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([z, s(nn2)])
() -> leq([z, z])
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)])
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2])
(leq([s(nn1), z])) -> BOT}
)
(length, F:
{() -> length([nil, z])
(length([ll, _yq])) -> length([cons(x, ll), s(_yq)])}
(length([_zq, _ar]) /\ length([_zq, _br])) -> eq_nat([_ar, _br])
)
(delete, F:
{() -> delete([x, nil, nil])
(delete([h, t, _cr])) -> delete([h, cons(h, t), _cr])
(delete([x, t, _dr]) /\ not eq_elt([x, h])) -> delete([x, cons(h, t), cons(h, _dr)])}
(delete([_er, _fr, _gr]) /\ delete([_er, _fr, _hr])) -> eq_eltlist([_gr, _hr])
)
}

properties:
{(delete([i, l, _ir]) /\ length([_ir, _jr]) /\ length([l, _kr])) -> leq([_jr, _kr])}


over-approximation: {delete, length}
under-approximation: {leq}

Clause system for inference is:

{
() -> delete([x, nil, nil]) -> 0
() -> length([nil, z]) -> 0
() -> leq([z, s(nn2)]) -> 0
() -> leq([z, z]) -> 0
(delete([h, t, _cr])) -> delete([h, cons(h, t), _cr]) -> 0
(delete([i, l, _ir]) /\ length([_ir, _jr]) /\ length([l, _kr])) -> leq([_jr, _kr]) -> 0
(delete([x, t, _dr]) /\ not eq_elt([x, h])) -> delete([x, cons(h, t), cons(h, _dr)]) -> 0
(length([ll, _yq])) -> length([cons(x, ll), s(_yq)]) -> 0
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 0
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 0
(leq([s(nn1), z])) -> BOT -> 0
}


Solving took 64.202353 seconds.
DontKnow. Stopped because: timeout
Working model:
|_
{
delete -> 
{{{
Q={q_gen_4617, q_gen_4622, q_gen_4623, q_gen_4624, q_gen_4625, q_gen_4626, q_gen_4627, q_gen_4630, q_gen_4633, q_gen_4634, q_gen_4635, q_gen_4636, q_gen_4645, q_gen_4646, q_gen_4647, q_gen_4648, q_gen_4651, q_gen_4652, q_gen_4653, q_gen_4654, q_gen_4656, q_gen_4657, q_gen_4658, q_gen_4665, q_gen_4666, q_gen_4674, q_gen_4675, q_gen_4689, q_gen_4690, q_gen_4691, q_gen_4692, q_gen_4699, q_gen_4700, q_gen_4701, q_gen_4705, q_gen_4706, q_gen_4707, q_gen_4708, q_gen_4712, q_gen_4716, q_gen_4717, q_gen_4718, q_gen_4719, q_gen_4720, q_gen_4725, q_gen_4736, q_gen_4737, q_gen_4738, q_gen_4739, q_gen_4746, q_gen_4751, q_gen_4752, q_gen_4757, q_gen_4768, q_gen_4769, q_gen_4770, q_gen_4771, q_gen_4779, q_gen_4786, q_gen_4789, q_gen_4790, q_gen_4791, q_gen_4795, q_gen_4799, q_gen_4800, q_gen_4801, q_gen_4802, q_gen_4803, q_gen_4807, q_gen_4808, q_gen_4809, q_gen_4815, q_gen_4816, q_gen_4817, q_gen_4818},
Q_f={},
Delta=
{
<nil>() -> q_gen_4626
<b>() -> q_gen_4627
<a>() -> q_gen_4636
<cons>(q_gen_4627, q_gen_4626) -> q_gen_4648
<cons>(q_gen_4636, q_gen_4626) -> q_gen_4701
<cons>(q_gen_4627, q_gen_4648) -> q_gen_4720
<cons>(q_gen_4636, q_gen_4648) -> q_gen_4803
<nil, nil>() -> q_gen_4623
<a, a>() -> q_gen_4624
<b, b>() -> q_gen_4634
<cons, nil>(q_gen_4636, q_gen_4626) -> q_gen_4646
<cons, cons>(q_gen_4634, q_gen_4623) -> q_gen_4653
<cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4657
<a, b>() -> q_gen_4658
<b, a>() -> q_gen_4666
<cons, cons>(q_gen_4634, q_gen_4653) -> q_gen_4675
<cons, cons>(q_gen_4634, q_gen_4691) -> q_gen_4690
<cons, cons>(q_gen_4634, q_gen_4692) -> q_gen_4691
<cons, nil>(q_gen_4627, q_gen_4648) -> q_gen_4692
<cons, nil>(q_gen_4627, q_gen_4701) -> q_gen_4700
<cons, cons>(q_gen_4658, q_gen_4623) -> q_gen_4706
<cons, cons>(q_gen_4658, q_gen_4646) -> q_gen_4708
<cons, cons>(q_gen_4634, q_gen_4718) -> q_gen_4717
<cons, cons>(q_gen_4634, q_gen_4719) -> q_gen_4718
<cons, nil>(q_gen_4627, q_gen_4720) -> q_gen_4719
<cons, cons>(q_gen_4634, q_gen_4738) -> q_gen_4737
<cons, cons>(q_gen_4634, q_gen_4739) -> q_gen_4738
<cons, cons>(q_gen_4634, q_gen_4657) -> q_gen_4739
<cons, cons>(q_gen_4634, q_gen_4717) -> q_gen_4752
<cons, cons>(q_gen_4634, q_gen_4770) -> q_gen_4769
<cons, cons>(q_gen_4624, q_gen_4771) -> q_gen_4770
<cons, nil>(q_gen_4636, q_gen_4701) -> q_gen_4771
<cons, cons>(q_gen_4658, q_gen_4791) -> q_gen_4790
<cons, cons>(q_gen_4624, q_gen_4719) -> q_gen_4791
<cons, cons>(q_gen_4634, q_gen_4801) -> q_gen_4800
<cons, cons>(q_gen_4634, q_gen_4802) -> q_gen_4801
<cons, nil>(q_gen_4627, q_gen_4803) -> q_gen_4802
<cons, cons>(q_gen_4634, q_gen_4809) -> q_gen_4808
<cons, cons>(q_gen_4634, q_gen_4646) -> q_gen_4809
<cons, cons>(q_gen_4634, q_gen_4675) -> q_gen_4816
<b, nil, nil>() -> q_gen_4617
<b, cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4622
<b, cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4625
<a, nil, nil>() -> q_gen_4630
<a, cons, cons>(q_gen_4634, q_gen_4623) -> q_gen_4633
<a, cons, nil>(q_gen_4636, q_gen_4626) -> q_gen_4635
<a, cons, cons>(q_gen_4634, q_gen_4646) -> q_gen_4645
<b, cons, nil>(q_gen_4627, q_gen_4648) -> q_gen_4647
<b, cons, cons>(q_gen_4634, q_gen_4623) -> q_gen_4651
<b, cons, cons>(q_gen_4624, q_gen_4653) -> q_gen_4652
<a, cons, cons>(q_gen_4634, q_gen_4653) -> q_gen_4654
<a, cons, cons>(q_gen_4658, q_gen_4657) -> q_gen_4656
<b, cons, cons>(q_gen_4666, q_gen_4646) -> q_gen_4665
<a, cons, cons>(q_gen_4634, q_gen_4675) -> q_gen_4674
<a, cons, cons>(q_gen_4634, q_gen_4690) -> q_gen_4689
<a, cons, cons>(q_gen_4634, q_gen_4700) -> q_gen_4699
<a, cons, cons>(q_gen_4658, q_gen_4706) -> q_gen_4705
<a, cons, cons>(q_gen_4658, q_gen_4708) -> q_gen_4707
<b, cons, cons>(q_gen_4666, q_gen_4675) -> q_gen_4712
<a, cons, cons>(q_gen_4634, q_gen_4717) -> q_gen_4716
<a, cons, cons>(q_gen_4624, q_gen_4657) -> q_gen_4725
<a, cons, cons>(q_gen_4634, q_gen_4737) -> q_gen_4736
<b, cons, cons>(q_gen_4634, q_gen_4739) -> q_gen_4746
<b, cons, cons>(q_gen_4634, q_gen_4752) -> q_gen_4751
<a, cons, cons>(q_gen_4666, q_gen_4739) -> q_gen_4757
<b, cons, cons>(q_gen_4634, q_gen_4769) -> q_gen_4768
<a, cons, cons>(q_gen_4658, q_gen_4623) -> q_gen_4779
<b, cons, cons>(q_gen_4666, q_gen_4739) -> q_gen_4786
<a, cons, cons>(q_gen_4634, q_gen_4790) -> q_gen_4789
<b, cons, cons>(q_gen_4634, q_gen_4675) -> q_gen_4795
<a, cons, cons>(q_gen_4634, q_gen_4800) -> q_gen_4799
<b, cons, cons>(q_gen_4634, q_gen_4808) -> q_gen_4807
<a, cons, cons>(q_gen_4634, q_gen_4816) -> q_gen_4815
<b, cons, cons>(q_gen_4658, q_gen_4706) -> q_gen_4817
<b, cons, cons>(q_gen_4634, q_gen_4708) -> q_gen_4818
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_4616, q_gen_4619, q_gen_4620, q_gen_4621, q_gen_4631, q_gen_4632, q_gen_4637, q_gen_4638, q_gen_4639, q_gen_4640, q_gen_4641, q_gen_4642, q_gen_4649, q_gen_4650, q_gen_4655, q_gen_4659, q_gen_4660, q_gen_4661, q_gen_4662, q_gen_4663, q_gen_4667, q_gen_4668, q_gen_4669, q_gen_4670, q_gen_4671, q_gen_4672, q_gen_4673, q_gen_4676, q_gen_4678, q_gen_4679, q_gen_4680, q_gen_4681, q_gen_4682, q_gen_4686, q_gen_4693, q_gen_4694, q_gen_4695, q_gen_4696, q_gen_4697, q_gen_4698, q_gen_4702, q_gen_4703, q_gen_4704, q_gen_4709, q_gen_4710, q_gen_4711, q_gen_4713, q_gen_4714, q_gen_4715, q_gen_4721, q_gen_4722, q_gen_4723, q_gen_4724, q_gen_4726, q_gen_4727, q_gen_4728, q_gen_4729, q_gen_4730, q_gen_4731, q_gen_4732, q_gen_4734, q_gen_4735, q_gen_4740, q_gen_4741, q_gen_4743, q_gen_4744, q_gen_4745, q_gen_4747, q_gen_4748, q_gen_4749, q_gen_4750, q_gen_4753, q_gen_4754, q_gen_4755, q_gen_4756, q_gen_4758, q_gen_4759, q_gen_4760, q_gen_4761, q_gen_4762, q_gen_4763, q_gen_4764, q_gen_4765, q_gen_4766, q_gen_4767, q_gen_4772, q_gen_4773, q_gen_4774, q_gen_4775, q_gen_4776, q_gen_4777, q_gen_4778, q_gen_4780, q_gen_4784, q_gen_4785, q_gen_4787, q_gen_4788, q_gen_4792, q_gen_4793, q_gen_4794, q_gen_4796, q_gen_4797, q_gen_4798, q_gen_4804, q_gen_4805, q_gen_4806, q_gen_4810, q_gen_4811, q_gen_4812, q_gen_4813, q_gen_4814},
Q_f={},
Delta=
{
<nil>() -> q_gen_4620
<cons>(q_gen_4639, q_gen_4620) -> q_gen_4638
<b>() -> q_gen_4639
<z>() -> q_gen_4641
<cons>(q_gen_4639, q_gen_4638) -> q_gen_4660
<s>(q_gen_4641) -> q_gen_4662
<s>(q_gen_4662) -> q_gen_4670
<cons>(q_gen_4673, q_gen_4620) -> q_gen_4672
<a>() -> q_gen_4673
<cons>(q_gen_4673, q_gen_4638) -> q_gen_4679
<cons>(q_gen_4639, q_gen_4679) -> q_gen_4681
<cons>(q_gen_4639, q_gen_4695) -> q_gen_4694
<cons>(q_gen_4639, q_gen_4660) -> q_gen_4695
<cons>(q_gen_4639, q_gen_4681) -> q_gen_4698
<cons>(q_gen_4639, q_gen_4672) -> q_gen_4703
<cons>(q_gen_4639, q_gen_4694) -> q_gen_4722
<cons>(q_gen_4673, q_gen_4695) -> q_gen_4729
<s>(q_gen_4670) -> q_gen_4731
<cons>(q_gen_4673, q_gen_4681) -> q_gen_4745
<cons>(q_gen_4639, q_gen_4722) -> q_gen_4754
<cons>(q_gen_4673, q_gen_4672) -> q_gen_4760
<cons>(q_gen_4639, q_gen_4760) -> q_gen_4762
<cons>(q_gen_4673, q_gen_4703) -> q_gen_4765
<cons>(q_gen_4639, q_gen_4765) -> q_gen_4767
<cons>(q_gen_4639, q_gen_4774) -> q_gen_4773
<cons>(q_gen_4673, q_gen_4760) -> q_gen_4774
<cons>(q_gen_4639, q_gen_4703) -> q_gen_4776
<cons>(q_gen_4639, q_gen_4776) -> q_gen_4778
<cons>(q_gen_4673, q_gen_4729) -> q_gen_4793
<cons>(q_gen_4673, q_gen_4694) -> q_gen_4798
<cons>(q_gen_4639, q_gen_4698) -> q_gen_4805
<cons>(q_gen_4673, q_gen_4698) -> q_gen_4814
<nil, z>() -> q_gen_4616
<cons, s>(q_gen_4621, q_gen_4620) -> q_gen_4619
<b, z>() -> q_gen_4621
<cons, s>(q_gen_4632, q_gen_4620) -> q_gen_4631
<a, z>() -> q_gen_4632
<cons, s>(q_gen_4640, q_gen_4638) -> q_gen_4637
<b, s>(q_gen_4641) -> q_gen_4640
<cons, s>(q_gen_4640, q_gen_4620) -> q_gen_4642
<cons, s>(q_gen_4650, q_gen_4638) -> q_gen_4649
<a, s>(q_gen_4641) -> q_gen_4650
<cons, s>(q_gen_4621, q_gen_4638) -> q_gen_4655
<cons, s>(q_gen_4661, q_gen_4660) -> q_gen_4659
<b, s>(q_gen_4662) -> q_gen_4661
<cons, s>(q_gen_4661, q_gen_4638) -> q_gen_4663
<cons, s>(q_gen_4661, q_gen_4620) -> q_gen_4667
<cons, s>(q_gen_4669, q_gen_4638) -> q_gen_4668
<b, s>(q_gen_4670) -> q_gen_4669
<cons, s>(q_gen_4640, q_gen_4672) -> q_gen_4671
<cons, s>(q_gen_4669, q_gen_4660) -> q_gen_4676
<cons, s>(q_gen_4661, q_gen_4679) -> q_gen_4678
<cons, s>(q_gen_4682, q_gen_4681) -> q_gen_4680
<a, s>(q_gen_4670) -> q_gen_4682
<cons, s>(q_gen_4669, q_gen_4681) -> q_gen_4686
<cons, s>(q_gen_4640, q_gen_4694) -> q_gen_4693
<cons, s>(q_gen_4621, q_gen_4681) -> q_gen_4696
<cons, s>(q_gen_4650, q_gen_4698) -> q_gen_4697
<cons, s>(q_gen_4661, q_gen_4703) -> q_gen_4702
<cons, s>(q_gen_4669, q_gen_4620) -> q_gen_4704
<cons, s>(q_gen_4669, q_gen_4695) -> q_gen_4709
<cons, s>(q_gen_4661, q_gen_4681) -> q_gen_4710
<cons, s>(q_gen_4682, q_gen_4698) -> q_gen_4711
<cons, s>(q_gen_4682, q_gen_4660) -> q_gen_4713
<cons, s>(q_gen_4640, q_gen_4681) -> q_gen_4714
<cons, s>(q_gen_4661, q_gen_4698) -> q_gen_4715
<cons, s>(q_gen_4640, q_gen_4722) -> q_gen_4721
<cons, s>(q_gen_4724, q_gen_4679) -> q_gen_4723
<a, s>(q_gen_4662) -> q_gen_4724
<cons, s>(q_gen_4724, q_gen_4620) -> q_gen_4726
<cons, s>(q_gen_4682, q_gen_4695) -> q_gen_4727
<cons, s>(q_gen_4730, q_gen_4729) -> q_gen_4728
<b, s>(q_gen_4731) -> q_gen_4730
<cons, s>(q_gen_4730, q_gen_4660) -> q_gen_4732
<cons, s>(q_gen_4724, q_gen_4638) -> q_gen_4734
<cons, s>(q_gen_4682, q_gen_4679) -> q_gen_4735
<cons, s>(q_gen_4669, q_gen_4694) -> q_gen_4740
<cons, s>(q_gen_4730, q_gen_4695) -> q_gen_4741
<cons, s>(q_gen_4724, q_gen_4681) -> q_gen_4743
<cons, s>(q_gen_4669, q_gen_4745) -> q_gen_4744
<cons, s>(q_gen_4730, q_gen_4638) -> q_gen_4747
<cons, s>(q_gen_4669, q_gen_4679) -> q_gen_4748
<cons, s>(q_gen_4750, q_gen_4681) -> q_gen_4749
<a, s>(q_gen_4731) -> q_gen_4750
<cons, s>(q_gen_4661, q_gen_4754) -> q_gen_4753
<cons, s>(q_gen_4669, q_gen_4672) -> q_gen_4755
<cons, s>(q_gen_4750, q_gen_4703) -> q_gen_4756
<cons, s>(q_gen_4682, q_gen_4638) -> q_gen_4758
<cons, s>(q_gen_4669, q_gen_4760) -> q_gen_4759
<cons, s>(q_gen_4730, q_gen_4762) -> q_gen_4761
<cons, s>(q_gen_4640, q_gen_4754) -> q_gen_4763
<cons, s>(q_gen_4669, q_gen_4765) -> q_gen_4764
<cons, s>(q_gen_4730, q_gen_4767) -> q_gen_4766
<cons, s>(q_gen_4640, q_gen_4773) -> q_gen_4772
<cons, s>(q_gen_4669, q_gen_4776) -> q_gen_4775
<cons, s>(q_gen_4730, q_gen_4778) -> q_gen_4777
<cons, s>(q_gen_4730, q_gen_4620) -> q_gen_4780
<cons, s>(q_gen_4682, q_gen_4672) -> q_gen_4784
<cons, s>(q_gen_4730, q_gen_4760) -> q_gen_4785
<cons, s>(q_gen_4640, q_gen_4660) -> q_gen_4787
<cons, s>(q_gen_4661, q_gen_4695) -> q_gen_4788
<cons, s>(q_gen_4640, q_gen_4793) -> q_gen_4792
<cons, s>(q_gen_4724, q_gen_4660) -> q_gen_4794
<cons, s>(q_gen_4682, q_gen_4694) -> q_gen_4796
<cons, s>(q_gen_4750, q_gen_4798) -> q_gen_4797
<cons, s>(q_gen_4640, q_gen_4805) -> q_gen_4804
<cons, s>(q_gen_4724, q_gen_4703) -> q_gen_4806
<cons, s>(q_gen_4640, q_gen_4776) -> q_gen_4810
<cons, s>(q_gen_4730, q_gen_4694) -> q_gen_4811
<cons, s>(q_gen_4621, q_gen_4660) -> q_gen_4812
<cons, s>(q_gen_4730, q_gen_4814) -> q_gen_4813
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_4613, q_gen_4614, q_gen_4615, q_gen_4618, q_gen_4628, q_gen_4629, q_gen_4643, q_gen_4644, q_gen_4664, q_gen_4677, q_gen_4683, q_gen_4684, q_gen_4685, q_gen_4687, q_gen_4688, q_gen_4733, q_gen_4742, q_gen_4781, q_gen_4782, q_gen_4783},
Q_f={},
Delta=
{
<z>() -> q_gen_4615
<s>(q_gen_4615) -> q_gen_4629
<s>(q_gen_4629) -> q_gen_4688
<s>(q_gen_4688) -> q_gen_4783
<z, z>() -> q_gen_4613
<z, s>(q_gen_4615) -> q_gen_4614
<s, s>(q_gen_4613) -> q_gen_4618
<z, s>(q_gen_4629) -> q_gen_4628
<s, s>(q_gen_4644) -> q_gen_4643
<s, z>(q_gen_4615) -> q_gen_4644
<s, s>(q_gen_4643) -> q_gen_4664
<s, s>(q_gen_4664) -> q_gen_4677
<s, s>(q_gen_4684) -> q_gen_4683
<s, s>(q_gen_4685) -> q_gen_4684
<s, z>(q_gen_4629) -> q_gen_4685
<z, s>(q_gen_4688) -> q_gen_4687
<s, s>(q_gen_4683) -> q_gen_4733
<s, s>(q_gen_4677) -> q_gen_4742
<s, s>(q_gen_4782) -> q_gen_4781
<s, z>(q_gen_4783) -> q_gen_4782
}

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

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

-------------------
STEPS:
-------------------------------------------
Step 0, which took 0.012818 s (model generation: 0.011855,  model checking: 0.000963):

Model:
|_
{
delete -> 
{{{
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: <nat, nat>
Convolution form: left
}}}

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

Teacher's answer:
New clause system:
{
() -> delete([x, nil, nil]) -> 0
() -> length([nil, z]) -> 0
() -> leq([z, s(nn2)]) -> 0
() -> leq([z, z]) -> 3
(delete([h, t, _cr])) -> delete([h, cons(h, t), _cr]) -> 1
(delete([i, l, _ir]) /\ length([_ir, _jr]) /\ length([l, _kr])) -> leq([_jr, _kr]) -> 1
(delete([x, t, _dr]) /\ not eq_elt([x, h])) -> delete([x, cons(h, t), cons(h, _dr)]) -> 1
(length([ll, _yq])) -> length([cons(x, ll), s(_yq)]) -> 1
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 1
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 1
(leq([s(nn1), z])) -> BOT -> 1
}
Sat witness: Found: (() -> leq([z, z]), {

})

-------------------------------------------
Step 1, which took 0.013788 s (model generation: 0.013696,  model checking: 0.000092):

Model:
|_
{
delete -> 
{{{
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_4613},
Q_f={q_gen_4613},
Delta=
{
<z, z>() -> q_gen_4613
}

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

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

Teacher's answer:
New clause system:
{
() -> delete([x, nil, nil]) -> 0
() -> length([nil, z]) -> 0
() -> leq([z, s(nn2)]) -> 3
() -> leq([z, z]) -> 3
(delete([h, t, _cr])) -> delete([h, cons(h, t), _cr]) -> 1
(delete([i, l, _ir]) /\ length([_ir, _jr]) /\ length([l, _kr])) -> leq([_jr, _kr]) -> 1
(delete([x, t, _dr]) /\ not eq_elt([x, h])) -> delete([x, cons(h, t), cons(h, _dr)]) -> 1
(length([ll, _yq])) -> length([cons(x, ll), s(_yq)]) -> 1
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 1
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 1
(leq([s(nn1), z])) -> BOT -> 1
}
Sat witness: Found: (() -> leq([z, s(nn2)]), {
nn2 -> z
})

-------------------------------------------
Step 2, which took 0.010398 s (model generation: 0.010316,  model checking: 0.000082):

Model:
|_
{
delete -> 
{{{
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_4613, q_gen_4615},
Q_f={q_gen_4613},
Delta=
{
<z>() -> q_gen_4615
<z, s>(q_gen_4615) -> q_gen_4613
<z, z>() -> q_gen_4613
}

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

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

Teacher's answer:
New clause system:
{
() -> delete([x, nil, nil]) -> 0
() -> length([nil, z]) -> 3
() -> leq([z, s(nn2)]) -> 3
() -> leq([z, z]) -> 3
(delete([h, t, _cr])) -> delete([h, cons(h, t), _cr]) -> 1
(delete([i, l, _ir]) /\ length([_ir, _jr]) /\ length([l, _kr])) -> leq([_jr, _kr]) -> 1
(delete([x, t, _dr]) /\ not eq_elt([x, h])) -> delete([x, cons(h, t), cons(h, _dr)]) -> 1
(length([ll, _yq])) -> length([cons(x, ll), s(_yq)]) -> 1
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 1
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 1
(leq([s(nn1), z])) -> BOT -> 1
}
Sat witness: Found: (() -> length([nil, z]), {

})

-------------------------------------------
Step 3, which took 0.012096 s (model generation: 0.011941,  model checking: 0.000155):

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

}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_4616},
Q_f={q_gen_4616},
Delta=
{
<nil, z>() -> q_gen_4616
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_4613, q_gen_4615},
Q_f={q_gen_4613},
Delta=
{
<z>() -> q_gen_4615
<z, s>(q_gen_4615) -> q_gen_4613
<z, z>() -> q_gen_4613
}

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

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

Teacher's answer:
New clause system:
{
() -> delete([x, nil, nil]) -> 3
() -> length([nil, z]) -> 3
() -> leq([z, s(nn2)]) -> 3
() -> leq([z, z]) -> 3
(delete([h, t, _cr])) -> delete([h, cons(h, t), _cr]) -> 1
(delete([i, l, _ir]) /\ length([_ir, _jr]) /\ length([l, _kr])) -> leq([_jr, _kr]) -> 1
(delete([x, t, _dr]) /\ not eq_elt([x, h])) -> delete([x, cons(h, t), cons(h, _dr)]) -> 1
(length([ll, _yq])) -> length([cons(x, ll), s(_yq)]) -> 1
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 1
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 1
(leq([s(nn1), z])) -> BOT -> 1
}
Sat witness: Found: (() -> delete([x, nil, nil]), {
x -> b
})

-------------------------------------------
Step 4, which took 0.009256 s (model generation: 0.009128,  model checking: 0.000128):

Model:
|_
{
delete -> 
{{{
Q={q_gen_4617},
Q_f={q_gen_4617},
Delta=
{
<b, nil, nil>() -> q_gen_4617
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_4616},
Q_f={q_gen_4616},
Delta=
{
<nil, z>() -> q_gen_4616
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_4613, q_gen_4615},
Q_f={q_gen_4613},
Delta=
{
<z>() -> q_gen_4615
<z, s>(q_gen_4615) -> q_gen_4613
<z, z>() -> q_gen_4613
}

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

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

Teacher's answer:
New clause system:
{
() -> delete([x, nil, nil]) -> 3
() -> length([nil, z]) -> 3
() -> leq([z, s(nn2)]) -> 3
() -> leq([z, z]) -> 3
(delete([h, t, _cr])) -> delete([h, cons(h, t), _cr]) -> 1
(delete([i, l, _ir]) /\ length([_ir, _jr]) /\ length([l, _kr])) -> leq([_jr, _kr]) -> 1
(delete([x, t, _dr]) /\ not eq_elt([x, h])) -> delete([x, cons(h, t), cons(h, _dr)]) -> 1
(length([ll, _yq])) -> length([cons(x, ll), s(_yq)]) -> 1
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 4
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 2
(leq([s(nn1), z])) -> BOT -> 2
}
Sat witness: Found: ((leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]), {
nn1 -> z  ;  nn2 -> z
})

-------------------------------------------
Step 5, which took 0.012158 s (model generation: 0.012061,  model checking: 0.000097):

Model:
|_
{
delete -> 
{{{
Q={q_gen_4617},
Q_f={q_gen_4617},
Delta=
{
<b, nil, nil>() -> q_gen_4617
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_4616},
Q_f={q_gen_4616},
Delta=
{
<nil, z>() -> q_gen_4616
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_4613, q_gen_4615},
Q_f={q_gen_4613},
Delta=
{
<z>() -> q_gen_4615
<s, s>(q_gen_4613) -> q_gen_4613
<z, s>(q_gen_4615) -> q_gen_4613
<z, z>() -> q_gen_4613
}

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

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

Teacher's answer:
New clause system:
{
() -> delete([x, nil, nil]) -> 3
() -> length([nil, z]) -> 3
() -> leq([z, s(nn2)]) -> 3
() -> leq([z, z]) -> 3
(delete([h, t, _cr])) -> delete([h, cons(h, t), _cr]) -> 1
(delete([i, l, _ir]) /\ length([_ir, _jr]) /\ length([l, _kr])) -> leq([_jr, _kr]) -> 1
(delete([x, t, _dr]) /\ not eq_elt([x, h])) -> delete([x, cons(h, t), cons(h, _dr)]) -> 1
(length([ll, _yq])) -> length([cons(x, ll), s(_yq)]) -> 4
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 4
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 2
(leq([s(nn1), z])) -> BOT -> 2
}
Sat witness: Found: ((length([ll, _yq])) -> length([cons(x, ll), s(_yq)]), {
_yq -> z  ;  ll -> nil  ;  x -> b
})

-------------------------------------------
Step 6, which took 0.014832 s (model generation: 0.014695,  model checking: 0.000137):

Model:
|_
{
delete -> 
{{{
Q={q_gen_4617},
Q_f={q_gen_4617},
Delta=
{
<b, nil, nil>() -> q_gen_4617
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_4616, q_gen_4620, q_gen_4621},
Q_f={q_gen_4616},
Delta=
{
<nil>() -> q_gen_4620
<cons, s>(q_gen_4621, q_gen_4620) -> q_gen_4616
<nil, z>() -> q_gen_4616
<b, z>() -> q_gen_4621
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_4613, q_gen_4615},
Q_f={q_gen_4613},
Delta=
{
<z>() -> q_gen_4615
<s, s>(q_gen_4613) -> q_gen_4613
<z, s>(q_gen_4615) -> q_gen_4613
<z, z>() -> q_gen_4613
}

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

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

Teacher's answer:
New clause system:
{
() -> delete([x, nil, nil]) -> 3
() -> length([nil, z]) -> 3
() -> leq([z, s(nn2)]) -> 3
() -> leq([z, z]) -> 3
(delete([h, t, _cr])) -> delete([h, cons(h, t), _cr]) -> 1
(delete([i, l, _ir]) /\ length([_ir, _jr]) /\ length([l, _kr])) -> leq([_jr, _kr]) -> 1
(delete([x, t, _dr]) /\ not eq_elt([x, h])) -> delete([x, cons(h, t), cons(h, _dr)]) -> 4
(length([ll, _yq])) -> length([cons(x, ll), s(_yq)]) -> 4
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 4
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 2
(leq([s(nn1), z])) -> BOT -> 2
}
Sat witness: Found: ((delete([x, t, _dr]) /\ not eq_elt([x, h])) -> delete([x, cons(h, t), cons(h, _dr)]), {
_dr -> nil  ;  h -> a  ;  t -> nil  ;  x -> b
})

-------------------------------------------
Step 7, which took 0.013289 s (model generation: 0.012942,  model checking: 0.000347):

Model:
|_
{
delete -> 
{{{
Q={q_gen_4617, q_gen_4623, q_gen_4624},
Q_f={q_gen_4617},
Delta=
{
<nil, nil>() -> q_gen_4623
<a, a>() -> q_gen_4624
<b, cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4617
<b, nil, nil>() -> q_gen_4617
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_4616, q_gen_4620, q_gen_4621},
Q_f={q_gen_4616},
Delta=
{
<nil>() -> q_gen_4620
<cons, s>(q_gen_4621, q_gen_4620) -> q_gen_4616
<nil, z>() -> q_gen_4616
<b, z>() -> q_gen_4621
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_4613, q_gen_4615},
Q_f={q_gen_4613},
Delta=
{
<z>() -> q_gen_4615
<s, s>(q_gen_4613) -> q_gen_4613
<z, s>(q_gen_4615) -> q_gen_4613
<z, z>() -> q_gen_4613
}

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

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

Teacher's answer:
New clause system:
{
() -> delete([x, nil, nil]) -> 3
() -> length([nil, z]) -> 3
() -> leq([z, s(nn2)]) -> 3
() -> leq([z, z]) -> 3
(delete([h, t, _cr])) -> delete([h, cons(h, t), _cr]) -> 4
(delete([i, l, _ir]) /\ length([_ir, _jr]) /\ length([l, _kr])) -> leq([_jr, _kr]) -> 2
(delete([x, t, _dr]) /\ not eq_elt([x, h])) -> delete([x, cons(h, t), cons(h, _dr)]) -> 4
(length([ll, _yq])) -> length([cons(x, ll), s(_yq)]) -> 4
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 4
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 2
(leq([s(nn1), z])) -> BOT -> 2
}
Sat witness: Found: ((delete([h, t, _cr])) -> delete([h, cons(h, t), _cr]), {
_cr -> nil  ;  h -> b  ;  t -> nil
})

-------------------------------------------
Step 8, which took 0.013362 s (model generation: 0.012346,  model checking: 0.001016):

Model:
|_
{
delete -> 
{{{
Q={q_gen_4617, q_gen_4623, q_gen_4624, q_gen_4626, q_gen_4627},
Q_f={q_gen_4617},
Delta=
{
<nil>() -> q_gen_4626
<b>() -> q_gen_4627
<nil, nil>() -> q_gen_4623
<a, a>() -> q_gen_4624
<b, cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4617
<b, cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4617
<b, nil, nil>() -> q_gen_4617
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_4616, q_gen_4620, q_gen_4621},
Q_f={q_gen_4616},
Delta=
{
<nil>() -> q_gen_4620
<cons, s>(q_gen_4621, q_gen_4620) -> q_gen_4616
<nil, z>() -> q_gen_4616
<b, z>() -> q_gen_4621
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_4613, q_gen_4615},
Q_f={q_gen_4613},
Delta=
{
<z>() -> q_gen_4615
<s, s>(q_gen_4613) -> q_gen_4613
<z, s>(q_gen_4615) -> q_gen_4613
<z, z>() -> q_gen_4613
}

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

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

Teacher's answer:
New clause system:
{
() -> delete([x, nil, nil]) -> 3
() -> length([nil, z]) -> 3
() -> leq([z, s(nn2)]) -> 6
() -> leq([z, z]) -> 4
(delete([h, t, _cr])) -> delete([h, cons(h, t), _cr]) -> 4
(delete([i, l, _ir]) /\ length([_ir, _jr]) /\ length([l, _kr])) -> leq([_jr, _kr]) -> 3
(delete([x, t, _dr]) /\ not eq_elt([x, h])) -> delete([x, cons(h, t), cons(h, _dr)]) -> 4
(length([ll, _yq])) -> length([cons(x, ll), s(_yq)]) -> 4
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 4
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 3
(leq([s(nn1), z])) -> BOT -> 3
}
Sat witness: Found: (() -> leq([z, s(nn2)]), {
nn2 -> s(z)
})

-------------------------------------------
Step 9, which took 0.011026 s (model generation: 0.010599,  model checking: 0.000427):

Model:
|_
{
delete -> 
{{{
Q={q_gen_4617, q_gen_4623, q_gen_4624, q_gen_4626, q_gen_4627},
Q_f={q_gen_4617},
Delta=
{
<nil>() -> q_gen_4626
<b>() -> q_gen_4627
<nil, nil>() -> q_gen_4623
<a, a>() -> q_gen_4624
<b, cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4617
<b, cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4617
<b, nil, nil>() -> q_gen_4617
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_4616, q_gen_4620, q_gen_4621},
Q_f={q_gen_4616},
Delta=
{
<nil>() -> q_gen_4620
<cons, s>(q_gen_4621, q_gen_4620) -> q_gen_4616
<nil, z>() -> q_gen_4616
<b, z>() -> q_gen_4621
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_4613, q_gen_4615},
Q_f={q_gen_4613},
Delta=
{
<s>(q_gen_4615) -> q_gen_4615
<z>() -> q_gen_4615
<s, s>(q_gen_4613) -> q_gen_4613
<z, s>(q_gen_4615) -> q_gen_4613
<z, z>() -> q_gen_4613
}

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

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

Teacher's answer:
New clause system:
{
() -> delete([x, nil, nil]) -> 6
() -> length([nil, z]) -> 4
() -> leq([z, s(nn2)]) -> 6
() -> leq([z, z]) -> 4
(delete([h, t, _cr])) -> delete([h, cons(h, t), _cr]) -> 4
(delete([i, l, _ir]) /\ length([_ir, _jr]) /\ length([l, _kr])) -> leq([_jr, _kr]) -> 4
(delete([x, t, _dr]) /\ not eq_elt([x, h])) -> delete([x, cons(h, t), cons(h, _dr)]) -> 4
(length([ll, _yq])) -> length([cons(x, ll), s(_yq)]) -> 4
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 4
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 4
(leq([s(nn1), z])) -> BOT -> 4
}
Sat witness: Found: (() -> delete([x, nil, nil]), {
x -> a
})

-------------------------------------------
Step 10, which took 0.013757 s (model generation: 0.013014,  model checking: 0.000743):

Model:
|_
{
delete -> 
{{{
Q={q_gen_4617, q_gen_4623, q_gen_4624, q_gen_4626, q_gen_4627},
Q_f={q_gen_4617},
Delta=
{
<nil>() -> q_gen_4626
<b>() -> q_gen_4627
<nil, nil>() -> q_gen_4623
<a, a>() -> q_gen_4624
<a, nil, nil>() -> q_gen_4617
<b, cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4617
<b, cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4617
<b, nil, nil>() -> q_gen_4617
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_4616, q_gen_4620, q_gen_4621},
Q_f={q_gen_4616},
Delta=
{
<nil>() -> q_gen_4620
<cons, s>(q_gen_4621, q_gen_4620) -> q_gen_4616
<nil, z>() -> q_gen_4616
<b, z>() -> q_gen_4621
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_4613, q_gen_4615},
Q_f={q_gen_4613},
Delta=
{
<s>(q_gen_4615) -> q_gen_4615
<z>() -> q_gen_4615
<s, s>(q_gen_4613) -> q_gen_4613
<z, s>(q_gen_4615) -> q_gen_4613
<z, z>() -> q_gen_4613
}

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

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

Teacher's answer:
New clause system:
{
() -> delete([x, nil, nil]) -> 6
() -> length([nil, z]) -> 4
() -> leq([z, s(nn2)]) -> 6
() -> leq([z, z]) -> 4
(delete([h, t, _cr])) -> delete([h, cons(h, t), _cr]) -> 4
(delete([i, l, _ir]) /\ length([_ir, _jr]) /\ length([l, _kr])) -> leq([_jr, _kr]) -> 4
(delete([x, t, _dr]) /\ not eq_elt([x, h])) -> delete([x, cons(h, t), cons(h, _dr)]) -> 4
(length([ll, _yq])) -> length([cons(x, ll), s(_yq)]) -> 7
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 5
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 5
(leq([s(nn1), z])) -> BOT -> 5
}
Sat witness: Found: ((length([ll, _yq])) -> length([cons(x, ll), s(_yq)]), {
_yq -> z  ;  ll -> nil  ;  x -> a
})

-------------------------------------------
Step 11, which took 0.012317 s (model generation: 0.011979,  model checking: 0.000338):

Model:
|_
{
delete -> 
{{{
Q={q_gen_4617, q_gen_4623, q_gen_4624, q_gen_4626, q_gen_4627},
Q_f={q_gen_4617},
Delta=
{
<nil>() -> q_gen_4626
<b>() -> q_gen_4627
<nil, nil>() -> q_gen_4623
<a, a>() -> q_gen_4624
<a, nil, nil>() -> q_gen_4617
<b, cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4617
<b, cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4617
<b, nil, nil>() -> q_gen_4617
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_4616, q_gen_4620, q_gen_4621},
Q_f={q_gen_4616},
Delta=
{
<nil>() -> q_gen_4620
<cons, s>(q_gen_4621, q_gen_4620) -> q_gen_4616
<nil, z>() -> q_gen_4616
<a, z>() -> q_gen_4621
<b, z>() -> q_gen_4621
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_4613, q_gen_4615},
Q_f={q_gen_4613},
Delta=
{
<s>(q_gen_4615) -> q_gen_4615
<z>() -> q_gen_4615
<s, s>(q_gen_4613) -> q_gen_4613
<z, s>(q_gen_4615) -> q_gen_4613
<z, z>() -> q_gen_4613
}

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

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

Teacher's answer:
New clause system:
{
() -> delete([x, nil, nil]) -> 6
() -> length([nil, z]) -> 4
() -> leq([z, s(nn2)]) -> 6
() -> leq([z, z]) -> 4
(delete([h, t, _cr])) -> delete([h, cons(h, t), _cr]) -> 4
(delete([i, l, _ir]) /\ length([_ir, _jr]) /\ length([l, _kr])) -> leq([_jr, _kr]) -> 4
(delete([x, t, _dr]) /\ not eq_elt([x, h])) -> delete([x, cons(h, t), cons(h, _dr)]) -> 7
(length([ll, _yq])) -> length([cons(x, ll), s(_yq)]) -> 7
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 5
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 5
(leq([s(nn1), z])) -> BOT -> 5
}
Sat witness: Found: ((delete([x, t, _dr]) /\ not eq_elt([x, h])) -> delete([x, cons(h, t), cons(h, _dr)]), {
_dr -> nil  ;  h -> b  ;  t -> nil  ;  x -> a
})

-------------------------------------------
Step 12, which took 0.012503 s (model generation: 0.012051,  model checking: 0.000452):

Model:
|_
{
delete -> 
{{{
Q={q_gen_4617, q_gen_4623, q_gen_4624, q_gen_4626, q_gen_4627},
Q_f={q_gen_4617},
Delta=
{
<nil>() -> q_gen_4626
<b>() -> q_gen_4627
<nil, nil>() -> q_gen_4623
<a, a>() -> q_gen_4624
<b, b>() -> q_gen_4624
<a, cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4617
<a, nil, nil>() -> q_gen_4617
<b, cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4617
<b, cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4617
<b, nil, nil>() -> q_gen_4617
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_4616, q_gen_4620, q_gen_4621},
Q_f={q_gen_4616},
Delta=
{
<nil>() -> q_gen_4620
<cons, s>(q_gen_4621, q_gen_4620) -> q_gen_4616
<nil, z>() -> q_gen_4616
<a, z>() -> q_gen_4621
<b, z>() -> q_gen_4621
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_4613, q_gen_4615},
Q_f={q_gen_4613},
Delta=
{
<s>(q_gen_4615) -> q_gen_4615
<z>() -> q_gen_4615
<s, s>(q_gen_4613) -> q_gen_4613
<z, s>(q_gen_4615) -> q_gen_4613
<z, z>() -> q_gen_4613
}

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

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

Teacher's answer:
New clause system:
{
() -> delete([x, nil, nil]) -> 6
() -> length([nil, z]) -> 4
() -> leq([z, s(nn2)]) -> 6
() -> leq([z, z]) -> 4
(delete([h, t, _cr])) -> delete([h, cons(h, t), _cr]) -> 7
(delete([i, l, _ir]) /\ length([_ir, _jr]) /\ length([l, _kr])) -> leq([_jr, _kr]) -> 5
(delete([x, t, _dr]) /\ not eq_elt([x, h])) -> delete([x, cons(h, t), cons(h, _dr)]) -> 7
(length([ll, _yq])) -> length([cons(x, ll), s(_yq)]) -> 7
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 5
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 5
(leq([s(nn1), z])) -> BOT -> 5
}
Sat witness: Found: ((delete([h, t, _cr])) -> delete([h, cons(h, t), _cr]), {
_cr -> nil  ;  h -> a  ;  t -> nil
})

-------------------------------------------
Step 13, which took 0.015893 s (model generation: 0.014974,  model checking: 0.000919):

Model:
|_
{
delete -> 
{{{
Q={q_gen_4617, q_gen_4623, q_gen_4624, q_gen_4626, q_gen_4627},
Q_f={q_gen_4617},
Delta=
{
<nil>() -> q_gen_4626
<a>() -> q_gen_4627
<b>() -> q_gen_4627
<nil, nil>() -> q_gen_4623
<a, a>() -> q_gen_4624
<b, b>() -> q_gen_4624
<a, cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4617
<a, cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4617
<a, nil, nil>() -> q_gen_4617
<b, cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4617
<b, cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4617
<b, nil, nil>() -> q_gen_4617
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_4616, q_gen_4620, q_gen_4621},
Q_f={q_gen_4616},
Delta=
{
<nil>() -> q_gen_4620
<cons, s>(q_gen_4621, q_gen_4620) -> q_gen_4616
<nil, z>() -> q_gen_4616
<a, z>() -> q_gen_4621
<b, z>() -> q_gen_4621
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_4613, q_gen_4615},
Q_f={q_gen_4613},
Delta=
{
<s>(q_gen_4615) -> q_gen_4615
<z>() -> q_gen_4615
<s, s>(q_gen_4613) -> q_gen_4613
<z, s>(q_gen_4615) -> q_gen_4613
<z, z>() -> q_gen_4613
}

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

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

Teacher's answer:
New clause system:
{
() -> delete([x, nil, nil]) -> 7
() -> length([nil, z]) -> 5
() -> leq([z, s(nn2)]) -> 7
() -> leq([z, z]) -> 5
(delete([h, t, _cr])) -> delete([h, cons(h, t), _cr]) -> 7
(delete([i, l, _ir]) /\ length([_ir, _jr]) /\ length([l, _kr])) -> leq([_jr, _kr]) -> 6
(delete([x, t, _dr]) /\ not eq_elt([x, h])) -> delete([x, cons(h, t), cons(h, _dr)]) -> 7
(length([ll, _yq])) -> length([cons(x, ll), s(_yq)]) -> 10
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 6
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 6
(leq([s(nn1), z])) -> BOT -> 6
}
Sat witness: Found: ((length([ll, _yq])) -> length([cons(x, ll), s(_yq)]), {
_yq -> s(z)  ;  ll -> cons(b, nil)  ;  x -> b
})

-------------------------------------------
Step 14, which took 0.016437 s (model generation: 0.015950,  model checking: 0.000487):

Model:
|_
{
delete -> 
{{{
Q={q_gen_4617, q_gen_4623, q_gen_4624, q_gen_4626, q_gen_4627},
Q_f={q_gen_4617},
Delta=
{
<nil>() -> q_gen_4626
<a>() -> q_gen_4627
<b>() -> q_gen_4627
<nil, nil>() -> q_gen_4623
<a, a>() -> q_gen_4624
<b, b>() -> q_gen_4624
<a, cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4617
<a, cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4617
<a, nil, nil>() -> q_gen_4617
<b, cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4617
<b, cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4617
<b, nil, nil>() -> q_gen_4617
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_4616, q_gen_4620, q_gen_4621, q_gen_4639, q_gen_4641},
Q_f={q_gen_4616},
Delta=
{
<cons>(q_gen_4639, q_gen_4620) -> q_gen_4620
<nil>() -> q_gen_4620
<b>() -> q_gen_4639
<z>() -> q_gen_4641
<cons, s>(q_gen_4621, q_gen_4620) -> q_gen_4616
<nil, z>() -> q_gen_4616
<a, z>() -> q_gen_4621
<b, s>(q_gen_4641) -> q_gen_4621
<b, z>() -> q_gen_4621
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_4613, q_gen_4615},
Q_f={q_gen_4613},
Delta=
{
<s>(q_gen_4615) -> q_gen_4615
<z>() -> q_gen_4615
<s, s>(q_gen_4613) -> q_gen_4613
<z, s>(q_gen_4615) -> q_gen_4613
<z, z>() -> q_gen_4613
}

