Solving ../../benchmarks/false/sort_bug_length_eq.smt2...

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, _oha]) /\ not leq([x, y])) -> insert([x, cons(y, z), _oha])
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))])}
(insert([_pha, _qha, _rha]) /\ insert([_pha, _qha, _sha])) -> eq_eltlist([_rha, _sha])
)
(sort, F:
{() -> sort([nil, nil])
(insert([y, _tha, _uha]) /\ sort([z, _tha])) -> sort([cons(y, z), _uha])}
(sort([_vha, _wha]) /\ sort([_vha, _xha])) -> eq_eltlist([_wha, _xha])
)
(length, F:
{() -> length([nil, z])
(length([ll, _yha])) -> length([cons(x, ll), s(_yha)])}
(length([_zha, _aia]) /\ length([_zha, _bia])) -> eq_nat([_aia, _bia])
)
}

properties:
{(length([_dia, _eia]) /\ length([l, _cia]) /\ sort([l, _dia])) -> eq_nat([_cia, _eia])}


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, _oha]) /\ not leq([x, y])) -> insert([x, cons(y, z), _oha]) -> 0
(insert([y, _tha, _uha]) /\ sort([z, _tha])) -> sort([cons(y, z), _uha]) -> 0
(length([_dia, _eia]) /\ length([l, _cia]) /\ sort([l, _dia])) -> eq_nat([_cia, _eia]) -> 0
(length([ll, _yha])) -> length([cons(x, ll), s(_yha)]) -> 0
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 0
(leq([b, a])) -> BOT -> 0
}


Solving took 66.170647 seconds.
DontKnow. Stopped because: timeout
Working model:
|_
{
insert -> 
{{{
Q={q_gen_8672, q_gen_8673, q_gen_8674, q_gen_8675, q_gen_8676, q_gen_8677, q_gen_8684, q_gen_8685, q_gen_8686, q_gen_8688, q_gen_8689, q_gen_8690, q_gen_8691, q_gen_8694, q_gen_8697, q_gen_8698, q_gen_8699, q_gen_8700, q_gen_8701, q_gen_8710, q_gen_8711, q_gen_8717, q_gen_8718, q_gen_8719, q_gen_8720, q_gen_8721, q_gen_8729, q_gen_8735, q_gen_8736, q_gen_8737, q_gen_8747, q_gen_8749, q_gen_8758, q_gen_8759, q_gen_8760, q_gen_8766, q_gen_8768, q_gen_8772, q_gen_8773, q_gen_8774, q_gen_8775, q_gen_8776, q_gen_8777, q_gen_8778, q_gen_8779, q_gen_8780, q_gen_8781, q_gen_8783, q_gen_8789, q_gen_8790, q_gen_8796, q_gen_8797, q_gen_8798, q_gen_8801, q_gen_8802, q_gen_8803, q_gen_8804, q_gen_8810, q_gen_8816, q_gen_8821, q_gen_8822, q_gen_8823, q_gen_8824, q_gen_8825, q_gen_8826, q_gen_8827, q_gen_8828, q_gen_8840, q_gen_8844, q_gen_8845},
Q_f={},
Delta=
{
<nil>() -> q_gen_8673
<b>() -> q_gen_8674
<a>() -> q_gen_8689
<cons>(q_gen_8674, q_gen_8673) -> q_gen_8721
<cons>(q_gen_8689, q_gen_8737) -> q_gen_8736
<cons>(q_gen_8689, q_gen_8673) -> q_gen_8737
<cons>(q_gen_8674, q_gen_8721) -> q_gen_8773
<nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8676
<b, b>() -> q_gen_8677
<nil, nil>() -> q_gen_8685
<a, b>() -> q_gen_8686
<b, a>() -> q_gen_8691
<a, a>() -> q_gen_8699
<cons, cons>(q_gen_8691, q_gen_8676) -> q_gen_8701
<cons, nil>(q_gen_8689, q_gen_8673) -> q_gen_8711
<cons, nil>(q_gen_8674, q_gen_8673) -> q_gen_8718
<cons, nil>(q_gen_8674, q_gen_8721) -> q_gen_8720
<nil, cons>(q_gen_8689, q_gen_8673) -> q_gen_8760
<nil, cons>(q_gen_8674, q_gen_8721) -> q_gen_8775
<cons, cons>(q_gen_8686, q_gen_8760) -> q_gen_8777
<nil, cons>(q_gen_8689, q_gen_8737) -> q_gen_8780
<nil, cons>(q_gen_8674, q_gen_8773) -> q_gen_8790
<cons, cons>(q_gen_8686, q_gen_8685) -> q_gen_8798
<cons, cons>(q_gen_8677, q_gen_8803) -> q_gen_8802
<cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8803
<cons, nil>(q_gen_8689, q_gen_8737) -> q_gen_8822
<cons, cons>(q_gen_8677, q_gen_8685) -> q_gen_8827
<cons, cons>(q_gen_8699, q_gen_8760) -> q_gen_8845
<b, nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8672
<b, cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8675
<b, cons, cons>(q_gen_8686, q_gen_8685) -> q_gen_8684
<a, nil, cons>(q_gen_8689, q_gen_8673) -> q_gen_8688
<a, cons, cons>(q_gen_8691, q_gen_8676) -> q_gen_8690
<a, nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8694
<b, nil, cons>(q_gen_8689, q_gen_8673) -> q_gen_8697
<b, cons, cons>(q_gen_8699, q_gen_8685) -> q_gen_8698
<a, cons, cons>(q_gen_8699, q_gen_8701) -> q_gen_8700
<b, cons, cons>(q_gen_8686, q_gen_8711) -> q_gen_8710
<b, cons, cons>(q_gen_8691, q_gen_8718) -> q_gen_8717
<b, cons, cons>(q_gen_8699, q_gen_8720) -> q_gen_8719
<a, nil, cons>(q_gen_8674, q_gen_8721) -> q_gen_8729
<a, nil, cons>(q_gen_8674, q_gen_8736) -> q_gen_8735
<a, cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8747
<b, cons, cons>(q_gen_8677, q_gen_8685) -> q_gen_8749
<b, nil, cons>(q_gen_8674, q_gen_8737) -> q_gen_8758
<b, cons, cons>(q_gen_8686, q_gen_8760) -> q_gen_8759
<a, nil, cons>(q_gen_8689, q_gen_8721) -> q_gen_8766
<a, cons, cons>(q_gen_8686, q_gen_8711) -> q_gen_8768
<b, nil, cons>(q_gen_8674, q_gen_8773) -> q_gen_8772
<b, cons, cons>(q_gen_8686, q_gen_8775) -> q_gen_8774
<b, cons, cons>(q_gen_8677, q_gen_8777) -> q_gen_8776
<b, nil, cons>(q_gen_8674, q_gen_8736) -> q_gen_8778
<b, cons, cons>(q_gen_8686, q_gen_8780) -> q_gen_8779
<a, nil, cons>(q_gen_8689, q_gen_8736) -> q_gen_8781
<a, cons, cons>(q_gen_8699, q_gen_8760) -> q_gen_8783
<a, cons, cons>(q_gen_8677, q_gen_8790) -> q_gen_8789
<b, cons, cons>(q_gen_8699, q_gen_8676) -> q_gen_8796
<b, cons, cons>(q_gen_8699, q_gen_8798) -> q_gen_8797
<b, cons, cons>(q_gen_8677, q_gen_8802) -> q_gen_8801
<a, cons, cons>(q_gen_8677, q_gen_8685) -> q_gen_8804
<b, cons, cons>(q_gen_8677, q_gen_8775) -> q_gen_8810
<b, cons, cons>(q_gen_8677, q_gen_8790) -> q_gen_8816
<b, cons, cons>(q_gen_8686, q_gen_8822) -> q_gen_8821
<b, nil, cons>(q_gen_8674, q_gen_8721) -> q_gen_8823
<b, cons, cons>(q_gen_8677, q_gen_8803) -> q_gen_8824
<b, cons, cons>(q_gen_8691, q_gen_8676) -> q_gen_8825
<b, cons, cons>(q_gen_8699, q_gen_8827) -> q_gen_8826
<b, cons, cons>(q_gen_8677, q_gen_8798) -> q_gen_8828
<b, cons, cons>(q_gen_8691, q_gen_8685) -> q_gen_8840
<a, cons, cons>(q_gen_8699, q_gen_8845) -> q_gen_8844
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_8671, q_gen_8678, q_gen_8679, q_gen_8680, q_gen_8692, q_gen_8693, q_gen_8702, q_gen_8703, q_gen_8704, q_gen_8705, q_gen_8706, q_gen_8707, q_gen_8712, q_gen_8713, q_gen_8714, q_gen_8722, q_gen_8723, q_gen_8724, q_gen_8725, q_gen_8726, q_gen_8727, q_gen_8734, q_gen_8742, q_gen_8743, q_gen_8744, q_gen_8752, q_gen_8753, q_gen_8754, q_gen_8755, q_gen_8762, q_gen_8763, q_gen_8784, q_gen_8785, q_gen_8786, q_gen_8787, q_gen_8788, q_gen_8793, q_gen_8794, q_gen_8795, q_gen_8807, q_gen_8812, q_gen_8831, q_gen_8833, q_gen_8834, q_gen_8835, q_gen_8836, q_gen_8842},
Q_f={},
Delta=
{
<nil>() -> q_gen_8679
<cons>(q_gen_8704, q_gen_8679) -> q_gen_8703
<b>() -> q_gen_8704
<z>() -> q_gen_8706
<cons>(q_gen_8704, q_gen_8703) -> q_gen_8723
<s>(q_gen_8706) -> q_gen_8725
<cons>(q_gen_8744, q_gen_8679) -> q_gen_8743
<a>() -> q_gen_8744
<s>(q_gen_8725) -> q_gen_8755
<cons>(q_gen_8744, q_gen_8703) -> q_gen_8785
<cons>(q_gen_8744, q_gen_8785) -> q_gen_8787
<cons>(q_gen_8704, q_gen_8785) -> q_gen_8795
<cons>(q_gen_8744, q_gen_8743) -> q_gen_8834
<cons>(q_gen_8704, q_gen_8723) -> q_gen_8836
<nil, z>() -> q_gen_8671
<cons, s>(q_gen_8680, q_gen_8679) -> q_gen_8678
<b, z>() -> q_gen_8680
<cons, s>(q_gen_8693, q_gen_8679) -> q_gen_8692
<a, z>() -> q_gen_8693
<cons, s>(q_gen_8705, q_gen_8703) -> q_gen_8702
<b, s>(q_gen_8706) -> q_gen_8705
<cons, s>(q_gen_8705, q_gen_8679) -> q_gen_8707
<cons, s>(q_gen_8713, q_gen_8703) -> q_gen_8712
<a, s>(q_gen_8706) -> q_gen_8713
<cons, s>(q_gen_8713, q_gen_8679) -> q_gen_8714
<cons, s>(q_gen_8724, q_gen_8723) -> q_gen_8722
<b, s>(q_gen_8725) -> q_gen_8724
<cons, s>(q_gen_8727, q_gen_8703) -> q_gen_8726
<a, s>(q_gen_8725) -> q_gen_8727
<cons, s>(q_gen_8727, q_gen_8723) -> q_gen_8734
<cons, s>(q_gen_8705, q_gen_8743) -> q_gen_8742
<cons, s>(q_gen_8724, q_gen_8679) -> q_gen_8752
<cons, s>(q_gen_8754, q_gen_8703) -> q_gen_8753
<b, s>(q_gen_8755) -> q_gen_8754
<cons, s>(q_gen_8727, q_gen_8679) -> q_gen_8762
<cons, s>(q_gen_8680, q_gen_8723) -> q_gen_8763
<cons, s>(q_gen_8727, q_gen_8785) -> q_gen_8784
<cons, s>(q_gen_8788, q_gen_8787) -> q_gen_8786
<a, s>(q_gen_8755) -> q_gen_8788
<cons, s>(q_gen_8705, q_gen_8785) -> q_gen_8793
<cons, s>(q_gen_8727, q_gen_8795) -> q_gen_8794
<cons, s>(q_gen_8713, q_gen_8723) -> q_gen_8807
<cons, s>(q_gen_8705, q_gen_8787) -> q_gen_8812
<cons, s>(q_gen_8754, q_gen_8723) -> q_gen_8831
<cons, s>(q_gen_8727, q_gen_8834) -> q_gen_8833
<cons, s>(q_gen_8713, q_gen_8836) -> q_gen_8835
<cons, s>(q_gen_8788, q_gen_8703) -> q_gen_8842
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_8669, q_gen_8670, q_gen_8683, q_gen_8687},
Q_f={},
Delta=
{
<b, b>() -> q_gen_8669
<a, b>() -> q_gen_8670
<b, a>() -> q_gen_8683
<a, a>() -> q_gen_8687
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_8668, q_gen_8681, q_gen_8682, q_gen_8695, q_gen_8696, q_gen_8708, q_gen_8709, q_gen_8715, q_gen_8716, q_gen_8728, q_gen_8730, q_gen_8731, q_gen_8732, q_gen_8733, q_gen_8738, q_gen_8739, q_gen_8740, q_gen_8741, q_gen_8745, q_gen_8746, q_gen_8748, q_gen_8750, q_gen_8751, q_gen_8756, q_gen_8757, q_gen_8761, q_gen_8764, q_gen_8765, q_gen_8767, q_gen_8769, q_gen_8770, q_gen_8771, q_gen_8782, q_gen_8791, q_gen_8792, q_gen_8799, q_gen_8800, q_gen_8805, q_gen_8806, q_gen_8808, q_gen_8809, q_gen_8811, q_gen_8813, q_gen_8814, q_gen_8815, q_gen_8817, q_gen_8818, q_gen_8819, q_gen_8820, q_gen_8829, q_gen_8830, q_gen_8832, q_gen_8837, q_gen_8838, q_gen_8839, q_gen_8841, q_gen_8843},
Q_f={},
Delta=
{
<nil>() -> q_gen_8732
<b>() -> q_gen_8733
<cons>(q_gen_8741, q_gen_8732) -> q_gen_8740
<a>() -> q_gen_8741
<cons>(q_gen_8733, q_gen_8732) -> q_gen_8757
<nil, nil>() -> q_gen_8668
<cons, cons>(q_gen_8682, q_gen_8668) -> q_gen_8681
<b, b>() -> q_gen_8682
<cons, cons>(q_gen_8696, q_gen_8668) -> q_gen_8695
<a, b>() -> q_gen_8696
<cons, cons>(q_gen_8709, q_gen_8668) -> q_gen_8708
<a, a>() -> q_gen_8709
<cons, cons>(q_gen_8716, q_gen_8668) -> q_gen_8715
<b, a>() -> q_gen_8716
<cons, cons>(q_gen_8709, q_gen_8681) -> q_gen_8728
<cons, cons>(q_gen_8696, q_gen_8731) -> q_gen_8730
<nil, cons>(q_gen_8733, q_gen_8732) -> q_gen_8731
<cons, cons>(q_gen_8696, q_gen_8739) -> q_gen_8738
<nil, cons>(q_gen_8741, q_gen_8740) -> q_gen_8739
<cons, cons>(q_gen_8716, q_gen_8746) -> q_gen_8745
<cons, cons>(q_gen_8682, q_gen_8731) -> q_gen_8746
<cons, cons>(q_gen_8696, q_gen_8695) -> q_gen_8748
<cons, cons>(q_gen_8682, q_gen_8751) -> q_gen_8750
<cons, nil>(q_gen_8741, q_gen_8732) -> q_gen_8751
<cons, nil>(q_gen_8741, q_gen_8757) -> q_gen_8756
<cons, nil>(q_gen_8733, q_gen_8732) -> q_gen_8761
<cons, cons>(q_gen_8716, q_gen_8765) -> q_gen_8764
<cons, nil>(q_gen_8733, q_gen_8757) -> q_gen_8765
<cons, cons>(q_gen_8709, q_gen_8731) -> q_gen_8767
<cons, cons>(q_gen_8709, q_gen_8770) -> q_gen_8769
<nil, cons>(q_gen_8741, q_gen_8732) -> q_gen_8770
<cons, cons>(q_gen_8696, q_gen_8751) -> q_gen_8771
<cons, cons>(q_gen_8709, q_gen_8739) -> q_gen_8782
<cons, cons>(q_gen_8696, q_gen_8792) -> q_gen_8791
<cons, cons>(q_gen_8696, q_gen_8730) -> q_gen_8792
<cons, cons>(q_gen_8709, q_gen_8800) -> q_gen_8799
<cons, cons>(q_gen_8716, q_gen_8731) -> q_gen_8800
<cons, cons>(q_gen_8682, q_gen_8761) -> q_gen_8805
<cons, cons>(q_gen_8696, q_gen_8765) -> q_gen_8806
<cons, cons>(q_gen_8709, q_gen_8809) -> q_gen_8808
<cons, cons>(q_gen_8682, q_gen_8681) -> q_gen_8809
<cons, cons>(q_gen_8682, q_gen_8730) -> q_gen_8811
<cons, cons>(q_gen_8716, q_gen_8814) -> q_gen_8813
<cons, cons>(q_gen_8696, q_gen_8815) -> q_gen_8814
<cons, cons>(q_gen_8696, q_gen_8761) -> q_gen_8815
<cons, cons>(q_gen_8682, q_gen_8818) -> q_gen_8817
<cons, cons>(q_gen_8682, q_gen_8746) -> q_gen_8818
<cons, cons>(q_gen_8696, q_gen_8746) -> q_gen_8819
<cons, cons>(q_gen_8709, q_gen_8761) -> q_gen_8820
<cons, cons>(q_gen_8682, q_gen_8708) -> q_gen_8829
<cons, cons>(q_gen_8682, q_gen_8750) -> q_gen_8830
<cons, cons>(q_gen_8682, q_gen_8809) -> q_gen_8832
<cons, cons>(q_gen_8709, q_gen_8838) -> q_gen_8837
<cons, cons>(q_gen_8716, q_gen_8839) -> q_gen_8838
<cons, cons>(q_gen_8716, q_gen_8761) -> q_gen_8839
<cons, cons>(q_gen_8716, q_gen_8751) -> q_gen_8841
<cons, cons>(q_gen_8682, q_gen_8695) -> q_gen_8843
}

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

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

-------------------
STEPS:
-------------------------------------------
Step 0, which took 0.015498 s (model generation: 0.014788,  model checking: 0.000710):

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, _oha]) /\ not leq([x, y])) -> insert([x, cons(y, z), _oha]) -> 1
(insert([y, _tha, _uha]) /\ sort([z, _tha])) -> sort([cons(y, z), _uha]) -> 1
(length([_dia, _eia]) /\ length([l, _cia]) /\ sort([l, _dia])) -> eq_nat([_cia, _eia]) -> 1
(length([ll, _yha])) -> length([cons(x, ll), s(_yha)]) -> 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 0.015073 s (model generation: 0.015008,  model checking: 0.000065):

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_8668},
Q_f={q_gen_8668},
Delta=
{
<nil, nil>() -> q_gen_8668
}

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, _oha]) /\ not leq([x, y])) -> insert([x, cons(y, z), _oha]) -> 1
(insert([y, _tha, _uha]) /\ sort([z, _tha])) -> sort([cons(y, z), _uha]) -> 1
(length([_dia, _eia]) /\ length([l, _cia]) /\ sort([l, _dia])) -> eq_nat([_cia, _eia]) -> 1
(length([ll, _yha])) -> length([cons(x, ll), s(_yha)]) -> 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 0.015051 s (model generation: 0.014969,  model checking: 0.000082):

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_8669},
Q_f={q_gen_8669},
Delta=
{
<b, b>() -> q_gen_8669
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_8668},
Q_f={q_gen_8668},
Delta=
{
<nil, nil>() -> q_gen_8668
}

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, _oha]) /\ not leq([x, y])) -> insert([x, cons(y, z), _oha]) -> 1
(insert([y, _tha, _uha]) /\ sort([z, _tha])) -> sort([cons(y, z), _uha]) -> 1
(length([_dia, _eia]) /\ length([l, _cia]) /\ sort([l, _dia])) -> eq_nat([_cia, _eia]) -> 1
(length([ll, _yha])) -> length([cons(x, ll), s(_yha)]) -> 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 0.016816 s (model generation: 0.016676,  model checking: 0.000140):

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_8669},
Q_f={q_gen_8669},
Delta=
{
<a, b>() -> q_gen_8669
<b, b>() -> q_gen_8669
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_8668},
Q_f={q_gen_8668},
Delta=
{
<nil, nil>() -> q_gen_8668
}

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, _oha]) /\ not leq([x, y])) -> insert([x, cons(y, z), _oha]) -> 1
(insert([y, _tha, _uha]) /\ sort([z, _tha])) -> sort([cons(y, z), _uha]) -> 1
(length([_dia, _eia]) /\ length([l, _cia]) /\ sort([l, _dia])) -> eq_nat([_cia, _eia]) -> 1
(length([ll, _yha])) -> length([cons(x, ll), s(_yha)]) -> 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 0.017653 s (model generation: 0.016739,  model checking: 0.000914):

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

}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_8671},
Q_f={q_gen_8671},
Delta=
{
<nil, z>() -> q_gen_8671
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_8669},
Q_f={q_gen_8669},
Delta=
{
<a, b>() -> q_gen_8669
<b, b>() -> q_gen_8669
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_8668},
Q_f={q_gen_8668},
Delta=
{
<nil, nil>() -> q_gen_8668
}

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, _oha]) /\ not leq([x, y])) -> insert([x, cons(y, z), _oha]) -> 1
(insert([y, _tha, _uha]) /\ sort([z, _tha])) -> sort([cons(y, z), _uha]) -> 1
(length([_dia, _eia]) /\ length([l, _cia]) /\ sort([l, _dia])) -> eq_nat([_cia, _eia]) -> 1
(length([ll, _yha])) -> length([cons(x, ll), s(_yha)]) -> 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 0.017490 s (model generation: 0.017002,  model checking: 0.000488):

Model:
|_
{
insert -> 
{{{
Q={q_gen_8672, q_gen_8673, q_gen_8674},
Q_f={q_gen_8672},
Delta=
{
<nil>() -> q_gen_8673
<b>() -> q_gen_8674
<b, nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8672
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_8671},
Q_f={q_gen_8671},
Delta=
{
<nil, z>() -> q_gen_8671
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_8669},
Q_f={q_gen_8669},
Delta=
{
<a, b>() -> q_gen_8669
<b, b>() -> q_gen_8669
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_8668},
Q_f={q_gen_8668},
Delta=
{
<nil, nil>() -> q_gen_8668
}

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, _oha]) /\ not leq([x, y])) -> insert([x, cons(y, z), _oha]) -> 1
(insert([y, _tha, _uha]) /\ sort([z, _tha])) -> sort([cons(y, z), _uha]) -> 1
(length([_dia, _eia]) /\ length([l, _cia]) /\ sort([l, _dia])) -> eq_nat([_cia, _eia]) -> 1
(length([ll, _yha])) -> length([cons(x, ll), s(_yha)]) -> 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 0.017220 s (model generation: 0.016875,  model checking: 0.000345):

Model:
|_
{
insert -> 
{{{
Q={q_gen_8672, q_gen_8673, q_gen_8674, q_gen_8676, q_gen_8677},
Q_f={q_gen_8672},
Delta=
{
<nil>() -> q_gen_8673
<b>() -> q_gen_8674
<nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8676
<b, b>() -> q_gen_8677
<b, cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8672
<b, nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8672
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_8671},
Q_f={q_gen_8671},
Delta=
{
<nil, z>() -> q_gen_8671
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_8669},
Q_f={q_gen_8669},
Delta=
{
<a, b>() -> q_gen_8669
<b, b>() -> q_gen_8669
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_8668},
Q_f={q_gen_8668},
Delta=
{
<nil, nil>() -> q_gen_8668
}

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, _oha]) /\ not leq([x, y])) -> insert([x, cons(y, z), _oha]) -> 1
(insert([y, _tha, _uha]) /\ sort([z, _tha])) -> sort([cons(y, z), _uha]) -> 1
(length([_dia, _eia]) /\ length([l, _cia]) /\ sort([l, _dia])) -> eq_nat([_cia, _eia]) -> 1
(length([ll, _yha])) -> length([cons(x, ll), s(_yha)]) -> 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, _yha])) -> length([cons(x, ll), s(_yha)]), {
_yha -> z  ;  ll -> nil  ;  x -> b
})

-------------------------------------------
Step 7, which took 0.017905 s (model generation: 0.017581,  model checking: 0.000324):

Model:
|_
{
insert -> 
{{{
Q={q_gen_8672, q_gen_8673, q_gen_8674, q_gen_8676, q_gen_8677},
Q_f={q_gen_8672},
Delta=
{
<nil>() -> q_gen_8673
<b>() -> q_gen_8674
<nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8676
<b, b>() -> q_gen_8677
<b, cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8672
<b, nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8672
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_8671, q_gen_8679, q_gen_8680},
Q_f={q_gen_8671},
Delta=
{
<nil>() -> q_gen_8679
<cons, s>(q_gen_8680, q_gen_8679) -> q_gen_8671
<nil, z>() -> q_gen_8671
<b, z>() -> q_gen_8680
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_8669},
Q_f={q_gen_8669},
Delta=
{
<a, b>() -> q_gen_8669
<b, b>() -> q_gen_8669
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_8668},
Q_f={q_gen_8668},
Delta=
{
<nil, nil>() -> q_gen_8668
}

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, _oha]) /\ not leq([x, y])) -> insert([x, cons(y, z), _oha]) -> 1
(insert([y, _tha, _uha]) /\ sort([z, _tha])) -> sort([cons(y, z), _uha]) -> 4
(length([_dia, _eia]) /\ length([l, _cia]) /\ sort([l, _dia])) -> eq_nat([_cia, _eia]) -> 2
(length([ll, _yha])) -> length([cons(x, ll), s(_yha)]) -> 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, _tha, _uha]) /\ sort([z, _tha])) -> sort([cons(y, z), _uha]), {
_tha -> nil  ;  _uha -> cons(b, nil)  ;  y -> b  ;  z -> nil
})

-------------------------------------------
Step 8, which took 0.019042 s (model generation: 0.018437,  model checking: 0.000605):

Model:
|_
{
insert -> 
{{{
Q={q_gen_8672, q_gen_8673, q_gen_8674, q_gen_8676, q_gen_8677},
Q_f={q_gen_8672},
Delta=
{
<nil>() -> q_gen_8673
<b>() -> q_gen_8674
<nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8676
<b, b>() -> q_gen_8677
<b, cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8672
<b, nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8672
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_8671, q_gen_8679, q_gen_8680},
Q_f={q_gen_8671},
Delta=
{
<nil>() -> q_gen_8679
<cons, s>(q_gen_8680, q_gen_8679) -> q_gen_8671
<nil, z>() -> q_gen_8671
<b, z>() -> q_gen_8680
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_8669},
Q_f={q_gen_8669},
Delta=
{
<a, b>() -> q_gen_8669
<b, b>() -> q_gen_8669
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_8668, q_gen_8682},
Q_f={q_gen_8668},
Delta=
{
<cons, cons>(q_gen_8682, q_gen_8668) -> q_gen_8668
<nil, nil>() -> q_gen_8668
<b, b>() -> q_gen_8682
}

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, _oha]) /\ not leq([x, y])) -> insert([x, cons(y, z), _oha]) -> 4
(insert([y, _tha, _uha]) /\ sort([z, _tha])) -> sort([cons(y, z), _uha]) -> 4
(length([_dia, _eia]) /\ length([l, _cia]) /\ sort([l, _dia])) -> eq_nat([_cia, _eia]) -> 2
(length([ll, _yha])) -> length([cons(x, ll), s(_yha)]) -> 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, _oha]) /\ not leq([x, y])) -> insert([x, cons(y, z), _oha]), {
_oha -> cons(b, nil)  ;  x -> b  ;  y -> a  ;  z -> nil
})

-------------------------------------------
Step 9, which took 0.021063 s (model generation: 0.021030,  model checking: 0.000033):

Model:
|_
{
insert -> 
{{{
Q={q_gen_8672, q_gen_8673, q_gen_8674, q_gen_8676, q_gen_8677},
Q_f={q_gen_8672},
Delta=
{
<nil>() -> q_gen_8673
<b>() -> q_gen_8674
<nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8676
<nil, nil>() -> q_gen_8676
<a, b>() -> q_gen_8677
<b, b>() -> q_gen_8677
<b, cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8672
<b, nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8672
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_8671, q_gen_8679, q_gen_8680},
Q_f={q_gen_8671},
Delta=
{
<nil>() -> q_gen_8679
<cons, s>(q_gen_8680, q_gen_8679) -> q_gen_8671
<nil, z>() -> q_gen_8671
<b, z>() -> q_gen_8680
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_8669},
Q_f={q_gen_8669},
Delta=
{
<a, b>() -> q_gen_8669
<b, a>() -> q_gen_8669
<b, b>() -> q_gen_8669
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_8668, q_gen_8682},
Q_f={q_gen_8668},
Delta=
{
<cons, cons>(q_gen_8682, q_gen_8668) -> q_gen_8668
<nil, nil>() -> q_gen_8668
<b, b>() -> q_gen_8682
}

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, _oha]) /\ not leq([x, y])) -> insert([x, cons(y, z), _oha]) -> 4
(insert([y, _tha, _uha]) /\ sort([z, _tha])) -> sort([cons(y, z), _uha]) -> 4
(length([_dia, _eia]) /\ length([l, _cia]) /\ sort([l, _dia])) -> eq_nat([_cia, _eia]) -> 2
(length([ll, _yha])) -> length([cons(x, ll), s(_yha)]) -> 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 0.020050 s (model generation: 0.019450,  model checking: 0.000600):

Model:
|_
{
insert -> 
{{{
Q={q_gen_8672, q_gen_8673, q_gen_8674, q_gen_8676, q_gen_8677},
Q_f={q_gen_8672},
Delta=
{
<nil>() -> q_gen_8673
<b>() -> q_gen_8674
<nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8676
<nil, nil>() -> q_gen_8676
<a, b>() -> q_gen_8677
<b, b>() -> q_gen_8677
<b, cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8672
<b, nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8672
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_8671, q_gen_8679, q_gen_8680},
Q_f={q_gen_8671},
Delta=
{
<nil>() -> q_gen_8679
<cons, s>(q_gen_8680, q_gen_8679) -> q_gen_8671
<nil, z>() -> q_gen_8671
<b, z>() -> q_gen_8680
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_8669, q_gen_8683},
Q_f={q_gen_8669},
Delta=
{
<a, b>() -> q_gen_8669
<b, b>() -> q_gen_8669
<b, a>() -> q_gen_8683
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_8668, q_gen_8682},
Q_f={q_gen_8668},
Delta=
{
<cons, cons>(q_gen_8682, q_gen_8668) -> q_gen_8668
<nil, nil>() -> q_gen_8668
<b, b>() -> q_gen_8682
}

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, _oha]) /\ not leq([x, y])) -> insert([x, cons(y, z), _oha]) -> 4
(insert([y, _tha, _uha]) /\ sort([z, _tha])) -> sort([cons(y, z), _uha]) -> 4
(length([_dia, _eia]) /\ length([l, _cia]) /\ sort([l, _dia])) -> eq_nat([_cia, _eia]) -> 3
(length([ll, _yha])) -> length([cons(x, ll), s(_yha)]) -> 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 0.020405 s (model generation: 0.019503,  model checking: 0.000902):

Model:
|_
{
insert -> 
{{{
Q={q_gen_8672, q_gen_8673, q_gen_8674, q_gen_8676, q_gen_8677},
Q_f={q_gen_8672},
Delta=
{
<nil>() -> q_gen_8673
<b>() -> q_gen_8674
<nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8676
<nil, nil>() -> q_gen_8676
<a, b>() -> q_gen_8677
<b, b>() -> q_gen_8677
<b, cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8672
<b, nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8672
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_8671, q_gen_8679, q_gen_8680},
Q_f={q_gen_8671},
Delta=
{
<nil>() -> q_gen_8679
<cons, s>(q_gen_8680, q_gen_8679) -> q_gen_8671
<nil, z>() -> q_gen_8671
<b, z>() -> q_gen_8680
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_8669, q_gen_8683},
Q_f={q_gen_8669},
Delta=
{
<a, a>() -> q_gen_8669
<a, b>() -> q_gen_8669
<b, b>() -> q_gen_8669
<b, a>() -> q_gen_8683
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_8668, q_gen_8682},
Q_f={q_gen_8668},
Delta=
{
<cons, cons>(q_gen_8682, q_gen_8668) -> q_gen_8668
<nil, nil>() -> q_gen_8668
<b, b>() -> q_gen_8682
}

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, _oha]) /\ not leq([x, y])) -> insert([x, cons(y, z), _oha]) -> 4
(insert([y, _tha, _uha]) /\ sort([z, _tha])) -> sort([cons(y, z), _uha]) -> 4
(length([_dia, _eia]) /\ length([l, _cia]) /\ sort([l, _dia])) -> eq_nat([_cia, _eia]) -> 4
(length([ll, _yha])) -> length([cons(x, ll), s(_yha)]) -> 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 0.021515 s (model generation: 0.020504,  model checking: 0.001011):

Model:
|_
{
insert -> 
{{{
Q={q_gen_8672, q_gen_8673, q_gen_8674, q_gen_8676, q_gen_8677},
Q_f={q_gen_8672},
Delta=
{
<nil>() -> q_gen_8673
<a>() -> q_gen_8674
<b>() -> q_gen_8674
<nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8676
<nil, nil>() -> q_gen_8676
<a, b>() -> q_gen_8677
<b, b>() -> q_gen_8677
<a, nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8672
<b, cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8672
<b, nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8672
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_8671, q_gen_8679, q_gen_8680},
Q_f={q_gen_8671},
Delta=
{
<nil>() -> q_gen_8679
<cons, s>(q_gen_8680, q_gen_8679) -> q_gen_8671
<nil, z>() -> q_gen_8671
<b, z>() -> q_gen_8680
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_8669, q_gen_8683},
Q_f={q_gen_8669},
Delta=
{
<a, a>() -> q_gen_8669
<a, b>() -> q_gen_8669
<b, b>() -> q_gen_8669
<b, a>() -> q_gen_8683
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_8668, q_gen_8682},
Q_f={q_gen_8668},
Delta=
{
<cons, cons>(q_gen_8682, q_gen_8668) -> q_gen_8668
<nil, nil>() -> q_gen_8668
<b, b>() -> q_gen_8682
}

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, _oha]) /\ not leq([x, y])) -> insert([x, cons(y, z), _oha]) -> 4
(insert([y, _tha, _uha]) /\ sort([z, _tha])) -> sort([cons(y, z), _uha]) -> 4
(length([_dia, _eia]) /\ length([l, _cia]) /\ sort([l, _dia])) -> eq_nat([_cia, _eia]) -> 4
(length([ll, _yha])) -> length([cons(x, ll), s(_yha)]) -> 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 0.020627 s (model generation: 0.020296,  model checking: 0.000331):

Model:
|_
{
insert -> 
{{{
Q={q_gen_8672, q_gen_8673, q_gen_8674, q_gen_8676, q_gen_8677},
Q_f={q_gen_8672},
Delta=
{
<nil>() -> q_gen_8673
<a>() -> q_gen_8674
<b>() -> q_gen_8674
<nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8676
<nil, nil>() -> q_gen_8676
<a, b>() -> q_gen_8677
<b, a>() -> q_gen_8677
<b, b>() -> q_gen_8677
<a, cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8672
<a, nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8672
<b, cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8672
<b, nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8672
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_8671, q_gen_8679, q_gen_8680},
Q_f={q_gen_8671},
Delta=
{
<nil>() -> q_gen_8679
<cons, s>(q_gen_8680, q_gen_8679) -> q_gen_8671
<nil, z>() -> q_gen_8671
<b, z>() -> q_gen_8680
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_8669, q_gen_8683},
Q_f={q_gen_8669},
Delta=
{
<a, a>() -> q_gen_8669
<a, b>() -> q_gen_8669
<b, b>() -> q_gen_8669
<b, a>() -> q_gen_8683
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_8668, q_gen_8682},
Q_f={q_gen_8668},
Delta=
{
<cons, cons>(q_gen_8682, q_gen_8668) -> q_gen_8668
<nil, nil>() -> q_gen_8668
<b, b>() -> q_gen_8682
}

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, _oha]) /\ not leq([x, y])) -> insert([x, cons(y, z), _oha]) -> 4
(insert([y, _tha, _uha]) /\ sort([z, _tha])) -> sort([cons(y, z), _uha]) -> 4
(length([_dia, _eia]) /\ length([l, _cia]) /\ sort([l, _dia])) -> eq_nat([_cia, _eia]) -> 4
(length([ll, _yha])) -> length([cons(x, ll), s(_yha)]) -> 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, _yha])) -> length([cons(x, ll), s(_yha)]), {
_yha -> z  ;  ll -> nil  ;  x -> a
})

-------------------------------------------
Step 14, which took 0.022423 s (model generation: 0.021466,  model checking: 0.000957):

Model:
|_
{
insert -> 
{{{
Q={q_gen_8672, q_gen_8673, q_gen_8674, q_gen_8676, q_gen_8677},
Q_f={q_gen_8672},
Delta=
{
<nil>() -> q_gen_8673
<a>() -> q_gen_8674
<b>() -> q_gen_8674
<nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8676
<nil, nil>() -> q_gen_8676
<a, b>() -> q_gen_8677
<b, a>() -> q_gen_8677
<b, b>() -> q_gen_8677
<a, cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8672
<a, nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8672
<b, cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8672
<b, nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8672
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_8671, q_gen_8679, q_gen_8680},
Q_f={q_gen_8671},
Delta=
{
<nil>() -> q_gen_8679
<cons, s>(q_gen_8680, q_gen_8679) -> q_gen_8671
<nil, z>() -> q_gen_8671
<a, z>() -> q_gen_8680
<b, z>() -> q_gen_8680
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_8669, q_gen_8683},
Q_f={q_gen_8669},
Delta=
{
<a, a>() -> q_gen_8669
<a, b>() -> q_gen_8669
<b, b>() -> q_gen_8669
<b, a>() -> q_gen_8683
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_8668, q_gen_8682},
Q_f={q_gen_8668},
Delta=
{
<cons, cons>(q_gen_8682, q_gen_8668) -> q_gen_8668
<nil, nil>() -> q_gen_8668
<b, b>() -> q_gen_8682
}

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, _oha]) /\ not leq([x, y])) -> insert([x, cons(y, z), _oha]) -> 4
(insert([y, _tha, _uha]) /\ sort([z, _tha])) -> sort([cons(y, z), _uha]) -> 7
(length([_dia, _eia]) /\ length([l, _cia]) /\ sort([l, _dia])) -> eq_nat([_cia, _eia]) -> 5
(length([ll, _yha])) -> length([cons(x, ll), s(_yha)]) -> 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, _tha, _uha]) /\ sort([z, _tha])) -> sort([cons(y, z), _uha]), {
_tha -> nil  ;  _uha -> cons(b, nil)  ;  y -> a  ;  z -> nil
})

-------------------------------------------
Step 15, which took 0.023313 s (model generation: 0.022506,  model checking: 0.000807):

Model:
|_
{
insert -> 
{{{
Q={q_gen_8672, q_gen_8673, q_gen_8674, q_gen_8676, q_gen_8677},
Q_f={q_gen_8672},
Delta=
{
<nil>() -> q_gen_8673
<a>() -> q_gen_8674
<b>() -> q_gen_8674
<nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8676
<nil, nil>() -> q_gen_8676
<a, b>() -> q_gen_8677
<b, a>() -> q_gen_8677
<b, b>() -> q_gen_8677
<a, cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8672
<a, nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8672
<b, cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8672
<b, nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8672
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_8671, q_gen_8679, q_gen_8680},
Q_f={q_gen_8671},
Delta=
{
<nil>() -> q_gen_8679
<cons, s>(q_gen_8680, q_gen_8679) -> q_gen_8671
<nil, z>() -> q_gen_8671
<a, z>() -> q_gen_8680
<b, z>() -> q_gen_8680
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_8669, q_gen_8683},
Q_f={q_gen_8669},
Delta=
{
<a, a>() -> q_gen_8669
<a, b>() -> q_gen_8669
<b, b>() -> q_gen_8669
<b, a>() -> q_gen_8683
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_8668, q_gen_8682},
Q_f={q_gen_8668},
Delta=
{
<cons, cons>(q_gen_8682, q_gen_8668) -> q_gen_8668
<nil, nil>() -> q_gen_8668
<a, b>() -> q_gen_8682
<b, b>() -> q_gen_8682
}

