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


Learning problem is:

env: {
nat -> {s, z}  ;  natlist -> {cons, nil}
}
definition:
{
(append, F:
{() -> append([nil, l2, l2])
(append([t1, l2, _nda])) -> append([cons(h1, t1), l2, cons(h1, _nda)])}
(append([_oda, _pda, _qda]) /\ append([_oda, _pda, _rda])) -> eq_natlist([_qda, _rda])
)
(reverse, F:
{() -> reverse([nil, nil])
(append([_sda, cons(h1, nil), _tda]) /\ reverse([t1, _sda])) -> reverse([cons(h1, t1), _tda])}
(reverse([_uda, _vda]) /\ reverse([_uda, _wda])) -> eq_natlist([_vda, _wda])
)
(leq, P:
{() -> leq([z, s(nn2)])
() -> leq([z, z])
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)])
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2])
(leq([s(nn1), z])) -> BOT}
)
(length, F:
{() -> length([nil, z])
(length([ll, _xda])) -> length([cons(x, ll), s(_xda)])}
(length([_yda, _aea]) /\ length([_yda, _zda])) -> eq_nat([_zda, _aea])
)
}

properties:
{(length([_cea, _dea]) /\ length([l1, _bea]) /\ reverse([l1, _cea])) -> leq([_bea, _dea])}


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

Clause system for inference is:

{
() -> append([nil, l2, l2]) -> 0
() -> length([nil, z]) -> 0
() -> leq([z, s(nn2)]) -> 0
() -> leq([z, z]) -> 0
() -> reverse([nil, nil]) -> 0
(append([_sda, cons(h1, nil), _tda]) /\ reverse([t1, _sda])) -> reverse([cons(h1, t1), _tda]) -> 0
(append([t1, l2, _nda])) -> append([cons(h1, t1), l2, cons(h1, _nda)]) -> 0
(length([_cea, _dea]) /\ length([l1, _bea]) /\ reverse([l1, _cea])) -> leq([_bea, _dea]) -> 0
(length([ll, _xda])) -> length([cons(x, ll), s(_xda)]) -> 0
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 0
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 0
(leq([s(nn1), z])) -> BOT -> 0
}


Solving took 60.004326 seconds.
DontKnow. Stopped because: timeout
Working model:
|_
{
append -> 
{{{
Q={q_gen_8087, q_gen_8092, q_gen_8093, q_gen_8094, q_gen_8097, q_gen_8098, q_gen_8099, q_gen_8100, q_gen_8106, q_gen_8107, q_gen_8108, q_gen_8109, q_gen_8110, q_gen_8111, q_gen_8117, q_gen_8118, q_gen_8119, q_gen_8130, q_gen_8131, q_gen_8132, q_gen_8133, q_gen_8134, q_gen_8148, q_gen_8149, q_gen_8150, q_gen_8156, q_gen_8157, q_gen_8158, q_gen_8159, q_gen_8160, q_gen_8161, q_gen_8162, q_gen_8163, q_gen_8171, q_gen_8172, q_gen_8176, q_gen_8177, q_gen_8178, q_gen_8187, q_gen_8188, q_gen_8189, q_gen_8192, q_gen_8193, q_gen_8201, q_gen_8202, q_gen_8203, q_gen_8204, q_gen_8205, q_gen_8212, q_gen_8213, q_gen_8214, q_gen_8215, q_gen_8216, q_gen_8217, q_gen_8221},
Q_f={},
Delta=
{
<nil>() -> q_gen_8108
<z>() -> q_gen_8109
<cons>(q_gen_8109, q_gen_8108) -> q_gen_8132
<s>(q_gen_8109) -> q_gen_8159
<cons>(q_gen_8159, q_gen_8108) -> q_gen_8163
<nil, nil>() -> q_gen_8093
<z, z>() -> q_gen_8094
<cons, cons>(q_gen_8099, q_gen_8093) -> q_gen_8098
<s, s>(q_gen_8094) -> q_gen_8099
<nil, cons>(q_gen_8109, q_gen_8108) -> q_gen_8118
<nil, cons>(q_gen_8109, q_gen_8132) -> q_gen_8134
<nil, cons>(q_gen_8159, q_gen_8163) -> q_gen_8162
<cons, cons>(q_gen_8094, q_gen_8093) -> q_gen_8188
<nil, cons>(q_gen_8159, q_gen_8108) -> q_gen_8215
<s, z>(q_gen_8109) -> q_gen_8216
<nil, nil, nil>() -> q_gen_8087
<cons, nil, cons>(q_gen_8094, q_gen_8093) -> q_gen_8092
<nil, cons, cons>(q_gen_8099, q_gen_8098) -> q_gen_8097
<nil, cons, cons>(q_gen_8094, q_gen_8093) -> q_gen_8100
<cons, cons, cons>(q_gen_8110, q_gen_8107) -> q_gen_8106
<nil, nil, cons>(q_gen_8109, q_gen_8108) -> q_gen_8107
<z, z, z>() -> q_gen_8110
<nil, cons, cons>(q_gen_8099, q_gen_8093) -> q_gen_8111
<cons, nil, cons>(q_gen_8094, q_gen_8118) -> q_gen_8117
<nil, cons, cons>(q_gen_8094, q_gen_8118) -> q_gen_8119
<cons, cons, cons>(q_gen_8110, q_gen_8131) -> q_gen_8130
<nil, nil, cons>(q_gen_8109, q_gen_8132) -> q_gen_8131
<nil, cons, cons>(q_gen_8094, q_gen_8134) -> q_gen_8133
<cons, cons, cons>(q_gen_8149, q_gen_8107) -> q_gen_8148
<s, z, s>(q_gen_8094) -> q_gen_8149
<cons, cons, cons>(q_gen_8110, q_gen_8087) -> q_gen_8150
<nil, cons, cons>(q_gen_8099, q_gen_8118) -> q_gen_8156
<cons, cons, cons>(q_gen_8160, q_gen_8158) -> q_gen_8157
<nil, nil, cons>(q_gen_8159, q_gen_8132) -> q_gen_8158
<s, s, s>(q_gen_8110) -> q_gen_8160
<nil, cons, cons>(q_gen_8094, q_gen_8162) -> q_gen_8161
<cons, cons, cons>(q_gen_8149, q_gen_8117) -> q_gen_8171
<cons, cons, cons>(q_gen_8110, q_gen_8092) -> q_gen_8172
<cons, cons, cons>(q_gen_8149, q_gen_8087) -> q_gen_8176
<cons, cons, cons>(q_gen_8110, q_gen_8178) -> q_gen_8177
<cons, nil, cons>(q_gen_8099, q_gen_8093) -> q_gen_8178
<nil, cons, cons>(q_gen_8094, q_gen_8188) -> q_gen_8187
<cons, cons, cons>(q_gen_8149, q_gen_8119) -> q_gen_8189
<cons, cons, cons>(q_gen_8110, q_gen_8119) -> q_gen_8192
<cons, cons, cons>(q_gen_8110, q_gen_8130) -> q_gen_8193
<cons, cons, cons>(q_gen_8160, q_gen_8092) -> q_gen_8201
<cons, cons, cons>(q_gen_8204, q_gen_8203) -> q_gen_8202
<cons, nil, cons>(q_gen_8099, q_gen_8188) -> q_gen_8203
<z, s, z>(q_gen_8109) -> q_gen_8204
<cons, cons, cons>(q_gen_8160, q_gen_8107) -> q_gen_8205
<nil, cons, cons>(q_gen_8094, q_gen_8098) -> q_gen_8212
<cons, cons, cons>(q_gen_8149, q_gen_8214) -> q_gen_8213
<nil, cons, cons>(q_gen_8216, q_gen_8215) -> q_gen_8214
<nil, cons, cons>(q_gen_8216, q_gen_8093) -> q_gen_8217
<cons, nil, cons>(q_gen_8094, q_gen_8134) -> q_gen_8221
}

Datatype: <natlist, natlist, natlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_8086, q_gen_8089, q_gen_8090, q_gen_8091, q_gen_8103, q_gen_8104, q_gen_8105, q_gen_8114, q_gen_8115, q_gen_8116, q_gen_8124, q_gen_8125, q_gen_8126, q_gen_8127, q_gen_8138, q_gen_8139, q_gen_8140, q_gen_8141, q_gen_8142, q_gen_8143, q_gen_8144, q_gen_8153, q_gen_8154, q_gen_8155, q_gen_8168, q_gen_8169, q_gen_8170, q_gen_8175, q_gen_8182, q_gen_8184, q_gen_8185, q_gen_8186, q_gen_8191, q_gen_8194, q_gen_8195, q_gen_8196, q_gen_8207, q_gen_8208, q_gen_8209, q_gen_8210, q_gen_8220, q_gen_8222, q_gen_8223, q_gen_8224, q_gen_8225},
Q_f={},
Delta=
{
<nil>() -> q_gen_8090
<z>() -> q_gen_8105
<s>(q_gen_8105) -> q_gen_8116
<cons>(q_gen_8105, q_gen_8090) -> q_gen_8125
<cons>(q_gen_8105, q_gen_8125) -> q_gen_8139
<cons>(q_gen_8116, q_gen_8090) -> q_gen_8155
<s>(q_gen_8116) -> q_gen_8186
<cons>(q_gen_8105, q_gen_8155) -> q_gen_8209
<cons>(q_gen_8116, q_gen_8155) -> q_gen_8224
<nil, z>() -> q_gen_8086
<cons, s>(q_gen_8091, q_gen_8090) -> q_gen_8089
<z, z>() -> q_gen_8091
<cons, s>(q_gen_8104, q_gen_8090) -> q_gen_8103
<s, z>(q_gen_8105) -> q_gen_8104
<cons, s>(q_gen_8115, q_gen_8090) -> q_gen_8114
<s, z>(q_gen_8116) -> q_gen_8115
<cons, s>(q_gen_8126, q_gen_8125) -> q_gen_8124
<z, s>(q_gen_8105) -> q_gen_8126
<cons, s>(q_gen_8126, q_gen_8090) -> q_gen_8127
<cons, s>(q_gen_8140, q_gen_8139) -> q_gen_8138
<s, s>(q_gen_8126) -> q_gen_8140
<cons, s>(q_gen_8140, q_gen_8125) -> q_gen_8141
<cons, s>(q_gen_8143, q_gen_8090) -> q_gen_8142
<s, s>(q_gen_8144) -> q_gen_8143
<z, s>(q_gen_8116) -> q_gen_8144
<cons, s>(q_gen_8140, q_gen_8090) -> q_gen_8153
<cons, s>(q_gen_8143, q_gen_8155) -> q_gen_8154
<cons, s>(q_gen_8169, q_gen_8139) -> q_gen_8168
<s, s>(q_gen_8170) -> q_gen_8169
<s, s>(q_gen_8091) -> q_gen_8170
<cons, s>(q_gen_8091, q_gen_8125) -> q_gen_8175
<cons, s>(q_gen_8170, q_gen_8125) -> q_gen_8182
<cons, s>(q_gen_8185, q_gen_8090) -> q_gen_8184
<s, z>(q_gen_8186) -> q_gen_8185
<cons, s>(q_gen_8144, q_gen_8090) -> q_gen_8191
<cons, s>(q_gen_8144, q_gen_8125) -> q_gen_8194
<cons, s>(q_gen_8196, q_gen_8139) -> q_gen_8195
<z, s>(q_gen_8186) -> q_gen_8196
<cons, s>(q_gen_8126, q_gen_8155) -> q_gen_8207
<cons, s>(q_gen_8144, q_gen_8209) -> q_gen_8208
<cons, s>(q_gen_8196, q_gen_8125) -> q_gen_8210
<cons, s>(q_gen_8196, q_gen_8155) -> q_gen_8220
<cons, s>(q_gen_8104, q_gen_8155) -> q_gen_8222
<cons, s>(q_gen_8170, q_gen_8224) -> q_gen_8223
<cons, s>(q_gen_8091, q_gen_8155) -> q_gen_8225
}

Datatype: <natlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_8083, q_gen_8084, q_gen_8085, q_gen_8088, q_gen_8095, q_gen_8096, q_gen_8128, q_gen_8129, q_gen_8146, q_gen_8147, q_gen_8199, q_gen_8200, q_gen_8211},
Q_f={},
Delta=
{
<z>() -> q_gen_8085
<s>(q_gen_8085) -> q_gen_8096
<z, z>() -> q_gen_8083
<z, s>(q_gen_8085) -> q_gen_8084
<s, s>(q_gen_8083) -> q_gen_8088
<z, s>(q_gen_8096) -> q_gen_8095
<s, s>(q_gen_8129) -> q_gen_8128
<s, z>(q_gen_8085) -> q_gen_8129
<s, s>(q_gen_8147) -> q_gen_8146
<s, s>(q_gen_8128) -> q_gen_8147
<s, s>(q_gen_8200) -> q_gen_8199
<s, z>(q_gen_8096) -> q_gen_8200
<s, s>(q_gen_8199) -> q_gen_8211
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_8082, q_gen_8101, q_gen_8102, q_gen_8112, q_gen_8113, q_gen_8120, q_gen_8121, q_gen_8122, q_gen_8123, q_gen_8135, q_gen_8136, q_gen_8137, q_gen_8145, q_gen_8151, q_gen_8152, q_gen_8164, q_gen_8165, q_gen_8166, q_gen_8167, q_gen_8173, q_gen_8174, q_gen_8179, q_gen_8180, q_gen_8181, q_gen_8183, q_gen_8190, q_gen_8197, q_gen_8198, q_gen_8206, q_gen_8218, q_gen_8219, q_gen_8226},
Q_f={},
Delta=
{
<nil>() -> q_gen_8122
<z>() -> q_gen_8123
<cons>(q_gen_8123, q_gen_8122) -> q_gen_8137
<cons>(q_gen_8167, q_gen_8122) -> q_gen_8166
<s>(q_gen_8123) -> q_gen_8167
<nil, nil>() -> q_gen_8082
<cons, cons>(q_gen_8102, q_gen_8082) -> q_gen_8101
<z, z>() -> q_gen_8102
<cons, cons>(q_gen_8113, q_gen_8082) -> q_gen_8112
<s, s>(q_gen_8102) -> q_gen_8113
<cons, cons>(q_gen_8102, q_gen_8121) -> q_gen_8120
<nil, cons>(q_gen_8123, q_gen_8122) -> q_gen_8121
<cons, cons>(q_gen_8102, q_gen_8136) -> q_gen_8135
<nil, cons>(q_gen_8123, q_gen_8137) -> q_gen_8136
<cons, cons>(q_gen_8113, q_gen_8121) -> q_gen_8145
<cons, cons>(q_gen_8102, q_gen_8152) -> q_gen_8151
<cons, nil>(q_gen_8123, q_gen_8122) -> q_gen_8152
<cons, cons>(q_gen_8102, q_gen_8165) -> q_gen_8164
<nil, cons>(q_gen_8167, q_gen_8166) -> q_gen_8165
<cons, cons>(q_gen_8102, q_gen_8101) -> q_gen_8173
<cons, cons>(q_gen_8102, q_gen_8151) -> q_gen_8174
<nil, cons>(q_gen_8167, q_gen_8122) -> q_gen_8179
<cons, cons>(q_gen_8181, q_gen_8121) -> q_gen_8180
<z, s>(q_gen_8123) -> q_gen_8181
<cons, cons>(q_gen_8113, q_gen_8101) -> q_gen_8183
<cons, cons>(q_gen_8102, q_gen_8120) -> q_gen_8190
<cons, cons>(q_gen_8198, q_gen_8082) -> q_gen_8197
<z, s>(q_gen_8167) -> q_gen_8198
<cons, cons>(q_gen_8181, q_gen_8082) -> q_gen_8206
<cons, cons>(q_gen_8219, q_gen_8082) -> q_gen_8218
<s, z>(q_gen_8123) -> q_gen_8219
<cons, cons>(q_gen_8219, q_gen_8179) -> q_gen_8226
}

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

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

-------------------
STEPS:
-------------------------------------------
Step 0, which took 0.007701 s (model generation: 0.007348,  model checking: 0.000353):

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

}

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

}

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

}

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

}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 0
() -> length([nil, z]) -> 0
() -> leq([z, s(nn2)]) -> 0
() -> leq([z, z]) -> 0
() -> reverse([nil, nil]) -> 3
(append([_sda, cons(h1, nil), _tda]) /\ reverse([t1, _sda])) -> reverse([cons(h1, t1), _tda]) -> 1
(append([t1, l2, _nda])) -> append([cons(h1, t1), l2, cons(h1, _nda)]) -> 1
(length([_cea, _dea]) /\ length([l1, _bea]) /\ reverse([l1, _cea])) -> leq([_bea, _dea]) -> 1
(length([ll, _xda])) -> length([cons(x, ll), s(_xda)]) -> 1
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 1
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 1
(leq([s(nn1), z])) -> BOT -> 1
}
Sat witness: Found: (() -> reverse([nil, nil]), {

})

-------------------------------------------
Step 1, which took 0.008238 s (model generation: 0.008131,  model checking: 0.000107):

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

}

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

}

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

}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_8082},
Q_f={q_gen_8082},
Delta=
{
<nil, nil>() -> q_gen_8082
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 0
() -> length([nil, z]) -> 0
() -> leq([z, s(nn2)]) -> 0
() -> leq([z, z]) -> 3
() -> reverse([nil, nil]) -> 3
(append([_sda, cons(h1, nil), _tda]) /\ reverse([t1, _sda])) -> reverse([cons(h1, t1), _tda]) -> 1
(append([t1, l2, _nda])) -> append([cons(h1, t1), l2, cons(h1, _nda)]) -> 1
(length([_cea, _dea]) /\ length([l1, _bea]) /\ reverse([l1, _cea])) -> leq([_bea, _dea]) -> 1
(length([ll, _xda])) -> length([cons(x, ll), s(_xda)]) -> 1
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 1
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 1
(leq([s(nn1), z])) -> BOT -> 1
}
Sat witness: Found: (() -> leq([z, z]), {

})

-------------------------------------------
Step 2, which took 0.010694 s (model generation: 0.010628,  model checking: 0.000066):

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

}

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

}

Datatype: <natlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_8083},
Q_f={q_gen_8083},
Delta=
{
<z, z>() -> q_gen_8083
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_8082},
Q_f={q_gen_8082},
Delta=
{
<nil, nil>() -> q_gen_8082
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 0
() -> length([nil, z]) -> 0
() -> leq([z, s(nn2)]) -> 3
() -> leq([z, z]) -> 3
() -> reverse([nil, nil]) -> 3
(append([_sda, cons(h1, nil), _tda]) /\ reverse([t1, _sda])) -> reverse([cons(h1, t1), _tda]) -> 1
(append([t1, l2, _nda])) -> append([cons(h1, t1), l2, cons(h1, _nda)]) -> 1
(length([_cea, _dea]) /\ length([l1, _bea]) /\ reverse([l1, _cea])) -> leq([_bea, _dea]) -> 1
(length([ll, _xda])) -> length([cons(x, ll), s(_xda)]) -> 1
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 1
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 1
(leq([s(nn1), z])) -> BOT -> 1
}
Sat witness: Found: (() -> leq([z, s(nn2)]), {
nn2 -> z
})

-------------------------------------------
Step 3, which took 0.012996 s (model generation: 0.012903,  model checking: 0.000093):

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

}

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

}

Datatype: <natlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_8083, q_gen_8085},
Q_f={q_gen_8083},
Delta=
{
<z>() -> q_gen_8085
<z, s>(q_gen_8085) -> q_gen_8083
<z, z>() -> q_gen_8083
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_8082},
Q_f={q_gen_8082},
Delta=
{
<nil, nil>() -> q_gen_8082
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 0
() -> length([nil, z]) -> 3
() -> leq([z, s(nn2)]) -> 3
() -> leq([z, z]) -> 3
() -> reverse([nil, nil]) -> 3
(append([_sda, cons(h1, nil), _tda]) /\ reverse([t1, _sda])) -> reverse([cons(h1, t1), _tda]) -> 1
(append([t1, l2, _nda])) -> append([cons(h1, t1), l2, cons(h1, _nda)]) -> 1
(length([_cea, _dea]) /\ length([l1, _bea]) /\ reverse([l1, _cea])) -> leq([_bea, _dea]) -> 1
(length([ll, _xda])) -> length([cons(x, ll), s(_xda)]) -> 1
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 1
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 1
(leq([s(nn1), z])) -> BOT -> 1
}
Sat witness: Found: (() -> length([nil, z]), {

})

-------------------------------------------
Step 4, which took 0.008799 s (model generation: 0.008638,  model checking: 0.000161):

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

}

Datatype: <natlist, natlist, natlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_8086},
Q_f={q_gen_8086},
Delta=
{
<nil, z>() -> q_gen_8086
}

Datatype: <natlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_8083, q_gen_8085},
Q_f={q_gen_8083},
Delta=
{
<z>() -> q_gen_8085
<z, s>(q_gen_8085) -> q_gen_8083
<z, z>() -> q_gen_8083
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_8082},
Q_f={q_gen_8082},
Delta=
{
<nil, nil>() -> q_gen_8082
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 3
() -> length([nil, z]) -> 3
() -> leq([z, s(nn2)]) -> 3
() -> leq([z, z]) -> 3
() -> reverse([nil, nil]) -> 3
(append([_sda, cons(h1, nil), _tda]) /\ reverse([t1, _sda])) -> reverse([cons(h1, t1), _tda]) -> 1
(append([t1, l2, _nda])) -> append([cons(h1, t1), l2, cons(h1, _nda)]) -> 1
(length([_cea, _dea]) /\ length([l1, _bea]) /\ reverse([l1, _cea])) -> leq([_bea, _dea]) -> 1
(length([ll, _xda])) -> length([cons(x, ll), s(_xda)]) -> 1
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 1
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 1
(leq([s(nn1), z])) -> BOT -> 1
}
Sat witness: Found: (() -> append([nil, l2, l2]), {
l2 -> nil
})

-------------------------------------------
Step 5, which took 0.008330 s (model generation: 0.007910,  model checking: 0.000420):

Model:
|_
{
append -> 
{{{
Q={q_gen_8087},
Q_f={q_gen_8087},
Delta=
{
<nil, nil, nil>() -> q_gen_8087
}

Datatype: <natlist, natlist, natlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_8086},
Q_f={q_gen_8086},
Delta=
{
<nil, z>() -> q_gen_8086
}

Datatype: <natlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_8083, q_gen_8085},
Q_f={q_gen_8083},
Delta=
{
<z>() -> q_gen_8085
<z, s>(q_gen_8085) -> q_gen_8083
<z, z>() -> q_gen_8083
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_8082},
Q_f={q_gen_8082},
Delta=
{
<nil, nil>() -> q_gen_8082
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 3
() -> length([nil, z]) -> 3
() -> leq([z, s(nn2)]) -> 3
() -> leq([z, z]) -> 3
() -> reverse([nil, nil]) -> 3
(append([_sda, cons(h1, nil), _tda]) /\ reverse([t1, _sda])) -> reverse([cons(h1, t1), _tda]) -> 1
(append([t1, l2, _nda])) -> append([cons(h1, t1), l2, cons(h1, _nda)]) -> 1
(length([_cea, _dea]) /\ length([l1, _bea]) /\ reverse([l1, _cea])) -> leq([_bea, _dea]) -> 1
(length([ll, _xda])) -> length([cons(x, ll), s(_xda)]) -> 1
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 4
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 2
(leq([s(nn1), z])) -> BOT -> 2
}
Sat witness: Found: ((leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]), {
nn1 -> z  ;  nn2 -> z
})

-------------------------------------------
Step 6, which took 0.008233 s (model generation: 0.008093,  model checking: 0.000140):

Model:
|_
{
append -> 
{{{
Q={q_gen_8087},
Q_f={q_gen_8087},
Delta=
{
<nil, nil, nil>() -> q_gen_8087
}

Datatype: <natlist, natlist, natlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_8086},
Q_f={q_gen_8086},
Delta=
{
<nil, z>() -> q_gen_8086
}

Datatype: <natlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_8083, q_gen_8085},
Q_f={q_gen_8083},
Delta=
{
<z>() -> q_gen_8085
<s, s>(q_gen_8083) -> q_gen_8083
<z, s>(q_gen_8085) -> q_gen_8083
<z, z>() -> q_gen_8083
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_8082},
Q_f={q_gen_8082},
Delta=
{
<nil, nil>() -> q_gen_8082
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 3
() -> length([nil, z]) -> 3
() -> leq([z, s(nn2)]) -> 3
() -> leq([z, z]) -> 3
() -> reverse([nil, nil]) -> 3
(append([_sda, cons(h1, nil), _tda]) /\ reverse([t1, _sda])) -> reverse([cons(h1, t1), _tda]) -> 1
(append([t1, l2, _nda])) -> append([cons(h1, t1), l2, cons(h1, _nda)]) -> 1
(length([_cea, _dea]) /\ length([l1, _bea]) /\ reverse([l1, _cea])) -> leq([_bea, _dea]) -> 1
(length([ll, _xda])) -> length([cons(x, ll), s(_xda)]) -> 4
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 4
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 2
(leq([s(nn1), z])) -> BOT -> 2
}
Sat witness: Found: ((length([ll, _xda])) -> length([cons(x, ll), s(_xda)]), {
_xda -> z  ;  ll -> nil  ;  x -> z
})

-------------------------------------------
Step 7, which took 0.013764 s (model generation: 0.013489,  model checking: 0.000275):

Model:
|_
{
append -> 
{{{
Q={q_gen_8087},
Q_f={q_gen_8087},
Delta=
{
<nil, nil, nil>() -> q_gen_8087
}

Datatype: <natlist, natlist, natlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_8086, q_gen_8090, q_gen_8091},
Q_f={q_gen_8086},
Delta=
{
<nil>() -> q_gen_8090
<cons, s>(q_gen_8091, q_gen_8090) -> q_gen_8086
<nil, z>() -> q_gen_8086
<z, z>() -> q_gen_8091
}

Datatype: <natlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_8083, q_gen_8085},
Q_f={q_gen_8083},
Delta=
{
<z>() -> q_gen_8085
<s, s>(q_gen_8083) -> q_gen_8083
<z, s>(q_gen_8085) -> q_gen_8083
<z, z>() -> q_gen_8083
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_8082},
Q_f={q_gen_8082},
Delta=
{
<nil, nil>() -> q_gen_8082
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 3
() -> length([nil, z]) -> 3
() -> leq([z, s(nn2)]) -> 3
() -> leq([z, z]) -> 3
() -> reverse([nil, nil]) -> 3
(append([_sda, cons(h1, nil), _tda]) /\ reverse([t1, _sda])) -> reverse([cons(h1, t1), _tda]) -> 1
(append([t1, l2, _nda])) -> append([cons(h1, t1), l2, cons(h1, _nda)]) -> 4
(length([_cea, _dea]) /\ length([l1, _bea]) /\ reverse([l1, _cea])) -> leq([_bea, _dea]) -> 2
(length([ll, _xda])) -> length([cons(x, ll), s(_xda)]) -> 4
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 4
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 2
(leq([s(nn1), z])) -> BOT -> 2
}
Sat witness: Found: ((append([t1, l2, _nda])) -> append([cons(h1, t1), l2, cons(h1, _nda)]), {
_nda -> nil  ;  h1 -> z  ;  l2 -> nil  ;  t1 -> nil
})

-------------------------------------------
Step 8, which took 0.017653 s (model generation: 0.017162,  model checking: 0.000491):

Model:
|_
{
append -> 
{{{
Q={q_gen_8087, q_gen_8093, q_gen_8094},
Q_f={q_gen_8087},
Delta=
{
<nil, nil>() -> q_gen_8093
<z, z>() -> q_gen_8094
<cons, nil, cons>(q_gen_8094, q_gen_8093) -> q_gen_8087
<nil, nil, nil>() -> q_gen_8087
}

Datatype: <natlist, natlist, natlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_8086, q_gen_8090, q_gen_8091},
Q_f={q_gen_8086},
Delta=
{
<nil>() -> q_gen_8090
<cons, s>(q_gen_8091, q_gen_8090) -> q_gen_8086
<nil, z>() -> q_gen_8086
<z, z>() -> q_gen_8091
}

Datatype: <natlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_8083, q_gen_8085},
Q_f={q_gen_8083},
Delta=
{
<z>() -> q_gen_8085
<s, s>(q_gen_8083) -> q_gen_8083
<z, s>(q_gen_8085) -> q_gen_8083
<z, z>() -> q_gen_8083
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_8082},
Q_f={q_gen_8082},
Delta=
{
<nil, nil>() -> q_gen_8082
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 3
() -> length([nil, z]) -> 3
() -> leq([z, s(nn2)]) -> 6
() -> leq([z, z]) -> 4
() -> reverse([nil, nil]) -> 4
(append([_sda, cons(h1, nil), _tda]) /\ reverse([t1, _sda])) -> reverse([cons(h1, t1), _tda]) -> 2
(append([t1, l2, _nda])) -> append([cons(h1, t1), l2, cons(h1, _nda)]) -> 4
(length([_cea, _dea]) /\ length([l1, _bea]) /\ reverse([l1, _cea])) -> leq([_bea, _dea]) -> 3
(length([ll, _xda])) -> length([cons(x, ll), s(_xda)]) -> 4
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 4
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 3
(leq([s(nn1), z])) -> BOT -> 3
}
Sat witness: Found: (() -> leq([z, s(nn2)]), {
nn2 -> s(z)
})

-------------------------------------------
Step 9, which took 0.009226 s (model generation: 0.008705,  model checking: 0.000521):

Model:
|_
{
append -> 
{{{
Q={q_gen_8087, q_gen_8093, q_gen_8094},
Q_f={q_gen_8087},
Delta=
{
<nil, nil>() -> q_gen_8093
<z, z>() -> q_gen_8094
<cons, nil, cons>(q_gen_8094, q_gen_8093) -> q_gen_8087
<nil, nil, nil>() -> q_gen_8087
}

Datatype: <natlist, natlist, natlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_8086, q_gen_8090, q_gen_8091},
Q_f={q_gen_8086},
Delta=
{
<nil>() -> q_gen_8090
<cons, s>(q_gen_8091, q_gen_8090) -> q_gen_8086
<nil, z>() -> q_gen_8086
<z, z>() -> q_gen_8091
}

Datatype: <natlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_8083, q_gen_8085},
Q_f={q_gen_8083},
Delta=
{
<s>(q_gen_8085) -> q_gen_8085
<z>() -> q_gen_8085
<s, s>(q_gen_8083) -> q_gen_8083
<z, s>(q_gen_8085) -> q_gen_8083
<z, z>() -> q_gen_8083
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_8082},
Q_f={q_gen_8082},
Delta=
{
<nil, nil>() -> q_gen_8082
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 6
() -> length([nil, z]) -> 4
() -> leq([z, s(nn2)]) -> 6
() -> leq([z, z]) -> 4
() -> reverse([nil, nil]) -> 4
(append([_sda, cons(h1, nil), _tda]) /\ reverse([t1, _sda])) -> reverse([cons(h1, t1), _tda]) -> 3
(append([t1, l2, _nda])) -> append([cons(h1, t1), l2, cons(h1, _nda)]) -> 4
(length([_cea, _dea]) /\ length([l1, _bea]) /\ reverse([l1, _cea])) -> leq([_bea, _dea]) -> 4
(length([ll, _xda])) -> length([cons(x, ll), s(_xda)]) -> 4
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 4
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 4
(leq([s(nn1), z])) -> BOT -> 4
}
Sat witness: Found: (() -> append([nil, l2, l2]), {
l2 -> cons(s(z), cons(s(z), nil))
})

-------------------------------------------
Step 10, which took 0.009653 s (model generation: 0.009488,  model checking: 0.000165):

Model:
|_
{
append -> 
{{{
Q={q_gen_8087, q_gen_8093, q_gen_8094},
Q_f={q_gen_8087},
Delta=
{
<cons, cons>(q_gen_8094, q_gen_8093) -> q_gen_8093
<nil, nil>() -> q_gen_8093
<s, s>(q_gen_8094) -> q_gen_8094
<z, z>() -> q_gen_8094
<cons, nil, cons>(q_gen_8094, q_gen_8093) -> q_gen_8087
<nil, cons, cons>(q_gen_8094, q_gen_8093) -> q_gen_8087
<nil, nil, nil>() -> q_gen_8087
}

Datatype: <natlist, natlist, natlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_8086, q_gen_8090, q_gen_8091},
Q_f={q_gen_8086},
Delta=
{
<nil>() -> q_gen_8090
<cons, s>(q_gen_8091, q_gen_8090) -> q_gen_8086
<nil, z>() -> q_gen_8086
<z, z>() -> q_gen_8091
}

Datatype: <natlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_8083, q_gen_8085},
Q_f={q_gen_8083},
Delta=
{
<s>(q_gen_8085) -> q_gen_8085
<z>() -> q_gen_8085
<s, s>(q_gen_8083) -> q_gen_8083
<z, s>(q_gen_8085) -> q_gen_8083
<z, z>() -> q_gen_8083
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_8082},
Q_f={q_gen_8082},
Delta=
{
<nil, nil>() -> q_gen_8082
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 6
() -> length([nil, z]) -> 4
() -> leq([z, s(nn2)]) -> 6
() -> leq([z, z]) -> 4
() -> reverse([nil, nil]) -> 4
(append([_sda, cons(h1, nil), _tda]) /\ reverse([t1, _sda])) -> reverse([cons(h1, t1), _tda]) -> 6
(append([t1, l2, _nda])) -> append([cons(h1, t1), l2, cons(h1, _nda)]) -> 4
(length([_cea, _dea]) /\ length([l1, _bea]) /\ reverse([l1, _cea])) -> leq([_bea, _dea]) -> 4
(length([ll, _xda])) -> length([cons(x, ll), s(_xda)]) -> 4
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 4
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 4
(leq([s(nn1), z])) -> BOT -> 4
}
Sat witness: Found: ((append([_sda, cons(h1, nil), _tda]) /\ reverse([t1, _sda])) -> reverse([cons(h1, t1), _tda]), {
_sda -> nil  ;  _tda -> cons(z, nil)  ;  h1 -> z  ;  t1 -> nil
})

-------------------------------------------
Step 11, which took 0.010286 s (model generation: 0.009982,  model checking: 0.000304):