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

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

Teacher's answer:
New clause system:
{
() -> delete([x, nil, nil]) -> 7
() -> length([nil, z]) -> 6
() -> leq([z, s(nn2)]) -> 7
() -> leq([z, z]) -> 6
(delete([h, t, _cr])) -> delete([h, cons(h, t), _cr]) -> 7
(delete([i, l, _ir]) /\ length([_ir, _jr]) /\ length([l, _kr])) -> leq([_jr, _kr]) -> 9
(delete([x, t, _dr]) /\ not eq_elt([x, h])) -> delete([x, cons(h, t), cons(h, _dr)]) -> 7
(length([ll, _yq])) -> length([cons(x, ll), s(_yq)]) -> 10
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 7
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 7
(leq([s(nn1), z])) -> BOT -> 7
}
Sat witness: Found: ((delete([i, l, _ir]) /\ length([_ir, _jr]) /\ length([l, _kr])) -> leq([_jr, _kr]), {
_ir -> cons(b, nil)  ;  _jr -> s(s(z))  ;  _kr -> s(z)  ;  i -> a  ;  l -> cons(b, nil)
})

-------------------------------------------
Step 15, which took 0.014258 s (model generation: 0.014105,  model checking: 0.000153):

Model:
|_
{
delete -> 
{{{
Q={q_gen_4617, q_gen_4623, q_gen_4624, q_gen_4626, q_gen_4627},
Q_f={q_gen_4617},
Delta=
{
<nil>() -> q_gen_4626
<a>() -> q_gen_4627
<b>() -> q_gen_4627
<nil, nil>() -> q_gen_4623
<a, a>() -> q_gen_4624
<b, b>() -> q_gen_4624
<a, cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4617
<a, cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4617
<a, nil, nil>() -> q_gen_4617
<b, cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4617
<b, cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4617
<b, nil, nil>() -> q_gen_4617
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_4616, q_gen_4620, q_gen_4621, q_gen_4639, q_gen_4641},
Q_f={q_gen_4616},
Delta=
{
<cons>(q_gen_4639, q_gen_4620) -> q_gen_4620
<nil>() -> q_gen_4620
<b>() -> q_gen_4639
<z>() -> q_gen_4641
<cons, s>(q_gen_4621, q_gen_4620) -> q_gen_4616
<nil, z>() -> q_gen_4616
<a, z>() -> q_gen_4621
<b, s>(q_gen_4641) -> q_gen_4621
<b, z>() -> q_gen_4621
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_4613, q_gen_4615},
Q_f={q_gen_4613},
Delta=
{
<s>(q_gen_4615) -> q_gen_4615
<z>() -> q_gen_4615
<s, s>(q_gen_4613) -> q_gen_4613
<s, z>(q_gen_4615) -> q_gen_4613
<z, s>(q_gen_4615) -> q_gen_4613
<z, z>() -> q_gen_4613
}

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

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

Teacher's answer:
New clause system:
{
() -> delete([x, nil, nil]) -> 7
() -> length([nil, z]) -> 7
() -> leq([z, s(nn2)]) -> 7
() -> leq([z, z]) -> 7
(delete([h, t, _cr])) -> delete([h, cons(h, t), _cr]) -> 7
(delete([i, l, _ir]) /\ length([_ir, _jr]) /\ length([l, _kr])) -> leq([_jr, _kr]) -> 9
(delete([x, t, _dr]) /\ not eq_elt([x, h])) -> delete([x, cons(h, t), cons(h, _dr)]) -> 7
(length([ll, _yq])) -> length([cons(x, ll), s(_yq)]) -> 10
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 7
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 7
(leq([s(nn1), z])) -> BOT -> 10
}
Sat witness: Found: ((leq([s(nn1), z])) -> BOT, {
nn1 -> z
})

-------------------------------------------
Step 16, which took 0.014575 s (model generation: 0.014484,  model checking: 0.000091):

Model:
|_
{
delete -> 
{{{
Q={q_gen_4617, q_gen_4623, q_gen_4624, q_gen_4626, q_gen_4627},
Q_f={q_gen_4617},
Delta=
{
<nil>() -> q_gen_4626
<a>() -> q_gen_4627
<b>() -> q_gen_4627
<nil, nil>() -> q_gen_4623
<a, a>() -> q_gen_4624
<b, b>() -> q_gen_4624
<a, cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4617
<a, cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4617
<a, nil, nil>() -> q_gen_4617
<b, cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4617
<b, cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4617
<b, nil, nil>() -> q_gen_4617
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_4616, q_gen_4620, q_gen_4621, q_gen_4639, q_gen_4641},
Q_f={q_gen_4616},
Delta=
{
<cons>(q_gen_4639, q_gen_4620) -> q_gen_4620
<nil>() -> q_gen_4620
<b>() -> q_gen_4639
<z>() -> q_gen_4641
<cons, s>(q_gen_4621, q_gen_4620) -> q_gen_4616
<nil, z>() -> q_gen_4616
<a, z>() -> q_gen_4621
<b, s>(q_gen_4641) -> q_gen_4621
<b, z>() -> q_gen_4621
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_4613, q_gen_4615, q_gen_4644},
Q_f={q_gen_4613},
Delta=
{
<s>(q_gen_4615) -> q_gen_4615
<z>() -> q_gen_4615
<s, s>(q_gen_4613) -> q_gen_4613
<s, s>(q_gen_4644) -> q_gen_4613
<z, s>(q_gen_4615) -> q_gen_4613
<z, z>() -> q_gen_4613
<s, z>(q_gen_4615) -> q_gen_4644
}

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

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

Teacher's answer:
New clause system:
{
() -> delete([x, nil, nil]) -> 7
() -> length([nil, z]) -> 7
() -> leq([z, s(nn2)]) -> 7
() -> leq([z, z]) -> 7
(delete([h, t, _cr])) -> delete([h, cons(h, t), _cr]) -> 7
(delete([i, l, _ir]) /\ length([_ir, _jr]) /\ length([l, _kr])) -> leq([_jr, _kr]) -> 9
(delete([x, t, _dr]) /\ not eq_elt([x, h])) -> delete([x, cons(h, t), cons(h, _dr)]) -> 7
(length([ll, _yq])) -> length([cons(x, ll), s(_yq)]) -> 10
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 7
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 10
(leq([s(nn1), z])) -> BOT -> 10
}
Sat witness: Found: ((leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]), {
nn1 -> s(z)  ;  nn2 -> z
})

-------------------------------------------
Step 17, which took 0.014408 s (model generation: 0.013764,  model checking: 0.000644):

Model:
|_
{
delete -> 
{{{
Q={q_gen_4617, q_gen_4623, q_gen_4624, q_gen_4626, q_gen_4627},
Q_f={q_gen_4617},
Delta=
{
<nil>() -> q_gen_4626
<a>() -> q_gen_4627
<b>() -> q_gen_4627
<nil, nil>() -> q_gen_4623
<a, a>() -> q_gen_4624
<b, b>() -> q_gen_4624
<a, cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4617
<a, cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4617
<a, nil, nil>() -> q_gen_4617
<b, cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4617
<b, cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4617
<b, nil, nil>() -> q_gen_4617
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_4616, q_gen_4620, q_gen_4621, q_gen_4638, q_gen_4639, q_gen_4640, q_gen_4641, q_gen_4642},
Q_f={q_gen_4616},
Delta=
{
<nil>() -> q_gen_4620
<cons>(q_gen_4639, q_gen_4620) -> q_gen_4638
<b>() -> q_gen_4639
<z>() -> q_gen_4641
<cons, s>(q_gen_4621, q_gen_4620) -> q_gen_4616
<cons, s>(q_gen_4640, q_gen_4638) -> q_gen_4616
<nil, z>() -> q_gen_4616
<a, z>() -> q_gen_4621
<b, z>() -> q_gen_4621
<b, s>(q_gen_4641) -> q_gen_4640
<cons, s>(q_gen_4640, q_gen_4620) -> q_gen_4642
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_4613, q_gen_4615, q_gen_4643},
Q_f={q_gen_4613},
Delta=
{
<s>(q_gen_4615) -> q_gen_4615
<z>() -> q_gen_4615
<s, s>(q_gen_4613) -> q_gen_4613
<z, s>(q_gen_4615) -> q_gen_4613
<z, z>() -> q_gen_4613
<s, s>(q_gen_4643) -> q_gen_4643
<s, z>(q_gen_4615) -> q_gen_4643
}

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

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

Teacher's answer:
New clause system:
{
() -> delete([x, nil, nil]) -> 7
() -> length([nil, z]) -> 7
() -> leq([z, s(nn2)]) -> 7
() -> leq([z, z]) -> 7
(delete([h, t, _cr])) -> delete([h, cons(h, t), _cr]) -> 7
(delete([i, l, _ir]) /\ length([_ir, _jr]) /\ length([l, _kr])) -> leq([_jr, _kr]) -> 9
(delete([x, t, _dr]) /\ not eq_elt([x, h])) -> delete([x, cons(h, t), cons(h, _dr)]) -> 10
(length([ll, _yq])) -> length([cons(x, ll), s(_yq)]) -> 10
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 8
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 10
(leq([s(nn1), z])) -> BOT -> 10
}
Sat witness: Found: ((delete([x, t, _dr]) /\ not eq_elt([x, h])) -> delete([x, cons(h, t), cons(h, _dr)]), {
_dr -> nil  ;  h -> b  ;  t -> cons(a, nil)  ;  x -> a
})

-------------------------------------------
Step 18, which took 0.015862 s (model generation: 0.015514,  model checking: 0.000348):

Model:
|_
{
delete -> 
{{{
Q={q_gen_4617, q_gen_4623, q_gen_4624, q_gen_4626, q_gen_4627},
Q_f={q_gen_4617},
Delta=
{
<nil>() -> q_gen_4626
<a>() -> q_gen_4627
<b>() -> q_gen_4627
<cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4623
<nil, nil>() -> q_gen_4623
<a, a>() -> q_gen_4624
<b, b>() -> q_gen_4624
<a, cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4617
<a, cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4617
<a, nil, nil>() -> q_gen_4617
<b, cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4617
<b, cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4617
<b, nil, nil>() -> q_gen_4617
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_4616, q_gen_4620, q_gen_4621, q_gen_4638, q_gen_4639, q_gen_4640, q_gen_4641, q_gen_4642},
Q_f={q_gen_4616},
Delta=
{
<nil>() -> q_gen_4620
<cons>(q_gen_4639, q_gen_4620) -> q_gen_4638
<b>() -> q_gen_4639
<z>() -> q_gen_4641
<cons, s>(q_gen_4621, q_gen_4620) -> q_gen_4616
<cons, s>(q_gen_4640, q_gen_4638) -> q_gen_4616
<nil, z>() -> q_gen_4616
<a, z>() -> q_gen_4621
<b, z>() -> q_gen_4621
<b, s>(q_gen_4641) -> q_gen_4640
<cons, s>(q_gen_4640, q_gen_4620) -> q_gen_4642
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_4613, q_gen_4615, q_gen_4643},
Q_f={q_gen_4613},
Delta=
{
<s>(q_gen_4615) -> q_gen_4615
<z>() -> q_gen_4615
<s, s>(q_gen_4613) -> q_gen_4613
<z, s>(q_gen_4615) -> q_gen_4613
<z, z>() -> q_gen_4613
<s, s>(q_gen_4643) -> q_gen_4643
<s, z>(q_gen_4615) -> q_gen_4643
}

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

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

Teacher's answer:
New clause system:
{
() -> delete([x, nil, nil]) -> 7
() -> length([nil, z]) -> 7
() -> leq([z, s(nn2)]) -> 7
() -> leq([z, z]) -> 7
(delete([h, t, _cr])) -> delete([h, cons(h, t), _cr]) -> 10
(delete([i, l, _ir]) /\ length([_ir, _jr]) /\ length([l, _kr])) -> leq([_jr, _kr]) -> 9
(delete([x, t, _dr]) /\ not eq_elt([x, h])) -> delete([x, cons(h, t), cons(h, _dr)]) -> 10
(length([ll, _yq])) -> length([cons(x, ll), s(_yq)]) -> 10
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 8
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 10
(leq([s(nn1), z])) -> BOT -> 10
}
Sat witness: Found: ((delete([h, t, _cr])) -> delete([h, cons(h, t), _cr]), {
_cr -> nil  ;  h -> b  ;  t -> cons(b, nil)
})

-------------------------------------------
Step 19, which took 0.016733 s (model generation: 0.015148,  model checking: 0.001585):

Model:
|_
{
delete -> 
{{{
Q={q_gen_4617, q_gen_4623, q_gen_4624, q_gen_4626, q_gen_4627},
Q_f={q_gen_4617},
Delta=
{
<cons>(q_gen_4627, q_gen_4626) -> q_gen_4626
<nil>() -> q_gen_4626
<a>() -> q_gen_4627
<b>() -> q_gen_4627
<cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4623
<nil, nil>() -> q_gen_4623
<a, a>() -> q_gen_4624
<b, b>() -> q_gen_4624
<a, cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4617
<a, cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4617
<a, nil, nil>() -> q_gen_4617
<b, cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4617
<b, cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4617
<b, nil, nil>() -> q_gen_4617
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_4616, q_gen_4620, q_gen_4621, q_gen_4638, q_gen_4639, q_gen_4640, q_gen_4641, q_gen_4642},
Q_f={q_gen_4616},
Delta=
{
<nil>() -> q_gen_4620
<cons>(q_gen_4639, q_gen_4620) -> q_gen_4638
<b>() -> q_gen_4639
<z>() -> q_gen_4641
<cons, s>(q_gen_4621, q_gen_4620) -> q_gen_4616
<cons, s>(q_gen_4640, q_gen_4638) -> q_gen_4616
<nil, z>() -> q_gen_4616
<a, z>() -> q_gen_4621
<b, z>() -> q_gen_4621
<b, s>(q_gen_4641) -> q_gen_4640
<cons, s>(q_gen_4640, q_gen_4620) -> q_gen_4642
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_4613, q_gen_4615, q_gen_4643},
Q_f={q_gen_4613},
Delta=
{
<s>(q_gen_4615) -> q_gen_4615
<z>() -> q_gen_4615
<s, s>(q_gen_4613) -> q_gen_4613
<z, s>(q_gen_4615) -> q_gen_4613
<z, z>() -> q_gen_4613
<s, s>(q_gen_4643) -> q_gen_4643
<s, z>(q_gen_4615) -> q_gen_4643
}

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

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

Teacher's answer:
New clause system:
{
() -> delete([x, nil, nil]) -> 8
() -> length([nil, z]) -> 8
() -> leq([z, s(nn2)]) -> 8
() -> leq([z, z]) -> 8
(delete([h, t, _cr])) -> delete([h, cons(h, t), _cr]) -> 10
(delete([i, l, _ir]) /\ length([_ir, _jr]) /\ length([l, _kr])) -> leq([_jr, _kr]) -> 10
(delete([x, t, _dr]) /\ not eq_elt([x, h])) -> delete([x, cons(h, t), cons(h, _dr)]) -> 10
(length([ll, _yq])) -> length([cons(x, ll), s(_yq)]) -> 13
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 9
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 11
(leq([s(nn1), z])) -> BOT -> 11
}
Sat witness: Found: ((length([ll, _yq])) -> length([cons(x, ll), s(_yq)]), {
_yq -> s(z)  ;  ll -> cons(b, nil)  ;  x -> a
})

-------------------------------------------
Step 20, which took 0.017128 s (model generation: 0.016040,  model checking: 0.001088):

Model:
|_
{
delete -> 
{{{
Q={q_gen_4617, q_gen_4623, q_gen_4624, q_gen_4626, q_gen_4627},
Q_f={q_gen_4617},
Delta=
{
<cons>(q_gen_4627, q_gen_4626) -> q_gen_4626
<nil>() -> q_gen_4626
<a>() -> q_gen_4627
<b>() -> q_gen_4627
<cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4623
<nil, nil>() -> q_gen_4623
<a, a>() -> q_gen_4624
<b, b>() -> q_gen_4624
<a, cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4617
<a, cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4617
<a, nil, nil>() -> q_gen_4617
<b, cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4617
<b, cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4617
<b, nil, nil>() -> q_gen_4617
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_4616, q_gen_4620, q_gen_4621, q_gen_4638, q_gen_4639, q_gen_4640, q_gen_4641, q_gen_4642},
Q_f={q_gen_4616},
Delta=
{
<nil>() -> q_gen_4620
<cons>(q_gen_4639, q_gen_4620) -> q_gen_4638
<b>() -> q_gen_4639
<z>() -> q_gen_4641
<cons, s>(q_gen_4621, q_gen_4620) -> q_gen_4616
<cons, s>(q_gen_4621, q_gen_4638) -> q_gen_4616
<cons, s>(q_gen_4640, q_gen_4638) -> q_gen_4616
<nil, z>() -> q_gen_4616
<a, s>(q_gen_4641) -> q_gen_4621
<a, z>() -> q_gen_4621
<b, z>() -> q_gen_4621
<b, s>(q_gen_4641) -> q_gen_4640
<cons, s>(q_gen_4640, q_gen_4620) -> q_gen_4642
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_4613, q_gen_4615, q_gen_4643},
Q_f={q_gen_4613},
Delta=
{
<s>(q_gen_4615) -> q_gen_4615
<z>() -> q_gen_4615
<s, s>(q_gen_4613) -> q_gen_4613
<z, s>(q_gen_4615) -> q_gen_4613
<z, z>() -> q_gen_4613
<s, s>(q_gen_4643) -> q_gen_4643
<s, z>(q_gen_4615) -> q_gen_4643
}

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

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

Teacher's answer:
New clause system:
{
() -> delete([x, nil, nil]) -> 9
() -> length([nil, z]) -> 9
() -> leq([z, s(nn2)]) -> 9
() -> leq([z, z]) -> 9
(delete([h, t, _cr])) -> delete([h, cons(h, t), _cr]) -> 10
(delete([i, l, _ir]) /\ length([_ir, _jr]) /\ length([l, _kr])) -> leq([_jr, _kr]) -> 10
(delete([x, t, _dr]) /\ not eq_elt([x, h])) -> delete([x, cons(h, t), cons(h, _dr)]) -> 13
(length([ll, _yq])) -> length([cons(x, ll), s(_yq)]) -> 13
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 10
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 11
(leq([s(nn1), z])) -> BOT -> 11
}
Sat witness: Found: ((delete([x, t, _dr]) /\ not eq_elt([x, h])) -> delete([x, cons(h, t), cons(h, _dr)]), {
_dr -> cons(b, nil)  ;  h -> a  ;  t -> cons(b, nil)  ;  x -> b
})

-------------------------------------------
Step 21, which took 0.018474 s (model generation: 0.017423,  model checking: 0.001051):

Model:
|_
{
delete -> 
{{{
Q={q_gen_4617, q_gen_4623, q_gen_4624, q_gen_4626, q_gen_4627},
Q_f={q_gen_4617},
Delta=
{
<cons>(q_gen_4627, q_gen_4626) -> q_gen_4626
<nil>() -> q_gen_4626
<a>() -> q_gen_4627
<b>() -> q_gen_4627
<cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4623
<cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4623
<nil, nil>() -> q_gen_4623
<a, a>() -> q_gen_4624
<b, b>() -> q_gen_4624
<a, cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4617
<a, cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4617
<a, nil, nil>() -> q_gen_4617
<b, cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4617
<b, cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4617
<b, nil, nil>() -> q_gen_4617
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_4616, q_gen_4620, q_gen_4621, q_gen_4638, q_gen_4639, q_gen_4640, q_gen_4641, q_gen_4642},
Q_f={q_gen_4616},
Delta=
{
<nil>() -> q_gen_4620
<cons>(q_gen_4639, q_gen_4620) -> q_gen_4638
<b>() -> q_gen_4639
<z>() -> q_gen_4641
<cons, s>(q_gen_4621, q_gen_4620) -> q_gen_4616
<cons, s>(q_gen_4621, q_gen_4638) -> q_gen_4616
<cons, s>(q_gen_4640, q_gen_4638) -> q_gen_4616
<nil, z>() -> q_gen_4616
<a, s>(q_gen_4641) -> q_gen_4621
<a, z>() -> q_gen_4621
<b, z>() -> q_gen_4621
<b, s>(q_gen_4641) -> q_gen_4640
<cons, s>(q_gen_4640, q_gen_4620) -> q_gen_4642
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_4613, q_gen_4615, q_gen_4643},
Q_f={q_gen_4613},
Delta=
{
<s>(q_gen_4615) -> q_gen_4615
<z>() -> q_gen_4615
<s, s>(q_gen_4613) -> q_gen_4613
<z, s>(q_gen_4615) -> q_gen_4613
<z, z>() -> q_gen_4613
<s, s>(q_gen_4643) -> q_gen_4643
<s, z>(q_gen_4615) -> q_gen_4643
}

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

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

Teacher's answer:
New clause system:
{
() -> delete([x, nil, nil]) -> 10
() -> length([nil, z]) -> 10
() -> leq([z, s(nn2)]) -> 10
() -> leq([z, z]) -> 10
(delete([h, t, _cr])) -> delete([h, cons(h, t), _cr]) -> 10
(delete([i, l, _ir]) /\ length([_ir, _jr]) /\ length([l, _kr])) -> leq([_jr, _kr]) -> 13
(delete([x, t, _dr]) /\ not eq_elt([x, h])) -> delete([x, cons(h, t), cons(h, _dr)]) -> 13
(length([ll, _yq])) -> length([cons(x, ll), s(_yq)]) -> 13
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 11
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 11
(leq([s(nn1), z])) -> BOT -> 11
}
Sat witness: Found: ((delete([i, l, _ir]) /\ length([_ir, _jr]) /\ length([l, _kr])) -> leq([_jr, _kr]), {
_ir -> cons(b, cons(b, nil))  ;  _jr -> s(s(z))  ;  _kr -> s(z)  ;  i -> a  ;  l -> cons(b, cons(b, nil))
})

-------------------------------------------
Step 22, which took 0.016446 s (model generation: 0.016048,  model checking: 0.000398):

Model:
|_
{
delete -> 
{{{
Q={q_gen_4617, q_gen_4623, q_gen_4624, q_gen_4626, q_gen_4627},
Q_f={q_gen_4617},
Delta=
{
<cons>(q_gen_4627, q_gen_4626) -> q_gen_4626
<nil>() -> q_gen_4626
<a>() -> q_gen_4627
<b>() -> q_gen_4627
<cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4623
<cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4623
<nil, nil>() -> q_gen_4623
<a, a>() -> q_gen_4624
<b, b>() -> q_gen_4624
<a, cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4617
<a, cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4617
<a, nil, nil>() -> q_gen_4617
<b, cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4617
<b, cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4617
<b, nil, nil>() -> q_gen_4617
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_4616, q_gen_4620, q_gen_4621, q_gen_4638, q_gen_4639, q_gen_4640, q_gen_4641, q_gen_4642},
Q_f={q_gen_4616},
Delta=
{
<nil>() -> q_gen_4620
<cons>(q_gen_4639, q_gen_4620) -> q_gen_4638
<b>() -> q_gen_4639
<z>() -> q_gen_4641
<cons, s>(q_gen_4621, q_gen_4620) -> q_gen_4616
<cons, s>(q_gen_4640, q_gen_4638) -> q_gen_4616
<nil, z>() -> q_gen_4616
<a, z>() -> q_gen_4621
<b, z>() -> q_gen_4621
<a, s>(q_gen_4641) -> q_gen_4640
<b, s>(q_gen_4641) -> q_gen_4640
<cons, s>(q_gen_4621, q_gen_4638) -> q_gen_4642
<cons, s>(q_gen_4640, q_gen_4620) -> q_gen_4642
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_4613, q_gen_4615, q_gen_4643},
Q_f={q_gen_4613},
Delta=
{
<s>(q_gen_4615) -> q_gen_4615
<z>() -> q_gen_4615
<s, s>(q_gen_4613) -> q_gen_4613
<z, s>(q_gen_4615) -> q_gen_4613
<z, z>() -> q_gen_4613
<s, s>(q_gen_4643) -> q_gen_4643
<s, z>(q_gen_4615) -> q_gen_4643
}

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

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

Teacher's answer:
New clause system:
{
() -> delete([x, nil, nil]) -> 10
() -> length([nil, z]) -> 10
() -> leq([z, s(nn2)]) -> 10
() -> leq([z, z]) -> 10
(delete([h, t, _cr])) -> delete([h, cons(h, t), _cr]) -> 13
(delete([i, l, _ir]) /\ length([_ir, _jr]) /\ length([l, _kr])) -> leq([_jr, _kr]) -> 13
(delete([x, t, _dr]) /\ not eq_elt([x, h])) -> delete([x, cons(h, t), cons(h, _dr)]) -> 13
(length([ll, _yq])) -> length([cons(x, ll), s(_yq)]) -> 13
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 11
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 11
(leq([s(nn1), z])) -> BOT -> 11
}
Sat witness: Found: ((delete([h, t, _cr])) -> delete([h, cons(h, t), _cr]), {
_cr -> cons(b, nil)  ;  h -> a  ;  t -> cons(b, nil)
})

-------------------------------------------
Step 23, which took 0.020418 s (model generation: 0.017700,  model checking: 0.002718):

Model:
|_
{
delete -> 
{{{
Q={q_gen_4617, q_gen_4623, q_gen_4624, q_gen_4626, q_gen_4627},
Q_f={q_gen_4617},
Delta=
{
<cons>(q_gen_4627, q_gen_4626) -> q_gen_4626
<nil>() -> q_gen_4626
<a>() -> q_gen_4627
<b>() -> q_gen_4627
<cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4623
<cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4623
<nil, nil>() -> q_gen_4623
<a, a>() -> q_gen_4624
<a, b>() -> q_gen_4624
<b, b>() -> q_gen_4624
<a, cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4617
<a, cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4617
<a, nil, nil>() -> q_gen_4617
<b, cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4617
<b, cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4617
<b, nil, nil>() -> q_gen_4617
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_4616, q_gen_4620, q_gen_4621, q_gen_4638, q_gen_4639, q_gen_4640, q_gen_4641, q_gen_4642},
Q_f={q_gen_4616},
Delta=
{
<nil>() -> q_gen_4620
<cons>(q_gen_4639, q_gen_4620) -> q_gen_4638
<b>() -> q_gen_4639
<z>() -> q_gen_4641
<cons, s>(q_gen_4621, q_gen_4620) -> q_gen_4616
<cons, s>(q_gen_4640, q_gen_4638) -> q_gen_4616
<nil, z>() -> q_gen_4616
<a, z>() -> q_gen_4621
<b, z>() -> q_gen_4621
<a, s>(q_gen_4641) -> q_gen_4640
<b, s>(q_gen_4641) -> q_gen_4640
<cons, s>(q_gen_4621, q_gen_4638) -> q_gen_4642
<cons, s>(q_gen_4640, q_gen_4620) -> q_gen_4642
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_4613, q_gen_4615, q_gen_4643},
Q_f={q_gen_4613},
Delta=
{
<s>(q_gen_4615) -> q_gen_4615
<z>() -> q_gen_4615
<s, s>(q_gen_4613) -> q_gen_4613
<z, s>(q_gen_4615) -> q_gen_4613
<z, z>() -> q_gen_4613
<s, s>(q_gen_4643) -> q_gen_4643
<s, z>(q_gen_4615) -> q_gen_4643
}

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

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

Teacher's answer:
New clause system:
{
() -> delete([x, nil, nil]) -> 11
() -> length([nil, z]) -> 11
() -> leq([z, s(nn2)]) -> 11
() -> leq([z, z]) -> 11
(delete([h, t, _cr])) -> delete([h, cons(h, t), _cr]) -> 13
(delete([i, l, _ir]) /\ length([_ir, _jr]) /\ length([l, _kr])) -> leq([_jr, _kr]) -> 13
(delete([x, t, _dr]) /\ not eq_elt([x, h])) -> delete([x, cons(h, t), cons(h, _dr)]) -> 13
(length([ll, _yq])) -> length([cons(x, ll), s(_yq)]) -> 16
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 12
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 12
(leq([s(nn1), z])) -> BOT -> 12
}
Sat witness: Found: ((length([ll, _yq])) -> length([cons(x, ll), s(_yq)]), {
_yq -> s(s(z))  ;  ll -> cons(b, cons(b, nil))  ;  x -> b
})

-------------------------------------------
Step 24, which took 0.024135 s (model generation: 0.022201,  model checking: 0.001934):

Model:
|_
{
delete -> 
{{{
Q={q_gen_4617, q_gen_4623, q_gen_4624, q_gen_4626, q_gen_4627},
Q_f={q_gen_4617},
Delta=
{
<cons>(q_gen_4627, q_gen_4626) -> q_gen_4626
<nil>() -> q_gen_4626
<a>() -> q_gen_4627
<b>() -> q_gen_4627
<cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4623
<cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4623
<nil, nil>() -> q_gen_4623
<a, a>() -> q_gen_4624
<a, b>() -> q_gen_4624
<b, b>() -> q_gen_4624
<a, cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4617
<a, cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4617
<a, nil, nil>() -> q_gen_4617
<b, cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4617
<b, cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4617
<b, nil, nil>() -> q_gen_4617
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_4616, q_gen_4620, q_gen_4621, q_gen_4638, q_gen_4639, q_gen_4640, q_gen_4641, q_gen_4642},
Q_f={q_gen_4616},
Delta=
{
<nil>() -> q_gen_4620
<cons>(q_gen_4639, q_gen_4620) -> q_gen_4638
<cons>(q_gen_4639, q_gen_4638) -> q_gen_4638
<b>() -> q_gen_4639
<s>(q_gen_4641) -> q_gen_4641
<z>() -> q_gen_4641
<cons, s>(q_gen_4621, q_gen_4620) -> q_gen_4616
<cons, s>(q_gen_4640, q_gen_4638) -> q_gen_4616
<nil, z>() -> q_gen_4616
<a, z>() -> q_gen_4621
<b, z>() -> q_gen_4621
<a, s>(q_gen_4641) -> q_gen_4640
<b, s>(q_gen_4641) -> q_gen_4640
<cons, s>(q_gen_4621, q_gen_4638) -> q_gen_4642
<cons, s>(q_gen_4640, q_gen_4620) -> q_gen_4642
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_4613, q_gen_4615, q_gen_4643},
Q_f={q_gen_4613},
Delta=
{
<s>(q_gen_4615) -> q_gen_4615
<z>() -> q_gen_4615
<s, s>(q_gen_4613) -> q_gen_4613
<z, s>(q_gen_4615) -> q_gen_4613
<z, z>() -> q_gen_4613
<s, s>(q_gen_4643) -> q_gen_4643
<s, z>(q_gen_4615) -> q_gen_4643
}

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

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

Teacher's answer:
New clause system:
{
() -> delete([x, nil, nil]) -> 12
() -> length([nil, z]) -> 12
() -> leq([z, s(nn2)]) -> 12
() -> leq([z, z]) -> 12
(delete([h, t, _cr])) -> delete([h, cons(h, t), _cr]) -> 13
(delete([i, l, _ir]) /\ length([_ir, _jr]) /\ length([l, _kr])) -> leq([_jr, _kr]) -> 16
(delete([x, t, _dr]) /\ not eq_elt([x, h])) -> delete([x, cons(h, t), cons(h, _dr)]) -> 14
(length([ll, _yq])) -> length([cons(x, ll), s(_yq)]) -> 16
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 13
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 13
(leq([s(nn1), z])) -> BOT -> 13
}
Sat witness: Found: ((delete([i, l, _ir]) /\ length([_ir, _jr]) /\ length([l, _kr])) -> leq([_jr, _kr]), {
_ir -> cons(b, cons(b, nil))  ;  _jr -> s(s(s(z)))  ;  _kr -> s(s(z))  ;  i -> a  ;  l -> cons(b, cons(b, nil))
})

-------------------------------------------
Step 25, which took 0.023674 s (model generation: 0.023143,  model checking: 0.000531):

Model:
|_
{
delete -> 
{{{
Q={q_gen_4617, q_gen_4623, q_gen_4624, q_gen_4626, q_gen_4627},
Q_f={q_gen_4617},
Delta=
{
<cons>(q_gen_4627, q_gen_4626) -> q_gen_4626
<nil>() -> q_gen_4626
<a>() -> q_gen_4627
<b>() -> q_gen_4627
<cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4623
<cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4623
<nil, nil>() -> q_gen_4623
<a, a>() -> q_gen_4624
<a, b>() -> q_gen_4624
<b, b>() -> q_gen_4624
<a, cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4617
<a, cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4617
<a, nil, nil>() -> q_gen_4617
<b, cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4617
<b, cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4617
<b, nil, nil>() -> q_gen_4617
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_4616, q_gen_4620, q_gen_4621, q_gen_4638, q_gen_4639, q_gen_4640, q_gen_4641, q_gen_4642},
Q_f={q_gen_4616},
Delta=
{
<nil>() -> q_gen_4620
<cons>(q_gen_4639, q_gen_4620) -> q_gen_4638
<cons>(q_gen_4639, q_gen_4638) -> q_gen_4638
<b>() -> q_gen_4639
<s>(q_gen_4641) -> q_gen_4641
<z>() -> q_gen_4641
<cons, s>(q_gen_4621, q_gen_4620) -> q_gen_4616
<cons, s>(q_gen_4640, q_gen_4638) -> q_gen_4616
<nil, z>() -> q_gen_4616
<a, z>() -> q_gen_4621
<b, z>() -> q_gen_4621
<a, s>(q_gen_4641) -> q_gen_4640
<b, s>(q_gen_4641) -> q_gen_4640
<cons, s>(q_gen_4621, q_gen_4638) -> q_gen_4642
<cons, s>(q_gen_4640, q_gen_4620) -> q_gen_4642
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_4613, q_gen_4615, q_gen_4643, q_gen_4644},
Q_f={q_gen_4613},
Delta=
{
<s>(q_gen_4615) -> q_gen_4615
<z>() -> q_gen_4615
<s, s>(q_gen_4613) -> q_gen_4613
<s, s>(q_gen_4643) -> q_gen_4613
<z, s>(q_gen_4615) -> q_gen_4613
<z, z>() -> q_gen_4613
<s, s>(q_gen_4644) -> q_gen_4643
<s, z>(q_gen_4615) -> q_gen_4644
}

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

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

Teacher's answer:
New clause system:
{
() -> delete([x, nil, nil]) -> 13
() -> length([nil, z]) -> 13
() -> leq([z, s(nn2)]) -> 13
() -> leq([z, z]) -> 13
(delete([h, t, _cr])) -> delete([h, cons(h, t), _cr]) -> 13
(delete([i, l, _ir]) /\ length([_ir, _jr]) /\ length([l, _kr])) -> leq([_jr, _kr]) -> 16
(delete([x, t, _dr]) /\ not eq_elt([x, h])) -> delete([x, cons(h, t), cons(h, _dr)]) -> 14
(length([ll, _yq])) -> length([cons(x, ll), s(_yq)]) -> 16
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 13
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 16
(leq([s(nn1), z])) -> BOT -> 14
}
Sat witness: Found: ((leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]), {
nn1 -> s(s(z))  ;  nn2 -> s(z)
})

-------------------------------------------
Step 26, which took 0.020675 s (model generation: 0.020204,  model checking: 0.000471):

Model:
|_
{
delete -> 
{{{
Q={q_gen_4617, q_gen_4623, q_gen_4624, q_gen_4626, q_gen_4627},
Q_f={q_gen_4617},
Delta=
{
<cons>(q_gen_4627, q_gen_4626) -> q_gen_4626
<nil>() -> q_gen_4626
<a>() -> q_gen_4627
<b>() -> q_gen_4627
<cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4623
<cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4623
<nil, nil>() -> q_gen_4623
<a, a>() -> q_gen_4624
<a, b>() -> q_gen_4624
<b, b>() -> q_gen_4624
<a, cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4617
<a, cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4617
<a, nil, nil>() -> q_gen_4617
<b, cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4617
<b, cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4617
<b, nil, nil>() -> q_gen_4617
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_4616, q_gen_4620, q_gen_4621, q_gen_4638, q_gen_4639, q_gen_4640, q_gen_4641, q_gen_4642, q_gen_4662},
Q_f={q_gen_4616},
Delta=
{
<cons>(q_gen_4639, q_gen_4638) -> q_gen_4620
<nil>() -> q_gen_4620
<cons>(q_gen_4639, q_gen_4620) -> q_gen_4638
<b>() -> q_gen_4639
<z>() -> q_gen_4641
<s>(q_gen_4641) -> q_gen_4662
<cons, s>(q_gen_4621, q_gen_4620) -> q_gen_4616
<cons, s>(q_gen_4640, q_gen_4638) -> q_gen_4616
<nil, z>() -> q_gen_4616
<a, z>() -> q_gen_4621
<b, s>(q_gen_4662) -> q_gen_4621
<b, z>() -> q_gen_4621
<a, s>(q_gen_4641) -> q_gen_4640
<b, s>(q_gen_4641) -> q_gen_4640
<cons, s>(q_gen_4621, q_gen_4638) -> q_gen_4642
<cons, s>(q_gen_4640, q_gen_4620) -> q_gen_4642
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_4613, q_gen_4615, q_gen_4643},
Q_f={q_gen_4613},
Delta=
{
<s>(q_gen_4615) -> q_gen_4615
<z>() -> q_gen_4615
<s, s>(q_gen_4613) -> q_gen_4613
<z, s>(q_gen_4615) -> q_gen_4613
<z, z>() -> q_gen_4613
<s, s>(q_gen_4643) -> q_gen_4643
<s, z>(q_gen_4615) -> q_gen_4643
}

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

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

Teacher's answer:
New clause system:
{
() -> delete([x, nil, nil]) -> 13
() -> length([nil, z]) -> 13
() -> leq([z, s(nn2)]) -> 13
() -> leq([z, z]) -> 13
(delete([h, t, _cr])) -> delete([h, cons(h, t), _cr]) -> 16
(delete([i, l, _ir]) /\ length([_ir, _jr]) /\ length([l, _kr])) -> leq([_jr, _kr]) -> 16
(delete([x, t, _dr]) /\ not eq_elt([x, h])) -> delete([x, cons(h, t), cons(h, _dr)]) -> 14
(length([ll, _yq])) -> length([cons(x, ll), s(_yq)]) -> 16
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 14
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 16
(leq([s(nn1), z])) -> BOT -> 14
}
Sat witness: Found: ((delete([h, t, _cr])) -> delete([h, cons(h, t), _cr]), {
_cr -> cons(a, nil)  ;  h -> b  ;  t -> cons(a, nil)
})

-------------------------------------------
Step 27, which took 0.023513 s (model generation: 0.021190,  model checking: 0.002323):

Model:
|_
{
delete -> 
{{{
Q={q_gen_4617, q_gen_4623, q_gen_4624, q_gen_4626, q_gen_4627},
Q_f={q_gen_4617},
Delta=
{
<cons>(q_gen_4627, q_gen_4626) -> q_gen_4626
<nil>() -> q_gen_4626
<a>() -> q_gen_4627
<b>() -> q_gen_4627
<cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4623
<cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4623
<nil, nil>() -> q_gen_4623
<a, a>() -> q_gen_4624
<a, b>() -> q_gen_4624
<b, a>() -> q_gen_4624
<b, b>() -> q_gen_4624
<a, cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4617
<a, cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4617
<a, nil, nil>() -> q_gen_4617
<b, cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4617
<b, cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4617
<b, nil, nil>() -> q_gen_4617
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_4616, q_gen_4620, q_gen_4621, q_gen_4638, q_gen_4639, q_gen_4640, q_gen_4641, q_gen_4642, q_gen_4662},
Q_f={q_gen_4616},
Delta=
{
<cons>(q_gen_4639, q_gen_4638) -> q_gen_4620
<nil>() -> q_gen_4620
<cons>(q_gen_4639, q_gen_4620) -> q_gen_4638
<b>() -> q_gen_4639
<z>() -> q_gen_4641
<s>(q_gen_4641) -> q_gen_4662
<cons, s>(q_gen_4621, q_gen_4620) -> q_gen_4616
<cons, s>(q_gen_4640, q_gen_4638) -> q_gen_4616
<nil, z>() -> q_gen_4616
<a, z>() -> q_gen_4621
<b, s>(q_gen_4662) -> q_gen_4621
<b, z>() -> q_gen_4621
<a, s>(q_gen_4641) -> q_gen_4640
<b, s>(q_gen_4641) -> q_gen_4640
<cons, s>(q_gen_4621, q_gen_4638) -> q_gen_4642
<cons, s>(q_gen_4640, q_gen_4620) -> q_gen_4642
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_4613, q_gen_4615, q_gen_4643},
Q_f={q_gen_4613},
Delta=
{
<s>(q_gen_4615) -> q_gen_4615
<z>() -> q_gen_4615
<s, s>(q_gen_4613) -> q_gen_4613
<z, s>(q_gen_4615) -> q_gen_4613
<z, z>() -> q_gen_4613
<s, s>(q_gen_4643) -> q_gen_4643
<s, z>(q_gen_4615) -> q_gen_4643
}

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

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

Teacher's answer:
New clause system:
{
() -> delete([x, nil, nil]) -> 14
() -> length([nil, z]) -> 14
() -> leq([z, s(nn2)]) -> 14
() -> leq([z, z]) -> 14
(delete([h, t, _cr])) -> delete([h, cons(h, t), _cr]) -> 16
(delete([i, l, _ir]) /\ length([_ir, _jr]) /\ length([l, _kr])) -> leq([_jr, _kr]) -> 16
(delete([x, t, _dr]) /\ not eq_elt([x, h])) -> delete([x, cons(h, t), cons(h, _dr)]) -> 15
(length([ll, _yq])) -> length([cons(x, ll), s(_yq)]) -> 19
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 15
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 17
(leq([s(nn1), z])) -> BOT -> 15
}
Sat witness: Found: ((length([ll, _yq])) -> length([cons(x, ll), s(_yq)]), {
_yq -> s(s(s(z)))  ;  ll -> cons(b, nil)  ;  x -> b
})

-------------------------------------------
Step 28, which took 0.025681 s (model generation: 0.024445,  model checking: 0.001236):

Model:
|_
{
delete -> 
{{{
Q={q_gen_4617, q_gen_4623, q_gen_4624, q_gen_4626, q_gen_4627},
Q_f={q_gen_4617},
Delta=
{
<cons>(q_gen_4627, q_gen_4626) -> q_gen_4626
<nil>() -> q_gen_4626
<a>() -> q_gen_4627
<b>() -> q_gen_4627
<cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4623
<cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4623
<nil, nil>() -> q_gen_4623
<a, a>() -> q_gen_4624
<a, b>() -> q_gen_4624
<b, a>() -> q_gen_4624
<b, b>() -> q_gen_4624
<a, cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4617
<a, cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4617
<a, nil, nil>() -> q_gen_4617
<b, cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4617
<b, cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4617
<b, nil, nil>() -> q_gen_4617
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_4616, q_gen_4620, q_gen_4621, q_gen_4638, q_gen_4639, q_gen_4640, q_gen_4641, q_gen_4642, q_gen_4662},
Q_f={q_gen_4616},
Delta=
{
<cons>(q_gen_4639, q_gen_4638) -> q_gen_4620
<nil>() -> q_gen_4620
<cons>(q_gen_4639, q_gen_4620) -> q_gen_4638
<b>() -> q_gen_4639
<s>(q_gen_4662) -> q_gen_4641
<z>() -> q_gen_4641
<s>(q_gen_4641) -> q_gen_4662
<cons, s>(q_gen_4621, q_gen_4620) -> q_gen_4616
<cons, s>(q_gen_4640, q_gen_4638) -> q_gen_4616
<nil, z>() -> q_gen_4616
<a, z>() -> q_gen_4621
<b, s>(q_gen_4662) -> q_gen_4621
<b, z>() -> q_gen_4621
<a, s>(q_gen_4641) -> q_gen_4640
<b, s>(q_gen_4641) -> q_gen_4640
<cons, s>(q_gen_4621, q_gen_4638) -> q_gen_4642
<cons, s>(q_gen_4640, q_gen_4620) -> q_gen_4642
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_4613, q_gen_4615, q_gen_4643},
Q_f={q_gen_4613},
Delta=
{
<s>(q_gen_4615) -> q_gen_4615
<z>() -> q_gen_4615
<s, s>(q_gen_4613) -> q_gen_4613
<z, s>(q_gen_4615) -> q_gen_4613
<z, z>() -> q_gen_4613
<s, s>(q_gen_4643) -> q_gen_4643
<s, z>(q_gen_4615) -> q_gen_4643
}

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

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

Teacher's answer:
New clause system:
{
() -> delete([x, nil, nil]) -> 15
() -> length([nil, z]) -> 15
() -> leq([z, s(nn2)]) -> 15
() -> leq([z, z]) -> 15
(delete([h, t, _cr])) -> delete([h, cons(h, t), _cr]) -> 16
(delete([i, l, _ir]) /\ length([_ir, _jr]) /\ length([l, _kr])) -> leq([_jr, _kr]) -> 19
(delete([x, t, _dr]) /\ not eq_elt([x, h])) -> delete([x, cons(h, t), cons(h, _dr)]) -> 16
(length([ll, _yq])) -> length([cons(x, ll), s(_yq)]) -> 19
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 16
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 17
(leq([s(nn1), z])) -> BOT -> 16
}
Sat witness: Found: ((delete([i, l, _ir]) /\ length([_ir, _jr]) /\ length([l, _kr])) -> leq([_jr, _kr]), {
_ir -> cons(b, nil)  ;  _jr -> s(s(s(z)))  ;  _kr -> s(s(z))  ;  i -> a  ;  l -> cons(a, cons(b, nil))
})

-------------------------------------------
Step 29, which took 0.025670 s (model generation: 0.024840,  model checking: 0.000830):

Model:
|_
{
delete -> 
{{{
Q={q_gen_4617, q_gen_4623, q_gen_4624, q_gen_4626, q_gen_4627, q_gen_4653, q_gen_4654},
Q_f={q_gen_4617},
Delta=
{
<cons>(q_gen_4627, q_gen_4626) -> q_gen_4626
<nil>() -> q_gen_4626
<a>() -> q_gen_4627
<b>() -> q_gen_4627
<cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4623
<nil, nil>() -> q_gen_4623
<a, a>() -> q_gen_4624
<a, b>() -> q_gen_4624
<b, a>() -> q_gen_4624
<b, b>() -> q_gen_4624
<cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4653
<a, cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4617
<a, cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4617
<a, nil, nil>() -> q_gen_4617
<b, cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4617
<b, cons, cons>(q_gen_4624, q_gen_4653) -> q_gen_4617
<b, cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4617
<b, nil, nil>() -> q_gen_4617
<a, cons, cons>(q_gen_4624, q_gen_4653) -> q_gen_4654
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_4616, q_gen_4620, q_gen_4621, q_gen_4638, q_gen_4639, q_gen_4640, q_gen_4641, q_gen_4642},
Q_f={q_gen_4616},
Delta=
{
<nil>() -> q_gen_4620
<cons>(q_gen_4639, q_gen_4620) -> q_gen_4638
<cons>(q_gen_4639, q_gen_4638) -> q_gen_4638
<b>() -> q_gen_4639
<s>(q_gen_4641) -> q_gen_4641
<z>() -> q_gen_4641
<cons, s>(q_gen_4621, q_gen_4620) -> q_gen_4616
<cons, s>(q_gen_4640, q_gen_4638) -> q_gen_4616
<nil, z>() -> q_gen_4616
<a, z>() -> q_gen_4621
<b, z>() -> q_gen_4621
<a, s>(q_gen_4641) -> q_gen_4640
<b, s>(q_gen_4641) -> q_gen_4640
<cons, s>(q_gen_4621, q_gen_4638) -> q_gen_4642
<cons, s>(q_gen_4640, q_gen_4620) -> q_gen_4642
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_4613, q_gen_4615, q_gen_4643},
Q_f={q_gen_4613},
Delta=
{
<s>(q_gen_4615) -> q_gen_4615
<z>() -> q_gen_4615
<s, s>(q_gen_4613) -> q_gen_4613
<z, s>(q_gen_4615) -> q_gen_4613
<z, z>() -> q_gen_4613
<s, s>(q_gen_4643) -> q_gen_4643
<s, z>(q_gen_4615) -> q_gen_4643
}

