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


Learning problem is:

env: {
elt -> {a, b}  ;  eltlist -> {cons, nil}  ;  nat -> {s, z}
}
definition:
{
(leq, P:
{() -> leq([a, n2])
() -> leq([b, b])
(leq([b, a])) -> BOT}
)
(leqnat, P:
{() -> leqnat([z, n2])
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)])
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2])
(leqnat([s(nn1), z])) -> BOT}
)
(merge, F:
{() -> merge([cons(z, xs), nil, cons(z, xs)])
() -> merge([nil, y, y])
(leq([z, y2]) /\ merge([xs, cons(y2, ys), _m])) -> merge([cons(z, xs), cons(y2, ys), cons(z, _m)])
(not leq([z, y2]) /\ merge([cons(z, xs), ys, _n])) -> merge([cons(z, xs), cons(y2, ys), cons(y2, _n)])}
(merge([_o, _p, _q]) /\ merge([_o, _p, _r])) -> eq_eltlist([_q, _r])
)
(append, F:
{() -> append([nil, l2, l2])
(append([t1, l2, _s])) -> append([cons(h1, t1), l2, cons(h1, _s)])}
(append([_t, _u, _v]) /\ append([_t, _u, _w])) -> eq_eltlist([_v, _w])
)
(plus, F:
{() -> plus([n, z, n])
(plus([n, mm, _x])) -> plus([n, s(mm), s(_x)])}
(plus([_y, _z, _aa]) /\ plus([_y, _z, _ba])) -> eq_nat([_aa, _ba])
)
(length, F:
{() -> length([nil, z])
(length([ll, _ca])) -> length([cons(x, ll), s(_ca)])}
(length([_da, _ea]) /\ length([_da, _fa])) -> eq_nat([_ea, _fa])
)
}

properties:
{(length([_ha, _ia]) /\ length([l1, _ga]) /\ merge([l1, l2, _ha])) -> leqnat([_ga, _ia]), (length([_ka, _la]) /\ length([l2, _ja]) /\ merge([l1, l2, _ka])) -> leqnat([_ja, _la])}


over-approximation: {append, length, merge, plus}
under-approximation: {append, leqnat, plus}

Clause system for inference is:

{
() -> append([nil, l2, l2]) -> 0
() -> length([nil, z]) -> 0
() -> leq([a, n2]) -> 0
() -> leq([b, b]) -> 0
() -> leqnat([z, n2]) -> 0
() -> merge([cons(z, xs), nil, cons(z, xs)]) -> 0
() -> merge([nil, y, y]) -> 0
() -> plus([n, z, n]) -> 0
(append([t1, l2, _s])) -> append([cons(h1, t1), l2, cons(h1, _s)]) -> 0
(length([_ha, _ia]) /\ length([l1, _ga]) /\ merge([l1, l2, _ha])) -> leqnat([_ga, _ia]) -> 0
(length([_ka, _la]) /\ length([l2, _ja]) /\ merge([l1, l2, _ka])) -> leqnat([_ja, _la]) -> 0
(length([ll, _ca])) -> length([cons(x, ll), s(_ca)]) -> 0
(leq([z, y2]) /\ merge([xs, cons(y2, ys), _m])) -> merge([cons(z, xs), cons(y2, ys), cons(z, _m)]) -> 0
(not leq([z, y2]) /\ merge([cons(z, xs), ys, _n])) -> merge([cons(z, xs), cons(y2, ys), cons(y2, _n)]) -> 0
(leq([b, a])) -> BOT -> 0
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 0
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 0
(leqnat([s(nn1), z])) -> BOT -> 0
(plus([n, mm, _x])) -> plus([n, s(mm), s(_x)]) -> 0
}


Solving took 66.606941 seconds.
DontKnow. Stopped because: timeout
Working model:
|_
{
append -> 
{{{
Q={q_gen_100, q_gen_109, q_gen_110, q_gen_111, q_gen_124, q_gen_125, q_gen_126, q_gen_127, q_gen_128, q_gen_129, q_gen_147, q_gen_148, q_gen_161, q_gen_162, q_gen_163, q_gen_185, q_gen_186, q_gen_187, q_gen_188, q_gen_189, q_gen_207, q_gen_208, q_gen_209, q_gen_221, q_gen_222, q_gen_223, q_gen_224, q_gen_235, q_gen_236, q_gen_237, q_gen_238, q_gen_239, q_gen_250, q_gen_251, q_gen_252, q_gen_253, q_gen_254, q_gen_78, q_gen_98, q_gen_99},
Q_f={},
Delta=
{
<nil>() -> q_gen_127
<b>() -> q_gen_128
<a>() -> q_gen_188
<cons>(q_gen_128, q_gen_127) -> q_gen_224
<b, b>() -> q_gen_100
<cons, cons>(q_gen_111, q_gen_99) -> q_gen_110
<a, a>() -> q_gen_111
<nil, cons>(q_gen_128, q_gen_127) -> q_gen_148
<cons, cons>(q_gen_100, q_gen_99) -> q_gen_236
<b, a>() -> q_gen_239
<nil, cons>(q_gen_188, q_gen_127) -> q_gen_253
<a, b>() -> q_gen_254
<nil, nil>() -> q_gen_99
<nil, cons, cons>(q_gen_111, q_gen_110) -> q_gen_109
<nil, cons, cons>(q_gen_100, q_gen_99) -> q_gen_124
<cons, cons, cons>(q_gen_129, q_gen_126) -> q_gen_125
<nil, nil, cons>(q_gen_128, q_gen_127) -> q_gen_126
<b, b, b>() -> q_gen_129
<cons, nil, cons>(q_gen_100, q_gen_148) -> q_gen_147
<cons, cons, cons>(q_gen_129, q_gen_78) -> q_gen_161
<cons, cons, cons>(q_gen_163, q_gen_98) -> q_gen_162
<a, b, a>() -> q_gen_163
<nil, cons, cons>(q_gen_111, q_gen_99) -> q_gen_185
<cons, cons, cons>(q_gen_189, q_gen_187) -> q_gen_186
<nil, nil, cons>(q_gen_188, q_gen_127) -> q_gen_187
<b, a, b>() -> q_gen_189
<cons, cons, cons>(q_gen_189, q_gen_78) -> q_gen_207
<cons, cons, cons>(q_gen_209, q_gen_98) -> q_gen_208
<a, a, a>() -> q_gen_209
<nil, cons, cons>(q_gen_100, q_gen_148) -> q_gen_221
<cons, cons, cons>(q_gen_163, q_gen_223) -> q_gen_222
<nil, nil, cons>(q_gen_128, q_gen_224) -> q_gen_223
<nil, cons, cons>(q_gen_111, q_gen_236) -> q_gen_235
<cons, cons, cons>(q_gen_189, q_gen_238) -> q_gen_237
<nil, cons, cons>(q_gen_239, q_gen_148) -> q_gen_238
<nil, cons, cons>(q_gen_100, q_gen_110) -> q_gen_250
<cons, cons, cons>(q_gen_163, q_gen_252) -> q_gen_251
<nil, cons, cons>(q_gen_254, q_gen_253) -> q_gen_252
<nil, nil, nil>() -> q_gen_78
<cons, nil, cons>(q_gen_100, q_gen_99) -> q_gen_98
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_122, q_gen_123, q_gen_138, q_gen_139, q_gen_140, q_gen_141, q_gen_142, q_gen_143, q_gen_149, q_gen_159, q_gen_160, q_gen_174, q_gen_175, q_gen_176, q_gen_177, q_gen_178, q_gen_179, q_gen_180, q_gen_181, q_gen_190, q_gen_204, q_gen_205, q_gen_211, q_gen_212, q_gen_213, q_gen_214, q_gen_215, q_gen_230, q_gen_233, q_gen_240, q_gen_241, q_gen_242, q_gen_248, q_gen_249, q_gen_255, q_gen_262, q_gen_265, q_gen_266, q_gen_77, q_gen_93, q_gen_94, q_gen_95},
Q_f={},
Delta=
{
<cons>(q_gen_140, q_gen_94) -> q_gen_139
<b>() -> q_gen_140
<z>() -> q_gen_142
<cons>(q_gen_176, q_gen_139) -> q_gen_175
<a>() -> q_gen_176
<s>(q_gen_142) -> q_gen_178
<cons>(q_gen_140, q_gen_139) -> q_gen_180
<cons>(q_gen_140, q_gen_175) -> q_gen_212
<s>(q_gen_178) -> q_gen_214
<cons>(q_gen_140, q_gen_180) -> q_gen_241
<cons>(q_gen_140, q_gen_241) -> q_gen_266
<nil>() -> q_gen_94
<cons, s>(q_gen_123, q_gen_94) -> q_gen_122
<a, z>() -> q_gen_123
<cons, s>(q_gen_141, q_gen_139) -> q_gen_138
<b, s>(q_gen_142) -> q_gen_141
<cons, s>(q_gen_141, q_gen_94) -> q_gen_143
<cons, s>(q_gen_95, q_gen_139) -> q_gen_149
<cons, s>(q_gen_160, q_gen_139) -> q_gen_159
<a, s>(q_gen_142) -> q_gen_160
<cons, s>(q_gen_177, q_gen_175) -> q_gen_174
<b, s>(q_gen_178) -> q_gen_177
<cons, s>(q_gen_141, q_gen_180) -> q_gen_179
<cons, s>(q_gen_177, q_gen_139) -> q_gen_181
<cons, s>(q_gen_177, q_gen_94) -> q_gen_190
<cons, s>(q_gen_205, q_gen_180) -> q_gen_204
<a, s>(q_gen_178) -> q_gen_205
<cons, s>(q_gen_213, q_gen_212) -> q_gen_211
<b, s>(q_gen_214) -> q_gen_213
<cons, s>(q_gen_213, q_gen_180) -> q_gen_215
<cons, s>(q_gen_177, q_gen_180) -> q_gen_230
<cons, s>(q_gen_95, q_gen_180) -> q_gen_233
<cons, s>(q_gen_141, q_gen_241) -> q_gen_240
<cons, s>(q_gen_213, q_gen_139) -> q_gen_242
<cons, s>(q_gen_177, q_gen_241) -> q_gen_248
<cons, s>(q_gen_205, q_gen_94) -> q_gen_249
<cons, s>(q_gen_95, q_gen_241) -> q_gen_255
<cons, s>(q_gen_205, q_gen_139) -> q_gen_262
<cons, s>(q_gen_95, q_gen_266) -> q_gen_265
<nil, z>() -> q_gen_77
<cons, s>(q_gen_95, q_gen_94) -> q_gen_93
<b, z>() -> q_gen_95
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_108, q_gen_75, q_gen_76, q_gen_82},
Q_f={},
Delta=
{
<a, a>() -> q_gen_108
<b, b>() -> q_gen_75
<a, b>() -> q_gen_76
<b, a>() -> q_gen_82
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  leqnat -> 
{{{
Q={q_gen_106, q_gen_107, q_gen_145, q_gen_146, q_gen_184, q_gen_218, q_gen_219, q_gen_220, q_gen_232, q_gen_246, q_gen_247, q_gen_74, q_gen_81, q_gen_96, q_gen_97},
Q_f={},
Delta=
{
<s>(q_gen_97) -> q_gen_107
<s>(q_gen_107) -> q_gen_247
<z>() -> q_gen_97
<z, s>(q_gen_107) -> q_gen_106
<s, s>(q_gen_146) -> q_gen_145
<s, z>(q_gen_97) -> q_gen_146
<s, s>(q_gen_145) -> q_gen_184
<s, s>(q_gen_219) -> q_gen_218
<s, s>(q_gen_220) -> q_gen_219
<s, z>(q_gen_107) -> q_gen_220
<s, s>(q_gen_184) -> q_gen_232
<z, s>(q_gen_247) -> q_gen_246
<z, z>() -> q_gen_74
<s, s>(q_gen_74) -> q_gen_81
<z, s>(q_gen_97) -> q_gen_96
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  merge -> 
{{{
Q={q_gen_103, q_gen_104, q_gen_105, q_gen_116, q_gen_117, q_gen_118, q_gen_119, q_gen_120, q_gen_121, q_gen_132, q_gen_133, q_gen_134, q_gen_135, q_gen_136, q_gen_137, q_gen_144, q_gen_154, q_gen_155, q_gen_156, q_gen_157, q_gen_158, q_gen_164, q_gen_165, q_gen_166, q_gen_167, q_gen_168, q_gen_169, q_gen_170, q_gen_171, q_gen_172, q_gen_173, q_gen_182, q_gen_183, q_gen_191, q_gen_192, q_gen_193, q_gen_194, q_gen_195, q_gen_196, q_gen_197, q_gen_198, q_gen_199, q_gen_200, q_gen_201, q_gen_202, q_gen_203, q_gen_206, q_gen_210, q_gen_216, q_gen_217, q_gen_225, q_gen_226, q_gen_227, q_gen_228, q_gen_229, q_gen_231, q_gen_234, q_gen_243, q_gen_244, q_gen_245, q_gen_256, q_gen_257, q_gen_258, q_gen_259, q_gen_260, q_gen_261, q_gen_263, q_gen_264, q_gen_267, q_gen_268, q_gen_269, q_gen_270, q_gen_271, q_gen_272, q_gen_273, q_gen_274, q_gen_275, q_gen_276, q_gen_277, q_gen_278, q_gen_70, q_gen_71, q_gen_72, q_gen_73, q_gen_83, q_gen_84, q_gen_85, q_gen_86, q_gen_87, q_gen_88, q_gen_89, q_gen_90, q_gen_91, q_gen_92},
Q_f={},
Delta=
{
<a>() -> q_gen_118
<cons>(q_gen_86, q_gen_85) -> q_gen_169
<cons>(q_gen_86, q_gen_169) -> q_gen_270
<nil>() -> q_gen_85
<b>() -> q_gen_86
<cons, cons>(q_gen_105, q_gen_72) -> q_gen_104
<a, a>() -> q_gen_105
<a, b>() -> q_gen_135
<nil, cons>(q_gen_86, q_gen_85) -> q_gen_156
<cons, cons>(q_gen_73, q_gen_72) -> q_gen_165
<cons, cons>(q_gen_73, q_gen_156) -> q_gen_183
<cons, cons>(q_gen_73, q_gen_165) -> q_gen_217
<cons, cons>(q_gen_73, q_gen_245) -> q_gen_244
<nil, cons>(q_gen_86, q_gen_169) -> q_gen_245
<cons, cons>(q_gen_91, q_gen_72) -> q_gen_260
<nil, cons>(q_gen_86, q_gen_270) -> q_gen_269
<nil, nil>() -> q_gen_72
<b, b>() -> q_gen_73
<b, a>() -> q_gen_91
<nil, cons, cons>(q_gen_105, q_gen_104) -> q_gen_103
<cons, cons, cons>(q_gen_87, q_gen_117) -> q_gen_116
<nil, nil, cons>(q_gen_118, q_gen_85) -> q_gen_117
<nil, cons, cons>(q_gen_73, q_gen_72) -> q_gen_119
<cons, cons, cons>(q_gen_121, q_gen_84) -> q_gen_120
<a, b, a>() -> q_gen_121
<cons, cons, cons>(q_gen_92, q_gen_70) -> q_gen_132
<cons, cons, cons>(q_gen_87, q_gen_134) -> q_gen_133
<nil, cons, cons>(q_gen_135, q_gen_72) -> q_gen_134
<cons, cons, cons>(q_gen_137, q_gen_84) -> q_gen_136
<b, b, b>() -> q_gen_137
<cons, cons, cons>(q_gen_121, q_gen_70) -> q_gen_144
<cons, cons, cons>(q_gen_87, q_gen_155) -> q_gen_154
<nil, cons, cons>(q_gen_73, q_gen_156) -> q_gen_155
<cons, cons, cons>(q_gen_158, q_gen_84) -> q_gen_157
<a, a, a>() -> q_gen_158
<nil, cons, cons>(q_gen_73, q_gen_165) -> q_gen_164
<cons, nil, cons>(q_gen_73, q_gen_156) -> q_gen_166
<cons, cons, cons>(q_gen_87, q_gen_168) -> q_gen_167
<nil, nil, cons>(q_gen_86, q_gen_169) -> q_gen_168
<cons, cons, cons>(q_gen_87, q_gen_119) -> q_gen_170
<cons, cons, cons>(q_gen_158, q_gen_172) -> q_gen_171
<cons, cons, cons>(q_gen_173, q_gen_84) -> q_gen_172
<b, b, a>() -> q_gen_173
<cons, nil, cons>(q_gen_73, q_gen_183) -> q_gen_182
<cons, cons, cons>(q_gen_92, q_gen_192) -> q_gen_191
<cons, cons, cons>(q_gen_92, q_gen_193) -> q_gen_192
<cons, nil, cons>(q_gen_135, q_gen_72) -> q_gen_193
<cons, cons, cons>(q_gen_87, q_gen_195) -> q_gen_194
<cons, cons, cons>(q_gen_92, q_gen_196) -> q_gen_195
<cons, cons, cons>(q_gen_197, q_gen_84) -> q_gen_196
<a, a, b>() -> q_gen_197
<cons, cons, cons>(q_gen_87, q_gen_199) -> q_gen_198
<cons, cons, cons>(q_gen_197, q_gen_119) -> q_gen_199
<cons, cons, cons>(q_gen_158, q_gen_201) -> q_gen_200
<cons, cons, cons>(q_gen_87, q_gen_202) -> q_gen_201
<cons, cons, cons>(q_gen_203, q_gen_84) -> q_gen_202
<a, b, b>() -> q_gen_203
<cons, cons, cons>(q_gen_137, q_gen_71) -> q_gen_206
<nil, cons, cons>(q_gen_105, q_gen_72) -> q_gen_210
<cons, nil, cons>(q_gen_73, q_gen_217) -> q_gen_216
<cons, nil, cons>(q_gen_73, q_gen_104) -> q_gen_225
<cons, cons, cons>(q_gen_137, q_gen_227) -> q_gen_226
<cons, cons, cons>(q_gen_137, q_gen_119) -> q_gen_227
<cons, cons, cons>(q_gen_87, q_gen_229) -> q_gen_228
<cons, cons, cons>(q_gen_137, q_gen_164) -> q_gen_229
<nil, cons, cons>(q_gen_73, q_gen_217) -> q_gen_231
<cons, cons, cons>(q_gen_137, q_gen_155) -> q_gen_234
<nil, cons, cons>(q_gen_73, q_gen_244) -> q_gen_243
<cons, cons, cons>(q_gen_87, q_gen_257) -> q_gen_256
<nil, cons, cons>(q_gen_91, q_gen_72) -> q_gen_257
<cons, cons, cons>(q_gen_87, q_gen_259) -> q_gen_258
<nil, cons, cons>(q_gen_105, q_gen_260) -> q_gen_259
<cons, cons, cons>(q_gen_158, q_gen_90) -> q_gen_261
<cons, cons, cons>(q_gen_137, q_gen_70) -> q_gen_263
<nil, cons, cons>(q_gen_135, q_gen_183) -> q_gen_264
<cons, cons, cons>(q_gen_137, q_gen_268) -> q_gen_267
<cons, nil, cons>(q_gen_73, q_gen_269) -> q_gen_268
<cons, cons, cons>(q_gen_173, q_gen_272) -> q_gen_271
<cons, cons, cons>(q_gen_203, q_gen_273) -> q_gen_272
<cons, cons, cons>(q_gen_203, q_gen_170) -> q_gen_273
<cons, cons, cons>(q_gen_87, q_gen_275) -> q_gen_274
<cons, cons, cons>(q_gen_121, q_gen_276) -> q_gen_275
<cons, cons, cons>(q_gen_203, q_gen_277) -> q_gen_276
<cons, cons, cons>(q_gen_137, q_gen_278) -> q_gen_277
<nil, cons, cons>(q_gen_105, q_gen_165) -> q_gen_278
<nil, nil, nil>() -> q_gen_70
<cons, nil, cons>(q_gen_73, q_gen_72) -> q_gen_71
<cons, cons, cons>(q_gen_87, q_gen_84) -> q_gen_83
<nil, nil, cons>(q_gen_86, q_gen_85) -> q_gen_84
<b, a, a>() -> q_gen_87
<cons, cons, cons>(q_gen_87, q_gen_70) -> q_gen_88
<cons, cons, cons>(q_gen_92, q_gen_90) -> q_gen_89
<cons, nil, cons>(q_gen_91, q_gen_72) -> q_gen_90
<b, a, b>() -> q_gen_92
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_101, q_gen_102, q_gen_112, q_gen_113, q_gen_114, q_gen_115, q_gen_130, q_gen_131, q_gen_150, q_gen_151, q_gen_152, q_gen_153, q_gen_69, q_gen_79, q_gen_80},
Q_f={},
Delta=
{
<z>() -> q_gen_115
<s>(q_gen_115) -> q_gen_153
<s, s>(q_gen_80) -> q_gen_102
<z, s>(q_gen_115) -> q_gen_131
<z, z>() -> q_gen_80
<s, z, s>(q_gen_102) -> q_gen_101
<s, z, s>(q_gen_80) -> q_gen_112
<s, s, s>(q_gen_114) -> q_gen_113
<z, z, s>(q_gen_115) -> q_gen_114
<z, s, s>(q_gen_131) -> q_gen_130
<s, z, s>(q_gen_131) -> q_gen_150
<s, s, s>(q_gen_152) -> q_gen_151
<z, z, s>(q_gen_153) -> q_gen_152
<z, z, z>() -> q_gen_69
<z, s, s>(q_gen_80) -> q_gen_79
}

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

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

-------------------
STEPS:
-------------------------------------------
Step 0, which took 0.010235 s (model generation: 0.008993,  model checking: 0.001242):

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

}

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

}

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

}

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

}

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

}

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

}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 0
() -> length([nil, z]) -> 0
() -> leq([a, n2]) -> 0
() -> leq([b, b]) -> 0
() -> leqnat([z, n2]) -> 0
() -> merge([cons(z, xs), nil, cons(z, xs)]) -> 0
() -> merge([nil, y, y]) -> 0
() -> plus([n, z, n]) -> 3
(append([t1, l2, _s])) -> append([cons(h1, t1), l2, cons(h1, _s)]) -> 1
(length([_ha, _ia]) /\ length([l1, _ga]) /\ merge([l1, l2, _ha])) -> leqnat([_ga, _ia]) -> 1
(length([_ka, _la]) /\ length([l2, _ja]) /\ merge([l1, l2, _ka])) -> leqnat([_ja, _la]) -> 1
(length([ll, _ca])) -> length([cons(x, ll), s(_ca)]) -> 1
(leq([z, y2]) /\ merge([xs, cons(y2, ys), _m])) -> merge([cons(z, xs), cons(y2, ys), cons(z, _m)]) -> 1
(not leq([z, y2]) /\ merge([cons(z, xs), ys, _n])) -> merge([cons(z, xs), cons(y2, ys), cons(y2, _n)]) -> 1
(leq([b, a])) -> BOT -> 1
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 1
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 1
(leqnat([s(nn1), z])) -> BOT -> 1
(plus([n, mm, _x])) -> plus([n, s(mm), s(_x)]) -> 1
}
Sat witness: Found: (() -> plus([n, z, n]), {
n -> z
})

-------------------------------------------
Step 1, which took 0.010887 s (model generation: 0.010714,  model checking: 0.000173):

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

}

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

}

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

}

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

}

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

}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_69},
Q_f={q_gen_69},
Delta=
{
<z, z, z>() -> q_gen_69
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 0
() -> length([nil, z]) -> 0
() -> leq([a, n2]) -> 0
() -> leq([b, b]) -> 0
() -> leqnat([z, n2]) -> 0
() -> merge([cons(z, xs), nil, cons(z, xs)]) -> 0
() -> merge([nil, y, y]) -> 3
() -> plus([n, z, n]) -> 3
(append([t1, l2, _s])) -> append([cons(h1, t1), l2, cons(h1, _s)]) -> 1
(length([_ha, _ia]) /\ length([l1, _ga]) /\ merge([l1, l2, _ha])) -> leqnat([_ga, _ia]) -> 1
(length([_ka, _la]) /\ length([l2, _ja]) /\ merge([l1, l2, _ka])) -> leqnat([_ja, _la]) -> 1
(length([ll, _ca])) -> length([cons(x, ll), s(_ca)]) -> 1
(leq([z, y2]) /\ merge([xs, cons(y2, ys), _m])) -> merge([cons(z, xs), cons(y2, ys), cons(z, _m)]) -> 1
(not leq([z, y2]) /\ merge([cons(z, xs), ys, _n])) -> merge([cons(z, xs), cons(y2, ys), cons(y2, _n)]) -> 1
(leq([b, a])) -> BOT -> 1
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 1
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 1
(leqnat([s(nn1), z])) -> BOT -> 1
(plus([n, mm, _x])) -> plus([n, s(mm), s(_x)]) -> 1
}
Sat witness: Found: (() -> merge([nil, y, y]), {
y -> nil
})

-------------------------------------------
Step 2, which took 0.010221 s (model generation: 0.010006,  model checking: 0.000215):

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

}

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

}

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

}

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

}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  merge -> 
{{{
Q={q_gen_70},
Q_f={q_gen_70},
Delta=
{
<nil, nil, nil>() -> q_gen_70
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_69},
Q_f={q_gen_69},
Delta=
{
<z, z, z>() -> q_gen_69
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 0
() -> length([nil, z]) -> 0
() -> leq([a, n2]) -> 0
() -> leq([b, b]) -> 0
() -> leqnat([z, n2]) -> 0
() -> merge([cons(z, xs), nil, cons(z, xs)]) -> 3
() -> merge([nil, y, y]) -> 3
() -> plus([n, z, n]) -> 3
(append([t1, l2, _s])) -> append([cons(h1, t1), l2, cons(h1, _s)]) -> 1
(length([_ha, _ia]) /\ length([l1, _ga]) /\ merge([l1, l2, _ha])) -> leqnat([_ga, _ia]) -> 1
(length([_ka, _la]) /\ length([l2, _ja]) /\ merge([l1, l2, _ka])) -> leqnat([_ja, _la]) -> 1
(length([ll, _ca])) -> length([cons(x, ll), s(_ca)]) -> 1
(leq([z, y2]) /\ merge([xs, cons(y2, ys), _m])) -> merge([cons(z, xs), cons(y2, ys), cons(z, _m)]) -> 1
(not leq([z, y2]) /\ merge([cons(z, xs), ys, _n])) -> merge([cons(z, xs), cons(y2, ys), cons(y2, _n)]) -> 1
(leq([b, a])) -> BOT -> 1
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 1
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 1
(leqnat([s(nn1), z])) -> BOT -> 1
(plus([n, mm, _x])) -> plus([n, s(mm), s(_x)]) -> 1
}
Sat witness: Found: (() -> merge([cons(z, xs), nil, cons(z, xs)]), {
xs -> nil  ;  z -> b
})

-------------------------------------------
Step 3, which took 0.010475 s (model generation: 0.010405,  model checking: 0.000070):

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

}

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

}

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

}

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

}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  merge -> 
{{{
Q={q_gen_70, q_gen_72, q_gen_73},
Q_f={q_gen_70},
Delta=
{
<nil, nil>() -> q_gen_72
<b, b>() -> q_gen_73
<cons, nil, cons>(q_gen_73, q_gen_72) -> q_gen_70
<nil, nil, nil>() -> q_gen_70
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_69},
Q_f={q_gen_69},
Delta=
{
<z, z, z>() -> q_gen_69
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 0
() -> length([nil, z]) -> 0
() -> leq([a, n2]) -> 0
() -> leq([b, b]) -> 0
() -> leqnat([z, n2]) -> 3
() -> merge([cons(z, xs), nil, cons(z, xs)]) -> 3
() -> merge([nil, y, y]) -> 3
() -> plus([n, z, n]) -> 3
(append([t1, l2, _s])) -> append([cons(h1, t1), l2, cons(h1, _s)]) -> 1
(length([_ha, _ia]) /\ length([l1, _ga]) /\ merge([l1, l2, _ha])) -> leqnat([_ga, _ia]) -> 1
(length([_ka, _la]) /\ length([l2, _ja]) /\ merge([l1, l2, _ka])) -> leqnat([_ja, _la]) -> 1
(length([ll, _ca])) -> length([cons(x, ll), s(_ca)]) -> 1
(leq([z, y2]) /\ merge([xs, cons(y2, ys), _m])) -> merge([cons(z, xs), cons(y2, ys), cons(z, _m)]) -> 1
(not leq([z, y2]) /\ merge([cons(z, xs), ys, _n])) -> merge([cons(z, xs), cons(y2, ys), cons(y2, _n)]) -> 1
(leq([b, a])) -> BOT -> 1
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 1
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 1
(leqnat([s(nn1), z])) -> BOT -> 1
(plus([n, mm, _x])) -> plus([n, s(mm), s(_x)]) -> 1
}
Sat witness: Found: (() -> leqnat([z, n2]), {
n2 -> z
})

-------------------------------------------
Step 4, which took 0.009017 s (model generation: 0.008975,  model checking: 0.000042):

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

}

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

}

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

}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  leqnat -> 
{{{
Q={q_gen_74},
Q_f={q_gen_74},
Delta=
{
<z, z>() -> q_gen_74
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  merge -> 
{{{
Q={q_gen_70, q_gen_72, q_gen_73},
Q_f={q_gen_70},
Delta=
{
<nil, nil>() -> q_gen_72
<b, b>() -> q_gen_73
<cons, nil, cons>(q_gen_73, q_gen_72) -> q_gen_70
<nil, nil, nil>() -> q_gen_70
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_69},
Q_f={q_gen_69},
Delta=
{
<z, z, z>() -> q_gen_69
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 0
() -> length([nil, z]) -> 0
() -> leq([a, n2]) -> 0
() -> leq([b, b]) -> 3
() -> leqnat([z, n2]) -> 3
() -> merge([cons(z, xs), nil, cons(z, xs)]) -> 3
() -> merge([nil, y, y]) -> 3
() -> plus([n, z, n]) -> 3
(append([t1, l2, _s])) -> append([cons(h1, t1), l2, cons(h1, _s)]) -> 1
(length([_ha, _ia]) /\ length([l1, _ga]) /\ merge([l1, l2, _ha])) -> leqnat([_ga, _ia]) -> 1
(length([_ka, _la]) /\ length([l2, _ja]) /\ merge([l1, l2, _ka])) -> leqnat([_ja, _la]) -> 1
(length([ll, _ca])) -> length([cons(x, ll), s(_ca)]) -> 1
(leq([z, y2]) /\ merge([xs, cons(y2, ys), _m])) -> merge([cons(z, xs), cons(y2, ys), cons(z, _m)]) -> 1
(not leq([z, y2]) /\ merge([cons(z, xs), ys, _n])) -> merge([cons(z, xs), cons(y2, ys), cons(y2, _n)]) -> 1
(leq([b, a])) -> BOT -> 1
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 1
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 1
(leqnat([s(nn1), z])) -> BOT -> 1
(plus([n, mm, _x])) -> plus([n, s(mm), s(_x)]) -> 1
}
Sat witness: Found: (() -> leq([b, b]), {

})

-------------------------------------------
Step 5, which took 0.009600 s (model generation: 0.009555,  model checking: 0.000045):

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

}

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

}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_75},
Q_f={q_gen_75},
Delta=
{
<b, b>() -> q_gen_75
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  leqnat -> 
{{{
Q={q_gen_74},
Q_f={q_gen_74},
Delta=
{
<z, z>() -> q_gen_74
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  merge -> 
{{{
Q={q_gen_70, q_gen_72, q_gen_73},
Q_f={q_gen_70},
Delta=
{
<nil, nil>() -> q_gen_72
<b, b>() -> q_gen_73
<cons, nil, cons>(q_gen_73, q_gen_72) -> q_gen_70
<nil, nil, nil>() -> q_gen_70
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_69},
Q_f={q_gen_69},
Delta=
{
<z, z, z>() -> q_gen_69
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 0
() -> length([nil, z]) -> 0
() -> leq([a, n2]) -> 3
() -> leq([b, b]) -> 3
() -> leqnat([z, n2]) -> 3
() -> merge([cons(z, xs), nil, cons(z, xs)]) -> 3
() -> merge([nil, y, y]) -> 3
() -> plus([n, z, n]) -> 3
(append([t1, l2, _s])) -> append([cons(h1, t1), l2, cons(h1, _s)]) -> 1
(length([_ha, _ia]) /\ length([l1, _ga]) /\ merge([l1, l2, _ha])) -> leqnat([_ga, _ia]) -> 1
(length([_ka, _la]) /\ length([l2, _ja]) /\ merge([l1, l2, _ka])) -> leqnat([_ja, _la]) -> 1
(length([ll, _ca])) -> length([cons(x, ll), s(_ca)]) -> 1
(leq([z, y2]) /\ merge([xs, cons(y2, ys), _m])) -> merge([cons(z, xs), cons(y2, ys), cons(z, _m)]) -> 1
(not leq([z, y2]) /\ merge([cons(z, xs), ys, _n])) -> merge([cons(z, xs), cons(y2, ys), cons(y2, _n)]) -> 1
(leq([b, a])) -> BOT -> 1
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 1
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 1
(leqnat([s(nn1), z])) -> BOT -> 1
(plus([n, mm, _x])) -> plus([n, s(mm), s(_x)]) -> 1
}
Sat witness: Found: (() -> leq([a, n2]), {
n2 -> b
})

-------------------------------------------
Step 6, which took 0.009869 s (model generation: 0.008245,  model checking: 0.001624):

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

}

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

}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_75},
Q_f={q_gen_75},
Delta=
{
<a, b>() -> q_gen_75
<b, b>() -> q_gen_75
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  leqnat -> 
{{{
Q={q_gen_74},
Q_f={q_gen_74},
Delta=
{
<z, z>() -> q_gen_74
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  merge -> 
{{{
Q={q_gen_70, q_gen_72, q_gen_73},
Q_f={q_gen_70},
Delta=
{
<nil, nil>() -> q_gen_72
<b, b>() -> q_gen_73
<cons, nil, cons>(q_gen_73, q_gen_72) -> q_gen_70
<nil, nil, nil>() -> q_gen_70
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_69},
Q_f={q_gen_69},
Delta=
{
<z, z, z>() -> q_gen_69
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 0
() -> length([nil, z]) -> 3
() -> leq([a, n2]) -> 3
() -> leq([b, b]) -> 3
() -> leqnat([z, n2]) -> 3
() -> merge([cons(z, xs), nil, cons(z, xs)]) -> 3
() -> merge([nil, y, y]) -> 3
() -> plus([n, z, n]) -> 3
(append([t1, l2, _s])) -> append([cons(h1, t1), l2, cons(h1, _s)]) -> 1
(length([_ha, _ia]) /\ length([l1, _ga]) /\ merge([l1, l2, _ha])) -> leqnat([_ga, _ia]) -> 1
(length([_ka, _la]) /\ length([l2, _ja]) /\ merge([l1, l2, _ka])) -> leqnat([_ja, _la]) -> 1
(length([ll, _ca])) -> length([cons(x, ll), s(_ca)]) -> 1
(leq([z, y2]) /\ merge([xs, cons(y2, ys), _m])) -> merge([cons(z, xs), cons(y2, ys), cons(z, _m)]) -> 1
(not leq([z, y2]) /\ merge([cons(z, xs), ys, _n])) -> merge([cons(z, xs), cons(y2, ys), cons(y2, _n)]) -> 1
(leq([b, a])) -> BOT -> 1
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 1
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 1
(leqnat([s(nn1), z])) -> BOT -> 1
(plus([n, mm, _x])) -> plus([n, s(mm), s(_x)]) -> 1
}
Sat witness: Found: (() -> length([nil, z]), {

})

-------------------------------------------
Step 7, which took 0.007933 s (model generation: 0.007795,  model checking: 0.000138):

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

}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_77},
Q_f={q_gen_77},
Delta=
{
<nil, z>() -> q_gen_77
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_75},
Q_f={q_gen_75},
Delta=
{
<a, b>() -> q_gen_75
<b, b>() -> q_gen_75
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  leqnat -> 
{{{
Q={q_gen_74},
Q_f={q_gen_74},
Delta=
{
<z, z>() -> q_gen_74
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  merge -> 
{{{
Q={q_gen_70, q_gen_72, q_gen_73},
Q_f={q_gen_70},
Delta=
{
<nil, nil>() -> q_gen_72
<b, b>() -> q_gen_73
<cons, nil, cons>(q_gen_73, q_gen_72) -> q_gen_70
<nil, nil, nil>() -> q_gen_70
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_69},
Q_f={q_gen_69},
Delta=
{
<z, z, z>() -> q_gen_69
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 3
() -> length([nil, z]) -> 3
() -> leq([a, n2]) -> 3
() -> leq([b, b]) -> 3
() -> leqnat([z, n2]) -> 3
() -> merge([cons(z, xs), nil, cons(z, xs)]) -> 3
() -> merge([nil, y, y]) -> 3
() -> plus([n, z, n]) -> 3
(append([t1, l2, _s])) -> append([cons(h1, t1), l2, cons(h1, _s)]) -> 1
(length([_ha, _ia]) /\ length([l1, _ga]) /\ merge([l1, l2, _ha])) -> leqnat([_ga, _ia]) -> 1
(length([_ka, _la]) /\ length([l2, _ja]) /\ merge([l1, l2, _ka])) -> leqnat([_ja, _la]) -> 1
(length([ll, _ca])) -> length([cons(x, ll), s(_ca)]) -> 1
(leq([z, y2]) /\ merge([xs, cons(y2, ys), _m])) -> merge([cons(z, xs), cons(y2, ys), cons(z, _m)]) -> 1
(not leq([z, y2]) /\ merge([cons(z, xs), ys, _n])) -> merge([cons(z, xs), cons(y2, ys), cons(y2, _n)]) -> 1
(leq([b, a])) -> BOT -> 1
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 1
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 1
(leqnat([s(nn1), z])) -> BOT -> 1
(plus([n, mm, _x])) -> plus([n, s(mm), s(_x)]) -> 1
}
Sat witness: Found: (() -> append([nil, l2, l2]), {
l2 -> nil
})

-------------------------------------------
Step 8, which took 0.008455 s (model generation: 0.008300,  model checking: 0.000155):

Model:
|_
{
append -> 
{{{
Q={q_gen_78},
Q_f={q_gen_78},
Delta=
{
<nil, nil, nil>() -> q_gen_78
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_77},
Q_f={q_gen_77},
Delta=
{
<nil, z>() -> q_gen_77
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_75},
Q_f={q_gen_75},
Delta=
{
<a, b>() -> q_gen_75
<b, b>() -> q_gen_75
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  leqnat -> 
{{{
Q={q_gen_74},
Q_f={q_gen_74},
Delta=
{
<z, z>() -> q_gen_74
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  merge -> 
{{{
Q={q_gen_70, q_gen_72, q_gen_73},
Q_f={q_gen_70},
Delta=
{
<nil, nil>() -> q_gen_72
<b, b>() -> q_gen_73
<cons, nil, cons>(q_gen_73, q_gen_72) -> q_gen_70
<nil, nil, nil>() -> q_gen_70
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_69},
Q_f={q_gen_69},
Delta=
{
<z, z, z>() -> q_gen_69
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 3
() -> length([nil, z]) -> 3
() -> leq([a, n2]) -> 3
() -> leq([b, b]) -> 3
() -> leqnat([z, n2]) -> 3
() -> merge([cons(z, xs), nil, cons(z, xs)]) -> 3
() -> merge([nil, y, y]) -> 3
() -> plus([n, z, n]) -> 3
(append([t1, l2, _s])) -> append([cons(h1, t1), l2, cons(h1, _s)]) -> 1
(length([_ha, _ia]) /\ length([l1, _ga]) /\ merge([l1, l2, _ha])) -> leqnat([_ga, _ia]) -> 1
(length([_ka, _la]) /\ length([l2, _ja]) /\ merge([l1, l2, _ka])) -> leqnat([_ja, _la]) -> 1
(length([ll, _ca])) -> length([cons(x, ll), s(_ca)]) -> 1
(leq([z, y2]) /\ merge([xs, cons(y2, ys), _m])) -> merge([cons(z, xs), cons(y2, ys), cons(z, _m)]) -> 1
(not leq([z, y2]) /\ merge([cons(z, xs), ys, _n])) -> merge([cons(z, xs), cons(y2, ys), cons(y2, _n)]) -> 1
(leq([b, a])) -> BOT -> 1
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 1
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 1
(leqnat([s(nn1), z])) -> BOT -> 1
(plus([n, mm, _x])) -> plus([n, s(mm), s(_x)]) -> 4
}
Sat witness: Found: ((plus([n, mm, _x])) -> plus([n, s(mm), s(_x)]), {
_x -> z  ;  mm -> z  ;  n -> z
})

-------------------------------------------
Step 9, which took 0.013576 s (model generation: 0.013416,  model checking: 0.000160):

Model:
|_
{
append -> 
{{{
Q={q_gen_78},
Q_f={q_gen_78},
Delta=
{
<nil, nil, nil>() -> q_gen_78
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_77},
Q_f={q_gen_77},
Delta=
{
<nil, z>() -> q_gen_77
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_75},
Q_f={q_gen_75},
Delta=
{
<a, b>() -> q_gen_75
<b, b>() -> q_gen_75
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  leqnat -> 
{{{
Q={q_gen_74},
Q_f={q_gen_74},
Delta=
{
<z, z>() -> q_gen_74
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  merge -> 
{{{
Q={q_gen_70, q_gen_72, q_gen_73},
Q_f={q_gen_70},
Delta=
{
<nil, nil>() -> q_gen_72
<b, b>() -> q_gen_73
<cons, nil, cons>(q_gen_73, q_gen_72) -> q_gen_70
<nil, nil, nil>() -> q_gen_70
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_69, q_gen_80},
Q_f={q_gen_69},
Delta=
{
<z, z>() -> q_gen_80
<z, s, s>(q_gen_80) -> q_gen_69
<z, z, z>() -> q_gen_69
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 3
() -> length([nil, z]) -> 3
() -> leq([a, n2]) -> 3
() -> leq([b, b]) -> 3
() -> leqnat([z, n2]) -> 3
() -> merge([cons(z, xs), nil, cons(z, xs)]) -> 3
() -> merge([nil, y, y]) -> 3
() -> plus([n, z, n]) -> 3
(append([t1, l2, _s])) -> append([cons(h1, t1), l2, cons(h1, _s)]) -> 1
(length([_ha, _ia]) /\ length([l1, _ga]) /\ merge([l1, l2, _ha])) -> leqnat([_ga, _ia]) -> 1
(length([_ka, _la]) /\ length([l2, _ja]) /\ merge([l1, l2, _ka])) -> leqnat([_ja, _la]) -> 1
(length([ll, _ca])) -> length([cons(x, ll), s(_ca)]) -> 1
(leq([z, y2]) /\ merge([xs, cons(y2, ys), _m])) -> merge([cons(z, xs), cons(y2, ys), cons(z, _m)]) -> 1
(not leq([z, y2]) /\ merge([cons(z, xs), ys, _n])) -> merge([cons(z, xs), cons(y2, ys), cons(y2, _n)]) -> 1
(leq([b, a])) -> BOT -> 1
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 4
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 2
(leqnat([s(nn1), z])) -> BOT -> 2
(plus([n, mm, _x])) -> plus([n, s(mm), s(_x)]) -> 4
}
Sat witness: Found: ((leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]), {
nn1 -> z  ;  nn2 -> z
})

-------------------------------------------
Step 10, which took 0.011319 s (model generation: 0.009544,  model checking: 0.001775):

Model:
|_
{
append -> 
{{{
Q={q_gen_78},
Q_f={q_gen_78},
Delta=
{
<nil, nil, nil>() -> q_gen_78
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_77},
Q_f={q_gen_77},
Delta=
{
<nil, z>() -> q_gen_77
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_75},
Q_f={q_gen_75},
Delta=
{
<a, b>() -> q_gen_75
<b, b>() -> q_gen_75
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  leqnat -> 
{{{
Q={q_gen_74},
Q_f={q_gen_74},
Delta=
{
<s, s>(q_gen_74) -> q_gen_74
<z, z>() -> q_gen_74
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  merge -> 
{{{
Q={q_gen_70, q_gen_72, q_gen_73},
Q_f={q_gen_70},
Delta=
{
<nil, nil>() -> q_gen_72
<b, b>() -> q_gen_73
<cons, nil, cons>(q_gen_73, q_gen_72) -> q_gen_70
<nil, nil, nil>() -> q_gen_70
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_69, q_gen_80},
Q_f={q_gen_69},
Delta=
{
<z, z>() -> q_gen_80
<z, s, s>(q_gen_80) -> q_gen_69
<z, z, z>() -> q_gen_69
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 3
() -> length([nil, z]) -> 3
() -> leq([a, n2]) -> 3
() -> leq([b, b]) -> 3
() -> leqnat([z, n2]) -> 3
() -> merge([cons(z, xs), nil, cons(z, xs)]) -> 3
() -> merge([nil, y, y]) -> 3
() -> plus([n, z, n]) -> 3
(append([t1, l2, _s])) -> append([cons(h1, t1), l2, cons(h1, _s)]) -> 1
(length([_ha, _ia]) /\ length([l1, _ga]) /\ merge([l1, l2, _ha])) -> leqnat([_ga, _ia]) -> 1
(length([_ka, _la]) /\ length([l2, _ja]) /\ merge([l1, l2, _ka])) -> leqnat([_ja, _la]) -> 1
(length([ll, _ca])) -> length([cons(x, ll), s(_ca)]) -> 1
(leq([z, y2]) /\ merge([xs, cons(y2, ys), _m])) -> merge([cons(z, xs), cons(y2, ys), cons(z, _m)]) -> 1
(not leq([z, y2]) /\ merge([cons(z, xs), ys, _n])) -> merge([cons(z, xs), cons(y2, ys), cons(y2, _n)]) -> 4
(leq([b, a])) -> BOT -> 2
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 4
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 2
(leqnat([s(nn1), z])) -> BOT -> 2
(plus([n, mm, _x])) -> plus([n, s(mm), s(_x)]) -> 4
}
Sat witness: Found: ((not leq([z, y2]) /\ merge([cons(z, xs), ys, _n])) -> merge([cons(z, xs), cons(y2, ys), cons(y2, _n)]), {
_n -> cons(b, nil)  ;  xs -> nil  ;  y2 -> a  ;  ys -> nil  ;  z -> b
})

-------------------------------------------
Step 11, which took 0.013805 s (model generation: 0.012372,  model checking: 0.001433):

Model:
|_
{
append -> 
{{{
Q={q_gen_78},
Q_f={q_gen_78},
Delta=
{
<nil, nil, nil>() -> q_gen_78
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_77},
Q_f={q_gen_77},
Delta=
{
<nil, z>() -> q_gen_77
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_75},
Q_f={q_gen_75},
Delta=
{
<a, b>() -> q_gen_75
<b, a>() -> q_gen_75
<b, b>() -> q_gen_75
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  leqnat -> 
{{{
Q={q_gen_74},
Q_f={q_gen_74},
Delta=
{
<s, s>(q_gen_74) -> q_gen_74
<z, z>() -> q_gen_74
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  merge -> 
{{{
Q={q_gen_70, q_gen_72, q_gen_73, q_gen_85, q_gen_86, q_gen_87},
Q_f={q_gen_70},
Delta=
{
<nil>() -> q_gen_85
<b>() -> q_gen_86
<nil, nil>() -> q_gen_72
<b, b>() -> q_gen_73
<cons, cons, cons>(q_gen_87, q_gen_70) -> q_gen_70
<cons, nil, cons>(q_gen_73, q_gen_72) -> q_gen_70
<nil, nil, cons>(q_gen_86, q_gen_85) -> q_gen_70
<nil, nil, nil>() -> q_gen_70
<b, a, a>() -> q_gen_87
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_69, q_gen_80},
Q_f={q_gen_69},
Delta=
{
<z, z>() -> q_gen_80
<z, s, s>(q_gen_80) -> q_gen_69
<z, z, z>() -> q_gen_69
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 3
() -> length([nil, z]) -> 3
() -> leq([a, n2]) -> 3
() -> leq([b, b]) -> 3
() -> leqnat([z, n2]) -> 3
() -> merge([cons(z, xs), nil, cons(z, xs)]) -> 3
() -> merge([nil, y, y]) -> 3
() -> plus([n, z, n]) -> 3
(append([t1, l2, _s])) -> append([cons(h1, t1), l2, cons(h1, _s)]) -> 1
(length([_ha, _ia]) /\ length([l1, _ga]) /\ merge([l1, l2, _ha])) -> leqnat([_ga, _ia]) -> 1
(length([_ka, _la]) /\ length([l2, _ja]) /\ merge([l1, l2, _ka])) -> leqnat([_ja, _la]) -> 1
(length([ll, _ca])) -> length([cons(x, ll), s(_ca)]) -> 1
(leq([z, y2]) /\ merge([xs, cons(y2, ys), _m])) -> merge([cons(z, xs), cons(y2, ys), cons(z, _m)]) -> 4
(not leq([z, y2]) /\ merge([cons(z, xs), ys, _n])) -> merge([cons(z, xs), cons(y2, ys), cons(y2, _n)]) -> 4
(leq([b, a])) -> BOT -> 2
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 4
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 2
(leqnat([s(nn1), z])) -> BOT -> 2
(plus([n, mm, _x])) -> plus([n, s(mm), s(_x)]) -> 4
}
Sat witness: Found: ((leq([z, y2]) /\ merge([xs, cons(y2, ys), _m])) -> merge([cons(z, xs), cons(y2, ys), cons(z, _m)]), {
_m -> cons(a, nil)  ;  xs -> cons(b, nil)  ;  y2 -> a  ;  ys -> nil  ;  z -> b
})

-------------------------------------------
Step 12, which took 0.016040 s (model generation: 0.015896,  model checking: 0.000144):

Model:
|_
{
append -> 
{{{
Q={q_gen_78},
Q_f={q_gen_78},
Delta=
{
<nil, nil, nil>() -> q_gen_78
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_77},
Q_f={q_gen_77},
Delta=
{
<nil, z>() -> q_gen_77
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_75},
Q_f={q_gen_75},
Delta=
{
<a, b>() -> q_gen_75
<b, a>() -> q_gen_75
<b, b>() -> q_gen_75
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  leqnat -> 
{{{
Q={q_gen_74},
Q_f={q_gen_74},
Delta=
{
<s, s>(q_gen_74) -> q_gen_74
<z, z>() -> q_gen_74
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  merge -> 
{{{
Q={q_gen_70, q_gen_72, q_gen_73, q_gen_85, q_gen_86, q_gen_87},
Q_f={q_gen_70},
Delta=
{
<nil>() -> q_gen_85
<b>() -> q_gen_86
<nil, nil>() -> q_gen_72
<b, a>() -> q_gen_73
<b, b>() -> q_gen_73
<cons, cons, cons>(q_gen_87, q_gen_70) -> q_gen_70
<cons, nil, cons>(q_gen_73, q_gen_72) -> q_gen_70
<nil, nil, cons>(q_gen_86, q_gen_85) -> q_gen_70
<nil, nil, nil>() -> q_gen_70
<b, a, a>() -> q_gen_87
<b, a, b>() -> q_gen_87
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_69, q_gen_80},
Q_f={q_gen_69},
Delta=
{
<z, z>() -> q_gen_80
<z, s, s>(q_gen_80) -> q_gen_69
<z, z, z>() -> q_gen_69
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 3
() -> length([nil, z]) -> 3
() -> leq([a, n2]) -> 3
() -> leq([b, b]) -> 3
() -> leqnat([z, n2]) -> 3
() -> merge([cons(z, xs), nil, cons(z, xs)]) -> 3
() -> merge([nil, y, y]) -> 3
() -> plus([n, z, n]) -> 3
(append([t1, l2, _s])) -> append([cons(h1, t1), l2, cons(h1, _s)]) -> 1
(length([_ha, _ia]) /\ length([l1, _ga]) /\ merge([l1, l2, _ha])) -> leqnat([_ga, _ia]) -> 1
(length([_ka, _la]) /\ length([l2, _ja]) /\ merge([l1, l2, _ka])) -> leqnat([_ja, _la]) -> 1
(length([ll, _ca])) -> length([cons(x, ll), s(_ca)]) -> 4
(leq([z, y2]) /\ merge([xs, cons(y2, ys), _m])) -> merge([cons(z, xs), cons(y2, ys), cons(z, _m)]) -> 4
(not leq([z, y2]) /\ merge([cons(z, xs), ys, _n])) -> merge([cons(z, xs), cons(y2, ys), cons(y2, _n)]) -> 4
(leq([b, a])) -> BOT -> 2
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 4
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 2
(leqnat([s(nn1), z])) -> BOT -> 2
(plus([n, mm, _x])) -> plus([n, s(mm), s(_x)]) -> 4
}
Sat witness: Found: ((length([ll, _ca])) -> length([cons(x, ll), s(_ca)]), {
_ca -> z  ;  ll -> nil  ;  x -> b
})

-------------------------------------------
Step 13, which took 0.013560 s (model generation: 0.013396,  model checking: 0.000164):

Model:
|_
{
append -> 
{{{
Q={q_gen_78},
Q_f={q_gen_78},
Delta=
{
<nil, nil, nil>() -> q_gen_78
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_77, q_gen_94, q_gen_95},
Q_f={q_gen_77},
Delta=
{
<nil>() -> q_gen_94
<cons, s>(q_gen_95, q_gen_94) -> q_gen_77
<nil, z>() -> q_gen_77
<b, z>() -> q_gen_95
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_75},
Q_f={q_gen_75},
Delta=
{
<a, b>() -> q_gen_75
<b, a>() -> q_gen_75
<b, b>() -> q_gen_75
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  leqnat -> 
{{{
Q={q_gen_74},
Q_f={q_gen_74},
Delta=
{
<s, s>(q_gen_74) -> q_gen_74
<z, z>() -> q_gen_74
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  merge -> 
{{{
Q={q_gen_70, q_gen_72, q_gen_73, q_gen_85, q_gen_86, q_gen_87},
Q_f={q_gen_70},
Delta=
{
<nil>() -> q_gen_85
<b>() -> q_gen_86
<nil, nil>() -> q_gen_72
<b, a>() -> q_gen_73
<b, b>() -> q_gen_73
<cons, cons, cons>(q_gen_87, q_gen_70) -> q_gen_70
<cons, nil, cons>(q_gen_73, q_gen_72) -> q_gen_70
<nil, nil, cons>(q_gen_86, q_gen_85) -> q_gen_70
<nil, nil, nil>() -> q_gen_70
<b, a, a>() -> q_gen_87
<b, a, b>() -> q_gen_87
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_69, q_gen_80},
Q_f={q_gen_69},
Delta=
{
<z, z>() -> q_gen_80
<z, s, s>(q_gen_80) -> q_gen_69
<z, z, z>() -> q_gen_69
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 3
() -> length([nil, z]) -> 3
() -> leq([a, n2]) -> 3
() -> leq([b, b]) -> 3
() -> leqnat([z, n2]) -> 3
() -> merge([cons(z, xs), nil, cons(z, xs)]) -> 3
() -> merge([nil, y, y]) -> 3
() -> plus([n, z, n]) -> 3
(append([t1, l2, _s])) -> append([cons(h1, t1), l2, cons(h1, _s)]) -> 1
(length([_ha, _ia]) /\ length([l1, _ga]) /\ merge([l1, l2, _ha])) -> leqnat([_ga, _ia]) -> 1
(length([_ka, _la]) /\ length([l2, _ja]) /\ merge([l1, l2, _ka])) -> leqnat([_ja, _la]) -> 4
(length([ll, _ca])) -> length([cons(x, ll), s(_ca)]) -> 4
(leq([z, y2]) /\ merge([xs, cons(y2, ys), _m])) -> merge([cons(z, xs), cons(y2, ys), cons(z, _m)]) -> 4
(not leq([z, y2]) /\ merge([cons(z, xs), ys, _n])) -> merge([cons(z, xs), cons(y2, ys), cons(y2, _n)]) -> 4
(leq([b, a])) -> BOT -> 2
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 4
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 2
(leqnat([s(nn1), z])) -> BOT -> 2
(plus([n, mm, _x])) -> plus([n, s(mm), s(_x)]) -> 4
}
Sat witness: Found: ((length([_ka, _la]) /\ length([l2, _ja]) /\ merge([l1, l2, _ka])) -> leqnat([_ja, _la]), {
_ja -> z  ;  _ka -> cons(b, nil)  ;  _la -> s(z)  ;  l1 -> nil  ;  l2 -> nil
})

-------------------------------------------
Step 14, which took 0.013457 s (model generation: 0.013117,  model checking: 0.000340):

Model:
|_
{
append -> 
{{{
Q={q_gen_78},
Q_f={q_gen_78},
Delta=
{
<nil, nil, nil>() -> q_gen_78
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_77, q_gen_94, q_gen_95},
Q_f={q_gen_77},
Delta=
{
<nil>() -> q_gen_94
<cons, s>(q_gen_95, q_gen_94) -> q_gen_77
<nil, z>() -> q_gen_77
<b, z>() -> q_gen_95
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_75},
Q_f={q_gen_75},
Delta=
{
<a, b>() -> q_gen_75
<b, a>() -> q_gen_75
<b, b>() -> q_gen_75
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  leqnat -> 
{{{
Q={q_gen_74, q_gen_97},
Q_f={q_gen_74},
Delta=
{
<z>() -> q_gen_97
<s, s>(q_gen_74) -> q_gen_74
<z, s>(q_gen_97) -> q_gen_74
<z, z>() -> q_gen_74
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  merge -> 
{{{
Q={q_gen_70, q_gen_72, q_gen_73, q_gen_85, q_gen_86, q_gen_87},
Q_f={q_gen_70},
Delta=
{
<nil>() -> q_gen_85
<b>() -> q_gen_86
<nil, nil>() -> q_gen_72
<b, a>() -> q_gen_73
<b, b>() -> q_gen_73
<cons, cons, cons>(q_gen_87, q_gen_70) -> q_gen_70
<cons, nil, cons>(q_gen_73, q_gen_72) -> q_gen_70
<nil, nil, cons>(q_gen_86, q_gen_85) -> q_gen_70
<nil, nil, nil>() -> q_gen_70
<b, a, a>() -> q_gen_87
<b, a, b>() -> q_gen_87
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_69, q_gen_80},
Q_f={q_gen_69},
Delta=
{
<z, z>() -> q_gen_80
<z, s, s>(q_gen_80) -> q_gen_69
<z, z, z>() -> q_gen_69
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 3
() -> length([nil, z]) -> 3
() -> leq([a, n2]) -> 3
() -> leq([b, b]) -> 3
() -> leqnat([z, n2]) -> 3
() -> merge([cons(z, xs), nil, cons(z, xs)]) -> 3
() -> merge([nil, y, y]) -> 3
() -> plus([n, z, n]) -> 3
(append([t1, l2, _s])) -> append([cons(h1, t1), l2, cons(h1, _s)]) -> 4
(length([_ha, _ia]) /\ length([l1, _ga]) /\ merge([l1, l2, _ha])) -> leqnat([_ga, _ia]) -> 2
(length([_ka, _la]) /\ length([l2, _ja]) /\ merge([l1, l2, _ka])) -> leqnat([_ja, _la]) -> 4
(length([ll, _ca])) -> length([cons(x, ll), s(_ca)]) -> 4
(leq([z, y2]) /\ merge([xs, cons(y2, ys), _m])) -> merge([cons(z, xs), cons(y2, ys), cons(z, _m)]) -> 4
(not leq([z, y2]) /\ merge([cons(z, xs), ys, _n])) -> merge([cons(z, xs), cons(y2, ys), cons(y2, _n)]) -> 4
(leq([b, a])) -> BOT -> 2
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 4
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 2
(leqnat([s(nn1), z])) -> BOT -> 2
(plus([n, mm, _x])) -> plus([n, s(mm), s(_x)]) -> 4
}
Sat witness: Found: ((append([t1, l2, _s])) -> append([cons(h1, t1), l2, cons(h1, _s)]), {
_s -> nil  ;  h1 -> b  ;  l2 -> nil  ;  t1 -> nil
})

