Solving ../../benchmarks/true/length_reverse_leq_leq.smt2...

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


Learning problem is:

env: {
elt -> {a, b}  ;  eltlist -> {cons, nil}  ;  nat -> {s, z}
}
definition:
{
(append, F:
{() -> append([nil, l2, l2])
(append([t1, l2, _rda])) -> append([cons(h1, t1), l2, cons(h1, _rda)])}
(append([_sda, _tda, _uda]) /\ append([_sda, _tda, _vda])) -> eq_eltlist([_uda, _vda])
)
(reverse, F:
{() -> reverse([nil, nil])
(append([_wda, cons(h1, nil), _xda]) /\ reverse([t1, _wda])) -> reverse([cons(h1, t1), _xda])}
(reverse([_yda, _aea]) /\ reverse([_yda, _zda])) -> eq_eltlist([_zda, _aea])
)
(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, _bea])) -> length([cons(x, ll), s(_bea)])}
(length([_cea, _dea]) /\ length([_cea, _eea])) -> eq_nat([_dea, _eea])
)
}

properties:
{(length([_gea, _hea]) /\ length([l1, _fea]) /\ reverse([l1, _gea])) -> leq([_fea, _hea]), (length([_iea, _jea]) /\ length([l1, _kea]) /\ reverse([l1, _iea])) -> leq([_jea, _kea])}