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

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

Teacher's answer:
New clause system:
{
() -> delete([x, nil, nil]) -> 16
() -> length([nil, z]) -> 16
() -> leq([z, s(nn2)]) -> 16
() -> leq([z, z]) -> 16
(delete([h, t, _cr])) -> delete([h, cons(h, t), _cr]) -> 16
(delete([i, l, _ir]) /\ length([_ir, _jr]) /\ length([l, _kr])) -> leq([_jr, _kr]) -> 19
(delete([x, t, _dr]) /\ not eq_elt([x, h])) -> delete([x, cons(h, t), cons(h, _dr)]) -> 19
(length([ll, _yq])) -> length([cons(x, ll), s(_yq)]) -> 19
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 17
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 17
(leq([s(nn1), z])) -> BOT -> 17
}
Sat witness: Found: ((delete([x, t, _dr]) /\ not eq_elt([x, h])) -> delete([x, cons(h, t), cons(h, _dr)]), {
_dr -> cons(b, nil)  ;  h -> b  ;  t -> cons(b, nil)  ;  x -> a
})

-------------------------------------------
Step 30, which took 0.029036 s (model generation: 0.026267,  model checking: 0.002769):

Model:
|_
{
delete -> 
{{{
Q={q_gen_4617, q_gen_4623, q_gen_4624, q_gen_4626, q_gen_4627},
Q_f={q_gen_4617},
Delta=
{
<cons>(q_gen_4627, q_gen_4626) -> q_gen_4626
<nil>() -> q_gen_4626
<a>() -> q_gen_4627
<b>() -> q_gen_4627
<cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4623
<cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4623
<nil, nil>() -> q_gen_4623
<a, a>() -> q_gen_4624
<a, b>() -> q_gen_4624
<b, a>() -> q_gen_4624
<b, b>() -> q_gen_4624
<a, cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4617
<a, cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4617
<a, nil, nil>() -> q_gen_4617
<b, cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4617
<b, cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4617
<b, nil, nil>() -> q_gen_4617
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_4616, q_gen_4620, q_gen_4621, q_gen_4638, q_gen_4639, q_gen_4640, q_gen_4641, q_gen_4642, q_gen_4660, q_gen_4661, q_gen_4662},
Q_f={q_gen_4616},
Delta=
{
<nil>() -> q_gen_4620
<cons>(q_gen_4639, q_gen_4620) -> q_gen_4638
<b>() -> q_gen_4639
<z>() -> q_gen_4641
<cons>(q_gen_4639, q_gen_4638) -> q_gen_4660
<s>(q_gen_4641) -> q_gen_4662
<s>(q_gen_4662) -> q_gen_4662
<cons, s>(q_gen_4621, q_gen_4620) -> q_gen_4616
<cons, s>(q_gen_4640, q_gen_4638) -> q_gen_4616
<cons, s>(q_gen_4661, q_gen_4660) -> q_gen_4616
<nil, z>() -> q_gen_4616
<a, z>() -> q_gen_4621
<b, z>() -> q_gen_4621
<a, s>(q_gen_4641) -> q_gen_4640
<b, s>(q_gen_4641) -> q_gen_4640
<cons, s>(q_gen_4621, q_gen_4638) -> q_gen_4642
<cons, s>(q_gen_4640, q_gen_4620) -> q_gen_4642
<cons, s>(q_gen_4661, q_gen_4620) -> q_gen_4642
<cons, s>(q_gen_4661, q_gen_4638) -> q_gen_4642
<b, s>(q_gen_4662) -> q_gen_4661
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_4613, q_gen_4615, q_gen_4643},
Q_f={q_gen_4613},
Delta=
{
<s>(q_gen_4615) -> q_gen_4615
<z>() -> q_gen_4615
<s, s>(q_gen_4613) -> q_gen_4613
<z, s>(q_gen_4615) -> q_gen_4613
<z, z>() -> q_gen_4613
<s, s>(q_gen_4643) -> q_gen_4643
<s, z>(q_gen_4615) -> q_gen_4643
}

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

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

Teacher's answer:
New clause system:
{
() -> delete([x, nil, nil]) -> 17
() -> length([nil, z]) -> 17
() -> leq([z, s(nn2)]) -> 17
() -> leq([z, z]) -> 17
(delete([h, t, _cr])) -> delete([h, cons(h, t), _cr]) -> 17
(delete([i, l, _ir]) /\ length([_ir, _jr]) /\ length([l, _kr])) -> leq([_jr, _kr]) -> 19
(delete([x, t, _dr]) /\ not eq_elt([x, h])) -> delete([x, cons(h, t), cons(h, _dr)]) -> 19
(length([ll, _yq])) -> length([cons(x, ll), s(_yq)]) -> 22
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 18
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 18
(leq([s(nn1), z])) -> BOT -> 18
}
Sat witness: Found: ((length([ll, _yq])) -> length([cons(x, ll), s(_yq)]), {
_yq -> s(z)  ;  ll -> cons(a, nil)  ;  x -> b
})

-------------------------------------------
Step 31, which took 0.028640 s (model generation: 0.026172,  model checking: 0.002468):

Model:
|_
{
delete -> 
{{{
Q={q_gen_4617, q_gen_4623, q_gen_4624, q_gen_4626, q_gen_4627},
Q_f={q_gen_4617},
Delta=
{
<cons>(q_gen_4627, q_gen_4626) -> q_gen_4626
<nil>() -> q_gen_4626
<a>() -> q_gen_4627
<b>() -> q_gen_4627
<cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4623
<cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4623
<nil, nil>() -> q_gen_4623
<a, a>() -> q_gen_4624
<a, b>() -> q_gen_4624
<b, a>() -> q_gen_4624
<b, b>() -> q_gen_4624
<a, cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4617
<a, cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4617
<a, nil, nil>() -> q_gen_4617
<b, cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4617
<b, cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4617
<b, nil, nil>() -> q_gen_4617
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_4616, q_gen_4620, q_gen_4621, q_gen_4638, q_gen_4639, q_gen_4640, q_gen_4641, q_gen_4642, q_gen_4660, q_gen_4661, q_gen_4662},
Q_f={q_gen_4616},
Delta=
{
<nil>() -> q_gen_4620
<cons>(q_gen_4639, q_gen_4620) -> q_gen_4638
<a>() -> q_gen_4639
<b>() -> q_gen_4639
<z>() -> q_gen_4641
<cons>(q_gen_4639, q_gen_4638) -> q_gen_4660
<s>(q_gen_4641) -> q_gen_4662
<s>(q_gen_4662) -> q_gen_4662
<cons, s>(q_gen_4621, q_gen_4620) -> q_gen_4616
<cons, s>(q_gen_4640, q_gen_4638) -> q_gen_4616
<cons, s>(q_gen_4661, q_gen_4660) -> q_gen_4616
<nil, z>() -> q_gen_4616
<a, z>() -> q_gen_4621
<b, z>() -> q_gen_4621
<a, s>(q_gen_4641) -> q_gen_4640
<b, s>(q_gen_4641) -> q_gen_4640
<cons, s>(q_gen_4621, q_gen_4638) -> q_gen_4642
<cons, s>(q_gen_4640, q_gen_4620) -> q_gen_4642
<cons, s>(q_gen_4661, q_gen_4620) -> q_gen_4642
<cons, s>(q_gen_4661, q_gen_4638) -> q_gen_4642
<b, s>(q_gen_4662) -> q_gen_4661
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_4613, q_gen_4615, q_gen_4643},
Q_f={q_gen_4613},
Delta=
{
<s>(q_gen_4615) -> q_gen_4615
<z>() -> q_gen_4615
<s, s>(q_gen_4613) -> q_gen_4613
<z, s>(q_gen_4615) -> q_gen_4613
<z, z>() -> q_gen_4613
<s, s>(q_gen_4643) -> q_gen_4643
<s, z>(q_gen_4615) -> q_gen_4643
}

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

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

Teacher's answer:
New clause system:
{
() -> delete([x, nil, nil]) -> 18
() -> length([nil, z]) -> 18
() -> leq([z, s(nn2)]) -> 18
() -> leq([z, z]) -> 18
(delete([h, t, _cr])) -> delete([h, cons(h, t), _cr]) -> 18
(delete([i, l, _ir]) /\ length([_ir, _jr]) /\ length([l, _kr])) -> leq([_jr, _kr]) -> 22
(delete([x, t, _dr]) /\ not eq_elt([x, h])) -> delete([x, cons(h, t), cons(h, _dr)]) -> 20
(length([ll, _yq])) -> length([cons(x, ll), s(_yq)]) -> 22
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 19
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 19
(leq([s(nn1), z])) -> BOT -> 19
}
Sat witness: Found: ((delete([i, l, _ir]) /\ length([_ir, _jr]) /\ length([l, _kr])) -> leq([_jr, _kr]), {
_ir -> cons(b, cons(b, cons(b, nil)))  ;  _jr -> s(s(s(s(z))))  ;  _kr -> s(s(s(z)))  ;  i -> a  ;  l -> cons(b, cons(b, cons(b, nil)))
})

-------------------------------------------
Step 32, which took 0.032107 s (model generation: 0.029090,  model checking: 0.003017):

Model:
|_
{
delete -> 
{{{
Q={q_gen_4617, q_gen_4623, q_gen_4624, q_gen_4626, q_gen_4627},
Q_f={q_gen_4617},
Delta=
{
<cons>(q_gen_4627, q_gen_4626) -> q_gen_4626
<nil>() -> q_gen_4626
<a>() -> q_gen_4627
<b>() -> q_gen_4627
<cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4623
<cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4623
<nil, nil>() -> q_gen_4623
<a, a>() -> q_gen_4624
<a, b>() -> q_gen_4624
<b, a>() -> q_gen_4624
<b, b>() -> q_gen_4624
<a, cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4617
<a, cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4617
<a, nil, nil>() -> q_gen_4617
<b, cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4617
<b, cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4617
<b, nil, nil>() -> q_gen_4617
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_4616, q_gen_4620, q_gen_4621, q_gen_4638, q_gen_4639, q_gen_4640, q_gen_4641, q_gen_4642, q_gen_4660, q_gen_4661, q_gen_4662},
Q_f={q_gen_4616},
Delta=
{
<nil>() -> q_gen_4620
<cons>(q_gen_4639, q_gen_4620) -> q_gen_4638
<a>() -> q_gen_4639
<b>() -> q_gen_4639
<s>(q_gen_4662) -> q_gen_4641
<z>() -> q_gen_4641
<cons>(q_gen_4639, q_gen_4638) -> q_gen_4660
<s>(q_gen_4641) -> q_gen_4662
<cons, s>(q_gen_4621, q_gen_4620) -> q_gen_4616
<cons, s>(q_gen_4640, q_gen_4638) -> q_gen_4616
<cons, s>(q_gen_4661, q_gen_4660) -> q_gen_4616
<nil, z>() -> q_gen_4616
<a, z>() -> q_gen_4621
<b, z>() -> q_gen_4621
<a, s>(q_gen_4641) -> q_gen_4640
<b, s>(q_gen_4641) -> q_gen_4640
<cons, s>(q_gen_4621, q_gen_4638) -> q_gen_4642
<cons, s>(q_gen_4640, q_gen_4620) -> q_gen_4642
<cons, s>(q_gen_4640, q_gen_4660) -> q_gen_4642
<cons, s>(q_gen_4661, q_gen_4620) -> q_gen_4642
<cons, s>(q_gen_4661, q_gen_4638) -> q_gen_4642
<b, s>(q_gen_4662) -> q_gen_4661
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_4613, q_gen_4615, q_gen_4643},
Q_f={q_gen_4613},
Delta=
{
<s>(q_gen_4615) -> q_gen_4615
<z>() -> q_gen_4615
<s, s>(q_gen_4613) -> q_gen_4613
<z, s>(q_gen_4615) -> q_gen_4613
<z, z>() -> q_gen_4613
<s, s>(q_gen_4643) -> q_gen_4643
<s, z>(q_gen_4615) -> q_gen_4643
}

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

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

Teacher's answer:
New clause system:
{
() -> delete([x, nil, nil]) -> 19
() -> length([nil, z]) -> 19
() -> leq([z, s(nn2)]) -> 19
() -> leq([z, z]) -> 19
(delete([h, t, _cr])) -> delete([h, cons(h, t), _cr]) -> 19
(delete([i, l, _ir]) /\ length([_ir, _jr]) /\ length([l, _kr])) -> leq([_jr, _kr]) -> 22
(delete([x, t, _dr]) /\ not eq_elt([x, h])) -> delete([x, cons(h, t), cons(h, _dr)]) -> 21
(length([ll, _yq])) -> length([cons(x, ll), s(_yq)]) -> 25
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 20
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 20
(leq([s(nn1), z])) -> BOT -> 20
}
Sat witness: Found: ((length([ll, _yq])) -> length([cons(x, ll), s(_yq)]), {
_yq -> s(s(s(z)))  ;  ll -> cons(b, cons(a, cons(b, nil)))  ;  x -> a
})

-------------------------------------------
Step 33, which took 0.033828 s (model generation: 0.031402,  model checking: 0.002426):

Model:
|_
{
delete -> 
{{{
Q={q_gen_4617, q_gen_4623, q_gen_4624, q_gen_4626, q_gen_4627},
Q_f={q_gen_4617},
Delta=
{
<cons>(q_gen_4627, q_gen_4626) -> q_gen_4626
<nil>() -> q_gen_4626
<a>() -> q_gen_4627
<b>() -> q_gen_4627
<cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4623
<cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4623
<nil, nil>() -> q_gen_4623
<a, a>() -> q_gen_4624
<a, b>() -> q_gen_4624
<b, a>() -> q_gen_4624
<b, b>() -> q_gen_4624
<a, cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4617
<a, cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4617
<a, nil, nil>() -> q_gen_4617
<b, cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4617
<b, cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4617
<b, nil, nil>() -> q_gen_4617
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_4616, q_gen_4620, q_gen_4621, q_gen_4638, q_gen_4639, q_gen_4640, q_gen_4641, q_gen_4642, q_gen_4660, q_gen_4661, q_gen_4662},
Q_f={q_gen_4616},
Delta=
{
<nil>() -> q_gen_4620
<cons>(q_gen_4639, q_gen_4620) -> q_gen_4638
<cons>(q_gen_4639, q_gen_4660) -> q_gen_4638
<a>() -> q_gen_4639
<b>() -> q_gen_4639
<s>(q_gen_4662) -> q_gen_4641
<z>() -> q_gen_4641
<cons>(q_gen_4639, q_gen_4638) -> q_gen_4660
<s>(q_gen_4641) -> q_gen_4662
<cons, s>(q_gen_4621, q_gen_4620) -> q_gen_4616
<cons, s>(q_gen_4640, q_gen_4638) -> q_gen_4616
<cons, s>(q_gen_4661, q_gen_4660) -> q_gen_4616
<nil, z>() -> q_gen_4616
<a, z>() -> q_gen_4621
<b, z>() -> q_gen_4621
<a, s>(q_gen_4641) -> q_gen_4640
<b, s>(q_gen_4641) -> q_gen_4640
<cons, s>(q_gen_4621, q_gen_4638) -> q_gen_4642
<cons, s>(q_gen_4640, q_gen_4620) -> q_gen_4642
<cons, s>(q_gen_4640, q_gen_4660) -> q_gen_4642
<cons, s>(q_gen_4661, q_gen_4620) -> q_gen_4642
<cons, s>(q_gen_4661, q_gen_4638) -> q_gen_4642
<b, s>(q_gen_4662) -> q_gen_4661
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_4613, q_gen_4615, q_gen_4643},
Q_f={q_gen_4613},
Delta=
{
<s>(q_gen_4615) -> q_gen_4615
<z>() -> q_gen_4615
<s, s>(q_gen_4613) -> q_gen_4613
<z, s>(q_gen_4615) -> q_gen_4613
<z, z>() -> q_gen_4613
<s, s>(q_gen_4643) -> q_gen_4643
<s, z>(q_gen_4615) -> q_gen_4643
}

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

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

Teacher's answer:
New clause system:
{
() -> delete([x, nil, nil]) -> 20
() -> length([nil, z]) -> 20
() -> leq([z, s(nn2)]) -> 20
() -> leq([z, z]) -> 20
(delete([h, t, _cr])) -> delete([h, cons(h, t), _cr]) -> 20
(delete([i, l, _ir]) /\ length([_ir, _jr]) /\ length([l, _kr])) -> leq([_jr, _kr]) -> 25
(delete([x, t, _dr]) /\ not eq_elt([x, h])) -> delete([x, cons(h, t), cons(h, _dr)]) -> 22
(length([ll, _yq])) -> length([cons(x, ll), s(_yq)]) -> 25
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 21
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 21
(leq([s(nn1), z])) -> BOT -> 21
}
Sat witness: Found: ((delete([i, l, _ir]) /\ length([_ir, _jr]) /\ length([l, _kr])) -> leq([_jr, _kr]), {
_ir -> cons(b, cons(b, nil))  ;  _jr -> s(s(s(s(z))))  ;  _kr -> s(s(z))  ;  i -> a  ;  l -> cons(b, cons(b, nil))
})

-------------------------------------------
Step 34, which took 0.044296 s (model generation: 0.041224,  model checking: 0.003072):

Model:
|_
{
delete -> 
{{{
Q={q_gen_4617, q_gen_4623, q_gen_4624, q_gen_4626, q_gen_4627},
Q_f={q_gen_4617},
Delta=
{
<cons>(q_gen_4627, q_gen_4626) -> q_gen_4626
<nil>() -> q_gen_4626
<a>() -> q_gen_4627
<b>() -> q_gen_4627
<cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4623
<cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4623
<nil, nil>() -> q_gen_4623
<a, a>() -> q_gen_4624
<a, b>() -> q_gen_4624
<b, a>() -> q_gen_4624
<b, b>() -> q_gen_4624
<a, cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4617
<a, cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4617
<a, nil, nil>() -> q_gen_4617
<b, cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4617
<b, cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4617
<b, nil, nil>() -> q_gen_4617
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_4616, q_gen_4620, q_gen_4621, q_gen_4638, q_gen_4639, q_gen_4640, q_gen_4641, q_gen_4642, q_gen_4660, q_gen_4661, q_gen_4662, q_gen_4670},
Q_f={q_gen_4616},
Delta=
{
<nil>() -> q_gen_4620
<cons>(q_gen_4639, q_gen_4620) -> q_gen_4638
<a>() -> q_gen_4639
<b>() -> q_gen_4639
<z>() -> q_gen_4641
<cons>(q_gen_4639, q_gen_4638) -> q_gen_4660
<cons>(q_gen_4639, q_gen_4660) -> q_gen_4660
<s>(q_gen_4641) -> q_gen_4662
<s>(q_gen_4662) -> q_gen_4670
<cons, s>(q_gen_4621, q_gen_4620) -> q_gen_4616
<cons, s>(q_gen_4640, q_gen_4638) -> q_gen_4616
<cons, s>(q_gen_4640, q_gen_4660) -> q_gen_4616
<cons, s>(q_gen_4661, q_gen_4660) -> q_gen_4616
<nil, z>() -> q_gen_4616
<a, z>() -> q_gen_4621
<b, s>(q_gen_4670) -> q_gen_4621
<b, z>() -> q_gen_4621
<a, s>(q_gen_4641) -> q_gen_4640
<a, s>(q_gen_4670) -> q_gen_4640
<b, s>(q_gen_4641) -> q_gen_4640
<cons, s>(q_gen_4621, q_gen_4638) -> q_gen_4642
<cons, s>(q_gen_4621, q_gen_4660) -> q_gen_4642
<cons, s>(q_gen_4640, q_gen_4620) -> q_gen_4642
<cons, s>(q_gen_4661, q_gen_4620) -> q_gen_4642
<cons, s>(q_gen_4661, q_gen_4638) -> q_gen_4642
<b, s>(q_gen_4662) -> q_gen_4661
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_4613, q_gen_4615, q_gen_4643},
Q_f={q_gen_4613},
Delta=
{
<s>(q_gen_4615) -> q_gen_4615
<z>() -> q_gen_4615
<s, s>(q_gen_4613) -> q_gen_4613
<z, s>(q_gen_4615) -> q_gen_4613
<z, z>() -> q_gen_4613
<s, s>(q_gen_4643) -> q_gen_4643
<s, z>(q_gen_4615) -> q_gen_4643
}

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

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

Teacher's answer:
New clause system:
{
() -> delete([x, nil, nil]) -> 21
() -> length([nil, z]) -> 21
() -> leq([z, s(nn2)]) -> 21
() -> leq([z, z]) -> 21
(delete([h, t, _cr])) -> delete([h, cons(h, t), _cr]) -> 21
(delete([i, l, _ir]) /\ length([_ir, _jr]) /\ length([l, _kr])) -> leq([_jr, _kr]) -> 25
(delete([x, t, _dr]) /\ not eq_elt([x, h])) -> delete([x, cons(h, t), cons(h, _dr)]) -> 23
(length([ll, _yq])) -> length([cons(x, ll), s(_yq)]) -> 28
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 22
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 22
(leq([s(nn1), z])) -> BOT -> 22
}
Sat witness: Found: ((length([ll, _yq])) -> length([cons(x, ll), s(_yq)]), {
_yq -> s(s(s(z)))  ;  ll -> cons(b, cons(a, cons(b, nil)))  ;  x -> b
})

-------------------------------------------
Step 35, which took 0.036756 s (model generation: 0.036231,  model checking: 0.000525):

Model:
|_
{
delete -> 
{{{
Q={q_gen_4617, q_gen_4623, q_gen_4624, q_gen_4626, q_gen_4627},
Q_f={q_gen_4617},
Delta=
{
<cons>(q_gen_4627, q_gen_4626) -> q_gen_4626
<nil>() -> q_gen_4626
<a>() -> q_gen_4627
<b>() -> q_gen_4627
<cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4623
<cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4623
<nil, nil>() -> q_gen_4623
<a, a>() -> q_gen_4624
<a, b>() -> q_gen_4624
<b, a>() -> q_gen_4624
<b, b>() -> q_gen_4624
<a, cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4617
<a, cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4617
<a, nil, nil>() -> q_gen_4617
<b, cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4617
<b, cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4617
<b, nil, nil>() -> q_gen_4617
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_4616, q_gen_4620, q_gen_4621, q_gen_4638, q_gen_4639, q_gen_4640, q_gen_4641, q_gen_4642, q_gen_4660, q_gen_4661, q_gen_4662},
Q_f={q_gen_4616},
Delta=
{
<nil>() -> q_gen_4620
<cons>(q_gen_4639, q_gen_4620) -> q_gen_4638
<cons>(q_gen_4639, q_gen_4660) -> q_gen_4638
<a>() -> q_gen_4639
<b>() -> q_gen_4639
<s>(q_gen_4662) -> q_gen_4641
<z>() -> q_gen_4641
<cons>(q_gen_4639, q_gen_4638) -> q_gen_4660
<s>(q_gen_4641) -> q_gen_4662
<cons, s>(q_gen_4621, q_gen_4620) -> q_gen_4616
<cons, s>(q_gen_4640, q_gen_4638) -> q_gen_4616
<cons, s>(q_gen_4661, q_gen_4660) -> q_gen_4616
<nil, z>() -> q_gen_4616
<a, z>() -> q_gen_4621
<b, z>() -> q_gen_4621
<a, s>(q_gen_4641) -> q_gen_4640
<b, s>(q_gen_4641) -> q_gen_4640
<cons, s>(q_gen_4621, q_gen_4638) -> q_gen_4642
<cons, s>(q_gen_4640, q_gen_4620) -> q_gen_4642
<cons, s>(q_gen_4640, q_gen_4660) -> q_gen_4642
<cons, s>(q_gen_4661, q_gen_4620) -> q_gen_4642
<cons, s>(q_gen_4661, q_gen_4638) -> q_gen_4642
<b, s>(q_gen_4662) -> q_gen_4661
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_4613, q_gen_4615, q_gen_4629, q_gen_4643},
Q_f={q_gen_4613},
Delta=
{
<z>() -> q_gen_4615
<s>(q_gen_4615) -> q_gen_4629
<s, s>(q_gen_4613) -> q_gen_4613
<s, z>(q_gen_4629) -> q_gen_4613
<z, s>(q_gen_4615) -> q_gen_4613
<z, s>(q_gen_4629) -> q_gen_4613
<z, z>() -> q_gen_4613
<s, s>(q_gen_4643) -> q_gen_4643
<s, z>(q_gen_4615) -> q_gen_4643
}

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

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

Teacher's answer:
New clause system:
{
() -> delete([x, nil, nil]) -> 21
() -> length([nil, z]) -> 21
() -> leq([z, s(nn2)]) -> 24
() -> leq([z, z]) -> 22
(delete([h, t, _cr])) -> delete([h, cons(h, t), _cr]) -> 22
(delete([i, l, _ir]) /\ length([_ir, _jr]) /\ length([l, _kr])) -> leq([_jr, _kr]) -> 25
(delete([x, t, _dr]) /\ not eq_elt([x, h])) -> delete([x, cons(h, t), cons(h, _dr)]) -> 23
(length([ll, _yq])) -> length([cons(x, ll), s(_yq)]) -> 28
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 22
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 22
(leq([s(nn1), z])) -> BOT -> 22
}
Sat witness: Found: (() -> leq([z, s(nn2)]), {
nn2 -> s(s(z))
})

-------------------------------------------
Step 36, which took 0.039760 s (model generation: 0.039364,  model checking: 0.000396):

Model:
|_
{
delete -> 
{{{
Q={q_gen_4617, q_gen_4623, q_gen_4624, q_gen_4626, q_gen_4627},
Q_f={q_gen_4617},
Delta=
{
<cons>(q_gen_4627, q_gen_4626) -> q_gen_4626
<nil>() -> q_gen_4626
<a>() -> q_gen_4627
<b>() -> q_gen_4627
<cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4623
<cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4623
<nil, nil>() -> q_gen_4623
<a, a>() -> q_gen_4624
<a, b>() -> q_gen_4624
<b, a>() -> q_gen_4624
<b, b>() -> q_gen_4624
<a, cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4617
<a, cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4617
<a, nil, nil>() -> q_gen_4617
<b, cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4617
<b, cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4617
<b, nil, nil>() -> q_gen_4617
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_4616, q_gen_4620, q_gen_4621, q_gen_4638, q_gen_4639, q_gen_4640, q_gen_4641, q_gen_4642, q_gen_4660, q_gen_4661, q_gen_4662},
Q_f={q_gen_4616},
Delta=
{
<nil>() -> q_gen_4620
<cons>(q_gen_4639, q_gen_4620) -> q_gen_4638
<cons>(q_gen_4639, q_gen_4660) -> q_gen_4638
<a>() -> q_gen_4639
<b>() -> q_gen_4639
<s>(q_gen_4662) -> q_gen_4641
<z>() -> q_gen_4641
<cons>(q_gen_4639, q_gen_4638) -> q_gen_4660
<s>(q_gen_4641) -> q_gen_4662
<cons, s>(q_gen_4621, q_gen_4620) -> q_gen_4616
<cons, s>(q_gen_4640, q_gen_4638) -> q_gen_4616
<cons, s>(q_gen_4661, q_gen_4660) -> q_gen_4616
<nil, z>() -> q_gen_4616
<a, z>() -> q_gen_4621
<b, z>() -> q_gen_4621
<a, s>(q_gen_4641) -> q_gen_4640
<b, s>(q_gen_4641) -> q_gen_4640
<cons, s>(q_gen_4621, q_gen_4638) -> q_gen_4642
<cons, s>(q_gen_4640, q_gen_4620) -> q_gen_4642
<cons, s>(q_gen_4640, q_gen_4660) -> q_gen_4642
<cons, s>(q_gen_4661, q_gen_4620) -> q_gen_4642
<cons, s>(q_gen_4661, q_gen_4638) -> q_gen_4642
<b, s>(q_gen_4662) -> q_gen_4661
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_4613, q_gen_4615, q_gen_4629, q_gen_4643},
Q_f={q_gen_4613},
Delta=
{
<z>() -> q_gen_4615
<s>(q_gen_4615) -> q_gen_4629
<s>(q_gen_4629) -> q_gen_4629
<s, s>(q_gen_4613) -> q_gen_4613
<s, z>(q_gen_4629) -> q_gen_4613
<z, s>(q_gen_4615) -> q_gen_4613
<z, s>(q_gen_4629) -> q_gen_4613
<z, z>() -> q_gen_4613
<s, s>(q_gen_4643) -> q_gen_4643
<s, z>(q_gen_4615) -> q_gen_4643
}

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

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

Teacher's answer:
New clause system:
{
() -> delete([x, nil, nil]) -> 22
() -> length([nil, z]) -> 22
() -> leq([z, s(nn2)]) -> 24
() -> leq([z, z]) -> 22
(delete([h, t, _cr])) -> delete([h, cons(h, t), _cr]) -> 22
(delete([i, l, _ir]) /\ length([_ir, _jr]) /\ length([l, _kr])) -> leq([_jr, _kr]) -> 25
(delete([x, t, _dr]) /\ not eq_elt([x, h])) -> delete([x, cons(h, t), cons(h, _dr)]) -> 23
(length([ll, _yq])) -> length([cons(x, ll), s(_yq)]) -> 28
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 22
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 22
(leq([s(nn1), z])) -> BOT -> 25
}
Sat witness: Found: ((leq([s(nn1), z])) -> BOT, {
nn1 -> s(z)
})

-------------------------------------------
Step 37, which took 0.040358 s (model generation: 0.038004,  model checking: 0.002354):

Model:
|_
{
delete -> 
{{{
Q={q_gen_4617, q_gen_4623, q_gen_4624, q_gen_4626, q_gen_4627},
Q_f={q_gen_4617},
Delta=
{
<cons>(q_gen_4627, q_gen_4626) -> q_gen_4626
<nil>() -> q_gen_4626
<a>() -> q_gen_4627
<b>() -> q_gen_4627
<cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4623
<cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4623
<nil, nil>() -> q_gen_4623
<a, a>() -> q_gen_4624
<a, b>() -> q_gen_4624
<b, a>() -> q_gen_4624
<b, b>() -> q_gen_4624
<a, cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4617
<a, cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4617
<a, nil, nil>() -> q_gen_4617
<b, cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4617
<b, cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4617
<b, nil, nil>() -> q_gen_4617
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_4616, q_gen_4620, q_gen_4621, q_gen_4638, q_gen_4639, q_gen_4640, q_gen_4641, q_gen_4642, q_gen_4660, q_gen_4661, q_gen_4662, q_gen_4670},
Q_f={q_gen_4616},
Delta=
{
<cons>(q_gen_4639, q_gen_4660) -> q_gen_4620
<nil>() -> q_gen_4620
<cons>(q_gen_4639, q_gen_4620) -> q_gen_4638
<a>() -> q_gen_4639
<b>() -> q_gen_4639
<z>() -> q_gen_4641
<cons>(q_gen_4639, q_gen_4638) -> q_gen_4660
<s>(q_gen_4641) -> q_gen_4662
<s>(q_gen_4662) -> q_gen_4670
<cons, s>(q_gen_4621, q_gen_4620) -> q_gen_4616
<cons, s>(q_gen_4640, q_gen_4638) -> q_gen_4616
<cons, s>(q_gen_4661, q_gen_4660) -> q_gen_4616
<nil, z>() -> q_gen_4616
<a, s>(q_gen_4670) -> q_gen_4621
<a, z>() -> q_gen_4621
<b, s>(q_gen_4670) -> q_gen_4621
<b, z>() -> q_gen_4621
<a, s>(q_gen_4641) -> q_gen_4640
<b, s>(q_gen_4641) -> q_gen_4640
<cons, s>(q_gen_4621, q_gen_4638) -> q_gen_4642
<cons, s>(q_gen_4621, q_gen_4660) -> q_gen_4642
<cons, s>(q_gen_4640, q_gen_4620) -> q_gen_4642
<cons, s>(q_gen_4661, q_gen_4620) -> q_gen_4642
<cons, s>(q_gen_4661, q_gen_4638) -> q_gen_4642
<b, s>(q_gen_4662) -> q_gen_4661
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_4613, q_gen_4615, q_gen_4643},
Q_f={q_gen_4613},
Delta=
{
<s>(q_gen_4615) -> q_gen_4615
<z>() -> q_gen_4615
<s, s>(q_gen_4613) -> q_gen_4613
<z, s>(q_gen_4615) -> q_gen_4613
<z, z>() -> q_gen_4613
<s, s>(q_gen_4643) -> q_gen_4643
<s, z>(q_gen_4615) -> q_gen_4643
}

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

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

Teacher's answer:
New clause system:
{
() -> delete([x, nil, nil]) -> 23
() -> length([nil, z]) -> 23
() -> leq([z, s(nn2)]) -> 25
() -> leq([z, z]) -> 23
(delete([h, t, _cr])) -> delete([h, cons(h, t), _cr]) -> 23
(delete([i, l, _ir]) /\ length([_ir, _jr]) /\ length([l, _kr])) -> leq([_jr, _kr]) -> 28
(delete([x, t, _dr]) /\ not eq_elt([x, h])) -> delete([x, cons(h, t), cons(h, _dr)]) -> 24
(length([ll, _yq])) -> length([cons(x, ll), s(_yq)]) -> 28
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 23
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 23
(leq([s(nn1), z])) -> BOT -> 26
}
Sat witness: Found: ((delete([i, l, _ir]) /\ length([_ir, _jr]) /\ length([l, _kr])) -> leq([_jr, _kr]), {
_ir -> cons(b, cons(b, cons(b, nil)))  ;  _jr -> s(s(s(z)))  ;  _kr -> s(s(z))  ;  i -> a  ;  l -> cons(b, cons(b, cons(b, cons(b, cons(b, nil)))))
})

-------------------------------------------
Step 38, which took 0.044683 s (model generation: 0.044567,  model checking: 0.000116):

Model:
|_
{
delete -> 
{{{
Q={q_gen_4617, q_gen_4623, q_gen_4624, q_gen_4626, q_gen_4627},
Q_f={q_gen_4617},
Delta=
{
<cons>(q_gen_4627, q_gen_4626) -> q_gen_4626
<nil>() -> q_gen_4626
<a>() -> q_gen_4627
<b>() -> q_gen_4627
<cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4623
<cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4623
<nil, nil>() -> q_gen_4623
<a, a>() -> q_gen_4624
<a, b>() -> q_gen_4624
<b, a>() -> q_gen_4624
<b, b>() -> q_gen_4624
<a, cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4617
<a, cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4617
<a, nil, nil>() -> q_gen_4617
<b, cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4617
<b, cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4617
<b, nil, nil>() -> q_gen_4617
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_4616, q_gen_4620, q_gen_4621, q_gen_4638, q_gen_4639, q_gen_4640, q_gen_4641, q_gen_4642, q_gen_4660, q_gen_4661, q_gen_4662},
Q_f={q_gen_4616},
Delta=
{
<nil>() -> q_gen_4620
<cons>(q_gen_4639, q_gen_4620) -> q_gen_4638
<cons>(q_gen_4639, q_gen_4660) -> q_gen_4638
<a>() -> q_gen_4639
<b>() -> q_gen_4639
<s>(q_gen_4662) -> q_gen_4641
<z>() -> q_gen_4641
<cons>(q_gen_4639, q_gen_4638) -> q_gen_4660
<s>(q_gen_4641) -> q_gen_4662
<cons, s>(q_gen_4621, q_gen_4620) -> q_gen_4616
<cons, s>(q_gen_4640, q_gen_4638) -> q_gen_4616
<cons, s>(q_gen_4661, q_gen_4660) -> q_gen_4616
<nil, z>() -> q_gen_4616
<a, z>() -> q_gen_4621
<b, z>() -> q_gen_4621
<a, s>(q_gen_4641) -> q_gen_4640
<b, s>(q_gen_4641) -> q_gen_4640
<cons, s>(q_gen_4621, q_gen_4638) -> q_gen_4642
<cons, s>(q_gen_4640, q_gen_4620) -> q_gen_4642
<cons, s>(q_gen_4640, q_gen_4660) -> q_gen_4642
<cons, s>(q_gen_4661, q_gen_4620) -> q_gen_4642
<cons, s>(q_gen_4661, q_gen_4638) -> q_gen_4642
<b, s>(q_gen_4662) -> q_gen_4661
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_4613, q_gen_4615, q_gen_4629, q_gen_4643, q_gen_4685},
Q_f={q_gen_4613},
Delta=
{
<z>() -> q_gen_4615
<s>(q_gen_4615) -> q_gen_4629
<s>(q_gen_4629) -> q_gen_4629
<s, s>(q_gen_4613) -> q_gen_4613
<s, s>(q_gen_4685) -> q_gen_4613
<z, s>(q_gen_4615) -> q_gen_4613
<z, s>(q_gen_4629) -> q_gen_4613
<z, z>() -> q_gen_4613
<s, s>(q_gen_4643) -> q_gen_4643
<s, z>(q_gen_4615) -> q_gen_4643
<s, z>(q_gen_4629) -> q_gen_4685
}

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

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

Teacher's answer:
New clause system:
{
() -> delete([x, nil, nil]) -> 23
() -> length([nil, z]) -> 23
() -> leq([z, s(nn2)]) -> 25
() -> leq([z, z]) -> 23
(delete([h, t, _cr])) -> delete([h, cons(h, t), _cr]) -> 23
(delete([i, l, _ir]) /\ length([_ir, _jr]) /\ length([l, _kr])) -> leq([_jr, _kr]) -> 28
(delete([x, t, _dr]) /\ not eq_elt([x, h])) -> delete([x, cons(h, t), cons(h, _dr)]) -> 24
(length([ll, _yq])) -> length([cons(x, ll), s(_yq)]) -> 28
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 23
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 26
(leq([s(nn1), z])) -> BOT -> 26
}
Sat witness: Found: ((leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]), {
nn1 -> s(s(z))  ;  nn2 -> z
})

-------------------------------------------
Step 39, which took 0.047899 s (model generation: 0.046432,  model checking: 0.001467):

Model:
|_
{
delete -> 
{{{
Q={q_gen_4617, q_gen_4623, q_gen_4624, q_gen_4626, q_gen_4627},
Q_f={q_gen_4617},
Delta=
{
<cons>(q_gen_4627, q_gen_4626) -> q_gen_4626
<nil>() -> q_gen_4626
<a>() -> q_gen_4627
<b>() -> q_gen_4627
<cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4623
<cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4623
<nil, nil>() -> q_gen_4623
<a, a>() -> q_gen_4624
<a, b>() -> q_gen_4624
<b, a>() -> q_gen_4624
<b, b>() -> q_gen_4624
<a, cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4617
<a, cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4617
<a, nil, nil>() -> q_gen_4617
<b, cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4617
<b, cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4617
<b, nil, nil>() -> q_gen_4617
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_4616, q_gen_4620, q_gen_4621, q_gen_4638, q_gen_4639, q_gen_4640, q_gen_4641, q_gen_4642, q_gen_4660, q_gen_4661, q_gen_4662},
Q_f={q_gen_4616},
Delta=
{
<nil>() -> q_gen_4620
<cons>(q_gen_4639, q_gen_4620) -> q_gen_4638
<a>() -> q_gen_4639
<b>() -> q_gen_4639
<z>() -> q_gen_4641
<cons>(q_gen_4639, q_gen_4638) -> q_gen_4660
<cons>(q_gen_4639, q_gen_4660) -> q_gen_4660
<s>(q_gen_4641) -> q_gen_4662
<s>(q_gen_4662) -> q_gen_4662
<cons, s>(q_gen_4621, q_gen_4620) -> q_gen_4616
<cons, s>(q_gen_4621, q_gen_4660) -> q_gen_4616
<cons, s>(q_gen_4640, q_gen_4638) -> q_gen_4616
<cons, s>(q_gen_4661, q_gen_4660) -> q_gen_4616
<nil, z>() -> q_gen_4616
<a, s>(q_gen_4662) -> q_gen_4621
<a, z>() -> q_gen_4621
<b, z>() -> q_gen_4621
<a, s>(q_gen_4641) -> q_gen_4640
<b, s>(q_gen_4641) -> q_gen_4640
<cons, s>(q_gen_4621, q_gen_4638) -> q_gen_4642
<cons, s>(q_gen_4640, q_gen_4620) -> q_gen_4642
<cons, s>(q_gen_4640, q_gen_4660) -> q_gen_4642
<cons, s>(q_gen_4661, q_gen_4620) -> q_gen_4642
<cons, s>(q_gen_4661, q_gen_4638) -> q_gen_4642
<b, s>(q_gen_4662) -> q_gen_4661
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_4613, q_gen_4615, q_gen_4643, q_gen_4644, q_gen_4664},
Q_f={q_gen_4613},
Delta=
{
<s>(q_gen_4615) -> q_gen_4615
<z>() -> q_gen_4615
<s, s>(q_gen_4613) -> q_gen_4613
<s, s>(q_gen_4664) -> q_gen_4613
<z, s>(q_gen_4615) -> q_gen_4613
<z, z>() -> q_gen_4613
<s, s>(q_gen_4644) -> q_gen_4643
<s, z>(q_gen_4615) -> q_gen_4644
<s, s>(q_gen_4643) -> q_gen_4664
}

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

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

Teacher's answer:
New clause system:
{
() -> delete([x, nil, nil]) -> 24
() -> length([nil, z]) -> 24
() -> leq([z, s(nn2)]) -> 26
() -> leq([z, z]) -> 24
(delete([h, t, _cr])) -> delete([h, cons(h, t), _cr]) -> 24
(delete([i, l, _ir]) /\ length([_ir, _jr]) /\ length([l, _kr])) -> leq([_jr, _kr]) -> 28
(delete([x, t, _dr]) /\ not eq_elt([x, h])) -> delete([x, cons(h, t), cons(h, _dr)]) -> 25
(length([ll, _yq])) -> length([cons(x, ll), s(_yq)]) -> 28
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 24
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 29
(leq([s(nn1), z])) -> BOT -> 27
}
Sat witness: Found: ((leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]), {
nn1 -> s(s(s(z)))  ;  nn2 -> s(s(z))
})

-------------------------------------------
Step 40, which took 0.049750 s (model generation: 0.045571,  model checking: 0.004179):

Model:
|_
{
delete -> 
{{{
Q={q_gen_4617, q_gen_4623, q_gen_4624, q_gen_4626, q_gen_4627},
Q_f={q_gen_4617},
Delta=
{
<cons>(q_gen_4627, q_gen_4626) -> q_gen_4626
<nil>() -> q_gen_4626
<a>() -> q_gen_4627
<b>() -> q_gen_4627
<cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4623
<cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4623
<nil, nil>() -> q_gen_4623
<a, a>() -> q_gen_4624
<a, b>() -> q_gen_4624
<b, a>() -> q_gen_4624
<b, b>() -> q_gen_4624
<a, cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4617
<a, cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4617
<a, nil, nil>() -> q_gen_4617
<b, cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4617
<b, cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4617
<b, nil, nil>() -> q_gen_4617
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_4616, q_gen_4620, q_gen_4621, q_gen_4638, q_gen_4639, q_gen_4640, q_gen_4641, q_gen_4642, q_gen_4660, q_gen_4661, q_gen_4662, q_gen_4670, q_gen_4681},
Q_f={q_gen_4616},
Delta=
{
<cons>(q_gen_4639, q_gen_4681) -> q_gen_4620
<nil>() -> q_gen_4620
<cons>(q_gen_4639, q_gen_4620) -> q_gen_4638
<a>() -> q_gen_4639
<b>() -> q_gen_4639
<z>() -> q_gen_4641
<cons>(q_gen_4639, q_gen_4638) -> q_gen_4660
<s>(q_gen_4641) -> q_gen_4662
<s>(q_gen_4662) -> q_gen_4670
<cons>(q_gen_4639, q_gen_4660) -> q_gen_4681
<cons, s>(q_gen_4621, q_gen_4620) -> q_gen_4616
<cons, s>(q_gen_4621, q_gen_4681) -> q_gen_4616
<cons, s>(q_gen_4640, q_gen_4638) -> q_gen_4616
<cons, s>(q_gen_4661, q_gen_4660) -> q_gen_4616
<nil, z>() -> q_gen_4616
<a, s>(q_gen_4670) -> q_gen_4621
<a, z>() -> q_gen_4621
<b, s>(q_gen_4670) -> q_gen_4621
<b, z>() -> q_gen_4621
<a, s>(q_gen_4641) -> q_gen_4640
<b, s>(q_gen_4641) -> q_gen_4640
<cons, s>(q_gen_4621, q_gen_4638) -> q_gen_4642
<cons, s>(q_gen_4621, q_gen_4660) -> q_gen_4642
<cons, s>(q_gen_4640, q_gen_4620) -> q_gen_4642
<cons, s>(q_gen_4661, q_gen_4620) -> q_gen_4642
<cons, s>(q_gen_4661, q_gen_4638) -> q_gen_4642
<b, s>(q_gen_4662) -> q_gen_4661
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_4613, q_gen_4615, q_gen_4643},
Q_f={q_gen_4613},
Delta=
{
<s>(q_gen_4615) -> q_gen_4615
<z>() -> q_gen_4615
<s, s>(q_gen_4613) -> q_gen_4613
<z, s>(q_gen_4615) -> q_gen_4613
<z, z>() -> q_gen_4613
<s, s>(q_gen_4643) -> q_gen_4643
<s, z>(q_gen_4615) -> q_gen_4643
}

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

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

Teacher's answer:
New clause system:
{
() -> delete([x, nil, nil]) -> 25
() -> length([nil, z]) -> 25
() -> leq([z, s(nn2)]) -> 27
() -> leq([z, z]) -> 25
(delete([h, t, _cr])) -> delete([h, cons(h, t), _cr]) -> 25
(delete([i, l, _ir]) /\ length([_ir, _jr]) /\ length([l, _kr])) -> leq([_jr, _kr]) -> 28
(delete([x, t, _dr]) /\ not eq_elt([x, h])) -> delete([x, cons(h, t), cons(h, _dr)]) -> 26
(length([ll, _yq])) -> length([cons(x, ll), s(_yq)]) -> 31
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 25
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 29
(leq([s(nn1), z])) -> BOT -> 28
}
Sat witness: Found: ((length([ll, _yq])) -> length([cons(x, ll), s(_yq)]), {
_yq -> s(z)  ;  ll -> cons(b, cons(b, cons(a, cons(b, nil))))  ;  x -> a
})

-------------------------------------------
Step 41, which took 0.057878 s (model generation: 0.055530,  model checking: 0.002348):

