons, s>(q_gen_7212, q_gen_7218) -> q_gen_7156
<cons, s>(q_gen_7232, q_gen_7192) -> q_gen_7156
<nil, z>() -> q_gen_7156
<s, s>(q_gen_7206) -> q_gen_7159
<s, z>(q_gen_7162) -> q_gen_7159
<s, z>(q_gen_7165) -> q_gen_7159
<s, z>(q_gen_7175) -> q_gen_7159
<s, z>(q_gen_7204) -> q_gen_7159
<s, z>(q_gen_7230) -> q_gen_7159
<z, z>() -> q_gen_7159
<s, s>(q_gen_7159) -> q_gen_7168
<z, s>(q_gen_7162) -> q_gen_7168
<cons, s>(q_gen_7159, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7159, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7159, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7159, q_gen_7186) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7186) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7192) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7218) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7206, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7206, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7206, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7206, q_gen_7186) -> q_gen_7169
<cons, s>(q_gen_7206, q_gen_7218) -> q_gen_7169
<cons, s>(q_gen_7212, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7212, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7212, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7212, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7212, q_gen_7186) -> q_gen_7169
<cons, s>(q_gen_7212, q_gen_7192) -> q_gen_7169
<cons, s>(q_gen_7232, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7232, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7232, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7232, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7232, q_gen_7186) -> q_gen_7169
<cons, s>(q_gen_7232, q_gen_7218) -> q_gen_7169
<s, s>(q_gen_7168) -> q_gen_7171
<z, s>(q_gen_7165) -> q_gen_7171
<s, s>(q_gen_7171) -> q_gen_7177
<s, s>(q_gen_7212) -> q_gen_7177
<z, s>(q_gen_7175) -> q_gen_7177
<s, s>(q_gen_7177) -> q_gen_7206
<z, s>(q_gen_7204) -> q_gen_7206
<s, s>(q_gen_7232) -> q_gen_7212
<z, s>(q_gen_7213) -> q_gen_7212
<z, s>(q_gen_7230) -> q_gen_7232
}

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

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

Teacher's answer:
New clause system:
{
() -> length([nil, z]) -> 71
(length([l, _cba]) /\ length([cons(z, cons(z, l)), _bba])) -> eq_nat([_bba, s(s(_cba))]) -> 111
(length([ll, _xaa])) -> length([cons(x, ll), s(_xaa)]) -> 109
}
Sat witness: Found: ((length([l, _cba]) /\ length([cons(z, cons(z, l)), _bba])) -> eq_nat([_bba, s(s(_cba))]), {
_bba -> s(s(s(s(s(s(s(s(z))))))))  ;  _cba -> s(s(s(s(s(z)))))  ;  l -> cons(z, cons(z, cons(z, cons(z, cons(z, nil)))))
})

-------------------------------------------
Step 71, which took 2.660094 s (model generation: 2.459044,  model checking: 0.201050):

Model:
|_
{
length -> 
{{{
Q={q_gen_7156, q_gen_7158, q_gen_7159, q_gen_7162, q_gen_7165, q_gen_7167, q_gen_7168, q_gen_7169, q_gen_7171, q_gen_7175, q_gen_7177, q_gen_7182, q_gen_7185, q_gen_7186, q_gen_7192, q_gen_7204, q_gen_7206, q_gen_7212, q_gen_7213, q_gen_7218, q_gen_7230, q_gen_7232},
Q_f={q_gen_7156},
Delta=
{
<nil>() -> q_gen_7158
<z>() -> q_gen_7162
<s>(q_gen_7162) -> q_gen_7165
<cons>(q_gen_7162, q_gen_7158) -> q_gen_7167
<s>(q_gen_7165) -> q_gen_7175
<cons>(q_gen_7162, q_gen_7167) -> q_gen_7182
<cons>(q_gen_7162, q_gen_7186) -> q_gen_7185
<cons>(q_gen_7162, q_gen_7192) -> q_gen_7185
<cons>(q_gen_7162, q_gen_7182) -> q_gen_7186
<cons>(q_gen_7162, q_gen_7218) -> q_gen_7192
<cons>(q_gen_7165, q_gen_7182) -> q_gen_7192
<s>(q_gen_7175) -> q_gen_7204
<s>(q_gen_7230) -> q_gen_7204
<s>(q_gen_7204) -> q_gen_7213
<cons>(q_gen_7162, q_gen_7185) -> q_gen_7218
<s>(q_gen_7213) -> q_gen_7230
<cons, s>(q_gen_7159, q_gen_7158) -> q_gen_7156
<cons, s>(q_gen_7159, q_gen_7192) -> q_gen_7156
<cons, s>(q_gen_7159, q_gen_7218) -> q_gen_7156
<cons, s>(q_gen_7168, q_gen_7167) -> q_gen_7156
<cons, s>(q_gen_7168, q_gen_7218) -> q_gen_7156
<cons, s>(q_gen_7171, q_gen_7182) -> q_gen_7156
<cons, s>(q_gen_7177, q_gen_7186) -> q_gen_7156
<cons, s>(q_gen_7177, q_gen_7192) -> q_gen_7156
<cons, s>(q_gen_7206, q_gen_7185) -> q_gen_7156
<cons, s>(q_gen_7212, q_gen_7218) -> q_gen_7156
<cons, s>(q_gen_7232, q_gen_7192) -> q_gen_7156
<nil, z>() -> q_gen_7156
<s, s>(q_gen_7206) -> q_gen_7159
<s, s>(q_gen_7212) -> q_gen_7159
<s, z>(q_gen_7162) -> q_gen_7159
<s, z>(q_gen_7165) -> q_gen_7159
<s, z>(q_gen_7175) -> q_gen_7159
<s, z>(q_gen_7204) -> q_gen_7159
<s, z>(q_gen_7230) -> q_gen_7159
<z, z>() -> q_gen_7159
<s, s>(q_gen_7159) -> q_gen_7168
<z, s>(q_gen_7162) -> q_gen_7168
<cons, s>(q_gen_7159, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7159, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7159, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7159, q_gen_7186) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7186) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7192) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7218) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7206, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7206, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7206, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7206, q_gen_7186) -> q_gen_7169
<cons, s>(q_gen_7206, q_gen_7192) -> q_gen_7169
<cons, s>(q_gen_7206, q_gen_7218) -> q_gen_7169
<cons, s>(q_gen_7212, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7212, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7212, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7212, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7212, q_gen_7186) -> q_gen_7169
<cons, s>(q_gen_7212, q_gen_7192) -> q_gen_7169
<cons, s>(q_gen_7232, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7232, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7232, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7232, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7232, q_gen_7186) -> q_gen_7169
<cons, s>(q_gen_7232, q_gen_7218) -> q_gen_7169
<s, s>(q_gen_7168) -> q_gen_7171
<z, s>(q_gen_7165) -> q_gen_7171
<s, s>(q_gen_7171) -> q_gen_7177
<z, s>(q_gen_7175) -> q_gen_7177
<s, s>(q_gen_7177) -> q_gen_7206
<z, s>(q_gen_7204) -> q_gen_7206
<s, s>(q_gen_7232) -> q_gen_7212
<z, s>(q_gen_7213) -> q_gen_7212
<z, s>(q_gen_7230) -> q_gen_7232
}