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, _oha]) /\ not leq([x, y])) -> insert([x, cons(y, z), _oha]) -> 7
(insert([y, _tha, _uha]) /\ sort([z, _tha])) -> sort([cons(y, z), _uha]) -> 7
(length([_dia, _eia]) /\ length([l, _cia]) /\ sort([l, _dia])) -> eq_nat([_cia, _eia]) -> 5
(length([ll, _yha])) -> length([cons(x, ll), s(_yha)]) -> 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, _oha]) /\ not leq([x, y])) -> insert([x, cons(y, z), _oha]), {
_oha -> cons(a, nil)  ;  x -> b  ;  y -> a  ;  z -> nil
})

-------------------------------------------
Step 16, which took 0.025779 s (model generation: 0.024287,  model checking: 0.001492):

Model:
|_
{
insert -> 
{{{
Q={q_gen_8672, q_gen_8673, q_gen_8674, q_gen_8676, q_gen_8677},
Q_f={q_gen_8672},
Delta=
{
<nil>() -> q_gen_8673
<a>() -> q_gen_8674
<b>() -> q_gen_8674
<nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8676
<nil, nil>() -> q_gen_8676
<a, a>() -> q_gen_8677
<a, b>() -> q_gen_8677
<b, a>() -> q_gen_8677
<b, b>() -> q_gen_8677
<a, cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8672
<a, nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8672
<b, cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8672
<b, nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8672
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_8671, q_gen_8679, q_gen_8680},
Q_f={q_gen_8671},
Delta=
{
<nil>() -> q_gen_8679
<cons, s>(q_gen_8680, q_gen_8679) -> q_gen_8671
<nil, z>() -> q_gen_8671
<a, z>() -> q_gen_8680
<b, z>() -> q_gen_8680
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_8669, q_gen_8683},
Q_f={q_gen_8669},
Delta=
{
<a, a>() -> q_gen_8669
<a, b>() -> q_gen_8669
<b, b>() -> q_gen_8669
<b, a>() -> q_gen_8683
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_8668, q_gen_8682},
Q_f={q_gen_8668},
Delta=
{
<cons, cons>(q_gen_8682, q_gen_8668) -> q_gen_8668
<nil, nil>() -> q_gen_8668
<a, b>() -> q_gen_8682
<b, b>() -> q_gen_8682
}

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, _oha]) /\ not leq([x, y])) -> insert([x, cons(y, z), _oha]) -> 7
(insert([y, _tha, _uha]) /\ sort([z, _tha])) -> sort([cons(y, z), _uha]) -> 7
(length([_dia, _eia]) /\ length([l, _cia]) /\ sort([l, _dia])) -> eq_nat([_cia, _eia]) -> 6
(length([ll, _yha])) -> length([cons(x, ll), s(_yha)]) -> 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 -> a  ;  y -> a  ;  z -> cons(b, nil)
})

-------------------------------------------
Step 17, which took 0.027416 s (model generation: 0.026187,  model checking: 0.001229):

Model:
|_
{
insert -> 
{{{
Q={q_gen_8672, q_gen_8673, q_gen_8674, q_gen_8676, q_gen_8677},
Q_f={q_gen_8672},
Delta=
{
<nil>() -> q_gen_8673
<a>() -> q_gen_8674
<b>() -> q_gen_8674
<cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8676
<nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8676
<nil, nil>() -> q_gen_8676
<a, a>() -> q_gen_8677
<a, b>() -> q_gen_8677
<b, a>() -> q_gen_8677
<b, b>() -> q_gen_8677
<a, cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8672
<a, nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8672
<b, cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8672
<b, nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8672
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_8671, q_gen_8679, q_gen_8680},
Q_f={q_gen_8671},
Delta=
{
<nil>() -> q_gen_8679
<cons, s>(q_gen_8680, q_gen_8679) -> q_gen_8671
<nil, z>() -> q_gen_8671
<a, z>() -> q_gen_8680
<b, z>() -> q_gen_8680
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_8669, q_gen_8683},
Q_f={q_gen_8669},
Delta=
{
<a, a>() -> q_gen_8669
<a, b>() -> q_gen_8669
<b, b>() -> q_gen_8669
<b, a>() -> q_gen_8683
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_8668, q_gen_8682},
Q_f={q_gen_8668},
Delta=
{
<cons, cons>(q_gen_8682, q_gen_8668) -> q_gen_8668
<nil, nil>() -> q_gen_8668
<a, b>() -> q_gen_8682
<b, b>() -> q_gen_8682
}

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, _oha]) /\ not leq([x, y])) -> insert([x, cons(y, z), _oha]) -> 7
(insert([y, _tha, _uha]) /\ sort([z, _tha])) -> sort([cons(y, z), _uha]) -> 7
(length([_dia, _eia]) /\ length([l, _cia]) /\ sort([l, _dia])) -> eq_nat([_cia, _eia]) -> 7
(length([ll, _yha])) -> length([cons(x, ll), s(_yha)]) -> 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, _yha])) -> length([cons(x, ll), s(_yha)]), {
_yha -> s(z)  ;  ll -> cons(b, nil)  ;  x -> b
})

-------------------------------------------
Step 18, which took 0.028230 s (model generation: 0.027457,  model checking: 0.000773):

Model:
|_
{
insert -> 
{{{
Q={q_gen_8672, q_gen_8673, q_gen_8674, q_gen_8676, q_gen_8677},
Q_f={q_gen_8672},
Delta=
{
<nil>() -> q_gen_8673
<a>() -> q_gen_8674
<b>() -> q_gen_8674
<cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8676
<nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8676
<nil, nil>() -> q_gen_8676
<a, a>() -> q_gen_8677
<a, b>() -> q_gen_8677
<b, a>() -> q_gen_8677
<b, b>() -> q_gen_8677
<a, cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8672
<a, nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8672
<b, cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8672
<b, nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8672
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_8671, q_gen_8679, q_gen_8680, q_gen_8704, q_gen_8706},
Q_f={q_gen_8671},
Delta=
{
<cons>(q_gen_8704, q_gen_8679) -> q_gen_8679
<nil>() -> q_gen_8679
<b>() -> q_gen_8704
<z>() -> q_gen_8706
<cons, s>(q_gen_8680, q_gen_8679) -> q_gen_8671
<nil, z>() -> q_gen_8671
<a, z>() -> q_gen_8680
<b, s>(q_gen_8706) -> q_gen_8680
<b, z>() -> q_gen_8680
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_8669, q_gen_8683},
Q_f={q_gen_8669},
Delta=
{
<a, a>() -> q_gen_8669
<a, b>() -> q_gen_8669
<b, b>() -> q_gen_8669
<b, a>() -> q_gen_8683
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_8668, q_gen_8682},
Q_f={q_gen_8668},
Delta=
{
<cons, cons>(q_gen_8682, q_gen_8668) -> q_gen_8668
<nil, nil>() -> q_gen_8668
<a, b>() -> q_gen_8682
<b, b>() -> q_gen_8682
}

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, _oha]) /\ not leq([x, y])) -> insert([x, cons(y, z), _oha]) -> 7
(insert([y, _tha, _uha]) /\ sort([z, _tha])) -> sort([cons(y, z), _uha]) -> 7
(length([_dia, _eia]) /\ length([l, _cia]) /\ sort([l, _dia])) -> eq_nat([_cia, _eia]) -> 10
(length([ll, _yha])) -> length([cons(x, ll), s(_yha)]) -> 10
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 10
(leq([b, a])) -> BOT -> 8
}
Sat witness: Found: ((length([_dia, _eia]) /\ length([l, _cia]) /\ sort([l, _dia])) -> eq_nat([_cia, _eia]), {
_cia -> s(z)  ;  _dia -> cons(b, nil)  ;  _eia -> s(s(z))  ;  l -> cons(a, nil)
})

-------------------------------------------
Step 19, which took 0.029788 s (model generation: 0.029086,  model checking: 0.000702):

Model:
|_
{
insert -> 
{{{
Q={q_gen_8672, q_gen_8673, q_gen_8674, q_gen_8676, q_gen_8677},
Q_f={q_gen_8672},
Delta=
{
<nil>() -> q_gen_8673
<a>() -> q_gen_8674
<b>() -> q_gen_8674
<cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8676
<nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8676
<nil, nil>() -> q_gen_8676
<a, a>() -> q_gen_8677
<a, b>() -> q_gen_8677
<b, a>() -> q_gen_8677
<b, b>() -> q_gen_8677
<a, cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8672
<a, nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8672
<b, cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8672
<b, nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8672
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_8671, q_gen_8679, q_gen_8680, q_gen_8703, q_gen_8704, q_gen_8705, q_gen_8706, q_gen_8707},
Q_f={q_gen_8671},
Delta=
{
<nil>() -> q_gen_8679
<cons>(q_gen_8704, q_gen_8679) -> q_gen_8703
<b>() -> q_gen_8704
<z>() -> q_gen_8706
<cons, s>(q_gen_8680, q_gen_8679) -> q_gen_8671
<cons, s>(q_gen_8705, q_gen_8703) -> q_gen_8671
<nil, z>() -> q_gen_8671
<a, z>() -> q_gen_8680
<b, z>() -> q_gen_8680
<b, s>(q_gen_8706) -> q_gen_8705
<cons, s>(q_gen_8705, q_gen_8679) -> q_gen_8707
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_8669, q_gen_8683},
Q_f={q_gen_8669},
Delta=
{
<a, a>() -> q_gen_8669
<a, b>() -> q_gen_8669
<b, b>() -> q_gen_8669
<b, a>() -> q_gen_8683
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_8668, q_gen_8682},
Q_f={q_gen_8668},
Delta=
{
<cons, cons>(q_gen_8682, q_gen_8668) -> q_gen_8668
<nil, nil>() -> q_gen_8668
<a, b>() -> q_gen_8682
<b, b>() -> q_gen_8682
}

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, _oha]) /\ not leq([x, y])) -> insert([x, cons(y, z), _oha]) -> 7
(insert([y, _tha, _uha]) /\ sort([z, _tha])) -> sort([cons(y, z), _uha]) -> 10
(length([_dia, _eia]) /\ length([l, _cia]) /\ sort([l, _dia])) -> eq_nat([_cia, _eia]) -> 10
(length([ll, _yha])) -> length([cons(x, ll), s(_yha)]) -> 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, _tha, _uha]) /\ sort([z, _tha])) -> sort([cons(y, z), _uha]), {
_tha -> nil  ;  _uha -> cons(a, nil)  ;  y -> a  ;  z -> nil
})

-------------------------------------------
Step 20, which took 0.031614 s (model generation: 0.030654,  model checking: 0.000960):

Model:
|_
{
insert -> 
{{{
Q={q_gen_8672, q_gen_8673, q_gen_8674, q_gen_8676, q_gen_8677},
Q_f={q_gen_8672},
Delta=
{
<nil>() -> q_gen_8673
<a>() -> q_gen_8674
<b>() -> q_gen_8674
<cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8676
<nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8676
<nil, nil>() -> q_gen_8676
<a, a>() -> q_gen_8677
<a, b>() -> q_gen_8677
<b, a>() -> q_gen_8677
<b, b>() -> q_gen_8677
<a, cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8672
<a, nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8672
<b, cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8672
<b, nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8672
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_8671, q_gen_8679, q_gen_8680, q_gen_8703, q_gen_8704, q_gen_8705, q_gen_8706, q_gen_8707},
Q_f={q_gen_8671},
Delta=
{
<nil>() -> q_gen_8679
<cons>(q_gen_8704, q_gen_8679) -> q_gen_8703
<b>() -> q_gen_8704
<z>() -> q_gen_8706
<cons, s>(q_gen_8680, q_gen_8679) -> q_gen_8671
<cons, s>(q_gen_8705, q_gen_8703) -> q_gen_8671
<nil, z>() -> q_gen_8671
<a, z>() -> q_gen_8680
<b, z>() -> q_gen_8680
<b, s>(q_gen_8706) -> q_gen_8705
<cons, s>(q_gen_8705, q_gen_8679) -> q_gen_8707
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_8669, q_gen_8683},
Q_f={q_gen_8669},
Delta=
{
<a, a>() -> q_gen_8669
<a, b>() -> q_gen_8669
<b, b>() -> q_gen_8669
<b, a>() -> q_gen_8683
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_8668, q_gen_8682},
Q_f={q_gen_8668},
Delta=
{
<cons, cons>(q_gen_8682, q_gen_8668) -> q_gen_8668
<nil, nil>() -> q_gen_8668
<a, a>() -> q_gen_8682
<a, b>() -> q_gen_8682
<b, b>() -> q_gen_8682
}

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, _oha]) /\ not leq([x, y])) -> insert([x, cons(y, z), _oha]) -> 10
(insert([y, _tha, _uha]) /\ sort([z, _tha])) -> sort([cons(y, z), _uha]) -> 10
(length([_dia, _eia]) /\ length([l, _cia]) /\ sort([l, _dia])) -> eq_nat([_cia, _eia]) -> 10
(length([ll, _yha])) -> length([cons(x, ll), s(_yha)]) -> 10
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 10
(leq([b, a])) -> BOT -> 8
}
Sat witness: Found: ((insert([x, z, _oha]) /\ not leq([x, y])) -> insert([x, cons(y, z), _oha]), {
_oha -> cons(b, nil)  ;  x -> b  ;  y -> a  ;  z -> cons(a, nil)
})

-------------------------------------------
Step 21, which took 0.034793 s (model generation: 0.031237,  model checking: 0.003556):

Model:
|_
{
insert -> 
{{{
Q={q_gen_8672, q_gen_8673, q_gen_8674, q_gen_8676, q_gen_8677},
Q_f={q_gen_8672},
Delta=
{
<nil>() -> q_gen_8673
<a>() -> q_gen_8674
<b>() -> q_gen_8674
<cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8676
<cons, nil>(q_gen_8674, q_gen_8673) -> q_gen_8676
<nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8676
<nil, nil>() -> q_gen_8676
<a, a>() -> q_gen_8677
<a, b>() -> q_gen_8677
<b, a>() -> q_gen_8677
<b, b>() -> q_gen_8677
<a, cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8672
<a, nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8672
<b, cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8672
<b, nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8672
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_8671, q_gen_8679, q_gen_8680, q_gen_8703, q_gen_8704, q_gen_8705, q_gen_8706, q_gen_8707},
Q_f={q_gen_8671},
Delta=
{
<nil>() -> q_gen_8679
<cons>(q_gen_8704, q_gen_8679) -> q_gen_8703
<b>() -> q_gen_8704
<z>() -> q_gen_8706
<cons, s>(q_gen_8680, q_gen_8679) -> q_gen_8671
<cons, s>(q_gen_8705, q_gen_8703) -> q_gen_8671
<nil, z>() -> q_gen_8671
<a, z>() -> q_gen_8680
<b, z>() -> q_gen_8680
<b, s>(q_gen_8706) -> q_gen_8705
<cons, s>(q_gen_8705, q_gen_8679) -> q_gen_8707
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_8669, q_gen_8683},
Q_f={q_gen_8669},
Delta=
{
<a, a>() -> q_gen_8669
<a, b>() -> q_gen_8669
<b, b>() -> q_gen_8669
<b, a>() -> q_gen_8683
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_8668, q_gen_8682},
Q_f={q_gen_8668},
Delta=
{
<cons, cons>(q_gen_8682, q_gen_8668) -> q_gen_8668
<nil, nil>() -> q_gen_8668
<a, a>() -> q_gen_8682
<a, b>() -> q_gen_8682
<b, b>() -> q_gen_8682
}

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, _oha]) /\ not leq([x, y])) -> insert([x, cons(y, z), _oha]) -> 10
(insert([y, _tha, _uha]) /\ sort([z, _tha])) -> sort([cons(y, z), _uha]) -> 10
(length([_dia, _eia]) /\ length([l, _cia]) /\ sort([l, _dia])) -> eq_nat([_cia, _eia]) -> 10
(length([ll, _yha])) -> length([cons(x, ll), s(_yha)]) -> 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, _yha])) -> length([cons(x, ll), s(_yha)]), {
_yha -> s(z)  ;  ll -> cons(b, nil)  ;  x -> a
})

-------------------------------------------
Step 22, which took 0.036074 s (model generation: 0.033999,  model checking: 0.002075):

Model:
|_
{
insert -> 
{{{
Q={q_gen_8672, q_gen_8673, q_gen_8674, q_gen_8676, q_gen_8677},
Q_f={q_gen_8672},
Delta=
{
<nil>() -> q_gen_8673
<a>() -> q_gen_8674
<b>() -> q_gen_8674
<cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8676
<cons, nil>(q_gen_8674, q_gen_8673) -> q_gen_8676
<nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8676
<nil, nil>() -> q_gen_8676
<a, a>() -> q_gen_8677
<a, b>() -> q_gen_8677
<b, a>() -> q_gen_8677
<b, b>() -> q_gen_8677
<a, cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8672
<a, nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8672
<b, cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8672
<b, nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8672
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_8671, q_gen_8679, q_gen_8680, q_gen_8703, q_gen_8704, q_gen_8705, q_gen_8706, q_gen_8707},
Q_f={q_gen_8671},
Delta=
{
<nil>() -> q_gen_8679
<cons>(q_gen_8704, q_gen_8679) -> q_gen_8703
<b>() -> q_gen_8704
<z>() -> q_gen_8706
<cons, s>(q_gen_8680, q_gen_8679) -> q_gen_8671
<cons, s>(q_gen_8680, q_gen_8703) -> q_gen_8671
<cons, s>(q_gen_8705, q_gen_8703) -> q_gen_8671
<nil, z>() -> q_gen_8671
<a, s>(q_gen_8706) -> q_gen_8680
<a, z>() -> q_gen_8680
<b, z>() -> q_gen_8680
<b, s>(q_gen_8706) -> q_gen_8705
<cons, s>(q_gen_8705, q_gen_8679) -> q_gen_8707
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_8669, q_gen_8683},
Q_f={q_gen_8669},
Delta=
{
<a, a>() -> q_gen_8669
<a, b>() -> q_gen_8669
<b, b>() -> q_gen_8669
<b, a>() -> q_gen_8683
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_8668, q_gen_8682},
Q_f={q_gen_8668},
Delta=
{
<cons, cons>(q_gen_8682, q_gen_8668) -> q_gen_8668
<nil, nil>() -> q_gen_8668
<a, a>() -> q_gen_8682
<a, b>() -> q_gen_8682
<b, b>() -> q_gen_8682
}

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, _oha]) /\ not leq([x, y])) -> insert([x, cons(y, z), _oha]) -> 10
(insert([y, _tha, _uha]) /\ sort([z, _tha])) -> sort([cons(y, z), _uha]) -> 10
(length([_dia, _eia]) /\ length([l, _cia]) /\ sort([l, _dia])) -> eq_nat([_cia, _eia]) -> 13
(length([ll, _yha])) -> length([cons(x, ll), s(_yha)]) -> 13
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 11
(leq([b, a])) -> BOT -> 10
}
Sat witness: Found: ((length([_dia, _eia]) /\ length([l, _cia]) /\ sort([l, _dia])) -> eq_nat([_cia, _eia]), {
_cia -> s(z)  ;  _dia -> cons(a, nil)  ;  _eia -> s(s(z))  ;  l -> cons(a, nil)
})

-------------------------------------------
Step 23, which took 0.036352 s (model generation: 0.034732,  model checking: 0.001620):

Model:
|_
{
insert -> 
{{{
Q={q_gen_8672, q_gen_8673, q_gen_8674, q_gen_8676, q_gen_8677},
Q_f={q_gen_8672},
Delta=
{
<nil>() -> q_gen_8673
<a>() -> q_gen_8674
<b>() -> q_gen_8674
<cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8676
<cons, nil>(q_gen_8674, q_gen_8673) -> q_gen_8676
<nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8676
<nil, nil>() -> q_gen_8676
<a, a>() -> q_gen_8677
<a, b>() -> q_gen_8677
<b, a>() -> q_gen_8677
<b, b>() -> q_gen_8677
<a, cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8672
<a, nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8672
<b, cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8672
<b, nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8672
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_8671, q_gen_8679, q_gen_8680, q_gen_8703, q_gen_8704, q_gen_8705, q_gen_8706, q_gen_8707},
Q_f={q_gen_8671},
Delta=
{
<nil>() -> q_gen_8679
<cons>(q_gen_8704, q_gen_8679) -> q_gen_8703
<b>() -> q_gen_8704
<z>() -> q_gen_8706
<cons, s>(q_gen_8680, q_gen_8679) -> q_gen_8671
<cons, s>(q_gen_8705, q_gen_8703) -> q_gen_8671
<nil, z>() -> q_gen_8671
<a, z>() -> q_gen_8680
<b, z>() -> q_gen_8680
<a, s>(q_gen_8706) -> q_gen_8705
<b, s>(q_gen_8706) -> q_gen_8705
<cons, s>(q_gen_8705, q_gen_8679) -> q_gen_8707
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_8669, q_gen_8683},
Q_f={q_gen_8669},
Delta=
{
<a, a>() -> q_gen_8669
<a, b>() -> q_gen_8669
<b, b>() -> q_gen_8669
<b, a>() -> q_gen_8683
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_8668, q_gen_8682},
Q_f={q_gen_8668},
Delta=
{
<cons, cons>(q_gen_8682, q_gen_8668) -> q_gen_8668
<nil, nil>() -> q_gen_8668
<a, a>() -> q_gen_8682
<a, b>() -> q_gen_8682
<b, b>() -> q_gen_8682
}

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, _oha]) /\ not leq([x, y])) -> insert([x, cons(y, z), _oha]) -> 10
(insert([y, _tha, _uha]) /\ sort([z, _tha])) -> sort([cons(y, z), _uha]) -> 13
(length([_dia, _eia]) /\ length([l, _cia]) /\ sort([l, _dia])) -> eq_nat([_cia, _eia]) -> 13
(length([ll, _yha])) -> length([cons(x, ll), s(_yha)]) -> 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, _tha, _uha]) /\ sort([z, _tha])) -> sort([cons(y, z), _uha]), {
_tha -> nil  ;  _uha -> cons(a, nil)  ;  y -> b  ;  z -> nil
})

-------------------------------------------
Step 24, which took 0.036954 s (model generation: 0.035812,  model checking: 0.001142):

Model:
|_
{
insert -> 
{{{
Q={q_gen_8672, q_gen_8673, q_gen_8674, q_gen_8676, q_gen_8677},
Q_f={q_gen_8672},
Delta=
{
<nil>() -> q_gen_8673
<a>() -> q_gen_8674
<b>() -> q_gen_8674
<cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8676
<cons, nil>(q_gen_8674, q_gen_8673) -> q_gen_8676
<nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8676
<nil, nil>() -> q_gen_8676
<a, a>() -> q_gen_8677
<a, b>() -> q_gen_8677
<b, a>() -> q_gen_8677
<b, b>() -> q_gen_8677
<a, cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8672
<a, nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8672
<b, cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8672
<b, nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8672
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_8671, q_gen_8679, q_gen_8680, q_gen_8703, q_gen_8704, q_gen_8705, q_gen_8706, q_gen_8707},
Q_f={q_gen_8671},
Delta=
{
<nil>() -> q_gen_8679
<cons>(q_gen_8704, q_gen_8679) -> q_gen_8703
<b>() -> q_gen_8704
<z>() -> q_gen_8706
<cons, s>(q_gen_8680, q_gen_8679) -> q_gen_8671
<cons, s>(q_gen_8705, q_gen_8703) -> q_gen_8671
<nil, z>() -> q_gen_8671
<a, z>() -> q_gen_8680
<b, z>() -> q_gen_8680
<a, s>(q_gen_8706) -> q_gen_8705
<b, s>(q_gen_8706) -> q_gen_8705
<cons, s>(q_gen_8705, q_gen_8679) -> q_gen_8707
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_8669, q_gen_8683},
Q_f={q_gen_8669},
Delta=
{
<a, a>() -> q_gen_8669
<a, b>() -> q_gen_8669
<b, b>() -> q_gen_8669
<b, a>() -> q_gen_8683
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_8668, q_gen_8682},
Q_f={q_gen_8668},
Delta=
{
<cons, cons>(q_gen_8682, q_gen_8668) -> q_gen_8668
<nil, nil>() -> q_gen_8668
<a, a>() -> q_gen_8682
<a, b>() -> q_gen_8682
<b, a>() -> q_gen_8682
<b, b>() -> q_gen_8682
}

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, _oha]) /\ not leq([x, y])) -> insert([x, cons(y, z), _oha]) -> 13
(insert([y, _tha, _uha]) /\ sort([z, _tha])) -> sort([cons(y, z), _uha]) -> 13
(length([_dia, _eia]) /\ length([l, _cia]) /\ sort([l, _dia])) -> eq_nat([_cia, _eia]) -> 13
(length([ll, _yha])) -> length([cons(x, ll), s(_yha)]) -> 13
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 11
(leq([b, a])) -> BOT -> 11
}
Sat witness: Found: ((insert([x, z, _oha]) /\ not leq([x, y])) -> insert([x, cons(y, z), _oha]), {
_oha -> cons(a, nil)  ;  x -> b  ;  y -> a  ;  z -> cons(b, cons(b, nil))
})

-------------------------------------------
Step 25, which took 0.044128 s (model generation: 0.040909,  model checking: 0.003219):

Model:
|_
{
insert -> 
{{{
Q={q_gen_8672, q_gen_8673, q_gen_8674, q_gen_8676, q_gen_8677},
Q_f={q_gen_8672},
Delta=
{
<cons>(q_gen_8674, q_gen_8673) -> q_gen_8673
<nil>() -> q_gen_8673
<a>() -> q_gen_8674
<b>() -> q_gen_8674
<cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8676
<cons, nil>(q_gen_8674, q_gen_8673) -> q_gen_8676
<nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8676
<nil, nil>() -> q_gen_8676
<a, a>() -> q_gen_8677
<a, b>() -> q_gen_8677
<b, a>() -> q_gen_8677
<b, b>() -> q_gen_8677
<a, cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8672
<a, nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8672
<b, cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8672
<b, nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8672
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_8671, q_gen_8679, q_gen_8680, q_gen_8703, q_gen_8704, q_gen_8705, q_gen_8706, q_gen_8707},
Q_f={q_gen_8671},
Delta=
{
<nil>() -> q_gen_8679
<cons>(q_gen_8704, q_gen_8679) -> q_gen_8703
<b>() -> q_gen_8704
<z>() -> q_gen_8706
<cons, s>(q_gen_8680, q_gen_8679) -> q_gen_8671
<cons, s>(q_gen_8705, q_gen_8703) -> q_gen_8671
<nil, z>() -> q_gen_8671
<a, z>() -> q_gen_8680
<b, z>() -> q_gen_8680
<a, s>(q_gen_8706) -> q_gen_8705
<b, s>(q_gen_8706) -> q_gen_8705
<cons, s>(q_gen_8705, q_gen_8679) -> q_gen_8707
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_8669, q_gen_8683},
Q_f={q_gen_8669},
Delta=
{
<a, a>() -> q_gen_8669
<a, b>() -> q_gen_8669
<b, b>() -> q_gen_8669
<b, a>() -> q_gen_8683
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_8668, q_gen_8682},
Q_f={q_gen_8668},
Delta=
{
<cons, cons>(q_gen_8682, q_gen_8668) -> q_gen_8668
<nil, nil>() -> q_gen_8668
<a, a>() -> q_gen_8682
<a, b>() -> q_gen_8682
<b, a>() -> q_gen_8682
<b, b>() -> q_gen_8682
}

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, _oha]) /\ not leq([x, y])) -> insert([x, cons(y, z), _oha]) -> 13
(insert([y, _tha, _uha]) /\ sort([z, _tha])) -> sort([cons(y, z), _uha]) -> 13
(length([_dia, _eia]) /\ length([l, _cia]) /\ sort([l, _dia])) -> eq_nat([_cia, _eia]) -> 13
(length([ll, _yha])) -> length([cons(x, ll), s(_yha)]) -> 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, _yha])) -> length([cons(x, ll), s(_yha)]), {
_yha -> s(s(z))  ;  ll -> cons(b, cons(b, nil))  ;  x -> b
})

-------------------------------------------
Step 26, which took 0.045058 s (model generation: 0.043122,  model checking: 0.001936):

Model:
|_
{
insert -> 
{{{
Q={q_gen_8672, q_gen_8673, q_gen_8674, q_gen_8676, q_gen_8677},
Q_f={q_gen_8672},
Delta=
{
<cons>(q_gen_8674, q_gen_8673) -> q_gen_8673
<nil>() -> q_gen_8673
<a>() -> q_gen_8674
<b>() -> q_gen_8674
<cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8676
<cons, nil>(q_gen_8674, q_gen_8673) -> q_gen_8676
<nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8676
<nil, nil>() -> q_gen_8676
<a, a>() -> q_gen_8677
<a, b>() -> q_gen_8677
<b, a>() -> q_gen_8677
<b, b>() -> q_gen_8677
<a, cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8672
<a, nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8672
<b, cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8672
<b, nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8672
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_8671, q_gen_8679, q_gen_8680, q_gen_8703, q_gen_8704, q_gen_8705, q_gen_8706, q_gen_8707},
Q_f={q_gen_8671},
Delta=
{
<nil>() -> q_gen_8679
<cons>(q_gen_8704, q_gen_8679) -> q_gen_8703
<cons>(q_gen_8704, q_gen_8703) -> q_gen_8703
<b>() -> q_gen_8704
<s>(q_gen_8706) -> q_gen_8706
<z>() -> q_gen_8706
<cons, s>(q_gen_8680, q_gen_8679) -> q_gen_8671
<cons, s>(q_gen_8705, q_gen_8703) -> q_gen_8671
<nil, z>() -> q_gen_8671
<a, z>() -> q_gen_8680
<b, z>() -> q_gen_8680
<a, s>(q_gen_8706) -> q_gen_8705
<b, s>(q_gen_8706) -> q_gen_8705
<cons, s>(q_gen_8705, q_gen_8679) -> q_gen_8707
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_8669, q_gen_8683},
Q_f={q_gen_8669},
Delta=
{
<a, a>() -> q_gen_8669
<a, b>() -> q_gen_8669
<b, b>() -> q_gen_8669
<b, a>() -> q_gen_8683
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_8668, q_gen_8682},
Q_f={q_gen_8668},
Delta=
{
<cons, cons>(q_gen_8682, q_gen_8668) -> q_gen_8668
<nil, nil>() -> q_gen_8668
<a, a>() -> q_gen_8682
<a, b>() -> q_gen_8682
<b, a>() -> q_gen_8682
<b, b>() -> q_gen_8682
}

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, _oha]) /\ not leq([x, y])) -> insert([x, cons(y, z), _oha]) -> 13
(insert([y, _tha, _uha]) /\ sort([z, _tha])) -> sort([cons(y, z), _uha]) -> 13
(length([_dia, _eia]) /\ length([l, _cia]) /\ sort([l, _dia])) -> eq_nat([_cia, _eia]) -> 16
(length([ll, _yha])) -> length([cons(x, ll), s(_yha)]) -> 16
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 13
(leq([b, a])) -> BOT -> 13
}
Sat witness: Found: ((length([_dia, _eia]) /\ length([l, _cia]) /\ sort([l, _dia])) -> eq_nat([_cia, _eia]), {
_cia -> s(s(z))  ;  _dia -> cons(a, cons(b, nil))  ;  _eia -> s(s(s(z)))  ;  l -> cons(a, cons(b, nil))
})

-------------------------------------------
Step 27, which took 0.048401 s (model generation: 0.046840,  model checking: 0.001561):

Model:
|_
{
insert -> 
{{{
Q={q_gen_8672, q_gen_8673, q_gen_8674, q_gen_8676, q_gen_8677},
Q_f={q_gen_8672},
Delta=
{
<cons>(q_gen_8674, q_gen_8673) -> q_gen_8673
<nil>() -> q_gen_8673
<a>() -> q_gen_8674
<b>() -> q_gen_8674
<cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8676
<cons, nil>(q_gen_8674, q_gen_8673) -> q_gen_8676
<nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8676
<nil, nil>() -> q_gen_8676
<a, a>() -> q_gen_8677
<a, b>() -> q_gen_8677
<b, a>() -> q_gen_8677
<b, b>() -> q_gen_8677
<a, cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8672
<a, nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8672
<b, cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8672
<b, nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8672
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_8671, q_gen_8679, q_gen_8680, q_gen_8703, q_gen_8704, q_gen_8705, q_gen_8706, q_gen_8707, q_gen_8725},
Q_f={q_gen_8671},
Delta=
{
<nil>() -> q_gen_8679
<cons>(q_gen_8704, q_gen_8679) -> q_gen_8703
<cons>(q_gen_8704, q_gen_8703) -> q_gen_8703
<b>() -> q_gen_8704
<z>() -> q_gen_8706
<s>(q_gen_8706) -> q_gen_8725
<cons, s>(q_gen_8680, q_gen_8679) -> q_gen_8671
<cons, s>(q_gen_8705, q_gen_8703) -> q_gen_8671
<nil, z>() -> q_gen_8671
<a, s>(q_gen_8725) -> q_gen_8680
<a, z>() -> q_gen_8680
<b, z>() -> q_gen_8680
<a, s>(q_gen_8706) -> q_gen_8705
<b, s>(q_gen_8706) -> q_gen_8705
<b, s>(q_gen_8725) -> q_gen_8705
<cons, s>(q_gen_8680, q_gen_8703) -> q_gen_8707
<cons, s>(q_gen_8705, q_gen_8679) -> q_gen_8707
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_8669, q_gen_8683},
Q_f={q_gen_8669},
Delta=
{
<a, a>() -> q_gen_8669
<a, b>() -> q_gen_8669
<b, b>() -> q_gen_8669
<b, a>() -> q_gen_8683
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_8668, q_gen_8682},
Q_f={q_gen_8668},
Delta=
{
<cons, cons>(q_gen_8682, q_gen_8668) -> q_gen_8668
<nil, nil>() -> q_gen_8668
<a, a>() -> q_gen_8682
<a, b>() -> q_gen_8682
<b, a>() -> q_gen_8682
<b, b>() -> q_gen_8682
}

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, _oha]) /\ not leq([x, y])) -> insert([x, cons(y, z), _oha]) -> 13
(insert([y, _tha, _uha]) /\ sort([z, _tha])) -> sort([cons(y, z), _uha]) -> 16
(length([_dia, _eia]) /\ length([l, _cia]) /\ sort([l, _dia])) -> eq_nat([_cia, _eia]) -> 16
(length([ll, _yha])) -> length([cons(x, ll), s(_yha)]) -> 16
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 14
(leq([b, a])) -> BOT -> 14
}
Sat witness: Found: ((insert([y, _tha, _uha]) /\ sort([z, _tha])) -> sort([cons(y, z), _uha]), {
_tha -> nil  ;  _uha -> cons(b, cons(b, nil))  ;  y -> a  ;  z -> nil
})

-------------------------------------------
Step 28, which took 0.055865 s (model generation: 0.053090,  model checking: 0.002775):

Model:
|_
{
insert -> 
{{{
Q={q_gen_8672, q_gen_8673, q_gen_8674, q_gen_8676, q_gen_8677},
Q_f={q_gen_8672},
Delta=
{
<cons>(q_gen_8674, q_gen_8673) -> q_gen_8673
<nil>() -> q_gen_8673
<a>() -> q_gen_8674
<b>() -> q_gen_8674
<cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8676
<cons, nil>(q_gen_8674, q_gen_8673) -> q_gen_8676
<nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8676
<nil, nil>() -> q_gen_8676
<a, a>() -> q_gen_8677
<a, b>() -> q_gen_8677
<b, a>() -> q_gen_8677
<b, b>() -> q_gen_8677
<a, cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8672
<a, nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8672
<b, cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8672
<b, nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8672
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_8671, q_gen_8679, q_gen_8680, q_gen_8703, q_gen_8704, q_gen_8705, q_gen_8706, q_gen_8707, q_gen_8725},
Q_f={q_gen_8671},
Delta=
{
<nil>() -> q_gen_8679
<cons>(q_gen_8704, q_gen_8679) -> q_gen_8703
<cons>(q_gen_8704, q_gen_8703) -> q_gen_8703
<b>() -> q_gen_8704
<z>() -> q_gen_8706
<s>(q_gen_8706) -> q_gen_8725
<cons, s>(q_gen_8680, q_gen_8679) -> q_gen_8671
<cons, s>(q_gen_8705, q_gen_8703) -> q_gen_8671
<nil, z>() -> q_gen_8671
<a, s>(q_gen_8725) -> q_gen_8680
<a, z>() -> q_gen_8680
<b, z>() -> q_gen_8680
<a, s>(q_gen_8706) -> q_gen_8705
<b, s>(q_gen_8706) -> q_gen_8705
<b, s>(q_gen_8725) -> q_gen_8705
<cons, s>(q_gen_8680, q_gen_8703) -> q_gen_8707
<cons, s>(q_gen_8705, q_gen_8679) -> q_gen_8707
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_8669, q_gen_8683},
Q_f={q_gen_8669},
Delta=
{
<a, a>() -> q_gen_8669
<a, b>() -> q_gen_8669
<b, b>() -> q_gen_8669
<b, a>() -> q_gen_8683
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_8668, q_gen_8682, q_gen_8732, q_gen_8733},
Q_f={q_gen_8668},
Delta=
{
<nil>() -> q_gen_8732
<b>() -> q_gen_8733
<cons, cons>(q_gen_8682, q_gen_8668) -> q_gen_8668
<nil, cons>(q_gen_8733, q_gen_8732) -> q_gen_8668
<nil, nil>() -> q_gen_8668
<a, a>() -> q_gen_8682
<a, b>() -> q_gen_8682
<b, a>() -> q_gen_8682
<b, b>() -> q_gen_8682
}

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, _oha]) /\ not leq([x, y])) -> insert([x, cons(y, z), _oha]) -> 14
(insert([y, _tha, _uha]) /\ sort([z, _tha])) -> sort([cons(y, z), _uha]) -> 16
(length([_dia, _eia]) /\ length([l, _cia]) /\ sort([l, _dia])) -> eq_nat([_cia, _eia]) -> 16
(length([ll, _yha])) -> length([cons(x, ll), s(_yha)]) -> 19
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 15
(leq([b, a])) -> BOT -> 15
}
Sat witness: Found: ((length([ll, _yha])) -> length([cons(x, ll), s(_yha)]), {
_yha -> s(s(z))  ;  ll -> cons(b, cons(b, nil))  ;  x -> a
})

-------------------------------------------
Step 29, which took 0.057377 s (model generation: 0.055016,  model checking: 0.002361):

Model:
|_
{
insert -> 
{{{
Q={q_gen_8672, q_gen_8673, q_gen_8674, q_gen_8676, q_gen_8677},
Q_f={q_gen_8672},
Delta=
{
<cons>(q_gen_8674, q_gen_8673) -> q_gen_8673
<nil>() -> q_gen_8673
<a>() -> q_gen_8674
<b>() -> q_gen_8674
<cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8676
<cons, nil>(q_gen_8674, q_gen_8673) -> q_gen_8676
<nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8676
<nil, nil>() -> q_gen_8676
<a, a>() -> q_gen_8677
<a, b>() -> q_gen_8677
<b, a>() -> q_gen_8677
<b, b>() -> q_gen_8677
<a, cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8672
<a, nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8672
<b, cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8672
<b, nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8672
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_8671, q_gen_8679, q_gen_8680, q_gen_8703, q_gen_8704, q_gen_8705, q_gen_8706, q_gen_8707, q_gen_8725},
Q_f={q_gen_8671},
Delta=
{
<cons>(q_gen_8704, q_gen_8703) -> q_gen_8679
<nil>() -> q_gen_8679
<cons>(q_gen_8704, q_gen_8679) -> q_gen_8703
<b>() -> q_gen_8704
<z>() -> q_gen_8706
<s>(q_gen_8706) -> q_gen_8725
<cons, s>(q_gen_8680, q_gen_8679) -> q_gen_8671
<cons, s>(q_gen_8705, q_gen_8703) -> q_gen_8671
<nil, z>() -> q_gen_8671
<a, s>(q_gen_8725) -> q_gen_8680
<a, z>() -> q_gen_8680
<b, s>(q_gen_8725) -> q_gen_8680
<b, z>() -> q_gen_8680
<a, s>(q_gen_8706) -> q_gen_8705
<b, s>(q_gen_8706) -> q_gen_8705
<cons, s>(q_gen_8680, q_gen_8703) -> q_gen_8707
<cons, s>(q_gen_8705, q_gen_8679) -> q_gen_8707
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_8669, q_gen_8683},
Q_f={q_gen_8669},
Delta=
{
<a, a>() -> q_gen_8669
<a, b>() -> q_gen_8669
<b, b>() -> q_gen_8669
<b, a>() -> q_gen_8683
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_8668, q_gen_8682, q_gen_8732, q_gen_8733},
Q_f={q_gen_8668},
Delta=
{
<nil>() -> q_gen_8732
<b>() -> q_gen_8733
<cons, cons>(q_gen_8682, q_gen_8668) -> q_gen_8668
<nil, cons>(q_gen_8733, q_gen_8732) -> q_gen_8668
<nil, nil>() -> q_gen_8668
<a, a>() -> q_gen_8682
<a, b>() -> q_gen_8682
<b, a>() -> q_gen_8682
<b, b>() -> q_gen_8682
}

