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


Learning problem is:

env: {
elt -> {a, b}  ;  eltlist -> {cons, nil}  ;  nat -> {s, z}
}
definition:
{
(leq, P:
{() -> leq([a, y])
() -> leq([b, b])
(leq([b, a])) -> BOT}
)
(insert, F:
{() -> insert([x, nil, cons(x, nil)])
(insert([x, z, _yc]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _yc)])
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))])}
(insert([_zc, _ad, _bd]) /\ insert([_zc, _ad, _cd])) -> eq_eltlist([_bd, _cd])
)
(sort, F:
{() -> sort([nil, nil])
(insert([y, _dd, _ed]) /\ sort([z, _dd])) -> sort([cons(y, z), _ed])}
(sort([_fd, _gd]) /\ sort([_fd, _hd])) -> eq_eltlist([_gd, _hd])
)
(length, F:
{() -> length([nil, z])
(length([ll, _id])) -> length([cons(x, ll), s(_id)])}
(length([_jd, _kd]) /\ length([_jd, _ld])) -> eq_nat([_kd, _ld])
)
}

properties:
{(length([_nd, _od]) /\ length([l, _md]) /\ sort([l, _nd])) -> eq_nat([_md, _od])}


over-approximation: {insert, length, sort}
under-approximation: {leq}

Clause system for inference is:

{
() -> insert([x, nil, cons(x, nil)]) -> 0
() -> length([nil, z]) -> 0
() -> leq([a, y]) -> 0
() -> leq([b, b]) -> 0
() -> sort([nil, nil]) -> 0
(insert([x, z, _yc]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _yc)]) -> 0
(insert([y, _dd, _ed]) /\ sort([z, _dd])) -> sort([cons(y, z), _ed]) -> 0
(length([_nd, _od]) /\ length([l, _md]) /\ sort([l, _nd])) -> eq_nat([_md, _od]) -> 0
(length([ll, _id])) -> length([cons(x, ll), s(_id)]) -> 0
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 0
(leq([b, a])) -> BOT -> 0
}


Solving took 66.587876 seconds.
DontKnow. Stopped because: timeout
Working model:
|_
{
insert -> 
{{{
Q={q_gen_741, q_gen_742, q_gen_743, q_gen_744, q_gen_745, q_gen_746, q_gen_753, q_gen_754, q_gen_756, q_gen_757, q_gen_758, q_gen_759, q_gen_762, q_gen_765, q_gen_766, q_gen_767, q_gen_768, q_gen_769, q_gen_770, q_gen_771, q_gen_783, q_gen_796, q_gen_798, q_gen_808, q_gen_837, q_gen_838, q_gen_849, q_gen_850, q_gen_882, q_gen_884, q_gen_885, q_gen_904, q_gen_909, q_gen_910, q_gen_926},
Q_f={},
Delta=
{
<nil>() -> q_gen_742
<b>() -> q_gen_743
<a>() -> q_gen_757
<nil, cons>(q_gen_743, q_gen_742) -> q_gen_745
<b, b>() -> q_gen_746
<a, a>() -> q_gen_754
<b, a>() -> q_gen_759
<nil, cons>(q_gen_757, q_gen_742) -> q_gen_766
<cons, cons>(q_gen_754, q_gen_766) -> q_gen_768
<cons, cons>(q_gen_771, q_gen_766) -> q_gen_770
<a, b>() -> q_gen_771
<cons, cons>(q_gen_759, q_gen_745) -> q_gen_838
<cons, cons>(q_gen_746, q_gen_745) -> q_gen_850
<cons, cons>(q_gen_771, q_gen_850) -> q_gen_910
<b, nil, cons>(q_gen_743, q_gen_742) -> q_gen_741
<b, cons, cons>(q_gen_746, q_gen_745) -> q_gen_744
<b, cons, cons>(q_gen_754, q_gen_745) -> q_gen_753
<a, nil, cons>(q_gen_757, q_gen_742) -> q_gen_756
<a, cons, cons>(q_gen_759, q_gen_745) -> q_gen_758
<a, nil, cons>(q_gen_743, q_gen_742) -> q_gen_762
<b, cons, cons>(q_gen_754, q_gen_766) -> q_gen_765
<b, cons, cons>(q_gen_754, q_gen_768) -> q_gen_767
<b, cons, cons>(q_gen_746, q_gen_770) -> q_gen_769
<b, nil, cons>(q_gen_757, q_gen_742) -> q_gen_783
<a, cons, cons>(q_gen_746, q_gen_745) -> q_gen_796
<b, cons, cons>(q_gen_771, q_gen_745) -> q_gen_798
<a, cons, cons>(q_gen_754, q_gen_766) -> q_gen_808
<b, cons, cons>(q_gen_771, q_gen_838) -> q_gen_837
<b, cons, cons>(q_gen_746, q_gen_850) -> q_gen_849
<a, cons, cons>(q_gen_771, q_gen_766) -> q_gen_882
<b, cons, cons>(q_gen_759, q_gen_745) -> q_gen_884
<b, cons, cons>(q_gen_754, q_gen_838) -> q_gen_885
<b, cons, cons>(q_gen_754, q_gen_850) -> q_gen_904
<a, cons, cons>(q_gen_771, q_gen_910) -> q_gen_909
<a, cons, cons>(q_gen_759, q_gen_770) -> q_gen_926
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_740, q_gen_747, q_gen_748, q_gen_749, q_gen_760, q_gen_761, q_gen_772, q_gen_773, q_gen_774, q_gen_775, q_gen_776, q_gen_777, q_gen_780, q_gen_781, q_gen_782, q_gen_786, q_gen_787, q_gen_788, q_gen_789, q_gen_790, q_gen_792, q_gen_793, q_gen_794, q_gen_795, q_gen_799, q_gen_800, q_gen_801, q_gen_802, q_gen_803, q_gen_804, q_gen_806, q_gen_807, q_gen_809, q_gen_810, q_gen_812, q_gen_813, q_gen_814, q_gen_815, q_gen_816, q_gen_817, q_gen_818, q_gen_819, q_gen_820, q_gen_821, q_gen_822, q_gen_823, q_gen_824, q_gen_826, q_gen_827, q_gen_828, q_gen_829, q_gen_830, q_gen_831, q_gen_835, q_gen_836, q_gen_840, q_gen_842, q_gen_843, q_gen_845, q_gen_846, q_gen_847, q_gen_848, q_gen_851, q_gen_852, q_gen_853, q_gen_856, q_gen_858, q_gen_859, q_gen_860, q_gen_861, q_gen_862, q_gen_863, q_gen_865, q_gen_867, q_gen_868, q_gen_869, q_gen_871, q_gen_872, q_gen_873, q_gen_874, q_gen_875, q_gen_876, q_gen_877, q_gen_879, q_gen_880, q_gen_881, q_gen_886, q_gen_887, q_gen_888, q_gen_889, q_gen_890, q_gen_891, q_gen_893, q_gen_894, q_gen_895, q_gen_896, q_gen_897, q_gen_898, q_gen_900, q_gen_901, q_gen_902, q_gen_905, q_gen_906, q_gen_907, q_gen_908, q_gen_915, q_gen_916, q_gen_917, q_gen_918, q_gen_920, q_gen_921, q_gen_922},
Q_f={},
Delta=
{
<nil>() -> q_gen_748
<cons>(q_gen_774, q_gen_748) -> q_gen_773
<b>() -> q_gen_774
<z>() -> q_gen_776
<cons>(q_gen_774, q_gen_773) -> q_gen_787
<s>(q_gen_776) -> q_gen_789
<s>(q_gen_789) -> q_gen_795
<cons>(q_gen_801, q_gen_748) -> q_gen_800
<a>() -> q_gen_801
<s>(q_gen_795) -> q_gen_804
<cons>(q_gen_801, q_gen_773) -> q_gen_813
<cons>(q_gen_774, q_gen_813) -> q_gen_815
<cons>(q_gen_774, q_gen_787) -> q_gen_820
<s>(q_gen_804) -> q_gen_824
<cons>(q_gen_774, q_gen_800) -> q_gen_827
<cons>(q_gen_774, q_gen_827) -> q_gen_829
<cons>(q_gen_801, q_gen_800) -> q_gen_847
<cons>(q_gen_801, q_gen_813) -> q_gen_861
<cons>(q_gen_774, q_gen_815) -> q_gen_868
<cons>(q_gen_774, q_gen_829) -> q_gen_873
<cons>(q_gen_774, q_gen_868) -> q_gen_888
<cons>(q_gen_774, q_gen_820) -> q_gen_890
<cons>(q_gen_801, q_gen_868) -> q_gen_896
<s>(q_gen_824) -> q_gen_902
<cons>(q_gen_801, q_gen_847) -> q_gen_907
<nil, z>() -> q_gen_740
<cons, s>(q_gen_749, q_gen_748) -> q_gen_747
<b, z>() -> q_gen_749
<cons, s>(q_gen_761, q_gen_748) -> q_gen_760
<a, z>() -> q_gen_761
<cons, s>(q_gen_775, q_gen_773) -> q_gen_772
<b, s>(q_gen_776) -> q_gen_775
<cons, s>(q_gen_775, q_gen_748) -> q_gen_777
<cons, s>(q_gen_781, q_gen_773) -> q_gen_780
<a, s>(q_gen_776) -> q_gen_781
<cons, s>(q_gen_781, q_gen_748) -> q_gen_782
<cons, s>(q_gen_788, q_gen_787) -> q_gen_786
<b, s>(q_gen_789) -> q_gen_788
<cons, s>(q_gen_788, q_gen_773) -> q_gen_790
<cons, s>(q_gen_788, q_gen_748) -> q_gen_792
<cons, s>(q_gen_794, q_gen_773) -> q_gen_793
<b, s>(q_gen_795) -> q_gen_794
<cons, s>(q_gen_775, q_gen_800) -> q_gen_799
<cons, s>(q_gen_803, q_gen_787) -> q_gen_802
<b, s>(q_gen_804) -> q_gen_803
<cons, s>(q_gen_794, q_gen_748) -> q_gen_806
<cons, s>(q_gen_803, q_gen_773) -> q_gen_807
<cons, s>(q_gen_810, q_gen_773) -> q_gen_809
<a, s>(q_gen_804) -> q_gen_810
<cons, s>(q_gen_794, q_gen_813) -> q_gen_812
<cons, s>(q_gen_803, q_gen_815) -> q_gen_814
<cons, s>(q_gen_794, q_gen_787) -> q_gen_816
<cons, s>(q_gen_788, q_gen_813) -> q_gen_817
<cons, s>(q_gen_794, q_gen_815) -> q_gen_818
<cons, s>(q_gen_821, q_gen_820) -> q_gen_819
<a, s>(q_gen_795) -> q_gen_821
<cons, s>(q_gen_823, q_gen_820) -> q_gen_822
<b, s>(q_gen_824) -> q_gen_823
<cons, s>(q_gen_788, q_gen_827) -> q_gen_826
<cons, s>(q_gen_821, q_gen_829) -> q_gen_828
<cons, s>(q_gen_761, q_gen_820) -> q_gen_830
<cons, s>(q_gen_788, q_gen_815) -> q_gen_831
<cons, s>(q_gen_788, q_gen_800) -> q_gen_835
<cons, s>(q_gen_821, q_gen_827) -> q_gen_836
<cons, s>(q_gen_781, q_gen_813) -> q_gen_840
<cons, s>(q_gen_821, q_gen_748) -> q_gen_842
<cons, s>(q_gen_803, q_gen_800) -> q_gen_843
<cons, s>(q_gen_781, q_gen_800) -> q_gen_845
<cons, s>(q_gen_788, q_gen_847) -> q_gen_846
<cons, s>(q_gen_749, q_gen_773) -> q_gen_848
<cons, s>(q_gen_794, q_gen_800) -> q_gen_851
<cons, s>(q_gen_810, q_gen_827) -> q_gen_852
<cons, s>(q_gen_781, q_gen_827) -> q_gen_853
<cons, s>(q_gen_761, q_gen_787) -> q_gen_856
<cons, s>(q_gen_810, q_gen_748) -> q_gen_858
<cons, s>(q_gen_810, q_gen_813) -> q_gen_859
<cons, s>(q_gen_823, q_gen_861) -> q_gen_860
<cons, s>(q_gen_810, q_gen_820) -> q_gen_862
<cons, s>(q_gen_794, q_gen_820) -> q_gen_863
<cons, s>(q_gen_775, q_gen_820) -> q_gen_865
<cons, s>(q_gen_794, q_gen_868) -> q_gen_867
<cons, s>(q_gen_823, q_gen_773) -> q_gen_869
<cons, s>(q_gen_794, q_gen_829) -> q_gen_871
<cons, s>(q_gen_803, q_gen_873) -> q_gen_872
<cons, s>(q_gen_803, q_gen_748) -> q_gen_874
<cons, s>(q_gen_876, q_gen_773) -> q_gen_875
<a, s>(q_gen_824) -> q_gen_876
<cons, s>(q_gen_810, q_gen_787) -> q_gen_877
<cons, s>(q_gen_880, q_gen_773) -> q_gen_879
<a, s>(q_gen_789) -> q_gen_880
<cons, s>(q_gen_810, q_gen_868) -> q_gen_881
<cons, s>(q_gen_880, q_gen_748) -> q_gen_886
<cons, s>(q_gen_803, q_gen_888) -> q_gen_887
<cons, s>(q_gen_810, q_gen_890) -> q_gen_889
<cons, s>(q_gen_775, q_gen_890) -> q_gen_891
<cons, s>(q_gen_880, q_gen_813) -> q_gen_893
<cons, s>(q_gen_823, q_gen_787) -> q_gen_894
<cons, s>(q_gen_823, q_gen_896) -> q_gen_895
<cons, s>(q_gen_876, q_gen_890) -> q_gen_897
<cons, s>(q_gen_794, q_gen_890) -> q_gen_898
<cons, s>(q_gen_901, q_gen_890) -> q_gen_900
<a, s>(q_gen_902) -> q_gen_901
<cons, s>(q_gen_821, q_gen_847) -> q_gen_905
<cons, s>(q_gen_810, q_gen_907) -> q_gen_906
<cons, s>(q_gen_880, q_gen_820) -> q_gen_908
<cons, s>(q_gen_876, q_gen_813) -> q_gen_915
<cons, s>(q_gen_917, q_gen_861) -> q_gen_916
<b, s>(q_gen_902) -> q_gen_917
<cons, s>(q_gen_880, q_gen_800) -> q_gen_918
<cons, s>(q_gen_803, q_gen_868) -> q_gen_920
<cons, s>(q_gen_876, q_gen_888) -> q_gen_921
<cons, s>(q_gen_781, q_gen_815) -> q_gen_922
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_738, q_gen_739, q_gen_752, q_gen_755},
Q_f={},
Delta=
{
<b, b>() -> q_gen_738
<a, b>() -> q_gen_739
<b, a>() -> q_gen_752
<a, a>() -> q_gen_755
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_737, q_gen_750, q_gen_751, q_gen_763, q_gen_764, q_gen_778, q_gen_779, q_gen_784, q_gen_785, q_gen_791, q_gen_797, q_gen_805, q_gen_811, q_gen_825, q_gen_832, q_gen_833, q_gen_834, q_gen_839, q_gen_841, q_gen_844, q_gen_854, q_gen_855, q_gen_857, q_gen_864, q_gen_866, q_gen_870, q_gen_878, q_gen_883, q_gen_892, q_gen_899, q_gen_903, q_gen_911, q_gen_912, q_gen_913, q_gen_914, q_gen_919, q_gen_923, q_gen_924, q_gen_925},
Q_f={},
Delta=
{
<nil, nil>() -> q_gen_737
<cons, cons>(q_gen_751, q_gen_737) -> q_gen_750
<b, b>() -> q_gen_751
<cons, cons>(q_gen_764, q_gen_737) -> q_gen_763
<a, b>() -> q_gen_764
<cons, cons>(q_gen_779, q_gen_737) -> q_gen_778
<a, a>() -> q_gen_779
<cons, cons>(q_gen_785, q_gen_737) -> q_gen_784
<b, a>() -> q_gen_785
<cons, cons>(q_gen_751, q_gen_750) -> q_gen_791
<cons, cons>(q_gen_764, q_gen_763) -> q_gen_797
<cons, cons>(q_gen_751, q_gen_791) -> q_gen_805
<cons, cons>(q_gen_779, q_gen_750) -> q_gen_811
<cons, cons>(q_gen_764, q_gen_805) -> q_gen_825
<cons, cons>(q_gen_764, q_gen_833) -> q_gen_832
<cons, cons>(q_gen_751, q_gen_834) -> q_gen_833
<cons, cons>(q_gen_785, q_gen_750) -> q_gen_834
<cons, cons>(q_gen_751, q_gen_811) -> q_gen_839
<cons, cons>(q_gen_785, q_gen_834) -> q_gen_841
<cons, cons>(q_gen_751, q_gen_763) -> q_gen_844
<cons, cons>(q_gen_785, q_gen_855) -> q_gen_854
<cons, cons>(q_gen_751, q_gen_784) -> q_gen_855
<cons, cons>(q_gen_785, q_gen_797) -> q_gen_857
<cons, cons>(q_gen_785, q_gen_805) -> q_gen_864
<cons, cons>(q_gen_751, q_gen_805) -> q_gen_866
<cons, cons>(q_gen_764, q_gen_750) -> q_gen_870
<cons, cons>(q_gen_785, q_gen_791) -> q_gen_878
<cons, cons>(q_gen_764, q_gen_778) -> q_gen_883
<cons, cons>(q_gen_785, q_gen_866) -> q_gen_892
<cons, cons>(q_gen_764, q_gen_866) -> q_gen_899
<cons, cons>(q_gen_779, q_gen_866) -> q_gen_903
<cons, cons>(q_gen_785, q_gen_912) -> q_gen_911
<cons, cons>(q_gen_779, q_gen_763) -> q_gen_912
<cons, cons>(q_gen_764, q_gen_914) -> q_gen_913
<cons, cons>(q_gen_751, q_gen_797) -> q_gen_914
<cons, cons>(q_gen_785, q_gen_784) -> q_gen_919
<cons, cons>(q_gen_785, q_gen_924) -> q_gen_923
<cons, cons>(q_gen_751, q_gen_925) -> q_gen_924
<cons, cons>(q_gen_785, q_gen_763) -> q_gen_925
}

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

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

-------------------
STEPS:
-------------------------------------------
Step 0, which took 0.007552 s (model generation: 0.007218,  model checking: 0.000334):

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

}

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

}

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

}

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

}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 0
() -> length([nil, z]) -> 0
() -> leq([a, y]) -> 0
() -> leq([b, b]) -> 0
() -> sort([nil, nil]) -> 3
(insert([x, z, _yc]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _yc)]) -> 1
(insert([y, _dd, _ed]) /\ sort([z, _dd])) -> sort([cons(y, z), _ed]) -> 1
(length([_nd, _od]) /\ length([l, _md]) /\ sort([l, _nd])) -> eq_nat([_md, _od]) -> 1
(length([ll, _id])) -> length([cons(x, ll), s(_id)]) -> 1
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 1
(leq([b, a])) -> BOT -> 1
}
Sat witness: Found: (() -> sort([nil, nil]), {

})

-------------------------------------------
Step 1, which took 0.009405 s (model generation: 0.009349,  model checking: 0.000056):

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

}

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

}

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

}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_737},
Q_f={q_gen_737},
Delta=
{
<nil, nil>() -> q_gen_737
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 0
() -> length([nil, z]) -> 0
() -> leq([a, y]) -> 0
() -> leq([b, b]) -> 3
() -> sort([nil, nil]) -> 3
(insert([x, z, _yc]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _yc)]) -> 1
(insert([y, _dd, _ed]) /\ sort([z, _dd])) -> sort([cons(y, z), _ed]) -> 1
(length([_nd, _od]) /\ length([l, _md]) /\ sort([l, _nd])) -> eq_nat([_md, _od]) -> 1
(length([ll, _id])) -> length([cons(x, ll), s(_id)]) -> 1
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 1
(leq([b, a])) -> BOT -> 1
}
Sat witness: Found: (() -> leq([b, b]), {

})

-------------------------------------------
Step 2, which took 0.009668 s (model generation: 0.009618,  model checking: 0.000050):

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

}

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

}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_738},
Q_f={q_gen_738},
Delta=
{
<b, b>() -> q_gen_738
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_737},
Q_f={q_gen_737},
Delta=
{
<nil, nil>() -> q_gen_737
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 0
() -> length([nil, z]) -> 0
() -> leq([a, y]) -> 3
() -> leq([b, b]) -> 3
() -> sort([nil, nil]) -> 3
(insert([x, z, _yc]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _yc)]) -> 1
(insert([y, _dd, _ed]) /\ sort([z, _dd])) -> sort([cons(y, z), _ed]) -> 1
(length([_nd, _od]) /\ length([l, _md]) /\ sort([l, _nd])) -> eq_nat([_md, _od]) -> 1
(length([ll, _id])) -> length([cons(x, ll), s(_id)]) -> 1
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 1
(leq([b, a])) -> BOT -> 1
}
Sat witness: Found: (() -> leq([a, y]), {
y -> b
})

-------------------------------------------
Step 3, which took 0.008165 s (model generation: 0.007838,  model checking: 0.000327):

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

}

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

}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_738},
Q_f={q_gen_738},
Delta=
{
<a, b>() -> q_gen_738
<b, b>() -> q_gen_738
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_737},
Q_f={q_gen_737},
Delta=
{
<nil, nil>() -> q_gen_737
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 0
() -> length([nil, z]) -> 3
() -> leq([a, y]) -> 3
() -> leq([b, b]) -> 3
() -> sort([nil, nil]) -> 3
(insert([x, z, _yc]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _yc)]) -> 1
(insert([y, _dd, _ed]) /\ sort([z, _dd])) -> sort([cons(y, z), _ed]) -> 1
(length([_nd, _od]) /\ length([l, _md]) /\ sort([l, _nd])) -> eq_nat([_md, _od]) -> 1
(length([ll, _id])) -> length([cons(x, ll), s(_id)]) -> 1
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 1
(leq([b, a])) -> BOT -> 1
}
Sat witness: Found: (() -> length([nil, z]), {

})

-------------------------------------------
Step 4, which took 0.007408 s (model generation: 0.007291,  model checking: 0.000117):

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

}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_740},
Q_f={q_gen_740},
Delta=
{
<nil, z>() -> q_gen_740
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_738},
Q_f={q_gen_738},
Delta=
{
<a, b>() -> q_gen_738
<b, b>() -> q_gen_738
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_737},
Q_f={q_gen_737},
Delta=
{
<nil, nil>() -> q_gen_737
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 3
() -> length([nil, z]) -> 3
() -> leq([a, y]) -> 3
() -> leq([b, b]) -> 3
() -> sort([nil, nil]) -> 3
(insert([x, z, _yc]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _yc)]) -> 1
(insert([y, _dd, _ed]) /\ sort([z, _dd])) -> sort([cons(y, z), _ed]) -> 1
(length([_nd, _od]) /\ length([l, _md]) /\ sort([l, _nd])) -> eq_nat([_md, _od]) -> 1
(length([ll, _id])) -> length([cons(x, ll), s(_id)]) -> 1
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 1
(leq([b, a])) -> BOT -> 1
}
Sat witness: Found: (() -> insert([x, nil, cons(x, nil)]), {
x -> b
})

-------------------------------------------
Step 5, which took 0.008015 s (model generation: 0.007730,  model checking: 0.000285):

Model:
|_
{
insert -> 
{{{
Q={q_gen_741, q_gen_742, q_gen_743},
Q_f={q_gen_741},
Delta=
{
<nil>() -> q_gen_742
<b>() -> q_gen_743
<b, nil, cons>(q_gen_743, q_gen_742) -> q_gen_741
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_740},
Q_f={q_gen_740},
Delta=
{
<nil, z>() -> q_gen_740
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_738},
Q_f={q_gen_738},
Delta=
{
<a, b>() -> q_gen_738
<b, b>() -> q_gen_738
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_737},
Q_f={q_gen_737},
Delta=
{
<nil, nil>() -> q_gen_737
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 3
() -> length([nil, z]) -> 3
() -> leq([a, y]) -> 3
() -> leq([b, b]) -> 3
() -> sort([nil, nil]) -> 3
(insert([x, z, _yc]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _yc)]) -> 1
(insert([y, _dd, _ed]) /\ sort([z, _dd])) -> sort([cons(y, z), _ed]) -> 1
(length([_nd, _od]) /\ length([l, _md]) /\ sort([l, _nd])) -> eq_nat([_md, _od]) -> 1
(length([ll, _id])) -> length([cons(x, ll), s(_id)]) -> 1
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 4
(leq([b, a])) -> BOT -> 2
}
Sat witness: Found: ((leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]), {
x -> b  ;  y -> b  ;  z -> nil
})

-------------------------------------------
Step 6, which took 0.008066 s (model generation: 0.007969,  model checking: 0.000097):

Model:
|_
{
insert -> 
{{{
Q={q_gen_741, q_gen_742, q_gen_743, q_gen_745, q_gen_746},
Q_f={q_gen_741},
Delta=
{
<nil>() -> q_gen_742
<b>() -> q_gen_743
<nil, cons>(q_gen_743, q_gen_742) -> q_gen_745
<b, b>() -> q_gen_746
<b, cons, cons>(q_gen_746, q_gen_745) -> q_gen_741
<b, nil, cons>(q_gen_743, q_gen_742) -> q_gen_741
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_740},
Q_f={q_gen_740},
Delta=
{
<nil, z>() -> q_gen_740
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_738},
Q_f={q_gen_738},
Delta=
{
<a, b>() -> q_gen_738
<b, b>() -> q_gen_738
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_737},
Q_f={q_gen_737},
Delta=
{
<nil, nil>() -> q_gen_737
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 3
() -> length([nil, z]) -> 3
() -> leq([a, y]) -> 3
() -> leq([b, b]) -> 3
() -> sort([nil, nil]) -> 3
(insert([x, z, _yc]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _yc)]) -> 1
(insert([y, _dd, _ed]) /\ sort([z, _dd])) -> sort([cons(y, z), _ed]) -> 1
(length([_nd, _od]) /\ length([l, _md]) /\ sort([l, _nd])) -> eq_nat([_md, _od]) -> 1
(length([ll, _id])) -> length([cons(x, ll), s(_id)]) -> 4
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 4
(leq([b, a])) -> BOT -> 2
}
Sat witness: Found: ((length([ll, _id])) -> length([cons(x, ll), s(_id)]), {
_id -> z  ;  ll -> nil  ;  x -> b
})

-------------------------------------------
Step 7, which took 0.008887 s (model generation: 0.008473,  model checking: 0.000414):

Model:
|_
{
insert -> 
{{{
Q={q_gen_741, q_gen_742, q_gen_743, q_gen_745, q_gen_746},
Q_f={q_gen_741},
Delta=
{
<nil>() -> q_gen_742
<b>() -> q_gen_743
<nil, cons>(q_gen_743, q_gen_742) -> q_gen_745
<b, b>() -> q_gen_746
<b, cons, cons>(q_gen_746, q_gen_745) -> q_gen_741
<b, nil, cons>(q_gen_743, q_gen_742) -> q_gen_741
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_740, q_gen_748, q_gen_749},
Q_f={q_gen_740},
Delta=
{
<nil>() -> q_gen_748
<cons, s>(q_gen_749, q_gen_748) -> q_gen_740
<nil, z>() -> q_gen_740
<b, z>() -> q_gen_749
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_738},
Q_f={q_gen_738},
Delta=
{
<a, b>() -> q_gen_738
<b, b>() -> q_gen_738
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_737},
Q_f={q_gen_737},
Delta=
{
<nil, nil>() -> q_gen_737
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 3
() -> length([nil, z]) -> 3
() -> leq([a, y]) -> 3
() -> leq([b, b]) -> 3
() -> sort([nil, nil]) -> 3
(insert([x, z, _yc]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _yc)]) -> 1
(insert([y, _dd, _ed]) /\ sort([z, _dd])) -> sort([cons(y, z), _ed]) -> 4
(length([_nd, _od]) /\ length([l, _md]) /\ sort([l, _nd])) -> eq_nat([_md, _od]) -> 2
(length([ll, _id])) -> length([cons(x, ll), s(_id)]) -> 4
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 4
(leq([b, a])) -> BOT -> 2
}
Sat witness: Found: ((insert([y, _dd, _ed]) /\ sort([z, _dd])) -> sort([cons(y, z), _ed]), {
_dd -> nil  ;  _ed -> cons(b, nil)  ;  y -> b  ;  z -> nil
})

-------------------------------------------
Step 8, which took 0.008917 s (model generation: 0.008500,  model checking: 0.000417):

Model:
|_
{
insert -> 
{{{
Q={q_gen_741, q_gen_742, q_gen_743, q_gen_745, q_gen_746},
Q_f={q_gen_741},
Delta=
{
<nil>() -> q_gen_742
<b>() -> q_gen_743
<nil, cons>(q_gen_743, q_gen_742) -> q_gen_745
<b, b>() -> q_gen_746
<b, cons, cons>(q_gen_746, q_gen_745) -> q_gen_741
<b, nil, cons>(q_gen_743, q_gen_742) -> q_gen_741
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_740, q_gen_748, q_gen_749},
Q_f={q_gen_740},
Delta=
{
<nil>() -> q_gen_748
<cons, s>(q_gen_749, q_gen_748) -> q_gen_740
<nil, z>() -> q_gen_740
<b, z>() -> q_gen_749
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_738},
Q_f={q_gen_738},
Delta=
{
<a, b>() -> q_gen_738
<b, b>() -> q_gen_738
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_737, q_gen_751},
Q_f={q_gen_737},
Delta=
{
<cons, cons>(q_gen_751, q_gen_737) -> q_gen_737
<nil, nil>() -> q_gen_737
<b, b>() -> q_gen_751
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 3
() -> length([nil, z]) -> 3
() -> leq([a, y]) -> 3
() -> leq([b, b]) -> 3
() -> sort([nil, nil]) -> 3
(insert([x, z, _yc]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _yc)]) -> 4
(insert([y, _dd, _ed]) /\ sort([z, _dd])) -> sort([cons(y, z), _ed]) -> 4
(length([_nd, _od]) /\ length([l, _md]) /\ sort([l, _nd])) -> eq_nat([_md, _od]) -> 2
(length([ll, _id])) -> length([cons(x, ll), s(_id)]) -> 4
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 4
(leq([b, a])) -> BOT -> 2
}
Sat witness: Found: ((insert([x, z, _yc]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _yc)]), {
_yc -> cons(b, nil)  ;  x -> b  ;  y -> a  ;  z -> nil
})

-------------------------------------------
Step 9, which took 0.009498 s (model generation: 0.009480,  model checking: 0.000018):

Model:
|_
{
insert -> 
{{{
Q={q_gen_741, q_gen_742, q_gen_743, q_gen_745, q_gen_746},
Q_f={q_gen_741},
Delta=
{
<nil>() -> q_gen_742
<b>() -> q_gen_743
<nil, cons>(q_gen_743, q_gen_742) -> q_gen_745
<a, a>() -> q_gen_746
<b, b>() -> q_gen_746
<b, cons, cons>(q_gen_746, q_gen_745) -> q_gen_741
<b, nil, cons>(q_gen_743, q_gen_742) -> q_gen_741
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_740, q_gen_748, q_gen_749},
Q_f={q_gen_740},
Delta=
{
<nil>() -> q_gen_748
<cons, s>(q_gen_749, q_gen_748) -> q_gen_740
<nil, z>() -> q_gen_740
<b, z>() -> q_gen_749
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_738},
Q_f={q_gen_738},
Delta=
{
<a, b>() -> q_gen_738
<b, a>() -> q_gen_738
<b, b>() -> q_gen_738
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_737, q_gen_751},
Q_f={q_gen_737},
Delta=
{
<cons, cons>(q_gen_751, q_gen_737) -> q_gen_737
<nil, nil>() -> q_gen_737
<b, b>() -> q_gen_751
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 3
() -> length([nil, z]) -> 3
() -> leq([a, y]) -> 3
() -> leq([b, b]) -> 3
() -> sort([nil, nil]) -> 3
(insert([x, z, _yc]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _yc)]) -> 4
(insert([y, _dd, _ed]) /\ sort([z, _dd])) -> sort([cons(y, z), _ed]) -> 4
(length([_nd, _od]) /\ length([l, _md]) /\ sort([l, _nd])) -> eq_nat([_md, _od]) -> 2
(length([ll, _id])) -> length([cons(x, ll), s(_id)]) -> 4
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 4
(leq([b, a])) -> BOT -> 5
}
Sat witness: Found: ((leq([b, a])) -> BOT, {

})

-------------------------------------------
Step 10, which took 0.010148 s (model generation: 0.009954,  model checking: 0.000194):

Model:
|_
{
insert -> 
{{{
Q={q_gen_741, q_gen_742, q_gen_743, q_gen_745, q_gen_746},
Q_f={q_gen_741},
Delta=
{
<nil>() -> q_gen_742
<b>() -> q_gen_743
<nil, cons>(q_gen_743, q_gen_742) -> q_gen_745
<a, a>() -> q_gen_746
<b, b>() -> q_gen_746
<b, cons, cons>(q_gen_746, q_gen_745) -> q_gen_741
<b, nil, cons>(q_gen_743, q_gen_742) -> q_gen_741
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_740, q_gen_748, q_gen_749},
Q_f={q_gen_740},
Delta=
{
<nil>() -> q_gen_748
<cons, s>(q_gen_749, q_gen_748) -> q_gen_740
<nil, z>() -> q_gen_740
<b, z>() -> q_gen_749
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_738, q_gen_752},
Q_f={q_gen_738},
Delta=
{
<a, b>() -> q_gen_738
<b, b>() -> q_gen_738
<b, a>() -> q_gen_752
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_737, q_gen_751},
Q_f={q_gen_737},
Delta=
{
<cons, cons>(q_gen_751, q_gen_737) -> q_gen_737
<nil, nil>() -> q_gen_737
<b, b>() -> q_gen_751
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 3
() -> length([nil, z]) -> 3
() -> leq([a, y]) -> 6
() -> leq([b, b]) -> 4
() -> sort([nil, nil]) -> 4
(insert([x, z, _yc]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _yc)]) -> 4
(insert([y, _dd, _ed]) /\ sort([z, _dd])) -> sort([cons(y, z), _ed]) -> 4
(length([_nd, _od]) /\ length([l, _md]) /\ sort([l, _nd])) -> eq_nat([_md, _od]) -> 3
(length([ll, _id])) -> length([cons(x, ll), s(_id)]) -> 4
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 4
(leq([b, a])) -> BOT -> 5
}
Sat witness: Found: (() -> leq([a, y]), {
y -> a
})

-------------------------------------------
Step 11, which took 0.009317 s (model generation: 0.008901,  model checking: 0.000416):

Model:
|_
{
insert -> 
{{{
Q={q_gen_741, q_gen_742, q_gen_743, q_gen_745, q_gen_746},
Q_f={q_gen_741},
Delta=
{
<nil>() -> q_gen_742
<b>() -> q_gen_743
<nil, cons>(q_gen_743, q_gen_742) -> q_gen_745
<a, a>() -> q_gen_746
<b, b>() -> q_gen_746
<b, cons, cons>(q_gen_746, q_gen_745) -> q_gen_741
<b, nil, cons>(q_gen_743, q_gen_742) -> q_gen_741
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_740, q_gen_748, q_gen_749},
Q_f={q_gen_740},
Delta=
{
<nil>() -> q_gen_748
<cons, s>(q_gen_749, q_gen_748) -> q_gen_740
<nil, z>() -> q_gen_740
<b, z>() -> q_gen_749
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_738, q_gen_752},
Q_f={q_gen_738},
Delta=
{
<a, a>() -> q_gen_738
<a, b>() -> q_gen_738
<b, b>() -> q_gen_738
<b, a>() -> q_gen_752
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_737, q_gen_751},
Q_f={q_gen_737},
Delta=
{
<cons, cons>(q_gen_751, q_gen_737) -> q_gen_737
<nil, nil>() -> q_gen_737
<b, b>() -> q_gen_751
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 6
() -> length([nil, z]) -> 4
() -> leq([a, y]) -> 6
() -> leq([b, b]) -> 4
() -> sort([nil, nil]) -> 4
(insert([x, z, _yc]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _yc)]) -> 4
(insert([y, _dd, _ed]) /\ sort([z, _dd])) -> sort([cons(y, z), _ed]) -> 4
(length([_nd, _od]) /\ length([l, _md]) /\ sort([l, _nd])) -> eq_nat([_md, _od]) -> 4
(length([ll, _id])) -> length([cons(x, ll), s(_id)]) -> 4
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 4
(leq([b, a])) -> BOT -> 5
}
Sat witness: Found: (() -> insert([x, nil, cons(x, nil)]), {
x -> a
})

-------------------------------------------
Step 12, which took 0.009981 s (model generation: 0.009513,  model checking: 0.000468):

Model:
|_
{
insert -> 
{{{
Q={q_gen_741, q_gen_742, q_gen_743, q_gen_745, q_gen_746},
Q_f={q_gen_741},
Delta=
{
<nil>() -> q_gen_742
<a>() -> q_gen_743
<b>() -> q_gen_743
<nil, cons>(q_gen_743, q_gen_742) -> q_gen_745
<a, a>() -> q_gen_746
<b, b>() -> q_gen_746
<a, nil, cons>(q_gen_743, q_gen_742) -> q_gen_741
<b, cons, cons>(q_gen_746, q_gen_745) -> q_gen_741
<b, nil, cons>(q_gen_743, q_gen_742) -> q_gen_741
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_740, q_gen_748, q_gen_749},
Q_f={q_gen_740},
Delta=
{
<nil>() -> q_gen_748
<cons, s>(q_gen_749, q_gen_748) -> q_gen_740
<nil, z>() -> q_gen_740
<b, z>() -> q_gen_749
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_738, q_gen_752},
Q_f={q_gen_738},
Delta=
{
<a, a>() -> q_gen_738
<a, b>() -> q_gen_738
<b, b>() -> q_gen_738
<b, a>() -> q_gen_752
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_737, q_gen_751},
Q_f={q_gen_737},
Delta=
{
<cons, cons>(q_gen_751, q_gen_737) -> q_gen_737
<nil, nil>() -> q_gen_737
<b, b>() -> q_gen_751
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 6
() -> length([nil, z]) -> 4
() -> leq([a, y]) -> 6
() -> leq([b, b]) -> 4
() -> sort([nil, nil]) -> 4
(insert([x, z, _yc]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _yc)]) -> 4
(insert([y, _dd, _ed]) /\ sort([z, _dd])) -> sort([cons(y, z), _ed]) -> 4
(length([_nd, _od]) /\ length([l, _md]) /\ sort([l, _nd])) -> eq_nat([_md, _od]) -> 4
(length([ll, _id])) -> length([cons(x, ll), s(_id)]) -> 4
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 7
(leq([b, a])) -> BOT -> 5
}
Sat witness: Found: ((leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]), {
x -> a  ;  y -> b  ;  z -> nil
})

-------------------------------------------
Step 13, which took 0.009811 s (model generation: 0.009513,  model checking: 0.000298):

Model:
|_
{
insert -> 
{{{
Q={q_gen_741, q_gen_742, q_gen_743, q_gen_745, q_gen_746},
Q_f={q_gen_741},
Delta=
{
<nil>() -> q_gen_742
<a>() -> q_gen_743
<b>() -> q_gen_743
<nil, cons>(q_gen_743, q_gen_742) -> q_gen_745
<a, a>() -> q_gen_746
<b, a>() -> q_gen_746
<b, b>() -> q_gen_746
<a, cons, cons>(q_gen_746, q_gen_745) -> q_gen_741
<a, nil, cons>(q_gen_743, q_gen_742) -> q_gen_741
<b, cons, cons>(q_gen_746, q_gen_745) -> q_gen_741
<b, nil, cons>(q_gen_743, q_gen_742) -> q_gen_741
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_740, q_gen_748, q_gen_749},
Q_f={q_gen_740},
Delta=
{
<nil>() -> q_gen_748
<cons, s>(q_gen_749, q_gen_748) -> q_gen_740
<nil, z>() -> q_gen_740
<b, z>() -> q_gen_749
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_738, q_gen_752},
Q_f={q_gen_738},
Delta=
{
<a, a>() -> q_gen_738
<a, b>() -> q_gen_738
<b, b>() -> q_gen_738
<b, a>() -> q_gen_752
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_737, q_gen_751},
Q_f={q_gen_737},
Delta=
{
<cons, cons>(q_gen_751, q_gen_737) -> q_gen_737
<nil, nil>() -> q_gen_737
<b, b>() -> q_gen_751
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 6
() -> length([nil, z]) -> 4
() -> leq([a, y]) -> 6
() -> leq([b, b]) -> 4
() -> sort([nil, nil]) -> 4
(insert([x, z, _yc]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _yc)]) -> 4
(insert([y, _dd, _ed]) /\ sort([z, _dd])) -> sort([cons(y, z), _ed]) -> 4
(length([_nd, _od]) /\ length([l, _md]) /\ sort([l, _nd])) -> eq_nat([_md, _od]) -> 4
(length([ll, _id])) -> length([cons(x, ll), s(_id)]) -> 7
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 7
(leq([b, a])) -> BOT -> 5
}
Sat witness: Found: ((length([ll, _id])) -> length([cons(x, ll), s(_id)]), {
_id -> z  ;  ll -> nil  ;  x -> a
})

-------------------------------------------
Step 14, which took 0.011165 s (model generation: 0.010735,  model checking: 0.000430):

Model:
|_
{
insert -> 
{{{
Q={q_gen_741, q_gen_742, q_gen_743, q_gen_745, q_gen_746},
Q_f={q_gen_741},
Delta=
{
<nil>() -> q_gen_742
<a>() -> q_gen_743
<b>() -> q_gen_743
<nil, cons>(q_gen_743, q_gen_742) -> q_gen_745
<a, a>() -> q_gen_746
<b, a>() -> q_gen_746
<b, b>() -> q_gen_746
<a, cons, cons>(q_gen_746, q_gen_745) -> q_gen_741
<a, nil, cons>(q_gen_743, q_gen_742) -> q_gen_741
<b, cons, cons>(q_gen_746, q_gen_745) -> q_gen_741
<b, nil, cons>(q_gen_743, q_gen_742) -> q_gen_741
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_740, q_gen_748, q_gen_749},
Q_f={q_gen_740},
Delta=
{
<nil>() -> q_gen_748
<cons, s>(q_gen_749, q_gen_748) -> q_gen_740
<nil, z>() -> q_gen_740
<a, z>() -> q_gen_749
<b, z>() -> q_gen_749
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_738, q_gen_752},
Q_f={q_gen_738},
Delta=
{
<a, a>() -> q_gen_738
<a, b>() -> q_gen_738
<b, b>() -> q_gen_738
<b, a>() -> q_gen_752
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_737, q_gen_751},
Q_f={q_gen_737},
Delta=
{
<cons, cons>(q_gen_751, q_gen_737) -> q_gen_737
<nil, nil>() -> q_gen_737
<b, b>() -> q_gen_751
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 6
() -> length([nil, z]) -> 4
() -> leq([a, y]) -> 6
() -> leq([b, b]) -> 4
() -> sort([nil, nil]) -> 4
(insert([x, z, _yc]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _yc)]) -> 4
(insert([y, _dd, _ed]) /\ sort([z, _dd])) -> sort([cons(y, z), _ed]) -> 7
(length([_nd, _od]) /\ length([l, _md]) /\ sort([l, _nd])) -> eq_nat([_md, _od]) -> 5
(length([ll, _id])) -> length([cons(x, ll), s(_id)]) -> 7
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 7
(leq([b, a])) -> BOT -> 5
}
Sat witness: Found: ((insert([y, _dd, _ed]) /\ sort([z, _dd])) -> sort([cons(y, z), _ed]), {
_dd -> nil  ;  _ed -> cons(b, nil)  ;  y -> a  ;  z -> nil
})

-------------------------------------------
Step 15, which took 0.011197 s (model generation: 0.010707,  model checking: 0.000490):

Model:
|_
{
insert -> 
{{{
Q={q_gen_741, q_gen_742, q_gen_743, q_gen_745, q_gen_746},
Q_f={q_gen_741},
Delta=
{
<nil>() -> q_gen_742
<a>() -> q_gen_743
<b>() -> q_gen_743
<nil, cons>(q_gen_743, q_gen_742) -> q_gen_745
<a, a>() -> q_gen_746
<b, a>() -> q_gen_746
<b, b>() -> q_gen_746
<a, cons, cons>(q_gen_746, q_gen_745) -> q_gen_741
<a, nil, cons>(q_gen_743, q_gen_742) -> q_gen_741
<b, cons, cons>(q_gen_746, q_gen_745) -> q_gen_741
<b, nil, cons>(q_gen_743, q_gen_742) -> q_gen_741
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_740, q_gen_748, q_gen_749},
Q_f={q_gen_740},
Delta=
{
<nil>() -> q_gen_748
<cons, s>(q_gen_749, q_gen_748) -> q_gen_740
<nil, z>() -> q_gen_740
<a, z>() -> q_gen_749
<b, z>() -> q_gen_749
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_738, q_gen_752},
Q_f={q_gen_738},
Delta=
{
<a, a>() -> q_gen_738
<a, b>() -> q_gen_738
<b, b>() -> q_gen_738
<b, a>() -> q_gen_752
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_737, q_gen_751},
Q_f={q_gen_737},
Delta=
{
<cons, cons>(q_gen_751, q_gen_737) -> q_gen_737
<nil, nil>() -> q_gen_737
<a, b>() -> q_gen_751
<b, b>() -> q_gen_751
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 6
() -> length([nil, z]) -> 4
() -> leq([a, y]) -> 6
() -> leq([b, b]) -> 4
() -> sort([nil, nil]) -> 4
(insert([x, z, _yc]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _yc)]) -> 7
(insert([y, _dd, _ed]) /\ sort([z, _dd])) -> sort([cons(y, z), _ed]) -> 7
(length([_nd, _od]) /\ length([l, _md]) /\ sort([l, _nd])) -> eq_nat([_md, _od]) -> 5
(length([ll, _id])) -> length([cons(x, ll), s(_id)]) -> 7
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 7
(leq([b, a])) -> BOT -> 5
}
Sat witness: Found: ((insert([x, z, _yc]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _yc)]), {
_yc -> cons(a, cons(a, nil))  ;  x -> b  ;  y -> a  ;  z -> cons(a, nil)
})

-------------------------------------------
Step 16, which took 0.013135 s (model generation: 0.012265,  model checking: 0.000870):

Model:
|_
{
insert -> 
{{{
Q={q_gen_741, q_gen_742, q_gen_743, q_gen_745, q_gen_746},
Q_f={q_gen_741},
Delta=
{
<nil>() -> q_gen_742
<a>() -> q_gen_743
<b>() -> q_gen_743
<cons, cons>(q_gen_746, q_gen_745) -> q_gen_745
<nil, cons>(q_gen_743, q_gen_742) -> q_gen_745
<a, a>() -> q_gen_746
<b, a>() -> q_gen_746
<b, b>() -> q_gen_746
<a, cons, cons>(q_gen_746, q_gen_745) -> q_gen_741
<a, nil, cons>(q_gen_743, q_gen_742) -> q_gen_741
<b, cons, cons>(q_gen_746, q_gen_745) -> q_gen_741
<b, nil, cons>(q_gen_743, q_gen_742) -> q_gen_741
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_740, q_gen_748, q_gen_749},
Q_f={q_gen_740},
Delta=
{
<nil>() -> q_gen_748
<cons, s>(q_gen_749, q_gen_748) -> q_gen_740
<nil, z>() -> q_gen_740
<a, z>() -> q_gen_749
<b, z>() -> q_gen_749
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_738, q_gen_752},
Q_f={q_gen_738},
Delta=
{
<a, a>() -> q_gen_738
<a, b>() -> q_gen_738
<b, b>() -> q_gen_738
<b, a>() -> q_gen_752
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_737, q_gen_751},
Q_f={q_gen_737},
Delta=
{
<cons, cons>(q_gen_751, q_gen_737) -> q_gen_737
<nil, nil>() -> q_gen_737
<a, b>() -> q_gen_751
<b, b>() -> q_gen_751
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 7
() -> length([nil, z]) -> 5
() -> leq([a, y]) -> 7
() -> leq([b, b]) -> 5
() -> sort([nil, nil]) -> 5
(insert([x, z, _yc]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _yc)]) -> 7
(insert([y, _dd, _ed]) /\ sort([z, _dd])) -> sort([cons(y, z), _ed]) -> 7
(length([_nd, _od]) /\ length([l, _md]) /\ sort([l, _nd])) -> eq_nat([_md, _od]) -> 6
(length([ll, _id])) -> length([cons(x, ll), s(_id)]) -> 7
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 10
(leq([b, a])) -> BOT -> 6
}
Sat witness: Found: ((leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]), {
x -> b  ;  y -> b  ;  z -> cons(a, nil)
})

-------------------------------------------
Step 17, which took 0.014242 s (model generation: 0.013504,  model checking: 0.000738):

Model:
|_
{
insert -> 
{{{
Q={q_gen_741, q_gen_742, q_gen_743, q_gen_745, q_gen_746},
Q_f={q_gen_741},
Delta=
{
<nil>() -> q_gen_742
<a>() -> q_gen_743
<b>() -> q_gen_743
<cons, cons>(q_gen_746, q_gen_745) -> q_gen_745
<nil, cons>(q_gen_743, q_gen_742) -> q_gen_745
<a, a>() -> q_gen_746
<a, b>() -> q_gen_746
<b, a>() -> q_gen_746
<b, b>() -> q_gen_746
<a, cons, cons>(q_gen_746, q_gen_745) -> q_gen_741
<a, nil, cons>(q_gen_743, q_gen_742) -> q_gen_741
<b, cons, cons>(q_gen_746, q_gen_745) -> q_gen_741
<b, nil, cons>(q_gen_743, q_gen_742) -> q_gen_741
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_740, q_gen_748, q_gen_749},
Q_f={q_gen_740},
Delta=
{
<nil>() -> q_gen_748
<cons, s>(q_gen_749, q_gen_748) -> q_gen_740
<nil, z>() -> q_gen_740
<a, z>() -> q_gen_749
<b, z>() -> q_gen_749
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_738, q_gen_752},
Q_f={q_gen_738},
Delta=
{
<a, a>() -> q_gen_738
<a, b>() -> q_gen_738
<b, b>() -> q_gen_738
<b, a>() -> q_gen_752
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_737, q_gen_751},
Q_f={q_gen_737},
Delta=
{
<cons, cons>(q_gen_751, q_gen_737) -> q_gen_737
<nil, nil>() -> q_gen_737
<a, b>() -> q_gen_751
<b, b>() -> q_gen_751
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 7
() -> length([nil, z]) -> 6
() -> leq([a, y]) -> 7
() -> leq([b, b]) -> 6
() -> sort([nil, nil]) -> 6
(insert([x, z, _yc]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _yc)]) -> 7
(insert([y, _dd, _ed]) /\ sort([z, _dd])) -> sort([cons(y, z), _ed]) -> 7
(length([_nd, _od]) /\ length([l, _md]) /\ sort([l, _nd])) -> eq_nat([_md, _od]) -> 7
(length([ll, _id])) -> length([cons(x, ll), s(_id)]) -> 10
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 10
(leq([b, a])) -> BOT -> 7
}
Sat witness: Found: ((length([ll, _id])) -> length([cons(x, ll), s(_id)]), {
_id -> s(z)  ;  ll -> cons(b, nil)  ;  x -> b
})