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

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

Teacher's answer:
New clause system:
{
() -> length([nil, z]) -> 72
(length([l, _cba]) /\ length([cons(z, cons(z, l)), _bba])) -> eq_nat([_bba, s(s(_cba))]) -> 111
(length([ll, _xaa])) -> length([cons(x, ll), s(_xaa)]) -> 112
}
Sat witness: Found: ((length([ll, _xaa])) -> length([cons(x, ll), s(_xaa)]), {
_xaa -> s(s(s(s(s(s(s(s(s(s(s(s(s(z)))))))))))))  ;  ll -> cons(z, cons(s(z), cons(z, cons(z, nil))))  ;  x -> s(s(s(s(s(s(s(s(s(z)))))))))
})

-------------------------------------------
Step 72, which took 2.406215 s (model generation: 2.388750,  model checking: 0.017465):

Model:
|_
{
length -> 
{{{
Q={q_gen_7156, q_gen_7158, q_gen_7159, q_gen_7162, q_gen_7165, q_gen_7167, q_gen_7168, q_gen_7169, q_gen_7171, q_gen_7175, q_gen_7177, q_gen_7182, q_gen_7185, q_gen_7186, q_gen_7192, q_gen_7197, q_gen_7204, q_gen_7206, q_gen_7212, q_gen_7213, q_gen_7230, q_gen_7232},
Q_f={q_gen_7156},
Delta=
{
<nil>() -> q_gen_7158
<z>() -> q_gen_7162
<s>(q_gen_7162) -> q_gen_7165
<cons>(q_gen_7162, q_gen_7158) -> q_gen_7167
<s>(q_gen_7165) -> q_gen_7175
<cons>(q_gen_7162, q_gen_7167) -> q_gen_7182
<cons>(q_gen_7162, q_gen_7186) -> q_gen_7185
<cons>(q_gen_7162, q_gen_7182) -> q_gen_7186
<cons>(q_gen_7162, q_gen_7197) -> q_gen_7192
<cons>(q_gen_7165, q_gen_7182) -> q_gen_7192
<cons>(q_gen_7162, q_gen_7185) -> q_gen_7197
<cons>(q_gen_7162, q_gen_7192) -> q_gen_7197
<s>(q_gen_7175) -> q_gen_7204
<s>(q_gen_7230) -> q_gen_7204
<s>(q_gen_7204) -> q_gen_7213
<s>(q_gen_7213) -> q_gen_7230
<cons, s>(q_gen_7159, q_gen_7158) -> q_gen_7156
<cons, s>(q_gen_7168, q_gen_7167) -> q_gen_7156
<cons, s>(q_gen_7168, q_gen_7197) -> q_gen_7156
<cons, s>(q_gen_7171, q_gen_7182) -> q_gen_7156
<cons, s>(q_gen_7177, q_gen_7186) -> q_gen_7156
<cons, s>(q_gen_7177, q_gen_7192) -> q_gen_7156
<cons, s>(q_gen_7206, q_gen_7185) -> q_gen_7156
<cons, s>(q_gen_7212, q_gen_7197) -> q_gen_7156
<cons, s>(q_gen_7232, q_gen_7192) -> q_gen_7156
<nil, z>() -> q_gen_7156
<s, z>(q_gen_7162) -> q_gen_7159
<s, z>(q_gen_7165) -> q_gen_7159
<s, z>(q_gen_7175) -> q_gen_7159
<s, z>(q_gen_7204) -> q_gen_7159
<s, z>(q_gen_7230) -> q_gen_7159
<z, z>() -> q_gen_7159
<s, s>(q_gen_7159) -> q_gen_7168
<s, s>(q_gen_7206) -> q_gen_7168
<z, s>(q_gen_7162) -> q_gen_7168
<cons, s>(q_gen_7159, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7159, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7159, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7159, q_gen_7186) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7186) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7192) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7197) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7197) -> q_gen_7169
<cons, s>(q_gen_7206, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7206, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7206, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7206, q_gen_7186) -> q_gen_7169
<cons, s>(q_gen_7206, q_gen_7192) -> q_gen_7169
<cons, s>(q_gen_7206, q_gen_7197) -> q_gen_7169
<cons, s>(q_gen_7212, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7212, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7212, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7212, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7212, q_gen_7186) -> q_gen_7169
<cons, s>(q_gen_7212, q_gen_7192) -> q_gen_7169
<cons, s>(q_gen_7232, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7232, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7232, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7232, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7232, q_gen_7186) -> q_gen_7169
<cons, s>(q_gen_7232, q_gen_7197) -> q_gen_7169
<s, s>(q_gen_7168) -> q_gen_7171
<s, s>(q_gen_7232) -> q_gen_7171
<z, s>(q_gen_7165) -> q_gen_7171
<s, s>(q_gen_7171) -> q_gen_7177
<z, s>(q_gen_7175) -> q_gen_7177
<s, s>(q_gen_7177) -> q_gen_7206
<z, s>(q_gen_7204) -> q_gen_7206
<z, s>(q_gen_7213) -> q_gen_7212
<s, s>(q_gen_7212) -> q_gen_7232
<z, s>(q_gen_7230) -> q_gen_7232
}