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([_wda, cons(h1, nil), _xda]) /\ reverse([t1, _wda])) -> reverse([cons(h1, t1), _xda]) -> 0  ;  (append([t1, l2, _rda])) -> append([cons(h1, t1), l2, cons(h1, _rda)]) -> 0  ;  (length([_gea, _hea]) /\ length([l1, _fea]) /\ reverse([l1, _gea])) -> leq([_fea, _hea]) -> 0  ;  (length([_iea, _jea]) /\ length([l1, _kea]) /\ reverse([l1, _iea])) -> leq([_jea, _kea]) -> 0  ;  (length([ll, _bea])) -> length([cons(x, ll), s(_bea)]) -> 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 30.000246 seconds.
DontKnow. Stopped because: timeout
Working model:
|_
{
append -> 
{{{
Q={q_gen_3556, q_gen_3560, q_gen_3561, q_gen_3562, q_gen_3563, q_gen_3564, q_gen_3567, q_gen_3568, q_gen_3569, q_gen_3570, q_gen_3571, q_gen_3578, q_gen_3579, q_gen_3580, q_gen_3581, q_gen_3582, q_gen_3583, q_gen_3584, q_gen_3589, q_gen_3590, q_gen_3591, q_gen_3592, q_gen_3593, q_gen_3597, q_gen_3598, q_gen_3599, q_gen_3600, q_gen_3601, q_gen_3602, q_gen_3603, q_gen_3604, q_gen_3607, q_gen_3608, q_gen_3609, q_gen_3610, q_gen_3611, q_gen_3612, q_gen_3613, q_gen_3614, q_gen_3615, q_gen_3625, q_gen_3626, q_gen_3627, q_gen_3628, q_gen_3635, q_gen_3636, q_gen_3637, q_gen_3638, q_gen_3639, q_gen_3640, q_gen_3641, q_gen_3642, q_gen_3643, q_gen_3650, q_gen_3651, q_gen_3652, q_gen_3653, q_gen_3654, q_gen_3655, q_gen_3656, q_gen_3657, q_gen_3658, q_gen_3659, q_gen_3660, q_gen_3661, q_gen_3663, q_gen_3664, q_gen_3665, q_gen_3666, q_gen_3667, q_gen_3668, q_gen_3669, q_gen_3670, q_gen_3671, q_gen_3672, q_gen_3673, q_gen_3674, q_gen_3675, q_gen_3676, q_gen_3677, q_gen_3678, q_gen_3682, q_gen_3683, q_gen_3684, q_gen_3685, q_gen_3686, q_gen_3694, q_gen_3699, q_gen_3700, q_gen_3701, q_gen_3702, q_gen_3703, q_gen_3704, q_gen_3705, q_gen_3706, q_gen_3707, q_gen_3708, q_gen_3711, q_gen_3712, q_gen_3713, q_gen_3714, q_gen_3715, q_gen_3716, q_gen_3717, q_gen_3718, q_gen_3719, q_gen_3720, q_gen_3721},
Q_f={},
Delta=
{
<nil>() -> q_gen_3582
<a>() -> q_gen_3583
<b>() -> q_gen_3592
<cons>(q_gen_3592, q_gen_3582) -> q_gen_3603
<cons>(q_gen_3583, q_gen_3603) -> q_gen_3668
<cons>(q_gen_3592, q_gen_3603) -> q_gen_3675
<cons>(q_gen_3583, q_gen_3582) -> q_gen_3718
<nil, nil>() -> q_gen_3561
<nil, b>() -> q_gen_3562
<b, nil>() -> q_gen_3563
<b, b>() -> q_gen_3564
<nil, a>() -> q_gen_3568
<a, nil>() -> q_gen_3569
<a, a>() -> q_gen_3570
<cons, cons>(q_gen_3570, q_gen_3569, q_gen_3568, q_gen_3561) -> q_gen_3580
<cons, b>(q_gen_3583, q_gen_3582) -> q_gen_3581
<b, cons>(q_gen_3583, q_gen_3582) -> q_gen_3584
<cons, cons>(q_gen_3564, q_gen_3563, q_gen_3562, q_gen_3561) -> q_gen_3590
<cons, b>(q_gen_3592, q_gen_3582) -> q_gen_3591
<b, cons>(q_gen_3592, q_gen_3582) -> q_gen_3593
<cons, a>(q_gen_3592, q_gen_3582) -> q_gen_3598
<a, cons>(q_gen_3592, q_gen_3582) -> q_gen_3599
<cons, cons>(q_gen_3570, q_gen_3599, q_gen_3598, q_gen_3590) -> q_gen_3601
<cons, b>(q_gen_3583, q_gen_3603) -> q_gen_3602
<b, cons>(q_gen_3583, q_gen_3603) -> q_gen_3604
<nil, cons>(q_gen_3583, q_gen_3582) -> q_gen_3627
<nil, cons>(q_gen_3592, q_gen_3603) -> q_gen_3642
<b, cons>(q_gen_3592, q_gen_3603) -> q_gen_3643
<cons, cons>(q_gen_3570, q_gen_3666, q_gen_3665, q_gen_3601) -> q_gen_3664
<cons, a>(q_gen_3583, q_gen_3603) -> q_gen_3665
<a, cons>(q_gen_3583, q_gen_3603) -> q_gen_3666
<cons, b>(q_gen_3583, q_gen_3668) -> q_gen_3667
<b, cons>(q_gen_3583, q_gen_3668) -> q_gen_3669
<a, cons>(q_gen_3592, q_gen_3603) -> q_gen_3671
<cons, cons>(q_gen_3570, q_gen_3671, q_gen_3568, q_gen_3642) -> q_gen_3673
<b, cons>(q_gen_3583, q_gen_3675) -> q_gen_3674
<nil, cons>(q_gen_3592, q_gen_3582) -> q_gen_3701
<cons, a>(q_gen_3583, q_gen_3582) -> q_gen_3712
<a, cons>(q_gen_3583, q_gen_3582) -> q_gen_3713
<nil, nil, nil>() -> q_gen_3556
<cons, nil, cons>(q_gen_3564, q_gen_3563, q_gen_3562, q_gen_3561) -> q_gen_3560
<nil, cons, cons>(q_gen_3570, q_gen_3569, q_gen_3568, q_gen_3561) -> q_gen_3567
<nil, cons, cons>(q_gen_3564, q_gen_3563, q_gen_3562, q_gen_3561) -> q_gen_3571
<cons, nil, cons>(q_gen_3570, q_gen_3569, q_gen_3568, q_gen_3561) -> q_gen_3578
<cons, nil, cons>(q_gen_3564, q_gen_3584, q_gen_3581, q_gen_3580) -> q_gen_3579
<nil, cons, cons>(q_gen_3564, q_gen_3593, q_gen_3591, q_gen_3590) -> q_gen_3589
<cons, nil, cons>(q_gen_3570, q_gen_3599, q_gen_3598, q_gen_3590) -> q_gen_3597
<nil, cons, cons>(q_gen_3564, q_gen_3604, q_gen_3602, q_gen_3601) -> q_gen_3600
<cons, cons, cons>(q_gen_3615, q_gen_3614, q_gen_3613, q_gen_3612, q_gen_3611, q_gen_3610, q_gen_3609, q_gen_3608) -> q_gen_3607
<nil, nil, cons>(q_gen_3592, q_gen_3582) -> q_gen_3608
<nil, nil, b>() -> q_gen_3609
<nil, b, cons>(q_gen_3592, q_gen_3582) -> q_gen_3610
<nil, b, b>() -> q_gen_3611
<b, nil, cons>(q_gen_3592, q_gen_3582) -> q_gen_3612
<b, nil, b>() -> q_gen_3613
<b, b, cons>(q_gen_3592, q_gen_3582) -> q_gen_3614
<b, b, b>() -> q_gen_3615
<nil, nil, cons>(q_gen_3583, q_gen_3582) -> q_gen_3625
<cons, nil, cons>(q_gen_3564, q_gen_3584, q_gen_3562, q_gen_3627) -> q_gen_3626
<nil, cons, cons>(q_gen_3564, q_gen_3584, q_gen_3562, q_gen_3627) -> q_gen_3628
<cons, cons, cons>(q_gen_3640, q_gen_3639, q_gen_3613, q_gen_3638, q_gen_3637, q_gen_3636, q_gen_3609, q_gen_3625) -> q_gen_3635
<nil, a, cons>(q_gen_3583, q_gen_3582) -> q_gen_3636
<nil, a, b>() -> q_gen_3637
<b, nil, cons>(q_gen_3583, q_gen_3582) -> q_gen_3638
<b, a, cons>(q_gen_3583, q_gen_3582) -> q_gen_3639
<b, a, b>() -> q_gen_3640
<nil, cons, cons>(q_gen_3564, q_gen_3643, q_gen_3562, q_gen_3642) -> q_gen_3641
<cons, cons, cons>(q_gen_3656, q_gen_3655, q_gen_3654, q_gen_3653, q_gen_3652, q_gen_3610, q_gen_3651, q_gen_3608) -> q_gen_3650
<nil, nil, a>() -> q_gen_3651
<nil, b, a>() -> q_gen_3652
<a, nil, cons>(q_gen_3592, q_gen_3582) -> q_gen_3653
<a, nil, a>() -> q_gen_3654
<a, b, cons>(q_gen_3592, q_gen_3582) -> q_gen_3655
<a, b, a>() -> q_gen_3656
<cons, cons, cons>(q_gen_3615, q_gen_3661, q_gen_3613, q_gen_3660, q_gen_3611, q_gen_3659, q_gen_3609, q_gen_3658) -> q_gen_3657
<nil, nil, cons>(q_gen_3592, q_gen_3603) -> q_gen_3658
<nil, b, cons>(q_gen_3592, q_gen_3603) -> q_gen_3659
<b, nil, cons>(q_gen_3592, q_gen_3603) -> q_gen_3660
<b, b, cons>(q_gen_3592, q_gen_3603) -> q_gen_3661
<nil, cons, cons>(q_gen_3564, q_gen_3669, q_gen_3667, q_gen_3664) -> q_gen_3663
<cons, nil, cons>(q_gen_3570, q_gen_3671, q_gen_3568, q_gen_3642) -> q_gen_3670
<cons, nil, cons>(q_gen_3564, q_gen_3674, q_gen_3581, q_gen_3673) -> q_gen_3672
<cons, cons, cons>(q_gen_3615, q_gen_3678, q_gen_3613, q_gen_3638, q_gen_3611, q_gen_3677, q_gen_3609, q_gen_3625) -> q_gen_3676
<nil, b, cons>(q_gen_3583, q_gen_3582) -> q_gen_3677
<b, b, cons>(q_gen_3583, q_gen_3582) -> q_gen_3678
<cons, cons, cons>(q_gen_3686, q_gen_3685, q_gen_3654, q_gen_3684, q_gen_3683, q_gen_3636, q_gen_3651, q_gen_3625) -> q_gen_3682
<nil, a, a>() -> q_gen_3683
<a, nil, cons>(q_gen_3583, q_gen_3582) -> q_gen_3684
<a, a, cons>(q_gen_3583, q_gen_3582) -> q_gen_3685
<a, a, a>() -> q_gen_3686
<cons, nil, cons>(q_gen_3564, q_gen_3643, q_gen_3562, q_gen_3642) -> q_gen_3694
<cons, cons, cons>(q_gen_3656, q_gen_3705, q_gen_3704, q_gen_3703, q_gen_3652, q_gen_3659, q_gen_3702, q_gen_3700) -> q_gen_3699
<nil, cons, cons>(q_gen_3564, q_gen_3593, q_gen_3562, q_gen_3701) -> q_gen_3700
<nil, cons, a>(q_gen_3592, q_gen_3582) -> q_gen_3702
<a, cons, cons>(q_gen_3564, q_gen_3593, q_gen_3562, q_gen_3701) -> q_gen_3703
<a, cons, a>(q_gen_3592, q_gen_3582) -> q_gen_3704
<a, b, cons>(q_gen_3592, q_gen_3603) -> q_gen_3705
<cons, cons, cons>(q_gen_3686, q_gen_3708, q_gen_3654, q_gen_3653, q_gen_3683, q_gen_3707, q_gen_3651, q_gen_3608) -> q_gen_3706
<nil, a, cons>(q_gen_3592, q_gen_3582) -> q_gen_3707
<a, a, cons>(q_gen_3592, q_gen_3582) -> q_gen_3708
<nil, cons, cons>(q_gen_3570, q_gen_3713, q_gen_3712, q_gen_3580) -> q_gen_3711
<cons, cons, cons>(q_gen_3640, q_gen_3721, q_gen_3720, q_gen_3719, q_gen_3637, q_gen_3717, q_gen_3716, q_gen_3715) -> q_gen_3714
<nil, cons, cons>(q_gen_3570, q_gen_3713, q_gen_3568, q_gen_3627) -> q_gen_3715
<nil, cons, b>(q_gen_3583, q_gen_3582) -> q_gen_3716
<nil, a, cons>(q_gen_3583, q_gen_3718) -> q_gen_3717
<b, cons, cons>(q_gen_3570, q_gen_3713, q_gen_3568, q_gen_3627) -> q_gen_3719
<b, cons, b>(q_gen_3583, q_gen_3582) -> q_gen_3720
<b, a, cons>(q_gen_3583, q_gen_3718) -> q_gen_3721
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_3555, q_gen_3558, q_gen_3559, q_gen_3576, q_gen_3577, q_gen_3594, q_gen_3595, q_gen_3596, q_gen_3605, q_gen_3606, q_gen_3621, q_gen_3622, q_gen_3623, q_gen_3624, q_gen_3689},
Q_f={},
Delta=
{
<z>() -> q_gen_3596
<s>(q_gen_3596) -> q_gen_3624
<nil, z>() -> q_gen_3555
<cons, s>(q_gen_3559, q_gen_3555) -> q_gen_3558
<b, z>() -> q_gen_3559
<cons, s>(q_gen_3577, q_gen_3555) -> q_gen_3576
<a, z>() -> q_gen_3577
<cons, s>(q_gen_3595, q_gen_3576) -> q_gen_3594
<b, s>(q_gen_3596) -> q_gen_3595
<cons, s>(q_gen_3606, q_gen_3558) -> q_gen_3605
<a, s>(q_gen_3596) -> q_gen_3606
<cons, s>(q_gen_3595, q_gen_3558) -> q_gen_3621
<cons, s>(q_gen_3623, q_gen_3621) -> q_gen_3622
<b, s>(q_gen_3624) -> q_gen_3623
<cons, s>(q_gen_3623, q_gen_3605) -> q_gen_3689
}

