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:
{
(append, F:
{() -> append([nil, l2, l2])
(append([t1, l2, _zn])) -> append([cons(h1, t1), l2, cons(h1, _zn)])}
(append([_ao, _bo, _co]) /\ append([_ao, _bo, _do])) -> eq_eltlist([_co, _do])
)
(reverse, F:
{() -> reverse([nil, nil])
(append([_eo, cons(h1, nil), _fo]) /\ reverse([t1, _eo])) -> reverse([cons(h1, t1), _fo])}
(reverse([_go, _ho]) /\ reverse([_go, _io])) -> eq_eltlist([_ho, _io])
)
(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, _jo])) -> length([cons(x, ll), s(_jo)])}
(length([_ko, _lo]) /\ length([_ko, _mo])) -> eq_nat([_lo, _mo])
)
}

properties:
{(length([_oo, _po]) /\ length([l1, _no]) /\ reverse([l1, _oo])) -> leq([_no, _po]), (length([_qo, _ro]) /\ length([l1, _so]) /\ reverse([l1, _qo])) -> leq([_ro, _so])}


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

Clause system for inference is:

{
() -> append([nil, l2, l2]) -> 0
() -> length([nil, z]) -> 0
() -> leq([z, s(nn2)]) -> 0
() -> leq([z, z]) -> 0
() -> reverse([nil, nil]) -> 0
(append([_eo, cons(h1, nil), _fo]) /\ reverse([t1, _eo])) -> reverse([cons(h1, t1), _fo]) -> 0
(append([t1, l2, _zn])) -> append([cons(h1, t1), l2, cons(h1, _zn)]) -> 0
(length([_oo, _po]) /\ length([l1, _no]) /\ reverse([l1, _oo])) -> leq([_no, _po]) -> 0
(length([_qo, _ro]) /\ length([l1, _so]) /\ reverse([l1, _qo])) -> leq([_ro, _so]) -> 0
(length([ll, _jo])) -> length([cons(x, ll), s(_jo)]) -> 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 65.155136 seconds.
DontKnow. Stopped because: timeout
Working model:
|_
{
append -> 
{{{
Q={q_gen_3638, q_gen_3643, q_gen_3644, q_gen_3645, q_gen_3648, q_gen_3649, q_gen_3650, q_gen_3651, q_gen_3656, q_gen_3657, q_gen_3658, q_gen_3659, q_gen_3660, q_gen_3661, q_gen_3672, q_gen_3673, q_gen_3674, q_gen_3681, q_gen_3682, q_gen_3685, q_gen_3695, q_gen_3696, q_gen_3700, q_gen_3711, q_gen_3721, q_gen_3729, q_gen_3730, q_gen_3731, q_gen_3732, q_gen_3736, q_gen_3737, q_gen_3747, q_gen_3748, q_gen_3749, q_gen_3750, q_gen_3751, q_gen_3752, q_gen_3753, q_gen_3754, q_gen_3762, q_gen_3763, q_gen_3764, q_gen_3765, q_gen_3774, q_gen_3775, q_gen_3776, q_gen_3777, q_gen_3778, q_gen_3779, q_gen_3780, q_gen_3798, q_gen_3799, q_gen_3813, q_gen_3814, q_gen_3815, q_gen_3816, q_gen_3817, q_gen_3818, q_gen_3819, q_gen_3827, q_gen_3828, q_gen_3829, q_gen_3830, q_gen_3831, q_gen_3837, q_gen_3839, q_gen_3840, q_gen_3841, q_gen_3851, q_gen_3852, q_gen_3853, q_gen_3854, q_gen_3855},
Q_f={},
Delta=
{
<nil>() -> q_gen_3658
<b>() -> q_gen_3659
<a>() -> q_gen_3731
<cons>(q_gen_3659, q_gen_3658) -> q_gen_3751
<cons>(q_gen_3659, q_gen_3751) -> q_gen_3754
<nil, nil>() -> q_gen_3644
<b, b>() -> q_gen_3645
<cons, cons>(q_gen_3650, q_gen_3644) -> q_gen_3649
<a, a>() -> q_gen_3650
<nil, cons>(q_gen_3659, q_gen_3658) -> q_gen_3673
<cons, cons>(q_gen_3645, q_gen_3673) -> q_gen_3696
<nil, cons>(q_gen_3731, q_gen_3658) -> q_gen_3764
<cons, cons>(q_gen_3650, q_gen_3649) -> q_gen_3776
<cons, cons>(q_gen_3650, q_gen_3764) -> q_gen_3779
<nil, cons>(q_gen_3659, q_gen_3751) -> q_gen_3799
<cons, cons>(q_gen_3645, q_gen_3644) -> q_gen_3814
<b, a>() -> q_gen_3817
<a, b>() -> q_gen_3829
<nil, nil, nil>() -> q_gen_3638
<cons, nil, cons>(q_gen_3645, q_gen_3644) -> q_gen_3643
<nil, cons, cons>(q_gen_3650, q_gen_3649) -> q_gen_3648
<nil, cons, cons>(q_gen_3645, q_gen_3644) -> q_gen_3651
<cons, cons, cons>(q_gen_3660, q_gen_3657) -> q_gen_3656
<nil, nil, cons>(q_gen_3659, q_gen_3658) -> q_gen_3657
<b, b, b>() -> q_gen_3660
<nil, cons, cons>(q_gen_3650, q_gen_3644) -> q_gen_3661
<cons, nil, cons>(q_gen_3645, q_gen_3673) -> q_gen_3672
<nil, cons, cons>(q_gen_3645, q_gen_3673) -> q_gen_3674
<cons, cons, cons>(q_gen_3682, q_gen_3657) -> q_gen_3681
<a, b, a>() -> q_gen_3682
<cons, cons, cons>(q_gen_3682, q_gen_3672) -> q_gen_3685
<cons, nil, cons>(q_gen_3645, q_gen_3696) -> q_gen_3695
<cons, cons, cons>(q_gen_3660, q_gen_3638) -> q_gen_3700
<cons, cons, cons>(q_gen_3660, q_gen_3672) -> q_gen_3711
<cons, cons, cons>(q_gen_3682, q_gen_3695) -> q_gen_3721
<cons, cons, cons>(q_gen_3732, q_gen_3730) -> q_gen_3729
<nil, nil, cons>(q_gen_3731, q_gen_3658) -> q_gen_3730
<b, a, b>() -> q_gen_3732
<cons, cons, cons>(q_gen_3737, q_gen_3730) -> q_gen_3736
<a, a, a>() -> q_gen_3737
<cons, cons, cons>(q_gen_3737, q_gen_3674) -> q_gen_3747
<cons, cons, cons>(q_gen_3737, q_gen_3749) -> q_gen_3748
<cons, cons, cons>(q_gen_3682, q_gen_3750) -> q_gen_3749
<nil, nil, cons>(q_gen_3659, q_gen_3751) -> q_gen_3750
<cons, cons, cons>(q_gen_3682, q_gen_3753) -> q_gen_3752
<nil, nil, cons>(q_gen_3731, q_gen_3754) -> q_gen_3753
<cons, cons, cons>(q_gen_3737, q_gen_3763) -> q_gen_3762
<nil, cons, cons>(q_gen_3650, q_gen_3764) -> q_gen_3763
<cons, cons, cons>(q_gen_3737, q_gen_3672) -> q_gen_3765
<nil, cons, cons>(q_gen_3645, q_gen_3649) -> q_gen_3774
<nil, cons, cons>(q_gen_3650, q_gen_3776) -> q_gen_3775
<cons, cons, cons>(q_gen_3737, q_gen_3778) -> q_gen_3777
<nil, cons, cons>(q_gen_3650, q_gen_3779) -> q_gen_3778
<cons, cons, cons>(q_gen_3660, q_gen_3750) -> q_gen_3780
<cons, nil, cons>(q_gen_3645, q_gen_3799) -> q_gen_3798
<nil, cons, cons>(q_gen_3650, q_gen_3814) -> q_gen_3813
<cons, cons, cons>(q_gen_3737, q_gen_3816) -> q_gen_3815
<nil, cons, cons>(q_gen_3817, q_gen_3673) -> q_gen_3816
<cons, cons, cons>(q_gen_3732, q_gen_3819) -> q_gen_3818
<cons, nil, cons>(q_gen_3645, q_gen_3764) -> q_gen_3819
<cons, cons, cons>(q_gen_3660, q_gen_3828) -> q_gen_3827
<nil, cons, cons>(q_gen_3829, q_gen_3764) -> q_gen_3828
<cons, cons, cons>(q_gen_3737, q_gen_3831) -> q_gen_3830
<cons, nil, cons>(q_gen_3817, q_gen_3673) -> q_gen_3831
<cons, cons, cons>(q_gen_3732, q_gen_3672) -> q_gen_3837
<nil, cons, cons>(q_gen_3645, q_gen_3799) -> q_gen_3839
<cons, cons, cons>(q_gen_3682, q_gen_3841) -> q_gen_3840
<nil, nil, cons>(q_gen_3659, q_gen_3754) -> q_gen_3841
<cons, cons, cons>(q_gen_3737, q_gen_3852) -> q_gen_3851
<cons, cons, cons>(q_gen_3682, q_gen_3638) -> q_gen_3852
<cons, cons, cons>(q_gen_3737, q_gen_3854) -> q_gen_3853
<cons, cons, cons>(q_gen_3682, q_gen_3855) -> q_gen_3854
<cons, nil, cons>(q_gen_3650, q_gen_3644) -> q_gen_3855
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_3637, q_gen_3640, q_gen_3641, q_gen_3642, q_gen_3654, q_gen_3655, q_gen_3664, q_gen_3665, q_gen_3666, q_gen_3667, q_gen_3668, q_gen_3669, q_gen_3679, q_gen_3680, q_gen_3683, q_gen_3691, q_gen_3692, q_gen_3693, q_gen_3694, q_gen_3697, q_gen_3705, q_gen_3706, q_gen_3707, q_gen_3708, q_gen_3712, q_gen_3714, q_gen_3715, q_gen_3716, q_gen_3717, q_gen_3725, q_gen_3726, q_gen_3733, q_gen_3734, q_gen_3738, q_gen_3741, q_gen_3742, q_gen_3743, q_gen_3744, q_gen_3758, q_gen_3759, q_gen_3760, q_gen_3769, q_gen_3770, q_gen_3771, q_gen_3782, q_gen_3783, q_gen_3784, q_gen_3785, q_gen_3786, q_gen_3787, q_gen_3788, q_gen_3789, q_gen_3795, q_gen_3802, q_gen_3803, q_gen_3807, q_gen_3811, q_gen_3812, q_gen_3821, q_gen_3822, q_gen_3825, q_gen_3826, q_gen_3833, q_gen_3834, q_gen_3835, q_gen_3842, q_gen_3843, q_gen_3844, q_gen_3846, q_gen_3856, q_gen_3857, q_gen_3858, q_gen_3859, q_gen_3860, q_gen_3861, q_gen_3862, q_gen_3863, q_gen_3868, q_gen_3869, q_gen_3870, q_gen_3871},
Q_f={},
Delta=
{
<nil>() -> q_gen_3641
<cons>(q_gen_3666, q_gen_3641) -> q_gen_3665
<b>() -> q_gen_3666
<z>() -> q_gen_3668
<cons>(q_gen_3666, q_gen_3665) -> q_gen_3692
<s>(q_gen_3668) -> q_gen_3694
<s>(q_gen_3694) -> q_gen_3708
<cons>(q_gen_3716, q_gen_3641) -> q_gen_3715
<a>() -> q_gen_3716
<cons>(q_gen_3716, q_gen_3665) -> q_gen_3726
<cons>(q_gen_3666, q_gen_3726) -> q_gen_3734
<s>(q_gen_3708) -> q_gen_3744
<cons>(q_gen_3666, q_gen_3715) -> q_gen_3770
<cons>(q_gen_3666, q_gen_3692) -> q_gen_3783
<cons>(q_gen_3666, q_gen_3783) -> q_gen_3785
<s>(q_gen_3789) -> q_gen_3788
<s>(q_gen_3744) -> q_gen_3789
<cons>(q_gen_3666, q_gen_3770) -> q_gen_3803
<cons>(q_gen_3666, q_gen_3734) -> q_gen_3826
<cons>(q_gen_3716, q_gen_3726) -> q_gen_3834
<cons>(q_gen_3666, q_gen_3860) -> q_gen_3859
<cons>(q_gen_3666, q_gen_3861) -> q_gen_3860
<cons>(q_gen_3716, q_gen_3715) -> q_gen_3861
<cons>(q_gen_3666, q_gen_3803) -> q_gen_3863
<cons>(q_gen_3666, q_gen_3834) -> q_gen_3869
<nil, z>() -> q_gen_3637
<cons, s>(q_gen_3642, q_gen_3641) -> q_gen_3640
<b, z>() -> q_gen_3642
<cons, s>(q_gen_3655, q_gen_3641) -> q_gen_3654
<a, z>() -> q_gen_3655
<cons, s>(q_gen_3667, q_gen_3665) -> q_gen_3664
<b, s>(q_gen_3668) -> q_gen_3667
<cons, s>(q_gen_3667, q_gen_3641) -> q_gen_3669
<cons, s>(q_gen_3680, q_gen_3665) -> q_gen_3679
<a, s>(q_gen_3668) -> q_gen_3680
<cons, s>(q_gen_3655, q_gen_3665) -> q_gen_3683
<cons, s>(q_gen_3693, q_gen_3692) -> q_gen_3691
<b, s>(q_gen_3694) -> q_gen_3693
<cons, s>(q_gen_3693, q_gen_3665) -> q_gen_3697
<cons, s>(q_gen_3693, q_gen_3641) -> q_gen_3705
<cons, s>(q_gen_3707, q_gen_3665) -> q_gen_3706
<b, s>(q_gen_3708) -> q_gen_3707
<cons, s>(q_gen_3680, q_gen_3641) -> q_gen_3712
<cons, s>(q_gen_3667, q_gen_3715) -> q_gen_3714
<cons, s>(q_gen_3642, q_gen_3692) -> q_gen_3717
<cons, s>(q_gen_3693, q_gen_3726) -> q_gen_3725
<cons, s>(q_gen_3707, q_gen_3734) -> q_gen_3733
<cons, s>(q_gen_3707, q_gen_3692) -> q_gen_3738
<cons, s>(q_gen_3707, q_gen_3641) -> q_gen_3741
<cons, s>(q_gen_3743, q_gen_3665) -> q_gen_3742
<b, s>(q_gen_3744) -> q_gen_3743
<cons, s>(q_gen_3759, q_gen_3726) -> q_gen_3758
<a, s>(q_gen_3694) -> q_gen_3759
<cons, s>(q_gen_3759, q_gen_3641) -> q_gen_3760
<cons, s>(q_gen_3693, q_gen_3770) -> q_gen_3769
<cons, s>(q_gen_3667, q_gen_3692) -> q_gen_3771
<cons, s>(q_gen_3707, q_gen_3783) -> q_gen_3782
<cons, s>(q_gen_3743, q_gen_3785) -> q_gen_3784
<cons, s>(q_gen_3787, q_gen_3641) -> q_gen_3786
<b, s>(q_gen_3788) -> q_gen_3787
<cons, s>(q_gen_3693, q_gen_3785) -> q_gen_3795
<cons, s>(q_gen_3693, q_gen_3803) -> q_gen_3802
<cons, s>(q_gen_3693, q_gen_3734) -> q_gen_3807
<cons, s>(q_gen_3642, q_gen_3726) -> q_gen_3811
<cons, s>(q_gen_3667, q_gen_3734) -> q_gen_3812
<cons, s>(q_gen_3743, q_gen_3783) -> q_gen_3821
<cons, s>(q_gen_3667, q_gen_3783) -> q_gen_3822
<cons, s>(q_gen_3707, q_gen_3826) -> q_gen_3825
<cons, s>(q_gen_3835, q_gen_3834) -> q_gen_3833
<a, s>(q_gen_3708) -> q_gen_3835
<cons, s>(q_gen_3835, q_gen_3641) -> q_gen_3842
<cons, s>(q_gen_3844, q_gen_3715) -> q_gen_3843
<a, s>(q_gen_3744) -> q_gen_3844
<cons, s>(q_gen_3743, q_gen_3692) -> q_gen_3846
<cons, s>(q_gen_3707, q_gen_3715) -> q_gen_3856
<cons, s>(q_gen_3743, q_gen_3770) -> q_gen_3857
<cons, s>(q_gen_3667, q_gen_3859) -> q_gen_3858
<cons, s>(q_gen_3642, q_gen_3863) -> q_gen_3862
<cons, s>(q_gen_3870, q_gen_3869) -> q_gen_3868
<b, s>(q_gen_3789) -> q_gen_3870
<cons, s>(q_gen_3667, q_gen_3869) -> q_gen_3871
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3634, q_gen_3635, q_gen_3636, q_gen_3639, q_gen_3646, q_gen_3647, q_gen_3670, q_gen_3671, q_gen_3699, q_gen_3709, q_gen_3710, q_gen_3722, q_gen_3723, q_gen_3735, q_gen_3740, q_gen_3745, q_gen_3746, q_gen_3790, q_gen_3791, q_gen_3792, q_gen_3793, q_gen_3794, q_gen_3824, q_gen_3836, q_gen_3847, q_gen_3874, q_gen_3875, q_gen_3876},
Q_f={},
Delta=
{
<z>() -> q_gen_3636
<s>(q_gen_3636) -> q_gen_3647
<s>(q_gen_3647) -> q_gen_3723
<s>(q_gen_3793) -> q_gen_3792
<s>(q_gen_3794) -> q_gen_3793
<s>(q_gen_3723) -> q_gen_3794
<z, z>() -> q_gen_3634
<z, s>(q_gen_3636) -> q_gen_3635
<s, s>(q_gen_3634) -> q_gen_3639
<z, s>(q_gen_3647) -> q_gen_3646
<s, s>(q_gen_3671) -> q_gen_3670
<s, z>(q_gen_3636) -> q_gen_3671
<s, s>(q_gen_3670) -> q_gen_3699
<s, s>(q_gen_3710) -> q_gen_3709
<s, z>(q_gen_3647) -> q_gen_3710
<z, s>(q_gen_3723) -> q_gen_3722
<s, s>(q_gen_3709) -> q_gen_3735
<s, s>(q_gen_3699) -> q_gen_3740
<s, s>(q_gen_3746) -> q_gen_3745
<s, z>(q_gen_3723) -> q_gen_3746
<s, s>(q_gen_3791) -> q_gen_3790
<z, s>(q_gen_3792) -> q_gen_3791
<s, s>(q_gen_3745) -> q_gen_3824
<s, s>(q_gen_3740) -> q_gen_3836
<s, s>(q_gen_3735) -> q_gen_3847
<s, s>(q_gen_3875) -> q_gen_3874
<s, s>(q_gen_3876) -> q_gen_3875
<s, z>(q_gen_3794) -> q_gen_3876
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3633, q_gen_3652, q_gen_3653, q_gen_3662, q_gen_3663, q_gen_3675, q_gen_3676, q_gen_3677, q_gen_3678, q_gen_3684, q_gen_3686, q_gen_3687, q_gen_3688, q_gen_3689, q_gen_3690, q_gen_3698, q_gen_3701, q_gen_3702, q_gen_3703, q_gen_3704, q_gen_3713, q_gen_3718, q_gen_3719, q_gen_3720, q_gen_3724, q_gen_3727, q_gen_3728, q_gen_3739, q_gen_3755, q_gen_3756, q_gen_3757, q_gen_3761, q_gen_3766, q_gen_3767, q_gen_3768, q_gen_3772, q_gen_3773, q_gen_3781, q_gen_3796, q_gen_3797, q_gen_3800, q_gen_3801, q_gen_3804, q_gen_3805, q_gen_3806, q_gen_3808, q_gen_3809, q_gen_3810, q_gen_3820, q_gen_3823, q_gen_3832, q_gen_3838, q_gen_3845, q_gen_3848, q_gen_3849, q_gen_3850, q_gen_3864, q_gen_3865, q_gen_3866, q_gen_3867, q_gen_3872, q_gen_3873},
Q_f={},
Delta=
{
<nil>() -> q_gen_3677
<b>() -> q_gen_3678
<a>() -> q_gen_3704
<cons>(q_gen_3678, q_gen_3677) -> q_gen_3850
<nil, nil>() -> q_gen_3633
<cons, cons>(q_gen_3653, q_gen_3633) -> q_gen_3652
<b, b>() -> q_gen_3653
<cons, cons>(q_gen_3663, q_gen_3633) -> q_gen_3662
<a, a>() -> q_gen_3663
<cons, cons>(q_gen_3653, q_gen_3676) -> q_gen_3675
<nil, cons>(q_gen_3678, q_gen_3677) -> q_gen_3676
<cons, cons>(q_gen_3663, q_gen_3652) -> q_gen_3684
<cons, cons>(q_gen_3663, q_gen_3676) -> q_gen_3686
<cons, cons>(q_gen_3690, q_gen_3688) -> q_gen_3687
<cons, cons>(q_gen_3689, q_gen_3676) -> q_gen_3688
<a, b>() -> q_gen_3689
<b, a>() -> q_gen_3690
<cons, cons>(q_gen_3653, q_gen_3652) -> q_gen_3698
<cons, cons>(q_gen_3689, q_gen_3633) -> q_gen_3701
<cons, cons>(q_gen_3653, q_gen_3703) -> q_gen_3702
<cons, nil>(q_gen_3704, q_gen_3677) -> q_gen_3703
<cons, cons>(q_gen_3690, q_gen_3701) -> q_gen_3713
<cons, cons>(q_gen_3653, q_gen_3719) -> q_gen_3718
<cons, cons>(q_gen_3653, q_gen_3720) -> q_gen_3719
<cons, nil>(q_gen_3678, q_gen_3677) -> q_gen_3720
<cons, cons>(q_gen_3653, q_gen_3701) -> q_gen_3724
<cons, cons>(q_gen_3653, q_gen_3728) -> q_gen_3727
<cons, cons>(q_gen_3690, q_gen_3676) -> q_gen_3728
<cons, cons>(q_gen_3653, q_gen_3698) -> q_gen_3739
<cons, cons>(q_gen_3690, q_gen_3703) -> q_gen_3755
<cons, cons>(q_gen_3690, q_gen_3687) -> q_gen_3756
<cons, cons>(q_gen_3689, q_gen_3720) -> q_gen_3757
<cons, cons>(q_gen_3690, q_gen_3633) -> q_gen_3761
<cons, cons>(q_gen_3663, q_gen_3701) -> q_gen_3766
<cons, cons>(q_gen_3663, q_gen_3768) -> q_gen_3767
<cons, cons>(q_gen_3689, q_gen_3701) -> q_gen_3768
<cons, cons>(q_gen_3653, q_gen_3773) -> q_gen_3772
<cons, cons>(q_gen_3653, q_gen_3761) -> q_gen_3773
<cons, cons>(q_gen_3653, q_gen_3675) -> q_gen_3781
<cons, cons>(q_gen_3653, q_gen_3797) -> q_gen_3796
<cons, cons>(q_gen_3653, q_gen_3718) -> q_gen_3797
<cons, cons>(q_gen_3690, q_gen_3652) -> q_gen_3800
<cons, cons>(q_gen_3690, q_gen_3698) -> q_gen_3801
<cons, cons>(q_gen_3653, q_gen_3805) -> q_gen_3804
<cons, cons>(q_gen_3653, q_gen_3806) -> q_gen_3805
<cons, cons>(q_gen_3689, q_gen_3761) -> q_gen_3806
<cons, cons>(q_gen_3653, q_gen_3809) -> q_gen_3808
<cons, cons>(q_gen_3653, q_gen_3810) -> q_gen_3809
<cons, cons>(q_gen_3689, q_gen_3652) -> q_gen_3810
<cons, cons>(q_gen_3689, q_gen_3806) -> q_gen_3820
<cons, cons>(q_gen_3653, q_gen_3739) -> q_gen_3823
<cons, cons>(q_gen_3663, q_gen_3684) -> q_gen_3832
<cons, cons>(q_gen_3689, q_gen_3810) -> q_gen_3838
<cons, cons>(q_gen_3653, q_gen_3800) -> q_gen_3845
<cons, cons>(q_gen_3653, q_gen_3849) -> q_gen_3848
<nil, cons>(q_gen_3678, q_gen_3850) -> q_gen_3849
<cons, cons>(q_gen_3653, q_gen_3865) -> q_gen_3864
<cons, cons>(q_gen_3653, q_gen_3866) -> q_gen_3865
<cons, cons>(q_gen_3653, q_gen_3867) -> q_gen_3866
<cons, cons>(q_gen_3690, q_gen_3662) -> q_gen_3867
<cons, cons>(q_gen_3653, q_gen_3873) -> q_gen_3872
<cons, cons>(q_gen_3653, q_gen_3832) -> q_gen_3873
}

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

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

-------------------
STEPS:
-------------------------------------------
Step 0, which took 0.009566 s (model generation: 0.009199,  model checking: 0.000367):

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

}

Datatype: <eltlist, 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
}}}
  ;  reverse -> 
{{{
Q={},
Q_f={},
Delta=
{

}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 0
() -> length([nil, z]) -> 0
() -> leq([z, s(nn2)]) -> 0
() -> leq([z, z]) -> 0
() -> reverse([nil, nil]) -> 3
(append([_eo, cons(h1, nil), _fo]) /\ reverse([t1, _eo])) -> reverse([cons(h1, t1), _fo]) -> 1
(append([t1, l2, _zn])) -> append([cons(h1, t1), l2, cons(h1, _zn)]) -> 1
(length([_oo, _po]) /\ length([l1, _no]) /\ reverse([l1, _oo])) -> leq([_no, _po]) -> 1
(length([_qo, _ro]) /\ length([l1, _so]) /\ reverse([l1, _qo])) -> leq([_ro, _so]) -> 1
(length([ll, _jo])) -> length([cons(x, ll), s(_jo)]) -> 1
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 1
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 1
(leq([s(nn1), z])) -> BOT -> 1
}
Sat witness: Found: (() -> reverse([nil, nil]), {

})

-------------------------------------------
Step 1, which took 0.008726 s (model generation: 0.008679,  model checking: 0.000047):

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

}

Datatype: <eltlist, 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
}}}
  ;  reverse -> 
{{{
Q={q_gen_3633},
Q_f={q_gen_3633},
Delta=
{
<nil, nil>() -> q_gen_3633
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 0
() -> length([nil, z]) -> 0
() -> leq([z, s(nn2)]) -> 0
() -> leq([z, z]) -> 3
() -> reverse([nil, nil]) -> 3
(append([_eo, cons(h1, nil), _fo]) /\ reverse([t1, _eo])) -> reverse([cons(h1, t1), _fo]) -> 1
(append([t1, l2, _zn])) -> append([cons(h1, t1), l2, cons(h1, _zn)]) -> 1
(length([_oo, _po]) /\ length([l1, _no]) /\ reverse([l1, _oo])) -> leq([_no, _po]) -> 1
(length([_qo, _ro]) /\ length([l1, _so]) /\ reverse([l1, _qo])) -> leq([_ro, _so]) -> 1
(length([ll, _jo])) -> length([cons(x, ll), s(_jo)]) -> 1
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 1
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 1
(leq([s(nn1), z])) -> BOT -> 1
}
Sat witness: Found: (() -> leq([z, z]), {

})

-------------------------------------------
Step 2, which took 0.007025 s (model generation: 0.006960,  model checking: 0.000065):

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

}

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

}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3634},
Q_f={q_gen_3634},
Delta=
{
<z, z>() -> q_gen_3634
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3633},
Q_f={q_gen_3633},
Delta=
{
<nil, nil>() -> q_gen_3633
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 0
() -> length([nil, z]) -> 0
() -> leq([z, s(nn2)]) -> 3
() -> leq([z, z]) -> 3
() -> reverse([nil, nil]) -> 3
(append([_eo, cons(h1, nil), _fo]) /\ reverse([t1, _eo])) -> reverse([cons(h1, t1), _fo]) -> 1
(append([t1, l2, _zn])) -> append([cons(h1, t1), l2, cons(h1, _zn)]) -> 1
(length([_oo, _po]) /\ length([l1, _no]) /\ reverse([l1, _oo])) -> leq([_no, _po]) -> 1
(length([_qo, _ro]) /\ length([l1, _so]) /\ reverse([l1, _qo])) -> leq([_ro, _so]) -> 1
(length([ll, _jo])) -> length([cons(x, ll), s(_jo)]) -> 1
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 1
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 1
(leq([s(nn1), z])) -> BOT -> 1
}
Sat witness: Found: (() -> leq([z, s(nn2)]), {
nn2 -> z
})

-------------------------------------------
Step 3, which took 0.008458 s (model generation: 0.008385,  model checking: 0.000073):

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

}

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

}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3634, q_gen_3636},
Q_f={q_gen_3634},
Delta=
{
<z>() -> q_gen_3636
<z, s>(q_gen_3636) -> q_gen_3634
<z, z>() -> q_gen_3634
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3633},
Q_f={q_gen_3633},
Delta=
{
<nil, nil>() -> q_gen_3633
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 0
() -> length([nil, z]) -> 3
() -> leq([z, s(nn2)]) -> 3
() -> leq([z, z]) -> 3
() -> reverse([nil, nil]) -> 3
(append([_eo, cons(h1, nil), _fo]) /\ reverse([t1, _eo])) -> reverse([cons(h1, t1), _fo]) -> 1
(append([t1, l2, _zn])) -> append([cons(h1, t1), l2, cons(h1, _zn)]) -> 1
(length([_oo, _po]) /\ length([l1, _no]) /\ reverse([l1, _oo])) -> leq([_no, _po]) -> 1
(length([_qo, _ro]) /\ length([l1, _so]) /\ reverse([l1, _qo])) -> leq([_ro, _so]) -> 1
(length([ll, _jo])) -> length([cons(x, ll), s(_jo)]) -> 1
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 1
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 1
(leq([s(nn1), z])) -> BOT -> 1
}
Sat witness: Found: (() -> length([nil, z]), {

})

-------------------------------------------
Step 4, which took 0.011591 s (model generation: 0.011434,  model checking: 0.000157):

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

}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_3637},
Q_f={q_gen_3637},
Delta=
{
<nil, z>() -> q_gen_3637
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3634, q_gen_3636},
Q_f={q_gen_3634},
Delta=
{
<z>() -> q_gen_3636
<z, s>(q_gen_3636) -> q_gen_3634
<z, z>() -> q_gen_3634
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3633},
Q_f={q_gen_3633},
Delta=
{
<nil, nil>() -> q_gen_3633
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 3
() -> length([nil, z]) -> 3
() -> leq([z, s(nn2)]) -> 3
() -> leq([z, z]) -> 3
() -> reverse([nil, nil]) -> 3
(append([_eo, cons(h1, nil), _fo]) /\ reverse([t1, _eo])) -> reverse([cons(h1, t1), _fo]) -> 1
(append([t1, l2, _zn])) -> append([cons(h1, t1), l2, cons(h1, _zn)]) -> 1
(length([_oo, _po]) /\ length([l1, _no]) /\ reverse([l1, _oo])) -> leq([_no, _po]) -> 1
(length([_qo, _ro]) /\ length([l1, _so]) /\ reverse([l1, _qo])) -> leq([_ro, _so]) -> 1
(length([ll, _jo])) -> length([cons(x, ll), s(_jo)]) -> 1
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 1
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 1
(leq([s(nn1), z])) -> BOT -> 1
}
Sat witness: Found: (() -> append([nil, l2, l2]), {
l2 -> nil
})

-------------------------------------------
Step 5, which took 0.010616 s (model generation: 0.010494,  model checking: 0.000122):

Model:
|_
{
append -> 
{{{
Q={q_gen_3638},
Q_f={q_gen_3638},
Delta=
{
<nil, nil, nil>() -> q_gen_3638
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_3637},
Q_f={q_gen_3637},
Delta=
{
<nil, z>() -> q_gen_3637
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3634, q_gen_3636},
Q_f={q_gen_3634},
Delta=
{
<z>() -> q_gen_3636
<z, s>(q_gen_3636) -> q_gen_3634
<z, z>() -> q_gen_3634
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3633},
Q_f={q_gen_3633},
Delta=
{
<nil, nil>() -> q_gen_3633
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 3
() -> length([nil, z]) -> 3
() -> leq([z, s(nn2)]) -> 3
() -> leq([z, z]) -> 3
() -> reverse([nil, nil]) -> 3
(append([_eo, cons(h1, nil), _fo]) /\ reverse([t1, _eo])) -> reverse([cons(h1, t1), _fo]) -> 1
(append([t1, l2, _zn])) -> append([cons(h1, t1), l2, cons(h1, _zn)]) -> 1
(length([_oo, _po]) /\ length([l1, _no]) /\ reverse([l1, _oo])) -> leq([_no, _po]) -> 1
(length([_qo, _ro]) /\ length([l1, _so]) /\ reverse([l1, _qo])) -> leq([_ro, _so]) -> 1
(length([ll, _jo])) -> length([cons(x, ll), s(_jo)]) -> 1
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 4
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 2
(leq([s(nn1), z])) -> BOT -> 2
}
Sat witness: Found: ((leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]), {
nn1 -> z  ;  nn2 -> z
})

-------------------------------------------
Step 6, which took 0.008185 s (model generation: 0.008041,  model checking: 0.000144):

Model:
|_
{
append -> 
{{{
Q={q_gen_3638},
Q_f={q_gen_3638},
Delta=
{
<nil, nil, nil>() -> q_gen_3638
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_3637},
Q_f={q_gen_3637},
Delta=
{
<nil, z>() -> q_gen_3637
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3634, q_gen_3636},
Q_f={q_gen_3634},
Delta=
{
<z>() -> q_gen_3636
<s, s>(q_gen_3634) -> q_gen_3634
<z, s>(q_gen_3636) -> q_gen_3634
<z, z>() -> q_gen_3634
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3633},
Q_f={q_gen_3633},
Delta=
{
<nil, nil>() -> q_gen_3633
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 3
() -> length([nil, z]) -> 3
() -> leq([z, s(nn2)]) -> 3
() -> leq([z, z]) -> 3
() -> reverse([nil, nil]) -> 3
(append([_eo, cons(h1, nil), _fo]) /\ reverse([t1, _eo])) -> reverse([cons(h1, t1), _fo]) -> 1
(append([t1, l2, _zn])) -> append([cons(h1, t1), l2, cons(h1, _zn)]) -> 1
(length([_oo, _po]) /\ length([l1, _no]) /\ reverse([l1, _oo])) -> leq([_no, _po]) -> 1
(length([_qo, _ro]) /\ length([l1, _so]) /\ reverse([l1, _qo])) -> leq([_ro, _so]) -> 1
(length([ll, _jo])) -> length([cons(x, ll), s(_jo)]) -> 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, _jo])) -> length([cons(x, ll), s(_jo)]), {
_jo -> z  ;  ll -> nil  ;  x -> b
})

-------------------------------------------
Step 7, which took 0.009430 s (model generation: 0.009189,  model checking: 0.000241):

Model:
|_
{
append -> 
{{{
Q={q_gen_3638},
Q_f={q_gen_3638},
Delta=
{
<nil, nil, nil>() -> q_gen_3638
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_3637, q_gen_3641, q_gen_3642},
Q_f={q_gen_3637},
Delta=
{
<nil>() -> q_gen_3641
<cons, s>(q_gen_3642, q_gen_3641) -> q_gen_3637
<nil, z>() -> q_gen_3637
<b, z>() -> q_gen_3642
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3634, q_gen_3636},
Q_f={q_gen_3634},
Delta=
{
<z>() -> q_gen_3636
<s, s>(q_gen_3634) -> q_gen_3634
<z, s>(q_gen_3636) -> q_gen_3634
<z, z>() -> q_gen_3634
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3633},
Q_f={q_gen_3633},
Delta=
{
<nil, nil>() -> q_gen_3633
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 3
() -> length([nil, z]) -> 3
() -> leq([z, s(nn2)]) -> 3
() -> leq([z, z]) -> 3
() -> reverse([nil, nil]) -> 3
(append([_eo, cons(h1, nil), _fo]) /\ reverse([t1, _eo])) -> reverse([cons(h1, t1), _fo]) -> 1
(append([t1, l2, _zn])) -> append([cons(h1, t1), l2, cons(h1, _zn)]) -> 4
(length([_oo, _po]) /\ length([l1, _no]) /\ reverse([l1, _oo])) -> leq([_no, _po]) -> 2
(length([_qo, _ro]) /\ length([l1, _so]) /\ reverse([l1, _qo])) -> leq([_ro, _so]) -> 2
(length([ll, _jo])) -> length([cons(x, ll), s(_jo)]) -> 4
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 4
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 2
(leq([s(nn1), z])) -> BOT -> 2
}
Sat witness: Found: ((append([t1, l2, _zn])) -> append([cons(h1, t1), l2, cons(h1, _zn)]), {
_zn -> nil  ;  h1 -> b  ;  l2 -> nil  ;  t1 -> nil
})

-------------------------------------------
Step 8, which took 0.011209 s (model generation: 0.010813,  model checking: 0.000396):

Model:
|_
{
append -> 
{{{
Q={q_gen_3638, q_gen_3644, q_gen_3645},
Q_f={q_gen_3638},
Delta=
{
<nil, nil>() -> q_gen_3644
<b, b>() -> q_gen_3645
<cons, nil, cons>(q_gen_3645, q_gen_3644) -> q_gen_3638
<nil, nil, nil>() -> q_gen_3638
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_3637, q_gen_3641, q_gen_3642},
Q_f={q_gen_3637},
Delta=
{
<nil>() -> q_gen_3641
<cons, s>(q_gen_3642, q_gen_3641) -> q_gen_3637
<nil, z>() -> q_gen_3637
<b, z>() -> q_gen_3642
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3634, q_gen_3636},
Q_f={q_gen_3634},
Delta=
{
<z>() -> q_gen_3636
<s, s>(q_gen_3634) -> q_gen_3634
<z, s>(q_gen_3636) -> q_gen_3634
<z, z>() -> q_gen_3634
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3633},
Q_f={q_gen_3633},
Delta=
{
<nil, nil>() -> q_gen_3633
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 3
() -> length([nil, z]) -> 3
() -> leq([z, s(nn2)]) -> 6
() -> leq([z, z]) -> 4
() -> reverse([nil, nil]) -> 4
(append([_eo, cons(h1, nil), _fo]) /\ reverse([t1, _eo])) -> reverse([cons(h1, t1), _fo]) -> 2
(append([t1, l2, _zn])) -> append([cons(h1, t1), l2, cons(h1, _zn)]) -> 4
(length([_oo, _po]) /\ length([l1, _no]) /\ reverse([l1, _oo])) -> leq([_no, _po]) -> 3
(length([_qo, _ro]) /\ length([l1, _so]) /\ reverse([l1, _qo])) -> leq([_ro, _so]) -> 3
(length([ll, _jo])) -> length([cons(x, ll), s(_jo)]) -> 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 0.011722 s (model generation: 0.011136,  model checking: 0.000586):

Model:
|_
{
append -> 
{{{
Q={q_gen_3638, q_gen_3644, q_gen_3645},
Q_f={q_gen_3638},
Delta=
{
<nil, nil>() -> q_gen_3644
<b, b>() -> q_gen_3645
<cons, nil, cons>(q_gen_3645, q_gen_3644) -> q_gen_3638
<nil, nil, nil>() -> q_gen_3638
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_3637, q_gen_3641, q_gen_3642},
Q_f={q_gen_3637},
Delta=
{
<nil>() -> q_gen_3641
<cons, s>(q_gen_3642, q_gen_3641) -> q_gen_3637
<nil, z>() -> q_gen_3637
<b, z>() -> q_gen_3642
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3634, q_gen_3636},
Q_f={q_gen_3634},
Delta=
{
<s>(q_gen_3636) -> q_gen_3636
<z>() -> q_gen_3636
<s, s>(q_gen_3634) -> q_gen_3634
<z, s>(q_gen_3636) -> q_gen_3634
<z, z>() -> q_gen_3634
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3633},
Q_f={q_gen_3633},
Delta=
{
<nil, nil>() -> q_gen_3633
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 6
() -> length([nil, z]) -> 4
() -> leq([z, s(nn2)]) -> 6
() -> leq([z, z]) -> 4
() -> reverse([nil, nil]) -> 4
(append([_eo, cons(h1, nil), _fo]) /\ reverse([t1, _eo])) -> reverse([cons(h1, t1), _fo]) -> 3
(append([t1, l2, _zn])) -> append([cons(h1, t1), l2, cons(h1, _zn)]) -> 4
(length([_oo, _po]) /\ length([l1, _no]) /\ reverse([l1, _oo])) -> leq([_no, _po]) -> 4
(length([_qo, _ro]) /\ length([l1, _so]) /\ reverse([l1, _qo])) -> leq([_ro, _so]) -> 4
(length([ll, _jo])) -> length([cons(x, ll), s(_jo)]) -> 4
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 4
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 4
(leq([s(nn1), z])) -> BOT -> 4
}
Sat witness: Found: (() -> append([nil, l2, l2]), {
l2 -> cons(a, cons(a, nil))
})

-------------------------------------------
Step 10, which took 0.011091 s (model generation: 0.010966,  model checking: 0.000125):

Model:
|_
{
append -> 
{{{
Q={q_gen_3638, q_gen_3644, q_gen_3645},
Q_f={q_gen_3638},
Delta=
{
<cons, cons>(q_gen_3645, q_gen_3644) -> q_gen_3644
<nil, nil>() -> q_gen_3644
<a, a>() -> q_gen_3645
<b, b>() -> q_gen_3645
<cons, nil, cons>(q_gen_3645, q_gen_3644) -> q_gen_3638
<nil, cons, cons>(q_gen_3645, q_gen_3644) -> q_gen_3638
<nil, nil, nil>() -> q_gen_3638
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_3637, q_gen_3641, q_gen_3642},
Q_f={q_gen_3637},
Delta=
{
<nil>() -> q_gen_3641
<cons, s>(q_gen_3642, q_gen_3641) -> q_gen_3637
<nil, z>() -> q_gen_3637
<b, z>() -> q_gen_3642
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3634, q_gen_3636},
Q_f={q_gen_3634},
Delta=
{
<s>(q_gen_3636) -> q_gen_3636
<z>() -> q_gen_3636
<s, s>(q_gen_3634) -> q_gen_3634
<z, s>(q_gen_3636) -> q_gen_3634
<z, z>() -> q_gen_3634
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3633},
Q_f={q_gen_3633},
Delta=
{
<nil, nil>() -> q_gen_3633
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 6
() -> length([nil, z]) -> 4
() -> leq([z, s(nn2)]) -> 6
() -> leq([z, z]) -> 4
() -> reverse([nil, nil]) -> 4
(append([_eo, cons(h1, nil), _fo]) /\ reverse([t1, _eo])) -> reverse([cons(h1, t1), _fo]) -> 6
(append([t1, l2, _zn])) -> append([cons(h1, t1), l2, cons(h1, _zn)]) -> 4
(length([_oo, _po]) /\ length([l1, _no]) /\ reverse([l1, _oo])) -> leq([_no, _po]) -> 4
(length([_qo, _ro]) /\ length([l1, _so]) /\ reverse([l1, _qo])) -> leq([_ro, _so]) -> 4
(length([ll, _jo])) -> length([cons(x, ll), s(_jo)]) -> 4
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 4
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 4
(leq([s(nn1), z])) -> BOT -> 4
}
Sat witness: Found: ((append([_eo, cons(h1, nil), _fo]) /\ reverse([t1, _eo])) -> reverse([cons(h1, t1), _fo]), {
_eo -> nil  ;  _fo -> cons(b, nil)  ;  h1 -> b  ;  t1 -> nil
})

-------------------------------------------
Step 11, which took 0.010197 s (model generation: 0.009817,  model checking: 0.000380):

Model:
|_
{
append -> 
{{{
Q={q_gen_3638, q_gen_3644, q_gen_3645},
Q_f={q_gen_3638},
Delta=
{
<cons, cons>(q_gen_3645, q_gen_3644) -> q_gen_3644
<nil, nil>() -> q_gen_3644
<a, a>() -> q_gen_3645
<b, b>() -> q_gen_3645
<cons, nil, cons>(q_gen_3645, q_gen_3644) -> q_gen_3638
<nil, cons, cons>(q_gen_3645, q_gen_3644) -> q_gen_3638
<nil, nil, nil>() -> q_gen_3638
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_3637, q_gen_3641, q_gen_3642},
Q_f={q_gen_3637},
Delta=
{
<nil>() -> q_gen_3641
<cons, s>(q_gen_3642, q_gen_3641) -> q_gen_3637
<nil, z>() -> q_gen_3637
<b, z>() -> q_gen_3642
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3634, q_gen_3636},
Q_f={q_gen_3634},
Delta=
{
<s>(q_gen_3636) -> q_gen_3636
<z>() -> q_gen_3636
<s, s>(q_gen_3634) -> q_gen_3634
<z, s>(q_gen_3636) -> q_gen_3634
<z, z>() -> q_gen_3634
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3633, q_gen_3653},
Q_f={q_gen_3633},
Delta=
{
<cons, cons>(q_gen_3653, q_gen_3633) -> q_gen_3633
<nil, nil>() -> q_gen_3633
<b, b>() -> q_gen_3653
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 6
() -> length([nil, z]) -> 4
() -> leq([z, s(nn2)]) -> 6
() -> leq([z, z]) -> 4
() -> reverse([nil, nil]) -> 4
(append([_eo, cons(h1, nil), _fo]) /\ reverse([t1, _eo])) -> reverse([cons(h1, t1), _fo]) -> 6
(append([t1, l2, _zn])) -> append([cons(h1, t1), l2, cons(h1, _zn)]) -> 4
(length([_oo, _po]) /\ length([l1, _no]) /\ reverse([l1, _oo])) -> leq([_no, _po]) -> 4
(length([_qo, _ro]) /\ length([l1, _so]) /\ reverse([l1, _qo])) -> leq([_ro, _so]) -> 4
(length([ll, _jo])) -> length([cons(x, ll), s(_jo)]) -> 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, _jo])) -> length([cons(x, ll), s(_jo)]), {
_jo -> z  ;  ll -> nil  ;  x -> a
})

-------------------------------------------
Step 12, which took 0.012171 s (model generation: 0.011102,  model checking: 0.001069):

Model:
|_
{
append -> 
{{{
Q={q_gen_3638, q_gen_3644, q_gen_3645},
Q_f={q_gen_3638},
Delta=
{
<cons, cons>(q_gen_3645, q_gen_3644) -> q_gen_3644
<nil, nil>() -> q_gen_3644
<a, a>() -> q_gen_3645
<b, b>() -> q_gen_3645
<cons, nil, cons>(q_gen_3645, q_gen_3644) -> q_gen_3638
<nil, cons, cons>(q_gen_3645, q_gen_3644) -> q_gen_3638
<nil, nil, nil>() -> q_gen_3638
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_3637, q_gen_3641, q_gen_3642},
Q_f={q_gen_3637},
Delta=
{
<nil>() -> q_gen_3641
<cons, s>(q_gen_3642, q_gen_3641) -> q_gen_3637
<nil, z>() -> q_gen_3637
<a, z>() -> q_gen_3642
<b, z>() -> q_gen_3642
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3634, q_gen_3636},
Q_f={q_gen_3634},
Delta=
{
<s>(q_gen_3636) -> q_gen_3636
<z>() -> q_gen_3636
<s, s>(q_gen_3634) -> q_gen_3634
<z, s>(q_gen_3636) -> q_gen_3634
<z, z>() -> q_gen_3634
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3633, q_gen_3653},
Q_f={q_gen_3633},
Delta=
{
<cons, cons>(q_gen_3653, q_gen_3633) -> q_gen_3633
<nil, nil>() -> q_gen_3633
<b, b>() -> q_gen_3653
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 6
() -> length([nil, z]) -> 4
() -> leq([z, s(nn2)]) -> 6
() -> leq([z, z]) -> 4
() -> reverse([nil, nil]) -> 4
(append([_eo, cons(h1, nil), _fo]) /\ reverse([t1, _eo])) -> reverse([cons(h1, t1), _fo]) -> 6
(append([t1, l2, _zn])) -> append([cons(h1, t1), l2, cons(h1, _zn)]) -> 7
(length([_oo, _po]) /\ length([l1, _no]) /\ reverse([l1, _oo])) -> leq([_no, _po]) -> 5
(length([_qo, _ro]) /\ length([l1, _so]) /\ reverse([l1, _qo])) -> leq([_ro, _so]) -> 5
(length([ll, _jo])) -> length([cons(x, ll), s(_jo)]) -> 7
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 5
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 5
(leq([s(nn1), z])) -> BOT -> 5
}
Sat witness: Found: ((append([t1, l2, _zn])) -> append([cons(h1, t1), l2, cons(h1, _zn)]), {
_zn -> cons(b, nil)  ;  h1 -> b  ;  l2 -> cons(b, nil)  ;  t1 -> nil
})

-------------------------------------------
Step 13, which took 0.017064 s (model generation: 0.016144,  model checking: 0.000920):

Model:
|_
{
append -> 
{{{
Q={q_gen_3638, q_gen_3644, q_gen_3645, q_gen_3658, q_gen_3659, q_gen_3660},
Q_f={q_gen_3638},
Delta=
{
<nil>() -> q_gen_3658
<b>() -> q_gen_3659
<cons, cons>(q_gen_3645, q_gen_3644) -> q_gen_3644
<nil, nil>() -> q_gen_3644
<a, a>() -> q_gen_3645
<b, b>() -> q_gen_3645
<cons, cons, cons>(q_gen_3660, q_gen_3638) -> q_gen_3638
<cons, nil, cons>(q_gen_3645, q_gen_3644) -> q_gen_3638
<nil, cons, cons>(q_gen_3645, q_gen_3644) -> q_gen_3638
<nil, nil, cons>(q_gen_3659, q_gen_3658) -> q_gen_3638
<nil, nil, nil>() -> q_gen_3638
<b, b, b>() -> q_gen_3660
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_3637, q_gen_3641, q_gen_3642},
Q_f={q_gen_3637},
Delta=
{
<nil>() -> q_gen_3641
<cons, s>(q_gen_3642, q_gen_3641) -> q_gen_3637
<nil, z>() -> q_gen_3637
<a, z>() -> q_gen_3642
<b, z>() -> q_gen_3642
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3634, q_gen_3636},
Q_f={q_gen_3634},
Delta=
{
<s>(q_gen_3636) -> q_gen_3636
<z>() -> q_gen_3636
<s, s>(q_gen_3634) -> q_gen_3634
<z, s>(q_gen_3636) -> q_gen_3634
<z, z>() -> q_gen_3634
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3633, q_gen_3653},
Q_f={q_gen_3633},
Delta=
{
<cons, cons>(q_gen_3653, q_gen_3633) -> q_gen_3633
<nil, nil>() -> q_gen_3633
<b, b>() -> q_gen_3653
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 6
() -> length([nil, z]) -> 5
() -> leq([z, s(nn2)]) -> 6
() -> leq([z, z]) -> 5
() -> reverse([nil, nil]) -> 5
(append([_eo, cons(h1, nil), _fo]) /\ reverse([t1, _eo])) -> reverse([cons(h1, t1), _fo]) -> 9
(append([t1, l2, _zn])) -> append([cons(h1, t1), l2, cons(h1, _zn)]) -> 7
(length([_oo, _po]) /\ length([l1, _no]) /\ reverse([l1, _oo])) -> leq([_no, _po]) -> 6
(length([_qo, _ro]) /\ length([l1, _so]) /\ reverse([l1, _qo])) -> leq([_ro, _so]) -> 6
(length([ll, _jo])) -> length([cons(x, ll), s(_jo)]) -> 7
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 6
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 6
(leq([s(nn1), z])) -> BOT -> 6
}
Sat witness: Found: ((append([_eo, cons(h1, nil), _fo]) /\ reverse([t1, _eo])) -> reverse([cons(h1, t1), _fo]), {
_eo -> nil  ;  _fo -> cons(a, nil)  ;  h1 -> a  ;  t1 -> nil
})

-------------------------------------------
Step 14, which took 0.015913 s (model generation: 0.014793,  model checking: 0.001120):

Model:
|_
{
append -> 
{{{
Q={q_gen_3638, q_gen_3644, q_gen_3645, q_gen_3658, q_gen_3659, q_gen_3660},
Q_f={q_gen_3638},
Delta=
{
<nil>() -> q_gen_3658
<b>() -> q_gen_3659
<cons, cons>(q_gen_3645, q_gen_3644) -> q_gen_3644
<nil, nil>() -> q_gen_3644
<a, a>() -> q_gen_3645
<b, b>() -> q_gen_3645
<cons, cons, cons>(q_gen_3660, q_gen_3638) -> q_gen_3638
<cons, nil, cons>(q_gen_3645, q_gen_3644) -> q_gen_3638
<nil, cons, cons>(q_gen_3645, q_gen_3644) -> q_gen_3638
<nil, nil, cons>(q_gen_3659, q_gen_3658) -> q_gen_3638
<nil, nil, nil>() -> q_gen_3638
<b, b, b>() -> q_gen_3660
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_3637, q_gen_3641, q_gen_3642},
Q_f={q_gen_3637},
Delta=
{
<nil>() -> q_gen_3641
<cons, s>(q_gen_3642, q_gen_3641) -> q_gen_3637
<nil, z>() -> q_gen_3637
<a, z>() -> q_gen_3642
<b, z>() -> q_gen_3642
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3634, q_gen_3636},
Q_f={q_gen_3634},
Delta=
{
<s>(q_gen_3636) -> q_gen_3636
<z>() -> q_gen_3636
<s, s>(q_gen_3634) -> q_gen_3634
<z, s>(q_gen_3636) -> q_gen_3634
<z, z>() -> q_gen_3634
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3633, q_gen_3653},
Q_f={q_gen_3633},
Delta=
{
<cons, cons>(q_gen_3653, q_gen_3633) -> q_gen_3633
<nil, nil>() -> q_gen_3633
<a, a>() -> q_gen_3653
<b, b>() -> q_gen_3653
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 7
() -> length([nil, z]) -> 6
() -> leq([z, s(nn2)]) -> 7
() -> leq([z, z]) -> 6
() -> reverse([nil, nil]) -> 6
(append([_eo, cons(h1, nil), _fo]) /\ reverse([t1, _eo])) -> reverse([cons(h1, t1), _fo]) -> 9
(append([t1, l2, _zn])) -> append([cons(h1, t1), l2, cons(h1, _zn)]) -> 7
(length([_oo, _po]) /\ length([l1, _no]) /\ reverse([l1, _oo])) -> leq([_no, _po]) -> 7
(length([_qo, _ro]) /\ length([l1, _so]) /\ reverse([l1, _qo])) -> leq([_ro, _so]) -> 7
(length([ll, _jo])) -> length([cons(x, ll), s(_jo)]) -> 10
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 7
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 7
(leq([s(nn1), z])) -> BOT -> 7
}
Sat witness: Found: ((length([ll, _jo])) -> length([cons(x, ll), s(_jo)]), {
_jo -> s(z)  ;  ll -> cons(b, nil)  ;  x -> b
})

-------------------------------------------
Step 15, which took 0.012323 s (model generation: 0.011842,  model checking: 0.000481):

Model:
|_
{
append -> 
{{{
Q={q_gen_3638, q_gen_3644, q_gen_3645, q_gen_3658, q_gen_3659, q_gen_3660},
Q_f={q_gen_3638},
Delta=
{
<nil>() -> q_gen_3658
<b>() -> q_gen_3659
<cons, cons>(q_gen_3645, q_gen_3644) -> q_gen_3644
<nil, nil>() -> q_gen_3644
<a, a>() -> q_gen_3645
<b, b>() -> q_gen_3645
<cons, cons, cons>(q_gen_3660, q_gen_3638) -> q_gen_3638
<cons, nil, cons>(q_gen_3645, q_gen_3644) -> q_gen_3638
<nil, cons, cons>(q_gen_3645, q_gen_3644) -> q_gen_3638
<nil, nil, cons>(q_gen_3659, q_gen_3658) -> q_gen_3638
<nil, nil, nil>() -> q_gen_3638
<b, b, b>() -> q_gen_3660
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_3637, q_gen_3641, q_gen_3642, q_gen_3666, q_gen_3668},
Q_f={q_gen_3637},
Delta=
{
<cons>(q_gen_3666, q_gen_3641) -> q_gen_3641
<nil>() -> q_gen_3641
<b>() -> q_gen_3666
<z>() -> q_gen_3668
<cons, s>(q_gen_3642, q_gen_3641) -> q_gen_3637
<nil, z>() -> q_gen_3637
<a, z>() -> q_gen_3642
<b, s>(q_gen_3668) -> q_gen_3642
<b, z>() -> q_gen_3642
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3634, q_gen_3636},
Q_f={q_gen_3634},
Delta=
{
<s>(q_gen_3636) -> q_gen_3636
<z>() -> q_gen_3636
<s, s>(q_gen_3634) -> q_gen_3634
<z, s>(q_gen_3636) -> q_gen_3634
<z, z>() -> q_gen_3634
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3633, q_gen_3653},
Q_f={q_gen_3633},
Delta=
{
<cons, cons>(q_gen_3653, q_gen_3633) -> q_gen_3633
<nil, nil>() -> q_gen_3633
<a, a>() -> q_gen_3653
<b, b>() -> q_gen_3653
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 7
() -> length([nil, z]) -> 7
() -> leq([z, s(nn2)]) -> 7
() -> leq([z, z]) -> 7
() -> reverse([nil, nil]) -> 7
(append([_eo, cons(h1, nil), _fo]) /\ reverse([t1, _eo])) -> reverse([cons(h1, t1), _fo]) -> 9
(append([t1, l2, _zn])) -> append([cons(h1, t1), l2, cons(h1, _zn)]) -> 7
(length([_oo, _po]) /\ length([l1, _no]) /\ reverse([l1, _oo])) -> leq([_no, _po]) -> 7
(length([_qo, _ro]) /\ length([l1, _so]) /\ reverse([l1, _qo])) -> leq([_ro, _so]) -> 10
(length([ll, _jo])) -> length([cons(x, ll), s(_jo)]) -> 10
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 8
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 8
(leq([s(nn1), z])) -> BOT -> 8
}
Sat witness: Found: ((length([_qo, _ro]) /\ length([l1, _so]) /\ reverse([l1, _qo])) -> leq([_ro, _so]), {
_qo -> cons(b, nil)  ;  _ro -> s(s(z))  ;  _so -> s(z)  ;  l1 -> cons(b, nil)
})

-------------------------------------------
Step 16, which took 0.014033 s (model generation: 0.013430,  model checking: 0.000603):

Model:
|_
{
append -> 
{{{
Q={q_gen_3638, q_gen_3644, q_gen_3645, q_gen_3658, q_gen_3659, q_gen_3660},
Q_f={q_gen_3638},
Delta=
{
<nil>() -> q_gen_3658
<b>() -> q_gen_3659
<cons, cons>(q_gen_3645, q_gen_3644) -> q_gen_3644
<nil, nil>() -> q_gen_3644
<a, a>() -> q_gen_3645
<b, b>() -> q_gen_3645
<cons, cons, cons>(q_gen_3660, q_gen_3638) -> q_gen_3638
<cons, nil, cons>(q_gen_3645, q_gen_3644) -> q_gen_3638
<nil, cons, cons>(q_gen_3645, q_gen_3644) -> q_gen_3638
<nil, nil, cons>(q_gen_3659, q_gen_3658) -> q_gen_3638
<nil, nil, nil>() -> q_gen_3638
<b, b, b>() -> q_gen_3660
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_3637, q_gen_3641, q_gen_3642, q_gen_3666, q_gen_3668},
Q_f={q_gen_3637},
Delta=
{
<cons>(q_gen_3666, q_gen_3641) -> q_gen_3641
<nil>() -> q_gen_3641
<b>() -> q_gen_3666
<z>() -> q_gen_3668
<cons, s>(q_gen_3642, q_gen_3641) -> q_gen_3637
<nil, z>() -> q_gen_3637
<a, z>() -> q_gen_3642
<b, s>(q_gen_3668) -> q_gen_3642
<b, z>() -> q_gen_3642
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3634, q_gen_3636},
Q_f={q_gen_3634},
Delta=
{
<s>(q_gen_3636) -> q_gen_3636
<z>() -> q_gen_3636
<s, s>(q_gen_3634) -> q_gen_3634
<s, z>(q_gen_3636) -> q_gen_3634
<z, s>(q_gen_3636) -> q_gen_3634
<z, z>() -> q_gen_3634
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3633, q_gen_3653},
Q_f={q_gen_3633},
Delta=
{
<cons, cons>(q_gen_3653, q_gen_3633) -> q_gen_3633
<nil, nil>() -> q_gen_3633
<a, a>() -> q_gen_3653
<b, b>() -> q_gen_3653
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 7
() -> length([nil, z]) -> 7
() -> leq([z, s(nn2)]) -> 7
() -> leq([z, z]) -> 7
() -> reverse([nil, nil]) -> 7
(append([_eo, cons(h1, nil), _fo]) /\ reverse([t1, _eo])) -> reverse([cons(h1, t1), _fo]) -> 9
(append([t1, l2, _zn])) -> append([cons(h1, t1), l2, cons(h1, _zn)]) -> 10
(length([_oo, _po]) /\ length([l1, _no]) /\ reverse([l1, _oo])) -> leq([_no, _po]) -> 8
(length([_qo, _ro]) /\ length([l1, _so]) /\ reverse([l1, _qo])) -> leq([_ro, _so]) -> 10
(length([ll, _jo])) -> length([cons(x, ll), s(_jo)]) -> 10
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 8
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 8
(leq([s(nn1), z])) -> BOT -> 8
}
Sat witness: Found: ((append([t1, l2, _zn])) -> append([cons(h1, t1), l2, cons(h1, _zn)]), {
_zn -> cons(b, nil)  ;  h1 -> b  ;  l2 -> nil  ;  t1 -> nil
})

-------------------------------------------
Step 17, which took 0.015703 s (model generation: 0.015058,  model checking: 0.000645):

Model:
|_
{
append -> 
{{{
Q={q_gen_3638, q_gen_3644, q_gen_3645, q_gen_3658, q_gen_3659, q_gen_3660},
Q_f={q_gen_3638},
Delta=
{
<nil>() -> q_gen_3658
<b>() -> q_gen_3659
<cons, cons>(q_gen_3645, q_gen_3644) -> q_gen_3644
<nil, cons>(q_gen_3659, q_gen_3658) -> q_gen_3644
<nil, nil>() -> q_gen_3644
<a, a>() -> q_gen_3645
<b, b>() -> q_gen_3645
<cons, cons, cons>(q_gen_3660, q_gen_3638) -> q_gen_3638
<cons, nil, cons>(q_gen_3645, q_gen_3644) -> q_gen_3638
<nil, cons, cons>(q_gen_3645, q_gen_3644) -> q_gen_3638
<nil, nil, cons>(q_gen_3659, q_gen_3658) -> q_gen_3638
<nil, nil, nil>() -> q_gen_3638
<b, b, b>() -> q_gen_3660
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_3637, q_gen_3641, q_gen_3642, q_gen_3666, q_gen_3668},
Q_f={q_gen_3637},
Delta=
{
<cons>(q_gen_3666, q_gen_3641) -> q_gen_3641
<nil>() -> q_gen_3641
<b>() -> q_gen_3666
<z>() -> q_gen_3668
<cons, s>(q_gen_3642, q_gen_3641) -> q_gen_3637
<nil, z>() -> q_gen_3637
<a, z>() -> q_gen_3642
<b, s>(q_gen_3668) -> q_gen_3642
<b, z>() -> q_gen_3642
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3634, q_gen_3636},
Q_f={q_gen_3634},
Delta=
{
<s>(q_gen_3636) -> q_gen_3636
<z>() -> q_gen_3636
<s, s>(q_gen_3634) -> q_gen_3634
<s, z>(q_gen_3636) -> q_gen_3634
<z, s>(q_gen_3636) -> q_gen_3634
<z, z>() -> q_gen_3634
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3633, q_gen_3653},
Q_f={q_gen_3633},
Delta=
{
<cons, cons>(q_gen_3653, q_gen_3633) -> q_gen_3633
<nil, nil>() -> q_gen_3633
<a, a>() -> q_gen_3653
<b, b>() -> q_gen_3653
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 8
() -> length([nil, z]) -> 8
() -> leq([z, s(nn2)]) -> 8
() -> leq([z, z]) -> 8
() -> reverse([nil, nil]) -> 8
(append([_eo, cons(h1, nil), _fo]) /\ reverse([t1, _eo])) -> reverse([cons(h1, t1), _fo]) -> 9
(append([t1, l2, _zn])) -> append([cons(h1, t1), l2, cons(h1, _zn)]) -> 10
(length([_oo, _po]) /\ length([l1, _no]) /\ reverse([l1, _oo])) -> leq([_no, _po]) -> 8
(length([_qo, _ro]) /\ length([l1, _so]) /\ reverse([l1, _qo])) -> leq([_ro, _so]) -> 10
(length([ll, _jo])) -> length([cons(x, ll), s(_jo)]) -> 10
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 8
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 8
(leq([s(nn1), z])) -> BOT -> 11
}
Sat witness: Found: ((leq([s(nn1), z])) -> BOT, {
nn1 -> z
})

-------------------------------------------
Step 18, which took 0.014729 s (model generation: 0.014577,  model checking: 0.000152):

Model:
|_
{
append -> 
{{{
Q={q_gen_3638, q_gen_3644, q_gen_3645, q_gen_3658, q_gen_3659, q_gen_3660},
Q_f={q_gen_3638},
Delta=
{
<nil>() -> q_gen_3658
<b>() -> q_gen_3659
<cons, cons>(q_gen_3645, q_gen_3644) -> q_gen_3644
<nil, cons>(q_gen_3659, q_gen_3658) -> q_gen_3644
<nil, nil>() -> q_gen_3644
<a, a>() -> q_gen_3645
<b, b>() -> q_gen_3645
<cons, cons, cons>(q_gen_3660, q_gen_3638) -> q_gen_3638
<cons, nil, cons>(q_gen_3645, q_gen_3644) -> q_gen_3638
<nil, cons, cons>(q_gen_3645, q_gen_3644) -> q_gen_3638
<nil, nil, cons>(q_gen_3659, q_gen_3658) -> q_gen_3638
<nil, nil, nil>() -> q_gen_3638
<b, b, b>() -> q_gen_3660
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_3637, q_gen_3641, q_gen_3642, q_gen_3666, q_gen_3668},
Q_f={q_gen_3637},
Delta=
{
<cons>(q_gen_3666, q_gen_3641) -> q_gen_3641
<nil>() -> q_gen_3641
<b>() -> q_gen_3666
<z>() -> q_gen_3668
<cons, s>(q_gen_3642, q_gen_3641) -> q_gen_3637
<nil, z>() -> q_gen_3637
<a, z>() -> q_gen_3642
<b, s>(q_gen_3668) -> q_gen_3642
<b, z>() -> q_gen_3642
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3634, q_gen_3636, q_gen_3671},
Q_f={q_gen_3634},
Delta=
{
<s>(q_gen_3636) -> q_gen_3636
<z>() -> q_gen_3636
<s, s>(q_gen_3634) -> q_gen_3634
<s, s>(q_gen_3671) -> q_gen_3634
<z, s>(q_gen_3636) -> q_gen_3634
<z, z>() -> q_gen_3634
<s, z>(q_gen_3636) -> q_gen_3671
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3633, q_gen_3653},
Q_f={q_gen_3633},
Delta=
{
<cons, cons>(q_gen_3653, q_gen_3633) -> q_gen_3633
<nil, nil>() -> q_gen_3633
<a, a>() -> q_gen_3653
<b, b>() -> q_gen_3653
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 8
() -> length([nil, z]) -> 8
() -> leq([z, s(nn2)]) -> 8
() -> leq([z, z]) -> 8
() -> reverse([nil, nil]) -> 8
(append([_eo, cons(h1, nil), _fo]) /\ reverse([t1, _eo])) -> reverse([cons(h1, t1), _fo]) -> 9
(append([t1, l2, _zn])) -> append([cons(h1, t1), l2, cons(h1, _zn)]) -> 10
(length([_oo, _po]) /\ length([l1, _no]) /\ reverse([l1, _oo])) -> leq([_no, _po]) -> 8
(length([_qo, _ro]) /\ length([l1, _so]) /\ reverse([l1, _qo])) -> leq([_ro, _so]) -> 10
(length([ll, _jo])) -> length([cons(x, ll), s(_jo)]) -> 10
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 8
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 11
(leq([s(nn1), z])) -> BOT -> 11
}
Sat witness: Found: ((leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]), {
nn1 -> s(z)  ;  nn2 -> z
})

-------------------------------------------
Step 19, which took 0.014906 s (model generation: 0.014272,  model checking: 0.000634):