Model:
|_
{
append -> 
{{{
Q={q_gen_8087, q_gen_8093, q_gen_8094},
Q_f={q_gen_8087},
Delta=
{
<cons, cons>(q_gen_8094, q_gen_8093) -> q_gen_8093
<nil, nil>() -> q_gen_8093
<s, s>(q_gen_8094) -> q_gen_8094
<z, z>() -> q_gen_8094
<cons, nil, cons>(q_gen_8094, q_gen_8093) -> q_gen_8087
<nil, cons, cons>(q_gen_8094, q_gen_8093) -> q_gen_8087
<nil, nil, nil>() -> q_gen_8087
}

Datatype: <natlist, natlist, natlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_8086, q_gen_8090, q_gen_8091},
Q_f={q_gen_8086},
Delta=
{
<nil>() -> q_gen_8090
<cons, s>(q_gen_8091, q_gen_8090) -> q_gen_8086
<nil, z>() -> q_gen_8086
<z, z>() -> q_gen_8091
}

Datatype: <natlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_8083, q_gen_8085},
Q_f={q_gen_8083},
Delta=
{
<s>(q_gen_8085) -> q_gen_8085
<z>() -> q_gen_8085
<s, s>(q_gen_8083) -> q_gen_8083
<z, s>(q_gen_8085) -> q_gen_8083
<z, z>() -> q_gen_8083
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_8082, q_gen_8102},
Q_f={q_gen_8082},
Delta=
{
<cons, cons>(q_gen_8102, q_gen_8082) -> q_gen_8082
<nil, nil>() -> q_gen_8082
<z, z>() -> q_gen_8102
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 6
() -> length([nil, z]) -> 4
() -> leq([z, s(nn2)]) -> 6
() -> leq([z, z]) -> 4
() -> reverse([nil, nil]) -> 4
(append([_sda, cons(h1, nil), _tda]) /\ reverse([t1, _sda])) -> reverse([cons(h1, t1), _tda]) -> 6
(append([t1, l2, _nda])) -> append([cons(h1, t1), l2, cons(h1, _nda)]) -> 4
(length([_cea, _dea]) /\ length([l1, _bea]) /\ reverse([l1, _cea])) -> leq([_bea, _dea]) -> 4
(length([ll, _xda])) -> length([cons(x, ll), s(_xda)]) -> 7
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 5
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 5
(leq([s(nn1), z])) -> BOT -> 5
}
Sat witness: Found: ((length([ll, _xda])) -> length([cons(x, ll), s(_xda)]), {
_xda -> z  ;  ll -> nil  ;  x -> s(z)
})

-------------------------------------------
Step 12, which took 0.011320 s (model generation: 0.010093,  model checking: 0.001227):

Model:
|_
{
append -> 
{{{
Q={q_gen_8087, q_gen_8093, q_gen_8094},
Q_f={q_gen_8087},
Delta=
{
<cons, cons>(q_gen_8094, q_gen_8093) -> q_gen_8093
<nil, nil>() -> q_gen_8093
<s, s>(q_gen_8094) -> q_gen_8094
<z, z>() -> q_gen_8094
<cons, nil, cons>(q_gen_8094, q_gen_8093) -> q_gen_8087
<nil, cons, cons>(q_gen_8094, q_gen_8093) -> q_gen_8087
<nil, nil, nil>() -> q_gen_8087
}

Datatype: <natlist, natlist, natlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_8086, q_gen_8090, q_gen_8091, q_gen_8105},
Q_f={q_gen_8086},
Delta=
{
<nil>() -> q_gen_8090
<z>() -> q_gen_8105
<cons, s>(q_gen_8091, q_gen_8090) -> q_gen_8086
<nil, z>() -> q_gen_8086
<s, z>(q_gen_8105) -> q_gen_8091
<z, z>() -> q_gen_8091
}

Datatype: <natlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_8083, q_gen_8085},
Q_f={q_gen_8083},
Delta=
{
<s>(q_gen_8085) -> q_gen_8085
<z>() -> q_gen_8085
<s, s>(q_gen_8083) -> q_gen_8083
<z, s>(q_gen_8085) -> q_gen_8083
<z, z>() -> q_gen_8083
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_8082, q_gen_8102},
Q_f={q_gen_8082},
Delta=
{
<cons, cons>(q_gen_8102, q_gen_8082) -> q_gen_8082
<nil, nil>() -> q_gen_8082
<z, z>() -> q_gen_8102
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 6
() -> length([nil, z]) -> 4
() -> leq([z, s(nn2)]) -> 6
() -> leq([z, z]) -> 4
() -> reverse([nil, nil]) -> 4
(append([_sda, cons(h1, nil), _tda]) /\ reverse([t1, _sda])) -> reverse([cons(h1, t1), _tda]) -> 6
(append([t1, l2, _nda])) -> append([cons(h1, t1), l2, cons(h1, _nda)]) -> 7
(length([_cea, _dea]) /\ length([l1, _bea]) /\ reverse([l1, _cea])) -> leq([_bea, _dea]) -> 5
(length([ll, _xda])) -> length([cons(x, ll), s(_xda)]) -> 7
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 5
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 5
(leq([s(nn1), z])) -> BOT -> 5
}
Sat witness: Found: ((append([t1, l2, _nda])) -> append([cons(h1, t1), l2, cons(h1, _nda)]), {
_nda -> cons(z, nil)  ;  h1 -> z  ;  l2 -> cons(z, nil)  ;  t1 -> nil
})

-------------------------------------------
Step 13, which took 0.011504 s (model generation: 0.010833,  model checking: 0.000671):

Model:
|_
{
append -> 
{{{
Q={q_gen_8087, q_gen_8093, q_gen_8094, q_gen_8108, q_gen_8109, q_gen_8110},
Q_f={q_gen_8087},
Delta=
{
<nil>() -> q_gen_8108
<z>() -> q_gen_8109
<cons, cons>(q_gen_8094, q_gen_8093) -> q_gen_8093
<nil, nil>() -> q_gen_8093
<s, s>(q_gen_8094) -> q_gen_8094
<z, z>() -> q_gen_8094
<cons, cons, cons>(q_gen_8110, q_gen_8087) -> q_gen_8087
<cons, nil, cons>(q_gen_8094, q_gen_8093) -> q_gen_8087
<nil, cons, cons>(q_gen_8094, q_gen_8093) -> q_gen_8087
<nil, nil, cons>(q_gen_8109, q_gen_8108) -> q_gen_8087
<nil, nil, nil>() -> q_gen_8087
<z, z, z>() -> q_gen_8110
}

Datatype: <natlist, natlist, natlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_8086, q_gen_8090, q_gen_8091, q_gen_8105},
Q_f={q_gen_8086},
Delta=
{
<nil>() -> q_gen_8090
<z>() -> q_gen_8105
<cons, s>(q_gen_8091, q_gen_8090) -> q_gen_8086
<nil, z>() -> q_gen_8086
<s, z>(q_gen_8105) -> q_gen_8091
<z, z>() -> q_gen_8091
}

Datatype: <natlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_8083, q_gen_8085},
Q_f={q_gen_8083},
Delta=
{
<s>(q_gen_8085) -> q_gen_8085
<z>() -> q_gen_8085
<s, s>(q_gen_8083) -> q_gen_8083
<z, s>(q_gen_8085) -> q_gen_8083
<z, z>() -> q_gen_8083
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_8082, q_gen_8102},
Q_f={q_gen_8082},
Delta=
{
<cons, cons>(q_gen_8102, q_gen_8082) -> q_gen_8082
<nil, nil>() -> q_gen_8082
<z, z>() -> q_gen_8102
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 6
() -> length([nil, z]) -> 5
() -> leq([z, s(nn2)]) -> 6
() -> leq([z, z]) -> 5
() -> reverse([nil, nil]) -> 5
(append([_sda, cons(h1, nil), _tda]) /\ reverse([t1, _sda])) -> reverse([cons(h1, t1), _tda]) -> 9
(append([t1, l2, _nda])) -> append([cons(h1, t1), l2, cons(h1, _nda)]) -> 7
(length([_cea, _dea]) /\ length([l1, _bea]) /\ reverse([l1, _cea])) -> leq([_bea, _dea]) -> 6
(length([ll, _xda])) -> length([cons(x, ll), s(_xda)]) -> 7
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 6
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 6
(leq([s(nn1), z])) -> BOT -> 6
}
Sat witness: Found: ((append([_sda, cons(h1, nil), _tda]) /\ reverse([t1, _sda])) -> reverse([cons(h1, t1), _tda]), {
_sda -> nil  ;  _tda -> cons(s(z), nil)  ;  h1 -> s(z)  ;  t1 -> nil
})

-------------------------------------------
Step 14, which took 0.012588 s (model generation: 0.011601,  model checking: 0.000987):

Model:
|_
{
append -> 
{{{
Q={q_gen_8087, q_gen_8093, q_gen_8094, q_gen_8108, q_gen_8109, q_gen_8110},
Q_f={q_gen_8087},
Delta=
{
<nil>() -> q_gen_8108
<z>() -> q_gen_8109
<cons, cons>(q_gen_8094, q_gen_8093) -> q_gen_8093
<nil, nil>() -> q_gen_8093
<s, s>(q_gen_8094) -> q_gen_8094
<z, z>() -> q_gen_8094
<cons, cons, cons>(q_gen_8110, q_gen_8087) -> q_gen_8087
<cons, nil, cons>(q_gen_8094, q_gen_8093) -> q_gen_8087
<nil, cons, cons>(q_gen_8094, q_gen_8093) -> q_gen_8087
<nil, nil, cons>(q_gen_8109, q_gen_8108) -> q_gen_8087
<nil, nil, nil>() -> q_gen_8087
<z, z, z>() -> q_gen_8110
}

Datatype: <natlist, natlist, natlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_8086, q_gen_8090, q_gen_8091, q_gen_8105},
Q_f={q_gen_8086},
Delta=
{
<nil>() -> q_gen_8090
<z>() -> q_gen_8105
<cons, s>(q_gen_8091, q_gen_8090) -> q_gen_8086
<nil, z>() -> q_gen_8086
<s, z>(q_gen_8105) -> q_gen_8091
<z, z>() -> q_gen_8091
}

Datatype: <natlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_8083, q_gen_8085},
Q_f={q_gen_8083},
Delta=
{
<s>(q_gen_8085) -> q_gen_8085
<z>() -> q_gen_8085
<s, s>(q_gen_8083) -> q_gen_8083
<z, s>(q_gen_8085) -> q_gen_8083
<z, z>() -> q_gen_8083
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_8082, q_gen_8102},
Q_f={q_gen_8082},
Delta=
{
<cons, cons>(q_gen_8102, q_gen_8082) -> q_gen_8082
<nil, nil>() -> q_gen_8082
<s, s>(q_gen_8102) -> q_gen_8102
<z, z>() -> q_gen_8102
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 7
() -> length([nil, z]) -> 6
() -> leq([z, s(nn2)]) -> 7
() -> leq([z, z]) -> 6
() -> reverse([nil, nil]) -> 6
(append([_sda, cons(h1, nil), _tda]) /\ reverse([t1, _sda])) -> reverse([cons(h1, t1), _tda]) -> 9
(append([t1, l2, _nda])) -> append([cons(h1, t1), l2, cons(h1, _nda)]) -> 7
(length([_cea, _dea]) /\ length([l1, _bea]) /\ reverse([l1, _cea])) -> leq([_bea, _dea]) -> 7
(length([ll, _xda])) -> length([cons(x, ll), s(_xda)]) -> 10
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 7
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 7
(leq([s(nn1), z])) -> BOT -> 7
}
Sat witness: Found: ((length([ll, _xda])) -> length([cons(x, ll), s(_xda)]), {
_xda -> z  ;  ll -> nil  ;  x -> s(s(z))
})

-------------------------------------------
Step 15, which took 0.013353 s (model generation: 0.012398,  model checking: 0.000955):

Model:
|_
{
append -> 
{{{
Q={q_gen_8087, q_gen_8093, q_gen_8094, q_gen_8108, q_gen_8109, q_gen_8110},
Q_f={q_gen_8087},
Delta=
{
<nil>() -> q_gen_8108
<z>() -> q_gen_8109
<cons, cons>(q_gen_8094, q_gen_8093) -> q_gen_8093
<nil, nil>() -> q_gen_8093
<s, s>(q_gen_8094) -> q_gen_8094
<z, z>() -> q_gen_8094
<cons, cons, cons>(q_gen_8110, q_gen_8087) -> q_gen_8087
<cons, nil, cons>(q_gen_8094, q_gen_8093) -> q_gen_8087
<nil, cons, cons>(q_gen_8094, q_gen_8093) -> q_gen_8087
<nil, nil, cons>(q_gen_8109, q_gen_8108) -> q_gen_8087
<nil, nil, nil>() -> q_gen_8087
<z, z, z>() -> q_gen_8110
}

Datatype: <natlist, natlist, natlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_8086, q_gen_8090, q_gen_8091, q_gen_8105},
Q_f={q_gen_8086},
Delta=
{
<nil>() -> q_gen_8090
<s>(q_gen_8105) -> q_gen_8105
<z>() -> q_gen_8105
<cons, s>(q_gen_8091, q_gen_8090) -> q_gen_8086
<nil, z>() -> q_gen_8086
<s, z>(q_gen_8105) -> q_gen_8091
<z, z>() -> q_gen_8091
}

Datatype: <natlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_8083, q_gen_8085},
Q_f={q_gen_8083},
Delta=
{
<s>(q_gen_8085) -> q_gen_8085
<z>() -> q_gen_8085
<s, s>(q_gen_8083) -> q_gen_8083
<z, s>(q_gen_8085) -> q_gen_8083
<z, z>() -> q_gen_8083
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_8082, q_gen_8102},
Q_f={q_gen_8082},
Delta=
{
<cons, cons>(q_gen_8102, q_gen_8082) -> q_gen_8082
<nil, nil>() -> q_gen_8082
<s, s>(q_gen_8102) -> q_gen_8102
<z, z>() -> q_gen_8102
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 7
() -> length([nil, z]) -> 7
() -> leq([z, s(nn2)]) -> 7
() -> leq([z, z]) -> 7
() -> reverse([nil, nil]) -> 7
(append([_sda, cons(h1, nil), _tda]) /\ reverse([t1, _sda])) -> reverse([cons(h1, t1), _tda]) -> 9
(append([t1, l2, _nda])) -> append([cons(h1, t1), l2, cons(h1, _nda)]) -> 10
(length([_cea, _dea]) /\ length([l1, _bea]) /\ reverse([l1, _cea])) -> leq([_bea, _dea]) -> 8
(length([ll, _xda])) -> length([cons(x, ll), s(_xda)]) -> 10
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 8
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 8
(leq([s(nn1), z])) -> BOT -> 8
}
Sat witness: Found: ((append([t1, l2, _nda])) -> append([cons(h1, t1), l2, cons(h1, _nda)]), {
_nda -> cons(z, nil)  ;  h1 -> z  ;  l2 -> nil  ;  t1 -> nil
})

-------------------------------------------
Step 16, which took 0.014568 s (model generation: 0.013504,  model checking: 0.001064):

Model:
|_
{
append -> 
{{{
Q={q_gen_8087, q_gen_8093, q_gen_8094, q_gen_8108, q_gen_8109, q_gen_8110},
Q_f={q_gen_8087},
Delta=
{
<nil>() -> q_gen_8108
<z>() -> q_gen_8109
<cons, cons>(q_gen_8094, q_gen_8093) -> q_gen_8093
<nil, cons>(q_gen_8109, q_gen_8108) -> q_gen_8093
<nil, nil>() -> q_gen_8093
<s, s>(q_gen_8094) -> q_gen_8094
<z, z>() -> q_gen_8094
<cons, cons, cons>(q_gen_8110, q_gen_8087) -> q_gen_8087
<cons, nil, cons>(q_gen_8094, q_gen_8093) -> q_gen_8087
<nil, cons, cons>(q_gen_8094, q_gen_8093) -> q_gen_8087
<nil, nil, cons>(q_gen_8109, q_gen_8108) -> q_gen_8087
<nil, nil, nil>() -> q_gen_8087
<z, z, z>() -> q_gen_8110
}

Datatype: <natlist, natlist, natlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_8086, q_gen_8090, q_gen_8091, q_gen_8105},
Q_f={q_gen_8086},
Delta=
{
<nil>() -> q_gen_8090
<s>(q_gen_8105) -> q_gen_8105
<z>() -> q_gen_8105
<cons, s>(q_gen_8091, q_gen_8090) -> q_gen_8086
<nil, z>() -> q_gen_8086
<s, z>(q_gen_8105) -> q_gen_8091
<z, z>() -> q_gen_8091
}

Datatype: <natlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_8083, q_gen_8085},
Q_f={q_gen_8083},
Delta=
{
<s>(q_gen_8085) -> q_gen_8085
<z>() -> q_gen_8085
<s, s>(q_gen_8083) -> q_gen_8083
<z, s>(q_gen_8085) -> q_gen_8083
<z, z>() -> q_gen_8083
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_8082, q_gen_8102},
Q_f={q_gen_8082},
Delta=
{
<cons, cons>(q_gen_8102, q_gen_8082) -> q_gen_8082
<nil, nil>() -> q_gen_8082
<s, s>(q_gen_8102) -> q_gen_8102
<z, z>() -> q_gen_8102
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 8
() -> length([nil, z]) -> 8
() -> leq([z, s(nn2)]) -> 8
() -> leq([z, z]) -> 8
() -> reverse([nil, nil]) -> 8
(append([_sda, cons(h1, nil), _tda]) /\ reverse([t1, _sda])) -> reverse([cons(h1, t1), _tda]) -> 12
(append([t1, l2, _nda])) -> append([cons(h1, t1), l2, cons(h1, _nda)]) -> 10
(length([_cea, _dea]) /\ length([l1, _bea]) /\ reverse([l1, _cea])) -> leq([_bea, _dea]) -> 9
(length([ll, _xda])) -> length([cons(x, ll), s(_xda)]) -> 10
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 9
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 9
(leq([s(nn1), z])) -> BOT -> 9
}
Sat witness: Found: ((append([_sda, cons(h1, nil), _tda]) /\ reverse([t1, _sda])) -> reverse([cons(h1, t1), _tda]), {
_sda -> nil  ;  _tda -> cons(z, cons(z, nil))  ;  h1 -> z  ;  t1 -> nil
})

-------------------------------------------
Step 17, which took 0.015199 s (model generation: 0.014086,  model checking: 0.001113):

Model:
|_
{
append -> 
{{{
Q={q_gen_8087, q_gen_8093, q_gen_8094, q_gen_8108, q_gen_8109, q_gen_8110},
Q_f={q_gen_8087},
Delta=
{
<nil>() -> q_gen_8108
<z>() -> q_gen_8109
<cons, cons>(q_gen_8094, q_gen_8093) -> q_gen_8093
<nil, cons>(q_gen_8109, q_gen_8108) -> q_gen_8093
<nil, nil>() -> q_gen_8093
<s, s>(q_gen_8094) -> q_gen_8094
<z, z>() -> q_gen_8094
<cons, cons, cons>(q_gen_8110, q_gen_8087) -> q_gen_8087
<cons, nil, cons>(q_gen_8094, q_gen_8093) -> q_gen_8087
<nil, cons, cons>(q_gen_8094, q_gen_8093) -> q_gen_8087
<nil, nil, cons>(q_gen_8109, q_gen_8108) -> q_gen_8087
<nil, nil, nil>() -> q_gen_8087
<z, z, z>() -> q_gen_8110
}

Datatype: <natlist, natlist, natlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_8086, q_gen_8090, q_gen_8091, q_gen_8105},
Q_f={q_gen_8086},
Delta=
{
<nil>() -> q_gen_8090
<s>(q_gen_8105) -> q_gen_8105
<z>() -> q_gen_8105
<cons, s>(q_gen_8091, q_gen_8090) -> q_gen_8086
<nil, z>() -> q_gen_8086
<s, z>(q_gen_8105) -> q_gen_8091
<z, z>() -> q_gen_8091
}

Datatype: <natlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_8083, q_gen_8085},
Q_f={q_gen_8083},
Delta=
{
<s>(q_gen_8085) -> q_gen_8085
<z>() -> q_gen_8085
<s, s>(q_gen_8083) -> q_gen_8083
<z, s>(q_gen_8085) -> q_gen_8083
<z, z>() -> q_gen_8083
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_8082, q_gen_8102, q_gen_8122, q_gen_8123},
Q_f={q_gen_8082},
Delta=
{
<nil>() -> q_gen_8122
<z>() -> q_gen_8123
<cons, cons>(q_gen_8102, q_gen_8082) -> q_gen_8082
<nil, cons>(q_gen_8123, q_gen_8122) -> q_gen_8082
<nil, nil>() -> q_gen_8082
<s, s>(q_gen_8102) -> q_gen_8102
<z, z>() -> q_gen_8102
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 9
() -> length([nil, z]) -> 9
() -> leq([z, s(nn2)]) -> 9
() -> leq([z, z]) -> 9
() -> reverse([nil, nil]) -> 9
(append([_sda, cons(h1, nil), _tda]) /\ reverse([t1, _sda])) -> reverse([cons(h1, t1), _tda]) -> 12
(append([t1, l2, _nda])) -> append([cons(h1, t1), l2, cons(h1, _nda)]) -> 10
(length([_cea, _dea]) /\ length([l1, _bea]) /\ reverse([l1, _cea])) -> leq([_bea, _dea]) -> 10
(length([ll, _xda])) -> length([cons(x, ll), s(_xda)]) -> 13
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 10
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 10
(leq([s(nn1), z])) -> BOT -> 10
}
Sat witness: Found: ((length([ll, _xda])) -> length([cons(x, ll), s(_xda)]), {
_xda -> s(z)  ;  ll -> cons(z, nil)  ;  x -> z
})

-------------------------------------------
Step 18, which took 0.016276 s (model generation: 0.015373,  model checking: 0.000903):

Model:
|_
{
append -> 
{{{
Q={q_gen_8087, q_gen_8093, q_gen_8094, q_gen_8108, q_gen_8109, q_gen_8110},
Q_f={q_gen_8087},
Delta=
{
<nil>() -> q_gen_8108
<z>() -> q_gen_8109
<cons, cons>(q_gen_8094, q_gen_8093) -> q_gen_8093
<nil, cons>(q_gen_8109, q_gen_8108) -> q_gen_8093
<nil, nil>() -> q_gen_8093
<s, s>(q_gen_8094) -> q_gen_8094
<z, z>() -> q_gen_8094
<cons, cons, cons>(q_gen_8110, q_gen_8087) -> q_gen_8087
<cons, nil, cons>(q_gen_8094, q_gen_8093) -> q_gen_8087
<nil, cons, cons>(q_gen_8094, q_gen_8093) -> q_gen_8087
<nil, nil, cons>(q_gen_8109, q_gen_8108) -> q_gen_8087
<nil, nil, nil>() -> q_gen_8087
<z, z, z>() -> q_gen_8110
}

Datatype: <natlist, natlist, natlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_8086, q_gen_8090, q_gen_8091, q_gen_8105},
Q_f={q_gen_8086},
Delta=
{
<cons>(q_gen_8105, q_gen_8090) -> q_gen_8090
<nil>() -> q_gen_8090
<s>(q_gen_8105) -> q_gen_8105
<z>() -> q_gen_8105
<cons, s>(q_gen_8091, q_gen_8090) -> q_gen_8086
<nil, z>() -> q_gen_8086
<s, z>(q_gen_8105) -> q_gen_8091
<z, s>(q_gen_8105) -> q_gen_8091
<z, z>() -> q_gen_8091
}

Datatype: <natlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_8083, q_gen_8085},
Q_f={q_gen_8083},
Delta=
{
<s>(q_gen_8085) -> q_gen_8085
<z>() -> q_gen_8085
<s, s>(q_gen_8083) -> q_gen_8083
<z, s>(q_gen_8085) -> q_gen_8083
<z, z>() -> q_gen_8083
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_8082, q_gen_8102, q_gen_8122, q_gen_8123},
Q_f={q_gen_8082},
Delta=
{
<nil>() -> q_gen_8122
<z>() -> q_gen_8123
<cons, cons>(q_gen_8102, q_gen_8082) -> q_gen_8082
<nil, cons>(q_gen_8123, q_gen_8122) -> q_gen_8082
<nil, nil>() -> q_gen_8082
<s, s>(q_gen_8102) -> q_gen_8102
<z, z>() -> q_gen_8102
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 10
() -> length([nil, z]) -> 10
() -> leq([z, s(nn2)]) -> 10
() -> leq([z, z]) -> 10
() -> reverse([nil, nil]) -> 10
(append([_sda, cons(h1, nil), _tda]) /\ reverse([t1, _sda])) -> reverse([cons(h1, t1), _tda]) -> 12
(append([t1, l2, _nda])) -> append([cons(h1, t1), l2, cons(h1, _nda)]) -> 10
(length([_cea, _dea]) /\ length([l1, _bea]) /\ reverse([l1, _cea])) -> leq([_bea, _dea]) -> 13
(length([ll, _xda])) -> length([cons(x, ll), s(_xda)]) -> 13
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 11
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 11
(leq([s(nn1), z])) -> BOT -> 11
}
Sat witness: Found: ((length([_cea, _dea]) /\ length([l1, _bea]) /\ reverse([l1, _cea])) -> leq([_bea, _dea]), {
_bea -> s(s(z))  ;  _cea -> cons(z, nil)  ;  _dea -> s(z)  ;  l1 -> cons(z, nil)
})

-------------------------------------------
Step 19, which took 0.023763 s (model generation: 0.022641,  model checking: 0.001122):

Model:
|_
{
append -> 
{{{
Q={q_gen_8087, q_gen_8093, q_gen_8094, q_gen_8108, q_gen_8109, q_gen_8110},
Q_f={q_gen_8087},
Delta=
{
<nil>() -> q_gen_8108
<z>() -> q_gen_8109
<cons, cons>(q_gen_8094, q_gen_8093) -> q_gen_8093
<nil, cons>(q_gen_8109, q_gen_8108) -> q_gen_8093
<nil, nil>() -> q_gen_8093
<s, s>(q_gen_8094) -> q_gen_8094
<z, z>() -> q_gen_8094
<cons, cons, cons>(q_gen_8110, q_gen_8087) -> q_gen_8087
<cons, nil, cons>(q_gen_8094, q_gen_8093) -> q_gen_8087
<nil, cons, cons>(q_gen_8094, q_gen_8093) -> q_gen_8087
<nil, nil, cons>(q_gen_8109, q_gen_8108) -> q_gen_8087
<nil, nil, nil>() -> q_gen_8087
<z, z, z>() -> q_gen_8110
}

Datatype: <natlist, natlist, natlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_8086, q_gen_8090, q_gen_8091, q_gen_8105},
Q_f={q_gen_8086},
Delta=
{
<cons>(q_gen_8105, q_gen_8090) -> q_gen_8090
<nil>() -> q_gen_8090
<s>(q_gen_8105) -> q_gen_8105
<z>() -> q_gen_8105
<cons, s>(q_gen_8091, q_gen_8090) -> q_gen_8086
<nil, z>() -> q_gen_8086
<s, z>(q_gen_8105) -> q_gen_8091
<z, s>(q_gen_8105) -> q_gen_8091
<z, z>() -> q_gen_8091
}

Datatype: <natlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_8083, q_gen_8085},
Q_f={q_gen_8083},
Delta=
{
<s>(q_gen_8085) -> q_gen_8085
<z>() -> q_gen_8085
<s, s>(q_gen_8083) -> q_gen_8083
<s, z>(q_gen_8085) -> q_gen_8083
<z, s>(q_gen_8085) -> q_gen_8083
<z, z>() -> q_gen_8083
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_8082, q_gen_8102, q_gen_8122, q_gen_8123},
Q_f={q_gen_8082},
Delta=
{
<nil>() -> q_gen_8122
<z>() -> q_gen_8123
<cons, cons>(q_gen_8102, q_gen_8082) -> q_gen_8082
<nil, cons>(q_gen_8123, q_gen_8122) -> q_gen_8082
<nil, nil>() -> q_gen_8082
<s, s>(q_gen_8102) -> q_gen_8102
<z, z>() -> q_gen_8102
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 10
() -> length([nil, z]) -> 10
() -> leq([z, s(nn2)]) -> 10
() -> leq([z, z]) -> 10
() -> reverse([nil, nil]) -> 10
(append([_sda, cons(h1, nil), _tda]) /\ reverse([t1, _sda])) -> reverse([cons(h1, t1), _tda]) -> 12
(append([t1, l2, _nda])) -> append([cons(h1, t1), l2, cons(h1, _nda)]) -> 13
(length([_cea, _dea]) /\ length([l1, _bea]) /\ reverse([l1, _cea])) -> leq([_bea, _dea]) -> 13
(length([ll, _xda])) -> length([cons(x, ll), s(_xda)]) -> 13
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 11
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 11
(leq([s(nn1), z])) -> BOT -> 11
}
Sat witness: Found: ((append([t1, l2, _nda])) -> append([cons(h1, t1), l2, cons(h1, _nda)]), {
_nda -> cons(z, cons(z, nil))  ;  h1 -> z  ;  l2 -> cons(z, nil)  ;  t1 -> nil
})

-------------------------------------------
Step 20, which took 0.017698 s (model generation: 0.017103,  model checking: 0.000595):

Model:
|_
{
append -> 
{{{
Q={q_gen_8087, q_gen_8093, q_gen_8094, q_gen_8108, q_gen_8109, q_gen_8110},
Q_f={q_gen_8087},
Delta=
{
<cons>(q_gen_8109, q_gen_8108) -> q_gen_8108
<nil>() -> q_gen_8108
<z>() -> q_gen_8109
<cons, cons>(q_gen_8094, q_gen_8093) -> q_gen_8093
<nil, cons>(q_gen_8109, q_gen_8108) -> q_gen_8093
<nil, nil>() -> q_gen_8093
<s, s>(q_gen_8094) -> q_gen_8094
<z, z>() -> q_gen_8094
<cons, cons, cons>(q_gen_8110, q_gen_8087) -> q_gen_8087
<cons, nil, cons>(q_gen_8094, q_gen_8093) -> q_gen_8087
<nil, cons, cons>(q_gen_8094, q_gen_8093) -> q_gen_8087
<nil, nil, cons>(q_gen_8109, q_gen_8108) -> q_gen_8087
<nil, nil, nil>() -> q_gen_8087
<z, z, z>() -> q_gen_8110
}

Datatype: <natlist, natlist, natlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_8086, q_gen_8090, q_gen_8091, q_gen_8105},
Q_f={q_gen_8086},
Delta=
{
<cons>(q_gen_8105, q_gen_8090) -> q_gen_8090
<nil>() -> q_gen_8090
<s>(q_gen_8105) -> q_gen_8105
<z>() -> q_gen_8105
<cons, s>(q_gen_8091, q_gen_8090) -> q_gen_8086
<nil, z>() -> q_gen_8086
<s, z>(q_gen_8105) -> q_gen_8091
<z, s>(q_gen_8105) -> q_gen_8091
<z, z>() -> q_gen_8091
}

Datatype: <natlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_8083, q_gen_8085},
Q_f={q_gen_8083},
Delta=
{
<s>(q_gen_8085) -> q_gen_8085
<z>() -> q_gen_8085
<s, s>(q_gen_8083) -> q_gen_8083
<s, z>(q_gen_8085) -> q_gen_8083
<z, s>(q_gen_8085) -> q_gen_8083
<z, z>() -> q_gen_8083
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_8082, q_gen_8102, q_gen_8122, q_gen_8123},
Q_f={q_gen_8082},
Delta=
{
<nil>() -> q_gen_8122
<z>() -> q_gen_8123
<cons, cons>(q_gen_8102, q_gen_8082) -> q_gen_8082
<nil, cons>(q_gen_8123, q_gen_8122) -> q_gen_8082
<nil, nil>() -> q_gen_8082
<s, s>(q_gen_8102) -> q_gen_8102
<z, z>() -> q_gen_8102
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 11
() -> length([nil, z]) -> 11
() -> leq([z, s(nn2)]) -> 11
() -> leq([z, z]) -> 11
() -> reverse([nil, nil]) -> 11
(append([_sda, cons(h1, nil), _tda]) /\ reverse([t1, _sda])) -> reverse([cons(h1, t1), _tda]) -> 12
(append([t1, l2, _nda])) -> append([cons(h1, t1), l2, cons(h1, _nda)]) -> 13
(length([_cea, _dea]) /\ length([l1, _bea]) /\ reverse([l1, _cea])) -> leq([_bea, _dea]) -> 13
(length([ll, _xda])) -> length([cons(x, ll), s(_xda)]) -> 13
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 11
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 11
(leq([s(nn1), z])) -> BOT -> 14
}
Sat witness: Found: ((leq([s(nn1), z])) -> BOT, {
nn1 -> z
})

-------------------------------------------
Step 21, which took 0.019678 s (model generation: 0.019557,  model checking: 0.000121):

Model:
|_
{
append -> 
{{{
Q={q_gen_8087, q_gen_8093, q_gen_8094, q_gen_8108, q_gen_8109, q_gen_8110},
Q_f={q_gen_8087},
Delta=
{
<cons>(q_gen_8109, q_gen_8108) -> q_gen_8108
<nil>() -> q_gen_8108
<z>() -> q_gen_8109
<cons, cons>(q_gen_8094, q_gen_8093) -> q_gen_8093
<nil, cons>(q_gen_8109, q_gen_8108) -> q_gen_8093
<nil, nil>() -> q_gen_8093
<s, s>(q_gen_8094) -> q_gen_8094
<z, z>() -> q_gen_8094
<cons, cons, cons>(q_gen_8110, q_gen_8087) -> q_gen_8087
<cons, nil, cons>(q_gen_8094, q_gen_8093) -> q_gen_8087
<nil, cons, cons>(q_gen_8094, q_gen_8093) -> q_gen_8087
<nil, nil, cons>(q_gen_8109, q_gen_8108) -> q_gen_8087
<nil, nil, nil>() -> q_gen_8087
<z, z, z>() -> q_gen_8110
}