Datatype: <eltlist, nat>
Convolution form: complete
}}}
  ;  leq -> 
{{{
Q={q_gen_3552, q_gen_3553, q_gen_3554, q_gen_3557, q_gen_3565, q_gen_3566, q_gen_3634, q_gen_3649, q_gen_3693},
Q_f={},
Delta=
{
<z>() -> q_gen_3554
<s>(q_gen_3554) -> q_gen_3566
<z, z>() -> q_gen_3552
<z, s>(q_gen_3554) -> q_gen_3553
<s, s>(q_gen_3552) -> q_gen_3557
<z, s>(q_gen_3566) -> q_gen_3565
<s, z>(q_gen_3554) -> q_gen_3634
<s, s>(q_gen_3634) -> q_gen_3649
<s, s>(q_gen_3649) -> q_gen_3693
}

Datatype: <nat, nat>
Convolution form: complete
}}}
  ;  reverse -> 
{{{
Q={q_gen_3551, q_gen_3572, q_gen_3573, q_gen_3574, q_gen_3575, q_gen_3585, q_gen_3586, q_gen_3587, q_gen_3588, q_gen_3616, q_gen_3617, q_gen_3618, q_gen_3619, q_gen_3620, q_gen_3629, q_gen_3630, q_gen_3631, q_gen_3632, q_gen_3633, q_gen_3644, q_gen_3645, q_gen_3646, q_gen_3647, q_gen_3648, q_gen_3662, q_gen_3679, q_gen_3680, q_gen_3681, q_gen_3687, q_gen_3688, q_gen_3690, q_gen_3691, q_gen_3692, q_gen_3695, q_gen_3696, q_gen_3697, q_gen_3698, q_gen_3709, q_gen_3710},
Q_f={},
Delta=
{
<nil>() -> q_gen_3618
<b>() -> q_gen_3619
<a>() -> q_gen_3631
<cons>(q_gen_3619, q_gen_3618) -> q_gen_3646
<nil, nil>() -> q_gen_3551
<cons, cons>(q_gen_3575, q_gen_3574, q_gen_3573, q_gen_3551) -> q_gen_3572
<nil, b>() -> q_gen_3573
<b, nil>() -> q_gen_3574
<b, b>() -> q_gen_3575
<cons, cons>(q_gen_3588, q_gen_3587, q_gen_3586, q_gen_3551) -> q_gen_3585
<nil, a>() -> q_gen_3586
<a, nil>() -> q_gen_3587
<a, a>() -> q_gen_3588
<cons, cons>(q_gen_3575, q_gen_3620, q_gen_3617, q_gen_3572) -> q_gen_3616
<cons, b>(q_gen_3619, q_gen_3618) -> q_gen_3617
<b, cons>(q_gen_3619, q_gen_3618) -> q_gen_3620
<cons, cons>(q_gen_3575, q_gen_3632, q_gen_3573, q_gen_3630) -> q_gen_3629
<nil, cons>(q_gen_3631, q_gen_3618) -> q_gen_3630
<b, cons>(q_gen_3631, q_gen_3618) -> q_gen_3632
<nil, cons>(q_gen_3619, q_gen_3618) -> q_gen_3633
<cons, cons>(q_gen_3575, q_gen_3647, q_gen_3573, q_gen_3645) -> q_gen_3644
<nil, cons>(q_gen_3619, q_gen_3646) -> q_gen_3645
<b, cons>(q_gen_3619, q_gen_3646) -> q_gen_3647
<cons, cons>(q_gen_3575, q_gen_3620, q_gen_3573, q_gen_3633) -> q_gen_3648
<cons, cons>(q_gen_3575, q_gen_3647, q_gen_3617, q_gen_3648) -> q_gen_3662
<cons, cons>(q_gen_3575, q_gen_3632, q_gen_3617, q_gen_3680) -> q_gen_3679
<cons, cons>(q_gen_3681, q_gen_3574, q_gen_3586, q_gen_3551) -> q_gen_3680
<b, a>() -> q_gen_3681
<cons, cons>(q_gen_3681, q_gen_3620, q_gen_3688, q_gen_3572) -> q_gen_3687
<cons, a>(q_gen_3619, q_gen_3618) -> q_gen_3688
<cons, cons>(q_gen_3575, q_gen_3692, q_gen_3617, q_gen_3691) -> q_gen_3690
<cons, cons>(q_gen_3681, q_gen_3620, q_gen_3586, q_gen_3633) -> q_gen_3691
<b, cons>(q_gen_3631, q_gen_3646) -> q_gen_3692
<cons, cons>(q_gen_3681, q_gen_3620, q_gen_3698, q_gen_3696) -> q_gen_3695
<cons, cons>(q_gen_3697, q_gen_3587, q_gen_3573, q_gen_3551) -> q_gen_3696
<a, b>() -> q_gen_3697
<cons, a>(q_gen_3631, q_gen_3618) -> q_gen_3698
<cons, cons>(q_gen_3588, q_gen_3710, q_gen_3688, q_gen_3572) -> q_gen_3709
<a, cons>(q_gen_3619, q_gen_3618) -> q_gen_3710
}