-------------------------------------------
Step 18, which took 0.014646 s (model generation: 0.014244,  model checking: 0.000402):

Model:
|_
{
insert -> 
{{{
Q={q_gen_741, q_gen_742, q_gen_743, q_gen_745, q_gen_746},
Q_f={q_gen_741},
Delta=
{
<nil>() -> q_gen_742
<a>() -> q_gen_743
<b>() -> q_gen_743
<cons, cons>(q_gen_746, q_gen_745) -> q_gen_745
<nil, cons>(q_gen_743, q_gen_742) -> q_gen_745
<a, a>() -> q_gen_746
<a, b>() -> q_gen_746
<b, a>() -> q_gen_746
<b, b>() -> q_gen_746
<a, cons, cons>(q_gen_746, q_gen_745) -> q_gen_741
<a, nil, cons>(q_gen_743, q_gen_742) -> q_gen_741
<b, cons, cons>(q_gen_746, q_gen_745) -> q_gen_741
<b, nil, cons>(q_gen_743, q_gen_742) -> q_gen_741
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_740, q_gen_748, q_gen_749, q_gen_774, q_gen_776},
Q_f={q_gen_740},
Delta=
{
<cons>(q_gen_774, q_gen_748) -> q_gen_748
<nil>() -> q_gen_748
<b>() -> q_gen_774
<z>() -> q_gen_776
<cons, s>(q_gen_749, q_gen_748) -> q_gen_740
<nil, z>() -> q_gen_740
<a, z>() -> q_gen_749
<b, s>(q_gen_776) -> q_gen_749
<b, z>() -> q_gen_749
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_738, q_gen_752},
Q_f={q_gen_738},
Delta=
{
<a, a>() -> q_gen_738
<a, b>() -> q_gen_738
<b, b>() -> q_gen_738
<b, a>() -> q_gen_752
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_737, q_gen_751},
Q_f={q_gen_737},
Delta=
{
<cons, cons>(q_gen_751, q_gen_737) -> q_gen_737
<nil, nil>() -> q_gen_737
<a, b>() -> q_gen_751
<b, b>() -> q_gen_751
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 7
() -> length([nil, z]) -> 7
() -> leq([a, y]) -> 7
() -> leq([b, b]) -> 7
() -> sort([nil, nil]) -> 7
(insert([x, z, _yc]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _yc)]) -> 7
(insert([y, _dd, _ed]) /\ sort([z, _dd])) -> sort([cons(y, z), _ed]) -> 7
(length([_nd, _od]) /\ length([l, _md]) /\ sort([l, _nd])) -> eq_nat([_md, _od]) -> 10
(length([ll, _id])) -> length([cons(x, ll), s(_id)]) -> 10
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 10
(leq([b, a])) -> BOT -> 8
}
Sat witness: Found: ((length([_nd, _od]) /\ length([l, _md]) /\ sort([l, _nd])) -> eq_nat([_md, _od]), {
_md -> s(z)  ;  _nd -> cons(b, nil)  ;  _od -> s(s(z))  ;  l -> cons(a, nil)
})

-------------------------------------------
Step 19, which took 0.015207 s (model generation: 0.014844,  model checking: 0.000363):

Model:
|_
{
insert -> 
{{{
Q={q_gen_741, q_gen_742, q_gen_743, q_gen_745, q_gen_746},
Q_f={q_gen_741},
Delta=
{
<nil>() -> q_gen_742
<a>() -> q_gen_743
<b>() -> q_gen_743
<cons, cons>(q_gen_746, q_gen_745) -> q_gen_745
<nil, cons>(q_gen_743, q_gen_742) -> q_gen_745
<a, a>() -> q_gen_746
<a, b>() -> q_gen_746
<b, a>() -> q_gen_746
<b, b>() -> q_gen_746
<a, cons, cons>(q_gen_746, q_gen_745) -> q_gen_741
<a, nil, cons>(q_gen_743, q_gen_742) -> q_gen_741
<b, cons, cons>(q_gen_746, q_gen_745) -> q_gen_741
<b, nil, cons>(q_gen_743, q_gen_742) -> q_gen_741
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_740, q_gen_748, q_gen_749, q_gen_773, q_gen_774, q_gen_775, q_gen_776, q_gen_777},
Q_f={q_gen_740},
Delta=
{
<nil>() -> q_gen_748
<cons>(q_gen_774, q_gen_748) -> q_gen_773
<b>() -> q_gen_774
<z>() -> q_gen_776
<cons, s>(q_gen_749, q_gen_748) -> q_gen_740
<cons, s>(q_gen_775, q_gen_773) -> q_gen_740
<nil, z>() -> q_gen_740
<a, z>() -> q_gen_749
<b, z>() -> q_gen_749
<b, s>(q_gen_776) -> q_gen_775
<cons, s>(q_gen_775, q_gen_748) -> q_gen_777
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_738, q_gen_752},
Q_f={q_gen_738},
Delta=
{
<a, a>() -> q_gen_738
<a, b>() -> q_gen_738
<b, b>() -> q_gen_738
<b, a>() -> q_gen_752
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_737, q_gen_751},
Q_f={q_gen_737},
Delta=
{
<cons, cons>(q_gen_751, q_gen_737) -> q_gen_737
<nil, nil>() -> q_gen_737
<a, b>() -> q_gen_751
<b, b>() -> q_gen_751
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 7
() -> length([nil, z]) -> 7
() -> leq([a, y]) -> 7
() -> leq([b, b]) -> 7
() -> sort([nil, nil]) -> 7
(insert([x, z, _yc]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _yc)]) -> 7
(insert([y, _dd, _ed]) /\ sort([z, _dd])) -> sort([cons(y, z), _ed]) -> 10
(length([_nd, _od]) /\ length([l, _md]) /\ sort([l, _nd])) -> eq_nat([_md, _od]) -> 10
(length([ll, _id])) -> length([cons(x, ll), s(_id)]) -> 10
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 10
(leq([b, a])) -> BOT -> 8
}
Sat witness: Found: ((insert([y, _dd, _ed]) /\ sort([z, _dd])) -> sort([cons(y, z), _ed]), {
_dd -> nil  ;  _ed -> cons(a, nil)  ;  y -> a  ;  z -> nil
})

-------------------------------------------
Step 20, which took 0.018235 s (model generation: 0.016284,  model checking: 0.001951):

Model:
|_
{
insert -> 
{{{
Q={q_gen_741, q_gen_742, q_gen_743, q_gen_745, q_gen_746},
Q_f={q_gen_741},
Delta=
{
<nil>() -> q_gen_742
<a>() -> q_gen_743
<b>() -> q_gen_743
<cons, cons>(q_gen_746, q_gen_745) -> q_gen_745
<nil, cons>(q_gen_743, q_gen_742) -> q_gen_745
<a, a>() -> q_gen_746
<a, b>() -> q_gen_746
<b, a>() -> q_gen_746
<b, b>() -> q_gen_746
<a, cons, cons>(q_gen_746, q_gen_745) -> q_gen_741
<a, nil, cons>(q_gen_743, q_gen_742) -> q_gen_741
<b, cons, cons>(q_gen_746, q_gen_745) -> q_gen_741
<b, nil, cons>(q_gen_743, q_gen_742) -> q_gen_741
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_740, q_gen_748, q_gen_749, q_gen_773, q_gen_774, q_gen_775, q_gen_776, q_gen_777},
Q_f={q_gen_740},
Delta=
{
<nil>() -> q_gen_748
<cons>(q_gen_774, q_gen_748) -> q_gen_773
<b>() -> q_gen_774
<z>() -> q_gen_776
<cons, s>(q_gen_749, q_gen_748) -> q_gen_740
<cons, s>(q_gen_775, q_gen_773) -> q_gen_740
<nil, z>() -> q_gen_740
<a, z>() -> q_gen_749
<b, z>() -> q_gen_749
<b, s>(q_gen_776) -> q_gen_775
<cons, s>(q_gen_775, q_gen_748) -> q_gen_777
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_738, q_gen_752},
Q_f={q_gen_738},
Delta=
{
<a, a>() -> q_gen_738
<a, b>() -> q_gen_738
<b, b>() -> q_gen_738
<b, a>() -> q_gen_752
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_737, q_gen_751},
Q_f={q_gen_737},
Delta=
{
<cons, cons>(q_gen_751, q_gen_737) -> q_gen_737
<nil, nil>() -> q_gen_737
<a, a>() -> q_gen_751
<a, b>() -> q_gen_751
<b, b>() -> q_gen_751
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 8
() -> length([nil, z]) -> 8
() -> leq([a, y]) -> 8
() -> leq([b, b]) -> 8
() -> sort([nil, nil]) -> 8
(insert([x, z, _yc]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _yc)]) -> 8
(insert([y, _dd, _ed]) /\ sort([z, _dd])) -> sort([cons(y, z), _ed]) -> 10
(length([_nd, _od]) /\ length([l, _md]) /\ sort([l, _nd])) -> eq_nat([_md, _od]) -> 10
(length([ll, _id])) -> length([cons(x, ll), s(_id)]) -> 13
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 11
(leq([b, a])) -> BOT -> 9
}
Sat witness: Found: ((length([ll, _id])) -> length([cons(x, ll), s(_id)]), {
_id -> s(z)  ;  ll -> cons(b, nil)  ;  x -> a
})

-------------------------------------------
Step 21, which took 0.017767 s (model generation: 0.016544,  model checking: 0.001223):

Model:
|_
{
insert -> 
{{{
Q={q_gen_741, q_gen_742, q_gen_743, q_gen_745, q_gen_746},
Q_f={q_gen_741},
Delta=
{
<nil>() -> q_gen_742
<a>() -> q_gen_743
<b>() -> q_gen_743
<cons, cons>(q_gen_746, q_gen_745) -> q_gen_745
<nil, cons>(q_gen_743, q_gen_742) -> q_gen_745
<a, a>() -> q_gen_746
<a, b>() -> q_gen_746
<b, a>() -> q_gen_746
<b, b>() -> q_gen_746
<a, cons, cons>(q_gen_746, q_gen_745) -> q_gen_741
<a, nil, cons>(q_gen_743, q_gen_742) -> q_gen_741
<b, cons, cons>(q_gen_746, q_gen_745) -> q_gen_741
<b, nil, cons>(q_gen_743, q_gen_742) -> q_gen_741
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_740, q_gen_748, q_gen_749, q_gen_773, q_gen_774, q_gen_775, q_gen_776, q_gen_777},
Q_f={q_gen_740},
Delta=
{
<nil>() -> q_gen_748
<cons>(q_gen_774, q_gen_748) -> q_gen_773
<b>() -> q_gen_774
<z>() -> q_gen_776
<cons, s>(q_gen_749, q_gen_748) -> q_gen_740
<cons, s>(q_gen_749, q_gen_773) -> q_gen_740
<cons, s>(q_gen_775, q_gen_773) -> q_gen_740
<nil, z>() -> q_gen_740
<a, s>(q_gen_776) -> q_gen_749
<a, z>() -> q_gen_749
<b, z>() -> q_gen_749
<b, s>(q_gen_776) -> q_gen_775
<cons, s>(q_gen_775, q_gen_748) -> q_gen_777
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_738, q_gen_752},
Q_f={q_gen_738},
Delta=
{
<a, a>() -> q_gen_738
<a, b>() -> q_gen_738
<b, b>() -> q_gen_738
<b, a>() -> q_gen_752
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_737, q_gen_751},
Q_f={q_gen_737},
Delta=
{
<cons, cons>(q_gen_751, q_gen_737) -> q_gen_737
<nil, nil>() -> q_gen_737
<a, a>() -> q_gen_751
<a, b>() -> q_gen_751
<b, b>() -> q_gen_751
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 9
() -> length([nil, z]) -> 9
() -> leq([a, y]) -> 9
() -> leq([b, b]) -> 9
() -> sort([nil, nil]) -> 9
(insert([x, z, _yc]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _yc)]) -> 9
(insert([y, _dd, _ed]) /\ sort([z, _dd])) -> sort([cons(y, z), _ed]) -> 10
(length([_nd, _od]) /\ length([l, _md]) /\ sort([l, _nd])) -> eq_nat([_md, _od]) -> 13
(length([ll, _id])) -> length([cons(x, ll), s(_id)]) -> 13
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 11
(leq([b, a])) -> BOT -> 10
}
Sat witness: Found: ((length([_nd, _od]) /\ length([l, _md]) /\ sort([l, _nd])) -> eq_nat([_md, _od]), {
_md -> s(z)  ;  _nd -> cons(a, nil)  ;  _od -> s(s(z))  ;  l -> cons(a, nil)
})

-------------------------------------------
Step 22, which took 0.017296 s (model generation: 0.016111,  model checking: 0.001185):

Model:
|_
{
insert -> 
{{{
Q={q_gen_741, q_gen_742, q_gen_743, q_gen_745, q_gen_746},
Q_f={q_gen_741},
Delta=
{
<nil>() -> q_gen_742
<a>() -> q_gen_743
<b>() -> q_gen_743
<cons, cons>(q_gen_746, q_gen_745) -> q_gen_745
<nil, cons>(q_gen_743, q_gen_742) -> q_gen_745
<a, a>() -> q_gen_746
<a, b>() -> q_gen_746
<b, a>() -> q_gen_746
<b, b>() -> q_gen_746
<a, cons, cons>(q_gen_746, q_gen_745) -> q_gen_741
<a, nil, cons>(q_gen_743, q_gen_742) -> q_gen_741
<b, cons, cons>(q_gen_746, q_gen_745) -> q_gen_741
<b, nil, cons>(q_gen_743, q_gen_742) -> q_gen_741
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_740, q_gen_748, q_gen_749, q_gen_773, q_gen_774, q_gen_775, q_gen_776, q_gen_777},
Q_f={q_gen_740},
Delta=
{
<nil>() -> q_gen_748
<cons>(q_gen_774, q_gen_748) -> q_gen_773
<b>() -> q_gen_774
<z>() -> q_gen_776
<cons, s>(q_gen_749, q_gen_748) -> q_gen_740
<cons, s>(q_gen_775, q_gen_773) -> q_gen_740
<nil, z>() -> q_gen_740
<a, z>() -> q_gen_749
<b, z>() -> q_gen_749
<a, s>(q_gen_776) -> q_gen_775
<b, s>(q_gen_776) -> q_gen_775
<cons, s>(q_gen_775, q_gen_748) -> q_gen_777
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_738, q_gen_752},
Q_f={q_gen_738},
Delta=
{
<a, a>() -> q_gen_738
<a, b>() -> q_gen_738
<b, b>() -> q_gen_738
<b, a>() -> q_gen_752
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_737, q_gen_751},
Q_f={q_gen_737},
Delta=
{
<cons, cons>(q_gen_751, q_gen_737) -> q_gen_737
<nil, nil>() -> q_gen_737
<a, a>() -> q_gen_751
<a, b>() -> q_gen_751
<b, b>() -> q_gen_751
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 10
() -> length([nil, z]) -> 10
() -> leq([a, y]) -> 10
() -> leq([b, b]) -> 10
() -> sort([nil, nil]) -> 10
(insert([x, z, _yc]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _yc)]) -> 10
(insert([y, _dd, _ed]) /\ sort([z, _dd])) -> sort([cons(y, z), _ed]) -> 13
(length([_nd, _od]) /\ length([l, _md]) /\ sort([l, _nd])) -> eq_nat([_md, _od]) -> 13
(length([ll, _id])) -> length([cons(x, ll), s(_id)]) -> 13
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 11
(leq([b, a])) -> BOT -> 11
}
Sat witness: Found: ((insert([y, _dd, _ed]) /\ sort([z, _dd])) -> sort([cons(y, z), _ed]), {
_dd -> nil  ;  _ed -> cons(a, nil)  ;  y -> b  ;  z -> nil
})

-------------------------------------------
Step 23, which took 0.019047 s (model generation: 0.017087,  model checking: 0.001960):

Model:
|_
{
insert -> 
{{{
Q={q_gen_741, q_gen_742, q_gen_743, q_gen_745, q_gen_746},
Q_f={q_gen_741},
Delta=
{
<nil>() -> q_gen_742
<a>() -> q_gen_743
<b>() -> q_gen_743
<cons, cons>(q_gen_746, q_gen_745) -> q_gen_745
<nil, cons>(q_gen_743, q_gen_742) -> q_gen_745
<a, a>() -> q_gen_746
<a, b>() -> q_gen_746
<b, a>() -> q_gen_746
<b, b>() -> q_gen_746
<a, cons, cons>(q_gen_746, q_gen_745) -> q_gen_741
<a, nil, cons>(q_gen_743, q_gen_742) -> q_gen_741
<b, cons, cons>(q_gen_746, q_gen_745) -> q_gen_741
<b, nil, cons>(q_gen_743, q_gen_742) -> q_gen_741
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_740, q_gen_748, q_gen_749, q_gen_773, q_gen_774, q_gen_775, q_gen_776, q_gen_777},
Q_f={q_gen_740},
Delta=
{
<nil>() -> q_gen_748
<cons>(q_gen_774, q_gen_748) -> q_gen_773
<b>() -> q_gen_774
<z>() -> q_gen_776
<cons, s>(q_gen_749, q_gen_748) -> q_gen_740
<cons, s>(q_gen_775, q_gen_773) -> q_gen_740
<nil, z>() -> q_gen_740
<a, z>() -> q_gen_749
<b, z>() -> q_gen_749
<a, s>(q_gen_776) -> q_gen_775
<b, s>(q_gen_776) -> q_gen_775
<cons, s>(q_gen_775, q_gen_748) -> q_gen_777
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_738, q_gen_752},
Q_f={q_gen_738},
Delta=
{
<a, a>() -> q_gen_738
<a, b>() -> q_gen_738
<b, b>() -> q_gen_738
<b, a>() -> q_gen_752
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_737, q_gen_751},
Q_f={q_gen_737},
Delta=
{
<cons, cons>(q_gen_751, q_gen_737) -> q_gen_737
<nil, nil>() -> q_gen_737
<a, a>() -> q_gen_751
<a, b>() -> q_gen_751
<b, a>() -> q_gen_751
<b, b>() -> q_gen_751
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 11
() -> length([nil, z]) -> 11
() -> leq([a, y]) -> 11
() -> leq([b, b]) -> 11
() -> sort([nil, nil]) -> 11
(insert([x, z, _yc]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _yc)]) -> 11
(insert([y, _dd, _ed]) /\ sort([z, _dd])) -> sort([cons(y, z), _ed]) -> 13
(length([_nd, _od]) /\ length([l, _md]) /\ sort([l, _nd])) -> eq_nat([_md, _od]) -> 13
(length([ll, _id])) -> length([cons(x, ll), s(_id)]) -> 16
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 12
(leq([b, a])) -> BOT -> 12
}
Sat witness: Found: ((length([ll, _id])) -> length([cons(x, ll), s(_id)]), {
_id -> s(s(z))  ;  ll -> cons(b, cons(b, nil))  ;  x -> b
})

-------------------------------------------
Step 24, which took 0.020378 s (model generation: 0.018946,  model checking: 0.001432):

Model:
|_
{
insert -> 
{{{
Q={q_gen_741, q_gen_742, q_gen_743, q_gen_745, q_gen_746},
Q_f={q_gen_741},
Delta=
{
<nil>() -> q_gen_742
<a>() -> q_gen_743
<b>() -> q_gen_743
<cons, cons>(q_gen_746, q_gen_745) -> q_gen_745
<nil, cons>(q_gen_743, q_gen_742) -> q_gen_745
<a, a>() -> q_gen_746
<a, b>() -> q_gen_746
<b, a>() -> q_gen_746
<b, b>() -> q_gen_746
<a, cons, cons>(q_gen_746, q_gen_745) -> q_gen_741
<a, nil, cons>(q_gen_743, q_gen_742) -> q_gen_741
<b, cons, cons>(q_gen_746, q_gen_745) -> q_gen_741
<b, nil, cons>(q_gen_743, q_gen_742) -> q_gen_741
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_740, q_gen_748, q_gen_749, q_gen_773, q_gen_774, q_gen_775, q_gen_776, q_gen_777},
Q_f={q_gen_740},
Delta=
{
<nil>() -> q_gen_748
<cons>(q_gen_774, q_gen_748) -> q_gen_773
<cons>(q_gen_774, q_gen_773) -> q_gen_773
<b>() -> q_gen_774
<s>(q_gen_776) -> q_gen_776
<z>() -> q_gen_776
<cons, s>(q_gen_749, q_gen_748) -> q_gen_740
<cons, s>(q_gen_775, q_gen_773) -> q_gen_740
<nil, z>() -> q_gen_740
<a, z>() -> q_gen_749
<b, z>() -> q_gen_749
<a, s>(q_gen_776) -> q_gen_775
<b, s>(q_gen_776) -> q_gen_775
<cons, s>(q_gen_775, q_gen_748) -> q_gen_777
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_738, q_gen_752},
Q_f={q_gen_738},
Delta=
{
<a, a>() -> q_gen_738
<a, b>() -> q_gen_738
<b, b>() -> q_gen_738
<b, a>() -> q_gen_752
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_737, q_gen_751},
Q_f={q_gen_737},
Delta=
{
<cons, cons>(q_gen_751, q_gen_737) -> q_gen_737
<nil, nil>() -> q_gen_737
<a, a>() -> q_gen_751
<a, b>() -> q_gen_751
<b, a>() -> q_gen_751
<b, b>() -> q_gen_751
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 12
() -> length([nil, z]) -> 12
() -> leq([a, y]) -> 12
() -> leq([b, b]) -> 12
() -> sort([nil, nil]) -> 12
(insert([x, z, _yc]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _yc)]) -> 12
(insert([y, _dd, _ed]) /\ sort([z, _dd])) -> sort([cons(y, z), _ed]) -> 13
(length([_nd, _od]) /\ length([l, _md]) /\ sort([l, _nd])) -> eq_nat([_md, _od]) -> 16
(length([ll, _id])) -> length([cons(x, ll), s(_id)]) -> 16
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 13
(leq([b, a])) -> BOT -> 13
}
Sat witness: Found: ((length([_nd, _od]) /\ length([l, _md]) /\ sort([l, _nd])) -> eq_nat([_md, _od]), {
_md -> s(s(z))  ;  _nd -> cons(b, cons(b, nil))  ;  _od -> s(s(s(z)))  ;  l -> cons(b, cons(b, nil))
})

-------------------------------------------
Step 25, which took 0.023087 s (model generation: 0.019871,  model checking: 0.003216):

Model:
|_
{
insert -> 
{{{
Q={q_gen_741, q_gen_742, q_gen_743, q_gen_745, q_gen_746},
Q_f={q_gen_741},
Delta=
{
<nil>() -> q_gen_742
<a>() -> q_gen_743
<b>() -> q_gen_743
<cons, cons>(q_gen_746, q_gen_745) -> q_gen_745
<nil, cons>(q_gen_743, q_gen_742) -> q_gen_745
<a, a>() -> q_gen_746
<a, b>() -> q_gen_746
<b, a>() -> q_gen_746
<b, b>() -> q_gen_746
<a, cons, cons>(q_gen_746, q_gen_745) -> q_gen_741
<a, nil, cons>(q_gen_743, q_gen_742) -> q_gen_741
<b, cons, cons>(q_gen_746, q_gen_745) -> q_gen_741
<b, nil, cons>(q_gen_743, q_gen_742) -> q_gen_741
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_740, q_gen_748, q_gen_749, q_gen_773, q_gen_774, q_gen_775, q_gen_776, q_gen_777, q_gen_789},
Q_f={q_gen_740},
Delta=
{
<cons>(q_gen_774, q_gen_773) -> q_gen_748
<nil>() -> q_gen_748
<cons>(q_gen_774, q_gen_748) -> q_gen_773
<b>() -> q_gen_774
<z>() -> q_gen_776
<s>(q_gen_776) -> q_gen_789
<cons, s>(q_gen_749, q_gen_748) -> q_gen_740
<cons, s>(q_gen_775, q_gen_773) -> q_gen_740
<nil, z>() -> q_gen_740
<a, z>() -> q_gen_749
<b, s>(q_gen_789) -> q_gen_749
<b, z>() -> q_gen_749
<a, s>(q_gen_776) -> q_gen_775
<b, s>(q_gen_776) -> q_gen_775
<cons, s>(q_gen_749, q_gen_773) -> q_gen_777
<cons, s>(q_gen_775, q_gen_748) -> q_gen_777
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_738, q_gen_752},
Q_f={q_gen_738},
Delta=
{
<a, a>() -> q_gen_738
<a, b>() -> q_gen_738
<b, b>() -> q_gen_738
<b, a>() -> q_gen_752
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_737, q_gen_751},
Q_f={q_gen_737},
Delta=
{
<cons, cons>(q_gen_751, q_gen_737) -> q_gen_737
<nil, nil>() -> q_gen_737
<a, a>() -> q_gen_751
<a, b>() -> q_gen_751
<b, a>() -> q_gen_751
<b, b>() -> q_gen_751
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 13
() -> length([nil, z]) -> 13
() -> leq([a, y]) -> 13
() -> leq([b, b]) -> 13
() -> sort([nil, nil]) -> 13
(insert([x, z, _yc]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _yc)]) -> 13
(insert([y, _dd, _ed]) /\ sort([z, _dd])) -> sort([cons(y, z), _ed]) -> 14
(length([_nd, _od]) /\ length([l, _md]) /\ sort([l, _nd])) -> eq_nat([_md, _od]) -> 16
(length([ll, _id])) -> length([cons(x, ll), s(_id)]) -> 19
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 14
(leq([b, a])) -> BOT -> 14
}
Sat witness: Found: ((length([ll, _id])) -> length([cons(x, ll), s(_id)]), {
_id -> s(s(s(z)))  ;  ll -> cons(b, nil)  ;  x -> b
})

-------------------------------------------
Step 26, which took 0.024719 s (model generation: 0.022532,  model checking: 0.002187):

Model:
|_
{
insert -> 
{{{
Q={q_gen_741, q_gen_742, q_gen_743, q_gen_745, q_gen_746},
Q_f={q_gen_741},
Delta=
{
<nil>() -> q_gen_742
<a>() -> q_gen_743
<b>() -> q_gen_743
<cons, cons>(q_gen_746, q_gen_745) -> q_gen_745
<nil, cons>(q_gen_743, q_gen_742) -> q_gen_745
<a, a>() -> q_gen_746
<a, b>() -> q_gen_746
<b, a>() -> q_gen_746
<b, b>() -> q_gen_746
<a, cons, cons>(q_gen_746, q_gen_745) -> q_gen_741
<a, nil, cons>(q_gen_743, q_gen_742) -> q_gen_741
<b, cons, cons>(q_gen_746, q_gen_745) -> q_gen_741
<b, nil, cons>(q_gen_743, q_gen_742) -> q_gen_741
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_740, q_gen_748, q_gen_749, q_gen_773, q_gen_774, q_gen_775, q_gen_776, q_gen_777, q_gen_789},
Q_f={q_gen_740},
Delta=
{
<cons>(q_gen_774, q_gen_773) -> q_gen_748
<nil>() -> q_gen_748
<cons>(q_gen_774, q_gen_748) -> q_gen_773
<b>() -> q_gen_774
<s>(q_gen_789) -> q_gen_776
<z>() -> q_gen_776
<s>(q_gen_776) -> q_gen_789
<cons, s>(q_gen_749, q_gen_748) -> q_gen_740
<cons, s>(q_gen_775, q_gen_773) -> q_gen_740
<nil, z>() -> q_gen_740
<a, z>() -> q_gen_749
<b, s>(q_gen_789) -> q_gen_749
<b, z>() -> q_gen_749
<a, s>(q_gen_776) -> q_gen_775
<b, s>(q_gen_776) -> q_gen_775
<cons, s>(q_gen_749, q_gen_773) -> q_gen_777
<cons, s>(q_gen_775, q_gen_748) -> q_gen_777
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_738, q_gen_752},
Q_f={q_gen_738},
Delta=
{
<a, a>() -> q_gen_738
<a, b>() -> q_gen_738
<b, b>() -> q_gen_738
<b, a>() -> q_gen_752
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_737, q_gen_751},
Q_f={q_gen_737},
Delta=
{
<cons, cons>(q_gen_751, q_gen_737) -> q_gen_737
<nil, nil>() -> q_gen_737
<a, a>() -> q_gen_751
<a, b>() -> q_gen_751
<b, a>() -> q_gen_751
<b, b>() -> q_gen_751
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 14
() -> length([nil, z]) -> 14
() -> leq([a, y]) -> 14
() -> leq([b, b]) -> 14
() -> sort([nil, nil]) -> 14
(insert([x, z, _yc]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _yc)]) -> 14
(insert([y, _dd, _ed]) /\ sort([z, _dd])) -> sort([cons(y, z), _ed]) -> 15
(length([_nd, _od]) /\ length([l, _md]) /\ sort([l, _nd])) -> eq_nat([_md, _od]) -> 19
(length([ll, _id])) -> length([cons(x, ll), s(_id)]) -> 19
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 15
(leq([b, a])) -> BOT -> 15
}
Sat witness: Found: ((length([_nd, _od]) /\ length([l, _md]) /\ sort([l, _nd])) -> eq_nat([_md, _od]), {
_md -> s(z)  ;  _nd -> cons(b, nil)  ;  _od -> s(s(s(z)))  ;  l -> cons(a, nil)
})

-------------------------------------------
Step 27, which took 0.024260 s (model generation: 0.022721,  model checking: 0.001539):

Model:
|_
{
insert -> 
{{{
Q={q_gen_741, q_gen_742, q_gen_743, q_gen_745, q_gen_746},
Q_f={q_gen_741},
Delta=
{
<nil>() -> q_gen_742
<a>() -> q_gen_743
<b>() -> q_gen_743
<cons, cons>(q_gen_746, q_gen_745) -> q_gen_745
<nil, cons>(q_gen_743, q_gen_742) -> q_gen_745
<a, a>() -> q_gen_746
<a, b>() -> q_gen_746
<b, a>() -> q_gen_746
<b, b>() -> q_gen_746
<a, cons, cons>(q_gen_746, q_gen_745) -> q_gen_741
<a, nil, cons>(q_gen_743, q_gen_742) -> q_gen_741
<b, cons, cons>(q_gen_746, q_gen_745) -> q_gen_741
<b, nil, cons>(q_gen_743, q_gen_742) -> q_gen_741
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_740, q_gen_748, q_gen_749, q_gen_773, q_gen_774, q_gen_775, q_gen_776, q_gen_777},
Q_f={q_gen_740},
Delta=
{
<nil>() -> q_gen_748
<cons>(q_gen_774, q_gen_748) -> q_gen_773
<cons>(q_gen_774, q_gen_773) -> q_gen_773
<b>() -> q_gen_774
<s>(q_gen_776) -> q_gen_776
<z>() -> q_gen_776
<cons, s>(q_gen_749, q_gen_748) -> q_gen_740
<cons, s>(q_gen_775, q_gen_773) -> q_gen_740
<nil, z>() -> q_gen_740
<a, z>() -> q_gen_749
<b, z>() -> q_gen_749
<a, s>(q_gen_776) -> q_gen_775
<b, s>(q_gen_776) -> q_gen_775
<cons, s>(q_gen_775, q_gen_748) -> q_gen_777
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_738, q_gen_752},
Q_f={q_gen_738},
Delta=
{
<a, a>() -> q_gen_738
<a, b>() -> q_gen_738
<b, b>() -> q_gen_738
<b, a>() -> q_gen_752
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_737, q_gen_750, q_gen_751, q_gen_791},
Q_f={q_gen_737, q_gen_750},
Delta=
{
<nil, nil>() -> q_gen_737
<cons, cons>(q_gen_751, q_gen_737) -> q_gen_750
<a, a>() -> q_gen_751
<a, b>() -> q_gen_751
<b, a>() -> q_gen_751
<b, b>() -> q_gen_751
<cons, cons>(q_gen_751, q_gen_750) -> q_gen_791
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 15
() -> length([nil, z]) -> 15
() -> leq([a, y]) -> 15
() -> leq([b, b]) -> 15
() -> sort([nil, nil]) -> 15
(insert([x, z, _yc]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _yc)]) -> 15
(insert([y, _dd, _ed]) /\ sort([z, _dd])) -> sort([cons(y, z), _ed]) -> 18
(length([_nd, _od]) /\ length([l, _md]) /\ sort([l, _nd])) -> eq_nat([_md, _od]) -> 19
(length([ll, _id])) -> length([cons(x, ll), s(_id)]) -> 19
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 16
(leq([b, a])) -> BOT -> 16
}
Sat witness: Found: ((insert([y, _dd, _ed]) /\ sort([z, _dd])) -> sort([cons(y, z), _ed]), {
_dd -> cons(b, nil)  ;  _ed -> cons(b, cons(b, nil))  ;  y -> a  ;  z -> cons(a, nil)
})

-------------------------------------------
Step 28, which took 0.025584 s (model generation: 0.024056,  model checking: 0.001528):

Model:
|_
{
insert -> 
{{{
Q={q_gen_741, q_gen_742, q_gen_743, q_gen_745, q_gen_746},
Q_f={q_gen_741},
Delta=
{
<nil>() -> q_gen_742
<a>() -> q_gen_743
<b>() -> q_gen_743
<cons, cons>(q_gen_746, q_gen_745) -> q_gen_745
<nil, cons>(q_gen_743, q_gen_742) -> q_gen_745
<a, a>() -> q_gen_746
<a, b>() -> q_gen_746
<b, a>() -> q_gen_746
<b, b>() -> q_gen_746
<a, cons, cons>(q_gen_746, q_gen_745) -> q_gen_741
<a, nil, cons>(q_gen_743, q_gen_742) -> q_gen_741
<b, cons, cons>(q_gen_746, q_gen_745) -> q_gen_741
<b, nil, cons>(q_gen_743, q_gen_742) -> q_gen_741
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_740, q_gen_748, q_gen_749, q_gen_773, q_gen_774, q_gen_775, q_gen_776, q_gen_777},
Q_f={q_gen_740},
Delta=
{
<nil>() -> q_gen_748
<cons>(q_gen_774, q_gen_748) -> q_gen_773
<cons>(q_gen_774, q_gen_773) -> q_gen_773
<b>() -> q_gen_774
<s>(q_gen_776) -> q_gen_776
<z>() -> q_gen_776
<cons, s>(q_gen_749, q_gen_748) -> q_gen_740
<cons, s>(q_gen_775, q_gen_773) -> q_gen_740
<nil, z>() -> q_gen_740
<a, z>() -> q_gen_749
<b, z>() -> q_gen_749
<a, s>(q_gen_776) -> q_gen_775
<b, s>(q_gen_776) -> q_gen_775
<cons, s>(q_gen_775, q_gen_748) -> q_gen_777
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_738, q_gen_752},
Q_f={q_gen_738},
Delta=
{
<a, a>() -> q_gen_738
<a, b>() -> q_gen_738
<b, b>() -> q_gen_738
<b, a>() -> q_gen_752
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_737, q_gen_750, q_gen_751, q_gen_764, q_gen_791},
Q_f={q_gen_737, q_gen_750},
Delta=
{
<cons, cons>(q_gen_764, q_gen_737) -> q_gen_737
<nil, nil>() -> q_gen_737
<cons, cons>(q_gen_751, q_gen_737) -> q_gen_750
<b, a>() -> q_gen_751
<b, b>() -> q_gen_751
<a, a>() -> q_gen_764
<a, b>() -> q_gen_764
<cons, cons>(q_gen_751, q_gen_750) -> q_gen_791
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 16
() -> length([nil, z]) -> 16
() -> leq([a, y]) -> 16
() -> leq([b, b]) -> 16
() -> sort([nil, nil]) -> 16
(insert([x, z, _yc]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _yc)]) -> 16
(insert([y, _dd, _ed]) /\ sort([z, _dd])) -> sort([cons(y, z), _ed]) -> 21
(length([_nd, _od]) /\ length([l, _md]) /\ sort([l, _nd])) -> eq_nat([_md, _od]) -> 19
(length([ll, _id])) -> length([cons(x, ll), s(_id)]) -> 19
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 17
(leq([b, a])) -> BOT -> 17
}
Sat witness: Found: ((insert([y, _dd, _ed]) /\ sort([z, _dd])) -> sort([cons(y, z), _ed]), {
_dd -> cons(a, nil)  ;  _ed -> cons(b, cons(b, nil))  ;  y -> b  ;  z -> cons(b, nil)
})

-------------------------------------------
Step 29, which took 0.029028 s (model generation: 0.025850,  model checking: 0.003178):

Model:
|_
{
insert -> 
{{{
Q={q_gen_741, q_gen_742, q_gen_743, q_gen_745, q_gen_746},
Q_f={q_gen_741},
Delta=
{
<nil>() -> q_gen_742
<a>() -> q_gen_743
<b>() -> q_gen_743
<cons, cons>(q_gen_746, q_gen_745) -> q_gen_745
<nil, cons>(q_gen_743, q_gen_742) -> q_gen_745
<a, a>() -> q_gen_746
<a, b>() -> q_gen_746
<b, a>() -> q_gen_746
<b, b>() -> q_gen_746
<a, cons, cons>(q_gen_746, q_gen_745) -> q_gen_741
<a, nil, cons>(q_gen_743, q_gen_742) -> q_gen_741
<b, cons, cons>(q_gen_746, q_gen_745) -> q_gen_741
<b, nil, cons>(q_gen_743, q_gen_742) -> q_gen_741
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_740, q_gen_748, q_gen_749, q_gen_773, q_gen_774, q_gen_775, q_gen_776, q_gen_777, q_gen_787, q_gen_788, q_gen_789},
Q_f={q_gen_740},
Delta=
{
<nil>() -> q_gen_748
<cons>(q_gen_774, q_gen_748) -> q_gen_773
<b>() -> q_gen_774
<s>(q_gen_789) -> q_gen_776
<z>() -> q_gen_776
<cons>(q_gen_774, q_gen_773) -> q_gen_787
<s>(q_gen_776) -> q_gen_789
<cons, s>(q_gen_749, q_gen_748) -> q_gen_740
<cons, s>(q_gen_775, q_gen_773) -> q_gen_740
<cons, s>(q_gen_788, q_gen_787) -> q_gen_740
<nil, z>() -> q_gen_740
<a, z>() -> q_gen_749
<b, z>() -> q_gen_749
<a, s>(q_gen_776) -> q_gen_775
<b, s>(q_gen_776) -> q_gen_775
<cons, s>(q_gen_775, q_gen_748) -> q_gen_777
<cons, s>(q_gen_788, q_gen_748) -> q_gen_777
<cons, s>(q_gen_788, q_gen_773) -> q_gen_777
<b, s>(q_gen_789) -> q_gen_788
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_738, q_gen_752},
Q_f={q_gen_738},
Delta=
{
<a, a>() -> q_gen_738
<a, b>() -> q_gen_738
<b, b>() -> q_gen_738
<b, a>() -> q_gen_752
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_737, q_gen_751},
Q_f={q_gen_737},
Delta=
{
<cons, cons>(q_gen_751, q_gen_737) -> q_gen_737
<nil, nil>() -> q_gen_737
<a, a>() -> q_gen_751
<a, b>() -> q_gen_751
<b, a>() -> q_gen_751
<b, b>() -> q_gen_751
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 17
() -> length([nil, z]) -> 17
() -> leq([a, y]) -> 17
() -> leq([b, b]) -> 17
() -> sort([nil, nil]) -> 17
(insert([x, z, _yc]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _yc)]) -> 17
(insert([y, _dd, _ed]) /\ sort([z, _dd])) -> sort([cons(y, z), _ed]) -> 21
(length([_nd, _od]) /\ length([l, _md]) /\ sort([l, _nd])) -> eq_nat([_md, _od]) -> 19
(length([ll, _id])) -> length([cons(x, ll), s(_id)]) -> 22
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 18
(leq([b, a])) -> BOT -> 18
}
Sat witness: Found: ((length([ll, _id])) -> length([cons(x, ll), s(_id)]), {
_id -> s(z)  ;  ll -> cons(a, nil)  ;  x -> b
})

-------------------------------------------
Step 30, which took 0.028827 s (model generation: 0.026837,  model checking: 0.001990):

Model:
|_
{
insert -> 
{{{
Q={q_gen_741, q_gen_742, q_gen_743, q_gen_745, q_gen_746},
Q_f={q_gen_741},
Delta=
{
<nil>() -> q_gen_742
<a>() -> q_gen_743
<b>() -> q_gen_743
<cons, cons>(q_gen_746, q_gen_745) -> q_gen_745
<nil, cons>(q_gen_743, q_gen_742) -> q_gen_745
<a, a>() -> q_gen_746
<a, b>() -> q_gen_746
<b, a>() -> q_gen_746
<b, b>() -> q_gen_746
<a, cons, cons>(q_gen_746, q_gen_745) -> q_gen_741
<a, nil, cons>(q_gen_743, q_gen_742) -> q_gen_741
<b, cons, cons>(q_gen_746, q_gen_745) -> q_gen_741
<b, nil, cons>(q_gen_743, q_gen_742) -> q_gen_741
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_740, q_gen_748, q_gen_749, q_gen_773, q_gen_774, q_gen_775, q_gen_776, q_gen_777, q_gen_787, q_gen_788, q_gen_789},
Q_f={q_gen_740},
Delta=
{
<nil>() -> q_gen_748
<cons>(q_gen_774, q_gen_748) -> q_gen_773
<a>() -> q_gen_774
<b>() -> q_gen_774
<s>(q_gen_789) -> q_gen_776
<z>() -> q_gen_776
<cons>(q_gen_774, q_gen_773) -> q_gen_787
<s>(q_gen_776) -> q_gen_789
<cons, s>(q_gen_749, q_gen_748) -> q_gen_740
<cons, s>(q_gen_775, q_gen_773) -> q_gen_740
<cons, s>(q_gen_788, q_gen_787) -> q_gen_740
<nil, z>() -> q_gen_740
<a, z>() -> q_gen_749
<b, z>() -> q_gen_749
<a, s>(q_gen_776) -> q_gen_775
<b, s>(q_gen_776) -> q_gen_775
<cons, s>(q_gen_775, q_gen_748) -> q_gen_777
<cons, s>(q_gen_788, q_gen_748) -> q_gen_777
<cons, s>(q_gen_788, q_gen_773) -> q_gen_777
<b, s>(q_gen_789) -> q_gen_788
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_738, q_gen_752},
Q_f={q_gen_738},
Delta=
{
<a, a>() -> q_gen_738
<a, b>() -> q_gen_738
<b, b>() -> q_gen_738
<b, a>() -> q_gen_752
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_737, q_gen_751},
Q_f={q_gen_737},
Delta=
{
<cons, cons>(q_gen_751, q_gen_737) -> q_gen_737
<nil, nil>() -> q_gen_737
<a, a>() -> q_gen_751
<a, b>() -> q_gen_751
<b, a>() -> q_gen_751
<b, b>() -> q_gen_751
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 18
() -> length([nil, z]) -> 18
() -> leq([a, y]) -> 18
() -> leq([b, b]) -> 18
() -> sort([nil, nil]) -> 18
(insert([x, z, _yc]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _yc)]) -> 18
(insert([y, _dd, _ed]) /\ sort([z, _dd])) -> sort([cons(y, z), _ed]) -> 21
(length([_nd, _od]) /\ length([l, _md]) /\ sort([l, _nd])) -> eq_nat([_md, _od]) -> 22
(length([ll, _id])) -> length([cons(x, ll), s(_id)]) -> 22
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 19
(leq([b, a])) -> BOT -> 19
}
Sat witness: Found: ((length([_nd, _od]) /\ length([l, _md]) /\ sort([l, _nd])) -> eq_nat([_md, _od]), {
_md -> s(s(s(z)))  ;  _nd -> cons(b, cons(b, cons(b, nil)))  ;  _od -> s(s(s(s(s(z)))))  ;  l -> cons(b, cons(b, cons(b, nil)))
})

-------------------------------------------
Step 31, which took 0.032899 s (model generation: 0.030303,  model checking: 0.002596):

Model:
|_
{
insert -> 
{{{
Q={q_gen_741, q_gen_742, q_gen_743, q_gen_745, q_gen_746},
Q_f={q_gen_741},
Delta=
{
<nil>() -> q_gen_742
<a>() -> q_gen_743
<b>() -> q_gen_743
<cons, cons>(q_gen_746, q_gen_745) -> q_gen_745
<nil, cons>(q_gen_743, q_gen_742) -> q_gen_745
<a, a>() -> q_gen_746
<a, b>() -> q_gen_746
<b, a>() -> q_gen_746
<b, b>() -> q_gen_746
<a, cons, cons>(q_gen_746, q_gen_745) -> q_gen_741
<a, nil, cons>(q_gen_743, q_gen_742) -> q_gen_741
<b, cons, cons>(q_gen_746, q_gen_745) -> q_gen_741
<b, nil, cons>(q_gen_743, q_gen_742) -> q_gen_741
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_740, q_gen_748, q_gen_749, q_gen_773, q_gen_774, q_gen_775, q_gen_776, q_gen_777, q_gen_787, q_gen_788, q_gen_789, q_gen_795},
Q_f={q_gen_740},
Delta=
{
<nil>() -> q_gen_748
<cons>(q_gen_774, q_gen_748) -> q_gen_773
<a>() -> q_gen_774
<b>() -> q_gen_774
<z>() -> q_gen_776
<cons>(q_gen_774, q_gen_773) -> q_gen_787
<s>(q_gen_776) -> q_gen_789
<s>(q_gen_789) -> q_gen_795
<s>(q_gen_795) -> q_gen_795
<cons, s>(q_gen_749, q_gen_748) -> q_gen_740
<cons, s>(q_gen_775, q_gen_773) -> q_gen_740
<cons, s>(q_gen_788, q_gen_787) -> q_gen_740
<nil, z>() -> q_gen_740
<a, z>() -> q_gen_749
<b, s>(q_gen_795) -> q_gen_749
<b, z>() -> q_gen_749
<a, s>(q_gen_776) -> q_gen_775
<b, s>(q_gen_776) -> q_gen_775
<cons, s>(q_gen_749, q_gen_773) -> q_gen_777
<cons, s>(q_gen_749, q_gen_787) -> q_gen_777
<cons, s>(q_gen_775, q_gen_748) -> q_gen_777
<cons, s>(q_gen_788, q_gen_748) -> q_gen_777
<cons, s>(q_gen_788, q_gen_773) -> q_gen_777
<b, s>(q_gen_789) -> q_gen_788
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_738, q_gen_752},
Q_f={q_gen_738},
Delta=
{
<a, a>() -> q_gen_738
<a, b>() -> q_gen_738
<b, b>() -> q_gen_738
<b, a>() -> q_gen_752
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_737, q_gen_751},
Q_f={q_gen_737},
Delta=
{
<cons, cons>(q_gen_751, q_gen_737) -> q_gen_737
<nil, nil>() -> q_gen_737
<a, a>() -> q_gen_751
<a, b>() -> q_gen_751
<b, a>() -> q_gen_751
<b, b>() -> q_gen_751
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 19
() -> length([nil, z]) -> 19
() -> leq([a, y]) -> 19
() -> leq([b, b]) -> 19
() -> sort([nil, nil]) -> 19
(insert([x, z, _yc]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _yc)]) -> 19
(insert([y, _dd, _ed]) /\ sort([z, _dd])) -> sort([cons(y, z), _ed]) -> 22
(length([_nd, _od]) /\ length([l, _md]) /\ sort([l, _nd])) -> eq_nat([_md, _od]) -> 22
(length([ll, _id])) -> length([cons(x, ll), s(_id)]) -> 25
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 20
(leq([b, a])) -> BOT -> 20
}
Sat witness: Found: ((length([ll, _id])) -> length([cons(x, ll), s(_id)]), {
_id -> s(s(s(s(z))))  ;  ll -> cons(b, nil)  ;  x -> b
})

-------------------------------------------
Step 32, which took 0.035837 s (model generation: 0.034134,  model checking: 0.001703):

Model:
|_
{
insert -> 
{{{
Q={q_gen_741, q_gen_742, q_gen_743, q_gen_745, q_gen_746, q_gen_759, q_gen_796},
Q_f={q_gen_741},
Delta=
{
<nil>() -> q_gen_742
<a>() -> q_gen_743
<b>() -> q_gen_743
<cons, cons>(q_gen_746, q_gen_745) -> q_gen_745
<cons, cons>(q_gen_759, q_gen_745) -> q_gen_745
<nil, cons>(q_gen_743, q_gen_742) -> q_gen_745
<a, a>() -> q_gen_746
<b, b>() -> q_gen_746
<a, b>() -> q_gen_759
<b, a>() -> q_gen_759
<a, cons, cons>(q_gen_759, q_gen_745) -> q_gen_741
<a, nil, cons>(q_gen_743, q_gen_742) -> q_gen_741
<b, cons, cons>(q_gen_746, q_gen_745) -> q_gen_741
<b, nil, cons>(q_gen_743, q_gen_742) -> q_gen_741
<a, cons, cons>(q_gen_746, q_gen_745) -> q_gen_796
<b, cons, cons>(q_gen_759, q_gen_745) -> q_gen_796
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_740, q_gen_748, q_gen_749, q_gen_773, q_gen_774, q_gen_775, q_gen_776, q_gen_777},
Q_f={q_gen_740},
Delta=
{
<nil>() -> q_gen_748
<cons>(q_gen_774, q_gen_748) -> q_gen_773
<cons>(q_gen_774, q_gen_773) -> q_gen_773
<a>() -> q_gen_774
<b>() -> q_gen_774
<s>(q_gen_776) -> q_gen_776
<z>() -> q_gen_776
<cons, s>(q_gen_749, q_gen_748) -> q_gen_740
<cons, s>(q_gen_775, q_gen_773) -> q_gen_740
<nil, z>() -> q_gen_740
<a, z>() -> q_gen_749
<b, z>() -> q_gen_749
<a, s>(q_gen_776) -> q_gen_775
<b, s>(q_gen_776) -> q_gen_775
<cons, s>(q_gen_775, q_gen_748) -> q_gen_777
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_738, q_gen_752},
Q_f={q_gen_738},
Delta=
{
<a, a>() -> q_gen_738
<a, b>() -> q_gen_738
<b, b>() -> q_gen_738
<b, a>() -> q_gen_752
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_737, q_gen_750, q_gen_751, q_gen_791},
Q_f={q_gen_737, q_gen_750},
Delta=
{
<nil, nil>() -> q_gen_737
<cons, cons>(q_gen_751, q_gen_737) -> q_gen_750
<a, a>() -> q_gen_751
<a, b>() -> q_gen_751
<b, a>() -> q_gen_751
<b, b>() -> q_gen_751
<cons, cons>(q_gen_751, q_gen_750) -> q_gen_791
<cons, cons>(q_gen_751, q_gen_791) -> q_gen_791
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 20
() -> length([nil, z]) -> 20
() -> leq([a, y]) -> 20
() -> leq([b, b]) -> 20
() -> sort([nil, nil]) -> 20
(insert([x, z, _yc]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _yc)]) -> 20
(insert([y, _dd, _ed]) /\ sort([z, _dd])) -> sort([cons(y, z), _ed]) -> 22
(length([_nd, _od]) /\ length([l, _md]) /\ sort([l, _nd])) -> eq_nat([_md, _od]) -> 22
(length([ll, _id])) -> length([cons(x, ll), s(_id)]) -> 25
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 23
(leq([b, a])) -> BOT -> 21
}
Sat witness: Found: ((leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]), {
x -> a  ;  y -> a  ;  z -> nil
})