Datatype: <natlist, natlist, natlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_8086, q_gen_8090, q_gen_8091, q_gen_8105},
Q_f={q_gen_8086},
Delta=
{
<cons>(q_gen_8105, q_gen_8090) -> q_gen_8090
<nil>() -> q_gen_8090
<s>(q_gen_8105) -> q_gen_8105
<z>() -> q_gen_8105
<cons, s>(q_gen_8091, q_gen_8090) -> q_gen_8086
<nil, z>() -> q_gen_8086
<s, z>(q_gen_8105) -> q_gen_8091
<z, s>(q_gen_8105) -> q_gen_8091
<z, z>() -> q_gen_8091
}

Datatype: <natlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_8083, q_gen_8085, q_gen_8129},
Q_f={q_gen_8083},
Delta=
{
<s>(q_gen_8085) -> q_gen_8085
<z>() -> q_gen_8085
<s, s>(q_gen_8083) -> q_gen_8083
<s, s>(q_gen_8129) -> q_gen_8083
<z, s>(q_gen_8085) -> q_gen_8083
<z, z>() -> q_gen_8083
<s, z>(q_gen_8085) -> q_gen_8129
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_8082, q_gen_8102, q_gen_8122, q_gen_8123},
Q_f={q_gen_8082},
Delta=
{
<nil>() -> q_gen_8122
<z>() -> q_gen_8123
<cons, cons>(q_gen_8102, q_gen_8082) -> q_gen_8082
<nil, cons>(q_gen_8123, q_gen_8122) -> q_gen_8082
<nil, nil>() -> q_gen_8082
<s, s>(q_gen_8102) -> q_gen_8102
<z, z>() -> q_gen_8102
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 11
() -> length([nil, z]) -> 11
() -> leq([z, s(nn2)]) -> 11
() -> leq([z, z]) -> 11
() -> reverse([nil, nil]) -> 11
(append([_sda, cons(h1, nil), _tda]) /\ reverse([t1, _sda])) -> reverse([cons(h1, t1), _tda]) -> 12
(append([t1, l2, _nda])) -> append([cons(h1, t1), l2, cons(h1, _nda)]) -> 13
(length([_cea, _dea]) /\ length([l1, _bea]) /\ reverse([l1, _cea])) -> leq([_bea, _dea]) -> 13
(length([ll, _xda])) -> length([cons(x, ll), s(_xda)]) -> 13
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 11
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 14
(leq([s(nn1), z])) -> BOT -> 14
}
Sat witness: Found: ((leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]), {
nn1 -> s(z)  ;  nn2 -> z
})

-------------------------------------------
Step 22, which took 0.019830 s (model generation: 0.019164,  model checking: 0.000666):

Model:
|_
{
append -> 
{{{
Q={q_gen_8087, q_gen_8093, q_gen_8094, q_gen_8098, q_gen_8100, q_gen_8108, q_gen_8109, q_gen_8110},
Q_f={q_gen_8087},
Delta=
{
<cons>(q_gen_8109, q_gen_8108) -> q_gen_8108
<nil>() -> q_gen_8108
<z>() -> q_gen_8109
<nil, cons>(q_gen_8109, q_gen_8108) -> q_gen_8093
<nil, nil>() -> q_gen_8093
<s, s>(q_gen_8094) -> q_gen_8094
<z, z>() -> q_gen_8094
<cons, cons>(q_gen_8094, q_gen_8093) -> q_gen_8098
<cons, cons, cons>(q_gen_8110, q_gen_8100) -> q_gen_8087
<cons, nil, cons>(q_gen_8094, q_gen_8093) -> q_gen_8087
<nil, cons, cons>(q_gen_8094, q_gen_8098) -> q_gen_8087
<nil, nil, nil>() -> q_gen_8087
<nil, cons, cons>(q_gen_8094, q_gen_8093) -> q_gen_8100
<nil, nil, cons>(q_gen_8109, q_gen_8108) -> q_gen_8100
<z, z, z>() -> q_gen_8110
}

Datatype: <natlist, natlist, natlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_8086, q_gen_8090, q_gen_8091, q_gen_8105},
Q_f={q_gen_8086},
Delta=
{
<cons>(q_gen_8105, q_gen_8090) -> q_gen_8090
<nil>() -> q_gen_8090
<s>(q_gen_8105) -> q_gen_8105
<z>() -> q_gen_8105
<cons, s>(q_gen_8091, q_gen_8090) -> q_gen_8086
<nil, z>() -> q_gen_8086
<s, z>(q_gen_8105) -> q_gen_8091
<z, s>(q_gen_8105) -> q_gen_8091
<z, z>() -> q_gen_8091
}

Datatype: <natlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_8083, q_gen_8085, q_gen_8128},
Q_f={q_gen_8083},
Delta=
{
<s>(q_gen_8085) -> q_gen_8085
<z>() -> q_gen_8085
<s, s>(q_gen_8083) -> q_gen_8083
<z, s>(q_gen_8085) -> q_gen_8083
<z, z>() -> q_gen_8083
<s, s>(q_gen_8128) -> q_gen_8128
<s, z>(q_gen_8085) -> q_gen_8128
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_8082, q_gen_8101, q_gen_8102, q_gen_8122, q_gen_8123},
Q_f={q_gen_8082},
Delta=
{
<nil>() -> q_gen_8122
<z>() -> q_gen_8123
<nil, cons>(q_gen_8123, q_gen_8122) -> q_gen_8082
<nil, nil>() -> q_gen_8082
<cons, cons>(q_gen_8102, q_gen_8082) -> q_gen_8101
<s, s>(q_gen_8102) -> q_gen_8102
<z, z>() -> q_gen_8102
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 14
() -> length([nil, z]) -> 12
() -> leq([z, s(nn2)]) -> 12
() -> leq([z, z]) -> 12
() -> reverse([nil, nil]) -> 12
(append([_sda, cons(h1, nil), _tda]) /\ reverse([t1, _sda])) -> reverse([cons(h1, t1), _tda]) -> 12
(append([t1, l2, _nda])) -> append([cons(h1, t1), l2, cons(h1, _nda)]) -> 13
(length([_cea, _dea]) /\ length([l1, _bea]) /\ reverse([l1, _cea])) -> leq([_bea, _dea]) -> 13
(length([ll, _xda])) -> length([cons(x, ll), s(_xda)]) -> 13
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 12
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 14
(leq([s(nn1), z])) -> BOT -> 14
}
Sat witness: Found: (() -> append([nil, l2, l2]), {
l2 -> cons(z, nil)
})

-------------------------------------------
Step 23, which took 0.027356 s (model generation: 0.026480,  model checking: 0.000876):

Model:
|_
{
append -> 
{{{
Q={q_gen_8087, q_gen_8093, q_gen_8094, q_gen_8108, q_gen_8109, q_gen_8110},
Q_f={q_gen_8087},
Delta=
{
<cons>(q_gen_8109, q_gen_8108) -> q_gen_8108
<nil>() -> q_gen_8108
<z>() -> q_gen_8109
<cons, cons>(q_gen_8094, q_gen_8093) -> q_gen_8093
<nil, cons>(q_gen_8109, q_gen_8108) -> q_gen_8093
<nil, nil>() -> q_gen_8093
<s, s>(q_gen_8094) -> q_gen_8094
<z, z>() -> q_gen_8094
<cons, cons, cons>(q_gen_8110, q_gen_8087) -> q_gen_8087
<cons, nil, cons>(q_gen_8094, q_gen_8093) -> q_gen_8087
<nil, cons, cons>(q_gen_8094, q_gen_8093) -> q_gen_8087
<nil, nil, cons>(q_gen_8109, q_gen_8108) -> q_gen_8087
<nil, nil, nil>() -> q_gen_8087
<z, z, z>() -> q_gen_8110
}

Datatype: <natlist, natlist, natlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_8086, q_gen_8090, q_gen_8091, q_gen_8105, q_gen_8125, q_gen_8126, q_gen_8127},
Q_f={q_gen_8086},
Delta=
{
<nil>() -> q_gen_8090
<s>(q_gen_8105) -> q_gen_8105
<z>() -> q_gen_8105
<cons>(q_gen_8105, q_gen_8090) -> q_gen_8125
<cons, s>(q_gen_8091, q_gen_8090) -> q_gen_8086
<cons, s>(q_gen_8126, q_gen_8125) -> q_gen_8086
<nil, z>() -> q_gen_8086
<s, z>(q_gen_8105) -> q_gen_8091
<z, z>() -> q_gen_8091
<z, s>(q_gen_8105) -> q_gen_8126
<cons, s>(q_gen_8126, q_gen_8090) -> q_gen_8127
}

Datatype: <natlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_8083, q_gen_8085, q_gen_8128},
Q_f={q_gen_8083},
Delta=
{
<s>(q_gen_8085) -> q_gen_8085
<z>() -> q_gen_8085
<s, s>(q_gen_8083) -> q_gen_8083
<z, s>(q_gen_8085) -> q_gen_8083
<z, z>() -> q_gen_8083
<s, s>(q_gen_8128) -> q_gen_8128
<s, z>(q_gen_8085) -> q_gen_8128
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_8082, q_gen_8102, q_gen_8122, q_gen_8123},
Q_f={q_gen_8082},
Delta=
{
<nil>() -> q_gen_8122
<z>() -> q_gen_8123
<cons, cons>(q_gen_8102, q_gen_8082) -> q_gen_8082
<nil, cons>(q_gen_8123, q_gen_8122) -> q_gen_8082
<nil, nil>() -> q_gen_8082
<s, s>(q_gen_8102) -> q_gen_8102
<z, z>() -> q_gen_8102
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 14
() -> length([nil, z]) -> 12
() -> leq([z, s(nn2)]) -> 12
() -> leq([z, z]) -> 12
() -> reverse([nil, nil]) -> 12
(append([_sda, cons(h1, nil), _tda]) /\ reverse([t1, _sda])) -> reverse([cons(h1, t1), _tda]) -> 15
(append([t1, l2, _nda])) -> append([cons(h1, t1), l2, cons(h1, _nda)]) -> 13
(length([_cea, _dea]) /\ length([l1, _bea]) /\ reverse([l1, _cea])) -> leq([_bea, _dea]) -> 13
(length([ll, _xda])) -> length([cons(x, ll), s(_xda)]) -> 13
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 13
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 14
(leq([s(nn1), z])) -> BOT -> 14
}
Sat witness: Found: ((append([_sda, cons(h1, nil), _tda]) /\ reverse([t1, _sda])) -> reverse([cons(h1, t1), _tda]), {
_sda -> nil  ;  _tda -> cons(z, cons(z, cons(z, nil)))  ;  h1 -> z  ;  t1 -> nil
})

-------------------------------------------
Step 24, which took 0.026323 s (model generation: 0.025130,  model checking: 0.001193):

Model:
|_
{
append -> 
{{{
Q={q_gen_8087, q_gen_8093, q_gen_8094, q_gen_8108, q_gen_8109, q_gen_8110},
Q_f={q_gen_8087},
Delta=
{
<cons>(q_gen_8109, q_gen_8108) -> q_gen_8108
<nil>() -> q_gen_8108
<z>() -> q_gen_8109
<cons, cons>(q_gen_8094, q_gen_8093) -> q_gen_8093
<nil, cons>(q_gen_8109, q_gen_8108) -> q_gen_8093
<nil, nil>() -> q_gen_8093
<s, s>(q_gen_8094) -> q_gen_8094
<z, z>() -> q_gen_8094
<cons, cons, cons>(q_gen_8110, q_gen_8087) -> q_gen_8087
<cons, nil, cons>(q_gen_8094, q_gen_8093) -> q_gen_8087
<nil, cons, cons>(q_gen_8094, q_gen_8093) -> q_gen_8087
<nil, nil, cons>(q_gen_8109, q_gen_8108) -> q_gen_8087
<nil, nil, nil>() -> q_gen_8087
<z, z, z>() -> q_gen_8110
}

Datatype: <natlist, natlist, natlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_8086, q_gen_8090, q_gen_8091, q_gen_8105, q_gen_8125, q_gen_8126, q_gen_8127},
Q_f={q_gen_8086},
Delta=
{
<nil>() -> q_gen_8090
<s>(q_gen_8105) -> q_gen_8105
<z>() -> q_gen_8105
<cons>(q_gen_8105, q_gen_8090) -> q_gen_8125
<cons, s>(q_gen_8091, q_gen_8090) -> q_gen_8086
<cons, s>(q_gen_8126, q_gen_8125) -> q_gen_8086
<nil, z>() -> q_gen_8086
<s, z>(q_gen_8105) -> q_gen_8091
<z, z>() -> q_gen_8091
<z, s>(q_gen_8105) -> q_gen_8126
<cons, s>(q_gen_8126, q_gen_8090) -> q_gen_8127
}

Datatype: <natlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_8083, q_gen_8085, q_gen_8128},
Q_f={q_gen_8083},
Delta=
{
<s>(q_gen_8085) -> q_gen_8085
<z>() -> q_gen_8085
<s, s>(q_gen_8083) -> q_gen_8083
<z, s>(q_gen_8085) -> q_gen_8083
<z, z>() -> q_gen_8083
<s, s>(q_gen_8128) -> q_gen_8128
<s, z>(q_gen_8085) -> q_gen_8128
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_8082, q_gen_8102, q_gen_8122, q_gen_8123},
Q_f={q_gen_8082},
Delta=
{
<cons>(q_gen_8123, q_gen_8122) -> q_gen_8122
<nil>() -> q_gen_8122
<z>() -> q_gen_8123
<cons, cons>(q_gen_8102, q_gen_8082) -> q_gen_8082
<nil, cons>(q_gen_8123, q_gen_8122) -> q_gen_8082
<nil, nil>() -> q_gen_8082
<s, s>(q_gen_8102) -> q_gen_8102
<z, z>() -> q_gen_8102
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 14
() -> length([nil, z]) -> 13
() -> leq([z, s(nn2)]) -> 13
() -> leq([z, z]) -> 13
() -> reverse([nil, nil]) -> 13
(append([_sda, cons(h1, nil), _tda]) /\ reverse([t1, _sda])) -> reverse([cons(h1, t1), _tda]) -> 15
(append([t1, l2, _nda])) -> append([cons(h1, t1), l2, cons(h1, _nda)]) -> 13
(length([_cea, _dea]) /\ length([l1, _bea]) /\ reverse([l1, _cea])) -> leq([_bea, _dea]) -> 13
(length([ll, _xda])) -> length([cons(x, ll), s(_xda)]) -> 16
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 14
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 14
(leq([s(nn1), z])) -> BOT -> 14
}
Sat witness: Found: ((length([ll, _xda])) -> length([cons(x, ll), s(_xda)]), {
_xda -> s(s(z))  ;  ll -> cons(z, cons(z, nil))  ;  x -> s(z)
})

-------------------------------------------
Step 25, which took 0.022019 s (model generation: 0.021417,  model checking: 0.000602):

Model:
|_
{
append -> 
{{{
Q={q_gen_8087, q_gen_8093, q_gen_8094, q_gen_8108, q_gen_8109, q_gen_8110},
Q_f={q_gen_8087},
Delta=
{
<cons>(q_gen_8109, q_gen_8108) -> q_gen_8108
<nil>() -> q_gen_8108
<z>() -> q_gen_8109
<cons, cons>(q_gen_8094, q_gen_8093) -> q_gen_8093
<nil, cons>(q_gen_8109, q_gen_8108) -> q_gen_8093
<nil, nil>() -> q_gen_8093
<s, s>(q_gen_8094) -> q_gen_8094
<z, z>() -> q_gen_8094
<cons, cons, cons>(q_gen_8110, q_gen_8087) -> q_gen_8087
<cons, nil, cons>(q_gen_8094, q_gen_8093) -> q_gen_8087
<nil, cons, cons>(q_gen_8094, q_gen_8093) -> q_gen_8087
<nil, nil, cons>(q_gen_8109, q_gen_8108) -> q_gen_8087
<nil, nil, nil>() -> q_gen_8087
<z, z, z>() -> q_gen_8110
}

Datatype: <natlist, natlist, natlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_8086, q_gen_8090, q_gen_8091, q_gen_8105, q_gen_8125, q_gen_8126, q_gen_8127},
Q_f={q_gen_8086},
Delta=
{
<nil>() -> q_gen_8090
<s>(q_gen_8105) -> q_gen_8105
<z>() -> q_gen_8105
<cons>(q_gen_8105, q_gen_8090) -> q_gen_8125
<cons>(q_gen_8105, q_gen_8125) -> q_gen_8125
<cons, s>(q_gen_8091, q_gen_8090) -> q_gen_8086
<cons, s>(q_gen_8091, q_gen_8125) -> q_gen_8086
<cons, s>(q_gen_8126, q_gen_8125) -> q_gen_8086
<nil, z>() -> q_gen_8086
<s, s>(q_gen_8126) -> q_gen_8091
<s, z>(q_gen_8105) -> q_gen_8091
<z, z>() -> q_gen_8091
<z, s>(q_gen_8105) -> q_gen_8126
<cons, s>(q_gen_8126, q_gen_8090) -> q_gen_8127
}

Datatype: <natlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_8083, q_gen_8085, q_gen_8128},
Q_f={q_gen_8083},
Delta=
{
<s>(q_gen_8085) -> q_gen_8085
<z>() -> q_gen_8085
<s, s>(q_gen_8083) -> q_gen_8083
<z, s>(q_gen_8085) -> q_gen_8083
<z, z>() -> q_gen_8083
<s, s>(q_gen_8128) -> q_gen_8128
<s, z>(q_gen_8085) -> q_gen_8128
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_8082, q_gen_8102, q_gen_8122, q_gen_8123},
Q_f={q_gen_8082},
Delta=
{
<cons>(q_gen_8123, q_gen_8122) -> q_gen_8122
<nil>() -> q_gen_8122
<z>() -> q_gen_8123
<cons, cons>(q_gen_8102, q_gen_8082) -> q_gen_8082
<nil, cons>(q_gen_8123, q_gen_8122) -> q_gen_8082
<nil, nil>() -> q_gen_8082
<s, s>(q_gen_8102) -> q_gen_8102
<z, z>() -> q_gen_8102
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 14
() -> length([nil, z]) -> 13
() -> leq([z, s(nn2)]) -> 13
() -> leq([z, z]) -> 13
() -> reverse([nil, nil]) -> 13
(append([_sda, cons(h1, nil), _tda]) /\ reverse([t1, _sda])) -> reverse([cons(h1, t1), _tda]) -> 15
(append([t1, l2, _nda])) -> append([cons(h1, t1), l2, cons(h1, _nda)]) -> 13
(length([_cea, _dea]) /\ length([l1, _bea]) /\ reverse([l1, _cea])) -> leq([_bea, _dea]) -> 16
(length([ll, _xda])) -> length([cons(x, ll), s(_xda)]) -> 16
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 14
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 14
(leq([s(nn1), z])) -> BOT -> 14
}
Sat witness: Found: ((length([_cea, _dea]) /\ length([l1, _bea]) /\ reverse([l1, _cea])) -> leq([_bea, _dea]), {
_bea -> s(s(s(s(z))))  ;  _cea -> cons(s(z), cons(z, nil))  ;  _dea -> s(s(s(z)))  ;  l1 -> cons(s(z), nil)
})

-------------------------------------------
Step 26, which took 0.028176 s (model generation: 0.025894,  model checking: 0.002282):

Model:
|_
{
append -> 
{{{
Q={q_gen_8087, q_gen_8093, q_gen_8094, q_gen_8108, q_gen_8109, q_gen_8110},
Q_f={q_gen_8087},
Delta=
{
<cons>(q_gen_8109, q_gen_8108) -> q_gen_8108
<nil>() -> q_gen_8108
<z>() -> q_gen_8109
<cons, cons>(q_gen_8094, q_gen_8093) -> q_gen_8093
<nil, cons>(q_gen_8109, q_gen_8108) -> q_gen_8093
<nil, nil>() -> q_gen_8093
<s, s>(q_gen_8094) -> q_gen_8094
<z, z>() -> q_gen_8094
<cons, cons, cons>(q_gen_8110, q_gen_8087) -> q_gen_8087
<cons, nil, cons>(q_gen_8094, q_gen_8093) -> q_gen_8087
<nil, cons, cons>(q_gen_8094, q_gen_8093) -> q_gen_8087
<nil, nil, cons>(q_gen_8109, q_gen_8108) -> q_gen_8087
<nil, nil, nil>() -> q_gen_8087
<z, z, z>() -> q_gen_8110
}

Datatype: <natlist, natlist, natlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_8086, q_gen_8090, q_gen_8091, q_gen_8105, q_gen_8125, q_gen_8126, q_gen_8127},
Q_f={q_gen_8086},
Delta=
{
<nil>() -> q_gen_8090
<s>(q_gen_8105) -> q_gen_8105
<z>() -> q_gen_8105
<cons>(q_gen_8105, q_gen_8090) -> q_gen_8125
<cons>(q_gen_8105, q_gen_8125) -> q_gen_8125
<cons, s>(q_gen_8091, q_gen_8090) -> q_gen_8086
<cons, s>(q_gen_8126, q_gen_8125) -> q_gen_8086
<nil, z>() -> q_gen_8086
<s, z>(q_gen_8105) -> q_gen_8091
<z, z>() -> q_gen_8091
<s, s>(q_gen_8126) -> q_gen_8126
<z, s>(q_gen_8105) -> q_gen_8126
<cons, s>(q_gen_8126, q_gen_8090) -> q_gen_8127
}

Datatype: <natlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_8083, q_gen_8085, q_gen_8128},
Q_f={q_gen_8083},
Delta=
{
<s>(q_gen_8085) -> q_gen_8085
<z>() -> q_gen_8085
<s, s>(q_gen_8083) -> q_gen_8083
<z, s>(q_gen_8085) -> q_gen_8083
<z, z>() -> q_gen_8083
<s, s>(q_gen_8128) -> q_gen_8128
<s, z>(q_gen_8085) -> q_gen_8128
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_8082, q_gen_8102, q_gen_8122, q_gen_8123},
Q_f={q_gen_8082},
Delta=
{
<cons>(q_gen_8123, q_gen_8122) -> q_gen_8122
<nil>() -> q_gen_8122
<z>() -> q_gen_8123
<cons, cons>(q_gen_8102, q_gen_8082) -> q_gen_8082
<nil, cons>(q_gen_8123, q_gen_8122) -> q_gen_8082
<nil, nil>() -> q_gen_8082
<s, s>(q_gen_8102) -> q_gen_8102
<z, z>() -> q_gen_8102
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 14
() -> length([nil, z]) -> 13
() -> leq([z, s(nn2)]) -> 13
() -> leq([z, z]) -> 13
() -> reverse([nil, nil]) -> 13
(append([_sda, cons(h1, nil), _tda]) /\ reverse([t1, _sda])) -> reverse([cons(h1, t1), _tda]) -> 15
(append([t1, l2, _nda])) -> append([cons(h1, t1), l2, cons(h1, _nda)]) -> 16
(length([_cea, _dea]) /\ length([l1, _bea]) /\ reverse([l1, _cea])) -> leq([_bea, _dea]) -> 16
(length([ll, _xda])) -> length([cons(x, ll), s(_xda)]) -> 16
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 14
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 14
(leq([s(nn1), z])) -> BOT -> 14
}
Sat witness: Found: ((append([t1, l2, _nda])) -> append([cons(h1, t1), l2, cons(h1, _nda)]), {
_nda -> cons(z, nil)  ;  h1 -> s(z)  ;  l2 -> cons(z, nil)  ;  t1 -> nil
})

-------------------------------------------
Step 27, which took 0.033019 s (model generation: 0.030865,  model checking: 0.002154):

Model:
|_
{
append -> 
{{{
Q={q_gen_8087, q_gen_8093, q_gen_8094, q_gen_8108, q_gen_8109, q_gen_8110},
Q_f={q_gen_8087},
Delta=
{
<cons>(q_gen_8109, q_gen_8108) -> q_gen_8108
<nil>() -> q_gen_8108
<z>() -> q_gen_8109
<cons, cons>(q_gen_8094, q_gen_8093) -> q_gen_8093
<nil, cons>(q_gen_8109, q_gen_8108) -> q_gen_8093
<nil, nil>() -> q_gen_8093
<s, s>(q_gen_8094) -> q_gen_8094
<z, z>() -> q_gen_8094
<cons, cons, cons>(q_gen_8110, q_gen_8087) -> q_gen_8087
<cons, nil, cons>(q_gen_8094, q_gen_8093) -> q_gen_8087
<nil, cons, cons>(q_gen_8094, q_gen_8093) -> q_gen_8087
<nil, nil, cons>(q_gen_8109, q_gen_8108) -> q_gen_8087
<nil, nil, nil>() -> q_gen_8087
<s, z, s>(q_gen_8094) -> q_gen_8110
<z, z, z>() -> q_gen_8110
}

Datatype: <natlist, natlist, natlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_8086, q_gen_8090, q_gen_8091, q_gen_8105, q_gen_8125, q_gen_8126, q_gen_8127},
Q_f={q_gen_8086},
Delta=
{
<cons>(q_gen_8105, q_gen_8125) -> q_gen_8090
<nil>() -> q_gen_8090
<s>(q_gen_8105) -> q_gen_8105
<z>() -> q_gen_8105
<cons>(q_gen_8105, q_gen_8090) -> q_gen_8125
<cons, s>(q_gen_8091, q_gen_8090) -> q_gen_8086
<cons, s>(q_gen_8126, q_gen_8125) -> q_gen_8086
<nil, z>() -> q_gen_8086
<s, s>(q_gen_8126) -> q_gen_8091
<s, z>(q_gen_8105) -> q_gen_8091
<z, z>() -> q_gen_8091
<z, s>(q_gen_8105) -> q_gen_8126
<cons, s>(q_gen_8091, q_gen_8125) -> q_gen_8127
<cons, s>(q_gen_8126, q_gen_8090) -> q_gen_8127
}

Datatype: <natlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_8083, q_gen_8085, q_gen_8128},
Q_f={q_gen_8083},
Delta=
{
<s>(q_gen_8085) -> q_gen_8085
<z>() -> q_gen_8085
<s, s>(q_gen_8083) -> q_gen_8083
<z, s>(q_gen_8085) -> q_gen_8083
<z, z>() -> q_gen_8083
<s, s>(q_gen_8128) -> q_gen_8128
<s, z>(q_gen_8085) -> q_gen_8128
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_8082, q_gen_8102, q_gen_8122, q_gen_8123},
Q_f={q_gen_8082},
Delta=
{
<cons>(q_gen_8123, q_gen_8122) -> q_gen_8122
<nil>() -> q_gen_8122
<z>() -> q_gen_8123
<cons, cons>(q_gen_8102, q_gen_8082) -> q_gen_8082
<nil, cons>(q_gen_8123, q_gen_8122) -> q_gen_8082
<nil, nil>() -> q_gen_8082
<s, s>(q_gen_8102) -> q_gen_8102
<z, z>() -> q_gen_8102
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 15
() -> length([nil, z]) -> 14
() -> leq([z, s(nn2)]) -> 14
() -> leq([z, z]) -> 14
() -> reverse([nil, nil]) -> 14
(append([_sda, cons(h1, nil), _tda]) /\ reverse([t1, _sda])) -> reverse([cons(h1, t1), _tda]) -> 18
(append([t1, l2, _nda])) -> append([cons(h1, t1), l2, cons(h1, _nda)]) -> 16
(length([_cea, _dea]) /\ length([l1, _bea]) /\ reverse([l1, _cea])) -> leq([_bea, _dea]) -> 16
(length([ll, _xda])) -> length([cons(x, ll), s(_xda)]) -> 16
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 15
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 15
(leq([s(nn1), z])) -> BOT -> 15
}
Sat witness: Found: ((append([_sda, cons(h1, nil), _tda]) /\ reverse([t1, _sda])) -> reverse([cons(h1, t1), _tda]), {
_sda -> cons(z, nil)  ;  _tda -> cons(z, nil)  ;  h1 -> z  ;  t1 -> cons(z, nil)
})

-------------------------------------------
Step 28, which took 0.035301 s (model generation: 0.033523,  model checking: 0.001778):

Model:
|_
{
append -> 
{{{
Q={q_gen_8087, q_gen_8093, q_gen_8094, q_gen_8108, q_gen_8109, q_gen_8110},
Q_f={q_gen_8087},
Delta=
{
<cons>(q_gen_8109, q_gen_8108) -> q_gen_8108
<nil>() -> q_gen_8108
<z>() -> q_gen_8109
<cons, cons>(q_gen_8094, q_gen_8093) -> q_gen_8093
<nil, cons>(q_gen_8109, q_gen_8108) -> q_gen_8093
<nil, nil>() -> q_gen_8093
<s, s>(q_gen_8094) -> q_gen_8094
<z, z>() -> q_gen_8094
<cons, cons, cons>(q_gen_8110, q_gen_8087) -> q_gen_8087
<cons, nil, cons>(q_gen_8094, q_gen_8093) -> q_gen_8087
<nil, cons, cons>(q_gen_8094, q_gen_8093) -> q_gen_8087
<nil, nil, cons>(q_gen_8109, q_gen_8108) -> q_gen_8087
<nil, nil, nil>() -> q_gen_8087
<s, z, s>(q_gen_8094) -> q_gen_8110
<z, z, z>() -> q_gen_8110
}

Datatype: <natlist, natlist, natlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_8086, q_gen_8090, q_gen_8091, q_gen_8105, q_gen_8125, q_gen_8126, q_gen_8127},
Q_f={q_gen_8086},
Delta=
{
<cons>(q_gen_8105, q_gen_8125) -> q_gen_8090
<nil>() -> q_gen_8090
<s>(q_gen_8105) -> q_gen_8105
<z>() -> q_gen_8105
<cons>(q_gen_8105, q_gen_8090) -> q_gen_8125
<cons, s>(q_gen_8091, q_gen_8090) -> q_gen_8086
<cons, s>(q_gen_8126, q_gen_8125) -> q_gen_8086
<nil, z>() -> q_gen_8086
<s, s>(q_gen_8126) -> q_gen_8091
<s, z>(q_gen_8105) -> q_gen_8091
<z, z>() -> q_gen_8091
<z, s>(q_gen_8105) -> q_gen_8126
<cons, s>(q_gen_8091, q_gen_8125) -> q_gen_8127
<cons, s>(q_gen_8126, q_gen_8090) -> q_gen_8127
}

Datatype: <natlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_8083, q_gen_8085, q_gen_8128},
Q_f={q_gen_8083},
Delta=
{
<s>(q_gen_8085) -> q_gen_8085
<z>() -> q_gen_8085
<s, s>(q_gen_8083) -> q_gen_8083
<z, s>(q_gen_8085) -> q_gen_8083
<z, z>() -> q_gen_8083
<s, s>(q_gen_8128) -> q_gen_8128
<s, z>(q_gen_8085) -> q_gen_8128
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_8082, q_gen_8102, q_gen_8122, q_gen_8123},
Q_f={q_gen_8082},
Delta=
{
<cons>(q_gen_8123, q_gen_8122) -> q_gen_8122
<nil>() -> q_gen_8122
<z>() -> q_gen_8123
<cons, cons>(q_gen_8102, q_gen_8082) -> q_gen_8082
<cons, nil>(q_gen_8123, q_gen_8122) -> q_gen_8082
<nil, cons>(q_gen_8123, q_gen_8122) -> q_gen_8082
<nil, nil>() -> q_gen_8082
<s, s>(q_gen_8102) -> q_gen_8102
<z, z>() -> q_gen_8102
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 16
() -> length([nil, z]) -> 15
() -> leq([z, s(nn2)]) -> 15
() -> leq([z, z]) -> 15
() -> reverse([nil, nil]) -> 15
(append([_sda, cons(h1, nil), _tda]) /\ reverse([t1, _sda])) -> reverse([cons(h1, t1), _tda]) -> 18
(append([t1, l2, _nda])) -> append([cons(h1, t1), l2, cons(h1, _nda)]) -> 16
(length([_cea, _dea]) /\ length([l1, _bea]) /\ reverse([l1, _cea])) -> leq([_bea, _dea]) -> 16
(length([ll, _xda])) -> length([cons(x, ll), s(_xda)]) -> 19
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 16
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 16
(leq([s(nn1), z])) -> BOT -> 16
}
Sat witness: Found: ((length([ll, _xda])) -> length([cons(x, ll), s(_xda)]), {
_xda -> s(s(s(z)))  ;  ll -> cons(s(z), nil)  ;  x -> s(z)
})

-------------------------------------------
Step 29, which took 0.042661 s (model generation: 0.041860,  model checking: 0.000801):

Model:
|_
{
append -> 
{{{
Q={q_gen_8087, q_gen_8093, q_gen_8094, q_gen_8108, q_gen_8109, q_gen_8110},
Q_f={q_gen_8087},
Delta=
{
<cons>(q_gen_8109, q_gen_8108) -> q_gen_8108
<nil>() -> q_gen_8108
<z>() -> q_gen_8109
<cons, cons>(q_gen_8094, q_gen_8093) -> q_gen_8093
<nil, cons>(q_gen_8109, q_gen_8108) -> q_gen_8093
<nil, nil>() -> q_gen_8093
<s, s>(q_gen_8094) -> q_gen_8094
<z, z>() -> q_gen_8094
<cons, cons, cons>(q_gen_8110, q_gen_8087) -> q_gen_8087
<cons, nil, cons>(q_gen_8094, q_gen_8093) -> q_gen_8087
<nil, cons, cons>(q_gen_8094, q_gen_8093) -> q_gen_8087
<nil, nil, cons>(q_gen_8109, q_gen_8108) -> q_gen_8087
<nil, nil, nil>() -> q_gen_8087
<s, z, s>(q_gen_8094) -> q_gen_8110
<z, z, z>() -> q_gen_8110
}

Datatype: <natlist, natlist, natlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_8086, q_gen_8090, q_gen_8091, q_gen_8105, q_gen_8125, q_gen_8126, q_gen_8127},
Q_f={q_gen_8086},
Delta=
{
<nil>() -> q_gen_8090
<s>(q_gen_8105) -> q_gen_8105
<z>() -> q_gen_8105
<cons>(q_gen_8105, q_gen_8090) -> q_gen_8125
<cons>(q_gen_8105, q_gen_8125) -> q_gen_8125
<cons, s>(q_gen_8091, q_gen_8090) -> q_gen_8086
<cons, s>(q_gen_8126, q_gen_8125) -> q_gen_8086
<nil, z>() -> q_gen_8086
<s, z>(q_gen_8105) -> q_gen_8091
<z, z>() -> q_gen_8091
<s, s>(q_gen_8126) -> q_gen_8126
<z, s>(q_gen_8105) -> q_gen_8126
<cons, s>(q_gen_8126, q_gen_8090) -> q_gen_8127
}