Model:
|_
{
append -> 
{{{
Q={q_gen_3638, q_gen_3644, q_gen_3645, q_gen_3649, q_gen_3651, q_gen_3658, q_gen_3659, q_gen_3660},
Q_f={q_gen_3638},
Delta=
{
<nil>() -> q_gen_3658
<b>() -> q_gen_3659
<nil, nil>() -> q_gen_3644
<a, a>() -> q_gen_3645
<b, b>() -> q_gen_3645
<cons, cons>(q_gen_3645, q_gen_3644) -> q_gen_3649
<nil, cons>(q_gen_3659, q_gen_3658) -> q_gen_3649
<cons, cons, cons>(q_gen_3660, q_gen_3651) -> q_gen_3638
<cons, nil, cons>(q_gen_3645, q_gen_3644) -> q_gen_3638
<nil, cons, cons>(q_gen_3645, q_gen_3649) -> q_gen_3638
<nil, nil, nil>() -> q_gen_3638
<cons, nil, cons>(q_gen_3645, q_gen_3649) -> q_gen_3651
<nil, cons, cons>(q_gen_3645, q_gen_3644) -> q_gen_3651
<nil, nil, cons>(q_gen_3659, q_gen_3658) -> q_gen_3651
<b, b, b>() -> q_gen_3660
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_3637, q_gen_3641, q_gen_3642, q_gen_3666, q_gen_3668},
Q_f={q_gen_3637},
Delta=
{
<cons>(q_gen_3666, q_gen_3641) -> q_gen_3641
<nil>() -> q_gen_3641
<b>() -> q_gen_3666
<z>() -> q_gen_3668
<cons, s>(q_gen_3642, q_gen_3641) -> q_gen_3637
<nil, z>() -> q_gen_3637
<a, z>() -> q_gen_3642
<b, s>(q_gen_3668) -> q_gen_3642
<b, z>() -> q_gen_3642
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3634, q_gen_3636, q_gen_3670},
Q_f={q_gen_3634},
Delta=
{
<s>(q_gen_3636) -> q_gen_3636
<z>() -> q_gen_3636
<s, s>(q_gen_3634) -> q_gen_3634
<z, s>(q_gen_3636) -> q_gen_3634
<z, z>() -> q_gen_3634
<s, s>(q_gen_3670) -> q_gen_3670
<s, z>(q_gen_3636) -> q_gen_3670
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3633, q_gen_3652, q_gen_3653},
Q_f={q_gen_3633},
Delta=
{
<nil, nil>() -> q_gen_3633
<cons, cons>(q_gen_3653, q_gen_3633) -> q_gen_3652
<a, a>() -> q_gen_3653
<b, b>() -> q_gen_3653
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 11
() -> length([nil, z]) -> 9
() -> leq([z, s(nn2)]) -> 9
() -> leq([z, z]) -> 9
() -> reverse([nil, nil]) -> 9
(append([_eo, cons(h1, nil), _fo]) /\ reverse([t1, _eo])) -> reverse([cons(h1, t1), _fo]) -> 9
(append([t1, l2, _zn])) -> append([cons(h1, t1), l2, cons(h1, _zn)]) -> 10
(length([_oo, _po]) /\ length([l1, _no]) /\ reverse([l1, _oo])) -> leq([_no, _po]) -> 9
(length([_qo, _ro]) /\ length([l1, _so]) /\ reverse([l1, _qo])) -> leq([_ro, _so]) -> 10
(length([ll, _jo])) -> length([cons(x, ll), s(_jo)]) -> 10
(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: (() -> append([nil, l2, l2]), {
l2 -> cons(b, nil)
})

-------------------------------------------
Step 20, which took 0.022764 s (model generation: 0.022126,  model checking: 0.000638):

Model:
|_
{
append -> 
{{{
Q={q_gen_3638, q_gen_3644, q_gen_3645, q_gen_3658, q_gen_3659, q_gen_3660},
Q_f={q_gen_3638},
Delta=
{
<nil>() -> q_gen_3658
<b>() -> q_gen_3659
<cons, cons>(q_gen_3645, q_gen_3644) -> q_gen_3644
<nil, cons>(q_gen_3659, q_gen_3658) -> q_gen_3644
<nil, nil>() -> q_gen_3644
<a, a>() -> q_gen_3645
<b, b>() -> q_gen_3645
<cons, cons, cons>(q_gen_3660, q_gen_3638) -> q_gen_3638
<cons, nil, cons>(q_gen_3645, q_gen_3644) -> q_gen_3638
<nil, cons, cons>(q_gen_3645, q_gen_3644) -> q_gen_3638
<nil, nil, cons>(q_gen_3659, q_gen_3658) -> q_gen_3638
<nil, nil, nil>() -> q_gen_3638
<b, b, b>() -> q_gen_3660
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_3637, q_gen_3641, q_gen_3642, q_gen_3665, q_gen_3666, q_gen_3667, q_gen_3668, q_gen_3669},
Q_f={q_gen_3637},
Delta=
{
<nil>() -> q_gen_3641
<cons>(q_gen_3666, q_gen_3641) -> q_gen_3665
<b>() -> q_gen_3666
<z>() -> q_gen_3668
<cons, s>(q_gen_3642, q_gen_3641) -> q_gen_3637
<cons, s>(q_gen_3667, q_gen_3665) -> q_gen_3637
<nil, z>() -> q_gen_3637
<a, z>() -> q_gen_3642
<b, z>() -> q_gen_3642
<b, s>(q_gen_3668) -> q_gen_3667
<cons, s>(q_gen_3667, q_gen_3641) -> q_gen_3669
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3634, q_gen_3636, q_gen_3670},
Q_f={q_gen_3634},
Delta=
{
<s>(q_gen_3636) -> q_gen_3636
<z>() -> q_gen_3636
<s, s>(q_gen_3634) -> q_gen_3634
<z, s>(q_gen_3636) -> q_gen_3634
<z, z>() -> q_gen_3634
<s, s>(q_gen_3670) -> q_gen_3670
<s, z>(q_gen_3636) -> q_gen_3670
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3633, q_gen_3653},
Q_f={q_gen_3633},
Delta=
{
<cons, cons>(q_gen_3653, q_gen_3633) -> q_gen_3633
<nil, nil>() -> q_gen_3633
<a, a>() -> q_gen_3653
<b, b>() -> q_gen_3653
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 11
() -> length([nil, z]) -> 9
() -> leq([z, s(nn2)]) -> 9
() -> leq([z, z]) -> 9
() -> reverse([nil, nil]) -> 9
(append([_eo, cons(h1, nil), _fo]) /\ reverse([t1, _eo])) -> reverse([cons(h1, t1), _fo]) -> 12
(append([t1, l2, _zn])) -> append([cons(h1, t1), l2, cons(h1, _zn)]) -> 10
(length([_oo, _po]) /\ length([l1, _no]) /\ reverse([l1, _oo])) -> leq([_no, _po]) -> 10
(length([_qo, _ro]) /\ length([l1, _so]) /\ reverse([l1, _qo])) -> leq([_ro, _so]) -> 10
(length([ll, _jo])) -> length([cons(x, ll), s(_jo)]) -> 10
(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: ((append([_eo, cons(h1, nil), _fo]) /\ reverse([t1, _eo])) -> reverse([cons(h1, t1), _fo]), {
_eo -> nil  ;  _fo -> cons(b, cons(b, nil))  ;  h1 -> b  ;  t1 -> nil
})

-------------------------------------------
Step 21, which took 0.017094 s (model generation: 0.015954,  model checking: 0.001140):

Model:
|_
{
append -> 
{{{
Q={q_gen_3638, q_gen_3644, q_gen_3645, q_gen_3658, q_gen_3659, q_gen_3660},
Q_f={q_gen_3638},
Delta=
{
<nil>() -> q_gen_3658
<b>() -> q_gen_3659
<cons, cons>(q_gen_3645, q_gen_3644) -> q_gen_3644
<nil, cons>(q_gen_3659, q_gen_3658) -> q_gen_3644
<nil, nil>() -> q_gen_3644
<a, a>() -> q_gen_3645
<b, b>() -> q_gen_3645
<cons, cons, cons>(q_gen_3660, q_gen_3638) -> q_gen_3638
<cons, nil, cons>(q_gen_3645, q_gen_3644) -> q_gen_3638
<nil, cons, cons>(q_gen_3645, q_gen_3644) -> q_gen_3638
<nil, nil, cons>(q_gen_3659, q_gen_3658) -> q_gen_3638
<nil, nil, nil>() -> q_gen_3638
<b, b, b>() -> q_gen_3660
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_3637, q_gen_3641, q_gen_3642, q_gen_3665, q_gen_3666, q_gen_3667, q_gen_3668, q_gen_3669},
Q_f={q_gen_3637},
Delta=
{
<nil>() -> q_gen_3641
<cons>(q_gen_3666, q_gen_3641) -> q_gen_3665
<b>() -> q_gen_3666
<z>() -> q_gen_3668
<cons, s>(q_gen_3642, q_gen_3641) -> q_gen_3637
<cons, s>(q_gen_3667, q_gen_3665) -> q_gen_3637
<nil, z>() -> q_gen_3637
<a, z>() -> q_gen_3642
<b, z>() -> q_gen_3642
<b, s>(q_gen_3668) -> q_gen_3667
<cons, s>(q_gen_3667, q_gen_3641) -> q_gen_3669
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3634, q_gen_3636, q_gen_3670},
Q_f={q_gen_3634},
Delta=
{
<s>(q_gen_3636) -> q_gen_3636
<z>() -> q_gen_3636
<s, s>(q_gen_3634) -> q_gen_3634
<z, s>(q_gen_3636) -> q_gen_3634
<z, z>() -> q_gen_3634
<s, s>(q_gen_3670) -> q_gen_3670
<s, z>(q_gen_3636) -> q_gen_3670
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3633, q_gen_3653, q_gen_3677, q_gen_3678},
Q_f={q_gen_3633},
Delta=
{
<nil>() -> q_gen_3677
<b>() -> q_gen_3678
<cons, cons>(q_gen_3653, q_gen_3633) -> q_gen_3633
<nil, cons>(q_gen_3678, q_gen_3677) -> q_gen_3633
<nil, nil>() -> q_gen_3633
<a, a>() -> q_gen_3653
<b, b>() -> q_gen_3653
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 11
() -> length([nil, z]) -> 10
() -> leq([z, s(nn2)]) -> 10
() -> leq([z, z]) -> 10
() -> reverse([nil, nil]) -> 10
(append([_eo, cons(h1, nil), _fo]) /\ reverse([t1, _eo])) -> reverse([cons(h1, t1), _fo]) -> 12
(append([t1, l2, _zn])) -> append([cons(h1, t1), l2, cons(h1, _zn)]) -> 10
(length([_oo, _po]) /\ length([l1, _no]) /\ reverse([l1, _oo])) -> leq([_no, _po]) -> 10
(length([_qo, _ro]) /\ length([l1, _so]) /\ reverse([l1, _qo])) -> leq([_ro, _so]) -> 10
(length([ll, _jo])) -> length([cons(x, ll), s(_jo)]) -> 13
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 11
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 11
(leq([s(nn1), z])) -> BOT -> 11
}
Sat witness: Found: ((length([ll, _jo])) -> length([cons(x, ll), s(_jo)]), {
_jo -> s(z)  ;  ll -> cons(b, nil)  ;  x -> a
})

-------------------------------------------
Step 22, which took 0.016737 s (model generation: 0.016282,  model checking: 0.000455):

Model:
|_
{
append -> 
{{{
Q={q_gen_3638, q_gen_3644, q_gen_3645, q_gen_3658, q_gen_3659, q_gen_3660},
Q_f={q_gen_3638},
Delta=
{
<nil>() -> q_gen_3658
<b>() -> q_gen_3659
<cons, cons>(q_gen_3645, q_gen_3644) -> q_gen_3644
<nil, cons>(q_gen_3659, q_gen_3658) -> q_gen_3644
<nil, nil>() -> q_gen_3644
<a, a>() -> q_gen_3645
<b, b>() -> q_gen_3645
<cons, cons, cons>(q_gen_3660, q_gen_3638) -> q_gen_3638
<cons, nil, cons>(q_gen_3645, q_gen_3644) -> q_gen_3638
<nil, cons, cons>(q_gen_3645, q_gen_3644) -> q_gen_3638
<nil, nil, cons>(q_gen_3659, q_gen_3658) -> q_gen_3638
<nil, nil, nil>() -> q_gen_3638
<b, b, b>() -> q_gen_3660
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_3637, q_gen_3641, q_gen_3642, q_gen_3665, q_gen_3666, q_gen_3667, q_gen_3668, q_gen_3669},
Q_f={q_gen_3637},
Delta=
{
<nil>() -> q_gen_3641
<cons>(q_gen_3666, q_gen_3641) -> q_gen_3665
<b>() -> q_gen_3666
<z>() -> q_gen_3668
<cons, s>(q_gen_3642, q_gen_3641) -> q_gen_3637
<cons, s>(q_gen_3642, q_gen_3665) -> q_gen_3637
<cons, s>(q_gen_3667, q_gen_3665) -> q_gen_3637
<nil, z>() -> q_gen_3637
<a, s>(q_gen_3668) -> q_gen_3642
<a, z>() -> q_gen_3642
<b, z>() -> q_gen_3642
<b, s>(q_gen_3668) -> q_gen_3667
<cons, s>(q_gen_3667, q_gen_3641) -> q_gen_3669
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3634, q_gen_3636, q_gen_3670},
Q_f={q_gen_3634},
Delta=
{
<s>(q_gen_3636) -> q_gen_3636
<z>() -> q_gen_3636
<s, s>(q_gen_3634) -> q_gen_3634
<z, s>(q_gen_3636) -> q_gen_3634
<z, z>() -> q_gen_3634
<s, s>(q_gen_3670) -> q_gen_3670
<s, z>(q_gen_3636) -> q_gen_3670
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3633, q_gen_3653, q_gen_3677, q_gen_3678},
Q_f={q_gen_3633},
Delta=
{
<nil>() -> q_gen_3677
<b>() -> q_gen_3678
<cons, cons>(q_gen_3653, q_gen_3633) -> q_gen_3633
<nil, cons>(q_gen_3678, q_gen_3677) -> q_gen_3633
<nil, nil>() -> q_gen_3633
<a, a>() -> q_gen_3653
<b, b>() -> q_gen_3653
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 11
() -> length([nil, z]) -> 10
() -> leq([z, s(nn2)]) -> 10
() -> leq([z, z]) -> 10
() -> reverse([nil, nil]) -> 10
(append([_eo, cons(h1, nil), _fo]) /\ reverse([t1, _eo])) -> reverse([cons(h1, t1), _fo]) -> 12
(append([t1, l2, _zn])) -> append([cons(h1, t1), l2, cons(h1, _zn)]) -> 10
(length([_oo, _po]) /\ length([l1, _no]) /\ reverse([l1, _oo])) -> leq([_no, _po]) -> 10
(length([_qo, _ro]) /\ length([l1, _so]) /\ reverse([l1, _qo])) -> leq([_ro, _so]) -> 13
(length([ll, _jo])) -> length([cons(x, ll), s(_jo)]) -> 13
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 11
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 11
(leq([s(nn1), z])) -> BOT -> 11
}
Sat witness: Found: ((length([_qo, _ro]) /\ length([l1, _so]) /\ reverse([l1, _qo])) -> leq([_ro, _so]), {
_qo -> cons(b, nil)  ;  _ro -> s(z)  ;  _so -> z  ;  l1 -> nil
})

-------------------------------------------
Step 23, which took 0.017484 s (model generation: 0.016037,  model checking: 0.001447):

Model:
|_
{
append -> 
{{{
Q={q_gen_3638, q_gen_3644, q_gen_3645, q_gen_3658, q_gen_3659, q_gen_3660},
Q_f={q_gen_3638},
Delta=
{
<nil>() -> q_gen_3658
<b>() -> q_gen_3659
<cons, cons>(q_gen_3645, q_gen_3644) -> q_gen_3644
<nil, cons>(q_gen_3659, q_gen_3658) -> q_gen_3644
<nil, nil>() -> q_gen_3644
<a, a>() -> q_gen_3645
<b, b>() -> q_gen_3645
<cons, cons, cons>(q_gen_3660, q_gen_3638) -> q_gen_3638
<cons, nil, cons>(q_gen_3645, q_gen_3644) -> q_gen_3638
<nil, cons, cons>(q_gen_3645, q_gen_3644) -> q_gen_3638
<nil, nil, cons>(q_gen_3659, q_gen_3658) -> q_gen_3638
<nil, nil, nil>() -> q_gen_3638
<b, b, b>() -> q_gen_3660
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_3637, q_gen_3641, q_gen_3642, q_gen_3665, q_gen_3666, q_gen_3667, q_gen_3668, q_gen_3669},
Q_f={q_gen_3637},
Delta=
{
<nil>() -> q_gen_3641
<cons>(q_gen_3666, q_gen_3641) -> q_gen_3665
<b>() -> q_gen_3666
<z>() -> q_gen_3668
<cons, s>(q_gen_3642, q_gen_3641) -> q_gen_3637
<cons, s>(q_gen_3667, q_gen_3665) -> q_gen_3637
<nil, z>() -> q_gen_3637
<a, z>() -> q_gen_3642
<b, z>() -> q_gen_3642
<a, s>(q_gen_3668) -> q_gen_3667
<b, s>(q_gen_3668) -> q_gen_3667
<cons, s>(q_gen_3667, q_gen_3641) -> q_gen_3669
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3634, q_gen_3636, q_gen_3670},
Q_f={q_gen_3634},
Delta=
{
<s>(q_gen_3636) -> q_gen_3636
<z>() -> q_gen_3636
<s, s>(q_gen_3634) -> q_gen_3634
<z, s>(q_gen_3636) -> q_gen_3634
<z, z>() -> q_gen_3634
<s, s>(q_gen_3670) -> q_gen_3670
<s, z>(q_gen_3636) -> q_gen_3670
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3633, q_gen_3653, q_gen_3676, q_gen_3677, q_gen_3678},
Q_f={q_gen_3633},
Delta=
{
<nil>() -> q_gen_3677
<b>() -> q_gen_3678
<cons, cons>(q_gen_3653, q_gen_3633) -> q_gen_3633
<cons, cons>(q_gen_3653, q_gen_3676) -> q_gen_3633
<nil, nil>() -> q_gen_3633
<a, a>() -> q_gen_3653
<b, b>() -> q_gen_3653
<nil, cons>(q_gen_3678, q_gen_3677) -> q_gen_3676
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 11
() -> length([nil, z]) -> 10
() -> leq([z, s(nn2)]) -> 10
() -> leq([z, z]) -> 10
() -> reverse([nil, nil]) -> 10
(append([_eo, cons(h1, nil), _fo]) /\ reverse([t1, _eo])) -> reverse([cons(h1, t1), _fo]) -> 12
(append([t1, l2, _zn])) -> append([cons(h1, t1), l2, cons(h1, _zn)]) -> 13
(length([_oo, _po]) /\ length([l1, _no]) /\ reverse([l1, _oo])) -> leq([_no, _po]) -> 11
(length([_qo, _ro]) /\ length([l1, _so]) /\ reverse([l1, _qo])) -> leq([_ro, _so]) -> 13
(length([ll, _jo])) -> length([cons(x, ll), s(_jo)]) -> 13
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 11
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 11
(leq([s(nn1), z])) -> BOT -> 11
}
Sat witness: Found: ((append([t1, l2, _zn])) -> append([cons(h1, t1), l2, cons(h1, _zn)]), {
_zn -> cons(b, nil)  ;  h1 -> a  ;  l2 -> cons(b, nil)  ;  t1 -> nil
})

-------------------------------------------
Step 24, which took 0.017580 s (model generation: 0.016450,  model checking: 0.001130):

Model:
|_
{
append -> 
{{{
Q={q_gen_3638, q_gen_3644, q_gen_3645, q_gen_3658, q_gen_3659, q_gen_3660},
Q_f={q_gen_3638},
Delta=
{
<nil>() -> q_gen_3658
<b>() -> q_gen_3659
<cons, cons>(q_gen_3645, q_gen_3644) -> q_gen_3644
<nil, cons>(q_gen_3659, q_gen_3658) -> q_gen_3644
<nil, nil>() -> q_gen_3644
<a, a>() -> q_gen_3645
<b, b>() -> q_gen_3645
<cons, cons, cons>(q_gen_3660, q_gen_3638) -> q_gen_3638
<cons, nil, cons>(q_gen_3645, q_gen_3644) -> q_gen_3638
<nil, cons, cons>(q_gen_3645, q_gen_3644) -> q_gen_3638
<nil, nil, cons>(q_gen_3659, q_gen_3658) -> q_gen_3638
<nil, nil, nil>() -> q_gen_3638
<a, b, a>() -> q_gen_3660
<b, b, b>() -> q_gen_3660
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_3637, q_gen_3641, q_gen_3642, q_gen_3665, q_gen_3666, q_gen_3667, q_gen_3668, q_gen_3669},
Q_f={q_gen_3637},
Delta=
{
<nil>() -> q_gen_3641
<cons>(q_gen_3666, q_gen_3641) -> q_gen_3665
<b>() -> q_gen_3666
<z>() -> q_gen_3668
<cons, s>(q_gen_3642, q_gen_3641) -> q_gen_3637
<cons, s>(q_gen_3642, q_gen_3665) -> q_gen_3637
<cons, s>(q_gen_3667, q_gen_3665) -> q_gen_3637
<nil, z>() -> q_gen_3637
<a, s>(q_gen_3668) -> q_gen_3642
<a, z>() -> q_gen_3642
<b, z>() -> q_gen_3642
<b, s>(q_gen_3668) -> q_gen_3667
<cons, s>(q_gen_3667, q_gen_3641) -> q_gen_3669
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3634, q_gen_3636, q_gen_3670},
Q_f={q_gen_3634},
Delta=
{
<s>(q_gen_3636) -> q_gen_3636
<z>() -> q_gen_3636
<s, s>(q_gen_3634) -> q_gen_3634
<z, s>(q_gen_3636) -> q_gen_3634
<z, z>() -> q_gen_3634
<s, s>(q_gen_3670) -> q_gen_3670
<s, z>(q_gen_3636) -> q_gen_3670
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3633, q_gen_3653, q_gen_3676, q_gen_3677, q_gen_3678},
Q_f={q_gen_3633},
Delta=
{
<nil>() -> q_gen_3677
<b>() -> q_gen_3678
<cons, cons>(q_gen_3653, q_gen_3633) -> q_gen_3633
<cons, cons>(q_gen_3653, q_gen_3676) -> q_gen_3633
<nil, nil>() -> q_gen_3633
<a, a>() -> q_gen_3653
<b, b>() -> q_gen_3653
<nil, cons>(q_gen_3678, q_gen_3677) -> q_gen_3676
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 11
() -> length([nil, z]) -> 11
() -> leq([z, s(nn2)]) -> 11
() -> leq([z, z]) -> 11
() -> reverse([nil, nil]) -> 11
(append([_eo, cons(h1, nil), _fo]) /\ reverse([t1, _eo])) -> reverse([cons(h1, t1), _fo]) -> 12
(append([t1, l2, _zn])) -> append([cons(h1, t1), l2, cons(h1, _zn)]) -> 13
(length([_oo, _po]) /\ length([l1, _no]) /\ reverse([l1, _oo])) -> leq([_no, _po]) -> 14
(length([_qo, _ro]) /\ length([l1, _so]) /\ reverse([l1, _qo])) -> leq([_ro, _so]) -> 13
(length([ll, _jo])) -> length([cons(x, ll), s(_jo)]) -> 13
(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([_oo, _po]) /\ length([l1, _no]) /\ reverse([l1, _oo])) -> leq([_no, _po]), {
_no -> s(s(z))  ;  _oo -> cons(a, cons(b, nil))  ;  _po -> s(z)  ;  l1 -> cons(a, cons(b, nil))
})

-------------------------------------------
Step 25, which took 0.019392 s (model generation: 0.017587,  model checking: 0.001805):

Model:
|_
{
append -> 
{{{
Q={q_gen_3638, q_gen_3644, q_gen_3645, q_gen_3658, q_gen_3659, q_gen_3660},
Q_f={q_gen_3638},
Delta=
{
<nil>() -> q_gen_3658
<b>() -> q_gen_3659
<cons, cons>(q_gen_3645, q_gen_3644) -> q_gen_3644
<nil, cons>(q_gen_3659, q_gen_3658) -> q_gen_3644
<nil, nil>() -> q_gen_3644
<a, a>() -> q_gen_3645
<b, b>() -> q_gen_3645
<cons, cons, cons>(q_gen_3660, q_gen_3638) -> q_gen_3638
<cons, nil, cons>(q_gen_3645, q_gen_3644) -> q_gen_3638
<nil, cons, cons>(q_gen_3645, q_gen_3644) -> q_gen_3638
<nil, nil, cons>(q_gen_3659, q_gen_3658) -> q_gen_3638
<nil, nil, nil>() -> q_gen_3638
<a, b, a>() -> q_gen_3660
<b, b, b>() -> q_gen_3660
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_3637, q_gen_3641, q_gen_3642, q_gen_3665, q_gen_3666, q_gen_3667, q_gen_3668, q_gen_3669},
Q_f={q_gen_3637},
Delta=
{
<nil>() -> q_gen_3641
<cons>(q_gen_3666, q_gen_3641) -> q_gen_3665
<b>() -> q_gen_3666
<z>() -> q_gen_3668
<cons, s>(q_gen_3642, q_gen_3641) -> q_gen_3637
<cons, s>(q_gen_3667, q_gen_3665) -> q_gen_3637
<nil, z>() -> q_gen_3637
<a, z>() -> q_gen_3642
<b, z>() -> q_gen_3642
<a, s>(q_gen_3668) -> q_gen_3667
<b, s>(q_gen_3668) -> q_gen_3667
<cons, s>(q_gen_3642, q_gen_3665) -> q_gen_3669
<cons, s>(q_gen_3667, q_gen_3641) -> q_gen_3669
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3634, q_gen_3636, q_gen_3670},
Q_f={q_gen_3634},
Delta=
{
<s>(q_gen_3636) -> q_gen_3636
<z>() -> q_gen_3636
<s, s>(q_gen_3634) -> q_gen_3634
<z, s>(q_gen_3636) -> q_gen_3634
<z, z>() -> q_gen_3634
<s, s>(q_gen_3670) -> q_gen_3670
<s, z>(q_gen_3636) -> q_gen_3670
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3633, q_gen_3653, q_gen_3676, q_gen_3677, q_gen_3678},
Q_f={q_gen_3633},
Delta=
{
<nil>() -> q_gen_3677
<b>() -> q_gen_3678
<cons, cons>(q_gen_3653, q_gen_3633) -> q_gen_3633
<cons, cons>(q_gen_3653, q_gen_3676) -> q_gen_3633
<nil, nil>() -> q_gen_3633
<a, a>() -> q_gen_3653
<b, b>() -> q_gen_3653
<nil, cons>(q_gen_3678, q_gen_3677) -> q_gen_3676
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 12
() -> length([nil, z]) -> 12
() -> leq([z, s(nn2)]) -> 12
() -> leq([z, z]) -> 12
() -> reverse([nil, nil]) -> 12
(append([_eo, cons(h1, nil), _fo]) /\ reverse([t1, _eo])) -> reverse([cons(h1, t1), _fo]) -> 15
(append([t1, l2, _zn])) -> append([cons(h1, t1), l2, cons(h1, _zn)]) -> 13
(length([_oo, _po]) /\ length([l1, _no]) /\ reverse([l1, _oo])) -> leq([_no, _po]) -> 14
(length([_qo, _ro]) /\ length([l1, _so]) /\ reverse([l1, _qo])) -> leq([_ro, _so]) -> 13
(length([ll, _jo])) -> length([cons(x, ll), s(_jo)]) -> 13
(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: ((append([_eo, cons(h1, nil), _fo]) /\ reverse([t1, _eo])) -> reverse([cons(h1, t1), _fo]), {
_eo -> cons(a, cons(b, nil))  ;  _fo -> cons(a, cons(b, cons(b, nil)))  ;  h1 -> b  ;  t1 -> cons(a, nil)
})

-------------------------------------------
Step 26, which took 0.022942 s (model generation: 0.021305,  model checking: 0.001637):

Model:
|_
{
append -> 
{{{
Q={q_gen_3638, q_gen_3644, q_gen_3645, q_gen_3658, q_gen_3659, q_gen_3660},
Q_f={q_gen_3638},
Delta=
{
<nil>() -> q_gen_3658
<b>() -> q_gen_3659
<cons, cons>(q_gen_3645, q_gen_3644) -> q_gen_3644
<nil, cons>(q_gen_3659, q_gen_3658) -> q_gen_3644
<nil, nil>() -> q_gen_3644
<a, a>() -> q_gen_3645
<b, b>() -> q_gen_3645
<cons, cons, cons>(q_gen_3660, q_gen_3638) -> q_gen_3638
<cons, nil, cons>(q_gen_3645, q_gen_3644) -> q_gen_3638
<nil, cons, cons>(q_gen_3645, q_gen_3644) -> q_gen_3638
<nil, nil, cons>(q_gen_3659, q_gen_3658) -> q_gen_3638
<nil, nil, nil>() -> q_gen_3638
<a, b, a>() -> q_gen_3660
<b, b, b>() -> q_gen_3660
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_3637, q_gen_3641, q_gen_3642, q_gen_3665, q_gen_3666, q_gen_3667, q_gen_3668, q_gen_3669},
Q_f={q_gen_3637},
Delta=
{
<nil>() -> q_gen_3641
<cons>(q_gen_3666, q_gen_3641) -> q_gen_3665
<b>() -> q_gen_3666
<z>() -> q_gen_3668
<cons, s>(q_gen_3642, q_gen_3641) -> q_gen_3637
<cons, s>(q_gen_3667, q_gen_3665) -> q_gen_3637
<nil, z>() -> q_gen_3637
<a, z>() -> q_gen_3642
<b, z>() -> q_gen_3642
<a, s>(q_gen_3668) -> q_gen_3667
<b, s>(q_gen_3668) -> q_gen_3667
<cons, s>(q_gen_3642, q_gen_3665) -> q_gen_3669
<cons, s>(q_gen_3667, q_gen_3641) -> q_gen_3669
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3634, q_gen_3636, q_gen_3670},
Q_f={q_gen_3634},
Delta=
{
<s>(q_gen_3636) -> q_gen_3636
<z>() -> q_gen_3636
<s, s>(q_gen_3634) -> q_gen_3634
<z, s>(q_gen_3636) -> q_gen_3634
<z, z>() -> q_gen_3634
<s, s>(q_gen_3670) -> q_gen_3670
<s, z>(q_gen_3636) -> q_gen_3670
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3633, q_gen_3653, q_gen_3676, q_gen_3677, q_gen_3678},
Q_f={q_gen_3633},
Delta=
{
<nil>() -> q_gen_3677
<b>() -> q_gen_3678
<cons, cons>(q_gen_3653, q_gen_3633) -> q_gen_3633
<cons, cons>(q_gen_3653, q_gen_3676) -> q_gen_3633
<nil, nil>() -> q_gen_3633
<a, a>() -> q_gen_3653
<a, b>() -> q_gen_3653
<b, a>() -> q_gen_3653
<b, b>() -> q_gen_3653
<nil, cons>(q_gen_3678, q_gen_3677) -> q_gen_3676
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 13
() -> length([nil, z]) -> 13
() -> leq([z, s(nn2)]) -> 13
() -> leq([z, z]) -> 13
() -> reverse([nil, nil]) -> 13
(append([_eo, cons(h1, nil), _fo]) /\ reverse([t1, _eo])) -> reverse([cons(h1, t1), _fo]) -> 15
(append([t1, l2, _zn])) -> append([cons(h1, t1), l2, cons(h1, _zn)]) -> 13
(length([_oo, _po]) /\ length([l1, _no]) /\ reverse([l1, _oo])) -> leq([_no, _po]) -> 14
(length([_qo, _ro]) /\ length([l1, _so]) /\ reverse([l1, _qo])) -> leq([_ro, _so]) -> 13
(length([ll, _jo])) -> length([cons(x, ll), s(_jo)]) -> 16
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 14
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 14
(leq([s(nn1), z])) -> BOT -> 14
}
Sat witness: Found: ((length([ll, _jo])) -> length([cons(x, ll), s(_jo)]), {
_jo -> s(s(z))  ;  ll -> cons(b, cons(b, nil))  ;  x -> b
})

-------------------------------------------
Step 27, which took 0.024029 s (model generation: 0.023320,  model checking: 0.000709):

Model:
|_
{
append -> 
{{{
Q={q_gen_3638, q_gen_3644, q_gen_3645, q_gen_3658, q_gen_3659, q_gen_3660},
Q_f={q_gen_3638},
Delta=
{
<nil>() -> q_gen_3658
<b>() -> q_gen_3659
<cons, cons>(q_gen_3645, q_gen_3644) -> q_gen_3644
<nil, cons>(q_gen_3659, q_gen_3658) -> q_gen_3644
<nil, nil>() -> q_gen_3644
<a, a>() -> q_gen_3645
<b, b>() -> q_gen_3645
<cons, cons, cons>(q_gen_3660, q_gen_3638) -> q_gen_3638
<cons, nil, cons>(q_gen_3645, q_gen_3644) -> q_gen_3638
<nil, cons, cons>(q_gen_3645, q_gen_3644) -> q_gen_3638
<nil, nil, cons>(q_gen_3659, q_gen_3658) -> q_gen_3638
<nil, nil, nil>() -> q_gen_3638
<a, b, a>() -> q_gen_3660
<b, b, b>() -> q_gen_3660
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_3637, q_gen_3641, q_gen_3642, q_gen_3665, q_gen_3666, q_gen_3667, q_gen_3668, q_gen_3669},
Q_f={q_gen_3637},
Delta=
{
<nil>() -> q_gen_3641
<cons>(q_gen_3666, q_gen_3641) -> q_gen_3665
<cons>(q_gen_3666, q_gen_3665) -> q_gen_3665
<b>() -> q_gen_3666
<s>(q_gen_3668) -> q_gen_3668
<z>() -> q_gen_3668
<cons, s>(q_gen_3642, q_gen_3641) -> q_gen_3637
<cons, s>(q_gen_3667, q_gen_3665) -> q_gen_3637
<nil, z>() -> q_gen_3637
<a, z>() -> q_gen_3642
<b, z>() -> q_gen_3642
<a, s>(q_gen_3668) -> q_gen_3667
<b, s>(q_gen_3668) -> q_gen_3667
<cons, s>(q_gen_3642, q_gen_3665) -> q_gen_3669
<cons, s>(q_gen_3667, q_gen_3641) -> q_gen_3669
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3634, q_gen_3636, q_gen_3670},
Q_f={q_gen_3634},
Delta=
{
<s>(q_gen_3636) -> q_gen_3636
<z>() -> q_gen_3636
<s, s>(q_gen_3634) -> q_gen_3634
<z, s>(q_gen_3636) -> q_gen_3634
<z, z>() -> q_gen_3634
<s, s>(q_gen_3670) -> q_gen_3670
<s, z>(q_gen_3636) -> q_gen_3670
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3633, q_gen_3653, q_gen_3676, q_gen_3677, q_gen_3678},
Q_f={q_gen_3633},
Delta=
{
<nil>() -> q_gen_3677
<b>() -> q_gen_3678
<cons, cons>(q_gen_3653, q_gen_3633) -> q_gen_3633
<cons, cons>(q_gen_3653, q_gen_3676) -> q_gen_3633
<nil, nil>() -> q_gen_3633
<a, a>() -> q_gen_3653
<a, b>() -> q_gen_3653
<b, a>() -> q_gen_3653
<b, b>() -> q_gen_3653
<nil, cons>(q_gen_3678, q_gen_3677) -> q_gen_3676
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 13
() -> length([nil, z]) -> 13
() -> leq([z, s(nn2)]) -> 13
() -> leq([z, z]) -> 13
() -> reverse([nil, nil]) -> 13
(append([_eo, cons(h1, nil), _fo]) /\ reverse([t1, _eo])) -> reverse([cons(h1, t1), _fo]) -> 15
(append([t1, l2, _zn])) -> append([cons(h1, t1), l2, cons(h1, _zn)]) -> 13
(length([_oo, _po]) /\ length([l1, _no]) /\ reverse([l1, _oo])) -> leq([_no, _po]) -> 14
(length([_qo, _ro]) /\ length([l1, _so]) /\ reverse([l1, _qo])) -> leq([_ro, _so]) -> 16
(length([ll, _jo])) -> length([cons(x, ll), s(_jo)]) -> 16
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 14
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 14
(leq([s(nn1), z])) -> BOT -> 14
}
Sat witness: Found: ((length([_qo, _ro]) /\ length([l1, _so]) /\ reverse([l1, _qo])) -> leq([_ro, _so]), {
_qo -> cons(b, cons(b, nil))  ;  _ro -> s(s(z))  ;  _so -> s(z)  ;  l1 -> cons(b, nil)
})

-------------------------------------------
Step 28, which took 0.024315 s (model generation: 0.023184,  model checking: 0.001131):

Model:
|_
{
append -> 
{{{
Q={q_gen_3638, q_gen_3644, q_gen_3645, q_gen_3658, q_gen_3659, q_gen_3660, q_gen_3673, q_gen_3674},
Q_f={q_gen_3638},
Delta=
{
<nil>() -> q_gen_3658
<b>() -> q_gen_3659
<cons, cons>(q_gen_3645, q_gen_3644) -> q_gen_3644
<nil, nil>() -> q_gen_3644
<a, a>() -> q_gen_3645
<b, b>() -> q_gen_3645
<nil, cons>(q_gen_3659, q_gen_3658) -> q_gen_3673
<cons, cons, cons>(q_gen_3660, q_gen_3638) -> q_gen_3638
<cons, nil, cons>(q_gen_3645, q_gen_3644) -> q_gen_3638
<cons, nil, cons>(q_gen_3645, q_gen_3673) -> q_gen_3638
<nil, cons, cons>(q_gen_3645, q_gen_3644) -> q_gen_3638
<nil, nil, cons>(q_gen_3659, q_gen_3658) -> q_gen_3638
<nil, nil, nil>() -> q_gen_3638
<a, b, a>() -> q_gen_3660
<b, b, b>() -> q_gen_3660
<nil, cons, cons>(q_gen_3645, q_gen_3673) -> q_gen_3674
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_3637, q_gen_3641, q_gen_3642, q_gen_3665, q_gen_3666, q_gen_3667, q_gen_3668, q_gen_3669},
Q_f={q_gen_3637},
Delta=
{
<nil>() -> q_gen_3641
<cons>(q_gen_3666, q_gen_3641) -> q_gen_3665
<cons>(q_gen_3666, q_gen_3665) -> q_gen_3665
<b>() -> q_gen_3666
<s>(q_gen_3668) -> q_gen_3668
<z>() -> q_gen_3668
<cons, s>(q_gen_3642, q_gen_3641) -> q_gen_3637
<cons, s>(q_gen_3667, q_gen_3665) -> q_gen_3637
<nil, z>() -> q_gen_3637
<a, z>() -> q_gen_3642
<b, z>() -> q_gen_3642
<a, s>(q_gen_3668) -> q_gen_3667
<b, s>(q_gen_3668) -> q_gen_3667
<cons, s>(q_gen_3642, q_gen_3665) -> q_gen_3669
<cons, s>(q_gen_3667, q_gen_3641) -> q_gen_3669
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3634, q_gen_3636, q_gen_3670},
Q_f={q_gen_3634},
Delta=
{
<s>(q_gen_3636) -> q_gen_3636
<z>() -> q_gen_3636
<s, s>(q_gen_3634) -> q_gen_3634
<z, s>(q_gen_3636) -> q_gen_3634
<z, z>() -> q_gen_3634
<s, s>(q_gen_3670) -> q_gen_3670
<s, z>(q_gen_3636) -> q_gen_3670
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3633, q_gen_3653, q_gen_3675, q_gen_3677, q_gen_3678},
Q_f={q_gen_3633},
Delta=
{
<nil>() -> q_gen_3677
<b>() -> q_gen_3678
<cons, cons>(q_gen_3653, q_gen_3633) -> q_gen_3633
<nil, nil>() -> q_gen_3633
<a, a>() -> q_gen_3653
<a, b>() -> q_gen_3653
<b, a>() -> q_gen_3653
<b, b>() -> q_gen_3653
<cons, cons>(q_gen_3653, q_gen_3675) -> q_gen_3675
<nil, cons>(q_gen_3678, q_gen_3677) -> q_gen_3675
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 13
() -> length([nil, z]) -> 13
() -> leq([z, s(nn2)]) -> 13
() -> leq([z, z]) -> 13
() -> reverse([nil, nil]) -> 13
(append([_eo, cons(h1, nil), _fo]) /\ reverse([t1, _eo])) -> reverse([cons(h1, t1), _fo]) -> 15
(append([t1, l2, _zn])) -> append([cons(h1, t1), l2, cons(h1, _zn)]) -> 16
(length([_oo, _po]) /\ length([l1, _no]) /\ reverse([l1, _oo])) -> leq([_no, _po]) -> 14
(length([_qo, _ro]) /\ length([l1, _so]) /\ reverse([l1, _qo])) -> leq([_ro, _so]) -> 16
(length([ll, _jo])) -> length([cons(x, ll), s(_jo)]) -> 16
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 14
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 14
(leq([s(nn1), z])) -> BOT -> 14
}
Sat witness: Found: ((append([t1, l2, _zn])) -> append([cons(h1, t1), l2, cons(h1, _zn)]), {
_zn -> cons(b, cons(b, nil))  ;  h1 -> b  ;  l2 -> nil  ;  t1 -> cons(b, nil)
})

-------------------------------------------
Step 29, which took 0.026182 s (model generation: 0.024828,  model checking: 0.001354):

Model:
|_
{
append -> 
{{{
Q={q_gen_3638, q_gen_3644, q_gen_3645, q_gen_3658, q_gen_3659, q_gen_3660, q_gen_3673, q_gen_3674},
Q_f={q_gen_3638},
Delta=
{
<nil>() -> q_gen_3658
<b>() -> q_gen_3659
<cons, cons>(q_gen_3645, q_gen_3644) -> q_gen_3644
<nil, nil>() -> q_gen_3644
<a, a>() -> q_gen_3645
<b, b>() -> q_gen_3645
<cons, cons>(q_gen_3645, q_gen_3673) -> q_gen_3673
<nil, cons>(q_gen_3659, q_gen_3658) -> q_gen_3673
<cons, cons, cons>(q_gen_3660, q_gen_3638) -> q_gen_3638
<cons, nil, cons>(q_gen_3645, q_gen_3644) -> q_gen_3638
<cons, nil, cons>(q_gen_3645, q_gen_3673) -> q_gen_3638
<nil, cons, cons>(q_gen_3645, q_gen_3644) -> q_gen_3638
<nil, nil, cons>(q_gen_3659, q_gen_3658) -> q_gen_3638
<nil, nil, nil>() -> q_gen_3638
<a, b, a>() -> q_gen_3660
<b, b, b>() -> q_gen_3660
<nil, cons, cons>(q_gen_3645, q_gen_3673) -> q_gen_3674
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_3637, q_gen_3641, q_gen_3642, q_gen_3665, q_gen_3666, q_gen_3667, q_gen_3668, q_gen_3669},
Q_f={q_gen_3637},
Delta=
{
<nil>() -> q_gen_3641
<cons>(q_gen_3666, q_gen_3641) -> q_gen_3665
<cons>(q_gen_3666, q_gen_3665) -> q_gen_3665
<b>() -> q_gen_3666
<s>(q_gen_3668) -> q_gen_3668
<z>() -> q_gen_3668
<cons, s>(q_gen_3642, q_gen_3641) -> q_gen_3637
<cons, s>(q_gen_3667, q_gen_3665) -> q_gen_3637
<nil, z>() -> q_gen_3637
<a, z>() -> q_gen_3642
<b, z>() -> q_gen_3642
<a, s>(q_gen_3668) -> q_gen_3667
<b, s>(q_gen_3668) -> q_gen_3667
<cons, s>(q_gen_3642, q_gen_3665) -> q_gen_3669
<cons, s>(q_gen_3667, q_gen_3641) -> q_gen_3669
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3634, q_gen_3636, q_gen_3670},
Q_f={q_gen_3634},
Delta=
{
<s>(q_gen_3636) -> q_gen_3636
<z>() -> q_gen_3636
<s, s>(q_gen_3634) -> q_gen_3634
<z, s>(q_gen_3636) -> q_gen_3634
<z, z>() -> q_gen_3634
<s, s>(q_gen_3670) -> q_gen_3670
<s, z>(q_gen_3636) -> q_gen_3670
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3633, q_gen_3653, q_gen_3675, q_gen_3677, q_gen_3678},
Q_f={q_gen_3633},
Delta=
{
<nil>() -> q_gen_3677
<b>() -> q_gen_3678
<cons, cons>(q_gen_3653, q_gen_3633) -> q_gen_3633
<nil, nil>() -> q_gen_3633
<a, a>() -> q_gen_3653
<a, b>() -> q_gen_3653
<b, a>() -> q_gen_3653
<b, b>() -> q_gen_3653
<cons, cons>(q_gen_3653, q_gen_3675) -> q_gen_3675
<nil, cons>(q_gen_3678, q_gen_3677) -> q_gen_3675
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 14
() -> length([nil, z]) -> 14
() -> leq([z, s(nn2)]) -> 14
() -> leq([z, z]) -> 14
() -> reverse([nil, nil]) -> 14
(append([_eo, cons(h1, nil), _fo]) /\ reverse([t1, _eo])) -> reverse([cons(h1, t1), _fo]) -> 15
(append([t1, l2, _zn])) -> append([cons(h1, t1), l2, cons(h1, _zn)]) -> 16
(length([_oo, _po]) /\ length([l1, _no]) /\ reverse([l1, _oo])) -> leq([_no, _po]) -> 17
(length([_qo, _ro]) /\ length([l1, _so]) /\ reverse([l1, _qo])) -> leq([_ro, _so]) -> 16
(length([ll, _jo])) -> length([cons(x, ll), s(_jo)]) -> 16
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 15
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 15
(leq([s(nn1), z])) -> BOT -> 15
}
Sat witness: Found: ((length([_oo, _po]) /\ length([l1, _no]) /\ reverse([l1, _oo])) -> leq([_no, _po]), {
_no -> s(s(s(z)))  ;  _oo -> cons(b, cons(b, nil))  ;  _po -> s(s(z))  ;  l1 -> cons(b, cons(b, nil))
})

-------------------------------------------
Step 30, which took 0.027652 s (model generation: 0.026819,  model checking: 0.000833):

Model:
|_
{
append -> 
{{{
Q={q_gen_3638, q_gen_3644, q_gen_3645, q_gen_3657, q_gen_3658, q_gen_3659, q_gen_3660, q_gen_3673},
Q_f={q_gen_3638},
Delta=
{
<nil>() -> q_gen_3658
<b>() -> q_gen_3659
<cons, cons>(q_gen_3645, q_gen_3644) -> q_gen_3644
<nil, nil>() -> q_gen_3644
<a, a>() -> q_gen_3645
<b, b>() -> q_gen_3645
<cons, cons>(q_gen_3645, q_gen_3673) -> q_gen_3673
<nil, cons>(q_gen_3659, q_gen_3658) -> q_gen_3673
<cons, cons, cons>(q_gen_3660, q_gen_3657) -> q_gen_3638
<cons, nil, cons>(q_gen_3645, q_gen_3644) -> q_gen_3638
<nil, cons, cons>(q_gen_3645, q_gen_3644) -> q_gen_3638
<nil, nil, nil>() -> q_gen_3638
<cons, nil, cons>(q_gen_3645, q_gen_3673) -> q_gen_3657
<nil, cons, cons>(q_gen_3645, q_gen_3673) -> q_gen_3657
<nil, nil, cons>(q_gen_3659, q_gen_3658) -> q_gen_3657
<a, b, a>() -> q_gen_3660
<b, b, b>() -> q_gen_3660
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_3637, q_gen_3641, q_gen_3642, q_gen_3665, q_gen_3666, q_gen_3667, q_gen_3668, q_gen_3669},
Q_f={q_gen_3637},
Delta=
{
<nil>() -> q_gen_3641
<cons>(q_gen_3666, q_gen_3641) -> q_gen_3665
<cons>(q_gen_3666, q_gen_3665) -> q_gen_3665
<b>() -> q_gen_3666
<s>(q_gen_3668) -> q_gen_3668
<z>() -> q_gen_3668
<cons, s>(q_gen_3642, q_gen_3641) -> q_gen_3637
<cons, s>(q_gen_3667, q_gen_3665) -> q_gen_3637
<nil, z>() -> q_gen_3637
<a, z>() -> q_gen_3642
<b, z>() -> q_gen_3642
<a, s>(q_gen_3668) -> q_gen_3667
<b, s>(q_gen_3668) -> q_gen_3667
<cons, s>(q_gen_3642, q_gen_3665) -> q_gen_3669
<cons, s>(q_gen_3667, q_gen_3641) -> q_gen_3669
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3634, q_gen_3636, q_gen_3670, q_gen_3671},
Q_f={q_gen_3634},
Delta=
{
<s>(q_gen_3636) -> q_gen_3636
<z>() -> q_gen_3636
<s, s>(q_gen_3634) -> q_gen_3634
<s, s>(q_gen_3670) -> q_gen_3634
<z, s>(q_gen_3636) -> q_gen_3634
<z, z>() -> q_gen_3634
<s, s>(q_gen_3671) -> q_gen_3670
<s, z>(q_gen_3636) -> q_gen_3671
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3633, q_gen_3653, q_gen_3675, q_gen_3677, q_gen_3678},
Q_f={q_gen_3633},
Delta=
{
<nil>() -> q_gen_3677
<b>() -> q_gen_3678
<cons, cons>(q_gen_3653, q_gen_3633) -> q_gen_3633
<nil, nil>() -> q_gen_3633
<a, a>() -> q_gen_3653
<a, b>() -> q_gen_3653
<b, a>() -> q_gen_3653
<b, b>() -> q_gen_3653
<cons, cons>(q_gen_3653, q_gen_3675) -> q_gen_3675
<nil, cons>(q_gen_3678, q_gen_3677) -> q_gen_3675
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 15
() -> length([nil, z]) -> 15
() -> leq([z, s(nn2)]) -> 15
() -> leq([z, z]) -> 15
() -> reverse([nil, nil]) -> 15
(append([_eo, cons(h1, nil), _fo]) /\ reverse([t1, _eo])) -> reverse([cons(h1, t1), _fo]) -> 15
(append([t1, l2, _zn])) -> append([cons(h1, t1), l2, cons(h1, _zn)]) -> 16
(length([_oo, _po]) /\ length([l1, _no]) /\ reverse([l1, _oo])) -> leq([_no, _po]) -> 17
(length([_qo, _ro]) /\ length([l1, _so]) /\ reverse([l1, _qo])) -> leq([_ro, _so]) -> 16
(length([ll, _jo])) -> length([cons(x, ll), s(_jo)]) -> 16
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 15
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 18
(leq([s(nn1), z])) -> BOT -> 16
}
Sat witness: Found: ((leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]), {
nn1 -> s(s(z))  ;  nn2 -> s(z)
})

-------------------------------------------
Step 31, which took 0.028473 s (model generation: 0.026554,  model checking: 0.001919):

Model:
|_
{
append -> 
{{{
Q={q_gen_3638, q_gen_3644, q_gen_3645, q_gen_3658, q_gen_3659, q_gen_3660, q_gen_3673, q_gen_3674},
Q_f={q_gen_3638},
Delta=
{
<nil>() -> q_gen_3658
<b>() -> q_gen_3659
<cons, cons>(q_gen_3645, q_gen_3644) -> q_gen_3644
<cons, cons>(q_gen_3645, q_gen_3673) -> q_gen_3644
<nil, nil>() -> q_gen_3644
<a, a>() -> q_gen_3645
<b, b>() -> q_gen_3645
<nil, cons>(q_gen_3659, q_gen_3658) -> q_gen_3673
<cons, cons, cons>(q_gen_3660, q_gen_3638) -> q_gen_3638
<cons, nil, cons>(q_gen_3645, q_gen_3644) -> q_gen_3638
<cons, nil, cons>(q_gen_3645, q_gen_3673) -> q_gen_3638
<nil, cons, cons>(q_gen_3645, q_gen_3644) -> q_gen_3638
<nil, nil, cons>(q_gen_3659, q_gen_3658) -> q_gen_3638
<nil, nil, nil>() -> q_gen_3638
<a, b, a>() -> q_gen_3660
<b, b, b>() -> q_gen_3660
<nil, cons, cons>(q_gen_3645, q_gen_3673) -> q_gen_3674
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_3637, q_gen_3641, q_gen_3642, q_gen_3665, q_gen_3666, q_gen_3667, q_gen_3668, q_gen_3669, q_gen_3694},
Q_f={q_gen_3637},
Delta=
{
<cons>(q_gen_3666, q_gen_3665) -> q_gen_3641
<nil>() -> q_gen_3641
<cons>(q_gen_3666, q_gen_3641) -> q_gen_3665
<b>() -> q_gen_3666
<z>() -> q_gen_3668
<s>(q_gen_3668) -> q_gen_3694
<cons, s>(q_gen_3642, q_gen_3641) -> q_gen_3637
<cons, s>(q_gen_3667, q_gen_3665) -> q_gen_3637
<nil, z>() -> q_gen_3637
<a, z>() -> q_gen_3642
<b, s>(q_gen_3694) -> q_gen_3642
<b, z>() -> q_gen_3642
<a, s>(q_gen_3668) -> q_gen_3667
<b, s>(q_gen_3668) -> q_gen_3667
<cons, s>(q_gen_3642, q_gen_3665) -> q_gen_3669
<cons, s>(q_gen_3667, q_gen_3641) -> q_gen_3669
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3634, q_gen_3636, q_gen_3670},
Q_f={q_gen_3634},
Delta=
{
<s>(q_gen_3636) -> q_gen_3636
<z>() -> q_gen_3636
<s, s>(q_gen_3634) -> q_gen_3634
<z, s>(q_gen_3636) -> q_gen_3634
<z, z>() -> q_gen_3634
<s, s>(q_gen_3670) -> q_gen_3670
<s, z>(q_gen_3636) -> q_gen_3670
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3633, q_gen_3653, q_gen_3675, q_gen_3677, q_gen_3678},
Q_f={q_gen_3633},
Delta=
{
<nil>() -> q_gen_3677
<b>() -> q_gen_3678
<cons, cons>(q_gen_3653, q_gen_3633) -> q_gen_3633
<nil, nil>() -> q_gen_3633
<a, a>() -> q_gen_3653
<a, b>() -> q_gen_3653
<b, a>() -> q_gen_3653
<b, b>() -> q_gen_3653
<cons, cons>(q_gen_3653, q_gen_3675) -> q_gen_3675
<nil, cons>(q_gen_3678, q_gen_3677) -> q_gen_3675
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 15
() -> length([nil, z]) -> 15
() -> leq([z, s(nn2)]) -> 15
() -> leq([z, z]) -> 15
() -> reverse([nil, nil]) -> 15
(append([_eo, cons(h1, nil), _fo]) /\ reverse([t1, _eo])) -> reverse([cons(h1, t1), _fo]) -> 18
(append([t1, l2, _zn])) -> append([cons(h1, t1), l2, cons(h1, _zn)]) -> 16
(length([_oo, _po]) /\ length([l1, _no]) /\ reverse([l1, _oo])) -> leq([_no, _po]) -> 17
(length([_qo, _ro]) /\ length([l1, _so]) /\ reverse([l1, _qo])) -> leq([_ro, _so]) -> 16
(length([ll, _jo])) -> length([cons(x, ll), s(_jo)]) -> 16
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 16
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 18
(leq([s(nn1), z])) -> BOT -> 16
}
Sat witness: Found: ((append([_eo, cons(h1, nil), _fo]) /\ reverse([t1, _eo])) -> reverse([cons(h1, t1), _fo]), {
_eo -> cons(b, nil)  ;  _fo -> cons(b, nil)  ;  h1 -> b  ;  t1 -> cons(a, nil)
})

-------------------------------------------
Step 32, which took 0.031641 s (model generation: 0.029461,  model checking: 0.002180):

Model:
|_
{
append -> 
{{{
Q={q_gen_3638, q_gen_3644, q_gen_3645, q_gen_3657, q_gen_3658, q_gen_3659, q_gen_3660, q_gen_3673},
Q_f={q_gen_3638},
Delta=
{
<nil>() -> q_gen_3658
<b>() -> q_gen_3659
<cons, cons>(q_gen_3645, q_gen_3644) -> q_gen_3644
<cons, cons>(q_gen_3645, q_gen_3673) -> q_gen_3644
<nil, nil>() -> q_gen_3644
<a, a>() -> q_gen_3645
<b, b>() -> q_gen_3645
<nil, cons>(q_gen_3659, q_gen_3658) -> q_gen_3673
<cons, cons, cons>(q_gen_3660, q_gen_3657) -> q_gen_3638
<cons, nil, cons>(q_gen_3645, q_gen_3644) -> q_gen_3638
<nil, cons, cons>(q_gen_3645, q_gen_3644) -> q_gen_3638
<nil, nil, nil>() -> q_gen_3638
<cons, cons, cons>(q_gen_3660, q_gen_3638) -> q_gen_3657
<cons, nil, cons>(q_gen_3645, q_gen_3673) -> q_gen_3657
<nil, cons, cons>(q_gen_3645, q_gen_3673) -> q_gen_3657
<nil, nil, cons>(q_gen_3659, q_gen_3658) -> q_gen_3657
<a, b, a>() -> q_gen_3660
<b, b, b>() -> q_gen_3660
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_3637, q_gen_3641, q_gen_3642, q_gen_3665, q_gen_3666, q_gen_3667, q_gen_3668, q_gen_3669, q_gen_3694},
Q_f={q_gen_3637},
Delta=
{
<cons>(q_gen_3666, q_gen_3665) -> q_gen_3641
<nil>() -> q_gen_3641
<cons>(q_gen_3666, q_gen_3641) -> q_gen_3665
<b>() -> q_gen_3666
<z>() -> q_gen_3668
<s>(q_gen_3668) -> q_gen_3694
<cons, s>(q_gen_3642, q_gen_3641) -> q_gen_3637
<cons, s>(q_gen_3667, q_gen_3665) -> q_gen_3637
<nil, z>() -> q_gen_3637
<a, z>() -> q_gen_3642
<b, s>(q_gen_3694) -> q_gen_3642
<b, z>() -> q_gen_3642
<a, s>(q_gen_3668) -> q_gen_3667
<b, s>(q_gen_3668) -> q_gen_3667
<cons, s>(q_gen_3642, q_gen_3665) -> q_gen_3669
<cons, s>(q_gen_3667, q_gen_3641) -> q_gen_3669
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3634, q_gen_3636, q_gen_3670},
Q_f={q_gen_3634},
Delta=
{
<s>(q_gen_3636) -> q_gen_3636
<z>() -> q_gen_3636
<s, s>(q_gen_3634) -> q_gen_3634
<z, s>(q_gen_3636) -> q_gen_3634
<z, z>() -> q_gen_3634
<s, s>(q_gen_3670) -> q_gen_3670
<s, z>(q_gen_3636) -> q_gen_3670
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3633, q_gen_3653, q_gen_3675, q_gen_3677, q_gen_3678},
Q_f={q_gen_3633},
Delta=
{
<nil>() -> q_gen_3677
<a>() -> q_gen_3678
<b>() -> q_gen_3678
<cons, cons>(q_gen_3653, q_gen_3633) -> q_gen_3633
<nil, nil>() -> q_gen_3633
<a, a>() -> q_gen_3653
<a, b>() -> q_gen_3653
<b, a>() -> q_gen_3653
<b, b>() -> q_gen_3653
<cons, cons>(q_gen_3653, q_gen_3675) -> q_gen_3675
<cons, nil>(q_gen_3678, q_gen_3677) -> q_gen_3675
<nil, cons>(q_gen_3678, q_gen_3677) -> q_gen_3675
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 16
() -> length([nil, z]) -> 16
() -> leq([z, s(nn2)]) -> 16
() -> leq([z, z]) -> 16
() -> reverse([nil, nil]) -> 16
(append([_eo, cons(h1, nil), _fo]) /\ reverse([t1, _eo])) -> reverse([cons(h1, t1), _fo]) -> 18
(append([t1, l2, _zn])) -> append([cons(h1, t1), l2, cons(h1, _zn)]) -> 16
(length([_oo, _po]) /\ length([l1, _no]) /\ reverse([l1, _oo])) -> leq([_no, _po]) -> 17
(length([_qo, _ro]) /\ length([l1, _so]) /\ reverse([l1, _qo])) -> leq([_ro, _so]) -> 16
(length([ll, _jo])) -> length([cons(x, ll), s(_jo)]) -> 19
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 17
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 18
(leq([s(nn1), z])) -> BOT -> 17
}
Sat witness: Found: ((length([ll, _jo])) -> length([cons(x, ll), s(_jo)]), {
_jo -> s(s(s(z)))  ;  ll -> cons(b, nil)  ;  x -> b
})

-------------------------------------------
Step 33, which took 0.034329 s (model generation: 0.033836,  model checking: 0.000493):

Model:
|_
{
append -> 
{{{
Q={q_gen_3638, q_gen_3644, q_gen_3645, q_gen_3657, q_gen_3658, q_gen_3659, q_gen_3660, q_gen_3673},
Q_f={q_gen_3638},
Delta=
{
<nil>() -> q_gen_3658
<b>() -> q_gen_3659
<cons, cons>(q_gen_3645, q_gen_3644) -> q_gen_3644
<cons, cons>(q_gen_3645, q_gen_3673) -> q_gen_3644
<nil, nil>() -> q_gen_3644
<a, a>() -> q_gen_3645
<b, b>() -> q_gen_3645
<nil, cons>(q_gen_3659, q_gen_3658) -> q_gen_3673
<cons, cons, cons>(q_gen_3660, q_gen_3638) -> q_gen_3638
<cons, cons, cons>(q_gen_3660, q_gen_3657) -> q_gen_3638
<cons, nil, cons>(q_gen_3645, q_gen_3644) -> q_gen_3638
<nil, cons, cons>(q_gen_3645, q_gen_3644) -> q_gen_3638
<nil, nil, nil>() -> q_gen_3638
<cons, nil, cons>(q_gen_3645, q_gen_3673) -> q_gen_3657
<nil, cons, cons>(q_gen_3645, q_gen_3673) -> q_gen_3657
<nil, nil, cons>(q_gen_3659, q_gen_3658) -> q_gen_3657
<a, b, a>() -> q_gen_3660
<b, b, b>() -> q_gen_3660
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_3637, q_gen_3641, q_gen_3642, q_gen_3665, q_gen_3666, q_gen_3667, q_gen_3668, q_gen_3669, q_gen_3694},
Q_f={q_gen_3637},
Delta=
{
<cons>(q_gen_3666, q_gen_3665) -> q_gen_3641
<nil>() -> q_gen_3641
<cons>(q_gen_3666, q_gen_3641) -> q_gen_3665
<b>() -> q_gen_3666
<s>(q_gen_3694) -> q_gen_3668
<z>() -> q_gen_3668
<s>(q_gen_3668) -> q_gen_3694
<cons, s>(q_gen_3642, q_gen_3641) -> q_gen_3637
<cons, s>(q_gen_3667, q_gen_3665) -> q_gen_3637
<nil, z>() -> q_gen_3637
<a, z>() -> q_gen_3642
<b, s>(q_gen_3694) -> q_gen_3642
<b, z>() -> q_gen_3642
<a, s>(q_gen_3668) -> q_gen_3667
<b, s>(q_gen_3668) -> q_gen_3667
<cons, s>(q_gen_3642, q_gen_3665) -> q_gen_3669
<cons, s>(q_gen_3667, q_gen_3641) -> q_gen_3669
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3634, q_gen_3636, q_gen_3670},
Q_f={q_gen_3634},
Delta=
{
<s>(q_gen_3636) -> q_gen_3636
<z>() -> q_gen_3636
<s, s>(q_gen_3634) -> q_gen_3634
<z, s>(q_gen_3636) -> q_gen_3634
<z, z>() -> q_gen_3634
<s, s>(q_gen_3670) -> q_gen_3670
<s, z>(q_gen_3636) -> q_gen_3670
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3633, q_gen_3653, q_gen_3675, q_gen_3677, q_gen_3678},
Q_f={q_gen_3633},
Delta=
{
<nil>() -> q_gen_3677
<a>() -> q_gen_3678
<b>() -> q_gen_3678
<cons, cons>(q_gen_3653, q_gen_3633) -> q_gen_3633
<cons, nil>(q_gen_3678, q_gen_3677) -> q_gen_3633
<nil, nil>() -> q_gen_3633
<a, a>() -> q_gen_3653
<a, b>() -> q_gen_3653
<b, a>() -> q_gen_3653
<b, b>() -> q_gen_3653
<cons, cons>(q_gen_3653, q_gen_3675) -> q_gen_3675
<nil, cons>(q_gen_3678, q_gen_3677) -> q_gen_3675
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 16
() -> length([nil, z]) -> 16
() -> leq([z, s(nn2)]) -> 16
() -> leq([z, z]) -> 16
() -> reverse([nil, nil]) -> 16
(append([_eo, cons(h1, nil), _fo]) /\ reverse([t1, _eo])) -> reverse([cons(h1, t1), _fo]) -> 18
(append([t1, l2, _zn])) -> append([cons(h1, t1), l2, cons(h1, _zn)]) -> 16
(length([_oo, _po]) /\ length([l1, _no]) /\ reverse([l1, _oo])) -> leq([_no, _po]) -> 17
(length([_qo, _ro]) /\ length([l1, _so]) /\ reverse([l1, _qo])) -> leq([_ro, _so]) -> 19
(length([ll, _jo])) -> length([cons(x, ll), s(_jo)]) -> 19
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 17
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 18
(leq([s(nn1), z])) -> BOT -> 17
}
Sat witness: Found: ((length([_qo, _ro]) /\ length([l1, _so]) /\ reverse([l1, _qo])) -> leq([_ro, _so]), {
_qo -> cons(b, nil)  ;  _ro -> s(s(s(z)))  ;  _so -> s(z)  ;  l1 -> cons(b, nil)
})

-------------------------------------------
Step 34, which took 0.034853 s (model generation: 0.034167,  model checking: 0.000686):

Model:
|_
{
append -> 
{{{
Q={q_gen_3638, q_gen_3644, q_gen_3645, q_gen_3657, q_gen_3658, q_gen_3659, q_gen_3660, q_gen_3673},
Q_f={q_gen_3638},
Delta=
{
<nil>() -> q_gen_3658
<b>() -> q_gen_3659
<cons, cons>(q_gen_3645, q_gen_3644) -> q_gen_3644
<nil, nil>() -> q_gen_3644
<a, a>() -> q_gen_3645
<b, b>() -> q_gen_3645
<cons, cons>(q_gen_3645, q_gen_3673) -> q_gen_3673
<nil, cons>(q_gen_3659, q_gen_3658) -> q_gen_3673
<cons, cons, cons>(q_gen_3660, q_gen_3657) -> q_gen_3638
<cons, nil, cons>(q_gen_3645, q_gen_3644) -> q_gen_3638
<cons, nil, cons>(q_gen_3645, q_gen_3673) -> q_gen_3638
<nil, cons, cons>(q_gen_3645, q_gen_3644) -> q_gen_3638
<nil, nil, nil>() -> q_gen_3638
<cons, cons, cons>(q_gen_3660, q_gen_3638) -> q_gen_3657
<nil, cons, cons>(q_gen_3645, q_gen_3673) -> q_gen_3657
<nil, nil, cons>(q_gen_3659, q_gen_3658) -> q_gen_3657
<a, b, a>() -> q_gen_3660
<b, b, b>() -> q_gen_3660
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_3637, q_gen_3641, q_gen_3642, q_gen_3665, q_gen_3666, q_gen_3667, q_gen_3668, q_gen_3669},
Q_f={q_gen_3637},
Delta=
{
<nil>() -> q_gen_3641
<cons>(q_gen_3666, q_gen_3641) -> q_gen_3665
<cons>(q_gen_3666, q_gen_3665) -> q_gen_3665
<b>() -> q_gen_3666
<s>(q_gen_3668) -> q_gen_3668
<z>() -> q_gen_3668
<cons, s>(q_gen_3642, q_gen_3641) -> q_gen_3637
<cons, s>(q_gen_3642, q_gen_3665) -> q_gen_3637
<cons, s>(q_gen_3667, q_gen_3665) -> q_gen_3637
<nil, z>() -> q_gen_3637
<a, s>(q_gen_3668) -> q_gen_3642
<a, z>() -> q_gen_3642
<b, z>() -> q_gen_3642
<b, s>(q_gen_3668) -> q_gen_3667
<cons, s>(q_gen_3667, q_gen_3641) -> q_gen_3669
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3634, q_gen_3636, q_gen_3670},
Q_f={q_gen_3634},
Delta=
{
<s>(q_gen_3636) -> q_gen_3636
<z>() -> q_gen_3636
<s, s>(q_gen_3634) -> q_gen_3634
<z, s>(q_gen_3636) -> q_gen_3634
<z, z>() -> q_gen_3634
<s, s>(q_gen_3670) -> q_gen_3670
<s, z>(q_gen_3636) -> q_gen_3670
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3633, q_gen_3652, q_gen_3653, q_gen_3675, q_gen_3677, q_gen_3678},
Q_f={q_gen_3633, q_gen_3652},
Delta=
{
<nil>() -> q_gen_3677
<a>() -> q_gen_3678
<b>() -> q_gen_3678
<nil, nil>() -> q_gen_3633
<cons, cons>(q_gen_3653, q_gen_3633) -> q_gen_3652
<a, a>() -> q_gen_3653
<a, b>() -> q_gen_3653
<b, a>() -> q_gen_3653
<b, b>() -> q_gen_3653
<cons, cons>(q_gen_3653, q_gen_3652) -> q_gen_3675
<cons, cons>(q_gen_3653, q_gen_3675) -> q_gen_3675
<cons, nil>(q_gen_3678, q_gen_3677) -> q_gen_3675
<nil, cons>(q_gen_3678, q_gen_3677) -> q_gen_3675
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 16
() -> length([nil, z]) -> 16
() -> leq([z, s(nn2)]) -> 16
() -> leq([z, z]) -> 16
() -> reverse([nil, nil]) -> 16
(append([_eo, cons(h1, nil), _fo]) /\ reverse([t1, _eo])) -> reverse([cons(h1, t1), _fo]) -> 18
(append([t1, l2, _zn])) -> append([cons(h1, t1), l2, cons(h1, _zn)]) -> 19
(length([_oo, _po]) /\ length([l1, _no]) /\ reverse([l1, _oo])) -> leq([_no, _po]) -> 17
(length([_qo, _ro]) /\ length([l1, _so]) /\ reverse([l1, _qo])) -> leq([_ro, _so]) -> 19
(length([ll, _jo])) -> length([cons(x, ll), s(_jo)]) -> 19
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 17
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 18
(leq([s(nn1), z])) -> BOT -> 17
}
Sat witness: Found: ((append([t1, l2, _zn])) -> append([cons(h1, t1), l2, cons(h1, _zn)]), {
_zn -> cons(b, cons(b, nil))  ;  h1 -> b  ;  l2 -> cons(b, nil)  ;  t1 -> cons(b, nil)
})

-------------------------------------------
Step 35, which took 0.035158 s (model generation: 0.033881,  model checking: 0.001277):