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

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

Teacher's answer:
New clause system:
{
() -> length([nil, z]) -> 73
(length([l, _cba]) /\ length([cons(z, cons(z, l)), _bba])) -> eq_nat([_bba, s(s(_cba))]) -> 114
(length([ll, _xaa])) -> length([cons(x, ll), s(_xaa)]) -> 112
}
Sat witness: Found: ((length([l, _cba]) /\ length([cons(z, cons(z, l)), _bba])) -> eq_nat([_bba, s(s(_cba))]), {
_bba -> s(s(s(s(s(s(s(s(z))))))))  ;  _cba -> s(s(s(z)))  ;  l -> cons(z, cons(z, cons(z, nil)))
})

-------------------------------------------
Step 73, which took 3.142294 s (model generation: 3.066375,  model checking: 0.075919):

Model:
|_
{
length -> 
{{{
Q={q_gen_7156, q_gen_7158, q_gen_7159, q_gen_7162, q_gen_7165, q_gen_7167, q_gen_7168, q_gen_7169, q_gen_7171, q_gen_7175, q_gen_7177, q_gen_7182, q_gen_7185, q_gen_7186, q_gen_7192, q_gen_7197, q_gen_7204, q_gen_7206, q_gen_7212, q_gen_7213, q_gen_7230, q_gen_7232, q_gen_7242},
Q_f={q_gen_7156},
Delta=
{
<nil>() -> q_gen_7158
<z>() -> q_gen_7162
<s>(q_gen_7162) -> q_gen_7165
<cons>(q_gen_7162, q_gen_7158) -> q_gen_7167
<s>(q_gen_7165) -> q_gen_7175
<cons>(q_gen_7162, q_gen_7167) -> q_gen_7182
<cons>(q_gen_7162, q_gen_7186) -> q_gen_7185
<cons>(q_gen_7162, q_gen_7197) -> q_gen_7185
<cons>(q_gen_7162, q_gen_7182) -> q_gen_7186
<cons>(q_gen_7162, q_gen_7185) -> q_gen_7192
<cons>(q_gen_7165, q_gen_7182) -> q_gen_7192
<cons>(q_gen_7162, q_gen_7192) -> q_gen_7197
<s>(q_gen_7175) -> q_gen_7204
<s>(q_gen_7204) -> q_gen_7213
<s>(q_gen_7213) -> q_gen_7230
<s>(q_gen_7230) -> q_gen_7242
<s>(q_gen_7242) -> q_gen_7242
<cons, s>(q_gen_7159, q_gen_7158) -> q_gen_7156
<cons, s>(q_gen_7168, q_gen_7167) -> q_gen_7156
<cons, s>(q_gen_7171, q_gen_7182) -> q_gen_7156
<cons, s>(q_gen_7177, q_gen_7186) -> q_gen_7156
<cons, s>(q_gen_7177, q_gen_7192) -> q_gen_7156
<cons, s>(q_gen_7206, q_gen_7185) -> q_gen_7156
<cons, s>(q_gen_7212, q_gen_7192) -> q_gen_7156
<cons, s>(q_gen_7232, q_gen_7197) -> q_gen_7156
<nil, z>() -> q_gen_7156
<s, s>(q_gen_7232) -> q_gen_7159
<s, z>(q_gen_7162) -> q_gen_7159
<s, z>(q_gen_7165) -> q_gen_7159
<s, z>(q_gen_7175) -> q_gen_7159
<s, z>(q_gen_7204) -> q_gen_7159
<s, z>(q_gen_7230) -> q_gen_7159
<z, s>(q_gen_7242) -> q_gen_7159
<z, z>() -> q_gen_7159
<s, s>(q_gen_7159) -> q_gen_7168
<z, s>(q_gen_7162) -> q_gen_7168
<cons, s>(q_gen_7159, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7159, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7159, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7159, q_gen_7186) -> q_gen_7169
<cons, s>(q_gen_7159, q_gen_7192) -> q_gen_7169
<cons, s>(q_gen_7159, q_gen_7197) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7186) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7192) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7192) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7197) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7206, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7206, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7206, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7206, q_gen_7186) -> q_gen_7169
<cons, s>(q_gen_7206, q_gen_7192) -> q_gen_7169
<cons, s>(q_gen_7212, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7212, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7212, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7212, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7212, q_gen_7186) -> q_gen_7169
<cons, s>(q_gen_7232, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7232, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7232, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7232, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7232, q_gen_7186) -> q_gen_7169
<cons, s>(q_gen_7232, q_gen_7192) -> q_gen_7169
<s, s>(q_gen_7168) -> q_gen_7171
<z, s>(q_gen_7165) -> q_gen_7171
<s, s>(q_gen_7171) -> q_gen_7177
<z, s>(q_gen_7175) -> q_gen_7177
<s, s>(q_gen_7177) -> q_gen_7206
<z, s>(q_gen_7204) -> q_gen_7206
<s, s>(q_gen_7206) -> q_gen_7212
<z, s>(q_gen_7213) -> q_gen_7212
<s, s>(q_gen_7212) -> q_gen_7232
<z, s>(q_gen_7230) -> q_gen_7232
}