-------------------------------------------
Step 15, which took 0.011667 s (model generation: 0.011554,  model checking: 0.000113):

Model:
|_
{
append -> 
{{{
Q={q_gen_100, q_gen_78, q_gen_99},
Q_f={q_gen_78},
Delta=
{
<b, b>() -> q_gen_100
<nil, nil>() -> q_gen_99
<cons, nil, cons>(q_gen_100, q_gen_99) -> q_gen_78
<nil, nil, nil>() -> q_gen_78
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_77, q_gen_94, q_gen_95},
Q_f={q_gen_77},
Delta=
{
<nil>() -> q_gen_94
<cons, s>(q_gen_95, q_gen_94) -> q_gen_77
<nil, z>() -> q_gen_77
<b, z>() -> q_gen_95
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_75},
Q_f={q_gen_75},
Delta=
{
<a, b>() -> q_gen_75
<b, a>() -> q_gen_75
<b, b>() -> q_gen_75
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  leqnat -> 
{{{
Q={q_gen_74, q_gen_97},
Q_f={q_gen_74},
Delta=
{
<z>() -> q_gen_97
<s, s>(q_gen_74) -> q_gen_74
<z, s>(q_gen_97) -> q_gen_74
<z, z>() -> q_gen_74
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  merge -> 
{{{
Q={q_gen_70, q_gen_72, q_gen_73, q_gen_85, q_gen_86, q_gen_87},
Q_f={q_gen_70},
Delta=
{
<nil>() -> q_gen_85
<b>() -> q_gen_86
<nil, nil>() -> q_gen_72
<b, a>() -> q_gen_73
<b, b>() -> q_gen_73
<cons, cons, cons>(q_gen_87, q_gen_70) -> q_gen_70
<cons, nil, cons>(q_gen_73, q_gen_72) -> q_gen_70
<nil, nil, cons>(q_gen_86, q_gen_85) -> q_gen_70
<nil, nil, nil>() -> q_gen_70
<b, a, a>() -> q_gen_87
<b, a, b>() -> q_gen_87
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_69, q_gen_80},
Q_f={q_gen_69},
Delta=
{
<z, z>() -> q_gen_80
<z, s, s>(q_gen_80) -> q_gen_69
<z, z, z>() -> q_gen_69
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 3
() -> length([nil, z]) -> 3
() -> leq([a, n2]) -> 3
() -> leq([b, b]) -> 3
() -> leqnat([z, n2]) -> 3
() -> merge([cons(z, xs), nil, cons(z, xs)]) -> 3
() -> merge([nil, y, y]) -> 3
() -> plus([n, z, n]) -> 3
(append([t1, l2, _s])) -> append([cons(h1, t1), l2, cons(h1, _s)]) -> 4
(length([_ha, _ia]) /\ length([l1, _ga]) /\ merge([l1, l2, _ha])) -> leqnat([_ga, _ia]) -> 2
(length([_ka, _la]) /\ length([l2, _ja]) /\ merge([l1, l2, _ka])) -> leqnat([_ja, _la]) -> 4
(length([ll, _ca])) -> length([cons(x, ll), s(_ca)]) -> 4
(leq([z, y2]) /\ merge([xs, cons(y2, ys), _m])) -> merge([cons(z, xs), cons(y2, ys), cons(z, _m)]) -> 4
(not leq([z, y2]) /\ merge([cons(z, xs), ys, _n])) -> merge([cons(z, xs), cons(y2, ys), cons(y2, _n)]) -> 4
(leq([b, a])) -> BOT -> 5
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 4
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 3
(leqnat([s(nn1), z])) -> BOT -> 3
(plus([n, mm, _x])) -> plus([n, s(mm), s(_x)]) -> 4
}
Sat witness: Found: ((leq([b, a])) -> BOT, {

})

-------------------------------------------
Step 16, which took 0.012059 s (model generation: 0.011213,  model checking: 0.000846):

Model:
|_
{
append -> 
{{{
Q={q_gen_100, q_gen_78, q_gen_99},
Q_f={q_gen_78},
Delta=
{
<b, b>() -> q_gen_100
<nil, nil>() -> q_gen_99
<cons, nil, cons>(q_gen_100, q_gen_99) -> q_gen_78
<nil, nil, nil>() -> q_gen_78
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_77, q_gen_94, q_gen_95},
Q_f={q_gen_77},
Delta=
{
<nil>() -> q_gen_94
<cons, s>(q_gen_95, q_gen_94) -> q_gen_77
<nil, z>() -> q_gen_77
<b, z>() -> q_gen_95
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_75, q_gen_82},
Q_f={q_gen_75},
Delta=
{
<a, b>() -> q_gen_75
<b, b>() -> q_gen_75
<b, a>() -> q_gen_82
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  leqnat -> 
{{{
Q={q_gen_74, q_gen_97},
Q_f={q_gen_74},
Delta=
{
<z>() -> q_gen_97
<s, s>(q_gen_74) -> q_gen_74
<z, s>(q_gen_97) -> q_gen_74
<z, z>() -> q_gen_74
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  merge -> 
{{{
Q={q_gen_70, q_gen_72, q_gen_73, q_gen_85, q_gen_86, q_gen_87},
Q_f={q_gen_70},
Delta=
{
<nil>() -> q_gen_85
<b>() -> q_gen_86
<nil, nil>() -> q_gen_72
<b, a>() -> q_gen_73
<b, b>() -> q_gen_73
<cons, cons, cons>(q_gen_87, q_gen_70) -> q_gen_70
<cons, nil, cons>(q_gen_73, q_gen_72) -> q_gen_70
<nil, nil, cons>(q_gen_86, q_gen_85) -> q_gen_70
<nil, nil, nil>() -> q_gen_70
<b, a, a>() -> q_gen_87
<b, a, b>() -> q_gen_87
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_69, q_gen_80},
Q_f={q_gen_69},
Delta=
{
<z, z>() -> q_gen_80
<z, s, s>(q_gen_80) -> q_gen_69
<z, z, z>() -> q_gen_69
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 3
() -> length([nil, z]) -> 3
() -> leq([a, n2]) -> 3
() -> leq([b, b]) -> 3
() -> leqnat([z, n2]) -> 3
() -> merge([cons(z, xs), nil, cons(z, xs)]) -> 3
() -> merge([nil, y, y]) -> 3
() -> plus([n, z, n]) -> 6
(append([t1, l2, _s])) -> append([cons(h1, t1), l2, cons(h1, _s)]) -> 4
(length([_ha, _ia]) /\ length([l1, _ga]) /\ merge([l1, l2, _ha])) -> leqnat([_ga, _ia]) -> 3
(length([_ka, _la]) /\ length([l2, _ja]) /\ merge([l1, l2, _ka])) -> leqnat([_ja, _la]) -> 4
(length([ll, _ca])) -> length([cons(x, ll), s(_ca)]) -> 4
(leq([z, y2]) /\ merge([xs, cons(y2, ys), _m])) -> merge([cons(z, xs), cons(y2, ys), cons(z, _m)]) -> 4
(not leq([z, y2]) /\ merge([cons(z, xs), ys, _n])) -> merge([cons(z, xs), cons(y2, ys), cons(y2, _n)]) -> 4
(leq([b, a])) -> BOT -> 5
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 4
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 4
(leqnat([s(nn1), z])) -> BOT -> 4
(plus([n, mm, _x])) -> plus([n, s(mm), s(_x)]) -> 4
}
Sat witness: Found: (() -> plus([n, z, n]), {
n -> s(s(z))
})

-------------------------------------------
Step 17, which took 0.012796 s (model generation: 0.012103,  model checking: 0.000693):

Model:
|_
{
append -> 
{{{
Q={q_gen_100, q_gen_78, q_gen_99},
Q_f={q_gen_78},
Delta=
{
<b, b>() -> q_gen_100
<nil, nil>() -> q_gen_99
<cons, nil, cons>(q_gen_100, q_gen_99) -> q_gen_78
<nil, nil, nil>() -> q_gen_78
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_77, q_gen_94, q_gen_95},
Q_f={q_gen_77},
Delta=
{
<nil>() -> q_gen_94
<cons, s>(q_gen_95, q_gen_94) -> q_gen_77
<nil, z>() -> q_gen_77
<b, z>() -> q_gen_95
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_75, q_gen_82},
Q_f={q_gen_75},
Delta=
{
<a, b>() -> q_gen_75
<b, b>() -> q_gen_75
<b, a>() -> q_gen_82
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  leqnat -> 
{{{
Q={q_gen_74, q_gen_97},
Q_f={q_gen_74},
Delta=
{
<z>() -> q_gen_97
<s, s>(q_gen_74) -> q_gen_74
<z, s>(q_gen_97) -> q_gen_74
<z, z>() -> q_gen_74
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  merge -> 
{{{
Q={q_gen_70, q_gen_72, q_gen_73, q_gen_85, q_gen_86, q_gen_87},
Q_f={q_gen_70},
Delta=
{
<nil>() -> q_gen_85
<b>() -> q_gen_86
<nil, nil>() -> q_gen_72
<b, a>() -> q_gen_73
<b, b>() -> q_gen_73
<cons, cons, cons>(q_gen_87, q_gen_70) -> q_gen_70
<cons, nil, cons>(q_gen_73, q_gen_72) -> q_gen_70
<nil, nil, cons>(q_gen_86, q_gen_85) -> q_gen_70
<nil, nil, nil>() -> q_gen_70
<b, a, a>() -> q_gen_87
<b, a, b>() -> q_gen_87
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_101, q_gen_102},
Q_f={q_gen_101},
Delta=
{
<s, s>(q_gen_102) -> q_gen_102
<z, z>() -> q_gen_102
<s, z, s>(q_gen_102) -> q_gen_101
<z, s, s>(q_gen_102) -> q_gen_101
<z, z, z>() -> q_gen_101
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 3
() -> length([nil, z]) -> 3
() -> leq([a, n2]) -> 3
() -> leq([b, b]) -> 3
() -> leqnat([z, n2]) -> 3
() -> merge([cons(z, xs), nil, cons(z, xs)]) -> 3
() -> merge([nil, y, y]) -> 6
() -> plus([n, z, n]) -> 6
(append([t1, l2, _s])) -> append([cons(h1, t1), l2, cons(h1, _s)]) -> 4
(length([_ha, _ia]) /\ length([l1, _ga]) /\ merge([l1, l2, _ha])) -> leqnat([_ga, _ia]) -> 4
(length([_ka, _la]) /\ length([l2, _ja]) /\ merge([l1, l2, _ka])) -> leqnat([_ja, _la]) -> 4
(length([ll, _ca])) -> length([cons(x, ll), s(_ca)]) -> 4
(leq([z, y2]) /\ merge([xs, cons(y2, ys), _m])) -> merge([cons(z, xs), cons(y2, ys), cons(z, _m)]) -> 4
(not leq([z, y2]) /\ merge([cons(z, xs), ys, _n])) -> merge([cons(z, xs), cons(y2, ys), cons(y2, _n)]) -> 4
(leq([b, a])) -> BOT -> 5
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 4
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 4
(leqnat([s(nn1), z])) -> BOT -> 4
(plus([n, mm, _x])) -> plus([n, s(mm), s(_x)]) -> 4
}
Sat witness: Found: (() -> merge([nil, y, y]), {
y -> cons(a, cons(a, nil))
})

-------------------------------------------
Step 18, which took 0.014993 s (model generation: 0.014621,  model checking: 0.000372):

Model:
|_
{
append -> 
{{{
Q={q_gen_100, q_gen_78, q_gen_99},
Q_f={q_gen_78},
Delta=
{
<b, b>() -> q_gen_100
<nil, nil>() -> q_gen_99
<cons, nil, cons>(q_gen_100, q_gen_99) -> q_gen_78
<nil, nil, nil>() -> q_gen_78
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_77, q_gen_94, q_gen_95},
Q_f={q_gen_77},
Delta=
{
<nil>() -> q_gen_94
<cons, s>(q_gen_95, q_gen_94) -> q_gen_77
<nil, z>() -> q_gen_77
<b, z>() -> q_gen_95
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_75, q_gen_82},
Q_f={q_gen_75},
Delta=
{
<a, b>() -> q_gen_75
<b, b>() -> q_gen_75
<b, a>() -> q_gen_82
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  leqnat -> 
{{{
Q={q_gen_74, q_gen_97},
Q_f={q_gen_74},
Delta=
{
<z>() -> q_gen_97
<s, s>(q_gen_74) -> q_gen_74
<z, s>(q_gen_97) -> q_gen_74
<z, z>() -> q_gen_74
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  merge -> 
{{{
Q={q_gen_103, q_gen_104, q_gen_105, q_gen_85, q_gen_86, q_gen_87},
Q_f={q_gen_103},
Delta=
{
<nil>() -> q_gen_85
<b>() -> q_gen_86
<cons, cons>(q_gen_105, q_gen_104) -> q_gen_104
<nil, nil>() -> q_gen_104
<a, a>() -> q_gen_105
<b, a>() -> q_gen_105
<b, b>() -> q_gen_105
<cons, cons, cons>(q_gen_87, q_gen_103) -> q_gen_103
<cons, nil, cons>(q_gen_105, q_gen_104) -> q_gen_103
<nil, cons, cons>(q_gen_105, q_gen_104) -> q_gen_103
<nil, nil, cons>(q_gen_86, q_gen_85) -> q_gen_103
<nil, nil, nil>() -> q_gen_103
<b, a, a>() -> q_gen_87
<b, a, b>() -> q_gen_87
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_101, q_gen_102},
Q_f={q_gen_101},
Delta=
{
<s, s>(q_gen_102) -> q_gen_102
<z, z>() -> q_gen_102
<s, z, s>(q_gen_102) -> q_gen_101
<z, s, s>(q_gen_102) -> q_gen_101
<z, z, z>() -> q_gen_101
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 3
() -> length([nil, z]) -> 3
() -> leq([a, n2]) -> 3
() -> leq([b, b]) -> 3
() -> leqnat([z, n2]) -> 6
() -> merge([cons(z, xs), nil, cons(z, xs)]) -> 4
() -> merge([nil, y, y]) -> 6
() -> plus([n, z, n]) -> 6
(append([t1, l2, _s])) -> append([cons(h1, t1), l2, cons(h1, _s)]) -> 4
(length([_ha, _ia]) /\ length([l1, _ga]) /\ merge([l1, l2, _ha])) -> leqnat([_ga, _ia]) -> 4
(length([_ka, _la]) /\ length([l2, _ja]) /\ merge([l1, l2, _ka])) -> leqnat([_ja, _la]) -> 4
(length([ll, _ca])) -> length([cons(x, ll), s(_ca)]) -> 4
(leq([z, y2]) /\ merge([xs, cons(y2, ys), _m])) -> merge([cons(z, xs), cons(y2, ys), cons(z, _m)]) -> 4
(not leq([z, y2]) /\ merge([cons(z, xs), ys, _n])) -> merge([cons(z, xs), cons(y2, ys), cons(y2, _n)]) -> 4
(leq([b, a])) -> BOT -> 5
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 4
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 4
(leqnat([s(nn1), z])) -> BOT -> 4
(plus([n, mm, _x])) -> plus([n, s(mm), s(_x)]) -> 4
}
Sat witness: Found: (() -> leqnat([z, n2]), {
n2 -> s(s(z))
})

-------------------------------------------
Step 19, which took 0.012839 s (model generation: 0.012785,  model checking: 0.000054):

Model:
|_
{
append -> 
{{{
Q={q_gen_100, q_gen_78, q_gen_99},
Q_f={q_gen_78},
Delta=
{
<b, b>() -> q_gen_100
<nil, nil>() -> q_gen_99
<cons, nil, cons>(q_gen_100, q_gen_99) -> q_gen_78
<nil, nil, nil>() -> q_gen_78
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_77, q_gen_94, q_gen_95},
Q_f={q_gen_77},
Delta=
{
<nil>() -> q_gen_94
<cons, s>(q_gen_95, q_gen_94) -> q_gen_77
<nil, z>() -> q_gen_77
<b, z>() -> q_gen_95
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_75, q_gen_82},
Q_f={q_gen_75},
Delta=
{
<a, b>() -> q_gen_75
<b, b>() -> q_gen_75
<b, a>() -> q_gen_82
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  leqnat -> 
{{{
Q={q_gen_106, q_gen_107},
Q_f={q_gen_106},
Delta=
{
<s>(q_gen_107) -> q_gen_107
<z>() -> q_gen_107
<s, s>(q_gen_106) -> q_gen_106
<z, s>(q_gen_107) -> q_gen_106
<z, z>() -> q_gen_106
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  merge -> 
{{{
Q={q_gen_103, q_gen_104, q_gen_105, q_gen_85, q_gen_86, q_gen_87},
Q_f={q_gen_103},
Delta=
{
<nil>() -> q_gen_85
<b>() -> q_gen_86
<cons, cons>(q_gen_105, q_gen_104) -> q_gen_104
<nil, nil>() -> q_gen_104
<a, a>() -> q_gen_105
<b, a>() -> q_gen_105
<b, b>() -> q_gen_105
<cons, cons, cons>(q_gen_87, q_gen_103) -> q_gen_103
<cons, nil, cons>(q_gen_105, q_gen_104) -> q_gen_103
<nil, cons, cons>(q_gen_105, q_gen_104) -> q_gen_103
<nil, nil, cons>(q_gen_86, q_gen_85) -> q_gen_103
<nil, nil, nil>() -> q_gen_103
<b, a, a>() -> q_gen_87
<b, a, b>() -> q_gen_87
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_101, q_gen_102},
Q_f={q_gen_101},
Delta=
{
<s, s>(q_gen_102) -> q_gen_102
<z, z>() -> q_gen_102
<s, z, s>(q_gen_102) -> q_gen_101
<z, s, s>(q_gen_102) -> q_gen_101
<z, z, z>() -> q_gen_101
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 3
() -> length([nil, z]) -> 3
() -> leq([a, n2]) -> 6
() -> leq([b, b]) -> 4
() -> leqnat([z, n2]) -> 6
() -> merge([cons(z, xs), nil, cons(z, xs)]) -> 4
() -> merge([nil, y, y]) -> 6
() -> plus([n, z, n]) -> 6
(append([t1, l2, _s])) -> append([cons(h1, t1), l2, cons(h1, _s)]) -> 4
(length([_ha, _ia]) /\ length([l1, _ga]) /\ merge([l1, l2, _ha])) -> leqnat([_ga, _ia]) -> 4
(length([_ka, _la]) /\ length([l2, _ja]) /\ merge([l1, l2, _ka])) -> leqnat([_ja, _la]) -> 4
(length([ll, _ca])) -> length([cons(x, ll), s(_ca)]) -> 4
(leq([z, y2]) /\ merge([xs, cons(y2, ys), _m])) -> merge([cons(z, xs), cons(y2, ys), cons(z, _m)]) -> 4
(not leq([z, y2]) /\ merge([cons(z, xs), ys, _n])) -> merge([cons(z, xs), cons(y2, ys), cons(y2, _n)]) -> 4
(leq([b, a])) -> BOT -> 5
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 4
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 4
(leqnat([s(nn1), z])) -> BOT -> 4
(plus([n, mm, _x])) -> plus([n, s(mm), s(_x)]) -> 4
}
Sat witness: Found: (() -> leq([a, n2]), {
n2 -> a
})

-------------------------------------------
Step 20, which took 0.013949 s (model generation: 0.013640,  model checking: 0.000309):

Model:
|_
{
append -> 
{{{
Q={q_gen_100, q_gen_78, q_gen_99},
Q_f={q_gen_78},
Delta=
{
<b, b>() -> q_gen_100
<nil, nil>() -> q_gen_99
<cons, nil, cons>(q_gen_100, q_gen_99) -> q_gen_78
<nil, nil, nil>() -> q_gen_78
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_77, q_gen_94, q_gen_95},
Q_f={q_gen_77},
Delta=
{
<nil>() -> q_gen_94
<cons, s>(q_gen_95, q_gen_94) -> q_gen_77
<nil, z>() -> q_gen_77
<b, z>() -> q_gen_95
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_108, q_gen_82},
Q_f={q_gen_108},
Delta=
{
<a, a>() -> q_gen_108
<a, b>() -> q_gen_108
<b, b>() -> q_gen_108
<b, a>() -> q_gen_82
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  leqnat -> 
{{{
Q={q_gen_106, q_gen_107},
Q_f={q_gen_106},
Delta=
{
<s>(q_gen_107) -> q_gen_107
<z>() -> q_gen_107
<s, s>(q_gen_106) -> q_gen_106
<z, s>(q_gen_107) -> q_gen_106
<z, z>() -> q_gen_106
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  merge -> 
{{{
Q={q_gen_103, q_gen_104, q_gen_105, q_gen_85, q_gen_86, q_gen_87},
Q_f={q_gen_103},
Delta=
{
<nil>() -> q_gen_85
<b>() -> q_gen_86
<cons, cons>(q_gen_105, q_gen_104) -> q_gen_104
<nil, nil>() -> q_gen_104
<a, a>() -> q_gen_105
<b, a>() -> q_gen_105
<b, b>() -> q_gen_105
<cons, cons, cons>(q_gen_87, q_gen_103) -> q_gen_103
<cons, nil, cons>(q_gen_105, q_gen_104) -> q_gen_103
<nil, cons, cons>(q_gen_105, q_gen_104) -> q_gen_103
<nil, nil, cons>(q_gen_86, q_gen_85) -> q_gen_103
<nil, nil, nil>() -> q_gen_103
<b, a, a>() -> q_gen_87
<b, a, b>() -> q_gen_87
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_101, q_gen_102},
Q_f={q_gen_101},
Delta=
{
<s, s>(q_gen_102) -> q_gen_102
<z, z>() -> q_gen_102
<s, z, s>(q_gen_102) -> q_gen_101
<z, s, s>(q_gen_102) -> q_gen_101
<z, z, z>() -> q_gen_101
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 6
() -> length([nil, z]) -> 4
() -> leq([a, n2]) -> 6
() -> leq([b, b]) -> 4
() -> leqnat([z, n2]) -> 6
() -> merge([cons(z, xs), nil, cons(z, xs)]) -> 4
() -> merge([nil, y, y]) -> 6
() -> plus([n, z, n]) -> 6
(append([t1, l2, _s])) -> append([cons(h1, t1), l2, cons(h1, _s)]) -> 4
(length([_ha, _ia]) /\ length([l1, _ga]) /\ merge([l1, l2, _ha])) -> leqnat([_ga, _ia]) -> 4
(length([_ka, _la]) /\ length([l2, _ja]) /\ merge([l1, l2, _ka])) -> leqnat([_ja, _la]) -> 4
(length([ll, _ca])) -> length([cons(x, ll), s(_ca)]) -> 4
(leq([z, y2]) /\ merge([xs, cons(y2, ys), _m])) -> merge([cons(z, xs), cons(y2, ys), cons(z, _m)]) -> 4
(not leq([z, y2]) /\ merge([cons(z, xs), ys, _n])) -> merge([cons(z, xs), cons(y2, ys), cons(y2, _n)]) -> 4
(leq([b, a])) -> BOT -> 5
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 4
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 4
(leqnat([s(nn1), z])) -> BOT -> 4
(plus([n, mm, _x])) -> plus([n, s(mm), s(_x)]) -> 4
}
Sat witness: Found: (() -> append([nil, l2, l2]), {
l2 -> cons(a, cons(a, nil))
})

-------------------------------------------
Step 21, which took 0.014768 s (model generation: 0.014614,  model checking: 0.000154):

Model:
|_
{
append -> 
{{{
Q={q_gen_100, q_gen_109, q_gen_110},
Q_f={q_gen_109},
Delta=
{
<a, a>() -> q_gen_100
<b, b>() -> q_gen_100
<cons, cons>(q_gen_100, q_gen_110) -> q_gen_110
<nil, nil>() -> q_gen_110
<cons, nil, cons>(q_gen_100, q_gen_110) -> q_gen_109
<nil, cons, cons>(q_gen_100, q_gen_110) -> q_gen_109
<nil, nil, nil>() -> q_gen_109
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_77, q_gen_94, q_gen_95},
Q_f={q_gen_77},
Delta=
{
<nil>() -> q_gen_94
<cons, s>(q_gen_95, q_gen_94) -> q_gen_77
<nil, z>() -> q_gen_77
<b, z>() -> q_gen_95
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_108, q_gen_82},
Q_f={q_gen_108},
Delta=
{
<a, a>() -> q_gen_108
<a, b>() -> q_gen_108
<b, b>() -> q_gen_108
<b, a>() -> q_gen_82
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  leqnat -> 
{{{
Q={q_gen_106, q_gen_107},
Q_f={q_gen_106},
Delta=
{
<s>(q_gen_107) -> q_gen_107
<z>() -> q_gen_107
<s, s>(q_gen_106) -> q_gen_106
<z, s>(q_gen_107) -> q_gen_106
<z, z>() -> q_gen_106
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  merge -> 
{{{
Q={q_gen_103, q_gen_104, q_gen_105, q_gen_85, q_gen_86, q_gen_87},
Q_f={q_gen_103},
Delta=
{
<nil>() -> q_gen_85
<b>() -> q_gen_86
<cons, cons>(q_gen_105, q_gen_104) -> q_gen_104
<nil, nil>() -> q_gen_104
<a, a>() -> q_gen_105
<b, a>() -> q_gen_105
<b, b>() -> q_gen_105
<cons, cons, cons>(q_gen_87, q_gen_103) -> q_gen_103
<cons, nil, cons>(q_gen_105, q_gen_104) -> q_gen_103
<nil, cons, cons>(q_gen_105, q_gen_104) -> q_gen_103
<nil, nil, cons>(q_gen_86, q_gen_85) -> q_gen_103
<nil, nil, nil>() -> q_gen_103
<b, a, a>() -> q_gen_87
<b, a, b>() -> q_gen_87
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_101, q_gen_102},
Q_f={q_gen_101},
Delta=
{
<s, s>(q_gen_102) -> q_gen_102
<z, z>() -> q_gen_102
<s, z, s>(q_gen_102) -> q_gen_101
<z, s, s>(q_gen_102) -> q_gen_101
<z, z, z>() -> q_gen_101
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 6
() -> length([nil, z]) -> 4
() -> leq([a, n2]) -> 6
() -> leq([b, b]) -> 4
() -> leqnat([z, n2]) -> 6
() -> merge([cons(z, xs), nil, cons(z, xs)]) -> 4
() -> merge([nil, y, y]) -> 6
() -> plus([n, z, n]) -> 6
(append([t1, l2, _s])) -> append([cons(h1, t1), l2, cons(h1, _s)]) -> 4
(length([_ha, _ia]) /\ length([l1, _ga]) /\ merge([l1, l2, _ha])) -> leqnat([_ga, _ia]) -> 4
(length([_ka, _la]) /\ length([l2, _ja]) /\ merge([l1, l2, _ka])) -> leqnat([_ja, _la]) -> 4
(length([ll, _ca])) -> length([cons(x, ll), s(_ca)]) -> 4
(leq([z, y2]) /\ merge([xs, cons(y2, ys), _m])) -> merge([cons(z, xs), cons(y2, ys), cons(z, _m)]) -> 4
(not leq([z, y2]) /\ merge([cons(z, xs), ys, _n])) -> merge([cons(z, xs), cons(y2, ys), cons(y2, _n)]) -> 4
(leq([b, a])) -> BOT -> 5
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 4
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 4
(leqnat([s(nn1), z])) -> BOT -> 4
(plus([n, mm, _x])) -> plus([n, s(mm), s(_x)]) -> 7
}
Sat witness: Found: ((plus([n, mm, _x])) -> plus([n, s(mm), s(_x)]), {
_x -> s(z)  ;  mm -> z  ;  n -> s(z)
})

-------------------------------------------
Step 22, which took 0.014839 s (model generation: 0.013996,  model checking: 0.000843):

Model:
|_
{
append -> 
{{{
Q={q_gen_100, q_gen_109, q_gen_110},
Q_f={q_gen_109},
Delta=
{
<a, a>() -> q_gen_100
<b, b>() -> q_gen_100
<cons, cons>(q_gen_100, q_gen_110) -> q_gen_110
<nil, nil>() -> q_gen_110
<cons, nil, cons>(q_gen_100, q_gen_110) -> q_gen_109
<nil, cons, cons>(q_gen_100, q_gen_110) -> q_gen_109
<nil, nil, nil>() -> q_gen_109
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_77, q_gen_94, q_gen_95},
Q_f={q_gen_77},
Delta=
{
<nil>() -> q_gen_94
<cons, s>(q_gen_95, q_gen_94) -> q_gen_77
<nil, z>() -> q_gen_77
<b, z>() -> q_gen_95
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_108, q_gen_82},
Q_f={q_gen_108},
Delta=
{
<a, a>() -> q_gen_108
<a, b>() -> q_gen_108
<b, b>() -> q_gen_108
<b, a>() -> q_gen_82
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  leqnat -> 
{{{
Q={q_gen_106, q_gen_107},
Q_f={q_gen_106},
Delta=
{
<s>(q_gen_107) -> q_gen_107
<z>() -> q_gen_107
<s, s>(q_gen_106) -> q_gen_106
<z, s>(q_gen_107) -> q_gen_106
<z, z>() -> q_gen_106
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  merge -> 
{{{
Q={q_gen_103, q_gen_104, q_gen_105, q_gen_85, q_gen_86, q_gen_87},
Q_f={q_gen_103},
Delta=
{
<nil>() -> q_gen_85
<b>() -> q_gen_86
<cons, cons>(q_gen_105, q_gen_104) -> q_gen_104
<nil, nil>() -> q_gen_104
<a, a>() -> q_gen_105
<b, a>() -> q_gen_105
<b, b>() -> q_gen_105
<cons, cons, cons>(q_gen_87, q_gen_103) -> q_gen_103
<cons, nil, cons>(q_gen_105, q_gen_104) -> q_gen_103
<nil, cons, cons>(q_gen_105, q_gen_104) -> q_gen_103
<nil, nil, cons>(q_gen_86, q_gen_85) -> q_gen_103
<nil, nil, nil>() -> q_gen_103
<b, a, a>() -> q_gen_87
<b, a, b>() -> q_gen_87
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_101, q_gen_102, q_gen_115},
Q_f={q_gen_101},
Delta=
{
<z>() -> q_gen_115
<s, s>(q_gen_102) -> q_gen_102
<z, z>() -> q_gen_102
<s, s, s>(q_gen_101) -> q_gen_101
<s, z, s>(q_gen_102) -> q_gen_101
<z, s, s>(q_gen_102) -> q_gen_101
<z, z, s>(q_gen_115) -> q_gen_101
<z, z, z>() -> q_gen_101
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 6
() -> length([nil, z]) -> 4
() -> leq([a, n2]) -> 6
() -> leq([b, b]) -> 4
() -> leqnat([z, n2]) -> 6
() -> merge([cons(z, xs), nil, cons(z, xs)]) -> 4
() -> merge([nil, y, y]) -> 6
() -> plus([n, z, n]) -> 6
(append([t1, l2, _s])) -> append([cons(h1, t1), l2, cons(h1, _s)]) -> 4
(length([_ha, _ia]) /\ length([l1, _ga]) /\ merge([l1, l2, _ha])) -> leqnat([_ga, _ia]) -> 4
(length([_ka, _la]) /\ length([l2, _ja]) /\ merge([l1, l2, _ka])) -> leqnat([_ja, _la]) -> 4
(length([ll, _ca])) -> length([cons(x, ll), s(_ca)]) -> 4
(leq([z, y2]) /\ merge([xs, cons(y2, ys), _m])) -> merge([cons(z, xs), cons(y2, ys), cons(z, _m)]) -> 4
(not leq([z, y2]) /\ merge([cons(z, xs), ys, _n])) -> merge([cons(z, xs), cons(y2, ys), cons(y2, _n)]) -> 7
(leq([b, a])) -> BOT -> 5
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 5
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 5
(leqnat([s(nn1), z])) -> BOT -> 5
(plus([n, mm, _x])) -> plus([n, s(mm), s(_x)]) -> 7
}
Sat witness: Found: ((not leq([z, y2]) /\ merge([cons(z, xs), ys, _n])) -> merge([cons(z, xs), cons(y2, ys), cons(y2, _n)]), {
_n -> cons(a, nil)  ;  xs -> nil  ;  y2 -> a  ;  ys -> nil  ;  z -> b
})

-------------------------------------------
Step 23, which took 0.015221 s (model generation: 0.014475,  model checking: 0.000746):

Model:
|_
{
append -> 
{{{
Q={q_gen_100, q_gen_109, q_gen_110},
Q_f={q_gen_109},
Delta=
{
<a, a>() -> q_gen_100
<b, b>() -> q_gen_100
<cons, cons>(q_gen_100, q_gen_110) -> q_gen_110
<nil, nil>() -> q_gen_110
<cons, nil, cons>(q_gen_100, q_gen_110) -> q_gen_109
<nil, cons, cons>(q_gen_100, q_gen_110) -> q_gen_109
<nil, nil, nil>() -> q_gen_109
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_77, q_gen_94, q_gen_95},
Q_f={q_gen_77},
Delta=
{
<nil>() -> q_gen_94
<cons, s>(q_gen_95, q_gen_94) -> q_gen_77
<nil, z>() -> q_gen_77
<b, z>() -> q_gen_95
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_108, q_gen_82},
Q_f={q_gen_108},
Delta=
{
<a, a>() -> q_gen_108
<a, b>() -> q_gen_108
<b, b>() -> q_gen_108
<b, a>() -> q_gen_82
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  leqnat -> 
{{{
Q={q_gen_106, q_gen_107},
Q_f={q_gen_106},
Delta=
{
<s>(q_gen_107) -> q_gen_107
<z>() -> q_gen_107
<s, s>(q_gen_106) -> q_gen_106
<z, s>(q_gen_107) -> q_gen_106
<z, z>() -> q_gen_106
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  merge -> 
{{{
Q={q_gen_103, q_gen_104, q_gen_105, q_gen_118, q_gen_85, q_gen_87},
Q_f={q_gen_103},
Delta=
{
<a>() -> q_gen_118
<b>() -> q_gen_118
<nil>() -> q_gen_85
<cons, cons>(q_gen_105, q_gen_104) -> q_gen_104
<nil, nil>() -> q_gen_104
<a, a>() -> q_gen_105
<b, a>() -> q_gen_105
<b, b>() -> q_gen_105
<cons, cons, cons>(q_gen_87, q_gen_103) -> q_gen_103
<cons, nil, cons>(q_gen_105, q_gen_104) -> q_gen_103
<nil, cons, cons>(q_gen_105, q_gen_104) -> q_gen_103
<nil, nil, cons>(q_gen_118, q_gen_85) -> q_gen_103
<nil, nil, nil>() -> q_gen_103
<b, a, a>() -> q_gen_87
<b, a, b>() -> q_gen_87
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_101, q_gen_102, q_gen_115},
Q_f={q_gen_101},
Delta=
{
<z>() -> q_gen_115
<s, s>(q_gen_102) -> q_gen_102
<z, z>() -> q_gen_102
<s, s, s>(q_gen_101) -> q_gen_101
<s, z, s>(q_gen_102) -> q_gen_101
<z, s, s>(q_gen_102) -> q_gen_101
<z, z, s>(q_gen_115) -> q_gen_101
<z, z, z>() -> q_gen_101
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 6
() -> length([nil, z]) -> 4
() -> leq([a, n2]) -> 6
() -> leq([b, b]) -> 4
() -> leqnat([z, n2]) -> 6
() -> merge([cons(z, xs), nil, cons(z, xs)]) -> 4
() -> merge([nil, y, y]) -> 6
() -> plus([n, z, n]) -> 6
(append([t1, l2, _s])) -> append([cons(h1, t1), l2, cons(h1, _s)]) -> 4
(length([_ha, _ia]) /\ length([l1, _ga]) /\ merge([l1, l2, _ha])) -> leqnat([_ga, _ia]) -> 4
(length([_ka, _la]) /\ length([l2, _ja]) /\ merge([l1, l2, _ka])) -> leqnat([_ja, _la]) -> 4
(length([ll, _ca])) -> length([cons(x, ll), s(_ca)]) -> 4
(leq([z, y2]) /\ merge([xs, cons(y2, ys), _m])) -> merge([cons(z, xs), cons(y2, ys), cons(z, _m)]) -> 7
(not leq([z, y2]) /\ merge([cons(z, xs), ys, _n])) -> merge([cons(z, xs), cons(y2, ys), cons(y2, _n)]) -> 7
(leq([b, a])) -> BOT -> 5
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 5
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 5
(leqnat([s(nn1), z])) -> BOT -> 5
(plus([n, mm, _x])) -> plus([n, s(mm), s(_x)]) -> 7
}
Sat witness: Found: ((leq([z, y2]) /\ merge([xs, cons(y2, ys), _m])) -> merge([cons(z, xs), cons(y2, ys), cons(z, _m)]), {
_m -> cons(b, nil)  ;  xs -> nil  ;  y2 -> b  ;  ys -> nil  ;  z -> a
})

-------------------------------------------
Step 24, which took 0.016148 s (model generation: 0.015978,  model checking: 0.000170):

Model:
|_
{
append -> 
{{{
Q={q_gen_100, q_gen_109, q_gen_110},
Q_f={q_gen_109},
Delta=
{
<a, a>() -> q_gen_100
<b, b>() -> q_gen_100
<cons, cons>(q_gen_100, q_gen_110) -> q_gen_110
<nil, nil>() -> q_gen_110
<cons, nil, cons>(q_gen_100, q_gen_110) -> q_gen_109
<nil, cons, cons>(q_gen_100, q_gen_110) -> q_gen_109
<nil, nil, nil>() -> q_gen_109
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_77, q_gen_94, q_gen_95},
Q_f={q_gen_77},
Delta=
{
<nil>() -> q_gen_94
<cons, s>(q_gen_95, q_gen_94) -> q_gen_77
<nil, z>() -> q_gen_77
<b, z>() -> q_gen_95
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_108, q_gen_82},
Q_f={q_gen_108},
Delta=
{
<a, a>() -> q_gen_108
<a, b>() -> q_gen_108
<b, b>() -> q_gen_108
<b, a>() -> q_gen_82
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  leqnat -> 
{{{
Q={q_gen_106, q_gen_107},
Q_f={q_gen_106},
Delta=
{
<s>(q_gen_107) -> q_gen_107
<z>() -> q_gen_107
<s, s>(q_gen_106) -> q_gen_106
<z, s>(q_gen_107) -> q_gen_106
<z, z>() -> q_gen_106
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  merge -> 
{{{
Q={q_gen_103, q_gen_104, q_gen_105, q_gen_118, q_gen_121, q_gen_85},
Q_f={q_gen_103},
Delta=
{
<a>() -> q_gen_118
<b>() -> q_gen_118
<nil>() -> q_gen_85
<cons, cons>(q_gen_105, q_gen_104) -> q_gen_104
<nil, nil>() -> q_gen_104
<a, a>() -> q_gen_105
<b, a>() -> q_gen_105
<b, b>() -> q_gen_105
<cons, cons, cons>(q_gen_121, q_gen_103) -> q_gen_103
<cons, nil, cons>(q_gen_105, q_gen_104) -> q_gen_103
<nil, cons, cons>(q_gen_105, q_gen_104) -> q_gen_103
<nil, nil, cons>(q_gen_118, q_gen_85) -> q_gen_103
<nil, nil, nil>() -> q_gen_103
<a, b, a>() -> q_gen_121
<b, a, a>() -> q_gen_121
<b, a, b>() -> q_gen_121
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_101, q_gen_102, q_gen_115},
Q_f={q_gen_101},
Delta=
{
<z>() -> q_gen_115
<s, s>(q_gen_102) -> q_gen_102
<z, z>() -> q_gen_102
<s, s, s>(q_gen_101) -> q_gen_101
<s, z, s>(q_gen_102) -> q_gen_101
<z, s, s>(q_gen_102) -> q_gen_101
<z, z, s>(q_gen_115) -> q_gen_101
<z, z, z>() -> q_gen_101
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 6
() -> length([nil, z]) -> 4
() -> leq([a, n2]) -> 6
() -> leq([b, b]) -> 4
() -> leqnat([z, n2]) -> 6
() -> merge([cons(z, xs), nil, cons(z, xs)]) -> 4
() -> merge([nil, y, y]) -> 6
() -> plus([n, z, n]) -> 6
(append([t1, l2, _s])) -> append([cons(h1, t1), l2, cons(h1, _s)]) -> 4
(length([_ha, _ia]) /\ length([l1, _ga]) /\ merge([l1, l2, _ha])) -> leqnat([_ga, _ia]) -> 4
(length([_ka, _la]) /\ length([l2, _ja]) /\ merge([l1, l2, _ka])) -> leqnat([_ja, _la]) -> 4
(length([ll, _ca])) -> length([cons(x, ll), s(_ca)]) -> 7
(leq([z, y2]) /\ merge([xs, cons(y2, ys), _m])) -> merge([cons(z, xs), cons(y2, ys), cons(z, _m)]) -> 7
(not leq([z, y2]) /\ merge([cons(z, xs), ys, _n])) -> merge([cons(z, xs), cons(y2, ys), cons(y2, _n)]) -> 7
(leq([b, a])) -> BOT -> 5
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 5
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 5
(leqnat([s(nn1), z])) -> BOT -> 5
(plus([n, mm, _x])) -> plus([n, s(mm), s(_x)]) -> 7
}
Sat witness: Found: ((length([ll, _ca])) -> length([cons(x, ll), s(_ca)]), {
_ca -> z  ;  ll -> nil  ;  x -> a
})

-------------------------------------------
Step 25, which took 0.017871 s (model generation: 0.016799,  model checking: 0.001072):

Model:
|_
{
append -> 
{{{
Q={q_gen_100, q_gen_109, q_gen_110},
Q_f={q_gen_109},
Delta=
{
<a, a>() -> q_gen_100
<b, b>() -> q_gen_100
<cons, cons>(q_gen_100, q_gen_110) -> q_gen_110
<nil, nil>() -> q_gen_110
<cons, nil, cons>(q_gen_100, q_gen_110) -> q_gen_109
<nil, cons, cons>(q_gen_100, q_gen_110) -> q_gen_109
<nil, nil, nil>() -> q_gen_109
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_122, q_gen_123, q_gen_94},
Q_f={q_gen_122},
Delta=
{
<nil>() -> q_gen_94
<cons, s>(q_gen_123, q_gen_94) -> q_gen_122
<nil, z>() -> q_gen_122
<a, z>() -> q_gen_123
<b, z>() -> q_gen_123
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_108, q_gen_82},
Q_f={q_gen_108},
Delta=
{
<a, a>() -> q_gen_108
<a, b>() -> q_gen_108
<b, b>() -> q_gen_108
<b, a>() -> q_gen_82
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  leqnat -> 
{{{
Q={q_gen_106, q_gen_107},
Q_f={q_gen_106},
Delta=
{
<s>(q_gen_107) -> q_gen_107
<z>() -> q_gen_107
<s, s>(q_gen_106) -> q_gen_106
<z, s>(q_gen_107) -> q_gen_106
<z, z>() -> q_gen_106
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  merge -> 
{{{
Q={q_gen_103, q_gen_104, q_gen_105, q_gen_118, q_gen_121, q_gen_85},
Q_f={q_gen_103},
Delta=
{
<a>() -> q_gen_118
<b>() -> q_gen_118
<nil>() -> q_gen_85
<cons, cons>(q_gen_105, q_gen_104) -> q_gen_104
<nil, nil>() -> q_gen_104
<a, a>() -> q_gen_105
<b, a>() -> q_gen_105
<b, b>() -> q_gen_105
<cons, cons, cons>(q_gen_121, q_gen_103) -> q_gen_103
<cons, nil, cons>(q_gen_105, q_gen_104) -> q_gen_103
<nil, cons, cons>(q_gen_105, q_gen_104) -> q_gen_103
<nil, nil, cons>(q_gen_118, q_gen_85) -> q_gen_103
<nil, nil, nil>() -> q_gen_103
<a, b, a>() -> q_gen_121
<b, a, a>() -> q_gen_121
<b, a, b>() -> q_gen_121
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_101, q_gen_102, q_gen_115},
Q_f={q_gen_101},
Delta=
{
<z>() -> q_gen_115
<s, s>(q_gen_102) -> q_gen_102
<z, z>() -> q_gen_102
<s, s, s>(q_gen_101) -> q_gen_101
<s, z, s>(q_gen_102) -> q_gen_101
<z, s, s>(q_gen_102) -> q_gen_101
<z, z, s>(q_gen_115) -> q_gen_101
<z, z, z>() -> q_gen_101
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 6
() -> length([nil, z]) -> 4
() -> leq([a, n2]) -> 6
() -> leq([b, b]) -> 4
() -> leqnat([z, n2]) -> 6
() -> merge([cons(z, xs), nil, cons(z, xs)]) -> 4
() -> merge([nil, y, y]) -> 6
() -> plus([n, z, n]) -> 6
(append([t1, l2, _s])) -> append([cons(h1, t1), l2, cons(h1, _s)]) -> 7
(length([_ha, _ia]) /\ length([l1, _ga]) /\ merge([l1, l2, _ha])) -> leqnat([_ga, _ia]) -> 5
(length([_ka, _la]) /\ length([l2, _ja]) /\ merge([l1, l2, _ka])) -> leqnat([_ja, _la]) -> 5
(length([ll, _ca])) -> length([cons(x, ll), s(_ca)]) -> 7
(leq([z, y2]) /\ merge([xs, cons(y2, ys), _m])) -> merge([cons(z, xs), cons(y2, ys), cons(z, _m)]) -> 7
(not leq([z, y2]) /\ merge([cons(z, xs), ys, _n])) -> merge([cons(z, xs), cons(y2, ys), cons(y2, _n)]) -> 7
(leq([b, a])) -> BOT -> 5
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 5
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 5
(leqnat([s(nn1), z])) -> BOT -> 5
(plus([n, mm, _x])) -> plus([n, s(mm), s(_x)]) -> 7
}
Sat witness: Found: ((append([t1, l2, _s])) -> append([cons(h1, t1), l2, cons(h1, _s)]), {
_s -> cons(b, nil)  ;  h1 -> b  ;  l2 -> cons(b, nil)  ;  t1 -> nil
})

-------------------------------------------
Step 26, which took 0.019622 s (model generation: 0.018020,  model checking: 0.001602):

Model:
|_
{
append -> 
{{{
Q={q_gen_100, q_gen_109, q_gen_110, q_gen_127, q_gen_128, q_gen_129},
Q_f={q_gen_109},
Delta=
{
<nil>() -> q_gen_127
<b>() -> q_gen_128
<a, a>() -> q_gen_100
<b, b>() -> q_gen_100
<cons, cons>(q_gen_100, q_gen_110) -> q_gen_110
<nil, nil>() -> q_gen_110
<cons, cons, cons>(q_gen_129, q_gen_109) -> q_gen_109
<cons, nil, cons>(q_gen_100, q_gen_110) -> q_gen_109
<nil, cons, cons>(q_gen_100, q_gen_110) -> q_gen_109
<nil, nil, cons>(q_gen_128, q_gen_127) -> q_gen_109
<nil, nil, nil>() -> q_gen_109
<b, b, b>() -> q_gen_129
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_122, q_gen_123, q_gen_94},
Q_f={q_gen_122},
Delta=
{
<nil>() -> q_gen_94
<cons, s>(q_gen_123, q_gen_94) -> q_gen_122
<nil, z>() -> q_gen_122
<a, z>() -> q_gen_123
<b, z>() -> q_gen_123
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_108, q_gen_82},
Q_f={q_gen_108},
Delta=
{
<a, a>() -> q_gen_108
<a, b>() -> q_gen_108
<b, b>() -> q_gen_108
<b, a>() -> q_gen_82
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  leqnat -> 
{{{
Q={q_gen_106, q_gen_107},
Q_f={q_gen_106},
Delta=
{
<s>(q_gen_107) -> q_gen_107
<z>() -> q_gen_107
<s, s>(q_gen_106) -> q_gen_106
<z, s>(q_gen_107) -> q_gen_106
<z, z>() -> q_gen_106
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  merge -> 
{{{
Q={q_gen_103, q_gen_104, q_gen_105, q_gen_118, q_gen_121, q_gen_85},
Q_f={q_gen_103},
Delta=
{
<a>() -> q_gen_118
<b>() -> q_gen_118
<nil>() -> q_gen_85
<cons, cons>(q_gen_105, q_gen_104) -> q_gen_104
<nil, nil>() -> q_gen_104
<a, a>() -> q_gen_105
<b, a>() -> q_gen_105
<b, b>() -> q_gen_105
<cons, cons, cons>(q_gen_121, q_gen_103) -> q_gen_103
<cons, nil, cons>(q_gen_105, q_gen_104) -> q_gen_103
<nil, cons, cons>(q_gen_105, q_gen_104) -> q_gen_103
<nil, nil, cons>(q_gen_118, q_gen_85) -> q_gen_103
<nil, nil, nil>() -> q_gen_103
<a, b, a>() -> q_gen_121
<b, a, a>() -> q_gen_121
<b, a, b>() -> q_gen_121
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_101, q_gen_102, q_gen_115},
Q_f={q_gen_101},
Delta=
{
<z>() -> q_gen_115
<s, s>(q_gen_102) -> q_gen_102
<z, z>() -> q_gen_102
<s, s, s>(q_gen_101) -> q_gen_101
<s, z, s>(q_gen_102) -> q_gen_101
<z, s, s>(q_gen_102) -> q_gen_101
<z, z, s>(q_gen_115) -> q_gen_101
<z, z, z>() -> q_gen_101
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 7
() -> length([nil, z]) -> 5
() -> leq([a, n2]) -> 7
() -> leq([b, b]) -> 5
() -> leqnat([z, n2]) -> 7
() -> merge([cons(z, xs), nil, cons(z, xs)]) -> 5
() -> merge([nil, y, y]) -> 7
() -> plus([n, z, n]) -> 7
(append([t1, l2, _s])) -> append([cons(h1, t1), l2, cons(h1, _s)]) -> 7
(length([_ha, _ia]) /\ length([l1, _ga]) /\ merge([l1, l2, _ha])) -> leqnat([_ga, _ia]) -> 6
(length([_ka, _la]) /\ length([l2, _ja]) /\ merge([l1, l2, _ka])) -> leqnat([_ja, _la]) -> 6
(length([ll, _ca])) -> length([cons(x, ll), s(_ca)]) -> 7
(leq([z, y2]) /\ merge([xs, cons(y2, ys), _m])) -> merge([cons(z, xs), cons(y2, ys), cons(z, _m)]) -> 7
(not leq([z, y2]) /\ merge([cons(z, xs), ys, _n])) -> merge([cons(z, xs), cons(y2, ys), cons(y2, _n)]) -> 7
(leq([b, a])) -> BOT -> 6
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 6
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 6
(leqnat([s(nn1), z])) -> BOT -> 6
(plus([n, mm, _x])) -> plus([n, s(mm), s(_x)]) -> 10
}
Sat witness: Found: ((plus([n, mm, _x])) -> plus([n, s(mm), s(_x)]), {
_x -> s(z)  ;  mm -> z  ;  n -> z
})

-------------------------------------------
Step 27, which took 0.019789 s (model generation: 0.018129,  model checking: 0.001660):

Model:
|_
{
append -> 
{{{
Q={q_gen_100, q_gen_109, q_gen_110, q_gen_127, q_gen_128, q_gen_129},
Q_f={q_gen_109},
Delta=
{
<nil>() -> q_gen_127
<b>() -> q_gen_128
<a, a>() -> q_gen_100
<b, b>() -> q_gen_100
<cons, cons>(q_gen_100, q_gen_110) -> q_gen_110
<nil, nil>() -> q_gen_110
<cons, cons, cons>(q_gen_129, q_gen_109) -> q_gen_109
<cons, nil, cons>(q_gen_100, q_gen_110) -> q_gen_109
<nil, cons, cons>(q_gen_100, q_gen_110) -> q_gen_109
<nil, nil, cons>(q_gen_128, q_gen_127) -> q_gen_109
<nil, nil, nil>() -> q_gen_109
<b, b, b>() -> q_gen_129
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_122, q_gen_123, q_gen_94},
Q_f={q_gen_122},
Delta=
{
<nil>() -> q_gen_94
<cons, s>(q_gen_123, q_gen_94) -> q_gen_122
<nil, z>() -> q_gen_122
<a, z>() -> q_gen_123
<b, z>() -> q_gen_123
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_108, q_gen_82},
Q_f={q_gen_108},
Delta=
{
<a, a>() -> q_gen_108
<a, b>() -> q_gen_108
<b, b>() -> q_gen_108
<b, a>() -> q_gen_82
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  leqnat -> 
{{{
Q={q_gen_106, q_gen_107},
Q_f={q_gen_106},
Delta=
{
<s>(q_gen_107) -> q_gen_107
<z>() -> q_gen_107
<s, s>(q_gen_106) -> q_gen_106
<z, s>(q_gen_107) -> q_gen_106
<z, z>() -> q_gen_106
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  merge -> 
{{{
Q={q_gen_103, q_gen_104, q_gen_105, q_gen_118, q_gen_121, q_gen_85},
Q_f={q_gen_103},
Delta=
{
<a>() -> q_gen_118
<b>() -> q_gen_118
<nil>() -> q_gen_85
<cons, cons>(q_gen_105, q_gen_104) -> q_gen_104
<nil, nil>() -> q_gen_104
<a, a>() -> q_gen_105
<b, a>() -> q_gen_105
<b, b>() -> q_gen_105
<cons, cons, cons>(q_gen_121, q_gen_103) -> q_gen_103
<cons, nil, cons>(q_gen_105, q_gen_104) -> q_gen_103
<nil, cons, cons>(q_gen_105, q_gen_104) -> q_gen_103
<nil, nil, cons>(q_gen_118, q_gen_85) -> q_gen_103
<nil, nil, nil>() -> q_gen_103
<a, b, a>() -> q_gen_121
<b, a, a>() -> q_gen_121
<b, a, b>() -> q_gen_121
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_101, q_gen_102, q_gen_115},
Q_f={q_gen_101},
Delta=
{
<z>() -> q_gen_115
<s, s>(q_gen_102) -> q_gen_102
<z, s>(q_gen_115) -> q_gen_102
<z, z>() -> q_gen_102
<s, s, s>(q_gen_101) -> q_gen_101
<s, z, s>(q_gen_102) -> q_gen_101
<z, s, s>(q_gen_102) -> q_gen_101
<z, z, s>(q_gen_115) -> q_gen_101
<z, z, z>() -> q_gen_101
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 7
() -> length([nil, z]) -> 6
() -> leq([a, n2]) -> 7
() -> leq([b, b]) -> 6
() -> leqnat([z, n2]) -> 7
() -> merge([cons(z, xs), nil, cons(z, xs)]) -> 6
() -> merge([nil, y, y]) -> 7
() -> plus([n, z, n]) -> 7
(append([t1, l2, _s])) -> append([cons(h1, t1), l2, cons(h1, _s)]) -> 7
(length([_ha, _ia]) /\ length([l1, _ga]) /\ merge([l1, l2, _ha])) -> leqnat([_ga, _ia]) -> 7
(length([_ka, _la]) /\ length([l2, _ja]) /\ merge([l1, l2, _ka])) -> leqnat([_ja, _la]) -> 7
(length([ll, _ca])) -> length([cons(x, ll), s(_ca)]) -> 7
(leq([z, y2]) /\ merge([xs, cons(y2, ys), _m])) -> merge([cons(z, xs), cons(y2, ys), cons(z, _m)]) -> 7
(not leq([z, y2]) /\ merge([cons(z, xs), ys, _n])) -> merge([cons(z, xs), cons(y2, ys), cons(y2, _n)]) -> 10
(leq([b, a])) -> BOT -> 7
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 7
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 7
(leqnat([s(nn1), z])) -> BOT -> 7
(plus([n, mm, _x])) -> plus([n, s(mm), s(_x)]) -> 10
}
Sat witness: Found: ((not leq([z, y2]) /\ merge([cons(z, xs), ys, _n])) -> merge([cons(z, xs), cons(y2, ys), cons(y2, _n)]), {
_n -> cons(b, nil)  ;  xs -> nil  ;  y2 -> a  ;  ys -> cons(a, nil)  ;  z -> b
})

-------------------------------------------
Step 28, which took 0.022217 s (model generation: 0.021230,  model checking: 0.000987):