Model:
|_
{
append -> 
{{{
Q={q_gen_3638, q_gen_3644, q_gen_3645, q_gen_3658, q_gen_3659, q_gen_3660, q_gen_3673, q_gen_3674},
Q_f={q_gen_3638},
Delta=
{
<nil>() -> q_gen_3658
<b>() -> q_gen_3659
<cons, cons>(q_gen_3645, q_gen_3644) -> q_gen_3644
<cons, cons>(q_gen_3645, q_gen_3673) -> q_gen_3644
<nil, nil>() -> q_gen_3644
<a, a>() -> q_gen_3645
<b, b>() -> q_gen_3645
<nil, cons>(q_gen_3659, q_gen_3658) -> q_gen_3673
<cons, cons, cons>(q_gen_3660, q_gen_3638) -> q_gen_3638
<cons, nil, cons>(q_gen_3645, q_gen_3644) -> q_gen_3638
<cons, nil, cons>(q_gen_3645, q_gen_3673) -> q_gen_3638
<nil, cons, cons>(q_gen_3645, q_gen_3644) -> q_gen_3638
<nil, nil, cons>(q_gen_3659, q_gen_3658) -> q_gen_3638
<nil, nil, nil>() -> q_gen_3638
<a, b, a>() -> q_gen_3660
<b, b, b>() -> q_gen_3660
<nil, cons, cons>(q_gen_3645, q_gen_3673) -> q_gen_3674
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_3637, q_gen_3641, q_gen_3642, q_gen_3665, q_gen_3666, q_gen_3667, q_gen_3668, q_gen_3669},
Q_f={q_gen_3637},
Delta=
{
<nil>() -> q_gen_3641
<cons>(q_gen_3666, q_gen_3641) -> q_gen_3665
<cons>(q_gen_3666, q_gen_3665) -> q_gen_3665
<b>() -> q_gen_3666
<s>(q_gen_3668) -> q_gen_3668
<z>() -> q_gen_3668
<cons, s>(q_gen_3642, q_gen_3641) -> q_gen_3637
<cons, s>(q_gen_3642, q_gen_3665) -> q_gen_3637
<cons, s>(q_gen_3667, q_gen_3665) -> q_gen_3637
<nil, z>() -> q_gen_3637
<a, s>(q_gen_3668) -> q_gen_3642
<a, z>() -> q_gen_3642
<b, z>() -> q_gen_3642
<b, s>(q_gen_3668) -> q_gen_3667
<cons, s>(q_gen_3667, q_gen_3641) -> q_gen_3669
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3634, q_gen_3636, q_gen_3670},
Q_f={q_gen_3634},
Delta=
{
<s>(q_gen_3636) -> q_gen_3636
<z>() -> q_gen_3636
<s, s>(q_gen_3634) -> q_gen_3634
<z, s>(q_gen_3636) -> q_gen_3634
<z, z>() -> q_gen_3634
<s, s>(q_gen_3670) -> q_gen_3670
<s, z>(q_gen_3636) -> q_gen_3670
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3633, q_gen_3652, q_gen_3653, q_gen_3675, q_gen_3677, q_gen_3678},
Q_f={q_gen_3633, q_gen_3652},
Delta=
{
<nil>() -> q_gen_3677
<a>() -> q_gen_3678
<b>() -> q_gen_3678
<cons, nil>(q_gen_3678, q_gen_3677) -> q_gen_3633
<nil, nil>() -> q_gen_3633
<cons, cons>(q_gen_3653, q_gen_3633) -> q_gen_3652
<a, a>() -> q_gen_3653
<a, b>() -> q_gen_3653
<b, a>() -> q_gen_3653
<b, b>() -> q_gen_3653
<cons, cons>(q_gen_3653, q_gen_3652) -> q_gen_3675
<cons, cons>(q_gen_3653, q_gen_3675) -> q_gen_3675
<nil, cons>(q_gen_3678, q_gen_3677) -> q_gen_3675
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 17
() -> length([nil, z]) -> 17
() -> leq([z, s(nn2)]) -> 17
() -> leq([z, z]) -> 17
() -> reverse([nil, nil]) -> 17
(append([_eo, cons(h1, nil), _fo]) /\ reverse([t1, _eo])) -> reverse([cons(h1, t1), _fo]) -> 18
(append([t1, l2, _zn])) -> append([cons(h1, t1), l2, cons(h1, _zn)]) -> 19
(length([_oo, _po]) /\ length([l1, _no]) /\ reverse([l1, _oo])) -> leq([_no, _po]) -> 20
(length([_qo, _ro]) /\ length([l1, _so]) /\ reverse([l1, _qo])) -> leq([_ro, _so]) -> 19
(length([ll, _jo])) -> length([cons(x, ll), s(_jo)]) -> 19
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 18
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 18
(leq([s(nn1), z])) -> BOT -> 18
}
Sat witness: Found: ((length([_oo, _po]) /\ length([l1, _no]) /\ reverse([l1, _oo])) -> leq([_no, _po]), {
_no -> s(s(z))  ;  _oo -> cons(a, nil)  ;  _po -> s(z)  ;  l1 -> cons(a, nil)
})

-------------------------------------------
Step 36, which took 0.037671 s (model generation: 0.036445,  model checking: 0.001226):

Model:
|_
{
append -> 
{{{
Q={q_gen_3638, q_gen_3644, q_gen_3645, q_gen_3658, q_gen_3659, q_gen_3660, q_gen_3673, q_gen_3674},
Q_f={q_gen_3638},
Delta=
{
<nil>() -> q_gen_3658
<b>() -> q_gen_3659
<cons, cons>(q_gen_3645, q_gen_3644) -> q_gen_3644
<cons, cons>(q_gen_3645, q_gen_3673) -> q_gen_3644
<nil, nil>() -> q_gen_3644
<a, a>() -> q_gen_3645
<b, b>() -> q_gen_3645
<nil, cons>(q_gen_3659, q_gen_3658) -> q_gen_3673
<cons, cons, cons>(q_gen_3660, q_gen_3638) -> q_gen_3638
<cons, nil, cons>(q_gen_3645, q_gen_3644) -> q_gen_3638
<cons, nil, cons>(q_gen_3645, q_gen_3673) -> q_gen_3638
<nil, cons, cons>(q_gen_3645, q_gen_3644) -> q_gen_3638
<nil, nil, cons>(q_gen_3659, q_gen_3658) -> q_gen_3638
<nil, nil, nil>() -> q_gen_3638
<a, b, a>() -> q_gen_3660
<b, b, b>() -> q_gen_3660
<nil, cons, cons>(q_gen_3645, q_gen_3673) -> q_gen_3674
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_3637, q_gen_3641, q_gen_3642, q_gen_3665, q_gen_3666, q_gen_3667, q_gen_3668, q_gen_3669},
Q_f={q_gen_3637},
Delta=
{
<nil>() -> q_gen_3641
<cons>(q_gen_3666, q_gen_3641) -> q_gen_3665
<cons>(q_gen_3666, q_gen_3665) -> q_gen_3665
<b>() -> q_gen_3666
<s>(q_gen_3668) -> q_gen_3668
<z>() -> q_gen_3668
<cons, s>(q_gen_3642, q_gen_3641) -> q_gen_3637
<cons, s>(q_gen_3667, q_gen_3665) -> q_gen_3637
<nil, z>() -> q_gen_3637
<a, z>() -> q_gen_3642
<b, z>() -> q_gen_3642
<a, s>(q_gen_3668) -> q_gen_3667
<b, s>(q_gen_3668) -> q_gen_3667
<cons, s>(q_gen_3642, q_gen_3665) -> q_gen_3669
<cons, s>(q_gen_3667, q_gen_3641) -> q_gen_3669
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3634, q_gen_3636, q_gen_3670},
Q_f={q_gen_3634},
Delta=
{
<s>(q_gen_3636) -> q_gen_3636
<z>() -> q_gen_3636
<s, s>(q_gen_3634) -> q_gen_3634
<z, s>(q_gen_3636) -> q_gen_3634
<z, z>() -> q_gen_3634
<s, s>(q_gen_3670) -> q_gen_3670
<s, z>(q_gen_3636) -> q_gen_3670
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3633, q_gen_3652, q_gen_3653, q_gen_3675, q_gen_3677, q_gen_3678},
Q_f={q_gen_3633, q_gen_3652},
Delta=
{
<nil>() -> q_gen_3677
<a>() -> q_gen_3678
<b>() -> q_gen_3678
<cons, nil>(q_gen_3678, q_gen_3677) -> q_gen_3633
<nil, nil>() -> q_gen_3633
<cons, cons>(q_gen_3653, q_gen_3633) -> q_gen_3652
<a, a>() -> q_gen_3653
<a, b>() -> q_gen_3653
<b, a>() -> q_gen_3653
<b, b>() -> q_gen_3653
<cons, cons>(q_gen_3653, q_gen_3652) -> q_gen_3675
<cons, cons>(q_gen_3653, q_gen_3675) -> q_gen_3675
<nil, cons>(q_gen_3678, q_gen_3677) -> q_gen_3675
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 18
() -> length([nil, z]) -> 18
() -> leq([z, s(nn2)]) -> 18
() -> leq([z, z]) -> 18
() -> reverse([nil, nil]) -> 18
(append([_eo, cons(h1, nil), _fo]) /\ reverse([t1, _eo])) -> reverse([cons(h1, t1), _fo]) -> 21
(append([t1, l2, _zn])) -> append([cons(h1, t1), l2, cons(h1, _zn)]) -> 19
(length([_oo, _po]) /\ length([l1, _no]) /\ reverse([l1, _oo])) -> leq([_no, _po]) -> 20
(length([_qo, _ro]) /\ length([l1, _so]) /\ reverse([l1, _qo])) -> leq([_ro, _so]) -> 19
(length([ll, _jo])) -> length([cons(x, ll), s(_jo)]) -> 19
(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: ((append([_eo, cons(h1, nil), _fo]) /\ reverse([t1, _eo])) -> reverse([cons(h1, t1), _fo]), {
_eo -> cons(a, nil)  ;  _fo -> cons(a, cons(b, nil))  ;  h1 -> b  ;  t1 -> cons(a, nil)
})

-------------------------------------------
Step 37, which took 0.047630 s (model generation: 0.045605,  model checking: 0.002025):

Model:
|_
{
append -> 
{{{
Q={q_gen_3638, q_gen_3644, q_gen_3645, q_gen_3657, q_gen_3658, q_gen_3659, q_gen_3660, q_gen_3673},
Q_f={q_gen_3638},
Delta=
{
<nil>() -> q_gen_3658
<b>() -> q_gen_3659
<cons, cons>(q_gen_3645, q_gen_3644) -> q_gen_3644
<cons, cons>(q_gen_3645, q_gen_3673) -> q_gen_3644
<nil, nil>() -> q_gen_3644
<a, a>() -> q_gen_3645
<b, b>() -> q_gen_3645
<nil, cons>(q_gen_3659, q_gen_3658) -> q_gen_3673
<cons, cons, cons>(q_gen_3660, q_gen_3657) -> q_gen_3638
<cons, nil, cons>(q_gen_3645, q_gen_3644) -> q_gen_3638
<nil, cons, cons>(q_gen_3645, q_gen_3644) -> q_gen_3638
<nil, nil, nil>() -> q_gen_3638
<cons, cons, cons>(q_gen_3660, q_gen_3638) -> q_gen_3657
<cons, nil, cons>(q_gen_3645, q_gen_3673) -> q_gen_3657
<nil, cons, cons>(q_gen_3645, q_gen_3673) -> q_gen_3657
<nil, nil, cons>(q_gen_3659, q_gen_3658) -> q_gen_3657
<a, b, a>() -> q_gen_3660
<b, b, b>() -> q_gen_3660
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_3637, q_gen_3641, q_gen_3642, q_gen_3665, q_gen_3666, q_gen_3667, q_gen_3668, q_gen_3669},
Q_f={q_gen_3637},
Delta=
{
<nil>() -> q_gen_3641
<cons>(q_gen_3666, q_gen_3641) -> q_gen_3665
<cons>(q_gen_3666, q_gen_3665) -> q_gen_3665
<b>() -> q_gen_3666
<s>(q_gen_3668) -> q_gen_3668
<z>() -> q_gen_3668
<cons, s>(q_gen_3642, q_gen_3641) -> q_gen_3637
<cons, s>(q_gen_3667, q_gen_3665) -> q_gen_3637
<nil, z>() -> q_gen_3637
<a, z>() -> q_gen_3642
<b, z>() -> q_gen_3642
<a, s>(q_gen_3668) -> q_gen_3667
<b, s>(q_gen_3668) -> q_gen_3667
<cons, s>(q_gen_3642, q_gen_3665) -> q_gen_3669
<cons, s>(q_gen_3667, q_gen_3641) -> q_gen_3669
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3634, q_gen_3636, q_gen_3670},
Q_f={q_gen_3634},
Delta=
{
<s>(q_gen_3636) -> q_gen_3636
<z>() -> q_gen_3636
<s, s>(q_gen_3634) -> q_gen_3634
<z, s>(q_gen_3636) -> q_gen_3634
<z, z>() -> q_gen_3634
<s, s>(q_gen_3670) -> q_gen_3670
<s, z>(q_gen_3636) -> q_gen_3670
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3633, q_gen_3652, q_gen_3653, q_gen_3675, q_gen_3677, q_gen_3678, q_gen_3690},
Q_f={q_gen_3633, q_gen_3652},
Delta=
{
<nil>() -> q_gen_3677
<a>() -> q_gen_3678
<b>() -> q_gen_3678
<cons, cons>(q_gen_3690, q_gen_3652) -> q_gen_3633
<cons, nil>(q_gen_3678, q_gen_3677) -> q_gen_3633
<nil, nil>() -> q_gen_3633
<cons, cons>(q_gen_3653, q_gen_3633) -> q_gen_3652
<a, a>() -> q_gen_3653
<a, b>() -> q_gen_3653
<b, b>() -> q_gen_3653
<cons, cons>(q_gen_3653, q_gen_3652) -> q_gen_3675
<cons, cons>(q_gen_3653, q_gen_3675) -> q_gen_3675
<cons, cons>(q_gen_3690, q_gen_3675) -> q_gen_3675
<nil, cons>(q_gen_3678, q_gen_3677) -> q_gen_3675
<b, a>() -> q_gen_3690
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 19
() -> length([nil, z]) -> 19
() -> leq([z, s(nn2)]) -> 19
() -> leq([z, z]) -> 19
() -> reverse([nil, nil]) -> 19
(append([_eo, cons(h1, nil), _fo]) /\ reverse([t1, _eo])) -> reverse([cons(h1, t1), _fo]) -> 21
(append([t1, l2, _zn])) -> append([cons(h1, t1), l2, cons(h1, _zn)]) -> 19
(length([_oo, _po]) /\ length([l1, _no]) /\ reverse([l1, _oo])) -> leq([_no, _po]) -> 20
(length([_qo, _ro]) /\ length([l1, _so]) /\ reverse([l1, _qo])) -> leq([_ro, _so]) -> 19
(length([ll, _jo])) -> length([cons(x, ll), s(_jo)]) -> 22
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 20
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 20
(leq([s(nn1), z])) -> BOT -> 20
}
Sat witness: Found: ((length([ll, _jo])) -> length([cons(x, ll), s(_jo)]), {
_jo -> s(z)  ;  ll -> cons(a, nil)  ;  x -> b
})

-------------------------------------------
Step 38, which took 0.040633 s (model generation: 0.040162,  model checking: 0.000471):

Model:
|_
{
append -> 
{{{
Q={q_gen_3638, q_gen_3644, q_gen_3645, q_gen_3657, q_gen_3658, q_gen_3659, q_gen_3660, q_gen_3673},
Q_f={q_gen_3638},
Delta=
{
<nil>() -> q_gen_3658
<b>() -> q_gen_3659
<cons, cons>(q_gen_3645, q_gen_3644) -> q_gen_3644
<cons, cons>(q_gen_3645, q_gen_3673) -> q_gen_3644
<nil, nil>() -> q_gen_3644
<a, a>() -> q_gen_3645
<b, b>() -> q_gen_3645
<nil, cons>(q_gen_3659, q_gen_3658) -> q_gen_3673
<cons, cons, cons>(q_gen_3660, q_gen_3638) -> q_gen_3638
<cons, cons, cons>(q_gen_3660, q_gen_3657) -> q_gen_3638
<cons, nil, cons>(q_gen_3645, q_gen_3644) -> q_gen_3638
<cons, nil, cons>(q_gen_3645, q_gen_3673) -> q_gen_3638
<nil, cons, cons>(q_gen_3645, q_gen_3644) -> q_gen_3638
<nil, nil, nil>() -> q_gen_3638
<nil, cons, cons>(q_gen_3645, q_gen_3673) -> q_gen_3657
<nil, nil, cons>(q_gen_3659, q_gen_3658) -> q_gen_3657
<a, b, a>() -> q_gen_3660
<b, b, b>() -> q_gen_3660
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_3637, q_gen_3641, q_gen_3642, q_gen_3665, q_gen_3666, q_gen_3667, q_gen_3668, q_gen_3669, q_gen_3694},
Q_f={q_gen_3637},
Delta=
{
<cons>(q_gen_3666, q_gen_3665) -> q_gen_3641
<nil>() -> q_gen_3641
<cons>(q_gen_3666, q_gen_3641) -> q_gen_3665
<a>() -> q_gen_3666
<b>() -> q_gen_3666
<s>(q_gen_3694) -> q_gen_3668
<z>() -> q_gen_3668
<s>(q_gen_3668) -> q_gen_3694
<cons, s>(q_gen_3642, q_gen_3641) -> q_gen_3637
<cons, s>(q_gen_3667, q_gen_3665) -> q_gen_3637
<nil, z>() -> q_gen_3637
<a, z>() -> q_gen_3642
<b, s>(q_gen_3694) -> q_gen_3642
<b, z>() -> q_gen_3642
<a, s>(q_gen_3668) -> q_gen_3667
<b, s>(q_gen_3668) -> q_gen_3667
<cons, s>(q_gen_3642, q_gen_3665) -> q_gen_3669
<cons, s>(q_gen_3667, q_gen_3641) -> q_gen_3669
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3634, q_gen_3636, q_gen_3647, q_gen_3670},
Q_f={q_gen_3634},
Delta=
{
<z>() -> q_gen_3636
<s>(q_gen_3636) -> q_gen_3647
<s, s>(q_gen_3634) -> q_gen_3634
<s, z>(q_gen_3647) -> q_gen_3634
<z, s>(q_gen_3636) -> q_gen_3634
<z, s>(q_gen_3647) -> q_gen_3634
<z, z>() -> q_gen_3634
<s, s>(q_gen_3670) -> q_gen_3670
<s, z>(q_gen_3636) -> q_gen_3670
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3633, q_gen_3653, q_gen_3675, q_gen_3677, q_gen_3678},
Q_f={q_gen_3633},
Delta=
{
<nil>() -> q_gen_3677
<a>() -> q_gen_3678
<b>() -> q_gen_3678
<cons, cons>(q_gen_3653, q_gen_3633) -> q_gen_3633
<cons, nil>(q_gen_3678, q_gen_3677) -> q_gen_3633
<nil, nil>() -> q_gen_3633
<a, a>() -> q_gen_3653
<a, b>() -> q_gen_3653
<b, a>() -> q_gen_3653
<b, b>() -> q_gen_3653
<cons, cons>(q_gen_3653, q_gen_3675) -> q_gen_3675
<nil, cons>(q_gen_3678, q_gen_3677) -> q_gen_3675
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 19
() -> length([nil, z]) -> 19
() -> leq([z, s(nn2)]) -> 19
() -> leq([z, z]) -> 19
() -> reverse([nil, nil]) -> 19
(append([_eo, cons(h1, nil), _fo]) /\ reverse([t1, _eo])) -> reverse([cons(h1, t1), _fo]) -> 21
(append([t1, l2, _zn])) -> append([cons(h1, t1), l2, cons(h1, _zn)]) -> 19
(length([_oo, _po]) /\ length([l1, _no]) /\ reverse([l1, _oo])) -> leq([_no, _po]) -> 20
(length([_qo, _ro]) /\ length([l1, _so]) /\ reverse([l1, _qo])) -> leq([_ro, _so]) -> 22
(length([ll, _jo])) -> length([cons(x, ll), s(_jo)]) -> 22
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 20
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 20
(leq([s(nn1), z])) -> BOT -> 20
}
Sat witness: Found: ((length([_qo, _ro]) /\ length([l1, _so]) /\ reverse([l1, _qo])) -> leq([_ro, _so]), {
_qo -> cons(b, cons(b, nil))  ;  _ro -> s(s(z))  ;  _so -> s(z)  ;  l1 -> cons(b, cons(b, cons(b, nil)))
})

-------------------------------------------
Step 39, which took 0.052340 s (model generation: 0.051604,  model checking: 0.000736):

Model:
|_
{
append -> 
{{{
Q={q_gen_3638, q_gen_3644, q_gen_3645, q_gen_3657, q_gen_3658, q_gen_3659, q_gen_3660, q_gen_3673},
Q_f={q_gen_3638},
Delta=
{
<nil>() -> q_gen_3658
<b>() -> q_gen_3659
<cons, cons>(q_gen_3645, q_gen_3644) -> q_gen_3644
<cons, cons>(q_gen_3645, q_gen_3673) -> q_gen_3644
<nil, nil>() -> q_gen_3644
<a, a>() -> q_gen_3645
<b, b>() -> q_gen_3645
<nil, cons>(q_gen_3659, q_gen_3658) -> q_gen_3673
<cons, cons, cons>(q_gen_3660, q_gen_3657) -> q_gen_3638
<cons, nil, cons>(q_gen_3645, q_gen_3644) -> q_gen_3638
<nil, cons, cons>(q_gen_3645, q_gen_3644) -> q_gen_3638
<nil, nil, nil>() -> q_gen_3638
<cons, cons, cons>(q_gen_3660, q_gen_3638) -> q_gen_3657
<cons, nil, cons>(q_gen_3645, q_gen_3673) -> q_gen_3657
<nil, cons, cons>(q_gen_3645, q_gen_3673) -> q_gen_3657
<nil, nil, cons>(q_gen_3659, q_gen_3658) -> q_gen_3657
<a, b, a>() -> q_gen_3660
<b, b, b>() -> q_gen_3660
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_3637, q_gen_3641, q_gen_3642, q_gen_3665, q_gen_3666, q_gen_3667, q_gen_3668, q_gen_3669, q_gen_3694},
Q_f={q_gen_3637},
Delta=
{
<cons>(q_gen_3666, q_gen_3665) -> q_gen_3641
<nil>() -> q_gen_3641
<cons>(q_gen_3666, q_gen_3641) -> q_gen_3665
<a>() -> q_gen_3666
<b>() -> q_gen_3666
<s>(q_gen_3694) -> q_gen_3668
<z>() -> q_gen_3668
<s>(q_gen_3668) -> q_gen_3694
<cons, s>(q_gen_3642, q_gen_3641) -> q_gen_3637
<cons, s>(q_gen_3667, q_gen_3665) -> q_gen_3637
<nil, z>() -> q_gen_3637
<a, z>() -> q_gen_3642
<b, s>(q_gen_3694) -> q_gen_3642
<b, z>() -> q_gen_3642
<a, s>(q_gen_3668) -> q_gen_3667
<b, s>(q_gen_3668) -> q_gen_3667
<cons, s>(q_gen_3642, q_gen_3665) -> q_gen_3669
<cons, s>(q_gen_3667, q_gen_3641) -> q_gen_3669
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3634, q_gen_3636, q_gen_3647, q_gen_3670},
Q_f={q_gen_3634},
Delta=
{
<z>() -> q_gen_3636
<s>(q_gen_3636) -> q_gen_3647
<s, s>(q_gen_3634) -> q_gen_3634
<s, z>(q_gen_3647) -> q_gen_3634
<z, s>(q_gen_3636) -> q_gen_3634
<z, s>(q_gen_3647) -> q_gen_3634
<z, z>() -> q_gen_3634
<s, s>(q_gen_3670) -> q_gen_3670
<s, z>(q_gen_3636) -> q_gen_3670
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3633, q_gen_3653, q_gen_3675, q_gen_3677, q_gen_3678},
Q_f={q_gen_3633},
Delta=
{
<nil>() -> q_gen_3677
<a>() -> q_gen_3678
<b>() -> q_gen_3678
<cons, cons>(q_gen_3653, q_gen_3633) -> q_gen_3633
<nil, nil>() -> q_gen_3633
<a, a>() -> q_gen_3653
<a, b>() -> q_gen_3653
<b, a>() -> q_gen_3653
<b, b>() -> q_gen_3653
<cons, cons>(q_gen_3653, q_gen_3675) -> q_gen_3675
<cons, nil>(q_gen_3678, q_gen_3677) -> q_gen_3675
<nil, cons>(q_gen_3678, q_gen_3677) -> q_gen_3675
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 19
() -> length([nil, z]) -> 19
() -> leq([z, s(nn2)]) -> 19
() -> leq([z, z]) -> 19
() -> reverse([nil, nil]) -> 19
(append([_eo, cons(h1, nil), _fo]) /\ reverse([t1, _eo])) -> reverse([cons(h1, t1), _fo]) -> 21
(append([t1, l2, _zn])) -> append([cons(h1, t1), l2, cons(h1, _zn)]) -> 22
(length([_oo, _po]) /\ length([l1, _no]) /\ reverse([l1, _oo])) -> leq([_no, _po]) -> 20
(length([_qo, _ro]) /\ length([l1, _so]) /\ reverse([l1, _qo])) -> leq([_ro, _so]) -> 22
(length([ll, _jo])) -> length([cons(x, ll), s(_jo)]) -> 22
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 20
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 20
(leq([s(nn1), z])) -> BOT -> 20
}
Sat witness: Found: ((append([t1, l2, _zn])) -> append([cons(h1, t1), l2, cons(h1, _zn)]), {
_zn -> cons(b, cons(b, cons(b, nil)))  ;  h1 -> a  ;  l2 -> cons(b, nil)  ;  t1 -> cons(b, cons(b, nil))
})

-------------------------------------------
Step 40, which took 0.047509 s (model generation: 0.047297,  model checking: 0.000212):

Model:
|_
{
append -> 
{{{
Q={q_gen_3638, q_gen_3644, q_gen_3645, q_gen_3657, q_gen_3658, q_gen_3659, q_gen_3660, q_gen_3673},
Q_f={q_gen_3638},
Delta=
{
<nil>() -> q_gen_3658
<b>() -> q_gen_3659
<cons, cons>(q_gen_3645, q_gen_3644) -> q_gen_3644
<nil, nil>() -> q_gen_3644
<a, a>() -> q_gen_3645
<b, b>() -> q_gen_3645
<cons, cons>(q_gen_3645, q_gen_3673) -> q_gen_3673
<nil, cons>(q_gen_3659, q_gen_3658) -> q_gen_3673
<cons, cons, cons>(q_gen_3660, q_gen_3657) -> q_gen_3638
<cons, nil, cons>(q_gen_3645, q_gen_3644) -> q_gen_3638
<nil, cons, cons>(q_gen_3645, q_gen_3644) -> q_gen_3638
<nil, nil, nil>() -> q_gen_3638
<cons, cons, cons>(q_gen_3660, q_gen_3638) -> q_gen_3657
<cons, nil, cons>(q_gen_3645, q_gen_3673) -> q_gen_3657
<nil, cons, cons>(q_gen_3645, q_gen_3673) -> q_gen_3657
<nil, nil, cons>(q_gen_3659, q_gen_3658) -> q_gen_3657
<a, b, a>() -> q_gen_3660
<b, b, b>() -> q_gen_3660
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_3637, q_gen_3641, q_gen_3642, q_gen_3665, q_gen_3666, q_gen_3667, q_gen_3668, q_gen_3669, q_gen_3694},
Q_f={q_gen_3637},
Delta=
{
<cons>(q_gen_3666, q_gen_3665) -> q_gen_3641
<nil>() -> q_gen_3641
<cons>(q_gen_3666, q_gen_3641) -> q_gen_3665
<a>() -> q_gen_3666
<b>() -> q_gen_3666
<s>(q_gen_3694) -> q_gen_3668
<z>() -> q_gen_3668
<s>(q_gen_3668) -> q_gen_3694
<cons, s>(q_gen_3642, q_gen_3641) -> q_gen_3637
<cons, s>(q_gen_3667, q_gen_3665) -> q_gen_3637
<nil, z>() -> q_gen_3637
<a, z>() -> q_gen_3642
<b, s>(q_gen_3694) -> q_gen_3642
<b, z>() -> q_gen_3642
<a, s>(q_gen_3668) -> q_gen_3667
<b, s>(q_gen_3668) -> q_gen_3667
<cons, s>(q_gen_3642, q_gen_3665) -> q_gen_3669
<cons, s>(q_gen_3667, q_gen_3641) -> q_gen_3669
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3634, q_gen_3636, q_gen_3647, q_gen_3670},
Q_f={q_gen_3634},
Delta=
{
<z>() -> q_gen_3636
<s>(q_gen_3636) -> q_gen_3647
<s, s>(q_gen_3634) -> q_gen_3634
<s, z>(q_gen_3647) -> q_gen_3634
<z, s>(q_gen_3636) -> q_gen_3634
<z, s>(q_gen_3647) -> q_gen_3634
<z, z>() -> q_gen_3634
<s, s>(q_gen_3670) -> q_gen_3670
<s, z>(q_gen_3636) -> q_gen_3670
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3633, q_gen_3653, q_gen_3675, q_gen_3677, q_gen_3678},
Q_f={q_gen_3633},
Delta=
{
<nil>() -> q_gen_3677
<a>() -> q_gen_3678
<b>() -> q_gen_3678
<cons, cons>(q_gen_3653, q_gen_3633) -> q_gen_3633
<nil, nil>() -> q_gen_3633
<a, a>() -> q_gen_3653
<a, b>() -> q_gen_3653
<b, a>() -> q_gen_3653
<b, b>() -> q_gen_3653
<cons, cons>(q_gen_3653, q_gen_3675) -> q_gen_3675
<cons, nil>(q_gen_3678, q_gen_3677) -> q_gen_3675
<nil, cons>(q_gen_3678, q_gen_3677) -> q_gen_3675
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 19
() -> length([nil, z]) -> 19
() -> leq([z, s(nn2)]) -> 22
() -> leq([z, z]) -> 20
() -> reverse([nil, nil]) -> 20
(append([_eo, cons(h1, nil), _fo]) /\ reverse([t1, _eo])) -> reverse([cons(h1, t1), _fo]) -> 21
(append([t1, l2, _zn])) -> append([cons(h1, t1), l2, cons(h1, _zn)]) -> 22
(length([_oo, _po]) /\ length([l1, _no]) /\ reverse([l1, _oo])) -> leq([_no, _po]) -> 20
(length([_qo, _ro]) /\ length([l1, _so]) /\ reverse([l1, _qo])) -> leq([_ro, _so]) -> 22
(length([ll, _jo])) -> length([cons(x, ll), s(_jo)]) -> 22
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 20
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 20
(leq([s(nn1), z])) -> BOT -> 20
}
Sat witness: Found: (() -> leq([z, s(nn2)]), {
nn2 -> s(s(z))
})

-------------------------------------------
Step 41, which took 0.049141 s (model generation: 0.048568,  model checking: 0.000573):

Model:
|_
{
append -> 
{{{
Q={q_gen_3638, q_gen_3644, q_gen_3645, q_gen_3657, q_gen_3658, q_gen_3659, q_gen_3660, q_gen_3673},
Q_f={q_gen_3638},
Delta=
{
<nil>() -> q_gen_3658
<b>() -> q_gen_3659
<cons, cons>(q_gen_3645, q_gen_3644) -> q_gen_3644
<nil, nil>() -> q_gen_3644
<a, a>() -> q_gen_3645
<b, b>() -> q_gen_3645
<cons, cons>(q_gen_3645, q_gen_3673) -> q_gen_3673
<nil, cons>(q_gen_3659, q_gen_3658) -> q_gen_3673
<cons, cons, cons>(q_gen_3660, q_gen_3657) -> q_gen_3638
<cons, nil, cons>(q_gen_3645, q_gen_3644) -> q_gen_3638
<nil, cons, cons>(q_gen_3645, q_gen_3644) -> q_gen_3638
<nil, nil, nil>() -> q_gen_3638
<cons, cons, cons>(q_gen_3660, q_gen_3638) -> q_gen_3657
<cons, nil, cons>(q_gen_3645, q_gen_3673) -> q_gen_3657
<nil, cons, cons>(q_gen_3645, q_gen_3673) -> q_gen_3657
<nil, nil, cons>(q_gen_3659, q_gen_3658) -> q_gen_3657
<a, b, a>() -> q_gen_3660
<b, b, b>() -> q_gen_3660
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_3637, q_gen_3641, q_gen_3642, q_gen_3665, q_gen_3666, q_gen_3667, q_gen_3668, q_gen_3669, q_gen_3694},
Q_f={q_gen_3637},
Delta=
{
<cons>(q_gen_3666, q_gen_3665) -> q_gen_3641
<nil>() -> q_gen_3641
<cons>(q_gen_3666, q_gen_3641) -> q_gen_3665
<a>() -> q_gen_3666
<b>() -> q_gen_3666
<s>(q_gen_3694) -> q_gen_3668
<z>() -> q_gen_3668
<s>(q_gen_3668) -> q_gen_3694
<cons, s>(q_gen_3642, q_gen_3641) -> q_gen_3637
<cons, s>(q_gen_3667, q_gen_3665) -> q_gen_3637
<nil, z>() -> q_gen_3637
<a, z>() -> q_gen_3642
<b, s>(q_gen_3694) -> q_gen_3642
<b, z>() -> q_gen_3642
<a, s>(q_gen_3668) -> q_gen_3667
<b, s>(q_gen_3668) -> q_gen_3667
<cons, s>(q_gen_3642, q_gen_3665) -> q_gen_3669
<cons, s>(q_gen_3667, q_gen_3641) -> q_gen_3669
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3634, q_gen_3636, q_gen_3647, q_gen_3670},
Q_f={q_gen_3634},
Delta=
{
<z>() -> q_gen_3636
<s>(q_gen_3636) -> q_gen_3647
<s>(q_gen_3647) -> q_gen_3647
<s, s>(q_gen_3634) -> q_gen_3634
<s, z>(q_gen_3647) -> q_gen_3634
<z, s>(q_gen_3636) -> q_gen_3634
<z, s>(q_gen_3647) -> q_gen_3634
<z, z>() -> q_gen_3634
<s, s>(q_gen_3670) -> q_gen_3670
<s, z>(q_gen_3636) -> q_gen_3670
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3633, q_gen_3653, q_gen_3675, q_gen_3677, q_gen_3678},
Q_f={q_gen_3633},
Delta=
{
<nil>() -> q_gen_3677
<a>() -> q_gen_3678
<b>() -> q_gen_3678
<cons, cons>(q_gen_3653, q_gen_3633) -> q_gen_3633
<nil, nil>() -> q_gen_3633
<a, a>() -> q_gen_3653
<a, b>() -> q_gen_3653
<b, a>() -> q_gen_3653
<b, b>() -> q_gen_3653
<cons, cons>(q_gen_3653, q_gen_3675) -> q_gen_3675
<cons, nil>(q_gen_3678, q_gen_3677) -> q_gen_3675
<nil, cons>(q_gen_3678, q_gen_3677) -> q_gen_3675
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 20
() -> length([nil, z]) -> 20
() -> leq([z, s(nn2)]) -> 22
() -> leq([z, z]) -> 20
() -> reverse([nil, nil]) -> 20
(append([_eo, cons(h1, nil), _fo]) /\ reverse([t1, _eo])) -> reverse([cons(h1, t1), _fo]) -> 21
(append([t1, l2, _zn])) -> append([cons(h1, t1), l2, cons(h1, _zn)]) -> 22
(length([_oo, _po]) /\ length([l1, _no]) /\ reverse([l1, _oo])) -> leq([_no, _po]) -> 20
(length([_qo, _ro]) /\ length([l1, _so]) /\ reverse([l1, _qo])) -> leq([_ro, _so]) -> 22
(length([ll, _jo])) -> length([cons(x, ll), s(_jo)]) -> 22
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 20
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 20
(leq([s(nn1), z])) -> BOT -> 23
}
Sat witness: Found: ((leq([s(nn1), z])) -> BOT, {
nn1 -> s(z)
})

-------------------------------------------
Step 42, which took 0.049887 s (model generation: 0.049208,  model checking: 0.000679):

Model:
|_
{
append -> 
{{{
Q={q_gen_3638, q_gen_3644, q_gen_3645, q_gen_3657, q_gen_3658, q_gen_3659, q_gen_3660, q_gen_3673},
Q_f={q_gen_3638},
Delta=
{
<nil>() -> q_gen_3658
<b>() -> q_gen_3659
<cons, cons>(q_gen_3645, q_gen_3644) -> q_gen_3644
<cons, cons>(q_gen_3645, q_gen_3673) -> q_gen_3644
<nil, nil>() -> q_gen_3644
<a, a>() -> q_gen_3645
<b, b>() -> q_gen_3645
<nil, cons>(q_gen_3659, q_gen_3658) -> q_gen_3673
<cons, cons, cons>(q_gen_3660, q_gen_3638) -> q_gen_3638
<cons, cons, cons>(q_gen_3660, q_gen_3657) -> q_gen_3638
<cons, nil, cons>(q_gen_3645, q_gen_3644) -> q_gen_3638
<nil, cons, cons>(q_gen_3645, q_gen_3644) -> q_gen_3638
<nil, nil, nil>() -> q_gen_3638
<cons, nil, cons>(q_gen_3645, q_gen_3673) -> q_gen_3657
<nil, cons, cons>(q_gen_3645, q_gen_3673) -> q_gen_3657
<nil, nil, cons>(q_gen_3659, q_gen_3658) -> q_gen_3657
<a, b, a>() -> q_gen_3660
<b, b, b>() -> q_gen_3660
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_3637, q_gen_3641, q_gen_3642, q_gen_3665, q_gen_3666, q_gen_3667, q_gen_3668, q_gen_3669},
Q_f={q_gen_3637},
Delta=
{
<nil>() -> q_gen_3641
<cons>(q_gen_3666, q_gen_3641) -> q_gen_3665
<cons>(q_gen_3666, q_gen_3665) -> q_gen_3665
<a>() -> q_gen_3666
<b>() -> q_gen_3666
<s>(q_gen_3668) -> q_gen_3668
<z>() -> q_gen_3668
<cons, s>(q_gen_3642, q_gen_3641) -> q_gen_3637
<cons, s>(q_gen_3667, q_gen_3665) -> q_gen_3637
<nil, z>() -> q_gen_3637
<a, z>() -> q_gen_3642
<b, z>() -> q_gen_3642
<a, s>(q_gen_3668) -> q_gen_3667
<b, s>(q_gen_3668) -> q_gen_3667
<cons, s>(q_gen_3642, q_gen_3665) -> q_gen_3669
<cons, s>(q_gen_3667, q_gen_3641) -> q_gen_3669
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3634, q_gen_3636, q_gen_3670},
Q_f={q_gen_3634},
Delta=
{
<s>(q_gen_3636) -> q_gen_3636
<z>() -> q_gen_3636
<s, s>(q_gen_3634) -> q_gen_3634
<z, s>(q_gen_3636) -> q_gen_3634
<z, z>() -> q_gen_3634
<s, s>(q_gen_3670) -> q_gen_3670
<s, z>(q_gen_3636) -> q_gen_3670
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3633, q_gen_3652, q_gen_3653, q_gen_3675, q_gen_3677, q_gen_3678, q_gen_3690},
Q_f={q_gen_3633, q_gen_3652},
Delta=
{
<nil>() -> q_gen_3677
<a>() -> q_gen_3678
<b>() -> q_gen_3678
<cons, cons>(q_gen_3690, q_gen_3652) -> q_gen_3633
<cons, cons>(q_gen_3690, q_gen_3675) -> q_gen_3633
<cons, nil>(q_gen_3678, q_gen_3677) -> q_gen_3633
<nil, nil>() -> q_gen_3633
<cons, cons>(q_gen_3653, q_gen_3633) -> q_gen_3652
<a, a>() -> q_gen_3653
<a, b>() -> q_gen_3653
<b, b>() -> q_gen_3653
<cons, cons>(q_gen_3653, q_gen_3652) -> q_gen_3675
<cons, cons>(q_gen_3653, q_gen_3675) -> q_gen_3675
<nil, cons>(q_gen_3678, q_gen_3677) -> q_gen_3675
<b, a>() -> q_gen_3690
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 20
() -> length([nil, z]) -> 20
() -> leq([z, s(nn2)]) -> 22
() -> leq([z, z]) -> 20
() -> reverse([nil, nil]) -> 20
(append([_eo, cons(h1, nil), _fo]) /\ reverse([t1, _eo])) -> reverse([cons(h1, t1), _fo]) -> 21
(append([t1, l2, _zn])) -> append([cons(h1, t1), l2, cons(h1, _zn)]) -> 22
(length([_oo, _po]) /\ length([l1, _no]) /\ reverse([l1, _oo])) -> leq([_no, _po]) -> 23
(length([_qo, _ro]) /\ length([l1, _so]) /\ reverse([l1, _qo])) -> leq([_ro, _so]) -> 22
(length([ll, _jo])) -> length([cons(x, ll), s(_jo)]) -> 22
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 21
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 21
(leq([s(nn1), z])) -> BOT -> 23
}
Sat witness: Found: ((length([_oo, _po]) /\ length([l1, _no]) /\ reverse([l1, _oo])) -> leq([_no, _po]), {
_no -> s(s(z))  ;  _oo -> cons(b, nil)  ;  _po -> s(z)  ;  l1 -> cons(b, cons(b, nil))
})

-------------------------------------------
Step 43, which took 0.057880 s (model generation: 0.056745,  model checking: 0.001135):

Model:
|_
{
append -> 
{{{
Q={q_gen_3638, q_gen_3644, q_gen_3645, q_gen_3657, q_gen_3658, q_gen_3659, q_gen_3660, q_gen_3673},
Q_f={q_gen_3638},
Delta=
{
<nil>() -> q_gen_3658
<b>() -> q_gen_3659
<cons, cons>(q_gen_3645, q_gen_3644) -> q_gen_3644
<nil, nil>() -> q_gen_3644
<a, a>() -> q_gen_3645
<b, b>() -> q_gen_3645
<cons, cons>(q_gen_3645, q_gen_3673) -> q_gen_3673
<nil, cons>(q_gen_3659, q_gen_3658) -> q_gen_3673
<cons, cons, cons>(q_gen_3660, q_gen_3657) -> q_gen_3638
<cons, nil, cons>(q_gen_3645, q_gen_3644) -> q_gen_3638
<nil, cons, cons>(q_gen_3645, q_gen_3644) -> q_gen_3638
<nil, nil, nil>() -> q_gen_3638
<cons, cons, cons>(q_gen_3660, q_gen_3638) -> q_gen_3657
<cons, nil, cons>(q_gen_3645, q_gen_3673) -> q_gen_3657
<nil, cons, cons>(q_gen_3645, q_gen_3673) -> q_gen_3657
<nil, nil, cons>(q_gen_3659, q_gen_3658) -> q_gen_3657
<a, b, a>() -> q_gen_3660
<b, b, b>() -> q_gen_3660
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_3637, q_gen_3641, q_gen_3642, q_gen_3665, q_gen_3666, q_gen_3667, q_gen_3668, q_gen_3669},
Q_f={q_gen_3637},
Delta=
{
<nil>() -> q_gen_3641
<cons>(q_gen_3666, q_gen_3641) -> q_gen_3665
<cons>(q_gen_3666, q_gen_3665) -> q_gen_3665
<a>() -> q_gen_3666
<b>() -> q_gen_3666
<s>(q_gen_3668) -> q_gen_3668
<z>() -> q_gen_3668
<cons, s>(q_gen_3642, q_gen_3641) -> q_gen_3637
<cons, s>(q_gen_3667, q_gen_3665) -> q_gen_3637
<nil, z>() -> q_gen_3637
<a, z>() -> q_gen_3642
<b, z>() -> q_gen_3642
<a, s>(q_gen_3668) -> q_gen_3667
<b, s>(q_gen_3668) -> q_gen_3667
<cons, s>(q_gen_3642, q_gen_3665) -> q_gen_3669
<cons, s>(q_gen_3667, q_gen_3641) -> q_gen_3669
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3634, q_gen_3636, q_gen_3670},
Q_f={q_gen_3634},
Delta=
{
<s>(q_gen_3636) -> q_gen_3636
<z>() -> q_gen_3636
<s, s>(q_gen_3634) -> q_gen_3634
<z, s>(q_gen_3636) -> q_gen_3634
<z, z>() -> q_gen_3634
<s, s>(q_gen_3670) -> q_gen_3670
<s, z>(q_gen_3636) -> q_gen_3670
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3633, q_gen_3652, q_gen_3653, q_gen_3675, q_gen_3677, q_gen_3678, q_gen_3690},
Q_f={q_gen_3633, q_gen_3652},
Delta=
{
<nil>() -> q_gen_3677
<a>() -> q_gen_3678
<b>() -> q_gen_3678
<cons, cons>(q_gen_3690, q_gen_3652) -> q_gen_3633
<cons, cons>(q_gen_3690, q_gen_3675) -> q_gen_3633
<nil, nil>() -> q_gen_3633
<cons, cons>(q_gen_3653, q_gen_3633) -> q_gen_3652
<a, a>() -> q_gen_3653
<a, b>() -> q_gen_3653
<b, b>() -> q_gen_3653
<cons, cons>(q_gen_3653, q_gen_3652) -> q_gen_3675
<cons, cons>(q_gen_3653, q_gen_3675) -> q_gen_3675
<cons, nil>(q_gen_3678, q_gen_3677) -> q_gen_3675
<nil, cons>(q_gen_3678, q_gen_3677) -> q_gen_3675
<b, a>() -> q_gen_3690
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 21
() -> length([nil, z]) -> 21
() -> leq([z, s(nn2)]) -> 22
() -> leq([z, z]) -> 21
() -> reverse([nil, nil]) -> 21
(append([_eo, cons(h1, nil), _fo]) /\ reverse([t1, _eo])) -> reverse([cons(h1, t1), _fo]) -> 24
(append([t1, l2, _zn])) -> append([cons(h1, t1), l2, cons(h1, _zn)]) -> 22
(length([_oo, _po]) /\ length([l1, _no]) /\ reverse([l1, _oo])) -> leq([_no, _po]) -> 23
(length([_qo, _ro]) /\ length([l1, _so]) /\ reverse([l1, _qo])) -> leq([_ro, _so]) -> 22
(length([ll, _jo])) -> length([cons(x, ll), s(_jo)]) -> 22
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 22
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 22
(leq([s(nn1), z])) -> BOT -> 23
}
Sat witness: Found: ((append([_eo, cons(h1, nil), _fo]) /\ reverse([t1, _eo])) -> reverse([cons(h1, t1), _fo]), {
_eo -> cons(b, nil)  ;  _fo -> cons(b, cons(b, nil))  ;  h1 -> b  ;  t1 -> cons(a, nil)
})

-------------------------------------------
Step 44, which took 0.052570 s (model generation: 0.050545,  model checking: 0.002025):

Model:
|_
{
append -> 
{{{
Q={q_gen_3638, q_gen_3644, q_gen_3645, q_gen_3658, q_gen_3659, q_gen_3660, q_gen_3673, q_gen_3674},
Q_f={q_gen_3638},
Delta=
{
<nil>() -> q_gen_3658
<b>() -> q_gen_3659
<cons, cons>(q_gen_3645, q_gen_3644) -> q_gen_3644
<cons, cons>(q_gen_3645, q_gen_3673) -> q_gen_3644
<nil, nil>() -> q_gen_3644
<a, a>() -> q_gen_3645
<b, b>() -> q_gen_3645
<nil, cons>(q_gen_3659, q_gen_3658) -> q_gen_3673
<cons, cons, cons>(q_gen_3660, q_gen_3638) -> q_gen_3638
<cons, nil, cons>(q_gen_3645, q_gen_3644) -> q_gen_3638
<cons, nil, cons>(q_gen_3645, q_gen_3673) -> q_gen_3638
<nil, cons, cons>(q_gen_3645, q_gen_3644) -> q_gen_3638
<nil, nil, cons>(q_gen_3659, q_gen_3658) -> q_gen_3638
<nil, nil, nil>() -> q_gen_3638
<a, b, a>() -> q_gen_3660
<b, b, b>() -> q_gen_3660
<nil, cons, cons>(q_gen_3645, q_gen_3673) -> q_gen_3674
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_3637, q_gen_3641, q_gen_3642, q_gen_3665, q_gen_3666, q_gen_3667, q_gen_3668, q_gen_3669},
Q_f={q_gen_3637},
Delta=
{
<nil>() -> q_gen_3641
<cons>(q_gen_3666, q_gen_3641) -> q_gen_3665
<cons>(q_gen_3666, q_gen_3665) -> q_gen_3665
<a>() -> q_gen_3666
<b>() -> q_gen_3666
<s>(q_gen_3668) -> q_gen_3668
<z>() -> q_gen_3668
<cons, s>(q_gen_3642, q_gen_3641) -> q_gen_3637
<cons, s>(q_gen_3667, q_gen_3665) -> q_gen_3637
<nil, z>() -> q_gen_3637
<a, z>() -> q_gen_3642
<b, z>() -> q_gen_3642
<a, s>(q_gen_3668) -> q_gen_3667
<b, s>(q_gen_3668) -> q_gen_3667
<cons, s>(q_gen_3642, q_gen_3665) -> q_gen_3669
<cons, s>(q_gen_3667, q_gen_3641) -> q_gen_3669
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3634, q_gen_3636, q_gen_3670},
Q_f={q_gen_3634},
Delta=
{
<s>(q_gen_3636) -> q_gen_3636
<z>() -> q_gen_3636
<s, s>(q_gen_3634) -> q_gen_3634
<z, s>(q_gen_3636) -> q_gen_3634
<z, z>() -> q_gen_3634
<s, s>(q_gen_3670) -> q_gen_3670
<s, z>(q_gen_3636) -> q_gen_3670
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3633, q_gen_3652, q_gen_3653, q_gen_3675, q_gen_3677, q_gen_3678, q_gen_3689},
Q_f={q_gen_3633, q_gen_3652},
Delta=
{
<nil>() -> q_gen_3677
<a>() -> q_gen_3678
<b>() -> q_gen_3678
<cons, cons>(q_gen_3689, q_gen_3675) -> q_gen_3633
<nil, nil>() -> q_gen_3633
<cons, cons>(q_gen_3653, q_gen_3633) -> q_gen_3652
<cons, nil>(q_gen_3678, q_gen_3677) -> q_gen_3652
<a, a>() -> q_gen_3653
<b, b>() -> q_gen_3653
<cons, cons>(q_gen_3653, q_gen_3652) -> q_gen_3675
<cons, cons>(q_gen_3653, q_gen_3675) -> q_gen_3675
<cons, cons>(q_gen_3689, q_gen_3633) -> q_gen_3675
<nil, cons>(q_gen_3678, q_gen_3677) -> q_gen_3675
<a, b>() -> q_gen_3689
<b, a>() -> q_gen_3689
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 22
() -> length([nil, z]) -> 22
() -> leq([z, s(nn2)]) -> 22
() -> leq([z, z]) -> 22
() -> reverse([nil, nil]) -> 22
(append([_eo, cons(h1, nil), _fo]) /\ reverse([t1, _eo])) -> reverse([cons(h1, t1), _fo]) -> 24
(append([t1, l2, _zn])) -> append([cons(h1, t1), l2, cons(h1, _zn)]) -> 22
(length([_oo, _po]) /\ length([l1, _no]) /\ reverse([l1, _oo])) -> leq([_no, _po]) -> 23
(length([_qo, _ro]) /\ length([l1, _so]) /\ reverse([l1, _qo])) -> leq([_ro, _so]) -> 25
(length([ll, _jo])) -> length([cons(x, ll), s(_jo)]) -> 23
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 23
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 23
(leq([s(nn1), z])) -> BOT -> 23
}
Sat witness: Found: ((length([_qo, _ro]) /\ length([l1, _so]) /\ reverse([l1, _qo])) -> leq([_ro, _so]), {
_qo -> cons(b, cons(a, cons(b, nil)))  ;  _ro -> s(s(s(z)))  ;  _so -> s(s(z))  ;  l1 -> cons(b, cons(b, nil))
})

-------------------------------------------
Step 45, which took 0.064141 s (model generation: 0.061136,  model checking: 0.003005):

Model:
|_
{
append -> 
{{{
Q={q_gen_3638, q_gen_3644, q_gen_3645, q_gen_3657, q_gen_3658, q_gen_3659, q_gen_3660, q_gen_3673},
Q_f={q_gen_3638},
Delta=
{
<nil>() -> q_gen_3658
<b>() -> q_gen_3659
<cons, cons>(q_gen_3645, q_gen_3644) -> q_gen_3644
<cons, cons>(q_gen_3645, q_gen_3673) -> q_gen_3644
<nil, nil>() -> q_gen_3644
<a, a>() -> q_gen_3645
<b, b>() -> q_gen_3645
<nil, cons>(q_gen_3659, q_gen_3658) -> q_gen_3673
<cons, cons, cons>(q_gen_3660, q_gen_3638) -> q_gen_3638
<cons, cons, cons>(q_gen_3660, q_gen_3657) -> q_gen_3638
<cons, nil, cons>(q_gen_3645, q_gen_3644) -> q_gen_3638
<nil, cons, cons>(q_gen_3645, q_gen_3644) -> q_gen_3638
<nil, nil, nil>() -> q_gen_3638
<cons, nil, cons>(q_gen_3645, q_gen_3673) -> q_gen_3657
<nil, cons, cons>(q_gen_3645, q_gen_3673) -> q_gen_3657
<nil, nil, cons>(q_gen_3659, q_gen_3658) -> q_gen_3657
<a, b, a>() -> q_gen_3660
<b, b, b>() -> q_gen_3660
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_3637, q_gen_3641, q_gen_3642, q_gen_3665, q_gen_3666, q_gen_3667, q_gen_3668, q_gen_3669},
Q_f={q_gen_3637},
Delta=
{
<nil>() -> q_gen_3641
<cons>(q_gen_3666, q_gen_3641) -> q_gen_3665
<cons>(q_gen_3666, q_gen_3665) -> q_gen_3665
<a>() -> q_gen_3666
<b>() -> q_gen_3666
<s>(q_gen_3668) -> q_gen_3668
<z>() -> q_gen_3668
<cons, s>(q_gen_3642, q_gen_3641) -> q_gen_3637
<cons, s>(q_gen_3667, q_gen_3665) -> q_gen_3637
<nil, z>() -> q_gen_3637
<a, z>() -> q_gen_3642
<b, z>() -> q_gen_3642
<a, s>(q_gen_3668) -> q_gen_3667
<b, s>(q_gen_3668) -> q_gen_3667
<cons, s>(q_gen_3642, q_gen_3665) -> q_gen_3669
<cons, s>(q_gen_3667, q_gen_3641) -> q_gen_3669
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3634, q_gen_3636, q_gen_3670},
Q_f={q_gen_3634},
Delta=
{
<s>(q_gen_3636) -> q_gen_3636
<z>() -> q_gen_3636
<s, s>(q_gen_3634) -> q_gen_3634
<z, s>(q_gen_3636) -> q_gen_3634
<z, z>() -> q_gen_3634
<s, s>(q_gen_3670) -> q_gen_3670
<s, z>(q_gen_3636) -> q_gen_3670
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3633, q_gen_3652, q_gen_3653, q_gen_3675, q_gen_3677, q_gen_3678, q_gen_3689},
Q_f={q_gen_3633, q_gen_3652},
Delta=
{
<nil>() -> q_gen_3677
<a>() -> q_gen_3678
<b>() -> q_gen_3678
<nil, nil>() -> q_gen_3633
<cons, cons>(q_gen_3653, q_gen_3633) -> q_gen_3652
<cons, cons>(q_gen_3689, q_gen_3675) -> q_gen_3652
<a, a>() -> q_gen_3653
<b, b>() -> q_gen_3653
<cons, cons>(q_gen_3653, q_gen_3652) -> q_gen_3675
<cons, cons>(q_gen_3653, q_gen_3675) -> q_gen_3675
<cons, cons>(q_gen_3689, q_gen_3633) -> q_gen_3675
<cons, cons>(q_gen_3689, q_gen_3652) -> q_gen_3675
<cons, nil>(q_gen_3678, q_gen_3677) -> q_gen_3675
<nil, cons>(q_gen_3678, q_gen_3677) -> q_gen_3675
<a, b>() -> q_gen_3689
<b, a>() -> q_gen_3689
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 22
() -> length([nil, z]) -> 22
() -> leq([z, s(nn2)]) -> 22
() -> leq([z, z]) -> 22
() -> reverse([nil, nil]) -> 22
(append([_eo, cons(h1, nil), _fo]) /\ reverse([t1, _eo])) -> reverse([cons(h1, t1), _fo]) -> 24
(append([t1, l2, _zn])) -> append([cons(h1, t1), l2, cons(h1, _zn)]) -> 25
(length([_oo, _po]) /\ length([l1, _no]) /\ reverse([l1, _oo])) -> leq([_no, _po]) -> 23
(length([_qo, _ro]) /\ length([l1, _so]) /\ reverse([l1, _qo])) -> leq([_ro, _so]) -> 25
(length([ll, _jo])) -> length([cons(x, ll), s(_jo)]) -> 23
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 23
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 23
(leq([s(nn1), z])) -> BOT -> 23
}
Sat witness: Found: ((append([t1, l2, _zn])) -> append([cons(h1, t1), l2, cons(h1, _zn)]), {
_zn -> cons(a, nil)  ;  h1 -> b  ;  l2 -> cons(a, nil)  ;  t1 -> nil
})

-------------------------------------------
Step 46, which took 0.063862 s (model generation: 0.062071,  model checking: 0.001791):

Model:
|_
{
append -> 
{{{
Q={q_gen_3638, q_gen_3644, q_gen_3645, q_gen_3657, q_gen_3658, q_gen_3659, q_gen_3660, q_gen_3673},
Q_f={q_gen_3638},
Delta=
{
<nil>() -> q_gen_3658
<a>() -> q_gen_3659
<b>() -> q_gen_3659
<cons, cons>(q_gen_3645, q_gen_3644) -> q_gen_3644
<cons, cons>(q_gen_3645, q_gen_3673) -> q_gen_3644
<nil, nil>() -> q_gen_3644
<a, a>() -> q_gen_3645
<b, b>() -> q_gen_3645
<nil, cons>(q_gen_3659, q_gen_3658) -> q_gen_3673
<cons, cons, cons>(q_gen_3660, q_gen_3638) -> q_gen_3638
<cons, cons, cons>(q_gen_3660, q_gen_3657) -> q_gen_3638
<cons, nil, cons>(q_gen_3645, q_gen_3644) -> q_gen_3638
<nil, cons, cons>(q_gen_3645, q_gen_3644) -> q_gen_3638
<nil, nil, nil>() -> q_gen_3638
<cons, nil, cons>(q_gen_3645, q_gen_3673) -> q_gen_3657
<nil, cons, cons>(q_gen_3645, q_gen_3673) -> q_gen_3657
<nil, nil, cons>(q_gen_3659, q_gen_3658) -> q_gen_3657
<a, b, a>() -> q_gen_3660
<b, a, b>() -> q_gen_3660
<b, b, b>() -> q_gen_3660
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_3637, q_gen_3641, q_gen_3642, q_gen_3665, q_gen_3666, q_gen_3667, q_gen_3668, q_gen_3669},
Q_f={q_gen_3637},
Delta=
{
<nil>() -> q_gen_3641
<cons>(q_gen_3666, q_gen_3641) -> q_gen_3665
<cons>(q_gen_3666, q_gen_3665) -> q_gen_3665
<a>() -> q_gen_3666
<b>() -> q_gen_3666
<s>(q_gen_3668) -> q_gen_3668
<z>() -> q_gen_3668
<cons, s>(q_gen_3642, q_gen_3641) -> q_gen_3637
<cons, s>(q_gen_3667, q_gen_3665) -> q_gen_3637
<nil, z>() -> q_gen_3637
<a, z>() -> q_gen_3642
<b, z>() -> q_gen_3642
<a, s>(q_gen_3668) -> q_gen_3667
<b, s>(q_gen_3668) -> q_gen_3667
<cons, s>(q_gen_3642, q_gen_3665) -> q_gen_3669
<cons, s>(q_gen_3667, q_gen_3641) -> q_gen_3669
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3634, q_gen_3636, q_gen_3670},
Q_f={q_gen_3634},
Delta=
{
<s>(q_gen_3636) -> q_gen_3636
<z>() -> q_gen_3636
<s, s>(q_gen_3634) -> q_gen_3634
<z, s>(q_gen_3636) -> q_gen_3634
<z, z>() -> q_gen_3634
<s, s>(q_gen_3670) -> q_gen_3670
<s, z>(q_gen_3636) -> q_gen_3670
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3633, q_gen_3652, q_gen_3653, q_gen_3675, q_gen_3677, q_gen_3678, q_gen_3689},
Q_f={q_gen_3633, q_gen_3652},
Delta=
{
<nil>() -> q_gen_3677
<a>() -> q_gen_3678
<b>() -> q_gen_3678
<nil, nil>() -> q_gen_3633
<cons, cons>(q_gen_3653, q_gen_3633) -> q_gen_3652
<cons, cons>(q_gen_3689, q_gen_3675) -> q_gen_3652
<cons, nil>(q_gen_3678, q_gen_3677) -> q_gen_3652
<a, a>() -> q_gen_3653
<b, b>() -> q_gen_3653
<cons, cons>(q_gen_3653, q_gen_3652) -> q_gen_3675
<cons, cons>(q_gen_3653, q_gen_3675) -> q_gen_3675
<cons, cons>(q_gen_3689, q_gen_3633) -> q_gen_3675
<cons, cons>(q_gen_3689, q_gen_3652) -> q_gen_3675
<nil, cons>(q_gen_3678, q_gen_3677) -> q_gen_3675
<a, b>() -> q_gen_3689
<b, a>() -> q_gen_3689
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 23
() -> length([nil, z]) -> 23
() -> leq([z, s(nn2)]) -> 23
() -> leq([z, z]) -> 23
() -> reverse([nil, nil]) -> 23
(append([_eo, cons(h1, nil), _fo]) /\ reverse([t1, _eo])) -> reverse([cons(h1, t1), _fo]) -> 24
(append([t1, l2, _zn])) -> append([cons(h1, t1), l2, cons(h1, _zn)]) -> 25
(length([_oo, _po]) /\ length([l1, _no]) /\ reverse([l1, _oo])) -> leq([_no, _po]) -> 26
(length([_qo, _ro]) /\ length([l1, _so]) /\ reverse([l1, _qo])) -> leq([_ro, _so]) -> 25
(length([ll, _jo])) -> length([cons(x, ll), s(_jo)]) -> 24
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 24
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 24
(leq([s(nn1), z])) -> BOT -> 24
}
Sat witness: Found: ((length([_oo, _po]) /\ length([l1, _no]) /\ reverse([l1, _oo])) -> leq([_no, _po]), {
_no -> s(z)  ;  _oo -> nil  ;  _po -> z  ;  l1 -> cons(b, nil)
})

-------------------------------------------
Step 47, which took 0.063463 s (model generation: 0.061621,  model checking: 0.001842):

Model:
|_
{
append -> 
{{{
Q={q_gen_3638, q_gen_3644, q_gen_3645, q_gen_3658, q_gen_3659, q_gen_3660, q_gen_3673, q_gen_3674},
Q_f={q_gen_3638},
Delta=
{
<nil>() -> q_gen_3658
<a>() -> q_gen_3659
<b>() -> q_gen_3659
<cons, cons>(q_gen_3645, q_gen_3644) -> q_gen_3644
<cons, cons>(q_gen_3645, q_gen_3673) -> q_gen_3644
<nil, nil>() -> q_gen_3644
<a, a>() -> q_gen_3645
<b, b>() -> q_gen_3645
<nil, cons>(q_gen_3659, q_gen_3658) -> q_gen_3673
<cons, cons, cons>(q_gen_3660, q_gen_3638) -> q_gen_3638
<cons, nil, cons>(q_gen_3645, q_gen_3644) -> q_gen_3638
<cons, nil, cons>(q_gen_3645, q_gen_3673) -> q_gen_3638
<nil, cons, cons>(q_gen_3645, q_gen_3644) -> q_gen_3638
<nil, nil, cons>(q_gen_3659, q_gen_3658) -> q_gen_3638
<nil, nil, nil>() -> q_gen_3638
<a, b, a>() -> q_gen_3660
<b, a, b>() -> q_gen_3660
<b, b, b>() -> q_gen_3660
<nil, cons, cons>(q_gen_3645, q_gen_3673) -> q_gen_3674
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_3637, q_gen_3641, q_gen_3642, q_gen_3665, q_gen_3666, q_gen_3667, q_gen_3668, q_gen_3669},
Q_f={q_gen_3637},
Delta=
{
<nil>() -> q_gen_3641
<cons>(q_gen_3666, q_gen_3641) -> q_gen_3665
<cons>(q_gen_3666, q_gen_3665) -> q_gen_3665
<a>() -> q_gen_3666
<b>() -> q_gen_3666
<s>(q_gen_3668) -> q_gen_3668
<z>() -> q_gen_3668
<cons, s>(q_gen_3642, q_gen_3641) -> q_gen_3637
<cons, s>(q_gen_3667, q_gen_3665) -> q_gen_3637
<nil, z>() -> q_gen_3637
<a, z>() -> q_gen_3642
<b, z>() -> q_gen_3642
<a, s>(q_gen_3668) -> q_gen_3667
<b, s>(q_gen_3668) -> q_gen_3667
<cons, s>(q_gen_3642, q_gen_3665) -> q_gen_3669
<cons, s>(q_gen_3667, q_gen_3641) -> q_gen_3669
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3634, q_gen_3636, q_gen_3670},
Q_f={q_gen_3634},
Delta=
{
<s>(q_gen_3636) -> q_gen_3636
<z>() -> q_gen_3636
<s, s>(q_gen_3634) -> q_gen_3634
<z, s>(q_gen_3636) -> q_gen_3634
<z, z>() -> q_gen_3634
<s, s>(q_gen_3670) -> q_gen_3670
<s, z>(q_gen_3636) -> q_gen_3670
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3633, q_gen_3652, q_gen_3653, q_gen_3675, q_gen_3677, q_gen_3678, q_gen_3689},
Q_f={q_gen_3633, q_gen_3652},
Delta=
{
<nil>() -> q_gen_3677
<a>() -> q_gen_3678
<b>() -> q_gen_3678
<nil, nil>() -> q_gen_3633
<cons, cons>(q_gen_3653, q_gen_3633) -> q_gen_3652
<cons, cons>(q_gen_3689, q_gen_3675) -> q_gen_3652
<a, a>() -> q_gen_3653
<b, b>() -> q_gen_3653
<cons, cons>(q_gen_3653, q_gen_3652) -> q_gen_3675
<cons, cons>(q_gen_3653, q_gen_3675) -> q_gen_3675
<cons, cons>(q_gen_3689, q_gen_3633) -> q_gen_3675
<cons, cons>(q_gen_3689, q_gen_3652) -> q_gen_3675
<cons, nil>(q_gen_3678, q_gen_3677) -> q_gen_3675
<nil, cons>(q_gen_3678, q_gen_3677) -> q_gen_3675
<a, b>() -> q_gen_3689
<b, a>() -> q_gen_3689
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 24
() -> length([nil, z]) -> 24
() -> leq([z, s(nn2)]) -> 24
() -> leq([z, z]) -> 24
() -> reverse([nil, nil]) -> 24
(append([_eo, cons(h1, nil), _fo]) /\ reverse([t1, _eo])) -> reverse([cons(h1, t1), _fo]) -> 27
(append([t1, l2, _zn])) -> append([cons(h1, t1), l2, cons(h1, _zn)]) -> 25
(length([_oo, _po]) /\ length([l1, _no]) /\ reverse([l1, _oo])) -> leq([_no, _po]) -> 26
(length([_qo, _ro]) /\ length([l1, _so]) /\ reverse([l1, _qo])) -> leq([_ro, _so]) -> 25
(length([ll, _jo])) -> length([cons(x, ll), s(_jo)]) -> 25
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 25
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 25
(leq([s(nn1), z])) -> BOT -> 25
}
Sat witness: Found: ((append([_eo, cons(h1, nil), _fo]) /\ reverse([t1, _eo])) -> reverse([cons(h1, t1), _fo]), {
_eo -> cons(b, nil)  ;  _fo -> cons(b, cons(b, nil))  ;  h1 -> b  ;  t1 -> cons(b, nil)
})

-------------------------------------------
Step 48, which took 0.068829 s (model generation: 0.067630,  model checking: 0.001199):