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

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

-------------------
STEPS:
-------------------------------------------
Step 0, which took 0.004360 s (model generation: 0.003907,  model checking: 0.000453):

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

}

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

}

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

}

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

}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 0  ;  () -> length([nil, z]) -> 0  ;  () -> leq([z, s(nn2)]) -> 0  ;  () -> leq([z, z]) -> 0  ;  () -> reverse([nil, nil]) -> 3  ;  (append([_wda, cons(h1, nil), _xda]) /\ reverse([t1, _wda])) -> reverse([cons(h1, t1), _xda]) -> 1  ;  (append([t1, l2, _rda])) -> append([cons(h1, t1), l2, cons(h1, _rda)]) -> 1  ;  (length([_gea, _hea]) /\ length([l1, _fea]) /\ reverse([l1, _gea])) -> leq([_fea, _hea]) -> 1  ;  (length([_iea, _jea]) /\ length([l1, _kea]) /\ reverse([l1, _iea])) -> leq([_jea, _kea]) -> 1  ;  (length([ll, _bea])) -> length([cons(x, ll), s(_bea)]) -> 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 0.003586 s (model generation: 0.003559,  model checking: 0.000027):

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

}

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

}

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

}

Datatype: <nat, nat>
Convolution form: complete
}}}
  ;  reverse -> 
{{{
Q={q_gen_3551},
Q_f={q_gen_3551},
Delta=
{
<nil, nil>() -> q_gen_3551
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 0  ;  () -> length([nil, z]) -> 0  ;  () -> leq([z, s(nn2)]) -> 0  ;  () -> leq([z, z]) -> 3  ;  () -> reverse([nil, nil]) -> 3  ;  (append([_wda, cons(h1, nil), _xda]) /\ reverse([t1, _wda])) -> reverse([cons(h1, t1), _xda]) -> 1  ;  (append([t1, l2, _rda])) -> append([cons(h1, t1), l2, cons(h1, _rda)]) -> 1  ;  (length([_gea, _hea]) /\ length([l1, _fea]) /\ reverse([l1, _gea])) -> leq([_fea, _hea]) -> 1  ;  (length([_iea, _jea]) /\ length([l1, _kea]) /\ reverse([l1, _iea])) -> leq([_jea, _kea]) -> 1  ;  (length([ll, _bea])) -> length([cons(x, ll), s(_bea)]) -> 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 0.003469 s (model generation: 0.003426,  model checking: 0.000043):

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

}

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

}

Datatype: <eltlist, nat>
Convolution form: complete
}}}
  ;  leq -> 
{{{
Q={q_gen_3552},
Q_f={q_gen_3552},
Delta=
{
<z, z>() -> q_gen_3552
}

Datatype: <nat, nat>
Convolution form: complete
}}}
  ;  reverse -> 
{{{
Q={q_gen_3551},
Q_f={q_gen_3551},
Delta=
{
<nil, nil>() -> q_gen_3551
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 0  ;  () -> length([nil, z]) -> 0  ;  () -> leq([z, s(nn2)]) -> 3  ;  () -> leq([z, z]) -> 3  ;  () -> reverse([nil, nil]) -> 3  ;  (append([_wda, cons(h1, nil), _xda]) /\ reverse([t1, _wda])) -> reverse([cons(h1, t1), _xda]) -> 1  ;  (append([t1, l2, _rda])) -> append([cons(h1, t1), l2, cons(h1, _rda)]) -> 1  ;  (length([_gea, _hea]) /\ length([l1, _fea]) /\ reverse([l1, _gea])) -> leq([_fea, _hea]) -> 1  ;  (length([_iea, _jea]) /\ length([l1, _kea]) /\ reverse([l1, _iea])) -> leq([_jea, _kea]) -> 1  ;  (length([ll, _bea])) -> length([cons(x, ll), s(_bea)]) -> 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 0.003416 s (model generation: 0.003374,  model checking: 0.000042):

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

}

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

}

Datatype: <eltlist, nat>
Convolution form: complete
}}}
  ;  leq -> 
{{{
Q={q_gen_3552, q_gen_3554},
Q_f={q_gen_3552},
Delta=
{
<z>() -> q_gen_3554
<z, s>(q_gen_3554) -> q_gen_3552
<z, z>() -> q_gen_3552
}

Datatype: <nat, nat>
Convolution form: complete
}}}
  ;  reverse -> 
{{{
Q={q_gen_3551},
Q_f={q_gen_3551},
Delta=
{
<nil, nil>() -> q_gen_3551
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 0  ;  () -> length([nil, z]) -> 3  ;  () -> leq([z, s(nn2)]) -> 3  ;  () -> leq([z, z]) -> 3  ;  () -> reverse([nil, nil]) -> 3  ;  (append([_wda, cons(h1, nil), _xda]) /\ reverse([t1, _wda])) -> reverse([cons(h1, t1), _xda]) -> 1  ;  (append([t1, l2, _rda])) -> append([cons(h1, t1), l2, cons(h1, _rda)]) -> 1  ;  (length([_gea, _hea]) /\ length([l1, _fea]) /\ reverse([l1, _gea])) -> leq([_fea, _hea]) -> 1  ;  (length([_iea, _jea]) /\ length([l1, _kea]) /\ reverse([l1, _iea])) -> leq([_jea, _kea]) -> 1  ;  (length([ll, _bea])) -> length([cons(x, ll), s(_bea)]) -> 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 0.004078 s (model generation: 0.003573,  model checking: 0.000505):

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

}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_3555},
Q_f={q_gen_3555},
Delta=
{
<nil, z>() -> q_gen_3555
}

Datatype: <eltlist, nat>
Convolution form: complete
}}}
  ;  leq -> 
{{{
Q={q_gen_3552, q_gen_3554},
Q_f={q_gen_3552},
Delta=
{
<z>() -> q_gen_3554
<z, s>(q_gen_3554) -> q_gen_3552
<z, z>() -> q_gen_3552
}