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

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

Teacher's answer:
New clause system:
{
() -> length([nil, z]) -> 74
(length([l, _cba]) /\ length([cons(z, cons(z, l)), _bba])) -> eq_nat([_bba, s(s(_cba))]) -> 114
(length([ll, _xaa])) -> length([cons(x, ll), s(_xaa)]) -> 115
}
Sat witness: Found: ((length([ll, _xaa])) -> length([cons(x, ll), s(_xaa)]), {
_xaa -> s(s(s(s(s(s(s(z)))))))  ;  ll -> cons(z, cons(z, cons(s(z), cons(z, cons(z, nil)))))  ;  x -> z
})

-------------------------------------------
Step 74, which took 3.061215 s (model generation: 3.033052,  model checking: 0.028163):

Model:
|_
{
length -> 
{{{
Q={q_gen_7156, q_gen_7158, q_gen_7159, q_gen_7162, q_gen_7165, q_gen_7167, q_gen_7168, q_gen_7169, q_gen_7171, q_gen_7175, q_gen_7177, q_gen_7182, q_gen_7185, q_gen_7186, q_gen_7192, q_gen_7197, q_gen_7204, q_gen_7206, q_gen_7212, q_gen_7213, q_gen_7230, q_gen_7232, q_gen_7243},
Q_f={q_gen_7156},
Delta=
{
<nil>() -> q_gen_7158
<z>() -> q_gen_7162
<s>(q_gen_7162) -> q_gen_7165
<cons>(q_gen_7162, q_gen_7158) -> q_gen_7167
<s>(q_gen_7165) -> q_gen_7175
<cons>(q_gen_7162, q_gen_7167) -> q_gen_7182
<cons>(q_gen_7162, q_gen_7186) -> q_gen_7185
<cons>(q_gen_7162, q_gen_7182) -> q_gen_7186
<cons>(q_gen_7162, q_gen_7197) -> q_gen_7192
<cons>(q_gen_7165, q_gen_7182) -> q_gen_7192
<cons>(q_gen_7162, q_gen_7185) -> q_gen_7197
<cons>(q_gen_7162, q_gen_7192) -> q_gen_7197
<s>(q_gen_7175) -> q_gen_7204
<s>(q_gen_7243) -> q_gen_7204
<s>(q_gen_7204) -> q_gen_7213
<s>(q_gen_7213) -> q_gen_7230
<s>(q_gen_7230) -> q_gen_7243
<cons, s>(q_gen_7159, q_gen_7158) -> q_gen_7156
<cons, s>(q_gen_7159, q_gen_7197) -> q_gen_7156
<cons, s>(q_gen_7168, q_gen_7167) -> q_gen_7156
<cons, s>(q_gen_7168, q_gen_7197) -> q_gen_7156
<cons, s>(q_gen_7171, q_gen_7182) -> q_gen_7156
<cons, s>(q_gen_7177, q_gen_7186) -> q_gen_7156
<cons, s>(q_gen_7177, q_gen_7192) -> q_gen_7156
<cons, s>(q_gen_7206, q_gen_7185) -> q_gen_7156
<cons, s>(q_gen_7212, q_gen_7197) -> q_gen_7156
<cons, s>(q_gen_7232, q_gen_7192) -> q_gen_7156
<nil, z>() -> q_gen_7156
<s, s>(q_gen_7206) -> q_gen_7159
<s, z>(q_gen_7162) -> q_gen_7159
<s, z>(q_gen_7165) -> q_gen_7159
<s, z>(q_gen_7175) -> q_gen_7159
<s, z>(q_gen_7204) -> q_gen_7159
<s, z>(q_gen_7230) -> q_gen_7159
<z, z>() -> q_gen_7159
<s, s>(q_gen_7159) -> q_gen_7168
<z, s>(q_gen_7162) -> q_gen_7168
<cons, s>(q_gen_7159, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7159, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7159, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7159, q_gen_7186) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7186) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7192) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7186) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7192) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7197) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7197) -> q_gen_7169
<cons, s>(q_gen_7206, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7206, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7206, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7206, q_gen_7186) -> q_gen_7169
<cons, s>(q_gen_7206, q_gen_7192) -> q_gen_7169
<cons, s>(q_gen_7206, q_gen_7197) -> q_gen_7169
<cons, s>(q_gen_7212, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7212, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7212, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7212, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7212, q_gen_7186) -> q_gen_7169
<cons, s>(q_gen_7212, q_gen_7192) -> q_gen_7169
<cons, s>(q_gen_7232, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7232, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7232, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7232, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7232, q_gen_7186) -> q_gen_7169
<cons, s>(q_gen_7232, q_gen_7197) -> q_gen_7169
<s, s>(q_gen_7168) -> q_gen_7171
<z, s>(q_gen_7165) -> q_gen_7171
<z, s>(q_gen_7243) -> q_gen_7171
<s, s>(q_gen_7171) -> q_gen_7177
<z, s>(q_gen_7175) -> q_gen_7177
<s, s>(q_gen_7177) -> q_gen_7206
<s, s>(q_gen_7232) -> q_gen_7206
<z, s>(q_gen_7204) -> q_gen_7206
<z, s>(q_gen_7213) -> q_gen_7212
<s, s>(q_gen_7212) -> q_gen_7232
<z, s>(q_gen_7230) -> q_gen_7232
}

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

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

Teacher's answer:
New clause system:
{
() -> length([nil, z]) -> 75
(length([l, _cba]) /\ length([cons(z, cons(z, l)), _bba])) -> eq_nat([_bba, s(s(_cba))]) -> 117
(length([ll, _xaa])) -> length([cons(x, ll), s(_xaa)]) -> 115
}
Sat witness: Found: ((length([l, _cba]) /\ length([cons(z, cons(z, l)), _bba])) -> eq_nat([_bba, s(s(_cba))]), {
_bba -> s(z)  ;  _cba -> s(s(s(s(z))))  ;  l -> cons(z, cons(z, cons(z, cons(z, nil))))
})