-------------------------------------------
Step 33, which took 0.036555 s (model generation: 0.034935,  model checking: 0.001620):

Model:
|_
{
insert -> 
{{{
Q={q_gen_741, q_gen_742, q_gen_743, q_gen_745, q_gen_746},
Q_f={q_gen_741},
Delta=
{
<nil>() -> q_gen_742
<a>() -> q_gen_743
<b>() -> q_gen_743
<cons, cons>(q_gen_746, q_gen_745) -> q_gen_745
<nil, cons>(q_gen_743, q_gen_742) -> q_gen_745
<a, a>() -> q_gen_746
<a, b>() -> q_gen_746
<b, a>() -> q_gen_746
<b, b>() -> q_gen_746
<a, cons, cons>(q_gen_746, q_gen_745) -> q_gen_741
<a, nil, cons>(q_gen_743, q_gen_742) -> q_gen_741
<b, cons, cons>(q_gen_746, q_gen_745) -> q_gen_741
<b, nil, cons>(q_gen_743, q_gen_742) -> q_gen_741
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_740, q_gen_748, q_gen_749, q_gen_773, q_gen_774, q_gen_775, q_gen_776, q_gen_777, q_gen_787, q_gen_788, q_gen_789, q_gen_795},
Q_f={q_gen_740},
Delta=
{
<nil>() -> q_gen_748
<cons>(q_gen_774, q_gen_748) -> q_gen_773
<a>() -> q_gen_774
<b>() -> q_gen_774
<z>() -> q_gen_776
<cons>(q_gen_774, q_gen_773) -> q_gen_787
<s>(q_gen_776) -> q_gen_789
<s>(q_gen_789) -> q_gen_795
<s>(q_gen_795) -> q_gen_795
<cons, s>(q_gen_749, q_gen_748) -> q_gen_740
<cons, s>(q_gen_749, q_gen_773) -> q_gen_740
<cons, s>(q_gen_775, q_gen_773) -> q_gen_740
<cons, s>(q_gen_788, q_gen_787) -> q_gen_740
<nil, z>() -> q_gen_740
<a, z>() -> q_gen_749
<b, s>(q_gen_795) -> q_gen_749
<b, z>() -> q_gen_749
<a, s>(q_gen_776) -> q_gen_775
<b, s>(q_gen_776) -> q_gen_775
<cons, s>(q_gen_749, q_gen_787) -> q_gen_777
<cons, s>(q_gen_775, q_gen_748) -> q_gen_777
<cons, s>(q_gen_788, q_gen_748) -> q_gen_777
<cons, s>(q_gen_788, q_gen_773) -> q_gen_777
<b, s>(q_gen_789) -> q_gen_788
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_738, q_gen_752},
Q_f={q_gen_738},
Delta=
{
<a, a>() -> q_gen_738
<a, b>() -> q_gen_738
<b, b>() -> q_gen_738
<b, a>() -> q_gen_752
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_737, q_gen_751},
Q_f={q_gen_737},
Delta=
{
<cons, cons>(q_gen_751, q_gen_737) -> q_gen_737
<nil, nil>() -> q_gen_737
<a, a>() -> q_gen_751
<a, b>() -> q_gen_751
<b, a>() -> q_gen_751
<b, b>() -> q_gen_751
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 21
() -> length([nil, z]) -> 21
() -> leq([a, y]) -> 21
() -> leq([b, b]) -> 21
() -> sort([nil, nil]) -> 21
(insert([x, z, _yc]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _yc)]) -> 21
(insert([y, _dd, _ed]) /\ sort([z, _dd])) -> sort([cons(y, z), _ed]) -> 22
(length([_nd, _od]) /\ length([l, _md]) /\ sort([l, _nd])) -> eq_nat([_md, _od]) -> 25
(length([ll, _id])) -> length([cons(x, ll), s(_id)]) -> 25
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 23
(leq([b, a])) -> BOT -> 22
}
Sat witness: Found: ((length([_nd, _od]) /\ length([l, _md]) /\ sort([l, _nd])) -> eq_nat([_md, _od]), {
_md -> s(z)  ;  _nd -> cons(b, nil)  ;  _od -> s(s(s(s(z))))  ;  l -> cons(a, nil)
})

-------------------------------------------
Step 34, which took 0.037579 s (model generation: 0.034230,  model checking: 0.003349):

Model:
|_
{
insert -> 
{{{
Q={q_gen_741, q_gen_742, q_gen_743, q_gen_745, q_gen_746},
Q_f={q_gen_741},
Delta=
{
<nil>() -> q_gen_742
<a>() -> q_gen_743
<b>() -> q_gen_743
<cons, cons>(q_gen_746, q_gen_745) -> q_gen_745
<nil, cons>(q_gen_743, q_gen_742) -> q_gen_745
<a, a>() -> q_gen_746
<a, b>() -> q_gen_746
<b, a>() -> q_gen_746
<b, b>() -> q_gen_746
<a, cons, cons>(q_gen_746, q_gen_745) -> q_gen_741
<a, nil, cons>(q_gen_743, q_gen_742) -> q_gen_741
<b, cons, cons>(q_gen_746, q_gen_745) -> q_gen_741
<b, nil, cons>(q_gen_743, q_gen_742) -> q_gen_741
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_740, q_gen_748, q_gen_749, q_gen_773, q_gen_774, q_gen_775, q_gen_776, q_gen_777, q_gen_787, q_gen_788, q_gen_789, q_gen_795},
Q_f={q_gen_740},
Delta=
{
<nil>() -> q_gen_748
<cons>(q_gen_774, q_gen_748) -> q_gen_773
<a>() -> q_gen_774
<b>() -> q_gen_774
<z>() -> q_gen_776
<cons>(q_gen_774, q_gen_773) -> q_gen_787
<s>(q_gen_776) -> q_gen_789
<s>(q_gen_789) -> q_gen_795
<s>(q_gen_795) -> q_gen_795
<cons, s>(q_gen_749, q_gen_748) -> q_gen_740
<cons, s>(q_gen_775, q_gen_773) -> q_gen_740
<cons, s>(q_gen_788, q_gen_787) -> q_gen_740
<nil, z>() -> q_gen_740
<a, z>() -> q_gen_749
<b, z>() -> q_gen_749
<a, s>(q_gen_776) -> q_gen_775
<b, s>(q_gen_776) -> q_gen_775
<b, s>(q_gen_795) -> q_gen_775
<cons, s>(q_gen_775, q_gen_748) -> q_gen_777
<cons, s>(q_gen_775, q_gen_787) -> q_gen_777
<cons, s>(q_gen_788, q_gen_748) -> q_gen_777
<cons, s>(q_gen_788, q_gen_773) -> q_gen_777
<b, s>(q_gen_789) -> q_gen_788
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_738, q_gen_752},
Q_f={q_gen_738},
Delta=
{
<a, a>() -> q_gen_738
<a, b>() -> q_gen_738
<b, b>() -> q_gen_738
<b, a>() -> q_gen_752
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_737, q_gen_751},
Q_f={q_gen_737},
Delta=
{
<cons, cons>(q_gen_751, q_gen_737) -> q_gen_737
<nil, nil>() -> q_gen_737
<a, a>() -> q_gen_751
<a, b>() -> q_gen_751
<b, a>() -> q_gen_751
<b, b>() -> q_gen_751
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 22
() -> length([nil, z]) -> 22
() -> leq([a, y]) -> 22
() -> leq([b, b]) -> 22
() -> sort([nil, nil]) -> 22
(insert([x, z, _yc]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _yc)]) -> 22
(insert([y, _dd, _ed]) /\ sort([z, _dd])) -> sort([cons(y, z), _ed]) -> 23
(length([_nd, _od]) /\ length([l, _md]) /\ sort([l, _nd])) -> eq_nat([_md, _od]) -> 25
(length([ll, _id])) -> length([cons(x, ll), s(_id)]) -> 28
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 24
(leq([b, a])) -> BOT -> 23
}
Sat witness: Found: ((length([ll, _id])) -> length([cons(x, ll), s(_id)]), {
_id -> s(s(s(s(z))))  ;  ll -> cons(b, cons(b, nil))  ;  x -> b
})

-------------------------------------------
Step 35, which took 0.038576 s (model generation: 0.035567,  model checking: 0.003009):

Model:
|_
{
insert -> 
{{{
Q={q_gen_741, q_gen_742, q_gen_743, q_gen_745, q_gen_746},
Q_f={q_gen_741},
Delta=
{
<nil>() -> q_gen_742
<a>() -> q_gen_743
<b>() -> q_gen_743
<cons, cons>(q_gen_746, q_gen_745) -> q_gen_745
<nil, cons>(q_gen_743, q_gen_742) -> q_gen_745
<a, a>() -> q_gen_746
<a, b>() -> q_gen_746
<b, a>() -> q_gen_746
<b, b>() -> q_gen_746
<a, cons, cons>(q_gen_746, q_gen_745) -> q_gen_741
<a, nil, cons>(q_gen_743, q_gen_742) -> q_gen_741
<b, cons, cons>(q_gen_746, q_gen_745) -> q_gen_741
<b, nil, cons>(q_gen_743, q_gen_742) -> q_gen_741
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_740, q_gen_748, q_gen_749, q_gen_773, q_gen_774, q_gen_775, q_gen_776, q_gen_777, q_gen_787, q_gen_788, q_gen_789, q_gen_795},
Q_f={q_gen_740},
Delta=
{
<nil>() -> q_gen_748
<cons>(q_gen_774, q_gen_748) -> q_gen_773
<a>() -> q_gen_774
<b>() -> q_gen_774
<s>(q_gen_795) -> q_gen_776
<z>() -> q_gen_776
<cons>(q_gen_774, q_gen_773) -> q_gen_787
<s>(q_gen_776) -> q_gen_789
<s>(q_gen_789) -> q_gen_795
<cons, s>(q_gen_749, q_gen_748) -> q_gen_740
<cons, s>(q_gen_775, q_gen_773) -> q_gen_740
<cons, s>(q_gen_788, q_gen_787) -> q_gen_740
<nil, z>() -> q_gen_740
<a, z>() -> q_gen_749
<b, z>() -> q_gen_749
<a, s>(q_gen_776) -> q_gen_775
<b, s>(q_gen_776) -> q_gen_775
<cons, s>(q_gen_775, q_gen_748) -> q_gen_777
<cons, s>(q_gen_775, q_gen_787) -> q_gen_777
<cons, s>(q_gen_788, q_gen_748) -> q_gen_777
<cons, s>(q_gen_788, q_gen_773) -> q_gen_777
<b, s>(q_gen_789) -> q_gen_788
<b, s>(q_gen_795) -> q_gen_788
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_738, q_gen_752},
Q_f={q_gen_738},
Delta=
{
<a, a>() -> q_gen_738
<a, b>() -> q_gen_738
<b, b>() -> q_gen_738
<b, a>() -> q_gen_752
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_737, q_gen_751},
Q_f={q_gen_737},
Delta=
{
<cons, cons>(q_gen_751, q_gen_737) -> q_gen_737
<nil, nil>() -> q_gen_737
<a, a>() -> q_gen_751
<a, b>() -> q_gen_751
<b, a>() -> q_gen_751
<b, b>() -> q_gen_751
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 23
() -> length([nil, z]) -> 23
() -> leq([a, y]) -> 23
() -> leq([b, b]) -> 23
() -> sort([nil, nil]) -> 23
(insert([x, z, _yc]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _yc)]) -> 23
(insert([y, _dd, _ed]) /\ sort([z, _dd])) -> sort([cons(y, z), _ed]) -> 24
(length([_nd, _od]) /\ length([l, _md]) /\ sort([l, _nd])) -> eq_nat([_md, _od]) -> 28
(length([ll, _id])) -> length([cons(x, ll), s(_id)]) -> 28
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 25
(leq([b, a])) -> BOT -> 24
}
Sat witness: Found: ((length([_nd, _od]) /\ length([l, _md]) /\ sort([l, _nd])) -> eq_nat([_md, _od]), {
_md -> s(s(z))  ;  _nd -> cons(a, cons(b, nil))  ;  _od -> s(s(s(s(s(z)))))  ;  l -> cons(a, cons(b, nil))
})

-------------------------------------------
Step 36, which took 0.040469 s (model generation: 0.038994,  model checking: 0.001475):

Model:
|_
{
insert -> 
{{{
Q={q_gen_741, q_gen_742, q_gen_743, q_gen_745, q_gen_746, q_gen_757, q_gen_762},
Q_f={q_gen_741},
Delta=
{
<nil>() -> q_gen_742
<b>() -> q_gen_743
<a>() -> q_gen_757
<cons, cons>(q_gen_746, q_gen_745) -> q_gen_745
<nil, cons>(q_gen_743, q_gen_742) -> q_gen_745
<nil, cons>(q_gen_757, q_gen_742) -> q_gen_745
<a, a>() -> q_gen_746
<a, b>() -> q_gen_746
<b, a>() -> q_gen_746
<b, b>() -> q_gen_746
<a, cons, cons>(q_gen_746, q_gen_745) -> q_gen_741
<a, nil, cons>(q_gen_757, q_gen_742) -> q_gen_741
<b, cons, cons>(q_gen_746, q_gen_745) -> q_gen_741
<b, nil, cons>(q_gen_743, q_gen_742) -> q_gen_741
<a, nil, cons>(q_gen_743, q_gen_742) -> q_gen_762
<b, nil, cons>(q_gen_757, q_gen_742) -> q_gen_762
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_740, q_gen_748, q_gen_749, q_gen_773, q_gen_774, q_gen_776, q_gen_781, q_gen_782},
Q_f={q_gen_740},
Delta=
{
<nil>() -> q_gen_748
<cons>(q_gen_774, q_gen_748) -> q_gen_773
<cons>(q_gen_774, q_gen_773) -> q_gen_773
<a>() -> q_gen_774
<b>() -> q_gen_774
<s>(q_gen_776) -> q_gen_776
<z>() -> q_gen_776
<cons, s>(q_gen_749, q_gen_748) -> q_gen_740
<cons, s>(q_gen_749, q_gen_773) -> q_gen_740
<cons, s>(q_gen_781, q_gen_773) -> q_gen_740
<nil, z>() -> q_gen_740
<a, z>() -> q_gen_749
<b, s>(q_gen_776) -> q_gen_749
<b, z>() -> q_gen_749
<a, s>(q_gen_776) -> q_gen_781
<cons, s>(q_gen_781, q_gen_748) -> q_gen_782
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_738, q_gen_752},
Q_f={q_gen_738},
Delta=
{
<a, a>() -> q_gen_738
<a, b>() -> q_gen_738
<b, b>() -> q_gen_738
<b, a>() -> q_gen_752
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_737, q_gen_750, q_gen_751, q_gen_763, q_gen_764},
Q_f={q_gen_737, q_gen_750},
Delta=
{
<nil, nil>() -> q_gen_737
<cons, cons>(q_gen_751, q_gen_737) -> q_gen_750
<a, a>() -> q_gen_751
<b, b>() -> q_gen_751
<cons, cons>(q_gen_751, q_gen_750) -> q_gen_763
<cons, cons>(q_gen_751, q_gen_763) -> q_gen_763
<cons, cons>(q_gen_764, q_gen_737) -> q_gen_763
<cons, cons>(q_gen_764, q_gen_763) -> q_gen_763
<a, b>() -> q_gen_764
<b, a>() -> q_gen_764
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 24
() -> length([nil, z]) -> 24
() -> leq([a, y]) -> 24
() -> leq([b, b]) -> 24
() -> sort([nil, nil]) -> 24
(insert([x, z, _yc]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _yc)]) -> 24
(insert([y, _dd, _ed]) /\ sort([z, _dd])) -> sort([cons(y, z), _ed]) -> 27
(length([_nd, _od]) /\ length([l, _md]) /\ sort([l, _nd])) -> eq_nat([_md, _od]) -> 28
(length([ll, _id])) -> length([cons(x, ll), s(_id)]) -> 28
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 25
(leq([b, a])) -> BOT -> 25
}
Sat witness: Found: ((insert([y, _dd, _ed]) /\ sort([z, _dd])) -> sort([cons(y, z), _ed]), {
_dd -> cons(b, nil)  ;  _ed -> cons(a, cons(b, nil))  ;  y -> a  ;  z -> cons(b, nil)
})

-------------------------------------------
Step 37, which took 0.043487 s (model generation: 0.039160,  model checking: 0.004327):

Model:
|_
{
insert -> 
{{{
Q={q_gen_741, q_gen_742, q_gen_743, q_gen_745, q_gen_746},
Q_f={q_gen_741},
Delta=
{
<nil>() -> q_gen_742
<a>() -> q_gen_743
<b>() -> q_gen_743
<cons, cons>(q_gen_746, q_gen_745) -> q_gen_745
<nil, cons>(q_gen_743, q_gen_742) -> q_gen_745
<a, a>() -> q_gen_746
<a, b>() -> q_gen_746
<b, a>() -> q_gen_746
<b, b>() -> q_gen_746
<a, cons, cons>(q_gen_746, q_gen_745) -> q_gen_741
<a, nil, cons>(q_gen_743, q_gen_742) -> q_gen_741
<b, cons, cons>(q_gen_746, q_gen_745) -> q_gen_741
<b, nil, cons>(q_gen_743, q_gen_742) -> q_gen_741
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_740, q_gen_748, q_gen_749, q_gen_773, q_gen_774, q_gen_775, q_gen_776, q_gen_777, q_gen_787, q_gen_788, q_gen_789, q_gen_795, q_gen_804},
Q_f={q_gen_740},
Delta=
{
<nil>() -> q_gen_748
<cons>(q_gen_774, q_gen_748) -> q_gen_773
<a>() -> q_gen_774
<b>() -> q_gen_774
<z>() -> q_gen_776
<cons>(q_gen_774, q_gen_773) -> q_gen_787
<s>(q_gen_776) -> q_gen_789
<s>(q_gen_789) -> q_gen_795
<s>(q_gen_795) -> q_gen_804
<cons, s>(q_gen_749, q_gen_748) -> q_gen_740
<cons, s>(q_gen_775, q_gen_773) -> q_gen_740
<cons, s>(q_gen_788, q_gen_787) -> q_gen_740
<nil, z>() -> q_gen_740
<a, z>() -> q_gen_749
<b, s>(q_gen_804) -> q_gen_749
<b, z>() -> q_gen_749
<a, s>(q_gen_776) -> q_gen_775
<b, s>(q_gen_776) -> q_gen_775
<cons, s>(q_gen_749, q_gen_773) -> q_gen_777
<cons, s>(q_gen_749, q_gen_787) -> q_gen_777
<cons, s>(q_gen_775, q_gen_748) -> q_gen_777
<cons, s>(q_gen_788, q_gen_748) -> q_gen_777
<cons, s>(q_gen_788, q_gen_773) -> q_gen_777
<a, s>(q_gen_804) -> q_gen_788
<b, s>(q_gen_789) -> q_gen_788
<b, s>(q_gen_795) -> q_gen_788
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_738, q_gen_752},
Q_f={q_gen_738},
Delta=
{
<a, a>() -> q_gen_738
<a, b>() -> q_gen_738
<b, b>() -> q_gen_738
<b, a>() -> q_gen_752
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_737, q_gen_751},
Q_f={q_gen_737},
Delta=
{
<cons, cons>(q_gen_751, q_gen_737) -> q_gen_737
<nil, nil>() -> q_gen_737
<a, a>() -> q_gen_751
<a, b>() -> q_gen_751
<b, a>() -> q_gen_751
<b, b>() -> q_gen_751
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 25
() -> length([nil, z]) -> 25
() -> leq([a, y]) -> 25
() -> leq([b, b]) -> 25
() -> sort([nil, nil]) -> 25
(insert([x, z, _yc]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _yc)]) -> 25
(insert([y, _dd, _ed]) /\ sort([z, _dd])) -> sort([cons(y, z), _ed]) -> 28
(length([_nd, _od]) /\ length([l, _md]) /\ sort([l, _nd])) -> eq_nat([_md, _od]) -> 28
(length([ll, _id])) -> length([cons(x, ll), s(_id)]) -> 31
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 26
(leq([b, a])) -> BOT -> 26
}
Sat witness: Found: ((length([ll, _id])) -> length([cons(x, ll), s(_id)]), {
_id -> s(s(s(s(z))))  ;  ll -> cons(b, cons(a, cons(b, nil)))  ;  x -> b
})

-------------------------------------------
Step 38, which took 0.046475 s (model generation: 0.044542,  model checking: 0.001933):

Model:
|_
{
insert -> 
{{{
Q={q_gen_741, q_gen_742, q_gen_743, q_gen_745, q_gen_746},
Q_f={q_gen_741},
Delta=
{
<nil>() -> q_gen_742
<a>() -> q_gen_743
<b>() -> q_gen_743
<cons, cons>(q_gen_746, q_gen_745) -> q_gen_745
<nil, cons>(q_gen_743, q_gen_742) -> q_gen_745
<a, a>() -> q_gen_746
<a, b>() -> q_gen_746
<b, a>() -> q_gen_746
<b, b>() -> q_gen_746
<a, cons, cons>(q_gen_746, q_gen_745) -> q_gen_741
<a, nil, cons>(q_gen_743, q_gen_742) -> q_gen_741
<b, cons, cons>(q_gen_746, q_gen_745) -> q_gen_741
<b, nil, cons>(q_gen_743, q_gen_742) -> q_gen_741
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_740, q_gen_748, q_gen_749, q_gen_773, q_gen_774, q_gen_775, q_gen_776, q_gen_777, q_gen_787, q_gen_788, q_gen_789, q_gen_795, q_gen_804},
Q_f={q_gen_740},
Delta=
{
<cons>(q_gen_774, q_gen_787) -> q_gen_748
<nil>() -> q_gen_748
<cons>(q_gen_774, q_gen_748) -> q_gen_773
<a>() -> q_gen_774
<b>() -> q_gen_774
<z>() -> q_gen_776
<cons>(q_gen_774, q_gen_773) -> q_gen_787
<s>(q_gen_776) -> q_gen_789
<s>(q_gen_789) -> q_gen_795
<s>(q_gen_795) -> q_gen_804
<cons, s>(q_gen_749, q_gen_748) -> q_gen_740
<cons, s>(q_gen_775, q_gen_773) -> q_gen_740
<cons, s>(q_gen_788, q_gen_787) -> q_gen_740
<nil, z>() -> q_gen_740
<a, s>(q_gen_804) -> q_gen_749
<a, z>() -> q_gen_749
<b, s>(q_gen_804) -> q_gen_749
<b, z>() -> q_gen_749
<a, s>(q_gen_776) -> q_gen_775
<b, s>(q_gen_776) -> q_gen_775
<cons, s>(q_gen_749, q_gen_773) -> q_gen_777
<cons, s>(q_gen_749, q_gen_787) -> q_gen_777
<cons, s>(q_gen_775, q_gen_748) -> q_gen_777
<cons, s>(q_gen_788, q_gen_748) -> q_gen_777
<cons, s>(q_gen_788, q_gen_773) -> q_gen_777
<b, s>(q_gen_789) -> q_gen_788
<b, s>(q_gen_795) -> q_gen_788
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_738, q_gen_752},
Q_f={q_gen_738},
Delta=
{
<a, a>() -> q_gen_738
<a, b>() -> q_gen_738
<b, b>() -> q_gen_738
<b, a>() -> q_gen_752
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_737, q_gen_751},
Q_f={q_gen_737},
Delta=
{
<cons, cons>(q_gen_751, q_gen_737) -> q_gen_737
<nil, nil>() -> q_gen_737
<a, a>() -> q_gen_751
<a, b>() -> q_gen_751
<b, a>() -> q_gen_751
<b, b>() -> q_gen_751
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 26
() -> length([nil, z]) -> 26
() -> leq([a, y]) -> 26
() -> leq([b, b]) -> 26
() -> sort([nil, nil]) -> 26
(insert([x, z, _yc]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _yc)]) -> 26
(insert([y, _dd, _ed]) /\ sort([z, _dd])) -> sort([cons(y, z), _ed]) -> 28
(length([_nd, _od]) /\ length([l, _md]) /\ sort([l, _nd])) -> eq_nat([_md, _od]) -> 31
(length([ll, _id])) -> length([cons(x, ll), s(_id)]) -> 31
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 27
(leq([b, a])) -> BOT -> 27
}
Sat witness: Found: ((length([_nd, _od]) /\ length([l, _md]) /\ sort([l, _nd])) -> eq_nat([_md, _od]), {
_md -> s(s(s(s(z))))  ;  _nd -> cons(b, cons(b, cons(b, nil)))  ;  _od -> s(s(s(z)))  ;  l -> cons(b, cons(b, cons(b, nil)))
})

-------------------------------------------
Step 39, which took 0.049039 s (model generation: 0.045760,  model checking: 0.003279):

Model:
|_
{
insert -> 
{{{
Q={q_gen_741, q_gen_742, q_gen_743, q_gen_745, q_gen_746},
Q_f={q_gen_741},
Delta=
{
<nil>() -> q_gen_742
<a>() -> q_gen_743
<b>() -> q_gen_743
<cons, cons>(q_gen_746, q_gen_745) -> q_gen_745
<nil, cons>(q_gen_743, q_gen_742) -> q_gen_745
<a, a>() -> q_gen_746
<a, b>() -> q_gen_746
<b, a>() -> q_gen_746
<b, b>() -> q_gen_746
<a, cons, cons>(q_gen_746, q_gen_745) -> q_gen_741
<a, nil, cons>(q_gen_743, q_gen_742) -> q_gen_741
<b, cons, cons>(q_gen_746, q_gen_745) -> q_gen_741
<b, nil, cons>(q_gen_743, q_gen_742) -> q_gen_741
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_740, q_gen_748, q_gen_749, q_gen_773, q_gen_774, q_gen_775, q_gen_776, q_gen_777, q_gen_787, q_gen_788, q_gen_789, q_gen_794, q_gen_795},
Q_f={q_gen_740},
Delta=
{
<cons>(q_gen_774, q_gen_787) -> q_gen_748
<nil>() -> q_gen_748
<cons>(q_gen_774, q_gen_748) -> q_gen_773
<a>() -> q_gen_774
<b>() -> q_gen_774
<z>() -> q_gen_776
<cons>(q_gen_774, q_gen_773) -> q_gen_787
<s>(q_gen_776) -> q_gen_789
<s>(q_gen_789) -> q_gen_795
<s>(q_gen_795) -> q_gen_795
<cons, s>(q_gen_749, q_gen_748) -> q_gen_740
<cons, s>(q_gen_775, q_gen_773) -> q_gen_740
<cons, s>(q_gen_788, q_gen_787) -> q_gen_740
<nil, z>() -> q_gen_740
<a, z>() -> q_gen_749
<b, z>() -> q_gen_749
<a, s>(q_gen_776) -> q_gen_775
<b, s>(q_gen_776) -> q_gen_775
<cons, s>(q_gen_775, q_gen_748) -> q_gen_777
<cons, s>(q_gen_788, q_gen_748) -> q_gen_777
<cons, s>(q_gen_788, q_gen_773) -> q_gen_777
<cons, s>(q_gen_794, q_gen_748) -> q_gen_777
<cons, s>(q_gen_794, q_gen_773) -> q_gen_777
<cons, s>(q_gen_794, q_gen_787) -> q_gen_777
<a, s>(q_gen_795) -> q_gen_788
<b, s>(q_gen_789) -> q_gen_788
<b, s>(q_gen_795) -> q_gen_794
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_738, q_gen_752},
Q_f={q_gen_738},
Delta=
{
<a, a>() -> q_gen_738
<a, b>() -> q_gen_738
<b, b>() -> q_gen_738
<b, a>() -> q_gen_752
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_737, q_gen_751},
Q_f={q_gen_737},
Delta=
{
<cons, cons>(q_gen_751, q_gen_737) -> q_gen_737
<nil, nil>() -> q_gen_737
<a, a>() -> q_gen_751
<a, b>() -> q_gen_751
<b, a>() -> q_gen_751
<b, b>() -> q_gen_751
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 27
() -> length([nil, z]) -> 27
() -> leq([a, y]) -> 27
() -> leq([b, b]) -> 27
() -> sort([nil, nil]) -> 27
(insert([x, z, _yc]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _yc)]) -> 27
(insert([y, _dd, _ed]) /\ sort([z, _dd])) -> sort([cons(y, z), _ed]) -> 29
(length([_nd, _od]) /\ length([l, _md]) /\ sort([l, _nd])) -> eq_nat([_md, _od]) -> 31
(length([ll, _id])) -> length([cons(x, ll), s(_id)]) -> 34
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 28
(leq([b, a])) -> BOT -> 28
}
Sat witness: Found: ((length([ll, _id])) -> length([cons(x, ll), s(_id)]), {
_id -> s(s(s(z)))  ;  ll -> cons(b, cons(a, cons(b, nil)))  ;  x -> b
})

-------------------------------------------
Step 40, which took 0.057104 s (model generation: 0.053338,  model checking: 0.003766):

Model:
|_
{
insert -> 
{{{
Q={q_gen_741, q_gen_742, q_gen_743, q_gen_745, q_gen_746},
Q_f={q_gen_741},
Delta=
{
<nil>() -> q_gen_742
<a>() -> q_gen_743
<b>() -> q_gen_743
<cons, cons>(q_gen_746, q_gen_745) -> q_gen_745
<nil, cons>(q_gen_743, q_gen_742) -> q_gen_745
<a, a>() -> q_gen_746
<a, b>() -> q_gen_746
<b, a>() -> q_gen_746
<b, b>() -> q_gen_746
<a, cons, cons>(q_gen_746, q_gen_745) -> q_gen_741
<a, nil, cons>(q_gen_743, q_gen_742) -> q_gen_741
<b, cons, cons>(q_gen_746, q_gen_745) -> q_gen_741
<b, nil, cons>(q_gen_743, q_gen_742) -> q_gen_741
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_740, q_gen_748, q_gen_749, q_gen_773, q_gen_774, q_gen_775, q_gen_776, q_gen_777, q_gen_787, q_gen_788, q_gen_789, q_gen_794, q_gen_795, q_gen_815},
Q_f={q_gen_740},
Delta=
{
<nil>() -> q_gen_748
<cons>(q_gen_774, q_gen_748) -> q_gen_773
<a>() -> q_gen_774
<b>() -> q_gen_774
<z>() -> q_gen_776
<cons>(q_gen_774, q_gen_773) -> q_gen_787
<s>(q_gen_776) -> q_gen_789
<s>(q_gen_789) -> q_gen_795
<s>(q_gen_795) -> q_gen_795
<cons>(q_gen_774, q_gen_787) -> q_gen_815
<cons, s>(q_gen_749, q_gen_748) -> q_gen_740
<cons, s>(q_gen_775, q_gen_773) -> q_gen_740
<cons, s>(q_gen_788, q_gen_787) -> q_gen_740
<cons, s>(q_gen_794, q_gen_815) -> q_gen_740
<nil, z>() -> q_gen_740
<a, z>() -> q_gen_749
<b, z>() -> q_gen_749
<a, s>(q_gen_776) -> q_gen_775
<b, s>(q_gen_776) -> q_gen_775
<cons, s>(q_gen_775, q_gen_748) -> q_gen_777
<cons, s>(q_gen_788, q_gen_748) -> q_gen_777
<cons, s>(q_gen_788, q_gen_773) -> q_gen_777
<cons, s>(q_gen_794, q_gen_748) -> q_gen_777
<cons, s>(q_gen_794, q_gen_773) -> q_gen_777
<cons, s>(q_gen_794, q_gen_787) -> q_gen_777
<b, s>(q_gen_789) -> q_gen_788
<a, s>(q_gen_795) -> q_gen_794
<b, s>(q_gen_795) -> q_gen_794
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_738, q_gen_752},
Q_f={q_gen_738},
Delta=
{
<a, a>() -> q_gen_738
<a, b>() -> q_gen_738
<b, b>() -> q_gen_738
<b, a>() -> q_gen_752
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_737, q_gen_751},
Q_f={q_gen_737},
Delta=
{
<cons, cons>(q_gen_751, q_gen_737) -> q_gen_737
<nil, nil>() -> q_gen_737
<a, a>() -> q_gen_751
<a, b>() -> q_gen_751
<b, a>() -> q_gen_751
<b, b>() -> q_gen_751
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 28
() -> length([nil, z]) -> 28
() -> leq([a, y]) -> 28
() -> leq([b, b]) -> 28
() -> sort([nil, nil]) -> 28
(insert([x, z, _yc]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _yc)]) -> 28
(insert([y, _dd, _ed]) /\ sort([z, _dd])) -> sort([cons(y, z), _ed]) -> 30
(length([_nd, _od]) /\ length([l, _md]) /\ sort([l, _nd])) -> eq_nat([_md, _od]) -> 34
(length([ll, _id])) -> length([cons(x, ll), s(_id)]) -> 34
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 29
(leq([b, a])) -> BOT -> 29
}
Sat witness: Found: ((length([_nd, _od]) /\ length([l, _md]) /\ sort([l, _nd])) -> eq_nat([_md, _od]), {
_md -> s(s(s(s(z))))  ;  _nd -> cons(b, cons(b, cons(b, cons(b, nil))))  ;  _od -> s(s(s(s(s(s(z))))))  ;  l -> cons(a, cons(b, cons(b, cons(b, nil))))
})

-------------------------------------------
Step 41, which took 0.067025 s (model generation: 0.062831,  model checking: 0.004194):

Model:
|_
{
insert -> 
{{{
Q={q_gen_741, q_gen_742, q_gen_743, q_gen_745, q_gen_746},
Q_f={q_gen_741},
Delta=
{
<nil>() -> q_gen_742
<a>() -> q_gen_743
<b>() -> q_gen_743
<cons, cons>(q_gen_746, q_gen_745) -> q_gen_745
<nil, cons>(q_gen_743, q_gen_742) -> q_gen_745
<a, a>() -> q_gen_746
<a, b>() -> q_gen_746
<b, a>() -> q_gen_746
<b, b>() -> q_gen_746
<a, cons, cons>(q_gen_746, q_gen_745) -> q_gen_741
<a, nil, cons>(q_gen_743, q_gen_742) -> q_gen_741
<b, cons, cons>(q_gen_746, q_gen_745) -> q_gen_741
<b, nil, cons>(q_gen_743, q_gen_742) -> q_gen_741
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_740, q_gen_748, q_gen_749, q_gen_773, q_gen_774, q_gen_775, q_gen_776, q_gen_777, q_gen_787, q_gen_788, q_gen_789, q_gen_794, q_gen_795, q_gen_801},
Q_f={q_gen_740},
Delta=
{
<cons>(q_gen_774, q_gen_787) -> q_gen_748
<cons>(q_gen_801, q_gen_773) -> q_gen_748
<nil>() -> q_gen_748
<cons>(q_gen_774, q_gen_748) -> q_gen_773
<cons>(q_gen_801, q_gen_748) -> q_gen_773
<b>() -> q_gen_774
<z>() -> q_gen_776
<cons>(q_gen_774, q_gen_773) -> q_gen_787
<s>(q_gen_776) -> q_gen_789
<s>(q_gen_789) -> q_gen_795
<s>(q_gen_795) -> q_gen_795
<a>() -> q_gen_801
<cons, s>(q_gen_749, q_gen_748) -> q_gen_740
<cons, s>(q_gen_775, q_gen_773) -> q_gen_740
<cons, s>(q_gen_788, q_gen_787) -> q_gen_740
<nil, z>() -> q_gen_740
<a, z>() -> q_gen_749
<b, z>() -> q_gen_749
<a, s>(q_gen_776) -> q_gen_775
<b, s>(q_gen_776) -> q_gen_775
<cons, s>(q_gen_775, q_gen_748) -> q_gen_777
<cons, s>(q_gen_788, q_gen_748) -> q_gen_777
<cons, s>(q_gen_788, q_gen_773) -> q_gen_777
<cons, s>(q_gen_794, q_gen_748) -> q_gen_777
<cons, s>(q_gen_794, q_gen_773) -> q_gen_777
<cons, s>(q_gen_794, q_gen_787) -> q_gen_777
<b, s>(q_gen_789) -> q_gen_788
<a, s>(q_gen_795) -> q_gen_794
<b, s>(q_gen_795) -> q_gen_794
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_738, q_gen_752},
Q_f={q_gen_738},
Delta=
{
<a, a>() -> q_gen_738
<a, b>() -> q_gen_738
<b, b>() -> q_gen_738
<b, a>() -> q_gen_752
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_737, q_gen_751},
Q_f={q_gen_737},
Delta=
{
<cons, cons>(q_gen_751, q_gen_737) -> q_gen_737
<nil, nil>() -> q_gen_737
<a, a>() -> q_gen_751
<a, b>() -> q_gen_751
<b, a>() -> q_gen_751
<b, b>() -> q_gen_751
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 29
() -> length([nil, z]) -> 29
() -> leq([a, y]) -> 29
() -> leq([b, b]) -> 29
() -> sort([nil, nil]) -> 29
(insert([x, z, _yc]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _yc)]) -> 29
(insert([y, _dd, _ed]) /\ sort([z, _dd])) -> sort([cons(y, z), _ed]) -> 31
(length([_nd, _od]) /\ length([l, _md]) /\ sort([l, _nd])) -> eq_nat([_md, _od]) -> 34
(length([ll, _id])) -> length([cons(x, ll), s(_id)]) -> 37
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 30
(leq([b, a])) -> BOT -> 30
}
Sat witness: Found: ((length([ll, _id])) -> length([cons(x, ll), s(_id)]), {
_id -> s(s(s(z)))  ;  ll -> cons(b, cons(b, cons(a, nil)))  ;  x -> a
})

-------------------------------------------
Step 42, which took 0.075064 s (model generation: 0.071589,  model checking: 0.003475):

Model:
|_
{
insert -> 
{{{
Q={q_gen_741, q_gen_742, q_gen_743, q_gen_745, q_gen_746},
Q_f={q_gen_741},
Delta=
{
<nil>() -> q_gen_742
<a>() -> q_gen_743
<b>() -> q_gen_743
<cons, cons>(q_gen_746, q_gen_745) -> q_gen_745
<nil, cons>(q_gen_743, q_gen_742) -> q_gen_745
<a, a>() -> q_gen_746
<a, b>() -> q_gen_746
<b, a>() -> q_gen_746
<b, b>() -> q_gen_746
<a, cons, cons>(q_gen_746, q_gen_745) -> q_gen_741
<a, nil, cons>(q_gen_743, q_gen_742) -> q_gen_741
<b, cons, cons>(q_gen_746, q_gen_745) -> q_gen_741
<b, nil, cons>(q_gen_743, q_gen_742) -> q_gen_741
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_740, q_gen_748, q_gen_749, q_gen_773, q_gen_774, q_gen_775, q_gen_776, q_gen_777, q_gen_787, q_gen_788, q_gen_789, q_gen_794, q_gen_795, q_gen_801},
Q_f={q_gen_740},
Delta=
{
<cons>(q_gen_774, q_gen_787) -> q_gen_748
<nil>() -> q_gen_748
<cons>(q_gen_774, q_gen_748) -> q_gen_773
<cons>(q_gen_801, q_gen_773) -> q_gen_773
<b>() -> q_gen_774
<z>() -> q_gen_776
<cons>(q_gen_774, q_gen_773) -> q_gen_787
<cons>(q_gen_801, q_gen_748) -> q_gen_787
<s>(q_gen_776) -> q_gen_789
<s>(q_gen_789) -> q_gen_795
<s>(q_gen_795) -> q_gen_795
<a>() -> q_gen_801
<cons, s>(q_gen_749, q_gen_748) -> q_gen_740
<cons, s>(q_gen_775, q_gen_773) -> q_gen_740
<cons, s>(q_gen_775, q_gen_787) -> q_gen_740
<cons, s>(q_gen_788, q_gen_787) -> q_gen_740
<nil, z>() -> q_gen_740
<a, z>() -> q_gen_749
<b, z>() -> q_gen_749
<a, s>(q_gen_776) -> q_gen_775
<b, s>(q_gen_776) -> q_gen_775
<cons, s>(q_gen_775, q_gen_748) -> q_gen_777
<cons, s>(q_gen_788, q_gen_748) -> q_gen_777
<cons, s>(q_gen_788, q_gen_773) -> q_gen_777
<cons, s>(q_gen_794, q_gen_748) -> q_gen_777
<cons, s>(q_gen_794, q_gen_773) -> q_gen_777
<cons, s>(q_gen_794, q_gen_787) -> q_gen_777
<b, s>(q_gen_789) -> q_gen_788
<a, s>(q_gen_795) -> q_gen_794
<b, s>(q_gen_795) -> q_gen_794
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_738, q_gen_752},
Q_f={q_gen_738},
Delta=
{
<a, a>() -> q_gen_738
<a, b>() -> q_gen_738
<b, b>() -> q_gen_738
<b, a>() -> q_gen_752
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_737, q_gen_751},
Q_f={q_gen_737},
Delta=
{
<cons, cons>(q_gen_751, q_gen_737) -> q_gen_737
<nil, nil>() -> q_gen_737
<a, a>() -> q_gen_751
<a, b>() -> q_gen_751
<b, a>() -> q_gen_751
<b, b>() -> q_gen_751
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 30
() -> length([nil, z]) -> 30
() -> leq([a, y]) -> 30
() -> leq([b, b]) -> 30
() -> sort([nil, nil]) -> 30
(insert([x, z, _yc]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _yc)]) -> 30
(insert([y, _dd, _ed]) /\ sort([z, _dd])) -> sort([cons(y, z), _ed]) -> 32
(length([_nd, _od]) /\ length([l, _md]) /\ sort([l, _nd])) -> eq_nat([_md, _od]) -> 37
(length([ll, _id])) -> length([cons(x, ll), s(_id)]) -> 37
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 31
(leq([b, a])) -> BOT -> 31
}
Sat witness: Found: ((length([_nd, _od]) /\ length([l, _md]) /\ sort([l, _nd])) -> eq_nat([_md, _od]), {
_md -> s(z)  ;  _nd -> cons(b, cons(b, cons(a, cons(b, nil))))  ;  _od -> s(s(s(z)))  ;  l -> cons(a, cons(b, cons(b, cons(b, nil))))
})

-------------------------------------------
Step 43, which took 0.088587 s (model generation: 0.084721,  model checking: 0.003866):

Model:
|_
{
insert -> 
{{{
Q={q_gen_741, q_gen_742, q_gen_743, q_gen_745, q_gen_746},
Q_f={q_gen_741},
Delta=
{
<nil>() -> q_gen_742
<a>() -> q_gen_743
<b>() -> q_gen_743
<cons, cons>(q_gen_746, q_gen_745) -> q_gen_745
<nil, cons>(q_gen_743, q_gen_742) -> q_gen_745
<a, a>() -> q_gen_746
<a, b>() -> q_gen_746
<b, a>() -> q_gen_746
<b, b>() -> q_gen_746
<a, cons, cons>(q_gen_746, q_gen_745) -> q_gen_741
<a, nil, cons>(q_gen_743, q_gen_742) -> q_gen_741
<b, cons, cons>(q_gen_746, q_gen_745) -> q_gen_741
<b, nil, cons>(q_gen_743, q_gen_742) -> q_gen_741
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_740, q_gen_748, q_gen_749, q_gen_773, q_gen_774, q_gen_775, q_gen_776, q_gen_777, q_gen_787, q_gen_788, q_gen_789, q_gen_794, q_gen_795, q_gen_801},
Q_f={q_gen_740},
Delta=
{
<nil>() -> q_gen_748
<cons>(q_gen_774, q_gen_748) -> q_gen_773
<cons>(q_gen_774, q_gen_787) -> q_gen_773
<cons>(q_gen_801, q_gen_773) -> q_gen_773
<b>() -> q_gen_774
<z>() -> q_gen_776
<cons>(q_gen_774, q_gen_773) -> q_gen_787
<cons>(q_gen_801, q_gen_748) -> q_gen_787
<s>(q_gen_776) -> q_gen_789
<s>(q_gen_789) -> q_gen_795
<s>(q_gen_795) -> q_gen_795
<a>() -> q_gen_801
<cons, s>(q_gen_749, q_gen_748) -> q_gen_740
<cons, s>(q_gen_775, q_gen_773) -> q_gen_740
<cons, s>(q_gen_775, q_gen_787) -> q_gen_740
<cons, s>(q_gen_788, q_gen_787) -> q_gen_740
<nil, z>() -> q_gen_740
<a, z>() -> q_gen_749
<b, z>() -> q_gen_749
<a, s>(q_gen_776) -> q_gen_775
<b, s>(q_gen_776) -> q_gen_775
<cons, s>(q_gen_749, q_gen_773) -> q_gen_777
<cons, s>(q_gen_775, q_gen_748) -> q_gen_777
<cons, s>(q_gen_788, q_gen_748) -> q_gen_777
<cons, s>(q_gen_788, q_gen_773) -> q_gen_777
<cons, s>(q_gen_794, q_gen_748) -> q_gen_777
<cons, s>(q_gen_794, q_gen_773) -> q_gen_777
<cons, s>(q_gen_794, q_gen_787) -> q_gen_777
<b, s>(q_gen_789) -> q_gen_788
<a, s>(q_gen_795) -> q_gen_794
<b, s>(q_gen_795) -> q_gen_794
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_738, q_gen_752},
Q_f={q_gen_738},
Delta=
{
<a, a>() -> q_gen_738
<a, b>() -> q_gen_738
<b, b>() -> q_gen_738
<b, a>() -> q_gen_752
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_737, q_gen_751},
Q_f={q_gen_737},
Delta=
{
<cons, cons>(q_gen_751, q_gen_737) -> q_gen_737
<nil, nil>() -> q_gen_737
<a, a>() -> q_gen_751
<a, b>() -> q_gen_751
<b, a>() -> q_gen_751
<b, b>() -> q_gen_751
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 31
() -> length([nil, z]) -> 31
() -> leq([a, y]) -> 31
() -> leq([b, b]) -> 31
() -> sort([nil, nil]) -> 31
(insert([x, z, _yc]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _yc)]) -> 31
(insert([y, _dd, _ed]) /\ sort([z, _dd])) -> sort([cons(y, z), _ed]) -> 33
(length([_nd, _od]) /\ length([l, _md]) /\ sort([l, _nd])) -> eq_nat([_md, _od]) -> 37
(length([ll, _id])) -> length([cons(x, ll), s(_id)]) -> 40
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 32
(leq([b, a])) -> BOT -> 32
}
Sat witness: Found: ((length([ll, _id])) -> length([cons(x, ll), s(_id)]), {
_id -> s(s(s(z)))  ;  ll -> cons(b, cons(a, nil))  ;  x -> a
})

-------------------------------------------
Step 44, which took 0.093610 s (model generation: 0.090611,  model checking: 0.002999):

Model:
|_
{
insert -> 
{{{
Q={q_gen_741, q_gen_742, q_gen_743, q_gen_745, q_gen_746, q_gen_771, q_gen_798},
Q_f={q_gen_741},
Delta=
{
<nil>() -> q_gen_742
<a>() -> q_gen_743
<b>() -> q_gen_743
<cons, cons>(q_gen_746, q_gen_745) -> q_gen_745
<cons, cons>(q_gen_771, q_gen_745) -> q_gen_745
<nil, cons>(q_gen_743, q_gen_742) -> q_gen_745
<a, a>() -> q_gen_746
<b, a>() -> q_gen_746
<b, b>() -> q_gen_746
<a, b>() -> q_gen_771
<a, cons, cons>(q_gen_746, q_gen_745) -> q_gen_741
<a, nil, cons>(q_gen_743, q_gen_742) -> q_gen_741
<b, cons, cons>(q_gen_746, q_gen_745) -> q_gen_741
<b, nil, cons>(q_gen_743, q_gen_742) -> q_gen_741
<b, cons, cons>(q_gen_771, q_gen_745) -> q_gen_798
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_740, q_gen_748, q_gen_749, q_gen_773, q_gen_774, q_gen_775, q_gen_776, q_gen_777, q_gen_789},
Q_f={q_gen_740},
Delta=
{
<nil>() -> q_gen_748
<cons>(q_gen_774, q_gen_748) -> q_gen_773
<cons>(q_gen_774, q_gen_773) -> q_gen_773
<a>() -> q_gen_774
<b>() -> q_gen_774
<s>(q_gen_789) -> q_gen_776
<z>() -> q_gen_776
<s>(q_gen_776) -> q_gen_789
<cons, s>(q_gen_749, q_gen_748) -> q_gen_740
<cons, s>(q_gen_775, q_gen_773) -> q_gen_740
<nil, z>() -> q_gen_740
<a, s>(q_gen_789) -> q_gen_749
<a, z>() -> q_gen_749
<b, z>() -> q_gen_749
<a, s>(q_gen_776) -> q_gen_775
<b, s>(q_gen_776) -> q_gen_775
<b, s>(q_gen_789) -> q_gen_775
<cons, s>(q_gen_749, q_gen_773) -> q_gen_777
<cons, s>(q_gen_775, q_gen_748) -> q_gen_777
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_738, q_gen_752},
Q_f={q_gen_738},
Delta=
{
<a, a>() -> q_gen_738
<a, b>() -> q_gen_738
<b, b>() -> q_gen_738
<b, a>() -> q_gen_752
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_737, q_gen_750, q_gen_751, q_gen_764, q_gen_791},
Q_f={q_gen_737, q_gen_750},
Delta=
{
<cons, cons>(q_gen_764, q_gen_750) -> q_gen_737
<nil, nil>() -> q_gen_737
<cons, cons>(q_gen_751, q_gen_737) -> q_gen_750
<cons, cons>(q_gen_764, q_gen_737) -> q_gen_750
<b, b>() -> q_gen_751
<a, a>() -> q_gen_764
<a, b>() -> q_gen_764
<b, a>() -> q_gen_764
<cons, cons>(q_gen_751, q_gen_750) -> q_gen_791
<cons, cons>(q_gen_751, q_gen_791) -> q_gen_791
<cons, cons>(q_gen_764, q_gen_791) -> q_gen_791
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 32
() -> length([nil, z]) -> 32
() -> leq([a, y]) -> 32
() -> leq([b, b]) -> 32
() -> sort([nil, nil]) -> 32
(insert([x, z, _yc]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _yc)]) -> 32
(insert([y, _dd, _ed]) /\ sort([z, _dd])) -> sort([cons(y, z), _ed]) -> 36
(length([_nd, _od]) /\ length([l, _md]) /\ sort([l, _nd])) -> eq_nat([_md, _od]) -> 37
(length([ll, _id])) -> length([cons(x, ll), s(_id)]) -> 40
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 33
(leq([b, a])) -> BOT -> 33
}
Sat witness: Found: ((insert([y, _dd, _ed]) /\ sort([z, _dd])) -> sort([cons(y, z), _ed]), {
_dd -> cons(b, nil)  ;  _ed -> cons(b, cons(b, nil))  ;  y -> b  ;  z -> cons(b, nil)
})