Model:
|_
{
append -> 
{{{
Q={q_gen_3638, q_gen_3644, q_gen_3645, q_gen_3657, q_gen_3658, q_gen_3659, q_gen_3660, q_gen_3673},
Q_f={q_gen_3638},
Delta=
{
<nil>() -> q_gen_3658
<a>() -> q_gen_3659
<b>() -> q_gen_3659
<cons, cons>(q_gen_3645, q_gen_3644) -> q_gen_3644
<nil, nil>() -> q_gen_3644
<a, a>() -> q_gen_3645
<b, b>() -> q_gen_3645
<cons, cons>(q_gen_3645, q_gen_3673) -> q_gen_3673
<nil, cons>(q_gen_3659, q_gen_3658) -> q_gen_3673
<cons, cons, cons>(q_gen_3660, q_gen_3657) -> q_gen_3638
<cons, nil, cons>(q_gen_3645, q_gen_3644) -> q_gen_3638
<nil, cons, cons>(q_gen_3645, q_gen_3644) -> q_gen_3638
<nil, nil, nil>() -> q_gen_3638
<cons, cons, cons>(q_gen_3660, q_gen_3638) -> q_gen_3657
<cons, nil, cons>(q_gen_3645, q_gen_3673) -> q_gen_3657
<nil, cons, cons>(q_gen_3645, q_gen_3673) -> q_gen_3657
<nil, nil, cons>(q_gen_3659, q_gen_3658) -> q_gen_3657
<a, b, a>() -> q_gen_3660
<b, a, b>() -> q_gen_3660
<b, b, b>() -> q_gen_3660
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_3637, q_gen_3641, q_gen_3642, q_gen_3665, q_gen_3666, q_gen_3667, q_gen_3668, q_gen_3669, q_gen_3694},
Q_f={q_gen_3637},
Delta=
{
<cons>(q_gen_3666, q_gen_3665) -> q_gen_3641
<nil>() -> q_gen_3641
<cons>(q_gen_3666, q_gen_3641) -> q_gen_3665
<a>() -> q_gen_3666
<b>() -> q_gen_3666
<s>(q_gen_3694) -> q_gen_3668
<z>() -> q_gen_3668
<s>(q_gen_3668) -> q_gen_3694
<cons, s>(q_gen_3642, q_gen_3641) -> q_gen_3637
<cons, s>(q_gen_3667, q_gen_3665) -> q_gen_3637
<nil, z>() -> q_gen_3637
<a, z>() -> q_gen_3642
<b, s>(q_gen_3694) -> q_gen_3642
<b, z>() -> q_gen_3642
<a, s>(q_gen_3668) -> q_gen_3667
<b, s>(q_gen_3668) -> q_gen_3667
<cons, s>(q_gen_3642, q_gen_3665) -> q_gen_3669
<cons, s>(q_gen_3667, q_gen_3641) -> q_gen_3669
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3634, q_gen_3636, q_gen_3647, q_gen_3670, q_gen_3710},
Q_f={q_gen_3634},
Delta=
{
<z>() -> q_gen_3636
<s>(q_gen_3636) -> q_gen_3647
<s>(q_gen_3647) -> q_gen_3647
<s, s>(q_gen_3634) -> q_gen_3634
<s, s>(q_gen_3710) -> q_gen_3634
<z, s>(q_gen_3636) -> q_gen_3634
<z, s>(q_gen_3647) -> q_gen_3634
<z, z>() -> q_gen_3634
<s, s>(q_gen_3670) -> q_gen_3670
<s, z>(q_gen_3636) -> q_gen_3670
<s, z>(q_gen_3647) -> q_gen_3710
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3633, q_gen_3653, q_gen_3675, q_gen_3677, q_gen_3678},
Q_f={q_gen_3633},
Delta=
{
<nil>() -> q_gen_3677
<a>() -> q_gen_3678
<b>() -> q_gen_3678
<cons, cons>(q_gen_3653, q_gen_3633) -> q_gen_3633
<nil, nil>() -> q_gen_3633
<a, a>() -> q_gen_3653
<a, b>() -> q_gen_3653
<b, a>() -> q_gen_3653
<b, b>() -> q_gen_3653
<cons, cons>(q_gen_3653, q_gen_3675) -> q_gen_3675
<cons, nil>(q_gen_3678, q_gen_3677) -> q_gen_3675
<nil, cons>(q_gen_3678, q_gen_3677) -> q_gen_3675
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 25
() -> length([nil, z]) -> 25
() -> leq([z, s(nn2)]) -> 25
() -> leq([z, z]) -> 25
() -> reverse([nil, nil]) -> 25
(append([_eo, cons(h1, nil), _fo]) /\ reverse([t1, _eo])) -> reverse([cons(h1, t1), _fo]) -> 27
(append([t1, l2, _zn])) -> append([cons(h1, t1), l2, cons(h1, _zn)]) -> 25
(length([_oo, _po]) /\ length([l1, _no]) /\ reverse([l1, _oo])) -> leq([_no, _po]) -> 26
(length([_qo, _ro]) /\ length([l1, _so]) /\ reverse([l1, _qo])) -> leq([_ro, _so]) -> 25
(length([ll, _jo])) -> length([cons(x, ll), s(_jo)]) -> 25
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 25
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 28
(leq([s(nn1), z])) -> BOT -> 26
}
Sat witness: Found: ((leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]), {
nn1 -> s(s(z))  ;  nn2 -> z
})

-------------------------------------------
Step 49, which took 0.065866 s (model generation: 0.062059,  model checking: 0.003807):

Model:
|_
{
append -> 
{{{
Q={q_gen_3638, q_gen_3644, q_gen_3645, q_gen_3657, q_gen_3658, q_gen_3659, q_gen_3660, q_gen_3673},
Q_f={q_gen_3638},
Delta=
{
<nil>() -> q_gen_3658
<a>() -> q_gen_3659
<b>() -> q_gen_3659
<cons, cons>(q_gen_3645, q_gen_3644) -> q_gen_3644
<nil, nil>() -> q_gen_3644
<a, a>() -> q_gen_3645
<b, b>() -> q_gen_3645
<cons, cons>(q_gen_3645, q_gen_3673) -> q_gen_3673
<nil, cons>(q_gen_3659, q_gen_3658) -> q_gen_3673
<cons, cons, cons>(q_gen_3660, q_gen_3657) -> q_gen_3638
<cons, nil, cons>(q_gen_3645, q_gen_3644) -> q_gen_3638
<nil, cons, cons>(q_gen_3645, q_gen_3644) -> q_gen_3638
<nil, nil, nil>() -> q_gen_3638
<cons, cons, cons>(q_gen_3660, q_gen_3638) -> q_gen_3657
<cons, nil, cons>(q_gen_3645, q_gen_3673) -> q_gen_3657
<nil, cons, cons>(q_gen_3645, q_gen_3673) -> q_gen_3657
<nil, nil, cons>(q_gen_3659, q_gen_3658) -> q_gen_3657
<a, b, a>() -> q_gen_3660
<b, a, b>() -> q_gen_3660
<b, b, b>() -> q_gen_3660
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_3637, q_gen_3641, q_gen_3642, q_gen_3665, q_gen_3666, q_gen_3667, q_gen_3668, q_gen_3669, q_gen_3692, q_gen_3693, q_gen_3694},
Q_f={q_gen_3637},
Delta=
{
<nil>() -> q_gen_3641
<cons>(q_gen_3666, q_gen_3641) -> q_gen_3665
<a>() -> q_gen_3666
<b>() -> q_gen_3666
<s>(q_gen_3694) -> q_gen_3668
<z>() -> q_gen_3668
<cons>(q_gen_3666, q_gen_3665) -> q_gen_3692
<s>(q_gen_3668) -> q_gen_3694
<cons, s>(q_gen_3642, q_gen_3641) -> q_gen_3637
<cons, s>(q_gen_3667, q_gen_3665) -> q_gen_3637
<cons, s>(q_gen_3693, q_gen_3692) -> q_gen_3637
<nil, z>() -> q_gen_3637
<a, z>() -> q_gen_3642
<b, z>() -> q_gen_3642
<a, s>(q_gen_3668) -> q_gen_3667
<b, s>(q_gen_3668) -> q_gen_3667
<cons, s>(q_gen_3642, q_gen_3665) -> q_gen_3669
<cons, s>(q_gen_3642, q_gen_3692) -> q_gen_3669
<cons, s>(q_gen_3667, q_gen_3641) -> q_gen_3669
<cons, s>(q_gen_3693, q_gen_3641) -> q_gen_3669
<cons, s>(q_gen_3693, q_gen_3665) -> q_gen_3669
<b, s>(q_gen_3694) -> q_gen_3693
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3634, q_gen_3636, q_gen_3670},
Q_f={q_gen_3634},
Delta=
{
<s>(q_gen_3636) -> q_gen_3636
<z>() -> q_gen_3636
<s, s>(q_gen_3634) -> q_gen_3634
<z, s>(q_gen_3636) -> q_gen_3634
<z, z>() -> q_gen_3634
<s, s>(q_gen_3670) -> q_gen_3670
<s, z>(q_gen_3636) -> q_gen_3670
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3633, q_gen_3653, q_gen_3675, q_gen_3677, q_gen_3678},
Q_f={q_gen_3633},
Delta=
{
<nil>() -> q_gen_3677
<a>() -> q_gen_3678
<b>() -> q_gen_3678
<cons, cons>(q_gen_3653, q_gen_3633) -> q_gen_3633
<nil, nil>() -> q_gen_3633
<a, a>() -> q_gen_3653
<a, b>() -> q_gen_3653
<b, a>() -> q_gen_3653
<b, b>() -> q_gen_3653
<cons, cons>(q_gen_3653, q_gen_3675) -> q_gen_3675
<cons, nil>(q_gen_3678, q_gen_3677) -> q_gen_3675
<nil, cons>(q_gen_3678, q_gen_3677) -> q_gen_3675
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 25
() -> length([nil, z]) -> 25
() -> leq([z, s(nn2)]) -> 25
() -> leq([z, z]) -> 25
() -> reverse([nil, nil]) -> 25
(append([_eo, cons(h1, nil), _fo]) /\ reverse([t1, _eo])) -> reverse([cons(h1, t1), _fo]) -> 27
(append([t1, l2, _zn])) -> append([cons(h1, t1), l2, cons(h1, _zn)]) -> 25
(length([_oo, _po]) /\ length([l1, _no]) /\ reverse([l1, _oo])) -> leq([_no, _po]) -> 26
(length([_qo, _ro]) /\ length([l1, _so]) /\ reverse([l1, _qo])) -> leq([_ro, _so]) -> 25
(length([ll, _jo])) -> length([cons(x, ll), s(_jo)]) -> 28
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 26
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 28
(leq([s(nn1), z])) -> BOT -> 26
}
Sat witness: Found: ((length([ll, _jo])) -> length([cons(x, ll), s(_jo)]), {
_jo -> s(s(s(z)))  ;  ll -> cons(b, cons(a, cons(b, nil)))  ;  x -> b
})

-------------------------------------------
Step 50, which took 0.067654 s (model generation: 0.066758,  model checking: 0.000896):

Model:
|_
{
append -> 
{{{
Q={q_gen_3638, q_gen_3644, q_gen_3645, q_gen_3657, q_gen_3658, q_gen_3659, q_gen_3660, q_gen_3673},
Q_f={q_gen_3638},
Delta=
{
<nil>() -> q_gen_3658
<a>() -> q_gen_3659
<b>() -> q_gen_3659
<cons, cons>(q_gen_3645, q_gen_3644) -> q_gen_3644
<nil, nil>() -> q_gen_3644
<a, a>() -> q_gen_3645
<b, b>() -> q_gen_3645
<cons, cons>(q_gen_3645, q_gen_3673) -> q_gen_3673
<nil, cons>(q_gen_3659, q_gen_3658) -> q_gen_3673
<cons, cons, cons>(q_gen_3660, q_gen_3657) -> q_gen_3638
<cons, nil, cons>(q_gen_3645, q_gen_3644) -> q_gen_3638
<nil, cons, cons>(q_gen_3645, q_gen_3644) -> q_gen_3638
<nil, nil, nil>() -> q_gen_3638
<cons, cons, cons>(q_gen_3660, q_gen_3638) -> q_gen_3657
<cons, nil, cons>(q_gen_3645, q_gen_3673) -> q_gen_3657
<nil, cons, cons>(q_gen_3645, q_gen_3673) -> q_gen_3657
<nil, nil, cons>(q_gen_3659, q_gen_3658) -> q_gen_3657
<a, b, a>() -> q_gen_3660
<b, a, b>() -> q_gen_3660
<b, b, b>() -> q_gen_3660
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_3637, q_gen_3641, q_gen_3642, q_gen_3665, q_gen_3666, q_gen_3667, q_gen_3668, q_gen_3669, q_gen_3692, q_gen_3693, q_gen_3694},
Q_f={q_gen_3637},
Delta=
{
<nil>() -> q_gen_3641
<cons>(q_gen_3666, q_gen_3641) -> q_gen_3665
<cons>(q_gen_3666, q_gen_3692) -> q_gen_3665
<a>() -> q_gen_3666
<b>() -> q_gen_3666
<s>(q_gen_3694) -> q_gen_3668
<z>() -> q_gen_3668
<cons>(q_gen_3666, q_gen_3665) -> q_gen_3692
<s>(q_gen_3668) -> q_gen_3694
<cons, s>(q_gen_3642, q_gen_3641) -> q_gen_3637
<cons, s>(q_gen_3667, q_gen_3665) -> q_gen_3637
<cons, s>(q_gen_3693, q_gen_3692) -> q_gen_3637
<nil, z>() -> q_gen_3637
<a, z>() -> q_gen_3642
<b, z>() -> q_gen_3642
<a, s>(q_gen_3668) -> q_gen_3667
<b, s>(q_gen_3668) -> q_gen_3667
<cons, s>(q_gen_3642, q_gen_3665) -> q_gen_3669
<cons, s>(q_gen_3642, q_gen_3692) -> q_gen_3669
<cons, s>(q_gen_3667, q_gen_3641) -> q_gen_3669
<cons, s>(q_gen_3693, q_gen_3641) -> q_gen_3669
<cons, s>(q_gen_3693, q_gen_3665) -> q_gen_3669
<b, s>(q_gen_3694) -> q_gen_3693
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3634, q_gen_3636, q_gen_3670},
Q_f={q_gen_3634},
Delta=
{
<s>(q_gen_3636) -> q_gen_3636
<z>() -> q_gen_3636
<s, s>(q_gen_3634) -> q_gen_3634
<z, s>(q_gen_3636) -> q_gen_3634
<z, z>() -> q_gen_3634
<s, s>(q_gen_3670) -> q_gen_3670
<s, z>(q_gen_3636) -> q_gen_3670
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3633, q_gen_3653, q_gen_3675, q_gen_3677, q_gen_3678},
Q_f={q_gen_3633},
Delta=
{
<nil>() -> q_gen_3677
<a>() -> q_gen_3678
<b>() -> q_gen_3678
<cons, cons>(q_gen_3653, q_gen_3633) -> q_gen_3633
<nil, nil>() -> q_gen_3633
<a, a>() -> q_gen_3653
<a, b>() -> q_gen_3653
<b, a>() -> q_gen_3653
<b, b>() -> q_gen_3653
<cons, cons>(q_gen_3653, q_gen_3675) -> q_gen_3675
<cons, nil>(q_gen_3678, q_gen_3677) -> q_gen_3675
<nil, cons>(q_gen_3678, q_gen_3677) -> q_gen_3675
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 25
() -> length([nil, z]) -> 25
() -> leq([z, s(nn2)]) -> 25
() -> leq([z, z]) -> 25
() -> reverse([nil, nil]) -> 25
(append([_eo, cons(h1, nil), _fo]) /\ reverse([t1, _eo])) -> reverse([cons(h1, t1), _fo]) -> 27
(append([t1, l2, _zn])) -> append([cons(h1, t1), l2, cons(h1, _zn)]) -> 25
(length([_oo, _po]) /\ length([l1, _no]) /\ reverse([l1, _oo])) -> leq([_no, _po]) -> 26
(length([_qo, _ro]) /\ length([l1, _so]) /\ reverse([l1, _qo])) -> leq([_ro, _so]) -> 28
(length([ll, _jo])) -> length([cons(x, ll), s(_jo)]) -> 28
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 26
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 28
(leq([s(nn1), z])) -> BOT -> 26
}
Sat witness: Found: ((length([_qo, _ro]) /\ length([l1, _so]) /\ reverse([l1, _qo])) -> leq([_ro, _so]), {
_qo -> cons(b, cons(b, nil))  ;  _ro -> s(s(s(s(z))))  ;  _so -> s(s(z))  ;  l1 -> cons(b, cons(b, nil))
})

-------------------------------------------
Step 51, which took 0.065811 s (model generation: 0.061988,  model checking: 0.003823):

Model:
|_
{
append -> 
{{{
Q={q_gen_3638, q_gen_3644, q_gen_3645, q_gen_3657, q_gen_3658, q_gen_3659, q_gen_3660, q_gen_3673},
Q_f={q_gen_3638},
Delta=
{
<nil>() -> q_gen_3658
<a>() -> q_gen_3659
<b>() -> q_gen_3659
<cons, cons>(q_gen_3645, q_gen_3644) -> q_gen_3644
<nil, nil>() -> q_gen_3644
<a, a>() -> q_gen_3645
<b, b>() -> q_gen_3645
<cons, cons>(q_gen_3645, q_gen_3673) -> q_gen_3673
<nil, cons>(q_gen_3659, q_gen_3658) -> q_gen_3673
<cons, cons, cons>(q_gen_3660, q_gen_3657) -> q_gen_3638
<cons, nil, cons>(q_gen_3645, q_gen_3644) -> q_gen_3638
<nil, cons, cons>(q_gen_3645, q_gen_3644) -> q_gen_3638
<nil, nil, nil>() -> q_gen_3638
<cons, cons, cons>(q_gen_3660, q_gen_3638) -> q_gen_3657
<cons, nil, cons>(q_gen_3645, q_gen_3673) -> q_gen_3657
<nil, cons, cons>(q_gen_3645, q_gen_3673) -> q_gen_3657
<nil, nil, cons>(q_gen_3659, q_gen_3658) -> q_gen_3657
<a, b, a>() -> q_gen_3660
<b, a, b>() -> q_gen_3660
<b, b, b>() -> q_gen_3660
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_3637, q_gen_3641, q_gen_3642, q_gen_3665, q_gen_3666, q_gen_3667, q_gen_3668, q_gen_3669, q_gen_3692, q_gen_3693, q_gen_3694},
Q_f={q_gen_3637},
Delta=
{
<nil>() -> q_gen_3641
<cons>(q_gen_3666, q_gen_3641) -> q_gen_3665
<a>() -> q_gen_3666
<b>() -> q_gen_3666
<z>() -> q_gen_3668
<cons>(q_gen_3666, q_gen_3665) -> q_gen_3692
<cons>(q_gen_3666, q_gen_3692) -> q_gen_3692
<s>(q_gen_3668) -> q_gen_3694
<s>(q_gen_3694) -> q_gen_3694
<cons, s>(q_gen_3642, q_gen_3641) -> q_gen_3637
<cons, s>(q_gen_3667, q_gen_3665) -> q_gen_3637
<cons, s>(q_gen_3693, q_gen_3692) -> q_gen_3637
<nil, z>() -> q_gen_3637
<a, z>() -> q_gen_3642
<b, z>() -> q_gen_3642
<a, s>(q_gen_3668) -> q_gen_3667
<b, s>(q_gen_3668) -> q_gen_3667
<cons, s>(q_gen_3642, q_gen_3665) -> q_gen_3669
<cons, s>(q_gen_3642, q_gen_3692) -> q_gen_3669
<cons, s>(q_gen_3667, q_gen_3641) -> q_gen_3669
<cons, s>(q_gen_3693, q_gen_3641) -> q_gen_3669
<cons, s>(q_gen_3693, q_gen_3665) -> q_gen_3669
<b, s>(q_gen_3694) -> q_gen_3693
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3634, q_gen_3636, q_gen_3670},
Q_f={q_gen_3634},
Delta=
{
<s>(q_gen_3636) -> q_gen_3636
<z>() -> q_gen_3636
<s, s>(q_gen_3634) -> q_gen_3634
<z, s>(q_gen_3636) -> q_gen_3634
<z, z>() -> q_gen_3634
<s, s>(q_gen_3670) -> q_gen_3670
<s, z>(q_gen_3636) -> q_gen_3670
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3633, q_gen_3653, q_gen_3675, q_gen_3677, q_gen_3678},
Q_f={q_gen_3633},
Delta=
{
<nil>() -> q_gen_3677
<a>() -> q_gen_3678
<b>() -> q_gen_3678
<cons, cons>(q_gen_3653, q_gen_3633) -> q_gen_3633
<nil, nil>() -> q_gen_3633
<a, a>() -> q_gen_3653
<a, b>() -> q_gen_3653
<b, a>() -> q_gen_3653
<b, b>() -> q_gen_3653
<cons, cons>(q_gen_3653, q_gen_3675) -> q_gen_3675
<cons, nil>(q_gen_3678, q_gen_3677) -> q_gen_3675
<nil, cons>(q_gen_3678, q_gen_3677) -> q_gen_3675
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 25
() -> length([nil, z]) -> 25
() -> leq([z, s(nn2)]) -> 25
() -> leq([z, z]) -> 25
() -> reverse([nil, nil]) -> 25
(append([_eo, cons(h1, nil), _fo]) /\ reverse([t1, _eo])) -> reverse([cons(h1, t1), _fo]) -> 27
(append([t1, l2, _zn])) -> append([cons(h1, t1), l2, cons(h1, _zn)]) -> 28
(length([_oo, _po]) /\ length([l1, _no]) /\ reverse([l1, _oo])) -> leq([_no, _po]) -> 26
(length([_qo, _ro]) /\ length([l1, _so]) /\ reverse([l1, _qo])) -> leq([_ro, _so]) -> 28
(length([ll, _jo])) -> length([cons(x, ll), s(_jo)]) -> 28
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 26
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 28
(leq([s(nn1), z])) -> BOT -> 26
}
Sat witness: Found: ((append([t1, l2, _zn])) -> append([cons(h1, t1), l2, cons(h1, _zn)]), {
_zn -> cons(a, nil)  ;  h1 -> a  ;  l2 -> cons(a, nil)  ;  t1 -> nil
})

-------------------------------------------
Step 52, which took 0.074438 s (model generation: 0.072473,  model checking: 0.001965):

Model:
|_
{
append -> 
{{{
Q={q_gen_3638, q_gen_3644, q_gen_3645, q_gen_3657, q_gen_3658, q_gen_3659, q_gen_3660, q_gen_3673},
Q_f={q_gen_3638},
Delta=
{
<nil>() -> q_gen_3658
<a>() -> q_gen_3659
<b>() -> q_gen_3659
<cons, cons>(q_gen_3645, q_gen_3644) -> q_gen_3644
<nil, nil>() -> q_gen_3644
<a, a>() -> q_gen_3645
<b, b>() -> q_gen_3645
<cons, cons>(q_gen_3645, q_gen_3673) -> q_gen_3673
<nil, cons>(q_gen_3659, q_gen_3658) -> q_gen_3673
<cons, cons, cons>(q_gen_3660, q_gen_3657) -> q_gen_3638
<cons, nil, cons>(q_gen_3645, q_gen_3644) -> q_gen_3638
<nil, cons, cons>(q_gen_3645, q_gen_3644) -> q_gen_3638
<nil, nil, nil>() -> q_gen_3638
<cons, cons, cons>(q_gen_3660, q_gen_3638) -> q_gen_3657
<cons, nil, cons>(q_gen_3645, q_gen_3673) -> q_gen_3657
<nil, cons, cons>(q_gen_3645, q_gen_3673) -> q_gen_3657
<nil, nil, cons>(q_gen_3659, q_gen_3658) -> q_gen_3657
<a, a, a>() -> q_gen_3660
<a, b, a>() -> q_gen_3660
<b, a, b>() -> q_gen_3660
<b, b, b>() -> q_gen_3660
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_3637, q_gen_3641, q_gen_3642, q_gen_3665, q_gen_3666, q_gen_3667, q_gen_3668, q_gen_3669, q_gen_3692, q_gen_3693, q_gen_3694},
Q_f={q_gen_3637},
Delta=
{
<nil>() -> q_gen_3641
<cons>(q_gen_3666, q_gen_3641) -> q_gen_3665
<a>() -> q_gen_3666
<b>() -> q_gen_3666
<z>() -> q_gen_3668
<cons>(q_gen_3666, q_gen_3665) -> q_gen_3692
<cons>(q_gen_3666, q_gen_3692) -> q_gen_3692
<s>(q_gen_3668) -> q_gen_3694
<s>(q_gen_3694) -> q_gen_3694
<cons, s>(q_gen_3642, q_gen_3641) -> q_gen_3637
<cons, s>(q_gen_3667, q_gen_3665) -> q_gen_3637
<cons, s>(q_gen_3693, q_gen_3692) -> q_gen_3637
<nil, z>() -> q_gen_3637
<a, z>() -> q_gen_3642
<b, z>() -> q_gen_3642
<a, s>(q_gen_3668) -> q_gen_3667
<b, s>(q_gen_3668) -> q_gen_3667
<cons, s>(q_gen_3642, q_gen_3665) -> q_gen_3669
<cons, s>(q_gen_3642, q_gen_3692) -> q_gen_3669
<cons, s>(q_gen_3667, q_gen_3641) -> q_gen_3669
<cons, s>(q_gen_3693, q_gen_3641) -> q_gen_3669
<cons, s>(q_gen_3693, q_gen_3665) -> q_gen_3669
<b, s>(q_gen_3694) -> q_gen_3693
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3634, q_gen_3636, q_gen_3670},
Q_f={q_gen_3634},
Delta=
{
<s>(q_gen_3636) -> q_gen_3636
<z>() -> q_gen_3636
<s, s>(q_gen_3634) -> q_gen_3634
<z, s>(q_gen_3636) -> q_gen_3634
<z, z>() -> q_gen_3634
<s, s>(q_gen_3670) -> q_gen_3670
<s, z>(q_gen_3636) -> q_gen_3670
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3633, q_gen_3653, q_gen_3675, q_gen_3677, q_gen_3678},
Q_f={q_gen_3633},
Delta=
{
<nil>() -> q_gen_3677
<a>() -> q_gen_3678
<b>() -> q_gen_3678
<cons, cons>(q_gen_3653, q_gen_3633) -> q_gen_3633
<nil, nil>() -> q_gen_3633
<a, a>() -> q_gen_3653
<a, b>() -> q_gen_3653
<b, a>() -> q_gen_3653
<b, b>() -> q_gen_3653
<cons, cons>(q_gen_3653, q_gen_3675) -> q_gen_3675
<cons, nil>(q_gen_3678, q_gen_3677) -> q_gen_3675
<nil, cons>(q_gen_3678, q_gen_3677) -> q_gen_3675
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 26
() -> length([nil, z]) -> 26
() -> leq([z, s(nn2)]) -> 26
() -> leq([z, z]) -> 26
() -> reverse([nil, nil]) -> 26
(append([_eo, cons(h1, nil), _fo]) /\ reverse([t1, _eo])) -> reverse([cons(h1, t1), _fo]) -> 27
(append([t1, l2, _zn])) -> append([cons(h1, t1), l2, cons(h1, _zn)]) -> 28
(length([_oo, _po]) /\ length([l1, _no]) /\ reverse([l1, _oo])) -> leq([_no, _po]) -> 29
(length([_qo, _ro]) /\ length([l1, _so]) /\ reverse([l1, _qo])) -> leq([_ro, _so]) -> 28
(length([ll, _jo])) -> length([cons(x, ll), s(_jo)]) -> 28
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 27
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 28
(leq([s(nn1), z])) -> BOT -> 27
}
Sat witness: Found: ((length([_oo, _po]) /\ length([l1, _no]) /\ reverse([l1, _oo])) -> leq([_no, _po]), {
_no -> s(s(s(s(z))))  ;  _oo -> cons(b, cons(b, cons(b, nil)))  ;  _po -> s(s(s(z)))  ;  l1 -> cons(b, cons(b, cons(b, nil)))
})

-------------------------------------------
Step 53, which took 0.090688 s (model generation: 0.084736,  model checking: 0.005952):

Model:
|_
{
append -> 
{{{
Q={q_gen_3638, q_gen_3644, q_gen_3645, q_gen_3657, q_gen_3658, q_gen_3659, q_gen_3660, q_gen_3673},
Q_f={q_gen_3638},
Delta=
{
<nil>() -> q_gen_3658
<a>() -> q_gen_3659
<b>() -> q_gen_3659
<cons, cons>(q_gen_3645, q_gen_3644) -> q_gen_3644
<nil, nil>() -> q_gen_3644
<a, a>() -> q_gen_3645
<b, b>() -> q_gen_3645
<cons, cons>(q_gen_3645, q_gen_3673) -> q_gen_3673
<nil, cons>(q_gen_3659, q_gen_3658) -> q_gen_3673
<cons, cons, cons>(q_gen_3660, q_gen_3657) -> q_gen_3638
<cons, nil, cons>(q_gen_3645, q_gen_3644) -> q_gen_3638
<nil, cons, cons>(q_gen_3645, q_gen_3644) -> q_gen_3638
<nil, nil, nil>() -> q_gen_3638
<cons, cons, cons>(q_gen_3660, q_gen_3638) -> q_gen_3657
<cons, nil, cons>(q_gen_3645, q_gen_3673) -> q_gen_3657
<nil, cons, cons>(q_gen_3645, q_gen_3673) -> q_gen_3657
<nil, nil, cons>(q_gen_3659, q_gen_3658) -> q_gen_3657
<a, a, a>() -> q_gen_3660
<a, b, a>() -> q_gen_3660
<b, a, b>() -> q_gen_3660
<b, b, b>() -> q_gen_3660
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_3637, q_gen_3641, q_gen_3642, q_gen_3665, q_gen_3666, q_gen_3667, q_gen_3668, q_gen_3669, q_gen_3692, q_gen_3693, q_gen_3694, q_gen_3708},
Q_f={q_gen_3637},
Delta=
{
<cons>(q_gen_3666, q_gen_3692) -> q_gen_3641
<nil>() -> q_gen_3641
<cons>(q_gen_3666, q_gen_3641) -> q_gen_3665
<a>() -> q_gen_3666
<b>() -> q_gen_3666
<z>() -> q_gen_3668
<cons>(q_gen_3666, q_gen_3665) -> q_gen_3692
<s>(q_gen_3668) -> q_gen_3694
<s>(q_gen_3694) -> q_gen_3708
<cons, s>(q_gen_3642, q_gen_3641) -> q_gen_3637
<cons, s>(q_gen_3667, q_gen_3665) -> q_gen_3637
<cons, s>(q_gen_3693, q_gen_3692) -> q_gen_3637
<nil, z>() -> q_gen_3637
<a, z>() -> q_gen_3642
<b, s>(q_gen_3708) -> q_gen_3642
<b, z>() -> q_gen_3642
<a, s>(q_gen_3668) -> q_gen_3667
<b, s>(q_gen_3668) -> q_gen_3667
<cons, s>(q_gen_3642, q_gen_3665) -> q_gen_3669
<cons, s>(q_gen_3642, q_gen_3692) -> q_gen_3669
<cons, s>(q_gen_3667, q_gen_3641) -> q_gen_3669
<cons, s>(q_gen_3693, q_gen_3641) -> q_gen_3669
<cons, s>(q_gen_3693, q_gen_3665) -> q_gen_3669
<b, s>(q_gen_3694) -> q_gen_3693
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3634, q_gen_3636, q_gen_3670},
Q_f={q_gen_3634},
Delta=
{
<s>(q_gen_3636) -> q_gen_3636
<z>() -> q_gen_3636
<s, s>(q_gen_3634) -> q_gen_3634
<z, s>(q_gen_3636) -> q_gen_3634
<z, z>() -> q_gen_3634
<s, s>(q_gen_3670) -> q_gen_3670
<s, z>(q_gen_3636) -> q_gen_3670
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3633, q_gen_3653, q_gen_3675, q_gen_3677, q_gen_3678},
Q_f={q_gen_3633},
Delta=
{
<nil>() -> q_gen_3677
<a>() -> q_gen_3678
<b>() -> q_gen_3678
<cons, cons>(q_gen_3653, q_gen_3633) -> q_gen_3633
<nil, nil>() -> q_gen_3633
<a, a>() -> q_gen_3653
<a, b>() -> q_gen_3653
<b, a>() -> q_gen_3653
<b, b>() -> q_gen_3653
<cons, cons>(q_gen_3653, q_gen_3675) -> q_gen_3675
<cons, nil>(q_gen_3678, q_gen_3677) -> q_gen_3675
<nil, cons>(q_gen_3678, q_gen_3677) -> q_gen_3675
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 27
() -> length([nil, z]) -> 27
() -> leq([z, s(nn2)]) -> 27
() -> leq([z, z]) -> 27
() -> reverse([nil, nil]) -> 27
(append([_eo, cons(h1, nil), _fo]) /\ reverse([t1, _eo])) -> reverse([cons(h1, t1), _fo]) -> 28
(append([t1, l2, _zn])) -> append([cons(h1, t1), l2, cons(h1, _zn)]) -> 28
(length([_oo, _po]) /\ length([l1, _no]) /\ reverse([l1, _oo])) -> leq([_no, _po]) -> 29
(length([_qo, _ro]) /\ length([l1, _so]) /\ reverse([l1, _qo])) -> leq([_ro, _so]) -> 28
(length([ll, _jo])) -> length([cons(x, ll), s(_jo)]) -> 31
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 28
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 29
(leq([s(nn1), z])) -> BOT -> 28
}
Sat witness: Found: ((length([ll, _jo])) -> length([cons(x, ll), s(_jo)]), {
_jo -> s(s(s(s(z))))  ;  ll -> cons(b, nil)  ;  x -> b
})

-------------------------------------------
Step 54, which took 0.093314 s (model generation: 0.091872,  model checking: 0.001442):

Model:
|_
{
append -> 
{{{
Q={q_gen_3638, q_gen_3644, q_gen_3645, q_gen_3657, q_gen_3658, q_gen_3659, q_gen_3660, q_gen_3673},
Q_f={q_gen_3638},
Delta=
{
<nil>() -> q_gen_3658
<a>() -> q_gen_3659
<b>() -> q_gen_3659
<cons, cons>(q_gen_3645, q_gen_3644) -> q_gen_3644
<nil, nil>() -> q_gen_3644
<a, a>() -> q_gen_3645
<b, b>() -> q_gen_3645
<cons, cons>(q_gen_3645, q_gen_3673) -> q_gen_3673
<nil, cons>(q_gen_3659, q_gen_3658) -> q_gen_3673
<cons, cons, cons>(q_gen_3660, q_gen_3657) -> q_gen_3638
<cons, nil, cons>(q_gen_3645, q_gen_3644) -> q_gen_3638
<nil, cons, cons>(q_gen_3645, q_gen_3644) -> q_gen_3638
<nil, nil, nil>() -> q_gen_3638
<cons, cons, cons>(q_gen_3660, q_gen_3638) -> q_gen_3657
<cons, nil, cons>(q_gen_3645, q_gen_3673) -> q_gen_3657
<nil, cons, cons>(q_gen_3645, q_gen_3673) -> q_gen_3657
<nil, nil, cons>(q_gen_3659, q_gen_3658) -> q_gen_3657
<a, a, a>() -> q_gen_3660
<a, b, a>() -> q_gen_3660
<b, a, b>() -> q_gen_3660
<b, b, b>() -> q_gen_3660
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_3637, q_gen_3641, q_gen_3642, q_gen_3665, q_gen_3666, q_gen_3667, q_gen_3668, q_gen_3669, q_gen_3692, q_gen_3693, q_gen_3694, q_gen_3708},
Q_f={q_gen_3637},
Delta=
{
<cons>(q_gen_3666, q_gen_3692) -> q_gen_3641
<nil>() -> q_gen_3641
<cons>(q_gen_3666, q_gen_3641) -> q_gen_3665
<a>() -> q_gen_3666
<b>() -> q_gen_3666
<s>(q_gen_3708) -> q_gen_3668
<z>() -> q_gen_3668
<cons>(q_gen_3666, q_gen_3665) -> q_gen_3692
<s>(q_gen_3668) -> q_gen_3694
<s>(q_gen_3694) -> q_gen_3708
<cons, s>(q_gen_3642, q_gen_3641) -> q_gen_3637
<cons, s>(q_gen_3667, q_gen_3665) -> q_gen_3637
<cons, s>(q_gen_3693, q_gen_3692) -> q_gen_3637
<nil, z>() -> q_gen_3637
<a, z>() -> q_gen_3642
<b, s>(q_gen_3708) -> q_gen_3642
<b, z>() -> q_gen_3642
<a, s>(q_gen_3668) -> q_gen_3667
<b, s>(q_gen_3668) -> q_gen_3667
<cons, s>(q_gen_3642, q_gen_3665) -> q_gen_3669
<cons, s>(q_gen_3642, q_gen_3692) -> q_gen_3669
<cons, s>(q_gen_3667, q_gen_3641) -> q_gen_3669
<cons, s>(q_gen_3693, q_gen_3641) -> q_gen_3669
<cons, s>(q_gen_3693, q_gen_3665) -> q_gen_3669
<b, s>(q_gen_3694) -> q_gen_3693
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3634, q_gen_3636, q_gen_3670},
Q_f={q_gen_3634},
Delta=
{
<s>(q_gen_3636) -> q_gen_3636
<z>() -> q_gen_3636
<s, s>(q_gen_3634) -> q_gen_3634
<z, s>(q_gen_3636) -> q_gen_3634
<z, z>() -> q_gen_3634
<s, s>(q_gen_3670) -> q_gen_3670
<s, z>(q_gen_3636) -> q_gen_3670
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3633, q_gen_3653, q_gen_3675, q_gen_3677, q_gen_3678},
Q_f={q_gen_3633},
Delta=
{
<nil>() -> q_gen_3677
<a>() -> q_gen_3678
<b>() -> q_gen_3678
<cons, cons>(q_gen_3653, q_gen_3633) -> q_gen_3633
<nil, nil>() -> q_gen_3633
<a, a>() -> q_gen_3653
<a, b>() -> q_gen_3653
<b, a>() -> q_gen_3653
<b, b>() -> q_gen_3653
<cons, cons>(q_gen_3653, q_gen_3675) -> q_gen_3675
<cons, nil>(q_gen_3678, q_gen_3677) -> q_gen_3675
<nil, cons>(q_gen_3678, q_gen_3677) -> q_gen_3675
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 28
() -> length([nil, z]) -> 28
() -> leq([z, s(nn2)]) -> 28
() -> leq([z, z]) -> 28
() -> reverse([nil, nil]) -> 28
(append([_eo, cons(h1, nil), _fo]) /\ reverse([t1, _eo])) -> reverse([cons(h1, t1), _fo]) -> 28
(append([t1, l2, _zn])) -> append([cons(h1, t1), l2, cons(h1, _zn)]) -> 28
(length([_oo, _po]) /\ length([l1, _no]) /\ reverse([l1, _oo])) -> leq([_no, _po]) -> 29
(length([_qo, _ro]) /\ length([l1, _so]) /\ reverse([l1, _qo])) -> leq([_ro, _so]) -> 31
(length([ll, _jo])) -> length([cons(x, ll), s(_jo)]) -> 31
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 29
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 29
(leq([s(nn1), z])) -> BOT -> 29
}
Sat witness: Found: ((length([_qo, _ro]) /\ length([l1, _so]) /\ reverse([l1, _qo])) -> leq([_ro, _so]), {
_qo -> cons(b, nil)  ;  _ro -> s(s(s(s(z))))  ;  _so -> s(z)  ;  l1 -> cons(b, nil)
})

-------------------------------------------
Step 55, which took 0.116156 s (model generation: 0.102028,  model checking: 0.014128):

Model:
|_
{
append -> 
{{{
Q={q_gen_3638, q_gen_3644, q_gen_3645, q_gen_3657, q_gen_3658, q_gen_3659, q_gen_3660, q_gen_3673},
Q_f={q_gen_3638},
Delta=
{
<nil>() -> q_gen_3658
<a>() -> q_gen_3659
<b>() -> q_gen_3659
<cons, cons>(q_gen_3645, q_gen_3644) -> q_gen_3644
<nil, nil>() -> q_gen_3644
<a, a>() -> q_gen_3645
<b, b>() -> q_gen_3645
<cons, cons>(q_gen_3645, q_gen_3673) -> q_gen_3673
<nil, cons>(q_gen_3659, q_gen_3658) -> q_gen_3673
<cons, cons, cons>(q_gen_3660, q_gen_3657) -> q_gen_3638
<cons, nil, cons>(q_gen_3645, q_gen_3644) -> q_gen_3638
<nil, cons, cons>(q_gen_3645, q_gen_3644) -> q_gen_3638
<nil, nil, nil>() -> q_gen_3638
<cons, cons, cons>(q_gen_3660, q_gen_3638) -> q_gen_3657
<cons, nil, cons>(q_gen_3645, q_gen_3673) -> q_gen_3657
<nil, cons, cons>(q_gen_3645, q_gen_3673) -> q_gen_3657
<nil, nil, cons>(q_gen_3659, q_gen_3658) -> q_gen_3657
<a, a, a>() -> q_gen_3660
<a, b, a>() -> q_gen_3660
<b, a, b>() -> q_gen_3660
<b, b, b>() -> q_gen_3660
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_3637, q_gen_3641, q_gen_3642, q_gen_3665, q_gen_3666, q_gen_3667, q_gen_3668, q_gen_3669, q_gen_3692, q_gen_3693, q_gen_3694},
Q_f={q_gen_3637},
Delta=
{
<nil>() -> q_gen_3641
<cons>(q_gen_3666, q_gen_3641) -> q_gen_3665
<a>() -> q_gen_3666
<b>() -> q_gen_3666
<z>() -> q_gen_3668
<cons>(q_gen_3666, q_gen_3665) -> q_gen_3692
<cons>(q_gen_3666, q_gen_3692) -> q_gen_3692
<s>(q_gen_3668) -> q_gen_3694
<s>(q_gen_3694) -> q_gen_3694
<cons, s>(q_gen_3642, q_gen_3641) -> q_gen_3637
<cons, s>(q_gen_3667, q_gen_3665) -> q_gen_3637
<cons, s>(q_gen_3693, q_gen_3692) -> q_gen_3637
<nil, z>() -> q_gen_3637
<a, z>() -> q_gen_3642
<b, z>() -> q_gen_3642
<a, s>(q_gen_3668) -> q_gen_3667
<b, s>(q_gen_3668) -> q_gen_3667
<cons, s>(q_gen_3642, q_gen_3665) -> q_gen_3669
<cons, s>(q_gen_3642, q_gen_3692) -> q_gen_3669
<cons, s>(q_gen_3667, q_gen_3641) -> q_gen_3669
<cons, s>(q_gen_3693, q_gen_3641) -> q_gen_3669
<cons, s>(q_gen_3693, q_gen_3665) -> q_gen_3669
<b, s>(q_gen_3694) -> q_gen_3693
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3634, q_gen_3636, q_gen_3670, q_gen_3671, q_gen_3699},
Q_f={q_gen_3634},
Delta=
{
<s>(q_gen_3636) -> q_gen_3636
<z>() -> q_gen_3636
<s, s>(q_gen_3634) -> q_gen_3634
<s, s>(q_gen_3699) -> q_gen_3634
<z, s>(q_gen_3636) -> q_gen_3634
<z, z>() -> q_gen_3634
<s, s>(q_gen_3671) -> q_gen_3670
<s, z>(q_gen_3636) -> q_gen_3671
<s, s>(q_gen_3670) -> q_gen_3699
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3633, q_gen_3653, q_gen_3675, q_gen_3677, q_gen_3678},
Q_f={q_gen_3633},
Delta=
{
<nil>() -> q_gen_3677
<a>() -> q_gen_3678
<b>() -> q_gen_3678
<cons, cons>(q_gen_3653, q_gen_3633) -> q_gen_3633
<nil, nil>() -> q_gen_3633
<a, a>() -> q_gen_3653
<a, b>() -> q_gen_3653
<b, a>() -> q_gen_3653
<b, b>() -> q_gen_3653
<cons, cons>(q_gen_3653, q_gen_3675) -> q_gen_3675
<cons, nil>(q_gen_3678, q_gen_3677) -> q_gen_3675
<nil, cons>(q_gen_3678, q_gen_3677) -> q_gen_3675
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 28
() -> length([nil, z]) -> 28
() -> leq([z, s(nn2)]) -> 28
() -> leq([z, z]) -> 28
() -> reverse([nil, nil]) -> 28
(append([_eo, cons(h1, nil), _fo]) /\ reverse([t1, _eo])) -> reverse([cons(h1, t1), _fo]) -> 28
(append([t1, l2, _zn])) -> append([cons(h1, t1), l2, cons(h1, _zn)]) -> 31
(length([_oo, _po]) /\ length([l1, _no]) /\ reverse([l1, _oo])) -> leq([_no, _po]) -> 29
(length([_qo, _ro]) /\ length([l1, _so]) /\ reverse([l1, _qo])) -> leq([_ro, _so]) -> 31
(length([ll, _jo])) -> length([cons(x, ll), s(_jo)]) -> 31
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 29
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 29
(leq([s(nn1), z])) -> BOT -> 29
}
Sat witness: Found: ((append([t1, l2, _zn])) -> append([cons(h1, t1), l2, cons(h1, _zn)]), {
_zn -> cons(a, cons(b, cons(b, nil)))  ;  h1 -> a  ;  l2 -> cons(a, cons(b, nil))  ;  t1 -> cons(a, nil)
})

-------------------------------------------
Step 56, which took 0.131188 s (model generation: 0.130135,  model checking: 0.001053):

Model:
|_
{
append -> 
{{{
Q={q_gen_3638, q_gen_3644, q_gen_3645, q_gen_3658, q_gen_3659, q_gen_3660, q_gen_3673, q_gen_3674},
Q_f={q_gen_3638},
Delta=
{
<cons>(q_gen_3659, q_gen_3658) -> q_gen_3658
<nil>() -> q_gen_3658
<a>() -> q_gen_3659
<b>() -> q_gen_3659
<cons, cons>(q_gen_3645, q_gen_3644) -> q_gen_3644
<cons, cons>(q_gen_3645, q_gen_3673) -> q_gen_3644
<nil, nil>() -> q_gen_3644
<a, a>() -> q_gen_3645
<b, b>() -> q_gen_3645
<nil, cons>(q_gen_3659, q_gen_3658) -> q_gen_3673
<cons, cons, cons>(q_gen_3660, q_gen_3638) -> q_gen_3638
<cons, nil, cons>(q_gen_3645, q_gen_3644) -> q_gen_3638
<cons, nil, cons>(q_gen_3645, q_gen_3673) -> q_gen_3638
<nil, cons, cons>(q_gen_3645, q_gen_3644) -> q_gen_3638
<nil, nil, cons>(q_gen_3659, q_gen_3658) -> q_gen_3638
<nil, nil, nil>() -> q_gen_3638
<a, a, a>() -> q_gen_3660
<a, b, a>() -> q_gen_3660
<b, a, b>() -> q_gen_3660
<b, b, b>() -> q_gen_3660
<cons, cons, cons>(q_gen_3660, q_gen_3674) -> q_gen_3674
<nil, cons, cons>(q_gen_3645, q_gen_3673) -> q_gen_3674
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_3637, q_gen_3641, q_gen_3642, q_gen_3665, q_gen_3666, q_gen_3667, q_gen_3668, q_gen_3669, q_gen_3692, q_gen_3693, q_gen_3694},
Q_f={q_gen_3637},
Delta=
{
<nil>() -> q_gen_3641
<cons>(q_gen_3666, q_gen_3641) -> q_gen_3665
<a>() -> q_gen_3666
<b>() -> q_gen_3666
<z>() -> q_gen_3668
<cons>(q_gen_3666, q_gen_3665) -> q_gen_3692
<cons>(q_gen_3666, q_gen_3692) -> q_gen_3692
<s>(q_gen_3668) -> q_gen_3694
<s>(q_gen_3694) -> q_gen_3694
<cons, s>(q_gen_3642, q_gen_3641) -> q_gen_3637
<cons, s>(q_gen_3667, q_gen_3665) -> q_gen_3637
<cons, s>(q_gen_3693, q_gen_3692) -> q_gen_3637
<nil, z>() -> q_gen_3637
<a, z>() -> q_gen_3642
<b, z>() -> q_gen_3642
<a, s>(q_gen_3668) -> q_gen_3667
<b, s>(q_gen_3668) -> q_gen_3667
<cons, s>(q_gen_3642, q_gen_3665) -> q_gen_3669
<cons, s>(q_gen_3642, q_gen_3692) -> q_gen_3669
<cons, s>(q_gen_3667, q_gen_3641) -> q_gen_3669
<cons, s>(q_gen_3693, q_gen_3641) -> q_gen_3669
<cons, s>(q_gen_3693, q_gen_3665) -> q_gen_3669
<b, s>(q_gen_3694) -> q_gen_3693
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3634, q_gen_3636, q_gen_3670},
Q_f={q_gen_3634},
Delta=
{
<s>(q_gen_3636) -> q_gen_3636
<z>() -> q_gen_3636
<s, s>(q_gen_3634) -> q_gen_3634
<z, s>(q_gen_3636) -> q_gen_3634
<z, z>() -> q_gen_3634
<s, s>(q_gen_3670) -> q_gen_3670
<s, z>(q_gen_3636) -> q_gen_3670
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3633, q_gen_3652, q_gen_3653, q_gen_3675, q_gen_3677, q_gen_3678, q_gen_3684, q_gen_3689},
Q_f={q_gen_3633, q_gen_3652, q_gen_3684},
Delta=
{
<nil>() -> q_gen_3677
<a>() -> q_gen_3678
<b>() -> q_gen_3678
<cons, cons>(q_gen_3689, q_gen_3684) -> q_gen_3633
<nil, nil>() -> q_gen_3633
<cons, cons>(q_gen_3653, q_gen_3633) -> q_gen_3652
<a, a>() -> q_gen_3653
<b, b>() -> q_gen_3653
<cons, cons>(q_gen_3653, q_gen_3675) -> q_gen_3675
<cons, cons>(q_gen_3653, q_gen_3684) -> q_gen_3675
<cons, cons>(q_gen_3689, q_gen_3633) -> q_gen_3675
<cons, nil>(q_gen_3678, q_gen_3677) -> q_gen_3675
<nil, cons>(q_gen_3678, q_gen_3677) -> q_gen_3675
<cons, cons>(q_gen_3653, q_gen_3652) -> q_gen_3684
<cons, cons>(q_gen_3689, q_gen_3675) -> q_gen_3684
<a, b>() -> q_gen_3689
<b, a>() -> q_gen_3689
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 28
() -> length([nil, z]) -> 28
() -> leq([z, s(nn2)]) -> 28
() -> leq([z, z]) -> 28
() -> reverse([nil, nil]) -> 28
(append([_eo, cons(h1, nil), _fo]) /\ reverse([t1, _eo])) -> reverse([cons(h1, t1), _fo]) -> 31
(append([t1, l2, _zn])) -> append([cons(h1, t1), l2, cons(h1, _zn)]) -> 31
(length([_oo, _po]) /\ length([l1, _no]) /\ reverse([l1, _oo])) -> leq([_no, _po]) -> 29
(length([_qo, _ro]) /\ length([l1, _so]) /\ reverse([l1, _qo])) -> leq([_ro, _so]) -> 31
(length([ll, _jo])) -> length([cons(x, ll), s(_jo)]) -> 31
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 29
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 29
(leq([s(nn1), z])) -> BOT -> 29
}
Sat witness: Found: ((append([_eo, cons(h1, nil), _fo]) /\ reverse([t1, _eo])) -> reverse([cons(h1, t1), _fo]), {
_eo -> cons(a, nil)  ;  _fo -> cons(a, cons(a, cons(b, cons(b, nil))))  ;  h1 -> b  ;  t1 -> cons(b, cons(a, nil))
})

-------------------------------------------
Step 57, which took 0.146760 s (model generation: 0.144423,  model checking: 0.002337):

Model:
|_
{
append -> 
{{{
Q={q_gen_3638, q_gen_3644, q_gen_3645, q_gen_3658, q_gen_3659, q_gen_3660, q_gen_3673, q_gen_3674},
Q_f={q_gen_3638},
Delta=
{
<cons>(q_gen_3659, q_gen_3658) -> q_gen_3658
<nil>() -> q_gen_3658
<a>() -> q_gen_3659
<b>() -> q_gen_3659
<cons, cons>(q_gen_3645, q_gen_3644) -> q_gen_3644
<nil, nil>() -> q_gen_3644
<a, a>() -> q_gen_3645
<b, b>() -> q_gen_3645
<cons, cons>(q_gen_3645, q_gen_3673) -> q_gen_3673
<nil, cons>(q_gen_3659, q_gen_3658) -> q_gen_3673
<cons, cons, cons>(q_gen_3660, q_gen_3638) -> q_gen_3638
<cons, nil, cons>(q_gen_3645, q_gen_3644) -> q_gen_3638
<cons, nil, cons>(q_gen_3645, q_gen_3673) -> q_gen_3638
<nil, cons, cons>(q_gen_3645, q_gen_3644) -> q_gen_3638
<nil, nil, cons>(q_gen_3659, q_gen_3658) -> q_gen_3638
<nil, nil, nil>() -> q_gen_3638
<a, a, a>() -> q_gen_3660
<a, b, a>() -> q_gen_3660
<b, a, b>() -> q_gen_3660
<b, b, b>() -> q_gen_3660
<cons, cons, cons>(q_gen_3660, q_gen_3674) -> q_gen_3674
<nil, cons, cons>(q_gen_3645, q_gen_3673) -> q_gen_3674
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_3637, q_gen_3641, q_gen_3642, q_gen_3665, q_gen_3666, q_gen_3667, q_gen_3668, q_gen_3669, q_gen_3692, q_gen_3693, q_gen_3694},
Q_f={q_gen_3637},
Delta=
{
<nil>() -> q_gen_3641
<cons>(q_gen_3666, q_gen_3641) -> q_gen_3665
<a>() -> q_gen_3666
<b>() -> q_gen_3666
<z>() -> q_gen_3668
<cons>(q_gen_3666, q_gen_3665) -> q_gen_3692
<cons>(q_gen_3666, q_gen_3692) -> q_gen_3692
<s>(q_gen_3668) -> q_gen_3694
<s>(q_gen_3694) -> q_gen_3694
<cons, s>(q_gen_3642, q_gen_3641) -> q_gen_3637
<cons, s>(q_gen_3667, q_gen_3665) -> q_gen_3637
<cons, s>(q_gen_3693, q_gen_3692) -> q_gen_3637
<nil, z>() -> q_gen_3637
<a, z>() -> q_gen_3642
<b, z>() -> q_gen_3642
<a, s>(q_gen_3668) -> q_gen_3667
<b, s>(q_gen_3668) -> q_gen_3667
<cons, s>(q_gen_3642, q_gen_3665) -> q_gen_3669
<cons, s>(q_gen_3642, q_gen_3692) -> q_gen_3669
<cons, s>(q_gen_3667, q_gen_3641) -> q_gen_3669
<cons, s>(q_gen_3693, q_gen_3641) -> q_gen_3669
<cons, s>(q_gen_3693, q_gen_3665) -> q_gen_3669
<b, s>(q_gen_3694) -> q_gen_3693
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3634, q_gen_3636, q_gen_3670},
Q_f={q_gen_3634},
Delta=
{
<s>(q_gen_3636) -> q_gen_3636
<z>() -> q_gen_3636
<s, s>(q_gen_3634) -> q_gen_3634
<z, s>(q_gen_3636) -> q_gen_3634
<z, z>() -> q_gen_3634
<s, s>(q_gen_3670) -> q_gen_3670
<s, z>(q_gen_3636) -> q_gen_3670
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3633, q_gen_3652, q_gen_3653, q_gen_3675, q_gen_3677, q_gen_3678, q_gen_3684, q_gen_3689},
Q_f={q_gen_3633, q_gen_3652, q_gen_3684},
Delta=
{
<nil>() -> q_gen_3677
<a>() -> q_gen_3678
<b>() -> q_gen_3678
<nil, nil>() -> q_gen_3633
<cons, cons>(q_gen_3653, q_gen_3633) -> q_gen_3652
<a, a>() -> q_gen_3653
<b, b>() -> q_gen_3653
<cons, cons>(q_gen_3653, q_gen_3675) -> q_gen_3675
<cons, cons>(q_gen_3653, q_gen_3684) -> q_gen_3675
<cons, cons>(q_gen_3689, q_gen_3633) -> q_gen_3675
<cons, cons>(q_gen_3689, q_gen_3684) -> q_gen_3675
<cons, nil>(q_gen_3678, q_gen_3677) -> q_gen_3675
<nil, cons>(q_gen_3678, q_gen_3677) -> q_gen_3675
<cons, cons>(q_gen_3653, q_gen_3652) -> q_gen_3684
<cons, cons>(q_gen_3689, q_gen_3675) -> q_gen_3684
<a, b>() -> q_gen_3689
<b, a>() -> q_gen_3689
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 29
() -> length([nil, z]) -> 29
() -> leq([z, s(nn2)]) -> 29
() -> leq([z, z]) -> 29
() -> reverse([nil, nil]) -> 29
(append([_eo, cons(h1, nil), _fo]) /\ reverse([t1, _eo])) -> reverse([cons(h1, t1), _fo]) -> 31
(append([t1, l2, _zn])) -> append([cons(h1, t1), l2, cons(h1, _zn)]) -> 31
(length([_oo, _po]) /\ length([l1, _no]) /\ reverse([l1, _oo])) -> leq([_no, _po]) -> 32
(length([_qo, _ro]) /\ length([l1, _so]) /\ reverse([l1, _qo])) -> leq([_ro, _so]) -> 31
(length([ll, _jo])) -> length([cons(x, ll), s(_jo)]) -> 31
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 30
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 30
(leq([s(nn1), z])) -> BOT -> 30
}
Sat witness: Found: ((length([_oo, _po]) /\ length([l1, _no]) /\ reverse([l1, _oo])) -> leq([_no, _po]), {
_no -> s(s(z))  ;  _oo -> cons(b, nil)  ;  _po -> s(z)  ;  l1 -> cons(a, cons(b, nil))
})

-------------------------------------------
Step 58, which took 0.149388 s (model generation: 0.146751,  model checking: 0.002637):

Model:
|_
{
append -> 
{{{
Q={q_gen_3638, q_gen_3643, q_gen_3644, q_gen_3645, q_gen_3658, q_gen_3659, q_gen_3660, q_gen_3673, q_gen_3674},
Q_f={q_gen_3638, q_gen_3643},
Delta=
{
<cons>(q_gen_3659, q_gen_3658) -> q_gen_3658
<nil>() -> q_gen_3658
<a>() -> q_gen_3659
<b>() -> q_gen_3659
<cons, cons>(q_gen_3645, q_gen_3644) -> q_gen_3644
<nil, nil>() -> q_gen_3644
<a, a>() -> q_gen_3645
<b, b>() -> q_gen_3645
<cons, cons>(q_gen_3645, q_gen_3673) -> q_gen_3673
<nil, cons>(q_gen_3659, q_gen_3658) -> q_gen_3673
<cons, cons, cons>(q_gen_3660, q_gen_3643) -> q_gen_3638
<nil, nil, nil>() -> q_gen_3638
<cons, nil, cons>(q_gen_3645, q_gen_3644) -> q_gen_3643
<cons, nil, cons>(q_gen_3645, q_gen_3673) -> q_gen_3643
<nil, cons, cons>(q_gen_3645, q_gen_3644) -> q_gen_3643
<nil, nil, cons>(q_gen_3659, q_gen_3658) -> q_gen_3643
<a, a, a>() -> q_gen_3660
<a, b, a>() -> q_gen_3660
<b, a, b>() -> q_gen_3660
<b, b, b>() -> q_gen_3660
<cons, cons, cons>(q_gen_3660, q_gen_3638) -> q_gen_3674
<cons, cons, cons>(q_gen_3660, q_gen_3674) -> q_gen_3674
<nil, cons, cons>(q_gen_3645, q_gen_3673) -> q_gen_3674
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_3637, q_gen_3641, q_gen_3642, q_gen_3665, q_gen_3666, q_gen_3667, q_gen_3668, q_gen_3669, q_gen_3692, q_gen_3693, q_gen_3694},
Q_f={q_gen_3637},
Delta=
{
<nil>() -> q_gen_3641
<cons>(q_gen_3666, q_gen_3641) -> q_gen_3665
<a>() -> q_gen_3666
<b>() -> q_gen_3666
<z>() -> q_gen_3668
<cons>(q_gen_3666, q_gen_3665) -> q_gen_3692
<cons>(q_gen_3666, q_gen_3692) -> q_gen_3692
<s>(q_gen_3668) -> q_gen_3694
<s>(q_gen_3694) -> q_gen_3694
<cons, s>(q_gen_3642, q_gen_3641) -> q_gen_3637
<cons, s>(q_gen_3667, q_gen_3665) -> q_gen_3637
<cons, s>(q_gen_3693, q_gen_3692) -> q_gen_3637
<nil, z>() -> q_gen_3637
<a, z>() -> q_gen_3642
<b, z>() -> q_gen_3642
<a, s>(q_gen_3668) -> q_gen_3667
<b, s>(q_gen_3668) -> q_gen_3667
<cons, s>(q_gen_3642, q_gen_3665) -> q_gen_3669
<cons, s>(q_gen_3642, q_gen_3692) -> q_gen_3669
<cons, s>(q_gen_3667, q_gen_3641) -> q_gen_3669
<cons, s>(q_gen_3693, q_gen_3641) -> q_gen_3669
<cons, s>(q_gen_3693, q_gen_3665) -> q_gen_3669
<b, s>(q_gen_3694) -> q_gen_3693
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3634, q_gen_3636, q_gen_3670},
Q_f={q_gen_3634},
Delta=
{
<s>(q_gen_3636) -> q_gen_3636
<z>() -> q_gen_3636
<s, s>(q_gen_3634) -> q_gen_3634
<z, s>(q_gen_3636) -> q_gen_3634
<z, z>() -> q_gen_3634
<s, s>(q_gen_3670) -> q_gen_3670
<s, z>(q_gen_3636) -> q_gen_3670
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3633, q_gen_3652, q_gen_3653, q_gen_3675, q_gen_3677, q_gen_3678, q_gen_3684},
Q_f={q_gen_3633, q_gen_3652, q_gen_3684},
Delta=
{
<nil>() -> q_gen_3677
<a>() -> q_gen_3678
<b>() -> q_gen_3678
<nil, nil>() -> q_gen_3633
<cons, cons>(q_gen_3653, q_gen_3633) -> q_gen_3652
<a, a>() -> q_gen_3653
<a, b>() -> q_gen_3653
<b, a>() -> q_gen_3653
<b, b>() -> q_gen_3653
<cons, cons>(q_gen_3653, q_gen_3675) -> q_gen_3675
<cons, cons>(q_gen_3653, q_gen_3684) -> q_gen_3675
<cons, nil>(q_gen_3678, q_gen_3677) -> q_gen_3675
<nil, cons>(q_gen_3678, q_gen_3677) -> q_gen_3675
<cons, cons>(q_gen_3653, q_gen_3652) -> q_gen_3684
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 30
() -> length([nil, z]) -> 30
() -> leq([z, s(nn2)]) -> 30
() -> leq([z, z]) -> 30
() -> reverse([nil, nil]) -> 30
(append([_eo, cons(h1, nil), _fo]) /\ reverse([t1, _eo])) -> reverse([cons(h1, t1), _fo]) -> 31
(append([t1, l2, _zn])) -> append([cons(h1, t1), l2, cons(h1, _zn)]) -> 31
(length([_oo, _po]) /\ length([l1, _no]) /\ reverse([l1, _oo])) -> leq([_no, _po]) -> 32
(length([_qo, _ro]) /\ length([l1, _so]) /\ reverse([l1, _qo])) -> leq([_ro, _so]) -> 31
(length([ll, _jo])) -> length([cons(x, ll), s(_jo)]) -> 34
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 31
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 31
(leq([s(nn1), z])) -> BOT -> 31
}
Sat witness: Found: ((length([ll, _jo])) -> length([cons(x, ll), s(_jo)]), {
_jo -> s(s(z))  ;  ll -> cons(a, cons(b, nil))  ;  x -> a
})

-------------------------------------------
Step 59, which took 0.170299 s (model generation: 0.167918,  model checking: 0.002381):

Model:
|_
{
append -> 
{{{
Q={q_gen_3638, q_gen_3643, q_gen_3644, q_gen_3645, q_gen_3658, q_gen_3659, q_gen_3660, q_gen_3673, q_gen_3674},
Q_f={q_gen_3638, q_gen_3643},
Delta=
{
<cons>(q_gen_3659, q_gen_3658) -> q_gen_3658
<nil>() -> q_gen_3658
<a>() -> q_gen_3659
<b>() -> q_gen_3659
<cons, cons>(q_gen_3645, q_gen_3644) -> q_gen_3644
<cons, cons>(q_gen_3645, q_gen_3673) -> q_gen_3644
<nil, nil>() -> q_gen_3644
<a, a>() -> q_gen_3645
<b, b>() -> q_gen_3645
<nil, cons>(q_gen_3659, q_gen_3658) -> q_gen_3673
<nil, cons, cons>(q_gen_3645, q_gen_3644) -> q_gen_3638
<nil, nil, nil>() -> q_gen_3638
<cons, cons, cons>(q_gen_3660, q_gen_3643) -> q_gen_3643
<cons, nil, cons>(q_gen_3645, q_gen_3644) -> q_gen_3643
<cons, nil, cons>(q_gen_3645, q_gen_3673) -> q_gen_3643
<nil, nil, cons>(q_gen_3659, q_gen_3658) -> q_gen_3643
<a, a, a>() -> q_gen_3660
<a, b, a>() -> q_gen_3660
<b, a, b>() -> q_gen_3660
<b, b, b>() -> q_gen_3660
<cons, cons, cons>(q_gen_3660, q_gen_3638) -> q_gen_3674
<cons, cons, cons>(q_gen_3660, q_gen_3674) -> q_gen_3674
<nil, cons, cons>(q_gen_3645, q_gen_3673) -> q_gen_3674
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_3637, q_gen_3641, q_gen_3642, q_gen_3665, q_gen_3666, q_gen_3667, q_gen_3668, q_gen_3669, q_gen_3692, q_gen_3693, q_gen_3694},
Q_f={q_gen_3637},
Delta=
{
<nil>() -> q_gen_3641
<cons>(q_gen_3666, q_gen_3641) -> q_gen_3665
<a>() -> q_gen_3666
<b>() -> q_gen_3666
<z>() -> q_gen_3668
<cons>(q_gen_3666, q_gen_3665) -> q_gen_3692
<cons>(q_gen_3666, q_gen_3692) -> q_gen_3692
<s>(q_gen_3668) -> q_gen_3694
<s>(q_gen_3694) -> q_gen_3694
<cons, s>(q_gen_3642, q_gen_3641) -> q_gen_3637
<cons, s>(q_gen_3642, q_gen_3692) -> q_gen_3637
<cons, s>(q_gen_3667, q_gen_3665) -> q_gen_3637
<cons, s>(q_gen_3693, q_gen_3692) -> q_gen_3637
<nil, z>() -> q_gen_3637
<a, s>(q_gen_3694) -> q_gen_3642
<a, z>() -> q_gen_3642
<b, z>() -> q_gen_3642
<a, s>(q_gen_3668) -> q_gen_3667
<b, s>(q_gen_3668) -> q_gen_3667
<cons, s>(q_gen_3642, q_gen_3665) -> q_gen_3669
<cons, s>(q_gen_3667, q_gen_3641) -> q_gen_3669
<cons, s>(q_gen_3693, q_gen_3641) -> q_gen_3669
<cons, s>(q_gen_3693, q_gen_3665) -> q_gen_3669
<b, s>(q_gen_3694) -> q_gen_3693
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3634, q_gen_3636, q_gen_3670},
Q_f={q_gen_3634},
Delta=
{
<s>(q_gen_3636) -> q_gen_3636
<z>() -> q_gen_3636
<s, s>(q_gen_3634) -> q_gen_3634
<z, s>(q_gen_3636) -> q_gen_3634
<z, z>() -> q_gen_3634
<s, s>(q_gen_3670) -> q_gen_3670
<s, z>(q_gen_3636) -> q_gen_3670
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3633, q_gen_3652, q_gen_3653, q_gen_3675, q_gen_3677, q_gen_3678, q_gen_3684},
Q_f={q_gen_3633, q_gen_3652, q_gen_3684},
Delta=
{
<nil>() -> q_gen_3677
<a>() -> q_gen_3678
<b>() -> q_gen_3678
<nil, nil>() -> q_gen_3633
<cons, cons>(q_gen_3653, q_gen_3633) -> q_gen_3652
<a, a>() -> q_gen_3653
<a, b>() -> q_gen_3653
<b, a>() -> q_gen_3653
<b, b>() -> q_gen_3653
<cons, cons>(q_gen_3653, q_gen_3675) -> q_gen_3675
<cons, cons>(q_gen_3653, q_gen_3684) -> q_gen_3675
<cons, nil>(q_gen_3678, q_gen_3677) -> q_gen_3675
<nil, cons>(q_gen_3678, q_gen_3677) -> q_gen_3675
<cons, cons>(q_gen_3653, q_gen_3652) -> q_gen_3684
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 31
() -> length([nil, z]) -> 31
() -> leq([z, s(nn2)]) -> 31
() -> leq([z, z]) -> 31
() -> reverse([nil, nil]) -> 31
(append([_eo, cons(h1, nil), _fo]) /\ reverse([t1, _eo])) -> reverse([cons(h1, t1), _fo]) -> 31
(append([t1, l2, _zn])) -> append([cons(h1, t1), l2, cons(h1, _zn)]) -> 31
(length([_oo, _po]) /\ length([l1, _no]) /\ reverse([l1, _oo])) -> leq([_no, _po]) -> 32
(length([_qo, _ro]) /\ length([l1, _so]) /\ reverse([l1, _qo])) -> leq([_ro, _so]) -> 34
(length([ll, _jo])) -> length([cons(x, ll), s(_jo)]) -> 34
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 32
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 32
(leq([s(nn1), z])) -> BOT -> 32
}
Sat witness: Found: ((length([_qo, _ro]) /\ length([l1, _so]) /\ reverse([l1, _qo])) -> leq([_ro, _so]), {
_qo -> cons(a, nil)  ;  _ro -> s(s(s(z)))  ;  _so -> s(z)  ;  l1 -> cons(b, nil)
})

-------------------------------------------
Step 60, which took 0.193249 s (model generation: 0.192098,  model checking: 0.001151):

