Solving ../../benchmarks/true/length_reverse_natlist.smt2...

Inference procedure has parameters:
Ice fuel: 200
Timeout: 30s
Convolution: complete


Learning problem is:

env: {
nat -> {s, z}  ;  natlist -> {cons, nil}
}
definition:
{
(append, F:
{() -> append([nil, l2, l2])
(append([t1, l2, _lea])) -> append([cons(h1, t1), l2, cons(h1, _lea)])}
(append([_mea, _nea, _oea]) /\ append([_mea, _nea, _pea])) -> eq_natlist([_oea, _pea])
)
(reverse, F:
{() -> reverse([nil, nil])
(append([_qea, cons(h1, nil), _rea]) /\ reverse([t1, _qea])) -> reverse([cons(h1, t1), _rea])}
(reverse([_sea, _tea]) /\ reverse([_sea, _uea])) -> eq_natlist([_tea, _uea])
)
(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, _vea])) -> length([cons(x, ll), s(_vea)])}
(length([_wea, _xea]) /\ length([_wea, _yea])) -> eq_nat([_xea, _yea])
)
}

properties:
{(length([_afa, _bfa]) /\ length([l1, _zea]) /\ reverse([l1, _afa])) -> leq([_zea, _bfa])}


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([_qea, cons(h1, nil), _rea]) /\ reverse([t1, _qea])) -> reverse([cons(h1, t1), _rea]) -> 0  ;  (append([t1, l2, _lea])) -> append([cons(h1, t1), l2, cons(h1, _lea)]) -> 0  ;  (length([_afa, _bfa]) /\ length([l1, _zea]) /\ reverse([l1, _afa])) -> leq([_zea, _bfa]) -> 0  ;  (length([ll, _vea])) -> length([cons(x, ll), s(_vea)]) -> 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 30.000092 seconds.
DontKnow. Stopped because: timeout
Working model:
|_
{
append -> 
{{{
Q={q_gen_3727, q_gen_3731, q_gen_3732, q_gen_3733, q_gen_3734, q_gen_3735, q_gen_3738, q_gen_3739, q_gen_3740, q_gen_3741, q_gen_3742, q_gen_3743, q_gen_3751, q_gen_3752, q_gen_3753, q_gen_3754, q_gen_3755, q_gen_3761, q_gen_3762, q_gen_3763, q_gen_3764, q_gen_3765, q_gen_3769, q_gen_3770, q_gen_3771, q_gen_3772, q_gen_3778, q_gen_3779, q_gen_3780, q_gen_3781, q_gen_3782, q_gen_3785, q_gen_3786, q_gen_3787, q_gen_3788, q_gen_3789, q_gen_3790, q_gen_3795, q_gen_3796, q_gen_3797, q_gen_3798, q_gen_3799, q_gen_3800, q_gen_3801, q_gen_3802, q_gen_3803, q_gen_3804, q_gen_3807, q_gen_3808, q_gen_3809, q_gen_3814, q_gen_3815, q_gen_3816, q_gen_3817, q_gen_3818, q_gen_3819, q_gen_3820, q_gen_3821, q_gen_3822, q_gen_3823, q_gen_3824, q_gen_3825, q_gen_3826, q_gen_3831, q_gen_3832, q_gen_3833, q_gen_3834, q_gen_3835, q_gen_3836, q_gen_3837, q_gen_3840, q_gen_3841, q_gen_3842, q_gen_3843, q_gen_3844, q_gen_3847, q_gen_3848, q_gen_3849, q_gen_3850, q_gen_3853, q_gen_3854, q_gen_3855, 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_3864, q_gen_3865, q_gen_3866, q_gen_3867, q_gen_3868, q_gen_3869, q_gen_3870, q_gen_3871, q_gen_3872, q_gen_3873, q_gen_3874, q_gen_3875, q_gen_3876, q_gen_3877, q_gen_3878, q_gen_3879, q_gen_3880, q_gen_3881, q_gen_3882, q_gen_3883, q_gen_3884, q_gen_3885, q_gen_3886, q_gen_3887, q_gen_3888, q_gen_3889, q_gen_3890, q_gen_3891, q_gen_3901, q_gen_3902, q_gen_3904, q_gen_3905, q_gen_3906, q_gen_3907, q_gen_3908},
Q_f={},
Delta=
{
<z>() -> q_gen_3740
<s>(q_gen_3740) -> q_gen_3753
<nil>() -> q_gen_3764
<cons>(q_gen_3740, q_gen_3764) -> q_gen_3781
<nil, nil>() -> q_gen_3732
<nil, z>() -> q_gen_3733
<z, nil>() -> q_gen_3734
<z, z>() -> q_gen_3735
<nil, s>(q_gen_3740) -> q_gen_3739
<s, nil>(q_gen_3740) -> q_gen_3741
<s, s>(q_gen_3735) -> q_gen_3742
<nil, s>(q_gen_3753) -> q_gen_3752
<s, nil>(q_gen_3753) -> q_gen_3754
<s, s>(q_gen_3742) -> q_gen_3755
<cons, cons>(q_gen_3735, q_gen_3734, q_gen_3733, q_gen_3732) -> q_gen_3762
<cons, z>(q_gen_3740, q_gen_3764) -> q_gen_3763
<z, cons>(q_gen_3740, q_gen_3764) -> q_gen_3765
<cons, s>(q_gen_3735, q_gen_3733) -> q_gen_3770
<s, cons>(q_gen_3735, q_gen_3734) -> q_gen_3771
<cons, cons>(q_gen_3735, q_gen_3765, q_gen_3763, q_gen_3762) -> q_gen_3779
<cons, z>(q_gen_3740, q_gen_3781) -> q_gen_3780
<z, cons>(q_gen_3740, q_gen_3781) -> q_gen_3782
<cons, s>(q_gen_3787, q_gen_3739) -> q_gen_3786
<z, s>(q_gen_3740) -> q_gen_3787
<s, cons>(q_gen_3789, q_gen_3741) -> q_gen_3788
<s, z>(q_gen_3740) -> q_gen_3789
<nil, cons>(q_gen_3740, q_gen_3764) -> q_gen_3808
<nil, cons>(q_gen_3740, q_gen_3781) -> q_gen_3826
<s, z>(q_gen_3753) -> q_gen_3854
<s, s>(q_gen_3789) -> q_gen_3874
<nil, nil, nil>() -> q_gen_3727
<cons, nil, cons>(q_gen_3735, q_gen_3734, q_gen_3733, q_gen_3732) -> q_gen_3731
<nil, cons, cons>(q_gen_3742, q_gen_3741, q_gen_3739, q_gen_3732) -> q_gen_3738
<nil, cons, cons>(q_gen_3735, q_gen_3734, q_gen_3733, q_gen_3732) -> q_gen_3743
<cons, nil, cons>(q_gen_3755, q_gen_3754, q_gen_3752, q_gen_3732) -> q_gen_3751
<nil, cons, cons>(q_gen_3735, q_gen_3765, q_gen_3763, q_gen_3762) -> q_gen_3761
<cons, nil, cons>(q_gen_3742, q_gen_3771, q_gen_3770, q_gen_3762) -> q_gen_3769
<nil, cons, cons>(q_gen_3755, q_gen_3754, q_gen_3752, q_gen_3732) -> q_gen_3772
<nil, cons, cons>(q_gen_3735, q_gen_3782, q_gen_3780, q_gen_3779) -> q_gen_3778
<cons, nil, cons>(q_gen_3755, q_gen_3788, q_gen_3786, q_gen_3762) -> q_gen_3785
<nil, cons, cons>(q_gen_3787, q_gen_3734, q_gen_3739, q_gen_3732) -> q_gen_3790
<cons, cons, cons>(q_gen_3803, q_gen_3802, q_gen_3801, q_gen_3800, q_gen_3799, q_gen_3798, q_gen_3797, q_gen_3796) -> q_gen_3795
<nil, nil, cons>(q_gen_3740, q_gen_3764) -> q_gen_3796
<nil, nil, z>() -> q_gen_3797
<nil, z, cons>(q_gen_3740, q_gen_3764) -> q_gen_3798
<nil, z, z>() -> q_gen_3799
<z, nil, cons>(q_gen_3740, q_gen_3764) -> q_gen_3800
<z, nil, z>() -> q_gen_3801
<z, z, cons>(q_gen_3740, q_gen_3764) -> q_gen_3802
<z, z, z>() -> q_gen_3803
<nil, cons, cons>(q_gen_3789, q_gen_3741, q_gen_3733, q_gen_3732) -> q_gen_3804
<cons, nil, cons>(q_gen_3735, q_gen_3765, q_gen_3733, q_gen_3808) -> q_gen_3807
<nil, cons, cons>(q_gen_3735, q_gen_3765, q_gen_3733, q_gen_3808) -> q_gen_3809
<cons, cons, cons>(q_gen_3823, q_gen_3820, q_gen_3819, q_gen_3818, q_gen_3817, q_gen_3816, q_gen_3815, q_gen_3796) -> q_gen_3814
<nil, nil, s>(q_gen_3753) -> q_gen_3815
<nil, s, cons>(q_gen_3735, q_gen_3734) -> q_gen_3816
<nil, s, s>(q_gen_3787) -> q_gen_3817
<s, nil, cons>(q_gen_3789, q_gen_3741) -> q_gen_3818
<s, nil, s>(q_gen_3742) -> q_gen_3819
<s, s, cons>(q_gen_3822, q_gen_3821) -> q_gen_3820
<s, z, nil>(q_gen_3740) -> q_gen_3821
<s, z, z>(q_gen_3740) -> q_gen_3822
<s, s, s>(q_gen_3824) -> q_gen_3823
<s, z, s>(q_gen_3735) -> q_gen_3824
<nil, cons, cons>(q_gen_3735, q_gen_3782, q_gen_3733, q_gen_3826) -> q_gen_3825
<cons, cons, cons>(q_gen_3824, q_gen_3836, q_gen_3835, q_gen_3834, q_gen_3833, q_gen_3798, q_gen_3832, q_gen_3796) -> q_gen_3831
<nil, nil, s>(q_gen_3740) -> q_gen_3832
<nil, z, s>(q_gen_3740) -> q_gen_3833
<s, nil, cons>(q_gen_3735, q_gen_3734) -> q_gen_3834
<s, nil, s>(q_gen_3735) -> q_gen_3835
<s, z, cons>(q_gen_3735, q_gen_3734) -> q_gen_3836
<nil, cons, cons>(q_gen_3789, q_gen_3771, q_gen_3733, q_gen_3808) -> q_gen_3837
<cons, cons, cons>(q_gen_3844, q_gen_3842, q_gen_3835, q_gen_3834, q_gen_3841, q_gen_3816, q_gen_3832, q_gen_3796) -> q_gen_3840
<nil, s, s>(q_gen_3735) -> q_gen_3841
<s, s, cons>(q_gen_3803, q_gen_3843) -> q_gen_3842
<z, z, nil>() -> q_gen_3843
<s, s, s>(q_gen_3803) -> q_gen_3844
<cons, cons, cons>(q_gen_3850, q_gen_3849, q_gen_3801, q_gen_3800, q_gen_3848, q_gen_3816, q_gen_3797, q_gen_3796) -> q_gen_3847
<nil, s, z>(q_gen_3740) -> q_gen_3848
<z, s, cons>(q_gen_3735, q_gen_3734) -> q_gen_3849
<z, s, z>(q_gen_3740) -> q_gen_3850
<nil, cons, cons>(q_gen_3854, q_gen_3754, q_gen_3733, q_gen_3732) -> q_gen_3853
<cons, cons, cons>(q_gen_3860, q_gen_3858, q_gen_3835, q_gen_3834, q_gen_3857, q_gen_3856, q_gen_3832, q_gen_3796) -> q_gen_3855
<nil, s, cons>(q_gen_3789, q_gen_3741) -> q_gen_3856
<nil, s, s>(q_gen_3789) -> q_gen_3857
<s, s, cons>(q_gen_3850, q_gen_3859) -> q_gen_3858
<z, s, nil>(q_gen_3740) -> q_gen_3859
<s, s, s>(q_gen_3850) -> q_gen_3860
<cons, cons, cons>(q_gen_3866, q_gen_3863, q_gen_3819, q_gen_3818, q_gen_3862, q_gen_3856, q_gen_3815, q_gen_3796) -> q_gen_3861
<nil, s, s>(q_gen_3742) -> q_gen_3862
<s, s, cons>(q_gen_3865, q_gen_3864) -> q_gen_3863
<s, s, nil>(q_gen_3735) -> q_gen_3864
<s, s, z>(q_gen_3735) -> q_gen_3865
<s, s, s>(q_gen_3844) -> q_gen_3866
<cons, cons, cons>(q_gen_3844, q_gen_3871, q_gen_3835, q_gen_3870, q_gen_3841, q_gen_3869, q_gen_3832, q_gen_3868) -> q_gen_3867
<nil, nil, cons>(q_gen_3753, q_gen_3764) -> q_gen_3868
<nil, s, cons>(q_gen_3787, q_gen_3734) -> q_gen_3869
<s, nil, cons>(q_gen_3787, q_gen_3734) -> q_gen_3870
<s, s, cons>(q_gen_3872, q_gen_3843) -> q_gen_3871
<z, z, s>(q_gen_3740) -> q_gen_3872
<nil, cons, cons>(q_gen_3874, q_gen_3754, q_gen_3739, q_gen_3732) -> q_gen_3873
<cons, cons, cons>(q_gen_3860, q_gen_3877, q_gen_3835, q_gen_3870, q_gen_3857, q_gen_3876, q_gen_3832, q_gen_3868) -> q_gen_3875
<nil, s, cons>(q_gen_3742, q_gen_3741) -> q_gen_3876
<s, s, cons>(q_gen_3878, q_gen_3859) -> q_gen_3877
<z, s, s>(q_gen_3735) -> q_gen_3878
<cons, cons, cons>(q_gen_3803, q_gen_3884, q_gen_3883, q_gen_3882, q_gen_3799, q_gen_3881, q_gen_3880, q_gen_3809) -> q_gen_3879
<nil, cons, z>(q_gen_3740, q_gen_3764) -> q_gen_3880
<nil, z, cons>(q_gen_3740, q_gen_3781) -> q_gen_3881
<z, cons, cons>(q_gen_3735, q_gen_3765, q_gen_3733, q_gen_3808) -> q_gen_3882
<z, cons, z>(q_gen_3740, q_gen_3764) -> q_gen_3883
<z, z, cons>(q_gen_3740, q_gen_3781) -> q_gen_3884
<cons, cons, cons>(q_gen_3803, q_gen_3884, q_gen_3801, q_gen_3889, q_gen_3888, q_gen_3887, q_gen_3886, q_gen_3807) -> q_gen_3885
<cons, nil, z>(q_gen_3740, q_gen_3764) -> q_gen_3886
<cons, z, cons>(q_gen_3735, q_gen_3765, q_gen_3733, q_gen_3808) -> q_gen_3887
<cons, z, z>(q_gen_3740, q_gen_3764) -> q_gen_3888
<z, nil, cons>(q_gen_3740, q_gen_3781) -> q_gen_3889
<cons, cons, cons>(q_gen_3803, q_gen_3802, q_gen_3801, q_gen_3800, q_gen_3888, q_gen_3891, q_gen_3886, q_gen_3731) -> q_gen_3890
<cons, z, cons>(q_gen_3735, q_gen_3734, q_gen_3733, q_gen_3732) -> q_gen_3891
<cons, cons, cons>(q_gen_3803, q_gen_3884, q_gen_3801, q_gen_3889, q_gen_3799, q_gen_3881, q_gen_3797, q_gen_3902) -> q_gen_3901
<nil, nil, cons>(q_gen_3740, q_gen_3781) -> q_gen_3902
<cons, cons, cons>(q_gen_3824, q_gen_3908, q_gen_3835, q_gen_3907, q_gen_3906, q_gen_3887, q_gen_3905, q_gen_3807) -> q_gen_3904
<cons, nil, s>(q_gen_3735, q_gen_3733) -> q_gen_3905
<cons, z, s>(q_gen_3735, q_gen_3733) -> q_gen_3906
<s, nil, cons>(q_gen_3735, q_gen_3765) -> q_gen_3907
<s, z, cons>(q_gen_3735, q_gen_3765) -> q_gen_3908
}

Datatype: <natlist, natlist, natlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_3726, q_gen_3729, q_gen_3730, q_gen_3748, q_gen_3749, q_gen_3750, q_gen_3766, q_gen_3767, q_gen_3768, q_gen_3783, q_gen_3784, q_gen_3793, q_gen_3794, q_gen_3898, q_gen_3899},
Q_f={},
Delta=
{
<z>() -> q_gen_3750
<s>(q_gen_3750) -> q_gen_3768
<nil, z>() -> q_gen_3726
<cons, s>(q_gen_3730, q_gen_3726) -> q_gen_3729
<z, z>() -> q_gen_3730
<cons, s>(q_gen_3749, q_gen_3726) -> q_gen_3748
<s, z>(q_gen_3750) -> q_gen_3749
<cons, s>(q_gen_3767, q_gen_3726) -> q_gen_3766
<s, z>(q_gen_3768) -> q_gen_3767
<cons, s>(q_gen_3784, q_gen_3729) -> q_gen_3783
<s, s>(q_gen_3730) -> q_gen_3784
<cons, s>(q_gen_3794, q_gen_3729) -> q_gen_3793
<z, s>(q_gen_3750) -> q_gen_3794
<cons, s>(q_gen_3899, q_gen_3793) -> q_gen_3898
<z, s>(q_gen_3768) -> q_gen_3899
}

Datatype: <natlist, nat>
Convolution form: complete
}}}
  ;  leq -> 
{{{
Q={q_gen_3723, q_gen_3724, q_gen_3725, q_gen_3728, q_gen_3736, q_gen_3737, q_gen_3896, q_gen_3897, q_gen_3900},
Q_f={},
Delta=
{
<z>() -> q_gen_3725
<s>(q_gen_3725) -> q_gen_3737
<z, z>() -> q_gen_3723
<z, s>(q_gen_3725) -> q_gen_3724
<s, s>(q_gen_3723) -> q_gen_3728
<z, s>(q_gen_3737) -> q_gen_3736
<s, z>(q_gen_3725) -> q_gen_3896
<s, s>(q_gen_3896) -> q_gen_3897
<s, s>(q_gen_3897) -> q_gen_3900
}

Datatype: <nat, nat>
Convolution form: complete
}}}
  ;  reverse -> 
{{{
Q={q_gen_3722, q_gen_3744, q_gen_3745, q_gen_3746, q_gen_3747, q_gen_3756, q_gen_3757, q_gen_3758, q_gen_3759, q_gen_3760, q_gen_3773, q_gen_3774, q_gen_3775, q_gen_3776, q_gen_3777, q_gen_3791, q_gen_3792, q_gen_3805, q_gen_3806, q_gen_3810, q_gen_3811, q_gen_3812, q_gen_3813, q_gen_3827, q_gen_3828, q_gen_3829, q_gen_3830, q_gen_3838, q_gen_3839, q_gen_3845, q_gen_3846, q_gen_3851, q_gen_3852, q_gen_3892, q_gen_3893, q_gen_3894, q_gen_3895, q_gen_3903},
Q_f={},
Delta=
{
<z>() -> q_gen_3758
<s>(q_gen_3758) -> q_gen_3775
<nil>() -> q_gen_3812
<cons>(q_gen_3758, q_gen_3812) -> q_gen_3829
<nil, nil>() -> q_gen_3722
<cons, cons>(q_gen_3747, q_gen_3746, q_gen_3745, q_gen_3722) -> q_gen_3744
<nil, z>() -> q_gen_3745
<z, nil>() -> q_gen_3746
<z, z>() -> q_gen_3747
<cons, cons>(q_gen_3760, q_gen_3759, q_gen_3757, q_gen_3722) -> q_gen_3756
<nil, s>(q_gen_3758) -> q_gen_3757
<s, nil>(q_gen_3758) -> q_gen_3759
<s, s>(q_gen_3747) -> q_gen_3760
<cons, cons>(q_gen_3777, q_gen_3776, q_gen_3774, q_gen_3722) -> q_gen_3773
<nil, s>(q_gen_3775) -> q_gen_3774
<s, nil>(q_gen_3775) -> q_gen_3776
<s, s>(q_gen_3760) -> q_gen_3777
<cons, cons>(q_gen_3792, q_gen_3746, q_gen_3757, q_gen_3722) -> q_gen_3791
<z, s>(q_gen_3758) -> q_gen_3792
<cons, cons>(q_gen_3806, q_gen_3759, q_gen_3745, q_gen_3722) -> q_gen_3805
<s, z>(q_gen_3758) -> q_gen_3806
<cons, cons>(q_gen_3747, q_gen_3813, q_gen_3745, q_gen_3811) -> q_gen_3810
<nil, cons>(q_gen_3758, q_gen_3812) -> q_gen_3811
<z, cons>(q_gen_3758, q_gen_3812) -> q_gen_3813
<cons, cons>(q_gen_3747, q_gen_3830, q_gen_3745, q_gen_3828) -> q_gen_3827
<nil, cons>(q_gen_3758, q_gen_3829) -> q_gen_3828
<z, cons>(q_gen_3758, q_gen_3829) -> q_gen_3830
<cons, cons>(q_gen_3806, q_gen_3839, q_gen_3745, q_gen_3811) -> q_gen_3838
<s, cons>(q_gen_3747, q_gen_3746) -> q_gen_3839
<cons, cons>(q_gen_3747, q_gen_3813, q_gen_3846, q_gen_3744) -> q_gen_3845
<cons, z>(q_gen_3758, q_gen_3812) -> q_gen_3846
<cons, cons>(q_gen_3792, q_gen_3813, q_gen_3852, q_gen_3744) -> q_gen_3851
<cons, s>(q_gen_3747, q_gen_3745) -> q_gen_3852
<cons, cons>(q_gen_3747, q_gen_3813, q_gen_3895, q_gen_3893) -> q_gen_3892
<cons, cons>(q_gen_3747, q_gen_3746, q_gen_3846, q_gen_3894) -> q_gen_3893
<cons, nil>(q_gen_3758, q_gen_3812) -> q_gen_3894
<cons, z>(q_gen_3758, q_gen_3829) -> q_gen_3895
<cons, cons>(q_gen_3747, q_gen_3830, q_gen_3846, q_gen_3810) -> q_gen_3903
}

Datatype: <natlist, natlist>
Convolution form: complete
}}}

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

-------------------
STEPS:
-------------------------------------------
Step 0, which took 0.004683 s (model generation: 0.003971,  model checking: 0.000712):

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

}

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

}

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

}

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

}

Datatype: <natlist, natlist>
Convolution form: complete
}}}

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

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([_qea, cons(h1, nil), _rea]) /\ reverse([t1, _qea])) -> reverse([cons(h1, t1), _rea]) -> 1  ;  (append([t1, l2, _lea])) -> append([cons(h1, t1), l2, cons(h1, _lea)]) -> 1  ;  (length([_afa, _bfa]) /\ length([l1, _zea]) /\ reverse([l1, _afa])) -> leq([_zea, _bfa]) -> 1  ;  (length([ll, _vea])) -> length([cons(x, ll), s(_vea)]) -> 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: Yes: (() -> reverse([nil, nil]), {

})

-------------------------------------------
Step 1, which took 0.003566 s (model generation: 0.003539,  model checking: 0.000027):

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

}

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

}

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

}

Datatype: <nat, nat>
Convolution form: complete
}}}
  ;  reverse -> 
{{{
Q={q_gen_3722},
Q_f={q_gen_3722},
Delta=
{
<nil, nil>() -> q_gen_3722
}

Datatype: <natlist, natlist>
Convolution form: complete
}}}

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

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([_qea, cons(h1, nil), _rea]) /\ reverse([t1, _qea])) -> reverse([cons(h1, t1), _rea]) -> 1  ;  (append([t1, l2, _lea])) -> append([cons(h1, t1), l2, cons(h1, _lea)]) -> 1  ;  (length([_afa, _bfa]) /\ length([l1, _zea]) /\ reverse([l1, _afa])) -> leq([_zea, _bfa]) -> 1  ;  (length([ll, _vea])) -> length([cons(x, ll), s(_vea)]) -> 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: Yes: (() -> leq([z, z]), {

})

-------------------------------------------
Step 2, which took 0.003415 s (model generation: 0.003372,  model checking: 0.000043):

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

}

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

}

Datatype: <natlist, nat>
Convolution form: complete
}}}
  ;  leq -> 
{{{
Q={q_gen_3723},
Q_f={q_gen_3723},
Delta=
{
<z, z>() -> q_gen_3723
}

Datatype: <nat, nat>
Convolution form: complete
}}}
  ;  reverse -> 
{{{
Q={q_gen_3722},
Q_f={q_gen_3722},
Delta=
{
<nil, nil>() -> q_gen_3722
}

Datatype: <natlist, natlist>
Convolution form: complete
}}}

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

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([_qea, cons(h1, nil), _rea]) /\ reverse([t1, _qea])) -> reverse([cons(h1, t1), _rea]) -> 1  ;  (append([t1, l2, _lea])) -> append([cons(h1, t1), l2, cons(h1, _lea)]) -> 1  ;  (length([_afa, _bfa]) /\ length([l1, _zea]) /\ reverse([l1, _afa])) -> leq([_zea, _bfa]) -> 1  ;  (length([ll, _vea])) -> length([cons(x, ll), s(_vea)]) -> 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: Yes: (() -> leq([z, s(nn2)]), {
nn2 -> z
})

-------------------------------------------
Step 3, which took 0.003446 s (model generation: 0.003388,  model checking: 0.000058):

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

}

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

}

Datatype: <natlist, nat>
Convolution form: complete
}}}
  ;  leq -> 
{{{
Q={q_gen_3723, q_gen_3725},
Q_f={q_gen_3723},
Delta=
{
<z>() -> q_gen_3725
<z, s>(q_gen_3725) -> q_gen_3723
<z, z>() -> q_gen_3723
}

Datatype: <nat, nat>
Convolution form: complete
}}}
  ;  reverse -> 
{{{
Q={q_gen_3722},
Q_f={q_gen_3722},
Delta=
{
<nil, nil>() -> q_gen_3722
}

Datatype: <natlist, natlist>
Convolution form: complete
}}}

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

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([_qea, cons(h1, nil), _rea]) /\ reverse([t1, _qea])) -> reverse([cons(h1, t1), _rea]) -> 1  ;  (append([t1, l2, _lea])) -> append([cons(h1, t1), l2, cons(h1, _lea)]) -> 1  ;  (length([_afa, _bfa]) /\ length([l1, _zea]) /\ reverse([l1, _afa])) -> leq([_zea, _bfa]) -> 1  ;  (length([ll, _vea])) -> length([cons(x, ll), s(_vea)]) -> 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: Yes: (() -> length([nil, z]), {

})

-------------------------------------------
Step 4, which took 0.004494 s (model generation: 0.003424,  model checking: 0.001070):

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

}

Datatype: <natlist, natlist, natlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_3726},
Q_f={q_gen_3726},
Delta=
{
<nil, z>() -> q_gen_3726
}

Datatype: <natlist, nat>
Convolution form: complete
}}}
  ;  leq -> 
{{{
Q={q_gen_3723, q_gen_3725},
Q_f={q_gen_3723},
Delta=
{
<z>() -> q_gen_3725
<z, s>(q_gen_3725) -> q_gen_3723
<z, z>() -> q_gen_3723
}

Datatype: <nat, nat>
Convolution form: complete
}}}
  ;  reverse -> 
{{{
Q={q_gen_3722},
Q_f={q_gen_3722},
Delta=
{
<nil, nil>() -> q_gen_3722
}

Datatype: <natlist, natlist>
Convolution form: complete
}}}

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

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([_qea, cons(h1, nil), _rea]) /\ reverse([t1, _qea])) -> reverse([cons(h1, t1), _rea]) -> 1  ;  (append([t1, l2, _lea])) -> append([cons(h1, t1), l2, cons(h1, _lea)]) -> 1  ;  (length([_afa, _bfa]) /\ length([l1, _zea]) /\ reverse([l1, _afa])) -> leq([_zea, _bfa]) -> 1  ;  (length([ll, _vea])) -> length([cons(x, ll), s(_vea)]) -> 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: Yes: (() -> append([nil, l2, l2]), {
l2 -> nil
})

-------------------------------------------
Step 5, which took 0.004884 s (model generation: 0.004774,  model checking: 0.000110):

Model:
|_
{
append -> 
{{{
Q={q_gen_3727},
Q_f={q_gen_3727},
Delta=
{
<nil, nil, nil>() -> q_gen_3727
}

Datatype: <natlist, natlist, natlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_3726},
Q_f={q_gen_3726},
Delta=
{
<nil, z>() -> q_gen_3726
}

Datatype: <natlist, nat>
Convolution form: complete
}}}
  ;  leq -> 
{{{
Q={q_gen_3723, q_gen_3725},
Q_f={q_gen_3723},
Delta=
{
<z>() -> q_gen_3725
<z, s>(q_gen_3725) -> q_gen_3723
<z, z>() -> q_gen_3723
}

Datatype: <nat, nat>
Convolution form: complete
}}}
  ;  reverse -> 
{{{
Q={q_gen_3722},
Q_f={q_gen_3722},
Delta=
{
<nil, nil>() -> q_gen_3722
}

Datatype: <natlist, natlist>
Convolution form: complete
}}}

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

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([_qea, cons(h1, nil), _rea]) /\ reverse([t1, _qea])) -> reverse([cons(h1, t1), _rea]) -> 1  ;  (append([t1, l2, _lea])) -> append([cons(h1, t1), l2, cons(h1, _lea)]) -> 1  ;  (length([_afa, _bfa]) /\ length([l1, _zea]) /\ reverse([l1, _afa])) -> leq([_zea, _bfa]) -> 1  ;  (length([ll, _vea])) -> length([cons(x, ll), s(_vea)]) -> 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: Yes: ((leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]), {
nn1 -> z  ;  nn2 -> z
})

-------------------------------------------
Step 6, which took 0.006350 s (model generation: 0.006175,  model checking: 0.000175):

Model:
|_
{
append -> 
{{{
Q={q_gen_3727},
Q_f={q_gen_3727},
Delta=
{
<nil, nil, nil>() -> q_gen_3727
}

Datatype: <natlist, natlist, natlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_3726},
Q_f={q_gen_3726},
Delta=
{
<nil, z>() -> q_gen_3726
}

Datatype: <natlist, nat>
Convolution form: complete
}}}
  ;  leq -> 
{{{
Q={q_gen_3723, q_gen_3725},
Q_f={q_gen_3723},
Delta=
{
<z>() -> q_gen_3725
<s, s>(q_gen_3723) -> q_gen_3723
<z, s>(q_gen_3725) -> q_gen_3723
<z, z>() -> q_gen_3723
}

Datatype: <nat, nat>
Convolution form: complete
}}}
  ;  reverse -> 
{{{
Q={q_gen_3722},
Q_f={q_gen_3722},
Delta=
{
<nil, nil>() -> q_gen_3722
}

Datatype: <natlist, natlist>
Convolution form: complete
}}}

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

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([_qea, cons(h1, nil), _rea]) /\ reverse([t1, _qea])) -> reverse([cons(h1, t1), _rea]) -> 1  ;  (append([t1, l2, _lea])) -> append([cons(h1, t1), l2, cons(h1, _lea)]) -> 1  ;  (length([_afa, _bfa]) /\ length([l1, _zea]) /\ reverse([l1, _afa])) -> leq([_zea, _bfa]) -> 1  ;  (length([ll, _vea])) -> length([cons(x, ll), s(_vea)]) -> 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: Yes: ((length([ll, _vea])) -> length([cons(x, ll), s(_vea)]), {
_vea -> z  ;  ll -> nil  ;  x -> z
})

-------------------------------------------
Step 7, which took 0.010495 s (model generation: 0.009544,  model checking: 0.000951):

Model:
|_
{
append -> 
{{{
Q={q_gen_3727},
Q_f={q_gen_3727},
Delta=
{
<nil, nil, nil>() -> q_gen_3727
}

Datatype: <natlist, natlist, natlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_3726, q_gen_3730},
Q_f={q_gen_3726},
Delta=
{
<cons, s>(q_gen_3730, q_gen_3726) -> q_gen_3726
<nil, z>() -> q_gen_3726
<z, z>() -> q_gen_3730
}

Datatype: <natlist, nat>
Convolution form: complete
}}}
  ;  leq -> 
{{{
Q={q_gen_3723, q_gen_3725},
Q_f={q_gen_3723},
Delta=
{
<z>() -> q_gen_3725
<s, s>(q_gen_3723) -> q_gen_3723
<z, s>(q_gen_3725) -> q_gen_3723
<z, z>() -> q_gen_3723
}

Datatype: <nat, nat>
Convolution form: complete
}}}
  ;  reverse -> 
{{{
Q={q_gen_3722},
Q_f={q_gen_3722},
Delta=
{
<nil, nil>() -> q_gen_3722
}

Datatype: <natlist, natlist>
Convolution form: complete
}}}

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

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([_qea, cons(h1, nil), _rea]) /\ reverse([t1, _qea])) -> reverse([cons(h1, t1), _rea]) -> 1  ;  (append([t1, l2, _lea])) -> append([cons(h1, t1), l2, cons(h1, _lea)]) -> 4  ;  (length([_afa, _bfa]) /\ length([l1, _zea]) /\ reverse([l1, _afa])) -> leq([_zea, _bfa]) -> 2  ;  (length([ll, _vea])) -> length([cons(x, ll), s(_vea)]) -> 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: Yes: ((append([t1, l2, _lea])) -> append([cons(h1, t1), l2, cons(h1, _lea)]), {
_lea -> nil  ;  h1 -> z  ;  l2 -> nil  ;  t1 -> nil
})

-------------------------------------------
Step 8, which took 0.009139 s (model generation: 0.007795,  model checking: 0.001344):

Model:
|_
{
append -> 
{{{
Q={q_gen_3727, q_gen_3732, q_gen_3733, q_gen_3734, q_gen_3735},
Q_f={q_gen_3727},
Delta=
{
<nil, nil>() -> q_gen_3732
<nil, z>() -> q_gen_3733
<z, nil>() -> q_gen_3734
<z, z>() -> q_gen_3735
<cons, nil, cons>(q_gen_3735, q_gen_3734, q_gen_3733, q_gen_3732) -> q_gen_3727
<nil, nil, nil>() -> q_gen_3727
}

Datatype: <natlist, natlist, natlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_3726, q_gen_3730},
Q_f={q_gen_3726},
Delta=
{
<cons, s>(q_gen_3730, q_gen_3726) -> q_gen_3726
<nil, z>() -> q_gen_3726
<z, z>() -> q_gen_3730
}

Datatype: <natlist, nat>
Convolution form: complete
}}}
  ;  leq -> 
{{{
Q={q_gen_3723, q_gen_3725},
Q_f={q_gen_3723},
Delta=
{
<z>() -> q_gen_3725
<s, s>(q_gen_3723) -> q_gen_3723
<z, s>(q_gen_3725) -> q_gen_3723
<z, z>() -> q_gen_3723
}

Datatype: <nat, nat>
Convolution form: complete
}}}
  ;  reverse -> 
{{{
Q={q_gen_3722},
Q_f={q_gen_3722},
Delta=
{
<nil, nil>() -> q_gen_3722
}

Datatype: <natlist, natlist>
Convolution form: complete
}}}

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

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([_qea, cons(h1, nil), _rea]) /\ reverse([t1, _qea])) -> reverse([cons(h1, t1), _rea]) -> 2  ;  (append([t1, l2, _lea])) -> append([cons(h1, t1), l2, cons(h1, _lea)]) -> 4  ;  (length([_afa, _bfa]) /\ length([l1, _zea]) /\ reverse([l1, _afa])) -> leq([_zea, _bfa]) -> 3  ;  (length([ll, _vea])) -> length([cons(x, ll), s(_vea)]) -> 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: Yes: (() -> leq([z, s(nn2)]), {
nn2 -> s(z)
})