-------------------------------------------
Step 75, which took 3.651017 s (model generation: 3.605349,  model checking: 0.045668):

Model:
|_
{
length -> 
{{{
Q={q_gen_7156, q_gen_7158, q_gen_7159, q_gen_7162, q_gen_7165, q_gen_7167, q_gen_7168, q_gen_7169, q_gen_7171, q_gen_7175, q_gen_7177, q_gen_7182, q_gen_7185, q_gen_7186, q_gen_7192, q_gen_7204, q_gen_7206, q_gen_7212, q_gen_7213, q_gen_7218, q_gen_7230, q_gen_7232, q_gen_7242},
Q_f={q_gen_7156},
Delta=
{
<nil>() -> q_gen_7158
<z>() -> q_gen_7162
<s>(q_gen_7162) -> q_gen_7165
<cons>(q_gen_7162, q_gen_7158) -> q_gen_7167
<cons>(q_gen_7162, q_gen_7192) -> q_gen_7167
<s>(q_gen_7165) -> q_gen_7175
<cons>(q_gen_7162, q_gen_7167) -> q_gen_7182
<cons>(q_gen_7162, q_gen_7186) -> q_gen_7185
<cons>(q_gen_7162, q_gen_7182) -> q_gen_7186
<cons>(q_gen_7162, q_gen_7218) -> q_gen_7192
<cons>(q_gen_7165, q_gen_7182) -> q_gen_7192
<s>(q_gen_7175) -> q_gen_7204
<s>(q_gen_7204) -> q_gen_7213
<cons>(q_gen_7162, q_gen_7185) -> q_gen_7218
<s>(q_gen_7213) -> q_gen_7230
<s>(q_gen_7230) -> q_gen_7242
<s>(q_gen_7242) -> q_gen_7242
<cons, s>(q_gen_7159, q_gen_7158) -> q_gen_7156
<cons, s>(q_gen_7168, q_gen_7167) -> q_gen_7156
<cons, s>(q_gen_7171, q_gen_7182) -> q_gen_7156
<cons, s>(q_gen_7177, q_gen_7186) -> q_gen_7156
<cons, s>(q_gen_7177, q_gen_7192) -> q_gen_7156
<cons, s>(q_gen_7206, q_gen_7185) -> q_gen_7156
<cons, s>(q_gen_7212, q_gen_7218) -> q_gen_7156
<cons, s>(q_gen_7232, q_gen_7192) -> q_gen_7156
<nil, z>() -> q_gen_7156
<s, z>(q_gen_7162) -> q_gen_7159
<s, z>(q_gen_7165) -> q_gen_7159
<s, z>(q_gen_7175) -> q_gen_7159
<s, z>(q_gen_7204) -> q_gen_7159
<s, z>(q_gen_7230) -> q_gen_7159
<z, z>() -> q_gen_7159
<s, s>(q_gen_7159) -> q_gen_7168
<z, s>(q_gen_7162) -> q_gen_7168
<cons, s>(q_gen_7159, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7159, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7159, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7159, q_gen_7186) -> q_gen_7169
<cons, s>(q_gen_7159, q_gen_7218) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7186) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7192) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7186) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7192) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7218) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7206, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7206, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7206, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7206, q_gen_7186) -> q_gen_7169
<cons, s>(q_gen_7206, q_gen_7218) -> q_gen_7169
<cons, s>(q_gen_7212, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7212, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7212, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7212, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7212, q_gen_7186) -> q_gen_7169
<cons, s>(q_gen_7212, q_gen_7192) -> q_gen_7169
<cons, s>(q_gen_7232, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7232, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7232, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7232, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7232, q_gen_7186) -> q_gen_7169
<cons, s>(q_gen_7232, q_gen_7218) -> q_gen_7169
<s, s>(q_gen_7168) -> q_gen_7171
<z, s>(q_gen_7165) -> q_gen_7171
<z, s>(q_gen_7242) -> q_gen_7171
<s, s>(q_gen_7171) -> q_gen_7177
<s, s>(q_gen_7212) -> q_gen_7177
<z, s>(q_gen_7175) -> q_gen_7177
<s, s>(q_gen_7177) -> q_gen_7206
<z, s>(q_gen_7204) -> q_gen_7206
<s, s>(q_gen_7206) -> q_gen_7212
<z, s>(q_gen_7213) -> q_gen_7212
<s, s>(q_gen_7232) -> q_gen_7232
<z, s>(q_gen_7230) -> q_gen_7232
}

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

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

Teacher's answer:
New clause system:
{
() -> length([nil, z]) -> 76
(length([l, _cba]) /\ length([cons(z, cons(z, l)), _bba])) -> eq_nat([_bba, s(s(_cba))]) -> 117
(length([ll, _xaa])) -> length([cons(x, ll), s(_xaa)]) -> 118
}
Sat witness: Found: ((length([ll, _xaa])) -> length([cons(x, ll), s(_xaa)]), {
_xaa -> s(s(s(s(s(s(s(s(s(s(z))))))))))  ;  ll -> cons(z, cons(z, cons(z, nil)))  ;  x -> s(s(s(z)))
})

-------------------------------------------
Step 76, which took 4.425157 s (model generation: 4.413195,  model checking: 0.011962):