Model:
|_
{
append -> 
{{{
Q={q_gen_100, q_gen_109, q_gen_110, q_gen_127, q_gen_128, q_gen_129},
Q_f={q_gen_109},
Delta=
{
<nil>() -> q_gen_127
<b>() -> q_gen_128
<a, a>() -> q_gen_100
<b, b>() -> q_gen_100
<cons, cons>(q_gen_100, q_gen_110) -> q_gen_110
<nil, nil>() -> q_gen_110
<cons, cons, cons>(q_gen_129, q_gen_109) -> q_gen_109
<cons, nil, cons>(q_gen_100, q_gen_110) -> q_gen_109
<nil, cons, cons>(q_gen_100, q_gen_110) -> q_gen_109
<nil, nil, cons>(q_gen_128, q_gen_127) -> q_gen_109
<nil, nil, nil>() -> q_gen_109
<b, b, b>() -> q_gen_129
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_122, q_gen_123, q_gen_94},
Q_f={q_gen_122},
Delta=
{
<nil>() -> q_gen_94
<cons, s>(q_gen_123, q_gen_94) -> q_gen_122
<nil, z>() -> q_gen_122
<a, z>() -> q_gen_123
<b, z>() -> q_gen_123
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_108, q_gen_82},
Q_f={q_gen_108},
Delta=
{
<a, a>() -> q_gen_108
<a, b>() -> q_gen_108
<b, b>() -> q_gen_108
<b, a>() -> q_gen_82
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  leqnat -> 
{{{
Q={q_gen_106, q_gen_107},
Q_f={q_gen_106},
Delta=
{
<s>(q_gen_107) -> q_gen_107
<z>() -> q_gen_107
<s, s>(q_gen_106) -> q_gen_106
<z, s>(q_gen_107) -> q_gen_106
<z, z>() -> q_gen_106
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  merge -> 
{{{
Q={q_gen_103, q_gen_104, q_gen_105, q_gen_118, q_gen_121, q_gen_85},
Q_f={q_gen_103},
Delta=
{
<a>() -> q_gen_118
<b>() -> q_gen_118
<nil>() -> q_gen_85
<cons, cons>(q_gen_105, q_gen_104) -> q_gen_104
<nil, nil>() -> q_gen_104
<a, a>() -> q_gen_105
<a, b>() -> q_gen_105
<b, a>() -> q_gen_105
<b, b>() -> q_gen_105
<cons, cons, cons>(q_gen_121, q_gen_103) -> q_gen_103
<cons, nil, cons>(q_gen_105, q_gen_104) -> q_gen_103
<nil, cons, cons>(q_gen_105, q_gen_104) -> q_gen_103
<nil, nil, cons>(q_gen_118, q_gen_85) -> q_gen_103
<nil, nil, nil>() -> q_gen_103
<a, b, a>() -> q_gen_121
<b, a, a>() -> q_gen_121
<b, a, b>() -> q_gen_121
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_101, q_gen_102, q_gen_115},
Q_f={q_gen_101},
Delta=
{
<z>() -> q_gen_115
<s, s>(q_gen_102) -> q_gen_102
<z, s>(q_gen_115) -> q_gen_102
<z, z>() -> q_gen_102
<s, s, s>(q_gen_101) -> q_gen_101
<s, z, s>(q_gen_102) -> q_gen_101
<z, s, s>(q_gen_102) -> q_gen_101
<z, z, s>(q_gen_115) -> q_gen_101
<z, z, z>() -> q_gen_101
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 7
() -> length([nil, z]) -> 7
() -> leq([a, n2]) -> 7
() -> leq([b, b]) -> 7
() -> leqnat([z, n2]) -> 7
() -> merge([cons(z, xs), nil, cons(z, xs)]) -> 7
() -> merge([nil, y, y]) -> 7
() -> plus([n, z, n]) -> 7
(append([t1, l2, _s])) -> append([cons(h1, t1), l2, cons(h1, _s)]) -> 7
(length([_ha, _ia]) /\ length([l1, _ga]) /\ merge([l1, l2, _ha])) -> leqnat([_ga, _ia]) -> 7
(length([_ka, _la]) /\ length([l2, _ja]) /\ merge([l1, l2, _ka])) -> leqnat([_ja, _la]) -> 7
(length([ll, _ca])) -> length([cons(x, ll), s(_ca)]) -> 7
(leq([z, y2]) /\ merge([xs, cons(y2, ys), _m])) -> merge([cons(z, xs), cons(y2, ys), cons(z, _m)]) -> 10
(not leq([z, y2]) /\ merge([cons(z, xs), ys, _n])) -> merge([cons(z, xs), cons(y2, ys), cons(y2, _n)]) -> 10
(leq([b, a])) -> BOT -> 8
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 8
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 8
(leqnat([s(nn1), z])) -> BOT -> 8
(plus([n, mm, _x])) -> plus([n, s(mm), s(_x)]) -> 10
}
Sat witness: Found: ((leq([z, y2]) /\ merge([xs, cons(y2, ys), _m])) -> merge([cons(z, xs), cons(y2, ys), cons(z, _m)]), {
_m -> cons(b, nil)  ;  xs -> nil  ;  y2 -> b  ;  ys -> nil  ;  z -> b
})

-------------------------------------------
Step 29, which took 0.024694 s (model generation: 0.024308,  model checking: 0.000386):

Model:
|_
{
append -> 
{{{
Q={q_gen_100, q_gen_109, q_gen_110, q_gen_127, q_gen_128, q_gen_129},
Q_f={q_gen_109},
Delta=
{
<nil>() -> q_gen_127
<b>() -> q_gen_128
<a, a>() -> q_gen_100
<b, b>() -> q_gen_100
<cons, cons>(q_gen_100, q_gen_110) -> q_gen_110
<nil, nil>() -> q_gen_110
<cons, cons, cons>(q_gen_129, q_gen_109) -> q_gen_109
<cons, nil, cons>(q_gen_100, q_gen_110) -> q_gen_109
<nil, cons, cons>(q_gen_100, q_gen_110) -> q_gen_109
<nil, nil, cons>(q_gen_128, q_gen_127) -> q_gen_109
<nil, nil, nil>() -> q_gen_109
<b, b, b>() -> q_gen_129
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_122, q_gen_123, q_gen_94},
Q_f={q_gen_122},
Delta=
{
<nil>() -> q_gen_94
<cons, s>(q_gen_123, q_gen_94) -> q_gen_122
<nil, z>() -> q_gen_122
<a, z>() -> q_gen_123
<b, z>() -> q_gen_123
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_108, q_gen_82},
Q_f={q_gen_108},
Delta=
{
<a, a>() -> q_gen_108
<a, b>() -> q_gen_108
<b, b>() -> q_gen_108
<b, a>() -> q_gen_82
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  leqnat -> 
{{{
Q={q_gen_106, q_gen_107},
Q_f={q_gen_106},
Delta=
{
<s>(q_gen_107) -> q_gen_107
<z>() -> q_gen_107
<s, s>(q_gen_106) -> q_gen_106
<z, s>(q_gen_107) -> q_gen_106
<z, z>() -> q_gen_106
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  merge -> 
{{{
Q={q_gen_103, q_gen_104, q_gen_105, q_gen_118, q_gen_121, q_gen_85},
Q_f={q_gen_103},
Delta=
{
<a>() -> q_gen_118
<b>() -> q_gen_118
<nil>() -> q_gen_85
<cons, cons>(q_gen_105, q_gen_104) -> q_gen_104
<nil, nil>() -> q_gen_104
<a, a>() -> q_gen_105
<a, b>() -> q_gen_105
<b, a>() -> q_gen_105
<b, b>() -> q_gen_105
<cons, cons, cons>(q_gen_121, q_gen_103) -> q_gen_103
<cons, nil, cons>(q_gen_105, q_gen_104) -> q_gen_103
<nil, cons, cons>(q_gen_105, q_gen_104) -> q_gen_103
<nil, nil, cons>(q_gen_118, q_gen_85) -> q_gen_103
<nil, nil, nil>() -> q_gen_103
<a, b, a>() -> q_gen_121
<b, a, a>() -> q_gen_121
<b, a, b>() -> q_gen_121
<b, b, b>() -> q_gen_121
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_101, q_gen_102, q_gen_115},
Q_f={q_gen_101},
Delta=
{
<z>() -> q_gen_115
<s, s>(q_gen_102) -> q_gen_102
<z, s>(q_gen_115) -> q_gen_102
<z, z>() -> q_gen_102
<s, s, s>(q_gen_101) -> q_gen_101
<s, z, s>(q_gen_102) -> q_gen_101
<z, s, s>(q_gen_102) -> q_gen_101
<z, z, s>(q_gen_115) -> q_gen_101
<z, z, z>() -> q_gen_101
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 7
() -> length([nil, z]) -> 7
() -> leq([a, n2]) -> 7
() -> leq([b, b]) -> 7
() -> leqnat([z, n2]) -> 7
() -> merge([cons(z, xs), nil, cons(z, xs)]) -> 7
() -> merge([nil, y, y]) -> 7
() -> plus([n, z, n]) -> 7
(append([t1, l2, _s])) -> append([cons(h1, t1), l2, cons(h1, _s)]) -> 7
(length([_ha, _ia]) /\ length([l1, _ga]) /\ merge([l1, l2, _ha])) -> leqnat([_ga, _ia]) -> 7
(length([_ka, _la]) /\ length([l2, _ja]) /\ merge([l1, l2, _ka])) -> leqnat([_ja, _la]) -> 7
(length([ll, _ca])) -> length([cons(x, ll), s(_ca)]) -> 10
(leq([z, y2]) /\ merge([xs, cons(y2, ys), _m])) -> merge([cons(z, xs), cons(y2, ys), cons(z, _m)]) -> 10
(not leq([z, y2]) /\ merge([cons(z, xs), ys, _n])) -> merge([cons(z, xs), cons(y2, ys), cons(y2, _n)]) -> 10
(leq([b, a])) -> BOT -> 8
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 8
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 8
(leqnat([s(nn1), z])) -> BOT -> 8
(plus([n, mm, _x])) -> plus([n, s(mm), s(_x)]) -> 10
}
Sat witness: Found: ((length([ll, _ca])) -> length([cons(x, ll), s(_ca)]), {
_ca -> s(z)  ;  ll -> cons(b, nil)  ;  x -> b
})

-------------------------------------------
Step 30, which took 0.023758 s (model generation: 0.023430,  model checking: 0.000328):

Model:
|_
{
append -> 
{{{
Q={q_gen_100, q_gen_109, q_gen_110, q_gen_127, q_gen_128, q_gen_129},
Q_f={q_gen_109},
Delta=
{
<nil>() -> q_gen_127
<b>() -> q_gen_128
<a, a>() -> q_gen_100
<b, b>() -> q_gen_100
<cons, cons>(q_gen_100, q_gen_110) -> q_gen_110
<nil, nil>() -> q_gen_110
<cons, cons, cons>(q_gen_129, q_gen_109) -> q_gen_109
<cons, nil, cons>(q_gen_100, q_gen_110) -> q_gen_109
<nil, cons, cons>(q_gen_100, q_gen_110) -> q_gen_109
<nil, nil, cons>(q_gen_128, q_gen_127) -> q_gen_109
<nil, nil, nil>() -> q_gen_109
<b, b, b>() -> q_gen_129
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_122, q_gen_123, q_gen_139, q_gen_140, q_gen_142},
Q_f={q_gen_122},
Delta=
{
<cons>(q_gen_140, q_gen_139) -> q_gen_139
<nil>() -> q_gen_139
<b>() -> q_gen_140
<z>() -> q_gen_142
<cons, s>(q_gen_123, q_gen_139) -> q_gen_122
<nil, z>() -> q_gen_122
<a, z>() -> q_gen_123
<b, s>(q_gen_142) -> q_gen_123
<b, z>() -> q_gen_123
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_108, q_gen_82},
Q_f={q_gen_108},
Delta=
{
<a, a>() -> q_gen_108
<a, b>() -> q_gen_108
<b, b>() -> q_gen_108
<b, a>() -> q_gen_82
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  leqnat -> 
{{{
Q={q_gen_106, q_gen_107},
Q_f={q_gen_106},
Delta=
{
<s>(q_gen_107) -> q_gen_107
<z>() -> q_gen_107
<s, s>(q_gen_106) -> q_gen_106
<z, s>(q_gen_107) -> q_gen_106
<z, z>() -> q_gen_106
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  merge -> 
{{{
Q={q_gen_103, q_gen_104, q_gen_105, q_gen_118, q_gen_121, q_gen_85},
Q_f={q_gen_103},
Delta=
{
<a>() -> q_gen_118
<b>() -> q_gen_118
<nil>() -> q_gen_85
<cons, cons>(q_gen_105, q_gen_104) -> q_gen_104
<nil, nil>() -> q_gen_104
<a, a>() -> q_gen_105
<a, b>() -> q_gen_105
<b, a>() -> q_gen_105
<b, b>() -> q_gen_105
<cons, cons, cons>(q_gen_121, q_gen_103) -> q_gen_103
<cons, nil, cons>(q_gen_105, q_gen_104) -> q_gen_103
<nil, cons, cons>(q_gen_105, q_gen_104) -> q_gen_103
<nil, nil, cons>(q_gen_118, q_gen_85) -> q_gen_103
<nil, nil, nil>() -> q_gen_103
<a, b, a>() -> q_gen_121
<b, a, a>() -> q_gen_121
<b, a, b>() -> q_gen_121
<b, b, b>() -> q_gen_121
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_101, q_gen_102, q_gen_115},
Q_f={q_gen_101},
Delta=
{
<z>() -> q_gen_115
<s, s>(q_gen_102) -> q_gen_102
<z, s>(q_gen_115) -> q_gen_102
<z, z>() -> q_gen_102
<s, s, s>(q_gen_101) -> q_gen_101
<s, z, s>(q_gen_102) -> q_gen_101
<z, s, s>(q_gen_102) -> q_gen_101
<z, z, s>(q_gen_115) -> q_gen_101
<z, z, z>() -> q_gen_101
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 7
() -> length([nil, z]) -> 7
() -> leq([a, n2]) -> 7
() -> leq([b, b]) -> 7
() -> leqnat([z, n2]) -> 7
() -> merge([cons(z, xs), nil, cons(z, xs)]) -> 7
() -> merge([nil, y, y]) -> 7
() -> plus([n, z, n]) -> 7
(append([t1, l2, _s])) -> append([cons(h1, t1), l2, cons(h1, _s)]) -> 7
(length([_ha, _ia]) /\ length([l1, _ga]) /\ merge([l1, l2, _ha])) -> leqnat([_ga, _ia]) -> 7
(length([_ka, _la]) /\ length([l2, _ja]) /\ merge([l1, l2, _ka])) -> leqnat([_ja, _la]) -> 10
(length([ll, _ca])) -> length([cons(x, ll), s(_ca)]) -> 10
(leq([z, y2]) /\ merge([xs, cons(y2, ys), _m])) -> merge([cons(z, xs), cons(y2, ys), cons(z, _m)]) -> 10
(not leq([z, y2]) /\ merge([cons(z, xs), ys, _n])) -> merge([cons(z, xs), cons(y2, ys), cons(y2, _n)]) -> 10
(leq([b, a])) -> BOT -> 8
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 8
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 8
(leqnat([s(nn1), z])) -> BOT -> 8
(plus([n, mm, _x])) -> plus([n, s(mm), s(_x)]) -> 10
}
Sat witness: Found: ((length([_ka, _la]) /\ length([l2, _ja]) /\ merge([l1, l2, _ka])) -> leqnat([_ja, _la]), {
_ja -> s(s(z))  ;  _ka -> cons(a, nil)  ;  _la -> s(z)  ;  l1 -> cons(a, nil)  ;  l2 -> cons(b, nil)
})

-------------------------------------------
Step 31, which took 0.026941 s (model generation: 0.026293,  model checking: 0.000648):

Model:
|_
{
append -> 
{{{
Q={q_gen_100, q_gen_109, q_gen_110, q_gen_127, q_gen_128, q_gen_129},
Q_f={q_gen_109},
Delta=
{
<nil>() -> q_gen_127
<b>() -> q_gen_128
<a, a>() -> q_gen_100
<b, b>() -> q_gen_100
<cons, cons>(q_gen_100, q_gen_110) -> q_gen_110
<nil, nil>() -> q_gen_110
<cons, cons, cons>(q_gen_129, q_gen_109) -> q_gen_109
<cons, nil, cons>(q_gen_100, q_gen_110) -> q_gen_109
<nil, cons, cons>(q_gen_100, q_gen_110) -> q_gen_109
<nil, nil, cons>(q_gen_128, q_gen_127) -> q_gen_109
<nil, nil, nil>() -> q_gen_109
<b, b, b>() -> q_gen_129
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_122, q_gen_123, q_gen_139, q_gen_140, q_gen_142},
Q_f={q_gen_122},
Delta=
{
<cons>(q_gen_140, q_gen_139) -> q_gen_139
<nil>() -> q_gen_139
<b>() -> q_gen_140
<z>() -> q_gen_142
<cons, s>(q_gen_123, q_gen_139) -> q_gen_122
<nil, z>() -> q_gen_122
<a, z>() -> q_gen_123
<b, s>(q_gen_142) -> q_gen_123
<b, z>() -> q_gen_123
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_108, q_gen_82},
Q_f={q_gen_108},
Delta=
{
<a, a>() -> q_gen_108
<a, b>() -> q_gen_108
<b, b>() -> q_gen_108
<b, a>() -> q_gen_82
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  leqnat -> 
{{{
Q={q_gen_106, q_gen_107},
Q_f={q_gen_106},
Delta=
{
<s>(q_gen_107) -> q_gen_107
<z>() -> q_gen_107
<s, s>(q_gen_106) -> q_gen_106
<s, z>(q_gen_107) -> q_gen_106
<z, s>(q_gen_107) -> q_gen_106
<z, z>() -> q_gen_106
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  merge -> 
{{{
Q={q_gen_103, q_gen_104, q_gen_105, q_gen_118, q_gen_121, q_gen_85},
Q_f={q_gen_103},
Delta=
{
<a>() -> q_gen_118
<b>() -> q_gen_118
<nil>() -> q_gen_85
<cons, cons>(q_gen_105, q_gen_104) -> q_gen_104
<nil, nil>() -> q_gen_104
<a, a>() -> q_gen_105
<a, b>() -> q_gen_105
<b, a>() -> q_gen_105
<b, b>() -> q_gen_105
<cons, cons, cons>(q_gen_121, q_gen_103) -> q_gen_103
<cons, nil, cons>(q_gen_105, q_gen_104) -> q_gen_103
<nil, cons, cons>(q_gen_105, q_gen_104) -> q_gen_103
<nil, nil, cons>(q_gen_118, q_gen_85) -> q_gen_103
<nil, nil, nil>() -> q_gen_103
<a, b, a>() -> q_gen_121
<b, a, a>() -> q_gen_121
<b, a, b>() -> q_gen_121
<b, b, b>() -> q_gen_121
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_101, q_gen_102, q_gen_115},
Q_f={q_gen_101},
Delta=
{
<z>() -> q_gen_115
<s, s>(q_gen_102) -> q_gen_102
<z, s>(q_gen_115) -> q_gen_102
<z, z>() -> q_gen_102
<s, s, s>(q_gen_101) -> q_gen_101
<s, z, s>(q_gen_102) -> q_gen_101
<z, s, s>(q_gen_102) -> q_gen_101
<z, z, s>(q_gen_115) -> q_gen_101
<z, z, z>() -> q_gen_101
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 7
() -> length([nil, z]) -> 7
() -> leq([a, n2]) -> 7
() -> leq([b, b]) -> 7
() -> leqnat([z, n2]) -> 7
() -> merge([cons(z, xs), nil, cons(z, xs)]) -> 7
() -> merge([nil, y, y]) -> 7
() -> plus([n, z, n]) -> 7
(append([t1, l2, _s])) -> append([cons(h1, t1), l2, cons(h1, _s)]) -> 10
(length([_ha, _ia]) /\ length([l1, _ga]) /\ merge([l1, l2, _ha])) -> leqnat([_ga, _ia]) -> 8
(length([_ka, _la]) /\ length([l2, _ja]) /\ merge([l1, l2, _ka])) -> leqnat([_ja, _la]) -> 10
(length([ll, _ca])) -> length([cons(x, ll), s(_ca)]) -> 10
(leq([z, y2]) /\ merge([xs, cons(y2, ys), _m])) -> merge([cons(z, xs), cons(y2, ys), cons(z, _m)]) -> 10
(not leq([z, y2]) /\ merge([cons(z, xs), ys, _n])) -> merge([cons(z, xs), cons(y2, ys), cons(y2, _n)]) -> 10
(leq([b, a])) -> BOT -> 8
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 8
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 8
(leqnat([s(nn1), z])) -> BOT -> 8
(plus([n, mm, _x])) -> plus([n, s(mm), s(_x)]) -> 10
}
Sat witness: Found: ((append([t1, l2, _s])) -> append([cons(h1, t1), l2, cons(h1, _s)]), {
_s -> cons(b, nil)  ;  h1 -> b  ;  l2 -> nil  ;  t1 -> nil
})

-------------------------------------------
Step 32, which took 0.027530 s (model generation: 0.026503,  model checking: 0.001027):

Model:
|_
{
append -> 
{{{
Q={q_gen_100, q_gen_109, q_gen_110, q_gen_127, q_gen_128, q_gen_129},
Q_f={q_gen_109},
Delta=
{
<nil>() -> q_gen_127
<b>() -> q_gen_128
<a, a>() -> q_gen_100
<b, b>() -> q_gen_100
<cons, cons>(q_gen_100, q_gen_110) -> q_gen_110
<nil, cons>(q_gen_128, q_gen_127) -> q_gen_110
<nil, nil>() -> q_gen_110
<cons, cons, cons>(q_gen_129, q_gen_109) -> q_gen_109
<cons, nil, cons>(q_gen_100, q_gen_110) -> q_gen_109
<nil, cons, cons>(q_gen_100, q_gen_110) -> q_gen_109
<nil, nil, cons>(q_gen_128, q_gen_127) -> q_gen_109
<nil, nil, nil>() -> q_gen_109
<b, b, b>() -> q_gen_129
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_122, q_gen_123, q_gen_139, q_gen_140, q_gen_142},
Q_f={q_gen_122},
Delta=
{
<cons>(q_gen_140, q_gen_139) -> q_gen_139
<nil>() -> q_gen_139
<b>() -> q_gen_140
<z>() -> q_gen_142
<cons, s>(q_gen_123, q_gen_139) -> q_gen_122
<nil, z>() -> q_gen_122
<a, z>() -> q_gen_123
<b, s>(q_gen_142) -> q_gen_123
<b, z>() -> q_gen_123
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_108, q_gen_82},
Q_f={q_gen_108},
Delta=
{
<a, a>() -> q_gen_108
<a, b>() -> q_gen_108
<b, b>() -> q_gen_108
<b, a>() -> q_gen_82
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  leqnat -> 
{{{
Q={q_gen_106, q_gen_107},
Q_f={q_gen_106},
Delta=
{
<s>(q_gen_107) -> q_gen_107
<z>() -> q_gen_107
<s, s>(q_gen_106) -> q_gen_106
<s, z>(q_gen_107) -> q_gen_106
<z, s>(q_gen_107) -> q_gen_106
<z, z>() -> q_gen_106
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  merge -> 
{{{
Q={q_gen_103, q_gen_104, q_gen_105, q_gen_118, q_gen_121, q_gen_85},
Q_f={q_gen_103},
Delta=
{
<a>() -> q_gen_118
<b>() -> q_gen_118
<nil>() -> q_gen_85
<cons, cons>(q_gen_105, q_gen_104) -> q_gen_104
<nil, nil>() -> q_gen_104
<a, a>() -> q_gen_105
<a, b>() -> q_gen_105
<b, a>() -> q_gen_105
<b, b>() -> q_gen_105
<cons, cons, cons>(q_gen_121, q_gen_103) -> q_gen_103
<cons, nil, cons>(q_gen_105, q_gen_104) -> q_gen_103
<nil, cons, cons>(q_gen_105, q_gen_104) -> q_gen_103
<nil, nil, cons>(q_gen_118, q_gen_85) -> q_gen_103
<nil, nil, nil>() -> q_gen_103
<a, b, a>() -> q_gen_121
<b, a, a>() -> q_gen_121
<b, a, b>() -> q_gen_121
<b, b, b>() -> q_gen_121
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_101, q_gen_102, q_gen_115},
Q_f={q_gen_101},
Delta=
{
<z>() -> q_gen_115
<s, s>(q_gen_102) -> q_gen_102
<z, s>(q_gen_115) -> q_gen_102
<z, z>() -> q_gen_102
<s, s, s>(q_gen_101) -> q_gen_101
<s, z, s>(q_gen_102) -> q_gen_101
<z, s, s>(q_gen_102) -> q_gen_101
<z, z, s>(q_gen_115) -> q_gen_101
<z, z, z>() -> q_gen_101
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 8
() -> length([nil, z]) -> 8
() -> leq([a, n2]) -> 8
() -> leq([b, b]) -> 8
() -> leqnat([z, n2]) -> 8
() -> merge([cons(z, xs), nil, cons(z, xs)]) -> 8
() -> merge([nil, y, y]) -> 8
() -> plus([n, z, n]) -> 8
(append([t1, l2, _s])) -> append([cons(h1, t1), l2, cons(h1, _s)]) -> 10
(length([_ha, _ia]) /\ length([l1, _ga]) /\ merge([l1, l2, _ha])) -> leqnat([_ga, _ia]) -> 8
(length([_ka, _la]) /\ length([l2, _ja]) /\ merge([l1, l2, _ka])) -> leqnat([_ja, _la]) -> 10
(length([ll, _ca])) -> length([cons(x, ll), s(_ca)]) -> 10
(leq([z, y2]) /\ merge([xs, cons(y2, ys), _m])) -> merge([cons(z, xs), cons(y2, ys), cons(z, _m)]) -> 10
(not leq([z, y2]) /\ merge([cons(z, xs), ys, _n])) -> merge([cons(z, xs), cons(y2, ys), cons(y2, _n)]) -> 10
(leq([b, a])) -> BOT -> 8
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 8
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 8
(leqnat([s(nn1), z])) -> BOT -> 11
(plus([n, mm, _x])) -> plus([n, s(mm), s(_x)]) -> 10
}
Sat witness: Found: ((leqnat([s(nn1), z])) -> BOT, {
nn1 -> z
})

-------------------------------------------
Step 33, which took 0.030498 s (model generation: 0.030404,  model checking: 0.000094):

Model:
|_
{
append -> 
{{{
Q={q_gen_100, q_gen_109, q_gen_110, q_gen_127, q_gen_128, q_gen_129},
Q_f={q_gen_109},
Delta=
{
<nil>() -> q_gen_127
<b>() -> q_gen_128
<a, a>() -> q_gen_100
<b, b>() -> q_gen_100
<cons, cons>(q_gen_100, q_gen_110) -> q_gen_110
<nil, cons>(q_gen_128, q_gen_127) -> q_gen_110
<nil, nil>() -> q_gen_110
<cons, cons, cons>(q_gen_129, q_gen_109) -> q_gen_109
<cons, nil, cons>(q_gen_100, q_gen_110) -> q_gen_109
<nil, cons, cons>(q_gen_100, q_gen_110) -> q_gen_109
<nil, nil, cons>(q_gen_128, q_gen_127) -> q_gen_109
<nil, nil, nil>() -> q_gen_109
<b, b, b>() -> q_gen_129
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_122, q_gen_123, q_gen_139, q_gen_140, q_gen_142},
Q_f={q_gen_122},
Delta=
{
<cons>(q_gen_140, q_gen_139) -> q_gen_139
<nil>() -> q_gen_139
<b>() -> q_gen_140
<z>() -> q_gen_142
<cons, s>(q_gen_123, q_gen_139) -> q_gen_122
<nil, z>() -> q_gen_122
<a, z>() -> q_gen_123
<b, s>(q_gen_142) -> q_gen_123
<b, z>() -> q_gen_123
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_108, q_gen_82},
Q_f={q_gen_108},
Delta=
{
<a, a>() -> q_gen_108
<a, b>() -> q_gen_108
<b, b>() -> q_gen_108
<b, a>() -> q_gen_82
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  leqnat -> 
{{{
Q={q_gen_106, q_gen_107, q_gen_146},
Q_f={q_gen_106},
Delta=
{
<s>(q_gen_107) -> q_gen_107
<z>() -> q_gen_107
<s, s>(q_gen_106) -> q_gen_106
<s, s>(q_gen_146) -> q_gen_106
<z, s>(q_gen_107) -> q_gen_106
<z, z>() -> q_gen_106
<s, z>(q_gen_107) -> q_gen_146
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  merge -> 
{{{
Q={q_gen_103, q_gen_104, q_gen_105, q_gen_118, q_gen_121, q_gen_85},
Q_f={q_gen_103},
Delta=
{
<a>() -> q_gen_118
<b>() -> q_gen_118
<nil>() -> q_gen_85
<cons, cons>(q_gen_105, q_gen_104) -> q_gen_104
<nil, nil>() -> q_gen_104
<a, a>() -> q_gen_105
<a, b>() -> q_gen_105
<b, a>() -> q_gen_105
<b, b>() -> q_gen_105
<cons, cons, cons>(q_gen_121, q_gen_103) -> q_gen_103
<cons, nil, cons>(q_gen_105, q_gen_104) -> q_gen_103
<nil, cons, cons>(q_gen_105, q_gen_104) -> q_gen_103
<nil, nil, cons>(q_gen_118, q_gen_85) -> q_gen_103
<nil, nil, nil>() -> q_gen_103
<a, b, a>() -> q_gen_121
<b, a, a>() -> q_gen_121
<b, a, b>() -> q_gen_121
<b, b, b>() -> q_gen_121
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_101, q_gen_102, q_gen_115},
Q_f={q_gen_101},
Delta=
{
<z>() -> q_gen_115
<s, s>(q_gen_102) -> q_gen_102
<z, s>(q_gen_115) -> q_gen_102
<z, z>() -> q_gen_102
<s, s, s>(q_gen_101) -> q_gen_101
<s, z, s>(q_gen_102) -> q_gen_101
<z, s, s>(q_gen_102) -> q_gen_101
<z, z, s>(q_gen_115) -> q_gen_101
<z, z, z>() -> q_gen_101
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 8
() -> length([nil, z]) -> 8
() -> leq([a, n2]) -> 8
() -> leq([b, b]) -> 8
() -> leqnat([z, n2]) -> 8
() -> merge([cons(z, xs), nil, cons(z, xs)]) -> 8
() -> merge([nil, y, y]) -> 8
() -> plus([n, z, n]) -> 8
(append([t1, l2, _s])) -> append([cons(h1, t1), l2, cons(h1, _s)]) -> 10
(length([_ha, _ia]) /\ length([l1, _ga]) /\ merge([l1, l2, _ha])) -> leqnat([_ga, _ia]) -> 8
(length([_ka, _la]) /\ length([l2, _ja]) /\ merge([l1, l2, _ka])) -> leqnat([_ja, _la]) -> 10
(length([ll, _ca])) -> length([cons(x, ll), s(_ca)]) -> 10
(leq([z, y2]) /\ merge([xs, cons(y2, ys), _m])) -> merge([cons(z, xs), cons(y2, ys), cons(z, _m)]) -> 10
(not leq([z, y2]) /\ merge([cons(z, xs), ys, _n])) -> merge([cons(z, xs), cons(y2, ys), cons(y2, _n)]) -> 10
(leq([b, a])) -> BOT -> 8
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 8
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 11
(leqnat([s(nn1), z])) -> BOT -> 11
(plus([n, mm, _x])) -> plus([n, s(mm), s(_x)]) -> 10
}
Sat witness: Found: ((leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]), {
nn1 -> s(z)  ;  nn2 -> z
})

-------------------------------------------
Step 34, which took 0.026873 s (model generation: 0.026401,  model checking: 0.000472):

Model:
|_
{
append -> 
{{{
Q={q_gen_100, q_gen_109, q_gen_110, q_gen_127, q_gen_128, q_gen_129},
Q_f={q_gen_109},
Delta=
{
<nil>() -> q_gen_127
<b>() -> q_gen_128
<a, a>() -> q_gen_100
<b, b>() -> q_gen_100
<cons, cons>(q_gen_100, q_gen_110) -> q_gen_110
<nil, cons>(q_gen_128, q_gen_127) -> q_gen_110
<nil, nil>() -> q_gen_110
<cons, cons, cons>(q_gen_129, q_gen_109) -> q_gen_109
<cons, nil, cons>(q_gen_100, q_gen_110) -> q_gen_109
<nil, cons, cons>(q_gen_100, q_gen_110) -> q_gen_109
<nil, nil, cons>(q_gen_128, q_gen_127) -> q_gen_109
<nil, nil, nil>() -> q_gen_109
<b, b, b>() -> q_gen_129
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_122, q_gen_123, q_gen_139, q_gen_140, q_gen_142},
Q_f={q_gen_122},
Delta=
{
<cons>(q_gen_140, q_gen_139) -> q_gen_139
<nil>() -> q_gen_139
<b>() -> q_gen_140
<z>() -> q_gen_142
<cons, s>(q_gen_123, q_gen_139) -> q_gen_122
<nil, z>() -> q_gen_122
<a, z>() -> q_gen_123
<b, s>(q_gen_142) -> q_gen_123
<b, z>() -> q_gen_123
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_108, q_gen_82},
Q_f={q_gen_108},
Delta=
{
<a, a>() -> q_gen_108
<a, b>() -> q_gen_108
<b, b>() -> q_gen_108
<b, a>() -> q_gen_82
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  leqnat -> 
{{{
Q={q_gen_106, q_gen_107, q_gen_145},
Q_f={q_gen_106},
Delta=
{
<s>(q_gen_107) -> q_gen_107
<z>() -> q_gen_107
<s, s>(q_gen_106) -> q_gen_106
<z, s>(q_gen_107) -> q_gen_106
<z, z>() -> q_gen_106
<s, s>(q_gen_145) -> q_gen_145
<s, z>(q_gen_107) -> q_gen_145
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  merge -> 
{{{
Q={q_gen_103, q_gen_104, q_gen_105, q_gen_117, q_gen_118, q_gen_121, q_gen_85},
Q_f={q_gen_103},
Delta=
{
<a>() -> q_gen_118
<b>() -> q_gen_118
<nil>() -> q_gen_85
<cons, cons>(q_gen_105, q_gen_104) -> q_gen_104
<nil, nil>() -> q_gen_104
<a, a>() -> q_gen_105
<a, b>() -> q_gen_105
<b, a>() -> q_gen_105
<b, b>() -> q_gen_105
<cons, cons, cons>(q_gen_121, q_gen_117) -> q_gen_103
<cons, nil, cons>(q_gen_105, q_gen_104) -> q_gen_103
<nil, cons, cons>(q_gen_105, q_gen_104) -> q_gen_103
<nil, nil, nil>() -> q_gen_103
<cons, cons, cons>(q_gen_121, q_gen_103) -> q_gen_117
<nil, nil, cons>(q_gen_118, q_gen_85) -> q_gen_117
<a, b, a>() -> q_gen_121
<b, a, a>() -> q_gen_121
<b, a, b>() -> q_gen_121
<b, b, b>() -> q_gen_121
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_101, q_gen_102, q_gen_115},
Q_f={q_gen_101},
Delta=
{
<z>() -> q_gen_115
<s, s>(q_gen_102) -> q_gen_102
<z, s>(q_gen_115) -> q_gen_102
<z, z>() -> q_gen_102
<s, s, s>(q_gen_101) -> q_gen_101
<s, z, s>(q_gen_102) -> q_gen_101
<z, s, s>(q_gen_102) -> q_gen_101
<z, z, s>(q_gen_115) -> q_gen_101
<z, z, z>() -> q_gen_101
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 8
() -> length([nil, z]) -> 8
() -> leq([a, n2]) -> 8
() -> leq([b, b]) -> 8
() -> leqnat([z, n2]) -> 8
() -> merge([cons(z, xs), nil, cons(z, xs)]) -> 8
() -> merge([nil, y, y]) -> 8
() -> plus([n, z, n]) -> 8
(append([t1, l2, _s])) -> append([cons(h1, t1), l2, cons(h1, _s)]) -> 10
(length([_ha, _ia]) /\ length([l1, _ga]) /\ merge([l1, l2, _ha])) -> leqnat([_ga, _ia]) -> 11
(length([_ka, _la]) /\ length([l2, _ja]) /\ merge([l1, l2, _ka])) -> leqnat([_ja, _la]) -> 10
(length([ll, _ca])) -> length([cons(x, ll), s(_ca)]) -> 10
(leq([z, y2]) /\ merge([xs, cons(y2, ys), _m])) -> merge([cons(z, xs), cons(y2, ys), cons(z, _m)]) -> 10
(not leq([z, y2]) /\ merge([cons(z, xs), ys, _n])) -> merge([cons(z, xs), cons(y2, ys), cons(y2, _n)]) -> 10
(leq([b, a])) -> BOT -> 9
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 9
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 11
(leqnat([s(nn1), z])) -> BOT -> 11
(plus([n, mm, _x])) -> plus([n, s(mm), s(_x)]) -> 10
}
Sat witness: Found: ((length([_ha, _ia]) /\ length([l1, _ga]) /\ merge([l1, l2, _ha])) -> leqnat([_ga, _ia]), {
_ga -> s(s(z))  ;  _ha -> cons(b, cons(b, nil))  ;  _ia -> s(z)  ;  l1 -> cons(b, nil)  ;  l2 -> cons(b, nil)
})

-------------------------------------------
Step 35, which took 0.028715 s (model generation: 0.027487,  model checking: 0.001228):

Model:
|_
{
append -> 
{{{
Q={q_gen_100, q_gen_109, q_gen_110, q_gen_127, q_gen_128, q_gen_129},
Q_f={q_gen_109},
Delta=
{
<nil>() -> q_gen_127
<b>() -> q_gen_128
<a, a>() -> q_gen_100
<b, b>() -> q_gen_100
<cons, cons>(q_gen_100, q_gen_110) -> q_gen_110
<nil, cons>(q_gen_128, q_gen_127) -> q_gen_110
<nil, nil>() -> q_gen_110
<cons, cons, cons>(q_gen_129, q_gen_109) -> q_gen_109
<cons, nil, cons>(q_gen_100, q_gen_110) -> q_gen_109
<nil, cons, cons>(q_gen_100, q_gen_110) -> q_gen_109
<nil, nil, cons>(q_gen_128, q_gen_127) -> q_gen_109
<nil, nil, nil>() -> q_gen_109
<b, b, b>() -> q_gen_129
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_122, q_gen_123, q_gen_139, q_gen_140, q_gen_141, q_gen_142, q_gen_143, q_gen_94},
Q_f={q_gen_122},
Delta=
{
<cons>(q_gen_140, q_gen_94) -> q_gen_139
<b>() -> q_gen_140
<z>() -> q_gen_142
<nil>() -> q_gen_94
<cons, s>(q_gen_123, q_gen_139) -> q_gen_122
<cons, s>(q_gen_123, q_gen_94) -> q_gen_122
<cons, s>(q_gen_141, q_gen_139) -> q_gen_122
<nil, z>() -> q_gen_122
<a, z>() -> q_gen_123
<b, z>() -> q_gen_123
<b, s>(q_gen_142) -> q_gen_141
<cons, s>(q_gen_141, q_gen_94) -> q_gen_143
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_108, q_gen_82},
Q_f={q_gen_108},
Delta=
{
<a, a>() -> q_gen_108
<a, b>() -> q_gen_108
<b, b>() -> q_gen_108
<b, a>() -> q_gen_82
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  leqnat -> 
{{{
Q={q_gen_106, q_gen_107, q_gen_145},
Q_f={q_gen_106},
Delta=
{
<s>(q_gen_107) -> q_gen_107
<z>() -> q_gen_107
<s, s>(q_gen_106) -> q_gen_106
<z, s>(q_gen_107) -> q_gen_106
<z, z>() -> q_gen_106
<s, s>(q_gen_145) -> q_gen_145
<s, z>(q_gen_107) -> q_gen_145
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  merge -> 
{{{
Q={q_gen_103, q_gen_104, q_gen_105, q_gen_118, q_gen_121, q_gen_85},
Q_f={q_gen_103},
Delta=
{
<a>() -> q_gen_118
<b>() -> q_gen_118
<nil>() -> q_gen_85
<cons, cons>(q_gen_105, q_gen_104) -> q_gen_104
<nil, nil>() -> q_gen_104
<a, a>() -> q_gen_105
<a, b>() -> q_gen_105
<b, a>() -> q_gen_105
<b, b>() -> q_gen_105
<cons, cons, cons>(q_gen_121, q_gen_103) -> q_gen_103
<cons, nil, cons>(q_gen_105, q_gen_104) -> q_gen_103
<nil, cons, cons>(q_gen_105, q_gen_104) -> q_gen_103
<nil, nil, cons>(q_gen_118, q_gen_85) -> q_gen_103
<nil, nil, nil>() -> q_gen_103
<a, b, a>() -> q_gen_121
<b, a, a>() -> q_gen_121
<b, a, b>() -> q_gen_121
<b, b, b>() -> q_gen_121
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_101, q_gen_102, q_gen_115},
Q_f={q_gen_101},
Delta=
{
<z>() -> q_gen_115
<s, s>(q_gen_102) -> q_gen_102
<z, s>(q_gen_115) -> q_gen_102
<z, z>() -> q_gen_102
<s, s, s>(q_gen_101) -> q_gen_101
<s, z, s>(q_gen_102) -> q_gen_101
<z, s, s>(q_gen_102) -> q_gen_101
<z, z, s>(q_gen_115) -> q_gen_101
<z, z, z>() -> q_gen_101
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 9
() -> length([nil, z]) -> 9
() -> leq([a, n2]) -> 9
() -> leq([b, b]) -> 9
() -> leqnat([z, n2]) -> 9
() -> merge([cons(z, xs), nil, cons(z, xs)]) -> 9
() -> merge([nil, y, y]) -> 9
() -> plus([n, z, n]) -> 9
(append([t1, l2, _s])) -> append([cons(h1, t1), l2, cons(h1, _s)]) -> 10
(length([_ha, _ia]) /\ length([l1, _ga]) /\ merge([l1, l2, _ha])) -> leqnat([_ga, _ia]) -> 11
(length([_ka, _la]) /\ length([l2, _ja]) /\ merge([l1, l2, _ka])) -> leqnat([_ja, _la]) -> 10
(length([ll, _ca])) -> length([cons(x, ll), s(_ca)]) -> 10
(leq([z, y2]) /\ merge([xs, cons(y2, ys), _m])) -> merge([cons(z, xs), cons(y2, ys), cons(z, _m)]) -> 10
(not leq([z, y2]) /\ merge([cons(z, xs), ys, _n])) -> merge([cons(z, xs), cons(y2, ys), cons(y2, _n)]) -> 10
(leq([b, a])) -> BOT -> 10
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 10
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 11
(leqnat([s(nn1), z])) -> BOT -> 11
(plus([n, mm, _x])) -> plus([n, s(mm), s(_x)]) -> 13
}
Sat witness: Found: ((plus([n, mm, _x])) -> plus([n, s(mm), s(_x)]), {
_x -> s(s(z))  ;  mm -> z  ;  n -> s(z)
})

-------------------------------------------
Step 36, which took 0.028743 s (model generation: 0.028349,  model checking: 0.000394):

Model:
|_
{
append -> 
{{{
Q={q_gen_100, q_gen_109, q_gen_110, q_gen_127, q_gen_128, q_gen_129},
Q_f={q_gen_109},
Delta=
{
<nil>() -> q_gen_127
<b>() -> q_gen_128
<a, a>() -> q_gen_100
<b, b>() -> q_gen_100
<cons, cons>(q_gen_100, q_gen_110) -> q_gen_110
<nil, cons>(q_gen_128, q_gen_127) -> q_gen_110
<nil, nil>() -> q_gen_110
<cons, cons, cons>(q_gen_129, q_gen_109) -> q_gen_109
<cons, nil, cons>(q_gen_100, q_gen_110) -> q_gen_109
<nil, cons, cons>(q_gen_100, q_gen_110) -> q_gen_109
<nil, nil, cons>(q_gen_128, q_gen_127) -> q_gen_109
<nil, nil, nil>() -> q_gen_109
<b, b, b>() -> q_gen_129
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_122, q_gen_123, q_gen_139, q_gen_140, q_gen_142},
Q_f={q_gen_122},
Delta=
{
<cons>(q_gen_140, q_gen_139) -> q_gen_139
<nil>() -> q_gen_139
<b>() -> q_gen_140
<z>() -> q_gen_142
<cons, s>(q_gen_123, q_gen_139) -> q_gen_122
<nil, z>() -> q_gen_122
<a, z>() -> q_gen_123
<b, s>(q_gen_142) -> q_gen_123
<b, z>() -> q_gen_123
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_108, q_gen_82},
Q_f={q_gen_108},
Delta=
{
<a, a>() -> q_gen_108
<a, b>() -> q_gen_108
<b, b>() -> q_gen_108
<b, a>() -> q_gen_82
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  leqnat -> 
{{{
Q={q_gen_106, q_gen_107, q_gen_145},
Q_f={q_gen_106},
Delta=
{
<s>(q_gen_107) -> q_gen_107
<z>() -> q_gen_107
<s, s>(q_gen_106) -> q_gen_106
<z, s>(q_gen_107) -> q_gen_106
<z, z>() -> q_gen_106
<s, s>(q_gen_145) -> q_gen_145
<s, z>(q_gen_107) -> q_gen_145
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  merge -> 
{{{
Q={q_gen_103, q_gen_104, q_gen_105, q_gen_117, q_gen_118, q_gen_121, q_gen_137, q_gen_73, q_gen_85},
Q_f={q_gen_103},
Delta=
{
<a>() -> q_gen_118
<b>() -> q_gen_118
<nil>() -> q_gen_85
<cons, cons>(q_gen_105, q_gen_104) -> q_gen_104
<nil, nil>() -> q_gen_104
<a, a>() -> q_gen_105
<a, b>() -> q_gen_105
<b, a>() -> q_gen_73
<b, b>() -> q_gen_73
<cons, cons, cons>(q_gen_121, q_gen_117) -> q_gen_103
<cons, nil, cons>(q_gen_73, q_gen_104) -> q_gen_103
<nil, cons, cons>(q_gen_105, q_gen_104) -> q_gen_103
<nil, nil, nil>() -> q_gen_103
<cons, cons, cons>(q_gen_121, q_gen_103) -> q_gen_117
<cons, cons, cons>(q_gen_137, q_gen_103) -> q_gen_117
<cons, cons, cons>(q_gen_137, q_gen_117) -> q_gen_117
<nil, cons, cons>(q_gen_73, q_gen_104) -> q_gen_117
<nil, nil, cons>(q_gen_118, q_gen_85) -> q_gen_117
<a, b, a>() -> q_gen_121
<b, a, a>() -> q_gen_121
<b, a, b>() -> q_gen_137
<b, b, b>() -> q_gen_137
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_101, q_gen_102, q_gen_115},
Q_f={q_gen_101},
Delta=
{
<s>(q_gen_115) -> q_gen_115
<z>() -> q_gen_115
<s, s>(q_gen_102) -> q_gen_102
<z, s>(q_gen_115) -> q_gen_102
<z, z>() -> q_gen_102
<s, s, s>(q_gen_101) -> q_gen_101
<s, z, s>(q_gen_102) -> q_gen_101
<z, s, s>(q_gen_102) -> q_gen_101
<z, z, s>(q_gen_115) -> q_gen_101
<z, z, z>() -> q_gen_101
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 9
() -> length([nil, z]) -> 9
() -> leq([a, n2]) -> 9
() -> leq([b, b]) -> 9
() -> leqnat([z, n2]) -> 9
() -> merge([cons(z, xs), nil, cons(z, xs)]) -> 9
() -> merge([nil, y, y]) -> 12
() -> plus([n, z, n]) -> 10
(append([t1, l2, _s])) -> append([cons(h1, t1), l2, cons(h1, _s)]) -> 10
(length([_ha, _ia]) /\ length([l1, _ga]) /\ merge([l1, l2, _ha])) -> leqnat([_ga, _ia]) -> 11
(length([_ka, _la]) /\ length([l2, _ja]) /\ merge([l1, l2, _ka])) -> leqnat([_ja, _la]) -> 10
(length([ll, _ca])) -> length([cons(x, ll), s(_ca)]) -> 10
(leq([z, y2]) /\ merge([xs, cons(y2, ys), _m])) -> merge([cons(z, xs), cons(y2, ys), cons(z, _m)]) -> 10
(not leq([z, y2]) /\ merge([cons(z, xs), ys, _n])) -> merge([cons(z, xs), cons(y2, ys), cons(y2, _n)]) -> 10
(leq([b, a])) -> BOT -> 10
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 10
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 11
(leqnat([s(nn1), z])) -> BOT -> 11
(plus([n, mm, _x])) -> plus([n, s(mm), s(_x)]) -> 13
}
Sat witness: Found: (() -> merge([nil, y, y]), {
y -> cons(b, nil)
})

-------------------------------------------
Step 37, which took 0.030838 s (model generation: 0.028975,  model checking: 0.001863):

Model:
|_
{
append -> 
{{{
Q={q_gen_100, q_gen_109, q_gen_110, q_gen_127, q_gen_128, q_gen_129},
Q_f={q_gen_109},
Delta=
{
<nil>() -> q_gen_127
<b>() -> q_gen_128
<a, a>() -> q_gen_100
<b, b>() -> q_gen_100
<cons, cons>(q_gen_100, q_gen_110) -> q_gen_110
<nil, cons>(q_gen_128, q_gen_127) -> q_gen_110
<nil, nil>() -> q_gen_110
<cons, cons, cons>(q_gen_129, q_gen_109) -> q_gen_109
<cons, nil, cons>(q_gen_100, q_gen_110) -> q_gen_109
<nil, cons, cons>(q_gen_100, q_gen_110) -> q_gen_109
<nil, nil, cons>(q_gen_128, q_gen_127) -> q_gen_109
<nil, nil, nil>() -> q_gen_109
<b, b, b>() -> q_gen_129
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_122, q_gen_123, q_gen_139, q_gen_140, q_gen_141, q_gen_142, q_gen_143, q_gen_94},
Q_f={q_gen_122},
Delta=
{
<cons>(q_gen_140, q_gen_94) -> q_gen_139
<b>() -> q_gen_140
<z>() -> q_gen_142
<nil>() -> q_gen_94
<cons, s>(q_gen_123, q_gen_94) -> q_gen_122
<cons, s>(q_gen_141, q_gen_139) -> q_gen_122
<nil, z>() -> q_gen_122
<a, z>() -> q_gen_123
<b, z>() -> q_gen_123
<b, s>(q_gen_142) -> q_gen_141
<cons, s>(q_gen_123, q_gen_139) -> q_gen_143
<cons, s>(q_gen_141, q_gen_94) -> q_gen_143
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_108, q_gen_82},
Q_f={q_gen_108},
Delta=
{
<a, a>() -> q_gen_108
<a, b>() -> q_gen_108
<b, b>() -> q_gen_108
<b, a>() -> q_gen_82
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  leqnat -> 
{{{
Q={q_gen_106, q_gen_107, q_gen_145},
Q_f={q_gen_106},
Delta=
{
<s>(q_gen_107) -> q_gen_107
<z>() -> q_gen_107
<s, s>(q_gen_106) -> q_gen_106
<z, s>(q_gen_107) -> q_gen_106
<z, z>() -> q_gen_106
<s, s>(q_gen_145) -> q_gen_145
<s, z>(q_gen_107) -> q_gen_145
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  merge -> 
{{{
Q={q_gen_103, q_gen_104, q_gen_105, q_gen_118, q_gen_121, q_gen_85},
Q_f={q_gen_103},
Delta=
{
<a>() -> q_gen_118
<b>() -> q_gen_118
<nil>() -> q_gen_85
<cons, cons>(q_gen_105, q_gen_104) -> q_gen_104
<nil, nil>() -> q_gen_104
<a, a>() -> q_gen_105
<a, b>() -> q_gen_105
<b, a>() -> q_gen_105
<b, b>() -> q_gen_105
<cons, cons, cons>(q_gen_121, q_gen_103) -> q_gen_103
<cons, nil, cons>(q_gen_105, q_gen_104) -> q_gen_103
<nil, cons, cons>(q_gen_105, q_gen_104) -> q_gen_103
<nil, nil, cons>(q_gen_118, q_gen_85) -> q_gen_103
<nil, nil, nil>() -> q_gen_103
<a, b, a>() -> q_gen_121
<b, a, a>() -> q_gen_121
<b, a, b>() -> q_gen_121
<b, b, b>() -> q_gen_121
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_101, q_gen_102, q_gen_115},
Q_f={q_gen_101},
Delta=
{
<s>(q_gen_115) -> q_gen_115
<z>() -> q_gen_115
<s, s>(q_gen_102) -> q_gen_102
<z, s>(q_gen_115) -> q_gen_102
<z, z>() -> q_gen_102
<s, s, s>(q_gen_101) -> q_gen_101
<s, z, s>(q_gen_102) -> q_gen_101
<z, s, s>(q_gen_102) -> q_gen_101
<z, z, s>(q_gen_115) -> q_gen_101
<z, z, z>() -> q_gen_101
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 10
() -> length([nil, z]) -> 10
() -> leq([a, n2]) -> 10
() -> leq([b, b]) -> 10
() -> leqnat([z, n2]) -> 10
() -> merge([cons(z, xs), nil, cons(z, xs)]) -> 10
() -> merge([nil, y, y]) -> 12
() -> plus([n, z, n]) -> 10
(append([t1, l2, _s])) -> append([cons(h1, t1), l2, cons(h1, _s)]) -> 10
(length([_ha, _ia]) /\ length([l1, _ga]) /\ merge([l1, l2, _ha])) -> leqnat([_ga, _ia]) -> 11
(length([_ka, _la]) /\ length([l2, _ja]) /\ merge([l1, l2, _ka])) -> leqnat([_ja, _la]) -> 10
(length([ll, _ca])) -> length([cons(x, ll), s(_ca)]) -> 10
(leq([z, y2]) /\ merge([xs, cons(y2, ys), _m])) -> merge([cons(z, xs), cons(y2, ys), cons(z, _m)]) -> 10
(not leq([z, y2]) /\ merge([cons(z, xs), ys, _n])) -> merge([cons(z, xs), cons(y2, ys), cons(y2, _n)]) -> 13
(leq([b, a])) -> BOT -> 11
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 11
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 11
(leqnat([s(nn1), z])) -> BOT -> 11
(plus([n, mm, _x])) -> plus([n, s(mm), s(_x)]) -> 13
}
Sat witness: Found: ((not leq([z, y2]) /\ merge([cons(z, xs), ys, _n])) -> merge([cons(z, xs), cons(y2, ys), cons(y2, _n)]), {
_n -> cons(b, cons(b, nil))  ;  xs -> nil  ;  y2 -> a  ;  ys -> cons(b, nil)  ;  z -> b
})

-------------------------------------------
Step 38, which took 0.035157 s (model generation: 0.034454,  model checking: 0.000703):

Model:
|_
{
append -> 
{{{
Q={q_gen_100, q_gen_109, q_gen_110, q_gen_127, q_gen_128, q_gen_129},
Q_f={q_gen_109},
Delta=
{
<nil>() -> q_gen_127
<b>() -> q_gen_128
<a, a>() -> q_gen_100
<b, b>() -> q_gen_100
<cons, cons>(q_gen_100, q_gen_110) -> q_gen_110
<nil, cons>(q_gen_128, q_gen_127) -> q_gen_110
<nil, nil>() -> q_gen_110
<cons, cons, cons>(q_gen_129, q_gen_109) -> q_gen_109
<cons, nil, cons>(q_gen_100, q_gen_110) -> q_gen_109
<nil, cons, cons>(q_gen_100, q_gen_110) -> q_gen_109
<nil, nil, cons>(q_gen_128, q_gen_127) -> q_gen_109
<nil, nil, nil>() -> q_gen_109
<b, b, b>() -> q_gen_129
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_122, q_gen_123, q_gen_139, q_gen_140, q_gen_141, q_gen_142, q_gen_143, q_gen_94},
Q_f={q_gen_122},
Delta=
{
<cons>(q_gen_140, q_gen_94) -> q_gen_139
<b>() -> q_gen_140
<z>() -> q_gen_142
<nil>() -> q_gen_94
<cons, s>(q_gen_123, q_gen_94) -> q_gen_122
<cons, s>(q_gen_141, q_gen_139) -> q_gen_122
<nil, z>() -> q_gen_122
<a, z>() -> q_gen_123
<b, z>() -> q_gen_123
<b, s>(q_gen_142) -> q_gen_141
<cons, s>(q_gen_123, q_gen_139) -> q_gen_143
<cons, s>(q_gen_141, q_gen_94) -> q_gen_143
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_108, q_gen_82},
Q_f={q_gen_108},
Delta=
{
<a, a>() -> q_gen_108
<a, b>() -> q_gen_108
<b, b>() -> q_gen_108
<b, a>() -> q_gen_82
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  leqnat -> 
{{{
Q={q_gen_106, q_gen_107, q_gen_145},
Q_f={q_gen_106},
Delta=
{
<s>(q_gen_107) -> q_gen_107
<z>() -> q_gen_107
<s, s>(q_gen_106) -> q_gen_106
<z, s>(q_gen_107) -> q_gen_106
<z, z>() -> q_gen_106
<s, s>(q_gen_145) -> q_gen_145
<s, z>(q_gen_107) -> q_gen_145
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  merge -> 
{{{
Q={q_gen_103, q_gen_104, q_gen_105, q_gen_118, q_gen_121, q_gen_85},
Q_f={q_gen_103},
Delta=
{
<a>() -> q_gen_118
<b>() -> q_gen_118
<nil>() -> q_gen_85
<cons, cons>(q_gen_105, q_gen_104) -> q_gen_104
<nil, cons>(q_gen_118, q_gen_85) -> q_gen_104
<nil, nil>() -> q_gen_104
<a, a>() -> q_gen_105
<a, b>() -> q_gen_105
<b, a>() -> q_gen_105
<b, b>() -> q_gen_105
<cons, cons, cons>(q_gen_121, q_gen_103) -> q_gen_103
<cons, nil, cons>(q_gen_105, q_gen_104) -> q_gen_103
<nil, cons, cons>(q_gen_105, q_gen_104) -> q_gen_103
<nil, nil, cons>(q_gen_118, q_gen_85) -> q_gen_103
<nil, nil, nil>() -> q_gen_103
<a, b, a>() -> q_gen_121
<b, a, a>() -> q_gen_121
<b, a, b>() -> q_gen_121
<b, b, b>() -> q_gen_121
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_101, q_gen_102, q_gen_115},
Q_f={q_gen_101},
Delta=
{
<s>(q_gen_115) -> q_gen_115
<z>() -> q_gen_115
<s, s>(q_gen_102) -> q_gen_102
<z, s>(q_gen_115) -> q_gen_102
<z, z>() -> q_gen_102
<s, s, s>(q_gen_101) -> q_gen_101
<s, z, s>(q_gen_102) -> q_gen_101
<z, s, s>(q_gen_102) -> q_gen_101
<z, z, s>(q_gen_115) -> q_gen_101
<z, z, z>() -> q_gen_101
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 10
() -> length([nil, z]) -> 10
() -> leq([a, n2]) -> 10
() -> leq([b, b]) -> 10
() -> leqnat([z, n2]) -> 10
() -> merge([cons(z, xs), nil, cons(z, xs)]) -> 10
() -> merge([nil, y, y]) -> 12
() -> plus([n, z, n]) -> 10
(append([t1, l2, _s])) -> append([cons(h1, t1), l2, cons(h1, _s)]) -> 10
(length([_ha, _ia]) /\ length([l1, _ga]) /\ merge([l1, l2, _ha])) -> leqnat([_ga, _ia]) -> 11
(length([_ka, _la]) /\ length([l2, _ja]) /\ merge([l1, l2, _ka])) -> leqnat([_ja, _la]) -> 10
(length([ll, _ca])) -> length([cons(x, ll), s(_ca)]) -> 10
(leq([z, y2]) /\ merge([xs, cons(y2, ys), _m])) -> merge([cons(z, xs), cons(y2, ys), cons(z, _m)]) -> 13
(not leq([z, y2]) /\ merge([cons(z, xs), ys, _n])) -> merge([cons(z, xs), cons(y2, ys), cons(y2, _n)]) -> 13
(leq([b, a])) -> BOT -> 11
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 11
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 11
(leqnat([s(nn1), z])) -> BOT -> 11
(plus([n, mm, _x])) -> plus([n, s(mm), s(_x)]) -> 13
}
Sat witness: Found: ((leq([z, y2]) /\ merge([xs, cons(y2, ys), _m])) -> merge([cons(z, xs), cons(y2, ys), cons(z, _m)]), {
_m -> cons(b, nil)  ;  xs -> nil  ;  y2 -> a  ;  ys -> nil  ;  z -> a
})