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, _oha]) /\ not leq([x, y])) -> insert([x, cons(y, z), _oha]) -> 15
(insert([y, _tha, _uha]) /\ sort([z, _tha])) -> sort([cons(y, z), _uha]) -> 16
(length([_dia, _eia]) /\ length([l, _cia]) /\ sort([l, _dia])) -> eq_nat([_cia, _eia]) -> 19
(length([ll, _yha])) -> length([cons(x, ll), s(_yha)]) -> 19
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 16
(leq([b, a])) -> BOT -> 16
}
Sat witness: Found: ((length([_dia, _eia]) /\ length([l, _cia]) /\ sort([l, _dia])) -> eq_nat([_cia, _eia]), {
_cia -> z  ;  _dia -> cons(b, nil)  ;  _eia -> s(z)  ;  l -> nil
})

-------------------------------------------
Step 30, which took 0.057411 s (model generation: 0.054735,  model checking: 0.002676):

Model:
|_
{
insert -> 
{{{
Q={q_gen_8672, q_gen_8673, q_gen_8674, q_gen_8676, q_gen_8677},
Q_f={q_gen_8672},
Delta=
{
<cons>(q_gen_8674, q_gen_8673) -> q_gen_8673
<nil>() -> q_gen_8673
<a>() -> q_gen_8674
<b>() -> q_gen_8674
<cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8676
<cons, nil>(q_gen_8674, q_gen_8673) -> q_gen_8676
<nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8676
<nil, nil>() -> q_gen_8676
<a, a>() -> q_gen_8677
<a, b>() -> q_gen_8677
<b, a>() -> q_gen_8677
<b, b>() -> q_gen_8677
<a, cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8672
<a, nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8672
<b, cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8672
<b, nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8672
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_8671, q_gen_8679, q_gen_8680, q_gen_8703, q_gen_8704, q_gen_8705, q_gen_8706, q_gen_8707, q_gen_8725},
Q_f={q_gen_8671},
Delta=
{
<cons>(q_gen_8704, q_gen_8703) -> q_gen_8679
<nil>() -> q_gen_8679
<cons>(q_gen_8704, q_gen_8679) -> q_gen_8703
<b>() -> q_gen_8704
<z>() -> q_gen_8706
<s>(q_gen_8706) -> q_gen_8725
<cons, s>(q_gen_8680, q_gen_8679) -> q_gen_8671
<cons, s>(q_gen_8705, q_gen_8703) -> q_gen_8671
<nil, z>() -> q_gen_8671
<a, s>(q_gen_8725) -> q_gen_8680
<a, z>() -> q_gen_8680
<b, s>(q_gen_8725) -> q_gen_8680
<b, z>() -> q_gen_8680
<a, s>(q_gen_8706) -> q_gen_8705
<b, s>(q_gen_8706) -> q_gen_8705
<cons, s>(q_gen_8680, q_gen_8703) -> q_gen_8707
<cons, s>(q_gen_8705, q_gen_8679) -> q_gen_8707
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_8669, q_gen_8683},
Q_f={q_gen_8669},
Delta=
{
<a, a>() -> q_gen_8669
<a, b>() -> q_gen_8669
<b, b>() -> q_gen_8669
<b, a>() -> q_gen_8683
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_8668, q_gen_8682, q_gen_8731, q_gen_8732, q_gen_8733},
Q_f={q_gen_8668},
Delta=
{
<nil>() -> q_gen_8732
<b>() -> q_gen_8733
<cons, cons>(q_gen_8682, q_gen_8668) -> q_gen_8668
<cons, cons>(q_gen_8682, q_gen_8731) -> q_gen_8668
<nil, nil>() -> q_gen_8668
<a, a>() -> q_gen_8682
<a, b>() -> q_gen_8682
<b, a>() -> q_gen_8682
<b, b>() -> q_gen_8682
<nil, cons>(q_gen_8733, q_gen_8732) -> q_gen_8731
}

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, _oha]) /\ not leq([x, y])) -> insert([x, cons(y, z), _oha]) -> 16
(insert([y, _tha, _uha]) /\ sort([z, _tha])) -> sort([cons(y, z), _uha]) -> 19
(length([_dia, _eia]) /\ length([l, _cia]) /\ sort([l, _dia])) -> eq_nat([_cia, _eia]) -> 19
(length([ll, _yha])) -> length([cons(x, ll), s(_yha)]) -> 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, _tha, _uha]) /\ sort([z, _tha])) -> sort([cons(y, z), _uha]), {
_tha -> nil  ;  _uha -> cons(b, cons(a, cons(a, nil)))  ;  y -> a  ;  z -> nil
})

-------------------------------------------
Step 31, which took 0.065249 s (model generation: 0.061083,  model checking: 0.004166):

Model:
|_
{
insert -> 
{{{
Q={q_gen_8672, q_gen_8673, q_gen_8674, q_gen_8676, q_gen_8677},
Q_f={q_gen_8672},
Delta=
{
<cons>(q_gen_8674, q_gen_8673) -> q_gen_8673
<nil>() -> q_gen_8673
<a>() -> q_gen_8674
<b>() -> q_gen_8674
<cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8676
<cons, nil>(q_gen_8674, q_gen_8673) -> q_gen_8676
<nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8676
<nil, nil>() -> q_gen_8676
<a, a>() -> q_gen_8677
<a, b>() -> q_gen_8677
<b, a>() -> q_gen_8677
<b, b>() -> q_gen_8677
<a, cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8672
<a, nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8672
<b, cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8672
<b, nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8672
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_8671, q_gen_8679, q_gen_8680, q_gen_8703, q_gen_8704, q_gen_8705, q_gen_8706, q_gen_8707},
Q_f={q_gen_8671},
Delta=
{
<nil>() -> q_gen_8679
<cons>(q_gen_8704, q_gen_8679) -> q_gen_8703
<cons>(q_gen_8704, q_gen_8703) -> q_gen_8703
<b>() -> q_gen_8704
<s>(q_gen_8706) -> q_gen_8706
<z>() -> q_gen_8706
<cons, s>(q_gen_8680, q_gen_8679) -> q_gen_8671
<cons, s>(q_gen_8705, q_gen_8703) -> q_gen_8671
<nil, z>() -> q_gen_8671
<a, z>() -> q_gen_8680
<b, z>() -> q_gen_8680
<a, s>(q_gen_8706) -> q_gen_8705
<b, s>(q_gen_8706) -> q_gen_8705
<cons, s>(q_gen_8705, q_gen_8679) -> q_gen_8707
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_8669, q_gen_8683},
Q_f={q_gen_8669},
Delta=
{
<a, a>() -> q_gen_8669
<a, b>() -> q_gen_8669
<b, b>() -> q_gen_8669
<b, a>() -> q_gen_8683
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_8668, q_gen_8681, q_gen_8682, q_gen_8728, q_gen_8732, q_gen_8733},
Q_f={q_gen_8668, q_gen_8681},
Delta=
{
<cons>(q_gen_8733, q_gen_8732) -> q_gen_8732
<nil>() -> q_gen_8732
<a>() -> q_gen_8733
<b>() -> q_gen_8733
<cons, cons>(q_gen_8682, q_gen_8728) -> q_gen_8668
<nil, nil>() -> q_gen_8668
<cons, cons>(q_gen_8682, q_gen_8668) -> q_gen_8681
<a, a>() -> q_gen_8682
<a, b>() -> q_gen_8682
<b, a>() -> q_gen_8682
<b, b>() -> q_gen_8682
<cons, cons>(q_gen_8682, q_gen_8681) -> q_gen_8728
<nil, cons>(q_gen_8733, q_gen_8732) -> q_gen_8728
}

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, _oha]) /\ not leq([x, y])) -> insert([x, cons(y, z), _oha]) -> 17
(insert([y, _tha, _uha]) /\ sort([z, _tha])) -> sort([cons(y, z), _uha]) -> 19
(length([_dia, _eia]) /\ length([l, _cia]) /\ sort([l, _dia])) -> eq_nat([_cia, _eia]) -> 19
(length([ll, _yha])) -> length([cons(x, ll), s(_yha)]) -> 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, _yha])) -> length([cons(x, ll), s(_yha)]), {
_yha -> s(z)  ;  ll -> cons(a, nil)  ;  x -> b
})

-------------------------------------------
Step 32, which took 0.068348 s (model generation: 0.065098,  model checking: 0.003250):

Model:
|_
{
insert -> 
{{{
Q={q_gen_8672, q_gen_8673, q_gen_8674, q_gen_8676, q_gen_8677},
Q_f={q_gen_8672},
Delta=
{
<cons>(q_gen_8674, q_gen_8673) -> q_gen_8673
<nil>() -> q_gen_8673
<a>() -> q_gen_8674
<b>() -> q_gen_8674
<cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8676
<cons, nil>(q_gen_8674, q_gen_8673) -> q_gen_8676
<nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8676
<nil, nil>() -> q_gen_8676
<a, a>() -> q_gen_8677
<a, b>() -> q_gen_8677
<b, a>() -> q_gen_8677
<b, b>() -> q_gen_8677
<a, cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8672
<a, nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8672
<b, cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8672
<b, nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8672
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_8671, q_gen_8679, q_gen_8680, q_gen_8703, q_gen_8704, q_gen_8705, q_gen_8706, q_gen_8707},
Q_f={q_gen_8671},
Delta=
{
<nil>() -> q_gen_8679
<cons>(q_gen_8704, q_gen_8679) -> q_gen_8703
<cons>(q_gen_8704, q_gen_8703) -> q_gen_8703
<a>() -> q_gen_8704
<b>() -> q_gen_8704
<s>(q_gen_8706) -> q_gen_8706
<z>() -> q_gen_8706
<cons, s>(q_gen_8680, q_gen_8679) -> q_gen_8671
<cons, s>(q_gen_8705, q_gen_8703) -> q_gen_8671
<nil, z>() -> q_gen_8671
<a, z>() -> q_gen_8680
<b, z>() -> q_gen_8680
<a, s>(q_gen_8706) -> q_gen_8705
<b, s>(q_gen_8706) -> q_gen_8705
<cons, s>(q_gen_8705, q_gen_8679) -> q_gen_8707
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_8669, q_gen_8683},
Q_f={q_gen_8669},
Delta=
{
<a, a>() -> q_gen_8669
<a, b>() -> q_gen_8669
<b, b>() -> q_gen_8669
<b, a>() -> q_gen_8683
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_8668, q_gen_8681, q_gen_8682, q_gen_8728, q_gen_8732, q_gen_8733},
Q_f={q_gen_8668, q_gen_8681},
Delta=
{
<cons>(q_gen_8733, q_gen_8732) -> q_gen_8732
<nil>() -> q_gen_8732
<a>() -> q_gen_8733
<b>() -> q_gen_8733
<cons, cons>(q_gen_8682, q_gen_8728) -> q_gen_8668
<nil, nil>() -> q_gen_8668
<cons, cons>(q_gen_8682, q_gen_8668) -> q_gen_8681
<a, a>() -> q_gen_8682
<a, b>() -> q_gen_8682
<b, a>() -> q_gen_8682
<b, b>() -> q_gen_8682
<cons, cons>(q_gen_8682, q_gen_8681) -> q_gen_8728
<nil, cons>(q_gen_8733, q_gen_8732) -> q_gen_8728
}

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, _oha]) /\ not leq([x, y])) -> insert([x, cons(y, z), _oha]) -> 18
(insert([y, _tha, _uha]) /\ sort([z, _tha])) -> sort([cons(y, z), _uha]) -> 19
(length([_dia, _eia]) /\ length([l, _cia]) /\ sort([l, _dia])) -> eq_nat([_cia, _eia]) -> 22
(length([ll, _yha])) -> length([cons(x, ll), s(_yha)]) -> 22
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 19
(leq([b, a])) -> BOT -> 19
}
Sat witness: Found: ((length([_dia, _eia]) /\ length([l, _cia]) /\ sort([l, _dia])) -> eq_nat([_cia, _eia]), {
_cia -> s(s(z))  ;  _dia -> cons(a, cons(b, cons(b, nil)))  ;  _eia -> s(s(s(z)))  ;  l -> cons(b, cons(b, nil))
})

-------------------------------------------
Step 33, which took 0.074092 s (model generation: 0.070468,  model checking: 0.003624):

Model:
|_
{
insert -> 
{{{
Q={q_gen_8672, q_gen_8673, q_gen_8674, q_gen_8676, q_gen_8677},
Q_f={q_gen_8672},
Delta=
{
<cons>(q_gen_8674, q_gen_8673) -> q_gen_8673
<nil>() -> q_gen_8673
<a>() -> q_gen_8674
<b>() -> q_gen_8674
<cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8676
<cons, nil>(q_gen_8674, q_gen_8673) -> q_gen_8676
<nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8676
<nil, nil>() -> q_gen_8676
<a, a>() -> q_gen_8677
<a, b>() -> q_gen_8677
<b, a>() -> q_gen_8677
<b, b>() -> q_gen_8677
<a, cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8672
<a, nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8672
<b, cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8672
<b, nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8672
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_8671, q_gen_8679, q_gen_8680, q_gen_8703, q_gen_8704, q_gen_8705, q_gen_8706, q_gen_8707},
Q_f={q_gen_8671},
Delta=
{
<nil>() -> q_gen_8679
<cons>(q_gen_8704, q_gen_8679) -> q_gen_8703
<cons>(q_gen_8704, q_gen_8703) -> q_gen_8703
<a>() -> q_gen_8704
<b>() -> q_gen_8704
<s>(q_gen_8706) -> q_gen_8706
<z>() -> q_gen_8706
<cons, s>(q_gen_8680, q_gen_8679) -> q_gen_8671
<cons, s>(q_gen_8705, q_gen_8703) -> q_gen_8671
<nil, z>() -> q_gen_8671
<a, z>() -> q_gen_8680
<b, z>() -> q_gen_8680
<a, s>(q_gen_8706) -> q_gen_8705
<b, s>(q_gen_8706) -> q_gen_8705
<cons, s>(q_gen_8705, q_gen_8679) -> q_gen_8707
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_8669, q_gen_8683},
Q_f={q_gen_8669},
Delta=
{
<a, a>() -> q_gen_8669
<a, b>() -> q_gen_8669
<b, b>() -> q_gen_8669
<b, a>() -> q_gen_8683
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_8668, q_gen_8681, q_gen_8682, q_gen_8728, q_gen_8732, q_gen_8733},
Q_f={q_gen_8668, q_gen_8681},
Delta=
{
<cons>(q_gen_8733, q_gen_8732) -> q_gen_8732
<nil>() -> q_gen_8732
<a>() -> q_gen_8733
<b>() -> q_gen_8733
<nil, nil>() -> q_gen_8668
<cons, cons>(q_gen_8682, q_gen_8668) -> q_gen_8681
<cons, cons>(q_gen_8682, q_gen_8728) -> q_gen_8681
<a, a>() -> q_gen_8682
<a, b>() -> q_gen_8682
<b, a>() -> q_gen_8682
<b, b>() -> q_gen_8682
<cons, cons>(q_gen_8682, q_gen_8681) -> q_gen_8728
<nil, cons>(q_gen_8733, q_gen_8732) -> q_gen_8728
}

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, _oha]) /\ not leq([x, y])) -> insert([x, cons(y, z), _oha]) -> 19
(insert([y, _tha, _uha]) /\ sort([z, _tha])) -> sort([cons(y, z), _uha]) -> 22
(length([_dia, _eia]) /\ length([l, _cia]) /\ sort([l, _dia])) -> eq_nat([_cia, _eia]) -> 22
(length([ll, _yha])) -> length([cons(x, ll), s(_yha)]) -> 22
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 20
(leq([b, a])) -> BOT -> 20
}
Sat witness: Found: ((insert([y, _tha, _uha]) /\ sort([z, _tha])) -> sort([cons(y, z), _uha]), {
_tha -> cons(b, nil)  ;  _uha -> cons(b, cons(b, nil))  ;  y -> a  ;  z -> cons(a, nil)
})

-------------------------------------------
Step 34, which took 0.085954 s (model generation: 0.082347,  model checking: 0.003607):

Model:
|_
{
insert -> 
{{{
Q={q_gen_8672, q_gen_8673, q_gen_8674, q_gen_8676, q_gen_8677},
Q_f={q_gen_8672},
Delta=
{
<cons>(q_gen_8674, q_gen_8673) -> q_gen_8673
<nil>() -> q_gen_8673
<a>() -> q_gen_8674
<b>() -> q_gen_8674
<cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8676
<cons, nil>(q_gen_8674, q_gen_8673) -> q_gen_8676
<nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8676
<nil, nil>() -> q_gen_8676
<a, a>() -> q_gen_8677
<a, b>() -> q_gen_8677
<b, a>() -> q_gen_8677
<b, b>() -> q_gen_8677
<a, cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8672
<a, nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8672
<b, cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8672
<b, nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8672
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_8671, q_gen_8679, q_gen_8680, q_gen_8703, q_gen_8704, q_gen_8705, q_gen_8706, q_gen_8707},
Q_f={q_gen_8671},
Delta=
{
<nil>() -> q_gen_8679
<cons>(q_gen_8704, q_gen_8679) -> q_gen_8703
<cons>(q_gen_8704, q_gen_8703) -> q_gen_8703
<a>() -> q_gen_8704
<b>() -> q_gen_8704
<s>(q_gen_8706) -> q_gen_8706
<z>() -> q_gen_8706
<cons, s>(q_gen_8680, q_gen_8679) -> q_gen_8671
<cons, s>(q_gen_8705, q_gen_8703) -> q_gen_8671
<nil, z>() -> q_gen_8671
<a, z>() -> q_gen_8680
<b, z>() -> q_gen_8680
<a, s>(q_gen_8706) -> q_gen_8705
<b, s>(q_gen_8706) -> q_gen_8705
<cons, s>(q_gen_8705, q_gen_8679) -> q_gen_8707
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_8669, q_gen_8683},
Q_f={q_gen_8669},
Delta=
{
<a, a>() -> q_gen_8669
<a, b>() -> q_gen_8669
<b, b>() -> q_gen_8669
<b, a>() -> q_gen_8683
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_8668, q_gen_8681, q_gen_8682, q_gen_8709, q_gen_8728, q_gen_8732, q_gen_8733},
Q_f={q_gen_8668, q_gen_8681},
Delta=
{
<cons>(q_gen_8733, q_gen_8732) -> q_gen_8732
<nil>() -> q_gen_8732
<a>() -> q_gen_8733
<b>() -> q_gen_8733
<cons, cons>(q_gen_8682, q_gen_8681) -> q_gen_8668
<nil, nil>() -> q_gen_8668
<cons, cons>(q_gen_8682, q_gen_8668) -> q_gen_8681
<cons, cons>(q_gen_8682, q_gen_8728) -> q_gen_8681
<cons, cons>(q_gen_8709, q_gen_8668) -> q_gen_8681
<a, b>() -> q_gen_8682
<b, b>() -> q_gen_8682
<a, a>() -> q_gen_8709
<b, a>() -> q_gen_8709
<cons, cons>(q_gen_8709, q_gen_8681) -> q_gen_8728
<nil, cons>(q_gen_8733, q_gen_8732) -> q_gen_8728
}

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, _oha]) /\ not leq([x, y])) -> insert([x, cons(y, z), _oha]) -> 20
(insert([y, _tha, _uha]) /\ sort([z, _tha])) -> sort([cons(y, z), _uha]) -> 22
(length([_dia, _eia]) /\ length([l, _cia]) /\ sort([l, _dia])) -> eq_nat([_cia, _eia]) -> 25
(length([ll, _yha])) -> length([cons(x, ll), s(_yha)]) -> 23
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 21
(leq([b, a])) -> BOT -> 21
}
Sat witness: Found: ((length([_dia, _eia]) /\ length([l, _cia]) /\ sort([l, _dia])) -> eq_nat([_cia, _eia]), {
_cia -> s(z)  ;  _dia -> cons(b, cons(b, nil))  ;  _eia -> s(s(z))  ;  l -> cons(a, nil)
})

-------------------------------------------
Step 35, which took 0.084242 s (model generation: 0.076720,  model checking: 0.007522):

Model:
|_
{
insert -> 
{{{
Q={q_gen_8672, q_gen_8673, q_gen_8674, q_gen_8676, q_gen_8677, q_gen_8721, q_gen_8729},
Q_f={q_gen_8672},
Delta=
{
<nil>() -> q_gen_8673
<a>() -> q_gen_8674
<b>() -> q_gen_8674
<cons>(q_gen_8674, q_gen_8673) -> q_gen_8721
<cons>(q_gen_8674, q_gen_8721) -> q_gen_8721
<cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8676
<cons, nil>(q_gen_8674, q_gen_8673) -> q_gen_8676
<cons, nil>(q_gen_8674, q_gen_8721) -> q_gen_8676
<nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8676
<nil, nil>() -> q_gen_8676
<a, a>() -> q_gen_8677
<a, b>() -> q_gen_8677
<b, a>() -> q_gen_8677
<b, b>() -> q_gen_8677
<a, cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8672
<a, nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8672
<b, cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8672
<b, nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8672
<a, nil, cons>(q_gen_8674, q_gen_8721) -> q_gen_8729
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_8671, q_gen_8679, q_gen_8680, q_gen_8703, q_gen_8704, q_gen_8705, q_gen_8706, q_gen_8707, q_gen_8725},
Q_f={q_gen_8671},
Delta=
{
<cons>(q_gen_8704, q_gen_8703) -> q_gen_8679
<nil>() -> q_gen_8679
<cons>(q_gen_8704, q_gen_8679) -> q_gen_8703
<a>() -> q_gen_8704
<b>() -> q_gen_8704
<z>() -> q_gen_8706
<s>(q_gen_8706) -> q_gen_8725
<cons, s>(q_gen_8680, q_gen_8679) -> q_gen_8671
<cons, s>(q_gen_8705, q_gen_8703) -> q_gen_8671
<nil, z>() -> q_gen_8671
<a, s>(q_gen_8725) -> q_gen_8680
<a, z>() -> q_gen_8680
<b, s>(q_gen_8725) -> q_gen_8680
<b, z>() -> q_gen_8680
<a, s>(q_gen_8706) -> q_gen_8705
<b, s>(q_gen_8706) -> q_gen_8705
<cons, s>(q_gen_8680, q_gen_8703) -> q_gen_8707
<cons, s>(q_gen_8705, q_gen_8679) -> q_gen_8707
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_8669, q_gen_8683},
Q_f={q_gen_8669},
Delta=
{
<a, a>() -> q_gen_8669
<a, b>() -> q_gen_8669
<b, b>() -> q_gen_8669
<b, a>() -> q_gen_8683
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_8668, q_gen_8682, q_gen_8730, q_gen_8732, q_gen_8733},
Q_f={q_gen_8668},
Delta=
{
<cons>(q_gen_8733, q_gen_8732) -> q_gen_8732
<nil>() -> q_gen_8732
<a>() -> q_gen_8733
<b>() -> q_gen_8733
<cons, cons>(q_gen_8682, q_gen_8668) -> q_gen_8668
<nil, nil>() -> q_gen_8668
<a, a>() -> q_gen_8682
<a, b>() -> q_gen_8682
<b, a>() -> q_gen_8682
<b, b>() -> q_gen_8682
<cons, cons>(q_gen_8682, q_gen_8730) -> q_gen_8730
<nil, cons>(q_gen_8733, q_gen_8732) -> q_gen_8730
}

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, _oha]) /\ not leq([x, y])) -> insert([x, cons(y, z), _oha]) -> 21
(insert([y, _tha, _uha]) /\ sort([z, _tha])) -> sort([cons(y, z), _uha]) -> 25
(length([_dia, _eia]) /\ length([l, _cia]) /\ sort([l, _dia])) -> eq_nat([_cia, _eia]) -> 25
(length([ll, _yha])) -> length([cons(x, ll), s(_yha)]) -> 23
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 22
(leq([b, a])) -> BOT -> 22
}
Sat witness: Found: ((insert([y, _tha, _uha]) /\ sort([z, _tha])) -> sort([cons(y, z), _uha]), {
_tha -> cons(b, nil)  ;  _uha -> cons(b, nil)  ;  y -> b  ;  z -> cons(a, nil)
})

-------------------------------------------
Step 36, which took 0.090291 s (model generation: 0.083635,  model checking: 0.006656):

Model:
|_
{
insert -> 
{{{
Q={q_gen_8672, q_gen_8673, q_gen_8674, q_gen_8676, q_gen_8677, q_gen_8721, q_gen_8729},
Q_f={q_gen_8672},
Delta=
{
<nil>() -> q_gen_8673
<a>() -> q_gen_8674
<b>() -> q_gen_8674
<cons>(q_gen_8674, q_gen_8673) -> q_gen_8721
<cons>(q_gen_8674, q_gen_8721) -> q_gen_8721
<cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8676
<cons, nil>(q_gen_8674, q_gen_8673) -> q_gen_8676
<cons, nil>(q_gen_8674, q_gen_8721) -> q_gen_8676
<nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8676
<nil, nil>() -> q_gen_8676
<a, a>() -> q_gen_8677
<a, b>() -> q_gen_8677
<b, a>() -> q_gen_8677
<b, b>() -> q_gen_8677
<a, cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8672
<a, nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8672
<b, cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8672
<b, nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8672
<a, nil, cons>(q_gen_8674, q_gen_8721) -> q_gen_8729
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_8671, q_gen_8679, q_gen_8680, q_gen_8703, q_gen_8704, q_gen_8705, q_gen_8706, q_gen_8707, q_gen_8725},
Q_f={q_gen_8671},
Delta=
{
<cons>(q_gen_8704, q_gen_8703) -> q_gen_8679
<nil>() -> q_gen_8679
<cons>(q_gen_8704, q_gen_8679) -> q_gen_8703
<a>() -> q_gen_8704
<b>() -> q_gen_8704
<z>() -> q_gen_8706
<s>(q_gen_8706) -> q_gen_8725
<cons, s>(q_gen_8680, q_gen_8679) -> q_gen_8671
<cons, s>(q_gen_8705, q_gen_8703) -> q_gen_8671
<nil, z>() -> q_gen_8671
<a, s>(q_gen_8725) -> q_gen_8680
<a, z>() -> q_gen_8680
<b, s>(q_gen_8725) -> q_gen_8680
<b, z>() -> q_gen_8680
<a, s>(q_gen_8706) -> q_gen_8705
<b, s>(q_gen_8706) -> q_gen_8705
<cons, s>(q_gen_8680, q_gen_8703) -> q_gen_8707
<cons, s>(q_gen_8705, q_gen_8679) -> q_gen_8707
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_8669, q_gen_8683},
Q_f={q_gen_8669},
Delta=
{
<a, a>() -> q_gen_8669
<a, b>() -> q_gen_8669
<b, b>() -> q_gen_8669
<b, a>() -> q_gen_8683
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_8668, q_gen_8682, q_gen_8730, q_gen_8732, q_gen_8733},
Q_f={q_gen_8668},
Delta=
{
<cons>(q_gen_8733, q_gen_8732) -> q_gen_8732
<nil>() -> q_gen_8732
<a>() -> q_gen_8733
<b>() -> q_gen_8733
<cons, cons>(q_gen_8682, q_gen_8668) -> q_gen_8668
<cons, nil>(q_gen_8733, q_gen_8732) -> q_gen_8668
<nil, nil>() -> q_gen_8668
<a, a>() -> q_gen_8682
<a, b>() -> q_gen_8682
<b, a>() -> q_gen_8682
<b, b>() -> q_gen_8682
<cons, cons>(q_gen_8682, q_gen_8730) -> q_gen_8730
<nil, cons>(q_gen_8733, q_gen_8732) -> q_gen_8730
}

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, _oha]) /\ not leq([x, y])) -> insert([x, cons(y, z), _oha]) -> 22
(insert([y, _tha, _uha]) /\ sort([z, _tha])) -> sort([cons(y, z), _uha]) -> 25
(length([_dia, _eia]) /\ length([l, _cia]) /\ sort([l, _dia])) -> eq_nat([_cia, _eia]) -> 25
(length([ll, _yha])) -> length([cons(x, ll), s(_yha)]) -> 26
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 23
(leq([b, a])) -> BOT -> 23
}
Sat witness: Found: ((length([ll, _yha])) -> length([cons(x, ll), s(_yha)]), {
_yha -> s(s(s(z)))  ;  ll -> cons(b, nil)  ;  x -> b
})

-------------------------------------------
Step 37, which took 0.097186 s (model generation: 0.093728,  model checking: 0.003458):

Model:
|_
{
insert -> 
{{{
Q={q_gen_8672, q_gen_8673, q_gen_8674, q_gen_8676, q_gen_8677, q_gen_8721, q_gen_8729},
Q_f={q_gen_8672},
Delta=
{
<nil>() -> q_gen_8673
<a>() -> q_gen_8674
<b>() -> q_gen_8674
<cons>(q_gen_8674, q_gen_8673) -> q_gen_8721
<cons>(q_gen_8674, q_gen_8721) -> q_gen_8721
<cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8676
<cons, nil>(q_gen_8674, q_gen_8673) -> q_gen_8676
<cons, nil>(q_gen_8674, q_gen_8721) -> q_gen_8676
<nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8676
<nil, nil>() -> q_gen_8676
<a, a>() -> q_gen_8677
<a, b>() -> q_gen_8677
<b, a>() -> q_gen_8677
<b, b>() -> q_gen_8677
<a, cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8672
<a, nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8672
<b, cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8672
<b, nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8672
<a, nil, cons>(q_gen_8674, q_gen_8721) -> q_gen_8729
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_8671, q_gen_8679, q_gen_8680, q_gen_8703, q_gen_8704, q_gen_8705, q_gen_8706, q_gen_8707, q_gen_8725},
Q_f={q_gen_8671},
Delta=
{
<cons>(q_gen_8704, q_gen_8703) -> q_gen_8679
<nil>() -> q_gen_8679
<cons>(q_gen_8704, q_gen_8679) -> q_gen_8703
<a>() -> q_gen_8704
<b>() -> q_gen_8704
<s>(q_gen_8725) -> q_gen_8706
<z>() -> q_gen_8706
<s>(q_gen_8706) -> q_gen_8725
<cons, s>(q_gen_8680, q_gen_8679) -> q_gen_8671
<cons, s>(q_gen_8705, q_gen_8703) -> q_gen_8671
<nil, z>() -> q_gen_8671
<a, s>(q_gen_8725) -> q_gen_8680
<a, z>() -> q_gen_8680
<b, s>(q_gen_8725) -> q_gen_8680
<b, z>() -> q_gen_8680
<a, s>(q_gen_8706) -> q_gen_8705
<b, s>(q_gen_8706) -> q_gen_8705
<cons, s>(q_gen_8680, q_gen_8703) -> q_gen_8707
<cons, s>(q_gen_8705, q_gen_8679) -> q_gen_8707
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_8669, q_gen_8683},
Q_f={q_gen_8669},
Delta=
{
<a, a>() -> q_gen_8669
<a, b>() -> q_gen_8669
<b, b>() -> q_gen_8669
<b, a>() -> q_gen_8683
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_8668, q_gen_8682, q_gen_8730, q_gen_8732, q_gen_8733},
Q_f={q_gen_8668},
Delta=
{
<cons>(q_gen_8733, q_gen_8732) -> q_gen_8732
<nil>() -> q_gen_8732
<a>() -> q_gen_8733
<b>() -> q_gen_8733
<cons, cons>(q_gen_8682, q_gen_8668) -> q_gen_8668
<cons, nil>(q_gen_8733, q_gen_8732) -> q_gen_8668
<nil, nil>() -> q_gen_8668
<a, a>() -> q_gen_8682
<a, b>() -> q_gen_8682
<b, a>() -> q_gen_8682
<b, b>() -> q_gen_8682
<cons, cons>(q_gen_8682, q_gen_8730) -> q_gen_8730
<nil, cons>(q_gen_8733, q_gen_8732) -> q_gen_8730
}

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, _oha]) /\ not leq([x, y])) -> insert([x, cons(y, z), _oha]) -> 23
(insert([y, _tha, _uha]) /\ sort([z, _tha])) -> sort([cons(y, z), _uha]) -> 25
(length([_dia, _eia]) /\ length([l, _cia]) /\ sort([l, _dia])) -> eq_nat([_cia, _eia]) -> 28
(length([ll, _yha])) -> length([cons(x, ll), s(_yha)]) -> 26
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 24
(leq([b, a])) -> BOT -> 24
}
Sat witness: Found: ((length([_dia, _eia]) /\ length([l, _cia]) /\ sort([l, _dia])) -> eq_nat([_cia, _eia]), {
_cia -> s(s(z))  ;  _dia -> nil  ;  _eia -> z  ;  l -> cons(a, cons(b, nil))
})

-------------------------------------------
Step 38, which took 0.095410 s (model generation: 0.094613,  model checking: 0.000797):

Model:
|_
{
insert -> 
{{{
Q={q_gen_8672, q_gen_8673, q_gen_8674, q_gen_8676, q_gen_8677, q_gen_8689, q_gen_8694},
Q_f={q_gen_8672},
Delta=
{
<cons>(q_gen_8674, q_gen_8673) -> q_gen_8673
<cons>(q_gen_8689, q_gen_8673) -> q_gen_8673
<nil>() -> q_gen_8673
<b>() -> q_gen_8674
<a>() -> q_gen_8689
<cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8676
<cons, nil>(q_gen_8674, q_gen_8673) -> q_gen_8676
<cons, nil>(q_gen_8689, q_gen_8673) -> q_gen_8676
<nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8676
<nil, nil>() -> q_gen_8676
<a, a>() -> q_gen_8677
<a, b>() -> q_gen_8677
<b, a>() -> q_gen_8677
<b, b>() -> q_gen_8677
<a, cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8672
<a, nil, cons>(q_gen_8689, q_gen_8673) -> q_gen_8672
<b, cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8672
<b, nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8672
<a, nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8694
<b, nil, cons>(q_gen_8689, q_gen_8673) -> q_gen_8694
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_8671, q_gen_8679, q_gen_8680, q_gen_8703, q_gen_8704, q_gen_8705, q_gen_8706, q_gen_8707, q_gen_8725},
Q_f={q_gen_8671},
Delta=
{
<cons>(q_gen_8704, q_gen_8703) -> q_gen_8679
<nil>() -> q_gen_8679
<cons>(q_gen_8704, q_gen_8679) -> q_gen_8703
<a>() -> q_gen_8704
<b>() -> q_gen_8704
<s>(q_gen_8725) -> q_gen_8706
<z>() -> q_gen_8706
<s>(q_gen_8706) -> q_gen_8725
<cons, s>(q_gen_8680, q_gen_8679) -> q_gen_8671
<cons, s>(q_gen_8705, q_gen_8703) -> q_gen_8671
<nil, z>() -> q_gen_8671
<a, s>(q_gen_8725) -> q_gen_8680
<a, z>() -> q_gen_8680
<b, s>(q_gen_8725) -> q_gen_8680
<b, z>() -> q_gen_8680
<a, s>(q_gen_8706) -> q_gen_8705
<b, s>(q_gen_8706) -> q_gen_8705
<cons, s>(q_gen_8680, q_gen_8703) -> q_gen_8707
<cons, s>(q_gen_8705, q_gen_8679) -> q_gen_8707
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_8669, q_gen_8683},
Q_f={q_gen_8669},
Delta=
{
<a, a>() -> q_gen_8669
<a, b>() -> q_gen_8669
<b, b>() -> q_gen_8669
<b, a>() -> q_gen_8683
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_8668, q_gen_8682, q_gen_8695, q_gen_8696, q_gen_8732, q_gen_8733},
Q_f={q_gen_8668},
Delta=
{
<cons>(q_gen_8733, q_gen_8732) -> q_gen_8732
<nil>() -> q_gen_8732
<a>() -> q_gen_8733
<b>() -> q_gen_8733
<cons, cons>(q_gen_8682, q_gen_8668) -> q_gen_8668
<nil, nil>() -> q_gen_8668
<a, a>() -> q_gen_8682
<b, b>() -> q_gen_8682
<cons, cons>(q_gen_8682, q_gen_8695) -> q_gen_8695
<cons, cons>(q_gen_8696, q_gen_8668) -> q_gen_8695
<cons, cons>(q_gen_8696, q_gen_8695) -> q_gen_8695
<cons, nil>(q_gen_8733, q_gen_8732) -> q_gen_8695
<nil, cons>(q_gen_8733, q_gen_8732) -> q_gen_8695
<a, b>() -> q_gen_8696
<b, a>() -> q_gen_8696
}

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, _oha]) /\ not leq([x, y])) -> insert([x, cons(y, z), _oha]) -> 26
(insert([y, _tha, _uha]) /\ sort([z, _tha])) -> sort([cons(y, z), _uha]) -> 25
(length([_dia, _eia]) /\ length([l, _cia]) /\ sort([l, _dia])) -> eq_nat([_cia, _eia]) -> 28
(length([ll, _yha])) -> length([cons(x, ll), s(_yha)]) -> 26
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 24
(leq([b, a])) -> BOT -> 24
}
Sat witness: Found: ((insert([x, z, _oha]) /\ not leq([x, y])) -> insert([x, cons(y, z), _oha]), {
_oha -> cons(b, cons(a, nil))  ;  x -> b  ;  y -> a  ;  z -> nil
})

-------------------------------------------
Step 39, which took 0.109691 s (model generation: 0.105992,  model checking: 0.003699):

Model:
|_
{
insert -> 
{{{
Q={q_gen_8672, q_gen_8673, q_gen_8674, q_gen_8676, q_gen_8677, q_gen_8689, q_gen_8694},
Q_f={q_gen_8672},
Delta=
{
<cons>(q_gen_8674, q_gen_8673) -> q_gen_8673
<cons>(q_gen_8689, q_gen_8673) -> q_gen_8673
<nil>() -> q_gen_8673
<b>() -> q_gen_8674
<a>() -> q_gen_8689
<cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8676
<cons, nil>(q_gen_8674, q_gen_8673) -> q_gen_8676
<cons, nil>(q_gen_8689, q_gen_8673) -> q_gen_8676
<nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8676
<nil, cons>(q_gen_8689, q_gen_8673) -> q_gen_8676
<nil, nil>() -> q_gen_8676
<a, a>() -> q_gen_8677
<a, b>() -> q_gen_8677
<b, a>() -> q_gen_8677
<b, b>() -> q_gen_8677
<a, cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8672
<a, nil, cons>(q_gen_8689, q_gen_8673) -> q_gen_8672
<b, cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8672
<b, nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8672
<a, nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8694
<b, nil, cons>(q_gen_8689, q_gen_8673) -> q_gen_8694
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_8671, q_gen_8679, q_gen_8680, q_gen_8703, q_gen_8704, q_gen_8706, q_gen_8713, q_gen_8714},
Q_f={q_gen_8671},
Delta=
{
<nil>() -> q_gen_8679
<cons>(q_gen_8704, q_gen_8679) -> q_gen_8703
<cons>(q_gen_8704, q_gen_8703) -> q_gen_8703
<a>() -> q_gen_8704
<b>() -> q_gen_8704
<s>(q_gen_8706) -> q_gen_8706
<z>() -> q_gen_8706
<cons, s>(q_gen_8680, q_gen_8679) -> q_gen_8671
<cons, s>(q_gen_8680, q_gen_8703) -> q_gen_8671
<cons, s>(q_gen_8713, q_gen_8703) -> q_gen_8671
<nil, z>() -> q_gen_8671
<a, z>() -> q_gen_8680
<b, s>(q_gen_8706) -> q_gen_8680
<b, z>() -> q_gen_8680
<a, s>(q_gen_8706) -> q_gen_8713
<cons, s>(q_gen_8713, q_gen_8679) -> q_gen_8714
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_8669, q_gen_8683},
Q_f={q_gen_8669},
Delta=
{
<a, a>() -> q_gen_8669
<a, b>() -> q_gen_8669
<b, b>() -> q_gen_8669
<b, a>() -> q_gen_8683
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_8668, q_gen_8681, q_gen_8682, q_gen_8695, q_gen_8696, q_gen_8732, q_gen_8733},
Q_f={q_gen_8668, q_gen_8681},
Delta=
{
<cons>(q_gen_8733, q_gen_8732) -> q_gen_8732
<nil>() -> q_gen_8732
<a>() -> q_gen_8733
<b>() -> q_gen_8733
<nil, nil>() -> q_gen_8668
<cons, cons>(q_gen_8682, q_gen_8668) -> q_gen_8681
<cons, cons>(q_gen_8682, q_gen_8695) -> q_gen_8681
<a, a>() -> q_gen_8682
<b, b>() -> q_gen_8682
<cons, cons>(q_gen_8682, q_gen_8681) -> q_gen_8695
<cons, cons>(q_gen_8696, q_gen_8668) -> q_gen_8695
<cons, cons>(q_gen_8696, q_gen_8681) -> q_gen_8695
<cons, cons>(q_gen_8696, q_gen_8695) -> q_gen_8695
<cons, nil>(q_gen_8733, q_gen_8732) -> q_gen_8695
<nil, cons>(q_gen_8733, q_gen_8732) -> q_gen_8695
<a, b>() -> q_gen_8696
<b, a>() -> q_gen_8696
}