Datatype: <natlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_8083, q_gen_8085, q_gen_8128},
Q_f={q_gen_8083},
Delta=
{
<s>(q_gen_8085) -> q_gen_8085
<z>() -> q_gen_8085
<s, s>(q_gen_8083) -> q_gen_8083
<z, s>(q_gen_8085) -> q_gen_8083
<z, z>() -> q_gen_8083
<s, s>(q_gen_8128) -> q_gen_8128
<s, z>(q_gen_8085) -> q_gen_8128
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_8082, q_gen_8102, q_gen_8122, q_gen_8123},
Q_f={q_gen_8082},
Delta=
{
<cons>(q_gen_8123, q_gen_8122) -> q_gen_8122
<nil>() -> q_gen_8122
<z>() -> q_gen_8123
<cons, cons>(q_gen_8102, q_gen_8082) -> q_gen_8082
<cons, nil>(q_gen_8123, q_gen_8122) -> q_gen_8082
<nil, cons>(q_gen_8123, q_gen_8122) -> q_gen_8082
<nil, nil>() -> q_gen_8082
<s, s>(q_gen_8102) -> q_gen_8102
<z, z>() -> q_gen_8102
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 16
() -> length([nil, z]) -> 16
() -> leq([z, s(nn2)]) -> 16
() -> leq([z, z]) -> 16
() -> reverse([nil, nil]) -> 16
(append([_sda, cons(h1, nil), _tda]) /\ reverse([t1, _sda])) -> reverse([cons(h1, t1), _tda]) -> 18
(append([t1, l2, _nda])) -> append([cons(h1, t1), l2, cons(h1, _nda)]) -> 16
(length([_cea, _dea]) /\ length([l1, _bea]) /\ reverse([l1, _cea])) -> leq([_bea, _dea]) -> 19
(length([ll, _xda])) -> length([cons(x, ll), s(_xda)]) -> 19
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 17
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 17
(leq([s(nn1), z])) -> BOT -> 17
}
Sat witness: Found: ((length([_cea, _dea]) /\ length([l1, _bea]) /\ reverse([l1, _cea])) -> leq([_bea, _dea]), {
_bea -> s(z)  ;  _cea -> nil  ;  _dea -> z  ;  l1 -> cons(z, nil)
})

-------------------------------------------
Step 30, which took 0.040252 s (model generation: 0.036800,  model checking: 0.003452):

Model:
|_
{
append -> 
{{{
Q={q_gen_8087, q_gen_8093, q_gen_8094, q_gen_8108, q_gen_8109, q_gen_8110},
Q_f={q_gen_8087},
Delta=
{
<cons>(q_gen_8109, q_gen_8108) -> q_gen_8108
<nil>() -> q_gen_8108
<z>() -> q_gen_8109
<cons, cons>(q_gen_8094, q_gen_8093) -> q_gen_8093
<nil, cons>(q_gen_8109, q_gen_8108) -> q_gen_8093
<nil, nil>() -> q_gen_8093
<s, s>(q_gen_8094) -> q_gen_8094
<z, z>() -> q_gen_8094
<cons, cons, cons>(q_gen_8110, q_gen_8087) -> q_gen_8087
<cons, nil, cons>(q_gen_8094, q_gen_8093) -> q_gen_8087
<nil, cons, cons>(q_gen_8094, q_gen_8093) -> q_gen_8087
<nil, nil, cons>(q_gen_8109, q_gen_8108) -> q_gen_8087
<nil, nil, nil>() -> q_gen_8087
<s, z, s>(q_gen_8094) -> q_gen_8110
<z, z, z>() -> q_gen_8110
}

Datatype: <natlist, natlist, natlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_8086, q_gen_8090, q_gen_8091, q_gen_8105, q_gen_8125, q_gen_8126, q_gen_8127},
Q_f={q_gen_8086},
Delta=
{
<nil>() -> q_gen_8090
<s>(q_gen_8105) -> q_gen_8105
<z>() -> q_gen_8105
<cons>(q_gen_8105, q_gen_8090) -> q_gen_8125
<cons>(q_gen_8105, q_gen_8125) -> q_gen_8125
<cons, s>(q_gen_8091, q_gen_8090) -> q_gen_8086
<cons, s>(q_gen_8126, q_gen_8125) -> q_gen_8086
<nil, z>() -> q_gen_8086
<s, z>(q_gen_8105) -> q_gen_8091
<z, z>() -> q_gen_8091
<s, s>(q_gen_8126) -> q_gen_8126
<z, s>(q_gen_8105) -> q_gen_8126
<cons, s>(q_gen_8126, q_gen_8090) -> q_gen_8127
}

Datatype: <natlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_8083, q_gen_8085, q_gen_8128},
Q_f={q_gen_8083},
Delta=
{
<s>(q_gen_8085) -> q_gen_8085
<z>() -> q_gen_8085
<s, s>(q_gen_8083) -> q_gen_8083
<z, s>(q_gen_8085) -> q_gen_8083
<z, z>() -> q_gen_8083
<s, s>(q_gen_8128) -> q_gen_8128
<s, z>(q_gen_8085) -> q_gen_8128
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_8082, q_gen_8102, q_gen_8121, q_gen_8122, q_gen_8123},
Q_f={q_gen_8082},
Delta=
{
<cons>(q_gen_8123, q_gen_8122) -> q_gen_8122
<nil>() -> q_gen_8122
<z>() -> q_gen_8123
<cons, cons>(q_gen_8102, q_gen_8082) -> q_gen_8082
<cons, cons>(q_gen_8102, q_gen_8121) -> q_gen_8082
<nil, nil>() -> q_gen_8082
<s, s>(q_gen_8102) -> q_gen_8102
<z, z>() -> q_gen_8102
<cons, nil>(q_gen_8123, q_gen_8122) -> q_gen_8121
<nil, cons>(q_gen_8123, q_gen_8122) -> q_gen_8121
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 16
() -> length([nil, z]) -> 16
() -> leq([z, s(nn2)]) -> 16
() -> leq([z, z]) -> 16
() -> reverse([nil, nil]) -> 16
(append([_sda, cons(h1, nil), _tda]) /\ reverse([t1, _sda])) -> reverse([cons(h1, t1), _tda]) -> 18
(append([t1, l2, _nda])) -> append([cons(h1, t1), l2, cons(h1, _nda)]) -> 19
(length([_cea, _dea]) /\ length([l1, _bea]) /\ reverse([l1, _cea])) -> leq([_bea, _dea]) -> 19
(length([ll, _xda])) -> length([cons(x, ll), s(_xda)]) -> 19
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 17
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 17
(leq([s(nn1), z])) -> BOT -> 17
}
Sat witness: Found: ((append([t1, l2, _nda])) -> append([cons(h1, t1), l2, cons(h1, _nda)]), {
_nda -> cons(s(z), cons(z, nil))  ;  h1 -> s(z)  ;  l2 -> cons(s(z), nil)  ;  t1 -> nil
})

-------------------------------------------
Step 31, which took 0.037463 s (model generation: 0.036237,  model checking: 0.001226):

Model:
|_
{
append -> 
{{{
Q={q_gen_8087, q_gen_8093, q_gen_8094, q_gen_8108, q_gen_8109, q_gen_8110},
Q_f={q_gen_8087},
Delta=
{
<cons>(q_gen_8109, q_gen_8108) -> q_gen_8108
<nil>() -> q_gen_8108
<s>(q_gen_8109) -> q_gen_8109
<z>() -> q_gen_8109
<cons, cons>(q_gen_8094, q_gen_8093) -> q_gen_8093
<nil, cons>(q_gen_8109, q_gen_8108) -> q_gen_8093
<nil, nil>() -> q_gen_8093
<s, s>(q_gen_8094) -> q_gen_8094
<z, z>() -> q_gen_8094
<cons, cons, cons>(q_gen_8110, q_gen_8087) -> q_gen_8087
<cons, nil, cons>(q_gen_8094, q_gen_8093) -> q_gen_8087
<nil, cons, cons>(q_gen_8094, q_gen_8093) -> q_gen_8087
<nil, nil, cons>(q_gen_8109, q_gen_8108) -> q_gen_8087
<nil, nil, nil>() -> q_gen_8087
<s, s, s>(q_gen_8110) -> q_gen_8110
<s, z, s>(q_gen_8094) -> q_gen_8110
<z, z, z>() -> q_gen_8110
}

Datatype: <natlist, natlist, natlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_8086, q_gen_8090, q_gen_8091, q_gen_8105, q_gen_8125, q_gen_8126, q_gen_8127},
Q_f={q_gen_8086},
Delta=
{
<nil>() -> q_gen_8090
<s>(q_gen_8105) -> q_gen_8105
<z>() -> q_gen_8105
<cons>(q_gen_8105, q_gen_8090) -> q_gen_8125
<cons>(q_gen_8105, q_gen_8125) -> q_gen_8125
<cons, s>(q_gen_8091, q_gen_8090) -> q_gen_8086
<cons, s>(q_gen_8126, q_gen_8125) -> q_gen_8086
<nil, z>() -> q_gen_8086
<s, z>(q_gen_8105) -> q_gen_8091
<z, z>() -> q_gen_8091
<s, s>(q_gen_8126) -> q_gen_8126
<z, s>(q_gen_8105) -> q_gen_8126
<cons, s>(q_gen_8126, q_gen_8090) -> q_gen_8127
}

Datatype: <natlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_8083, q_gen_8085, q_gen_8128},
Q_f={q_gen_8083},
Delta=
{
<s>(q_gen_8085) -> q_gen_8085
<z>() -> q_gen_8085
<s, s>(q_gen_8083) -> q_gen_8083
<z, s>(q_gen_8085) -> q_gen_8083
<z, z>() -> q_gen_8083
<s, s>(q_gen_8128) -> q_gen_8128
<s, z>(q_gen_8085) -> q_gen_8128
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_8082, q_gen_8102, q_gen_8121, q_gen_8122, q_gen_8123},
Q_f={q_gen_8082},
Delta=
{
<cons>(q_gen_8123, q_gen_8122) -> q_gen_8122
<nil>() -> q_gen_8122
<z>() -> q_gen_8123
<cons, cons>(q_gen_8102, q_gen_8082) -> q_gen_8082
<cons, cons>(q_gen_8102, q_gen_8121) -> q_gen_8082
<nil, nil>() -> q_gen_8082
<s, s>(q_gen_8102) -> q_gen_8102
<z, z>() -> q_gen_8102
<cons, nil>(q_gen_8123, q_gen_8122) -> q_gen_8121
<nil, cons>(q_gen_8123, q_gen_8122) -> q_gen_8121
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 17
() -> length([nil, z]) -> 17
() -> leq([z, s(nn2)]) -> 17
() -> leq([z, z]) -> 17
() -> reverse([nil, nil]) -> 17
(append([_sda, cons(h1, nil), _tda]) /\ reverse([t1, _sda])) -> reverse([cons(h1, t1), _tda]) -> 21
(append([t1, l2, _nda])) -> append([cons(h1, t1), l2, cons(h1, _nda)]) -> 19
(length([_cea, _dea]) /\ length([l1, _bea]) /\ reverse([l1, _cea])) -> leq([_bea, _dea]) -> 19
(length([ll, _xda])) -> length([cons(x, ll), s(_xda)]) -> 19
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 18
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 18
(leq([s(nn1), z])) -> BOT -> 18
}
Sat witness: Found: ((append([_sda, cons(h1, nil), _tda]) /\ reverse([t1, _sda])) -> reverse([cons(h1, t1), _tda]), {
_sda -> nil  ;  _tda -> cons(z, cons(s(z), cons(s(z), nil)))  ;  h1 -> z  ;  t1 -> nil
})

-------------------------------------------
Step 32, which took 0.054173 s (model generation: 0.052413,  model checking: 0.001760):

Model:
|_
{
append -> 
{{{
Q={q_gen_8087, q_gen_8093, q_gen_8094, q_gen_8108, q_gen_8109, q_gen_8110},
Q_f={q_gen_8087},
Delta=
{
<cons>(q_gen_8109, q_gen_8108) -> q_gen_8108
<nil>() -> q_gen_8108
<s>(q_gen_8109) -> q_gen_8109
<z>() -> q_gen_8109
<cons, cons>(q_gen_8094, q_gen_8093) -> q_gen_8093
<nil, cons>(q_gen_8109, q_gen_8108) -> q_gen_8093
<nil, nil>() -> q_gen_8093
<s, s>(q_gen_8094) -> q_gen_8094
<z, z>() -> q_gen_8094
<cons, cons, cons>(q_gen_8110, q_gen_8087) -> q_gen_8087
<cons, nil, cons>(q_gen_8094, q_gen_8093) -> q_gen_8087
<nil, cons, cons>(q_gen_8094, q_gen_8093) -> q_gen_8087
<nil, nil, cons>(q_gen_8109, q_gen_8108) -> q_gen_8087
<nil, nil, nil>() -> q_gen_8087
<s, s, s>(q_gen_8110) -> q_gen_8110
<s, z, s>(q_gen_8094) -> q_gen_8110
<z, z, z>() -> q_gen_8110
}

Datatype: <natlist, natlist, natlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_8086, q_gen_8090, q_gen_8091, q_gen_8105, q_gen_8125, q_gen_8126, q_gen_8127},
Q_f={q_gen_8086},
Delta=
{
<nil>() -> q_gen_8090
<s>(q_gen_8105) -> q_gen_8105
<z>() -> q_gen_8105
<cons>(q_gen_8105, q_gen_8090) -> q_gen_8125
<cons>(q_gen_8105, q_gen_8125) -> q_gen_8125
<cons, s>(q_gen_8091, q_gen_8090) -> q_gen_8086
<cons, s>(q_gen_8126, q_gen_8125) -> q_gen_8086
<nil, z>() -> q_gen_8086
<s, z>(q_gen_8105) -> q_gen_8091
<z, z>() -> q_gen_8091
<s, s>(q_gen_8126) -> q_gen_8126
<z, s>(q_gen_8105) -> q_gen_8126
<cons, s>(q_gen_8126, q_gen_8090) -> q_gen_8127
}

Datatype: <natlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_8083, q_gen_8085, q_gen_8128},
Q_f={q_gen_8083},
Delta=
{
<s>(q_gen_8085) -> q_gen_8085
<z>() -> q_gen_8085
<s, s>(q_gen_8083) -> q_gen_8083
<z, s>(q_gen_8085) -> q_gen_8083
<z, z>() -> q_gen_8083
<s, s>(q_gen_8128) -> q_gen_8128
<s, z>(q_gen_8085) -> q_gen_8128
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_8082, q_gen_8102, q_gen_8121, q_gen_8122, q_gen_8123},
Q_f={q_gen_8082},
Delta=
{
<cons>(q_gen_8123, q_gen_8122) -> q_gen_8122
<nil>() -> q_gen_8122
<s>(q_gen_8123) -> q_gen_8123
<z>() -> q_gen_8123
<cons, cons>(q_gen_8102, q_gen_8082) -> q_gen_8082
<cons, cons>(q_gen_8102, q_gen_8121) -> q_gen_8082
<nil, nil>() -> q_gen_8082
<s, s>(q_gen_8102) -> q_gen_8102
<z, z>() -> q_gen_8102
<cons, nil>(q_gen_8123, q_gen_8122) -> q_gen_8121
<nil, cons>(q_gen_8123, q_gen_8122) -> q_gen_8121
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 18
() -> length([nil, z]) -> 18
() -> leq([z, s(nn2)]) -> 18
() -> leq([z, z]) -> 18
() -> reverse([nil, nil]) -> 18
(append([_sda, cons(h1, nil), _tda]) /\ reverse([t1, _sda])) -> reverse([cons(h1, t1), _tda]) -> 21
(append([t1, l2, _nda])) -> append([cons(h1, t1), l2, cons(h1, _nda)]) -> 19
(length([_cea, _dea]) /\ length([l1, _bea]) /\ reverse([l1, _cea])) -> leq([_bea, _dea]) -> 19
(length([ll, _xda])) -> length([cons(x, ll), s(_xda)]) -> 22
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 19
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 19
(leq([s(nn1), z])) -> BOT -> 19
}
Sat witness: Found: ((length([ll, _xda])) -> length([cons(x, ll), s(_xda)]), {
_xda -> s(s(z))  ;  ll -> cons(z, cons(z, nil))  ;  x -> s(s(z))
})

-------------------------------------------
Step 33, which took 0.067358 s (model generation: 0.065640,  model checking: 0.001718):

Model:
|_
{
append -> 
{{{
Q={q_gen_8087, q_gen_8093, q_gen_8094, q_gen_8108, q_gen_8109, q_gen_8110},
Q_f={q_gen_8087},
Delta=
{
<cons>(q_gen_8109, q_gen_8108) -> q_gen_8108
<nil>() -> q_gen_8108
<s>(q_gen_8109) -> q_gen_8109
<z>() -> q_gen_8109
<cons, cons>(q_gen_8094, q_gen_8093) -> q_gen_8093
<nil, cons>(q_gen_8109, q_gen_8108) -> q_gen_8093
<nil, nil>() -> q_gen_8093
<s, s>(q_gen_8094) -> q_gen_8094
<z, z>() -> q_gen_8094
<cons, cons, cons>(q_gen_8110, q_gen_8087) -> q_gen_8087
<cons, nil, cons>(q_gen_8094, q_gen_8093) -> q_gen_8087
<nil, cons, cons>(q_gen_8094, q_gen_8093) -> q_gen_8087
<nil, nil, cons>(q_gen_8109, q_gen_8108) -> q_gen_8087
<nil, nil, nil>() -> q_gen_8087
<s, s, s>(q_gen_8110) -> q_gen_8110
<s, z, s>(q_gen_8094) -> q_gen_8110
<z, z, z>() -> q_gen_8110
}

Datatype: <natlist, natlist, natlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_8086, q_gen_8090, q_gen_8091, q_gen_8105, q_gen_8125, q_gen_8126, q_gen_8127},
Q_f={q_gen_8086},
Delta=
{
<nil>() -> q_gen_8090
<s>(q_gen_8105) -> q_gen_8105
<z>() -> q_gen_8105
<cons>(q_gen_8105, q_gen_8090) -> q_gen_8125
<cons>(q_gen_8105, q_gen_8125) -> q_gen_8125
<cons, s>(q_gen_8091, q_gen_8090) -> q_gen_8086
<cons, s>(q_gen_8091, q_gen_8125) -> q_gen_8086
<cons, s>(q_gen_8126, q_gen_8125) -> q_gen_8086
<nil, z>() -> q_gen_8086
<s, s>(q_gen_8091) -> q_gen_8091
<s, z>(q_gen_8105) -> q_gen_8091
<z, z>() -> q_gen_8091
<s, s>(q_gen_8126) -> q_gen_8126
<z, s>(q_gen_8105) -> q_gen_8126
<cons, s>(q_gen_8126, q_gen_8090) -> q_gen_8127
}

Datatype: <natlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_8083, q_gen_8085, q_gen_8128},
Q_f={q_gen_8083},
Delta=
{
<s>(q_gen_8085) -> q_gen_8085
<z>() -> q_gen_8085
<s, s>(q_gen_8083) -> q_gen_8083
<z, s>(q_gen_8085) -> q_gen_8083
<z, z>() -> q_gen_8083
<s, s>(q_gen_8128) -> q_gen_8128
<s, z>(q_gen_8085) -> q_gen_8128
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_8082, q_gen_8102, q_gen_8121, q_gen_8122, q_gen_8123},
Q_f={q_gen_8082},
Delta=
{
<cons>(q_gen_8123, q_gen_8122) -> q_gen_8122
<nil>() -> q_gen_8122
<s>(q_gen_8123) -> q_gen_8123
<z>() -> q_gen_8123
<cons, cons>(q_gen_8102, q_gen_8082) -> q_gen_8082
<cons, cons>(q_gen_8102, q_gen_8121) -> q_gen_8082
<nil, nil>() -> q_gen_8082
<s, s>(q_gen_8102) -> q_gen_8102
<z, z>() -> q_gen_8102
<cons, nil>(q_gen_8123, q_gen_8122) -> q_gen_8121
<nil, cons>(q_gen_8123, q_gen_8122) -> q_gen_8121
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 19
() -> length([nil, z]) -> 19
() -> leq([z, s(nn2)]) -> 19
() -> leq([z, z]) -> 19
() -> reverse([nil, nil]) -> 19
(append([_sda, cons(h1, nil), _tda]) /\ reverse([t1, _sda])) -> reverse([cons(h1, t1), _tda]) -> 21
(append([t1, l2, _nda])) -> append([cons(h1, t1), l2, cons(h1, _nda)]) -> 19
(length([_cea, _dea]) /\ length([l1, _bea]) /\ reverse([l1, _cea])) -> leq([_bea, _dea]) -> 22
(length([ll, _xda])) -> length([cons(x, ll), s(_xda)]) -> 22
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 20
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 20
(leq([s(nn1), z])) -> BOT -> 20
}
Sat witness: Found: ((length([_cea, _dea]) /\ length([l1, _bea]) /\ reverse([l1, _cea])) -> leq([_bea, _dea]), {
_bea -> s(s(z))  ;  _cea -> cons(z, nil)  ;  _dea -> s(z)  ;  l1 -> cons(z, cons(z, nil))
})

-------------------------------------------
Step 34, which took 0.059932 s (model generation: 0.059192,  model checking: 0.000740):

Model:
|_
{
append -> 
{{{
Q={q_gen_8087, q_gen_8093, q_gen_8094, q_gen_8107, q_gen_8108, q_gen_8109, q_gen_8110},
Q_f={q_gen_8087},
Delta=
{
<cons>(q_gen_8109, q_gen_8108) -> q_gen_8108
<nil>() -> q_gen_8108
<s>(q_gen_8109) -> q_gen_8109
<z>() -> q_gen_8109
<cons, cons>(q_gen_8094, q_gen_8093) -> q_gen_8093
<nil, cons>(q_gen_8109, q_gen_8108) -> q_gen_8093
<nil, nil>() -> q_gen_8093
<s, s>(q_gen_8094) -> q_gen_8094
<z, z>() -> q_gen_8094
<cons, cons, cons>(q_gen_8110, q_gen_8107) -> q_gen_8087
<cons, nil, cons>(q_gen_8094, q_gen_8093) -> q_gen_8087
<nil, cons, cons>(q_gen_8094, q_gen_8093) -> q_gen_8087
<nil, nil, nil>() -> q_gen_8087
<cons, cons, cons>(q_gen_8110, q_gen_8087) -> q_gen_8107
<nil, nil, cons>(q_gen_8109, q_gen_8108) -> q_gen_8107
<s, s, s>(q_gen_8110) -> q_gen_8110
<s, z, s>(q_gen_8094) -> q_gen_8110
<z, z, z>() -> q_gen_8110
}

Datatype: <natlist, natlist, natlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_8086, q_gen_8090, q_gen_8091, q_gen_8105, q_gen_8125, q_gen_8126, q_gen_8127},
Q_f={q_gen_8086},
Delta=
{
<nil>() -> q_gen_8090
<s>(q_gen_8105) -> q_gen_8105
<z>() -> q_gen_8105
<cons>(q_gen_8105, q_gen_8090) -> q_gen_8125
<cons>(q_gen_8105, q_gen_8125) -> q_gen_8125
<cons, s>(q_gen_8091, q_gen_8090) -> q_gen_8086
<cons, s>(q_gen_8091, q_gen_8125) -> q_gen_8086
<cons, s>(q_gen_8126, q_gen_8125) -> q_gen_8086
<nil, z>() -> q_gen_8086
<s, s>(q_gen_8091) -> q_gen_8091
<s, z>(q_gen_8105) -> q_gen_8091
<z, z>() -> q_gen_8091
<s, s>(q_gen_8126) -> q_gen_8126
<z, s>(q_gen_8105) -> q_gen_8126
<cons, s>(q_gen_8126, q_gen_8090) -> q_gen_8127
}

Datatype: <natlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_8083, q_gen_8085, q_gen_8128},
Q_f={q_gen_8083},
Delta=
{
<s>(q_gen_8085) -> q_gen_8085
<z>() -> q_gen_8085
<s, s>(q_gen_8083) -> q_gen_8083
<z, s>(q_gen_8085) -> q_gen_8083
<z, z>() -> q_gen_8083
<s, s>(q_gen_8128) -> q_gen_8128
<s, z>(q_gen_8085) -> q_gen_8128
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_8082, q_gen_8102, q_gen_8122, q_gen_8123, q_gen_8151},
Q_f={q_gen_8082},
Delta=
{
<cons>(q_gen_8123, q_gen_8122) -> q_gen_8122
<nil>() -> q_gen_8122
<s>(q_gen_8123) -> q_gen_8123
<z>() -> q_gen_8123
<cons, cons>(q_gen_8102, q_gen_8082) -> q_gen_8082
<nil, cons>(q_gen_8123, q_gen_8122) -> q_gen_8082
<nil, nil>() -> q_gen_8082
<s, s>(q_gen_8102) -> q_gen_8102
<z, z>() -> q_gen_8102
<cons, cons>(q_gen_8102, q_gen_8151) -> q_gen_8151
<cons, nil>(q_gen_8123, q_gen_8122) -> q_gen_8151
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 19
() -> length([nil, z]) -> 19
() -> leq([z, s(nn2)]) -> 19
() -> leq([z, z]) -> 19
() -> reverse([nil, nil]) -> 19
(append([_sda, cons(h1, nil), _tda]) /\ reverse([t1, _sda])) -> reverse([cons(h1, t1), _tda]) -> 21
(append([t1, l2, _nda])) -> append([cons(h1, t1), l2, cons(h1, _nda)]) -> 22
(length([_cea, _dea]) /\ length([l1, _bea]) /\ reverse([l1, _cea])) -> leq([_bea, _dea]) -> 22
(length([ll, _xda])) -> length([cons(x, ll), s(_xda)]) -> 22
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 20
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 20
(leq([s(nn1), z])) -> BOT -> 20
}
Sat witness: Found: ((append([t1, l2, _nda])) -> append([cons(h1, t1), l2, cons(h1, _nda)]), {
_nda -> cons(z, cons(z, nil))  ;  h1 -> s(z)  ;  l2 -> cons(z, nil)  ;  t1 -> cons(z, nil)
})

-------------------------------------------
Step 35, which took 0.102316 s (model generation: 0.099911,  model checking: 0.002405):

Model:
|_
{
append -> 
{{{
Q={q_gen_8087, q_gen_8092, q_gen_8093, q_gen_8094, q_gen_8108, q_gen_8109, q_gen_8110, q_gen_8150},
Q_f={q_gen_8087, q_gen_8092},
Delta=
{
<cons>(q_gen_8109, q_gen_8108) -> q_gen_8108
<nil>() -> q_gen_8108
<s>(q_gen_8109) -> q_gen_8109
<z>() -> q_gen_8109
<cons, cons>(q_gen_8094, q_gen_8093) -> q_gen_8093
<nil, cons>(q_gen_8109, q_gen_8108) -> q_gen_8093
<nil, nil>() -> q_gen_8093
<s, s>(q_gen_8094) -> q_gen_8094
<z, z>() -> q_gen_8094
<nil, nil, nil>() -> q_gen_8087
<cons, cons, cons>(q_gen_8110, q_gen_8092) -> q_gen_8092
<cons, nil, cons>(q_gen_8094, q_gen_8093) -> q_gen_8092
<nil, cons, cons>(q_gen_8094, q_gen_8093) -> q_gen_8092
<nil, nil, cons>(q_gen_8109, q_gen_8108) -> q_gen_8092
<s, s, s>(q_gen_8110) -> q_gen_8110
<s, z, s>(q_gen_8094) -> q_gen_8110
<z, z, z>() -> q_gen_8110
<cons, cons, cons>(q_gen_8110, q_gen_8087) -> q_gen_8150
}

Datatype: <natlist, natlist, natlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_8086, q_gen_8090, q_gen_8091, q_gen_8105, q_gen_8125, q_gen_8126, q_gen_8127},
Q_f={q_gen_8086},
Delta=
{
<nil>() -> q_gen_8090
<s>(q_gen_8105) -> q_gen_8105
<z>() -> q_gen_8105
<cons>(q_gen_8105, q_gen_8090) -> q_gen_8125
<cons>(q_gen_8105, q_gen_8125) -> q_gen_8125
<cons, s>(q_gen_8091, q_gen_8090) -> q_gen_8086
<cons, s>(q_gen_8091, q_gen_8125) -> q_gen_8086
<cons, s>(q_gen_8126, q_gen_8125) -> q_gen_8086
<nil, z>() -> q_gen_8086
<s, s>(q_gen_8091) -> q_gen_8091
<s, z>(q_gen_8105) -> q_gen_8091
<z, z>() -> q_gen_8091
<s, s>(q_gen_8126) -> q_gen_8126
<z, s>(q_gen_8105) -> q_gen_8126
<cons, s>(q_gen_8126, q_gen_8090) -> q_gen_8127
}

Datatype: <natlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_8083, q_gen_8085, q_gen_8128},
Q_f={q_gen_8083},
Delta=
{
<s>(q_gen_8085) -> q_gen_8085
<z>() -> q_gen_8085
<s, s>(q_gen_8083) -> q_gen_8083
<z, s>(q_gen_8085) -> q_gen_8083
<z, z>() -> q_gen_8083
<s, s>(q_gen_8128) -> q_gen_8128
<s, z>(q_gen_8085) -> q_gen_8128
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_8082, q_gen_8102, q_gen_8122, q_gen_8123, q_gen_8151},
Q_f={q_gen_8082},
Delta=
{
<cons>(q_gen_8123, q_gen_8122) -> q_gen_8122
<nil>() -> q_gen_8122
<s>(q_gen_8123) -> q_gen_8123
<z>() -> q_gen_8123
<cons, cons>(q_gen_8102, q_gen_8082) -> q_gen_8082
<nil, cons>(q_gen_8123, q_gen_8122) -> q_gen_8082
<nil, nil>() -> q_gen_8082
<s, s>(q_gen_8102) -> q_gen_8102
<z, z>() -> q_gen_8102
<cons, cons>(q_gen_8102, q_gen_8151) -> q_gen_8151
<cons, nil>(q_gen_8123, q_gen_8122) -> q_gen_8151
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 20
() -> length([nil, z]) -> 20
() -> leq([z, s(nn2)]) -> 20
() -> leq([z, z]) -> 20
() -> reverse([nil, nil]) -> 20
(append([_sda, cons(h1, nil), _tda]) /\ reverse([t1, _sda])) -> reverse([cons(h1, t1), _tda]) -> 24
(append([t1, l2, _nda])) -> append([cons(h1, t1), l2, cons(h1, _nda)]) -> 22
(length([_cea, _dea]) /\ length([l1, _bea]) /\ reverse([l1, _cea])) -> leq([_bea, _dea]) -> 22
(length([ll, _xda])) -> length([cons(x, ll), s(_xda)]) -> 22
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 21
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 21
(leq([s(nn1), z])) -> BOT -> 21
}
Sat witness: Found: ((append([_sda, cons(h1, nil), _tda]) /\ reverse([t1, _sda])) -> reverse([cons(h1, t1), _tda]), {
_sda -> cons(z, cons(z, nil))  ;  _tda -> cons(z, cons(z, nil))  ;  h1 -> z  ;  t1 -> cons(z, cons(z, nil))
})

-------------------------------------------
Step 36, which took 0.140509 s (model generation: 0.138940,  model checking: 0.001569):

Model:
|_
{
append -> 
{{{
Q={q_gen_8087, q_gen_8093, q_gen_8094, q_gen_8107, q_gen_8108, q_gen_8109, q_gen_8110, q_gen_8118},
Q_f={q_gen_8087},
Delta=
{
<cons>(q_gen_8109, q_gen_8108) -> q_gen_8108
<nil>() -> q_gen_8108
<s>(q_gen_8109) -> q_gen_8109
<z>() -> q_gen_8109
<cons, cons>(q_gen_8094, q_gen_8093) -> q_gen_8093
<nil, nil>() -> q_gen_8093
<s, s>(q_gen_8094) -> q_gen_8094
<z, z>() -> q_gen_8094
<nil, cons>(q_gen_8109, q_gen_8108) -> q_gen_8118
<cons, cons, cons>(q_gen_8110, q_gen_8107) -> q_gen_8087
<cons, nil, cons>(q_gen_8094, q_gen_8093) -> q_gen_8087
<nil, cons, cons>(q_gen_8094, q_gen_8093) -> q_gen_8087
<nil, nil, nil>() -> q_gen_8087
<cons, cons, cons>(q_gen_8110, q_gen_8087) -> q_gen_8107
<cons, nil, cons>(q_gen_8094, q_gen_8118) -> q_gen_8107
<nil, cons, cons>(q_gen_8094, q_gen_8118) -> q_gen_8107
<nil, nil, cons>(q_gen_8109, q_gen_8108) -> q_gen_8107
<s, s, s>(q_gen_8110) -> q_gen_8110
<s, z, s>(q_gen_8094) -> q_gen_8110
<z, z, z>() -> q_gen_8110
}

Datatype: <natlist, natlist, natlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_8086, q_gen_8090, q_gen_8091, q_gen_8105, q_gen_8125, q_gen_8126, q_gen_8127},
Q_f={q_gen_8086},
Delta=
{
<nil>() -> q_gen_8090
<s>(q_gen_8105) -> q_gen_8105
<z>() -> q_gen_8105
<cons>(q_gen_8105, q_gen_8090) -> q_gen_8125
<cons>(q_gen_8105, q_gen_8125) -> q_gen_8125
<cons, s>(q_gen_8091, q_gen_8090) -> q_gen_8086
<cons, s>(q_gen_8091, q_gen_8125) -> q_gen_8086
<cons, s>(q_gen_8126, q_gen_8125) -> q_gen_8086
<nil, z>() -> q_gen_8086
<s, s>(q_gen_8091) -> q_gen_8091
<s, z>(q_gen_8105) -> q_gen_8091
<z, z>() -> q_gen_8091
<s, s>(q_gen_8126) -> q_gen_8126
<z, s>(q_gen_8105) -> q_gen_8126
<cons, s>(q_gen_8126, q_gen_8090) -> q_gen_8127
}