-------------------------------------------
Step 39, which took 0.036718 s (model generation: 0.036034,  model checking: 0.000684):

Model:
|_
{
append -> 
{{{
Q={q_gen_100, q_gen_109, q_gen_110, q_gen_127, q_gen_128, q_gen_129},
Q_f={q_gen_109},
Delta=
{
<nil>() -> q_gen_127
<b>() -> q_gen_128
<a, a>() -> q_gen_100
<b, b>() -> q_gen_100
<cons, cons>(q_gen_100, q_gen_110) -> q_gen_110
<nil, cons>(q_gen_128, q_gen_127) -> q_gen_110
<nil, nil>() -> q_gen_110
<cons, cons, cons>(q_gen_129, q_gen_109) -> q_gen_109
<cons, nil, cons>(q_gen_100, q_gen_110) -> q_gen_109
<nil, cons, cons>(q_gen_100, q_gen_110) -> q_gen_109
<nil, nil, cons>(q_gen_128, q_gen_127) -> q_gen_109
<nil, nil, nil>() -> q_gen_109
<b, b, b>() -> q_gen_129
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_122, q_gen_123, q_gen_139, q_gen_140, q_gen_141, q_gen_142, q_gen_143, q_gen_94},
Q_f={q_gen_122},
Delta=
{
<cons>(q_gen_140, q_gen_94) -> q_gen_139
<b>() -> q_gen_140
<z>() -> q_gen_142
<nil>() -> q_gen_94
<cons, s>(q_gen_123, q_gen_94) -> q_gen_122
<cons, s>(q_gen_141, q_gen_139) -> q_gen_122
<nil, z>() -> q_gen_122
<a, z>() -> q_gen_123
<b, z>() -> q_gen_123
<b, s>(q_gen_142) -> q_gen_141
<cons, s>(q_gen_123, q_gen_139) -> q_gen_143
<cons, s>(q_gen_141, q_gen_94) -> q_gen_143
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_108, q_gen_82},
Q_f={q_gen_108},
Delta=
{
<a, a>() -> q_gen_108
<a, b>() -> q_gen_108
<b, b>() -> q_gen_108
<b, a>() -> q_gen_82
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  leqnat -> 
{{{
Q={q_gen_106, q_gen_107, q_gen_145},
Q_f={q_gen_106},
Delta=
{
<s>(q_gen_107) -> q_gen_107
<z>() -> q_gen_107
<s, s>(q_gen_106) -> q_gen_106
<z, s>(q_gen_107) -> q_gen_106
<z, z>() -> q_gen_106
<s, s>(q_gen_145) -> q_gen_145
<s, z>(q_gen_107) -> q_gen_145
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  merge -> 
{{{
Q={q_gen_103, q_gen_104, q_gen_105, q_gen_118, q_gen_121, q_gen_85},
Q_f={q_gen_103},
Delta=
{
<a>() -> q_gen_118
<b>() -> q_gen_118
<nil>() -> q_gen_85
<cons, cons>(q_gen_105, q_gen_104) -> q_gen_104
<nil, cons>(q_gen_118, q_gen_85) -> q_gen_104
<nil, nil>() -> q_gen_104
<a, a>() -> q_gen_105
<a, b>() -> q_gen_105
<b, a>() -> q_gen_105
<b, b>() -> q_gen_105
<cons, cons, cons>(q_gen_121, q_gen_103) -> q_gen_103
<cons, nil, cons>(q_gen_105, q_gen_104) -> q_gen_103
<nil, cons, cons>(q_gen_105, q_gen_104) -> q_gen_103
<nil, nil, cons>(q_gen_118, q_gen_85) -> q_gen_103
<nil, nil, nil>() -> q_gen_103
<a, a, a>() -> q_gen_121
<a, b, a>() -> q_gen_121
<b, a, a>() -> q_gen_121
<b, a, b>() -> q_gen_121
<b, b, b>() -> q_gen_121
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_101, q_gen_102, q_gen_115},
Q_f={q_gen_101},
Delta=
{
<s>(q_gen_115) -> q_gen_115
<z>() -> q_gen_115
<s, s>(q_gen_102) -> q_gen_102
<z, s>(q_gen_115) -> q_gen_102
<z, z>() -> q_gen_102
<s, s, s>(q_gen_101) -> q_gen_101
<s, z, s>(q_gen_102) -> q_gen_101
<z, s, s>(q_gen_102) -> q_gen_101
<z, z, s>(q_gen_115) -> q_gen_101
<z, z, z>() -> q_gen_101
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 10
() -> length([nil, z]) -> 10
() -> leq([a, n2]) -> 10
() -> leq([b, b]) -> 10
() -> leqnat([z, n2]) -> 10
() -> merge([cons(z, xs), nil, cons(z, xs)]) -> 10
() -> merge([nil, y, y]) -> 12
() -> plus([n, z, n]) -> 10
(append([t1, l2, _s])) -> append([cons(h1, t1), l2, cons(h1, _s)]) -> 10
(length([_ha, _ia]) /\ length([l1, _ga]) /\ merge([l1, l2, _ha])) -> leqnat([_ga, _ia]) -> 11
(length([_ka, _la]) /\ length([l2, _ja]) /\ merge([l1, l2, _ka])) -> leqnat([_ja, _la]) -> 10
(length([ll, _ca])) -> length([cons(x, ll), s(_ca)]) -> 13
(leq([z, y2]) /\ merge([xs, cons(y2, ys), _m])) -> merge([cons(z, xs), cons(y2, ys), cons(z, _m)]) -> 13
(not leq([z, y2]) /\ merge([cons(z, xs), ys, _n])) -> merge([cons(z, xs), cons(y2, ys), cons(y2, _n)]) -> 13
(leq([b, a])) -> BOT -> 11
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 11
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 11
(leqnat([s(nn1), z])) -> BOT -> 11
(plus([n, mm, _x])) -> plus([n, s(mm), s(_x)]) -> 13
}
Sat witness: Found: ((length([ll, _ca])) -> length([cons(x, ll), s(_ca)]), {
_ca -> s(z)  ;  ll -> cons(b, nil)  ;  x -> a
})

-------------------------------------------
Step 40, which took 0.039640 s (model generation: 0.037173,  model checking: 0.002467):

Model:
|_
{
append -> 
{{{
Q={q_gen_100, q_gen_109, q_gen_110, q_gen_127, q_gen_128, q_gen_129},
Q_f={q_gen_109},
Delta=
{
<nil>() -> q_gen_127
<b>() -> q_gen_128
<a, a>() -> q_gen_100
<b, b>() -> q_gen_100
<cons, cons>(q_gen_100, q_gen_110) -> q_gen_110
<nil, cons>(q_gen_128, q_gen_127) -> q_gen_110
<nil, nil>() -> q_gen_110
<cons, cons, cons>(q_gen_129, q_gen_109) -> q_gen_109
<cons, nil, cons>(q_gen_100, q_gen_110) -> q_gen_109
<nil, cons, cons>(q_gen_100, q_gen_110) -> q_gen_109
<nil, nil, cons>(q_gen_128, q_gen_127) -> q_gen_109
<nil, nil, nil>() -> q_gen_109
<b, b, b>() -> q_gen_129
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_122, q_gen_123, q_gen_139, q_gen_140, q_gen_141, q_gen_142, q_gen_143, q_gen_94},
Q_f={q_gen_122},
Delta=
{
<cons>(q_gen_140, q_gen_94) -> q_gen_139
<b>() -> q_gen_140
<z>() -> q_gen_142
<nil>() -> q_gen_94
<cons, s>(q_gen_123, q_gen_94) -> q_gen_122
<cons, s>(q_gen_141, q_gen_139) -> q_gen_122
<nil, z>() -> q_gen_122
<a, z>() -> q_gen_123
<b, z>() -> q_gen_123
<a, s>(q_gen_142) -> q_gen_141
<b, s>(q_gen_142) -> q_gen_141
<cons, s>(q_gen_123, q_gen_139) -> q_gen_143
<cons, s>(q_gen_141, q_gen_94) -> q_gen_143
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_108, q_gen_82},
Q_f={q_gen_108},
Delta=
{
<a, a>() -> q_gen_108
<a, b>() -> q_gen_108
<b, b>() -> q_gen_108
<b, a>() -> q_gen_82
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  leqnat -> 
{{{
Q={q_gen_106, q_gen_107, q_gen_145},
Q_f={q_gen_106},
Delta=
{
<s>(q_gen_107) -> q_gen_107
<z>() -> q_gen_107
<s, s>(q_gen_106) -> q_gen_106
<z, s>(q_gen_107) -> q_gen_106
<z, z>() -> q_gen_106
<s, s>(q_gen_145) -> q_gen_145
<s, z>(q_gen_107) -> q_gen_145
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  merge -> 
{{{
Q={q_gen_103, q_gen_104, q_gen_105, q_gen_118, q_gen_121, q_gen_85},
Q_f={q_gen_103},
Delta=
{
<a>() -> q_gen_118
<b>() -> q_gen_118
<nil>() -> q_gen_85
<cons, cons>(q_gen_105, q_gen_104) -> q_gen_104
<nil, cons>(q_gen_118, q_gen_85) -> q_gen_104
<nil, nil>() -> q_gen_104
<a, a>() -> q_gen_105
<a, b>() -> q_gen_105
<b, a>() -> q_gen_105
<b, b>() -> q_gen_105
<cons, cons, cons>(q_gen_121, q_gen_103) -> q_gen_103
<cons, nil, cons>(q_gen_105, q_gen_104) -> q_gen_103
<nil, cons, cons>(q_gen_105, q_gen_104) -> q_gen_103
<nil, nil, cons>(q_gen_118, q_gen_85) -> q_gen_103
<nil, nil, nil>() -> q_gen_103
<a, a, a>() -> q_gen_121
<a, b, a>() -> q_gen_121
<b, a, a>() -> q_gen_121
<b, a, b>() -> q_gen_121
<b, b, b>() -> q_gen_121
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_101, q_gen_102, q_gen_115},
Q_f={q_gen_101},
Delta=
{
<s>(q_gen_115) -> q_gen_115
<z>() -> q_gen_115
<s, s>(q_gen_102) -> q_gen_102
<z, s>(q_gen_115) -> q_gen_102
<z, z>() -> q_gen_102
<s, s, s>(q_gen_101) -> q_gen_101
<s, z, s>(q_gen_102) -> q_gen_101
<z, s, s>(q_gen_102) -> q_gen_101
<z, z, s>(q_gen_115) -> q_gen_101
<z, z, z>() -> q_gen_101
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 10
() -> length([nil, z]) -> 10
() -> leq([a, n2]) -> 10
() -> leq([b, b]) -> 10
() -> leqnat([z, n2]) -> 10
() -> merge([cons(z, xs), nil, cons(z, xs)]) -> 10
() -> merge([nil, y, y]) -> 12
() -> plus([n, z, n]) -> 10
(append([t1, l2, _s])) -> append([cons(h1, t1), l2, cons(h1, _s)]) -> 13
(length([_ha, _ia]) /\ length([l1, _ga]) /\ merge([l1, l2, _ha])) -> leqnat([_ga, _ia]) -> 11
(length([_ka, _la]) /\ length([l2, _ja]) /\ merge([l1, l2, _ka])) -> leqnat([_ja, _la]) -> 11
(length([ll, _ca])) -> length([cons(x, ll), s(_ca)]) -> 13
(leq([z, y2]) /\ merge([xs, cons(y2, ys), _m])) -> merge([cons(z, xs), cons(y2, ys), cons(z, _m)]) -> 13
(not leq([z, y2]) /\ merge([cons(z, xs), ys, _n])) -> merge([cons(z, xs), cons(y2, ys), cons(y2, _n)]) -> 13
(leq([b, a])) -> BOT -> 11
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 11
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 11
(leqnat([s(nn1), z])) -> BOT -> 11
(plus([n, mm, _x])) -> plus([n, s(mm), s(_x)]) -> 13
}
Sat witness: Found: ((append([t1, l2, _s])) -> append([cons(h1, t1), l2, cons(h1, _s)]), {
_s -> cons(b, nil)  ;  h1 -> a  ;  l2 -> cons(b, nil)  ;  t1 -> cons(b, nil)
})

-------------------------------------------
Step 41, which took 0.038647 s (model generation: 0.036739,  model checking: 0.001908):

Model:
|_
{
append -> 
{{{
Q={q_gen_100, q_gen_109, q_gen_110, q_gen_127, q_gen_128, q_gen_129},
Q_f={q_gen_109},
Delta=
{
<nil>() -> q_gen_127
<b>() -> q_gen_128
<a, a>() -> q_gen_100
<b, b>() -> q_gen_100
<cons, cons>(q_gen_100, q_gen_110) -> q_gen_110
<nil, cons>(q_gen_128, q_gen_127) -> q_gen_110
<nil, nil>() -> q_gen_110
<cons, cons, cons>(q_gen_129, q_gen_109) -> q_gen_109
<cons, nil, cons>(q_gen_100, q_gen_110) -> q_gen_109
<nil, cons, cons>(q_gen_100, q_gen_110) -> q_gen_109
<nil, nil, cons>(q_gen_128, q_gen_127) -> q_gen_109
<nil, nil, nil>() -> q_gen_109
<a, b, a>() -> q_gen_129
<b, b, b>() -> q_gen_129
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_122, q_gen_123, q_gen_139, q_gen_140, q_gen_141, q_gen_142, q_gen_143, q_gen_94},
Q_f={q_gen_122},
Delta=
{
<cons>(q_gen_140, q_gen_94) -> q_gen_139
<b>() -> q_gen_140
<z>() -> q_gen_142
<nil>() -> q_gen_94
<cons, s>(q_gen_123, q_gen_139) -> q_gen_122
<cons, s>(q_gen_123, q_gen_94) -> q_gen_122
<cons, s>(q_gen_141, q_gen_139) -> q_gen_122
<nil, z>() -> q_gen_122
<a, z>() -> q_gen_123
<b, z>() -> q_gen_123
<a, s>(q_gen_142) -> q_gen_141
<b, s>(q_gen_142) -> q_gen_141
<cons, s>(q_gen_141, q_gen_94) -> q_gen_143
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_108, q_gen_82},
Q_f={q_gen_108},
Delta=
{
<a, a>() -> q_gen_108
<a, b>() -> q_gen_108
<b, b>() -> q_gen_108
<b, a>() -> q_gen_82
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  leqnat -> 
{{{
Q={q_gen_106, q_gen_107, q_gen_145},
Q_f={q_gen_106},
Delta=
{
<s>(q_gen_107) -> q_gen_107
<z>() -> q_gen_107
<s, s>(q_gen_106) -> q_gen_106
<z, s>(q_gen_107) -> q_gen_106
<z, z>() -> q_gen_106
<s, s>(q_gen_145) -> q_gen_145
<s, z>(q_gen_107) -> q_gen_145
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  merge -> 
{{{
Q={q_gen_103, q_gen_104, q_gen_105, q_gen_118, q_gen_121, q_gen_85},
Q_f={q_gen_103},
Delta=
{
<a>() -> q_gen_118
<b>() -> q_gen_118
<nil>() -> q_gen_85
<cons, cons>(q_gen_105, q_gen_104) -> q_gen_104
<nil, cons>(q_gen_118, q_gen_85) -> q_gen_104
<nil, nil>() -> q_gen_104
<a, a>() -> q_gen_105
<a, b>() -> q_gen_105
<b, a>() -> q_gen_105
<b, b>() -> q_gen_105
<cons, cons, cons>(q_gen_121, q_gen_103) -> q_gen_103
<cons, nil, cons>(q_gen_105, q_gen_104) -> q_gen_103
<nil, cons, cons>(q_gen_105, q_gen_104) -> q_gen_103
<nil, nil, cons>(q_gen_118, q_gen_85) -> q_gen_103
<nil, nil, nil>() -> q_gen_103
<a, a, a>() -> q_gen_121
<a, b, a>() -> q_gen_121
<b, a, a>() -> q_gen_121
<b, a, b>() -> q_gen_121
<b, b, b>() -> q_gen_121
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_101, q_gen_102, q_gen_115},
Q_f={q_gen_101},
Delta=
{
<s>(q_gen_115) -> q_gen_115
<z>() -> q_gen_115
<s, s>(q_gen_102) -> q_gen_102
<z, s>(q_gen_115) -> q_gen_102
<z, z>() -> q_gen_102
<s, s, s>(q_gen_101) -> q_gen_101
<s, z, s>(q_gen_102) -> q_gen_101
<z, s, s>(q_gen_102) -> q_gen_101
<z, z, s>(q_gen_115) -> q_gen_101
<z, z, z>() -> q_gen_101
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 11
() -> length([nil, z]) -> 11
() -> leq([a, n2]) -> 11
() -> leq([b, b]) -> 11
() -> leqnat([z, n2]) -> 11
() -> merge([cons(z, xs), nil, cons(z, xs)]) -> 11
() -> merge([nil, y, y]) -> 12
() -> plus([n, z, n]) -> 11
(append([t1, l2, _s])) -> append([cons(h1, t1), l2, cons(h1, _s)]) -> 13
(length([_ha, _ia]) /\ length([l1, _ga]) /\ merge([l1, l2, _ha])) -> leqnat([_ga, _ia]) -> 11
(length([_ka, _la]) /\ length([l2, _ja]) /\ merge([l1, l2, _ka])) -> leqnat([_ja, _la]) -> 14
(length([ll, _ca])) -> length([cons(x, ll), s(_ca)]) -> 13
(leq([z, y2]) /\ merge([xs, cons(y2, ys), _m])) -> merge([cons(z, xs), cons(y2, ys), cons(z, _m)]) -> 13
(not leq([z, y2]) /\ merge([cons(z, xs), ys, _n])) -> merge([cons(z, xs), cons(y2, ys), cons(y2, _n)]) -> 13
(leq([b, a])) -> BOT -> 12
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 12
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 12
(leqnat([s(nn1), z])) -> BOT -> 12
(plus([n, mm, _x])) -> plus([n, s(mm), s(_x)]) -> 13
}
Sat witness: Found: ((length([_ka, _la]) /\ length([l2, _ja]) /\ merge([l1, l2, _ka])) -> leqnat([_ja, _la]), {
_ja -> s(s(z))  ;  _ka -> cons(b, cons(b, nil))  ;  _la -> s(z)  ;  l1 -> nil  ;  l2 -> cons(b, cons(b, nil))
})

-------------------------------------------
Step 42, which took 0.041748 s (model generation: 0.037993,  model checking: 0.003755):

Model:
|_
{
append -> 
{{{
Q={q_gen_100, q_gen_109, q_gen_110, q_gen_127, q_gen_128, q_gen_129},
Q_f={q_gen_109},
Delta=
{
<nil>() -> q_gen_127
<b>() -> q_gen_128
<a, a>() -> q_gen_100
<b, b>() -> q_gen_100
<cons, cons>(q_gen_100, q_gen_110) -> q_gen_110
<nil, cons>(q_gen_128, q_gen_127) -> q_gen_110
<nil, nil>() -> q_gen_110
<cons, cons, cons>(q_gen_129, q_gen_109) -> q_gen_109
<cons, nil, cons>(q_gen_100, q_gen_110) -> q_gen_109
<nil, cons, cons>(q_gen_100, q_gen_110) -> q_gen_109
<nil, nil, cons>(q_gen_128, q_gen_127) -> q_gen_109
<nil, nil, nil>() -> q_gen_109
<a, b, a>() -> q_gen_129
<b, b, b>() -> q_gen_129
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_122, q_gen_123, q_gen_139, q_gen_140, q_gen_141, q_gen_142, q_gen_143, q_gen_94},
Q_f={q_gen_122},
Delta=
{
<cons>(q_gen_140, q_gen_94) -> q_gen_139
<b>() -> q_gen_140
<z>() -> q_gen_142
<nil>() -> q_gen_94
<cons, s>(q_gen_123, q_gen_94) -> q_gen_122
<cons, s>(q_gen_141, q_gen_139) -> q_gen_122
<nil, z>() -> q_gen_122
<a, z>() -> q_gen_123
<b, z>() -> q_gen_123
<a, s>(q_gen_142) -> q_gen_141
<b, s>(q_gen_142) -> q_gen_141
<cons, s>(q_gen_123, q_gen_139) -> q_gen_143
<cons, s>(q_gen_141, q_gen_94) -> q_gen_143
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_108, q_gen_82},
Q_f={q_gen_108},
Delta=
{
<a, a>() -> q_gen_108
<a, b>() -> q_gen_108
<b, b>() -> q_gen_108
<b, a>() -> q_gen_82
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  leqnat -> 
{{{
Q={q_gen_106, q_gen_107, q_gen_145},
Q_f={q_gen_106},
Delta=
{
<s>(q_gen_107) -> q_gen_107
<z>() -> q_gen_107
<s, s>(q_gen_106) -> q_gen_106
<z, s>(q_gen_107) -> q_gen_106
<z, z>() -> q_gen_106
<s, s>(q_gen_145) -> q_gen_145
<s, z>(q_gen_107) -> q_gen_145
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  merge -> 
{{{
Q={q_gen_103, q_gen_104, q_gen_105, q_gen_118, q_gen_121, q_gen_85},
Q_f={q_gen_103},
Delta=
{
<a>() -> q_gen_118
<b>() -> q_gen_118
<nil>() -> q_gen_85
<cons, cons>(q_gen_105, q_gen_104) -> q_gen_104
<nil, cons>(q_gen_118, q_gen_85) -> q_gen_104
<nil, nil>() -> q_gen_104
<a, a>() -> q_gen_105
<a, b>() -> q_gen_105
<b, a>() -> q_gen_105
<b, b>() -> q_gen_105
<cons, cons, cons>(q_gen_121, q_gen_103) -> q_gen_103
<cons, nil, cons>(q_gen_105, q_gen_104) -> q_gen_103
<nil, cons, cons>(q_gen_105, q_gen_104) -> q_gen_103
<nil, nil, cons>(q_gen_118, q_gen_85) -> q_gen_103
<nil, nil, nil>() -> q_gen_103
<a, a, a>() -> q_gen_121
<a, b, a>() -> q_gen_121
<b, a, a>() -> q_gen_121
<b, a, b>() -> q_gen_121
<b, b, b>() -> q_gen_121
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_101, q_gen_102, q_gen_115},
Q_f={q_gen_101},
Delta=
{
<s>(q_gen_115) -> q_gen_115
<z>() -> q_gen_115
<s, s>(q_gen_102) -> q_gen_102
<z, s>(q_gen_115) -> q_gen_102
<z, z>() -> q_gen_102
<s, s, s>(q_gen_101) -> q_gen_101
<s, z, s>(q_gen_102) -> q_gen_101
<z, s, s>(q_gen_102) -> q_gen_101
<z, z, s>(q_gen_115) -> q_gen_101
<z, z, z>() -> q_gen_101
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 12
() -> length([nil, z]) -> 12
() -> leq([a, n2]) -> 12
() -> leq([b, b]) -> 12
() -> leqnat([z, n2]) -> 12
() -> merge([cons(z, xs), nil, cons(z, xs)]) -> 12
() -> merge([nil, y, y]) -> 13
() -> plus([n, z, n]) -> 12
(append([t1, l2, _s])) -> append([cons(h1, t1), l2, cons(h1, _s)]) -> 13
(length([_ha, _ia]) /\ length([l1, _ga]) /\ merge([l1, l2, _ha])) -> leqnat([_ga, _ia]) -> 12
(length([_ka, _la]) /\ length([l2, _ja]) /\ merge([l1, l2, _ka])) -> leqnat([_ja, _la]) -> 14
(length([ll, _ca])) -> length([cons(x, ll), s(_ca)]) -> 13
(leq([z, y2]) /\ merge([xs, cons(y2, ys), _m])) -> merge([cons(z, xs), cons(y2, ys), cons(z, _m)]) -> 13
(not leq([z, y2]) /\ merge([cons(z, xs), ys, _n])) -> merge([cons(z, xs), cons(y2, ys), cons(y2, _n)]) -> 16
(leq([b, a])) -> BOT -> 13
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 13
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 13
(leqnat([s(nn1), z])) -> BOT -> 13
(plus([n, mm, _x])) -> plus([n, s(mm), s(_x)]) -> 14
}
Sat witness: Found: ((not leq([z, y2]) /\ merge([cons(z, xs), ys, _n])) -> merge([cons(z, xs), cons(y2, ys), cons(y2, _n)]), {
_n -> cons(b, cons(b, nil))  ;  xs -> nil  ;  y2 -> a  ;  ys -> nil  ;  z -> b
})

-------------------------------------------
Step 43, which took 0.049373 s (model generation: 0.044837,  model checking: 0.004536):

Model:
|_
{
append -> 
{{{
Q={q_gen_100, q_gen_109, q_gen_110, q_gen_127, q_gen_128, q_gen_129},
Q_f={q_gen_109},
Delta=
{
<nil>() -> q_gen_127
<b>() -> q_gen_128
<a, a>() -> q_gen_100
<b, b>() -> q_gen_100
<cons, cons>(q_gen_100, q_gen_110) -> q_gen_110
<nil, cons>(q_gen_128, q_gen_127) -> q_gen_110
<nil, nil>() -> q_gen_110
<cons, cons, cons>(q_gen_129, q_gen_109) -> q_gen_109
<cons, nil, cons>(q_gen_100, q_gen_110) -> q_gen_109
<nil, cons, cons>(q_gen_100, q_gen_110) -> q_gen_109
<nil, nil, cons>(q_gen_128, q_gen_127) -> q_gen_109
<nil, nil, nil>() -> q_gen_109
<a, b, a>() -> q_gen_129
<b, b, b>() -> q_gen_129
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_122, q_gen_123, q_gen_139, q_gen_140, q_gen_141, q_gen_142, q_gen_143, q_gen_94},
Q_f={q_gen_122},
Delta=
{
<cons>(q_gen_140, q_gen_94) -> q_gen_139
<b>() -> q_gen_140
<z>() -> q_gen_142
<nil>() -> q_gen_94
<cons, s>(q_gen_123, q_gen_94) -> q_gen_122
<cons, s>(q_gen_141, q_gen_139) -> q_gen_122
<nil, z>() -> q_gen_122
<a, z>() -> q_gen_123
<b, z>() -> q_gen_123
<a, s>(q_gen_142) -> q_gen_141
<b, s>(q_gen_142) -> q_gen_141
<cons, s>(q_gen_123, q_gen_139) -> q_gen_143
<cons, s>(q_gen_141, q_gen_94) -> q_gen_143
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_108, q_gen_82},
Q_f={q_gen_108},
Delta=
{
<a, a>() -> q_gen_108
<a, b>() -> q_gen_108
<b, b>() -> q_gen_108
<b, a>() -> q_gen_82
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  leqnat -> 
{{{
Q={q_gen_106, q_gen_107, q_gen_145},
Q_f={q_gen_106},
Delta=
{
<s>(q_gen_107) -> q_gen_107
<z>() -> q_gen_107
<s, s>(q_gen_106) -> q_gen_106
<z, s>(q_gen_107) -> q_gen_106
<z, z>() -> q_gen_106
<s, s>(q_gen_145) -> q_gen_145
<s, z>(q_gen_107) -> q_gen_145
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  merge -> 
{{{
Q={q_gen_103, q_gen_104, q_gen_105, q_gen_118, q_gen_121, q_gen_169},
Q_f={q_gen_103},
Delta=
{
<a>() -> q_gen_118
<b>() -> q_gen_118
<cons>(q_gen_118, q_gen_169) -> q_gen_169
<nil>() -> q_gen_169
<cons, cons>(q_gen_105, q_gen_104) -> q_gen_104
<nil, cons>(q_gen_118, q_gen_169) -> q_gen_104
<nil, nil>() -> q_gen_104
<a, a>() -> q_gen_105
<a, b>() -> q_gen_105
<b, a>() -> q_gen_105
<b, b>() -> q_gen_105
<cons, cons, cons>(q_gen_121, q_gen_103) -> q_gen_103
<cons, nil, cons>(q_gen_105, q_gen_104) -> q_gen_103
<nil, cons, cons>(q_gen_105, q_gen_104) -> q_gen_103
<nil, nil, cons>(q_gen_118, q_gen_169) -> q_gen_103
<nil, nil, nil>() -> q_gen_103
<a, a, a>() -> q_gen_121
<a, b, a>() -> q_gen_121
<b, a, a>() -> q_gen_121
<b, a, b>() -> q_gen_121
<b, b, b>() -> q_gen_121
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_101, q_gen_102, q_gen_115},
Q_f={q_gen_101},
Delta=
{
<s>(q_gen_115) -> q_gen_115
<z>() -> q_gen_115
<s, s>(q_gen_102) -> q_gen_102
<z, s>(q_gen_115) -> q_gen_102
<z, z>() -> q_gen_102
<s, s, s>(q_gen_101) -> q_gen_101
<s, z, s>(q_gen_102) -> q_gen_101
<z, s, s>(q_gen_102) -> q_gen_101
<z, z, s>(q_gen_115) -> q_gen_101
<z, z, z>() -> q_gen_101
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 13
() -> length([nil, z]) -> 13
() -> leq([a, n2]) -> 13
() -> leq([b, b]) -> 13
() -> leqnat([z, n2]) -> 13
() -> merge([cons(z, xs), nil, cons(z, xs)]) -> 13
() -> merge([nil, y, y]) -> 13
() -> plus([n, z, n]) -> 13
(append([t1, l2, _s])) -> append([cons(h1, t1), l2, cons(h1, _s)]) -> 13
(length([_ha, _ia]) /\ length([l1, _ga]) /\ merge([l1, l2, _ha])) -> leqnat([_ga, _ia]) -> 13
(length([_ka, _la]) /\ length([l2, _ja]) /\ merge([l1, l2, _ka])) -> leqnat([_ja, _la]) -> 14
(length([ll, _ca])) -> length([cons(x, ll), s(_ca)]) -> 13
(leq([z, y2]) /\ merge([xs, cons(y2, ys), _m])) -> merge([cons(z, xs), cons(y2, ys), cons(z, _m)]) -> 16
(not leq([z, y2]) /\ merge([cons(z, xs), ys, _n])) -> merge([cons(z, xs), cons(y2, ys), cons(y2, _n)]) -> 16
(leq([b, a])) -> BOT -> 14
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 14
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 14
(leqnat([s(nn1), z])) -> BOT -> 14
(plus([n, mm, _x])) -> plus([n, s(mm), s(_x)]) -> 14
}
Sat witness: Found: ((leq([z, y2]) /\ merge([xs, cons(y2, ys), _m])) -> merge([cons(z, xs), cons(y2, ys), cons(z, _m)]), {
_m -> cons(a, cons(b, nil))  ;  xs -> cons(b, nil)  ;  y2 -> a  ;  ys -> cons(b, nil)  ;  z -> a
})

-------------------------------------------
Step 44, which took 0.056595 s (model generation: 0.055227,  model checking: 0.001368):

Model:
|_
{
append -> 
{{{
Q={q_gen_100, q_gen_109, q_gen_110, q_gen_127, q_gen_128, q_gen_129},
Q_f={q_gen_109},
Delta=
{
<nil>() -> q_gen_127
<b>() -> q_gen_128
<a, a>() -> q_gen_100
<b, b>() -> q_gen_100
<cons, cons>(q_gen_100, q_gen_110) -> q_gen_110
<nil, cons>(q_gen_128, q_gen_127) -> q_gen_110
<nil, nil>() -> q_gen_110
<cons, cons, cons>(q_gen_129, q_gen_109) -> q_gen_109
<cons, nil, cons>(q_gen_100, q_gen_110) -> q_gen_109
<nil, cons, cons>(q_gen_100, q_gen_110) -> q_gen_109
<nil, nil, cons>(q_gen_128, q_gen_127) -> q_gen_109
<nil, nil, nil>() -> q_gen_109
<a, b, a>() -> q_gen_129
<b, b, b>() -> q_gen_129
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_122, q_gen_123, q_gen_139, q_gen_140, q_gen_141, q_gen_142, q_gen_143, q_gen_94},
Q_f={q_gen_122},
Delta=
{
<cons>(q_gen_140, q_gen_94) -> q_gen_139
<b>() -> q_gen_140
<z>() -> q_gen_142
<nil>() -> q_gen_94
<cons, s>(q_gen_123, q_gen_94) -> q_gen_122
<cons, s>(q_gen_141, q_gen_139) -> q_gen_122
<nil, z>() -> q_gen_122
<a, z>() -> q_gen_123
<b, z>() -> q_gen_123
<a, s>(q_gen_142) -> q_gen_141
<b, s>(q_gen_142) -> q_gen_141
<cons, s>(q_gen_123, q_gen_139) -> q_gen_143
<cons, s>(q_gen_141, q_gen_94) -> q_gen_143
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_108, q_gen_82},
Q_f={q_gen_108},
Delta=
{
<a, a>() -> q_gen_108
<a, b>() -> q_gen_108
<b, b>() -> q_gen_108
<b, a>() -> q_gen_82
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  leqnat -> 
{{{
Q={q_gen_106, q_gen_107, q_gen_145},
Q_f={q_gen_106},
Delta=
{
<s>(q_gen_107) -> q_gen_107
<z>() -> q_gen_107
<s, s>(q_gen_106) -> q_gen_106
<z, s>(q_gen_107) -> q_gen_106
<z, z>() -> q_gen_106
<s, s>(q_gen_145) -> q_gen_145
<s, z>(q_gen_107) -> q_gen_145
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  merge -> 
{{{
Q={q_gen_103, q_gen_104, q_gen_105, q_gen_118, q_gen_121, q_gen_169},
Q_f={q_gen_103},
Delta=
{
<a>() -> q_gen_118
<b>() -> q_gen_118
<cons>(q_gen_118, q_gen_169) -> q_gen_169
<nil>() -> q_gen_169
<cons, cons>(q_gen_105, q_gen_104) -> q_gen_104
<nil, cons>(q_gen_118, q_gen_169) -> q_gen_104
<nil, nil>() -> q_gen_104
<a, a>() -> q_gen_105
<a, b>() -> q_gen_105
<b, a>() -> q_gen_105
<b, b>() -> q_gen_105
<cons, cons, cons>(q_gen_121, q_gen_103) -> q_gen_103
<cons, nil, cons>(q_gen_105, q_gen_104) -> q_gen_103
<nil, cons, cons>(q_gen_105, q_gen_104) -> q_gen_103
<nil, nil, cons>(q_gen_118, q_gen_169) -> q_gen_103
<nil, nil, nil>() -> q_gen_103
<a, a, a>() -> q_gen_121
<a, b, a>() -> q_gen_121
<b, a, a>() -> q_gen_121
<b, a, b>() -> q_gen_121
<b, b, a>() -> q_gen_121
<b, b, b>() -> q_gen_121
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_101, q_gen_102, q_gen_115},
Q_f={q_gen_101},
Delta=
{
<s>(q_gen_115) -> q_gen_115
<z>() -> q_gen_115
<s, s>(q_gen_102) -> q_gen_102
<z, s>(q_gen_115) -> q_gen_102
<z, z>() -> q_gen_102
<s, s, s>(q_gen_101) -> q_gen_101
<s, z, s>(q_gen_102) -> q_gen_101
<z, s, s>(q_gen_102) -> q_gen_101
<z, z, s>(q_gen_115) -> q_gen_101
<z, z, z>() -> q_gen_101
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 13
() -> length([nil, z]) -> 13
() -> leq([a, n2]) -> 13
() -> leq([b, b]) -> 13
() -> leqnat([z, n2]) -> 13
() -> merge([cons(z, xs), nil, cons(z, xs)]) -> 13
() -> merge([nil, y, y]) -> 13
() -> plus([n, z, n]) -> 13
(append([t1, l2, _s])) -> append([cons(h1, t1), l2, cons(h1, _s)]) -> 13
(length([_ha, _ia]) /\ length([l1, _ga]) /\ merge([l1, l2, _ha])) -> leqnat([_ga, _ia]) -> 13
(length([_ka, _la]) /\ length([l2, _ja]) /\ merge([l1, l2, _ka])) -> leqnat([_ja, _la]) -> 14
(length([ll, _ca])) -> length([cons(x, ll), s(_ca)]) -> 16
(leq([z, y2]) /\ merge([xs, cons(y2, ys), _m])) -> merge([cons(z, xs), cons(y2, ys), cons(z, _m)]) -> 16
(not leq([z, y2]) /\ merge([cons(z, xs), ys, _n])) -> merge([cons(z, xs), cons(y2, ys), cons(y2, _n)]) -> 16
(leq([b, a])) -> BOT -> 14
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 14
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 14
(leqnat([s(nn1), z])) -> BOT -> 14
(plus([n, mm, _x])) -> plus([n, s(mm), s(_x)]) -> 14
}
Sat witness: Found: ((length([ll, _ca])) -> length([cons(x, ll), s(_ca)]), {
_ca -> s(s(z))  ;  ll -> cons(a, cons(b, nil))  ;  x -> b
})

-------------------------------------------
Step 45, which took 0.080180 s (model generation: 0.078824,  model checking: 0.001356):

Model:
|_
{
append -> 
{{{
Q={q_gen_100, q_gen_109, q_gen_110, q_gen_127, q_gen_128, q_gen_129},
Q_f={q_gen_109},
Delta=
{
<nil>() -> q_gen_127
<b>() -> q_gen_128
<a, a>() -> q_gen_100
<b, b>() -> q_gen_100
<cons, cons>(q_gen_100, q_gen_110) -> q_gen_110
<nil, cons>(q_gen_128, q_gen_127) -> q_gen_110
<nil, nil>() -> q_gen_110
<cons, cons, cons>(q_gen_129, q_gen_109) -> q_gen_109
<cons, nil, cons>(q_gen_100, q_gen_110) -> q_gen_109
<nil, cons, cons>(q_gen_100, q_gen_110) -> q_gen_109
<nil, nil, cons>(q_gen_128, q_gen_127) -> q_gen_109
<nil, nil, nil>() -> q_gen_109
<a, b, a>() -> q_gen_129
<b, b, b>() -> q_gen_129
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_122, q_gen_123, q_gen_139, q_gen_140, q_gen_141, q_gen_142, q_gen_143, q_gen_94},
Q_f={q_gen_122},
Delta=
{
<cons>(q_gen_140, q_gen_139) -> q_gen_139
<cons>(q_gen_140, q_gen_94) -> q_gen_139
<a>() -> q_gen_140
<b>() -> q_gen_140
<s>(q_gen_142) -> q_gen_142
<z>() -> q_gen_142
<nil>() -> q_gen_94
<cons, s>(q_gen_123, q_gen_94) -> q_gen_122
<cons, s>(q_gen_141, q_gen_139) -> q_gen_122
<nil, z>() -> q_gen_122
<a, z>() -> q_gen_123
<b, z>() -> q_gen_123
<a, s>(q_gen_142) -> q_gen_141
<b, s>(q_gen_142) -> q_gen_141
<cons, s>(q_gen_123, q_gen_139) -> q_gen_143
<cons, s>(q_gen_141, q_gen_94) -> q_gen_143
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_108, q_gen_82},
Q_f={q_gen_108},
Delta=
{
<a, a>() -> q_gen_108
<a, b>() -> q_gen_108
<b, b>() -> q_gen_108
<b, a>() -> q_gen_82
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  leqnat -> 
{{{
Q={q_gen_106, q_gen_107, q_gen_145},
Q_f={q_gen_106},
Delta=
{
<s>(q_gen_107) -> q_gen_107
<z>() -> q_gen_107
<s, s>(q_gen_106) -> q_gen_106
<z, s>(q_gen_107) -> q_gen_106
<z, z>() -> q_gen_106
<s, s>(q_gen_145) -> q_gen_145
<s, z>(q_gen_107) -> q_gen_145
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  merge -> 
{{{
Q={q_gen_103, q_gen_104, q_gen_105, q_gen_118, q_gen_121, q_gen_169},
Q_f={q_gen_103},
Delta=
{
<a>() -> q_gen_118
<b>() -> q_gen_118
<cons>(q_gen_118, q_gen_169) -> q_gen_169
<nil>() -> q_gen_169
<cons, cons>(q_gen_105, q_gen_104) -> q_gen_104
<nil, cons>(q_gen_118, q_gen_169) -> q_gen_104
<nil, nil>() -> q_gen_104
<a, a>() -> q_gen_105
<a, b>() -> q_gen_105
<b, a>() -> q_gen_105
<b, b>() -> q_gen_105
<cons, cons, cons>(q_gen_121, q_gen_103) -> q_gen_103
<cons, nil, cons>(q_gen_105, q_gen_104) -> q_gen_103
<nil, cons, cons>(q_gen_105, q_gen_104) -> q_gen_103
<nil, nil, cons>(q_gen_118, q_gen_169) -> q_gen_103
<nil, nil, nil>() -> q_gen_103
<a, a, a>() -> q_gen_121
<a, b, a>() -> q_gen_121
<b, a, a>() -> q_gen_121
<b, a, b>() -> q_gen_121
<b, b, a>() -> q_gen_121
<b, b, b>() -> q_gen_121
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_101, q_gen_102, q_gen_115},
Q_f={q_gen_101},
Delta=
{
<s>(q_gen_115) -> q_gen_115
<z>() -> q_gen_115
<s, s>(q_gen_102) -> q_gen_102
<z, s>(q_gen_115) -> q_gen_102
<z, z>() -> q_gen_102
<s, s, s>(q_gen_101) -> q_gen_101
<s, z, s>(q_gen_102) -> q_gen_101
<z, s, s>(q_gen_102) -> q_gen_101
<z, z, s>(q_gen_115) -> q_gen_101
<z, z, z>() -> q_gen_101
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 13
() -> length([nil, z]) -> 13
() -> leq([a, n2]) -> 13
() -> leq([b, b]) -> 13
() -> leqnat([z, n2]) -> 13
() -> merge([cons(z, xs), nil, cons(z, xs)]) -> 13
() -> merge([nil, y, y]) -> 13
() -> plus([n, z, n]) -> 13
(append([t1, l2, _s])) -> append([cons(h1, t1), l2, cons(h1, _s)]) -> 13
(length([_ha, _ia]) /\ length([l1, _ga]) /\ merge([l1, l2, _ha])) -> leqnat([_ga, _ia]) -> 16
(length([_ka, _la]) /\ length([l2, _ja]) /\ merge([l1, l2, _ka])) -> leqnat([_ja, _la]) -> 14
(length([ll, _ca])) -> length([cons(x, ll), s(_ca)]) -> 16
(leq([z, y2]) /\ merge([xs, cons(y2, ys), _m])) -> merge([cons(z, xs), cons(y2, ys), cons(z, _m)]) -> 16
(not leq([z, y2]) /\ merge([cons(z, xs), ys, _n])) -> merge([cons(z, xs), cons(y2, ys), cons(y2, _n)]) -> 16
(leq([b, a])) -> BOT -> 14
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 14
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 14
(leqnat([s(nn1), z])) -> BOT -> 14
(plus([n, mm, _x])) -> plus([n, s(mm), s(_x)]) -> 14
}
Sat witness: Found: ((length([_ha, _ia]) /\ length([l1, _ga]) /\ merge([l1, l2, _ha])) -> leqnat([_ga, _ia]), {
_ga -> s(s(s(z)))  ;  _ha -> cons(b, cons(b, cons(b, nil)))  ;  _ia -> s(s(z))  ;  l1 -> cons(b, cons(b, nil))  ;  l2 -> nil
})

-------------------------------------------
Step 46, which took 0.127510 s (model generation: 0.125780,  model checking: 0.001730):

Model:
|_
{
append -> 
{{{
Q={q_gen_100, q_gen_109, q_gen_110, q_gen_127, q_gen_128, q_gen_129},
Q_f={q_gen_109},
Delta=
{
<nil>() -> q_gen_127
<b>() -> q_gen_128
<a, a>() -> q_gen_100
<b, b>() -> q_gen_100
<cons, cons>(q_gen_100, q_gen_110) -> q_gen_110
<nil, cons>(q_gen_128, q_gen_127) -> q_gen_110
<nil, nil>() -> q_gen_110
<cons, cons, cons>(q_gen_129, q_gen_109) -> q_gen_109
<cons, nil, cons>(q_gen_100, q_gen_110) -> q_gen_109
<nil, cons, cons>(q_gen_100, q_gen_110) -> q_gen_109
<nil, nil, cons>(q_gen_128, q_gen_127) -> q_gen_109
<nil, nil, nil>() -> q_gen_109
<a, b, a>() -> q_gen_129
<b, b, b>() -> q_gen_129
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_122, q_gen_123, q_gen_139, q_gen_140, q_gen_141, q_gen_142, q_gen_143, q_gen_94},
Q_f={q_gen_122},
Delta=
{
<cons>(q_gen_140, q_gen_139) -> q_gen_139
<cons>(q_gen_140, q_gen_94) -> q_gen_139
<a>() -> q_gen_140
<b>() -> q_gen_140
<s>(q_gen_142) -> q_gen_142
<z>() -> q_gen_142
<nil>() -> q_gen_94
<cons, s>(q_gen_123, q_gen_94) -> q_gen_122
<cons, s>(q_gen_141, q_gen_139) -> q_gen_122
<nil, z>() -> q_gen_122
<a, z>() -> q_gen_123
<b, z>() -> q_gen_123
<a, s>(q_gen_142) -> q_gen_141
<b, s>(q_gen_142) -> q_gen_141
<cons, s>(q_gen_123, q_gen_139) -> q_gen_143
<cons, s>(q_gen_141, q_gen_94) -> q_gen_143
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_108, q_gen_82},
Q_f={q_gen_108},
Delta=
{
<a, a>() -> q_gen_108
<a, b>() -> q_gen_108
<b, b>() -> q_gen_108
<b, a>() -> q_gen_82
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  leqnat -> 
{{{
Q={q_gen_106, q_gen_107, q_gen_145, q_gen_146},
Q_f={q_gen_106},
Delta=
{
<s>(q_gen_107) -> q_gen_107
<z>() -> q_gen_107
<s, s>(q_gen_106) -> q_gen_106
<s, s>(q_gen_145) -> q_gen_106
<z, s>(q_gen_107) -> q_gen_106
<z, z>() -> q_gen_106
<s, s>(q_gen_146) -> q_gen_145
<s, z>(q_gen_107) -> q_gen_146
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  merge -> 
{{{
Q={q_gen_103, q_gen_104, q_gen_105, q_gen_118, q_gen_121, q_gen_169},
Q_f={q_gen_103},
Delta=
{
<a>() -> q_gen_118
<b>() -> q_gen_118
<cons>(q_gen_118, q_gen_169) -> q_gen_169
<nil>() -> q_gen_169
<cons, cons>(q_gen_105, q_gen_104) -> q_gen_104
<nil, cons>(q_gen_118, q_gen_169) -> q_gen_104
<nil, nil>() -> q_gen_104
<a, a>() -> q_gen_105
<a, b>() -> q_gen_105
<b, a>() -> q_gen_105
<b, b>() -> q_gen_105
<cons, cons, cons>(q_gen_121, q_gen_103) -> q_gen_103
<cons, nil, cons>(q_gen_105, q_gen_104) -> q_gen_103
<nil, cons, cons>(q_gen_105, q_gen_104) -> q_gen_103
<nil, nil, cons>(q_gen_118, q_gen_169) -> q_gen_103
<nil, nil, nil>() -> q_gen_103
<a, a, a>() -> q_gen_121
<a, b, a>() -> q_gen_121
<b, a, a>() -> q_gen_121
<b, a, b>() -> q_gen_121
<b, b, a>() -> q_gen_121
<b, b, b>() -> q_gen_121
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_101, q_gen_102, q_gen_115},
Q_f={q_gen_101},
Delta=
{
<s>(q_gen_115) -> q_gen_115
<z>() -> q_gen_115
<s, s>(q_gen_102) -> q_gen_102
<z, s>(q_gen_115) -> q_gen_102
<z, z>() -> q_gen_102
<s, s, s>(q_gen_101) -> q_gen_101
<s, z, s>(q_gen_102) -> q_gen_101
<z, s, s>(q_gen_102) -> q_gen_101
<z, z, s>(q_gen_115) -> q_gen_101
<z, z, z>() -> q_gen_101
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 13
() -> length([nil, z]) -> 13
() -> leq([a, n2]) -> 13
() -> leq([b, b]) -> 13
() -> leqnat([z, n2]) -> 13
() -> merge([cons(z, xs), nil, cons(z, xs)]) -> 13
() -> merge([nil, y, y]) -> 13
() -> plus([n, z, n]) -> 13
(append([t1, l2, _s])) -> append([cons(h1, t1), l2, cons(h1, _s)]) -> 16
(length([_ha, _ia]) /\ length([l1, _ga]) /\ merge([l1, l2, _ha])) -> leqnat([_ga, _ia]) -> 16
(length([_ka, _la]) /\ length([l2, _ja]) /\ merge([l1, l2, _ka])) -> leqnat([_ja, _la]) -> 14
(length([ll, _ca])) -> length([cons(x, ll), s(_ca)]) -> 16
(leq([z, y2]) /\ merge([xs, cons(y2, ys), _m])) -> merge([cons(z, xs), cons(y2, ys), cons(z, _m)]) -> 16
(not leq([z, y2]) /\ merge([cons(z, xs), ys, _n])) -> merge([cons(z, xs), cons(y2, ys), cons(y2, _n)]) -> 16
(leq([b, a])) -> BOT -> 14
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 14
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 14
(leqnat([s(nn1), z])) -> BOT -> 14
(plus([n, mm, _x])) -> plus([n, s(mm), s(_x)]) -> 14
}
Sat witness: Found: ((append([t1, l2, _s])) -> append([cons(h1, t1), l2, cons(h1, _s)]), {
_s -> cons(a, nil)  ;  h1 -> b  ;  l2 -> cons(a, nil)  ;  t1 -> nil
})

-------------------------------------------
Step 47, which took 0.115840 s (model generation: 0.112544,  model checking: 0.003296):

Model:
|_
{
append -> 
{{{
Q={q_gen_100, q_gen_109, q_gen_110, q_gen_127, q_gen_128, q_gen_129},
Q_f={q_gen_109},
Delta=
{
<nil>() -> q_gen_127
<a>() -> q_gen_128
<b>() -> q_gen_128
<a, a>() -> q_gen_100
<b, b>() -> q_gen_100
<cons, cons>(q_gen_100, q_gen_110) -> q_gen_110
<nil, cons>(q_gen_128, q_gen_127) -> q_gen_110
<nil, nil>() -> q_gen_110
<cons, cons, cons>(q_gen_129, q_gen_109) -> q_gen_109
<cons, nil, cons>(q_gen_100, q_gen_110) -> q_gen_109
<nil, cons, cons>(q_gen_100, q_gen_110) -> q_gen_109
<nil, nil, cons>(q_gen_128, q_gen_127) -> q_gen_109
<nil, nil, nil>() -> q_gen_109
<a, b, a>() -> q_gen_129
<b, a, b>() -> q_gen_129
<b, b, b>() -> q_gen_129
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_122, q_gen_123, q_gen_139, q_gen_140, q_gen_141, q_gen_142, q_gen_143, q_gen_175, q_gen_178},
Q_f={q_gen_122},
Delta=
{
<cons>(q_gen_140, q_gen_175) -> q_gen_139
<a>() -> q_gen_140
<b>() -> q_gen_140
<z>() -> q_gen_142
<cons>(q_gen_140, q_gen_139) -> q_gen_175
<nil>() -> q_gen_175
<s>(q_gen_142) -> q_gen_178
<cons, s>(q_gen_123, q_gen_175) -> q_gen_122
<cons, s>(q_gen_141, q_gen_139) -> q_gen_122
<nil, z>() -> q_gen_122
<a, z>() -> q_gen_123
<b, s>(q_gen_178) -> q_gen_123
<b, z>() -> q_gen_123
<a, s>(q_gen_142) -> q_gen_141
<b, s>(q_gen_142) -> q_gen_141
<cons, s>(q_gen_123, q_gen_139) -> q_gen_143
<cons, s>(q_gen_141, q_gen_175) -> q_gen_143
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_108, q_gen_82},
Q_f={q_gen_108},
Delta=
{
<a, a>() -> q_gen_108
<a, b>() -> q_gen_108
<b, b>() -> q_gen_108
<b, a>() -> q_gen_82
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  leqnat -> 
{{{
Q={q_gen_106, q_gen_107, q_gen_145},
Q_f={q_gen_106},
Delta=
{
<s>(q_gen_107) -> q_gen_107
<z>() -> q_gen_107
<s, s>(q_gen_106) -> q_gen_106
<z, s>(q_gen_107) -> q_gen_106
<z, z>() -> q_gen_106
<s, s>(q_gen_145) -> q_gen_145
<s, z>(q_gen_107) -> q_gen_145
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  merge -> 
{{{
Q={q_gen_103, q_gen_104, q_gen_105, q_gen_118, q_gen_121, q_gen_169},
Q_f={q_gen_103},
Delta=
{
<a>() -> q_gen_118
<b>() -> q_gen_118
<cons>(q_gen_118, q_gen_169) -> q_gen_169
<nil>() -> q_gen_169
<cons, cons>(q_gen_105, q_gen_104) -> q_gen_104
<nil, cons>(q_gen_118, q_gen_169) -> q_gen_104
<nil, nil>() -> q_gen_104
<a, a>() -> q_gen_105
<a, b>() -> q_gen_105
<b, a>() -> q_gen_105
<b, b>() -> q_gen_105
<cons, cons, cons>(q_gen_121, q_gen_103) -> q_gen_103
<cons, nil, cons>(q_gen_105, q_gen_104) -> q_gen_103
<nil, cons, cons>(q_gen_105, q_gen_104) -> q_gen_103
<nil, nil, cons>(q_gen_118, q_gen_169) -> q_gen_103
<nil, nil, nil>() -> q_gen_103
<a, a, a>() -> q_gen_121
<a, b, a>() -> q_gen_121
<b, a, a>() -> q_gen_121
<b, a, b>() -> q_gen_121
<b, b, a>() -> q_gen_121
<b, b, b>() -> q_gen_121
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_101, q_gen_102, q_gen_115},
Q_f={q_gen_101},
Delta=
{
<s>(q_gen_115) -> q_gen_115
<z>() -> q_gen_115
<s, s>(q_gen_102) -> q_gen_102
<z, s>(q_gen_115) -> q_gen_102
<z, z>() -> q_gen_102
<s, s, s>(q_gen_101) -> q_gen_101
<s, z, s>(q_gen_102) -> q_gen_101
<z, s, s>(q_gen_102) -> q_gen_101
<z, z, s>(q_gen_115) -> q_gen_101
<z, z, z>() -> q_gen_101
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 14
() -> length([nil, z]) -> 14
() -> leq([a, n2]) -> 14
() -> leq([b, b]) -> 14
() -> leqnat([z, n2]) -> 14
() -> merge([cons(z, xs), nil, cons(z, xs)]) -> 14
() -> merge([nil, y, y]) -> 14
() -> plus([n, z, n]) -> 14
(append([t1, l2, _s])) -> append([cons(h1, t1), l2, cons(h1, _s)]) -> 16
(length([_ha, _ia]) /\ length([l1, _ga]) /\ merge([l1, l2, _ha])) -> leqnat([_ga, _ia]) -> 16
(length([_ka, _la]) /\ length([l2, _ja]) /\ merge([l1, l2, _ka])) -> leqnat([_ja, _la]) -> 17
(length([ll, _ca])) -> length([cons(x, ll), s(_ca)]) -> 16
(leq([z, y2]) /\ merge([xs, cons(y2, ys), _m])) -> merge([cons(z, xs), cons(y2, ys), cons(z, _m)]) -> 16
(not leq([z, y2]) /\ merge([cons(z, xs), ys, _n])) -> merge([cons(z, xs), cons(y2, ys), cons(y2, _n)]) -> 16
(leq([b, a])) -> BOT -> 15
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 15
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 15
(leqnat([s(nn1), z])) -> BOT -> 15
(plus([n, mm, _x])) -> plus([n, s(mm), s(_x)]) -> 15
}
Sat witness: Found: ((length([_ka, _la]) /\ length([l2, _ja]) /\ merge([l1, l2, _ka])) -> leqnat([_ja, _la]), {
_ja -> s(s(s(z)))  ;  _ka -> cons(b, cons(b, nil))  ;  _la -> s(s(z))  ;  l1 -> nil  ;  l2 -> cons(b, nil)
})

-------------------------------------------
Step 48, which took 0.109420 s (model generation: 0.107834,  model checking: 0.001586):