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, _oha]) /\ not leq([x, y])) -> insert([x, cons(y, z), _oha]) -> 26
(insert([y, _tha, _uha]) /\ sort([z, _tha])) -> sort([cons(y, z), _uha]) -> 28
(length([_dia, _eia]) /\ length([l, _cia]) /\ sort([l, _dia])) -> eq_nat([_cia, _eia]) -> 28
(length([ll, _yha])) -> length([cons(x, ll), s(_yha)]) -> 26
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 25
(leq([b, a])) -> BOT -> 25
}
Sat witness: Found: ((insert([y, _tha, _uha]) /\ sort([z, _tha])) -> sort([cons(y, z), _uha]), {
_tha -> cons(b, nil)  ;  _uha -> cons(a, cons(b, nil))  ;  y -> a  ;  z -> cons(b, nil)
})

-------------------------------------------
Step 40, which took 0.111473 s (model generation: 0.104099,  model checking: 0.007374):

Model:
|_
{
insert -> 
{{{
Q={q_gen_8672, q_gen_8673, q_gen_8674, q_gen_8676, q_gen_8677, q_gen_8721, q_gen_8729},
Q_f={q_gen_8672},
Delta=
{
<nil>() -> q_gen_8673
<a>() -> q_gen_8674
<b>() -> q_gen_8674
<cons>(q_gen_8674, q_gen_8673) -> q_gen_8721
<cons>(q_gen_8674, q_gen_8721) -> q_gen_8721
<cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8676
<cons, nil>(q_gen_8674, q_gen_8673) -> q_gen_8676
<cons, nil>(q_gen_8674, q_gen_8721) -> q_gen_8676
<nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8676
<nil, nil>() -> q_gen_8676
<a, a>() -> q_gen_8677
<a, b>() -> q_gen_8677
<b, a>() -> q_gen_8677
<b, b>() -> q_gen_8677
<a, cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8672
<a, nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8672
<b, cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8672
<b, nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8672
<a, nil, cons>(q_gen_8674, q_gen_8721) -> q_gen_8729
<b, nil, cons>(q_gen_8674, q_gen_8721) -> q_gen_8729
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_8671, q_gen_8679, q_gen_8680, q_gen_8703, q_gen_8704, q_gen_8705, q_gen_8706, q_gen_8707, q_gen_8725},
Q_f={q_gen_8671},
Delta=
{
<cons>(q_gen_8704, q_gen_8703) -> q_gen_8679
<nil>() -> q_gen_8679
<cons>(q_gen_8704, q_gen_8679) -> q_gen_8703
<a>() -> q_gen_8704
<b>() -> q_gen_8704
<s>(q_gen_8725) -> q_gen_8706
<z>() -> q_gen_8706
<s>(q_gen_8706) -> q_gen_8725
<cons, s>(q_gen_8680, q_gen_8679) -> q_gen_8671
<cons, s>(q_gen_8705, q_gen_8703) -> q_gen_8671
<nil, z>() -> q_gen_8671
<a, s>(q_gen_8725) -> q_gen_8680
<a, z>() -> q_gen_8680
<b, s>(q_gen_8725) -> q_gen_8680
<b, z>() -> q_gen_8680
<a, s>(q_gen_8706) -> q_gen_8705
<b, s>(q_gen_8706) -> q_gen_8705
<cons, s>(q_gen_8680, q_gen_8703) -> q_gen_8707
<cons, s>(q_gen_8705, q_gen_8679) -> q_gen_8707
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_8669, q_gen_8683},
Q_f={q_gen_8669},
Delta=
{
<a, a>() -> q_gen_8669
<a, b>() -> q_gen_8669
<b, b>() -> q_gen_8669
<b, a>() -> q_gen_8683
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_8668, q_gen_8682, q_gen_8730, q_gen_8732, q_gen_8733, q_gen_8740},
Q_f={q_gen_8668},
Delta=
{
<nil>() -> q_gen_8732
<a>() -> q_gen_8733
<b>() -> q_gen_8733
<cons>(q_gen_8733, q_gen_8732) -> q_gen_8740
<cons, cons>(q_gen_8682, q_gen_8668) -> q_gen_8668
<cons, nil>(q_gen_8733, q_gen_8732) -> q_gen_8668
<nil, nil>() -> q_gen_8668
<a, a>() -> q_gen_8682
<a, b>() -> q_gen_8682
<b, a>() -> q_gen_8682
<b, b>() -> q_gen_8682
<cons, cons>(q_gen_8682, q_gen_8730) -> q_gen_8730
<cons, nil>(q_gen_8733, q_gen_8740) -> q_gen_8730
<nil, cons>(q_gen_8733, q_gen_8732) -> q_gen_8730
<nil, cons>(q_gen_8733, q_gen_8740) -> q_gen_8730
}

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, _oha]) /\ not leq([x, y])) -> insert([x, cons(y, z), _oha]) -> 27
(insert([y, _tha, _uha]) /\ sort([z, _tha])) -> sort([cons(y, z), _uha]) -> 28
(length([_dia, _eia]) /\ length([l, _cia]) /\ sort([l, _dia])) -> eq_nat([_cia, _eia]) -> 31
(length([ll, _yha])) -> length([cons(x, ll), s(_yha)]) -> 27
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 26
(leq([b, a])) -> BOT -> 26
}
Sat witness: Found: ((length([_dia, _eia]) /\ length([l, _cia]) /\ sort([l, _dia])) -> eq_nat([_cia, _eia]), {
_cia -> s(z)  ;  _dia -> nil  ;  _eia -> z  ;  l -> cons(b, nil)
})

-------------------------------------------
Step 41, which took 0.117536 s (model generation: 0.104212,  model checking: 0.013324):

Model:
|_
{
insert -> 
{{{
Q={q_gen_8672, q_gen_8673, q_gen_8674, q_gen_8676, q_gen_8677, q_gen_8721, q_gen_8729},
Q_f={q_gen_8672},
Delta=
{
<nil>() -> q_gen_8673
<a>() -> q_gen_8674
<b>() -> q_gen_8674
<cons>(q_gen_8674, q_gen_8673) -> q_gen_8721
<cons>(q_gen_8674, q_gen_8721) -> q_gen_8721
<cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8676
<cons, nil>(q_gen_8674, q_gen_8673) -> q_gen_8676
<cons, nil>(q_gen_8674, q_gen_8721) -> q_gen_8676
<nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8676
<nil, nil>() -> q_gen_8676
<a, a>() -> q_gen_8677
<a, b>() -> q_gen_8677
<b, a>() -> q_gen_8677
<b, b>() -> q_gen_8677
<a, cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8672
<a, nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8672
<b, cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8672
<b, nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8672
<a, nil, cons>(q_gen_8674, q_gen_8721) -> q_gen_8729
<b, nil, cons>(q_gen_8674, q_gen_8721) -> q_gen_8729
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_8671, q_gen_8679, q_gen_8680, q_gen_8703, q_gen_8704, q_gen_8705, q_gen_8706, q_gen_8707, q_gen_8725},
Q_f={q_gen_8671},
Delta=
{
<cons>(q_gen_8704, q_gen_8703) -> q_gen_8679
<nil>() -> q_gen_8679
<cons>(q_gen_8704, q_gen_8679) -> q_gen_8703
<a>() -> q_gen_8704
<b>() -> q_gen_8704
<s>(q_gen_8725) -> q_gen_8706
<z>() -> q_gen_8706
<s>(q_gen_8706) -> q_gen_8725
<cons, s>(q_gen_8680, q_gen_8679) -> q_gen_8671
<cons, s>(q_gen_8705, q_gen_8703) -> q_gen_8671
<nil, z>() -> q_gen_8671
<a, s>(q_gen_8725) -> q_gen_8680
<a, z>() -> q_gen_8680
<b, s>(q_gen_8725) -> q_gen_8680
<b, z>() -> q_gen_8680
<a, s>(q_gen_8706) -> q_gen_8705
<b, s>(q_gen_8706) -> q_gen_8705
<cons, s>(q_gen_8680, q_gen_8703) -> q_gen_8707
<cons, s>(q_gen_8705, q_gen_8679) -> q_gen_8707
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_8669, q_gen_8683},
Q_f={q_gen_8669},
Delta=
{
<a, a>() -> q_gen_8669
<a, b>() -> q_gen_8669
<b, b>() -> q_gen_8669
<b, a>() -> q_gen_8683
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_8668, q_gen_8682, q_gen_8730, q_gen_8732, q_gen_8733, q_gen_8751},
Q_f={q_gen_8668},
Delta=
{
<cons>(q_gen_8733, q_gen_8732) -> q_gen_8732
<nil>() -> q_gen_8732
<a>() -> q_gen_8733
<b>() -> q_gen_8733
<cons, cons>(q_gen_8682, q_gen_8668) -> q_gen_8668
<cons, cons>(q_gen_8682, q_gen_8751) -> q_gen_8668
<nil, nil>() -> q_gen_8668
<a, a>() -> q_gen_8682
<a, b>() -> q_gen_8682
<b, a>() -> q_gen_8682
<b, b>() -> q_gen_8682
<cons, cons>(q_gen_8682, q_gen_8730) -> q_gen_8730
<nil, cons>(q_gen_8733, q_gen_8732) -> q_gen_8730
<cons, nil>(q_gen_8733, q_gen_8732) -> q_gen_8751
}

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, _oha]) /\ not leq([x, y])) -> insert([x, cons(y, z), _oha]) -> 28
(insert([y, _tha, _uha]) /\ sort([z, _tha])) -> sort([cons(y, z), _uha]) -> 29
(length([_dia, _eia]) /\ length([l, _cia]) /\ sort([l, _dia])) -> eq_nat([_cia, _eia]) -> 34
(length([ll, _yha])) -> length([cons(x, ll), s(_yha)]) -> 28
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 27
(leq([b, a])) -> BOT -> 27
}
Sat witness: Found: ((length([_dia, _eia]) /\ length([l, _cia]) /\ sort([l, _dia])) -> eq_nat([_cia, _eia]), {
_cia -> s(z)  ;  _dia -> cons(a, nil)  ;  _eia -> s(s(s(z)))  ;  l -> cons(b, cons(b, cons(b, nil)))
})

-------------------------------------------
Step 42, which took 0.136202 s (model generation: 0.130776,  model checking: 0.005426):

Model:
|_
{
insert -> 
{{{
Q={q_gen_8672, q_gen_8673, q_gen_8674, q_gen_8676, q_gen_8677, q_gen_8689, q_gen_8694},
Q_f={q_gen_8672},
Delta=
{
<cons>(q_gen_8674, q_gen_8673) -> q_gen_8673
<cons>(q_gen_8689, q_gen_8673) -> q_gen_8673
<nil>() -> q_gen_8673
<b>() -> q_gen_8674
<a>() -> q_gen_8689
<cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8676
<cons, nil>(q_gen_8674, q_gen_8673) -> q_gen_8676
<cons, nil>(q_gen_8689, q_gen_8673) -> q_gen_8676
<nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8676
<nil, cons>(q_gen_8689, q_gen_8673) -> q_gen_8676
<nil, nil>() -> q_gen_8676
<a, a>() -> q_gen_8677
<a, b>() -> q_gen_8677
<b, a>() -> q_gen_8677
<b, b>() -> q_gen_8677
<a, cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8672
<a, nil, cons>(q_gen_8689, q_gen_8673) -> q_gen_8672
<b, cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8672
<b, nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8672
<a, nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8694
<b, nil, cons>(q_gen_8689, q_gen_8673) -> q_gen_8694
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_8671, q_gen_8679, q_gen_8680, q_gen_8703, q_gen_8704, q_gen_8705, q_gen_8706, q_gen_8707, q_gen_8725},
Q_f={q_gen_8671},
Delta=
{
<cons>(q_gen_8704, q_gen_8703) -> q_gen_8679
<nil>() -> q_gen_8679
<cons>(q_gen_8704, q_gen_8679) -> q_gen_8703
<a>() -> q_gen_8704
<b>() -> q_gen_8704
<s>(q_gen_8725) -> q_gen_8706
<z>() -> q_gen_8706
<s>(q_gen_8706) -> q_gen_8725
<cons, s>(q_gen_8680, q_gen_8679) -> q_gen_8671
<cons, s>(q_gen_8705, q_gen_8703) -> q_gen_8671
<nil, z>() -> q_gen_8671
<a, s>(q_gen_8725) -> q_gen_8680
<a, z>() -> q_gen_8680
<b, s>(q_gen_8725) -> q_gen_8680
<b, z>() -> q_gen_8680
<a, s>(q_gen_8706) -> q_gen_8705
<b, s>(q_gen_8706) -> q_gen_8705
<cons, s>(q_gen_8680, q_gen_8703) -> q_gen_8707
<cons, s>(q_gen_8705, q_gen_8679) -> q_gen_8707
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_8669, q_gen_8683},
Q_f={q_gen_8669},
Delta=
{
<a, a>() -> q_gen_8669
<a, b>() -> q_gen_8669
<b, b>() -> q_gen_8669
<b, a>() -> q_gen_8683
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_8668, q_gen_8682, q_gen_8695, q_gen_8696, q_gen_8732, q_gen_8733},
Q_f={q_gen_8668},
Delta=
{
<cons>(q_gen_8733, q_gen_8732) -> q_gen_8732
<nil>() -> q_gen_8732
<a>() -> q_gen_8733
<b>() -> q_gen_8733
<cons, cons>(q_gen_8682, q_gen_8668) -> q_gen_8668
<nil, nil>() -> q_gen_8668
<a, a>() -> q_gen_8682
<b, b>() -> q_gen_8682
<cons, cons>(q_gen_8682, q_gen_8695) -> q_gen_8695
<cons, cons>(q_gen_8696, q_gen_8668) -> q_gen_8695
<cons, cons>(q_gen_8696, q_gen_8695) -> q_gen_8695
<cons, nil>(q_gen_8733, q_gen_8732) -> q_gen_8695
<nil, cons>(q_gen_8733, q_gen_8732) -> q_gen_8695
<a, b>() -> q_gen_8696
<b, a>() -> q_gen_8696
}

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, _oha]) /\ not leq([x, y])) -> insert([x, cons(y, z), _oha]) -> 29
(insert([y, _tha, _uha]) /\ sort([z, _tha])) -> sort([cons(y, z), _uha]) -> 32
(length([_dia, _eia]) /\ length([l, _cia]) /\ sort([l, _dia])) -> eq_nat([_cia, _eia]) -> 34
(length([ll, _yha])) -> length([cons(x, ll), s(_yha)]) -> 29
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 28
(leq([b, a])) -> BOT -> 28
}
Sat witness: Found: ((insert([y, _tha, _uha]) /\ sort([z, _tha])) -> sort([cons(y, z), _uha]), {
_tha -> nil  ;  _uha -> cons(a, cons(b, nil))  ;  y -> a  ;  z -> nil
})

-------------------------------------------
Step 43, which took 0.150030 s (model generation: 0.142561,  model checking: 0.007469):

Model:
|_
{
insert -> 
{{{
Q={q_gen_8672, q_gen_8673, q_gen_8674, q_gen_8676, q_gen_8677, q_gen_8689, q_gen_8694},
Q_f={q_gen_8672},
Delta=
{
<cons>(q_gen_8674, q_gen_8673) -> q_gen_8673
<cons>(q_gen_8689, q_gen_8673) -> q_gen_8673
<nil>() -> q_gen_8673
<b>() -> q_gen_8674
<a>() -> q_gen_8689
<cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8676
<cons, nil>(q_gen_8674, q_gen_8673) -> q_gen_8676
<cons, nil>(q_gen_8689, q_gen_8673) -> q_gen_8676
<nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8676
<nil, cons>(q_gen_8689, q_gen_8673) -> q_gen_8676
<nil, nil>() -> q_gen_8676
<a, a>() -> q_gen_8677
<a, b>() -> q_gen_8677
<b, a>() -> q_gen_8677
<b, b>() -> q_gen_8677
<a, cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8672
<a, nil, cons>(q_gen_8689, q_gen_8673) -> q_gen_8672
<b, cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8672
<b, nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8672
<a, nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8694
<b, nil, cons>(q_gen_8689, q_gen_8673) -> q_gen_8694
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_8671, q_gen_8679, q_gen_8680, q_gen_8703, q_gen_8704, q_gen_8705, q_gen_8706, q_gen_8707, q_gen_8725},
Q_f={q_gen_8671},
Delta=
{
<cons>(q_gen_8704, q_gen_8703) -> q_gen_8679
<nil>() -> q_gen_8679
<cons>(q_gen_8704, q_gen_8679) -> q_gen_8703
<a>() -> q_gen_8704
<b>() -> q_gen_8704
<s>(q_gen_8725) -> q_gen_8706
<z>() -> q_gen_8706
<s>(q_gen_8706) -> q_gen_8725
<cons, s>(q_gen_8680, q_gen_8679) -> q_gen_8671
<cons, s>(q_gen_8705, q_gen_8703) -> q_gen_8671
<nil, z>() -> q_gen_8671
<a, s>(q_gen_8725) -> q_gen_8680
<a, z>() -> q_gen_8680
<b, s>(q_gen_8725) -> q_gen_8680
<b, z>() -> q_gen_8680
<a, s>(q_gen_8706) -> q_gen_8705
<b, s>(q_gen_8706) -> q_gen_8705
<cons, s>(q_gen_8680, q_gen_8703) -> q_gen_8707
<cons, s>(q_gen_8705, q_gen_8679) -> q_gen_8707
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_8669, q_gen_8683},
Q_f={q_gen_8669},
Delta=
{
<a, a>() -> q_gen_8669
<a, b>() -> q_gen_8669
<b, b>() -> q_gen_8669
<b, a>() -> q_gen_8683
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_8668, q_gen_8682, q_gen_8695, q_gen_8696, q_gen_8732, q_gen_8733},
Q_f={q_gen_8668},
Delta=
{
<cons>(q_gen_8733, q_gen_8732) -> q_gen_8732
<nil>() -> q_gen_8732
<a>() -> q_gen_8733
<b>() -> q_gen_8733
<cons, cons>(q_gen_8682, q_gen_8668) -> q_gen_8668
<cons, cons>(q_gen_8682, q_gen_8695) -> q_gen_8668
<nil, nil>() -> q_gen_8668
<a, a>() -> q_gen_8682
<b, b>() -> q_gen_8682
<cons, cons>(q_gen_8696, q_gen_8668) -> q_gen_8695
<cons, cons>(q_gen_8696, q_gen_8695) -> q_gen_8695
<cons, nil>(q_gen_8733, q_gen_8732) -> q_gen_8695
<nil, cons>(q_gen_8733, q_gen_8732) -> q_gen_8695
<a, b>() -> q_gen_8696
<b, a>() -> q_gen_8696
}

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, _oha]) /\ not leq([x, y])) -> insert([x, cons(y, z), _oha]) -> 30
(insert([y, _tha, _uha]) /\ sort([z, _tha])) -> sort([cons(y, z), _uha]) -> 35
(length([_dia, _eia]) /\ length([l, _cia]) /\ sort([l, _dia])) -> eq_nat([_cia, _eia]) -> 34
(length([ll, _yha])) -> length([cons(x, ll), s(_yha)]) -> 30
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 29
(leq([b, a])) -> BOT -> 29
}
Sat witness: Found: ((insert([y, _tha, _uha]) /\ sort([z, _tha])) -> sort([cons(y, z), _uha]), {
_tha -> cons(a, cons(a, nil))  ;  _uha -> cons(b, nil)  ;  y -> a  ;  z -> cons(a, nil)
})

-------------------------------------------
Step 44, which took 0.150119 s (model generation: 0.145604,  model checking: 0.004515):

Model:
|_
{
insert -> 
{{{
Q={q_gen_8672, q_gen_8673, q_gen_8674, q_gen_8676, q_gen_8677, q_gen_8721, q_gen_8729},
Q_f={q_gen_8672},
Delta=
{
<cons>(q_gen_8674, q_gen_8721) -> q_gen_8673
<nil>() -> q_gen_8673
<a>() -> q_gen_8674
<b>() -> q_gen_8674
<cons>(q_gen_8674, q_gen_8673) -> q_gen_8721
<cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8676
<cons, nil>(q_gen_8674, q_gen_8673) -> q_gen_8676
<cons, nil>(q_gen_8674, q_gen_8721) -> q_gen_8676
<nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8676
<nil, nil>() -> q_gen_8676
<a, a>() -> q_gen_8677
<a, b>() -> q_gen_8677
<b, a>() -> q_gen_8677
<b, b>() -> q_gen_8677
<a, cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8672
<a, nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8672
<b, cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8672
<b, nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8672
<a, nil, cons>(q_gen_8674, q_gen_8721) -> q_gen_8729
<b, nil, cons>(q_gen_8674, q_gen_8721) -> q_gen_8729
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_8671, q_gen_8679, q_gen_8680, q_gen_8703, q_gen_8704, q_gen_8705, q_gen_8706, q_gen_8707, q_gen_8725},
Q_f={q_gen_8671},
Delta=
{
<cons>(q_gen_8704, q_gen_8703) -> q_gen_8679
<nil>() -> q_gen_8679
<cons>(q_gen_8704, q_gen_8679) -> q_gen_8703
<a>() -> q_gen_8704
<b>() -> q_gen_8704
<s>(q_gen_8725) -> q_gen_8706
<z>() -> q_gen_8706
<s>(q_gen_8706) -> q_gen_8725
<cons, s>(q_gen_8680, q_gen_8679) -> q_gen_8671
<cons, s>(q_gen_8705, q_gen_8703) -> q_gen_8671
<nil, z>() -> q_gen_8671
<a, s>(q_gen_8725) -> q_gen_8680
<a, z>() -> q_gen_8680
<b, s>(q_gen_8725) -> q_gen_8680
<b, z>() -> q_gen_8680
<a, s>(q_gen_8706) -> q_gen_8705
<b, s>(q_gen_8706) -> q_gen_8705
<cons, s>(q_gen_8680, q_gen_8703) -> q_gen_8707
<cons, s>(q_gen_8705, q_gen_8679) -> q_gen_8707
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_8669, q_gen_8683},
Q_f={q_gen_8669},
Delta=
{
<a, a>() -> q_gen_8669
<a, b>() -> q_gen_8669
<b, b>() -> q_gen_8669
<b, a>() -> q_gen_8683
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_8668, q_gen_8682, q_gen_8730, q_gen_8732, q_gen_8733, q_gen_8741, q_gen_8757},
Q_f={q_gen_8668},
Delta=
{
<cons>(q_gen_8741, q_gen_8732) -> q_gen_8732
<nil>() -> q_gen_8732
<b>() -> q_gen_8733
<a>() -> q_gen_8741
<cons>(q_gen_8733, q_gen_8732) -> q_gen_8757
<cons, cons>(q_gen_8682, q_gen_8668) -> q_gen_8668
<cons, nil>(q_gen_8741, q_gen_8732) -> q_gen_8668
<nil, cons>(q_gen_8741, q_gen_8732) -> q_gen_8668
<nil, nil>() -> q_gen_8668
<a, a>() -> q_gen_8682
<a, b>() -> q_gen_8682
<b, a>() -> q_gen_8682
<b, b>() -> q_gen_8682
<cons, cons>(q_gen_8682, q_gen_8730) -> q_gen_8730
<cons, nil>(q_gen_8733, q_gen_8732) -> q_gen_8730
<cons, nil>(q_gen_8733, q_gen_8757) -> q_gen_8730
<cons, nil>(q_gen_8741, q_gen_8757) -> q_gen_8730
<nil, cons>(q_gen_8733, q_gen_8732) -> q_gen_8730
}

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, _oha]) /\ not leq([x, y])) -> insert([x, cons(y, z), _oha]) -> 33
(insert([y, _tha, _uha]) /\ sort([z, _tha])) -> sort([cons(y, z), _uha]) -> 35
(length([_dia, _eia]) /\ length([l, _cia]) /\ sort([l, _dia])) -> eq_nat([_cia, _eia]) -> 34
(length([ll, _yha])) -> length([cons(x, ll), s(_yha)]) -> 31
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 30
(leq([b, a])) -> BOT -> 30
}
Sat witness: Found: ((insert([x, z, _oha]) /\ not leq([x, y])) -> insert([x, cons(y, z), _oha]), {
_oha -> cons(b, cons(b, cons(b, nil)))  ;  x -> b  ;  y -> a  ;  z -> nil
})

-------------------------------------------
Step 45, which took 0.165232 s (model generation: 0.162673,  model checking: 0.002559):

Model:
|_
{
insert -> 
{{{
Q={q_gen_8672, q_gen_8673, q_gen_8674, q_gen_8676, q_gen_8677, q_gen_8685, q_gen_8686, q_gen_8721, q_gen_8729},
Q_f={q_gen_8672},
Delta=
{
<nil>() -> q_gen_8673
<a>() -> q_gen_8674
<b>() -> q_gen_8674
<cons>(q_gen_8674, q_gen_8673) -> q_gen_8721
<cons>(q_gen_8674, q_gen_8721) -> q_gen_8721
<cons, nil>(q_gen_8674, q_gen_8673) -> q_gen_8676
<nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8676
<nil, cons>(q_gen_8674, q_gen_8721) -> q_gen_8676
<b, b>() -> q_gen_8677
<cons, cons>(q_gen_8686, q_gen_8676) -> q_gen_8685
<cons, nil>(q_gen_8674, q_gen_8721) -> q_gen_8685
<nil, nil>() -> q_gen_8685
<a, a>() -> q_gen_8686
<a, b>() -> q_gen_8686
<b, a>() -> q_gen_8686
<a, cons, cons>(q_gen_8686, q_gen_8676) -> q_gen_8672
<a, cons, cons>(q_gen_8686, q_gen_8685) -> q_gen_8672
<a, nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8672
<b, cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8672
<b, cons, cons>(q_gen_8686, q_gen_8676) -> q_gen_8672
<b, cons, cons>(q_gen_8686, q_gen_8685) -> q_gen_8672
<b, nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8672
<a, cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8729
<a, nil, cons>(q_gen_8674, q_gen_8721) -> q_gen_8729
<b, cons, cons>(q_gen_8677, q_gen_8685) -> q_gen_8729
<b, nil, cons>(q_gen_8674, q_gen_8721) -> q_gen_8729
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_8671, q_gen_8679, q_gen_8680, q_gen_8703, q_gen_8704, q_gen_8705, q_gen_8706, q_gen_8707, q_gen_8725},
Q_f={q_gen_8671},
Delta=
{
<cons>(q_gen_8704, q_gen_8703) -> q_gen_8679
<nil>() -> q_gen_8679
<cons>(q_gen_8704, q_gen_8679) -> q_gen_8703
<a>() -> q_gen_8704
<b>() -> q_gen_8704
<s>(q_gen_8725) -> q_gen_8706
<z>() -> q_gen_8706
<s>(q_gen_8706) -> q_gen_8725
<cons, s>(q_gen_8680, q_gen_8679) -> q_gen_8671
<cons, s>(q_gen_8705, q_gen_8703) -> q_gen_8671
<nil, z>() -> q_gen_8671
<a, s>(q_gen_8725) -> q_gen_8680
<a, z>() -> q_gen_8680
<b, s>(q_gen_8725) -> q_gen_8680
<b, z>() -> q_gen_8680
<a, s>(q_gen_8706) -> q_gen_8705
<b, s>(q_gen_8706) -> q_gen_8705
<cons, s>(q_gen_8680, q_gen_8703) -> q_gen_8707
<cons, s>(q_gen_8705, q_gen_8679) -> q_gen_8707
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_8669, q_gen_8683},
Q_f={q_gen_8669},
Delta=
{
<a, a>() -> q_gen_8669
<a, b>() -> q_gen_8669
<b, b>() -> q_gen_8669
<b, a>() -> q_gen_8683
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_8668, q_gen_8682, q_gen_8730, q_gen_8732, q_gen_8733},
Q_f={q_gen_8668},
Delta=
{
<cons>(q_gen_8733, q_gen_8732) -> q_gen_8732
<nil>() -> q_gen_8732
<a>() -> q_gen_8733
<b>() -> q_gen_8733
<cons, cons>(q_gen_8682, q_gen_8668) -> q_gen_8668
<nil, nil>() -> q_gen_8668
<a, a>() -> q_gen_8682
<a, b>() -> q_gen_8682
<b, a>() -> q_gen_8682
<b, b>() -> q_gen_8682
<cons, cons>(q_gen_8682, q_gen_8730) -> q_gen_8730
<cons, nil>(q_gen_8733, q_gen_8732) -> q_gen_8730
<nil, cons>(q_gen_8733, q_gen_8732) -> q_gen_8730
}

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, _oha]) /\ not leq([x, y])) -> insert([x, cons(y, z), _oha]) -> 33
(insert([y, _tha, _uha]) /\ sort([z, _tha])) -> sort([cons(y, z), _uha]) -> 35
(length([_dia, _eia]) /\ length([l, _cia]) /\ sort([l, _dia])) -> eq_nat([_cia, _eia]) -> 34
(length([ll, _yha])) -> length([cons(x, ll), s(_yha)]) -> 31
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 33
(leq([b, a])) -> BOT -> 31
}
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 46, which took 0.269544 s (model generation: 0.262278,  model checking: 0.007266):

Model:
|_
{
insert -> 
{{{
Q={q_gen_8672, q_gen_8673, q_gen_8674, q_gen_8676, q_gen_8677, q_gen_8721, q_gen_8729},
Q_f={q_gen_8672},
Delta=
{
<nil>() -> q_gen_8673
<a>() -> q_gen_8674
<b>() -> q_gen_8674
<cons>(q_gen_8674, q_gen_8673) -> q_gen_8721
<cons>(q_gen_8674, q_gen_8721) -> q_gen_8721
<cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8676
<cons, nil>(q_gen_8674, q_gen_8673) -> q_gen_8676
<cons, nil>(q_gen_8674, q_gen_8721) -> q_gen_8676
<nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8676
<nil, cons>(q_gen_8674, q_gen_8721) -> q_gen_8676
<nil, nil>() -> q_gen_8676
<a, a>() -> q_gen_8677
<a, b>() -> q_gen_8677
<b, a>() -> q_gen_8677
<b, b>() -> q_gen_8677
<a, cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8672
<a, nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8672
<b, cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8672
<b, nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8672
<a, nil, cons>(q_gen_8674, q_gen_8721) -> q_gen_8729
<b, nil, cons>(q_gen_8674, q_gen_8721) -> q_gen_8729
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_8671, q_gen_8679, q_gen_8680, q_gen_8703, q_gen_8704, q_gen_8705, q_gen_8706, q_gen_8707, q_gen_8725},
Q_f={q_gen_8671},
Delta=
{
<cons>(q_gen_8704, q_gen_8703) -> q_gen_8679
<nil>() -> q_gen_8679
<cons>(q_gen_8704, q_gen_8679) -> q_gen_8703
<a>() -> q_gen_8704
<b>() -> q_gen_8704
<s>(q_gen_8725) -> q_gen_8706
<z>() -> q_gen_8706
<s>(q_gen_8706) -> q_gen_8725
<cons, s>(q_gen_8680, q_gen_8679) -> q_gen_8671
<cons, s>(q_gen_8705, q_gen_8703) -> q_gen_8671
<nil, z>() -> q_gen_8671
<a, s>(q_gen_8725) -> q_gen_8680
<a, z>() -> q_gen_8680
<b, s>(q_gen_8725) -> q_gen_8680
<b, z>() -> q_gen_8680
<a, s>(q_gen_8706) -> q_gen_8705
<b, s>(q_gen_8706) -> q_gen_8705
<cons, s>(q_gen_8680, q_gen_8703) -> q_gen_8707
<cons, s>(q_gen_8705, q_gen_8679) -> q_gen_8707
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_8669, q_gen_8683},
Q_f={q_gen_8669},
Delta=
{
<a, a>() -> q_gen_8669
<a, b>() -> q_gen_8669
<b, b>() -> q_gen_8669
<b, a>() -> q_gen_8683
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_8668, q_gen_8682, q_gen_8696, q_gen_8730, q_gen_8731, q_gen_8732, q_gen_8733},
Q_f={q_gen_8668},
Delta=
{
<cons>(q_gen_8733, q_gen_8732) -> q_gen_8732
<nil>() -> q_gen_8732
<a>() -> q_gen_8733
<b>() -> q_gen_8733
<cons, cons>(q_gen_8682, q_gen_8668) -> q_gen_8668
<cons, cons>(q_gen_8682, q_gen_8730) -> q_gen_8668
<cons, cons>(q_gen_8696, q_gen_8668) -> q_gen_8668
<nil, nil>() -> q_gen_8668
<a, a>() -> q_gen_8682
<b, b>() -> q_gen_8682
<a, b>() -> q_gen_8696
<b, a>() -> q_gen_8696
<cons, cons>(q_gen_8682, q_gen_8731) -> q_gen_8730
<cons, cons>(q_gen_8696, q_gen_8731) -> q_gen_8730
<cons, nil>(q_gen_8733, q_gen_8732) -> q_gen_8730
<cons, cons>(q_gen_8696, q_gen_8730) -> q_gen_8731
<nil, cons>(q_gen_8733, q_gen_8732) -> q_gen_8731
}

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, _oha]) /\ not leq([x, y])) -> insert([x, cons(y, z), _oha]) -> 34
(insert([y, _tha, _uha]) /\ sort([z, _tha])) -> sort([cons(y, z), _uha]) -> 35
(length([_dia, _eia]) /\ length([l, _cia]) /\ sort([l, _dia])) -> eq_nat([_cia, _eia]) -> 37
(length([ll, _yha])) -> length([cons(x, ll), s(_yha)]) -> 32
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 34
(leq([b, a])) -> BOT -> 32
}
Sat witness: Found: ((length([_dia, _eia]) /\ length([l, _cia]) /\ sort([l, _dia])) -> eq_nat([_cia, _eia]), {
_cia -> s(z)  ;  _dia -> cons(b, nil)  ;  _eia -> s(s(s(z)))  ;  l -> cons(a, nil)
})

-------------------------------------------
Step 47, which took 0.270170 s (model generation: 0.264094,  model checking: 0.006076):

Model:
|_
{
insert -> 
{{{
Q={q_gen_8672, q_gen_8673, q_gen_8674, q_gen_8676, q_gen_8677, q_gen_8689, q_gen_8694, q_gen_8721},
Q_f={q_gen_8672},
Delta=
{
<cons>(q_gen_8674, q_gen_8721) -> q_gen_8673
<nil>() -> q_gen_8673
<b>() -> q_gen_8674
<a>() -> q_gen_8689
<cons>(q_gen_8674, q_gen_8673) -> q_gen_8721
<cons>(q_gen_8689, q_gen_8673) -> q_gen_8721
<cons>(q_gen_8689, q_gen_8721) -> q_gen_8721
<cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8676
<cons, nil>(q_gen_8674, q_gen_8673) -> q_gen_8676
<cons, nil>(q_gen_8674, q_gen_8721) -> q_gen_8676
<cons, nil>(q_gen_8689, q_gen_8673) -> q_gen_8676
<nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8676
<nil, cons>(q_gen_8674, q_gen_8721) -> q_gen_8676
<nil, cons>(q_gen_8689, q_gen_8673) -> q_gen_8676
<nil, nil>() -> q_gen_8676
<a, a>() -> q_gen_8677
<a, b>() -> q_gen_8677
<b, a>() -> q_gen_8677
<b, b>() -> q_gen_8677
<a, cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8672
<a, nil, cons>(q_gen_8689, q_gen_8673) -> q_gen_8672
<b, cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8672
<b, nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8672
<b, nil, cons>(q_gen_8674, q_gen_8721) -> q_gen_8672
<a, nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8694
<a, nil, cons>(q_gen_8674, q_gen_8721) -> q_gen_8694
<a, nil, cons>(q_gen_8689, q_gen_8721) -> q_gen_8694
<b, nil, cons>(q_gen_8689, q_gen_8673) -> q_gen_8694
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_8671, q_gen_8679, q_gen_8680, q_gen_8703, q_gen_8704, q_gen_8705, q_gen_8706, q_gen_8707, q_gen_8725},
Q_f={q_gen_8671},
Delta=
{
<cons>(q_gen_8704, q_gen_8703) -> q_gen_8679
<nil>() -> q_gen_8679
<cons>(q_gen_8704, q_gen_8679) -> q_gen_8703
<a>() -> q_gen_8704
<b>() -> q_gen_8704
<s>(q_gen_8725) -> q_gen_8706
<z>() -> q_gen_8706
<s>(q_gen_8706) -> q_gen_8725
<cons, s>(q_gen_8680, q_gen_8679) -> q_gen_8671
<cons, s>(q_gen_8705, q_gen_8703) -> q_gen_8671
<nil, z>() -> q_gen_8671
<a, s>(q_gen_8725) -> q_gen_8680
<a, z>() -> q_gen_8680
<b, s>(q_gen_8725) -> q_gen_8680
<b, z>() -> q_gen_8680
<a, s>(q_gen_8706) -> q_gen_8705
<b, s>(q_gen_8706) -> q_gen_8705
<cons, s>(q_gen_8680, q_gen_8703) -> q_gen_8707
<cons, s>(q_gen_8705, q_gen_8679) -> q_gen_8707
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_8669, q_gen_8683},
Q_f={q_gen_8669},
Delta=
{
<a, a>() -> q_gen_8669
<a, b>() -> q_gen_8669
<b, b>() -> q_gen_8669
<b, a>() -> q_gen_8683
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_8668, q_gen_8682, q_gen_8695, q_gen_8696, q_gen_8732, q_gen_8733},
Q_f={q_gen_8668},
Delta=
{
<cons>(q_gen_8733, q_gen_8732) -> q_gen_8732
<nil>() -> q_gen_8732
<a>() -> q_gen_8733
<b>() -> q_gen_8733
<cons, cons>(q_gen_8682, q_gen_8668) -> q_gen_8668
<nil, nil>() -> q_gen_8668
<a, a>() -> q_gen_8682
<b, b>() -> q_gen_8682
<cons, cons>(q_gen_8682, q_gen_8695) -> q_gen_8695
<cons, cons>(q_gen_8696, q_gen_8668) -> q_gen_8695
<cons, cons>(q_gen_8696, q_gen_8695) -> q_gen_8695
<cons, nil>(q_gen_8733, q_gen_8732) -> q_gen_8695
<nil, cons>(q_gen_8733, q_gen_8732) -> q_gen_8695
<a, b>() -> q_gen_8696
<b, a>() -> q_gen_8696
}