Datatype: <nat, nat>
Convolution form: complete
}}}
  ;  reverse -> 
{{{
Q={q_gen_3551},
Q_f={q_gen_3551},
Delta=
{
<nil, nil>() -> q_gen_3551
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 3  ;  () -> length([nil, z]) -> 3  ;  () -> leq([z, s(nn2)]) -> 3  ;  () -> leq([z, z]) -> 3  ;  () -> reverse([nil, nil]) -> 3  ;  (append([_wda, cons(h1, nil), _xda]) /\ reverse([t1, _wda])) -> reverse([cons(h1, t1), _xda]) -> 1  ;  (append([t1, l2, _rda])) -> append([cons(h1, t1), l2, cons(h1, _rda)]) -> 1  ;  (length([_gea, _hea]) /\ length([l1, _fea]) /\ reverse([l1, _gea])) -> leq([_fea, _hea]) -> 1  ;  (length([_iea, _jea]) /\ length([l1, _kea]) /\ reverse([l1, _iea])) -> leq([_jea, _kea]) -> 1  ;  (length([ll, _bea])) -> length([cons(x, ll), s(_bea)]) -> 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 0.004675 s (model generation: 0.004563,  model checking: 0.000112):

Model:
|_
{
append -> 
{{{
Q={q_gen_3556},
Q_f={q_gen_3556},
Delta=
{
<nil, nil, nil>() -> q_gen_3556
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_3555},
Q_f={q_gen_3555},
Delta=
{
<nil, z>() -> q_gen_3555
}

Datatype: <eltlist, nat>
Convolution form: complete
}}}
  ;  leq -> 
{{{
Q={q_gen_3552, q_gen_3554},
Q_f={q_gen_3552},
Delta=
{
<z>() -> q_gen_3554
<z, s>(q_gen_3554) -> q_gen_3552
<z, z>() -> q_gen_3552
}

Datatype: <nat, nat>
Convolution form: complete
}}}
  ;  reverse -> 
{{{
Q={q_gen_3551},
Q_f={q_gen_3551},
Delta=
{
<nil, nil>() -> q_gen_3551
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 3  ;  () -> length([nil, z]) -> 3  ;  () -> leq([z, s(nn2)]) -> 3  ;  () -> leq([z, z]) -> 3  ;  () -> reverse([nil, nil]) -> 3  ;  (append([_wda, cons(h1, nil), _xda]) /\ reverse([t1, _wda])) -> reverse([cons(h1, t1), _xda]) -> 1  ;  (append([t1, l2, _rda])) -> append([cons(h1, t1), l2, cons(h1, _rda)]) -> 1  ;  (length([_gea, _hea]) /\ length([l1, _fea]) /\ reverse([l1, _gea])) -> leq([_fea, _hea]) -> 1  ;  (length([_iea, _jea]) /\ length([l1, _kea]) /\ reverse([l1, _iea])) -> leq([_jea, _kea]) -> 1  ;  (length([ll, _bea])) -> length([cons(x, ll), s(_bea)]) -> 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 0.007117 s (model generation: 0.006919,  model checking: 0.000198):

Model:
|_
{
append -> 
{{{
Q={q_gen_3556},
Q_f={q_gen_3556},
Delta=
{
<nil, nil, nil>() -> q_gen_3556
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_3555},
Q_f={q_gen_3555},
Delta=
{
<nil, z>() -> q_gen_3555
}

Datatype: <eltlist, nat>
Convolution form: complete
}}}
  ;  leq -> 
{{{
Q={q_gen_3552, q_gen_3554},
Q_f={q_gen_3552},
Delta=
{
<z>() -> q_gen_3554
<s, s>(q_gen_3552) -> q_gen_3552
<z, s>(q_gen_3554) -> q_gen_3552
<z, z>() -> q_gen_3552
}

Datatype: <nat, nat>
Convolution form: complete
}}}
  ;  reverse -> 
{{{
Q={q_gen_3551},
Q_f={q_gen_3551},
Delta=
{
<nil, nil>() -> q_gen_3551
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 3  ;  () -> length([nil, z]) -> 3  ;  () -> leq([z, s(nn2)]) -> 3  ;  () -> leq([z, z]) -> 3  ;  () -> reverse([nil, nil]) -> 3  ;  (append([_wda, cons(h1, nil), _xda]) /\ reverse([t1, _wda])) -> reverse([cons(h1, t1), _xda]) -> 1  ;  (append([t1, l2, _rda])) -> append([cons(h1, t1), l2, cons(h1, _rda)]) -> 1  ;  (length([_gea, _hea]) /\ length([l1, _fea]) /\ reverse([l1, _gea])) -> leq([_fea, _hea]) -> 1  ;  (length([_iea, _jea]) /\ length([l1, _kea]) /\ reverse([l1, _iea])) -> leq([_jea, _kea]) -> 1  ;  (length([ll, _bea])) -> length([cons(x, ll), s(_bea)]) -> 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, _bea])) -> length([cons(x, ll), s(_bea)]), {
_bea -> z  ;  ll -> nil  ;  x -> b
})

-------------------------------------------
Step 7, which took 0.011329 s (model generation: 0.010121,  model checking: 0.001208):

Model:
|_
{
append -> 
{{{
Q={q_gen_3556},
Q_f={q_gen_3556},
Delta=
{
<nil, nil, nil>() -> q_gen_3556
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_3555, q_gen_3559},
Q_f={q_gen_3555},
Delta=
{
<cons, s>(q_gen_3559, q_gen_3555) -> q_gen_3555
<nil, z>() -> q_gen_3555
<b, z>() -> q_gen_3559
}

Datatype: <eltlist, nat>
Convolution form: complete
}}}
  ;  leq -> 
{{{
Q={q_gen_3552, q_gen_3554},
Q_f={q_gen_3552},
Delta=
{
<z>() -> q_gen_3554
<s, s>(q_gen_3552) -> q_gen_3552
<z, s>(q_gen_3554) -> q_gen_3552
<z, z>() -> q_gen_3552
}

Datatype: <nat, nat>
Convolution form: complete
}}}
  ;  reverse -> 
{{{
Q={q_gen_3551},
Q_f={q_gen_3551},
Delta=
{
<nil, nil>() -> q_gen_3551
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 3  ;  () -> length([nil, z]) -> 3  ;  () -> leq([z, s(nn2)]) -> 3  ;  () -> leq([z, z]) -> 3  ;  () -> reverse([nil, nil]) -> 3  ;  (append([_wda, cons(h1, nil), _xda]) /\ reverse([t1, _wda])) -> reverse([cons(h1, t1), _xda]) -> 1  ;  (append([t1, l2, _rda])) -> append([cons(h1, t1), l2, cons(h1, _rda)]) -> 4  ;  (length([_gea, _hea]) /\ length([l1, _fea]) /\ reverse([l1, _gea])) -> leq([_fea, _hea]) -> 2  ;  (length([_iea, _jea]) /\ length([l1, _kea]) /\ reverse([l1, _iea])) -> leq([_jea, _kea]) -> 2  ;  (length([ll, _bea])) -> length([cons(x, ll), s(_bea)]) -> 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, _rda])) -> append([cons(h1, t1), l2, cons(h1, _rda)]), {
_rda -> nil  ;  h1 -> b  ;  l2 -> nil  ;  t1 -> nil
})