Model:
|_
{
append -> 
{{{
Q={q_gen_3638, q_gen_3643, q_gen_3644, q_gen_3645, q_gen_3658, q_gen_3659, q_gen_3660, q_gen_3673, q_gen_3674},
Q_f={q_gen_3638, q_gen_3643},
Delta=
{
<cons>(q_gen_3659, q_gen_3658) -> q_gen_3658
<nil>() -> q_gen_3658
<a>() -> q_gen_3659
<b>() -> q_gen_3659
<cons, cons>(q_gen_3645, q_gen_3644) -> q_gen_3644
<cons, cons>(q_gen_3645, q_gen_3673) -> q_gen_3644
<nil, nil>() -> q_gen_3644
<a, a>() -> q_gen_3645
<b, b>() -> q_gen_3645
<nil, cons>(q_gen_3659, q_gen_3658) -> q_gen_3673
<nil, nil, nil>() -> q_gen_3638
<cons, cons, cons>(q_gen_3660, q_gen_3643) -> q_gen_3643
<cons, nil, cons>(q_gen_3645, q_gen_3644) -> q_gen_3643
<cons, nil, cons>(q_gen_3645, q_gen_3673) -> q_gen_3643
<nil, cons, cons>(q_gen_3645, q_gen_3644) -> q_gen_3643
<nil, nil, cons>(q_gen_3659, q_gen_3658) -> q_gen_3643
<a, a, a>() -> q_gen_3660
<a, b, a>() -> q_gen_3660
<b, a, b>() -> q_gen_3660
<b, b, b>() -> q_gen_3660
<cons, cons, cons>(q_gen_3660, q_gen_3638) -> q_gen_3674
<cons, cons, cons>(q_gen_3660, q_gen_3674) -> q_gen_3674
<nil, cons, cons>(q_gen_3645, q_gen_3673) -> q_gen_3674
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_3637, q_gen_3641, q_gen_3642, q_gen_3665, q_gen_3666, q_gen_3667, q_gen_3668, q_gen_3669, q_gen_3692, q_gen_3693, q_gen_3694},
Q_f={q_gen_3637},
Delta=
{
<nil>() -> q_gen_3641
<cons>(q_gen_3666, q_gen_3641) -> q_gen_3665
<a>() -> q_gen_3666
<b>() -> q_gen_3666
<z>() -> q_gen_3668
<cons>(q_gen_3666, q_gen_3665) -> q_gen_3692
<cons>(q_gen_3666, q_gen_3692) -> q_gen_3692
<s>(q_gen_3668) -> q_gen_3694
<s>(q_gen_3694) -> q_gen_3694
<cons, s>(q_gen_3642, q_gen_3641) -> q_gen_3637
<cons, s>(q_gen_3667, q_gen_3665) -> q_gen_3637
<cons, s>(q_gen_3667, q_gen_3692) -> q_gen_3637
<cons, s>(q_gen_3693, q_gen_3692) -> q_gen_3637
<nil, z>() -> q_gen_3637
<a, z>() -> q_gen_3642
<b, z>() -> q_gen_3642
<a, s>(q_gen_3668) -> q_gen_3667
<a, s>(q_gen_3694) -> q_gen_3667
<b, s>(q_gen_3668) -> q_gen_3667
<cons, s>(q_gen_3642, q_gen_3665) -> q_gen_3669
<cons, s>(q_gen_3642, q_gen_3692) -> q_gen_3669
<cons, s>(q_gen_3667, q_gen_3641) -> q_gen_3669
<cons, s>(q_gen_3693, q_gen_3641) -> q_gen_3669
<cons, s>(q_gen_3693, q_gen_3665) -> q_gen_3669
<b, s>(q_gen_3694) -> q_gen_3693
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3634, q_gen_3636, q_gen_3670},
Q_f={q_gen_3634},
Delta=
{
<s>(q_gen_3636) -> q_gen_3636
<z>() -> q_gen_3636
<s, s>(q_gen_3634) -> q_gen_3634
<z, s>(q_gen_3636) -> q_gen_3634
<z, z>() -> q_gen_3634
<s, s>(q_gen_3670) -> q_gen_3670
<s, z>(q_gen_3636) -> q_gen_3670
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3633, q_gen_3652, q_gen_3653, q_gen_3675, q_gen_3677, q_gen_3678, q_gen_3684},
Q_f={q_gen_3633, q_gen_3652, q_gen_3684},
Delta=
{
<nil>() -> q_gen_3677
<a>() -> q_gen_3678
<b>() -> q_gen_3678
<nil, nil>() -> q_gen_3633
<cons, cons>(q_gen_3653, q_gen_3633) -> q_gen_3652
<a, a>() -> q_gen_3653
<a, b>() -> q_gen_3653
<b, a>() -> q_gen_3653
<b, b>() -> q_gen_3653
<cons, cons>(q_gen_3653, q_gen_3675) -> q_gen_3675
<cons, cons>(q_gen_3653, q_gen_3684) -> q_gen_3675
<cons, nil>(q_gen_3678, q_gen_3677) -> q_gen_3675
<nil, cons>(q_gen_3678, q_gen_3677) -> q_gen_3675
<cons, cons>(q_gen_3653, q_gen_3652) -> q_gen_3684
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 31
() -> length([nil, z]) -> 31
() -> leq([z, s(nn2)]) -> 31
() -> leq([z, z]) -> 31
() -> reverse([nil, nil]) -> 31
(append([_eo, cons(h1, nil), _fo]) /\ reverse([t1, _eo])) -> reverse([cons(h1, t1), _fo]) -> 31
(append([t1, l2, _zn])) -> append([cons(h1, t1), l2, cons(h1, _zn)]) -> 34
(length([_oo, _po]) /\ length([l1, _no]) /\ reverse([l1, _oo])) -> leq([_no, _po]) -> 32
(length([_qo, _ro]) /\ length([l1, _so]) /\ reverse([l1, _qo])) -> leq([_ro, _so]) -> 34
(length([ll, _jo])) -> length([cons(x, ll), s(_jo)]) -> 34
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 32
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 32
(leq([s(nn1), z])) -> BOT -> 32
}
Sat witness: Found: ((append([t1, l2, _zn])) -> append([cons(h1, t1), l2, cons(h1, _zn)]), {
_zn -> cons(a, cons(a, nil))  ;  h1 -> a  ;  l2 -> cons(a, cons(a, nil))  ;  t1 -> nil
})

-------------------------------------------
Step 61, which took 0.202354 s (model generation: 0.200876,  model checking: 0.001478):

Model:
|_
{
append -> 
{{{
Q={q_gen_3638, q_gen_3643, q_gen_3644, q_gen_3645, q_gen_3658, q_gen_3659, q_gen_3660, q_gen_3673, q_gen_3674},
Q_f={q_gen_3638, q_gen_3643},
Delta=
{
<cons>(q_gen_3659, q_gen_3658) -> q_gen_3658
<nil>() -> q_gen_3658
<a>() -> q_gen_3659
<b>() -> q_gen_3659
<cons, cons>(q_gen_3645, q_gen_3644) -> q_gen_3644
<cons, cons>(q_gen_3645, q_gen_3673) -> q_gen_3644
<nil, nil>() -> q_gen_3644
<a, a>() -> q_gen_3645
<b, b>() -> q_gen_3645
<nil, cons>(q_gen_3659, q_gen_3658) -> q_gen_3673
<cons, cons, cons>(q_gen_3660, q_gen_3674) -> q_gen_3638
<nil, nil, nil>() -> q_gen_3638
<cons, cons, cons>(q_gen_3660, q_gen_3643) -> q_gen_3643
<cons, nil, cons>(q_gen_3645, q_gen_3644) -> q_gen_3643
<cons, nil, cons>(q_gen_3645, q_gen_3673) -> q_gen_3643
<nil, cons, cons>(q_gen_3645, q_gen_3644) -> q_gen_3643
<nil, nil, cons>(q_gen_3659, q_gen_3658) -> q_gen_3643
<a, a, a>() -> q_gen_3660
<a, b, a>() -> q_gen_3660
<b, a, b>() -> q_gen_3660
<b, b, b>() -> q_gen_3660
<cons, cons, cons>(q_gen_3660, q_gen_3638) -> q_gen_3674
<nil, cons, cons>(q_gen_3645, q_gen_3673) -> q_gen_3674
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_3637, q_gen_3641, q_gen_3642, q_gen_3665, q_gen_3666, q_gen_3667, q_gen_3668, q_gen_3669, q_gen_3692, q_gen_3693, q_gen_3694},
Q_f={q_gen_3637},
Delta=
{
<nil>() -> q_gen_3641
<cons>(q_gen_3666, q_gen_3641) -> q_gen_3665
<a>() -> q_gen_3666
<b>() -> q_gen_3666
<z>() -> q_gen_3668
<cons>(q_gen_3666, q_gen_3665) -> q_gen_3692
<cons>(q_gen_3666, q_gen_3692) -> q_gen_3692
<s>(q_gen_3668) -> q_gen_3694
<s>(q_gen_3694) -> q_gen_3694
<cons, s>(q_gen_3642, q_gen_3641) -> q_gen_3637
<cons, s>(q_gen_3667, q_gen_3665) -> q_gen_3637
<cons, s>(q_gen_3667, q_gen_3692) -> q_gen_3637
<cons, s>(q_gen_3693, q_gen_3692) -> q_gen_3637
<nil, z>() -> q_gen_3637
<a, z>() -> q_gen_3642
<b, z>() -> q_gen_3642
<a, s>(q_gen_3668) -> q_gen_3667
<a, s>(q_gen_3694) -> q_gen_3667
<b, s>(q_gen_3668) -> q_gen_3667
<cons, s>(q_gen_3642, q_gen_3665) -> q_gen_3669
<cons, s>(q_gen_3642, q_gen_3692) -> q_gen_3669
<cons, s>(q_gen_3667, q_gen_3641) -> q_gen_3669
<cons, s>(q_gen_3693, q_gen_3641) -> q_gen_3669
<cons, s>(q_gen_3693, q_gen_3665) -> q_gen_3669
<b, s>(q_gen_3694) -> q_gen_3693
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3634, q_gen_3636, q_gen_3670},
Q_f={q_gen_3634},
Delta=
{
<s>(q_gen_3636) -> q_gen_3636
<z>() -> q_gen_3636
<s, s>(q_gen_3634) -> q_gen_3634
<z, s>(q_gen_3636) -> q_gen_3634
<z, z>() -> q_gen_3634
<s, s>(q_gen_3670) -> q_gen_3670
<s, z>(q_gen_3636) -> q_gen_3670
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3633, q_gen_3652, q_gen_3653, q_gen_3675, q_gen_3677, q_gen_3678, q_gen_3684},
Q_f={q_gen_3633, q_gen_3652, q_gen_3684},
Delta=
{
<nil>() -> q_gen_3677
<a>() -> q_gen_3678
<b>() -> q_gen_3678
<nil, nil>() -> q_gen_3633
<cons, cons>(q_gen_3653, q_gen_3633) -> q_gen_3652
<a, a>() -> q_gen_3653
<a, b>() -> q_gen_3653
<b, a>() -> q_gen_3653
<b, b>() -> q_gen_3653
<cons, cons>(q_gen_3653, q_gen_3675) -> q_gen_3675
<cons, cons>(q_gen_3653, q_gen_3684) -> q_gen_3675
<cons, nil>(q_gen_3678, q_gen_3677) -> q_gen_3675
<nil, cons>(q_gen_3678, q_gen_3677) -> q_gen_3675
<cons, cons>(q_gen_3653, q_gen_3652) -> q_gen_3684
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 31
() -> length([nil, z]) -> 31
() -> leq([z, s(nn2)]) -> 31
() -> leq([z, z]) -> 31
() -> reverse([nil, nil]) -> 31
(append([_eo, cons(h1, nil), _fo]) /\ reverse([t1, _eo])) -> reverse([cons(h1, t1), _fo]) -> 34
(append([t1, l2, _zn])) -> append([cons(h1, t1), l2, cons(h1, _zn)]) -> 34
(length([_oo, _po]) /\ length([l1, _no]) /\ reverse([l1, _oo])) -> leq([_no, _po]) -> 32
(length([_qo, _ro]) /\ length([l1, _so]) /\ reverse([l1, _qo])) -> leq([_ro, _so]) -> 34
(length([ll, _jo])) -> length([cons(x, ll), s(_jo)]) -> 34
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 32
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 32
(leq([s(nn1), z])) -> BOT -> 32
}
Sat witness: Found: ((append([_eo, cons(h1, nil), _fo]) /\ reverse([t1, _eo])) -> reverse([cons(h1, t1), _fo]), {
_eo -> cons(a, cons(b, nil))  ;  _fo -> cons(a, cons(b, cons(b, nil)))  ;  h1 -> a  ;  t1 -> cons(a, cons(a, nil))
})

-------------------------------------------
Step 62, which took 0.284122 s (model generation: 0.283185,  model checking: 0.000937):

Model:
|_
{
append -> 
{{{
Q={q_gen_3638, q_gen_3643, q_gen_3644, q_gen_3645, q_gen_3658, q_gen_3659, q_gen_3660, q_gen_3673, q_gen_3674},
Q_f={q_gen_3638, q_gen_3643},
Delta=
{
<cons>(q_gen_3659, q_gen_3658) -> q_gen_3658
<nil>() -> q_gen_3658
<a>() -> q_gen_3659
<b>() -> q_gen_3659
<cons, cons>(q_gen_3645, q_gen_3644) -> q_gen_3644
<nil, nil>() -> q_gen_3644
<a, a>() -> q_gen_3645
<b, b>() -> q_gen_3645
<cons, cons>(q_gen_3645, q_gen_3673) -> q_gen_3673
<nil, cons>(q_gen_3659, q_gen_3658) -> q_gen_3673
<cons, cons, cons>(q_gen_3660, q_gen_3674) -> q_gen_3638
<nil, cons, cons>(q_gen_3645, q_gen_3644) -> q_gen_3638
<nil, nil, nil>() -> q_gen_3638
<cons, cons, cons>(q_gen_3660, q_gen_3643) -> q_gen_3643
<cons, nil, cons>(q_gen_3645, q_gen_3644) -> q_gen_3643
<cons, nil, cons>(q_gen_3645, q_gen_3673) -> q_gen_3643
<nil, nil, cons>(q_gen_3659, q_gen_3658) -> q_gen_3643
<a, a, a>() -> q_gen_3660
<a, b, a>() -> q_gen_3660
<b, a, b>() -> q_gen_3660
<b, b, b>() -> q_gen_3660
<cons, cons, cons>(q_gen_3660, q_gen_3638) -> q_gen_3674
<nil, cons, cons>(q_gen_3645, q_gen_3673) -> q_gen_3674
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_3637, q_gen_3641, q_gen_3642, q_gen_3665, q_gen_3666, q_gen_3667, q_gen_3668, q_gen_3669, q_gen_3692, q_gen_3693, q_gen_3694},
Q_f={q_gen_3637},
Delta=
{
<nil>() -> q_gen_3641
<cons>(q_gen_3666, q_gen_3641) -> q_gen_3665
<a>() -> q_gen_3666
<b>() -> q_gen_3666
<z>() -> q_gen_3668
<cons>(q_gen_3666, q_gen_3665) -> q_gen_3692
<cons>(q_gen_3666, q_gen_3692) -> q_gen_3692
<s>(q_gen_3668) -> q_gen_3694
<s>(q_gen_3694) -> q_gen_3694
<cons, s>(q_gen_3642, q_gen_3641) -> q_gen_3637
<cons, s>(q_gen_3667, q_gen_3665) -> q_gen_3637
<cons, s>(q_gen_3667, q_gen_3692) -> q_gen_3637
<cons, s>(q_gen_3693, q_gen_3692) -> q_gen_3637
<nil, z>() -> q_gen_3637
<a, z>() -> q_gen_3642
<b, z>() -> q_gen_3642
<a, s>(q_gen_3668) -> q_gen_3667
<a, s>(q_gen_3694) -> q_gen_3667
<b, s>(q_gen_3668) -> q_gen_3667
<cons, s>(q_gen_3642, q_gen_3665) -> q_gen_3669
<cons, s>(q_gen_3642, q_gen_3692) -> q_gen_3669
<cons, s>(q_gen_3667, q_gen_3641) -> q_gen_3669
<cons, s>(q_gen_3693, q_gen_3641) -> q_gen_3669
<cons, s>(q_gen_3693, q_gen_3665) -> q_gen_3669
<b, s>(q_gen_3694) -> q_gen_3693
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3634, q_gen_3636, q_gen_3670, q_gen_3671, q_gen_3699},
Q_f={q_gen_3634},
Delta=
{
<s>(q_gen_3636) -> q_gen_3636
<z>() -> q_gen_3636
<s, s>(q_gen_3634) -> q_gen_3634
<s, s>(q_gen_3699) -> q_gen_3634
<z, s>(q_gen_3636) -> q_gen_3634
<z, z>() -> q_gen_3634
<s, s>(q_gen_3671) -> q_gen_3670
<s, z>(q_gen_3636) -> q_gen_3671
<s, s>(q_gen_3670) -> q_gen_3699
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3633, q_gen_3653, q_gen_3675, q_gen_3677, q_gen_3678},
Q_f={q_gen_3633},
Delta=
{
<nil>() -> q_gen_3677
<a>() -> q_gen_3678
<b>() -> q_gen_3678
<cons, cons>(q_gen_3653, q_gen_3633) -> q_gen_3633
<nil, nil>() -> q_gen_3633
<a, a>() -> q_gen_3653
<a, b>() -> q_gen_3653
<b, a>() -> q_gen_3653
<b, b>() -> q_gen_3653
<cons, cons>(q_gen_3653, q_gen_3675) -> q_gen_3675
<cons, nil>(q_gen_3678, q_gen_3677) -> q_gen_3675
<nil, cons>(q_gen_3678, q_gen_3677) -> q_gen_3675
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 32
() -> length([nil, z]) -> 32
() -> leq([z, s(nn2)]) -> 32
() -> leq([z, z]) -> 32
() -> reverse([nil, nil]) -> 32
(append([_eo, cons(h1, nil), _fo]) /\ reverse([t1, _eo])) -> reverse([cons(h1, t1), _fo]) -> 34
(append([t1, l2, _zn])) -> append([cons(h1, t1), l2, cons(h1, _zn)]) -> 34
(length([_oo, _po]) /\ length([l1, _no]) /\ reverse([l1, _oo])) -> leq([_no, _po]) -> 32
(length([_qo, _ro]) /\ length([l1, _so]) /\ reverse([l1, _qo])) -> leq([_ro, _so]) -> 34
(length([ll, _jo])) -> length([cons(x, ll), s(_jo)]) -> 34
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 32
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 35
(leq([s(nn1), z])) -> BOT -> 33
}
Sat witness: Found: ((leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]), {
nn1 -> s(s(s(z)))  ;  nn2 -> s(s(z))
})

-------------------------------------------
Step 63, which took 0.324629 s (model generation: 0.323454,  model checking: 0.001175):

Model:
|_
{
append -> 
{{{
Q={q_gen_3638, q_gen_3644, q_gen_3645, q_gen_3658, q_gen_3659, q_gen_3660, q_gen_3673, q_gen_3674},
Q_f={q_gen_3638},
Delta=
{
<cons>(q_gen_3659, q_gen_3658) -> q_gen_3658
<nil>() -> q_gen_3658
<a>() -> q_gen_3659
<b>() -> q_gen_3659
<cons, cons>(q_gen_3645, q_gen_3644) -> q_gen_3644
<cons, cons>(q_gen_3645, q_gen_3673) -> q_gen_3644
<nil, nil>() -> q_gen_3644
<a, a>() -> q_gen_3645
<b, b>() -> q_gen_3645
<nil, cons>(q_gen_3659, q_gen_3658) -> q_gen_3673
<cons, cons, cons>(q_gen_3660, q_gen_3638) -> q_gen_3638
<cons, cons, cons>(q_gen_3660, q_gen_3674) -> q_gen_3638
<cons, nil, cons>(q_gen_3645, q_gen_3644) -> q_gen_3638
<cons, nil, cons>(q_gen_3645, q_gen_3673) -> q_gen_3638
<nil, cons, cons>(q_gen_3645, q_gen_3644) -> q_gen_3638
<nil, nil, cons>(q_gen_3659, q_gen_3658) -> q_gen_3638
<nil, nil, nil>() -> q_gen_3638
<a, a, a>() -> q_gen_3660
<a, b, a>() -> q_gen_3660
<b, a, b>() -> q_gen_3660
<b, b, b>() -> q_gen_3660
<nil, cons, cons>(q_gen_3645, q_gen_3673) -> q_gen_3674
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_3637, q_gen_3641, q_gen_3642, q_gen_3665, q_gen_3666, q_gen_3667, q_gen_3668, q_gen_3669, q_gen_3692, q_gen_3693, q_gen_3694},
Q_f={q_gen_3637},
Delta=
{
<nil>() -> q_gen_3641
<cons>(q_gen_3666, q_gen_3641) -> q_gen_3665
<a>() -> q_gen_3666
<b>() -> q_gen_3666
<z>() -> q_gen_3668
<cons>(q_gen_3666, q_gen_3665) -> q_gen_3692
<cons>(q_gen_3666, q_gen_3692) -> q_gen_3692
<s>(q_gen_3668) -> q_gen_3694
<s>(q_gen_3694) -> q_gen_3694
<cons, s>(q_gen_3642, q_gen_3641) -> q_gen_3637
<cons, s>(q_gen_3667, q_gen_3665) -> q_gen_3637
<cons, s>(q_gen_3667, q_gen_3692) -> q_gen_3637
<cons, s>(q_gen_3693, q_gen_3692) -> q_gen_3637
<nil, z>() -> q_gen_3637
<a, z>() -> q_gen_3642
<b, z>() -> q_gen_3642
<a, s>(q_gen_3668) -> q_gen_3667
<a, s>(q_gen_3694) -> q_gen_3667
<b, s>(q_gen_3668) -> q_gen_3667
<cons, s>(q_gen_3642, q_gen_3665) -> q_gen_3669
<cons, s>(q_gen_3642, q_gen_3692) -> q_gen_3669
<cons, s>(q_gen_3667, q_gen_3641) -> q_gen_3669
<cons, s>(q_gen_3693, q_gen_3641) -> q_gen_3669
<cons, s>(q_gen_3693, q_gen_3665) -> q_gen_3669
<b, s>(q_gen_3694) -> q_gen_3693
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3634, q_gen_3636, q_gen_3670},
Q_f={q_gen_3634},
Delta=
{
<s>(q_gen_3636) -> q_gen_3636
<z>() -> q_gen_3636
<s, s>(q_gen_3634) -> q_gen_3634
<z, s>(q_gen_3636) -> q_gen_3634
<z, z>() -> q_gen_3634
<s, s>(q_gen_3670) -> q_gen_3670
<s, z>(q_gen_3636) -> q_gen_3670
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3633, q_gen_3652, q_gen_3653, q_gen_3663, q_gen_3675, q_gen_3677, q_gen_3678, q_gen_3698, q_gen_3704},
Q_f={q_gen_3633, q_gen_3652, q_gen_3698},
Delta=
{
<nil>() -> q_gen_3677
<b>() -> q_gen_3678
<a>() -> q_gen_3704
<cons, cons>(q_gen_3663, q_gen_3633) -> q_gen_3633
<nil, nil>() -> q_gen_3633
<cons, cons>(q_gen_3653, q_gen_3633) -> q_gen_3652
<cons, nil>(q_gen_3704, q_gen_3677) -> q_gen_3652
<b, b>() -> q_gen_3653
<a, a>() -> q_gen_3663
<a, b>() -> q_gen_3663
<b, a>() -> q_gen_3663
<cons, cons>(q_gen_3653, q_gen_3675) -> q_gen_3675
<cons, cons>(q_gen_3653, q_gen_3698) -> q_gen_3675
<cons, cons>(q_gen_3663, q_gen_3652) -> q_gen_3675
<cons, cons>(q_gen_3663, q_gen_3675) -> q_gen_3675
<cons, nil>(q_gen_3678, q_gen_3677) -> q_gen_3675
<nil, cons>(q_gen_3678, q_gen_3677) -> q_gen_3675
<cons, cons>(q_gen_3653, q_gen_3652) -> q_gen_3698
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 32
() -> length([nil, z]) -> 32
() -> leq([z, s(nn2)]) -> 32
() -> leq([z, z]) -> 32
() -> reverse([nil, nil]) -> 32
(append([_eo, cons(h1, nil), _fo]) /\ reverse([t1, _eo])) -> reverse([cons(h1, t1), _fo]) -> 34
(append([t1, l2, _zn])) -> append([cons(h1, t1), l2, cons(h1, _zn)]) -> 34
(length([_oo, _po]) /\ length([l1, _no]) /\ reverse([l1, _oo])) -> leq([_no, _po]) -> 35
(length([_qo, _ro]) /\ length([l1, _so]) /\ reverse([l1, _qo])) -> leq([_ro, _so]) -> 34
(length([ll, _jo])) -> length([cons(x, ll), s(_jo)]) -> 34
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 33
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 35
(leq([s(nn1), z])) -> BOT -> 33
}
Sat witness: Found: ((length([_oo, _po]) /\ length([l1, _no]) /\ reverse([l1, _oo])) -> leq([_no, _po]), {
_no -> s(s(z))  ;  _oo -> cons(b, nil)  ;  _po -> s(z)  ;  l1 -> cons(b, cons(a, nil))
})

-------------------------------------------
Step 64, which took 0.245827 s (model generation: 0.242566,  model checking: 0.003261):

Model:
|_
{
append -> 
{{{
Q={q_gen_3638, q_gen_3643, q_gen_3644, q_gen_3645, q_gen_3658, q_gen_3659, q_gen_3660, q_gen_3673, q_gen_3674},
Q_f={q_gen_3638, q_gen_3643},
Delta=
{
<cons>(q_gen_3659, q_gen_3658) -> q_gen_3658
<nil>() -> q_gen_3658
<a>() -> q_gen_3659
<b>() -> q_gen_3659
<cons, cons>(q_gen_3645, q_gen_3644) -> q_gen_3644
<nil, nil>() -> q_gen_3644
<a, a>() -> q_gen_3645
<b, b>() -> q_gen_3645
<cons, cons>(q_gen_3645, q_gen_3673) -> q_gen_3673
<nil, cons>(q_gen_3659, q_gen_3658) -> q_gen_3673
<nil, cons, cons>(q_gen_3645, q_gen_3644) -> q_gen_3638
<nil, nil, nil>() -> q_gen_3638
<cons, cons, cons>(q_gen_3660, q_gen_3643) -> q_gen_3643
<cons, cons, cons>(q_gen_3660, q_gen_3674) -> q_gen_3643
<cons, nil, cons>(q_gen_3645, q_gen_3644) -> q_gen_3643
<cons, nil, cons>(q_gen_3645, q_gen_3673) -> q_gen_3643
<nil, nil, cons>(q_gen_3659, q_gen_3658) -> q_gen_3643
<a, a, a>() -> q_gen_3660
<a, b, a>() -> q_gen_3660
<b, a, b>() -> q_gen_3660
<b, b, b>() -> q_gen_3660
<cons, cons, cons>(q_gen_3660, q_gen_3638) -> q_gen_3674
<nil, cons, cons>(q_gen_3645, q_gen_3673) -> q_gen_3674
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_3637, q_gen_3641, q_gen_3642, q_gen_3665, q_gen_3666, q_gen_3667, q_gen_3668, q_gen_3669, q_gen_3692, q_gen_3693, q_gen_3694},
Q_f={q_gen_3637},
Delta=
{
<nil>() -> q_gen_3641
<cons>(q_gen_3666, q_gen_3641) -> q_gen_3665
<a>() -> q_gen_3666
<b>() -> q_gen_3666
<z>() -> q_gen_3668
<cons>(q_gen_3666, q_gen_3665) -> q_gen_3692
<cons>(q_gen_3666, q_gen_3692) -> q_gen_3692
<s>(q_gen_3668) -> q_gen_3694
<s>(q_gen_3694) -> q_gen_3694
<cons, s>(q_gen_3642, q_gen_3641) -> q_gen_3637
<cons, s>(q_gen_3667, q_gen_3665) -> q_gen_3637
<cons, s>(q_gen_3667, q_gen_3692) -> q_gen_3637
<cons, s>(q_gen_3693, q_gen_3692) -> q_gen_3637
<nil, z>() -> q_gen_3637
<a, z>() -> q_gen_3642
<b, z>() -> q_gen_3642
<a, s>(q_gen_3668) -> q_gen_3667
<a, s>(q_gen_3694) -> q_gen_3667
<b, s>(q_gen_3668) -> q_gen_3667
<cons, s>(q_gen_3642, q_gen_3665) -> q_gen_3669
<cons, s>(q_gen_3642, q_gen_3692) -> q_gen_3669
<cons, s>(q_gen_3667, q_gen_3641) -> q_gen_3669
<cons, s>(q_gen_3693, q_gen_3641) -> q_gen_3669
<cons, s>(q_gen_3693, q_gen_3665) -> q_gen_3669
<b, s>(q_gen_3694) -> q_gen_3693
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3634, q_gen_3636, q_gen_3670},
Q_f={q_gen_3634},
Delta=
{
<s>(q_gen_3636) -> q_gen_3636
<z>() -> q_gen_3636
<s, s>(q_gen_3634) -> q_gen_3634
<z, s>(q_gen_3636) -> q_gen_3634
<z, z>() -> q_gen_3634
<s, s>(q_gen_3670) -> q_gen_3670
<s, z>(q_gen_3636) -> q_gen_3670
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3633, q_gen_3652, q_gen_3653, q_gen_3663, q_gen_3675, q_gen_3677, q_gen_3678, q_gen_3698},
Q_f={q_gen_3633, q_gen_3652, q_gen_3698},
Delta=
{
<nil>() -> q_gen_3677
<a>() -> q_gen_3678
<b>() -> q_gen_3678
<cons, cons>(q_gen_3663, q_gen_3633) -> q_gen_3633
<nil, nil>() -> q_gen_3633
<cons, cons>(q_gen_3653, q_gen_3633) -> q_gen_3652
<cons, cons>(q_gen_3663, q_gen_3652) -> q_gen_3652
<b, b>() -> q_gen_3653
<a, a>() -> q_gen_3663
<a, b>() -> q_gen_3663
<b, a>() -> q_gen_3663
<cons, cons>(q_gen_3653, q_gen_3675) -> q_gen_3675
<cons, cons>(q_gen_3653, q_gen_3698) -> q_gen_3675
<cons, cons>(q_gen_3663, q_gen_3675) -> q_gen_3675
<cons, nil>(q_gen_3678, q_gen_3677) -> q_gen_3675
<nil, cons>(q_gen_3678, q_gen_3677) -> q_gen_3675
<cons, cons>(q_gen_3653, q_gen_3652) -> q_gen_3698
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 33
() -> length([nil, z]) -> 33
() -> leq([z, s(nn2)]) -> 33
() -> leq([z, z]) -> 33
() -> reverse([nil, nil]) -> 33
(append([_eo, cons(h1, nil), _fo]) /\ reverse([t1, _eo])) -> reverse([cons(h1, t1), _fo]) -> 34
(append([t1, l2, _zn])) -> append([cons(h1, t1), l2, cons(h1, _zn)]) -> 34
(length([_oo, _po]) /\ length([l1, _no]) /\ reverse([l1, _oo])) -> leq([_no, _po]) -> 35
(length([_qo, _ro]) /\ length([l1, _so]) /\ reverse([l1, _qo])) -> leq([_ro, _so]) -> 37
(length([ll, _jo])) -> length([cons(x, ll), s(_jo)]) -> 35
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 34
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 35
(leq([s(nn1), z])) -> BOT -> 34
}
Sat witness: Found: ((length([_qo, _ro]) /\ length([l1, _so]) /\ reverse([l1, _qo])) -> leq([_ro, _so]), {
_qo -> cons(b, cons(b, cons(a, nil)))  ;  _ro -> s(s(s(z)))  ;  _so -> s(s(z))  ;  l1 -> cons(b, cons(b, cons(b, nil)))
})

-------------------------------------------
Step 65, which took 0.249517 s (model generation: 0.248792,  model checking: 0.000725):

Model:
|_
{
append -> 
{{{
Q={q_gen_3638, q_gen_3644, q_gen_3645, q_gen_3649, q_gen_3650, q_gen_3658, q_gen_3659, q_gen_3660, q_gen_3661},
Q_f={q_gen_3638},
Delta=
{
<cons>(q_gen_3659, q_gen_3658) -> q_gen_3658
<nil>() -> q_gen_3658
<a>() -> q_gen_3659
<b>() -> q_gen_3659
<cons, cons>(q_gen_3645, q_gen_3649) -> q_gen_3644
<nil, nil>() -> q_gen_3644
<b, b>() -> q_gen_3645
<cons, cons>(q_gen_3650, q_gen_3644) -> q_gen_3649
<nil, cons>(q_gen_3659, q_gen_3658) -> q_gen_3649
<a, a>() -> q_gen_3650
<cons, cons, cons>(q_gen_3660, q_gen_3638) -> q_gen_3638
<cons, nil, cons>(q_gen_3645, q_gen_3644) -> q_gen_3638
<cons, nil, cons>(q_gen_3645, q_gen_3649) -> q_gen_3638
<nil, cons, cons>(q_gen_3645, q_gen_3644) -> q_gen_3638
<nil, cons, cons>(q_gen_3650, q_gen_3649) -> q_gen_3638
<nil, nil, cons>(q_gen_3659, q_gen_3658) -> q_gen_3638
<nil, nil, nil>() -> q_gen_3638
<a, a, a>() -> q_gen_3660
<a, b, a>() -> q_gen_3660
<b, a, b>() -> q_gen_3660
<b, b, b>() -> q_gen_3660
<cons, cons, cons>(q_gen_3660, q_gen_3661) -> q_gen_3661
<nil, cons, cons>(q_gen_3645, q_gen_3649) -> q_gen_3661
<nil, cons, cons>(q_gen_3650, q_gen_3644) -> q_gen_3661
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_3637, q_gen_3641, q_gen_3642, q_gen_3665, q_gen_3666, q_gen_3667, q_gen_3668, q_gen_3669, q_gen_3692, q_gen_3693, q_gen_3694},
Q_f={q_gen_3637},
Delta=
{
<nil>() -> q_gen_3641
<cons>(q_gen_3666, q_gen_3641) -> q_gen_3665
<a>() -> q_gen_3666
<b>() -> q_gen_3666
<z>() -> q_gen_3668
<cons>(q_gen_3666, q_gen_3665) -> q_gen_3692
<cons>(q_gen_3666, q_gen_3692) -> q_gen_3692
<s>(q_gen_3668) -> q_gen_3694
<s>(q_gen_3694) -> q_gen_3694
<cons, s>(q_gen_3642, q_gen_3641) -> q_gen_3637
<cons, s>(q_gen_3667, q_gen_3665) -> q_gen_3637
<cons, s>(q_gen_3693, q_gen_3692) -> q_gen_3637
<nil, z>() -> q_gen_3637
<a, z>() -> q_gen_3642
<b, z>() -> q_gen_3642
<a, s>(q_gen_3668) -> q_gen_3667
<b, s>(q_gen_3668) -> q_gen_3667
<cons, s>(q_gen_3642, q_gen_3665) -> q_gen_3669
<cons, s>(q_gen_3642, q_gen_3692) -> q_gen_3669
<cons, s>(q_gen_3667, q_gen_3641) -> q_gen_3669
<cons, s>(q_gen_3667, q_gen_3692) -> q_gen_3669
<cons, s>(q_gen_3693, q_gen_3641) -> q_gen_3669
<cons, s>(q_gen_3693, q_gen_3665) -> q_gen_3669
<a, s>(q_gen_3694) -> q_gen_3693
<b, s>(q_gen_3694) -> q_gen_3693
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3634, q_gen_3636, q_gen_3670},
Q_f={q_gen_3634},
Delta=
{
<s>(q_gen_3636) -> q_gen_3636
<z>() -> q_gen_3636
<s, s>(q_gen_3634) -> q_gen_3634
<z, s>(q_gen_3636) -> q_gen_3634
<z, z>() -> q_gen_3634
<s, s>(q_gen_3670) -> q_gen_3670
<s, z>(q_gen_3636) -> q_gen_3670
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3633, q_gen_3652, q_gen_3653, q_gen_3662, q_gen_3663, q_gen_3677, q_gen_3678, q_gen_3698},
Q_f={q_gen_3633, q_gen_3652, q_gen_3698},
Delta=
{
<nil>() -> q_gen_3677
<a>() -> q_gen_3678
<b>() -> q_gen_3678
<nil, nil>() -> q_gen_3633
<cons, cons>(q_gen_3653, q_gen_3633) -> q_gen_3652
<cons, cons>(q_gen_3663, q_gen_3652) -> q_gen_3652
<b, b>() -> q_gen_3653
<cons, cons>(q_gen_3653, q_gen_3662) -> q_gen_3662
<cons, cons>(q_gen_3653, q_gen_3698) -> q_gen_3662
<cons, cons>(q_gen_3663, q_gen_3633) -> q_gen_3662
<cons, cons>(q_gen_3663, q_gen_3662) -> q_gen_3662
<cons, nil>(q_gen_3678, q_gen_3677) -> q_gen_3662
<nil, cons>(q_gen_3678, q_gen_3677) -> q_gen_3662
<a, a>() -> q_gen_3663
<a, b>() -> q_gen_3663
<b, a>() -> q_gen_3663
<cons, cons>(q_gen_3653, q_gen_3652) -> q_gen_3698
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 36
() -> length([nil, z]) -> 34
() -> leq([z, s(nn2)]) -> 34
() -> leq([z, z]) -> 34
() -> reverse([nil, nil]) -> 34
(append([_eo, cons(h1, nil), _fo]) /\ reverse([t1, _eo])) -> reverse([cons(h1, t1), _fo]) -> 34
(append([t1, l2, _zn])) -> append([cons(h1, t1), l2, cons(h1, _zn)]) -> 34
(length([_oo, _po]) /\ length([l1, _no]) /\ reverse([l1, _oo])) -> leq([_no, _po]) -> 35
(length([_qo, _ro]) /\ length([l1, _so]) /\ reverse([l1, _qo])) -> leq([_ro, _so]) -> 37
(length([ll, _jo])) -> length([cons(x, ll), s(_jo)]) -> 35
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 34
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 35
(leq([s(nn1), z])) -> BOT -> 34
}
Sat witness: Found: (() -> append([nil, l2, l2]), {
l2 -> cons(b, cons(a, nil))
})

-------------------------------------------
Step 66, which took 0.256070 s (model generation: 0.245734,  model checking: 0.010336):

Model:
|_
{
append -> 
{{{
Q={q_gen_3638, q_gen_3643, q_gen_3644, q_gen_3645, q_gen_3658, q_gen_3659, q_gen_3660, q_gen_3673, q_gen_3674},
Q_f={q_gen_3638, q_gen_3643},
Delta=
{
<cons>(q_gen_3659, q_gen_3658) -> q_gen_3658
<nil>() -> q_gen_3658
<a>() -> q_gen_3659
<b>() -> q_gen_3659
<cons, cons>(q_gen_3645, q_gen_3644) -> q_gen_3644
<cons, cons>(q_gen_3645, q_gen_3673) -> q_gen_3644
<nil, nil>() -> q_gen_3644
<a, a>() -> q_gen_3645
<b, b>() -> q_gen_3645
<nil, cons>(q_gen_3659, q_gen_3658) -> q_gen_3673
<cons, cons, cons>(q_gen_3660, q_gen_3674) -> q_gen_3638
<nil, cons, cons>(q_gen_3645, q_gen_3644) -> q_gen_3638
<nil, nil, nil>() -> q_gen_3638
<cons, cons, cons>(q_gen_3660, q_gen_3643) -> q_gen_3643
<cons, nil, cons>(q_gen_3645, q_gen_3644) -> q_gen_3643
<cons, nil, cons>(q_gen_3645, q_gen_3673) -> q_gen_3643
<nil, nil, cons>(q_gen_3659, q_gen_3658) -> q_gen_3643
<a, a, a>() -> q_gen_3660
<a, b, a>() -> q_gen_3660
<b, a, b>() -> q_gen_3660
<b, b, b>() -> q_gen_3660
<cons, cons, cons>(q_gen_3660, q_gen_3638) -> q_gen_3674
<nil, cons, cons>(q_gen_3645, q_gen_3673) -> q_gen_3674
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_3637, q_gen_3641, q_gen_3642, q_gen_3665, q_gen_3666, q_gen_3667, q_gen_3668, q_gen_3669, q_gen_3692, q_gen_3693, q_gen_3694},
Q_f={q_gen_3637},
Delta=
{
<nil>() -> q_gen_3641
<cons>(q_gen_3666, q_gen_3641) -> q_gen_3665
<a>() -> q_gen_3666
<b>() -> q_gen_3666
<z>() -> q_gen_3668
<cons>(q_gen_3666, q_gen_3665) -> q_gen_3692
<cons>(q_gen_3666, q_gen_3692) -> q_gen_3692
<s>(q_gen_3668) -> q_gen_3694
<s>(q_gen_3694) -> q_gen_3694
<cons, s>(q_gen_3642, q_gen_3641) -> q_gen_3637
<cons, s>(q_gen_3642, q_gen_3665) -> q_gen_3637
<cons, s>(q_gen_3667, q_gen_3665) -> q_gen_3637
<cons, s>(q_gen_3667, q_gen_3692) -> q_gen_3637
<cons, s>(q_gen_3693, q_gen_3692) -> q_gen_3637
<nil, z>() -> q_gen_3637
<a, z>() -> q_gen_3642
<b, z>() -> q_gen_3642
<a, s>(q_gen_3668) -> q_gen_3667
<a, s>(q_gen_3694) -> q_gen_3667
<b, s>(q_gen_3668) -> q_gen_3667
<cons, s>(q_gen_3642, q_gen_3692) -> q_gen_3669
<cons, s>(q_gen_3667, q_gen_3641) -> q_gen_3669
<cons, s>(q_gen_3693, q_gen_3641) -> q_gen_3669
<cons, s>(q_gen_3693, q_gen_3665) -> q_gen_3669
<b, s>(q_gen_3694) -> q_gen_3693
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3634, q_gen_3636, q_gen_3670},
Q_f={q_gen_3634},
Delta=
{
<s>(q_gen_3636) -> q_gen_3636
<z>() -> q_gen_3636
<s, s>(q_gen_3634) -> q_gen_3634
<z, s>(q_gen_3636) -> q_gen_3634
<z, z>() -> q_gen_3634
<s, s>(q_gen_3670) -> q_gen_3670
<s, z>(q_gen_3636) -> q_gen_3670
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3633, q_gen_3652, q_gen_3653, q_gen_3663, q_gen_3675, q_gen_3677, q_gen_3678, q_gen_3698},
Q_f={q_gen_3633, q_gen_3652, q_gen_3698},
Delta=
{
<nil>() -> q_gen_3677
<a>() -> q_gen_3678
<b>() -> q_gen_3678
<cons, cons>(q_gen_3663, q_gen_3633) -> q_gen_3633
<cons, cons>(q_gen_3663, q_gen_3698) -> q_gen_3633
<nil, nil>() -> q_gen_3633
<cons, cons>(q_gen_3653, q_gen_3633) -> q_gen_3652
<a, b>() -> q_gen_3653
<b, a>() -> q_gen_3653
<b, b>() -> q_gen_3653
<a, a>() -> q_gen_3663
<cons, cons>(q_gen_3653, q_gen_3675) -> q_gen_3675
<cons, cons>(q_gen_3653, q_gen_3698) -> q_gen_3675
<cons, cons>(q_gen_3663, q_gen_3652) -> q_gen_3675
<cons, cons>(q_gen_3663, q_gen_3675) -> q_gen_3675
<cons, nil>(q_gen_3678, q_gen_3677) -> q_gen_3675
<nil, cons>(q_gen_3678, q_gen_3677) -> q_gen_3675
<cons, cons>(q_gen_3653, q_gen_3652) -> q_gen_3698
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 36
() -> length([nil, z]) -> 34
() -> leq([z, s(nn2)]) -> 34
() -> leq([z, z]) -> 34
() -> reverse([nil, nil]) -> 34
(append([_eo, cons(h1, nil), _fo]) /\ reverse([t1, _eo])) -> reverse([cons(h1, t1), _fo]) -> 34
(append([t1, l2, _zn])) -> append([cons(h1, t1), l2, cons(h1, _zn)]) -> 37
(length([_oo, _po]) /\ length([l1, _no]) /\ reverse([l1, _oo])) -> leq([_no, _po]) -> 35
(length([_qo, _ro]) /\ length([l1, _so]) /\ reverse([l1, _qo])) -> leq([_ro, _so]) -> 37
(length([ll, _jo])) -> length([cons(x, ll), s(_jo)]) -> 35
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 35
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 35
(leq([s(nn1), z])) -> BOT -> 35
}
Sat witness: Found: ((append([t1, l2, _zn])) -> append([cons(h1, t1), l2, cons(h1, _zn)]), {
_zn -> cons(a, cons(a, cons(a, nil)))  ;  h1 -> a  ;  l2 -> cons(a, cons(a, cons(a, nil)))  ;  t1 -> nil
})

-------------------------------------------
Step 67, which took 0.302400 s (model generation: 0.301680,  model checking: 0.000720):

Model:
|_
{
append -> 
{{{
Q={q_gen_3638, q_gen_3643, q_gen_3644, q_gen_3645, q_gen_3658, q_gen_3659, q_gen_3660, q_gen_3673, q_gen_3674},
Q_f={q_gen_3638, q_gen_3643},
Delta=
{
<cons>(q_gen_3659, q_gen_3658) -> q_gen_3658
<nil>() -> q_gen_3658
<a>() -> q_gen_3659
<b>() -> q_gen_3659
<cons, cons>(q_gen_3645, q_gen_3644) -> q_gen_3644
<nil, nil>() -> q_gen_3644
<a, a>() -> q_gen_3645
<b, b>() -> q_gen_3645
<cons, cons>(q_gen_3645, q_gen_3673) -> q_gen_3673
<nil, cons>(q_gen_3659, q_gen_3658) -> q_gen_3673
<cons, cons, cons>(q_gen_3660, q_gen_3674) -> q_gen_3638
<nil, cons, cons>(q_gen_3645, q_gen_3644) -> q_gen_3638
<nil, nil, nil>() -> q_gen_3638
<cons, cons, cons>(q_gen_3660, q_gen_3643) -> q_gen_3643
<cons, nil, cons>(q_gen_3645, q_gen_3644) -> q_gen_3643
<cons, nil, cons>(q_gen_3645, q_gen_3673) -> q_gen_3643
<nil, nil, cons>(q_gen_3659, q_gen_3658) -> q_gen_3643
<a, a, a>() -> q_gen_3660
<a, b, a>() -> q_gen_3660
<b, a, b>() -> q_gen_3660
<b, b, b>() -> q_gen_3660
<cons, cons, cons>(q_gen_3660, q_gen_3638) -> q_gen_3674
<nil, cons, cons>(q_gen_3645, q_gen_3673) -> q_gen_3674
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_3637, q_gen_3641, q_gen_3642, q_gen_3665, q_gen_3666, q_gen_3667, q_gen_3668, q_gen_3669, q_gen_3692, q_gen_3693, q_gen_3694, q_gen_3707, q_gen_3708, q_gen_3716},
Q_f={q_gen_3637},
Delta=
{
<nil>() -> q_gen_3641
<cons>(q_gen_3666, q_gen_3641) -> q_gen_3665
<cons>(q_gen_3716, q_gen_3641) -> q_gen_3665
<cons>(q_gen_3716, q_gen_3665) -> q_gen_3665
<b>() -> q_gen_3666
<z>() -> q_gen_3668
<cons>(q_gen_3666, q_gen_3665) -> q_gen_3692
<s>(q_gen_3668) -> q_gen_3694
<s>(q_gen_3708) -> q_gen_3694
<s>(q_gen_3694) -> q_gen_3708
<a>() -> q_gen_3716
<cons, s>(q_gen_3642, q_gen_3641) -> q_gen_3637
<cons, s>(q_gen_3667, q_gen_3665) -> q_gen_3637
<cons, s>(q_gen_3693, q_gen_3692) -> q_gen_3637
<nil, z>() -> q_gen_3637
<a, z>() -> q_gen_3642
<b, z>() -> q_gen_3642
<a, s>(q_gen_3668) -> q_gen_3667
<a, s>(q_gen_3694) -> q_gen_3667
<b, s>(q_gen_3668) -> q_gen_3667
<cons, s>(q_gen_3642, q_gen_3665) -> q_gen_3669
<cons, s>(q_gen_3642, q_gen_3692) -> q_gen_3669
<cons, s>(q_gen_3667, q_gen_3641) -> q_gen_3669
<cons, s>(q_gen_3667, q_gen_3692) -> q_gen_3669
<cons, s>(q_gen_3693, q_gen_3641) -> q_gen_3669
<cons, s>(q_gen_3693, q_gen_3665) -> q_gen_3669
<cons, s>(q_gen_3707, q_gen_3641) -> q_gen_3669
<cons, s>(q_gen_3707, q_gen_3665) -> q_gen_3669
<cons, s>(q_gen_3707, q_gen_3692) -> q_gen_3669
<b, s>(q_gen_3694) -> q_gen_3693
<b, s>(q_gen_3708) -> q_gen_3707
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3634, q_gen_3636, q_gen_3670},
Q_f={q_gen_3634},
Delta=
{
<s>(q_gen_3636) -> q_gen_3636
<z>() -> q_gen_3636
<s, s>(q_gen_3634) -> q_gen_3634
<z, s>(q_gen_3636) -> q_gen_3634
<z, z>() -> q_gen_3634
<s, s>(q_gen_3670) -> q_gen_3670
<s, z>(q_gen_3636) -> q_gen_3670
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3633, q_gen_3653, q_gen_3675, q_gen_3677, q_gen_3678},
Q_f={q_gen_3633},
Delta=
{
<nil>() -> q_gen_3677
<a>() -> q_gen_3678
<b>() -> q_gen_3678
<cons, cons>(q_gen_3653, q_gen_3633) -> q_gen_3633
<nil, nil>() -> q_gen_3633
<a, a>() -> q_gen_3653
<a, b>() -> q_gen_3653
<b, a>() -> q_gen_3653
<b, b>() -> q_gen_3653
<cons, cons>(q_gen_3653, q_gen_3675) -> q_gen_3675
<cons, nil>(q_gen_3678, q_gen_3677) -> q_gen_3675
<nil, cons>(q_gen_3678, q_gen_3677) -> q_gen_3675
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 36
() -> length([nil, z]) -> 34
() -> leq([z, s(nn2)]) -> 34
() -> leq([z, z]) -> 34
() -> reverse([nil, nil]) -> 34
(append([_eo, cons(h1, nil), _fo]) /\ reverse([t1, _eo])) -> reverse([cons(h1, t1), _fo]) -> 37
(append([t1, l2, _zn])) -> append([cons(h1, t1), l2, cons(h1, _zn)]) -> 37
(length([_oo, _po]) /\ length([l1, _no]) /\ reverse([l1, _oo])) -> leq([_no, _po]) -> 35
(length([_qo, _ro]) /\ length([l1, _so]) /\ reverse([l1, _qo])) -> leq([_ro, _so]) -> 37
(length([ll, _jo])) -> length([cons(x, ll), s(_jo)]) -> 35
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 35
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 35
(leq([s(nn1), z])) -> BOT -> 35
}
Sat witness: Found: ((append([_eo, cons(h1, nil), _fo]) /\ reverse([t1, _eo])) -> reverse([cons(h1, t1), _fo]), {
_eo -> cons(b, nil)  ;  _fo -> cons(b, cons(b, cons(b, nil)))  ;  h1 -> b  ;  t1 -> cons(b, nil)
})

-------------------------------------------
Step 68, which took 0.334258 s (model generation: 0.326451,  model checking: 0.007807):

Model:
|_
{
append -> 
{{{
Q={q_gen_3638, q_gen_3644, q_gen_3645, q_gen_3657, q_gen_3658, q_gen_3659, q_gen_3660, q_gen_3673, q_gen_3751},
Q_f={q_gen_3638},
Delta=
{
<cons>(q_gen_3659, q_gen_3751) -> q_gen_3658
<nil>() -> q_gen_3658
<a>() -> q_gen_3659
<b>() -> q_gen_3659
<cons>(q_gen_3659, q_gen_3658) -> q_gen_3751
<cons, cons>(q_gen_3645, q_gen_3644) -> q_gen_3644
<nil, nil>() -> q_gen_3644
<a, a>() -> q_gen_3645
<b, b>() -> q_gen_3645
<cons, cons>(q_gen_3645, q_gen_3673) -> q_gen_3673
<nil, cons>(q_gen_3659, q_gen_3658) -> q_gen_3673
<cons, cons, cons>(q_gen_3660, q_gen_3657) -> q_gen_3638
<cons, nil, cons>(q_gen_3645, q_gen_3644) -> q_gen_3638
<nil, cons, cons>(q_gen_3645, q_gen_3644) -> q_gen_3638
<nil, nil, cons>(q_gen_3659, q_gen_3751) -> q_gen_3638
<nil, nil, nil>() -> q_gen_3638
<cons, cons, cons>(q_gen_3660, q_gen_3638) -> q_gen_3657
<cons, nil, cons>(q_gen_3645, q_gen_3673) -> q_gen_3657
<nil, cons, cons>(q_gen_3645, q_gen_3673) -> q_gen_3657
<nil, nil, cons>(q_gen_3659, q_gen_3658) -> q_gen_3657
<a, a, a>() -> q_gen_3660
<a, b, a>() -> q_gen_3660
<b, a, b>() -> q_gen_3660
<b, b, b>() -> q_gen_3660
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_3637, q_gen_3641, q_gen_3642, q_gen_3665, q_gen_3666, q_gen_3667, q_gen_3668, q_gen_3669, q_gen_3692, q_gen_3693, q_gen_3694, q_gen_3707, q_gen_3708, q_gen_3734},
Q_f={q_gen_3637},
Delta=
{
<nil>() -> q_gen_3641
<cons>(q_gen_3666, q_gen_3641) -> q_gen_3665
<a>() -> q_gen_3666
<b>() -> q_gen_3666
<z>() -> q_gen_3668
<cons>(q_gen_3666, q_gen_3665) -> q_gen_3692
<s>(q_gen_3668) -> q_gen_3694
<s>(q_gen_3694) -> q_gen_3708
<s>(q_gen_3708) -> q_gen_3708
<cons>(q_gen_3666, q_gen_3692) -> q_gen_3734
<cons, s>(q_gen_3642, q_gen_3641) -> q_gen_3637
<cons, s>(q_gen_3667, q_gen_3665) -> q_gen_3637
<cons, s>(q_gen_3693, q_gen_3692) -> q_gen_3637
<cons, s>(q_gen_3707, q_gen_3734) -> q_gen_3637
<nil, z>() -> q_gen_3637
<a, z>() -> q_gen_3642
<b, z>() -> q_gen_3642
<a, s>(q_gen_3668) -> q_gen_3667
<b, s>(q_gen_3668) -> q_gen_3667
<cons, s>(q_gen_3642, q_gen_3665) -> q_gen_3669
<cons, s>(q_gen_3642, q_gen_3692) -> q_gen_3669
<cons, s>(q_gen_3667, q_gen_3641) -> q_gen_3669
<cons, s>(q_gen_3667, q_gen_3692) -> q_gen_3669
<cons, s>(q_gen_3693, q_gen_3641) -> q_gen_3669
<cons, s>(q_gen_3693, q_gen_3665) -> q_gen_3669
<cons, s>(q_gen_3707, q_gen_3641) -> q_gen_3669
<cons, s>(q_gen_3707, q_gen_3665) -> q_gen_3669
<cons, s>(q_gen_3707, q_gen_3692) -> q_gen_3669
<a, s>(q_gen_3694) -> q_gen_3693
<b, s>(q_gen_3694) -> q_gen_3693
<b, s>(q_gen_3708) -> q_gen_3707
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3634, q_gen_3636, q_gen_3670},
Q_f={q_gen_3634},
Delta=
{
<s>(q_gen_3636) -> q_gen_3636
<z>() -> q_gen_3636
<s, s>(q_gen_3634) -> q_gen_3634
<z, s>(q_gen_3636) -> q_gen_3634
<z, z>() -> q_gen_3634
<s, s>(q_gen_3670) -> q_gen_3670
<s, z>(q_gen_3636) -> q_gen_3670
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3633, q_gen_3653, q_gen_3675, q_gen_3677, q_gen_3678},
Q_f={q_gen_3633},
Delta=
{
<nil>() -> q_gen_3677
<a>() -> q_gen_3678
<b>() -> q_gen_3678
<cons, cons>(q_gen_3653, q_gen_3633) -> q_gen_3633
<nil, nil>() -> q_gen_3633
<a, a>() -> q_gen_3653
<a, b>() -> q_gen_3653
<b, a>() -> q_gen_3653
<b, b>() -> q_gen_3653
<cons, cons>(q_gen_3653, q_gen_3675) -> q_gen_3675
<cons, nil>(q_gen_3678, q_gen_3677) -> q_gen_3675
<nil, cons>(q_gen_3678, q_gen_3677) -> q_gen_3675
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 36
() -> length([nil, z]) -> 35
() -> leq([z, s(nn2)]) -> 35
() -> leq([z, z]) -> 35
() -> reverse([nil, nil]) -> 35
(append([_eo, cons(h1, nil), _fo]) /\ reverse([t1, _eo])) -> reverse([cons(h1, t1), _fo]) -> 37
(append([t1, l2, _zn])) -> append([cons(h1, t1), l2, cons(h1, _zn)]) -> 37
(length([_oo, _po]) /\ length([l1, _no]) /\ reverse([l1, _oo])) -> leq([_no, _po]) -> 35
(length([_qo, _ro]) /\ length([l1, _so]) /\ reverse([l1, _qo])) -> leq([_ro, _so]) -> 37
(length([ll, _jo])) -> length([cons(x, ll), s(_jo)]) -> 38
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 36
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 36
(leq([s(nn1), z])) -> BOT -> 36
}
Sat witness: Found: ((length([ll, _jo])) -> length([cons(x, ll), s(_jo)]), {
_jo -> s(s(s(s(z))))  ;  ll -> cons(b, cons(b, cons(b, cons(b, nil))))  ;  x -> b
})

-------------------------------------------
Step 69, which took 0.297560 s (model generation: 0.294602,  model checking: 0.002958):

Model:
|_
{
append -> 
{{{
Q={q_gen_3638, q_gen_3644, q_gen_3645, q_gen_3657, q_gen_3658, q_gen_3659, q_gen_3660, q_gen_3673, q_gen_3751},
Q_f={q_gen_3638},
Delta=
{
<nil>() -> q_gen_3658
<a>() -> q_gen_3659
<b>() -> q_gen_3659
<cons>(q_gen_3659, q_gen_3658) -> q_gen_3751
<cons>(q_gen_3659, q_gen_3751) -> q_gen_3751
<cons, cons>(q_gen_3645, q_gen_3644) -> q_gen_3644
<nil, nil>() -> q_gen_3644
<a, a>() -> q_gen_3645
<b, b>() -> q_gen_3645
<cons, cons>(q_gen_3645, q_gen_3673) -> q_gen_3673
<nil, cons>(q_gen_3659, q_gen_3658) -> q_gen_3673
<cons, cons, cons>(q_gen_3660, q_gen_3657) -> q_gen_3638
<cons, nil, cons>(q_gen_3645, q_gen_3644) -> q_gen_3638
<nil, cons, cons>(q_gen_3645, q_gen_3644) -> q_gen_3638
<nil, nil, cons>(q_gen_3659, q_gen_3751) -> q_gen_3638
<nil, nil, nil>() -> q_gen_3638
<cons, cons, cons>(q_gen_3660, q_gen_3638) -> q_gen_3657
<cons, nil, cons>(q_gen_3645, q_gen_3673) -> q_gen_3657
<nil, cons, cons>(q_gen_3645, q_gen_3673) -> q_gen_3657
<nil, nil, cons>(q_gen_3659, q_gen_3658) -> q_gen_3657
<a, a, a>() -> q_gen_3660
<a, b, a>() -> q_gen_3660
<b, a, b>() -> q_gen_3660
<b, b, b>() -> q_gen_3660
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_3637, q_gen_3641, q_gen_3642, q_gen_3665, q_gen_3666, q_gen_3667, q_gen_3668, q_gen_3669, q_gen_3692, q_gen_3693, q_gen_3694, q_gen_3708},
Q_f={q_gen_3637},
Delta=
{
<cons>(q_gen_3666, q_gen_3692) -> q_gen_3641
<nil>() -> q_gen_3641
<cons>(q_gen_3666, q_gen_3641) -> q_gen_3665
<a>() -> q_gen_3666
<b>() -> q_gen_3666
<s>(q_gen_3708) -> q_gen_3668
<z>() -> q_gen_3668
<cons>(q_gen_3666, q_gen_3665) -> q_gen_3692
<s>(q_gen_3668) -> q_gen_3694
<s>(q_gen_3694) -> q_gen_3708
<cons, s>(q_gen_3642, q_gen_3641) -> q_gen_3637
<cons, s>(q_gen_3667, q_gen_3665) -> q_gen_3637
<cons, s>(q_gen_3693, q_gen_3692) -> q_gen_3637
<nil, z>() -> q_gen_3637
<a, z>() -> q_gen_3642
<b, s>(q_gen_3708) -> q_gen_3642
<b, z>() -> q_gen_3642
<a, s>(q_gen_3668) -> q_gen_3667
<b, s>(q_gen_3668) -> q_gen_3667
<cons, s>(q_gen_3642, q_gen_3665) -> q_gen_3669
<cons, s>(q_gen_3642, q_gen_3692) -> q_gen_3669
<cons, s>(q_gen_3667, q_gen_3641) -> q_gen_3669
<cons, s>(q_gen_3667, q_gen_3692) -> q_gen_3669
<cons, s>(q_gen_3693, q_gen_3641) -> q_gen_3669
<cons, s>(q_gen_3693, q_gen_3665) -> q_gen_3669
<a, s>(q_gen_3694) -> q_gen_3693
<b, s>(q_gen_3694) -> q_gen_3693
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3634, q_gen_3636, q_gen_3647, q_gen_3670, q_gen_3723},
Q_f={q_gen_3634},
Delta=
{
<z>() -> q_gen_3636
<s>(q_gen_3636) -> q_gen_3647
<s>(q_gen_3647) -> q_gen_3723
<s, s>(q_gen_3634) -> q_gen_3634
<s, z>(q_gen_3723) -> q_gen_3634
<z, s>(q_gen_3636) -> q_gen_3634
<z, s>(q_gen_3647) -> q_gen_3634
<z, s>(q_gen_3723) -> q_gen_3634
<z, z>() -> q_gen_3634
<s, s>(q_gen_3670) -> q_gen_3670
<s, z>(q_gen_3636) -> q_gen_3670
<s, z>(q_gen_3647) -> q_gen_3670
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3633, q_gen_3653, q_gen_3675, q_gen_3677, q_gen_3678},
Q_f={q_gen_3633},
Delta=
{
<nil>() -> q_gen_3677
<a>() -> q_gen_3678
<b>() -> q_gen_3678
<cons, cons>(q_gen_3653, q_gen_3633) -> q_gen_3633
<nil, nil>() -> q_gen_3633
<a, a>() -> q_gen_3653
<a, b>() -> q_gen_3653
<b, a>() -> q_gen_3653
<b, b>() -> q_gen_3653
<cons, cons>(q_gen_3653, q_gen_3675) -> q_gen_3675
<cons, nil>(q_gen_3678, q_gen_3677) -> q_gen_3675
<nil, cons>(q_gen_3678, q_gen_3677) -> q_gen_3675
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 36
() -> length([nil, z]) -> 35
() -> leq([z, s(nn2)]) -> 35
() -> leq([z, z]) -> 35
() -> reverse([nil, nil]) -> 35
(append([_eo, cons(h1, nil), _fo]) /\ reverse([t1, _eo])) -> reverse([cons(h1, t1), _fo]) -> 37
(append([t1, l2, _zn])) -> append([cons(h1, t1), l2, cons(h1, _zn)]) -> 37
(length([_oo, _po]) /\ length([l1, _no]) /\ reverse([l1, _oo])) -> leq([_no, _po]) -> 38
(length([_qo, _ro]) /\ length([l1, _so]) /\ reverse([l1, _qo])) -> leq([_ro, _so]) -> 37
(length([ll, _jo])) -> length([cons(x, ll), s(_jo)]) -> 38
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 36
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 36
(leq([s(nn1), z])) -> BOT -> 36
}
Sat witness: Found: ((length([_oo, _po]) /\ length([l1, _no]) /\ reverse([l1, _oo])) -> leq([_no, _po]), {
_no -> s(z)  ;  _oo -> cons(b, nil)  ;  _po -> s(s(s(s(s(s(s(z)))))))  ;  l1 -> cons(a, nil)
})

-------------------------------------------
Step 70, which took 0.369976 s (model generation: 0.366591,  model checking: 0.003385):

Model:
|_
{
append -> 
{{{
Q={q_gen_3638, q_gen_3644, q_gen_3645, q_gen_3658, q_gen_3659, q_gen_3660, q_gen_3673, q_gen_3674},
Q_f={q_gen_3638},
Delta=
{
<cons>(q_gen_3659, q_gen_3658) -> q_gen_3658
<nil>() -> q_gen_3658
<a>() -> q_gen_3659
<b>() -> q_gen_3659
<cons, cons>(q_gen_3645, q_gen_3644) -> q_gen_3644
<nil, nil>() -> q_gen_3644
<a, a>() -> q_gen_3645
<b, b>() -> q_gen_3645
<cons, cons>(q_gen_3645, q_gen_3673) -> q_gen_3673
<nil, cons>(q_gen_3659, q_gen_3658) -> q_gen_3673
<cons, cons, cons>(q_gen_3660, q_gen_3638) -> q_gen_3638
<cons, cons, cons>(q_gen_3660, q_gen_3674) -> q_gen_3638
<cons, nil, cons>(q_gen_3645, q_gen_3644) -> q_gen_3638
<cons, nil, cons>(q_gen_3645, q_gen_3673) -> q_gen_3638
<nil, cons, cons>(q_gen_3645, q_gen_3644) -> q_gen_3638
<nil, nil, cons>(q_gen_3659, q_gen_3658) -> q_gen_3638
<nil, nil, nil>() -> q_gen_3638
<a, a, a>() -> q_gen_3660
<a, b, a>() -> q_gen_3660
<b, a, b>() -> q_gen_3660
<b, b, b>() -> q_gen_3660
<nil, cons, cons>(q_gen_3645, q_gen_3673) -> q_gen_3674
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_3637, q_gen_3641, q_gen_3642, q_gen_3665, q_gen_3666, q_gen_3667, q_gen_3668, q_gen_3669, q_gen_3692, q_gen_3693, q_gen_3694},
Q_f={q_gen_3637},
Delta=
{
<nil>() -> q_gen_3641
<cons>(q_gen_3666, q_gen_3641) -> q_gen_3665
<a>() -> q_gen_3666
<b>() -> q_gen_3666
<z>() -> q_gen_3668
<cons>(q_gen_3666, q_gen_3665) -> q_gen_3692
<cons>(q_gen_3666, q_gen_3692) -> q_gen_3692
<s>(q_gen_3668) -> q_gen_3694
<s>(q_gen_3694) -> q_gen_3694
<cons, s>(q_gen_3642, q_gen_3641) -> q_gen_3637
<cons, s>(q_gen_3667, q_gen_3665) -> q_gen_3637
<cons, s>(q_gen_3693, q_gen_3692) -> q_gen_3637
<nil, z>() -> q_gen_3637
<a, z>() -> q_gen_3642
<b, z>() -> q_gen_3642
<a, s>(q_gen_3668) -> q_gen_3667
<b, s>(q_gen_3668) -> q_gen_3667
<cons, s>(q_gen_3642, q_gen_3665) -> q_gen_3669
<cons, s>(q_gen_3642, q_gen_3692) -> q_gen_3669
<cons, s>(q_gen_3667, q_gen_3641) -> q_gen_3669
<cons, s>(q_gen_3667, q_gen_3692) -> q_gen_3669
<cons, s>(q_gen_3693, q_gen_3641) -> q_gen_3669
<cons, s>(q_gen_3693, q_gen_3665) -> q_gen_3669
<a, s>(q_gen_3694) -> q_gen_3693
<b, s>(q_gen_3694) -> q_gen_3693
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3634, q_gen_3636, q_gen_3670},
Q_f={q_gen_3634},
Delta=
{
<s>(q_gen_3636) -> q_gen_3636
<z>() -> q_gen_3636
<s, s>(q_gen_3634) -> q_gen_3634
<z, s>(q_gen_3636) -> q_gen_3634
<z, z>() -> q_gen_3634
<s, s>(q_gen_3670) -> q_gen_3670
<s, z>(q_gen_3636) -> q_gen_3670
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3633, q_gen_3652, q_gen_3653, q_gen_3675, q_gen_3676, q_gen_3677, q_gen_3678, q_gen_3684, q_gen_3689},
Q_f={q_gen_3633, q_gen_3652, q_gen_3684},
Delta=
{
<nil>() -> q_gen_3677
<a>() -> q_gen_3678
<b>() -> q_gen_3678
<cons, cons>(q_gen_3653, q_gen_3675) -> q_gen_3633
<nil, nil>() -> q_gen_3633
<cons, cons>(q_gen_3653, q_gen_3633) -> q_gen_3652
<cons, cons>(q_gen_3689, q_gen_3675) -> q_gen_3652
<a, a>() -> q_gen_3653
<b, b>() -> q_gen_3653
<cons, cons>(q_gen_3653, q_gen_3676) -> q_gen_3675
<cons, cons>(q_gen_3653, q_gen_3684) -> q_gen_3675
<cons, cons>(q_gen_3689, q_gen_3633) -> q_gen_3675
<cons, cons>(q_gen_3689, q_gen_3676) -> q_gen_3676
<cons, nil>(q_gen_3678, q_gen_3677) -> q_gen_3676
<nil, cons>(q_gen_3678, q_gen_3677) -> q_gen_3676
<cons, cons>(q_gen_3653, q_gen_3652) -> q_gen_3684
<a, b>() -> q_gen_3689
<b, a>() -> q_gen_3689
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 37
() -> length([nil, z]) -> 36
() -> leq([z, s(nn2)]) -> 36
() -> leq([z, z]) -> 36
() -> reverse([nil, nil]) -> 36
(append([_eo, cons(h1, nil), _fo]) /\ reverse([t1, _eo])) -> reverse([cons(h1, t1), _fo]) -> 37
(append([t1, l2, _zn])) -> append([cons(h1, t1), l2, cons(h1, _zn)]) -> 37
(length([_oo, _po]) /\ length([l1, _no]) /\ reverse([l1, _oo])) -> leq([_no, _po]) -> 38
(length([_qo, _ro]) /\ length([l1, _so]) /\ reverse([l1, _qo])) -> leq([_ro, _so]) -> 40
(length([ll, _jo])) -> length([cons(x, ll), s(_jo)]) -> 38
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 37
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 37
(leq([s(nn1), z])) -> BOT -> 37
}
Sat witness: Found: ((length([_qo, _ro]) /\ length([l1, _so]) /\ reverse([l1, _qo])) -> leq([_ro, _so]), {
_qo -> cons(b, cons(b, cons(b, cons(b, nil))))  ;  _ro -> s(s(s(s(z))))  ;  _so -> s(s(s(z)))  ;  l1 -> cons(b, cons(b, cons(b, cons(b, cons(b, nil)))))
})

-------------------------------------------
Step 71, which took 0.420683 s (model generation: 0.413597,  model checking: 0.007086):

