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


Learning problem is:

env: {
nat -> {s, z}  ;  natlist -> {cons, nil}
}
definition:
{
(le, P:
{() -> le([z, s(nn2)])
(le([nn1, nn2])) -> le([s(nn1), s(nn2)])
(le([s(nn1), s(nn2)])) -> le([nn1, nn2])
(le([s(nn1), z])) -> BOT
(le([z, z])) -> BOT}
)
(length, F:
{() -> length([nil, z])
(length([ll, _uca])) -> length([cons(x, ll), s(_uca)])}
(length([_vca, _wca]) /\ length([_vca, _xca])) -> eq_nat([_wca, _xca])
)
}

properties:
{(length([l, _yca]) /\ length([cons(x, l), _zca])) -> le([_yca, _zca])}


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

Clause system for inference is:

{
() -> le([z, s(nn2)]) -> 0
() -> length([nil, z]) -> 0
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 0
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 0
(le([s(nn1), z])) -> BOT -> 0
(le([z, z])) -> BOT -> 0
(length([l, _yca]) /\ length([cons(x, l), _zca])) -> le([_yca, _zca]) -> 0
(length([ll, _uca])) -> length([cons(x, ll), s(_uca)]) -> 0
}


Solving took 2104.585646 seconds.
DontKnow. Stopped because: timeout
Working model:
|_
{
le -> 
{{{
Q={q_gen_7879, q_gen_7880, q_gen_7884, q_gen_7885, q_gen_7886, q_gen_7897, q_gen_7898, q_gen_7903, q_gen_7910, q_gen_7911, q_gen_7912, q_gen_7918, q_gen_7926, q_gen_7927, q_gen_7928, q_gen_7929, q_gen_7930, q_gen_7938, q_gen_7939, q_gen_7947, q_gen_7961, q_gen_7975, q_gen_7976, q_gen_7977, q_gen_7987, q_gen_7988, q_gen_8003},
Q_f={},
Delta=
{
<z>() -> q_gen_7880
<s>(q_gen_7880) -> q_gen_7886
<s>(q_gen_7886) -> q_gen_7930
<s>(q_gen_7930) -> q_gen_7988
<z, s>(q_gen_7880) -> q_gen_7879
<s, s>(q_gen_7879) -> q_gen_7884
<z, s>(q_gen_7886) -> q_gen_7885
<s, s>(q_gen_7898) -> q_gen_7897
<z, z>() -> q_gen_7898
<s, s>(q_gen_7897) -> q_gen_7903
<s, s>(q_gen_7911) -> q_gen_7910
<s, s>(q_gen_7912) -> q_gen_7911
<s, z>(q_gen_7880) -> q_gen_7912
<s, s>(q_gen_7903) -> q_gen_7918
<s, s>(q_gen_7927) -> q_gen_7926
<s, s>(q_gen_7928) -> q_gen_7927
<s, z>(q_gen_7886) -> q_gen_7928
<z, s>(q_gen_7930) -> q_gen_7929
<s, s>(q_gen_7939) -> q_gen_7938
<s, s>(q_gen_7910) -> q_gen_7939
<s, s>(q_gen_7926) -> q_gen_7947
<s, s>(q_gen_7918) -> q_gen_7961
<s, s>(q_gen_7976) -> q_gen_7975
<s, s>(q_gen_7977) -> q_gen_7976
<s, z>(q_gen_7930) -> q_gen_7977
<z, s>(q_gen_7988) -> q_gen_7987
<s, s>(q_gen_7947) -> q_gen_8003
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_7878, q_gen_7881, q_gen_7882, q_gen_7883, q_gen_7887, q_gen_7888, q_gen_7889, q_gen_7890, q_gen_7891, q_gen_7892, q_gen_7893, q_gen_7894, q_gen_7895, q_gen_7896, q_gen_7899, q_gen_7900, q_gen_7901, q_gen_7902, q_gen_7904, q_gen_7905, q_gen_7906, q_gen_7907, q_gen_7908, q_gen_7909, q_gen_7913, q_gen_7914, q_gen_7915, q_gen_7916, q_gen_7917, q_gen_7919, q_gen_7920, q_gen_7921, q_gen_7922, q_gen_7923, q_gen_7924, q_gen_7925, q_gen_7931, q_gen_7932, q_gen_7933, q_gen_7934, q_gen_7935, q_gen_7936, q_gen_7937, q_gen_7940, q_gen_7941, q_gen_7942, q_gen_7943, q_gen_7944, q_gen_7945, q_gen_7946, q_gen_7948, q_gen_7949, q_gen_7950, q_gen_7951, q_gen_7952, q_gen_7953, q_gen_7954, q_gen_7955, q_gen_7956, q_gen_7957, q_gen_7958, q_gen_7959, q_gen_7960, q_gen_7962, q_gen_7963, q_gen_7964, q_gen_7965, q_gen_7966, q_gen_7967, q_gen_7968, q_gen_7969, q_gen_7970, q_gen_7971, q_gen_7972, q_gen_7973, q_gen_7974, q_gen_7978, q_gen_7979, q_gen_7980, q_gen_7981, q_gen_7982, q_gen_7983, q_gen_7984, q_gen_7985, q_gen_7986, q_gen_7989, q_gen_7990, q_gen_7991, q_gen_7992, q_gen_7993, q_gen_7994, q_gen_7995, q_gen_7996, q_gen_7997, q_gen_7998, q_gen_7999, q_gen_8000, q_gen_8001, q_gen_8002, q_gen_8004, q_gen_8005, q_gen_8006, q_gen_8007, q_gen_8008, q_gen_8009, q_gen_8010, q_gen_8011, q_gen_8012, q_gen_8013, q_gen_8014, q_gen_8015, q_gen_8016, q_gen_8017, q_gen_8018, q_gen_8019, q_gen_8020, q_gen_8021, q_gen_8022, q_gen_8023, q_gen_8024},
Q_f={},
Delta=
{
<nil>() -> q_gen_7882
<z>() -> q_gen_7889
<s>(q_gen_7889) -> q_gen_7892
<cons>(q_gen_7889, q_gen_7882) -> q_gen_7894
<cons>(q_gen_7889, q_gen_7894) -> q_gen_7900
<s>(q_gen_7892) -> q_gen_7907
<cons>(q_gen_7889, q_gen_7900) -> q_gen_7909
<cons>(q_gen_7907, q_gen_7882) -> q_gen_7920
<s>(q_gen_7907) -> q_gen_7924
<cons>(q_gen_7924, q_gen_7882) -> q_gen_7932
<cons>(q_gen_7889, q_gen_7920) -> q_gen_7934
<cons>(q_gen_7889, q_gen_7934) -> q_gen_7937
<cons>(q_gen_7892, q_gen_7882) -> q_gen_7941
<cons>(q_gen_7889, q_gen_7941) -> q_gen_7949
<cons>(q_gen_7889, q_gen_7949) -> q_gen_7951
<cons>(q_gen_7889, q_gen_7951) -> q_gen_7956
<cons>(q_gen_7889, q_gen_7959) -> q_gen_7958
<cons>(q_gen_7889, q_gen_7937) -> q_gen_7959
<cons>(q_gen_7889, q_gen_7909) -> q_gen_7966
<cons>(q_gen_7889, q_gen_7966) -> q_gen_7968
<cons>(q_gen_7892, q_gen_7951) -> q_gen_7983
<cons>(q_gen_7892, q_gen_7894) -> q_gen_7986
<cons>(q_gen_7889, q_gen_7991) -> q_gen_7990
<cons>(q_gen_7892, q_gen_7909) -> q_gen_7991
<cons>(q_gen_7889, q_gen_7990) -> q_gen_7993
<cons>(q_gen_7889, q_gen_7996) -> q_gen_7995
<cons>(q_gen_7892, q_gen_7941) -> q_gen_7996
<s>(q_gen_7924) -> q_gen_8000
<cons>(q_gen_7889, q_gen_8006) -> q_gen_8005
<cons>(q_gen_7889, q_gen_8007) -> q_gen_8006
<cons>(q_gen_7892, q_gen_7932) -> q_gen_8007
<cons>(q_gen_7889, q_gen_8005) -> q_gen_8009
<cons>(q_gen_7889, q_gen_8013) -> q_gen_8012
<cons>(q_gen_7889, q_gen_8014) -> q_gen_8013
<cons>(q_gen_7889, q_gen_7986) -> q_gen_8014
<cons>(q_gen_7889, q_gen_8012) -> q_gen_8016
<cons>(q_gen_8000, q_gen_7920) -> q_gen_8024
<nil, z>() -> q_gen_7878
<cons, s>(q_gen_7883, q_gen_7882) -> q_gen_7881
<z, z>() -> q_gen_7883
<cons, s>(q_gen_7888, q_gen_7882) -> q_gen_7887
<s, z>(q_gen_7889) -> q_gen_7888
<cons, s>(q_gen_7891, q_gen_7882) -> q_gen_7890
<s, z>(q_gen_7892) -> q_gen_7891
<cons, s>(q_gen_7895, q_gen_7894) -> q_gen_7893
<z, s>(q_gen_7889) -> q_gen_7895
<cons, s>(q_gen_7883, q_gen_7894) -> q_gen_7896
<cons, s>(q_gen_7901, q_gen_7900) -> q_gen_7899
<z, s>(q_gen_7892) -> q_gen_7901
<cons, s>(q_gen_7895, q_gen_7882) -> q_gen_7902
<cons, s>(q_gen_7895, q_gen_7900) -> q_gen_7904
<cons, s>(q_gen_7906, q_gen_7882) -> q_gen_7905
<s, z>(q_gen_7907) -> q_gen_7906
<cons, s>(q_gen_7895, q_gen_7909) -> q_gen_7908
<cons, s>(q_gen_7901, q_gen_7882) -> q_gen_7913
<cons, s>(q_gen_7915, q_gen_7894) -> q_gen_7914
<z, s>(q_gen_7907) -> q_gen_7915
<cons, s>(q_gen_7915, q_gen_7909) -> q_gen_7916
<cons, s>(q_gen_7901, q_gen_7894) -> q_gen_7917
<cons, s>(q_gen_7895, q_gen_7920) -> q_gen_7919
<cons, s>(q_gen_7901, q_gen_7909) -> q_gen_7921
<cons, s>(q_gen_7923, q_gen_7882) -> q_gen_7922
<s, z>(q_gen_7924) -> q_gen_7923
<cons, s>(q_gen_7915, q_gen_7882) -> q_gen_7925
<cons, s>(q_gen_7895, q_gen_7932) -> q_gen_7931
<cons, s>(q_gen_7935, q_gen_7934) -> q_gen_7933
<z, s>(q_gen_7924) -> q_gen_7935
<cons, s>(q_gen_7915, q_gen_7937) -> q_gen_7936
<cons, s>(q_gen_7942, q_gen_7941) -> q_gen_7940
<s, s>(q_gen_7883) -> q_gen_7942
<cons, s>(q_gen_7883, q_gen_7941) -> q_gen_7943
<cons, s>(q_gen_7895, q_gen_7941) -> q_gen_7944
<cons, s>(q_gen_7935, q_gen_7920) -> q_gen_7945
<cons, s>(q_gen_7901, q_gen_7934) -> q_gen_7946
<cons, s>(q_gen_7901, q_gen_7949) -> q_gen_7948
<cons, s>(q_gen_7952, q_gen_7951) -> q_gen_7950
<s, s>(q_gen_7901) -> q_gen_7952
<cons, s>(q_gen_7952, q_gen_7882) -> q_gen_7953
<cons, s>(q_gen_7915, q_gen_7951) -> q_gen_7954
<cons, s>(q_gen_7935, q_gen_7956) -> q_gen_7955
<cons, s>(q_gen_7952, q_gen_7958) -> q_gen_7957
<cons, s>(q_gen_7915, q_gen_7959) -> q_gen_7960
<cons, s>(q_gen_7915, q_gen_7920) -> q_gen_7962
<cons, s>(q_gen_7942, q_gen_7949) -> q_gen_7963
<cons, s>(q_gen_7888, q_gen_7934) -> q_gen_7964
<cons, s>(q_gen_7915, q_gen_7966) -> q_gen_7965
<cons, s>(q_gen_7935, q_gen_7968) -> q_gen_7967
<cons, s>(q_gen_7935, q_gen_7941) -> q_gen_7969
<cons, s>(q_gen_7901, q_gen_7920) -> q_gen_7970
<cons, s>(q_gen_7915, q_gen_7934) -> q_gen_7971
<cons, s>(q_gen_7895, q_gen_7934) -> q_gen_7972
<cons, s>(q_gen_7942, q_gen_7894) -> q_gen_7973
<cons, s>(q_gen_7935, q_gen_7882) -> q_gen_7974
<cons, s>(q_gen_7935, q_gen_7966) -> q_gen_7978
<cons, s>(q_gen_7895, q_gen_7937) -> q_gen_7979
<cons, s>(q_gen_7935, q_gen_7894) -> q_gen_7980
<cons, s>(q_gen_7952, q_gen_7909) -> q_gen_7981
<cons, s>(q_gen_7935, q_gen_7983) -> q_gen_7982
<cons, s>(q_gen_7942, q_gen_7909) -> q_gen_7984
<cons, s>(q_gen_7901, q_gen_7986) -> q_gen_7985
<cons, s>(q_gen_7901, q_gen_7990) -> q_gen_7989
<cons, s>(q_gen_7952, q_gen_7993) -> q_gen_7992
<cons, s>(q_gen_7942, q_gen_7995) -> q_gen_7994
<cons, s>(q_gen_7901, q_gen_7996) -> q_gen_7997
<cons, s>(q_gen_7999, q_gen_7882) -> q_gen_7998
<s, z>(q_gen_8000) -> q_gen_7999
<cons, s>(q_gen_8002, q_gen_7934) -> q_gen_8001
<z, s>(q_gen_8000) -> q_gen_8002
<cons, s>(q_gen_7935, q_gen_8005) -> q_gen_8004
<cons, s>(q_gen_8002, q_gen_8009) -> q_gen_8008
<cons, s>(q_gen_8002, q_gen_7920) -> q_gen_8010
<cons, s>(q_gen_8002, q_gen_8012) -> q_gen_8011
<cons, s>(q_gen_8017, q_gen_8016) -> q_gen_8015
<s, s>(q_gen_8018) -> q_gen_8017
<s, s>(q_gen_7935) -> q_gen_8018
<cons, s>(q_gen_8020, q_gen_7920) -> q_gen_8019
<s, s>(q_gen_8021) -> q_gen_8020
<s, s>(q_gen_8022) -> q_gen_8021
<s, s>(q_gen_7888) -> q_gen_8022
<cons, s>(q_gen_7901, q_gen_8024) -> q_gen_8023
}

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

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

-------------------
STEPS:
-------------------------------------------
Step 0, which took 0.029702 s (model generation: 0.029531,  model checking: 0.000171):

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

}

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

}

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

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 0
() -> length([nil, z]) -> 3
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 1
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 1
(le([s(nn1), z])) -> BOT -> 1
(le([z, z])) -> BOT -> 1
(length([l, _yca]) /\ length([cons(x, l), _zca])) -> le([_yca, _zca]) -> 1
(length([ll, _uca])) -> length([cons(x, ll), s(_uca)]) -> 1
}
Sat witness: Found: (() -> length([nil, z]), {

})

-------------------------------------------
Step 1, which took 0.010703 s (model generation: 0.010204,  model checking: 0.000499):

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

}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_7878},
Q_f={q_gen_7878},
Delta=
{
<nil, z>() -> q_gen_7878
}

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

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 3
() -> length([nil, z]) -> 3
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 1
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 1
(le([s(nn1), z])) -> BOT -> 1
(le([z, z])) -> BOT -> 1
(length([l, _yca]) /\ length([cons(x, l), _zca])) -> le([_yca, _zca]) -> 1
(length([ll, _uca])) -> length([cons(x, ll), s(_uca)]) -> 1
}
Sat witness: Found: (() -> le([z, s(nn2)]), {
nn2 -> z
})

-------------------------------------------
Step 2, which took 0.009573 s (model generation: 0.009413,  model checking: 0.000160):

Model:
|_
{
le -> 
{{{
Q={q_gen_7879, q_gen_7880},
Q_f={q_gen_7879},
Delta=
{
<z>() -> q_gen_7880
<z, s>(q_gen_7880) -> q_gen_7879
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_7878},
Q_f={q_gen_7878},
Delta=
{
<nil, z>() -> q_gen_7878
}

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

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 3
() -> length([nil, z]) -> 3
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 1
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 1
(le([s(nn1), z])) -> BOT -> 1
(le([z, z])) -> BOT -> 1
(length([l, _yca]) /\ length([cons(x, l), _zca])) -> le([_yca, _zca]) -> 1
(length([ll, _uca])) -> length([cons(x, ll), s(_uca)]) -> 4
}
Sat witness: Found: ((length([ll, _uca])) -> length([cons(x, ll), s(_uca)]), {
_uca -> z  ;  ll -> nil  ;  x -> z
})

-------------------------------------------
Step 3, which took 0.012195 s (model generation: 0.011927,  model checking: 0.000268):

Model:
|_
{
le -> 
{{{
Q={q_gen_7879, q_gen_7880},
Q_f={q_gen_7879},
Delta=
{
<z>() -> q_gen_7880
<z, s>(q_gen_7880) -> q_gen_7879
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_7878, q_gen_7882, q_gen_7883},
Q_f={q_gen_7878},
Delta=
{
<nil>() -> q_gen_7882
<cons, s>(q_gen_7883, q_gen_7882) -> q_gen_7878
<nil, z>() -> q_gen_7878
<z, z>() -> q_gen_7883
}

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

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 3
() -> length([nil, z]) -> 3
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 4
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 2
(le([s(nn1), z])) -> BOT -> 2
(le([z, z])) -> BOT -> 2
(length([l, _yca]) /\ length([cons(x, l), _zca])) -> le([_yca, _zca]) -> 2
(length([ll, _uca])) -> length([cons(x, ll), s(_uca)]) -> 4
}
Sat witness: Found: ((le([nn1, nn2])) -> le([s(nn1), s(nn2)]), {
nn1 -> z  ;  nn2 -> s(z)
})

-------------------------------------------
Step 4, which took 0.025466 s (model generation: 0.025048,  model checking: 0.000418):

Model:
|_
{
le -> 
{{{
Q={q_gen_7879, q_gen_7880},
Q_f={q_gen_7879},
Delta=
{
<z>() -> q_gen_7880
<s, s>(q_gen_7879) -> q_gen_7879
<z, s>(q_gen_7880) -> q_gen_7879
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_7878, q_gen_7882, q_gen_7883},
Q_f={q_gen_7878},
Delta=
{
<nil>() -> q_gen_7882
<cons, s>(q_gen_7883, q_gen_7882) -> q_gen_7878
<nil, z>() -> q_gen_7878
<z, z>() -> q_gen_7883
}

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

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 6
() -> length([nil, z]) -> 4
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 4
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 3
(le([s(nn1), z])) -> BOT -> 3
(le([z, z])) -> BOT -> 3
(length([l, _yca]) /\ length([cons(x, l), _zca])) -> le([_yca, _zca]) -> 3
(length([ll, _uca])) -> length([cons(x, ll), s(_uca)]) -> 4
}
Sat witness: Found: (() -> le([z, s(nn2)]), {
nn2 -> s(z)
})

-------------------------------------------
Step 5, which took 0.020483 s (model generation: 0.020031,  model checking: 0.000452):

Model:
|_
{
le -> 
{{{
Q={q_gen_7879, q_gen_7880},
Q_f={q_gen_7879},
Delta=
{
<s>(q_gen_7880) -> q_gen_7880
<z>() -> q_gen_7880
<s, s>(q_gen_7879) -> q_gen_7879
<z, s>(q_gen_7880) -> q_gen_7879
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_7878, q_gen_7882, q_gen_7883},
Q_f={q_gen_7878},
Delta=
{
<nil>() -> q_gen_7882
<cons, s>(q_gen_7883, q_gen_7882) -> q_gen_7878
<nil, z>() -> q_gen_7878
<z, z>() -> q_gen_7883
}

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

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 6
() -> length([nil, z]) -> 4
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 4
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 4
(le([s(nn1), z])) -> BOT -> 4
(le([z, z])) -> BOT -> 4
(length([l, _yca]) /\ length([cons(x, l), _zca])) -> le([_yca, _zca]) -> 4
(length([ll, _uca])) -> length([cons(x, ll), s(_uca)]) -> 7
}
Sat witness: Found: ((length([ll, _uca])) -> length([cons(x, ll), s(_uca)]), {
_uca -> z  ;  ll -> nil  ;  x -> s(z)
})

-------------------------------------------
Step 6, which took 0.014588 s (model generation: 0.013472,  model checking: 0.001116):

Model:
|_
{
le -> 
{{{
Q={q_gen_7879, q_gen_7880},
Q_f={q_gen_7879},
Delta=
{
<s>(q_gen_7880) -> q_gen_7880
<z>() -> q_gen_7880
<s, s>(q_gen_7879) -> q_gen_7879
<z, s>(q_gen_7880) -> q_gen_7879
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_7878, q_gen_7882, q_gen_7883, q_gen_7889},
Q_f={q_gen_7878},
Delta=
{
<nil>() -> q_gen_7882
<z>() -> q_gen_7889
<cons, s>(q_gen_7883, q_gen_7882) -> q_gen_7878
<nil, z>() -> q_gen_7878
<s, z>(q_gen_7889) -> q_gen_7883
<z, z>() -> q_gen_7883
}

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

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 7
() -> length([nil, z]) -> 5
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 5
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 5
(le([s(nn1), z])) -> BOT -> 5
(le([z, z])) -> BOT -> 5
(length([l, _yca]) /\ length([cons(x, l), _zca])) -> le([_yca, _zca]) -> 5
(length([ll, _uca])) -> length([cons(x, ll), s(_uca)]) -> 10
}
Sat witness: Found: ((length([ll, _uca])) -> length([cons(x, ll), s(_uca)]), {
_uca -> z  ;  ll -> nil  ;  x -> s(s(z))
})

-------------------------------------------
Step 7, which took 0.011680 s (model generation: 0.011104,  model checking: 0.000576):

Model:
|_
{
le -> 
{{{
Q={q_gen_7879, q_gen_7880},
Q_f={q_gen_7879},
Delta=
{
<s>(q_gen_7880) -> q_gen_7880
<z>() -> q_gen_7880
<s, s>(q_gen_7879) -> q_gen_7879
<z, s>(q_gen_7880) -> q_gen_7879
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_7878, q_gen_7882, q_gen_7883, q_gen_7889},
Q_f={q_gen_7878},
Delta=
{
<nil>() -> q_gen_7882
<s>(q_gen_7889) -> q_gen_7889
<z>() -> q_gen_7889
<cons, s>(q_gen_7883, q_gen_7882) -> q_gen_7878
<nil, z>() -> q_gen_7878
<s, z>(q_gen_7889) -> q_gen_7883
<z, z>() -> q_gen_7883
}

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

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 8
() -> length([nil, z]) -> 6
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 6
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 6
(le([s(nn1), z])) -> BOT -> 6
(le([z, z])) -> BOT -> 6
(length([l, _yca]) /\ length([cons(x, l), _zca])) -> le([_yca, _zca]) -> 6
(length([ll, _uca])) -> length([cons(x, ll), s(_uca)]) -> 13
}
Sat witness: Found: ((length([ll, _uca])) -> length([cons(x, ll), s(_uca)]), {
_uca -> s(z)  ;  ll -> cons(z, nil)  ;  x -> z
})

-------------------------------------------
Step 8, which took 0.010474 s (model generation: 0.010106,  model checking: 0.000368):

Model:
|_
{
le -> 
{{{
Q={q_gen_7879, q_gen_7880},
Q_f={q_gen_7879},
Delta=
{
<s>(q_gen_7880) -> q_gen_7880
<z>() -> q_gen_7880
<s, s>(q_gen_7879) -> q_gen_7879
<z, s>(q_gen_7880) -> q_gen_7879
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_7878, q_gen_7882, q_gen_7883, q_gen_7889},
Q_f={q_gen_7878},
Delta=
{
<cons>(q_gen_7889, q_gen_7882) -> q_gen_7882
<nil>() -> q_gen_7882
<s>(q_gen_7889) -> q_gen_7889
<z>() -> q_gen_7889
<cons, s>(q_gen_7883, q_gen_7882) -> q_gen_7878
<nil, z>() -> q_gen_7878
<s, z>(q_gen_7889) -> q_gen_7883
<z, s>(q_gen_7889) -> q_gen_7883
<z, z>() -> q_gen_7883
}

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

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 8
() -> length([nil, z]) -> 6
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 6
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 6
(le([s(nn1), z])) -> BOT -> 6
(le([z, z])) -> BOT -> 6
(length([l, _yca]) /\ length([cons(x, l), _zca])) -> le([_yca, _zca]) -> 9
(length([ll, _uca])) -> length([cons(x, ll), s(_uca)]) -> 13
}
Sat witness: Found: ((length([l, _yca]) /\ length([cons(x, l), _zca])) -> le([_yca, _zca]), {
_yca -> s(z)  ;  _zca -> s(z)  ;  l -> cons(z, nil)  ;  x -> z
})

-------------------------------------------
Step 9, which took 0.010554 s (model generation: 0.010537,  model checking: 0.000017):

Model:
|_
{
le -> 
{{{
Q={q_gen_7879, q_gen_7880},
Q_f={q_gen_7879},
Delta=
{
<s>(q_gen_7880) -> q_gen_7880
<z>() -> q_gen_7880
<s, s>(q_gen_7879) -> q_gen_7879
<z, s>(q_gen_7880) -> q_gen_7879
<z, z>() -> q_gen_7879
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_7878, q_gen_7882, q_gen_7883, q_gen_7889},
Q_f={q_gen_7878},
Delta=
{
<cons>(q_gen_7889, q_gen_7882) -> q_gen_7882
<nil>() -> q_gen_7882
<s>(q_gen_7889) -> q_gen_7889
<z>() -> q_gen_7889
<cons, s>(q_gen_7883, q_gen_7882) -> q_gen_7878
<nil, z>() -> q_gen_7878
<s, z>(q_gen_7889) -> q_gen_7883
<z, s>(q_gen_7889) -> q_gen_7883
<z, z>() -> q_gen_7883
}

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

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 8
() -> length([nil, z]) -> 6
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 6
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 6
(le([s(nn1), z])) -> BOT -> 6
(le([z, z])) -> BOT -> 9
(length([l, _yca]) /\ length([cons(x, l), _zca])) -> le([_yca, _zca]) -> 9
(length([ll, _uca])) -> length([cons(x, ll), s(_uca)]) -> 13
}
Sat witness: Found: ((le([z, z])) -> BOT, {

})

-------------------------------------------
Step 10, which took 0.011763 s (model generation: 0.011686,  model checking: 0.000077):

Model:
|_
{
le -> 
{{{
Q={q_gen_7879, q_gen_7880, q_gen_7898},
Q_f={q_gen_7879},
Delta=
{
<s>(q_gen_7880) -> q_gen_7880
<z>() -> q_gen_7880
<s, s>(q_gen_7879) -> q_gen_7879
<s, s>(q_gen_7898) -> q_gen_7879
<z, s>(q_gen_7880) -> q_gen_7879
<z, z>() -> q_gen_7898
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_7878, q_gen_7882, q_gen_7883, q_gen_7889},
Q_f={q_gen_7878},
Delta=
{
<cons>(q_gen_7889, q_gen_7882) -> q_gen_7882
<nil>() -> q_gen_7882
<s>(q_gen_7889) -> q_gen_7889
<z>() -> q_gen_7889
<cons, s>(q_gen_7883, q_gen_7882) -> q_gen_7878
<nil, z>() -> q_gen_7878
<s, z>(q_gen_7889) -> q_gen_7883
<z, s>(q_gen_7889) -> q_gen_7883
<z, z>() -> q_gen_7883
}

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

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 8
() -> length([nil, z]) -> 6
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 6
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 9
(le([s(nn1), z])) -> BOT -> 7
(le([z, z])) -> BOT -> 9
(length([l, _yca]) /\ length([cons(x, l), _zca])) -> le([_yca, _zca]) -> 9
(length([ll, _uca])) -> length([cons(x, ll), s(_uca)]) -> 13
}
Sat witness: Found: ((le([s(nn1), s(nn2)])) -> le([nn1, nn2]), {
nn1 -> z  ;  nn2 -> z
})

-------------------------------------------
Step 11, which took 0.012810 s (model generation: 0.011108,  model checking: 0.001702):

Model:
|_
{
le -> 
{{{
Q={q_gen_7879, q_gen_7880, q_gen_7897},
Q_f={q_gen_7879},
Delta=
{
<s>(q_gen_7880) -> q_gen_7880
<z>() -> q_gen_7880
<s, s>(q_gen_7879) -> q_gen_7879
<z, s>(q_gen_7880) -> q_gen_7879
<s, s>(q_gen_7897) -> q_gen_7897
<z, z>() -> q_gen_7897
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_7878, q_gen_7882, q_gen_7883, q_gen_7889, q_gen_7894, q_gen_7895, q_gen_7896},
Q_f={q_gen_7878},
Delta=
{
<nil>() -> q_gen_7882
<s>(q_gen_7889) -> q_gen_7889
<z>() -> q_gen_7889
<cons>(q_gen_7889, q_gen_7882) -> q_gen_7894
<cons, s>(q_gen_7883, q_gen_7882) -> q_gen_7878
<cons, s>(q_gen_7895, q_gen_7894) -> q_gen_7878
<nil, z>() -> q_gen_7878
<s, z>(q_gen_7889) -> q_gen_7883
<z, z>() -> q_gen_7883
<z, s>(q_gen_7889) -> q_gen_7895
<cons, s>(q_gen_7883, q_gen_7894) -> q_gen_7896
}

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

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 9
() -> length([nil, z]) -> 7
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 7
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 10
(le([s(nn1), z])) -> BOT -> 8
(le([z, z])) -> BOT -> 10
(length([l, _yca]) /\ length([cons(x, l), _zca])) -> le([_yca, _zca]) -> 10
(length([ll, _uca])) -> length([cons(x, ll), s(_uca)]) -> 16
}
Sat witness: Found: ((length([ll, _uca])) -> length([cons(x, ll), s(_uca)]), {
_uca -> s(s(z))  ;  ll -> cons(z, cons(z, nil))  ;  x -> z
})

-------------------------------------------
Step 12, which took 0.013013 s (model generation: 0.012008,  model checking: 0.001005):

Model:
|_
{
le -> 
{{{
Q={q_gen_7879, q_gen_7880, q_gen_7897},
Q_f={q_gen_7879},
Delta=
{
<s>(q_gen_7880) -> q_gen_7880
<z>() -> q_gen_7880
<s, s>(q_gen_7879) -> q_gen_7879
<z, s>(q_gen_7880) -> q_gen_7879
<s, s>(q_gen_7897) -> q_gen_7897
<z, z>() -> q_gen_7897
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_7878, q_gen_7882, q_gen_7883, q_gen_7889, q_gen_7894, q_gen_7895, q_gen_7896},
Q_f={q_gen_7878},
Delta=
{
<cons>(q_gen_7889, q_gen_7894) -> q_gen_7882
<nil>() -> q_gen_7882
<s>(q_gen_7889) -> q_gen_7889
<z>() -> q_gen_7889
<cons>(q_gen_7889, q_gen_7882) -> q_gen_7894
<cons, s>(q_gen_7883, q_gen_7882) -> q_gen_7878
<cons, s>(q_gen_7895, q_gen_7882) -> q_gen_7878
<cons, s>(q_gen_7895, q_gen_7894) -> q_gen_7878
<nil, z>() -> q_gen_7878
<s, z>(q_gen_7889) -> q_gen_7883
<z, z>() -> q_gen_7883
<z, s>(q_gen_7889) -> q_gen_7895
<cons, s>(q_gen_7883, q_gen_7894) -> q_gen_7896
}

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

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 10
() -> length([nil, z]) -> 8
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 8
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 10
(le([s(nn1), z])) -> BOT -> 9
(le([z, z])) -> BOT -> 10
(length([l, _yca]) /\ length([cons(x, l), _zca])) -> le([_yca, _zca]) -> 13
(length([ll, _uca])) -> length([cons(x, ll), s(_uca)]) -> 16
}
Sat witness: Found: ((length([l, _yca]) /\ length([cons(x, l), _zca])) -> le([_yca, _zca]), {
_yca -> s(s(z))  ;  _zca -> s(s(z))  ;  l -> cons(z, nil)  ;  x -> z
})

-------------------------------------------
Step 13, which took 0.013486 s (model generation: 0.012854,  model checking: 0.000632):

Model:
|_
{
le -> 
{{{
Q={q_gen_7879, q_gen_7880, q_gen_7897},
Q_f={q_gen_7879},
Delta=
{
<s>(q_gen_7880) -> q_gen_7880
<z>() -> q_gen_7880
<s, s>(q_gen_7879) -> q_gen_7879
<z, s>(q_gen_7880) -> q_gen_7879
<s, s>(q_gen_7897) -> q_gen_7897
<z, z>() -> q_gen_7897
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_7878, q_gen_7882, q_gen_7883, q_gen_7889, q_gen_7894, q_gen_7895, q_gen_7896},
Q_f={q_gen_7878},
Delta=
{
<nil>() -> q_gen_7882
<s>(q_gen_7889) -> q_gen_7889
<z>() -> q_gen_7889
<cons>(q_gen_7889, q_gen_7882) -> q_gen_7894
<cons>(q_gen_7889, q_gen_7894) -> q_gen_7894
<cons, s>(q_gen_7883, q_gen_7882) -> q_gen_7878
<cons, s>(q_gen_7895, q_gen_7894) -> q_gen_7878
<nil, z>() -> q_gen_7878
<s, z>(q_gen_7889) -> q_gen_7883
<z, z>() -> q_gen_7883
<z, s>(q_gen_7889) -> q_gen_7895
<cons, s>(q_gen_7883, q_gen_7894) -> q_gen_7896
<cons, s>(q_gen_7895, q_gen_7882) -> q_gen_7896
}