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, _oha]) /\ not leq([x, y])) -> insert([x, cons(y, z), _oha]) -> 37
(insert([y, _tha, _uha]) /\ sort([z, _tha])) -> sort([cons(y, z), _uha]) -> 35
(length([_dia, _eia]) /\ length([l, _cia]) /\ sort([l, _dia])) -> eq_nat([_cia, _eia]) -> 37
(length([ll, _yha])) -> length([cons(x, ll), s(_yha)]) -> 33
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 35
(leq([b, a])) -> BOT -> 33
}
Sat witness: Found: ((insert([x, z, _oha]) /\ not leq([x, y])) -> insert([x, cons(y, z), _oha]), {
_oha -> cons(b, cons(a, cons(a, nil)))  ;  x -> b  ;  y -> a  ;  z -> nil
})

-------------------------------------------
Step 48, which took 0.307548 s (model generation: 0.301265,  model checking: 0.006283):

Model:
|_
{
insert -> 
{{{
Q={q_gen_8672, q_gen_8673, q_gen_8674, q_gen_8676, q_gen_8677, q_gen_8689, q_gen_8694, q_gen_8721},
Q_f={q_gen_8672},
Delta=
{
<cons>(q_gen_8689, q_gen_8721) -> q_gen_8673
<nil>() -> q_gen_8673
<b>() -> q_gen_8674
<a>() -> q_gen_8689
<cons>(q_gen_8674, q_gen_8673) -> q_gen_8721
<cons>(q_gen_8674, q_gen_8721) -> q_gen_8721
<cons>(q_gen_8689, q_gen_8673) -> q_gen_8721
<cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8676
<cons, nil>(q_gen_8674, q_gen_8673) -> q_gen_8676
<cons, nil>(q_gen_8674, q_gen_8721) -> q_gen_8676
<cons, nil>(q_gen_8689, q_gen_8673) -> q_gen_8676
<nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8676
<nil, cons>(q_gen_8674, q_gen_8721) -> q_gen_8676
<nil, cons>(q_gen_8689, q_gen_8673) -> q_gen_8676
<nil, cons>(q_gen_8689, q_gen_8721) -> q_gen_8676
<nil, nil>() -> q_gen_8676
<a, a>() -> q_gen_8677
<a, b>() -> q_gen_8677
<b, a>() -> q_gen_8677
<b, b>() -> q_gen_8677
<a, cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8672
<a, nil, cons>(q_gen_8689, q_gen_8673) -> q_gen_8672
<b, cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8672
<b, nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8672
<a, nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8694
<a, nil, cons>(q_gen_8674, q_gen_8721) -> q_gen_8694
<a, nil, cons>(q_gen_8689, q_gen_8721) -> q_gen_8694
<b, nil, cons>(q_gen_8674, q_gen_8721) -> q_gen_8694
<b, nil, cons>(q_gen_8689, q_gen_8673) -> q_gen_8694
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_8671, q_gen_8679, q_gen_8680, q_gen_8703, q_gen_8704, q_gen_8705, q_gen_8706, q_gen_8707, q_gen_8725},
Q_f={q_gen_8671},
Delta=
{
<cons>(q_gen_8704, q_gen_8703) -> q_gen_8679
<nil>() -> q_gen_8679
<cons>(q_gen_8704, q_gen_8679) -> q_gen_8703
<a>() -> q_gen_8704
<b>() -> q_gen_8704
<s>(q_gen_8725) -> q_gen_8706
<z>() -> q_gen_8706
<s>(q_gen_8706) -> q_gen_8725
<cons, s>(q_gen_8680, q_gen_8679) -> q_gen_8671
<cons, s>(q_gen_8705, q_gen_8703) -> q_gen_8671
<nil, z>() -> q_gen_8671
<a, s>(q_gen_8725) -> q_gen_8680
<a, z>() -> q_gen_8680
<b, s>(q_gen_8725) -> q_gen_8680
<b, z>() -> q_gen_8680
<a, s>(q_gen_8706) -> q_gen_8705
<b, s>(q_gen_8706) -> q_gen_8705
<cons, s>(q_gen_8680, q_gen_8703) -> q_gen_8707
<cons, s>(q_gen_8705, q_gen_8679) -> q_gen_8707
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_8669, q_gen_8683},
Q_f={q_gen_8669},
Delta=
{
<a, a>() -> q_gen_8669
<a, b>() -> q_gen_8669
<b, b>() -> q_gen_8669
<b, a>() -> q_gen_8683
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_8668, q_gen_8682, q_gen_8695, q_gen_8696, q_gen_8732, q_gen_8733},
Q_f={q_gen_8668},
Delta=
{
<cons>(q_gen_8733, q_gen_8732) -> q_gen_8732
<nil>() -> q_gen_8732
<a>() -> q_gen_8733
<b>() -> q_gen_8733
<cons, cons>(q_gen_8682, q_gen_8668) -> q_gen_8668
<nil, nil>() -> q_gen_8668
<a, a>() -> q_gen_8682
<b, b>() -> q_gen_8682
<cons, cons>(q_gen_8682, q_gen_8695) -> q_gen_8695
<cons, cons>(q_gen_8696, q_gen_8668) -> q_gen_8695
<cons, cons>(q_gen_8696, q_gen_8695) -> q_gen_8695
<cons, nil>(q_gen_8733, q_gen_8732) -> q_gen_8695
<nil, cons>(q_gen_8733, q_gen_8732) -> q_gen_8695
<a, b>() -> q_gen_8696
<b, a>() -> q_gen_8696
}

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, _oha]) /\ not leq([x, y])) -> insert([x, cons(y, z), _oha]) -> 37
(insert([y, _tha, _uha]) /\ sort([z, _tha])) -> sort([cons(y, z), _uha]) -> 38
(length([_dia, _eia]) /\ length([l, _cia]) /\ sort([l, _dia])) -> eq_nat([_cia, _eia]) -> 37
(length([ll, _yha])) -> length([cons(x, ll), s(_yha)]) -> 34
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 36
(leq([b, a])) -> BOT -> 34
}
Sat witness: Found: ((insert([y, _tha, _uha]) /\ sort([z, _tha])) -> sort([cons(y, z), _uha]), {
_tha -> nil  ;  _uha -> cons(a, cons(a, cons(a, nil)))  ;  y -> a  ;  z -> nil
})

-------------------------------------------
Step 49, which took 0.298448 s (model generation: 0.293652,  model checking: 0.004796):

Model:
|_
{
insert -> 
{{{
Q={q_gen_8672, q_gen_8673, q_gen_8674, q_gen_8676, q_gen_8677, q_gen_8685, q_gen_8689, q_gen_8694},
Q_f={q_gen_8672},
Delta=
{
<cons>(q_gen_8674, q_gen_8673) -> q_gen_8673
<cons>(q_gen_8689, q_gen_8673) -> q_gen_8673
<nil>() -> q_gen_8673
<b>() -> q_gen_8674
<a>() -> q_gen_8689
<cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8676
<nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8676
<a, a>() -> q_gen_8677
<a, b>() -> q_gen_8677
<b, a>() -> q_gen_8677
<b, b>() -> q_gen_8677
<cons, cons>(q_gen_8677, q_gen_8685) -> q_gen_8685
<cons, nil>(q_gen_8674, q_gen_8673) -> q_gen_8685
<cons, nil>(q_gen_8689, q_gen_8673) -> q_gen_8685
<nil, cons>(q_gen_8689, q_gen_8673) -> q_gen_8685
<nil, nil>() -> q_gen_8685
<a, cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8672
<a, nil, cons>(q_gen_8689, q_gen_8673) -> q_gen_8672
<b, cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8672
<b, cons, cons>(q_gen_8677, q_gen_8685) -> q_gen_8672
<b, nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8672
<a, cons, cons>(q_gen_8677, q_gen_8685) -> q_gen_8694
<a, nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8694
<b, nil, cons>(q_gen_8689, q_gen_8673) -> q_gen_8694
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_8671, q_gen_8679, q_gen_8680, q_gen_8703, q_gen_8704, q_gen_8705, q_gen_8706, q_gen_8707, q_gen_8725},
Q_f={q_gen_8671},
Delta=
{
<cons>(q_gen_8704, q_gen_8703) -> q_gen_8679
<nil>() -> q_gen_8679
<cons>(q_gen_8704, q_gen_8679) -> q_gen_8703
<a>() -> q_gen_8704
<b>() -> q_gen_8704
<s>(q_gen_8725) -> q_gen_8706
<z>() -> q_gen_8706
<s>(q_gen_8706) -> q_gen_8725
<cons, s>(q_gen_8680, q_gen_8679) -> q_gen_8671
<cons, s>(q_gen_8705, q_gen_8703) -> q_gen_8671
<nil, z>() -> q_gen_8671
<a, s>(q_gen_8725) -> q_gen_8680
<a, z>() -> q_gen_8680
<b, s>(q_gen_8725) -> q_gen_8680
<b, z>() -> q_gen_8680
<a, s>(q_gen_8706) -> q_gen_8705
<b, s>(q_gen_8706) -> q_gen_8705
<cons, s>(q_gen_8680, q_gen_8703) -> q_gen_8707
<cons, s>(q_gen_8705, q_gen_8679) -> q_gen_8707
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_8669, q_gen_8683},
Q_f={q_gen_8669},
Delta=
{
<a, a>() -> q_gen_8669
<a, b>() -> q_gen_8669
<b, b>() -> q_gen_8669
<b, a>() -> q_gen_8683
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_8668, q_gen_8682, q_gen_8695, q_gen_8696, q_gen_8732, q_gen_8733},
Q_f={q_gen_8668},
Delta=
{
<cons>(q_gen_8733, q_gen_8732) -> q_gen_8732
<nil>() -> q_gen_8732
<a>() -> q_gen_8733
<b>() -> q_gen_8733
<cons, cons>(q_gen_8682, q_gen_8668) -> q_gen_8668
<cons, cons>(q_gen_8682, q_gen_8695) -> q_gen_8668
<nil, nil>() -> q_gen_8668
<a, a>() -> q_gen_8682
<b, b>() -> q_gen_8682
<cons, cons>(q_gen_8696, q_gen_8668) -> q_gen_8695
<cons, cons>(q_gen_8696, q_gen_8695) -> q_gen_8695
<cons, nil>(q_gen_8733, q_gen_8732) -> q_gen_8695
<nil, cons>(q_gen_8733, q_gen_8732) -> q_gen_8695
<a, b>() -> q_gen_8696
<b, a>() -> q_gen_8696
}

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, _oha]) /\ not leq([x, y])) -> insert([x, cons(y, z), _oha]) -> 37
(insert([y, _tha, _uha]) /\ sort([z, _tha])) -> sort([cons(y, z), _uha]) -> 38
(length([_dia, _eia]) /\ length([l, _cia]) /\ sort([l, _dia])) -> eq_nat([_cia, _eia]) -> 37
(length([ll, _yha])) -> length([cons(x, ll), s(_yha)]) -> 35
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 39
(leq([b, a])) -> BOT -> 35
}
Sat witness: Found: ((leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]), {
x -> a  ;  y -> a  ;  z -> nil
})

-------------------------------------------
Step 50, which took 0.331635 s (model generation: 0.327631,  model checking: 0.004004):

Model:
|_
{
insert -> 
{{{
Q={q_gen_8672, q_gen_8673, q_gen_8674, q_gen_8676, q_gen_8677, q_gen_8689, q_gen_8694, q_gen_8721},
Q_f={q_gen_8672},
Delta=
{
<cons>(q_gen_8674, q_gen_8721) -> q_gen_8673
<nil>() -> q_gen_8673
<b>() -> q_gen_8674
<a>() -> q_gen_8689
<cons>(q_gen_8674, q_gen_8673) -> q_gen_8721
<cons>(q_gen_8689, q_gen_8673) -> q_gen_8721
<cons>(q_gen_8689, q_gen_8721) -> q_gen_8721
<cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8676
<cons, nil>(q_gen_8674, q_gen_8673) -> q_gen_8676
<cons, nil>(q_gen_8674, q_gen_8721) -> q_gen_8676
<cons, nil>(q_gen_8689, q_gen_8673) -> q_gen_8676
<nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8676
<nil, cons>(q_gen_8674, q_gen_8721) -> q_gen_8676
<nil, cons>(q_gen_8689, q_gen_8673) -> q_gen_8676
<nil, cons>(q_gen_8689, q_gen_8721) -> q_gen_8676
<nil, nil>() -> q_gen_8676
<a, a>() -> q_gen_8677
<a, b>() -> q_gen_8677
<b, a>() -> q_gen_8677
<b, b>() -> q_gen_8677
<a, cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8672
<a, nil, cons>(q_gen_8689, q_gen_8673) -> q_gen_8672
<b, cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8672
<b, nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8672
<a, nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8694
<a, nil, cons>(q_gen_8674, q_gen_8721) -> q_gen_8694
<a, nil, cons>(q_gen_8689, q_gen_8721) -> q_gen_8694
<b, nil, cons>(q_gen_8674, q_gen_8721) -> q_gen_8694
<b, nil, cons>(q_gen_8689, q_gen_8673) -> q_gen_8694
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_8671, q_gen_8679, q_gen_8680, q_gen_8703, q_gen_8704, q_gen_8705, q_gen_8706, q_gen_8707, q_gen_8725},
Q_f={q_gen_8671},
Delta=
{
<cons>(q_gen_8704, q_gen_8703) -> q_gen_8679
<nil>() -> q_gen_8679
<cons>(q_gen_8704, q_gen_8679) -> q_gen_8703
<a>() -> q_gen_8704
<b>() -> q_gen_8704
<s>(q_gen_8725) -> q_gen_8706
<z>() -> q_gen_8706
<s>(q_gen_8706) -> q_gen_8725
<cons, s>(q_gen_8680, q_gen_8679) -> q_gen_8671
<cons, s>(q_gen_8705, q_gen_8703) -> q_gen_8671
<nil, z>() -> q_gen_8671
<a, s>(q_gen_8725) -> q_gen_8680
<a, z>() -> q_gen_8680
<b, s>(q_gen_8725) -> q_gen_8680
<b, z>() -> q_gen_8680
<a, s>(q_gen_8706) -> q_gen_8705
<b, s>(q_gen_8706) -> q_gen_8705
<cons, s>(q_gen_8680, q_gen_8703) -> q_gen_8707
<cons, s>(q_gen_8705, q_gen_8679) -> q_gen_8707
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_8669, q_gen_8683},
Q_f={q_gen_8669},
Delta=
{
<a, a>() -> q_gen_8669
<a, b>() -> q_gen_8669
<b, b>() -> q_gen_8669
<b, a>() -> q_gen_8683
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_8668, q_gen_8682, q_gen_8695, q_gen_8696, q_gen_8732, q_gen_8733},
Q_f={q_gen_8668},
Delta=
{
<cons>(q_gen_8733, q_gen_8732) -> q_gen_8732
<nil>() -> q_gen_8732
<a>() -> q_gen_8733
<b>() -> q_gen_8733
<cons, cons>(q_gen_8682, q_gen_8668) -> q_gen_8668
<nil, nil>() -> q_gen_8668
<a, a>() -> q_gen_8682
<b, b>() -> q_gen_8682
<cons, cons>(q_gen_8682, q_gen_8695) -> q_gen_8695
<cons, cons>(q_gen_8696, q_gen_8668) -> q_gen_8695
<cons, cons>(q_gen_8696, q_gen_8695) -> q_gen_8695
<cons, nil>(q_gen_8733, q_gen_8732) -> q_gen_8695
<nil, cons>(q_gen_8733, q_gen_8732) -> q_gen_8695
<a, b>() -> q_gen_8696
<b, a>() -> q_gen_8696
}

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, _oha]) /\ not leq([x, y])) -> insert([x, cons(y, z), _oha]) -> 37
(insert([y, _tha, _uha]) /\ sort([z, _tha])) -> sort([cons(y, z), _uha]) -> 38
(length([_dia, _eia]) /\ length([l, _cia]) /\ sort([l, _dia])) -> eq_nat([_cia, _eia]) -> 40
(length([ll, _yha])) -> length([cons(x, ll), s(_yha)]) -> 36
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 39
(leq([b, a])) -> BOT -> 36
}
Sat witness: Found: ((length([_dia, _eia]) /\ length([l, _cia]) /\ sort([l, _dia])) -> eq_nat([_cia, _eia]), {
_cia -> s(z)  ;  _dia -> cons(a, nil)  ;  _eia -> s(s(s(z)))  ;  l -> cons(a, nil)
})

-------------------------------------------
Step 51, which took 0.322943 s (model generation: 0.314272,  model checking: 0.008671):

Model:
|_
{
insert -> 
{{{
Q={q_gen_8672, q_gen_8673, q_gen_8674, q_gen_8676, q_gen_8677, q_gen_8721, q_gen_8729},
Q_f={q_gen_8672},
Delta=
{
<nil>() -> q_gen_8673
<a>() -> q_gen_8674
<b>() -> q_gen_8674
<cons>(q_gen_8674, q_gen_8673) -> q_gen_8721
<cons>(q_gen_8674, q_gen_8721) -> q_gen_8721
<cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8676
<cons, nil>(q_gen_8674, q_gen_8673) -> q_gen_8676
<cons, nil>(q_gen_8674, q_gen_8721) -> q_gen_8676
<nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8676
<nil, cons>(q_gen_8674, q_gen_8721) -> q_gen_8676
<nil, nil>() -> q_gen_8676
<a, a>() -> q_gen_8677
<a, b>() -> q_gen_8677
<b, a>() -> q_gen_8677
<b, b>() -> q_gen_8677
<a, cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8672
<a, nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8672
<b, cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8672
<b, nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8672
<a, nil, cons>(q_gen_8674, q_gen_8721) -> q_gen_8729
<b, nil, cons>(q_gen_8674, q_gen_8721) -> q_gen_8729
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_8671, q_gen_8679, q_gen_8680, q_gen_8703, q_gen_8704, q_gen_8705, q_gen_8706, q_gen_8707, q_gen_8723, q_gen_8725, q_gen_8727},
Q_f={q_gen_8671},
Delta=
{
<nil>() -> q_gen_8679
<cons>(q_gen_8704, q_gen_8679) -> q_gen_8703
<a>() -> q_gen_8704
<b>() -> q_gen_8704
<z>() -> q_gen_8706
<cons>(q_gen_8704, q_gen_8703) -> q_gen_8723
<s>(q_gen_8706) -> q_gen_8725
<s>(q_gen_8725) -> q_gen_8725
<cons, s>(q_gen_8680, q_gen_8679) -> q_gen_8671
<cons, s>(q_gen_8705, q_gen_8703) -> q_gen_8671
<cons, s>(q_gen_8705, q_gen_8723) -> q_gen_8671
<cons, s>(q_gen_8727, q_gen_8723) -> q_gen_8671
<nil, z>() -> q_gen_8671
<a, z>() -> q_gen_8680
<b, z>() -> q_gen_8680
<a, s>(q_gen_8706) -> q_gen_8705
<b, s>(q_gen_8706) -> q_gen_8705
<b, s>(q_gen_8725) -> q_gen_8705
<cons, s>(q_gen_8680, q_gen_8723) -> q_gen_8707
<cons, s>(q_gen_8705, q_gen_8679) -> q_gen_8707
<cons, s>(q_gen_8727, q_gen_8679) -> q_gen_8707
<cons, s>(q_gen_8727, q_gen_8703) -> q_gen_8707
<a, s>(q_gen_8725) -> q_gen_8727
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_8669, q_gen_8683},
Q_f={q_gen_8669},
Delta=
{
<a, a>() -> q_gen_8669
<a, b>() -> q_gen_8669
<b, b>() -> q_gen_8669
<b, a>() -> q_gen_8683
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_8668, q_gen_8682, q_gen_8730, q_gen_8732, q_gen_8733, q_gen_8751},
Q_f={q_gen_8668},
Delta=
{
<cons>(q_gen_8733, q_gen_8732) -> q_gen_8732
<nil>() -> q_gen_8732
<a>() -> q_gen_8733
<b>() -> q_gen_8733
<cons, cons>(q_gen_8682, q_gen_8668) -> q_gen_8668
<cons, cons>(q_gen_8682, q_gen_8751) -> q_gen_8668
<nil, nil>() -> q_gen_8668
<a, a>() -> q_gen_8682
<a, b>() -> q_gen_8682
<b, a>() -> q_gen_8682
<b, b>() -> q_gen_8682
<cons, cons>(q_gen_8682, q_gen_8730) -> q_gen_8730
<nil, cons>(q_gen_8733, q_gen_8732) -> q_gen_8730
<cons, nil>(q_gen_8733, q_gen_8732) -> q_gen_8751
}

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, _oha]) /\ not leq([x, y])) -> insert([x, cons(y, z), _oha]) -> 37
(insert([y, _tha, _uha]) /\ sort([z, _tha])) -> sort([cons(y, z), _uha]) -> 38
(length([_dia, _eia]) /\ length([l, _cia]) /\ sort([l, _dia])) -> eq_nat([_cia, _eia]) -> 40
(length([ll, _yha])) -> length([cons(x, ll), s(_yha)]) -> 39
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 39
(leq([b, a])) -> BOT -> 37
}
Sat witness: Found: ((length([ll, _yha])) -> length([cons(x, ll), s(_yha)]), {
_yha -> s(s(s(z)))  ;  ll -> cons(a, cons(a, cons(b, nil)))  ;  x -> a
})

-------------------------------------------
Step 52, which took 0.309828 s (model generation: 0.305758,  model checking: 0.004070):

Model:
|_
{
insert -> 
{{{
Q={q_gen_8672, q_gen_8673, q_gen_8674, q_gen_8676, q_gen_8677, q_gen_8721, q_gen_8729},
Q_f={q_gen_8672},
Delta=
{
<nil>() -> q_gen_8673
<a>() -> q_gen_8674
<b>() -> q_gen_8674
<cons>(q_gen_8674, q_gen_8673) -> q_gen_8721
<cons>(q_gen_8674, q_gen_8721) -> q_gen_8721
<cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8676
<cons, nil>(q_gen_8674, q_gen_8673) -> q_gen_8676
<cons, nil>(q_gen_8674, q_gen_8721) -> q_gen_8676
<nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8676
<nil, cons>(q_gen_8674, q_gen_8721) -> q_gen_8676
<nil, nil>() -> q_gen_8676
<a, a>() -> q_gen_8677
<a, b>() -> q_gen_8677
<b, a>() -> q_gen_8677
<b, b>() -> q_gen_8677
<a, cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8672
<a, nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8672
<b, cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8672
<b, nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8672
<a, nil, cons>(q_gen_8674, q_gen_8721) -> q_gen_8729
<b, nil, cons>(q_gen_8674, q_gen_8721) -> q_gen_8729
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_8671, q_gen_8679, q_gen_8680, q_gen_8703, q_gen_8704, q_gen_8705, q_gen_8706, q_gen_8707, q_gen_8723, q_gen_8725, q_gen_8727},
Q_f={q_gen_8671},
Delta=
{
<nil>() -> q_gen_8679
<cons>(q_gen_8704, q_gen_8679) -> q_gen_8703
<a>() -> q_gen_8704
<b>() -> q_gen_8704
<s>(q_gen_8725) -> q_gen_8706
<z>() -> q_gen_8706
<cons>(q_gen_8704, q_gen_8703) -> q_gen_8723
<cons>(q_gen_8704, q_gen_8723) -> q_gen_8723
<s>(q_gen_8706) -> q_gen_8725
<cons, s>(q_gen_8680, q_gen_8679) -> q_gen_8671
<cons, s>(q_gen_8705, q_gen_8703) -> q_gen_8671
<cons, s>(q_gen_8705, q_gen_8723) -> q_gen_8671
<cons, s>(q_gen_8727, q_gen_8723) -> q_gen_8671
<nil, z>() -> q_gen_8671
<a, z>() -> q_gen_8680
<b, z>() -> q_gen_8680
<a, s>(q_gen_8706) -> q_gen_8705
<b, s>(q_gen_8706) -> q_gen_8705
<b, s>(q_gen_8725) -> q_gen_8705
<cons, s>(q_gen_8680, q_gen_8723) -> q_gen_8707
<cons, s>(q_gen_8705, q_gen_8679) -> q_gen_8707
<cons, s>(q_gen_8727, q_gen_8679) -> q_gen_8707
<cons, s>(q_gen_8727, q_gen_8703) -> q_gen_8707
<a, s>(q_gen_8725) -> q_gen_8727
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_8669, q_gen_8683},
Q_f={q_gen_8669},
Delta=
{
<a, a>() -> q_gen_8669
<a, b>() -> q_gen_8669
<b, b>() -> q_gen_8669
<b, a>() -> q_gen_8683
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_8668, q_gen_8682, q_gen_8730, q_gen_8732, q_gen_8733, q_gen_8751},
Q_f={q_gen_8668},
Delta=
{
<cons>(q_gen_8733, q_gen_8732) -> q_gen_8732
<nil>() -> q_gen_8732
<a>() -> q_gen_8733
<b>() -> q_gen_8733
<cons, cons>(q_gen_8682, q_gen_8668) -> q_gen_8668
<cons, cons>(q_gen_8682, q_gen_8751) -> q_gen_8668
<nil, nil>() -> q_gen_8668
<a, a>() -> q_gen_8682
<a, b>() -> q_gen_8682
<b, a>() -> q_gen_8682
<b, b>() -> q_gen_8682
<cons, cons>(q_gen_8682, q_gen_8730) -> q_gen_8730
<nil, cons>(q_gen_8733, q_gen_8732) -> q_gen_8730
<cons, nil>(q_gen_8733, q_gen_8732) -> q_gen_8751
}

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, _oha]) /\ not leq([x, y])) -> insert([x, cons(y, z), _oha]) -> 38
(insert([y, _tha, _uha]) /\ sort([z, _tha])) -> sort([cons(y, z), _uha]) -> 41
(length([_dia, _eia]) /\ length([l, _cia]) /\ sort([l, _dia])) -> eq_nat([_cia, _eia]) -> 40
(length([ll, _yha])) -> length([cons(x, ll), s(_yha)]) -> 39
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 39
(leq([b, a])) -> BOT -> 38
}
Sat witness: Found: ((insert([y, _tha, _uha]) /\ sort([z, _tha])) -> sort([cons(y, z), _uha]), {
_tha -> cons(b, nil)  ;  _uha -> cons(b, cons(b, cons(b, cons(b, nil))))  ;  y -> a  ;  z -> cons(a, cons(a, nil))
})

-------------------------------------------
Step 53, which took 0.349398 s (model generation: 0.343823,  model checking: 0.005575):

Model:
|_
{
insert -> 
{{{
Q={q_gen_8672, q_gen_8673, q_gen_8674, q_gen_8676, q_gen_8677, q_gen_8689, q_gen_8694},
Q_f={q_gen_8672},
Delta=
{
<cons>(q_gen_8674, q_gen_8673) -> q_gen_8673
<cons>(q_gen_8689, q_gen_8673) -> q_gen_8673
<nil>() -> q_gen_8673
<b>() -> q_gen_8674
<a>() -> q_gen_8689
<cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8676
<cons, nil>(q_gen_8674, q_gen_8673) -> q_gen_8676
<cons, nil>(q_gen_8689, q_gen_8673) -> q_gen_8676
<nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8676
<nil, cons>(q_gen_8689, q_gen_8673) -> q_gen_8676
<nil, nil>() -> q_gen_8676
<a, a>() -> q_gen_8677
<a, b>() -> q_gen_8677
<b, a>() -> q_gen_8677
<b, b>() -> q_gen_8677
<a, cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8672
<a, nil, cons>(q_gen_8689, q_gen_8673) -> q_gen_8672
<b, cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8672
<b, nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8672
<a, nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8694
<b, nil, cons>(q_gen_8689, q_gen_8673) -> q_gen_8694
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_8671, q_gen_8679, q_gen_8680, q_gen_8703, q_gen_8704, q_gen_8705, q_gen_8706, q_gen_8707, q_gen_8723, q_gen_8725, q_gen_8727},
Q_f={q_gen_8671},
Delta=
{
<nil>() -> q_gen_8679
<cons>(q_gen_8704, q_gen_8679) -> q_gen_8703
<cons>(q_gen_8704, q_gen_8723) -> q_gen_8703
<a>() -> q_gen_8704
<b>() -> q_gen_8704
<s>(q_gen_8725) -> q_gen_8706
<z>() -> q_gen_8706
<cons>(q_gen_8704, q_gen_8703) -> q_gen_8723
<s>(q_gen_8706) -> q_gen_8725
<cons, s>(q_gen_8680, q_gen_8679) -> q_gen_8671
<cons, s>(q_gen_8705, q_gen_8703) -> q_gen_8671
<cons, s>(q_gen_8705, q_gen_8723) -> q_gen_8671
<cons, s>(q_gen_8727, q_gen_8723) -> q_gen_8671
<nil, z>() -> q_gen_8671
<a, z>() -> q_gen_8680
<b, z>() -> q_gen_8680
<a, s>(q_gen_8706) -> q_gen_8705
<b, s>(q_gen_8706) -> q_gen_8705
<b, s>(q_gen_8725) -> q_gen_8705
<cons, s>(q_gen_8680, q_gen_8723) -> q_gen_8707
<cons, s>(q_gen_8705, q_gen_8679) -> q_gen_8707
<cons, s>(q_gen_8727, q_gen_8679) -> q_gen_8707
<cons, s>(q_gen_8727, q_gen_8703) -> q_gen_8707
<a, s>(q_gen_8725) -> q_gen_8727
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_8669, q_gen_8683},
Q_f={q_gen_8669},
Delta=
{
<a, a>() -> q_gen_8669
<a, b>() -> q_gen_8669
<b, b>() -> q_gen_8669
<b, a>() -> q_gen_8683
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_8668, q_gen_8682, q_gen_8709, q_gen_8730, q_gen_8731, q_gen_8732, q_gen_8733},
Q_f={q_gen_8668},
Delta=
{
<cons>(q_gen_8733, q_gen_8732) -> q_gen_8732
<nil>() -> q_gen_8732
<a>() -> q_gen_8733
<b>() -> q_gen_8733
<cons, cons>(q_gen_8682, q_gen_8668) -> q_gen_8668
<cons, cons>(q_gen_8682, q_gen_8730) -> q_gen_8668
<cons, cons>(q_gen_8709, q_gen_8668) -> q_gen_8668
<cons, cons>(q_gen_8709, q_gen_8731) -> q_gen_8668
<nil, nil>() -> q_gen_8668
<a, b>() -> q_gen_8682
<b, b>() -> q_gen_8682
<a, a>() -> q_gen_8709
<b, a>() -> q_gen_8709
<cons, cons>(q_gen_8682, q_gen_8731) -> q_gen_8730
<cons, cons>(q_gen_8709, q_gen_8730) -> q_gen_8730
<cons, nil>(q_gen_8733, q_gen_8732) -> q_gen_8730
<nil, cons>(q_gen_8733, q_gen_8732) -> q_gen_8731
}

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, _oha]) /\ not leq([x, y])) -> insert([x, cons(y, z), _oha]) -> 39
(insert([y, _tha, _uha]) /\ sort([z, _tha])) -> sort([cons(y, z), _uha]) -> 41
(length([_dia, _eia]) /\ length([l, _cia]) /\ sort([l, _dia])) -> eq_nat([_cia, _eia]) -> 40
(length([ll, _yha])) -> length([cons(x, ll), s(_yha)]) -> 42
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 40
(leq([b, a])) -> BOT -> 39
}
Sat witness: Found: ((length([ll, _yha])) -> length([cons(x, ll), s(_yha)]), {
_yha -> s(s(z))  ;  ll -> cons(b, cons(a, cons(b, nil)))  ;  x -> a
})

-------------------------------------------
Step 54, which took 0.350312 s (model generation: 0.347901,  model checking: 0.002411):

Model:
|_
{
insert -> 
{{{
Q={q_gen_8672, q_gen_8673, q_gen_8674, q_gen_8676, q_gen_8677, q_gen_8685, q_gen_8689, q_gen_8694},
Q_f={q_gen_8672},
Delta=
{
<cons>(q_gen_8674, q_gen_8673) -> q_gen_8673
<cons>(q_gen_8689, q_gen_8673) -> q_gen_8673
<nil>() -> q_gen_8673
<b>() -> q_gen_8674
<a>() -> q_gen_8689
<cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8676
<nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8676
<nil, cons>(q_gen_8689, q_gen_8673) -> q_gen_8676
<a, a>() -> q_gen_8677
<a, b>() -> q_gen_8677
<b, a>() -> q_gen_8677
<b, b>() -> q_gen_8677
<cons, nil>(q_gen_8674, q_gen_8673) -> q_gen_8685
<cons, nil>(q_gen_8689, q_gen_8673) -> q_gen_8685
<nil, nil>() -> q_gen_8685
<a, cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8672
<a, nil, cons>(q_gen_8689, q_gen_8673) -> q_gen_8672
<b, cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8672
<b, cons, cons>(q_gen_8677, q_gen_8685) -> q_gen_8672
<b, nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8672
<a, cons, cons>(q_gen_8677, q_gen_8685) -> q_gen_8694
<a, nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8694
<b, nil, cons>(q_gen_8689, q_gen_8673) -> q_gen_8694
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_8671, q_gen_8679, q_gen_8680, q_gen_8703, q_gen_8704, q_gen_8706, q_gen_8713, q_gen_8714, q_gen_8723, q_gen_8725, q_gen_8727},
Q_f={q_gen_8671},
Delta=
{
<nil>() -> q_gen_8679
<cons>(q_gen_8704, q_gen_8679) -> q_gen_8703
<a>() -> q_gen_8704
<b>() -> q_gen_8704
<z>() -> q_gen_8706
<cons>(q_gen_8704, q_gen_8703) -> q_gen_8723
<cons>(q_gen_8704, q_gen_8723) -> q_gen_8723
<s>(q_gen_8706) -> q_gen_8725
<s>(q_gen_8725) -> q_gen_8725
<cons, s>(q_gen_8680, q_gen_8679) -> q_gen_8671
<cons, s>(q_gen_8680, q_gen_8703) -> q_gen_8671
<cons, s>(q_gen_8680, q_gen_8723) -> q_gen_8671
<cons, s>(q_gen_8713, q_gen_8703) -> q_gen_8671
<cons, s>(q_gen_8727, q_gen_8723) -> q_gen_8671
<nil, z>() -> q_gen_8671
<a, z>() -> q_gen_8680
<b, s>(q_gen_8706) -> q_gen_8680
<b, s>(q_gen_8725) -> q_gen_8680
<b, z>() -> q_gen_8680
<a, s>(q_gen_8706) -> q_gen_8713
<cons, s>(q_gen_8713, q_gen_8679) -> q_gen_8714
<cons, s>(q_gen_8727, q_gen_8679) -> q_gen_8714
<cons, s>(q_gen_8727, q_gen_8703) -> q_gen_8714
<a, s>(q_gen_8725) -> q_gen_8727
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_8669, q_gen_8683},
Q_f={q_gen_8669},
Delta=
{
<a, a>() -> q_gen_8669
<a, b>() -> q_gen_8669
<b, b>() -> q_gen_8669
<b, a>() -> q_gen_8683
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_8668, q_gen_8682, q_gen_8695, q_gen_8696, q_gen_8732, q_gen_8733},
Q_f={q_gen_8668},
Delta=
{
<cons>(q_gen_8733, q_gen_8732) -> q_gen_8732
<nil>() -> q_gen_8732
<a>() -> q_gen_8733
<b>() -> q_gen_8733
<cons, cons>(q_gen_8682, q_gen_8668) -> q_gen_8668
<cons, cons>(q_gen_8682, q_gen_8695) -> q_gen_8668
<nil, nil>() -> q_gen_8668
<a, a>() -> q_gen_8682
<b, b>() -> q_gen_8682
<cons, cons>(q_gen_8696, q_gen_8668) -> q_gen_8695
<cons, cons>(q_gen_8696, q_gen_8695) -> q_gen_8695
<cons, nil>(q_gen_8733, q_gen_8732) -> q_gen_8695
<nil, cons>(q_gen_8733, q_gen_8732) -> q_gen_8695
<a, b>() -> q_gen_8696
<b, a>() -> q_gen_8696
}

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, _oha]) /\ not leq([x, y])) -> insert([x, cons(y, z), _oha]) -> 42
(insert([y, _tha, _uha]) /\ sort([z, _tha])) -> sort([cons(y, z), _uha]) -> 41
(length([_dia, _eia]) /\ length([l, _cia]) /\ sort([l, _dia])) -> eq_nat([_cia, _eia]) -> 40
(length([ll, _yha])) -> length([cons(x, ll), s(_yha)]) -> 42
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 40
(leq([b, a])) -> BOT -> 40
}
Sat witness: Found: ((insert([x, z, _oha]) /\ not leq([x, y])) -> insert([x, cons(y, z), _oha]), {
_oha -> cons(a, cons(b, nil))  ;  x -> b  ;  y -> a  ;  z -> cons(a, nil)
})

-------------------------------------------
Step 55, which took 0.353655 s (model generation: 0.344734,  model checking: 0.008921):

Model:
|_
{
insert -> 
{{{
Q={q_gen_8672, q_gen_8673, q_gen_8674, q_gen_8676, q_gen_8677, q_gen_8685, q_gen_8689, q_gen_8694},
Q_f={q_gen_8672},
Delta=
{
<cons>(q_gen_8674, q_gen_8673) -> q_gen_8673
<cons>(q_gen_8689, q_gen_8673) -> q_gen_8673
<nil>() -> q_gen_8673
<b>() -> q_gen_8674
<a>() -> q_gen_8689
<cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8676
<cons, cons>(q_gen_8677, q_gen_8685) -> q_gen_8676
<nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8676
<nil, cons>(q_gen_8689, q_gen_8673) -> q_gen_8676
<a, a>() -> q_gen_8677
<a, b>() -> q_gen_8677
<b, a>() -> q_gen_8677
<b, b>() -> q_gen_8677
<cons, nil>(q_gen_8674, q_gen_8673) -> q_gen_8685
<cons, nil>(q_gen_8689, q_gen_8673) -> q_gen_8685
<nil, nil>() -> q_gen_8685
<a, cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8672
<a, nil, cons>(q_gen_8689, q_gen_8673) -> q_gen_8672
<b, cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8672
<b, cons, cons>(q_gen_8677, q_gen_8685) -> q_gen_8672
<b, nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8672
<a, cons, cons>(q_gen_8677, q_gen_8685) -> q_gen_8694
<a, nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8694
<b, nil, cons>(q_gen_8689, q_gen_8673) -> q_gen_8694
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_8671, q_gen_8679, q_gen_8680, q_gen_8703, q_gen_8704, q_gen_8706, q_gen_8713, q_gen_8714, q_gen_8723, q_gen_8725, q_gen_8727},
Q_f={q_gen_8671},
Delta=
{
<nil>() -> q_gen_8679
<cons>(q_gen_8704, q_gen_8679) -> q_gen_8703
<a>() -> q_gen_8704
<b>() -> q_gen_8704
<z>() -> q_gen_8706
<cons>(q_gen_8704, q_gen_8703) -> q_gen_8723
<cons>(q_gen_8704, q_gen_8723) -> q_gen_8723
<s>(q_gen_8706) -> q_gen_8725
<s>(q_gen_8725) -> q_gen_8725
<cons, s>(q_gen_8680, q_gen_8679) -> q_gen_8671
<cons, s>(q_gen_8680, q_gen_8703) -> q_gen_8671
<cons, s>(q_gen_8713, q_gen_8703) -> q_gen_8671
<cons, s>(q_gen_8713, q_gen_8723) -> q_gen_8671
<cons, s>(q_gen_8727, q_gen_8723) -> q_gen_8671
<nil, z>() -> q_gen_8671
<a, z>() -> q_gen_8680
<b, s>(q_gen_8706) -> q_gen_8680
<b, z>() -> q_gen_8680
<a, s>(q_gen_8706) -> q_gen_8713
<b, s>(q_gen_8725) -> q_gen_8713
<cons, s>(q_gen_8680, q_gen_8723) -> q_gen_8714
<cons, s>(q_gen_8713, q_gen_8679) -> q_gen_8714
<cons, s>(q_gen_8727, q_gen_8679) -> q_gen_8714
<cons, s>(q_gen_8727, q_gen_8703) -> q_gen_8714
<a, s>(q_gen_8725) -> q_gen_8727
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_8669, q_gen_8683},
Q_f={q_gen_8669},
Delta=
{
<a, a>() -> q_gen_8669
<a, b>() -> q_gen_8669
<b, b>() -> q_gen_8669
<b, a>() -> q_gen_8683
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_8668, q_gen_8682, q_gen_8695, q_gen_8696, q_gen_8732, q_gen_8733},
Q_f={q_gen_8668},
Delta=
{
<cons>(q_gen_8733, q_gen_8732) -> q_gen_8732
<nil>() -> q_gen_8732
<a>() -> q_gen_8733
<b>() -> q_gen_8733
<cons, cons>(q_gen_8682, q_gen_8668) -> q_gen_8668
<cons, cons>(q_gen_8682, q_gen_8695) -> q_gen_8668
<nil, nil>() -> q_gen_8668
<a, a>() -> q_gen_8682
<b, b>() -> q_gen_8682
<cons, cons>(q_gen_8696, q_gen_8668) -> q_gen_8695
<cons, cons>(q_gen_8696, q_gen_8695) -> q_gen_8695
<cons, nil>(q_gen_8733, q_gen_8732) -> q_gen_8695
<nil, cons>(q_gen_8733, q_gen_8732) -> q_gen_8695
<a, b>() -> q_gen_8696
<b, a>() -> q_gen_8696
}