-------------------------------------------
Step 45, which took 0.104838 s (model generation: 0.102060,  model checking: 0.002778):

Model:
|_
{
insert -> 
{{{
Q={q_gen_741, q_gen_742, q_gen_743, q_gen_745, q_gen_746},
Q_f={q_gen_741},
Delta=
{
<nil>() -> q_gen_742
<a>() -> q_gen_743
<b>() -> q_gen_743
<cons, cons>(q_gen_746, q_gen_745) -> q_gen_745
<nil, cons>(q_gen_743, q_gen_742) -> q_gen_745
<a, a>() -> q_gen_746
<a, b>() -> q_gen_746
<b, a>() -> q_gen_746
<b, b>() -> q_gen_746
<a, cons, cons>(q_gen_746, q_gen_745) -> q_gen_741
<a, nil, cons>(q_gen_743, q_gen_742) -> q_gen_741
<b, cons, cons>(q_gen_746, q_gen_745) -> q_gen_741
<b, nil, cons>(q_gen_743, q_gen_742) -> q_gen_741
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_740, q_gen_748, q_gen_749, q_gen_773, q_gen_774, q_gen_775, q_gen_776, q_gen_777, q_gen_787, q_gen_788, q_gen_789},
Q_f={q_gen_740},
Delta=
{
<nil>() -> q_gen_748
<cons>(q_gen_774, q_gen_748) -> q_gen_773
<a>() -> q_gen_774
<b>() -> q_gen_774
<z>() -> q_gen_776
<cons>(q_gen_774, q_gen_773) -> q_gen_787
<cons>(q_gen_774, q_gen_787) -> q_gen_787
<s>(q_gen_776) -> q_gen_789
<s>(q_gen_789) -> q_gen_789
<cons, s>(q_gen_749, q_gen_748) -> q_gen_740
<cons, s>(q_gen_749, q_gen_787) -> q_gen_740
<cons, s>(q_gen_775, q_gen_773) -> q_gen_740
<cons, s>(q_gen_788, q_gen_787) -> q_gen_740
<nil, z>() -> q_gen_740
<a, z>() -> q_gen_749
<b, z>() -> q_gen_749
<a, s>(q_gen_776) -> q_gen_775
<b, s>(q_gen_776) -> q_gen_775
<cons, s>(q_gen_775, q_gen_748) -> q_gen_777
<cons, s>(q_gen_788, q_gen_748) -> q_gen_777
<cons, s>(q_gen_788, q_gen_773) -> q_gen_777
<a, s>(q_gen_789) -> q_gen_788
<b, s>(q_gen_789) -> q_gen_788
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_738, q_gen_752},
Q_f={q_gen_738},
Delta=
{
<a, a>() -> q_gen_738
<a, b>() -> q_gen_738
<b, b>() -> q_gen_738
<b, a>() -> q_gen_752
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_737, q_gen_750, q_gen_751, q_gen_791, q_gen_805},
Q_f={q_gen_737, q_gen_750, q_gen_791},
Delta=
{
<nil, nil>() -> q_gen_737
<cons, cons>(q_gen_751, q_gen_737) -> q_gen_750
<a, a>() -> q_gen_751
<a, b>() -> q_gen_751
<b, a>() -> q_gen_751
<b, b>() -> q_gen_751
<cons, cons>(q_gen_751, q_gen_750) -> q_gen_791
<cons, cons>(q_gen_751, q_gen_791) -> q_gen_805
<cons, cons>(q_gen_751, q_gen_805) -> q_gen_805
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 33
() -> length([nil, z]) -> 33
() -> leq([a, y]) -> 33
() -> leq([b, b]) -> 33
() -> sort([nil, nil]) -> 33
(insert([x, z, _yc]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _yc)]) -> 33
(insert([y, _dd, _ed]) /\ sort([z, _dd])) -> sort([cons(y, z), _ed]) -> 39
(length([_nd, _od]) /\ length([l, _md]) /\ sort([l, _nd])) -> eq_nat([_md, _od]) -> 37
(length([ll, _id])) -> length([cons(x, ll), s(_id)]) -> 40
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 34
(leq([b, a])) -> BOT -> 34
}
Sat witness: Found: ((insert([y, _dd, _ed]) /\ sort([z, _dd])) -> sort([cons(y, z), _ed]), {
_dd -> cons(a, cons(b, nil))  ;  _ed -> cons(b, cons(a, cons(b, nil)))  ;  y -> b  ;  z -> cons(a, cons(b, nil))
})

-------------------------------------------
Step 46, which took 0.117920 s (model generation: 0.115680,  model checking: 0.002240):

Model:
|_
{
insert -> 
{{{
Q={q_gen_741, q_gen_742, q_gen_743, q_gen_745, q_gen_746},
Q_f={q_gen_741},
Delta=
{
<nil>() -> q_gen_742
<a>() -> q_gen_743
<b>() -> q_gen_743
<cons, cons>(q_gen_746, q_gen_745) -> q_gen_745
<nil, cons>(q_gen_743, q_gen_742) -> q_gen_745
<a, a>() -> q_gen_746
<a, b>() -> q_gen_746
<b, a>() -> q_gen_746
<b, b>() -> q_gen_746
<a, cons, cons>(q_gen_746, q_gen_745) -> q_gen_741
<a, nil, cons>(q_gen_743, q_gen_742) -> q_gen_741
<b, cons, cons>(q_gen_746, q_gen_745) -> q_gen_741
<b, nil, cons>(q_gen_743, q_gen_742) -> q_gen_741
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_740, q_gen_748, q_gen_749, q_gen_773, q_gen_774, q_gen_775, q_gen_776, q_gen_777, q_gen_787, q_gen_788, q_gen_789, q_gen_794, q_gen_795, q_gen_801},
Q_f={q_gen_740},
Delta=
{
<nil>() -> q_gen_748
<cons>(q_gen_774, q_gen_748) -> q_gen_773
<cons>(q_gen_801, q_gen_748) -> q_gen_773
<cons>(q_gen_801, q_gen_773) -> q_gen_773
<b>() -> q_gen_774
<z>() -> q_gen_776
<cons>(q_gen_774, q_gen_773) -> q_gen_787
<cons>(q_gen_774, q_gen_787) -> q_gen_787
<s>(q_gen_776) -> q_gen_789
<s>(q_gen_789) -> q_gen_795
<s>(q_gen_795) -> q_gen_795
<a>() -> q_gen_801
<cons, s>(q_gen_749, q_gen_748) -> q_gen_740
<cons, s>(q_gen_775, q_gen_773) -> q_gen_740
<cons, s>(q_gen_788, q_gen_787) -> q_gen_740
<nil, z>() -> q_gen_740
<a, z>() -> q_gen_749
<b, z>() -> q_gen_749
<a, s>(q_gen_776) -> q_gen_775
<b, s>(q_gen_776) -> q_gen_775
<cons, s>(q_gen_749, q_gen_787) -> q_gen_777
<cons, s>(q_gen_775, q_gen_748) -> q_gen_777
<cons, s>(q_gen_788, q_gen_748) -> q_gen_777
<cons, s>(q_gen_788, q_gen_773) -> q_gen_777
<cons, s>(q_gen_794, q_gen_748) -> q_gen_777
<cons, s>(q_gen_794, q_gen_773) -> q_gen_777
<cons, s>(q_gen_794, q_gen_787) -> q_gen_777
<a, s>(q_gen_795) -> q_gen_788
<b, s>(q_gen_789) -> q_gen_788
<b, s>(q_gen_795) -> q_gen_794
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_738, q_gen_752},
Q_f={q_gen_738},
Delta=
{
<a, a>() -> q_gen_738
<a, b>() -> q_gen_738
<b, b>() -> q_gen_738
<b, a>() -> q_gen_752
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_737, q_gen_751},
Q_f={q_gen_737},
Delta=
{
<cons, cons>(q_gen_751, q_gen_737) -> q_gen_737
<nil, nil>() -> q_gen_737
<a, a>() -> q_gen_751
<a, b>() -> q_gen_751
<b, a>() -> q_gen_751
<b, b>() -> q_gen_751
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 34
() -> length([nil, z]) -> 34
() -> leq([a, y]) -> 34
() -> leq([b, b]) -> 34
() -> sort([nil, nil]) -> 34
(insert([x, z, _yc]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _yc)]) -> 34
(insert([y, _dd, _ed]) /\ sort([z, _dd])) -> sort([cons(y, z), _ed]) -> 39
(length([_nd, _od]) /\ length([l, _md]) /\ sort([l, _nd])) -> eq_nat([_md, _od]) -> 40
(length([ll, _id])) -> length([cons(x, ll), s(_id)]) -> 40
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 35
(leq([b, a])) -> BOT -> 35
}
Sat witness: Found: ((length([_nd, _od]) /\ length([l, _md]) /\ sort([l, _nd])) -> eq_nat([_md, _od]), {
_md -> s(s(s(z)))  ;  _nd -> cons(a, cons(a, cons(b, nil)))  ;  _od -> s(s(z))  ;  l -> cons(b, cons(b, cons(b, nil)))
})

-------------------------------------------
Step 47, which took 0.105033 s (model generation: 0.101606,  model checking: 0.003427):

Model:
|_
{
insert -> 
{{{
Q={q_gen_741, q_gen_742, q_gen_743, q_gen_745, q_gen_746},
Q_f={q_gen_741},
Delta=
{
<nil>() -> q_gen_742
<a>() -> q_gen_743
<b>() -> q_gen_743
<cons, cons>(q_gen_746, q_gen_745) -> q_gen_745
<nil, cons>(q_gen_743, q_gen_742) -> q_gen_745
<a, a>() -> q_gen_746
<a, b>() -> q_gen_746
<b, a>() -> q_gen_746
<b, b>() -> q_gen_746
<a, cons, cons>(q_gen_746, q_gen_745) -> q_gen_741
<a, nil, cons>(q_gen_743, q_gen_742) -> q_gen_741
<b, cons, cons>(q_gen_746, q_gen_745) -> q_gen_741
<b, nil, cons>(q_gen_743, q_gen_742) -> q_gen_741
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_740, q_gen_748, q_gen_749, q_gen_773, q_gen_774, q_gen_775, q_gen_776, q_gen_777, q_gen_787, q_gen_788, q_gen_789, q_gen_794, q_gen_795, q_gen_801},
Q_f={q_gen_740},
Delta=
{
<cons>(q_gen_774, q_gen_787) -> q_gen_748
<cons>(q_gen_801, q_gen_773) -> q_gen_748
<nil>() -> q_gen_748
<cons>(q_gen_774, q_gen_748) -> q_gen_773
<b>() -> q_gen_774
<z>() -> q_gen_776
<cons>(q_gen_774, q_gen_773) -> q_gen_787
<cons>(q_gen_801, q_gen_748) -> q_gen_787
<s>(q_gen_776) -> q_gen_789
<s>(q_gen_789) -> q_gen_795
<s>(q_gen_795) -> q_gen_795
<a>() -> q_gen_801
<cons, s>(q_gen_749, q_gen_748) -> q_gen_740
<cons, s>(q_gen_775, q_gen_773) -> q_gen_740
<cons, s>(q_gen_775, q_gen_787) -> q_gen_740
<cons, s>(q_gen_788, q_gen_787) -> q_gen_740
<nil, z>() -> q_gen_740
<a, s>(q_gen_795) -> q_gen_749
<a, z>() -> q_gen_749
<b, z>() -> q_gen_749
<a, s>(q_gen_776) -> q_gen_775
<b, s>(q_gen_776) -> q_gen_775
<cons, s>(q_gen_749, q_gen_773) -> q_gen_777
<cons, s>(q_gen_775, q_gen_748) -> q_gen_777
<cons, s>(q_gen_788, q_gen_748) -> q_gen_777
<cons, s>(q_gen_788, q_gen_773) -> q_gen_777
<cons, s>(q_gen_794, q_gen_748) -> q_gen_777
<cons, s>(q_gen_794, q_gen_773) -> q_gen_777
<cons, s>(q_gen_794, q_gen_787) -> q_gen_777
<b, s>(q_gen_789) -> q_gen_788
<b, s>(q_gen_795) -> q_gen_794
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_738, q_gen_752},
Q_f={q_gen_738},
Delta=
{
<a, a>() -> q_gen_738
<a, b>() -> q_gen_738
<b, b>() -> q_gen_738
<b, a>() -> q_gen_752
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_737, q_gen_751},
Q_f={q_gen_737},
Delta=
{
<cons, cons>(q_gen_751, q_gen_737) -> q_gen_737
<nil, nil>() -> q_gen_737
<a, a>() -> q_gen_751
<a, b>() -> q_gen_751
<b, a>() -> q_gen_751
<b, b>() -> q_gen_751
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 35
() -> length([nil, z]) -> 35
() -> leq([a, y]) -> 35
() -> leq([b, b]) -> 35
() -> sort([nil, nil]) -> 35
(insert([x, z, _yc]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _yc)]) -> 35
(insert([y, _dd, _ed]) /\ sort([z, _dd])) -> sort([cons(y, z), _ed]) -> 40
(length([_nd, _od]) /\ length([l, _md]) /\ sort([l, _nd])) -> eq_nat([_md, _od]) -> 40
(length([ll, _id])) -> length([cons(x, ll), s(_id)]) -> 43
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 36
(leq([b, a])) -> BOT -> 36
}
Sat witness: Found: ((length([ll, _id])) -> length([cons(x, ll), s(_id)]), {
_id -> s(s(s(s(z))))  ;  ll -> cons(a, nil)  ;  x -> b
})

-------------------------------------------
Step 48, which took 0.134387 s (model generation: 0.131937,  model checking: 0.002450):

Model:
|_
{
insert -> 
{{{
Q={q_gen_741, q_gen_742, q_gen_743, q_gen_745, q_gen_746},
Q_f={q_gen_741},
Delta=
{
<nil>() -> q_gen_742
<a>() -> q_gen_743
<b>() -> q_gen_743
<cons, cons>(q_gen_746, q_gen_745) -> q_gen_745
<nil, cons>(q_gen_743, q_gen_742) -> q_gen_745
<a, a>() -> q_gen_746
<a, b>() -> q_gen_746
<b, a>() -> q_gen_746
<b, b>() -> q_gen_746
<a, cons, cons>(q_gen_746, q_gen_745) -> q_gen_741
<a, nil, cons>(q_gen_743, q_gen_742) -> q_gen_741
<b, cons, cons>(q_gen_746, q_gen_745) -> q_gen_741
<b, nil, cons>(q_gen_743, q_gen_742) -> q_gen_741
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_740, q_gen_748, q_gen_749, q_gen_773, q_gen_774, q_gen_775, q_gen_776, q_gen_777, q_gen_787, q_gen_788, q_gen_789, q_gen_794, q_gen_795, q_gen_801},
Q_f={q_gen_740},
Delta=
{
<cons>(q_gen_801, q_gen_773) -> q_gen_748
<nil>() -> q_gen_748
<cons>(q_gen_774, q_gen_748) -> q_gen_773
<b>() -> q_gen_774
<z>() -> q_gen_776
<cons>(q_gen_774, q_gen_773) -> q_gen_787
<cons>(q_gen_774, q_gen_787) -> q_gen_787
<cons>(q_gen_801, q_gen_748) -> q_gen_787
<s>(q_gen_776) -> q_gen_789
<s>(q_gen_789) -> q_gen_795
<s>(q_gen_795) -> q_gen_795
<a>() -> q_gen_801
<cons, s>(q_gen_749, q_gen_748) -> q_gen_740
<cons, s>(q_gen_775, q_gen_773) -> q_gen_740
<cons, s>(q_gen_775, q_gen_787) -> q_gen_740
<cons, s>(q_gen_788, q_gen_787) -> q_gen_740
<nil, z>() -> q_gen_740
<a, z>() -> q_gen_749
<b, z>() -> q_gen_749
<a, s>(q_gen_776) -> q_gen_775
<b, s>(q_gen_776) -> q_gen_775
<cons, s>(q_gen_749, q_gen_787) -> q_gen_777
<cons, s>(q_gen_775, q_gen_748) -> q_gen_777
<cons, s>(q_gen_788, q_gen_748) -> q_gen_777
<cons, s>(q_gen_788, q_gen_773) -> q_gen_777
<cons, s>(q_gen_794, q_gen_748) -> q_gen_777
<cons, s>(q_gen_794, q_gen_773) -> q_gen_777
<cons, s>(q_gen_794, q_gen_787) -> q_gen_777
<a, s>(q_gen_795) -> q_gen_788
<b, s>(q_gen_789) -> q_gen_788
<b, s>(q_gen_795) -> q_gen_794
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_738, q_gen_752},
Q_f={q_gen_738},
Delta=
{
<a, a>() -> q_gen_738
<a, b>() -> q_gen_738
<b, b>() -> q_gen_738
<b, a>() -> q_gen_752
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_737, q_gen_751},
Q_f={q_gen_737},
Delta=
{
<cons, cons>(q_gen_751, q_gen_737) -> q_gen_737
<nil, nil>() -> q_gen_737
<a, a>() -> q_gen_751
<a, b>() -> q_gen_751
<b, a>() -> q_gen_751
<b, b>() -> q_gen_751
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 36
() -> length([nil, z]) -> 36
() -> leq([a, y]) -> 36
() -> leq([b, b]) -> 36
() -> sort([nil, nil]) -> 36
(insert([x, z, _yc]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _yc)]) -> 36
(insert([y, _dd, _ed]) /\ sort([z, _dd])) -> sort([cons(y, z), _ed]) -> 40
(length([_nd, _od]) /\ length([l, _md]) /\ sort([l, _nd])) -> eq_nat([_md, _od]) -> 43
(length([ll, _id])) -> length([cons(x, ll), s(_id)]) -> 43
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 37
(leq([b, a])) -> BOT -> 37
}
Sat witness: Found: ((length([_nd, _od]) /\ length([l, _md]) /\ sort([l, _nd])) -> eq_nat([_md, _od]), {
_md -> s(s(s(z)))  ;  _nd -> cons(b, cons(b, nil))  ;  _od -> s(s(z))  ;  l -> cons(b, cons(a, nil))
})

-------------------------------------------
Step 49, which took 0.144391 s (model generation: 0.140847,  model checking: 0.003544):

Model:
|_
{
insert -> 
{{{
Q={q_gen_741, q_gen_742, q_gen_743, q_gen_745, q_gen_746},
Q_f={q_gen_741},
Delta=
{
<nil>() -> q_gen_742
<a>() -> q_gen_743
<b>() -> q_gen_743
<cons, cons>(q_gen_746, q_gen_745) -> q_gen_745
<nil, cons>(q_gen_743, q_gen_742) -> q_gen_745
<a, a>() -> q_gen_746
<a, b>() -> q_gen_746
<b, a>() -> q_gen_746
<b, b>() -> q_gen_746
<a, cons, cons>(q_gen_746, q_gen_745) -> q_gen_741
<a, nil, cons>(q_gen_743, q_gen_742) -> q_gen_741
<b, cons, cons>(q_gen_746, q_gen_745) -> q_gen_741
<b, nil, cons>(q_gen_743, q_gen_742) -> q_gen_741
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_740, q_gen_748, q_gen_749, q_gen_773, q_gen_774, q_gen_775, q_gen_776, q_gen_777, q_gen_787, q_gen_788, q_gen_789, q_gen_794, q_gen_795, q_gen_801},
Q_f={q_gen_740},
Delta=
{
<cons>(q_gen_801, q_gen_773) -> q_gen_748
<nil>() -> q_gen_748
<cons>(q_gen_774, q_gen_748) -> q_gen_773
<cons>(q_gen_801, q_gen_748) -> q_gen_773
<b>() -> q_gen_774
<z>() -> q_gen_776
<cons>(q_gen_774, q_gen_773) -> q_gen_787
<cons>(q_gen_774, q_gen_787) -> q_gen_787
<s>(q_gen_776) -> q_gen_789
<s>(q_gen_789) -> q_gen_795
<s>(q_gen_795) -> q_gen_795
<a>() -> q_gen_801
<cons, s>(q_gen_749, q_gen_748) -> q_gen_740
<cons, s>(q_gen_775, q_gen_773) -> q_gen_740
<cons, s>(q_gen_788, q_gen_787) -> q_gen_740
<nil, z>() -> q_gen_740
<a, z>() -> q_gen_749
<b, z>() -> q_gen_749
<a, s>(q_gen_776) -> q_gen_775
<b, s>(q_gen_776) -> q_gen_775
<cons, s>(q_gen_749, q_gen_787) -> q_gen_777
<cons, s>(q_gen_775, q_gen_748) -> q_gen_777
<cons, s>(q_gen_788, q_gen_748) -> q_gen_777
<cons, s>(q_gen_788, q_gen_773) -> q_gen_777
<cons, s>(q_gen_794, q_gen_748) -> q_gen_777
<cons, s>(q_gen_794, q_gen_773) -> q_gen_777
<cons, s>(q_gen_794, q_gen_787) -> q_gen_777
<a, s>(q_gen_795) -> q_gen_788
<b, s>(q_gen_789) -> q_gen_788
<b, s>(q_gen_795) -> q_gen_794
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_738, q_gen_752},
Q_f={q_gen_738},
Delta=
{
<a, a>() -> q_gen_738
<a, b>() -> q_gen_738
<b, b>() -> q_gen_738
<b, a>() -> q_gen_752
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_737, q_gen_751},
Q_f={q_gen_737},
Delta=
{
<cons, cons>(q_gen_751, q_gen_737) -> q_gen_737
<nil, nil>() -> q_gen_737
<a, a>() -> q_gen_751
<a, b>() -> q_gen_751
<b, a>() -> q_gen_751
<b, b>() -> q_gen_751
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 37
() -> length([nil, z]) -> 37
() -> leq([a, y]) -> 37
() -> leq([b, b]) -> 37
() -> sort([nil, nil]) -> 37
(insert([x, z, _yc]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _yc)]) -> 37
(insert([y, _dd, _ed]) /\ sort([z, _dd])) -> sort([cons(y, z), _ed]) -> 41
(length([_nd, _od]) /\ length([l, _md]) /\ sort([l, _nd])) -> eq_nat([_md, _od]) -> 43
(length([ll, _id])) -> length([cons(x, ll), s(_id)]) -> 46
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 38
(leq([b, a])) -> BOT -> 38
}
Sat witness: Found: ((length([ll, _id])) -> length([cons(x, ll), s(_id)]), {
_id -> s(s(z))  ;  ll -> cons(a, cons(a, nil))  ;  x -> b
})

-------------------------------------------
Step 50, which took 0.181175 s (model generation: 0.179294,  model checking: 0.001881):

Model:
|_
{
insert -> 
{{{
Q={q_gen_741, q_gen_742, q_gen_743, q_gen_745, q_gen_746},
Q_f={q_gen_741},
Delta=
{
<nil>() -> q_gen_742
<a>() -> q_gen_743
<b>() -> q_gen_743
<cons, cons>(q_gen_746, q_gen_745) -> q_gen_745
<nil, cons>(q_gen_743, q_gen_742) -> q_gen_745
<a, a>() -> q_gen_746
<a, b>() -> q_gen_746
<b, a>() -> q_gen_746
<b, b>() -> q_gen_746
<a, cons, cons>(q_gen_746, q_gen_745) -> q_gen_741
<a, nil, cons>(q_gen_743, q_gen_742) -> q_gen_741
<b, cons, cons>(q_gen_746, q_gen_745) -> q_gen_741
<b, nil, cons>(q_gen_743, q_gen_742) -> q_gen_741
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_740, q_gen_748, q_gen_749, q_gen_773, q_gen_774, q_gen_775, q_gen_776, q_gen_777, q_gen_787, q_gen_788, q_gen_789},
Q_f={q_gen_740},
Delta=
{
<nil>() -> q_gen_748
<cons>(q_gen_774, q_gen_748) -> q_gen_773
<a>() -> q_gen_774
<b>() -> q_gen_774
<z>() -> q_gen_776
<cons>(q_gen_774, q_gen_773) -> q_gen_787
<cons>(q_gen_774, q_gen_787) -> q_gen_787
<s>(q_gen_776) -> q_gen_789
<s>(q_gen_789) -> q_gen_789
<cons, s>(q_gen_749, q_gen_748) -> q_gen_740
<cons, s>(q_gen_775, q_gen_773) -> q_gen_740
<cons, s>(q_gen_788, q_gen_787) -> q_gen_740
<nil, z>() -> q_gen_740
<a, z>() -> q_gen_749
<b, z>() -> q_gen_749
<a, s>(q_gen_776) -> q_gen_775
<b, s>(q_gen_776) -> q_gen_775
<cons, s>(q_gen_749, q_gen_787) -> q_gen_777
<cons, s>(q_gen_775, q_gen_748) -> q_gen_777
<cons, s>(q_gen_775, q_gen_787) -> q_gen_777
<cons, s>(q_gen_788, q_gen_748) -> q_gen_777
<cons, s>(q_gen_788, q_gen_773) -> q_gen_777
<a, s>(q_gen_789) -> q_gen_788
<b, s>(q_gen_789) -> q_gen_788
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_738, q_gen_752},
Q_f={q_gen_738},
Delta=
{
<a, a>() -> q_gen_738
<a, b>() -> q_gen_738
<b, b>() -> q_gen_738
<b, a>() -> q_gen_752
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_737, q_gen_750, q_gen_751, q_gen_763, q_gen_764, q_gen_805},
Q_f={q_gen_737, q_gen_750, q_gen_763},
Delta=
{
<cons, cons>(q_gen_764, q_gen_750) -> q_gen_737
<nil, nil>() -> q_gen_737
<cons, cons>(q_gen_751, q_gen_737) -> q_gen_750
<b, b>() -> q_gen_751
<cons, cons>(q_gen_751, q_gen_750) -> q_gen_763
<cons, cons>(q_gen_764, q_gen_737) -> q_gen_763
<cons, cons>(q_gen_764, q_gen_763) -> q_gen_763
<a, a>() -> q_gen_764
<a, b>() -> q_gen_764
<b, a>() -> q_gen_764
<cons, cons>(q_gen_751, q_gen_763) -> q_gen_805
<cons, cons>(q_gen_764, q_gen_805) -> q_gen_805
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 38
() -> length([nil, z]) -> 38
() -> leq([a, y]) -> 38
() -> leq([b, b]) -> 38
() -> sort([nil, nil]) -> 38
(insert([x, z, _yc]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _yc)]) -> 38
(insert([y, _dd, _ed]) /\ sort([z, _dd])) -> sort([cons(y, z), _ed]) -> 44
(length([_nd, _od]) /\ length([l, _md]) /\ sort([l, _nd])) -> eq_nat([_md, _od]) -> 43
(length([ll, _id])) -> length([cons(x, ll), s(_id)]) -> 46
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 39
(leq([b, a])) -> BOT -> 39
}
Sat witness: Found: ((insert([y, _dd, _ed]) /\ sort([z, _dd])) -> sort([cons(y, z), _ed]), {
_dd -> cons(a, nil)  ;  _ed -> cons(b, cons(b, nil))  ;  y -> b  ;  z -> cons(a, nil)
})

-------------------------------------------
Step 51, which took 0.169867 s (model generation: 0.167389,  model checking: 0.002478):

Model:
|_
{
insert -> 
{{{
Q={q_gen_741, q_gen_742, q_gen_743, q_gen_745, q_gen_746},
Q_f={q_gen_741},
Delta=
{
<nil>() -> q_gen_742
<a>() -> q_gen_743
<b>() -> q_gen_743
<cons, cons>(q_gen_746, q_gen_745) -> q_gen_745
<nil, cons>(q_gen_743, q_gen_742) -> q_gen_745
<a, a>() -> q_gen_746
<a, b>() -> q_gen_746
<b, a>() -> q_gen_746
<b, b>() -> q_gen_746
<a, cons, cons>(q_gen_746, q_gen_745) -> q_gen_741
<a, nil, cons>(q_gen_743, q_gen_742) -> q_gen_741
<b, cons, cons>(q_gen_746, q_gen_745) -> q_gen_741
<b, nil, cons>(q_gen_743, q_gen_742) -> q_gen_741
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_740, q_gen_748, q_gen_749, q_gen_773, q_gen_774, q_gen_775, q_gen_776, q_gen_777, q_gen_787, q_gen_788, q_gen_789},
Q_f={q_gen_740},
Delta=
{
<nil>() -> q_gen_748
<cons>(q_gen_774, q_gen_748) -> q_gen_773
<cons>(q_gen_774, q_gen_787) -> q_gen_773
<a>() -> q_gen_774
<b>() -> q_gen_774
<s>(q_gen_789) -> q_gen_776
<z>() -> q_gen_776
<cons>(q_gen_774, q_gen_773) -> q_gen_787
<s>(q_gen_776) -> q_gen_789
<cons, s>(q_gen_749, q_gen_748) -> q_gen_740
<cons, s>(q_gen_749, q_gen_773) -> q_gen_740
<cons, s>(q_gen_775, q_gen_773) -> q_gen_740
<cons, s>(q_gen_788, q_gen_787) -> q_gen_740
<nil, z>() -> q_gen_740
<a, z>() -> q_gen_749
<b, z>() -> q_gen_749
<a, s>(q_gen_776) -> q_gen_775
<b, s>(q_gen_776) -> q_gen_775
<cons, s>(q_gen_775, q_gen_748) -> q_gen_777
<cons, s>(q_gen_775, q_gen_787) -> q_gen_777
<cons, s>(q_gen_788, q_gen_748) -> q_gen_777
<cons, s>(q_gen_788, q_gen_773) -> q_gen_777
<a, s>(q_gen_789) -> q_gen_788
<b, s>(q_gen_789) -> q_gen_788
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_738, q_gen_752},
Q_f={q_gen_738},
Delta=
{
<a, a>() -> q_gen_738
<a, b>() -> q_gen_738
<b, b>() -> q_gen_738
<b, a>() -> q_gen_752
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_737, q_gen_750, q_gen_751, q_gen_764, q_gen_791, q_gen_805},
Q_f={q_gen_737, q_gen_750, q_gen_791},
Delta=
{
<cons, cons>(q_gen_764, q_gen_750) -> q_gen_737
<nil, nil>() -> q_gen_737
<cons, cons>(q_gen_751, q_gen_737) -> q_gen_750
<cons, cons>(q_gen_764, q_gen_737) -> q_gen_750
<b, b>() -> q_gen_751
<a, a>() -> q_gen_764
<a, b>() -> q_gen_764
<b, a>() -> q_gen_764
<cons, cons>(q_gen_751, q_gen_750) -> q_gen_791
<cons, cons>(q_gen_751, q_gen_791) -> q_gen_805
<cons, cons>(q_gen_764, q_gen_805) -> q_gen_805
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 39
() -> length([nil, z]) -> 39
() -> leq([a, y]) -> 39
() -> leq([b, b]) -> 39
() -> sort([nil, nil]) -> 39
(insert([x, z, _yc]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _yc)]) -> 39
(insert([y, _dd, _ed]) /\ sort([z, _dd])) -> sort([cons(y, z), _ed]) -> 44
(length([_nd, _od]) /\ length([l, _md]) /\ sort([l, _nd])) -> eq_nat([_md, _od]) -> 46
(length([ll, _id])) -> length([cons(x, ll), s(_id)]) -> 46
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 40
(leq([b, a])) -> BOT -> 40
}
Sat witness: Found: ((length([_nd, _od]) /\ length([l, _md]) /\ sort([l, _nd])) -> eq_nat([_md, _od]), {
_md -> s(s(z))  ;  _nd -> cons(b, cons(b, nil))  ;  _od -> s(z)  ;  l -> cons(b, cons(b, nil))
})

-------------------------------------------
Step 52, which took 0.179207 s (model generation: 0.177183,  model checking: 0.002024):

Model:
|_
{
insert -> 
{{{
Q={q_gen_741, q_gen_742, q_gen_743, q_gen_745, q_gen_746},
Q_f={q_gen_741},
Delta=
{
<nil>() -> q_gen_742
<a>() -> q_gen_743
<b>() -> q_gen_743
<cons, cons>(q_gen_746, q_gen_745) -> q_gen_745
<nil, cons>(q_gen_743, q_gen_742) -> q_gen_745
<a, a>() -> q_gen_746
<a, b>() -> q_gen_746
<b, a>() -> q_gen_746
<b, b>() -> q_gen_746
<a, cons, cons>(q_gen_746, q_gen_745) -> q_gen_741
<a, nil, cons>(q_gen_743, q_gen_742) -> q_gen_741
<b, cons, cons>(q_gen_746, q_gen_745) -> q_gen_741
<b, nil, cons>(q_gen_743, q_gen_742) -> q_gen_741
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_740, q_gen_748, q_gen_749, q_gen_773, q_gen_774, q_gen_775, q_gen_776, q_gen_777, q_gen_787, q_gen_788, q_gen_789},
Q_f={q_gen_740},
Delta=
{
<nil>() -> q_gen_748
<cons>(q_gen_774, q_gen_748) -> q_gen_773
<a>() -> q_gen_774
<b>() -> q_gen_774
<z>() -> q_gen_776
<cons>(q_gen_774, q_gen_773) -> q_gen_787
<cons>(q_gen_774, q_gen_787) -> q_gen_787
<s>(q_gen_776) -> q_gen_789
<s>(q_gen_789) -> q_gen_789
<cons, s>(q_gen_749, q_gen_748) -> q_gen_740
<cons, s>(q_gen_775, q_gen_773) -> q_gen_740
<cons, s>(q_gen_788, q_gen_787) -> q_gen_740
<nil, z>() -> q_gen_740
<a, z>() -> q_gen_749
<b, z>() -> q_gen_749
<a, s>(q_gen_776) -> q_gen_775
<b, s>(q_gen_776) -> q_gen_775
<cons, s>(q_gen_749, q_gen_773) -> q_gen_777
<cons, s>(q_gen_749, q_gen_787) -> q_gen_777
<cons, s>(q_gen_775, q_gen_748) -> q_gen_777
<cons, s>(q_gen_775, q_gen_787) -> q_gen_777
<cons, s>(q_gen_788, q_gen_748) -> q_gen_777
<cons, s>(q_gen_788, q_gen_773) -> q_gen_777
<a, s>(q_gen_789) -> q_gen_788
<b, s>(q_gen_789) -> q_gen_788
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_738, q_gen_752},
Q_f={q_gen_738},
Delta=
{
<a, a>() -> q_gen_738
<a, b>() -> q_gen_738
<b, b>() -> q_gen_738
<b, a>() -> q_gen_752
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_737, q_gen_750, q_gen_751, q_gen_764, q_gen_791, q_gen_805},
Q_f={q_gen_737, q_gen_750, q_gen_791},
Delta=
{
<cons, cons>(q_gen_764, q_gen_737) -> q_gen_737
<nil, nil>() -> q_gen_737
<cons, cons>(q_gen_751, q_gen_737) -> q_gen_750
<cons, cons>(q_gen_764, q_gen_750) -> q_gen_750
<cons, cons>(q_gen_764, q_gen_791) -> q_gen_750
<b, b>() -> q_gen_751
<a, a>() -> q_gen_764
<a, b>() -> q_gen_764
<b, a>() -> q_gen_764
<cons, cons>(q_gen_751, q_gen_750) -> q_gen_791
<cons, cons>(q_gen_751, q_gen_791) -> q_gen_805
<cons, cons>(q_gen_764, q_gen_805) -> q_gen_805
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 40
() -> length([nil, z]) -> 40
() -> leq([a, y]) -> 40
() -> leq([b, b]) -> 40
() -> sort([nil, nil]) -> 40
(insert([x, z, _yc]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _yc)]) -> 40
(insert([y, _dd, _ed]) /\ sort([z, _dd])) -> sort([cons(y, z), _ed]) -> 47
(length([_nd, _od]) /\ length([l, _md]) /\ sort([l, _nd])) -> eq_nat([_md, _od]) -> 46
(length([ll, _id])) -> length([cons(x, ll), s(_id)]) -> 46
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 41
(leq([b, a])) -> BOT -> 41
}
Sat witness: Found: ((insert([y, _dd, _ed]) /\ sort([z, _dd])) -> sort([cons(y, z), _ed]), {
_dd -> cons(b, cons(b, nil))  ;  _ed -> cons(b, cons(b, cons(b, nil)))  ;  y -> b  ;  z -> cons(b, cons(b, nil))
})

-------------------------------------------
Step 53, which took 0.155434 s (model generation: 0.152278,  model checking: 0.003156):

Model:
|_
{
insert -> 
{{{
Q={q_gen_741, q_gen_742, q_gen_743, q_gen_745, q_gen_746},
Q_f={q_gen_741},
Delta=
{
<nil>() -> q_gen_742
<a>() -> q_gen_743
<b>() -> q_gen_743
<cons, cons>(q_gen_746, q_gen_745) -> q_gen_745
<nil, cons>(q_gen_743, q_gen_742) -> q_gen_745
<a, a>() -> q_gen_746
<a, b>() -> q_gen_746
<b, a>() -> q_gen_746
<b, b>() -> q_gen_746
<a, cons, cons>(q_gen_746, q_gen_745) -> q_gen_741
<a, nil, cons>(q_gen_743, q_gen_742) -> q_gen_741
<b, cons, cons>(q_gen_746, q_gen_745) -> q_gen_741
<b, nil, cons>(q_gen_743, q_gen_742) -> q_gen_741
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_740, q_gen_748, q_gen_749, q_gen_773, q_gen_774, q_gen_775, q_gen_776, q_gen_777, q_gen_787, q_gen_788, q_gen_789, q_gen_794, q_gen_795, q_gen_800, q_gen_801},
Q_f={q_gen_740},
Delta=
{
<nil>() -> q_gen_748
<cons>(q_gen_774, q_gen_748) -> q_gen_773
<b>() -> q_gen_774
<z>() -> q_gen_776
<cons>(q_gen_774, q_gen_773) -> q_gen_787
<cons>(q_gen_801, q_gen_773) -> q_gen_787
<cons>(q_gen_801, q_gen_800) -> q_gen_787
<s>(q_gen_776) -> q_gen_789
<s>(q_gen_789) -> q_gen_795
<s>(q_gen_795) -> q_gen_795
<cons>(q_gen_774, q_gen_787) -> q_gen_800
<cons>(q_gen_774, q_gen_800) -> q_gen_800
<cons>(q_gen_801, q_gen_748) -> q_gen_800
<a>() -> q_gen_801
<cons, s>(q_gen_749, q_gen_748) -> q_gen_740
<cons, s>(q_gen_775, q_gen_773) -> q_gen_740
<cons, s>(q_gen_775, q_gen_800) -> q_gen_740
<cons, s>(q_gen_788, q_gen_787) -> q_gen_740
<cons, s>(q_gen_794, q_gen_800) -> q_gen_740
<nil, z>() -> q_gen_740
<a, s>(q_gen_795) -> q_gen_749
<a, z>() -> q_gen_749
<b, z>() -> q_gen_749
<a, s>(q_gen_776) -> q_gen_775
<b, s>(q_gen_776) -> q_gen_775
<cons, s>(q_gen_749, q_gen_773) -> q_gen_777
<cons, s>(q_gen_749, q_gen_800) -> q_gen_777
<cons, s>(q_gen_775, q_gen_748) -> q_gen_777
<cons, s>(q_gen_775, q_gen_787) -> q_gen_777
<cons, s>(q_gen_788, q_gen_748) -> q_gen_777
<cons, s>(q_gen_788, q_gen_773) -> q_gen_777
<cons, s>(q_gen_788, q_gen_800) -> q_gen_777
<cons, s>(q_gen_794, q_gen_748) -> q_gen_777
<cons, s>(q_gen_794, q_gen_773) -> q_gen_777
<cons, s>(q_gen_794, q_gen_787) -> q_gen_777
<b, s>(q_gen_789) -> q_gen_788
<b, s>(q_gen_795) -> q_gen_794
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_738, q_gen_752},
Q_f={q_gen_738},
Delta=
{
<a, a>() -> q_gen_738
<a, b>() -> q_gen_738
<b, b>() -> q_gen_738
<b, a>() -> q_gen_752
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_737, q_gen_751},
Q_f={q_gen_737},
Delta=
{
<cons, cons>(q_gen_751, q_gen_737) -> q_gen_737
<nil, nil>() -> q_gen_737
<a, a>() -> q_gen_751
<a, b>() -> q_gen_751
<b, a>() -> q_gen_751
<b, b>() -> q_gen_751
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 41
() -> length([nil, z]) -> 41
() -> leq([a, y]) -> 41
() -> leq([b, b]) -> 41
() -> sort([nil, nil]) -> 41
(insert([x, z, _yc]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _yc)]) -> 41
(insert([y, _dd, _ed]) /\ sort([z, _dd])) -> sort([cons(y, z), _ed]) -> 47
(length([_nd, _od]) /\ length([l, _md]) /\ sort([l, _nd])) -> eq_nat([_md, _od]) -> 46
(length([ll, _id])) -> length([cons(x, ll), s(_id)]) -> 49
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 42
(leq([b, a])) -> BOT -> 42
}
Sat witness: Found: ((length([ll, _id])) -> length([cons(x, ll), s(_id)]), {
_id -> s(s(s(s(z))))  ;  ll -> cons(b, cons(a, nil))  ;  x -> a
})

-------------------------------------------
Step 54, which took 0.203728 s (model generation: 0.200050,  model checking: 0.003678):

Model:
|_
{
insert -> 
{{{
Q={q_gen_741, q_gen_742, q_gen_743, q_gen_745, q_gen_746},
Q_f={q_gen_741},
Delta=
{
<nil>() -> q_gen_742
<a>() -> q_gen_743
<b>() -> q_gen_743
<cons, cons>(q_gen_746, q_gen_745) -> q_gen_745
<nil, cons>(q_gen_743, q_gen_742) -> q_gen_745
<a, a>() -> q_gen_746
<a, b>() -> q_gen_746
<b, a>() -> q_gen_746
<b, b>() -> q_gen_746
<a, cons, cons>(q_gen_746, q_gen_745) -> q_gen_741
<a, nil, cons>(q_gen_743, q_gen_742) -> q_gen_741
<b, cons, cons>(q_gen_746, q_gen_745) -> q_gen_741
<b, nil, cons>(q_gen_743, q_gen_742) -> q_gen_741
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_740, q_gen_748, q_gen_749, q_gen_773, q_gen_774, q_gen_775, q_gen_776, q_gen_777, q_gen_787, q_gen_788, q_gen_789, q_gen_794, q_gen_795, q_gen_800, q_gen_801},
Q_f={q_gen_740},
Delta=
{
<cons>(q_gen_801, q_gen_773) -> q_gen_748
<nil>() -> q_gen_748
<cons>(q_gen_774, q_gen_748) -> q_gen_773
<b>() -> q_gen_774
<z>() -> q_gen_776
<cons>(q_gen_774, q_gen_773) -> q_gen_787
<cons>(q_gen_774, q_gen_787) -> q_gen_787
<cons>(q_gen_801, q_gen_800) -> q_gen_787
<s>(q_gen_776) -> q_gen_789
<s>(q_gen_789) -> q_gen_795
<s>(q_gen_795) -> q_gen_795
<cons>(q_gen_774, q_gen_800) -> q_gen_800
<cons>(q_gen_801, q_gen_748) -> q_gen_800
<a>() -> q_gen_801
<cons, s>(q_gen_749, q_gen_748) -> q_gen_740
<cons, s>(q_gen_749, q_gen_787) -> q_gen_740
<cons, s>(q_gen_775, q_gen_773) -> q_gen_740
<cons, s>(q_gen_775, q_gen_800) -> q_gen_740
<cons, s>(q_gen_788, q_gen_787) -> q_gen_740
<nil, z>() -> q_gen_740
<a, z>() -> q_gen_749
<b, z>() -> q_gen_749
<a, s>(q_gen_776) -> q_gen_775
<b, s>(q_gen_776) -> q_gen_775
<cons, s>(q_gen_749, q_gen_773) -> q_gen_777
<cons, s>(q_gen_775, q_gen_748) -> q_gen_777
<cons, s>(q_gen_788, q_gen_748) -> q_gen_777
<cons, s>(q_gen_788, q_gen_773) -> q_gen_777
<cons, s>(q_gen_788, q_gen_800) -> q_gen_777
<cons, s>(q_gen_794, q_gen_748) -> q_gen_777
<cons, s>(q_gen_794, q_gen_773) -> q_gen_777
<cons, s>(q_gen_794, q_gen_787) -> q_gen_777
<cons, s>(q_gen_794, q_gen_800) -> q_gen_777
<a, s>(q_gen_795) -> q_gen_788
<b, s>(q_gen_789) -> q_gen_788
<b, s>(q_gen_795) -> q_gen_794
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_738, q_gen_752},
Q_f={q_gen_738},
Delta=
{
<a, a>() -> q_gen_738
<a, b>() -> q_gen_738
<b, b>() -> q_gen_738
<b, a>() -> q_gen_752
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_737, q_gen_751},
Q_f={q_gen_737},
Delta=
{
<cons, cons>(q_gen_751, q_gen_737) -> q_gen_737
<nil, nil>() -> q_gen_737
<a, a>() -> q_gen_751
<a, b>() -> q_gen_751
<b, a>() -> q_gen_751
<b, b>() -> q_gen_751
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 42
() -> length([nil, z]) -> 42
() -> leq([a, y]) -> 42
() -> leq([b, b]) -> 42
() -> sort([nil, nil]) -> 42
(insert([x, z, _yc]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _yc)]) -> 42
(insert([y, _dd, _ed]) /\ sort([z, _dd])) -> sort([cons(y, z), _ed]) -> 47
(length([_nd, _od]) /\ length([l, _md]) /\ sort([l, _nd])) -> eq_nat([_md, _od]) -> 49
(length([ll, _id])) -> length([cons(x, ll), s(_id)]) -> 49
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 43
(leq([b, a])) -> BOT -> 43
}
Sat witness: Found: ((length([_nd, _od]) /\ length([l, _md]) /\ sort([l, _nd])) -> eq_nat([_md, _od]), {
_md -> s(s(s(z)))  ;  _nd -> cons(a, cons(b, cons(a, nil)))  ;  _od -> s(s(z))  ;  l -> cons(b, cons(b, cons(b, nil)))
})

-------------------------------------------
Step 55, which took 0.222677 s (model generation: 0.217395,  model checking: 0.005282):

Model:
|_
{
insert -> 
{{{
Q={q_gen_741, q_gen_742, q_gen_743, q_gen_745, q_gen_746},
Q_f={q_gen_741},
Delta=
{
<nil>() -> q_gen_742
<a>() -> q_gen_743
<b>() -> q_gen_743
<cons, cons>(q_gen_746, q_gen_745) -> q_gen_745
<nil, cons>(q_gen_743, q_gen_742) -> q_gen_745
<a, a>() -> q_gen_746
<a, b>() -> q_gen_746
<b, a>() -> q_gen_746
<b, b>() -> q_gen_746
<a, cons, cons>(q_gen_746, q_gen_745) -> q_gen_741
<a, nil, cons>(q_gen_743, q_gen_742) -> q_gen_741
<b, cons, cons>(q_gen_746, q_gen_745) -> q_gen_741
<b, nil, cons>(q_gen_743, q_gen_742) -> q_gen_741
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_740, q_gen_748, q_gen_749, q_gen_773, q_gen_774, q_gen_775, q_gen_776, q_gen_777, q_gen_787, q_gen_788, q_gen_789, q_gen_794, q_gen_795, q_gen_800, q_gen_801},
Q_f={q_gen_740},
Delta=
{
<cons>(q_gen_774, q_gen_800) -> q_gen_748
<cons>(q_gen_801, q_gen_773) -> q_gen_748
<nil>() -> q_gen_748
<cons>(q_gen_774, q_gen_748) -> q_gen_773
<b>() -> q_gen_774
<z>() -> q_gen_776
<cons>(q_gen_774, q_gen_773) -> q_gen_787
<cons>(q_gen_774, q_gen_787) -> q_gen_787
<cons>(q_gen_801, q_gen_800) -> q_gen_787
<s>(q_gen_776) -> q_gen_789
<s>(q_gen_789) -> q_gen_795
<s>(q_gen_795) -> q_gen_795
<cons>(q_gen_801, q_gen_748) -> q_gen_800
<a>() -> q_gen_801
<cons, s>(q_gen_749, q_gen_748) -> q_gen_740
<cons, s>(q_gen_749, q_gen_787) -> q_gen_740
<cons, s>(q_gen_775, q_gen_773) -> q_gen_740
<cons, s>(q_gen_775, q_gen_800) -> q_gen_740
<cons, s>(q_gen_788, q_gen_787) -> q_gen_740
<nil, z>() -> q_gen_740
<a, z>() -> q_gen_749
<b, z>() -> q_gen_749
<a, s>(q_gen_776) -> q_gen_775
<b, s>(q_gen_776) -> q_gen_775
<cons, s>(q_gen_749, q_gen_773) -> q_gen_777
<cons, s>(q_gen_775, q_gen_748) -> q_gen_777
<cons, s>(q_gen_788, q_gen_748) -> q_gen_777
<cons, s>(q_gen_788, q_gen_773) -> q_gen_777
<cons, s>(q_gen_788, q_gen_800) -> q_gen_777
<cons, s>(q_gen_794, q_gen_748) -> q_gen_777
<cons, s>(q_gen_794, q_gen_773) -> q_gen_777
<cons, s>(q_gen_794, q_gen_787) -> q_gen_777
<cons, s>(q_gen_794, q_gen_800) -> q_gen_777
<b, s>(q_gen_789) -> q_gen_788
<a, s>(q_gen_795) -> q_gen_794
<b, s>(q_gen_795) -> q_gen_794
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_738, q_gen_752},
Q_f={q_gen_738},
Delta=
{
<a, a>() -> q_gen_738
<a, b>() -> q_gen_738
<b, b>() -> q_gen_738
<b, a>() -> q_gen_752
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_737, q_gen_751},
Q_f={q_gen_737},
Delta=
{
<cons, cons>(q_gen_751, q_gen_737) -> q_gen_737
<nil, nil>() -> q_gen_737
<a, a>() -> q_gen_751
<a, b>() -> q_gen_751
<b, a>() -> q_gen_751
<b, b>() -> q_gen_751
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 43
() -> length([nil, z]) -> 43
() -> leq([a, y]) -> 43
() -> leq([b, b]) -> 43
() -> sort([nil, nil]) -> 43
(insert([x, z, _yc]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _yc)]) -> 43
(insert([y, _dd, _ed]) /\ sort([z, _dd])) -> sort([cons(y, z), _ed]) -> 48
(length([_nd, _od]) /\ length([l, _md]) /\ sort([l, _nd])) -> eq_nat([_md, _od]) -> 49
(length([ll, _id])) -> length([cons(x, ll), s(_id)]) -> 52
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 44
(leq([b, a])) -> BOT -> 44
}
Sat witness: Found: ((length([ll, _id])) -> length([cons(x, ll), s(_id)]), {
_id -> s(s(z))  ;  ll -> cons(b, cons(a, nil))  ;  x -> b
})