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

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 11
() -> length([nil, z]) -> 9
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 9
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 11
(le([s(nn1), z])) -> BOT -> 10
(le([z, z])) -> BOT -> 11
(length([l, _yca]) /\ length([cons(x, l), _zca])) -> le([_yca, _zca]) -> 16
(length([ll, _uca])) -> length([cons(x, ll), s(_uca)]) -> 16
}
Sat witness: Found: ((length([l, _yca]) /\ length([cons(x, l), _zca])) -> le([_yca, _zca]), {
_yca -> s(s(z))  ;  _zca -> s(s(z))  ;  l -> cons(z, cons(z, nil))  ;  x -> z
})

-------------------------------------------
Step 14, which took 0.017542 s (model generation: 0.015908,  model checking: 0.001634):

Model:
|_
{
le -> 
{{{
Q={q_gen_7879, q_gen_7880, q_gen_7897},
Q_f={q_gen_7879},
Delta=
{
<s>(q_gen_7880) -> q_gen_7880
<z>() -> q_gen_7880
<s, s>(q_gen_7879) -> q_gen_7879
<z, s>(q_gen_7880) -> q_gen_7879
<s, s>(q_gen_7897) -> q_gen_7897
<z, z>() -> q_gen_7897
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_7878, q_gen_7882, q_gen_7883, q_gen_7889, q_gen_7892, q_gen_7894, q_gen_7895, q_gen_7896},
Q_f={q_gen_7878},
Delta=
{
<cons>(q_gen_7889, q_gen_7894) -> q_gen_7882
<nil>() -> q_gen_7882
<z>() -> q_gen_7889
<s>(q_gen_7889) -> q_gen_7892
<cons>(q_gen_7889, q_gen_7882) -> q_gen_7894
<cons, s>(q_gen_7883, q_gen_7882) -> q_gen_7878
<cons, s>(q_gen_7895, q_gen_7894) -> q_gen_7878
<nil, z>() -> q_gen_7878
<s, z>(q_gen_7889) -> q_gen_7883
<s, z>(q_gen_7892) -> q_gen_7883
<z, s>(q_gen_7892) -> q_gen_7883
<z, z>() -> q_gen_7883
<z, s>(q_gen_7889) -> q_gen_7895
<cons, s>(q_gen_7883, q_gen_7894) -> q_gen_7896
<cons, s>(q_gen_7895, q_gen_7882) -> q_gen_7896
}

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

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 12
() -> length([nil, z]) -> 10
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 10
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 12
(le([s(nn1), z])) -> BOT -> 11
(le([z, z])) -> BOT -> 12
(length([l, _yca]) /\ length([cons(x, l), _zca])) -> le([_yca, _zca]) -> 16
(length([ll, _uca])) -> length([cons(x, ll), s(_uca)]) -> 19
}
Sat witness: Found: ((length([ll, _uca])) -> length([cons(x, ll), s(_uca)]), {
_uca -> z  ;  ll -> nil  ;  x -> s(s(s(z)))
})

-------------------------------------------
Step 15, which took 0.016222 s (model generation: 0.015852,  model checking: 0.000370):

Model:
|_
{
le -> 
{{{
Q={q_gen_7879, q_gen_7880, q_gen_7897, q_gen_7898},
Q_f={q_gen_7879},
Delta=
{
<s>(q_gen_7880) -> q_gen_7880
<z>() -> q_gen_7880
<s, s>(q_gen_7879) -> q_gen_7879
<s, s>(q_gen_7897) -> q_gen_7879
<z, s>(q_gen_7880) -> q_gen_7879
<s, s>(q_gen_7898) -> q_gen_7897
<z, z>() -> q_gen_7898
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_7878, q_gen_7882, q_gen_7883, q_gen_7888, q_gen_7889, q_gen_7894, q_gen_7896},
Q_f={q_gen_7878},
Delta=
{
<nil>() -> q_gen_7882
<s>(q_gen_7889) -> q_gen_7889
<z>() -> q_gen_7889
<cons>(q_gen_7889, q_gen_7882) -> q_gen_7894
<cons>(q_gen_7889, q_gen_7894) -> q_gen_7894
<cons, s>(q_gen_7883, q_gen_7882) -> q_gen_7878
<cons, s>(q_gen_7888, q_gen_7882) -> q_gen_7878
<cons, s>(q_gen_7888, q_gen_7894) -> q_gen_7878
<nil, z>() -> q_gen_7878
<z, z>() -> q_gen_7883
<s, z>(q_gen_7889) -> q_gen_7888
<z, s>(q_gen_7889) -> q_gen_7888
<cons, s>(q_gen_7883, q_gen_7894) -> q_gen_7896
}

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

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 12
() -> length([nil, z]) -> 11
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 11
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 15
(le([s(nn1), z])) -> BOT -> 12
(le([z, z])) -> BOT -> 13
(length([l, _yca]) /\ length([cons(x, l), _zca])) -> le([_yca, _zca]) -> 16
(length([ll, _uca])) -> length([cons(x, ll), s(_uca)]) -> 19
}
Sat witness: Found: ((le([s(nn1), s(nn2)])) -> le([nn1, nn2]), {
nn1 -> s(z)  ;  nn2 -> s(z)
})

-------------------------------------------
Step 16, which took 0.023754 s (model generation: 0.021312,  model checking: 0.002442):

Model:
|_
{
le -> 
{{{
Q={q_gen_7879, q_gen_7880, q_gen_7897},
Q_f={q_gen_7879},
Delta=
{
<s>(q_gen_7880) -> q_gen_7880
<z>() -> q_gen_7880
<s, s>(q_gen_7879) -> q_gen_7879
<z, s>(q_gen_7880) -> q_gen_7879
<s, s>(q_gen_7897) -> q_gen_7897
<z, z>() -> q_gen_7897
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_7878, q_gen_7882, q_gen_7883, q_gen_7889, q_gen_7892, q_gen_7894, q_gen_7895, q_gen_7896},
Q_f={q_gen_7878},
Delta=
{
<cons>(q_gen_7889, q_gen_7894) -> q_gen_7882
<nil>() -> q_gen_7882
<s>(q_gen_7892) -> q_gen_7889
<z>() -> q_gen_7889
<s>(q_gen_7889) -> q_gen_7892
<cons>(q_gen_7889, q_gen_7882) -> q_gen_7894
<cons, s>(q_gen_7883, q_gen_7882) -> q_gen_7878
<cons, s>(q_gen_7895, q_gen_7894) -> q_gen_7878
<nil, z>() -> q_gen_7878
<s, z>(q_gen_7889) -> q_gen_7883
<s, z>(q_gen_7892) -> q_gen_7883
<z, s>(q_gen_7892) -> q_gen_7883
<z, z>() -> q_gen_7883
<z, s>(q_gen_7889) -> q_gen_7895
<cons, s>(q_gen_7883, q_gen_7894) -> q_gen_7896
<cons, s>(q_gen_7895, q_gen_7882) -> q_gen_7896
}

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

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 13
() -> length([nil, z]) -> 12
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 12
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 16
(le([s(nn1), z])) -> BOT -> 13
(le([z, z])) -> BOT -> 14
(length([l, _yca]) /\ length([cons(x, l), _zca])) -> le([_yca, _zca]) -> 19
(length([ll, _uca])) -> length([cons(x, ll), s(_uca)]) -> 19
}
Sat witness: Found: ((length([l, _yca]) /\ length([cons(x, l), _zca])) -> le([_yca, _zca]), {
_yca -> s(s(s(z)))  ;  _zca -> s(s(z))  ;  l -> cons(z, cons(z, cons(z, nil)))  ;  x -> z
})

-------------------------------------------
Step 17, which took 0.018689 s (model generation: 0.018466,  model checking: 0.000223):

Model:
|_
{
le -> 
{{{
Q={q_gen_7879, q_gen_7880, q_gen_7897},
Q_f={q_gen_7879},
Delta=
{
<s>(q_gen_7880) -> q_gen_7880
<z>() -> q_gen_7880
<s, s>(q_gen_7879) -> q_gen_7879
<s, z>(q_gen_7880) -> q_gen_7879
<z, s>(q_gen_7880) -> q_gen_7879
<s, s>(q_gen_7897) -> q_gen_7897
<z, z>() -> q_gen_7897
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_7878, q_gen_7882, q_gen_7883, q_gen_7889, q_gen_7892, q_gen_7894, q_gen_7895, q_gen_7896},
Q_f={q_gen_7878},
Delta=
{
<cons>(q_gen_7889, q_gen_7894) -> q_gen_7882
<nil>() -> q_gen_7882
<z>() -> q_gen_7889
<s>(q_gen_7889) -> q_gen_7892
<s>(q_gen_7892) -> q_gen_7892
<cons>(q_gen_7889, q_gen_7882) -> q_gen_7894
<cons, s>(q_gen_7883, q_gen_7882) -> q_gen_7878
<cons, s>(q_gen_7895, q_gen_7894) -> q_gen_7878
<nil, z>() -> q_gen_7878
<s, z>(q_gen_7889) -> q_gen_7883
<s, z>(q_gen_7892) -> q_gen_7883
<z, s>(q_gen_7892) -> q_gen_7883
<z, z>() -> q_gen_7883
<z, s>(q_gen_7889) -> q_gen_7895
<cons, s>(q_gen_7883, q_gen_7894) -> q_gen_7896
<cons, s>(q_gen_7895, q_gen_7882) -> q_gen_7896
}

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

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 13
() -> length([nil, z]) -> 13
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 13
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 16
(le([s(nn1), z])) -> BOT -> 16
(le([z, z])) -> BOT -> 14
(length([l, _yca]) /\ length([cons(x, l), _zca])) -> le([_yca, _zca]) -> 19
(length([ll, _uca])) -> length([cons(x, ll), s(_uca)]) -> 19
}
Sat witness: Found: ((le([s(nn1), z])) -> BOT, {
nn1 -> z
})

-------------------------------------------
Step 18, which took 0.021790 s (model generation: 0.020166,  model checking: 0.001624):

Model:
|_
{
le -> 
{{{
Q={q_gen_7879, q_gen_7880, q_gen_7897},
Q_f={q_gen_7879},
Delta=
{
<s>(q_gen_7880) -> q_gen_7880
<z>() -> q_gen_7880
<s, s>(q_gen_7879) -> q_gen_7879
<z, s>(q_gen_7880) -> q_gen_7879
<s, s>(q_gen_7897) -> q_gen_7897
<s, z>(q_gen_7880) -> q_gen_7897
<z, z>() -> q_gen_7897
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_7878, q_gen_7882, q_gen_7883, q_gen_7889, q_gen_7892, q_gen_7894, q_gen_7895, q_gen_7896, q_gen_7900},
Q_f={q_gen_7878},
Delta=
{
<nil>() -> q_gen_7882
<z>() -> q_gen_7889
<s>(q_gen_7889) -> q_gen_7892
<s>(q_gen_7892) -> q_gen_7892
<cons>(q_gen_7889, q_gen_7882) -> q_gen_7894
<cons>(q_gen_7889, q_gen_7894) -> q_gen_7900
<cons>(q_gen_7889, q_gen_7900) -> q_gen_7900
<cons, s>(q_gen_7883, q_gen_7882) -> q_gen_7878
<cons, s>(q_gen_7883, q_gen_7900) -> q_gen_7878
<cons, s>(q_gen_7895, q_gen_7894) -> q_gen_7878
<nil, z>() -> q_gen_7878
<s, z>(q_gen_7889) -> q_gen_7883
<s, z>(q_gen_7892) -> q_gen_7883
<z, s>(q_gen_7892) -> q_gen_7883
<z, z>() -> q_gen_7883
<z, s>(q_gen_7889) -> q_gen_7895
<cons, s>(q_gen_7883, q_gen_7894) -> q_gen_7896
<cons, s>(q_gen_7895, q_gen_7882) -> q_gen_7896
<cons, s>(q_gen_7895, q_gen_7900) -> q_gen_7896
}

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

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 14
() -> length([nil, z]) -> 14
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 14
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 17
(le([s(nn1), z])) -> BOT -> 17
(le([z, z])) -> BOT -> 15
(length([l, _yca]) /\ length([cons(x, l), _zca])) -> le([_yca, _zca]) -> 19
(length([ll, _uca])) -> length([cons(x, ll), s(_uca)]) -> 22
}
Sat witness: Found: ((length([ll, _uca])) -> length([cons(x, ll), s(_uca)]), {
_uca -> s(s(s(z)))  ;  ll -> cons(z, nil)  ;  x -> z
})

-------------------------------------------
Step 19, which took 0.023164 s (model generation: 0.021729,  model checking: 0.001435):

Model:
|_
{
le -> 
{{{
Q={q_gen_7879, q_gen_7880, q_gen_7897},
Q_f={q_gen_7879},
Delta=
{
<s>(q_gen_7880) -> q_gen_7880
<z>() -> q_gen_7880
<s, s>(q_gen_7879) -> q_gen_7879
<z, s>(q_gen_7880) -> q_gen_7879
<s, s>(q_gen_7897) -> q_gen_7897
<s, z>(q_gen_7880) -> q_gen_7897
<z, z>() -> q_gen_7897
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_7878, q_gen_7882, q_gen_7883, q_gen_7889, q_gen_7892, q_gen_7894, q_gen_7895, q_gen_7896, q_gen_7900},
Q_f={q_gen_7878},
Delta=
{
<nil>() -> q_gen_7882
<s>(q_gen_7892) -> q_gen_7889
<z>() -> q_gen_7889
<s>(q_gen_7889) -> q_gen_7892
<cons>(q_gen_7889, q_gen_7882) -> q_gen_7894
<cons>(q_gen_7889, q_gen_7894) -> q_gen_7900
<cons>(q_gen_7889, q_gen_7900) -> q_gen_7900
<cons, s>(q_gen_7883, q_gen_7882) -> q_gen_7878
<cons, s>(q_gen_7883, q_gen_7900) -> q_gen_7878
<cons, s>(q_gen_7895, q_gen_7894) -> q_gen_7878
<nil, z>() -> q_gen_7878
<s, z>(q_gen_7889) -> q_gen_7883
<s, z>(q_gen_7892) -> q_gen_7883
<z, s>(q_gen_7892) -> q_gen_7883
<z, z>() -> q_gen_7883
<z, s>(q_gen_7889) -> q_gen_7895
<cons, s>(q_gen_7883, q_gen_7894) -> q_gen_7896
<cons, s>(q_gen_7895, q_gen_7882) -> q_gen_7896
<cons, s>(q_gen_7895, q_gen_7900) -> q_gen_7896
}

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

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 15
() -> length([nil, z]) -> 15
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 15
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 18
(le([s(nn1), z])) -> BOT -> 18
(le([z, z])) -> BOT -> 16
(length([l, _yca]) /\ length([cons(x, l), _zca])) -> le([_yca, _zca]) -> 22
(length([ll, _uca])) -> length([cons(x, ll), s(_uca)]) -> 22
}
Sat witness: Found: ((length([l, _yca]) /\ length([cons(x, l), _zca])) -> le([_yca, _zca]), {
_yca -> s(s(s(z)))  ;  _zca -> s(s(z))  ;  l -> cons(z, nil)  ;  x -> z
})

-------------------------------------------
Step 20, which took 0.023479 s (model generation: 0.022770,  model checking: 0.000709):

Model:
|_
{
le -> 
{{{
Q={q_gen_7879, q_gen_7880, q_gen_7897, q_gen_7912},
Q_f={q_gen_7879},
Delta=
{
<s>(q_gen_7880) -> q_gen_7880
<z>() -> q_gen_7880
<s, s>(q_gen_7879) -> q_gen_7879
<s, s>(q_gen_7912) -> q_gen_7879
<z, s>(q_gen_7880) -> q_gen_7879
<s, s>(q_gen_7897) -> q_gen_7897
<z, z>() -> q_gen_7897
<s, z>(q_gen_7880) -> q_gen_7912
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_7878, q_gen_7882, q_gen_7883, q_gen_7889, q_gen_7892, q_gen_7894, q_gen_7895, q_gen_7896},
Q_f={q_gen_7878},
Delta=
{
<cons>(q_gen_7889, q_gen_7894) -> q_gen_7882
<nil>() -> q_gen_7882
<s>(q_gen_7892) -> q_gen_7889
<z>() -> q_gen_7889
<s>(q_gen_7889) -> q_gen_7892
<cons>(q_gen_7889, q_gen_7882) -> q_gen_7894
<cons, s>(q_gen_7883, q_gen_7882) -> q_gen_7878
<cons, s>(q_gen_7895, q_gen_7894) -> q_gen_7878
<nil, z>() -> q_gen_7878
<s, z>(q_gen_7889) -> q_gen_7883
<s, z>(q_gen_7892) -> q_gen_7883
<z, s>(q_gen_7892) -> q_gen_7883
<z, z>() -> q_gen_7883
<z, s>(q_gen_7889) -> q_gen_7895
<cons, s>(q_gen_7883, q_gen_7894) -> q_gen_7896
<cons, s>(q_gen_7895, q_gen_7882) -> q_gen_7896
}

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

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 16
() -> length([nil, z]) -> 16
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 16
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 21
(le([s(nn1), z])) -> BOT -> 19
(le([z, z])) -> BOT -> 17
(length([l, _yca]) /\ length([cons(x, l), _zca])) -> le([_yca, _zca]) -> 22
(length([ll, _uca])) -> length([cons(x, ll), s(_uca)]) -> 22
}
Sat witness: Found: ((le([s(nn1), s(nn2)])) -> le([nn1, nn2]), {
nn1 -> s(z)  ;  nn2 -> z
})

-------------------------------------------
Step 21, which took 0.021896 s (model generation: 0.021412,  model checking: 0.000484):

Model:
|_
{
le -> 
{{{
Q={q_gen_7879, q_gen_7880, q_gen_7897, q_gen_7911, q_gen_7912},
Q_f={q_gen_7879},
Delta=
{
<s>(q_gen_7880) -> q_gen_7880
<z>() -> q_gen_7880
<s, s>(q_gen_7879) -> q_gen_7879
<s, s>(q_gen_7911) -> q_gen_7879
<z, s>(q_gen_7880) -> q_gen_7879
<s, s>(q_gen_7897) -> q_gen_7897
<z, z>() -> q_gen_7897
<s, s>(q_gen_7912) -> q_gen_7911
<s, z>(q_gen_7880) -> q_gen_7912
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_7878, q_gen_7882, q_gen_7883, q_gen_7889, q_gen_7892, q_gen_7894, q_gen_7895, q_gen_7896},
Q_f={q_gen_7878},
Delta=
{
<cons>(q_gen_7889, q_gen_7894) -> q_gen_7882
<nil>() -> q_gen_7882
<s>(q_gen_7892) -> q_gen_7889
<z>() -> q_gen_7889
<s>(q_gen_7889) -> q_gen_7892
<cons>(q_gen_7889, q_gen_7882) -> q_gen_7894
<cons, s>(q_gen_7883, q_gen_7882) -> q_gen_7878
<cons, s>(q_gen_7895, q_gen_7894) -> q_gen_7878
<nil, z>() -> q_gen_7878
<s, z>(q_gen_7889) -> q_gen_7883
<s, z>(q_gen_7892) -> q_gen_7883
<z, s>(q_gen_7892) -> q_gen_7883
<z, z>() -> q_gen_7883
<z, s>(q_gen_7889) -> q_gen_7895
<cons, s>(q_gen_7883, q_gen_7894) -> q_gen_7896
<cons, s>(q_gen_7895, q_gen_7882) -> q_gen_7896
}

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

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 17
() -> length([nil, z]) -> 17
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 17
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 24
(le([s(nn1), z])) -> BOT -> 20
(le([z, z])) -> BOT -> 18
(length([l, _yca]) /\ length([cons(x, l), _zca])) -> le([_yca, _zca]) -> 22
(length([ll, _uca])) -> length([cons(x, ll), s(_uca)]) -> 22
}
Sat witness: Found: ((le([s(nn1), s(nn2)])) -> le([nn1, nn2]), {
nn1 -> s(s(z))  ;  nn2 -> s(z)
})

-------------------------------------------
Step 22, which took 0.022738 s (model generation: 0.020865,  model checking: 0.001873):

Model:
|_
{
le -> 
{{{
Q={q_gen_7879, q_gen_7880, q_gen_7897},
Q_f={q_gen_7879},
Delta=
{
<s>(q_gen_7880) -> q_gen_7880
<z>() -> q_gen_7880
<s, s>(q_gen_7879) -> q_gen_7879
<z, s>(q_gen_7880) -> q_gen_7879
<s, s>(q_gen_7897) -> q_gen_7897
<s, z>(q_gen_7880) -> q_gen_7897
<z, z>() -> q_gen_7897
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_7878, q_gen_7882, q_gen_7883, q_gen_7889, q_gen_7892, q_gen_7894, q_gen_7895, q_gen_7896, q_gen_7900, q_gen_7901},
Q_f={q_gen_7878},
Delta=
{
<cons>(q_gen_7889, q_gen_7900) -> q_gen_7882
<nil>() -> q_gen_7882
<s>(q_gen_7892) -> q_gen_7889
<z>() -> q_gen_7889
<s>(q_gen_7889) -> q_gen_7892
<cons>(q_gen_7889, q_gen_7882) -> q_gen_7894
<cons>(q_gen_7889, q_gen_7894) -> q_gen_7900
<cons, s>(q_gen_7883, q_gen_7882) -> q_gen_7878
<cons, s>(q_gen_7895, q_gen_7894) -> q_gen_7878
<cons, s>(q_gen_7901, q_gen_7900) -> q_gen_7878
<nil, z>() -> q_gen_7878
<s, z>(q_gen_7889) -> q_gen_7883
<s, z>(q_gen_7892) -> q_gen_7883
<z, z>() -> q_gen_7883
<z, s>(q_gen_7889) -> q_gen_7895
<cons, s>(q_gen_7883, q_gen_7894) -> q_gen_7896
<cons, s>(q_gen_7895, q_gen_7882) -> q_gen_7896
<cons, s>(q_gen_7895, q_gen_7900) -> q_gen_7896
<cons, s>(q_gen_7901, q_gen_7882) -> q_gen_7896
<z, s>(q_gen_7892) -> q_gen_7901
}

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

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 18
() -> length([nil, z]) -> 18
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 18
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 24
(le([s(nn1), z])) -> BOT -> 21
(le([z, z])) -> BOT -> 19
(length([l, _yca]) /\ length([cons(x, l), _zca])) -> le([_yca, _zca]) -> 22
(length([ll, _uca])) -> length([cons(x, ll), s(_uca)]) -> 25
}
Sat witness: Found: ((length([ll, _uca])) -> length([cons(x, ll), s(_uca)]), {
_uca -> s(s(s(z)))  ;  ll -> cons(z, cons(z, cons(z, nil)))  ;  x -> z
})

-------------------------------------------
Step 23, which took 0.023820 s (model generation: 0.022220,  model checking: 0.001600):

Model:
|_
{
le -> 
{{{
Q={q_gen_7879, q_gen_7880, q_gen_7897},
Q_f={q_gen_7879},
Delta=
{
<s>(q_gen_7880) -> q_gen_7880
<z>() -> q_gen_7880
<s, s>(q_gen_7879) -> q_gen_7879
<z, s>(q_gen_7880) -> q_gen_7879
<s, s>(q_gen_7897) -> q_gen_7897
<s, z>(q_gen_7880) -> q_gen_7897
<z, z>() -> q_gen_7897
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_7878, q_gen_7882, q_gen_7883, q_gen_7889, q_gen_7892, q_gen_7894, q_gen_7895, q_gen_7896, q_gen_7900, q_gen_7901},
Q_f={q_gen_7878},
Delta=
{
<nil>() -> q_gen_7882
<z>() -> q_gen_7889
<s>(q_gen_7889) -> q_gen_7892
<s>(q_gen_7892) -> q_gen_7892
<cons>(q_gen_7889, q_gen_7882) -> q_gen_7894
<cons>(q_gen_7889, q_gen_7894) -> q_gen_7900
<cons>(q_gen_7889, q_gen_7900) -> q_gen_7900
<cons, s>(q_gen_7883, q_gen_7882) -> q_gen_7878
<cons, s>(q_gen_7895, q_gen_7894) -> q_gen_7878
<cons, s>(q_gen_7901, q_gen_7894) -> q_gen_7878
<cons, s>(q_gen_7901, q_gen_7900) -> q_gen_7878
<nil, z>() -> q_gen_7878
<s, z>(q_gen_7889) -> q_gen_7883
<s, z>(q_gen_7892) -> q_gen_7883
<z, z>() -> q_gen_7883
<z, s>(q_gen_7889) -> q_gen_7895
<cons, s>(q_gen_7883, q_gen_7894) -> q_gen_7896
<cons, s>(q_gen_7895, q_gen_7882) -> q_gen_7896
<cons, s>(q_gen_7895, q_gen_7900) -> q_gen_7896
<cons, s>(q_gen_7901, q_gen_7882) -> q_gen_7896
<z, s>(q_gen_7892) -> q_gen_7901
}

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

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 19
() -> length([nil, z]) -> 19
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 19
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 24
(le([s(nn1), z])) -> BOT -> 22
(le([z, z])) -> BOT -> 20
(length([l, _yca]) /\ length([cons(x, l), _zca])) -> le([_yca, _zca]) -> 25
(length([ll, _uca])) -> length([cons(x, ll), s(_uca)]) -> 25
}
Sat witness: Found: ((length([l, _yca]) /\ length([cons(x, l), _zca])) -> le([_yca, _zca]), {
_yca -> s(s(s(z)))  ;  _zca -> s(s(s(z)))  ;  l -> cons(z, cons(z, nil))  ;  x -> z
})

-------------------------------------------
Step 24, which took 0.027859 s (model generation: 0.024684,  model checking: 0.003175):

Model:
|_
{
le -> 
{{{
Q={q_gen_7879, q_gen_7880, q_gen_7897},
Q_f={q_gen_7879},
Delta=
{
<s>(q_gen_7880) -> q_gen_7880
<z>() -> q_gen_7880
<s, s>(q_gen_7879) -> q_gen_7879
<z, s>(q_gen_7880) -> q_gen_7879
<s, s>(q_gen_7897) -> q_gen_7897
<s, z>(q_gen_7880) -> q_gen_7897
<z, z>() -> q_gen_7897
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_7878, q_gen_7882, q_gen_7883, q_gen_7889, q_gen_7892, q_gen_7894, q_gen_7895, q_gen_7896, q_gen_7900, q_gen_7901},
Q_f={q_gen_7878},
Delta=
{
<nil>() -> q_gen_7882
<z>() -> q_gen_7889
<s>(q_gen_7889) -> q_gen_7892
<s>(q_gen_7892) -> q_gen_7892
<cons>(q_gen_7889, q_gen_7882) -> q_gen_7894
<cons>(q_gen_7889, q_gen_7894) -> q_gen_7900
<cons>(q_gen_7889, q_gen_7900) -> q_gen_7900
<cons, s>(q_gen_7883, q_gen_7882) -> q_gen_7878
<cons, s>(q_gen_7895, q_gen_7894) -> q_gen_7878
<cons, s>(q_gen_7901, q_gen_7900) -> q_gen_7878
<nil, z>() -> q_gen_7878
<s, z>(q_gen_7889) -> q_gen_7883
<s, z>(q_gen_7892) -> q_gen_7883
<z, z>() -> q_gen_7883
<z, s>(q_gen_7889) -> q_gen_7895
<cons, s>(q_gen_7883, q_gen_7894) -> q_gen_7896
<cons, s>(q_gen_7895, q_gen_7882) -> q_gen_7896
<cons, s>(q_gen_7895, q_gen_7900) -> q_gen_7896
<cons, s>(q_gen_7901, q_gen_7882) -> q_gen_7896
<cons, s>(q_gen_7901, q_gen_7894) -> q_gen_7896
<z, s>(q_gen_7892) -> q_gen_7901
}

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

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 20
() -> length([nil, z]) -> 20
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 20
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 25
(le([s(nn1), z])) -> BOT -> 23
(le([z, z])) -> BOT -> 21
(length([l, _yca]) /\ length([cons(x, l), _zca])) -> le([_yca, _zca]) -> 25
(length([ll, _uca])) -> length([cons(x, ll), s(_uca)]) -> 28
}
Sat witness: Found: ((length([ll, _uca])) -> length([cons(x, ll), s(_uca)]), {
_uca -> s(z)  ;  ll -> cons(s(s(z)), nil)  ;  x -> z
})

-------------------------------------------
Step 25, which took 0.027851 s (model generation: 0.025945,  model checking: 0.001906):

Model:
|_
{
le -> 
{{{
Q={q_gen_7879, q_gen_7880, q_gen_7897},
Q_f={q_gen_7879},
Delta=
{
<s>(q_gen_7880) -> q_gen_7880
<z>() -> q_gen_7880
<s, s>(q_gen_7879) -> q_gen_7879
<z, s>(q_gen_7880) -> q_gen_7879
<s, s>(q_gen_7897) -> q_gen_7897
<s, z>(q_gen_7880) -> q_gen_7897
<z, z>() -> q_gen_7897
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_7878, q_gen_7882, q_gen_7883, q_gen_7889, q_gen_7892, q_gen_7894, q_gen_7895, q_gen_7896, q_gen_7900, q_gen_7901},
Q_f={q_gen_7878},
Delta=
{
<nil>() -> q_gen_7882
<z>() -> q_gen_7889
<s>(q_gen_7889) -> q_gen_7892
<s>(q_gen_7892) -> q_gen_7892
<cons>(q_gen_7889, q_gen_7882) -> q_gen_7894
<cons>(q_gen_7892, q_gen_7882) -> q_gen_7894
<cons>(q_gen_7889, q_gen_7894) -> q_gen_7900
<cons>(q_gen_7889, q_gen_7900) -> q_gen_7900
<cons, s>(q_gen_7883, q_gen_7882) -> q_gen_7878
<cons, s>(q_gen_7895, q_gen_7894) -> q_gen_7878
<cons, s>(q_gen_7901, q_gen_7900) -> q_gen_7878
<nil, z>() -> q_gen_7878
<s, z>(q_gen_7889) -> q_gen_7883
<s, z>(q_gen_7892) -> q_gen_7883
<z, z>() -> q_gen_7883
<z, s>(q_gen_7889) -> q_gen_7895
<cons, s>(q_gen_7883, q_gen_7894) -> q_gen_7896
<cons, s>(q_gen_7895, q_gen_7882) -> q_gen_7896
<cons, s>(q_gen_7895, q_gen_7900) -> q_gen_7896
<cons, s>(q_gen_7901, q_gen_7882) -> q_gen_7896
<cons, s>(q_gen_7901, q_gen_7894) -> q_gen_7896
<z, s>(q_gen_7892) -> q_gen_7901
}

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

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 21
() -> length([nil, z]) -> 21
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 21
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 25
(le([s(nn1), z])) -> BOT -> 24
(le([z, z])) -> BOT -> 22
(length([l, _yca]) /\ length([cons(x, l), _zca])) -> le([_yca, _zca]) -> 28
(length([ll, _uca])) -> length([cons(x, ll), s(_uca)]) -> 28
}
Sat witness: Found: ((length([l, _yca]) /\ length([cons(x, l), _zca])) -> le([_yca, _zca]), {
_yca -> s(s(s(z)))  ;  _zca -> s(s(s(z)))  ;  l -> cons(z, cons(z, cons(z, nil)))  ;  x -> z
})

-------------------------------------------
Step 26, which took 0.032555 s (model generation: 0.028305,  model checking: 0.004250):

Model:
|_
{
le -> 
{{{
Q={q_gen_7879, q_gen_7880, q_gen_7897},
Q_f={q_gen_7879},
Delta=
{
<s>(q_gen_7880) -> q_gen_7880
<z>() -> q_gen_7880
<s, s>(q_gen_7879) -> q_gen_7879
<z, s>(q_gen_7880) -> q_gen_7879
<s, s>(q_gen_7897) -> q_gen_7897
<s, z>(q_gen_7880) -> q_gen_7897
<z, z>() -> q_gen_7897
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_7878, q_gen_7882, q_gen_7883, q_gen_7889, q_gen_7892, q_gen_7894, q_gen_7895, q_gen_7896, q_gen_7900, q_gen_7901, q_gen_7907},
Q_f={q_gen_7878},
Delta=
{
<cons>(q_gen_7889, q_gen_7900) -> q_gen_7882
<nil>() -> q_gen_7882
<z>() -> q_gen_7889
<s>(q_gen_7889) -> q_gen_7892
<cons>(q_gen_7889, q_gen_7882) -> q_gen_7894
<cons>(q_gen_7907, q_gen_7882) -> q_gen_7894
<cons>(q_gen_7889, q_gen_7894) -> q_gen_7900
<s>(q_gen_7892) -> q_gen_7907
<cons, s>(q_gen_7883, q_gen_7882) -> q_gen_7878
<cons, s>(q_gen_7895, q_gen_7894) -> q_gen_7878
<cons, s>(q_gen_7901, q_gen_7900) -> q_gen_7878
<nil, z>() -> q_gen_7878
<s, z>(q_gen_7889) -> q_gen_7883
<s, z>(q_gen_7892) -> q_gen_7883
<s, z>(q_gen_7907) -> q_gen_7883
<z, s>(q_gen_7907) -> q_gen_7883
<z, z>() -> q_gen_7883
<z, s>(q_gen_7889) -> q_gen_7895
<cons, s>(q_gen_7883, q_gen_7894) -> q_gen_7896
<cons, s>(q_gen_7895, q_gen_7882) -> q_gen_7896
<cons, s>(q_gen_7895, q_gen_7900) -> q_gen_7896
<cons, s>(q_gen_7901, q_gen_7882) -> q_gen_7896
<cons, s>(q_gen_7901, q_gen_7894) -> q_gen_7896
<z, s>(q_gen_7892) -> q_gen_7901
}