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, _oha]) /\ not leq([x, y])) -> insert([x, cons(y, z), _oha]) -> 42
(insert([y, _tha, _uha]) /\ sort([z, _tha])) -> sort([cons(y, z), _uha]) -> 41
(length([_dia, _eia]) /\ length([l, _cia]) /\ sort([l, _dia])) -> eq_nat([_cia, _eia]) -> 43
(length([ll, _yha])) -> length([cons(x, ll), s(_yha)]) -> 42
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 41
(leq([b, a])) -> BOT -> 41
}
Sat witness: Found: ((length([_dia, _eia]) /\ length([l, _cia]) /\ sort([l, _dia])) -> eq_nat([_cia, _eia]), {
_cia -> s(s(z))  ;  _dia -> cons(a, cons(a, cons(b, nil)))  ;  _eia -> s(s(s(z)))  ;  l -> cons(a, cons(b, nil))
})

-------------------------------------------
Step 56, which took 0.488136 s (model generation: 0.484841,  model checking: 0.003295):

Model:
|_
{
insert -> 
{{{
Q={q_gen_8672, q_gen_8673, q_gen_8674, q_gen_8676, q_gen_8677, q_gen_8685, q_gen_8686, q_gen_8721, q_gen_8729},
Q_f={q_gen_8672},
Delta=
{
<nil>() -> q_gen_8673
<a>() -> q_gen_8674
<b>() -> q_gen_8674
<cons>(q_gen_8674, q_gen_8673) -> q_gen_8721
<cons>(q_gen_8674, q_gen_8721) -> q_gen_8721
<cons, cons>(q_gen_8686, q_gen_8676) -> q_gen_8676
<cons, cons>(q_gen_8686, q_gen_8685) -> q_gen_8676
<cons, nil>(q_gen_8674, q_gen_8673) -> q_gen_8676
<nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8676
<nil, cons>(q_gen_8674, q_gen_8721) -> q_gen_8676
<b, b>() -> q_gen_8677
<cons, nil>(q_gen_8674, q_gen_8721) -> q_gen_8685
<nil, nil>() -> q_gen_8685
<a, a>() -> q_gen_8686
<a, b>() -> q_gen_8686
<b, a>() -> q_gen_8686
<a, cons, cons>(q_gen_8686, q_gen_8676) -> q_gen_8672
<a, nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8672
<b, cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8672
<b, cons, cons>(q_gen_8686, q_gen_8676) -> q_gen_8672
<b, cons, cons>(q_gen_8686, q_gen_8685) -> q_gen_8672
<b, nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8672
<a, cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8729
<a, nil, cons>(q_gen_8674, q_gen_8721) -> q_gen_8729
<b, cons, cons>(q_gen_8677, q_gen_8685) -> q_gen_8729
<b, nil, cons>(q_gen_8674, q_gen_8721) -> q_gen_8729
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_8671, q_gen_8679, q_gen_8680, q_gen_8703, q_gen_8704, q_gen_8705, q_gen_8706, q_gen_8707, q_gen_8723, q_gen_8725, q_gen_8727},
Q_f={q_gen_8671},
Delta=
{
<nil>() -> q_gen_8679
<cons>(q_gen_8704, q_gen_8679) -> q_gen_8703
<a>() -> q_gen_8704
<b>() -> q_gen_8704
<z>() -> q_gen_8706
<cons>(q_gen_8704, q_gen_8703) -> q_gen_8723
<cons>(q_gen_8704, q_gen_8723) -> q_gen_8723
<s>(q_gen_8706) -> q_gen_8725
<s>(q_gen_8725) -> q_gen_8725
<cons, s>(q_gen_8680, q_gen_8679) -> q_gen_8671
<cons, s>(q_gen_8705, q_gen_8703) -> q_gen_8671
<cons, s>(q_gen_8705, q_gen_8723) -> q_gen_8671
<cons, s>(q_gen_8727, q_gen_8723) -> q_gen_8671
<nil, z>() -> q_gen_8671
<a, z>() -> q_gen_8680
<b, z>() -> q_gen_8680
<a, s>(q_gen_8706) -> q_gen_8705
<b, s>(q_gen_8706) -> q_gen_8705
<b, s>(q_gen_8725) -> q_gen_8705
<cons, s>(q_gen_8680, q_gen_8723) -> q_gen_8707
<cons, s>(q_gen_8705, q_gen_8679) -> q_gen_8707
<cons, s>(q_gen_8727, q_gen_8679) -> q_gen_8707
<cons, s>(q_gen_8727, q_gen_8703) -> q_gen_8707
<a, s>(q_gen_8725) -> q_gen_8727
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_8669, q_gen_8683},
Q_f={q_gen_8669},
Delta=
{
<a, a>() -> q_gen_8669
<a, b>() -> q_gen_8669
<b, b>() -> q_gen_8669
<b, a>() -> q_gen_8683
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_8668, q_gen_8682, q_gen_8730, q_gen_8732, q_gen_8733},
Q_f={q_gen_8668},
Delta=
{
<cons>(q_gen_8733, q_gen_8732) -> q_gen_8732
<nil>() -> q_gen_8732
<a>() -> q_gen_8733
<b>() -> q_gen_8733
<cons, cons>(q_gen_8682, q_gen_8668) -> q_gen_8668
<nil, nil>() -> q_gen_8668
<a, a>() -> q_gen_8682
<a, b>() -> q_gen_8682
<b, a>() -> q_gen_8682
<b, b>() -> q_gen_8682
<cons, cons>(q_gen_8682, q_gen_8730) -> q_gen_8730
<cons, nil>(q_gen_8733, q_gen_8732) -> q_gen_8730
<nil, cons>(q_gen_8733, q_gen_8732) -> q_gen_8730
}

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, _oha]) /\ not leq([x, y])) -> insert([x, cons(y, z), _oha]) -> 42
(insert([y, _tha, _uha]) /\ sort([z, _tha])) -> sort([cons(y, z), _uha]) -> 41
(length([_dia, _eia]) /\ length([l, _cia]) /\ sort([l, _dia])) -> eq_nat([_cia, _eia]) -> 43
(length([ll, _yha])) -> length([cons(x, ll), s(_yha)]) -> 42
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 44
(leq([b, a])) -> BOT -> 42
}
Sat witness: Found: ((leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]), {
x -> b  ;  y -> b  ;  z -> cons(b, cons(b, nil))
})

-------------------------------------------
Step 57, which took 1.234112 s (model generation: 1.231960,  model checking: 0.002152):

Model:
|_
{
insert -> 
{{{
Q={q_gen_8672, q_gen_8673, q_gen_8674, q_gen_8676, q_gen_8677, q_gen_8721, q_gen_8729},
Q_f={q_gen_8672},
Delta=
{
<nil>() -> q_gen_8673
<a>() -> q_gen_8674
<b>() -> q_gen_8674
<cons>(q_gen_8674, q_gen_8673) -> q_gen_8721
<cons>(q_gen_8674, q_gen_8721) -> q_gen_8721
<cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8676
<cons, nil>(q_gen_8674, q_gen_8673) -> q_gen_8676
<cons, nil>(q_gen_8674, q_gen_8721) -> q_gen_8676
<nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8676
<nil, cons>(q_gen_8674, q_gen_8721) -> q_gen_8676
<nil, nil>() -> q_gen_8676
<a, a>() -> q_gen_8677
<a, b>() -> q_gen_8677
<b, a>() -> q_gen_8677
<b, b>() -> q_gen_8677
<a, cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8672
<a, nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8672
<b, cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8672
<b, nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8672
<a, nil, cons>(q_gen_8674, q_gen_8721) -> q_gen_8729
<b, nil, cons>(q_gen_8674, q_gen_8721) -> q_gen_8729
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_8671, q_gen_8679, q_gen_8680, q_gen_8703, q_gen_8704, q_gen_8705, q_gen_8706, q_gen_8707, q_gen_8723, q_gen_8725, q_gen_8727},
Q_f={q_gen_8671},
Delta=
{
<nil>() -> q_gen_8679
<cons>(q_gen_8704, q_gen_8679) -> q_gen_8703
<a>() -> q_gen_8704
<b>() -> q_gen_8704
<z>() -> q_gen_8706
<cons>(q_gen_8704, q_gen_8703) -> q_gen_8723
<cons>(q_gen_8704, q_gen_8723) -> q_gen_8723
<s>(q_gen_8706) -> q_gen_8725
<s>(q_gen_8725) -> q_gen_8725
<cons, s>(q_gen_8680, q_gen_8679) -> q_gen_8671
<cons, s>(q_gen_8705, q_gen_8703) -> q_gen_8671
<cons, s>(q_gen_8705, q_gen_8723) -> q_gen_8671
<cons, s>(q_gen_8727, q_gen_8723) -> q_gen_8671
<nil, z>() -> q_gen_8671
<a, z>() -> q_gen_8680
<b, z>() -> q_gen_8680
<a, s>(q_gen_8706) -> q_gen_8705
<b, s>(q_gen_8706) -> q_gen_8705
<b, s>(q_gen_8725) -> q_gen_8705
<cons, s>(q_gen_8680, q_gen_8723) -> q_gen_8707
<cons, s>(q_gen_8705, q_gen_8679) -> q_gen_8707
<cons, s>(q_gen_8727, q_gen_8679) -> q_gen_8707
<cons, s>(q_gen_8727, q_gen_8703) -> q_gen_8707
<a, s>(q_gen_8725) -> q_gen_8727
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_8669, q_gen_8683},
Q_f={q_gen_8669},
Delta=
{
<a, a>() -> q_gen_8669
<a, b>() -> q_gen_8669
<b, b>() -> q_gen_8669
<b, a>() -> q_gen_8683
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_8668, q_gen_8682, q_gen_8696, q_gen_8730, q_gen_8731, q_gen_8732, q_gen_8733},
Q_f={q_gen_8668},
Delta=
{
<cons>(q_gen_8733, q_gen_8732) -> q_gen_8732
<nil>() -> q_gen_8732
<a>() -> q_gen_8733
<b>() -> q_gen_8733
<cons, cons>(q_gen_8682, q_gen_8668) -> q_gen_8668
<cons, cons>(q_gen_8682, q_gen_8730) -> q_gen_8668
<cons, cons>(q_gen_8696, q_gen_8668) -> q_gen_8668
<nil, nil>() -> q_gen_8668
<b, b>() -> q_gen_8682
<a, a>() -> q_gen_8696
<a, b>() -> q_gen_8696
<b, a>() -> q_gen_8696
<cons, cons>(q_gen_8682, q_gen_8731) -> q_gen_8730
<cons, cons>(q_gen_8696, q_gen_8731) -> q_gen_8730
<cons, nil>(q_gen_8733, q_gen_8732) -> q_gen_8730
<cons, cons>(q_gen_8696, q_gen_8730) -> q_gen_8731
<nil, cons>(q_gen_8733, q_gen_8732) -> q_gen_8731
}

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, _oha]) /\ not leq([x, y])) -> insert([x, cons(y, z), _oha]) -> 42
(insert([y, _tha, _uha]) /\ sort([z, _tha])) -> sort([cons(y, z), _uha]) -> 44
(length([_dia, _eia]) /\ length([l, _cia]) /\ sort([l, _dia])) -> eq_nat([_cia, _eia]) -> 43
(length([ll, _yha])) -> length([cons(x, ll), s(_yha)]) -> 42
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 44
(leq([b, a])) -> BOT -> 42
}
Sat witness: Found: ((insert([y, _tha, _uha]) /\ sort([z, _tha])) -> sort([cons(y, z), _uha]), {
_tha -> cons(b, nil)  ;  _uha -> cons(b, nil)  ;  y -> a  ;  z -> cons(b, cons(b, nil))
})

-------------------------------------------
Step 58, which took 0.924948 s (model generation: 0.915591,  model checking: 0.009357):

Model:
|_
{
insert -> 
{{{
Q={q_gen_8672, q_gen_8673, q_gen_8674, q_gen_8676, q_gen_8677, q_gen_8721, q_gen_8729},
Q_f={q_gen_8672},
Delta=
{
<nil>() -> q_gen_8673
<a>() -> q_gen_8674
<b>() -> q_gen_8674
<cons>(q_gen_8674, q_gen_8673) -> q_gen_8721
<cons>(q_gen_8674, q_gen_8721) -> q_gen_8721
<cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8676
<cons, nil>(q_gen_8674, q_gen_8673) -> q_gen_8676
<cons, nil>(q_gen_8674, q_gen_8721) -> q_gen_8676
<nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8676
<nil, cons>(q_gen_8674, q_gen_8721) -> q_gen_8676
<nil, nil>() -> q_gen_8676
<a, a>() -> q_gen_8677
<a, b>() -> q_gen_8677
<b, a>() -> q_gen_8677
<b, b>() -> q_gen_8677
<a, cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8672
<a, nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8672
<b, cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8672
<b, nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8672
<b, nil, cons>(q_gen_8674, q_gen_8721) -> q_gen_8672
<a, nil, cons>(q_gen_8674, q_gen_8721) -> q_gen_8729
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_8671, q_gen_8679, q_gen_8680, q_gen_8703, q_gen_8704, q_gen_8705, q_gen_8706, q_gen_8707, q_gen_8723, q_gen_8725, q_gen_8727},
Q_f={q_gen_8671},
Delta=
{
<nil>() -> q_gen_8679
<cons>(q_gen_8704, q_gen_8679) -> q_gen_8703
<a>() -> q_gen_8704
<b>() -> q_gen_8704
<z>() -> q_gen_8706
<cons>(q_gen_8704, q_gen_8703) -> q_gen_8723
<cons>(q_gen_8704, q_gen_8723) -> q_gen_8723
<s>(q_gen_8706) -> q_gen_8725
<s>(q_gen_8725) -> q_gen_8725
<cons, s>(q_gen_8680, q_gen_8679) -> q_gen_8671
<cons, s>(q_gen_8705, q_gen_8703) -> q_gen_8671
<cons, s>(q_gen_8705, q_gen_8723) -> q_gen_8671
<cons, s>(q_gen_8727, q_gen_8723) -> q_gen_8671
<nil, z>() -> q_gen_8671
<a, z>() -> q_gen_8680
<b, z>() -> q_gen_8680
<a, s>(q_gen_8706) -> q_gen_8705
<b, s>(q_gen_8706) -> q_gen_8705
<b, s>(q_gen_8725) -> q_gen_8705
<cons, s>(q_gen_8680, q_gen_8723) -> q_gen_8707
<cons, s>(q_gen_8705, q_gen_8679) -> q_gen_8707
<cons, s>(q_gen_8727, q_gen_8679) -> q_gen_8707
<cons, s>(q_gen_8727, q_gen_8703) -> q_gen_8707
<a, s>(q_gen_8725) -> q_gen_8727
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_8669, q_gen_8683},
Q_f={q_gen_8669},
Delta=
{
<a, a>() -> q_gen_8669
<a, b>() -> q_gen_8669
<b, b>() -> q_gen_8669
<b, a>() -> q_gen_8683
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_8668, q_gen_8682, q_gen_8730, q_gen_8731, q_gen_8732, q_gen_8733, q_gen_8745},
Q_f={q_gen_8668},
Delta=
{
<cons>(q_gen_8733, q_gen_8732) -> q_gen_8732
<nil>() -> q_gen_8732
<a>() -> q_gen_8733
<b>() -> q_gen_8733
<cons, cons>(q_gen_8682, q_gen_8668) -> q_gen_8668
<cons, cons>(q_gen_8682, q_gen_8745) -> q_gen_8668
<nil, nil>() -> q_gen_8668
<a, a>() -> q_gen_8682
<a, b>() -> q_gen_8682
<b, a>() -> q_gen_8682
<b, b>() -> q_gen_8682
<cons, cons>(q_gen_8682, q_gen_8731) -> q_gen_8730
<nil, cons>(q_gen_8733, q_gen_8732) -> q_gen_8731
<cons, cons>(q_gen_8682, q_gen_8730) -> q_gen_8745
<cons, nil>(q_gen_8733, q_gen_8732) -> q_gen_8745
}

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, _oha]) /\ not leq([x, y])) -> insert([x, cons(y, z), _oha]) -> 43
(insert([y, _tha, _uha]) /\ sort([z, _tha])) -> sort([cons(y, z), _uha]) -> 44
(length([_dia, _eia]) /\ length([l, _cia]) /\ sort([l, _dia])) -> eq_nat([_cia, _eia]) -> 46
(length([ll, _yha])) -> length([cons(x, ll), s(_yha)]) -> 43
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 44
(leq([b, a])) -> BOT -> 43
}
Sat witness: Found: ((length([_dia, _eia]) /\ length([l, _cia]) /\ sort([l, _dia])) -> eq_nat([_cia, _eia]), {
_cia -> s(s(z))  ;  _dia -> cons(a, cons(b, cons(b, nil)))  ;  _eia -> s(s(s(z)))  ;  l -> cons(a, cons(b, cons(b, nil)))
})

-------------------------------------------
Step 59, which took 1.437375 s (model generation: 1.432927,  model checking: 0.004448):

Model:
|_
{
insert -> 
{{{
Q={q_gen_8672, q_gen_8673, q_gen_8674, q_gen_8676, q_gen_8677, q_gen_8689, q_gen_8694, q_gen_8721},
Q_f={q_gen_8672},
Delta=
{
<nil>() -> q_gen_8673
<b>() -> q_gen_8674
<a>() -> q_gen_8689
<cons>(q_gen_8674, q_gen_8673) -> q_gen_8721
<cons>(q_gen_8674, q_gen_8721) -> q_gen_8721
<cons>(q_gen_8689, q_gen_8673) -> q_gen_8721
<cons>(q_gen_8689, q_gen_8721) -> q_gen_8721
<cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8676
<cons, nil>(q_gen_8674, q_gen_8673) -> q_gen_8676
<cons, nil>(q_gen_8674, q_gen_8721) -> q_gen_8676
<cons, nil>(q_gen_8689, q_gen_8673) -> q_gen_8676
<nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8676
<nil, cons>(q_gen_8674, q_gen_8721) -> q_gen_8676
<nil, cons>(q_gen_8689, q_gen_8673) -> q_gen_8676
<nil, cons>(q_gen_8689, q_gen_8721) -> q_gen_8676
<nil, nil>() -> q_gen_8676
<a, a>() -> q_gen_8677
<a, b>() -> q_gen_8677
<b, a>() -> q_gen_8677
<b, b>() -> q_gen_8677
<a, cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8672
<a, nil, cons>(q_gen_8689, q_gen_8673) -> q_gen_8672
<b, cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8672
<b, nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8672
<a, nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8694
<a, nil, cons>(q_gen_8674, q_gen_8721) -> q_gen_8694
<a, nil, cons>(q_gen_8689, q_gen_8721) -> q_gen_8694
<b, nil, cons>(q_gen_8674, q_gen_8721) -> q_gen_8694
<b, nil, cons>(q_gen_8689, q_gen_8673) -> q_gen_8694
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_8671, q_gen_8679, q_gen_8680, q_gen_8703, q_gen_8704, q_gen_8706, q_gen_8713, q_gen_8714, q_gen_8723, q_gen_8724, q_gen_8725},
Q_f={q_gen_8671},
Delta=
{
<nil>() -> q_gen_8679
<cons>(q_gen_8704, q_gen_8679) -> q_gen_8703
<a>() -> q_gen_8704
<b>() -> q_gen_8704
<z>() -> q_gen_8706
<cons>(q_gen_8704, q_gen_8703) -> q_gen_8723
<cons>(q_gen_8704, q_gen_8723) -> q_gen_8723
<s>(q_gen_8706) -> q_gen_8725
<s>(q_gen_8725) -> q_gen_8725
<cons, s>(q_gen_8680, q_gen_8679) -> q_gen_8671
<cons, s>(q_gen_8680, q_gen_8703) -> q_gen_8671
<cons, s>(q_gen_8680, q_gen_8723) -> q_gen_8671
<cons, s>(q_gen_8713, q_gen_8703) -> q_gen_8671
<cons, s>(q_gen_8724, q_gen_8723) -> q_gen_8671
<nil, z>() -> q_gen_8671
<a, z>() -> q_gen_8680
<b, s>(q_gen_8706) -> q_gen_8680
<b, z>() -> q_gen_8680
<a, s>(q_gen_8706) -> q_gen_8713
<cons, s>(q_gen_8713, q_gen_8679) -> q_gen_8714
<cons, s>(q_gen_8713, q_gen_8723) -> q_gen_8714
<cons, s>(q_gen_8724, q_gen_8679) -> q_gen_8714
<cons, s>(q_gen_8724, q_gen_8703) -> q_gen_8714
<a, s>(q_gen_8725) -> q_gen_8724
<b, s>(q_gen_8725) -> q_gen_8724
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_8669, q_gen_8683},
Q_f={q_gen_8669},
Delta=
{
<a, a>() -> q_gen_8669
<a, b>() -> q_gen_8669
<b, b>() -> q_gen_8669
<b, a>() -> q_gen_8683
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_8668, q_gen_8682, q_gen_8695, q_gen_8696, q_gen_8732, q_gen_8733},
Q_f={q_gen_8668},
Delta=
{
<cons>(q_gen_8733, q_gen_8732) -> q_gen_8732
<nil>() -> q_gen_8732
<a>() -> q_gen_8733
<b>() -> q_gen_8733
<cons, cons>(q_gen_8682, q_gen_8668) -> q_gen_8668
<nil, nil>() -> q_gen_8668
<a, a>() -> q_gen_8682
<b, a>() -> q_gen_8682
<b, b>() -> q_gen_8682
<cons, cons>(q_gen_8682, q_gen_8695) -> q_gen_8695
<cons, cons>(q_gen_8696, q_gen_8668) -> q_gen_8695
<cons, cons>(q_gen_8696, q_gen_8695) -> q_gen_8695
<cons, nil>(q_gen_8733, q_gen_8732) -> q_gen_8695
<nil, cons>(q_gen_8733, q_gen_8732) -> q_gen_8695
<a, b>() -> q_gen_8696
}

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, _oha]) /\ not leq([x, y])) -> insert([x, cons(y, z), _oha]) -> 43
(insert([y, _tha, _uha]) /\ sort([z, _tha])) -> sort([cons(y, z), _uha]) -> 44
(length([_dia, _eia]) /\ length([l, _cia]) /\ sort([l, _dia])) -> eq_nat([_cia, _eia]) -> 46
(length([ll, _yha])) -> length([cons(x, ll), s(_yha)]) -> 46
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 44
(leq([b, a])) -> BOT -> 44
}
Sat witness: Found: ((length([ll, _yha])) -> length([cons(x, ll), s(_yha)]), {
_yha -> s(s(z))  ;  ll -> cons(b, nil)  ;  x -> a
})

-------------------------------------------
Step 60, which took 1.045353 s (model generation: 1.038941,  model checking: 0.006412):

Model:
|_
{
insert -> 
{{{
Q={q_gen_8672, q_gen_8673, q_gen_8674, q_gen_8676, q_gen_8677, q_gen_8721, q_gen_8729},
Q_f={q_gen_8672},
Delta=
{
<nil>() -> q_gen_8673
<a>() -> q_gen_8674
<b>() -> q_gen_8674
<cons>(q_gen_8674, q_gen_8673) -> q_gen_8721
<cons>(q_gen_8674, q_gen_8721) -> q_gen_8721
<cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8676
<cons, nil>(q_gen_8674, q_gen_8673) -> q_gen_8676
<cons, nil>(q_gen_8674, q_gen_8721) -> q_gen_8676
<nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8676
<nil, cons>(q_gen_8674, q_gen_8721) -> q_gen_8676
<nil, nil>() -> q_gen_8676
<a, a>() -> q_gen_8677
<a, b>() -> q_gen_8677
<b, a>() -> q_gen_8677
<b, b>() -> q_gen_8677
<a, cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8672
<a, nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8672
<b, cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8672
<b, nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8672
<a, nil, cons>(q_gen_8674, q_gen_8721) -> q_gen_8729
<b, nil, cons>(q_gen_8674, q_gen_8721) -> q_gen_8729
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_8671, q_gen_8679, q_gen_8680, q_gen_8703, q_gen_8704, q_gen_8705, q_gen_8706, q_gen_8707, q_gen_8723, q_gen_8724, q_gen_8725},
Q_f={q_gen_8671},
Delta=
{
<nil>() -> q_gen_8679
<cons>(q_gen_8704, q_gen_8679) -> q_gen_8703
<a>() -> q_gen_8704
<b>() -> q_gen_8704
<z>() -> q_gen_8706
<cons>(q_gen_8704, q_gen_8703) -> q_gen_8723
<cons>(q_gen_8704, q_gen_8723) -> q_gen_8723
<s>(q_gen_8706) -> q_gen_8725
<s>(q_gen_8725) -> q_gen_8725
<cons, s>(q_gen_8680, q_gen_8679) -> q_gen_8671
<cons, s>(q_gen_8705, q_gen_8703) -> q_gen_8671
<cons, s>(q_gen_8724, q_gen_8723) -> q_gen_8671
<nil, z>() -> q_gen_8671
<a, z>() -> q_gen_8680
<b, z>() -> q_gen_8680
<a, s>(q_gen_8706) -> q_gen_8705
<b, s>(q_gen_8706) -> q_gen_8705
<cons, s>(q_gen_8680, q_gen_8723) -> q_gen_8707
<cons, s>(q_gen_8705, q_gen_8679) -> q_gen_8707
<cons, s>(q_gen_8705, q_gen_8723) -> q_gen_8707
<cons, s>(q_gen_8724, q_gen_8679) -> q_gen_8707
<cons, s>(q_gen_8724, q_gen_8703) -> q_gen_8707
<a, s>(q_gen_8725) -> q_gen_8724
<b, s>(q_gen_8725) -> q_gen_8724
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_8669, q_gen_8683},
Q_f={q_gen_8669},
Delta=
{
<a, a>() -> q_gen_8669
<a, b>() -> q_gen_8669
<b, b>() -> q_gen_8669
<b, a>() -> q_gen_8683
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_8668, q_gen_8682, q_gen_8730, q_gen_8731, q_gen_8732, q_gen_8733, q_gen_8745},
Q_f={q_gen_8668},
Delta=
{
<cons>(q_gen_8733, q_gen_8732) -> q_gen_8732
<nil>() -> q_gen_8732
<a>() -> q_gen_8733
<b>() -> q_gen_8733
<cons, cons>(q_gen_8682, q_gen_8668) -> q_gen_8668
<cons, cons>(q_gen_8682, q_gen_8745) -> q_gen_8668
<nil, nil>() -> q_gen_8668
<a, a>() -> q_gen_8682
<a, b>() -> q_gen_8682
<b, a>() -> q_gen_8682
<b, b>() -> q_gen_8682
<cons, cons>(q_gen_8682, q_gen_8731) -> q_gen_8730
<nil, cons>(q_gen_8733, q_gen_8732) -> q_gen_8731
<cons, cons>(q_gen_8682, q_gen_8730) -> q_gen_8745
<cons, nil>(q_gen_8733, q_gen_8732) -> q_gen_8745
}

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, _oha]) /\ not leq([x, y])) -> insert([x, cons(y, z), _oha]) -> 44
(insert([y, _tha, _uha]) /\ sort([z, _tha])) -> sort([cons(y, z), _uha]) -> 47
(length([_dia, _eia]) /\ length([l, _cia]) /\ sort([l, _dia])) -> eq_nat([_cia, _eia]) -> 46
(length([ll, _yha])) -> length([cons(x, ll), s(_yha)]) -> 46
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 45
(leq([b, a])) -> BOT -> 45
}
Sat witness: Found: ((insert([y, _tha, _uha]) /\ sort([z, _tha])) -> sort([cons(y, z), _uha]), {
_tha -> cons(b, nil)  ;  _uha -> cons(b, cons(b, cons(b, nil)))  ;  y -> b  ;  z -> cons(a, nil)
})

-------------------------------------------
Step 61, which took 2.152872 s (model generation: 2.139579,  model checking: 0.013293):

Model:
|_
{
insert -> 
{{{
Q={q_gen_8672, q_gen_8673, q_gen_8674, q_gen_8676, q_gen_8677, q_gen_8721, q_gen_8729},
Q_f={q_gen_8672},
Delta=
{
<nil>() -> q_gen_8673
<a>() -> q_gen_8674
<b>() -> q_gen_8674
<cons>(q_gen_8674, q_gen_8673) -> q_gen_8721
<cons>(q_gen_8674, q_gen_8721) -> q_gen_8721
<cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8676
<cons, nil>(q_gen_8674, q_gen_8673) -> q_gen_8676
<cons, nil>(q_gen_8674, q_gen_8721) -> q_gen_8676
<nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8676
<nil, cons>(q_gen_8674, q_gen_8721) -> q_gen_8676
<nil, nil>() -> q_gen_8676
<a, a>() -> q_gen_8677
<a, b>() -> q_gen_8677
<b, a>() -> q_gen_8677
<b, b>() -> q_gen_8677
<a, cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8672
<a, nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8672
<b, cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8672
<b, nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8672
<a, nil, cons>(q_gen_8674, q_gen_8721) -> q_gen_8729
<b, nil, cons>(q_gen_8674, q_gen_8721) -> q_gen_8729
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_8671, q_gen_8679, q_gen_8680, q_gen_8703, q_gen_8704, q_gen_8705, q_gen_8706, q_gen_8707, q_gen_8723, q_gen_8724, q_gen_8725},
Q_f={q_gen_8671},
Delta=
{
<nil>() -> q_gen_8679
<cons>(q_gen_8704, q_gen_8679) -> q_gen_8703
<cons>(q_gen_8704, q_gen_8723) -> q_gen_8703
<a>() -> q_gen_8704
<b>() -> q_gen_8704
<s>(q_gen_8725) -> q_gen_8706
<z>() -> q_gen_8706
<cons>(q_gen_8704, q_gen_8703) -> q_gen_8723
<s>(q_gen_8706) -> q_gen_8725
<cons, s>(q_gen_8680, q_gen_8679) -> q_gen_8671
<cons, s>(q_gen_8705, q_gen_8703) -> q_gen_8671
<cons, s>(q_gen_8724, q_gen_8723) -> q_gen_8671
<nil, z>() -> q_gen_8671
<a, z>() -> q_gen_8680
<b, z>() -> q_gen_8680
<a, s>(q_gen_8706) -> q_gen_8705
<b, s>(q_gen_8706) -> q_gen_8705
<cons, s>(q_gen_8680, q_gen_8723) -> q_gen_8707
<cons, s>(q_gen_8705, q_gen_8679) -> q_gen_8707
<cons, s>(q_gen_8705, q_gen_8723) -> q_gen_8707
<cons, s>(q_gen_8724, q_gen_8679) -> q_gen_8707
<cons, s>(q_gen_8724, q_gen_8703) -> q_gen_8707
<a, s>(q_gen_8725) -> q_gen_8724
<b, s>(q_gen_8725) -> q_gen_8724
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_8669, q_gen_8683},
Q_f={q_gen_8669},
Delta=
{
<a, a>() -> q_gen_8669
<a, b>() -> q_gen_8669
<b, b>() -> q_gen_8669
<b, a>() -> q_gen_8683
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_8668, q_gen_8682, q_gen_8696, q_gen_8730, q_gen_8731, q_gen_8732, q_gen_8733},
Q_f={q_gen_8668},
Delta=
{
<cons>(q_gen_8733, q_gen_8732) -> q_gen_8732
<nil>() -> q_gen_8732
<a>() -> q_gen_8733
<b>() -> q_gen_8733
<cons, cons>(q_gen_8682, q_gen_8668) -> q_gen_8668
<cons, cons>(q_gen_8682, q_gen_8730) -> q_gen_8668
<cons, cons>(q_gen_8696, q_gen_8668) -> q_gen_8668
<cons, cons>(q_gen_8696, q_gen_8730) -> q_gen_8668
<nil, nil>() -> q_gen_8668
<b, a>() -> q_gen_8682
<b, b>() -> q_gen_8682
<a, a>() -> q_gen_8696
<a, b>() -> q_gen_8696
<cons, cons>(q_gen_8696, q_gen_8731) -> q_gen_8730
<cons, nil>(q_gen_8733, q_gen_8732) -> q_gen_8730
<cons, cons>(q_gen_8682, q_gen_8731) -> q_gen_8731
<nil, cons>(q_gen_8733, q_gen_8732) -> q_gen_8731
}

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, _oha]) /\ not leq([x, y])) -> insert([x, cons(y, z), _oha]) -> 45
(insert([y, _tha, _uha]) /\ sort([z, _tha])) -> sort([cons(y, z), _uha]) -> 47
(length([_dia, _eia]) /\ length([l, _cia]) /\ sort([l, _dia])) -> eq_nat([_cia, _eia]) -> 49
(length([ll, _yha])) -> length([cons(x, ll), s(_yha)]) -> 47
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 46
(leq([b, a])) -> BOT -> 46
}
Sat witness: Found: ((length([_dia, _eia]) /\ length([l, _cia]) /\ sort([l, _dia])) -> eq_nat([_cia, _eia]), {
_cia -> s(s(z))  ;  _dia -> cons(a, cons(b, cons(b, nil)))  ;  _eia -> s(s(s(z)))  ;  l -> cons(b, cons(a, cons(a, cons(b, nil))))
})

-------------------------------------------
Step 62, which took 1.516266 s (model generation: 1.508056,  model checking: 0.008210):

Model:
|_
{
insert -> 
{{{
Q={q_gen_8672, q_gen_8673, q_gen_8674, q_gen_8676, q_gen_8677, q_gen_8721, q_gen_8729},
Q_f={q_gen_8672},
Delta=
{
<nil>() -> q_gen_8673
<a>() -> q_gen_8674
<b>() -> q_gen_8674
<cons>(q_gen_8674, q_gen_8673) -> q_gen_8721
<cons>(q_gen_8674, q_gen_8721) -> q_gen_8721
<cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8676
<cons, nil>(q_gen_8674, q_gen_8673) -> q_gen_8676
<cons, nil>(q_gen_8674, q_gen_8721) -> q_gen_8676
<nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8676
<nil, cons>(q_gen_8674, q_gen_8721) -> q_gen_8676
<nil, nil>() -> q_gen_8676
<a, a>() -> q_gen_8677
<a, b>() -> q_gen_8677
<b, a>() -> q_gen_8677
<b, b>() -> q_gen_8677
<a, cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8672
<a, nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8672
<b, cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8672
<b, nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8672
<a, nil, cons>(q_gen_8674, q_gen_8721) -> q_gen_8729
<b, nil, cons>(q_gen_8674, q_gen_8721) -> q_gen_8729
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_8671, q_gen_8679, q_gen_8680, q_gen_8703, q_gen_8704, q_gen_8705, q_gen_8706, q_gen_8707, q_gen_8723, q_gen_8724, q_gen_8725},
Q_f={q_gen_8671},
Delta=
{
<nil>() -> q_gen_8679
<cons>(q_gen_8704, q_gen_8679) -> q_gen_8703
<a>() -> q_gen_8704
<b>() -> q_gen_8704
<z>() -> q_gen_8706
<cons>(q_gen_8704, q_gen_8703) -> q_gen_8723
<cons>(q_gen_8704, q_gen_8723) -> q_gen_8723
<s>(q_gen_8706) -> q_gen_8725
<s>(q_gen_8725) -> q_gen_8725
<cons, s>(q_gen_8680, q_gen_8679) -> q_gen_8671
<cons, s>(q_gen_8705, q_gen_8703) -> q_gen_8671
<cons, s>(q_gen_8724, q_gen_8723) -> q_gen_8671
<nil, z>() -> q_gen_8671
<a, z>() -> q_gen_8680
<b, z>() -> q_gen_8680
<a, s>(q_gen_8706) -> q_gen_8705
<b, s>(q_gen_8706) -> q_gen_8705
<cons, s>(q_gen_8680, q_gen_8723) -> q_gen_8707
<cons, s>(q_gen_8705, q_gen_8679) -> q_gen_8707
<cons, s>(q_gen_8705, q_gen_8723) -> q_gen_8707
<cons, s>(q_gen_8724, q_gen_8679) -> q_gen_8707
<cons, s>(q_gen_8724, q_gen_8703) -> q_gen_8707
<a, s>(q_gen_8725) -> q_gen_8724
<b, s>(q_gen_8725) -> q_gen_8724
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_8669, q_gen_8683},
Q_f={q_gen_8669},
Delta=
{
<a, a>() -> q_gen_8669
<a, b>() -> q_gen_8669
<b, b>() -> q_gen_8669
<b, a>() -> q_gen_8683
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_8668, q_gen_8682, q_gen_8696, q_gen_8730, q_gen_8731, q_gen_8732, q_gen_8733},
Q_f={q_gen_8668},
Delta=
{
<cons>(q_gen_8733, q_gen_8732) -> q_gen_8732
<nil>() -> q_gen_8732
<a>() -> q_gen_8733
<b>() -> q_gen_8733
<cons, cons>(q_gen_8682, q_gen_8668) -> q_gen_8668
<cons, cons>(q_gen_8682, q_gen_8730) -> q_gen_8668
<cons, cons>(q_gen_8696, q_gen_8668) -> q_gen_8668
<cons, cons>(q_gen_8696, q_gen_8730) -> q_gen_8668
<nil, nil>() -> q_gen_8668
<b, a>() -> q_gen_8682
<b, b>() -> q_gen_8682
<a, a>() -> q_gen_8696
<a, b>() -> q_gen_8696
<cons, cons>(q_gen_8696, q_gen_8731) -> q_gen_8730
<cons, nil>(q_gen_8733, q_gen_8732) -> q_gen_8730
<cons, cons>(q_gen_8682, q_gen_8731) -> q_gen_8731
<nil, cons>(q_gen_8733, q_gen_8732) -> q_gen_8731
}

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, _oha]) /\ not leq([x, y])) -> insert([x, cons(y, z), _oha]) -> 46
(insert([y, _tha, _uha]) /\ sort([z, _tha])) -> sort([cons(y, z), _uha]) -> 50
(length([_dia, _eia]) /\ length([l, _cia]) /\ sort([l, _dia])) -> eq_nat([_cia, _eia]) -> 49
(length([ll, _yha])) -> length([cons(x, ll), s(_yha)]) -> 48
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 47
(leq([b, a])) -> BOT -> 47
}
Sat witness: Found: ((insert([y, _tha, _uha]) /\ sort([z, _tha])) -> sort([cons(y, z), _uha]), {
_tha -> cons(b, nil)  ;  _uha -> cons(b, cons(b, cons(b, cons(b, nil))))  ;  y -> b  ;  z -> cons(b, cons(b, nil))
})

-------------------------------------------
Step 63, which took 2.208554 s (model generation: 2.196570,  model checking: 0.011984):