-------------------------------------------
Step 56, which took 0.249232 s (model generation: 0.244568,  model checking: 0.004664):

Model:
|_
{
insert -> 
{{{
Q={q_gen_741, q_gen_742, q_gen_743, q_gen_745, q_gen_746},
Q_f={q_gen_741},
Delta=
{
<nil>() -> q_gen_742
<a>() -> q_gen_743
<b>() -> q_gen_743
<cons, cons>(q_gen_746, q_gen_745) -> q_gen_745
<nil, cons>(q_gen_743, q_gen_742) -> q_gen_745
<a, a>() -> q_gen_746
<a, b>() -> q_gen_746
<b, a>() -> q_gen_746
<b, b>() -> q_gen_746
<a, cons, cons>(q_gen_746, q_gen_745) -> q_gen_741
<a, nil, cons>(q_gen_743, q_gen_742) -> q_gen_741
<b, cons, cons>(q_gen_746, q_gen_745) -> q_gen_741
<b, nil, cons>(q_gen_743, q_gen_742) -> q_gen_741
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_740, q_gen_748, q_gen_749, q_gen_773, q_gen_774, q_gen_775, q_gen_776, q_gen_777, q_gen_787, q_gen_788, q_gen_789, q_gen_794, q_gen_795, q_gen_800, q_gen_801},
Q_f={q_gen_740},
Delta=
{
<cons>(q_gen_801, q_gen_773) -> q_gen_748
<nil>() -> q_gen_748
<cons>(q_gen_774, q_gen_748) -> q_gen_773
<b>() -> q_gen_774
<z>() -> q_gen_776
<cons>(q_gen_774, q_gen_773) -> q_gen_787
<cons>(q_gen_774, q_gen_787) -> q_gen_787
<cons>(q_gen_774, q_gen_800) -> q_gen_787
<cons>(q_gen_801, q_gen_800) -> q_gen_787
<s>(q_gen_776) -> q_gen_789
<s>(q_gen_789) -> q_gen_795
<s>(q_gen_795) -> q_gen_795
<cons>(q_gen_801, q_gen_748) -> q_gen_800
<a>() -> q_gen_801
<cons, s>(q_gen_749, q_gen_748) -> q_gen_740
<cons, s>(q_gen_749, q_gen_787) -> q_gen_740
<cons, s>(q_gen_775, q_gen_773) -> q_gen_740
<cons, s>(q_gen_775, q_gen_800) -> q_gen_740
<cons, s>(q_gen_788, q_gen_787) -> q_gen_740
<cons, s>(q_gen_794, q_gen_800) -> q_gen_740
<nil, z>() -> q_gen_740
<a, s>(q_gen_795) -> q_gen_749
<a, z>() -> q_gen_749
<b, z>() -> q_gen_749
<a, s>(q_gen_776) -> q_gen_775
<b, s>(q_gen_776) -> q_gen_775
<cons, s>(q_gen_749, q_gen_773) -> q_gen_777
<cons, s>(q_gen_775, q_gen_748) -> q_gen_777
<cons, s>(q_gen_775, q_gen_787) -> q_gen_777
<cons, s>(q_gen_788, q_gen_748) -> q_gen_777
<cons, s>(q_gen_788, q_gen_773) -> q_gen_777
<cons, s>(q_gen_788, q_gen_800) -> q_gen_777
<cons, s>(q_gen_794, q_gen_748) -> q_gen_777
<cons, s>(q_gen_794, q_gen_773) -> q_gen_777
<cons, s>(q_gen_794, q_gen_787) -> q_gen_777
<b, s>(q_gen_789) -> q_gen_788
<b, s>(q_gen_795) -> q_gen_794
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_738, q_gen_752},
Q_f={q_gen_738},
Delta=
{
<a, a>() -> q_gen_738
<a, b>() -> q_gen_738
<b, b>() -> q_gen_738
<b, a>() -> q_gen_752
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_737, q_gen_751},
Q_f={q_gen_737},
Delta=
{
<cons, cons>(q_gen_751, q_gen_737) -> q_gen_737
<nil, nil>() -> q_gen_737
<a, a>() -> q_gen_751
<a, b>() -> q_gen_751
<b, a>() -> q_gen_751
<b, b>() -> q_gen_751
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 44
() -> length([nil, z]) -> 44
() -> leq([a, y]) -> 44
() -> leq([b, b]) -> 44
() -> sort([nil, nil]) -> 44
(insert([x, z, _yc]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _yc)]) -> 44
(insert([y, _dd, _ed]) /\ sort([z, _dd])) -> sort([cons(y, z), _ed]) -> 49
(length([_nd, _od]) /\ length([l, _md]) /\ sort([l, _nd])) -> eq_nat([_md, _od]) -> 52
(length([ll, _id])) -> length([cons(x, ll), s(_id)]) -> 52
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 45
(leq([b, a])) -> BOT -> 45
}
Sat witness: Found: ((length([_nd, _od]) /\ length([l, _md]) /\ sort([l, _nd])) -> eq_nat([_md, _od]), {
_md -> s(s(s(z)))  ;  _nd -> cons(a, cons(b, cons(b, nil)))  ;  _od -> s(z)  ;  l -> cons(b, cons(a, cons(a, nil)))
})

-------------------------------------------
Step 57, which took 0.474546 s (model generation: 0.469974,  model checking: 0.004572):

Model:
|_
{
insert -> 
{{{
Q={q_gen_741, q_gen_742, q_gen_743, q_gen_745, q_gen_746},
Q_f={q_gen_741},
Delta=
{
<nil>() -> q_gen_742
<a>() -> q_gen_743
<b>() -> q_gen_743
<cons, cons>(q_gen_746, q_gen_745) -> q_gen_745
<nil, cons>(q_gen_743, q_gen_742) -> q_gen_745
<a, a>() -> q_gen_746
<a, b>() -> q_gen_746
<b, a>() -> q_gen_746
<b, b>() -> q_gen_746
<a, cons, cons>(q_gen_746, q_gen_745) -> q_gen_741
<a, nil, cons>(q_gen_743, q_gen_742) -> q_gen_741
<b, cons, cons>(q_gen_746, q_gen_745) -> q_gen_741
<b, nil, cons>(q_gen_743, q_gen_742) -> q_gen_741
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_740, q_gen_748, q_gen_749, q_gen_773, q_gen_774, q_gen_775, q_gen_776, q_gen_777, q_gen_787, q_gen_788, q_gen_789, q_gen_794, q_gen_795, q_gen_800, q_gen_801},
Q_f={q_gen_740},
Delta=
{
<cons>(q_gen_801, q_gen_773) -> q_gen_748
<nil>() -> q_gen_748
<cons>(q_gen_774, q_gen_748) -> q_gen_773
<b>() -> q_gen_774
<z>() -> q_gen_776
<cons>(q_gen_774, q_gen_773) -> q_gen_787
<cons>(q_gen_774, q_gen_787) -> q_gen_787
<cons>(q_gen_774, q_gen_800) -> q_gen_787
<cons>(q_gen_801, q_gen_800) -> q_gen_787
<s>(q_gen_776) -> q_gen_789
<s>(q_gen_789) -> q_gen_795
<s>(q_gen_795) -> q_gen_795
<cons>(q_gen_801, q_gen_748) -> q_gen_800
<a>() -> q_gen_801
<cons, s>(q_gen_749, q_gen_748) -> q_gen_740
<cons, s>(q_gen_775, q_gen_773) -> q_gen_740
<cons, s>(q_gen_775, q_gen_800) -> q_gen_740
<cons, s>(q_gen_788, q_gen_787) -> q_gen_740
<cons, s>(q_gen_794, q_gen_800) -> q_gen_740
<nil, z>() -> q_gen_740
<a, z>() -> q_gen_749
<b, z>() -> q_gen_749
<a, s>(q_gen_776) -> q_gen_775
<b, s>(q_gen_776) -> q_gen_775
<cons, s>(q_gen_749, q_gen_773) -> q_gen_777
<cons, s>(q_gen_749, q_gen_787) -> q_gen_777
<cons, s>(q_gen_775, q_gen_748) -> q_gen_777
<cons, s>(q_gen_775, q_gen_787) -> q_gen_777
<cons, s>(q_gen_788, q_gen_748) -> q_gen_777
<cons, s>(q_gen_788, q_gen_773) -> q_gen_777
<cons, s>(q_gen_788, q_gen_800) -> q_gen_777
<cons, s>(q_gen_794, q_gen_748) -> q_gen_777
<cons, s>(q_gen_794, q_gen_773) -> q_gen_777
<cons, s>(q_gen_794, q_gen_787) -> q_gen_777
<a, s>(q_gen_795) -> q_gen_788
<b, s>(q_gen_789) -> q_gen_788
<b, s>(q_gen_795) -> q_gen_794
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_738, q_gen_752},
Q_f={q_gen_738},
Delta=
{
<a, a>() -> q_gen_738
<a, b>() -> q_gen_738
<b, b>() -> q_gen_738
<b, a>() -> q_gen_752
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_737, q_gen_751},
Q_f={q_gen_737},
Delta=
{
<cons, cons>(q_gen_751, q_gen_737) -> q_gen_737
<nil, nil>() -> q_gen_737
<a, a>() -> q_gen_751
<a, b>() -> q_gen_751
<b, a>() -> q_gen_751
<b, b>() -> q_gen_751
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 45
() -> length([nil, z]) -> 45
() -> leq([a, y]) -> 45
() -> leq([b, b]) -> 45
() -> sort([nil, nil]) -> 45
(insert([x, z, _yc]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _yc)]) -> 45
(insert([y, _dd, _ed]) /\ sort([z, _dd])) -> sort([cons(y, z), _ed]) -> 50
(length([_nd, _od]) /\ length([l, _md]) /\ sort([l, _nd])) -> eq_nat([_md, _od]) -> 52
(length([ll, _id])) -> length([cons(x, ll), s(_id)]) -> 55
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 46
(leq([b, a])) -> BOT -> 46
}
Sat witness: Found: ((length([ll, _id])) -> length([cons(x, ll), s(_id)]), {
_id -> s(s(z))  ;  ll -> cons(a, cons(b, nil))  ;  x -> b
})

-------------------------------------------
Step 58, which took 0.278427 s (model generation: 0.274448,  model checking: 0.003979):

Model:
|_
{
insert -> 
{{{
Q={q_gen_741, q_gen_742, q_gen_743, q_gen_745, q_gen_746},
Q_f={q_gen_741},
Delta=
{
<nil>() -> q_gen_742
<a>() -> q_gen_743
<b>() -> q_gen_743
<cons, cons>(q_gen_746, q_gen_745) -> q_gen_745
<nil, cons>(q_gen_743, q_gen_742) -> q_gen_745
<a, a>() -> q_gen_746
<a, b>() -> q_gen_746
<b, a>() -> q_gen_746
<b, b>() -> q_gen_746
<a, cons, cons>(q_gen_746, q_gen_745) -> q_gen_741
<a, nil, cons>(q_gen_743, q_gen_742) -> q_gen_741
<b, cons, cons>(q_gen_746, q_gen_745) -> q_gen_741
<b, nil, cons>(q_gen_743, q_gen_742) -> q_gen_741
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_740, q_gen_748, q_gen_749, q_gen_773, q_gen_774, q_gen_775, q_gen_776, q_gen_777, q_gen_787, q_gen_788, q_gen_789, q_gen_794, q_gen_795, q_gen_804, q_gen_815},
Q_f={q_gen_740},
Delta=
{
<nil>() -> q_gen_748
<cons>(q_gen_774, q_gen_748) -> q_gen_773
<a>() -> q_gen_774
<b>() -> q_gen_774
<z>() -> q_gen_776
<cons>(q_gen_774, q_gen_773) -> q_gen_787
<s>(q_gen_776) -> q_gen_789
<s>(q_gen_804) -> q_gen_789
<s>(q_gen_789) -> q_gen_795
<s>(q_gen_795) -> q_gen_804
<cons>(q_gen_774, q_gen_787) -> q_gen_815
<cons, s>(q_gen_749, q_gen_748) -> q_gen_740
<cons, s>(q_gen_749, q_gen_815) -> q_gen_740
<cons, s>(q_gen_775, q_gen_773) -> q_gen_740
<cons, s>(q_gen_788, q_gen_787) -> q_gen_740
<cons, s>(q_gen_794, q_gen_815) -> q_gen_740
<nil, z>() -> q_gen_740
<a, s>(q_gen_795) -> q_gen_749
<a, s>(q_gen_804) -> q_gen_749
<a, z>() -> q_gen_749
<b, z>() -> q_gen_749
<a, s>(q_gen_776) -> q_gen_775
<b, s>(q_gen_776) -> q_gen_775
<b, s>(q_gen_804) -> q_gen_775
<cons, s>(q_gen_749, q_gen_773) -> q_gen_777
<cons, s>(q_gen_749, q_gen_787) -> q_gen_777
<cons, s>(q_gen_775, q_gen_748) -> q_gen_777
<cons, s>(q_gen_775, q_gen_787) -> q_gen_777
<cons, s>(q_gen_775, q_gen_815) -> q_gen_777
<cons, s>(q_gen_788, q_gen_748) -> q_gen_777
<cons, s>(q_gen_788, q_gen_773) -> q_gen_777
<cons, s>(q_gen_788, q_gen_815) -> q_gen_777
<cons, s>(q_gen_794, q_gen_748) -> q_gen_777
<cons, s>(q_gen_794, q_gen_773) -> q_gen_777
<cons, s>(q_gen_794, q_gen_787) -> q_gen_777
<b, s>(q_gen_789) -> q_gen_788
<b, s>(q_gen_795) -> q_gen_794
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_738, q_gen_752},
Q_f={q_gen_738},
Delta=
{
<a, a>() -> q_gen_738
<a, b>() -> q_gen_738
<b, b>() -> q_gen_738
<b, a>() -> q_gen_752
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_737, q_gen_751},
Q_f={q_gen_737},
Delta=
{
<cons, cons>(q_gen_751, q_gen_737) -> q_gen_737
<nil, nil>() -> q_gen_737
<a, a>() -> q_gen_751
<a, b>() -> q_gen_751
<b, a>() -> q_gen_751
<b, b>() -> q_gen_751
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 46
() -> length([nil, z]) -> 46
() -> leq([a, y]) -> 46
() -> leq([b, b]) -> 46
() -> sort([nil, nil]) -> 46
(insert([x, z, _yc]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _yc)]) -> 46
(insert([y, _dd, _ed]) /\ sort([z, _dd])) -> sort([cons(y, z), _ed]) -> 51
(length([_nd, _od]) /\ length([l, _md]) /\ sort([l, _nd])) -> eq_nat([_md, _od]) -> 55
(length([ll, _id])) -> length([cons(x, ll), s(_id)]) -> 55
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 47
(leq([b, a])) -> BOT -> 47
}
Sat witness: Found: ((length([_nd, _od]) /\ length([l, _md]) /\ sort([l, _nd])) -> eq_nat([_md, _od]), {
_md -> s(z)  ;  _nd -> cons(a, nil)  ;  _od -> s(s(s(s(s(z)))))  ;  l -> cons(b, nil)
})

-------------------------------------------
Step 59, which took 0.275430 s (model generation: 0.269155,  model checking: 0.006275):

Model:
|_
{
insert -> 
{{{
Q={q_gen_741, q_gen_742, q_gen_743, q_gen_745, q_gen_746},
Q_f={q_gen_741},
Delta=
{
<nil>() -> q_gen_742
<a>() -> q_gen_743
<b>() -> q_gen_743
<cons, cons>(q_gen_746, q_gen_745) -> q_gen_745
<nil, cons>(q_gen_743, q_gen_742) -> q_gen_745
<a, a>() -> q_gen_746
<a, b>() -> q_gen_746
<b, a>() -> q_gen_746
<b, b>() -> q_gen_746
<a, cons, cons>(q_gen_746, q_gen_745) -> q_gen_741
<a, nil, cons>(q_gen_743, q_gen_742) -> q_gen_741
<b, cons, cons>(q_gen_746, q_gen_745) -> q_gen_741
<b, nil, cons>(q_gen_743, q_gen_742) -> q_gen_741
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_740, q_gen_748, q_gen_749, q_gen_773, q_gen_774, q_gen_775, q_gen_776, q_gen_777, q_gen_787, q_gen_788, q_gen_789, q_gen_794, q_gen_795, q_gen_804, q_gen_815},
Q_f={q_gen_740},
Delta=
{
<nil>() -> q_gen_748
<cons>(q_gen_774, q_gen_748) -> q_gen_773
<a>() -> q_gen_774
<b>() -> q_gen_774
<z>() -> q_gen_776
<cons>(q_gen_774, q_gen_773) -> q_gen_787
<s>(q_gen_776) -> q_gen_789
<s>(q_gen_804) -> q_gen_789
<s>(q_gen_789) -> q_gen_795
<s>(q_gen_795) -> q_gen_804
<cons>(q_gen_774, q_gen_787) -> q_gen_815
<cons, s>(q_gen_749, q_gen_748) -> q_gen_740
<cons, s>(q_gen_775, q_gen_773) -> q_gen_740
<cons, s>(q_gen_775, q_gen_815) -> q_gen_740
<cons, s>(q_gen_788, q_gen_787) -> q_gen_740
<cons, s>(q_gen_794, q_gen_815) -> q_gen_740
<nil, z>() -> q_gen_740
<a, z>() -> q_gen_749
<b, z>() -> q_gen_749
<a, s>(q_gen_776) -> q_gen_775
<b, s>(q_gen_776) -> q_gen_775
<b, s>(q_gen_804) -> q_gen_775
<cons, s>(q_gen_749, q_gen_773) -> q_gen_777
<cons, s>(q_gen_749, q_gen_787) -> q_gen_777
<cons, s>(q_gen_749, q_gen_815) -> q_gen_777
<cons, s>(q_gen_775, q_gen_748) -> q_gen_777
<cons, s>(q_gen_775, q_gen_787) -> q_gen_777
<cons, s>(q_gen_788, q_gen_748) -> q_gen_777
<cons, s>(q_gen_788, q_gen_773) -> q_gen_777
<cons, s>(q_gen_788, q_gen_815) -> q_gen_777
<cons, s>(q_gen_794, q_gen_748) -> q_gen_777
<cons, s>(q_gen_794, q_gen_773) -> q_gen_777
<cons, s>(q_gen_794, q_gen_787) -> q_gen_777
<a, s>(q_gen_804) -> q_gen_788
<b, s>(q_gen_789) -> q_gen_788
<a, s>(q_gen_795) -> q_gen_794
<b, s>(q_gen_795) -> q_gen_794
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_738, q_gen_752},
Q_f={q_gen_738},
Delta=
{
<a, a>() -> q_gen_738
<a, b>() -> q_gen_738
<b, b>() -> q_gen_738
<b, a>() -> q_gen_752
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_737, q_gen_751},
Q_f={q_gen_737},
Delta=
{
<cons, cons>(q_gen_751, q_gen_737) -> q_gen_737
<nil, nil>() -> q_gen_737
<a, a>() -> q_gen_751
<a, b>() -> q_gen_751
<b, a>() -> q_gen_751
<b, b>() -> q_gen_751
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 47
() -> length([nil, z]) -> 47
() -> leq([a, y]) -> 47
() -> leq([b, b]) -> 47
() -> sort([nil, nil]) -> 47
(insert([x, z, _yc]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _yc)]) -> 47
(insert([y, _dd, _ed]) /\ sort([z, _dd])) -> sort([cons(y, z), _ed]) -> 52
(length([_nd, _od]) /\ length([l, _md]) /\ sort([l, _nd])) -> eq_nat([_md, _od]) -> 55
(length([ll, _id])) -> length([cons(x, ll), s(_id)]) -> 58
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 48
(leq([b, a])) -> BOT -> 48
}
Sat witness: Found: ((length([ll, _id])) -> length([cons(x, ll), s(_id)]), {
_id -> s(s(s(s(s(z)))))  ;  ll -> cons(a, cons(a, cons(b, nil)))  ;  x -> b
})

-------------------------------------------
Step 60, which took 0.305700 s (model generation: 0.301605,  model checking: 0.004095):

Model:
|_
{
insert -> 
{{{
Q={q_gen_741, q_gen_742, q_gen_743, q_gen_745, q_gen_746},
Q_f={q_gen_741},
Delta=
{
<nil>() -> q_gen_742
<a>() -> q_gen_743
<b>() -> q_gen_743
<cons, cons>(q_gen_746, q_gen_745) -> q_gen_745
<nil, cons>(q_gen_743, q_gen_742) -> q_gen_745
<a, a>() -> q_gen_746
<a, b>() -> q_gen_746
<b, a>() -> q_gen_746
<b, b>() -> q_gen_746
<a, cons, cons>(q_gen_746, q_gen_745) -> q_gen_741
<a, nil, cons>(q_gen_743, q_gen_742) -> q_gen_741
<b, cons, cons>(q_gen_746, q_gen_745) -> q_gen_741
<b, nil, cons>(q_gen_743, q_gen_742) -> q_gen_741
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_740, q_gen_748, q_gen_749, q_gen_773, q_gen_774, q_gen_775, q_gen_776, q_gen_777, q_gen_787, q_gen_788, q_gen_789, q_gen_794, q_gen_795, q_gen_804, q_gen_815},
Q_f={q_gen_740},
Delta=
{
<nil>() -> q_gen_748
<cons>(q_gen_774, q_gen_748) -> q_gen_773
<a>() -> q_gen_774
<b>() -> q_gen_774
<z>() -> q_gen_776
<cons>(q_gen_774, q_gen_773) -> q_gen_787
<s>(q_gen_776) -> q_gen_789
<s>(q_gen_804) -> q_gen_789
<s>(q_gen_789) -> q_gen_795
<s>(q_gen_795) -> q_gen_804
<cons>(q_gen_774, q_gen_787) -> q_gen_815
<cons, s>(q_gen_749, q_gen_748) -> q_gen_740
<cons, s>(q_gen_775, q_gen_773) -> q_gen_740
<cons, s>(q_gen_788, q_gen_787) -> q_gen_740
<cons, s>(q_gen_794, q_gen_815) -> q_gen_740
<nil, z>() -> q_gen_740
<a, z>() -> q_gen_749
<b, z>() -> q_gen_749
<a, s>(q_gen_776) -> q_gen_775
<b, s>(q_gen_776) -> q_gen_775
<b, s>(q_gen_804) -> q_gen_775
<cons, s>(q_gen_749, q_gen_773) -> q_gen_777
<cons, s>(q_gen_749, q_gen_787) -> q_gen_777
<cons, s>(q_gen_749, q_gen_815) -> q_gen_777
<cons, s>(q_gen_775, q_gen_748) -> q_gen_777
<cons, s>(q_gen_775, q_gen_787) -> q_gen_777
<cons, s>(q_gen_775, q_gen_815) -> q_gen_777
<cons, s>(q_gen_788, q_gen_748) -> q_gen_777
<cons, s>(q_gen_788, q_gen_773) -> q_gen_777
<cons, s>(q_gen_788, q_gen_815) -> q_gen_777
<cons, s>(q_gen_794, q_gen_748) -> q_gen_777
<cons, s>(q_gen_794, q_gen_773) -> q_gen_777
<cons, s>(q_gen_794, q_gen_787) -> q_gen_777
<b, s>(q_gen_789) -> q_gen_788
<a, s>(q_gen_795) -> q_gen_794
<a, s>(q_gen_804) -> q_gen_794
<b, s>(q_gen_795) -> q_gen_794
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_738, q_gen_752},
Q_f={q_gen_738},
Delta=
{
<a, a>() -> q_gen_738
<a, b>() -> q_gen_738
<b, b>() -> q_gen_738
<b, a>() -> q_gen_752
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_737, q_gen_751},
Q_f={q_gen_737},
Delta=
{
<cons, cons>(q_gen_751, q_gen_737) -> q_gen_737
<nil, nil>() -> q_gen_737
<a, a>() -> q_gen_751
<a, b>() -> q_gen_751
<b, a>() -> q_gen_751
<b, b>() -> q_gen_751
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 48
() -> length([nil, z]) -> 48
() -> leq([a, y]) -> 48
() -> leq([b, b]) -> 48
() -> sort([nil, nil]) -> 48
(insert([x, z, _yc]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _yc)]) -> 48
(insert([y, _dd, _ed]) /\ sort([z, _dd])) -> sort([cons(y, z), _ed]) -> 53
(length([_nd, _od]) /\ length([l, _md]) /\ sort([l, _nd])) -> eq_nat([_md, _od]) -> 58
(length([ll, _id])) -> length([cons(x, ll), s(_id)]) -> 58
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 49
(leq([b, a])) -> BOT -> 49
}
Sat witness: Found: ((length([_nd, _od]) /\ length([l, _md]) /\ sort([l, _nd])) -> eq_nat([_md, _od]), {
_md -> s(s(s(s(z))))  ;  _nd -> cons(a, cons(b, cons(b, cons(b, nil))))  ;  _od -> s(s(s(s(s(z)))))  ;  l -> cons(b, cons(b, cons(b, cons(b, nil))))
})

-------------------------------------------
Step 61, which took 0.378613 s (model generation: 0.369025,  model checking: 0.009588):

Model:
|_
{
insert -> 
{{{
Q={q_gen_741, q_gen_742, q_gen_743, q_gen_745, q_gen_746},
Q_f={q_gen_741},
Delta=
{
<nil>() -> q_gen_742
<a>() -> q_gen_743
<b>() -> q_gen_743
<cons, cons>(q_gen_746, q_gen_745) -> q_gen_745
<nil, cons>(q_gen_743, q_gen_742) -> q_gen_745
<a, a>() -> q_gen_746
<a, b>() -> q_gen_746
<b, a>() -> q_gen_746
<b, b>() -> q_gen_746
<a, cons, cons>(q_gen_746, q_gen_745) -> q_gen_741
<a, nil, cons>(q_gen_743, q_gen_742) -> q_gen_741
<b, cons, cons>(q_gen_746, q_gen_745) -> q_gen_741
<b, nil, cons>(q_gen_743, q_gen_742) -> q_gen_741
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_740, q_gen_748, q_gen_749, q_gen_773, q_gen_774, q_gen_775, q_gen_776, q_gen_777, q_gen_787, q_gen_788, q_gen_789, q_gen_794, q_gen_795, q_gen_801, q_gen_813},
Q_f={q_gen_740},
Delta=
{
<nil>() -> q_gen_748
<cons>(q_gen_774, q_gen_748) -> q_gen_773
<cons>(q_gen_801, q_gen_748) -> q_gen_773
<b>() -> q_gen_774
<z>() -> q_gen_776
<cons>(q_gen_774, q_gen_773) -> q_gen_787
<cons>(q_gen_774, q_gen_787) -> q_gen_787
<s>(q_gen_776) -> q_gen_789
<s>(q_gen_789) -> q_gen_795
<s>(q_gen_795) -> q_gen_795
<a>() -> q_gen_801
<cons>(q_gen_774, q_gen_813) -> q_gen_813
<cons>(q_gen_801, q_gen_773) -> q_gen_813
<cons>(q_gen_801, q_gen_813) -> q_gen_813
<cons, s>(q_gen_749, q_gen_748) -> q_gen_740
<cons, s>(q_gen_775, q_gen_773) -> q_gen_740
<cons, s>(q_gen_788, q_gen_787) -> q_gen_740
<cons, s>(q_gen_788, q_gen_813) -> q_gen_740
<cons, s>(q_gen_794, q_gen_813) -> q_gen_740
<nil, z>() -> q_gen_740
<a, z>() -> q_gen_749
<b, z>() -> q_gen_749
<a, s>(q_gen_776) -> q_gen_775
<b, s>(q_gen_776) -> q_gen_775
<cons, s>(q_gen_749, q_gen_773) -> q_gen_777
<cons, s>(q_gen_749, q_gen_787) -> q_gen_777
<cons, s>(q_gen_775, q_gen_748) -> q_gen_777
<cons, s>(q_gen_775, q_gen_787) -> q_gen_777
<cons, s>(q_gen_775, q_gen_813) -> q_gen_777
<cons, s>(q_gen_788, q_gen_748) -> q_gen_777
<cons, s>(q_gen_788, q_gen_773) -> q_gen_777
<cons, s>(q_gen_794, q_gen_748) -> q_gen_777
<cons, s>(q_gen_794, q_gen_773) -> q_gen_777
<cons, s>(q_gen_794, q_gen_787) -> q_gen_777
<a, s>(q_gen_795) -> q_gen_788
<b, s>(q_gen_789) -> q_gen_788
<b, s>(q_gen_795) -> q_gen_794
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_738, q_gen_752},
Q_f={q_gen_738},
Delta=
{
<a, a>() -> q_gen_738
<a, b>() -> q_gen_738
<b, b>() -> q_gen_738
<b, a>() -> q_gen_752
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_737, q_gen_751},
Q_f={q_gen_737},
Delta=
{
<cons, cons>(q_gen_751, q_gen_737) -> q_gen_737
<nil, nil>() -> q_gen_737
<a, a>() -> q_gen_751
<a, b>() -> q_gen_751
<b, a>() -> q_gen_751
<b, b>() -> q_gen_751
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 49
() -> length([nil, z]) -> 49
() -> leq([a, y]) -> 49
() -> leq([b, b]) -> 49
() -> sort([nil, nil]) -> 49
(insert([x, z, _yc]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _yc)]) -> 49
(insert([y, _dd, _ed]) /\ sort([z, _dd])) -> sort([cons(y, z), _ed]) -> 54
(length([_nd, _od]) /\ length([l, _md]) /\ sort([l, _nd])) -> eq_nat([_md, _od]) -> 58
(length([ll, _id])) -> length([cons(x, ll), s(_id)]) -> 61
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 50
(leq([b, a])) -> BOT -> 50
}
Sat witness: Found: ((length([ll, _id])) -> length([cons(x, ll), s(_id)]), {
_id -> s(s(s(z)))  ;  ll -> cons(b, cons(b, cons(b, nil)))  ;  x -> b
})

-------------------------------------------
Step 62, which took 0.648321 s (model generation: 0.644077,  model checking: 0.004244):

Model:
|_
{
insert -> 
{{{
Q={q_gen_741, q_gen_742, q_gen_743, q_gen_745, q_gen_746},
Q_f={q_gen_741},
Delta=
{
<nil>() -> q_gen_742
<a>() -> q_gen_743
<b>() -> q_gen_743
<cons, cons>(q_gen_746, q_gen_745) -> q_gen_745
<nil, cons>(q_gen_743, q_gen_742) -> q_gen_745
<a, a>() -> q_gen_746
<a, b>() -> q_gen_746
<b, a>() -> q_gen_746
<b, b>() -> q_gen_746
<a, cons, cons>(q_gen_746, q_gen_745) -> q_gen_741
<a, nil, cons>(q_gen_743, q_gen_742) -> q_gen_741
<b, cons, cons>(q_gen_746, q_gen_745) -> q_gen_741
<b, nil, cons>(q_gen_743, q_gen_742) -> q_gen_741
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_740, q_gen_748, q_gen_749, q_gen_773, q_gen_774, q_gen_775, q_gen_776, q_gen_777, q_gen_787, q_gen_788, q_gen_789, q_gen_794, q_gen_795, q_gen_801, q_gen_804, q_gen_815},
Q_f={q_gen_740},
Delta=
{
<nil>() -> q_gen_748
<cons>(q_gen_774, q_gen_748) -> q_gen_773
<cons>(q_gen_801, q_gen_748) -> q_gen_773
<b>() -> q_gen_774
<z>() -> q_gen_776
<cons>(q_gen_774, q_gen_773) -> q_gen_787
<cons>(q_gen_801, q_gen_773) -> q_gen_787
<cons>(q_gen_801, q_gen_787) -> q_gen_787
<s>(q_gen_776) -> q_gen_789
<s>(q_gen_804) -> q_gen_789
<s>(q_gen_789) -> q_gen_795
<a>() -> q_gen_801
<s>(q_gen_795) -> q_gen_804
<cons>(q_gen_774, q_gen_787) -> q_gen_815
<cons, s>(q_gen_749, q_gen_748) -> q_gen_740
<cons, s>(q_gen_775, q_gen_773) -> q_gen_740
<cons, s>(q_gen_775, q_gen_815) -> q_gen_740
<cons, s>(q_gen_788, q_gen_787) -> q_gen_740
<cons, s>(q_gen_794, q_gen_815) -> q_gen_740
<nil, z>() -> q_gen_740
<a, z>() -> q_gen_749
<b, s>(q_gen_804) -> q_gen_749
<b, z>() -> q_gen_749
<a, s>(q_gen_776) -> q_gen_775
<a, s>(q_gen_795) -> q_gen_775
<b, s>(q_gen_776) -> q_gen_775
<cons, s>(q_gen_749, q_gen_773) -> q_gen_777
<cons, s>(q_gen_749, q_gen_787) -> q_gen_777
<cons, s>(q_gen_749, q_gen_815) -> q_gen_777
<cons, s>(q_gen_775, q_gen_748) -> q_gen_777
<cons, s>(q_gen_775, q_gen_787) -> q_gen_777
<cons, s>(q_gen_788, q_gen_748) -> q_gen_777
<cons, s>(q_gen_788, q_gen_773) -> q_gen_777
<cons, s>(q_gen_788, q_gen_815) -> q_gen_777
<cons, s>(q_gen_794, q_gen_748) -> q_gen_777
<cons, s>(q_gen_794, q_gen_773) -> q_gen_777
<cons, s>(q_gen_794, q_gen_787) -> q_gen_777
<a, s>(q_gen_804) -> q_gen_788
<b, s>(q_gen_789) -> q_gen_788
<b, s>(q_gen_795) -> q_gen_794
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_738, q_gen_752},
Q_f={q_gen_738},
Delta=
{
<a, a>() -> q_gen_738
<a, b>() -> q_gen_738
<b, b>() -> q_gen_738
<b, a>() -> q_gen_752
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_737, q_gen_751},
Q_f={q_gen_737},
Delta=
{
<cons, cons>(q_gen_751, q_gen_737) -> q_gen_737
<nil, nil>() -> q_gen_737
<a, a>() -> q_gen_751
<a, b>() -> q_gen_751
<b, a>() -> q_gen_751
<b, b>() -> q_gen_751
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 50
() -> length([nil, z]) -> 50
() -> leq([a, y]) -> 50
() -> leq([b, b]) -> 50
() -> sort([nil, nil]) -> 50
(insert([x, z, _yc]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _yc)]) -> 50
(insert([y, _dd, _ed]) /\ sort([z, _dd])) -> sort([cons(y, z), _ed]) -> 55
(length([_nd, _od]) /\ length([l, _md]) /\ sort([l, _nd])) -> eq_nat([_md, _od]) -> 61
(length([ll, _id])) -> length([cons(x, ll), s(_id)]) -> 61
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 51
(leq([b, a])) -> BOT -> 51
}
Sat witness: Found: ((length([_nd, _od]) /\ length([l, _md]) /\ sort([l, _nd])) -> eq_nat([_md, _od]), {
_md -> s(s(z))  ;  _nd -> cons(b, cons(b, cons(b, cons(b, nil))))  ;  _od -> s(s(s(s(z))))  ;  l -> cons(b, cons(b, cons(b, cons(b, nil))))
})

-------------------------------------------
Step 63, which took 0.446239 s (model generation: 0.435429,  model checking: 0.010810):

Model:
|_
{
insert -> 
{{{
Q={q_gen_741, q_gen_742, q_gen_743, q_gen_745, q_gen_746},
Q_f={q_gen_741},
Delta=
{
<nil>() -> q_gen_742
<a>() -> q_gen_743
<b>() -> q_gen_743
<cons, cons>(q_gen_746, q_gen_745) -> q_gen_745
<nil, cons>(q_gen_743, q_gen_742) -> q_gen_745
<a, a>() -> q_gen_746
<a, b>() -> q_gen_746
<b, a>() -> q_gen_746
<b, b>() -> q_gen_746
<a, cons, cons>(q_gen_746, q_gen_745) -> q_gen_741
<a, nil, cons>(q_gen_743, q_gen_742) -> q_gen_741
<b, cons, cons>(q_gen_746, q_gen_745) -> q_gen_741
<b, nil, cons>(q_gen_743, q_gen_742) -> q_gen_741
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_740, q_gen_748, q_gen_749, q_gen_773, q_gen_774, q_gen_775, q_gen_776, q_gen_777, q_gen_787, q_gen_788, q_gen_789, q_gen_794, q_gen_795, q_gen_803, q_gen_804, q_gen_815},
Q_f={q_gen_740},
Delta=
{
<nil>() -> q_gen_748
<cons>(q_gen_774, q_gen_748) -> q_gen_773
<a>() -> q_gen_774
<b>() -> q_gen_774
<s>(q_gen_804) -> q_gen_776
<z>() -> q_gen_776
<cons>(q_gen_774, q_gen_773) -> q_gen_787
<s>(q_gen_776) -> q_gen_789
<s>(q_gen_789) -> q_gen_795
<s>(q_gen_795) -> q_gen_804
<cons>(q_gen_774, q_gen_787) -> q_gen_815
<cons, s>(q_gen_749, q_gen_748) -> q_gen_740
<cons, s>(q_gen_775, q_gen_773) -> q_gen_740
<cons, s>(q_gen_788, q_gen_787) -> q_gen_740
<cons, s>(q_gen_788, q_gen_815) -> q_gen_740
<cons, s>(q_gen_794, q_gen_815) -> q_gen_740
<nil, z>() -> q_gen_740
<a, z>() -> q_gen_749
<b, z>() -> q_gen_749
<a, s>(q_gen_776) -> q_gen_775
<b, s>(q_gen_776) -> q_gen_775
<cons, s>(q_gen_749, q_gen_773) -> q_gen_777
<cons, s>(q_gen_749, q_gen_787) -> q_gen_777
<cons, s>(q_gen_749, q_gen_815) -> q_gen_777
<cons, s>(q_gen_775, q_gen_748) -> q_gen_777
<cons, s>(q_gen_775, q_gen_787) -> q_gen_777
<cons, s>(q_gen_775, q_gen_815) -> q_gen_777
<cons, s>(q_gen_788, q_gen_748) -> q_gen_777
<cons, s>(q_gen_788, q_gen_773) -> q_gen_777
<cons, s>(q_gen_794, q_gen_748) -> q_gen_777
<cons, s>(q_gen_794, q_gen_773) -> q_gen_777
<cons, s>(q_gen_794, q_gen_787) -> q_gen_777
<cons, s>(q_gen_803, q_gen_748) -> q_gen_777
<cons, s>(q_gen_803, q_gen_773) -> q_gen_777
<cons, s>(q_gen_803, q_gen_787) -> q_gen_777
<cons, s>(q_gen_803, q_gen_815) -> q_gen_777
<b, s>(q_gen_789) -> q_gen_788
<a, s>(q_gen_795) -> q_gen_794
<b, s>(q_gen_795) -> q_gen_794
<a, s>(q_gen_804) -> q_gen_803
<b, s>(q_gen_804) -> q_gen_803
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_738, q_gen_752},
Q_f={q_gen_738},
Delta=
{
<a, a>() -> q_gen_738
<a, b>() -> q_gen_738
<b, b>() -> q_gen_738
<b, a>() -> q_gen_752
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_737, q_gen_751},
Q_f={q_gen_737},
Delta=
{
<cons, cons>(q_gen_751, q_gen_737) -> q_gen_737
<nil, nil>() -> q_gen_737
<a, a>() -> q_gen_751
<a, b>() -> q_gen_751
<b, a>() -> q_gen_751
<b, b>() -> q_gen_751
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 51
() -> length([nil, z]) -> 51
() -> leq([a, y]) -> 51
() -> leq([b, b]) -> 51
() -> sort([nil, nil]) -> 51
(insert([x, z, _yc]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _yc)]) -> 51
(insert([y, _dd, _ed]) /\ sort([z, _dd])) -> sort([cons(y, z), _ed]) -> 56
(length([_nd, _od]) /\ length([l, _md]) /\ sort([l, _nd])) -> eq_nat([_md, _od]) -> 61
(length([ll, _id])) -> length([cons(x, ll), s(_id)]) -> 64
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 52
(leq([b, a])) -> BOT -> 52
}
Sat witness: Found: ((length([ll, _id])) -> length([cons(x, ll), s(_id)]), {
_id -> s(s(s(z)))  ;  ll -> cons(b, cons(b, cons(a, cons(b, nil))))  ;  x -> b
})

-------------------------------------------
Step 64, which took 0.861670 s (model generation: 0.856715,  model checking: 0.004955):

Model:
|_
{
insert -> 
{{{
Q={q_gen_741, q_gen_742, q_gen_743, q_gen_745, q_gen_746},
Q_f={q_gen_741},
Delta=
{
<nil>() -> q_gen_742
<a>() -> q_gen_743
<b>() -> q_gen_743
<cons, cons>(q_gen_746, q_gen_745) -> q_gen_745
<nil, cons>(q_gen_743, q_gen_742) -> q_gen_745
<a, a>() -> q_gen_746
<a, b>() -> q_gen_746
<b, a>() -> q_gen_746
<b, b>() -> q_gen_746
<a, cons, cons>(q_gen_746, q_gen_745) -> q_gen_741
<a, nil, cons>(q_gen_743, q_gen_742) -> q_gen_741
<b, cons, cons>(q_gen_746, q_gen_745) -> q_gen_741
<b, nil, cons>(q_gen_743, q_gen_742) -> q_gen_741
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_740, q_gen_748, q_gen_749, q_gen_773, q_gen_774, q_gen_775, q_gen_776, q_gen_777, q_gen_787, q_gen_788, q_gen_789, q_gen_794, q_gen_795, q_gen_801, q_gen_804, q_gen_815},
Q_f={q_gen_740},
Delta=
{
<nil>() -> q_gen_748
<cons>(q_gen_774, q_gen_748) -> q_gen_773
<cons>(q_gen_801, q_gen_748) -> q_gen_773
<cons>(q_gen_801, q_gen_787) -> q_gen_773
<b>() -> q_gen_774
<s>(q_gen_804) -> q_gen_776
<z>() -> q_gen_776
<cons>(q_gen_774, q_gen_773) -> q_gen_787
<cons>(q_gen_774, q_gen_815) -> q_gen_787
<cons>(q_gen_801, q_gen_773) -> q_gen_787
<s>(q_gen_776) -> q_gen_789
<s>(q_gen_789) -> q_gen_795
<a>() -> q_gen_801
<s>(q_gen_795) -> q_gen_804
<cons>(q_gen_774, q_gen_787) -> q_gen_815
<cons, s>(q_gen_749, q_gen_748) -> q_gen_740
<cons, s>(q_gen_775, q_gen_773) -> q_gen_740
<cons, s>(q_gen_788, q_gen_787) -> q_gen_740
<cons, s>(q_gen_794, q_gen_815) -> q_gen_740
<nil, z>() -> q_gen_740
<a, z>() -> q_gen_749
<b, z>() -> q_gen_749
<a, s>(q_gen_776) -> q_gen_775
<b, s>(q_gen_776) -> q_gen_775
<cons, s>(q_gen_749, q_gen_773) -> q_gen_777
<cons, s>(q_gen_749, q_gen_787) -> q_gen_777
<cons, s>(q_gen_749, q_gen_815) -> q_gen_777
<cons, s>(q_gen_775, q_gen_748) -> q_gen_777
<cons, s>(q_gen_775, q_gen_787) -> q_gen_777
<cons, s>(q_gen_775, q_gen_815) -> q_gen_777
<cons, s>(q_gen_788, q_gen_748) -> q_gen_777
<cons, s>(q_gen_788, q_gen_773) -> q_gen_777
<cons, s>(q_gen_788, q_gen_815) -> q_gen_777
<cons, s>(q_gen_794, q_gen_748) -> q_gen_777
<cons, s>(q_gen_794, q_gen_773) -> q_gen_777
<cons, s>(q_gen_794, q_gen_787) -> q_gen_777
<a, s>(q_gen_804) -> q_gen_788
<b, s>(q_gen_789) -> q_gen_788
<a, s>(q_gen_795) -> q_gen_794
<b, s>(q_gen_795) -> q_gen_794
<b, s>(q_gen_804) -> q_gen_794
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_738, q_gen_752},
Q_f={q_gen_738},
Delta=
{
<a, a>() -> q_gen_738
<a, b>() -> q_gen_738
<b, b>() -> q_gen_738
<b, a>() -> q_gen_752
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_737, q_gen_751},
Q_f={q_gen_737},
Delta=
{
<cons, cons>(q_gen_751, q_gen_737) -> q_gen_737
<nil, nil>() -> q_gen_737
<a, a>() -> q_gen_751
<a, b>() -> q_gen_751
<b, a>() -> q_gen_751
<b, b>() -> q_gen_751
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 52
() -> length([nil, z]) -> 52
() -> leq([a, y]) -> 52
() -> leq([b, b]) -> 52
() -> sort([nil, nil]) -> 52
(insert([x, z, _yc]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _yc)]) -> 52
(insert([y, _dd, _ed]) /\ sort([z, _dd])) -> sort([cons(y, z), _ed]) -> 57
(length([_nd, _od]) /\ length([l, _md]) /\ sort([l, _nd])) -> eq_nat([_md, _od]) -> 64
(length([ll, _id])) -> length([cons(x, ll), s(_id)]) -> 64
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 53
(leq([b, a])) -> BOT -> 53
}
Sat witness: Found: ((length([_nd, _od]) /\ length([l, _md]) /\ sort([l, _nd])) -> eq_nat([_md, _od]), {
_md -> s(s(z))  ;  _nd -> cons(b, cons(b, nil))  ;  _od -> s(s(s(s(s(s(z))))))  ;  l -> cons(a, cons(b, nil))
})

-------------------------------------------
Step 65, which took 0.975030 s (model generation: 0.967868,  model checking: 0.007162):

Model:
|_
{
insert -> 
{{{
Q={q_gen_741, q_gen_742, q_gen_743, q_gen_745, q_gen_746},
Q_f={q_gen_741},
Delta=
{
<nil>() -> q_gen_742
<a>() -> q_gen_743
<b>() -> q_gen_743
<cons, cons>(q_gen_746, q_gen_745) -> q_gen_745
<nil, cons>(q_gen_743, q_gen_742) -> q_gen_745
<a, a>() -> q_gen_746
<a, b>() -> q_gen_746
<b, a>() -> q_gen_746
<b, b>() -> q_gen_746
<a, cons, cons>(q_gen_746, q_gen_745) -> q_gen_741
<a, nil, cons>(q_gen_743, q_gen_742) -> q_gen_741
<b, cons, cons>(q_gen_746, q_gen_745) -> q_gen_741
<b, nil, cons>(q_gen_743, q_gen_742) -> q_gen_741
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_740, q_gen_748, q_gen_749, q_gen_773, q_gen_774, q_gen_775, q_gen_776, q_gen_777, q_gen_787, q_gen_788, q_gen_789, q_gen_794, q_gen_795, q_gen_801, q_gen_804, q_gen_815},
Q_f={q_gen_740},
Delta=
{
<cons>(q_gen_801, q_gen_787) -> q_gen_748
<nil>() -> q_gen_748
<cons>(q_gen_774, q_gen_748) -> q_gen_773
<cons>(q_gen_801, q_gen_748) -> q_gen_773
<b>() -> q_gen_774
<z>() -> q_gen_776
<cons>(q_gen_774, q_gen_773) -> q_gen_787
<cons>(q_gen_801, q_gen_773) -> q_gen_787
<s>(q_gen_776) -> q_gen_789
<s>(q_gen_789) -> q_gen_795
<a>() -> q_gen_801
<s>(q_gen_795) -> q_gen_804
<s>(q_gen_804) -> q_gen_804
<cons>(q_gen_774, q_gen_787) -> q_gen_815
<cons>(q_gen_774, q_gen_815) -> q_gen_815
<cons, s>(q_gen_749, q_gen_748) -> q_gen_740
<cons, s>(q_gen_775, q_gen_773) -> q_gen_740
<cons, s>(q_gen_788, q_gen_787) -> q_gen_740
<cons, s>(q_gen_794, q_gen_815) -> q_gen_740
<nil, z>() -> q_gen_740
<a, z>() -> q_gen_749
<b, s>(q_gen_804) -> q_gen_749
<b, z>() -> q_gen_749
<a, s>(q_gen_776) -> q_gen_775
<b, s>(q_gen_776) -> q_gen_775
<cons, s>(q_gen_749, q_gen_773) -> q_gen_777
<cons, s>(q_gen_749, q_gen_787) -> q_gen_777
<cons, s>(q_gen_749, q_gen_815) -> q_gen_777
<cons, s>(q_gen_775, q_gen_748) -> q_gen_777
<cons, s>(q_gen_775, q_gen_787) -> q_gen_777
<cons, s>(q_gen_775, q_gen_815) -> q_gen_777
<cons, s>(q_gen_788, q_gen_748) -> q_gen_777
<cons, s>(q_gen_788, q_gen_773) -> q_gen_777
<cons, s>(q_gen_788, q_gen_815) -> q_gen_777
<cons, s>(q_gen_794, q_gen_748) -> q_gen_777
<cons, s>(q_gen_794, q_gen_773) -> q_gen_777
<cons, s>(q_gen_794, q_gen_787) -> q_gen_777
<a, s>(q_gen_804) -> q_gen_788
<b, s>(q_gen_789) -> q_gen_788
<a, s>(q_gen_795) -> q_gen_794
<b, s>(q_gen_795) -> q_gen_794
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_738, q_gen_752},
Q_f={q_gen_738},
Delta=
{
<a, a>() -> q_gen_738
<a, b>() -> q_gen_738
<b, b>() -> q_gen_738
<b, a>() -> q_gen_752
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_737, q_gen_751},
Q_f={q_gen_737},
Delta=
{
<cons, cons>(q_gen_751, q_gen_737) -> q_gen_737
<nil, nil>() -> q_gen_737
<a, a>() -> q_gen_751
<a, b>() -> q_gen_751
<b, a>() -> q_gen_751
<b, b>() -> q_gen_751
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 53
() -> length([nil, z]) -> 53
() -> leq([a, y]) -> 53
() -> leq([b, b]) -> 53
() -> sort([nil, nil]) -> 53
(insert([x, z, _yc]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _yc)]) -> 53
(insert([y, _dd, _ed]) /\ sort([z, _dd])) -> sort([cons(y, z), _ed]) -> 58
(length([_nd, _od]) /\ length([l, _md]) /\ sort([l, _nd])) -> eq_nat([_md, _od]) -> 64
(length([ll, _id])) -> length([cons(x, ll), s(_id)]) -> 67
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 54
(leq([b, a])) -> BOT -> 54
}
Sat witness: Found: ((length([ll, _id])) -> length([cons(x, ll), s(_id)]), {
_id -> s(s(s(s(z))))  ;  ll -> cons(b, cons(b, cons(b, cons(a, nil))))  ;  x -> b
})