Model:
|_
{
append -> 
{{{
Q={q_gen_100, q_gen_109, q_gen_110, q_gen_127, q_gen_128, q_gen_129},
Q_f={q_gen_109},
Delta=
{
<nil>() -> q_gen_127
<a>() -> q_gen_128
<b>() -> q_gen_128
<a, a>() -> q_gen_100
<b, b>() -> q_gen_100
<cons, cons>(q_gen_100, q_gen_110) -> q_gen_110
<nil, cons>(q_gen_128, q_gen_127) -> q_gen_110
<nil, nil>() -> q_gen_110
<cons, cons, cons>(q_gen_129, q_gen_109) -> q_gen_109
<cons, nil, cons>(q_gen_100, q_gen_110) -> q_gen_109
<nil, cons, cons>(q_gen_100, q_gen_110) -> q_gen_109
<nil, nil, cons>(q_gen_128, q_gen_127) -> q_gen_109
<nil, nil, nil>() -> q_gen_109
<a, b, a>() -> q_gen_129
<b, a, b>() -> q_gen_129
<b, b, b>() -> q_gen_129
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_122, q_gen_123, q_gen_139, q_gen_140, q_gen_141, q_gen_142, q_gen_143, q_gen_94},
Q_f={q_gen_122},
Delta=
{
<cons>(q_gen_140, q_gen_139) -> q_gen_139
<cons>(q_gen_140, q_gen_94) -> q_gen_139
<a>() -> q_gen_140
<b>() -> q_gen_140
<s>(q_gen_142) -> q_gen_142
<z>() -> q_gen_142
<nil>() -> q_gen_94
<cons, s>(q_gen_123, q_gen_94) -> q_gen_122
<cons, s>(q_gen_141, q_gen_139) -> q_gen_122
<nil, z>() -> q_gen_122
<a, z>() -> q_gen_123
<b, z>() -> q_gen_123
<a, s>(q_gen_142) -> q_gen_141
<b, s>(q_gen_142) -> q_gen_141
<cons, s>(q_gen_123, q_gen_139) -> q_gen_143
<cons, s>(q_gen_141, q_gen_94) -> q_gen_143
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_108, q_gen_82},
Q_f={q_gen_108},
Delta=
{
<a, a>() -> q_gen_108
<a, b>() -> q_gen_108
<b, b>() -> q_gen_108
<b, a>() -> q_gen_82
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  leqnat -> 
{{{
Q={q_gen_106, q_gen_107, q_gen_145, q_gen_146},
Q_f={q_gen_106},
Delta=
{
<s>(q_gen_107) -> q_gen_107
<z>() -> q_gen_107
<s, s>(q_gen_106) -> q_gen_106
<s, s>(q_gen_145) -> q_gen_106
<z, s>(q_gen_107) -> q_gen_106
<z, z>() -> q_gen_106
<s, s>(q_gen_146) -> q_gen_145
<s, z>(q_gen_107) -> q_gen_146
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  merge -> 
{{{
Q={q_gen_103, q_gen_104, q_gen_105, q_gen_118, q_gen_121, q_gen_169},
Q_f={q_gen_103},
Delta=
{
<a>() -> q_gen_118
<b>() -> q_gen_118
<cons>(q_gen_118, q_gen_169) -> q_gen_169
<nil>() -> q_gen_169
<cons, cons>(q_gen_105, q_gen_104) -> q_gen_104
<nil, cons>(q_gen_118, q_gen_169) -> q_gen_104
<nil, nil>() -> q_gen_104
<a, a>() -> q_gen_105
<a, b>() -> q_gen_105
<b, a>() -> q_gen_105
<b, b>() -> q_gen_105
<cons, cons, cons>(q_gen_121, q_gen_103) -> q_gen_103
<cons, nil, cons>(q_gen_105, q_gen_104) -> q_gen_103
<nil, cons, cons>(q_gen_105, q_gen_104) -> q_gen_103
<nil, nil, cons>(q_gen_118, q_gen_169) -> q_gen_103
<nil, nil, nil>() -> q_gen_103
<a, a, a>() -> q_gen_121
<a, b, a>() -> q_gen_121
<b, a, a>() -> q_gen_121
<b, a, b>() -> q_gen_121
<b, b, a>() -> q_gen_121
<b, b, b>() -> q_gen_121
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_101, q_gen_102, q_gen_115},
Q_f={q_gen_101},
Delta=
{
<s>(q_gen_115) -> q_gen_115
<z>() -> q_gen_115
<s, s>(q_gen_102) -> q_gen_102
<z, s>(q_gen_115) -> q_gen_102
<z, z>() -> q_gen_102
<s, s, s>(q_gen_101) -> q_gen_101
<s, z, s>(q_gen_102) -> q_gen_101
<z, s, s>(q_gen_102) -> q_gen_101
<z, z, s>(q_gen_115) -> q_gen_101
<z, z, z>() -> q_gen_101
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 15
() -> length([nil, z]) -> 15
() -> leq([a, n2]) -> 15
() -> leq([b, b]) -> 15
() -> leqnat([z, n2]) -> 15
() -> merge([cons(z, xs), nil, cons(z, xs)]) -> 15
() -> merge([nil, y, y]) -> 15
() -> plus([n, z, n]) -> 15
(append([t1, l2, _s])) -> append([cons(h1, t1), l2, cons(h1, _s)]) -> 16
(length([_ha, _ia]) /\ length([l1, _ga]) /\ merge([l1, l2, _ha])) -> leqnat([_ga, _ia]) -> 16
(length([_ka, _la]) /\ length([l2, _ja]) /\ merge([l1, l2, _ka])) -> leqnat([_ja, _la]) -> 17
(length([ll, _ca])) -> length([cons(x, ll), s(_ca)]) -> 16
(leq([z, y2]) /\ merge([xs, cons(y2, ys), _m])) -> merge([cons(z, xs), cons(y2, ys), cons(z, _m)]) -> 16
(not leq([z, y2]) /\ merge([cons(z, xs), ys, _n])) -> merge([cons(z, xs), cons(y2, ys), cons(y2, _n)]) -> 16
(leq([b, a])) -> BOT -> 15
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 15
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 18
(leqnat([s(nn1), z])) -> BOT -> 16
(plus([n, mm, _x])) -> plus([n, s(mm), s(_x)]) -> 16
}
Sat witness: Found: ((leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]), {
nn1 -> s(s(z))  ;  nn2 -> s(z)
})

-------------------------------------------
Step 49, which took 0.101352 s (model generation: 0.096756,  model checking: 0.004596):

Model:
|_
{
append -> 
{{{
Q={q_gen_100, q_gen_109, q_gen_110, q_gen_127, q_gen_128, q_gen_129},
Q_f={q_gen_109},
Delta=
{
<nil>() -> q_gen_127
<a>() -> q_gen_128
<b>() -> q_gen_128
<a, a>() -> q_gen_100
<b, b>() -> q_gen_100
<cons, cons>(q_gen_100, q_gen_110) -> q_gen_110
<nil, cons>(q_gen_128, q_gen_127) -> q_gen_110
<nil, nil>() -> q_gen_110
<cons, cons, cons>(q_gen_129, q_gen_109) -> q_gen_109
<cons, nil, cons>(q_gen_100, q_gen_110) -> q_gen_109
<nil, cons, cons>(q_gen_100, q_gen_110) -> q_gen_109
<nil, nil, cons>(q_gen_128, q_gen_127) -> q_gen_109
<nil, nil, nil>() -> q_gen_109
<a, b, a>() -> q_gen_129
<b, a, b>() -> q_gen_129
<b, b, b>() -> q_gen_129
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_122, q_gen_123, q_gen_139, q_gen_140, q_gen_141, q_gen_142, q_gen_143, q_gen_176, q_gen_180},
Q_f={q_gen_122},
Delta=
{
<cons>(q_gen_140, q_gen_180) -> q_gen_139
<cons>(q_gen_176, q_gen_139) -> q_gen_139
<b>() -> q_gen_140
<s>(q_gen_142) -> q_gen_142
<z>() -> q_gen_142
<a>() -> q_gen_176
<cons>(q_gen_140, q_gen_139) -> q_gen_180
<nil>() -> q_gen_180
<cons, s>(q_gen_123, q_gen_180) -> q_gen_122
<cons, s>(q_gen_141, q_gen_139) -> q_gen_122
<nil, z>() -> q_gen_122
<a, z>() -> q_gen_123
<b, z>() -> q_gen_123
<a, s>(q_gen_142) -> q_gen_141
<b, s>(q_gen_142) -> q_gen_141
<cons, s>(q_gen_123, q_gen_139) -> q_gen_143
<cons, s>(q_gen_141, q_gen_180) -> q_gen_143
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_108, q_gen_82},
Q_f={q_gen_108},
Delta=
{
<a, a>() -> q_gen_108
<a, b>() -> q_gen_108
<b, b>() -> q_gen_108
<b, a>() -> q_gen_82
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  leqnat -> 
{{{
Q={q_gen_106, q_gen_107, q_gen_145},
Q_f={q_gen_106},
Delta=
{
<s>(q_gen_107) -> q_gen_107
<z>() -> q_gen_107
<s, s>(q_gen_106) -> q_gen_106
<z, s>(q_gen_107) -> q_gen_106
<z, z>() -> q_gen_106
<s, s>(q_gen_145) -> q_gen_145
<s, z>(q_gen_107) -> q_gen_145
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  merge -> 
{{{
Q={q_gen_103, q_gen_104, q_gen_105, q_gen_118, q_gen_121, q_gen_169},
Q_f={q_gen_103},
Delta=
{
<a>() -> q_gen_118
<b>() -> q_gen_118
<cons>(q_gen_118, q_gen_169) -> q_gen_169
<nil>() -> q_gen_169
<cons, cons>(q_gen_105, q_gen_104) -> q_gen_104
<nil, cons>(q_gen_118, q_gen_169) -> q_gen_104
<nil, nil>() -> q_gen_104
<a, a>() -> q_gen_105
<a, b>() -> q_gen_105
<b, a>() -> q_gen_105
<b, b>() -> q_gen_105
<cons, cons, cons>(q_gen_121, q_gen_103) -> q_gen_103
<cons, nil, cons>(q_gen_105, q_gen_104) -> q_gen_103
<nil, cons, cons>(q_gen_105, q_gen_104) -> q_gen_103
<nil, nil, cons>(q_gen_118, q_gen_169) -> q_gen_103
<nil, nil, nil>() -> q_gen_103
<a, a, a>() -> q_gen_121
<a, b, a>() -> q_gen_121
<b, a, a>() -> q_gen_121
<b, a, b>() -> q_gen_121
<b, b, a>() -> q_gen_121
<b, b, b>() -> q_gen_121
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_101, q_gen_102, q_gen_115},
Q_f={q_gen_101},
Delta=
{
<s>(q_gen_115) -> q_gen_115
<z>() -> q_gen_115
<s, s>(q_gen_102) -> q_gen_102
<z, s>(q_gen_115) -> q_gen_102
<z, z>() -> q_gen_102
<s, s, s>(q_gen_101) -> q_gen_101
<s, z, s>(q_gen_102) -> q_gen_101
<z, s, s>(q_gen_102) -> q_gen_101
<z, z, s>(q_gen_115) -> q_gen_101
<z, z, z>() -> q_gen_101
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 16
() -> length([nil, z]) -> 16
() -> leq([a, n2]) -> 16
() -> leq([b, b]) -> 16
() -> leqnat([z, n2]) -> 16
() -> merge([cons(z, xs), nil, cons(z, xs)]) -> 16
() -> merge([nil, y, y]) -> 16
() -> plus([n, z, n]) -> 16
(append([t1, l2, _s])) -> append([cons(h1, t1), l2, cons(h1, _s)]) -> 16
(length([_ha, _ia]) /\ length([l1, _ga]) /\ merge([l1, l2, _ha])) -> leqnat([_ga, _ia]) -> 16
(length([_ka, _la]) /\ length([l2, _ja]) /\ merge([l1, l2, _ka])) -> leqnat([_ja, _la]) -> 17
(length([ll, _ca])) -> length([cons(x, ll), s(_ca)]) -> 16
(leq([z, y2]) /\ merge([xs, cons(y2, ys), _m])) -> merge([cons(z, xs), cons(y2, ys), cons(z, _m)]) -> 16
(not leq([z, y2]) /\ merge([cons(z, xs), ys, _n])) -> merge([cons(z, xs), cons(y2, ys), cons(y2, _n)]) -> 19
(leq([b, a])) -> BOT -> 16
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 16
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 18
(leqnat([s(nn1), z])) -> BOT -> 17
(plus([n, mm, _x])) -> plus([n, s(mm), s(_x)]) -> 17
}
Sat witness: Found: ((not leq([z, y2]) /\ merge([cons(z, xs), ys, _n])) -> merge([cons(z, xs), cons(y2, ys), cons(y2, _n)]), {
_n -> cons(b, cons(b, cons(b, nil)))  ;  xs -> cons(b, cons(a, nil))  ;  y2 -> a  ;  ys -> cons(a, cons(a, nil))  ;  z -> b
})

-------------------------------------------
Step 50, which took 0.273786 s (model generation: 0.262893,  model checking: 0.010893):

Model:
|_
{
append -> 
{{{
Q={q_gen_100, q_gen_109, q_gen_110, q_gen_127, q_gen_128, q_gen_129},
Q_f={q_gen_109},
Delta=
{
<nil>() -> q_gen_127
<a>() -> q_gen_128
<b>() -> q_gen_128
<a, a>() -> q_gen_100
<b, b>() -> q_gen_100
<cons, cons>(q_gen_100, q_gen_110) -> q_gen_110
<nil, cons>(q_gen_128, q_gen_127) -> q_gen_110
<nil, nil>() -> q_gen_110
<cons, cons, cons>(q_gen_129, q_gen_109) -> q_gen_109
<cons, nil, cons>(q_gen_100, q_gen_110) -> q_gen_109
<nil, cons, cons>(q_gen_100, q_gen_110) -> q_gen_109
<nil, nil, cons>(q_gen_128, q_gen_127) -> q_gen_109
<nil, nil, nil>() -> q_gen_109
<a, b, a>() -> q_gen_129
<b, a, b>() -> q_gen_129
<b, b, b>() -> q_gen_129
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_122, q_gen_123, q_gen_139, q_gen_140, q_gen_141, q_gen_142, q_gen_143, q_gen_176, q_gen_180},
Q_f={q_gen_122},
Delta=
{
<cons>(q_gen_140, q_gen_180) -> q_gen_139
<cons>(q_gen_176, q_gen_139) -> q_gen_139
<b>() -> q_gen_140
<s>(q_gen_142) -> q_gen_142
<z>() -> q_gen_142
<a>() -> q_gen_176
<cons>(q_gen_140, q_gen_139) -> q_gen_180
<nil>() -> q_gen_180
<cons, s>(q_gen_123, q_gen_180) -> q_gen_122
<cons, s>(q_gen_141, q_gen_139) -> q_gen_122
<nil, z>() -> q_gen_122
<a, z>() -> q_gen_123
<b, z>() -> q_gen_123
<a, s>(q_gen_142) -> q_gen_141
<b, s>(q_gen_142) -> q_gen_141
<cons, s>(q_gen_123, q_gen_139) -> q_gen_143
<cons, s>(q_gen_141, q_gen_180) -> q_gen_143
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_108, q_gen_82},
Q_f={q_gen_108},
Delta=
{
<a, a>() -> q_gen_108
<a, b>() -> q_gen_108
<b, b>() -> q_gen_108
<b, a>() -> q_gen_82
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  leqnat -> 
{{{
Q={q_gen_106, q_gen_107, q_gen_145},
Q_f={q_gen_106},
Delta=
{
<s>(q_gen_107) -> q_gen_107
<z>() -> q_gen_107
<s, s>(q_gen_106) -> q_gen_106
<z, s>(q_gen_107) -> q_gen_106
<z, z>() -> q_gen_106
<s, s>(q_gen_145) -> q_gen_145
<s, z>(q_gen_107) -> q_gen_145
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  merge -> 
{{{
Q={q_gen_103, q_gen_104, q_gen_105, q_gen_118, q_gen_121, q_gen_169},
Q_f={q_gen_103},
Delta=
{
<a>() -> q_gen_118
<b>() -> q_gen_118
<cons>(q_gen_118, q_gen_169) -> q_gen_169
<nil>() -> q_gen_169
<cons, cons>(q_gen_105, q_gen_104) -> q_gen_104
<nil, cons>(q_gen_118, q_gen_169) -> q_gen_104
<nil, nil>() -> q_gen_104
<a, a>() -> q_gen_105
<a, b>() -> q_gen_105
<b, a>() -> q_gen_105
<b, b>() -> q_gen_105
<cons, cons, cons>(q_gen_121, q_gen_103) -> q_gen_103
<cons, nil, cons>(q_gen_105, q_gen_104) -> q_gen_103
<nil, cons, cons>(q_gen_105, q_gen_104) -> q_gen_103
<nil, nil, cons>(q_gen_118, q_gen_169) -> q_gen_103
<nil, nil, nil>() -> q_gen_103
<a, a, a>() -> q_gen_121
<a, a, b>() -> q_gen_121
<a, b, a>() -> q_gen_121
<b, a, a>() -> q_gen_121
<b, a, b>() -> q_gen_121
<b, b, a>() -> q_gen_121
<b, b, b>() -> q_gen_121
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_101, q_gen_102, q_gen_115},
Q_f={q_gen_101},
Delta=
{
<s>(q_gen_115) -> q_gen_115
<z>() -> q_gen_115
<s, s>(q_gen_102) -> q_gen_102
<z, s>(q_gen_115) -> q_gen_102
<z, z>() -> q_gen_102
<s, s, s>(q_gen_101) -> q_gen_101
<s, z, s>(q_gen_102) -> q_gen_101
<z, s, s>(q_gen_102) -> q_gen_101
<z, z, s>(q_gen_115) -> q_gen_101
<z, z, z>() -> q_gen_101
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 16
() -> length([nil, z]) -> 16
() -> leq([a, n2]) -> 16
() -> leq([b, b]) -> 16
() -> leqnat([z, n2]) -> 16
() -> merge([cons(z, xs), nil, cons(z, xs)]) -> 16
() -> merge([nil, y, y]) -> 16
() -> plus([n, z, n]) -> 16
(append([t1, l2, _s])) -> append([cons(h1, t1), l2, cons(h1, _s)]) -> 16
(length([_ha, _ia]) /\ length([l1, _ga]) /\ merge([l1, l2, _ha])) -> leqnat([_ga, _ia]) -> 16
(length([_ka, _la]) /\ length([l2, _ja]) /\ merge([l1, l2, _ka])) -> leqnat([_ja, _la]) -> 17
(length([ll, _ca])) -> length([cons(x, ll), s(_ca)]) -> 16
(leq([z, y2]) /\ merge([xs, cons(y2, ys), _m])) -> merge([cons(z, xs), cons(y2, ys), cons(z, _m)]) -> 19
(not leq([z, y2]) /\ merge([cons(z, xs), ys, _n])) -> merge([cons(z, xs), cons(y2, ys), cons(y2, _n)]) -> 19
(leq([b, a])) -> BOT -> 17
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 17
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 18
(leqnat([s(nn1), z])) -> BOT -> 17
(plus([n, mm, _x])) -> plus([n, s(mm), s(_x)]) -> 17
}
Sat witness: Found: ((leq([z, y2]) /\ merge([xs, cons(y2, ys), _m])) -> merge([cons(z, xs), cons(y2, ys), cons(z, _m)]), {
_m -> cons(a, cons(b, cons(b, nil)))  ;  xs -> cons(b, cons(a, nil))  ;  y2 -> a  ;  ys -> cons(a, cons(b, nil))  ;  z -> a
})

-------------------------------------------
Step 51, which took 0.263166 s (model generation: 0.262498,  model checking: 0.000668):

Model:
|_
{
append -> 
{{{
Q={q_gen_100, q_gen_109, q_gen_110, q_gen_127, q_gen_128, q_gen_129},
Q_f={q_gen_109},
Delta=
{
<nil>() -> q_gen_127
<a>() -> q_gen_128
<b>() -> q_gen_128
<a, a>() -> q_gen_100
<b, b>() -> q_gen_100
<cons, cons>(q_gen_100, q_gen_110) -> q_gen_110
<nil, cons>(q_gen_128, q_gen_127) -> q_gen_110
<nil, nil>() -> q_gen_110
<cons, cons, cons>(q_gen_129, q_gen_109) -> q_gen_109
<cons, nil, cons>(q_gen_100, q_gen_110) -> q_gen_109
<nil, cons, cons>(q_gen_100, q_gen_110) -> q_gen_109
<nil, nil, cons>(q_gen_128, q_gen_127) -> q_gen_109
<nil, nil, nil>() -> q_gen_109
<a, b, a>() -> q_gen_129
<b, a, b>() -> q_gen_129
<b, b, b>() -> q_gen_129
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_122, q_gen_123, q_gen_139, q_gen_140, q_gen_141, q_gen_142, q_gen_143, q_gen_176, q_gen_180},
Q_f={q_gen_122},
Delta=
{
<cons>(q_gen_140, q_gen_180) -> q_gen_139
<cons>(q_gen_176, q_gen_139) -> q_gen_139
<b>() -> q_gen_140
<s>(q_gen_142) -> q_gen_142
<z>() -> q_gen_142
<a>() -> q_gen_176
<cons>(q_gen_140, q_gen_139) -> q_gen_180
<nil>() -> q_gen_180
<cons, s>(q_gen_123, q_gen_180) -> q_gen_122
<cons, s>(q_gen_141, q_gen_139) -> q_gen_122
<nil, z>() -> q_gen_122
<a, z>() -> q_gen_123
<b, z>() -> q_gen_123
<a, s>(q_gen_142) -> q_gen_141
<b, s>(q_gen_142) -> q_gen_141
<cons, s>(q_gen_123, q_gen_139) -> q_gen_143
<cons, s>(q_gen_141, q_gen_180) -> q_gen_143
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_108, q_gen_82},
Q_f={q_gen_108},
Delta=
{
<a, a>() -> q_gen_108
<a, b>() -> q_gen_108
<b, b>() -> q_gen_108
<b, a>() -> q_gen_82
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  leqnat -> 
{{{
Q={q_gen_106, q_gen_107, q_gen_145},
Q_f={q_gen_106},
Delta=
{
<s>(q_gen_107) -> q_gen_107
<z>() -> q_gen_107
<s, s>(q_gen_106) -> q_gen_106
<z, s>(q_gen_107) -> q_gen_106
<z, z>() -> q_gen_106
<s, s>(q_gen_145) -> q_gen_145
<s, z>(q_gen_107) -> q_gen_145
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  merge -> 
{{{
Q={q_gen_103, q_gen_104, q_gen_105, q_gen_118, q_gen_121, q_gen_169},
Q_f={q_gen_103},
Delta=
{
<a>() -> q_gen_118
<b>() -> q_gen_118
<cons>(q_gen_118, q_gen_169) -> q_gen_169
<nil>() -> q_gen_169
<cons, cons>(q_gen_105, q_gen_104) -> q_gen_104
<nil, cons>(q_gen_118, q_gen_169) -> q_gen_104
<nil, nil>() -> q_gen_104
<a, a>() -> q_gen_105
<a, b>() -> q_gen_105
<b, a>() -> q_gen_105
<b, b>() -> q_gen_105
<cons, cons, cons>(q_gen_121, q_gen_103) -> q_gen_103
<cons, nil, cons>(q_gen_105, q_gen_104) -> q_gen_103
<nil, cons, cons>(q_gen_105, q_gen_104) -> q_gen_103
<nil, nil, cons>(q_gen_118, q_gen_169) -> q_gen_103
<nil, nil, nil>() -> q_gen_103
<a, a, a>() -> q_gen_121
<a, a, b>() -> q_gen_121
<a, b, a>() -> q_gen_121
<a, b, b>() -> q_gen_121
<b, a, a>() -> q_gen_121
<b, a, b>() -> q_gen_121
<b, b, a>() -> q_gen_121
<b, b, b>() -> q_gen_121
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_101, q_gen_102, q_gen_115},
Q_f={q_gen_101},
Delta=
{
<s>(q_gen_115) -> q_gen_115
<z>() -> q_gen_115
<s, s>(q_gen_102) -> q_gen_102
<z, s>(q_gen_115) -> q_gen_102
<z, z>() -> q_gen_102
<s, s, s>(q_gen_101) -> q_gen_101
<s, z, s>(q_gen_102) -> q_gen_101
<z, s, s>(q_gen_102) -> q_gen_101
<z, z, s>(q_gen_115) -> q_gen_101
<z, z, z>() -> q_gen_101
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 16
() -> length([nil, z]) -> 16
() -> leq([a, n2]) -> 16
() -> leq([b, b]) -> 16
() -> leqnat([z, n2]) -> 16
() -> merge([cons(z, xs), nil, cons(z, xs)]) -> 16
() -> merge([nil, y, y]) -> 16
() -> plus([n, z, n]) -> 16
(append([t1, l2, _s])) -> append([cons(h1, t1), l2, cons(h1, _s)]) -> 16
(length([_ha, _ia]) /\ length([l1, _ga]) /\ merge([l1, l2, _ha])) -> leqnat([_ga, _ia]) -> 16
(length([_ka, _la]) /\ length([l2, _ja]) /\ merge([l1, l2, _ka])) -> leqnat([_ja, _la]) -> 17
(length([ll, _ca])) -> length([cons(x, ll), s(_ca)]) -> 19
(leq([z, y2]) /\ merge([xs, cons(y2, ys), _m])) -> merge([cons(z, xs), cons(y2, ys), cons(z, _m)]) -> 19
(not leq([z, y2]) /\ merge([cons(z, xs), ys, _n])) -> merge([cons(z, xs), cons(y2, ys), cons(y2, _n)]) -> 19
(leq([b, a])) -> BOT -> 17
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 17
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 18
(leqnat([s(nn1), z])) -> BOT -> 17
(plus([n, mm, _x])) -> plus([n, s(mm), s(_x)]) -> 17
}
Sat witness: Found: ((length([ll, _ca])) -> length([cons(x, ll), s(_ca)]), {
_ca -> s(s(z))  ;  ll -> cons(b, cons(b, nil))  ;  x -> a
})

-------------------------------------------
Step 52, which took 0.369400 s (model generation: 0.368204,  model checking: 0.001196):

Model:
|_
{
append -> 
{{{
Q={q_gen_100, q_gen_109, q_gen_110, q_gen_127, q_gen_128, q_gen_129},
Q_f={q_gen_109},
Delta=
{
<nil>() -> q_gen_127
<a>() -> q_gen_128
<b>() -> q_gen_128
<a, a>() -> q_gen_100
<b, b>() -> q_gen_100
<cons, cons>(q_gen_100, q_gen_110) -> q_gen_110
<nil, cons>(q_gen_128, q_gen_127) -> q_gen_110
<nil, nil>() -> q_gen_110
<cons, cons, cons>(q_gen_129, q_gen_109) -> q_gen_109
<cons, nil, cons>(q_gen_100, q_gen_110) -> q_gen_109
<nil, cons, cons>(q_gen_100, q_gen_110) -> q_gen_109
<nil, nil, cons>(q_gen_128, q_gen_127) -> q_gen_109
<nil, nil, nil>() -> q_gen_109
<a, b, a>() -> q_gen_129
<b, a, b>() -> q_gen_129
<b, b, b>() -> q_gen_129
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_122, q_gen_123, q_gen_139, q_gen_140, q_gen_141, q_gen_142, q_gen_143, q_gen_94},
Q_f={q_gen_122},
Delta=
{
<cons>(q_gen_140, q_gen_139) -> q_gen_139
<cons>(q_gen_140, q_gen_94) -> q_gen_139
<a>() -> q_gen_140
<b>() -> q_gen_140
<s>(q_gen_142) -> q_gen_142
<z>() -> q_gen_142
<nil>() -> q_gen_94
<cons, s>(q_gen_123, q_gen_94) -> q_gen_122
<cons, s>(q_gen_141, q_gen_139) -> q_gen_122
<nil, z>() -> q_gen_122
<a, z>() -> q_gen_123
<b, z>() -> q_gen_123
<a, s>(q_gen_142) -> q_gen_141
<b, s>(q_gen_142) -> q_gen_141
<cons, s>(q_gen_123, q_gen_139) -> q_gen_143
<cons, s>(q_gen_141, q_gen_94) -> q_gen_143
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_108, q_gen_82},
Q_f={q_gen_108},
Delta=
{
<a, a>() -> q_gen_108
<a, b>() -> q_gen_108
<b, b>() -> q_gen_108
<b, a>() -> q_gen_82
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  leqnat -> 
{{{
Q={q_gen_106, q_gen_107, q_gen_145},
Q_f={q_gen_106},
Delta=
{
<s>(q_gen_107) -> q_gen_107
<z>() -> q_gen_107
<s, s>(q_gen_106) -> q_gen_106
<z, s>(q_gen_107) -> q_gen_106
<z, z>() -> q_gen_106
<s, s>(q_gen_145) -> q_gen_145
<s, z>(q_gen_107) -> q_gen_145
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  merge -> 
{{{
Q={q_gen_103, q_gen_104, q_gen_105, q_gen_118, q_gen_121, q_gen_166, q_gen_169, q_gen_72},
Q_f={q_gen_103},
Delta=
{
<a>() -> q_gen_118
<b>() -> q_gen_118
<cons>(q_gen_118, q_gen_169) -> q_gen_169
<nil>() -> q_gen_169
<cons, cons>(q_gen_105, q_gen_104) -> q_gen_104
<cons, cons>(q_gen_105, q_gen_72) -> q_gen_104
<nil, cons>(q_gen_118, q_gen_169) -> q_gen_104
<a, a>() -> q_gen_105
<a, b>() -> q_gen_105
<b, a>() -> q_gen_105
<b, b>() -> q_gen_105
<nil, nil>() -> q_gen_72
<cons, cons, cons>(q_gen_121, q_gen_103) -> q_gen_103
<cons, nil, cons>(q_gen_105, q_gen_72) -> q_gen_103
<nil, cons, cons>(q_gen_105, q_gen_104) -> q_gen_103
<nil, cons, cons>(q_gen_105, q_gen_72) -> q_gen_103
<nil, nil, cons>(q_gen_118, q_gen_169) -> q_gen_103
<nil, nil, nil>() -> q_gen_103
<a, a, a>() -> q_gen_121
<a, a, b>() -> q_gen_121
<a, b, a>() -> q_gen_121
<a, b, b>() -> q_gen_121
<b, a, a>() -> q_gen_121
<b, a, b>() -> q_gen_121
<b, b, a>() -> q_gen_121
<b, b, b>() -> q_gen_121
<cons, nil, cons>(q_gen_105, q_gen_104) -> q_gen_166
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_101, q_gen_102, q_gen_115},
Q_f={q_gen_101},
Delta=
{
<s>(q_gen_115) -> q_gen_115
<z>() -> q_gen_115
<s, s>(q_gen_102) -> q_gen_102
<z, s>(q_gen_115) -> q_gen_102
<z, z>() -> q_gen_102
<s, s, s>(q_gen_101) -> q_gen_101
<s, z, s>(q_gen_102) -> q_gen_101
<z, s, s>(q_gen_102) -> q_gen_101
<z, z, s>(q_gen_115) -> q_gen_101
<z, z, z>() -> q_gen_101
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 16
() -> length([nil, z]) -> 16
() -> leq([a, n2]) -> 16
() -> leq([b, b]) -> 16
() -> leqnat([z, n2]) -> 16
() -> merge([cons(z, xs), nil, cons(z, xs)]) -> 16
() -> merge([nil, y, y]) -> 16
() -> plus([n, z, n]) -> 16
(append([t1, l2, _s])) -> append([cons(h1, t1), l2, cons(h1, _s)]) -> 16
(length([_ha, _ia]) /\ length([l1, _ga]) /\ merge([l1, l2, _ha])) -> leqnat([_ga, _ia]) -> 19
(length([_ka, _la]) /\ length([l2, _ja]) /\ merge([l1, l2, _ka])) -> leqnat([_ja, _la]) -> 17
(length([ll, _ca])) -> length([cons(x, ll), s(_ca)]) -> 19
(leq([z, y2]) /\ merge([xs, cons(y2, ys), _m])) -> merge([cons(z, xs), cons(y2, ys), cons(z, _m)]) -> 19
(not leq([z, y2]) /\ merge([cons(z, xs), ys, _n])) -> merge([cons(z, xs), cons(y2, ys), cons(y2, _n)]) -> 19
(leq([b, a])) -> BOT -> 17
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 17
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 18
(leqnat([s(nn1), z])) -> BOT -> 17
(plus([n, mm, _x])) -> plus([n, s(mm), s(_x)]) -> 17
}
Sat witness: Found: ((length([_ha, _ia]) /\ length([l1, _ga]) /\ merge([l1, l2, _ha])) -> leqnat([_ga, _ia]), {
_ga -> s(s(s(z)))  ;  _ha -> cons(b, cons(b, nil))  ;  _ia -> s(s(z))  ;  l1 -> cons(b, cons(b, nil))  ;  l2 -> cons(b, nil)
})

-------------------------------------------
Step 53, which took 0.752062 s (model generation: 0.750731,  model checking: 0.001331):

Model:
|_
{
append -> 
{{{
Q={q_gen_100, q_gen_109, q_gen_110, q_gen_127, q_gen_128, q_gen_129},
Q_f={q_gen_109},
Delta=
{
<nil>() -> q_gen_127
<a>() -> q_gen_128
<b>() -> q_gen_128
<a, a>() -> q_gen_100
<b, b>() -> q_gen_100
<cons, cons>(q_gen_100, q_gen_110) -> q_gen_110
<nil, cons>(q_gen_128, q_gen_127) -> q_gen_110
<nil, nil>() -> q_gen_110
<cons, cons, cons>(q_gen_129, q_gen_109) -> q_gen_109
<cons, nil, cons>(q_gen_100, q_gen_110) -> q_gen_109
<nil, cons, cons>(q_gen_100, q_gen_110) -> q_gen_109
<nil, nil, cons>(q_gen_128, q_gen_127) -> q_gen_109
<nil, nil, nil>() -> q_gen_109
<a, b, a>() -> q_gen_129
<b, a, b>() -> q_gen_129
<b, b, b>() -> q_gen_129
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_122, q_gen_123, q_gen_139, q_gen_140, q_gen_141, q_gen_142, q_gen_143, q_gen_94},
Q_f={q_gen_122},
Delta=
{
<cons>(q_gen_140, q_gen_139) -> q_gen_139
<cons>(q_gen_140, q_gen_94) -> q_gen_139
<a>() -> q_gen_140
<b>() -> q_gen_140
<s>(q_gen_142) -> q_gen_142
<z>() -> q_gen_142
<nil>() -> q_gen_94
<cons, s>(q_gen_123, q_gen_94) -> q_gen_122
<cons, s>(q_gen_141, q_gen_139) -> q_gen_122
<nil, z>() -> q_gen_122
<a, z>() -> q_gen_123
<b, z>() -> q_gen_123
<a, s>(q_gen_142) -> q_gen_141
<b, s>(q_gen_142) -> q_gen_141
<cons, s>(q_gen_123, q_gen_139) -> q_gen_143
<cons, s>(q_gen_141, q_gen_94) -> q_gen_143
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_108, q_gen_82},
Q_f={q_gen_108},
Delta=
{
<a, a>() -> q_gen_108
<a, b>() -> q_gen_108
<b, b>() -> q_gen_108
<b, a>() -> q_gen_82
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  leqnat -> 
{{{
Q={q_gen_106, q_gen_107, q_gen_145},
Q_f={q_gen_106},
Delta=
{
<s>(q_gen_107) -> q_gen_107
<z>() -> q_gen_107
<s, s>(q_gen_106) -> q_gen_106
<z, s>(q_gen_107) -> q_gen_106
<z, z>() -> q_gen_106
<s, s>(q_gen_145) -> q_gen_145
<s, z>(q_gen_107) -> q_gen_145
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  merge -> 
{{{
Q={q_gen_103, q_gen_104, q_gen_105, q_gen_117, q_gen_118, q_gen_121, q_gen_156, q_gen_169},
Q_f={q_gen_103},
Delta=
{
<a>() -> q_gen_118
<b>() -> q_gen_118
<cons>(q_gen_118, q_gen_169) -> q_gen_169
<nil>() -> q_gen_169
<cons, cons>(q_gen_105, q_gen_104) -> q_gen_104
<nil, nil>() -> q_gen_104
<a, a>() -> q_gen_105
<a, b>() -> q_gen_105
<b, a>() -> q_gen_105
<b, b>() -> q_gen_105
<cons, cons>(q_gen_105, q_gen_156) -> q_gen_156
<nil, cons>(q_gen_118, q_gen_169) -> q_gen_156
<cons, cons, cons>(q_gen_121, q_gen_117) -> q_gen_103
<cons, nil, cons>(q_gen_105, q_gen_104) -> q_gen_103
<nil, cons, cons>(q_gen_105, q_gen_104) -> q_gen_103
<nil, nil, nil>() -> q_gen_103
<cons, cons, cons>(q_gen_121, q_gen_103) -> q_gen_117
<cons, nil, cons>(q_gen_105, q_gen_156) -> q_gen_117
<nil, cons, cons>(q_gen_105, q_gen_156) -> q_gen_117
<nil, nil, cons>(q_gen_118, q_gen_169) -> q_gen_117
<a, a, a>() -> q_gen_121
<a, a, b>() -> q_gen_121
<a, b, a>() -> q_gen_121
<a, b, b>() -> q_gen_121
<b, a, a>() -> q_gen_121
<b, a, b>() -> q_gen_121
<b, b, a>() -> q_gen_121
<b, b, b>() -> q_gen_121
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_101, q_gen_102, q_gen_115},
Q_f={q_gen_101},
Delta=
{
<s>(q_gen_115) -> q_gen_115
<z>() -> q_gen_115
<s, s>(q_gen_102) -> q_gen_102
<z, s>(q_gen_115) -> q_gen_102
<z, z>() -> q_gen_102
<s, s, s>(q_gen_101) -> q_gen_101
<s, z, s>(q_gen_102) -> q_gen_101
<z, s, s>(q_gen_102) -> q_gen_101
<z, z, s>(q_gen_115) -> q_gen_101
<z, z, z>() -> q_gen_101
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 16
() -> length([nil, z]) -> 16
() -> leq([a, n2]) -> 16
() -> leq([b, b]) -> 16
() -> leqnat([z, n2]) -> 16
() -> merge([cons(z, xs), nil, cons(z, xs)]) -> 16
() -> merge([nil, y, y]) -> 16
() -> plus([n, z, n]) -> 16
(append([t1, l2, _s])) -> append([cons(h1, t1), l2, cons(h1, _s)]) -> 19
(length([_ha, _ia]) /\ length([l1, _ga]) /\ merge([l1, l2, _ha])) -> leqnat([_ga, _ia]) -> 19
(length([_ka, _la]) /\ length([l2, _ja]) /\ merge([l1, l2, _ka])) -> leqnat([_ja, _la]) -> 17
(length([ll, _ca])) -> length([cons(x, ll), s(_ca)]) -> 19
(leq([z, y2]) /\ merge([xs, cons(y2, ys), _m])) -> merge([cons(z, xs), cons(y2, ys), cons(z, _m)]) -> 19
(not leq([z, y2]) /\ merge([cons(z, xs), ys, _n])) -> merge([cons(z, xs), cons(y2, ys), cons(y2, _n)]) -> 19
(leq([b, a])) -> BOT -> 17
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 17
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 18
(leqnat([s(nn1), z])) -> BOT -> 17
(plus([n, mm, _x])) -> plus([n, s(mm), s(_x)]) -> 17
}
Sat witness: Found: ((append([t1, l2, _s])) -> append([cons(h1, t1), l2, cons(h1, _s)]), {
_s -> cons(b, nil)  ;  h1 -> a  ;  l2 -> cons(a, nil)  ;  t1 -> cons(b, nil)
})

-------------------------------------------
Step 54, which took 0.301600 s (model generation: 0.298821,  model checking: 0.002779):

Model:
|_
{
append -> 
{{{
Q={q_gen_100, q_gen_109, q_gen_110, q_gen_127, q_gen_128, q_gen_129},
Q_f={q_gen_109},
Delta=
{
<nil>() -> q_gen_127
<a>() -> q_gen_128
<b>() -> q_gen_128
<a, a>() -> q_gen_100
<b, b>() -> q_gen_100
<cons, cons>(q_gen_100, q_gen_110) -> q_gen_110
<nil, cons>(q_gen_128, q_gen_127) -> q_gen_110
<nil, nil>() -> q_gen_110
<cons, cons, cons>(q_gen_129, q_gen_109) -> q_gen_109
<cons, nil, cons>(q_gen_100, q_gen_110) -> q_gen_109
<nil, cons, cons>(q_gen_100, q_gen_110) -> q_gen_109
<nil, nil, cons>(q_gen_128, q_gen_127) -> q_gen_109
<nil, nil, nil>() -> q_gen_109
<a, a, a>() -> q_gen_129
<a, b, a>() -> q_gen_129
<b, a, b>() -> q_gen_129
<b, b, b>() -> q_gen_129
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_122, q_gen_123, q_gen_139, q_gen_140, q_gen_141, q_gen_142, q_gen_143, q_gen_94},
Q_f={q_gen_122},
Delta=
{
<cons>(q_gen_140, q_gen_139) -> q_gen_139
<cons>(q_gen_140, q_gen_94) -> q_gen_139
<a>() -> q_gen_140
<b>() -> q_gen_140
<s>(q_gen_142) -> q_gen_142
<z>() -> q_gen_142
<nil>() -> q_gen_94
<cons, s>(q_gen_123, q_gen_94) -> q_gen_122
<cons, s>(q_gen_141, q_gen_139) -> q_gen_122
<nil, z>() -> q_gen_122
<a, z>() -> q_gen_123
<b, z>() -> q_gen_123
<a, s>(q_gen_142) -> q_gen_141
<b, s>(q_gen_142) -> q_gen_141
<cons, s>(q_gen_123, q_gen_139) -> q_gen_143
<cons, s>(q_gen_141, q_gen_94) -> q_gen_143
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_108, q_gen_82},
Q_f={q_gen_108},
Delta=
{
<a, a>() -> q_gen_108
<a, b>() -> q_gen_108
<b, b>() -> q_gen_108
<b, a>() -> q_gen_82
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  leqnat -> 
{{{
Q={q_gen_106, q_gen_107, q_gen_145},
Q_f={q_gen_106},
Delta=
{
<s>(q_gen_107) -> q_gen_107
<z>() -> q_gen_107
<s, s>(q_gen_106) -> q_gen_106
<z, s>(q_gen_107) -> q_gen_106
<z, z>() -> q_gen_106
<s, s>(q_gen_145) -> q_gen_145
<s, z>(q_gen_107) -> q_gen_145
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  merge -> 
{{{
Q={q_gen_103, q_gen_104, q_gen_105, q_gen_117, q_gen_118, q_gen_121, q_gen_156, q_gen_169},
Q_f={q_gen_103},
Delta=
{
<a>() -> q_gen_118
<b>() -> q_gen_118
<cons>(q_gen_118, q_gen_169) -> q_gen_169
<nil>() -> q_gen_169
<cons, cons>(q_gen_105, q_gen_104) -> q_gen_104
<nil, nil>() -> q_gen_104
<a, a>() -> q_gen_105
<a, b>() -> q_gen_105
<b, a>() -> q_gen_105
<b, b>() -> q_gen_105
<cons, cons>(q_gen_105, q_gen_156) -> q_gen_156
<nil, cons>(q_gen_118, q_gen_169) -> q_gen_156
<cons, cons, cons>(q_gen_121, q_gen_117) -> q_gen_103
<cons, nil, cons>(q_gen_105, q_gen_104) -> q_gen_103
<nil, cons, cons>(q_gen_105, q_gen_104) -> q_gen_103
<nil, nil, nil>() -> q_gen_103
<cons, cons, cons>(q_gen_121, q_gen_103) -> q_gen_117
<cons, nil, cons>(q_gen_105, q_gen_156) -> q_gen_117
<nil, cons, cons>(q_gen_105, q_gen_156) -> q_gen_117
<nil, nil, cons>(q_gen_118, q_gen_169) -> q_gen_117
<a, a, a>() -> q_gen_121
<a, a, b>() -> q_gen_121
<a, b, a>() -> q_gen_121
<a, b, b>() -> q_gen_121
<b, a, a>() -> q_gen_121
<b, a, b>() -> q_gen_121
<b, b, a>() -> q_gen_121
<b, b, b>() -> q_gen_121
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_101, q_gen_102, q_gen_115},
Q_f={q_gen_101},
Delta=
{
<s>(q_gen_115) -> q_gen_115
<z>() -> q_gen_115
<s, s>(q_gen_102) -> q_gen_102
<z, s>(q_gen_115) -> q_gen_102
<z, z>() -> q_gen_102
<s, s, s>(q_gen_101) -> q_gen_101
<s, z, s>(q_gen_102) -> q_gen_101
<z, s, s>(q_gen_102) -> q_gen_101
<z, z, s>(q_gen_115) -> q_gen_101
<z, z, z>() -> q_gen_101
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 17
() -> length([nil, z]) -> 17
() -> leq([a, n2]) -> 17
() -> leq([b, b]) -> 17
() -> leqnat([z, n2]) -> 17
() -> merge([cons(z, xs), nil, cons(z, xs)]) -> 17
() -> merge([nil, y, y]) -> 17
() -> plus([n, z, n]) -> 17
(append([t1, l2, _s])) -> append([cons(h1, t1), l2, cons(h1, _s)]) -> 19
(length([_ha, _ia]) /\ length([l1, _ga]) /\ merge([l1, l2, _ha])) -> leqnat([_ga, _ia]) -> 19
(length([_ka, _la]) /\ length([l2, _ja]) /\ merge([l1, l2, _ka])) -> leqnat([_ja, _la]) -> 20
(length([ll, _ca])) -> length([cons(x, ll), s(_ca)]) -> 19
(leq([z, y2]) /\ merge([xs, cons(y2, ys), _m])) -> merge([cons(z, xs), cons(y2, ys), cons(z, _m)]) -> 19
(not leq([z, y2]) /\ merge([cons(z, xs), ys, _n])) -> merge([cons(z, xs), cons(y2, ys), cons(y2, _n)]) -> 19
(leq([b, a])) -> BOT -> 18
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 18
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 18
(leqnat([s(nn1), z])) -> BOT -> 18
(plus([n, mm, _x])) -> plus([n, s(mm), s(_x)]) -> 18
}
Sat witness: Found: ((length([_ka, _la]) /\ length([l2, _ja]) /\ merge([l1, l2, _ka])) -> leqnat([_ja, _la]), {
_ja -> s(s(s(z)))  ;  _ka -> cons(b, cons(b, nil))  ;  _la -> s(s(z))  ;  l1 -> nil  ;  l2 -> cons(b, cons(b, nil))
})

-------------------------------------------
Step 55, which took 0.263204 s (model generation: 0.262510,  model checking: 0.000694):

Model:
|_
{
append -> 
{{{
Q={q_gen_100, q_gen_109, q_gen_110, q_gen_127, q_gen_128, q_gen_129},
Q_f={q_gen_109},
Delta=
{
<nil>() -> q_gen_127
<a>() -> q_gen_128
<b>() -> q_gen_128
<a, a>() -> q_gen_100
<b, b>() -> q_gen_100
<cons, cons>(q_gen_100, q_gen_110) -> q_gen_110
<nil, cons>(q_gen_128, q_gen_127) -> q_gen_110
<nil, nil>() -> q_gen_110
<cons, cons, cons>(q_gen_129, q_gen_109) -> q_gen_109
<cons, nil, cons>(q_gen_100, q_gen_110) -> q_gen_109
<nil, cons, cons>(q_gen_100, q_gen_110) -> q_gen_109
<nil, nil, cons>(q_gen_128, q_gen_127) -> q_gen_109
<nil, nil, nil>() -> q_gen_109
<a, a, a>() -> q_gen_129
<a, b, a>() -> q_gen_129
<b, a, b>() -> q_gen_129
<b, b, b>() -> q_gen_129
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_122, q_gen_123, q_gen_139, q_gen_140, q_gen_142, q_gen_149, q_gen_94, q_gen_95},
Q_f={q_gen_122},
Delta=
{
<cons>(q_gen_140, q_gen_139) -> q_gen_139
<cons>(q_gen_140, q_gen_94) -> q_gen_139
<a>() -> q_gen_140
<b>() -> q_gen_140
<s>(q_gen_142) -> q_gen_142
<z>() -> q_gen_142
<nil>() -> q_gen_94
<cons, s>(q_gen_123, q_gen_139) -> q_gen_122
<cons, s>(q_gen_123, q_gen_94) -> q_gen_122
<cons, s>(q_gen_95, q_gen_94) -> q_gen_122
<nil, z>() -> q_gen_122
<a, s>(q_gen_142) -> q_gen_123
<a, z>() -> q_gen_123
<b, s>(q_gen_142) -> q_gen_123
<cons, s>(q_gen_95, q_gen_139) -> q_gen_149
<b, z>() -> q_gen_95
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_108, q_gen_82},
Q_f={q_gen_108},
Delta=
{
<a, a>() -> q_gen_108
<a, b>() -> q_gen_108
<b, b>() -> q_gen_108
<b, a>() -> q_gen_82
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  leqnat -> 
{{{
Q={q_gen_106, q_gen_107, q_gen_145},
Q_f={q_gen_106},
Delta=
{
<s>(q_gen_107) -> q_gen_107
<z>() -> q_gen_107
<s, s>(q_gen_106) -> q_gen_106
<z, s>(q_gen_107) -> q_gen_106
<z, z>() -> q_gen_106
<s, s>(q_gen_145) -> q_gen_145
<s, z>(q_gen_107) -> q_gen_145
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  merge -> 
{{{
Q={q_gen_103, q_gen_104, q_gen_105, q_gen_117, q_gen_118, q_gen_121, q_gen_169, q_gen_72, q_gen_73},
Q_f={q_gen_103},
Delta=
{
<a>() -> q_gen_118
<b>() -> q_gen_118
<cons>(q_gen_118, q_gen_169) -> q_gen_169
<nil>() -> q_gen_169
<cons, cons>(q_gen_105, q_gen_72) -> q_gen_104
<cons, cons>(q_gen_73, q_gen_104) -> q_gen_104
<cons, cons>(q_gen_73, q_gen_72) -> q_gen_104
<nil, cons>(q_gen_118, q_gen_169) -> q_gen_104
<a, a>() -> q_gen_105
<a, b>() -> q_gen_105
<nil, nil>() -> q_gen_72
<b, a>() -> q_gen_73
<b, b>() -> q_gen_73
<cons, cons, cons>(q_gen_121, q_gen_117) -> q_gen_103
<cons, nil, cons>(q_gen_105, q_gen_72) -> q_gen_103
<cons, nil, cons>(q_gen_73, q_gen_72) -> q_gen_103
<nil, cons, cons>(q_gen_105, q_gen_104) -> q_gen_103
<nil, cons, cons>(q_gen_73, q_gen_72) -> q_gen_103
<nil, nil, nil>() -> q_gen_103
<cons, cons, cons>(q_gen_121, q_gen_103) -> q_gen_117
<cons, nil, cons>(q_gen_73, q_gen_104) -> q_gen_117
<nil, cons, cons>(q_gen_105, q_gen_72) -> q_gen_117
<nil, cons, cons>(q_gen_73, q_gen_104) -> q_gen_117
<nil, nil, cons>(q_gen_118, q_gen_169) -> q_gen_117
<a, a, a>() -> q_gen_121
<a, a, b>() -> q_gen_121
<a, b, a>() -> q_gen_121
<a, b, b>() -> q_gen_121
<b, a, a>() -> q_gen_121
<b, a, b>() -> q_gen_121
<b, b, a>() -> q_gen_121
<b, b, b>() -> q_gen_121
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_101, q_gen_102, q_gen_115},
Q_f={q_gen_101},
Delta=
{
<s>(q_gen_115) -> q_gen_115
<z>() -> q_gen_115
<s, s>(q_gen_102) -> q_gen_102
<z, s>(q_gen_115) -> q_gen_102
<z, z>() -> q_gen_102
<s, s, s>(q_gen_101) -> q_gen_101
<s, z, s>(q_gen_102) -> q_gen_101
<z, s, s>(q_gen_102) -> q_gen_101
<z, z, s>(q_gen_115) -> q_gen_101
<z, z, z>() -> q_gen_101
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 17
() -> length([nil, z]) -> 17
() -> leq([a, n2]) -> 17
() -> leq([b, b]) -> 17
() -> leqnat([z, n2]) -> 17
() -> merge([cons(z, xs), nil, cons(z, xs)]) -> 17
() -> merge([nil, y, y]) -> 20
() -> plus([n, z, n]) -> 18
(append([t1, l2, _s])) -> append([cons(h1, t1), l2, cons(h1, _s)]) -> 19
(length([_ha, _ia]) /\ length([l1, _ga]) /\ merge([l1, l2, _ha])) -> leqnat([_ga, _ia]) -> 19
(length([_ka, _la]) /\ length([l2, _ja]) /\ merge([l1, l2, _ka])) -> leqnat([_ja, _la]) -> 20
(length([ll, _ca])) -> length([cons(x, ll), s(_ca)]) -> 19
(leq([z, y2]) /\ merge([xs, cons(y2, ys), _m])) -> merge([cons(z, xs), cons(y2, ys), cons(z, _m)]) -> 19
(not leq([z, y2]) /\ merge([cons(z, xs), ys, _n])) -> merge([cons(z, xs), cons(y2, ys), cons(y2, _n)]) -> 19
(leq([b, a])) -> BOT -> 18
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 18
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 18
(leqnat([s(nn1), z])) -> BOT -> 18
(plus([n, mm, _x])) -> plus([n, s(mm), s(_x)]) -> 18
}
Sat witness: Found: (() -> merge([nil, y, y]), {
y -> cons(a, nil)
})

-------------------------------------------
Step 56, which took 0.600652 s (model generation: 0.536462,  model checking: 0.064190):

Model:
|_
{
append -> 
{{{
Q={q_gen_100, q_gen_109, q_gen_110, q_gen_127, q_gen_128, q_gen_129},
Q_f={q_gen_109},
Delta=
{
<nil>() -> q_gen_127
<a>() -> q_gen_128
<b>() -> q_gen_128
<a, a>() -> q_gen_100
<b, b>() -> q_gen_100
<cons, cons>(q_gen_100, q_gen_110) -> q_gen_110
<nil, cons>(q_gen_128, q_gen_127) -> q_gen_110
<nil, nil>() -> q_gen_110
<cons, cons, cons>(q_gen_129, q_gen_109) -> q_gen_109
<cons, nil, cons>(q_gen_100, q_gen_110) -> q_gen_109
<nil, cons, cons>(q_gen_100, q_gen_110) -> q_gen_109
<nil, nil, cons>(q_gen_128, q_gen_127) -> q_gen_109
<nil, nil, nil>() -> q_gen_109
<a, a, a>() -> q_gen_129
<a, b, a>() -> q_gen_129
<b, a, b>() -> q_gen_129
<b, b, b>() -> q_gen_129
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_122, q_gen_123, q_gen_139, q_gen_140, q_gen_141, q_gen_142, q_gen_143, q_gen_175, q_gen_177, q_gen_178, q_gen_94},
Q_f={q_gen_122},
Delta=
{
<cons>(q_gen_140, q_gen_94) -> q_gen_139
<a>() -> q_gen_140
<b>() -> q_gen_140
<z>() -> q_gen_142
<cons>(q_gen_140, q_gen_139) -> q_gen_175
<s>(q_gen_142) -> q_gen_178
<nil>() -> q_gen_94
<cons, s>(q_gen_123, q_gen_94) -> q_gen_122
<cons, s>(q_gen_141, q_gen_139) -> q_gen_122
<cons, s>(q_gen_141, q_gen_175) -> q_gen_122
<cons, s>(q_gen_177, q_gen_175) -> q_gen_122
<nil, z>() -> q_gen_122
<a, z>() -> q_gen_123
<b, z>() -> q_gen_123
<a, s>(q_gen_142) -> q_gen_141
<b, s>(q_gen_142) -> q_gen_141
<cons, s>(q_gen_123, q_gen_139) -> q_gen_143
<cons, s>(q_gen_141, q_gen_94) -> q_gen_143
<cons, s>(q_gen_177, q_gen_139) -> q_gen_143
<cons, s>(q_gen_177, q_gen_94) -> q_gen_143
<a, s>(q_gen_178) -> q_gen_177
<b, s>(q_gen_178) -> q_gen_177
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_108, q_gen_82},
Q_f={q_gen_108},
Delta=
{
<a, a>() -> q_gen_108
<a, b>() -> q_gen_108
<b, b>() -> q_gen_108
<b, a>() -> q_gen_82
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  leqnat -> 
{{{
Q={q_gen_106, q_gen_107, q_gen_145},
Q_f={q_gen_106},
Delta=
{
<s>(q_gen_107) -> q_gen_107
<z>() -> q_gen_107
<s, s>(q_gen_106) -> q_gen_106
<z, s>(q_gen_107) -> q_gen_106
<z, z>() -> q_gen_106
<s, s>(q_gen_145) -> q_gen_145
<s, z>(q_gen_107) -> q_gen_145
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  merge -> 
{{{
Q={q_gen_103, q_gen_104, q_gen_105, q_gen_118, q_gen_121, q_gen_169},
Q_f={q_gen_103},
Delta=
{
<a>() -> q_gen_118
<b>() -> q_gen_118
<cons>(q_gen_118, q_gen_169) -> q_gen_169
<nil>() -> q_gen_169
<cons, cons>(q_gen_105, q_gen_104) -> q_gen_104
<nil, cons>(q_gen_118, q_gen_169) -> q_gen_104
<nil, nil>() -> q_gen_104
<a, a>() -> q_gen_105
<a, b>() -> q_gen_105
<b, a>() -> q_gen_105
<b, b>() -> q_gen_105
<cons, cons, cons>(q_gen_121, q_gen_103) -> q_gen_103
<cons, nil, cons>(q_gen_105, q_gen_104) -> q_gen_103
<nil, cons, cons>(q_gen_105, q_gen_104) -> q_gen_103
<nil, nil, cons>(q_gen_118, q_gen_169) -> q_gen_103
<nil, nil, nil>() -> q_gen_103
<a, a, a>() -> q_gen_121
<a, a, b>() -> q_gen_121
<a, b, a>() -> q_gen_121
<a, b, b>() -> q_gen_121
<b, a, a>() -> q_gen_121
<b, a, b>() -> q_gen_121
<b, b, a>() -> q_gen_121
<b, b, b>() -> q_gen_121
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_101, q_gen_102, q_gen_115},
Q_f={q_gen_101},
Delta=
{
<s>(q_gen_115) -> q_gen_115
<z>() -> q_gen_115
<s, s>(q_gen_102) -> q_gen_102
<z, s>(q_gen_115) -> q_gen_102
<z, z>() -> q_gen_102
<s, s, s>(q_gen_101) -> q_gen_101
<s, z, s>(q_gen_102) -> q_gen_101
<z, s, s>(q_gen_102) -> q_gen_101
<z, z, s>(q_gen_115) -> q_gen_101
<z, z, z>() -> q_gen_101
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 18
() -> length([nil, z]) -> 18
() -> leq([a, n2]) -> 18
() -> leq([b, b]) -> 18
() -> leqnat([z, n2]) -> 18
() -> merge([cons(z, xs), nil, cons(z, xs)]) -> 18
() -> merge([nil, y, y]) -> 20
() -> plus([n, z, n]) -> 19
(append([t1, l2, _s])) -> append([cons(h1, t1), l2, cons(h1, _s)]) -> 19
(length([_ha, _ia]) /\ length([l1, _ga]) /\ merge([l1, l2, _ha])) -> leqnat([_ga, _ia]) -> 19
(length([_ka, _la]) /\ length([l2, _ja]) /\ merge([l1, l2, _ka])) -> leqnat([_ja, _la]) -> 20
(length([ll, _ca])) -> length([cons(x, ll), s(_ca)]) -> 22
(leq([z, y2]) /\ merge([xs, cons(y2, ys), _m])) -> merge([cons(z, xs), cons(y2, ys), cons(z, _m)]) -> 20
(not leq([z, y2]) /\ merge([cons(z, xs), ys, _n])) -> merge([cons(z, xs), cons(y2, ys), cons(y2, _n)]) -> 20
(leq([b, a])) -> BOT -> 19
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 19
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 19
(leqnat([s(nn1), z])) -> BOT -> 19
(plus([n, mm, _x])) -> plus([n, s(mm), s(_x)]) -> 19
}
Sat witness: Found: ((length([ll, _ca])) -> length([cons(x, ll), s(_ca)]), {
_ca -> s(s(s(z)))  ;  ll -> cons(b, cons(a, cons(b, nil)))  ;  x -> b
})