Model:
|_
{
append -> 
{{{
Q={q_gen_3638, q_gen_3644, q_gen_3645, q_gen_3657, q_gen_3658, q_gen_3659, q_gen_3660, q_gen_3673, q_gen_3751},
Q_f={q_gen_3638},
Delta=
{
<cons>(q_gen_3659, q_gen_3751) -> q_gen_3658
<nil>() -> q_gen_3658
<a>() -> q_gen_3659
<b>() -> q_gen_3659
<cons>(q_gen_3659, q_gen_3658) -> q_gen_3751
<cons, cons>(q_gen_3645, q_gen_3644) -> q_gen_3644
<nil, nil>() -> q_gen_3644
<a, a>() -> q_gen_3645
<b, b>() -> q_gen_3645
<cons, cons>(q_gen_3645, q_gen_3673) -> q_gen_3673
<nil, cons>(q_gen_3659, q_gen_3658) -> q_gen_3673
<cons, cons, cons>(q_gen_3660, q_gen_3657) -> q_gen_3638
<cons, nil, cons>(q_gen_3645, q_gen_3644) -> q_gen_3638
<nil, cons, cons>(q_gen_3645, q_gen_3644) -> q_gen_3638
<nil, nil, cons>(q_gen_3659, q_gen_3751) -> q_gen_3638
<nil, nil, nil>() -> q_gen_3638
<cons, cons, cons>(q_gen_3660, q_gen_3638) -> q_gen_3657
<cons, nil, cons>(q_gen_3645, q_gen_3673) -> q_gen_3657
<nil, cons, cons>(q_gen_3645, q_gen_3673) -> q_gen_3657
<nil, nil, cons>(q_gen_3659, q_gen_3658) -> q_gen_3657
<a, a, a>() -> q_gen_3660
<a, b, a>() -> q_gen_3660
<b, a, b>() -> q_gen_3660
<b, b, b>() -> q_gen_3660
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_3637, q_gen_3641, q_gen_3642, q_gen_3665, q_gen_3666, q_gen_3667, q_gen_3668, q_gen_3669, q_gen_3692, q_gen_3693, q_gen_3694, q_gen_3707, q_gen_3708, q_gen_3716},
Q_f={q_gen_3637},
Delta=
{
<nil>() -> q_gen_3641
<cons>(q_gen_3666, q_gen_3641) -> q_gen_3665
<cons>(q_gen_3666, q_gen_3692) -> q_gen_3665
<cons>(q_gen_3716, q_gen_3665) -> q_gen_3665
<b>() -> q_gen_3666
<z>() -> q_gen_3668
<cons>(q_gen_3666, q_gen_3665) -> q_gen_3692
<cons>(q_gen_3716, q_gen_3641) -> q_gen_3692
<s>(q_gen_3668) -> q_gen_3694
<s>(q_gen_3694) -> q_gen_3708
<s>(q_gen_3708) -> q_gen_3708
<a>() -> q_gen_3716
<cons, s>(q_gen_3642, q_gen_3641) -> q_gen_3637
<cons, s>(q_gen_3642, q_gen_3692) -> q_gen_3637
<cons, s>(q_gen_3667, q_gen_3665) -> q_gen_3637
<cons, s>(q_gen_3667, q_gen_3692) -> q_gen_3637
<cons, s>(q_gen_3693, q_gen_3692) -> q_gen_3637
<nil, z>() -> q_gen_3637
<a, z>() -> q_gen_3642
<b, z>() -> q_gen_3642
<a, s>(q_gen_3668) -> q_gen_3667
<a, s>(q_gen_3694) -> q_gen_3667
<b, s>(q_gen_3668) -> q_gen_3667
<cons, s>(q_gen_3642, q_gen_3665) -> q_gen_3669
<cons, s>(q_gen_3667, q_gen_3641) -> q_gen_3669
<cons, s>(q_gen_3693, q_gen_3641) -> q_gen_3669
<cons, s>(q_gen_3693, q_gen_3665) -> q_gen_3669
<cons, s>(q_gen_3707, q_gen_3641) -> q_gen_3669
<cons, s>(q_gen_3707, q_gen_3665) -> q_gen_3669
<cons, s>(q_gen_3707, q_gen_3692) -> q_gen_3669
<b, s>(q_gen_3694) -> q_gen_3693
<b, s>(q_gen_3708) -> q_gen_3707
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3634, q_gen_3636, q_gen_3670},
Q_f={q_gen_3634},
Delta=
{
<s>(q_gen_3636) -> q_gen_3636
<z>() -> q_gen_3636
<s, s>(q_gen_3634) -> q_gen_3634
<z, s>(q_gen_3636) -> q_gen_3634
<z, z>() -> q_gen_3634
<s, s>(q_gen_3670) -> q_gen_3670
<s, z>(q_gen_3636) -> q_gen_3670
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3633, q_gen_3653, q_gen_3675, q_gen_3677, q_gen_3678},
Q_f={q_gen_3633},
Delta=
{
<nil>() -> q_gen_3677
<a>() -> q_gen_3678
<b>() -> q_gen_3678
<cons, cons>(q_gen_3653, q_gen_3633) -> q_gen_3633
<nil, nil>() -> q_gen_3633
<a, a>() -> q_gen_3653
<a, b>() -> q_gen_3653
<b, a>() -> q_gen_3653
<b, b>() -> q_gen_3653
<cons, cons>(q_gen_3653, q_gen_3675) -> q_gen_3675
<cons, nil>(q_gen_3678, q_gen_3677) -> q_gen_3675
<nil, cons>(q_gen_3678, q_gen_3677) -> q_gen_3675
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 37
() -> length([nil, z]) -> 37
() -> leq([z, s(nn2)]) -> 37
() -> leq([z, z]) -> 37
() -> reverse([nil, nil]) -> 37
(append([_eo, cons(h1, nil), _fo]) /\ reverse([t1, _eo])) -> reverse([cons(h1, t1), _fo]) -> 37
(append([t1, l2, _zn])) -> append([cons(h1, t1), l2, cons(h1, _zn)]) -> 40
(length([_oo, _po]) /\ length([l1, _no]) /\ reverse([l1, _oo])) -> leq([_no, _po]) -> 38
(length([_qo, _ro]) /\ length([l1, _so]) /\ reverse([l1, _qo])) -> leq([_ro, _so]) -> 40
(length([ll, _jo])) -> length([cons(x, ll), s(_jo)]) -> 38
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 38
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 38
(leq([s(nn1), z])) -> BOT -> 38
}
Sat witness: Found: ((append([t1, l2, _zn])) -> append([cons(h1, t1), l2, cons(h1, _zn)]), {
_zn -> cons(b, cons(b, nil))  ;  h1 -> b  ;  l2 -> nil  ;  t1 -> nil
})

-------------------------------------------
Step 72, which took 0.431276 s (model generation: 0.429215,  model checking: 0.002061):

Model:
|_
{
append -> 
{{{
Q={q_gen_3638, q_gen_3644, q_gen_3645, q_gen_3657, q_gen_3658, q_gen_3659, q_gen_3660, q_gen_3673, q_gen_3751},
Q_f={q_gen_3638},
Delta=
{
<cons>(q_gen_3659, q_gen_3751) -> q_gen_3658
<nil>() -> q_gen_3658
<a>() -> q_gen_3659
<b>() -> q_gen_3659
<cons>(q_gen_3659, q_gen_3658) -> q_gen_3751
<cons, cons>(q_gen_3645, q_gen_3644) -> q_gen_3644
<nil, cons>(q_gen_3659, q_gen_3751) -> q_gen_3644
<nil, nil>() -> q_gen_3644
<a, a>() -> q_gen_3645
<b, b>() -> q_gen_3645
<cons, cons>(q_gen_3645, q_gen_3673) -> q_gen_3673
<nil, cons>(q_gen_3659, q_gen_3658) -> q_gen_3673
<cons, cons, cons>(q_gen_3660, q_gen_3657) -> q_gen_3638
<cons, nil, cons>(q_gen_3645, q_gen_3644) -> q_gen_3638
<nil, cons, cons>(q_gen_3645, q_gen_3644) -> q_gen_3638
<nil, nil, cons>(q_gen_3659, q_gen_3751) -> q_gen_3638
<nil, nil, nil>() -> q_gen_3638
<cons, cons, cons>(q_gen_3660, q_gen_3638) -> q_gen_3657
<cons, nil, cons>(q_gen_3645, q_gen_3673) -> q_gen_3657
<nil, cons, cons>(q_gen_3645, q_gen_3673) -> q_gen_3657
<nil, nil, cons>(q_gen_3659, q_gen_3658) -> q_gen_3657
<a, a, a>() -> q_gen_3660
<a, b, a>() -> q_gen_3660
<b, a, b>() -> q_gen_3660
<b, b, b>() -> q_gen_3660
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_3637, q_gen_3641, q_gen_3642, q_gen_3665, q_gen_3666, q_gen_3667, q_gen_3668, q_gen_3669, q_gen_3692, q_gen_3693, q_gen_3694},
Q_f={q_gen_3637},
Delta=
{
<nil>() -> q_gen_3641
<cons>(q_gen_3666, q_gen_3641) -> q_gen_3665
<a>() -> q_gen_3666
<b>() -> q_gen_3666
<z>() -> q_gen_3668
<cons>(q_gen_3666, q_gen_3665) -> q_gen_3692
<cons>(q_gen_3666, q_gen_3692) -> q_gen_3692
<s>(q_gen_3668) -> q_gen_3694
<s>(q_gen_3694) -> q_gen_3694
<cons, s>(q_gen_3642, q_gen_3641) -> q_gen_3637
<cons, s>(q_gen_3667, q_gen_3665) -> q_gen_3637
<cons, s>(q_gen_3667, q_gen_3692) -> q_gen_3637
<cons, s>(q_gen_3693, q_gen_3692) -> q_gen_3637
<nil, z>() -> q_gen_3637
<a, z>() -> q_gen_3642
<b, z>() -> q_gen_3642
<a, s>(q_gen_3668) -> q_gen_3667
<a, s>(q_gen_3694) -> q_gen_3667
<b, s>(q_gen_3668) -> q_gen_3667
<cons, s>(q_gen_3642, q_gen_3665) -> q_gen_3669
<cons, s>(q_gen_3642, q_gen_3692) -> q_gen_3669
<cons, s>(q_gen_3667, q_gen_3641) -> q_gen_3669
<cons, s>(q_gen_3693, q_gen_3641) -> q_gen_3669
<cons, s>(q_gen_3693, q_gen_3665) -> q_gen_3669
<b, s>(q_gen_3694) -> q_gen_3693
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3634, q_gen_3636, q_gen_3670},
Q_f={q_gen_3634},
Delta=
{
<s>(q_gen_3636) -> q_gen_3636
<z>() -> q_gen_3636
<s, s>(q_gen_3634) -> q_gen_3634
<z, s>(q_gen_3636) -> q_gen_3634
<z, z>() -> q_gen_3634
<s, s>(q_gen_3670) -> q_gen_3670
<s, z>(q_gen_3636) -> q_gen_3670
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3633, q_gen_3652, q_gen_3653, q_gen_3663, q_gen_3675, q_gen_3677, q_gen_3678, q_gen_3698},
Q_f={q_gen_3633, q_gen_3652, q_gen_3698},
Delta=
{
<nil>() -> q_gen_3677
<a>() -> q_gen_3678
<b>() -> q_gen_3678
<nil, nil>() -> q_gen_3633
<cons, cons>(q_gen_3653, q_gen_3633) -> q_gen_3652
<cons, cons>(q_gen_3663, q_gen_3633) -> q_gen_3652
<b, a>() -> q_gen_3653
<b, b>() -> q_gen_3653
<a, a>() -> q_gen_3663
<a, b>() -> q_gen_3663
<cons, cons>(q_gen_3653, q_gen_3675) -> q_gen_3675
<cons, cons>(q_gen_3653, q_gen_3698) -> q_gen_3675
<cons, cons>(q_gen_3663, q_gen_3652) -> q_gen_3675
<cons, cons>(q_gen_3663, q_gen_3675) -> q_gen_3675
<cons, nil>(q_gen_3678, q_gen_3677) -> q_gen_3675
<nil, cons>(q_gen_3678, q_gen_3677) -> q_gen_3675
<cons, cons>(q_gen_3653, q_gen_3652) -> q_gen_3698
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 37
() -> length([nil, z]) -> 37
() -> leq([z, s(nn2)]) -> 37
() -> leq([z, z]) -> 37
() -> reverse([nil, nil]) -> 37
(append([_eo, cons(h1, nil), _fo]) /\ reverse([t1, _eo])) -> reverse([cons(h1, t1), _fo]) -> 40
(append([t1, l2, _zn])) -> append([cons(h1, t1), l2, cons(h1, _zn)]) -> 40
(length([_oo, _po]) /\ length([l1, _no]) /\ reverse([l1, _oo])) -> leq([_no, _po]) -> 38
(length([_qo, _ro]) /\ length([l1, _so]) /\ reverse([l1, _qo])) -> leq([_ro, _so]) -> 40
(length([ll, _jo])) -> length([cons(x, ll), s(_jo)]) -> 38
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 38
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 38
(leq([s(nn1), z])) -> BOT -> 38
}
Sat witness: Found: ((append([_eo, cons(h1, nil), _fo]) /\ reverse([t1, _eo])) -> reverse([cons(h1, t1), _fo]), {
_eo -> cons(a, cons(b, nil))  ;  _fo -> cons(a, cons(b, cons(b, nil)))  ;  h1 -> b  ;  t1 -> cons(b, cons(b, nil))
})

-------------------------------------------
Step 73, which took 0.476298 s (model generation: 0.471656,  model checking: 0.004642):

Model:
|_
{
append -> 
{{{
Q={q_gen_3638, q_gen_3644, q_gen_3645, q_gen_3658, q_gen_3659, q_gen_3660, q_gen_3673, q_gen_3674},
Q_f={q_gen_3638},
Delta=
{
<cons>(q_gen_3659, q_gen_3658) -> q_gen_3658
<nil>() -> q_gen_3658
<a>() -> q_gen_3659
<b>() -> q_gen_3659
<cons, cons>(q_gen_3645, q_gen_3644) -> q_gen_3644
<cons, cons>(q_gen_3645, q_gen_3673) -> q_gen_3644
<nil, nil>() -> q_gen_3644
<a, a>() -> q_gen_3645
<b, b>() -> q_gen_3645
<nil, cons>(q_gen_3659, q_gen_3658) -> q_gen_3673
<cons, cons, cons>(q_gen_3660, q_gen_3638) -> q_gen_3638
<cons, cons, cons>(q_gen_3660, q_gen_3674) -> q_gen_3638
<cons, nil, cons>(q_gen_3645, q_gen_3644) -> q_gen_3638
<cons, nil, cons>(q_gen_3645, q_gen_3673) -> q_gen_3638
<nil, cons, cons>(q_gen_3645, q_gen_3644) -> q_gen_3638
<nil, nil, cons>(q_gen_3659, q_gen_3658) -> q_gen_3638
<nil, nil, nil>() -> q_gen_3638
<a, a, a>() -> q_gen_3660
<a, b, a>() -> q_gen_3660
<b, a, b>() -> q_gen_3660
<b, b, b>() -> q_gen_3660
<nil, cons, cons>(q_gen_3645, q_gen_3673) -> q_gen_3674
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_3637, q_gen_3641, q_gen_3642, q_gen_3665, q_gen_3666, q_gen_3667, q_gen_3668, q_gen_3669, q_gen_3692, q_gen_3693, q_gen_3694},
Q_f={q_gen_3637},
Delta=
{
<nil>() -> q_gen_3641
<cons>(q_gen_3666, q_gen_3641) -> q_gen_3665
<a>() -> q_gen_3666
<b>() -> q_gen_3666
<z>() -> q_gen_3668
<cons>(q_gen_3666, q_gen_3665) -> q_gen_3692
<cons>(q_gen_3666, q_gen_3692) -> q_gen_3692
<s>(q_gen_3668) -> q_gen_3694
<s>(q_gen_3694) -> q_gen_3694
<cons, s>(q_gen_3642, q_gen_3641) -> q_gen_3637
<cons, s>(q_gen_3667, q_gen_3665) -> q_gen_3637
<cons, s>(q_gen_3693, q_gen_3692) -> q_gen_3637
<nil, z>() -> q_gen_3637
<a, z>() -> q_gen_3642
<b, z>() -> q_gen_3642
<a, s>(q_gen_3668) -> q_gen_3667
<b, s>(q_gen_3668) -> q_gen_3667
<cons, s>(q_gen_3642, q_gen_3665) -> q_gen_3669
<cons, s>(q_gen_3642, q_gen_3692) -> q_gen_3669
<cons, s>(q_gen_3667, q_gen_3641) -> q_gen_3669
<cons, s>(q_gen_3667, q_gen_3692) -> q_gen_3669
<cons, s>(q_gen_3693, q_gen_3641) -> q_gen_3669
<cons, s>(q_gen_3693, q_gen_3665) -> q_gen_3669
<a, s>(q_gen_3694) -> q_gen_3693
<b, s>(q_gen_3694) -> q_gen_3693
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3634, q_gen_3636, q_gen_3670},
Q_f={q_gen_3634},
Delta=
{
<s>(q_gen_3636) -> q_gen_3636
<z>() -> q_gen_3636
<s, s>(q_gen_3634) -> q_gen_3634
<z, s>(q_gen_3636) -> q_gen_3634
<z, z>() -> q_gen_3634
<s, s>(q_gen_3670) -> q_gen_3670
<s, z>(q_gen_3636) -> q_gen_3670
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3633, q_gen_3652, q_gen_3653, q_gen_3675, q_gen_3676, q_gen_3677, q_gen_3678, q_gen_3684, q_gen_3689},
Q_f={q_gen_3633, q_gen_3652, q_gen_3684},
Delta=
{
<nil>() -> q_gen_3677
<a>() -> q_gen_3678
<b>() -> q_gen_3678
<cons, cons>(q_gen_3689, q_gen_3675) -> q_gen_3633
<cons, cons>(q_gen_3689, q_gen_3684) -> q_gen_3633
<nil, nil>() -> q_gen_3633
<cons, cons>(q_gen_3653, q_gen_3633) -> q_gen_3652
<cons, cons>(q_gen_3653, q_gen_3675) -> q_gen_3652
<a, a>() -> q_gen_3653
<b, b>() -> q_gen_3653
<cons, cons>(q_gen_3653, q_gen_3676) -> q_gen_3675
<cons, cons>(q_gen_3653, q_gen_3684) -> q_gen_3675
<cons, cons>(q_gen_3689, q_gen_3633) -> q_gen_3675
<cons, cons>(q_gen_3689, q_gen_3652) -> q_gen_3676
<cons, cons>(q_gen_3689, q_gen_3676) -> q_gen_3676
<cons, nil>(q_gen_3678, q_gen_3677) -> q_gen_3676
<nil, cons>(q_gen_3678, q_gen_3677) -> q_gen_3676
<cons, cons>(q_gen_3653, q_gen_3652) -> q_gen_3684
<a, b>() -> q_gen_3689
<b, a>() -> q_gen_3689
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 38
() -> length([nil, z]) -> 38
() -> leq([z, s(nn2)]) -> 38
() -> leq([z, z]) -> 38
() -> reverse([nil, nil]) -> 38
(append([_eo, cons(h1, nil), _fo]) /\ reverse([t1, _eo])) -> reverse([cons(h1, t1), _fo]) -> 40
(append([t1, l2, _zn])) -> append([cons(h1, t1), l2, cons(h1, _zn)]) -> 40
(length([_oo, _po]) /\ length([l1, _no]) /\ reverse([l1, _oo])) -> leq([_no, _po]) -> 41
(length([_qo, _ro]) /\ length([l1, _so]) /\ reverse([l1, _qo])) -> leq([_ro, _so]) -> 40
(length([ll, _jo])) -> length([cons(x, ll), s(_jo)]) -> 39
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 39
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 39
(leq([s(nn1), z])) -> BOT -> 39
}
Sat witness: Found: ((length([_oo, _po]) /\ length([l1, _no]) /\ reverse([l1, _oo])) -> leq([_no, _po]), {
_no -> s(s(s(s(z))))  ;  _oo -> cons(b, cons(b, cons(b, cons(a, nil))))  ;  _po -> s(s(s(z)))  ;  l1 -> cons(b, cons(b, cons(a, cons(b, nil))))
})

-------------------------------------------
Step 74, which took 0.502672 s (model generation: 0.497266,  model checking: 0.005406):

Model:
|_
{
append -> 
{{{
Q={q_gen_3638, q_gen_3644, q_gen_3645, q_gen_3658, q_gen_3659, q_gen_3660, q_gen_3673, q_gen_3674},
Q_f={q_gen_3638},
Delta=
{
<cons>(q_gen_3659, q_gen_3658) -> q_gen_3658
<nil>() -> q_gen_3658
<a>() -> q_gen_3659
<b>() -> q_gen_3659
<cons, cons>(q_gen_3645, q_gen_3644) -> q_gen_3644
<nil, nil>() -> q_gen_3644
<a, a>() -> q_gen_3645
<b, b>() -> q_gen_3645
<cons, cons>(q_gen_3645, q_gen_3673) -> q_gen_3673
<nil, cons>(q_gen_3659, q_gen_3658) -> q_gen_3673
<cons, cons, cons>(q_gen_3660, q_gen_3638) -> q_gen_3638
<cons, cons, cons>(q_gen_3660, q_gen_3674) -> q_gen_3638
<cons, nil, cons>(q_gen_3645, q_gen_3644) -> q_gen_3638
<cons, nil, cons>(q_gen_3645, q_gen_3673) -> q_gen_3638
<nil, cons, cons>(q_gen_3645, q_gen_3644) -> q_gen_3638
<nil, nil, cons>(q_gen_3659, q_gen_3658) -> q_gen_3638
<nil, nil, nil>() -> q_gen_3638
<a, a, a>() -> q_gen_3660
<a, b, a>() -> q_gen_3660
<b, a, b>() -> q_gen_3660
<b, b, b>() -> q_gen_3660
<nil, cons, cons>(q_gen_3645, q_gen_3673) -> q_gen_3674
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_3637, q_gen_3641, q_gen_3642, q_gen_3665, q_gen_3666, q_gen_3667, q_gen_3668, q_gen_3669, q_gen_3692, q_gen_3693, q_gen_3694},
Q_f={q_gen_3637},
Delta=
{
<nil>() -> q_gen_3641
<cons>(q_gen_3666, q_gen_3641) -> q_gen_3665
<a>() -> q_gen_3666
<b>() -> q_gen_3666
<z>() -> q_gen_3668
<cons>(q_gen_3666, q_gen_3665) -> q_gen_3692
<cons>(q_gen_3666, q_gen_3692) -> q_gen_3692
<s>(q_gen_3668) -> q_gen_3694
<s>(q_gen_3694) -> q_gen_3694
<cons, s>(q_gen_3642, q_gen_3641) -> q_gen_3637
<cons, s>(q_gen_3667, q_gen_3665) -> q_gen_3637
<cons, s>(q_gen_3693, q_gen_3692) -> q_gen_3637
<nil, z>() -> q_gen_3637
<a, z>() -> q_gen_3642
<b, z>() -> q_gen_3642
<a, s>(q_gen_3668) -> q_gen_3667
<b, s>(q_gen_3668) -> q_gen_3667
<cons, s>(q_gen_3642, q_gen_3665) -> q_gen_3669
<cons, s>(q_gen_3642, q_gen_3692) -> q_gen_3669
<cons, s>(q_gen_3667, q_gen_3641) -> q_gen_3669
<cons, s>(q_gen_3667, q_gen_3692) -> q_gen_3669
<cons, s>(q_gen_3693, q_gen_3641) -> q_gen_3669
<cons, s>(q_gen_3693, q_gen_3665) -> q_gen_3669
<a, s>(q_gen_3694) -> q_gen_3693
<b, s>(q_gen_3694) -> q_gen_3693
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3634, q_gen_3636, q_gen_3670},
Q_f={q_gen_3634},
Delta=
{
<s>(q_gen_3636) -> q_gen_3636
<z>() -> q_gen_3636
<s, s>(q_gen_3634) -> q_gen_3634
<z, s>(q_gen_3636) -> q_gen_3634
<z, z>() -> q_gen_3634
<s, s>(q_gen_3670) -> q_gen_3670
<s, z>(q_gen_3636) -> q_gen_3670
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3633, q_gen_3652, q_gen_3653, q_gen_3675, q_gen_3676, q_gen_3677, q_gen_3678, q_gen_3684, q_gen_3689},
Q_f={q_gen_3633, q_gen_3652, q_gen_3684},
Delta=
{
<nil>() -> q_gen_3677
<a>() -> q_gen_3678
<b>() -> q_gen_3678
<cons, cons>(q_gen_3689, q_gen_3652) -> q_gen_3633
<cons, cons>(q_gen_3689, q_gen_3684) -> q_gen_3633
<nil, nil>() -> q_gen_3633
<cons, cons>(q_gen_3653, q_gen_3633) -> q_gen_3652
<cons, cons>(q_gen_3653, q_gen_3675) -> q_gen_3652
<cons, cons>(q_gen_3689, q_gen_3675) -> q_gen_3652
<a, a>() -> q_gen_3653
<b, b>() -> q_gen_3653
<cons, cons>(q_gen_3653, q_gen_3676) -> q_gen_3675
<cons, cons>(q_gen_3653, q_gen_3684) -> q_gen_3675
<cons, cons>(q_gen_3689, q_gen_3633) -> q_gen_3675
<cons, cons>(q_gen_3689, q_gen_3676) -> q_gen_3676
<cons, nil>(q_gen_3678, q_gen_3677) -> q_gen_3676
<nil, cons>(q_gen_3678, q_gen_3677) -> q_gen_3676
<cons, cons>(q_gen_3653, q_gen_3652) -> q_gen_3684
<a, b>() -> q_gen_3689
<b, a>() -> q_gen_3689
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 39
() -> length([nil, z]) -> 39
() -> leq([z, s(nn2)]) -> 39
() -> leq([z, z]) -> 39
() -> reverse([nil, nil]) -> 39
(append([_eo, cons(h1, nil), _fo]) /\ reverse([t1, _eo])) -> reverse([cons(h1, t1), _fo]) -> 40
(append([t1, l2, _zn])) -> append([cons(h1, t1), l2, cons(h1, _zn)]) -> 40
(length([_oo, _po]) /\ length([l1, _no]) /\ reverse([l1, _oo])) -> leq([_no, _po]) -> 41
(length([_qo, _ro]) /\ length([l1, _so]) /\ reverse([l1, _qo])) -> leq([_ro, _so]) -> 43
(length([ll, _jo])) -> length([cons(x, ll), s(_jo)]) -> 40
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 40
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 40
(leq([s(nn1), z])) -> BOT -> 40
}
Sat witness: Found: ((length([_qo, _ro]) /\ length([l1, _so]) /\ reverse([l1, _qo])) -> leq([_ro, _so]), {
_qo -> cons(b, cons(b, cons(b, cons(b, nil))))  ;  _ro -> s(s(s(s(z))))  ;  _so -> s(s(s(z)))  ;  l1 -> cons(b, cons(b, cons(a, cons(b, nil))))
})

-------------------------------------------
Step 75, which took 0.878671 s (model generation: 0.875766,  model checking: 0.002905):

Model:
|_
{
append -> 
{{{
Q={q_gen_3638, q_gen_3644, q_gen_3645, q_gen_3657, q_gen_3658, q_gen_3659, q_gen_3660, q_gen_3673, q_gen_3751},
Q_f={q_gen_3638},
Delta=
{
<cons>(q_gen_3659, q_gen_3751) -> q_gen_3658
<nil>() -> q_gen_3658
<a>() -> q_gen_3659
<b>() -> q_gen_3659
<cons>(q_gen_3659, q_gen_3658) -> q_gen_3751
<cons, cons>(q_gen_3645, q_gen_3644) -> q_gen_3644
<nil, cons>(q_gen_3659, q_gen_3751) -> q_gen_3644
<nil, nil>() -> q_gen_3644
<a, a>() -> q_gen_3645
<b, b>() -> q_gen_3645
<cons, cons>(q_gen_3645, q_gen_3673) -> q_gen_3673
<nil, cons>(q_gen_3659, q_gen_3658) -> q_gen_3673
<cons, cons, cons>(q_gen_3660, q_gen_3657) -> q_gen_3638
<cons, nil, cons>(q_gen_3645, q_gen_3644) -> q_gen_3638
<nil, cons, cons>(q_gen_3645, q_gen_3644) -> q_gen_3638
<nil, nil, cons>(q_gen_3659, q_gen_3751) -> q_gen_3638
<nil, nil, nil>() -> q_gen_3638
<cons, cons, cons>(q_gen_3660, q_gen_3638) -> q_gen_3657
<cons, nil, cons>(q_gen_3645, q_gen_3673) -> q_gen_3657
<nil, cons, cons>(q_gen_3645, q_gen_3673) -> q_gen_3657
<nil, nil, cons>(q_gen_3659, q_gen_3658) -> q_gen_3657
<a, a, a>() -> q_gen_3660
<a, b, a>() -> q_gen_3660
<b, a, b>() -> q_gen_3660
<b, b, b>() -> q_gen_3660
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_3637, q_gen_3641, q_gen_3642, q_gen_3665, q_gen_3666, q_gen_3667, q_gen_3668, q_gen_3669, q_gen_3692, q_gen_3693, q_gen_3694},
Q_f={q_gen_3637},
Delta=
{
<nil>() -> q_gen_3641
<cons>(q_gen_3666, q_gen_3641) -> q_gen_3665
<a>() -> q_gen_3666
<b>() -> q_gen_3666
<z>() -> q_gen_3668
<cons>(q_gen_3666, q_gen_3665) -> q_gen_3692
<cons>(q_gen_3666, q_gen_3692) -> q_gen_3692
<s>(q_gen_3668) -> q_gen_3694
<s>(q_gen_3694) -> q_gen_3694
<cons, s>(q_gen_3642, q_gen_3641) -> q_gen_3637
<cons, s>(q_gen_3642, q_gen_3692) -> q_gen_3637
<cons, s>(q_gen_3667, q_gen_3665) -> q_gen_3637
<cons, s>(q_gen_3693, q_gen_3692) -> q_gen_3637
<nil, z>() -> q_gen_3637
<a, z>() -> q_gen_3642
<b, z>() -> q_gen_3642
<a, s>(q_gen_3668) -> q_gen_3667
<b, s>(q_gen_3668) -> q_gen_3667
<cons, s>(q_gen_3642, q_gen_3665) -> q_gen_3669
<cons, s>(q_gen_3667, q_gen_3641) -> q_gen_3669
<cons, s>(q_gen_3667, q_gen_3692) -> q_gen_3669
<cons, s>(q_gen_3693, q_gen_3641) -> q_gen_3669
<cons, s>(q_gen_3693, q_gen_3665) -> q_gen_3669
<a, s>(q_gen_3694) -> q_gen_3693
<b, s>(q_gen_3694) -> q_gen_3693
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3634, q_gen_3636, q_gen_3670},
Q_f={q_gen_3634},
Delta=
{
<s>(q_gen_3636) -> q_gen_3636
<z>() -> q_gen_3636
<s, s>(q_gen_3634) -> q_gen_3634
<z, s>(q_gen_3636) -> q_gen_3634
<z, z>() -> q_gen_3634
<s, s>(q_gen_3670) -> q_gen_3670
<s, z>(q_gen_3636) -> q_gen_3670
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3633, q_gen_3652, q_gen_3653, q_gen_3663, q_gen_3675, q_gen_3677, q_gen_3678, q_gen_3698},
Q_f={q_gen_3633, q_gen_3652, q_gen_3698},
Delta=
{
<nil>() -> q_gen_3677
<a>() -> q_gen_3678
<b>() -> q_gen_3678
<cons, cons>(q_gen_3663, q_gen_3652) -> q_gen_3633
<cons, cons>(q_gen_3663, q_gen_3698) -> q_gen_3633
<nil, nil>() -> q_gen_3633
<cons, cons>(q_gen_3653, q_gen_3633) -> q_gen_3652
<cons, cons>(q_gen_3663, q_gen_3633) -> q_gen_3652
<a, b>() -> q_gen_3653
<b, b>() -> q_gen_3653
<a, a>() -> q_gen_3663
<b, a>() -> q_gen_3663
<cons, cons>(q_gen_3653, q_gen_3675) -> q_gen_3675
<cons, cons>(q_gen_3653, q_gen_3698) -> q_gen_3675
<cons, cons>(q_gen_3663, q_gen_3675) -> q_gen_3675
<cons, nil>(q_gen_3678, q_gen_3677) -> q_gen_3675
<nil, cons>(q_gen_3678, q_gen_3677) -> q_gen_3675
<cons, cons>(q_gen_3653, q_gen_3652) -> q_gen_3698
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 40
() -> length([nil, z]) -> 40
() -> leq([z, s(nn2)]) -> 40
() -> leq([z, z]) -> 40
() -> reverse([nil, nil]) -> 40
(append([_eo, cons(h1, nil), _fo]) /\ reverse([t1, _eo])) -> reverse([cons(h1, t1), _fo]) -> 40
(append([t1, l2, _zn])) -> append([cons(h1, t1), l2, cons(h1, _zn)]) -> 40
(length([_oo, _po]) /\ length([l1, _no]) /\ reverse([l1, _oo])) -> leq([_no, _po]) -> 41
(length([_qo, _ro]) /\ length([l1, _so]) /\ reverse([l1, _qo])) -> leq([_ro, _so]) -> 43
(length([ll, _jo])) -> length([cons(x, ll), s(_jo)]) -> 43
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 41
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 41
(leq([s(nn1), z])) -> BOT -> 41
}
Sat witness: Found: ((length([ll, _jo])) -> length([cons(x, ll), s(_jo)]), {
_jo -> s(z)  ;  ll -> cons(b, cons(a, cons(b, nil)))  ;  x -> b
})

-------------------------------------------
Step 76, which took 0.745998 s (model generation: 0.730683,  model checking: 0.015315):

Model:
|_
{
append -> 
{{{
Q={q_gen_3638, q_gen_3644, q_gen_3645, q_gen_3657, q_gen_3658, q_gen_3659, q_gen_3660, q_gen_3673, q_gen_3751},
Q_f={q_gen_3638},
Delta=
{
<cons>(q_gen_3659, q_gen_3751) -> q_gen_3658
<nil>() -> q_gen_3658
<a>() -> q_gen_3659
<b>() -> q_gen_3659
<cons>(q_gen_3659, q_gen_3658) -> q_gen_3751
<cons, cons>(q_gen_3645, q_gen_3644) -> q_gen_3644
<nil, cons>(q_gen_3659, q_gen_3751) -> q_gen_3644
<nil, nil>() -> q_gen_3644
<a, a>() -> q_gen_3645
<b, b>() -> q_gen_3645
<cons, cons>(q_gen_3645, q_gen_3673) -> q_gen_3673
<nil, cons>(q_gen_3659, q_gen_3658) -> q_gen_3673
<cons, cons, cons>(q_gen_3660, q_gen_3657) -> q_gen_3638
<cons, nil, cons>(q_gen_3645, q_gen_3644) -> q_gen_3638
<nil, cons, cons>(q_gen_3645, q_gen_3644) -> q_gen_3638
<nil, nil, cons>(q_gen_3659, q_gen_3751) -> q_gen_3638
<nil, nil, nil>() -> q_gen_3638
<cons, cons, cons>(q_gen_3660, q_gen_3638) -> q_gen_3657
<cons, nil, cons>(q_gen_3645, q_gen_3673) -> q_gen_3657
<nil, cons, cons>(q_gen_3645, q_gen_3673) -> q_gen_3657
<nil, nil, cons>(q_gen_3659, q_gen_3658) -> q_gen_3657
<a, a, a>() -> q_gen_3660
<a, b, a>() -> q_gen_3660
<b, a, b>() -> q_gen_3660
<b, b, b>() -> q_gen_3660
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_3637, q_gen_3641, q_gen_3642, q_gen_3665, q_gen_3666, q_gen_3667, q_gen_3668, q_gen_3669, q_gen_3692, q_gen_3693, q_gen_3694},
Q_f={q_gen_3637},
Delta=
{
<nil>() -> q_gen_3641
<cons>(q_gen_3666, q_gen_3641) -> q_gen_3665
<a>() -> q_gen_3666
<b>() -> q_gen_3666
<z>() -> q_gen_3668
<cons>(q_gen_3666, q_gen_3665) -> q_gen_3692
<cons>(q_gen_3666, q_gen_3692) -> q_gen_3692
<s>(q_gen_3668) -> q_gen_3694
<s>(q_gen_3694) -> q_gen_3694
<cons, s>(q_gen_3642, q_gen_3641) -> q_gen_3637
<cons, s>(q_gen_3667, q_gen_3665) -> q_gen_3637
<cons, s>(q_gen_3693, q_gen_3692) -> q_gen_3637
<nil, z>() -> q_gen_3637
<a, z>() -> q_gen_3642
<b, z>() -> q_gen_3642
<a, s>(q_gen_3668) -> q_gen_3667
<b, s>(q_gen_3668) -> q_gen_3667
<cons, s>(q_gen_3642, q_gen_3665) -> q_gen_3669
<cons, s>(q_gen_3642, q_gen_3692) -> q_gen_3669
<cons, s>(q_gen_3667, q_gen_3641) -> q_gen_3669
<cons, s>(q_gen_3667, q_gen_3692) -> q_gen_3669
<cons, s>(q_gen_3693, q_gen_3641) -> q_gen_3669
<cons, s>(q_gen_3693, q_gen_3665) -> q_gen_3669
<a, s>(q_gen_3694) -> q_gen_3693
<b, s>(q_gen_3694) -> q_gen_3693
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3634, q_gen_3636, q_gen_3670},
Q_f={q_gen_3634},
Delta=
{
<s>(q_gen_3636) -> q_gen_3636
<z>() -> q_gen_3636
<s, s>(q_gen_3634) -> q_gen_3634
<z, s>(q_gen_3636) -> q_gen_3634
<z, z>() -> q_gen_3634
<s, s>(q_gen_3670) -> q_gen_3670
<s, z>(q_gen_3636) -> q_gen_3670
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3633, q_gen_3652, q_gen_3653, q_gen_3675, q_gen_3677, q_gen_3678, q_gen_3684, q_gen_3689},
Q_f={q_gen_3633, q_gen_3652, q_gen_3684},
Delta=
{
<nil>() -> q_gen_3677
<a>() -> q_gen_3678
<b>() -> q_gen_3678
<nil, nil>() -> q_gen_3633
<cons, cons>(q_gen_3653, q_gen_3633) -> q_gen_3652
<cons, cons>(q_gen_3689, q_gen_3633) -> q_gen_3652
<cons, cons>(q_gen_3689, q_gen_3652) -> q_gen_3652
<a, a>() -> q_gen_3653
<b, b>() -> q_gen_3653
<cons, cons>(q_gen_3653, q_gen_3675) -> q_gen_3675
<cons, cons>(q_gen_3653, q_gen_3684) -> q_gen_3675
<cons, cons>(q_gen_3689, q_gen_3675) -> q_gen_3675
<cons, nil>(q_gen_3678, q_gen_3677) -> q_gen_3675
<nil, cons>(q_gen_3678, q_gen_3677) -> q_gen_3675
<cons, cons>(q_gen_3653, q_gen_3652) -> q_gen_3684
<cons, cons>(q_gen_3689, q_gen_3684) -> q_gen_3684
<a, b>() -> q_gen_3689
<b, a>() -> q_gen_3689
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 40
() -> length([nil, z]) -> 40
() -> leq([z, s(nn2)]) -> 40
() -> leq([z, z]) -> 40
() -> reverse([nil, nil]) -> 40
(append([_eo, cons(h1, nil), _fo]) /\ reverse([t1, _eo])) -> reverse([cons(h1, t1), _fo]) -> 40
(append([t1, l2, _zn])) -> append([cons(h1, t1), l2, cons(h1, _zn)]) -> 43
(length([_oo, _po]) /\ length([l1, _no]) /\ reverse([l1, _oo])) -> leq([_no, _po]) -> 41
(length([_qo, _ro]) /\ length([l1, _so]) /\ reverse([l1, _qo])) -> leq([_ro, _so]) -> 43
(length([ll, _jo])) -> length([cons(x, ll), s(_jo)]) -> 43
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 41
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 41
(leq([s(nn1), z])) -> BOT -> 41
}
Sat witness: Found: ((append([t1, l2, _zn])) -> append([cons(h1, t1), l2, cons(h1, _zn)]), {
_zn -> cons(a, cons(b, nil))  ;  h1 -> a  ;  l2 -> cons(a, cons(b, nil))  ;  t1 -> nil
})

-------------------------------------------
Step 77, which took 0.857708 s (model generation: 0.855984,  model checking: 0.001724):

Model:
|_
{
append -> 
{{{
Q={q_gen_3638, q_gen_3644, q_gen_3645, q_gen_3657, q_gen_3658, q_gen_3659, q_gen_3660, q_gen_3673, q_gen_3751},
Q_f={q_gen_3638},
Delta=
{
<nil>() -> q_gen_3658
<a>() -> q_gen_3659
<b>() -> q_gen_3659
<cons>(q_gen_3659, q_gen_3658) -> q_gen_3751
<cons>(q_gen_3659, q_gen_3751) -> q_gen_3751
<cons, cons>(q_gen_3645, q_gen_3644) -> q_gen_3644
<nil, cons>(q_gen_3659, q_gen_3751) -> q_gen_3644
<nil, nil>() -> q_gen_3644
<a, a>() -> q_gen_3645
<b, a>() -> q_gen_3645
<b, b>() -> q_gen_3645
<cons, cons>(q_gen_3645, q_gen_3673) -> q_gen_3673
<nil, cons>(q_gen_3659, q_gen_3658) -> q_gen_3673
<cons, cons, cons>(q_gen_3660, q_gen_3657) -> q_gen_3638
<cons, nil, cons>(q_gen_3645, q_gen_3644) -> q_gen_3638
<nil, cons, cons>(q_gen_3645, q_gen_3644) -> q_gen_3638
<nil, nil, cons>(q_gen_3659, q_gen_3751) -> q_gen_3638
<nil, nil, nil>() -> q_gen_3638
<cons, cons, cons>(q_gen_3660, q_gen_3638) -> q_gen_3657
<cons, nil, cons>(q_gen_3645, q_gen_3673) -> q_gen_3657
<nil, cons, cons>(q_gen_3645, q_gen_3673) -> q_gen_3657
<nil, nil, cons>(q_gen_3659, q_gen_3658) -> q_gen_3657
<a, a, a>() -> q_gen_3660
<a, b, a>() -> q_gen_3660
<b, a, b>() -> q_gen_3660
<b, b, b>() -> q_gen_3660
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_3637, q_gen_3641, q_gen_3642, q_gen_3665, q_gen_3666, q_gen_3667, q_gen_3668, q_gen_3669, q_gen_3692, q_gen_3693, q_gen_3694},
Q_f={q_gen_3637},
Delta=
{
<nil>() -> q_gen_3641
<cons>(q_gen_3666, q_gen_3641) -> q_gen_3665
<a>() -> q_gen_3666
<b>() -> q_gen_3666
<z>() -> q_gen_3668
<cons>(q_gen_3666, q_gen_3665) -> q_gen_3692
<cons>(q_gen_3666, q_gen_3692) -> q_gen_3692
<s>(q_gen_3668) -> q_gen_3694
<s>(q_gen_3694) -> q_gen_3694
<cons, s>(q_gen_3642, q_gen_3641) -> q_gen_3637
<cons, s>(q_gen_3642, q_gen_3692) -> q_gen_3637
<cons, s>(q_gen_3667, q_gen_3665) -> q_gen_3637
<cons, s>(q_gen_3667, q_gen_3692) -> q_gen_3637
<cons, s>(q_gen_3693, q_gen_3692) -> q_gen_3637
<nil, z>() -> q_gen_3637
<a, z>() -> q_gen_3642
<b, z>() -> q_gen_3642
<a, s>(q_gen_3668) -> q_gen_3667
<a, s>(q_gen_3694) -> q_gen_3667
<b, s>(q_gen_3668) -> q_gen_3667
<cons, s>(q_gen_3642, q_gen_3665) -> q_gen_3669
<cons, s>(q_gen_3667, q_gen_3641) -> q_gen_3669
<cons, s>(q_gen_3693, q_gen_3641) -> q_gen_3669
<cons, s>(q_gen_3693, q_gen_3665) -> q_gen_3669
<b, s>(q_gen_3694) -> q_gen_3693
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3634, q_gen_3636, q_gen_3670},
Q_f={q_gen_3634},
Delta=
{
<s>(q_gen_3636) -> q_gen_3636
<z>() -> q_gen_3636
<s, s>(q_gen_3634) -> q_gen_3634
<z, s>(q_gen_3636) -> q_gen_3634
<z, z>() -> q_gen_3634
<s, s>(q_gen_3670) -> q_gen_3670
<s, z>(q_gen_3636) -> q_gen_3670
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3633, q_gen_3652, q_gen_3653, q_gen_3663, q_gen_3675, q_gen_3677, q_gen_3678, q_gen_3698},
Q_f={q_gen_3633, q_gen_3652, q_gen_3698},
Delta=
{
<nil>() -> q_gen_3677
<a>() -> q_gen_3678
<b>() -> q_gen_3678
<cons, cons>(q_gen_3663, q_gen_3652) -> q_gen_3633
<cons, cons>(q_gen_3663, q_gen_3698) -> q_gen_3633
<nil, nil>() -> q_gen_3633
<cons, cons>(q_gen_3653, q_gen_3633) -> q_gen_3652
<cons, cons>(q_gen_3663, q_gen_3633) -> q_gen_3652
<a, b>() -> q_gen_3653
<b, b>() -> q_gen_3653
<a, a>() -> q_gen_3663
<b, a>() -> q_gen_3663
<cons, cons>(q_gen_3653, q_gen_3675) -> q_gen_3675
<cons, cons>(q_gen_3653, q_gen_3698) -> q_gen_3675
<cons, cons>(q_gen_3663, q_gen_3675) -> q_gen_3675
<cons, nil>(q_gen_3678, q_gen_3677) -> q_gen_3675
<nil, cons>(q_gen_3678, q_gen_3677) -> q_gen_3675
<cons, cons>(q_gen_3653, q_gen_3652) -> q_gen_3698
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 40
() -> length([nil, z]) -> 40
() -> leq([z, s(nn2)]) -> 40
() -> leq([z, z]) -> 40
() -> reverse([nil, nil]) -> 40
(append([_eo, cons(h1, nil), _fo]) /\ reverse([t1, _eo])) -> reverse([cons(h1, t1), _fo]) -> 43
(append([t1, l2, _zn])) -> append([cons(h1, t1), l2, cons(h1, _zn)]) -> 43
(length([_oo, _po]) /\ length([l1, _no]) /\ reverse([l1, _oo])) -> leq([_no, _po]) -> 41
(length([_qo, _ro]) /\ length([l1, _so]) /\ reverse([l1, _qo])) -> leq([_ro, _so]) -> 43
(length([ll, _jo])) -> length([cons(x, ll), s(_jo)]) -> 43
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 41
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 41
(leq([s(nn1), z])) -> BOT -> 41
}
Sat witness: Found: ((append([_eo, cons(h1, nil), _fo]) /\ reverse([t1, _eo])) -> reverse([cons(h1, t1), _fo]), {
_eo -> cons(b, cons(b, nil))  ;  _fo -> cons(b, cons(b, cons(a, nil)))  ;  h1 -> a  ;  t1 -> cons(a, cons(b, nil))
})

-------------------------------------------
Step 78, which took 1.706112 s (model generation: 1.703217,  model checking: 0.002895):

Model:
|_
{
append -> 
{{{
Q={q_gen_3638, q_gen_3644, q_gen_3645, q_gen_3657, q_gen_3658, q_gen_3659, q_gen_3660, q_gen_3673, q_gen_3751},
Q_f={q_gen_3638},
Delta=
{
<nil>() -> q_gen_3658
<a>() -> q_gen_3659
<b>() -> q_gen_3659
<cons>(q_gen_3659, q_gen_3658) -> q_gen_3751
<cons>(q_gen_3659, q_gen_3751) -> q_gen_3751
<cons, cons>(q_gen_3645, q_gen_3644) -> q_gen_3644
<nil, cons>(q_gen_3659, q_gen_3751) -> q_gen_3644
<nil, nil>() -> q_gen_3644
<a, a>() -> q_gen_3645
<b, a>() -> q_gen_3645
<b, b>() -> q_gen_3645
<cons, cons>(q_gen_3645, q_gen_3673) -> q_gen_3673
<nil, cons>(q_gen_3659, q_gen_3658) -> q_gen_3673
<cons, cons, cons>(q_gen_3660, q_gen_3657) -> q_gen_3638
<cons, nil, cons>(q_gen_3645, q_gen_3644) -> q_gen_3638
<nil, cons, cons>(q_gen_3645, q_gen_3644) -> q_gen_3638
<nil, nil, cons>(q_gen_3659, q_gen_3751) -> q_gen_3638
<nil, nil, nil>() -> q_gen_3638
<cons, cons, cons>(q_gen_3660, q_gen_3638) -> q_gen_3657
<cons, nil, cons>(q_gen_3645, q_gen_3673) -> q_gen_3657
<nil, cons, cons>(q_gen_3645, q_gen_3673) -> q_gen_3657
<nil, nil, cons>(q_gen_3659, q_gen_3658) -> q_gen_3657
<a, a, a>() -> q_gen_3660
<a, b, a>() -> q_gen_3660
<b, a, b>() -> q_gen_3660
<b, b, b>() -> q_gen_3660
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_3637, q_gen_3641, q_gen_3642, q_gen_3665, q_gen_3666, q_gen_3667, q_gen_3668, q_gen_3669, q_gen_3692, q_gen_3693, q_gen_3694, q_gen_3707, q_gen_3708, q_gen_3734},
Q_f={q_gen_3637},
Delta=
{
<nil>() -> q_gen_3641
<cons>(q_gen_3666, q_gen_3641) -> q_gen_3665
<a>() -> q_gen_3666
<b>() -> q_gen_3666
<s>(q_gen_3708) -> q_gen_3668
<z>() -> q_gen_3668
<cons>(q_gen_3666, q_gen_3665) -> q_gen_3692
<s>(q_gen_3668) -> q_gen_3694
<s>(q_gen_3694) -> q_gen_3708
<cons>(q_gen_3666, q_gen_3692) -> q_gen_3734
<cons>(q_gen_3666, q_gen_3734) -> q_gen_3734
<cons, s>(q_gen_3642, q_gen_3641) -> q_gen_3637
<cons, s>(q_gen_3667, q_gen_3665) -> q_gen_3637
<cons, s>(q_gen_3667, q_gen_3734) -> q_gen_3637
<cons, s>(q_gen_3693, q_gen_3692) -> q_gen_3637
<cons, s>(q_gen_3707, q_gen_3734) -> q_gen_3637
<nil, z>() -> q_gen_3637
<a, z>() -> q_gen_3642
<b, z>() -> q_gen_3642
<a, s>(q_gen_3668) -> q_gen_3667
<b, s>(q_gen_3668) -> q_gen_3667
<cons, s>(q_gen_3642, q_gen_3665) -> q_gen_3669
<cons, s>(q_gen_3642, q_gen_3692) -> q_gen_3669
<cons, s>(q_gen_3667, q_gen_3641) -> q_gen_3669
<cons, s>(q_gen_3667, q_gen_3692) -> q_gen_3669
<cons, s>(q_gen_3693, q_gen_3641) -> q_gen_3669
<cons, s>(q_gen_3693, q_gen_3665) -> q_gen_3669
<cons, s>(q_gen_3693, q_gen_3734) -> q_gen_3669
<cons, s>(q_gen_3707, q_gen_3641) -> q_gen_3669
<cons, s>(q_gen_3707, q_gen_3665) -> q_gen_3669
<cons, s>(q_gen_3707, q_gen_3692) -> q_gen_3669
<a, s>(q_gen_3694) -> q_gen_3693
<b, s>(q_gen_3694) -> q_gen_3693
<b, s>(q_gen_3708) -> q_gen_3707
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3634, q_gen_3636, q_gen_3670},
Q_f={q_gen_3634},
Delta=
{
<s>(q_gen_3636) -> q_gen_3636
<z>() -> q_gen_3636
<s, s>(q_gen_3634) -> q_gen_3634
<z, s>(q_gen_3636) -> q_gen_3634
<z, z>() -> q_gen_3634
<s, s>(q_gen_3670) -> q_gen_3670
<s, z>(q_gen_3636) -> q_gen_3670
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3633, q_gen_3653, q_gen_3675, q_gen_3677, q_gen_3678},
Q_f={q_gen_3633},
Delta=
{
<nil>() -> q_gen_3677
<a>() -> q_gen_3678
<b>() -> q_gen_3678
<cons, cons>(q_gen_3653, q_gen_3633) -> q_gen_3633
<nil, nil>() -> q_gen_3633
<a, a>() -> q_gen_3653
<a, b>() -> q_gen_3653
<b, a>() -> q_gen_3653
<b, b>() -> q_gen_3653
<cons, cons>(q_gen_3653, q_gen_3675) -> q_gen_3675
<cons, nil>(q_gen_3678, q_gen_3677) -> q_gen_3675
<nil, cons>(q_gen_3678, q_gen_3677) -> q_gen_3675
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 41
() -> length([nil, z]) -> 41
() -> leq([z, s(nn2)]) -> 41
() -> leq([z, z]) -> 41
() -> reverse([nil, nil]) -> 41
(append([_eo, cons(h1, nil), _fo]) /\ reverse([t1, _eo])) -> reverse([cons(h1, t1), _fo]) -> 43
(append([t1, l2, _zn])) -> append([cons(h1, t1), l2, cons(h1, _zn)]) -> 43
(length([_oo, _po]) /\ length([l1, _no]) /\ reverse([l1, _oo])) -> leq([_no, _po]) -> 44
(length([_qo, _ro]) /\ length([l1, _so]) /\ reverse([l1, _qo])) -> leq([_ro, _so]) -> 43
(length([ll, _jo])) -> length([cons(x, ll), s(_jo)]) -> 43
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 42
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 42
(leq([s(nn1), z])) -> BOT -> 42
}
Sat witness: Found: ((length([_oo, _po]) /\ length([l1, _no]) /\ reverse([l1, _oo])) -> leq([_no, _po]), {
_no -> s(s(s(s(s(z)))))  ;  _oo -> cons(b, cons(b, cons(b, cons(b, nil))))  ;  _po -> s(s(z))  ;  l1 -> cons(b, cons(b, cons(b, cons(b, nil))))
})

-------------------------------------------
Step 79, which took 0.985928 s (model generation: 0.979250,  model checking: 0.006678):

Model:
|_
{
append -> 
{{{
Q={q_gen_3638, q_gen_3644, q_gen_3645, q_gen_3657, q_gen_3658, q_gen_3659, q_gen_3660, q_gen_3673, q_gen_3751},
Q_f={q_gen_3638},
Delta=
{
<nil>() -> q_gen_3658
<a>() -> q_gen_3659
<b>() -> q_gen_3659
<cons>(q_gen_3659, q_gen_3658) -> q_gen_3751
<cons>(q_gen_3659, q_gen_3751) -> q_gen_3751
<cons, cons>(q_gen_3645, q_gen_3644) -> q_gen_3644
<nil, cons>(q_gen_3659, q_gen_3751) -> q_gen_3644
<nil, nil>() -> q_gen_3644
<a, a>() -> q_gen_3645
<b, a>() -> q_gen_3645
<b, b>() -> q_gen_3645
<cons, cons>(q_gen_3645, q_gen_3673) -> q_gen_3673
<nil, cons>(q_gen_3659, q_gen_3658) -> q_gen_3673
<cons, cons, cons>(q_gen_3660, q_gen_3657) -> q_gen_3638
<cons, nil, cons>(q_gen_3645, q_gen_3644) -> q_gen_3638
<nil, cons, cons>(q_gen_3645, q_gen_3644) -> q_gen_3638
<nil, nil, cons>(q_gen_3659, q_gen_3751) -> q_gen_3638
<nil, nil, nil>() -> q_gen_3638
<cons, cons, cons>(q_gen_3660, q_gen_3638) -> q_gen_3657
<cons, nil, cons>(q_gen_3645, q_gen_3673) -> q_gen_3657
<nil, cons, cons>(q_gen_3645, q_gen_3673) -> q_gen_3657
<nil, nil, cons>(q_gen_3659, q_gen_3658) -> q_gen_3657
<a, a, a>() -> q_gen_3660
<a, b, a>() -> q_gen_3660
<b, a, b>() -> q_gen_3660
<b, b, b>() -> q_gen_3660
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_3637, q_gen_3641, q_gen_3642, q_gen_3665, q_gen_3666, q_gen_3667, q_gen_3668, q_gen_3669, q_gen_3692, q_gen_3693, q_gen_3694, q_gen_3707, q_gen_3708, q_gen_3716},
Q_f={q_gen_3637},
Delta=
{
<nil>() -> q_gen_3641
<cons>(q_gen_3666, q_gen_3641) -> q_gen_3665
<cons>(q_gen_3666, q_gen_3692) -> q_gen_3665
<cons>(q_gen_3716, q_gen_3665) -> q_gen_3665
<b>() -> q_gen_3666
<z>() -> q_gen_3668
<cons>(q_gen_3666, q_gen_3665) -> q_gen_3692
<cons>(q_gen_3716, q_gen_3641) -> q_gen_3692
<s>(q_gen_3668) -> q_gen_3694
<s>(q_gen_3708) -> q_gen_3694
<s>(q_gen_3694) -> q_gen_3708
<a>() -> q_gen_3716
<cons, s>(q_gen_3642, q_gen_3641) -> q_gen_3637
<cons, s>(q_gen_3642, q_gen_3692) -> q_gen_3637
<cons, s>(q_gen_3667, q_gen_3665) -> q_gen_3637
<cons, s>(q_gen_3667, q_gen_3692) -> q_gen_3637
<cons, s>(q_gen_3693, q_gen_3692) -> q_gen_3637
<nil, z>() -> q_gen_3637
<a, z>() -> q_gen_3642
<b, z>() -> q_gen_3642
<a, s>(q_gen_3668) -> q_gen_3667
<a, s>(q_gen_3694) -> q_gen_3667
<b, s>(q_gen_3668) -> q_gen_3667
<cons, s>(q_gen_3642, q_gen_3665) -> q_gen_3669
<cons, s>(q_gen_3667, q_gen_3641) -> q_gen_3669
<cons, s>(q_gen_3693, q_gen_3641) -> q_gen_3669
<cons, s>(q_gen_3693, q_gen_3665) -> q_gen_3669
<cons, s>(q_gen_3707, q_gen_3641) -> q_gen_3669
<cons, s>(q_gen_3707, q_gen_3665) -> q_gen_3669
<cons, s>(q_gen_3707, q_gen_3692) -> q_gen_3669
<b, s>(q_gen_3694) -> q_gen_3693
<b, s>(q_gen_3708) -> q_gen_3707
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3634, q_gen_3636, q_gen_3670},
Q_f={q_gen_3634},
Delta=
{
<s>(q_gen_3636) -> q_gen_3636
<z>() -> q_gen_3636
<s, s>(q_gen_3634) -> q_gen_3634
<z, s>(q_gen_3636) -> q_gen_3634
<z, z>() -> q_gen_3634
<s, s>(q_gen_3670) -> q_gen_3670
<s, z>(q_gen_3636) -> q_gen_3670
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3633, q_gen_3653, q_gen_3675, q_gen_3677, q_gen_3678},
Q_f={q_gen_3633},
Delta=
{
<nil>() -> q_gen_3677
<a>() -> q_gen_3678
<b>() -> q_gen_3678
<cons, cons>(q_gen_3653, q_gen_3633) -> q_gen_3633
<nil, nil>() -> q_gen_3633
<a, a>() -> q_gen_3653
<a, b>() -> q_gen_3653
<b, a>() -> q_gen_3653
<b, b>() -> q_gen_3653
<cons, cons>(q_gen_3653, q_gen_3675) -> q_gen_3675
<cons, nil>(q_gen_3678, q_gen_3677) -> q_gen_3675
<nil, cons>(q_gen_3678, q_gen_3677) -> q_gen_3675
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 42
() -> length([nil, z]) -> 42
() -> leq([z, s(nn2)]) -> 42
() -> leq([z, z]) -> 42
() -> reverse([nil, nil]) -> 42
(append([_eo, cons(h1, nil), _fo]) /\ reverse([t1, _eo])) -> reverse([cons(h1, t1), _fo]) -> 43
(append([t1, l2, _zn])) -> append([cons(h1, t1), l2, cons(h1, _zn)]) -> 43
(length([_oo, _po]) /\ length([l1, _no]) /\ reverse([l1, _oo])) -> leq([_no, _po]) -> 44
(length([_qo, _ro]) /\ length([l1, _so]) /\ reverse([l1, _qo])) -> leq([_ro, _so]) -> 43
(length([ll, _jo])) -> length([cons(x, ll), s(_jo)]) -> 46
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 43
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 43
(leq([s(nn1), z])) -> BOT -> 43
}
Sat witness: Found: ((length([ll, _jo])) -> length([cons(x, ll), s(_jo)]), {
_jo -> s(s(s(z)))  ;  ll -> cons(b, cons(b, cons(a, cons(b, nil))))  ;  x -> b
})

-------------------------------------------
Step 80, which took 1.095852 s (model generation: 1.092455,  model checking: 0.003397):

Model:
|_
{
append -> 
{{{
Q={q_gen_3638, q_gen_3644, q_gen_3645, q_gen_3658, q_gen_3659, q_gen_3660, q_gen_3673, q_gen_3674},
Q_f={q_gen_3638},
Delta=
{
<cons>(q_gen_3659, q_gen_3658) -> q_gen_3658
<nil>() -> q_gen_3658
<a>() -> q_gen_3659
<b>() -> q_gen_3659
<cons, cons>(q_gen_3645, q_gen_3644) -> q_gen_3644
<nil, nil>() -> q_gen_3644
<a, a>() -> q_gen_3645
<b, a>() -> q_gen_3645
<b, b>() -> q_gen_3645
<cons, cons>(q_gen_3645, q_gen_3673) -> q_gen_3673
<nil, cons>(q_gen_3659, q_gen_3658) -> q_gen_3673
<cons, cons, cons>(q_gen_3660, q_gen_3638) -> q_gen_3638
<cons, cons, cons>(q_gen_3660, q_gen_3674) -> q_gen_3638
<cons, nil, cons>(q_gen_3645, q_gen_3644) -> q_gen_3638
<cons, nil, cons>(q_gen_3645, q_gen_3673) -> q_gen_3638
<nil, cons, cons>(q_gen_3645, q_gen_3644) -> q_gen_3638
<nil, nil, cons>(q_gen_3659, q_gen_3658) -> q_gen_3638
<nil, nil, nil>() -> q_gen_3638
<a, a, a>() -> q_gen_3660
<a, b, a>() -> q_gen_3660
<b, a, b>() -> q_gen_3660
<b, b, b>() -> q_gen_3660
<nil, cons, cons>(q_gen_3645, q_gen_3673) -> q_gen_3674
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_3637, q_gen_3641, q_gen_3642, q_gen_3665, q_gen_3666, q_gen_3667, q_gen_3668, q_gen_3669, q_gen_3692, q_gen_3693, q_gen_3694},
Q_f={q_gen_3637},
Delta=
{
<nil>() -> q_gen_3641
<cons>(q_gen_3666, q_gen_3641) -> q_gen_3665
<a>() -> q_gen_3666
<b>() -> q_gen_3666
<z>() -> q_gen_3668
<cons>(q_gen_3666, q_gen_3665) -> q_gen_3692
<cons>(q_gen_3666, q_gen_3692) -> q_gen_3692
<s>(q_gen_3668) -> q_gen_3694
<s>(q_gen_3694) -> q_gen_3694
<cons, s>(q_gen_3642, q_gen_3641) -> q_gen_3637
<cons, s>(q_gen_3667, q_gen_3665) -> q_gen_3637
<cons, s>(q_gen_3693, q_gen_3692) -> q_gen_3637
<nil, z>() -> q_gen_3637
<a, z>() -> q_gen_3642
<b, z>() -> q_gen_3642
<a, s>(q_gen_3668) -> q_gen_3667
<b, s>(q_gen_3668) -> q_gen_3667
<cons, s>(q_gen_3642, q_gen_3665) -> q_gen_3669
<cons, s>(q_gen_3642, q_gen_3692) -> q_gen_3669
<cons, s>(q_gen_3667, q_gen_3641) -> q_gen_3669
<cons, s>(q_gen_3667, q_gen_3692) -> q_gen_3669
<cons, s>(q_gen_3693, q_gen_3641) -> q_gen_3669
<cons, s>(q_gen_3693, q_gen_3665) -> q_gen_3669
<a, s>(q_gen_3694) -> q_gen_3693
<b, s>(q_gen_3694) -> q_gen_3693
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3634, q_gen_3636, q_gen_3670},
Q_f={q_gen_3634},
Delta=
{
<s>(q_gen_3636) -> q_gen_3636
<z>() -> q_gen_3636
<s, s>(q_gen_3634) -> q_gen_3634
<z, s>(q_gen_3636) -> q_gen_3634
<z, z>() -> q_gen_3634
<s, s>(q_gen_3670) -> q_gen_3670
<s, z>(q_gen_3636) -> q_gen_3670
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3633, q_gen_3652, q_gen_3653, q_gen_3675, q_gen_3676, q_gen_3677, q_gen_3678, q_gen_3684, q_gen_3689},
Q_f={q_gen_3633, q_gen_3652, q_gen_3684},
Delta=
{
<nil>() -> q_gen_3677
<a>() -> q_gen_3678
<b>() -> q_gen_3678
<cons, cons>(q_gen_3689, q_gen_3684) -> q_gen_3633
<nil, nil>() -> q_gen_3633
<cons, cons>(q_gen_3653, q_gen_3633) -> q_gen_3652
<cons, cons>(q_gen_3689, q_gen_3675) -> q_gen_3652
<a, a>() -> q_gen_3653
<b, b>() -> q_gen_3653
<cons, cons>(q_gen_3653, q_gen_3676) -> q_gen_3675
<cons, cons>(q_gen_3689, q_gen_3633) -> q_gen_3675
<cons, cons>(q_gen_3689, q_gen_3652) -> q_gen_3675
<cons, cons>(q_gen_3653, q_gen_3684) -> q_gen_3676
<cons, cons>(q_gen_3689, q_gen_3676) -> q_gen_3676
<cons, nil>(q_gen_3678, q_gen_3677) -> q_gen_3676
<nil, cons>(q_gen_3678, q_gen_3677) -> q_gen_3676
<cons, cons>(q_gen_3653, q_gen_3652) -> q_gen_3684
<cons, cons>(q_gen_3653, q_gen_3675) -> q_gen_3684
<a, b>() -> q_gen_3689
<b, a>() -> q_gen_3689
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 43
() -> length([nil, z]) -> 43
() -> leq([z, s(nn2)]) -> 43
() -> leq([z, z]) -> 43
() -> reverse([nil, nil]) -> 43
(append([_eo, cons(h1, nil), _fo]) /\ reverse([t1, _eo])) -> reverse([cons(h1, t1), _fo]) -> 43
(append([t1, l2, _zn])) -> append([cons(h1, t1), l2, cons(h1, _zn)]) -> 43
(length([_oo, _po]) /\ length([l1, _no]) /\ reverse([l1, _oo])) -> leq([_no, _po]) -> 44
(length([_qo, _ro]) /\ length([l1, _so]) /\ reverse([l1, _qo])) -> leq([_ro, _so]) -> 46
(length([ll, _jo])) -> length([cons(x, ll), s(_jo)]) -> 46
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 44
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 44
(leq([s(nn1), z])) -> BOT -> 44
}
Sat witness: Found: ((length([_qo, _ro]) /\ length([l1, _so]) /\ reverse([l1, _qo])) -> leq([_ro, _so]), {
_qo -> cons(b, cons(b, cons(b, nil)))  ;  _ro -> s(s(s(z)))  ;  _so -> s(s(z))  ;  l1 -> cons(b, cons(b, nil))
})

-------------------------------------------
Step 81, which took 0.833122 s (model generation: 0.809943,  model checking: 0.023179):