-------------------------------------------
Step 66, which took 0.541919 s (model generation: 0.537703,  model checking: 0.004216):

Model:
|_
{
insert -> 
{{{
Q={q_gen_741, q_gen_742, q_gen_743, q_gen_745, q_gen_746},
Q_f={q_gen_741},
Delta=
{
<nil>() -> q_gen_742
<a>() -> q_gen_743
<b>() -> q_gen_743
<cons, cons>(q_gen_746, q_gen_745) -> q_gen_745
<nil, cons>(q_gen_743, q_gen_742) -> q_gen_745
<a, a>() -> q_gen_746
<a, b>() -> q_gen_746
<b, a>() -> q_gen_746
<b, b>() -> q_gen_746
<a, cons, cons>(q_gen_746, q_gen_745) -> q_gen_741
<a, nil, cons>(q_gen_743, q_gen_742) -> q_gen_741
<b, cons, cons>(q_gen_746, q_gen_745) -> q_gen_741
<b, nil, cons>(q_gen_743, q_gen_742) -> q_gen_741
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_740, q_gen_748, q_gen_749, q_gen_773, q_gen_774, q_gen_775, q_gen_776, q_gen_777, q_gen_787, q_gen_788, q_gen_789, q_gen_794, q_gen_795, q_gen_804, q_gen_810, q_gen_815},
Q_f={q_gen_740},
Delta=
{
<nil>() -> q_gen_748
<cons>(q_gen_774, q_gen_748) -> q_gen_773
<cons>(q_gen_774, q_gen_815) -> q_gen_773
<a>() -> q_gen_774
<b>() -> q_gen_774
<z>() -> q_gen_776
<cons>(q_gen_774, q_gen_773) -> q_gen_787
<s>(q_gen_776) -> q_gen_789
<s>(q_gen_804) -> q_gen_789
<s>(q_gen_789) -> q_gen_795
<s>(q_gen_795) -> q_gen_804
<cons>(q_gen_774, q_gen_787) -> q_gen_815
<cons, s>(q_gen_749, q_gen_748) -> q_gen_740
<cons, s>(q_gen_749, q_gen_815) -> q_gen_740
<cons, s>(q_gen_775, q_gen_773) -> q_gen_740
<cons, s>(q_gen_788, q_gen_787) -> q_gen_740
<cons, s>(q_gen_794, q_gen_815) -> q_gen_740
<nil, z>() -> q_gen_740
<a, s>(q_gen_795) -> q_gen_749
<a, z>() -> q_gen_749
<b, z>() -> q_gen_749
<a, s>(q_gen_776) -> q_gen_775
<b, s>(q_gen_776) -> q_gen_775
<b, s>(q_gen_804) -> q_gen_775
<cons, s>(q_gen_749, q_gen_773) -> q_gen_777
<cons, s>(q_gen_749, q_gen_787) -> q_gen_777
<cons, s>(q_gen_775, q_gen_748) -> q_gen_777
<cons, s>(q_gen_775, q_gen_787) -> q_gen_777
<cons, s>(q_gen_775, q_gen_815) -> q_gen_777
<cons, s>(q_gen_788, q_gen_748) -> q_gen_777
<cons, s>(q_gen_788, q_gen_773) -> q_gen_777
<cons, s>(q_gen_788, q_gen_815) -> q_gen_777
<cons, s>(q_gen_794, q_gen_748) -> q_gen_777
<cons, s>(q_gen_794, q_gen_773) -> q_gen_777
<cons, s>(q_gen_794, q_gen_787) -> q_gen_777
<cons, s>(q_gen_810, q_gen_748) -> q_gen_777
<cons, s>(q_gen_810, q_gen_773) -> q_gen_777
<cons, s>(q_gen_810, q_gen_787) -> q_gen_777
<cons, s>(q_gen_810, q_gen_815) -> q_gen_777
<b, s>(q_gen_789) -> q_gen_788
<b, s>(q_gen_795) -> q_gen_794
<a, s>(q_gen_804) -> q_gen_810
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_738, q_gen_752},
Q_f={q_gen_738},
Delta=
{
<a, a>() -> q_gen_738
<a, b>() -> q_gen_738
<b, b>() -> q_gen_738
<b, a>() -> q_gen_752
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_737, q_gen_751},
Q_f={q_gen_737},
Delta=
{
<cons, cons>(q_gen_751, q_gen_737) -> q_gen_737
<nil, nil>() -> q_gen_737
<a, a>() -> q_gen_751
<a, b>() -> q_gen_751
<b, a>() -> q_gen_751
<b, b>() -> q_gen_751
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 54
() -> length([nil, z]) -> 54
() -> leq([a, y]) -> 54
() -> leq([b, b]) -> 54
() -> sort([nil, nil]) -> 54
(insert([x, z, _yc]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _yc)]) -> 54
(insert([y, _dd, _ed]) /\ sort([z, _dd])) -> sort([cons(y, z), _ed]) -> 59
(length([_nd, _od]) /\ length([l, _md]) /\ sort([l, _nd])) -> eq_nat([_md, _od]) -> 67
(length([ll, _id])) -> length([cons(x, ll), s(_id)]) -> 67
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 55
(leq([b, a])) -> BOT -> 55
}
Sat witness: Found: ((length([_nd, _od]) /\ length([l, _md]) /\ sort([l, _nd])) -> eq_nat([_md, _od]), {
_md -> s(z)  ;  _nd -> cons(a, nil)  ;  _od -> s(s(s(s(z))))  ;  l -> cons(a, nil)
})

-------------------------------------------
Step 67, which took 0.489290 s (model generation: 0.482573,  model checking: 0.006717):

Model:
|_
{
insert -> 
{{{
Q={q_gen_741, q_gen_742, q_gen_743, q_gen_745, q_gen_746},
Q_f={q_gen_741},
Delta=
{
<nil>() -> q_gen_742
<a>() -> q_gen_743
<b>() -> q_gen_743
<cons, cons>(q_gen_746, q_gen_745) -> q_gen_745
<nil, cons>(q_gen_743, q_gen_742) -> q_gen_745
<a, a>() -> q_gen_746
<a, b>() -> q_gen_746
<b, a>() -> q_gen_746
<b, b>() -> q_gen_746
<a, cons, cons>(q_gen_746, q_gen_745) -> q_gen_741
<a, nil, cons>(q_gen_743, q_gen_742) -> q_gen_741
<b, cons, cons>(q_gen_746, q_gen_745) -> q_gen_741
<b, nil, cons>(q_gen_743, q_gen_742) -> q_gen_741
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_740, q_gen_748, q_gen_749, q_gen_773, q_gen_774, q_gen_775, q_gen_776, q_gen_777, q_gen_787, q_gen_788, q_gen_789, q_gen_794, q_gen_795, q_gen_801, q_gen_804, q_gen_815},
Q_f={q_gen_740},
Delta=
{
<cons>(q_gen_774, q_gen_815) -> q_gen_748
<cons>(q_gen_801, q_gen_787) -> q_gen_748
<nil>() -> q_gen_748
<cons>(q_gen_774, q_gen_748) -> q_gen_773
<cons>(q_gen_801, q_gen_748) -> q_gen_773
<b>() -> q_gen_774
<z>() -> q_gen_776
<cons>(q_gen_774, q_gen_773) -> q_gen_787
<cons>(q_gen_801, q_gen_773) -> q_gen_787
<s>(q_gen_776) -> q_gen_789
<s>(q_gen_789) -> q_gen_795
<a>() -> q_gen_801
<s>(q_gen_795) -> q_gen_804
<s>(q_gen_804) -> q_gen_804
<cons>(q_gen_774, q_gen_787) -> q_gen_815
<cons, s>(q_gen_749, q_gen_748) -> q_gen_740
<cons, s>(q_gen_775, q_gen_773) -> q_gen_740
<cons, s>(q_gen_788, q_gen_787) -> q_gen_740
<cons, s>(q_gen_794, q_gen_815) -> q_gen_740
<nil, z>() -> q_gen_740
<a, z>() -> q_gen_749
<b, s>(q_gen_804) -> q_gen_749
<b, z>() -> q_gen_749
<a, s>(q_gen_776) -> q_gen_775
<b, s>(q_gen_776) -> q_gen_775
<cons, s>(q_gen_749, q_gen_773) -> q_gen_777
<cons, s>(q_gen_749, q_gen_787) -> q_gen_777
<cons, s>(q_gen_749, q_gen_815) -> q_gen_777
<cons, s>(q_gen_775, q_gen_748) -> q_gen_777
<cons, s>(q_gen_775, q_gen_787) -> q_gen_777
<cons, s>(q_gen_775, q_gen_815) -> q_gen_777
<cons, s>(q_gen_788, q_gen_748) -> q_gen_777
<cons, s>(q_gen_788, q_gen_773) -> q_gen_777
<cons, s>(q_gen_788, q_gen_815) -> q_gen_777
<cons, s>(q_gen_794, q_gen_748) -> q_gen_777
<cons, s>(q_gen_794, q_gen_773) -> q_gen_777
<cons, s>(q_gen_794, q_gen_787) -> q_gen_777
<a, s>(q_gen_804) -> q_gen_788
<b, s>(q_gen_789) -> q_gen_788
<a, s>(q_gen_795) -> q_gen_794
<b, s>(q_gen_795) -> q_gen_794
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_738, q_gen_752},
Q_f={q_gen_738},
Delta=
{
<a, a>() -> q_gen_738
<a, b>() -> q_gen_738
<b, b>() -> q_gen_738
<b, a>() -> q_gen_752
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_737, q_gen_751},
Q_f={q_gen_737},
Delta=
{
<cons, cons>(q_gen_751, q_gen_737) -> q_gen_737
<nil, nil>() -> q_gen_737
<a, a>() -> q_gen_751
<a, b>() -> q_gen_751
<b, a>() -> q_gen_751
<b, b>() -> q_gen_751
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 55
() -> length([nil, z]) -> 55
() -> leq([a, y]) -> 55
() -> leq([b, b]) -> 55
() -> sort([nil, nil]) -> 55
(insert([x, z, _yc]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _yc)]) -> 55
(insert([y, _dd, _ed]) /\ sort([z, _dd])) -> sort([cons(y, z), _ed]) -> 60
(length([_nd, _od]) /\ length([l, _md]) /\ sort([l, _nd])) -> eq_nat([_md, _od]) -> 67
(length([ll, _id])) -> length([cons(x, ll), s(_id)]) -> 70
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 56
(leq([b, a])) -> BOT -> 56
}
Sat witness: Found: ((length([ll, _id])) -> length([cons(x, ll), s(_id)]), {
_id -> s(s(s(s(s(z)))))  ;  ll -> cons(b, nil)  ;  x -> a
})

-------------------------------------------
Step 68, which took 0.672779 s (model generation: 0.667557,  model checking: 0.005222):

Model:
|_
{
insert -> 
{{{
Q={q_gen_741, q_gen_742, q_gen_743, q_gen_745, q_gen_746},
Q_f={q_gen_741},
Delta=
{
<nil>() -> q_gen_742
<a>() -> q_gen_743
<b>() -> q_gen_743
<cons, cons>(q_gen_746, q_gen_745) -> q_gen_745
<nil, cons>(q_gen_743, q_gen_742) -> q_gen_745
<a, a>() -> q_gen_746
<a, b>() -> q_gen_746
<b, a>() -> q_gen_746
<b, b>() -> q_gen_746
<a, cons, cons>(q_gen_746, q_gen_745) -> q_gen_741
<a, nil, cons>(q_gen_743, q_gen_742) -> q_gen_741
<b, cons, cons>(q_gen_746, q_gen_745) -> q_gen_741
<b, nil, cons>(q_gen_743, q_gen_742) -> q_gen_741
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_740, q_gen_748, q_gen_749, q_gen_773, q_gen_774, q_gen_775, q_gen_776, q_gen_777, q_gen_787, q_gen_788, q_gen_789, q_gen_794, q_gen_795, q_gen_801, q_gen_804, q_gen_815},
Q_f={q_gen_740},
Delta=
{
<nil>() -> q_gen_748
<cons>(q_gen_774, q_gen_748) -> q_gen_773
<cons>(q_gen_801, q_gen_748) -> q_gen_773
<b>() -> q_gen_774
<z>() -> q_gen_776
<cons>(q_gen_774, q_gen_773) -> q_gen_787
<cons>(q_gen_801, q_gen_773) -> q_gen_787
<cons>(q_gen_801, q_gen_787) -> q_gen_787
<s>(q_gen_776) -> q_gen_789
<s>(q_gen_804) -> q_gen_789
<s>(q_gen_789) -> q_gen_795
<a>() -> q_gen_801
<s>(q_gen_795) -> q_gen_804
<cons>(q_gen_774, q_gen_787) -> q_gen_815
<cons>(q_gen_774, q_gen_815) -> q_gen_815
<cons, s>(q_gen_749, q_gen_748) -> q_gen_740
<cons, s>(q_gen_775, q_gen_773) -> q_gen_740
<cons, s>(q_gen_788, q_gen_787) -> q_gen_740
<cons, s>(q_gen_794, q_gen_815) -> q_gen_740
<nil, z>() -> q_gen_740
<a, z>() -> q_gen_749
<b, z>() -> q_gen_749
<a, s>(q_gen_776) -> q_gen_775
<a, s>(q_gen_789) -> q_gen_775
<b, s>(q_gen_776) -> q_gen_775
<cons, s>(q_gen_749, q_gen_773) -> q_gen_777
<cons, s>(q_gen_749, q_gen_787) -> q_gen_777
<cons, s>(q_gen_749, q_gen_815) -> q_gen_777
<cons, s>(q_gen_775, q_gen_748) -> q_gen_777
<cons, s>(q_gen_775, q_gen_787) -> q_gen_777
<cons, s>(q_gen_775, q_gen_815) -> q_gen_777
<cons, s>(q_gen_788, q_gen_748) -> q_gen_777
<cons, s>(q_gen_788, q_gen_773) -> q_gen_777
<cons, s>(q_gen_788, q_gen_815) -> q_gen_777
<cons, s>(q_gen_794, q_gen_748) -> q_gen_777
<cons, s>(q_gen_794, q_gen_773) -> q_gen_777
<cons, s>(q_gen_794, q_gen_787) -> q_gen_777
<a, s>(q_gen_804) -> q_gen_788
<b, s>(q_gen_789) -> q_gen_788
<a, s>(q_gen_795) -> q_gen_794
<b, s>(q_gen_795) -> q_gen_794
<b, s>(q_gen_804) -> q_gen_794
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_738, q_gen_752},
Q_f={q_gen_738},
Delta=
{
<a, a>() -> q_gen_738
<a, b>() -> q_gen_738
<b, b>() -> q_gen_738
<b, a>() -> q_gen_752
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_737, q_gen_751},
Q_f={q_gen_737},
Delta=
{
<cons, cons>(q_gen_751, q_gen_737) -> q_gen_737
<nil, nil>() -> q_gen_737
<a, a>() -> q_gen_751
<a, b>() -> q_gen_751
<b, a>() -> q_gen_751
<b, b>() -> q_gen_751
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 56
() -> length([nil, z]) -> 56
() -> leq([a, y]) -> 56
() -> leq([b, b]) -> 56
() -> sort([nil, nil]) -> 56
(insert([x, z, _yc]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _yc)]) -> 56
(insert([y, _dd, _ed]) /\ sort([z, _dd])) -> sort([cons(y, z), _ed]) -> 61
(length([_nd, _od]) /\ length([l, _md]) /\ sort([l, _nd])) -> eq_nat([_md, _od]) -> 70
(length([ll, _id])) -> length([cons(x, ll), s(_id)]) -> 70
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 57
(leq([b, a])) -> BOT -> 57
}
Sat witness: Found: ((length([_nd, _od]) /\ length([l, _md]) /\ sort([l, _nd])) -> eq_nat([_md, _od]), {
_md -> s(s(s(z)))  ;  _nd -> cons(a, cons(b, cons(b, nil)))  ;  _od -> s(s(s(s(s(z)))))  ;  l -> cons(b, cons(b, cons(b, nil)))
})

-------------------------------------------
Step 69, which took 0.651027 s (model generation: 0.644288,  model checking: 0.006739):

Model:
|_
{
insert -> 
{{{
Q={q_gen_741, q_gen_742, q_gen_743, q_gen_745, q_gen_746},
Q_f={q_gen_741},
Delta=
{
<nil>() -> q_gen_742
<a>() -> q_gen_743
<b>() -> q_gen_743
<cons, cons>(q_gen_746, q_gen_745) -> q_gen_745
<nil, cons>(q_gen_743, q_gen_742) -> q_gen_745
<a, a>() -> q_gen_746
<a, b>() -> q_gen_746
<b, a>() -> q_gen_746
<b, b>() -> q_gen_746
<a, cons, cons>(q_gen_746, q_gen_745) -> q_gen_741
<a, nil, cons>(q_gen_743, q_gen_742) -> q_gen_741
<b, cons, cons>(q_gen_746, q_gen_745) -> q_gen_741
<b, nil, cons>(q_gen_743, q_gen_742) -> q_gen_741
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_740, q_gen_748, q_gen_749, q_gen_773, q_gen_774, q_gen_775, q_gen_776, q_gen_777, q_gen_787, q_gen_788, q_gen_789, q_gen_794, q_gen_795, q_gen_804, q_gen_810, q_gen_815},
Q_f={q_gen_740},
Delta=
{
<cons>(q_gen_774, q_gen_815) -> q_gen_748
<nil>() -> q_gen_748
<cons>(q_gen_774, q_gen_748) -> q_gen_773
<a>() -> q_gen_774
<b>() -> q_gen_774
<z>() -> q_gen_776
<cons>(q_gen_774, q_gen_773) -> q_gen_787
<s>(q_gen_776) -> q_gen_789
<s>(q_gen_804) -> q_gen_789
<s>(q_gen_789) -> q_gen_795
<s>(q_gen_795) -> q_gen_804
<cons>(q_gen_774, q_gen_787) -> q_gen_815
<cons, s>(q_gen_749, q_gen_748) -> q_gen_740
<cons, s>(q_gen_749, q_gen_815) -> q_gen_740
<cons, s>(q_gen_775, q_gen_773) -> q_gen_740
<cons, s>(q_gen_788, q_gen_787) -> q_gen_740
<cons, s>(q_gen_794, q_gen_815) -> q_gen_740
<nil, z>() -> q_gen_740
<a, z>() -> q_gen_749
<b, s>(q_gen_804) -> q_gen_749
<b, z>() -> q_gen_749
<a, s>(q_gen_776) -> q_gen_775
<a, s>(q_gen_789) -> q_gen_775
<b, s>(q_gen_776) -> q_gen_775
<cons, s>(q_gen_749, q_gen_773) -> q_gen_777
<cons, s>(q_gen_749, q_gen_787) -> q_gen_777
<cons, s>(q_gen_775, q_gen_748) -> q_gen_777
<cons, s>(q_gen_775, q_gen_787) -> q_gen_777
<cons, s>(q_gen_775, q_gen_815) -> q_gen_777
<cons, s>(q_gen_788, q_gen_748) -> q_gen_777
<cons, s>(q_gen_788, q_gen_773) -> q_gen_777
<cons, s>(q_gen_788, q_gen_815) -> q_gen_777
<cons, s>(q_gen_794, q_gen_748) -> q_gen_777
<cons, s>(q_gen_794, q_gen_773) -> q_gen_777
<cons, s>(q_gen_794, q_gen_787) -> q_gen_777
<cons, s>(q_gen_810, q_gen_748) -> q_gen_777
<cons, s>(q_gen_810, q_gen_773) -> q_gen_777
<cons, s>(q_gen_810, q_gen_787) -> q_gen_777
<cons, s>(q_gen_810, q_gen_815) -> q_gen_777
<b, s>(q_gen_789) -> q_gen_788
<a, s>(q_gen_795) -> q_gen_794
<b, s>(q_gen_795) -> q_gen_794
<a, s>(q_gen_804) -> q_gen_810
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_738, q_gen_752},
Q_f={q_gen_738},
Delta=
{
<a, a>() -> q_gen_738
<a, b>() -> q_gen_738
<b, b>() -> q_gen_738
<b, a>() -> q_gen_752
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_737, q_gen_751},
Q_f={q_gen_737},
Delta=
{
<cons, cons>(q_gen_751, q_gen_737) -> q_gen_737
<nil, nil>() -> q_gen_737
<a, a>() -> q_gen_751
<a, b>() -> q_gen_751
<b, a>() -> q_gen_751
<b, b>() -> q_gen_751
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 57
() -> length([nil, z]) -> 57
() -> leq([a, y]) -> 57
() -> leq([b, b]) -> 57
() -> sort([nil, nil]) -> 57
(insert([x, z, _yc]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _yc)]) -> 57
(insert([y, _dd, _ed]) /\ sort([z, _dd])) -> sort([cons(y, z), _ed]) -> 62
(length([_nd, _od]) /\ length([l, _md]) /\ sort([l, _nd])) -> eq_nat([_md, _od]) -> 70
(length([ll, _id])) -> length([cons(x, ll), s(_id)]) -> 73
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 58
(leq([b, a])) -> BOT -> 58
}
Sat witness: Found: ((length([ll, _id])) -> length([cons(x, ll), s(_id)]), {
_id -> s(s(s(s(s(z)))))  ;  ll -> cons(b, nil)  ;  x -> b
})

-------------------------------------------
Step 70, which took 0.668161 s (model generation: 0.664015,  model checking: 0.004146):

Model:
|_
{
insert -> 
{{{
Q={q_gen_741, q_gen_742, q_gen_743, q_gen_745, q_gen_746},
Q_f={q_gen_741},
Delta=
{
<nil>() -> q_gen_742
<a>() -> q_gen_743
<b>() -> q_gen_743
<cons, cons>(q_gen_746, q_gen_745) -> q_gen_745
<nil, cons>(q_gen_743, q_gen_742) -> q_gen_745
<a, a>() -> q_gen_746
<a, b>() -> q_gen_746
<b, a>() -> q_gen_746
<b, b>() -> q_gen_746
<a, cons, cons>(q_gen_746, q_gen_745) -> q_gen_741
<a, nil, cons>(q_gen_743, q_gen_742) -> q_gen_741
<b, cons, cons>(q_gen_746, q_gen_745) -> q_gen_741
<b, nil, cons>(q_gen_743, q_gen_742) -> q_gen_741
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_740, q_gen_748, q_gen_749, q_gen_773, q_gen_774, q_gen_775, q_gen_776, q_gen_777, q_gen_787, q_gen_788, q_gen_789, q_gen_794, q_gen_795, q_gen_804, q_gen_810, q_gen_815},
Q_f={q_gen_740},
Delta=
{
<nil>() -> q_gen_748
<cons>(q_gen_774, q_gen_748) -> q_gen_773
<a>() -> q_gen_774
<b>() -> q_gen_774
<z>() -> q_gen_776
<cons>(q_gen_774, q_gen_773) -> q_gen_787
<s>(q_gen_776) -> q_gen_789
<s>(q_gen_804) -> q_gen_789
<s>(q_gen_789) -> q_gen_795
<s>(q_gen_795) -> q_gen_804
<cons>(q_gen_774, q_gen_787) -> q_gen_815
<cons>(q_gen_774, q_gen_815) -> q_gen_815
<cons, s>(q_gen_749, q_gen_748) -> q_gen_740
<cons, s>(q_gen_775, q_gen_773) -> q_gen_740
<cons, s>(q_gen_788, q_gen_787) -> q_gen_740
<cons, s>(q_gen_794, q_gen_815) -> q_gen_740
<nil, z>() -> q_gen_740
<a, z>() -> q_gen_749
<b, z>() -> q_gen_749
<a, s>(q_gen_776) -> q_gen_775
<a, s>(q_gen_789) -> q_gen_775
<b, s>(q_gen_776) -> q_gen_775
<cons, s>(q_gen_749, q_gen_773) -> q_gen_777
<cons, s>(q_gen_749, q_gen_787) -> q_gen_777
<cons, s>(q_gen_749, q_gen_815) -> q_gen_777
<cons, s>(q_gen_775, q_gen_748) -> q_gen_777
<cons, s>(q_gen_775, q_gen_787) -> q_gen_777
<cons, s>(q_gen_775, q_gen_815) -> q_gen_777
<cons, s>(q_gen_788, q_gen_748) -> q_gen_777
<cons, s>(q_gen_788, q_gen_773) -> q_gen_777
<cons, s>(q_gen_788, q_gen_815) -> q_gen_777
<cons, s>(q_gen_794, q_gen_748) -> q_gen_777
<cons, s>(q_gen_794, q_gen_773) -> q_gen_777
<cons, s>(q_gen_794, q_gen_787) -> q_gen_777
<cons, s>(q_gen_810, q_gen_748) -> q_gen_777
<cons, s>(q_gen_810, q_gen_773) -> q_gen_777
<cons, s>(q_gen_810, q_gen_787) -> q_gen_777
<cons, s>(q_gen_810, q_gen_815) -> q_gen_777
<b, s>(q_gen_789) -> q_gen_788
<a, s>(q_gen_795) -> q_gen_794
<b, s>(q_gen_795) -> q_gen_794
<b, s>(q_gen_804) -> q_gen_794
<a, s>(q_gen_804) -> q_gen_810
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_738, q_gen_752},
Q_f={q_gen_738},
Delta=
{
<a, a>() -> q_gen_738
<a, b>() -> q_gen_738
<b, b>() -> q_gen_738
<b, a>() -> q_gen_752
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_737, q_gen_751},
Q_f={q_gen_737},
Delta=
{
<cons, cons>(q_gen_751, q_gen_737) -> q_gen_737
<nil, nil>() -> q_gen_737
<a, a>() -> q_gen_751
<a, b>() -> q_gen_751
<b, a>() -> q_gen_751
<b, b>() -> q_gen_751
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 58
() -> length([nil, z]) -> 58
() -> leq([a, y]) -> 58
() -> leq([b, b]) -> 58
() -> sort([nil, nil]) -> 58
(insert([x, z, _yc]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _yc)]) -> 58
(insert([y, _dd, _ed]) /\ sort([z, _dd])) -> sort([cons(y, z), _ed]) -> 63
(length([_nd, _od]) /\ length([l, _md]) /\ sort([l, _nd])) -> eq_nat([_md, _od]) -> 73
(length([ll, _id])) -> length([cons(x, ll), s(_id)]) -> 73
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 59
(leq([b, a])) -> BOT -> 59
}
Sat witness: Found: ((length([_nd, _od]) /\ length([l, _md]) /\ sort([l, _nd])) -> eq_nat([_md, _od]), {
_md -> s(s(s(z)))  ;  _nd -> cons(a, cons(b, nil))  ;  _od -> s(s(z))  ;  l -> cons(a, cons(b, nil))
})

-------------------------------------------
Step 71, which took 0.675859 s (model generation: 0.664887,  model checking: 0.010972):

Model:
|_
{
insert -> 
{{{
Q={q_gen_741, q_gen_742, q_gen_743, q_gen_745, q_gen_746},
Q_f={q_gen_741},
Delta=
{
<nil>() -> q_gen_742
<a>() -> q_gen_743
<b>() -> q_gen_743
<cons, cons>(q_gen_746, q_gen_745) -> q_gen_745
<nil, cons>(q_gen_743, q_gen_742) -> q_gen_745
<a, a>() -> q_gen_746
<a, b>() -> q_gen_746
<b, a>() -> q_gen_746
<b, b>() -> q_gen_746
<a, cons, cons>(q_gen_746, q_gen_745) -> q_gen_741
<a, nil, cons>(q_gen_743, q_gen_742) -> q_gen_741
<b, cons, cons>(q_gen_746, q_gen_745) -> q_gen_741
<b, nil, cons>(q_gen_743, q_gen_742) -> q_gen_741
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_740, q_gen_748, q_gen_749, q_gen_773, q_gen_774, q_gen_775, q_gen_776, q_gen_777, q_gen_787, q_gen_788, q_gen_789, q_gen_794, q_gen_795, q_gen_804, q_gen_810, q_gen_815},
Q_f={q_gen_740},
Delta=
{
<nil>() -> q_gen_748
<cons>(q_gen_774, q_gen_748) -> q_gen_773
<a>() -> q_gen_774
<b>() -> q_gen_774
<z>() -> q_gen_776
<cons>(q_gen_774, q_gen_773) -> q_gen_787
<s>(q_gen_776) -> q_gen_789
<s>(q_gen_804) -> q_gen_789
<s>(q_gen_789) -> q_gen_795
<s>(q_gen_795) -> q_gen_804
<cons>(q_gen_774, q_gen_787) -> q_gen_815
<cons>(q_gen_774, q_gen_815) -> q_gen_815
<cons, s>(q_gen_749, q_gen_748) -> q_gen_740
<cons, s>(q_gen_775, q_gen_773) -> q_gen_740
<cons, s>(q_gen_788, q_gen_787) -> q_gen_740
<cons, s>(q_gen_794, q_gen_815) -> q_gen_740
<nil, z>() -> q_gen_740
<a, z>() -> q_gen_749
<b, z>() -> q_gen_749
<a, s>(q_gen_776) -> q_gen_775
<b, s>(q_gen_776) -> q_gen_775
<cons, s>(q_gen_749, q_gen_773) -> q_gen_777
<cons, s>(q_gen_749, q_gen_787) -> q_gen_777
<cons, s>(q_gen_749, q_gen_815) -> q_gen_777
<cons, s>(q_gen_775, q_gen_748) -> q_gen_777
<cons, s>(q_gen_775, q_gen_787) -> q_gen_777
<cons, s>(q_gen_775, q_gen_815) -> q_gen_777
<cons, s>(q_gen_788, q_gen_748) -> q_gen_777
<cons, s>(q_gen_788, q_gen_773) -> q_gen_777
<cons, s>(q_gen_788, q_gen_815) -> q_gen_777
<cons, s>(q_gen_794, q_gen_748) -> q_gen_777
<cons, s>(q_gen_794, q_gen_773) -> q_gen_777
<cons, s>(q_gen_794, q_gen_787) -> q_gen_777
<cons, s>(q_gen_810, q_gen_748) -> q_gen_777
<cons, s>(q_gen_810, q_gen_773) -> q_gen_777
<cons, s>(q_gen_810, q_gen_787) -> q_gen_777
<cons, s>(q_gen_810, q_gen_815) -> q_gen_777
<a, s>(q_gen_789) -> q_gen_788
<b, s>(q_gen_789) -> q_gen_788
<a, s>(q_gen_795) -> q_gen_794
<b, s>(q_gen_795) -> q_gen_794
<b, s>(q_gen_804) -> q_gen_794
<a, s>(q_gen_804) -> q_gen_810
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_738, q_gen_752},
Q_f={q_gen_738},
Delta=
{
<a, a>() -> q_gen_738
<a, b>() -> q_gen_738
<b, b>() -> q_gen_738
<b, a>() -> q_gen_752
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_737, q_gen_751},
Q_f={q_gen_737},
Delta=
{
<cons, cons>(q_gen_751, q_gen_737) -> q_gen_737
<nil, nil>() -> q_gen_737
<a, a>() -> q_gen_751
<a, b>() -> q_gen_751
<b, a>() -> q_gen_751
<b, b>() -> q_gen_751
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 59
() -> length([nil, z]) -> 59
() -> leq([a, y]) -> 59
() -> leq([b, b]) -> 59
() -> sort([nil, nil]) -> 59
(insert([x, z, _yc]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _yc)]) -> 59
(insert([y, _dd, _ed]) /\ sort([z, _dd])) -> sort([cons(y, z), _ed]) -> 64
(length([_nd, _od]) /\ length([l, _md]) /\ sort([l, _nd])) -> eq_nat([_md, _od]) -> 73
(length([ll, _id])) -> length([cons(x, ll), s(_id)]) -> 76
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 60
(leq([b, a])) -> BOT -> 60
}
Sat witness: Found: ((length([ll, _id])) -> length([cons(x, ll), s(_id)]), {
_id -> s(s(s(s(z))))  ;  ll -> cons(b, cons(b, cons(a, cons(b, nil))))  ;  x -> a
})

-------------------------------------------
Step 72, which took 0.732727 s (model generation: 0.730970,  model checking: 0.001757):

Model:
|_
{
insert -> 
{{{
Q={q_gen_741, q_gen_742, q_gen_743, q_gen_745, q_gen_746},
Q_f={q_gen_741},
Delta=
{
<nil>() -> q_gen_742
<a>() -> q_gen_743
<b>() -> q_gen_743
<cons, cons>(q_gen_746, q_gen_745) -> q_gen_745
<nil, cons>(q_gen_743, q_gen_742) -> q_gen_745
<a, a>() -> q_gen_746
<a, b>() -> q_gen_746
<b, a>() -> q_gen_746
<b, b>() -> q_gen_746
<a, cons, cons>(q_gen_746, q_gen_745) -> q_gen_741
<a, nil, cons>(q_gen_743, q_gen_742) -> q_gen_741
<b, cons, cons>(q_gen_746, q_gen_745) -> q_gen_741
<b, nil, cons>(q_gen_743, q_gen_742) -> q_gen_741
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_740, q_gen_748, q_gen_749, q_gen_773, q_gen_774, q_gen_775, q_gen_776, q_gen_777, q_gen_787, q_gen_788, q_gen_789, q_gen_794, q_gen_795, q_gen_815},
Q_f={q_gen_740},
Delta=
{
<nil>() -> q_gen_748
<cons>(q_gen_774, q_gen_748) -> q_gen_773
<a>() -> q_gen_774
<b>() -> q_gen_774
<z>() -> q_gen_776
<cons>(q_gen_774, q_gen_773) -> q_gen_787
<s>(q_gen_776) -> q_gen_789
<s>(q_gen_789) -> q_gen_795
<s>(q_gen_795) -> q_gen_795
<cons>(q_gen_774, q_gen_787) -> q_gen_815
<cons>(q_gen_774, q_gen_815) -> q_gen_815
<cons, s>(q_gen_749, q_gen_748) -> q_gen_740
<cons, s>(q_gen_775, q_gen_773) -> q_gen_740
<cons, s>(q_gen_788, q_gen_787) -> q_gen_740
<cons, s>(q_gen_788, q_gen_815) -> q_gen_740
<cons, s>(q_gen_794, q_gen_815) -> q_gen_740
<nil, z>() -> q_gen_740
<a, z>() -> q_gen_749
<b, z>() -> q_gen_749
<a, s>(q_gen_776) -> q_gen_775
<b, s>(q_gen_776) -> q_gen_775
<cons, s>(q_gen_749, q_gen_773) -> q_gen_777
<cons, s>(q_gen_749, q_gen_787) -> q_gen_777
<cons, s>(q_gen_749, q_gen_815) -> q_gen_777
<cons, s>(q_gen_775, q_gen_748) -> q_gen_777
<cons, s>(q_gen_775, q_gen_787) -> q_gen_777
<cons, s>(q_gen_775, q_gen_815) -> q_gen_777
<cons, s>(q_gen_788, q_gen_748) -> q_gen_777
<cons, s>(q_gen_788, q_gen_773) -> q_gen_777
<cons, s>(q_gen_794, q_gen_748) -> q_gen_777
<cons, s>(q_gen_794, q_gen_773) -> q_gen_777
<cons, s>(q_gen_794, q_gen_787) -> q_gen_777
<a, s>(q_gen_789) -> q_gen_788
<a, s>(q_gen_795) -> q_gen_788
<b, s>(q_gen_789) -> q_gen_788
<b, s>(q_gen_795) -> q_gen_794
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_738, q_gen_752},
Q_f={q_gen_738},
Delta=
{
<a, a>() -> q_gen_738
<a, b>() -> q_gen_738
<b, b>() -> q_gen_738
<b, a>() -> q_gen_752
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_737, q_gen_750, q_gen_751, q_gen_764, q_gen_825},
Q_f={q_gen_737, q_gen_750},
Delta=
{
<cons, cons>(q_gen_764, q_gen_737) -> q_gen_737
<nil, nil>() -> q_gen_737
<cons, cons>(q_gen_751, q_gen_737) -> q_gen_750
<cons, cons>(q_gen_751, q_gen_750) -> q_gen_750
<cons, cons>(q_gen_751, q_gen_825) -> q_gen_750
<cons, cons>(q_gen_764, q_gen_825) -> q_gen_750
<a, a>() -> q_gen_751
<b, b>() -> q_gen_751
<a, b>() -> q_gen_764
<b, a>() -> q_gen_764
<cons, cons>(q_gen_764, q_gen_750) -> q_gen_825
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 60
() -> length([nil, z]) -> 60
() -> leq([a, y]) -> 60
() -> leq([b, b]) -> 60
() -> sort([nil, nil]) -> 60
(insert([x, z, _yc]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _yc)]) -> 60
(insert([y, _dd, _ed]) /\ sort([z, _dd])) -> sort([cons(y, z), _ed]) -> 67
(length([_nd, _od]) /\ length([l, _md]) /\ sort([l, _nd])) -> eq_nat([_md, _od]) -> 73
(length([ll, _id])) -> length([cons(x, ll), s(_id)]) -> 76
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 61
(leq([b, a])) -> BOT -> 61
}
Sat witness: Found: ((insert([y, _dd, _ed]) /\ sort([z, _dd])) -> sort([cons(y, z), _ed]), {
_dd -> cons(a, nil)  ;  _ed -> cons(b, cons(a, nil))  ;  y -> a  ;  z -> cons(a, nil)
})

-------------------------------------------
Step 73, which took 0.854622 s (model generation: 0.853886,  model checking: 0.000736):

Model:
|_
{
insert -> 
{{{
Q={q_gen_741, q_gen_742, q_gen_743, q_gen_745, q_gen_746, q_gen_757, q_gen_762, q_gen_766},
Q_f={q_gen_741},
Delta=
{
<nil>() -> q_gen_742
<b>() -> q_gen_743
<a>() -> q_gen_757
<cons, cons>(q_gen_746, q_gen_766) -> q_gen_745
<nil, cons>(q_gen_743, q_gen_742) -> q_gen_745
<a, a>() -> q_gen_746
<a, b>() -> q_gen_746
<b, a>() -> q_gen_746
<b, b>() -> q_gen_746
<cons, cons>(q_gen_746, q_gen_745) -> q_gen_766
<nil, cons>(q_gen_757, q_gen_742) -> q_gen_766
<a, cons, cons>(q_gen_746, q_gen_745) -> q_gen_741
<a, cons, cons>(q_gen_746, q_gen_766) -> q_gen_741
<a, nil, cons>(q_gen_757, q_gen_742) -> q_gen_741
<b, cons, cons>(q_gen_746, q_gen_745) -> q_gen_741
<b, nil, cons>(q_gen_743, q_gen_742) -> q_gen_741
<a, nil, cons>(q_gen_743, q_gen_742) -> q_gen_762
<b, cons, cons>(q_gen_746, q_gen_766) -> q_gen_762
<b, nil, cons>(q_gen_757, q_gen_742) -> q_gen_762
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_740, q_gen_748, q_gen_749, q_gen_773, q_gen_774, q_gen_775, q_gen_776, q_gen_777, q_gen_787, q_gen_788, q_gen_789},
Q_f={q_gen_740},
Delta=
{
<nil>() -> q_gen_748
<cons>(q_gen_774, q_gen_748) -> q_gen_773
<a>() -> q_gen_774
<b>() -> q_gen_774
<z>() -> q_gen_776
<cons>(q_gen_774, q_gen_773) -> q_gen_787
<cons>(q_gen_774, q_gen_787) -> q_gen_787
<s>(q_gen_776) -> q_gen_789
<s>(q_gen_789) -> q_gen_789
<cons, s>(q_gen_749, q_gen_748) -> q_gen_740
<cons, s>(q_gen_775, q_gen_773) -> q_gen_740
<cons, s>(q_gen_788, q_gen_787) -> q_gen_740
<nil, z>() -> q_gen_740
<a, z>() -> q_gen_749
<b, z>() -> q_gen_749
<a, s>(q_gen_776) -> q_gen_775
<b, s>(q_gen_776) -> q_gen_775
<cons, s>(q_gen_749, q_gen_773) -> q_gen_777
<cons, s>(q_gen_749, q_gen_787) -> q_gen_777
<cons, s>(q_gen_775, q_gen_748) -> q_gen_777
<cons, s>(q_gen_775, q_gen_787) -> q_gen_777
<cons, s>(q_gen_788, q_gen_748) -> q_gen_777
<cons, s>(q_gen_788, q_gen_773) -> q_gen_777
<a, s>(q_gen_789) -> q_gen_788
<b, s>(q_gen_789) -> q_gen_788
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_738, q_gen_752},
Q_f={q_gen_738},
Delta=
{
<a, a>() -> q_gen_738
<a, b>() -> q_gen_738
<b, b>() -> q_gen_738
<b, a>() -> q_gen_752
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_737, q_gen_750, q_gen_751, q_gen_791, q_gen_805},
Q_f={q_gen_737, q_gen_750, q_gen_791},
Delta=
{
<nil, nil>() -> q_gen_737
<cons, cons>(q_gen_751, q_gen_737) -> q_gen_750
<a, a>() -> q_gen_751
<a, b>() -> q_gen_751
<b, a>() -> q_gen_751
<b, b>() -> q_gen_751
<cons, cons>(q_gen_751, q_gen_750) -> q_gen_791
<cons, cons>(q_gen_751, q_gen_791) -> q_gen_805
<cons, cons>(q_gen_751, q_gen_805) -> q_gen_805
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 60
() -> length([nil, z]) -> 60
() -> leq([a, y]) -> 60
() -> leq([b, b]) -> 60
() -> sort([nil, nil]) -> 60
(insert([x, z, _yc]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _yc)]) -> 63
(insert([y, _dd, _ed]) /\ sort([z, _dd])) -> sort([cons(y, z), _ed]) -> 67
(length([_nd, _od]) /\ length([l, _md]) /\ sort([l, _nd])) -> eq_nat([_md, _od]) -> 73
(length([ll, _id])) -> length([cons(x, ll), s(_id)]) -> 76
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 61
(leq([b, a])) -> BOT -> 61
}
Sat witness: Found: ((insert([x, z, _yc]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _yc)]), {
_yc -> cons(a, cons(b, nil))  ;  x -> b  ;  y -> a  ;  z -> cons(b, nil)
})

-------------------------------------------
Step 74, which took 1.071760 s (model generation: 1.070398,  model checking: 0.001362):

Model:
|_
{
insert -> 
{{{
Q={q_gen_741, q_gen_742, q_gen_743, q_gen_745, q_gen_746, q_gen_757, q_gen_759, q_gen_762, q_gen_766},
Q_f={q_gen_741},
Delta=
{
<nil>() -> q_gen_742
<b>() -> q_gen_743
<a>() -> q_gen_757
<cons, cons>(q_gen_759, q_gen_745) -> q_gen_745
<cons, cons>(q_gen_759, q_gen_766) -> q_gen_745
<nil, cons>(q_gen_743, q_gen_742) -> q_gen_745
<a, a>() -> q_gen_746
<b, b>() -> q_gen_746
<a, b>() -> q_gen_759
<b, a>() -> q_gen_759
<cons, cons>(q_gen_746, q_gen_745) -> q_gen_766
<cons, cons>(q_gen_746, q_gen_766) -> q_gen_766
<nil, cons>(q_gen_757, q_gen_742) -> q_gen_766
<a, cons, cons>(q_gen_746, q_gen_766) -> q_gen_741
<a, cons, cons>(q_gen_759, q_gen_745) -> q_gen_741
<a, nil, cons>(q_gen_757, q_gen_742) -> q_gen_741
<b, cons, cons>(q_gen_746, q_gen_745) -> q_gen_741
<b, nil, cons>(q_gen_743, q_gen_742) -> q_gen_741
<a, cons, cons>(q_gen_746, q_gen_745) -> q_gen_762
<a, cons, cons>(q_gen_759, q_gen_766) -> q_gen_762
<a, nil, cons>(q_gen_743, q_gen_742) -> q_gen_762
<b, cons, cons>(q_gen_746, q_gen_766) -> q_gen_762
<b, cons, cons>(q_gen_759, q_gen_745) -> q_gen_762
<b, nil, cons>(q_gen_757, q_gen_742) -> q_gen_762
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_740, q_gen_748, q_gen_749, q_gen_773, q_gen_774, q_gen_775, q_gen_776, q_gen_777, q_gen_789},
Q_f={q_gen_740},
Delta=
{
<cons>(q_gen_774, q_gen_773) -> q_gen_748
<nil>() -> q_gen_748
<cons>(q_gen_774, q_gen_748) -> q_gen_773
<a>() -> q_gen_774
<b>() -> q_gen_774
<s>(q_gen_789) -> q_gen_776
<z>() -> q_gen_776
<s>(q_gen_776) -> q_gen_789
<cons, s>(q_gen_749, q_gen_748) -> q_gen_740
<cons, s>(q_gen_775, q_gen_773) -> q_gen_740
<nil, z>() -> q_gen_740
<a, s>(q_gen_789) -> q_gen_749
<a, z>() -> q_gen_749
<b, s>(q_gen_789) -> q_gen_749
<b, z>() -> q_gen_749
<a, s>(q_gen_776) -> q_gen_775
<b, s>(q_gen_776) -> q_gen_775
<cons, s>(q_gen_749, q_gen_773) -> q_gen_777
<cons, s>(q_gen_775, q_gen_748) -> q_gen_777
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_738, q_gen_752},
Q_f={q_gen_738},
Delta=
{
<a, a>() -> q_gen_738
<a, b>() -> q_gen_738
<b, b>() -> q_gen_738
<b, a>() -> q_gen_752
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_737, q_gen_750, q_gen_751, q_gen_763, q_gen_764, q_gen_791},
Q_f={q_gen_737, q_gen_750, q_gen_791},
Delta=
{
<nil, nil>() -> q_gen_737
<cons, cons>(q_gen_751, q_gen_737) -> q_gen_750
<a, a>() -> q_gen_751
<b, b>() -> q_gen_751
<cons, cons>(q_gen_751, q_gen_763) -> q_gen_763
<cons, cons>(q_gen_751, q_gen_791) -> q_gen_763
<cons, cons>(q_gen_764, q_gen_737) -> q_gen_763
<cons, cons>(q_gen_764, q_gen_750) -> q_gen_763
<cons, cons>(q_gen_764, q_gen_763) -> q_gen_763
<cons, cons>(q_gen_764, q_gen_791) -> q_gen_763
<a, b>() -> q_gen_764
<b, a>() -> q_gen_764
<cons, cons>(q_gen_751, q_gen_750) -> q_gen_791
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 61
() -> length([nil, z]) -> 61
() -> leq([a, y]) -> 61
() -> leq([b, b]) -> 61
() -> sort([nil, nil]) -> 61
(insert([x, z, _yc]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _yc)]) -> 63
(insert([y, _dd, _ed]) /\ sort([z, _dd])) -> sort([cons(y, z), _ed]) -> 67
(length([_nd, _od]) /\ length([l, _md]) /\ sort([l, _nd])) -> eq_nat([_md, _od]) -> 73
(length([ll, _id])) -> length([cons(x, ll), s(_id)]) -> 76
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 64
(leq([b, a])) -> BOT -> 62
}
Sat witness: Found: ((leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]), {
x -> b  ;  y -> b  ;  z -> cons(b, nil)
})

-------------------------------------------
Step 75, which took 1.094310 s (model generation: 1.088233,  model checking: 0.006077):

Model:
|_
{
insert -> 
{{{
Q={q_gen_741, q_gen_742, q_gen_743, q_gen_745, q_gen_746},
Q_f={q_gen_741},
Delta=
{
<nil>() -> q_gen_742
<a>() -> q_gen_743
<b>() -> q_gen_743
<cons, cons>(q_gen_746, q_gen_745) -> q_gen_745
<nil, cons>(q_gen_743, q_gen_742) -> q_gen_745
<a, a>() -> q_gen_746
<a, b>() -> q_gen_746
<b, a>() -> q_gen_746
<b, b>() -> q_gen_746
<a, cons, cons>(q_gen_746, q_gen_745) -> q_gen_741
<a, nil, cons>(q_gen_743, q_gen_742) -> q_gen_741
<b, cons, cons>(q_gen_746, q_gen_745) -> q_gen_741
<b, nil, cons>(q_gen_743, q_gen_742) -> q_gen_741
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_740, q_gen_748, q_gen_749, q_gen_773, q_gen_774, q_gen_775, q_gen_776, q_gen_777, q_gen_787, q_gen_788, q_gen_789, q_gen_794, q_gen_795, q_gen_804, q_gen_810, q_gen_815, q_gen_868},
Q_f={q_gen_740},
Delta=
{
<nil>() -> q_gen_748
<cons>(q_gen_774, q_gen_748) -> q_gen_773
<a>() -> q_gen_774
<b>() -> q_gen_774
<z>() -> q_gen_776
<cons>(q_gen_774, q_gen_773) -> q_gen_787
<s>(q_gen_776) -> q_gen_789
<s>(q_gen_804) -> q_gen_789
<s>(q_gen_789) -> q_gen_795
<s>(q_gen_795) -> q_gen_804
<cons>(q_gen_774, q_gen_787) -> q_gen_815
<cons>(q_gen_774, q_gen_815) -> q_gen_868
<cons, s>(q_gen_749, q_gen_748) -> q_gen_740
<cons, s>(q_gen_775, q_gen_773) -> q_gen_740
<cons, s>(q_gen_788, q_gen_787) -> q_gen_740
<cons, s>(q_gen_794, q_gen_815) -> q_gen_740
<cons, s>(q_gen_794, q_gen_868) -> q_gen_740
<cons, s>(q_gen_810, q_gen_868) -> q_gen_740
<nil, z>() -> q_gen_740
<a, s>(q_gen_789) -> q_gen_749
<a, z>() -> q_gen_749
<b, z>() -> q_gen_749
<a, s>(q_gen_776) -> q_gen_775
<b, s>(q_gen_776) -> q_gen_775
<cons, s>(q_gen_749, q_gen_773) -> q_gen_777
<cons, s>(q_gen_749, q_gen_787) -> q_gen_777
<cons, s>(q_gen_749, q_gen_815) -> q_gen_777
<cons, s>(q_gen_775, q_gen_748) -> q_gen_777
<cons, s>(q_gen_775, q_gen_787) -> q_gen_777
<cons, s>(q_gen_775, q_gen_815) -> q_gen_777
<cons, s>(q_gen_788, q_gen_748) -> q_gen_777
<cons, s>(q_gen_788, q_gen_773) -> q_gen_777
<cons, s>(q_gen_788, q_gen_815) -> q_gen_777
<cons, s>(q_gen_794, q_gen_748) -> q_gen_777
<cons, s>(q_gen_794, q_gen_773) -> q_gen_777
<cons, s>(q_gen_794, q_gen_787) -> q_gen_777
<cons, s>(q_gen_810, q_gen_748) -> q_gen_777
<cons, s>(q_gen_810, q_gen_773) -> q_gen_777
<cons, s>(q_gen_810, q_gen_787) -> q_gen_777
<cons, s>(q_gen_810, q_gen_815) -> q_gen_777
<b, s>(q_gen_789) -> q_gen_788
<a, s>(q_gen_795) -> q_gen_794
<b, s>(q_gen_795) -> q_gen_794
<b, s>(q_gen_804) -> q_gen_794
<a, s>(q_gen_804) -> q_gen_810
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_738, q_gen_752},
Q_f={q_gen_738},
Delta=
{
<a, a>() -> q_gen_738
<a, b>() -> q_gen_738
<b, b>() -> q_gen_738
<b, a>() -> q_gen_752
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_737, q_gen_751},
Q_f={q_gen_737},
Delta=
{
<cons, cons>(q_gen_751, q_gen_737) -> q_gen_737
<nil, nil>() -> q_gen_737
<a, a>() -> q_gen_751
<a, b>() -> q_gen_751
<b, a>() -> q_gen_751
<b, b>() -> q_gen_751
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 62
() -> length([nil, z]) -> 62
() -> leq([a, y]) -> 62
() -> leq([b, b]) -> 62
() -> sort([nil, nil]) -> 62
(insert([x, z, _yc]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _yc)]) -> 64
(insert([y, _dd, _ed]) /\ sort([z, _dd])) -> sort([cons(y, z), _ed]) -> 68
(length([_nd, _od]) /\ length([l, _md]) /\ sort([l, _nd])) -> eq_nat([_md, _od]) -> 76
(length([ll, _id])) -> length([cons(x, ll), s(_id)]) -> 76
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 65
(leq([b, a])) -> BOT -> 63
}
Sat witness: Found: ((length([_nd, _od]) /\ length([l, _md]) /\ sort([l, _nd])) -> eq_nat([_md, _od]), {
_md -> s(z)  ;  _nd -> cons(a, nil)  ;  _od -> s(s(s(z)))  ;  l -> cons(b, nil)
})