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

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 22
() -> length([nil, z]) -> 22
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 22
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 26
(le([s(nn1), z])) -> BOT -> 25
(le([z, z])) -> BOT -> 23
(length([l, _yca]) /\ length([cons(x, l), _zca])) -> le([_yca, _zca]) -> 28
(length([ll, _uca])) -> length([cons(x, ll), s(_uca)]) -> 31
}
Sat witness: Found: ((length([ll, _uca])) -> length([cons(x, ll), s(_uca)]), {
_uca -> z  ;  ll -> nil  ;  x -> s(s(s(s(z))))
})

-------------------------------------------
Step 27, which took 0.033240 s (model generation: 0.031100,  model checking: 0.002140):

Model:
|_
{
le -> 
{{{
Q={q_gen_7879, q_gen_7880, q_gen_7897},
Q_f={q_gen_7879},
Delta=
{
<s>(q_gen_7880) -> q_gen_7880
<z>() -> q_gen_7880
<s, s>(q_gen_7879) -> q_gen_7879
<z, s>(q_gen_7880) -> q_gen_7879
<s, s>(q_gen_7897) -> q_gen_7897
<s, z>(q_gen_7880) -> q_gen_7897
<z, z>() -> q_gen_7897
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_7878, q_gen_7882, q_gen_7883, q_gen_7889, q_gen_7892, q_gen_7894, q_gen_7895, q_gen_7896, q_gen_7900, q_gen_7901, q_gen_7907},
Q_f={q_gen_7878},
Delta=
{
<cons>(q_gen_7889, q_gen_7900) -> q_gen_7882
<nil>() -> q_gen_7882
<z>() -> q_gen_7889
<s>(q_gen_7889) -> q_gen_7892
<s>(q_gen_7907) -> q_gen_7892
<cons>(q_gen_7889, q_gen_7882) -> q_gen_7894
<cons>(q_gen_7907, q_gen_7882) -> q_gen_7894
<cons>(q_gen_7889, q_gen_7894) -> q_gen_7900
<s>(q_gen_7892) -> q_gen_7907
<cons, s>(q_gen_7883, q_gen_7882) -> q_gen_7878
<cons, s>(q_gen_7895, q_gen_7894) -> q_gen_7878
<cons, s>(q_gen_7901, q_gen_7900) -> q_gen_7878
<nil, z>() -> q_gen_7878
<s, z>(q_gen_7889) -> q_gen_7883
<s, z>(q_gen_7892) -> q_gen_7883
<s, z>(q_gen_7907) -> q_gen_7883
<z, s>(q_gen_7907) -> q_gen_7883
<z, z>() -> q_gen_7883
<z, s>(q_gen_7889) -> q_gen_7895
<cons, s>(q_gen_7883, q_gen_7894) -> q_gen_7896
<cons, s>(q_gen_7895, q_gen_7882) -> q_gen_7896
<cons, s>(q_gen_7895, q_gen_7900) -> q_gen_7896
<cons, s>(q_gen_7901, q_gen_7882) -> q_gen_7896
<cons, s>(q_gen_7901, q_gen_7894) -> q_gen_7896
<z, s>(q_gen_7892) -> q_gen_7901
}

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

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 23
() -> length([nil, z]) -> 23
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 23
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 27
(le([s(nn1), z])) -> BOT -> 26
(le([z, z])) -> BOT -> 24
(length([l, _yca]) /\ length([cons(x, l), _zca])) -> le([_yca, _zca]) -> 31
(length([ll, _uca])) -> length([cons(x, ll), s(_uca)]) -> 31
}
Sat witness: Found: ((length([l, _yca]) /\ length([cons(x, l), _zca])) -> le([_yca, _zca]), {
_yca -> s(s(s(s(z))))  ;  _zca -> s(s(z))  ;  l -> cons(z, nil)  ;  x -> z
})

-------------------------------------------
Step 28, which took 0.035750 s (model generation: 0.035180,  model checking: 0.000570):

Model:
|_
{
le -> 
{{{
Q={q_gen_7879, q_gen_7880, q_gen_7886, q_gen_7897},
Q_f={q_gen_7879},
Delta=
{
<z>() -> q_gen_7880
<s>(q_gen_7880) -> q_gen_7886
<s, s>(q_gen_7879) -> q_gen_7879
<s, z>(q_gen_7886) -> q_gen_7879
<z, s>(q_gen_7880) -> q_gen_7879
<z, s>(q_gen_7886) -> q_gen_7879
<s, s>(q_gen_7897) -> q_gen_7897
<s, z>(q_gen_7880) -> q_gen_7897
<z, z>() -> q_gen_7897
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_7878, q_gen_7882, q_gen_7883, q_gen_7889, q_gen_7892, q_gen_7894, q_gen_7895, q_gen_7896, q_gen_7900, q_gen_7901, q_gen_7907},
Q_f={q_gen_7878},
Delta=
{
<cons>(q_gen_7889, q_gen_7900) -> q_gen_7882
<nil>() -> q_gen_7882
<z>() -> q_gen_7889
<s>(q_gen_7889) -> q_gen_7892
<s>(q_gen_7907) -> q_gen_7892
<cons>(q_gen_7889, q_gen_7882) -> q_gen_7894
<cons>(q_gen_7907, q_gen_7882) -> q_gen_7894
<cons>(q_gen_7889, q_gen_7894) -> q_gen_7900
<s>(q_gen_7892) -> q_gen_7907
<cons, s>(q_gen_7883, q_gen_7882) -> q_gen_7878
<cons, s>(q_gen_7895, q_gen_7894) -> q_gen_7878
<cons, s>(q_gen_7901, q_gen_7900) -> q_gen_7878
<nil, z>() -> q_gen_7878
<s, z>(q_gen_7889) -> q_gen_7883
<s, z>(q_gen_7892) -> q_gen_7883
<s, z>(q_gen_7907) -> q_gen_7883
<z, s>(q_gen_7907) -> q_gen_7883
<z, z>() -> q_gen_7883
<z, s>(q_gen_7889) -> q_gen_7895
<cons, s>(q_gen_7883, q_gen_7894) -> q_gen_7896
<cons, s>(q_gen_7895, q_gen_7882) -> q_gen_7896
<cons, s>(q_gen_7895, q_gen_7900) -> q_gen_7896
<cons, s>(q_gen_7901, q_gen_7882) -> q_gen_7896
<cons, s>(q_gen_7901, q_gen_7894) -> q_gen_7896
<z, s>(q_gen_7892) -> q_gen_7901
}

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

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 26
() -> length([nil, z]) -> 24
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 24
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 27
(le([s(nn1), z])) -> BOT -> 26
(le([z, z])) -> BOT -> 24
(length([l, _yca]) /\ length([cons(x, l), _zca])) -> le([_yca, _zca]) -> 31
(length([ll, _uca])) -> length([cons(x, ll), s(_uca)]) -> 31
}
Sat witness: Found: (() -> le([z, s(nn2)]), {
nn2 -> s(s(z))
})

-------------------------------------------
Step 29, which took 0.037545 s (model generation: 0.037149,  model checking: 0.000396):

Model:
|_
{
le -> 
{{{
Q={q_gen_7879, q_gen_7880, q_gen_7886, q_gen_7897},
Q_f={q_gen_7879},
Delta=
{
<z>() -> q_gen_7880
<s>(q_gen_7880) -> q_gen_7886
<s>(q_gen_7886) -> q_gen_7886
<s, s>(q_gen_7879) -> q_gen_7879
<s, z>(q_gen_7886) -> q_gen_7879
<z, s>(q_gen_7880) -> q_gen_7879
<z, s>(q_gen_7886) -> q_gen_7879
<s, s>(q_gen_7897) -> q_gen_7897
<s, z>(q_gen_7880) -> q_gen_7897
<z, z>() -> q_gen_7897
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_7878, q_gen_7882, q_gen_7883, q_gen_7889, q_gen_7892, q_gen_7894, q_gen_7895, q_gen_7896, q_gen_7900, q_gen_7901, q_gen_7907},
Q_f={q_gen_7878},
Delta=
{
<cons>(q_gen_7889, q_gen_7900) -> q_gen_7882
<nil>() -> q_gen_7882
<z>() -> q_gen_7889
<s>(q_gen_7889) -> q_gen_7892
<s>(q_gen_7907) -> q_gen_7892
<cons>(q_gen_7889, q_gen_7882) -> q_gen_7894
<cons>(q_gen_7907, q_gen_7882) -> q_gen_7894
<cons>(q_gen_7889, q_gen_7894) -> q_gen_7900
<s>(q_gen_7892) -> q_gen_7907
<cons, s>(q_gen_7883, q_gen_7882) -> q_gen_7878
<cons, s>(q_gen_7895, q_gen_7894) -> q_gen_7878
<cons, s>(q_gen_7901, q_gen_7900) -> q_gen_7878
<nil, z>() -> q_gen_7878
<s, z>(q_gen_7889) -> q_gen_7883
<s, z>(q_gen_7892) -> q_gen_7883
<s, z>(q_gen_7907) -> q_gen_7883
<z, s>(q_gen_7907) -> q_gen_7883
<z, z>() -> q_gen_7883
<z, s>(q_gen_7889) -> q_gen_7895
<cons, s>(q_gen_7883, q_gen_7894) -> q_gen_7896
<cons, s>(q_gen_7895, q_gen_7882) -> q_gen_7896
<cons, s>(q_gen_7895, q_gen_7900) -> q_gen_7896
<cons, s>(q_gen_7901, q_gen_7882) -> q_gen_7896
<cons, s>(q_gen_7901, q_gen_7894) -> q_gen_7896
<z, s>(q_gen_7892) -> q_gen_7901
}

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

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 26
() -> length([nil, z]) -> 25
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 25
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 27
(le([s(nn1), z])) -> BOT -> 29
(le([z, z])) -> BOT -> 25
(length([l, _yca]) /\ length([cons(x, l), _zca])) -> le([_yca, _zca]) -> 31
(length([ll, _uca])) -> length([cons(x, ll), s(_uca)]) -> 31
}
Sat witness: Found: ((le([s(nn1), z])) -> BOT, {
nn1 -> s(z)
})

-------------------------------------------
Step 30, which took 0.037363 s (model generation: 0.036819,  model checking: 0.000544):

Model:
|_
{
le -> 
{{{
Q={q_gen_7879, q_gen_7880, q_gen_7897, q_gen_7898, q_gen_7903},
Q_f={q_gen_7879},
Delta=
{
<s>(q_gen_7880) -> q_gen_7880
<z>() -> q_gen_7880
<s, s>(q_gen_7879) -> q_gen_7879
<s, s>(q_gen_7903) -> q_gen_7879
<z, s>(q_gen_7880) -> q_gen_7879
<s, s>(q_gen_7898) -> q_gen_7897
<s, z>(q_gen_7880) -> q_gen_7898
<z, z>() -> q_gen_7898
<s, s>(q_gen_7897) -> q_gen_7903
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_7878, q_gen_7882, q_gen_7883, q_gen_7889, q_gen_7892, q_gen_7894, q_gen_7895, q_gen_7896, q_gen_7900, q_gen_7901},
Q_f={q_gen_7878},
Delta=
{
<nil>() -> q_gen_7882
<z>() -> q_gen_7889
<s>(q_gen_7889) -> q_gen_7892
<s>(q_gen_7892) -> q_gen_7892
<cons>(q_gen_7889, q_gen_7882) -> q_gen_7894
<cons>(q_gen_7892, q_gen_7882) -> q_gen_7894
<cons>(q_gen_7889, q_gen_7894) -> q_gen_7900
<cons>(q_gen_7889, q_gen_7900) -> q_gen_7900
<cons, s>(q_gen_7883, q_gen_7882) -> q_gen_7878
<cons, s>(q_gen_7895, q_gen_7894) -> q_gen_7878
<cons, s>(q_gen_7901, q_gen_7900) -> q_gen_7878
<nil, z>() -> q_gen_7878
<s, z>(q_gen_7889) -> q_gen_7883
<s, z>(q_gen_7892) -> q_gen_7883
<z, z>() -> q_gen_7883
<z, s>(q_gen_7889) -> q_gen_7895
<cons, s>(q_gen_7883, q_gen_7894) -> q_gen_7896
<cons, s>(q_gen_7895, q_gen_7882) -> q_gen_7896
<cons, s>(q_gen_7895, q_gen_7900) -> q_gen_7896
<cons, s>(q_gen_7901, q_gen_7882) -> q_gen_7896
<cons, s>(q_gen_7901, q_gen_7894) -> q_gen_7896
<z, s>(q_gen_7892) -> q_gen_7901
}

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

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 27
() -> length([nil, z]) -> 26
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 26
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 30
(le([s(nn1), z])) -> BOT -> 29
(le([z, z])) -> BOT -> 26
(length([l, _yca]) /\ length([cons(x, l), _zca])) -> le([_yca, _zca]) -> 31
(length([ll, _uca])) -> length([cons(x, ll), s(_uca)]) -> 31
}
Sat witness: Found: ((le([s(nn1), s(nn2)])) -> le([nn1, nn2]), {
nn1 -> s(s(z))  ;  nn2 -> s(s(z))
})

-------------------------------------------
Step 31, which took 0.045359 s (model generation: 0.036650,  model checking: 0.008709):

Model:
|_
{
le -> 
{{{
Q={q_gen_7879, q_gen_7880, q_gen_7897},
Q_f={q_gen_7879},
Delta=
{
<s>(q_gen_7880) -> q_gen_7880
<z>() -> q_gen_7880
<s, s>(q_gen_7879) -> q_gen_7879
<z, s>(q_gen_7880) -> q_gen_7879
<s, s>(q_gen_7897) -> q_gen_7897
<s, z>(q_gen_7880) -> q_gen_7897
<z, z>() -> q_gen_7897
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_7878, q_gen_7882, q_gen_7883, q_gen_7889, q_gen_7892, q_gen_7894, q_gen_7895, q_gen_7896, q_gen_7900, q_gen_7901, q_gen_7907, q_gen_7909, q_gen_7915},
Q_f={q_gen_7878},
Delta=
{
<nil>() -> q_gen_7882
<z>() -> q_gen_7889
<s>(q_gen_7889) -> q_gen_7892
<s>(q_gen_7907) -> q_gen_7892
<cons>(q_gen_7889, q_gen_7882) -> q_gen_7894
<cons>(q_gen_7907, q_gen_7882) -> q_gen_7894
<cons>(q_gen_7889, q_gen_7894) -> q_gen_7900
<s>(q_gen_7892) -> q_gen_7907
<cons>(q_gen_7889, q_gen_7900) -> q_gen_7909
<cons, s>(q_gen_7883, q_gen_7882) -> q_gen_7878
<cons, s>(q_gen_7895, q_gen_7894) -> q_gen_7878
<cons, s>(q_gen_7901, q_gen_7900) -> q_gen_7878
<cons, s>(q_gen_7915, q_gen_7909) -> q_gen_7878
<nil, z>() -> q_gen_7878
<s, z>(q_gen_7889) -> q_gen_7883
<s, z>(q_gen_7892) -> q_gen_7883
<s, z>(q_gen_7907) -> q_gen_7883
<z, z>() -> q_gen_7883
<z, s>(q_gen_7889) -> q_gen_7895
<cons, s>(q_gen_7883, q_gen_7894) -> q_gen_7896
<cons, s>(q_gen_7895, q_gen_7882) -> q_gen_7896
<cons, s>(q_gen_7895, q_gen_7900) -> q_gen_7896
<cons, s>(q_gen_7895, q_gen_7909) -> q_gen_7896
<cons, s>(q_gen_7901, q_gen_7882) -> q_gen_7896
<cons, s>(q_gen_7901, q_gen_7894) -> q_gen_7896
<cons, s>(q_gen_7901, q_gen_7909) -> q_gen_7896
<cons, s>(q_gen_7915, q_gen_7882) -> q_gen_7896
<cons, s>(q_gen_7915, q_gen_7894) -> q_gen_7896
<z, s>(q_gen_7892) -> q_gen_7901
<z, s>(q_gen_7907) -> q_gen_7915
}

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

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 28
() -> length([nil, z]) -> 27
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 27
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 31
(le([s(nn1), z])) -> BOT -> 30
(le([z, z])) -> BOT -> 27
(length([l, _yca]) /\ length([cons(x, l), _zca])) -> le([_yca, _zca]) -> 31
(length([ll, _uca])) -> length([cons(x, ll), s(_uca)]) -> 34
}
Sat witness: Found: ((length([ll, _uca])) -> length([cons(x, ll), s(_uca)]), {
_uca -> s(z)  ;  ll -> cons(s(s(s(z))), nil)  ;  x -> z
})

-------------------------------------------
Step 32, which took 0.042097 s (model generation: 0.038975,  model checking: 0.003122):

Model:
|_
{
le -> 
{{{
Q={q_gen_7879, q_gen_7880, q_gen_7897},
Q_f={q_gen_7879},
Delta=
{
<s>(q_gen_7880) -> q_gen_7880
<z>() -> q_gen_7880
<s, s>(q_gen_7879) -> q_gen_7879
<z, s>(q_gen_7880) -> q_gen_7879
<s, s>(q_gen_7897) -> q_gen_7897
<s, z>(q_gen_7880) -> q_gen_7897
<z, z>() -> q_gen_7897
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_7878, q_gen_7882, q_gen_7883, q_gen_7889, q_gen_7892, q_gen_7894, q_gen_7895, q_gen_7896, q_gen_7900, q_gen_7901, q_gen_7907, q_gen_7909, q_gen_7915},
Q_f={q_gen_7878},
Delta=
{
<nil>() -> q_gen_7882
<z>() -> q_gen_7889
<s>(q_gen_7889) -> q_gen_7892
<s>(q_gen_7907) -> q_gen_7892
<cons>(q_gen_7889, q_gen_7882) -> q_gen_7894
<cons>(q_gen_7892, q_gen_7882) -> q_gen_7894
<cons>(q_gen_7907, q_gen_7882) -> q_gen_7894
<cons>(q_gen_7889, q_gen_7894) -> q_gen_7900
<s>(q_gen_7892) -> q_gen_7907
<cons>(q_gen_7889, q_gen_7900) -> q_gen_7909
<cons, s>(q_gen_7883, q_gen_7882) -> q_gen_7878
<cons, s>(q_gen_7895, q_gen_7894) -> q_gen_7878
<cons, s>(q_gen_7901, q_gen_7900) -> q_gen_7878
<cons, s>(q_gen_7915, q_gen_7909) -> q_gen_7878
<nil, z>() -> q_gen_7878
<s, z>(q_gen_7889) -> q_gen_7883
<s, z>(q_gen_7892) -> q_gen_7883
<s, z>(q_gen_7907) -> q_gen_7883
<z, z>() -> q_gen_7883
<z, s>(q_gen_7889) -> q_gen_7895
<cons, s>(q_gen_7883, q_gen_7894) -> q_gen_7896
<cons, s>(q_gen_7895, q_gen_7882) -> q_gen_7896
<cons, s>(q_gen_7895, q_gen_7900) -> q_gen_7896
<cons, s>(q_gen_7895, q_gen_7909) -> q_gen_7896
<cons, s>(q_gen_7901, q_gen_7882) -> q_gen_7896
<cons, s>(q_gen_7901, q_gen_7894) -> q_gen_7896
<cons, s>(q_gen_7901, q_gen_7909) -> q_gen_7896
<cons, s>(q_gen_7915, q_gen_7882) -> q_gen_7896
<cons, s>(q_gen_7915, q_gen_7894) -> q_gen_7896
<z, s>(q_gen_7892) -> q_gen_7901
<z, s>(q_gen_7907) -> q_gen_7915
}

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

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 29
() -> length([nil, z]) -> 28
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 28
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 31
(le([s(nn1), z])) -> BOT -> 31
(le([z, z])) -> BOT -> 28
(length([l, _yca]) /\ length([cons(x, l), _zca])) -> le([_yca, _zca]) -> 34
(length([ll, _uca])) -> length([cons(x, ll), s(_uca)]) -> 34
}
Sat witness: Found: ((length([l, _yca]) /\ length([cons(x, l), _zca])) -> le([_yca, _zca]), {
_yca -> s(s(s(s(s(z)))))  ;  _zca -> s(s(s(s(z))))  ;  l -> cons(z, cons(z, cons(s(s(z)), nil)))  ;  x -> z
})

-------------------------------------------
Step 33, which took 0.050806 s (model generation: 0.050037,  model checking: 0.000769):

Model:
|_
{
le -> 
{{{
Q={q_gen_7879, q_gen_7880, q_gen_7886, q_gen_7897, q_gen_7928},
Q_f={q_gen_7879},
Delta=
{
<z>() -> q_gen_7880
<s>(q_gen_7880) -> q_gen_7886
<s>(q_gen_7886) -> q_gen_7886
<s, s>(q_gen_7879) -> q_gen_7879
<s, s>(q_gen_7928) -> q_gen_7879
<z, s>(q_gen_7880) -> q_gen_7879
<z, s>(q_gen_7886) -> q_gen_7879
<s, s>(q_gen_7897) -> q_gen_7897
<s, z>(q_gen_7880) -> q_gen_7897
<z, z>() -> q_gen_7897
<s, z>(q_gen_7886) -> q_gen_7928
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_7878, q_gen_7882, q_gen_7883, q_gen_7889, q_gen_7892, q_gen_7894, q_gen_7895, q_gen_7896, q_gen_7900, q_gen_7901, q_gen_7907},
Q_f={q_gen_7878},
Delta=
{
<cons>(q_gen_7889, q_gen_7900) -> q_gen_7882
<nil>() -> q_gen_7882
<s>(q_gen_7907) -> q_gen_7889
<z>() -> q_gen_7889
<s>(q_gen_7889) -> q_gen_7892
<cons>(q_gen_7889, q_gen_7882) -> q_gen_7894
<cons>(q_gen_7907, q_gen_7882) -> q_gen_7894
<cons>(q_gen_7889, q_gen_7894) -> q_gen_7900
<s>(q_gen_7892) -> q_gen_7907
<cons, s>(q_gen_7883, q_gen_7882) -> q_gen_7878
<cons, s>(q_gen_7895, q_gen_7894) -> q_gen_7878
<cons, s>(q_gen_7901, q_gen_7900) -> q_gen_7878
<nil, z>() -> q_gen_7878
<s, z>(q_gen_7889) -> q_gen_7883
<s, z>(q_gen_7892) -> q_gen_7883
<s, z>(q_gen_7907) -> q_gen_7883
<z, s>(q_gen_7907) -> q_gen_7883
<z, z>() -> q_gen_7883
<z, s>(q_gen_7889) -> q_gen_7895
<cons, s>(q_gen_7883, q_gen_7894) -> q_gen_7896
<cons, s>(q_gen_7895, q_gen_7882) -> q_gen_7896
<cons, s>(q_gen_7895, q_gen_7900) -> q_gen_7896
<cons, s>(q_gen_7901, q_gen_7882) -> q_gen_7896
<cons, s>(q_gen_7901, q_gen_7894) -> q_gen_7896
<z, s>(q_gen_7892) -> q_gen_7901
}

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

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 30
() -> length([nil, z]) -> 29
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 29
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 34
(le([s(nn1), z])) -> BOT -> 32
(le([z, z])) -> BOT -> 29
(length([l, _yca]) /\ length([cons(x, l), _zca])) -> le([_yca, _zca]) -> 34
(length([ll, _uca])) -> length([cons(x, ll), s(_uca)]) -> 34
}
Sat witness: Found: ((le([s(nn1), s(nn2)])) -> le([nn1, nn2]), {
nn1 -> s(s(z))  ;  nn2 -> z
})

-------------------------------------------
Step 34, which took 0.066770 s (model generation: 0.051543,  model checking: 0.015227):

Model:
|_
{
le -> 
{{{
Q={q_gen_7879, q_gen_7880, q_gen_7897},
Q_f={q_gen_7879},
Delta=
{
<s>(q_gen_7880) -> q_gen_7880
<z>() -> q_gen_7880
<s, s>(q_gen_7879) -> q_gen_7879
<z, s>(q_gen_7880) -> q_gen_7879
<s, s>(q_gen_7897) -> q_gen_7897
<s, z>(q_gen_7880) -> q_gen_7897
<z, z>() -> q_gen_7897
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_7878, q_gen_7882, q_gen_7883, q_gen_7889, q_gen_7892, q_gen_7894, q_gen_7895, q_gen_7896, q_gen_7900, q_gen_7901, q_gen_7907, q_gen_7909, q_gen_7915},
Q_f={q_gen_7878},
Delta=
{
<nil>() -> q_gen_7882
<s>(q_gen_7907) -> q_gen_7889
<z>() -> q_gen_7889
<s>(q_gen_7889) -> q_gen_7892
<cons>(q_gen_7889, q_gen_7882) -> q_gen_7894
<cons>(q_gen_7907, q_gen_7882) -> q_gen_7894
<cons>(q_gen_7889, q_gen_7894) -> q_gen_7900
<s>(q_gen_7892) -> q_gen_7907
<cons>(q_gen_7889, q_gen_7900) -> q_gen_7909
<cons, s>(q_gen_7883, q_gen_7882) -> q_gen_7878
<cons, s>(q_gen_7895, q_gen_7894) -> q_gen_7878
<cons, s>(q_gen_7901, q_gen_7900) -> q_gen_7878
<cons, s>(q_gen_7915, q_gen_7909) -> q_gen_7878
<nil, z>() -> q_gen_7878
<s, z>(q_gen_7889) -> q_gen_7883
<s, z>(q_gen_7892) -> q_gen_7883
<s, z>(q_gen_7907) -> q_gen_7883
<z, z>() -> q_gen_7883
<z, s>(q_gen_7889) -> q_gen_7895
<cons, s>(q_gen_7883, q_gen_7894) -> q_gen_7896
<cons, s>(q_gen_7895, q_gen_7882) -> q_gen_7896
<cons, s>(q_gen_7895, q_gen_7900) -> q_gen_7896
<cons, s>(q_gen_7895, q_gen_7909) -> q_gen_7896
<cons, s>(q_gen_7901, q_gen_7882) -> q_gen_7896
<cons, s>(q_gen_7901, q_gen_7894) -> q_gen_7896
<cons, s>(q_gen_7901, q_gen_7909) -> q_gen_7896
<cons, s>(q_gen_7915, q_gen_7882) -> q_gen_7896
<cons, s>(q_gen_7915, q_gen_7894) -> q_gen_7896
<z, s>(q_gen_7892) -> q_gen_7901
<z, s>(q_gen_7907) -> q_gen_7915
}

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

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 31
() -> length([nil, z]) -> 30
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 30
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 34
(le([s(nn1), z])) -> BOT -> 33
(le([z, z])) -> BOT -> 30
(length([l, _yca]) /\ length([cons(x, l), _zca])) -> le([_yca, _zca]) -> 34
(length([ll, _uca])) -> length([cons(x, ll), s(_uca)]) -> 37
}
Sat witness: Found: ((length([ll, _uca])) -> length([cons(x, ll), s(_uca)]), {
_uca -> s(z)  ;  ll -> cons(s(z), nil)  ;  x -> s(z)
})

-------------------------------------------
Step 35, which took 0.056346 s (model generation: 0.054222,  model checking: 0.002124):

Model:
|_
{
le -> 
{{{
Q={q_gen_7879, q_gen_7880, q_gen_7897},
Q_f={q_gen_7879},
Delta=
{
<s>(q_gen_7880) -> q_gen_7880
<z>() -> q_gen_7880
<s, s>(q_gen_7879) -> q_gen_7879
<z, s>(q_gen_7880) -> q_gen_7879
<s, s>(q_gen_7897) -> q_gen_7897
<s, z>(q_gen_7880) -> q_gen_7897
<z, z>() -> q_gen_7897
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_7878, q_gen_7882, q_gen_7883, q_gen_7889, q_gen_7892, q_gen_7894, q_gen_7895, q_gen_7896, q_gen_7900, q_gen_7901, q_gen_7907, q_gen_7909, q_gen_7915},
Q_f={q_gen_7878},
Delta=
{
<nil>() -> q_gen_7882
<s>(q_gen_7907) -> q_gen_7889
<z>() -> q_gen_7889
<s>(q_gen_7889) -> q_gen_7892
<cons>(q_gen_7889, q_gen_7882) -> q_gen_7894
<cons>(q_gen_7907, q_gen_7882) -> q_gen_7894
<cons>(q_gen_7889, q_gen_7894) -> q_gen_7900
<s>(q_gen_7892) -> q_gen_7907
<cons>(q_gen_7889, q_gen_7900) -> q_gen_7909
<cons>(q_gen_7892, q_gen_7882) -> q_gen_7909
<cons, s>(q_gen_7883, q_gen_7882) -> q_gen_7878
<cons, s>(q_gen_7883, q_gen_7909) -> q_gen_7878
<cons, s>(q_gen_7895, q_gen_7894) -> q_gen_7878
<cons, s>(q_gen_7901, q_gen_7900) -> q_gen_7878
<cons, s>(q_gen_7915, q_gen_7909) -> q_gen_7878
<nil, z>() -> q_gen_7878
<s, s>(q_gen_7883) -> q_gen_7883
<s, z>(q_gen_7889) -> q_gen_7883
<s, z>(q_gen_7892) -> q_gen_7883
<s, z>(q_gen_7907) -> q_gen_7883
<z, z>() -> q_gen_7883
<z, s>(q_gen_7889) -> q_gen_7895
<cons, s>(q_gen_7883, q_gen_7894) -> q_gen_7896
<cons, s>(q_gen_7895, q_gen_7882) -> q_gen_7896
<cons, s>(q_gen_7895, q_gen_7900) -> q_gen_7896
<cons, s>(q_gen_7895, q_gen_7909) -> q_gen_7896
<cons, s>(q_gen_7901, q_gen_7882) -> q_gen_7896
<cons, s>(q_gen_7901, q_gen_7894) -> q_gen_7896
<cons, s>(q_gen_7901, q_gen_7909) -> q_gen_7896
<cons, s>(q_gen_7915, q_gen_7882) -> q_gen_7896
<cons, s>(q_gen_7915, q_gen_7894) -> q_gen_7896
<z, s>(q_gen_7892) -> q_gen_7901
<z, s>(q_gen_7907) -> q_gen_7915
}

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

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 32
() -> length([nil, z]) -> 31
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 31
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 34
(le([s(nn1), z])) -> BOT -> 34
(le([z, z])) -> BOT -> 31
(length([l, _yca]) /\ length([cons(x, l), _zca])) -> le([_yca, _zca]) -> 37
(length([ll, _uca])) -> length([cons(x, ll), s(_uca)]) -> 37
}
Sat witness: Found: ((length([l, _yca]) /\ length([cons(x, l), _zca])) -> le([_yca, _zca]), {
_yca -> s(z)  ;  _zca -> s(z)  ;  l -> cons(s(z), nil)  ;  x -> z
})

-------------------------------------------
Step 36, which took 0.077180 s (model generation: 0.073100,  model checking: 0.004080):

Model:
|_
{
le -> 
{{{
Q={q_gen_7879, q_gen_7880, q_gen_7897},
Q_f={q_gen_7879},
Delta=
{
<s>(q_gen_7880) -> q_gen_7880
<z>() -> q_gen_7880
<s, s>(q_gen_7879) -> q_gen_7879
<z, s>(q_gen_7880) -> q_gen_7879
<s, s>(q_gen_7897) -> q_gen_7897
<s, z>(q_gen_7880) -> q_gen_7897
<z, z>() -> q_gen_7897
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_7878, q_gen_7882, q_gen_7883, q_gen_7889, q_gen_7892, q_gen_7894, q_gen_7895, q_gen_7896, q_gen_7900, q_gen_7901, q_gen_7907, q_gen_7909, q_gen_7915},
Q_f={q_gen_7878},
Delta=
{
<nil>() -> q_gen_7882
<s>(q_gen_7907) -> q_gen_7889
<z>() -> q_gen_7889
<s>(q_gen_7889) -> q_gen_7892
<cons>(q_gen_7889, q_gen_7882) -> q_gen_7894
<cons>(q_gen_7907, q_gen_7882) -> q_gen_7894
<cons>(q_gen_7889, q_gen_7894) -> q_gen_7900
<s>(q_gen_7892) -> q_gen_7907
<cons>(q_gen_7889, q_gen_7900) -> q_gen_7909
<cons>(q_gen_7892, q_gen_7882) -> q_gen_7909
<cons, s>(q_gen_7883, q_gen_7882) -> q_gen_7878
<cons, s>(q_gen_7895, q_gen_7894) -> q_gen_7878
<cons, s>(q_gen_7901, q_gen_7900) -> q_gen_7878
<cons, s>(q_gen_7915, q_gen_7909) -> q_gen_7878
<nil, z>() -> q_gen_7878
<s, z>(q_gen_7889) -> q_gen_7883
<s, z>(q_gen_7892) -> q_gen_7883
<s, z>(q_gen_7907) -> q_gen_7883
<z, z>() -> q_gen_7883
<z, s>(q_gen_7889) -> q_gen_7895
<cons, s>(q_gen_7883, q_gen_7894) -> q_gen_7896
<cons, s>(q_gen_7883, q_gen_7909) -> q_gen_7896
<cons, s>(q_gen_7895, q_gen_7882) -> q_gen_7896
<cons, s>(q_gen_7895, q_gen_7900) -> q_gen_7896
<cons, s>(q_gen_7895, q_gen_7909) -> q_gen_7896
<cons, s>(q_gen_7901, q_gen_7882) -> q_gen_7896
<cons, s>(q_gen_7901, q_gen_7894) -> q_gen_7896
<cons, s>(q_gen_7901, q_gen_7909) -> q_gen_7896
<cons, s>(q_gen_7915, q_gen_7882) -> q_gen_7896
<cons, s>(q_gen_7915, q_gen_7894) -> q_gen_7896
<z, s>(q_gen_7892) -> q_gen_7901
<s, s>(q_gen_7883) -> q_gen_7915
<z, s>(q_gen_7907) -> q_gen_7915
}

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

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 33
() -> length([nil, z]) -> 32
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 32
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 35
(le([s(nn1), z])) -> BOT -> 35
(le([z, z])) -> BOT -> 32
(length([l, _yca]) /\ length([cons(x, l), _zca])) -> le([_yca, _zca]) -> 37
(length([ll, _uca])) -> length([cons(x, ll), s(_uca)]) -> 40
}
Sat witness: Found: ((length([ll, _uca])) -> length([cons(x, ll), s(_uca)]), {
_uca -> s(z)  ;  ll -> cons(s(z), nil)  ;  x -> z
})