-------------------------------------------
Step 9, which took 0.032196 s (model generation: 0.011043,  model checking: 0.021153):

Model:
|_
{
append -> 
{{{
Q={q_gen_3727, q_gen_3732, q_gen_3733, q_gen_3734, q_gen_3735},
Q_f={q_gen_3727},
Delta=
{
<nil, nil>() -> q_gen_3732
<nil, z>() -> q_gen_3733
<z, nil>() -> q_gen_3734
<z, z>() -> q_gen_3735
<cons, nil, cons>(q_gen_3735, q_gen_3734, q_gen_3733, q_gen_3732) -> q_gen_3727
<nil, nil, nil>() -> q_gen_3727
}

Datatype: <natlist, natlist, natlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_3726, q_gen_3730},
Q_f={q_gen_3726},
Delta=
{
<cons, s>(q_gen_3730, q_gen_3726) -> q_gen_3726
<nil, z>() -> q_gen_3726
<z, z>() -> q_gen_3730
}

Datatype: <natlist, nat>
Convolution form: complete
}}}
  ;  leq -> 
{{{
Q={q_gen_3723, q_gen_3725},
Q_f={q_gen_3723},
Delta=
{
<s>(q_gen_3725) -> q_gen_3725
<z>() -> q_gen_3725
<s, s>(q_gen_3723) -> q_gen_3723
<z, s>(q_gen_3725) -> q_gen_3723
<z, z>() -> q_gen_3723
}

Datatype: <nat, nat>
Convolution form: complete
}}}
  ;  reverse -> 
{{{
Q={q_gen_3722},
Q_f={q_gen_3722},
Delta=
{
<nil, nil>() -> q_gen_3722
}

Datatype: <natlist, natlist>
Convolution form: complete
}}}

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

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([_qea, cons(h1, nil), _rea]) /\ reverse([t1, _qea])) -> reverse([cons(h1, t1), _rea]) -> 3  ;  (append([t1, l2, _lea])) -> append([cons(h1, t1), l2, cons(h1, _lea)]) -> 4  ;  (length([_afa, _bfa]) /\ length([l1, _zea]) /\ reverse([l1, _afa])) -> leq([_zea, _bfa]) -> 4  ;  (length([ll, _vea])) -> length([cons(x, ll), s(_vea)]) -> 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: Yes: (() -> append([nil, l2, l2]), {
l2 -> cons(s(z), nil)
})

-------------------------------------------
Step 10, which took 0.004389 s (model generation: 0.004242,  model checking: 0.000147):

Model:
|_
{
append -> 
{{{
Q={q_gen_3727, q_gen_3732, q_gen_3733, q_gen_3734, q_gen_3735, q_gen_3740},
Q_f={q_gen_3727},
Delta=
{
<z>() -> q_gen_3740
<nil, nil>() -> q_gen_3732
<nil, s>(q_gen_3740) -> q_gen_3733
<nil, z>() -> q_gen_3733
<s, nil>(q_gen_3740) -> q_gen_3734
<z, nil>() -> q_gen_3734
<s, s>(q_gen_3735) -> q_gen_3735
<z, z>() -> q_gen_3735
<cons, nil, cons>(q_gen_3735, q_gen_3734, q_gen_3733, q_gen_3732) -> q_gen_3727
<nil, cons, cons>(q_gen_3735, q_gen_3734, q_gen_3733, q_gen_3732) -> q_gen_3727
<nil, nil, nil>() -> q_gen_3727
}

Datatype: <natlist, natlist, natlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_3726, q_gen_3730},
Q_f={q_gen_3726},
Delta=
{
<cons, s>(q_gen_3730, q_gen_3726) -> q_gen_3726
<nil, z>() -> q_gen_3726
<z, z>() -> q_gen_3730
}

Datatype: <natlist, nat>
Convolution form: complete
}}}
  ;  leq -> 
{{{
Q={q_gen_3723, q_gen_3725},
Q_f={q_gen_3723},
Delta=
{
<s>(q_gen_3725) -> q_gen_3725
<z>() -> q_gen_3725
<s, s>(q_gen_3723) -> q_gen_3723
<z, s>(q_gen_3725) -> q_gen_3723
<z, z>() -> q_gen_3723
}

Datatype: <nat, nat>
Convolution form: complete
}}}
  ;  reverse -> 
{{{
Q={q_gen_3722},
Q_f={q_gen_3722},
Delta=
{
<nil, nil>() -> q_gen_3722
}

Datatype: <natlist, natlist>
Convolution form: complete
}}}

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

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([_qea, cons(h1, nil), _rea]) /\ reverse([t1, _qea])) -> reverse([cons(h1, t1), _rea]) -> 6  ;  (append([t1, l2, _lea])) -> append([cons(h1, t1), l2, cons(h1, _lea)]) -> 4  ;  (length([_afa, _bfa]) /\ length([l1, _zea]) /\ reverse([l1, _afa])) -> leq([_zea, _bfa]) -> 4  ;  (length([ll, _vea])) -> length([cons(x, ll), s(_vea)]) -> 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: Yes: ((append([_qea, cons(h1, nil), _rea]) /\ reverse([t1, _qea])) -> reverse([cons(h1, t1), _rea]), {
_qea -> nil  ;  _rea -> cons(z, nil)  ;  h1 -> z  ;  t1 -> nil
})

-------------------------------------------
Step 11, which took 0.005075 s (model generation: 0.004476,  model checking: 0.000599):

Model:
|_
{
append -> 
{{{
Q={q_gen_3727, q_gen_3732, q_gen_3733, q_gen_3734, q_gen_3735, q_gen_3740},
Q_f={q_gen_3727},
Delta=
{
<z>() -> q_gen_3740
<nil, nil>() -> q_gen_3732
<nil, s>(q_gen_3740) -> q_gen_3733
<nil, z>() -> q_gen_3733
<s, nil>(q_gen_3740) -> q_gen_3734
<z, nil>() -> q_gen_3734
<s, s>(q_gen_3735) -> q_gen_3735
<z, z>() -> q_gen_3735
<cons, nil, cons>(q_gen_3735, q_gen_3734, q_gen_3733, q_gen_3732) -> q_gen_3727
<nil, cons, cons>(q_gen_3735, q_gen_3734, q_gen_3733, q_gen_3732) -> q_gen_3727
<nil, nil, nil>() -> q_gen_3727
}

Datatype: <natlist, natlist, natlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_3726, q_gen_3730},
Q_f={q_gen_3726},
Delta=
{
<cons, s>(q_gen_3730, q_gen_3726) -> q_gen_3726
<nil, z>() -> q_gen_3726
<z, z>() -> q_gen_3730
}

Datatype: <natlist, nat>
Convolution form: complete
}}}
  ;  leq -> 
{{{
Q={q_gen_3723, q_gen_3725},
Q_f={q_gen_3723},
Delta=
{
<s>(q_gen_3725) -> q_gen_3725
<z>() -> q_gen_3725
<s, s>(q_gen_3723) -> q_gen_3723
<z, s>(q_gen_3725) -> q_gen_3723
<z, z>() -> q_gen_3723
}

Datatype: <nat, nat>
Convolution form: complete
}}}
  ;  reverse -> 
{{{
Q={q_gen_3722, q_gen_3745, q_gen_3746, q_gen_3747},
Q_f={q_gen_3722},
Delta=
{
<cons, cons>(q_gen_3747, q_gen_3746, q_gen_3745, q_gen_3722) -> q_gen_3722
<nil, nil>() -> q_gen_3722
<nil, z>() -> q_gen_3745
<z, nil>() -> q_gen_3746
<z, z>() -> q_gen_3747
}

Datatype: <natlist, natlist>
Convolution form: complete
}}}

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

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([_qea, cons(h1, nil), _rea]) /\ reverse([t1, _qea])) -> reverse([cons(h1, t1), _rea]) -> 6  ;  (append([t1, l2, _lea])) -> append([cons(h1, t1), l2, cons(h1, _lea)]) -> 4  ;  (length([_afa, _bfa]) /\ length([l1, _zea]) /\ reverse([l1, _afa])) -> leq([_zea, _bfa]) -> 4  ;  (length([ll, _vea])) -> length([cons(x, ll), s(_vea)]) -> 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: Yes: ((length([ll, _vea])) -> length([cons(x, ll), s(_vea)]), {
_vea -> z  ;  ll -> nil  ;  x -> s(z)
})

-------------------------------------------
Step 12, which took 0.009457 s (model generation: 0.006231,  model checking: 0.003226):

Model:
|_
{
append -> 
{{{
Q={q_gen_3727, q_gen_3732, q_gen_3733, q_gen_3734, q_gen_3735, q_gen_3740},
Q_f={q_gen_3727},
Delta=
{
<z>() -> q_gen_3740
<nil, nil>() -> q_gen_3732
<nil, s>(q_gen_3740) -> q_gen_3733
<nil, z>() -> q_gen_3733
<s, nil>(q_gen_3740) -> q_gen_3734
<z, nil>() -> q_gen_3734
<s, s>(q_gen_3735) -> q_gen_3735
<z, z>() -> q_gen_3735
<cons, nil, cons>(q_gen_3735, q_gen_3734, q_gen_3733, q_gen_3732) -> q_gen_3727
<nil, cons, cons>(q_gen_3735, q_gen_3734, q_gen_3733, q_gen_3732) -> q_gen_3727
<nil, nil, nil>() -> q_gen_3727
}

Datatype: <natlist, natlist, natlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_3726, q_gen_3730, q_gen_3750},
Q_f={q_gen_3726},
Delta=
{
<z>() -> q_gen_3750
<cons, s>(q_gen_3730, q_gen_3726) -> q_gen_3726
<nil, z>() -> q_gen_3726
<s, z>(q_gen_3750) -> q_gen_3730
<z, z>() -> q_gen_3730
}

Datatype: <natlist, nat>
Convolution form: complete
}}}
  ;  leq -> 
{{{
Q={q_gen_3723, q_gen_3725},
Q_f={q_gen_3723},
Delta=
{
<s>(q_gen_3725) -> q_gen_3725
<z>() -> q_gen_3725
<s, s>(q_gen_3723) -> q_gen_3723
<z, s>(q_gen_3725) -> q_gen_3723
<z, z>() -> q_gen_3723
}

Datatype: <nat, nat>
Convolution form: complete
}}}
  ;  reverse -> 
{{{
Q={q_gen_3722, q_gen_3745, q_gen_3746, q_gen_3747},
Q_f={q_gen_3722},
Delta=
{
<cons, cons>(q_gen_3747, q_gen_3746, q_gen_3745, q_gen_3722) -> q_gen_3722
<nil, nil>() -> q_gen_3722
<nil, z>() -> q_gen_3745
<z, nil>() -> q_gen_3746
<z, z>() -> q_gen_3747
}

Datatype: <natlist, natlist>
Convolution form: complete
}}}

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

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([_qea, cons(h1, nil), _rea]) /\ reverse([t1, _qea])) -> reverse([cons(h1, t1), _rea]) -> 6  ;  (append([t1, l2, _lea])) -> append([cons(h1, t1), l2, cons(h1, _lea)]) -> 7  ;  (length([_afa, _bfa]) /\ length([l1, _zea]) /\ reverse([l1, _afa])) -> leq([_zea, _bfa]) -> 5  ;  (length([ll, _vea])) -> length([cons(x, ll), s(_vea)]) -> 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: Yes: ((append([t1, l2, _lea])) -> append([cons(h1, t1), l2, cons(h1, _lea)]), {
_lea -> nil  ;  h1 -> s(s(z))  ;  l2 -> nil  ;  t1 -> nil
})

-------------------------------------------
Step 13, which took 0.012239 s (model generation: 0.009678,  model checking: 0.002561):

Model:
|_
{
append -> 
{{{
Q={q_gen_3727, q_gen_3732, q_gen_3733, q_gen_3734, q_gen_3735, q_gen_3740},
Q_f={q_gen_3727},
Delta=
{
<s>(q_gen_3740) -> q_gen_3740
<z>() -> q_gen_3740
<nil, nil>() -> q_gen_3732
<nil, s>(q_gen_3740) -> q_gen_3733
<nil, z>() -> q_gen_3733
<s, nil>(q_gen_3740) -> q_gen_3734
<z, nil>() -> q_gen_3734
<s, s>(q_gen_3735) -> q_gen_3735
<z, z>() -> q_gen_3735
<cons, nil, cons>(q_gen_3735, q_gen_3734, q_gen_3733, q_gen_3732) -> q_gen_3727
<nil, cons, cons>(q_gen_3735, q_gen_3734, q_gen_3733, q_gen_3732) -> q_gen_3727
<nil, nil, nil>() -> q_gen_3727
}

Datatype: <natlist, natlist, natlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_3726, q_gen_3730, q_gen_3750},
Q_f={q_gen_3726},
Delta=
{
<z>() -> q_gen_3750
<cons, s>(q_gen_3730, q_gen_3726) -> q_gen_3726
<nil, z>() -> q_gen_3726
<s, z>(q_gen_3750) -> q_gen_3730
<z, z>() -> q_gen_3730
}

Datatype: <natlist, nat>
Convolution form: complete
}}}
  ;  leq -> 
{{{
Q={q_gen_3723, q_gen_3725},
Q_f={q_gen_3723},
Delta=
{
<s>(q_gen_3725) -> q_gen_3725
<z>() -> q_gen_3725
<s, s>(q_gen_3723) -> q_gen_3723
<z, s>(q_gen_3725) -> q_gen_3723
<z, z>() -> q_gen_3723
}

Datatype: <nat, nat>
Convolution form: complete
}}}
  ;  reverse -> 
{{{
Q={q_gen_3722, q_gen_3745, q_gen_3746, q_gen_3747},
Q_f={q_gen_3722},
Delta=
{
<cons, cons>(q_gen_3747, q_gen_3746, q_gen_3745, q_gen_3722) -> q_gen_3722
<nil, nil>() -> q_gen_3722
<nil, z>() -> q_gen_3745
<z, nil>() -> q_gen_3746
<z, z>() -> q_gen_3747
}

Datatype: <natlist, natlist>
Convolution form: complete
}}}

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

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([_qea, cons(h1, nil), _rea]) /\ reverse([t1, _qea])) -> reverse([cons(h1, t1), _rea]) -> 9  ;  (append([t1, l2, _lea])) -> append([cons(h1, t1), l2, cons(h1, _lea)]) -> 7  ;  (length([_afa, _bfa]) /\ length([l1, _zea]) /\ reverse([l1, _afa])) -> leq([_zea, _bfa]) -> 6  ;  (length([ll, _vea])) -> length([cons(x, ll), s(_vea)]) -> 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: Yes: ((append([_qea, cons(h1, nil), _rea]) /\ reverse([t1, _qea])) -> reverse([cons(h1, t1), _rea]), {
_qea -> nil  ;  _rea -> cons(s(z), nil)  ;  h1 -> s(z)  ;  t1 -> nil
})

-------------------------------------------
Step 14, which took 0.041928 s (model generation: 0.011858,  model checking: 0.030070):

Model:
|_
{
append -> 
{{{
Q={q_gen_3727, q_gen_3732, q_gen_3733, q_gen_3734, q_gen_3735, q_gen_3740},
Q_f={q_gen_3727},
Delta=
{
<s>(q_gen_3740) -> q_gen_3740
<z>() -> q_gen_3740
<nil, nil>() -> q_gen_3732
<nil, s>(q_gen_3740) -> q_gen_3733
<nil, z>() -> q_gen_3733
<s, nil>(q_gen_3740) -> q_gen_3734
<z, nil>() -> q_gen_3734
<s, s>(q_gen_3735) -> q_gen_3735
<z, z>() -> q_gen_3735
<cons, nil, cons>(q_gen_3735, q_gen_3734, q_gen_3733, q_gen_3732) -> q_gen_3727
<nil, cons, cons>(q_gen_3735, q_gen_3734, q_gen_3733, q_gen_3732) -> q_gen_3727
<nil, nil, nil>() -> q_gen_3727
}

Datatype: <natlist, natlist, natlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_3726, q_gen_3730, q_gen_3750},
Q_f={q_gen_3726},
Delta=
{
<z>() -> q_gen_3750
<cons, s>(q_gen_3730, q_gen_3726) -> q_gen_3726
<nil, z>() -> q_gen_3726
<s, z>(q_gen_3750) -> q_gen_3730
<z, z>() -> q_gen_3730
}

Datatype: <natlist, nat>
Convolution form: complete
}}}
  ;  leq -> 
{{{
Q={q_gen_3723, q_gen_3725},
Q_f={q_gen_3723},
Delta=
{
<s>(q_gen_3725) -> q_gen_3725
<z>() -> q_gen_3725
<s, s>(q_gen_3723) -> q_gen_3723
<z, s>(q_gen_3725) -> q_gen_3723
<z, z>() -> q_gen_3723
}

Datatype: <nat, nat>
Convolution form: complete
}}}
  ;  reverse -> 
{{{
Q={q_gen_3722, q_gen_3745, q_gen_3746, q_gen_3747, q_gen_3758},
Q_f={q_gen_3722},
Delta=
{
<z>() -> q_gen_3758
<cons, cons>(q_gen_3747, q_gen_3746, q_gen_3745, q_gen_3722) -> q_gen_3722
<nil, nil>() -> q_gen_3722
<nil, s>(q_gen_3758) -> q_gen_3745
<nil, z>() -> q_gen_3745
<s, nil>(q_gen_3758) -> q_gen_3746
<z, nil>() -> q_gen_3746
<s, s>(q_gen_3747) -> q_gen_3747
<z, z>() -> q_gen_3747
}

Datatype: <natlist, natlist>
Convolution form: complete
}}}

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 9  ;  () -> length([nil, z]) -> 6  ;  () -> leq([z, s(nn2)]) -> 7  ;  () -> leq([z, z]) -> 6  ;  () -> reverse([nil, nil]) -> 6  ;  (append([_qea, cons(h1, nil), _rea]) /\ reverse([t1, _qea])) -> reverse([cons(h1, t1), _rea]) -> 9  ;  (append([t1, l2, _lea])) -> append([cons(h1, t1), l2, cons(h1, _lea)]) -> 7  ;  (length([_afa, _bfa]) /\ length([l1, _zea]) /\ reverse([l1, _afa])) -> leq([_zea, _bfa]) -> 7  ;  (length([ll, _vea])) -> length([cons(x, ll), s(_vea)]) -> 7  ;  (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: Yes: (() -> append([nil, l2, l2]), {
l2 -> cons(z, cons(z, nil))
})

-------------------------------------------
Step 15, which took 0.006183 s (model generation: 0.005617,  model checking: 0.000566):

Model:
|_
{
append -> 
{{{
Q={q_gen_3727, q_gen_3732, q_gen_3733, q_gen_3734, q_gen_3735, q_gen_3740, q_gen_3764},
Q_f={q_gen_3727},
Delta=
{
<s>(q_gen_3740) -> q_gen_3740
<z>() -> q_gen_3740
<nil>() -> q_gen_3764
<cons, cons>(q_gen_3735, q_gen_3734, q_gen_3733, q_gen_3732) -> q_gen_3732
<nil, nil>() -> q_gen_3732
<cons, z>(q_gen_3740, q_gen_3764) -> q_gen_3733
<nil, s>(q_gen_3740) -> q_gen_3733
<nil, z>() -> q_gen_3733
<s, nil>(q_gen_3740) -> q_gen_3734
<z, cons>(q_gen_3740, q_gen_3764) -> q_gen_3734
<z, nil>() -> q_gen_3734
<s, s>(q_gen_3735) -> q_gen_3735
<z, z>() -> q_gen_3735
<cons, nil, cons>(q_gen_3735, q_gen_3734, q_gen_3733, q_gen_3732) -> q_gen_3727
<nil, cons, cons>(q_gen_3735, q_gen_3734, q_gen_3733, q_gen_3732) -> q_gen_3727
<nil, nil, nil>() -> q_gen_3727
}

Datatype: <natlist, natlist, natlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_3726, q_gen_3730, q_gen_3750},
Q_f={q_gen_3726},
Delta=
{
<z>() -> q_gen_3750
<cons, s>(q_gen_3730, q_gen_3726) -> q_gen_3726
<nil, z>() -> q_gen_3726
<s, z>(q_gen_3750) -> q_gen_3730
<z, z>() -> q_gen_3730
}

Datatype: <natlist, nat>
Convolution form: complete
}}}
  ;  leq -> 
{{{
Q={q_gen_3723, q_gen_3725},
Q_f={q_gen_3723},
Delta=
{
<s>(q_gen_3725) -> q_gen_3725
<z>() -> q_gen_3725
<s, s>(q_gen_3723) -> q_gen_3723
<z, s>(q_gen_3725) -> q_gen_3723
<z, z>() -> q_gen_3723
}

Datatype: <nat, nat>
Convolution form: complete
}}}
  ;  reverse -> 
{{{
Q={q_gen_3722, q_gen_3745, q_gen_3746, q_gen_3747, q_gen_3758},
Q_f={q_gen_3722},
Delta=
{
<z>() -> q_gen_3758
<cons, cons>(q_gen_3747, q_gen_3746, q_gen_3745, q_gen_3722) -> q_gen_3722
<nil, nil>() -> q_gen_3722
<nil, s>(q_gen_3758) -> q_gen_3745
<nil, z>() -> q_gen_3745
<s, nil>(q_gen_3758) -> q_gen_3746
<z, nil>() -> q_gen_3746
<s, s>(q_gen_3747) -> q_gen_3747
<z, z>() -> q_gen_3747
}

Datatype: <natlist, natlist>
Convolution form: complete
}}}

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 9  ;  () -> length([nil, z]) -> 7  ;  () -> leq([z, s(nn2)]) -> 7  ;  () -> leq([z, z]) -> 7  ;  () -> reverse([nil, nil]) -> 7  ;  (append([_qea, cons(h1, nil), _rea]) /\ reverse([t1, _qea])) -> reverse([cons(h1, t1), _rea]) -> 9  ;  (append([t1, l2, _lea])) -> append([cons(h1, t1), l2, cons(h1, _lea)]) -> 7  ;  (length([_afa, _bfa]) /\ length([l1, _zea]) /\ reverse([l1, _afa])) -> leq([_zea, _bfa]) -> 7  ;  (length([ll, _vea])) -> length([cons(x, ll), s(_vea)]) -> 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: Yes: ((length([ll, _vea])) -> length([cons(x, ll), s(_vea)]), {
_vea -> z  ;  ll -> nil  ;  x -> s(s(z))
})

-------------------------------------------
Step 16, which took 0.009558 s (model generation: 0.005736,  model checking: 0.003822):

Model:
|_
{
append -> 
{{{
Q={q_gen_3727, q_gen_3732, q_gen_3733, q_gen_3734, q_gen_3735, q_gen_3740, q_gen_3764},
Q_f={q_gen_3727},
Delta=
{
<s>(q_gen_3740) -> q_gen_3740
<z>() -> q_gen_3740
<nil>() -> q_gen_3764
<cons, cons>(q_gen_3735, q_gen_3734, q_gen_3733, q_gen_3732) -> q_gen_3732
<nil, nil>() -> q_gen_3732
<cons, z>(q_gen_3740, q_gen_3764) -> q_gen_3733
<nil, s>(q_gen_3740) -> q_gen_3733
<nil, z>() -> q_gen_3733
<s, nil>(q_gen_3740) -> q_gen_3734
<z, cons>(q_gen_3740, q_gen_3764) -> q_gen_3734
<z, nil>() -> q_gen_3734
<s, s>(q_gen_3735) -> q_gen_3735
<z, z>() -> q_gen_3735
<cons, nil, cons>(q_gen_3735, q_gen_3734, q_gen_3733, q_gen_3732) -> q_gen_3727
<nil, cons, cons>(q_gen_3735, q_gen_3734, q_gen_3733, q_gen_3732) -> q_gen_3727
<nil, nil, nil>() -> q_gen_3727
}

Datatype: <natlist, natlist, natlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_3726, q_gen_3730, q_gen_3750},
Q_f={q_gen_3726},
Delta=
{
<s>(q_gen_3750) -> q_gen_3750
<z>() -> q_gen_3750
<cons, s>(q_gen_3730, q_gen_3726) -> q_gen_3726
<nil, z>() -> q_gen_3726
<s, z>(q_gen_3750) -> q_gen_3730
<z, z>() -> q_gen_3730
}

Datatype: <natlist, nat>
Convolution form: complete
}}}
  ;  leq -> 
{{{
Q={q_gen_3723, q_gen_3725},
Q_f={q_gen_3723},
Delta=
{
<s>(q_gen_3725) -> q_gen_3725
<z>() -> q_gen_3725
<s, s>(q_gen_3723) -> q_gen_3723
<z, s>(q_gen_3725) -> q_gen_3723
<z, z>() -> q_gen_3723
}

Datatype: <nat, nat>
Convolution form: complete
}}}
  ;  reverse -> 
{{{
Q={q_gen_3722, q_gen_3745, q_gen_3746, q_gen_3747, q_gen_3758},
Q_f={q_gen_3722},
Delta=
{
<z>() -> q_gen_3758
<cons, cons>(q_gen_3747, q_gen_3746, q_gen_3745, q_gen_3722) -> q_gen_3722
<nil, nil>() -> q_gen_3722
<nil, s>(q_gen_3758) -> q_gen_3745
<nil, z>() -> q_gen_3745
<s, nil>(q_gen_3758) -> q_gen_3746
<z, nil>() -> q_gen_3746
<s, s>(q_gen_3747) -> q_gen_3747
<z, z>() -> q_gen_3747
}

Datatype: <natlist, natlist>
Convolution form: complete
}}}

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 9  ;  () -> length([nil, z]) -> 7  ;  () -> leq([z, s(nn2)]) -> 7  ;  () -> leq([z, z]) -> 7  ;  () -> reverse([nil, nil]) -> 7  ;  (append([_qea, cons(h1, nil), _rea]) /\ reverse([t1, _qea])) -> reverse([cons(h1, t1), _rea]) -> 9  ;  (append([t1, l2, _lea])) -> append([cons(h1, t1), l2, cons(h1, _lea)]) -> 10  ;  (length([_afa, _bfa]) /\ length([l1, _zea]) /\ reverse([l1, _afa])) -> leq([_zea, _bfa]) -> 8  ;  (length([ll, _vea])) -> length([cons(x, ll), s(_vea)]) -> 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: Yes: ((append([t1, l2, _lea])) -> append([cons(h1, t1), l2, cons(h1, _lea)]), {
_lea -> cons(z, nil)  ;  h1 -> s(z)  ;  l2 -> nil  ;  t1 -> cons(z, nil)
})

-------------------------------------------
Step 17, which took 0.007395 s (model generation: 0.006078,  model checking: 0.001317):

Model:
|_
{
append -> 
{{{
Q={q_gen_3727, q_gen_3732, q_gen_3733, q_gen_3734, q_gen_3735, q_gen_3740, q_gen_3764},
Q_f={q_gen_3727},
Delta=
{
<s>(q_gen_3740) -> q_gen_3740
<z>() -> q_gen_3740
<nil>() -> q_gen_3764
<cons, cons>(q_gen_3735, q_gen_3734, q_gen_3733, q_gen_3732) -> q_gen_3732
<nil, nil>() -> q_gen_3732
<cons, s>(q_gen_3735, q_gen_3733) -> q_gen_3733
<cons, z>(q_gen_3740, q_gen_3764) -> q_gen_3733
<nil, s>(q_gen_3740) -> q_gen_3733
<nil, z>() -> q_gen_3733
<s, cons>(q_gen_3735, q_gen_3734) -> q_gen_3734
<s, nil>(q_gen_3740) -> q_gen_3734
<z, cons>(q_gen_3740, q_gen_3764) -> q_gen_3734
<z, nil>() -> q_gen_3734
<s, s>(q_gen_3735) -> q_gen_3735
<z, z>() -> q_gen_3735
<cons, nil, cons>(q_gen_3735, q_gen_3734, q_gen_3733, q_gen_3732) -> q_gen_3727
<nil, cons, cons>(q_gen_3735, q_gen_3734, q_gen_3733, q_gen_3732) -> q_gen_3727
<nil, nil, nil>() -> q_gen_3727
}

Datatype: <natlist, natlist, natlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_3726, q_gen_3730, q_gen_3750},
Q_f={q_gen_3726},
Delta=
{
<s>(q_gen_3750) -> q_gen_3750
<z>() -> q_gen_3750
<cons, s>(q_gen_3730, q_gen_3726) -> q_gen_3726
<nil, z>() -> q_gen_3726
<s, z>(q_gen_3750) -> q_gen_3730
<z, z>() -> q_gen_3730
}

Datatype: <natlist, nat>
Convolution form: complete
}}}
  ;  leq -> 
{{{
Q={q_gen_3723, q_gen_3725},
Q_f={q_gen_3723},
Delta=
{
<s>(q_gen_3725) -> q_gen_3725
<z>() -> q_gen_3725
<s, s>(q_gen_3723) -> q_gen_3723
<z, s>(q_gen_3725) -> q_gen_3723
<z, z>() -> q_gen_3723
}

Datatype: <nat, nat>
Convolution form: complete
}}}
  ;  reverse -> 
{{{
Q={q_gen_3722, q_gen_3745, q_gen_3746, q_gen_3747, q_gen_3758},
Q_f={q_gen_3722},
Delta=
{
<z>() -> q_gen_3758
<cons, cons>(q_gen_3747, q_gen_3746, q_gen_3745, q_gen_3722) -> q_gen_3722
<nil, nil>() -> q_gen_3722
<nil, s>(q_gen_3758) -> q_gen_3745
<nil, z>() -> q_gen_3745
<s, nil>(q_gen_3758) -> q_gen_3746
<z, nil>() -> q_gen_3746
<s, s>(q_gen_3747) -> q_gen_3747
<z, z>() -> q_gen_3747
}

Datatype: <natlist, natlist>
Convolution form: complete
}}}

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 9  ;  () -> length([nil, z]) -> 8  ;  () -> leq([z, s(nn2)]) -> 8  ;  () -> leq([z, z]) -> 8  ;  () -> reverse([nil, nil]) -> 8  ;  (append([_qea, cons(h1, nil), _rea]) /\ reverse([t1, _qea])) -> reverse([cons(h1, t1), _rea]) -> 12  ;  (append([t1, l2, _lea])) -> append([cons(h1, t1), l2, cons(h1, _lea)]) -> 10  ;  (length([_afa, _bfa]) /\ length([l1, _zea]) /\ reverse([l1, _afa])) -> leq([_zea, _bfa]) -> 9  ;  (length([ll, _vea])) -> length([cons(x, ll), s(_vea)]) -> 10  ;  (leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 9  ;  (leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 9  ;  (leq([s(nn1), z])) -> BOT -> 9
}
Sat witness: Yes: ((append([_qea, cons(h1, nil), _rea]) /\ reverse([t1, _qea])) -> reverse([cons(h1, t1), _rea]), {
_qea -> nil  ;  _rea -> cons(s(s(z)), nil)  ;  h1 -> s(s(z))  ;  t1 -> nil
})

-------------------------------------------
Step 18, which took 0.052308 s (model generation: 0.008257,  model checking: 0.044051):

Model:
|_
{
append -> 
{{{
Q={q_gen_3727, q_gen_3732, q_gen_3733, q_gen_3734, q_gen_3735, q_gen_3740, q_gen_3764},
Q_f={q_gen_3727},
Delta=
{
<s>(q_gen_3740) -> q_gen_3740
<z>() -> q_gen_3740
<nil>() -> q_gen_3764
<cons, cons>(q_gen_3735, q_gen_3734, q_gen_3733, q_gen_3732) -> q_gen_3732
<nil, nil>() -> q_gen_3732
<cons, s>(q_gen_3735, q_gen_3733) -> q_gen_3733
<cons, z>(q_gen_3740, q_gen_3764) -> q_gen_3733
<nil, s>(q_gen_3740) -> q_gen_3733
<nil, z>() -> q_gen_3733
<s, cons>(q_gen_3735, q_gen_3734) -> q_gen_3734
<s, nil>(q_gen_3740) -> q_gen_3734
<z, cons>(q_gen_3740, q_gen_3764) -> q_gen_3734
<z, nil>() -> q_gen_3734
<s, s>(q_gen_3735) -> q_gen_3735
<z, z>() -> q_gen_3735
<cons, nil, cons>(q_gen_3735, q_gen_3734, q_gen_3733, q_gen_3732) -> q_gen_3727
<nil, cons, cons>(q_gen_3735, q_gen_3734, q_gen_3733, q_gen_3732) -> q_gen_3727
<nil, nil, nil>() -> q_gen_3727
}

Datatype: <natlist, natlist, natlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_3726, q_gen_3730, q_gen_3750},
Q_f={q_gen_3726},
Delta=
{
<s>(q_gen_3750) -> q_gen_3750
<z>() -> q_gen_3750
<cons, s>(q_gen_3730, q_gen_3726) -> q_gen_3726
<nil, z>() -> q_gen_3726
<s, z>(q_gen_3750) -> q_gen_3730
<z, z>() -> q_gen_3730
}

Datatype: <natlist, nat>
Convolution form: complete
}}}
  ;  leq -> 
{{{
Q={q_gen_3723, q_gen_3725},
Q_f={q_gen_3723},
Delta=
{
<s>(q_gen_3725) -> q_gen_3725
<z>() -> q_gen_3725
<s, s>(q_gen_3723) -> q_gen_3723
<z, s>(q_gen_3725) -> q_gen_3723
<z, z>() -> q_gen_3723
}

Datatype: <nat, nat>
Convolution form: complete
}}}
  ;  reverse -> 
{{{
Q={q_gen_3722, q_gen_3745, q_gen_3746, q_gen_3747, q_gen_3758},
Q_f={q_gen_3722},
Delta=
{
<s>(q_gen_3758) -> q_gen_3758
<z>() -> q_gen_3758
<cons, cons>(q_gen_3747, q_gen_3746, q_gen_3745, q_gen_3722) -> q_gen_3722
<nil, nil>() -> q_gen_3722
<nil, s>(q_gen_3758) -> q_gen_3745
<nil, z>() -> q_gen_3745
<s, nil>(q_gen_3758) -> q_gen_3746
<z, nil>() -> q_gen_3746
<s, s>(q_gen_3747) -> q_gen_3747
<z, z>() -> q_gen_3747
}

Datatype: <natlist, natlist>
Convolution form: complete
}}}

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 12  ;  () -> length([nil, z]) -> 9  ;  () -> leq([z, s(nn2)]) -> 9  ;  () -> leq([z, z]) -> 9  ;  () -> reverse([nil, nil]) -> 9  ;  (append([_qea, cons(h1, nil), _rea]) /\ reverse([t1, _qea])) -> reverse([cons(h1, t1), _rea]) -> 12  ;  (append([t1, l2, _lea])) -> append([cons(h1, t1), l2, cons(h1, _lea)]) -> 10  ;  (length([_afa, _bfa]) /\ length([l1, _zea]) /\ reverse([l1, _afa])) -> leq([_zea, _bfa]) -> 10  ;  (length([ll, _vea])) -> length([cons(x, ll), s(_vea)]) -> 10  ;  (leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 10  ;  (leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 10  ;  (leq([s(nn1), z])) -> BOT -> 10
}
Sat witness: Yes: (() -> append([nil, l2, l2]), {
l2 -> cons(z, cons(z, cons(z, nil)))
})

-------------------------------------------
Step 19, which took 0.008679 s (model generation: 0.008199,  model checking: 0.000480):