-------------------------------------------
Step 57, which took 0.440111 s (model generation: 0.435543,  model checking: 0.004568):

Model:
|_
{
append -> 
{{{
Q={q_gen_100, q_gen_109, q_gen_110, q_gen_127, q_gen_128, q_gen_129},
Q_f={q_gen_109},
Delta=
{
<nil>() -> q_gen_127
<a>() -> q_gen_128
<b>() -> q_gen_128
<a, a>() -> q_gen_100
<b, b>() -> q_gen_100
<cons, cons>(q_gen_100, q_gen_110) -> q_gen_110
<nil, cons>(q_gen_128, q_gen_127) -> q_gen_110
<nil, nil>() -> q_gen_110
<cons, cons, cons>(q_gen_129, q_gen_109) -> q_gen_109
<cons, nil, cons>(q_gen_100, q_gen_110) -> q_gen_109
<nil, cons, cons>(q_gen_100, q_gen_110) -> q_gen_109
<nil, nil, cons>(q_gen_128, q_gen_127) -> q_gen_109
<nil, nil, nil>() -> q_gen_109
<a, a, a>() -> q_gen_129
<a, b, a>() -> q_gen_129
<b, a, b>() -> q_gen_129
<b, b, b>() -> q_gen_129
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_122, q_gen_123, q_gen_139, q_gen_140, q_gen_141, q_gen_142, q_gen_143, q_gen_175, q_gen_177, q_gen_178, q_gen_94},
Q_f={q_gen_122},
Delta=
{
<cons>(q_gen_140, q_gen_94) -> q_gen_139
<a>() -> q_gen_140
<b>() -> q_gen_140
<s>(q_gen_178) -> q_gen_142
<z>() -> q_gen_142
<cons>(q_gen_140, q_gen_139) -> q_gen_175
<cons>(q_gen_140, q_gen_175) -> q_gen_175
<s>(q_gen_142) -> q_gen_178
<nil>() -> q_gen_94
<cons, s>(q_gen_123, q_gen_94) -> q_gen_122
<cons, s>(q_gen_141, q_gen_139) -> q_gen_122
<cons, s>(q_gen_141, q_gen_175) -> q_gen_122
<cons, s>(q_gen_177, q_gen_175) -> q_gen_122
<nil, z>() -> q_gen_122
<a, z>() -> q_gen_123
<b, z>() -> q_gen_123
<a, s>(q_gen_142) -> q_gen_141
<a, s>(q_gen_178) -> q_gen_141
<b, s>(q_gen_142) -> q_gen_141
<cons, s>(q_gen_123, q_gen_139) -> q_gen_143
<cons, s>(q_gen_141, q_gen_94) -> q_gen_143
<cons, s>(q_gen_177, q_gen_139) -> q_gen_143
<cons, s>(q_gen_177, q_gen_94) -> q_gen_143
<b, s>(q_gen_178) -> q_gen_177
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_108, q_gen_82},
Q_f={q_gen_108},
Delta=
{
<a, a>() -> q_gen_108
<a, b>() -> q_gen_108
<b, b>() -> q_gen_108
<b, a>() -> q_gen_82
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  leqnat -> 
{{{
Q={q_gen_106, q_gen_107, q_gen_145},
Q_f={q_gen_106},
Delta=
{
<s>(q_gen_107) -> q_gen_107
<z>() -> q_gen_107
<s, s>(q_gen_106) -> q_gen_106
<z, s>(q_gen_107) -> q_gen_106
<z, z>() -> q_gen_106
<s, s>(q_gen_145) -> q_gen_145
<s, z>(q_gen_107) -> q_gen_145
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  merge -> 
{{{
Q={q_gen_103, q_gen_104, q_gen_105, q_gen_118, q_gen_121, q_gen_169},
Q_f={q_gen_103},
Delta=
{
<a>() -> q_gen_118
<b>() -> q_gen_118
<cons>(q_gen_118, q_gen_169) -> q_gen_169
<nil>() -> q_gen_169
<cons, cons>(q_gen_105, q_gen_104) -> q_gen_104
<nil, cons>(q_gen_118, q_gen_169) -> q_gen_104
<nil, nil>() -> q_gen_104
<a, a>() -> q_gen_105
<a, b>() -> q_gen_105
<b, a>() -> q_gen_105
<b, b>() -> q_gen_105
<cons, cons, cons>(q_gen_121, q_gen_103) -> q_gen_103
<cons, nil, cons>(q_gen_105, q_gen_104) -> q_gen_103
<nil, cons, cons>(q_gen_105, q_gen_104) -> q_gen_103
<nil, nil, cons>(q_gen_118, q_gen_169) -> q_gen_103
<nil, nil, nil>() -> q_gen_103
<a, a, a>() -> q_gen_121
<a, a, b>() -> q_gen_121
<a, b, a>() -> q_gen_121
<a, b, b>() -> q_gen_121
<b, a, a>() -> q_gen_121
<b, a, b>() -> q_gen_121
<b, b, a>() -> q_gen_121
<b, b, b>() -> q_gen_121
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_101, q_gen_102, q_gen_115},
Q_f={q_gen_101},
Delta=
{
<s>(q_gen_115) -> q_gen_115
<z>() -> q_gen_115
<s, s>(q_gen_102) -> q_gen_102
<z, s>(q_gen_115) -> q_gen_102
<z, z>() -> q_gen_102
<s, s, s>(q_gen_101) -> q_gen_101
<s, z, s>(q_gen_102) -> q_gen_101
<z, s, s>(q_gen_102) -> q_gen_101
<z, z, s>(q_gen_115) -> q_gen_101
<z, z, z>() -> q_gen_101
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 19
() -> length([nil, z]) -> 19
() -> leq([a, n2]) -> 19
() -> leq([b, b]) -> 19
() -> leqnat([z, n2]) -> 19
() -> merge([cons(z, xs), nil, cons(z, xs)]) -> 19
() -> merge([nil, y, y]) -> 20
() -> plus([n, z, n]) -> 19
(append([t1, l2, _s])) -> append([cons(h1, t1), l2, cons(h1, _s)]) -> 19
(length([_ha, _ia]) /\ length([l1, _ga]) /\ merge([l1, l2, _ha])) -> leqnat([_ga, _ia]) -> 22
(length([_ka, _la]) /\ length([l2, _ja]) /\ merge([l1, l2, _ka])) -> leqnat([_ja, _la]) -> 20
(length([ll, _ca])) -> length([cons(x, ll), s(_ca)]) -> 22
(leq([z, y2]) /\ merge([xs, cons(y2, ys), _m])) -> merge([cons(z, xs), cons(y2, ys), cons(z, _m)]) -> 20
(not leq([z, y2]) /\ merge([cons(z, xs), ys, _n])) -> merge([cons(z, xs), cons(y2, ys), cons(y2, _n)]) -> 20
(leq([b, a])) -> BOT -> 20
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 20
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 20
(leqnat([s(nn1), z])) -> BOT -> 20
(plus([n, mm, _x])) -> plus([n, s(mm), s(_x)]) -> 20
}
Sat witness: Found: ((length([_ha, _ia]) /\ length([l1, _ga]) /\ merge([l1, l2, _ha])) -> leqnat([_ga, _ia]), {
_ga -> s(s(s(s(z))))  ;  _ha -> cons(b, cons(b, cons(b, nil)))  ;  _ia -> s(s(z))  ;  l1 -> cons(b, cons(b, cons(b, nil)))  ;  l2 -> nil
})

-------------------------------------------
Step 58, which took 0.739849 s (model generation: 0.738418,  model checking: 0.001431):

Model:
|_
{
append -> 
{{{
Q={q_gen_100, q_gen_109, q_gen_110, q_gen_127, q_gen_128, q_gen_129},
Q_f={q_gen_109},
Delta=
{
<nil>() -> q_gen_127
<a>() -> q_gen_128
<b>() -> q_gen_128
<a, a>() -> q_gen_100
<b, b>() -> q_gen_100
<cons, cons>(q_gen_100, q_gen_110) -> q_gen_110
<nil, cons>(q_gen_128, q_gen_127) -> q_gen_110
<nil, nil>() -> q_gen_110
<cons, cons, cons>(q_gen_129, q_gen_109) -> q_gen_109
<cons, nil, cons>(q_gen_100, q_gen_110) -> q_gen_109
<nil, cons, cons>(q_gen_100, q_gen_110) -> q_gen_109
<nil, nil, cons>(q_gen_128, q_gen_127) -> q_gen_109
<nil, nil, nil>() -> q_gen_109
<a, a, a>() -> q_gen_129
<a, b, a>() -> q_gen_129
<b, a, b>() -> q_gen_129
<b, b, b>() -> q_gen_129
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_122, q_gen_123, q_gen_139, q_gen_140, q_gen_141, q_gen_142, q_gen_143, q_gen_175, q_gen_178},
Q_f={q_gen_122},
Delta=
{
<cons>(q_gen_140, q_gen_175) -> q_gen_139
<a>() -> q_gen_140
<b>() -> q_gen_140
<s>(q_gen_178) -> q_gen_142
<z>() -> q_gen_142
<cons>(q_gen_140, q_gen_139) -> q_gen_175
<nil>() -> q_gen_175
<s>(q_gen_142) -> q_gen_178
<cons, s>(q_gen_123, q_gen_175) -> q_gen_122
<cons, s>(q_gen_141, q_gen_139) -> q_gen_122
<nil, z>() -> q_gen_122
<a, s>(q_gen_178) -> q_gen_123
<a, z>() -> q_gen_123
<b, s>(q_gen_178) -> q_gen_123
<b, z>() -> q_gen_123
<a, s>(q_gen_142) -> q_gen_141
<b, s>(q_gen_142) -> q_gen_141
<cons, s>(q_gen_123, q_gen_139) -> q_gen_143
<cons, s>(q_gen_141, q_gen_175) -> q_gen_143
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_108, q_gen_82},
Q_f={q_gen_108},
Delta=
{
<a, a>() -> q_gen_108
<a, b>() -> q_gen_108
<b, b>() -> q_gen_108
<b, a>() -> q_gen_82
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  leqnat -> 
{{{
Q={q_gen_106, q_gen_107, q_gen_145},
Q_f={q_gen_106},
Delta=
{
<s>(q_gen_107) -> q_gen_107
<z>() -> q_gen_107
<s, s>(q_gen_106) -> q_gen_106
<z, s>(q_gen_107) -> q_gen_106
<z, z>() -> q_gen_106
<s, s>(q_gen_145) -> q_gen_145
<s, z>(q_gen_107) -> q_gen_145
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  merge -> 
{{{
Q={q_gen_103, q_gen_104, q_gen_105, q_gen_118, q_gen_121, q_gen_155, q_gen_156, q_gen_169},
Q_f={q_gen_103},
Delta=
{
<a>() -> q_gen_118
<b>() -> q_gen_118
<cons>(q_gen_118, q_gen_169) -> q_gen_169
<nil>() -> q_gen_169
<cons, cons>(q_gen_105, q_gen_104) -> q_gen_104
<nil, nil>() -> q_gen_104
<a, a>() -> q_gen_105
<a, b>() -> q_gen_105
<b, a>() -> q_gen_105
<b, b>() -> q_gen_105
<cons, cons>(q_gen_105, q_gen_156) -> q_gen_156
<nil, cons>(q_gen_118, q_gen_169) -> q_gen_156
<cons, cons, cons>(q_gen_121, q_gen_103) -> q_gen_103
<cons, cons, cons>(q_gen_121, q_gen_155) -> q_gen_103
<cons, nil, cons>(q_gen_105, q_gen_104) -> q_gen_103
<nil, cons, cons>(q_gen_105, q_gen_104) -> q_gen_103
<nil, nil, cons>(q_gen_118, q_gen_169) -> q_gen_103
<nil, nil, nil>() -> q_gen_103
<a, a, a>() -> q_gen_121
<a, a, b>() -> q_gen_121
<a, b, a>() -> q_gen_121
<a, b, b>() -> q_gen_121
<b, a, a>() -> q_gen_121
<b, a, b>() -> q_gen_121
<b, b, a>() -> q_gen_121
<b, b, b>() -> q_gen_121
<cons, nil, cons>(q_gen_105, q_gen_156) -> q_gen_155
<nil, cons, cons>(q_gen_105, q_gen_156) -> q_gen_155
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_101, q_gen_102, q_gen_115},
Q_f={q_gen_101},
Delta=
{
<s>(q_gen_115) -> q_gen_115
<z>() -> q_gen_115
<s, s>(q_gen_102) -> q_gen_102
<z, s>(q_gen_115) -> q_gen_102
<z, z>() -> q_gen_102
<s, s, s>(q_gen_101) -> q_gen_101
<s, z, s>(q_gen_102) -> q_gen_101
<z, s, s>(q_gen_102) -> q_gen_101
<z, z, s>(q_gen_115) -> q_gen_101
<z, z, z>() -> q_gen_101
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 19
() -> length([nil, z]) -> 19
() -> leq([a, n2]) -> 19
() -> leq([b, b]) -> 19
() -> leqnat([z, n2]) -> 19
() -> merge([cons(z, xs), nil, cons(z, xs)]) -> 19
() -> merge([nil, y, y]) -> 20
() -> plus([n, z, n]) -> 19
(append([t1, l2, _s])) -> append([cons(h1, t1), l2, cons(h1, _s)]) -> 22
(length([_ha, _ia]) /\ length([l1, _ga]) /\ merge([l1, l2, _ha])) -> leqnat([_ga, _ia]) -> 22
(length([_ka, _la]) /\ length([l2, _ja]) /\ merge([l1, l2, _ka])) -> leqnat([_ja, _la]) -> 20
(length([ll, _ca])) -> length([cons(x, ll), s(_ca)]) -> 22
(leq([z, y2]) /\ merge([xs, cons(y2, ys), _m])) -> merge([cons(z, xs), cons(y2, ys), cons(z, _m)]) -> 20
(not leq([z, y2]) /\ merge([cons(z, xs), ys, _n])) -> merge([cons(z, xs), cons(y2, ys), cons(y2, _n)]) -> 20
(leq([b, a])) -> BOT -> 20
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 20
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 20
(leqnat([s(nn1), z])) -> BOT -> 20
(plus([n, mm, _x])) -> plus([n, s(mm), s(_x)]) -> 20
}
Sat witness: Found: ((append([t1, l2, _s])) -> append([cons(h1, t1), l2, cons(h1, _s)]), {
_s -> cons(b, cons(b, nil))  ;  h1 -> a  ;  l2 -> cons(b, nil)  ;  t1 -> nil
})

-------------------------------------------
Step 59, which took 0.391282 s (model generation: 0.390222,  model checking: 0.001060):

Model:
|_
{
append -> 
{{{
Q={q_gen_100, q_gen_109, q_gen_110, q_gen_127, q_gen_128, q_gen_129},
Q_f={q_gen_109},
Delta=
{
<cons>(q_gen_128, q_gen_127) -> q_gen_127
<nil>() -> q_gen_127
<a>() -> q_gen_128
<b>() -> q_gen_128
<a, a>() -> q_gen_100
<b, b>() -> q_gen_100
<cons, cons>(q_gen_100, q_gen_110) -> q_gen_110
<nil, cons>(q_gen_128, q_gen_127) -> q_gen_110
<nil, nil>() -> q_gen_110
<cons, cons, cons>(q_gen_129, q_gen_109) -> q_gen_109
<cons, nil, cons>(q_gen_100, q_gen_110) -> q_gen_109
<nil, cons, cons>(q_gen_100, q_gen_110) -> q_gen_109
<nil, nil, cons>(q_gen_128, q_gen_127) -> q_gen_109
<nil, nil, nil>() -> q_gen_109
<a, a, a>() -> q_gen_129
<a, b, a>() -> q_gen_129
<b, a, b>() -> q_gen_129
<b, b, b>() -> q_gen_129
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_122, q_gen_123, q_gen_139, q_gen_140, q_gen_141, q_gen_142, q_gen_143, q_gen_94},
Q_f={q_gen_122},
Delta=
{
<cons>(q_gen_140, q_gen_139) -> q_gen_139
<cons>(q_gen_140, q_gen_94) -> q_gen_139
<a>() -> q_gen_140
<b>() -> q_gen_140
<s>(q_gen_142) -> q_gen_142
<z>() -> q_gen_142
<nil>() -> q_gen_94
<cons, s>(q_gen_123, q_gen_139) -> q_gen_122
<cons, s>(q_gen_123, q_gen_94) -> q_gen_122
<cons, s>(q_gen_141, q_gen_139) -> q_gen_122
<nil, z>() -> q_gen_122
<a, s>(q_gen_142) -> q_gen_123
<a, z>() -> q_gen_123
<b, z>() -> q_gen_123
<b, s>(q_gen_142) -> q_gen_141
<cons, s>(q_gen_141, q_gen_94) -> q_gen_143
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_108, q_gen_82},
Q_f={q_gen_108},
Delta=
{
<a, a>() -> q_gen_108
<a, b>() -> q_gen_108
<b, b>() -> q_gen_108
<b, a>() -> q_gen_82
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  leqnat -> 
{{{
Q={q_gen_106, q_gen_107, q_gen_145},
Q_f={q_gen_106},
Delta=
{
<s>(q_gen_107) -> q_gen_107
<z>() -> q_gen_107
<s, s>(q_gen_106) -> q_gen_106
<z, s>(q_gen_107) -> q_gen_106
<z, z>() -> q_gen_106
<s, s>(q_gen_145) -> q_gen_145
<s, z>(q_gen_107) -> q_gen_145
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  merge -> 
{{{
Q={q_gen_103, q_gen_104, q_gen_105, q_gen_117, q_gen_118, q_gen_121, q_gen_169, q_gen_72, q_gen_73},
Q_f={q_gen_103},
Delta=
{
<a>() -> q_gen_118
<b>() -> q_gen_118
<cons>(q_gen_118, q_gen_169) -> q_gen_169
<nil>() -> q_gen_169
<cons, cons>(q_gen_105, q_gen_72) -> q_gen_104
<cons, cons>(q_gen_73, q_gen_104) -> q_gen_104
<cons, cons>(q_gen_73, q_gen_72) -> q_gen_104
<nil, cons>(q_gen_118, q_gen_169) -> q_gen_104
<a, a>() -> q_gen_105
<a, b>() -> q_gen_105
<b, a>() -> q_gen_105
<nil, nil>() -> q_gen_72
<b, b>() -> q_gen_73
<cons, cons, cons>(q_gen_121, q_gen_117) -> q_gen_103
<cons, nil, cons>(q_gen_105, q_gen_72) -> q_gen_103
<cons, nil, cons>(q_gen_73, q_gen_72) -> q_gen_103
<nil, cons, cons>(q_gen_105, q_gen_104) -> q_gen_103
<nil, cons, cons>(q_gen_105, q_gen_72) -> q_gen_103
<nil, cons, cons>(q_gen_73, q_gen_72) -> q_gen_103
<nil, nil, nil>() -> q_gen_103
<cons, cons, cons>(q_gen_121, q_gen_103) -> q_gen_117
<cons, nil, cons>(q_gen_73, q_gen_104) -> q_gen_117
<nil, cons, cons>(q_gen_73, q_gen_104) -> q_gen_117
<nil, nil, cons>(q_gen_118, q_gen_169) -> q_gen_117
<a, a, a>() -> q_gen_121
<a, a, b>() -> q_gen_121
<a, b, a>() -> q_gen_121
<a, b, b>() -> q_gen_121
<b, a, a>() -> q_gen_121
<b, a, b>() -> q_gen_121
<b, b, a>() -> q_gen_121
<b, b, b>() -> q_gen_121
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_101, q_gen_102, q_gen_115},
Q_f={q_gen_101},
Delta=
{
<s>(q_gen_115) -> q_gen_115
<z>() -> q_gen_115
<s, s>(q_gen_102) -> q_gen_102
<z, s>(q_gen_115) -> q_gen_102
<z, z>() -> q_gen_102
<s, s, s>(q_gen_101) -> q_gen_101
<s, z, s>(q_gen_102) -> q_gen_101
<z, s, s>(q_gen_102) -> q_gen_101
<z, z, s>(q_gen_115) -> q_gen_101
<z, z, z>() -> q_gen_101
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 19
() -> length([nil, z]) -> 19
() -> leq([a, n2]) -> 19
() -> leq([b, b]) -> 19
() -> leqnat([z, n2]) -> 19
() -> merge([cons(z, xs), nil, cons(z, xs)]) -> 22
() -> merge([nil, y, y]) -> 20
() -> plus([n, z, n]) -> 20
(append([t1, l2, _s])) -> append([cons(h1, t1), l2, cons(h1, _s)]) -> 22
(length([_ha, _ia]) /\ length([l1, _ga]) /\ merge([l1, l2, _ha])) -> leqnat([_ga, _ia]) -> 22
(length([_ka, _la]) /\ length([l2, _ja]) /\ merge([l1, l2, _ka])) -> leqnat([_ja, _la]) -> 20
(length([ll, _ca])) -> length([cons(x, ll), s(_ca)]) -> 22
(leq([z, y2]) /\ merge([xs, cons(y2, ys), _m])) -> merge([cons(z, xs), cons(y2, ys), cons(z, _m)]) -> 20
(not leq([z, y2]) /\ merge([cons(z, xs), ys, _n])) -> merge([cons(z, xs), cons(y2, ys), cons(y2, _n)]) -> 20
(leq([b, a])) -> BOT -> 20
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 20
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 20
(leqnat([s(nn1), z])) -> BOT -> 20
(plus([n, mm, _x])) -> plus([n, s(mm), s(_x)]) -> 20
}
Sat witness: Found: (() -> merge([cons(z, xs), nil, cons(z, xs)]), {
xs -> cons(a, nil)  ;  z -> b
})

-------------------------------------------
Step 60, which took 0.391444 s (model generation: 0.389296,  model checking: 0.002148):

Model:
|_
{
append -> 
{{{
Q={q_gen_100, q_gen_109, q_gen_110, q_gen_127, q_gen_128, q_gen_129},
Q_f={q_gen_109},
Delta=
{
<cons>(q_gen_128, q_gen_127) -> q_gen_127
<nil>() -> q_gen_127
<a>() -> q_gen_128
<b>() -> q_gen_128
<a, a>() -> q_gen_100
<b, b>() -> q_gen_100
<cons, cons>(q_gen_100, q_gen_110) -> q_gen_110
<nil, cons>(q_gen_128, q_gen_127) -> q_gen_110
<nil, nil>() -> q_gen_110
<cons, cons, cons>(q_gen_129, q_gen_109) -> q_gen_109
<cons, nil, cons>(q_gen_100, q_gen_110) -> q_gen_109
<nil, cons, cons>(q_gen_100, q_gen_110) -> q_gen_109
<nil, nil, cons>(q_gen_128, q_gen_127) -> q_gen_109
<nil, nil, nil>() -> q_gen_109
<a, a, a>() -> q_gen_129
<a, b, a>() -> q_gen_129
<b, a, b>() -> q_gen_129
<b, b, b>() -> q_gen_129
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_122, q_gen_123, q_gen_139, q_gen_140, q_gen_141, q_gen_142, q_gen_143, q_gen_94},
Q_f={q_gen_122},
Delta=
{
<cons>(q_gen_140, q_gen_139) -> q_gen_139
<cons>(q_gen_140, q_gen_94) -> q_gen_139
<a>() -> q_gen_140
<b>() -> q_gen_140
<s>(q_gen_142) -> q_gen_142
<z>() -> q_gen_142
<nil>() -> q_gen_94
<cons, s>(q_gen_123, q_gen_94) -> q_gen_122
<cons, s>(q_gen_141, q_gen_139) -> q_gen_122
<nil, z>() -> q_gen_122
<a, z>() -> q_gen_123
<b, z>() -> q_gen_123
<a, s>(q_gen_142) -> q_gen_141
<b, s>(q_gen_142) -> q_gen_141
<cons, s>(q_gen_123, q_gen_139) -> q_gen_143
<cons, s>(q_gen_141, q_gen_94) -> q_gen_143
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_108, q_gen_82},
Q_f={q_gen_108},
Delta=
{
<a, a>() -> q_gen_108
<a, b>() -> q_gen_108
<b, b>() -> q_gen_108
<b, a>() -> q_gen_82
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  leqnat -> 
{{{
Q={q_gen_106, q_gen_107, q_gen_145},
Q_f={q_gen_106},
Delta=
{
<s>(q_gen_107) -> q_gen_107
<z>() -> q_gen_107
<s, s>(q_gen_106) -> q_gen_106
<z, s>(q_gen_107) -> q_gen_106
<z, z>() -> q_gen_106
<s, s>(q_gen_145) -> q_gen_145
<s, z>(q_gen_107) -> q_gen_145
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  merge -> 
{{{
Q={q_gen_103, q_gen_104, q_gen_105, q_gen_117, q_gen_118, q_gen_121, q_gen_156, q_gen_169, q_gen_73},
Q_f={q_gen_103},
Delta=
{
<a>() -> q_gen_118
<b>() -> q_gen_118
<cons>(q_gen_118, q_gen_169) -> q_gen_169
<nil>() -> q_gen_169
<cons, cons>(q_gen_105, q_gen_104) -> q_gen_104
<nil, nil>() -> q_gen_104
<a, a>() -> q_gen_105
<a, b>() -> q_gen_105
<b, a>() -> q_gen_105
<cons, cons>(q_gen_73, q_gen_104) -> q_gen_156
<cons, cons>(q_gen_73, q_gen_156) -> q_gen_156
<nil, cons>(q_gen_118, q_gen_169) -> q_gen_156
<b, b>() -> q_gen_73
<cons, cons, cons>(q_gen_121, q_gen_117) -> q_gen_103
<cons, nil, cons>(q_gen_73, q_gen_104) -> q_gen_103
<nil, cons, cons>(q_gen_105, q_gen_104) -> q_gen_103
<nil, cons, cons>(q_gen_73, q_gen_104) -> q_gen_103
<nil, nil, nil>() -> q_gen_103
<cons, cons, cons>(q_gen_121, q_gen_103) -> q_gen_117
<cons, nil, cons>(q_gen_105, q_gen_104) -> q_gen_117
<cons, nil, cons>(q_gen_73, q_gen_156) -> q_gen_117
<nil, cons, cons>(q_gen_73, q_gen_156) -> q_gen_117
<nil, nil, cons>(q_gen_118, q_gen_169) -> q_gen_117
<a, a, a>() -> q_gen_121
<a, a, b>() -> q_gen_121
<a, b, a>() -> q_gen_121
<a, b, b>() -> q_gen_121
<b, a, a>() -> q_gen_121
<b, a, b>() -> q_gen_121
<b, b, a>() -> q_gen_121
<b, b, b>() -> q_gen_121
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_101, q_gen_102, q_gen_115},
Q_f={q_gen_101},
Delta=
{
<s>(q_gen_115) -> q_gen_115
<z>() -> q_gen_115
<s, s>(q_gen_102) -> q_gen_102
<z, s>(q_gen_115) -> q_gen_102
<z, z>() -> q_gen_102
<s, s, s>(q_gen_101) -> q_gen_101
<s, z, s>(q_gen_102) -> q_gen_101
<z, s, s>(q_gen_102) -> q_gen_101
<z, z, s>(q_gen_115) -> q_gen_101
<z, z, z>() -> q_gen_101
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 20
() -> length([nil, z]) -> 20
() -> leq([a, n2]) -> 20
() -> leq([b, b]) -> 20
() -> leqnat([z, n2]) -> 20
() -> merge([cons(z, xs), nil, cons(z, xs)]) -> 22
() -> merge([nil, y, y]) -> 20
() -> plus([n, z, n]) -> 20
(append([t1, l2, _s])) -> append([cons(h1, t1), l2, cons(h1, _s)]) -> 22
(length([_ha, _ia]) /\ length([l1, _ga]) /\ merge([l1, l2, _ha])) -> leqnat([_ga, _ia]) -> 22
(length([_ka, _la]) /\ length([l2, _ja]) /\ merge([l1, l2, _ka])) -> leqnat([_ja, _la]) -> 20
(length([ll, _ca])) -> length([cons(x, ll), s(_ca)]) -> 22
(leq([z, y2]) /\ merge([xs, cons(y2, ys), _m])) -> merge([cons(z, xs), cons(y2, ys), cons(z, _m)]) -> 20
(not leq([z, y2]) /\ merge([cons(z, xs), ys, _n])) -> merge([cons(z, xs), cons(y2, ys), cons(y2, _n)]) -> 23
(leq([b, a])) -> BOT -> 21
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 21
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 21
(leqnat([s(nn1), z])) -> BOT -> 21
(plus([n, mm, _x])) -> plus([n, s(mm), s(_x)]) -> 21
}
Sat witness: Found: ((not leq([z, y2]) /\ merge([cons(z, xs), ys, _n])) -> merge([cons(z, xs), cons(y2, ys), cons(y2, _n)]), {
_n -> cons(b, cons(b, cons(b, nil)))  ;  xs -> cons(b, nil)  ;  y2 -> a  ;  ys -> cons(b, cons(b, cons(b, nil)))  ;  z -> b
})

-------------------------------------------
Step 61, which took 0.612623 s (model generation: 0.573561,  model checking: 0.039062):

Model:
|_
{
append -> 
{{{
Q={q_gen_100, q_gen_109, q_gen_110, q_gen_127, q_gen_128, q_gen_129},
Q_f={q_gen_109},
Delta=
{
<cons>(q_gen_128, q_gen_127) -> q_gen_127
<nil>() -> q_gen_127
<a>() -> q_gen_128
<b>() -> q_gen_128
<a, a>() -> q_gen_100
<b, b>() -> q_gen_100
<cons, cons>(q_gen_100, q_gen_110) -> q_gen_110
<nil, cons>(q_gen_128, q_gen_127) -> q_gen_110
<nil, nil>() -> q_gen_110
<cons, cons, cons>(q_gen_129, q_gen_109) -> q_gen_109
<cons, nil, cons>(q_gen_100, q_gen_110) -> q_gen_109
<nil, cons, cons>(q_gen_100, q_gen_110) -> q_gen_109
<nil, nil, cons>(q_gen_128, q_gen_127) -> q_gen_109
<nil, nil, nil>() -> q_gen_109
<a, a, a>() -> q_gen_129
<a, b, a>() -> q_gen_129
<b, a, b>() -> q_gen_129
<b, b, b>() -> q_gen_129
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_122, q_gen_123, q_gen_139, q_gen_140, q_gen_141, q_gen_142, q_gen_143, q_gen_175, q_gen_177, q_gen_178, q_gen_94},
Q_f={q_gen_122},
Delta=
{
<cons>(q_gen_140, q_gen_94) -> q_gen_139
<a>() -> q_gen_140
<b>() -> q_gen_140
<z>() -> q_gen_142
<cons>(q_gen_140, q_gen_139) -> q_gen_175
<cons>(q_gen_140, q_gen_175) -> q_gen_175
<s>(q_gen_142) -> q_gen_178
<s>(q_gen_178) -> q_gen_178
<nil>() -> q_gen_94
<cons, s>(q_gen_123, q_gen_94) -> q_gen_122
<cons, s>(q_gen_141, q_gen_139) -> q_gen_122
<cons, s>(q_gen_177, q_gen_175) -> q_gen_122
<nil, z>() -> q_gen_122
<a, z>() -> q_gen_123
<b, z>() -> q_gen_123
<a, s>(q_gen_142) -> q_gen_141
<b, s>(q_gen_142) -> q_gen_141
<cons, s>(q_gen_123, q_gen_139) -> q_gen_143
<cons, s>(q_gen_141, q_gen_175) -> q_gen_143
<cons, s>(q_gen_141, q_gen_94) -> q_gen_143
<cons, s>(q_gen_177, q_gen_139) -> q_gen_143
<cons, s>(q_gen_177, q_gen_94) -> q_gen_143
<a, s>(q_gen_178) -> q_gen_177
<b, s>(q_gen_178) -> q_gen_177
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_108, q_gen_82},
Q_f={q_gen_108},
Delta=
{
<a, a>() -> q_gen_108
<a, b>() -> q_gen_108
<b, b>() -> q_gen_108
<b, a>() -> q_gen_82
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  leqnat -> 
{{{
Q={q_gen_106, q_gen_107, q_gen_145},
Q_f={q_gen_106},
Delta=
{
<s>(q_gen_107) -> q_gen_107
<z>() -> q_gen_107
<s, s>(q_gen_106) -> q_gen_106
<z, s>(q_gen_107) -> q_gen_106
<z, z>() -> q_gen_106
<s, s>(q_gen_145) -> q_gen_145
<s, z>(q_gen_107) -> q_gen_145
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  merge -> 
{{{
Q={q_gen_103, q_gen_104, q_gen_105, q_gen_118, q_gen_121, q_gen_169},
Q_f={q_gen_103},
Delta=
{
<a>() -> q_gen_118
<b>() -> q_gen_118
<cons>(q_gen_118, q_gen_169) -> q_gen_169
<nil>() -> q_gen_169
<cons, cons>(q_gen_105, q_gen_104) -> q_gen_104
<nil, cons>(q_gen_118, q_gen_169) -> q_gen_104
<nil, nil>() -> q_gen_104
<a, a>() -> q_gen_105
<a, b>() -> q_gen_105
<b, a>() -> q_gen_105
<b, b>() -> q_gen_105
<cons, cons, cons>(q_gen_121, q_gen_103) -> q_gen_103
<cons, nil, cons>(q_gen_105, q_gen_104) -> q_gen_103
<nil, cons, cons>(q_gen_105, q_gen_104) -> q_gen_103
<nil, nil, cons>(q_gen_118, q_gen_169) -> q_gen_103
<nil, nil, nil>() -> q_gen_103
<a, a, a>() -> q_gen_121
<a, a, b>() -> q_gen_121
<a, b, a>() -> q_gen_121
<a, b, b>() -> q_gen_121
<b, a, a>() -> q_gen_121
<b, a, b>() -> q_gen_121
<b, b, a>() -> q_gen_121
<b, b, b>() -> q_gen_121
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_101, q_gen_102, q_gen_115},
Q_f={q_gen_101},
Delta=
{
<s>(q_gen_115) -> q_gen_115
<z>() -> q_gen_115
<s, s>(q_gen_102) -> q_gen_102
<z, s>(q_gen_115) -> q_gen_102
<z, z>() -> q_gen_102
<s, s, s>(q_gen_101) -> q_gen_101
<s, z, s>(q_gen_102) -> q_gen_101
<z, s, s>(q_gen_102) -> q_gen_101
<z, z, s>(q_gen_115) -> q_gen_101
<z, z, z>() -> q_gen_101
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 20
() -> length([nil, z]) -> 20
() -> leq([a, n2]) -> 20
() -> leq([b, b]) -> 20
() -> leqnat([z, n2]) -> 20
() -> merge([cons(z, xs), nil, cons(z, xs)]) -> 22
() -> merge([nil, y, y]) -> 20
() -> plus([n, z, n]) -> 20
(append([t1, l2, _s])) -> append([cons(h1, t1), l2, cons(h1, _s)]) -> 22
(length([_ha, _ia]) /\ length([l1, _ga]) /\ merge([l1, l2, _ha])) -> leqnat([_ga, _ia]) -> 22
(length([_ka, _la]) /\ length([l2, _ja]) /\ merge([l1, l2, _ka])) -> leqnat([_ja, _la]) -> 23
(length([ll, _ca])) -> length([cons(x, ll), s(_ca)]) -> 22
(leq([z, y2]) /\ merge([xs, cons(y2, ys), _m])) -> merge([cons(z, xs), cons(y2, ys), cons(z, _m)]) -> 21
(not leq([z, y2]) /\ merge([cons(z, xs), ys, _n])) -> merge([cons(z, xs), cons(y2, ys), cons(y2, _n)]) -> 23
(leq([b, a])) -> BOT -> 21
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 21
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 21
(leqnat([s(nn1), z])) -> BOT -> 21
(plus([n, mm, _x])) -> plus([n, s(mm), s(_x)]) -> 21
}
Sat witness: Found: ((length([_ka, _la]) /\ length([l2, _ja]) /\ merge([l1, l2, _ka])) -> leqnat([_ja, _la]), {
_ja -> s(s(s(s(z))))  ;  _ka -> cons(b, cons(b, cons(b, nil)))  ;  _la -> s(s(s(z)))  ;  l1 -> nil  ;  l2 -> cons(b, cons(b, cons(b, nil)))
})

-------------------------------------------
Step 62, which took 1.538484 s (model generation: 1.454377,  model checking: 0.084107):

Model:
|_
{
append -> 
{{{
Q={q_gen_100, q_gen_109, q_gen_110, q_gen_127, q_gen_128, q_gen_129},
Q_f={q_gen_109},
Delta=
{
<cons>(q_gen_128, q_gen_127) -> q_gen_127
<nil>() -> q_gen_127
<a>() -> q_gen_128
<b>() -> q_gen_128
<a, a>() -> q_gen_100
<b, b>() -> q_gen_100
<cons, cons>(q_gen_100, q_gen_110) -> q_gen_110
<nil, cons>(q_gen_128, q_gen_127) -> q_gen_110
<nil, nil>() -> q_gen_110
<cons, cons, cons>(q_gen_129, q_gen_109) -> q_gen_109
<cons, nil, cons>(q_gen_100, q_gen_110) -> q_gen_109
<nil, cons, cons>(q_gen_100, q_gen_110) -> q_gen_109
<nil, nil, cons>(q_gen_128, q_gen_127) -> q_gen_109
<nil, nil, nil>() -> q_gen_109
<a, a, a>() -> q_gen_129
<a, b, a>() -> q_gen_129
<b, a, b>() -> q_gen_129
<b, b, b>() -> q_gen_129
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_122, q_gen_123, q_gen_139, q_gen_140, q_gen_141, q_gen_142, q_gen_143, q_gen_175, q_gen_178},
Q_f={q_gen_122},
Delta=
{
<cons>(q_gen_140, q_gen_175) -> q_gen_139
<a>() -> q_gen_140
<b>() -> q_gen_140
<s>(q_gen_178) -> q_gen_142
<z>() -> q_gen_142
<cons>(q_gen_140, q_gen_139) -> q_gen_175
<nil>() -> q_gen_175
<s>(q_gen_142) -> q_gen_178
<cons, s>(q_gen_123, q_gen_175) -> q_gen_122
<cons, s>(q_gen_141, q_gen_139) -> q_gen_122
<nil, z>() -> q_gen_122
<a, s>(q_gen_178) -> q_gen_123
<a, z>() -> q_gen_123
<b, s>(q_gen_178) -> q_gen_123
<b, z>() -> q_gen_123
<a, s>(q_gen_142) -> q_gen_141
<b, s>(q_gen_142) -> q_gen_141
<cons, s>(q_gen_123, q_gen_139) -> q_gen_143
<cons, s>(q_gen_141, q_gen_175) -> q_gen_143
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_108, q_gen_82},
Q_f={q_gen_108},
Delta=
{
<a, a>() -> q_gen_108
<a, b>() -> q_gen_108
<b, b>() -> q_gen_108
<b, a>() -> q_gen_82
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  leqnat -> 
{{{
Q={q_gen_106, q_gen_107, q_gen_145},
Q_f={q_gen_106},
Delta=
{
<s>(q_gen_107) -> q_gen_107
<z>() -> q_gen_107
<s, s>(q_gen_106) -> q_gen_106
<z, s>(q_gen_107) -> q_gen_106
<z, z>() -> q_gen_106
<s, s>(q_gen_145) -> q_gen_145
<s, z>(q_gen_107) -> q_gen_145
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  merge -> 
{{{
Q={q_gen_103, q_gen_104, q_gen_105, q_gen_118, q_gen_121, q_gen_155, q_gen_156, q_gen_169},
Q_f={q_gen_103},
Delta=
{
<a>() -> q_gen_118
<b>() -> q_gen_118
<cons>(q_gen_118, q_gen_169) -> q_gen_169
<nil>() -> q_gen_169
<cons, cons>(q_gen_105, q_gen_104) -> q_gen_104
<cons, cons>(q_gen_105, q_gen_156) -> q_gen_104
<nil, nil>() -> q_gen_104
<a, a>() -> q_gen_105
<a, b>() -> q_gen_105
<b, a>() -> q_gen_105
<b, b>() -> q_gen_105
<nil, cons>(q_gen_118, q_gen_169) -> q_gen_156
<cons, cons, cons>(q_gen_121, q_gen_103) -> q_gen_103
<cons, cons, cons>(q_gen_121, q_gen_155) -> q_gen_103
<cons, nil, cons>(q_gen_105, q_gen_104) -> q_gen_103
<nil, cons, cons>(q_gen_105, q_gen_104) -> q_gen_103
<nil, nil, cons>(q_gen_118, q_gen_169) -> q_gen_103
<nil, nil, nil>() -> q_gen_103
<a, a, a>() -> q_gen_121
<a, a, b>() -> q_gen_121
<a, b, a>() -> q_gen_121
<a, b, b>() -> q_gen_121
<b, a, a>() -> q_gen_121
<b, a, b>() -> q_gen_121
<b, b, a>() -> q_gen_121
<b, b, b>() -> q_gen_121
<cons, nil, cons>(q_gen_105, q_gen_156) -> q_gen_155
<nil, cons, cons>(q_gen_105, q_gen_156) -> q_gen_155
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_101, q_gen_102, q_gen_115},
Q_f={q_gen_101},
Delta=
{
<s>(q_gen_115) -> q_gen_115
<z>() -> q_gen_115
<s, s>(q_gen_102) -> q_gen_102
<z, s>(q_gen_115) -> q_gen_102
<z, z>() -> q_gen_102
<s, s, s>(q_gen_101) -> q_gen_101
<s, z, s>(q_gen_102) -> q_gen_101
<z, s, s>(q_gen_102) -> q_gen_101
<z, z, s>(q_gen_115) -> q_gen_101
<z, z, z>() -> q_gen_101
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 21
() -> length([nil, z]) -> 21
() -> leq([a, n2]) -> 21
() -> leq([b, b]) -> 21
() -> leqnat([z, n2]) -> 21
() -> merge([cons(z, xs), nil, cons(z, xs)]) -> 22
() -> merge([nil, y, y]) -> 21
() -> plus([n, z, n]) -> 21
(append([t1, l2, _s])) -> append([cons(h1, t1), l2, cons(h1, _s)]) -> 22
(length([_ha, _ia]) /\ length([l1, _ga]) /\ merge([l1, l2, _ha])) -> leqnat([_ga, _ia]) -> 25
(length([_ka, _la]) /\ length([l2, _ja]) /\ merge([l1, l2, _ka])) -> leqnat([_ja, _la]) -> 23
(length([ll, _ca])) -> length([cons(x, ll), s(_ca)]) -> 23
(leq([z, y2]) /\ merge([xs, cons(y2, ys), _m])) -> merge([cons(z, xs), cons(y2, ys), cons(z, _m)]) -> 22
(not leq([z, y2]) /\ merge([cons(z, xs), ys, _n])) -> merge([cons(z, xs), cons(y2, ys), cons(y2, _n)]) -> 23
(leq([b, a])) -> BOT -> 22
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 22
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 22
(leqnat([s(nn1), z])) -> BOT -> 22
(plus([n, mm, _x])) -> plus([n, s(mm), s(_x)]) -> 22
}
Sat witness: Found: ((length([_ha, _ia]) /\ length([l1, _ga]) /\ merge([l1, l2, _ha])) -> leqnat([_ga, _ia]), {
_ga -> s(s(s(z)))  ;  _ha -> cons(b, cons(b, cons(b, nil)))  ;  _ia -> s(z)  ;  l1 -> cons(b, nil)  ;  l2 -> cons(b, cons(b, nil))
})

-------------------------------------------
Step 63, which took 0.621714 s (model generation: 0.579307,  model checking: 0.042407):

Model:
|_
{
append -> 
{{{
Q={q_gen_100, q_gen_109, q_gen_110, q_gen_127, q_gen_128, q_gen_129},
Q_f={q_gen_109},
Delta=
{
<cons>(q_gen_128, q_gen_127) -> q_gen_127
<nil>() -> q_gen_127
<a>() -> q_gen_128
<b>() -> q_gen_128
<a, a>() -> q_gen_100
<b, b>() -> q_gen_100
<cons, cons>(q_gen_100, q_gen_110) -> q_gen_110
<nil, cons>(q_gen_128, q_gen_127) -> q_gen_110
<nil, nil>() -> q_gen_110
<cons, cons, cons>(q_gen_129, q_gen_109) -> q_gen_109
<cons, nil, cons>(q_gen_100, q_gen_110) -> q_gen_109
<nil, cons, cons>(q_gen_100, q_gen_110) -> q_gen_109
<nil, nil, cons>(q_gen_128, q_gen_127) -> q_gen_109
<nil, nil, nil>() -> q_gen_109
<a, a, a>() -> q_gen_129
<a, b, a>() -> q_gen_129
<b, a, b>() -> q_gen_129
<b, b, b>() -> q_gen_129
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_122, q_gen_123, q_gen_139, q_gen_140, q_gen_141, q_gen_142, q_gen_143, q_gen_175, q_gen_177, q_gen_178, q_gen_94},
Q_f={q_gen_122},
Delta=
{
<cons>(q_gen_140, q_gen_175) -> q_gen_139
<cons>(q_gen_140, q_gen_94) -> q_gen_139
<a>() -> q_gen_140
<b>() -> q_gen_140
<s>(q_gen_178) -> q_gen_142
<z>() -> q_gen_142
<cons>(q_gen_140, q_gen_139) -> q_gen_175
<s>(q_gen_142) -> q_gen_178
<nil>() -> q_gen_94
<cons, s>(q_gen_123, q_gen_175) -> q_gen_122
<cons, s>(q_gen_123, q_gen_94) -> q_gen_122
<cons, s>(q_gen_141, q_gen_139) -> q_gen_122
<cons, s>(q_gen_177, q_gen_175) -> q_gen_122
<nil, z>() -> q_gen_122
<a, z>() -> q_gen_123
<b, z>() -> q_gen_123
<a, s>(q_gen_142) -> q_gen_141
<b, s>(q_gen_142) -> q_gen_141
<cons, s>(q_gen_123, q_gen_139) -> q_gen_143
<cons, s>(q_gen_141, q_gen_175) -> q_gen_143
<cons, s>(q_gen_141, q_gen_94) -> q_gen_143
<cons, s>(q_gen_177, q_gen_139) -> q_gen_143
<cons, s>(q_gen_177, q_gen_94) -> q_gen_143
<a, s>(q_gen_178) -> q_gen_177
<b, s>(q_gen_178) -> q_gen_177
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_108, q_gen_82},
Q_f={q_gen_108},
Delta=
{
<a, a>() -> q_gen_108
<a, b>() -> q_gen_108
<b, b>() -> q_gen_108
<b, a>() -> q_gen_82
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  leqnat -> 
{{{
Q={q_gen_106, q_gen_107, q_gen_145},
Q_f={q_gen_106},
Delta=
{
<s>(q_gen_107) -> q_gen_107
<z>() -> q_gen_107
<s, s>(q_gen_106) -> q_gen_106
<z, s>(q_gen_107) -> q_gen_106
<z, z>() -> q_gen_106
<s, s>(q_gen_145) -> q_gen_145
<s, z>(q_gen_107) -> q_gen_145
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  merge -> 
{{{
Q={q_gen_103, q_gen_104, q_gen_105, q_gen_118, q_gen_121, q_gen_169},
Q_f={q_gen_103},
Delta=
{
<a>() -> q_gen_118
<b>() -> q_gen_118
<cons>(q_gen_118, q_gen_169) -> q_gen_169
<nil>() -> q_gen_169
<cons, cons>(q_gen_105, q_gen_104) -> q_gen_104
<nil, cons>(q_gen_118, q_gen_169) -> q_gen_104
<nil, nil>() -> q_gen_104
<a, a>() -> q_gen_105
<a, b>() -> q_gen_105
<b, a>() -> q_gen_105
<b, b>() -> q_gen_105
<cons, cons, cons>(q_gen_121, q_gen_103) -> q_gen_103
<cons, nil, cons>(q_gen_105, q_gen_104) -> q_gen_103
<nil, cons, cons>(q_gen_105, q_gen_104) -> q_gen_103
<nil, nil, cons>(q_gen_118, q_gen_169) -> q_gen_103
<nil, nil, nil>() -> q_gen_103
<a, a, a>() -> q_gen_121
<a, a, b>() -> q_gen_121
<a, b, a>() -> q_gen_121
<a, b, b>() -> q_gen_121
<b, a, a>() -> q_gen_121
<b, a, b>() -> q_gen_121
<b, b, a>() -> q_gen_121
<b, b, b>() -> q_gen_121
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_101, q_gen_102, q_gen_115},
Q_f={q_gen_101},
Delta=
{
<s>(q_gen_115) -> q_gen_115
<z>() -> q_gen_115
<s, s>(q_gen_102) -> q_gen_102
<z, s>(q_gen_115) -> q_gen_102
<z, z>() -> q_gen_102
<s, s, s>(q_gen_101) -> q_gen_101
<s, z, s>(q_gen_102) -> q_gen_101
<z, s, s>(q_gen_102) -> q_gen_101
<z, z, s>(q_gen_115) -> q_gen_101
<z, z, z>() -> q_gen_101
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 22
() -> length([nil, z]) -> 22
() -> leq([a, n2]) -> 22
() -> leq([b, b]) -> 22
() -> leqnat([z, n2]) -> 22
() -> merge([cons(z, xs), nil, cons(z, xs)]) -> 22
() -> merge([nil, y, y]) -> 22
() -> plus([n, z, n]) -> 22
(append([t1, l2, _s])) -> append([cons(h1, t1), l2, cons(h1, _s)]) -> 25
(length([_ha, _ia]) /\ length([l1, _ga]) /\ merge([l1, l2, _ha])) -> leqnat([_ga, _ia]) -> 25
(length([_ka, _la]) /\ length([l2, _ja]) /\ merge([l1, l2, _ka])) -> leqnat([_ja, _la]) -> 23
(length([ll, _ca])) -> length([cons(x, ll), s(_ca)]) -> 23
(leq([z, y2]) /\ merge([xs, cons(y2, ys), _m])) -> merge([cons(z, xs), cons(y2, ys), cons(z, _m)]) -> 23
(not leq([z, y2]) /\ merge([cons(z, xs), ys, _n])) -> merge([cons(z, xs), cons(y2, ys), cons(y2, _n)]) -> 23
(leq([b, a])) -> BOT -> 23
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 23
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 23
(leqnat([s(nn1), z])) -> BOT -> 23
(plus([n, mm, _x])) -> plus([n, s(mm), s(_x)]) -> 23
}
Sat witness: Found: ((append([t1, l2, _s])) -> append([cons(h1, t1), l2, cons(h1, _s)]), {
_s -> cons(a, cons(b, nil))  ;  h1 -> b  ;  l2 -> cons(a, cons(b, nil))  ;  t1 -> nil
})

-------------------------------------------
Step 64, which took 0.723589 s (model generation: 0.660887,  model checking: 0.062702):

Model:
|_
{
append -> 
{{{
Q={q_gen_100, q_gen_109, q_gen_110, q_gen_127, q_gen_128, q_gen_129},
Q_f={q_gen_109},
Delta=
{
<cons>(q_gen_128, q_gen_127) -> q_gen_127
<nil>() -> q_gen_127
<a>() -> q_gen_128
<b>() -> q_gen_128
<a, a>() -> q_gen_100
<b, a>() -> q_gen_100
<b, b>() -> q_gen_100
<cons, cons>(q_gen_100, q_gen_110) -> q_gen_110
<nil, cons>(q_gen_128, q_gen_127) -> q_gen_110
<nil, nil>() -> q_gen_110
<cons, cons, cons>(q_gen_129, q_gen_109) -> q_gen_109
<cons, nil, cons>(q_gen_100, q_gen_110) -> q_gen_109
<nil, cons, cons>(q_gen_100, q_gen_110) -> q_gen_109
<nil, nil, cons>(q_gen_128, q_gen_127) -> q_gen_109
<nil, nil, nil>() -> q_gen_109
<a, a, a>() -> q_gen_129
<a, b, a>() -> q_gen_129
<b, a, b>() -> q_gen_129
<b, b, b>() -> q_gen_129
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_122, q_gen_123, q_gen_139, q_gen_140, q_gen_141, q_gen_142, q_gen_143, q_gen_175, q_gen_177, q_gen_178, q_gen_94},
Q_f={q_gen_122},
Delta=
{
<cons>(q_gen_140, q_gen_175) -> q_gen_139
<cons>(q_gen_140, q_gen_94) -> q_gen_139
<a>() -> q_gen_140
<b>() -> q_gen_140
<s>(q_gen_178) -> q_gen_142
<z>() -> q_gen_142
<cons>(q_gen_140, q_gen_139) -> q_gen_175
<s>(q_gen_142) -> q_gen_178
<nil>() -> q_gen_94
<cons, s>(q_gen_123, q_gen_94) -> q_gen_122
<cons, s>(q_gen_141, q_gen_139) -> q_gen_122
<cons, s>(q_gen_177, q_gen_175) -> q_gen_122
<nil, z>() -> q_gen_122
<a, z>() -> q_gen_123
<b, z>() -> q_gen_123
<a, s>(q_gen_142) -> q_gen_141
<b, s>(q_gen_142) -> q_gen_141
<cons, s>(q_gen_123, q_gen_139) -> q_gen_143
<cons, s>(q_gen_123, q_gen_175) -> q_gen_143
<cons, s>(q_gen_141, q_gen_175) -> q_gen_143
<cons, s>(q_gen_141, q_gen_94) -> q_gen_143
<cons, s>(q_gen_177, q_gen_139) -> q_gen_143
<cons, s>(q_gen_177, q_gen_94) -> q_gen_143
<a, s>(q_gen_178) -> q_gen_177
<b, s>(q_gen_178) -> q_gen_177
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_108, q_gen_82},
Q_f={q_gen_108},
Delta=
{
<a, a>() -> q_gen_108
<a, b>() -> q_gen_108
<b, b>() -> q_gen_108
<b, a>() -> q_gen_82
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  leqnat -> 
{{{
Q={q_gen_106, q_gen_107, q_gen_145},
Q_f={q_gen_106},
Delta=
{
<s>(q_gen_107) -> q_gen_107
<z>() -> q_gen_107
<s, s>(q_gen_106) -> q_gen_106
<z, s>(q_gen_107) -> q_gen_106
<z, z>() -> q_gen_106
<s, s>(q_gen_145) -> q_gen_145
<s, z>(q_gen_107) -> q_gen_145
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  merge -> 
{{{
Q={q_gen_103, q_gen_104, q_gen_105, q_gen_118, q_gen_121, q_gen_169},
Q_f={q_gen_103},
Delta=
{
<a>() -> q_gen_118
<b>() -> q_gen_118
<cons>(q_gen_118, q_gen_169) -> q_gen_169
<nil>() -> q_gen_169
<cons, cons>(q_gen_105, q_gen_104) -> q_gen_104
<nil, cons>(q_gen_118, q_gen_169) -> q_gen_104
<nil, nil>() -> q_gen_104
<a, a>() -> q_gen_105
<a, b>() -> q_gen_105
<b, a>() -> q_gen_105
<b, b>() -> q_gen_105
<cons, cons, cons>(q_gen_121, q_gen_103) -> q_gen_103
<cons, nil, cons>(q_gen_105, q_gen_104) -> q_gen_103
<nil, cons, cons>(q_gen_105, q_gen_104) -> q_gen_103
<nil, nil, cons>(q_gen_118, q_gen_169) -> q_gen_103
<nil, nil, nil>() -> q_gen_103
<a, a, a>() -> q_gen_121
<a, a, b>() -> q_gen_121
<a, b, a>() -> q_gen_121
<a, b, b>() -> q_gen_121
<b, a, a>() -> q_gen_121
<b, a, b>() -> q_gen_121
<b, b, a>() -> q_gen_121
<b, b, b>() -> q_gen_121
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_101, q_gen_102, q_gen_115},
Q_f={q_gen_101},
Delta=
{
<s>(q_gen_115) -> q_gen_115
<z>() -> q_gen_115
<s, s>(q_gen_102) -> q_gen_102
<z, s>(q_gen_115) -> q_gen_102
<z, z>() -> q_gen_102
<s, s, s>(q_gen_101) -> q_gen_101
<s, z, s>(q_gen_102) -> q_gen_101
<z, s, s>(q_gen_102) -> q_gen_101
<z, z, s>(q_gen_115) -> q_gen_101
<z, z, z>() -> q_gen_101
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 23
() -> length([nil, z]) -> 23
() -> leq([a, n2]) -> 23
() -> leq([b, b]) -> 23
() -> leqnat([z, n2]) -> 23
() -> merge([cons(z, xs), nil, cons(z, xs)]) -> 23
() -> merge([nil, y, y]) -> 23
() -> plus([n, z, n]) -> 23
(append([t1, l2, _s])) -> append([cons(h1, t1), l2, cons(h1, _s)]) -> 25
(length([_ha, _ia]) /\ length([l1, _ga]) /\ merge([l1, l2, _ha])) -> leqnat([_ga, _ia]) -> 25
(length([_ka, _la]) /\ length([l2, _ja]) /\ merge([l1, l2, _ka])) -> leqnat([_ja, _la]) -> 26
(length([ll, _ca])) -> length([cons(x, ll), s(_ca)]) -> 24
(leq([z, y2]) /\ merge([xs, cons(y2, ys), _m])) -> merge([cons(z, xs), cons(y2, ys), cons(z, _m)]) -> 24
(not leq([z, y2]) /\ merge([cons(z, xs), ys, _n])) -> merge([cons(z, xs), cons(y2, ys), cons(y2, _n)]) -> 24
(leq([b, a])) -> BOT -> 24
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 24
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 24
(leqnat([s(nn1), z])) -> BOT -> 24
(plus([n, mm, _x])) -> plus([n, s(mm), s(_x)]) -> 24
}
Sat witness: Found: ((length([_ka, _la]) /\ length([l2, _ja]) /\ merge([l1, l2, _ka])) -> leqnat([_ja, _la]), {
_ja -> s(s(s(s(z))))  ;  _ka -> cons(b, cons(b, cons(b, cons(b, nil))))  ;  _la -> s(s(z))  ;  l1 -> nil  ;  l2 -> cons(b, cons(b, nil))
})