Model:
|_
{
delete -> 
{{{
Q={q_gen_4617, q_gen_4623, q_gen_4624, q_gen_4626, q_gen_4627},
Q_f={q_gen_4617},
Delta=
{
<cons>(q_gen_4627, q_gen_4626) -> q_gen_4626
<nil>() -> q_gen_4626
<a>() -> q_gen_4627
<b>() -> q_gen_4627
<cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4623
<cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4623
<nil, nil>() -> q_gen_4623
<a, a>() -> q_gen_4624
<a, b>() -> q_gen_4624
<b, a>() -> q_gen_4624
<b, b>() -> q_gen_4624
<a, cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4617
<a, cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4617
<a, nil, nil>() -> q_gen_4617
<b, cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4617
<b, cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4617
<b, nil, nil>() -> q_gen_4617
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_4616, q_gen_4620, q_gen_4621, q_gen_4638, q_gen_4639, q_gen_4640, q_gen_4641, q_gen_4642, q_gen_4660, q_gen_4661, q_gen_4662, q_gen_4670, q_gen_4673},
Q_f={q_gen_4616},
Delta=
{
<cons>(q_gen_4673, q_gen_4638) -> q_gen_4620
<nil>() -> q_gen_4620
<cons>(q_gen_4639, q_gen_4620) -> q_gen_4638
<cons>(q_gen_4673, q_gen_4620) -> q_gen_4638
<b>() -> q_gen_4639
<z>() -> q_gen_4641
<cons>(q_gen_4639, q_gen_4638) -> q_gen_4660
<cons>(q_gen_4639, q_gen_4660) -> q_gen_4660
<s>(q_gen_4641) -> q_gen_4662
<s>(q_gen_4662) -> q_gen_4670
<a>() -> q_gen_4673
<cons, s>(q_gen_4621, q_gen_4620) -> q_gen_4616
<cons, s>(q_gen_4640, q_gen_4638) -> q_gen_4616
<cons, s>(q_gen_4661, q_gen_4660) -> q_gen_4616
<nil, z>() -> q_gen_4616
<a, s>(q_gen_4670) -> q_gen_4621
<a, z>() -> q_gen_4621
<b, s>(q_gen_4670) -> q_gen_4621
<b, z>() -> q_gen_4621
<a, s>(q_gen_4641) -> q_gen_4640
<b, s>(q_gen_4641) -> q_gen_4640
<cons, s>(q_gen_4621, q_gen_4638) -> q_gen_4642
<cons, s>(q_gen_4621, q_gen_4660) -> q_gen_4642
<cons, s>(q_gen_4640, q_gen_4620) -> q_gen_4642
<cons, s>(q_gen_4640, q_gen_4660) -> q_gen_4642
<cons, s>(q_gen_4661, q_gen_4620) -> q_gen_4642
<cons, s>(q_gen_4661, q_gen_4638) -> q_gen_4642
<b, s>(q_gen_4662) -> q_gen_4661
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_4613, q_gen_4615, q_gen_4643},
Q_f={q_gen_4613},
Delta=
{
<s>(q_gen_4615) -> q_gen_4615
<z>() -> q_gen_4615
<s, s>(q_gen_4613) -> q_gen_4613
<z, s>(q_gen_4615) -> q_gen_4613
<z, z>() -> q_gen_4613
<s, s>(q_gen_4643) -> q_gen_4643
<s, z>(q_gen_4615) -> q_gen_4643
}

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

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

Teacher's answer:
New clause system:
{
() -> delete([x, nil, nil]) -> 26
() -> length([nil, z]) -> 26
() -> leq([z, s(nn2)]) -> 28
() -> leq([z, z]) -> 26
(delete([h, t, _cr])) -> delete([h, cons(h, t), _cr]) -> 26
(delete([i, l, _ir]) /\ length([_ir, _jr]) /\ length([l, _kr])) -> leq([_jr, _kr]) -> 31
(delete([x, t, _dr]) /\ not eq_elt([x, h])) -> delete([x, cons(h, t), cons(h, _dr)]) -> 27
(length([ll, _yq])) -> length([cons(x, ll), s(_yq)]) -> 31
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 26
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 29
(leq([s(nn1), z])) -> BOT -> 29
}
Sat witness: Found: ((delete([i, l, _ir]) /\ length([_ir, _jr]) /\ length([l, _kr])) -> leq([_jr, _kr]), {
_ir -> cons(b, nil)  ;  _jr -> s(s(s(s(z))))  ;  _kr -> s(s(s(z)))  ;  i -> a  ;  l -> cons(b, cons(b, cons(a, nil)))
})

-------------------------------------------
Step 42, which took 0.065646 s (model generation: 0.064196,  model checking: 0.001450):

Model:
|_
{
delete -> 
{{{
Q={q_gen_4617, q_gen_4623, q_gen_4624, q_gen_4626, q_gen_4627},
Q_f={q_gen_4617},
Delta=
{
<cons>(q_gen_4627, q_gen_4626) -> q_gen_4626
<nil>() -> q_gen_4626
<a>() -> q_gen_4627
<b>() -> q_gen_4627
<cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4623
<cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4623
<nil, nil>() -> q_gen_4623
<a, a>() -> q_gen_4624
<a, b>() -> q_gen_4624
<b, a>() -> q_gen_4624
<b, b>() -> q_gen_4624
<a, cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4617
<a, cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4617
<a, nil, nil>() -> q_gen_4617
<b, cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4617
<b, cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4617
<b, nil, nil>() -> q_gen_4617
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_4616, q_gen_4620, q_gen_4621, q_gen_4638, q_gen_4639, q_gen_4640, q_gen_4641, q_gen_4642, q_gen_4660, q_gen_4661, q_gen_4662},
Q_f={q_gen_4616},
Delta=
{
<nil>() -> q_gen_4620
<cons>(q_gen_4639, q_gen_4620) -> q_gen_4638
<cons>(q_gen_4639, q_gen_4660) -> q_gen_4638
<a>() -> q_gen_4639
<b>() -> q_gen_4639
<s>(q_gen_4662) -> q_gen_4641
<z>() -> q_gen_4641
<cons>(q_gen_4639, q_gen_4638) -> q_gen_4660
<s>(q_gen_4641) -> q_gen_4662
<cons, s>(q_gen_4621, q_gen_4620) -> q_gen_4616
<cons, s>(q_gen_4640, q_gen_4638) -> q_gen_4616
<cons, s>(q_gen_4661, q_gen_4660) -> q_gen_4616
<nil, z>() -> q_gen_4616
<a, z>() -> q_gen_4621
<b, z>() -> q_gen_4621
<a, s>(q_gen_4641) -> q_gen_4640
<b, s>(q_gen_4641) -> q_gen_4640
<cons, s>(q_gen_4621, q_gen_4638) -> q_gen_4642
<cons, s>(q_gen_4640, q_gen_4620) -> q_gen_4642
<cons, s>(q_gen_4640, q_gen_4660) -> q_gen_4642
<cons, s>(q_gen_4661, q_gen_4620) -> q_gen_4642
<cons, s>(q_gen_4661, q_gen_4638) -> q_gen_4642
<b, s>(q_gen_4662) -> q_gen_4661
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_4613, q_gen_4615, q_gen_4629, q_gen_4643, q_gen_4684, q_gen_4685},
Q_f={q_gen_4613},
Delta=
{
<z>() -> q_gen_4615
<s>(q_gen_4615) -> q_gen_4629
<s>(q_gen_4629) -> q_gen_4629
<s, s>(q_gen_4613) -> q_gen_4613
<s, s>(q_gen_4684) -> q_gen_4613
<z, s>(q_gen_4615) -> q_gen_4613
<z, s>(q_gen_4629) -> q_gen_4613
<z, z>() -> q_gen_4613
<s, s>(q_gen_4643) -> q_gen_4643
<s, z>(q_gen_4615) -> q_gen_4643
<s, s>(q_gen_4685) -> q_gen_4684
<s, z>(q_gen_4629) -> q_gen_4685
}

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

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

Teacher's answer:
New clause system:
{
() -> delete([x, nil, nil]) -> 27
() -> length([nil, z]) -> 27
() -> leq([z, s(nn2)]) -> 29
() -> leq([z, z]) -> 27
(delete([h, t, _cr])) -> delete([h, cons(h, t), _cr]) -> 27
(delete([i, l, _ir]) /\ length([_ir, _jr]) /\ length([l, _kr])) -> leq([_jr, _kr]) -> 31
(delete([x, t, _dr]) /\ not eq_elt([x, h])) -> delete([x, cons(h, t), cons(h, _dr)]) -> 28
(length([ll, _yq])) -> length([cons(x, ll), s(_yq)]) -> 31
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 27
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 32
(leq([s(nn1), z])) -> BOT -> 30
}
Sat witness: Found: ((leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]), {
nn1 -> s(s(s(z)))  ;  nn2 -> s(z)
})

-------------------------------------------
Step 43, which took 0.062736 s (model generation: 0.062201,  model checking: 0.000535):

Model:
|_
{
delete -> 
{{{
Q={q_gen_4617, q_gen_4623, q_gen_4624, q_gen_4626, q_gen_4627, q_gen_4646, q_gen_4674, q_gen_4675},
Q_f={q_gen_4617},
Delta=
{
<cons>(q_gen_4627, q_gen_4626) -> q_gen_4626
<nil>() -> q_gen_4626
<a>() -> q_gen_4627
<b>() -> q_gen_4627
<nil, nil>() -> q_gen_4623
<a, a>() -> q_gen_4624
<a, b>() -> q_gen_4624
<b, a>() -> q_gen_4624
<b, b>() -> q_gen_4624
<cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4646
<cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4646
<cons, cons>(q_gen_4624, q_gen_4646) -> q_gen_4675
<cons, cons>(q_gen_4624, q_gen_4675) -> q_gen_4675
<a, cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4617
<a, cons, cons>(q_gen_4624, q_gen_4646) -> q_gen_4617
<a, cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4617
<a, nil, nil>() -> q_gen_4617
<b, cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4617
<b, cons, cons>(q_gen_4624, q_gen_4646) -> q_gen_4617
<b, cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4617
<b, nil, nil>() -> q_gen_4617
<a, cons, cons>(q_gen_4624, q_gen_4675) -> q_gen_4674
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_4616, q_gen_4620, q_gen_4621, q_gen_4638, q_gen_4639, q_gen_4640, q_gen_4641, q_gen_4642, q_gen_4660, q_gen_4661, q_gen_4662},
Q_f={q_gen_4616},
Delta=
{
<nil>() -> q_gen_4620
<cons>(q_gen_4639, q_gen_4620) -> q_gen_4638
<a>() -> q_gen_4639
<b>() -> q_gen_4639
<z>() -> q_gen_4641
<cons>(q_gen_4639, q_gen_4638) -> q_gen_4660
<cons>(q_gen_4639, q_gen_4660) -> q_gen_4660
<s>(q_gen_4641) -> q_gen_4662
<s>(q_gen_4662) -> q_gen_4662
<cons, s>(q_gen_4621, q_gen_4620) -> q_gen_4616
<cons, s>(q_gen_4640, q_gen_4638) -> q_gen_4616
<cons, s>(q_gen_4640, q_gen_4660) -> q_gen_4616
<cons, s>(q_gen_4661, q_gen_4660) -> q_gen_4616
<nil, z>() -> q_gen_4616
<a, z>() -> q_gen_4621
<b, z>() -> q_gen_4621
<a, s>(q_gen_4641) -> q_gen_4640
<b, s>(q_gen_4641) -> q_gen_4640
<cons, s>(q_gen_4621, q_gen_4638) -> q_gen_4642
<cons, s>(q_gen_4621, q_gen_4660) -> q_gen_4642
<cons, s>(q_gen_4640, q_gen_4620) -> q_gen_4642
<cons, s>(q_gen_4661, q_gen_4620) -> q_gen_4642
<cons, s>(q_gen_4661, q_gen_4638) -> q_gen_4642
<a, s>(q_gen_4662) -> q_gen_4661
<b, s>(q_gen_4662) -> q_gen_4661
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_4613, q_gen_4615, q_gen_4643},
Q_f={q_gen_4613},
Delta=
{
<s>(q_gen_4615) -> q_gen_4615
<z>() -> q_gen_4615
<s, s>(q_gen_4613) -> q_gen_4613
<z, s>(q_gen_4615) -> q_gen_4613
<z, z>() -> q_gen_4613
<s, s>(q_gen_4643) -> q_gen_4643
<s, z>(q_gen_4615) -> q_gen_4643
}

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

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

Teacher's answer:
New clause system:
{
() -> delete([x, nil, nil]) -> 27
() -> length([nil, z]) -> 27
() -> leq([z, s(nn2)]) -> 29
() -> leq([z, z]) -> 27
(delete([h, t, _cr])) -> delete([h, cons(h, t), _cr]) -> 30
(delete([i, l, _ir]) /\ length([_ir, _jr]) /\ length([l, _kr])) -> leq([_jr, _kr]) -> 31
(delete([x, t, _dr]) /\ not eq_elt([x, h])) -> delete([x, cons(h, t), cons(h, _dr)]) -> 28
(length([ll, _yq])) -> length([cons(x, ll), s(_yq)]) -> 31
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 28
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 32
(leq([s(nn1), z])) -> BOT -> 30
}
Sat witness: Found: ((delete([h, t, _cr])) -> delete([h, cons(h, t), _cr]), {
_cr -> cons(b, cons(b, nil))  ;  h -> a  ;  t -> cons(a, cons(a, nil))
})

-------------------------------------------
Step 44, which took 0.069511 s (model generation: 0.068414,  model checking: 0.001097):

Model:
|_
{
delete -> 
{{{
Q={q_gen_4617, q_gen_4623, q_gen_4624, q_gen_4626, q_gen_4627, q_gen_4653, q_gen_4674, q_gen_4675},
Q_f={q_gen_4617},
Delta=
{
<cons>(q_gen_4627, q_gen_4626) -> q_gen_4626
<nil>() -> q_gen_4626
<a>() -> q_gen_4627
<b>() -> q_gen_4627
<cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4623
<nil, nil>() -> q_gen_4623
<a, a>() -> q_gen_4624
<a, b>() -> q_gen_4624
<b, a>() -> q_gen_4624
<b, b>() -> q_gen_4624
<cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4653
<cons, cons>(q_gen_4624, q_gen_4653) -> q_gen_4675
<a, cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4617
<a, cons, cons>(q_gen_4624, q_gen_4653) -> q_gen_4617
<a, cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4617
<a, nil, nil>() -> q_gen_4617
<b, cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4617
<b, cons, cons>(q_gen_4624, q_gen_4653) -> q_gen_4617
<b, cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4617
<b, nil, nil>() -> q_gen_4617
<a, cons, cons>(q_gen_4624, q_gen_4675) -> q_gen_4674
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_4616, q_gen_4620, q_gen_4621, q_gen_4638, q_gen_4639, q_gen_4640, q_gen_4641, q_gen_4642, q_gen_4660, q_gen_4661, q_gen_4662},
Q_f={q_gen_4616},
Delta=
{
<nil>() -> q_gen_4620
<cons>(q_gen_4639, q_gen_4620) -> q_gen_4638
<a>() -> q_gen_4639
<b>() -> q_gen_4639
<z>() -> q_gen_4641
<cons>(q_gen_4639, q_gen_4638) -> q_gen_4660
<cons>(q_gen_4639, q_gen_4660) -> q_gen_4660
<s>(q_gen_4641) -> q_gen_4662
<s>(q_gen_4662) -> q_gen_4662
<cons, s>(q_gen_4621, q_gen_4620) -> q_gen_4616
<cons, s>(q_gen_4640, q_gen_4638) -> q_gen_4616
<cons, s>(q_gen_4640, q_gen_4660) -> q_gen_4616
<cons, s>(q_gen_4661, q_gen_4660) -> q_gen_4616
<nil, z>() -> q_gen_4616
<a, z>() -> q_gen_4621
<b, z>() -> q_gen_4621
<a, s>(q_gen_4641) -> q_gen_4640
<b, s>(q_gen_4641) -> q_gen_4640
<cons, s>(q_gen_4621, q_gen_4638) -> q_gen_4642
<cons, s>(q_gen_4621, q_gen_4660) -> q_gen_4642
<cons, s>(q_gen_4640, q_gen_4620) -> q_gen_4642
<cons, s>(q_gen_4661, q_gen_4620) -> q_gen_4642
<cons, s>(q_gen_4661, q_gen_4638) -> q_gen_4642
<a, s>(q_gen_4662) -> q_gen_4661
<b, s>(q_gen_4662) -> q_gen_4661
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_4613, q_gen_4615, q_gen_4643},
Q_f={q_gen_4613},
Delta=
{
<s>(q_gen_4615) -> q_gen_4615
<z>() -> q_gen_4615
<s, s>(q_gen_4613) -> q_gen_4613
<z, s>(q_gen_4615) -> q_gen_4613
<z, z>() -> q_gen_4613
<s, s>(q_gen_4643) -> q_gen_4643
<s, z>(q_gen_4615) -> q_gen_4643
}

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

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

Teacher's answer:
New clause system:
{
() -> delete([x, nil, nil]) -> 28
() -> length([nil, z]) -> 28
() -> leq([z, s(nn2)]) -> 29
() -> leq([z, z]) -> 28
(delete([h, t, _cr])) -> delete([h, cons(h, t), _cr]) -> 30
(delete([i, l, _ir]) /\ length([_ir, _jr]) /\ length([l, _kr])) -> leq([_jr, _kr]) -> 31
(delete([x, t, _dr]) /\ not eq_elt([x, h])) -> delete([x, cons(h, t), cons(h, _dr)]) -> 31
(length([ll, _yq])) -> length([cons(x, ll), s(_yq)]) -> 31
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 29
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 32
(leq([s(nn1), z])) -> BOT -> 30
}
Sat witness: Found: ((delete([x, t, _dr]) /\ not eq_elt([x, h])) -> delete([x, cons(h, t), cons(h, _dr)]), {
_dr -> cons(b, cons(b, nil))  ;  h -> b  ;  t -> cons(b, cons(b, nil))  ;  x -> a
})

-------------------------------------------
Step 45, which took 0.067583 s (model generation: 0.064025,  model checking: 0.003558):

Model:
|_
{
delete -> 
{{{
Q={q_gen_4617, q_gen_4623, q_gen_4624, q_gen_4626, q_gen_4627},
Q_f={q_gen_4617},
Delta=
{
<cons>(q_gen_4627, q_gen_4626) -> q_gen_4626
<nil>() -> q_gen_4626
<a>() -> q_gen_4627
<b>() -> q_gen_4627
<cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4623
<cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4623
<nil, nil>() -> q_gen_4623
<a, a>() -> q_gen_4624
<a, b>() -> q_gen_4624
<b, a>() -> q_gen_4624
<b, b>() -> q_gen_4624
<a, cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4617
<a, cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4617
<a, nil, nil>() -> q_gen_4617
<b, cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4617
<b, cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4617
<b, nil, nil>() -> q_gen_4617
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_4616, q_gen_4620, q_gen_4621, q_gen_4638, q_gen_4639, q_gen_4640, q_gen_4641, q_gen_4642, q_gen_4660, q_gen_4661, q_gen_4662, q_gen_4670, q_gen_4673, q_gen_4679},
Q_f={q_gen_4616},
Delta=
{
<nil>() -> q_gen_4620
<cons>(q_gen_4639, q_gen_4620) -> q_gen_4638
<b>() -> q_gen_4639
<z>() -> q_gen_4641
<cons>(q_gen_4639, q_gen_4638) -> q_gen_4660
<cons>(q_gen_4673, q_gen_4620) -> q_gen_4660
<s>(q_gen_4641) -> q_gen_4662
<s>(q_gen_4662) -> q_gen_4670
<a>() -> q_gen_4673
<cons>(q_gen_4639, q_gen_4660) -> q_gen_4679
<cons>(q_gen_4639, q_gen_4679) -> q_gen_4679
<cons>(q_gen_4673, q_gen_4638) -> q_gen_4679
<cons, s>(q_gen_4621, q_gen_4620) -> q_gen_4616
<cons, s>(q_gen_4640, q_gen_4638) -> q_gen_4616
<cons, s>(q_gen_4640, q_gen_4660) -> q_gen_4616
<cons, s>(q_gen_4661, q_gen_4660) -> q_gen_4616
<nil, z>() -> q_gen_4616
<a, z>() -> q_gen_4621
<b, s>(q_gen_4670) -> q_gen_4621
<b, z>() -> q_gen_4621
<a, s>(q_gen_4641) -> q_gen_4640
<a, s>(q_gen_4670) -> q_gen_4640
<b, s>(q_gen_4641) -> q_gen_4640
<cons, s>(q_gen_4621, q_gen_4638) -> q_gen_4642
<cons, s>(q_gen_4621, q_gen_4660) -> q_gen_4642
<cons, s>(q_gen_4621, q_gen_4679) -> q_gen_4642
<cons, s>(q_gen_4640, q_gen_4620) -> q_gen_4642
<cons, s>(q_gen_4640, q_gen_4679) -> q_gen_4642
<cons, s>(q_gen_4661, q_gen_4620) -> q_gen_4642
<cons, s>(q_gen_4661, q_gen_4638) -> q_gen_4642
<cons, s>(q_gen_4661, q_gen_4679) -> q_gen_4642
<b, s>(q_gen_4662) -> q_gen_4661
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_4613, q_gen_4615, q_gen_4643},
Q_f={q_gen_4613},
Delta=
{
<s>(q_gen_4615) -> q_gen_4615
<z>() -> q_gen_4615
<s, s>(q_gen_4613) -> q_gen_4613
<z, s>(q_gen_4615) -> q_gen_4613
<z, z>() -> q_gen_4613
<s, s>(q_gen_4643) -> q_gen_4643
<s, z>(q_gen_4615) -> q_gen_4643
}

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

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

Teacher's answer:
New clause system:
{
() -> delete([x, nil, nil]) -> 29
() -> length([nil, z]) -> 29
() -> leq([z, s(nn2)]) -> 30
() -> leq([z, z]) -> 29
(delete([h, t, _cr])) -> delete([h, cons(h, t), _cr]) -> 31
(delete([i, l, _ir]) /\ length([_ir, _jr]) /\ length([l, _kr])) -> leq([_jr, _kr]) -> 31
(delete([x, t, _dr]) /\ not eq_elt([x, h])) -> delete([x, cons(h, t), cons(h, _dr)]) -> 31
(length([ll, _yq])) -> length([cons(x, ll), s(_yq)]) -> 34
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 30
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 32
(leq([s(nn1), z])) -> BOT -> 31
}
Sat witness: Found: ((length([ll, _yq])) -> length([cons(x, ll), s(_yq)]), {
_yq -> s(s(s(z)))  ;  ll -> cons(b, cons(b, cons(b, nil)))  ;  x -> b
})

-------------------------------------------
Step 46, which took 0.073991 s (model generation: 0.070177,  model checking: 0.003814):

Model:
|_
{
delete -> 
{{{
Q={q_gen_4617, q_gen_4623, q_gen_4624, q_gen_4626, q_gen_4627},
Q_f={q_gen_4617},
Delta=
{
<cons>(q_gen_4627, q_gen_4626) -> q_gen_4626
<nil>() -> q_gen_4626
<a>() -> q_gen_4627
<b>() -> q_gen_4627
<cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4623
<cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4623
<nil, nil>() -> q_gen_4623
<a, a>() -> q_gen_4624
<a, b>() -> q_gen_4624
<b, a>() -> q_gen_4624
<b, b>() -> q_gen_4624
<a, cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4617
<a, cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4617
<a, nil, nil>() -> q_gen_4617
<b, cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4617
<b, cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4617
<b, nil, nil>() -> q_gen_4617
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_4616, q_gen_4620, q_gen_4621, q_gen_4638, q_gen_4639, q_gen_4640, q_gen_4641, q_gen_4642, q_gen_4660, q_gen_4661, q_gen_4662, q_gen_4670, q_gen_4673, q_gen_4694},
Q_f={q_gen_4616},
Delta=
{
<nil>() -> q_gen_4620
<cons>(q_gen_4639, q_gen_4620) -> q_gen_4638
<cons>(q_gen_4673, q_gen_4638) -> q_gen_4638
<b>() -> q_gen_4639
<z>() -> q_gen_4641
<cons>(q_gen_4639, q_gen_4638) -> q_gen_4660
<cons>(q_gen_4673, q_gen_4620) -> q_gen_4660
<s>(q_gen_4641) -> q_gen_4662
<s>(q_gen_4662) -> q_gen_4670
<a>() -> q_gen_4673
<cons>(q_gen_4639, q_gen_4660) -> q_gen_4694
<cons>(q_gen_4639, q_gen_4694) -> q_gen_4694
<cons, s>(q_gen_4621, q_gen_4620) -> q_gen_4616
<cons, s>(q_gen_4621, q_gen_4694) -> q_gen_4616
<cons, s>(q_gen_4640, q_gen_4638) -> q_gen_4616
<cons, s>(q_gen_4640, q_gen_4660) -> q_gen_4616
<cons, s>(q_gen_4661, q_gen_4660) -> q_gen_4616
<nil, z>() -> q_gen_4616
<a, s>(q_gen_4670) -> q_gen_4621
<a, z>() -> q_gen_4621
<b, s>(q_gen_4670) -> q_gen_4621
<b, z>() -> q_gen_4621
<a, s>(q_gen_4641) -> q_gen_4640
<b, s>(q_gen_4641) -> q_gen_4640
<cons, s>(q_gen_4621, q_gen_4638) -> q_gen_4642
<cons, s>(q_gen_4621, q_gen_4660) -> q_gen_4642
<cons, s>(q_gen_4640, q_gen_4620) -> q_gen_4642
<cons, s>(q_gen_4640, q_gen_4694) -> q_gen_4642
<cons, s>(q_gen_4661, q_gen_4620) -> q_gen_4642
<cons, s>(q_gen_4661, q_gen_4638) -> q_gen_4642
<cons, s>(q_gen_4661, q_gen_4694) -> q_gen_4642
<b, s>(q_gen_4662) -> q_gen_4661
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_4613, q_gen_4615, q_gen_4643},
Q_f={q_gen_4613},
Delta=
{
<s>(q_gen_4615) -> q_gen_4615
<z>() -> q_gen_4615
<s, s>(q_gen_4613) -> q_gen_4613
<z, s>(q_gen_4615) -> q_gen_4613
<z, z>() -> q_gen_4613
<s, s>(q_gen_4643) -> q_gen_4643
<s, z>(q_gen_4615) -> q_gen_4643
}

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

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

Teacher's answer:
New clause system:
{
() -> delete([x, nil, nil]) -> 30
() -> length([nil, z]) -> 30
() -> leq([z, s(nn2)]) -> 31
() -> leq([z, z]) -> 30
(delete([h, t, _cr])) -> delete([h, cons(h, t), _cr]) -> 31
(delete([i, l, _ir]) /\ length([_ir, _jr]) /\ length([l, _kr])) -> leq([_jr, _kr]) -> 34
(delete([x, t, _dr]) /\ not eq_elt([x, h])) -> delete([x, cons(h, t), cons(h, _dr)]) -> 32
(length([ll, _yq])) -> length([cons(x, ll), s(_yq)]) -> 34
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 31
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 32
(leq([s(nn1), z])) -> BOT -> 32
}
Sat witness: Found: ((delete([i, l, _ir]) /\ length([_ir, _jr]) /\ length([l, _kr])) -> leq([_jr, _kr]), {
_ir -> cons(b, nil)  ;  _jr -> s(s(s(s(z))))  ;  _kr -> s(s(z))  ;  i -> a  ;  l -> cons(a, cons(b, nil))
})

-------------------------------------------
Step 47, which took 0.068825 s (model generation: 0.063083,  model checking: 0.005742):

Model:
|_
{
delete -> 
{{{
Q={q_gen_4617, q_gen_4623, q_gen_4624, q_gen_4626, q_gen_4627},
Q_f={q_gen_4617},
Delta=
{
<cons>(q_gen_4627, q_gen_4626) -> q_gen_4626
<nil>() -> q_gen_4626
<a>() -> q_gen_4627
<b>() -> q_gen_4627
<cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4623
<cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4623
<nil, nil>() -> q_gen_4623
<a, a>() -> q_gen_4624
<a, b>() -> q_gen_4624
<b, a>() -> q_gen_4624
<b, b>() -> q_gen_4624
<a, cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4617
<a, cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4617
<a, nil, nil>() -> q_gen_4617
<b, cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4617
<b, cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4617
<b, nil, nil>() -> q_gen_4617
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_4616, q_gen_4620, q_gen_4621, q_gen_4638, q_gen_4639, q_gen_4640, q_gen_4641, q_gen_4642, q_gen_4660, q_gen_4661, q_gen_4662, q_gen_4669, q_gen_4670, q_gen_4681},
Q_f={q_gen_4616},
Delta=
{
<cons>(q_gen_4639, q_gen_4681) -> q_gen_4620
<nil>() -> q_gen_4620
<cons>(q_gen_4639, q_gen_4620) -> q_gen_4638
<a>() -> q_gen_4639
<b>() -> q_gen_4639
<z>() -> q_gen_4641
<cons>(q_gen_4639, q_gen_4638) -> q_gen_4660
<s>(q_gen_4641) -> q_gen_4662
<s>(q_gen_4662) -> q_gen_4670
<cons>(q_gen_4639, q_gen_4660) -> q_gen_4681
<cons, s>(q_gen_4621, q_gen_4620) -> q_gen_4616
<cons, s>(q_gen_4640, q_gen_4638) -> q_gen_4616
<cons, s>(q_gen_4661, q_gen_4660) -> q_gen_4616
<cons, s>(q_gen_4661, q_gen_4681) -> q_gen_4616
<cons, s>(q_gen_4669, q_gen_4681) -> q_gen_4616
<nil, z>() -> q_gen_4616
<a, z>() -> q_gen_4621
<b, z>() -> q_gen_4621
<a, s>(q_gen_4641) -> q_gen_4640
<b, s>(q_gen_4641) -> q_gen_4640
<cons, s>(q_gen_4621, q_gen_4638) -> q_gen_4642
<cons, s>(q_gen_4621, q_gen_4681) -> q_gen_4642
<cons, s>(q_gen_4640, q_gen_4620) -> q_gen_4642
<cons, s>(q_gen_4661, q_gen_4620) -> q_gen_4642
<cons, s>(q_gen_4661, q_gen_4638) -> q_gen_4642
<cons, s>(q_gen_4669, q_gen_4620) -> q_gen_4642
<cons, s>(q_gen_4669, q_gen_4638) -> q_gen_4642
<cons, s>(q_gen_4669, q_gen_4660) -> q_gen_4642
<a, s>(q_gen_4670) -> q_gen_4661
<b, s>(q_gen_4662) -> q_gen_4661
<b, s>(q_gen_4670) -> q_gen_4669
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_4613, q_gen_4615, q_gen_4643},
Q_f={q_gen_4613},
Delta=
{
<s>(q_gen_4615) -> q_gen_4615
<z>() -> q_gen_4615
<s, s>(q_gen_4613) -> q_gen_4613
<z, s>(q_gen_4615) -> q_gen_4613
<z, z>() -> q_gen_4613
<s, s>(q_gen_4643) -> q_gen_4643
<s, z>(q_gen_4615) -> q_gen_4643
}

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

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

Teacher's answer:
New clause system:
{
() -> delete([x, nil, nil]) -> 31
() -> length([nil, z]) -> 31
() -> leq([z, s(nn2)]) -> 32
() -> leq([z, z]) -> 31
(delete([h, t, _cr])) -> delete([h, cons(h, t), _cr]) -> 32
(delete([i, l, _ir]) /\ length([_ir, _jr]) /\ length([l, _kr])) -> leq([_jr, _kr]) -> 34
(delete([x, t, _dr]) /\ not eq_elt([x, h])) -> delete([x, cons(h, t), cons(h, _dr)]) -> 33
(length([ll, _yq])) -> length([cons(x, ll), s(_yq)]) -> 37
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 32
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 33
(leq([s(nn1), z])) -> BOT -> 33
}
Sat witness: Found: ((length([ll, _yq])) -> length([cons(x, ll), s(_yq)]), {
_yq -> s(s(s(z)))  ;  ll -> cons(b, cons(b, cons(a, cons(b, nil))))  ;  x -> a
})

-------------------------------------------
Step 48, which took 0.079461 s (model generation: 0.074420,  model checking: 0.005041):

Model:
|_
{
delete -> 
{{{
Q={q_gen_4617, q_gen_4623, q_gen_4624, q_gen_4626, q_gen_4627},
Q_f={q_gen_4617},
Delta=
{
<cons>(q_gen_4627, q_gen_4626) -> q_gen_4626
<nil>() -> q_gen_4626
<a>() -> q_gen_4627
<b>() -> q_gen_4627
<cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4623
<cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4623
<nil, nil>() -> q_gen_4623
<a, a>() -> q_gen_4624
<a, b>() -> q_gen_4624
<b, a>() -> q_gen_4624
<b, b>() -> q_gen_4624
<a, cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4617
<a, cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4617
<a, nil, nil>() -> q_gen_4617
<b, cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4617
<b, cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4617
<b, nil, nil>() -> q_gen_4617
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_4616, q_gen_4620, q_gen_4621, q_gen_4638, q_gen_4639, q_gen_4640, q_gen_4641, q_gen_4642, q_gen_4660, q_gen_4661, q_gen_4662, q_gen_4669, q_gen_4670, q_gen_4681},
Q_f={q_gen_4616},
Delta=
{
<nil>() -> q_gen_4620
<cons>(q_gen_4639, q_gen_4620) -> q_gen_4638
<a>() -> q_gen_4639
<b>() -> q_gen_4639
<z>() -> q_gen_4641
<cons>(q_gen_4639, q_gen_4638) -> q_gen_4660
<s>(q_gen_4641) -> q_gen_4662
<s>(q_gen_4662) -> q_gen_4670
<cons>(q_gen_4639, q_gen_4660) -> q_gen_4681
<cons>(q_gen_4639, q_gen_4681) -> q_gen_4681
<cons, s>(q_gen_4621, q_gen_4620) -> q_gen_4616
<cons, s>(q_gen_4640, q_gen_4638) -> q_gen_4616
<cons, s>(q_gen_4661, q_gen_4660) -> q_gen_4616
<cons, s>(q_gen_4661, q_gen_4681) -> q_gen_4616
<cons, s>(q_gen_4669, q_gen_4681) -> q_gen_4616
<nil, z>() -> q_gen_4616
<a, z>() -> q_gen_4621
<b, z>() -> q_gen_4621
<a, s>(q_gen_4641) -> q_gen_4640
<b, s>(q_gen_4641) -> q_gen_4640
<cons, s>(q_gen_4621, q_gen_4638) -> q_gen_4642
<cons, s>(q_gen_4621, q_gen_4681) -> q_gen_4642
<cons, s>(q_gen_4640, q_gen_4620) -> q_gen_4642
<cons, s>(q_gen_4640, q_gen_4681) -> q_gen_4642
<cons, s>(q_gen_4661, q_gen_4620) -> q_gen_4642
<cons, s>(q_gen_4661, q_gen_4638) -> q_gen_4642
<cons, s>(q_gen_4669, q_gen_4620) -> q_gen_4642
<cons, s>(q_gen_4669, q_gen_4638) -> q_gen_4642
<cons, s>(q_gen_4669, q_gen_4660) -> q_gen_4642
<a, s>(q_gen_4670) -> q_gen_4661
<b, s>(q_gen_4662) -> q_gen_4661
<b, s>(q_gen_4670) -> q_gen_4669
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_4613, q_gen_4615, q_gen_4643},
Q_f={q_gen_4613},
Delta=
{
<s>(q_gen_4615) -> q_gen_4615
<z>() -> q_gen_4615
<s, s>(q_gen_4613) -> q_gen_4613
<z, s>(q_gen_4615) -> q_gen_4613
<z, z>() -> q_gen_4613
<s, s>(q_gen_4643) -> q_gen_4643
<s, z>(q_gen_4615) -> q_gen_4643
}

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

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

Teacher's answer:
New clause system:
{
() -> delete([x, nil, nil]) -> 32
() -> length([nil, z]) -> 32
() -> leq([z, s(nn2)]) -> 33
() -> leq([z, z]) -> 32
(delete([h, t, _cr])) -> delete([h, cons(h, t), _cr]) -> 33
(delete([i, l, _ir]) /\ length([_ir, _jr]) /\ length([l, _kr])) -> leq([_jr, _kr]) -> 37
(delete([x, t, _dr]) /\ not eq_elt([x, h])) -> delete([x, cons(h, t), cons(h, _dr)]) -> 34
(length([ll, _yq])) -> length([cons(x, ll), s(_yq)]) -> 37
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 33
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 34
(leq([s(nn1), z])) -> BOT -> 34
}
Sat witness: Found: ((delete([i, l, _ir]) /\ length([_ir, _jr]) /\ length([l, _kr])) -> leq([_jr, _kr]), {
_ir -> cons(a, cons(b, cons(b, nil)))  ;  _jr -> s(s(s(s(z))))  ;  _kr -> s(s(s(z)))  ;  i -> b  ;  l -> cons(b, cons(b, cons(b, nil)))
})

-------------------------------------------
Step 49, which took 0.080908 s (model generation: 0.074419,  model checking: 0.006489):

Model:
|_
{
delete -> 
{{{
Q={q_gen_4617, q_gen_4623, q_gen_4624, q_gen_4626, q_gen_4627},
Q_f={q_gen_4617},
Delta=
{
<cons>(q_gen_4627, q_gen_4626) -> q_gen_4626
<nil>() -> q_gen_4626
<a>() -> q_gen_4627
<b>() -> q_gen_4627
<cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4623
<cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4623
<nil, nil>() -> q_gen_4623
<a, a>() -> q_gen_4624
<a, b>() -> q_gen_4624
<b, a>() -> q_gen_4624
<b, b>() -> q_gen_4624
<a, cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4617
<a, cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4617
<a, nil, nil>() -> q_gen_4617
<b, cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4617
<b, cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4617
<b, nil, nil>() -> q_gen_4617
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_4616, q_gen_4620, q_gen_4621, q_gen_4638, q_gen_4639, q_gen_4640, q_gen_4641, q_gen_4642, q_gen_4660, q_gen_4661, q_gen_4662, q_gen_4669, q_gen_4670, q_gen_4681},
Q_f={q_gen_4616},
Delta=
{
<cons>(q_gen_4639, q_gen_4681) -> q_gen_4620
<nil>() -> q_gen_4620
<cons>(q_gen_4639, q_gen_4620) -> q_gen_4638
<a>() -> q_gen_4639
<b>() -> q_gen_4639
<z>() -> q_gen_4641
<cons>(q_gen_4639, q_gen_4638) -> q_gen_4660
<s>(q_gen_4641) -> q_gen_4662
<s>(q_gen_4662) -> q_gen_4670
<cons>(q_gen_4639, q_gen_4660) -> q_gen_4681
<cons, s>(q_gen_4621, q_gen_4620) -> q_gen_4616
<cons, s>(q_gen_4640, q_gen_4638) -> q_gen_4616
<cons, s>(q_gen_4640, q_gen_4681) -> q_gen_4616
<cons, s>(q_gen_4661, q_gen_4660) -> q_gen_4616
<cons, s>(q_gen_4669, q_gen_4681) -> q_gen_4616
<nil, z>() -> q_gen_4616
<a, z>() -> q_gen_4621
<b, z>() -> q_gen_4621
<a, s>(q_gen_4641) -> q_gen_4640
<a, s>(q_gen_4670) -> q_gen_4640
<b, s>(q_gen_4641) -> q_gen_4640
<cons, s>(q_gen_4621, q_gen_4638) -> q_gen_4642
<cons, s>(q_gen_4621, q_gen_4681) -> q_gen_4642
<cons, s>(q_gen_4640, q_gen_4620) -> q_gen_4642
<cons, s>(q_gen_4640, q_gen_4660) -> q_gen_4642
<cons, s>(q_gen_4661, q_gen_4620) -> q_gen_4642
<cons, s>(q_gen_4661, q_gen_4638) -> q_gen_4642
<cons, s>(q_gen_4661, q_gen_4681) -> q_gen_4642
<cons, s>(q_gen_4669, q_gen_4620) -> q_gen_4642
<cons, s>(q_gen_4669, q_gen_4638) -> q_gen_4642
<cons, s>(q_gen_4669, q_gen_4660) -> q_gen_4642
<b, s>(q_gen_4662) -> q_gen_4661
<b, s>(q_gen_4670) -> q_gen_4669
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_4613, q_gen_4615, q_gen_4643},
Q_f={q_gen_4613},
Delta=
{
<s>(q_gen_4615) -> q_gen_4615
<z>() -> q_gen_4615
<s, s>(q_gen_4613) -> q_gen_4613
<z, s>(q_gen_4615) -> q_gen_4613
<z, z>() -> q_gen_4613
<s, s>(q_gen_4643) -> q_gen_4643
<s, z>(q_gen_4615) -> q_gen_4643
}

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

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

Teacher's answer:
New clause system:
{
() -> delete([x, nil, nil]) -> 33
() -> length([nil, z]) -> 33
() -> leq([z, s(nn2)]) -> 34
() -> leq([z, z]) -> 33
(delete([h, t, _cr])) -> delete([h, cons(h, t), _cr]) -> 34
(delete([i, l, _ir]) /\ length([_ir, _jr]) /\ length([l, _kr])) -> leq([_jr, _kr]) -> 37
(delete([x, t, _dr]) /\ not eq_elt([x, h])) -> delete([x, cons(h, t), cons(h, _dr)]) -> 35
(length([ll, _yq])) -> length([cons(x, ll), s(_yq)]) -> 40
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 34
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 35
(leq([s(nn1), z])) -> BOT -> 35
}
Sat witness: Found: ((length([ll, _yq])) -> length([cons(x, ll), s(_yq)]), {
_yq -> s(s(z))  ;  ll -> cons(b, cons(b, cons(a, cons(b, nil))))  ;  x -> b
})

-------------------------------------------
Step 50, which took 0.089122 s (model generation: 0.085518,  model checking: 0.003604):

Model:
|_
{
delete -> 
{{{
Q={q_gen_4617, q_gen_4623, q_gen_4624, q_gen_4626, q_gen_4627},
Q_f={q_gen_4617},
Delta=
{
<cons>(q_gen_4627, q_gen_4626) -> q_gen_4626
<nil>() -> q_gen_4626
<a>() -> q_gen_4627
<b>() -> q_gen_4627
<cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4623
<cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4623
<nil, nil>() -> q_gen_4623
<a, a>() -> q_gen_4624
<a, b>() -> q_gen_4624
<b, a>() -> q_gen_4624
<b, b>() -> q_gen_4624
<a, cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4617
<a, cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4617
<a, nil, nil>() -> q_gen_4617
<b, cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4617
<b, cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4617
<b, nil, nil>() -> q_gen_4617
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_4616, q_gen_4620, q_gen_4621, q_gen_4638, q_gen_4639, q_gen_4640, q_gen_4641, q_gen_4642, q_gen_4660, q_gen_4661, q_gen_4662, q_gen_4669, q_gen_4670, q_gen_4681},
Q_f={q_gen_4616},
Delta=
{
<cons>(q_gen_4639, q_gen_4681) -> q_gen_4620
<nil>() -> q_gen_4620
<cons>(q_gen_4639, q_gen_4620) -> q_gen_4638
<a>() -> q_gen_4639
<b>() -> q_gen_4639
<z>() -> q_gen_4641
<cons>(q_gen_4639, q_gen_4638) -> q_gen_4660
<s>(q_gen_4641) -> q_gen_4662
<s>(q_gen_4662) -> q_gen_4670
<cons>(q_gen_4639, q_gen_4660) -> q_gen_4681
<cons, s>(q_gen_4621, q_gen_4620) -> q_gen_4616
<cons, s>(q_gen_4640, q_gen_4638) -> q_gen_4616
<cons, s>(q_gen_4661, q_gen_4660) -> q_gen_4616
<cons, s>(q_gen_4669, q_gen_4681) -> q_gen_4616
<nil, z>() -> q_gen_4616
<a, z>() -> q_gen_4621
<b, z>() -> q_gen_4621
<a, s>(q_gen_4641) -> q_gen_4640
<b, s>(q_gen_4641) -> q_gen_4640
<cons, s>(q_gen_4621, q_gen_4638) -> q_gen_4642
<cons, s>(q_gen_4621, q_gen_4681) -> q_gen_4642
<cons, s>(q_gen_4640, q_gen_4620) -> q_gen_4642
<cons, s>(q_gen_4640, q_gen_4681) -> q_gen_4642
<cons, s>(q_gen_4661, q_gen_4620) -> q_gen_4642
<cons, s>(q_gen_4661, q_gen_4638) -> q_gen_4642
<cons, s>(q_gen_4661, q_gen_4681) -> q_gen_4642
<cons, s>(q_gen_4669, q_gen_4620) -> q_gen_4642
<cons, s>(q_gen_4669, q_gen_4638) -> q_gen_4642
<cons, s>(q_gen_4669, q_gen_4660) -> q_gen_4642
<b, s>(q_gen_4662) -> q_gen_4661
<a, s>(q_gen_4670) -> q_gen_4669
<b, s>(q_gen_4670) -> q_gen_4669
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_4613, q_gen_4615, q_gen_4643},
Q_f={q_gen_4613},
Delta=
{
<s>(q_gen_4615) -> q_gen_4615
<z>() -> q_gen_4615
<s, s>(q_gen_4613) -> q_gen_4613
<z, s>(q_gen_4615) -> q_gen_4613
<z, z>() -> q_gen_4613
<s, s>(q_gen_4643) -> q_gen_4643
<s, z>(q_gen_4615) -> q_gen_4643
}

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

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

Teacher's answer:
New clause system:
{
() -> delete([x, nil, nil]) -> 34
() -> length([nil, z]) -> 34
() -> leq([z, s(nn2)]) -> 35
() -> leq([z, z]) -> 34
(delete([h, t, _cr])) -> delete([h, cons(h, t), _cr]) -> 35
(delete([i, l, _ir]) /\ length([_ir, _jr]) /\ length([l, _kr])) -> leq([_jr, _kr]) -> 40
(delete([x, t, _dr]) /\ not eq_elt([x, h])) -> delete([x, cons(h, t), cons(h, _dr)]) -> 36
(length([ll, _yq])) -> length([cons(x, ll), s(_yq)]) -> 40
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 35
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 36
(leq([s(nn1), z])) -> BOT -> 36
}
Sat witness: Found: ((delete([i, l, _ir]) /\ length([_ir, _jr]) /\ length([l, _kr])) -> leq([_jr, _kr]), {
_ir -> cons(b, cons(b, cons(b, nil)))  ;  _jr -> s(s(s(z)))  ;  _kr -> s(s(z))  ;  i -> a  ;  l -> cons(b, cons(b, cons(b, cons(b, cons(b, cons(b, nil))))))
})

-------------------------------------------
Step 51, which took 0.101043 s (model generation: 0.094505,  model checking: 0.006538):