Datatype: <natlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_8083, q_gen_8085, q_gen_8128},
Q_f={q_gen_8083},
Delta=
{
<s>(q_gen_8085) -> q_gen_8085
<z>() -> q_gen_8085
<s, s>(q_gen_8083) -> q_gen_8083
<z, s>(q_gen_8085) -> q_gen_8083
<z, z>() -> q_gen_8083
<s, s>(q_gen_8128) -> q_gen_8128
<s, z>(q_gen_8085) -> q_gen_8128
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_8082, q_gen_8102, q_gen_8120, q_gen_8122, q_gen_8123},
Q_f={q_gen_8082},
Delta=
{
<cons>(q_gen_8123, q_gen_8122) -> q_gen_8122
<nil>() -> q_gen_8122
<s>(q_gen_8123) -> q_gen_8123
<z>() -> q_gen_8123
<cons, cons>(q_gen_8102, q_gen_8082) -> q_gen_8082
<nil, nil>() -> q_gen_8082
<s, s>(q_gen_8102) -> q_gen_8102
<z, z>() -> q_gen_8102
<cons, cons>(q_gen_8102, q_gen_8120) -> q_gen_8120
<cons, nil>(q_gen_8123, q_gen_8122) -> q_gen_8120
<nil, cons>(q_gen_8123, q_gen_8122) -> q_gen_8120
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 21
() -> length([nil, z]) -> 21
() -> leq([z, s(nn2)]) -> 21
() -> leq([z, z]) -> 21
() -> reverse([nil, nil]) -> 21
(append([_sda, cons(h1, nil), _tda]) /\ reverse([t1, _sda])) -> reverse([cons(h1, t1), _tda]) -> 24
(append([t1, l2, _nda])) -> append([cons(h1, t1), l2, cons(h1, _nda)]) -> 22
(length([_cea, _dea]) /\ length([l1, _bea]) /\ reverse([l1, _cea])) -> leq([_bea, _dea]) -> 25
(length([ll, _xda])) -> length([cons(x, ll), s(_xda)]) -> 23
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 22
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 22
(leq([s(nn1), z])) -> BOT -> 22
}
Sat witness: Found: ((length([_cea, _dea]) /\ length([l1, _bea]) /\ reverse([l1, _cea])) -> leq([_bea, _dea]), {
_bea -> s(s(z))  ;  _cea -> cons(z, cons(z, nil))  ;  _dea -> s(z)  ;  l1 -> cons(z, cons(z, nil))
})

-------------------------------------------
Step 37, which took 0.109146 s (model generation: 0.107603,  model checking: 0.001543):

Model:
|_
{
append -> 
{{{
Q={q_gen_8087, q_gen_8093, q_gen_8094, q_gen_8107, q_gen_8108, q_gen_8109, q_gen_8110, q_gen_8149},
Q_f={q_gen_8087},
Delta=
{
<cons>(q_gen_8109, q_gen_8108) -> q_gen_8108
<nil>() -> q_gen_8108
<s>(q_gen_8109) -> q_gen_8109
<z>() -> q_gen_8109
<cons, cons>(q_gen_8094, q_gen_8093) -> q_gen_8093
<nil, cons>(q_gen_8109, q_gen_8108) -> q_gen_8093
<nil, nil>() -> q_gen_8093
<s, s>(q_gen_8094) -> q_gen_8094
<z, z>() -> q_gen_8094
<cons, cons, cons>(q_gen_8110, q_gen_8107) -> q_gen_8087
<cons, cons, cons>(q_gen_8149, q_gen_8087) -> q_gen_8087
<cons, cons, cons>(q_gen_8149, q_gen_8107) -> q_gen_8087
<cons, nil, cons>(q_gen_8094, q_gen_8093) -> q_gen_8087
<nil, cons, cons>(q_gen_8094, q_gen_8093) -> q_gen_8087
<nil, nil, nil>() -> q_gen_8087
<cons, cons, cons>(q_gen_8110, q_gen_8087) -> q_gen_8107
<nil, nil, cons>(q_gen_8109, q_gen_8108) -> q_gen_8107
<z, z, z>() -> q_gen_8110
<s, s, s>(q_gen_8110) -> q_gen_8149
<s, z, s>(q_gen_8094) -> q_gen_8149
}

Datatype: <natlist, natlist, natlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_8086, q_gen_8090, q_gen_8091, q_gen_8105, q_gen_8125, q_gen_8126, q_gen_8127},
Q_f={q_gen_8086},
Delta=
{
<nil>() -> q_gen_8090
<s>(q_gen_8105) -> q_gen_8105
<z>() -> q_gen_8105
<cons>(q_gen_8105, q_gen_8090) -> q_gen_8125
<cons>(q_gen_8105, q_gen_8125) -> q_gen_8125
<cons, s>(q_gen_8091, q_gen_8090) -> q_gen_8086
<cons, s>(q_gen_8126, q_gen_8125) -> q_gen_8086
<nil, z>() -> q_gen_8086
<s, z>(q_gen_8105) -> q_gen_8091
<z, z>() -> q_gen_8091
<s, s>(q_gen_8091) -> q_gen_8126
<s, s>(q_gen_8126) -> q_gen_8126
<z, s>(q_gen_8105) -> q_gen_8126
<cons, s>(q_gen_8091, q_gen_8125) -> q_gen_8127
<cons, s>(q_gen_8126, q_gen_8090) -> q_gen_8127
}

Datatype: <natlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_8083, q_gen_8085, q_gen_8128},
Q_f={q_gen_8083},
Delta=
{
<s>(q_gen_8085) -> q_gen_8085
<z>() -> q_gen_8085
<s, s>(q_gen_8083) -> q_gen_8083
<z, s>(q_gen_8085) -> q_gen_8083
<z, z>() -> q_gen_8083
<s, s>(q_gen_8128) -> q_gen_8128
<s, z>(q_gen_8085) -> q_gen_8128
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_8082, q_gen_8102, q_gen_8122, q_gen_8123, q_gen_8151},
Q_f={q_gen_8082},
Delta=
{
<cons>(q_gen_8123, q_gen_8122) -> q_gen_8122
<nil>() -> q_gen_8122
<s>(q_gen_8123) -> q_gen_8123
<z>() -> q_gen_8123
<cons, cons>(q_gen_8102, q_gen_8082) -> q_gen_8082
<nil, cons>(q_gen_8123, q_gen_8122) -> q_gen_8082
<nil, nil>() -> q_gen_8082
<s, s>(q_gen_8102) -> q_gen_8102
<z, z>() -> q_gen_8102
<cons, cons>(q_gen_8102, q_gen_8151) -> q_gen_8151
<cons, nil>(q_gen_8123, q_gen_8122) -> q_gen_8151
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 22
() -> length([nil, z]) -> 22
() -> leq([z, s(nn2)]) -> 22
() -> leq([z, z]) -> 22
() -> reverse([nil, nil]) -> 22
(append([_sda, cons(h1, nil), _tda]) /\ reverse([t1, _sda])) -> reverse([cons(h1, t1), _tda]) -> 24
(append([t1, l2, _nda])) -> append([cons(h1, t1), l2, cons(h1, _nda)]) -> 25
(length([_cea, _dea]) /\ length([l1, _bea]) /\ reverse([l1, _cea])) -> leq([_bea, _dea]) -> 25
(length([ll, _xda])) -> length([cons(x, ll), s(_xda)]) -> 23
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 23
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 23
(leq([s(nn1), z])) -> BOT -> 23
}
Sat witness: Found: ((append([t1, l2, _nda])) -> append([cons(h1, t1), l2, cons(h1, _nda)]), {
_nda -> cons(s(z), nil)  ;  h1 -> z  ;  l2 -> cons(z, nil)  ;  t1 -> cons(s(z), nil)
})

-------------------------------------------
Step 38, which took 0.159772 s (model generation: 0.157740,  model checking: 0.002032):

Model:
|_
{
append -> 
{{{
Q={q_gen_8087, q_gen_8093, q_gen_8094, q_gen_8107, q_gen_8108, q_gen_8109, q_gen_8110, q_gen_8118},
Q_f={q_gen_8087},
Delta=
{
<cons>(q_gen_8109, q_gen_8108) -> q_gen_8108
<nil>() -> q_gen_8108
<s>(q_gen_8109) -> q_gen_8109
<z>() -> q_gen_8109
<cons, cons>(q_gen_8094, q_gen_8093) -> q_gen_8093
<nil, nil>() -> q_gen_8093
<s, s>(q_gen_8094) -> q_gen_8094
<z, z>() -> q_gen_8094
<nil, cons>(q_gen_8109, q_gen_8108) -> q_gen_8118
<cons, cons, cons>(q_gen_8110, q_gen_8107) -> q_gen_8087
<cons, nil, cons>(q_gen_8094, q_gen_8093) -> q_gen_8087
<nil, cons, cons>(q_gen_8094, q_gen_8093) -> q_gen_8087
<nil, nil, nil>() -> q_gen_8087
<cons, cons, cons>(q_gen_8110, q_gen_8087) -> q_gen_8107
<cons, nil, cons>(q_gen_8094, q_gen_8118) -> q_gen_8107
<nil, cons, cons>(q_gen_8094, q_gen_8118) -> q_gen_8107
<nil, nil, cons>(q_gen_8109, q_gen_8108) -> q_gen_8107
<s, s, s>(q_gen_8110) -> q_gen_8110
<s, z, s>(q_gen_8094) -> q_gen_8110
<z, z, z>() -> q_gen_8110
}

Datatype: <natlist, natlist, natlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_8086, q_gen_8090, q_gen_8091, q_gen_8105, q_gen_8125, q_gen_8126, q_gen_8127},
Q_f={q_gen_8086},
Delta=
{
<nil>() -> q_gen_8090
<s>(q_gen_8105) -> q_gen_8105
<z>() -> q_gen_8105
<cons>(q_gen_8105, q_gen_8090) -> q_gen_8125
<cons>(q_gen_8105, q_gen_8125) -> q_gen_8125
<cons, s>(q_gen_8091, q_gen_8090) -> q_gen_8086
<cons, s>(q_gen_8126, q_gen_8125) -> q_gen_8086
<nil, z>() -> q_gen_8086
<s, z>(q_gen_8105) -> q_gen_8091
<z, z>() -> q_gen_8091
<s, s>(q_gen_8091) -> q_gen_8126
<s, s>(q_gen_8126) -> q_gen_8126
<z, s>(q_gen_8105) -> q_gen_8126
<cons, s>(q_gen_8091, q_gen_8125) -> q_gen_8127
<cons, s>(q_gen_8126, q_gen_8090) -> q_gen_8127
}

Datatype: <natlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_8083, q_gen_8085, q_gen_8128},
Q_f={q_gen_8083},
Delta=
{
<s>(q_gen_8085) -> q_gen_8085
<z>() -> q_gen_8085
<s, s>(q_gen_8083) -> q_gen_8083
<z, s>(q_gen_8085) -> q_gen_8083
<z, z>() -> q_gen_8083
<s, s>(q_gen_8128) -> q_gen_8128
<s, z>(q_gen_8085) -> q_gen_8128
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_8082, q_gen_8102, q_gen_8122, q_gen_8123, q_gen_8151},
Q_f={q_gen_8082},
Delta=
{
<cons>(q_gen_8123, q_gen_8122) -> q_gen_8122
<nil>() -> q_gen_8122
<s>(q_gen_8123) -> q_gen_8123
<z>() -> q_gen_8123
<cons, cons>(q_gen_8102, q_gen_8082) -> q_gen_8082
<nil, cons>(q_gen_8123, q_gen_8122) -> q_gen_8082
<nil, nil>() -> q_gen_8082
<s, s>(q_gen_8102) -> q_gen_8102
<z, z>() -> q_gen_8102
<cons, cons>(q_gen_8102, q_gen_8151) -> q_gen_8151
<cons, nil>(q_gen_8123, q_gen_8122) -> q_gen_8151
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 23
() -> length([nil, z]) -> 23
() -> leq([z, s(nn2)]) -> 23
() -> leq([z, z]) -> 23
() -> reverse([nil, nil]) -> 23
(append([_sda, cons(h1, nil), _tda]) /\ reverse([t1, _sda])) -> reverse([cons(h1, t1), _tda]) -> 27
(append([t1, l2, _nda])) -> append([cons(h1, t1), l2, cons(h1, _nda)]) -> 25
(length([_cea, _dea]) /\ length([l1, _bea]) /\ reverse([l1, _cea])) -> leq([_bea, _dea]) -> 25
(length([ll, _xda])) -> length([cons(x, ll), s(_xda)]) -> 24
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 24
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 24
(leq([s(nn1), z])) -> BOT -> 24
}
Sat witness: Found: ((append([_sda, cons(h1, nil), _tda]) /\ reverse([t1, _sda])) -> reverse([cons(h1, t1), _tda]), {
_sda -> cons(s(z), nil)  ;  _tda -> cons(s(z), cons(z, nil))  ;  h1 -> z  ;  t1 -> nil
})

-------------------------------------------
Step 39, which took 0.473450 s (model generation: 0.472021,  model checking: 0.001429):

Model:
|_
{
append -> 
{{{
Q={q_gen_8087, q_gen_8093, q_gen_8094, q_gen_8107, q_gen_8108, q_gen_8109, q_gen_8110, q_gen_8118},
Q_f={q_gen_8087},
Delta=
{
<cons>(q_gen_8109, q_gen_8108) -> q_gen_8108
<nil>() -> q_gen_8108
<s>(q_gen_8109) -> q_gen_8109
<z>() -> q_gen_8109
<cons, cons>(q_gen_8094, q_gen_8093) -> q_gen_8093
<nil, nil>() -> q_gen_8093
<s, s>(q_gen_8094) -> q_gen_8094
<z, z>() -> q_gen_8094
<nil, cons>(q_gen_8109, q_gen_8108) -> q_gen_8118
<cons, cons, cons>(q_gen_8110, q_gen_8107) -> q_gen_8087
<cons, nil, cons>(q_gen_8094, q_gen_8093) -> q_gen_8087
<nil, cons, cons>(q_gen_8094, q_gen_8093) -> q_gen_8087
<nil, nil, nil>() -> q_gen_8087
<cons, cons, cons>(q_gen_8110, q_gen_8087) -> q_gen_8107
<cons, nil, cons>(q_gen_8094, q_gen_8118) -> q_gen_8107
<nil, cons, cons>(q_gen_8094, q_gen_8118) -> q_gen_8107
<nil, nil, cons>(q_gen_8109, q_gen_8108) -> q_gen_8107
<s, s, s>(q_gen_8110) -> q_gen_8110
<s, z, s>(q_gen_8094) -> q_gen_8110
<z, z, z>() -> q_gen_8110
}

Datatype: <natlist, natlist, natlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_8086, q_gen_8090, q_gen_8091, q_gen_8105, q_gen_8125, q_gen_8126, q_gen_8127},
Q_f={q_gen_8086},
Delta=
{
<nil>() -> q_gen_8090
<s>(q_gen_8105) -> q_gen_8105
<z>() -> q_gen_8105
<cons>(q_gen_8105, q_gen_8090) -> q_gen_8125
<cons>(q_gen_8105, q_gen_8125) -> q_gen_8125
<cons, s>(q_gen_8091, q_gen_8090) -> q_gen_8086
<cons, s>(q_gen_8126, q_gen_8125) -> q_gen_8086
<nil, z>() -> q_gen_8086
<s, z>(q_gen_8105) -> q_gen_8091
<z, z>() -> q_gen_8091
<s, s>(q_gen_8091) -> q_gen_8126
<s, s>(q_gen_8126) -> q_gen_8126
<z, s>(q_gen_8105) -> q_gen_8126
<cons, s>(q_gen_8091, q_gen_8125) -> q_gen_8127
<cons, s>(q_gen_8126, q_gen_8090) -> q_gen_8127
}

Datatype: <natlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_8083, q_gen_8085, q_gen_8128},
Q_f={q_gen_8083},
Delta=
{
<s>(q_gen_8085) -> q_gen_8085
<z>() -> q_gen_8085
<s, s>(q_gen_8083) -> q_gen_8083
<z, s>(q_gen_8085) -> q_gen_8083
<z, z>() -> q_gen_8083
<s, s>(q_gen_8128) -> q_gen_8128
<s, z>(q_gen_8085) -> q_gen_8128
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_8082, q_gen_8102, q_gen_8120, q_gen_8122, q_gen_8123},
Q_f={q_gen_8082},
Delta=
{
<cons>(q_gen_8123, q_gen_8122) -> q_gen_8122
<nil>() -> q_gen_8122
<s>(q_gen_8123) -> q_gen_8123
<z>() -> q_gen_8123
<cons, cons>(q_gen_8102, q_gen_8082) -> q_gen_8082
<nil, nil>() -> q_gen_8082
<s, s>(q_gen_8102) -> q_gen_8102
<z, s>(q_gen_8123) -> q_gen_8102
<z, z>() -> q_gen_8102
<cons, cons>(q_gen_8102, q_gen_8120) -> q_gen_8120
<cons, nil>(q_gen_8123, q_gen_8122) -> q_gen_8120
<nil, cons>(q_gen_8123, q_gen_8122) -> q_gen_8120
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 24
() -> length([nil, z]) -> 24
() -> leq([z, s(nn2)]) -> 24
() -> leq([z, z]) -> 24
() -> reverse([nil, nil]) -> 24
(append([_sda, cons(h1, nil), _tda]) /\ reverse([t1, _sda])) -> reverse([cons(h1, t1), _tda]) -> 27
(append([t1, l2, _nda])) -> append([cons(h1, t1), l2, cons(h1, _nda)]) -> 25
(length([_cea, _dea]) /\ length([l1, _bea]) /\ reverse([l1, _cea])) -> leq([_bea, _dea]) -> 28
(length([ll, _xda])) -> length([cons(x, ll), s(_xda)]) -> 25
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 25
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 25
(leq([s(nn1), z])) -> BOT -> 25
}
Sat witness: Found: ((length([_cea, _dea]) /\ length([l1, _bea]) /\ reverse([l1, _cea])) -> leq([_bea, _dea]), {
_bea -> s(s(s(z)))  ;  _cea -> cons(s(z), cons(z, nil))  ;  _dea -> s(s(z))  ;  l1 -> cons(s(z), cons(z, nil))
})

-------------------------------------------
Step 40, which took 0.107869 s (model generation: 0.104257,  model checking: 0.003612):

Model:
|_
{
append -> 
{{{
Q={q_gen_8087, q_gen_8093, q_gen_8094, q_gen_8107, q_gen_8108, q_gen_8109, q_gen_8110, q_gen_8118},
Q_f={q_gen_8087},
Delta=
{
<cons>(q_gen_8109, q_gen_8108) -> q_gen_8108
<nil>() -> q_gen_8108
<s>(q_gen_8109) -> q_gen_8109
<z>() -> q_gen_8109
<cons, cons>(q_gen_8094, q_gen_8093) -> q_gen_8093
<nil, nil>() -> q_gen_8093
<s, s>(q_gen_8094) -> q_gen_8094
<z, z>() -> q_gen_8094
<nil, cons>(q_gen_8109, q_gen_8108) -> q_gen_8118
<cons, cons, cons>(q_gen_8110, q_gen_8107) -> q_gen_8087
<cons, nil, cons>(q_gen_8094, q_gen_8093) -> q_gen_8087
<nil, cons, cons>(q_gen_8094, q_gen_8093) -> q_gen_8087
<nil, nil, nil>() -> q_gen_8087
<cons, cons, cons>(q_gen_8110, q_gen_8087) -> q_gen_8107
<cons, nil, cons>(q_gen_8094, q_gen_8118) -> q_gen_8107
<nil, cons, cons>(q_gen_8094, q_gen_8118) -> q_gen_8107
<nil, nil, cons>(q_gen_8109, q_gen_8108) -> q_gen_8107
<s, s, s>(q_gen_8110) -> q_gen_8110
<s, z, s>(q_gen_8094) -> q_gen_8110
<z, z, z>() -> q_gen_8110
}

Datatype: <natlist, natlist, natlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_8086, q_gen_8090, q_gen_8091, q_gen_8105, q_gen_8116, q_gen_8125, q_gen_8126, q_gen_8127},
Q_f={q_gen_8086},
Delta=
{
<cons>(q_gen_8105, q_gen_8125) -> q_gen_8090
<nil>() -> q_gen_8090
<z>() -> q_gen_8105
<s>(q_gen_8105) -> q_gen_8116
<cons>(q_gen_8105, q_gen_8090) -> q_gen_8125
<cons>(q_gen_8116, q_gen_8090) -> q_gen_8125
<cons, s>(q_gen_8091, q_gen_8090) -> q_gen_8086
<cons, s>(q_gen_8126, q_gen_8125) -> q_gen_8086
<nil, z>() -> q_gen_8086
<s, s>(q_gen_8126) -> q_gen_8091
<s, z>(q_gen_8105) -> q_gen_8091
<s, z>(q_gen_8116) -> q_gen_8091
<z, s>(q_gen_8116) -> q_gen_8091
<z, z>() -> q_gen_8091
<s, s>(q_gen_8091) -> q_gen_8126
<z, s>(q_gen_8105) -> q_gen_8126
<cons, s>(q_gen_8091, q_gen_8125) -> q_gen_8127
<cons, s>(q_gen_8126, q_gen_8090) -> q_gen_8127
}

Datatype: <natlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_8083, q_gen_8085, q_gen_8128},
Q_f={q_gen_8083},
Delta=
{
<s>(q_gen_8085) -> q_gen_8085
<z>() -> q_gen_8085
<s, s>(q_gen_8083) -> q_gen_8083
<z, s>(q_gen_8085) -> q_gen_8083
<z, z>() -> q_gen_8083
<s, s>(q_gen_8128) -> q_gen_8128
<s, z>(q_gen_8085) -> q_gen_8128
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_8082, q_gen_8102, q_gen_8120, q_gen_8122, q_gen_8123},
Q_f={q_gen_8082},
Delta=
{
<cons>(q_gen_8123, q_gen_8122) -> q_gen_8122
<nil>() -> q_gen_8122
<s>(q_gen_8123) -> q_gen_8123
<z>() -> q_gen_8123
<cons, cons>(q_gen_8102, q_gen_8082) -> q_gen_8082
<nil, nil>() -> q_gen_8082
<s, s>(q_gen_8102) -> q_gen_8102
<z, s>(q_gen_8123) -> q_gen_8102
<z, z>() -> q_gen_8102
<cons, cons>(q_gen_8102, q_gen_8120) -> q_gen_8120
<cons, nil>(q_gen_8123, q_gen_8122) -> q_gen_8120
<nil, cons>(q_gen_8123, q_gen_8122) -> q_gen_8120
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 25
() -> length([nil, z]) -> 25
() -> leq([z, s(nn2)]) -> 25
() -> leq([z, z]) -> 25
() -> reverse([nil, nil]) -> 25
(append([_sda, cons(h1, nil), _tda]) /\ reverse([t1, _sda])) -> reverse([cons(h1, t1), _tda]) -> 27
(append([t1, l2, _nda])) -> append([cons(h1, t1), l2, cons(h1, _nda)]) -> 25
(length([_cea, _dea]) /\ length([l1, _bea]) /\ reverse([l1, _cea])) -> leq([_bea, _dea]) -> 28
(length([ll, _xda])) -> length([cons(x, ll), s(_xda)]) -> 28
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 26
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 26
(leq([s(nn1), z])) -> BOT -> 26
}
Sat witness: Found: ((length([ll, _xda])) -> length([cons(x, ll), s(_xda)]), {
_xda -> z  ;  ll -> nil  ;  x -> s(s(s(z)))
})

-------------------------------------------
Step 41, which took 0.401858 s (model generation: 0.400377,  model checking: 0.001481):

Model:
|_
{
append -> 
{{{
Q={q_gen_8087, q_gen_8092, q_gen_8093, q_gen_8094, q_gen_8108, q_gen_8109, q_gen_8110, q_gen_8150},
Q_f={q_gen_8087, q_gen_8092},
Delta=
{
<cons>(q_gen_8109, q_gen_8108) -> q_gen_8108
<nil>() -> q_gen_8108
<s>(q_gen_8109) -> q_gen_8109
<z>() -> q_gen_8109
<cons, cons>(q_gen_8094, q_gen_8093) -> q_gen_8093
<nil, cons>(q_gen_8109, q_gen_8108) -> q_gen_8093
<nil, nil>() -> q_gen_8093
<s, s>(q_gen_8094) -> q_gen_8094
<z, z>() -> q_gen_8094
<cons, cons, cons>(q_gen_8110, q_gen_8092) -> q_gen_8087
<nil, cons, cons>(q_gen_8094, q_gen_8093) -> q_gen_8087
<nil, nil, nil>() -> q_gen_8087
<cons, nil, cons>(q_gen_8094, q_gen_8093) -> q_gen_8092
<nil, nil, cons>(q_gen_8109, q_gen_8108) -> q_gen_8092
<s, s, s>(q_gen_8110) -> q_gen_8110
<s, z, s>(q_gen_8094) -> q_gen_8110
<z, z, z>() -> q_gen_8110
<cons, cons, cons>(q_gen_8110, q_gen_8087) -> q_gen_8150
}

Datatype: <natlist, natlist, natlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_8086, q_gen_8090, q_gen_8091, q_gen_8105, q_gen_8125, q_gen_8126, q_gen_8127},
Q_f={q_gen_8086},
Delta=
{
<nil>() -> q_gen_8090
<s>(q_gen_8105) -> q_gen_8105
<z>() -> q_gen_8105
<cons>(q_gen_8105, q_gen_8090) -> q_gen_8125
<cons>(q_gen_8105, q_gen_8125) -> q_gen_8125
<cons, s>(q_gen_8091, q_gen_8090) -> q_gen_8086
<cons, s>(q_gen_8126, q_gen_8125) -> q_gen_8086
<nil, z>() -> q_gen_8086
<s, z>(q_gen_8105) -> q_gen_8091
<z, z>() -> q_gen_8091
<s, s>(q_gen_8091) -> q_gen_8126
<s, s>(q_gen_8126) -> q_gen_8126
<z, s>(q_gen_8105) -> q_gen_8126
<cons, s>(q_gen_8091, q_gen_8125) -> q_gen_8127
<cons, s>(q_gen_8126, q_gen_8090) -> q_gen_8127
}

Datatype: <natlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_8083, q_gen_8085, q_gen_8128},
Q_f={q_gen_8083},
Delta=
{
<s>(q_gen_8085) -> q_gen_8085
<z>() -> q_gen_8085
<s, s>(q_gen_8083) -> q_gen_8083
<z, s>(q_gen_8085) -> q_gen_8083
<z, z>() -> q_gen_8083
<s, s>(q_gen_8128) -> q_gen_8128
<s, z>(q_gen_8085) -> q_gen_8128
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_8082, q_gen_8101, q_gen_8102, q_gen_8122, q_gen_8123, q_gen_8151},
Q_f={q_gen_8082, q_gen_8101},
Delta=
{
<cons>(q_gen_8123, q_gen_8122) -> q_gen_8122
<nil>() -> q_gen_8122
<s>(q_gen_8123) -> q_gen_8123
<z>() -> q_gen_8123
<nil, cons>(q_gen_8123, q_gen_8122) -> q_gen_8082
<nil, nil>() -> q_gen_8082
<cons, cons>(q_gen_8102, q_gen_8082) -> q_gen_8101
<s, s>(q_gen_8102) -> q_gen_8102
<z, s>(q_gen_8123) -> q_gen_8102
<z, z>() -> q_gen_8102
<cons, cons>(q_gen_8102, q_gen_8101) -> q_gen_8151
<cons, cons>(q_gen_8102, q_gen_8151) -> q_gen_8151
<cons, nil>(q_gen_8123, q_gen_8122) -> q_gen_8151
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 25
() -> length([nil, z]) -> 25
() -> leq([z, s(nn2)]) -> 25
() -> leq([z, z]) -> 25
() -> reverse([nil, nil]) -> 25
(append([_sda, cons(h1, nil), _tda]) /\ reverse([t1, _sda])) -> reverse([cons(h1, t1), _tda]) -> 27
(append([t1, l2, _nda])) -> append([cons(h1, t1), l2, cons(h1, _nda)]) -> 28
(length([_cea, _dea]) /\ length([l1, _bea]) /\ reverse([l1, _cea])) -> leq([_bea, _dea]) -> 28
(length([ll, _xda])) -> length([cons(x, ll), s(_xda)]) -> 28
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 26
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 26
(leq([s(nn1), z])) -> BOT -> 26
}
Sat witness: Found: ((append([t1, l2, _nda])) -> append([cons(h1, t1), l2, cons(h1, _nda)]), {
_nda -> cons(z, cons(z, nil))  ;  h1 -> s(z)  ;  l2 -> cons(z, cons(z, nil))  ;  t1 -> nil
})

-------------------------------------------
Step 42, which took 0.481121 s (model generation: 0.477744,  model checking: 0.003377):

Model:
|_
{
append -> 
{{{
Q={q_gen_8087, q_gen_8093, q_gen_8094, q_gen_8107, q_gen_8108, q_gen_8109, q_gen_8110, q_gen_8118},
Q_f={q_gen_8087},
Delta=
{
<cons>(q_gen_8109, q_gen_8108) -> q_gen_8108
<nil>() -> q_gen_8108
<s>(q_gen_8109) -> q_gen_8109
<z>() -> q_gen_8109
<cons, cons>(q_gen_8094, q_gen_8093) -> q_gen_8093
<nil, nil>() -> q_gen_8093
<s, s>(q_gen_8094) -> q_gen_8094
<z, z>() -> q_gen_8094
<nil, cons>(q_gen_8109, q_gen_8108) -> q_gen_8118
<cons, cons, cons>(q_gen_8110, q_gen_8107) -> q_gen_8087
<cons, nil, cons>(q_gen_8094, q_gen_8093) -> q_gen_8087
<nil, cons, cons>(q_gen_8094, q_gen_8093) -> q_gen_8087
<nil, nil, nil>() -> q_gen_8087
<cons, cons, cons>(q_gen_8110, q_gen_8087) -> q_gen_8107
<cons, nil, cons>(q_gen_8094, q_gen_8118) -> q_gen_8107
<nil, cons, cons>(q_gen_8094, q_gen_8118) -> q_gen_8107
<nil, nil, cons>(q_gen_8109, q_gen_8108) -> q_gen_8107
<s, s, s>(q_gen_8110) -> q_gen_8110
<s, z, s>(q_gen_8094) -> q_gen_8110
<z, z, z>() -> q_gen_8110
}

Datatype: <natlist, natlist, natlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_8086, q_gen_8090, q_gen_8091, q_gen_8104, q_gen_8105, q_gen_8125, q_gen_8126, q_gen_8127},
Q_f={q_gen_8086},
Delta=
{
<cons>(q_gen_8105, q_gen_8125) -> q_gen_8090
<nil>() -> q_gen_8090
<s>(q_gen_8105) -> q_gen_8105
<z>() -> q_gen_8105
<cons>(q_gen_8105, q_gen_8090) -> q_gen_8125
<cons, s>(q_gen_8091, q_gen_8090) -> q_gen_8086
<cons, s>(q_gen_8104, q_gen_8090) -> q_gen_8086
<cons, s>(q_gen_8104, q_gen_8125) -> q_gen_8086
<cons, s>(q_gen_8126, q_gen_8125) -> q_gen_8086
<nil, z>() -> q_gen_8086
<s, s>(q_gen_8091) -> q_gen_8091
<z, z>() -> q_gen_8091
<s, s>(q_gen_8126) -> q_gen_8104
<s, z>(q_gen_8105) -> q_gen_8104
<z, s>(q_gen_8105) -> q_gen_8126
<cons, s>(q_gen_8091, q_gen_8125) -> q_gen_8127
<cons, s>(q_gen_8126, q_gen_8090) -> q_gen_8127
}

Datatype: <natlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_8083, q_gen_8085, q_gen_8128},
Q_f={q_gen_8083},
Delta=
{
<s>(q_gen_8085) -> q_gen_8085
<z>() -> q_gen_8085
<s, s>(q_gen_8083) -> q_gen_8083
<z, s>(q_gen_8085) -> q_gen_8083
<z, z>() -> q_gen_8083
<s, s>(q_gen_8128) -> q_gen_8128
<s, z>(q_gen_8085) -> q_gen_8128
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_8082, q_gen_8102, q_gen_8120, q_gen_8122, q_gen_8123},
Q_f={q_gen_8082},
Delta=
{
<cons>(q_gen_8123, q_gen_8122) -> q_gen_8122
<nil>() -> q_gen_8122
<s>(q_gen_8123) -> q_gen_8123
<z>() -> q_gen_8123
<cons, cons>(q_gen_8102, q_gen_8082) -> q_gen_8082
<nil, nil>() -> q_gen_8082
<s, s>(q_gen_8102) -> q_gen_8102
<z, s>(q_gen_8123) -> q_gen_8102
<z, z>() -> q_gen_8102
<cons, cons>(q_gen_8102, q_gen_8120) -> q_gen_8120
<cons, nil>(q_gen_8123, q_gen_8122) -> q_gen_8120
<nil, cons>(q_gen_8123, q_gen_8122) -> q_gen_8120
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 26
() -> length([nil, z]) -> 26
() -> leq([z, s(nn2)]) -> 26
() -> leq([z, z]) -> 26
() -> reverse([nil, nil]) -> 26
(append([_sda, cons(h1, nil), _tda]) /\ reverse([t1, _sda])) -> reverse([cons(h1, t1), _tda]) -> 30
(append([t1, l2, _nda])) -> append([cons(h1, t1), l2, cons(h1, _nda)]) -> 28
(length([_cea, _dea]) /\ length([l1, _bea]) /\ reverse([l1, _cea])) -> leq([_bea, _dea]) -> 28
(length([ll, _xda])) -> length([cons(x, ll), s(_xda)]) -> 28
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 27
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 27
(leq([s(nn1), z])) -> BOT -> 27
}
Sat witness: Found: ((append([_sda, cons(h1, nil), _tda]) /\ reverse([t1, _sda])) -> reverse([cons(h1, t1), _tda]), {
_sda -> cons(z, nil)  ;  _tda -> cons(z, cons(z, cons(z, nil)))  ;  h1 -> z  ;  t1 -> cons(z, nil)
})

-------------------------------------------
Step 43, which took 0.687124 s (model generation: 0.685777,  model checking: 0.001347):