-------------------------------------------
Step 8, which took 0.010026 s (model generation: 0.009686,  model checking: 0.000340):

Model:
|_
{
append -> 
{{{
Q={q_gen_3556, q_gen_3561, q_gen_3562, q_gen_3563, q_gen_3564},
Q_f={q_gen_3556},
Delta=
{
<nil, nil>() -> q_gen_3561
<nil, b>() -> q_gen_3562
<b, nil>() -> q_gen_3563
<b, b>() -> q_gen_3564
<cons, nil, cons>(q_gen_3564, q_gen_3563, q_gen_3562, q_gen_3561) -> q_gen_3556
<nil, nil, nil>() -> q_gen_3556
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_3555, q_gen_3559},
Q_f={q_gen_3555},
Delta=
{
<cons, s>(q_gen_3559, q_gen_3555) -> q_gen_3555
<nil, z>() -> q_gen_3555
<b, z>() -> q_gen_3559
}

Datatype: <eltlist, nat>
Convolution form: complete
}}}
  ;  leq -> 
{{{
Q={q_gen_3552, q_gen_3554},
Q_f={q_gen_3552},
Delta=
{
<z>() -> q_gen_3554
<s, s>(q_gen_3552) -> q_gen_3552
<z, s>(q_gen_3554) -> q_gen_3552
<z, z>() -> q_gen_3552
}

Datatype: <nat, nat>
Convolution form: complete
}}}
  ;  reverse -> 
{{{
Q={q_gen_3551},
Q_f={q_gen_3551},
Delta=
{
<nil, nil>() -> q_gen_3551
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 3  ;  () -> length([nil, z]) -> 3  ;  () -> leq([z, s(nn2)]) -> 6  ;  () -> leq([z, z]) -> 4  ;  () -> reverse([nil, nil]) -> 4  ;  (append([_wda, cons(h1, nil), _xda]) /\ reverse([t1, _wda])) -> reverse([cons(h1, t1), _xda]) -> 2  ;  (append([t1, l2, _rda])) -> append([cons(h1, t1), l2, cons(h1, _rda)]) -> 4  ;  (length([_gea, _hea]) /\ length([l1, _fea]) /\ reverse([l1, _gea])) -> leq([_fea, _hea]) -> 3  ;  (length([_iea, _jea]) /\ length([l1, _kea]) /\ reverse([l1, _iea])) -> leq([_jea, _kea]) -> 3  ;  (length([ll, _bea])) -> length([cons(x, ll), s(_bea)]) -> 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 0.010554 s (model generation: 0.009298,  model checking: 0.001256):

Model:
|_
{
append -> 
{{{
Q={q_gen_3556, q_gen_3561, q_gen_3562, q_gen_3563, q_gen_3564},
Q_f={q_gen_3556},
Delta=
{
<nil, nil>() -> q_gen_3561
<nil, b>() -> q_gen_3562
<b, nil>() -> q_gen_3563
<b, b>() -> q_gen_3564
<cons, nil, cons>(q_gen_3564, q_gen_3563, q_gen_3562, q_gen_3561) -> q_gen_3556
<nil, nil, nil>() -> q_gen_3556
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_3555, q_gen_3559},
Q_f={q_gen_3555},
Delta=
{
<cons, s>(q_gen_3559, q_gen_3555) -> q_gen_3555
<nil, z>() -> q_gen_3555
<b, z>() -> q_gen_3559
}

Datatype: <eltlist, nat>
Convolution form: complete
}}}
  ;  leq -> 
{{{
Q={q_gen_3552, q_gen_3554},
Q_f={q_gen_3552},
Delta=
{
<s>(q_gen_3554) -> q_gen_3554
<z>() -> q_gen_3554
<s, s>(q_gen_3552) -> q_gen_3552
<z, s>(q_gen_3554) -> q_gen_3552
<z, z>() -> q_gen_3552
}

Datatype: <nat, nat>
Convolution form: complete
}}}
  ;  reverse -> 
{{{
Q={q_gen_3551},
Q_f={q_gen_3551},
Delta=
{
<nil, nil>() -> q_gen_3551
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 6  ;  () -> length([nil, z]) -> 4  ;  () -> leq([z, s(nn2)]) -> 6  ;  () -> leq([z, z]) -> 4  ;  () -> reverse([nil, nil]) -> 4  ;  (append([_wda, cons(h1, nil), _xda]) /\ reverse([t1, _wda])) -> reverse([cons(h1, t1), _xda]) -> 3  ;  (append([t1, l2, _rda])) -> append([cons(h1, t1), l2, cons(h1, _rda)]) -> 4  ;  (length([_gea, _hea]) /\ length([l1, _fea]) /\ reverse([l1, _gea])) -> leq([_fea, _hea]) -> 4  ;  (length([_iea, _jea]) /\ length([l1, _kea]) /\ reverse([l1, _iea])) -> leq([_jea, _kea]) -> 4  ;  (length([ll, _bea])) -> length([cons(x, ll), s(_bea)]) -> 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(a, nil)
})

-------------------------------------------
Step 10, which took 0.012240 s (model generation: 0.011763,  model checking: 0.000477):

Model:
|_
{
append -> 
{{{
Q={q_gen_3556, q_gen_3561, q_gen_3562, q_gen_3563, q_gen_3564},
Q_f={q_gen_3556},
Delta=
{
<nil, nil>() -> q_gen_3561
<nil, a>() -> q_gen_3562
<nil, b>() -> q_gen_3562
<a, nil>() -> q_gen_3563
<b, nil>() -> q_gen_3563
<a, a>() -> q_gen_3564
<b, b>() -> q_gen_3564
<cons, nil, cons>(q_gen_3564, q_gen_3563, q_gen_3562, q_gen_3561) -> q_gen_3556
<nil, cons, cons>(q_gen_3564, q_gen_3563, q_gen_3562, q_gen_3561) -> q_gen_3556
<nil, nil, nil>() -> q_gen_3556
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_3555, q_gen_3559},
Q_f={q_gen_3555},
Delta=
{
<cons, s>(q_gen_3559, q_gen_3555) -> q_gen_3555
<nil, z>() -> q_gen_3555
<b, z>() -> q_gen_3559
}

Datatype: <eltlist, nat>
Convolution form: complete
}}}
  ;  leq -> 
{{{
Q={q_gen_3552, q_gen_3554},
Q_f={q_gen_3552},
Delta=
{
<s>(q_gen_3554) -> q_gen_3554
<z>() -> q_gen_3554
<s, s>(q_gen_3552) -> q_gen_3552
<z, s>(q_gen_3554) -> q_gen_3552
<z, z>() -> q_gen_3552
}