Model:
|_
{
delete -> 
{{{
Q={q_gen_4617, q_gen_4623, q_gen_4624, q_gen_4626, q_gen_4627},
Q_f={q_gen_4617},
Delta=
{
<cons>(q_gen_4627, q_gen_4626) -> q_gen_4626
<nil>() -> q_gen_4626
<a>() -> q_gen_4627
<b>() -> q_gen_4627
<cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4623
<cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4623
<nil, nil>() -> q_gen_4623
<a, a>() -> q_gen_4624
<a, b>() -> q_gen_4624
<b, a>() -> q_gen_4624
<b, b>() -> q_gen_4624
<a, cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4617
<a, cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4617
<a, nil, nil>() -> q_gen_4617
<b, cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4617
<b, cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4617
<b, nil, nil>() -> q_gen_4617
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_4616, q_gen_4620, q_gen_4621, q_gen_4638, q_gen_4639, q_gen_4640, q_gen_4641, q_gen_4642, q_gen_4660, q_gen_4661, q_gen_4662, q_gen_4669, q_gen_4670, q_gen_4681},
Q_f={q_gen_4616},
Delta=
{
<nil>() -> q_gen_4620
<cons>(q_gen_4639, q_gen_4620) -> q_gen_4638
<a>() -> q_gen_4639
<b>() -> q_gen_4639
<z>() -> q_gen_4641
<cons>(q_gen_4639, q_gen_4638) -> q_gen_4660
<s>(q_gen_4641) -> q_gen_4662
<s>(q_gen_4662) -> q_gen_4670
<cons>(q_gen_4639, q_gen_4660) -> q_gen_4681
<cons>(q_gen_4639, q_gen_4681) -> q_gen_4681
<cons, s>(q_gen_4621, q_gen_4620) -> q_gen_4616
<cons, s>(q_gen_4640, q_gen_4638) -> q_gen_4616
<cons, s>(q_gen_4661, q_gen_4660) -> q_gen_4616
<cons, s>(q_gen_4669, q_gen_4681) -> q_gen_4616
<nil, z>() -> q_gen_4616
<a, z>() -> q_gen_4621
<b, z>() -> q_gen_4621
<a, s>(q_gen_4641) -> q_gen_4640
<b, s>(q_gen_4641) -> q_gen_4640
<cons, s>(q_gen_4621, q_gen_4638) -> q_gen_4642
<cons, s>(q_gen_4621, q_gen_4681) -> q_gen_4642
<cons, s>(q_gen_4640, q_gen_4620) -> q_gen_4642
<cons, s>(q_gen_4640, q_gen_4681) -> q_gen_4642
<cons, s>(q_gen_4661, q_gen_4620) -> q_gen_4642
<cons, s>(q_gen_4661, q_gen_4638) -> q_gen_4642
<cons, s>(q_gen_4661, q_gen_4681) -> q_gen_4642
<cons, s>(q_gen_4669, q_gen_4620) -> q_gen_4642
<cons, s>(q_gen_4669, q_gen_4638) -> q_gen_4642
<cons, s>(q_gen_4669, q_gen_4660) -> q_gen_4642
<b, s>(q_gen_4662) -> q_gen_4661
<a, s>(q_gen_4670) -> q_gen_4669
<b, s>(q_gen_4670) -> q_gen_4669
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_4613, q_gen_4615, q_gen_4643},
Q_f={q_gen_4613},
Delta=
{
<s>(q_gen_4615) -> q_gen_4615
<z>() -> q_gen_4615
<s, s>(q_gen_4613) -> q_gen_4613
<z, s>(q_gen_4615) -> q_gen_4613
<z, z>() -> q_gen_4613
<s, s>(q_gen_4643) -> q_gen_4643
<s, z>(q_gen_4615) -> q_gen_4643
}

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

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

Teacher's answer:
New clause system:
{
() -> delete([x, nil, nil]) -> 35
() -> length([nil, z]) -> 35
() -> leq([z, s(nn2)]) -> 36
() -> leq([z, z]) -> 35
(delete([h, t, _cr])) -> delete([h, cons(h, t), _cr]) -> 36
(delete([i, l, _ir]) /\ length([_ir, _jr]) /\ length([l, _kr])) -> leq([_jr, _kr]) -> 40
(delete([x, t, _dr]) /\ not eq_elt([x, h])) -> delete([x, cons(h, t), cons(h, _dr)]) -> 37
(length([ll, _yq])) -> length([cons(x, ll), s(_yq)]) -> 43
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 36
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 37
(leq([s(nn1), z])) -> BOT -> 37
}
Sat witness: Found: ((length([ll, _yq])) -> length([cons(x, ll), s(_yq)]), {
_yq -> s(s(z))  ;  ll -> cons(a, cons(b, nil))  ;  x -> a
})

-------------------------------------------
Step 52, which took 0.103420 s (model generation: 0.098655,  model checking: 0.004765):

Model:
|_
{
delete -> 
{{{
Q={q_gen_4617, q_gen_4623, q_gen_4624, q_gen_4626, q_gen_4627},
Q_f={q_gen_4617},
Delta=
{
<cons>(q_gen_4627, q_gen_4626) -> q_gen_4626
<nil>() -> q_gen_4626
<a>() -> q_gen_4627
<b>() -> q_gen_4627
<cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4623
<cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4623
<nil, nil>() -> q_gen_4623
<a, a>() -> q_gen_4624
<a, b>() -> q_gen_4624
<b, a>() -> q_gen_4624
<b, b>() -> q_gen_4624
<a, cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4617
<a, cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4617
<a, nil, nil>() -> q_gen_4617
<b, cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4617
<b, cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4617
<b, nil, nil>() -> q_gen_4617
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_4616, q_gen_4620, q_gen_4621, q_gen_4638, q_gen_4639, q_gen_4640, q_gen_4641, q_gen_4642, q_gen_4660, q_gen_4661, q_gen_4662, q_gen_4669, q_gen_4670, q_gen_4681},
Q_f={q_gen_4616},
Delta=
{
<nil>() -> q_gen_4620
<cons>(q_gen_4639, q_gen_4620) -> q_gen_4638
<a>() -> q_gen_4639
<b>() -> q_gen_4639
<z>() -> q_gen_4641
<cons>(q_gen_4639, q_gen_4638) -> q_gen_4660
<s>(q_gen_4641) -> q_gen_4662
<s>(q_gen_4662) -> q_gen_4670
<cons>(q_gen_4639, q_gen_4660) -> q_gen_4681
<cons>(q_gen_4639, q_gen_4681) -> q_gen_4681
<cons, s>(q_gen_4621, q_gen_4620) -> q_gen_4616
<cons, s>(q_gen_4621, q_gen_4660) -> q_gen_4616
<cons, s>(q_gen_4640, q_gen_4638) -> q_gen_4616
<cons, s>(q_gen_4661, q_gen_4660) -> q_gen_4616
<cons, s>(q_gen_4669, q_gen_4681) -> q_gen_4616
<nil, z>() -> q_gen_4616
<a, s>(q_gen_4662) -> q_gen_4621
<a, z>() -> q_gen_4621
<b, z>() -> q_gen_4621
<a, s>(q_gen_4641) -> q_gen_4640
<b, s>(q_gen_4641) -> q_gen_4640
<cons, s>(q_gen_4621, q_gen_4638) -> q_gen_4642
<cons, s>(q_gen_4621, q_gen_4681) -> q_gen_4642
<cons, s>(q_gen_4640, q_gen_4620) -> q_gen_4642
<cons, s>(q_gen_4640, q_gen_4681) -> q_gen_4642
<cons, s>(q_gen_4661, q_gen_4620) -> q_gen_4642
<cons, s>(q_gen_4661, q_gen_4638) -> q_gen_4642
<cons, s>(q_gen_4661, q_gen_4681) -> q_gen_4642
<cons, s>(q_gen_4669, q_gen_4620) -> q_gen_4642
<cons, s>(q_gen_4669, q_gen_4638) -> q_gen_4642
<cons, s>(q_gen_4669, q_gen_4660) -> q_gen_4642
<b, s>(q_gen_4662) -> q_gen_4661
<a, s>(q_gen_4670) -> q_gen_4669
<b, s>(q_gen_4670) -> q_gen_4669
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_4613, q_gen_4615, q_gen_4643},
Q_f={q_gen_4613},
Delta=
{
<s>(q_gen_4615) -> q_gen_4615
<z>() -> q_gen_4615
<s, s>(q_gen_4613) -> q_gen_4613
<z, s>(q_gen_4615) -> q_gen_4613
<z, z>() -> q_gen_4613
<s, s>(q_gen_4643) -> q_gen_4643
<s, z>(q_gen_4615) -> q_gen_4643
}

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

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

Teacher's answer:
New clause system:
{
() -> delete([x, nil, nil]) -> 36
() -> length([nil, z]) -> 36
() -> leq([z, s(nn2)]) -> 37
() -> leq([z, z]) -> 36
(delete([h, t, _cr])) -> delete([h, cons(h, t), _cr]) -> 37
(delete([i, l, _ir]) /\ length([_ir, _jr]) /\ length([l, _kr])) -> leq([_jr, _kr]) -> 43
(delete([x, t, _dr]) /\ not eq_elt([x, h])) -> delete([x, cons(h, t), cons(h, _dr)]) -> 38
(length([ll, _yq])) -> length([cons(x, ll), s(_yq)]) -> 43
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 37
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 38
(leq([s(nn1), z])) -> BOT -> 38
}
Sat witness: Found: ((delete([i, l, _ir]) /\ length([_ir, _jr]) /\ length([l, _kr])) -> leq([_jr, _kr]), {
_ir -> cons(a, nil)  ;  _jr -> s(s(s(z)))  ;  _kr -> s(s(z))  ;  i -> a  ;  l -> cons(a, cons(b, nil))
})

-------------------------------------------
Step 53, which took 0.123598 s (model generation: 0.115145,  model checking: 0.008453):

Model:
|_
{
delete -> 
{{{
Q={q_gen_4617, q_gen_4623, q_gen_4624, q_gen_4626, q_gen_4627},
Q_f={q_gen_4617},
Delta=
{
<cons>(q_gen_4627, q_gen_4626) -> q_gen_4626
<nil>() -> q_gen_4626
<a>() -> q_gen_4627
<b>() -> q_gen_4627
<cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4623
<cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4623
<nil, nil>() -> q_gen_4623
<a, a>() -> q_gen_4624
<a, b>() -> q_gen_4624
<b, a>() -> q_gen_4624
<b, b>() -> q_gen_4624
<a, cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4617
<a, cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4617
<a, nil, nil>() -> q_gen_4617
<b, cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4617
<b, cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4617
<b, nil, nil>() -> q_gen_4617
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_4616, q_gen_4620, q_gen_4621, q_gen_4638, q_gen_4639, q_gen_4640, q_gen_4641, q_gen_4642, q_gen_4660, q_gen_4661, q_gen_4662, q_gen_4669, q_gen_4670, q_gen_4681},
Q_f={q_gen_4616},
Delta=
{
<nil>() -> q_gen_4620
<cons>(q_gen_4639, q_gen_4620) -> q_gen_4638
<a>() -> q_gen_4639
<b>() -> q_gen_4639
<z>() -> q_gen_4641
<cons>(q_gen_4639, q_gen_4638) -> q_gen_4660
<cons>(q_gen_4639, q_gen_4681) -> q_gen_4660
<s>(q_gen_4641) -> q_gen_4662
<s>(q_gen_4662) -> q_gen_4670
<cons>(q_gen_4639, q_gen_4660) -> q_gen_4681
<cons, s>(q_gen_4621, q_gen_4620) -> q_gen_4616
<cons, s>(q_gen_4640, q_gen_4638) -> q_gen_4616
<cons, s>(q_gen_4661, q_gen_4660) -> q_gen_4616
<cons, s>(q_gen_4669, q_gen_4681) -> q_gen_4616
<nil, z>() -> q_gen_4616
<a, z>() -> q_gen_4621
<b, z>() -> q_gen_4621
<a, s>(q_gen_4641) -> q_gen_4640
<b, s>(q_gen_4641) -> q_gen_4640
<cons, s>(q_gen_4621, q_gen_4638) -> q_gen_4642
<cons, s>(q_gen_4621, q_gen_4681) -> q_gen_4642
<cons, s>(q_gen_4640, q_gen_4620) -> q_gen_4642
<cons, s>(q_gen_4640, q_gen_4660) -> q_gen_4642
<cons, s>(q_gen_4640, q_gen_4681) -> q_gen_4642
<cons, s>(q_gen_4661, q_gen_4620) -> q_gen_4642
<cons, s>(q_gen_4661, q_gen_4638) -> q_gen_4642
<cons, s>(q_gen_4661, q_gen_4681) -> q_gen_4642
<cons, s>(q_gen_4669, q_gen_4620) -> q_gen_4642
<cons, s>(q_gen_4669, q_gen_4638) -> q_gen_4642
<cons, s>(q_gen_4669, q_gen_4660) -> q_gen_4642
<a, s>(q_gen_4662) -> q_gen_4661
<b, s>(q_gen_4662) -> q_gen_4661
<a, s>(q_gen_4670) -> q_gen_4669
<b, s>(q_gen_4670) -> q_gen_4669
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_4613, q_gen_4615, q_gen_4643},
Q_f={q_gen_4613},
Delta=
{
<s>(q_gen_4615) -> q_gen_4615
<z>() -> q_gen_4615
<s, s>(q_gen_4613) -> q_gen_4613
<z, s>(q_gen_4615) -> q_gen_4613
<z, z>() -> q_gen_4613
<s, s>(q_gen_4643) -> q_gen_4643
<s, z>(q_gen_4615) -> q_gen_4643
}

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

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

Teacher's answer:
New clause system:
{
() -> delete([x, nil, nil]) -> 37
() -> length([nil, z]) -> 37
() -> leq([z, s(nn2)]) -> 38
() -> leq([z, z]) -> 37
(delete([h, t, _cr])) -> delete([h, cons(h, t), _cr]) -> 38
(delete([i, l, _ir]) /\ length([_ir, _jr]) /\ length([l, _kr])) -> leq([_jr, _kr]) -> 43
(delete([x, t, _dr]) /\ not eq_elt([x, h])) -> delete([x, cons(h, t), cons(h, _dr)]) -> 39
(length([ll, _yq])) -> length([cons(x, ll), s(_yq)]) -> 46
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 38
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 39
(leq([s(nn1), z])) -> BOT -> 39
}
Sat witness: Found: ((length([ll, _yq])) -> length([cons(x, ll), s(_yq)]), {
_yq -> s(s(s(s(z))))  ;  ll -> cons(a, cons(b, cons(b, cons(b, nil))))  ;  x -> b
})

-------------------------------------------
Step 54, which took 0.118933 s (model generation: 0.114734,  model checking: 0.004199):

Model:
|_
{
delete -> 
{{{
Q={q_gen_4617, q_gen_4623, q_gen_4624, q_gen_4626, q_gen_4627},
Q_f={q_gen_4617},
Delta=
{
<cons>(q_gen_4627, q_gen_4626) -> q_gen_4626
<nil>() -> q_gen_4626
<a>() -> q_gen_4627
<b>() -> q_gen_4627
<cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4623
<cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4623
<nil, nil>() -> q_gen_4623
<a, a>() -> q_gen_4624
<a, b>() -> q_gen_4624
<b, a>() -> q_gen_4624
<b, b>() -> q_gen_4624
<a, cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4617
<a, cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4617
<a, nil, nil>() -> q_gen_4617
<b, cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4617
<b, cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4617
<b, nil, nil>() -> q_gen_4617
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_4616, q_gen_4620, q_gen_4621, q_gen_4638, q_gen_4639, q_gen_4640, q_gen_4641, q_gen_4642, q_gen_4660, q_gen_4661, q_gen_4662, q_gen_4669, q_gen_4670, q_gen_4681},
Q_f={q_gen_4616},
Delta=
{
<nil>() -> q_gen_4620
<cons>(q_gen_4639, q_gen_4620) -> q_gen_4638
<a>() -> q_gen_4639
<b>() -> q_gen_4639
<z>() -> q_gen_4641
<cons>(q_gen_4639, q_gen_4638) -> q_gen_4660
<cons>(q_gen_4639, q_gen_4681) -> q_gen_4660
<s>(q_gen_4641) -> q_gen_4662
<s>(q_gen_4670) -> q_gen_4662
<s>(q_gen_4662) -> q_gen_4670
<cons>(q_gen_4639, q_gen_4660) -> q_gen_4681
<cons, s>(q_gen_4621, q_gen_4620) -> q_gen_4616
<cons, s>(q_gen_4640, q_gen_4638) -> q_gen_4616
<cons, s>(q_gen_4661, q_gen_4660) -> q_gen_4616
<cons, s>(q_gen_4669, q_gen_4681) -> q_gen_4616
<nil, z>() -> q_gen_4616
<a, z>() -> q_gen_4621
<b, z>() -> q_gen_4621
<a, s>(q_gen_4641) -> q_gen_4640
<b, s>(q_gen_4641) -> q_gen_4640
<cons, s>(q_gen_4621, q_gen_4638) -> q_gen_4642
<cons, s>(q_gen_4621, q_gen_4681) -> q_gen_4642
<cons, s>(q_gen_4640, q_gen_4620) -> q_gen_4642
<cons, s>(q_gen_4640, q_gen_4660) -> q_gen_4642
<cons, s>(q_gen_4640, q_gen_4681) -> q_gen_4642
<cons, s>(q_gen_4661, q_gen_4620) -> q_gen_4642
<cons, s>(q_gen_4661, q_gen_4638) -> q_gen_4642
<cons, s>(q_gen_4661, q_gen_4681) -> q_gen_4642
<cons, s>(q_gen_4669, q_gen_4620) -> q_gen_4642
<cons, s>(q_gen_4669, q_gen_4638) -> q_gen_4642
<cons, s>(q_gen_4669, q_gen_4660) -> q_gen_4642
<a, s>(q_gen_4662) -> q_gen_4661
<b, s>(q_gen_4662) -> q_gen_4661
<a, s>(q_gen_4670) -> q_gen_4669
<b, s>(q_gen_4670) -> q_gen_4669
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_4613, q_gen_4615, q_gen_4643},
Q_f={q_gen_4613},
Delta=
{
<s>(q_gen_4615) -> q_gen_4615
<z>() -> q_gen_4615
<s, s>(q_gen_4613) -> q_gen_4613
<z, s>(q_gen_4615) -> q_gen_4613
<z, z>() -> q_gen_4613
<s, s>(q_gen_4643) -> q_gen_4643
<s, z>(q_gen_4615) -> q_gen_4643
}

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

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

Teacher's answer:
New clause system:
{
() -> delete([x, nil, nil]) -> 38
() -> length([nil, z]) -> 38
() -> leq([z, s(nn2)]) -> 39
() -> leq([z, z]) -> 38
(delete([h, t, _cr])) -> delete([h, cons(h, t), _cr]) -> 39
(delete([i, l, _ir]) /\ length([_ir, _jr]) /\ length([l, _kr])) -> leq([_jr, _kr]) -> 46
(delete([x, t, _dr]) /\ not eq_elt([x, h])) -> delete([x, cons(h, t), cons(h, _dr)]) -> 40
(length([ll, _yq])) -> length([cons(x, ll), s(_yq)]) -> 46
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 39
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 40
(leq([s(nn1), z])) -> BOT -> 40
}
Sat witness: Found: ((delete([i, l, _ir]) /\ length([_ir, _jr]) /\ length([l, _kr])) -> leq([_jr, _kr]), {
_ir -> cons(b, cons(b, cons(b, nil)))  ;  _jr -> s(s(s(s(s(z)))))  ;  _kr -> s(s(s(z)))  ;  i -> a  ;  l -> cons(b, cons(b, cons(b, nil)))
})

-------------------------------------------
Step 55, which took 0.141751 s (model generation: 0.134839,  model checking: 0.006912):

Model:
|_
{
delete -> 
{{{
Q={q_gen_4617, q_gen_4623, q_gen_4624, q_gen_4626, q_gen_4627},
Q_f={q_gen_4617},
Delta=
{
<cons>(q_gen_4627, q_gen_4626) -> q_gen_4626
<nil>() -> q_gen_4626
<a>() -> q_gen_4627
<b>() -> q_gen_4627
<cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4623
<cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4623
<nil, nil>() -> q_gen_4623
<a, a>() -> q_gen_4624
<a, b>() -> q_gen_4624
<b, a>() -> q_gen_4624
<b, b>() -> q_gen_4624
<a, cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4617
<a, cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4617
<a, nil, nil>() -> q_gen_4617
<b, cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4617
<b, cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4617
<b, nil, nil>() -> q_gen_4617
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_4616, q_gen_4620, q_gen_4621, q_gen_4638, q_gen_4639, q_gen_4640, q_gen_4641, q_gen_4642, q_gen_4660, q_gen_4661, q_gen_4662, q_gen_4669, q_gen_4670, q_gen_4681},
Q_f={q_gen_4616},
Delta=
{
<nil>() -> q_gen_4620
<cons>(q_gen_4639, q_gen_4620) -> q_gen_4638
<a>() -> q_gen_4639
<b>() -> q_gen_4639
<z>() -> q_gen_4641
<cons>(q_gen_4639, q_gen_4638) -> q_gen_4660
<s>(q_gen_4641) -> q_gen_4662
<s>(q_gen_4662) -> q_gen_4670
<s>(q_gen_4670) -> q_gen_4670
<cons>(q_gen_4639, q_gen_4660) -> q_gen_4681
<cons>(q_gen_4639, q_gen_4681) -> q_gen_4681
<cons, s>(q_gen_4621, q_gen_4620) -> q_gen_4616
<cons, s>(q_gen_4640, q_gen_4638) -> q_gen_4616
<cons, s>(q_gen_4640, q_gen_4660) -> q_gen_4616
<cons, s>(q_gen_4661, q_gen_4660) -> q_gen_4616
<cons, s>(q_gen_4669, q_gen_4681) -> q_gen_4616
<nil, z>() -> q_gen_4616
<a, z>() -> q_gen_4621
<b, z>() -> q_gen_4621
<a, s>(q_gen_4641) -> q_gen_4640
<a, s>(q_gen_4662) -> q_gen_4640
<b, s>(q_gen_4641) -> q_gen_4640
<cons, s>(q_gen_4621, q_gen_4638) -> q_gen_4642
<cons, s>(q_gen_4621, q_gen_4681) -> q_gen_4642
<cons, s>(q_gen_4640, q_gen_4620) -> q_gen_4642
<cons, s>(q_gen_4640, q_gen_4681) -> q_gen_4642
<cons, s>(q_gen_4661, q_gen_4620) -> q_gen_4642
<cons, s>(q_gen_4661, q_gen_4638) -> q_gen_4642
<cons, s>(q_gen_4661, q_gen_4681) -> q_gen_4642
<cons, s>(q_gen_4669, q_gen_4620) -> q_gen_4642
<cons, s>(q_gen_4669, q_gen_4638) -> q_gen_4642
<cons, s>(q_gen_4669, q_gen_4660) -> q_gen_4642
<b, s>(q_gen_4662) -> q_gen_4661
<a, s>(q_gen_4670) -> q_gen_4669
<b, s>(q_gen_4670) -> q_gen_4669
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_4613, q_gen_4615, q_gen_4643},
Q_f={q_gen_4613},
Delta=
{
<s>(q_gen_4615) -> q_gen_4615
<z>() -> q_gen_4615
<s, s>(q_gen_4613) -> q_gen_4613
<z, s>(q_gen_4615) -> q_gen_4613
<z, z>() -> q_gen_4613
<s, s>(q_gen_4643) -> q_gen_4643
<s, z>(q_gen_4615) -> q_gen_4643
}

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

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

Teacher's answer:
New clause system:
{
() -> delete([x, nil, nil]) -> 39
() -> length([nil, z]) -> 39
() -> leq([z, s(nn2)]) -> 40
() -> leq([z, z]) -> 39
(delete([h, t, _cr])) -> delete([h, cons(h, t), _cr]) -> 40
(delete([i, l, _ir]) /\ length([_ir, _jr]) /\ length([l, _kr])) -> leq([_jr, _kr]) -> 46
(delete([x, t, _dr]) /\ not eq_elt([x, h])) -> delete([x, cons(h, t), cons(h, _dr)]) -> 41
(length([ll, _yq])) -> length([cons(x, ll), s(_yq)]) -> 49
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 40
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 41
(leq([s(nn1), z])) -> BOT -> 41
}
Sat witness: Found: ((length([ll, _yq])) -> length([cons(x, ll), s(_yq)]), {
_yq -> s(s(s(z)))  ;  ll -> cons(a, cons(b, nil))  ;  x -> a
})

-------------------------------------------
Step 56, which took 0.143680 s (model generation: 0.139163,  model checking: 0.004517):

Model:
|_
{
delete -> 
{{{
Q={q_gen_4617, q_gen_4623, q_gen_4624, q_gen_4626, q_gen_4627},
Q_f={q_gen_4617},
Delta=
{
<cons>(q_gen_4627, q_gen_4626) -> q_gen_4626
<nil>() -> q_gen_4626
<a>() -> q_gen_4627
<b>() -> q_gen_4627
<cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4623
<cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4623
<nil, nil>() -> q_gen_4623
<a, a>() -> q_gen_4624
<a, b>() -> q_gen_4624
<b, a>() -> q_gen_4624
<b, b>() -> q_gen_4624
<a, cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4617
<a, cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4617
<a, nil, nil>() -> q_gen_4617
<b, cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4617
<b, cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4617
<b, nil, nil>() -> q_gen_4617
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_4616, q_gen_4620, q_gen_4621, q_gen_4638, q_gen_4639, q_gen_4640, q_gen_4641, q_gen_4642, q_gen_4660, q_gen_4661, q_gen_4662, q_gen_4669, q_gen_4670, q_gen_4681},
Q_f={q_gen_4616},
Delta=
{
<nil>() -> q_gen_4620
<cons>(q_gen_4639, q_gen_4620) -> q_gen_4638
<a>() -> q_gen_4639
<b>() -> q_gen_4639
<z>() -> q_gen_4641
<cons>(q_gen_4639, q_gen_4638) -> q_gen_4660
<s>(q_gen_4641) -> q_gen_4662
<s>(q_gen_4662) -> q_gen_4670
<s>(q_gen_4670) -> q_gen_4670
<cons>(q_gen_4639, q_gen_4660) -> q_gen_4681
<cons>(q_gen_4639, q_gen_4681) -> q_gen_4681
<cons, s>(q_gen_4621, q_gen_4620) -> q_gen_4616
<cons, s>(q_gen_4640, q_gen_4638) -> q_gen_4616
<cons, s>(q_gen_4661, q_gen_4660) -> q_gen_4616
<cons, s>(q_gen_4669, q_gen_4681) -> q_gen_4616
<nil, z>() -> q_gen_4616
<a, z>() -> q_gen_4621
<b, z>() -> q_gen_4621
<a, s>(q_gen_4641) -> q_gen_4640
<b, s>(q_gen_4641) -> q_gen_4640
<cons, s>(q_gen_4621, q_gen_4638) -> q_gen_4642
<cons, s>(q_gen_4621, q_gen_4681) -> q_gen_4642
<cons, s>(q_gen_4640, q_gen_4620) -> q_gen_4642
<cons, s>(q_gen_4640, q_gen_4681) -> q_gen_4642
<cons, s>(q_gen_4661, q_gen_4620) -> q_gen_4642
<cons, s>(q_gen_4661, q_gen_4638) -> q_gen_4642
<cons, s>(q_gen_4661, q_gen_4681) -> q_gen_4642
<cons, s>(q_gen_4669, q_gen_4620) -> q_gen_4642
<cons, s>(q_gen_4669, q_gen_4638) -> q_gen_4642
<cons, s>(q_gen_4669, q_gen_4660) -> q_gen_4642
<a, s>(q_gen_4662) -> q_gen_4661
<b, s>(q_gen_4662) -> q_gen_4661
<a, s>(q_gen_4670) -> q_gen_4669
<b, s>(q_gen_4670) -> q_gen_4669
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_4613, q_gen_4615, q_gen_4643},
Q_f={q_gen_4613},
Delta=
{
<s>(q_gen_4615) -> q_gen_4615
<z>() -> q_gen_4615
<s, s>(q_gen_4613) -> q_gen_4613
<z, s>(q_gen_4615) -> q_gen_4613
<z, z>() -> q_gen_4613
<s, s>(q_gen_4643) -> q_gen_4643
<s, z>(q_gen_4615) -> q_gen_4643
}

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

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

Teacher's answer:
New clause system:
{
() -> delete([x, nil, nil]) -> 40
() -> length([nil, z]) -> 40
() -> leq([z, s(nn2)]) -> 41
() -> leq([z, z]) -> 40
(delete([h, t, _cr])) -> delete([h, cons(h, t), _cr]) -> 41
(delete([i, l, _ir]) /\ length([_ir, _jr]) /\ length([l, _kr])) -> leq([_jr, _kr]) -> 49
(delete([x, t, _dr]) /\ not eq_elt([x, h])) -> delete([x, cons(h, t), cons(h, _dr)]) -> 42
(length([ll, _yq])) -> length([cons(x, ll), s(_yq)]) -> 49
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 41
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 42
(leq([s(nn1), z])) -> BOT -> 42
}
Sat witness: Found: ((delete([i, l, _ir]) /\ length([_ir, _jr]) /\ length([l, _kr])) -> leq([_jr, _kr]), {
_ir -> cons(b, cons(b, cons(b, cons(b, nil))))  ;  _jr -> s(s(s(s(s(z)))))  ;  _kr -> s(s(s(s(z))))  ;  i -> a  ;  l -> cons(b, cons(b, cons(b, cons(b, cons(b, nil)))))
})

-------------------------------------------
Step 57, which took 0.204128 s (model generation: 0.198378,  model checking: 0.005750):

Model:
|_
{
delete -> 
{{{
Q={q_gen_4617, q_gen_4623, q_gen_4624, q_gen_4626, q_gen_4627},
Q_f={q_gen_4617},
Delta=
{
<cons>(q_gen_4627, q_gen_4626) -> q_gen_4626
<nil>() -> q_gen_4626
<a>() -> q_gen_4627
<b>() -> q_gen_4627
<cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4623
<cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4623
<nil, nil>() -> q_gen_4623
<a, a>() -> q_gen_4624
<a, b>() -> q_gen_4624
<b, a>() -> q_gen_4624
<b, b>() -> q_gen_4624
<a, cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4617
<a, cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4617
<a, nil, nil>() -> q_gen_4617
<b, cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4617
<b, cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4617
<b, nil, nil>() -> q_gen_4617
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_4616, q_gen_4620, q_gen_4621, q_gen_4638, q_gen_4639, q_gen_4640, q_gen_4641, q_gen_4642, q_gen_4660, q_gen_4661, q_gen_4662, q_gen_4669, q_gen_4670, q_gen_4673, q_gen_4679},
Q_f={q_gen_4616},
Delta=
{
<nil>() -> q_gen_4620
<cons>(q_gen_4639, q_gen_4620) -> q_gen_4638
<cons>(q_gen_4673, q_gen_4620) -> q_gen_4638
<b>() -> q_gen_4639
<s>(q_gen_4670) -> q_gen_4641
<z>() -> q_gen_4641
<cons>(q_gen_4639, q_gen_4638) -> q_gen_4660
<cons>(q_gen_4673, q_gen_4679) -> q_gen_4660
<s>(q_gen_4641) -> q_gen_4662
<s>(q_gen_4662) -> q_gen_4670
<a>() -> q_gen_4673
<cons>(q_gen_4639, q_gen_4660) -> q_gen_4679
<cons>(q_gen_4639, q_gen_4679) -> q_gen_4679
<cons>(q_gen_4673, q_gen_4638) -> q_gen_4679
<cons, s>(q_gen_4621, q_gen_4620) -> q_gen_4616
<cons, s>(q_gen_4640, q_gen_4638) -> q_gen_4616
<cons, s>(q_gen_4661, q_gen_4660) -> q_gen_4616
<cons, s>(q_gen_4669, q_gen_4679) -> q_gen_4616
<nil, z>() -> q_gen_4616
<a, z>() -> q_gen_4621
<b, z>() -> q_gen_4621
<a, s>(q_gen_4641) -> q_gen_4640
<a, s>(q_gen_4670) -> q_gen_4640
<b, s>(q_gen_4641) -> q_gen_4640
<cons, s>(q_gen_4621, q_gen_4638) -> q_gen_4642
<cons, s>(q_gen_4621, q_gen_4679) -> q_gen_4642
<cons, s>(q_gen_4640, q_gen_4620) -> q_gen_4642
<cons, s>(q_gen_4640, q_gen_4660) -> q_gen_4642
<cons, s>(q_gen_4640, q_gen_4679) -> q_gen_4642
<cons, s>(q_gen_4661, q_gen_4620) -> q_gen_4642
<cons, s>(q_gen_4661, q_gen_4638) -> q_gen_4642
<cons, s>(q_gen_4661, q_gen_4679) -> q_gen_4642
<cons, s>(q_gen_4669, q_gen_4620) -> q_gen_4642
<cons, s>(q_gen_4669, q_gen_4638) -> q_gen_4642
<cons, s>(q_gen_4669, q_gen_4660) -> q_gen_4642
<b, s>(q_gen_4662) -> q_gen_4661
<a, s>(q_gen_4662) -> q_gen_4669
<b, s>(q_gen_4670) -> q_gen_4669
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_4613, q_gen_4615, q_gen_4643},
Q_f={q_gen_4613},
Delta=
{
<s>(q_gen_4615) -> q_gen_4615
<z>() -> q_gen_4615
<s, s>(q_gen_4613) -> q_gen_4613
<z, s>(q_gen_4615) -> q_gen_4613
<z, z>() -> q_gen_4613
<s, s>(q_gen_4643) -> q_gen_4643
<s, z>(q_gen_4615) -> q_gen_4643
}

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

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

Teacher's answer:
New clause system:
{
() -> delete([x, nil, nil]) -> 41
() -> length([nil, z]) -> 41
() -> leq([z, s(nn2)]) -> 42
() -> leq([z, z]) -> 41
(delete([h, t, _cr])) -> delete([h, cons(h, t), _cr]) -> 42
(delete([i, l, _ir]) /\ length([_ir, _jr]) /\ length([l, _kr])) -> leq([_jr, _kr]) -> 49
(delete([x, t, _dr]) /\ not eq_elt([x, h])) -> delete([x, cons(h, t), cons(h, _dr)]) -> 43
(length([ll, _yq])) -> length([cons(x, ll), s(_yq)]) -> 52
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 42
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 43
(leq([s(nn1), z])) -> BOT -> 43
}
Sat witness: Found: ((length([ll, _yq])) -> length([cons(x, ll), s(_yq)]), {
_yq -> s(s(s(z)))  ;  ll -> cons(a, cons(b, cons(a, cons(b, nil))))  ;  x -> b
})

-------------------------------------------
Step 58, which took 0.195687 s (model generation: 0.191645,  model checking: 0.004042):

Model:
|_
{
delete -> 
{{{
Q={q_gen_4617, q_gen_4623, q_gen_4624, q_gen_4626, q_gen_4627},
Q_f={q_gen_4617},
Delta=
{
<cons>(q_gen_4627, q_gen_4626) -> q_gen_4626
<nil>() -> q_gen_4626
<a>() -> q_gen_4627
<b>() -> q_gen_4627
<cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4623
<cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4623
<nil, nil>() -> q_gen_4623
<a, a>() -> q_gen_4624
<a, b>() -> q_gen_4624
<b, a>() -> q_gen_4624
<b, b>() -> q_gen_4624
<a, cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4617
<a, cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4617
<a, nil, nil>() -> q_gen_4617
<b, cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4617
<b, cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4617
<b, nil, nil>() -> q_gen_4617
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_4616, q_gen_4620, q_gen_4621, q_gen_4638, q_gen_4639, q_gen_4640, q_gen_4641, q_gen_4642, q_gen_4660, q_gen_4661, q_gen_4662, q_gen_4669, q_gen_4670, q_gen_4673, q_gen_4681},
Q_f={q_gen_4616},
Delta=
{
<nil>() -> q_gen_4620
<cons>(q_gen_4639, q_gen_4620) -> q_gen_4638
<cons>(q_gen_4673, q_gen_4620) -> q_gen_4638
<cons>(q_gen_4673, q_gen_4681) -> q_gen_4638
<b>() -> q_gen_4639
<s>(q_gen_4670) -> q_gen_4641
<z>() -> q_gen_4641
<cons>(q_gen_4639, q_gen_4638) -> q_gen_4660
<cons>(q_gen_4673, q_gen_4638) -> q_gen_4660
<s>(q_gen_4641) -> q_gen_4662
<s>(q_gen_4662) -> q_gen_4670
<a>() -> q_gen_4673
<cons>(q_gen_4639, q_gen_4660) -> q_gen_4681
<cons>(q_gen_4639, q_gen_4681) -> q_gen_4681
<cons, s>(q_gen_4621, q_gen_4620) -> q_gen_4616
<cons, s>(q_gen_4640, q_gen_4638) -> q_gen_4616
<cons, s>(q_gen_4661, q_gen_4660) -> q_gen_4616
<cons, s>(q_gen_4669, q_gen_4681) -> q_gen_4616
<nil, z>() -> q_gen_4616
<a, z>() -> q_gen_4621
<b, z>() -> q_gen_4621
<a, s>(q_gen_4641) -> q_gen_4640
<b, s>(q_gen_4641) -> q_gen_4640
<cons, s>(q_gen_4621, q_gen_4638) -> q_gen_4642
<cons, s>(q_gen_4621, q_gen_4681) -> q_gen_4642
<cons, s>(q_gen_4640, q_gen_4620) -> q_gen_4642
<cons, s>(q_gen_4640, q_gen_4660) -> q_gen_4642
<cons, s>(q_gen_4640, q_gen_4681) -> q_gen_4642
<cons, s>(q_gen_4661, q_gen_4620) -> q_gen_4642
<cons, s>(q_gen_4661, q_gen_4638) -> q_gen_4642
<cons, s>(q_gen_4661, q_gen_4681) -> q_gen_4642
<cons, s>(q_gen_4669, q_gen_4620) -> q_gen_4642
<cons, s>(q_gen_4669, q_gen_4638) -> q_gen_4642
<cons, s>(q_gen_4669, q_gen_4660) -> q_gen_4642
<a, s>(q_gen_4662) -> q_gen_4661
<b, s>(q_gen_4662) -> q_gen_4661
<a, s>(q_gen_4670) -> q_gen_4669
<b, s>(q_gen_4670) -> q_gen_4669
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_4613, q_gen_4615, q_gen_4643},
Q_f={q_gen_4613},
Delta=
{
<s>(q_gen_4615) -> q_gen_4615
<z>() -> q_gen_4615
<s, s>(q_gen_4613) -> q_gen_4613
<z, s>(q_gen_4615) -> q_gen_4613
<z, z>() -> q_gen_4613
<s, s>(q_gen_4643) -> q_gen_4643
<s, z>(q_gen_4615) -> q_gen_4643
}

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

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

Teacher's answer:
New clause system:
{
() -> delete([x, nil, nil]) -> 42
() -> length([nil, z]) -> 42
() -> leq([z, s(nn2)]) -> 43
() -> leq([z, z]) -> 42
(delete([h, t, _cr])) -> delete([h, cons(h, t), _cr]) -> 43
(delete([i, l, _ir]) /\ length([_ir, _jr]) /\ length([l, _kr])) -> leq([_jr, _kr]) -> 52
(delete([x, t, _dr]) /\ not eq_elt([x, h])) -> delete([x, cons(h, t), cons(h, _dr)]) -> 44
(length([ll, _yq])) -> length([cons(x, ll), s(_yq)]) -> 52
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 43
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 44
(leq([s(nn1), z])) -> BOT -> 44
}
Sat witness: Found: ((delete([i, l, _ir]) /\ length([_ir, _jr]) /\ length([l, _kr])) -> leq([_jr, _kr]), {
_ir -> cons(b, cons(b, nil))  ;  _jr -> s(s(s(s(s(z)))))  ;  _kr -> s(s(s(z)))  ;  i -> b  ;  l -> cons(b, cons(b, cons(b, nil)))
})

-------------------------------------------
Step 59, which took 0.198378 s (model generation: 0.192872,  model checking: 0.005506):

Model:
|_
{
delete -> 
{{{
Q={q_gen_4617, q_gen_4623, q_gen_4624, q_gen_4626, q_gen_4627},
Q_f={q_gen_4617},
Delta=
{
<cons>(q_gen_4627, q_gen_4626) -> q_gen_4626
<nil>() -> q_gen_4626
<a>() -> q_gen_4627
<b>() -> q_gen_4627
<cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4623
<cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4623
<nil, nil>() -> q_gen_4623
<a, a>() -> q_gen_4624
<a, b>() -> q_gen_4624
<b, a>() -> q_gen_4624
<b, b>() -> q_gen_4624
<a, cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4617
<a, cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4617
<a, nil, nil>() -> q_gen_4617
<b, cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4617
<b, cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4617
<b, nil, nil>() -> q_gen_4617
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_4616, q_gen_4620, q_gen_4621, q_gen_4638, q_gen_4639, q_gen_4640, q_gen_4641, q_gen_4642, q_gen_4660, q_gen_4661, q_gen_4662, q_gen_4669, q_gen_4670, q_gen_4673, q_gen_4679},
Q_f={q_gen_4616},
Delta=
{
<cons>(q_gen_4673, q_gen_4660) -> q_gen_4620
<nil>() -> q_gen_4620
<cons>(q_gen_4639, q_gen_4620) -> q_gen_4638
<cons>(q_gen_4673, q_gen_4620) -> q_gen_4638
<b>() -> q_gen_4639
<z>() -> q_gen_4641
<cons>(q_gen_4639, q_gen_4638) -> q_gen_4660
<cons>(q_gen_4639, q_gen_4679) -> q_gen_4660
<s>(q_gen_4641) -> q_gen_4662
<s>(q_gen_4662) -> q_gen_4670
<s>(q_gen_4670) -> q_gen_4670
<a>() -> q_gen_4673
<cons>(q_gen_4639, q_gen_4660) -> q_gen_4679
<cons>(q_gen_4673, q_gen_4638) -> q_gen_4679
<cons>(q_gen_4673, q_gen_4679) -> q_gen_4679
<cons, s>(q_gen_4621, q_gen_4620) -> q_gen_4616
<cons, s>(q_gen_4621, q_gen_4679) -> q_gen_4616
<cons, s>(q_gen_4640, q_gen_4638) -> q_gen_4616
<cons, s>(q_gen_4661, q_gen_4660) -> q_gen_4616
<cons, s>(q_gen_4669, q_gen_4679) -> q_gen_4616
<nil, z>() -> q_gen_4616
<a, s>(q_gen_4670) -> q_gen_4621
<a, z>() -> q_gen_4621
<b, z>() -> q_gen_4621
<a, s>(q_gen_4641) -> q_gen_4640
<b, s>(q_gen_4641) -> q_gen_4640
<cons, s>(q_gen_4621, q_gen_4638) -> q_gen_4642
<cons, s>(q_gen_4621, q_gen_4660) -> q_gen_4642
<cons, s>(q_gen_4640, q_gen_4620) -> q_gen_4642
<cons, s>(q_gen_4640, q_gen_4660) -> q_gen_4642
<cons, s>(q_gen_4640, q_gen_4679) -> q_gen_4642
<cons, s>(q_gen_4661, q_gen_4620) -> q_gen_4642
<cons, s>(q_gen_4661, q_gen_4638) -> q_gen_4642
<cons, s>(q_gen_4661, q_gen_4679) -> q_gen_4642
<cons, s>(q_gen_4669, q_gen_4620) -> q_gen_4642
<cons, s>(q_gen_4669, q_gen_4638) -> q_gen_4642
<cons, s>(q_gen_4669, q_gen_4660) -> q_gen_4642
<b, s>(q_gen_4662) -> q_gen_4661
<a, s>(q_gen_4662) -> q_gen_4669
<b, s>(q_gen_4670) -> q_gen_4669
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_4613, q_gen_4615, q_gen_4643},
Q_f={q_gen_4613},
Delta=
{
<s>(q_gen_4615) -> q_gen_4615
<z>() -> q_gen_4615
<s, s>(q_gen_4613) -> q_gen_4613
<z, s>(q_gen_4615) -> q_gen_4613
<z, z>() -> q_gen_4613
<s, s>(q_gen_4643) -> q_gen_4643
<s, z>(q_gen_4615) -> q_gen_4643
}

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

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

Teacher's answer:
New clause system:
{
() -> delete([x, nil, nil]) -> 43
() -> length([nil, z]) -> 43
() -> leq([z, s(nn2)]) -> 44
() -> leq([z, z]) -> 43
(delete([h, t, _cr])) -> delete([h, cons(h, t), _cr]) -> 44
(delete([i, l, _ir]) /\ length([_ir, _jr]) /\ length([l, _kr])) -> leq([_jr, _kr]) -> 52
(delete([x, t, _dr]) /\ not eq_elt([x, h])) -> delete([x, cons(h, t), cons(h, _dr)]) -> 45
(length([ll, _yq])) -> length([cons(x, ll), s(_yq)]) -> 55
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 44
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 45
(leq([s(nn1), z])) -> BOT -> 45
}
Sat witness: Found: ((length([ll, _yq])) -> length([cons(x, ll), s(_yq)]), {
_yq -> s(s(s(s(z))))  ;  ll -> cons(b, cons(a, cons(b, nil)))  ;  x -> a
})

-------------------------------------------
Step 60, which took 0.241394 s (model generation: 0.236892,  model checking: 0.004502):