-------------------------------------------
Step 37, which took 0.062876 s (model generation: 0.058431,  model checking: 0.004445):

Model:
|_
{
le -> 
{{{
Q={q_gen_7879, q_gen_7880, q_gen_7897},
Q_f={q_gen_7879},
Delta=
{
<s>(q_gen_7880) -> q_gen_7880
<z>() -> q_gen_7880
<s, s>(q_gen_7879) -> q_gen_7879
<z, s>(q_gen_7880) -> q_gen_7879
<s, s>(q_gen_7897) -> q_gen_7897
<s, z>(q_gen_7880) -> q_gen_7897
<z, z>() -> q_gen_7897
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_7878, q_gen_7882, q_gen_7883, q_gen_7889, q_gen_7892, q_gen_7894, q_gen_7895, q_gen_7896, q_gen_7900, q_gen_7901, q_gen_7907, q_gen_7909, q_gen_7915},
Q_f={q_gen_7878},
Delta=
{
<nil>() -> q_gen_7882
<s>(q_gen_7907) -> q_gen_7889
<z>() -> q_gen_7889
<s>(q_gen_7889) -> q_gen_7892
<cons>(q_gen_7889, q_gen_7882) -> q_gen_7894
<cons>(q_gen_7892, q_gen_7882) -> q_gen_7894
<cons>(q_gen_7907, q_gen_7882) -> q_gen_7894
<cons>(q_gen_7889, q_gen_7894) -> q_gen_7900
<s>(q_gen_7892) -> q_gen_7907
<cons>(q_gen_7889, q_gen_7900) -> q_gen_7909
<cons, s>(q_gen_7883, q_gen_7882) -> q_gen_7878
<cons, s>(q_gen_7895, q_gen_7894) -> q_gen_7878
<cons, s>(q_gen_7901, q_gen_7900) -> q_gen_7878
<cons, s>(q_gen_7915, q_gen_7909) -> q_gen_7878
<nil, z>() -> q_gen_7878
<s, z>(q_gen_7889) -> q_gen_7883
<s, z>(q_gen_7892) -> q_gen_7883
<s, z>(q_gen_7907) -> q_gen_7883
<z, z>() -> q_gen_7883
<s, s>(q_gen_7883) -> q_gen_7895
<z, s>(q_gen_7889) -> q_gen_7895
<cons, s>(q_gen_7883, q_gen_7894) -> q_gen_7896
<cons, s>(q_gen_7895, q_gen_7882) -> q_gen_7896
<cons, s>(q_gen_7895, q_gen_7900) -> q_gen_7896
<cons, s>(q_gen_7895, q_gen_7909) -> q_gen_7896
<cons, s>(q_gen_7901, q_gen_7882) -> q_gen_7896
<cons, s>(q_gen_7901, q_gen_7894) -> q_gen_7896
<cons, s>(q_gen_7901, q_gen_7909) -> q_gen_7896
<cons, s>(q_gen_7915, q_gen_7882) -> q_gen_7896
<cons, s>(q_gen_7915, q_gen_7894) -> q_gen_7896
<z, s>(q_gen_7892) -> q_gen_7901
<z, s>(q_gen_7907) -> q_gen_7915
}

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

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 34
() -> length([nil, z]) -> 33
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 33
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 36
(le([s(nn1), z])) -> BOT -> 36
(le([z, z])) -> BOT -> 33
(length([l, _yca]) /\ length([cons(x, l), _zca])) -> le([_yca, _zca]) -> 40
(length([ll, _uca])) -> length([cons(x, ll), s(_uca)]) -> 40
}
Sat witness: Found: ((length([l, _yca]) /\ length([cons(x, l), _zca])) -> le([_yca, _zca]), {
_yca -> s(s(s(s(s(z)))))  ;  _zca -> s(s(s(z)))  ;  l -> cons(z, cons(s(s(z)), nil))  ;  x -> z
})

-------------------------------------------
Step 38, which took 0.080430 s (model generation: 0.066807,  model checking: 0.013623):

Model:
|_
{
le -> 
{{{
Q={q_gen_7879, q_gen_7880, q_gen_7897},
Q_f={q_gen_7879},
Delta=
{
<s>(q_gen_7880) -> q_gen_7880
<z>() -> q_gen_7880
<s, s>(q_gen_7879) -> q_gen_7879
<z, s>(q_gen_7880) -> q_gen_7879
<s, s>(q_gen_7897) -> q_gen_7897
<s, z>(q_gen_7880) -> q_gen_7897
<z, z>() -> q_gen_7897
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_7878, q_gen_7882, q_gen_7883, q_gen_7889, q_gen_7892, q_gen_7894, q_gen_7895, q_gen_7896, q_gen_7900, q_gen_7901, q_gen_7907, q_gen_7909, q_gen_7915},
Q_f={q_gen_7878},
Delta=
{
<nil>() -> q_gen_7882
<z>() -> q_gen_7889
<s>(q_gen_7889) -> q_gen_7892
<cons>(q_gen_7889, q_gen_7882) -> q_gen_7894
<cons>(q_gen_7892, q_gen_7882) -> q_gen_7894
<cons>(q_gen_7907, q_gen_7882) -> q_gen_7894
<cons>(q_gen_7889, q_gen_7894) -> q_gen_7900
<s>(q_gen_7892) -> q_gen_7907
<s>(q_gen_7907) -> q_gen_7907
<cons>(q_gen_7889, q_gen_7900) -> q_gen_7909
<cons, s>(q_gen_7883, q_gen_7882) -> q_gen_7878
<cons, s>(q_gen_7895, q_gen_7894) -> q_gen_7878
<cons, s>(q_gen_7901, q_gen_7900) -> q_gen_7878
<cons, s>(q_gen_7915, q_gen_7909) -> q_gen_7878
<nil, z>() -> q_gen_7878
<s, z>(q_gen_7889) -> q_gen_7883
<s, z>(q_gen_7892) -> q_gen_7883
<s, z>(q_gen_7907) -> q_gen_7883
<z, z>() -> q_gen_7883
<s, s>(q_gen_7883) -> q_gen_7895
<z, s>(q_gen_7889) -> q_gen_7895
<cons, s>(q_gen_7883, q_gen_7894) -> q_gen_7896
<cons, s>(q_gen_7895, q_gen_7882) -> q_gen_7896
<cons, s>(q_gen_7895, q_gen_7900) -> q_gen_7896
<cons, s>(q_gen_7895, q_gen_7909) -> q_gen_7896
<cons, s>(q_gen_7901, q_gen_7882) -> q_gen_7896
<cons, s>(q_gen_7901, q_gen_7894) -> q_gen_7896
<cons, s>(q_gen_7901, q_gen_7909) -> q_gen_7896
<cons, s>(q_gen_7915, q_gen_7882) -> q_gen_7896
<cons, s>(q_gen_7915, q_gen_7894) -> q_gen_7896
<cons, s>(q_gen_7915, q_gen_7900) -> q_gen_7896
<z, s>(q_gen_7892) -> q_gen_7901
<z, s>(q_gen_7907) -> q_gen_7915
}

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

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 35
() -> length([nil, z]) -> 34
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 34
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 37
(le([s(nn1), z])) -> BOT -> 37
(le([z, z])) -> BOT -> 34
(length([l, _yca]) /\ length([cons(x, l), _zca])) -> le([_yca, _zca]) -> 40
(length([ll, _uca])) -> length([cons(x, ll), s(_uca)]) -> 43
}
Sat witness: Found: ((length([ll, _uca])) -> length([cons(x, ll), s(_uca)]), {
_uca -> s(s(s(z)))  ;  ll -> cons(z, cons(z, cons(s(z), nil)))  ;  x -> s(z)
})

-------------------------------------------
Step 39, which took 0.085160 s (model generation: 0.081130,  model checking: 0.004030):

Model:
|_
{
le -> 
{{{
Q={q_gen_7879, q_gen_7880, q_gen_7897},
Q_f={q_gen_7879},
Delta=
{
<s>(q_gen_7880) -> q_gen_7880
<z>() -> q_gen_7880
<s, s>(q_gen_7879) -> q_gen_7879
<z, s>(q_gen_7880) -> q_gen_7879
<s, s>(q_gen_7897) -> q_gen_7897
<s, z>(q_gen_7880) -> q_gen_7897
<z, z>() -> q_gen_7897
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_7878, q_gen_7882, q_gen_7883, q_gen_7889, q_gen_7892, q_gen_7894, q_gen_7895, q_gen_7896, q_gen_7900, q_gen_7901, q_gen_7907, q_gen_7909, q_gen_7915},
Q_f={q_gen_7878},
Delta=
{
<nil>() -> q_gen_7882
<z>() -> q_gen_7889
<s>(q_gen_7889) -> q_gen_7892
<cons>(q_gen_7889, q_gen_7882) -> q_gen_7894
<cons>(q_gen_7892, q_gen_7882) -> q_gen_7894
<cons>(q_gen_7907, q_gen_7882) -> q_gen_7894
<cons>(q_gen_7889, q_gen_7894) -> q_gen_7900
<s>(q_gen_7892) -> q_gen_7907
<s>(q_gen_7907) -> q_gen_7907
<cons>(q_gen_7889, q_gen_7900) -> q_gen_7909
<cons, s>(q_gen_7883, q_gen_7882) -> q_gen_7878
<cons, s>(q_gen_7883, q_gen_7909) -> q_gen_7878
<cons, s>(q_gen_7895, q_gen_7894) -> q_gen_7878
<cons, s>(q_gen_7901, q_gen_7900) -> q_gen_7878
<cons, s>(q_gen_7915, q_gen_7909) -> q_gen_7878
<nil, z>() -> q_gen_7878
<s, s>(q_gen_7901) -> q_gen_7883
<s, z>(q_gen_7889) -> q_gen_7883
<s, z>(q_gen_7892) -> q_gen_7883
<s, z>(q_gen_7907) -> q_gen_7883
<z, z>() -> q_gen_7883
<s, s>(q_gen_7883) -> q_gen_7895
<z, s>(q_gen_7889) -> q_gen_7895
<cons, s>(q_gen_7883, q_gen_7894) -> q_gen_7896
<cons, s>(q_gen_7895, q_gen_7882) -> q_gen_7896
<cons, s>(q_gen_7895, q_gen_7900) -> q_gen_7896
<cons, s>(q_gen_7895, q_gen_7909) -> q_gen_7896
<cons, s>(q_gen_7901, q_gen_7882) -> q_gen_7896
<cons, s>(q_gen_7901, q_gen_7894) -> q_gen_7896
<cons, s>(q_gen_7901, q_gen_7909) -> q_gen_7896
<cons, s>(q_gen_7915, q_gen_7882) -> q_gen_7896
<cons, s>(q_gen_7915, q_gen_7894) -> q_gen_7896
<cons, s>(q_gen_7915, q_gen_7900) -> q_gen_7896
<z, s>(q_gen_7892) -> q_gen_7901
<z, s>(q_gen_7907) -> q_gen_7915
}

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

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 36
() -> length([nil, z]) -> 35
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 35
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 38
(le([s(nn1), z])) -> BOT -> 38
(le([z, z])) -> BOT -> 35
(length([l, _yca]) /\ length([cons(x, l), _zca])) -> le([_yca, _zca]) -> 43
(length([ll, _uca])) -> length([cons(x, ll), s(_uca)]) -> 43
}
Sat witness: Found: ((length([l, _yca]) /\ length([cons(x, l), _zca])) -> le([_yca, _zca]), {
_yca -> s(s(s(s(z))))  ;  _zca -> s(s(z))  ;  l -> cons(s(z), nil)  ;  x -> s(z)
})

-------------------------------------------
Step 40, which took 0.091211 s (model generation: 0.081110,  model checking: 0.010101):

Model:
|_
{
le -> 
{{{
Q={q_gen_7879, q_gen_7880, q_gen_7897},
Q_f={q_gen_7879},
Delta=
{
<s>(q_gen_7880) -> q_gen_7880
<z>() -> q_gen_7880
<s, s>(q_gen_7879) -> q_gen_7879
<z, s>(q_gen_7880) -> q_gen_7879
<s, s>(q_gen_7897) -> q_gen_7897
<s, z>(q_gen_7880) -> q_gen_7897
<z, z>() -> q_gen_7897
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_7878, q_gen_7882, q_gen_7883, q_gen_7889, q_gen_7892, q_gen_7894, q_gen_7895, q_gen_7896, q_gen_7900, q_gen_7901, q_gen_7907, q_gen_7909, q_gen_7915},
Q_f={q_gen_7878},
Delta=
{
<nil>() -> q_gen_7882
<z>() -> q_gen_7889
<s>(q_gen_7889) -> q_gen_7892
<cons>(q_gen_7889, q_gen_7882) -> q_gen_7894
<cons>(q_gen_7892, q_gen_7882) -> q_gen_7894
<cons>(q_gen_7907, q_gen_7882) -> q_gen_7894
<cons>(q_gen_7889, q_gen_7894) -> q_gen_7900
<s>(q_gen_7892) -> q_gen_7907
<s>(q_gen_7907) -> q_gen_7907
<cons>(q_gen_7889, q_gen_7900) -> q_gen_7909
<cons, s>(q_gen_7883, q_gen_7882) -> q_gen_7878
<cons, s>(q_gen_7895, q_gen_7894) -> q_gen_7878
<cons, s>(q_gen_7901, q_gen_7900) -> q_gen_7878
<cons, s>(q_gen_7915, q_gen_7909) -> q_gen_7878
<nil, z>() -> q_gen_7878
<s, z>(q_gen_7889) -> q_gen_7883
<s, z>(q_gen_7892) -> q_gen_7883
<s, z>(q_gen_7907) -> q_gen_7883
<z, z>() -> q_gen_7883
<s, s>(q_gen_7883) -> q_gen_7895
<z, s>(q_gen_7889) -> q_gen_7895
<cons, s>(q_gen_7883, q_gen_7894) -> q_gen_7896
<cons, s>(q_gen_7895, q_gen_7882) -> q_gen_7896
<cons, s>(q_gen_7895, q_gen_7900) -> q_gen_7896
<cons, s>(q_gen_7895, q_gen_7909) -> q_gen_7896
<cons, s>(q_gen_7901, q_gen_7882) -> q_gen_7896
<cons, s>(q_gen_7901, q_gen_7894) -> q_gen_7896
<cons, s>(q_gen_7901, q_gen_7909) -> q_gen_7896
<cons, s>(q_gen_7915, q_gen_7882) -> q_gen_7896
<cons, s>(q_gen_7915, q_gen_7894) -> q_gen_7896
<cons, s>(q_gen_7915, q_gen_7900) -> q_gen_7896
<z, s>(q_gen_7892) -> q_gen_7901
<s, s>(q_gen_7901) -> q_gen_7915
<z, s>(q_gen_7907) -> q_gen_7915
}

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

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 37
() -> length([nil, z]) -> 36
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 36
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 39
(le([s(nn1), z])) -> BOT -> 39
(le([z, z])) -> BOT -> 36
(length([l, _yca]) /\ length([cons(x, l), _zca])) -> le([_yca, _zca]) -> 43
(length([ll, _uca])) -> length([cons(x, ll), s(_uca)]) -> 46
}
Sat witness: Found: ((length([ll, _uca])) -> length([cons(x, ll), s(_uca)]), {
_uca -> s(s(s(s(z))))  ;  ll -> cons(z, cons(z, cons(z, cons(s(z), nil))))  ;  x -> z
})

-------------------------------------------
Step 41, which took 0.104852 s (model generation: 0.098756,  model checking: 0.006096):

Model:
|_
{
le -> 
{{{
Q={q_gen_7879, q_gen_7880, q_gen_7897},
Q_f={q_gen_7879},
Delta=
{
<s>(q_gen_7880) -> q_gen_7880
<z>() -> q_gen_7880
<s, s>(q_gen_7879) -> q_gen_7879
<z, s>(q_gen_7880) -> q_gen_7879
<s, s>(q_gen_7897) -> q_gen_7897
<s, z>(q_gen_7880) -> q_gen_7897
<z, z>() -> q_gen_7897
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_7878, q_gen_7882, q_gen_7883, q_gen_7889, q_gen_7892, q_gen_7894, q_gen_7895, q_gen_7896, q_gen_7900, q_gen_7901, q_gen_7907, q_gen_7909, q_gen_7915},
Q_f={q_gen_7878},
Delta=
{
<nil>() -> q_gen_7882
<z>() -> q_gen_7889
<s>(q_gen_7889) -> q_gen_7892
<cons>(q_gen_7889, q_gen_7882) -> q_gen_7894
<cons>(q_gen_7892, q_gen_7882) -> q_gen_7894
<cons>(q_gen_7907, q_gen_7882) -> q_gen_7894
<cons>(q_gen_7889, q_gen_7894) -> q_gen_7900
<s>(q_gen_7892) -> q_gen_7907
<s>(q_gen_7907) -> q_gen_7907
<cons>(q_gen_7889, q_gen_7900) -> q_gen_7909
<cons>(q_gen_7889, q_gen_7909) -> q_gen_7909
<cons, s>(q_gen_7883, q_gen_7882) -> q_gen_7878
<cons, s>(q_gen_7895, q_gen_7894) -> q_gen_7878
<cons, s>(q_gen_7901, q_gen_7900) -> q_gen_7878
<cons, s>(q_gen_7915, q_gen_7909) -> q_gen_7878
<nil, z>() -> q_gen_7878
<s, z>(q_gen_7889) -> q_gen_7883
<s, z>(q_gen_7892) -> q_gen_7883
<s, z>(q_gen_7907) -> q_gen_7883
<z, z>() -> q_gen_7883
<s, s>(q_gen_7883) -> q_gen_7895
<z, s>(q_gen_7889) -> q_gen_7895
<cons, s>(q_gen_7883, q_gen_7894) -> q_gen_7896
<cons, s>(q_gen_7895, q_gen_7882) -> q_gen_7896
<cons, s>(q_gen_7895, q_gen_7900) -> q_gen_7896
<cons, s>(q_gen_7895, q_gen_7909) -> q_gen_7896
<cons, s>(q_gen_7901, q_gen_7882) -> q_gen_7896
<cons, s>(q_gen_7901, q_gen_7894) -> q_gen_7896
<cons, s>(q_gen_7901, q_gen_7909) -> q_gen_7896
<cons, s>(q_gen_7915, q_gen_7882) -> q_gen_7896
<cons, s>(q_gen_7915, q_gen_7894) -> q_gen_7896
<cons, s>(q_gen_7915, q_gen_7900) -> q_gen_7896
<z, s>(q_gen_7892) -> q_gen_7901
<s, s>(q_gen_7901) -> q_gen_7915
<z, s>(q_gen_7907) -> q_gen_7915
}

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

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 38
() -> length([nil, z]) -> 37
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 37
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 40
(le([s(nn1), z])) -> BOT -> 40
(le([z, z])) -> BOT -> 37
(length([l, _yca]) /\ length([cons(x, l), _zca])) -> le([_yca, _zca]) -> 46
(length([ll, _uca])) -> length([cons(x, ll), s(_uca)]) -> 46
}
Sat witness: Found: ((length([l, _yca]) /\ length([cons(x, l), _zca])) -> le([_yca, _zca]), {
_yca -> s(s(s(s(z))))  ;  _zca -> s(s(s(s(z))))  ;  l -> cons(z, cons(z, cons(z, cons(z, cons(s(s(z)), nil)))))  ;  x -> s(z)
})

-------------------------------------------
Step 42, which took 0.120465 s (model generation: 0.110785,  model checking: 0.009680):

Model:
|_
{
le -> 
{{{
Q={q_gen_7879, q_gen_7880, q_gen_7897},
Q_f={q_gen_7879},
Delta=
{
<s>(q_gen_7880) -> q_gen_7880
<z>() -> q_gen_7880
<s, s>(q_gen_7879) -> q_gen_7879
<z, s>(q_gen_7880) -> q_gen_7879
<s, s>(q_gen_7897) -> q_gen_7897
<s, z>(q_gen_7880) -> q_gen_7897
<z, z>() -> q_gen_7897
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_7878, q_gen_7882, q_gen_7883, q_gen_7889, q_gen_7892, q_gen_7894, q_gen_7895, q_gen_7896, q_gen_7900, q_gen_7901, q_gen_7907, q_gen_7909, q_gen_7915, q_gen_7920},
Q_f={q_gen_7878},
Delta=
{
<cons>(q_gen_7889, q_gen_7920) -> q_gen_7882
<nil>() -> q_gen_7882
<z>() -> q_gen_7889
<s>(q_gen_7889) -> q_gen_7892
<cons>(q_gen_7889, q_gen_7882) -> q_gen_7894
<cons>(q_gen_7892, q_gen_7882) -> q_gen_7894
<cons>(q_gen_7889, q_gen_7894) -> q_gen_7900
<s>(q_gen_7892) -> q_gen_7907
<s>(q_gen_7907) -> q_gen_7907
<cons>(q_gen_7889, q_gen_7900) -> q_gen_7909
<cons>(q_gen_7889, q_gen_7909) -> q_gen_7920
<cons>(q_gen_7907, q_gen_7882) -> q_gen_7920
<cons, s>(q_gen_7883, q_gen_7882) -> q_gen_7878
<cons, s>(q_gen_7895, q_gen_7894) -> q_gen_7878
<cons, s>(q_gen_7895, q_gen_7920) -> q_gen_7878
<cons, s>(q_gen_7901, q_gen_7900) -> q_gen_7878
<cons, s>(q_gen_7915, q_gen_7909) -> q_gen_7878
<cons, s>(q_gen_7915, q_gen_7920) -> q_gen_7878
<nil, z>() -> q_gen_7878
<s, z>(q_gen_7889) -> q_gen_7883
<s, z>(q_gen_7892) -> q_gen_7883
<s, z>(q_gen_7907) -> q_gen_7883
<z, z>() -> q_gen_7883
<s, s>(q_gen_7883) -> q_gen_7895
<z, s>(q_gen_7889) -> q_gen_7895
<cons, s>(q_gen_7883, q_gen_7894) -> q_gen_7896
<cons, s>(q_gen_7895, q_gen_7882) -> q_gen_7896
<cons, s>(q_gen_7895, q_gen_7900) -> q_gen_7896
<cons, s>(q_gen_7895, q_gen_7909) -> q_gen_7896
<cons, s>(q_gen_7901, q_gen_7882) -> q_gen_7896
<cons, s>(q_gen_7901, q_gen_7894) -> q_gen_7896
<cons, s>(q_gen_7901, q_gen_7909) -> q_gen_7896
<cons, s>(q_gen_7915, q_gen_7882) -> q_gen_7896
<cons, s>(q_gen_7915, q_gen_7894) -> q_gen_7896
<cons, s>(q_gen_7915, q_gen_7900) -> q_gen_7896
<z, s>(q_gen_7892) -> q_gen_7901
<s, s>(q_gen_7901) -> q_gen_7915
<z, s>(q_gen_7907) -> q_gen_7915
}

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

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 39
() -> length([nil, z]) -> 38
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 38
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 41
(le([s(nn1), z])) -> BOT -> 41
(le([z, z])) -> BOT -> 38
(length([l, _yca]) /\ length([cons(x, l), _zca])) -> le([_yca, _zca]) -> 46
(length([ll, _uca])) -> length([cons(x, ll), s(_uca)]) -> 49
}
Sat witness: Found: ((length([ll, _uca])) -> length([cons(x, ll), s(_uca)]), {
_uca -> s(s(s(s(z))))  ;  ll -> cons(z, cons(s(s(z)), nil))  ;  x -> z
})

-------------------------------------------
Step 43, which took 0.143140 s (model generation: 0.135736,  model checking: 0.007404):

Model:
|_
{
le -> 
{{{
Q={q_gen_7879, q_gen_7880, q_gen_7897},
Q_f={q_gen_7879},
Delta=
{
<s>(q_gen_7880) -> q_gen_7880
<z>() -> q_gen_7880
<s, s>(q_gen_7879) -> q_gen_7879
<z, s>(q_gen_7880) -> q_gen_7879
<s, s>(q_gen_7897) -> q_gen_7897
<s, z>(q_gen_7880) -> q_gen_7897
<z, z>() -> q_gen_7897
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_7878, q_gen_7882, q_gen_7883, q_gen_7889, q_gen_7892, q_gen_7894, q_gen_7895, q_gen_7896, q_gen_7900, q_gen_7901, q_gen_7907, q_gen_7909, q_gen_7915, q_gen_7941},
Q_f={q_gen_7878},
Delta=
{
<nil>() -> q_gen_7882
<z>() -> q_gen_7889
<s>(q_gen_7889) -> q_gen_7892
<cons>(q_gen_7889, q_gen_7882) -> q_gen_7894
<cons>(q_gen_7889, q_gen_7909) -> q_gen_7894
<cons>(q_gen_7907, q_gen_7882) -> q_gen_7894
<cons>(q_gen_7889, q_gen_7894) -> q_gen_7900
<s>(q_gen_7892) -> q_gen_7907
<s>(q_gen_7907) -> q_gen_7907
<cons>(q_gen_7889, q_gen_7900) -> q_gen_7909
<cons>(q_gen_7889, q_gen_7941) -> q_gen_7909
<cons>(q_gen_7892, q_gen_7882) -> q_gen_7941
<cons, s>(q_gen_7883, q_gen_7882) -> q_gen_7878
<cons, s>(q_gen_7895, q_gen_7894) -> q_gen_7878
<cons, s>(q_gen_7895, q_gen_7941) -> q_gen_7878
<cons, s>(q_gen_7901, q_gen_7900) -> q_gen_7878
<cons, s>(q_gen_7915, q_gen_7909) -> q_gen_7878
<cons, s>(q_gen_7915, q_gen_7941) -> q_gen_7878
<nil, z>() -> q_gen_7878
<s, z>(q_gen_7889) -> q_gen_7883
<s, z>(q_gen_7892) -> q_gen_7883
<s, z>(q_gen_7907) -> q_gen_7883
<z, z>() -> q_gen_7883
<s, s>(q_gen_7901) -> q_gen_7895
<z, s>(q_gen_7889) -> q_gen_7895
<cons, s>(q_gen_7883, q_gen_7894) -> q_gen_7896
<cons, s>(q_gen_7883, q_gen_7941) -> q_gen_7896
<cons, s>(q_gen_7895, q_gen_7882) -> q_gen_7896
<cons, s>(q_gen_7895, q_gen_7900) -> q_gen_7896
<cons, s>(q_gen_7895, q_gen_7909) -> q_gen_7896
<cons, s>(q_gen_7901, q_gen_7882) -> q_gen_7896
<cons, s>(q_gen_7901, q_gen_7894) -> q_gen_7896
<cons, s>(q_gen_7901, q_gen_7909) -> q_gen_7896
<cons, s>(q_gen_7915, q_gen_7882) -> q_gen_7896
<cons, s>(q_gen_7915, q_gen_7894) -> q_gen_7896
<cons, s>(q_gen_7915, q_gen_7900) -> q_gen_7896
<z, s>(q_gen_7892) -> q_gen_7901
<s, s>(q_gen_7883) -> q_gen_7915
<z, s>(q_gen_7907) -> q_gen_7915
}

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

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 40
() -> length([nil, z]) -> 39
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 39
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 42
(le([s(nn1), z])) -> BOT -> 42
(le([z, z])) -> BOT -> 39
(length([l, _yca]) /\ length([cons(x, l), _zca])) -> le([_yca, _zca]) -> 49
(length([ll, _uca])) -> length([cons(x, ll), s(_uca)]) -> 49
}
Sat witness: Found: ((length([l, _yca]) /\ length([cons(x, l), _zca])) -> le([_yca, _zca]), {
_yca -> s(s(z))  ;  _zca -> s(s(z))  ;  l -> cons(z, cons(s(z), nil))  ;  x -> s(z)
})

-------------------------------------------
Step 44, which took 0.115732 s (model generation: 0.115118,  model checking: 0.000614):

Model:
|_
{
le -> 
{{{
Q={q_gen_7879, q_gen_7880, q_gen_7886, q_gen_7897, q_gen_7927, q_gen_7928},
Q_f={q_gen_7879},
Delta=
{
<z>() -> q_gen_7880
<s>(q_gen_7880) -> q_gen_7886
<s>(q_gen_7886) -> q_gen_7886
<s, s>(q_gen_7879) -> q_gen_7879
<s, s>(q_gen_7927) -> q_gen_7879
<z, s>(q_gen_7880) -> q_gen_7879
<z, s>(q_gen_7886) -> q_gen_7879
<s, s>(q_gen_7897) -> q_gen_7897
<s, z>(q_gen_7880) -> q_gen_7897
<z, z>() -> q_gen_7897
<s, s>(q_gen_7928) -> q_gen_7927
<s, z>(q_gen_7886) -> q_gen_7928
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_7878, q_gen_7882, q_gen_7883, q_gen_7889, q_gen_7892, q_gen_7894, q_gen_7895, q_gen_7896, q_gen_7900, q_gen_7901, q_gen_7907},
Q_f={q_gen_7878},
Delta=
{
<cons>(q_gen_7889, q_gen_7900) -> q_gen_7882
<nil>() -> q_gen_7882
<s>(q_gen_7907) -> q_gen_7889
<z>() -> q_gen_7889
<s>(q_gen_7889) -> q_gen_7892
<cons>(q_gen_7889, q_gen_7882) -> q_gen_7894
<cons>(q_gen_7892, q_gen_7882) -> q_gen_7894
<cons>(q_gen_7907, q_gen_7882) -> q_gen_7894
<cons>(q_gen_7889, q_gen_7894) -> q_gen_7900
<s>(q_gen_7892) -> q_gen_7907
<cons, s>(q_gen_7883, q_gen_7882) -> q_gen_7878
<cons, s>(q_gen_7883, q_gen_7900) -> q_gen_7878
<cons, s>(q_gen_7895, q_gen_7894) -> q_gen_7878
<cons, s>(q_gen_7901, q_gen_7900) -> q_gen_7878
<nil, z>() -> q_gen_7878
<s, s>(q_gen_7901) -> q_gen_7883
<s, z>(q_gen_7889) -> q_gen_7883
<s, z>(q_gen_7892) -> q_gen_7883
<s, z>(q_gen_7907) -> q_gen_7883
<z, s>(q_gen_7907) -> q_gen_7883
<z, z>() -> q_gen_7883
<s, s>(q_gen_7883) -> q_gen_7895
<z, s>(q_gen_7889) -> q_gen_7895
<cons, s>(q_gen_7883, q_gen_7894) -> q_gen_7896
<cons, s>(q_gen_7895, q_gen_7882) -> q_gen_7896
<cons, s>(q_gen_7895, q_gen_7900) -> q_gen_7896
<cons, s>(q_gen_7901, q_gen_7882) -> q_gen_7896
<cons, s>(q_gen_7901, q_gen_7894) -> q_gen_7896
<z, s>(q_gen_7892) -> q_gen_7901
}

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

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 41
() -> length([nil, z]) -> 40
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 40
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 45
(le([s(nn1), z])) -> BOT -> 43
(le([z, z])) -> BOT -> 40
(length([l, _yca]) /\ length([cons(x, l), _zca])) -> le([_yca, _zca]) -> 49
(length([ll, _uca])) -> length([cons(x, ll), s(_uca)]) -> 49
}
Sat witness: Found: ((le([s(nn1), s(nn2)])) -> le([nn1, nn2]), {
nn1 -> s(s(s(z)))  ;  nn2 -> s(z)
})

-------------------------------------------
Step 45, which took 0.131339 s (model generation: 0.124510,  model checking: 0.006829):

Model:
|_
{
le -> 
{{{
Q={q_gen_7879, q_gen_7880, q_gen_7897},
Q_f={q_gen_7879},
Delta=
{
<s>(q_gen_7880) -> q_gen_7880
<z>() -> q_gen_7880
<s, s>(q_gen_7879) -> q_gen_7879
<z, s>(q_gen_7880) -> q_gen_7879
<s, s>(q_gen_7897) -> q_gen_7897
<s, z>(q_gen_7880) -> q_gen_7897
<z, z>() -> q_gen_7897
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_7878, q_gen_7882, q_gen_7883, q_gen_7889, q_gen_7892, q_gen_7894, q_gen_7895, q_gen_7896, q_gen_7900, q_gen_7901, q_gen_7907, q_gen_7909, q_gen_7915, q_gen_7920},
Q_f={q_gen_7878},
Delta=
{
<cons>(q_gen_7889, q_gen_7920) -> q_gen_7882
<nil>() -> q_gen_7882
<s>(q_gen_7907) -> q_gen_7889
<z>() -> q_gen_7889
<s>(q_gen_7889) -> q_gen_7892
<cons>(q_gen_7889, q_gen_7882) -> q_gen_7894
<cons>(q_gen_7889, q_gen_7894) -> q_gen_7900
<s>(q_gen_7892) -> q_gen_7907
<cons>(q_gen_7889, q_gen_7900) -> q_gen_7909
<cons>(q_gen_7892, q_gen_7882) -> q_gen_7920
<cons>(q_gen_7907, q_gen_7882) -> q_gen_7920
<cons, s>(q_gen_7883, q_gen_7882) -> q_gen_7878
<cons, s>(q_gen_7895, q_gen_7894) -> q_gen_7878
<cons, s>(q_gen_7895, q_gen_7920) -> q_gen_7878
<cons, s>(q_gen_7901, q_gen_7900) -> q_gen_7878
<cons, s>(q_gen_7915, q_gen_7900) -> q_gen_7878
<cons, s>(q_gen_7915, q_gen_7909) -> q_gen_7878
<nil, z>() -> q_gen_7878
<s, z>(q_gen_7889) -> q_gen_7883
<s, z>(q_gen_7892) -> q_gen_7883
<s, z>(q_gen_7907) -> q_gen_7883
<z, z>() -> q_gen_7883
<s, s>(q_gen_7883) -> q_gen_7895
<s, s>(q_gen_7901) -> q_gen_7895
<z, s>(q_gen_7889) -> q_gen_7895
<cons, s>(q_gen_7883, q_gen_7894) -> q_gen_7896
<cons, s>(q_gen_7883, q_gen_7920) -> q_gen_7896
<cons, s>(q_gen_7895, q_gen_7882) -> q_gen_7896
<cons, s>(q_gen_7895, q_gen_7900) -> q_gen_7896
<cons, s>(q_gen_7895, q_gen_7909) -> q_gen_7896
<cons, s>(q_gen_7901, q_gen_7882) -> q_gen_7896
<cons, s>(q_gen_7901, q_gen_7894) -> q_gen_7896
<cons, s>(q_gen_7901, q_gen_7909) -> q_gen_7896
<cons, s>(q_gen_7915, q_gen_7882) -> q_gen_7896
<cons, s>(q_gen_7915, q_gen_7894) -> q_gen_7896
<cons, s>(q_gen_7915, q_gen_7920) -> q_gen_7896
<z, s>(q_gen_7892) -> q_gen_7901
<z, s>(q_gen_7907) -> q_gen_7915
}