-------------------------------------------
Step 65, which took 0.735570 s (model generation: 0.735124,  model checking: 0.000446):

Model:
|_
{
append -> 
{{{
Q={q_gen_100, q_gen_109, q_gen_110, q_gen_127, q_gen_128, q_gen_129},
Q_f={q_gen_109},
Delta=
{
<cons>(q_gen_128, q_gen_127) -> q_gen_127
<nil>() -> q_gen_127
<a>() -> q_gen_128
<b>() -> q_gen_128
<a, a>() -> q_gen_100
<b, a>() -> q_gen_100
<b, b>() -> q_gen_100
<cons, cons>(q_gen_100, q_gen_110) -> q_gen_110
<nil, cons>(q_gen_128, q_gen_127) -> q_gen_110
<nil, nil>() -> q_gen_110
<cons, cons, cons>(q_gen_129, q_gen_109) -> q_gen_109
<cons, nil, cons>(q_gen_100, q_gen_110) -> q_gen_109
<nil, cons, cons>(q_gen_100, q_gen_110) -> q_gen_109
<nil, nil, cons>(q_gen_128, q_gen_127) -> q_gen_109
<nil, nil, nil>() -> q_gen_109
<a, a, a>() -> q_gen_129
<a, b, a>() -> q_gen_129
<b, a, b>() -> q_gen_129
<b, b, b>() -> q_gen_129
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_122, q_gen_123, q_gen_139, q_gen_140, q_gen_141, q_gen_142, q_gen_143, q_gen_94},
Q_f={q_gen_122},
Delta=
{
<cons>(q_gen_140, q_gen_139) -> q_gen_139
<cons>(q_gen_140, q_gen_94) -> q_gen_139
<a>() -> q_gen_140
<b>() -> q_gen_140
<s>(q_gen_142) -> q_gen_142
<z>() -> q_gen_142
<nil>() -> q_gen_94
<cons, s>(q_gen_123, q_gen_94) -> q_gen_122
<cons, s>(q_gen_141, q_gen_139) -> q_gen_122
<nil, z>() -> q_gen_122
<a, z>() -> q_gen_123
<b, z>() -> q_gen_123
<a, s>(q_gen_142) -> q_gen_141
<b, s>(q_gen_142) -> q_gen_141
<cons, s>(q_gen_123, q_gen_139) -> q_gen_143
<cons, s>(q_gen_141, q_gen_94) -> q_gen_143
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_108, q_gen_82},
Q_f={q_gen_108},
Delta=
{
<a, a>() -> q_gen_108
<a, b>() -> q_gen_108
<b, b>() -> q_gen_108
<b, a>() -> q_gen_82
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  leqnat -> 
{{{
Q={q_gen_106, q_gen_107, q_gen_145},
Q_f={q_gen_106},
Delta=
{
<s>(q_gen_107) -> q_gen_107
<z>() -> q_gen_107
<s, s>(q_gen_106) -> q_gen_106
<z, s>(q_gen_107) -> q_gen_106
<z, z>() -> q_gen_106
<s, s>(q_gen_145) -> q_gen_145
<s, z>(q_gen_107) -> q_gen_145
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  merge -> 
{{{
Q={q_gen_103, q_gen_104, q_gen_105, q_gen_116, q_gen_118, q_gen_121, q_gen_135, q_gen_155, q_gen_156, q_gen_169},
Q_f={q_gen_103, q_gen_116},
Delta=
{
<a>() -> q_gen_118
<b>() -> q_gen_118
<cons>(q_gen_118, q_gen_169) -> q_gen_169
<nil>() -> q_gen_169
<cons, cons>(q_gen_105, q_gen_104) -> q_gen_104
<nil, nil>() -> q_gen_104
<a, a>() -> q_gen_105
<b, a>() -> q_gen_105
<a, b>() -> q_gen_135
<b, b>() -> q_gen_135
<cons, cons>(q_gen_135, q_gen_104) -> q_gen_156
<cons, cons>(q_gen_135, q_gen_156) -> q_gen_156
<nil, cons>(q_gen_118, q_gen_169) -> q_gen_156
<cons, nil, cons>(q_gen_105, q_gen_104) -> q_gen_103
<cons, nil, cons>(q_gen_135, q_gen_104) -> q_gen_103
<nil, cons, cons>(q_gen_105, q_gen_104) -> q_gen_103
<cons, cons, cons>(q_gen_121, q_gen_116) -> q_gen_116
<cons, cons, cons>(q_gen_121, q_gen_155) -> q_gen_116
<nil, cons, cons>(q_gen_135, q_gen_104) -> q_gen_116
<nil, nil, cons>(q_gen_118, q_gen_169) -> q_gen_116
<nil, nil, nil>() -> q_gen_116
<a, a, a>() -> q_gen_121
<a, a, b>() -> q_gen_121
<a, b, a>() -> q_gen_121
<a, b, b>() -> q_gen_121
<b, a, a>() -> q_gen_121
<b, a, b>() -> q_gen_121
<b, b, a>() -> q_gen_121
<b, b, b>() -> q_gen_121
<cons, cons, cons>(q_gen_121, q_gen_103) -> q_gen_155
<cons, nil, cons>(q_gen_135, q_gen_156) -> q_gen_155
<nil, cons, cons>(q_gen_135, q_gen_156) -> q_gen_155
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_101, q_gen_102, q_gen_115},
Q_f={q_gen_101},
Delta=
{
<s>(q_gen_115) -> q_gen_115
<z>() -> q_gen_115
<s, s>(q_gen_102) -> q_gen_102
<z, s>(q_gen_115) -> q_gen_102
<z, z>() -> q_gen_102
<s, s, s>(q_gen_101) -> q_gen_101
<s, z, s>(q_gen_102) -> q_gen_101
<z, s, s>(q_gen_102) -> q_gen_101
<z, z, s>(q_gen_115) -> q_gen_101
<z, z, z>() -> q_gen_101
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 23
() -> length([nil, z]) -> 23
() -> leq([a, n2]) -> 23
() -> leq([b, b]) -> 23
() -> leqnat([z, n2]) -> 23
() -> merge([cons(z, xs), nil, cons(z, xs)]) -> 23
() -> merge([nil, y, y]) -> 26
() -> plus([n, z, n]) -> 24
(append([t1, l2, _s])) -> append([cons(h1, t1), l2, cons(h1, _s)]) -> 25
(length([_ha, _ia]) /\ length([l1, _ga]) /\ merge([l1, l2, _ha])) -> leqnat([_ga, _ia]) -> 25
(length([_ka, _la]) /\ length([l2, _ja]) /\ merge([l1, l2, _ka])) -> leqnat([_ja, _la]) -> 26
(length([ll, _ca])) -> length([cons(x, ll), s(_ca)]) -> 24
(leq([z, y2]) /\ merge([xs, cons(y2, ys), _m])) -> merge([cons(z, xs), cons(y2, ys), cons(z, _m)]) -> 24
(not leq([z, y2]) /\ merge([cons(z, xs), ys, _n])) -> merge([cons(z, xs), cons(y2, ys), cons(y2, _n)]) -> 24
(leq([b, a])) -> BOT -> 24
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 24
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 24
(leqnat([s(nn1), z])) -> BOT -> 24
(plus([n, mm, _x])) -> plus([n, s(mm), s(_x)]) -> 24
}
Sat witness: Found: (() -> merge([nil, y, y]), {
y -> cons(b, cons(b, nil))
})

-------------------------------------------
Step 66, which took 0.753923 s (model generation: 0.753629,  model checking: 0.000294):

Model:
|_
{
append -> 
{{{
Q={q_gen_100, q_gen_109, q_gen_110, q_gen_127, q_gen_128, q_gen_129},
Q_f={q_gen_109},
Delta=
{
<cons>(q_gen_128, q_gen_127) -> q_gen_127
<nil>() -> q_gen_127
<a>() -> q_gen_128
<b>() -> q_gen_128
<a, a>() -> q_gen_100
<b, a>() -> q_gen_100
<b, b>() -> q_gen_100
<cons, cons>(q_gen_100, q_gen_110) -> q_gen_110
<nil, cons>(q_gen_128, q_gen_127) -> q_gen_110
<nil, nil>() -> q_gen_110
<cons, cons, cons>(q_gen_129, q_gen_109) -> q_gen_109
<cons, nil, cons>(q_gen_100, q_gen_110) -> q_gen_109
<nil, cons, cons>(q_gen_100, q_gen_110) -> q_gen_109
<nil, nil, cons>(q_gen_128, q_gen_127) -> q_gen_109
<nil, nil, nil>() -> q_gen_109
<a, a, a>() -> q_gen_129
<a, b, a>() -> q_gen_129
<b, a, b>() -> q_gen_129
<b, b, b>() -> q_gen_129
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_122, q_gen_123, q_gen_139, q_gen_140, q_gen_141, q_gen_142, q_gen_143, q_gen_175, q_gen_177, q_gen_178, q_gen_94},
Q_f={q_gen_122},
Delta=
{
<cons>(q_gen_140, q_gen_175) -> q_gen_139
<cons>(q_gen_140, q_gen_94) -> q_gen_139
<a>() -> q_gen_140
<b>() -> q_gen_140
<s>(q_gen_178) -> q_gen_142
<z>() -> q_gen_142
<cons>(q_gen_140, q_gen_139) -> q_gen_175
<s>(q_gen_142) -> q_gen_178
<nil>() -> q_gen_94
<cons, s>(q_gen_123, q_gen_175) -> q_gen_122
<cons, s>(q_gen_123, q_gen_94) -> q_gen_122
<cons, s>(q_gen_141, q_gen_139) -> q_gen_122
<cons, s>(q_gen_177, q_gen_175) -> q_gen_122
<nil, z>() -> q_gen_122
<a, z>() -> q_gen_123
<b, z>() -> q_gen_123
<a, s>(q_gen_142) -> q_gen_141
<b, s>(q_gen_142) -> q_gen_141
<cons, s>(q_gen_123, q_gen_139) -> q_gen_143
<cons, s>(q_gen_141, q_gen_175) -> q_gen_143
<cons, s>(q_gen_141, q_gen_94) -> q_gen_143
<cons, s>(q_gen_177, q_gen_139) -> q_gen_143
<cons, s>(q_gen_177, q_gen_94) -> q_gen_143
<a, s>(q_gen_178) -> q_gen_177
<b, s>(q_gen_178) -> q_gen_177
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_108, q_gen_82},
Q_f={q_gen_108},
Delta=
{
<a, a>() -> q_gen_108
<a, b>() -> q_gen_108
<b, b>() -> q_gen_108
<b, a>() -> q_gen_82
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  leqnat -> 
{{{
Q={q_gen_106, q_gen_107, q_gen_145, q_gen_97},
Q_f={q_gen_106},
Delta=
{
<s>(q_gen_97) -> q_gen_107
<z>() -> q_gen_97
<s, s>(q_gen_106) -> q_gen_106
<s, z>(q_gen_107) -> q_gen_106
<z, s>(q_gen_107) -> q_gen_106
<z, s>(q_gen_97) -> q_gen_106
<z, z>() -> q_gen_106
<s, s>(q_gen_145) -> q_gen_145
<s, z>(q_gen_97) -> q_gen_145
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  merge -> 
{{{
Q={q_gen_103, q_gen_104, q_gen_105, q_gen_118, q_gen_121, q_gen_169},
Q_f={q_gen_103},
Delta=
{
<a>() -> q_gen_118
<b>() -> q_gen_118
<cons>(q_gen_118, q_gen_169) -> q_gen_169
<nil>() -> q_gen_169
<cons, cons>(q_gen_105, q_gen_104) -> q_gen_104
<nil, cons>(q_gen_118, q_gen_169) -> q_gen_104
<nil, nil>() -> q_gen_104
<a, a>() -> q_gen_105
<a, b>() -> q_gen_105
<b, a>() -> q_gen_105
<b, b>() -> q_gen_105
<cons, cons, cons>(q_gen_121, q_gen_103) -> q_gen_103
<cons, nil, cons>(q_gen_105, q_gen_104) -> q_gen_103
<nil, cons, cons>(q_gen_105, q_gen_104) -> q_gen_103
<nil, nil, cons>(q_gen_118, q_gen_169) -> q_gen_103
<nil, nil, nil>() -> q_gen_103
<a, a, a>() -> q_gen_121
<a, a, b>() -> q_gen_121
<a, b, a>() -> q_gen_121
<a, b, b>() -> q_gen_121
<b, a, a>() -> q_gen_121
<b, a, b>() -> q_gen_121
<b, b, a>() -> q_gen_121
<b, b, b>() -> q_gen_121
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_101, q_gen_102, q_gen_115},
Q_f={q_gen_101},
Delta=
{
<s>(q_gen_115) -> q_gen_115
<z>() -> q_gen_115
<s, s>(q_gen_102) -> q_gen_102
<z, s>(q_gen_115) -> q_gen_102
<z, z>() -> q_gen_102
<s, s, s>(q_gen_101) -> q_gen_101
<s, z, s>(q_gen_102) -> q_gen_101
<z, s, s>(q_gen_102) -> q_gen_101
<z, z, s>(q_gen_115) -> q_gen_101
<z, z, z>() -> q_gen_101
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 23
() -> length([nil, z]) -> 23
() -> leq([a, n2]) -> 23
() -> leq([b, b]) -> 23
() -> leqnat([z, n2]) -> 26
() -> merge([cons(z, xs), nil, cons(z, xs)]) -> 24
() -> merge([nil, y, y]) -> 26
() -> plus([n, z, n]) -> 24
(append([t1, l2, _s])) -> append([cons(h1, t1), l2, cons(h1, _s)]) -> 25
(length([_ha, _ia]) /\ length([l1, _ga]) /\ merge([l1, l2, _ha])) -> leqnat([_ga, _ia]) -> 25
(length([_ka, _la]) /\ length([l2, _ja]) /\ merge([l1, l2, _ka])) -> leqnat([_ja, _la]) -> 26
(length([ll, _ca])) -> length([cons(x, ll), s(_ca)]) -> 24
(leq([z, y2]) /\ merge([xs, cons(y2, ys), _m])) -> merge([cons(z, xs), cons(y2, ys), cons(z, _m)]) -> 24
(not leq([z, y2]) /\ merge([cons(z, xs), ys, _n])) -> merge([cons(z, xs), cons(y2, ys), cons(y2, _n)]) -> 24
(leq([b, a])) -> BOT -> 24
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 24
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 24
(leqnat([s(nn1), z])) -> BOT -> 24
(plus([n, mm, _x])) -> plus([n, s(mm), s(_x)]) -> 24
}
Sat witness: Found: (() -> leqnat([z, n2]), {
n2 -> s(s(s(z)))
})

-------------------------------------------
Step 67, which took 1.358202 s (model generation: 1.357036,  model checking: 0.001166):

Model:
|_
{
append -> 
{{{
Q={q_gen_100, q_gen_109, q_gen_110, q_gen_127, q_gen_128, q_gen_129},
Q_f={q_gen_109},
Delta=
{
<cons>(q_gen_128, q_gen_127) -> q_gen_127
<nil>() -> q_gen_127
<a>() -> q_gen_128
<b>() -> q_gen_128
<a, a>() -> q_gen_100
<b, a>() -> q_gen_100
<b, b>() -> q_gen_100
<cons, cons>(q_gen_100, q_gen_110) -> q_gen_110
<nil, cons>(q_gen_128, q_gen_127) -> q_gen_110
<nil, nil>() -> q_gen_110
<cons, cons, cons>(q_gen_129, q_gen_109) -> q_gen_109
<cons, nil, cons>(q_gen_100, q_gen_110) -> q_gen_109
<nil, cons, cons>(q_gen_100, q_gen_110) -> q_gen_109
<nil, nil, cons>(q_gen_128, q_gen_127) -> q_gen_109
<nil, nil, nil>() -> q_gen_109
<a, a, a>() -> q_gen_129
<a, b, a>() -> q_gen_129
<b, a, b>() -> q_gen_129
<b, b, b>() -> q_gen_129
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_122, q_gen_123, q_gen_139, q_gen_140, q_gen_141, q_gen_142, q_gen_143, q_gen_175, q_gen_177, q_gen_178, q_gen_94},
Q_f={q_gen_122},
Delta=
{
<cons>(q_gen_140, q_gen_175) -> q_gen_139
<cons>(q_gen_140, q_gen_94) -> q_gen_139
<a>() -> q_gen_140
<b>() -> q_gen_140
<s>(q_gen_178) -> q_gen_142
<z>() -> q_gen_142
<cons>(q_gen_140, q_gen_139) -> q_gen_175
<s>(q_gen_142) -> q_gen_178
<nil>() -> q_gen_94
<cons, s>(q_gen_123, q_gen_175) -> q_gen_122
<cons, s>(q_gen_123, q_gen_94) -> q_gen_122
<cons, s>(q_gen_141, q_gen_139) -> q_gen_122
<cons, s>(q_gen_177, q_gen_175) -> q_gen_122
<nil, z>() -> q_gen_122
<a, s>(q_gen_178) -> q_gen_123
<a, z>() -> q_gen_123
<b, z>() -> q_gen_123
<a, s>(q_gen_142) -> q_gen_141
<b, s>(q_gen_142) -> q_gen_141
<cons, s>(q_gen_123, q_gen_139) -> q_gen_143
<cons, s>(q_gen_141, q_gen_175) -> q_gen_143
<cons, s>(q_gen_141, q_gen_94) -> q_gen_143
<cons, s>(q_gen_177, q_gen_139) -> q_gen_143
<cons, s>(q_gen_177, q_gen_94) -> q_gen_143
<b, s>(q_gen_178) -> q_gen_177
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_108, q_gen_82},
Q_f={q_gen_108},
Delta=
{
<a, a>() -> q_gen_108
<a, b>() -> q_gen_108
<b, b>() -> q_gen_108
<b, a>() -> q_gen_82
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  leqnat -> 
{{{
Q={q_gen_106, q_gen_107, q_gen_145, q_gen_247},
Q_f={q_gen_106},
Delta=
{
<s>(q_gen_247) -> q_gen_107
<s>(q_gen_107) -> q_gen_247
<z>() -> q_gen_247
<s, s>(q_gen_106) -> q_gen_106
<s, z>(q_gen_107) -> q_gen_106
<z, s>(q_gen_107) -> q_gen_106
<z, s>(q_gen_247) -> q_gen_106
<z, z>() -> q_gen_106
<s, s>(q_gen_145) -> q_gen_145
<s, z>(q_gen_247) -> q_gen_145
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  merge -> 
{{{
Q={q_gen_103, q_gen_104, q_gen_105, q_gen_118, q_gen_121, q_gen_169},
Q_f={q_gen_103},
Delta=
{
<a>() -> q_gen_118
<b>() -> q_gen_118
<cons>(q_gen_118, q_gen_169) -> q_gen_169
<nil>() -> q_gen_169
<cons, cons>(q_gen_105, q_gen_104) -> q_gen_104
<nil, cons>(q_gen_118, q_gen_169) -> q_gen_104
<nil, nil>() -> q_gen_104
<a, a>() -> q_gen_105
<a, b>() -> q_gen_105
<b, a>() -> q_gen_105
<b, b>() -> q_gen_105
<cons, cons, cons>(q_gen_121, q_gen_103) -> q_gen_103
<cons, nil, cons>(q_gen_105, q_gen_104) -> q_gen_103
<nil, cons, cons>(q_gen_105, q_gen_104) -> q_gen_103
<nil, nil, cons>(q_gen_118, q_gen_169) -> q_gen_103
<nil, nil, nil>() -> q_gen_103
<a, a, a>() -> q_gen_121
<a, a, b>() -> q_gen_121
<a, b, a>() -> q_gen_121
<a, b, b>() -> q_gen_121
<b, a, a>() -> q_gen_121
<b, a, b>() -> q_gen_121
<b, b, a>() -> q_gen_121
<b, b, b>() -> q_gen_121
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_101, q_gen_102, q_gen_115},
Q_f={q_gen_101},
Delta=
{
<s>(q_gen_115) -> q_gen_115
<z>() -> q_gen_115
<s, s>(q_gen_102) -> q_gen_102
<z, s>(q_gen_115) -> q_gen_102
<z, z>() -> q_gen_102
<s, s, s>(q_gen_101) -> q_gen_101
<s, z, s>(q_gen_102) -> q_gen_101
<z, s, s>(q_gen_102) -> q_gen_101
<z, z, s>(q_gen_115) -> q_gen_101
<z, z, z>() -> q_gen_101
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 24
() -> length([nil, z]) -> 24
() -> leq([a, n2]) -> 24
() -> leq([b, b]) -> 24
() -> leqnat([z, n2]) -> 26
() -> merge([cons(z, xs), nil, cons(z, xs)]) -> 24
() -> merge([nil, y, y]) -> 26
() -> plus([n, z, n]) -> 24
(append([t1, l2, _s])) -> append([cons(h1, t1), l2, cons(h1, _s)]) -> 25
(length([_ha, _ia]) /\ length([l1, _ga]) /\ merge([l1, l2, _ha])) -> leqnat([_ga, _ia]) -> 25
(length([_ka, _la]) /\ length([l2, _ja]) /\ merge([l1, l2, _ka])) -> leqnat([_ja, _la]) -> 26
(length([ll, _ca])) -> length([cons(x, ll), s(_ca)]) -> 24
(leq([z, y2]) /\ merge([xs, cons(y2, ys), _m])) -> merge([cons(z, xs), cons(y2, ys), cons(z, _m)]) -> 24
(not leq([z, y2]) /\ merge([cons(z, xs), ys, _n])) -> merge([cons(z, xs), cons(y2, ys), cons(y2, _n)]) -> 24
(leq([b, a])) -> BOT -> 24
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 24
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 24
(leqnat([s(nn1), z])) -> BOT -> 27
(plus([n, mm, _x])) -> plus([n, s(mm), s(_x)]) -> 25
}
Sat witness: Found: ((leqnat([s(nn1), z])) -> BOT, {
nn1 -> s(z)
})

-------------------------------------------
Step 68, which took 2.928211 s (model generation: 2.864462,  model checking: 0.063749):

Model:
|_
{
append -> 
{{{
Q={q_gen_100, q_gen_109, q_gen_110, q_gen_127, q_gen_128, q_gen_129},
Q_f={q_gen_109},
Delta=
{
<cons>(q_gen_128, q_gen_127) -> q_gen_127
<nil>() -> q_gen_127
<a>() -> q_gen_128
<b>() -> q_gen_128
<a, a>() -> q_gen_100
<b, a>() -> q_gen_100
<b, b>() -> q_gen_100
<cons, cons>(q_gen_100, q_gen_110) -> q_gen_110
<nil, cons>(q_gen_128, q_gen_127) -> q_gen_110
<nil, nil>() -> q_gen_110
<cons, cons, cons>(q_gen_129, q_gen_109) -> q_gen_109
<cons, nil, cons>(q_gen_100, q_gen_110) -> q_gen_109
<nil, cons, cons>(q_gen_100, q_gen_110) -> q_gen_109
<nil, nil, cons>(q_gen_128, q_gen_127) -> q_gen_109
<nil, nil, nil>() -> q_gen_109
<a, a, a>() -> q_gen_129
<a, b, a>() -> q_gen_129
<b, a, b>() -> q_gen_129
<b, b, b>() -> q_gen_129
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_122, q_gen_123, q_gen_139, q_gen_140, q_gen_141, q_gen_142, q_gen_143, q_gen_175, q_gen_176, q_gen_177, q_gen_178, q_gen_94},
Q_f={q_gen_122},
Delta=
{
<cons>(q_gen_140, q_gen_139) -> q_gen_139
<cons>(q_gen_140, q_gen_94) -> q_gen_139
<b>() -> q_gen_140
<z>() -> q_gen_142
<cons>(q_gen_140, q_gen_175) -> q_gen_175
<cons>(q_gen_176, q_gen_139) -> q_gen_175
<a>() -> q_gen_176
<s>(q_gen_142) -> q_gen_178
<s>(q_gen_178) -> q_gen_178
<nil>() -> q_gen_94
<cons, s>(q_gen_123, q_gen_94) -> q_gen_122
<cons, s>(q_gen_141, q_gen_139) -> q_gen_122
<cons, s>(q_gen_177, q_gen_175) -> q_gen_122
<nil, z>() -> q_gen_122
<a, z>() -> q_gen_123
<b, z>() -> q_gen_123
<a, s>(q_gen_142) -> q_gen_141
<a, s>(q_gen_178) -> q_gen_141
<b, s>(q_gen_142) -> q_gen_141
<cons, s>(q_gen_123, q_gen_139) -> q_gen_143
<cons, s>(q_gen_141, q_gen_94) -> q_gen_143
<cons, s>(q_gen_177, q_gen_139) -> q_gen_143
<cons, s>(q_gen_177, q_gen_94) -> q_gen_143
<b, s>(q_gen_178) -> q_gen_177
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_108, q_gen_82},
Q_f={q_gen_108},
Delta=
{
<a, a>() -> q_gen_108
<a, b>() -> q_gen_108
<b, b>() -> q_gen_108
<b, a>() -> q_gen_82
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  leqnat -> 
{{{
Q={q_gen_106, q_gen_107, q_gen_145},
Q_f={q_gen_106},
Delta=
{
<s>(q_gen_107) -> q_gen_107
<z>() -> q_gen_107
<s, s>(q_gen_106) -> q_gen_106
<z, s>(q_gen_107) -> q_gen_106
<z, z>() -> q_gen_106
<s, s>(q_gen_145) -> q_gen_145
<s, z>(q_gen_107) -> q_gen_145
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  merge -> 
{{{
Q={q_gen_103, q_gen_104, q_gen_105, q_gen_118, q_gen_121, q_gen_169},
Q_f={q_gen_103},
Delta=
{
<a>() -> q_gen_118
<b>() -> q_gen_118
<cons>(q_gen_118, q_gen_169) -> q_gen_169
<nil>() -> q_gen_169
<cons, cons>(q_gen_105, q_gen_104) -> q_gen_104
<nil, cons>(q_gen_118, q_gen_169) -> q_gen_104
<nil, nil>() -> q_gen_104
<a, a>() -> q_gen_105
<a, b>() -> q_gen_105
<b, a>() -> q_gen_105
<b, b>() -> q_gen_105
<cons, cons, cons>(q_gen_121, q_gen_103) -> q_gen_103
<cons, nil, cons>(q_gen_105, q_gen_104) -> q_gen_103
<nil, cons, cons>(q_gen_105, q_gen_104) -> q_gen_103
<nil, nil, cons>(q_gen_118, q_gen_169) -> q_gen_103
<nil, nil, nil>() -> q_gen_103
<a, a, a>() -> q_gen_121
<a, a, b>() -> q_gen_121
<a, b, a>() -> q_gen_121
<a, b, b>() -> q_gen_121
<b, a, a>() -> q_gen_121
<b, a, b>() -> q_gen_121
<b, b, a>() -> q_gen_121
<b, b, b>() -> q_gen_121
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_101, q_gen_102, q_gen_115},
Q_f={q_gen_101},
Delta=
{
<s>(q_gen_115) -> q_gen_115
<z>() -> q_gen_115
<s, s>(q_gen_102) -> q_gen_102
<z, s>(q_gen_115) -> q_gen_102
<z, z>() -> q_gen_102
<s, s, s>(q_gen_101) -> q_gen_101
<s, z, s>(q_gen_102) -> q_gen_101
<z, s, s>(q_gen_102) -> q_gen_101
<z, z, s>(q_gen_115) -> q_gen_101
<z, z, z>() -> q_gen_101
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 24
() -> length([nil, z]) -> 24
() -> leq([a, n2]) -> 24
() -> leq([b, b]) -> 24
() -> leqnat([z, n2]) -> 26
() -> merge([cons(z, xs), nil, cons(z, xs)]) -> 24
() -> merge([nil, y, y]) -> 26
() -> plus([n, z, n]) -> 24
(append([t1, l2, _s])) -> append([cons(h1, t1), l2, cons(h1, _s)]) -> 25
(length([_ha, _ia]) /\ length([l1, _ga]) /\ merge([l1, l2, _ha])) -> leqnat([_ga, _ia]) -> 25
(length([_ka, _la]) /\ length([l2, _ja]) /\ merge([l1, l2, _ka])) -> leqnat([_ja, _la]) -> 26
(length([ll, _ca])) -> length([cons(x, ll), s(_ca)]) -> 27
(leq([z, y2]) /\ merge([xs, cons(y2, ys), _m])) -> merge([cons(z, xs), cons(y2, ys), cons(z, _m)]) -> 25
(not leq([z, y2]) /\ merge([cons(z, xs), ys, _n])) -> merge([cons(z, xs), cons(y2, ys), cons(y2, _n)]) -> 25
(leq([b, a])) -> BOT -> 25
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 25
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 25
(leqnat([s(nn1), z])) -> BOT -> 27
(plus([n, mm, _x])) -> plus([n, s(mm), s(_x)]) -> 25
}
Sat witness: Found: ((length([ll, _ca])) -> length([cons(x, ll), s(_ca)]), {
_ca -> s(s(z))  ;  ll -> cons(b, cons(b, cons(b, nil)))  ;  x -> b
})

-------------------------------------------
Step 69, which took 0.874440 s (model generation: 0.812183,  model checking: 0.062257):

Model:
|_
{
append -> 
{{{
Q={q_gen_100, q_gen_109, q_gen_110, q_gen_127, q_gen_128, q_gen_129},
Q_f={q_gen_109},
Delta=
{
<cons>(q_gen_128, q_gen_127) -> q_gen_127
<nil>() -> q_gen_127
<a>() -> q_gen_128
<b>() -> q_gen_128
<a, a>() -> q_gen_100
<b, a>() -> q_gen_100
<b, b>() -> q_gen_100
<cons, cons>(q_gen_100, q_gen_110) -> q_gen_110
<nil, cons>(q_gen_128, q_gen_127) -> q_gen_110
<nil, nil>() -> q_gen_110
<cons, cons, cons>(q_gen_129, q_gen_109) -> q_gen_109
<cons, nil, cons>(q_gen_100, q_gen_110) -> q_gen_109
<nil, cons, cons>(q_gen_100, q_gen_110) -> q_gen_109
<nil, nil, cons>(q_gen_128, q_gen_127) -> q_gen_109
<nil, nil, nil>() -> q_gen_109
<a, a, a>() -> q_gen_129
<a, b, a>() -> q_gen_129
<b, a, b>() -> q_gen_129
<b, b, b>() -> q_gen_129
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_122, q_gen_123, q_gen_139, q_gen_140, q_gen_141, q_gen_142, q_gen_143, q_gen_175, q_gen_176, q_gen_177, q_gen_178, q_gen_180},
Q_f={q_gen_122},
Delta=
{
<cons>(q_gen_140, q_gen_180) -> q_gen_139
<b>() -> q_gen_140
<z>() -> q_gen_142
<cons>(q_gen_140, q_gen_175) -> q_gen_175
<cons>(q_gen_176, q_gen_139) -> q_gen_175
<a>() -> q_gen_176
<s>(q_gen_142) -> q_gen_178
<s>(q_gen_178) -> q_gen_178
<cons>(q_gen_140, q_gen_139) -> q_gen_180
<nil>() -> q_gen_180
<cons, s>(q_gen_123, q_gen_180) -> q_gen_122
<cons, s>(q_gen_141, q_gen_139) -> q_gen_122
<cons, s>(q_gen_177, q_gen_175) -> q_gen_122
<nil, z>() -> q_gen_122
<a, s>(q_gen_178) -> q_gen_123
<a, z>() -> q_gen_123
<b, z>() -> q_gen_123
<a, s>(q_gen_142) -> q_gen_141
<b, s>(q_gen_142) -> q_gen_141
<cons, s>(q_gen_123, q_gen_139) -> q_gen_143
<cons, s>(q_gen_141, q_gen_180) -> q_gen_143
<cons, s>(q_gen_177, q_gen_139) -> q_gen_143
<cons, s>(q_gen_177, q_gen_180) -> q_gen_143
<b, s>(q_gen_178) -> q_gen_177
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_108, q_gen_82},
Q_f={q_gen_108},
Delta=
{
<a, a>() -> q_gen_108
<a, b>() -> q_gen_108
<b, b>() -> q_gen_108
<b, a>() -> q_gen_82
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  leqnat -> 
{{{
Q={q_gen_106, q_gen_107, q_gen_145},
Q_f={q_gen_106},
Delta=
{
<s>(q_gen_107) -> q_gen_107
<z>() -> q_gen_107
<s, s>(q_gen_106) -> q_gen_106
<z, s>(q_gen_107) -> q_gen_106
<z, z>() -> q_gen_106
<s, s>(q_gen_145) -> q_gen_145
<s, z>(q_gen_107) -> q_gen_145
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  merge -> 
{{{
Q={q_gen_103, q_gen_104, q_gen_105, q_gen_118, q_gen_121, q_gen_169},
Q_f={q_gen_103},
Delta=
{
<a>() -> q_gen_118
<b>() -> q_gen_118
<cons>(q_gen_118, q_gen_169) -> q_gen_169
<nil>() -> q_gen_169
<cons, cons>(q_gen_105, q_gen_104) -> q_gen_104
<nil, cons>(q_gen_118, q_gen_169) -> q_gen_104
<nil, nil>() -> q_gen_104
<a, a>() -> q_gen_105
<a, b>() -> q_gen_105
<b, a>() -> q_gen_105
<b, b>() -> q_gen_105
<cons, cons, cons>(q_gen_121, q_gen_103) -> q_gen_103
<cons, nil, cons>(q_gen_105, q_gen_104) -> q_gen_103
<nil, cons, cons>(q_gen_105, q_gen_104) -> q_gen_103
<nil, nil, cons>(q_gen_118, q_gen_169) -> q_gen_103
<nil, nil, nil>() -> q_gen_103
<a, a, a>() -> q_gen_121
<a, a, b>() -> q_gen_121
<a, b, a>() -> q_gen_121
<a, b, b>() -> q_gen_121
<b, a, a>() -> q_gen_121
<b, a, b>() -> q_gen_121
<b, b, a>() -> q_gen_121
<b, b, b>() -> q_gen_121
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_101, q_gen_102, q_gen_115},
Q_f={q_gen_101},
Delta=
{
<s>(q_gen_115) -> q_gen_115
<z>() -> q_gen_115
<s, s>(q_gen_102) -> q_gen_102
<z, s>(q_gen_115) -> q_gen_102
<z, z>() -> q_gen_102
<s, s, s>(q_gen_101) -> q_gen_101
<s, z, s>(q_gen_102) -> q_gen_101
<z, s, s>(q_gen_102) -> q_gen_101
<z, z, s>(q_gen_115) -> q_gen_101
<z, z, z>() -> q_gen_101
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 25
() -> length([nil, z]) -> 25
() -> leq([a, n2]) -> 25
() -> leq([b, b]) -> 25
() -> leqnat([z, n2]) -> 26
() -> merge([cons(z, xs), nil, cons(z, xs)]) -> 25
() -> merge([nil, y, y]) -> 26
() -> plus([n, z, n]) -> 25
(append([t1, l2, _s])) -> append([cons(h1, t1), l2, cons(h1, _s)]) -> 25
(length([_ha, _ia]) /\ length([l1, _ga]) /\ merge([l1, l2, _ha])) -> leqnat([_ga, _ia]) -> 28
(length([_ka, _la]) /\ length([l2, _ja]) /\ merge([l1, l2, _ka])) -> leqnat([_ja, _la]) -> 26
(length([ll, _ca])) -> length([cons(x, ll), s(_ca)]) -> 27
(leq([z, y2]) /\ merge([xs, cons(y2, ys), _m])) -> merge([cons(z, xs), cons(y2, ys), cons(z, _m)]) -> 26
(not leq([z, y2]) /\ merge([cons(z, xs), ys, _n])) -> merge([cons(z, xs), cons(y2, ys), cons(y2, _n)]) -> 26
(leq([b, a])) -> BOT -> 26
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 26
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 26
(leqnat([s(nn1), z])) -> BOT -> 27
(plus([n, mm, _x])) -> plus([n, s(mm), s(_x)]) -> 26
}
Sat witness: Found: ((length([_ha, _ia]) /\ length([l1, _ga]) /\ merge([l1, l2, _ha])) -> leqnat([_ga, _ia]), {
_ga -> s(s(s(z)))  ;  _ha -> cons(b, nil)  ;  _ia -> s(z)  ;  l1 -> cons(a, nil)  ;  l2 -> nil
})

-------------------------------------------
Step 70, which took 2.084100 s (model generation: 2.076837,  model checking: 0.007263):

Model:
|_
{
append -> 
{{{
Q={q_gen_100, q_gen_109, q_gen_110, q_gen_127, q_gen_128, q_gen_129},
Q_f={q_gen_109},
Delta=
{
<cons>(q_gen_128, q_gen_127) -> q_gen_127
<nil>() -> q_gen_127
<a>() -> q_gen_128
<b>() -> q_gen_128
<a, a>() -> q_gen_100
<b, a>() -> q_gen_100
<b, b>() -> q_gen_100
<cons, cons>(q_gen_100, q_gen_110) -> q_gen_110
<nil, cons>(q_gen_128, q_gen_127) -> q_gen_110
<nil, nil>() -> q_gen_110
<cons, cons, cons>(q_gen_129, q_gen_109) -> q_gen_109
<cons, nil, cons>(q_gen_100, q_gen_110) -> q_gen_109
<nil, cons, cons>(q_gen_100, q_gen_110) -> q_gen_109
<nil, nil, cons>(q_gen_128, q_gen_127) -> q_gen_109
<nil, nil, nil>() -> q_gen_109
<a, a, a>() -> q_gen_129
<a, b, a>() -> q_gen_129
<b, a, b>() -> q_gen_129
<b, b, b>() -> q_gen_129
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_122, q_gen_123, q_gen_139, q_gen_140, q_gen_141, q_gen_142, q_gen_143, q_gen_175, q_gen_177, q_gen_178, q_gen_212, q_gen_214},
Q_f={q_gen_122},
Delta=
{
<cons>(q_gen_140, q_gen_212) -> q_gen_139
<a>() -> q_gen_140
<b>() -> q_gen_140
<z>() -> q_gen_142
<cons>(q_gen_140, q_gen_139) -> q_gen_175
<s>(q_gen_142) -> q_gen_178
<cons>(q_gen_140, q_gen_175) -> q_gen_212
<nil>() -> q_gen_212
<s>(q_gen_178) -> q_gen_214
<cons, s>(q_gen_123, q_gen_212) -> q_gen_122
<cons, s>(q_gen_141, q_gen_139) -> q_gen_122
<cons, s>(q_gen_177, q_gen_175) -> q_gen_122
<nil, z>() -> q_gen_122
<a, z>() -> q_gen_123
<b, s>(q_gen_214) -> q_gen_123
<b, z>() -> q_gen_123
<a, s>(q_gen_142) -> q_gen_141
<b, s>(q_gen_142) -> q_gen_141
<cons, s>(q_gen_123, q_gen_139) -> q_gen_143
<cons, s>(q_gen_123, q_gen_175) -> q_gen_143
<cons, s>(q_gen_141, q_gen_175) -> q_gen_143
<cons, s>(q_gen_141, q_gen_212) -> q_gen_143
<cons, s>(q_gen_177, q_gen_139) -> q_gen_143
<cons, s>(q_gen_177, q_gen_212) -> q_gen_143
<a, s>(q_gen_178) -> q_gen_177
<b, s>(q_gen_178) -> q_gen_177
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_108, q_gen_82},
Q_f={q_gen_108},
Delta=
{
<a, a>() -> q_gen_108
<a, b>() -> q_gen_108
<b, b>() -> q_gen_108
<b, a>() -> q_gen_82
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  leqnat -> 
{{{
Q={q_gen_106, q_gen_107, q_gen_145},
Q_f={q_gen_106},
Delta=
{
<s>(q_gen_107) -> q_gen_107
<z>() -> q_gen_107
<s, s>(q_gen_106) -> q_gen_106
<z, s>(q_gen_107) -> q_gen_106
<z, z>() -> q_gen_106
<s, s>(q_gen_145) -> q_gen_145
<s, z>(q_gen_107) -> q_gen_145
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  merge -> 
{{{
Q={q_gen_103, q_gen_104, q_gen_105, q_gen_118, q_gen_121, q_gen_169},
Q_f={q_gen_103},
Delta=
{
<a>() -> q_gen_118
<b>() -> q_gen_118
<cons>(q_gen_118, q_gen_169) -> q_gen_169
<nil>() -> q_gen_169
<cons, cons>(q_gen_105, q_gen_104) -> q_gen_104
<nil, cons>(q_gen_118, q_gen_169) -> q_gen_104
<nil, nil>() -> q_gen_104
<a, a>() -> q_gen_105
<a, b>() -> q_gen_105
<b, a>() -> q_gen_105
<b, b>() -> q_gen_105
<cons, cons, cons>(q_gen_121, q_gen_103) -> q_gen_103
<cons, nil, cons>(q_gen_105, q_gen_104) -> q_gen_103
<nil, cons, cons>(q_gen_105, q_gen_104) -> q_gen_103
<nil, nil, cons>(q_gen_118, q_gen_169) -> q_gen_103
<nil, nil, nil>() -> q_gen_103
<a, a, a>() -> q_gen_121
<a, a, b>() -> q_gen_121
<a, b, a>() -> q_gen_121
<a, b, b>() -> q_gen_121
<b, a, a>() -> q_gen_121
<b, a, b>() -> q_gen_121
<b, b, a>() -> q_gen_121
<b, b, b>() -> q_gen_121
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_101, q_gen_102, q_gen_115},
Q_f={q_gen_101},
Delta=
{
<s>(q_gen_115) -> q_gen_115
<z>() -> q_gen_115
<s, s>(q_gen_102) -> q_gen_102
<z, s>(q_gen_115) -> q_gen_102
<z, z>() -> q_gen_102
<s, s, s>(q_gen_101) -> q_gen_101
<s, z, s>(q_gen_102) -> q_gen_101
<z, s, s>(q_gen_102) -> q_gen_101
<z, z, s>(q_gen_115) -> q_gen_101
<z, z, z>() -> q_gen_101
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 25
() -> length([nil, z]) -> 25
() -> leq([a, n2]) -> 25
() -> leq([b, b]) -> 25
() -> leqnat([z, n2]) -> 26
() -> merge([cons(z, xs), nil, cons(z, xs)]) -> 25
() -> merge([nil, y, y]) -> 26
() -> plus([n, z, n]) -> 25
(append([t1, l2, _s])) -> append([cons(h1, t1), l2, cons(h1, _s)]) -> 28
(length([_ha, _ia]) /\ length([l1, _ga]) /\ merge([l1, l2, _ha])) -> leqnat([_ga, _ia]) -> 28
(length([_ka, _la]) /\ length([l2, _ja]) /\ merge([l1, l2, _ka])) -> leqnat([_ja, _la]) -> 26
(length([ll, _ca])) -> length([cons(x, ll), s(_ca)]) -> 27
(leq([z, y2]) /\ merge([xs, cons(y2, ys), _m])) -> merge([cons(z, xs), cons(y2, ys), cons(z, _m)]) -> 26
(not leq([z, y2]) /\ merge([cons(z, xs), ys, _n])) -> merge([cons(z, xs), cons(y2, ys), cons(y2, _n)]) -> 26
(leq([b, a])) -> BOT -> 26
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 26
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 26
(leqnat([s(nn1), z])) -> BOT -> 27
(plus([n, mm, _x])) -> plus([n, s(mm), s(_x)]) -> 26
}
Sat witness: Found: ((append([t1, l2, _s])) -> append([cons(h1, t1), l2, cons(h1, _s)]), {
_s -> cons(b, cons(a, nil))  ;  h1 -> a  ;  l2 -> cons(b, cons(a, nil))  ;  t1 -> nil
})

-------------------------------------------
Step 71, which took 1.868400 s (model generation: 1.808173,  model checking: 0.060227):

Model:
|_
{
append -> 
{{{
Q={q_gen_100, q_gen_109, q_gen_110, q_gen_127, q_gen_128, q_gen_129},
Q_f={q_gen_109},
Delta=
{
<cons>(q_gen_128, q_gen_127) -> q_gen_127
<nil>() -> q_gen_127
<a>() -> q_gen_128
<b>() -> q_gen_128
<a, a>() -> q_gen_100
<a, b>() -> q_gen_100
<b, a>() -> q_gen_100
<b, b>() -> q_gen_100
<cons, cons>(q_gen_100, q_gen_110) -> q_gen_110
<nil, cons>(q_gen_128, q_gen_127) -> q_gen_110
<nil, nil>() -> q_gen_110
<cons, cons, cons>(q_gen_129, q_gen_109) -> q_gen_109
<cons, nil, cons>(q_gen_100, q_gen_110) -> q_gen_109
<nil, cons, cons>(q_gen_100, q_gen_110) -> q_gen_109
<nil, nil, cons>(q_gen_128, q_gen_127) -> q_gen_109
<nil, nil, nil>() -> q_gen_109
<a, a, a>() -> q_gen_129
<a, b, a>() -> q_gen_129
<b, a, b>() -> q_gen_129
<b, b, b>() -> q_gen_129
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_122, q_gen_123, q_gen_139, q_gen_140, q_gen_141, q_gen_142, q_gen_143, q_gen_175, q_gen_177, q_gen_178, q_gen_212, q_gen_214},
Q_f={q_gen_122},
Delta=
{
<cons>(q_gen_140, q_gen_212) -> q_gen_139
<a>() -> q_gen_140
<b>() -> q_gen_140
<z>() -> q_gen_142
<cons>(q_gen_140, q_gen_139) -> q_gen_175
<s>(q_gen_142) -> q_gen_178
<cons>(q_gen_140, q_gen_175) -> q_gen_212
<nil>() -> q_gen_212
<s>(q_gen_178) -> q_gen_214
<cons, s>(q_gen_123, q_gen_212) -> q_gen_122
<cons, s>(q_gen_141, q_gen_139) -> q_gen_122
<cons, s>(q_gen_177, q_gen_175) -> q_gen_122
<nil, z>() -> q_gen_122
<a, z>() -> q_gen_123
<b, s>(q_gen_214) -> q_gen_123
<b, z>() -> q_gen_123
<a, s>(q_gen_142) -> q_gen_141
<b, s>(q_gen_142) -> q_gen_141
<cons, s>(q_gen_123, q_gen_139) -> q_gen_143
<cons, s>(q_gen_123, q_gen_175) -> q_gen_143
<cons, s>(q_gen_141, q_gen_175) -> q_gen_143
<cons, s>(q_gen_141, q_gen_212) -> q_gen_143
<cons, s>(q_gen_177, q_gen_139) -> q_gen_143
<cons, s>(q_gen_177, q_gen_212) -> q_gen_143
<a, s>(q_gen_178) -> q_gen_177
<b, s>(q_gen_178) -> q_gen_177
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_108, q_gen_82},
Q_f={q_gen_108},
Delta=
{
<a, a>() -> q_gen_108
<a, b>() -> q_gen_108
<b, b>() -> q_gen_108
<b, a>() -> q_gen_82
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  leqnat -> 
{{{
Q={q_gen_106, q_gen_107, q_gen_145},
Q_f={q_gen_106},
Delta=
{
<s>(q_gen_107) -> q_gen_107
<z>() -> q_gen_107
<s, s>(q_gen_106) -> q_gen_106
<z, s>(q_gen_107) -> q_gen_106
<z, z>() -> q_gen_106
<s, s>(q_gen_145) -> q_gen_145
<s, z>(q_gen_107) -> q_gen_145
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  merge -> 
{{{
Q={q_gen_103, q_gen_104, q_gen_105, q_gen_118, q_gen_121, q_gen_169},
Q_f={q_gen_103},
Delta=
{
<a>() -> q_gen_118
<b>() -> q_gen_118
<cons>(q_gen_118, q_gen_169) -> q_gen_169
<nil>() -> q_gen_169
<cons, cons>(q_gen_105, q_gen_104) -> q_gen_104
<nil, cons>(q_gen_118, q_gen_169) -> q_gen_104
<nil, nil>() -> q_gen_104
<a, a>() -> q_gen_105
<a, b>() -> q_gen_105
<b, a>() -> q_gen_105
<b, b>() -> q_gen_105
<cons, cons, cons>(q_gen_121, q_gen_103) -> q_gen_103
<cons, nil, cons>(q_gen_105, q_gen_104) -> q_gen_103
<nil, cons, cons>(q_gen_105, q_gen_104) -> q_gen_103
<nil, nil, cons>(q_gen_118, q_gen_169) -> q_gen_103
<nil, nil, nil>() -> q_gen_103
<a, a, a>() -> q_gen_121
<a, a, b>() -> q_gen_121
<a, b, a>() -> q_gen_121
<a, b, b>() -> q_gen_121
<b, a, a>() -> q_gen_121
<b, a, b>() -> q_gen_121
<b, b, a>() -> q_gen_121
<b, b, b>() -> q_gen_121
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_101, q_gen_102, q_gen_115},
Q_f={q_gen_101},
Delta=
{
<s>(q_gen_115) -> q_gen_115
<z>() -> q_gen_115
<s, s>(q_gen_102) -> q_gen_102
<z, s>(q_gen_115) -> q_gen_102
<z, z>() -> q_gen_102
<s, s, s>(q_gen_101) -> q_gen_101
<s, z, s>(q_gen_102) -> q_gen_101
<z, s, s>(q_gen_102) -> q_gen_101
<z, z, s>(q_gen_115) -> q_gen_101
<z, z, z>() -> q_gen_101
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 26
() -> length([nil, z]) -> 26
() -> leq([a, n2]) -> 26
() -> leq([b, b]) -> 26
() -> leqnat([z, n2]) -> 26
() -> merge([cons(z, xs), nil, cons(z, xs)]) -> 26
() -> merge([nil, y, y]) -> 26
() -> plus([n, z, n]) -> 26
(append([t1, l2, _s])) -> append([cons(h1, t1), l2, cons(h1, _s)]) -> 28
(length([_ha, _ia]) /\ length([l1, _ga]) /\ merge([l1, l2, _ha])) -> leqnat([_ga, _ia]) -> 28
(length([_ka, _la]) /\ length([l2, _ja]) /\ merge([l1, l2, _ka])) -> leqnat([_ja, _la]) -> 29
(length([ll, _ca])) -> length([cons(x, ll), s(_ca)]) -> 27
(leq([z, y2]) /\ merge([xs, cons(y2, ys), _m])) -> merge([cons(z, xs), cons(y2, ys), cons(z, _m)]) -> 27
(not leq([z, y2]) /\ merge([cons(z, xs), ys, _n])) -> merge([cons(z, xs), cons(y2, ys), cons(y2, _n)]) -> 27
(leq([b, a])) -> BOT -> 27
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 27
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 27
(leqnat([s(nn1), z])) -> BOT -> 27
(plus([n, mm, _x])) -> plus([n, s(mm), s(_x)]) -> 27
}
Sat witness: Found: ((length([_ka, _la]) /\ length([l2, _ja]) /\ merge([l1, l2, _ka])) -> leqnat([_ja, _la]), {
_ja -> s(s(z))  ;  _ka -> cons(b, cons(b, cons(b, cons(b, nil))))  ;  _la -> s(z)  ;  l1 -> nil  ;  l2 -> cons(b, cons(b, nil))
})

-------------------------------------------
Step 72, which took 3.527269 s (model generation: 3.522795,  model checking: 0.004474):

Model:
|_
{
append -> 
{{{
Q={q_gen_100, q_gen_109, q_gen_110, q_gen_127, q_gen_128, q_gen_129},
Q_f={q_gen_109},
Delta=
{
<cons>(q_gen_128, q_gen_127) -> q_gen_127
<nil>() -> q_gen_127
<a>() -> q_gen_128
<b>() -> q_gen_128
<a, a>() -> q_gen_100
<a, b>() -> q_gen_100
<b, a>() -> q_gen_100
<b, b>() -> q_gen_100
<cons, cons>(q_gen_100, q_gen_110) -> q_gen_110
<nil, cons>(q_gen_128, q_gen_127) -> q_gen_110
<nil, nil>() -> q_gen_110
<cons, cons, cons>(q_gen_129, q_gen_109) -> q_gen_109
<cons, nil, cons>(q_gen_100, q_gen_110) -> q_gen_109
<nil, cons, cons>(q_gen_100, q_gen_110) -> q_gen_109
<nil, nil, cons>(q_gen_128, q_gen_127) -> q_gen_109
<nil, nil, nil>() -> q_gen_109
<a, a, a>() -> q_gen_129
<a, b, a>() -> q_gen_129
<b, a, b>() -> q_gen_129
<b, b, b>() -> q_gen_129
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_122, q_gen_123, q_gen_139, q_gen_140, q_gen_141, q_gen_142, q_gen_143, q_gen_175, q_gen_178},
Q_f={q_gen_122},
Delta=
{
<cons>(q_gen_140, q_gen_175) -> q_gen_139
<a>() -> q_gen_140
<b>() -> q_gen_140
<s>(q_gen_178) -> q_gen_142
<z>() -> q_gen_142
<cons>(q_gen_140, q_gen_139) -> q_gen_175
<nil>() -> q_gen_175
<s>(q_gen_142) -> q_gen_178
<cons, s>(q_gen_123, q_gen_175) -> q_gen_122
<cons, s>(q_gen_141, q_gen_139) -> q_gen_122
<nil, z>() -> q_gen_122
<a, s>(q_gen_178) -> q_gen_123
<a, z>() -> q_gen_123
<b, s>(q_gen_178) -> q_gen_123
<b, z>() -> q_gen_123
<a, s>(q_gen_142) -> q_gen_141
<b, s>(q_gen_142) -> q_gen_141
<cons, s>(q_gen_123, q_gen_139) -> q_gen_143
<cons, s>(q_gen_141, q_gen_175) -> q_gen_143
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_108, q_gen_82},
Q_f={q_gen_108},
Delta=
{
<a, a>() -> q_gen_108
<a, b>() -> q_gen_108
<b, b>() -> q_gen_108
<b, a>() -> q_gen_82
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  leqnat -> 
{{{
Q={q_gen_106, q_gen_107, q_gen_145},
Q_f={q_gen_106},
Delta=
{
<s>(q_gen_107) -> q_gen_107
<z>() -> q_gen_107
<s, s>(q_gen_106) -> q_gen_106
<z, s>(q_gen_107) -> q_gen_106
<z, z>() -> q_gen_106
<s, s>(q_gen_145) -> q_gen_145
<s, z>(q_gen_107) -> q_gen_145
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  merge -> 
{{{
Q={q_gen_103, q_gen_104, q_gen_105, q_gen_118, q_gen_121, q_gen_135, q_gen_155, q_gen_156, q_gen_169, q_gen_197},
Q_f={q_gen_103},
Delta=
{
<a>() -> q_gen_118
<b>() -> q_gen_118
<cons>(q_gen_118, q_gen_169) -> q_gen_169
<nil>() -> q_gen_169
<cons, cons>(q_gen_105, q_gen_104) -> q_gen_104
<nil, nil>() -> q_gen_104
<a, a>() -> q_gen_105
<b, b>() -> q_gen_105
<a, b>() -> q_gen_135
<b, a>() -> q_gen_135
<cons, cons>(q_gen_105, q_gen_156) -> q_gen_156
<nil, cons>(q_gen_118, q_gen_169) -> q_gen_156
<cons, cons, cons>(q_gen_121, q_gen_103) -> q_gen_103
<cons, cons, cons>(q_gen_197, q_gen_103) -> q_gen_103
<cons, cons, cons>(q_gen_197, q_gen_155) -> q_gen_103
<cons, nil, cons>(q_gen_105, q_gen_104) -> q_gen_103
<cons, nil, cons>(q_gen_105, q_gen_156) -> q_gen_103
<nil, cons, cons>(q_gen_105, q_gen_104) -> q_gen_103
<nil, cons, cons>(q_gen_135, q_gen_104) -> q_gen_103
<nil, nil, cons>(q_gen_118, q_gen_169) -> q_gen_103
<nil, nil, nil>() -> q_gen_103
<a, a, a>() -> q_gen_121
<a, b, a>() -> q_gen_121
<b, a, b>() -> q_gen_121
<b, b, a>() -> q_gen_121
<b, b, b>() -> q_gen_121
<cons, cons, cons>(q_gen_121, q_gen_155) -> q_gen_155
<cons, nil, cons>(q_gen_135, q_gen_104) -> q_gen_155
<nil, cons, cons>(q_gen_105, q_gen_156) -> q_gen_155
<a, a, b>() -> q_gen_197
<a, b, b>() -> q_gen_197
<b, a, a>() -> q_gen_197
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_101, q_gen_102, q_gen_115},
Q_f={q_gen_101},
Delta=
{
<s>(q_gen_115) -> q_gen_115
<z>() -> q_gen_115
<s, s>(q_gen_102) -> q_gen_102
<z, s>(q_gen_115) -> q_gen_102
<z, z>() -> q_gen_102
<s, s, s>(q_gen_101) -> q_gen_101
<s, z, s>(q_gen_102) -> q_gen_101
<z, s, s>(q_gen_102) -> q_gen_101
<z, z, s>(q_gen_115) -> q_gen_101
<z, z, z>() -> q_gen_101
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 27
() -> length([nil, z]) -> 27
() -> leq([a, n2]) -> 27
() -> leq([b, b]) -> 27
() -> leqnat([z, n2]) -> 27
() -> merge([cons(z, xs), nil, cons(z, xs)]) -> 27
() -> merge([nil, y, y]) -> 27
() -> plus([n, z, n]) -> 27
(append([t1, l2, _s])) -> append([cons(h1, t1), l2, cons(h1, _s)]) -> 28
(length([_ha, _ia]) /\ length([l1, _ga]) /\ merge([l1, l2, _ha])) -> leqnat([_ga, _ia]) -> 28
(length([_ka, _la]) /\ length([l2, _ja]) /\ merge([l1, l2, _ka])) -> leqnat([_ja, _la]) -> 29
(length([ll, _ca])) -> length([cons(x, ll), s(_ca)]) -> 27
(leq([z, y2]) /\ merge([xs, cons(y2, ys), _m])) -> merge([cons(z, xs), cons(y2, ys), cons(z, _m)]) -> 27
(not leq([z, y2]) /\ merge([cons(z, xs), ys, _n])) -> merge([cons(z, xs), cons(y2, ys), cons(y2, _n)]) -> 30
(leq([b, a])) -> BOT -> 28
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 28
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 28
(leqnat([s(nn1), z])) -> BOT -> 28
(plus([n, mm, _x])) -> plus([n, s(mm), s(_x)]) -> 28
}
Sat witness: Found: ((not leq([z, y2]) /\ merge([cons(z, xs), ys, _n])) -> merge([cons(z, xs), cons(y2, ys), cons(y2, _n)]), {
_n -> cons(a, cons(a, nil))  ;  xs -> nil  ;  y2 -> a  ;  ys -> cons(a, cons(b, nil))  ;  z -> b
})