Model:
|_
{
insert -> 
{{{
Q={q_gen_8672, q_gen_8673, q_gen_8674, q_gen_8676, q_gen_8677, q_gen_8721, q_gen_8729},
Q_f={q_gen_8672},
Delta=
{
<nil>() -> q_gen_8673
<a>() -> q_gen_8674
<b>() -> q_gen_8674
<cons>(q_gen_8674, q_gen_8673) -> q_gen_8721
<cons>(q_gen_8674, q_gen_8721) -> q_gen_8721
<cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8676
<cons, nil>(q_gen_8674, q_gen_8673) -> q_gen_8676
<cons, nil>(q_gen_8674, q_gen_8721) -> q_gen_8676
<nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8676
<nil, cons>(q_gen_8674, q_gen_8721) -> q_gen_8676
<nil, nil>() -> q_gen_8676
<a, a>() -> q_gen_8677
<a, b>() -> q_gen_8677
<b, a>() -> q_gen_8677
<b, b>() -> q_gen_8677
<a, cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8672
<a, nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8672
<b, cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8672
<b, nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8672
<a, nil, cons>(q_gen_8674, q_gen_8721) -> q_gen_8729
<b, nil, cons>(q_gen_8674, q_gen_8721) -> q_gen_8729
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_8671, q_gen_8679, q_gen_8680, q_gen_8703, q_gen_8704, q_gen_8705, q_gen_8706, q_gen_8707, q_gen_8723, q_gen_8724, q_gen_8725},
Q_f={q_gen_8671},
Delta=
{
<nil>() -> q_gen_8679
<cons>(q_gen_8704, q_gen_8679) -> q_gen_8703
<a>() -> q_gen_8704
<b>() -> q_gen_8704
<z>() -> q_gen_8706
<cons>(q_gen_8704, q_gen_8703) -> q_gen_8723
<cons>(q_gen_8704, q_gen_8723) -> q_gen_8723
<s>(q_gen_8706) -> q_gen_8725
<s>(q_gen_8725) -> q_gen_8725
<cons, s>(q_gen_8680, q_gen_8679) -> q_gen_8671
<cons, s>(q_gen_8705, q_gen_8703) -> q_gen_8671
<cons, s>(q_gen_8724, q_gen_8723) -> q_gen_8671
<nil, z>() -> q_gen_8671
<a, z>() -> q_gen_8680
<b, z>() -> q_gen_8680
<a, s>(q_gen_8706) -> q_gen_8705
<b, s>(q_gen_8706) -> q_gen_8705
<cons, s>(q_gen_8680, q_gen_8723) -> q_gen_8707
<cons, s>(q_gen_8705, q_gen_8679) -> q_gen_8707
<cons, s>(q_gen_8705, q_gen_8723) -> q_gen_8707
<cons, s>(q_gen_8724, q_gen_8679) -> q_gen_8707
<cons, s>(q_gen_8724, q_gen_8703) -> q_gen_8707
<a, s>(q_gen_8725) -> q_gen_8724
<b, s>(q_gen_8725) -> q_gen_8724
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_8669, q_gen_8683},
Q_f={q_gen_8669},
Delta=
{
<a, a>() -> q_gen_8669
<a, b>() -> q_gen_8669
<b, b>() -> q_gen_8669
<b, a>() -> q_gen_8683
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_8668, q_gen_8682, q_gen_8709, q_gen_8730, q_gen_8731, q_gen_8732, q_gen_8733},
Q_f={q_gen_8668},
Delta=
{
<cons>(q_gen_8733, q_gen_8732) -> q_gen_8732
<nil>() -> q_gen_8732
<a>() -> q_gen_8733
<b>() -> q_gen_8733
<cons, cons>(q_gen_8682, q_gen_8668) -> q_gen_8668
<cons, cons>(q_gen_8682, q_gen_8730) -> q_gen_8668
<cons, cons>(q_gen_8709, q_gen_8668) -> q_gen_8668
<nil, nil>() -> q_gen_8668
<a, b>() -> q_gen_8682
<b, b>() -> q_gen_8682
<a, a>() -> q_gen_8709
<b, a>() -> q_gen_8709
<cons, cons>(q_gen_8682, q_gen_8731) -> q_gen_8730
<cons, cons>(q_gen_8709, q_gen_8730) -> q_gen_8730
<cons, cons>(q_gen_8709, q_gen_8731) -> q_gen_8730
<cons, nil>(q_gen_8733, q_gen_8732) -> q_gen_8730
<nil, cons>(q_gen_8733, q_gen_8732) -> q_gen_8731
}

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, _oha]) /\ not leq([x, y])) -> insert([x, cons(y, z), _oha]) -> 47
(insert([y, _tha, _uha]) /\ sort([z, _tha])) -> sort([cons(y, z), _uha]) -> 50
(length([_dia, _eia]) /\ length([l, _cia]) /\ sort([l, _dia])) -> eq_nat([_cia, _eia]) -> 52
(length([ll, _yha])) -> length([cons(x, ll), s(_yha)]) -> 49
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 48
(leq([b, a])) -> BOT -> 48
}
Sat witness: Found: ((length([_dia, _eia]) /\ length([l, _cia]) /\ sort([l, _dia])) -> eq_nat([_cia, _eia]), {
_cia -> s(s(z))  ;  _dia -> cons(b, cons(b, cons(b, nil)))  ;  _eia -> s(s(s(z)))  ;  l -> cons(a, cons(b, nil))
})

-------------------------------------------
Step 64, which took 2.448285 s (model generation: 2.434748,  model checking: 0.013537):

Model:
|_
{
insert -> 
{{{
Q={q_gen_8672, q_gen_8673, q_gen_8674, q_gen_8676, q_gen_8677, q_gen_8721, q_gen_8729, q_gen_8775},
Q_f={q_gen_8672},
Delta=
{
<nil>() -> q_gen_8673
<a>() -> q_gen_8674
<b>() -> q_gen_8674
<cons>(q_gen_8674, q_gen_8673) -> q_gen_8721
<cons>(q_gen_8674, q_gen_8721) -> q_gen_8721
<cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8676
<cons, nil>(q_gen_8674, q_gen_8673) -> q_gen_8676
<cons, nil>(q_gen_8674, q_gen_8721) -> q_gen_8676
<nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8676
<nil, nil>() -> q_gen_8676
<a, a>() -> q_gen_8677
<a, b>() -> q_gen_8677
<b, a>() -> q_gen_8677
<b, b>() -> q_gen_8677
<nil, cons>(q_gen_8674, q_gen_8721) -> q_gen_8775
<a, cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8672
<a, nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8672
<b, cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8672
<b, nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8672
<a, cons, cons>(q_gen_8677, q_gen_8775) -> q_gen_8729
<a, nil, cons>(q_gen_8674, q_gen_8721) -> q_gen_8729
<b, cons, cons>(q_gen_8677, q_gen_8775) -> q_gen_8729
<b, nil, cons>(q_gen_8674, q_gen_8721) -> q_gen_8729
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_8671, q_gen_8679, q_gen_8680, q_gen_8703, q_gen_8704, q_gen_8705, q_gen_8706, q_gen_8707, q_gen_8723, q_gen_8724, q_gen_8725},
Q_f={q_gen_8671},
Delta=
{
<nil>() -> q_gen_8679
<cons>(q_gen_8704, q_gen_8679) -> q_gen_8703
<a>() -> q_gen_8704
<b>() -> q_gen_8704
<z>() -> q_gen_8706
<cons>(q_gen_8704, q_gen_8703) -> q_gen_8723
<cons>(q_gen_8704, q_gen_8723) -> q_gen_8723
<s>(q_gen_8706) -> q_gen_8725
<s>(q_gen_8725) -> q_gen_8725
<cons, s>(q_gen_8680, q_gen_8679) -> q_gen_8671
<cons, s>(q_gen_8705, q_gen_8703) -> q_gen_8671
<cons, s>(q_gen_8724, q_gen_8723) -> q_gen_8671
<nil, z>() -> q_gen_8671
<a, z>() -> q_gen_8680
<b, z>() -> q_gen_8680
<a, s>(q_gen_8706) -> q_gen_8705
<b, s>(q_gen_8706) -> q_gen_8705
<cons, s>(q_gen_8680, q_gen_8723) -> q_gen_8707
<cons, s>(q_gen_8705, q_gen_8679) -> q_gen_8707
<cons, s>(q_gen_8705, q_gen_8723) -> q_gen_8707
<cons, s>(q_gen_8724, q_gen_8679) -> q_gen_8707
<cons, s>(q_gen_8724, q_gen_8703) -> q_gen_8707
<a, s>(q_gen_8725) -> q_gen_8724
<b, s>(q_gen_8725) -> q_gen_8724
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_8669, q_gen_8683},
Q_f={q_gen_8669},
Delta=
{
<a, a>() -> q_gen_8669
<a, b>() -> q_gen_8669
<b, b>() -> q_gen_8669
<b, a>() -> q_gen_8683
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_8668, q_gen_8682, q_gen_8730, q_gen_8732, q_gen_8733, q_gen_8751},
Q_f={q_gen_8668},
Delta=
{
<cons>(q_gen_8733, q_gen_8732) -> q_gen_8732
<nil>() -> q_gen_8732
<a>() -> q_gen_8733
<b>() -> q_gen_8733
<cons, cons>(q_gen_8682, q_gen_8668) -> q_gen_8668
<cons, cons>(q_gen_8682, q_gen_8751) -> q_gen_8668
<nil, nil>() -> q_gen_8668
<a, a>() -> q_gen_8682
<a, b>() -> q_gen_8682
<b, a>() -> q_gen_8682
<b, b>() -> q_gen_8682
<cons, cons>(q_gen_8682, q_gen_8730) -> q_gen_8730
<nil, cons>(q_gen_8733, q_gen_8732) -> q_gen_8730
<cons, nil>(q_gen_8733, q_gen_8732) -> q_gen_8751
}

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, _oha]) /\ not leq([x, y])) -> insert([x, cons(y, z), _oha]) -> 48
(insert([y, _tha, _uha]) /\ sort([z, _tha])) -> sort([cons(y, z), _uha]) -> 51
(length([_dia, _eia]) /\ length([l, _cia]) /\ sort([l, _dia])) -> eq_nat([_cia, _eia]) -> 55
(length([ll, _yha])) -> length([cons(x, ll), s(_yha)]) -> 50
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 49
(leq([b, a])) -> BOT -> 49
}
Sat witness: Found: ((length([_dia, _eia]) /\ length([l, _cia]) /\ sort([l, _dia])) -> eq_nat([_cia, _eia]), {
_cia -> s(s(z))  ;  _dia -> cons(a, nil)  ;  _eia -> s(z)  ;  l -> cons(a, cons(b, nil))
})

-------------------------------------------
Step 65, which took 2.189293 s (model generation: 2.187278,  model checking: 0.002015):

Model:
|_
{
insert -> 
{{{
Q={q_gen_8672, q_gen_8673, q_gen_8674, q_gen_8676, q_gen_8677, q_gen_8689, q_gen_8694, q_gen_8721},
Q_f={q_gen_8672},
Delta=
{
<nil>() -> q_gen_8673
<b>() -> q_gen_8674
<a>() -> q_gen_8689
<cons>(q_gen_8674, q_gen_8673) -> q_gen_8721
<cons>(q_gen_8674, q_gen_8721) -> q_gen_8721
<cons>(q_gen_8689, q_gen_8673) -> q_gen_8721
<cons>(q_gen_8689, q_gen_8721) -> q_gen_8721
<cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8676
<cons, nil>(q_gen_8674, q_gen_8673) -> q_gen_8676
<cons, nil>(q_gen_8674, q_gen_8721) -> q_gen_8676
<cons, nil>(q_gen_8689, q_gen_8673) -> q_gen_8676
<nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8676
<nil, cons>(q_gen_8674, q_gen_8721) -> q_gen_8676
<nil, cons>(q_gen_8689, q_gen_8673) -> q_gen_8676
<nil, cons>(q_gen_8689, q_gen_8721) -> q_gen_8676
<nil, nil>() -> q_gen_8676
<a, a>() -> q_gen_8677
<a, b>() -> q_gen_8677
<b, a>() -> q_gen_8677
<b, b>() -> q_gen_8677
<a, cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8672
<a, nil, cons>(q_gen_8689, q_gen_8673) -> q_gen_8672
<b, cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8672
<b, nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8672
<b, nil, cons>(q_gen_8689, q_gen_8673) -> q_gen_8672
<a, nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8694
<a, nil, cons>(q_gen_8674, q_gen_8721) -> q_gen_8694
<a, nil, cons>(q_gen_8689, q_gen_8721) -> q_gen_8694
<b, nil, cons>(q_gen_8674, q_gen_8721) -> q_gen_8694
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_8671, q_gen_8679, q_gen_8680, q_gen_8703, q_gen_8704, q_gen_8705, q_gen_8706, q_gen_8707, q_gen_8723, q_gen_8725, q_gen_8727},
Q_f={q_gen_8671},
Delta=
{
<nil>() -> q_gen_8679
<cons>(q_gen_8704, q_gen_8679) -> q_gen_8703
<cons>(q_gen_8704, q_gen_8723) -> q_gen_8703
<a>() -> q_gen_8704
<b>() -> q_gen_8704
<s>(q_gen_8725) -> q_gen_8706
<z>() -> q_gen_8706
<cons>(q_gen_8704, q_gen_8703) -> q_gen_8723
<s>(q_gen_8706) -> q_gen_8725
<cons, s>(q_gen_8680, q_gen_8679) -> q_gen_8671
<cons, s>(q_gen_8680, q_gen_8723) -> q_gen_8671
<cons, s>(q_gen_8705, q_gen_8703) -> q_gen_8671
<cons, s>(q_gen_8727, q_gen_8723) -> q_gen_8671
<nil, z>() -> q_gen_8671
<a, z>() -> q_gen_8680
<b, s>(q_gen_8725) -> q_gen_8680
<b, z>() -> q_gen_8680
<a, s>(q_gen_8706) -> q_gen_8705
<b, s>(q_gen_8706) -> q_gen_8705
<cons, s>(q_gen_8705, q_gen_8679) -> q_gen_8707
<cons, s>(q_gen_8705, q_gen_8723) -> q_gen_8707
<cons, s>(q_gen_8727, q_gen_8679) -> q_gen_8707
<cons, s>(q_gen_8727, q_gen_8703) -> q_gen_8707
<a, s>(q_gen_8725) -> q_gen_8727
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_8669, q_gen_8683},
Q_f={q_gen_8669},
Delta=
{
<a, a>() -> q_gen_8669
<a, b>() -> q_gen_8669
<b, b>() -> q_gen_8669
<b, a>() -> q_gen_8683
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_8668, q_gen_8682, q_gen_8695, q_gen_8696, q_gen_8732, q_gen_8733},
Q_f={q_gen_8668},
Delta=
{
<cons>(q_gen_8733, q_gen_8732) -> q_gen_8732
<nil>() -> q_gen_8732
<a>() -> q_gen_8733
<b>() -> q_gen_8733
<cons, cons>(q_gen_8682, q_gen_8668) -> q_gen_8668
<nil, nil>() -> q_gen_8668
<a, a>() -> q_gen_8682
<b, a>() -> q_gen_8682
<b, b>() -> q_gen_8682
<cons, cons>(q_gen_8682, q_gen_8695) -> q_gen_8695
<cons, cons>(q_gen_8696, q_gen_8668) -> q_gen_8695
<cons, cons>(q_gen_8696, q_gen_8695) -> q_gen_8695
<cons, nil>(q_gen_8733, q_gen_8732) -> q_gen_8695
<nil, cons>(q_gen_8733, q_gen_8732) -> q_gen_8695
<a, b>() -> q_gen_8696
}

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, _oha]) /\ not leq([x, y])) -> insert([x, cons(y, z), _oha]) -> 51
(insert([y, _tha, _uha]) /\ sort([z, _tha])) -> sort([cons(y, z), _uha]) -> 51
(length([_dia, _eia]) /\ length([l, _cia]) /\ sort([l, _dia])) -> eq_nat([_cia, _eia]) -> 55
(length([ll, _yha])) -> length([cons(x, ll), s(_yha)]) -> 50
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 49
(leq([b, a])) -> BOT -> 49
}
Sat witness: Found: ((insert([x, z, _oha]) /\ not leq([x, y])) -> insert([x, cons(y, z), _oha]), {
_oha -> cons(b, nil)  ;  x -> b  ;  y -> a  ;  z -> cons(a, cons(a, nil))
})

-------------------------------------------
Step 66, which took 2.662864 s (model generation: 2.653190,  model checking: 0.009674):

Model:
|_
{
insert -> 
{{{
Q={q_gen_8672, q_gen_8673, q_gen_8674, q_gen_8676, q_gen_8677, q_gen_8685, q_gen_8686, q_gen_8721, q_gen_8729},
Q_f={q_gen_8672},
Delta=
{
<nil>() -> q_gen_8673
<a>() -> q_gen_8674
<b>() -> q_gen_8674
<cons>(q_gen_8674, q_gen_8673) -> q_gen_8721
<cons>(q_gen_8674, q_gen_8721) -> q_gen_8721
<cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8676
<cons, cons>(q_gen_8686, q_gen_8676) -> q_gen_8676
<cons, nil>(q_gen_8674, q_gen_8673) -> q_gen_8676
<cons, nil>(q_gen_8674, q_gen_8721) -> q_gen_8676
<nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8676
<b, a>() -> q_gen_8677
<b, b>() -> q_gen_8677
<cons, cons>(q_gen_8686, q_gen_8685) -> q_gen_8685
<nil, cons>(q_gen_8674, q_gen_8721) -> q_gen_8685
<nil, nil>() -> q_gen_8685
<a, a>() -> q_gen_8686
<a, b>() -> q_gen_8686
<a, cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8672
<a, cons, cons>(q_gen_8677, q_gen_8685) -> q_gen_8672
<a, cons, cons>(q_gen_8686, q_gen_8676) -> q_gen_8672
<a, nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8672
<b, cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8672
<b, cons, cons>(q_gen_8686, q_gen_8676) -> q_gen_8672
<b, cons, cons>(q_gen_8686, q_gen_8685) -> q_gen_8672
<b, nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8672
<b, nil, cons>(q_gen_8674, q_gen_8721) -> q_gen_8672
<a, nil, cons>(q_gen_8674, q_gen_8721) -> q_gen_8729
<b, cons, cons>(q_gen_8677, q_gen_8685) -> q_gen_8729
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_8671, q_gen_8679, q_gen_8680, q_gen_8703, q_gen_8704, q_gen_8705, q_gen_8706, q_gen_8707, q_gen_8723, q_gen_8724, q_gen_8725},
Q_f={q_gen_8671},
Delta=
{
<nil>() -> q_gen_8679
<cons>(q_gen_8704, q_gen_8679) -> q_gen_8703
<cons>(q_gen_8704, q_gen_8723) -> q_gen_8703
<a>() -> q_gen_8704
<b>() -> q_gen_8704
<s>(q_gen_8725) -> q_gen_8706
<z>() -> q_gen_8706
<cons>(q_gen_8704, q_gen_8703) -> q_gen_8723
<s>(q_gen_8706) -> q_gen_8725
<cons, s>(q_gen_8680, q_gen_8679) -> q_gen_8671
<cons, s>(q_gen_8705, q_gen_8703) -> q_gen_8671
<cons, s>(q_gen_8724, q_gen_8723) -> q_gen_8671
<nil, z>() -> q_gen_8671
<a, z>() -> q_gen_8680
<b, z>() -> q_gen_8680
<a, s>(q_gen_8706) -> q_gen_8705
<b, s>(q_gen_8706) -> q_gen_8705
<cons, s>(q_gen_8680, q_gen_8723) -> q_gen_8707
<cons, s>(q_gen_8705, q_gen_8679) -> q_gen_8707
<cons, s>(q_gen_8705, q_gen_8723) -> q_gen_8707
<cons, s>(q_gen_8724, q_gen_8679) -> q_gen_8707
<cons, s>(q_gen_8724, q_gen_8703) -> q_gen_8707
<a, s>(q_gen_8725) -> q_gen_8724
<b, s>(q_gen_8725) -> q_gen_8724
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_8669, q_gen_8683},
Q_f={q_gen_8669},
Delta=
{
<a, a>() -> q_gen_8669
<a, b>() -> q_gen_8669
<b, b>() -> q_gen_8669
<b, a>() -> q_gen_8683
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_8668, q_gen_8682, q_gen_8730, q_gen_8732, q_gen_8733},
Q_f={q_gen_8668},
Delta=
{
<cons>(q_gen_8733, q_gen_8732) -> q_gen_8732
<nil>() -> q_gen_8732
<a>() -> q_gen_8733
<b>() -> q_gen_8733
<cons, cons>(q_gen_8682, q_gen_8668) -> q_gen_8668
<nil, nil>() -> q_gen_8668
<a, a>() -> q_gen_8682
<a, b>() -> q_gen_8682
<b, a>() -> q_gen_8682
<b, b>() -> q_gen_8682
<cons, cons>(q_gen_8682, q_gen_8730) -> q_gen_8730
<cons, nil>(q_gen_8733, q_gen_8732) -> q_gen_8730
<nil, cons>(q_gen_8733, q_gen_8732) -> q_gen_8730
}

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, _oha]) /\ not leq([x, y])) -> insert([x, cons(y, z), _oha]) -> 51
(insert([y, _tha, _uha]) /\ sort([z, _tha])) -> sort([cons(y, z), _uha]) -> 54
(length([_dia, _eia]) /\ length([l, _cia]) /\ sort([l, _dia])) -> eq_nat([_cia, _eia]) -> 55
(length([ll, _yha])) -> length([cons(x, ll), s(_yha)]) -> 51
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 50
(leq([b, a])) -> BOT -> 50
}
Sat witness: Found: ((insert([y, _tha, _uha]) /\ sort([z, _tha])) -> sort([cons(y, z), _uha]), {
_tha -> nil  ;  _uha -> cons(b, cons(b, nil))  ;  y -> b  ;  z -> nil
})

-------------------------------------------
Step 67, which took 1.983913 s (model generation: 1.982024,  model checking: 0.001889):

Model:
|_
{
insert -> 
{{{
Q={q_gen_8672, q_gen_8673, q_gen_8674, q_gen_8676, q_gen_8677, q_gen_8685, q_gen_8686, q_gen_8717, q_gen_8721},
Q_f={q_gen_8672},
Delta=
{
<nil>() -> q_gen_8673
<a>() -> q_gen_8674
<b>() -> q_gen_8674
<cons>(q_gen_8674, q_gen_8673) -> q_gen_8721
<cons>(q_gen_8674, q_gen_8721) -> q_gen_8721
<cons, cons>(q_gen_8677, q_gen_8685) -> q_gen_8676
<cons, cons>(q_gen_8686, q_gen_8676) -> q_gen_8676
<cons, cons>(q_gen_8686, q_gen_8685) -> q_gen_8676
<nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8676
<b, a>() -> q_gen_8677
<b, b>() -> q_gen_8677
<cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8685
<cons, nil>(q_gen_8674, q_gen_8673) -> q_gen_8685
<cons, nil>(q_gen_8674, q_gen_8721) -> q_gen_8685
<nil, cons>(q_gen_8674, q_gen_8721) -> q_gen_8685
<nil, nil>() -> q_gen_8685
<a, a>() -> q_gen_8686
<a, b>() -> q_gen_8686
<a, cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8672
<a, cons, cons>(q_gen_8686, q_gen_8676) -> q_gen_8672
<a, cons, cons>(q_gen_8686, q_gen_8685) -> q_gen_8672
<a, nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8672
<b, cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8672
<b, cons, cons>(q_gen_8686, q_gen_8685) -> q_gen_8672
<b, nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8672
<a, cons, cons>(q_gen_8677, q_gen_8685) -> q_gen_8717
<a, nil, cons>(q_gen_8674, q_gen_8721) -> q_gen_8717
<b, cons, cons>(q_gen_8677, q_gen_8685) -> q_gen_8717
<b, cons, cons>(q_gen_8686, q_gen_8676) -> q_gen_8717
<b, nil, cons>(q_gen_8674, q_gen_8721) -> q_gen_8717
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_8671, q_gen_8679, q_gen_8680, q_gen_8703, q_gen_8704, q_gen_8705, q_gen_8706, q_gen_8707, q_gen_8723, q_gen_8724, q_gen_8725},
Q_f={q_gen_8671},
Delta=
{
<nil>() -> q_gen_8679
<cons>(q_gen_8704, q_gen_8679) -> q_gen_8703
<cons>(q_gen_8704, q_gen_8723) -> q_gen_8703
<a>() -> q_gen_8704
<b>() -> q_gen_8704
<s>(q_gen_8725) -> q_gen_8706
<z>() -> q_gen_8706
<cons>(q_gen_8704, q_gen_8703) -> q_gen_8723
<s>(q_gen_8706) -> q_gen_8725
<cons, s>(q_gen_8680, q_gen_8679) -> q_gen_8671
<cons, s>(q_gen_8705, q_gen_8703) -> q_gen_8671
<cons, s>(q_gen_8724, q_gen_8723) -> q_gen_8671
<nil, z>() -> q_gen_8671
<a, z>() -> q_gen_8680
<b, z>() -> q_gen_8680
<a, s>(q_gen_8706) -> q_gen_8705
<b, s>(q_gen_8706) -> q_gen_8705
<cons, s>(q_gen_8680, q_gen_8723) -> q_gen_8707
<cons, s>(q_gen_8705, q_gen_8679) -> q_gen_8707
<cons, s>(q_gen_8705, q_gen_8723) -> q_gen_8707
<cons, s>(q_gen_8724, q_gen_8679) -> q_gen_8707
<cons, s>(q_gen_8724, q_gen_8703) -> q_gen_8707
<a, s>(q_gen_8725) -> q_gen_8724
<b, s>(q_gen_8725) -> q_gen_8724
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_8669, q_gen_8683},
Q_f={q_gen_8669},
Delta=
{
<a, a>() -> q_gen_8669
<a, b>() -> q_gen_8669
<b, b>() -> q_gen_8669
<b, a>() -> q_gen_8683
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_8668, q_gen_8682, q_gen_8730, q_gen_8732, q_gen_8733},
Q_f={q_gen_8668},
Delta=
{
<cons>(q_gen_8733, q_gen_8732) -> q_gen_8732
<nil>() -> q_gen_8732
<a>() -> q_gen_8733
<b>() -> q_gen_8733
<cons, cons>(q_gen_8682, q_gen_8668) -> q_gen_8668
<nil, nil>() -> q_gen_8668
<a, a>() -> q_gen_8682
<a, b>() -> q_gen_8682
<b, a>() -> q_gen_8682
<b, b>() -> q_gen_8682
<cons, cons>(q_gen_8682, q_gen_8730) -> q_gen_8730
<cons, nil>(q_gen_8733, q_gen_8732) -> q_gen_8730
<nil, cons>(q_gen_8733, q_gen_8732) -> q_gen_8730
}

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, _oha]) /\ not leq([x, y])) -> insert([x, cons(y, z), _oha]) -> 51
(insert([y, _tha, _uha]) /\ sort([z, _tha])) -> sort([cons(y, z), _uha]) -> 54
(length([_dia, _eia]) /\ length([l, _cia]) /\ sort([l, _dia])) -> eq_nat([_cia, _eia]) -> 55
(length([ll, _yha])) -> length([cons(x, ll), s(_yha)]) -> 51
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 53
(leq([b, a])) -> BOT -> 51
}
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 68, which took 1.365891 s (model generation: 1.359130,  model checking: 0.006761):

Model:
|_
{
insert -> 
{{{
Q={q_gen_8672, q_gen_8673, q_gen_8674, q_gen_8676, q_gen_8677, q_gen_8685, q_gen_8686, q_gen_8717, q_gen_8721},
Q_f={q_gen_8672},
Delta=
{
<nil>() -> q_gen_8673
<a>() -> q_gen_8674
<b>() -> q_gen_8674
<cons>(q_gen_8674, q_gen_8673) -> q_gen_8721
<cons>(q_gen_8674, q_gen_8721) -> q_gen_8721
<cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8676
<cons, cons>(q_gen_8686, q_gen_8676) -> q_gen_8676
<cons, cons>(q_gen_8686, q_gen_8685) -> q_gen_8676
<nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8676
<b, a>() -> q_gen_8677
<b, b>() -> q_gen_8677
<cons, nil>(q_gen_8674, q_gen_8673) -> q_gen_8685
<cons, nil>(q_gen_8674, q_gen_8721) -> q_gen_8685
<nil, cons>(q_gen_8674, q_gen_8721) -> q_gen_8685
<nil, nil>() -> q_gen_8685
<a, a>() -> q_gen_8686
<a, b>() -> q_gen_8686
<a, cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8672
<a, cons, cons>(q_gen_8677, q_gen_8685) -> q_gen_8672
<a, cons, cons>(q_gen_8686, q_gen_8676) -> q_gen_8672
<a, cons, cons>(q_gen_8686, q_gen_8685) -> q_gen_8672
<a, nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8672
<b, cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8672
<b, cons, cons>(q_gen_8686, q_gen_8676) -> q_gen_8672
<b, cons, cons>(q_gen_8686, q_gen_8685) -> q_gen_8672
<b, nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8672
<a, nil, cons>(q_gen_8674, q_gen_8721) -> q_gen_8717
<b, cons, cons>(q_gen_8677, q_gen_8685) -> q_gen_8717
<b, nil, cons>(q_gen_8674, q_gen_8721) -> q_gen_8717
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_8671, q_gen_8679, q_gen_8680, q_gen_8703, q_gen_8704, q_gen_8705, q_gen_8706, q_gen_8707, q_gen_8723, q_gen_8724, q_gen_8725},
Q_f={q_gen_8671},
Delta=
{
<nil>() -> q_gen_8679
<cons>(q_gen_8704, q_gen_8679) -> q_gen_8703
<a>() -> q_gen_8704
<b>() -> q_gen_8704
<z>() -> q_gen_8706
<cons>(q_gen_8704, q_gen_8703) -> q_gen_8723
<cons>(q_gen_8704, q_gen_8723) -> q_gen_8723
<s>(q_gen_8706) -> q_gen_8725
<s>(q_gen_8725) -> q_gen_8725
<cons, s>(q_gen_8680, q_gen_8679) -> q_gen_8671
<cons, s>(q_gen_8705, q_gen_8703) -> q_gen_8671
<cons, s>(q_gen_8724, q_gen_8723) -> q_gen_8671
<nil, z>() -> q_gen_8671
<a, z>() -> q_gen_8680
<b, z>() -> q_gen_8680
<a, s>(q_gen_8706) -> q_gen_8705
<b, s>(q_gen_8706) -> q_gen_8705
<cons, s>(q_gen_8680, q_gen_8723) -> q_gen_8707
<cons, s>(q_gen_8705, q_gen_8679) -> q_gen_8707
<cons, s>(q_gen_8705, q_gen_8723) -> q_gen_8707
<cons, s>(q_gen_8724, q_gen_8679) -> q_gen_8707
<cons, s>(q_gen_8724, q_gen_8703) -> q_gen_8707
<a, s>(q_gen_8725) -> q_gen_8724
<b, s>(q_gen_8725) -> q_gen_8724
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_8669, q_gen_8683},
Q_f={q_gen_8669},
Delta=
{
<a, a>() -> q_gen_8669
<a, b>() -> q_gen_8669
<b, b>() -> q_gen_8669
<b, a>() -> q_gen_8683
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_8668, q_gen_8682, q_gen_8730, q_gen_8732, q_gen_8733},
Q_f={q_gen_8668},
Delta=
{
<cons>(q_gen_8733, q_gen_8732) -> q_gen_8732
<nil>() -> q_gen_8732
<a>() -> q_gen_8733
<b>() -> q_gen_8733
<cons, cons>(q_gen_8682, q_gen_8668) -> q_gen_8668
<nil, nil>() -> q_gen_8668
<a, a>() -> q_gen_8682
<a, b>() -> q_gen_8682
<b, a>() -> q_gen_8682
<b, b>() -> q_gen_8682
<cons, cons>(q_gen_8682, q_gen_8730) -> q_gen_8730
<cons, nil>(q_gen_8733, q_gen_8732) -> q_gen_8730
<nil, cons>(q_gen_8733, q_gen_8732) -> q_gen_8730
}

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, _oha]) /\ not leq([x, y])) -> insert([x, cons(y, z), _oha]) -> 54
(insert([y, _tha, _uha]) /\ sort([z, _tha])) -> sort([cons(y, z), _uha]) -> 54
(length([_dia, _eia]) /\ length([l, _cia]) /\ sort([l, _dia])) -> eq_nat([_cia, _eia]) -> 55
(length([ll, _yha])) -> length([cons(x, ll), s(_yha)]) -> 52
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 53
(leq([b, a])) -> BOT -> 52
}
Sat witness: Found: ((insert([x, z, _oha]) /\ not leq([x, y])) -> insert([x, cons(y, z), _oha]), {
_oha -> cons(a, cons(b, nil))  ;  x -> b  ;  y -> a  ;  z -> cons(b, nil)
})

-------------------------------------------
Step 69, which took 2.179227 s (model generation: 2.171775,  model checking: 0.007452):

Model:
|_
{
insert -> 
{{{
Q={q_gen_8672, q_gen_8673, q_gen_8674, q_gen_8676, q_gen_8677, q_gen_8685, q_gen_8686, q_gen_8717, q_gen_8721},
Q_f={q_gen_8672},
Delta=
{
<nil>() -> q_gen_8673
<a>() -> q_gen_8674
<b>() -> q_gen_8674
<cons>(q_gen_8674, q_gen_8673) -> q_gen_8721
<cons>(q_gen_8674, q_gen_8721) -> q_gen_8721
<cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8676
<cons, cons>(q_gen_8686, q_gen_8676) -> q_gen_8676
<cons, cons>(q_gen_8686, q_gen_8685) -> q_gen_8676
<nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8676
<b, a>() -> q_gen_8677
<b, b>() -> q_gen_8677
<cons, cons>(q_gen_8677, q_gen_8685) -> q_gen_8685
<cons, nil>(q_gen_8674, q_gen_8673) -> q_gen_8685
<cons, nil>(q_gen_8674, q_gen_8721) -> q_gen_8685
<nil, cons>(q_gen_8674, q_gen_8721) -> q_gen_8685
<nil, nil>() -> q_gen_8685
<a, a>() -> q_gen_8686
<a, b>() -> q_gen_8686
<a, cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8672
<a, cons, cons>(q_gen_8677, q_gen_8685) -> q_gen_8672
<a, cons, cons>(q_gen_8686, q_gen_8676) -> q_gen_8672
<a, nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8672
<b, cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8672
<b, cons, cons>(q_gen_8686, q_gen_8685) -> q_gen_8672
<b, nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8672
<a, cons, cons>(q_gen_8686, q_gen_8685) -> q_gen_8717
<a, nil, cons>(q_gen_8674, q_gen_8721) -> q_gen_8717
<b, cons, cons>(q_gen_8677, q_gen_8685) -> q_gen_8717
<b, cons, cons>(q_gen_8686, q_gen_8676) -> q_gen_8717
<b, nil, cons>(q_gen_8674, q_gen_8721) -> q_gen_8717
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_8671, q_gen_8679, q_gen_8680, q_gen_8703, q_gen_8704, q_gen_8705, q_gen_8706, q_gen_8707, q_gen_8723, q_gen_8724, q_gen_8725},
Q_f={q_gen_8671},
Delta=
{
<nil>() -> q_gen_8679
<cons>(q_gen_8704, q_gen_8679) -> q_gen_8703
<a>() -> q_gen_8704
<b>() -> q_gen_8704
<z>() -> q_gen_8706
<cons>(q_gen_8704, q_gen_8703) -> q_gen_8723
<cons>(q_gen_8704, q_gen_8723) -> q_gen_8723
<s>(q_gen_8706) -> q_gen_8725
<s>(q_gen_8725) -> q_gen_8725
<cons, s>(q_gen_8680, q_gen_8679) -> q_gen_8671
<cons, s>(q_gen_8705, q_gen_8703) -> q_gen_8671
<cons, s>(q_gen_8724, q_gen_8723) -> q_gen_8671
<nil, z>() -> q_gen_8671
<a, z>() -> q_gen_8680
<b, z>() -> q_gen_8680
<a, s>(q_gen_8706) -> q_gen_8705
<b, s>(q_gen_8706) -> q_gen_8705
<cons, s>(q_gen_8680, q_gen_8723) -> q_gen_8707
<cons, s>(q_gen_8705, q_gen_8679) -> q_gen_8707
<cons, s>(q_gen_8705, q_gen_8723) -> q_gen_8707
<cons, s>(q_gen_8724, q_gen_8679) -> q_gen_8707
<cons, s>(q_gen_8724, q_gen_8703) -> q_gen_8707
<a, s>(q_gen_8725) -> q_gen_8724
<b, s>(q_gen_8725) -> q_gen_8724
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_8669, q_gen_8683},
Q_f={q_gen_8669},
Delta=
{
<a, a>() -> q_gen_8669
<a, b>() -> q_gen_8669
<b, b>() -> q_gen_8669
<b, a>() -> q_gen_8683
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_8668, q_gen_8682, q_gen_8730, q_gen_8732, q_gen_8733},
Q_f={q_gen_8668},
Delta=
{
<cons>(q_gen_8733, q_gen_8732) -> q_gen_8732
<nil>() -> q_gen_8732
<a>() -> q_gen_8733
<b>() -> q_gen_8733
<cons, cons>(q_gen_8682, q_gen_8668) -> q_gen_8668
<nil, nil>() -> q_gen_8668
<a, a>() -> q_gen_8682
<a, b>() -> q_gen_8682
<b, a>() -> q_gen_8682
<b, b>() -> q_gen_8682
<cons, cons>(q_gen_8682, q_gen_8730) -> q_gen_8730
<cons, nil>(q_gen_8733, q_gen_8732) -> q_gen_8730
<nil, cons>(q_gen_8733, q_gen_8732) -> q_gen_8730
}

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, _oha]) /\ not leq([x, y])) -> insert([x, cons(y, z), _oha]) -> 54
(insert([y, _tha, _uha]) /\ sort([z, _tha])) -> sort([cons(y, z), _uha]) -> 57
(length([_dia, _eia]) /\ length([l, _cia]) /\ sort([l, _dia])) -> eq_nat([_cia, _eia]) -> 55
(length([ll, _yha])) -> length([cons(x, ll), s(_yha)]) -> 53
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 54
(leq([b, a])) -> BOT -> 53
}
Sat witness: Found: ((insert([y, _tha, _uha]) /\ sort([z, _tha])) -> sort([cons(y, z), _uha]), {
_tha -> cons(b, cons(a, nil))  ;  _uha -> cons(b, cons(b, nil))  ;  y -> b  ;  z -> cons(b, cons(a, nil))
})

-------------------------------------------
Step 70, which took 4.882299 s (model generation: 4.874895,  model checking: 0.007404):