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

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 42
() -> length([nil, z]) -> 41
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 41
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 46
(le([s(nn1), z])) -> BOT -> 44
(le([z, z])) -> BOT -> 41
(length([l, _yca]) /\ length([cons(x, l), _zca])) -> le([_yca, _zca]) -> 49
(length([ll, _uca])) -> length([cons(x, ll), s(_uca)]) -> 52
}
Sat witness: Found: ((length([ll, _uca])) -> length([cons(x, ll), s(_uca)]), {
_uca -> s(s(z))  ;  ll -> cons(z, cons(s(z), nil))  ;  x -> z
})

-------------------------------------------
Step 46, which took 0.125316 s (model generation: 0.122893,  model checking: 0.002423):

Model:
|_
{
le -> 
{{{
Q={q_gen_7879, q_gen_7880, q_gen_7897},
Q_f={q_gen_7879},
Delta=
{
<s>(q_gen_7880) -> q_gen_7880
<z>() -> q_gen_7880
<s, s>(q_gen_7879) -> q_gen_7879
<z, s>(q_gen_7880) -> q_gen_7879
<s, s>(q_gen_7897) -> q_gen_7897
<s, z>(q_gen_7880) -> q_gen_7897
<z, z>() -> q_gen_7897
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_7878, q_gen_7882, q_gen_7883, q_gen_7889, q_gen_7892, q_gen_7894, q_gen_7895, q_gen_7896, q_gen_7900, q_gen_7901, q_gen_7907, q_gen_7909, q_gen_7915, q_gen_7920},
Q_f={q_gen_7878},
Delta=
{
<cons>(q_gen_7889, q_gen_7920) -> q_gen_7882
<nil>() -> q_gen_7882
<z>() -> q_gen_7889
<s>(q_gen_7889) -> q_gen_7892
<cons>(q_gen_7889, q_gen_7882) -> q_gen_7894
<cons>(q_gen_7892, q_gen_7882) -> q_gen_7894
<cons>(q_gen_7889, q_gen_7894) -> q_gen_7900
<s>(q_gen_7892) -> q_gen_7907
<s>(q_gen_7907) -> q_gen_7907
<cons>(q_gen_7889, q_gen_7900) -> q_gen_7909
<cons>(q_gen_7889, q_gen_7909) -> q_gen_7909
<cons>(q_gen_7907, q_gen_7882) -> q_gen_7920
<cons, s>(q_gen_7883, q_gen_7882) -> q_gen_7878
<cons, s>(q_gen_7895, q_gen_7894) -> q_gen_7878
<cons, s>(q_gen_7895, q_gen_7920) -> q_gen_7878
<cons, s>(q_gen_7901, q_gen_7900) -> q_gen_7878
<cons, s>(q_gen_7915, q_gen_7909) -> q_gen_7878
<nil, z>() -> q_gen_7878
<s, z>(q_gen_7889) -> q_gen_7883
<s, z>(q_gen_7892) -> q_gen_7883
<s, z>(q_gen_7907) -> q_gen_7883
<z, z>() -> q_gen_7883
<s, s>(q_gen_7883) -> q_gen_7895
<z, s>(q_gen_7889) -> q_gen_7895
<cons, s>(q_gen_7883, q_gen_7894) -> q_gen_7896
<cons, s>(q_gen_7895, q_gen_7882) -> q_gen_7896
<cons, s>(q_gen_7895, q_gen_7900) -> q_gen_7896
<cons, s>(q_gen_7895, q_gen_7909) -> q_gen_7896
<cons, s>(q_gen_7901, q_gen_7882) -> q_gen_7896
<cons, s>(q_gen_7901, q_gen_7894) -> q_gen_7896
<cons, s>(q_gen_7901, q_gen_7909) -> q_gen_7896
<cons, s>(q_gen_7915, q_gen_7882) -> q_gen_7896
<cons, s>(q_gen_7915, q_gen_7894) -> q_gen_7896
<cons, s>(q_gen_7915, q_gen_7900) -> q_gen_7896
<cons, s>(q_gen_7915, q_gen_7920) -> q_gen_7896
<z, s>(q_gen_7892) -> q_gen_7901
<s, s>(q_gen_7901) -> q_gen_7915
<z, s>(q_gen_7907) -> q_gen_7915
}

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

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 43
() -> length([nil, z]) -> 42
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 42
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 47
(le([s(nn1), z])) -> BOT -> 45
(le([z, z])) -> BOT -> 42
(length([l, _yca]) /\ length([cons(x, l), _zca])) -> le([_yca, _zca]) -> 52
(length([ll, _uca])) -> length([cons(x, ll), s(_uca)]) -> 52
}
Sat witness: Found: ((length([l, _yca]) /\ length([cons(x, l), _zca])) -> le([_yca, _zca]), {
_yca -> s(s(z))  ;  _zca -> s(z)  ;  l -> cons(z, cons(s(s(z)), nil))  ;  x -> s(z)
})

-------------------------------------------
Step 47, which took 0.147647 s (model generation: 0.132721,  model checking: 0.014926):

Model:
|_
{
le -> 
{{{
Q={q_gen_7879, q_gen_7880, q_gen_7897},
Q_f={q_gen_7879},
Delta=
{
<s>(q_gen_7880) -> q_gen_7880
<z>() -> q_gen_7880
<s, s>(q_gen_7879) -> q_gen_7879
<z, s>(q_gen_7880) -> q_gen_7879
<s, s>(q_gen_7897) -> q_gen_7897
<s, z>(q_gen_7880) -> q_gen_7897
<z, z>() -> q_gen_7897
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_7878, q_gen_7882, q_gen_7883, q_gen_7889, q_gen_7892, q_gen_7894, q_gen_7895, q_gen_7896, q_gen_7900, q_gen_7901, q_gen_7907, q_gen_7909, q_gen_7915, q_gen_7956},
Q_f={q_gen_7878},
Delta=
{
<cons>(q_gen_7889, q_gen_7956) -> q_gen_7882
<nil>() -> q_gen_7882
<z>() -> q_gen_7889
<s>(q_gen_7889) -> q_gen_7892
<cons>(q_gen_7889, q_gen_7882) -> q_gen_7894
<cons>(q_gen_7892, q_gen_7882) -> q_gen_7894
<cons>(q_gen_7907, q_gen_7882) -> q_gen_7894
<cons>(q_gen_7889, q_gen_7894) -> q_gen_7900
<s>(q_gen_7892) -> q_gen_7907
<s>(q_gen_7907) -> q_gen_7907
<cons>(q_gen_7889, q_gen_7900) -> q_gen_7909
<cons>(q_gen_7889, q_gen_7909) -> q_gen_7956
<cons, s>(q_gen_7883, q_gen_7882) -> q_gen_7878
<cons, s>(q_gen_7895, q_gen_7894) -> q_gen_7878
<cons, s>(q_gen_7901, q_gen_7900) -> q_gen_7878
<cons, s>(q_gen_7915, q_gen_7909) -> q_gen_7878
<cons, s>(q_gen_7915, q_gen_7956) -> q_gen_7878
<nil, z>() -> q_gen_7878
<s, z>(q_gen_7889) -> q_gen_7883
<s, z>(q_gen_7892) -> q_gen_7883
<s, z>(q_gen_7907) -> q_gen_7883
<z, z>() -> q_gen_7883
<s, s>(q_gen_7883) -> q_gen_7895
<z, s>(q_gen_7889) -> q_gen_7895
<cons, s>(q_gen_7883, q_gen_7894) -> q_gen_7896
<cons, s>(q_gen_7883, q_gen_7900) -> q_gen_7896
<cons, s>(q_gen_7895, q_gen_7882) -> q_gen_7896
<cons, s>(q_gen_7895, q_gen_7900) -> q_gen_7896
<cons, s>(q_gen_7895, q_gen_7909) -> q_gen_7896
<cons, s>(q_gen_7901, q_gen_7882) -> q_gen_7896
<cons, s>(q_gen_7901, q_gen_7894) -> q_gen_7896
<cons, s>(q_gen_7901, q_gen_7909) -> q_gen_7896
<cons, s>(q_gen_7915, q_gen_7882) -> q_gen_7896
<cons, s>(q_gen_7915, q_gen_7894) -> q_gen_7896
<cons, s>(q_gen_7915, q_gen_7900) -> q_gen_7896
<z, s>(q_gen_7892) -> q_gen_7901
<s, s>(q_gen_7901) -> q_gen_7915
<z, s>(q_gen_7907) -> q_gen_7915
}

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

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 44
() -> length([nil, z]) -> 43
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 43
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 48
(le([s(nn1), z])) -> BOT -> 46
(le([z, z])) -> BOT -> 43
(length([l, _yca]) /\ length([cons(x, l), _zca])) -> le([_yca, _zca]) -> 52
(length([ll, _uca])) -> length([cons(x, ll), s(_uca)]) -> 55
}
Sat witness: Found: ((length([ll, _uca])) -> length([cons(x, ll), s(_uca)]), {
_uca -> s(s(s(s(z))))  ;  ll -> cons(z, cons(z, cons(z, cons(z, cons(z, nil)))))  ;  x -> z
})

-------------------------------------------
Step 48, which took 0.163534 s (model generation: 0.158114,  model checking: 0.005420):

Model:
|_
{
le -> 
{{{
Q={q_gen_7879, q_gen_7880, q_gen_7897},
Q_f={q_gen_7879},
Delta=
{
<s>(q_gen_7880) -> q_gen_7880
<z>() -> q_gen_7880
<s, s>(q_gen_7879) -> q_gen_7879
<z, s>(q_gen_7880) -> q_gen_7879
<s, s>(q_gen_7897) -> q_gen_7897
<s, z>(q_gen_7880) -> q_gen_7897
<z, z>() -> q_gen_7897
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_7878, q_gen_7882, q_gen_7883, q_gen_7889, q_gen_7892, q_gen_7894, q_gen_7895, q_gen_7896, q_gen_7900, q_gen_7901, q_gen_7907, q_gen_7909, q_gen_7915, q_gen_7920},
Q_f={q_gen_7878},
Delta=
{
<nil>() -> q_gen_7882
<s>(q_gen_7907) -> q_gen_7889
<z>() -> q_gen_7889
<s>(q_gen_7889) -> q_gen_7892
<cons>(q_gen_7889, q_gen_7882) -> q_gen_7894
<cons>(q_gen_7892, q_gen_7882) -> q_gen_7894
<cons>(q_gen_7889, q_gen_7894) -> q_gen_7900
<s>(q_gen_7892) -> q_gen_7907
<cons>(q_gen_7889, q_gen_7900) -> q_gen_7909
<cons>(q_gen_7889, q_gen_7909) -> q_gen_7920
<cons>(q_gen_7889, q_gen_7920) -> q_gen_7920
<cons>(q_gen_7907, q_gen_7882) -> q_gen_7920
<cons, s>(q_gen_7883, q_gen_7882) -> q_gen_7878
<cons, s>(q_gen_7895, q_gen_7894) -> q_gen_7878
<cons, s>(q_gen_7895, q_gen_7920) -> q_gen_7878
<cons, s>(q_gen_7901, q_gen_7900) -> q_gen_7878
<cons, s>(q_gen_7915, q_gen_7894) -> q_gen_7878
<cons, s>(q_gen_7915, q_gen_7909) -> q_gen_7878
<nil, z>() -> q_gen_7878
<s, z>(q_gen_7889) -> q_gen_7883
<s, z>(q_gen_7892) -> q_gen_7883
<s, z>(q_gen_7907) -> q_gen_7883
<z, z>() -> q_gen_7883
<s, s>(q_gen_7883) -> q_gen_7895
<z, s>(q_gen_7889) -> q_gen_7895
<cons, s>(q_gen_7883, q_gen_7894) -> q_gen_7896
<cons, s>(q_gen_7883, q_gen_7920) -> q_gen_7896
<cons, s>(q_gen_7895, q_gen_7882) -> q_gen_7896
<cons, s>(q_gen_7895, q_gen_7900) -> q_gen_7896
<cons, s>(q_gen_7895, q_gen_7909) -> q_gen_7896
<cons, s>(q_gen_7901, q_gen_7882) -> q_gen_7896
<cons, s>(q_gen_7901, q_gen_7894) -> q_gen_7896
<cons, s>(q_gen_7901, q_gen_7909) -> q_gen_7896
<cons, s>(q_gen_7901, q_gen_7920) -> q_gen_7896
<cons, s>(q_gen_7915, q_gen_7882) -> q_gen_7896
<cons, s>(q_gen_7915, q_gen_7920) -> q_gen_7896
<z, s>(q_gen_7892) -> q_gen_7901
<s, s>(q_gen_7901) -> q_gen_7915
<z, s>(q_gen_7907) -> q_gen_7915
}

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

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 45
() -> length([nil, z]) -> 44
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 44
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 49
(le([s(nn1), z])) -> BOT -> 47
(le([z, z])) -> BOT -> 44
(length([l, _yca]) /\ length([cons(x, l), _zca])) -> le([_yca, _zca]) -> 55
(length([ll, _uca])) -> length([cons(x, ll), s(_uca)]) -> 55
}
Sat witness: Found: ((length([l, _yca]) /\ length([cons(x, l), _zca])) -> le([_yca, _zca]), {
_yca -> s(s(s(s(s(z)))))  ;  _zca -> s(s(s(z)))  ;  l -> cons(z, cons(s(z), nil))  ;  x -> z
})

-------------------------------------------
Step 49, which took 0.186084 s (model generation: 0.181229,  model checking: 0.004855):

Model:
|_
{
le -> 
{{{
Q={q_gen_7879, q_gen_7880, q_gen_7897},
Q_f={q_gen_7879},
Delta=
{
<s>(q_gen_7880) -> q_gen_7880
<z>() -> q_gen_7880
<s, s>(q_gen_7879) -> q_gen_7879
<z, s>(q_gen_7880) -> q_gen_7879
<s, s>(q_gen_7897) -> q_gen_7897
<s, z>(q_gen_7880) -> q_gen_7897
<z, z>() -> q_gen_7897
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_7878, q_gen_7882, q_gen_7883, q_gen_7889, q_gen_7892, q_gen_7894, q_gen_7895, q_gen_7896, q_gen_7900, q_gen_7901, q_gen_7907, q_gen_7909, q_gen_7915, q_gen_7920},
Q_f={q_gen_7878},
Delta=
{
<nil>() -> q_gen_7882
<z>() -> q_gen_7889
<s>(q_gen_7889) -> q_gen_7892
<s>(q_gen_7907) -> q_gen_7892
<cons>(q_gen_7889, q_gen_7882) -> q_gen_7894
<cons>(q_gen_7889, q_gen_7920) -> q_gen_7894
<cons>(q_gen_7892, q_gen_7882) -> q_gen_7894
<cons>(q_gen_7889, q_gen_7894) -> q_gen_7900
<s>(q_gen_7892) -> q_gen_7907
<cons>(q_gen_7889, q_gen_7900) -> q_gen_7909
<cons>(q_gen_7889, q_gen_7909) -> q_gen_7920
<cons>(q_gen_7907, q_gen_7882) -> q_gen_7920
<cons, s>(q_gen_7883, q_gen_7882) -> q_gen_7878
<cons, s>(q_gen_7895, q_gen_7894) -> q_gen_7878
<cons, s>(q_gen_7895, q_gen_7920) -> q_gen_7878
<cons, s>(q_gen_7901, q_gen_7900) -> q_gen_7878
<cons, s>(q_gen_7901, q_gen_7920) -> q_gen_7878
<cons, s>(q_gen_7915, q_gen_7909) -> q_gen_7878
<nil, z>() -> q_gen_7878
<s, z>(q_gen_7889) -> q_gen_7883
<s, z>(q_gen_7892) -> q_gen_7883
<s, z>(q_gen_7907) -> q_gen_7883
<z, z>() -> q_gen_7883
<s, s>(q_gen_7883) -> q_gen_7895
<z, s>(q_gen_7889) -> q_gen_7895
<cons, s>(q_gen_7883, q_gen_7894) -> q_gen_7896
<cons, s>(q_gen_7895, q_gen_7882) -> q_gen_7896
<cons, s>(q_gen_7895, q_gen_7900) -> q_gen_7896
<cons, s>(q_gen_7895, q_gen_7909) -> q_gen_7896
<cons, s>(q_gen_7901, q_gen_7882) -> q_gen_7896
<cons, s>(q_gen_7901, q_gen_7894) -> q_gen_7896
<cons, s>(q_gen_7901, q_gen_7909) -> q_gen_7896
<cons, s>(q_gen_7915, q_gen_7882) -> q_gen_7896
<cons, s>(q_gen_7915, q_gen_7894) -> q_gen_7896
<cons, s>(q_gen_7915, q_gen_7900) -> q_gen_7896
<cons, s>(q_gen_7915, q_gen_7920) -> q_gen_7896
<z, s>(q_gen_7892) -> q_gen_7901
<s, s>(q_gen_7901) -> q_gen_7915
<z, s>(q_gen_7907) -> q_gen_7915
}

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

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 46
() -> length([nil, z]) -> 45
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 45
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 50
(le([s(nn1), z])) -> BOT -> 48
(le([z, z])) -> BOT -> 45
(length([l, _yca]) /\ length([cons(x, l), _zca])) -> le([_yca, _zca]) -> 55
(length([ll, _uca])) -> length([cons(x, ll), s(_uca)]) -> 58
}
Sat witness: Found: ((length([ll, _uca])) -> length([cons(x, ll), s(_uca)]), {
_uca -> s(s(s(z)))  ;  ll -> cons(z, cons(s(s(z)), nil))  ;  x -> z
})

-------------------------------------------
Step 50, which took 0.179850 s (model generation: 0.173448,  model checking: 0.006402):

Model:
|_
{
le -> 
{{{
Q={q_gen_7879, q_gen_7880, q_gen_7897},
Q_f={q_gen_7879},
Delta=
{
<s>(q_gen_7880) -> q_gen_7880
<z>() -> q_gen_7880
<s, s>(q_gen_7879) -> q_gen_7879
<z, s>(q_gen_7880) -> q_gen_7879
<s, s>(q_gen_7897) -> q_gen_7897
<s, z>(q_gen_7880) -> q_gen_7897
<z, z>() -> q_gen_7897
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_7878, q_gen_7882, q_gen_7883, q_gen_7889, q_gen_7892, q_gen_7894, q_gen_7895, q_gen_7896, q_gen_7900, q_gen_7901, q_gen_7907, q_gen_7909, q_gen_7915, q_gen_7920},
Q_f={q_gen_7878},
Delta=
{
<nil>() -> q_gen_7882
<z>() -> q_gen_7889
<s>(q_gen_7889) -> q_gen_7892
<cons>(q_gen_7889, q_gen_7882) -> q_gen_7894
<cons>(q_gen_7892, q_gen_7882) -> q_gen_7894
<cons>(q_gen_7889, q_gen_7894) -> q_gen_7900
<cons>(q_gen_7889, q_gen_7909) -> q_gen_7900
<s>(q_gen_7892) -> q_gen_7907
<s>(q_gen_7907) -> q_gen_7907
<cons>(q_gen_7889, q_gen_7900) -> q_gen_7909
<cons>(q_gen_7889, q_gen_7920) -> q_gen_7920
<cons>(q_gen_7907, q_gen_7882) -> q_gen_7920
<cons, s>(q_gen_7883, q_gen_7882) -> q_gen_7878
<cons, s>(q_gen_7895, q_gen_7894) -> q_gen_7878
<cons, s>(q_gen_7895, q_gen_7920) -> q_gen_7878
<cons, s>(q_gen_7901, q_gen_7900) -> q_gen_7878
<cons, s>(q_gen_7915, q_gen_7900) -> q_gen_7878
<cons, s>(q_gen_7915, q_gen_7909) -> q_gen_7878
<nil, z>() -> q_gen_7878
<s, z>(q_gen_7889) -> q_gen_7883
<s, z>(q_gen_7892) -> q_gen_7883
<s, z>(q_gen_7907) -> q_gen_7883
<z, z>() -> q_gen_7883
<s, s>(q_gen_7883) -> q_gen_7895
<z, s>(q_gen_7889) -> q_gen_7895
<cons, s>(q_gen_7883, q_gen_7894) -> q_gen_7896
<cons, s>(q_gen_7883, q_gen_7920) -> q_gen_7896
<cons, s>(q_gen_7895, q_gen_7882) -> q_gen_7896
<cons, s>(q_gen_7895, q_gen_7900) -> q_gen_7896
<cons, s>(q_gen_7895, q_gen_7909) -> q_gen_7896
<cons, s>(q_gen_7901, q_gen_7882) -> q_gen_7896
<cons, s>(q_gen_7901, q_gen_7894) -> q_gen_7896
<cons, s>(q_gen_7901, q_gen_7909) -> q_gen_7896
<cons, s>(q_gen_7901, q_gen_7920) -> q_gen_7896
<cons, s>(q_gen_7915, q_gen_7882) -> q_gen_7896
<cons, s>(q_gen_7915, q_gen_7894) -> q_gen_7896
<cons, s>(q_gen_7915, q_gen_7920) -> q_gen_7896
<z, s>(q_gen_7892) -> q_gen_7901
<s, s>(q_gen_7901) -> q_gen_7915
<z, s>(q_gen_7907) -> q_gen_7915
}

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

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 47
() -> length([nil, z]) -> 46
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 46
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 51
(le([s(nn1), z])) -> BOT -> 49
(le([z, z])) -> BOT -> 46
(length([l, _yca]) /\ length([cons(x, l), _zca])) -> le([_yca, _zca]) -> 58
(length([ll, _uca])) -> length([cons(x, ll), s(_uca)]) -> 58
}
Sat witness: Found: ((length([l, _yca]) /\ length([cons(x, l), _zca])) -> le([_yca, _zca]), {
_yca -> s(s(z))  ;  _zca -> s(s(z))  ;  l -> cons(z, cons(s(s(z)), nil))  ;  x -> z
})

-------------------------------------------
Step 51, which took 0.180848 s (model generation: 0.176141,  model checking: 0.004707):

Model:
|_
{
le -> 
{{{
Q={q_gen_7879, q_gen_7880, q_gen_7897},
Q_f={q_gen_7879},
Delta=
{
<s>(q_gen_7880) -> q_gen_7880
<z>() -> q_gen_7880
<s, s>(q_gen_7879) -> q_gen_7879
<z, s>(q_gen_7880) -> q_gen_7879
<s, s>(q_gen_7897) -> q_gen_7897
<s, z>(q_gen_7880) -> q_gen_7897
<z, z>() -> q_gen_7897
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_7878, q_gen_7882, q_gen_7883, q_gen_7889, q_gen_7892, q_gen_7894, q_gen_7895, q_gen_7896, q_gen_7900, q_gen_7901, q_gen_7907, q_gen_7909, q_gen_7915, q_gen_7920},
Q_f={q_gen_7878},
Delta=
{
<nil>() -> q_gen_7882
<z>() -> q_gen_7889
<s>(q_gen_7889) -> q_gen_7892
<s>(q_gen_7907) -> q_gen_7892
<cons>(q_gen_7889, q_gen_7882) -> q_gen_7894
<cons>(q_gen_7892, q_gen_7882) -> q_gen_7894
<cons>(q_gen_7889, q_gen_7894) -> q_gen_7900
<s>(q_gen_7892) -> q_gen_7907
<cons>(q_gen_7889, q_gen_7900) -> q_gen_7909
<cons>(q_gen_7889, q_gen_7920) -> q_gen_7909
<cons>(q_gen_7889, q_gen_7909) -> q_gen_7920
<cons>(q_gen_7907, q_gen_7882) -> q_gen_7920
<cons, s>(q_gen_7883, q_gen_7882) -> q_gen_7878
<cons, s>(q_gen_7895, q_gen_7894) -> q_gen_7878
<cons, s>(q_gen_7895, q_gen_7920) -> q_gen_7878
<cons, s>(q_gen_7901, q_gen_7900) -> q_gen_7878
<cons, s>(q_gen_7901, q_gen_7920) -> q_gen_7878
<cons, s>(q_gen_7915, q_gen_7909) -> q_gen_7878
<nil, z>() -> q_gen_7878
<s, z>(q_gen_7889) -> q_gen_7883
<s, z>(q_gen_7892) -> q_gen_7883
<s, z>(q_gen_7907) -> q_gen_7883
<z, z>() -> q_gen_7883
<s, s>(q_gen_7883) -> q_gen_7895
<z, s>(q_gen_7889) -> q_gen_7895
<cons, s>(q_gen_7883, q_gen_7894) -> q_gen_7896
<cons, s>(q_gen_7883, q_gen_7909) -> q_gen_7896
<cons, s>(q_gen_7895, q_gen_7882) -> q_gen_7896
<cons, s>(q_gen_7895, q_gen_7900) -> q_gen_7896
<cons, s>(q_gen_7895, q_gen_7909) -> q_gen_7896
<cons, s>(q_gen_7901, q_gen_7882) -> q_gen_7896
<cons, s>(q_gen_7901, q_gen_7894) -> q_gen_7896
<cons, s>(q_gen_7901, q_gen_7909) -> q_gen_7896
<cons, s>(q_gen_7915, q_gen_7882) -> q_gen_7896
<cons, s>(q_gen_7915, q_gen_7894) -> q_gen_7896
<cons, s>(q_gen_7915, q_gen_7920) -> q_gen_7896
<z, s>(q_gen_7892) -> q_gen_7901
<s, s>(q_gen_7901) -> q_gen_7915
<z, s>(q_gen_7907) -> q_gen_7915
}

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

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 48
() -> length([nil, z]) -> 47
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 47
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 52
(le([s(nn1), z])) -> BOT -> 50
(le([z, z])) -> BOT -> 47
(length([l, _yca]) /\ length([cons(x, l), _zca])) -> le([_yca, _zca]) -> 58
(length([ll, _uca])) -> length([cons(x, ll), s(_uca)]) -> 61
}
Sat witness: Found: ((length([ll, _uca])) -> length([cons(x, ll), s(_uca)]), {
_uca -> s(s(z))  ;  ll -> cons(z, cons(s(s(z)), nil))  ;  x -> z
})

-------------------------------------------
Step 52, which took 0.189739 s (model generation: 0.184628,  model checking: 0.005111):

Model:
|_
{
le -> 
{{{
Q={q_gen_7879, q_gen_7880, q_gen_7897},
Q_f={q_gen_7879},
Delta=
{
<s>(q_gen_7880) -> q_gen_7880
<z>() -> q_gen_7880
<s, s>(q_gen_7879) -> q_gen_7879
<z, s>(q_gen_7880) -> q_gen_7879
<s, s>(q_gen_7897) -> q_gen_7897
<s, z>(q_gen_7880) -> q_gen_7897
<z, z>() -> q_gen_7897
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_7878, q_gen_7882, q_gen_7883, q_gen_7889, q_gen_7892, q_gen_7894, q_gen_7895, q_gen_7896, q_gen_7900, q_gen_7901, q_gen_7907, q_gen_7909, q_gen_7915, q_gen_7924},
Q_f={q_gen_7878},
Delta=
{
<cons>(q_gen_7889, q_gen_7909) -> q_gen_7882
<nil>() -> q_gen_7882
<z>() -> q_gen_7889
<s>(q_gen_7889) -> q_gen_7892
<cons>(q_gen_7889, q_gen_7882) -> q_gen_7894
<cons>(q_gen_7892, q_gen_7882) -> q_gen_7894
<cons>(q_gen_7907, q_gen_7882) -> q_gen_7894
<cons>(q_gen_7924, q_gen_7882) -> q_gen_7894
<cons>(q_gen_7889, q_gen_7894) -> q_gen_7900
<s>(q_gen_7892) -> q_gen_7907
<cons>(q_gen_7889, q_gen_7900) -> q_gen_7909
<s>(q_gen_7907) -> q_gen_7924
<cons, s>(q_gen_7883, q_gen_7882) -> q_gen_7878
<cons, s>(q_gen_7895, q_gen_7894) -> q_gen_7878
<cons, s>(q_gen_7901, q_gen_7900) -> q_gen_7878
<cons, s>(q_gen_7915, q_gen_7909) -> q_gen_7878
<nil, z>() -> q_gen_7878
<s, z>(q_gen_7889) -> q_gen_7883
<s, z>(q_gen_7892) -> q_gen_7883
<s, z>(q_gen_7907) -> q_gen_7883
<s, z>(q_gen_7924) -> q_gen_7883
<z, s>(q_gen_7924) -> q_gen_7883
<z, z>() -> q_gen_7883
<s, s>(q_gen_7883) -> q_gen_7895
<z, s>(q_gen_7889) -> q_gen_7895
<cons, s>(q_gen_7883, q_gen_7894) -> q_gen_7896
<cons, s>(q_gen_7883, q_gen_7900) -> q_gen_7896
<cons, s>(q_gen_7895, q_gen_7882) -> q_gen_7896
<cons, s>(q_gen_7895, q_gen_7900) -> q_gen_7896
<cons, s>(q_gen_7895, q_gen_7909) -> q_gen_7896
<cons, s>(q_gen_7901, q_gen_7882) -> q_gen_7896
<cons, s>(q_gen_7901, q_gen_7894) -> q_gen_7896
<cons, s>(q_gen_7901, q_gen_7909) -> q_gen_7896
<cons, s>(q_gen_7915, q_gen_7882) -> q_gen_7896
<cons, s>(q_gen_7915, q_gen_7894) -> q_gen_7896
<cons, s>(q_gen_7915, q_gen_7900) -> q_gen_7896
<z, s>(q_gen_7892) -> q_gen_7901
<s, s>(q_gen_7901) -> q_gen_7915
<z, s>(q_gen_7907) -> q_gen_7915
}

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

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 49
() -> length([nil, z]) -> 48
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 48
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 53
(le([s(nn1), z])) -> BOT -> 51
(le([z, z])) -> BOT -> 48
(length([l, _yca]) /\ length([cons(x, l), _zca])) -> le([_yca, _zca]) -> 61
(length([ll, _uca])) -> length([cons(x, ll), s(_uca)]) -> 61
}
Sat witness: Found: ((length([l, _yca]) /\ length([cons(x, l), _zca])) -> le([_yca, _zca]), {
_yca -> s(s(s(s(s(z)))))  ;  _zca -> s(s(z))  ;  l -> cons(z, nil)  ;  x -> s(z)
})

-------------------------------------------
Step 53, which took 0.231882 s (model generation: 0.209513,  model checking: 0.022369):

Model:
|_
{
le -> 
{{{
Q={q_gen_7879, q_gen_7880, q_gen_7897},
Q_f={q_gen_7879},
Delta=
{
<s>(q_gen_7880) -> q_gen_7880
<z>() -> q_gen_7880
<s, s>(q_gen_7879) -> q_gen_7879
<z, s>(q_gen_7880) -> q_gen_7879
<s, s>(q_gen_7897) -> q_gen_7897
<s, z>(q_gen_7880) -> q_gen_7897
<z, z>() -> q_gen_7897
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_7878, q_gen_7882, q_gen_7883, q_gen_7889, q_gen_7892, q_gen_7894, q_gen_7895, q_gen_7896, q_gen_7900, q_gen_7901, q_gen_7907, q_gen_7909, q_gen_7915, q_gen_7920, q_gen_7934},
Q_f={q_gen_7878},
Delta=
{
<cons>(q_gen_7889, q_gen_7909) -> q_gen_7882
<nil>() -> q_gen_7882
<z>() -> q_gen_7889
<s>(q_gen_7889) -> q_gen_7892
<cons>(q_gen_7889, q_gen_7882) -> q_gen_7894
<cons>(q_gen_7889, q_gen_7894) -> q_gen_7900
<cons>(q_gen_7889, q_gen_7934) -> q_gen_7900
<s>(q_gen_7892) -> q_gen_7907
<s>(q_gen_7907) -> q_gen_7907
<cons>(q_gen_7889, q_gen_7900) -> q_gen_7909
<cons>(q_gen_7892, q_gen_7882) -> q_gen_7920
<cons>(q_gen_7907, q_gen_7882) -> q_gen_7920
<cons>(q_gen_7889, q_gen_7920) -> q_gen_7934
<cons, s>(q_gen_7883, q_gen_7882) -> q_gen_7878
<cons, s>(q_gen_7895, q_gen_7894) -> q_gen_7878
<cons, s>(q_gen_7895, q_gen_7920) -> q_gen_7878
<cons, s>(q_gen_7901, q_gen_7900) -> q_gen_7878
<cons, s>(q_gen_7901, q_gen_7934) -> q_gen_7878
<cons, s>(q_gen_7915, q_gen_7900) -> q_gen_7878
<cons, s>(q_gen_7915, q_gen_7909) -> q_gen_7878
<nil, z>() -> q_gen_7878
<s, z>(q_gen_7889) -> q_gen_7883
<s, z>(q_gen_7892) -> q_gen_7883
<s, z>(q_gen_7907) -> q_gen_7883
<z, z>() -> q_gen_7883
<s, s>(q_gen_7883) -> q_gen_7895
<z, s>(q_gen_7889) -> q_gen_7895
<cons, s>(q_gen_7883, q_gen_7894) -> q_gen_7896
<cons, s>(q_gen_7883, q_gen_7920) -> q_gen_7896
<cons, s>(q_gen_7883, q_gen_7934) -> q_gen_7896
<cons, s>(q_gen_7895, q_gen_7882) -> q_gen_7896
<cons, s>(q_gen_7895, q_gen_7900) -> q_gen_7896
<cons, s>(q_gen_7895, q_gen_7909) -> q_gen_7896
<cons, s>(q_gen_7895, q_gen_7934) -> q_gen_7896
<cons, s>(q_gen_7901, q_gen_7882) -> q_gen_7896
<cons, s>(q_gen_7901, q_gen_7894) -> q_gen_7896
<cons, s>(q_gen_7901, q_gen_7909) -> q_gen_7896
<cons, s>(q_gen_7901, q_gen_7920) -> q_gen_7896
<cons, s>(q_gen_7915, q_gen_7882) -> q_gen_7896
<cons, s>(q_gen_7915, q_gen_7894) -> q_gen_7896
<cons, s>(q_gen_7915, q_gen_7920) -> q_gen_7896
<cons, s>(q_gen_7915, q_gen_7934) -> q_gen_7896
<z, s>(q_gen_7892) -> q_gen_7901
<s, s>(q_gen_7901) -> q_gen_7915
<z, s>(q_gen_7907) -> q_gen_7915
}