Model:
|_
{
append -> 
{{{
Q={q_gen_3727, q_gen_3732, q_gen_3733, q_gen_3734, q_gen_3735, q_gen_3740, q_gen_3764},
Q_f={q_gen_3727},
Delta=
{
<s>(q_gen_3740) -> q_gen_3740
<z>() -> q_gen_3740
<cons>(q_gen_3740, q_gen_3764) -> q_gen_3764
<nil>() -> q_gen_3764
<cons, cons>(q_gen_3735, q_gen_3734, q_gen_3733, q_gen_3732) -> q_gen_3732
<nil, nil>() -> q_gen_3732
<cons, s>(q_gen_3735, q_gen_3733) -> q_gen_3733
<cons, z>(q_gen_3740, q_gen_3764) -> q_gen_3733
<nil, s>(q_gen_3740) -> q_gen_3733
<nil, z>() -> q_gen_3733
<s, cons>(q_gen_3735, q_gen_3734) -> q_gen_3734
<s, nil>(q_gen_3740) -> q_gen_3734
<z, cons>(q_gen_3740, q_gen_3764) -> q_gen_3734
<z, nil>() -> q_gen_3734
<s, s>(q_gen_3735) -> q_gen_3735
<z, z>() -> q_gen_3735
<cons, nil, cons>(q_gen_3735, q_gen_3734, q_gen_3733, q_gen_3732) -> q_gen_3727
<nil, cons, cons>(q_gen_3735, q_gen_3734, q_gen_3733, q_gen_3732) -> q_gen_3727
<nil, nil, nil>() -> q_gen_3727
}

Datatype: <natlist, natlist, natlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_3726, q_gen_3730, q_gen_3750},
Q_f={q_gen_3726},
Delta=
{
<s>(q_gen_3750) -> q_gen_3750
<z>() -> q_gen_3750
<cons, s>(q_gen_3730, q_gen_3726) -> q_gen_3726
<nil, z>() -> q_gen_3726
<s, z>(q_gen_3750) -> q_gen_3730
<z, z>() -> q_gen_3730
}

Datatype: <natlist, nat>
Convolution form: complete
}}}
  ;  leq -> 
{{{
Q={q_gen_3723, q_gen_3725},
Q_f={q_gen_3723},
Delta=
{
<s>(q_gen_3725) -> q_gen_3725
<z>() -> q_gen_3725
<s, s>(q_gen_3723) -> q_gen_3723
<z, s>(q_gen_3725) -> q_gen_3723
<z, z>() -> q_gen_3723
}

Datatype: <nat, nat>
Convolution form: complete
}}}
  ;  reverse -> 
{{{
Q={q_gen_3722, q_gen_3745, q_gen_3746, q_gen_3747, q_gen_3758},
Q_f={q_gen_3722},
Delta=
{
<s>(q_gen_3758) -> q_gen_3758
<z>() -> q_gen_3758
<cons, cons>(q_gen_3747, q_gen_3746, q_gen_3745, q_gen_3722) -> q_gen_3722
<nil, nil>() -> q_gen_3722
<nil, s>(q_gen_3758) -> q_gen_3745
<nil, z>() -> q_gen_3745
<s, nil>(q_gen_3758) -> q_gen_3746
<z, nil>() -> q_gen_3746
<s, s>(q_gen_3747) -> q_gen_3747
<z, z>() -> q_gen_3747
}

Datatype: <natlist, natlist>
Convolution form: complete
}}}

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 12  ;  () -> length([nil, z]) -> 10  ;  () -> leq([z, s(nn2)]) -> 10  ;  () -> leq([z, z]) -> 10  ;  () -> reverse([nil, nil]) -> 10  ;  (append([_qea, cons(h1, nil), _rea]) /\ reverse([t1, _qea])) -> reverse([cons(h1, t1), _rea]) -> 12  ;  (append([t1, l2, _lea])) -> append([cons(h1, t1), l2, cons(h1, _lea)]) -> 10  ;  (length([_afa, _bfa]) /\ length([l1, _zea]) /\ reverse([l1, _afa])) -> leq([_zea, _bfa]) -> 10  ;  (length([ll, _vea])) -> length([cons(x, ll), s(_vea)]) -> 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: Yes: ((length([ll, _vea])) -> length([cons(x, ll), s(_vea)]), {
_vea -> s(z)  ;  ll -> cons(z, nil)  ;  x -> s(z)
})

-------------------------------------------
Step 20, which took 0.012152 s (model generation: 0.008029,  model checking: 0.004123):

Model:
|_
{
append -> 
{{{
Q={q_gen_3727, q_gen_3732, q_gen_3733, q_gen_3734, q_gen_3735, q_gen_3740, q_gen_3764},
Q_f={q_gen_3727},
Delta=
{
<s>(q_gen_3740) -> q_gen_3740
<z>() -> q_gen_3740
<cons>(q_gen_3740, q_gen_3764) -> q_gen_3764
<nil>() -> q_gen_3764
<cons, cons>(q_gen_3735, q_gen_3734, q_gen_3733, q_gen_3732) -> q_gen_3732
<nil, nil>() -> q_gen_3732
<cons, s>(q_gen_3735, q_gen_3733) -> q_gen_3733
<cons, z>(q_gen_3740, q_gen_3764) -> q_gen_3733
<nil, s>(q_gen_3740) -> q_gen_3733
<nil, z>() -> q_gen_3733
<s, cons>(q_gen_3735, q_gen_3734) -> q_gen_3734
<s, nil>(q_gen_3740) -> q_gen_3734
<z, cons>(q_gen_3740, q_gen_3764) -> q_gen_3734
<z, nil>() -> q_gen_3734
<s, s>(q_gen_3735) -> q_gen_3735
<z, z>() -> q_gen_3735
<cons, nil, cons>(q_gen_3735, q_gen_3734, q_gen_3733, q_gen_3732) -> q_gen_3727
<nil, cons, cons>(q_gen_3735, q_gen_3734, q_gen_3733, q_gen_3732) -> q_gen_3727
<nil, nil, nil>() -> q_gen_3727
}

Datatype: <natlist, natlist, natlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_3726, q_gen_3730, q_gen_3750},
Q_f={q_gen_3726},
Delta=
{
<s>(q_gen_3750) -> q_gen_3750
<z>() -> q_gen_3750
<cons, s>(q_gen_3730, q_gen_3726) -> q_gen_3726
<nil, z>() -> q_gen_3726
<s, s>(q_gen_3730) -> q_gen_3730
<s, z>(q_gen_3750) -> q_gen_3730
<z, z>() -> q_gen_3730
}

Datatype: <natlist, nat>
Convolution form: complete
}}}
  ;  leq -> 
{{{
Q={q_gen_3723, q_gen_3725},
Q_f={q_gen_3723},
Delta=
{
<s>(q_gen_3725) -> q_gen_3725
<z>() -> q_gen_3725
<s, s>(q_gen_3723) -> q_gen_3723
<z, s>(q_gen_3725) -> q_gen_3723
<z, z>() -> q_gen_3723
}

Datatype: <nat, nat>
Convolution form: complete
}}}
  ;  reverse -> 
{{{
Q={q_gen_3722, q_gen_3745, q_gen_3746, q_gen_3747, q_gen_3758},
Q_f={q_gen_3722},
Delta=
{
<s>(q_gen_3758) -> q_gen_3758
<z>() -> q_gen_3758
<cons, cons>(q_gen_3747, q_gen_3746, q_gen_3745, q_gen_3722) -> q_gen_3722
<nil, nil>() -> q_gen_3722
<nil, s>(q_gen_3758) -> q_gen_3745
<nil, z>() -> q_gen_3745
<s, nil>(q_gen_3758) -> q_gen_3746
<z, nil>() -> q_gen_3746
<s, s>(q_gen_3747) -> q_gen_3747
<z, z>() -> q_gen_3747
}

Datatype: <natlist, natlist>
Convolution form: complete
}}}

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 12  ;  () -> length([nil, z]) -> 10  ;  () -> leq([z, s(nn2)]) -> 10  ;  () -> leq([z, z]) -> 10  ;  () -> reverse([nil, nil]) -> 10  ;  (append([_qea, cons(h1, nil), _rea]) /\ reverse([t1, _qea])) -> reverse([cons(h1, t1), _rea]) -> 12  ;  (append([t1, l2, _lea])) -> append([cons(h1, t1), l2, cons(h1, _lea)]) -> 13  ;  (length([_afa, _bfa]) /\ length([l1, _zea]) /\ reverse([l1, _afa])) -> leq([_zea, _bfa]) -> 11  ;  (length([ll, _vea])) -> length([cons(x, ll), s(_vea)]) -> 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: Yes: ((append([t1, l2, _lea])) -> append([cons(h1, t1), l2, cons(h1, _lea)]), {
_lea -> cons(z, nil)  ;  h1 -> s(s(z))  ;  l2 -> nil  ;  t1 -> cons(z, nil)
})

-------------------------------------------
Step 21, which took 0.009649 s (model generation: 0.008676,  model checking: 0.000973):

Model:
|_
{
append -> 
{{{
Q={q_gen_3727, q_gen_3732, q_gen_3733, q_gen_3734, q_gen_3735, q_gen_3740, q_gen_3764},
Q_f={q_gen_3727},
Delta=
{
<s>(q_gen_3740) -> q_gen_3740
<z>() -> q_gen_3740
<cons>(q_gen_3740, q_gen_3764) -> q_gen_3764
<nil>() -> q_gen_3764
<cons, cons>(q_gen_3735, q_gen_3734, q_gen_3733, q_gen_3732) -> q_gen_3732
<nil, nil>() -> q_gen_3732
<cons, s>(q_gen_3735, q_gen_3733) -> q_gen_3733
<cons, z>(q_gen_3740, q_gen_3764) -> q_gen_3733
<nil, s>(q_gen_3740) -> q_gen_3733
<nil, z>() -> q_gen_3733
<s, cons>(q_gen_3735, q_gen_3734) -> q_gen_3734
<s, nil>(q_gen_3740) -> q_gen_3734
<z, cons>(q_gen_3740, q_gen_3764) -> q_gen_3734
<z, nil>() -> q_gen_3734
<s, s>(q_gen_3735) -> q_gen_3735
<s, z>(q_gen_3740) -> q_gen_3735
<z, s>(q_gen_3740) -> q_gen_3735
<z, z>() -> q_gen_3735
<cons, nil, cons>(q_gen_3735, q_gen_3734, q_gen_3733, q_gen_3732) -> q_gen_3727
<nil, cons, cons>(q_gen_3735, q_gen_3734, q_gen_3733, q_gen_3732) -> q_gen_3727
<nil, nil, nil>() -> q_gen_3727
}

Datatype: <natlist, natlist, natlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_3726, q_gen_3730, q_gen_3750},
Q_f={q_gen_3726},
Delta=
{
<s>(q_gen_3750) -> q_gen_3750
<z>() -> q_gen_3750
<cons, s>(q_gen_3730, q_gen_3726) -> q_gen_3726
<nil, z>() -> q_gen_3726
<s, s>(q_gen_3730) -> q_gen_3730
<s, z>(q_gen_3750) -> q_gen_3730
<z, z>() -> q_gen_3730
}

Datatype: <natlist, nat>
Convolution form: complete
}}}
  ;  leq -> 
{{{
Q={q_gen_3723, q_gen_3725},
Q_f={q_gen_3723},
Delta=
{
<s>(q_gen_3725) -> q_gen_3725
<z>() -> q_gen_3725
<s, s>(q_gen_3723) -> q_gen_3723
<z, s>(q_gen_3725) -> q_gen_3723
<z, z>() -> q_gen_3723
}

Datatype: <nat, nat>
Convolution form: complete
}}}
  ;  reverse -> 
{{{
Q={q_gen_3722, q_gen_3745, q_gen_3746, q_gen_3747, q_gen_3758},
Q_f={q_gen_3722},
Delta=
{
<s>(q_gen_3758) -> q_gen_3758
<z>() -> q_gen_3758
<cons, cons>(q_gen_3747, q_gen_3746, q_gen_3745, q_gen_3722) -> q_gen_3722
<nil, nil>() -> q_gen_3722
<nil, s>(q_gen_3758) -> q_gen_3745
<nil, z>() -> q_gen_3745
<s, nil>(q_gen_3758) -> q_gen_3746
<z, nil>() -> q_gen_3746
<s, s>(q_gen_3747) -> q_gen_3747
<z, z>() -> q_gen_3747
}

Datatype: <natlist, natlist>
Convolution form: complete
}}}

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 12  ;  () -> length([nil, z]) -> 11  ;  () -> leq([z, s(nn2)]) -> 11  ;  () -> leq([z, z]) -> 11  ;  () -> reverse([nil, nil]) -> 11  ;  (append([_qea, cons(h1, nil), _rea]) /\ reverse([t1, _qea])) -> reverse([cons(h1, t1), _rea]) -> 15  ;  (append([t1, l2, _lea])) -> append([cons(h1, t1), l2, cons(h1, _lea)]) -> 13  ;  (length([_afa, _bfa]) /\ length([l1, _zea]) /\ reverse([l1, _afa])) -> leq([_zea, _bfa]) -> 12  ;  (length([ll, _vea])) -> length([cons(x, ll), s(_vea)]) -> 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: Yes: ((append([_qea, cons(h1, nil), _rea]) /\ reverse([t1, _qea])) -> reverse([cons(h1, t1), _rea]), {
_qea -> nil  ;  _rea -> cons(s(z), nil)  ;  h1 -> z  ;  t1 -> nil
})

-------------------------------------------
Step 22, which took 0.018219 s (model generation: 0.015678,  model checking: 0.002541):

Model:
|_
{
append -> 
{{{
Q={q_gen_3727, q_gen_3732, q_gen_3733, q_gen_3734, q_gen_3735, q_gen_3740, q_gen_3764},
Q_f={q_gen_3727},
Delta=
{
<s>(q_gen_3740) -> q_gen_3740
<z>() -> q_gen_3740
<cons>(q_gen_3740, q_gen_3764) -> q_gen_3764
<nil>() -> q_gen_3764
<cons, cons>(q_gen_3735, q_gen_3734, q_gen_3733, q_gen_3732) -> q_gen_3732
<nil, nil>() -> q_gen_3732
<cons, s>(q_gen_3735, q_gen_3733) -> q_gen_3733
<cons, z>(q_gen_3740, q_gen_3764) -> q_gen_3733
<nil, s>(q_gen_3740) -> q_gen_3733
<nil, z>() -> q_gen_3733
<s, cons>(q_gen_3735, q_gen_3734) -> q_gen_3734
<s, nil>(q_gen_3740) -> q_gen_3734
<z, cons>(q_gen_3740, q_gen_3764) -> q_gen_3734
<z, nil>() -> q_gen_3734
<s, s>(q_gen_3735) -> q_gen_3735
<s, z>(q_gen_3740) -> q_gen_3735
<z, s>(q_gen_3740) -> q_gen_3735
<z, z>() -> q_gen_3735
<cons, nil, cons>(q_gen_3735, q_gen_3734, q_gen_3733, q_gen_3732) -> q_gen_3727
<nil, cons, cons>(q_gen_3735, q_gen_3734, q_gen_3733, q_gen_3732) -> q_gen_3727
<nil, nil, nil>() -> q_gen_3727
}

Datatype: <natlist, natlist, natlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_3726, q_gen_3730, q_gen_3750},
Q_f={q_gen_3726},
Delta=
{
<s>(q_gen_3750) -> q_gen_3750
<z>() -> q_gen_3750
<cons, s>(q_gen_3730, q_gen_3726) -> q_gen_3726
<nil, z>() -> q_gen_3726
<s, s>(q_gen_3730) -> q_gen_3730
<s, z>(q_gen_3750) -> q_gen_3730
<z, z>() -> q_gen_3730
}

Datatype: <natlist, nat>
Convolution form: complete
}}}
  ;  leq -> 
{{{
Q={q_gen_3723, q_gen_3725},
Q_f={q_gen_3723},
Delta=
{
<s>(q_gen_3725) -> q_gen_3725
<z>() -> q_gen_3725
<s, s>(q_gen_3723) -> q_gen_3723
<z, s>(q_gen_3725) -> q_gen_3723
<z, z>() -> q_gen_3723
}

Datatype: <nat, nat>
Convolution form: complete
}}}
  ;  reverse -> 
{{{
Q={q_gen_3722, q_gen_3745, q_gen_3746, q_gen_3747, q_gen_3758},
Q_f={q_gen_3722},
Delta=
{
<s>(q_gen_3758) -> q_gen_3758
<z>() -> q_gen_3758
<cons, cons>(q_gen_3747, q_gen_3746, q_gen_3745, q_gen_3722) -> q_gen_3722
<nil, nil>() -> q_gen_3722
<nil, s>(q_gen_3758) -> q_gen_3745
<nil, z>() -> q_gen_3745
<s, nil>(q_gen_3758) -> q_gen_3746
<z, nil>() -> q_gen_3746
<s, s>(q_gen_3747) -> q_gen_3747
<z, s>(q_gen_3758) -> q_gen_3747
<z, z>() -> q_gen_3747
}

Datatype: <natlist, natlist>
Convolution form: complete
}}}

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 13  ;  () -> length([nil, z]) -> 12  ;  () -> leq([z, s(nn2)]) -> 12  ;  () -> leq([z, z]) -> 12  ;  () -> reverse([nil, nil]) -> 12  ;  (append([_qea, cons(h1, nil), _rea]) /\ reverse([t1, _qea])) -> reverse([cons(h1, t1), _rea]) -> 15  ;  (append([t1, l2, _lea])) -> append([cons(h1, t1), l2, cons(h1, _lea)]) -> 13  ;  (length([_afa, _bfa]) /\ length([l1, _zea]) /\ reverse([l1, _afa])) -> leq([_zea, _bfa]) -> 13  ;  (length([ll, _vea])) -> length([cons(x, ll), s(_vea)]) -> 16  ;  (leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 13  ;  (leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 13  ;  (leq([s(nn1), z])) -> BOT -> 13
}
Sat witness: Yes: ((length([ll, _vea])) -> length([cons(x, ll), s(_vea)]), {
_vea -> s(z)  ;  ll -> cons(z, nil)  ;  x -> z
})

-------------------------------------------
Step 23, which took 0.020609 s (model generation: 0.015280,  model checking: 0.005329):

Model:
|_
{
append -> 
{{{
Q={q_gen_3727, q_gen_3732, q_gen_3733, q_gen_3734, q_gen_3735, q_gen_3740, q_gen_3764},
Q_f={q_gen_3727},
Delta=
{
<s>(q_gen_3740) -> q_gen_3740
<z>() -> q_gen_3740
<cons>(q_gen_3740, q_gen_3764) -> q_gen_3764
<nil>() -> q_gen_3764
<cons, cons>(q_gen_3735, q_gen_3734, q_gen_3733, q_gen_3732) -> q_gen_3732
<nil, nil>() -> q_gen_3732
<cons, s>(q_gen_3735, q_gen_3733) -> q_gen_3733
<cons, z>(q_gen_3740, q_gen_3764) -> q_gen_3733
<nil, s>(q_gen_3740) -> q_gen_3733
<nil, z>() -> q_gen_3733
<s, cons>(q_gen_3735, q_gen_3734) -> q_gen_3734
<s, nil>(q_gen_3740) -> q_gen_3734
<z, cons>(q_gen_3740, q_gen_3764) -> q_gen_3734
<z, nil>() -> q_gen_3734
<s, s>(q_gen_3735) -> q_gen_3735
<s, z>(q_gen_3740) -> q_gen_3735
<z, s>(q_gen_3740) -> q_gen_3735
<z, z>() -> q_gen_3735
<cons, nil, cons>(q_gen_3735, q_gen_3734, q_gen_3733, q_gen_3732) -> q_gen_3727
<nil, cons, cons>(q_gen_3735, q_gen_3734, q_gen_3733, q_gen_3732) -> q_gen_3727
<nil, nil, nil>() -> q_gen_3727
}

Datatype: <natlist, natlist, natlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_3726, q_gen_3730, q_gen_3750},
Q_f={q_gen_3726},
Delta=
{
<s>(q_gen_3750) -> q_gen_3750
<z>() -> q_gen_3750
<cons, s>(q_gen_3730, q_gen_3726) -> q_gen_3726
<nil, z>() -> q_gen_3726
<s, s>(q_gen_3730) -> q_gen_3730
<s, z>(q_gen_3750) -> q_gen_3730
<z, s>(q_gen_3750) -> q_gen_3730
<z, z>() -> q_gen_3730
}

Datatype: <natlist, nat>
Convolution form: complete
}}}
  ;  leq -> 
{{{
Q={q_gen_3723, q_gen_3725},
Q_f={q_gen_3723},
Delta=
{
<s>(q_gen_3725) -> q_gen_3725
<z>() -> q_gen_3725
<s, s>(q_gen_3723) -> q_gen_3723
<z, s>(q_gen_3725) -> q_gen_3723
<z, z>() -> q_gen_3723
}

Datatype: <nat, nat>
Convolution form: complete
}}}
  ;  reverse -> 
{{{
Q={q_gen_3722, q_gen_3745, q_gen_3746, q_gen_3747, q_gen_3758},
Q_f={q_gen_3722},
Delta=
{
<s>(q_gen_3758) -> q_gen_3758
<z>() -> q_gen_3758
<cons, cons>(q_gen_3747, q_gen_3746, q_gen_3745, q_gen_3722) -> q_gen_3722
<nil, nil>() -> q_gen_3722
<nil, s>(q_gen_3758) -> q_gen_3745
<nil, z>() -> q_gen_3745
<s, nil>(q_gen_3758) -> q_gen_3746
<z, nil>() -> q_gen_3746
<s, s>(q_gen_3747) -> q_gen_3747
<z, s>(q_gen_3758) -> q_gen_3747
<z, z>() -> q_gen_3747
}

Datatype: <natlist, natlist>
Convolution form: complete
}}}

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

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([_qea, cons(h1, nil), _rea]) /\ reverse([t1, _qea])) -> reverse([cons(h1, t1), _rea]) -> 15  ;  (append([t1, l2, _lea])) -> append([cons(h1, t1), l2, cons(h1, _lea)]) -> 16  ;  (length([_afa, _bfa]) /\ length([l1, _zea]) /\ reverse([l1, _afa])) -> leq([_zea, _bfa]) -> 14  ;  (length([ll, _vea])) -> length([cons(x, ll), s(_vea)]) -> 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: Yes: ((append([t1, l2, _lea])) -> append([cons(h1, t1), l2, cons(h1, _lea)]), {
_lea -> cons(z, nil)  ;  h1 -> z  ;  l2 -> cons(z, nil)  ;  t1 -> nil
})

-------------------------------------------
Step 24, which took 0.022385 s (model generation: 0.015992,  model checking: 0.006393):

Model:
|_
{
append -> 
{{{
Q={q_gen_3727, q_gen_3732, q_gen_3733, q_gen_3734, q_gen_3735, q_gen_3740, q_gen_3764, q_gen_3797, q_gen_3798, q_gen_3799, q_gen_3800, q_gen_3801, q_gen_3802, q_gen_3803},
Q_f={q_gen_3727},
Delta=
{
<s>(q_gen_3740) -> q_gen_3740
<z>() -> q_gen_3740
<cons>(q_gen_3740, q_gen_3764) -> q_gen_3764
<nil>() -> q_gen_3764
<cons, cons>(q_gen_3735, q_gen_3734, q_gen_3733, q_gen_3732) -> q_gen_3732
<nil, nil>() -> q_gen_3732
<cons, s>(q_gen_3735, q_gen_3733) -> q_gen_3733
<cons, z>(q_gen_3740, q_gen_3764) -> q_gen_3733
<nil, s>(q_gen_3740) -> q_gen_3733
<nil, z>() -> q_gen_3733
<s, cons>(q_gen_3735, q_gen_3734) -> q_gen_3734
<s, nil>(q_gen_3740) -> q_gen_3734
<z, cons>(q_gen_3740, q_gen_3764) -> q_gen_3734
<z, nil>() -> q_gen_3734
<s, s>(q_gen_3735) -> q_gen_3735
<s, z>(q_gen_3740) -> q_gen_3735
<z, s>(q_gen_3740) -> q_gen_3735
<z, z>() -> q_gen_3735
<cons, cons, cons>(q_gen_3803, q_gen_3802, q_gen_3801, q_gen_3800, q_gen_3799, q_gen_3798, q_gen_3797, q_gen_3727) -> q_gen_3727
<cons, nil, cons>(q_gen_3735, q_gen_3734, q_gen_3733, q_gen_3732) -> q_gen_3727
<nil, cons, cons>(q_gen_3735, q_gen_3734, q_gen_3733, q_gen_3732) -> q_gen_3727
<nil, nil, cons>(q_gen_3740, q_gen_3764) -> q_gen_3727
<nil, nil, nil>() -> q_gen_3727
<nil, nil, z>() -> q_gen_3797
<nil, z, cons>(q_gen_3740, q_gen_3764) -> q_gen_3798
<nil, z, z>() -> q_gen_3799
<z, nil, cons>(q_gen_3740, q_gen_3764) -> q_gen_3800
<z, nil, z>() -> q_gen_3801
<z, z, cons>(q_gen_3740, q_gen_3764) -> q_gen_3802
<z, z, z>() -> q_gen_3803
}

Datatype: <natlist, natlist, natlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_3726, q_gen_3730, q_gen_3750},
Q_f={q_gen_3726},
Delta=
{
<s>(q_gen_3750) -> q_gen_3750
<z>() -> q_gen_3750
<cons, s>(q_gen_3730, q_gen_3726) -> q_gen_3726
<nil, z>() -> q_gen_3726
<s, s>(q_gen_3730) -> q_gen_3730
<s, z>(q_gen_3750) -> q_gen_3730
<z, s>(q_gen_3750) -> q_gen_3730
<z, z>() -> q_gen_3730
}

Datatype: <natlist, nat>
Convolution form: complete
}}}
  ;  leq -> 
{{{
Q={q_gen_3723, q_gen_3725},
Q_f={q_gen_3723},
Delta=
{
<s>(q_gen_3725) -> q_gen_3725
<z>() -> q_gen_3725
<s, s>(q_gen_3723) -> q_gen_3723
<z, s>(q_gen_3725) -> q_gen_3723
<z, z>() -> q_gen_3723
}

Datatype: <nat, nat>
Convolution form: complete
}}}
  ;  reverse -> 
{{{
Q={q_gen_3722, q_gen_3745, q_gen_3746, q_gen_3747, q_gen_3758},
Q_f={q_gen_3722},
Delta=
{
<s>(q_gen_3758) -> q_gen_3758
<z>() -> q_gen_3758
<cons, cons>(q_gen_3747, q_gen_3746, q_gen_3745, q_gen_3722) -> q_gen_3722
<nil, nil>() -> q_gen_3722
<nil, s>(q_gen_3758) -> q_gen_3745
<nil, z>() -> q_gen_3745
<s, nil>(q_gen_3758) -> q_gen_3746
<z, nil>() -> q_gen_3746
<s, s>(q_gen_3747) -> q_gen_3747
<z, s>(q_gen_3758) -> q_gen_3747
<z, z>() -> q_gen_3747
}

Datatype: <natlist, natlist>
Convolution form: complete
}}}

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

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([_qea, cons(h1, nil), _rea]) /\ reverse([t1, _qea])) -> reverse([cons(h1, t1), _rea]) -> 18  ;  (append([t1, l2, _lea])) -> append([cons(h1, t1), l2, cons(h1, _lea)]) -> 16  ;  (length([_afa, _bfa]) /\ length([l1, _zea]) /\ reverse([l1, _afa])) -> leq([_zea, _bfa]) -> 15  ;  (length([ll, _vea])) -> length([cons(x, ll), s(_vea)]) -> 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: Yes: ((append([_qea, cons(h1, nil), _rea]) /\ reverse([t1, _qea])) -> reverse([cons(h1, t1), _rea]), {
_qea -> nil  ;  _rea -> cons(z, nil)  ;  h1 -> s(z)  ;  t1 -> nil
})

-------------------------------------------
Step 25, which took 0.053865 s (model generation: 0.021082,  model checking: 0.032783):

Model:
|_
{
append -> 
{{{
Q={q_gen_3727, q_gen_3732, q_gen_3733, q_gen_3734, q_gen_3735, q_gen_3740, q_gen_3764, q_gen_3797, q_gen_3798, q_gen_3799, q_gen_3800, q_gen_3801, q_gen_3802, q_gen_3803},
Q_f={q_gen_3727},
Delta=
{
<s>(q_gen_3740) -> q_gen_3740
<z>() -> q_gen_3740
<cons>(q_gen_3740, q_gen_3764) -> q_gen_3764
<nil>() -> q_gen_3764
<cons, cons>(q_gen_3735, q_gen_3734, q_gen_3733, q_gen_3732) -> q_gen_3732
<nil, nil>() -> q_gen_3732
<cons, s>(q_gen_3735, q_gen_3733) -> q_gen_3733
<cons, z>(q_gen_3740, q_gen_3764) -> q_gen_3733
<nil, s>(q_gen_3740) -> q_gen_3733
<nil, z>() -> q_gen_3733
<s, cons>(q_gen_3735, q_gen_3734) -> q_gen_3734
<s, nil>(q_gen_3740) -> q_gen_3734
<z, cons>(q_gen_3740, q_gen_3764) -> q_gen_3734
<z, nil>() -> q_gen_3734
<s, s>(q_gen_3735) -> q_gen_3735
<s, z>(q_gen_3740) -> q_gen_3735
<z, s>(q_gen_3740) -> q_gen_3735
<z, z>() -> q_gen_3735
<cons, cons, cons>(q_gen_3803, q_gen_3802, q_gen_3801, q_gen_3800, q_gen_3799, q_gen_3798, q_gen_3797, q_gen_3727) -> q_gen_3727
<cons, nil, cons>(q_gen_3735, q_gen_3734, q_gen_3733, q_gen_3732) -> q_gen_3727
<nil, cons, cons>(q_gen_3735, q_gen_3734, q_gen_3733, q_gen_3732) -> q_gen_3727
<nil, nil, cons>(q_gen_3740, q_gen_3764) -> q_gen_3727
<nil, nil, nil>() -> q_gen_3727
<nil, nil, z>() -> q_gen_3797
<nil, z, cons>(q_gen_3740, q_gen_3764) -> q_gen_3798
<nil, z, z>() -> q_gen_3799
<z, nil, cons>(q_gen_3740, q_gen_3764) -> q_gen_3800
<z, nil, z>() -> q_gen_3801
<z, z, cons>(q_gen_3740, q_gen_3764) -> q_gen_3802
<z, z, z>() -> q_gen_3803
}

Datatype: <natlist, natlist, natlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_3726, q_gen_3730, q_gen_3750},
Q_f={q_gen_3726},
Delta=
{
<s>(q_gen_3750) -> q_gen_3750
<z>() -> q_gen_3750
<cons, s>(q_gen_3730, q_gen_3726) -> q_gen_3726
<nil, z>() -> q_gen_3726
<s, s>(q_gen_3730) -> q_gen_3730
<s, z>(q_gen_3750) -> q_gen_3730
<z, s>(q_gen_3750) -> q_gen_3730
<z, z>() -> q_gen_3730
}

Datatype: <natlist, nat>
Convolution form: complete
}}}
  ;  leq -> 
{{{
Q={q_gen_3723, q_gen_3725},
Q_f={q_gen_3723},
Delta=
{
<s>(q_gen_3725) -> q_gen_3725
<z>() -> q_gen_3725
<s, s>(q_gen_3723) -> q_gen_3723
<z, s>(q_gen_3725) -> q_gen_3723
<z, z>() -> q_gen_3723
}

Datatype: <nat, nat>
Convolution form: complete
}}}
  ;  reverse -> 
{{{
Q={q_gen_3722, q_gen_3745, q_gen_3746, q_gen_3747, q_gen_3758},
Q_f={q_gen_3722},
Delta=
{
<s>(q_gen_3758) -> q_gen_3758
<z>() -> q_gen_3758
<cons, cons>(q_gen_3747, q_gen_3746, q_gen_3745, q_gen_3722) -> q_gen_3722
<nil, nil>() -> q_gen_3722
<nil, s>(q_gen_3758) -> q_gen_3745
<nil, z>() -> q_gen_3745
<s, nil>(q_gen_3758) -> q_gen_3746
<z, nil>() -> q_gen_3746
<s, s>(q_gen_3747) -> q_gen_3747
<s, z>(q_gen_3758) -> q_gen_3747
<z, s>(q_gen_3758) -> q_gen_3747
<z, z>() -> q_gen_3747
}

Datatype: <natlist, natlist>
Convolution form: complete
}}}

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

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([_qea, cons(h1, nil), _rea]) /\ reverse([t1, _qea])) -> reverse([cons(h1, t1), _rea]) -> 18  ;  (append([t1, l2, _lea])) -> append([cons(h1, t1), l2, cons(h1, _lea)]) -> 19  ;  (length([_afa, _bfa]) /\ length([l1, _zea]) /\ reverse([l1, _afa])) -> leq([_zea, _bfa]) -> 16  ;  (length([ll, _vea])) -> length([cons(x, ll), s(_vea)]) -> 17  ;  (leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 16  ;  (leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 16  ;  (leq([s(nn1), z])) -> BOT -> 16
}
Sat witness: Yes: ((append([t1, l2, _lea])) -> append([cons(h1, t1), l2, cons(h1, _lea)]), {
_lea -> cons(z, nil)  ;  h1 -> z  ;  l2 -> nil  ;  t1 -> nil
})

-------------------------------------------
Step 26, which took 0.015820 s (model generation: 0.012454,  model checking: 0.003366):

Model:
|_
{
append -> 
{{{
Q={q_gen_3727, q_gen_3732, q_gen_3733, q_gen_3734, q_gen_3735, q_gen_3740, q_gen_3764, q_gen_3797, q_gen_3798, q_gen_3799, q_gen_3800, q_gen_3801, q_gen_3802, q_gen_3803},
Q_f={q_gen_3727},
Delta=
{
<s>(q_gen_3740) -> q_gen_3740
<z>() -> q_gen_3740
<cons>(q_gen_3740, q_gen_3764) -> q_gen_3764
<nil>() -> q_gen_3764
<cons, cons>(q_gen_3735, q_gen_3734, q_gen_3733, q_gen_3732) -> q_gen_3732
<nil, cons>(q_gen_3740, q_gen_3764) -> q_gen_3732
<nil, nil>() -> q_gen_3732
<cons, s>(q_gen_3735, q_gen_3733) -> q_gen_3733
<cons, z>(q_gen_3740, q_gen_3764) -> q_gen_3733
<nil, s>(q_gen_3740) -> q_gen_3733
<nil, z>() -> q_gen_3733
<s, cons>(q_gen_3735, q_gen_3734) -> q_gen_3734
<s, nil>(q_gen_3740) -> q_gen_3734
<z, cons>(q_gen_3740, q_gen_3764) -> q_gen_3734
<z, nil>() -> q_gen_3734
<s, s>(q_gen_3735) -> q_gen_3735
<s, z>(q_gen_3740) -> q_gen_3735
<z, s>(q_gen_3740) -> q_gen_3735
<z, z>() -> q_gen_3735
<cons, cons, cons>(q_gen_3803, q_gen_3802, q_gen_3801, q_gen_3800, q_gen_3799, q_gen_3798, q_gen_3797, q_gen_3727) -> q_gen_3727
<cons, nil, cons>(q_gen_3735, q_gen_3734, q_gen_3733, q_gen_3732) -> q_gen_3727
<nil, cons, cons>(q_gen_3735, q_gen_3734, q_gen_3733, q_gen_3732) -> q_gen_3727
<nil, nil, cons>(q_gen_3740, q_gen_3764) -> q_gen_3727
<nil, nil, nil>() -> q_gen_3727
<nil, nil, z>() -> q_gen_3797
<nil, z, cons>(q_gen_3740, q_gen_3764) -> q_gen_3798
<nil, z, z>() -> q_gen_3799
<z, nil, cons>(q_gen_3740, q_gen_3764) -> q_gen_3800
<z, nil, z>() -> q_gen_3801
<z, z, cons>(q_gen_3740, q_gen_3764) -> q_gen_3802
<z, z, z>() -> q_gen_3803
}

Datatype: <natlist, natlist, natlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_3726, q_gen_3730, q_gen_3750},
Q_f={q_gen_3726},
Delta=
{
<s>(q_gen_3750) -> q_gen_3750
<z>() -> q_gen_3750
<cons, s>(q_gen_3730, q_gen_3726) -> q_gen_3726
<nil, z>() -> q_gen_3726
<s, s>(q_gen_3730) -> q_gen_3730
<s, z>(q_gen_3750) -> q_gen_3730
<z, s>(q_gen_3750) -> q_gen_3730
<z, z>() -> q_gen_3730
}