Model:
|_
{
length -> 
{{{
Q={q_gen_7156, q_gen_7158, q_gen_7159, q_gen_7162, q_gen_7165, q_gen_7167, q_gen_7168, q_gen_7169, q_gen_7171, q_gen_7175, q_gen_7177, q_gen_7182, q_gen_7185, q_gen_7186, q_gen_7192, q_gen_7197, q_gen_7204, q_gen_7206, q_gen_7212, q_gen_7213, q_gen_7230, q_gen_7232, q_gen_7243},
Q_f={q_gen_7156},
Delta=
{
<cons>(q_gen_7162, q_gen_7197) -> q_gen_7158
<nil>() -> q_gen_7158
<z>() -> q_gen_7162
<s>(q_gen_7162) -> q_gen_7165
<cons>(q_gen_7162, q_gen_7158) -> q_gen_7167
<s>(q_gen_7165) -> q_gen_7175
<cons>(q_gen_7162, q_gen_7167) -> q_gen_7182
<cons>(q_gen_7162, q_gen_7186) -> q_gen_7185
<cons>(q_gen_7162, q_gen_7182) -> q_gen_7186
<cons>(q_gen_7162, q_gen_7185) -> q_gen_7192
<cons>(q_gen_7165, q_gen_7182) -> q_gen_7192
<cons>(q_gen_7162, q_gen_7192) -> q_gen_7197
<s>(q_gen_7175) -> q_gen_7204
<s>(q_gen_7204) -> q_gen_7213
<s>(q_gen_7213) -> q_gen_7230
<s>(q_gen_7243) -> q_gen_7230
<s>(q_gen_7230) -> q_gen_7243
<cons, s>(q_gen_7159, q_gen_7158) -> q_gen_7156
<cons, s>(q_gen_7168, q_gen_7167) -> q_gen_7156
<cons, s>(q_gen_7168, q_gen_7182) -> q_gen_7156
<cons, s>(q_gen_7171, q_gen_7182) -> q_gen_7156
<cons, s>(q_gen_7177, q_gen_7186) -> q_gen_7156
<cons, s>(q_gen_7177, q_gen_7192) -> q_gen_7156
<cons, s>(q_gen_7206, q_gen_7185) -> q_gen_7156
<cons, s>(q_gen_7212, q_gen_7192) -> q_gen_7156
<cons, s>(q_gen_7232, q_gen_7197) -> q_gen_7156
<nil, z>() -> q_gen_7156
<s, s>(q_gen_7232) -> q_gen_7159
<s, z>(q_gen_7162) -> q_gen_7159
<s, z>(q_gen_7165) -> q_gen_7159
<s, z>(q_gen_7175) -> q_gen_7159
<s, z>(q_gen_7204) -> q_gen_7159
<s, z>(q_gen_7230) -> q_gen_7159
<z, s>(q_gen_7243) -> q_gen_7159
<z, z>() -> q_gen_7159
<s, s>(q_gen_7159) -> q_gen_7168
<z, s>(q_gen_7162) -> q_gen_7168
<cons, s>(q_gen_7159, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7159, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7159, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7159, q_gen_7186) -> q_gen_7169
<cons, s>(q_gen_7159, q_gen_7192) -> q_gen_7169
<cons, s>(q_gen_7159, q_gen_7197) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7186) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7192) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7192) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7197) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7206, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7206, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7206, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7206, q_gen_7186) -> q_gen_7169
<cons, s>(q_gen_7206, q_gen_7192) -> q_gen_7169
<cons, s>(q_gen_7212, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7212, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7212, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7212, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7212, q_gen_7186) -> q_gen_7169
<cons, s>(q_gen_7232, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7232, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7232, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7232, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7232, q_gen_7186) -> q_gen_7169
<cons, s>(q_gen_7232, q_gen_7192) -> q_gen_7169
<s, s>(q_gen_7168) -> q_gen_7171
<z, s>(q_gen_7165) -> q_gen_7171
<s, s>(q_gen_7171) -> q_gen_7177
<z, s>(q_gen_7175) -> q_gen_7177
<s, s>(q_gen_7177) -> q_gen_7206
<z, s>(q_gen_7204) -> q_gen_7206
<s, s>(q_gen_7206) -> q_gen_7212
<z, s>(q_gen_7213) -> q_gen_7212
<s, s>(q_gen_7212) -> q_gen_7232
<z, s>(q_gen_7230) -> q_gen_7232
}

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

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

Teacher's answer:
New clause system:
{
() -> length([nil, z]) -> 77
(length([l, _cba]) /\ length([cons(z, cons(z, l)), _bba])) -> eq_nat([_bba, s(s(_cba))]) -> 120
(length([ll, _xaa])) -> length([cons(x, ll), s(_xaa)]) -> 118
}
Sat witness: Found: ((length([l, _cba]) /\ length([cons(z, cons(z, l)), _bba])) -> eq_nat([_bba, s(s(_cba))]), {
_bba -> s(s(s(s(s(z)))))  ;  _cba -> s(s(z))  ;  l -> cons(z, cons(z, cons(z, nil)))
})

-------------------------------------------
Step 77, which took 3.382425 s (model generation: 3.335933,  model checking: 0.046492):