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

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 50
() -> length([nil, z]) -> 49
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 49
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 54
(le([s(nn1), z])) -> BOT -> 52
(le([z, z])) -> BOT -> 49
(length([l, _yca]) /\ length([cons(x, l), _zca])) -> le([_yca, _zca]) -> 61
(length([ll, _uca])) -> length([cons(x, ll), s(_uca)]) -> 64
}
Sat witness: Found: ((length([ll, _uca])) -> length([cons(x, ll), s(_uca)]), {
_uca -> s(s(s(s(z))))  ;  ll -> cons(z, cons(z, cons(z, cons(z, nil))))  ;  x -> z
})

-------------------------------------------
Step 54, which took 0.240590 s (model generation: 0.229256,  model checking: 0.011334):

Model:
|_
{
le -> 
{{{
Q={q_gen_7879, q_gen_7880, q_gen_7897},
Q_f={q_gen_7879},
Delta=
{
<s>(q_gen_7880) -> q_gen_7880
<z>() -> q_gen_7880
<s, s>(q_gen_7879) -> q_gen_7879
<z, s>(q_gen_7880) -> q_gen_7879
<s, s>(q_gen_7897) -> q_gen_7897
<s, z>(q_gen_7880) -> q_gen_7897
<z, z>() -> q_gen_7897
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_7878, q_gen_7882, q_gen_7883, q_gen_7889, q_gen_7892, q_gen_7894, q_gen_7895, q_gen_7896, q_gen_7900, q_gen_7901, q_gen_7907, q_gen_7909, q_gen_7915, q_gen_7920, q_gen_7934},
Q_f={q_gen_7878},
Delta=
{
<nil>() -> q_gen_7882
<z>() -> q_gen_7889
<s>(q_gen_7889) -> q_gen_7892
<s>(q_gen_7907) -> q_gen_7892
<cons>(q_gen_7889, q_gen_7882) -> q_gen_7894
<cons>(q_gen_7889, q_gen_7934) -> q_gen_7894
<cons>(q_gen_7889, q_gen_7894) -> q_gen_7900
<cons>(q_gen_7889, q_gen_7909) -> q_gen_7900
<s>(q_gen_7892) -> q_gen_7907
<cons>(q_gen_7889, q_gen_7900) -> q_gen_7909
<cons>(q_gen_7892, q_gen_7882) -> q_gen_7920
<cons>(q_gen_7907, q_gen_7882) -> q_gen_7920
<cons>(q_gen_7889, q_gen_7920) -> q_gen_7934
<cons, s>(q_gen_7883, q_gen_7882) -> q_gen_7878
<cons, s>(q_gen_7895, q_gen_7894) -> q_gen_7878
<cons, s>(q_gen_7895, q_gen_7920) -> q_gen_7878
<cons, s>(q_gen_7901, q_gen_7900) -> q_gen_7878
<cons, s>(q_gen_7901, q_gen_7934) -> q_gen_7878
<cons, s>(q_gen_7915, q_gen_7909) -> q_gen_7878
<nil, z>() -> q_gen_7878
<s, z>(q_gen_7889) -> q_gen_7883
<s, z>(q_gen_7892) -> q_gen_7883
<s, z>(q_gen_7907) -> q_gen_7883
<z, z>() -> q_gen_7883
<s, s>(q_gen_7883) -> q_gen_7895
<s, s>(q_gen_7901) -> q_gen_7895
<z, s>(q_gen_7889) -> q_gen_7895
<cons, s>(q_gen_7883, q_gen_7894) -> q_gen_7896
<cons, s>(q_gen_7883, q_gen_7920) -> q_gen_7896
<cons, s>(q_gen_7883, q_gen_7934) -> q_gen_7896
<cons, s>(q_gen_7895, q_gen_7882) -> q_gen_7896
<cons, s>(q_gen_7895, q_gen_7900) -> q_gen_7896
<cons, s>(q_gen_7895, q_gen_7909) -> q_gen_7896
<cons, s>(q_gen_7895, q_gen_7934) -> q_gen_7896
<cons, s>(q_gen_7901, q_gen_7882) -> q_gen_7896
<cons, s>(q_gen_7901, q_gen_7894) -> q_gen_7896
<cons, s>(q_gen_7901, q_gen_7909) -> q_gen_7896
<cons, s>(q_gen_7901, q_gen_7920) -> q_gen_7896
<cons, s>(q_gen_7915, q_gen_7882) -> q_gen_7896
<cons, s>(q_gen_7915, q_gen_7894) -> q_gen_7896
<cons, s>(q_gen_7915, q_gen_7900) -> q_gen_7896
<cons, s>(q_gen_7915, q_gen_7920) -> q_gen_7896
<cons, s>(q_gen_7915, q_gen_7934) -> q_gen_7896
<z, s>(q_gen_7892) -> q_gen_7901
<z, s>(q_gen_7907) -> q_gen_7915
}

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

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 51
() -> length([nil, z]) -> 50
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 50
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 55
(le([s(nn1), z])) -> BOT -> 53
(le([z, z])) -> BOT -> 50
(length([l, _yca]) /\ length([cons(x, l), _zca])) -> le([_yca, _zca]) -> 64
(length([ll, _uca])) -> length([cons(x, ll), s(_uca)]) -> 64
}
Sat witness: Found: ((length([l, _yca]) /\ length([cons(x, l), _zca])) -> le([_yca, _zca]), {
_yca -> s(s(s(z)))  ;  _zca -> s(s(z))  ;  l -> cons(z, cons(z, cons(s(s(z)), nil)))  ;  x -> z
})

-------------------------------------------
Step 55, which took 0.231485 s (model generation: 0.225741,  model checking: 0.005744):

Model:
|_
{
le -> 
{{{
Q={q_gen_7879, q_gen_7880, q_gen_7897},
Q_f={q_gen_7879},
Delta=
{
<s>(q_gen_7880) -> q_gen_7880
<z>() -> q_gen_7880
<s, s>(q_gen_7879) -> q_gen_7879
<z, s>(q_gen_7880) -> q_gen_7879
<s, s>(q_gen_7897) -> q_gen_7897
<s, z>(q_gen_7880) -> q_gen_7897
<z, z>() -> q_gen_7897
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_7878, q_gen_7882, q_gen_7883, q_gen_7889, q_gen_7892, q_gen_7894, q_gen_7895, q_gen_7896, q_gen_7900, q_gen_7901, q_gen_7907, q_gen_7909, q_gen_7915, q_gen_7920, q_gen_7934},
Q_f={q_gen_7878},
Delta=
{
<nil>() -> q_gen_7882
<z>() -> q_gen_7889
<s>(q_gen_7889) -> q_gen_7892
<cons>(q_gen_7889, q_gen_7882) -> q_gen_7894
<cons>(q_gen_7889, q_gen_7894) -> q_gen_7900
<cons>(q_gen_7889, q_gen_7934) -> q_gen_7900
<s>(q_gen_7892) -> q_gen_7907
<s>(q_gen_7907) -> q_gen_7907
<cons>(q_gen_7889, q_gen_7900) -> q_gen_7909
<cons>(q_gen_7889, q_gen_7909) -> q_gen_7909
<cons>(q_gen_7892, q_gen_7882) -> q_gen_7920
<cons>(q_gen_7907, q_gen_7882) -> q_gen_7920
<cons>(q_gen_7889, q_gen_7920) -> q_gen_7934
<cons, s>(q_gen_7883, q_gen_7882) -> q_gen_7878
<cons, s>(q_gen_7895, q_gen_7894) -> q_gen_7878
<cons, s>(q_gen_7895, q_gen_7920) -> q_gen_7878
<cons, s>(q_gen_7901, q_gen_7900) -> q_gen_7878
<cons, s>(q_gen_7901, q_gen_7934) -> q_gen_7878
<cons, s>(q_gen_7915, q_gen_7909) -> q_gen_7878
<nil, z>() -> q_gen_7878
<s, z>(q_gen_7889) -> q_gen_7883
<s, z>(q_gen_7892) -> q_gen_7883
<s, z>(q_gen_7907) -> q_gen_7883
<z, z>() -> q_gen_7883
<s, s>(q_gen_7883) -> q_gen_7895
<z, s>(q_gen_7889) -> q_gen_7895
<cons, s>(q_gen_7883, q_gen_7894) -> q_gen_7896
<cons, s>(q_gen_7883, q_gen_7920) -> q_gen_7896
<cons, s>(q_gen_7883, q_gen_7934) -> q_gen_7896
<cons, s>(q_gen_7895, q_gen_7882) -> q_gen_7896
<cons, s>(q_gen_7895, q_gen_7900) -> q_gen_7896
<cons, s>(q_gen_7895, q_gen_7909) -> q_gen_7896
<cons, s>(q_gen_7895, q_gen_7934) -> q_gen_7896
<cons, s>(q_gen_7901, q_gen_7882) -> q_gen_7896
<cons, s>(q_gen_7901, q_gen_7894) -> q_gen_7896
<cons, s>(q_gen_7901, q_gen_7909) -> q_gen_7896
<cons, s>(q_gen_7901, q_gen_7920) -> q_gen_7896
<cons, s>(q_gen_7915, q_gen_7882) -> q_gen_7896
<cons, s>(q_gen_7915, q_gen_7894) -> q_gen_7896
<cons, s>(q_gen_7915, q_gen_7900) -> q_gen_7896
<cons, s>(q_gen_7915, q_gen_7920) -> q_gen_7896
<cons, s>(q_gen_7915, q_gen_7934) -> q_gen_7896
<s, s>(q_gen_7901) -> q_gen_7901
<z, s>(q_gen_7892) -> q_gen_7901
<z, s>(q_gen_7907) -> q_gen_7915
}

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

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 52
() -> length([nil, z]) -> 51
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 51
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 56
(le([s(nn1), z])) -> BOT -> 54
(le([z, z])) -> BOT -> 51
(length([l, _yca]) /\ length([cons(x, l), _zca])) -> le([_yca, _zca]) -> 64
(length([ll, _uca])) -> length([cons(x, ll), s(_uca)]) -> 67
}
Sat witness: Found: ((length([ll, _uca])) -> length([cons(x, ll), s(_uca)]), {
_uca -> s(s(s(z)))  ;  ll -> cons(z, cons(z, cons(s(s(z)), nil)))  ;  x -> z
})

-------------------------------------------
Step 56, which took 0.230615 s (model generation: 0.223204,  model checking: 0.007411):

Model:
|_
{
le -> 
{{{
Q={q_gen_7879, q_gen_7880, q_gen_7897},
Q_f={q_gen_7879},
Delta=
{
<s>(q_gen_7880) -> q_gen_7880
<z>() -> q_gen_7880
<s, s>(q_gen_7879) -> q_gen_7879
<z, s>(q_gen_7880) -> q_gen_7879
<s, s>(q_gen_7897) -> q_gen_7897
<s, z>(q_gen_7880) -> q_gen_7897
<z, z>() -> q_gen_7897
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_7878, q_gen_7882, q_gen_7883, q_gen_7889, q_gen_7892, q_gen_7894, q_gen_7895, q_gen_7896, q_gen_7900, q_gen_7901, q_gen_7907, q_gen_7909, q_gen_7915, q_gen_7920, q_gen_7934},
Q_f={q_gen_7878},
Delta=
{
<nil>() -> q_gen_7882
<z>() -> q_gen_7889
<s>(q_gen_7889) -> q_gen_7892
<cons>(q_gen_7889, q_gen_7882) -> q_gen_7894
<cons>(q_gen_7889, q_gen_7894) -> q_gen_7900
<cons>(q_gen_7889, q_gen_7934) -> q_gen_7900
<s>(q_gen_7892) -> q_gen_7907
<s>(q_gen_7907) -> q_gen_7907
<cons>(q_gen_7889, q_gen_7900) -> q_gen_7909
<cons>(q_gen_7889, q_gen_7909) -> q_gen_7909
<cons>(q_gen_7892, q_gen_7882) -> q_gen_7920
<cons>(q_gen_7907, q_gen_7882) -> q_gen_7920
<cons>(q_gen_7889, q_gen_7920) -> q_gen_7934
<cons, s>(q_gen_7883, q_gen_7882) -> q_gen_7878
<cons, s>(q_gen_7895, q_gen_7894) -> q_gen_7878
<cons, s>(q_gen_7895, q_gen_7920) -> q_gen_7878
<cons, s>(q_gen_7901, q_gen_7900) -> q_gen_7878
<cons, s>(q_gen_7901, q_gen_7934) -> q_gen_7878
<cons, s>(q_gen_7915, q_gen_7894) -> q_gen_7878
<cons, s>(q_gen_7915, q_gen_7900) -> q_gen_7878
<cons, s>(q_gen_7915, q_gen_7909) -> q_gen_7878
<nil, z>() -> q_gen_7878
<s, z>(q_gen_7889) -> q_gen_7883
<s, z>(q_gen_7892) -> q_gen_7883
<s, z>(q_gen_7907) -> q_gen_7883
<z, z>() -> q_gen_7883
<s, s>(q_gen_7883) -> q_gen_7895
<z, s>(q_gen_7889) -> q_gen_7895
<cons, s>(q_gen_7883, q_gen_7894) -> q_gen_7896
<cons, s>(q_gen_7883, q_gen_7920) -> q_gen_7896
<cons, s>(q_gen_7883, q_gen_7934) -> q_gen_7896
<cons, s>(q_gen_7895, q_gen_7882) -> q_gen_7896
<cons, s>(q_gen_7895, q_gen_7900) -> q_gen_7896
<cons, s>(q_gen_7895, q_gen_7909) -> q_gen_7896
<cons, s>(q_gen_7895, q_gen_7934) -> q_gen_7896
<cons, s>(q_gen_7901, q_gen_7882) -> q_gen_7896
<cons, s>(q_gen_7901, q_gen_7894) -> q_gen_7896
<cons, s>(q_gen_7901, q_gen_7909) -> q_gen_7896
<cons, s>(q_gen_7901, q_gen_7920) -> q_gen_7896
<cons, s>(q_gen_7915, q_gen_7882) -> q_gen_7896
<cons, s>(q_gen_7915, q_gen_7920) -> q_gen_7896
<cons, s>(q_gen_7915, q_gen_7934) -> q_gen_7896
<s, s>(q_gen_7901) -> q_gen_7901
<z, s>(q_gen_7892) -> q_gen_7901
<z, s>(q_gen_7907) -> q_gen_7915
}

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

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 53
() -> length([nil, z]) -> 52
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 52
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 57
(le([s(nn1), z])) -> BOT -> 55
(le([z, z])) -> BOT -> 52
(length([l, _yca]) /\ length([cons(x, l), _zca])) -> le([_yca, _zca]) -> 67
(length([ll, _uca])) -> length([cons(x, ll), s(_uca)]) -> 67
}
Sat witness: Found: ((length([l, _yca]) /\ length([cons(x, l), _zca])) -> le([_yca, _zca]), {
_yca -> s(s(s(s(s(z)))))  ;  _zca -> s(s(s(z)))  ;  l -> cons(z, cons(z, nil))  ;  x -> z
})

-------------------------------------------
Step 57, which took 0.280528 s (model generation: 0.266827,  model checking: 0.013701):

Model:
|_
{
le -> 
{{{
Q={q_gen_7879, q_gen_7880, q_gen_7897},
Q_f={q_gen_7879},
Delta=
{
<s>(q_gen_7880) -> q_gen_7880
<z>() -> q_gen_7880
<s, s>(q_gen_7879) -> q_gen_7879
<z, s>(q_gen_7880) -> q_gen_7879
<s, s>(q_gen_7897) -> q_gen_7897
<s, z>(q_gen_7880) -> q_gen_7897
<z, z>() -> q_gen_7897
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_7878, q_gen_7882, q_gen_7883, q_gen_7889, q_gen_7892, q_gen_7894, q_gen_7895, q_gen_7896, q_gen_7900, q_gen_7901, q_gen_7907, q_gen_7909, q_gen_7915, q_gen_7920, q_gen_7934},
Q_f={q_gen_7878},
Delta=
{
<nil>() -> q_gen_7882
<z>() -> q_gen_7889
<s>(q_gen_7889) -> q_gen_7892
<cons>(q_gen_7889, q_gen_7882) -> q_gen_7894
<cons>(q_gen_7889, q_gen_7894) -> q_gen_7900
<cons>(q_gen_7889, q_gen_7934) -> q_gen_7900
<s>(q_gen_7892) -> q_gen_7907
<s>(q_gen_7907) -> q_gen_7907
<cons>(q_gen_7889, q_gen_7900) -> q_gen_7909
<cons>(q_gen_7889, q_gen_7909) -> q_gen_7909
<cons>(q_gen_7892, q_gen_7882) -> q_gen_7920
<cons>(q_gen_7907, q_gen_7882) -> q_gen_7920
<cons>(q_gen_7889, q_gen_7920) -> q_gen_7934
<cons, s>(q_gen_7883, q_gen_7882) -> q_gen_7878
<cons, s>(q_gen_7895, q_gen_7894) -> q_gen_7878
<cons, s>(q_gen_7895, q_gen_7920) -> q_gen_7878
<cons, s>(q_gen_7901, q_gen_7900) -> q_gen_7878
<cons, s>(q_gen_7901, q_gen_7934) -> q_gen_7878
<cons, s>(q_gen_7915, q_gen_7900) -> q_gen_7878
<cons, s>(q_gen_7915, q_gen_7909) -> q_gen_7878
<nil, z>() -> q_gen_7878
<s, z>(q_gen_7889) -> q_gen_7883
<s, z>(q_gen_7892) -> q_gen_7883
<s, z>(q_gen_7907) -> q_gen_7883
<z, z>() -> q_gen_7883
<s, s>(q_gen_7883) -> q_gen_7895
<z, s>(q_gen_7889) -> q_gen_7895
<cons, s>(q_gen_7883, q_gen_7894) -> q_gen_7896
<cons, s>(q_gen_7883, q_gen_7920) -> q_gen_7896
<cons, s>(q_gen_7883, q_gen_7934) -> q_gen_7896
<cons, s>(q_gen_7895, q_gen_7882) -> q_gen_7896
<cons, s>(q_gen_7895, q_gen_7900) -> q_gen_7896
<cons, s>(q_gen_7895, q_gen_7909) -> q_gen_7896
<cons, s>(q_gen_7895, q_gen_7934) -> q_gen_7896
<cons, s>(q_gen_7901, q_gen_7882) -> q_gen_7896
<cons, s>(q_gen_7901, q_gen_7894) -> q_gen_7896
<cons, s>(q_gen_7901, q_gen_7909) -> q_gen_7896
<cons, s>(q_gen_7901, q_gen_7920) -> q_gen_7896
<cons, s>(q_gen_7915, q_gen_7882) -> q_gen_7896
<cons, s>(q_gen_7915, q_gen_7894) -> q_gen_7896
<cons, s>(q_gen_7915, q_gen_7920) -> q_gen_7896
<cons, s>(q_gen_7915, q_gen_7934) -> q_gen_7896
<s, s>(q_gen_7901) -> q_gen_7901
<z, s>(q_gen_7892) -> q_gen_7901
<z, s>(q_gen_7907) -> q_gen_7915
}

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

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 54
() -> length([nil, z]) -> 53
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 53
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 58
(le([s(nn1), z])) -> BOT -> 56
(le([z, z])) -> BOT -> 53
(length([l, _yca]) /\ length([cons(x, l), _zca])) -> le([_yca, _zca]) -> 67
(length([ll, _uca])) -> length([cons(x, ll), s(_uca)]) -> 70
}
Sat witness: Found: ((length([ll, _uca])) -> length([cons(x, ll), s(_uca)]), {
_uca -> s(s(s(z)))  ;  ll -> cons(z, cons(z, cons(z, nil)))  ;  x -> s(z)
})

-------------------------------------------
Step 58, which took 0.260706 s (model generation: 0.256270,  model checking: 0.004436):

Model:
|_
{
le -> 
{{{
Q={q_gen_7879, q_gen_7880, q_gen_7897},
Q_f={q_gen_7879},
Delta=
{
<s>(q_gen_7880) -> q_gen_7880
<z>() -> q_gen_7880
<s, s>(q_gen_7879) -> q_gen_7879
<z, s>(q_gen_7880) -> q_gen_7879
<s, s>(q_gen_7897) -> q_gen_7897
<s, z>(q_gen_7880) -> q_gen_7897
<z, z>() -> q_gen_7897
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_7878, q_gen_7882, q_gen_7883, q_gen_7889, q_gen_7892, q_gen_7894, q_gen_7895, q_gen_7896, q_gen_7900, q_gen_7901, q_gen_7907, q_gen_7909, q_gen_7915, q_gen_7924, q_gen_7932},
Q_f={q_gen_7878},
Delta=
{
<cons>(q_gen_7889, q_gen_7909) -> q_gen_7882
<nil>() -> q_gen_7882
<z>() -> q_gen_7889
<s>(q_gen_7889) -> q_gen_7892
<cons>(q_gen_7889, q_gen_7882) -> q_gen_7894
<cons>(q_gen_7907, q_gen_7882) -> q_gen_7894
<cons>(q_gen_7889, q_gen_7894) -> q_gen_7900
<cons>(q_gen_7889, q_gen_7932) -> q_gen_7900
<s>(q_gen_7892) -> q_gen_7907
<cons>(q_gen_7889, q_gen_7900) -> q_gen_7909
<s>(q_gen_7907) -> q_gen_7924
<cons>(q_gen_7892, q_gen_7882) -> q_gen_7932
<cons>(q_gen_7924, q_gen_7882) -> q_gen_7932
<cons, s>(q_gen_7883, q_gen_7882) -> q_gen_7878
<cons, s>(q_gen_7895, q_gen_7894) -> q_gen_7878
<cons, s>(q_gen_7895, q_gen_7932) -> q_gen_7878
<cons, s>(q_gen_7901, q_gen_7900) -> q_gen_7878
<cons, s>(q_gen_7915, q_gen_7909) -> q_gen_7878
<cons, s>(q_gen_7915, q_gen_7932) -> q_gen_7878
<nil, z>() -> q_gen_7878
<s, z>(q_gen_7889) -> q_gen_7883
<s, z>(q_gen_7892) -> q_gen_7883
<s, z>(q_gen_7907) -> q_gen_7883
<s, z>(q_gen_7924) -> q_gen_7883
<z, s>(q_gen_7924) -> q_gen_7883
<z, z>() -> q_gen_7883
<z, s>(q_gen_7889) -> q_gen_7895
<cons, s>(q_gen_7883, q_gen_7894) -> q_gen_7896
<cons, s>(q_gen_7883, q_gen_7900) -> q_gen_7896
<cons, s>(q_gen_7883, q_gen_7932) -> q_gen_7896
<cons, s>(q_gen_7895, q_gen_7882) -> q_gen_7896
<cons, s>(q_gen_7895, q_gen_7900) -> q_gen_7896
<cons, s>(q_gen_7895, q_gen_7909) -> q_gen_7896
<cons, s>(q_gen_7901, q_gen_7882) -> q_gen_7896
<cons, s>(q_gen_7901, q_gen_7894) -> q_gen_7896
<cons, s>(q_gen_7901, q_gen_7909) -> q_gen_7896
<cons, s>(q_gen_7915, q_gen_7882) -> q_gen_7896
<cons, s>(q_gen_7915, q_gen_7894) -> q_gen_7896
<cons, s>(q_gen_7915, q_gen_7900) -> q_gen_7896
<z, s>(q_gen_7892) -> q_gen_7901
<s, s>(q_gen_7883) -> q_gen_7915
<s, s>(q_gen_7901) -> q_gen_7915
<z, s>(q_gen_7907) -> q_gen_7915
}

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

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 55
() -> length([nil, z]) -> 54
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 54
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 59
(le([s(nn1), z])) -> BOT -> 57
(le([z, z])) -> BOT -> 54
(length([l, _yca]) /\ length([cons(x, l), _zca])) -> le([_yca, _zca]) -> 70
(length([ll, _uca])) -> length([cons(x, ll), s(_uca)]) -> 70
}
Sat witness: Found: ((length([l, _yca]) /\ length([cons(x, l), _zca])) -> le([_yca, _zca]), {
_yca -> s(s(s(s(s(z)))))  ;  _zca -> s(s(z))  ;  l -> cons(z, nil)  ;  x -> z
})

-------------------------------------------
Step 59, which took 0.284847 s (model generation: 0.263012,  model checking: 0.021835):

Model:
|_
{
le -> 
{{{
Q={q_gen_7879, q_gen_7880, q_gen_7897},
Q_f={q_gen_7879},
Delta=
{
<s>(q_gen_7880) -> q_gen_7880
<z>() -> q_gen_7880
<s, s>(q_gen_7879) -> q_gen_7879
<z, s>(q_gen_7880) -> q_gen_7879
<s, s>(q_gen_7897) -> q_gen_7897
<s, z>(q_gen_7880) -> q_gen_7897
<z, z>() -> q_gen_7897
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_7878, q_gen_7882, q_gen_7883, q_gen_7889, q_gen_7892, q_gen_7894, q_gen_7895, q_gen_7896, q_gen_7900, q_gen_7901, q_gen_7907, q_gen_7909, q_gen_7915, q_gen_7952, q_gen_7956},
Q_f={q_gen_7878},
Delta=
{
<nil>() -> q_gen_7882
<z>() -> q_gen_7889
<s>(q_gen_7889) -> q_gen_7892
<cons>(q_gen_7889, q_gen_7882) -> q_gen_7894
<cons>(q_gen_7892, q_gen_7882) -> q_gen_7894
<cons>(q_gen_7907, q_gen_7882) -> q_gen_7894
<cons>(q_gen_7889, q_gen_7894) -> q_gen_7900
<s>(q_gen_7892) -> q_gen_7907
<s>(q_gen_7907) -> q_gen_7907
<cons>(q_gen_7889, q_gen_7900) -> q_gen_7909
<cons>(q_gen_7889, q_gen_7909) -> q_gen_7956
<cons>(q_gen_7889, q_gen_7956) -> q_gen_7956
<cons, s>(q_gen_7883, q_gen_7882) -> q_gen_7878
<cons, s>(q_gen_7895, q_gen_7894) -> q_gen_7878
<cons, s>(q_gen_7901, q_gen_7900) -> q_gen_7878
<cons, s>(q_gen_7915, q_gen_7909) -> q_gen_7878
<cons, s>(q_gen_7915, q_gen_7956) -> q_gen_7878
<cons, s>(q_gen_7952, q_gen_7909) -> q_gen_7878
<nil, z>() -> q_gen_7878
<s, z>(q_gen_7889) -> q_gen_7883
<s, z>(q_gen_7892) -> q_gen_7883
<s, z>(q_gen_7907) -> q_gen_7883
<z, z>() -> q_gen_7883
<s, s>(q_gen_7883) -> q_gen_7895
<z, s>(q_gen_7889) -> q_gen_7895
<cons, s>(q_gen_7883, q_gen_7894) -> q_gen_7896
<cons, s>(q_gen_7883, q_gen_7900) -> q_gen_7896
<cons, s>(q_gen_7895, q_gen_7882) -> q_gen_7896
<cons, s>(q_gen_7895, q_gen_7900) -> q_gen_7896
<cons, s>(q_gen_7895, q_gen_7909) -> q_gen_7896
<cons, s>(q_gen_7901, q_gen_7882) -> q_gen_7896
<cons, s>(q_gen_7901, q_gen_7894) -> q_gen_7896
<cons, s>(q_gen_7901, q_gen_7909) -> q_gen_7896
<cons, s>(q_gen_7915, q_gen_7882) -> q_gen_7896
<cons, s>(q_gen_7915, q_gen_7894) -> q_gen_7896
<cons, s>(q_gen_7915, q_gen_7900) -> q_gen_7896
<cons, s>(q_gen_7952, q_gen_7882) -> q_gen_7896
<cons, s>(q_gen_7952, q_gen_7956) -> q_gen_7896
<z, s>(q_gen_7892) -> q_gen_7901
<z, s>(q_gen_7907) -> q_gen_7915
<s, s>(q_gen_7901) -> q_gen_7952
}

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

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 56
() -> length([nil, z]) -> 55
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 55
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 60
(le([s(nn1), z])) -> BOT -> 58
(le([z, z])) -> BOT -> 55
(length([l, _yca]) /\ length([cons(x, l), _zca])) -> le([_yca, _zca]) -> 70
(length([ll, _uca])) -> length([cons(x, ll), s(_uca)]) -> 73
}
Sat witness: Found: ((length([ll, _uca])) -> length([cons(x, ll), s(_uca)]), {
_uca -> s(s(s(s(z))))  ;  ll -> cons(s(z), cons(z, cons(z, cons(s(z), nil))))  ;  x -> z
})

-------------------------------------------
Step 60, which took 0.294498 s (model generation: 0.284393,  model checking: 0.010105):

Model:
|_
{
le -> 
{{{
Q={q_gen_7879, q_gen_7880, q_gen_7897},
Q_f={q_gen_7879},
Delta=
{
<s>(q_gen_7880) -> q_gen_7880
<z>() -> q_gen_7880
<s, s>(q_gen_7879) -> q_gen_7879
<z, s>(q_gen_7880) -> q_gen_7879
<s, s>(q_gen_7897) -> q_gen_7897
<s, z>(q_gen_7880) -> q_gen_7897
<z, z>() -> q_gen_7897
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_7878, q_gen_7882, q_gen_7883, q_gen_7889, q_gen_7892, q_gen_7894, q_gen_7895, q_gen_7896, q_gen_7900, q_gen_7901, q_gen_7907, q_gen_7909, q_gen_7915, q_gen_7942, q_gen_7956},
Q_f={q_gen_7878},
Delta=
{
<nil>() -> q_gen_7882
<z>() -> q_gen_7889
<s>(q_gen_7889) -> q_gen_7892
<cons>(q_gen_7889, q_gen_7882) -> q_gen_7894
<cons>(q_gen_7892, q_gen_7882) -> q_gen_7894
<cons>(q_gen_7907, q_gen_7882) -> q_gen_7894
<cons>(q_gen_7889, q_gen_7894) -> q_gen_7900
<s>(q_gen_7892) -> q_gen_7907
<s>(q_gen_7907) -> q_gen_7907
<cons>(q_gen_7889, q_gen_7900) -> q_gen_7909
<cons>(q_gen_7892, q_gen_7909) -> q_gen_7909
<cons>(q_gen_7889, q_gen_7909) -> q_gen_7956
<cons>(q_gen_7889, q_gen_7956) -> q_gen_7956
<cons, s>(q_gen_7883, q_gen_7882) -> q_gen_7878
<cons, s>(q_gen_7895, q_gen_7894) -> q_gen_7878
<cons, s>(q_gen_7901, q_gen_7900) -> q_gen_7878
<cons, s>(q_gen_7915, q_gen_7909) -> q_gen_7878
<cons, s>(q_gen_7915, q_gen_7956) -> q_gen_7878
<cons, s>(q_gen_7942, q_gen_7894) -> q_gen_7878
<cons, s>(q_gen_7942, q_gen_7909) -> q_gen_7878
<nil, z>() -> q_gen_7878
<s, z>(q_gen_7889) -> q_gen_7883
<s, z>(q_gen_7892) -> q_gen_7883
<s, z>(q_gen_7907) -> q_gen_7883
<z, z>() -> q_gen_7883
<z, s>(q_gen_7889) -> q_gen_7895
<cons, s>(q_gen_7883, q_gen_7894) -> q_gen_7896
<cons, s>(q_gen_7883, q_gen_7900) -> q_gen_7896
<cons, s>(q_gen_7895, q_gen_7882) -> q_gen_7896
<cons, s>(q_gen_7895, q_gen_7900) -> q_gen_7896
<cons, s>(q_gen_7895, q_gen_7909) -> q_gen_7896
<cons, s>(q_gen_7901, q_gen_7882) -> q_gen_7896
<cons, s>(q_gen_7901, q_gen_7894) -> q_gen_7896
<cons, s>(q_gen_7901, q_gen_7909) -> q_gen_7896
<cons, s>(q_gen_7915, q_gen_7882) -> q_gen_7896
<cons, s>(q_gen_7915, q_gen_7894) -> q_gen_7896
<cons, s>(q_gen_7915, q_gen_7900) -> q_gen_7896
<cons, s>(q_gen_7942, q_gen_7882) -> q_gen_7896
<cons, s>(q_gen_7942, q_gen_7900) -> q_gen_7896
<cons, s>(q_gen_7942, q_gen_7956) -> q_gen_7896
<z, s>(q_gen_7892) -> q_gen_7901
<z, s>(q_gen_7907) -> q_gen_7915
<s, s>(q_gen_7883) -> q_gen_7942
<s, s>(q_gen_7901) -> q_gen_7942
}