Datatype: <natlist, nat>
Convolution form: complete
}}}
  ;  leq -> 
{{{
Q={q_gen_3723, q_gen_3725},
Q_f={q_gen_3723},
Delta=
{
<s>(q_gen_3725) -> q_gen_3725
<z>() -> q_gen_3725
<s, s>(q_gen_3723) -> q_gen_3723
<z, s>(q_gen_3725) -> q_gen_3723
<z, z>() -> q_gen_3723
}

Datatype: <nat, nat>
Convolution form: complete
}}}
  ;  reverse -> 
{{{
Q={q_gen_3722, q_gen_3745, q_gen_3746, q_gen_3747, q_gen_3758},
Q_f={q_gen_3722},
Delta=
{
<s>(q_gen_3758) -> q_gen_3758
<z>() -> q_gen_3758
<cons, cons>(q_gen_3747, q_gen_3746, q_gen_3745, q_gen_3722) -> q_gen_3722
<nil, nil>() -> q_gen_3722
<nil, s>(q_gen_3758) -> q_gen_3745
<nil, z>() -> q_gen_3745
<s, nil>(q_gen_3758) -> q_gen_3746
<z, nil>() -> q_gen_3746
<s, s>(q_gen_3747) -> q_gen_3747
<s, z>(q_gen_3758) -> q_gen_3747
<z, s>(q_gen_3758) -> q_gen_3747
<z, z>() -> q_gen_3747
}

Datatype: <natlist, natlist>
Convolution form: complete
}}}

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

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([_qea, cons(h1, nil), _rea]) /\ reverse([t1, _qea])) -> reverse([cons(h1, t1), _rea]) -> 21  ;  (append([t1, l2, _lea])) -> append([cons(h1, t1), l2, cons(h1, _lea)]) -> 19  ;  (length([_afa, _bfa]) /\ length([l1, _zea]) /\ reverse([l1, _afa])) -> leq([_zea, _bfa]) -> 17  ;  (length([ll, _vea])) -> length([cons(x, ll), s(_vea)]) -> 18  ;  (leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 17  ;  (leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 17  ;  (leq([s(nn1), z])) -> BOT -> 17
}
Sat witness: Yes: ((append([_qea, cons(h1, nil), _rea]) /\ reverse([t1, _qea])) -> reverse([cons(h1, t1), _rea]), {
_qea -> nil  ;  _rea -> cons(z, cons(z, nil))  ;  h1 -> z  ;  t1 -> nil
})

-------------------------------------------
Step 27, which took 0.552367 s (model generation: 0.016527,  model checking: 0.535840):

Model:
|_
{
append -> 
{{{
Q={q_gen_3727, q_gen_3732, q_gen_3733, q_gen_3734, q_gen_3735, q_gen_3740, q_gen_3764, q_gen_3797, q_gen_3798, q_gen_3799, q_gen_3800, q_gen_3801, q_gen_3802, q_gen_3803},
Q_f={q_gen_3727},
Delta=
{
<s>(q_gen_3740) -> q_gen_3740
<z>() -> q_gen_3740
<cons>(q_gen_3740, q_gen_3764) -> q_gen_3764
<nil>() -> q_gen_3764
<cons, cons>(q_gen_3735, q_gen_3734, q_gen_3733, q_gen_3732) -> q_gen_3732
<nil, cons>(q_gen_3740, q_gen_3764) -> q_gen_3732
<nil, nil>() -> q_gen_3732
<cons, s>(q_gen_3735, q_gen_3733) -> q_gen_3733
<cons, z>(q_gen_3740, q_gen_3764) -> q_gen_3733
<nil, s>(q_gen_3740) -> q_gen_3733
<nil, z>() -> q_gen_3733
<s, cons>(q_gen_3735, q_gen_3734) -> q_gen_3734
<s, nil>(q_gen_3740) -> q_gen_3734
<z, cons>(q_gen_3740, q_gen_3764) -> q_gen_3734
<z, nil>() -> q_gen_3734
<s, s>(q_gen_3735) -> q_gen_3735
<s, z>(q_gen_3740) -> q_gen_3735
<z, s>(q_gen_3740) -> q_gen_3735
<z, z>() -> q_gen_3735
<cons, cons, cons>(q_gen_3803, q_gen_3802, q_gen_3801, q_gen_3800, q_gen_3799, q_gen_3798, q_gen_3797, q_gen_3727) -> q_gen_3727
<cons, nil, cons>(q_gen_3735, q_gen_3734, q_gen_3733, q_gen_3732) -> q_gen_3727
<nil, cons, cons>(q_gen_3735, q_gen_3734, q_gen_3733, q_gen_3732) -> q_gen_3727
<nil, nil, cons>(q_gen_3740, q_gen_3764) -> q_gen_3727
<nil, nil, nil>() -> q_gen_3727
<nil, nil, z>() -> q_gen_3797
<nil, z, cons>(q_gen_3740, q_gen_3764) -> q_gen_3798
<nil, z, z>() -> q_gen_3799
<z, nil, cons>(q_gen_3740, q_gen_3764) -> q_gen_3800
<z, nil, z>() -> q_gen_3801
<z, z, cons>(q_gen_3740, q_gen_3764) -> q_gen_3802
<z, z, z>() -> q_gen_3803
}

Datatype: <natlist, natlist, natlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_3726, q_gen_3730, q_gen_3750},
Q_f={q_gen_3726},
Delta=
{
<s>(q_gen_3750) -> q_gen_3750
<z>() -> q_gen_3750
<cons, s>(q_gen_3730, q_gen_3726) -> q_gen_3726
<nil, z>() -> q_gen_3726
<s, s>(q_gen_3730) -> q_gen_3730
<s, z>(q_gen_3750) -> q_gen_3730
<z, s>(q_gen_3750) -> q_gen_3730
<z, z>() -> q_gen_3730
}

Datatype: <natlist, nat>
Convolution form: complete
}}}
  ;  leq -> 
{{{
Q={q_gen_3723, q_gen_3725},
Q_f={q_gen_3723},
Delta=
{
<s>(q_gen_3725) -> q_gen_3725
<z>() -> q_gen_3725
<s, s>(q_gen_3723) -> q_gen_3723
<z, s>(q_gen_3725) -> q_gen_3723
<z, z>() -> q_gen_3723
}

Datatype: <nat, nat>
Convolution form: complete
}}}
  ;  reverse -> 
{{{
Q={q_gen_3722, q_gen_3745, q_gen_3746, q_gen_3747, q_gen_3758, q_gen_3812},
Q_f={q_gen_3722},
Delta=
{
<s>(q_gen_3758) -> q_gen_3758
<z>() -> q_gen_3758
<nil>() -> q_gen_3812
<cons, cons>(q_gen_3747, q_gen_3746, q_gen_3745, q_gen_3722) -> q_gen_3722
<nil, cons>(q_gen_3758, q_gen_3812) -> q_gen_3722
<nil, nil>() -> q_gen_3722
<nil, s>(q_gen_3758) -> q_gen_3745
<nil, z>() -> q_gen_3745
<s, nil>(q_gen_3758) -> q_gen_3746
<z, cons>(q_gen_3758, q_gen_3812) -> q_gen_3746
<z, nil>() -> q_gen_3746
<s, s>(q_gen_3747) -> q_gen_3747
<s, z>(q_gen_3758) -> q_gen_3747
<z, s>(q_gen_3758) -> q_gen_3747
<z, z>() -> q_gen_3747
}

Datatype: <natlist, natlist>
Convolution form: complete
}}}

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

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([_qea, cons(h1, nil), _rea]) /\ reverse([t1, _qea])) -> reverse([cons(h1, t1), _rea]) -> 21  ;  (append([t1, l2, _lea])) -> append([cons(h1, t1), l2, cons(h1, _lea)]) -> 22  ;  (length([_afa, _bfa]) /\ length([l1, _zea]) /\ reverse([l1, _afa])) -> leq([_zea, _bfa]) -> 18  ;  (length([ll, _vea])) -> length([cons(x, ll), s(_vea)]) -> 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: Yes: ((append([t1, l2, _lea])) -> append([cons(h1, t1), l2, cons(h1, _lea)]), {
_lea -> cons(z, nil)  ;  h1 -> s(s(z))  ;  l2 -> cons(s(z), nil)  ;  t1 -> nil
})

-------------------------------------------
Step 28, which took 0.019633 s (model generation: 0.015844,  model checking: 0.003789):

Model:
|_
{
append -> 
{{{
Q={q_gen_3727, q_gen_3732, q_gen_3733, q_gen_3734, q_gen_3735, q_gen_3740, q_gen_3764, q_gen_3797, q_gen_3798, q_gen_3799, q_gen_3800, q_gen_3801, q_gen_3802, q_gen_3803},
Q_f={q_gen_3727},
Delta=
{
<s>(q_gen_3740) -> q_gen_3740
<z>() -> q_gen_3740
<cons>(q_gen_3740, q_gen_3764) -> q_gen_3764
<nil>() -> q_gen_3764
<cons, cons>(q_gen_3735, q_gen_3734, q_gen_3733, q_gen_3732) -> q_gen_3732
<nil, cons>(q_gen_3740, q_gen_3764) -> q_gen_3732
<nil, nil>() -> q_gen_3732
<cons, s>(q_gen_3735, q_gen_3733) -> q_gen_3733
<cons, z>(q_gen_3740, q_gen_3764) -> q_gen_3733
<nil, s>(q_gen_3740) -> q_gen_3733
<nil, z>() -> q_gen_3733
<s, cons>(q_gen_3735, q_gen_3734) -> q_gen_3734
<s, nil>(q_gen_3740) -> q_gen_3734
<z, cons>(q_gen_3740, q_gen_3764) -> q_gen_3734
<z, nil>() -> q_gen_3734
<s, s>(q_gen_3735) -> q_gen_3735
<s, z>(q_gen_3740) -> q_gen_3735
<z, s>(q_gen_3740) -> q_gen_3735
<z, z>() -> q_gen_3735
<cons, cons, cons>(q_gen_3803, q_gen_3802, q_gen_3801, q_gen_3800, q_gen_3799, q_gen_3798, q_gen_3797, q_gen_3727) -> q_gen_3727
<cons, nil, cons>(q_gen_3735, q_gen_3734, q_gen_3733, q_gen_3732) -> q_gen_3727
<nil, cons, cons>(q_gen_3735, q_gen_3734, q_gen_3733, q_gen_3732) -> q_gen_3727
<nil, nil, cons>(q_gen_3740, q_gen_3764) -> q_gen_3727
<nil, nil, nil>() -> q_gen_3727
<nil, nil, s>(q_gen_3740) -> q_gen_3797
<nil, nil, z>() -> q_gen_3797
<nil, s, cons>(q_gen_3735, q_gen_3734) -> q_gen_3798
<nil, z, cons>(q_gen_3740, q_gen_3764) -> q_gen_3798
<nil, s, s>(q_gen_3735) -> q_gen_3799
<nil, z, z>() -> q_gen_3799
<s, nil, cons>(q_gen_3735, q_gen_3734) -> q_gen_3800
<z, nil, cons>(q_gen_3740, q_gen_3764) -> q_gen_3800
<s, nil, s>(q_gen_3735) -> q_gen_3801
<z, nil, z>() -> q_gen_3801
<s, s, cons>(q_gen_3803, q_gen_3802) -> q_gen_3802
<s, z, nil>(q_gen_3740) -> q_gen_3802
<z, z, cons>(q_gen_3740, q_gen_3764) -> q_gen_3802
<s, s, s>(q_gen_3803) -> q_gen_3803
<s, z, s>(q_gen_3735) -> q_gen_3803
<s, z, z>(q_gen_3740) -> q_gen_3803
<z, z, z>() -> q_gen_3803
}

Datatype: <natlist, natlist, natlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_3726, q_gen_3730, q_gen_3750},
Q_f={q_gen_3726},
Delta=
{
<s>(q_gen_3750) -> q_gen_3750
<z>() -> q_gen_3750
<cons, s>(q_gen_3730, q_gen_3726) -> q_gen_3726
<nil, z>() -> q_gen_3726
<s, s>(q_gen_3730) -> q_gen_3730
<s, z>(q_gen_3750) -> q_gen_3730
<z, s>(q_gen_3750) -> q_gen_3730
<z, z>() -> q_gen_3730
}

Datatype: <natlist, nat>
Convolution form: complete
}}}
  ;  leq -> 
{{{
Q={q_gen_3723, q_gen_3725},
Q_f={q_gen_3723},
Delta=
{
<s>(q_gen_3725) -> q_gen_3725
<z>() -> q_gen_3725
<s, s>(q_gen_3723) -> q_gen_3723
<z, s>(q_gen_3725) -> q_gen_3723
<z, z>() -> q_gen_3723
}

Datatype: <nat, nat>
Convolution form: complete
}}}
  ;  reverse -> 
{{{
Q={q_gen_3722, q_gen_3745, q_gen_3746, q_gen_3747, q_gen_3758, q_gen_3812},
Q_f={q_gen_3722},
Delta=
{
<s>(q_gen_3758) -> q_gen_3758
<z>() -> q_gen_3758
<nil>() -> q_gen_3812
<cons, cons>(q_gen_3747, q_gen_3746, q_gen_3745, q_gen_3722) -> q_gen_3722
<nil, cons>(q_gen_3758, q_gen_3812) -> q_gen_3722
<nil, nil>() -> q_gen_3722
<nil, s>(q_gen_3758) -> q_gen_3745
<nil, z>() -> q_gen_3745
<s, nil>(q_gen_3758) -> q_gen_3746
<z, cons>(q_gen_3758, q_gen_3812) -> q_gen_3746
<z, nil>() -> q_gen_3746
<s, s>(q_gen_3747) -> q_gen_3747
<s, z>(q_gen_3758) -> q_gen_3747
<z, s>(q_gen_3758) -> q_gen_3747
<z, z>() -> q_gen_3747
}

Datatype: <natlist, natlist>
Convolution form: complete
}}}

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

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([_qea, cons(h1, nil), _rea]) /\ reverse([t1, _qea])) -> reverse([cons(h1, t1), _rea]) -> 24  ;  (append([t1, l2, _lea])) -> append([cons(h1, t1), l2, cons(h1, _lea)]) -> 22  ;  (length([_afa, _bfa]) /\ length([l1, _zea]) /\ reverse([l1, _afa])) -> leq([_zea, _bfa]) -> 19  ;  (length([ll, _vea])) -> length([cons(x, ll), s(_vea)]) -> 20  ;  (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: Yes: ((append([_qea, cons(h1, nil), _rea]) /\ reverse([t1, _qea])) -> reverse([cons(h1, t1), _rea]), {
_qea -> nil  ;  _rea -> cons(z, cons(z, cons(z, nil)))  ;  h1 -> z  ;  t1 -> nil
})

-------------------------------------------
Step 29, which took 0.181374 s (model generation: 0.016953,  model checking: 0.164421):

Model:
|_
{
append -> 
{{{
Q={q_gen_3727, q_gen_3732, q_gen_3733, q_gen_3734, q_gen_3735, q_gen_3740, q_gen_3764, q_gen_3797, q_gen_3798, q_gen_3799, q_gen_3800, q_gen_3801, q_gen_3802, q_gen_3803},
Q_f={q_gen_3727},
Delta=
{
<s>(q_gen_3740) -> q_gen_3740
<z>() -> q_gen_3740
<cons>(q_gen_3740, q_gen_3764) -> q_gen_3764
<nil>() -> q_gen_3764
<cons, cons>(q_gen_3735, q_gen_3734, q_gen_3733, q_gen_3732) -> q_gen_3732
<nil, cons>(q_gen_3740, q_gen_3764) -> q_gen_3732
<nil, nil>() -> q_gen_3732
<cons, s>(q_gen_3735, q_gen_3733) -> q_gen_3733
<cons, z>(q_gen_3740, q_gen_3764) -> q_gen_3733
<nil, s>(q_gen_3740) -> q_gen_3733
<nil, z>() -> q_gen_3733
<s, cons>(q_gen_3735, q_gen_3734) -> q_gen_3734
<s, nil>(q_gen_3740) -> q_gen_3734
<z, cons>(q_gen_3740, q_gen_3764) -> q_gen_3734
<z, nil>() -> q_gen_3734
<s, s>(q_gen_3735) -> q_gen_3735
<s, z>(q_gen_3740) -> q_gen_3735
<z, s>(q_gen_3740) -> q_gen_3735
<z, z>() -> q_gen_3735
<cons, cons, cons>(q_gen_3803, q_gen_3802, q_gen_3801, q_gen_3800, q_gen_3799, q_gen_3798, q_gen_3797, q_gen_3727) -> q_gen_3727
<cons, nil, cons>(q_gen_3735, q_gen_3734, q_gen_3733, q_gen_3732) -> q_gen_3727
<nil, cons, cons>(q_gen_3735, q_gen_3734, q_gen_3733, q_gen_3732) -> q_gen_3727
<nil, nil, cons>(q_gen_3740, q_gen_3764) -> q_gen_3727
<nil, nil, nil>() -> q_gen_3727
<nil, nil, s>(q_gen_3740) -> q_gen_3797
<nil, nil, z>() -> q_gen_3797
<nil, s, cons>(q_gen_3735, q_gen_3734) -> q_gen_3798
<nil, z, cons>(q_gen_3740, q_gen_3764) -> q_gen_3798
<nil, s, s>(q_gen_3735) -> q_gen_3799
<nil, z, z>() -> q_gen_3799
<s, nil, cons>(q_gen_3735, q_gen_3734) -> q_gen_3800
<z, nil, cons>(q_gen_3740, q_gen_3764) -> q_gen_3800
<s, nil, s>(q_gen_3735) -> q_gen_3801
<z, nil, z>() -> q_gen_3801
<s, s, cons>(q_gen_3803, q_gen_3802) -> q_gen_3802
<s, z, nil>(q_gen_3740) -> q_gen_3802
<z, z, cons>(q_gen_3740, q_gen_3764) -> q_gen_3802
<s, s, s>(q_gen_3803) -> q_gen_3803
<s, z, s>(q_gen_3735) -> q_gen_3803
<s, z, z>(q_gen_3740) -> q_gen_3803
<z, z, z>() -> q_gen_3803
}

Datatype: <natlist, natlist, natlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_3726, q_gen_3730, q_gen_3750},
Q_f={q_gen_3726},
Delta=
{
<s>(q_gen_3750) -> q_gen_3750
<z>() -> q_gen_3750
<cons, s>(q_gen_3730, q_gen_3726) -> q_gen_3726
<nil, z>() -> q_gen_3726
<s, s>(q_gen_3730) -> q_gen_3730
<s, z>(q_gen_3750) -> q_gen_3730
<z, s>(q_gen_3750) -> q_gen_3730
<z, z>() -> q_gen_3730
}

Datatype: <natlist, nat>
Convolution form: complete
}}}
  ;  leq -> 
{{{
Q={q_gen_3723, q_gen_3725},
Q_f={q_gen_3723},
Delta=
{
<s>(q_gen_3725) -> q_gen_3725
<z>() -> q_gen_3725
<s, s>(q_gen_3723) -> q_gen_3723
<z, s>(q_gen_3725) -> q_gen_3723
<z, z>() -> q_gen_3723
}

Datatype: <nat, nat>
Convolution form: complete
}}}
  ;  reverse -> 
{{{
Q={q_gen_3722, q_gen_3745, q_gen_3746, q_gen_3747, q_gen_3758, q_gen_3812},
Q_f={q_gen_3722},
Delta=
{
<s>(q_gen_3758) -> q_gen_3758
<z>() -> q_gen_3758
<cons>(q_gen_3758, q_gen_3812) -> q_gen_3812
<nil>() -> q_gen_3812
<cons, cons>(q_gen_3747, q_gen_3746, q_gen_3745, q_gen_3722) -> q_gen_3722
<nil, cons>(q_gen_3758, q_gen_3812) -> q_gen_3722
<nil, nil>() -> q_gen_3722
<nil, s>(q_gen_3758) -> q_gen_3745
<nil, z>() -> q_gen_3745
<s, nil>(q_gen_3758) -> q_gen_3746
<z, cons>(q_gen_3758, q_gen_3812) -> q_gen_3746
<z, nil>() -> q_gen_3746
<s, s>(q_gen_3747) -> q_gen_3747
<s, z>(q_gen_3758) -> q_gen_3747
<z, s>(q_gen_3758) -> q_gen_3747
<z, z>() -> q_gen_3747
}

Datatype: <natlist, natlist>
Convolution form: complete
}}}

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

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([_qea, cons(h1, nil), _rea]) /\ reverse([t1, _qea])) -> reverse([cons(h1, t1), _rea]) -> 24  ;  (append([t1, l2, _lea])) -> append([cons(h1, t1), l2, cons(h1, _lea)]) -> 25  ;  (length([_afa, _bfa]) /\ length([l1, _zea]) /\ reverse([l1, _afa])) -> leq([_zea, _bfa]) -> 20  ;  (length([ll, _vea])) -> length([cons(x, ll), s(_vea)]) -> 21  ;  (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: Yes: ((append([t1, l2, _lea])) -> append([cons(h1, t1), l2, cons(h1, _lea)]), {
_lea -> cons(z, nil)  ;  h1 -> s(z)  ;  l2 -> cons(z, nil)  ;  t1 -> nil
})

-------------------------------------------
Step 30, which took 0.023054 s (model generation: 0.019052,  model checking: 0.004002):

Model:
|_
{
append -> 
{{{
Q={q_gen_3727, q_gen_3732, q_gen_3733, q_gen_3734, q_gen_3735, q_gen_3740, q_gen_3764, q_gen_3797, q_gen_3798, q_gen_3799, q_gen_3800, q_gen_3801, q_gen_3802, q_gen_3803},
Q_f={q_gen_3727},
Delta=
{
<s>(q_gen_3740) -> q_gen_3740
<z>() -> q_gen_3740
<cons>(q_gen_3740, q_gen_3764) -> q_gen_3764
<nil>() -> q_gen_3764
<cons, cons>(q_gen_3735, q_gen_3734, q_gen_3733, q_gen_3732) -> q_gen_3732
<nil, cons>(q_gen_3740, q_gen_3764) -> q_gen_3732
<nil, nil>() -> q_gen_3732
<cons, s>(q_gen_3735, q_gen_3733) -> q_gen_3733
<cons, z>(q_gen_3740, q_gen_3764) -> q_gen_3733
<nil, s>(q_gen_3740) -> q_gen_3733
<nil, z>() -> q_gen_3733
<s, cons>(q_gen_3735, q_gen_3734) -> q_gen_3734
<s, nil>(q_gen_3740) -> q_gen_3734
<z, cons>(q_gen_3740, q_gen_3764) -> q_gen_3734
<z, nil>() -> q_gen_3734
<s, s>(q_gen_3735) -> q_gen_3735
<s, z>(q_gen_3740) -> q_gen_3735
<z, s>(q_gen_3740) -> q_gen_3735
<z, z>() -> q_gen_3735
<cons, cons, cons>(q_gen_3803, q_gen_3802, q_gen_3801, q_gen_3800, q_gen_3799, q_gen_3798, q_gen_3797, q_gen_3727) -> q_gen_3727
<cons, nil, cons>(q_gen_3735, q_gen_3734, q_gen_3733, q_gen_3732) -> q_gen_3727
<nil, cons, cons>(q_gen_3735, q_gen_3734, q_gen_3733, q_gen_3732) -> q_gen_3727
<nil, nil, cons>(q_gen_3740, q_gen_3764) -> q_gen_3727
<nil, nil, nil>() -> q_gen_3727
<nil, nil, s>(q_gen_3740) -> q_gen_3797
<nil, nil, z>() -> q_gen_3797
<nil, s, cons>(q_gen_3735, q_gen_3734) -> q_gen_3798
<nil, z, cons>(q_gen_3740, q_gen_3764) -> q_gen_3798
<nil, s, s>(q_gen_3735) -> q_gen_3799
<nil, z, s>(q_gen_3740) -> q_gen_3799
<nil, z, z>() -> q_gen_3799
<s, nil, cons>(q_gen_3735, q_gen_3734) -> q_gen_3800
<z, nil, cons>(q_gen_3740, q_gen_3764) -> q_gen_3800
<s, nil, s>(q_gen_3735) -> q_gen_3801
<z, nil, z>() -> q_gen_3801
<s, s, cons>(q_gen_3803, q_gen_3802) -> q_gen_3802
<s, z, cons>(q_gen_3735, q_gen_3734) -> q_gen_3802
<s, z, nil>(q_gen_3740) -> q_gen_3802
<z, z, cons>(q_gen_3740, q_gen_3764) -> q_gen_3802
<s, s, s>(q_gen_3803) -> q_gen_3803
<s, z, s>(q_gen_3735) -> q_gen_3803
<s, z, z>(q_gen_3740) -> q_gen_3803
<z, z, z>() -> q_gen_3803
}

Datatype: <natlist, natlist, natlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_3726, q_gen_3730, q_gen_3750},
Q_f={q_gen_3726},
Delta=
{
<s>(q_gen_3750) -> q_gen_3750
<z>() -> q_gen_3750
<cons, s>(q_gen_3730, q_gen_3726) -> q_gen_3726
<nil, z>() -> q_gen_3726
<s, s>(q_gen_3730) -> q_gen_3730
<s, z>(q_gen_3750) -> q_gen_3730
<z, s>(q_gen_3750) -> q_gen_3730
<z, z>() -> q_gen_3730
}

Datatype: <natlist, nat>
Convolution form: complete
}}}
  ;  leq -> 
{{{
Q={q_gen_3723, q_gen_3725},
Q_f={q_gen_3723},
Delta=
{
<s>(q_gen_3725) -> q_gen_3725
<z>() -> q_gen_3725
<s, s>(q_gen_3723) -> q_gen_3723
<z, s>(q_gen_3725) -> q_gen_3723
<z, z>() -> q_gen_3723
}

Datatype: <nat, nat>
Convolution form: complete
}}}
  ;  reverse -> 
{{{
Q={q_gen_3722, q_gen_3745, q_gen_3746, q_gen_3747, q_gen_3758, q_gen_3812},
Q_f={q_gen_3722},
Delta=
{
<s>(q_gen_3758) -> q_gen_3758
<z>() -> q_gen_3758
<cons>(q_gen_3758, q_gen_3812) -> q_gen_3812
<nil>() -> q_gen_3812
<cons, cons>(q_gen_3747, q_gen_3746, q_gen_3745, q_gen_3722) -> q_gen_3722
<nil, cons>(q_gen_3758, q_gen_3812) -> q_gen_3722
<nil, nil>() -> q_gen_3722
<nil, s>(q_gen_3758) -> q_gen_3745
<nil, z>() -> q_gen_3745
<s, nil>(q_gen_3758) -> q_gen_3746
<z, cons>(q_gen_3758, q_gen_3812) -> q_gen_3746
<z, nil>() -> q_gen_3746
<s, s>(q_gen_3747) -> q_gen_3747
<s, z>(q_gen_3758) -> q_gen_3747
<z, s>(q_gen_3758) -> q_gen_3747
<z, z>() -> q_gen_3747
}

Datatype: <natlist, natlist>
Convolution form: complete
}}}

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 20  ;  () -> length([nil, z]) -> 20  ;  () -> leq([z, s(nn2)]) -> 20  ;  () -> leq([z, z]) -> 20  ;  () -> reverse([nil, nil]) -> 20  ;  (append([_qea, cons(h1, nil), _rea]) /\ reverse([t1, _qea])) -> reverse([cons(h1, t1), _rea]) -> 27  ;  (append([t1, l2, _lea])) -> append([cons(h1, t1), l2, cons(h1, _lea)]) -> 25  ;  (length([_afa, _bfa]) /\ length([l1, _zea]) /\ reverse([l1, _afa])) -> leq([_zea, _bfa]) -> 21  ;  (length([ll, _vea])) -> length([cons(x, ll), s(_vea)]) -> 22  ;  (leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 21  ;  (leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 21  ;  (leq([s(nn1), z])) -> BOT -> 21
}
Sat witness: Yes: ((append([_qea, cons(h1, nil), _rea]) /\ reverse([t1, _qea])) -> reverse([cons(h1, t1), _rea]), {
_qea -> nil  ;  _rea -> cons(z, cons(z, nil))  ;  h1 -> s(z)  ;  t1 -> nil
})

-------------------------------------------
Step 31, which took 0.186360 s (model generation: 0.020179,  model checking: 0.166181):

Model:
|_
{
append -> 
{{{
Q={q_gen_3727, q_gen_3732, q_gen_3733, q_gen_3734, q_gen_3735, q_gen_3740, q_gen_3764, q_gen_3797, q_gen_3798, q_gen_3799, q_gen_3800, q_gen_3801, q_gen_3802, q_gen_3803},
Q_f={q_gen_3727},
Delta=
{
<s>(q_gen_3740) -> q_gen_3740
<z>() -> q_gen_3740
<cons>(q_gen_3740, q_gen_3764) -> q_gen_3764
<nil>() -> q_gen_3764
<cons, cons>(q_gen_3735, q_gen_3734, q_gen_3733, q_gen_3732) -> q_gen_3732
<nil, cons>(q_gen_3740, q_gen_3764) -> q_gen_3732
<nil, nil>() -> q_gen_3732
<cons, s>(q_gen_3735, q_gen_3733) -> q_gen_3733
<cons, z>(q_gen_3740, q_gen_3764) -> q_gen_3733
<nil, s>(q_gen_3740) -> q_gen_3733
<nil, z>() -> q_gen_3733
<s, cons>(q_gen_3735, q_gen_3734) -> q_gen_3734
<s, nil>(q_gen_3740) -> q_gen_3734
<z, cons>(q_gen_3740, q_gen_3764) -> q_gen_3734
<z, nil>() -> q_gen_3734
<s, s>(q_gen_3735) -> q_gen_3735
<s, z>(q_gen_3740) -> q_gen_3735
<z, s>(q_gen_3740) -> q_gen_3735
<z, z>() -> q_gen_3735
<cons, cons, cons>(q_gen_3803, q_gen_3802, q_gen_3801, q_gen_3800, q_gen_3799, q_gen_3798, q_gen_3797, q_gen_3727) -> q_gen_3727
<cons, nil, cons>(q_gen_3735, q_gen_3734, q_gen_3733, q_gen_3732) -> q_gen_3727
<nil, cons, cons>(q_gen_3735, q_gen_3734, q_gen_3733, q_gen_3732) -> q_gen_3727
<nil, nil, cons>(q_gen_3740, q_gen_3764) -> q_gen_3727
<nil, nil, nil>() -> q_gen_3727
<nil, nil, s>(q_gen_3740) -> q_gen_3797
<nil, nil, z>() -> q_gen_3797
<nil, s, cons>(q_gen_3735, q_gen_3734) -> q_gen_3798
<nil, z, cons>(q_gen_3740, q_gen_3764) -> q_gen_3798
<nil, s, s>(q_gen_3735) -> q_gen_3799
<nil, z, s>(q_gen_3740) -> q_gen_3799
<nil, z, z>() -> q_gen_3799
<s, nil, cons>(q_gen_3735, q_gen_3734) -> q_gen_3800
<z, nil, cons>(q_gen_3740, q_gen_3764) -> q_gen_3800
<s, nil, s>(q_gen_3735) -> q_gen_3801
<z, nil, z>() -> q_gen_3801
<s, s, cons>(q_gen_3803, q_gen_3802) -> q_gen_3802
<s, z, cons>(q_gen_3735, q_gen_3734) -> q_gen_3802
<s, z, nil>(q_gen_3740) -> q_gen_3802
<z, z, cons>(q_gen_3740, q_gen_3764) -> q_gen_3802
<s, s, s>(q_gen_3803) -> q_gen_3803
<s, z, s>(q_gen_3735) -> q_gen_3803
<s, z, z>(q_gen_3740) -> q_gen_3803
<z, z, z>() -> q_gen_3803
}

Datatype: <natlist, natlist, natlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_3726, q_gen_3730, q_gen_3750},
Q_f={q_gen_3726},
Delta=
{
<s>(q_gen_3750) -> q_gen_3750
<z>() -> q_gen_3750
<cons, s>(q_gen_3730, q_gen_3726) -> q_gen_3726
<nil, z>() -> q_gen_3726
<s, s>(q_gen_3730) -> q_gen_3730
<s, z>(q_gen_3750) -> q_gen_3730
<z, s>(q_gen_3750) -> q_gen_3730
<z, z>() -> q_gen_3730
}

Datatype: <natlist, nat>
Convolution form: complete
}}}
  ;  leq -> 
{{{
Q={q_gen_3723, q_gen_3725},
Q_f={q_gen_3723},
Delta=
{
<s>(q_gen_3725) -> q_gen_3725
<z>() -> q_gen_3725
<s, s>(q_gen_3723) -> q_gen_3723
<z, s>(q_gen_3725) -> q_gen_3723
<z, z>() -> q_gen_3723
}

Datatype: <nat, nat>
Convolution form: complete
}}}
  ;  reverse -> 
{{{
Q={q_gen_3722, q_gen_3745, q_gen_3746, q_gen_3747, q_gen_3758, q_gen_3812},
Q_f={q_gen_3722},
Delta=
{
<s>(q_gen_3758) -> q_gen_3758
<z>() -> q_gen_3758
<cons>(q_gen_3758, q_gen_3812) -> q_gen_3812
<nil>() -> q_gen_3812
<cons, cons>(q_gen_3747, q_gen_3746, q_gen_3745, q_gen_3722) -> q_gen_3722
<nil, cons>(q_gen_3758, q_gen_3812) -> q_gen_3722
<nil, nil>() -> q_gen_3722
<nil, s>(q_gen_3758) -> q_gen_3745
<nil, z>() -> q_gen_3745
<s, cons>(q_gen_3747, q_gen_3746) -> q_gen_3746
<s, nil>(q_gen_3758) -> q_gen_3746
<z, cons>(q_gen_3758, q_gen_3812) -> q_gen_3746
<z, nil>() -> q_gen_3746
<s, s>(q_gen_3747) -> q_gen_3747
<s, z>(q_gen_3758) -> q_gen_3747
<z, s>(q_gen_3758) -> q_gen_3747
<z, z>() -> q_gen_3747
}

Datatype: <natlist, natlist>
Convolution form: complete
}}}

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 21  ;  () -> length([nil, z]) -> 21  ;  () -> leq([z, s(nn2)]) -> 21  ;  () -> leq([z, z]) -> 21  ;  () -> reverse([nil, nil]) -> 21  ;  (append([_qea, cons(h1, nil), _rea]) /\ reverse([t1, _qea])) -> reverse([cons(h1, t1), _rea]) -> 27  ;  (append([t1, l2, _lea])) -> append([cons(h1, t1), l2, cons(h1, _lea)]) -> 28  ;  (length([_afa, _bfa]) /\ length([l1, _zea]) /\ reverse([l1, _afa])) -> leq([_zea, _bfa]) -> 22  ;  (length([ll, _vea])) -> length([cons(x, ll), s(_vea)]) -> 23  ;  (leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 22  ;  (leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 22  ;  (leq([s(nn1), z])) -> BOT -> 22
}
Sat witness: Yes: ((append([t1, l2, _lea])) -> append([cons(h1, t1), l2, cons(h1, _lea)]), {
_lea -> cons(z, nil)  ;  h1 -> s(z)  ;  l2 -> cons(s(z), nil)  ;  t1 -> nil
})

-------------------------------------------
Step 32, which took 0.027356 s (model generation: 0.020685,  model checking: 0.006671):