-------------------------------------------
Step 76, which took 0.853220 s (model generation: 0.830820,  model checking: 0.022400):

Model:
|_
{
insert -> 
{{{
Q={q_gen_741, q_gen_742, q_gen_743, q_gen_745, q_gen_746},
Q_f={q_gen_741},
Delta=
{
<nil>() -> q_gen_742
<a>() -> q_gen_743
<b>() -> q_gen_743
<cons, cons>(q_gen_746, q_gen_745) -> q_gen_745
<nil, cons>(q_gen_743, q_gen_742) -> q_gen_745
<a, a>() -> q_gen_746
<a, b>() -> q_gen_746
<b, a>() -> q_gen_746
<b, b>() -> q_gen_746
<a, cons, cons>(q_gen_746, q_gen_745) -> q_gen_741
<a, nil, cons>(q_gen_743, q_gen_742) -> q_gen_741
<b, cons, cons>(q_gen_746, q_gen_745) -> q_gen_741
<b, nil, cons>(q_gen_743, q_gen_742) -> q_gen_741
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_740, q_gen_748, q_gen_749, q_gen_773, q_gen_774, q_gen_775, q_gen_776, q_gen_777, q_gen_787, q_gen_788, q_gen_789, q_gen_794, q_gen_795, q_gen_804, q_gen_810, q_gen_815, q_gen_868},
Q_f={q_gen_740},
Delta=
{
<nil>() -> q_gen_748
<cons>(q_gen_774, q_gen_748) -> q_gen_773
<a>() -> q_gen_774
<b>() -> q_gen_774
<z>() -> q_gen_776
<cons>(q_gen_774, q_gen_773) -> q_gen_787
<s>(q_gen_776) -> q_gen_789
<s>(q_gen_804) -> q_gen_789
<s>(q_gen_789) -> q_gen_795
<s>(q_gen_795) -> q_gen_804
<cons>(q_gen_774, q_gen_787) -> q_gen_815
<cons>(q_gen_774, q_gen_815) -> q_gen_868
<cons, s>(q_gen_749, q_gen_748) -> q_gen_740
<cons, s>(q_gen_775, q_gen_773) -> q_gen_740
<cons, s>(q_gen_788, q_gen_787) -> q_gen_740
<cons, s>(q_gen_794, q_gen_815) -> q_gen_740
<cons, s>(q_gen_794, q_gen_868) -> q_gen_740
<cons, s>(q_gen_810, q_gen_868) -> q_gen_740
<nil, z>() -> q_gen_740
<a, z>() -> q_gen_749
<b, z>() -> q_gen_749
<a, s>(q_gen_776) -> q_gen_775
<b, s>(q_gen_776) -> q_gen_775
<cons, s>(q_gen_749, q_gen_773) -> q_gen_777
<cons, s>(q_gen_749, q_gen_787) -> q_gen_777
<cons, s>(q_gen_749, q_gen_815) -> q_gen_777
<cons, s>(q_gen_775, q_gen_748) -> q_gen_777
<cons, s>(q_gen_775, q_gen_787) -> q_gen_777
<cons, s>(q_gen_775, q_gen_815) -> q_gen_777
<cons, s>(q_gen_788, q_gen_748) -> q_gen_777
<cons, s>(q_gen_788, q_gen_773) -> q_gen_777
<cons, s>(q_gen_788, q_gen_815) -> q_gen_777
<cons, s>(q_gen_794, q_gen_748) -> q_gen_777
<cons, s>(q_gen_794, q_gen_773) -> q_gen_777
<cons, s>(q_gen_794, q_gen_787) -> q_gen_777
<cons, s>(q_gen_810, q_gen_748) -> q_gen_777
<cons, s>(q_gen_810, q_gen_773) -> q_gen_777
<cons, s>(q_gen_810, q_gen_787) -> q_gen_777
<cons, s>(q_gen_810, q_gen_815) -> q_gen_777
<a, s>(q_gen_789) -> q_gen_788
<b, s>(q_gen_789) -> q_gen_788
<a, s>(q_gen_795) -> q_gen_794
<b, s>(q_gen_795) -> q_gen_794
<b, s>(q_gen_804) -> q_gen_794
<a, s>(q_gen_804) -> q_gen_810
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_738, q_gen_752},
Q_f={q_gen_738},
Delta=
{
<a, a>() -> q_gen_738
<a, b>() -> q_gen_738
<b, b>() -> q_gen_738
<b, a>() -> q_gen_752
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_737, q_gen_751},
Q_f={q_gen_737},
Delta=
{
<cons, cons>(q_gen_751, q_gen_737) -> q_gen_737
<nil, nil>() -> q_gen_737
<a, a>() -> q_gen_751
<a, b>() -> q_gen_751
<b, a>() -> q_gen_751
<b, b>() -> q_gen_751
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 63
() -> length([nil, z]) -> 63
() -> leq([a, y]) -> 63
() -> leq([b, b]) -> 63
() -> sort([nil, nil]) -> 63
(insert([x, z, _yc]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _yc)]) -> 65
(insert([y, _dd, _ed]) /\ sort([z, _dd])) -> sort([cons(y, z), _ed]) -> 69
(length([_nd, _od]) /\ length([l, _md]) /\ sort([l, _nd])) -> eq_nat([_md, _od]) -> 76
(length([ll, _id])) -> length([cons(x, ll), s(_id)]) -> 79
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 66
(leq([b, a])) -> BOT -> 64
}
Sat witness: Found: ((length([ll, _id])) -> length([cons(x, ll), s(_id)]), {
_id -> s(s(s(s(z))))  ;  ll -> cons(b, cons(b, cons(b, cons(a, cons(b, nil)))))  ;  x -> b
})

-------------------------------------------
Step 77, which took 1.240650 s (model generation: 1.235236,  model checking: 0.005414):

Model:
|_
{
insert -> 
{{{
Q={q_gen_741, q_gen_742, q_gen_743, q_gen_745, q_gen_746},
Q_f={q_gen_741},
Delta=
{
<nil>() -> q_gen_742
<a>() -> q_gen_743
<b>() -> q_gen_743
<cons, cons>(q_gen_746, q_gen_745) -> q_gen_745
<nil, cons>(q_gen_743, q_gen_742) -> q_gen_745
<a, a>() -> q_gen_746
<a, b>() -> q_gen_746
<b, a>() -> q_gen_746
<b, b>() -> q_gen_746
<a, cons, cons>(q_gen_746, q_gen_745) -> q_gen_741
<a, nil, cons>(q_gen_743, q_gen_742) -> q_gen_741
<b, cons, cons>(q_gen_746, q_gen_745) -> q_gen_741
<b, nil, cons>(q_gen_743, q_gen_742) -> q_gen_741
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_740, q_gen_748, q_gen_749, q_gen_773, q_gen_774, q_gen_775, q_gen_776, q_gen_777, q_gen_787, q_gen_788, q_gen_789, q_gen_794, q_gen_795, q_gen_804, q_gen_810, q_gen_815, q_gen_868},
Q_f={q_gen_740},
Delta=
{
<nil>() -> q_gen_748
<cons>(q_gen_774, q_gen_748) -> q_gen_773
<a>() -> q_gen_774
<b>() -> q_gen_774
<z>() -> q_gen_776
<cons>(q_gen_774, q_gen_773) -> q_gen_787
<s>(q_gen_776) -> q_gen_789
<s>(q_gen_804) -> q_gen_789
<s>(q_gen_789) -> q_gen_795
<s>(q_gen_795) -> q_gen_804
<cons>(q_gen_774, q_gen_787) -> q_gen_815
<cons>(q_gen_774, q_gen_815) -> q_gen_868
<cons>(q_gen_774, q_gen_868) -> q_gen_868
<cons, s>(q_gen_749, q_gen_748) -> q_gen_740
<cons, s>(q_gen_775, q_gen_773) -> q_gen_740
<cons, s>(q_gen_775, q_gen_868) -> q_gen_740
<cons, s>(q_gen_788, q_gen_787) -> q_gen_740
<cons, s>(q_gen_794, q_gen_815) -> q_gen_740
<cons, s>(q_gen_810, q_gen_868) -> q_gen_740
<nil, z>() -> q_gen_740
<a, z>() -> q_gen_749
<b, z>() -> q_gen_749
<a, s>(q_gen_776) -> q_gen_775
<b, s>(q_gen_776) -> q_gen_775
<b, s>(q_gen_804) -> q_gen_775
<cons, s>(q_gen_749, q_gen_773) -> q_gen_777
<cons, s>(q_gen_749, q_gen_787) -> q_gen_777
<cons, s>(q_gen_749, q_gen_815) -> q_gen_777
<cons, s>(q_gen_775, q_gen_748) -> q_gen_777
<cons, s>(q_gen_775, q_gen_787) -> q_gen_777
<cons, s>(q_gen_775, q_gen_815) -> q_gen_777
<cons, s>(q_gen_788, q_gen_748) -> q_gen_777
<cons, s>(q_gen_788, q_gen_773) -> q_gen_777
<cons, s>(q_gen_788, q_gen_815) -> q_gen_777
<cons, s>(q_gen_794, q_gen_748) -> q_gen_777
<cons, s>(q_gen_794, q_gen_773) -> q_gen_777
<cons, s>(q_gen_794, q_gen_787) -> q_gen_777
<cons, s>(q_gen_794, q_gen_868) -> q_gen_777
<cons, s>(q_gen_810, q_gen_748) -> q_gen_777
<cons, s>(q_gen_810, q_gen_773) -> q_gen_777
<cons, s>(q_gen_810, q_gen_787) -> q_gen_777
<cons, s>(q_gen_810, q_gen_815) -> q_gen_777
<a, s>(q_gen_789) -> q_gen_788
<b, s>(q_gen_789) -> q_gen_788
<a, s>(q_gen_795) -> q_gen_794
<b, s>(q_gen_795) -> q_gen_794
<a, s>(q_gen_804) -> q_gen_810
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_738, q_gen_752},
Q_f={q_gen_738},
Delta=
{
<a, a>() -> q_gen_738
<a, b>() -> q_gen_738
<b, b>() -> q_gen_738
<b, a>() -> q_gen_752
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_737, q_gen_751},
Q_f={q_gen_737},
Delta=
{
<cons, cons>(q_gen_751, q_gen_737) -> q_gen_737
<nil, nil>() -> q_gen_737
<a, a>() -> q_gen_751
<a, b>() -> q_gen_751
<b, a>() -> q_gen_751
<b, b>() -> q_gen_751
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 64
() -> length([nil, z]) -> 64
() -> leq([a, y]) -> 64
() -> leq([b, b]) -> 64
() -> sort([nil, nil]) -> 64
(insert([x, z, _yc]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _yc)]) -> 66
(insert([y, _dd, _ed]) /\ sort([z, _dd])) -> sort([cons(y, z), _ed]) -> 70
(length([_nd, _od]) /\ length([l, _md]) /\ sort([l, _nd])) -> eq_nat([_md, _od]) -> 79
(length([ll, _id])) -> length([cons(x, ll), s(_id)]) -> 79
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 67
(leq([b, a])) -> BOT -> 65
}
Sat witness: Found: ((length([_nd, _od]) /\ length([l, _md]) /\ sort([l, _nd])) -> eq_nat([_md, _od]), {
_md -> s(s(z))  ;  _nd -> cons(a, cons(b, cons(b, cons(b, cons(b, nil)))))  ;  _od -> s(s(s(s(s(z)))))  ;  l -> cons(b, cons(b, cons(b, cons(b, cons(b, nil)))))
})

-------------------------------------------
Step 78, which took 1.769795 s (model generation: 1.747510,  model checking: 0.022285):

Model:
|_
{
insert -> 
{{{
Q={q_gen_741, q_gen_742, q_gen_743, q_gen_745, q_gen_746},
Q_f={q_gen_741},
Delta=
{
<nil>() -> q_gen_742
<a>() -> q_gen_743
<b>() -> q_gen_743
<cons, cons>(q_gen_746, q_gen_745) -> q_gen_745
<nil, cons>(q_gen_743, q_gen_742) -> q_gen_745
<a, a>() -> q_gen_746
<a, b>() -> q_gen_746
<b, a>() -> q_gen_746
<b, b>() -> q_gen_746
<a, cons, cons>(q_gen_746, q_gen_745) -> q_gen_741
<a, nil, cons>(q_gen_743, q_gen_742) -> q_gen_741
<b, cons, cons>(q_gen_746, q_gen_745) -> q_gen_741
<b, nil, cons>(q_gen_743, q_gen_742) -> q_gen_741
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_740, q_gen_748, q_gen_749, q_gen_773, q_gen_774, q_gen_775, q_gen_776, q_gen_777, q_gen_787, q_gen_788, q_gen_789, q_gen_794, q_gen_795, q_gen_804, q_gen_810, q_gen_815, q_gen_868},
Q_f={q_gen_740},
Delta=
{
<nil>() -> q_gen_748
<cons>(q_gen_774, q_gen_748) -> q_gen_773
<a>() -> q_gen_774
<b>() -> q_gen_774
<z>() -> q_gen_776
<cons>(q_gen_774, q_gen_773) -> q_gen_787
<s>(q_gen_776) -> q_gen_789
<s>(q_gen_804) -> q_gen_789
<s>(q_gen_789) -> q_gen_795
<s>(q_gen_795) -> q_gen_804
<cons>(q_gen_774, q_gen_787) -> q_gen_815
<cons>(q_gen_774, q_gen_815) -> q_gen_868
<cons>(q_gen_774, q_gen_868) -> q_gen_868
<cons, s>(q_gen_749, q_gen_748) -> q_gen_740
<cons, s>(q_gen_749, q_gen_815) -> q_gen_740
<cons, s>(q_gen_775, q_gen_773) -> q_gen_740
<cons, s>(q_gen_788, q_gen_787) -> q_gen_740
<cons, s>(q_gen_794, q_gen_815) -> q_gen_740
<cons, s>(q_gen_794, q_gen_868) -> q_gen_740
<cons, s>(q_gen_810, q_gen_868) -> q_gen_740
<nil, z>() -> q_gen_740
<a, z>() -> q_gen_749
<b, z>() -> q_gen_749
<a, s>(q_gen_776) -> q_gen_775
<b, s>(q_gen_776) -> q_gen_775
<cons, s>(q_gen_749, q_gen_773) -> q_gen_777
<cons, s>(q_gen_749, q_gen_787) -> q_gen_777
<cons, s>(q_gen_775, q_gen_748) -> q_gen_777
<cons, s>(q_gen_775, q_gen_787) -> q_gen_777
<cons, s>(q_gen_775, q_gen_815) -> q_gen_777
<cons, s>(q_gen_775, q_gen_868) -> q_gen_777
<cons, s>(q_gen_788, q_gen_748) -> q_gen_777
<cons, s>(q_gen_788, q_gen_773) -> q_gen_777
<cons, s>(q_gen_788, q_gen_815) -> q_gen_777
<cons, s>(q_gen_794, q_gen_748) -> q_gen_777
<cons, s>(q_gen_794, q_gen_773) -> q_gen_777
<cons, s>(q_gen_794, q_gen_787) -> q_gen_777
<cons, s>(q_gen_810, q_gen_748) -> q_gen_777
<cons, s>(q_gen_810, q_gen_773) -> q_gen_777
<cons, s>(q_gen_810, q_gen_787) -> q_gen_777
<cons, s>(q_gen_810, q_gen_815) -> q_gen_777
<b, s>(q_gen_789) -> q_gen_788
<a, s>(q_gen_789) -> q_gen_794
<a, s>(q_gen_795) -> q_gen_794
<b, s>(q_gen_795) -> q_gen_794
<b, s>(q_gen_804) -> q_gen_794
<a, s>(q_gen_804) -> q_gen_810
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_738, q_gen_752},
Q_f={q_gen_738},
Delta=
{
<a, a>() -> q_gen_738
<a, b>() -> q_gen_738
<b, b>() -> q_gen_738
<b, a>() -> q_gen_752
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_737, q_gen_751},
Q_f={q_gen_737},
Delta=
{
<cons, cons>(q_gen_751, q_gen_737) -> q_gen_737
<nil, nil>() -> q_gen_737
<a, a>() -> q_gen_751
<a, b>() -> q_gen_751
<b, a>() -> q_gen_751
<b, b>() -> q_gen_751
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 65
() -> length([nil, z]) -> 65
() -> leq([a, y]) -> 65
() -> leq([b, b]) -> 65
() -> sort([nil, nil]) -> 65
(insert([x, z, _yc]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _yc)]) -> 67
(insert([y, _dd, _ed]) /\ sort([z, _dd])) -> sort([cons(y, z), _ed]) -> 71
(length([_nd, _od]) /\ length([l, _md]) /\ sort([l, _nd])) -> eq_nat([_md, _od]) -> 79
(length([ll, _id])) -> length([cons(x, ll), s(_id)]) -> 82
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 68
(leq([b, a])) -> BOT -> 66
}
Sat witness: Found: ((length([ll, _id])) -> length([cons(x, ll), s(_id)]), {
_id -> s(s(z))  ;  ll -> cons(a, cons(b, nil))  ;  x -> a
})

-------------------------------------------
Step 79, which took 2.438954 s (model generation: 2.433521,  model checking: 0.005433):

Model:
|_
{
insert -> 
{{{
Q={q_gen_741, q_gen_742, q_gen_743, q_gen_745, q_gen_746},
Q_f={q_gen_741},
Delta=
{
<nil>() -> q_gen_742
<a>() -> q_gen_743
<b>() -> q_gen_743
<cons, cons>(q_gen_746, q_gen_745) -> q_gen_745
<nil, cons>(q_gen_743, q_gen_742) -> q_gen_745
<a, a>() -> q_gen_746
<a, b>() -> q_gen_746
<b, a>() -> q_gen_746
<b, b>() -> q_gen_746
<a, cons, cons>(q_gen_746, q_gen_745) -> q_gen_741
<a, nil, cons>(q_gen_743, q_gen_742) -> q_gen_741
<b, cons, cons>(q_gen_746, q_gen_745) -> q_gen_741
<b, nil, cons>(q_gen_743, q_gen_742) -> q_gen_741
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_740, q_gen_748, q_gen_749, q_gen_773, q_gen_774, q_gen_775, q_gen_776, q_gen_777, q_gen_787, q_gen_788, q_gen_789, q_gen_794, q_gen_795, q_gen_803, q_gen_804, q_gen_815, q_gen_868},
Q_f={q_gen_740},
Delta=
{
<nil>() -> q_gen_748
<cons>(q_gen_774, q_gen_748) -> q_gen_773
<a>() -> q_gen_774
<b>() -> q_gen_774
<z>() -> q_gen_776
<cons>(q_gen_774, q_gen_773) -> q_gen_787
<s>(q_gen_776) -> q_gen_789
<s>(q_gen_804) -> q_gen_789
<s>(q_gen_789) -> q_gen_795
<s>(q_gen_795) -> q_gen_804
<cons>(q_gen_774, q_gen_787) -> q_gen_815
<cons>(q_gen_774, q_gen_815) -> q_gen_868
<cons>(q_gen_774, q_gen_868) -> q_gen_868
<cons, s>(q_gen_749, q_gen_748) -> q_gen_740
<cons, s>(q_gen_775, q_gen_773) -> q_gen_740
<cons, s>(q_gen_788, q_gen_787) -> q_gen_740
<cons, s>(q_gen_794, q_gen_815) -> q_gen_740
<cons, s>(q_gen_803, q_gen_868) -> q_gen_740
<nil, z>() -> q_gen_740
<a, z>() -> q_gen_749
<b, z>() -> q_gen_749
<a, s>(q_gen_776) -> q_gen_775
<b, s>(q_gen_776) -> q_gen_775
<cons, s>(q_gen_749, q_gen_773) -> q_gen_777
<cons, s>(q_gen_749, q_gen_787) -> q_gen_777
<cons, s>(q_gen_749, q_gen_815) -> q_gen_777
<cons, s>(q_gen_775, q_gen_748) -> q_gen_777
<cons, s>(q_gen_775, q_gen_787) -> q_gen_777
<cons, s>(q_gen_775, q_gen_815) -> q_gen_777
<cons, s>(q_gen_775, q_gen_868) -> q_gen_777
<cons, s>(q_gen_788, q_gen_748) -> q_gen_777
<cons, s>(q_gen_788, q_gen_773) -> q_gen_777
<cons, s>(q_gen_788, q_gen_815) -> q_gen_777
<cons, s>(q_gen_794, q_gen_748) -> q_gen_777
<cons, s>(q_gen_794, q_gen_773) -> q_gen_777
<cons, s>(q_gen_794, q_gen_787) -> q_gen_777
<cons, s>(q_gen_794, q_gen_868) -> q_gen_777
<cons, s>(q_gen_803, q_gen_748) -> q_gen_777
<cons, s>(q_gen_803, q_gen_773) -> q_gen_777
<cons, s>(q_gen_803, q_gen_787) -> q_gen_777
<cons, s>(q_gen_803, q_gen_815) -> q_gen_777
<a, s>(q_gen_789) -> q_gen_788
<b, s>(q_gen_789) -> q_gen_788
<a, s>(q_gen_795) -> q_gen_794
<b, s>(q_gen_795) -> q_gen_794
<a, s>(q_gen_804) -> q_gen_803
<b, s>(q_gen_804) -> q_gen_803
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_738, q_gen_752},
Q_f={q_gen_738},
Delta=
{
<a, a>() -> q_gen_738
<a, b>() -> q_gen_738
<b, b>() -> q_gen_738
<b, a>() -> q_gen_752
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_737, q_gen_751},
Q_f={q_gen_737},
Delta=
{
<cons, cons>(q_gen_751, q_gen_737) -> q_gen_737
<nil, nil>() -> q_gen_737
<a, a>() -> q_gen_751
<a, b>() -> q_gen_751
<b, a>() -> q_gen_751
<b, b>() -> q_gen_751
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 66
() -> length([nil, z]) -> 66
() -> leq([a, y]) -> 66
() -> leq([b, b]) -> 66
() -> sort([nil, nil]) -> 66
(insert([x, z, _yc]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _yc)]) -> 68
(insert([y, _dd, _ed]) /\ sort([z, _dd])) -> sort([cons(y, z), _ed]) -> 72
(length([_nd, _od]) /\ length([l, _md]) /\ sort([l, _nd])) -> eq_nat([_md, _od]) -> 82
(length([ll, _id])) -> length([cons(x, ll), s(_id)]) -> 82
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 69
(leq([b, a])) -> BOT -> 67
}
Sat witness: Found: ((length([_nd, _od]) /\ length([l, _md]) /\ sort([l, _nd])) -> eq_nat([_md, _od]), {
_md -> s(s(s(z)))  ;  _nd -> cons(b, cons(b, cons(b, nil)))  ;  _od -> s(s(s(s(s(s(z))))))  ;  l -> cons(b, cons(b, cons(b, nil)))
})

-------------------------------------------
Step 80, which took 1.903383 s (model generation: 1.885898,  model checking: 0.017485):

Model:
|_
{
insert -> 
{{{
Q={q_gen_741, q_gen_742, q_gen_743, q_gen_745, q_gen_746},
Q_f={q_gen_741},
Delta=
{
<nil>() -> q_gen_742
<a>() -> q_gen_743
<b>() -> q_gen_743
<cons, cons>(q_gen_746, q_gen_745) -> q_gen_745
<nil, cons>(q_gen_743, q_gen_742) -> q_gen_745
<a, a>() -> q_gen_746
<a, b>() -> q_gen_746
<b, a>() -> q_gen_746
<b, b>() -> q_gen_746
<a, cons, cons>(q_gen_746, q_gen_745) -> q_gen_741
<a, nil, cons>(q_gen_743, q_gen_742) -> q_gen_741
<b, cons, cons>(q_gen_746, q_gen_745) -> q_gen_741
<b, nil, cons>(q_gen_743, q_gen_742) -> q_gen_741
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_740, q_gen_748, q_gen_749, q_gen_773, q_gen_774, q_gen_775, q_gen_776, q_gen_777, q_gen_787, q_gen_788, q_gen_789, q_gen_794, q_gen_795, q_gen_803, q_gen_804, q_gen_815, q_gen_868},
Q_f={q_gen_740},
Delta=
{
<nil>() -> q_gen_748
<cons>(q_gen_774, q_gen_748) -> q_gen_773
<a>() -> q_gen_774
<b>() -> q_gen_774
<z>() -> q_gen_776
<cons>(q_gen_774, q_gen_773) -> q_gen_787
<s>(q_gen_776) -> q_gen_789
<s>(q_gen_789) -> q_gen_795
<s>(q_gen_795) -> q_gen_804
<s>(q_gen_804) -> q_gen_804
<cons>(q_gen_774, q_gen_787) -> q_gen_815
<cons>(q_gen_774, q_gen_868) -> q_gen_815
<cons>(q_gen_774, q_gen_815) -> q_gen_868
<cons, s>(q_gen_749, q_gen_748) -> q_gen_740
<cons, s>(q_gen_775, q_gen_773) -> q_gen_740
<cons, s>(q_gen_788, q_gen_787) -> q_gen_740
<cons, s>(q_gen_794, q_gen_815) -> q_gen_740
<cons, s>(q_gen_803, q_gen_868) -> q_gen_740
<nil, z>() -> q_gen_740
<a, z>() -> q_gen_749
<b, z>() -> q_gen_749
<a, s>(q_gen_776) -> q_gen_775
<b, s>(q_gen_776) -> q_gen_775
<cons, s>(q_gen_749, q_gen_773) -> q_gen_777
<cons, s>(q_gen_749, q_gen_787) -> q_gen_777
<cons, s>(q_gen_749, q_gen_815) -> q_gen_777
<cons, s>(q_gen_775, q_gen_748) -> q_gen_777
<cons, s>(q_gen_775, q_gen_787) -> q_gen_777
<cons, s>(q_gen_775, q_gen_815) -> q_gen_777
<cons, s>(q_gen_775, q_gen_868) -> q_gen_777
<cons, s>(q_gen_788, q_gen_748) -> q_gen_777
<cons, s>(q_gen_788, q_gen_773) -> q_gen_777
<cons, s>(q_gen_788, q_gen_815) -> q_gen_777
<cons, s>(q_gen_794, q_gen_748) -> q_gen_777
<cons, s>(q_gen_794, q_gen_773) -> q_gen_777
<cons, s>(q_gen_794, q_gen_787) -> q_gen_777
<cons, s>(q_gen_794, q_gen_868) -> q_gen_777
<cons, s>(q_gen_803, q_gen_748) -> q_gen_777
<cons, s>(q_gen_803, q_gen_773) -> q_gen_777
<cons, s>(q_gen_803, q_gen_787) -> q_gen_777
<cons, s>(q_gen_803, q_gen_815) -> q_gen_777
<a, s>(q_gen_789) -> q_gen_788
<b, s>(q_gen_789) -> q_gen_788
<a, s>(q_gen_795) -> q_gen_794
<b, s>(q_gen_795) -> q_gen_794
<a, s>(q_gen_804) -> q_gen_803
<b, s>(q_gen_804) -> q_gen_803
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_738, q_gen_752},
Q_f={q_gen_738},
Delta=
{
<a, a>() -> q_gen_738
<a, b>() -> q_gen_738
<b, b>() -> q_gen_738
<b, a>() -> q_gen_752
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_737, q_gen_751},
Q_f={q_gen_737},
Delta=
{
<cons, cons>(q_gen_751, q_gen_737) -> q_gen_737
<nil, nil>() -> q_gen_737
<a, a>() -> q_gen_751
<a, b>() -> q_gen_751
<b, a>() -> q_gen_751
<b, b>() -> q_gen_751
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 67
() -> length([nil, z]) -> 67
() -> leq([a, y]) -> 67
() -> leq([b, b]) -> 67
() -> sort([nil, nil]) -> 67
(insert([x, z, _yc]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _yc)]) -> 69
(insert([y, _dd, _ed]) /\ sort([z, _dd])) -> sort([cons(y, z), _ed]) -> 73
(length([_nd, _od]) /\ length([l, _md]) /\ sort([l, _nd])) -> eq_nat([_md, _od]) -> 82
(length([ll, _id])) -> length([cons(x, ll), s(_id)]) -> 85
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 70
(leq([b, a])) -> BOT -> 68
}
Sat witness: Found: ((length([ll, _id])) -> length([cons(x, ll), s(_id)]), {
_id -> s(s(s(s(s(z)))))  ;  ll -> cons(a, cons(b, cons(b, cons(a, cons(b, nil)))))  ;  x -> b
})

-------------------------------------------
Step 81, which took 1.745311 s (model generation: 1.739202,  model checking: 0.006109):

Model:
|_
{
insert -> 
{{{
Q={q_gen_741, q_gen_742, q_gen_743, q_gen_745, q_gen_746},
Q_f={q_gen_741},
Delta=
{
<nil>() -> q_gen_742
<a>() -> q_gen_743
<b>() -> q_gen_743
<cons, cons>(q_gen_746, q_gen_745) -> q_gen_745
<nil, cons>(q_gen_743, q_gen_742) -> q_gen_745
<a, a>() -> q_gen_746
<a, b>() -> q_gen_746
<b, a>() -> q_gen_746
<b, b>() -> q_gen_746
<a, cons, cons>(q_gen_746, q_gen_745) -> q_gen_741
<a, nil, cons>(q_gen_743, q_gen_742) -> q_gen_741
<b, cons, cons>(q_gen_746, q_gen_745) -> q_gen_741
<b, nil, cons>(q_gen_743, q_gen_742) -> q_gen_741
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_740, q_gen_748, q_gen_749, q_gen_773, q_gen_774, q_gen_775, q_gen_776, q_gen_777, q_gen_787, q_gen_788, q_gen_789, q_gen_794, q_gen_795, q_gen_803, q_gen_804, q_gen_815, q_gen_868},
Q_f={q_gen_740},
Delta=
{
<nil>() -> q_gen_748
<cons>(q_gen_774, q_gen_748) -> q_gen_773
<a>() -> q_gen_774
<b>() -> q_gen_774
<z>() -> q_gen_776
<cons>(q_gen_774, q_gen_773) -> q_gen_787
<s>(q_gen_776) -> q_gen_789
<s>(q_gen_789) -> q_gen_795
<s>(q_gen_795) -> q_gen_804
<s>(q_gen_804) -> q_gen_804
<cons>(q_gen_774, q_gen_787) -> q_gen_815
<cons>(q_gen_774, q_gen_815) -> q_gen_868
<cons>(q_gen_774, q_gen_868) -> q_gen_868
<cons, s>(q_gen_749, q_gen_748) -> q_gen_740
<cons, s>(q_gen_775, q_gen_773) -> q_gen_740
<cons, s>(q_gen_788, q_gen_787) -> q_gen_740
<cons, s>(q_gen_788, q_gen_815) -> q_gen_740
<cons, s>(q_gen_794, q_gen_815) -> q_gen_740
<cons, s>(q_gen_794, q_gen_868) -> q_gen_740
<cons, s>(q_gen_803, q_gen_868) -> q_gen_740
<nil, z>() -> q_gen_740
<a, z>() -> q_gen_749
<b, z>() -> q_gen_749
<a, s>(q_gen_776) -> q_gen_775
<b, s>(q_gen_776) -> q_gen_775
<cons, s>(q_gen_749, q_gen_773) -> q_gen_777
<cons, s>(q_gen_749, q_gen_787) -> q_gen_777
<cons, s>(q_gen_749, q_gen_815) -> q_gen_777
<cons, s>(q_gen_775, q_gen_748) -> q_gen_777
<cons, s>(q_gen_775, q_gen_787) -> q_gen_777
<cons, s>(q_gen_775, q_gen_815) -> q_gen_777
<cons, s>(q_gen_775, q_gen_868) -> q_gen_777
<cons, s>(q_gen_788, q_gen_748) -> q_gen_777
<cons, s>(q_gen_788, q_gen_773) -> q_gen_777
<cons, s>(q_gen_794, q_gen_748) -> q_gen_777
<cons, s>(q_gen_794, q_gen_773) -> q_gen_777
<cons, s>(q_gen_794, q_gen_787) -> q_gen_777
<cons, s>(q_gen_803, q_gen_748) -> q_gen_777
<cons, s>(q_gen_803, q_gen_773) -> q_gen_777
<cons, s>(q_gen_803, q_gen_787) -> q_gen_777
<cons, s>(q_gen_803, q_gen_815) -> q_gen_777
<a, s>(q_gen_789) -> q_gen_788
<a, s>(q_gen_795) -> q_gen_788
<b, s>(q_gen_789) -> q_gen_788
<b, s>(q_gen_795) -> q_gen_794
<a, s>(q_gen_804) -> q_gen_803
<b, s>(q_gen_804) -> q_gen_803
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_738, q_gen_752},
Q_f={q_gen_738},
Delta=
{
<a, a>() -> q_gen_738
<a, b>() -> q_gen_738
<b, b>() -> q_gen_738
<b, a>() -> q_gen_752
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_737, q_gen_751},
Q_f={q_gen_737},
Delta=
{
<cons, cons>(q_gen_751, q_gen_737) -> q_gen_737
<nil, nil>() -> q_gen_737
<a, a>() -> q_gen_751
<a, b>() -> q_gen_751
<b, a>() -> q_gen_751
<b, b>() -> q_gen_751
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 68
() -> length([nil, z]) -> 68
() -> leq([a, y]) -> 68
() -> leq([b, b]) -> 68
() -> sort([nil, nil]) -> 68
(insert([x, z, _yc]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _yc)]) -> 70
(insert([y, _dd, _ed]) /\ sort([z, _dd])) -> sort([cons(y, z), _ed]) -> 74
(length([_nd, _od]) /\ length([l, _md]) /\ sort([l, _nd])) -> eq_nat([_md, _od]) -> 85
(length([ll, _id])) -> length([cons(x, ll), s(_id)]) -> 85
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 71
(leq([b, a])) -> BOT -> 69
}
Sat witness: Found: ((length([_nd, _od]) /\ length([l, _md]) /\ sort([l, _nd])) -> eq_nat([_md, _od]), {
_md -> s(s(s(s(s(s(z))))))  ;  _nd -> cons(b, cons(b, cons(b, cons(b, cons(b, nil)))))  ;  _od -> s(s(s(s(z))))  ;  l -> cons(a, cons(b, cons(b, cons(b, cons(b, nil)))))
})

-------------------------------------------
Step 82, which took 2.516657 s (model generation: 2.493303,  model checking: 0.023354):

Model:
|_
{
insert -> 
{{{
Q={q_gen_741, q_gen_742, q_gen_743, q_gen_745, q_gen_746},
Q_f={q_gen_741},
Delta=
{
<nil>() -> q_gen_742
<a>() -> q_gen_743
<b>() -> q_gen_743
<cons, cons>(q_gen_746, q_gen_745) -> q_gen_745
<nil, cons>(q_gen_743, q_gen_742) -> q_gen_745
<a, a>() -> q_gen_746
<a, b>() -> q_gen_746
<b, a>() -> q_gen_746
<b, b>() -> q_gen_746
<a, cons, cons>(q_gen_746, q_gen_745) -> q_gen_741
<a, nil, cons>(q_gen_743, q_gen_742) -> q_gen_741
<b, cons, cons>(q_gen_746, q_gen_745) -> q_gen_741
<b, nil, cons>(q_gen_743, q_gen_742) -> q_gen_741
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_740, q_gen_748, q_gen_749, q_gen_773, q_gen_774, q_gen_775, q_gen_776, q_gen_777, q_gen_787, q_gen_788, q_gen_789, q_gen_794, q_gen_795, q_gen_803, q_gen_804, q_gen_815, q_gen_868},
Q_f={q_gen_740},
Delta=
{
<nil>() -> q_gen_748
<cons>(q_gen_774, q_gen_748) -> q_gen_773
<a>() -> q_gen_774
<b>() -> q_gen_774
<z>() -> q_gen_776
<cons>(q_gen_774, q_gen_773) -> q_gen_787
<s>(q_gen_776) -> q_gen_789
<s>(q_gen_789) -> q_gen_795
<s>(q_gen_795) -> q_gen_804
<s>(q_gen_804) -> q_gen_804
<cons>(q_gen_774, q_gen_787) -> q_gen_815
<cons>(q_gen_774, q_gen_815) -> q_gen_868
<cons>(q_gen_774, q_gen_868) -> q_gen_868
<cons, s>(q_gen_749, q_gen_748) -> q_gen_740
<cons, s>(q_gen_775, q_gen_773) -> q_gen_740
<cons, s>(q_gen_788, q_gen_787) -> q_gen_740
<cons, s>(q_gen_794, q_gen_815) -> q_gen_740
<cons, s>(q_gen_803, q_gen_868) -> q_gen_740
<nil, z>() -> q_gen_740
<a, z>() -> q_gen_749
<b, z>() -> q_gen_749
<a, s>(q_gen_776) -> q_gen_775
<b, s>(q_gen_776) -> q_gen_775
<cons, s>(q_gen_749, q_gen_773) -> q_gen_777
<cons, s>(q_gen_749, q_gen_787) -> q_gen_777
<cons, s>(q_gen_749, q_gen_815) -> q_gen_777
<cons, s>(q_gen_775, q_gen_748) -> q_gen_777
<cons, s>(q_gen_775, q_gen_787) -> q_gen_777
<cons, s>(q_gen_775, q_gen_815) -> q_gen_777
<cons, s>(q_gen_775, q_gen_868) -> q_gen_777
<cons, s>(q_gen_788, q_gen_748) -> q_gen_777
<cons, s>(q_gen_788, q_gen_773) -> q_gen_777
<cons, s>(q_gen_788, q_gen_815) -> q_gen_777
<cons, s>(q_gen_794, q_gen_748) -> q_gen_777
<cons, s>(q_gen_794, q_gen_773) -> q_gen_777
<cons, s>(q_gen_794, q_gen_787) -> q_gen_777
<cons, s>(q_gen_794, q_gen_868) -> q_gen_777
<cons, s>(q_gen_803, q_gen_748) -> q_gen_777
<cons, s>(q_gen_803, q_gen_773) -> q_gen_777
<cons, s>(q_gen_803, q_gen_787) -> q_gen_777
<cons, s>(q_gen_803, q_gen_815) -> q_gen_777
<a, s>(q_gen_789) -> q_gen_788
<b, s>(q_gen_789) -> q_gen_788
<a, s>(q_gen_795) -> q_gen_794
<b, s>(q_gen_795) -> q_gen_794
<a, s>(q_gen_804) -> q_gen_803
<b, s>(q_gen_804) -> q_gen_803
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_738, q_gen_752},
Q_f={q_gen_738},
Delta=
{
<a, a>() -> q_gen_738
<a, b>() -> q_gen_738
<b, b>() -> q_gen_738
<b, a>() -> q_gen_752
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_737, q_gen_751},
Q_f={q_gen_737},
Delta=
{
<cons, cons>(q_gen_751, q_gen_737) -> q_gen_737
<nil, nil>() -> q_gen_737
<a, a>() -> q_gen_751
<a, b>() -> q_gen_751
<b, a>() -> q_gen_751
<b, b>() -> q_gen_751
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 69
() -> length([nil, z]) -> 69
() -> leq([a, y]) -> 69
() -> leq([b, b]) -> 69
() -> sort([nil, nil]) -> 69
(insert([x, z, _yc]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _yc)]) -> 71
(insert([y, _dd, _ed]) /\ sort([z, _dd])) -> sort([cons(y, z), _ed]) -> 75
(length([_nd, _od]) /\ length([l, _md]) /\ sort([l, _nd])) -> eq_nat([_md, _od]) -> 88
(length([ll, _id])) -> length([cons(x, ll), s(_id)]) -> 86
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 72
(leq([b, a])) -> BOT -> 70
}
Sat witness: Found: ((length([_nd, _od]) /\ length([l, _md]) /\ sort([l, _nd])) -> eq_nat([_md, _od]), {
_md -> s(s(s(s(s(s(s(z)))))))  ;  _nd -> cons(a, cons(b, cons(b, cons(b, cons(b, nil)))))  ;  _od -> s(s(s(s(s(z)))))  ;  l -> cons(a, cons(b, cons(b, cons(b, cons(b, nil)))))
})

-------------------------------------------
Step 83, which took 2.665674 s (model generation: 2.661803,  model checking: 0.003871):

Model:
|_
{
insert -> 
{{{
Q={q_gen_741, q_gen_742, q_gen_743, q_gen_745, q_gen_746},
Q_f={q_gen_741},
Delta=
{
<nil>() -> q_gen_742
<a>() -> q_gen_743
<b>() -> q_gen_743
<cons, cons>(q_gen_746, q_gen_745) -> q_gen_745
<nil, cons>(q_gen_743, q_gen_742) -> q_gen_745
<a, a>() -> q_gen_746
<a, b>() -> q_gen_746
<b, a>() -> q_gen_746
<b, b>() -> q_gen_746
<a, cons, cons>(q_gen_746, q_gen_745) -> q_gen_741
<a, nil, cons>(q_gen_743, q_gen_742) -> q_gen_741
<b, cons, cons>(q_gen_746, q_gen_745) -> q_gen_741
<b, nil, cons>(q_gen_743, q_gen_742) -> q_gen_741
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_740, q_gen_748, q_gen_749, q_gen_773, q_gen_774, q_gen_775, q_gen_776, q_gen_777, q_gen_787, q_gen_788, q_gen_789, q_gen_794, q_gen_795, q_gen_815},
Q_f={q_gen_740},
Delta=
{
<nil>() -> q_gen_748
<cons>(q_gen_774, q_gen_748) -> q_gen_773
<a>() -> q_gen_774
<b>() -> q_gen_774
<z>() -> q_gen_776
<cons>(q_gen_774, q_gen_773) -> q_gen_787
<s>(q_gen_776) -> q_gen_789
<s>(q_gen_789) -> q_gen_795
<s>(q_gen_795) -> q_gen_795
<cons>(q_gen_774, q_gen_787) -> q_gen_815
<cons>(q_gen_774, q_gen_815) -> q_gen_815
<cons, s>(q_gen_749, q_gen_748) -> q_gen_740
<cons, s>(q_gen_775, q_gen_773) -> q_gen_740
<cons, s>(q_gen_788, q_gen_787) -> q_gen_740
<cons, s>(q_gen_788, q_gen_815) -> q_gen_740
<cons, s>(q_gen_794, q_gen_815) -> q_gen_740
<nil, z>() -> q_gen_740
<a, z>() -> q_gen_749
<b, z>() -> q_gen_749
<a, s>(q_gen_776) -> q_gen_775
<b, s>(q_gen_776) -> q_gen_775
<cons, s>(q_gen_749, q_gen_773) -> q_gen_777
<cons, s>(q_gen_749, q_gen_787) -> q_gen_777
<cons, s>(q_gen_749, q_gen_815) -> q_gen_777
<cons, s>(q_gen_775, q_gen_748) -> q_gen_777
<cons, s>(q_gen_775, q_gen_787) -> q_gen_777
<cons, s>(q_gen_775, q_gen_815) -> q_gen_777
<cons, s>(q_gen_788, q_gen_748) -> q_gen_777
<cons, s>(q_gen_788, q_gen_773) -> q_gen_777
<cons, s>(q_gen_794, q_gen_748) -> q_gen_777
<cons, s>(q_gen_794, q_gen_773) -> q_gen_777
<cons, s>(q_gen_794, q_gen_787) -> q_gen_777
<a, s>(q_gen_789) -> q_gen_788
<a, s>(q_gen_795) -> q_gen_788
<b, s>(q_gen_789) -> q_gen_788
<b, s>(q_gen_795) -> q_gen_794
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_738, q_gen_752},
Q_f={q_gen_738},
Delta=
{
<a, a>() -> q_gen_738
<a, b>() -> q_gen_738
<b, b>() -> q_gen_738
<b, a>() -> q_gen_752
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_737, q_gen_750, q_gen_751, q_gen_764, q_gen_791, q_gen_825},
Q_f={q_gen_737, q_gen_750, q_gen_791},
Delta=
{
<cons, cons>(q_gen_764, q_gen_737) -> q_gen_737
<nil, nil>() -> q_gen_737
<cons, cons>(q_gen_751, q_gen_737) -> q_gen_750
<b, b>() -> q_gen_751
<a, a>() -> q_gen_764
<a, b>() -> q_gen_764
<b, a>() -> q_gen_764
<cons, cons>(q_gen_751, q_gen_750) -> q_gen_791
<cons, cons>(q_gen_751, q_gen_791) -> q_gen_791
<cons, cons>(q_gen_764, q_gen_750) -> q_gen_791
<cons, cons>(q_gen_764, q_gen_791) -> q_gen_825
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 70
() -> length([nil, z]) -> 70
() -> leq([a, y]) -> 70
() -> leq([b, b]) -> 70
() -> sort([nil, nil]) -> 70
(insert([x, z, _yc]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _yc)]) -> 72
(insert([y, _dd, _ed]) /\ sort([z, _dd])) -> sort([cons(y, z), _ed]) -> 78
(length([_nd, _od]) /\ length([l, _md]) /\ sort([l, _nd])) -> eq_nat([_md, _od]) -> 88
(length([ll, _id])) -> length([cons(x, ll), s(_id)]) -> 86
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 73
(leq([b, a])) -> BOT -> 71
}
Sat witness: Found: ((insert([y, _dd, _ed]) /\ sort([z, _dd])) -> sort([cons(y, z), _ed]), {
_dd -> cons(a, cons(b, nil))  ;  _ed -> cons(a, cons(b, cons(b, nil)))  ;  y -> b  ;  z -> cons(b, cons(b, nil))
})

-------------------------------------------
Step 84, which took 1.285278 s (model generation: 1.253466,  model checking: 0.031812):

Model:
|_
{
insert -> 
{{{
Q={q_gen_741, q_gen_742, q_gen_743, q_gen_745, q_gen_746},
Q_f={q_gen_741},
Delta=
{
<nil>() -> q_gen_742
<a>() -> q_gen_743
<b>() -> q_gen_743
<cons, cons>(q_gen_746, q_gen_745) -> q_gen_745
<nil, cons>(q_gen_743, q_gen_742) -> q_gen_745
<a, a>() -> q_gen_746
<a, b>() -> q_gen_746
<b, a>() -> q_gen_746
<b, b>() -> q_gen_746
<a, cons, cons>(q_gen_746, q_gen_745) -> q_gen_741
<a, nil, cons>(q_gen_743, q_gen_742) -> q_gen_741
<b, cons, cons>(q_gen_746, q_gen_745) -> q_gen_741
<b, nil, cons>(q_gen_743, q_gen_742) -> q_gen_741
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_740, q_gen_748, q_gen_749, q_gen_773, q_gen_774, q_gen_775, q_gen_776, q_gen_777, q_gen_787, q_gen_788, q_gen_789, q_gen_794, q_gen_795, q_gen_800, q_gen_801, q_gen_810, q_gen_813, q_gen_820},
Q_f={q_gen_740},
Delta=
{
<cons>(q_gen_774, q_gen_820) -> q_gen_748
<nil>() -> q_gen_748
<cons>(q_gen_774, q_gen_748) -> q_gen_773
<b>() -> q_gen_774
<z>() -> q_gen_776
<cons>(q_gen_774, q_gen_773) -> q_gen_787
<s>(q_gen_776) -> q_gen_789
<s>(q_gen_789) -> q_gen_795
<s>(q_gen_795) -> q_gen_795
<cons>(q_gen_774, q_gen_813) -> q_gen_800
<cons>(q_gen_801, q_gen_748) -> q_gen_800
<a>() -> q_gen_801
<cons>(q_gen_774, q_gen_800) -> q_gen_813
<cons>(q_gen_801, q_gen_773) -> q_gen_813
<cons>(q_gen_801, q_gen_800) -> q_gen_813
<cons>(q_gen_774, q_gen_787) -> q_gen_820
<cons>(q_gen_801, q_gen_813) -> q_gen_820
<cons, s>(q_gen_749, q_gen_748) -> q_gen_740
<cons, s>(q_gen_749, q_gen_820) -> q_gen_740
<cons, s>(q_gen_775, q_gen_773) -> q_gen_740
<cons, s>(q_gen_775, q_gen_800) -> q_gen_740
<cons, s>(q_gen_788, q_gen_787) -> q_gen_740
<cons, s>(q_gen_788, q_gen_813) -> q_gen_740
<cons, s>(q_gen_794, q_gen_800) -> q_gen_740
<cons, s>(q_gen_794, q_gen_813) -> q_gen_740
<cons, s>(q_gen_794, q_gen_820) -> q_gen_740
<cons, s>(q_gen_810, q_gen_800) -> q_gen_740
<cons, s>(q_gen_810, q_gen_813) -> q_gen_740
<nil, z>() -> q_gen_740
<a, z>() -> q_gen_749
<b, z>() -> q_gen_749
<a, s>(q_gen_776) -> q_gen_775
<b, s>(q_gen_776) -> q_gen_775
<cons, s>(q_gen_749, q_gen_773) -> q_gen_777
<cons, s>(q_gen_749, q_gen_787) -> q_gen_777
<cons, s>(q_gen_775, q_gen_748) -> q_gen_777
<cons, s>(q_gen_775, q_gen_813) -> q_gen_777
<cons, s>(q_gen_775, q_gen_820) -> q_gen_777
<cons, s>(q_gen_788, q_gen_748) -> q_gen_777
<cons, s>(q_gen_788, q_gen_773) -> q_gen_777
<cons, s>(q_gen_788, q_gen_800) -> q_gen_777
<cons, s>(q_gen_794, q_gen_748) -> q_gen_777
<cons, s>(q_gen_794, q_gen_773) -> q_gen_777
<cons, s>(q_gen_794, q_gen_787) -> q_gen_777
<cons, s>(q_gen_810, q_gen_748) -> q_gen_777
<cons, s>(q_gen_810, q_gen_773) -> q_gen_777
<cons, s>(q_gen_810, q_gen_787) -> q_gen_777
<cons, s>(q_gen_810, q_gen_820) -> q_gen_777
<b, s>(q_gen_789) -> q_gen_788
<b, s>(q_gen_795) -> q_gen_794
<a, s>(q_gen_789) -> q_gen_810
<a, s>(q_gen_795) -> q_gen_810
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_738, q_gen_752},
Q_f={q_gen_738},
Delta=
{
<a, a>() -> q_gen_738
<a, b>() -> q_gen_738
<b, b>() -> q_gen_738
<b, a>() -> q_gen_752
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_737, q_gen_751},
Q_f={q_gen_737},
Delta=
{
<cons, cons>(q_gen_751, q_gen_737) -> q_gen_737
<nil, nil>() -> q_gen_737
<a, a>() -> q_gen_751
<a, b>() -> q_gen_751
<b, a>() -> q_gen_751
<b, b>() -> q_gen_751
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 71
() -> length([nil, z]) -> 71
() -> leq([a, y]) -> 71
() -> leq([b, b]) -> 71
() -> sort([nil, nil]) -> 71
(insert([x, z, _yc]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _yc)]) -> 73
(insert([y, _dd, _ed]) /\ sort([z, _dd])) -> sort([cons(y, z), _ed]) -> 79
(length([_nd, _od]) /\ length([l, _md]) /\ sort([l, _nd])) -> eq_nat([_md, _od]) -> 88
(length([ll, _id])) -> length([cons(x, ll), s(_id)]) -> 89
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 74
(leq([b, a])) -> BOT -> 72
}
Sat witness: Found: ((length([ll, _id])) -> length([cons(x, ll), s(_id)]), {
_id -> s(s(s(s(z))))  ;  ll -> cons(a, cons(a, cons(a, nil)))  ;  x -> a
})