Datatype: <nat, nat>
Convolution form: complete
}}}
  ;  reverse -> 
{{{
Q={q_gen_3551},
Q_f={q_gen_3551},
Delta=
{
<nil, nil>() -> q_gen_3551
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 6  ;  () -> length([nil, z]) -> 4  ;  () -> leq([z, s(nn2)]) -> 6  ;  () -> leq([z, z]) -> 4  ;  () -> reverse([nil, nil]) -> 4  ;  (append([_wda, cons(h1, nil), _xda]) /\ reverse([t1, _wda])) -> reverse([cons(h1, t1), _xda]) -> 6  ;  (append([t1, l2, _rda])) -> append([cons(h1, t1), l2, cons(h1, _rda)]) -> 4  ;  (length([_gea, _hea]) /\ length([l1, _fea]) /\ reverse([l1, _gea])) -> leq([_fea, _hea]) -> 4  ;  (length([_iea, _jea]) /\ length([l1, _kea]) /\ reverse([l1, _iea])) -> leq([_jea, _kea]) -> 4  ;  (length([ll, _bea])) -> length([cons(x, ll), s(_bea)]) -> 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([_wda, cons(h1, nil), _xda]) /\ reverse([t1, _wda])) -> reverse([cons(h1, t1), _xda]), {
_wda -> nil  ;  _xda -> cons(b, nil)  ;  h1 -> b  ;  t1 -> nil
})

-------------------------------------------
Step 11, which took 0.015149 s (model generation: 0.013344,  model checking: 0.001805):

Model:
|_
{
append -> 
{{{
Q={q_gen_3556, q_gen_3561, q_gen_3562, q_gen_3563, q_gen_3564},
Q_f={q_gen_3556},
Delta=
{
<nil, nil>() -> q_gen_3561
<nil, a>() -> q_gen_3562
<nil, b>() -> q_gen_3562
<a, nil>() -> q_gen_3563
<b, nil>() -> q_gen_3563
<a, a>() -> q_gen_3564
<b, b>() -> q_gen_3564
<cons, nil, cons>(q_gen_3564, q_gen_3563, q_gen_3562, q_gen_3561) -> q_gen_3556
<nil, cons, cons>(q_gen_3564, q_gen_3563, q_gen_3562, q_gen_3561) -> q_gen_3556
<nil, nil, nil>() -> q_gen_3556
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_3555, q_gen_3559},
Q_f={q_gen_3555},
Delta=
{
<cons, s>(q_gen_3559, q_gen_3555) -> q_gen_3555
<nil, z>() -> q_gen_3555
<b, z>() -> q_gen_3559
}

Datatype: <eltlist, nat>
Convolution form: complete
}}}
  ;  leq -> 
{{{
Q={q_gen_3552, q_gen_3554},
Q_f={q_gen_3552},
Delta=
{
<s>(q_gen_3554) -> q_gen_3554
<z>() -> q_gen_3554
<s, s>(q_gen_3552) -> q_gen_3552
<z, s>(q_gen_3554) -> q_gen_3552
<z, z>() -> q_gen_3552
}

Datatype: <nat, nat>
Convolution form: complete
}}}
  ;  reverse -> 
{{{
Q={q_gen_3551, q_gen_3573, q_gen_3574, q_gen_3575},
Q_f={q_gen_3551},
Delta=
{
<cons, cons>(q_gen_3575, q_gen_3574, q_gen_3573, q_gen_3551) -> q_gen_3551
<nil, nil>() -> q_gen_3551
<nil, b>() -> q_gen_3573
<b, nil>() -> q_gen_3574
<b, b>() -> q_gen_3575
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 6  ;  () -> length([nil, z]) -> 4  ;  () -> leq([z, s(nn2)]) -> 6  ;  () -> leq([z, z]) -> 4  ;  () -> reverse([nil, nil]) -> 4  ;  (append([_wda, cons(h1, nil), _xda]) /\ reverse([t1, _wda])) -> reverse([cons(h1, t1), _xda]) -> 6  ;  (append([t1, l2, _rda])) -> append([cons(h1, t1), l2, cons(h1, _rda)]) -> 4  ;  (length([_gea, _hea]) /\ length([l1, _fea]) /\ reverse([l1, _gea])) -> leq([_fea, _hea]) -> 4  ;  (length([_iea, _jea]) /\ length([l1, _kea]) /\ reverse([l1, _iea])) -> leq([_jea, _kea]) -> 4  ;  (length([ll, _bea])) -> length([cons(x, ll), s(_bea)]) -> 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, _bea])) -> length([cons(x, ll), s(_bea)]), {
_bea -> z  ;  ll -> nil  ;  x -> a
})

-------------------------------------------
Step 12, which took 0.019702 s (model generation: 0.011566,  model checking: 0.008136):

Model:
|_
{
append -> 
{{{
Q={q_gen_3556, q_gen_3561, q_gen_3562, q_gen_3563, q_gen_3564},
Q_f={q_gen_3556},
Delta=
{
<nil, nil>() -> q_gen_3561
<nil, a>() -> q_gen_3562
<nil, b>() -> q_gen_3562
<a, nil>() -> q_gen_3563
<b, nil>() -> q_gen_3563
<a, a>() -> q_gen_3564
<b, b>() -> q_gen_3564
<cons, nil, cons>(q_gen_3564, q_gen_3563, q_gen_3562, q_gen_3561) -> q_gen_3556
<nil, cons, cons>(q_gen_3564, q_gen_3563, q_gen_3562, q_gen_3561) -> q_gen_3556
<nil, nil, nil>() -> q_gen_3556
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_3555, q_gen_3559},
Q_f={q_gen_3555},
Delta=
{
<cons, s>(q_gen_3559, q_gen_3555) -> q_gen_3555
<nil, z>() -> q_gen_3555
<a, z>() -> q_gen_3559
<b, z>() -> q_gen_3559
}

Datatype: <eltlist, nat>
Convolution form: complete
}}}
  ;  leq -> 
{{{
Q={q_gen_3552, q_gen_3554},
Q_f={q_gen_3552},
Delta=
{
<s>(q_gen_3554) -> q_gen_3554
<z>() -> q_gen_3554
<s, s>(q_gen_3552) -> q_gen_3552
<z, s>(q_gen_3554) -> q_gen_3552
<z, z>() -> q_gen_3552
}