Model:
|_
{
length -> 
{{{
Q={q_gen_7156, q_gen_7158, q_gen_7159, q_gen_7162, q_gen_7165, q_gen_7167, q_gen_7168, q_gen_7169, q_gen_7171, q_gen_7175, q_gen_7177, q_gen_7182, q_gen_7185, q_gen_7186, q_gen_7192, q_gen_7204, q_gen_7206, q_gen_7212, q_gen_7213, q_gen_7218, q_gen_7230, q_gen_7232, q_gen_7243},
Q_f={q_gen_7156},
Delta=
{
<nil>() -> q_gen_7158
<z>() -> q_gen_7162
<s>(q_gen_7162) -> q_gen_7165
<cons>(q_gen_7162, q_gen_7158) -> q_gen_7167
<cons>(q_gen_7162, q_gen_7192) -> q_gen_7167
<s>(q_gen_7165) -> q_gen_7175
<cons>(q_gen_7162, q_gen_7167) -> q_gen_7182
<cons>(q_gen_7162, q_gen_7186) -> q_gen_7185
<cons>(q_gen_7162, q_gen_7182) -> q_gen_7186
<cons>(q_gen_7162, q_gen_7218) -> q_gen_7192
<cons>(q_gen_7165, q_gen_7182) -> q_gen_7192
<s>(q_gen_7175) -> q_gen_7204
<s>(q_gen_7204) -> q_gen_7213
<s>(q_gen_7243) -> q_gen_7213
<cons>(q_gen_7162, q_gen_7185) -> q_gen_7218
<s>(q_gen_7213) -> q_gen_7230
<s>(q_gen_7230) -> q_gen_7243
<cons, s>(q_gen_7159, q_gen_7158) -> q_gen_7156
<cons, s>(q_gen_7168, q_gen_7167) -> q_gen_7156
<cons, s>(q_gen_7168, q_gen_7218) -> q_gen_7156
<cons, s>(q_gen_7171, q_gen_7182) -> q_gen_7156
<cons, s>(q_gen_7177, q_gen_7186) -> q_gen_7156
<cons, s>(q_gen_7177, q_gen_7192) -> q_gen_7156
<cons, s>(q_gen_7206, q_gen_7185) -> q_gen_7156
<cons, s>(q_gen_7212, q_gen_7218) -> q_gen_7156
<cons, s>(q_gen_7232, q_gen_7192) -> q_gen_7156
<nil, z>() -> q_gen_7156
<s, z>(q_gen_7162) -> q_gen_7159
<s, z>(q_gen_7165) -> q_gen_7159
<s, z>(q_gen_7175) -> q_gen_7159
<s, z>(q_gen_7204) -> q_gen_7159
<s, z>(q_gen_7230) -> q_gen_7159
<z, z>() -> q_gen_7159
<s, s>(q_gen_7159) -> q_gen_7168
<s, s>(q_gen_7206) -> q_gen_7168
<z, s>(q_gen_7162) -> q_gen_7168
<cons, s>(q_gen_7159, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7159, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7159, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7159, q_gen_7186) -> q_gen_7169
<cons, s>(q_gen_7159, q_gen_7218) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7186) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7192) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7186) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7192) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7218) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7206, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7206, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7206, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7206, q_gen_7186) -> q_gen_7169
<cons, s>(q_gen_7206, q_gen_7218) -> q_gen_7169
<cons, s>(q_gen_7212, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7212, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7212, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7212, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7212, q_gen_7186) -> q_gen_7169
<cons, s>(q_gen_7212, q_gen_7192) -> q_gen_7169
<cons, s>(q_gen_7232, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7232, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7232, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7232, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7232, q_gen_7186) -> q_gen_7169
<cons, s>(q_gen_7232, q_gen_7218) -> q_gen_7169
<s, s>(q_gen_7168) -> q_gen_7171
<z, s>(q_gen_7165) -> q_gen_7171
<z, s>(q_gen_7243) -> q_gen_7171
<s, s>(q_gen_7171) -> q_gen_7177
<s, s>(q_gen_7232) -> q_gen_7177
<z, s>(q_gen_7175) -> q_gen_7177
<s, s>(q_gen_7177) -> q_gen_7206
<z, s>(q_gen_7204) -> q_gen_7206
<z, s>(q_gen_7213) -> q_gen_7212
<s, s>(q_gen_7212) -> q_gen_7232
<z, s>(q_gen_7230) -> q_gen_7232
}

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

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

Teacher's answer:
New clause system:
{
() -> length([nil, z]) -> 78
(length([l, _cba]) /\ length([cons(z, cons(z, l)), _bba])) -> eq_nat([_bba, s(s(_cba))]) -> 120
(length([ll, _xaa])) -> length([cons(x, ll), s(_xaa)]) -> 121
}
Sat witness: Found: ((length([ll, _xaa])) -> length([cons(x, ll), s(_xaa)]), {
_xaa -> s(s(s(s(s(s(s(s(s(s(s(z)))))))))))  ;  ll -> cons(z, cons(z, cons(z, nil)))  ;  x -> s(s(s(s(z))))
})

-------------------------------------------
Step 78, which took 3.151350 s (model generation: 3.038531,  model checking: 0.112819):