Model:
|_
{
append -> 
{{{
Q={q_gen_3727, q_gen_3732, q_gen_3733, q_gen_3734, q_gen_3735, q_gen_3740, q_gen_3764, q_gen_3797, q_gen_3798, q_gen_3799, q_gen_3800, q_gen_3801, q_gen_3802, q_gen_3803},
Q_f={q_gen_3727},
Delta=
{
<s>(q_gen_3740) -> q_gen_3740
<z>() -> q_gen_3740
<cons>(q_gen_3740, q_gen_3764) -> q_gen_3764
<nil>() -> q_gen_3764
<cons, cons>(q_gen_3735, q_gen_3734, q_gen_3733, q_gen_3732) -> q_gen_3732
<nil, cons>(q_gen_3740, q_gen_3764) -> q_gen_3732
<nil, nil>() -> q_gen_3732
<cons, s>(q_gen_3735, q_gen_3733) -> q_gen_3733
<cons, z>(q_gen_3740, q_gen_3764) -> q_gen_3733
<nil, s>(q_gen_3740) -> q_gen_3733
<nil, z>() -> q_gen_3733
<s, cons>(q_gen_3735, q_gen_3734) -> q_gen_3734
<s, nil>(q_gen_3740) -> q_gen_3734
<z, cons>(q_gen_3740, q_gen_3764) -> q_gen_3734
<z, nil>() -> q_gen_3734
<s, s>(q_gen_3735) -> q_gen_3735
<s, z>(q_gen_3740) -> q_gen_3735
<z, s>(q_gen_3740) -> q_gen_3735
<z, z>() -> q_gen_3735
<cons, cons, cons>(q_gen_3803, q_gen_3802, q_gen_3801, q_gen_3800, q_gen_3799, q_gen_3798, q_gen_3797, q_gen_3727) -> q_gen_3727
<cons, nil, cons>(q_gen_3735, q_gen_3734, q_gen_3733, q_gen_3732) -> q_gen_3727
<nil, cons, cons>(q_gen_3735, q_gen_3734, q_gen_3733, q_gen_3732) -> q_gen_3727
<nil, nil, cons>(q_gen_3740, q_gen_3764) -> q_gen_3727
<nil, nil, nil>() -> q_gen_3727
<nil, nil, s>(q_gen_3740) -> q_gen_3797
<nil, nil, z>() -> q_gen_3797
<nil, s, cons>(q_gen_3735, q_gen_3734) -> q_gen_3798
<nil, z, cons>(q_gen_3740, q_gen_3764) -> q_gen_3798
<nil, s, s>(q_gen_3735) -> q_gen_3799
<nil, z, s>(q_gen_3740) -> q_gen_3799
<nil, z, z>() -> q_gen_3799
<s, nil, cons>(q_gen_3735, q_gen_3734) -> q_gen_3800
<z, nil, cons>(q_gen_3740, q_gen_3764) -> q_gen_3800
<s, nil, s>(q_gen_3735) -> q_gen_3801
<z, nil, z>() -> q_gen_3801
<s, s, cons>(q_gen_3803, q_gen_3802) -> q_gen_3802
<s, z, cons>(q_gen_3735, q_gen_3734) -> q_gen_3802
<s, z, nil>(q_gen_3740) -> q_gen_3802
<z, z, cons>(q_gen_3740, q_gen_3764) -> q_gen_3802
<z, z, nil>() -> q_gen_3802
<s, s, s>(q_gen_3803) -> q_gen_3803
<s, z, s>(q_gen_3735) -> q_gen_3803
<s, z, z>(q_gen_3740) -> q_gen_3803
<z, z, z>() -> q_gen_3803
}

Datatype: <natlist, natlist, natlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_3726, q_gen_3730, q_gen_3750},
Q_f={q_gen_3726},
Delta=
{
<s>(q_gen_3750) -> q_gen_3750
<z>() -> q_gen_3750
<cons, s>(q_gen_3730, q_gen_3726) -> q_gen_3726
<nil, z>() -> q_gen_3726
<s, s>(q_gen_3730) -> q_gen_3730
<s, z>(q_gen_3750) -> q_gen_3730
<z, s>(q_gen_3750) -> q_gen_3730
<z, z>() -> q_gen_3730
}

Datatype: <natlist, nat>
Convolution form: complete
}}}
  ;  leq -> 
{{{
Q={q_gen_3723, q_gen_3725},
Q_f={q_gen_3723},
Delta=
{
<s>(q_gen_3725) -> q_gen_3725
<z>() -> q_gen_3725
<s, s>(q_gen_3723) -> q_gen_3723
<z, s>(q_gen_3725) -> q_gen_3723
<z, z>() -> q_gen_3723
}

Datatype: <nat, nat>
Convolution form: complete
}}}
  ;  reverse -> 
{{{
Q={q_gen_3722, q_gen_3745, q_gen_3746, q_gen_3747, q_gen_3758, q_gen_3812},
Q_f={q_gen_3722},
Delta=
{
<s>(q_gen_3758) -> q_gen_3758
<z>() -> q_gen_3758
<cons>(q_gen_3758, q_gen_3812) -> q_gen_3812
<nil>() -> q_gen_3812
<cons, cons>(q_gen_3747, q_gen_3746, q_gen_3745, q_gen_3722) -> q_gen_3722
<nil, cons>(q_gen_3758, q_gen_3812) -> q_gen_3722
<nil, nil>() -> q_gen_3722
<nil, s>(q_gen_3758) -> q_gen_3745
<nil, z>() -> q_gen_3745
<s, cons>(q_gen_3747, q_gen_3746) -> q_gen_3746
<s, nil>(q_gen_3758) -> q_gen_3746
<z, cons>(q_gen_3758, q_gen_3812) -> q_gen_3746
<z, nil>() -> q_gen_3746
<s, s>(q_gen_3747) -> q_gen_3747
<s, z>(q_gen_3758) -> q_gen_3747
<z, s>(q_gen_3758) -> q_gen_3747
<z, z>() -> q_gen_3747
}

Datatype: <natlist, natlist>
Convolution form: complete
}}}

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

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([_qea, cons(h1, nil), _rea]) /\ reverse([t1, _qea])) -> reverse([cons(h1, t1), _rea]) -> 30  ;  (append([t1, l2, _lea])) -> append([cons(h1, t1), l2, cons(h1, _lea)]) -> 28  ;  (length([_afa, _bfa]) /\ length([l1, _zea]) /\ reverse([l1, _afa])) -> leq([_zea, _bfa]) -> 23  ;  (length([ll, _vea])) -> length([cons(x, ll), s(_vea)]) -> 24  ;  (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: Yes: ((append([_qea, cons(h1, nil), _rea]) /\ reverse([t1, _qea])) -> reverse([cons(h1, t1), _rea]), {
_qea -> cons(z, nil)  ;  _rea -> cons(z, cons(z, nil))  ;  h1 -> z  ;  t1 -> cons(z, nil)
})

-------------------------------------------
Step 33, which took 0.218237 s (model generation: 0.024022,  model checking: 0.194215):

Model:
|_
{
append -> 
{{{
Q={q_gen_3727, q_gen_3732, q_gen_3733, q_gen_3734, q_gen_3735, q_gen_3740, q_gen_3764, q_gen_3797, q_gen_3798, q_gen_3799, q_gen_3800, q_gen_3801, q_gen_3802, q_gen_3803},
Q_f={q_gen_3727},
Delta=
{
<s>(q_gen_3740) -> q_gen_3740
<z>() -> q_gen_3740
<cons>(q_gen_3740, q_gen_3764) -> q_gen_3764
<nil>() -> q_gen_3764
<cons, cons>(q_gen_3735, q_gen_3734, q_gen_3733, q_gen_3732) -> q_gen_3732
<nil, cons>(q_gen_3740, q_gen_3764) -> q_gen_3732
<nil, nil>() -> q_gen_3732
<cons, s>(q_gen_3735, q_gen_3733) -> q_gen_3733
<cons, z>(q_gen_3740, q_gen_3764) -> q_gen_3733
<nil, s>(q_gen_3740) -> q_gen_3733
<nil, z>() -> q_gen_3733
<s, cons>(q_gen_3735, q_gen_3734) -> q_gen_3734
<s, nil>(q_gen_3740) -> q_gen_3734
<z, cons>(q_gen_3740, q_gen_3764) -> q_gen_3734
<z, nil>() -> q_gen_3734
<s, s>(q_gen_3735) -> q_gen_3735
<s, z>(q_gen_3740) -> q_gen_3735
<z, s>(q_gen_3740) -> q_gen_3735
<z, z>() -> q_gen_3735
<cons, cons, cons>(q_gen_3803, q_gen_3802, q_gen_3801, q_gen_3800, q_gen_3799, q_gen_3798, q_gen_3797, q_gen_3727) -> q_gen_3727
<cons, nil, cons>(q_gen_3735, q_gen_3734, q_gen_3733, q_gen_3732) -> q_gen_3727
<nil, cons, cons>(q_gen_3735, q_gen_3734, q_gen_3733, q_gen_3732) -> q_gen_3727
<nil, nil, cons>(q_gen_3740, q_gen_3764) -> q_gen_3727
<nil, nil, nil>() -> q_gen_3727
<nil, nil, s>(q_gen_3740) -> q_gen_3797
<nil, nil, z>() -> q_gen_3797
<nil, s, cons>(q_gen_3735, q_gen_3734) -> q_gen_3798
<nil, z, cons>(q_gen_3740, q_gen_3764) -> q_gen_3798
<nil, s, s>(q_gen_3735) -> q_gen_3799
<nil, z, s>(q_gen_3740) -> q_gen_3799
<nil, z, z>() -> q_gen_3799
<s, nil, cons>(q_gen_3735, q_gen_3734) -> q_gen_3800
<z, nil, cons>(q_gen_3740, q_gen_3764) -> q_gen_3800
<s, nil, s>(q_gen_3735) -> q_gen_3801
<z, nil, z>() -> q_gen_3801
<s, s, cons>(q_gen_3803, q_gen_3802) -> q_gen_3802
<s, z, cons>(q_gen_3735, q_gen_3734) -> q_gen_3802
<s, z, nil>(q_gen_3740) -> q_gen_3802
<z, z, cons>(q_gen_3740, q_gen_3764) -> q_gen_3802
<z, z, nil>() -> q_gen_3802
<s, s, s>(q_gen_3803) -> q_gen_3803
<s, z, s>(q_gen_3735) -> q_gen_3803
<s, z, z>(q_gen_3740) -> q_gen_3803
<z, z, z>() -> q_gen_3803
}

Datatype: <natlist, natlist, natlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_3726, q_gen_3730, q_gen_3750},
Q_f={q_gen_3726},
Delta=
{
<s>(q_gen_3750) -> q_gen_3750
<z>() -> q_gen_3750
<cons, s>(q_gen_3730, q_gen_3726) -> q_gen_3726
<nil, z>() -> q_gen_3726
<s, s>(q_gen_3730) -> q_gen_3730
<s, z>(q_gen_3750) -> q_gen_3730
<z, s>(q_gen_3750) -> q_gen_3730
<z, z>() -> q_gen_3730
}

Datatype: <natlist, nat>
Convolution form: complete
}}}
  ;  leq -> 
{{{
Q={q_gen_3723, q_gen_3725},
Q_f={q_gen_3723},
Delta=
{
<s>(q_gen_3725) -> q_gen_3725
<z>() -> q_gen_3725
<s, s>(q_gen_3723) -> q_gen_3723
<z, s>(q_gen_3725) -> q_gen_3723
<z, z>() -> q_gen_3723
}

Datatype: <nat, nat>
Convolution form: complete
}}}
  ;  reverse -> 
{{{
Q={q_gen_3722, q_gen_3745, q_gen_3746, q_gen_3747, q_gen_3758, q_gen_3812},
Q_f={q_gen_3722},
Delta=
{
<s>(q_gen_3758) -> q_gen_3758
<z>() -> q_gen_3758
<cons>(q_gen_3758, q_gen_3812) -> q_gen_3812
<nil>() -> q_gen_3812
<cons, cons>(q_gen_3747, q_gen_3746, q_gen_3745, q_gen_3722) -> q_gen_3722
<nil, cons>(q_gen_3758, q_gen_3812) -> q_gen_3722
<nil, nil>() -> q_gen_3722
<cons, z>(q_gen_3758, q_gen_3812) -> q_gen_3745
<nil, s>(q_gen_3758) -> q_gen_3745
<nil, z>() -> q_gen_3745
<s, cons>(q_gen_3747, q_gen_3746) -> q_gen_3746
<s, nil>(q_gen_3758) -> q_gen_3746
<z, cons>(q_gen_3758, q_gen_3812) -> q_gen_3746
<z, nil>() -> q_gen_3746
<s, s>(q_gen_3747) -> q_gen_3747
<s, z>(q_gen_3758) -> q_gen_3747
<z, s>(q_gen_3758) -> q_gen_3747
<z, z>() -> q_gen_3747
}

Datatype: <natlist, natlist>
Convolution form: complete
}}}

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

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([_qea, cons(h1, nil), _rea]) /\ reverse([t1, _qea])) -> reverse([cons(h1, t1), _rea]) -> 30  ;  (append([t1, l2, _lea])) -> append([cons(h1, t1), l2, cons(h1, _lea)]) -> 31  ;  (length([_afa, _bfa]) /\ length([l1, _zea]) /\ reverse([l1, _afa])) -> leq([_zea, _bfa]) -> 24  ;  (length([ll, _vea])) -> length([cons(x, ll), s(_vea)]) -> 25  ;  (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: Yes: ((append([t1, l2, _lea])) -> append([cons(h1, t1), l2, cons(h1, _lea)]), {
_lea -> cons(z, nil)  ;  h1 -> z  ;  l2 -> cons(s(z), nil)  ;  t1 -> nil
})

-------------------------------------------
Step 34, which took 0.031021 s (model generation: 0.023383,  model checking: 0.007638):

Model:
|_
{
append -> 
{{{
Q={q_gen_3727, q_gen_3732, q_gen_3733, q_gen_3734, q_gen_3735, q_gen_3740, q_gen_3764, q_gen_3797, q_gen_3798, q_gen_3799, q_gen_3800, q_gen_3801, q_gen_3802, q_gen_3803},
Q_f={q_gen_3727},
Delta=
{
<s>(q_gen_3740) -> q_gen_3740
<z>() -> q_gen_3740
<cons>(q_gen_3740, q_gen_3764) -> q_gen_3764
<nil>() -> q_gen_3764
<cons, cons>(q_gen_3735, q_gen_3734, q_gen_3733, q_gen_3732) -> q_gen_3732
<nil, cons>(q_gen_3740, q_gen_3764) -> q_gen_3732
<nil, nil>() -> q_gen_3732
<cons, s>(q_gen_3735, q_gen_3733) -> q_gen_3733
<cons, z>(q_gen_3740, q_gen_3764) -> q_gen_3733
<nil, s>(q_gen_3740) -> q_gen_3733
<nil, z>() -> q_gen_3733
<s, cons>(q_gen_3735, q_gen_3734) -> q_gen_3734
<s, nil>(q_gen_3740) -> q_gen_3734
<z, cons>(q_gen_3740, q_gen_3764) -> q_gen_3734
<z, nil>() -> q_gen_3734
<s, s>(q_gen_3735) -> q_gen_3735
<s, z>(q_gen_3740) -> q_gen_3735
<z, s>(q_gen_3740) -> q_gen_3735
<z, z>() -> q_gen_3735
<cons, cons, cons>(q_gen_3803, q_gen_3802, q_gen_3801, q_gen_3800, q_gen_3799, q_gen_3798, q_gen_3797, q_gen_3727) -> q_gen_3727
<cons, nil, cons>(q_gen_3735, q_gen_3734, q_gen_3733, q_gen_3732) -> q_gen_3727
<nil, cons, cons>(q_gen_3735, q_gen_3734, q_gen_3733, q_gen_3732) -> q_gen_3727
<nil, nil, cons>(q_gen_3740, q_gen_3764) -> q_gen_3727
<nil, nil, nil>() -> q_gen_3727
<nil, nil, s>(q_gen_3740) -> q_gen_3797
<nil, nil, z>() -> q_gen_3797
<nil, s, cons>(q_gen_3735, q_gen_3734) -> q_gen_3798
<nil, z, cons>(q_gen_3740, q_gen_3764) -> q_gen_3798
<nil, s, s>(q_gen_3735) -> q_gen_3799
<nil, s, z>(q_gen_3740) -> q_gen_3799
<nil, z, s>(q_gen_3740) -> q_gen_3799
<nil, z, z>() -> q_gen_3799
<s, nil, cons>(q_gen_3735, q_gen_3734) -> q_gen_3800
<z, nil, cons>(q_gen_3740, q_gen_3764) -> q_gen_3800
<s, nil, s>(q_gen_3735) -> q_gen_3801
<z, nil, z>() -> q_gen_3801
<s, s, cons>(q_gen_3803, q_gen_3802) -> q_gen_3802
<s, z, cons>(q_gen_3735, q_gen_3734) -> q_gen_3802
<s, z, nil>(q_gen_3740) -> q_gen_3802
<z, s, cons>(q_gen_3735, q_gen_3734) -> q_gen_3802
<z, z, cons>(q_gen_3740, q_gen_3764) -> q_gen_3802
<z, z, nil>() -> q_gen_3802
<s, s, s>(q_gen_3803) -> q_gen_3803
<s, z, s>(q_gen_3735) -> q_gen_3803
<s, z, z>(q_gen_3740) -> q_gen_3803
<z, s, z>(q_gen_3740) -> q_gen_3803
<z, z, z>() -> q_gen_3803
}

Datatype: <natlist, natlist, natlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_3726, q_gen_3730, q_gen_3750},
Q_f={q_gen_3726},
Delta=
{
<s>(q_gen_3750) -> q_gen_3750
<z>() -> q_gen_3750
<cons, s>(q_gen_3730, q_gen_3726) -> q_gen_3726
<nil, z>() -> q_gen_3726
<s, s>(q_gen_3730) -> q_gen_3730
<s, z>(q_gen_3750) -> q_gen_3730
<z, s>(q_gen_3750) -> q_gen_3730
<z, z>() -> q_gen_3730
}

Datatype: <natlist, nat>
Convolution form: complete
}}}
  ;  leq -> 
{{{
Q={q_gen_3723, q_gen_3725},
Q_f={q_gen_3723},
Delta=
{
<s>(q_gen_3725) -> q_gen_3725
<z>() -> q_gen_3725
<s, s>(q_gen_3723) -> q_gen_3723
<z, s>(q_gen_3725) -> q_gen_3723
<z, z>() -> q_gen_3723
}

Datatype: <nat, nat>
Convolution form: complete
}}}
  ;  reverse -> 
{{{
Q={q_gen_3722, q_gen_3745, q_gen_3746, q_gen_3747, q_gen_3758, q_gen_3812},
Q_f={q_gen_3722},
Delta=
{
<s>(q_gen_3758) -> q_gen_3758
<z>() -> q_gen_3758
<cons>(q_gen_3758, q_gen_3812) -> q_gen_3812
<nil>() -> q_gen_3812
<cons, cons>(q_gen_3747, q_gen_3746, q_gen_3745, q_gen_3722) -> q_gen_3722
<nil, cons>(q_gen_3758, q_gen_3812) -> q_gen_3722
<nil, nil>() -> q_gen_3722
<cons, z>(q_gen_3758, q_gen_3812) -> q_gen_3745
<nil, s>(q_gen_3758) -> q_gen_3745
<nil, z>() -> q_gen_3745
<s, cons>(q_gen_3747, q_gen_3746) -> q_gen_3746
<s, nil>(q_gen_3758) -> q_gen_3746
<z, cons>(q_gen_3758, q_gen_3812) -> q_gen_3746
<z, nil>() -> q_gen_3746
<s, s>(q_gen_3747) -> q_gen_3747
<s, z>(q_gen_3758) -> q_gen_3747
<z, s>(q_gen_3758) -> q_gen_3747
<z, z>() -> q_gen_3747
}

Datatype: <natlist, natlist>
Convolution form: complete
}}}

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

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([_qea, cons(h1, nil), _rea]) /\ reverse([t1, _qea])) -> reverse([cons(h1, t1), _rea]) -> 33  ;  (append([t1, l2, _lea])) -> append([cons(h1, t1), l2, cons(h1, _lea)]) -> 31  ;  (length([_afa, _bfa]) /\ length([l1, _zea]) /\ reverse([l1, _afa])) -> leq([_zea, _bfa]) -> 25  ;  (length([ll, _vea])) -> length([cons(x, ll), s(_vea)]) -> 26  ;  (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: Yes: ((append([_qea, cons(h1, nil), _rea]) /\ reverse([t1, _qea])) -> reverse([cons(h1, t1), _rea]), {
_qea -> cons(s(z), nil)  ;  _rea -> cons(s(z), cons(z, nil))  ;  h1 -> z  ;  t1 -> cons(z, nil)
})

-------------------------------------------
Step 35, which took 0.180204 s (model generation: 0.023988,  model checking: 0.156216):

Model:
|_
{
append -> 
{{{
Q={q_gen_3727, q_gen_3732, q_gen_3733, q_gen_3734, q_gen_3735, q_gen_3740, q_gen_3764, q_gen_3797, q_gen_3798, q_gen_3799, q_gen_3800, q_gen_3801, q_gen_3802, q_gen_3803},
Q_f={q_gen_3727},
Delta=
{
<s>(q_gen_3740) -> q_gen_3740
<z>() -> q_gen_3740
<cons>(q_gen_3740, q_gen_3764) -> q_gen_3764
<nil>() -> q_gen_3764
<cons, cons>(q_gen_3735, q_gen_3734, q_gen_3733, q_gen_3732) -> q_gen_3732
<nil, cons>(q_gen_3740, q_gen_3764) -> q_gen_3732
<nil, nil>() -> q_gen_3732
<cons, s>(q_gen_3735, q_gen_3733) -> q_gen_3733
<cons, z>(q_gen_3740, q_gen_3764) -> q_gen_3733
<nil, s>(q_gen_3740) -> q_gen_3733
<nil, z>() -> q_gen_3733
<s, cons>(q_gen_3735, q_gen_3734) -> q_gen_3734
<s, nil>(q_gen_3740) -> q_gen_3734
<z, cons>(q_gen_3740, q_gen_3764) -> q_gen_3734
<z, nil>() -> q_gen_3734
<s, s>(q_gen_3735) -> q_gen_3735
<s, z>(q_gen_3740) -> q_gen_3735
<z, s>(q_gen_3740) -> q_gen_3735
<z, z>() -> q_gen_3735
<cons, cons, cons>(q_gen_3803, q_gen_3802, q_gen_3801, q_gen_3800, q_gen_3799, q_gen_3798, q_gen_3797, q_gen_3727) -> q_gen_3727
<cons, nil, cons>(q_gen_3735, q_gen_3734, q_gen_3733, q_gen_3732) -> q_gen_3727
<nil, cons, cons>(q_gen_3735, q_gen_3734, q_gen_3733, q_gen_3732) -> q_gen_3727
<nil, nil, cons>(q_gen_3740, q_gen_3764) -> q_gen_3727
<nil, nil, nil>() -> q_gen_3727
<nil, nil, s>(q_gen_3740) -> q_gen_3797
<nil, nil, z>() -> q_gen_3797
<nil, s, cons>(q_gen_3735, q_gen_3734) -> q_gen_3798
<nil, z, cons>(q_gen_3740, q_gen_3764) -> q_gen_3798
<nil, s, s>(q_gen_3735) -> q_gen_3799
<nil, s, z>(q_gen_3740) -> q_gen_3799
<nil, z, s>(q_gen_3740) -> q_gen_3799
<nil, z, z>() -> q_gen_3799
<s, nil, cons>(q_gen_3735, q_gen_3734) -> q_gen_3800
<z, nil, cons>(q_gen_3740, q_gen_3764) -> q_gen_3800
<s, nil, s>(q_gen_3735) -> q_gen_3801
<z, nil, z>() -> q_gen_3801
<s, s, cons>(q_gen_3803, q_gen_3802) -> q_gen_3802
<s, z, cons>(q_gen_3735, q_gen_3734) -> q_gen_3802
<s, z, nil>(q_gen_3740) -> q_gen_3802
<z, s, cons>(q_gen_3735, q_gen_3734) -> q_gen_3802
<z, z, cons>(q_gen_3740, q_gen_3764) -> q_gen_3802
<z, z, nil>() -> q_gen_3802
<s, s, s>(q_gen_3803) -> q_gen_3803
<s, z, s>(q_gen_3735) -> q_gen_3803
<s, z, z>(q_gen_3740) -> q_gen_3803
<z, s, z>(q_gen_3740) -> q_gen_3803
<z, z, z>() -> q_gen_3803
}

Datatype: <natlist, natlist, natlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_3726, q_gen_3730, q_gen_3750},
Q_f={q_gen_3726},
Delta=
{
<s>(q_gen_3750) -> q_gen_3750
<z>() -> q_gen_3750
<cons, s>(q_gen_3730, q_gen_3726) -> q_gen_3726
<nil, z>() -> q_gen_3726
<s, s>(q_gen_3730) -> q_gen_3730
<s, z>(q_gen_3750) -> q_gen_3730
<z, s>(q_gen_3750) -> q_gen_3730
<z, z>() -> q_gen_3730
}

Datatype: <natlist, nat>
Convolution form: complete
}}}
  ;  leq -> 
{{{
Q={q_gen_3723, q_gen_3725},
Q_f={q_gen_3723},
Delta=
{
<s>(q_gen_3725) -> q_gen_3725
<z>() -> q_gen_3725
<s, s>(q_gen_3723) -> q_gen_3723
<z, s>(q_gen_3725) -> q_gen_3723
<z, z>() -> q_gen_3723
}

Datatype: <nat, nat>
Convolution form: complete
}}}
  ;  reverse -> 
{{{
Q={q_gen_3722, q_gen_3745, q_gen_3746, q_gen_3747, q_gen_3758, q_gen_3812},
Q_f={q_gen_3722},
Delta=
{
<s>(q_gen_3758) -> q_gen_3758
<z>() -> q_gen_3758
<cons>(q_gen_3758, q_gen_3812) -> q_gen_3812
<nil>() -> q_gen_3812
<cons, cons>(q_gen_3747, q_gen_3746, q_gen_3745, q_gen_3722) -> q_gen_3722
<nil, cons>(q_gen_3758, q_gen_3812) -> q_gen_3722
<nil, nil>() -> q_gen_3722
<cons, s>(q_gen_3747, q_gen_3745) -> q_gen_3745
<cons, z>(q_gen_3758, q_gen_3812) -> q_gen_3745
<nil, s>(q_gen_3758) -> q_gen_3745
<nil, z>() -> q_gen_3745
<s, cons>(q_gen_3747, q_gen_3746) -> q_gen_3746
<s, nil>(q_gen_3758) -> q_gen_3746
<z, cons>(q_gen_3758, q_gen_3812) -> q_gen_3746
<z, nil>() -> q_gen_3746
<s, s>(q_gen_3747) -> q_gen_3747
<s, z>(q_gen_3758) -> q_gen_3747
<z, s>(q_gen_3758) -> q_gen_3747
<z, z>() -> q_gen_3747
}

Datatype: <natlist, natlist>
Convolution form: complete
}}}

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

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([_qea, cons(h1, nil), _rea]) /\ reverse([t1, _qea])) -> reverse([cons(h1, t1), _rea]) -> 33  ;  (append([t1, l2, _lea])) -> append([cons(h1, t1), l2, cons(h1, _lea)]) -> 34  ;  (length([_afa, _bfa]) /\ length([l1, _zea]) /\ reverse([l1, _afa])) -> leq([_zea, _bfa]) -> 26  ;  (length([ll, _vea])) -> length([cons(x, ll), s(_vea)]) -> 27  ;  (leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 26  ;  (leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 26  ;  (leq([s(nn1), z])) -> BOT -> 26
}
Sat witness: Yes: ((append([t1, l2, _lea])) -> append([cons(h1, t1), l2, cons(h1, _lea)]), {
_lea -> cons(z, nil)  ;  h1 -> s(z)  ;  l2 -> cons(s(s(z)), nil)  ;  t1 -> nil
})

-------------------------------------------
Step 36, which took 0.400421 s (model generation: 0.035360,  model checking: 0.365061):

Model:
|_
{
append -> 
{{{
Q={q_gen_3727, q_gen_3732, q_gen_3733, q_gen_3734, q_gen_3735, q_gen_3740, q_gen_3764, q_gen_3797, q_gen_3798, q_gen_3799, q_gen_3800, q_gen_3801, q_gen_3802, q_gen_3803},
Q_f={q_gen_3727},
Delta=
{
<s>(q_gen_3740) -> q_gen_3740
<z>() -> q_gen_3740
<cons>(q_gen_3740, q_gen_3764) -> q_gen_3764
<nil>() -> q_gen_3764
<cons, cons>(q_gen_3735, q_gen_3734, q_gen_3733, q_gen_3732) -> q_gen_3732
<nil, cons>(q_gen_3740, q_gen_3764) -> q_gen_3732
<nil, nil>() -> q_gen_3732
<cons, s>(q_gen_3735, q_gen_3733) -> q_gen_3733
<cons, z>(q_gen_3740, q_gen_3764) -> q_gen_3733
<nil, s>(q_gen_3740) -> q_gen_3733
<nil, z>() -> q_gen_3733
<s, cons>(q_gen_3735, q_gen_3734) -> q_gen_3734
<s, nil>(q_gen_3740) -> q_gen_3734
<z, cons>(q_gen_3740, q_gen_3764) -> q_gen_3734
<z, nil>() -> q_gen_3734
<s, s>(q_gen_3735) -> q_gen_3735
<s, z>(q_gen_3740) -> q_gen_3735
<z, s>(q_gen_3740) -> q_gen_3735
<z, z>() -> q_gen_3735
<cons, cons, cons>(q_gen_3803, q_gen_3802, q_gen_3801, q_gen_3800, q_gen_3799, q_gen_3798, q_gen_3797, q_gen_3727) -> q_gen_3727
<cons, nil, cons>(q_gen_3735, q_gen_3734, q_gen_3733, q_gen_3732) -> q_gen_3727
<nil, cons, cons>(q_gen_3735, q_gen_3734, q_gen_3733, q_gen_3732) -> q_gen_3727
<nil, nil, cons>(q_gen_3740, q_gen_3764) -> q_gen_3727
<nil, nil, nil>() -> q_gen_3727
<nil, nil, s>(q_gen_3740) -> q_gen_3797
<nil, nil, z>() -> q_gen_3797
<nil, s, cons>(q_gen_3735, q_gen_3734) -> q_gen_3798
<nil, z, cons>(q_gen_3740, q_gen_3764) -> q_gen_3798
<nil, s, s>(q_gen_3735) -> q_gen_3799
<nil, s, z>(q_gen_3740) -> q_gen_3799
<nil, z, s>(q_gen_3740) -> q_gen_3799
<nil, z, z>() -> q_gen_3799
<s, nil, cons>(q_gen_3735, q_gen_3734) -> q_gen_3800
<z, nil, cons>(q_gen_3740, q_gen_3764) -> q_gen_3800
<s, nil, s>(q_gen_3735) -> q_gen_3801
<z, nil, z>() -> q_gen_3801
<s, s, cons>(q_gen_3803, q_gen_3802) -> q_gen_3802
<s, z, cons>(q_gen_3735, q_gen_3734) -> q_gen_3802
<s, z, nil>(q_gen_3740) -> q_gen_3802
<z, s, cons>(q_gen_3735, q_gen_3734) -> q_gen_3802
<z, s, nil>(q_gen_3740) -> q_gen_3802
<z, z, cons>(q_gen_3740, q_gen_3764) -> q_gen_3802
<z, z, nil>() -> q_gen_3802
<s, s, s>(q_gen_3803) -> q_gen_3803
<s, z, s>(q_gen_3735) -> q_gen_3803
<s, z, z>(q_gen_3740) -> q_gen_3803
<z, s, z>(q_gen_3740) -> q_gen_3803
<z, z, z>() -> q_gen_3803
}

Datatype: <natlist, natlist, natlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_3726, q_gen_3730, q_gen_3750},
Q_f={q_gen_3726},
Delta=
{
<s>(q_gen_3750) -> q_gen_3750
<z>() -> q_gen_3750
<cons, s>(q_gen_3730, q_gen_3726) -> q_gen_3726
<nil, z>() -> q_gen_3726
<s, s>(q_gen_3730) -> q_gen_3730
<s, z>(q_gen_3750) -> q_gen_3730
<z, s>(q_gen_3750) -> q_gen_3730
<z, z>() -> q_gen_3730
}

Datatype: <natlist, nat>
Convolution form: complete
}}}
  ;  leq -> 
{{{
Q={q_gen_3723, q_gen_3725},
Q_f={q_gen_3723},
Delta=
{
<s>(q_gen_3725) -> q_gen_3725
<z>() -> q_gen_3725
<s, s>(q_gen_3723) -> q_gen_3723
<z, s>(q_gen_3725) -> q_gen_3723
<z, z>() -> q_gen_3723
}

Datatype: <nat, nat>
Convolution form: complete
}}}
  ;  reverse -> 
{{{
Q={q_gen_3722, q_gen_3745, q_gen_3746, q_gen_3747, q_gen_3758, q_gen_3812},
Q_f={q_gen_3722},
Delta=
{
<s>(q_gen_3758) -> q_gen_3758
<z>() -> q_gen_3758
<cons>(q_gen_3758, q_gen_3812) -> q_gen_3812
<nil>() -> q_gen_3812
<cons, cons>(q_gen_3747, q_gen_3746, q_gen_3745, q_gen_3722) -> q_gen_3722
<nil, cons>(q_gen_3758, q_gen_3812) -> q_gen_3722
<nil, nil>() -> q_gen_3722
<cons, s>(q_gen_3747, q_gen_3745) -> q_gen_3745
<cons, z>(q_gen_3758, q_gen_3812) -> q_gen_3745
<nil, s>(q_gen_3758) -> q_gen_3745
<nil, z>() -> q_gen_3745
<s, cons>(q_gen_3747, q_gen_3746) -> q_gen_3746
<s, nil>(q_gen_3758) -> q_gen_3746
<z, cons>(q_gen_3758, q_gen_3812) -> q_gen_3746
<z, nil>() -> q_gen_3746
<s, s>(q_gen_3747) -> q_gen_3747
<s, z>(q_gen_3758) -> q_gen_3747
<z, s>(q_gen_3758) -> q_gen_3747
<z, z>() -> q_gen_3747
}

Datatype: <natlist, natlist>
Convolution form: complete
}}}

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

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([_qea, cons(h1, nil), _rea]) /\ reverse([t1, _qea])) -> reverse([cons(h1, t1), _rea]) -> 34  ;  (append([t1, l2, _lea])) -> append([cons(h1, t1), l2, cons(h1, _lea)]) -> 37  ;  (length([_afa, _bfa]) /\ length([l1, _zea]) /\ reverse([l1, _afa])) -> leq([_zea, _bfa]) -> 27  ;  (length([ll, _vea])) -> length([cons(x, ll), s(_vea)]) -> 28  ;  (leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 27  ;  (leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 27  ;  (leq([s(nn1), z])) -> BOT -> 27
}
Sat witness: Yes: ((append([t1, l2, _lea])) -> append([cons(h1, t1), l2, cons(h1, _lea)]), {
_lea -> cons(z, nil)  ;  h1 -> s(s(z))  ;  l2 -> cons(s(s(z)), nil)  ;  t1 -> nil
})

-------------------------------------------
Step 37, which took 0.544164 s (model generation: 0.030824,  model checking: 0.513340):