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

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 57
() -> length([nil, z]) -> 56
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 56
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 61
(le([s(nn1), z])) -> BOT -> 59
(le([z, z])) -> BOT -> 56
(length([l, _yca]) /\ length([cons(x, l), _zca])) -> le([_yca, _zca]) -> 73
(length([ll, _uca])) -> length([cons(x, ll), s(_uca)]) -> 73
}
Sat witness: Found: ((length([l, _yca]) /\ length([cons(x, l), _zca])) -> le([_yca, _zca]), {
_yca -> s(s(s(z)))  ;  _zca -> s(s(z))  ;  l -> cons(z, cons(z, cons(z, nil)))  ;  x -> s(z)
})

-------------------------------------------
Step 61, which took 0.414092 s (model generation: 0.390102,  model checking: 0.023990):

Model:
|_
{
le -> 
{{{
Q={q_gen_7879, q_gen_7880, q_gen_7897},
Q_f={q_gen_7879},
Delta=
{
<s>(q_gen_7880) -> q_gen_7880
<z>() -> q_gen_7880
<s, s>(q_gen_7879) -> q_gen_7879
<z, s>(q_gen_7880) -> q_gen_7879
<s, s>(q_gen_7897) -> q_gen_7897
<s, z>(q_gen_7880) -> q_gen_7897
<z, z>() -> q_gen_7897
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_7878, q_gen_7882, q_gen_7883, q_gen_7889, q_gen_7892, q_gen_7894, q_gen_7895, q_gen_7896, q_gen_7900, q_gen_7901, q_gen_7907, q_gen_7909, q_gen_7915, q_gen_7952, q_gen_7956},
Q_f={q_gen_7878},
Delta=
{
<nil>() -> q_gen_7882
<z>() -> q_gen_7889
<s>(q_gen_7889) -> q_gen_7892
<cons>(q_gen_7889, q_gen_7882) -> q_gen_7894
<cons>(q_gen_7892, q_gen_7882) -> q_gen_7894
<cons>(q_gen_7907, q_gen_7882) -> q_gen_7894
<cons>(q_gen_7889, q_gen_7894) -> q_gen_7900
<s>(q_gen_7892) -> q_gen_7907
<s>(q_gen_7907) -> q_gen_7907
<cons>(q_gen_7889, q_gen_7900) -> q_gen_7909
<cons>(q_gen_7892, q_gen_7909) -> q_gen_7909
<cons>(q_gen_7889, q_gen_7909) -> q_gen_7956
<cons>(q_gen_7889, q_gen_7956) -> q_gen_7956
<cons, s>(q_gen_7883, q_gen_7882) -> q_gen_7878
<cons, s>(q_gen_7895, q_gen_7894) -> q_gen_7878
<cons, s>(q_gen_7901, q_gen_7900) -> q_gen_7878
<cons, s>(q_gen_7915, q_gen_7909) -> q_gen_7878
<cons, s>(q_gen_7915, q_gen_7956) -> q_gen_7878
<cons, s>(q_gen_7952, q_gen_7909) -> q_gen_7878
<nil, z>() -> q_gen_7878
<s, z>(q_gen_7889) -> q_gen_7883
<s, z>(q_gen_7892) -> q_gen_7883
<s, z>(q_gen_7907) -> q_gen_7883
<z, z>() -> q_gen_7883
<s, s>(q_gen_7883) -> q_gen_7895
<z, s>(q_gen_7889) -> q_gen_7895
<cons, s>(q_gen_7883, q_gen_7894) -> q_gen_7896
<cons, s>(q_gen_7883, q_gen_7900) -> q_gen_7896
<cons, s>(q_gen_7895, q_gen_7882) -> q_gen_7896
<cons, s>(q_gen_7895, q_gen_7900) -> q_gen_7896
<cons, s>(q_gen_7895, q_gen_7909) -> q_gen_7896
<cons, s>(q_gen_7901, q_gen_7882) -> q_gen_7896
<cons, s>(q_gen_7901, q_gen_7894) -> q_gen_7896
<cons, s>(q_gen_7901, q_gen_7909) -> q_gen_7896
<cons, s>(q_gen_7915, q_gen_7882) -> q_gen_7896
<cons, s>(q_gen_7915, q_gen_7894) -> q_gen_7896
<cons, s>(q_gen_7915, q_gen_7900) -> q_gen_7896
<cons, s>(q_gen_7952, q_gen_7882) -> q_gen_7896
<cons, s>(q_gen_7952, q_gen_7956) -> q_gen_7896
<z, s>(q_gen_7892) -> q_gen_7901
<z, s>(q_gen_7907) -> q_gen_7915
<s, s>(q_gen_7901) -> q_gen_7952
}

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

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 58
() -> length([nil, z]) -> 57
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 57
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 62
(le([s(nn1), z])) -> BOT -> 60
(le([z, z])) -> BOT -> 57
(length([l, _yca]) /\ length([cons(x, l), _zca])) -> le([_yca, _zca]) -> 73
(length([ll, _uca])) -> length([cons(x, ll), s(_uca)]) -> 76
}
Sat witness: Found: ((length([ll, _uca])) -> length([cons(x, ll), s(_uca)]), {
_uca -> s(s(z))  ;  ll -> cons(s(z), cons(z, nil))  ;  x -> z
})

-------------------------------------------
Step 62, which took 0.393326 s (model generation: 0.384493,  model checking: 0.008833):

Model:
|_
{
le -> 
{{{
Q={q_gen_7879, q_gen_7880, q_gen_7897},
Q_f={q_gen_7879},
Delta=
{
<s>(q_gen_7880) -> q_gen_7880
<z>() -> q_gen_7880
<s, s>(q_gen_7879) -> q_gen_7879
<z, s>(q_gen_7880) -> q_gen_7879
<s, s>(q_gen_7897) -> q_gen_7897
<s, z>(q_gen_7880) -> q_gen_7897
<z, z>() -> q_gen_7897
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_7878, q_gen_7882, q_gen_7883, q_gen_7889, q_gen_7892, q_gen_7894, q_gen_7895, q_gen_7896, q_gen_7900, q_gen_7901, q_gen_7907, q_gen_7909, q_gen_7915, q_gen_7952, q_gen_7956},
Q_f={q_gen_7878},
Delta=
{
<nil>() -> q_gen_7882
<z>() -> q_gen_7889
<s>(q_gen_7889) -> q_gen_7892
<cons>(q_gen_7889, q_gen_7882) -> q_gen_7894
<cons>(q_gen_7892, q_gen_7882) -> q_gen_7894
<cons>(q_gen_7907, q_gen_7882) -> q_gen_7894
<cons>(q_gen_7889, q_gen_7894) -> q_gen_7900
<cons>(q_gen_7892, q_gen_7894) -> q_gen_7900
<s>(q_gen_7892) -> q_gen_7907
<s>(q_gen_7907) -> q_gen_7907
<cons>(q_gen_7889, q_gen_7900) -> q_gen_7909
<cons>(q_gen_7889, q_gen_7909) -> q_gen_7956
<cons>(q_gen_7889, q_gen_7956) -> q_gen_7956
<cons>(q_gen_7892, q_gen_7909) -> q_gen_7956
<cons, s>(q_gen_7883, q_gen_7882) -> q_gen_7878
<cons, s>(q_gen_7895, q_gen_7894) -> q_gen_7878
<cons, s>(q_gen_7901, q_gen_7900) -> q_gen_7878
<cons, s>(q_gen_7915, q_gen_7909) -> q_gen_7878
<cons, s>(q_gen_7915, q_gen_7956) -> q_gen_7878
<cons, s>(q_gen_7952, q_gen_7909) -> q_gen_7878
<nil, z>() -> q_gen_7878
<s, z>(q_gen_7889) -> q_gen_7883
<s, z>(q_gen_7892) -> q_gen_7883
<s, z>(q_gen_7907) -> q_gen_7883
<z, z>() -> q_gen_7883
<s, s>(q_gen_7883) -> q_gen_7895
<z, s>(q_gen_7889) -> q_gen_7895
<cons, s>(q_gen_7883, q_gen_7894) -> q_gen_7896
<cons, s>(q_gen_7883, q_gen_7900) -> q_gen_7896
<cons, s>(q_gen_7895, q_gen_7882) -> q_gen_7896
<cons, s>(q_gen_7895, q_gen_7900) -> q_gen_7896
<cons, s>(q_gen_7895, q_gen_7909) -> q_gen_7896
<cons, s>(q_gen_7901, q_gen_7882) -> q_gen_7896
<cons, s>(q_gen_7901, q_gen_7894) -> q_gen_7896
<cons, s>(q_gen_7901, q_gen_7909) -> q_gen_7896
<cons, s>(q_gen_7915, q_gen_7882) -> q_gen_7896
<cons, s>(q_gen_7915, q_gen_7894) -> q_gen_7896
<cons, s>(q_gen_7915, q_gen_7900) -> q_gen_7896
<cons, s>(q_gen_7952, q_gen_7882) -> q_gen_7896
<cons, s>(q_gen_7952, q_gen_7956) -> q_gen_7896
<z, s>(q_gen_7892) -> q_gen_7901
<z, s>(q_gen_7907) -> q_gen_7915
<s, s>(q_gen_7901) -> q_gen_7952
}

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

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 59
() -> length([nil, z]) -> 58
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 58
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 63
(le([s(nn1), z])) -> BOT -> 61
(le([z, z])) -> BOT -> 58
(length([l, _yca]) /\ length([cons(x, l), _zca])) -> le([_yca, _zca]) -> 76
(length([ll, _uca])) -> length([cons(x, ll), s(_uca)]) -> 76
}
Sat witness: Found: ((length([l, _yca]) /\ length([cons(x, l), _zca])) -> le([_yca, _zca]), {
_yca -> s(s(s(s(z))))  ;  _zca -> s(s(s(s(z))))  ;  l -> cons(z, cons(z, cons(z, cons(z, nil))))  ;  x -> z
})

-------------------------------------------
Step 63, which took 0.365100 s (model generation: 0.364240,  model checking: 0.000860):

Model:
|_
{
le -> 
{{{
Q={q_gen_7879, q_gen_7880, q_gen_7897, q_gen_7910, q_gen_7911, q_gen_7912},
Q_f={q_gen_7879},
Delta=
{
<s>(q_gen_7880) -> q_gen_7880
<z>() -> q_gen_7880
<s, s>(q_gen_7879) -> q_gen_7879
<s, s>(q_gen_7910) -> q_gen_7879
<z, s>(q_gen_7880) -> q_gen_7879
<s, s>(q_gen_7897) -> q_gen_7897
<z, z>() -> q_gen_7897
<s, s>(q_gen_7911) -> q_gen_7910
<s, s>(q_gen_7912) -> q_gen_7911
<s, z>(q_gen_7880) -> q_gen_7912
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_7878, q_gen_7882, q_gen_7883, q_gen_7889, q_gen_7892, q_gen_7894, q_gen_7895, q_gen_7896, q_gen_7900, q_gen_7901, q_gen_7907, q_gen_7909, q_gen_7915},
Q_f={q_gen_7878},
Delta=
{
<nil>() -> q_gen_7882
<s>(q_gen_7907) -> q_gen_7889
<z>() -> q_gen_7889
<s>(q_gen_7889) -> q_gen_7892
<cons>(q_gen_7889, q_gen_7882) -> q_gen_7894
<cons>(q_gen_7889, q_gen_7909) -> q_gen_7894
<cons>(q_gen_7892, q_gen_7882) -> q_gen_7894
<cons>(q_gen_7892, q_gen_7909) -> q_gen_7894
<cons>(q_gen_7907, q_gen_7882) -> q_gen_7894
<cons>(q_gen_7889, q_gen_7894) -> q_gen_7900
<cons>(q_gen_7892, q_gen_7894) -> q_gen_7900
<s>(q_gen_7892) -> q_gen_7907
<cons>(q_gen_7889, q_gen_7900) -> q_gen_7909
<cons, s>(q_gen_7883, q_gen_7882) -> q_gen_7878
<cons, s>(q_gen_7895, q_gen_7894) -> q_gen_7878
<cons, s>(q_gen_7901, q_gen_7900) -> q_gen_7878
<cons, s>(q_gen_7915, q_gen_7909) -> q_gen_7878
<nil, z>() -> q_gen_7878
<s, z>(q_gen_7889) -> q_gen_7883
<s, z>(q_gen_7892) -> q_gen_7883
<s, z>(q_gen_7907) -> q_gen_7883
<z, z>() -> q_gen_7883
<s, s>(q_gen_7883) -> q_gen_7895
<z, s>(q_gen_7889) -> q_gen_7895
<cons, s>(q_gen_7883, q_gen_7894) -> q_gen_7896
<cons, s>(q_gen_7883, q_gen_7900) -> q_gen_7896
<cons, s>(q_gen_7895, q_gen_7882) -> q_gen_7896
<cons, s>(q_gen_7895, q_gen_7900) -> q_gen_7896
<cons, s>(q_gen_7895, q_gen_7909) -> q_gen_7896
<cons, s>(q_gen_7901, q_gen_7882) -> q_gen_7896
<cons, s>(q_gen_7901, q_gen_7894) -> q_gen_7896
<cons, s>(q_gen_7901, q_gen_7909) -> q_gen_7896
<cons, s>(q_gen_7915, q_gen_7882) -> q_gen_7896
<cons, s>(q_gen_7915, q_gen_7894) -> q_gen_7896
<cons, s>(q_gen_7915, q_gen_7900) -> q_gen_7896
<z, s>(q_gen_7892) -> q_gen_7901
<s, s>(q_gen_7901) -> q_gen_7915
<z, s>(q_gen_7907) -> q_gen_7915
}

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

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 60
() -> length([nil, z]) -> 59
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 59
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 66
(le([s(nn1), z])) -> BOT -> 62
(le([z, z])) -> BOT -> 59
(length([l, _yca]) /\ length([cons(x, l), _zca])) -> le([_yca, _zca]) -> 76
(length([ll, _uca])) -> length([cons(x, ll), s(_uca)]) -> 76
}
Sat witness: Found: ((le([s(nn1), s(nn2)])) -> le([nn1, nn2]), {
nn1 -> s(s(s(z)))  ;  nn2 -> s(s(z))
})

-------------------------------------------
Step 64, which took 0.302399 s (model generation: 0.301365,  model checking: 0.001034):

Model:
|_
{
le -> 
{{{
Q={q_gen_7879, q_gen_7880, q_gen_7897, q_gen_7898, q_gen_7903, q_gen_7918},
Q_f={q_gen_7879},
Delta=
{
<s>(q_gen_7880) -> q_gen_7880
<z>() -> q_gen_7880
<s, s>(q_gen_7879) -> q_gen_7879
<s, s>(q_gen_7918) -> q_gen_7879
<z, s>(q_gen_7880) -> q_gen_7879
<s, s>(q_gen_7898) -> q_gen_7897
<s, z>(q_gen_7880) -> q_gen_7898
<z, z>() -> q_gen_7898
<s, s>(q_gen_7897) -> q_gen_7903
<s, s>(q_gen_7903) -> q_gen_7918
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_7878, q_gen_7882, q_gen_7883, q_gen_7889, q_gen_7892, q_gen_7894, q_gen_7895, q_gen_7896, q_gen_7900, q_gen_7901, q_gen_7907, q_gen_7909, q_gen_7915},
Q_f={q_gen_7878},
Delta=
{
<nil>() -> q_gen_7882
<z>() -> q_gen_7889
<s>(q_gen_7889) -> q_gen_7892
<s>(q_gen_7907) -> q_gen_7892
<cons>(q_gen_7889, q_gen_7882) -> q_gen_7894
<cons>(q_gen_7892, q_gen_7882) -> q_gen_7894
<cons>(q_gen_7907, q_gen_7882) -> q_gen_7894
<cons>(q_gen_7889, q_gen_7894) -> q_gen_7900
<cons>(q_gen_7889, q_gen_7909) -> q_gen_7900
<cons>(q_gen_7892, q_gen_7894) -> q_gen_7900
<cons>(q_gen_7892, q_gen_7909) -> q_gen_7900
<s>(q_gen_7892) -> q_gen_7907
<cons>(q_gen_7889, q_gen_7900) -> q_gen_7909
<cons, s>(q_gen_7883, q_gen_7882) -> q_gen_7878
<cons, s>(q_gen_7895, q_gen_7894) -> q_gen_7878
<cons, s>(q_gen_7901, q_gen_7900) -> q_gen_7878
<cons, s>(q_gen_7915, q_gen_7909) -> q_gen_7878
<nil, z>() -> q_gen_7878
<s, z>(q_gen_7889) -> q_gen_7883
<s, z>(q_gen_7892) -> q_gen_7883
<s, z>(q_gen_7907) -> q_gen_7883
<z, z>() -> q_gen_7883
<s, s>(q_gen_7883) -> q_gen_7895
<z, s>(q_gen_7889) -> q_gen_7895
<cons, s>(q_gen_7883, q_gen_7894) -> q_gen_7896
<cons, s>(q_gen_7883, q_gen_7900) -> q_gen_7896
<cons, s>(q_gen_7895, q_gen_7882) -> q_gen_7896
<cons, s>(q_gen_7895, q_gen_7900) -> q_gen_7896
<cons, s>(q_gen_7895, q_gen_7909) -> q_gen_7896
<cons, s>(q_gen_7901, q_gen_7882) -> q_gen_7896
<cons, s>(q_gen_7901, q_gen_7894) -> q_gen_7896
<cons, s>(q_gen_7901, q_gen_7909) -> q_gen_7896
<cons, s>(q_gen_7915, q_gen_7882) -> q_gen_7896
<cons, s>(q_gen_7915, q_gen_7894) -> q_gen_7896
<cons, s>(q_gen_7915, q_gen_7900) -> q_gen_7896
<z, s>(q_gen_7892) -> q_gen_7901
<s, s>(q_gen_7901) -> q_gen_7915
<z, s>(q_gen_7907) -> q_gen_7915
}

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

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 61
() -> length([nil, z]) -> 60
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 60
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 69
(le([s(nn1), z])) -> BOT -> 63
(le([z, z])) -> BOT -> 60
(length([l, _yca]) /\ length([cons(x, l), _zca])) -> le([_yca, _zca]) -> 76
(length([ll, _uca])) -> length([cons(x, ll), s(_uca)]) -> 76
}
Sat witness: Found: ((le([s(nn1), s(nn2)])) -> le([nn1, nn2]), {
nn1 -> s(s(s(z)))  ;  nn2 -> s(s(s(z)))
})

-------------------------------------------
Step 65, which took 0.319302 s (model generation: 0.318534,  model checking: 0.000768):

Model:
|_
{
le -> 
{{{
Q={q_gen_7879, q_gen_7880, q_gen_7886, q_gen_7897, q_gen_7930},
Q_f={q_gen_7879},
Delta=
{
<z>() -> q_gen_7880
<s>(q_gen_7880) -> q_gen_7886
<s>(q_gen_7886) -> q_gen_7930
<s, s>(q_gen_7879) -> q_gen_7879
<s, z>(q_gen_7930) -> q_gen_7879
<z, s>(q_gen_7880) -> q_gen_7879
<z, s>(q_gen_7886) -> q_gen_7879
<z, s>(q_gen_7930) -> q_gen_7879
<s, s>(q_gen_7897) -> q_gen_7897
<s, z>(q_gen_7880) -> q_gen_7897
<s, z>(q_gen_7886) -> q_gen_7897
<z, z>() -> q_gen_7897
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_7878, q_gen_7882, q_gen_7883, q_gen_7889, q_gen_7892, q_gen_7894, q_gen_7895, q_gen_7896, q_gen_7900, q_gen_7901, q_gen_7907, q_gen_7909, q_gen_7915, q_gen_7924},
Q_f={q_gen_7878},
Delta=
{
<cons>(q_gen_7889, q_gen_7909) -> q_gen_7882
<cons>(q_gen_7892, q_gen_7909) -> q_gen_7882
<nil>() -> q_gen_7882
<z>() -> q_gen_7889
<s>(q_gen_7889) -> q_gen_7892
<cons>(q_gen_7889, q_gen_7882) -> q_gen_7894
<cons>(q_gen_7892, q_gen_7882) -> q_gen_7894
<cons>(q_gen_7907, q_gen_7882) -> q_gen_7894
<cons>(q_gen_7924, q_gen_7882) -> q_gen_7894
<cons>(q_gen_7889, q_gen_7894) -> q_gen_7900
<cons>(q_gen_7892, q_gen_7894) -> q_gen_7900
<s>(q_gen_7892) -> q_gen_7907
<cons>(q_gen_7889, q_gen_7900) -> q_gen_7909
<s>(q_gen_7907) -> q_gen_7924
<cons, s>(q_gen_7883, q_gen_7882) -> q_gen_7878
<cons, s>(q_gen_7895, q_gen_7894) -> q_gen_7878
<cons, s>(q_gen_7901, q_gen_7900) -> q_gen_7878
<cons, s>(q_gen_7915, q_gen_7909) -> q_gen_7878
<nil, z>() -> q_gen_7878
<s, z>(q_gen_7889) -> q_gen_7883
<s, z>(q_gen_7892) -> q_gen_7883
<s, z>(q_gen_7907) -> q_gen_7883
<s, z>(q_gen_7924) -> q_gen_7883
<z, s>(q_gen_7924) -> q_gen_7883
<z, z>() -> q_gen_7883
<s, s>(q_gen_7883) -> q_gen_7895
<z, s>(q_gen_7889) -> q_gen_7895
<cons, s>(q_gen_7883, q_gen_7894) -> q_gen_7896
<cons, s>(q_gen_7883, q_gen_7900) -> q_gen_7896
<cons, s>(q_gen_7895, q_gen_7882) -> q_gen_7896
<cons, s>(q_gen_7895, q_gen_7900) -> q_gen_7896
<cons, s>(q_gen_7895, q_gen_7909) -> q_gen_7896
<cons, s>(q_gen_7901, q_gen_7882) -> q_gen_7896
<cons, s>(q_gen_7901, q_gen_7894) -> q_gen_7896
<cons, s>(q_gen_7901, q_gen_7909) -> q_gen_7896
<cons, s>(q_gen_7915, q_gen_7882) -> q_gen_7896
<cons, s>(q_gen_7915, q_gen_7894) -> q_gen_7896
<cons, s>(q_gen_7915, q_gen_7900) -> q_gen_7896
<z, s>(q_gen_7892) -> q_gen_7901
<s, s>(q_gen_7901) -> q_gen_7915
<z, s>(q_gen_7907) -> q_gen_7915
}

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

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 64
() -> length([nil, z]) -> 61
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 61
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 69
(le([s(nn1), z])) -> BOT -> 63
(le([z, z])) -> BOT -> 61
(length([l, _yca]) /\ length([cons(x, l), _zca])) -> le([_yca, _zca]) -> 76
(length([ll, _uca])) -> length([cons(x, ll), s(_uca)]) -> 76
}
Sat witness: Found: (() -> le([z, s(nn2)]), {
nn2 -> s(s(s(z)))
})

-------------------------------------------
Step 66, which took 0.597102 s (model generation: 0.568693,  model checking: 0.028409):

Model:
|_
{
le -> 
{{{
Q={q_gen_7879, q_gen_7880, q_gen_7897},
Q_f={q_gen_7879},
Delta=
{
<s>(q_gen_7880) -> q_gen_7880
<z>() -> q_gen_7880
<s, s>(q_gen_7879) -> q_gen_7879
<z, s>(q_gen_7880) -> q_gen_7879
<s, s>(q_gen_7897) -> q_gen_7897
<s, z>(q_gen_7880) -> q_gen_7897
<z, z>() -> q_gen_7897
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_7878, q_gen_7882, q_gen_7883, q_gen_7889, q_gen_7892, q_gen_7894, q_gen_7895, q_gen_7896, q_gen_7900, q_gen_7901, q_gen_7907, q_gen_7909, q_gen_7915, q_gen_7924, q_gen_7935, q_gen_7956},
Q_f={q_gen_7878},
Delta=
{
<cons>(q_gen_7889, q_gen_7956) -> q_gen_7882
<nil>() -> q_gen_7882
<z>() -> q_gen_7889
<s>(q_gen_7889) -> q_gen_7892
<cons>(q_gen_7889, q_gen_7882) -> q_gen_7894
<cons>(q_gen_7892, q_gen_7882) -> q_gen_7894
<cons>(q_gen_7907, q_gen_7882) -> q_gen_7894
<cons>(q_gen_7924, q_gen_7882) -> q_gen_7894
<cons>(q_gen_7889, q_gen_7894) -> q_gen_7900
<s>(q_gen_7892) -> q_gen_7907
<cons>(q_gen_7889, q_gen_7900) -> q_gen_7909
<cons>(q_gen_7892, q_gen_7909) -> q_gen_7909
<s>(q_gen_7907) -> q_gen_7924
<cons>(q_gen_7889, q_gen_7909) -> q_gen_7956
<cons>(q_gen_7892, q_gen_7894) -> q_gen_7956
<cons, s>(q_gen_7883, q_gen_7882) -> q_gen_7878
<cons, s>(q_gen_7895, q_gen_7894) -> q_gen_7878
<cons, s>(q_gen_7901, q_gen_7900) -> q_gen_7878
<cons, s>(q_gen_7901, q_gen_7956) -> q_gen_7878
<cons, s>(q_gen_7915, q_gen_7900) -> q_gen_7878
<cons, s>(q_gen_7915, q_gen_7909) -> q_gen_7878
<cons, s>(q_gen_7935, q_gen_7909) -> q_gen_7878
<cons, s>(q_gen_7935, q_gen_7956) -> q_gen_7878
<nil, z>() -> q_gen_7878
<s, z>(q_gen_7889) -> q_gen_7883
<s, z>(q_gen_7892) -> q_gen_7883
<s, z>(q_gen_7907) -> q_gen_7883
<s, z>(q_gen_7924) -> q_gen_7883
<z, z>() -> q_gen_7883
<s, s>(q_gen_7883) -> q_gen_7895
<z, s>(q_gen_7889) -> q_gen_7895
<cons, s>(q_gen_7883, q_gen_7894) -> q_gen_7896
<cons, s>(q_gen_7883, q_gen_7900) -> q_gen_7896
<cons, s>(q_gen_7895, q_gen_7882) -> q_gen_7896
<cons, s>(q_gen_7895, q_gen_7900) -> q_gen_7896
<cons, s>(q_gen_7895, q_gen_7909) -> q_gen_7896
<cons, s>(q_gen_7901, q_gen_7882) -> q_gen_7896
<cons, s>(q_gen_7901, q_gen_7894) -> q_gen_7896
<cons, s>(q_gen_7901, q_gen_7909) -> q_gen_7896
<cons, s>(q_gen_7915, q_gen_7882) -> q_gen_7896
<cons, s>(q_gen_7915, q_gen_7894) -> q_gen_7896
<cons, s>(q_gen_7915, q_gen_7956) -> q_gen_7896
<cons, s>(q_gen_7935, q_gen_7882) -> q_gen_7896
<cons, s>(q_gen_7935, q_gen_7894) -> q_gen_7896
<cons, s>(q_gen_7935, q_gen_7900) -> q_gen_7896
<z, s>(q_gen_7892) -> q_gen_7901
<s, s>(q_gen_7901) -> q_gen_7915
<z, s>(q_gen_7907) -> q_gen_7915
<z, s>(q_gen_7924) -> q_gen_7935
}

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

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 65
() -> length([nil, z]) -> 62
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 62
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 70
(le([s(nn1), z])) -> BOT -> 64
(le([z, z])) -> BOT -> 62
(length([l, _yca]) /\ length([cons(x, l), _zca])) -> le([_yca, _zca]) -> 76
(length([ll, _uca])) -> length([cons(x, ll), s(_uca)]) -> 79
}
Sat witness: Found: ((length([ll, _uca])) -> length([cons(x, ll), s(_uca)]), {
_uca -> s(s(s(z)))  ;  ll -> cons(z, cons(z, cons(s(z), cons(z, cons(z, cons(z, nil))))))  ;  x -> s(z)
})

-------------------------------------------
Step 67, which took 0.546874 s (model generation: 0.546105,  model checking: 0.000769):

Model:
|_
{
le -> 
{{{
Q={q_gen_7879, q_gen_7880, q_gen_7886, q_gen_7897, q_gen_7930},
Q_f={q_gen_7879},
Delta=
{
<s>(q_gen_7930) -> q_gen_7880
<z>() -> q_gen_7880
<s>(q_gen_7880) -> q_gen_7886
<s>(q_gen_7886) -> q_gen_7930
<s, s>(q_gen_7879) -> q_gen_7879
<s, z>(q_gen_7930) -> q_gen_7879
<z, s>(q_gen_7880) -> q_gen_7879
<z, s>(q_gen_7886) -> q_gen_7879
<z, s>(q_gen_7930) -> q_gen_7879
<s, s>(q_gen_7897) -> q_gen_7897
<s, z>(q_gen_7880) -> q_gen_7897
<s, z>(q_gen_7886) -> q_gen_7897
<z, z>() -> q_gen_7897
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_7878, q_gen_7882, q_gen_7883, q_gen_7889, q_gen_7892, q_gen_7894, q_gen_7895, q_gen_7896, q_gen_7900, q_gen_7901, q_gen_7907, q_gen_7909, q_gen_7915, q_gen_7924},
Q_f={q_gen_7878},
Delta=
{
<cons>(q_gen_7889, q_gen_7909) -> q_gen_7882
<cons>(q_gen_7892, q_gen_7909) -> q_gen_7882
<nil>() -> q_gen_7882
<z>() -> q_gen_7889
<s>(q_gen_7889) -> q_gen_7892
<cons>(q_gen_7889, q_gen_7882) -> q_gen_7894
<cons>(q_gen_7892, q_gen_7882) -> q_gen_7894
<cons>(q_gen_7907, q_gen_7882) -> q_gen_7894
<cons>(q_gen_7924, q_gen_7882) -> q_gen_7894
<cons>(q_gen_7889, q_gen_7894) -> q_gen_7900
<cons>(q_gen_7892, q_gen_7894) -> q_gen_7900
<s>(q_gen_7892) -> q_gen_7907
<cons>(q_gen_7889, q_gen_7900) -> q_gen_7909
<s>(q_gen_7907) -> q_gen_7924
<cons, s>(q_gen_7883, q_gen_7882) -> q_gen_7878
<cons, s>(q_gen_7895, q_gen_7894) -> q_gen_7878
<cons, s>(q_gen_7901, q_gen_7900) -> q_gen_7878
<cons, s>(q_gen_7915, q_gen_7909) -> q_gen_7878
<nil, z>() -> q_gen_7878
<s, z>(q_gen_7889) -> q_gen_7883
<s, z>(q_gen_7892) -> q_gen_7883
<s, z>(q_gen_7907) -> q_gen_7883
<s, z>(q_gen_7924) -> q_gen_7883
<z, s>(q_gen_7924) -> q_gen_7883
<z, z>() -> q_gen_7883
<s, s>(q_gen_7883) -> q_gen_7895
<z, s>(q_gen_7889) -> q_gen_7895
<cons, s>(q_gen_7883, q_gen_7894) -> q_gen_7896
<cons, s>(q_gen_7883, q_gen_7900) -> q_gen_7896
<cons, s>(q_gen_7895, q_gen_7882) -> q_gen_7896
<cons, s>(q_gen_7895, q_gen_7900) -> q_gen_7896
<cons, s>(q_gen_7895, q_gen_7909) -> q_gen_7896
<cons, s>(q_gen_7901, q_gen_7882) -> q_gen_7896
<cons, s>(q_gen_7901, q_gen_7894) -> q_gen_7896
<cons, s>(q_gen_7901, q_gen_7909) -> q_gen_7896
<cons, s>(q_gen_7915, q_gen_7882) -> q_gen_7896
<cons, s>(q_gen_7915, q_gen_7894) -> q_gen_7896
<cons, s>(q_gen_7915, q_gen_7900) -> q_gen_7896
<z, s>(q_gen_7892) -> q_gen_7901
<s, s>(q_gen_7901) -> q_gen_7915
<z, s>(q_gen_7907) -> q_gen_7915
}

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

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 65
() -> length([nil, z]) -> 63
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 63
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 70
(le([s(nn1), z])) -> BOT -> 67
(le([z, z])) -> BOT -> 63
(length([l, _yca]) /\ length([cons(x, l), _zca])) -> le([_yca, _zca]) -> 76
(length([ll, _uca])) -> length([cons(x, ll), s(_uca)]) -> 79
}
Sat witness: Found: ((le([s(nn1), z])) -> BOT, {
nn1 -> s(s(z))
})

-------------------------------------------
Step 68, which took 5.688467 s (model generation: 5.563644,  model checking: 0.124823):