Model:
|_
{
append -> 
{{{
Q={q_gen_8087, q_gen_8093, q_gen_8094, q_gen_8107, q_gen_8108, q_gen_8109, q_gen_8110, q_gen_8118},
Q_f={q_gen_8087},
Delta=
{
<cons>(q_gen_8109, q_gen_8108) -> q_gen_8108
<nil>() -> q_gen_8108
<s>(q_gen_8109) -> q_gen_8109
<z>() -> q_gen_8109
<cons, cons>(q_gen_8094, q_gen_8093) -> q_gen_8093
<nil, nil>() -> q_gen_8093
<s, s>(q_gen_8094) -> q_gen_8094
<z, z>() -> q_gen_8094
<nil, cons>(q_gen_8109, q_gen_8108) -> q_gen_8118
<cons, cons, cons>(q_gen_8110, q_gen_8107) -> q_gen_8087
<cons, nil, cons>(q_gen_8094, q_gen_8093) -> q_gen_8087
<nil, cons, cons>(q_gen_8094, q_gen_8093) -> q_gen_8087
<nil, nil, nil>() -> q_gen_8087
<cons, cons, cons>(q_gen_8110, q_gen_8087) -> q_gen_8107
<cons, nil, cons>(q_gen_8094, q_gen_8118) -> q_gen_8107
<nil, cons, cons>(q_gen_8094, q_gen_8118) -> q_gen_8107
<nil, nil, cons>(q_gen_8109, q_gen_8108) -> q_gen_8107
<s, s, s>(q_gen_8110) -> q_gen_8110
<s, z, s>(q_gen_8094) -> q_gen_8110
<z, z, z>() -> q_gen_8110
}

Datatype: <natlist, natlist, natlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_8086, q_gen_8090, q_gen_8091, q_gen_8104, q_gen_8105, q_gen_8125, q_gen_8126, q_gen_8127},
Q_f={q_gen_8086},
Delta=
{
<nil>() -> q_gen_8090
<s>(q_gen_8105) -> q_gen_8105
<z>() -> q_gen_8105
<cons>(q_gen_8105, q_gen_8090) -> q_gen_8125
<cons>(q_gen_8105, q_gen_8125) -> q_gen_8125
<cons, s>(q_gen_8091, q_gen_8090) -> q_gen_8086
<cons, s>(q_gen_8104, q_gen_8090) -> q_gen_8086
<cons, s>(q_gen_8126, q_gen_8125) -> q_gen_8086
<nil, z>() -> q_gen_8086
<z, z>() -> q_gen_8091
<s, s>(q_gen_8091) -> q_gen_8104
<s, z>(q_gen_8105) -> q_gen_8104
<s, s>(q_gen_8104) -> q_gen_8126
<s, s>(q_gen_8126) -> q_gen_8126
<z, s>(q_gen_8105) -> q_gen_8126
<cons, s>(q_gen_8091, q_gen_8125) -> q_gen_8127
<cons, s>(q_gen_8104, q_gen_8125) -> q_gen_8127
<cons, s>(q_gen_8126, q_gen_8090) -> q_gen_8127
}

Datatype: <natlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_8083, q_gen_8085, q_gen_8128},
Q_f={q_gen_8083},
Delta=
{
<s>(q_gen_8085) -> q_gen_8085
<z>() -> q_gen_8085
<s, s>(q_gen_8083) -> q_gen_8083
<z, s>(q_gen_8085) -> q_gen_8083
<z, z>() -> q_gen_8083
<s, s>(q_gen_8128) -> q_gen_8128
<s, z>(q_gen_8085) -> q_gen_8128
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_8082, q_gen_8102, q_gen_8122, q_gen_8123, q_gen_8151},
Q_f={q_gen_8082},
Delta=
{
<cons>(q_gen_8123, q_gen_8122) -> q_gen_8122
<nil>() -> q_gen_8122
<s>(q_gen_8123) -> q_gen_8123
<z>() -> q_gen_8123
<cons, cons>(q_gen_8102, q_gen_8082) -> q_gen_8082
<nil, cons>(q_gen_8123, q_gen_8122) -> q_gen_8082
<nil, nil>() -> q_gen_8082
<s, s>(q_gen_8102) -> q_gen_8102
<z, s>(q_gen_8123) -> q_gen_8102
<z, z>() -> q_gen_8102
<cons, cons>(q_gen_8102, q_gen_8151) -> q_gen_8151
<cons, nil>(q_gen_8123, q_gen_8122) -> q_gen_8151
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 27
() -> length([nil, z]) -> 27
() -> leq([z, s(nn2)]) -> 27
() -> leq([z, z]) -> 27
() -> reverse([nil, nil]) -> 27
(append([_sda, cons(h1, nil), _tda]) /\ reverse([t1, _sda])) -> reverse([cons(h1, t1), _tda]) -> 30
(append([t1, l2, _nda])) -> append([cons(h1, t1), l2, cons(h1, _nda)]) -> 28
(length([_cea, _dea]) /\ length([l1, _bea]) /\ reverse([l1, _cea])) -> leq([_bea, _dea]) -> 28
(length([ll, _xda])) -> length([cons(x, ll), s(_xda)]) -> 31
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 28
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 28
(leq([s(nn1), z])) -> BOT -> 28
}
Sat witness: Found: ((length([ll, _xda])) -> length([cons(x, ll), s(_xda)]), {
_xda -> s(z)  ;  ll -> cons(z, nil)  ;  x -> s(z)
})

-------------------------------------------
Step 44, which took 1.085095 s (model generation: 1.084007,  model checking: 0.001088):

Model:
|_
{
append -> 
{{{
Q={q_gen_8087, q_gen_8093, q_gen_8094, q_gen_8107, q_gen_8108, q_gen_8109, q_gen_8110, q_gen_8118},
Q_f={q_gen_8087},
Delta=
{
<cons>(q_gen_8109, q_gen_8108) -> q_gen_8108
<nil>() -> q_gen_8108
<s>(q_gen_8109) -> q_gen_8109
<z>() -> q_gen_8109
<cons, cons>(q_gen_8094, q_gen_8093) -> q_gen_8093
<nil, nil>() -> q_gen_8093
<s, s>(q_gen_8094) -> q_gen_8094
<z, z>() -> q_gen_8094
<nil, cons>(q_gen_8109, q_gen_8108) -> q_gen_8118
<cons, cons, cons>(q_gen_8110, q_gen_8107) -> q_gen_8087
<cons, nil, cons>(q_gen_8094, q_gen_8093) -> q_gen_8087
<nil, cons, cons>(q_gen_8094, q_gen_8093) -> q_gen_8087
<nil, nil, nil>() -> q_gen_8087
<cons, cons, cons>(q_gen_8110, q_gen_8087) -> q_gen_8107
<cons, nil, cons>(q_gen_8094, q_gen_8118) -> q_gen_8107
<nil, cons, cons>(q_gen_8094, q_gen_8118) -> q_gen_8107
<nil, nil, cons>(q_gen_8109, q_gen_8108) -> q_gen_8107
<s, s, s>(q_gen_8110) -> q_gen_8110
<s, z, s>(q_gen_8094) -> q_gen_8110
<z, z, z>() -> q_gen_8110
}

Datatype: <natlist, natlist, natlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_8086, q_gen_8090, q_gen_8091, q_gen_8105, q_gen_8125, q_gen_8126, q_gen_8127},
Q_f={q_gen_8086},
Delta=
{
<nil>() -> q_gen_8090
<s>(q_gen_8105) -> q_gen_8105
<z>() -> q_gen_8105
<cons>(q_gen_8105, q_gen_8090) -> q_gen_8125
<cons>(q_gen_8105, q_gen_8125) -> q_gen_8125
<cons, s>(q_gen_8091, q_gen_8090) -> q_gen_8086
<cons, s>(q_gen_8126, q_gen_8125) -> q_gen_8086
<nil, z>() -> q_gen_8086
<s, z>(q_gen_8105) -> q_gen_8091
<z, z>() -> q_gen_8091
<s, s>(q_gen_8091) -> q_gen_8126
<s, s>(q_gen_8126) -> q_gen_8126
<z, s>(q_gen_8105) -> q_gen_8126
<cons, s>(q_gen_8091, q_gen_8125) -> q_gen_8127
<cons, s>(q_gen_8126, q_gen_8090) -> q_gen_8127
}

Datatype: <natlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_8083, q_gen_8085, q_gen_8128, q_gen_8129},
Q_f={q_gen_8083},
Delta=
{
<s>(q_gen_8085) -> q_gen_8085
<z>() -> q_gen_8085
<s, s>(q_gen_8083) -> q_gen_8083
<s, s>(q_gen_8128) -> q_gen_8083
<z, s>(q_gen_8085) -> q_gen_8083
<z, z>() -> q_gen_8083
<s, s>(q_gen_8129) -> q_gen_8128
<s, z>(q_gen_8085) -> q_gen_8129
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_8082, q_gen_8102, q_gen_8122, q_gen_8123, q_gen_8151},
Q_f={q_gen_8082},
Delta=
{
<cons>(q_gen_8123, q_gen_8122) -> q_gen_8122
<nil>() -> q_gen_8122
<s>(q_gen_8123) -> q_gen_8123
<z>() -> q_gen_8123
<cons, cons>(q_gen_8102, q_gen_8082) -> q_gen_8082
<nil, cons>(q_gen_8123, q_gen_8122) -> q_gen_8082
<nil, nil>() -> q_gen_8082
<s, s>(q_gen_8102) -> q_gen_8102
<z, s>(q_gen_8123) -> q_gen_8102
<z, z>() -> q_gen_8102
<cons, cons>(q_gen_8102, q_gen_8151) -> q_gen_8151
<cons, nil>(q_gen_8123, q_gen_8122) -> q_gen_8151
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 28
() -> length([nil, z]) -> 28
() -> leq([z, s(nn2)]) -> 28
() -> leq([z, z]) -> 28
() -> reverse([nil, nil]) -> 28
(append([_sda, cons(h1, nil), _tda]) /\ reverse([t1, _sda])) -> reverse([cons(h1, t1), _tda]) -> 30
(append([t1, l2, _nda])) -> append([cons(h1, t1), l2, cons(h1, _nda)]) -> 28
(length([_cea, _dea]) /\ length([l1, _bea]) /\ reverse([l1, _cea])) -> leq([_bea, _dea]) -> 28
(length([ll, _xda])) -> length([cons(x, ll), s(_xda)]) -> 31
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 28
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 31
(leq([s(nn1), z])) -> BOT -> 29
}
Sat witness: Found: ((leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]), {
nn1 -> s(s(z))  ;  nn2 -> s(z)
})

-------------------------------------------
Step 45, which took 0.178557 s (model generation: 0.177767,  model checking: 0.000790):

Model:
|_
{
append -> 
{{{
Q={q_gen_8087, q_gen_8093, q_gen_8094, q_gen_8107, q_gen_8108, q_gen_8109, q_gen_8110, q_gen_8118},
Q_f={q_gen_8087},
Delta=
{
<cons>(q_gen_8109, q_gen_8108) -> q_gen_8108
<nil>() -> q_gen_8108
<s>(q_gen_8109) -> q_gen_8109
<z>() -> q_gen_8109
<cons, cons>(q_gen_8094, q_gen_8093) -> q_gen_8093
<nil, nil>() -> q_gen_8093
<s, s>(q_gen_8094) -> q_gen_8094
<z, z>() -> q_gen_8094
<nil, cons>(q_gen_8109, q_gen_8108) -> q_gen_8118
<cons, cons, cons>(q_gen_8110, q_gen_8107) -> q_gen_8087
<cons, nil, cons>(q_gen_8094, q_gen_8093) -> q_gen_8087
<nil, cons, cons>(q_gen_8094, q_gen_8093) -> q_gen_8087
<nil, nil, nil>() -> q_gen_8087
<cons, cons, cons>(q_gen_8110, q_gen_8087) -> q_gen_8107
<cons, nil, cons>(q_gen_8094, q_gen_8118) -> q_gen_8107
<nil, cons, cons>(q_gen_8094, q_gen_8118) -> q_gen_8107
<nil, nil, cons>(q_gen_8109, q_gen_8108) -> q_gen_8107
<s, s, s>(q_gen_8110) -> q_gen_8110
<s, z, s>(q_gen_8094) -> q_gen_8110
<z, z, z>() -> q_gen_8110
}

Datatype: <natlist, natlist, natlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_8086, q_gen_8090, q_gen_8091, q_gen_8105, q_gen_8116, q_gen_8125, q_gen_8126, q_gen_8127},
Q_f={q_gen_8086},
Delta=
{
<cons>(q_gen_8105, q_gen_8125) -> q_gen_8090
<nil>() -> q_gen_8090
<z>() -> q_gen_8105
<s>(q_gen_8105) -> q_gen_8116
<s>(q_gen_8116) -> q_gen_8116
<cons>(q_gen_8105, q_gen_8090) -> q_gen_8125
<cons>(q_gen_8116, q_gen_8090) -> q_gen_8125
<cons, s>(q_gen_8091, q_gen_8090) -> q_gen_8086
<cons, s>(q_gen_8126, q_gen_8125) -> q_gen_8086
<nil, z>() -> q_gen_8086
<s, s>(q_gen_8126) -> q_gen_8091
<s, z>(q_gen_8105) -> q_gen_8091
<s, z>(q_gen_8116) -> q_gen_8091
<z, s>(q_gen_8116) -> q_gen_8091
<z, z>() -> q_gen_8091
<s, s>(q_gen_8091) -> q_gen_8126
<z, s>(q_gen_8105) -> q_gen_8126
<cons, s>(q_gen_8091, q_gen_8125) -> q_gen_8127
<cons, s>(q_gen_8126, q_gen_8090) -> q_gen_8127
}

Datatype: <natlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_8083, q_gen_8085, q_gen_8128},
Q_f={q_gen_8083},
Delta=
{
<s>(q_gen_8085) -> q_gen_8085
<z>() -> q_gen_8085
<s, s>(q_gen_8083) -> q_gen_8083
<z, s>(q_gen_8085) -> q_gen_8083
<z, z>() -> q_gen_8083
<s, s>(q_gen_8128) -> q_gen_8128
<s, z>(q_gen_8085) -> q_gen_8128
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_8082, q_gen_8102, q_gen_8122, q_gen_8123, q_gen_8151},
Q_f={q_gen_8082},
Delta=
{
<cons>(q_gen_8123, q_gen_8122) -> q_gen_8122
<nil>() -> q_gen_8122
<s>(q_gen_8123) -> q_gen_8123
<z>() -> q_gen_8123
<cons, cons>(q_gen_8102, q_gen_8082) -> q_gen_8082
<nil, cons>(q_gen_8123, q_gen_8122) -> q_gen_8082
<nil, nil>() -> q_gen_8082
<s, s>(q_gen_8102) -> q_gen_8102
<z, s>(q_gen_8123) -> q_gen_8102
<z, z>() -> q_gen_8102
<cons, cons>(q_gen_8102, q_gen_8151) -> q_gen_8151
<cons, nil>(q_gen_8123, q_gen_8122) -> q_gen_8151
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 28
() -> length([nil, z]) -> 28
() -> leq([z, s(nn2)]) -> 28
() -> leq([z, z]) -> 28
() -> reverse([nil, nil]) -> 28
(append([_sda, cons(h1, nil), _tda]) /\ reverse([t1, _sda])) -> reverse([cons(h1, t1), _tda]) -> 30
(append([t1, l2, _nda])) -> append([cons(h1, t1), l2, cons(h1, _nda)]) -> 28
(length([_cea, _dea]) /\ length([l1, _bea]) /\ reverse([l1, _cea])) -> leq([_bea, _dea]) -> 31
(length([ll, _xda])) -> length([cons(x, ll), s(_xda)]) -> 31
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 29
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 31
(leq([s(nn1), z])) -> BOT -> 29
}
Sat witness: Found: ((length([_cea, _dea]) /\ length([l1, _bea]) /\ reverse([l1, _cea])) -> leq([_bea, _dea]), {
_bea -> s(s(s(z)))  ;  _cea -> cons(z, cons(z, nil))  ;  _dea -> s(s(z))  ;  l1 -> cons(z, nil)
})

-------------------------------------------
Step 46, which took 0.150254 s (model generation: 0.148917,  model checking: 0.001337):

Model:
|_
{
append -> 
{{{
Q={q_gen_8087, q_gen_8093, q_gen_8094, q_gen_8107, q_gen_8108, q_gen_8109, q_gen_8110, q_gen_8118},
Q_f={q_gen_8087},
Delta=
{
<cons>(q_gen_8109, q_gen_8108) -> q_gen_8108
<nil>() -> q_gen_8108
<s>(q_gen_8109) -> q_gen_8109
<z>() -> q_gen_8109
<cons, cons>(q_gen_8094, q_gen_8093) -> q_gen_8093
<nil, nil>() -> q_gen_8093
<s, s>(q_gen_8094) -> q_gen_8094
<z, z>() -> q_gen_8094
<nil, cons>(q_gen_8109, q_gen_8108) -> q_gen_8118
<cons, cons, cons>(q_gen_8110, q_gen_8107) -> q_gen_8087
<cons, nil, cons>(q_gen_8094, q_gen_8093) -> q_gen_8087
<nil, cons, cons>(q_gen_8094, q_gen_8093) -> q_gen_8087
<nil, nil, nil>() -> q_gen_8087
<cons, cons, cons>(q_gen_8110, q_gen_8087) -> q_gen_8107
<cons, nil, cons>(q_gen_8094, q_gen_8118) -> q_gen_8107
<nil, cons, cons>(q_gen_8094, q_gen_8118) -> q_gen_8107
<nil, nil, cons>(q_gen_8109, q_gen_8108) -> q_gen_8107
<s, s, s>(q_gen_8110) -> q_gen_8110
<s, z, s>(q_gen_8094) -> q_gen_8110
<z, z, z>() -> q_gen_8110
}

Datatype: <natlist, natlist, natlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_8086, q_gen_8090, q_gen_8091, q_gen_8105, q_gen_8116, q_gen_8125, q_gen_8126, q_gen_8127},
Q_f={q_gen_8086},
Delta=
{
<cons>(q_gen_8105, q_gen_8125) -> q_gen_8090
<cons>(q_gen_8116, q_gen_8090) -> q_gen_8090
<nil>() -> q_gen_8090
<s>(q_gen_8116) -> q_gen_8105
<z>() -> q_gen_8105
<s>(q_gen_8105) -> q_gen_8116
<cons>(q_gen_8105, q_gen_8090) -> q_gen_8125
<cons, s>(q_gen_8091, q_gen_8090) -> q_gen_8086
<cons, s>(q_gen_8126, q_gen_8125) -> q_gen_8086
<nil, z>() -> q_gen_8086
<s, s>(q_gen_8126) -> q_gen_8091
<s, z>(q_gen_8105) -> q_gen_8091
<s, z>(q_gen_8116) -> q_gen_8091
<z, z>() -> q_gen_8091
<s, s>(q_gen_8091) -> q_gen_8126
<z, s>(q_gen_8105) -> q_gen_8126
<z, s>(q_gen_8116) -> q_gen_8126
<cons, s>(q_gen_8091, q_gen_8125) -> q_gen_8127
<cons, s>(q_gen_8126, q_gen_8090) -> q_gen_8127
}

Datatype: <natlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_8083, q_gen_8085, q_gen_8128},
Q_f={q_gen_8083},
Delta=
{
<s>(q_gen_8085) -> q_gen_8085
<z>() -> q_gen_8085
<s, s>(q_gen_8083) -> q_gen_8083
<z, s>(q_gen_8085) -> q_gen_8083
<z, z>() -> q_gen_8083
<s, s>(q_gen_8128) -> q_gen_8128
<s, z>(q_gen_8085) -> q_gen_8128
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_8082, q_gen_8102, q_gen_8122, q_gen_8123, q_gen_8151},
Q_f={q_gen_8082},
Delta=
{
<cons>(q_gen_8123, q_gen_8122) -> q_gen_8122
<nil>() -> q_gen_8122
<s>(q_gen_8123) -> q_gen_8123
<z>() -> q_gen_8123
<cons, cons>(q_gen_8102, q_gen_8082) -> q_gen_8082
<nil, cons>(q_gen_8123, q_gen_8122) -> q_gen_8082
<nil, nil>() -> q_gen_8082
<s, s>(q_gen_8102) -> q_gen_8102
<z, s>(q_gen_8123) -> q_gen_8102
<z, z>() -> q_gen_8102
<cons, cons>(q_gen_8102, q_gen_8151) -> q_gen_8151
<cons, nil>(q_gen_8123, q_gen_8122) -> q_gen_8151
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 28
() -> length([nil, z]) -> 28
() -> leq([z, s(nn2)]) -> 28
() -> leq([z, z]) -> 28
() -> reverse([nil, nil]) -> 28
(append([_sda, cons(h1, nil), _tda]) /\ reverse([t1, _sda])) -> reverse([cons(h1, t1), _tda]) -> 30
(append([t1, l2, _nda])) -> append([cons(h1, t1), l2, cons(h1, _nda)]) -> 31
(length([_cea, _dea]) /\ length([l1, _bea]) /\ reverse([l1, _cea])) -> leq([_bea, _dea]) -> 31
(length([ll, _xda])) -> length([cons(x, ll), s(_xda)]) -> 31
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 29
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 31
(leq([s(nn1), z])) -> BOT -> 29
}
Sat witness: Found: ((append([t1, l2, _nda])) -> append([cons(h1, t1), l2, cons(h1, _nda)]), {
_nda -> cons(z, cons(z, cons(z, nil)))  ;  h1 -> z  ;  l2 -> cons(z, cons(z, nil))  ;  t1 -> cons(z, nil)
})

-------------------------------------------
Step 47, which took 0.155941 s (model generation: 0.154713,  model checking: 0.001228):

Model:
|_
{
append -> 
{{{
Q={q_gen_8087, q_gen_8092, q_gen_8093, q_gen_8094, q_gen_8108, q_gen_8109, q_gen_8110, q_gen_8150},
Q_f={q_gen_8087, q_gen_8092},
Delta=
{
<cons>(q_gen_8109, q_gen_8108) -> q_gen_8108
<nil>() -> q_gen_8108
<s>(q_gen_8109) -> q_gen_8109
<z>() -> q_gen_8109
<cons, cons>(q_gen_8094, q_gen_8093) -> q_gen_8093
<nil, cons>(q_gen_8109, q_gen_8108) -> q_gen_8093
<nil, nil>() -> q_gen_8093
<s, s>(q_gen_8094) -> q_gen_8094
<z, z>() -> q_gen_8094
<nil, nil, nil>() -> q_gen_8087
<cons, cons, cons>(q_gen_8110, q_gen_8092) -> q_gen_8092
<cons, nil, cons>(q_gen_8094, q_gen_8093) -> q_gen_8092
<nil, cons, cons>(q_gen_8094, q_gen_8093) -> q_gen_8092
<nil, nil, cons>(q_gen_8109, q_gen_8108) -> q_gen_8092
<s, s, s>(q_gen_8110) -> q_gen_8110
<s, z, s>(q_gen_8094) -> q_gen_8110
<z, z, z>() -> q_gen_8110
<cons, cons, cons>(q_gen_8110, q_gen_8087) -> q_gen_8150
}

Datatype: <natlist, natlist, natlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_8086, q_gen_8090, q_gen_8091, q_gen_8105, q_gen_8125, q_gen_8126, q_gen_8127},
Q_f={q_gen_8086},
Delta=
{
<nil>() -> q_gen_8090
<s>(q_gen_8105) -> q_gen_8105
<z>() -> q_gen_8105
<cons>(q_gen_8105, q_gen_8090) -> q_gen_8125
<cons>(q_gen_8105, q_gen_8125) -> q_gen_8125
<cons, s>(q_gen_8091, q_gen_8090) -> q_gen_8086
<cons, s>(q_gen_8126, q_gen_8125) -> q_gen_8086
<nil, z>() -> q_gen_8086
<s, z>(q_gen_8105) -> q_gen_8091
<z, z>() -> q_gen_8091
<s, s>(q_gen_8091) -> q_gen_8126
<s, s>(q_gen_8126) -> q_gen_8126
<z, s>(q_gen_8105) -> q_gen_8126
<cons, s>(q_gen_8091, q_gen_8125) -> q_gen_8127
<cons, s>(q_gen_8126, q_gen_8090) -> q_gen_8127
}

Datatype: <natlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_8083, q_gen_8085, q_gen_8128},
Q_f={q_gen_8083},
Delta=
{
<s>(q_gen_8085) -> q_gen_8085
<z>() -> q_gen_8085
<s, s>(q_gen_8083) -> q_gen_8083
<z, s>(q_gen_8085) -> q_gen_8083
<z, z>() -> q_gen_8083
<s, s>(q_gen_8128) -> q_gen_8128
<s, z>(q_gen_8085) -> q_gen_8128
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_8082, q_gen_8101, q_gen_8102, q_gen_8121, q_gen_8122, q_gen_8123, q_gen_8152},
Q_f={q_gen_8082, q_gen_8101},
Delta=
{
<cons>(q_gen_8123, q_gen_8122) -> q_gen_8122
<nil>() -> q_gen_8122
<s>(q_gen_8123) -> q_gen_8123
<z>() -> q_gen_8123
<cons, cons>(q_gen_8102, q_gen_8121) -> q_gen_8082
<nil, nil>() -> q_gen_8082
<cons, cons>(q_gen_8102, q_gen_8082) -> q_gen_8101
<s, s>(q_gen_8102) -> q_gen_8102
<z, s>(q_gen_8123) -> q_gen_8102
<z, z>() -> q_gen_8102
<cons, cons>(q_gen_8102, q_gen_8101) -> q_gen_8121
<cons, cons>(q_gen_8102, q_gen_8152) -> q_gen_8121
<nil, cons>(q_gen_8123, q_gen_8122) -> q_gen_8121
<cons, nil>(q_gen_8123, q_gen_8122) -> q_gen_8152
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 29
() -> length([nil, z]) -> 29
() -> leq([z, s(nn2)]) -> 29
() -> leq([z, z]) -> 29
() -> reverse([nil, nil]) -> 29
(append([_sda, cons(h1, nil), _tda]) /\ reverse([t1, _sda])) -> reverse([cons(h1, t1), _tda]) -> 33
(append([t1, l2, _nda])) -> append([cons(h1, t1), l2, cons(h1, _nda)]) -> 31
(length([_cea, _dea]) /\ length([l1, _bea]) /\ reverse([l1, _cea])) -> leq([_bea, _dea]) -> 31
(length([ll, _xda])) -> length([cons(x, ll), s(_xda)]) -> 31
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 30
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 31
(leq([s(nn1), z])) -> BOT -> 30
}
Sat witness: Found: ((append([_sda, cons(h1, nil), _tda]) /\ reverse([t1, _sda])) -> reverse([cons(h1, t1), _tda]), {
_sda -> cons(z, nil)  ;  _tda -> cons(z, cons(z, nil))  ;  h1 -> z  ;  t1 -> cons(z, nil)
})

-------------------------------------------
Step 48, which took 0.187359 s (model generation: 0.185014,  model checking: 0.002345):

Model:
|_
{
append -> 
{{{
Q={q_gen_8087, q_gen_8092, q_gen_8093, q_gen_8094, q_gen_8108, q_gen_8109, q_gen_8110, q_gen_8150},
Q_f={q_gen_8087, q_gen_8092},
Delta=
{
<cons>(q_gen_8109, q_gen_8108) -> q_gen_8108
<nil>() -> q_gen_8108
<s>(q_gen_8109) -> q_gen_8109
<z>() -> q_gen_8109
<cons, cons>(q_gen_8094, q_gen_8093) -> q_gen_8093
<nil, cons>(q_gen_8109, q_gen_8108) -> q_gen_8093
<nil, nil>() -> q_gen_8093
<s, s>(q_gen_8094) -> q_gen_8094
<z, z>() -> q_gen_8094
<nil, nil, nil>() -> q_gen_8087
<cons, cons, cons>(q_gen_8110, q_gen_8092) -> q_gen_8092
<cons, nil, cons>(q_gen_8094, q_gen_8093) -> q_gen_8092
<nil, cons, cons>(q_gen_8094, q_gen_8093) -> q_gen_8092
<nil, nil, cons>(q_gen_8109, q_gen_8108) -> q_gen_8092
<s, s, s>(q_gen_8110) -> q_gen_8110
<s, z, s>(q_gen_8094) -> q_gen_8110
<z, z, z>() -> q_gen_8110
<cons, cons, cons>(q_gen_8110, q_gen_8087) -> q_gen_8150
}

Datatype: <natlist, natlist, natlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_8086, q_gen_8090, q_gen_8091, q_gen_8105, q_gen_8116, q_gen_8125, q_gen_8126, q_gen_8127},
Q_f={q_gen_8086},
Delta=
{
<cons>(q_gen_8105, q_gen_8125) -> q_gen_8090
<cons>(q_gen_8116, q_gen_8090) -> q_gen_8090
<nil>() -> q_gen_8090
<z>() -> q_gen_8105
<s>(q_gen_8105) -> q_gen_8116
<s>(q_gen_8116) -> q_gen_8116
<cons>(q_gen_8105, q_gen_8090) -> q_gen_8125
<cons, s>(q_gen_8091, q_gen_8090) -> q_gen_8086
<cons, s>(q_gen_8126, q_gen_8125) -> q_gen_8086
<nil, z>() -> q_gen_8086
<s, s>(q_gen_8126) -> q_gen_8091
<s, z>(q_gen_8105) -> q_gen_8091
<s, z>(q_gen_8116) -> q_gen_8091
<z, z>() -> q_gen_8091
<s, s>(q_gen_8091) -> q_gen_8126
<z, s>(q_gen_8105) -> q_gen_8126
<z, s>(q_gen_8116) -> q_gen_8126
<cons, s>(q_gen_8091, q_gen_8125) -> q_gen_8127
<cons, s>(q_gen_8126, q_gen_8090) -> q_gen_8127
}

Datatype: <natlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_8083, q_gen_8085, q_gen_8128},
Q_f={q_gen_8083},
Delta=
{
<s>(q_gen_8085) -> q_gen_8085
<z>() -> q_gen_8085
<s, s>(q_gen_8083) -> q_gen_8083
<z, s>(q_gen_8085) -> q_gen_8083
<z, z>() -> q_gen_8083
<s, s>(q_gen_8128) -> q_gen_8128
<s, z>(q_gen_8085) -> q_gen_8128
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_8082, q_gen_8102, q_gen_8121, q_gen_8122, q_gen_8123, q_gen_8152},
Q_f={q_gen_8082},
Delta=
{
<cons>(q_gen_8123, q_gen_8122) -> q_gen_8122
<nil>() -> q_gen_8122
<s>(q_gen_8123) -> q_gen_8123
<z>() -> q_gen_8123
<cons, cons>(q_gen_8102, q_gen_8082) -> q_gen_8082
<cons, cons>(q_gen_8102, q_gen_8121) -> q_gen_8082
<nil, nil>() -> q_gen_8082
<s, s>(q_gen_8102) -> q_gen_8102
<z, s>(q_gen_8123) -> q_gen_8102
<z, z>() -> q_gen_8102
<cons, cons>(q_gen_8102, q_gen_8152) -> q_gen_8121
<nil, cons>(q_gen_8123, q_gen_8122) -> q_gen_8121
<cons, nil>(q_gen_8123, q_gen_8122) -> q_gen_8152
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 30
() -> length([nil, z]) -> 30
() -> leq([z, s(nn2)]) -> 30
() -> leq([z, z]) -> 30
() -> reverse([nil, nil]) -> 30
(append([_sda, cons(h1, nil), _tda]) /\ reverse([t1, _sda])) -> reverse([cons(h1, t1), _tda]) -> 33
(append([t1, l2, _nda])) -> append([cons(h1, t1), l2, cons(h1, _nda)]) -> 31
(length([_cea, _dea]) /\ length([l1, _bea]) /\ reverse([l1, _cea])) -> leq([_bea, _dea]) -> 31
(length([ll, _xda])) -> length([cons(x, ll), s(_xda)]) -> 34
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 31
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 32
(leq([s(nn1), z])) -> BOT -> 31
}
Sat witness: Found: ((length([ll, _xda])) -> length([cons(x, ll), s(_xda)]), {
_xda -> s(s(s(z)))  ;  ll -> cons(z, cons(z, nil))  ;  x -> z
})

-------------------------------------------
Step 49, which took 0.230673 s (model generation: 0.229174,  model checking: 0.001499):

Model:
|_
{
append -> 
{{{
Q={q_gen_8087, q_gen_8093, q_gen_8094, q_gen_8107, q_gen_8108, q_gen_8109, q_gen_8110, q_gen_8118, q_gen_8132},
Q_f={q_gen_8087},
Delta=
{
<nil>() -> q_gen_8108
<s>(q_gen_8109) -> q_gen_8109
<z>() -> q_gen_8109
<cons>(q_gen_8109, q_gen_8108) -> q_gen_8132
<cons, cons>(q_gen_8094, q_gen_8093) -> q_gen_8093
<nil, nil>() -> q_gen_8093
<s, s>(q_gen_8094) -> q_gen_8094
<z, z>() -> q_gen_8094
<nil, cons>(q_gen_8109, q_gen_8108) -> q_gen_8118
<nil, cons>(q_gen_8109, q_gen_8132) -> q_gen_8118
<cons, cons, cons>(q_gen_8110, q_gen_8107) -> q_gen_8087
<cons, nil, cons>(q_gen_8094, q_gen_8093) -> q_gen_8087
<nil, cons, cons>(q_gen_8094, q_gen_8093) -> q_gen_8087
<nil, nil, cons>(q_gen_8109, q_gen_8132) -> q_gen_8087
<nil, nil, nil>() -> q_gen_8087
<cons, cons, cons>(q_gen_8110, q_gen_8087) -> q_gen_8107
<cons, nil, cons>(q_gen_8094, q_gen_8118) -> q_gen_8107
<nil, cons, cons>(q_gen_8094, q_gen_8118) -> q_gen_8107
<nil, nil, cons>(q_gen_8109, q_gen_8108) -> q_gen_8107
<s, s, s>(q_gen_8110) -> q_gen_8110
<s, z, s>(q_gen_8094) -> q_gen_8110
<z, z, z>() -> q_gen_8110
}