Model:
|_
{
append -> 
{{{
Q={q_gen_3727, q_gen_3732, q_gen_3733, q_gen_3734, q_gen_3735, q_gen_3740, q_gen_3764, q_gen_3797, q_gen_3798, q_gen_3799, q_gen_3800, q_gen_3801, q_gen_3802, q_gen_3803},
Q_f={q_gen_3727},
Delta=
{
<s>(q_gen_3740) -> q_gen_3740
<z>() -> q_gen_3740
<cons>(q_gen_3740, q_gen_3764) -> q_gen_3764
<nil>() -> q_gen_3764
<cons, cons>(q_gen_3735, q_gen_3734, q_gen_3733, q_gen_3732) -> q_gen_3732
<nil, cons>(q_gen_3740, q_gen_3764) -> q_gen_3732
<nil, nil>() -> q_gen_3732
<cons, s>(q_gen_3735, q_gen_3733) -> q_gen_3733
<cons, z>(q_gen_3740, q_gen_3764) -> q_gen_3733
<nil, s>(q_gen_3740) -> q_gen_3733
<nil, z>() -> q_gen_3733
<s, cons>(q_gen_3735, q_gen_3734) -> q_gen_3734
<s, nil>(q_gen_3740) -> q_gen_3734
<z, cons>(q_gen_3740, q_gen_3764) -> q_gen_3734
<z, nil>() -> q_gen_3734
<s, s>(q_gen_3735) -> q_gen_3735
<s, z>(q_gen_3740) -> q_gen_3735
<z, s>(q_gen_3740) -> q_gen_3735
<z, z>() -> q_gen_3735
<cons, cons, cons>(q_gen_3803, q_gen_3802, q_gen_3801, q_gen_3800, q_gen_3799, q_gen_3798, q_gen_3797, q_gen_3727) -> q_gen_3727
<cons, nil, cons>(q_gen_3735, q_gen_3734, q_gen_3733, q_gen_3732) -> q_gen_3727
<nil, cons, cons>(q_gen_3735, q_gen_3734, q_gen_3733, q_gen_3732) -> q_gen_3727
<nil, nil, cons>(q_gen_3740, q_gen_3764) -> q_gen_3727
<nil, nil, nil>() -> q_gen_3727
<nil, nil, s>(q_gen_3740) -> q_gen_3797
<nil, nil, z>() -> q_gen_3797
<nil, s, cons>(q_gen_3735, q_gen_3734) -> q_gen_3798
<nil, z, cons>(q_gen_3740, q_gen_3764) -> q_gen_3798
<nil, s, s>(q_gen_3735) -> q_gen_3799
<nil, s, z>(q_gen_3740) -> q_gen_3799
<nil, z, s>(q_gen_3740) -> q_gen_3799
<nil, z, z>() -> q_gen_3799
<s, nil, cons>(q_gen_3735, q_gen_3734) -> q_gen_3800
<z, nil, cons>(q_gen_3740, q_gen_3764) -> q_gen_3800
<s, nil, s>(q_gen_3735) -> q_gen_3801
<z, nil, z>() -> q_gen_3801
<s, s, cons>(q_gen_3803, q_gen_3802) -> q_gen_3802
<s, s, nil>(q_gen_3735) -> q_gen_3802
<s, z, cons>(q_gen_3735, q_gen_3734) -> q_gen_3802
<s, z, nil>(q_gen_3740) -> q_gen_3802
<z, s, cons>(q_gen_3735, q_gen_3734) -> q_gen_3802
<z, s, nil>(q_gen_3740) -> q_gen_3802
<z, z, cons>(q_gen_3740, q_gen_3764) -> q_gen_3802
<z, z, nil>() -> q_gen_3802
<s, s, s>(q_gen_3803) -> q_gen_3803
<s, s, z>(q_gen_3735) -> q_gen_3803
<s, z, s>(q_gen_3735) -> q_gen_3803
<s, z, z>(q_gen_3740) -> q_gen_3803
<z, s, z>(q_gen_3740) -> q_gen_3803
<z, z, z>() -> q_gen_3803
}

Datatype: <natlist, natlist, natlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_3726, q_gen_3730, q_gen_3750},
Q_f={q_gen_3726},
Delta=
{
<s>(q_gen_3750) -> q_gen_3750
<z>() -> q_gen_3750
<cons, s>(q_gen_3730, q_gen_3726) -> q_gen_3726
<nil, z>() -> q_gen_3726
<s, s>(q_gen_3730) -> q_gen_3730
<s, z>(q_gen_3750) -> q_gen_3730
<z, s>(q_gen_3750) -> q_gen_3730
<z, z>() -> q_gen_3730
}

Datatype: <natlist, nat>
Convolution form: complete
}}}
  ;  leq -> 
{{{
Q={q_gen_3723, q_gen_3725},
Q_f={q_gen_3723},
Delta=
{
<s>(q_gen_3725) -> q_gen_3725
<z>() -> q_gen_3725
<s, s>(q_gen_3723) -> q_gen_3723
<z, s>(q_gen_3725) -> q_gen_3723
<z, z>() -> q_gen_3723
}

Datatype: <nat, nat>
Convolution form: complete
}}}
  ;  reverse -> 
{{{
Q={q_gen_3722, q_gen_3745, q_gen_3746, q_gen_3747, q_gen_3758, q_gen_3812},
Q_f={q_gen_3722},
Delta=
{
<s>(q_gen_3758) -> q_gen_3758
<z>() -> q_gen_3758
<cons>(q_gen_3758, q_gen_3812) -> q_gen_3812
<nil>() -> q_gen_3812
<cons, cons>(q_gen_3747, q_gen_3746, q_gen_3745, q_gen_3722) -> q_gen_3722
<nil, cons>(q_gen_3758, q_gen_3812) -> q_gen_3722
<nil, nil>() -> q_gen_3722
<cons, s>(q_gen_3747, q_gen_3745) -> q_gen_3745
<cons, z>(q_gen_3758, q_gen_3812) -> q_gen_3745
<nil, s>(q_gen_3758) -> q_gen_3745
<nil, z>() -> q_gen_3745
<s, cons>(q_gen_3747, q_gen_3746) -> q_gen_3746
<s, nil>(q_gen_3758) -> q_gen_3746
<z, cons>(q_gen_3758, q_gen_3812) -> q_gen_3746
<z, nil>() -> q_gen_3746
<s, s>(q_gen_3747) -> q_gen_3747
<s, z>(q_gen_3758) -> q_gen_3747
<z, s>(q_gen_3758) -> q_gen_3747
<z, z>() -> q_gen_3747
}

Datatype: <natlist, natlist>
Convolution form: complete
}}}

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

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([_qea, cons(h1, nil), _rea]) /\ reverse([t1, _qea])) -> reverse([cons(h1, t1), _rea]) -> 35  ;  (append([t1, l2, _lea])) -> append([cons(h1, t1), l2, cons(h1, _lea)]) -> 40  ;  (length([_afa, _bfa]) /\ length([l1, _zea]) /\ reverse([l1, _afa])) -> leq([_zea, _bfa]) -> 28  ;  (length([ll, _vea])) -> length([cons(x, ll), s(_vea)]) -> 29  ;  (leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 28  ;  (leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 28  ;  (leq([s(nn1), z])) -> BOT -> 28
}
Sat witness: Yes: ((append([t1, l2, _lea])) -> append([cons(h1, t1), l2, cons(h1, _lea)]), {
_lea -> cons(s(z), nil)  ;  h1 -> s(z)  ;  l2 -> cons(s(z), nil)  ;  t1 -> nil
})

-------------------------------------------
Step 38, which took 0.560905 s (model generation: 0.034553,  model checking: 0.526352):

Model:
|_
{
append -> 
{{{
Q={q_gen_3727, q_gen_3732, q_gen_3733, q_gen_3734, q_gen_3735, q_gen_3740, q_gen_3764, q_gen_3797, q_gen_3798, q_gen_3799, q_gen_3800, q_gen_3801, q_gen_3802, q_gen_3803},
Q_f={q_gen_3727},
Delta=
{
<s>(q_gen_3740) -> q_gen_3740
<z>() -> q_gen_3740
<cons>(q_gen_3740, q_gen_3764) -> q_gen_3764
<nil>() -> q_gen_3764
<cons, cons>(q_gen_3735, q_gen_3734, q_gen_3733, q_gen_3732) -> q_gen_3732
<nil, cons>(q_gen_3740, q_gen_3764) -> q_gen_3732
<nil, nil>() -> q_gen_3732
<cons, s>(q_gen_3735, q_gen_3733) -> q_gen_3733
<cons, z>(q_gen_3740, q_gen_3764) -> q_gen_3733
<nil, s>(q_gen_3740) -> q_gen_3733
<nil, z>() -> q_gen_3733
<s, cons>(q_gen_3735, q_gen_3734) -> q_gen_3734
<s, nil>(q_gen_3740) -> q_gen_3734
<z, cons>(q_gen_3740, q_gen_3764) -> q_gen_3734
<z, nil>() -> q_gen_3734
<s, s>(q_gen_3735) -> q_gen_3735
<s, z>(q_gen_3740) -> q_gen_3735
<z, s>(q_gen_3740) -> q_gen_3735
<z, z>() -> q_gen_3735
<cons, cons, cons>(q_gen_3803, q_gen_3802, q_gen_3801, q_gen_3800, q_gen_3799, q_gen_3798, q_gen_3797, q_gen_3727) -> q_gen_3727
<cons, nil, cons>(q_gen_3735, q_gen_3734, q_gen_3733, q_gen_3732) -> q_gen_3727
<nil, cons, cons>(q_gen_3735, q_gen_3734, q_gen_3733, q_gen_3732) -> q_gen_3727
<nil, nil, cons>(q_gen_3740, q_gen_3764) -> q_gen_3727
<nil, nil, nil>() -> q_gen_3727
<nil, nil, s>(q_gen_3740) -> q_gen_3797
<nil, nil, z>() -> q_gen_3797
<nil, s, cons>(q_gen_3735, q_gen_3734) -> q_gen_3798
<nil, z, cons>(q_gen_3740, q_gen_3764) -> q_gen_3798
<nil, s, s>(q_gen_3735) -> q_gen_3799
<nil, s, z>(q_gen_3740) -> q_gen_3799
<nil, z, s>(q_gen_3740) -> q_gen_3799
<nil, z, z>() -> q_gen_3799
<s, nil, cons>(q_gen_3735, q_gen_3734) -> q_gen_3800
<z, nil, cons>(q_gen_3740, q_gen_3764) -> q_gen_3800
<s, nil, s>(q_gen_3735) -> q_gen_3801
<z, nil, z>() -> q_gen_3801
<s, s, cons>(q_gen_3803, q_gen_3802) -> q_gen_3802
<s, s, nil>(q_gen_3735) -> q_gen_3802
<s, z, cons>(q_gen_3735, q_gen_3734) -> q_gen_3802
<s, z, nil>(q_gen_3740) -> q_gen_3802
<z, s, cons>(q_gen_3735, q_gen_3734) -> q_gen_3802
<z, s, nil>(q_gen_3740) -> q_gen_3802
<z, z, cons>(q_gen_3740, q_gen_3764) -> q_gen_3802
<z, z, nil>() -> q_gen_3802
<s, s, s>(q_gen_3803) -> q_gen_3803
<s, s, z>(q_gen_3735) -> q_gen_3803
<s, z, s>(q_gen_3735) -> q_gen_3803
<s, z, z>(q_gen_3740) -> q_gen_3803
<z, s, z>(q_gen_3740) -> q_gen_3803
<z, z, s>(q_gen_3740) -> q_gen_3803
<z, z, z>() -> q_gen_3803
}

Datatype: <natlist, natlist, natlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_3726, q_gen_3730, q_gen_3750},
Q_f={q_gen_3726},
Delta=
{
<s>(q_gen_3750) -> q_gen_3750
<z>() -> q_gen_3750
<cons, s>(q_gen_3730, q_gen_3726) -> q_gen_3726
<nil, z>() -> q_gen_3726
<s, s>(q_gen_3730) -> q_gen_3730
<s, z>(q_gen_3750) -> q_gen_3730
<z, s>(q_gen_3750) -> q_gen_3730
<z, z>() -> q_gen_3730
}

Datatype: <natlist, nat>
Convolution form: complete
}}}
  ;  leq -> 
{{{
Q={q_gen_3723, q_gen_3725},
Q_f={q_gen_3723},
Delta=
{
<s>(q_gen_3725) -> q_gen_3725
<z>() -> q_gen_3725
<s, s>(q_gen_3723) -> q_gen_3723
<z, s>(q_gen_3725) -> q_gen_3723
<z, z>() -> q_gen_3723
}

Datatype: <nat, nat>
Convolution form: complete
}}}
  ;  reverse -> 
{{{
Q={q_gen_3722, q_gen_3745, q_gen_3746, q_gen_3747, q_gen_3758, q_gen_3812},
Q_f={q_gen_3722},
Delta=
{
<s>(q_gen_3758) -> q_gen_3758
<z>() -> q_gen_3758
<cons>(q_gen_3758, q_gen_3812) -> q_gen_3812
<nil>() -> q_gen_3812
<cons, cons>(q_gen_3747, q_gen_3746, q_gen_3745, q_gen_3722) -> q_gen_3722
<nil, cons>(q_gen_3758, q_gen_3812) -> q_gen_3722
<nil, nil>() -> q_gen_3722
<cons, s>(q_gen_3747, q_gen_3745) -> q_gen_3745
<cons, z>(q_gen_3758, q_gen_3812) -> q_gen_3745
<nil, s>(q_gen_3758) -> q_gen_3745
<nil, z>() -> q_gen_3745
<s, cons>(q_gen_3747, q_gen_3746) -> q_gen_3746
<s, nil>(q_gen_3758) -> q_gen_3746
<z, cons>(q_gen_3758, q_gen_3812) -> q_gen_3746
<z, nil>() -> q_gen_3746
<s, s>(q_gen_3747) -> q_gen_3747
<s, z>(q_gen_3758) -> q_gen_3747
<z, s>(q_gen_3758) -> q_gen_3747
<z, z>() -> q_gen_3747
}

Datatype: <natlist, natlist>
Convolution form: complete
}}}

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

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([_qea, cons(h1, nil), _rea]) /\ reverse([t1, _qea])) -> reverse([cons(h1, t1), _rea]) -> 36  ;  (append([t1, l2, _lea])) -> append([cons(h1, t1), l2, cons(h1, _lea)]) -> 43  ;  (length([_afa, _bfa]) /\ length([l1, _zea]) /\ reverse([l1, _afa])) -> leq([_zea, _bfa]) -> 29  ;  (length([ll, _vea])) -> length([cons(x, ll), s(_vea)]) -> 30  ;  (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: Yes: ((append([t1, l2, _lea])) -> append([cons(h1, t1), l2, cons(h1, _lea)]), {
_lea -> cons(s(z), nil)  ;  h1 -> s(z)  ;  l2 -> cons(s(s(z)), nil)  ;  t1 -> nil
})

-------------------------------------------
Step 39, which took 0.814265 s (model generation: 0.056895,  model checking: 0.757370):

Model:
|_
{
append -> 
{{{
Q={q_gen_3727, q_gen_3732, q_gen_3733, q_gen_3734, q_gen_3735, q_gen_3740, q_gen_3764, q_gen_3797, q_gen_3798, q_gen_3799, q_gen_3800, q_gen_3801, q_gen_3802, q_gen_3803},
Q_f={q_gen_3727},
Delta=
{
<s>(q_gen_3740) -> q_gen_3740
<z>() -> q_gen_3740
<cons>(q_gen_3740, q_gen_3764) -> q_gen_3764
<nil>() -> q_gen_3764
<cons, cons>(q_gen_3735, q_gen_3734, q_gen_3733, q_gen_3732) -> q_gen_3732
<nil, cons>(q_gen_3740, q_gen_3764) -> q_gen_3732
<nil, nil>() -> q_gen_3732
<cons, s>(q_gen_3735, q_gen_3733) -> q_gen_3733
<cons, z>(q_gen_3740, q_gen_3764) -> q_gen_3733
<nil, s>(q_gen_3740) -> q_gen_3733
<nil, z>() -> q_gen_3733
<s, cons>(q_gen_3735, q_gen_3734) -> q_gen_3734
<s, nil>(q_gen_3740) -> q_gen_3734
<z, cons>(q_gen_3740, q_gen_3764) -> q_gen_3734
<z, nil>() -> q_gen_3734
<s, s>(q_gen_3735) -> q_gen_3735
<s, z>(q_gen_3740) -> q_gen_3735
<z, s>(q_gen_3740) -> q_gen_3735
<z, z>() -> q_gen_3735
<cons, cons, cons>(q_gen_3803, q_gen_3802, q_gen_3801, q_gen_3800, q_gen_3799, q_gen_3798, q_gen_3797, q_gen_3727) -> q_gen_3727
<cons, nil, cons>(q_gen_3735, q_gen_3734, q_gen_3733, q_gen_3732) -> q_gen_3727
<nil, cons, cons>(q_gen_3735, q_gen_3734, q_gen_3733, q_gen_3732) -> q_gen_3727
<nil, nil, cons>(q_gen_3740, q_gen_3764) -> q_gen_3727
<nil, nil, nil>() -> q_gen_3727
<nil, nil, s>(q_gen_3740) -> q_gen_3797
<nil, nil, z>() -> q_gen_3797
<nil, s, cons>(q_gen_3735, q_gen_3734) -> q_gen_3798
<nil, z, cons>(q_gen_3740, q_gen_3764) -> q_gen_3798
<nil, s, s>(q_gen_3735) -> q_gen_3799
<nil, s, z>(q_gen_3740) -> q_gen_3799
<nil, z, s>(q_gen_3740) -> q_gen_3799
<nil, z, z>() -> q_gen_3799
<s, nil, cons>(q_gen_3735, q_gen_3734) -> q_gen_3800
<z, nil, cons>(q_gen_3740, q_gen_3764) -> q_gen_3800
<s, nil, s>(q_gen_3735) -> q_gen_3801
<z, nil, z>() -> q_gen_3801
<s, s, cons>(q_gen_3803, q_gen_3802) -> q_gen_3802
<s, s, nil>(q_gen_3735) -> q_gen_3802
<s, z, cons>(q_gen_3735, q_gen_3734) -> q_gen_3802
<s, z, nil>(q_gen_3740) -> q_gen_3802
<z, s, cons>(q_gen_3735, q_gen_3734) -> q_gen_3802
<z, s, nil>(q_gen_3740) -> q_gen_3802
<z, z, cons>(q_gen_3740, q_gen_3764) -> q_gen_3802
<z, z, nil>() -> q_gen_3802
<s, s, s>(q_gen_3803) -> q_gen_3803
<s, s, z>(q_gen_3735) -> q_gen_3803
<s, z, s>(q_gen_3735) -> q_gen_3803
<s, z, z>(q_gen_3740) -> q_gen_3803
<z, s, s>(q_gen_3735) -> q_gen_3803
<z, s, z>(q_gen_3740) -> q_gen_3803
<z, z, s>(q_gen_3740) -> q_gen_3803
<z, z, z>() -> q_gen_3803
}

Datatype: <natlist, natlist, natlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_3726, q_gen_3730, q_gen_3750},
Q_f={q_gen_3726},
Delta=
{
<s>(q_gen_3750) -> q_gen_3750
<z>() -> q_gen_3750
<cons, s>(q_gen_3730, q_gen_3726) -> q_gen_3726
<nil, z>() -> q_gen_3726
<s, s>(q_gen_3730) -> q_gen_3730
<s, z>(q_gen_3750) -> q_gen_3730
<z, s>(q_gen_3750) -> q_gen_3730
<z, z>() -> q_gen_3730
}

Datatype: <natlist, nat>
Convolution form: complete
}}}
  ;  leq -> 
{{{
Q={q_gen_3723, q_gen_3725},
Q_f={q_gen_3723},
Delta=
{
<s>(q_gen_3725) -> q_gen_3725
<z>() -> q_gen_3725
<s, s>(q_gen_3723) -> q_gen_3723
<z, s>(q_gen_3725) -> q_gen_3723
<z, z>() -> q_gen_3723
}

Datatype: <nat, nat>
Convolution form: complete
}}}
  ;  reverse -> 
{{{
Q={q_gen_3722, q_gen_3745, q_gen_3746, q_gen_3747, q_gen_3758, q_gen_3812},
Q_f={q_gen_3722},
Delta=
{
<s>(q_gen_3758) -> q_gen_3758
<z>() -> q_gen_3758
<cons>(q_gen_3758, q_gen_3812) -> q_gen_3812
<nil>() -> q_gen_3812
<cons, cons>(q_gen_3747, q_gen_3746, q_gen_3745, q_gen_3722) -> q_gen_3722
<nil, cons>(q_gen_3758, q_gen_3812) -> q_gen_3722
<nil, nil>() -> q_gen_3722
<cons, s>(q_gen_3747, q_gen_3745) -> q_gen_3745
<cons, z>(q_gen_3758, q_gen_3812) -> q_gen_3745
<nil, s>(q_gen_3758) -> q_gen_3745
<nil, z>() -> q_gen_3745
<s, cons>(q_gen_3747, q_gen_3746) -> q_gen_3746
<s, nil>(q_gen_3758) -> q_gen_3746
<z, cons>(q_gen_3758, q_gen_3812) -> q_gen_3746
<z, nil>() -> q_gen_3746
<s, s>(q_gen_3747) -> q_gen_3747
<s, z>(q_gen_3758) -> q_gen_3747
<z, s>(q_gen_3758) -> q_gen_3747
<z, z>() -> q_gen_3747
}

Datatype: <natlist, natlist>
Convolution form: complete
}}}

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

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([_qea, cons(h1, nil), _rea]) /\ reverse([t1, _qea])) -> reverse([cons(h1, t1), _rea]) -> 37  ;  (append([t1, l2, _lea])) -> append([cons(h1, t1), l2, cons(h1, _lea)]) -> 46  ;  (length([_afa, _bfa]) /\ length([l1, _zea]) /\ reverse([l1, _afa])) -> leq([_zea, _bfa]) -> 30  ;  (length([ll, _vea])) -> length([cons(x, ll), s(_vea)]) -> 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: Yes: ((append([t1, l2, _lea])) -> append([cons(h1, t1), l2, cons(h1, _lea)]), {
_lea -> cons(z, cons(z, nil))  ;  h1 -> z  ;  l2 -> cons(z, cons(z, nil))  ;  t1 -> nil
})

-------------------------------------------
Step 40, which took 1.705466 s (model generation: 0.067573,  model checking: 1.637893):

Model:
|_
{
append -> 
{{{
Q={q_gen_3727, q_gen_3732, q_gen_3733, q_gen_3734, q_gen_3735, q_gen_3740, q_gen_3764, q_gen_3797, q_gen_3798, q_gen_3799, q_gen_3800, q_gen_3801, q_gen_3802, q_gen_3803},
Q_f={q_gen_3727},
Delta=
{
<s>(q_gen_3740) -> q_gen_3740
<z>() -> q_gen_3740
<cons>(q_gen_3740, q_gen_3764) -> q_gen_3764
<nil>() -> q_gen_3764
<cons, cons>(q_gen_3735, q_gen_3734, q_gen_3733, q_gen_3732) -> q_gen_3732
<nil, cons>(q_gen_3740, q_gen_3764) -> q_gen_3732
<nil, nil>() -> q_gen_3732
<cons, s>(q_gen_3735, q_gen_3733) -> q_gen_3733
<cons, z>(q_gen_3740, q_gen_3764) -> q_gen_3733
<nil, s>(q_gen_3740) -> q_gen_3733
<nil, z>() -> q_gen_3733
<s, cons>(q_gen_3735, q_gen_3734) -> q_gen_3734
<s, nil>(q_gen_3740) -> q_gen_3734
<z, cons>(q_gen_3740, q_gen_3764) -> q_gen_3734
<z, nil>() -> q_gen_3734
<s, s>(q_gen_3735) -> q_gen_3735
<s, z>(q_gen_3740) -> q_gen_3735
<z, s>(q_gen_3740) -> q_gen_3735
<z, z>() -> q_gen_3735
<cons, cons, cons>(q_gen_3803, q_gen_3802, q_gen_3801, q_gen_3800, q_gen_3799, q_gen_3798, q_gen_3797, q_gen_3727) -> q_gen_3727
<cons, nil, cons>(q_gen_3735, q_gen_3734, q_gen_3733, q_gen_3732) -> q_gen_3727
<nil, cons, cons>(q_gen_3735, q_gen_3734, q_gen_3733, q_gen_3732) -> q_gen_3727
<nil, nil, cons>(q_gen_3740, q_gen_3764) -> q_gen_3727
<nil, nil, nil>() -> q_gen_3727
<nil, cons, z>(q_gen_3740, q_gen_3764) -> q_gen_3797
<nil, nil, s>(q_gen_3740) -> q_gen_3797
<nil, nil, z>() -> q_gen_3797
<nil, s, cons>(q_gen_3735, q_gen_3734) -> q_gen_3798
<nil, z, cons>(q_gen_3740, q_gen_3764) -> q_gen_3798
<nil, s, s>(q_gen_3735) -> q_gen_3799
<nil, s, z>(q_gen_3740) -> q_gen_3799
<nil, z, s>(q_gen_3740) -> q_gen_3799
<nil, z, z>() -> q_gen_3799
<s, nil, cons>(q_gen_3735, q_gen_3734) -> q_gen_3800
<z, cons, cons>(q_gen_3735, q_gen_3734, q_gen_3733, q_gen_3732) -> q_gen_3800
<z, nil, cons>(q_gen_3740, q_gen_3764) -> q_gen_3800
<s, nil, s>(q_gen_3735) -> q_gen_3801
<z, cons, z>(q_gen_3740, q_gen_3764) -> q_gen_3801
<z, nil, z>() -> q_gen_3801
<s, s, cons>(q_gen_3803, q_gen_3802) -> q_gen_3802
<s, s, nil>(q_gen_3735) -> q_gen_3802
<s, z, cons>(q_gen_3735, q_gen_3734) -> q_gen_3802
<s, z, nil>(q_gen_3740) -> q_gen_3802
<z, s, cons>(q_gen_3735, q_gen_3734) -> q_gen_3802
<z, s, nil>(q_gen_3740) -> q_gen_3802
<z, z, cons>(q_gen_3740, q_gen_3764) -> q_gen_3802
<z, z, nil>() -> q_gen_3802
<s, s, s>(q_gen_3803) -> q_gen_3803
<s, s, z>(q_gen_3735) -> q_gen_3803
<s, z, s>(q_gen_3735) -> q_gen_3803
<s, z, z>(q_gen_3740) -> q_gen_3803
<z, s, s>(q_gen_3735) -> q_gen_3803
<z, s, z>(q_gen_3740) -> q_gen_3803
<z, z, s>(q_gen_3740) -> q_gen_3803
<z, z, z>() -> q_gen_3803
}

Datatype: <natlist, natlist, natlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_3726, q_gen_3730, q_gen_3750},
Q_f={q_gen_3726},
Delta=
{
<s>(q_gen_3750) -> q_gen_3750
<z>() -> q_gen_3750
<cons, s>(q_gen_3730, q_gen_3726) -> q_gen_3726
<nil, z>() -> q_gen_3726
<s, s>(q_gen_3730) -> q_gen_3730
<s, z>(q_gen_3750) -> q_gen_3730
<z, s>(q_gen_3750) -> q_gen_3730
<z, z>() -> q_gen_3730
}

Datatype: <natlist, nat>
Convolution form: complete
}}}
  ;  leq -> 
{{{
Q={q_gen_3723, q_gen_3725},
Q_f={q_gen_3723},
Delta=
{
<s>(q_gen_3725) -> q_gen_3725
<z>() -> q_gen_3725
<s, s>(q_gen_3723) -> q_gen_3723
<z, s>(q_gen_3725) -> q_gen_3723
<z, z>() -> q_gen_3723
}

Datatype: <nat, nat>
Convolution form: complete
}}}
  ;  reverse -> 
{{{
Q={q_gen_3722, q_gen_3745, q_gen_3746, q_gen_3747, q_gen_3758, q_gen_3812},
Q_f={q_gen_3722},
Delta=
{
<s>(q_gen_3758) -> q_gen_3758
<z>() -> q_gen_3758
<cons>(q_gen_3758, q_gen_3812) -> q_gen_3812
<nil>() -> q_gen_3812
<cons, cons>(q_gen_3747, q_gen_3746, q_gen_3745, q_gen_3722) -> q_gen_3722
<nil, cons>(q_gen_3758, q_gen_3812) -> q_gen_3722
<nil, nil>() -> q_gen_3722
<cons, s>(q_gen_3747, q_gen_3745) -> q_gen_3745
<cons, z>(q_gen_3758, q_gen_3812) -> q_gen_3745
<nil, s>(q_gen_3758) -> q_gen_3745
<nil, z>() -> q_gen_3745
<s, cons>(q_gen_3747, q_gen_3746) -> q_gen_3746
<s, nil>(q_gen_3758) -> q_gen_3746
<z, cons>(q_gen_3758, q_gen_3812) -> q_gen_3746
<z, nil>() -> q_gen_3746
<s, s>(q_gen_3747) -> q_gen_3747
<s, z>(q_gen_3758) -> q_gen_3747
<z, s>(q_gen_3758) -> q_gen_3747
<z, z>() -> q_gen_3747
}

Datatype: <natlist, natlist>
Convolution form: complete
}}}

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

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([_qea, cons(h1, nil), _rea]) /\ reverse([t1, _qea])) -> reverse([cons(h1, t1), _rea]) -> 38  ;  (append([t1, l2, _lea])) -> append([cons(h1, t1), l2, cons(h1, _lea)]) -> 49  ;  (length([_afa, _bfa]) /\ length([l1, _zea]) /\ reverse([l1, _afa])) -> leq([_zea, _bfa]) -> 31  ;  (length([ll, _vea])) -> length([cons(x, ll), s(_vea)]) -> 32  ;  (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: Yes: ((append([t1, l2, _lea])) -> append([cons(h1, t1), l2, cons(h1, _lea)]), {
_lea -> cons(z, cons(z, nil))  ;  h1 -> z  ;  l2 -> cons(z, nil)  ;  t1 -> cons(z, nil)
})

-------------------------------------------
Step 41, which took 0.081261 s (model generation: 0.075276,  model checking: 0.005985):

Model:
|_
{
append -> 
{{{
Q={q_gen_3727, q_gen_3732, q_gen_3733, q_gen_3734, q_gen_3735, q_gen_3740, q_gen_3764, q_gen_3797, q_gen_3798, q_gen_3799, q_gen_3800, q_gen_3801, q_gen_3802, q_gen_3803},
Q_f={q_gen_3727},
Delta=
{
<s>(q_gen_3740) -> q_gen_3740
<z>() -> q_gen_3740
<cons>(q_gen_3740, q_gen_3764) -> q_gen_3764
<nil>() -> q_gen_3764
<cons, cons>(q_gen_3735, q_gen_3734, q_gen_3733, q_gen_3732) -> q_gen_3732
<nil, cons>(q_gen_3740, q_gen_3764) -> q_gen_3732
<nil, nil>() -> q_gen_3732
<cons, s>(q_gen_3735, q_gen_3733) -> q_gen_3733
<cons, z>(q_gen_3740, q_gen_3764) -> q_gen_3733
<nil, s>(q_gen_3740) -> q_gen_3733
<nil, z>() -> q_gen_3733
<s, cons>(q_gen_3735, q_gen_3734) -> q_gen_3734
<s, nil>(q_gen_3740) -> q_gen_3734
<z, cons>(q_gen_3740, q_gen_3764) -> q_gen_3734
<z, nil>() -> q_gen_3734
<s, s>(q_gen_3735) -> q_gen_3735
<s, z>(q_gen_3740) -> q_gen_3735
<z, s>(q_gen_3740) -> q_gen_3735
<z, z>() -> q_gen_3735
<cons, cons, cons>(q_gen_3803, q_gen_3802, q_gen_3801, q_gen_3800, q_gen_3799, q_gen_3798, q_gen_3797, q_gen_3727) -> q_gen_3727
<cons, nil, cons>(q_gen_3735, q_gen_3734, q_gen_3733, q_gen_3732) -> q_gen_3727
<nil, cons, cons>(q_gen_3735, q_gen_3734, q_gen_3733, q_gen_3732) -> q_gen_3727
<nil, nil, cons>(q_gen_3740, q_gen_3764) -> q_gen_3727
<nil, nil, nil>() -> q_gen_3727
<cons, nil, z>(q_gen_3740, q_gen_3764) -> q_gen_3797
<nil, cons, z>(q_gen_3740, q_gen_3764) -> q_gen_3797
<nil, nil, s>(q_gen_3740) -> q_gen_3797
<nil, nil, z>() -> q_gen_3797
<cons, z, cons>(q_gen_3735, q_gen_3734, q_gen_3733, q_gen_3732) -> q_gen_3798
<nil, s, cons>(q_gen_3735, q_gen_3734) -> q_gen_3798
<nil, z, cons>(q_gen_3740, q_gen_3764) -> q_gen_3798
<cons, z, z>(q_gen_3740, q_gen_3764) -> q_gen_3799
<nil, s, s>(q_gen_3735) -> q_gen_3799
<nil, s, z>(q_gen_3740) -> q_gen_3799
<nil, z, s>(q_gen_3740) -> q_gen_3799
<nil, z, z>() -> q_gen_3799
<s, nil, cons>(q_gen_3735, q_gen_3734) -> q_gen_3800
<z, cons, cons>(q_gen_3735, q_gen_3734, q_gen_3733, q_gen_3732) -> q_gen_3800
<z, nil, cons>(q_gen_3740, q_gen_3764) -> q_gen_3800
<s, nil, s>(q_gen_3735) -> q_gen_3801
<z, cons, z>(q_gen_3740, q_gen_3764) -> q_gen_3801
<z, nil, z>() -> q_gen_3801
<s, s, cons>(q_gen_3803, q_gen_3802) -> q_gen_3802
<s, s, nil>(q_gen_3735) -> q_gen_3802
<s, z, cons>(q_gen_3735, q_gen_3734) -> q_gen_3802
<s, z, nil>(q_gen_3740) -> q_gen_3802
<z, s, cons>(q_gen_3735, q_gen_3734) -> q_gen_3802
<z, s, nil>(q_gen_3740) -> q_gen_3802
<z, z, cons>(q_gen_3740, q_gen_3764) -> q_gen_3802
<z, z, nil>() -> q_gen_3802
<s, s, s>(q_gen_3803) -> q_gen_3803
<s, s, z>(q_gen_3735) -> q_gen_3803
<s, z, s>(q_gen_3735) -> q_gen_3803
<s, z, z>(q_gen_3740) -> q_gen_3803
<z, s, s>(q_gen_3735) -> q_gen_3803
<z, s, z>(q_gen_3740) -> q_gen_3803
<z, z, s>(q_gen_3740) -> q_gen_3803
<z, z, z>() -> q_gen_3803
}

Datatype: <natlist, natlist, natlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_3726, q_gen_3730, q_gen_3750},
Q_f={q_gen_3726},
Delta=
{
<s>(q_gen_3750) -> q_gen_3750
<z>() -> q_gen_3750
<cons, s>(q_gen_3730, q_gen_3726) -> q_gen_3726
<nil, z>() -> q_gen_3726
<s, s>(q_gen_3730) -> q_gen_3730
<s, z>(q_gen_3750) -> q_gen_3730
<z, s>(q_gen_3750) -> q_gen_3730
<z, z>() -> q_gen_3730
}

Datatype: <natlist, nat>
Convolution form: complete
}}}
  ;  leq -> 
{{{
Q={q_gen_3723, q_gen_3725},
Q_f={q_gen_3723},
Delta=
{
<s>(q_gen_3725) -> q_gen_3725
<z>() -> q_gen_3725
<s, s>(q_gen_3723) -> q_gen_3723
<z, s>(q_gen_3725) -> q_gen_3723
<z, z>() -> q_gen_3723
}

Datatype: <nat, nat>
Convolution form: complete
}}}
  ;  reverse -> 
{{{
Q={q_gen_3722, q_gen_3745, q_gen_3746, q_gen_3747, q_gen_3758, q_gen_3812},
Q_f={q_gen_3722},
Delta=
{
<s>(q_gen_3758) -> q_gen_3758
<z>() -> q_gen_3758
<cons>(q_gen_3758, q_gen_3812) -> q_gen_3812
<nil>() -> q_gen_3812
<cons, cons>(q_gen_3747, q_gen_3746, q_gen_3745, q_gen_3722) -> q_gen_3722
<nil, cons>(q_gen_3758, q_gen_3812) -> q_gen_3722
<nil, nil>() -> q_gen_3722
<cons, s>(q_gen_3747, q_gen_3745) -> q_gen_3745
<cons, z>(q_gen_3758, q_gen_3812) -> q_gen_3745
<nil, s>(q_gen_3758) -> q_gen_3745
<nil, z>() -> q_gen_3745
<s, cons>(q_gen_3747, q_gen_3746) -> q_gen_3746
<s, nil>(q_gen_3758) -> q_gen_3746
<z, cons>(q_gen_3758, q_gen_3812) -> q_gen_3746
<z, nil>() -> q_gen_3746
<s, s>(q_gen_3747) -> q_gen_3747
<s, z>(q_gen_3758) -> q_gen_3747
<z, s>(q_gen_3758) -> q_gen_3747
<z, z>() -> q_gen_3747
}