Model:
|_
{
append -> 
{{{
Q={q_gen_3638, q_gen_3644, q_gen_3645, q_gen_3657, q_gen_3658, q_gen_3659, q_gen_3660, q_gen_3673, q_gen_3751},
Q_f={q_gen_3638},
Delta=
{
<cons>(q_gen_3659, q_gen_3751) -> q_gen_3658
<nil>() -> q_gen_3658
<a>() -> q_gen_3659
<b>() -> q_gen_3659
<cons>(q_gen_3659, q_gen_3658) -> q_gen_3751
<cons, cons>(q_gen_3645, q_gen_3644) -> q_gen_3644
<nil, cons>(q_gen_3659, q_gen_3751) -> q_gen_3644
<nil, nil>() -> q_gen_3644
<a, a>() -> q_gen_3645
<b, a>() -> q_gen_3645
<b, b>() -> q_gen_3645
<cons, cons>(q_gen_3645, q_gen_3673) -> q_gen_3673
<nil, cons>(q_gen_3659, q_gen_3658) -> q_gen_3673
<cons, cons, cons>(q_gen_3660, q_gen_3657) -> q_gen_3638
<cons, nil, cons>(q_gen_3645, q_gen_3644) -> q_gen_3638
<nil, cons, cons>(q_gen_3645, q_gen_3644) -> q_gen_3638
<nil, nil, cons>(q_gen_3659, q_gen_3751) -> q_gen_3638
<nil, nil, nil>() -> q_gen_3638
<cons, cons, cons>(q_gen_3660, q_gen_3638) -> q_gen_3657
<cons, nil, cons>(q_gen_3645, q_gen_3673) -> q_gen_3657
<nil, cons, cons>(q_gen_3645, q_gen_3673) -> q_gen_3657
<nil, nil, cons>(q_gen_3659, q_gen_3658) -> q_gen_3657
<a, a, a>() -> q_gen_3660
<a, b, a>() -> q_gen_3660
<b, a, b>() -> q_gen_3660
<b, b, b>() -> q_gen_3660
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_3637, q_gen_3641, q_gen_3642, q_gen_3665, q_gen_3666, q_gen_3667, q_gen_3668, q_gen_3669, q_gen_3692, q_gen_3693, q_gen_3694},
Q_f={q_gen_3637},
Delta=
{
<nil>() -> q_gen_3641
<cons>(q_gen_3666, q_gen_3641) -> q_gen_3665
<a>() -> q_gen_3666
<b>() -> q_gen_3666
<z>() -> q_gen_3668
<cons>(q_gen_3666, q_gen_3665) -> q_gen_3692
<cons>(q_gen_3666, q_gen_3692) -> q_gen_3692
<s>(q_gen_3668) -> q_gen_3694
<s>(q_gen_3694) -> q_gen_3694
<cons, s>(q_gen_3642, q_gen_3641) -> q_gen_3637
<cons, s>(q_gen_3667, q_gen_3665) -> q_gen_3637
<cons, s>(q_gen_3693, q_gen_3692) -> q_gen_3637
<nil, z>() -> q_gen_3637
<a, z>() -> q_gen_3642
<b, z>() -> q_gen_3642
<a, s>(q_gen_3668) -> q_gen_3667
<b, s>(q_gen_3668) -> q_gen_3667
<cons, s>(q_gen_3642, q_gen_3665) -> q_gen_3669
<cons, s>(q_gen_3642, q_gen_3692) -> q_gen_3669
<cons, s>(q_gen_3667, q_gen_3641) -> q_gen_3669
<cons, s>(q_gen_3667, q_gen_3692) -> q_gen_3669
<cons, s>(q_gen_3693, q_gen_3641) -> q_gen_3669
<cons, s>(q_gen_3693, q_gen_3665) -> q_gen_3669
<a, s>(q_gen_3694) -> q_gen_3693
<b, s>(q_gen_3694) -> q_gen_3693
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3634, q_gen_3636, q_gen_3670},
Q_f={q_gen_3634},
Delta=
{
<s>(q_gen_3636) -> q_gen_3636
<z>() -> q_gen_3636
<s, s>(q_gen_3634) -> q_gen_3634
<z, s>(q_gen_3636) -> q_gen_3634
<z, z>() -> q_gen_3634
<s, s>(q_gen_3670) -> q_gen_3670
<s, z>(q_gen_3636) -> q_gen_3670
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3633, q_gen_3652, q_gen_3653, q_gen_3663, q_gen_3675, q_gen_3677, q_gen_3678, q_gen_3698},
Q_f={q_gen_3633, q_gen_3652, q_gen_3698},
Delta=
{
<nil>() -> q_gen_3677
<a>() -> q_gen_3678
<b>() -> q_gen_3678
<cons, cons>(q_gen_3663, q_gen_3698) -> q_gen_3633
<nil, nil>() -> q_gen_3633
<cons, cons>(q_gen_3653, q_gen_3633) -> q_gen_3652
<cons, cons>(q_gen_3663, q_gen_3633) -> q_gen_3652
<cons, cons>(q_gen_3663, q_gen_3652) -> q_gen_3652
<b, b>() -> q_gen_3653
<a, a>() -> q_gen_3663
<a, b>() -> q_gen_3663
<b, a>() -> q_gen_3663
<cons, cons>(q_gen_3653, q_gen_3675) -> q_gen_3675
<cons, cons>(q_gen_3653, q_gen_3698) -> q_gen_3675
<cons, cons>(q_gen_3663, q_gen_3675) -> q_gen_3675
<cons, nil>(q_gen_3678, q_gen_3677) -> q_gen_3675
<nil, cons>(q_gen_3678, q_gen_3677) -> q_gen_3675
<cons, cons>(q_gen_3653, q_gen_3652) -> q_gen_3698
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 43
() -> length([nil, z]) -> 43
() -> leq([z, s(nn2)]) -> 43
() -> leq([z, z]) -> 43
() -> reverse([nil, nil]) -> 43
(append([_eo, cons(h1, nil), _fo]) /\ reverse([t1, _eo])) -> reverse([cons(h1, t1), _fo]) -> 43
(append([t1, l2, _zn])) -> append([cons(h1, t1), l2, cons(h1, _zn)]) -> 46
(length([_oo, _po]) /\ length([l1, _no]) /\ reverse([l1, _oo])) -> leq([_no, _po]) -> 44
(length([_qo, _ro]) /\ length([l1, _so]) /\ reverse([l1, _qo])) -> leq([_ro, _so]) -> 46
(length([ll, _jo])) -> length([cons(x, ll), s(_jo)]) -> 46
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 44
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 44
(leq([s(nn1), z])) -> BOT -> 44
}
Sat witness: Found: ((append([t1, l2, _zn])) -> append([cons(h1, t1), l2, cons(h1, _zn)]), {
_zn -> cons(b, cons(a, nil))  ;  h1 -> b  ;  l2 -> cons(b, cons(a, nil))  ;  t1 -> nil
})

-------------------------------------------
Step 82, which took 1.551977 s (model generation: 1.550064,  model checking: 0.001913):

Model:
|_
{
append -> 
{{{
Q={q_gen_3638, q_gen_3644, q_gen_3645, q_gen_3657, q_gen_3658, q_gen_3659, q_gen_3660, q_gen_3673, q_gen_3751},
Q_f={q_gen_3638},
Delta=
{
<nil>() -> q_gen_3658
<a>() -> q_gen_3659
<b>() -> q_gen_3659
<cons>(q_gen_3659, q_gen_3658) -> q_gen_3751
<cons>(q_gen_3659, q_gen_3751) -> q_gen_3751
<cons, cons>(q_gen_3645, q_gen_3644) -> q_gen_3644
<nil, cons>(q_gen_3659, q_gen_3751) -> q_gen_3644
<nil, nil>() -> q_gen_3644
<a, a>() -> q_gen_3645
<a, b>() -> q_gen_3645
<b, a>() -> q_gen_3645
<b, b>() -> q_gen_3645
<cons, cons>(q_gen_3645, q_gen_3673) -> q_gen_3673
<nil, cons>(q_gen_3659, q_gen_3658) -> q_gen_3673
<cons, cons, cons>(q_gen_3660, q_gen_3657) -> q_gen_3638
<cons, nil, cons>(q_gen_3645, q_gen_3644) -> q_gen_3638
<nil, cons, cons>(q_gen_3645, q_gen_3644) -> q_gen_3638
<nil, nil, cons>(q_gen_3659, q_gen_3751) -> q_gen_3638
<nil, nil, nil>() -> q_gen_3638
<cons, cons, cons>(q_gen_3660, q_gen_3638) -> q_gen_3657
<cons, nil, cons>(q_gen_3645, q_gen_3673) -> q_gen_3657
<nil, cons, cons>(q_gen_3645, q_gen_3673) -> q_gen_3657
<nil, nil, cons>(q_gen_3659, q_gen_3658) -> q_gen_3657
<a, a, a>() -> q_gen_3660
<a, b, a>() -> q_gen_3660
<b, a, b>() -> q_gen_3660
<b, b, b>() -> q_gen_3660
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_3637, q_gen_3641, q_gen_3642, q_gen_3665, q_gen_3666, q_gen_3667, q_gen_3668, q_gen_3669, q_gen_3692, q_gen_3693, q_gen_3694},
Q_f={q_gen_3637},
Delta=
{
<nil>() -> q_gen_3641
<cons>(q_gen_3666, q_gen_3641) -> q_gen_3665
<a>() -> q_gen_3666
<b>() -> q_gen_3666
<z>() -> q_gen_3668
<cons>(q_gen_3666, q_gen_3665) -> q_gen_3692
<cons>(q_gen_3666, q_gen_3692) -> q_gen_3692
<s>(q_gen_3668) -> q_gen_3694
<s>(q_gen_3694) -> q_gen_3694
<cons, s>(q_gen_3642, q_gen_3641) -> q_gen_3637
<cons, s>(q_gen_3667, q_gen_3665) -> q_gen_3637
<cons, s>(q_gen_3667, q_gen_3692) -> q_gen_3637
<cons, s>(q_gen_3693, q_gen_3692) -> q_gen_3637
<nil, z>() -> q_gen_3637
<a, z>() -> q_gen_3642
<b, z>() -> q_gen_3642
<a, s>(q_gen_3668) -> q_gen_3667
<a, s>(q_gen_3694) -> q_gen_3667
<b, s>(q_gen_3668) -> q_gen_3667
<cons, s>(q_gen_3642, q_gen_3665) -> q_gen_3669
<cons, s>(q_gen_3642, q_gen_3692) -> q_gen_3669
<cons, s>(q_gen_3667, q_gen_3641) -> q_gen_3669
<cons, s>(q_gen_3693, q_gen_3641) -> q_gen_3669
<cons, s>(q_gen_3693, q_gen_3665) -> q_gen_3669
<b, s>(q_gen_3694) -> q_gen_3693
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3634, q_gen_3636, q_gen_3670},
Q_f={q_gen_3634},
Delta=
{
<s>(q_gen_3636) -> q_gen_3636
<z>() -> q_gen_3636
<s, s>(q_gen_3634) -> q_gen_3634
<z, s>(q_gen_3636) -> q_gen_3634
<z, z>() -> q_gen_3634
<s, s>(q_gen_3670) -> q_gen_3670
<s, z>(q_gen_3636) -> q_gen_3670
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3633, q_gen_3652, q_gen_3653, q_gen_3675, q_gen_3677, q_gen_3678, q_gen_3684, q_gen_3689},
Q_f={q_gen_3633, q_gen_3652, q_gen_3684},
Delta=
{
<nil>() -> q_gen_3677
<a>() -> q_gen_3678
<b>() -> q_gen_3678
<cons, cons>(q_gen_3689, q_gen_3684) -> q_gen_3633
<nil, nil>() -> q_gen_3633
<cons, cons>(q_gen_3653, q_gen_3633) -> q_gen_3652
<cons, cons>(q_gen_3689, q_gen_3633) -> q_gen_3652
<cons, cons>(q_gen_3689, q_gen_3652) -> q_gen_3652
<a, a>() -> q_gen_3653
<b, b>() -> q_gen_3653
<cons, cons>(q_gen_3653, q_gen_3675) -> q_gen_3675
<cons, cons>(q_gen_3653, q_gen_3684) -> q_gen_3675
<cons, cons>(q_gen_3689, q_gen_3675) -> q_gen_3675
<cons, nil>(q_gen_3678, q_gen_3677) -> q_gen_3675
<nil, cons>(q_gen_3678, q_gen_3677) -> q_gen_3675
<cons, cons>(q_gen_3653, q_gen_3652) -> q_gen_3684
<a, b>() -> q_gen_3689
<b, a>() -> q_gen_3689
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 43
() -> length([nil, z]) -> 43
() -> leq([z, s(nn2)]) -> 43
() -> leq([z, z]) -> 43
() -> reverse([nil, nil]) -> 43
(append([_eo, cons(h1, nil), _fo]) /\ reverse([t1, _eo])) -> reverse([cons(h1, t1), _fo]) -> 46
(append([t1, l2, _zn])) -> append([cons(h1, t1), l2, cons(h1, _zn)]) -> 46
(length([_oo, _po]) /\ length([l1, _no]) /\ reverse([l1, _oo])) -> leq([_no, _po]) -> 44
(length([_qo, _ro]) /\ length([l1, _so]) /\ reverse([l1, _qo])) -> leq([_ro, _so]) -> 46
(length([ll, _jo])) -> length([cons(x, ll), s(_jo)]) -> 46
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 44
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 44
(leq([s(nn1), z])) -> BOT -> 44
}
Sat witness: Found: ((append([_eo, cons(h1, nil), _fo]) /\ reverse([t1, _eo])) -> reverse([cons(h1, t1), _fo]), {
_eo -> cons(a, cons(b, nil))  ;  _fo -> cons(a, cons(a, cons(b, nil)))  ;  h1 -> a  ;  t1 -> cons(a, cons(b, nil))
})

-------------------------------------------
Step 83, which took 0.922198 s (model generation: 0.919287,  model checking: 0.002911):

Model:
|_
{
append -> 
{{{
Q={q_gen_3638, q_gen_3644, q_gen_3645, q_gen_3657, q_gen_3658, q_gen_3659, q_gen_3660, q_gen_3673, q_gen_3751},
Q_f={q_gen_3638},
Delta=
{
<nil>() -> q_gen_3658
<a>() -> q_gen_3659
<b>() -> q_gen_3659
<cons>(q_gen_3659, q_gen_3658) -> q_gen_3751
<cons>(q_gen_3659, q_gen_3751) -> q_gen_3751
<cons, cons>(q_gen_3645, q_gen_3644) -> q_gen_3644
<nil, cons>(q_gen_3659, q_gen_3751) -> q_gen_3644
<nil, nil>() -> q_gen_3644
<a, a>() -> q_gen_3645
<a, b>() -> q_gen_3645
<b, a>() -> q_gen_3645
<b, b>() -> q_gen_3645
<cons, cons>(q_gen_3645, q_gen_3673) -> q_gen_3673
<nil, cons>(q_gen_3659, q_gen_3658) -> q_gen_3673
<cons, cons, cons>(q_gen_3660, q_gen_3657) -> q_gen_3638
<cons, nil, cons>(q_gen_3645, q_gen_3644) -> q_gen_3638
<nil, cons, cons>(q_gen_3645, q_gen_3644) -> q_gen_3638
<nil, nil, cons>(q_gen_3659, q_gen_3751) -> q_gen_3638
<nil, nil, nil>() -> q_gen_3638
<cons, cons, cons>(q_gen_3660, q_gen_3638) -> q_gen_3657
<cons, nil, cons>(q_gen_3645, q_gen_3673) -> q_gen_3657
<nil, cons, cons>(q_gen_3645, q_gen_3673) -> q_gen_3657
<nil, nil, cons>(q_gen_3659, q_gen_3658) -> q_gen_3657
<a, a, a>() -> q_gen_3660
<a, b, a>() -> q_gen_3660
<b, a, b>() -> q_gen_3660
<b, b, b>() -> q_gen_3660
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_3637, q_gen_3641, q_gen_3642, q_gen_3665, q_gen_3666, q_gen_3667, q_gen_3668, q_gen_3669, q_gen_3692, q_gen_3693, q_gen_3694, q_gen_3707, q_gen_3708, q_gen_3734},
Q_f={q_gen_3637},
Delta=
{
<nil>() -> q_gen_3641
<cons>(q_gen_3666, q_gen_3641) -> q_gen_3665
<a>() -> q_gen_3666
<b>() -> q_gen_3666
<z>() -> q_gen_3668
<cons>(q_gen_3666, q_gen_3665) -> q_gen_3692
<cons>(q_gen_3666, q_gen_3734) -> q_gen_3692
<s>(q_gen_3668) -> q_gen_3694
<s>(q_gen_3708) -> q_gen_3694
<s>(q_gen_3694) -> q_gen_3708
<cons>(q_gen_3666, q_gen_3692) -> q_gen_3734
<cons, s>(q_gen_3642, q_gen_3641) -> q_gen_3637
<cons, s>(q_gen_3667, q_gen_3665) -> q_gen_3637
<cons, s>(q_gen_3667, q_gen_3734) -> q_gen_3637
<cons, s>(q_gen_3693, q_gen_3692) -> q_gen_3637
<cons, s>(q_gen_3707, q_gen_3734) -> q_gen_3637
<nil, z>() -> q_gen_3637
<a, z>() -> q_gen_3642
<b, z>() -> q_gen_3642
<a, s>(q_gen_3668) -> q_gen_3667
<b, s>(q_gen_3668) -> q_gen_3667
<cons, s>(q_gen_3642, q_gen_3665) -> q_gen_3669
<cons, s>(q_gen_3642, q_gen_3692) -> q_gen_3669
<cons, s>(q_gen_3667, q_gen_3641) -> q_gen_3669
<cons, s>(q_gen_3667, q_gen_3692) -> q_gen_3669
<cons, s>(q_gen_3693, q_gen_3641) -> q_gen_3669
<cons, s>(q_gen_3693, q_gen_3665) -> q_gen_3669
<cons, s>(q_gen_3693, q_gen_3734) -> q_gen_3669
<cons, s>(q_gen_3707, q_gen_3641) -> q_gen_3669
<cons, s>(q_gen_3707, q_gen_3665) -> q_gen_3669
<cons, s>(q_gen_3707, q_gen_3692) -> q_gen_3669
<a, s>(q_gen_3694) -> q_gen_3693
<b, s>(q_gen_3694) -> q_gen_3693
<b, s>(q_gen_3708) -> q_gen_3707
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3634, q_gen_3636, q_gen_3670},
Q_f={q_gen_3634},
Delta=
{
<s>(q_gen_3636) -> q_gen_3636
<z>() -> q_gen_3636
<s, s>(q_gen_3634) -> q_gen_3634
<z, s>(q_gen_3636) -> q_gen_3634
<z, z>() -> q_gen_3634
<s, s>(q_gen_3670) -> q_gen_3670
<s, z>(q_gen_3636) -> q_gen_3670
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3633, q_gen_3653, q_gen_3675, q_gen_3677, q_gen_3678},
Q_f={q_gen_3633},
Delta=
{
<nil>() -> q_gen_3677
<a>() -> q_gen_3678
<b>() -> q_gen_3678
<cons, cons>(q_gen_3653, q_gen_3633) -> q_gen_3633
<nil, nil>() -> q_gen_3633
<a, a>() -> q_gen_3653
<a, b>() -> q_gen_3653
<b, a>() -> q_gen_3653
<b, b>() -> q_gen_3653
<cons, cons>(q_gen_3653, q_gen_3675) -> q_gen_3675
<cons, nil>(q_gen_3678, q_gen_3677) -> q_gen_3675
<nil, cons>(q_gen_3678, q_gen_3677) -> q_gen_3675
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 44
() -> length([nil, z]) -> 44
() -> leq([z, s(nn2)]) -> 44
() -> leq([z, z]) -> 44
() -> reverse([nil, nil]) -> 44
(append([_eo, cons(h1, nil), _fo]) /\ reverse([t1, _eo])) -> reverse([cons(h1, t1), _fo]) -> 46
(append([t1, l2, _zn])) -> append([cons(h1, t1), l2, cons(h1, _zn)]) -> 46
(length([_oo, _po]) /\ length([l1, _no]) /\ reverse([l1, _oo])) -> leq([_no, _po]) -> 47
(length([_qo, _ro]) /\ length([l1, _so]) /\ reverse([l1, _qo])) -> leq([_ro, _so]) -> 46
(length([ll, _jo])) -> length([cons(x, ll), s(_jo)]) -> 46
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 45
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 45
(leq([s(nn1), z])) -> BOT -> 45
}
Sat witness: Found: ((length([_oo, _po]) /\ length([l1, _no]) /\ reverse([l1, _oo])) -> leq([_no, _po]), {
_no -> s(s(s(s(z))))  ;  _oo -> cons(b, cons(b, cons(b, cons(b, nil))))  ;  _po -> s(s(z))  ;  l1 -> cons(b, cons(b, cons(b, cons(b, nil))))
})

-------------------------------------------
Step 84, which took 4.261044 s (model generation: 4.254477,  model checking: 0.006567):

Model:
|_
{
append -> 
{{{
Q={q_gen_3638, q_gen_3644, q_gen_3645, q_gen_3657, q_gen_3658, q_gen_3659, q_gen_3660, q_gen_3673, q_gen_3751},
Q_f={q_gen_3638},
Delta=
{
<nil>() -> q_gen_3658
<a>() -> q_gen_3659
<b>() -> q_gen_3659
<cons>(q_gen_3659, q_gen_3658) -> q_gen_3751
<cons>(q_gen_3659, q_gen_3751) -> q_gen_3751
<cons, cons>(q_gen_3645, q_gen_3644) -> q_gen_3644
<nil, cons>(q_gen_3659, q_gen_3751) -> q_gen_3644
<nil, nil>() -> q_gen_3644
<a, a>() -> q_gen_3645
<a, b>() -> q_gen_3645
<b, a>() -> q_gen_3645
<b, b>() -> q_gen_3645
<cons, cons>(q_gen_3645, q_gen_3673) -> q_gen_3673
<nil, cons>(q_gen_3659, q_gen_3658) -> q_gen_3673
<cons, cons, cons>(q_gen_3660, q_gen_3657) -> q_gen_3638
<cons, nil, cons>(q_gen_3645, q_gen_3644) -> q_gen_3638
<nil, cons, cons>(q_gen_3645, q_gen_3644) -> q_gen_3638
<nil, nil, cons>(q_gen_3659, q_gen_3751) -> q_gen_3638
<nil, nil, nil>() -> q_gen_3638
<cons, cons, cons>(q_gen_3660, q_gen_3638) -> q_gen_3657
<cons, nil, cons>(q_gen_3645, q_gen_3673) -> q_gen_3657
<nil, cons, cons>(q_gen_3645, q_gen_3673) -> q_gen_3657
<nil, nil, cons>(q_gen_3659, q_gen_3658) -> q_gen_3657
<a, a, a>() -> q_gen_3660
<a, b, a>() -> q_gen_3660
<b, a, b>() -> q_gen_3660
<b, b, b>() -> q_gen_3660
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_3637, q_gen_3641, q_gen_3642, q_gen_3665, q_gen_3666, q_gen_3667, q_gen_3668, q_gen_3669, q_gen_3692, q_gen_3693, q_gen_3694, q_gen_3707, q_gen_3708, q_gen_3734},
Q_f={q_gen_3637},
Delta=
{
<nil>() -> q_gen_3641
<cons>(q_gen_3666, q_gen_3641) -> q_gen_3665
<cons>(q_gen_3666, q_gen_3734) -> q_gen_3665
<a>() -> q_gen_3666
<b>() -> q_gen_3666
<s>(q_gen_3708) -> q_gen_3668
<z>() -> q_gen_3668
<cons>(q_gen_3666, q_gen_3665) -> q_gen_3692
<s>(q_gen_3668) -> q_gen_3694
<s>(q_gen_3694) -> q_gen_3708
<cons>(q_gen_3666, q_gen_3692) -> q_gen_3734
<cons, s>(q_gen_3642, q_gen_3641) -> q_gen_3637
<cons, s>(q_gen_3667, q_gen_3665) -> q_gen_3637
<cons, s>(q_gen_3693, q_gen_3692) -> q_gen_3637
<cons, s>(q_gen_3707, q_gen_3734) -> q_gen_3637
<nil, z>() -> q_gen_3637
<a, z>() -> q_gen_3642
<b, z>() -> q_gen_3642
<a, s>(q_gen_3668) -> q_gen_3667
<b, s>(q_gen_3668) -> q_gen_3667
<cons, s>(q_gen_3642, q_gen_3665) -> q_gen_3669
<cons, s>(q_gen_3642, q_gen_3692) -> q_gen_3669
<cons, s>(q_gen_3667, q_gen_3641) -> q_gen_3669
<cons, s>(q_gen_3667, q_gen_3692) -> q_gen_3669
<cons, s>(q_gen_3667, q_gen_3734) -> q_gen_3669
<cons, s>(q_gen_3693, q_gen_3641) -> q_gen_3669
<cons, s>(q_gen_3693, q_gen_3665) -> q_gen_3669
<cons, s>(q_gen_3693, q_gen_3734) -> q_gen_3669
<cons, s>(q_gen_3707, q_gen_3641) -> q_gen_3669
<cons, s>(q_gen_3707, q_gen_3665) -> q_gen_3669
<cons, s>(q_gen_3707, q_gen_3692) -> q_gen_3669
<a, s>(q_gen_3694) -> q_gen_3693
<b, s>(q_gen_3694) -> q_gen_3693
<b, s>(q_gen_3708) -> q_gen_3707
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3634, q_gen_3636, q_gen_3670},
Q_f={q_gen_3634},
Delta=
{
<s>(q_gen_3636) -> q_gen_3636
<z>() -> q_gen_3636
<s, s>(q_gen_3634) -> q_gen_3634
<z, s>(q_gen_3636) -> q_gen_3634
<z, z>() -> q_gen_3634
<s, s>(q_gen_3670) -> q_gen_3670
<s, z>(q_gen_3636) -> q_gen_3670
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3633, q_gen_3653, q_gen_3675, q_gen_3677, q_gen_3678},
Q_f={q_gen_3633},
Delta=
{
<nil>() -> q_gen_3677
<a>() -> q_gen_3678
<b>() -> q_gen_3678
<cons, cons>(q_gen_3653, q_gen_3633) -> q_gen_3633
<nil, nil>() -> q_gen_3633
<a, a>() -> q_gen_3653
<a, b>() -> q_gen_3653
<b, a>() -> q_gen_3653
<b, b>() -> q_gen_3653
<cons, cons>(q_gen_3653, q_gen_3675) -> q_gen_3675
<cons, nil>(q_gen_3678, q_gen_3677) -> q_gen_3675
<nil, cons>(q_gen_3678, q_gen_3677) -> q_gen_3675
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 45
() -> length([nil, z]) -> 45
() -> leq([z, s(nn2)]) -> 45
() -> leq([z, z]) -> 45
() -> reverse([nil, nil]) -> 45
(append([_eo, cons(h1, nil), _fo]) /\ reverse([t1, _eo])) -> reverse([cons(h1, t1), _fo]) -> 46
(append([t1, l2, _zn])) -> append([cons(h1, t1), l2, cons(h1, _zn)]) -> 46
(length([_oo, _po]) /\ length([l1, _no]) /\ reverse([l1, _oo])) -> leq([_no, _po]) -> 47
(length([_qo, _ro]) /\ length([l1, _so]) /\ reverse([l1, _qo])) -> leq([_ro, _so]) -> 46
(length([ll, _jo])) -> length([cons(x, ll), s(_jo)]) -> 49
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 46
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 46
(leq([s(nn1), z])) -> BOT -> 46
}
Sat witness: Found: ((length([ll, _jo])) -> length([cons(x, ll), s(_jo)]), {
_jo -> s(s(s(z)))  ;  ll -> cons(a, cons(a, cons(b, nil)))  ;  x -> a
})

-------------------------------------------
Step 85, which took 0.965157 s (model generation: 0.962541,  model checking: 0.002616):

Model:
|_
{
append -> 
{{{
Q={q_gen_3638, q_gen_3644, q_gen_3645, q_gen_3657, q_gen_3658, q_gen_3659, q_gen_3660, q_gen_3673, q_gen_3751},
Q_f={q_gen_3638},
Delta=
{
<nil>() -> q_gen_3658
<a>() -> q_gen_3659
<b>() -> q_gen_3659
<cons>(q_gen_3659, q_gen_3658) -> q_gen_3751
<cons>(q_gen_3659, q_gen_3751) -> q_gen_3751
<cons, cons>(q_gen_3645, q_gen_3644) -> q_gen_3644
<nil, cons>(q_gen_3659, q_gen_3751) -> q_gen_3644
<nil, nil>() -> q_gen_3644
<a, a>() -> q_gen_3645
<a, b>() -> q_gen_3645
<b, a>() -> q_gen_3645
<b, b>() -> q_gen_3645
<cons, cons>(q_gen_3645, q_gen_3673) -> q_gen_3673
<nil, cons>(q_gen_3659, q_gen_3658) -> q_gen_3673
<cons, cons, cons>(q_gen_3660, q_gen_3657) -> q_gen_3638
<cons, nil, cons>(q_gen_3645, q_gen_3644) -> q_gen_3638
<nil, cons, cons>(q_gen_3645, q_gen_3644) -> q_gen_3638
<nil, nil, cons>(q_gen_3659, q_gen_3751) -> q_gen_3638
<nil, nil, nil>() -> q_gen_3638
<cons, cons, cons>(q_gen_3660, q_gen_3638) -> q_gen_3657
<cons, nil, cons>(q_gen_3645, q_gen_3673) -> q_gen_3657
<nil, cons, cons>(q_gen_3645, q_gen_3673) -> q_gen_3657
<nil, nil, cons>(q_gen_3659, q_gen_3658) -> q_gen_3657
<a, a, a>() -> q_gen_3660
<a, b, a>() -> q_gen_3660
<b, a, b>() -> q_gen_3660
<b, b, b>() -> q_gen_3660
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_3637, q_gen_3641, q_gen_3642, q_gen_3665, q_gen_3666, q_gen_3667, q_gen_3668, q_gen_3669, q_gen_3692, q_gen_3693, q_gen_3694, q_gen_3707, q_gen_3708, q_gen_3734},
Q_f={q_gen_3637},
Delta=
{
<nil>() -> q_gen_3641
<cons>(q_gen_3666, q_gen_3641) -> q_gen_3665
<a>() -> q_gen_3666
<b>() -> q_gen_3666
<z>() -> q_gen_3668
<cons>(q_gen_3666, q_gen_3665) -> q_gen_3692
<s>(q_gen_3668) -> q_gen_3694
<s>(q_gen_3694) -> q_gen_3708
<s>(q_gen_3708) -> q_gen_3708
<cons>(q_gen_3666, q_gen_3692) -> q_gen_3734
<cons>(q_gen_3666, q_gen_3734) -> q_gen_3734
<cons, s>(q_gen_3642, q_gen_3641) -> q_gen_3637
<cons, s>(q_gen_3667, q_gen_3665) -> q_gen_3637
<cons, s>(q_gen_3693, q_gen_3692) -> q_gen_3637
<cons, s>(q_gen_3707, q_gen_3734) -> q_gen_3637
<nil, z>() -> q_gen_3637
<a, z>() -> q_gen_3642
<b, z>() -> q_gen_3642
<a, s>(q_gen_3668) -> q_gen_3667
<b, s>(q_gen_3668) -> q_gen_3667
<cons, s>(q_gen_3642, q_gen_3665) -> q_gen_3669
<cons, s>(q_gen_3642, q_gen_3692) -> q_gen_3669
<cons, s>(q_gen_3667, q_gen_3641) -> q_gen_3669
<cons, s>(q_gen_3667, q_gen_3692) -> q_gen_3669
<cons, s>(q_gen_3667, q_gen_3734) -> q_gen_3669
<cons, s>(q_gen_3693, q_gen_3641) -> q_gen_3669
<cons, s>(q_gen_3693, q_gen_3665) -> q_gen_3669
<cons, s>(q_gen_3693, q_gen_3734) -> q_gen_3669
<cons, s>(q_gen_3707, q_gen_3641) -> q_gen_3669
<cons, s>(q_gen_3707, q_gen_3665) -> q_gen_3669
<cons, s>(q_gen_3707, q_gen_3692) -> q_gen_3669
<a, s>(q_gen_3694) -> q_gen_3693
<b, s>(q_gen_3694) -> q_gen_3693
<a, s>(q_gen_3708) -> q_gen_3707
<b, s>(q_gen_3708) -> q_gen_3707
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3634, q_gen_3636, q_gen_3670},
Q_f={q_gen_3634},
Delta=
{
<s>(q_gen_3636) -> q_gen_3636
<z>() -> q_gen_3636
<s, s>(q_gen_3634) -> q_gen_3634
<z, s>(q_gen_3636) -> q_gen_3634
<z, z>() -> q_gen_3634
<s, s>(q_gen_3670) -> q_gen_3670
<s, z>(q_gen_3636) -> q_gen_3670
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3633, q_gen_3653, q_gen_3675, q_gen_3677, q_gen_3678},
Q_f={q_gen_3633},
Delta=
{
<nil>() -> q_gen_3677
<a>() -> q_gen_3678
<b>() -> q_gen_3678
<cons, cons>(q_gen_3653, q_gen_3633) -> q_gen_3633
<nil, nil>() -> q_gen_3633
<a, a>() -> q_gen_3653
<a, b>() -> q_gen_3653
<b, a>() -> q_gen_3653
<b, b>() -> q_gen_3653
<cons, cons>(q_gen_3653, q_gen_3675) -> q_gen_3675
<cons, nil>(q_gen_3678, q_gen_3677) -> q_gen_3675
<nil, cons>(q_gen_3678, q_gen_3677) -> q_gen_3675
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 46
() -> length([nil, z]) -> 46
() -> leq([z, s(nn2)]) -> 46
() -> leq([z, z]) -> 46
() -> reverse([nil, nil]) -> 46
(append([_eo, cons(h1, nil), _fo]) /\ reverse([t1, _eo])) -> reverse([cons(h1, t1), _fo]) -> 46
(append([t1, l2, _zn])) -> append([cons(h1, t1), l2, cons(h1, _zn)]) -> 46
(length([_oo, _po]) /\ length([l1, _no]) /\ reverse([l1, _oo])) -> leq([_no, _po]) -> 47
(length([_qo, _ro]) /\ length([l1, _so]) /\ reverse([l1, _qo])) -> leq([_ro, _so]) -> 49
(length([ll, _jo])) -> length([cons(x, ll), s(_jo)]) -> 49
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 47
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 47
(leq([s(nn1), z])) -> BOT -> 47
}
Sat witness: Found: ((length([_qo, _ro]) /\ length([l1, _so]) /\ reverse([l1, _qo])) -> leq([_ro, _so]), {
_qo -> cons(b, cons(b, cons(b, cons(b, nil))))  ;  _ro -> s(s(s(s(s(z)))))  ;  _so -> s(s(s(s(z))))  ;  l1 -> cons(b, cons(b, cons(b, cons(b, nil))))
})

-------------------------------------------
Step 86, which took 1.036667 s (model generation: 1.008511,  model checking: 0.028156):

Model:
|_
{
append -> 
{{{
Q={q_gen_3638, q_gen_3644, q_gen_3645, q_gen_3657, q_gen_3658, q_gen_3659, q_gen_3660, q_gen_3673, q_gen_3751},
Q_f={q_gen_3638},
Delta=
{
<cons>(q_gen_3659, q_gen_3751) -> q_gen_3658
<nil>() -> q_gen_3658
<a>() -> q_gen_3659
<b>() -> q_gen_3659
<cons>(q_gen_3659, q_gen_3658) -> q_gen_3751
<cons, cons>(q_gen_3645, q_gen_3644) -> q_gen_3644
<nil, cons>(q_gen_3659, q_gen_3751) -> q_gen_3644
<nil, nil>() -> q_gen_3644
<a, a>() -> q_gen_3645
<a, b>() -> q_gen_3645
<b, a>() -> q_gen_3645
<b, b>() -> q_gen_3645
<cons, cons>(q_gen_3645, q_gen_3673) -> q_gen_3673
<nil, cons>(q_gen_3659, q_gen_3658) -> q_gen_3673
<cons, cons, cons>(q_gen_3660, q_gen_3657) -> q_gen_3638
<cons, nil, cons>(q_gen_3645, q_gen_3644) -> q_gen_3638
<nil, cons, cons>(q_gen_3645, q_gen_3644) -> q_gen_3638
<nil, nil, cons>(q_gen_3659, q_gen_3751) -> q_gen_3638
<nil, nil, nil>() -> q_gen_3638
<cons, cons, cons>(q_gen_3660, q_gen_3638) -> q_gen_3657
<cons, nil, cons>(q_gen_3645, q_gen_3673) -> q_gen_3657
<nil, cons, cons>(q_gen_3645, q_gen_3673) -> q_gen_3657
<nil, nil, cons>(q_gen_3659, q_gen_3658) -> q_gen_3657
<a, a, a>() -> q_gen_3660
<a, b, a>() -> q_gen_3660
<b, a, b>() -> q_gen_3660
<b, b, b>() -> q_gen_3660
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_3637, q_gen_3641, q_gen_3642, q_gen_3665, q_gen_3666, q_gen_3667, q_gen_3668, q_gen_3669, q_gen_3692, q_gen_3693, q_gen_3694},
Q_f={q_gen_3637},
Delta=
{
<nil>() -> q_gen_3641
<cons>(q_gen_3666, q_gen_3641) -> q_gen_3665
<a>() -> q_gen_3666
<b>() -> q_gen_3666
<z>() -> q_gen_3668
<cons>(q_gen_3666, q_gen_3665) -> q_gen_3692
<cons>(q_gen_3666, q_gen_3692) -> q_gen_3692
<s>(q_gen_3668) -> q_gen_3694
<s>(q_gen_3694) -> q_gen_3694
<cons, s>(q_gen_3642, q_gen_3641) -> q_gen_3637
<cons, s>(q_gen_3667, q_gen_3665) -> q_gen_3637
<cons, s>(q_gen_3693, q_gen_3692) -> q_gen_3637
<nil, z>() -> q_gen_3637
<a, z>() -> q_gen_3642
<b, z>() -> q_gen_3642
<a, s>(q_gen_3668) -> q_gen_3667
<b, s>(q_gen_3668) -> q_gen_3667
<cons, s>(q_gen_3642, q_gen_3665) -> q_gen_3669
<cons, s>(q_gen_3642, q_gen_3692) -> q_gen_3669
<cons, s>(q_gen_3667, q_gen_3641) -> q_gen_3669
<cons, s>(q_gen_3667, q_gen_3692) -> q_gen_3669
<cons, s>(q_gen_3693, q_gen_3641) -> q_gen_3669
<cons, s>(q_gen_3693, q_gen_3665) -> q_gen_3669
<a, s>(q_gen_3694) -> q_gen_3693
<b, s>(q_gen_3694) -> q_gen_3693
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3634, q_gen_3636, q_gen_3670},
Q_f={q_gen_3634},
Delta=
{
<s>(q_gen_3636) -> q_gen_3636
<z>() -> q_gen_3636
<s, s>(q_gen_3634) -> q_gen_3634
<z, s>(q_gen_3636) -> q_gen_3634
<z, z>() -> q_gen_3634
<s, s>(q_gen_3670) -> q_gen_3670
<s, z>(q_gen_3636) -> q_gen_3670
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3633, q_gen_3652, q_gen_3653, q_gen_3663, q_gen_3675, q_gen_3677, q_gen_3678, q_gen_3698},
Q_f={q_gen_3633, q_gen_3652, q_gen_3698},
Delta=
{
<nil>() -> q_gen_3677
<a>() -> q_gen_3678
<b>() -> q_gen_3678
<cons, cons>(q_gen_3663, q_gen_3633) -> q_gen_3633
<cons, cons>(q_gen_3663, q_gen_3652) -> q_gen_3633
<nil, nil>() -> q_gen_3633
<cons, cons>(q_gen_3653, q_gen_3633) -> q_gen_3652
<a, b>() -> q_gen_3653
<b, b>() -> q_gen_3653
<a, a>() -> q_gen_3663
<b, a>() -> q_gen_3663
<cons, cons>(q_gen_3653, q_gen_3675) -> q_gen_3675
<cons, cons>(q_gen_3653, q_gen_3698) -> q_gen_3675
<cons, cons>(q_gen_3663, q_gen_3675) -> q_gen_3675
<cons, nil>(q_gen_3678, q_gen_3677) -> q_gen_3675
<nil, cons>(q_gen_3678, q_gen_3677) -> q_gen_3675
<cons, cons>(q_gen_3653, q_gen_3652) -> q_gen_3698
<cons, cons>(q_gen_3663, q_gen_3698) -> q_gen_3698
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 46
() -> length([nil, z]) -> 46
() -> leq([z, s(nn2)]) -> 46
() -> leq([z, z]) -> 46
() -> reverse([nil, nil]) -> 46
(append([_eo, cons(h1, nil), _fo]) /\ reverse([t1, _eo])) -> reverse([cons(h1, t1), _fo]) -> 49
(append([t1, l2, _zn])) -> append([cons(h1, t1), l2, cons(h1, _zn)]) -> 47
(length([_oo, _po]) /\ length([l1, _no]) /\ reverse([l1, _oo])) -> leq([_no, _po]) -> 47
(length([_qo, _ro]) /\ length([l1, _so]) /\ reverse([l1, _qo])) -> leq([_ro, _so]) -> 49
(length([ll, _jo])) -> length([cons(x, ll), s(_jo)]) -> 49
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 47
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 47
(leq([s(nn1), z])) -> BOT -> 47
}
Sat witness: Found: ((append([_eo, cons(h1, nil), _fo]) /\ reverse([t1, _eo])) -> reverse([cons(h1, t1), _fo]), {
_eo -> cons(b, cons(b, nil))  ;  _fo -> cons(b, cons(b, cons(b, nil)))  ;  h1 -> a  ;  t1 -> cons(a, cons(b, nil))
})

-------------------------------------------
Step 87, which took 2.869112 s (model generation: 2.867042,  model checking: 0.002070):

Model:
|_
{
append -> 
{{{
Q={q_gen_3638, q_gen_3644, q_gen_3645, q_gen_3657, q_gen_3658, q_gen_3659, q_gen_3660, q_gen_3673, q_gen_3751},
Q_f={q_gen_3638},
Delta=
{
<nil>() -> q_gen_3658
<a>() -> q_gen_3659
<b>() -> q_gen_3659
<cons>(q_gen_3659, q_gen_3658) -> q_gen_3751
<cons>(q_gen_3659, q_gen_3751) -> q_gen_3751
<cons, cons>(q_gen_3645, q_gen_3644) -> q_gen_3644
<nil, cons>(q_gen_3659, q_gen_3751) -> q_gen_3644
<nil, nil>() -> q_gen_3644
<a, a>() -> q_gen_3645
<a, b>() -> q_gen_3645
<b, a>() -> q_gen_3645
<b, b>() -> q_gen_3645
<cons, cons>(q_gen_3645, q_gen_3673) -> q_gen_3673
<nil, cons>(q_gen_3659, q_gen_3658) -> q_gen_3673
<cons, cons, cons>(q_gen_3660, q_gen_3657) -> q_gen_3638
<cons, nil, cons>(q_gen_3645, q_gen_3644) -> q_gen_3638
<nil, cons, cons>(q_gen_3645, q_gen_3644) -> q_gen_3638
<nil, nil, cons>(q_gen_3659, q_gen_3751) -> q_gen_3638
<nil, nil, nil>() -> q_gen_3638
<cons, cons, cons>(q_gen_3660, q_gen_3638) -> q_gen_3657
<cons, nil, cons>(q_gen_3645, q_gen_3673) -> q_gen_3657
<nil, cons, cons>(q_gen_3645, q_gen_3673) -> q_gen_3657
<nil, nil, cons>(q_gen_3659, q_gen_3658) -> q_gen_3657
<a, a, a>() -> q_gen_3660
<a, b, a>() -> q_gen_3660
<b, a, b>() -> q_gen_3660
<b, b, b>() -> q_gen_3660
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_3637, q_gen_3641, q_gen_3642, q_gen_3665, q_gen_3666, q_gen_3667, q_gen_3668, q_gen_3669, q_gen_3692, q_gen_3693, q_gen_3694, q_gen_3707, q_gen_3708, q_gen_3734},
Q_f={q_gen_3637},
Delta=
{
<nil>() -> q_gen_3641
<cons>(q_gen_3666, q_gen_3641) -> q_gen_3665
<cons>(q_gen_3666, q_gen_3734) -> q_gen_3665
<a>() -> q_gen_3666
<b>() -> q_gen_3666
<s>(q_gen_3708) -> q_gen_3668
<z>() -> q_gen_3668
<cons>(q_gen_3666, q_gen_3665) -> q_gen_3692
<s>(q_gen_3668) -> q_gen_3694
<s>(q_gen_3694) -> q_gen_3708
<cons>(q_gen_3666, q_gen_3692) -> q_gen_3734
<cons, s>(q_gen_3642, q_gen_3641) -> q_gen_3637
<cons, s>(q_gen_3667, q_gen_3665) -> q_gen_3637
<cons, s>(q_gen_3693, q_gen_3692) -> q_gen_3637
<cons, s>(q_gen_3707, q_gen_3734) -> q_gen_3637
<nil, z>() -> q_gen_3637
<a, z>() -> q_gen_3642
<b, z>() -> q_gen_3642
<a, s>(q_gen_3668) -> q_gen_3667
<b, s>(q_gen_3668) -> q_gen_3667
<cons, s>(q_gen_3642, q_gen_3665) -> q_gen_3669
<cons, s>(q_gen_3642, q_gen_3692) -> q_gen_3669
<cons, s>(q_gen_3667, q_gen_3641) -> q_gen_3669
<cons, s>(q_gen_3667, q_gen_3692) -> q_gen_3669
<cons, s>(q_gen_3667, q_gen_3734) -> q_gen_3669
<cons, s>(q_gen_3693, q_gen_3641) -> q_gen_3669
<cons, s>(q_gen_3693, q_gen_3665) -> q_gen_3669
<cons, s>(q_gen_3693, q_gen_3734) -> q_gen_3669
<cons, s>(q_gen_3707, q_gen_3641) -> q_gen_3669
<cons, s>(q_gen_3707, q_gen_3665) -> q_gen_3669
<cons, s>(q_gen_3707, q_gen_3692) -> q_gen_3669
<a, s>(q_gen_3694) -> q_gen_3693
<b, s>(q_gen_3694) -> q_gen_3693
<a, s>(q_gen_3708) -> q_gen_3707
<b, s>(q_gen_3708) -> q_gen_3707
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3634, q_gen_3636, q_gen_3670},
Q_f={q_gen_3634},
Delta=
{
<s>(q_gen_3636) -> q_gen_3636
<z>() -> q_gen_3636
<s, s>(q_gen_3634) -> q_gen_3634
<z, s>(q_gen_3636) -> q_gen_3634
<z, z>() -> q_gen_3634
<s, s>(q_gen_3670) -> q_gen_3670
<s, z>(q_gen_3636) -> q_gen_3670
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3633, q_gen_3653, q_gen_3675, q_gen_3677, q_gen_3678},
Q_f={q_gen_3633},
Delta=
{
<nil>() -> q_gen_3677
<a>() -> q_gen_3678
<b>() -> q_gen_3678
<cons, cons>(q_gen_3653, q_gen_3633) -> q_gen_3633
<nil, nil>() -> q_gen_3633
<a, a>() -> q_gen_3653
<a, b>() -> q_gen_3653
<b, a>() -> q_gen_3653
<b, b>() -> q_gen_3653
<cons, cons>(q_gen_3653, q_gen_3675) -> q_gen_3675
<cons, nil>(q_gen_3678, q_gen_3677) -> q_gen_3675
<nil, cons>(q_gen_3678, q_gen_3677) -> q_gen_3675
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 47
() -> length([nil, z]) -> 47
() -> leq([z, s(nn2)]) -> 47
() -> leq([z, z]) -> 47
() -> reverse([nil, nil]) -> 47
(append([_eo, cons(h1, nil), _fo]) /\ reverse([t1, _eo])) -> reverse([cons(h1, t1), _fo]) -> 49
(append([t1, l2, _zn])) -> append([cons(h1, t1), l2, cons(h1, _zn)]) -> 47
(length([_oo, _po]) /\ length([l1, _no]) /\ reverse([l1, _oo])) -> leq([_no, _po]) -> 50
(length([_qo, _ro]) /\ length([l1, _so]) /\ reverse([l1, _qo])) -> leq([_ro, _so]) -> 49
(length([ll, _jo])) -> length([cons(x, ll), s(_jo)]) -> 49
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 48
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 48
(leq([s(nn1), z])) -> BOT -> 48
}
Sat witness: Found: ((length([_oo, _po]) /\ length([l1, _no]) /\ reverse([l1, _oo])) -> leq([_no, _po]), {
_no -> s(s(s(s(s(z)))))  ;  _oo -> cons(b, cons(b, nil))  ;  _po -> s(s(z))  ;  l1 -> cons(b, cons(b, nil))
})

-------------------------------------------
Step 88, which took 2.135142 s (model generation: 2.130556,  model checking: 0.004586):

Model:
|_
{
append -> 
{{{
Q={q_gen_3638, q_gen_3644, q_gen_3645, q_gen_3657, q_gen_3658, q_gen_3659, q_gen_3660, q_gen_3673, q_gen_3751},
Q_f={q_gen_3638},
Delta=
{
<nil>() -> q_gen_3658
<a>() -> q_gen_3659
<b>() -> q_gen_3659
<cons>(q_gen_3659, q_gen_3658) -> q_gen_3751
<cons>(q_gen_3659, q_gen_3751) -> q_gen_3751
<cons, cons>(q_gen_3645, q_gen_3644) -> q_gen_3644
<nil, cons>(q_gen_3659, q_gen_3751) -> q_gen_3644
<nil, nil>() -> q_gen_3644
<a, a>() -> q_gen_3645
<a, b>() -> q_gen_3645
<b, a>() -> q_gen_3645
<b, b>() -> q_gen_3645
<cons, cons>(q_gen_3645, q_gen_3673) -> q_gen_3673
<nil, cons>(q_gen_3659, q_gen_3658) -> q_gen_3673
<cons, cons, cons>(q_gen_3660, q_gen_3657) -> q_gen_3638
<cons, nil, cons>(q_gen_3645, q_gen_3644) -> q_gen_3638
<nil, cons, cons>(q_gen_3645, q_gen_3644) -> q_gen_3638
<nil, nil, cons>(q_gen_3659, q_gen_3751) -> q_gen_3638
<nil, nil, nil>() -> q_gen_3638
<cons, cons, cons>(q_gen_3660, q_gen_3638) -> q_gen_3657
<cons, nil, cons>(q_gen_3645, q_gen_3673) -> q_gen_3657
<nil, cons, cons>(q_gen_3645, q_gen_3673) -> q_gen_3657
<nil, nil, cons>(q_gen_3659, q_gen_3658) -> q_gen_3657
<a, a, a>() -> q_gen_3660
<a, b, a>() -> q_gen_3660
<b, a, b>() -> q_gen_3660
<b, b, b>() -> q_gen_3660
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_3637, q_gen_3641, q_gen_3642, q_gen_3665, q_gen_3666, q_gen_3667, q_gen_3668, q_gen_3669, q_gen_3692, q_gen_3693, q_gen_3694},
Q_f={q_gen_3637},
Delta=
{
<nil>() -> q_gen_3641
<cons>(q_gen_3666, q_gen_3641) -> q_gen_3665
<a>() -> q_gen_3666
<b>() -> q_gen_3666
<z>() -> q_gen_3668
<cons>(q_gen_3666, q_gen_3665) -> q_gen_3692
<cons>(q_gen_3666, q_gen_3692) -> q_gen_3692
<s>(q_gen_3668) -> q_gen_3694
<s>(q_gen_3694) -> q_gen_3694
<cons, s>(q_gen_3642, q_gen_3641) -> q_gen_3637
<cons, s>(q_gen_3667, q_gen_3665) -> q_gen_3637
<cons, s>(q_gen_3667, q_gen_3692) -> q_gen_3637
<cons, s>(q_gen_3693, q_gen_3692) -> q_gen_3637
<nil, z>() -> q_gen_3637
<a, z>() -> q_gen_3642
<b, z>() -> q_gen_3642
<a, s>(q_gen_3668) -> q_gen_3667
<a, s>(q_gen_3694) -> q_gen_3667
<b, s>(q_gen_3668) -> q_gen_3667
<cons, s>(q_gen_3642, q_gen_3665) -> q_gen_3669
<cons, s>(q_gen_3642, q_gen_3692) -> q_gen_3669
<cons, s>(q_gen_3667, q_gen_3641) -> q_gen_3669
<cons, s>(q_gen_3693, q_gen_3641) -> q_gen_3669
<cons, s>(q_gen_3693, q_gen_3665) -> q_gen_3669
<b, s>(q_gen_3694) -> q_gen_3693
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3634, q_gen_3636, q_gen_3670},
Q_f={q_gen_3634},
Delta=
{
<s>(q_gen_3636) -> q_gen_3636
<z>() -> q_gen_3636
<s, s>(q_gen_3634) -> q_gen_3634
<z, s>(q_gen_3636) -> q_gen_3634
<z, z>() -> q_gen_3634
<s, s>(q_gen_3670) -> q_gen_3670
<s, z>(q_gen_3636) -> q_gen_3670
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3633, q_gen_3652, q_gen_3653, q_gen_3663, q_gen_3675, q_gen_3677, q_gen_3678, q_gen_3698},
Q_f={q_gen_3633, q_gen_3652, q_gen_3698},
Delta=
{
<nil>() -> q_gen_3677
<a>() -> q_gen_3678
<b>() -> q_gen_3678
<nil, nil>() -> q_gen_3633
<cons, cons>(q_gen_3653, q_gen_3633) -> q_gen_3652
<cons, cons>(q_gen_3663, q_gen_3633) -> q_gen_3652
<cons, cons>(q_gen_3663, q_gen_3652) -> q_gen_3652
<b, b>() -> q_gen_3653
<a, a>() -> q_gen_3663
<a, b>() -> q_gen_3663
<b, a>() -> q_gen_3663
<cons, cons>(q_gen_3653, q_gen_3675) -> q_gen_3675
<cons, cons>(q_gen_3653, q_gen_3698) -> q_gen_3675
<cons, cons>(q_gen_3663, q_gen_3675) -> q_gen_3675
<cons, nil>(q_gen_3678, q_gen_3677) -> q_gen_3675
<nil, cons>(q_gen_3678, q_gen_3677) -> q_gen_3675
<cons, cons>(q_gen_3653, q_gen_3652) -> q_gen_3698
<cons, cons>(q_gen_3663, q_gen_3698) -> q_gen_3698
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 47
() -> length([nil, z]) -> 47
() -> leq([z, s(nn2)]) -> 47
() -> leq([z, z]) -> 47
() -> reverse([nil, nil]) -> 47
(append([_eo, cons(h1, nil), _fo]) /\ reverse([t1, _eo])) -> reverse([cons(h1, t1), _fo]) -> 49
(append([t1, l2, _zn])) -> append([cons(h1, t1), l2, cons(h1, _zn)]) -> 50
(length([_oo, _po]) /\ length([l1, _no]) /\ reverse([l1, _oo])) -> leq([_no, _po]) -> 50
(length([_qo, _ro]) /\ length([l1, _so]) /\ reverse([l1, _qo])) -> leq([_ro, _so]) -> 49
(length([ll, _jo])) -> length([cons(x, ll), s(_jo)]) -> 49
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 48
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 48
(leq([s(nn1), z])) -> BOT -> 48
}
Sat witness: Found: ((append([t1, l2, _zn])) -> append([cons(h1, t1), l2, cons(h1, _zn)]), {
_zn -> cons(b, cons(b, cons(b, nil)))  ;  h1 -> a  ;  l2 -> cons(b, nil)  ;  t1 -> nil
})

-------------------------------------------
Step 89, which took 2.827506 s (model generation: 2.824365,  model checking: 0.003141):

Model:
|_
{
append -> 
{{{
Q={q_gen_3638, q_gen_3644, q_gen_3645, q_gen_3657, q_gen_3658, q_gen_3659, q_gen_3660, q_gen_3673, q_gen_3751},
Q_f={q_gen_3638},
Delta=
{
<cons>(q_gen_3659, q_gen_3751) -> q_gen_3658
<nil>() -> q_gen_3658
<a>() -> q_gen_3659
<b>() -> q_gen_3659
<cons>(q_gen_3659, q_gen_3658) -> q_gen_3751
<cons, cons>(q_gen_3645, q_gen_3644) -> q_gen_3644
<nil, cons>(q_gen_3659, q_gen_3751) -> q_gen_3644
<nil, nil>() -> q_gen_3644
<a, a>() -> q_gen_3645
<a, b>() -> q_gen_3645
<b, a>() -> q_gen_3645
<b, b>() -> q_gen_3645
<cons, cons>(q_gen_3645, q_gen_3673) -> q_gen_3673
<nil, cons>(q_gen_3659, q_gen_3658) -> q_gen_3673
<cons, cons, cons>(q_gen_3660, q_gen_3657) -> q_gen_3638
<cons, nil, cons>(q_gen_3645, q_gen_3644) -> q_gen_3638
<nil, cons, cons>(q_gen_3645, q_gen_3644) -> q_gen_3638
<nil, nil, cons>(q_gen_3659, q_gen_3751) -> q_gen_3638
<nil, nil, nil>() -> q_gen_3638
<cons, cons, cons>(q_gen_3660, q_gen_3638) -> q_gen_3657
<cons, nil, cons>(q_gen_3645, q_gen_3673) -> q_gen_3657
<nil, cons, cons>(q_gen_3645, q_gen_3673) -> q_gen_3657
<nil, nil, cons>(q_gen_3659, q_gen_3658) -> q_gen_3657
<a, a, a>() -> q_gen_3660
<a, b, a>() -> q_gen_3660
<b, a, b>() -> q_gen_3660
<b, b, b>() -> q_gen_3660
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_3637, q_gen_3641, q_gen_3642, q_gen_3665, q_gen_3666, q_gen_3667, q_gen_3668, q_gen_3669, q_gen_3692, q_gen_3693, q_gen_3694, q_gen_3707, q_gen_3708, q_gen_3734},
Q_f={q_gen_3637},
Delta=
{
<nil>() -> q_gen_3641
<cons>(q_gen_3666, q_gen_3641) -> q_gen_3665
<a>() -> q_gen_3666
<b>() -> q_gen_3666
<z>() -> q_gen_3668
<cons>(q_gen_3666, q_gen_3665) -> q_gen_3692
<cons>(q_gen_3666, q_gen_3734) -> q_gen_3692
<s>(q_gen_3668) -> q_gen_3694
<s>(q_gen_3708) -> q_gen_3694
<s>(q_gen_3694) -> q_gen_3708
<cons>(q_gen_3666, q_gen_3692) -> q_gen_3734
<cons, s>(q_gen_3642, q_gen_3641) -> q_gen_3637
<cons, s>(q_gen_3642, q_gen_3734) -> q_gen_3637
<cons, s>(q_gen_3667, q_gen_3665) -> q_gen_3637
<cons, s>(q_gen_3693, q_gen_3692) -> q_gen_3637
<cons, s>(q_gen_3707, q_gen_3734) -> q_gen_3637
<nil, z>() -> q_gen_3637
<a, s>(q_gen_3708) -> q_gen_3642
<a, z>() -> q_gen_3642
<b, z>() -> q_gen_3642
<a, s>(q_gen_3668) -> q_gen_3667
<b, s>(q_gen_3668) -> q_gen_3667
<cons, s>(q_gen_3642, q_gen_3665) -> q_gen_3669
<cons, s>(q_gen_3642, q_gen_3692) -> q_gen_3669
<cons, s>(q_gen_3667, q_gen_3641) -> q_gen_3669
<cons, s>(q_gen_3667, q_gen_3692) -> q_gen_3669
<cons, s>(q_gen_3667, q_gen_3734) -> q_gen_3669
<cons, s>(q_gen_3693, q_gen_3641) -> q_gen_3669
<cons, s>(q_gen_3693, q_gen_3665) -> q_gen_3669
<cons, s>(q_gen_3693, q_gen_3734) -> q_gen_3669
<cons, s>(q_gen_3707, q_gen_3641) -> q_gen_3669
<cons, s>(q_gen_3707, q_gen_3665) -> q_gen_3669
<cons, s>(q_gen_3707, q_gen_3692) -> q_gen_3669
<a, s>(q_gen_3694) -> q_gen_3693
<b, s>(q_gen_3694) -> q_gen_3693
<b, s>(q_gen_3708) -> q_gen_3707
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3634, q_gen_3636, q_gen_3670},
Q_f={q_gen_3634},
Delta=
{
<s>(q_gen_3636) -> q_gen_3636
<z>() -> q_gen_3636
<s, s>(q_gen_3634) -> q_gen_3634
<z, s>(q_gen_3636) -> q_gen_3634
<z, z>() -> q_gen_3634
<s, s>(q_gen_3670) -> q_gen_3670
<s, z>(q_gen_3636) -> q_gen_3670
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3633, q_gen_3653, q_gen_3675, q_gen_3677, q_gen_3678},
Q_f={q_gen_3633},
Delta=
{
<nil>() -> q_gen_3677
<a>() -> q_gen_3678
<b>() -> q_gen_3678
<cons, cons>(q_gen_3653, q_gen_3633) -> q_gen_3633
<nil, nil>() -> q_gen_3633
<a, a>() -> q_gen_3653
<a, b>() -> q_gen_3653
<b, a>() -> q_gen_3653
<b, b>() -> q_gen_3653
<cons, cons>(q_gen_3653, q_gen_3675) -> q_gen_3675
<cons, nil>(q_gen_3678, q_gen_3677) -> q_gen_3675
<nil, cons>(q_gen_3678, q_gen_3677) -> q_gen_3675
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 48
() -> length([nil, z]) -> 48
() -> leq([z, s(nn2)]) -> 48
() -> leq([z, z]) -> 48
() -> reverse([nil, nil]) -> 48
(append([_eo, cons(h1, nil), _fo]) /\ reverse([t1, _eo])) -> reverse([cons(h1, t1), _fo]) -> 49
(append([t1, l2, _zn])) -> append([cons(h1, t1), l2, cons(h1, _zn)]) -> 50
(length([_oo, _po]) /\ length([l1, _no]) /\ reverse([l1, _oo])) -> leq([_no, _po]) -> 50
(length([_qo, _ro]) /\ length([l1, _so]) /\ reverse([l1, _qo])) -> leq([_ro, _so]) -> 49
(length([ll, _jo])) -> length([cons(x, ll), s(_jo)]) -> 52
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 49
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 49
(leq([s(nn1), z])) -> BOT -> 49
}
Sat witness: Found: ((length([ll, _jo])) -> length([cons(x, ll), s(_jo)]), {
_jo -> s(s(s(s(z))))  ;  ll -> cons(a, nil)  ;  x -> a
})

-------------------------------------------
Step 90, which took 2.156382 s (model generation: 2.154449,  model checking: 0.001933):

Model:
|_
{
append -> 
{{{
Q={q_gen_3638, q_gen_3644, q_gen_3645, q_gen_3657, q_gen_3658, q_gen_3659, q_gen_3660, q_gen_3673, q_gen_3751},
Q_f={q_gen_3638},
Delta=
{
<cons>(q_gen_3659, q_gen_3751) -> q_gen_3658
<nil>() -> q_gen_3658
<a>() -> q_gen_3659
<b>() -> q_gen_3659
<cons>(q_gen_3659, q_gen_3658) -> q_gen_3751
<cons, cons>(q_gen_3645, q_gen_3644) -> q_gen_3644
<nil, cons>(q_gen_3659, q_gen_3751) -> q_gen_3644
<nil, nil>() -> q_gen_3644
<a, a>() -> q_gen_3645
<a, b>() -> q_gen_3645
<b, a>() -> q_gen_3645
<b, b>() -> q_gen_3645
<cons, cons>(q_gen_3645, q_gen_3673) -> q_gen_3673
<nil, cons>(q_gen_3659, q_gen_3658) -> q_gen_3673
<cons, cons, cons>(q_gen_3660, q_gen_3657) -> q_gen_3638
<cons, nil, cons>(q_gen_3645, q_gen_3644) -> q_gen_3638
<nil, cons, cons>(q_gen_3645, q_gen_3644) -> q_gen_3638
<nil, nil, cons>(q_gen_3659, q_gen_3751) -> q_gen_3638
<nil, nil, nil>() -> q_gen_3638
<cons, cons, cons>(q_gen_3660, q_gen_3638) -> q_gen_3657
<cons, nil, cons>(q_gen_3645, q_gen_3673) -> q_gen_3657
<nil, cons, cons>(q_gen_3645, q_gen_3673) -> q_gen_3657
<nil, nil, cons>(q_gen_3659, q_gen_3658) -> q_gen_3657
<a, a, a>() -> q_gen_3660
<a, b, a>() -> q_gen_3660
<b, a, b>() -> q_gen_3660
<b, b, b>() -> q_gen_3660
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_3637, q_gen_3641, q_gen_3642, q_gen_3665, q_gen_3666, q_gen_3667, q_gen_3668, q_gen_3669, q_gen_3692, q_gen_3693, q_gen_3694},
Q_f={q_gen_3637},
Delta=
{
<nil>() -> q_gen_3641
<cons>(q_gen_3666, q_gen_3641) -> q_gen_3665
<a>() -> q_gen_3666
<b>() -> q_gen_3666
<z>() -> q_gen_3668
<cons>(q_gen_3666, q_gen_3665) -> q_gen_3692
<cons>(q_gen_3666, q_gen_3692) -> q_gen_3692
<s>(q_gen_3668) -> q_gen_3694
<s>(q_gen_3694) -> q_gen_3694
<cons, s>(q_gen_3642, q_gen_3641) -> q_gen_3637
<cons, s>(q_gen_3667, q_gen_3665) -> q_gen_3637
<cons, s>(q_gen_3667, q_gen_3692) -> q_gen_3637
<cons, s>(q_gen_3693, q_gen_3692) -> q_gen_3637
<nil, z>() -> q_gen_3637
<a, z>() -> q_gen_3642
<b, z>() -> q_gen_3642
<a, s>(q_gen_3668) -> q_gen_3667
<a, s>(q_gen_3694) -> q_gen_3667
<b, s>(q_gen_3668) -> q_gen_3667
<cons, s>(q_gen_3642, q_gen_3665) -> q_gen_3669
<cons, s>(q_gen_3642, q_gen_3692) -> q_gen_3669
<cons, s>(q_gen_3667, q_gen_3641) -> q_gen_3669
<cons, s>(q_gen_3693, q_gen_3641) -> q_gen_3669
<cons, s>(q_gen_3693, q_gen_3665) -> q_gen_3669
<b, s>(q_gen_3694) -> q_gen_3693
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3634, q_gen_3636, q_gen_3670},
Q_f={q_gen_3634},
Delta=
{
<s>(q_gen_3636) -> q_gen_3636
<z>() -> q_gen_3636
<s, s>(q_gen_3634) -> q_gen_3634
<z, s>(q_gen_3636) -> q_gen_3634
<z, z>() -> q_gen_3634
<s, s>(q_gen_3670) -> q_gen_3670
<s, z>(q_gen_3636) -> q_gen_3670
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3633, q_gen_3652, q_gen_3653, q_gen_3663, q_gen_3675, q_gen_3677, q_gen_3678, q_gen_3698},
Q_f={q_gen_3633, q_gen_3652, q_gen_3698},
Delta=
{
<nil>() -> q_gen_3677
<a>() -> q_gen_3678
<b>() -> q_gen_3678
<cons, cons>(q_gen_3663, q_gen_3698) -> q_gen_3633
<nil, nil>() -> q_gen_3633
<cons, cons>(q_gen_3653, q_gen_3633) -> q_gen_3652
<cons, cons>(q_gen_3663, q_gen_3633) -> q_gen_3652
<cons, cons>(q_gen_3663, q_gen_3652) -> q_gen_3652
<b, b>() -> q_gen_3653
<a, a>() -> q_gen_3663
<a, b>() -> q_gen_3663
<b, a>() -> q_gen_3663
<cons, cons>(q_gen_3653, q_gen_3675) -> q_gen_3675
<cons, cons>(q_gen_3653, q_gen_3698) -> q_gen_3675
<cons, cons>(q_gen_3663, q_gen_3675) -> q_gen_3675
<cons, nil>(q_gen_3678, q_gen_3677) -> q_gen_3675
<nil, cons>(q_gen_3678, q_gen_3677) -> q_gen_3675
<cons, cons>(q_gen_3653, q_gen_3652) -> q_gen_3698
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 49
() -> length([nil, z]) -> 49
() -> leq([z, s(nn2)]) -> 49
() -> leq([z, z]) -> 49
() -> reverse([nil, nil]) -> 49
(append([_eo, cons(h1, nil), _fo]) /\ reverse([t1, _eo])) -> reverse([cons(h1, t1), _fo]) -> 49
(append([t1, l2, _zn])) -> append([cons(h1, t1), l2, cons(h1, _zn)]) -> 50
(length([_oo, _po]) /\ length([l1, _no]) /\ reverse([l1, _oo])) -> leq([_no, _po]) -> 50
(length([_qo, _ro]) /\ length([l1, _so]) /\ reverse([l1, _qo])) -> leq([_ro, _so]) -> 52
(length([ll, _jo])) -> length([cons(x, ll), s(_jo)]) -> 52
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 50
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 50
(leq([s(nn1), z])) -> BOT -> 50
}
Sat witness: Found: ((length([_qo, _ro]) /\ length([l1, _so]) /\ reverse([l1, _qo])) -> leq([_ro, _so]), {
_qo -> cons(b, cons(a, cons(b, nil)))  ;  _ro -> s(s(s(z)))  ;  _so -> s(s(z))  ;  l1 -> cons(b, cons(b, cons(b, nil)))
})

-------------------------------------------
Step 91, which took 2.442104 s (model generation: 2.440917,  model checking: 0.001187):