Model:
|_
{
delete -> 
{{{
Q={q_gen_4617, q_gen_4623, q_gen_4624, q_gen_4626, q_gen_4627},
Q_f={q_gen_4617},
Delta=
{
<cons>(q_gen_4627, q_gen_4626) -> q_gen_4626
<nil>() -> q_gen_4626
<a>() -> q_gen_4627
<b>() -> q_gen_4627
<cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4623
<cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4623
<nil, nil>() -> q_gen_4623
<a, a>() -> q_gen_4624
<a, b>() -> q_gen_4624
<b, a>() -> q_gen_4624
<b, b>() -> q_gen_4624
<a, cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4617
<a, cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4617
<a, nil, nil>() -> q_gen_4617
<b, cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4617
<b, cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4617
<b, nil, nil>() -> q_gen_4617
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_4616, q_gen_4620, q_gen_4621, q_gen_4638, q_gen_4639, q_gen_4640, q_gen_4641, q_gen_4642, q_gen_4660, q_gen_4661, q_gen_4662, q_gen_4669, q_gen_4670, q_gen_4673, q_gen_4681},
Q_f={q_gen_4616},
Delta=
{
<nil>() -> q_gen_4620
<cons>(q_gen_4639, q_gen_4620) -> q_gen_4638
<cons>(q_gen_4673, q_gen_4620) -> q_gen_4638
<b>() -> q_gen_4639
<z>() -> q_gen_4641
<cons>(q_gen_4639, q_gen_4638) -> q_gen_4660
<cons>(q_gen_4639, q_gen_4681) -> q_gen_4660
<cons>(q_gen_4673, q_gen_4638) -> q_gen_4660
<s>(q_gen_4641) -> q_gen_4662
<s>(q_gen_4662) -> q_gen_4670
<s>(q_gen_4670) -> q_gen_4670
<a>() -> q_gen_4673
<cons>(q_gen_4639, q_gen_4660) -> q_gen_4681
<cons>(q_gen_4673, q_gen_4681) -> q_gen_4681
<cons, s>(q_gen_4621, q_gen_4620) -> q_gen_4616
<cons, s>(q_gen_4640, q_gen_4638) -> q_gen_4616
<cons, s>(q_gen_4661, q_gen_4660) -> q_gen_4616
<cons, s>(q_gen_4669, q_gen_4681) -> q_gen_4616
<nil, z>() -> q_gen_4616
<a, z>() -> q_gen_4621
<b, z>() -> q_gen_4621
<a, s>(q_gen_4641) -> q_gen_4640
<b, s>(q_gen_4641) -> q_gen_4640
<cons, s>(q_gen_4621, q_gen_4638) -> q_gen_4642
<cons, s>(q_gen_4621, q_gen_4681) -> q_gen_4642
<cons, s>(q_gen_4640, q_gen_4620) -> q_gen_4642
<cons, s>(q_gen_4640, q_gen_4660) -> q_gen_4642
<cons, s>(q_gen_4640, q_gen_4681) -> q_gen_4642
<cons, s>(q_gen_4661, q_gen_4620) -> q_gen_4642
<cons, s>(q_gen_4661, q_gen_4638) -> q_gen_4642
<cons, s>(q_gen_4661, q_gen_4681) -> q_gen_4642
<cons, s>(q_gen_4669, q_gen_4620) -> q_gen_4642
<cons, s>(q_gen_4669, q_gen_4638) -> q_gen_4642
<cons, s>(q_gen_4669, q_gen_4660) -> q_gen_4642
<a, s>(q_gen_4662) -> q_gen_4661
<b, s>(q_gen_4662) -> q_gen_4661
<a, s>(q_gen_4670) -> q_gen_4669
<b, s>(q_gen_4670) -> q_gen_4669
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_4613, q_gen_4615, q_gen_4643},
Q_f={q_gen_4613},
Delta=
{
<s>(q_gen_4615) -> q_gen_4615
<z>() -> q_gen_4615
<s, s>(q_gen_4613) -> q_gen_4613
<z, s>(q_gen_4615) -> q_gen_4613
<z, z>() -> q_gen_4613
<s, s>(q_gen_4643) -> q_gen_4643
<s, z>(q_gen_4615) -> q_gen_4643
}

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

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

Teacher's answer:
New clause system:
{
() -> delete([x, nil, nil]) -> 44
() -> length([nil, z]) -> 44
() -> leq([z, s(nn2)]) -> 45
() -> leq([z, z]) -> 44
(delete([h, t, _cr])) -> delete([h, cons(h, t), _cr]) -> 45
(delete([i, l, _ir]) /\ length([_ir, _jr]) /\ length([l, _kr])) -> leq([_jr, _kr]) -> 55
(delete([x, t, _dr]) /\ not eq_elt([x, h])) -> delete([x, cons(h, t), cons(h, _dr)]) -> 46
(length([ll, _yq])) -> length([cons(x, ll), s(_yq)]) -> 55
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 45
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 46
(leq([s(nn1), z])) -> BOT -> 46
}
Sat witness: Found: ((delete([i, l, _ir]) /\ length([_ir, _jr]) /\ length([l, _kr])) -> leq([_jr, _kr]), {
_ir -> cons(b, cons(b, cons(b, cons(b, nil))))  ;  _jr -> s(s(s(s(z))))  ;  _kr -> s(s(s(z)))  ;  i -> b  ;  l -> cons(b, cons(b, cons(b, cons(b, cons(b, cons(b, cons(b, nil)))))))
})

-------------------------------------------
Step 61, which took 0.309629 s (model generation: 0.300011,  model checking: 0.009618):

Model:
|_
{
delete -> 
{{{
Q={q_gen_4617, q_gen_4623, q_gen_4624, q_gen_4626, q_gen_4627},
Q_f={q_gen_4617},
Delta=
{
<cons>(q_gen_4627, q_gen_4626) -> q_gen_4626
<nil>() -> q_gen_4626
<a>() -> q_gen_4627
<b>() -> q_gen_4627
<cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4623
<cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4623
<nil, nil>() -> q_gen_4623
<a, a>() -> q_gen_4624
<a, b>() -> q_gen_4624
<b, a>() -> q_gen_4624
<b, b>() -> q_gen_4624
<a, cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4617
<a, cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4617
<a, nil, nil>() -> q_gen_4617
<b, cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4617
<b, cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4617
<b, nil, nil>() -> q_gen_4617
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_4616, q_gen_4620, q_gen_4621, q_gen_4638, q_gen_4639, q_gen_4640, q_gen_4641, q_gen_4642, q_gen_4660, q_gen_4661, q_gen_4662, q_gen_4669, q_gen_4670, q_gen_4672, q_gen_4673, q_gen_4694},
Q_f={q_gen_4616},
Delta=
{
<cons>(q_gen_4639, q_gen_4694) -> q_gen_4620
<cons>(q_gen_4673, q_gen_4660) -> q_gen_4620
<nil>() -> q_gen_4620
<cons>(q_gen_4639, q_gen_4620) -> q_gen_4638
<cons>(q_gen_4673, q_gen_4638) -> q_gen_4638
<b>() -> q_gen_4639
<z>() -> q_gen_4641
<cons>(q_gen_4639, q_gen_4638) -> q_gen_4660
<s>(q_gen_4641) -> q_gen_4662
<s>(q_gen_4662) -> q_gen_4670
<s>(q_gen_4670) -> q_gen_4670
<cons>(q_gen_4639, q_gen_4660) -> q_gen_4672
<cons>(q_gen_4673, q_gen_4620) -> q_gen_4672
<cons>(q_gen_4673, q_gen_4672) -> q_gen_4672
<a>() -> q_gen_4673
<cons>(q_gen_4639, q_gen_4672) -> q_gen_4694
<cons, s>(q_gen_4621, q_gen_4620) -> q_gen_4616
<cons, s>(q_gen_4640, q_gen_4638) -> q_gen_4616
<cons, s>(q_gen_4640, q_gen_4672) -> q_gen_4616
<cons, s>(q_gen_4661, q_gen_4660) -> q_gen_4616
<cons, s>(q_gen_4669, q_gen_4672) -> q_gen_4616
<nil, z>() -> q_gen_4616
<a, z>() -> q_gen_4621
<b, z>() -> q_gen_4621
<a, s>(q_gen_4641) -> q_gen_4640
<a, s>(q_gen_4662) -> q_gen_4640
<a, s>(q_gen_4670) -> q_gen_4640
<b, s>(q_gen_4641) -> q_gen_4640
<cons, s>(q_gen_4621, q_gen_4638) -> q_gen_4642
<cons, s>(q_gen_4621, q_gen_4660) -> q_gen_4642
<cons, s>(q_gen_4640, q_gen_4620) -> q_gen_4642
<cons, s>(q_gen_4640, q_gen_4660) -> q_gen_4642
<cons, s>(q_gen_4640, q_gen_4694) -> q_gen_4642
<cons, s>(q_gen_4661, q_gen_4620) -> q_gen_4642
<cons, s>(q_gen_4661, q_gen_4638) -> q_gen_4642
<cons, s>(q_gen_4661, q_gen_4672) -> q_gen_4642
<cons, s>(q_gen_4661, q_gen_4694) -> q_gen_4642
<cons, s>(q_gen_4669, q_gen_4620) -> q_gen_4642
<cons, s>(q_gen_4669, q_gen_4638) -> q_gen_4642
<cons, s>(q_gen_4669, q_gen_4660) -> q_gen_4642
<cons, s>(q_gen_4669, q_gen_4694) -> q_gen_4642
<b, s>(q_gen_4662) -> q_gen_4661
<b, s>(q_gen_4670) -> q_gen_4669
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_4613, q_gen_4615, q_gen_4643},
Q_f={q_gen_4613},
Delta=
{
<s>(q_gen_4615) -> q_gen_4615
<z>() -> q_gen_4615
<s, s>(q_gen_4613) -> q_gen_4613
<z, s>(q_gen_4615) -> q_gen_4613
<z, z>() -> q_gen_4613
<s, s>(q_gen_4643) -> q_gen_4643
<s, z>(q_gen_4615) -> q_gen_4643
}

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

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

Teacher's answer:
New clause system:
{
() -> delete([x, nil, nil]) -> 45
() -> length([nil, z]) -> 45
() -> leq([z, s(nn2)]) -> 46
() -> leq([z, z]) -> 45
(delete([h, t, _cr])) -> delete([h, cons(h, t), _cr]) -> 46
(delete([i, l, _ir]) /\ length([_ir, _jr]) /\ length([l, _kr])) -> leq([_jr, _kr]) -> 55
(delete([x, t, _dr]) /\ not eq_elt([x, h])) -> delete([x, cons(h, t), cons(h, _dr)]) -> 47
(length([ll, _yq])) -> length([cons(x, ll), s(_yq)]) -> 58
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 46
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 47
(leq([s(nn1), z])) -> BOT -> 47
}
Sat witness: Found: ((length([ll, _yq])) -> length([cons(x, ll), s(_yq)]), {
_yq -> s(s(s(s(z))))  ;  ll -> cons(b, cons(a, nil))  ;  x -> a
})

-------------------------------------------
Step 62, which took 0.407309 s (model generation: 0.402527,  model checking: 0.004782):

Model:
|_
{
delete -> 
{{{
Q={q_gen_4617, q_gen_4623, q_gen_4624, q_gen_4626, q_gen_4627},
Q_f={q_gen_4617},
Delta=
{
<cons>(q_gen_4627, q_gen_4626) -> q_gen_4626
<nil>() -> q_gen_4626
<a>() -> q_gen_4627
<b>() -> q_gen_4627
<cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4623
<cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4623
<nil, nil>() -> q_gen_4623
<a, a>() -> q_gen_4624
<a, b>() -> q_gen_4624
<b, a>() -> q_gen_4624
<b, b>() -> q_gen_4624
<a, cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4617
<a, cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4617
<a, nil, nil>() -> q_gen_4617
<b, cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4617
<b, cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4617
<b, nil, nil>() -> q_gen_4617
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_4616, q_gen_4620, q_gen_4621, q_gen_4638, q_gen_4639, q_gen_4640, q_gen_4641, q_gen_4642, q_gen_4660, q_gen_4661, q_gen_4662, q_gen_4669, q_gen_4670, q_gen_4673, q_gen_4694, q_gen_4695},
Q_f={q_gen_4616},
Delta=
{
<cons>(q_gen_4639, q_gen_4694) -> q_gen_4620
<nil>() -> q_gen_4620
<cons>(q_gen_4639, q_gen_4620) -> q_gen_4638
<cons>(q_gen_4673, q_gen_4620) -> q_gen_4638
<cons>(q_gen_4673, q_gen_4638) -> q_gen_4638
<b>() -> q_gen_4639
<z>() -> q_gen_4641
<cons>(q_gen_4639, q_gen_4638) -> q_gen_4660
<s>(q_gen_4641) -> q_gen_4662
<s>(q_gen_4662) -> q_gen_4670
<s>(q_gen_4670) -> q_gen_4670
<a>() -> q_gen_4673
<cons>(q_gen_4639, q_gen_4695) -> q_gen_4694
<cons>(q_gen_4639, q_gen_4660) -> q_gen_4695
<cons>(q_gen_4673, q_gen_4660) -> q_gen_4695
<cons>(q_gen_4673, q_gen_4695) -> q_gen_4695
<cons, s>(q_gen_4621, q_gen_4620) -> q_gen_4616
<cons, s>(q_gen_4640, q_gen_4638) -> q_gen_4616
<cons, s>(q_gen_4640, q_gen_4695) -> q_gen_4616
<cons, s>(q_gen_4661, q_gen_4660) -> q_gen_4616
<cons, s>(q_gen_4669, q_gen_4695) -> q_gen_4616
<nil, z>() -> q_gen_4616
<a, z>() -> q_gen_4621
<b, z>() -> q_gen_4621
<a, s>(q_gen_4641) -> q_gen_4640
<a, s>(q_gen_4662) -> q_gen_4640
<a, s>(q_gen_4670) -> q_gen_4640
<b, s>(q_gen_4641) -> q_gen_4640
<cons, s>(q_gen_4621, q_gen_4638) -> q_gen_4642
<cons, s>(q_gen_4621, q_gen_4660) -> q_gen_4642
<cons, s>(q_gen_4640, q_gen_4620) -> q_gen_4642
<cons, s>(q_gen_4640, q_gen_4660) -> q_gen_4642
<cons, s>(q_gen_4640, q_gen_4694) -> q_gen_4642
<cons, s>(q_gen_4661, q_gen_4620) -> q_gen_4642
<cons, s>(q_gen_4661, q_gen_4638) -> q_gen_4642
<cons, s>(q_gen_4661, q_gen_4695) -> q_gen_4642
<cons, s>(q_gen_4669, q_gen_4620) -> q_gen_4642
<cons, s>(q_gen_4669, q_gen_4638) -> q_gen_4642
<cons, s>(q_gen_4669, q_gen_4660) -> q_gen_4642
<cons, s>(q_gen_4669, q_gen_4694) -> q_gen_4642
<b, s>(q_gen_4662) -> q_gen_4661
<b, s>(q_gen_4670) -> q_gen_4669
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_4613, q_gen_4615, q_gen_4643},
Q_f={q_gen_4613},
Delta=
{
<s>(q_gen_4615) -> q_gen_4615
<z>() -> q_gen_4615
<s, s>(q_gen_4613) -> q_gen_4613
<z, s>(q_gen_4615) -> q_gen_4613
<z, z>() -> q_gen_4613
<s, s>(q_gen_4643) -> q_gen_4643
<s, z>(q_gen_4615) -> q_gen_4643
}

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

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

Teacher's answer:
New clause system:
{
() -> delete([x, nil, nil]) -> 46
() -> length([nil, z]) -> 46
() -> leq([z, s(nn2)]) -> 47
() -> leq([z, z]) -> 46
(delete([h, t, _cr])) -> delete([h, cons(h, t), _cr]) -> 47
(delete([i, l, _ir]) /\ length([_ir, _jr]) /\ length([l, _kr])) -> leq([_jr, _kr]) -> 58
(delete([x, t, _dr]) /\ not eq_elt([x, h])) -> delete([x, cons(h, t), cons(h, _dr)]) -> 48
(length([ll, _yq])) -> length([cons(x, ll), s(_yq)]) -> 58
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 47
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 48
(leq([s(nn1), z])) -> BOT -> 48
}
Sat witness: Found: ((delete([i, l, _ir]) /\ length([_ir, _jr]) /\ length([l, _kr])) -> leq([_jr, _kr]), {
_ir -> cons(a, cons(b, nil))  ;  _jr -> s(s(s(s(z))))  ;  _kr -> s(s(s(z)))  ;  i -> a  ;  l -> cons(b, cons(b, cons(b, nil)))
})

-------------------------------------------
Step 63, which took 0.390927 s (model generation: 0.384144,  model checking: 0.006783):

Model:
|_
{
delete -> 
{{{
Q={q_gen_4617, q_gen_4623, q_gen_4624, q_gen_4626, q_gen_4627},
Q_f={q_gen_4617},
Delta=
{
<cons>(q_gen_4627, q_gen_4626) -> q_gen_4626
<nil>() -> q_gen_4626
<a>() -> q_gen_4627
<b>() -> q_gen_4627
<cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4623
<cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4623
<nil, nil>() -> q_gen_4623
<a, a>() -> q_gen_4624
<a, b>() -> q_gen_4624
<b, a>() -> q_gen_4624
<b, b>() -> q_gen_4624
<a, cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4617
<a, cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4617
<a, nil, nil>() -> q_gen_4617
<b, cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4617
<b, cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4617
<b, nil, nil>() -> q_gen_4617
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_4616, q_gen_4620, q_gen_4621, q_gen_4638, q_gen_4639, q_gen_4640, q_gen_4641, q_gen_4642, q_gen_4660, q_gen_4661, q_gen_4662, q_gen_4669, q_gen_4670, q_gen_4673, q_gen_4679, q_gen_4731},
Q_f={q_gen_4616},
Delta=
{
<nil>() -> q_gen_4620
<cons>(q_gen_4639, q_gen_4620) -> q_gen_4638
<cons>(q_gen_4673, q_gen_4620) -> q_gen_4638
<b>() -> q_gen_4639
<z>() -> q_gen_4641
<cons>(q_gen_4639, q_gen_4638) -> q_gen_4660
<s>(q_gen_4641) -> q_gen_4662
<s>(q_gen_4662) -> q_gen_4670
<a>() -> q_gen_4673
<cons>(q_gen_4639, q_gen_4660) -> q_gen_4679
<cons>(q_gen_4639, q_gen_4679) -> q_gen_4679
<cons>(q_gen_4673, q_gen_4638) -> q_gen_4679
<cons>(q_gen_4673, q_gen_4679) -> q_gen_4679
<s>(q_gen_4670) -> q_gen_4731
<cons, s>(q_gen_4621, q_gen_4620) -> q_gen_4616
<cons, s>(q_gen_4640, q_gen_4638) -> q_gen_4616
<cons, s>(q_gen_4661, q_gen_4660) -> q_gen_4616
<cons, s>(q_gen_4669, q_gen_4679) -> q_gen_4616
<nil, z>() -> q_gen_4616
<a, s>(q_gen_4670) -> q_gen_4621
<a, z>() -> q_gen_4621
<b, s>(q_gen_4731) -> q_gen_4621
<b, z>() -> q_gen_4621
<a, s>(q_gen_4641) -> q_gen_4640
<b, s>(q_gen_4641) -> q_gen_4640
<cons, s>(q_gen_4621, q_gen_4638) -> q_gen_4642
<cons, s>(q_gen_4621, q_gen_4660) -> q_gen_4642
<cons, s>(q_gen_4621, q_gen_4679) -> q_gen_4642
<cons, s>(q_gen_4640, q_gen_4620) -> q_gen_4642
<cons, s>(q_gen_4640, q_gen_4679) -> q_gen_4642
<cons, s>(q_gen_4661, q_gen_4620) -> q_gen_4642
<cons, s>(q_gen_4661, q_gen_4638) -> q_gen_4642
<cons, s>(q_gen_4661, q_gen_4679) -> q_gen_4642
<cons, s>(q_gen_4669, q_gen_4620) -> q_gen_4642
<cons, s>(q_gen_4669, q_gen_4638) -> q_gen_4642
<cons, s>(q_gen_4669, q_gen_4660) -> q_gen_4642
<b, s>(q_gen_4662) -> q_gen_4661
<a, s>(q_gen_4662) -> q_gen_4669
<a, s>(q_gen_4731) -> q_gen_4669
<b, s>(q_gen_4670) -> q_gen_4669
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_4613, q_gen_4615, q_gen_4643},
Q_f={q_gen_4613},
Delta=
{
<s>(q_gen_4615) -> q_gen_4615
<z>() -> q_gen_4615
<s, s>(q_gen_4613) -> q_gen_4613
<z, s>(q_gen_4615) -> q_gen_4613
<z, z>() -> q_gen_4613
<s, s>(q_gen_4643) -> q_gen_4643
<s, z>(q_gen_4615) -> q_gen_4643
}

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

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

Teacher's answer:
New clause system:
{
() -> delete([x, nil, nil]) -> 47
() -> length([nil, z]) -> 47
() -> leq([z, s(nn2)]) -> 48
() -> leq([z, z]) -> 47
(delete([h, t, _cr])) -> delete([h, cons(h, t), _cr]) -> 48
(delete([i, l, _ir]) /\ length([_ir, _jr]) /\ length([l, _kr])) -> leq([_jr, _kr]) -> 58
(delete([x, t, _dr]) /\ not eq_elt([x, h])) -> delete([x, cons(h, t), cons(h, _dr)]) -> 49
(length([ll, _yq])) -> length([cons(x, ll), s(_yq)]) -> 61
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 48
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 49
(leq([s(nn1), z])) -> BOT -> 49
}
Sat witness: Found: ((length([ll, _yq])) -> length([cons(x, ll), s(_yq)]), {
_yq -> s(s(s(s(z))))  ;  ll -> cons(b, cons(a, cons(a, nil)))  ;  x -> b
})

-------------------------------------------
Step 64, which took 0.656516 s (model generation: 0.651614,  model checking: 0.004902):

Model:
|_
{
delete -> 
{{{
Q={q_gen_4617, q_gen_4623, q_gen_4624, q_gen_4626, q_gen_4627},
Q_f={q_gen_4617},
Delta=
{
<cons>(q_gen_4627, q_gen_4626) -> q_gen_4626
<nil>() -> q_gen_4626
<a>() -> q_gen_4627
<b>() -> q_gen_4627
<cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4623
<cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4623
<nil, nil>() -> q_gen_4623
<a, a>() -> q_gen_4624
<a, b>() -> q_gen_4624
<b, a>() -> q_gen_4624
<b, b>() -> q_gen_4624
<a, cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4617
<a, cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4617
<a, nil, nil>() -> q_gen_4617
<b, cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4617
<b, cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4617
<b, nil, nil>() -> q_gen_4617
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_4616, q_gen_4620, q_gen_4621, q_gen_4638, q_gen_4639, q_gen_4640, q_gen_4641, q_gen_4642, q_gen_4660, q_gen_4661, q_gen_4662, q_gen_4669, q_gen_4670, q_gen_4673, q_gen_4681, q_gen_4694},
Q_f={q_gen_4616},
Delta=
{
<cons>(q_gen_4639, q_gen_4694) -> q_gen_4620
<nil>() -> q_gen_4620
<cons>(q_gen_4639, q_gen_4620) -> q_gen_4638
<cons>(q_gen_4673, q_gen_4620) -> q_gen_4638
<b>() -> q_gen_4639
<z>() -> q_gen_4641
<cons>(q_gen_4639, q_gen_4638) -> q_gen_4660
<cons>(q_gen_4673, q_gen_4638) -> q_gen_4660
<s>(q_gen_4641) -> q_gen_4662
<s>(q_gen_4662) -> q_gen_4670
<s>(q_gen_4670) -> q_gen_4670
<a>() -> q_gen_4673
<cons>(q_gen_4639, q_gen_4660) -> q_gen_4681
<cons>(q_gen_4673, q_gen_4681) -> q_gen_4681
<cons>(q_gen_4639, q_gen_4681) -> q_gen_4694
<cons, s>(q_gen_4621, q_gen_4620) -> q_gen_4616
<cons, s>(q_gen_4640, q_gen_4638) -> q_gen_4616
<cons, s>(q_gen_4661, q_gen_4660) -> q_gen_4616
<cons, s>(q_gen_4669, q_gen_4681) -> q_gen_4616
<nil, z>() -> q_gen_4616
<a, z>() -> q_gen_4621
<b, z>() -> q_gen_4621
<a, s>(q_gen_4641) -> q_gen_4640
<b, s>(q_gen_4641) -> q_gen_4640
<cons, s>(q_gen_4621, q_gen_4638) -> q_gen_4642
<cons, s>(q_gen_4621, q_gen_4681) -> q_gen_4642
<cons, s>(q_gen_4640, q_gen_4620) -> q_gen_4642
<cons, s>(q_gen_4640, q_gen_4681) -> q_gen_4642
<cons, s>(q_gen_4640, q_gen_4694) -> q_gen_4642
<cons, s>(q_gen_4661, q_gen_4620) -> q_gen_4642
<cons, s>(q_gen_4661, q_gen_4638) -> q_gen_4642
<cons, s>(q_gen_4661, q_gen_4681) -> q_gen_4642
<cons, s>(q_gen_4661, q_gen_4694) -> q_gen_4642
<cons, s>(q_gen_4669, q_gen_4620) -> q_gen_4642
<cons, s>(q_gen_4669, q_gen_4638) -> q_gen_4642
<cons, s>(q_gen_4669, q_gen_4660) -> q_gen_4642
<cons, s>(q_gen_4669, q_gen_4694) -> q_gen_4642
<a, s>(q_gen_4662) -> q_gen_4661
<b, s>(q_gen_4662) -> q_gen_4661
<a, s>(q_gen_4670) -> q_gen_4669
<b, s>(q_gen_4670) -> q_gen_4669
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_4613, q_gen_4615, q_gen_4643},
Q_f={q_gen_4613},
Delta=
{
<s>(q_gen_4615) -> q_gen_4615
<z>() -> q_gen_4615
<s, s>(q_gen_4613) -> q_gen_4613
<z, s>(q_gen_4615) -> q_gen_4613
<z, z>() -> q_gen_4613
<s, s>(q_gen_4643) -> q_gen_4643
<s, z>(q_gen_4615) -> q_gen_4643
}

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

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

Teacher's answer:
New clause system:
{
() -> delete([x, nil, nil]) -> 48
() -> length([nil, z]) -> 48
() -> leq([z, s(nn2)]) -> 49
() -> leq([z, z]) -> 48
(delete([h, t, _cr])) -> delete([h, cons(h, t), _cr]) -> 49
(delete([i, l, _ir]) /\ length([_ir, _jr]) /\ length([l, _kr])) -> leq([_jr, _kr]) -> 61
(delete([x, t, _dr]) /\ not eq_elt([x, h])) -> delete([x, cons(h, t), cons(h, _dr)]) -> 50
(length([ll, _yq])) -> length([cons(x, ll), s(_yq)]) -> 61
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 49
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 50
(leq([s(nn1), z])) -> BOT -> 50
}
Sat witness: Found: ((delete([i, l, _ir]) /\ length([_ir, _jr]) /\ length([l, _kr])) -> leq([_jr, _kr]), {
_ir -> cons(b, cons(b, cons(b, cons(b, nil))))  ;  _jr -> s(s(s(s(z))))  ;  _kr -> s(s(z))  ;  i -> b  ;  l -> cons(b, cons(b, cons(b, cons(b, cons(b, cons(b, cons(b, nil)))))))
})

-------------------------------------------
Step 65, which took 0.825104 s (model generation: 0.812394,  model checking: 0.012710):

Model:
|_
{
delete -> 
{{{
Q={q_gen_4617, q_gen_4623, q_gen_4624, q_gen_4626, q_gen_4627},
Q_f={q_gen_4617},
Delta=
{
<cons>(q_gen_4627, q_gen_4626) -> q_gen_4626
<nil>() -> q_gen_4626
<a>() -> q_gen_4627
<b>() -> q_gen_4627
<cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4623
<cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4623
<nil, nil>() -> q_gen_4623
<a, a>() -> q_gen_4624
<a, b>() -> q_gen_4624
<b, a>() -> q_gen_4624
<b, b>() -> q_gen_4624
<a, cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4617
<a, cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4617
<a, nil, nil>() -> q_gen_4617
<b, cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4617
<b, cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4617
<b, nil, nil>() -> q_gen_4617
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_4616, q_gen_4620, q_gen_4621, q_gen_4638, q_gen_4639, q_gen_4640, q_gen_4641, q_gen_4642, q_gen_4660, q_gen_4661, q_gen_4662, q_gen_4669, q_gen_4670, q_gen_4673, q_gen_4681, q_gen_4694},
Q_f={q_gen_4616},
Delta=
{
<nil>() -> q_gen_4620
<cons>(q_gen_4639, q_gen_4620) -> q_gen_4638
<b>() -> q_gen_4639
<z>() -> q_gen_4641
<cons>(q_gen_4639, q_gen_4638) -> q_gen_4660
<cons>(q_gen_4673, q_gen_4620) -> q_gen_4660
<cons>(q_gen_4673, q_gen_4638) -> q_gen_4660
<s>(q_gen_4641) -> q_gen_4662
<s>(q_gen_4662) -> q_gen_4670
<s>(q_gen_4670) -> q_gen_4670
<a>() -> q_gen_4673
<cons>(q_gen_4639, q_gen_4660) -> q_gen_4681
<cons>(q_gen_4639, q_gen_4694) -> q_gen_4681
<cons>(q_gen_4673, q_gen_4681) -> q_gen_4681
<cons>(q_gen_4639, q_gen_4681) -> q_gen_4694
<cons>(q_gen_4673, q_gen_4660) -> q_gen_4694
<cons, s>(q_gen_4621, q_gen_4620) -> q_gen_4616
<cons, s>(q_gen_4640, q_gen_4638) -> q_gen_4616
<cons, s>(q_gen_4640, q_gen_4660) -> q_gen_4616
<cons, s>(q_gen_4661, q_gen_4660) -> q_gen_4616
<cons, s>(q_gen_4669, q_gen_4681) -> q_gen_4616
<nil, z>() -> q_gen_4616
<a, z>() -> q_gen_4621
<b, z>() -> q_gen_4621
<a, s>(q_gen_4641) -> q_gen_4640
<b, s>(q_gen_4641) -> q_gen_4640
<cons, s>(q_gen_4621, q_gen_4638) -> q_gen_4642
<cons, s>(q_gen_4621, q_gen_4681) -> q_gen_4642
<cons, s>(q_gen_4640, q_gen_4620) -> q_gen_4642
<cons, s>(q_gen_4640, q_gen_4681) -> q_gen_4642
<cons, s>(q_gen_4640, q_gen_4694) -> q_gen_4642
<cons, s>(q_gen_4661, q_gen_4620) -> q_gen_4642
<cons, s>(q_gen_4661, q_gen_4638) -> q_gen_4642
<cons, s>(q_gen_4661, q_gen_4681) -> q_gen_4642
<cons, s>(q_gen_4661, q_gen_4694) -> q_gen_4642
<cons, s>(q_gen_4669, q_gen_4620) -> q_gen_4642
<cons, s>(q_gen_4669, q_gen_4638) -> q_gen_4642
<cons, s>(q_gen_4669, q_gen_4660) -> q_gen_4642
<cons, s>(q_gen_4669, q_gen_4694) -> q_gen_4642
<a, s>(q_gen_4662) -> q_gen_4661
<b, s>(q_gen_4662) -> q_gen_4661
<a, s>(q_gen_4670) -> q_gen_4669
<b, s>(q_gen_4670) -> q_gen_4669
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_4613, q_gen_4615, q_gen_4643},
Q_f={q_gen_4613},
Delta=
{
<s>(q_gen_4615) -> q_gen_4615
<z>() -> q_gen_4615
<s, s>(q_gen_4613) -> q_gen_4613
<z, s>(q_gen_4615) -> q_gen_4613
<z, z>() -> q_gen_4613
<s, s>(q_gen_4643) -> q_gen_4643
<s, z>(q_gen_4615) -> q_gen_4643
}

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

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

Teacher's answer:
New clause system:
{
() -> delete([x, nil, nil]) -> 49
() -> length([nil, z]) -> 49
() -> leq([z, s(nn2)]) -> 50
() -> leq([z, z]) -> 49
(delete([h, t, _cr])) -> delete([h, cons(h, t), _cr]) -> 50
(delete([i, l, _ir]) /\ length([_ir, _jr]) /\ length([l, _kr])) -> leq([_jr, _kr]) -> 61
(delete([x, t, _dr]) /\ not eq_elt([x, h])) -> delete([x, cons(h, t), cons(h, _dr)]) -> 51
(length([ll, _yq])) -> length([cons(x, ll), s(_yq)]) -> 64
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 50
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 51
(leq([s(nn1), z])) -> BOT -> 51
}
Sat witness: Found: ((length([ll, _yq])) -> length([cons(x, ll), s(_yq)]), {
_yq -> s(s(s(s(z))))  ;  ll -> cons(b, cons(a, cons(b, cons(a, nil))))  ;  x -> b
})

-------------------------------------------
Step 66, which took 0.797174 s (model generation: 0.792900,  model checking: 0.004274):

Model:
|_
{
delete -> 
{{{
Q={q_gen_4617, q_gen_4623, q_gen_4624, q_gen_4626, q_gen_4627},
Q_f={q_gen_4617},
Delta=
{
<cons>(q_gen_4627, q_gen_4626) -> q_gen_4626
<nil>() -> q_gen_4626
<a>() -> q_gen_4627
<b>() -> q_gen_4627
<cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4623
<cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4623
<nil, nil>() -> q_gen_4623
<a, a>() -> q_gen_4624
<a, b>() -> q_gen_4624
<b, a>() -> q_gen_4624
<b, b>() -> q_gen_4624
<a, cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4617
<a, cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4617
<a, nil, nil>() -> q_gen_4617
<b, cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4617
<b, cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4617
<b, nil, nil>() -> q_gen_4617
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_4616, q_gen_4620, q_gen_4621, q_gen_4638, q_gen_4639, q_gen_4640, q_gen_4641, q_gen_4642, q_gen_4660, q_gen_4661, q_gen_4662, q_gen_4669, q_gen_4670, q_gen_4673, q_gen_4681, q_gen_4731},
Q_f={q_gen_4616},
Delta=
{
<cons>(q_gen_4673, q_gen_4660) -> q_gen_4620
<cons>(q_gen_4673, q_gen_4681) -> q_gen_4620
<nil>() -> q_gen_4620
<cons>(q_gen_4639, q_gen_4620) -> q_gen_4638
<cons>(q_gen_4673, q_gen_4620) -> q_gen_4638
<b>() -> q_gen_4639
<z>() -> q_gen_4641
<cons>(q_gen_4639, q_gen_4638) -> q_gen_4660
<cons>(q_gen_4673, q_gen_4638) -> q_gen_4660
<s>(q_gen_4641) -> q_gen_4662
<s>(q_gen_4662) -> q_gen_4670
<a>() -> q_gen_4673
<cons>(q_gen_4639, q_gen_4660) -> q_gen_4681
<cons>(q_gen_4639, q_gen_4681) -> q_gen_4681
<s>(q_gen_4670) -> q_gen_4731
<cons, s>(q_gen_4621, q_gen_4620) -> q_gen_4616
<cons, s>(q_gen_4640, q_gen_4638) -> q_gen_4616
<cons, s>(q_gen_4661, q_gen_4660) -> q_gen_4616
<cons, s>(q_gen_4669, q_gen_4681) -> q_gen_4616
<nil, z>() -> q_gen_4616
<a, s>(q_gen_4731) -> q_gen_4621
<a, z>() -> q_gen_4621
<b, s>(q_gen_4731) -> q_gen_4621
<b, z>() -> q_gen_4621
<a, s>(q_gen_4641) -> q_gen_4640
<b, s>(q_gen_4641) -> q_gen_4640
<cons, s>(q_gen_4621, q_gen_4638) -> q_gen_4642
<cons, s>(q_gen_4621, q_gen_4660) -> q_gen_4642
<cons, s>(q_gen_4621, q_gen_4681) -> q_gen_4642
<cons, s>(q_gen_4640, q_gen_4620) -> q_gen_4642
<cons, s>(q_gen_4640, q_gen_4681) -> q_gen_4642
<cons, s>(q_gen_4661, q_gen_4620) -> q_gen_4642
<cons, s>(q_gen_4661, q_gen_4638) -> q_gen_4642
<cons, s>(q_gen_4661, q_gen_4681) -> q_gen_4642
<cons, s>(q_gen_4669, q_gen_4620) -> q_gen_4642
<cons, s>(q_gen_4669, q_gen_4638) -> q_gen_4642
<cons, s>(q_gen_4669, q_gen_4660) -> q_gen_4642
<a, s>(q_gen_4662) -> q_gen_4661
<b, s>(q_gen_4662) -> q_gen_4661
<a, s>(q_gen_4670) -> q_gen_4669
<b, s>(q_gen_4670) -> q_gen_4669
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_4613, q_gen_4615, q_gen_4643},
Q_f={q_gen_4613},
Delta=
{
<s>(q_gen_4615) -> q_gen_4615
<z>() -> q_gen_4615
<s, s>(q_gen_4613) -> q_gen_4613
<z, s>(q_gen_4615) -> q_gen_4613
<z, z>() -> q_gen_4613
<s, s>(q_gen_4643) -> q_gen_4643
<s, z>(q_gen_4615) -> q_gen_4643
}

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

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

Teacher's answer:
New clause system:
{
() -> delete([x, nil, nil]) -> 50
() -> length([nil, z]) -> 50
() -> leq([z, s(nn2)]) -> 51
() -> leq([z, z]) -> 50
(delete([h, t, _cr])) -> delete([h, cons(h, t), _cr]) -> 51
(delete([i, l, _ir]) /\ length([_ir, _jr]) /\ length([l, _kr])) -> leq([_jr, _kr]) -> 64
(delete([x, t, _dr]) /\ not eq_elt([x, h])) -> delete([x, cons(h, t), cons(h, _dr)]) -> 52
(length([ll, _yq])) -> length([cons(x, ll), s(_yq)]) -> 64
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 51
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 52
(leq([s(nn1), z])) -> BOT -> 52
}
Sat witness: Found: ((delete([i, l, _ir]) /\ length([_ir, _jr]) /\ length([l, _kr])) -> leq([_jr, _kr]), {
_ir -> cons(b, cons(b, cons(a, nil)))  ;  _jr -> s(s(s(z)))  ;  _kr -> s(s(z))  ;  i -> b  ;  l -> cons(b, cons(b, cons(a, cons(a, cons(a, nil)))))
})

-------------------------------------------
Step 67, which took 0.831534 s (model generation: 0.819720,  model checking: 0.011814):

Model:
|_
{
delete -> 
{{{
Q={q_gen_4617, q_gen_4623, q_gen_4624, q_gen_4626, q_gen_4627},
Q_f={q_gen_4617},
Delta=
{
<cons>(q_gen_4627, q_gen_4626) -> q_gen_4626
<nil>() -> q_gen_4626
<a>() -> q_gen_4627
<b>() -> q_gen_4627
<cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4623
<cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4623
<nil, nil>() -> q_gen_4623
<a, a>() -> q_gen_4624
<a, b>() -> q_gen_4624
<b, a>() -> q_gen_4624
<b, b>() -> q_gen_4624
<a, cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4617
<a, cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4617
<a, nil, nil>() -> q_gen_4617
<b, cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4617
<b, cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4617
<b, nil, nil>() -> q_gen_4617
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_4616, q_gen_4620, q_gen_4621, q_gen_4638, q_gen_4639, q_gen_4640, q_gen_4641, q_gen_4642, q_gen_4660, q_gen_4661, q_gen_4662, q_gen_4669, q_gen_4670, q_gen_4673, q_gen_4681, q_gen_4731},
Q_f={q_gen_4616},
Delta=
{
<cons>(q_gen_4673, q_gen_4681) -> q_gen_4620
<nil>() -> q_gen_4620
<cons>(q_gen_4639, q_gen_4620) -> q_gen_4638
<cons>(q_gen_4673, q_gen_4620) -> q_gen_4638
<cons>(q_gen_4673, q_gen_4660) -> q_gen_4638
<b>() -> q_gen_4639
<z>() -> q_gen_4641
<cons>(q_gen_4639, q_gen_4638) -> q_gen_4660
<cons>(q_gen_4673, q_gen_4638) -> q_gen_4660
<s>(q_gen_4641) -> q_gen_4662
<s>(q_gen_4662) -> q_gen_4670
<a>() -> q_gen_4673
<cons>(q_gen_4639, q_gen_4660) -> q_gen_4681
<cons>(q_gen_4639, q_gen_4681) -> q_gen_4681
<s>(q_gen_4670) -> q_gen_4731
<cons, s>(q_gen_4621, q_gen_4620) -> q_gen_4616
<cons, s>(q_gen_4640, q_gen_4638) -> q_gen_4616
<cons, s>(q_gen_4661, q_gen_4660) -> q_gen_4616
<cons, s>(q_gen_4669, q_gen_4681) -> q_gen_4616
<nil, z>() -> q_gen_4616
<a, s>(q_gen_4731) -> q_gen_4621
<a, z>() -> q_gen_4621
<b, s>(q_gen_4731) -> q_gen_4621
<b, z>() -> q_gen_4621
<a, s>(q_gen_4641) -> q_gen_4640
<b, s>(q_gen_4641) -> q_gen_4640
<cons, s>(q_gen_4621, q_gen_4638) -> q_gen_4642
<cons, s>(q_gen_4621, q_gen_4660) -> q_gen_4642
<cons, s>(q_gen_4621, q_gen_4681) -> q_gen_4642
<cons, s>(q_gen_4640, q_gen_4620) -> q_gen_4642
<cons, s>(q_gen_4640, q_gen_4660) -> q_gen_4642
<cons, s>(q_gen_4640, q_gen_4681) -> q_gen_4642
<cons, s>(q_gen_4661, q_gen_4620) -> q_gen_4642
<cons, s>(q_gen_4661, q_gen_4638) -> q_gen_4642
<cons, s>(q_gen_4661, q_gen_4681) -> q_gen_4642
<cons, s>(q_gen_4669, q_gen_4620) -> q_gen_4642
<cons, s>(q_gen_4669, q_gen_4638) -> q_gen_4642
<cons, s>(q_gen_4669, q_gen_4660) -> q_gen_4642
<a, s>(q_gen_4662) -> q_gen_4661
<b, s>(q_gen_4662) -> q_gen_4661
<a, s>(q_gen_4670) -> q_gen_4669
<b, s>(q_gen_4670) -> q_gen_4669
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_4613, q_gen_4615, q_gen_4643},
Q_f={q_gen_4613},
Delta=
{
<s>(q_gen_4615) -> q_gen_4615
<z>() -> q_gen_4615
<s, s>(q_gen_4613) -> q_gen_4613
<z, s>(q_gen_4615) -> q_gen_4613
<z, z>() -> q_gen_4613
<s, s>(q_gen_4643) -> q_gen_4643
<s, z>(q_gen_4615) -> q_gen_4643
}

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

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

Teacher's answer:
New clause system:
{
() -> delete([x, nil, nil]) -> 51
() -> length([nil, z]) -> 51
() -> leq([z, s(nn2)]) -> 52
() -> leq([z, z]) -> 51
(delete([h, t, _cr])) -> delete([h, cons(h, t), _cr]) -> 52
(delete([i, l, _ir]) /\ length([_ir, _jr]) /\ length([l, _kr])) -> leq([_jr, _kr]) -> 64
(delete([x, t, _dr]) /\ not eq_elt([x, h])) -> delete([x, cons(h, t), cons(h, _dr)]) -> 53
(length([ll, _yq])) -> length([cons(x, ll), s(_yq)]) -> 67
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 52
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 53
(leq([s(nn1), z])) -> BOT -> 53
}
Sat witness: Found: ((length([ll, _yq])) -> length([cons(x, ll), s(_yq)]), {
_yq -> s(s(s(s(z))))  ;  ll -> cons(b, cons(b, cons(b, cons(a, nil))))  ;  x -> b
})

-------------------------------------------
Step 68, which took 1.423660 s (model generation: 1.418516,  model checking: 0.005144):

Model:
|_
{
delete -> 
{{{
Q={q_gen_4617, q_gen_4623, q_gen_4624, q_gen_4626, q_gen_4627},
Q_f={q_gen_4617},
Delta=
{
<cons>(q_gen_4627, q_gen_4626) -> q_gen_4626
<nil>() -> q_gen_4626
<a>() -> q_gen_4627
<b>() -> q_gen_4627
<cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4623
<cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4623
<nil, nil>() -> q_gen_4623
<a, a>() -> q_gen_4624
<a, b>() -> q_gen_4624
<b, a>() -> q_gen_4624
<b, b>() -> q_gen_4624
<a, cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4617
<a, cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4617
<a, nil, nil>() -> q_gen_4617
<b, cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4617
<b, cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4617
<b, nil, nil>() -> q_gen_4617
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_4616, q_gen_4620, q_gen_4621, q_gen_4638, q_gen_4639, q_gen_4640, q_gen_4641, q_gen_4642, q_gen_4660, q_gen_4661, q_gen_4662, q_gen_4669, q_gen_4670, q_gen_4681, q_gen_4694, q_gen_4731},
Q_f={q_gen_4616},
Delta=
{
<nil>() -> q_gen_4620
<cons>(q_gen_4639, q_gen_4620) -> q_gen_4638
<a>() -> q_gen_4639
<b>() -> q_gen_4639
<z>() -> q_gen_4641
<cons>(q_gen_4639, q_gen_4638) -> q_gen_4660
<s>(q_gen_4641) -> q_gen_4662
<s>(q_gen_4662) -> q_gen_4670
<cons>(q_gen_4639, q_gen_4660) -> q_gen_4681
<cons>(q_gen_4639, q_gen_4681) -> q_gen_4694
<cons>(q_gen_4639, q_gen_4694) -> q_gen_4694
<s>(q_gen_4670) -> q_gen_4731
<cons, s>(q_gen_4621, q_gen_4620) -> q_gen_4616
<cons, s>(q_gen_4621, q_gen_4694) -> q_gen_4616
<cons, s>(q_gen_4640, q_gen_4638) -> q_gen_4616
<cons, s>(q_gen_4640, q_gen_4660) -> q_gen_4616
<cons, s>(q_gen_4661, q_gen_4660) -> q_gen_4616
<cons, s>(q_gen_4669, q_gen_4681) -> q_gen_4616
<nil, z>() -> q_gen_4616
<a, z>() -> q_gen_4621
<b, s>(q_gen_4731) -> q_gen_4621
<b, z>() -> q_gen_4621
<a, s>(q_gen_4641) -> q_gen_4640
<a, s>(q_gen_4731) -> q_gen_4640
<b, s>(q_gen_4641) -> q_gen_4640
<cons, s>(q_gen_4621, q_gen_4638) -> q_gen_4642
<cons, s>(q_gen_4621, q_gen_4660) -> q_gen_4642
<cons, s>(q_gen_4621, q_gen_4681) -> q_gen_4642
<cons, s>(q_gen_4640, q_gen_4620) -> q_gen_4642
<cons, s>(q_gen_4640, q_gen_4681) -> q_gen_4642
<cons, s>(q_gen_4640, q_gen_4694) -> q_gen_4642
<cons, s>(q_gen_4661, q_gen_4620) -> q_gen_4642
<cons, s>(q_gen_4661, q_gen_4638) -> q_gen_4642
<cons, s>(q_gen_4661, q_gen_4681) -> q_gen_4642
<cons, s>(q_gen_4661, q_gen_4694) -> q_gen_4642
<cons, s>(q_gen_4669, q_gen_4620) -> q_gen_4642
<cons, s>(q_gen_4669, q_gen_4638) -> q_gen_4642
<cons, s>(q_gen_4669, q_gen_4660) -> q_gen_4642
<cons, s>(q_gen_4669, q_gen_4694) -> q_gen_4642
<a, s>(q_gen_4662) -> q_gen_4661
<b, s>(q_gen_4662) -> q_gen_4661
<a, s>(q_gen_4670) -> q_gen_4669
<b, s>(q_gen_4670) -> q_gen_4669
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_4613, q_gen_4615, q_gen_4643},
Q_f={q_gen_4613},
Delta=
{
<s>(q_gen_4615) -> q_gen_4615
<z>() -> q_gen_4615
<s, s>(q_gen_4613) -> q_gen_4613
<z, s>(q_gen_4615) -> q_gen_4613
<z, z>() -> q_gen_4613
<s, s>(q_gen_4643) -> q_gen_4643
<s, z>(q_gen_4615) -> q_gen_4643
}