Datatype: <natlist, natlist>
Convolution form: complete
}}}

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

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([_qea, cons(h1, nil), _rea]) /\ reverse([t1, _qea])) -> reverse([cons(h1, t1), _rea]) -> 41  ;  (append([t1, l2, _lea])) -> append([cons(h1, t1), l2, cons(h1, _lea)]) -> 49  ;  (length([_afa, _bfa]) /\ length([l1, _zea]) /\ reverse([l1, _afa])) -> leq([_zea, _bfa]) -> 32  ;  (length([ll, _vea])) -> length([cons(x, ll), s(_vea)]) -> 33  ;  (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: Yes: ((append([_qea, cons(h1, nil), _rea]) /\ reverse([t1, _qea])) -> reverse([cons(h1, t1), _rea]), {
_qea -> cons(z, cons(z, nil))  ;  _rea -> cons(z, cons(z, nil))  ;  h1 -> z  ;  t1 -> cons(z, cons(z, nil))
})

-------------------------------------------
Step 42, which took 0.091089 s (model generation: 0.088712,  model checking: 0.002377):

Model:
|_
{
append -> 
{{{
Q={q_gen_3727, q_gen_3732, q_gen_3733, q_gen_3734, q_gen_3735, q_gen_3740, q_gen_3764, q_gen_3797, q_gen_3798, q_gen_3799, q_gen_3800, q_gen_3801, q_gen_3802, q_gen_3803},
Q_f={q_gen_3727},
Delta=
{
<s>(q_gen_3740) -> q_gen_3740
<z>() -> q_gen_3740
<cons>(q_gen_3740, q_gen_3764) -> q_gen_3764
<nil>() -> q_gen_3764
<cons, cons>(q_gen_3735, q_gen_3734, q_gen_3733, q_gen_3732) -> q_gen_3732
<nil, cons>(q_gen_3740, q_gen_3764) -> q_gen_3732
<nil, nil>() -> q_gen_3732
<cons, s>(q_gen_3735, q_gen_3733) -> q_gen_3733
<cons, z>(q_gen_3740, q_gen_3764) -> q_gen_3733
<nil, s>(q_gen_3740) -> q_gen_3733
<nil, z>() -> q_gen_3733
<s, cons>(q_gen_3735, q_gen_3734) -> q_gen_3734
<s, nil>(q_gen_3740) -> q_gen_3734
<z, cons>(q_gen_3740, q_gen_3764) -> q_gen_3734
<z, nil>() -> q_gen_3734
<s, s>(q_gen_3735) -> q_gen_3735
<s, z>(q_gen_3740) -> q_gen_3735
<z, s>(q_gen_3740) -> q_gen_3735
<z, z>() -> q_gen_3735
<cons, cons, cons>(q_gen_3803, q_gen_3802, q_gen_3801, q_gen_3800, q_gen_3799, q_gen_3798, q_gen_3797, q_gen_3727) -> q_gen_3727
<cons, nil, cons>(q_gen_3735, q_gen_3734, q_gen_3733, q_gen_3732) -> q_gen_3727
<nil, cons, cons>(q_gen_3735, q_gen_3734, q_gen_3733, q_gen_3732) -> q_gen_3727
<nil, nil, cons>(q_gen_3740, q_gen_3764) -> q_gen_3727
<nil, nil, nil>() -> q_gen_3727
<cons, nil, z>(q_gen_3740, q_gen_3764) -> q_gen_3797
<nil, cons, z>(q_gen_3740, q_gen_3764) -> q_gen_3797
<nil, nil, s>(q_gen_3740) -> q_gen_3797
<nil, nil, z>() -> q_gen_3797
<cons, z, cons>(q_gen_3735, q_gen_3734, q_gen_3733, q_gen_3732) -> q_gen_3798
<nil, s, cons>(q_gen_3735, q_gen_3734) -> q_gen_3798
<nil, z, cons>(q_gen_3740, q_gen_3764) -> q_gen_3798
<cons, z, z>(q_gen_3740, q_gen_3764) -> q_gen_3799
<nil, s, s>(q_gen_3735) -> q_gen_3799
<nil, s, z>(q_gen_3740) -> q_gen_3799
<nil, z, s>(q_gen_3740) -> q_gen_3799
<nil, z, z>() -> q_gen_3799
<s, nil, cons>(q_gen_3735, q_gen_3734) -> q_gen_3800
<z, cons, cons>(q_gen_3735, q_gen_3734, q_gen_3733, q_gen_3732) -> q_gen_3800
<z, nil, cons>(q_gen_3740, q_gen_3764) -> q_gen_3800
<s, nil, s>(q_gen_3735) -> q_gen_3801
<z, cons, z>(q_gen_3740, q_gen_3764) -> q_gen_3801
<z, nil, z>() -> q_gen_3801
<s, s, cons>(q_gen_3803, q_gen_3802) -> q_gen_3802
<s, s, nil>(q_gen_3735) -> q_gen_3802
<s, z, cons>(q_gen_3735, q_gen_3734) -> q_gen_3802
<s, z, nil>(q_gen_3740) -> q_gen_3802
<z, s, cons>(q_gen_3735, q_gen_3734) -> q_gen_3802
<z, s, nil>(q_gen_3740) -> q_gen_3802
<z, z, cons>(q_gen_3740, q_gen_3764) -> q_gen_3802
<z, z, nil>() -> q_gen_3802
<s, s, s>(q_gen_3803) -> q_gen_3803
<s, s, z>(q_gen_3735) -> q_gen_3803
<s, z, s>(q_gen_3735) -> q_gen_3803
<s, z, z>(q_gen_3740) -> q_gen_3803
<z, s, s>(q_gen_3735) -> q_gen_3803
<z, s, z>(q_gen_3740) -> q_gen_3803
<z, z, s>(q_gen_3740) -> q_gen_3803
<z, z, z>() -> q_gen_3803
}

Datatype: <natlist, natlist, natlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_3726, q_gen_3730, q_gen_3750},
Q_f={q_gen_3726},
Delta=
{
<s>(q_gen_3750) -> q_gen_3750
<z>() -> q_gen_3750
<cons, s>(q_gen_3730, q_gen_3726) -> q_gen_3726
<nil, z>() -> q_gen_3726
<s, s>(q_gen_3730) -> q_gen_3730
<s, z>(q_gen_3750) -> q_gen_3730
<z, s>(q_gen_3750) -> q_gen_3730
<z, z>() -> q_gen_3730
}

Datatype: <natlist, nat>
Convolution form: complete
}}}
  ;  leq -> 
{{{
Q={q_gen_3723, q_gen_3725},
Q_f={q_gen_3723},
Delta=
{
<s>(q_gen_3725) -> q_gen_3725
<z>() -> q_gen_3725
<s, s>(q_gen_3723) -> q_gen_3723
<z, s>(q_gen_3725) -> q_gen_3723
<z, z>() -> q_gen_3723
}

Datatype: <nat, nat>
Convolution form: complete
}}}
  ;  reverse -> 
{{{
Q={q_gen_3722, q_gen_3745, q_gen_3746, q_gen_3747, q_gen_3758, q_gen_3812},
Q_f={q_gen_3722},
Delta=
{
<s>(q_gen_3758) -> q_gen_3758
<z>() -> q_gen_3758
<cons>(q_gen_3758, q_gen_3812) -> q_gen_3812
<nil>() -> q_gen_3812
<cons, cons>(q_gen_3747, q_gen_3746, q_gen_3745, q_gen_3722) -> q_gen_3722
<cons, nil>(q_gen_3758, q_gen_3812) -> q_gen_3722
<nil, cons>(q_gen_3758, q_gen_3812) -> q_gen_3722
<nil, nil>() -> q_gen_3722
<cons, s>(q_gen_3747, q_gen_3745) -> q_gen_3745
<cons, z>(q_gen_3758, q_gen_3812) -> q_gen_3745
<nil, s>(q_gen_3758) -> q_gen_3745
<nil, z>() -> q_gen_3745
<s, cons>(q_gen_3747, q_gen_3746) -> q_gen_3746
<s, nil>(q_gen_3758) -> q_gen_3746
<z, cons>(q_gen_3758, q_gen_3812) -> q_gen_3746
<z, nil>() -> q_gen_3746
<s, s>(q_gen_3747) -> q_gen_3747
<s, z>(q_gen_3758) -> q_gen_3747
<z, s>(q_gen_3758) -> q_gen_3747
<z, z>() -> q_gen_3747
}

Datatype: <natlist, natlist>
Convolution form: complete
}}}

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

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([_qea, cons(h1, nil), _rea]) /\ reverse([t1, _qea])) -> reverse([cons(h1, t1), _rea]) -> 41  ;  (append([t1, l2, _lea])) -> append([cons(h1, t1), l2, cons(h1, _lea)]) -> 49  ;  (length([_afa, _bfa]) /\ length([l1, _zea]) /\ reverse([l1, _afa])) -> leq([_zea, _bfa]) -> 35  ;  (length([ll, _vea])) -> length([cons(x, ll), s(_vea)]) -> 33  ;  (leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 33  ;  (leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 33  ;  (leq([s(nn1), z])) -> BOT -> 33
}
Sat witness: Yes: ((length([_afa, _bfa]) /\ length([l1, _zea]) /\ reverse([l1, _afa])) -> leq([_zea, _bfa]), {
_afa -> nil  ;  _bfa -> z  ;  _zea -> s(z)  ;  l1 -> cons(z, nil)
})

-------------------------------------------
Step 43, which took 0.091415 s (model generation: 0.089232,  model checking: 0.002183):

Model:
|_
{
append -> 
{{{
Q={q_gen_3727, q_gen_3732, q_gen_3733, q_gen_3734, q_gen_3735, q_gen_3740, q_gen_3764, q_gen_3797, q_gen_3798, q_gen_3799, q_gen_3800, q_gen_3801, q_gen_3802, q_gen_3803},
Q_f={q_gen_3727},
Delta=
{
<s>(q_gen_3740) -> q_gen_3740
<z>() -> q_gen_3740
<cons>(q_gen_3740, q_gen_3764) -> q_gen_3764
<nil>() -> q_gen_3764
<cons, cons>(q_gen_3735, q_gen_3734, q_gen_3733, q_gen_3732) -> q_gen_3732
<nil, cons>(q_gen_3740, q_gen_3764) -> q_gen_3732
<nil, nil>() -> q_gen_3732
<cons, s>(q_gen_3735, q_gen_3733) -> q_gen_3733
<cons, z>(q_gen_3740, q_gen_3764) -> q_gen_3733
<nil, s>(q_gen_3740) -> q_gen_3733
<nil, z>() -> q_gen_3733
<s, cons>(q_gen_3735, q_gen_3734) -> q_gen_3734
<s, nil>(q_gen_3740) -> q_gen_3734
<z, cons>(q_gen_3740, q_gen_3764) -> q_gen_3734
<z, nil>() -> q_gen_3734
<s, s>(q_gen_3735) -> q_gen_3735
<s, z>(q_gen_3740) -> q_gen_3735
<z, s>(q_gen_3740) -> q_gen_3735
<z, z>() -> q_gen_3735
<cons, cons, cons>(q_gen_3803, q_gen_3802, q_gen_3801, q_gen_3800, q_gen_3799, q_gen_3798, q_gen_3797, q_gen_3727) -> q_gen_3727
<cons, nil, cons>(q_gen_3735, q_gen_3734, q_gen_3733, q_gen_3732) -> q_gen_3727
<nil, cons, cons>(q_gen_3735, q_gen_3734, q_gen_3733, q_gen_3732) -> q_gen_3727
<nil, nil, cons>(q_gen_3740, q_gen_3764) -> q_gen_3727
<nil, nil, nil>() -> q_gen_3727
<cons, nil, z>(q_gen_3740, q_gen_3764) -> q_gen_3797
<nil, cons, z>(q_gen_3740, q_gen_3764) -> q_gen_3797
<nil, nil, s>(q_gen_3740) -> q_gen_3797
<nil, nil, z>() -> q_gen_3797
<cons, z, cons>(q_gen_3735, q_gen_3734, q_gen_3733, q_gen_3732) -> q_gen_3798
<nil, s, cons>(q_gen_3735, q_gen_3734) -> q_gen_3798
<nil, z, cons>(q_gen_3740, q_gen_3764) -> q_gen_3798
<cons, z, z>(q_gen_3740, q_gen_3764) -> q_gen_3799
<nil, s, s>(q_gen_3735) -> q_gen_3799
<nil, s, z>(q_gen_3740) -> q_gen_3799
<nil, z, s>(q_gen_3740) -> q_gen_3799
<nil, z, z>() -> q_gen_3799
<s, nil, cons>(q_gen_3735, q_gen_3734) -> q_gen_3800
<z, cons, cons>(q_gen_3735, q_gen_3734, q_gen_3733, q_gen_3732) -> q_gen_3800
<z, nil, cons>(q_gen_3740, q_gen_3764) -> q_gen_3800
<s, nil, s>(q_gen_3735) -> q_gen_3801
<z, cons, z>(q_gen_3740, q_gen_3764) -> q_gen_3801
<z, nil, z>() -> q_gen_3801
<s, s, cons>(q_gen_3803, q_gen_3802) -> q_gen_3802
<s, s, nil>(q_gen_3735) -> q_gen_3802
<s, z, cons>(q_gen_3735, q_gen_3734) -> q_gen_3802
<s, z, nil>(q_gen_3740) -> q_gen_3802
<z, s, cons>(q_gen_3735, q_gen_3734) -> q_gen_3802
<z, s, nil>(q_gen_3740) -> q_gen_3802
<z, z, cons>(q_gen_3740, q_gen_3764) -> q_gen_3802
<z, z, nil>() -> q_gen_3802
<s, s, s>(q_gen_3803) -> q_gen_3803
<s, s, z>(q_gen_3735) -> q_gen_3803
<s, z, s>(q_gen_3735) -> q_gen_3803
<s, z, z>(q_gen_3740) -> q_gen_3803
<z, s, s>(q_gen_3735) -> q_gen_3803
<z, s, z>(q_gen_3740) -> q_gen_3803
<z, z, s>(q_gen_3740) -> q_gen_3803
<z, z, z>() -> q_gen_3803
}

Datatype: <natlist, natlist, natlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_3726, q_gen_3730, q_gen_3750},
Q_f={q_gen_3726},
Delta=
{
<s>(q_gen_3750) -> q_gen_3750
<z>() -> q_gen_3750
<cons, s>(q_gen_3730, q_gen_3726) -> q_gen_3726
<nil, z>() -> q_gen_3726
<s, s>(q_gen_3730) -> q_gen_3730
<s, z>(q_gen_3750) -> q_gen_3730
<z, s>(q_gen_3750) -> q_gen_3730
<z, z>() -> q_gen_3730
}

Datatype: <natlist, nat>
Convolution form: complete
}}}
  ;  leq -> 
{{{
Q={q_gen_3723, q_gen_3725},
Q_f={q_gen_3723},
Delta=
{
<s>(q_gen_3725) -> q_gen_3725
<z>() -> q_gen_3725
<s, s>(q_gen_3723) -> q_gen_3723
<s, z>(q_gen_3725) -> q_gen_3723
<z, s>(q_gen_3725) -> q_gen_3723
<z, z>() -> q_gen_3723
}

Datatype: <nat, nat>
Convolution form: complete
}}}
  ;  reverse -> 
{{{
Q={q_gen_3722, q_gen_3745, q_gen_3746, q_gen_3747, q_gen_3758, q_gen_3812},
Q_f={q_gen_3722},
Delta=
{
<s>(q_gen_3758) -> q_gen_3758
<z>() -> q_gen_3758
<cons>(q_gen_3758, q_gen_3812) -> q_gen_3812
<nil>() -> q_gen_3812
<cons, cons>(q_gen_3747, q_gen_3746, q_gen_3745, q_gen_3722) -> q_gen_3722
<cons, nil>(q_gen_3758, q_gen_3812) -> q_gen_3722
<nil, cons>(q_gen_3758, q_gen_3812) -> q_gen_3722
<nil, nil>() -> q_gen_3722
<cons, s>(q_gen_3747, q_gen_3745) -> q_gen_3745
<cons, z>(q_gen_3758, q_gen_3812) -> q_gen_3745
<nil, s>(q_gen_3758) -> q_gen_3745
<nil, z>() -> q_gen_3745
<s, cons>(q_gen_3747, q_gen_3746) -> q_gen_3746
<s, nil>(q_gen_3758) -> q_gen_3746
<z, cons>(q_gen_3758, q_gen_3812) -> q_gen_3746
<z, nil>() -> q_gen_3746
<s, s>(q_gen_3747) -> q_gen_3747
<s, z>(q_gen_3758) -> q_gen_3747
<z, s>(q_gen_3758) -> q_gen_3747
<z, z>() -> q_gen_3747
}

Datatype: <natlist, natlist>
Convolution form: complete
}}}

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

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([_qea, cons(h1, nil), _rea]) /\ reverse([t1, _qea])) -> reverse([cons(h1, t1), _rea]) -> 41  ;  (append([t1, l2, _lea])) -> append([cons(h1, t1), l2, cons(h1, _lea)]) -> 49  ;  (length([_afa, _bfa]) /\ length([l1, _zea]) /\ reverse([l1, _afa])) -> leq([_zea, _bfa]) -> 35  ;  (length([ll, _vea])) -> length([cons(x, ll), s(_vea)]) -> 33  ;  (leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 33  ;  (leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 33  ;  (leq([s(nn1), z])) -> BOT -> 36
}
Sat witness: Yes: ((leq([s(nn1), z])) -> BOT, {
nn1 -> z
})

-------------------------------------------
Step 44, which took 0.180745 s (model generation: 0.177534,  model checking: 0.003211):

Model:
|_
{
append -> 
{{{
Q={q_gen_3727, q_gen_3732, q_gen_3733, q_gen_3734, q_gen_3735, q_gen_3740, q_gen_3764, q_gen_3797, q_gen_3798, q_gen_3799, q_gen_3800, q_gen_3801, q_gen_3802, q_gen_3803},
Q_f={q_gen_3727},
Delta=
{
<s>(q_gen_3740) -> q_gen_3740
<z>() -> q_gen_3740
<cons>(q_gen_3740, q_gen_3764) -> q_gen_3764
<nil>() -> q_gen_3764
<cons, cons>(q_gen_3735, q_gen_3734, q_gen_3733, q_gen_3732) -> q_gen_3732
<nil, cons>(q_gen_3740, q_gen_3764) -> q_gen_3732
<nil, nil>() -> q_gen_3732
<cons, s>(q_gen_3735, q_gen_3733) -> q_gen_3733
<cons, z>(q_gen_3740, q_gen_3764) -> q_gen_3733
<nil, s>(q_gen_3740) -> q_gen_3733
<nil, z>() -> q_gen_3733
<s, cons>(q_gen_3735, q_gen_3734) -> q_gen_3734
<s, nil>(q_gen_3740) -> q_gen_3734
<z, cons>(q_gen_3740, q_gen_3764) -> q_gen_3734
<z, nil>() -> q_gen_3734
<s, s>(q_gen_3735) -> q_gen_3735
<s, z>(q_gen_3740) -> q_gen_3735
<z, s>(q_gen_3740) -> q_gen_3735
<z, z>() -> q_gen_3735
<cons, cons, cons>(q_gen_3803, q_gen_3802, q_gen_3801, q_gen_3800, q_gen_3799, q_gen_3798, q_gen_3797, q_gen_3727) -> q_gen_3727
<cons, nil, cons>(q_gen_3735, q_gen_3734, q_gen_3733, q_gen_3732) -> q_gen_3727
<nil, cons, cons>(q_gen_3735, q_gen_3734, q_gen_3733, q_gen_3732) -> q_gen_3727
<nil, nil, cons>(q_gen_3740, q_gen_3764) -> q_gen_3727
<nil, nil, nil>() -> q_gen_3727
<cons, nil, z>(q_gen_3740, q_gen_3764) -> q_gen_3797
<nil, cons, z>(q_gen_3740, q_gen_3764) -> q_gen_3797
<nil, nil, s>(q_gen_3740) -> q_gen_3797
<nil, nil, z>() -> q_gen_3797
<cons, z, cons>(q_gen_3735, q_gen_3734, q_gen_3733, q_gen_3732) -> q_gen_3798
<nil, s, cons>(q_gen_3735, q_gen_3734) -> q_gen_3798
<nil, z, cons>(q_gen_3740, q_gen_3764) -> q_gen_3798
<cons, z, z>(q_gen_3740, q_gen_3764) -> q_gen_3799
<nil, s, s>(q_gen_3735) -> q_gen_3799
<nil, s, z>(q_gen_3740) -> q_gen_3799
<nil, z, s>(q_gen_3740) -> q_gen_3799
<nil, z, z>() -> q_gen_3799
<s, nil, cons>(q_gen_3735, q_gen_3734) -> q_gen_3800
<z, cons, cons>(q_gen_3735, q_gen_3734, q_gen_3733, q_gen_3732) -> q_gen_3800
<z, nil, cons>(q_gen_3740, q_gen_3764) -> q_gen_3800
<s, nil, s>(q_gen_3735) -> q_gen_3801
<z, cons, z>(q_gen_3740, q_gen_3764) -> q_gen_3801
<z, nil, z>() -> q_gen_3801
<s, s, cons>(q_gen_3803, q_gen_3802) -> q_gen_3802
<s, s, nil>(q_gen_3735) -> q_gen_3802
<s, z, cons>(q_gen_3735, q_gen_3734) -> q_gen_3802
<s, z, nil>(q_gen_3740) -> q_gen_3802
<z, s, cons>(q_gen_3735, q_gen_3734) -> q_gen_3802
<z, s, nil>(q_gen_3740) -> q_gen_3802
<z, z, cons>(q_gen_3740, q_gen_3764) -> q_gen_3802
<z, z, nil>() -> q_gen_3802
<s, s, s>(q_gen_3803) -> q_gen_3803
<s, s, z>(q_gen_3735) -> q_gen_3803
<s, z, s>(q_gen_3735) -> q_gen_3803
<s, z, z>(q_gen_3740) -> q_gen_3803
<z, s, s>(q_gen_3735) -> q_gen_3803
<z, s, z>(q_gen_3740) -> q_gen_3803
<z, z, s>(q_gen_3740) -> q_gen_3803
<z, z, z>() -> q_gen_3803
}

Datatype: <natlist, natlist, natlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_3726, q_gen_3730, q_gen_3750},
Q_f={q_gen_3726},
Delta=
{
<s>(q_gen_3750) -> q_gen_3750
<z>() -> q_gen_3750
<cons, s>(q_gen_3730, q_gen_3726) -> q_gen_3726
<nil, z>() -> q_gen_3726
<s, s>(q_gen_3730) -> q_gen_3730
<s, z>(q_gen_3750) -> q_gen_3730
<z, s>(q_gen_3750) -> q_gen_3730
<z, z>() -> q_gen_3730
}

Datatype: <natlist, nat>
Convolution form: complete
}}}
  ;  leq -> 
{{{
Q={q_gen_3723, q_gen_3725, q_gen_3896},
Q_f={q_gen_3723},
Delta=
{
<s>(q_gen_3725) -> q_gen_3725
<z>() -> q_gen_3725
<s, s>(q_gen_3723) -> q_gen_3723
<z, s>(q_gen_3725) -> q_gen_3723
<z, z>() -> q_gen_3723
<s, z>(q_gen_3725) -> q_gen_3896
}

Datatype: <nat, nat>
Convolution form: complete
}}}
  ;  reverse -> 
{{{
Q={q_gen_3722, q_gen_3745, q_gen_3746, q_gen_3747, q_gen_3758, q_gen_3811, q_gen_3812},
Q_f={q_gen_3722},
Delta=
{
<s>(q_gen_3758) -> q_gen_3758
<z>() -> q_gen_3758
<cons>(q_gen_3758, q_gen_3812) -> q_gen_3812
<nil>() -> q_gen_3812
<cons, cons>(q_gen_3747, q_gen_3746, q_gen_3745, q_gen_3722) -> q_gen_3722
<cons, cons>(q_gen_3747, q_gen_3746, q_gen_3745, q_gen_3811) -> q_gen_3722
<nil, nil>() -> q_gen_3722
<cons, s>(q_gen_3747, q_gen_3745) -> q_gen_3745
<cons, z>(q_gen_3758, q_gen_3812) -> q_gen_3745
<nil, s>(q_gen_3758) -> q_gen_3745
<nil, z>() -> q_gen_3745
<s, cons>(q_gen_3747, q_gen_3746) -> q_gen_3746
<s, nil>(q_gen_3758) -> q_gen_3746
<z, cons>(q_gen_3758, q_gen_3812) -> q_gen_3746
<z, nil>() -> q_gen_3746
<s, s>(q_gen_3747) -> q_gen_3747
<s, z>(q_gen_3758) -> q_gen_3747
<z, s>(q_gen_3758) -> q_gen_3747
<z, z>() -> q_gen_3747
<cons, nil>(q_gen_3758, q_gen_3812) -> q_gen_3811
<nil, cons>(q_gen_3758, q_gen_3812) -> q_gen_3811
}

Datatype: <natlist, natlist>
Convolution form: complete
}}}

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 34  ;  () -> length([nil, z]) -> 34  ;  () -> leq([z, s(nn2)]) -> 34  ;  () -> leq([z, z]) -> 34  ;  () -> reverse([nil, nil]) -> 34  ;  (append([_qea, cons(h1, nil), _rea]) /\ reverse([t1, _qea])) -> reverse([cons(h1, t1), _rea]) -> 41  ;  (append([t1, l2, _lea])) -> append([cons(h1, t1), l2, cons(h1, _lea)]) -> 49  ;  (length([_afa, _bfa]) /\ length([l1, _zea]) /\ reverse([l1, _afa])) -> leq([_zea, _bfa]) -> 38  ;  (length([ll, _vea])) -> length([cons(x, ll), s(_vea)]) -> 34  ;  (leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 34  ;  (leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 34  ;  (leq([s(nn1), z])) -> BOT -> 36
}
Sat witness: Yes: ((length([_afa, _bfa]) /\ length([l1, _zea]) /\ reverse([l1, _afa])) -> leq([_zea, _bfa]), {
_afa -> cons(z, nil)  ;  _bfa -> s(z)  ;  _zea -> s(s(z))  ;  l1 -> cons(z, cons(z, nil))
})

-------------------------------------------
Step 45, which took 0.231557 s (model generation: 0.231471,  model checking: 0.000086):

Model:
|_
{
append -> 
{{{
Q={q_gen_3727, q_gen_3732, q_gen_3733, q_gen_3734, q_gen_3735, q_gen_3740, q_gen_3764, q_gen_3797, q_gen_3798, q_gen_3799, q_gen_3800, q_gen_3801, q_gen_3802, q_gen_3803},
Q_f={q_gen_3727},
Delta=
{
<s>(q_gen_3740) -> q_gen_3740
<z>() -> q_gen_3740
<cons>(q_gen_3740, q_gen_3764) -> q_gen_3764
<nil>() -> q_gen_3764
<cons, cons>(q_gen_3735, q_gen_3734, q_gen_3733, q_gen_3732) -> q_gen_3732
<nil, cons>(q_gen_3740, q_gen_3764) -> q_gen_3732
<nil, nil>() -> q_gen_3732
<cons, s>(q_gen_3735, q_gen_3733) -> q_gen_3733
<cons, z>(q_gen_3740, q_gen_3764) -> q_gen_3733
<nil, s>(q_gen_3740) -> q_gen_3733
<nil, z>() -> q_gen_3733
<s, cons>(q_gen_3735, q_gen_3734) -> q_gen_3734
<s, nil>(q_gen_3740) -> q_gen_3734
<z, cons>(q_gen_3740, q_gen_3764) -> q_gen_3734
<z, nil>() -> q_gen_3734
<s, s>(q_gen_3735) -> q_gen_3735
<s, z>(q_gen_3740) -> q_gen_3735
<z, s>(q_gen_3740) -> q_gen_3735
<z, z>() -> q_gen_3735
<cons, cons, cons>(q_gen_3803, q_gen_3802, q_gen_3801, q_gen_3800, q_gen_3799, q_gen_3798, q_gen_3797, q_gen_3727) -> q_gen_3727
<cons, nil, cons>(q_gen_3735, q_gen_3734, q_gen_3733, q_gen_3732) -> q_gen_3727
<nil, cons, cons>(q_gen_3735, q_gen_3734, q_gen_3733, q_gen_3732) -> q_gen_3727
<nil, nil, cons>(q_gen_3740, q_gen_3764) -> q_gen_3727
<nil, nil, nil>() -> q_gen_3727
<cons, nil, z>(q_gen_3740, q_gen_3764) -> q_gen_3797
<nil, cons, z>(q_gen_3740, q_gen_3764) -> q_gen_3797
<nil, nil, s>(q_gen_3740) -> q_gen_3797
<nil, nil, z>() -> q_gen_3797
<cons, z, cons>(q_gen_3735, q_gen_3734, q_gen_3733, q_gen_3732) -> q_gen_3798
<nil, s, cons>(q_gen_3735, q_gen_3734) -> q_gen_3798
<nil, z, cons>(q_gen_3740, q_gen_3764) -> q_gen_3798
<cons, z, z>(q_gen_3740, q_gen_3764) -> q_gen_3799
<nil, s, s>(q_gen_3735) -> q_gen_3799
<nil, s, z>(q_gen_3740) -> q_gen_3799
<nil, z, s>(q_gen_3740) -> q_gen_3799
<nil, z, z>() -> q_gen_3799
<s, nil, cons>(q_gen_3735, q_gen_3734) -> q_gen_3800
<z, cons, cons>(q_gen_3735, q_gen_3734, q_gen_3733, q_gen_3732) -> q_gen_3800
<z, nil, cons>(q_gen_3740, q_gen_3764) -> q_gen_3800
<s, nil, s>(q_gen_3735) -> q_gen_3801
<z, cons, z>(q_gen_3740, q_gen_3764) -> q_gen_3801
<z, nil, z>() -> q_gen_3801
<s, s, cons>(q_gen_3803, q_gen_3802) -> q_gen_3802
<s, s, nil>(q_gen_3735) -> q_gen_3802
<s, z, cons>(q_gen_3735, q_gen_3734) -> q_gen_3802
<s, z, nil>(q_gen_3740) -> q_gen_3802
<z, s, cons>(q_gen_3735, q_gen_3734) -> q_gen_3802
<z, s, nil>(q_gen_3740) -> q_gen_3802
<z, z, cons>(q_gen_3740, q_gen_3764) -> q_gen_3802
<z, z, nil>() -> q_gen_3802
<s, s, s>(q_gen_3803) -> q_gen_3803
<s, s, z>(q_gen_3735) -> q_gen_3803
<s, z, s>(q_gen_3735) -> q_gen_3803
<s, z, z>(q_gen_3740) -> q_gen_3803
<z, s, s>(q_gen_3735) -> q_gen_3803
<z, s, z>(q_gen_3740) -> q_gen_3803
<z, z, s>(q_gen_3740) -> q_gen_3803
<z, z, z>() -> q_gen_3803
}

Datatype: <natlist, natlist, natlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_3726, q_gen_3730, q_gen_3750},
Q_f={q_gen_3726},
Delta=
{
<s>(q_gen_3750) -> q_gen_3750
<z>() -> q_gen_3750
<cons, s>(q_gen_3730, q_gen_3726) -> q_gen_3726
<nil, z>() -> q_gen_3726
<s, s>(q_gen_3730) -> q_gen_3730
<s, z>(q_gen_3750) -> q_gen_3730
<z, s>(q_gen_3750) -> q_gen_3730
<z, z>() -> q_gen_3730
}

Datatype: <natlist, nat>
Convolution form: complete
}}}
  ;  leq -> 
{{{
Q={q_gen_3723, q_gen_3725, q_gen_3896},
Q_f={q_gen_3723},
Delta=
{
<s>(q_gen_3725) -> q_gen_3725
<z>() -> q_gen_3725
<s, s>(q_gen_3723) -> q_gen_3723
<s, s>(q_gen_3896) -> q_gen_3723
<z, s>(q_gen_3725) -> q_gen_3723
<z, z>() -> q_gen_3723
<s, z>(q_gen_3725) -> q_gen_3896
}

Datatype: <nat, nat>
Convolution form: complete
}}}
  ;  reverse -> 
{{{
Q={q_gen_3722, q_gen_3745, q_gen_3746, q_gen_3747, q_gen_3758, q_gen_3811, q_gen_3812},
Q_f={q_gen_3722},
Delta=
{
<s>(q_gen_3758) -> q_gen_3758
<z>() -> q_gen_3758
<cons>(q_gen_3758, q_gen_3812) -> q_gen_3812
<nil>() -> q_gen_3812
<cons, cons>(q_gen_3747, q_gen_3746, q_gen_3745, q_gen_3722) -> q_gen_3722
<cons, cons>(q_gen_3747, q_gen_3746, q_gen_3745, q_gen_3811) -> q_gen_3722
<nil, nil>() -> q_gen_3722
<cons, s>(q_gen_3747, q_gen_3745) -> q_gen_3745
<cons, z>(q_gen_3758, q_gen_3812) -> q_gen_3745
<nil, s>(q_gen_3758) -> q_gen_3745
<nil, z>() -> q_gen_3745
<s, cons>(q_gen_3747, q_gen_3746) -> q_gen_3746
<s, nil>(q_gen_3758) -> q_gen_3746
<z, cons>(q_gen_3758, q_gen_3812) -> q_gen_3746
<z, nil>() -> q_gen_3746
<s, s>(q_gen_3747) -> q_gen_3747
<s, z>(q_gen_3758) -> q_gen_3747
<z, s>(q_gen_3758) -> q_gen_3747
<z, z>() -> q_gen_3747
<cons, nil>(q_gen_3758, q_gen_3812) -> q_gen_3811
<nil, cons>(q_gen_3758, q_gen_3812) -> q_gen_3811
}

Datatype: <natlist, natlist>
Convolution form: complete
}}}

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 34  ;  () -> length([nil, z]) -> 34  ;  () -> leq([z, s(nn2)]) -> 34  ;  () -> leq([z, z]) -> 34  ;  () -> reverse([nil, nil]) -> 34  ;  (append([_qea, cons(h1, nil), _rea]) /\ reverse([t1, _qea])) -> reverse([cons(h1, t1), _rea]) -> 41  ;  (append([t1, l2, _lea])) -> append([cons(h1, t1), l2, cons(h1, _lea)]) -> 49  ;  (length([_afa, _bfa]) /\ length([l1, _zea]) /\ reverse([l1, _afa])) -> leq([_zea, _bfa]) -> 38  ;  (length([ll, _vea])) -> length([cons(x, ll), s(_vea)]) -> 34  ;  (leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 34  ;  (leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 37  ;  (leq([s(nn1), z])) -> BOT -> 36
}
Sat witness: Yes: ((leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]), {
nn1 -> s(z)  ;  nn2 -> z
})

-------------------------------------------
Step 46, which took 0.274605 s (model generation: 0.271598,  model checking: 0.003007):