Model:
|_
{
length -> 
{{{
Q={q_gen_7156, q_gen_7158, q_gen_7159, q_gen_7161, q_gen_7162, q_gen_7165, q_gen_7167, q_gen_7168, q_gen_7169, q_gen_7171, q_gen_7175, q_gen_7177, q_gen_7182, q_gen_7185, q_gen_7186, q_gen_7192, q_gen_7204, q_gen_7206, q_gen_7208, q_gen_7212, q_gen_7213, q_gen_7218, q_gen_7221, q_gen_7229, q_gen_7230, q_gen_7241, q_gen_7242, q_gen_7243, q_gen_7254, q_gen_7255, q_gen_7256, q_gen_7291, q_gen_7293},
Q_f={q_gen_7156},
Delta=
{
<nil>() -> q_gen_7158
<z>() -> q_gen_7162
<s>(q_gen_7162) -> q_gen_7165
<cons>(q_gen_7162, q_gen_7158) -> q_gen_7167
<cons>(q_gen_7162, q_gen_7192) -> q_gen_7167
<s>(q_gen_7165) -> q_gen_7175
<cons>(q_gen_7162, q_gen_7167) -> q_gen_7182
<cons>(q_gen_7162, q_gen_7186) -> q_gen_7185
<cons>(q_gen_7162, q_gen_7182) -> q_gen_7186
<cons>(q_gen_7162, q_gen_7218) -> q_gen_7192
<cons>(q_gen_7165, q_gen_7182) -> q_gen_7192
<s>(q_gen_7175) -> q_gen_7204
<s>(q_gen_7204) -> q_gen_7213
<cons>(q_gen_7162, q_gen_7185) -> q_gen_7218
<s>(q_gen_7213) -> q_gen_7230
<s>(q_gen_7243) -> q_gen_7242
<s>(q_gen_7230) -> q_gen_7243
<s>(q_gen_7256) -> q_gen_7255
<s>(q_gen_7242) -> q_gen_7256
<s>(q_gen_7255) -> q_gen_7256
<cons, s>(q_gen_7159, q_gen_7158) -> q_gen_7156
<cons, s>(q_gen_7161, q_gen_7158) -> q_gen_7156
<cons, s>(q_gen_7161, q_gen_7167) -> q_gen_7156
<cons, s>(q_gen_7168, q_gen_7167) -> q_gen_7156
<cons, s>(q_gen_7171, q_gen_7182) -> q_gen_7156
<cons, s>(q_gen_7177, q_gen_7186) -> q_gen_7156
<cons, s>(q_gen_7177, q_gen_7192) -> q_gen_7156
<cons, s>(q_gen_7206, q_gen_7185) -> q_gen_7156
<cons, s>(q_gen_7206, q_gen_7192) -> q_gen_7156
<cons, s>(q_gen_7208, q_gen_7167) -> q_gen_7156
<cons, s>(q_gen_7208, q_gen_7185) -> q_gen_7156
<cons, s>(q_gen_7208, q_gen_7186) -> q_gen_7156
<cons, s>(q_gen_7208, q_gen_7218) -> q_gen_7156
<cons, s>(q_gen_7212, q_gen_7218) -> q_gen_7156
<cons, s>(q_gen_7221, q_gen_7192) -> q_gen_7156
<cons, s>(q_gen_7229, q_gen_7158) -> q_gen_7156
<nil, z>() -> q_gen_7156
<s, s>(q_gen_7241) -> q_gen_7159
<s, z>(q_gen_7204) -> q_gen_7159
<z, z>() -> q_gen_7159
<s, s>(q_gen_7159) -> q_gen_7161
<s, z>(q_gen_7162) -> q_gen_7161
<s, z>(q_gen_7165) -> q_gen_7161
<s, z>(q_gen_7175) -> q_gen_7161
<z, s>(q_gen_7162) -> q_gen_7168
<cons, s>(q_gen_7159, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7159, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7159, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7159, q_gen_7186) -> q_gen_7169
<cons, s>(q_gen_7159, q_gen_7218) -> q_gen_7169
<cons, s>(q_gen_7161, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7161, q_gen_7186) -> q_gen_7169
<cons, s>(q_gen_7161, q_gen_7218) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7186) -> q_gen_7169
<cons, s>(q_gen_7168, q_gen_7192) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7171, q_gen_7218) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7177, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7206, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7206, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7206, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7206, q_gen_7186) -> q_gen_7169
<cons, s>(q_gen_7206, q_gen_7218) -> q_gen_7169
<cons, s>(q_gen_7212, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7212, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7212, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7212, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7212, q_gen_7186) -> q_gen_7169
<cons, s>(q_gen_7212, q_gen_7192) -> q_gen_7169
<cons, s>(q_gen_7221, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7221, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7221, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7221, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7221, q_gen_7186) -> q_gen_7169
<cons, s>(q_gen_7221, q_gen_7218) -> q_gen_7169
<cons, s>(q_gen_7229, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7229, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7229, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7229, q_gen_7186) -> q_gen_7169
<cons, s>(q_gen_7229, q_gen_7192) -> q_gen_7169
<cons, s>(q_gen_7229, q_gen_7218) -> q_gen_7169
<cons, s>(q_gen_7241, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7241, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7241, q_gen_7186) -> q_gen_7169
<cons, s>(q_gen_7254, q_gen_7158) -> q_gen_7169
<cons, s>(q_gen_7254, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7254, q_gen_7192) -> q_gen_7169
<cons, s>(q_gen_7291, q_gen_7182) -> q_gen_7169
<cons, s>(q_gen_7291, q_gen_7185) -> q_gen_7169
<cons, s>(q_gen_7293, q_gen_7167) -> q_gen_7169
<cons, s>(q_gen_7293, q_gen_7218) -> q_gen_7169
<s, s>(q_gen_7168) -> q_gen_7171
<z, s>(q_gen_7165) -> q_gen_7171
<z, s>(q_gen_7175) -> q_gen_7177
<s, s>(q_gen_7177) -> q_gen_7206
<s, s>(q_gen_7212) -> q_gen_7206
<z, s>(q_gen_7204) -> q_gen_7206
<s, s>(q_gen_7171) -> q_gen_7208
<s, s>(q_gen_7208) -> q_gen_7208
<z, s>(q_gen_7213) -> q_gen_7212
<s, s>(q_gen_7206) -> q_gen_7221
<s, s>(q_gen_7229) -> q_gen_7221
<z, s>(q_gen_7230) -> q_gen_7221
<s, z>(q_gen_7230) -> q_gen_7229
<z, s>(q_gen_7243) -> q_gen_7229
<s, s>(q_gen_7221) -> q_gen_7241
<z, s>(q_gen_7242) -> q_gen_7241
<z, s>(q_gen_7255) -> q_gen_7254
<s, s>(q_gen_7161) -> q_gen_7291
<z, s>(q_gen_7256) -> q_gen_7291
<s, s>(q_gen_7291) -> q_gen_7293
<s, s>(q_gen_7293) -> q_gen_7293
}

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

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

Teacher's answer:
New clause system:
{
() -> length([nil, z]) -> 79
(length([l, _cba]) /\ length([cons(z, cons(z, l)), _bba])) -> eq_nat([_bba, s(s(_cba))]) -> 123
(length([ll, _xaa])) -> length([cons(x, ll), s(_xaa)]) -> 121
}
Sat witness: Found: ((length([l, _cba]) /\ length([cons(z, cons(z, l)), _bba])) -> eq_nat([_bba, s(s(_cba))]), {
_bba -> s(s(s(z)))  ;  _cba -> s(s(s(s(s(s(s(s(z))))))))  ;  l -> cons(z, nil)
})

Total time: 63.535443
Reason for stopping: DontKnow. Stopped because: timeout