Model:
|_
{
le -> 
{{{
Q={q_gen_7879, q_gen_7880, q_gen_7897},
Q_f={q_gen_7879},
Delta=
{
<s>(q_gen_7880) -> q_gen_7880
<z>() -> q_gen_7880
<s, s>(q_gen_7879) -> q_gen_7879
<z, s>(q_gen_7880) -> q_gen_7879
<s, s>(q_gen_7897) -> q_gen_7897
<s, z>(q_gen_7880) -> q_gen_7897
<z, z>() -> q_gen_7897
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_7878, q_gen_7882, q_gen_7883, q_gen_7889, q_gen_7892, q_gen_7894, q_gen_7895, q_gen_7896, q_gen_7900, q_gen_7901, q_gen_7907, q_gen_7909, q_gen_7915, q_gen_7924, q_gen_7935, q_gen_7956},
Q_f={q_gen_7878},
Delta=
{
<nil>() -> q_gen_7882
<z>() -> q_gen_7889
<s>(q_gen_7889) -> q_gen_7892
<cons>(q_gen_7889, q_gen_7882) -> q_gen_7894
<cons>(q_gen_7889, q_gen_7956) -> q_gen_7894
<cons>(q_gen_7892, q_gen_7882) -> q_gen_7894
<cons>(q_gen_7907, q_gen_7882) -> q_gen_7894
<cons>(q_gen_7924, q_gen_7882) -> q_gen_7894
<cons>(q_gen_7889, q_gen_7894) -> q_gen_7900
<s>(q_gen_7892) -> q_gen_7907
<cons>(q_gen_7889, q_gen_7900) -> q_gen_7909
<s>(q_gen_7907) -> q_gen_7924
<cons>(q_gen_7889, q_gen_7909) -> q_gen_7956
<cons>(q_gen_7892, q_gen_7894) -> q_gen_7956
<cons>(q_gen_7892, q_gen_7909) -> q_gen_7956
<cons, s>(q_gen_7883, q_gen_7882) -> q_gen_7878
<cons, s>(q_gen_7895, q_gen_7894) -> q_gen_7878
<cons, s>(q_gen_7901, q_gen_7900) -> q_gen_7878
<cons, s>(q_gen_7901, q_gen_7956) -> q_gen_7878
<cons, s>(q_gen_7915, q_gen_7909) -> q_gen_7878
<cons, s>(q_gen_7935, q_gen_7956) -> q_gen_7878
<nil, z>() -> q_gen_7878
<s, z>(q_gen_7889) -> q_gen_7883
<s, z>(q_gen_7892) -> q_gen_7883
<s, z>(q_gen_7907) -> q_gen_7883
<s, z>(q_gen_7924) -> q_gen_7883
<z, z>() -> q_gen_7883
<s, s>(q_gen_7883) -> q_gen_7895
<z, s>(q_gen_7889) -> q_gen_7895
<cons, s>(q_gen_7883, q_gen_7894) -> q_gen_7896
<cons, s>(q_gen_7883, q_gen_7900) -> q_gen_7896
<cons, s>(q_gen_7895, q_gen_7882) -> q_gen_7896
<cons, s>(q_gen_7895, q_gen_7900) -> q_gen_7896
<cons, s>(q_gen_7895, q_gen_7909) -> q_gen_7896
<cons, s>(q_gen_7901, q_gen_7882) -> q_gen_7896
<cons, s>(q_gen_7901, q_gen_7894) -> q_gen_7896
<cons, s>(q_gen_7901, q_gen_7909) -> q_gen_7896
<cons, s>(q_gen_7915, q_gen_7882) -> q_gen_7896
<cons, s>(q_gen_7915, q_gen_7894) -> q_gen_7896
<cons, s>(q_gen_7915, q_gen_7900) -> q_gen_7896
<cons, s>(q_gen_7915, q_gen_7956) -> q_gen_7896
<cons, s>(q_gen_7935, q_gen_7882) -> q_gen_7896
<cons, s>(q_gen_7935, q_gen_7894) -> q_gen_7896
<cons, s>(q_gen_7935, q_gen_7900) -> q_gen_7896
<z, s>(q_gen_7892) -> q_gen_7901
<s, s>(q_gen_7901) -> q_gen_7915
<z, s>(q_gen_7907) -> q_gen_7915
<z, s>(q_gen_7924) -> q_gen_7935
}

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

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 66
() -> length([nil, z]) -> 64
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 64
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 71
(le([s(nn1), z])) -> BOT -> 68
(le([z, z])) -> BOT -> 64
(length([l, _yca]) /\ length([cons(x, l), _zca])) -> le([_yca, _zca]) -> 79
(length([ll, _uca])) -> length([cons(x, ll), s(_uca)]) -> 79
}
Sat witness: Found: ((length([l, _yca]) /\ length([cons(x, l), _zca])) -> le([_yca, _zca]), {
_yca -> s(s(s(z)))  ;  _zca -> s(s(z))  ;  l -> cons(z, cons(s(z), cons(s(z), nil)))  ;  x -> s(z)
})

-------------------------------------------
Step 69, which took 5.837011 s (model generation: 5.401484,  model checking: 0.435527):

Model:
|_
{
le -> 
{{{
Q={q_gen_7879, q_gen_7880, q_gen_7897},
Q_f={q_gen_7879},
Delta=
{
<s>(q_gen_7880) -> q_gen_7880
<z>() -> q_gen_7880
<s, s>(q_gen_7879) -> q_gen_7879
<z, s>(q_gen_7880) -> q_gen_7879
<s, s>(q_gen_7897) -> q_gen_7897
<s, z>(q_gen_7880) -> q_gen_7897
<z, z>() -> q_gen_7897
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_7878, q_gen_7882, q_gen_7883, q_gen_7889, q_gen_7892, q_gen_7894, q_gen_7895, q_gen_7896, q_gen_7900, q_gen_7901, q_gen_7907, q_gen_7909, q_gen_7915, q_gen_7924, q_gen_7935, q_gen_7956},
Q_f={q_gen_7878},
Delta=
{
<nil>() -> q_gen_7882
<z>() -> q_gen_7889
<s>(q_gen_7889) -> q_gen_7892
<cons>(q_gen_7889, q_gen_7882) -> q_gen_7894
<cons>(q_gen_7892, q_gen_7882) -> q_gen_7894
<cons>(q_gen_7907, q_gen_7882) -> q_gen_7894
<cons>(q_gen_7924, q_gen_7882) -> q_gen_7894
<cons>(q_gen_7889, q_gen_7894) -> q_gen_7900
<cons>(q_gen_7889, q_gen_7956) -> q_gen_7900
<cons>(q_gen_7892, q_gen_7894) -> q_gen_7900
<s>(q_gen_7892) -> q_gen_7907
<cons>(q_gen_7889, q_gen_7900) -> q_gen_7909
<s>(q_gen_7907) -> q_gen_7924
<cons>(q_gen_7889, q_gen_7909) -> q_gen_7956
<cons>(q_gen_7892, q_gen_7909) -> q_gen_7956
<cons, s>(q_gen_7883, q_gen_7882) -> q_gen_7878
<cons, s>(q_gen_7895, q_gen_7894) -> q_gen_7878
<cons, s>(q_gen_7901, q_gen_7900) -> q_gen_7878
<cons, s>(q_gen_7915, q_gen_7900) -> q_gen_7878
<cons, s>(q_gen_7915, q_gen_7909) -> q_gen_7878
<cons, s>(q_gen_7935, q_gen_7909) -> q_gen_7878
<cons, s>(q_gen_7935, q_gen_7956) -> q_gen_7878
<nil, z>() -> q_gen_7878
<s, z>(q_gen_7889) -> q_gen_7883
<s, z>(q_gen_7892) -> q_gen_7883
<s, z>(q_gen_7907) -> q_gen_7883
<s, z>(q_gen_7924) -> q_gen_7883
<z, z>() -> q_gen_7883
<s, s>(q_gen_7883) -> q_gen_7895
<z, s>(q_gen_7889) -> q_gen_7895
<cons, s>(q_gen_7883, q_gen_7894) -> q_gen_7896
<cons, s>(q_gen_7883, q_gen_7900) -> q_gen_7896
<cons, s>(q_gen_7895, q_gen_7882) -> q_gen_7896
<cons, s>(q_gen_7895, q_gen_7900) -> q_gen_7896
<cons, s>(q_gen_7895, q_gen_7909) -> q_gen_7896
<cons, s>(q_gen_7901, q_gen_7882) -> q_gen_7896
<cons, s>(q_gen_7901, q_gen_7894) -> q_gen_7896
<cons, s>(q_gen_7901, q_gen_7909) -> q_gen_7896
<cons, s>(q_gen_7915, q_gen_7882) -> q_gen_7896
<cons, s>(q_gen_7915, q_gen_7894) -> q_gen_7896
<cons, s>(q_gen_7915, q_gen_7956) -> q_gen_7896
<cons, s>(q_gen_7935, q_gen_7882) -> q_gen_7896
<cons, s>(q_gen_7935, q_gen_7894) -> q_gen_7896
<cons, s>(q_gen_7935, q_gen_7900) -> q_gen_7896
<z, s>(q_gen_7892) -> q_gen_7901
<z, s>(q_gen_7907) -> q_gen_7915
<s, s>(q_gen_7901) -> q_gen_7935
<z, s>(q_gen_7924) -> q_gen_7935
}

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

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 67
() -> length([nil, z]) -> 65
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 65
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 72
(le([s(nn1), z])) -> BOT -> 69
(le([z, z])) -> BOT -> 65
(length([l, _yca]) /\ length([cons(x, l), _zca])) -> le([_yca, _zca]) -> 79
(length([ll, _uca])) -> length([cons(x, ll), s(_uca)]) -> 82
}
Sat witness: Found: ((length([ll, _uca])) -> length([cons(x, ll), s(_uca)]), {
_uca -> z  ;  ll -> nil  ;  x -> s(s(s(s(s(z)))))
})

-------------------------------------------
Step 70, which took 5.298160 s (model generation: 5.132775,  model checking: 0.165385):

Model:
|_
{
le -> 
{{{
Q={q_gen_7879, q_gen_7880, q_gen_7897},
Q_f={q_gen_7879},
Delta=
{
<s>(q_gen_7880) -> q_gen_7880
<z>() -> q_gen_7880
<s, s>(q_gen_7879) -> q_gen_7879
<z, s>(q_gen_7880) -> q_gen_7879
<s, s>(q_gen_7897) -> q_gen_7897
<s, z>(q_gen_7880) -> q_gen_7897
<z, z>() -> q_gen_7897
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_7878, q_gen_7882, q_gen_7883, q_gen_7889, q_gen_7892, q_gen_7894, q_gen_7895, q_gen_7896, q_gen_7900, q_gen_7901, q_gen_7907, q_gen_7909, q_gen_7915, q_gen_7924, q_gen_7935, q_gen_7956},
Q_f={q_gen_7878},
Delta=
{
<nil>() -> q_gen_7882
<z>() -> q_gen_7889
<s>(q_gen_7889) -> q_gen_7892
<s>(q_gen_7924) -> q_gen_7892
<cons>(q_gen_7889, q_gen_7882) -> q_gen_7894
<cons>(q_gen_7892, q_gen_7882) -> q_gen_7894
<cons>(q_gen_7907, q_gen_7882) -> q_gen_7894
<cons>(q_gen_7924, q_gen_7882) -> q_gen_7894
<cons>(q_gen_7889, q_gen_7894) -> q_gen_7900
<cons>(q_gen_7889, q_gen_7956) -> q_gen_7900
<cons>(q_gen_7892, q_gen_7894) -> q_gen_7900
<s>(q_gen_7892) -> q_gen_7907
<cons>(q_gen_7889, q_gen_7900) -> q_gen_7909
<s>(q_gen_7907) -> q_gen_7924
<cons>(q_gen_7889, q_gen_7909) -> q_gen_7956
<cons>(q_gen_7892, q_gen_7909) -> q_gen_7956
<cons, s>(q_gen_7883, q_gen_7882) -> q_gen_7878
<cons, s>(q_gen_7895, q_gen_7894) -> q_gen_7878
<cons, s>(q_gen_7901, q_gen_7900) -> q_gen_7878
<cons, s>(q_gen_7915, q_gen_7909) -> q_gen_7878
<cons, s>(q_gen_7935, q_gen_7909) -> q_gen_7878
<cons, s>(q_gen_7935, q_gen_7956) -> q_gen_7878
<nil, z>() -> q_gen_7878
<s, z>(q_gen_7889) -> q_gen_7883
<s, z>(q_gen_7892) -> q_gen_7883
<s, z>(q_gen_7907) -> q_gen_7883
<s, z>(q_gen_7924) -> q_gen_7883
<z, z>() -> q_gen_7883
<s, s>(q_gen_7883) -> q_gen_7895
<z, s>(q_gen_7889) -> q_gen_7895
<cons, s>(q_gen_7883, q_gen_7894) -> q_gen_7896
<cons, s>(q_gen_7883, q_gen_7900) -> q_gen_7896
<cons, s>(q_gen_7895, q_gen_7882) -> q_gen_7896
<cons, s>(q_gen_7895, q_gen_7900) -> q_gen_7896
<cons, s>(q_gen_7895, q_gen_7909) -> q_gen_7896
<cons, s>(q_gen_7901, q_gen_7882) -> q_gen_7896
<cons, s>(q_gen_7901, q_gen_7894) -> q_gen_7896
<cons, s>(q_gen_7901, q_gen_7909) -> q_gen_7896
<cons, s>(q_gen_7915, q_gen_7882) -> q_gen_7896
<cons, s>(q_gen_7915, q_gen_7894) -> q_gen_7896
<cons, s>(q_gen_7915, q_gen_7900) -> q_gen_7896
<cons, s>(q_gen_7915, q_gen_7956) -> q_gen_7896
<cons, s>(q_gen_7935, q_gen_7882) -> q_gen_7896
<cons, s>(q_gen_7935, q_gen_7894) -> q_gen_7896
<cons, s>(q_gen_7935, q_gen_7900) -> q_gen_7896
<z, s>(q_gen_7892) -> q_gen_7901
<z, s>(q_gen_7907) -> q_gen_7915
<s, s>(q_gen_7901) -> q_gen_7935
<z, s>(q_gen_7924) -> q_gen_7935
}

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

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 68
() -> length([nil, z]) -> 66
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 66
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 73
(le([s(nn1), z])) -> BOT -> 70
(le([z, z])) -> BOT -> 66
(length([l, _yca]) /\ length([cons(x, l), _zca])) -> le([_yca, _zca]) -> 82
(length([ll, _uca])) -> length([cons(x, ll), s(_uca)]) -> 82
}
Sat witness: Found: ((length([l, _yca]) /\ length([cons(x, l), _zca])) -> le([_yca, _zca]), {
_yca -> s(s(s(s(s(s(z))))))  ;  _zca -> s(s(s(s(z))))  ;  l -> cons(z, cons(z, cons(s(s(z)), nil)))  ;  x -> z
})

-------------------------------------------
Step 71, which took 6.340577 s (model generation: 5.987525,  model checking: 0.353052):

Model:
|_
{
le -> 
{{{
Q={q_gen_7879, q_gen_7880, q_gen_7897},
Q_f={q_gen_7879},
Delta=
{
<s>(q_gen_7880) -> q_gen_7880
<z>() -> q_gen_7880
<s, s>(q_gen_7879) -> q_gen_7879
<z, s>(q_gen_7880) -> q_gen_7879
<s, s>(q_gen_7897) -> q_gen_7897
<s, z>(q_gen_7880) -> q_gen_7897
<z, z>() -> q_gen_7897
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_7878, q_gen_7882, q_gen_7883, q_gen_7889, q_gen_7892, q_gen_7894, q_gen_7895, q_gen_7896, q_gen_7900, q_gen_7901, q_gen_7907, q_gen_7909, q_gen_7915, q_gen_7924, q_gen_7935, q_gen_7956},
Q_f={q_gen_7878},
Delta=
{
<cons>(q_gen_7889, q_gen_7956) -> q_gen_7882
<nil>() -> q_gen_7882
<z>() -> q_gen_7889
<s>(q_gen_7889) -> q_gen_7892
<cons>(q_gen_7889, q_gen_7882) -> q_gen_7894
<cons>(q_gen_7892, q_gen_7882) -> q_gen_7894
<cons>(q_gen_7907, q_gen_7882) -> q_gen_7894
<cons>(q_gen_7924, q_gen_7882) -> q_gen_7894
<cons>(q_gen_7889, q_gen_7894) -> q_gen_7900
<cons>(q_gen_7892, q_gen_7894) -> q_gen_7900
<s>(q_gen_7892) -> q_gen_7907
<cons>(q_gen_7889, q_gen_7900) -> q_gen_7909
<cons>(q_gen_7892, q_gen_7909) -> q_gen_7909
<s>(q_gen_7907) -> q_gen_7924
<s>(q_gen_7924) -> q_gen_7924
<cons>(q_gen_7889, q_gen_7909) -> q_gen_7956
<cons, s>(q_gen_7883, q_gen_7882) -> q_gen_7878
<cons, s>(q_gen_7895, q_gen_7894) -> q_gen_7878
<cons, s>(q_gen_7901, q_gen_7900) -> q_gen_7878
<cons, s>(q_gen_7915, q_gen_7909) -> q_gen_7878
<cons, s>(q_gen_7935, q_gen_7909) -> q_gen_7878
<cons, s>(q_gen_7935, q_gen_7956) -> q_gen_7878
<nil, z>() -> q_gen_7878
<s, z>(q_gen_7889) -> q_gen_7883
<s, z>(q_gen_7892) -> q_gen_7883
<s, z>(q_gen_7907) -> q_gen_7883
<s, z>(q_gen_7924) -> q_gen_7883
<z, z>() -> q_gen_7883
<s, s>(q_gen_7883) -> q_gen_7895
<z, s>(q_gen_7889) -> q_gen_7895
<cons, s>(q_gen_7883, q_gen_7894) -> q_gen_7896
<cons, s>(q_gen_7883, q_gen_7900) -> q_gen_7896
<cons, s>(q_gen_7895, q_gen_7882) -> q_gen_7896
<cons, s>(q_gen_7895, q_gen_7900) -> q_gen_7896
<cons, s>(q_gen_7895, q_gen_7909) -> q_gen_7896
<cons, s>(q_gen_7901, q_gen_7882) -> q_gen_7896
<cons, s>(q_gen_7901, q_gen_7894) -> q_gen_7896
<cons, s>(q_gen_7901, q_gen_7909) -> q_gen_7896
<cons, s>(q_gen_7901, q_gen_7956) -> q_gen_7896
<cons, s>(q_gen_7915, q_gen_7882) -> q_gen_7896
<cons, s>(q_gen_7915, q_gen_7894) -> q_gen_7896
<cons, s>(q_gen_7915, q_gen_7900) -> q_gen_7896
<cons, s>(q_gen_7915, q_gen_7956) -> q_gen_7896
<cons, s>(q_gen_7935, q_gen_7882) -> q_gen_7896
<cons, s>(q_gen_7935, q_gen_7894) -> q_gen_7896
<cons, s>(q_gen_7935, q_gen_7900) -> q_gen_7896
<z, s>(q_gen_7892) -> q_gen_7901
<z, s>(q_gen_7907) -> q_gen_7915
<s, s>(q_gen_7901) -> q_gen_7935
<z, s>(q_gen_7924) -> q_gen_7935
}

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

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 69
() -> length([nil, z]) -> 67
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 67
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 74
(le([s(nn1), z])) -> BOT -> 71
(le([z, z])) -> BOT -> 67
(length([l, _yca]) /\ length([cons(x, l), _zca])) -> le([_yca, _zca]) -> 82
(length([ll, _uca])) -> length([cons(x, ll), s(_uca)]) -> 85
}
Sat witness: Found: ((length([ll, _uca])) -> length([cons(x, ll), s(_uca)]), {
_uca -> s(s(s(s(s(z)))))  ;  ll -> cons(z, cons(z, cons(z, cons(s(z), cons(s(s(s(z))), nil)))))  ;  x -> z
})

-------------------------------------------
Step 72, which took 6.828110 s (model generation: 6.674133,  model checking: 0.153977):

Model:
|_
{
le -> 
{{{
Q={q_gen_7879, q_gen_7880, q_gen_7897},
Q_f={q_gen_7879},
Delta=
{
<s>(q_gen_7880) -> q_gen_7880
<z>() -> q_gen_7880
<s, s>(q_gen_7879) -> q_gen_7879
<z, s>(q_gen_7880) -> q_gen_7879
<s, s>(q_gen_7897) -> q_gen_7897
<s, z>(q_gen_7880) -> q_gen_7897
<z, z>() -> q_gen_7897
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_7878, q_gen_7882, q_gen_7883, q_gen_7889, q_gen_7892, q_gen_7894, q_gen_7895, q_gen_7896, q_gen_7900, q_gen_7901, q_gen_7907, q_gen_7909, q_gen_7915, q_gen_7924, q_gen_7935, q_gen_7956},
Q_f={q_gen_7878},
Delta=
{
<nil>() -> q_gen_7882
<s>(q_gen_7924) -> q_gen_7889
<z>() -> q_gen_7889
<s>(q_gen_7889) -> q_gen_7892
<cons>(q_gen_7889, q_gen_7882) -> q_gen_7894
<cons>(q_gen_7889, q_gen_7956) -> q_gen_7894
<cons>(q_gen_7892, q_gen_7882) -> q_gen_7894
<cons>(q_gen_7907, q_gen_7882) -> q_gen_7894
<cons>(q_gen_7924, q_gen_7882) -> q_gen_7894
<cons>(q_gen_7889, q_gen_7894) -> q_gen_7900
<cons>(q_gen_7892, q_gen_7894) -> q_gen_7900
<s>(q_gen_7892) -> q_gen_7907
<cons>(q_gen_7889, q_gen_7900) -> q_gen_7909
<cons>(q_gen_7892, q_gen_7909) -> q_gen_7909
<s>(q_gen_7907) -> q_gen_7924
<cons>(q_gen_7889, q_gen_7909) -> q_gen_7956
<cons, s>(q_gen_7883, q_gen_7882) -> q_gen_7878
<cons, s>(q_gen_7895, q_gen_7894) -> q_gen_7878
<cons, s>(q_gen_7901, q_gen_7900) -> q_gen_7878
<cons, s>(q_gen_7915, q_gen_7900) -> q_gen_7878
<cons, s>(q_gen_7915, q_gen_7909) -> q_gen_7878
<cons, s>(q_gen_7935, q_gen_7909) -> q_gen_7878
<cons, s>(q_gen_7935, q_gen_7956) -> q_gen_7878
<nil, z>() -> q_gen_7878
<s, z>(q_gen_7889) -> q_gen_7883
<s, z>(q_gen_7892) -> q_gen_7883
<s, z>(q_gen_7907) -> q_gen_7883
<s, z>(q_gen_7924) -> q_gen_7883
<z, z>() -> q_gen_7883
<s, s>(q_gen_7883) -> q_gen_7895
<z, s>(q_gen_7889) -> q_gen_7895
<cons, s>(q_gen_7883, q_gen_7894) -> q_gen_7896
<cons, s>(q_gen_7883, q_gen_7900) -> q_gen_7896
<cons, s>(q_gen_7895, q_gen_7882) -> q_gen_7896
<cons, s>(q_gen_7895, q_gen_7900) -> q_gen_7896
<cons, s>(q_gen_7895, q_gen_7909) -> q_gen_7896
<cons, s>(q_gen_7901, q_gen_7882) -> q_gen_7896
<cons, s>(q_gen_7901, q_gen_7894) -> q_gen_7896
<cons, s>(q_gen_7901, q_gen_7909) -> q_gen_7896
<cons, s>(q_gen_7901, q_gen_7956) -> q_gen_7896
<cons, s>(q_gen_7915, q_gen_7882) -> q_gen_7896
<cons, s>(q_gen_7915, q_gen_7894) -> q_gen_7896
<cons, s>(q_gen_7915, q_gen_7956) -> q_gen_7896
<cons, s>(q_gen_7935, q_gen_7882) -> q_gen_7896
<cons, s>(q_gen_7935, q_gen_7894) -> q_gen_7896
<cons, s>(q_gen_7935, q_gen_7900) -> q_gen_7896
<z, s>(q_gen_7892) -> q_gen_7901
<z, s>(q_gen_7907) -> q_gen_7915
<s, s>(q_gen_7901) -> q_gen_7935
<z, s>(q_gen_7924) -> q_gen_7935
}

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

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 70
() -> length([nil, z]) -> 68
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 68
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 75
(le([s(nn1), z])) -> BOT -> 72
(le([z, z])) -> BOT -> 68
(length([l, _yca]) /\ length([cons(x, l), _zca])) -> le([_yca, _zca]) -> 85
(length([ll, _uca])) -> length([cons(x, ll), s(_uca)]) -> 85
}
Sat witness: Found: ((length([l, _yca]) /\ length([cons(x, l), _zca])) -> le([_yca, _zca]), {
_yca -> s(s(s(s(s(s(z))))))  ;  _zca -> s(s(s(s(z))))  ;  l -> cons(z, cons(s(s(z)), nil))  ;  x -> z
})

-------------------------------------------
Step 73, which took 7.533874 s (model generation: 6.827370,  model checking: 0.706504):

Model:
|_
{
le -> 
{{{
Q={q_gen_7879, q_gen_7880, q_gen_7897},
Q_f={q_gen_7879},
Delta=
{
<s>(q_gen_7880) -> q_gen_7880
<z>() -> q_gen_7880
<s, s>(q_gen_7879) -> q_gen_7879
<z, s>(q_gen_7880) -> q_gen_7879
<s, s>(q_gen_7897) -> q_gen_7897
<s, z>(q_gen_7880) -> q_gen_7897
<z, z>() -> q_gen_7897
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_7878, q_gen_7882, q_gen_7883, q_gen_7889, q_gen_7892, q_gen_7894, q_gen_7895, q_gen_7896, q_gen_7900, q_gen_7901, q_gen_7907, q_gen_7909, q_gen_7915, q_gen_7924, q_gen_7935, q_gen_7956},
Q_f={q_gen_7878},
Delta=
{
<nil>() -> q_gen_7882
<z>() -> q_gen_7889
<s>(q_gen_7889) -> q_gen_7892
<cons>(q_gen_7889, q_gen_7882) -> q_gen_7894
<cons>(q_gen_7892, q_gen_7882) -> q_gen_7894
<cons>(q_gen_7907, q_gen_7882) -> q_gen_7894
<cons>(q_gen_7924, q_gen_7882) -> q_gen_7894
<cons>(q_gen_7889, q_gen_7894) -> q_gen_7900
<cons>(q_gen_7892, q_gen_7894) -> q_gen_7900
<s>(q_gen_7892) -> q_gen_7907
<cons>(q_gen_7889, q_gen_7900) -> q_gen_7909
<cons>(q_gen_7892, q_gen_7909) -> q_gen_7909
<s>(q_gen_7907) -> q_gen_7924
<s>(q_gen_7924) -> q_gen_7924
<cons>(q_gen_7889, q_gen_7909) -> q_gen_7956
<cons>(q_gen_7889, q_gen_7956) -> q_gen_7956
<cons, s>(q_gen_7883, q_gen_7882) -> q_gen_7878
<cons, s>(q_gen_7895, q_gen_7894) -> q_gen_7878
<cons, s>(q_gen_7901, q_gen_7900) -> q_gen_7878
<cons, s>(q_gen_7915, q_gen_7900) -> q_gen_7878
<cons, s>(q_gen_7915, q_gen_7909) -> q_gen_7878
<cons, s>(q_gen_7935, q_gen_7909) -> q_gen_7878
<cons, s>(q_gen_7935, q_gen_7956) -> q_gen_7878
<nil, z>() -> q_gen_7878
<s, z>(q_gen_7889) -> q_gen_7883
<s, z>(q_gen_7892) -> q_gen_7883
<s, z>(q_gen_7907) -> q_gen_7883
<s, z>(q_gen_7924) -> q_gen_7883
<z, z>() -> q_gen_7883
<s, s>(q_gen_7883) -> q_gen_7895
<z, s>(q_gen_7889) -> q_gen_7895
<cons, s>(q_gen_7883, q_gen_7894) -> q_gen_7896
<cons, s>(q_gen_7883, q_gen_7900) -> q_gen_7896
<cons, s>(q_gen_7895, q_gen_7882) -> q_gen_7896
<cons, s>(q_gen_7895, q_gen_7900) -> q_gen_7896
<cons, s>(q_gen_7895, q_gen_7909) -> q_gen_7896
<cons, s>(q_gen_7901, q_gen_7882) -> q_gen_7896
<cons, s>(q_gen_7901, q_gen_7894) -> q_gen_7896
<cons, s>(q_gen_7901, q_gen_7909) -> q_gen_7896
<cons, s>(q_gen_7901, q_gen_7956) -> q_gen_7896
<cons, s>(q_gen_7915, q_gen_7882) -> q_gen_7896
<cons, s>(q_gen_7915, q_gen_7894) -> q_gen_7896
<cons, s>(q_gen_7915, q_gen_7956) -> q_gen_7896
<cons, s>(q_gen_7935, q_gen_7882) -> q_gen_7896
<cons, s>(q_gen_7935, q_gen_7894) -> q_gen_7896
<cons, s>(q_gen_7935, q_gen_7900) -> q_gen_7896
<z, s>(q_gen_7892) -> q_gen_7901
<s, s>(q_gen_7901) -> q_gen_7915
<z, s>(q_gen_7907) -> q_gen_7915
<z, s>(q_gen_7924) -> q_gen_7935
}

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

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 71
() -> length([nil, z]) -> 69
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 69
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 76
(le([s(nn1), z])) -> BOT -> 73
(le([z, z])) -> BOT -> 69
(length([l, _yca]) /\ length([cons(x, l), _zca])) -> le([_yca, _zca]) -> 85
(length([ll, _uca])) -> length([cons(x, ll), s(_uca)]) -> 88
}
Sat witness: Found: ((length([ll, _uca])) -> length([cons(x, ll), s(_uca)]), {
_uca -> s(s(s(s(s(s(z))))))  ;  ll -> cons(z, cons(z, cons(z, cons(z, cons(s(z), cons(z, nil))))))  ;  x -> s(s(z))
})

-------------------------------------------
Step 74, which took 6.600398 s (model generation: 6.396814,  model checking: 0.203584):

Model:
|_
{
le -> 
{{{
Q={q_gen_7879, q_gen_7880, q_gen_7897},
Q_f={q_gen_7879},
Delta=
{
<s>(q_gen_7880) -> q_gen_7880
<z>() -> q_gen_7880
<s, s>(q_gen_7879) -> q_gen_7879
<z, s>(q_gen_7880) -> q_gen_7879
<s, s>(q_gen_7897) -> q_gen_7897
<s, z>(q_gen_7880) -> q_gen_7897
<z, z>() -> q_gen_7897
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_7878, q_gen_7882, q_gen_7883, q_gen_7889, q_gen_7892, q_gen_7894, q_gen_7895, q_gen_7896, q_gen_7900, q_gen_7901, q_gen_7907, q_gen_7909, q_gen_7915, q_gen_7924, q_gen_7935, q_gen_7956},
Q_f={q_gen_7878},
Delta=
{
<nil>() -> q_gen_7882
<s>(q_gen_7924) -> q_gen_7889
<z>() -> q_gen_7889
<s>(q_gen_7889) -> q_gen_7892
<cons>(q_gen_7889, q_gen_7882) -> q_gen_7894
<cons>(q_gen_7892, q_gen_7882) -> q_gen_7894
<cons>(q_gen_7907, q_gen_7882) -> q_gen_7894
<cons>(q_gen_7924, q_gen_7882) -> q_gen_7894
<cons>(q_gen_7889, q_gen_7894) -> q_gen_7900
<cons>(q_gen_7889, q_gen_7956) -> q_gen_7900
<s>(q_gen_7892) -> q_gen_7907
<cons>(q_gen_7889, q_gen_7900) -> q_gen_7909
<s>(q_gen_7907) -> q_gen_7924
<cons>(q_gen_7889, q_gen_7909) -> q_gen_7956
<cons>(q_gen_7892, q_gen_7894) -> q_gen_7956
<cons>(q_gen_7892, q_gen_7909) -> q_gen_7956
<cons, s>(q_gen_7883, q_gen_7882) -> q_gen_7878
<cons, s>(q_gen_7895, q_gen_7894) -> q_gen_7878
<cons, s>(q_gen_7901, q_gen_7900) -> q_gen_7878
<cons, s>(q_gen_7901, q_gen_7956) -> q_gen_7878
<cons, s>(q_gen_7915, q_gen_7909) -> q_gen_7878
<cons, s>(q_gen_7935, q_gen_7956) -> q_gen_7878
<nil, z>() -> q_gen_7878
<s, z>(q_gen_7889) -> q_gen_7883
<s, z>(q_gen_7892) -> q_gen_7883
<s, z>(q_gen_7907) -> q_gen_7883
<s, z>(q_gen_7924) -> q_gen_7883
<z, z>() -> q_gen_7883
<s, s>(q_gen_7883) -> q_gen_7895
<s, s>(q_gen_7895) -> q_gen_7895
<s, s>(q_gen_7935) -> q_gen_7895
<z, s>(q_gen_7889) -> q_gen_7895
<cons, s>(q_gen_7883, q_gen_7894) -> q_gen_7896
<cons, s>(q_gen_7883, q_gen_7900) -> q_gen_7896
<cons, s>(q_gen_7895, q_gen_7882) -> q_gen_7896
<cons, s>(q_gen_7895, q_gen_7900) -> q_gen_7896
<cons, s>(q_gen_7895, q_gen_7909) -> q_gen_7896
<cons, s>(q_gen_7895, q_gen_7956) -> q_gen_7896
<cons, s>(q_gen_7901, q_gen_7882) -> q_gen_7896
<cons, s>(q_gen_7901, q_gen_7894) -> q_gen_7896
<cons, s>(q_gen_7901, q_gen_7909) -> q_gen_7896
<cons, s>(q_gen_7915, q_gen_7882) -> q_gen_7896
<cons, s>(q_gen_7915, q_gen_7894) -> q_gen_7896
<cons, s>(q_gen_7915, q_gen_7900) -> q_gen_7896
<cons, s>(q_gen_7915, q_gen_7956) -> q_gen_7896
<cons, s>(q_gen_7935, q_gen_7882) -> q_gen_7896
<cons, s>(q_gen_7935, q_gen_7894) -> q_gen_7896
<cons, s>(q_gen_7935, q_gen_7900) -> q_gen_7896
<cons, s>(q_gen_7935, q_gen_7909) -> q_gen_7896
<z, s>(q_gen_7892) -> q_gen_7901
<s, s>(q_gen_7901) -> q_gen_7915
<z, s>(q_gen_7907) -> q_gen_7915
<z, s>(q_gen_7924) -> q_gen_7935
}

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

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 72
() -> length([nil, z]) -> 70
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 70
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 77
(le([s(nn1), z])) -> BOT -> 74
(le([z, z])) -> BOT -> 70
(length([l, _yca]) /\ length([cons(x, l), _zca])) -> le([_yca, _zca]) -> 88
(length([ll, _uca])) -> length([cons(x, ll), s(_uca)]) -> 88
}
Sat witness: Found: ((length([l, _yca]) /\ length([cons(x, l), _zca])) -> le([_yca, _zca]), {
_yca -> s(s(s(s(z))))  ;  _zca -> s(s(s(z)))  ;  l -> cons(s(s(s(s(z)))), cons(s(s(z)), nil))  ;  x -> z
})

Total time: 2104.585646
Reason for stopping: DontKnow. Stopped because: timeout