Datatype: <natlist, natlist, natlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_8086, q_gen_8090, q_gen_8091, q_gen_8105, q_gen_8116, q_gen_8125, q_gen_8126, q_gen_8127},
Q_f={q_gen_8086},
Delta=
{
<cons>(q_gen_8105, q_gen_8125) -> q_gen_8090
<nil>() -> q_gen_8090
<s>(q_gen_8116) -> q_gen_8105
<z>() -> q_gen_8105
<s>(q_gen_8105) -> q_gen_8116
<cons>(q_gen_8105, q_gen_8090) -> q_gen_8125
<cons>(q_gen_8116, q_gen_8090) -> q_gen_8125
<cons, s>(q_gen_8091, q_gen_8090) -> q_gen_8086
<cons, s>(q_gen_8126, q_gen_8125) -> q_gen_8086
<nil, z>() -> q_gen_8086
<s, s>(q_gen_8126) -> q_gen_8091
<s, z>(q_gen_8105) -> q_gen_8091
<s, z>(q_gen_8116) -> q_gen_8091
<z, s>(q_gen_8116) -> q_gen_8091
<z, z>() -> q_gen_8091
<s, s>(q_gen_8091) -> q_gen_8126
<z, s>(q_gen_8105) -> q_gen_8126
<cons, s>(q_gen_8091, q_gen_8125) -> q_gen_8127
<cons, s>(q_gen_8126, q_gen_8090) -> q_gen_8127
}

Datatype: <natlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_8083, q_gen_8085, q_gen_8128},
Q_f={q_gen_8083},
Delta=
{
<s>(q_gen_8085) -> q_gen_8085
<z>() -> q_gen_8085
<s, s>(q_gen_8083) -> q_gen_8083
<z, s>(q_gen_8085) -> q_gen_8083
<z, z>() -> q_gen_8083
<s, s>(q_gen_8128) -> q_gen_8128
<s, z>(q_gen_8085) -> q_gen_8128
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_8082, q_gen_8102, q_gen_8120, q_gen_8122, q_gen_8123},
Q_f={q_gen_8082},
Delta=
{
<cons>(q_gen_8123, q_gen_8122) -> q_gen_8122
<nil>() -> q_gen_8122
<s>(q_gen_8123) -> q_gen_8123
<z>() -> q_gen_8123
<cons, cons>(q_gen_8102, q_gen_8082) -> q_gen_8082
<nil, nil>() -> q_gen_8082
<s, s>(q_gen_8102) -> q_gen_8102
<z, s>(q_gen_8123) -> q_gen_8102
<z, z>() -> q_gen_8102
<cons, cons>(q_gen_8102, q_gen_8120) -> q_gen_8120
<cons, nil>(q_gen_8123, q_gen_8122) -> q_gen_8120
<nil, cons>(q_gen_8123, q_gen_8122) -> q_gen_8120
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 31
() -> length([nil, z]) -> 31
() -> leq([z, s(nn2)]) -> 31
() -> leq([z, z]) -> 31
() -> reverse([nil, nil]) -> 31
(append([_sda, cons(h1, nil), _tda]) /\ reverse([t1, _sda])) -> reverse([cons(h1, t1), _tda]) -> 33
(append([t1, l2, _nda])) -> append([cons(h1, t1), l2, cons(h1, _nda)]) -> 31
(length([_cea, _dea]) /\ length([l1, _bea]) /\ reverse([l1, _cea])) -> leq([_bea, _dea]) -> 34
(length([ll, _xda])) -> length([cons(x, ll), s(_xda)]) -> 34
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 32
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 32
(leq([s(nn1), z])) -> BOT -> 32
}
Sat witness: Found: ((length([_cea, _dea]) /\ length([l1, _bea]) /\ reverse([l1, _cea])) -> leq([_bea, _dea]), {
_bea -> s(s(s(z)))  ;  _cea -> cons(s(s(z)), nil)  ;  _dea -> s(z)  ;  l1 -> cons(z, nil)
})

-------------------------------------------
Step 50, which took 0.244259 s (model generation: 0.242274,  model checking: 0.001985):

Model:
|_
{
append -> 
{{{
Q={q_gen_8087, q_gen_8092, q_gen_8093, q_gen_8094, q_gen_8108, q_gen_8109, q_gen_8110, q_gen_8150},
Q_f={q_gen_8087, q_gen_8092},
Delta=
{
<cons>(q_gen_8109, q_gen_8108) -> q_gen_8108
<nil>() -> q_gen_8108
<s>(q_gen_8109) -> q_gen_8109
<z>() -> q_gen_8109
<cons, cons>(q_gen_8094, q_gen_8093) -> q_gen_8093
<nil, cons>(q_gen_8109, q_gen_8108) -> q_gen_8093
<nil, nil>() -> q_gen_8093
<s, s>(q_gen_8094) -> q_gen_8094
<z, z>() -> q_gen_8094
<nil, nil, nil>() -> q_gen_8087
<cons, cons, cons>(q_gen_8110, q_gen_8092) -> q_gen_8092
<cons, nil, cons>(q_gen_8094, q_gen_8093) -> q_gen_8092
<nil, cons, cons>(q_gen_8094, q_gen_8093) -> q_gen_8092
<nil, nil, cons>(q_gen_8109, q_gen_8108) -> q_gen_8092
<s, s, s>(q_gen_8110) -> q_gen_8110
<s, z, s>(q_gen_8094) -> q_gen_8110
<z, z, z>() -> q_gen_8110
<cons, cons, cons>(q_gen_8110, q_gen_8087) -> q_gen_8150
}

Datatype: <natlist, natlist, natlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_8086, q_gen_8090, q_gen_8091, q_gen_8105, q_gen_8125, q_gen_8126, q_gen_8127},
Q_f={q_gen_8086},
Delta=
{
<nil>() -> q_gen_8090
<s>(q_gen_8105) -> q_gen_8105
<z>() -> q_gen_8105
<cons>(q_gen_8105, q_gen_8090) -> q_gen_8125
<cons>(q_gen_8105, q_gen_8125) -> q_gen_8125
<cons, s>(q_gen_8091, q_gen_8090) -> q_gen_8086
<cons, s>(q_gen_8126, q_gen_8125) -> q_gen_8086
<nil, z>() -> q_gen_8086
<s, z>(q_gen_8105) -> q_gen_8091
<z, z>() -> q_gen_8091
<s, s>(q_gen_8091) -> q_gen_8126
<s, s>(q_gen_8126) -> q_gen_8126
<z, s>(q_gen_8105) -> q_gen_8126
<cons, s>(q_gen_8091, q_gen_8125) -> q_gen_8127
<cons, s>(q_gen_8126, q_gen_8090) -> q_gen_8127
}

Datatype: <natlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_8083, q_gen_8085, q_gen_8128},
Q_f={q_gen_8083},
Delta=
{
<s>(q_gen_8085) -> q_gen_8085
<z>() -> q_gen_8085
<s, s>(q_gen_8083) -> q_gen_8083
<z, s>(q_gen_8085) -> q_gen_8083
<z, z>() -> q_gen_8083
<s, s>(q_gen_8128) -> q_gen_8128
<s, z>(q_gen_8085) -> q_gen_8128
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_8082, q_gen_8101, q_gen_8102, q_gen_8113, q_gen_8122, q_gen_8123, q_gen_8145, q_gen_8151},
Q_f={q_gen_8082, q_gen_8101},
Delta=
{
<cons>(q_gen_8123, q_gen_8122) -> q_gen_8122
<nil>() -> q_gen_8122
<s>(q_gen_8123) -> q_gen_8123
<z>() -> q_gen_8123
<cons, cons>(q_gen_8102, q_gen_8151) -> q_gen_8082
<nil, nil>() -> q_gen_8082
<cons, cons>(q_gen_8102, q_gen_8082) -> q_gen_8101
<cons, cons>(q_gen_8102, q_gen_8101) -> q_gen_8101
<cons, cons>(q_gen_8113, q_gen_8082) -> q_gen_8101
<nil, cons>(q_gen_8123, q_gen_8122) -> q_gen_8101
<z, s>(q_gen_8123) -> q_gen_8102
<z, z>() -> q_gen_8102
<s, s>(q_gen_8102) -> q_gen_8113
<cons, cons>(q_gen_8113, q_gen_8101) -> q_gen_8145
<cons, nil>(q_gen_8123, q_gen_8122) -> q_gen_8145
<cons, cons>(q_gen_8102, q_gen_8145) -> q_gen_8151
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 31
() -> length([nil, z]) -> 31
() -> leq([z, s(nn2)]) -> 31
() -> leq([z, z]) -> 31
() -> reverse([nil, nil]) -> 31
(append([_sda, cons(h1, nil), _tda]) /\ reverse([t1, _sda])) -> reverse([cons(h1, t1), _tda]) -> 33
(append([t1, l2, _nda])) -> append([cons(h1, t1), l2, cons(h1, _nda)]) -> 34
(length([_cea, _dea]) /\ length([l1, _bea]) /\ reverse([l1, _cea])) -> leq([_bea, _dea]) -> 34
(length([ll, _xda])) -> length([cons(x, ll), s(_xda)]) -> 34
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 32
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 32
(leq([s(nn1), z])) -> BOT -> 32
}
Sat witness: Found: ((append([t1, l2, _nda])) -> append([cons(h1, t1), l2, cons(h1, _nda)]), {
_nda -> cons(s(z), cons(z, nil))  ;  h1 -> z  ;  l2 -> cons(s(z), nil)  ;  t1 -> cons(s(z), cons(z, nil))
})

-------------------------------------------
Step 51, which took 0.280237 s (model generation: 0.278014,  model checking: 0.002223):

Model:
|_
{
append -> 
{{{
Q={q_gen_8087, q_gen_8092, q_gen_8093, q_gen_8094, q_gen_8108, q_gen_8109, q_gen_8110, q_gen_8150},
Q_f={q_gen_8087, q_gen_8092},
Delta=
{
<cons>(q_gen_8109, q_gen_8108) -> q_gen_8108
<nil>() -> q_gen_8108
<s>(q_gen_8109) -> q_gen_8109
<z>() -> q_gen_8109
<cons, cons>(q_gen_8094, q_gen_8093) -> q_gen_8093
<nil, cons>(q_gen_8109, q_gen_8108) -> q_gen_8093
<nil, nil>() -> q_gen_8093
<s, s>(q_gen_8094) -> q_gen_8094
<z, z>() -> q_gen_8094
<nil, nil, nil>() -> q_gen_8087
<cons, cons, cons>(q_gen_8110, q_gen_8092) -> q_gen_8092
<cons, nil, cons>(q_gen_8094, q_gen_8093) -> q_gen_8092
<nil, cons, cons>(q_gen_8094, q_gen_8093) -> q_gen_8092
<nil, nil, cons>(q_gen_8109, q_gen_8108) -> q_gen_8092
<s, s, s>(q_gen_8110) -> q_gen_8110
<s, z, s>(q_gen_8094) -> q_gen_8110
<z, s, z>(q_gen_8109) -> q_gen_8110
<z, z, z>() -> q_gen_8110
<cons, cons, cons>(q_gen_8110, q_gen_8087) -> q_gen_8150
}

Datatype: <natlist, natlist, natlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_8086, q_gen_8090, q_gen_8091, q_gen_8105, q_gen_8125, q_gen_8126, q_gen_8127},
Q_f={q_gen_8086},
Delta=
{
<nil>() -> q_gen_8090
<s>(q_gen_8105) -> q_gen_8105
<z>() -> q_gen_8105
<cons>(q_gen_8105, q_gen_8090) -> q_gen_8125
<cons>(q_gen_8105, q_gen_8125) -> q_gen_8125
<cons, s>(q_gen_8091, q_gen_8090) -> q_gen_8086
<cons, s>(q_gen_8126, q_gen_8125) -> q_gen_8086
<nil, z>() -> q_gen_8086
<s, z>(q_gen_8105) -> q_gen_8091
<z, z>() -> q_gen_8091
<s, s>(q_gen_8091) -> q_gen_8126
<s, s>(q_gen_8126) -> q_gen_8126
<z, s>(q_gen_8105) -> q_gen_8126
<cons, s>(q_gen_8091, q_gen_8125) -> q_gen_8127
<cons, s>(q_gen_8126, q_gen_8090) -> q_gen_8127
}

Datatype: <natlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_8083, q_gen_8085, q_gen_8128},
Q_f={q_gen_8083},
Delta=
{
<s>(q_gen_8085) -> q_gen_8085
<z>() -> q_gen_8085
<s, s>(q_gen_8083) -> q_gen_8083
<z, s>(q_gen_8085) -> q_gen_8083
<z, z>() -> q_gen_8083
<s, s>(q_gen_8128) -> q_gen_8128
<s, z>(q_gen_8085) -> q_gen_8128
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_8082, q_gen_8101, q_gen_8102, q_gen_8113, q_gen_8122, q_gen_8123, q_gen_8151, q_gen_8152},
Q_f={q_gen_8082, q_gen_8101},
Delta=
{
<cons>(q_gen_8123, q_gen_8122) -> q_gen_8122
<nil>() -> q_gen_8122
<s>(q_gen_8123) -> q_gen_8123
<z>() -> q_gen_8123
<cons, cons>(q_gen_8102, q_gen_8151) -> q_gen_8082
<nil, cons>(q_gen_8123, q_gen_8122) -> q_gen_8082
<nil, nil>() -> q_gen_8082
<cons, cons>(q_gen_8102, q_gen_8082) -> q_gen_8101
<cons, cons>(q_gen_8102, q_gen_8101) -> q_gen_8101
<cons, cons>(q_gen_8113, q_gen_8082) -> q_gen_8101
<z, z>() -> q_gen_8102
<s, s>(q_gen_8102) -> q_gen_8113
<z, s>(q_gen_8123) -> q_gen_8113
<cons, cons>(q_gen_8102, q_gen_8152) -> q_gen_8151
<cons, cons>(q_gen_8113, q_gen_8101) -> q_gen_8152
<cons, nil>(q_gen_8123, q_gen_8122) -> q_gen_8152
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 32
() -> length([nil, z]) -> 32
() -> leq([z, s(nn2)]) -> 32
() -> leq([z, z]) -> 32
() -> reverse([nil, nil]) -> 32
(append([_sda, cons(h1, nil), _tda]) /\ reverse([t1, _sda])) -> reverse([cons(h1, t1), _tda]) -> 36
(append([t1, l2, _nda])) -> append([cons(h1, t1), l2, cons(h1, _nda)]) -> 34
(length([_cea, _dea]) /\ length([l1, _bea]) /\ reverse([l1, _cea])) -> leq([_bea, _dea]) -> 34
(length([ll, _xda])) -> length([cons(x, ll), s(_xda)]) -> 34
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 33
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 33
(leq([s(nn1), z])) -> BOT -> 33
}
Sat witness: Found: ((append([_sda, cons(h1, nil), _tda]) /\ reverse([t1, _sda])) -> reverse([cons(h1, t1), _tda]), {
_sda -> cons(s(z), nil)  ;  _tda -> cons(s(z), cons(z, nil))  ;  h1 -> s(z)  ;  t1 -> cons(z, nil)
})

-------------------------------------------
Step 52, which took 0.565148 s (model generation: 0.561358,  model checking: 0.003790):

Model:
|_
{
append -> 
{{{
Q={q_gen_8087, q_gen_8093, q_gen_8094, q_gen_8107, q_gen_8108, q_gen_8109, q_gen_8110, q_gen_8118, q_gen_8132},
Q_f={q_gen_8087},
Delta=
{
<nil>() -> q_gen_8108
<s>(q_gen_8109) -> q_gen_8109
<z>() -> q_gen_8109
<cons>(q_gen_8109, q_gen_8108) -> q_gen_8132
<cons, cons>(q_gen_8094, q_gen_8093) -> q_gen_8093
<nil, nil>() -> q_gen_8093
<s, s>(q_gen_8094) -> q_gen_8094
<z, z>() -> q_gen_8094
<nil, cons>(q_gen_8109, q_gen_8108) -> q_gen_8118
<nil, cons>(q_gen_8109, q_gen_8132) -> q_gen_8118
<cons, cons, cons>(q_gen_8110, q_gen_8107) -> q_gen_8087
<cons, nil, cons>(q_gen_8094, q_gen_8093) -> q_gen_8087
<nil, cons, cons>(q_gen_8094, q_gen_8093) -> q_gen_8087
<nil, nil, cons>(q_gen_8109, q_gen_8132) -> q_gen_8087
<nil, nil, nil>() -> q_gen_8087
<cons, cons, cons>(q_gen_8110, q_gen_8087) -> q_gen_8107
<cons, nil, cons>(q_gen_8094, q_gen_8118) -> q_gen_8107
<nil, cons, cons>(q_gen_8094, q_gen_8118) -> q_gen_8107
<nil, nil, cons>(q_gen_8109, q_gen_8108) -> q_gen_8107
<s, s, s>(q_gen_8110) -> q_gen_8110
<s, z, s>(q_gen_8094) -> q_gen_8110
<z, s, z>(q_gen_8109) -> q_gen_8110
<z, z, z>() -> q_gen_8110
}

Datatype: <natlist, natlist, natlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_8086, q_gen_8090, q_gen_8091, q_gen_8105, q_gen_8116, q_gen_8125, q_gen_8126, q_gen_8127, q_gen_8144},
Q_f={q_gen_8086},
Delta=
{
<cons>(q_gen_8105, q_gen_8125) -> q_gen_8090
<nil>() -> q_gen_8090
<s>(q_gen_8116) -> q_gen_8105
<z>() -> q_gen_8105
<s>(q_gen_8105) -> q_gen_8116
<cons>(q_gen_8105, q_gen_8090) -> q_gen_8125
<cons>(q_gen_8116, q_gen_8090) -> q_gen_8125
<cons, s>(q_gen_8091, q_gen_8090) -> q_gen_8086
<cons, s>(q_gen_8126, q_gen_8125) -> q_gen_8086
<nil, z>() -> q_gen_8086
<s, s>(q_gen_8126) -> q_gen_8091
<s, z>(q_gen_8105) -> q_gen_8091
<s, z>(q_gen_8116) -> q_gen_8091
<z, z>() -> q_gen_8091
<s, s>(q_gen_8091) -> q_gen_8126
<s, s>(q_gen_8144) -> q_gen_8126
<z, s>(q_gen_8105) -> q_gen_8126
<cons, s>(q_gen_8091, q_gen_8125) -> q_gen_8127
<cons, s>(q_gen_8126, q_gen_8090) -> q_gen_8127
<cons, s>(q_gen_8144, q_gen_8090) -> q_gen_8127
<cons, s>(q_gen_8144, q_gen_8125) -> q_gen_8127
<z, s>(q_gen_8116) -> q_gen_8144
}

Datatype: <natlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_8083, q_gen_8085, q_gen_8128},
Q_f={q_gen_8083},
Delta=
{
<s>(q_gen_8085) -> q_gen_8085
<z>() -> q_gen_8085
<s, s>(q_gen_8083) -> q_gen_8083
<z, s>(q_gen_8085) -> q_gen_8083
<z, z>() -> q_gen_8083
<s, s>(q_gen_8128) -> q_gen_8128
<s, z>(q_gen_8085) -> q_gen_8128
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_8082, q_gen_8102, q_gen_8122, q_gen_8123, q_gen_8151},
Q_f={q_gen_8082},
Delta=
{
<cons>(q_gen_8123, q_gen_8122) -> q_gen_8122
<nil>() -> q_gen_8122
<s>(q_gen_8123) -> q_gen_8123
<z>() -> q_gen_8123
<cons, cons>(q_gen_8102, q_gen_8082) -> q_gen_8082
<nil, cons>(q_gen_8123, q_gen_8122) -> q_gen_8082
<nil, nil>() -> q_gen_8082
<s, s>(q_gen_8102) -> q_gen_8102
<z, s>(q_gen_8123) -> q_gen_8102
<z, z>() -> q_gen_8102
<cons, cons>(q_gen_8102, q_gen_8151) -> q_gen_8151
<cons, nil>(q_gen_8123, q_gen_8122) -> q_gen_8151
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 33
() -> length([nil, z]) -> 33
() -> leq([z, s(nn2)]) -> 33
() -> leq([z, z]) -> 33
() -> reverse([nil, nil]) -> 33
(append([_sda, cons(h1, nil), _tda]) /\ reverse([t1, _sda])) -> reverse([cons(h1, t1), _tda]) -> 36
(append([t1, l2, _nda])) -> append([cons(h1, t1), l2, cons(h1, _nda)]) -> 34
(length([_cea, _dea]) /\ length([l1, _bea]) /\ reverse([l1, _cea])) -> leq([_bea, _dea]) -> 34
(length([ll, _xda])) -> length([cons(x, ll), s(_xda)]) -> 37
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 34
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 34
(leq([s(nn1), z])) -> BOT -> 34
}
Sat witness: Found: ((length([ll, _xda])) -> length([cons(x, ll), s(_xda)]), {
_xda -> s(s(z))  ;  ll -> cons(z, cons(s(z), nil))  ;  x -> z
})

-------------------------------------------
Step 53, which took 0.486921 s (model generation: 0.483090,  model checking: 0.003831):

Model:
|_
{
append -> 
{{{
Q={q_gen_8087, q_gen_8092, q_gen_8093, q_gen_8094, q_gen_8108, q_gen_8109, q_gen_8110, q_gen_8150},
Q_f={q_gen_8087, q_gen_8092},
Delta=
{
<cons>(q_gen_8109, q_gen_8108) -> q_gen_8108
<nil>() -> q_gen_8108
<s>(q_gen_8109) -> q_gen_8109
<z>() -> q_gen_8109
<cons, cons>(q_gen_8094, q_gen_8093) -> q_gen_8093
<nil, cons>(q_gen_8109, q_gen_8108) -> q_gen_8093
<nil, nil>() -> q_gen_8093
<s, s>(q_gen_8094) -> q_gen_8094
<z, z>() -> q_gen_8094
<nil, nil, nil>() -> q_gen_8087
<cons, cons, cons>(q_gen_8110, q_gen_8092) -> q_gen_8092
<cons, nil, cons>(q_gen_8094, q_gen_8093) -> q_gen_8092
<nil, cons, cons>(q_gen_8094, q_gen_8093) -> q_gen_8092
<nil, nil, cons>(q_gen_8109, q_gen_8108) -> q_gen_8092
<s, s, s>(q_gen_8110) -> q_gen_8110
<s, z, s>(q_gen_8094) -> q_gen_8110
<z, s, z>(q_gen_8109) -> q_gen_8110
<z, z, z>() -> q_gen_8110
<cons, cons, cons>(q_gen_8110, q_gen_8087) -> q_gen_8150
}

Datatype: <natlist, natlist, natlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_8086, q_gen_8090, q_gen_8091, q_gen_8105, q_gen_8116, q_gen_8125, q_gen_8126, q_gen_8127, q_gen_8139},
Q_f={q_gen_8086},
Delta=
{
<nil>() -> q_gen_8090
<s>(q_gen_8116) -> q_gen_8105
<z>() -> q_gen_8105
<s>(q_gen_8105) -> q_gen_8116
<cons>(q_gen_8105, q_gen_8090) -> q_gen_8125
<cons>(q_gen_8105, q_gen_8125) -> q_gen_8139
<cons>(q_gen_8105, q_gen_8139) -> q_gen_8139
<cons>(q_gen_8116, q_gen_8090) -> q_gen_8139
<cons, s>(q_gen_8091, q_gen_8090) -> q_gen_8086
<cons, s>(q_gen_8091, q_gen_8139) -> q_gen_8086
<cons, s>(q_gen_8126, q_gen_8125) -> q_gen_8086
<cons, s>(q_gen_8126, q_gen_8139) -> q_gen_8086
<nil, z>() -> q_gen_8086
<s, s>(q_gen_8126) -> q_gen_8091
<s, z>(q_gen_8105) -> q_gen_8091
<s, z>(q_gen_8116) -> q_gen_8091
<z, z>() -> q_gen_8091
<s, s>(q_gen_8091) -> q_gen_8126
<z, s>(q_gen_8105) -> q_gen_8126
<z, s>(q_gen_8116) -> q_gen_8126
<cons, s>(q_gen_8091, q_gen_8125) -> q_gen_8127
<cons, s>(q_gen_8126, q_gen_8090) -> q_gen_8127
}

Datatype: <natlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_8083, q_gen_8085, q_gen_8128},
Q_f={q_gen_8083},
Delta=
{
<s>(q_gen_8085) -> q_gen_8085
<z>() -> q_gen_8085
<s, s>(q_gen_8083) -> q_gen_8083
<z, s>(q_gen_8085) -> q_gen_8083
<z, z>() -> q_gen_8083
<s, s>(q_gen_8128) -> q_gen_8128
<s, z>(q_gen_8085) -> q_gen_8128
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_8082, q_gen_8102, q_gen_8122, q_gen_8123, q_gen_8151, q_gen_8152},
Q_f={q_gen_8082},
Delta=
{
<cons>(q_gen_8123, q_gen_8122) -> q_gen_8122
<nil>() -> q_gen_8122
<s>(q_gen_8123) -> q_gen_8123
<z>() -> q_gen_8123
<cons, cons>(q_gen_8102, q_gen_8082) -> q_gen_8082
<cons, cons>(q_gen_8102, q_gen_8151) -> q_gen_8082
<nil, cons>(q_gen_8123, q_gen_8122) -> q_gen_8082
<nil, nil>() -> q_gen_8082
<s, s>(q_gen_8102) -> q_gen_8102
<z, s>(q_gen_8123) -> q_gen_8102
<z, z>() -> q_gen_8102
<cons, cons>(q_gen_8102, q_gen_8152) -> q_gen_8151
<cons, nil>(q_gen_8123, q_gen_8122) -> q_gen_8152
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 34
() -> length([nil, z]) -> 34
() -> leq([z, s(nn2)]) -> 34
() -> leq([z, z]) -> 34
() -> reverse([nil, nil]) -> 34
(append([_sda, cons(h1, nil), _tda]) /\ reverse([t1, _sda])) -> reverse([cons(h1, t1), _tda]) -> 36
(append([t1, l2, _nda])) -> append([cons(h1, t1), l2, cons(h1, _nda)]) -> 34
(length([_cea, _dea]) /\ length([l1, _bea]) /\ reverse([l1, _cea])) -> leq([_bea, _dea]) -> 37
(length([ll, _xda])) -> length([cons(x, ll), s(_xda)]) -> 37
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 35
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 35
(leq([s(nn1), z])) -> BOT -> 35
}
Sat witness: Found: ((length([_cea, _dea]) /\ length([l1, _bea]) /\ reverse([l1, _cea])) -> leq([_bea, _dea]), {
_bea -> s(s(s(s(z))))  ;  _cea -> cons(z, cons(z, nil))  ;  _dea -> s(s(z))  ;  l1 -> cons(z, cons(z, nil))
})

-------------------------------------------
Step 54, which took 0.622114 s (model generation: 0.609863,  model checking: 0.012251):

Model:
|_
{
append -> 
{{{
Q={q_gen_8087, q_gen_8092, q_gen_8093, q_gen_8094, q_gen_8108, q_gen_8109, q_gen_8110, q_gen_8150},
Q_f={q_gen_8087, q_gen_8092},
Delta=
{
<cons>(q_gen_8109, q_gen_8108) -> q_gen_8108
<nil>() -> q_gen_8108
<s>(q_gen_8109) -> q_gen_8109
<z>() -> q_gen_8109
<cons, cons>(q_gen_8094, q_gen_8093) -> q_gen_8093
<nil, cons>(q_gen_8109, q_gen_8108) -> q_gen_8093
<nil, nil>() -> q_gen_8093
<s, s>(q_gen_8094) -> q_gen_8094
<z, z>() -> q_gen_8094
<nil, nil, nil>() -> q_gen_8087
<cons, cons, cons>(q_gen_8110, q_gen_8092) -> q_gen_8092
<cons, nil, cons>(q_gen_8094, q_gen_8093) -> q_gen_8092
<nil, cons, cons>(q_gen_8094, q_gen_8093) -> q_gen_8092
<nil, nil, cons>(q_gen_8109, q_gen_8108) -> q_gen_8092
<s, s, s>(q_gen_8110) -> q_gen_8110
<s, z, s>(q_gen_8094) -> q_gen_8110
<z, s, z>(q_gen_8109) -> q_gen_8110
<z, z, z>() -> q_gen_8110
<cons, cons, cons>(q_gen_8110, q_gen_8087) -> q_gen_8150
}

Datatype: <natlist, natlist, natlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_8086, q_gen_8090, q_gen_8091, q_gen_8105, q_gen_8116, q_gen_8125, q_gen_8126, q_gen_8127, q_gen_8144},
Q_f={q_gen_8086},
Delta=
{
<cons>(q_gen_8105, q_gen_8125) -> q_gen_8090
<cons>(q_gen_8116, q_gen_8090) -> q_gen_8090
<nil>() -> q_gen_8090
<z>() -> q_gen_8105
<s>(q_gen_8105) -> q_gen_8116
<s>(q_gen_8116) -> q_gen_8116
<cons>(q_gen_8105, q_gen_8090) -> q_gen_8125
<cons, s>(q_gen_8091, q_gen_8090) -> q_gen_8086
<cons, s>(q_gen_8126, q_gen_8125) -> q_gen_8086
<nil, z>() -> q_gen_8086
<s, s>(q_gen_8126) -> q_gen_8091
<s, s>(q_gen_8144) -> q_gen_8091
<s, z>(q_gen_8105) -> q_gen_8091
<s, z>(q_gen_8116) -> q_gen_8091
<z, z>() -> q_gen_8091
<s, s>(q_gen_8091) -> q_gen_8126
<z, s>(q_gen_8105) -> q_gen_8126
<cons, s>(q_gen_8091, q_gen_8125) -> q_gen_8127
<cons, s>(q_gen_8126, q_gen_8090) -> q_gen_8127
<cons, s>(q_gen_8144, q_gen_8090) -> q_gen_8127
<cons, s>(q_gen_8144, q_gen_8125) -> q_gen_8127
<z, s>(q_gen_8116) -> q_gen_8144
}

Datatype: <natlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_8083, q_gen_8085, q_gen_8128},
Q_f={q_gen_8083},
Delta=
{
<s>(q_gen_8085) -> q_gen_8085
<z>() -> q_gen_8085
<s, s>(q_gen_8083) -> q_gen_8083
<z, s>(q_gen_8085) -> q_gen_8083
<z, z>() -> q_gen_8083
<s, s>(q_gen_8128) -> q_gen_8128
<s, z>(q_gen_8085) -> q_gen_8128
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_8082, q_gen_8102, q_gen_8122, q_gen_8123, q_gen_8151, q_gen_8152},
Q_f={q_gen_8082},
Delta=
{
<cons>(q_gen_8123, q_gen_8122) -> q_gen_8122
<nil>() -> q_gen_8122
<s>(q_gen_8123) -> q_gen_8123
<z>() -> q_gen_8123
<cons, cons>(q_gen_8102, q_gen_8082) -> q_gen_8082
<cons, cons>(q_gen_8102, q_gen_8151) -> q_gen_8082
<nil, cons>(q_gen_8123, q_gen_8122) -> q_gen_8082
<nil, nil>() -> q_gen_8082
<s, s>(q_gen_8102) -> q_gen_8102
<z, s>(q_gen_8123) -> q_gen_8102
<z, z>() -> q_gen_8102
<cons, cons>(q_gen_8102, q_gen_8152) -> q_gen_8151
<cons, nil>(q_gen_8123, q_gen_8122) -> q_gen_8152
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 34
() -> length([nil, z]) -> 34
() -> leq([z, s(nn2)]) -> 34
() -> leq([z, z]) -> 34
() -> reverse([nil, nil]) -> 34
(append([_sda, cons(h1, nil), _tda]) /\ reverse([t1, _sda])) -> reverse([cons(h1, t1), _tda]) -> 36
(append([t1, l2, _nda])) -> append([cons(h1, t1), l2, cons(h1, _nda)]) -> 37
(length([_cea, _dea]) /\ length([l1, _bea]) /\ reverse([l1, _cea])) -> leq([_bea, _dea]) -> 37
(length([ll, _xda])) -> length([cons(x, ll), s(_xda)]) -> 37
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 35
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 35
(leq([s(nn1), z])) -> BOT -> 35
}
Sat witness: Found: ((append([t1, l2, _nda])) -> append([cons(h1, t1), l2, cons(h1, _nda)]), {
_nda -> cons(z, cons(s(z), nil))  ;  h1 -> s(z)  ;  l2 -> cons(z, cons(s(z), nil))  ;  t1 -> nil
})

-------------------------------------------
Step 55, which took 1.058067 s (model generation: 1.056329,  model checking: 0.001738):

Model:
|_
{
append -> 
{{{
Q={q_gen_8087, q_gen_8092, q_gen_8093, q_gen_8094, q_gen_8108, q_gen_8109, q_gen_8110, q_gen_8150},
Q_f={q_gen_8087, q_gen_8092},
Delta=
{
<cons>(q_gen_8109, q_gen_8108) -> q_gen_8108
<nil>() -> q_gen_8108
<s>(q_gen_8109) -> q_gen_8109
<z>() -> q_gen_8109
<cons, cons>(q_gen_8094, q_gen_8093) -> q_gen_8093
<nil, cons>(q_gen_8109, q_gen_8108) -> q_gen_8093
<nil, nil>() -> q_gen_8093
<s, s>(q_gen_8094) -> q_gen_8094
<s, z>(q_gen_8109) -> q_gen_8094
<z, z>() -> q_gen_8094
<nil, nil, nil>() -> q_gen_8087
<cons, cons, cons>(q_gen_8110, q_gen_8092) -> q_gen_8092
<cons, nil, cons>(q_gen_8094, q_gen_8093) -> q_gen_8092
<nil, cons, cons>(q_gen_8094, q_gen_8093) -> q_gen_8092
<nil, nil, cons>(q_gen_8109, q_gen_8108) -> q_gen_8092
<s, s, s>(q_gen_8110) -> q_gen_8110
<s, z, s>(q_gen_8094) -> q_gen_8110
<z, s, z>(q_gen_8109) -> q_gen_8110
<z, z, z>() -> q_gen_8110
<cons, cons, cons>(q_gen_8110, q_gen_8087) -> q_gen_8150
}