Model:
|_
{
append -> 
{{{
Q={q_gen_3727, q_gen_3732, q_gen_3733, q_gen_3734, q_gen_3735, q_gen_3740, q_gen_3764, q_gen_3797, q_gen_3798, q_gen_3799, q_gen_3800, q_gen_3801, q_gen_3802, q_gen_3803},
Q_f={q_gen_3727},
Delta=
{
<s>(q_gen_3740) -> q_gen_3740
<z>() -> q_gen_3740
<cons>(q_gen_3740, q_gen_3764) -> q_gen_3764
<nil>() -> q_gen_3764
<cons, cons>(q_gen_3735, q_gen_3734, q_gen_3733, q_gen_3732) -> q_gen_3732
<nil, cons>(q_gen_3740, q_gen_3764) -> q_gen_3732
<nil, nil>() -> q_gen_3732
<cons, s>(q_gen_3735, q_gen_3733) -> q_gen_3733
<cons, z>(q_gen_3740, q_gen_3764) -> q_gen_3733
<nil, s>(q_gen_3740) -> q_gen_3733
<nil, z>() -> q_gen_3733
<s, cons>(q_gen_3735, q_gen_3734) -> q_gen_3734
<s, nil>(q_gen_3740) -> q_gen_3734
<z, cons>(q_gen_3740, q_gen_3764) -> q_gen_3734
<z, nil>() -> q_gen_3734
<s, s>(q_gen_3735) -> q_gen_3735
<s, z>(q_gen_3740) -> q_gen_3735
<z, s>(q_gen_3740) -> q_gen_3735
<z, z>() -> q_gen_3735
<cons, cons, cons>(q_gen_3803, q_gen_3802, q_gen_3801, q_gen_3800, q_gen_3799, q_gen_3798, q_gen_3797, q_gen_3727) -> q_gen_3727
<cons, nil, cons>(q_gen_3735, q_gen_3734, q_gen_3733, q_gen_3732) -> q_gen_3727
<nil, cons, cons>(q_gen_3735, q_gen_3734, q_gen_3733, q_gen_3732) -> q_gen_3727
<nil, nil, cons>(q_gen_3740, q_gen_3764) -> q_gen_3727
<nil, nil, nil>() -> q_gen_3727
<cons, nil, z>(q_gen_3740, q_gen_3764) -> q_gen_3797
<nil, cons, z>(q_gen_3740, q_gen_3764) -> q_gen_3797
<nil, nil, s>(q_gen_3740) -> q_gen_3797
<nil, nil, z>() -> q_gen_3797
<cons, z, cons>(q_gen_3735, q_gen_3734, q_gen_3733, q_gen_3732) -> q_gen_3798
<nil, s, cons>(q_gen_3735, q_gen_3734) -> q_gen_3798
<nil, z, cons>(q_gen_3740, q_gen_3764) -> q_gen_3798
<cons, z, z>(q_gen_3740, q_gen_3764) -> q_gen_3799
<nil, s, s>(q_gen_3735) -> q_gen_3799
<nil, s, z>(q_gen_3740) -> q_gen_3799
<nil, z, s>(q_gen_3740) -> q_gen_3799
<nil, z, z>() -> q_gen_3799
<s, nil, cons>(q_gen_3735, q_gen_3734) -> q_gen_3800
<z, cons, cons>(q_gen_3735, q_gen_3734, q_gen_3733, q_gen_3732) -> q_gen_3800
<z, nil, cons>(q_gen_3740, q_gen_3764) -> q_gen_3800
<s, nil, s>(q_gen_3735) -> q_gen_3801
<z, cons, z>(q_gen_3740, q_gen_3764) -> q_gen_3801
<z, nil, z>() -> q_gen_3801
<s, s, cons>(q_gen_3803, q_gen_3802) -> q_gen_3802
<s, s, nil>(q_gen_3735) -> q_gen_3802
<s, z, cons>(q_gen_3735, q_gen_3734) -> q_gen_3802
<s, z, nil>(q_gen_3740) -> q_gen_3802
<z, s, cons>(q_gen_3735, q_gen_3734) -> q_gen_3802
<z, s, nil>(q_gen_3740) -> q_gen_3802
<z, z, cons>(q_gen_3740, q_gen_3764) -> q_gen_3802
<z, z, nil>() -> q_gen_3802
<s, s, s>(q_gen_3803) -> q_gen_3803
<s, s, z>(q_gen_3735) -> q_gen_3803
<s, z, s>(q_gen_3735) -> q_gen_3803
<s, z, z>(q_gen_3740) -> q_gen_3803
<z, s, s>(q_gen_3735) -> q_gen_3803
<z, s, z>(q_gen_3740) -> q_gen_3803
<z, z, s>(q_gen_3740) -> q_gen_3803
<z, z, z>() -> q_gen_3803
}

Datatype: <natlist, natlist, natlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_3726, q_gen_3730, q_gen_3750},
Q_f={q_gen_3726},
Delta=
{
<s>(q_gen_3750) -> q_gen_3750
<z>() -> q_gen_3750
<cons, s>(q_gen_3730, q_gen_3726) -> q_gen_3726
<nil, z>() -> q_gen_3726
<s, s>(q_gen_3730) -> q_gen_3730
<s, z>(q_gen_3750) -> q_gen_3730
<z, s>(q_gen_3750) -> q_gen_3730
<z, z>() -> q_gen_3730
}

Datatype: <natlist, nat>
Convolution form: complete
}}}
  ;  leq -> 
{{{
Q={q_gen_3723, q_gen_3725, q_gen_3896},
Q_f={q_gen_3723},
Delta=
{
<s>(q_gen_3725) -> q_gen_3725
<z>() -> q_gen_3725
<s, s>(q_gen_3723) -> q_gen_3723
<z, s>(q_gen_3725) -> q_gen_3723
<z, z>() -> q_gen_3723
<s, s>(q_gen_3896) -> q_gen_3896
<s, z>(q_gen_3725) -> q_gen_3896
}

Datatype: <nat, nat>
Convolution form: complete
}}}
  ;  reverse -> 
{{{
Q={q_gen_3722, q_gen_3745, q_gen_3746, q_gen_3747, q_gen_3758, q_gen_3811, q_gen_3812, q_gen_3813},
Q_f={q_gen_3722},
Delta=
{
<s>(q_gen_3758) -> q_gen_3758
<z>() -> q_gen_3758
<cons>(q_gen_3758, q_gen_3812) -> q_gen_3812
<nil>() -> q_gen_3812
<cons, cons>(q_gen_3747, q_gen_3746, q_gen_3745, q_gen_3722) -> q_gen_3722
<cons, cons>(q_gen_3747, q_gen_3813, q_gen_3745, q_gen_3722) -> q_gen_3722
<cons, cons>(q_gen_3747, q_gen_3813, q_gen_3745, q_gen_3811) -> q_gen_3722
<nil, nil>() -> q_gen_3722
<cons, s>(q_gen_3747, q_gen_3745) -> q_gen_3745
<cons, z>(q_gen_3758, q_gen_3812) -> q_gen_3745
<nil, s>(q_gen_3758) -> q_gen_3745
<nil, z>() -> q_gen_3745
<s, nil>(q_gen_3758) -> q_gen_3746
<z, nil>() -> q_gen_3746
<s, s>(q_gen_3747) -> q_gen_3747
<s, z>(q_gen_3758) -> q_gen_3747
<z, s>(q_gen_3758) -> q_gen_3747
<z, z>() -> q_gen_3747
<cons, cons>(q_gen_3747, q_gen_3746, q_gen_3745, q_gen_3811) -> q_gen_3811
<cons, nil>(q_gen_3758, q_gen_3812) -> q_gen_3811
<nil, cons>(q_gen_3758, q_gen_3812) -> q_gen_3811
<s, cons>(q_gen_3747, q_gen_3746) -> q_gen_3813
<z, cons>(q_gen_3758, q_gen_3812) -> q_gen_3813
}

Datatype: <natlist, natlist>
Convolution form: complete
}}}

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 35  ;  () -> length([nil, z]) -> 35  ;  () -> leq([z, s(nn2)]) -> 35  ;  () -> leq([z, z]) -> 35  ;  () -> reverse([nil, nil]) -> 35  ;  (append([_qea, cons(h1, nil), _rea]) /\ reverse([t1, _qea])) -> reverse([cons(h1, t1), _rea]) -> 41  ;  (append([t1, l2, _lea])) -> append([cons(h1, t1), l2, cons(h1, _lea)]) -> 49  ;  (length([_afa, _bfa]) /\ length([l1, _zea]) /\ reverse([l1, _afa])) -> leq([_zea, _bfa]) -> 41  ;  (length([ll, _vea])) -> length([cons(x, ll), s(_vea)]) -> 35  ;  (leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 35  ;  (leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 38  ;  (leq([s(nn1), z])) -> BOT -> 37
}
Sat witness: Yes: ((length([_afa, _bfa]) /\ length([l1, _zea]) /\ reverse([l1, _afa])) -> leq([_zea, _bfa]), {
_afa -> cons(z, cons(z, nil))  ;  _bfa -> s(s(z))  ;  _zea -> s(s(s(z)))  ;  l1 -> cons(z, cons(z, cons(z, nil)))
})

-------------------------------------------
Step 47, which took 0.344418 s (model generation: 0.339627,  model checking: 0.004791):

Model:
|_
{
append -> 
{{{
Q={q_gen_3727, q_gen_3732, q_gen_3733, q_gen_3734, q_gen_3735, q_gen_3740, q_gen_3764, q_gen_3796, q_gen_3797, q_gen_3798, q_gen_3799, q_gen_3800, q_gen_3801, q_gen_3802, q_gen_3803, q_gen_3808},
Q_f={q_gen_3727},
Delta=
{
<s>(q_gen_3740) -> q_gen_3740
<z>() -> q_gen_3740
<cons>(q_gen_3740, q_gen_3764) -> q_gen_3764
<nil>() -> q_gen_3764
<cons, cons>(q_gen_3735, q_gen_3734, q_gen_3733, q_gen_3732) -> q_gen_3732
<nil, nil>() -> q_gen_3732
<cons, s>(q_gen_3735, q_gen_3733) -> q_gen_3733
<cons, z>(q_gen_3740, q_gen_3764) -> q_gen_3733
<nil, s>(q_gen_3740) -> q_gen_3733
<nil, z>() -> q_gen_3733
<s, cons>(q_gen_3735, q_gen_3734) -> q_gen_3734
<s, nil>(q_gen_3740) -> q_gen_3734
<z, cons>(q_gen_3740, q_gen_3764) -> q_gen_3734
<z, nil>() -> q_gen_3734
<s, s>(q_gen_3735) -> q_gen_3735
<s, z>(q_gen_3740) -> q_gen_3735
<z, s>(q_gen_3740) -> q_gen_3735
<z, z>() -> q_gen_3735
<nil, cons>(q_gen_3740, q_gen_3764) -> q_gen_3808
<cons, cons, cons>(q_gen_3803, q_gen_3802, q_gen_3801, q_gen_3800, q_gen_3799, q_gen_3798, q_gen_3797, q_gen_3796) -> q_gen_3727
<cons, nil, cons>(q_gen_3735, q_gen_3734, q_gen_3733, q_gen_3732) -> q_gen_3727
<nil, cons, cons>(q_gen_3735, q_gen_3734, q_gen_3733, q_gen_3732) -> q_gen_3727
<nil, nil, nil>() -> q_gen_3727
<cons, cons, cons>(q_gen_3803, q_gen_3802, q_gen_3801, q_gen_3800, q_gen_3799, q_gen_3798, q_gen_3797, q_gen_3727) -> q_gen_3796
<cons, nil, cons>(q_gen_3735, q_gen_3734, q_gen_3733, q_gen_3808) -> q_gen_3796
<nil, cons, cons>(q_gen_3735, q_gen_3734, q_gen_3733, q_gen_3808) -> q_gen_3796
<nil, nil, cons>(q_gen_3740, q_gen_3764) -> q_gen_3796
<cons, nil, z>(q_gen_3740, q_gen_3764) -> q_gen_3797
<nil, cons, z>(q_gen_3740, q_gen_3764) -> q_gen_3797
<nil, nil, s>(q_gen_3740) -> q_gen_3797
<nil, nil, z>() -> q_gen_3797
<cons, z, cons>(q_gen_3735, q_gen_3734, q_gen_3733, q_gen_3732) -> q_gen_3798
<cons, z, cons>(q_gen_3735, q_gen_3734, q_gen_3733, q_gen_3808) -> q_gen_3798
<nil, s, cons>(q_gen_3735, q_gen_3734) -> q_gen_3798
<nil, z, cons>(q_gen_3740, q_gen_3764) -> q_gen_3798
<cons, z, z>(q_gen_3740, q_gen_3764) -> q_gen_3799
<nil, s, s>(q_gen_3735) -> q_gen_3799
<nil, s, z>(q_gen_3740) -> q_gen_3799
<nil, z, s>(q_gen_3740) -> q_gen_3799
<nil, z, z>() -> q_gen_3799
<s, nil, cons>(q_gen_3735, q_gen_3734) -> q_gen_3800
<z, cons, cons>(q_gen_3735, q_gen_3734, q_gen_3733, q_gen_3808) -> q_gen_3800
<z, nil, cons>(q_gen_3740, q_gen_3764) -> q_gen_3800
<s, nil, s>(q_gen_3735) -> q_gen_3801
<z, cons, z>(q_gen_3740, q_gen_3764) -> q_gen_3801
<z, nil, z>() -> q_gen_3801
<s, s, cons>(q_gen_3803, q_gen_3802) -> q_gen_3802
<s, s, nil>(q_gen_3735) -> q_gen_3802
<s, z, cons>(q_gen_3735, q_gen_3734) -> q_gen_3802
<s, z, nil>(q_gen_3740) -> q_gen_3802
<z, s, cons>(q_gen_3735, q_gen_3734) -> q_gen_3802
<z, s, nil>(q_gen_3740) -> q_gen_3802
<z, z, cons>(q_gen_3740, q_gen_3764) -> q_gen_3802
<z, z, nil>() -> q_gen_3802
<s, s, s>(q_gen_3803) -> q_gen_3803
<s, s, z>(q_gen_3735) -> q_gen_3803
<s, z, s>(q_gen_3735) -> q_gen_3803
<s, z, z>(q_gen_3740) -> q_gen_3803
<z, s, s>(q_gen_3735) -> q_gen_3803
<z, s, z>(q_gen_3740) -> q_gen_3803
<z, z, s>(q_gen_3740) -> q_gen_3803
<z, z, z>() -> q_gen_3803
}

Datatype: <natlist, natlist, natlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_3726, q_gen_3730, q_gen_3750},
Q_f={q_gen_3726},
Delta=
{
<s>(q_gen_3750) -> q_gen_3750
<z>() -> q_gen_3750
<cons, s>(q_gen_3730, q_gen_3726) -> q_gen_3726
<nil, z>() -> q_gen_3726
<s, s>(q_gen_3730) -> q_gen_3730
<s, z>(q_gen_3750) -> q_gen_3730
<z, s>(q_gen_3750) -> q_gen_3730
<z, z>() -> q_gen_3730
}

Datatype: <natlist, nat>
Convolution form: complete
}}}
  ;  leq -> 
{{{
Q={q_gen_3723, q_gen_3725, q_gen_3896},
Q_f={q_gen_3723},
Delta=
{
<s>(q_gen_3725) -> q_gen_3725
<z>() -> q_gen_3725
<s, s>(q_gen_3723) -> q_gen_3723
<z, s>(q_gen_3725) -> q_gen_3723
<z, z>() -> q_gen_3723
<s, s>(q_gen_3896) -> q_gen_3896
<s, z>(q_gen_3725) -> q_gen_3896
}

Datatype: <nat, nat>
Convolution form: complete
}}}
  ;  reverse -> 
{{{
Q={q_gen_3722, q_gen_3745, q_gen_3746, q_gen_3747, q_gen_3758, q_gen_3810, q_gen_3812},
Q_f={q_gen_3722},
Delta=
{
<s>(q_gen_3758) -> q_gen_3758
<z>() -> q_gen_3758
<cons>(q_gen_3758, q_gen_3812) -> q_gen_3812
<nil>() -> q_gen_3812
<cons, cons>(q_gen_3747, q_gen_3746, q_gen_3745, q_gen_3722) -> q_gen_3722
<nil, nil>() -> q_gen_3722
<cons, s>(q_gen_3747, q_gen_3745) -> q_gen_3745
<cons, z>(q_gen_3758, q_gen_3812) -> q_gen_3745
<nil, s>(q_gen_3758) -> q_gen_3745
<nil, z>() -> q_gen_3745
<s, cons>(q_gen_3747, q_gen_3746) -> q_gen_3746
<s, nil>(q_gen_3758) -> q_gen_3746
<z, cons>(q_gen_3758, q_gen_3812) -> q_gen_3746
<z, nil>() -> q_gen_3746
<s, s>(q_gen_3747) -> q_gen_3747
<s, z>(q_gen_3758) -> q_gen_3747
<z, s>(q_gen_3758) -> q_gen_3747
<z, z>() -> q_gen_3747
<cons, cons>(q_gen_3747, q_gen_3746, q_gen_3745, q_gen_3810) -> q_gen_3810
<cons, nil>(q_gen_3758, q_gen_3812) -> q_gen_3810
<nil, cons>(q_gen_3758, q_gen_3812) -> q_gen_3810
}

Datatype: <natlist, natlist>
Convolution form: complete
}}}

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 36  ;  () -> length([nil, z]) -> 36  ;  () -> leq([z, s(nn2)]) -> 36  ;  () -> leq([z, z]) -> 36  ;  () -> reverse([nil, nil]) -> 36  ;  (append([_qea, cons(h1, nil), _rea]) /\ reverse([t1, _qea])) -> reverse([cons(h1, t1), _rea]) -> 44  ;  (append([t1, l2, _lea])) -> append([cons(h1, t1), l2, cons(h1, _lea)]) -> 49  ;  (length([_afa, _bfa]) /\ length([l1, _zea]) /\ reverse([l1, _afa])) -> leq([_zea, _bfa]) -> 42  ;  (length([ll, _vea])) -> length([cons(x, ll), s(_vea)]) -> 36  ;  (leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 36  ;  (leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 39  ;  (leq([s(nn1), z])) -> BOT -> 38
}
Sat witness: Yes: ((append([_qea, cons(h1, nil), _rea]) /\ reverse([t1, _qea])) -> reverse([cons(h1, t1), _rea]), {
_qea -> cons(z, nil)  ;  _rea -> cons(z, cons(z, cons(z, nil)))  ;  h1 -> z  ;  t1 -> cons(z, nil)
})

-------------------------------------------
Step 48, which took 18.997771 s (model generation: 0.679572,  model checking: 18.318199):

Model:
|_
{
append -> 
{{{
Q={q_gen_3727, q_gen_3732, q_gen_3733, q_gen_3734, q_gen_3735, q_gen_3740, q_gen_3764, q_gen_3796, q_gen_3797, q_gen_3798, q_gen_3799, q_gen_3800, q_gen_3801, q_gen_3802, q_gen_3803, q_gen_3808},
Q_f={q_gen_3727},
Delta=
{
<s>(q_gen_3740) -> q_gen_3740
<z>() -> q_gen_3740
<cons>(q_gen_3740, q_gen_3764) -> q_gen_3764
<nil>() -> q_gen_3764
<cons, cons>(q_gen_3735, q_gen_3734, q_gen_3733, q_gen_3732) -> q_gen_3732
<nil, nil>() -> q_gen_3732
<cons, s>(q_gen_3735, q_gen_3733) -> q_gen_3733
<cons, z>(q_gen_3740, q_gen_3764) -> q_gen_3733
<nil, s>(q_gen_3740) -> q_gen_3733
<nil, z>() -> q_gen_3733
<s, cons>(q_gen_3735, q_gen_3734) -> q_gen_3734
<s, nil>(q_gen_3740) -> q_gen_3734
<z, cons>(q_gen_3740, q_gen_3764) -> q_gen_3734
<z, nil>() -> q_gen_3734
<s, s>(q_gen_3735) -> q_gen_3735
<s, z>(q_gen_3740) -> q_gen_3735
<z, s>(q_gen_3740) -> q_gen_3735
<z, z>() -> q_gen_3735
<nil, cons>(q_gen_3740, q_gen_3764) -> q_gen_3808
<cons, cons, cons>(q_gen_3803, q_gen_3802, q_gen_3801, q_gen_3800, q_gen_3799, q_gen_3798, q_gen_3797, q_gen_3796) -> q_gen_3727
<cons, nil, cons>(q_gen_3735, q_gen_3734, q_gen_3733, q_gen_3732) -> q_gen_3727
<nil, cons, cons>(q_gen_3735, q_gen_3734, q_gen_3733, q_gen_3732) -> q_gen_3727
<nil, nil, nil>() -> q_gen_3727
<cons, cons, cons>(q_gen_3803, q_gen_3802, q_gen_3801, q_gen_3800, q_gen_3799, q_gen_3798, q_gen_3797, q_gen_3727) -> q_gen_3796
<cons, nil, cons>(q_gen_3735, q_gen_3734, q_gen_3733, q_gen_3808) -> q_gen_3796
<nil, cons, cons>(q_gen_3735, q_gen_3734, q_gen_3733, q_gen_3808) -> q_gen_3796
<nil, nil, cons>(q_gen_3740, q_gen_3764) -> q_gen_3796
<cons, nil, z>(q_gen_3740, q_gen_3764) -> q_gen_3797
<nil, cons, z>(q_gen_3740, q_gen_3764) -> q_gen_3797
<nil, nil, s>(q_gen_3740) -> q_gen_3797
<nil, nil, z>() -> q_gen_3797
<cons, z, cons>(q_gen_3735, q_gen_3734, q_gen_3733, q_gen_3732) -> q_gen_3798
<cons, z, cons>(q_gen_3735, q_gen_3734, q_gen_3733, q_gen_3808) -> q_gen_3798
<nil, s, cons>(q_gen_3735, q_gen_3734) -> q_gen_3798
<nil, z, cons>(q_gen_3740, q_gen_3764) -> q_gen_3798
<cons, z, z>(q_gen_3740, q_gen_3764) -> q_gen_3799
<nil, s, s>(q_gen_3735) -> q_gen_3799
<nil, s, z>(q_gen_3740) -> q_gen_3799
<nil, z, s>(q_gen_3740) -> q_gen_3799
<nil, z, z>() -> q_gen_3799
<s, nil, cons>(q_gen_3735, q_gen_3734) -> q_gen_3800
<z, cons, cons>(q_gen_3735, q_gen_3734, q_gen_3733, q_gen_3808) -> q_gen_3800
<z, nil, cons>(q_gen_3740, q_gen_3764) -> q_gen_3800
<s, nil, s>(q_gen_3735) -> q_gen_3801
<z, cons, z>(q_gen_3740, q_gen_3764) -> q_gen_3801
<z, nil, z>() -> q_gen_3801
<s, s, cons>(q_gen_3803, q_gen_3802) -> q_gen_3802
<s, s, nil>(q_gen_3735) -> q_gen_3802
<s, z, cons>(q_gen_3735, q_gen_3734) -> q_gen_3802
<s, z, nil>(q_gen_3740) -> q_gen_3802
<z, s, cons>(q_gen_3735, q_gen_3734) -> q_gen_3802
<z, s, nil>(q_gen_3740) -> q_gen_3802
<z, z, cons>(q_gen_3740, q_gen_3764) -> q_gen_3802
<z, z, nil>() -> q_gen_3802
<s, s, s>(q_gen_3803) -> q_gen_3803
<s, s, z>(q_gen_3735) -> q_gen_3803
<s, z, s>(q_gen_3735) -> q_gen_3803
<s, z, z>(q_gen_3740) -> q_gen_3803
<z, s, s>(q_gen_3735) -> q_gen_3803
<z, s, z>(q_gen_3740) -> q_gen_3803
<z, z, s>(q_gen_3740) -> q_gen_3803
<z, z, z>() -> q_gen_3803
}

Datatype: <natlist, natlist, natlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_3726, q_gen_3730, q_gen_3750},
Q_f={q_gen_3726},
Delta=
{
<s>(q_gen_3750) -> q_gen_3750
<z>() -> q_gen_3750
<cons, s>(q_gen_3730, q_gen_3726) -> q_gen_3726
<nil, z>() -> q_gen_3726
<s, s>(q_gen_3730) -> q_gen_3730
<s, z>(q_gen_3750) -> q_gen_3730
<z, s>(q_gen_3750) -> q_gen_3730
<z, z>() -> q_gen_3730
}

Datatype: <natlist, nat>
Convolution form: complete
}}}
  ;  leq -> 
{{{
Q={q_gen_3723, q_gen_3725, q_gen_3896},
Q_f={q_gen_3723},
Delta=
{
<s>(q_gen_3725) -> q_gen_3725
<z>() -> q_gen_3725
<s, s>(q_gen_3723) -> q_gen_3723
<z, s>(q_gen_3725) -> q_gen_3723
<z, z>() -> q_gen_3723
<s, s>(q_gen_3896) -> q_gen_3896
<s, z>(q_gen_3725) -> q_gen_3896
}

Datatype: <nat, nat>
Convolution form: complete
}}}
  ;  reverse -> 
{{{
Q={q_gen_3722, q_gen_3745, q_gen_3746, q_gen_3747, q_gen_3758, q_gen_3812, q_gen_3892},
Q_f={q_gen_3722},
Delta=
{
<s>(q_gen_3758) -> q_gen_3758
<z>() -> q_gen_3758
<cons>(q_gen_3758, q_gen_3812) -> q_gen_3812
<nil>() -> q_gen_3812
<cons, cons>(q_gen_3747, q_gen_3746, q_gen_3745, q_gen_3722) -> q_gen_3722
<nil, cons>(q_gen_3758, q_gen_3812) -> q_gen_3722
<nil, nil>() -> q_gen_3722
<cons, s>(q_gen_3747, q_gen_3745) -> q_gen_3745
<cons, z>(q_gen_3758, q_gen_3812) -> q_gen_3745
<nil, s>(q_gen_3758) -> q_gen_3745
<nil, z>() -> q_gen_3745
<s, cons>(q_gen_3747, q_gen_3746) -> q_gen_3746
<s, nil>(q_gen_3758) -> q_gen_3746
<z, cons>(q_gen_3758, q_gen_3812) -> q_gen_3746
<z, nil>() -> q_gen_3746
<s, s>(q_gen_3747) -> q_gen_3747
<s, z>(q_gen_3758) -> q_gen_3747
<z, s>(q_gen_3758) -> q_gen_3747
<z, z>() -> q_gen_3747
<cons, cons>(q_gen_3747, q_gen_3746, q_gen_3745, q_gen_3892) -> q_gen_3892
<cons, nil>(q_gen_3758, q_gen_3812) -> q_gen_3892
}

Datatype: <natlist, natlist>
Convolution form: complete
}}}

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

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([_qea, cons(h1, nil), _rea]) /\ reverse([t1, _qea])) -> reverse([cons(h1, t1), _rea]) -> 45  ;  (append([t1, l2, _lea])) -> append([cons(h1, t1), l2, cons(h1, _lea)]) -> 52  ;  (length([_afa, _bfa]) /\ length([l1, _zea]) /\ reverse([l1, _afa])) -> leq([_zea, _bfa]) -> 43  ;  (length([ll, _vea])) -> length([cons(x, ll), s(_vea)]) -> 37  ;  (leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 37  ;  (leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 40  ;  (leq([s(nn1), z])) -> BOT -> 39
}
Sat witness: Yes: ((append([t1, l2, _lea])) -> append([cons(h1, t1), l2, cons(h1, _lea)]), {
_lea -> cons(z, cons(z, nil))  ;  h1 -> s(z)  ;  l2 -> cons(z, nil)  ;  t1 -> cons(z, nil)
})

-------------------------------------------
Step 49, which took 0.628397 s (model generation: 0.625722,  model checking: 0.002675):

Model:
|_
{
append -> 
{{{
Q={q_gen_3727, q_gen_3732, q_gen_3733, q_gen_3734, q_gen_3735, q_gen_3740, q_gen_3764, q_gen_3797, q_gen_3798, q_gen_3799, q_gen_3800, q_gen_3801, q_gen_3802, q_gen_3803},
Q_f={q_gen_3727},
Delta=
{
<s>(q_gen_3740) -> q_gen_3740
<z>() -> q_gen_3740
<cons>(q_gen_3740, q_gen_3764) -> q_gen_3764
<nil>() -> q_gen_3764
<cons, cons>(q_gen_3735, q_gen_3734, q_gen_3733, q_gen_3732) -> q_gen_3732
<nil, cons>(q_gen_3740, q_gen_3764) -> q_gen_3732
<nil, nil>() -> q_gen_3732
<cons, s>(q_gen_3735, q_gen_3733) -> q_gen_3733
<cons, z>(q_gen_3740, q_gen_3764) -> q_gen_3733
<nil, s>(q_gen_3740) -> q_gen_3733
<nil, z>() -> q_gen_3733
<s, cons>(q_gen_3735, q_gen_3734) -> q_gen_3734
<s, nil>(q_gen_3740) -> q_gen_3734
<z, cons>(q_gen_3740, q_gen_3764) -> q_gen_3734
<z, nil>() -> q_gen_3734
<s, s>(q_gen_3735) -> q_gen_3735
<s, z>(q_gen_3740) -> q_gen_3735
<z, s>(q_gen_3740) -> q_gen_3735
<z, z>() -> q_gen_3735
<cons, cons, cons>(q_gen_3803, q_gen_3802, q_gen_3801, q_gen_3800, q_gen_3799, q_gen_3798, q_gen_3797, q_gen_3727) -> q_gen_3727
<cons, nil, cons>(q_gen_3735, q_gen_3734, q_gen_3733, q_gen_3732) -> q_gen_3727
<nil, cons, cons>(q_gen_3735, q_gen_3734, q_gen_3733, q_gen_3732) -> q_gen_3727
<nil, nil, cons>(q_gen_3740, q_gen_3764) -> q_gen_3727
<nil, nil, nil>() -> q_gen_3727
<cons, nil, s>(q_gen_3735, q_gen_3733) -> q_gen_3797
<cons, nil, z>(q_gen_3740, q_gen_3764) -> q_gen_3797
<nil, cons, z>(q_gen_3740, q_gen_3764) -> q_gen_3797
<nil, nil, s>(q_gen_3740) -> q_gen_3797
<nil, nil, z>() -> q_gen_3797
<cons, z, cons>(q_gen_3735, q_gen_3734, q_gen_3733, q_gen_3732) -> q_gen_3798
<nil, s, cons>(q_gen_3735, q_gen_3734) -> q_gen_3798
<nil, z, cons>(q_gen_3740, q_gen_3764) -> q_gen_3798
<cons, z, s>(q_gen_3735, q_gen_3733) -> q_gen_3799
<cons, z, z>(q_gen_3740, q_gen_3764) -> q_gen_3799
<nil, s, s>(q_gen_3735) -> q_gen_3799
<nil, s, z>(q_gen_3740) -> q_gen_3799
<nil, z, s>(q_gen_3740) -> q_gen_3799
<nil, z, z>() -> q_gen_3799
<s, nil, cons>(q_gen_3735, q_gen_3734) -> q_gen_3800
<z, cons, cons>(q_gen_3735, q_gen_3734, q_gen_3733, q_gen_3732) -> q_gen_3800
<z, nil, cons>(q_gen_3740, q_gen_3764) -> q_gen_3800
<s, nil, s>(q_gen_3735) -> q_gen_3801
<z, cons, z>(q_gen_3740, q_gen_3764) -> q_gen_3801
<z, nil, z>() -> q_gen_3801
<s, s, cons>(q_gen_3803, q_gen_3802) -> q_gen_3802
<s, s, nil>(q_gen_3735) -> q_gen_3802
<s, z, cons>(q_gen_3735, q_gen_3734) -> q_gen_3802
<s, z, nil>(q_gen_3740) -> q_gen_3802
<z, s, cons>(q_gen_3735, q_gen_3734) -> q_gen_3802
<z, s, nil>(q_gen_3740) -> q_gen_3802
<z, z, cons>(q_gen_3740, q_gen_3764) -> q_gen_3802
<z, z, nil>() -> q_gen_3802
<s, s, s>(q_gen_3803) -> q_gen_3803
<s, s, z>(q_gen_3735) -> q_gen_3803
<s, z, s>(q_gen_3735) -> q_gen_3803
<s, z, z>(q_gen_3740) -> q_gen_3803
<z, s, s>(q_gen_3735) -> q_gen_3803
<z, s, z>(q_gen_3740) -> q_gen_3803
<z, z, s>(q_gen_3740) -> q_gen_3803
<z, z, z>() -> q_gen_3803
}

Datatype: <natlist, natlist, natlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_3726, q_gen_3730, q_gen_3750},
Q_f={q_gen_3726},
Delta=
{
<s>(q_gen_3750) -> q_gen_3750
<z>() -> q_gen_3750
<cons, s>(q_gen_3730, q_gen_3726) -> q_gen_3726
<nil, z>() -> q_gen_3726
<s, s>(q_gen_3730) -> q_gen_3730
<s, z>(q_gen_3750) -> q_gen_3730
<z, s>(q_gen_3750) -> q_gen_3730
<z, z>() -> q_gen_3730
}

Datatype: <natlist, nat>
Convolution form: complete
}}}
  ;  leq -> 
{{{
Q={q_gen_3723, q_gen_3725, q_gen_3896, q_gen_3897},
Q_f={q_gen_3723},
Delta=
{
<s>(q_gen_3725) -> q_gen_3725
<z>() -> q_gen_3725
<s, s>(q_gen_3723) -> q_gen_3723
<s, s>(q_gen_3897) -> q_gen_3723
<z, s>(q_gen_3725) -> q_gen_3723
<z, z>() -> q_gen_3723
<s, z>(q_gen_3725) -> q_gen_3896
<s, s>(q_gen_3896) -> q_gen_3897
}

Datatype: <nat, nat>
Convolution form: complete
}}}
  ;  reverse -> 
{{{
Q={q_gen_3722, q_gen_3745, q_gen_3746, q_gen_3747, q_gen_3758, q_gen_3811, q_gen_3812, q_gen_3894},
Q_f={q_gen_3722},
Delta=
{
<s>(q_gen_3758) -> q_gen_3758
<z>() -> q_gen_3758
<cons>(q_gen_3758, q_gen_3812) -> q_gen_3812
<nil>() -> q_gen_3812
<cons, cons>(q_gen_3747, q_gen_3746, q_gen_3745, q_gen_3722) -> q_gen_3722
<cons, cons>(q_gen_3747, q_gen_3746, q_gen_3745, q_gen_3811) -> q_gen_3722
<nil, nil>() -> q_gen_3722
<cons, s>(q_gen_3747, q_gen_3745) -> q_gen_3745
<cons, z>(q_gen_3758, q_gen_3812) -> q_gen_3745
<nil, s>(q_gen_3758) -> q_gen_3745
<nil, z>() -> q_gen_3745
<s, cons>(q_gen_3747, q_gen_3746) -> q_gen_3746
<s, nil>(q_gen_3758) -> q_gen_3746
<z, cons>(q_gen_3758, q_gen_3812) -> q_gen_3746
<z, nil>() -> q_gen_3746
<s, s>(q_gen_3747) -> q_gen_3747
<s, z>(q_gen_3758) -> q_gen_3747
<z, s>(q_gen_3758) -> q_gen_3747
<z, z>() -> q_gen_3747
<cons, cons>(q_gen_3747, q_gen_3746, q_gen_3745, q_gen_3894) -> q_gen_3811
<nil, cons>(q_gen_3758, q_gen_3812) -> q_gen_3811
<cons, nil>(q_gen_3758, q_gen_3812) -> q_gen_3894
}

Datatype: <natlist, natlist>
Convolution form: complete
}}}

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

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([_qea, cons(h1, nil), _rea]) /\ reverse([t1, _qea])) -> reverse([cons(h1, t1), _rea]) -> 45  ;  (append([t1, l2, _lea])) -> append([cons(h1, t1), l2, cons(h1, _lea)]) -> 52  ;  (length([_afa, _bfa]) /\ length([l1, _zea]) /\ reverse([l1, _afa])) -> leq([_zea, _bfa]) -> 43  ;  (length([ll, _vea])) -> length([cons(x, ll), s(_vea)]) -> 38  ;  (leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 38  ;  (leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 43  ;  (leq([s(nn1), z])) -> BOT -> 40
}
Sat witness: Yes: ((leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]), {
nn1 -> s(s(z))  ;  nn2 -> s(z)
})

Total time: 30.000092
Reason for stopping: DontKnow. Stopped because: timeout