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

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

Teacher's answer:
New clause system:
{
() -> delete([x, nil, nil]) -> 52
() -> length([nil, z]) -> 52
() -> leq([z, s(nn2)]) -> 53
() -> leq([z, z]) -> 52
(delete([h, t, _cr])) -> delete([h, cons(h, t), _cr]) -> 53
(delete([i, l, _ir]) /\ length([_ir, _jr]) /\ length([l, _kr])) -> leq([_jr, _kr]) -> 67
(delete([x, t, _dr]) /\ not eq_elt([x, h])) -> delete([x, cons(h, t), cons(h, _dr)]) -> 54
(length([ll, _yq])) -> length([cons(x, ll), s(_yq)]) -> 67
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 53
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 54
(leq([s(nn1), z])) -> BOT -> 54
}
Sat witness: Found: ((delete([i, l, _ir]) /\ length([_ir, _jr]) /\ length([l, _kr])) -> leq([_jr, _kr]), {
_ir -> cons(b, nil)  ;  _jr -> s(s(s(s(s(z)))))  ;  _kr -> s(z)  ;  i -> a  ;  l -> cons(a, nil)
})

-------------------------------------------
Step 69, which took 1.283572 s (model generation: 1.276626,  model checking: 0.006946):

Model:
|_
{
delete -> 
{{{
Q={q_gen_4617, q_gen_4623, q_gen_4624, q_gen_4626, q_gen_4627},
Q_f={q_gen_4617},
Delta=
{
<cons>(q_gen_4627, q_gen_4626) -> q_gen_4626
<nil>() -> q_gen_4626
<a>() -> q_gen_4627
<b>() -> q_gen_4627
<cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4623
<cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4623
<nil, nil>() -> q_gen_4623
<a, a>() -> q_gen_4624
<a, b>() -> q_gen_4624
<b, a>() -> q_gen_4624
<b, b>() -> q_gen_4624
<a, cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4617
<a, cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4617
<a, nil, nil>() -> q_gen_4617
<b, cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4617
<b, cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4617
<b, nil, nil>() -> q_gen_4617
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_4616, q_gen_4620, q_gen_4621, q_gen_4638, q_gen_4639, q_gen_4640, q_gen_4641, q_gen_4642, q_gen_4660, q_gen_4661, q_gen_4662, q_gen_4669, q_gen_4670, q_gen_4672, q_gen_4673, q_gen_4694, q_gen_4695},
Q_f={q_gen_4616},
Delta=
{
<cons>(q_gen_4639, q_gen_4672) -> q_gen_4620
<nil>() -> q_gen_4620
<cons>(q_gen_4639, q_gen_4620) -> q_gen_4638
<cons>(q_gen_4673, q_gen_4694) -> q_gen_4638
<b>() -> q_gen_4639
<z>() -> q_gen_4641
<cons>(q_gen_4639, q_gen_4638) -> q_gen_4660
<s>(q_gen_4641) -> q_gen_4662
<s>(q_gen_4662) -> q_gen_4670
<s>(q_gen_4670) -> q_gen_4670
<cons>(q_gen_4673, q_gen_4620) -> q_gen_4672
<cons>(q_gen_4673, q_gen_4638) -> q_gen_4672
<a>() -> q_gen_4673
<cons>(q_gen_4639, q_gen_4695) -> q_gen_4694
<cons>(q_gen_4673, q_gen_4672) -> q_gen_4694
<cons>(q_gen_4639, q_gen_4660) -> q_gen_4695
<cons>(q_gen_4639, q_gen_4694) -> q_gen_4695
<cons>(q_gen_4673, q_gen_4695) -> q_gen_4695
<cons, s>(q_gen_4621, q_gen_4620) -> q_gen_4616
<cons, s>(q_gen_4621, q_gen_4672) -> q_gen_4616
<cons, s>(q_gen_4621, q_gen_4695) -> q_gen_4616
<cons, s>(q_gen_4640, q_gen_4638) -> q_gen_4616
<cons, s>(q_gen_4640, q_gen_4660) -> q_gen_4616
<cons, s>(q_gen_4640, q_gen_4672) -> q_gen_4616
<cons, s>(q_gen_4661, q_gen_4660) -> q_gen_4616
<cons, s>(q_gen_4669, q_gen_4695) -> q_gen_4616
<nil, z>() -> q_gen_4616
<a, s>(q_gen_4670) -> q_gen_4621
<a, z>() -> q_gen_4621
<b, z>() -> q_gen_4621
<a, s>(q_gen_4641) -> q_gen_4640
<a, s>(q_gen_4662) -> q_gen_4640
<b, s>(q_gen_4641) -> q_gen_4640
<cons, s>(q_gen_4621, q_gen_4638) -> q_gen_4642
<cons, s>(q_gen_4621, q_gen_4660) -> q_gen_4642
<cons, s>(q_gen_4640, q_gen_4620) -> q_gen_4642
<cons, s>(q_gen_4640, q_gen_4694) -> q_gen_4642
<cons, s>(q_gen_4640, q_gen_4695) -> q_gen_4642
<cons, s>(q_gen_4661, q_gen_4620) -> q_gen_4642
<cons, s>(q_gen_4661, q_gen_4638) -> q_gen_4642
<cons, s>(q_gen_4661, q_gen_4672) -> q_gen_4642
<cons, s>(q_gen_4661, q_gen_4694) -> q_gen_4642
<cons, s>(q_gen_4669, q_gen_4620) -> q_gen_4642
<cons, s>(q_gen_4669, q_gen_4638) -> q_gen_4642
<cons, s>(q_gen_4669, q_gen_4660) -> q_gen_4642
<cons, s>(q_gen_4669, q_gen_4672) -> q_gen_4642
<cons, s>(q_gen_4669, q_gen_4694) -> q_gen_4642
<b, s>(q_gen_4662) -> q_gen_4661
<b, s>(q_gen_4670) -> q_gen_4669
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_4613, q_gen_4615, q_gen_4643},
Q_f={q_gen_4613},
Delta=
{
<s>(q_gen_4615) -> q_gen_4615
<z>() -> q_gen_4615
<s, s>(q_gen_4613) -> q_gen_4613
<z, s>(q_gen_4615) -> q_gen_4613
<z, z>() -> q_gen_4613
<s, s>(q_gen_4643) -> q_gen_4643
<s, z>(q_gen_4615) -> q_gen_4643
}

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

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

Teacher's answer:
New clause system:
{
() -> delete([x, nil, nil]) -> 53
() -> length([nil, z]) -> 53
() -> leq([z, s(nn2)]) -> 54
() -> leq([z, z]) -> 53
(delete([h, t, _cr])) -> delete([h, cons(h, t), _cr]) -> 54
(delete([i, l, _ir]) /\ length([_ir, _jr]) /\ length([l, _kr])) -> leq([_jr, _kr]) -> 67
(delete([x, t, _dr]) /\ not eq_elt([x, h])) -> delete([x, cons(h, t), cons(h, _dr)]) -> 55
(length([ll, _yq])) -> length([cons(x, ll), s(_yq)]) -> 70
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 54
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 55
(leq([s(nn1), z])) -> BOT -> 55
}
Sat witness: Found: ((length([ll, _yq])) -> length([cons(x, ll), s(_yq)]), {
_yq -> s(s(s(s(z))))  ;  ll -> cons(a, cons(a, nil))  ;  x -> b
})

-------------------------------------------
Step 70, which took 2.896732 s (model generation: 2.887746,  model checking: 0.008986):

Model:
|_
{
delete -> 
{{{
Q={q_gen_4617, q_gen_4623, q_gen_4624, q_gen_4626, q_gen_4627},
Q_f={q_gen_4617},
Delta=
{
<cons>(q_gen_4627, q_gen_4626) -> q_gen_4626
<nil>() -> q_gen_4626
<a>() -> q_gen_4627
<b>() -> q_gen_4627
<cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4623
<cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4623
<nil, nil>() -> q_gen_4623
<a, a>() -> q_gen_4624
<a, b>() -> q_gen_4624
<b, a>() -> q_gen_4624
<b, b>() -> q_gen_4624
<a, cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4617
<a, cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4617
<a, nil, nil>() -> q_gen_4617
<b, cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4617
<b, cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4617
<b, nil, nil>() -> q_gen_4617
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_4616, q_gen_4620, q_gen_4621, q_gen_4638, q_gen_4639, q_gen_4640, q_gen_4641, q_gen_4642, q_gen_4660, q_gen_4661, q_gen_4662, q_gen_4669, q_gen_4670, q_gen_4673, q_gen_4679, q_gen_4694, q_gen_4695},
Q_f={q_gen_4616},
Delta=
{
<cons>(q_gen_4673, q_gen_4660) -> q_gen_4620
<nil>() -> q_gen_4620
<cons>(q_gen_4639, q_gen_4620) -> q_gen_4638
<b>() -> q_gen_4639
<z>() -> q_gen_4641
<cons>(q_gen_4639, q_gen_4638) -> q_gen_4660
<cons>(q_gen_4673, q_gen_4620) -> q_gen_4660
<s>(q_gen_4641) -> q_gen_4662
<s>(q_gen_4662) -> q_gen_4670
<s>(q_gen_4670) -> q_gen_4670
<a>() -> q_gen_4673
<cons>(q_gen_4639, q_gen_4679) -> q_gen_4679
<cons>(q_gen_4673, q_gen_4638) -> q_gen_4679
<cons>(q_gen_4673, q_gen_4695) -> q_gen_4679
<cons>(q_gen_4639, q_gen_4694) -> q_gen_4694
<cons>(q_gen_4639, q_gen_4695) -> q_gen_4694
<cons>(q_gen_4639, q_gen_4660) -> q_gen_4695
<cons>(q_gen_4673, q_gen_4679) -> q_gen_4695
<cons, s>(q_gen_4621, q_gen_4620) -> q_gen_4616
<cons, s>(q_gen_4640, q_gen_4638) -> q_gen_4616
<cons, s>(q_gen_4640, q_gen_4660) -> q_gen_4616
<cons, s>(q_gen_4640, q_gen_4679) -> q_gen_4616
<cons, s>(q_gen_4661, q_gen_4660) -> q_gen_4616
<cons, s>(q_gen_4661, q_gen_4679) -> q_gen_4616
<cons, s>(q_gen_4661, q_gen_4695) -> q_gen_4616
<cons, s>(q_gen_4669, q_gen_4679) -> q_gen_4616
<cons, s>(q_gen_4669, q_gen_4695) -> q_gen_4616
<nil, z>() -> q_gen_4616
<a, z>() -> q_gen_4621
<b, z>() -> q_gen_4621
<a, s>(q_gen_4641) -> q_gen_4640
<a, s>(q_gen_4662) -> q_gen_4640
<b, s>(q_gen_4641) -> q_gen_4640
<cons, s>(q_gen_4621, q_gen_4638) -> q_gen_4642
<cons, s>(q_gen_4621, q_gen_4679) -> q_gen_4642
<cons, s>(q_gen_4640, q_gen_4620) -> q_gen_4642
<cons, s>(q_gen_4640, q_gen_4694) -> q_gen_4642
<cons, s>(q_gen_4640, q_gen_4695) -> q_gen_4642
<cons, s>(q_gen_4661, q_gen_4620) -> q_gen_4642
<cons, s>(q_gen_4661, q_gen_4638) -> q_gen_4642
<cons, s>(q_gen_4661, q_gen_4694) -> q_gen_4642
<cons, s>(q_gen_4669, q_gen_4620) -> q_gen_4642
<cons, s>(q_gen_4669, q_gen_4638) -> q_gen_4642
<cons, s>(q_gen_4669, q_gen_4660) -> q_gen_4642
<cons, s>(q_gen_4669, q_gen_4694) -> q_gen_4642
<b, s>(q_gen_4662) -> q_gen_4661
<a, s>(q_gen_4670) -> q_gen_4669
<b, s>(q_gen_4670) -> q_gen_4669
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_4613, q_gen_4615, q_gen_4643},
Q_f={q_gen_4613},
Delta=
{
<s>(q_gen_4615) -> q_gen_4615
<z>() -> q_gen_4615
<s, s>(q_gen_4613) -> q_gen_4613
<z, s>(q_gen_4615) -> q_gen_4613
<z, z>() -> q_gen_4613
<s, s>(q_gen_4643) -> q_gen_4643
<s, z>(q_gen_4615) -> q_gen_4643
}

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

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

Teacher's answer:
New clause system:
{
() -> delete([x, nil, nil]) -> 54
() -> length([nil, z]) -> 54
() -> leq([z, s(nn2)]) -> 55
() -> leq([z, z]) -> 54
(delete([h, t, _cr])) -> delete([h, cons(h, t), _cr]) -> 55
(delete([i, l, _ir]) /\ length([_ir, _jr]) /\ length([l, _kr])) -> leq([_jr, _kr]) -> 70
(delete([x, t, _dr]) /\ not eq_elt([x, h])) -> delete([x, cons(h, t), cons(h, _dr)]) -> 56
(length([ll, _yq])) -> length([cons(x, ll), s(_yq)]) -> 70
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 55
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 56
(leq([s(nn1), z])) -> BOT -> 56
}
Sat witness: Found: ((delete([i, l, _ir]) /\ length([_ir, _jr]) /\ length([l, _kr])) -> leq([_jr, _kr]), {
_ir -> cons(a, cons(b, nil))  ;  _jr -> s(s(s(z)))  ;  _kr -> s(s(z))  ;  i -> b  ;  l -> cons(b, cons(b, cons(b, nil)))
})

-------------------------------------------
Step 71, which took 1.792736 s (model generation: 1.774112,  model checking: 0.018624):

Model:
|_
{
delete -> 
{{{
Q={q_gen_4617, q_gen_4623, q_gen_4624, q_gen_4626, q_gen_4627},
Q_f={q_gen_4617},
Delta=
{
<cons>(q_gen_4627, q_gen_4626) -> q_gen_4626
<nil>() -> q_gen_4626
<a>() -> q_gen_4627
<b>() -> q_gen_4627
<cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4623
<cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4623
<nil, nil>() -> q_gen_4623
<a, a>() -> q_gen_4624
<a, b>() -> q_gen_4624
<b, a>() -> q_gen_4624
<b, b>() -> q_gen_4624
<a, cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4617
<a, cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4617
<a, nil, nil>() -> q_gen_4617
<b, cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4617
<b, cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4617
<b, nil, nil>() -> q_gen_4617
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_4616, q_gen_4620, q_gen_4621, q_gen_4638, q_gen_4639, q_gen_4640, q_gen_4641, q_gen_4642, q_gen_4660, q_gen_4661, q_gen_4662, q_gen_4669, q_gen_4670, q_gen_4673, q_gen_4681, q_gen_4694, q_gen_4722},
Q_f={q_gen_4616},
Delta=
{
<nil>() -> q_gen_4620
<cons>(q_gen_4639, q_gen_4620) -> q_gen_4638
<b>() -> q_gen_4639
<z>() -> q_gen_4641
<cons>(q_gen_4639, q_gen_4638) -> q_gen_4660
<cons>(q_gen_4673, q_gen_4620) -> q_gen_4660
<cons>(q_gen_4673, q_gen_4638) -> q_gen_4660
<cons>(q_gen_4673, q_gen_4660) -> q_gen_4660
<s>(q_gen_4641) -> q_gen_4662
<s>(q_gen_4662) -> q_gen_4670
<s>(q_gen_4670) -> q_gen_4670
<a>() -> q_gen_4673
<cons>(q_gen_4639, q_gen_4660) -> q_gen_4681
<cons>(q_gen_4639, q_gen_4681) -> q_gen_4694
<cons>(q_gen_4639, q_gen_4694) -> q_gen_4722
<cons>(q_gen_4639, q_gen_4722) -> q_gen_4722
<cons>(q_gen_4673, q_gen_4681) -> q_gen_4722
<cons, s>(q_gen_4621, q_gen_4620) -> q_gen_4616
<cons, s>(q_gen_4640, q_gen_4638) -> q_gen_4616
<cons, s>(q_gen_4640, q_gen_4660) -> q_gen_4616
<cons, s>(q_gen_4661, q_gen_4660) -> q_gen_4616
<cons, s>(q_gen_4669, q_gen_4681) -> q_gen_4616
<cons, s>(q_gen_4669, q_gen_4722) -> q_gen_4616
<nil, z>() -> q_gen_4616
<a, z>() -> q_gen_4621
<b, z>() -> q_gen_4621
<a, s>(q_gen_4641) -> q_gen_4640
<b, s>(q_gen_4641) -> q_gen_4640
<cons, s>(q_gen_4621, q_gen_4638) -> q_gen_4642
<cons, s>(q_gen_4621, q_gen_4681) -> q_gen_4642
<cons, s>(q_gen_4640, q_gen_4620) -> q_gen_4642
<cons, s>(q_gen_4640, q_gen_4681) -> q_gen_4642
<cons, s>(q_gen_4640, q_gen_4694) -> q_gen_4642
<cons, s>(q_gen_4640, q_gen_4722) -> q_gen_4642
<cons, s>(q_gen_4661, q_gen_4620) -> q_gen_4642
<cons, s>(q_gen_4661, q_gen_4638) -> q_gen_4642
<cons, s>(q_gen_4661, q_gen_4681) -> q_gen_4642
<cons, s>(q_gen_4661, q_gen_4694) -> q_gen_4642
<cons, s>(q_gen_4661, q_gen_4722) -> q_gen_4642
<cons, s>(q_gen_4669, q_gen_4620) -> q_gen_4642
<cons, s>(q_gen_4669, q_gen_4638) -> q_gen_4642
<cons, s>(q_gen_4669, q_gen_4660) -> q_gen_4642
<cons, s>(q_gen_4669, q_gen_4694) -> q_gen_4642
<a, s>(q_gen_4662) -> q_gen_4661
<b, s>(q_gen_4662) -> q_gen_4661
<a, s>(q_gen_4670) -> q_gen_4669
<b, s>(q_gen_4670) -> q_gen_4669
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_4613, q_gen_4615, q_gen_4643},
Q_f={q_gen_4613},
Delta=
{
<s>(q_gen_4615) -> q_gen_4615
<z>() -> q_gen_4615
<s, s>(q_gen_4613) -> q_gen_4613
<z, s>(q_gen_4615) -> q_gen_4613
<z, z>() -> q_gen_4613
<s, s>(q_gen_4643) -> q_gen_4643
<s, z>(q_gen_4615) -> q_gen_4643
}

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

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

Teacher's answer:
New clause system:
{
() -> delete([x, nil, nil]) -> 55
() -> length([nil, z]) -> 55
() -> leq([z, s(nn2)]) -> 56
() -> leq([z, z]) -> 55
(delete([h, t, _cr])) -> delete([h, cons(h, t), _cr]) -> 56
(delete([i, l, _ir]) /\ length([_ir, _jr]) /\ length([l, _kr])) -> leq([_jr, _kr]) -> 70
(delete([x, t, _dr]) /\ not eq_elt([x, h])) -> delete([x, cons(h, t), cons(h, _dr)]) -> 57
(length([ll, _yq])) -> length([cons(x, ll), s(_yq)]) -> 73
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 56
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 57
(leq([s(nn1), z])) -> BOT -> 57
}
Sat witness: Found: ((length([ll, _yq])) -> length([cons(x, ll), s(_yq)]), {
_yq -> s(s(z))  ;  ll -> cons(b, cons(b, cons(b, nil)))  ;  x -> b
})

-------------------------------------------
Step 72, which took 1.363015 s (model generation: 1.354082,  model checking: 0.008933):

Model:
|_
{
delete -> 
{{{
Q={q_gen_4617, q_gen_4623, q_gen_4624, q_gen_4626, q_gen_4627},
Q_f={q_gen_4617},
Delta=
{
<cons>(q_gen_4627, q_gen_4626) -> q_gen_4626
<nil>() -> q_gen_4626
<a>() -> q_gen_4627
<b>() -> q_gen_4627
<cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4623
<cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4623
<nil, nil>() -> q_gen_4623
<a, a>() -> q_gen_4624
<a, b>() -> q_gen_4624
<b, a>() -> q_gen_4624
<b, b>() -> q_gen_4624
<a, cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4617
<a, cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4617
<a, nil, nil>() -> q_gen_4617
<b, cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4617
<b, cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4617
<b, nil, nil>() -> q_gen_4617
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_4616, q_gen_4620, q_gen_4621, q_gen_4638, q_gen_4639, q_gen_4640, q_gen_4641, q_gen_4642, q_gen_4660, q_gen_4661, q_gen_4662, q_gen_4669, q_gen_4670, q_gen_4673, q_gen_4679, q_gen_4694, q_gen_4695},
Q_f={q_gen_4616},
Delta=
{
<cons>(q_gen_4639, q_gen_4679) -> q_gen_4620
<cons>(q_gen_4673, q_gen_4695) -> q_gen_4620
<nil>() -> q_gen_4620
<cons>(q_gen_4639, q_gen_4620) -> q_gen_4638
<b>() -> q_gen_4639
<z>() -> q_gen_4641
<cons>(q_gen_4639, q_gen_4638) -> q_gen_4660
<cons>(q_gen_4673, q_gen_4620) -> q_gen_4660
<s>(q_gen_4641) -> q_gen_4662
<s>(q_gen_4662) -> q_gen_4670
<s>(q_gen_4670) -> q_gen_4670
<a>() -> q_gen_4673
<cons>(q_gen_4673, q_gen_4638) -> q_gen_4679
<cons>(q_gen_4639, q_gen_4694) -> q_gen_4694
<cons>(q_gen_4639, q_gen_4695) -> q_gen_4694
<cons>(q_gen_4673, q_gen_4660) -> q_gen_4694
<cons>(q_gen_4639, q_gen_4660) -> q_gen_4695
<cons>(q_gen_4673, q_gen_4694) -> q_gen_4695
<cons, s>(q_gen_4621, q_gen_4620) -> q_gen_4616
<cons, s>(q_gen_4621, q_gen_4679) -> q_gen_4616
<cons, s>(q_gen_4640, q_gen_4638) -> q_gen_4616
<cons, s>(q_gen_4640, q_gen_4660) -> q_gen_4616
<cons, s>(q_gen_4661, q_gen_4660) -> q_gen_4616
<cons, s>(q_gen_4661, q_gen_4695) -> q_gen_4616
<cons, s>(q_gen_4669, q_gen_4679) -> q_gen_4616
<cons, s>(q_gen_4669, q_gen_4695) -> q_gen_4616
<nil, z>() -> q_gen_4616
<a, s>(q_gen_4670) -> q_gen_4621
<a, z>() -> q_gen_4621
<b, z>() -> q_gen_4621
<a, s>(q_gen_4641) -> q_gen_4640
<b, s>(q_gen_4641) -> q_gen_4640
<cons, s>(q_gen_4621, q_gen_4638) -> q_gen_4642
<cons, s>(q_gen_4621, q_gen_4660) -> q_gen_4642
<cons, s>(q_gen_4621, q_gen_4695) -> q_gen_4642
<cons, s>(q_gen_4640, q_gen_4620) -> q_gen_4642
<cons, s>(q_gen_4640, q_gen_4694) -> q_gen_4642
<cons, s>(q_gen_4661, q_gen_4620) -> q_gen_4642
<cons, s>(q_gen_4661, q_gen_4638) -> q_gen_4642
<cons, s>(q_gen_4661, q_gen_4679) -> q_gen_4642
<cons, s>(q_gen_4661, q_gen_4694) -> q_gen_4642
<cons, s>(q_gen_4669, q_gen_4620) -> q_gen_4642
<cons, s>(q_gen_4669, q_gen_4638) -> q_gen_4642
<cons, s>(q_gen_4669, q_gen_4660) -> q_gen_4642
<cons, s>(q_gen_4669, q_gen_4694) -> q_gen_4642
<b, s>(q_gen_4662) -> q_gen_4661
<a, s>(q_gen_4662) -> q_gen_4669
<b, s>(q_gen_4670) -> q_gen_4669
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_4613, q_gen_4615, q_gen_4643},
Q_f={q_gen_4613},
Delta=
{
<s>(q_gen_4615) -> q_gen_4615
<z>() -> q_gen_4615
<s, s>(q_gen_4613) -> q_gen_4613
<z, s>(q_gen_4615) -> q_gen_4613
<z, z>() -> q_gen_4613
<s, s>(q_gen_4643) -> q_gen_4643
<s, z>(q_gen_4615) -> q_gen_4643
}

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

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

Teacher's answer:
New clause system:
{
() -> delete([x, nil, nil]) -> 56
() -> length([nil, z]) -> 56
() -> leq([z, s(nn2)]) -> 57
() -> leq([z, z]) -> 56
(delete([h, t, _cr])) -> delete([h, cons(h, t), _cr]) -> 57
(delete([i, l, _ir]) /\ length([_ir, _jr]) /\ length([l, _kr])) -> leq([_jr, _kr]) -> 73
(delete([x, t, _dr]) /\ not eq_elt([x, h])) -> delete([x, cons(h, t), cons(h, _dr)]) -> 58
(length([ll, _yq])) -> length([cons(x, ll), s(_yq)]) -> 73
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 57
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 58
(leq([s(nn1), z])) -> BOT -> 58
}
Sat witness: Found: ((delete([i, l, _ir]) /\ length([_ir, _jr]) /\ length([l, _kr])) -> leq([_jr, _kr]), {
_ir -> cons(b, cons(b, cons(a, nil)))  ;  _jr -> s(s(s(z)))  ;  _kr -> s(s(z))  ;  i -> a  ;  l -> cons(b, cons(a, cons(a, cons(b, cons(b, cons(b, nil))))))
})

-------------------------------------------
Step 73, which took 5.009271 s (model generation: 4.988174,  model checking: 0.021097):

Model:
|_
{
delete -> 
{{{
Q={q_gen_4617, q_gen_4623, q_gen_4624, q_gen_4626, q_gen_4627},
Q_f={q_gen_4617},
Delta=
{
<cons>(q_gen_4627, q_gen_4626) -> q_gen_4626
<nil>() -> q_gen_4626
<a>() -> q_gen_4627
<b>() -> q_gen_4627
<cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4623
<cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4623
<nil, nil>() -> q_gen_4623
<a, a>() -> q_gen_4624
<a, b>() -> q_gen_4624
<b, a>() -> q_gen_4624
<b, b>() -> q_gen_4624
<a, cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4617
<a, cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4617
<a, nil, nil>() -> q_gen_4617
<b, cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4617
<b, cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4617
<b, nil, nil>() -> q_gen_4617
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_4616, q_gen_4620, q_gen_4621, q_gen_4638, q_gen_4639, q_gen_4640, q_gen_4641, q_gen_4642, q_gen_4660, q_gen_4661, q_gen_4662, q_gen_4669, q_gen_4670, q_gen_4673, q_gen_4679, q_gen_4694, q_gen_4695},
Q_f={q_gen_4616},
Delta=
{
<cons>(q_gen_4673, q_gen_4660) -> q_gen_4620
<nil>() -> q_gen_4620
<cons>(q_gen_4639, q_gen_4620) -> q_gen_4638
<b>() -> q_gen_4639
<z>() -> q_gen_4641
<cons>(q_gen_4639, q_gen_4638) -> q_gen_4660
<cons>(q_gen_4673, q_gen_4620) -> q_gen_4660
<s>(q_gen_4641) -> q_gen_4662
<s>(q_gen_4662) -> q_gen_4670
<s>(q_gen_4670) -> q_gen_4670
<a>() -> q_gen_4673
<cons>(q_gen_4639, q_gen_4679) -> q_gen_4679
<cons>(q_gen_4673, q_gen_4638) -> q_gen_4679
<cons>(q_gen_4673, q_gen_4679) -> q_gen_4679
<cons>(q_gen_4673, q_gen_4695) -> q_gen_4679
<cons>(q_gen_4639, q_gen_4695) -> q_gen_4694
<cons>(q_gen_4639, q_gen_4660) -> q_gen_4695
<cons>(q_gen_4639, q_gen_4694) -> q_gen_4695
<cons, s>(q_gen_4621, q_gen_4620) -> q_gen_4616
<cons, s>(q_gen_4640, q_gen_4638) -> q_gen_4616
<cons, s>(q_gen_4640, q_gen_4660) -> q_gen_4616
<cons, s>(q_gen_4661, q_gen_4660) -> q_gen_4616
<cons, s>(q_gen_4661, q_gen_4679) -> q_gen_4616
<cons, s>(q_gen_4661, q_gen_4695) -> q_gen_4616
<cons, s>(q_gen_4669, q_gen_4679) -> q_gen_4616
<cons, s>(q_gen_4669, q_gen_4695) -> q_gen_4616
<nil, z>() -> q_gen_4616
<a, z>() -> q_gen_4621
<b, z>() -> q_gen_4621
<a, s>(q_gen_4641) -> q_gen_4640
<b, s>(q_gen_4641) -> q_gen_4640
<cons, s>(q_gen_4621, q_gen_4638) -> q_gen_4642
<cons, s>(q_gen_4621, q_gen_4679) -> q_gen_4642
<cons, s>(q_gen_4640, q_gen_4620) -> q_gen_4642
<cons, s>(q_gen_4640, q_gen_4679) -> q_gen_4642
<cons, s>(q_gen_4640, q_gen_4694) -> q_gen_4642
<cons, s>(q_gen_4640, q_gen_4695) -> q_gen_4642
<cons, s>(q_gen_4661, q_gen_4620) -> q_gen_4642
<cons, s>(q_gen_4661, q_gen_4638) -> q_gen_4642
<cons, s>(q_gen_4661, q_gen_4694) -> q_gen_4642
<cons, s>(q_gen_4669, q_gen_4620) -> q_gen_4642
<cons, s>(q_gen_4669, q_gen_4638) -> q_gen_4642
<cons, s>(q_gen_4669, q_gen_4660) -> q_gen_4642
<cons, s>(q_gen_4669, q_gen_4694) -> q_gen_4642
<b, s>(q_gen_4662) -> q_gen_4661
<a, s>(q_gen_4662) -> q_gen_4669
<a, s>(q_gen_4670) -> q_gen_4669
<b, s>(q_gen_4670) -> q_gen_4669
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_4613, q_gen_4615, q_gen_4643},
Q_f={q_gen_4613},
Delta=
{
<s>(q_gen_4615) -> q_gen_4615
<z>() -> q_gen_4615
<s, s>(q_gen_4613) -> q_gen_4613
<z, s>(q_gen_4615) -> q_gen_4613
<z, z>() -> q_gen_4613
<s, s>(q_gen_4643) -> q_gen_4643
<s, z>(q_gen_4615) -> q_gen_4643
}

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

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

Teacher's answer:
New clause system:
{
() -> delete([x, nil, nil]) -> 57
() -> length([nil, z]) -> 57
() -> leq([z, s(nn2)]) -> 58
() -> leq([z, z]) -> 57
(delete([h, t, _cr])) -> delete([h, cons(h, t), _cr]) -> 58
(delete([i, l, _ir]) /\ length([_ir, _jr]) /\ length([l, _kr])) -> leq([_jr, _kr]) -> 73
(delete([x, t, _dr]) /\ not eq_elt([x, h])) -> delete([x, cons(h, t), cons(h, _dr)]) -> 59
(length([ll, _yq])) -> length([cons(x, ll), s(_yq)]) -> 76
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 58
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 59
(leq([s(nn1), z])) -> BOT -> 59
}
Sat witness: Found: ((length([ll, _yq])) -> length([cons(x, ll), s(_yq)]), {
_yq -> s(s(z))  ;  ll -> cons(b, cons(b, nil))  ;  x -> a
})

-------------------------------------------
Step 74, which took 2.985284 s (model generation: 2.974593,  model checking: 0.010691):

Model:
|_
{
delete -> 
{{{
Q={q_gen_4617, q_gen_4623, q_gen_4624, q_gen_4626, q_gen_4627},
Q_f={q_gen_4617},
Delta=
{
<cons>(q_gen_4627, q_gen_4626) -> q_gen_4626
<nil>() -> q_gen_4626
<a>() -> q_gen_4627
<b>() -> q_gen_4627
<cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4623
<cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4623
<nil, nil>() -> q_gen_4623
<a, a>() -> q_gen_4624
<a, b>() -> q_gen_4624
<b, a>() -> q_gen_4624
<b, b>() -> q_gen_4624
<a, cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4617
<a, cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4617
<a, nil, nil>() -> q_gen_4617
<b, cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4617
<b, cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4617
<b, nil, nil>() -> q_gen_4617
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_4616, q_gen_4620, q_gen_4621, q_gen_4638, q_gen_4639, q_gen_4640, q_gen_4641, q_gen_4642, q_gen_4660, q_gen_4661, q_gen_4662, q_gen_4669, q_gen_4670, q_gen_4673, q_gen_4679, q_gen_4694, q_gen_4695},
Q_f={q_gen_4616},
Delta=
{
<nil>() -> q_gen_4620
<cons>(q_gen_4639, q_gen_4620) -> q_gen_4638
<cons>(q_gen_4673, q_gen_4660) -> q_gen_4638
<b>() -> q_gen_4639
<z>() -> q_gen_4641
<cons>(q_gen_4639, q_gen_4638) -> q_gen_4660
<cons>(q_gen_4673, q_gen_4620) -> q_gen_4660
<s>(q_gen_4641) -> q_gen_4662
<s>(q_gen_4662) -> q_gen_4670
<s>(q_gen_4670) -> q_gen_4670
<a>() -> q_gen_4673
<cons>(q_gen_4639, q_gen_4679) -> q_gen_4679
<cons>(q_gen_4673, q_gen_4638) -> q_gen_4679
<cons>(q_gen_4673, q_gen_4695) -> q_gen_4679
<cons>(q_gen_4639, q_gen_4695) -> q_gen_4694
<cons>(q_gen_4639, q_gen_4660) -> q_gen_4695
<cons>(q_gen_4639, q_gen_4694) -> q_gen_4695
<cons>(q_gen_4673, q_gen_4679) -> q_gen_4695
<cons, s>(q_gen_4621, q_gen_4620) -> q_gen_4616
<cons, s>(q_gen_4640, q_gen_4638) -> q_gen_4616
<cons, s>(q_gen_4640, q_gen_4660) -> q_gen_4616
<cons, s>(q_gen_4661, q_gen_4660) -> q_gen_4616
<cons, s>(q_gen_4661, q_gen_4679) -> q_gen_4616
<cons, s>(q_gen_4661, q_gen_4695) -> q_gen_4616
<cons, s>(q_gen_4669, q_gen_4679) -> q_gen_4616
<cons, s>(q_gen_4669, q_gen_4695) -> q_gen_4616
<nil, z>() -> q_gen_4616
<a, z>() -> q_gen_4621
<b, z>() -> q_gen_4621
<a, s>(q_gen_4641) -> q_gen_4640
<b, s>(q_gen_4641) -> q_gen_4640
<cons, s>(q_gen_4621, q_gen_4638) -> q_gen_4642
<cons, s>(q_gen_4621, q_gen_4679) -> q_gen_4642
<cons, s>(q_gen_4640, q_gen_4620) -> q_gen_4642
<cons, s>(q_gen_4640, q_gen_4679) -> q_gen_4642
<cons, s>(q_gen_4640, q_gen_4694) -> q_gen_4642
<cons, s>(q_gen_4640, q_gen_4695) -> q_gen_4642
<cons, s>(q_gen_4661, q_gen_4620) -> q_gen_4642
<cons, s>(q_gen_4661, q_gen_4638) -> q_gen_4642
<cons, s>(q_gen_4661, q_gen_4694) -> q_gen_4642
<cons, s>(q_gen_4669, q_gen_4620) -> q_gen_4642
<cons, s>(q_gen_4669, q_gen_4638) -> q_gen_4642
<cons, s>(q_gen_4669, q_gen_4660) -> q_gen_4642
<cons, s>(q_gen_4669, q_gen_4694) -> q_gen_4642
<a, s>(q_gen_4662) -> q_gen_4661
<b, s>(q_gen_4662) -> q_gen_4661
<a, s>(q_gen_4670) -> q_gen_4669
<b, s>(q_gen_4670) -> q_gen_4669
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_4613, q_gen_4615, q_gen_4643},
Q_f={q_gen_4613},
Delta=
{
<s>(q_gen_4615) -> q_gen_4615
<z>() -> q_gen_4615
<s, s>(q_gen_4613) -> q_gen_4613
<z, s>(q_gen_4615) -> q_gen_4613
<z, z>() -> q_gen_4613
<s, s>(q_gen_4643) -> q_gen_4643
<s, z>(q_gen_4615) -> q_gen_4643
}

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

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

Teacher's answer:
New clause system:
{
() -> delete([x, nil, nil]) -> 58
() -> length([nil, z]) -> 58
() -> leq([z, s(nn2)]) -> 59
() -> leq([z, z]) -> 58
(delete([h, t, _cr])) -> delete([h, cons(h, t), _cr]) -> 59
(delete([i, l, _ir]) /\ length([_ir, _jr]) /\ length([l, _kr])) -> leq([_jr, _kr]) -> 76
(delete([x, t, _dr]) /\ not eq_elt([x, h])) -> delete([x, cons(h, t), cons(h, _dr)]) -> 60
(length([ll, _yq])) -> length([cons(x, ll), s(_yq)]) -> 76
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 59
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 60
(leq([s(nn1), z])) -> BOT -> 60
}
Sat witness: Found: ((delete([i, l, _ir]) /\ length([_ir, _jr]) /\ length([l, _kr])) -> leq([_jr, _kr]), {
_ir -> cons(b, cons(b, cons(b, nil)))  ;  _jr -> s(s(s(z)))  ;  _kr -> s(s(z))  ;  i -> b  ;  l -> cons(b, cons(b, cons(b, nil)))
})

-------------------------------------------
Step 75, which took 3.248588 s (model generation: 3.233172,  model checking: 0.015416):

Model:
|_
{
delete -> 
{{{
Q={q_gen_4617, q_gen_4623, q_gen_4624, q_gen_4626, q_gen_4627},
Q_f={q_gen_4617},
Delta=
{
<cons>(q_gen_4627, q_gen_4626) -> q_gen_4626
<nil>() -> q_gen_4626
<a>() -> q_gen_4627
<b>() -> q_gen_4627
<cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4623
<cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4623
<nil, nil>() -> q_gen_4623
<a, a>() -> q_gen_4624
<a, b>() -> q_gen_4624
<b, a>() -> q_gen_4624
<b, b>() -> q_gen_4624
<a, cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4617
<a, cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4617
<a, nil, nil>() -> q_gen_4617
<b, cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4617
<b, cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4617
<b, nil, nil>() -> q_gen_4617
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_4616, q_gen_4620, q_gen_4621, q_gen_4638, q_gen_4639, q_gen_4640, q_gen_4641, q_gen_4642, q_gen_4660, q_gen_4661, q_gen_4662, q_gen_4669, q_gen_4670, q_gen_4681, q_gen_4682, q_gen_4694, q_gen_4731},
Q_f={q_gen_4616},
Delta=
{
<nil>() -> q_gen_4620
<cons>(q_gen_4639, q_gen_4620) -> q_gen_4638
<a>() -> q_gen_4639
<b>() -> q_gen_4639
<z>() -> q_gen_4641
<cons>(q_gen_4639, q_gen_4638) -> q_gen_4660
<cons>(q_gen_4639, q_gen_4694) -> q_gen_4660
<s>(q_gen_4641) -> q_gen_4662
<s>(q_gen_4662) -> q_gen_4670
<cons>(q_gen_4639, q_gen_4660) -> q_gen_4681
<cons>(q_gen_4639, q_gen_4681) -> q_gen_4694
<s>(q_gen_4670) -> q_gen_4731
<cons, s>(q_gen_4621, q_gen_4620) -> q_gen_4616
<cons, s>(q_gen_4640, q_gen_4638) -> q_gen_4616
<cons, s>(q_gen_4661, q_gen_4660) -> q_gen_4616
<cons, s>(q_gen_4669, q_gen_4681) -> q_gen_4616
<cons, s>(q_gen_4682, q_gen_4681) -> q_gen_4616
<cons, s>(q_gen_4682, q_gen_4694) -> q_gen_4616
<nil, z>() -> q_gen_4616
<a, z>() -> q_gen_4621
<b, z>() -> q_gen_4621
<a, s>(q_gen_4641) -> q_gen_4640
<b, s>(q_gen_4641) -> q_gen_4640
<cons, s>(q_gen_4621, q_gen_4638) -> q_gen_4642
<cons, s>(q_gen_4621, q_gen_4681) -> q_gen_4642
<cons, s>(q_gen_4640, q_gen_4620) -> q_gen_4642
<cons, s>(q_gen_4640, q_gen_4660) -> q_gen_4642
<cons, s>(q_gen_4640, q_gen_4681) -> q_gen_4642
<cons, s>(q_gen_4640, q_gen_4694) -> q_gen_4642
<cons, s>(q_gen_4661, q_gen_4620) -> q_gen_4642
<cons, s>(q_gen_4661, q_gen_4638) -> q_gen_4642
<cons, s>(q_gen_4661, q_gen_4681) -> q_gen_4642
<cons, s>(q_gen_4661, q_gen_4694) -> q_gen_4642
<cons, s>(q_gen_4669, q_gen_4620) -> q_gen_4642
<cons, s>(q_gen_4669, q_gen_4638) -> q_gen_4642
<cons, s>(q_gen_4669, q_gen_4660) -> q_gen_4642
<cons, s>(q_gen_4669, q_gen_4694) -> q_gen_4642
<cons, s>(q_gen_4682, q_gen_4620) -> q_gen_4642
<cons, s>(q_gen_4682, q_gen_4638) -> q_gen_4642
<cons, s>(q_gen_4682, q_gen_4660) -> q_gen_4642
<a, s>(q_gen_4662) -> q_gen_4661
<b, s>(q_gen_4662) -> q_gen_4661
<a, s>(q_gen_4731) -> q_gen_4669
<b, s>(q_gen_4670) -> q_gen_4669
<a, s>(q_gen_4670) -> q_gen_4682
<b, s>(q_gen_4731) -> q_gen_4682
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_4613, q_gen_4615, q_gen_4643},
Q_f={q_gen_4613},
Delta=
{
<s>(q_gen_4615) -> q_gen_4615
<z>() -> q_gen_4615
<s, s>(q_gen_4613) -> q_gen_4613
<z, s>(q_gen_4615) -> q_gen_4613
<z, z>() -> q_gen_4613
<s, s>(q_gen_4643) -> q_gen_4643
<s, z>(q_gen_4615) -> q_gen_4643
}

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

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

Teacher's answer:
New clause system:
{
() -> delete([x, nil, nil]) -> 59
() -> length([nil, z]) -> 59
() -> leq([z, s(nn2)]) -> 60
() -> leq([z, z]) -> 59
(delete([h, t, _cr])) -> delete([h, cons(h, t), _cr]) -> 60
(delete([i, l, _ir]) /\ length([_ir, _jr]) /\ length([l, _kr])) -> leq([_jr, _kr]) -> 76
(delete([x, t, _dr]) /\ not eq_elt([x, h])) -> delete([x, cons(h, t), cons(h, _dr)]) -> 61
(length([ll, _yq])) -> length([cons(x, ll), s(_yq)]) -> 79
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 60
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 61
(leq([s(nn1), z])) -> BOT -> 61
}
Sat witness: Found: ((length([ll, _yq])) -> length([cons(x, ll), s(_yq)]), {
_yq -> s(s(s(s(z))))  ;  ll -> cons(a, cons(b, cons(b, cons(b, cons(b, nil)))))  ;  x -> a
})

-------------------------------------------
Step 76, which took 3.444306 s (model generation: 3.432156,  model checking: 0.012150):

Model:
|_
{
delete -> 
{{{
Q={q_gen_4617, q_gen_4623, q_gen_4624, q_gen_4626, q_gen_4627},
Q_f={q_gen_4617},
Delta=
{
<cons>(q_gen_4627, q_gen_4626) -> q_gen_4626
<nil>() -> q_gen_4626
<a>() -> q_gen_4627
<b>() -> q_gen_4627
<cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4623
<cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4623
<nil, nil>() -> q_gen_4623
<a, a>() -> q_gen_4624
<a, b>() -> q_gen_4624
<b, a>() -> q_gen_4624
<b, b>() -> q_gen_4624
<a, cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4617
<a, cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4617
<a, nil, nil>() -> q_gen_4617
<b, cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4617
<b, cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4617
<b, nil, nil>() -> q_gen_4617
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_4616, q_gen_4620, q_gen_4621, q_gen_4638, q_gen_4639, q_gen_4640, q_gen_4641, q_gen_4642, q_gen_4660, q_gen_4661, q_gen_4662, q_gen_4669, q_gen_4670, q_gen_4672, q_gen_4673, q_gen_4679, q_gen_4694},
Q_f={q_gen_4616},
Delta=
{
<cons>(q_gen_4673, q_gen_4672) -> q_gen_4620
<nil>() -> q_gen_4620
<cons>(q_gen_4639, q_gen_4620) -> q_gen_4638
<b>() -> q_gen_4639
<z>() -> q_gen_4641
<cons>(q_gen_4639, q_gen_4638) -> q_gen_4660
<s>(q_gen_4641) -> q_gen_4662
<s>(q_gen_4662) -> q_gen_4670
<s>(q_gen_4670) -> q_gen_4670
<cons>(q_gen_4639, q_gen_4660) -> q_gen_4672
<cons>(q_gen_4673, q_gen_4620) -> q_gen_4672
<a>() -> q_gen_4673
<cons>(q_gen_4639, q_gen_4679) -> q_gen_4679
<cons>(q_gen_4673, q_gen_4638) -> q_gen_4679
<cons>(q_gen_4673, q_gen_4679) -> q_gen_4679
<cons>(q_gen_4673, q_gen_4694) -> q_gen_4679
<cons>(q_gen_4639, q_gen_4672) -> q_gen_4694
<cons>(q_gen_4639, q_gen_4694) -> q_gen_4694
<cons, s>(q_gen_4621, q_gen_4620) -> q_gen_4616
<cons, s>(q_gen_4621, q_gen_4679) -> q_gen_4616
<cons, s>(q_gen_4621, q_gen_4694) -> q_gen_4616
<cons, s>(q_gen_4640, q_gen_4638) -> q_gen_4616
<cons, s>(q_gen_4640, q_gen_4672) -> q_gen_4616
<cons, s>(q_gen_4640, q_gen_4679) -> q_gen_4616
<cons, s>(q_gen_4661, q_gen_4660) -> q_gen_4616
<cons, s>(q_gen_4661, q_gen_4672) -> q_gen_4616
<cons, s>(q_gen_4661, q_gen_4679) -> q_gen_4616
<cons, s>(q_gen_4669, q_gen_4672) -> q_gen_4616
<cons, s>(q_gen_4669, q_gen_4679) -> q_gen_4616
<nil, z>() -> q_gen_4616
<a, s>(q_gen_4670) -> q_gen_4621
<a, z>() -> q_gen_4621
<b, z>() -> q_gen_4621
<a, s>(q_gen_4641) -> q_gen_4640
<b, s>(q_gen_4641) -> q_gen_4640
<cons, s>(q_gen_4621, q_gen_4638) -> q_gen_4642
<cons, s>(q_gen_4621, q_gen_4660) -> q_gen_4642
<cons, s>(q_gen_4621, q_gen_4672) -> q_gen_4642
<cons, s>(q_gen_4640, q_gen_4620) -> q_gen_4642
<cons, s>(q_gen_4640, q_gen_4660) -> q_gen_4642
<cons, s>(q_gen_4640, q_gen_4694) -> q_gen_4642
<cons, s>(q_gen_4661, q_gen_4620) -> q_gen_4642
<cons, s>(q_gen_4661, q_gen_4638) -> q_gen_4642
<cons, s>(q_gen_4661, q_gen_4694) -> q_gen_4642
<cons, s>(q_gen_4669, q_gen_4620) -> q_gen_4642
<cons, s>(q_gen_4669, q_gen_4638) -> q_gen_4642
<cons, s>(q_gen_4669, q_gen_4660) -> q_gen_4642
<cons, s>(q_gen_4669, q_gen_4694) -> q_gen_4642
<a, s>(q_gen_4662) -> q_gen_4661
<b, s>(q_gen_4662) -> q_gen_4661
<b, s>(q_gen_4670) -> q_gen_4669
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_4613, q_gen_4615, q_gen_4643},
Q_f={q_gen_4613},
Delta=
{
<s>(q_gen_4615) -> q_gen_4615
<z>() -> q_gen_4615
<s, s>(q_gen_4613) -> q_gen_4613
<z, s>(q_gen_4615) -> q_gen_4613
<z, z>() -> q_gen_4613
<s, s>(q_gen_4643) -> q_gen_4643
<s, z>(q_gen_4615) -> q_gen_4643
}