-------------------------------------------
Step 73, which took 7.223820 s (model generation: 7.223112,  model checking: 0.000708):

Model:
|_
{
append -> 
{{{
Q={q_gen_100, q_gen_109, q_gen_110, q_gen_127, q_gen_128, q_gen_129},
Q_f={q_gen_109},
Delta=
{
<cons>(q_gen_128, q_gen_127) -> q_gen_127
<nil>() -> q_gen_127
<a>() -> q_gen_128
<b>() -> q_gen_128
<a, a>() -> q_gen_100
<a, b>() -> q_gen_100
<b, a>() -> q_gen_100
<b, b>() -> q_gen_100
<cons, cons>(q_gen_100, q_gen_110) -> q_gen_110
<nil, cons>(q_gen_128, q_gen_127) -> q_gen_110
<nil, nil>() -> q_gen_110
<cons, cons, cons>(q_gen_129, q_gen_109) -> q_gen_109
<cons, nil, cons>(q_gen_100, q_gen_110) -> q_gen_109
<nil, cons, cons>(q_gen_100, q_gen_110) -> q_gen_109
<nil, nil, cons>(q_gen_128, q_gen_127) -> q_gen_109
<nil, nil, nil>() -> q_gen_109
<a, a, a>() -> q_gen_129
<a, b, a>() -> q_gen_129
<b, a, b>() -> q_gen_129
<b, b, b>() -> q_gen_129
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_122, q_gen_123, q_gen_139, q_gen_140, q_gen_141, q_gen_142, q_gen_143, q_gen_175, q_gen_178},
Q_f={q_gen_122},
Delta=
{
<cons>(q_gen_140, q_gen_175) -> q_gen_139
<a>() -> q_gen_140
<b>() -> q_gen_140
<s>(q_gen_178) -> q_gen_142
<z>() -> q_gen_142
<cons>(q_gen_140, q_gen_139) -> q_gen_175
<nil>() -> q_gen_175
<s>(q_gen_142) -> q_gen_178
<cons, s>(q_gen_123, q_gen_175) -> q_gen_122
<cons, s>(q_gen_141, q_gen_139) -> q_gen_122
<nil, z>() -> q_gen_122
<a, s>(q_gen_178) -> q_gen_123
<a, z>() -> q_gen_123
<b, s>(q_gen_178) -> q_gen_123
<b, z>() -> q_gen_123
<a, s>(q_gen_142) -> q_gen_141
<b, s>(q_gen_142) -> q_gen_141
<cons, s>(q_gen_123, q_gen_139) -> q_gen_143
<cons, s>(q_gen_141, q_gen_175) -> q_gen_143
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_108, q_gen_82},
Q_f={q_gen_108},
Delta=
{
<a, a>() -> q_gen_108
<a, b>() -> q_gen_108
<b, b>() -> q_gen_108
<b, a>() -> q_gen_82
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  leqnat -> 
{{{
Q={q_gen_106, q_gen_107, q_gen_145},
Q_f={q_gen_106},
Delta=
{
<s>(q_gen_107) -> q_gen_107
<z>() -> q_gen_107
<s, s>(q_gen_106) -> q_gen_106
<z, s>(q_gen_107) -> q_gen_106
<z, z>() -> q_gen_106
<s, s>(q_gen_145) -> q_gen_145
<s, z>(q_gen_107) -> q_gen_145
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  merge -> 
{{{
Q={q_gen_103, q_gen_104, q_gen_105, q_gen_118, q_gen_121, q_gen_135, q_gen_155, q_gen_156, q_gen_169, q_gen_87},
Q_f={q_gen_103},
Delta=
{
<a>() -> q_gen_118
<b>() -> q_gen_118
<cons>(q_gen_118, q_gen_169) -> q_gen_169
<nil>() -> q_gen_169
<cons, cons>(q_gen_105, q_gen_104) -> q_gen_104
<nil, nil>() -> q_gen_104
<a, a>() -> q_gen_105
<b, b>() -> q_gen_105
<a, b>() -> q_gen_135
<b, a>() -> q_gen_135
<cons, cons>(q_gen_105, q_gen_156) -> q_gen_156
<cons, cons>(q_gen_135, q_gen_104) -> q_gen_156
<nil, cons>(q_gen_118, q_gen_169) -> q_gen_156
<cons, cons, cons>(q_gen_121, q_gen_103) -> q_gen_103
<cons, cons, cons>(q_gen_87, q_gen_103) -> q_gen_103
<cons, cons, cons>(q_gen_87, q_gen_155) -> q_gen_103
<cons, nil, cons>(q_gen_105, q_gen_104) -> q_gen_103
<nil, cons, cons>(q_gen_105, q_gen_104) -> q_gen_103
<nil, cons, cons>(q_gen_135, q_gen_104) -> q_gen_103
<nil, nil, cons>(q_gen_118, q_gen_169) -> q_gen_103
<nil, nil, nil>() -> q_gen_103
<a, a, a>() -> q_gen_121
<a, a, b>() -> q_gen_121
<a, b, a>() -> q_gen_121
<a, b, b>() -> q_gen_121
<b, a, b>() -> q_gen_121
<b, b, a>() -> q_gen_121
<b, b, b>() -> q_gen_121
<cons, cons, cons>(q_gen_121, q_gen_155) -> q_gen_155
<cons, nil, cons>(q_gen_105, q_gen_156) -> q_gen_155
<cons, nil, cons>(q_gen_135, q_gen_104) -> q_gen_155
<nil, cons, cons>(q_gen_105, q_gen_156) -> q_gen_155
<b, a, a>() -> q_gen_87
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_101, q_gen_102, q_gen_115},
Q_f={q_gen_101},
Delta=
{
<s>(q_gen_115) -> q_gen_115
<z>() -> q_gen_115
<s, s>(q_gen_102) -> q_gen_102
<z, s>(q_gen_115) -> q_gen_102
<z, z>() -> q_gen_102
<s, s, s>(q_gen_101) -> q_gen_101
<s, z, s>(q_gen_102) -> q_gen_101
<z, s, s>(q_gen_102) -> q_gen_101
<z, z, s>(q_gen_115) -> q_gen_101
<z, z, z>() -> q_gen_101
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 27
() -> length([nil, z]) -> 27
() -> leq([a, n2]) -> 27
() -> leq([b, b]) -> 27
() -> leqnat([z, n2]) -> 27
() -> merge([cons(z, xs), nil, cons(z, xs)]) -> 27
() -> merge([nil, y, y]) -> 27
() -> plus([n, z, n]) -> 27
(append([t1, l2, _s])) -> append([cons(h1, t1), l2, cons(h1, _s)]) -> 28
(length([_ha, _ia]) /\ length([l1, _ga]) /\ merge([l1, l2, _ha])) -> leqnat([_ga, _ia]) -> 28
(length([_ka, _la]) /\ length([l2, _ja]) /\ merge([l1, l2, _ka])) -> leqnat([_ja, _la]) -> 29
(length([ll, _ca])) -> length([cons(x, ll), s(_ca)]) -> 27
(leq([z, y2]) /\ merge([xs, cons(y2, ys), _m])) -> merge([cons(z, xs), cons(y2, ys), cons(z, _m)]) -> 30
(not leq([z, y2]) /\ merge([cons(z, xs), ys, _n])) -> merge([cons(z, xs), cons(y2, ys), cons(y2, _n)]) -> 30
(leq([b, a])) -> BOT -> 28
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 28
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 28
(leqnat([s(nn1), z])) -> BOT -> 28
(plus([n, mm, _x])) -> plus([n, s(mm), s(_x)]) -> 28
}
Sat witness: Found: ((leq([z, y2]) /\ merge([xs, cons(y2, ys), _m])) -> merge([cons(z, xs), cons(y2, ys), cons(z, _m)]), {
_m -> cons(a, nil)  ;  xs -> cons(b, nil)  ;  y2 -> a  ;  ys -> nil  ;  z -> a
})

-------------------------------------------
Step 74, which took 4.694433 s (model generation: 4.693699,  model checking: 0.000734):

Model:
|_
{
append -> 
{{{
Q={q_gen_100, q_gen_109, q_gen_110, q_gen_127, q_gen_128, q_gen_129},
Q_f={q_gen_109},
Delta=
{
<cons>(q_gen_128, q_gen_127) -> q_gen_127
<nil>() -> q_gen_127
<a>() -> q_gen_128
<b>() -> q_gen_128
<a, a>() -> q_gen_100
<a, b>() -> q_gen_100
<b, a>() -> q_gen_100
<b, b>() -> q_gen_100
<cons, cons>(q_gen_100, q_gen_110) -> q_gen_110
<nil, cons>(q_gen_128, q_gen_127) -> q_gen_110
<nil, nil>() -> q_gen_110
<cons, cons, cons>(q_gen_129, q_gen_109) -> q_gen_109
<cons, nil, cons>(q_gen_100, q_gen_110) -> q_gen_109
<nil, cons, cons>(q_gen_100, q_gen_110) -> q_gen_109
<nil, nil, cons>(q_gen_128, q_gen_127) -> q_gen_109
<nil, nil, nil>() -> q_gen_109
<a, a, a>() -> q_gen_129
<a, b, a>() -> q_gen_129
<b, a, b>() -> q_gen_129
<b, b, b>() -> q_gen_129
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_122, q_gen_123, q_gen_139, q_gen_140, q_gen_141, q_gen_142, q_gen_149, q_gen_175, q_gen_177, q_gen_178, q_gen_94},
Q_f={q_gen_122},
Delta=
{
<cons>(q_gen_140, q_gen_175) -> q_gen_139
<cons>(q_gen_140, q_gen_94) -> q_gen_139
<a>() -> q_gen_140
<b>() -> q_gen_140
<s>(q_gen_178) -> q_gen_142
<z>() -> q_gen_142
<cons>(q_gen_140, q_gen_139) -> q_gen_175
<s>(q_gen_142) -> q_gen_178
<nil>() -> q_gen_94
<cons, s>(q_gen_123, q_gen_175) -> q_gen_122
<cons, s>(q_gen_123, q_gen_94) -> q_gen_122
<cons, s>(q_gen_141, q_gen_139) -> q_gen_122
<cons, s>(q_gen_141, q_gen_94) -> q_gen_122
<cons, s>(q_gen_177, q_gen_175) -> q_gen_122
<nil, z>() -> q_gen_122
<a, z>() -> q_gen_123
<b, z>() -> q_gen_123
<a, s>(q_gen_142) -> q_gen_141
<b, s>(q_gen_142) -> q_gen_141
<cons, s>(q_gen_123, q_gen_139) -> q_gen_149
<cons, s>(q_gen_141, q_gen_175) -> q_gen_149
<cons, s>(q_gen_177, q_gen_139) -> q_gen_149
<cons, s>(q_gen_177, q_gen_94) -> q_gen_149
<a, s>(q_gen_178) -> q_gen_177
<b, s>(q_gen_178) -> q_gen_177
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_108, q_gen_82},
Q_f={q_gen_108},
Delta=
{
<a, a>() -> q_gen_108
<a, b>() -> q_gen_108
<b, b>() -> q_gen_108
<b, a>() -> q_gen_82
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  leqnat -> 
{{{
Q={q_gen_106, q_gen_107, q_gen_145},
Q_f={q_gen_106},
Delta=
{
<s>(q_gen_107) -> q_gen_107
<z>() -> q_gen_107
<s, s>(q_gen_106) -> q_gen_106
<z, s>(q_gen_107) -> q_gen_106
<z, z>() -> q_gen_106
<s, s>(q_gen_145) -> q_gen_145
<s, z>(q_gen_107) -> q_gen_145
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  merge -> 
{{{
Q={q_gen_103, q_gen_104, q_gen_105, q_gen_117, q_gen_118, q_gen_121, q_gen_156, q_gen_169},
Q_f={q_gen_103},
Delta=
{
<a>() -> q_gen_118
<b>() -> q_gen_118
<cons>(q_gen_118, q_gen_169) -> q_gen_169
<nil>() -> q_gen_169
<cons, cons>(q_gen_105, q_gen_104) -> q_gen_104
<nil, nil>() -> q_gen_104
<a, a>() -> q_gen_105
<a, b>() -> q_gen_105
<b, a>() -> q_gen_105
<b, b>() -> q_gen_105
<cons, cons>(q_gen_105, q_gen_156) -> q_gen_156
<nil, cons>(q_gen_118, q_gen_169) -> q_gen_156
<cons, cons, cons>(q_gen_121, q_gen_117) -> q_gen_103
<cons, nil, cons>(q_gen_105, q_gen_104) -> q_gen_103
<nil, cons, cons>(q_gen_105, q_gen_104) -> q_gen_103
<nil, nil, nil>() -> q_gen_103
<cons, cons, cons>(q_gen_121, q_gen_103) -> q_gen_117
<cons, nil, cons>(q_gen_105, q_gen_156) -> q_gen_117
<nil, cons, cons>(q_gen_105, q_gen_156) -> q_gen_117
<nil, nil, cons>(q_gen_118, q_gen_169) -> q_gen_117
<a, a, a>() -> q_gen_121
<a, a, b>() -> q_gen_121
<a, b, a>() -> q_gen_121
<a, b, b>() -> q_gen_121
<b, a, a>() -> q_gen_121
<b, a, b>() -> q_gen_121
<b, b, a>() -> q_gen_121
<b, b, b>() -> q_gen_121
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_101, q_gen_102, q_gen_115},
Q_f={q_gen_101},
Delta=
{
<s>(q_gen_115) -> q_gen_115
<z>() -> q_gen_115
<s, s>(q_gen_102) -> q_gen_102
<z, s>(q_gen_115) -> q_gen_102
<z, z>() -> q_gen_102
<s, s, s>(q_gen_101) -> q_gen_101
<s, z, s>(q_gen_102) -> q_gen_101
<z, s, s>(q_gen_102) -> q_gen_101
<z, z, s>(q_gen_115) -> q_gen_101
<z, z, z>() -> q_gen_101
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 27
() -> length([nil, z]) -> 27
() -> leq([a, n2]) -> 27
() -> leq([b, b]) -> 27
() -> leqnat([z, n2]) -> 27
() -> merge([cons(z, xs), nil, cons(z, xs)]) -> 27
() -> merge([nil, y, y]) -> 27
() -> plus([n, z, n]) -> 27
(append([t1, l2, _s])) -> append([cons(h1, t1), l2, cons(h1, _s)]) -> 28
(length([_ha, _ia]) /\ length([l1, _ga]) /\ merge([l1, l2, _ha])) -> leqnat([_ga, _ia]) -> 28
(length([_ka, _la]) /\ length([l2, _ja]) /\ merge([l1, l2, _ka])) -> leqnat([_ja, _la]) -> 29
(length([ll, _ca])) -> length([cons(x, ll), s(_ca)]) -> 30
(leq([z, y2]) /\ merge([xs, cons(y2, ys), _m])) -> merge([cons(z, xs), cons(y2, ys), cons(z, _m)]) -> 30
(not leq([z, y2]) /\ merge([cons(z, xs), ys, _n])) -> merge([cons(z, xs), cons(y2, ys), cons(y2, _n)]) -> 30
(leq([b, a])) -> BOT -> 28
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 28
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 28
(leqnat([s(nn1), z])) -> BOT -> 28
(plus([n, mm, _x])) -> plus([n, s(mm), s(_x)]) -> 28
}
Sat witness: Found: ((length([ll, _ca])) -> length([cons(x, ll), s(_ca)]), {
_ca -> s(s(z))  ;  ll -> cons(b, nil)  ;  x -> a
})

-------------------------------------------
Step 75, which took 5.217367 s (model generation: 5.213923,  model checking: 0.003444):

Model:
|_
{
append -> 
{{{
Q={q_gen_100, q_gen_109, q_gen_110, q_gen_127, q_gen_128, q_gen_129},
Q_f={q_gen_109},
Delta=
{
<cons>(q_gen_128, q_gen_127) -> q_gen_127
<nil>() -> q_gen_127
<a>() -> q_gen_128
<b>() -> q_gen_128
<a, a>() -> q_gen_100
<a, b>() -> q_gen_100
<b, a>() -> q_gen_100
<b, b>() -> q_gen_100
<cons, cons>(q_gen_100, q_gen_110) -> q_gen_110
<nil, cons>(q_gen_128, q_gen_127) -> q_gen_110
<nil, nil>() -> q_gen_110
<cons, cons, cons>(q_gen_129, q_gen_109) -> q_gen_109
<cons, nil, cons>(q_gen_100, q_gen_110) -> q_gen_109
<nil, cons, cons>(q_gen_100, q_gen_110) -> q_gen_109
<nil, nil, cons>(q_gen_128, q_gen_127) -> q_gen_109
<nil, nil, nil>() -> q_gen_109
<a, a, a>() -> q_gen_129
<a, b, a>() -> q_gen_129
<b, a, b>() -> q_gen_129
<b, b, b>() -> q_gen_129
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_122, q_gen_123, q_gen_139, q_gen_140, q_gen_141, q_gen_142, q_gen_143, q_gen_175, q_gen_178},
Q_f={q_gen_122},
Delta=
{
<cons>(q_gen_140, q_gen_175) -> q_gen_139
<a>() -> q_gen_140
<b>() -> q_gen_140
<s>(q_gen_178) -> q_gen_142
<z>() -> q_gen_142
<cons>(q_gen_140, q_gen_139) -> q_gen_175
<nil>() -> q_gen_175
<s>(q_gen_142) -> q_gen_178
<cons, s>(q_gen_123, q_gen_175) -> q_gen_122
<cons, s>(q_gen_141, q_gen_139) -> q_gen_122
<nil, z>() -> q_gen_122
<a, s>(q_gen_178) -> q_gen_123
<a, z>() -> q_gen_123
<b, s>(q_gen_178) -> q_gen_123
<b, z>() -> q_gen_123
<a, s>(q_gen_142) -> q_gen_141
<b, s>(q_gen_142) -> q_gen_141
<cons, s>(q_gen_123, q_gen_139) -> q_gen_143
<cons, s>(q_gen_141, q_gen_175) -> q_gen_143
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_108, q_gen_82},
Q_f={q_gen_108},
Delta=
{
<a, a>() -> q_gen_108
<a, b>() -> q_gen_108
<b, b>() -> q_gen_108
<b, a>() -> q_gen_82
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  leqnat -> 
{{{
Q={q_gen_106, q_gen_107, q_gen_145},
Q_f={q_gen_106},
Delta=
{
<s>(q_gen_107) -> q_gen_107
<z>() -> q_gen_107
<s, s>(q_gen_106) -> q_gen_106
<z, s>(q_gen_107) -> q_gen_106
<z, z>() -> q_gen_106
<s, s>(q_gen_145) -> q_gen_145
<s, z>(q_gen_107) -> q_gen_145
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  merge -> 
{{{
Q={q_gen_103, q_gen_104, q_gen_105, q_gen_118, q_gen_121, q_gen_135, q_gen_155, q_gen_156, q_gen_158, q_gen_169},
Q_f={q_gen_103},
Delta=
{
<a>() -> q_gen_118
<b>() -> q_gen_118
<cons>(q_gen_118, q_gen_169) -> q_gen_169
<nil>() -> q_gen_169
<cons, cons>(q_gen_105, q_gen_104) -> q_gen_104
<nil, nil>() -> q_gen_104
<a, a>() -> q_gen_105
<b, a>() -> q_gen_105
<b, b>() -> q_gen_105
<a, b>() -> q_gen_135
<cons, cons>(q_gen_105, q_gen_156) -> q_gen_156
<nil, cons>(q_gen_118, q_gen_169) -> q_gen_156
<cons, cons, cons>(q_gen_121, q_gen_103) -> q_gen_103
<cons, cons, cons>(q_gen_158, q_gen_103) -> q_gen_103
<cons, cons, cons>(q_gen_158, q_gen_155) -> q_gen_103
<cons, nil, cons>(q_gen_105, q_gen_104) -> q_gen_103
<nil, cons, cons>(q_gen_105, q_gen_104) -> q_gen_103
<nil, cons, cons>(q_gen_135, q_gen_104) -> q_gen_103
<nil, nil, cons>(q_gen_118, q_gen_169) -> q_gen_103
<nil, nil, nil>() -> q_gen_103
<a, a, b>() -> q_gen_121
<a, b, a>() -> q_gen_121
<a, b, b>() -> q_gen_121
<b, a, b>() -> q_gen_121
<b, b, a>() -> q_gen_121
<b, b, b>() -> q_gen_121
<cons, cons, cons>(q_gen_121, q_gen_155) -> q_gen_155
<cons, nil, cons>(q_gen_105, q_gen_156) -> q_gen_155
<cons, nil, cons>(q_gen_135, q_gen_104) -> q_gen_155
<nil, cons, cons>(q_gen_105, q_gen_156) -> q_gen_155
<a, a, a>() -> q_gen_158
<b, a, a>() -> q_gen_158
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_101, q_gen_102, q_gen_115},
Q_f={q_gen_101},
Delta=
{
<s>(q_gen_115) -> q_gen_115
<z>() -> q_gen_115
<s, s>(q_gen_102) -> q_gen_102
<z, s>(q_gen_115) -> q_gen_102
<z, z>() -> q_gen_102
<s, s, s>(q_gen_101) -> q_gen_101
<s, z, s>(q_gen_102) -> q_gen_101
<z, s, s>(q_gen_102) -> q_gen_101
<z, z, s>(q_gen_115) -> q_gen_101
<z, z, z>() -> q_gen_101
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 28
() -> length([nil, z]) -> 28
() -> leq([a, n2]) -> 28
() -> leq([b, b]) -> 28
() -> leqnat([z, n2]) -> 28
() -> merge([cons(z, xs), nil, cons(z, xs)]) -> 28
() -> merge([nil, y, y]) -> 28
() -> plus([n, z, n]) -> 28
(append([t1, l2, _s])) -> append([cons(h1, t1), l2, cons(h1, _s)]) -> 28
(length([_ha, _ia]) /\ length([l1, _ga]) /\ merge([l1, l2, _ha])) -> leqnat([_ga, _ia]) -> 31
(length([_ka, _la]) /\ length([l2, _ja]) /\ merge([l1, l2, _ka])) -> leqnat([_ja, _la]) -> 29
(length([ll, _ca])) -> length([cons(x, ll), s(_ca)]) -> 30
(leq([z, y2]) /\ merge([xs, cons(y2, ys), _m])) -> merge([cons(z, xs), cons(y2, ys), cons(z, _m)]) -> 30
(not leq([z, y2]) /\ merge([cons(z, xs), ys, _n])) -> merge([cons(z, xs), cons(y2, ys), cons(y2, _n)]) -> 30
(leq([b, a])) -> BOT -> 29
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 29
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 29
(leqnat([s(nn1), z])) -> BOT -> 29
(plus([n, mm, _x])) -> plus([n, s(mm), s(_x)]) -> 29
}
Sat witness: Found: ((length([_ha, _ia]) /\ length([l1, _ga]) /\ merge([l1, l2, _ha])) -> leqnat([_ga, _ia]), {
_ga -> s(s(s(z)))  ;  _ha -> cons(b, nil)  ;  _ia -> s(z)  ;  l1 -> cons(b, nil)  ;  l2 -> cons(b, nil)
})

-------------------------------------------
Step 76, which took 2.464824 s (model generation: 2.451629,  model checking: 0.013195):

Model:
|_
{
append -> 
{{{
Q={q_gen_100, q_gen_109, q_gen_110, q_gen_127, q_gen_128, q_gen_129},
Q_f={q_gen_109},
Delta=
{
<cons>(q_gen_128, q_gen_127) -> q_gen_127
<nil>() -> q_gen_127
<a>() -> q_gen_128
<b>() -> q_gen_128
<a, a>() -> q_gen_100
<a, b>() -> q_gen_100
<b, a>() -> q_gen_100
<b, b>() -> q_gen_100
<cons, cons>(q_gen_100, q_gen_110) -> q_gen_110
<nil, cons>(q_gen_128, q_gen_127) -> q_gen_110
<nil, nil>() -> q_gen_110
<cons, cons, cons>(q_gen_129, q_gen_109) -> q_gen_109
<cons, nil, cons>(q_gen_100, q_gen_110) -> q_gen_109
<nil, cons, cons>(q_gen_100, q_gen_110) -> q_gen_109
<nil, nil, cons>(q_gen_128, q_gen_127) -> q_gen_109
<nil, nil, nil>() -> q_gen_109
<a, a, a>() -> q_gen_129
<a, b, a>() -> q_gen_129
<b, a, b>() -> q_gen_129
<b, b, b>() -> q_gen_129
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_122, q_gen_123, q_gen_139, q_gen_140, q_gen_141, q_gen_142, q_gen_143, q_gen_175, q_gen_176, q_gen_177, q_gen_178, q_gen_180, q_gen_94},
Q_f={q_gen_122},
Delta=
{
<cons>(q_gen_140, q_gen_94) -> q_gen_139
<b>() -> q_gen_140
<z>() -> q_gen_142
<cons>(q_gen_140, q_gen_175) -> q_gen_175
<cons>(q_gen_140, q_gen_180) -> q_gen_175
<cons>(q_gen_176, q_gen_139) -> q_gen_175
<a>() -> q_gen_176
<s>(q_gen_142) -> q_gen_178
<s>(q_gen_178) -> q_gen_178
<cons>(q_gen_140, q_gen_139) -> q_gen_180
<nil>() -> q_gen_94
<cons, s>(q_gen_123, q_gen_94) -> q_gen_122
<cons, s>(q_gen_141, q_gen_139) -> q_gen_122
<cons, s>(q_gen_141, q_gen_180) -> q_gen_122
<cons, s>(q_gen_177, q_gen_175) -> q_gen_122
<nil, z>() -> q_gen_122
<a, z>() -> q_gen_123
<b, z>() -> q_gen_123
<a, s>(q_gen_142) -> q_gen_141
<a, s>(q_gen_178) -> q_gen_141
<b, s>(q_gen_142) -> q_gen_141
<cons, s>(q_gen_123, q_gen_139) -> q_gen_143
<cons, s>(q_gen_123, q_gen_175) -> q_gen_143
<cons, s>(q_gen_123, q_gen_180) -> q_gen_143
<cons, s>(q_gen_141, q_gen_175) -> q_gen_143
<cons, s>(q_gen_141, q_gen_94) -> q_gen_143
<cons, s>(q_gen_177, q_gen_139) -> q_gen_143
<cons, s>(q_gen_177, q_gen_180) -> q_gen_143
<cons, s>(q_gen_177, q_gen_94) -> q_gen_143
<b, s>(q_gen_178) -> q_gen_177
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_108, q_gen_82},
Q_f={q_gen_108},
Delta=
{
<a, a>() -> q_gen_108
<a, b>() -> q_gen_108
<b, b>() -> q_gen_108
<b, a>() -> q_gen_82
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  leqnat -> 
{{{
Q={q_gen_106, q_gen_107, q_gen_145},
Q_f={q_gen_106},
Delta=
{
<s>(q_gen_107) -> q_gen_107
<z>() -> q_gen_107
<s, s>(q_gen_106) -> q_gen_106
<z, s>(q_gen_107) -> q_gen_106
<z, z>() -> q_gen_106
<s, s>(q_gen_145) -> q_gen_145
<s, z>(q_gen_107) -> q_gen_145
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  merge -> 
{{{
Q={q_gen_103, q_gen_104, q_gen_105, q_gen_118, q_gen_121, q_gen_169},
Q_f={q_gen_103},
Delta=
{
<a>() -> q_gen_118
<b>() -> q_gen_118
<cons>(q_gen_118, q_gen_169) -> q_gen_169
<nil>() -> q_gen_169
<cons, cons>(q_gen_105, q_gen_104) -> q_gen_104
<nil, cons>(q_gen_118, q_gen_169) -> q_gen_104
<nil, nil>() -> q_gen_104
<a, a>() -> q_gen_105
<a, b>() -> q_gen_105
<b, a>() -> q_gen_105
<b, b>() -> q_gen_105
<cons, cons, cons>(q_gen_121, q_gen_103) -> q_gen_103
<cons, nil, cons>(q_gen_105, q_gen_104) -> q_gen_103
<nil, cons, cons>(q_gen_105, q_gen_104) -> q_gen_103
<nil, nil, cons>(q_gen_118, q_gen_169) -> q_gen_103
<nil, nil, nil>() -> q_gen_103
<a, a, a>() -> q_gen_121
<a, a, b>() -> q_gen_121
<a, b, a>() -> q_gen_121
<a, b, b>() -> q_gen_121
<b, a, a>() -> q_gen_121
<b, a, b>() -> q_gen_121
<b, b, a>() -> q_gen_121
<b, b, b>() -> q_gen_121
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_101, q_gen_102, q_gen_115},
Q_f={q_gen_101},
Delta=
{
<s>(q_gen_115) -> q_gen_115
<z>() -> q_gen_115
<s, s>(q_gen_102) -> q_gen_102
<z, s>(q_gen_115) -> q_gen_102
<z, z>() -> q_gen_102
<s, s, s>(q_gen_101) -> q_gen_101
<s, z, s>(q_gen_102) -> q_gen_101
<z, s, s>(q_gen_102) -> q_gen_101
<z, z, s>(q_gen_115) -> q_gen_101
<z, z, z>() -> q_gen_101
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 29
() -> length([nil, z]) -> 29
() -> leq([a, n2]) -> 29
() -> leq([b, b]) -> 29
() -> leqnat([z, n2]) -> 29
() -> merge([cons(z, xs), nil, cons(z, xs)]) -> 29
() -> merge([nil, y, y]) -> 29
() -> plus([n, z, n]) -> 29
(append([t1, l2, _s])) -> append([cons(h1, t1), l2, cons(h1, _s)]) -> 29
(length([_ha, _ia]) /\ length([l1, _ga]) /\ merge([l1, l2, _ha])) -> leqnat([_ga, _ia]) -> 31
(length([_ka, _la]) /\ length([l2, _ja]) /\ merge([l1, l2, _ka])) -> leqnat([_ja, _la]) -> 32
(length([ll, _ca])) -> length([cons(x, ll), s(_ca)]) -> 30
(leq([z, y2]) /\ merge([xs, cons(y2, ys), _m])) -> merge([cons(z, xs), cons(y2, ys), cons(z, _m)]) -> 30
(not leq([z, y2]) /\ merge([cons(z, xs), ys, _n])) -> merge([cons(z, xs), cons(y2, ys), cons(y2, _n)]) -> 30
(leq([b, a])) -> BOT -> 30
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 30
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 30
(leqnat([s(nn1), z])) -> BOT -> 30
(plus([n, mm, _x])) -> plus([n, s(mm), s(_x)]) -> 30
}
Sat witness: Found: ((length([_ka, _la]) /\ length([l2, _ja]) /\ merge([l1, l2, _ka])) -> leqnat([_ja, _la]), {
_ja -> s(s(s(z)))  ;  _ka -> cons(b, cons(b, cons(b, nil)))  ;  _la -> s(s(z))  ;  l1 -> nil  ;  l2 -> cons(a, cons(b, nil))
})

-------------------------------------------
Step 77, which took 4.424367 s (model generation: 4.186811,  model checking: 0.237556):

Model:
|_
{
append -> 
{{{
Q={q_gen_100, q_gen_109, q_gen_110, q_gen_127, q_gen_128, q_gen_129},
Q_f={q_gen_109},
Delta=
{
<cons>(q_gen_128, q_gen_127) -> q_gen_127
<nil>() -> q_gen_127
<a>() -> q_gen_128
<b>() -> q_gen_128
<a, a>() -> q_gen_100
<a, b>() -> q_gen_100
<b, a>() -> q_gen_100
<b, b>() -> q_gen_100
<cons, cons>(q_gen_100, q_gen_110) -> q_gen_110
<nil, cons>(q_gen_128, q_gen_127) -> q_gen_110
<nil, nil>() -> q_gen_110
<cons, cons, cons>(q_gen_129, q_gen_109) -> q_gen_109
<cons, nil, cons>(q_gen_100, q_gen_110) -> q_gen_109
<nil, cons, cons>(q_gen_100, q_gen_110) -> q_gen_109
<nil, nil, cons>(q_gen_128, q_gen_127) -> q_gen_109
<nil, nil, nil>() -> q_gen_109
<a, a, a>() -> q_gen_129
<a, b, a>() -> q_gen_129
<b, a, b>() -> q_gen_129
<b, b, b>() -> q_gen_129
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_122, q_gen_123, q_gen_139, q_gen_140, q_gen_141, q_gen_142, q_gen_143, q_gen_175, q_gen_177, q_gen_178, q_gen_94},
Q_f={q_gen_122},
Delta=
{
<cons>(q_gen_140, q_gen_175) -> q_gen_139
<cons>(q_gen_140, q_gen_94) -> q_gen_139
<a>() -> q_gen_140
<b>() -> q_gen_140
<s>(q_gen_178) -> q_gen_142
<z>() -> q_gen_142
<cons>(q_gen_140, q_gen_139) -> q_gen_175
<s>(q_gen_142) -> q_gen_178
<nil>() -> q_gen_94
<cons, s>(q_gen_123, q_gen_175) -> q_gen_122
<cons, s>(q_gen_123, q_gen_94) -> q_gen_122
<cons, s>(q_gen_141, q_gen_139) -> q_gen_122
<cons, s>(q_gen_177, q_gen_175) -> q_gen_122
<nil, z>() -> q_gen_122
<a, z>() -> q_gen_123
<b, z>() -> q_gen_123
<a, s>(q_gen_142) -> q_gen_141
<b, s>(q_gen_142) -> q_gen_141
<cons, s>(q_gen_123, q_gen_139) -> q_gen_143
<cons, s>(q_gen_141, q_gen_175) -> q_gen_143
<cons, s>(q_gen_141, q_gen_94) -> q_gen_143
<cons, s>(q_gen_177, q_gen_139) -> q_gen_143
<cons, s>(q_gen_177, q_gen_94) -> q_gen_143
<a, s>(q_gen_178) -> q_gen_177
<b, s>(q_gen_178) -> q_gen_177
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_108, q_gen_82},
Q_f={q_gen_108},
Delta=
{
<a, a>() -> q_gen_108
<a, b>() -> q_gen_108
<b, b>() -> q_gen_108
<b, a>() -> q_gen_82
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  leqnat -> 
{{{
Q={q_gen_106, q_gen_107, q_gen_145},
Q_f={q_gen_106},
Delta=
{
<s>(q_gen_107) -> q_gen_107
<z>() -> q_gen_107
<s, s>(q_gen_106) -> q_gen_106
<z, s>(q_gen_107) -> q_gen_106
<z, z>() -> q_gen_106
<s, s>(q_gen_145) -> q_gen_145
<s, z>(q_gen_107) -> q_gen_145
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  merge -> 
{{{
Q={q_gen_103, q_gen_104, q_gen_105, q_gen_118, q_gen_121, q_gen_155, q_gen_156, q_gen_169},
Q_f={q_gen_103},
Delta=
{
<a>() -> q_gen_118
<b>() -> q_gen_118
<cons>(q_gen_118, q_gen_169) -> q_gen_169
<nil>() -> q_gen_169
<cons, cons>(q_gen_105, q_gen_104) -> q_gen_104
<nil, nil>() -> q_gen_104
<a, a>() -> q_gen_105
<a, b>() -> q_gen_105
<b, a>() -> q_gen_105
<b, b>() -> q_gen_105
<cons, cons>(q_gen_105, q_gen_156) -> q_gen_156
<nil, cons>(q_gen_118, q_gen_169) -> q_gen_156
<cons, cons, cons>(q_gen_121, q_gen_103) -> q_gen_103
<cons, cons, cons>(q_gen_121, q_gen_155) -> q_gen_103
<cons, nil, cons>(q_gen_105, q_gen_104) -> q_gen_103
<cons, nil, cons>(q_gen_105, q_gen_156) -> q_gen_103
<nil, cons, cons>(q_gen_105, q_gen_104) -> q_gen_103
<nil, nil, cons>(q_gen_118, q_gen_169) -> q_gen_103
<nil, nil, nil>() -> q_gen_103
<a, a, a>() -> q_gen_121
<a, a, b>() -> q_gen_121
<a, b, a>() -> q_gen_121
<a, b, b>() -> q_gen_121
<b, a, a>() -> q_gen_121
<b, a, b>() -> q_gen_121
<b, b, a>() -> q_gen_121
<b, b, b>() -> q_gen_121
<nil, cons, cons>(q_gen_105, q_gen_156) -> q_gen_155
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_101, q_gen_102, q_gen_115},
Q_f={q_gen_101},
Delta=
{
<s>(q_gen_115) -> q_gen_115
<z>() -> q_gen_115
<s, s>(q_gen_102) -> q_gen_102
<z, s>(q_gen_115) -> q_gen_102
<z, z>() -> q_gen_102
<s, s, s>(q_gen_101) -> q_gen_101
<s, z, s>(q_gen_102) -> q_gen_101
<z, s, s>(q_gen_102) -> q_gen_101
<z, z, s>(q_gen_115) -> q_gen_101
<z, z, z>() -> q_gen_101
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 30
() -> length([nil, z]) -> 30
() -> leq([a, n2]) -> 30
() -> leq([b, b]) -> 30
() -> leqnat([z, n2]) -> 30
() -> merge([cons(z, xs), nil, cons(z, xs)]) -> 30
() -> merge([nil, y, y]) -> 30
() -> plus([n, z, n]) -> 30
(append([t1, l2, _s])) -> append([cons(h1, t1), l2, cons(h1, _s)]) -> 30
(length([_ha, _ia]) /\ length([l1, _ga]) /\ merge([l1, l2, _ha])) -> leqnat([_ga, _ia]) -> 34
(length([_ka, _la]) /\ length([l2, _ja]) /\ merge([l1, l2, _ka])) -> leqnat([_ja, _la]) -> 32
(length([ll, _ca])) -> length([cons(x, ll), s(_ca)]) -> 31
(leq([z, y2]) /\ merge([xs, cons(y2, ys), _m])) -> merge([cons(z, xs), cons(y2, ys), cons(z, _m)]) -> 31
(not leq([z, y2]) /\ merge([cons(z, xs), ys, _n])) -> merge([cons(z, xs), cons(y2, ys), cons(y2, _n)]) -> 31
(leq([b, a])) -> BOT -> 31
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 31
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 31
(leqnat([s(nn1), z])) -> BOT -> 31
(plus([n, mm, _x])) -> plus([n, s(mm), s(_x)]) -> 31
}
Sat witness: Found: ((length([_ha, _ia]) /\ length([l1, _ga]) /\ merge([l1, l2, _ha])) -> leqnat([_ga, _ia]), {
_ga -> s(s(z))  ;  _ha -> cons(b, cons(b, cons(b, cons(b, cons(b, nil)))))  ;  _ia -> s(z)  ;  l1 -> cons(b, cons(b, nil))  ;  l2 -> cons(b, nil)
})

-------------------------------------------
Step 78, which took 5.167113 s (model generation: 5.161004,  model checking: 0.006109):

Model:
|_
{
append -> 
{{{
Q={q_gen_100, q_gen_109, q_gen_110, q_gen_127, q_gen_128, q_gen_129},
Q_f={q_gen_109},
Delta=
{
<cons>(q_gen_128, q_gen_127) -> q_gen_127
<nil>() -> q_gen_127
<a>() -> q_gen_128
<b>() -> q_gen_128
<a, a>() -> q_gen_100
<a, b>() -> q_gen_100
<b, a>() -> q_gen_100
<b, b>() -> q_gen_100
<cons, cons>(q_gen_100, q_gen_110) -> q_gen_110
<nil, cons>(q_gen_128, q_gen_127) -> q_gen_110
<nil, nil>() -> q_gen_110
<cons, cons, cons>(q_gen_129, q_gen_109) -> q_gen_109
<cons, nil, cons>(q_gen_100, q_gen_110) -> q_gen_109
<nil, cons, cons>(q_gen_100, q_gen_110) -> q_gen_109
<nil, nil, cons>(q_gen_128, q_gen_127) -> q_gen_109
<nil, nil, nil>() -> q_gen_109
<a, a, a>() -> q_gen_129
<a, b, a>() -> q_gen_129
<b, a, b>() -> q_gen_129
<b, b, b>() -> q_gen_129
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_122, q_gen_123, q_gen_139, q_gen_140, q_gen_141, q_gen_142, q_gen_143, q_gen_175, q_gen_178},
Q_f={q_gen_122},
Delta=
{
<cons>(q_gen_140, q_gen_175) -> q_gen_139
<a>() -> q_gen_140
<b>() -> q_gen_140
<s>(q_gen_178) -> q_gen_142
<z>() -> q_gen_142
<cons>(q_gen_140, q_gen_139) -> q_gen_175
<nil>() -> q_gen_175
<s>(q_gen_142) -> q_gen_178
<cons, s>(q_gen_123, q_gen_175) -> q_gen_122
<cons, s>(q_gen_141, q_gen_139) -> q_gen_122
<nil, z>() -> q_gen_122
<a, s>(q_gen_178) -> q_gen_123
<a, z>() -> q_gen_123
<b, s>(q_gen_178) -> q_gen_123
<b, z>() -> q_gen_123
<a, s>(q_gen_142) -> q_gen_141
<b, s>(q_gen_142) -> q_gen_141
<cons, s>(q_gen_123, q_gen_139) -> q_gen_143
<cons, s>(q_gen_141, q_gen_175) -> q_gen_143
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_108, q_gen_82},
Q_f={q_gen_108},
Delta=
{
<a, a>() -> q_gen_108
<a, b>() -> q_gen_108
<b, b>() -> q_gen_108
<b, a>() -> q_gen_82
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  leqnat -> 
{{{
Q={q_gen_106, q_gen_107, q_gen_145, q_gen_220, q_gen_247},
Q_f={q_gen_106},
Delta=
{
<s>(q_gen_247) -> q_gen_107
<s>(q_gen_107) -> q_gen_247
<z>() -> q_gen_247
<s, s>(q_gen_106) -> q_gen_106
<s, s>(q_gen_220) -> q_gen_106
<z, s>(q_gen_107) -> q_gen_106
<z, s>(q_gen_247) -> q_gen_106
<z, z>() -> q_gen_106
<s, s>(q_gen_145) -> q_gen_145
<s, z>(q_gen_247) -> q_gen_145
<s, z>(q_gen_107) -> q_gen_220
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  merge -> 
{{{
Q={q_gen_103, q_gen_104, q_gen_105, q_gen_117, q_gen_118, q_gen_121, q_gen_156, q_gen_169},
Q_f={q_gen_103},
Delta=
{
<a>() -> q_gen_118
<b>() -> q_gen_118
<cons>(q_gen_118, q_gen_169) -> q_gen_169
<nil>() -> q_gen_169
<cons, cons>(q_gen_105, q_gen_104) -> q_gen_104
<cons, cons>(q_gen_105, q_gen_156) -> q_gen_104
<nil, nil>() -> q_gen_104
<a, a>() -> q_gen_105
<a, b>() -> q_gen_105
<b, a>() -> q_gen_105
<b, b>() -> q_gen_105
<nil, cons>(q_gen_118, q_gen_169) -> q_gen_156
<cons, cons, cons>(q_gen_121, q_gen_117) -> q_gen_103
<cons, nil, cons>(q_gen_105, q_gen_104) -> q_gen_103
<cons, nil, cons>(q_gen_105, q_gen_156) -> q_gen_103
<nil, cons, cons>(q_gen_105, q_gen_104) -> q_gen_103
<nil, nil, nil>() -> q_gen_103
<cons, cons, cons>(q_gen_121, q_gen_103) -> q_gen_117
<nil, cons, cons>(q_gen_105, q_gen_156) -> q_gen_117
<nil, nil, cons>(q_gen_118, q_gen_169) -> q_gen_117
<a, a, a>() -> q_gen_121
<a, a, b>() -> q_gen_121
<a, b, a>() -> q_gen_121
<a, b, b>() -> q_gen_121
<b, a, a>() -> q_gen_121
<b, a, b>() -> q_gen_121
<b, b, a>() -> q_gen_121
<b, b, b>() -> q_gen_121
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_101, q_gen_102, q_gen_115},
Q_f={q_gen_101},
Delta=
{
<s>(q_gen_115) -> q_gen_115
<z>() -> q_gen_115
<s, s>(q_gen_102) -> q_gen_102
<z, s>(q_gen_115) -> q_gen_102
<z, z>() -> q_gen_102
<s, s, s>(q_gen_101) -> q_gen_101
<s, z, s>(q_gen_102) -> q_gen_101
<z, s, s>(q_gen_102) -> q_gen_101
<z, z, s>(q_gen_115) -> q_gen_101
<z, z, z>() -> q_gen_101
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 31
() -> length([nil, z]) -> 31
() -> leq([a, n2]) -> 31
() -> leq([b, b]) -> 31
() -> leqnat([z, n2]) -> 31
() -> merge([cons(z, xs), nil, cons(z, xs)]) -> 31
() -> merge([nil, y, y]) -> 31
() -> plus([n, z, n]) -> 31
(append([t1, l2, _s])) -> append([cons(h1, t1), l2, cons(h1, _s)]) -> 31
(length([_ha, _ia]) /\ length([l1, _ga]) /\ merge([l1, l2, _ha])) -> leqnat([_ga, _ia]) -> 34
(length([_ka, _la]) /\ length([l2, _ja]) /\ merge([l1, l2, _ka])) -> leqnat([_ja, _la]) -> 32
(length([ll, _ca])) -> length([cons(x, ll), s(_ca)]) -> 31
(leq([z, y2]) /\ merge([xs, cons(y2, ys), _m])) -> merge([cons(z, xs), cons(y2, ys), cons(z, _m)]) -> 31
(not leq([z, y2]) /\ merge([cons(z, xs), ys, _n])) -> merge([cons(z, xs), cons(y2, ys), cons(y2, _n)]) -> 31
(leq([b, a])) -> BOT -> 31
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 31
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 34
(leqnat([s(nn1), z])) -> BOT -> 32
(plus([n, mm, _x])) -> plus([n, s(mm), s(_x)]) -> 32
}
Sat witness: Found: ((leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]), {
nn1 -> s(s(z))  ;  nn2 -> z
})

-------------------------------------------
Step 79, which took 6.022453 s (model generation: 6.016246,  model checking: 0.006207):

Model:
|_
{
append -> 
{{{
Q={q_gen_100, q_gen_109, q_gen_110, q_gen_127, q_gen_128, q_gen_129, q_gen_148, q_gen_162, q_gen_163, q_gen_187, q_gen_188, q_gen_207, q_gen_208},
Q_f={q_gen_109, q_gen_162, q_gen_187, q_gen_208},
Delta=
{
<cons>(q_gen_128, q_gen_127) -> q_gen_127
<nil>() -> q_gen_127
<b>() -> q_gen_128
<a>() -> q_gen_188
<a, a>() -> q_gen_100
<a, b>() -> q_gen_100
<b, a>() -> q_gen_100
<b, b>() -> q_gen_100
<cons, cons>(q_gen_100, q_gen_110) -> q_gen_110
<nil, nil>() -> q_gen_110
<nil, cons>(q_gen_128, q_gen_127) -> q_gen_148
<nil, cons>(q_gen_188, q_gen_127) -> q_gen_148
<cons, cons, cons>(q_gen_129, q_gen_109) -> q_gen_109
<cons, cons, cons>(q_gen_129, q_gen_162) -> q_gen_109
<cons, cons, cons>(q_gen_163, q_gen_187) -> q_gen_109
<cons, nil, cons>(q_gen_100, q_gen_148) -> q_gen_109
<nil, cons, cons>(q_gen_100, q_gen_110) -> q_gen_109
<nil, nil, cons>(q_gen_128, q_gen_127) -> q_gen_109
<a, a, a>() -> q_gen_129
<b, b, b>() -> q_gen_129
<cons, cons, cons>(q_gen_163, q_gen_208) -> q_gen_162
<nil, nil, nil>() -> q_gen_162
<a, b, a>() -> q_gen_163
<b, a, b>() -> q_gen_163
<cons, cons, cons>(q_gen_163, q_gen_207) -> q_gen_187
<nil, nil, cons>(q_gen_188, q_gen_127) -> q_gen_187
<cons, cons, cons>(q_gen_163, q_gen_162) -> q_gen_207
<nil, cons, cons>(q_gen_100, q_gen_148) -> q_gen_207
<cons, cons, cons>(q_gen_129, q_gen_208) -> q_gen_208
<cons, cons, cons>(q_gen_163, q_gen_109) -> q_gen_208
<cons, nil, cons>(q_gen_100, q_gen_110) -> q_gen_208
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_122, q_gen_123, q_gen_139, q_gen_140, q_gen_142, q_gen_149, q_gen_175, q_gen_177, q_gen_178, q_gen_205, q_gen_94, q_gen_95},
Q_f={q_gen_122},
Delta=
{
<cons>(q_gen_140, q_gen_94) -> q_gen_139
<a>() -> q_gen_140
<b>() -> q_gen_140
<z>() -> q_gen_142
<cons>(q_gen_140, q_gen_139) -> q_gen_175
<cons>(q_gen_140, q_gen_175) -> q_gen_175
<s>(q_gen_142) -> q_gen_178
<s>(q_gen_178) -> q_gen_178
<nil>() -> q_gen_94
<cons, s>(q_gen_123, q_gen_139) -> q_gen_122
<cons, s>(q_gen_123, q_gen_94) -> q_gen_122
<cons, s>(q_gen_177, q_gen_175) -> q_gen_122
<cons, s>(q_gen_205, q_gen_139) -> q_gen_122
<cons, s>(q_gen_205, q_gen_175) -> q_gen_122
<cons, s>(q_gen_95, q_gen_94) -> q_gen_122
<nil, z>() -> q_gen_122
<a, s>(q_gen_142) -> q_gen_123
<a, z>() -> q_gen_123
<b, s>(q_gen_142) -> q_gen_123
<cons, s>(q_gen_123, q_gen_175) -> q_gen_149
<cons, s>(q_gen_177, q_gen_139) -> q_gen_149
<cons, s>(q_gen_177, q_gen_94) -> q_gen_149
<cons, s>(q_gen_205, q_gen_94) -> q_gen_149
<cons, s>(q_gen_95, q_gen_139) -> q_gen_149
<cons, s>(q_gen_95, q_gen_175) -> q_gen_149
<b, s>(q_gen_178) -> q_gen_177
<a, s>(q_gen_178) -> q_gen_205
<b, z>() -> q_gen_95
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_108, q_gen_82},
Q_f={q_gen_108},
Delta=
{
<a, a>() -> q_gen_108
<a, b>() -> q_gen_108
<b, b>() -> q_gen_108
<b, a>() -> q_gen_82
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  leqnat -> 
{{{
Q={q_gen_106, q_gen_107, q_gen_145, q_gen_146, q_gen_219, q_gen_220, q_gen_97},
Q_f={q_gen_106},
Delta=
{
<s>(q_gen_107) -> q_gen_107
<s>(q_gen_97) -> q_gen_107
<z>() -> q_gen_97
<s, s>(q_gen_106) -> q_gen_106
<s, s>(q_gen_219) -> q_gen_106
<z, s>(q_gen_107) -> q_gen_106
<z, s>(q_gen_97) -> q_gen_106
<z, z>() -> q_gen_106
<s, s>(q_gen_146) -> q_gen_145
<s, s>(q_gen_145) -> q_gen_146
<s, z>(q_gen_97) -> q_gen_146
<s, s>(q_gen_220) -> q_gen_219
<s, z>(q_gen_107) -> q_gen_220
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  merge -> 
{{{
Q={q_gen_103, q_gen_104, q_gen_105, q_gen_116, q_gen_118, q_gen_121, q_gen_144, q_gen_156, q_gen_169, q_gen_172, q_gen_173, q_gen_194, q_gen_195, q_gen_206, q_gen_217, q_gen_226, q_gen_231, q_gen_245, q_gen_258, q_gen_268, q_gen_85, q_gen_87, q_gen_91},
Q_f={q_gen_103, q_gen_116, q_gen_195, q_gen_206, q_gen_226, q_gen_268},
Delta=
{
<a>() -> q_gen_118
<b>() -> q_gen_118
<cons>(q_gen_118, q_gen_169) -> q_gen_169
<cons>(q_gen_118, q_gen_85) -> q_gen_169
<nil>() -> q_gen_85
<cons, cons>(q_gen_105, q_gen_156) -> q_gen_104
<a, a>() -> q_gen_105
<a, b>() -> q_gen_105
<b, b>() -> q_gen_105
<cons, cons>(q_gen_105, q_gen_245) -> q_gen_156
<nil, cons>(q_gen_118, q_gen_85) -> q_gen_156
<nil, nil>() -> q_gen_156
<cons, cons>(q_gen_105, q_gen_104) -> q_gen_217
<cons, cons>(q_gen_91, q_gen_156) -> q_gen_245
<nil, cons>(q_gen_118, q_gen_169) -> q_gen_245
<b, a>() -> q_gen_91
<cons, cons, cons>(q_gen_87, q_gen_103) -> q_gen_103
<cons, nil, cons>(q_gen_105, q_gen_104) -> q_gen_103
<cons, nil, cons>(q_gen_105, q_gen_156) -> q_gen_103
<nil, cons, cons>(q_gen_105, q_gen_104) -> q_gen_103
<nil, cons, cons>(q_gen_105, q_gen_156) -> q_gen_103
<cons, cons, cons>(q_gen_121, q_gen_116) -> q_gen_116
<cons, cons, cons>(q_gen_121, q_gen_172) -> q_gen_116
<cons, cons, cons>(q_gen_173, q_gen_195) -> q_gen_116
<cons, cons, cons>(q_gen_87, q_gen_116) -> q_gen_116
<cons, cons, cons>(q_gen_87, q_gen_144) -> q_gen_116
<nil, nil, cons>(q_gen_118, q_gen_85) -> q_gen_116
<a, a, a>() -> q_gen_121
<a, b, a>() -> q_gen_121
<a, b, b>() -> q_gen_121
<b, b, b>() -> q_gen_121
<cons, cons, cons>(q_gen_121, q_gen_195) -> q_gen_144
<cons, cons, cons>(q_gen_173, q_gen_103) -> q_gen_144
<nil, nil, cons>(q_gen_118, q_gen_169) -> q_gen_144
<cons, cons, cons>(q_gen_173, q_gen_116) -> q_gen_172
<cons, cons, cons>(q_gen_173, q_gen_144) -> q_gen_172
<a, a, b>() -> q_gen_173
<b, a, b>() -> q_gen_173
<b, b, a>() -> q_gen_173
<cons, cons, cons>(q_gen_87, q_gen_195) -> q_gen_194
<cons, cons, cons>(q_gen_121, q_gen_268) -> q_gen_195
<cons, cons, cons>(q_gen_173, q_gen_172) -> q_gen_195
<nil, nil, nil>() -> q_gen_195
<cons, cons, cons>(q_gen_121, q_gen_103) -> q_gen_206
<cons, nil, cons>(q_gen_105, q_gen_217) -> q_gen_206
<cons, cons, cons>(q_gen_121, q_gen_206) -> q_gen_226
<cons, cons, cons>(q_gen_87, q_gen_206) -> q_gen_226
<cons, nil, cons>(q_gen_91, q_gen_156) -> q_gen_226
<cons, cons, cons>(q_gen_121, q_gen_226) -> q_gen_231
<cons, cons, cons>(q_gen_87, q_gen_231) -> q_gen_231
<nil, cons, cons>(q_gen_105, q_gen_217) -> q_gen_231
<nil, cons, cons>(q_gen_91, q_gen_156) -> q_gen_231
<cons, cons, cons>(q_gen_87, q_gen_258) -> q_gen_258
<nil, cons, cons>(q_gen_105, q_gen_245) -> q_gen_258
<cons, cons, cons>(q_gen_173, q_gen_226) -> q_gen_268
<cons, nil, cons>(q_gen_105, q_gen_245) -> q_gen_268
<b, a, a>() -> q_gen_87
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_101, q_gen_102, q_gen_115},
Q_f={q_gen_101},
Delta=
{
<s>(q_gen_115) -> q_gen_115
<z>() -> q_gen_115
<s, s>(q_gen_102) -> q_gen_102
<z, s>(q_gen_115) -> q_gen_102
<z, z>() -> q_gen_102
<s, s, s>(q_gen_101) -> q_gen_101
<s, z, s>(q_gen_102) -> q_gen_101
<z, s, s>(q_gen_102) -> q_gen_101
<z, z, s>(q_gen_115) -> q_gen_101
<z, z, z>() -> q_gen_101
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 31
() -> length([nil, z]) -> 31
() -> leq([a, n2]) -> 31
() -> leq([b, b]) -> 31
() -> leqnat([z, n2]) -> 31
() -> merge([cons(z, xs), nil, cons(z, xs)]) -> 31
() -> merge([nil, y, y]) -> 31
() -> plus([n, z, n]) -> 31
(append([t1, l2, _s])) -> append([cons(h1, t1), l2, cons(h1, _s)]) -> 31
(length([_ha, _ia]) /\ length([l1, _ga]) /\ merge([l1, l2, _ha])) -> leqnat([_ga, _ia]) -> 34
(length([_ka, _la]) /\ length([l2, _ja]) /\ merge([l1, l2, _ka])) -> leqnat([_ja, _la]) -> 32
(length([ll, _ca])) -> length([cons(x, ll), s(_ca)]) -> 31
(leq([z, y2]) /\ merge([xs, cons(y2, ys), _m])) -> merge([cons(z, xs), cons(y2, ys), cons(z, _m)]) -> 31
(not leq([z, y2]) /\ merge([cons(z, xs), ys, _n])) -> merge([cons(z, xs), cons(y2, ys), cons(y2, _n)]) -> 34
(leq([b, a])) -> BOT -> 32
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 32
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 34
(leqnat([s(nn1), z])) -> BOT -> 32
(plus([n, mm, _x])) -> plus([n, s(mm), s(_x)]) -> 32
}
Sat witness: Found: ((not leq([z, y2]) /\ merge([cons(z, xs), ys, _n])) -> merge([cons(z, xs), cons(y2, ys), cons(y2, _n)]), {
_n -> cons(a, cons(b, cons(b, cons(a, cons(b, nil)))))  ;  xs -> cons(a, cons(a, cons(b, nil)))  ;  y2 -> a  ;  ys -> cons(b, cons(b, cons(b, cons(a, cons(b, nil)))))  ;  z -> b
})

Total time: 66.606941
Reason for stopping: DontKnow. Stopped because: timeout