Model:
|_
{
append -> 
{{{
Q={q_gen_3638, q_gen_3644, q_gen_3645, q_gen_3657, q_gen_3658, q_gen_3659, q_gen_3660, q_gen_3673, q_gen_3751},
Q_f={q_gen_3638},
Delta=
{
<cons>(q_gen_3659, q_gen_3751) -> q_gen_3658
<nil>() -> q_gen_3658
<a>() -> q_gen_3659
<b>() -> q_gen_3659
<cons>(q_gen_3659, q_gen_3658) -> q_gen_3751
<cons, cons>(q_gen_3645, q_gen_3644) -> q_gen_3644
<nil, cons>(q_gen_3659, q_gen_3751) -> q_gen_3644
<nil, nil>() -> q_gen_3644
<a, a>() -> q_gen_3645
<a, b>() -> q_gen_3645
<b, a>() -> q_gen_3645
<b, b>() -> q_gen_3645
<cons, cons>(q_gen_3645, q_gen_3673) -> q_gen_3673
<nil, cons>(q_gen_3659, q_gen_3658) -> q_gen_3673
<cons, cons, cons>(q_gen_3660, q_gen_3657) -> q_gen_3638
<cons, nil, cons>(q_gen_3645, q_gen_3644) -> q_gen_3638
<nil, cons, cons>(q_gen_3645, q_gen_3644) -> q_gen_3638
<nil, nil, cons>(q_gen_3659, q_gen_3751) -> q_gen_3638
<nil, nil, nil>() -> q_gen_3638
<cons, cons, cons>(q_gen_3660, q_gen_3638) -> q_gen_3657
<cons, nil, cons>(q_gen_3645, q_gen_3673) -> q_gen_3657
<nil, cons, cons>(q_gen_3645, q_gen_3673) -> q_gen_3657
<nil, nil, cons>(q_gen_3659, q_gen_3658) -> q_gen_3657
<a, a, a>() -> q_gen_3660
<a, b, a>() -> q_gen_3660
<b, a, b>() -> q_gen_3660
<b, b, b>() -> q_gen_3660
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_3637, q_gen_3641, q_gen_3642, q_gen_3665, q_gen_3666, q_gen_3667, q_gen_3668, q_gen_3669, q_gen_3692, q_gen_3693, q_gen_3694},
Q_f={q_gen_3637},
Delta=
{
<nil>() -> q_gen_3641
<cons>(q_gen_3666, q_gen_3641) -> q_gen_3665
<a>() -> q_gen_3666
<b>() -> q_gen_3666
<z>() -> q_gen_3668
<cons>(q_gen_3666, q_gen_3665) -> q_gen_3692
<cons>(q_gen_3666, q_gen_3692) -> q_gen_3692
<s>(q_gen_3668) -> q_gen_3694
<s>(q_gen_3694) -> q_gen_3694
<cons, s>(q_gen_3642, q_gen_3641) -> q_gen_3637
<cons, s>(q_gen_3667, q_gen_3665) -> q_gen_3637
<cons, s>(q_gen_3693, q_gen_3692) -> q_gen_3637
<nil, z>() -> q_gen_3637
<a, z>() -> q_gen_3642
<b, z>() -> q_gen_3642
<a, s>(q_gen_3668) -> q_gen_3667
<b, s>(q_gen_3668) -> q_gen_3667
<cons, s>(q_gen_3642, q_gen_3665) -> q_gen_3669
<cons, s>(q_gen_3642, q_gen_3692) -> q_gen_3669
<cons, s>(q_gen_3667, q_gen_3641) -> q_gen_3669
<cons, s>(q_gen_3667, q_gen_3692) -> q_gen_3669
<cons, s>(q_gen_3693, q_gen_3641) -> q_gen_3669
<cons, s>(q_gen_3693, q_gen_3665) -> q_gen_3669
<a, s>(q_gen_3694) -> q_gen_3693
<b, s>(q_gen_3694) -> q_gen_3693
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3634, q_gen_3636, q_gen_3670},
Q_f={q_gen_3634},
Delta=
{
<s>(q_gen_3636) -> q_gen_3636
<z>() -> q_gen_3636
<s, s>(q_gen_3634) -> q_gen_3634
<z, s>(q_gen_3636) -> q_gen_3634
<z, z>() -> q_gen_3634
<s, s>(q_gen_3670) -> q_gen_3670
<s, z>(q_gen_3636) -> q_gen_3670
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3633, q_gen_3652, q_gen_3653, q_gen_3663, q_gen_3675, q_gen_3677, q_gen_3678, q_gen_3698},
Q_f={q_gen_3633, q_gen_3652, q_gen_3698},
Delta=
{
<nil>() -> q_gen_3677
<a>() -> q_gen_3678
<b>() -> q_gen_3678
<cons, cons>(q_gen_3663, q_gen_3698) -> q_gen_3633
<nil, nil>() -> q_gen_3633
<cons, cons>(q_gen_3653, q_gen_3633) -> q_gen_3652
<cons, cons>(q_gen_3663, q_gen_3633) -> q_gen_3652
<cons, cons>(q_gen_3663, q_gen_3652) -> q_gen_3652
<b, b>() -> q_gen_3653
<a, a>() -> q_gen_3663
<a, b>() -> q_gen_3663
<b, a>() -> q_gen_3663
<cons, cons>(q_gen_3653, q_gen_3675) -> q_gen_3675
<cons, cons>(q_gen_3653, q_gen_3698) -> q_gen_3675
<cons, cons>(q_gen_3663, q_gen_3675) -> q_gen_3675
<cons, nil>(q_gen_3678, q_gen_3677) -> q_gen_3675
<nil, cons>(q_gen_3678, q_gen_3677) -> q_gen_3675
<cons, cons>(q_gen_3653, q_gen_3652) -> q_gen_3698
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 49
() -> length([nil, z]) -> 49
() -> leq([z, s(nn2)]) -> 49
() -> leq([z, z]) -> 49
() -> reverse([nil, nil]) -> 49
(append([_eo, cons(h1, nil), _fo]) /\ reverse([t1, _eo])) -> reverse([cons(h1, t1), _fo]) -> 52
(append([t1, l2, _zn])) -> append([cons(h1, t1), l2, cons(h1, _zn)]) -> 50
(length([_oo, _po]) /\ length([l1, _no]) /\ reverse([l1, _oo])) -> leq([_no, _po]) -> 50
(length([_qo, _ro]) /\ length([l1, _so]) /\ reverse([l1, _qo])) -> leq([_ro, _so]) -> 52
(length([ll, _jo])) -> length([cons(x, ll), s(_jo)]) -> 52
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 50
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 50
(leq([s(nn1), z])) -> BOT -> 50
}
Sat witness: Found: ((append([_eo, cons(h1, nil), _fo]) /\ reverse([t1, _eo])) -> reverse([cons(h1, t1), _fo]), {
_eo -> cons(b, cons(b, nil))  ;  _fo -> cons(b, cons(b, cons(b, nil)))  ;  h1 -> b  ;  t1 -> cons(b, cons(b, nil))
})

-------------------------------------------
Step 92, which took 2.809046 s (model generation: 2.808160,  model checking: 0.000886):

Model:
|_
{
append -> 
{{{
Q={q_gen_3638, q_gen_3644, q_gen_3645, q_gen_3657, q_gen_3658, q_gen_3659, q_gen_3660, q_gen_3673, q_gen_3751},
Q_f={q_gen_3638},
Delta=
{
<cons>(q_gen_3659, q_gen_3751) -> q_gen_3658
<nil>() -> q_gen_3658
<a>() -> q_gen_3659
<b>() -> q_gen_3659
<cons>(q_gen_3659, q_gen_3658) -> q_gen_3751
<cons, cons>(q_gen_3645, q_gen_3644) -> q_gen_3644
<nil, cons>(q_gen_3659, q_gen_3751) -> q_gen_3644
<nil, nil>() -> q_gen_3644
<a, a>() -> q_gen_3645
<a, b>() -> q_gen_3645
<b, a>() -> q_gen_3645
<b, b>() -> q_gen_3645
<cons, cons>(q_gen_3645, q_gen_3673) -> q_gen_3673
<nil, cons>(q_gen_3659, q_gen_3658) -> q_gen_3673
<cons, cons, cons>(q_gen_3660, q_gen_3657) -> q_gen_3638
<cons, nil, cons>(q_gen_3645, q_gen_3644) -> q_gen_3638
<nil, cons, cons>(q_gen_3645, q_gen_3644) -> q_gen_3638
<nil, nil, cons>(q_gen_3659, q_gen_3751) -> q_gen_3638
<nil, nil, nil>() -> q_gen_3638
<cons, cons, cons>(q_gen_3660, q_gen_3638) -> q_gen_3657
<cons, nil, cons>(q_gen_3645, q_gen_3673) -> q_gen_3657
<nil, cons, cons>(q_gen_3645, q_gen_3673) -> q_gen_3657
<nil, nil, cons>(q_gen_3659, q_gen_3658) -> q_gen_3657
<a, a, a>() -> q_gen_3660
<a, b, a>() -> q_gen_3660
<b, a, b>() -> q_gen_3660
<b, b, b>() -> q_gen_3660
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_3637, q_gen_3641, q_gen_3642, q_gen_3665, q_gen_3666, q_gen_3667, q_gen_3668, q_gen_3669, q_gen_3692, q_gen_3693, q_gen_3694, q_gen_3708},
Q_f={q_gen_3637},
Delta=
{
<cons>(q_gen_3666, q_gen_3692) -> q_gen_3641
<nil>() -> q_gen_3641
<cons>(q_gen_3666, q_gen_3641) -> q_gen_3665
<a>() -> q_gen_3666
<b>() -> q_gen_3666
<s>(q_gen_3708) -> q_gen_3668
<z>() -> q_gen_3668
<cons>(q_gen_3666, q_gen_3665) -> q_gen_3692
<s>(q_gen_3668) -> q_gen_3694
<s>(q_gen_3694) -> q_gen_3708
<cons, s>(q_gen_3642, q_gen_3641) -> q_gen_3637
<cons, s>(q_gen_3667, q_gen_3665) -> q_gen_3637
<cons, s>(q_gen_3693, q_gen_3692) -> q_gen_3637
<nil, z>() -> q_gen_3637
<a, s>(q_gen_3708) -> q_gen_3642
<a, z>() -> q_gen_3642
<b, s>(q_gen_3708) -> q_gen_3642
<b, z>() -> q_gen_3642
<a, s>(q_gen_3668) -> q_gen_3667
<b, s>(q_gen_3668) -> q_gen_3667
<cons, s>(q_gen_3642, q_gen_3665) -> q_gen_3669
<cons, s>(q_gen_3642, q_gen_3692) -> q_gen_3669
<cons, s>(q_gen_3667, q_gen_3641) -> q_gen_3669
<cons, s>(q_gen_3667, q_gen_3692) -> q_gen_3669
<cons, s>(q_gen_3693, q_gen_3641) -> q_gen_3669
<cons, s>(q_gen_3693, q_gen_3665) -> q_gen_3669
<a, s>(q_gen_3694) -> q_gen_3693
<b, s>(q_gen_3694) -> q_gen_3693
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3634, q_gen_3636, q_gen_3647, q_gen_3670, q_gen_3723},
Q_f={q_gen_3634},
Delta=
{
<z>() -> q_gen_3636
<s>(q_gen_3636) -> q_gen_3647
<s>(q_gen_3723) -> q_gen_3647
<s>(q_gen_3647) -> q_gen_3723
<s, s>(q_gen_3634) -> q_gen_3634
<s, z>(q_gen_3723) -> q_gen_3634
<z, s>(q_gen_3636) -> q_gen_3634
<z, s>(q_gen_3647) -> q_gen_3634
<z, s>(q_gen_3723) -> q_gen_3634
<z, z>() -> q_gen_3634
<s, s>(q_gen_3670) -> q_gen_3670
<s, z>(q_gen_3636) -> q_gen_3670
<s, z>(q_gen_3647) -> q_gen_3670
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3633, q_gen_3653, q_gen_3675, q_gen_3677, q_gen_3678},
Q_f={q_gen_3633},
Delta=
{
<nil>() -> q_gen_3677
<a>() -> q_gen_3678
<b>() -> q_gen_3678
<cons, cons>(q_gen_3653, q_gen_3633) -> q_gen_3633
<nil, nil>() -> q_gen_3633
<a, a>() -> q_gen_3653
<a, b>() -> q_gen_3653
<b, a>() -> q_gen_3653
<b, b>() -> q_gen_3653
<cons, cons>(q_gen_3653, q_gen_3675) -> q_gen_3675
<cons, nil>(q_gen_3678, q_gen_3677) -> q_gen_3675
<nil, cons>(q_gen_3678, q_gen_3677) -> q_gen_3675
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 50
() -> length([nil, z]) -> 50
() -> leq([z, s(nn2)]) -> 50
() -> leq([z, z]) -> 50
() -> reverse([nil, nil]) -> 50
(append([_eo, cons(h1, nil), _fo]) /\ reverse([t1, _eo])) -> reverse([cons(h1, t1), _fo]) -> 52
(append([t1, l2, _zn])) -> append([cons(h1, t1), l2, cons(h1, _zn)]) -> 50
(length([_oo, _po]) /\ length([l1, _no]) /\ reverse([l1, _oo])) -> leq([_no, _po]) -> 50
(length([_qo, _ro]) /\ length([l1, _so]) /\ reverse([l1, _qo])) -> leq([_ro, _so]) -> 52
(length([ll, _jo])) -> length([cons(x, ll), s(_jo)]) -> 52
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 50
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 50
(leq([s(nn1), z])) -> BOT -> 53
}
Sat witness: Found: ((leq([s(nn1), z])) -> BOT, {
nn1 -> s(s(z))
})

-------------------------------------------
Step 93, which took 1.326015 s (model generation: 1.323080,  model checking: 0.002935):

Model:
|_
{
append -> 
{{{
Q={q_gen_3638, q_gen_3644, q_gen_3645, q_gen_3657, q_gen_3658, q_gen_3659, q_gen_3660, q_gen_3673, q_gen_3751},
Q_f={q_gen_3638},
Delta=
{
<cons>(q_gen_3659, q_gen_3751) -> q_gen_3658
<nil>() -> q_gen_3658
<a>() -> q_gen_3659
<b>() -> q_gen_3659
<cons>(q_gen_3659, q_gen_3658) -> q_gen_3751
<cons, cons>(q_gen_3645, q_gen_3644) -> q_gen_3644
<nil, cons>(q_gen_3659, q_gen_3751) -> q_gen_3644
<nil, nil>() -> q_gen_3644
<a, a>() -> q_gen_3645
<a, b>() -> q_gen_3645
<b, a>() -> q_gen_3645
<b, b>() -> q_gen_3645
<cons, cons>(q_gen_3645, q_gen_3673) -> q_gen_3673
<nil, cons>(q_gen_3659, q_gen_3658) -> q_gen_3673
<cons, cons, cons>(q_gen_3660, q_gen_3657) -> q_gen_3638
<cons, nil, cons>(q_gen_3645, q_gen_3644) -> q_gen_3638
<nil, cons, cons>(q_gen_3645, q_gen_3644) -> q_gen_3638
<nil, nil, cons>(q_gen_3659, q_gen_3751) -> q_gen_3638
<nil, nil, nil>() -> q_gen_3638
<cons, cons, cons>(q_gen_3660, q_gen_3638) -> q_gen_3657
<cons, nil, cons>(q_gen_3645, q_gen_3673) -> q_gen_3657
<nil, cons, cons>(q_gen_3645, q_gen_3673) -> q_gen_3657
<nil, nil, cons>(q_gen_3659, q_gen_3658) -> q_gen_3657
<a, a, a>() -> q_gen_3660
<a, b, a>() -> q_gen_3660
<b, a, b>() -> q_gen_3660
<b, b, b>() -> q_gen_3660
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_3637, q_gen_3641, q_gen_3642, q_gen_3665, q_gen_3666, q_gen_3667, q_gen_3668, q_gen_3669, q_gen_3692, q_gen_3693, q_gen_3694, q_gen_3707, q_gen_3708, q_gen_3734},
Q_f={q_gen_3637},
Delta=
{
<nil>() -> q_gen_3641
<cons>(q_gen_3666, q_gen_3641) -> q_gen_3665
<a>() -> q_gen_3666
<b>() -> q_gen_3666
<z>() -> q_gen_3668
<cons>(q_gen_3666, q_gen_3665) -> q_gen_3692
<cons>(q_gen_3666, q_gen_3734) -> q_gen_3692
<s>(q_gen_3668) -> q_gen_3694
<s>(q_gen_3708) -> q_gen_3694
<s>(q_gen_3694) -> q_gen_3708
<cons>(q_gen_3666, q_gen_3692) -> q_gen_3734
<cons, s>(q_gen_3642, q_gen_3641) -> q_gen_3637
<cons, s>(q_gen_3667, q_gen_3665) -> q_gen_3637
<cons, s>(q_gen_3693, q_gen_3692) -> q_gen_3637
<cons, s>(q_gen_3707, q_gen_3734) -> q_gen_3637
<nil, z>() -> q_gen_3637
<a, z>() -> q_gen_3642
<b, z>() -> q_gen_3642
<a, s>(q_gen_3668) -> q_gen_3667
<b, s>(q_gen_3668) -> q_gen_3667
<cons, s>(q_gen_3642, q_gen_3665) -> q_gen_3669
<cons, s>(q_gen_3642, q_gen_3692) -> q_gen_3669
<cons, s>(q_gen_3667, q_gen_3641) -> q_gen_3669
<cons, s>(q_gen_3667, q_gen_3692) -> q_gen_3669
<cons, s>(q_gen_3667, q_gen_3734) -> q_gen_3669
<cons, s>(q_gen_3693, q_gen_3641) -> q_gen_3669
<cons, s>(q_gen_3693, q_gen_3665) -> q_gen_3669
<cons, s>(q_gen_3693, q_gen_3734) -> q_gen_3669
<cons, s>(q_gen_3707, q_gen_3641) -> q_gen_3669
<cons, s>(q_gen_3707, q_gen_3665) -> q_gen_3669
<cons, s>(q_gen_3707, q_gen_3692) -> q_gen_3669
<a, s>(q_gen_3694) -> q_gen_3693
<b, s>(q_gen_3694) -> q_gen_3693
<a, s>(q_gen_3708) -> q_gen_3707
<b, s>(q_gen_3708) -> q_gen_3707
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3634, q_gen_3636, q_gen_3670},
Q_f={q_gen_3634},
Delta=
{
<s>(q_gen_3636) -> q_gen_3636
<z>() -> q_gen_3636
<s, s>(q_gen_3634) -> q_gen_3634
<z, s>(q_gen_3636) -> q_gen_3634
<z, z>() -> q_gen_3634
<s, s>(q_gen_3670) -> q_gen_3670
<s, z>(q_gen_3636) -> q_gen_3670
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3633, q_gen_3653, q_gen_3675, q_gen_3677, q_gen_3678},
Q_f={q_gen_3633},
Delta=
{
<nil>() -> q_gen_3677
<a>() -> q_gen_3678
<b>() -> q_gen_3678
<cons, cons>(q_gen_3653, q_gen_3633) -> q_gen_3633
<nil, nil>() -> q_gen_3633
<a, a>() -> q_gen_3653
<a, b>() -> q_gen_3653
<b, a>() -> q_gen_3653
<b, b>() -> q_gen_3653
<cons, cons>(q_gen_3653, q_gen_3675) -> q_gen_3675
<cons, nil>(q_gen_3678, q_gen_3677) -> q_gen_3675
<nil, cons>(q_gen_3678, q_gen_3677) -> q_gen_3675
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 50
() -> length([nil, z]) -> 50
() -> leq([z, s(nn2)]) -> 50
() -> leq([z, z]) -> 50
() -> reverse([nil, nil]) -> 50
(append([_eo, cons(h1, nil), _fo]) /\ reverse([t1, _eo])) -> reverse([cons(h1, t1), _fo]) -> 52
(append([t1, l2, _zn])) -> append([cons(h1, t1), l2, cons(h1, _zn)]) -> 50
(length([_oo, _po]) /\ length([l1, _no]) /\ reverse([l1, _oo])) -> leq([_no, _po]) -> 53
(length([_qo, _ro]) /\ length([l1, _so]) /\ reverse([l1, _qo])) -> leq([_ro, _so]) -> 52
(length([ll, _jo])) -> length([cons(x, ll), s(_jo)]) -> 52
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 51
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 51
(leq([s(nn1), z])) -> BOT -> 53
}
Sat witness: Found: ((length([_oo, _po]) /\ length([l1, _no]) /\ reverse([l1, _oo])) -> leq([_no, _po]), {
_no -> s(s(s(s(s(z)))))  ;  _oo -> cons(b, cons(b, cons(b, nil)))  ;  _po -> s(s(s(z)))  ;  l1 -> cons(b, cons(b, cons(b, nil)))
})

-------------------------------------------
Step 94, which took 1.573249 s (model generation: 1.546427,  model checking: 0.026822):

Model:
|_
{
append -> 
{{{
Q={q_gen_3638, q_gen_3644, q_gen_3645, q_gen_3657, q_gen_3658, q_gen_3659, q_gen_3660, q_gen_3673, q_gen_3751},
Q_f={q_gen_3638},
Delta=
{
<cons>(q_gen_3659, q_gen_3751) -> q_gen_3658
<nil>() -> q_gen_3658
<a>() -> q_gen_3659
<b>() -> q_gen_3659
<cons>(q_gen_3659, q_gen_3658) -> q_gen_3751
<cons, cons>(q_gen_3645, q_gen_3644) -> q_gen_3644
<nil, cons>(q_gen_3659, q_gen_3751) -> q_gen_3644
<nil, nil>() -> q_gen_3644
<a, a>() -> q_gen_3645
<a, b>() -> q_gen_3645
<b, a>() -> q_gen_3645
<b, b>() -> q_gen_3645
<cons, cons>(q_gen_3645, q_gen_3673) -> q_gen_3673
<nil, cons>(q_gen_3659, q_gen_3658) -> q_gen_3673
<cons, cons, cons>(q_gen_3660, q_gen_3657) -> q_gen_3638
<cons, nil, cons>(q_gen_3645, q_gen_3644) -> q_gen_3638
<nil, cons, cons>(q_gen_3645, q_gen_3644) -> q_gen_3638
<nil, nil, cons>(q_gen_3659, q_gen_3751) -> q_gen_3638
<nil, nil, nil>() -> q_gen_3638
<cons, cons, cons>(q_gen_3660, q_gen_3638) -> q_gen_3657
<cons, nil, cons>(q_gen_3645, q_gen_3673) -> q_gen_3657
<nil, cons, cons>(q_gen_3645, q_gen_3673) -> q_gen_3657
<nil, nil, cons>(q_gen_3659, q_gen_3658) -> q_gen_3657
<a, a, a>() -> q_gen_3660
<a, b, a>() -> q_gen_3660
<b, a, b>() -> q_gen_3660
<b, b, b>() -> q_gen_3660
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_3637, q_gen_3641, q_gen_3642, q_gen_3665, q_gen_3666, q_gen_3667, q_gen_3668, q_gen_3669, q_gen_3692, q_gen_3693, q_gen_3694},
Q_f={q_gen_3637},
Delta=
{
<nil>() -> q_gen_3641
<cons>(q_gen_3666, q_gen_3641) -> q_gen_3665
<cons>(q_gen_3666, q_gen_3692) -> q_gen_3665
<a>() -> q_gen_3666
<b>() -> q_gen_3666
<s>(q_gen_3694) -> q_gen_3668
<z>() -> q_gen_3668
<cons>(q_gen_3666, q_gen_3665) -> q_gen_3692
<s>(q_gen_3668) -> q_gen_3694
<cons, s>(q_gen_3642, q_gen_3641) -> q_gen_3637
<cons, s>(q_gen_3667, q_gen_3665) -> q_gen_3637
<cons, s>(q_gen_3693, q_gen_3692) -> q_gen_3637
<nil, z>() -> q_gen_3637
<a, z>() -> q_gen_3642
<b, z>() -> q_gen_3642
<a, s>(q_gen_3668) -> q_gen_3667
<b, s>(q_gen_3668) -> q_gen_3667
<cons, s>(q_gen_3642, q_gen_3665) -> q_gen_3669
<cons, s>(q_gen_3642, q_gen_3692) -> q_gen_3669
<cons, s>(q_gen_3667, q_gen_3641) -> q_gen_3669
<cons, s>(q_gen_3667, q_gen_3692) -> q_gen_3669
<cons, s>(q_gen_3693, q_gen_3641) -> q_gen_3669
<cons, s>(q_gen_3693, q_gen_3665) -> q_gen_3669
<a, s>(q_gen_3694) -> q_gen_3693
<b, s>(q_gen_3694) -> q_gen_3693
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3634, q_gen_3636, q_gen_3647, q_gen_3670, q_gen_3709, q_gen_3710},
Q_f={q_gen_3634},
Delta=
{
<s>(q_gen_3647) -> q_gen_3636
<z>() -> q_gen_3636
<s>(q_gen_3636) -> q_gen_3647
<s, s>(q_gen_3634) -> q_gen_3634
<s, s>(q_gen_3709) -> q_gen_3634
<z, s>(q_gen_3636) -> q_gen_3634
<z, s>(q_gen_3647) -> q_gen_3634
<z, z>() -> q_gen_3634
<s, s>(q_gen_3670) -> q_gen_3670
<s, z>(q_gen_3636) -> q_gen_3670
<s, s>(q_gen_3710) -> q_gen_3709
<s, z>(q_gen_3647) -> q_gen_3710
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3633, q_gen_3653, q_gen_3675, q_gen_3677, q_gen_3678},
Q_f={q_gen_3633},
Delta=
{
<nil>() -> q_gen_3677
<a>() -> q_gen_3678
<b>() -> q_gen_3678
<cons, cons>(q_gen_3653, q_gen_3633) -> q_gen_3633
<nil, nil>() -> q_gen_3633
<a, a>() -> q_gen_3653
<a, b>() -> q_gen_3653
<b, a>() -> q_gen_3653
<b, b>() -> q_gen_3653
<cons, cons>(q_gen_3653, q_gen_3675) -> q_gen_3675
<cons, nil>(q_gen_3678, q_gen_3677) -> q_gen_3675
<nil, cons>(q_gen_3678, q_gen_3677) -> q_gen_3675
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 51
() -> length([nil, z]) -> 51
() -> leq([z, s(nn2)]) -> 51
() -> leq([z, z]) -> 51
() -> reverse([nil, nil]) -> 51
(append([_eo, cons(h1, nil), _fo]) /\ reverse([t1, _eo])) -> reverse([cons(h1, t1), _fo]) -> 52
(append([t1, l2, _zn])) -> append([cons(h1, t1), l2, cons(h1, _zn)]) -> 51
(length([_oo, _po]) /\ length([l1, _no]) /\ reverse([l1, _oo])) -> leq([_no, _po]) -> 53
(length([_qo, _ro]) /\ length([l1, _so]) /\ reverse([l1, _qo])) -> leq([_ro, _so]) -> 52
(length([ll, _jo])) -> length([cons(x, ll), s(_jo)]) -> 52
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 51
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 54
(leq([s(nn1), z])) -> BOT -> 53
}
Sat witness: Found: ((leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]), {
nn1 -> s(s(s(z)))  ;  nn2 -> s(z)
})

-------------------------------------------
Step 95, which took 5.836063 s (model generation: 5.804568,  model checking: 0.031495):

Model:
|_
{
append -> 
{{{
Q={q_gen_3638, q_gen_3644, q_gen_3645, q_gen_3657, q_gen_3658, q_gen_3659, q_gen_3660, q_gen_3673, q_gen_3751},
Q_f={q_gen_3638},
Delta=
{
<cons>(q_gen_3659, q_gen_3751) -> q_gen_3658
<nil>() -> q_gen_3658
<a>() -> q_gen_3659
<b>() -> q_gen_3659
<cons>(q_gen_3659, q_gen_3658) -> q_gen_3751
<cons, cons>(q_gen_3645, q_gen_3644) -> q_gen_3644
<nil, cons>(q_gen_3659, q_gen_3751) -> q_gen_3644
<nil, nil>() -> q_gen_3644
<a, a>() -> q_gen_3645
<a, b>() -> q_gen_3645
<b, a>() -> q_gen_3645
<b, b>() -> q_gen_3645
<cons, cons>(q_gen_3645, q_gen_3673) -> q_gen_3673
<nil, cons>(q_gen_3659, q_gen_3658) -> q_gen_3673
<cons, cons, cons>(q_gen_3660, q_gen_3657) -> q_gen_3638
<cons, nil, cons>(q_gen_3645, q_gen_3644) -> q_gen_3638
<nil, cons, cons>(q_gen_3645, q_gen_3644) -> q_gen_3638
<nil, nil, cons>(q_gen_3659, q_gen_3751) -> q_gen_3638
<nil, nil, nil>() -> q_gen_3638
<cons, cons, cons>(q_gen_3660, q_gen_3638) -> q_gen_3657
<cons, nil, cons>(q_gen_3645, q_gen_3673) -> q_gen_3657
<nil, cons, cons>(q_gen_3645, q_gen_3673) -> q_gen_3657
<nil, nil, cons>(q_gen_3659, q_gen_3658) -> q_gen_3657
<a, a, a>() -> q_gen_3660
<a, b, a>() -> q_gen_3660
<b, a, b>() -> q_gen_3660
<b, b, b>() -> q_gen_3660
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_3637, q_gen_3641, q_gen_3642, q_gen_3665, q_gen_3666, q_gen_3667, q_gen_3668, q_gen_3669, q_gen_3692, q_gen_3693, q_gen_3694, q_gen_3708},
Q_f={q_gen_3637},
Delta=
{
<cons>(q_gen_3666, q_gen_3692) -> q_gen_3641
<nil>() -> q_gen_3641
<cons>(q_gen_3666, q_gen_3641) -> q_gen_3665
<a>() -> q_gen_3666
<b>() -> q_gen_3666
<s>(q_gen_3708) -> q_gen_3668
<z>() -> q_gen_3668
<cons>(q_gen_3666, q_gen_3665) -> q_gen_3692
<s>(q_gen_3668) -> q_gen_3694
<s>(q_gen_3694) -> q_gen_3708
<cons, s>(q_gen_3642, q_gen_3641) -> q_gen_3637
<cons, s>(q_gen_3667, q_gen_3665) -> q_gen_3637
<cons, s>(q_gen_3693, q_gen_3692) -> q_gen_3637
<nil, z>() -> q_gen_3637
<a, s>(q_gen_3708) -> q_gen_3642
<a, z>() -> q_gen_3642
<b, s>(q_gen_3708) -> q_gen_3642
<b, z>() -> q_gen_3642
<a, s>(q_gen_3668) -> q_gen_3667
<b, s>(q_gen_3668) -> q_gen_3667
<cons, s>(q_gen_3642, q_gen_3665) -> q_gen_3669
<cons, s>(q_gen_3642, q_gen_3692) -> q_gen_3669
<cons, s>(q_gen_3667, q_gen_3641) -> q_gen_3669
<cons, s>(q_gen_3667, q_gen_3692) -> q_gen_3669
<cons, s>(q_gen_3693, q_gen_3641) -> q_gen_3669
<cons, s>(q_gen_3693, q_gen_3665) -> q_gen_3669
<a, s>(q_gen_3694) -> q_gen_3693
<b, s>(q_gen_3694) -> q_gen_3693
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3634, q_gen_3636, q_gen_3647, q_gen_3670, q_gen_3723, q_gen_3746},
Q_f={q_gen_3634},
Delta=
{
<z>() -> q_gen_3636
<s>(q_gen_3636) -> q_gen_3647
<s>(q_gen_3647) -> q_gen_3723
<s>(q_gen_3723) -> q_gen_3723
<s, s>(q_gen_3634) -> q_gen_3634
<s, s>(q_gen_3746) -> q_gen_3634
<z, s>(q_gen_3636) -> q_gen_3634
<z, s>(q_gen_3647) -> q_gen_3634
<z, s>(q_gen_3723) -> q_gen_3634
<z, z>() -> q_gen_3634
<s, s>(q_gen_3670) -> q_gen_3670
<s, z>(q_gen_3636) -> q_gen_3670
<s, z>(q_gen_3647) -> q_gen_3670
<s, z>(q_gen_3723) -> q_gen_3746
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3633, q_gen_3653, q_gen_3675, q_gen_3677, q_gen_3678},
Q_f={q_gen_3633},
Delta=
{
<nil>() -> q_gen_3677
<a>() -> q_gen_3678
<b>() -> q_gen_3678
<cons, cons>(q_gen_3653, q_gen_3633) -> q_gen_3633
<nil, nil>() -> q_gen_3633
<a, a>() -> q_gen_3653
<a, b>() -> q_gen_3653
<b, a>() -> q_gen_3653
<b, b>() -> q_gen_3653
<cons, cons>(q_gen_3653, q_gen_3675) -> q_gen_3675
<cons, nil>(q_gen_3678, q_gen_3677) -> q_gen_3675
<nil, cons>(q_gen_3678, q_gen_3677) -> q_gen_3675
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 52
() -> length([nil, z]) -> 52
() -> leq([z, s(nn2)]) -> 52
() -> leq([z, z]) -> 52
() -> reverse([nil, nil]) -> 52
(append([_eo, cons(h1, nil), _fo]) /\ reverse([t1, _eo])) -> reverse([cons(h1, t1), _fo]) -> 55
(append([t1, l2, _zn])) -> append([cons(h1, t1), l2, cons(h1, _zn)]) -> 52
(length([_oo, _po]) /\ length([l1, _no]) /\ reverse([l1, _oo])) -> leq([_no, _po]) -> 53
(length([_qo, _ro]) /\ length([l1, _so]) /\ reverse([l1, _qo])) -> leq([_ro, _so]) -> 53
(length([ll, _jo])) -> length([cons(x, ll), s(_jo)]) -> 53
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 52
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 54
(leq([s(nn1), z])) -> BOT -> 53
}
Sat witness: Found: ((append([_eo, cons(h1, nil), _fo]) /\ reverse([t1, _eo])) -> reverse([cons(h1, t1), _fo]), {
_eo -> nil  ;  _fo -> cons(b, cons(b, cons(b, nil)))  ;  h1 -> b  ;  t1 -> nil
})

-------------------------------------------
Step 96, which took 1.375928 s (model generation: 1.374846,  model checking: 0.001082):

Model:
|_
{
append -> 
{{{
Q={q_gen_3638, q_gen_3643, q_gen_3644, q_gen_3645, q_gen_3658, q_gen_3659, q_gen_3660, q_gen_3673, q_gen_3674, q_gen_3751},
Q_f={q_gen_3638, q_gen_3643},
Delta=
{
<cons>(q_gen_3659, q_gen_3751) -> q_gen_3658
<nil>() -> q_gen_3658
<a>() -> q_gen_3659
<b>() -> q_gen_3659
<cons>(q_gen_3659, q_gen_3658) -> q_gen_3751
<cons, cons>(q_gen_3645, q_gen_3644) -> q_gen_3644
<nil, nil>() -> q_gen_3644
<a, a>() -> q_gen_3645
<a, b>() -> q_gen_3645
<b, a>() -> q_gen_3645
<b, b>() -> q_gen_3645
<cons, cons>(q_gen_3645, q_gen_3673) -> q_gen_3673
<nil, cons>(q_gen_3659, q_gen_3658) -> q_gen_3673
<nil, cons>(q_gen_3659, q_gen_3751) -> q_gen_3673
<cons, cons, cons>(q_gen_3660, q_gen_3643) -> q_gen_3638
<nil, cons, cons>(q_gen_3645, q_gen_3644) -> q_gen_3638
<nil, nil, cons>(q_gen_3659, q_gen_3751) -> q_gen_3638
<nil, nil, nil>() -> q_gen_3638
<cons, cons, cons>(q_gen_3660, q_gen_3674) -> q_gen_3643
<cons, nil, cons>(q_gen_3645, q_gen_3644) -> q_gen_3643
<cons, nil, cons>(q_gen_3645, q_gen_3673) -> q_gen_3643
<nil, nil, cons>(q_gen_3659, q_gen_3658) -> q_gen_3643
<a, a, a>() -> q_gen_3660
<a, b, a>() -> q_gen_3660
<b, a, b>() -> q_gen_3660
<b, b, b>() -> q_gen_3660
<cons, cons, cons>(q_gen_3660, q_gen_3638) -> q_gen_3674
<nil, cons, cons>(q_gen_3645, q_gen_3673) -> q_gen_3674
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_3637, q_gen_3641, q_gen_3642, q_gen_3665, q_gen_3666, q_gen_3667, q_gen_3668, q_gen_3669, q_gen_3692, q_gen_3693, q_gen_3694, q_gen_3707, q_gen_3708, q_gen_3715, q_gen_3716},
Q_f={q_gen_3637},
Delta=
{
<nil>() -> q_gen_3641
<cons>(q_gen_3666, q_gen_3641) -> q_gen_3665
<cons>(q_gen_3666, q_gen_3715) -> q_gen_3665
<cons>(q_gen_3716, q_gen_3715) -> q_gen_3665
<b>() -> q_gen_3666
<z>() -> q_gen_3668
<cons>(q_gen_3666, q_gen_3665) -> q_gen_3692
<cons>(q_gen_3666, q_gen_3692) -> q_gen_3692
<s>(q_gen_3668) -> q_gen_3694
<s>(q_gen_3694) -> q_gen_3708
<s>(q_gen_3708) -> q_gen_3708
<cons>(q_gen_3716, q_gen_3641) -> q_gen_3715
<cons>(q_gen_3716, q_gen_3665) -> q_gen_3715
<a>() -> q_gen_3716
<cons, s>(q_gen_3642, q_gen_3641) -> q_gen_3637
<cons, s>(q_gen_3667, q_gen_3665) -> q_gen_3637
<cons, s>(q_gen_3667, q_gen_3692) -> q_gen_3637
<cons, s>(q_gen_3667, q_gen_3715) -> q_gen_3637
<cons, s>(q_gen_3693, q_gen_3692) -> q_gen_3637
<nil, z>() -> q_gen_3637
<a, z>() -> q_gen_3642
<b, z>() -> q_gen_3642
<a, s>(q_gen_3668) -> q_gen_3667
<a, s>(q_gen_3694) -> q_gen_3667
<a, s>(q_gen_3708) -> q_gen_3667
<b, s>(q_gen_3668) -> q_gen_3667
<cons, s>(q_gen_3642, q_gen_3665) -> q_gen_3669
<cons, s>(q_gen_3642, q_gen_3692) -> q_gen_3669
<cons, s>(q_gen_3642, q_gen_3715) -> q_gen_3669
<cons, s>(q_gen_3667, q_gen_3641) -> q_gen_3669
<cons, s>(q_gen_3693, q_gen_3641) -> q_gen_3669
<cons, s>(q_gen_3693, q_gen_3665) -> q_gen_3669
<cons, s>(q_gen_3693, q_gen_3715) -> q_gen_3669
<cons, s>(q_gen_3707, q_gen_3641) -> q_gen_3669
<cons, s>(q_gen_3707, q_gen_3665) -> q_gen_3669
<cons, s>(q_gen_3707, q_gen_3692) -> q_gen_3669
<b, s>(q_gen_3694) -> q_gen_3693
<b, s>(q_gen_3708) -> q_gen_3707
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3634, q_gen_3636, q_gen_3670},
Q_f={q_gen_3634},
Delta=
{
<s>(q_gen_3636) -> q_gen_3636
<z>() -> q_gen_3636
<s, s>(q_gen_3634) -> q_gen_3634
<z, s>(q_gen_3636) -> q_gen_3634
<z, z>() -> q_gen_3634
<s, s>(q_gen_3670) -> q_gen_3670
<s, z>(q_gen_3636) -> q_gen_3670
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3633, q_gen_3653, q_gen_3675, q_gen_3677, q_gen_3678},
Q_f={q_gen_3633},
Delta=
{
<cons>(q_gen_3678, q_gen_3677) -> q_gen_3677
<nil>() -> q_gen_3677
<a>() -> q_gen_3678
<b>() -> q_gen_3678
<cons, cons>(q_gen_3653, q_gen_3633) -> q_gen_3633
<nil, nil>() -> q_gen_3633
<a, a>() -> q_gen_3653
<a, b>() -> q_gen_3653
<b, a>() -> q_gen_3653
<b, b>() -> q_gen_3653
<cons, cons>(q_gen_3653, q_gen_3675) -> q_gen_3675
<cons, nil>(q_gen_3678, q_gen_3677) -> q_gen_3675
<nil, cons>(q_gen_3678, q_gen_3677) -> q_gen_3675
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 52
() -> length([nil, z]) -> 52
() -> leq([z, s(nn2)]) -> 52
() -> leq([z, z]) -> 52
() -> reverse([nil, nil]) -> 52
(append([_eo, cons(h1, nil), _fo]) /\ reverse([t1, _eo])) -> reverse([cons(h1, t1), _fo]) -> 55
(append([t1, l2, _zn])) -> append([cons(h1, t1), l2, cons(h1, _zn)]) -> 55
(length([_oo, _po]) /\ length([l1, _no]) /\ reverse([l1, _oo])) -> leq([_no, _po]) -> 53
(length([_qo, _ro]) /\ length([l1, _so]) /\ reverse([l1, _qo])) -> leq([_ro, _so]) -> 53
(length([ll, _jo])) -> length([cons(x, ll), s(_jo)]) -> 53
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 53
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 54
(leq([s(nn1), z])) -> BOT -> 53
}
Sat witness: Found: ((append([t1, l2, _zn])) -> append([cons(h1, t1), l2, cons(h1, _zn)]), {
_zn -> cons(a, cons(a, nil))  ;  h1 -> a  ;  l2 -> cons(a, cons(b, nil))  ;  t1 -> cons(a, cons(a, nil))
})

-------------------------------------------
Step 97, which took 4.372084 s (model generation: 4.367128,  model checking: 0.004956):

Model:
|_
{
append -> 
{{{
Q={q_gen_3638, q_gen_3643, q_gen_3644, q_gen_3645, q_gen_3658, q_gen_3659, q_gen_3660, q_gen_3673, q_gen_3674, q_gen_3751},
Q_f={q_gen_3638, q_gen_3643},
Delta=
{
<cons>(q_gen_3659, q_gen_3751) -> q_gen_3658
<nil>() -> q_gen_3658
<a>() -> q_gen_3659
<b>() -> q_gen_3659
<cons>(q_gen_3659, q_gen_3658) -> q_gen_3751
<cons, cons>(q_gen_3645, q_gen_3644) -> q_gen_3644
<nil, nil>() -> q_gen_3644
<a, a>() -> q_gen_3645
<a, b>() -> q_gen_3645
<b, a>() -> q_gen_3645
<b, b>() -> q_gen_3645
<cons, cons>(q_gen_3645, q_gen_3673) -> q_gen_3673
<nil, cons>(q_gen_3659, q_gen_3658) -> q_gen_3673
<nil, cons>(q_gen_3659, q_gen_3751) -> q_gen_3673
<cons, cons, cons>(q_gen_3660, q_gen_3674) -> q_gen_3638
<nil, cons, cons>(q_gen_3645, q_gen_3644) -> q_gen_3638
<nil, nil, cons>(q_gen_3659, q_gen_3751) -> q_gen_3638
<nil, nil, nil>() -> q_gen_3638
<cons, cons, cons>(q_gen_3660, q_gen_3643) -> q_gen_3643
<cons, nil, cons>(q_gen_3645, q_gen_3644) -> q_gen_3643
<cons, nil, cons>(q_gen_3645, q_gen_3673) -> q_gen_3643
<nil, nil, cons>(q_gen_3659, q_gen_3658) -> q_gen_3643
<a, a, a>() -> q_gen_3660
<a, b, a>() -> q_gen_3660
<b, a, b>() -> q_gen_3660
<b, b, b>() -> q_gen_3660
<cons, cons, cons>(q_gen_3660, q_gen_3638) -> q_gen_3674
<nil, cons, cons>(q_gen_3645, q_gen_3673) -> q_gen_3674
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_3637, q_gen_3641, q_gen_3642, q_gen_3665, q_gen_3666, q_gen_3667, q_gen_3668, q_gen_3669, q_gen_3692, q_gen_3693, q_gen_3694, q_gen_3707, q_gen_3708, q_gen_3715, q_gen_3716},
Q_f={q_gen_3637},
Delta=
{
<cons>(q_gen_3666, q_gen_3692) -> q_gen_3641
<nil>() -> q_gen_3641
<cons>(q_gen_3666, q_gen_3641) -> q_gen_3665
<cons>(q_gen_3666, q_gen_3715) -> q_gen_3665
<b>() -> q_gen_3666
<z>() -> q_gen_3668
<cons>(q_gen_3666, q_gen_3665) -> q_gen_3692
<s>(q_gen_3668) -> q_gen_3694
<s>(q_gen_3694) -> q_gen_3708
<s>(q_gen_3708) -> q_gen_3708
<cons>(q_gen_3716, q_gen_3641) -> q_gen_3715
<cons>(q_gen_3716, q_gen_3665) -> q_gen_3715
<cons>(q_gen_3716, q_gen_3715) -> q_gen_3715
<a>() -> q_gen_3716
<cons, s>(q_gen_3642, q_gen_3641) -> q_gen_3637
<cons, s>(q_gen_3642, q_gen_3715) -> q_gen_3637
<cons, s>(q_gen_3667, q_gen_3665) -> q_gen_3637
<cons, s>(q_gen_3667, q_gen_3715) -> q_gen_3637
<cons, s>(q_gen_3693, q_gen_3692) -> q_gen_3637
<cons, s>(q_gen_3707, q_gen_3715) -> q_gen_3637
<nil, z>() -> q_gen_3637
<a, z>() -> q_gen_3642
<b, z>() -> q_gen_3642
<a, s>(q_gen_3668) -> q_gen_3667
<a, s>(q_gen_3708) -> q_gen_3667
<b, s>(q_gen_3668) -> q_gen_3667
<cons, s>(q_gen_3642, q_gen_3665) -> q_gen_3669
<cons, s>(q_gen_3642, q_gen_3692) -> q_gen_3669
<cons, s>(q_gen_3667, q_gen_3641) -> q_gen_3669
<cons, s>(q_gen_3667, q_gen_3692) -> q_gen_3669
<cons, s>(q_gen_3693, q_gen_3641) -> q_gen_3669
<cons, s>(q_gen_3693, q_gen_3665) -> q_gen_3669
<cons, s>(q_gen_3693, q_gen_3715) -> q_gen_3669
<cons, s>(q_gen_3707, q_gen_3641) -> q_gen_3669
<cons, s>(q_gen_3707, q_gen_3665) -> q_gen_3669
<cons, s>(q_gen_3707, q_gen_3692) -> q_gen_3669
<b, s>(q_gen_3694) -> q_gen_3693
<a, s>(q_gen_3694) -> q_gen_3707
<b, s>(q_gen_3708) -> q_gen_3707
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3634, q_gen_3636, q_gen_3670},
Q_f={q_gen_3634},
Delta=
{
<s>(q_gen_3636) -> q_gen_3636
<z>() -> q_gen_3636
<s, s>(q_gen_3634) -> q_gen_3634
<z, s>(q_gen_3636) -> q_gen_3634
<z, z>() -> q_gen_3634
<s, s>(q_gen_3670) -> q_gen_3670
<s, z>(q_gen_3636) -> q_gen_3670
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3633, q_gen_3653, q_gen_3675, q_gen_3677, q_gen_3678},
Q_f={q_gen_3633},
Delta=
{
<cons>(q_gen_3678, q_gen_3677) -> q_gen_3677
<nil>() -> q_gen_3677
<a>() -> q_gen_3678
<b>() -> q_gen_3678
<cons, cons>(q_gen_3653, q_gen_3633) -> q_gen_3633
<nil, nil>() -> q_gen_3633
<a, a>() -> q_gen_3653
<a, b>() -> q_gen_3653
<b, a>() -> q_gen_3653
<b, b>() -> q_gen_3653
<cons, cons>(q_gen_3653, q_gen_3675) -> q_gen_3675
<cons, nil>(q_gen_3678, q_gen_3677) -> q_gen_3675
<nil, cons>(q_gen_3678, q_gen_3677) -> q_gen_3675
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 53
() -> length([nil, z]) -> 53
() -> leq([z, s(nn2)]) -> 53
() -> leq([z, z]) -> 53
() -> reverse([nil, nil]) -> 53
(append([_eo, cons(h1, nil), _fo]) /\ reverse([t1, _eo])) -> reverse([cons(h1, t1), _fo]) -> 55
(append([t1, l2, _zn])) -> append([cons(h1, t1), l2, cons(h1, _zn)]) -> 55
(length([_oo, _po]) /\ length([l1, _no]) /\ reverse([l1, _oo])) -> leq([_no, _po]) -> 53
(length([_qo, _ro]) /\ length([l1, _so]) /\ reverse([l1, _qo])) -> leq([_ro, _so]) -> 53
(length([ll, _jo])) -> length([cons(x, ll), s(_jo)]) -> 56
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 54
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 54
(leq([s(nn1), z])) -> BOT -> 54
}
Sat witness: Found: ((length([ll, _jo])) -> length([cons(x, ll), s(_jo)]), {
_jo -> s(s(s(s(z))))  ;  ll -> cons(b, cons(a, nil))  ;  x -> b
})

-------------------------------------------
Step 98, which took 3.408501 s (model generation: 3.406585,  model checking: 0.001916):

Model:
|_
{
append -> 
{{{
Q={q_gen_3638, q_gen_3644, q_gen_3645, q_gen_3648, q_gen_3658, q_gen_3659, q_gen_3660, q_gen_3673, q_gen_3674, q_gen_3751},
Q_f={q_gen_3638, q_gen_3648},
Delta=
{
<nil>() -> q_gen_3658
<a>() -> q_gen_3659
<b>() -> q_gen_3659
<cons>(q_gen_3659, q_gen_3658) -> q_gen_3751
<cons>(q_gen_3659, q_gen_3751) -> q_gen_3751
<cons, cons>(q_gen_3645, q_gen_3644) -> q_gen_3644
<nil, nil>() -> q_gen_3644
<a, a>() -> q_gen_3645
<a, b>() -> q_gen_3645
<b, a>() -> q_gen_3645
<b, b>() -> q_gen_3645
<cons, cons>(q_gen_3645, q_gen_3673) -> q_gen_3673
<nil, cons>(q_gen_3659, q_gen_3658) -> q_gen_3673
<nil, cons>(q_gen_3659, q_gen_3751) -> q_gen_3673
<cons, cons, cons>(q_gen_3660, q_gen_3648) -> q_gen_3638
<cons, nil, cons>(q_gen_3645, q_gen_3644) -> q_gen_3638
<nil, nil, cons>(q_gen_3659, q_gen_3751) -> q_gen_3638
<nil, nil, nil>() -> q_gen_3638
<cons, cons, cons>(q_gen_3660, q_gen_3674) -> q_gen_3648
<cons, nil, cons>(q_gen_3645, q_gen_3673) -> q_gen_3648
<nil, cons, cons>(q_gen_3645, q_gen_3644) -> q_gen_3648
<nil, nil, cons>(q_gen_3659, q_gen_3658) -> q_gen_3648
<a, a, a>() -> q_gen_3660
<a, b, a>() -> q_gen_3660
<b, a, b>() -> q_gen_3660
<b, b, b>() -> q_gen_3660
<cons, cons, cons>(q_gen_3660, q_gen_3638) -> q_gen_3674
<nil, cons, cons>(q_gen_3645, q_gen_3673) -> q_gen_3674
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_3637, q_gen_3641, q_gen_3642, q_gen_3665, q_gen_3666, q_gen_3667, q_gen_3668, q_gen_3669, q_gen_3692, q_gen_3693, q_gen_3694, q_gen_3707, q_gen_3708, q_gen_3715, q_gen_3716},
Q_f={q_gen_3637},
Delta=
{
<cons>(q_gen_3666, q_gen_3692) -> q_gen_3641
<nil>() -> q_gen_3641
<cons>(q_gen_3666, q_gen_3641) -> q_gen_3665
<cons>(q_gen_3666, q_gen_3715) -> q_gen_3665
<b>() -> q_gen_3666
<z>() -> q_gen_3668
<cons>(q_gen_3666, q_gen_3665) -> q_gen_3692
<cons>(q_gen_3716, q_gen_3715) -> q_gen_3692
<s>(q_gen_3668) -> q_gen_3694
<s>(q_gen_3694) -> q_gen_3708
<s>(q_gen_3708) -> q_gen_3708
<cons>(q_gen_3716, q_gen_3641) -> q_gen_3715
<cons>(q_gen_3716, q_gen_3665) -> q_gen_3715
<a>() -> q_gen_3716
<cons, s>(q_gen_3642, q_gen_3641) -> q_gen_3637
<cons, s>(q_gen_3667, q_gen_3665) -> q_gen_3637
<cons, s>(q_gen_3667, q_gen_3715) -> q_gen_3637
<cons, s>(q_gen_3693, q_gen_3692) -> q_gen_3637
<nil, z>() -> q_gen_3637
<a, z>() -> q_gen_3642
<b, z>() -> q_gen_3642
<a, s>(q_gen_3668) -> q_gen_3667
<a, s>(q_gen_3694) -> q_gen_3667
<b, s>(q_gen_3668) -> q_gen_3667
<cons, s>(q_gen_3642, q_gen_3665) -> q_gen_3669
<cons, s>(q_gen_3642, q_gen_3692) -> q_gen_3669
<cons, s>(q_gen_3642, q_gen_3715) -> q_gen_3669
<cons, s>(q_gen_3667, q_gen_3641) -> q_gen_3669
<cons, s>(q_gen_3667, q_gen_3692) -> q_gen_3669
<cons, s>(q_gen_3693, q_gen_3641) -> q_gen_3669
<cons, s>(q_gen_3693, q_gen_3665) -> q_gen_3669
<cons, s>(q_gen_3693, q_gen_3715) -> q_gen_3669
<cons, s>(q_gen_3707, q_gen_3641) -> q_gen_3669
<cons, s>(q_gen_3707, q_gen_3665) -> q_gen_3669
<cons, s>(q_gen_3707, q_gen_3692) -> q_gen_3669
<cons, s>(q_gen_3707, q_gen_3715) -> q_gen_3669
<a, s>(q_gen_3708) -> q_gen_3693
<b, s>(q_gen_3694) -> q_gen_3693
<b, s>(q_gen_3708) -> q_gen_3707
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3634, q_gen_3636, q_gen_3670},
Q_f={q_gen_3634},
Delta=
{
<s>(q_gen_3636) -> q_gen_3636
<z>() -> q_gen_3636
<s, s>(q_gen_3634) -> q_gen_3634
<z, s>(q_gen_3636) -> q_gen_3634
<z, z>() -> q_gen_3634
<s, s>(q_gen_3670) -> q_gen_3670
<s, z>(q_gen_3636) -> q_gen_3670
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3633, q_gen_3653, q_gen_3675, q_gen_3677, q_gen_3678},
Q_f={q_gen_3633},
Delta=
{
<cons>(q_gen_3678, q_gen_3677) -> q_gen_3677
<nil>() -> q_gen_3677
<a>() -> q_gen_3678
<b>() -> q_gen_3678
<cons, cons>(q_gen_3653, q_gen_3633) -> q_gen_3633
<nil, nil>() -> q_gen_3633
<a, a>() -> q_gen_3653
<a, b>() -> q_gen_3653
<b, a>() -> q_gen_3653
<b, b>() -> q_gen_3653
<cons, cons>(q_gen_3653, q_gen_3675) -> q_gen_3675
<cons, nil>(q_gen_3678, q_gen_3677) -> q_gen_3675
<nil, cons>(q_gen_3678, q_gen_3677) -> q_gen_3675
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 53
() -> length([nil, z]) -> 53
() -> leq([z, s(nn2)]) -> 53
() -> leq([z, z]) -> 53
() -> reverse([nil, nil]) -> 53
(append([_eo, cons(h1, nil), _fo]) /\ reverse([t1, _eo])) -> reverse([cons(h1, t1), _fo]) -> 55
(append([t1, l2, _zn])) -> append([cons(h1, t1), l2, cons(h1, _zn)]) -> 55
(length([_oo, _po]) /\ length([l1, _no]) /\ reverse([l1, _oo])) -> leq([_no, _po]) -> 53
(length([_qo, _ro]) /\ length([l1, _so]) /\ reverse([l1, _qo])) -> leq([_ro, _so]) -> 56
(length([ll, _jo])) -> length([cons(x, ll), s(_jo)]) -> 56
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 54
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 54
(leq([s(nn1), z])) -> BOT -> 54
}
Sat witness: Found: ((length([_qo, _ro]) /\ length([l1, _so]) /\ reverse([l1, _qo])) -> leq([_ro, _so]), {
_qo -> cons(b, cons(b, cons(b, cons(a, cons(a, nil)))))  ;  _ro -> s(s(z))  ;  _so -> s(z)  ;  l1 -> cons(b, cons(b, cons(b, cons(b, cons(a, nil)))))
})

-------------------------------------------
Step 99, which took 3.035995 s (model generation: 3.026662,  model checking: 0.009333):

Model:
|_
{
append -> 
{{{
Q={q_gen_3638, q_gen_3643, q_gen_3644, q_gen_3645, q_gen_3649, q_gen_3650, q_gen_3658, q_gen_3659, q_gen_3660, q_gen_3661, q_gen_3672, q_gen_3673, q_gen_3674, q_gen_3695, q_gen_3696, q_gen_3729, q_gen_3731, q_gen_3737, q_gen_3749, q_gen_3751, q_gen_3752, q_gen_3763, q_gen_3764, q_gen_3765, q_gen_3774, q_gen_3775, q_gen_3777, q_gen_3813, q_gen_3815, q_gen_3816, q_gen_3817, q_gen_3819, q_gen_3827},
Q_f={q_gen_3638, q_gen_3643, q_gen_3672, q_gen_3695, q_gen_3774, q_gen_3827},
Delta=
{
<nil>() -> q_gen_3658
<b>() -> q_gen_3659
<a>() -> q_gen_3731
<cons>(q_gen_3659, q_gen_3658) -> q_gen_3751
<cons>(q_gen_3659, q_gen_3751) -> q_gen_3751
<nil, nil>() -> q_gen_3644
<b, b>() -> q_gen_3645
<cons, cons>(q_gen_3650, q_gen_3644) -> q_gen_3649
<a, a>() -> q_gen_3650
<cons, cons>(q_gen_3650, q_gen_3649) -> q_gen_3673
<cons, cons>(q_gen_3650, q_gen_3764) -> q_gen_3673
<nil, cons>(q_gen_3659, q_gen_3658) -> q_gen_3673
<cons, cons>(q_gen_3645, q_gen_3644) -> q_gen_3696
<cons, cons>(q_gen_3645, q_gen_3673) -> q_gen_3696
<nil, cons>(q_gen_3659, q_gen_3751) -> q_gen_3696
<nil, cons>(q_gen_3731, q_gen_3658) -> q_gen_3764
<a, b>() -> q_gen_3817
<b, a>() -> q_gen_3817
<cons, cons, cons>(q_gen_3660, q_gen_3672) -> q_gen_3638
<cons, cons, cons>(q_gen_3660, q_gen_3695) -> q_gen_3638
<cons, cons, cons>(q_gen_3737, q_gen_3763) -> q_gen_3638
<nil, nil, nil>() -> q_gen_3638
<cons, cons, cons>(q_gen_3660, q_gen_3643) -> q_gen_3643
<cons, nil, cons>(q_gen_3645, q_gen_3644) -> q_gen_3643
<nil, cons, cons>(q_gen_3645, q_gen_3644) -> q_gen_3643
<nil, cons, cons>(q_gen_3650, q_gen_3649) -> q_gen_3643
<nil, nil, cons>(q_gen_3659, q_gen_3658) -> q_gen_3643
<a, b, a>() -> q_gen_3660
<b, a, b>() -> q_gen_3660
<b, b, b>() -> q_gen_3660
<nil, cons, cons>(q_gen_3650, q_gen_3644) -> q_gen_3661
<cons, cons, cons>(q_gen_3660, q_gen_3638) -> q_gen_3672
<cons, nil, cons>(q_gen_3645, q_gen_3673) -> q_gen_3672
<cons, cons, cons>(q_gen_3737, q_gen_3674) -> q_gen_3674
<cons, cons, cons>(q_gen_3737, q_gen_3749) -> q_gen_3674
<nil, cons, cons>(q_gen_3645, q_gen_3673) -> q_gen_3674
<nil, nil, cons>(q_gen_3731, q_gen_3658) -> q_gen_3674
<cons, nil, cons>(q_gen_3645, q_gen_3696) -> q_gen_3695
<cons, cons, cons>(q_gen_3660, q_gen_3674) -> q_gen_3729
<a, a, a>() -> q_gen_3737
<cons, cons, cons>(q_gen_3660, q_gen_3749) -> q_gen_3749
<nil, nil, cons>(q_gen_3659, q_gen_3751) -> q_gen_3749
<cons, cons, cons>(q_gen_3660, q_gen_3752) -> q_gen_3752
<nil, nil, cons>(q_gen_3731, q_gen_3751) -> q_gen_3752
<nil, cons, cons>(q_gen_3650, q_gen_3764) -> q_gen_3763
<cons, cons, cons>(q_gen_3737, q_gen_3672) -> q_gen_3765
<nil, cons, cons>(q_gen_3645, q_gen_3649) -> q_gen_3774
<nil, cons, cons>(q_gen_3650, q_gen_3673) -> q_gen_3775
<cons, cons, cons>(q_gen_3737, q_gen_3775) -> q_gen_3777
<nil, cons, cons>(q_gen_3650, q_gen_3696) -> q_gen_3813
<cons, cons, cons>(q_gen_3737, q_gen_3816) -> q_gen_3815
<cons, cons, cons>(q_gen_3660, q_gen_3819) -> q_gen_3816
<nil, cons, cons>(q_gen_3817, q_gen_3673) -> q_gen_3816
<nil, cons, cons>(q_gen_3817, q_gen_3764) -> q_gen_3816
<cons, cons, cons>(q_gen_3660, q_gen_3827) -> q_gen_3819
<cons, cons, cons>(q_gen_3737, q_gen_3819) -> q_gen_3819
<cons, nil, cons>(q_gen_3645, q_gen_3764) -> q_gen_3819
<cons, nil, cons>(q_gen_3817, q_gen_3673) -> q_gen_3819
<nil, cons, cons>(q_gen_3645, q_gen_3696) -> q_gen_3819
<cons, cons, cons>(q_gen_3660, q_gen_3816) -> q_gen_3827
<cons, nil, cons>(q_gen_3650, q_gen_3644) -> q_gen_3827
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_3637, q_gen_3640, q_gen_3641, q_gen_3642, q_gen_3665, q_gen_3666, q_gen_3667, q_gen_3668, q_gen_3669, q_gen_3692, q_gen_3693, q_gen_3694, q_gen_3707, q_gen_3708, q_gen_3716, q_gen_3743, q_gen_3744, q_gen_3770, q_gen_3782, q_gen_3784, q_gen_3821, q_gen_3822},
Q_f={q_gen_3637, q_gen_3640, q_gen_3821, q_gen_3822},
Delta=
{
<cons>(q_gen_3716, q_gen_3665) -> q_gen_3641
<nil>() -> q_gen_3641
<cons>(q_gen_3666, q_gen_3641) -> q_gen_3665
<cons>(q_gen_3716, q_gen_3692) -> q_gen_3665
<b>() -> q_gen_3666
<s>(q_gen_3744) -> q_gen_3668
<z>() -> q_gen_3668
<cons>(q_gen_3666, q_gen_3665) -> q_gen_3692
<cons>(q_gen_3666, q_gen_3770) -> q_gen_3692
<cons>(q_gen_3716, q_gen_3641) -> q_gen_3692
<s>(q_gen_3668) -> q_gen_3694
<s>(q_gen_3694) -> q_gen_3708
<a>() -> q_gen_3716
<s>(q_gen_3708) -> q_gen_3744
<cons>(q_gen_3666, q_gen_3692) -> q_gen_3770
<cons, s>(q_gen_3667, q_gen_3692) -> q_gen_3637
<cons, s>(q_gen_3743, q_gen_3641) -> q_gen_3637
<nil, z>() -> q_gen_3637
<cons, s>(q_gen_3642, q_gen_3641) -> q_gen_3640
<cons, s>(q_gen_3667, q_gen_3665) -> q_gen_3640
<cons, s>(q_gen_3693, q_gen_3692) -> q_gen_3640
<a, z>() -> q_gen_3642
<b, z>() -> q_gen_3642
<a, s>(q_gen_3668) -> q_gen_3667
<a, s>(q_gen_3708) -> q_gen_3667
<b, s>(q_gen_3668) -> q_gen_3667
<cons, s>(q_gen_3642, q_gen_3665) -> q_gen_3669
<cons, s>(q_gen_3642, q_gen_3692) -> q_gen_3669
<cons, s>(q_gen_3642, q_gen_3770) -> q_gen_3669
<cons, s>(q_gen_3667, q_gen_3641) -> q_gen_3669
<cons, s>(q_gen_3693, q_gen_3641) -> q_gen_3669
<cons, s>(q_gen_3693, q_gen_3665) -> q_gen_3669
<cons, s>(q_gen_3693, q_gen_3770) -> q_gen_3669
<cons, s>(q_gen_3707, q_gen_3641) -> q_gen_3669
<cons, s>(q_gen_3707, q_gen_3665) -> q_gen_3669
<cons, s>(q_gen_3707, q_gen_3692) -> q_gen_3669
<cons, s>(q_gen_3743, q_gen_3665) -> q_gen_3669
<b, s>(q_gen_3694) -> q_gen_3693
<a, s>(q_gen_3744) -> q_gen_3707
<b, s>(q_gen_3708) -> q_gen_3707
<a, s>(q_gen_3694) -> q_gen_3743
<b, s>(q_gen_3744) -> q_gen_3743
<cons, s>(q_gen_3707, q_gen_3770) -> q_gen_3782
<cons, s>(q_gen_3743, q_gen_3692) -> q_gen_3784
<cons, s>(q_gen_3743, q_gen_3770) -> q_gen_3821
<cons, s>(q_gen_3667, q_gen_3770) -> q_gen_3822
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_3634, q_gen_3636, q_gen_3647, q_gen_3670, q_gen_3709},
Q_f={q_gen_3634},
Delta=
{
<z>() -> q_gen_3636
<s>(q_gen_3636) -> q_gen_3647
<s>(q_gen_3647) -> q_gen_3647
<s, s>(q_gen_3634) -> q_gen_3634
<z, s>(q_gen_3636) -> q_gen_3634
<z, s>(q_gen_3647) -> q_gen_3634
<z, z>() -> q_gen_3634
<s, s>(q_gen_3670) -> q_gen_3670
<s, z>(q_gen_3636) -> q_gen_3670
<s, s>(q_gen_3709) -> q_gen_3709
<s, z>(q_gen_3647) -> q_gen_3709
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_3633, q_gen_3652, q_gen_3653, q_gen_3663, q_gen_3675, q_gen_3677, q_gen_3678, q_gen_3688, q_gen_3689, q_gen_3690, q_gen_3698, q_gen_3701, q_gen_3702, q_gen_3704, q_gen_3713, q_gen_3718, q_gen_3719, q_gen_3728, q_gen_3739, q_gen_3755, q_gen_3756, q_gen_3757, q_gen_3766, q_gen_3768, q_gen_3773, q_gen_3796, q_gen_3800, q_gen_3801, q_gen_3805, q_gen_3806, q_gen_3808, q_gen_3809, q_gen_3820, q_gen_3823},
Q_f={q_gen_3633, q_gen_3652, q_gen_3698, q_gen_3713, q_gen_3739},
Delta=
{
<cons>(q_gen_3678, q_gen_3677) -> q_gen_3677
<nil>() -> q_gen_3677
<b>() -> q_gen_3678
<a>() -> q_gen_3704
<cons, cons>(q_gen_3663, q_gen_3633) -> q_gen_3633
<cons, cons>(q_gen_3663, q_gen_3675) -> q_gen_3633
<cons, cons>(q_gen_3690, q_gen_3688) -> q_gen_3633
<nil, nil>() -> q_gen_3633
<cons, cons>(q_gen_3653, q_gen_3633) -> q_gen_3652
<cons, cons>(q_gen_3663, q_gen_3652) -> q_gen_3652
<b, b>() -> q_gen_3653
<a, a>() -> q_gen_3663
<cons, cons>(q_gen_3653, q_gen_3675) -> q_gen_3675
<nil, cons>(q_gen_3678, q_gen_3677) -> q_gen_3675
<cons, cons>(q_gen_3689, q_gen_3675) -> q_gen_3688
<cons, nil>(q_gen_3678, q_gen_3677) -> q_gen_3688
<a, b>() -> q_gen_3689
<b, a>() -> q_gen_3690
<cons, cons>(q_gen_3653, q_gen_3652) -> q_gen_3698
<cons, cons>(q_gen_3689, q_gen_3633) -> q_gen_3701
<cons, cons>(q_gen_3653, q_gen_3702) -> q_gen_3702
<cons, nil>(q_gen_3704, q_gen_3677) -> q_gen_3702
<cons, cons>(q_gen_3690, q_gen_3701) -> q_gen_3713
<cons, cons>(q_gen_3653, q_gen_3719) -> q_gen_3718
<cons, cons>(q_gen_3653, q_gen_3688) -> q_gen_3719
<cons, cons>(q_gen_3653, q_gen_3701) -> q_gen_3719
<cons, cons>(q_gen_3653, q_gen_3728) -> q_gen_3719
<cons, cons>(q_gen_3690, q_gen_3675) -> q_gen_3728
<cons, cons>(q_gen_3653, q_gen_3698) -> q_gen_3739
<cons, cons>(q_gen_3690, q_gen_3702) -> q_gen_3755
<cons, cons>(q_gen_3690, q_gen_3633) -> q_gen_3756
<cons, cons>(q_gen_3663, q_gen_3768) -> q_gen_3757
<cons, cons>(q_gen_3689, q_gen_3688) -> q_gen_3757
<cons, cons>(q_gen_3663, q_gen_3701) -> q_gen_3766
<cons, cons>(q_gen_3653, q_gen_3773) -> q_gen_3768
<cons, cons>(q_gen_3689, q_gen_3701) -> q_gen_3768
<cons, cons>(q_gen_3653, q_gen_3756) -> q_gen_3773
<cons, cons>(q_gen_3653, q_gen_3718) -> q_gen_3796
<cons, cons>(q_gen_3653, q_gen_3796) -> q_gen_3796
<cons, cons>(q_gen_3690, q_gen_3652) -> q_gen_3800
<cons, cons>(q_gen_3653, q_gen_3805) -> q_gen_3801
<cons, cons>(q_gen_3690, q_gen_3698) -> q_gen_3801
<cons, cons>(q_gen_3653, q_gen_3806) -> q_gen_3805
<cons, cons>(q_gen_3689, q_gen_3756) -> q_gen_3806
<cons, cons>(q_gen_3653, q_gen_3809) -> q_gen_3808
<cons, cons>(q_gen_3689, q_gen_3652) -> q_gen_3808
<cons, cons>(q_gen_3653, q_gen_3808) -> q_gen_3809
<cons, cons>(q_gen_3689, q_gen_3806) -> q_gen_3820
<cons, cons>(q_gen_3653, q_gen_3739) -> q_gen_3823
<cons, cons>(q_gen_3653, q_gen_3768) -> q_gen_3823
<cons, cons>(q_gen_3653, q_gen_3800) -> q_gen_3823
<cons, cons>(q_gen_3689, q_gen_3808) -> q_gen_3823
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 53
() -> length([nil, z]) -> 53
() -> leq([z, s(nn2)]) -> 53
() -> leq([z, z]) -> 53
() -> reverse([nil, nil]) -> 53
(append([_eo, cons(h1, nil), _fo]) /\ reverse([t1, _eo])) -> reverse([cons(h1, t1), _fo]) -> 55
(append([t1, l2, _zn])) -> append([cons(h1, t1), l2, cons(h1, _zn)]) -> 55
(length([_oo, _po]) /\ length([l1, _no]) /\ reverse([l1, _oo])) -> leq([_no, _po]) -> 56
(length([_qo, _ro]) /\ length([l1, _so]) /\ reverse([l1, _qo])) -> leq([_ro, _so]) -> 56
(length([ll, _jo])) -> length([cons(x, ll), s(_jo)]) -> 56
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 54
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 54
(leq([s(nn1), z])) -> BOT -> 54
}
Sat witness: Found: ((length([_oo, _po]) /\ length([l1, _no]) /\ reverse([l1, _oo])) -> leq([_no, _po]), {
_no -> s(s(s(s(s(s(z))))))  ;  _oo -> cons(b, cons(b, cons(a, cons(a, cons(b, nil)))))  ;  _po -> s(s(z))  ;  l1 -> cons(b, cons(b, cons(a, cons(a, cons(b, nil)))))
})

Total time: 65.155136
Reason for stopping: DontKnow. Stopped because: timeout