Model:
|_
{
insert -> 
{{{
Q={q_gen_8672, q_gen_8673, q_gen_8674, q_gen_8676, q_gen_8677, q_gen_8685, q_gen_8686, q_gen_8721, q_gen_8729},
Q_f={q_gen_8672},
Delta=
{
<nil>() -> q_gen_8673
<a>() -> q_gen_8674
<b>() -> q_gen_8674
<cons>(q_gen_8674, q_gen_8673) -> q_gen_8721
<cons>(q_gen_8674, q_gen_8721) -> q_gen_8721
<cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8676
<cons, cons>(q_gen_8677, q_gen_8685) -> q_gen_8676
<cons, cons>(q_gen_8686, q_gen_8676) -> q_gen_8676
<cons, nil>(q_gen_8674, q_gen_8721) -> q_gen_8676
<nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8676
<b, b>() -> q_gen_8677
<cons, cons>(q_gen_8686, q_gen_8685) -> q_gen_8685
<cons, nil>(q_gen_8674, q_gen_8673) -> q_gen_8685
<nil, cons>(q_gen_8674, q_gen_8721) -> q_gen_8685
<nil, nil>() -> q_gen_8685
<a, a>() -> q_gen_8686
<a, b>() -> q_gen_8686
<b, a>() -> q_gen_8686
<a, cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8672
<a, cons, cons>(q_gen_8686, q_gen_8676) -> q_gen_8672
<a, nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8672
<b, cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8672
<b, cons, cons>(q_gen_8686, q_gen_8676) -> q_gen_8672
<b, cons, cons>(q_gen_8686, q_gen_8685) -> q_gen_8672
<b, nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8672
<a, cons, cons>(q_gen_8677, q_gen_8685) -> q_gen_8729
<a, cons, cons>(q_gen_8686, q_gen_8685) -> q_gen_8729
<a, nil, cons>(q_gen_8674, q_gen_8721) -> q_gen_8729
<b, cons, cons>(q_gen_8677, q_gen_8685) -> q_gen_8729
<b, nil, cons>(q_gen_8674, q_gen_8721) -> q_gen_8729
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_8671, q_gen_8679, q_gen_8680, q_gen_8703, q_gen_8704, q_gen_8705, q_gen_8706, q_gen_8707, q_gen_8723, q_gen_8724, q_gen_8725},
Q_f={q_gen_8671},
Delta=
{
<nil>() -> q_gen_8679
<cons>(q_gen_8704, q_gen_8679) -> q_gen_8703
<a>() -> q_gen_8704
<b>() -> q_gen_8704
<z>() -> q_gen_8706
<cons>(q_gen_8704, q_gen_8703) -> q_gen_8723
<cons>(q_gen_8704, q_gen_8723) -> q_gen_8723
<s>(q_gen_8706) -> q_gen_8725
<s>(q_gen_8725) -> q_gen_8725
<cons, s>(q_gen_8680, q_gen_8679) -> q_gen_8671
<cons, s>(q_gen_8705, q_gen_8703) -> q_gen_8671
<cons, s>(q_gen_8724, q_gen_8723) -> q_gen_8671
<nil, z>() -> q_gen_8671
<a, z>() -> q_gen_8680
<b, z>() -> q_gen_8680
<a, s>(q_gen_8706) -> q_gen_8705
<b, s>(q_gen_8706) -> q_gen_8705
<cons, s>(q_gen_8680, q_gen_8723) -> q_gen_8707
<cons, s>(q_gen_8705, q_gen_8679) -> q_gen_8707
<cons, s>(q_gen_8705, q_gen_8723) -> q_gen_8707
<cons, s>(q_gen_8724, q_gen_8679) -> q_gen_8707
<cons, s>(q_gen_8724, q_gen_8703) -> q_gen_8707
<a, s>(q_gen_8725) -> q_gen_8724
<b, s>(q_gen_8725) -> q_gen_8724
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_8669, q_gen_8683},
Q_f={q_gen_8669},
Delta=
{
<a, a>() -> q_gen_8669
<a, b>() -> q_gen_8669
<b, b>() -> q_gen_8669
<b, a>() -> q_gen_8683
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_8668, q_gen_8682, q_gen_8730, q_gen_8732, q_gen_8733},
Q_f={q_gen_8668},
Delta=
{
<cons>(q_gen_8733, q_gen_8732) -> q_gen_8732
<nil>() -> q_gen_8732
<a>() -> q_gen_8733
<b>() -> q_gen_8733
<cons, cons>(q_gen_8682, q_gen_8668) -> q_gen_8668
<nil, nil>() -> q_gen_8668
<a, a>() -> q_gen_8682
<a, b>() -> q_gen_8682
<b, a>() -> q_gen_8682
<b, b>() -> q_gen_8682
<cons, cons>(q_gen_8682, q_gen_8730) -> q_gen_8730
<cons, nil>(q_gen_8733, q_gen_8732) -> q_gen_8730
<nil, cons>(q_gen_8733, q_gen_8732) -> q_gen_8730
}

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, _oha]) /\ not leq([x, y])) -> insert([x, cons(y, z), _oha]) -> 55
(insert([y, _tha, _uha]) /\ sort([z, _tha])) -> sort([cons(y, z), _uha]) -> 57
(length([_dia, _eia]) /\ length([l, _cia]) /\ sort([l, _dia])) -> eq_nat([_cia, _eia]) -> 58
(length([ll, _yha])) -> length([cons(x, ll), s(_yha)]) -> 54
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 55
(leq([b, a])) -> BOT -> 54
}
Sat witness: Found: ((length([_dia, _eia]) /\ length([l, _cia]) /\ sort([l, _dia])) -> eq_nat([_cia, _eia]), {
_cia -> s(s(s(z)))  ;  _dia -> cons(b, cons(b, cons(b, nil)))  ;  _eia -> s(s(s(s(z))))  ;  l -> cons(b, cons(b, cons(b, nil)))
})

-------------------------------------------
Step 71, which took 4.333900 s (model generation: 4.324695,  model checking: 0.009205):

Model:
|_
{
insert -> 
{{{
Q={q_gen_8672, q_gen_8673, q_gen_8674, q_gen_8676, q_gen_8677, q_gen_8685, q_gen_8686, q_gen_8717, q_gen_8721},
Q_f={q_gen_8672},
Delta=
{
<nil>() -> q_gen_8673
<a>() -> q_gen_8674
<b>() -> q_gen_8674
<cons>(q_gen_8674, q_gen_8673) -> q_gen_8721
<cons>(q_gen_8674, q_gen_8721) -> q_gen_8721
<cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8676
<cons, cons>(q_gen_8686, q_gen_8676) -> q_gen_8676
<cons, nil>(q_gen_8674, q_gen_8721) -> q_gen_8676
<nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8676
<b, a>() -> q_gen_8677
<b, b>() -> q_gen_8677
<cons, cons>(q_gen_8677, q_gen_8685) -> q_gen_8685
<cons, cons>(q_gen_8686, q_gen_8685) -> q_gen_8685
<cons, nil>(q_gen_8674, q_gen_8673) -> q_gen_8685
<nil, cons>(q_gen_8674, q_gen_8721) -> q_gen_8685
<nil, nil>() -> q_gen_8685
<a, a>() -> q_gen_8686
<a, b>() -> q_gen_8686
<a, cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8672
<a, cons, cons>(q_gen_8686, q_gen_8676) -> q_gen_8672
<a, nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8672
<b, cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8672
<b, cons, cons>(q_gen_8686, q_gen_8676) -> q_gen_8672
<b, cons, cons>(q_gen_8686, q_gen_8685) -> q_gen_8672
<b, nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8672
<a, cons, cons>(q_gen_8677, q_gen_8685) -> q_gen_8717
<a, cons, cons>(q_gen_8686, q_gen_8685) -> q_gen_8717
<a, nil, cons>(q_gen_8674, q_gen_8721) -> q_gen_8717
<b, cons, cons>(q_gen_8677, q_gen_8685) -> q_gen_8717
<b, nil, cons>(q_gen_8674, q_gen_8721) -> q_gen_8717
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_8671, q_gen_8679, q_gen_8680, q_gen_8703, q_gen_8704, q_gen_8705, q_gen_8706, q_gen_8707, q_gen_8723, q_gen_8724, q_gen_8725},
Q_f={q_gen_8671},
Delta=
{
<nil>() -> q_gen_8679
<cons>(q_gen_8704, q_gen_8679) -> q_gen_8703
<cons>(q_gen_8704, q_gen_8723) -> q_gen_8703
<a>() -> q_gen_8704
<b>() -> q_gen_8704
<s>(q_gen_8725) -> q_gen_8706
<z>() -> q_gen_8706
<cons>(q_gen_8704, q_gen_8703) -> q_gen_8723
<s>(q_gen_8706) -> q_gen_8725
<cons, s>(q_gen_8680, q_gen_8679) -> q_gen_8671
<cons, s>(q_gen_8705, q_gen_8703) -> q_gen_8671
<cons, s>(q_gen_8724, q_gen_8723) -> q_gen_8671
<nil, z>() -> q_gen_8671
<a, z>() -> q_gen_8680
<b, z>() -> q_gen_8680
<a, s>(q_gen_8706) -> q_gen_8705
<b, s>(q_gen_8706) -> q_gen_8705
<cons, s>(q_gen_8680, q_gen_8723) -> q_gen_8707
<cons, s>(q_gen_8705, q_gen_8679) -> q_gen_8707
<cons, s>(q_gen_8705, q_gen_8723) -> q_gen_8707
<cons, s>(q_gen_8724, q_gen_8679) -> q_gen_8707
<cons, s>(q_gen_8724, q_gen_8703) -> q_gen_8707
<a, s>(q_gen_8725) -> q_gen_8724
<b, s>(q_gen_8725) -> q_gen_8724
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_8669, q_gen_8683},
Q_f={q_gen_8669},
Delta=
{
<a, a>() -> q_gen_8669
<a, b>() -> q_gen_8669
<b, b>() -> q_gen_8669
<b, a>() -> q_gen_8683
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_8668, q_gen_8682, q_gen_8730, q_gen_8732, q_gen_8733},
Q_f={q_gen_8668},
Delta=
{
<cons>(q_gen_8733, q_gen_8732) -> q_gen_8732
<nil>() -> q_gen_8732
<a>() -> q_gen_8733
<b>() -> q_gen_8733
<cons, cons>(q_gen_8682, q_gen_8668) -> q_gen_8668
<nil, nil>() -> q_gen_8668
<a, a>() -> q_gen_8682
<a, b>() -> q_gen_8682
<b, a>() -> q_gen_8682
<b, b>() -> q_gen_8682
<cons, cons>(q_gen_8682, q_gen_8730) -> q_gen_8730
<cons, nil>(q_gen_8733, q_gen_8732) -> q_gen_8730
<nil, cons>(q_gen_8733, q_gen_8732) -> q_gen_8730
}

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, _oha]) /\ not leq([x, y])) -> insert([x, cons(y, z), _oha]) -> 56
(insert([y, _tha, _uha]) /\ sort([z, _tha])) -> sort([cons(y, z), _uha]) -> 60
(length([_dia, _eia]) /\ length([l, _cia]) /\ sort([l, _dia])) -> eq_nat([_cia, _eia]) -> 58
(length([ll, _yha])) -> length([cons(x, ll), s(_yha)]) -> 55
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 56
(leq([b, a])) -> BOT -> 55
}
Sat witness: Found: ((insert([y, _tha, _uha]) /\ sort([z, _tha])) -> sort([cons(y, z), _uha]), {
_tha -> cons(a, nil)  ;  _uha -> cons(b, nil)  ;  y -> b  ;  z -> cons(b, nil)
})

-------------------------------------------
Step 72, which took 4.681280 s (model generation: 4.666776,  model checking: 0.014504):

Model:
|_
{
insert -> 
{{{
Q={q_gen_8672, q_gen_8673, q_gen_8674, q_gen_8676, q_gen_8677, q_gen_8689, q_gen_8694},
Q_f={q_gen_8672},
Delta=
{
<cons>(q_gen_8674, q_gen_8673) -> q_gen_8673
<cons>(q_gen_8689, q_gen_8673) -> q_gen_8673
<nil>() -> q_gen_8673
<b>() -> q_gen_8674
<a>() -> q_gen_8689
<cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8676
<cons, nil>(q_gen_8674, q_gen_8673) -> q_gen_8676
<cons, nil>(q_gen_8689, q_gen_8673) -> q_gen_8676
<nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8676
<nil, cons>(q_gen_8689, q_gen_8673) -> q_gen_8676
<nil, nil>() -> q_gen_8676
<a, a>() -> q_gen_8677
<a, b>() -> q_gen_8677
<b, a>() -> q_gen_8677
<b, b>() -> q_gen_8677
<a, cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8672
<a, nil, cons>(q_gen_8689, q_gen_8673) -> q_gen_8672
<b, cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8672
<b, nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8672
<a, nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8694
<b, nil, cons>(q_gen_8689, q_gen_8673) -> q_gen_8694
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_8671, q_gen_8679, q_gen_8680, q_gen_8703, q_gen_8704, q_gen_8705, q_gen_8706, q_gen_8707, q_gen_8723, q_gen_8725, q_gen_8727},
Q_f={q_gen_8671},
Delta=
{
<nil>() -> q_gen_8679
<cons>(q_gen_8704, q_gen_8679) -> q_gen_8703
<cons>(q_gen_8704, q_gen_8723) -> q_gen_8703
<a>() -> q_gen_8704
<b>() -> q_gen_8704
<s>(q_gen_8725) -> q_gen_8706
<z>() -> q_gen_8706
<cons>(q_gen_8704, q_gen_8703) -> q_gen_8723
<s>(q_gen_8706) -> q_gen_8725
<cons, s>(q_gen_8680, q_gen_8679) -> q_gen_8671
<cons, s>(q_gen_8680, q_gen_8723) -> q_gen_8671
<cons, s>(q_gen_8705, q_gen_8703) -> q_gen_8671
<cons, s>(q_gen_8727, q_gen_8723) -> q_gen_8671
<nil, z>() -> q_gen_8671
<a, z>() -> q_gen_8680
<b, s>(q_gen_8725) -> q_gen_8680
<b, z>() -> q_gen_8680
<a, s>(q_gen_8706) -> q_gen_8705
<b, s>(q_gen_8706) -> q_gen_8705
<cons, s>(q_gen_8705, q_gen_8679) -> q_gen_8707
<cons, s>(q_gen_8705, q_gen_8723) -> q_gen_8707
<cons, s>(q_gen_8727, q_gen_8679) -> q_gen_8707
<cons, s>(q_gen_8727, q_gen_8703) -> q_gen_8707
<a, s>(q_gen_8725) -> q_gen_8727
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_8669, q_gen_8683},
Q_f={q_gen_8669},
Delta=
{
<a, a>() -> q_gen_8669
<a, b>() -> q_gen_8669
<b, b>() -> q_gen_8669
<b, a>() -> q_gen_8683
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_8668, q_gen_8681, q_gen_8682, q_gen_8695, q_gen_8696, q_gen_8730, q_gen_8732, q_gen_8733},
Q_f={q_gen_8668, q_gen_8681},
Delta=
{
<cons>(q_gen_8733, q_gen_8732) -> q_gen_8732
<nil>() -> q_gen_8732
<a>() -> q_gen_8733
<b>() -> q_gen_8733
<cons, cons>(q_gen_8682, q_gen_8695) -> q_gen_8668
<cons, cons>(q_gen_8696, q_gen_8681) -> q_gen_8668
<nil, nil>() -> q_gen_8668
<cons, cons>(q_gen_8682, q_gen_8668) -> q_gen_8681
<cons, cons>(q_gen_8682, q_gen_8681) -> q_gen_8681
<cons, cons>(q_gen_8696, q_gen_8730) -> q_gen_8681
<a, a>() -> q_gen_8682
<b, b>() -> q_gen_8682
<cons, cons>(q_gen_8682, q_gen_8730) -> q_gen_8695
<cons, cons>(q_gen_8696, q_gen_8668) -> q_gen_8695
<nil, cons>(q_gen_8733, q_gen_8732) -> q_gen_8695
<a, b>() -> q_gen_8696
<b, a>() -> q_gen_8696
<cons, cons>(q_gen_8696, q_gen_8695) -> q_gen_8730
<cons, nil>(q_gen_8733, q_gen_8732) -> q_gen_8730
}

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, _oha]) /\ not leq([x, y])) -> insert([x, cons(y, z), _oha]) -> 57
(insert([y, _tha, _uha]) /\ sort([z, _tha])) -> sort([cons(y, z), _uha]) -> 60
(length([_dia, _eia]) /\ length([l, _cia]) /\ sort([l, _dia])) -> eq_nat([_cia, _eia]) -> 61
(length([ll, _yha])) -> length([cons(x, ll), s(_yha)]) -> 56
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 57
(leq([b, a])) -> BOT -> 56
}
Sat witness: Found: ((length([_dia, _eia]) /\ length([l, _cia]) /\ sort([l, _dia])) -> eq_nat([_cia, _eia]), {
_cia -> s(s(z))  ;  _dia -> cons(a, cons(a, cons(a, nil)))  ;  _eia -> s(s(s(z)))  ;  l -> cons(a, cons(b, cons(b, cons(b, nil))))
})

-------------------------------------------
Step 73, which took 2.389031 s (model generation: 2.379515,  model checking: 0.009516):

Model:
|_
{
insert -> 
{{{
Q={q_gen_8672, q_gen_8673, q_gen_8674, q_gen_8676, q_gen_8677, q_gen_8686, q_gen_8721, q_gen_8729},
Q_f={q_gen_8672},
Delta=
{
<nil>() -> q_gen_8673
<a>() -> q_gen_8674
<b>() -> q_gen_8674
<cons>(q_gen_8674, q_gen_8673) -> q_gen_8721
<cons>(q_gen_8674, q_gen_8721) -> q_gen_8721
<cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8676
<cons, cons>(q_gen_8686, q_gen_8676) -> q_gen_8676
<cons, nil>(q_gen_8674, q_gen_8673) -> q_gen_8676
<cons, nil>(q_gen_8674, q_gen_8721) -> q_gen_8676
<nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8676
<nil, cons>(q_gen_8674, q_gen_8721) -> q_gen_8676
<nil, nil>() -> q_gen_8676
<b, b>() -> q_gen_8677
<a, a>() -> q_gen_8686
<a, b>() -> q_gen_8686
<b, a>() -> q_gen_8686
<a, cons, cons>(q_gen_8686, q_gen_8676) -> q_gen_8672
<a, nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8672
<b, cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8672
<b, cons, cons>(q_gen_8686, q_gen_8676) -> q_gen_8672
<b, nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8672
<a, cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8729
<a, nil, cons>(q_gen_8674, q_gen_8721) -> q_gen_8729
<b, nil, cons>(q_gen_8674, q_gen_8721) -> q_gen_8729
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_8671, q_gen_8679, q_gen_8680, q_gen_8703, q_gen_8704, q_gen_8705, q_gen_8706, q_gen_8707, q_gen_8723, q_gen_8724, q_gen_8725},
Q_f={q_gen_8671},
Delta=
{
<nil>() -> q_gen_8679
<cons>(q_gen_8704, q_gen_8679) -> q_gen_8703
<cons>(q_gen_8704, q_gen_8723) -> q_gen_8703
<a>() -> q_gen_8704
<b>() -> q_gen_8704
<s>(q_gen_8725) -> q_gen_8706
<z>() -> q_gen_8706
<cons>(q_gen_8704, q_gen_8703) -> q_gen_8723
<s>(q_gen_8706) -> q_gen_8725
<cons, s>(q_gen_8680, q_gen_8679) -> q_gen_8671
<cons, s>(q_gen_8705, q_gen_8703) -> q_gen_8671
<cons, s>(q_gen_8724, q_gen_8723) -> q_gen_8671
<nil, z>() -> q_gen_8671
<a, z>() -> q_gen_8680
<b, z>() -> q_gen_8680
<a, s>(q_gen_8706) -> q_gen_8705
<b, s>(q_gen_8706) -> q_gen_8705
<cons, s>(q_gen_8680, q_gen_8723) -> q_gen_8707
<cons, s>(q_gen_8705, q_gen_8679) -> q_gen_8707
<cons, s>(q_gen_8705, q_gen_8723) -> q_gen_8707
<cons, s>(q_gen_8724, q_gen_8679) -> q_gen_8707
<cons, s>(q_gen_8724, q_gen_8703) -> q_gen_8707
<a, s>(q_gen_8725) -> q_gen_8724
<b, s>(q_gen_8725) -> q_gen_8724
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_8669, q_gen_8683},
Q_f={q_gen_8669},
Delta=
{
<a, a>() -> q_gen_8669
<a, b>() -> q_gen_8669
<b, b>() -> q_gen_8669
<b, a>() -> q_gen_8683
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_8668, q_gen_8682, q_gen_8696, q_gen_8730, q_gen_8731, q_gen_8732, q_gen_8733},
Q_f={q_gen_8668},
Delta=
{
<cons>(q_gen_8733, q_gen_8732) -> q_gen_8732
<nil>() -> q_gen_8732
<a>() -> q_gen_8733
<b>() -> q_gen_8733
<cons, cons>(q_gen_8682, q_gen_8668) -> q_gen_8668
<cons, cons>(q_gen_8682, q_gen_8730) -> q_gen_8668
<cons, cons>(q_gen_8696, q_gen_8668) -> q_gen_8668
<nil, nil>() -> q_gen_8668
<b, b>() -> q_gen_8682
<a, a>() -> q_gen_8696
<a, b>() -> q_gen_8696
<b, a>() -> q_gen_8696
<cons, cons>(q_gen_8682, q_gen_8731) -> q_gen_8730
<cons, cons>(q_gen_8696, q_gen_8731) -> q_gen_8730
<cons, nil>(q_gen_8733, q_gen_8732) -> q_gen_8730
<cons, cons>(q_gen_8696, q_gen_8730) -> q_gen_8731
<nil, cons>(q_gen_8733, q_gen_8732) -> q_gen_8731
}

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, _oha]) /\ not leq([x, y])) -> insert([x, cons(y, z), _oha]) -> 58
(insert([y, _tha, _uha]) /\ sort([z, _tha])) -> sort([cons(y, z), _uha]) -> 63
(length([_dia, _eia]) /\ length([l, _cia]) /\ sort([l, _dia])) -> eq_nat([_cia, _eia]) -> 61
(length([ll, _yha])) -> length([cons(x, ll), s(_yha)]) -> 57
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 58
(leq([b, a])) -> BOT -> 57
}
Sat witness: Found: ((insert([y, _tha, _uha]) /\ sort([z, _tha])) -> sort([cons(y, z), _uha]), {
_tha -> cons(b, nil)  ;  _uha -> cons(a, nil)  ;  y -> b  ;  z -> cons(a, nil)
})

-------------------------------------------
Step 74, which took 4.525249 s (model generation: 4.515278,  model checking: 0.009971):

Model:
|_
{
insert -> 
{{{
Q={q_gen_8672, q_gen_8673, q_gen_8674, q_gen_8676, q_gen_8677, q_gen_8689, q_gen_8694, q_gen_8721},
Q_f={q_gen_8672},
Delta=
{
<cons>(q_gen_8674, q_gen_8721) -> q_gen_8673
<nil>() -> q_gen_8673
<b>() -> q_gen_8674
<a>() -> q_gen_8689
<cons>(q_gen_8674, q_gen_8673) -> q_gen_8721
<cons>(q_gen_8689, q_gen_8673) -> q_gen_8721
<cons>(q_gen_8689, q_gen_8721) -> q_gen_8721
<cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8676
<cons, nil>(q_gen_8674, q_gen_8673) -> q_gen_8676
<cons, nil>(q_gen_8674, q_gen_8721) -> q_gen_8676
<cons, nil>(q_gen_8689, q_gen_8673) -> q_gen_8676
<cons, nil>(q_gen_8689, q_gen_8721) -> q_gen_8676
<nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8676
<nil, cons>(q_gen_8674, q_gen_8721) -> q_gen_8676
<nil, cons>(q_gen_8689, q_gen_8673) -> q_gen_8676
<nil, cons>(q_gen_8689, q_gen_8721) -> q_gen_8676
<nil, nil>() -> q_gen_8676
<a, a>() -> q_gen_8677
<a, b>() -> q_gen_8677
<b, a>() -> q_gen_8677
<b, b>() -> q_gen_8677
<a, cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8672
<a, nil, cons>(q_gen_8689, q_gen_8673) -> q_gen_8672
<b, cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8672
<b, nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8672
<a, nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8694
<a, nil, cons>(q_gen_8674, q_gen_8721) -> q_gen_8694
<a, nil, cons>(q_gen_8689, q_gen_8721) -> q_gen_8694
<b, nil, cons>(q_gen_8674, q_gen_8721) -> q_gen_8694
<b, nil, cons>(q_gen_8689, q_gen_8673) -> q_gen_8694
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_8671, q_gen_8679, q_gen_8680, q_gen_8703, q_gen_8704, q_gen_8705, q_gen_8706, q_gen_8707, q_gen_8723, q_gen_8724, q_gen_8725},
Q_f={q_gen_8671},
Delta=
{
<nil>() -> q_gen_8679
<cons>(q_gen_8704, q_gen_8679) -> q_gen_8703
<cons>(q_gen_8704, q_gen_8723) -> q_gen_8703
<a>() -> q_gen_8704
<b>() -> q_gen_8704
<s>(q_gen_8725) -> q_gen_8706
<z>() -> q_gen_8706
<cons>(q_gen_8704, q_gen_8703) -> q_gen_8723
<s>(q_gen_8706) -> q_gen_8725
<cons, s>(q_gen_8680, q_gen_8679) -> q_gen_8671
<cons, s>(q_gen_8705, q_gen_8703) -> q_gen_8671
<cons, s>(q_gen_8724, q_gen_8723) -> q_gen_8671
<nil, z>() -> q_gen_8671
<a, z>() -> q_gen_8680
<b, z>() -> q_gen_8680
<a, s>(q_gen_8706) -> q_gen_8705
<b, s>(q_gen_8706) -> q_gen_8705
<cons, s>(q_gen_8680, q_gen_8723) -> q_gen_8707
<cons, s>(q_gen_8705, q_gen_8679) -> q_gen_8707
<cons, s>(q_gen_8705, q_gen_8723) -> q_gen_8707
<cons, s>(q_gen_8724, q_gen_8679) -> q_gen_8707
<cons, s>(q_gen_8724, q_gen_8703) -> q_gen_8707
<a, s>(q_gen_8725) -> q_gen_8724
<b, s>(q_gen_8725) -> q_gen_8724
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_8669, q_gen_8683},
Q_f={q_gen_8669},
Delta=
{
<a, a>() -> q_gen_8669
<a, b>() -> q_gen_8669
<b, b>() -> q_gen_8669
<b, a>() -> q_gen_8683
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_8668, q_gen_8682, q_gen_8695, q_gen_8696, q_gen_8730, q_gen_8732, q_gen_8733},
Q_f={q_gen_8668},
Delta=
{
<cons>(q_gen_8733, q_gen_8732) -> q_gen_8732
<nil>() -> q_gen_8732
<a>() -> q_gen_8733
<b>() -> q_gen_8733
<cons, cons>(q_gen_8682, q_gen_8668) -> q_gen_8668
<cons, cons>(q_gen_8682, q_gen_8695) -> q_gen_8668
<nil, nil>() -> q_gen_8668
<a, a>() -> q_gen_8682
<b, b>() -> q_gen_8682
<cons, cons>(q_gen_8682, q_gen_8730) -> q_gen_8695
<cons, cons>(q_gen_8696, q_gen_8668) -> q_gen_8695
<a, b>() -> q_gen_8696
<b, a>() -> q_gen_8696
<cons, cons>(q_gen_8696, q_gen_8695) -> q_gen_8730
<cons, cons>(q_gen_8696, q_gen_8730) -> q_gen_8730
<cons, nil>(q_gen_8733, q_gen_8732) -> q_gen_8730
<nil, cons>(q_gen_8733, q_gen_8732) -> q_gen_8730
}

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, _oha]) /\ not leq([x, y])) -> insert([x, cons(y, z), _oha]) -> 59
(insert([y, _tha, _uha]) /\ sort([z, _tha])) -> sort([cons(y, z), _uha]) -> 63
(length([_dia, _eia]) /\ length([l, _cia]) /\ sort([l, _dia])) -> eq_nat([_cia, _eia]) -> 64
(length([ll, _yha])) -> length([cons(x, ll), s(_yha)]) -> 58
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 59
(leq([b, a])) -> BOT -> 58
}
Sat witness: Found: ((length([_dia, _eia]) /\ length([l, _cia]) /\ sort([l, _dia])) -> eq_nat([_cia, _eia]), {
_cia -> s(s(z))  ;  _dia -> cons(a, cons(b, nil))  ;  _eia -> s(s(s(s(z))))  ;  l -> cons(a, cons(b, nil))
})

-------------------------------------------
Step 75, which took 4.265575 s (model generation: 4.257016,  model checking: 0.008559):

Model:
|_
{
insert -> 
{{{
Q={q_gen_8672, q_gen_8673, q_gen_8674, q_gen_8676, q_gen_8677, q_gen_8686, q_gen_8721, q_gen_8729},
Q_f={q_gen_8672},
Delta=
{
<nil>() -> q_gen_8673
<a>() -> q_gen_8674
<b>() -> q_gen_8674
<cons>(q_gen_8674, q_gen_8673) -> q_gen_8721
<cons>(q_gen_8674, q_gen_8721) -> q_gen_8721
<cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8676
<cons, cons>(q_gen_8686, q_gen_8676) -> q_gen_8676
<cons, nil>(q_gen_8674, q_gen_8673) -> q_gen_8676
<cons, nil>(q_gen_8674, q_gen_8721) -> q_gen_8676
<nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8676
<nil, cons>(q_gen_8674, q_gen_8721) -> q_gen_8676
<nil, nil>() -> q_gen_8676
<b, b>() -> q_gen_8677
<a, a>() -> q_gen_8686
<a, b>() -> q_gen_8686
<b, a>() -> q_gen_8686
<a, cons, cons>(q_gen_8686, q_gen_8676) -> q_gen_8672
<a, nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8672
<b, cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8672
<b, cons, cons>(q_gen_8686, q_gen_8676) -> q_gen_8672
<b, nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8672
<a, cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8729
<a, nil, cons>(q_gen_8674, q_gen_8721) -> q_gen_8729
<b, nil, cons>(q_gen_8674, q_gen_8721) -> q_gen_8729
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_8671, q_gen_8679, q_gen_8680, q_gen_8703, q_gen_8704, q_gen_8705, q_gen_8706, q_gen_8707, q_gen_8723, q_gen_8724, q_gen_8725},
Q_f={q_gen_8671},
Delta=
{
<nil>() -> q_gen_8679
<cons>(q_gen_8704, q_gen_8679) -> q_gen_8703
<a>() -> q_gen_8704
<b>() -> q_gen_8704
<z>() -> q_gen_8706
<cons>(q_gen_8704, q_gen_8703) -> q_gen_8723
<cons>(q_gen_8704, q_gen_8723) -> q_gen_8723
<s>(q_gen_8706) -> q_gen_8725
<s>(q_gen_8725) -> q_gen_8725
<cons, s>(q_gen_8680, q_gen_8679) -> q_gen_8671
<cons, s>(q_gen_8705, q_gen_8703) -> q_gen_8671
<cons, s>(q_gen_8724, q_gen_8723) -> q_gen_8671
<nil, z>() -> q_gen_8671
<a, z>() -> q_gen_8680
<b, z>() -> q_gen_8680
<a, s>(q_gen_8706) -> q_gen_8705
<b, s>(q_gen_8706) -> q_gen_8705
<cons, s>(q_gen_8680, q_gen_8723) -> q_gen_8707
<cons, s>(q_gen_8705, q_gen_8679) -> q_gen_8707
<cons, s>(q_gen_8705, q_gen_8723) -> q_gen_8707
<cons, s>(q_gen_8724, q_gen_8679) -> q_gen_8707
<cons, s>(q_gen_8724, q_gen_8703) -> q_gen_8707
<a, s>(q_gen_8725) -> q_gen_8724
<b, s>(q_gen_8725) -> q_gen_8724
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_8669, q_gen_8683},
Q_f={q_gen_8669},
Delta=
{
<a, a>() -> q_gen_8669
<a, b>() -> q_gen_8669
<b, b>() -> q_gen_8669
<b, a>() -> q_gen_8683
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_8668, q_gen_8681, q_gen_8682, q_gen_8695, q_gen_8696, q_gen_8730, q_gen_8732, q_gen_8733},
Q_f={q_gen_8668, q_gen_8681, q_gen_8695},
Delta=
{
<cons>(q_gen_8733, q_gen_8732) -> q_gen_8732
<nil>() -> q_gen_8732
<a>() -> q_gen_8733
<b>() -> q_gen_8733
<nil, nil>() -> q_gen_8668
<cons, cons>(q_gen_8682, q_gen_8668) -> q_gen_8681
<cons, cons>(q_gen_8696, q_gen_8681) -> q_gen_8681
<b, a>() -> q_gen_8682
<b, b>() -> q_gen_8682
<cons, cons>(q_gen_8682, q_gen_8681) -> q_gen_8695
<cons, cons>(q_gen_8682, q_gen_8730) -> q_gen_8695
<cons, cons>(q_gen_8696, q_gen_8668) -> q_gen_8695
<a, a>() -> q_gen_8696
<a, b>() -> q_gen_8696
<cons, cons>(q_gen_8682, q_gen_8695) -> q_gen_8730
<cons, cons>(q_gen_8696, q_gen_8695) -> q_gen_8730
<cons, cons>(q_gen_8696, q_gen_8730) -> q_gen_8730
<cons, nil>(q_gen_8733, q_gen_8732) -> q_gen_8730
<nil, cons>(q_gen_8733, q_gen_8732) -> q_gen_8730
}

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, _oha]) /\ not leq([x, y])) -> insert([x, cons(y, z), _oha]) -> 60
(insert([y, _tha, _uha]) /\ sort([z, _tha])) -> sort([cons(y, z), _uha]) -> 66
(length([_dia, _eia]) /\ length([l, _cia]) /\ sort([l, _dia])) -> eq_nat([_cia, _eia]) -> 64
(length([ll, _yha])) -> length([cons(x, ll), s(_yha)]) -> 59
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 60
(leq([b, a])) -> BOT -> 59
}
Sat witness: Found: ((insert([y, _tha, _uha]) /\ sort([z, _tha])) -> sort([cons(y, z), _uha]), {
_tha -> cons(b, nil)  ;  _uha -> cons(b, cons(b, nil))  ;  y -> b  ;  z -> cons(a, nil)
})

-------------------------------------------
Step 76, which took 5.046503 s (model generation: 5.037141,  model checking: 0.009362):

Model:
|_
{
insert -> 
{{{
Q={q_gen_8672, q_gen_8673, q_gen_8674, q_gen_8676, q_gen_8677, q_gen_8685, q_gen_8689, q_gen_8691, q_gen_8694, q_gen_8721, q_gen_8729, q_gen_8773, q_gen_8775, q_gen_8783, q_gen_8789, q_gen_8796, q_gen_8797},
Q_f={q_gen_8672, q_gen_8783, q_gen_8797},
Delta=
{
<nil>() -> q_gen_8673
<b>() -> q_gen_8674
<a>() -> q_gen_8689
<cons>(q_gen_8674, q_gen_8673) -> q_gen_8721
<cons>(q_gen_8689, q_gen_8673) -> q_gen_8721
<cons>(q_gen_8689, q_gen_8721) -> q_gen_8721
<cons>(q_gen_8674, q_gen_8721) -> q_gen_8773
<cons, cons>(q_gen_8677, q_gen_8775) -> q_gen_8676
<cons, cons>(q_gen_8691, q_gen_8676) -> q_gen_8676
<cons, nil>(q_gen_8689, q_gen_8673) -> q_gen_8676
<nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8676
<a, b>() -> q_gen_8677
<b, b>() -> q_gen_8677
<cons, nil>(q_gen_8674, q_gen_8673) -> q_gen_8685
<cons, nil>(q_gen_8674, q_gen_8721) -> q_gen_8685
<cons, nil>(q_gen_8689, q_gen_8721) -> q_gen_8685
<nil, cons>(q_gen_8674, q_gen_8773) -> q_gen_8685
<nil, cons>(q_gen_8689, q_gen_8673) -> q_gen_8685
<nil, cons>(q_gen_8689, q_gen_8721) -> q_gen_8685
<nil, nil>() -> q_gen_8685
<a, a>() -> q_gen_8691
<b, a>() -> q_gen_8691
<cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8775
<cons, cons>(q_gen_8677, q_gen_8685) -> q_gen_8775
<nil, cons>(q_gen_8674, q_gen_8721) -> q_gen_8775
<a, cons, cons>(q_gen_8691, q_gen_8676) -> q_gen_8672
<a, nil, cons>(q_gen_8689, q_gen_8673) -> q_gen_8672
<b, cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8672
<b, cons, cons>(q_gen_8677, q_gen_8685) -> q_gen_8672
<b, cons, cons>(q_gen_8677, q_gen_8775) -> q_gen_8672
<b, nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8672
<a, nil, cons>(q_gen_8674, q_gen_8673) -> q_gen_8694
<a, nil, cons>(q_gen_8689, q_gen_8721) -> q_gen_8694
<b, cons, cons>(q_gen_8691, q_gen_8685) -> q_gen_8694
<b, nil, cons>(q_gen_8674, q_gen_8773) -> q_gen_8694
<b, nil, cons>(q_gen_8689, q_gen_8673) -> q_gen_8694
<a, cons, cons>(q_gen_8677, q_gen_8676) -> q_gen_8729
<a, nil, cons>(q_gen_8674, q_gen_8721) -> q_gen_8729
<b, nil, cons>(q_gen_8674, q_gen_8721) -> q_gen_8729
<a, cons, cons>(q_gen_8691, q_gen_8685) -> q_gen_8783
<a, cons, cons>(q_gen_8677, q_gen_8685) -> q_gen_8789
<b, cons, cons>(q_gen_8691, q_gen_8676) -> q_gen_8796
<b, cons, cons>(q_gen_8691, q_gen_8775) -> q_gen_8797
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_8671, q_gen_8679, q_gen_8680, q_gen_8703, q_gen_8704, q_gen_8705, q_gen_8706, q_gen_8707, q_gen_8723, q_gen_8724, q_gen_8725},
Q_f={q_gen_8671},
Delta=
{
<nil>() -> q_gen_8679
<cons>(q_gen_8704, q_gen_8679) -> q_gen_8703
<a>() -> q_gen_8704
<b>() -> q_gen_8704
<z>() -> q_gen_8706
<cons>(q_gen_8704, q_gen_8703) -> q_gen_8723
<cons>(q_gen_8704, q_gen_8723) -> q_gen_8723
<s>(q_gen_8706) -> q_gen_8725
<s>(q_gen_8725) -> q_gen_8725
<cons, s>(q_gen_8680, q_gen_8679) -> q_gen_8671
<cons, s>(q_gen_8705, q_gen_8703) -> q_gen_8671
<cons, s>(q_gen_8724, q_gen_8723) -> q_gen_8671
<nil, z>() -> q_gen_8671
<a, z>() -> q_gen_8680
<b, z>() -> q_gen_8680
<a, s>(q_gen_8706) -> q_gen_8705
<b, s>(q_gen_8706) -> q_gen_8705
<cons, s>(q_gen_8680, q_gen_8723) -> q_gen_8707
<cons, s>(q_gen_8705, q_gen_8679) -> q_gen_8707
<cons, s>(q_gen_8705, q_gen_8723) -> q_gen_8707
<cons, s>(q_gen_8724, q_gen_8679) -> q_gen_8707
<cons, s>(q_gen_8724, q_gen_8703) -> q_gen_8707
<a, s>(q_gen_8725) -> q_gen_8724
<b, s>(q_gen_8725) -> q_gen_8724
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_8669, q_gen_8683},
Q_f={q_gen_8669},
Delta=
{
<a, a>() -> q_gen_8669
<a, b>() -> q_gen_8669
<b, b>() -> q_gen_8669
<b, a>() -> q_gen_8683
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  sort -> 
{{{
Q={q_gen_8668, q_gen_8681, q_gen_8682, q_gen_8696, q_gen_8715, q_gen_8716, q_gen_8731, q_gen_8732, q_gen_8733},
Q_f={q_gen_8668, q_gen_8681},
Delta=
{
<cons>(q_gen_8733, q_gen_8732) -> q_gen_8732
<nil>() -> q_gen_8732
<a>() -> q_gen_8733
<b>() -> q_gen_8733
<cons, cons>(q_gen_8682, q_gen_8715) -> q_gen_8668
<cons, cons>(q_gen_8696, q_gen_8668) -> q_gen_8668
<nil, nil>() -> q_gen_8668
<cons, cons>(q_gen_8682, q_gen_8668) -> q_gen_8681
<cons, cons>(q_gen_8696, q_gen_8681) -> q_gen_8681
<b, b>() -> q_gen_8682
<a, a>() -> q_gen_8696
<a, b>() -> q_gen_8696
<cons, cons>(q_gen_8682, q_gen_8731) -> q_gen_8715
<cons, cons>(q_gen_8696, q_gen_8731) -> q_gen_8715
<cons, cons>(q_gen_8716, q_gen_8668) -> q_gen_8715
<cons, cons>(q_gen_8716, q_gen_8715) -> q_gen_8715
<cons, cons>(q_gen_8716, q_gen_8731) -> q_gen_8715
<cons, nil>(q_gen_8733, q_gen_8732) -> q_gen_8715
<b, a>() -> q_gen_8716
<cons, cons>(q_gen_8682, q_gen_8681) -> q_gen_8731
<cons, cons>(q_gen_8696, q_gen_8715) -> q_gen_8731
<nil, cons>(q_gen_8733, q_gen_8732) -> q_gen_8731
}

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, _oha]) /\ not leq([x, y])) -> insert([x, cons(y, z), _oha]) -> 60
(insert([y, _tha, _uha]) /\ sort([z, _tha])) -> sort([cons(y, z), _uha]) -> 66
(length([_dia, _eia]) /\ length([l, _cia]) /\ sort([l, _dia])) -> eq_nat([_cia, _eia]) -> 64
(length([ll, _yha])) -> length([cons(x, ll), s(_yha)]) -> 60
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 63
(leq([b, a])) -> BOT -> 60
}
Sat witness: Found: ((leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]), {
x -> a  ;  y -> a  ;  z -> cons(a, nil)
})

Total time: 66.170647
Reason for stopping: DontKnow. Stopped because: timeout