Datatype: <natlist, natlist, natlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_8086, q_gen_8090, q_gen_8091, q_gen_8105, q_gen_8116, q_gen_8125, q_gen_8126, q_gen_8127, q_gen_8144},
Q_f={q_gen_8086},
Delta=
{
<cons>(q_gen_8105, q_gen_8125) -> q_gen_8090
<cons>(q_gen_8116, q_gen_8090) -> q_gen_8090
<nil>() -> q_gen_8090
<z>() -> q_gen_8105
<s>(q_gen_8105) -> q_gen_8116
<s>(q_gen_8116) -> q_gen_8116
<cons>(q_gen_8105, q_gen_8090) -> q_gen_8125
<cons, s>(q_gen_8091, q_gen_8090) -> q_gen_8086
<cons, s>(q_gen_8126, q_gen_8125) -> q_gen_8086
<nil, z>() -> q_gen_8086
<s, s>(q_gen_8126) -> q_gen_8091
<s, s>(q_gen_8144) -> q_gen_8091
<s, z>(q_gen_8105) -> q_gen_8091
<s, z>(q_gen_8116) -> q_gen_8091
<z, z>() -> q_gen_8091
<s, s>(q_gen_8091) -> q_gen_8126
<z, s>(q_gen_8105) -> q_gen_8126
<cons, s>(q_gen_8091, q_gen_8125) -> q_gen_8127
<cons, s>(q_gen_8126, q_gen_8090) -> q_gen_8127
<cons, s>(q_gen_8144, q_gen_8090) -> q_gen_8127
<cons, s>(q_gen_8144, q_gen_8125) -> q_gen_8127
<z, s>(q_gen_8116) -> q_gen_8144
}

Datatype: <natlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_8083, q_gen_8085, q_gen_8128},
Q_f={q_gen_8083},
Delta=
{
<s>(q_gen_8085) -> q_gen_8085
<z>() -> q_gen_8085
<s, s>(q_gen_8083) -> q_gen_8083
<z, s>(q_gen_8085) -> q_gen_8083
<z, z>() -> q_gen_8083
<s, s>(q_gen_8128) -> q_gen_8128
<s, z>(q_gen_8085) -> q_gen_8128
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_8082, q_gen_8102, q_gen_8122, q_gen_8123, q_gen_8151, q_gen_8152},
Q_f={q_gen_8082},
Delta=
{
<cons>(q_gen_8123, q_gen_8122) -> q_gen_8122
<nil>() -> q_gen_8122
<s>(q_gen_8123) -> q_gen_8123
<z>() -> q_gen_8123
<cons, cons>(q_gen_8102, q_gen_8082) -> q_gen_8082
<cons, cons>(q_gen_8102, q_gen_8151) -> q_gen_8082
<nil, cons>(q_gen_8123, q_gen_8122) -> q_gen_8082
<nil, nil>() -> q_gen_8082
<s, s>(q_gen_8102) -> q_gen_8102
<z, s>(q_gen_8123) -> q_gen_8102
<z, z>() -> q_gen_8102
<cons, cons>(q_gen_8102, q_gen_8152) -> q_gen_8151
<cons, nil>(q_gen_8123, q_gen_8122) -> q_gen_8152
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 35
() -> length([nil, z]) -> 35
() -> leq([z, s(nn2)]) -> 35
() -> leq([z, z]) -> 35
() -> reverse([nil, nil]) -> 35
(append([_sda, cons(h1, nil), _tda]) /\ reverse([t1, _sda])) -> reverse([cons(h1, t1), _tda]) -> 39
(append([t1, l2, _nda])) -> append([cons(h1, t1), l2, cons(h1, _nda)]) -> 37
(length([_cea, _dea]) /\ length([l1, _bea]) /\ reverse([l1, _cea])) -> leq([_bea, _dea]) -> 37
(length([ll, _xda])) -> length([cons(x, ll), s(_xda)]) -> 37
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 36
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 36
(leq([s(nn1), z])) -> BOT -> 36
}
Sat witness: Found: ((append([_sda, cons(h1, nil), _tda]) /\ reverse([t1, _sda])) -> reverse([cons(h1, t1), _tda]), {
_sda -> nil  ;  _tda -> cons(z, nil)  ;  h1 -> s(z)  ;  t1 -> nil
})

-------------------------------------------
Step 56, which took 0.859251 s (model generation: 0.814440,  model checking: 0.044811):

Model:
|_
{
append -> 
{{{
Q={q_gen_8087, q_gen_8092, q_gen_8093, q_gen_8094, q_gen_8108, q_gen_8109, q_gen_8110, q_gen_8150},
Q_f={q_gen_8087, q_gen_8092},
Delta=
{
<cons>(q_gen_8109, q_gen_8108) -> q_gen_8108
<nil>() -> q_gen_8108
<s>(q_gen_8109) -> q_gen_8109
<z>() -> q_gen_8109
<cons, cons>(q_gen_8094, q_gen_8093) -> q_gen_8093
<nil, cons>(q_gen_8109, q_gen_8108) -> q_gen_8093
<nil, nil>() -> q_gen_8093
<s, s>(q_gen_8094) -> q_gen_8094
<s, z>(q_gen_8109) -> q_gen_8094
<z, z>() -> q_gen_8094
<nil, nil, nil>() -> q_gen_8087
<cons, cons, cons>(q_gen_8110, q_gen_8092) -> q_gen_8092
<cons, nil, cons>(q_gen_8094, q_gen_8093) -> q_gen_8092
<nil, cons, cons>(q_gen_8094, q_gen_8093) -> q_gen_8092
<nil, nil, cons>(q_gen_8109, q_gen_8108) -> q_gen_8092
<s, s, s>(q_gen_8110) -> q_gen_8110
<s, z, s>(q_gen_8094) -> q_gen_8110
<z, s, z>(q_gen_8109) -> q_gen_8110
<z, z, z>() -> q_gen_8110
<cons, cons, cons>(q_gen_8110, q_gen_8087) -> q_gen_8150
}

Datatype: <natlist, natlist, natlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_8086, q_gen_8090, q_gen_8091, q_gen_8105, q_gen_8116, q_gen_8125, q_gen_8126, q_gen_8127, q_gen_8144},
Q_f={q_gen_8086},
Delta=
{
<cons>(q_gen_8105, q_gen_8125) -> q_gen_8090
<cons>(q_gen_8116, q_gen_8090) -> q_gen_8090
<nil>() -> q_gen_8090
<z>() -> q_gen_8105
<s>(q_gen_8105) -> q_gen_8116
<s>(q_gen_8116) -> q_gen_8116
<cons>(q_gen_8105, q_gen_8090) -> q_gen_8125
<cons, s>(q_gen_8091, q_gen_8090) -> q_gen_8086
<cons, s>(q_gen_8126, q_gen_8125) -> q_gen_8086
<nil, z>() -> q_gen_8086
<s, s>(q_gen_8126) -> q_gen_8091
<s, s>(q_gen_8144) -> q_gen_8091
<s, z>(q_gen_8105) -> q_gen_8091
<s, z>(q_gen_8116) -> q_gen_8091
<z, z>() -> q_gen_8091
<s, s>(q_gen_8091) -> q_gen_8126
<z, s>(q_gen_8105) -> q_gen_8126
<cons, s>(q_gen_8091, q_gen_8125) -> q_gen_8127
<cons, s>(q_gen_8126, q_gen_8090) -> q_gen_8127
<cons, s>(q_gen_8144, q_gen_8090) -> q_gen_8127
<cons, s>(q_gen_8144, q_gen_8125) -> q_gen_8127
<z, s>(q_gen_8116) -> q_gen_8144
}

Datatype: <natlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_8083, q_gen_8085, q_gen_8128},
Q_f={q_gen_8083},
Delta=
{
<s>(q_gen_8085) -> q_gen_8085
<z>() -> q_gen_8085
<s, s>(q_gen_8083) -> q_gen_8083
<z, s>(q_gen_8085) -> q_gen_8083
<z, z>() -> q_gen_8083
<s, s>(q_gen_8128) -> q_gen_8128
<s, z>(q_gen_8085) -> q_gen_8128
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_8082, q_gen_8102, q_gen_8122, q_gen_8123, q_gen_8151, q_gen_8152},
Q_f={q_gen_8082},
Delta=
{
<cons>(q_gen_8123, q_gen_8122) -> q_gen_8122
<nil>() -> q_gen_8122
<s>(q_gen_8123) -> q_gen_8123
<z>() -> q_gen_8123
<cons, cons>(q_gen_8102, q_gen_8082) -> q_gen_8082
<cons, cons>(q_gen_8102, q_gen_8151) -> q_gen_8082
<nil, cons>(q_gen_8123, q_gen_8122) -> q_gen_8082
<nil, nil>() -> q_gen_8082
<s, s>(q_gen_8102) -> q_gen_8102
<s, z>(q_gen_8123) -> q_gen_8102
<z, s>(q_gen_8123) -> q_gen_8102
<z, z>() -> q_gen_8102
<cons, cons>(q_gen_8102, q_gen_8152) -> q_gen_8151
<cons, nil>(q_gen_8123, q_gen_8122) -> q_gen_8152
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 36
() -> length([nil, z]) -> 36
() -> leq([z, s(nn2)]) -> 36
() -> leq([z, z]) -> 36
() -> reverse([nil, nil]) -> 36
(append([_sda, cons(h1, nil), _tda]) /\ reverse([t1, _sda])) -> reverse([cons(h1, t1), _tda]) -> 39
(append([t1, l2, _nda])) -> append([cons(h1, t1), l2, cons(h1, _nda)]) -> 37
(length([_cea, _dea]) /\ length([l1, _bea]) /\ reverse([l1, _cea])) -> leq([_bea, _dea]) -> 37
(length([ll, _xda])) -> length([cons(x, ll), s(_xda)]) -> 40
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 37
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 37
(leq([s(nn1), z])) -> BOT -> 37
}
Sat witness: Found: ((length([ll, _xda])) -> length([cons(x, ll), s(_xda)]), {
_xda -> s(s(s(z)))  ;  ll -> cons(s(z), nil)  ;  x -> z
})

-------------------------------------------
Step 57, which took 7.138043 s (model generation: 7.108435,  model checking: 0.029608):

Model:
|_
{
append -> 
{{{
Q={q_gen_8087, q_gen_8092, q_gen_8093, q_gen_8094, q_gen_8108, q_gen_8109, q_gen_8110, q_gen_8150},
Q_f={q_gen_8087, q_gen_8092},
Delta=
{
<cons>(q_gen_8109, q_gen_8108) -> q_gen_8108
<nil>() -> q_gen_8108
<s>(q_gen_8109) -> q_gen_8109
<z>() -> q_gen_8109
<cons, cons>(q_gen_8094, q_gen_8093) -> q_gen_8093
<nil, cons>(q_gen_8109, q_gen_8108) -> q_gen_8093
<nil, nil>() -> q_gen_8093
<s, s>(q_gen_8094) -> q_gen_8094
<s, z>(q_gen_8109) -> q_gen_8094
<z, z>() -> q_gen_8094
<nil, nil, nil>() -> q_gen_8087
<cons, cons, cons>(q_gen_8110, q_gen_8092) -> q_gen_8092
<cons, nil, cons>(q_gen_8094, q_gen_8093) -> q_gen_8092
<nil, cons, cons>(q_gen_8094, q_gen_8093) -> q_gen_8092
<nil, nil, cons>(q_gen_8109, q_gen_8108) -> q_gen_8092
<s, s, s>(q_gen_8110) -> q_gen_8110
<s, z, s>(q_gen_8094) -> q_gen_8110
<z, s, z>(q_gen_8109) -> q_gen_8110
<z, z, z>() -> q_gen_8110
<cons, cons, cons>(q_gen_8110, q_gen_8087) -> q_gen_8150
}

Datatype: <natlist, natlist, natlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_8086, q_gen_8090, q_gen_8091, q_gen_8105, q_gen_8116, q_gen_8125, q_gen_8126, q_gen_8127, q_gen_8186},
Q_f={q_gen_8086},
Delta=
{
<cons>(q_gen_8105, q_gen_8125) -> q_gen_8090
<cons>(q_gen_8116, q_gen_8090) -> q_gen_8090
<nil>() -> q_gen_8090
<z>() -> q_gen_8105
<s>(q_gen_8105) -> q_gen_8116
<cons>(q_gen_8105, q_gen_8090) -> q_gen_8125
<s>(q_gen_8116) -> q_gen_8186
<cons, s>(q_gen_8091, q_gen_8090) -> q_gen_8086
<cons, s>(q_gen_8126, q_gen_8125) -> q_gen_8086
<nil, z>() -> q_gen_8086
<s, s>(q_gen_8126) -> q_gen_8091
<s, z>(q_gen_8105) -> q_gen_8091
<s, z>(q_gen_8116) -> q_gen_8091
<s, z>(q_gen_8186) -> q_gen_8091
<z, s>(q_gen_8186) -> q_gen_8091
<z, z>() -> q_gen_8091
<s, s>(q_gen_8091) -> q_gen_8126
<z, s>(q_gen_8105) -> q_gen_8126
<z, s>(q_gen_8116) -> q_gen_8126
<cons, s>(q_gen_8091, q_gen_8125) -> q_gen_8127
<cons, s>(q_gen_8126, q_gen_8090) -> q_gen_8127
}

Datatype: <natlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_8083, q_gen_8085, q_gen_8128},
Q_f={q_gen_8083},
Delta=
{
<s>(q_gen_8085) -> q_gen_8085
<z>() -> q_gen_8085
<s, s>(q_gen_8083) -> q_gen_8083
<z, s>(q_gen_8085) -> q_gen_8083
<z, z>() -> q_gen_8083
<s, s>(q_gen_8128) -> q_gen_8128
<s, z>(q_gen_8085) -> q_gen_8128
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_8082, q_gen_8102, q_gen_8122, q_gen_8123, q_gen_8151, q_gen_8152},
Q_f={q_gen_8082},
Delta=
{
<cons>(q_gen_8123, q_gen_8122) -> q_gen_8122
<nil>() -> q_gen_8122
<s>(q_gen_8123) -> q_gen_8123
<z>() -> q_gen_8123
<cons, cons>(q_gen_8102, q_gen_8082) -> q_gen_8082
<cons, cons>(q_gen_8102, q_gen_8151) -> q_gen_8082
<nil, cons>(q_gen_8123, q_gen_8122) -> q_gen_8082
<nil, nil>() -> q_gen_8082
<s, s>(q_gen_8102) -> q_gen_8102
<s, z>(q_gen_8123) -> q_gen_8102
<z, s>(q_gen_8123) -> q_gen_8102
<z, z>() -> q_gen_8102
<cons, cons>(q_gen_8102, q_gen_8152) -> q_gen_8151
<cons, nil>(q_gen_8123, q_gen_8122) -> q_gen_8152
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 37
() -> length([nil, z]) -> 37
() -> leq([z, s(nn2)]) -> 37
() -> leq([z, z]) -> 37
() -> reverse([nil, nil]) -> 37
(append([_sda, cons(h1, nil), _tda]) /\ reverse([t1, _sda])) -> reverse([cons(h1, t1), _tda]) -> 39
(append([t1, l2, _nda])) -> append([cons(h1, t1), l2, cons(h1, _nda)]) -> 37
(length([_cea, _dea]) /\ length([l1, _bea]) /\ reverse([l1, _cea])) -> leq([_bea, _dea]) -> 40
(length([ll, _xda])) -> length([cons(x, ll), s(_xda)]) -> 40
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 38
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 38
(leq([s(nn1), z])) -> BOT -> 38
}
Sat witness: Found: ((length([_cea, _dea]) /\ length([l1, _bea]) /\ reverse([l1, _cea])) -> leq([_bea, _dea]), {
_bea -> s(s(s(z)))  ;  _cea -> cons(z, cons(z, nil))  ;  _dea -> s(s(z))  ;  l1 -> cons(z, cons(z, nil))
})

-------------------------------------------
Step 58, which took 7.844005 s (model generation: 7.834874,  model checking: 0.009131):

Model:
|_
{
append -> 
{{{
Q={q_gen_8087, q_gen_8093, q_gen_8094, q_gen_8107, q_gen_8108, q_gen_8109, q_gen_8110, q_gen_8118, q_gen_8132},
Q_f={q_gen_8087},
Delta=
{
<nil>() -> q_gen_8108
<s>(q_gen_8109) -> q_gen_8109
<z>() -> q_gen_8109
<cons>(q_gen_8109, q_gen_8108) -> q_gen_8132
<cons, cons>(q_gen_8094, q_gen_8093) -> q_gen_8093
<nil, nil>() -> q_gen_8093
<s, s>(q_gen_8094) -> q_gen_8094
<s, z>(q_gen_8109) -> q_gen_8094
<z, z>() -> q_gen_8094
<nil, cons>(q_gen_8109, q_gen_8108) -> q_gen_8118
<nil, cons>(q_gen_8109, q_gen_8132) -> q_gen_8118
<cons, cons, cons>(q_gen_8110, q_gen_8107) -> q_gen_8087
<cons, nil, cons>(q_gen_8094, q_gen_8093) -> q_gen_8087
<nil, cons, cons>(q_gen_8094, q_gen_8093) -> q_gen_8087
<nil, nil, cons>(q_gen_8109, q_gen_8132) -> q_gen_8087
<nil, nil, nil>() -> q_gen_8087
<cons, cons, cons>(q_gen_8110, q_gen_8087) -> q_gen_8107
<cons, nil, cons>(q_gen_8094, q_gen_8118) -> q_gen_8107
<nil, cons, cons>(q_gen_8094, q_gen_8118) -> q_gen_8107
<nil, nil, cons>(q_gen_8109, q_gen_8108) -> q_gen_8107
<s, s, s>(q_gen_8110) -> q_gen_8110
<s, z, s>(q_gen_8094) -> q_gen_8110
<z, s, z>(q_gen_8109) -> q_gen_8110
<z, z, z>() -> q_gen_8110
}

Datatype: <natlist, natlist, natlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_8086, q_gen_8090, q_gen_8091, q_gen_8105, q_gen_8116, q_gen_8125, q_gen_8126, q_gen_8127},
Q_f={q_gen_8086},
Delta=
{
<cons>(q_gen_8105, q_gen_8125) -> q_gen_8090
<nil>() -> q_gen_8090
<s>(q_gen_8116) -> q_gen_8105
<z>() -> q_gen_8105
<s>(q_gen_8105) -> q_gen_8116
<cons>(q_gen_8105, q_gen_8090) -> q_gen_8125
<cons>(q_gen_8116, q_gen_8090) -> q_gen_8125
<cons, s>(q_gen_8091, q_gen_8090) -> q_gen_8086
<cons, s>(q_gen_8126, q_gen_8125) -> q_gen_8086
<nil, z>() -> q_gen_8086
<s, s>(q_gen_8126) -> q_gen_8091
<s, z>(q_gen_8105) -> q_gen_8091
<s, z>(q_gen_8116) -> q_gen_8091
<z, s>(q_gen_8116) -> q_gen_8091
<z, z>() -> q_gen_8091
<s, s>(q_gen_8091) -> q_gen_8126
<z, s>(q_gen_8105) -> q_gen_8126
<cons, s>(q_gen_8091, q_gen_8125) -> q_gen_8127
<cons, s>(q_gen_8126, q_gen_8090) -> q_gen_8127
}

Datatype: <natlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_8083, q_gen_8085, q_gen_8096, q_gen_8128},
Q_f={q_gen_8083},
Delta=
{
<z>() -> q_gen_8085
<s>(q_gen_8085) -> q_gen_8096
<s, s>(q_gen_8083) -> q_gen_8083
<s, z>(q_gen_8096) -> q_gen_8083
<z, s>(q_gen_8085) -> q_gen_8083
<z, s>(q_gen_8096) -> q_gen_8083
<z, z>() -> q_gen_8083
<s, s>(q_gen_8128) -> q_gen_8128
<s, z>(q_gen_8085) -> q_gen_8128
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_8082, q_gen_8102, q_gen_8120, q_gen_8122, q_gen_8123},
Q_f={q_gen_8082},
Delta=
{
<cons>(q_gen_8123, q_gen_8122) -> q_gen_8122
<nil>() -> q_gen_8122
<s>(q_gen_8123) -> q_gen_8123
<z>() -> q_gen_8123
<cons, cons>(q_gen_8102, q_gen_8082) -> q_gen_8082
<nil, nil>() -> q_gen_8082
<s, s>(q_gen_8102) -> q_gen_8102
<s, z>(q_gen_8123) -> q_gen_8102
<z, s>(q_gen_8123) -> q_gen_8102
<z, z>() -> q_gen_8102
<cons, cons>(q_gen_8102, q_gen_8120) -> q_gen_8120
<cons, nil>(q_gen_8123, q_gen_8122) -> q_gen_8120
<nil, cons>(q_gen_8123, q_gen_8122) -> q_gen_8120
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 37
() -> length([nil, z]) -> 37
() -> leq([z, s(nn2)]) -> 37
() -> leq([z, z]) -> 37
() -> reverse([nil, nil]) -> 37
(append([_sda, cons(h1, nil), _tda]) /\ reverse([t1, _sda])) -> reverse([cons(h1, t1), _tda]) -> 39
(append([t1, l2, _nda])) -> append([cons(h1, t1), l2, cons(h1, _nda)]) -> 40
(length([_cea, _dea]) /\ length([l1, _bea]) /\ reverse([l1, _cea])) -> leq([_bea, _dea]) -> 40
(length([ll, _xda])) -> length([cons(x, ll), s(_xda)]) -> 40
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 38
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 38
(leq([s(nn1), z])) -> BOT -> 38
}
Sat witness: Found: ((append([t1, l2, _nda])) -> append([cons(h1, t1), l2, cons(h1, _nda)]), {
_nda -> cons(z, cons(z, nil))  ;  h1 -> z  ;  l2 -> nil  ;  t1 -> nil
})

-------------------------------------------
Step 59, which took 8.637352 s (model generation: 8.543653,  model checking: 0.093699):

Model:
|_
{
append -> 
{{{
Q={q_gen_8087, q_gen_8092, q_gen_8093, q_gen_8094, q_gen_8108, q_gen_8109, q_gen_8110, q_gen_8150},
Q_f={q_gen_8087, q_gen_8092},
Delta=
{
<cons>(q_gen_8109, q_gen_8108) -> q_gen_8108
<nil>() -> q_gen_8108
<s>(q_gen_8109) -> q_gen_8109
<z>() -> q_gen_8109
<cons, cons>(q_gen_8094, q_gen_8093) -> q_gen_8093
<nil, cons>(q_gen_8109, q_gen_8108) -> q_gen_8093
<nil, nil>() -> q_gen_8093
<s, s>(q_gen_8094) -> q_gen_8094
<s, z>(q_gen_8109) -> q_gen_8094
<z, z>() -> q_gen_8094
<nil, nil, nil>() -> q_gen_8087
<cons, cons, cons>(q_gen_8110, q_gen_8092) -> q_gen_8092
<cons, nil, cons>(q_gen_8094, q_gen_8093) -> q_gen_8092
<nil, cons, cons>(q_gen_8094, q_gen_8093) -> q_gen_8092
<nil, nil, cons>(q_gen_8109, q_gen_8108) -> q_gen_8092
<s, s, s>(q_gen_8110) -> q_gen_8110
<s, z, s>(q_gen_8094) -> q_gen_8110
<z, s, z>(q_gen_8109) -> q_gen_8110
<z, z, z>() -> q_gen_8110
<cons, cons, cons>(q_gen_8110, q_gen_8087) -> q_gen_8150
}

Datatype: <natlist, natlist, natlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_8086, q_gen_8090, q_gen_8091, q_gen_8105, q_gen_8116, q_gen_8125, q_gen_8126, q_gen_8127, q_gen_8144, q_gen_8186},
Q_f={q_gen_8086},
Delta=
{
<cons>(q_gen_8105, q_gen_8125) -> q_gen_8090
<cons>(q_gen_8116, q_gen_8090) -> q_gen_8090
<nil>() -> q_gen_8090
<z>() -> q_gen_8105
<s>(q_gen_8105) -> q_gen_8116
<cons>(q_gen_8105, q_gen_8090) -> q_gen_8125
<s>(q_gen_8116) -> q_gen_8186
<cons, s>(q_gen_8091, q_gen_8090) -> q_gen_8086
<cons, s>(q_gen_8126, q_gen_8125) -> q_gen_8086
<nil, z>() -> q_gen_8086
<s, s>(q_gen_8126) -> q_gen_8091
<s, s>(q_gen_8144) -> q_gen_8091
<s, z>(q_gen_8105) -> q_gen_8091
<s, z>(q_gen_8116) -> q_gen_8091
<s, z>(q_gen_8186) -> q_gen_8091
<z, s>(q_gen_8186) -> q_gen_8091
<z, z>() -> q_gen_8091
<s, s>(q_gen_8091) -> q_gen_8126
<z, s>(q_gen_8105) -> q_gen_8126
<cons, s>(q_gen_8091, q_gen_8125) -> q_gen_8127
<cons, s>(q_gen_8126, q_gen_8090) -> q_gen_8127
<cons, s>(q_gen_8144, q_gen_8090) -> q_gen_8127
<cons, s>(q_gen_8144, q_gen_8125) -> q_gen_8127
<z, s>(q_gen_8116) -> q_gen_8144
}

Datatype: <natlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_8083, q_gen_8085, q_gen_8128},
Q_f={q_gen_8083},
Delta=
{
<s>(q_gen_8085) -> q_gen_8085
<z>() -> q_gen_8085
<s, s>(q_gen_8083) -> q_gen_8083
<z, s>(q_gen_8085) -> q_gen_8083
<z, z>() -> q_gen_8083
<s, s>(q_gen_8128) -> q_gen_8128
<s, z>(q_gen_8085) -> q_gen_8128
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_8082, q_gen_8102, q_gen_8121, q_gen_8122, q_gen_8123, q_gen_8152},
Q_f={q_gen_8082},
Delta=
{
<cons>(q_gen_8123, q_gen_8122) -> q_gen_8122
<nil>() -> q_gen_8122
<s>(q_gen_8123) -> q_gen_8123
<z>() -> q_gen_8123
<cons, cons>(q_gen_8102, q_gen_8082) -> q_gen_8082
<cons, cons>(q_gen_8102, q_gen_8121) -> q_gen_8082
<nil, nil>() -> q_gen_8082
<s, s>(q_gen_8102) -> q_gen_8102
<s, z>(q_gen_8123) -> q_gen_8102
<z, s>(q_gen_8123) -> q_gen_8102
<z, z>() -> q_gen_8102
<cons, cons>(q_gen_8102, q_gen_8152) -> q_gen_8121
<nil, cons>(q_gen_8123, q_gen_8122) -> q_gen_8121
<cons, nil>(q_gen_8123, q_gen_8122) -> q_gen_8152
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 38
() -> length([nil, z]) -> 38
() -> leq([z, s(nn2)]) -> 38
() -> leq([z, z]) -> 38
() -> reverse([nil, nil]) -> 38
(append([_sda, cons(h1, nil), _tda]) /\ reverse([t1, _sda])) -> reverse([cons(h1, t1), _tda]) -> 40
(append([t1, l2, _nda])) -> append([cons(h1, t1), l2, cons(h1, _nda)]) -> 40
(length([_cea, _dea]) /\ length([l1, _bea]) /\ reverse([l1, _cea])) -> leq([_bea, _dea]) -> 40
(length([ll, _xda])) -> length([cons(x, ll), s(_xda)]) -> 43
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 39
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 39
(leq([s(nn1), z])) -> BOT -> 39
}
Sat witness: Found: ((length([ll, _xda])) -> length([cons(x, ll), s(_xda)]), {
_xda -> s(z)  ;  ll -> cons(s(z), cons(s(z), nil))  ;  x -> s(z)
})

-------------------------------------------
Step 60, which took 9.257794 s (model generation: 9.226696,  model checking: 0.031098):

Model:
|_
{
append -> 
{{{
Q={q_gen_8087, q_gen_8093, q_gen_8094, q_gen_8097, q_gen_8108, q_gen_8109, q_gen_8110, q_gen_8118, q_gen_8119},
Q_f={q_gen_8087, q_gen_8097},
Delta=
{
<cons>(q_gen_8109, q_gen_8108) -> q_gen_8108
<nil>() -> q_gen_8108
<s>(q_gen_8109) -> q_gen_8109
<z>() -> q_gen_8109
<cons, cons>(q_gen_8094, q_gen_8093) -> q_gen_8093
<nil, nil>() -> q_gen_8093
<s, s>(q_gen_8094) -> q_gen_8094
<s, z>(q_gen_8109) -> q_gen_8094
<z, z>() -> q_gen_8094
<nil, cons>(q_gen_8109, q_gen_8108) -> q_gen_8118
<cons, cons, cons>(q_gen_8110, q_gen_8119) -> q_gen_8087
<cons, nil, cons>(q_gen_8094, q_gen_8093) -> q_gen_8087
<nil, nil, nil>() -> q_gen_8087
<cons, cons, cons>(q_gen_8110, q_gen_8097) -> q_gen_8097
<cons, nil, cons>(q_gen_8094, q_gen_8118) -> q_gen_8097
<nil, cons, cons>(q_gen_8094, q_gen_8093) -> q_gen_8097
<nil, nil, cons>(q_gen_8109, q_gen_8108) -> q_gen_8097
<s, s, s>(q_gen_8110) -> q_gen_8110
<s, z, s>(q_gen_8094) -> q_gen_8110
<z, s, z>(q_gen_8109) -> q_gen_8110
<z, z, z>() -> q_gen_8110
<cons, cons, cons>(q_gen_8110, q_gen_8087) -> q_gen_8119
<nil, cons, cons>(q_gen_8094, q_gen_8118) -> q_gen_8119
}

Datatype: <natlist, natlist, natlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_8086, q_gen_8090, q_gen_8091, q_gen_8105, q_gen_8116, q_gen_8125, q_gen_8126, q_gen_8127, q_gen_8139, q_gen_8144},
Q_f={q_gen_8086},
Delta=
{
<nil>() -> q_gen_8090
<z>() -> q_gen_8105
<s>(q_gen_8105) -> q_gen_8116
<s>(q_gen_8116) -> q_gen_8116
<cons>(q_gen_8105, q_gen_8090) -> q_gen_8125
<cons>(q_gen_8105, q_gen_8125) -> q_gen_8139
<cons>(q_gen_8105, q_gen_8139) -> q_gen_8139
<cons>(q_gen_8116, q_gen_8090) -> q_gen_8139
<cons>(q_gen_8116, q_gen_8139) -> q_gen_8139
<cons, s>(q_gen_8091, q_gen_8090) -> q_gen_8086
<cons, s>(q_gen_8091, q_gen_8139) -> q_gen_8086
<cons, s>(q_gen_8126, q_gen_8125) -> q_gen_8086
<cons, s>(q_gen_8126, q_gen_8139) -> q_gen_8086
<cons, s>(q_gen_8144, q_gen_8139) -> q_gen_8086
<nil, z>() -> q_gen_8086
<s, s>(q_gen_8126) -> q_gen_8091
<s, z>(q_gen_8105) -> q_gen_8091
<s, z>(q_gen_8116) -> q_gen_8091
<z, z>() -> q_gen_8091
<s, s>(q_gen_8091) -> q_gen_8126
<s, s>(q_gen_8144) -> q_gen_8126
<z, s>(q_gen_8105) -> q_gen_8126
<cons, s>(q_gen_8091, q_gen_8125) -> q_gen_8127
<cons, s>(q_gen_8126, q_gen_8090) -> q_gen_8127
<cons, s>(q_gen_8144, q_gen_8090) -> q_gen_8127
<cons, s>(q_gen_8144, q_gen_8125) -> q_gen_8127
<z, s>(q_gen_8116) -> q_gen_8144
}

Datatype: <natlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_8083, q_gen_8085, q_gen_8128},
Q_f={q_gen_8083},
Delta=
{
<s>(q_gen_8085) -> q_gen_8085
<z>() -> q_gen_8085
<s, s>(q_gen_8083) -> q_gen_8083
<z, s>(q_gen_8085) -> q_gen_8083
<z, z>() -> q_gen_8083
<s, s>(q_gen_8128) -> q_gen_8128
<s, z>(q_gen_8085) -> q_gen_8128
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_8082, q_gen_8102, q_gen_8122, q_gen_8123, q_gen_8151},
Q_f={q_gen_8082},
Delta=
{
<cons>(q_gen_8123, q_gen_8122) -> q_gen_8122
<nil>() -> q_gen_8122
<s>(q_gen_8123) -> q_gen_8123
<z>() -> q_gen_8123
<cons, cons>(q_gen_8102, q_gen_8082) -> q_gen_8082
<nil, cons>(q_gen_8123, q_gen_8122) -> q_gen_8082
<nil, nil>() -> q_gen_8082
<s, s>(q_gen_8102) -> q_gen_8102
<s, z>(q_gen_8123) -> q_gen_8102
<z, s>(q_gen_8123) -> q_gen_8102
<z, z>() -> q_gen_8102
<cons, cons>(q_gen_8102, q_gen_8151) -> q_gen_8151
<cons, nil>(q_gen_8123, q_gen_8122) -> q_gen_8151
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 39
() -> length([nil, z]) -> 39
() -> leq([z, s(nn2)]) -> 39
() -> leq([z, z]) -> 39
() -> reverse([nil, nil]) -> 39
(append([_sda, cons(h1, nil), _tda]) /\ reverse([t1, _sda])) -> reverse([cons(h1, t1), _tda]) -> 40
(append([t1, l2, _nda])) -> append([cons(h1, t1), l2, cons(h1, _nda)]) -> 40
(length([_cea, _dea]) /\ length([l1, _bea]) /\ reverse([l1, _cea])) -> leq([_bea, _dea]) -> 43
(length([ll, _xda])) -> length([cons(x, ll), s(_xda)]) -> 43
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 40
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 40
(leq([s(nn1), z])) -> BOT -> 40
}
Sat witness: Found: ((length([_cea, _dea]) /\ length([l1, _bea]) /\ reverse([l1, _cea])) -> leq([_bea, _dea]), {
_bea -> s(s(s(z)))  ;  _cea -> cons(z, cons(s(z), nil))  ;  _dea -> s(z)  ;  l1 -> cons(s(z), nil)
})

Total time: 60.004326
Reason for stopping: DontKnow. Stopped because: timeout