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

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

Teacher's answer:
New clause system:
{
() -> delete([x, nil, nil]) -> 60
() -> length([nil, z]) -> 60
() -> leq([z, s(nn2)]) -> 61
() -> leq([z, z]) -> 60
(delete([h, t, _cr])) -> delete([h, cons(h, t), _cr]) -> 61
(delete([i, l, _ir]) /\ length([_ir, _jr]) /\ length([l, _kr])) -> leq([_jr, _kr]) -> 79
(delete([x, t, _dr]) /\ not eq_elt([x, h])) -> delete([x, cons(h, t), cons(h, _dr)]) -> 62
(length([ll, _yq])) -> length([cons(x, ll), s(_yq)]) -> 79
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 61
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 62
(leq([s(nn1), z])) -> BOT -> 62
}
Sat witness: Found: ((delete([i, l, _ir]) /\ length([_ir, _jr]) /\ length([l, _kr])) -> leq([_jr, _kr]), {
_ir -> cons(b, cons(b, cons(b, nil)))  ;  _jr -> s(s(s(z)))  ;  _kr -> s(s(z))  ;  i -> a  ;  l -> cons(b, cons(b, cons(b, cons(b, cons(a, cons(b, nil))))))
})

-------------------------------------------
Step 77, which took 2.564291 s (model generation: 2.550563,  model checking: 0.013728):

Model:
|_
{
delete -> 
{{{
Q={q_gen_4617, q_gen_4623, q_gen_4624, q_gen_4626, q_gen_4627},
Q_f={q_gen_4617},
Delta=
{
<cons>(q_gen_4627, q_gen_4626) -> q_gen_4626
<nil>() -> q_gen_4626
<a>() -> q_gen_4627
<b>() -> q_gen_4627
<cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4623
<cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4623
<nil, nil>() -> q_gen_4623
<a, a>() -> q_gen_4624
<a, b>() -> q_gen_4624
<b, a>() -> q_gen_4624
<b, b>() -> q_gen_4624
<a, cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4617
<a, cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4617
<a, nil, nil>() -> q_gen_4617
<b, cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4617
<b, cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4617
<b, nil, nil>() -> q_gen_4617
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_4616, q_gen_4620, q_gen_4621, q_gen_4638, q_gen_4639, q_gen_4640, q_gen_4641, q_gen_4642, q_gen_4660, q_gen_4661, q_gen_4662, q_gen_4669, q_gen_4670, q_gen_4672, q_gen_4673, q_gen_4681, q_gen_4694},
Q_f={q_gen_4616},
Delta=
{
<cons>(q_gen_4673, q_gen_4694) -> q_gen_4620
<nil>() -> q_gen_4620
<cons>(q_gen_4639, q_gen_4620) -> q_gen_4638
<b>() -> q_gen_4639
<z>() -> q_gen_4641
<cons>(q_gen_4639, q_gen_4638) -> q_gen_4660
<cons>(q_gen_4639, q_gen_4694) -> q_gen_4660
<cons>(q_gen_4673, q_gen_4638) -> q_gen_4660
<s>(q_gen_4641) -> q_gen_4662
<s>(q_gen_4662) -> q_gen_4670
<s>(q_gen_4670) -> q_gen_4670
<cons>(q_gen_4673, q_gen_4620) -> q_gen_4672
<cons>(q_gen_4673, q_gen_4672) -> q_gen_4672
<cons>(q_gen_4673, q_gen_4681) -> q_gen_4672
<a>() -> q_gen_4673
<cons>(q_gen_4639, q_gen_4660) -> q_gen_4681
<cons>(q_gen_4639, q_gen_4672) -> q_gen_4681
<cons>(q_gen_4639, q_gen_4681) -> q_gen_4694
<cons, s>(q_gen_4621, q_gen_4620) -> q_gen_4616
<cons, s>(q_gen_4640, q_gen_4638) -> q_gen_4616
<cons, s>(q_gen_4640, q_gen_4672) -> q_gen_4616
<cons, s>(q_gen_4661, q_gen_4660) -> q_gen_4616
<cons, s>(q_gen_4661, q_gen_4694) -> q_gen_4616
<cons, s>(q_gen_4669, q_gen_4672) -> q_gen_4616
<cons, s>(q_gen_4669, q_gen_4681) -> q_gen_4616
<nil, z>() -> q_gen_4616
<a, z>() -> q_gen_4621
<b, z>() -> q_gen_4621
<a, s>(q_gen_4641) -> q_gen_4640
<b, s>(q_gen_4641) -> q_gen_4640
<cons, s>(q_gen_4621, q_gen_4638) -> q_gen_4642
<cons, s>(q_gen_4621, q_gen_4681) -> q_gen_4642
<cons, s>(q_gen_4640, q_gen_4620) -> q_gen_4642
<cons, s>(q_gen_4640, q_gen_4660) -> q_gen_4642
<cons, s>(q_gen_4640, q_gen_4681) -> q_gen_4642
<cons, s>(q_gen_4640, q_gen_4694) -> q_gen_4642
<cons, s>(q_gen_4661, q_gen_4620) -> q_gen_4642
<cons, s>(q_gen_4661, q_gen_4638) -> q_gen_4642
<cons, s>(q_gen_4661, q_gen_4681) -> q_gen_4642
<cons, s>(q_gen_4669, q_gen_4620) -> q_gen_4642
<cons, s>(q_gen_4669, q_gen_4638) -> q_gen_4642
<cons, s>(q_gen_4669, q_gen_4660) -> q_gen_4642
<cons, s>(q_gen_4669, q_gen_4694) -> q_gen_4642
<a, s>(q_gen_4662) -> q_gen_4661
<b, s>(q_gen_4662) -> q_gen_4661
<a, s>(q_gen_4670) -> q_gen_4669
<b, s>(q_gen_4670) -> q_gen_4669
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_4613, q_gen_4615, q_gen_4643},
Q_f={q_gen_4613},
Delta=
{
<s>(q_gen_4615) -> q_gen_4615
<z>() -> q_gen_4615
<s, s>(q_gen_4613) -> q_gen_4613
<z, s>(q_gen_4615) -> q_gen_4613
<z, z>() -> q_gen_4613
<s, s>(q_gen_4643) -> q_gen_4643
<s, z>(q_gen_4615) -> q_gen_4643
}

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

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

Teacher's answer:
New clause system:
{
() -> delete([x, nil, nil]) -> 61
() -> length([nil, z]) -> 61
() -> leq([z, s(nn2)]) -> 62
() -> leq([z, z]) -> 61
(delete([h, t, _cr])) -> delete([h, cons(h, t), _cr]) -> 62
(delete([i, l, _ir]) /\ length([_ir, _jr]) /\ length([l, _kr])) -> leq([_jr, _kr]) -> 79
(delete([x, t, _dr]) /\ not eq_elt([x, h])) -> delete([x, cons(h, t), cons(h, _dr)]) -> 63
(length([ll, _yq])) -> length([cons(x, ll), s(_yq)]) -> 82
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 62
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 63
(leq([s(nn1), z])) -> BOT -> 63
}
Sat witness: Found: ((length([ll, _yq])) -> length([cons(x, ll), s(_yq)]), {
_yq -> s(s(z))  ;  ll -> cons(b, cons(a, nil))  ;  x -> a
})

-------------------------------------------
Step 78, which took 2.963809 s (model generation: 2.957275,  model checking: 0.006534):

Model:
|_
{
delete -> 
{{{
Q={q_gen_4617, q_gen_4623, q_gen_4624, q_gen_4626, q_gen_4627},
Q_f={q_gen_4617},
Delta=
{
<cons>(q_gen_4627, q_gen_4626) -> q_gen_4626
<nil>() -> q_gen_4626
<a>() -> q_gen_4627
<b>() -> q_gen_4627
<cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4623
<cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4623
<nil, nil>() -> q_gen_4623
<a, a>() -> q_gen_4624
<a, b>() -> q_gen_4624
<b, a>() -> q_gen_4624
<b, b>() -> q_gen_4624
<a, cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4617
<a, cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4617
<a, nil, nil>() -> q_gen_4617
<b, cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4617
<b, cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4617
<b, nil, nil>() -> q_gen_4617
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_4616, q_gen_4620, q_gen_4621, q_gen_4638, q_gen_4639, q_gen_4640, q_gen_4641, q_gen_4642, q_gen_4660, q_gen_4661, q_gen_4662, q_gen_4669, q_gen_4670, q_gen_4672, q_gen_4673, q_gen_4681, q_gen_4694},
Q_f={q_gen_4616},
Delta=
{
<nil>() -> q_gen_4620
<cons>(q_gen_4639, q_gen_4620) -> q_gen_4638
<cons>(q_gen_4673, q_gen_4672) -> q_gen_4638
<b>() -> q_gen_4639
<z>() -> q_gen_4641
<cons>(q_gen_4639, q_gen_4638) -> q_gen_4660
<cons>(q_gen_4673, q_gen_4638) -> q_gen_4660
<s>(q_gen_4641) -> q_gen_4662
<s>(q_gen_4662) -> q_gen_4670
<s>(q_gen_4670) -> q_gen_4670
<cons>(q_gen_4639, q_gen_4672) -> q_gen_4672
<cons>(q_gen_4673, q_gen_4620) -> q_gen_4672
<a>() -> q_gen_4673
<cons>(q_gen_4639, q_gen_4660) -> q_gen_4681
<cons>(q_gen_4673, q_gen_4681) -> q_gen_4681
<cons>(q_gen_4673, q_gen_4694) -> q_gen_4681
<cons>(q_gen_4639, q_gen_4681) -> q_gen_4694
<cons>(q_gen_4639, q_gen_4694) -> q_gen_4694
<cons, s>(q_gen_4621, q_gen_4620) -> q_gen_4616
<cons, s>(q_gen_4640, q_gen_4638) -> q_gen_4616
<cons, s>(q_gen_4640, q_gen_4672) -> q_gen_4616
<cons, s>(q_gen_4661, q_gen_4660) -> q_gen_4616
<cons, s>(q_gen_4661, q_gen_4672) -> q_gen_4616
<cons, s>(q_gen_4669, q_gen_4681) -> q_gen_4616
<nil, z>() -> q_gen_4616
<a, z>() -> q_gen_4621
<b, z>() -> q_gen_4621
<a, s>(q_gen_4641) -> q_gen_4640
<b, s>(q_gen_4641) -> q_gen_4640
<cons, s>(q_gen_4621, q_gen_4638) -> q_gen_4642
<cons, s>(q_gen_4621, q_gen_4681) -> q_gen_4642
<cons, s>(q_gen_4640, q_gen_4620) -> q_gen_4642
<cons, s>(q_gen_4640, q_gen_4660) -> q_gen_4642
<cons, s>(q_gen_4640, q_gen_4681) -> q_gen_4642
<cons, s>(q_gen_4640, q_gen_4694) -> q_gen_4642
<cons, s>(q_gen_4661, q_gen_4620) -> q_gen_4642
<cons, s>(q_gen_4661, q_gen_4638) -> q_gen_4642
<cons, s>(q_gen_4661, q_gen_4681) -> q_gen_4642
<cons, s>(q_gen_4661, q_gen_4694) -> q_gen_4642
<cons, s>(q_gen_4669, q_gen_4620) -> q_gen_4642
<cons, s>(q_gen_4669, q_gen_4638) -> q_gen_4642
<cons, s>(q_gen_4669, q_gen_4660) -> q_gen_4642
<cons, s>(q_gen_4669, q_gen_4672) -> q_gen_4642
<cons, s>(q_gen_4669, q_gen_4694) -> q_gen_4642
<a, s>(q_gen_4662) -> q_gen_4661
<b, s>(q_gen_4662) -> q_gen_4661
<a, s>(q_gen_4670) -> q_gen_4669
<b, s>(q_gen_4670) -> q_gen_4669
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_4613, q_gen_4615, q_gen_4643},
Q_f={q_gen_4613},
Delta=
{
<s>(q_gen_4615) -> q_gen_4615
<z>() -> q_gen_4615
<s, s>(q_gen_4613) -> q_gen_4613
<z, s>(q_gen_4615) -> q_gen_4613
<z, z>() -> q_gen_4613
<s, s>(q_gen_4643) -> q_gen_4643
<s, z>(q_gen_4615) -> q_gen_4643
}

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

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

Teacher's answer:
New clause system:
{
() -> delete([x, nil, nil]) -> 62
() -> length([nil, z]) -> 62
() -> leq([z, s(nn2)]) -> 63
() -> leq([z, z]) -> 62
(delete([h, t, _cr])) -> delete([h, cons(h, t), _cr]) -> 63
(delete([i, l, _ir]) /\ length([_ir, _jr]) /\ length([l, _kr])) -> leq([_jr, _kr]) -> 82
(delete([x, t, _dr]) /\ not eq_elt([x, h])) -> delete([x, cons(h, t), cons(h, _dr)]) -> 64
(length([ll, _yq])) -> length([cons(x, ll), s(_yq)]) -> 82
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 63
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 64
(leq([s(nn1), z])) -> BOT -> 64
}
Sat witness: Found: ((delete([i, l, _ir]) /\ length([_ir, _jr]) /\ length([l, _kr])) -> leq([_jr, _kr]), {
_ir -> cons(b, cons(b, cons(b, nil)))  ;  _jr -> s(s(s(z)))  ;  _kr -> s(s(z))  ;  i -> b  ;  l -> cons(b, cons(b, cons(b, cons(a, nil))))
})

-------------------------------------------
Step 79, which took 5.245946 s (model generation: 5.210627,  model checking: 0.035319):

Model:
|_
{
delete -> 
{{{
Q={q_gen_4617, q_gen_4623, q_gen_4624, q_gen_4626, q_gen_4627},
Q_f={q_gen_4617},
Delta=
{
<cons>(q_gen_4627, q_gen_4626) -> q_gen_4626
<nil>() -> q_gen_4626
<a>() -> q_gen_4627
<b>() -> q_gen_4627
<cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4623
<cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4623
<nil, nil>() -> q_gen_4623
<a, a>() -> q_gen_4624
<a, b>() -> q_gen_4624
<b, a>() -> q_gen_4624
<b, b>() -> q_gen_4624
<a, cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4617
<a, cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4617
<a, nil, nil>() -> q_gen_4617
<b, cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4617
<b, cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4617
<b, nil, nil>() -> q_gen_4617
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_4616, q_gen_4620, q_gen_4621, q_gen_4638, q_gen_4639, q_gen_4640, q_gen_4641, q_gen_4642, q_gen_4660, q_gen_4661, q_gen_4662, q_gen_4669, q_gen_4670, q_gen_4672, q_gen_4673, q_gen_4681, q_gen_4694},
Q_f={q_gen_4616},
Delta=
{
<nil>() -> q_gen_4620
<cons>(q_gen_4639, q_gen_4620) -> q_gen_4638
<b>() -> q_gen_4639
<z>() -> q_gen_4641
<cons>(q_gen_4639, q_gen_4638) -> q_gen_4660
<cons>(q_gen_4639, q_gen_4694) -> q_gen_4660
<cons>(q_gen_4673, q_gen_4638) -> q_gen_4660
<cons>(q_gen_4673, q_gen_4694) -> q_gen_4660
<s>(q_gen_4641) -> q_gen_4662
<s>(q_gen_4662) -> q_gen_4670
<s>(q_gen_4670) -> q_gen_4670
<cons>(q_gen_4673, q_gen_4620) -> q_gen_4672
<a>() -> q_gen_4673
<cons>(q_gen_4639, q_gen_4660) -> q_gen_4681
<cons>(q_gen_4673, q_gen_4681) -> q_gen_4681
<cons>(q_gen_4639, q_gen_4672) -> q_gen_4694
<cons>(q_gen_4639, q_gen_4681) -> q_gen_4694
<cons>(q_gen_4673, q_gen_4672) -> q_gen_4694
<cons, s>(q_gen_4621, q_gen_4620) -> q_gen_4616
<cons, s>(q_gen_4640, q_gen_4638) -> q_gen_4616
<cons, s>(q_gen_4640, q_gen_4672) -> q_gen_4616
<cons, s>(q_gen_4661, q_gen_4660) -> q_gen_4616
<cons, s>(q_gen_4661, q_gen_4694) -> q_gen_4616
<cons, s>(q_gen_4669, q_gen_4681) -> q_gen_4616
<nil, z>() -> q_gen_4616
<a, z>() -> q_gen_4621
<b, z>() -> q_gen_4621
<a, s>(q_gen_4641) -> q_gen_4640
<b, s>(q_gen_4641) -> q_gen_4640
<cons, s>(q_gen_4621, q_gen_4638) -> q_gen_4642
<cons, s>(q_gen_4621, q_gen_4681) -> q_gen_4642
<cons, s>(q_gen_4640, q_gen_4620) -> q_gen_4642
<cons, s>(q_gen_4640, q_gen_4660) -> q_gen_4642
<cons, s>(q_gen_4640, q_gen_4681) -> q_gen_4642
<cons, s>(q_gen_4640, q_gen_4694) -> q_gen_4642
<cons, s>(q_gen_4661, q_gen_4620) -> q_gen_4642
<cons, s>(q_gen_4661, q_gen_4638) -> q_gen_4642
<cons, s>(q_gen_4661, q_gen_4681) -> q_gen_4642
<cons, s>(q_gen_4669, q_gen_4620) -> q_gen_4642
<cons, s>(q_gen_4669, q_gen_4638) -> q_gen_4642
<cons, s>(q_gen_4669, q_gen_4660) -> q_gen_4642
<cons, s>(q_gen_4669, q_gen_4672) -> q_gen_4642
<cons, s>(q_gen_4669, q_gen_4694) -> q_gen_4642
<a, s>(q_gen_4662) -> q_gen_4661
<b, s>(q_gen_4662) -> q_gen_4661
<a, s>(q_gen_4670) -> q_gen_4669
<b, s>(q_gen_4670) -> q_gen_4669
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_4613, q_gen_4615, q_gen_4643},
Q_f={q_gen_4613},
Delta=
{
<s>(q_gen_4615) -> q_gen_4615
<z>() -> q_gen_4615
<s, s>(q_gen_4613) -> q_gen_4613
<z, s>(q_gen_4615) -> q_gen_4613
<z, z>() -> q_gen_4613
<s, s>(q_gen_4643) -> q_gen_4643
<s, z>(q_gen_4615) -> q_gen_4643
}

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

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

Teacher's answer:
New clause system:
{
() -> delete([x, nil, nil]) -> 63
() -> length([nil, z]) -> 63
() -> leq([z, s(nn2)]) -> 64
() -> leq([z, z]) -> 63
(delete([h, t, _cr])) -> delete([h, cons(h, t), _cr]) -> 64
(delete([i, l, _ir]) /\ length([_ir, _jr]) /\ length([l, _kr])) -> leq([_jr, _kr]) -> 82
(delete([x, t, _dr]) /\ not eq_elt([x, h])) -> delete([x, cons(h, t), cons(h, _dr)]) -> 65
(length([ll, _yq])) -> length([cons(x, ll), s(_yq)]) -> 85
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 64
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 65
(leq([s(nn1), z])) -> BOT -> 65
}
Sat witness: Found: ((length([ll, _yq])) -> length([cons(x, ll), s(_yq)]), {
_yq -> s(s(s(s(z))))  ;  ll -> cons(b, cons(b, cons(b, cons(b, nil))))  ;  x -> b
})

-------------------------------------------
Step 80, which took 3.418900 s (model generation: 3.411122,  model checking: 0.007778):

Model:
|_
{
delete -> 
{{{
Q={q_gen_4617, q_gen_4623, q_gen_4624, q_gen_4626, q_gen_4627},
Q_f={q_gen_4617},
Delta=
{
<cons>(q_gen_4627, q_gen_4626) -> q_gen_4626
<nil>() -> q_gen_4626
<a>() -> q_gen_4627
<b>() -> q_gen_4627
<cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4623
<cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4623
<nil, nil>() -> q_gen_4623
<a, a>() -> q_gen_4624
<a, b>() -> q_gen_4624
<b, a>() -> q_gen_4624
<b, b>() -> q_gen_4624
<a, cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4617
<a, cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4617
<a, nil, nil>() -> q_gen_4617
<b, cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4617
<b, cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4617
<b, nil, nil>() -> q_gen_4617
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_4616, q_gen_4620, q_gen_4621, q_gen_4638, q_gen_4639, q_gen_4640, q_gen_4641, q_gen_4642, q_gen_4660, q_gen_4661, q_gen_4662, q_gen_4669, q_gen_4670, q_gen_4681, q_gen_4682, q_gen_4694, q_gen_4731},
Q_f={q_gen_4616},
Delta=
{
<nil>() -> q_gen_4620
<cons>(q_gen_4639, q_gen_4620) -> q_gen_4638
<a>() -> q_gen_4639
<b>() -> q_gen_4639
<z>() -> q_gen_4641
<cons>(q_gen_4639, q_gen_4638) -> q_gen_4660
<cons>(q_gen_4639, q_gen_4694) -> q_gen_4660
<s>(q_gen_4641) -> q_gen_4662
<s>(q_gen_4662) -> q_gen_4670
<cons>(q_gen_4639, q_gen_4660) -> q_gen_4681
<cons>(q_gen_4639, q_gen_4681) -> q_gen_4694
<s>(q_gen_4670) -> q_gen_4731
<cons, s>(q_gen_4621, q_gen_4620) -> q_gen_4616
<cons, s>(q_gen_4621, q_gen_4660) -> q_gen_4616
<cons, s>(q_gen_4640, q_gen_4638) -> q_gen_4616
<cons, s>(q_gen_4661, q_gen_4660) -> q_gen_4616
<cons, s>(q_gen_4661, q_gen_4694) -> q_gen_4616
<cons, s>(q_gen_4669, q_gen_4681) -> q_gen_4616
<cons, s>(q_gen_4682, q_gen_4681) -> q_gen_4616
<cons, s>(q_gen_4682, q_gen_4694) -> q_gen_4616
<nil, z>() -> q_gen_4616
<a, s>(q_gen_4731) -> q_gen_4621
<a, z>() -> q_gen_4621
<b, z>() -> q_gen_4621
<a, s>(q_gen_4641) -> q_gen_4640
<b, s>(q_gen_4641) -> q_gen_4640
<cons, s>(q_gen_4621, q_gen_4638) -> q_gen_4642
<cons, s>(q_gen_4621, q_gen_4681) -> q_gen_4642
<cons, s>(q_gen_4640, q_gen_4620) -> q_gen_4642
<cons, s>(q_gen_4640, q_gen_4660) -> q_gen_4642
<cons, s>(q_gen_4640, q_gen_4681) -> q_gen_4642
<cons, s>(q_gen_4640, q_gen_4694) -> q_gen_4642
<cons, s>(q_gen_4661, q_gen_4620) -> q_gen_4642
<cons, s>(q_gen_4661, q_gen_4638) -> q_gen_4642
<cons, s>(q_gen_4661, q_gen_4681) -> q_gen_4642
<cons, s>(q_gen_4669, q_gen_4620) -> q_gen_4642
<cons, s>(q_gen_4669, q_gen_4638) -> q_gen_4642
<cons, s>(q_gen_4669, q_gen_4660) -> q_gen_4642
<cons, s>(q_gen_4669, q_gen_4694) -> q_gen_4642
<cons, s>(q_gen_4682, q_gen_4620) -> q_gen_4642
<cons, s>(q_gen_4682, q_gen_4638) -> q_gen_4642
<cons, s>(q_gen_4682, q_gen_4660) -> q_gen_4642
<a, s>(q_gen_4662) -> q_gen_4661
<b, s>(q_gen_4662) -> q_gen_4661
<b, s>(q_gen_4670) -> q_gen_4669
<a, s>(q_gen_4670) -> q_gen_4682
<b, s>(q_gen_4731) -> q_gen_4682
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_4613, q_gen_4615, q_gen_4643},
Q_f={q_gen_4613},
Delta=
{
<s>(q_gen_4615) -> q_gen_4615
<z>() -> q_gen_4615
<s, s>(q_gen_4613) -> q_gen_4613
<z, s>(q_gen_4615) -> q_gen_4613
<z, z>() -> q_gen_4613
<s, s>(q_gen_4643) -> q_gen_4643
<s, z>(q_gen_4615) -> q_gen_4643
}

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

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

Teacher's answer:
New clause system:
{
() -> delete([x, nil, nil]) -> 64
() -> length([nil, z]) -> 64
() -> leq([z, s(nn2)]) -> 65
() -> leq([z, z]) -> 64
(delete([h, t, _cr])) -> delete([h, cons(h, t), _cr]) -> 65
(delete([i, l, _ir]) /\ length([_ir, _jr]) /\ length([l, _kr])) -> leq([_jr, _kr]) -> 85
(delete([x, t, _dr]) /\ not eq_elt([x, h])) -> delete([x, cons(h, t), cons(h, _dr)]) -> 66
(length([ll, _yq])) -> length([cons(x, ll), s(_yq)]) -> 85
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 65
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 66
(leq([s(nn1), z])) -> BOT -> 66
}
Sat witness: Found: ((delete([i, l, _ir]) /\ length([_ir, _jr]) /\ length([l, _kr])) -> leq([_jr, _kr]), {
_ir -> cons(b, cons(b, cons(b, nil)))  ;  _jr -> s(s(s(z)))  ;  _kr -> s(z)  ;  i -> a  ;  l -> cons(b, cons(b, cons(b, nil)))
})

-------------------------------------------
Step 81, which took 4.814234 s (model generation: 4.797484,  model checking: 0.016750):

Model:
|_
{
delete -> 
{{{
Q={q_gen_4617, q_gen_4623, q_gen_4624, q_gen_4626, q_gen_4627},
Q_f={q_gen_4617},
Delta=
{
<cons>(q_gen_4627, q_gen_4626) -> q_gen_4626
<nil>() -> q_gen_4626
<a>() -> q_gen_4627
<b>() -> q_gen_4627
<cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4623
<cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4623
<nil, nil>() -> q_gen_4623
<a, a>() -> q_gen_4624
<a, b>() -> q_gen_4624
<b, a>() -> q_gen_4624
<b, b>() -> q_gen_4624
<a, cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4617
<a, cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4617
<a, nil, nil>() -> q_gen_4617
<b, cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4617
<b, cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4617
<b, nil, nil>() -> q_gen_4617
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_4616, q_gen_4620, q_gen_4621, q_gen_4638, q_gen_4639, q_gen_4640, q_gen_4641, q_gen_4642, q_gen_4660, q_gen_4661, q_gen_4662, q_gen_4669, q_gen_4670, q_gen_4681, q_gen_4682, q_gen_4694, q_gen_4731},
Q_f={q_gen_4616},
Delta=
{
<nil>() -> q_gen_4620
<cons>(q_gen_4639, q_gen_4620) -> q_gen_4638
<a>() -> q_gen_4639
<b>() -> q_gen_4639
<z>() -> q_gen_4641
<cons>(q_gen_4639, q_gen_4638) -> q_gen_4660
<cons>(q_gen_4639, q_gen_4694) -> q_gen_4660
<s>(q_gen_4641) -> q_gen_4662
<s>(q_gen_4662) -> q_gen_4670
<cons>(q_gen_4639, q_gen_4660) -> q_gen_4681
<cons>(q_gen_4639, q_gen_4681) -> q_gen_4694
<s>(q_gen_4670) -> q_gen_4731
<cons, s>(q_gen_4621, q_gen_4620) -> q_gen_4616
<cons, s>(q_gen_4640, q_gen_4638) -> q_gen_4616
<cons, s>(q_gen_4661, q_gen_4660) -> q_gen_4616
<cons, s>(q_gen_4661, q_gen_4694) -> q_gen_4616
<cons, s>(q_gen_4669, q_gen_4681) -> q_gen_4616
<cons, s>(q_gen_4682, q_gen_4681) -> q_gen_4616
<cons, s>(q_gen_4682, q_gen_4694) -> q_gen_4616
<nil, z>() -> q_gen_4616
<a, z>() -> q_gen_4621
<b, z>() -> q_gen_4621
<a, s>(q_gen_4641) -> q_gen_4640
<b, s>(q_gen_4641) -> q_gen_4640
<cons, s>(q_gen_4621, q_gen_4638) -> q_gen_4642
<cons, s>(q_gen_4621, q_gen_4660) -> q_gen_4642
<cons, s>(q_gen_4621, q_gen_4681) -> q_gen_4642
<cons, s>(q_gen_4640, q_gen_4620) -> q_gen_4642
<cons, s>(q_gen_4640, q_gen_4660) -> q_gen_4642
<cons, s>(q_gen_4640, q_gen_4681) -> q_gen_4642
<cons, s>(q_gen_4640, q_gen_4694) -> q_gen_4642
<cons, s>(q_gen_4661, q_gen_4620) -> q_gen_4642
<cons, s>(q_gen_4661, q_gen_4638) -> q_gen_4642
<cons, s>(q_gen_4661, q_gen_4681) -> q_gen_4642
<cons, s>(q_gen_4669, q_gen_4620) -> q_gen_4642
<cons, s>(q_gen_4669, q_gen_4638) -> q_gen_4642
<cons, s>(q_gen_4669, q_gen_4660) -> q_gen_4642
<cons, s>(q_gen_4669, q_gen_4694) -> q_gen_4642
<cons, s>(q_gen_4682, q_gen_4620) -> q_gen_4642
<cons, s>(q_gen_4682, q_gen_4638) -> q_gen_4642
<cons, s>(q_gen_4682, q_gen_4660) -> q_gen_4642
<a, s>(q_gen_4662) -> q_gen_4661
<a, s>(q_gen_4731) -> q_gen_4661
<b, s>(q_gen_4662) -> q_gen_4661
<b, s>(q_gen_4670) -> q_gen_4669
<a, s>(q_gen_4670) -> q_gen_4682
<b, s>(q_gen_4731) -> q_gen_4682
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_4613, q_gen_4615, q_gen_4643},
Q_f={q_gen_4613},
Delta=
{
<s>(q_gen_4615) -> q_gen_4615
<z>() -> q_gen_4615
<s, s>(q_gen_4613) -> q_gen_4613
<z, s>(q_gen_4615) -> q_gen_4613
<z, z>() -> q_gen_4613
<s, s>(q_gen_4643) -> q_gen_4643
<s, z>(q_gen_4615) -> q_gen_4643
}

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

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

Teacher's answer:
New clause system:
{
() -> delete([x, nil, nil]) -> 65
() -> length([nil, z]) -> 65
() -> leq([z, s(nn2)]) -> 66
() -> leq([z, z]) -> 65
(delete([h, t, _cr])) -> delete([h, cons(h, t), _cr]) -> 66
(delete([i, l, _ir]) /\ length([_ir, _jr]) /\ length([l, _kr])) -> leq([_jr, _kr]) -> 85
(delete([x, t, _dr]) /\ not eq_elt([x, h])) -> delete([x, cons(h, t), cons(h, _dr)]) -> 67
(length([ll, _yq])) -> length([cons(x, ll), s(_yq)]) -> 88
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 66
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 67
(leq([s(nn1), z])) -> BOT -> 67
}
Sat witness: Found: ((length([ll, _yq])) -> length([cons(x, ll), s(_yq)]), {
_yq -> s(s(s(s(z))))  ;  ll -> cons(a, cons(b, cons(b, cons(a, cons(b, nil)))))  ;  x -> b
})

-------------------------------------------
Step 82, which took 5.763084 s (model generation: 5.755973,  model checking: 0.007111):

Model:
|_
{
delete -> 
{{{
Q={q_gen_4617, q_gen_4623, q_gen_4624, q_gen_4626, q_gen_4627},
Q_f={q_gen_4617},
Delta=
{
<cons>(q_gen_4627, q_gen_4626) -> q_gen_4626
<nil>() -> q_gen_4626
<a>() -> q_gen_4627
<b>() -> q_gen_4627
<cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4623
<cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4623
<nil, nil>() -> q_gen_4623
<a, a>() -> q_gen_4624
<a, b>() -> q_gen_4624
<b, a>() -> q_gen_4624
<b, b>() -> q_gen_4624
<a, cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4617
<a, cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4617
<a, nil, nil>() -> q_gen_4617
<b, cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4617
<b, cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4617
<b, nil, nil>() -> q_gen_4617
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_4616, q_gen_4620, q_gen_4621, q_gen_4638, q_gen_4639, q_gen_4640, q_gen_4641, q_gen_4642, q_gen_4660, q_gen_4661, q_gen_4662, q_gen_4669, q_gen_4670, q_gen_4681, q_gen_4694, q_gen_4730, q_gen_4731},
Q_f={q_gen_4616},
Delta=
{
<nil>() -> q_gen_4620
<cons>(q_gen_4639, q_gen_4620) -> q_gen_4638
<a>() -> q_gen_4639
<b>() -> q_gen_4639
<z>() -> q_gen_4641
<cons>(q_gen_4639, q_gen_4638) -> q_gen_4660
<s>(q_gen_4641) -> q_gen_4662
<s>(q_gen_4662) -> q_gen_4670
<cons>(q_gen_4639, q_gen_4660) -> q_gen_4681
<cons>(q_gen_4639, q_gen_4681) -> q_gen_4694
<cons>(q_gen_4639, q_gen_4694) -> q_gen_4694
<s>(q_gen_4670) -> q_gen_4731
<cons, s>(q_gen_4621, q_gen_4620) -> q_gen_4616
<cons, s>(q_gen_4640, q_gen_4638) -> q_gen_4616
<cons, s>(q_gen_4661, q_gen_4660) -> q_gen_4616
<cons, s>(q_gen_4661, q_gen_4681) -> q_gen_4616
<cons, s>(q_gen_4669, q_gen_4681) -> q_gen_4616
<cons, s>(q_gen_4669, q_gen_4694) -> q_gen_4616
<cons, s>(q_gen_4730, q_gen_4694) -> q_gen_4616
<nil, z>() -> q_gen_4616
<a, z>() -> q_gen_4621
<b, z>() -> q_gen_4621
<a, s>(q_gen_4641) -> q_gen_4640
<b, s>(q_gen_4641) -> q_gen_4640
<cons, s>(q_gen_4621, q_gen_4638) -> q_gen_4642
<cons, s>(q_gen_4621, q_gen_4660) -> q_gen_4642
<cons, s>(q_gen_4621, q_gen_4681) -> q_gen_4642
<cons, s>(q_gen_4640, q_gen_4620) -> q_gen_4642
<cons, s>(q_gen_4640, q_gen_4660) -> q_gen_4642
<cons, s>(q_gen_4640, q_gen_4681) -> q_gen_4642
<cons, s>(q_gen_4640, q_gen_4694) -> q_gen_4642
<cons, s>(q_gen_4661, q_gen_4620) -> q_gen_4642
<cons, s>(q_gen_4661, q_gen_4638) -> q_gen_4642
<cons, s>(q_gen_4661, q_gen_4694) -> q_gen_4642
<cons, s>(q_gen_4669, q_gen_4620) -> q_gen_4642
<cons, s>(q_gen_4669, q_gen_4638) -> q_gen_4642
<cons, s>(q_gen_4669, q_gen_4660) -> q_gen_4642
<cons, s>(q_gen_4730, q_gen_4620) -> q_gen_4642
<cons, s>(q_gen_4730, q_gen_4638) -> q_gen_4642
<cons, s>(q_gen_4730, q_gen_4660) -> q_gen_4642
<cons, s>(q_gen_4730, q_gen_4681) -> q_gen_4642
<a, s>(q_gen_4662) -> q_gen_4661
<b, s>(q_gen_4662) -> q_gen_4661
<a, s>(q_gen_4670) -> q_gen_4669
<b, s>(q_gen_4670) -> q_gen_4669
<a, s>(q_gen_4731) -> q_gen_4730
<b, s>(q_gen_4731) -> q_gen_4730
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_4613, q_gen_4615, q_gen_4643},
Q_f={q_gen_4613},
Delta=
{
<s>(q_gen_4615) -> q_gen_4615
<z>() -> q_gen_4615
<s, s>(q_gen_4613) -> q_gen_4613
<z, s>(q_gen_4615) -> q_gen_4613
<z, z>() -> q_gen_4613
<s, s>(q_gen_4643) -> q_gen_4643
<s, z>(q_gen_4615) -> q_gen_4643
}

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

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

Teacher's answer:
New clause system:
{
() -> delete([x, nil, nil]) -> 66
() -> length([nil, z]) -> 66
() -> leq([z, s(nn2)]) -> 67
() -> leq([z, z]) -> 66
(delete([h, t, _cr])) -> delete([h, cons(h, t), _cr]) -> 67
(delete([i, l, _ir]) /\ length([_ir, _jr]) /\ length([l, _kr])) -> leq([_jr, _kr]) -> 88
(delete([x, t, _dr]) /\ not eq_elt([x, h])) -> delete([x, cons(h, t), cons(h, _dr)]) -> 68
(length([ll, _yq])) -> length([cons(x, ll), s(_yq)]) -> 88
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 67
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 68
(leq([s(nn1), z])) -> BOT -> 68
}
Sat witness: Found: ((delete([i, l, _ir]) /\ length([_ir, _jr]) /\ length([l, _kr])) -> leq([_jr, _kr]), {
_ir -> cons(b, cons(b, cons(b, cons(b, nil))))  ;  _jr -> s(s(s(s(z))))  ;  _kr -> s(s(s(z)))  ;  i -> a  ;  l -> cons(b, cons(b, cons(b, cons(b, nil))))
})

-------------------------------------------
Step 83, which took 4.033580 s (model generation: 4.031322,  model checking: 0.002258):

Model:
|_
{
delete -> 
{{{
Q={q_gen_4617, q_gen_4623, q_gen_4624, q_gen_4626, q_gen_4627, q_gen_4636, q_gen_4646, q_gen_4653, q_gen_4654, q_gen_4658, q_gen_4699, q_gen_4700, q_gen_4701},
Q_f={q_gen_4617, q_gen_4654},
Delta=
{
<cons>(q_gen_4627, q_gen_4626) -> q_gen_4626
<nil>() -> q_gen_4626
<b>() -> q_gen_4627
<a>() -> q_gen_4636
<cons>(q_gen_4636, q_gen_4626) -> q_gen_4701
<cons, cons>(q_gen_4624, q_gen_4700) -> q_gen_4623
<cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4623
<nil, nil>() -> q_gen_4623
<a, a>() -> q_gen_4624
<b, b>() -> q_gen_4624
<cons, cons>(q_gen_4624, q_gen_4653) -> q_gen_4646
<cons, cons>(q_gen_4658, q_gen_4623) -> q_gen_4646
<cons, cons>(q_gen_4658, q_gen_4646) -> q_gen_4646
<cons, nil>(q_gen_4636, q_gen_4626) -> q_gen_4646
<cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4653
<cons, nil>(q_gen_4636, q_gen_4701) -> q_gen_4653
<a, b>() -> q_gen_4658
<b, a>() -> q_gen_4658
<cons, cons>(q_gen_4624, q_gen_4646) -> q_gen_4700
<cons, cons>(q_gen_4658, q_gen_4653) -> q_gen_4700
<cons, nil>(q_gen_4627, q_gen_4701) -> q_gen_4700
<a, cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4617
<a, cons, cons>(q_gen_4624, q_gen_4646) -> q_gen_4617
<a, cons, cons>(q_gen_4658, q_gen_4623) -> q_gen_4617
<a, cons, nil>(q_gen_4636, q_gen_4626) -> q_gen_4617
<a, nil, nil>() -> q_gen_4617
<b, cons, cons>(q_gen_4624, q_gen_4623) -> q_gen_4617
<b, cons, cons>(q_gen_4624, q_gen_4653) -> q_gen_4617
<b, cons, nil>(q_gen_4627, q_gen_4626) -> q_gen_4617
<b, nil, nil>() -> q_gen_4617
<a, cons, cons>(q_gen_4624, q_gen_4653) -> q_gen_4654
<b, cons, cons>(q_gen_4658, q_gen_4646) -> q_gen_4654
<a, cons, cons>(q_gen_4624, q_gen_4700) -> q_gen_4699
<a, cons, cons>(q_gen_4658, q_gen_4646) -> q_gen_4699
<a, cons, cons>(q_gen_4658, q_gen_4653) -> q_gen_4699
<b, cons, cons>(q_gen_4624, q_gen_4646) -> q_gen_4699
<b, cons, cons>(q_gen_4624, q_gen_4700) -> q_gen_4699
<b, cons, cons>(q_gen_4658, q_gen_4653) -> q_gen_4699
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_4616, q_gen_4619, q_gen_4620, q_gen_4621, q_gen_4638, q_gen_4639, q_gen_4640, q_gen_4641, q_gen_4642, q_gen_4660, q_gen_4661, q_gen_4662, q_gen_4669, q_gen_4670, q_gen_4673, q_gen_4682, q_gen_4694, q_gen_4695, q_gen_4711, q_gen_4722, q_gen_4723, q_gen_4724, q_gen_4728},
Q_f={q_gen_4616, q_gen_4619, q_gen_4711, q_gen_4723, q_gen_4728},
Delta=
{
<nil>() -> q_gen_4620
<cons>(q_gen_4639, q_gen_4620) -> q_gen_4638
<cons>(q_gen_4673, q_gen_4638) -> q_gen_4638
<cons>(q_gen_4673, q_gen_4694) -> q_gen_4638
<b>() -> q_gen_4639
<z>() -> q_gen_4641
<cons>(q_gen_4639, q_gen_4638) -> q_gen_4660
<cons>(q_gen_4673, q_gen_4620) -> q_gen_4660
<cons>(q_gen_4673, q_gen_4722) -> q_gen_4660
<s>(q_gen_4641) -> q_gen_4662
<s>(q_gen_4662) -> q_gen_4670
<s>(q_gen_4670) -> q_gen_4670
<a>() -> q_gen_4673
<cons>(q_gen_4639, q_gen_4695) -> q_gen_4694
<cons>(q_gen_4639, q_gen_4722) -> q_gen_4694
<cons>(q_gen_4639, q_gen_4660) -> q_gen_4695
<cons>(q_gen_4673, q_gen_4660) -> q_gen_4695
<cons>(q_gen_4639, q_gen_4694) -> q_gen_4722
<cons>(q_gen_4673, q_gen_4695) -> q_gen_4722
<cons, s>(q_gen_4640, q_gen_4638) -> q_gen_4616
<cons, s>(q_gen_4640, q_gen_4660) -> q_gen_4616
<cons, s>(q_gen_4661, q_gen_4660) -> q_gen_4616
<cons, s>(q_gen_4669, q_gen_4695) -> q_gen_4616
<nil, z>() -> q_gen_4616
<cons, s>(q_gen_4621, q_gen_4620) -> q_gen_4619
<cons, s>(q_gen_4661, q_gen_4695) -> q_gen_4619
<cons, s>(q_gen_4682, q_gen_4638) -> q_gen_4619
<a, z>() -> q_gen_4621
<b, z>() -> q_gen_4621
<a, s>(q_gen_4641) -> q_gen_4640
<b, s>(q_gen_4641) -> q_gen_4640
<cons, s>(q_gen_4621, q_gen_4638) -> q_gen_4642
<cons, s>(q_gen_4621, q_gen_4660) -> q_gen_4642
<cons, s>(q_gen_4640, q_gen_4620) -> q_gen_4642
<cons, s>(q_gen_4640, q_gen_4694) -> q_gen_4642
<cons, s>(q_gen_4640, q_gen_4695) -> q_gen_4642
<cons, s>(q_gen_4640, q_gen_4722) -> q_gen_4642
<cons, s>(q_gen_4661, q_gen_4620) -> q_gen_4642
<cons, s>(q_gen_4661, q_gen_4638) -> q_gen_4642
<cons, s>(q_gen_4669, q_gen_4620) -> q_gen_4642
<cons, s>(q_gen_4669, q_gen_4638) -> q_gen_4642
<cons, s>(q_gen_4669, q_gen_4660) -> q_gen_4642
<cons, s>(q_gen_4682, q_gen_4660) -> q_gen_4642
<cons, s>(q_gen_4724, q_gen_4620) -> q_gen_4642
<b, s>(q_gen_4662) -> q_gen_4661
<b, s>(q_gen_4670) -> q_gen_4669
<a, s>(q_gen_4670) -> q_gen_4682
<cons, s>(q_gen_4661, q_gen_4694) -> q_gen_4711
<cons, s>(q_gen_4682, q_gen_4695) -> q_gen_4711
<cons, s>(q_gen_4669, q_gen_4694) -> q_gen_4723
<cons, s>(q_gen_4724, q_gen_4638) -> q_gen_4723
<a, s>(q_gen_4662) -> q_gen_4724
<cons, s>(q_gen_4669, q_gen_4722) -> q_gen_4728
<cons, s>(q_gen_4682, q_gen_4694) -> q_gen_4728
<cons, s>(q_gen_4724, q_gen_4660) -> q_gen_4728
<cons, s>(q_gen_4724, q_gen_4695) -> q_gen_4728
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_4613, q_gen_4615, q_gen_4643},
Q_f={q_gen_4613},
Delta=
{
<s>(q_gen_4615) -> q_gen_4615
<z>() -> q_gen_4615
<s, s>(q_gen_4613) -> q_gen_4613
<z, s>(q_gen_4615) -> q_gen_4613
<z, z>() -> q_gen_4613
<s, s>(q_gen_4643) -> q_gen_4643
<s, z>(q_gen_4615) -> q_gen_4643
}

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

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

Teacher's answer:
New clause system:
{
() -> delete([x, nil, nil]) -> 67
() -> length([nil, z]) -> 67
() -> leq([z, s(nn2)]) -> 67
() -> leq([z, z]) -> 67
(delete([h, t, _cr])) -> delete([h, cons(h, t), _cr]) -> 70
(delete([i, l, _ir]) /\ length([_ir, _jr]) /\ length([l, _kr])) -> leq([_jr, _kr]) -> 88
(delete([x, t, _dr]) /\ not eq_elt([x, h])) -> delete([x, cons(h, t), cons(h, _dr)]) -> 68
(length([ll, _yq])) -> length([cons(x, ll), s(_yq)]) -> 88
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 68
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 68
(leq([s(nn1), z])) -> BOT -> 68
}
Sat witness: Found: ((delete([h, t, _cr])) -> delete([h, cons(h, t), _cr]), {
_cr -> cons(b, cons(b, nil))  ;  h -> b  ;  t -> cons(a, cons(a, nil))
})

Total time: 64.202353
Reason for stopping: DontKnow. Stopped because: timeout