-------------------------------------------
Step 85, which took 2.946738 s (model generation: 2.929795,  model checking: 0.016943):

Model:
|_
{
insert -> 
{{{
Q={q_gen_741, q_gen_742, q_gen_743, q_gen_745, q_gen_746},
Q_f={q_gen_741},
Delta=
{
<nil>() -> q_gen_742
<a>() -> q_gen_743
<b>() -> q_gen_743
<cons, cons>(q_gen_746, q_gen_745) -> q_gen_745
<nil, cons>(q_gen_743, q_gen_742) -> q_gen_745
<a, a>() -> q_gen_746
<a, b>() -> q_gen_746
<b, a>() -> q_gen_746
<b, b>() -> q_gen_746
<a, cons, cons>(q_gen_746, q_gen_745) -> q_gen_741
<a, nil, cons>(q_gen_743, q_gen_742) -> q_gen_741
<b, cons, cons>(q_gen_746, q_gen_745) -> q_gen_741
<b, nil, cons>(q_gen_743, q_gen_742) -> q_gen_741
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_740, q_gen_748, q_gen_749, q_gen_773, q_gen_774, q_gen_775, q_gen_776, q_gen_777, q_gen_787, q_gen_788, q_gen_789, q_gen_794, q_gen_795, q_gen_800, q_gen_801, q_gen_810, q_gen_813, q_gen_820},
Q_f={q_gen_740},
Delta=
{
<nil>() -> q_gen_748
<cons>(q_gen_774, q_gen_748) -> q_gen_773
<b>() -> q_gen_774
<z>() -> q_gen_776
<cons>(q_gen_774, q_gen_773) -> q_gen_787
<s>(q_gen_776) -> q_gen_789
<s>(q_gen_789) -> q_gen_795
<s>(q_gen_795) -> q_gen_795
<cons>(q_gen_801, q_gen_748) -> q_gen_800
<a>() -> q_gen_801
<cons>(q_gen_774, q_gen_800) -> q_gen_813
<cons>(q_gen_774, q_gen_813) -> q_gen_813
<cons>(q_gen_801, q_gen_773) -> q_gen_813
<cons>(q_gen_801, q_gen_800) -> q_gen_813
<cons>(q_gen_801, q_gen_813) -> q_gen_813
<cons>(q_gen_774, q_gen_787) -> q_gen_820
<cons>(q_gen_774, q_gen_820) -> q_gen_820
<cons, s>(q_gen_749, q_gen_748) -> q_gen_740
<cons, s>(q_gen_775, q_gen_773) -> q_gen_740
<cons, s>(q_gen_775, q_gen_800) -> q_gen_740
<cons, s>(q_gen_788, q_gen_787) -> q_gen_740
<cons, s>(q_gen_788, q_gen_813) -> q_gen_740
<cons, s>(q_gen_794, q_gen_813) -> q_gen_740
<cons, s>(q_gen_794, q_gen_820) -> q_gen_740
<cons, s>(q_gen_810, q_gen_813) -> q_gen_740
<nil, z>() -> q_gen_740
<a, z>() -> q_gen_749
<b, z>() -> q_gen_749
<a, s>(q_gen_776) -> q_gen_775
<b, s>(q_gen_776) -> q_gen_775
<cons, s>(q_gen_749, q_gen_773) -> q_gen_777
<cons, s>(q_gen_749, q_gen_787) -> q_gen_777
<cons, s>(q_gen_749, q_gen_820) -> q_gen_777
<cons, s>(q_gen_775, q_gen_748) -> q_gen_777
<cons, s>(q_gen_775, q_gen_813) -> q_gen_777
<cons, s>(q_gen_775, q_gen_820) -> q_gen_777
<cons, s>(q_gen_788, q_gen_748) -> q_gen_777
<cons, s>(q_gen_788, q_gen_773) -> q_gen_777
<cons, s>(q_gen_788, q_gen_800) -> q_gen_777
<cons, s>(q_gen_794, q_gen_748) -> q_gen_777
<cons, s>(q_gen_794, q_gen_773) -> q_gen_777
<cons, s>(q_gen_794, q_gen_787) -> q_gen_777
<cons, s>(q_gen_794, q_gen_800) -> q_gen_777
<cons, s>(q_gen_810, q_gen_748) -> q_gen_777
<cons, s>(q_gen_810, q_gen_773) -> q_gen_777
<cons, s>(q_gen_810, q_gen_787) -> q_gen_777
<cons, s>(q_gen_810, q_gen_820) -> q_gen_777
<b, s>(q_gen_789) -> q_gen_788
<a, s>(q_gen_789) -> q_gen_794
<b, s>(q_gen_795) -> q_gen_794
<a, s>(q_gen_795) -> q_gen_810
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_738, q_gen_752},
Q_f={q_gen_738},
Delta=
{
<a, a>() -> q_gen_738
<a, b>() -> q_gen_738
<b, b>() -> q_gen_738
<b, a>() -> q_gen_752
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_737, q_gen_751},
Q_f={q_gen_737},
Delta=
{
<cons, cons>(q_gen_751, q_gen_737) -> q_gen_737
<nil, nil>() -> q_gen_737
<a, a>() -> q_gen_751
<a, b>() -> q_gen_751
<b, a>() -> q_gen_751
<b, b>() -> q_gen_751
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 72
() -> length([nil, z]) -> 72
() -> leq([a, y]) -> 72
() -> leq([b, b]) -> 72
() -> sort([nil, nil]) -> 72
(insert([x, z, _yc]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _yc)]) -> 74
(insert([y, _dd, _ed]) /\ sort([z, _dd])) -> sort([cons(y, z), _ed]) -> 80
(length([_nd, _od]) /\ length([l, _md]) /\ sort([l, _nd])) -> eq_nat([_md, _od]) -> 91
(length([ll, _id])) -> length([cons(x, ll), s(_id)]) -> 89
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 75
(leq([b, a])) -> BOT -> 73
}
Sat witness: Found: ((length([_nd, _od]) /\ length([l, _md]) /\ sort([l, _nd])) -> eq_nat([_md, _od]), {
_md -> s(s(s(s(z))))  ;  _nd -> cons(a, cons(b, cons(b, cons(b, nil))))  ;  _od -> s(s(s(z)))  ;  l -> cons(b, cons(b, cons(b, cons(b, nil))))
})

-------------------------------------------
Step 86, which took 4.152271 s (model generation: 4.147338,  model checking: 0.004933):

Model:
|_
{
insert -> 
{{{
Q={q_gen_741, q_gen_742, q_gen_743, q_gen_745, q_gen_746},
Q_f={q_gen_741},
Delta=
{
<nil>() -> q_gen_742
<a>() -> q_gen_743
<b>() -> q_gen_743
<cons, cons>(q_gen_746, q_gen_745) -> q_gen_745
<nil, cons>(q_gen_743, q_gen_742) -> q_gen_745
<a, a>() -> q_gen_746
<a, b>() -> q_gen_746
<b, a>() -> q_gen_746
<b, b>() -> q_gen_746
<a, cons, cons>(q_gen_746, q_gen_745) -> q_gen_741
<a, nil, cons>(q_gen_743, q_gen_742) -> q_gen_741
<b, cons, cons>(q_gen_746, q_gen_745) -> q_gen_741
<b, nil, cons>(q_gen_743, q_gen_742) -> q_gen_741
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_740, q_gen_748, q_gen_749, q_gen_773, q_gen_774, q_gen_775, q_gen_776, q_gen_777, q_gen_787, q_gen_788, q_gen_789, q_gen_794, q_gen_795, q_gen_815},
Q_f={q_gen_740},
Delta=
{
<nil>() -> q_gen_748
<cons>(q_gen_774, q_gen_748) -> q_gen_773
<a>() -> q_gen_774
<b>() -> q_gen_774
<z>() -> q_gen_776
<cons>(q_gen_774, q_gen_773) -> q_gen_787
<s>(q_gen_776) -> q_gen_789
<s>(q_gen_789) -> q_gen_795
<s>(q_gen_795) -> q_gen_795
<cons>(q_gen_774, q_gen_787) -> q_gen_815
<cons>(q_gen_774, q_gen_815) -> q_gen_815
<cons, s>(q_gen_749, q_gen_748) -> q_gen_740
<cons, s>(q_gen_775, q_gen_773) -> q_gen_740
<cons, s>(q_gen_788, q_gen_787) -> q_gen_740
<cons, s>(q_gen_794, q_gen_815) -> q_gen_740
<nil, z>() -> q_gen_740
<a, z>() -> q_gen_749
<b, z>() -> q_gen_749
<a, s>(q_gen_776) -> q_gen_775
<b, s>(q_gen_776) -> q_gen_775
<cons, s>(q_gen_749, q_gen_773) -> q_gen_777
<cons, s>(q_gen_749, q_gen_787) -> q_gen_777
<cons, s>(q_gen_749, q_gen_815) -> q_gen_777
<cons, s>(q_gen_775, q_gen_748) -> q_gen_777
<cons, s>(q_gen_775, q_gen_787) -> q_gen_777
<cons, s>(q_gen_775, q_gen_815) -> q_gen_777
<cons, s>(q_gen_788, q_gen_748) -> q_gen_777
<cons, s>(q_gen_788, q_gen_773) -> q_gen_777
<cons, s>(q_gen_788, q_gen_815) -> q_gen_777
<cons, s>(q_gen_794, q_gen_748) -> q_gen_777
<cons, s>(q_gen_794, q_gen_773) -> q_gen_777
<cons, s>(q_gen_794, q_gen_787) -> q_gen_777
<a, s>(q_gen_789) -> q_gen_788
<b, s>(q_gen_789) -> q_gen_788
<a, s>(q_gen_795) -> q_gen_794
<b, s>(q_gen_795) -> q_gen_794
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_738, q_gen_752},
Q_f={q_gen_738},
Delta=
{
<a, a>() -> q_gen_738
<a, b>() -> q_gen_738
<b, b>() -> q_gen_738
<b, a>() -> q_gen_752
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_737, q_gen_750, q_gen_751, q_gen_791, q_gen_805, q_gen_825},
Q_f={q_gen_737, q_gen_750, q_gen_791, q_gen_805},
Delta=
{
<nil, nil>() -> q_gen_737
<cons, cons>(q_gen_751, q_gen_737) -> q_gen_750
<a, a>() -> q_gen_751
<a, b>() -> q_gen_751
<b, a>() -> q_gen_751
<b, b>() -> q_gen_751
<cons, cons>(q_gen_751, q_gen_750) -> q_gen_791
<cons, cons>(q_gen_751, q_gen_791) -> q_gen_805
<cons, cons>(q_gen_751, q_gen_805) -> q_gen_825
<cons, cons>(q_gen_751, q_gen_825) -> q_gen_825
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 73
() -> length([nil, z]) -> 73
() -> leq([a, y]) -> 73
() -> leq([b, b]) -> 73
() -> sort([nil, nil]) -> 73
(insert([x, z, _yc]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _yc)]) -> 75
(insert([y, _dd, _ed]) /\ sort([z, _dd])) -> sort([cons(y, z), _ed]) -> 83
(length([_nd, _od]) /\ length([l, _md]) /\ sort([l, _nd])) -> eq_nat([_md, _od]) -> 91
(length([ll, _id])) -> length([cons(x, ll), s(_id)]) -> 89
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 76
(leq([b, a])) -> BOT -> 74
}
Sat witness: Found: ((insert([y, _dd, _ed]) /\ sort([z, _dd])) -> sort([cons(y, z), _ed]), {
_dd -> cons(a, cons(a, cons(b, nil)))  ;  _ed -> cons(b, cons(b, cons(b, cons(b, nil))))  ;  y -> a  ;  z -> cons(b, cons(a, cons(a, nil)))
})

-------------------------------------------
Step 87, which took 3.181754 s (model generation: 3.158917,  model checking: 0.022837):

Model:
|_
{
insert -> 
{{{
Q={q_gen_741, q_gen_742, q_gen_743, q_gen_745, q_gen_746},
Q_f={q_gen_741},
Delta=
{
<nil>() -> q_gen_742
<a>() -> q_gen_743
<b>() -> q_gen_743
<cons, cons>(q_gen_746, q_gen_745) -> q_gen_745
<nil, cons>(q_gen_743, q_gen_742) -> q_gen_745
<a, a>() -> q_gen_746
<a, b>() -> q_gen_746
<b, a>() -> q_gen_746
<b, b>() -> q_gen_746
<a, cons, cons>(q_gen_746, q_gen_745) -> q_gen_741
<a, nil, cons>(q_gen_743, q_gen_742) -> q_gen_741
<b, cons, cons>(q_gen_746, q_gen_745) -> q_gen_741
<b, nil, cons>(q_gen_743, q_gen_742) -> q_gen_741
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_740, q_gen_748, q_gen_749, q_gen_773, q_gen_774, q_gen_775, q_gen_776, q_gen_777, q_gen_787, q_gen_788, q_gen_789, q_gen_794, q_gen_795, q_gen_804, q_gen_810, q_gen_815, q_gen_824, q_gen_868},
Q_f={q_gen_740},
Delta=
{
<nil>() -> q_gen_748
<cons>(q_gen_774, q_gen_748) -> q_gen_773
<a>() -> q_gen_774
<b>() -> q_gen_774
<s>(q_gen_824) -> q_gen_776
<z>() -> q_gen_776
<cons>(q_gen_774, q_gen_773) -> q_gen_787
<s>(q_gen_776) -> q_gen_789
<s>(q_gen_789) -> q_gen_795
<s>(q_gen_795) -> q_gen_804
<cons>(q_gen_774, q_gen_787) -> q_gen_815
<s>(q_gen_804) -> q_gen_824
<cons>(q_gen_774, q_gen_815) -> q_gen_868
<cons>(q_gen_774, q_gen_868) -> q_gen_868
<cons, s>(q_gen_749, q_gen_748) -> q_gen_740
<cons, s>(q_gen_749, q_gen_868) -> q_gen_740
<cons, s>(q_gen_775, q_gen_773) -> q_gen_740
<cons, s>(q_gen_788, q_gen_787) -> q_gen_740
<cons, s>(q_gen_794, q_gen_815) -> q_gen_740
<cons, s>(q_gen_794, q_gen_868) -> q_gen_740
<cons, s>(q_gen_810, q_gen_868) -> q_gen_740
<nil, z>() -> q_gen_740
<a, z>() -> q_gen_749
<b, s>(q_gen_824) -> q_gen_749
<b, z>() -> q_gen_749
<a, s>(q_gen_776) -> q_gen_775
<b, s>(q_gen_776) -> q_gen_775
<cons, s>(q_gen_749, q_gen_773) -> q_gen_777
<cons, s>(q_gen_749, q_gen_787) -> q_gen_777
<cons, s>(q_gen_749, q_gen_815) -> q_gen_777
<cons, s>(q_gen_775, q_gen_748) -> q_gen_777
<cons, s>(q_gen_775, q_gen_787) -> q_gen_777
<cons, s>(q_gen_775, q_gen_815) -> q_gen_777
<cons, s>(q_gen_775, q_gen_868) -> q_gen_777
<cons, s>(q_gen_788, q_gen_748) -> q_gen_777
<cons, s>(q_gen_788, q_gen_773) -> q_gen_777
<cons, s>(q_gen_788, q_gen_815) -> q_gen_777
<cons, s>(q_gen_788, q_gen_868) -> q_gen_777
<cons, s>(q_gen_794, q_gen_748) -> q_gen_777
<cons, s>(q_gen_794, q_gen_773) -> q_gen_777
<cons, s>(q_gen_794, q_gen_787) -> q_gen_777
<cons, s>(q_gen_810, q_gen_748) -> q_gen_777
<cons, s>(q_gen_810, q_gen_773) -> q_gen_777
<cons, s>(q_gen_810, q_gen_787) -> q_gen_777
<cons, s>(q_gen_810, q_gen_815) -> q_gen_777
<a, s>(q_gen_789) -> q_gen_788
<a, s>(q_gen_824) -> q_gen_788
<b, s>(q_gen_789) -> q_gen_788
<a, s>(q_gen_795) -> q_gen_794
<b, s>(q_gen_795) -> q_gen_794
<b, s>(q_gen_804) -> q_gen_794
<a, s>(q_gen_804) -> q_gen_810
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_738, q_gen_752},
Q_f={q_gen_738},
Delta=
{
<a, a>() -> q_gen_738
<a, b>() -> q_gen_738
<b, b>() -> q_gen_738
<b, a>() -> q_gen_752
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_737, q_gen_751},
Q_f={q_gen_737},
Delta=
{
<cons, cons>(q_gen_751, q_gen_737) -> q_gen_737
<nil, nil>() -> q_gen_737
<a, a>() -> q_gen_751
<a, b>() -> q_gen_751
<b, a>() -> q_gen_751
<b, b>() -> q_gen_751
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 74
() -> length([nil, z]) -> 74
() -> leq([a, y]) -> 74
() -> leq([b, b]) -> 74
() -> sort([nil, nil]) -> 74
(insert([x, z, _yc]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _yc)]) -> 76
(insert([y, _dd, _ed]) /\ sort([z, _dd])) -> sort([cons(y, z), _ed]) -> 84
(length([_nd, _od]) /\ length([l, _md]) /\ sort([l, _nd])) -> eq_nat([_md, _od]) -> 91
(length([ll, _id])) -> length([cons(x, ll), s(_id)]) -> 92
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 77
(leq([b, a])) -> BOT -> 75
}
Sat witness: Found: ((length([ll, _id])) -> length([cons(x, ll), s(_id)]), {
_id -> s(s(s(s(s(s(z))))))  ;  ll -> cons(a, cons(a, cons(b, nil)))  ;  x -> b
})

-------------------------------------------
Step 88, which took 4.991600 s (model generation: 4.977853,  model checking: 0.013747):

Model:
|_
{
insert -> 
{{{
Q={q_gen_741, q_gen_742, q_gen_743, q_gen_745, q_gen_746},
Q_f={q_gen_741},
Delta=
{
<nil>() -> q_gen_742
<a>() -> q_gen_743
<b>() -> q_gen_743
<cons, cons>(q_gen_746, q_gen_745) -> q_gen_745
<nil, cons>(q_gen_743, q_gen_742) -> q_gen_745
<a, a>() -> q_gen_746
<a, b>() -> q_gen_746
<b, a>() -> q_gen_746
<b, b>() -> q_gen_746
<a, cons, cons>(q_gen_746, q_gen_745) -> q_gen_741
<a, nil, cons>(q_gen_743, q_gen_742) -> q_gen_741
<b, cons, cons>(q_gen_746, q_gen_745) -> q_gen_741
<b, nil, cons>(q_gen_743, q_gen_742) -> q_gen_741
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_740, q_gen_748, q_gen_749, q_gen_773, q_gen_774, q_gen_775, q_gen_776, q_gen_777, q_gen_787, q_gen_788, q_gen_789, q_gen_794, q_gen_795, q_gen_800, q_gen_801, q_gen_810, q_gen_813, q_gen_820},
Q_f={q_gen_740},
Delta=
{
<nil>() -> q_gen_748
<cons>(q_gen_774, q_gen_748) -> q_gen_773
<b>() -> q_gen_774
<z>() -> q_gen_776
<cons>(q_gen_774, q_gen_773) -> q_gen_787
<cons>(q_gen_774, q_gen_820) -> q_gen_787
<s>(q_gen_776) -> q_gen_789
<s>(q_gen_789) -> q_gen_795
<s>(q_gen_795) -> q_gen_795
<cons>(q_gen_801, q_gen_748) -> q_gen_800
<cons>(q_gen_801, q_gen_813) -> q_gen_800
<cons>(q_gen_801, q_gen_820) -> q_gen_800
<a>() -> q_gen_801
<cons>(q_gen_774, q_gen_800) -> q_gen_813
<cons>(q_gen_774, q_gen_813) -> q_gen_813
<cons>(q_gen_801, q_gen_773) -> q_gen_813
<cons>(q_gen_774, q_gen_787) -> q_gen_820
<cons>(q_gen_801, q_gen_800) -> q_gen_820
<cons, s>(q_gen_749, q_gen_748) -> q_gen_740
<cons, s>(q_gen_775, q_gen_773) -> q_gen_740
<cons, s>(q_gen_775, q_gen_787) -> q_gen_740
<cons, s>(q_gen_775, q_gen_800) -> q_gen_740
<cons, s>(q_gen_788, q_gen_787) -> q_gen_740
<cons, s>(q_gen_788, q_gen_813) -> q_gen_740
<cons, s>(q_gen_788, q_gen_820) -> q_gen_740
<cons, s>(q_gen_794, q_gen_800) -> q_gen_740
<cons, s>(q_gen_794, q_gen_813) -> q_gen_740
<cons, s>(q_gen_794, q_gen_820) -> q_gen_740
<cons, s>(q_gen_810, q_gen_800) -> q_gen_740
<cons, s>(q_gen_810, q_gen_813) -> q_gen_740
<nil, z>() -> q_gen_740
<a, z>() -> q_gen_749
<b, z>() -> q_gen_749
<a, s>(q_gen_776) -> q_gen_775
<b, s>(q_gen_776) -> q_gen_775
<cons, s>(q_gen_749, q_gen_773) -> q_gen_777
<cons, s>(q_gen_749, q_gen_787) -> q_gen_777
<cons, s>(q_gen_749, q_gen_820) -> q_gen_777
<cons, s>(q_gen_775, q_gen_748) -> q_gen_777
<cons, s>(q_gen_775, q_gen_813) -> q_gen_777
<cons, s>(q_gen_775, q_gen_820) -> q_gen_777
<cons, s>(q_gen_788, q_gen_748) -> q_gen_777
<cons, s>(q_gen_788, q_gen_773) -> q_gen_777
<cons, s>(q_gen_788, q_gen_800) -> q_gen_777
<cons, s>(q_gen_794, q_gen_748) -> q_gen_777
<cons, s>(q_gen_794, q_gen_773) -> q_gen_777
<cons, s>(q_gen_794, q_gen_787) -> q_gen_777
<cons, s>(q_gen_810, q_gen_748) -> q_gen_777
<cons, s>(q_gen_810, q_gen_773) -> q_gen_777
<cons, s>(q_gen_810, q_gen_787) -> q_gen_777
<cons, s>(q_gen_810, q_gen_820) -> q_gen_777
<b, s>(q_gen_789) -> q_gen_788
<b, s>(q_gen_795) -> q_gen_794
<a, s>(q_gen_789) -> q_gen_810
<a, s>(q_gen_795) -> q_gen_810
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_738, q_gen_752},
Q_f={q_gen_738},
Delta=
{
<a, a>() -> q_gen_738
<a, b>() -> q_gen_738
<b, b>() -> q_gen_738
<b, a>() -> q_gen_752
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_737, q_gen_751},
Q_f={q_gen_737},
Delta=
{
<cons, cons>(q_gen_751, q_gen_737) -> q_gen_737
<nil, nil>() -> q_gen_737
<a, a>() -> q_gen_751
<a, b>() -> q_gen_751
<b, a>() -> q_gen_751
<b, b>() -> q_gen_751
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 75
() -> length([nil, z]) -> 75
() -> leq([a, y]) -> 75
() -> leq([b, b]) -> 75
() -> sort([nil, nil]) -> 75
(insert([x, z, _yc]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _yc)]) -> 77
(insert([y, _dd, _ed]) /\ sort([z, _dd])) -> sort([cons(y, z), _ed]) -> 85
(length([_nd, _od]) /\ length([l, _md]) /\ sort([l, _nd])) -> eq_nat([_md, _od]) -> 94
(length([ll, _id])) -> length([cons(x, ll), s(_id)]) -> 92
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 78
(leq([b, a])) -> BOT -> 76
}
Sat witness: Found: ((length([_nd, _od]) /\ length([l, _md]) /\ sort([l, _nd])) -> eq_nat([_md, _od]), {
_md -> s(s(z))  ;  _nd -> cons(a, cons(a, nil))  ;  _od -> s(s(s(z)))  ;  l -> cons(b, cons(b, nil))
})

-------------------------------------------
Step 89, which took 6.158012 s (model generation: 6.143490,  model checking: 0.014522):

Model:
|_
{
insert -> 
{{{
Q={q_gen_741, q_gen_742, q_gen_743, q_gen_745, q_gen_746},
Q_f={q_gen_741},
Delta=
{
<nil>() -> q_gen_742
<a>() -> q_gen_743
<b>() -> q_gen_743
<cons, cons>(q_gen_746, q_gen_745) -> q_gen_745
<nil, cons>(q_gen_743, q_gen_742) -> q_gen_745
<a, a>() -> q_gen_746
<a, b>() -> q_gen_746
<b, a>() -> q_gen_746
<b, b>() -> q_gen_746
<a, cons, cons>(q_gen_746, q_gen_745) -> q_gen_741
<a, nil, cons>(q_gen_743, q_gen_742) -> q_gen_741
<b, cons, cons>(q_gen_746, q_gen_745) -> q_gen_741
<b, nil, cons>(q_gen_743, q_gen_742) -> q_gen_741
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_740, q_gen_748, q_gen_749, q_gen_773, q_gen_774, q_gen_775, q_gen_776, q_gen_777, q_gen_787, q_gen_788, q_gen_789, q_gen_794, q_gen_795, q_gen_803, q_gen_804, q_gen_815, q_gen_824, q_gen_868},
Q_f={q_gen_740},
Delta=
{
<cons>(q_gen_774, q_gen_868) -> q_gen_748
<nil>() -> q_gen_748
<cons>(q_gen_774, q_gen_748) -> q_gen_773
<a>() -> q_gen_774
<b>() -> q_gen_774
<z>() -> q_gen_776
<cons>(q_gen_774, q_gen_773) -> q_gen_787
<s>(q_gen_776) -> q_gen_789
<s>(q_gen_824) -> q_gen_789
<s>(q_gen_789) -> q_gen_795
<s>(q_gen_795) -> q_gen_804
<cons>(q_gen_774, q_gen_787) -> q_gen_815
<s>(q_gen_804) -> q_gen_824
<cons>(q_gen_774, q_gen_815) -> q_gen_868
<cons, s>(q_gen_749, q_gen_748) -> q_gen_740
<cons, s>(q_gen_775, q_gen_773) -> q_gen_740
<cons, s>(q_gen_788, q_gen_787) -> q_gen_740
<cons, s>(q_gen_794, q_gen_815) -> q_gen_740
<cons, s>(q_gen_803, q_gen_868) -> q_gen_740
<nil, z>() -> q_gen_740
<a, z>() -> q_gen_749
<b, s>(q_gen_824) -> q_gen_749
<b, z>() -> q_gen_749
<a, s>(q_gen_776) -> q_gen_775
<a, s>(q_gen_824) -> q_gen_775
<b, s>(q_gen_776) -> q_gen_775
<cons, s>(q_gen_749, q_gen_773) -> q_gen_777
<cons, s>(q_gen_749, q_gen_787) -> q_gen_777
<cons, s>(q_gen_749, q_gen_815) -> q_gen_777
<cons, s>(q_gen_775, q_gen_748) -> q_gen_777
<cons, s>(q_gen_775, q_gen_787) -> q_gen_777
<cons, s>(q_gen_775, q_gen_815) -> q_gen_777
<cons, s>(q_gen_775, q_gen_868) -> q_gen_777
<cons, s>(q_gen_788, q_gen_748) -> q_gen_777
<cons, s>(q_gen_788, q_gen_773) -> q_gen_777
<cons, s>(q_gen_788, q_gen_815) -> q_gen_777
<cons, s>(q_gen_788, q_gen_868) -> q_gen_777
<cons, s>(q_gen_794, q_gen_748) -> q_gen_777
<cons, s>(q_gen_794, q_gen_773) -> q_gen_777
<cons, s>(q_gen_794, q_gen_787) -> q_gen_777
<cons, s>(q_gen_794, q_gen_868) -> q_gen_777
<cons, s>(q_gen_803, q_gen_748) -> q_gen_777
<cons, s>(q_gen_803, q_gen_773) -> q_gen_777
<cons, s>(q_gen_803, q_gen_787) -> q_gen_777
<cons, s>(q_gen_803, q_gen_815) -> q_gen_777
<a, s>(q_gen_789) -> q_gen_788
<b, s>(q_gen_789) -> q_gen_788
<a, s>(q_gen_795) -> q_gen_794
<b, s>(q_gen_795) -> q_gen_794
<a, s>(q_gen_804) -> q_gen_803
<b, s>(q_gen_804) -> q_gen_803
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_738, q_gen_752},
Q_f={q_gen_738},
Delta=
{
<a, a>() -> q_gen_738
<a, b>() -> q_gen_738
<b, b>() -> q_gen_738
<b, a>() -> q_gen_752
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_737, q_gen_751},
Q_f={q_gen_737},
Delta=
{
<cons, cons>(q_gen_751, q_gen_737) -> q_gen_737
<nil, nil>() -> q_gen_737
<a, a>() -> q_gen_751
<a, b>() -> q_gen_751
<b, a>() -> q_gen_751
<b, b>() -> q_gen_751
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 76
() -> length([nil, z]) -> 76
() -> leq([a, y]) -> 76
() -> leq([b, b]) -> 76
() -> sort([nil, nil]) -> 76
(insert([x, z, _yc]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _yc)]) -> 78
(insert([y, _dd, _ed]) /\ sort([z, _dd])) -> sort([cons(y, z), _ed]) -> 86
(length([_nd, _od]) /\ length([l, _md]) /\ sort([l, _nd])) -> eq_nat([_md, _od]) -> 94
(length([ll, _id])) -> length([cons(x, ll), s(_id)]) -> 95
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 79
(leq([b, a])) -> BOT -> 77
}
Sat witness: Found: ((length([ll, _id])) -> length([cons(x, ll), s(_id)]), {
_id -> s(s(s(s(s(z)))))  ;  ll -> cons(b, cons(b, cons(b, cons(a, cons(b, nil)))))  ;  x -> a
})

-------------------------------------------
Step 90, which took 4.924315 s (model generation: 4.911573,  model checking: 0.012742):

Model:
|_
{
insert -> 
{{{
Q={q_gen_741, q_gen_742, q_gen_743, q_gen_745, q_gen_746},
Q_f={q_gen_741},
Delta=
{
<nil>() -> q_gen_742
<a>() -> q_gen_743
<b>() -> q_gen_743
<cons, cons>(q_gen_746, q_gen_745) -> q_gen_745
<nil, cons>(q_gen_743, q_gen_742) -> q_gen_745
<a, a>() -> q_gen_746
<a, b>() -> q_gen_746
<b, a>() -> q_gen_746
<b, b>() -> q_gen_746
<a, cons, cons>(q_gen_746, q_gen_745) -> q_gen_741
<a, nil, cons>(q_gen_743, q_gen_742) -> q_gen_741
<b, cons, cons>(q_gen_746, q_gen_745) -> q_gen_741
<b, nil, cons>(q_gen_743, q_gen_742) -> q_gen_741
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_740, q_gen_748, q_gen_749, q_gen_773, q_gen_774, q_gen_775, q_gen_776, q_gen_777, q_gen_787, q_gen_788, q_gen_789, q_gen_794, q_gen_795, q_gen_800, q_gen_801, q_gen_810, q_gen_813, q_gen_820},
Q_f={q_gen_740},
Delta=
{
<nil>() -> q_gen_748
<cons>(q_gen_774, q_gen_748) -> q_gen_773
<b>() -> q_gen_774
<z>() -> q_gen_776
<cons>(q_gen_774, q_gen_773) -> q_gen_787
<cons>(q_gen_801, q_gen_800) -> q_gen_787
<s>(q_gen_776) -> q_gen_789
<s>(q_gen_789) -> q_gen_795
<s>(q_gen_795) -> q_gen_795
<cons>(q_gen_774, q_gen_813) -> q_gen_800
<cons>(q_gen_801, q_gen_748) -> q_gen_800
<a>() -> q_gen_801
<cons>(q_gen_774, q_gen_800) -> q_gen_813
<cons>(q_gen_801, q_gen_773) -> q_gen_813
<cons>(q_gen_774, q_gen_787) -> q_gen_820
<cons>(q_gen_774, q_gen_820) -> q_gen_820
<cons>(q_gen_801, q_gen_787) -> q_gen_820
<cons>(q_gen_801, q_gen_813) -> q_gen_820
<cons, s>(q_gen_749, q_gen_748) -> q_gen_740
<cons, s>(q_gen_775, q_gen_773) -> q_gen_740
<cons, s>(q_gen_775, q_gen_800) -> q_gen_740
<cons, s>(q_gen_788, q_gen_787) -> q_gen_740
<cons, s>(q_gen_788, q_gen_813) -> q_gen_740
<cons, s>(q_gen_794, q_gen_800) -> q_gen_740
<cons, s>(q_gen_794, q_gen_813) -> q_gen_740
<cons, s>(q_gen_794, q_gen_820) -> q_gen_740
<cons, s>(q_gen_810, q_gen_800) -> q_gen_740
<cons, s>(q_gen_810, q_gen_813) -> q_gen_740
<nil, z>() -> q_gen_740
<a, z>() -> q_gen_749
<b, z>() -> q_gen_749
<a, s>(q_gen_776) -> q_gen_775
<b, s>(q_gen_776) -> q_gen_775
<cons, s>(q_gen_749, q_gen_773) -> q_gen_777
<cons, s>(q_gen_749, q_gen_787) -> q_gen_777
<cons, s>(q_gen_749, q_gen_820) -> q_gen_777
<cons, s>(q_gen_775, q_gen_748) -> q_gen_777
<cons, s>(q_gen_775, q_gen_813) -> q_gen_777
<cons, s>(q_gen_775, q_gen_820) -> q_gen_777
<cons, s>(q_gen_788, q_gen_748) -> q_gen_777
<cons, s>(q_gen_788, q_gen_773) -> q_gen_777
<cons, s>(q_gen_788, q_gen_800) -> q_gen_777
<cons, s>(q_gen_788, q_gen_820) -> q_gen_777
<cons, s>(q_gen_794, q_gen_748) -> q_gen_777
<cons, s>(q_gen_794, q_gen_773) -> q_gen_777
<cons, s>(q_gen_794, q_gen_787) -> q_gen_777
<cons, s>(q_gen_810, q_gen_748) -> q_gen_777
<cons, s>(q_gen_810, q_gen_773) -> q_gen_777
<cons, s>(q_gen_810, q_gen_787) -> q_gen_777
<cons, s>(q_gen_810, q_gen_820) -> q_gen_777
<a, s>(q_gen_789) -> q_gen_788
<b, s>(q_gen_789) -> q_gen_788
<b, s>(q_gen_795) -> q_gen_794
<a, s>(q_gen_795) -> q_gen_810
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_738, q_gen_752},
Q_f={q_gen_738},
Delta=
{
<a, a>() -> q_gen_738
<a, b>() -> q_gen_738
<b, b>() -> q_gen_738
<b, a>() -> q_gen_752
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_737, q_gen_751},
Q_f={q_gen_737},
Delta=
{
<cons, cons>(q_gen_751, q_gen_737) -> q_gen_737
<nil, nil>() -> q_gen_737
<a, a>() -> q_gen_751
<a, b>() -> q_gen_751
<b, a>() -> q_gen_751
<b, b>() -> q_gen_751
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 77
() -> length([nil, z]) -> 77
() -> leq([a, y]) -> 77
() -> leq([b, b]) -> 77
() -> sort([nil, nil]) -> 77
(insert([x, z, _yc]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _yc)]) -> 79
(insert([y, _dd, _ed]) /\ sort([z, _dd])) -> sort([cons(y, z), _ed]) -> 87
(length([_nd, _od]) /\ length([l, _md]) /\ sort([l, _nd])) -> eq_nat([_md, _od]) -> 97
(length([ll, _id])) -> length([cons(x, ll), s(_id)]) -> 95
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 80
(leq([b, a])) -> BOT -> 78
}
Sat witness: Found: ((length([_nd, _od]) /\ length([l, _md]) /\ sort([l, _nd])) -> eq_nat([_md, _od]), {
_md -> s(s(s(s(z))))  ;  _nd -> cons(a, cons(b, cons(a, cons(b, nil))))  ;  _od -> s(s(z))  ;  l -> cons(b, cons(b, cons(b, cons(a, nil))))
})

-------------------------------------------
Step 91, which took 1.032836 s (model generation: 1.029363,  model checking: 0.003473):

Model:
|_
{
insert -> 
{{{
Q={q_gen_741, q_gen_742, q_gen_743, q_gen_744, q_gen_745, q_gen_746, q_gen_757, q_gen_762, q_gen_765, q_gen_766, q_gen_768},
Q_f={q_gen_741, q_gen_744},
Delta=
{
<nil>() -> q_gen_742
<b>() -> q_gen_743
<a>() -> q_gen_757
<nil, cons>(q_gen_743, q_gen_742) -> q_gen_745
<a, a>() -> q_gen_746
<a, b>() -> q_gen_746
<b, a>() -> q_gen_746
<b, b>() -> q_gen_746
<nil, cons>(q_gen_757, q_gen_742) -> q_gen_766
<cons, cons>(q_gen_746, q_gen_745) -> q_gen_768
<cons, cons>(q_gen_746, q_gen_766) -> q_gen_768
<cons, cons>(q_gen_746, q_gen_768) -> q_gen_768
<a, cons, cons>(q_gen_746, q_gen_745) -> q_gen_741
<a, cons, cons>(q_gen_746, q_gen_766) -> q_gen_741
<b, nil, cons>(q_gen_743, q_gen_742) -> q_gen_741
<a, nil, cons>(q_gen_757, q_gen_742) -> q_gen_744
<b, cons, cons>(q_gen_746, q_gen_745) -> q_gen_744
<b, cons, cons>(q_gen_746, q_gen_768) -> q_gen_744
<a, nil, cons>(q_gen_743, q_gen_742) -> q_gen_762
<a, cons, cons>(q_gen_746, q_gen_768) -> q_gen_765
<b, cons, cons>(q_gen_746, q_gen_766) -> q_gen_765
<b, nil, cons>(q_gen_757, q_gen_742) -> q_gen_765
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_740, q_gen_747, q_gen_748, q_gen_749, q_gen_761, q_gen_773, q_gen_774, q_gen_775, q_gen_776, q_gen_781, q_gen_782, q_gen_787, q_gen_788, q_gen_789, q_gen_790, q_gen_792, q_gen_793, q_gen_794, q_gen_795, q_gen_800, q_gen_801, q_gen_802, q_gen_803, q_gen_804, q_gen_809, q_gen_810, q_gen_813, q_gen_815, q_gen_816, q_gen_820, q_gen_821, q_gen_824, q_gen_827, q_gen_829, q_gen_835, q_gen_836, q_gen_840, q_gen_842, q_gen_843, q_gen_845, q_gen_848, q_gen_858, q_gen_859, q_gen_860, q_gen_862, q_gen_863, q_gen_865, q_gen_867, q_gen_868, q_gen_869, q_gen_871, q_gen_872, q_gen_874, q_gen_875, q_gen_877, q_gen_880, q_gen_881, q_gen_889, q_gen_891},
Q_f={q_gen_740, q_gen_747, q_gen_863, q_gen_881},
Delta=
{
<nil>() -> q_gen_748
<cons>(q_gen_774, q_gen_748) -> q_gen_773
<cons>(q_gen_774, q_gen_868) -> q_gen_773
<b>() -> q_gen_774
<s>(q_gen_824) -> q_gen_776
<z>() -> q_gen_776
<cons>(q_gen_774, q_gen_773) -> q_gen_787
<s>(q_gen_776) -> q_gen_789
<s>(q_gen_789) -> q_gen_795
<cons>(q_gen_801, q_gen_748) -> q_gen_800
<cons>(q_gen_801, q_gen_827) -> q_gen_800
<cons>(q_gen_801, q_gen_868) -> q_gen_800
<a>() -> q_gen_801
<s>(q_gen_795) -> q_gen_804
<cons>(q_gen_801, q_gen_773) -> q_gen_813
<cons>(q_gen_801, q_gen_813) -> q_gen_813
<cons>(q_gen_774, q_gen_813) -> q_gen_815
<cons>(q_gen_774, q_gen_820) -> q_gen_815
<cons>(q_gen_774, q_gen_787) -> q_gen_820
<s>(q_gen_804) -> q_gen_824
<cons>(q_gen_774, q_gen_800) -> q_gen_827
<cons>(q_gen_801, q_gen_800) -> q_gen_827
<cons>(q_gen_774, q_gen_827) -> q_gen_829
<cons>(q_gen_774, q_gen_829) -> q_gen_829
<cons>(q_gen_774, q_gen_815) -> q_gen_868
<cons, s>(q_gen_775, q_gen_800) -> q_gen_740
<cons, s>(q_gen_788, q_gen_827) -> q_gen_740
<cons, s>(q_gen_794, q_gen_815) -> q_gen_740
<cons, s>(q_gen_821, q_gen_829) -> q_gen_740
<nil, z>() -> q_gen_740
<cons, s>(q_gen_749, q_gen_748) -> q_gen_747
<cons, s>(q_gen_761, q_gen_748) -> q_gen_747
<cons, s>(q_gen_775, q_gen_748) -> q_gen_747
<cons, s>(q_gen_775, q_gen_773) -> q_gen_747
<cons, s>(q_gen_781, q_gen_773) -> q_gen_747
<cons, s>(q_gen_788, q_gen_787) -> q_gen_747
<cons, s>(q_gen_788, q_gen_813) -> q_gen_747
<b, z>() -> q_gen_749
<a, s>(q_gen_824) -> q_gen_761
<a, z>() -> q_gen_761
<b, s>(q_gen_776) -> q_gen_775
<a, s>(q_gen_776) -> q_gen_781
<cons, s>(q_gen_781, q_gen_748) -> q_gen_782
<b, s>(q_gen_789) -> q_gen_788
<cons, s>(q_gen_788, q_gen_773) -> q_gen_790
<cons, s>(q_gen_788, q_gen_748) -> q_gen_792
<cons, s>(q_gen_794, q_gen_773) -> q_gen_793
<b, s>(q_gen_795) -> q_gen_794
<cons, s>(q_gen_794, q_gen_748) -> q_gen_802
<cons, s>(q_gen_803, q_gen_773) -> q_gen_802
<cons, s>(q_gen_803, q_gen_787) -> q_gen_802
<b, s>(q_gen_804) -> q_gen_803
<cons, s>(q_gen_794, q_gen_813) -> q_gen_809
<cons, s>(q_gen_803, q_gen_815) -> q_gen_809
<cons, s>(q_gen_810, q_gen_773) -> q_gen_809
<a, s>(q_gen_804) -> q_gen_810
<cons, s>(q_gen_761, q_gen_820) -> q_gen_816
<cons, s>(q_gen_788, q_gen_815) -> q_gen_816
<cons, s>(q_gen_794, q_gen_787) -> q_gen_816
<cons, s>(q_gen_821, q_gen_820) -> q_gen_816
<a, s>(q_gen_795) -> q_gen_821
<b, s>(q_gen_824) -> q_gen_821
<cons, s>(q_gen_788, q_gen_800) -> q_gen_835
<cons, s>(q_gen_821, q_gen_827) -> q_gen_836
<cons, s>(q_gen_781, q_gen_813) -> q_gen_840
<cons, s>(q_gen_821, q_gen_748) -> q_gen_842
<cons, s>(q_gen_803, q_gen_800) -> q_gen_843
<cons, s>(q_gen_781, q_gen_800) -> q_gen_845
<cons, s>(q_gen_749, q_gen_773) -> q_gen_848
<cons, s>(q_gen_761, q_gen_787) -> q_gen_848
<cons, s>(q_gen_781, q_gen_827) -> q_gen_848
<cons, s>(q_gen_794, q_gen_800) -> q_gen_848
<cons, s>(q_gen_810, q_gen_827) -> q_gen_848
<cons, s>(q_gen_821, q_gen_787) -> q_gen_848
<cons, s>(q_gen_810, q_gen_748) -> q_gen_858
<cons, s>(q_gen_810, q_gen_813) -> q_gen_859
<cons, s>(q_gen_821, q_gen_813) -> q_gen_860
<cons, s>(q_gen_810, q_gen_820) -> q_gen_862
<cons, s>(q_gen_794, q_gen_820) -> q_gen_863
<cons, s>(q_gen_775, q_gen_820) -> q_gen_865
<cons, s>(q_gen_794, q_gen_868) -> q_gen_867
<cons, s>(q_gen_821, q_gen_773) -> q_gen_869
<cons, s>(q_gen_794, q_gen_829) -> q_gen_871
<cons, s>(q_gen_803, q_gen_829) -> q_gen_872
<cons, s>(q_gen_803, q_gen_868) -> q_gen_872
<cons, s>(q_gen_803, q_gen_748) -> q_gen_874
<cons, s>(q_gen_761, q_gen_773) -> q_gen_875
<cons, s>(q_gen_810, q_gen_787) -> q_gen_877
<cons, s>(q_gen_880, q_gen_748) -> q_gen_877
<cons, s>(q_gen_880, q_gen_773) -> q_gen_877
<a, s>(q_gen_789) -> q_gen_880
<cons, s>(q_gen_810, q_gen_868) -> q_gen_881
<cons, s>(q_gen_821, q_gen_800) -> q_gen_881
<cons, s>(q_gen_880, q_gen_813) -> q_gen_881
<cons, s>(q_gen_810, q_gen_815) -> q_gen_889
<cons, s>(q_gen_761, q_gen_813) -> q_gen_891
<cons, s>(q_gen_761, q_gen_815) -> q_gen_891
<cons, s>(q_gen_775, q_gen_813) -> q_gen_891
<cons, s>(q_gen_775, q_gen_815) -> q_gen_891
<cons, s>(q_gen_781, q_gen_815) -> q_gen_891
<cons, s>(q_gen_810, q_gen_800) -> q_gen_891
<cons, s>(q_gen_880, q_gen_800) -> q_gen_891
<cons, s>(q_gen_880, q_gen_820) -> q_gen_891
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_738, q_gen_752},
Q_f={q_gen_738},
Delta=
{
<a, a>() -> q_gen_738
<a, b>() -> q_gen_738
<b, b>() -> q_gen_738
<b, a>() -> q_gen_752
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_737, q_gen_750, q_gen_751, q_gen_763, q_gen_764, q_gen_779, q_gen_785, q_gen_797, q_gen_811, q_gen_825, q_gen_832, q_gen_833, q_gen_834, q_gen_839, q_gen_841, q_gen_844, q_gen_854},
Q_f={q_gen_737, q_gen_750, q_gen_811, q_gen_825, q_gen_839, q_gen_844},
Delta=
{
<nil, nil>() -> q_gen_737
<cons, cons>(q_gen_751, q_gen_737) -> q_gen_750
<cons, cons>(q_gen_751, q_gen_750) -> q_gen_750
<cons, cons>(q_gen_779, q_gen_737) -> q_gen_750
<b, b>() -> q_gen_751
<cons, cons>(q_gen_764, q_gen_737) -> q_gen_763
<cons, cons>(q_gen_785, q_gen_737) -> q_gen_763
<a, b>() -> q_gen_764
<a, a>() -> q_gen_779
<b, a>() -> q_gen_785
<cons, cons>(q_gen_764, q_gen_763) -> q_gen_797
<cons, cons>(q_gen_779, q_gen_750) -> q_gen_811
<cons, cons>(q_gen_764, q_gen_750) -> q_gen_825
<cons, cons>(q_gen_764, q_gen_833) -> q_gen_832
<cons, cons>(q_gen_751, q_gen_834) -> q_gen_833
<cons, cons>(q_gen_785, q_gen_750) -> q_gen_834
<cons, cons>(q_gen_751, q_gen_811) -> q_gen_839
<cons, cons>(q_gen_785, q_gen_834) -> q_gen_841
<cons, cons>(q_gen_751, q_gen_763) -> q_gen_844
<cons, cons>(q_gen_751, q_gen_797) -> q_gen_854
<cons, cons>(q_gen_751, q_gen_854) -> q_gen_854
<cons, cons>(q_gen_764, q_gen_854) -> q_gen_854
<cons, cons>(q_gen_779, q_gen_763) -> q_gen_854
<cons, cons>(q_gen_785, q_gen_763) -> q_gen_854
<cons, cons>(q_gen_785, q_gen_797) -> q_gen_854
<cons, cons>(q_gen_785, q_gen_844) -> q_gen_854
<cons, cons>(q_gen_785, q_gen_854) -> q_gen_854
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 78
() -> length([nil, z]) -> 78
() -> leq([a, y]) -> 78
() -> leq([b, b]) -> 78
() -> sort([nil, nil]) -> 78
(insert([x, z, _yc]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _yc)]) -> 80
(insert([y, _dd, _ed]) /\ sort([z, _dd])) -> sort([cons(y, z), _ed]) -> 87
(length([_nd, _od]) /\ length([l, _md]) /\ sort([l, _nd])) -> eq_nat([_md, _od]) -> 97
(length([ll, _id])) -> length([cons(x, ll), s(_id)]) -> 95
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 83
(leq([b, a])) -> BOT -> 79
}
Sat witness: Found: ((leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]), {
x -> a  ;  y -> b  ;  z -> cons(a, nil)
})

Total time: 66.587876
Reason for stopping: DontKnow. Stopped because: timeout