Datatype: <nat, nat>
Convolution form: complete
}}}
  ;  reverse -> 
{{{
Q={q_gen_3551, q_gen_3573, q_gen_3574, q_gen_3575},
Q_f={q_gen_3551},
Delta=
{
<cons, cons>(q_gen_3575, q_gen_3574, q_gen_3573, q_gen_3551) -> q_gen_3551
<nil, nil>() -> q_gen_3551
<nil, b>() -> q_gen_3573
<b, nil>() -> q_gen_3574
<b, b>() -> q_gen_3575
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 6  ;  () -> length([nil, z]) -> 4  ;  () -> leq([z, s(nn2)]) -> 6  ;  () -> leq([z, z]) -> 4  ;  () -> reverse([nil, nil]) -> 4  ;  (append([_wda, cons(h1, nil), _xda]) /\ reverse([t1, _wda])) -> reverse([cons(h1, t1), _xda]) -> 6  ;  (append([t1, l2, _rda])) -> append([cons(h1, t1), l2, cons(h1, _rda)]) -> 7  ;  (length([_gea, _hea]) /\ length([l1, _fea]) /\ reverse([l1, _gea])) -> leq([_fea, _hea]) -> 5  ;  (length([_iea, _jea]) /\ length([l1, _kea]) /\ reverse([l1, _iea])) -> leq([_jea, _kea]) -> 5  ;  (length([ll, _bea])) -> length([cons(x, ll), s(_bea)]) -> 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, _rda])) -> append([cons(h1, t1), l2, cons(h1, _rda)]), {
_rda -> cons(a, nil)  ;  h1 -> b  ;  l2 -> nil  ;  t1 -> cons(a, nil)
})

-------------------------------------------
Step 13, which took 0.018374 s (model generation: 0.015436,  model checking: 0.002938):

Model:
|_
{
append -> 
{{{
Q={q_gen_3556, q_gen_3561, q_gen_3562, q_gen_3563, q_gen_3564, q_gen_3582, q_gen_3583},
Q_f={q_gen_3556},
Delta=
{
<nil>() -> q_gen_3582
<a>() -> q_gen_3583
<cons, cons>(q_gen_3564, q_gen_3563, q_gen_3562, q_gen_3561) -> q_gen_3561
<nil, nil>() -> q_gen_3561
<cons, b>(q_gen_3583, q_gen_3582) -> q_gen_3562
<nil, a>() -> q_gen_3562
<nil, b>() -> q_gen_3562
<a, nil>() -> q_gen_3563
<b, cons>(q_gen_3583, q_gen_3582) -> q_gen_3563
<b, nil>() -> q_gen_3563
<a, a>() -> q_gen_3564
<b, b>() -> q_gen_3564
<cons, nil, cons>(q_gen_3564, q_gen_3563, q_gen_3562, q_gen_3561) -> q_gen_3556
<nil, cons, cons>(q_gen_3564, q_gen_3563, q_gen_3562, q_gen_3561) -> q_gen_3556
<nil, nil, nil>() -> q_gen_3556
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_3555, q_gen_3559},
Q_f={q_gen_3555},
Delta=
{
<cons, s>(q_gen_3559, q_gen_3555) -> q_gen_3555
<nil, z>() -> q_gen_3555
<a, z>() -> q_gen_3559
<b, z>() -> q_gen_3559
}

Datatype: <eltlist, nat>
Convolution form: complete
}}}
  ;  leq -> 
{{{
Q={q_gen_3552, q_gen_3554},
Q_f={q_gen_3552},
Delta=
{
<s>(q_gen_3554) -> q_gen_3554
<z>() -> q_gen_3554
<s, s>(q_gen_3552) -> q_gen_3552
<z, s>(q_gen_3554) -> q_gen_3552
<z, z>() -> q_gen_3552
}

Datatype: <nat, nat>
Convolution form: complete
}}}
  ;  reverse -> 
{{{
Q={q_gen_3551, q_gen_3573, q_gen_3574, q_gen_3575},
Q_f={q_gen_3551},
Delta=
{
<cons, cons>(q_gen_3575, q_gen_3574, q_gen_3573, q_gen_3551) -> q_gen_3551
<nil, nil>() -> q_gen_3551
<nil, b>() -> q_gen_3573
<b, nil>() -> q_gen_3574
<b, b>() -> q_gen_3575
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 6  ;  () -> length([nil, z]) -> 5  ;  () -> leq([z, s(nn2)]) -> 6  ;  () -> leq([z, z]) -> 5  ;  () -> reverse([nil, nil]) -> 5  ;  (append([_wda, cons(h1, nil), _xda]) /\ reverse([t1, _wda])) -> reverse([cons(h1, t1), _xda]) -> 9  ;  (append([t1, l2, _rda])) -> append([cons(h1, t1), l2, cons(h1, _rda)]) -> 7  ;  (length([_gea, _hea]) /\ length([l1, _fea]) /\ reverse([l1, _gea])) -> leq([_fea, _hea]) -> 6  ;  (length([_iea, _jea]) /\ length([l1, _kea]) /\ reverse([l1, _iea])) -> leq([_jea, _kea]) -> 6  ;  (length([ll, _bea])) -> length([cons(x, ll), s(_bea)]) -> 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([_wda, cons(h1, nil), _xda]) /\ reverse([t1, _wda])) -> reverse([cons(h1, t1), _xda]), {
_wda -> nil  ;  _xda -> cons(a, nil)  ;  h1 -> a  ;  t1 -> nil
})

-------------------------------------------
Step 14, which took 0.038643 s (model generation: 0.016044,  model checking: 0.022599):

Model:
|_
{
append -> 
{{{
Q={q_gen_3556, q_gen_3561, q_gen_3562, q_gen_3563, q_gen_3564, q_gen_3582, q_gen_3583},
Q_f={q_gen_3556},
Delta=
{
<nil>() -> q_gen_3582
<a>() -> q_gen_3583
<cons, cons>(q_gen_3564, q_gen_3563, q_gen_3562, q_gen_3561) -> q_gen_3561
<nil, nil>() -> q_gen_3561
<cons, b>(q_gen_3583, q_gen_3582) -> q_gen_3562
<nil, a>() -> q_gen_3562
<nil, b>() -> q_gen_3562
<a, nil>() -> q_gen_3563
<b, cons>(q_gen_3583, q_gen_3582) -> q_gen_3563
<b, nil>() -> q_gen_3563
<a, a>() -> q_gen_3564
<b, b>() -> q_gen_3564
<cons, nil, cons>(q_gen_3564, q_gen_3563, q_gen_3562, q_gen_3561) -> q_gen_3556
<nil, cons, cons>(q_gen_3564, q_gen_3563, q_gen_3562, q_gen_3561) -> q_gen_3556
<nil, nil, nil>() -> q_gen_3556
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_3555, q_gen_3559},
Q_f={q_gen_3555},
Delta=
{
<cons, s>(q_gen_3559, q_gen_3555) -> q_gen_3555
<nil, z>() -> q_gen_3555
<a, z>() -> q_gen_3559
<b, z>() -> q_gen_3559
}

Datatype: <eltlist, nat>
Convolution form: complete
}}}
  ;  leq -> 
{{{
Q={q_gen_3552, q_gen_3554},
Q_f={q_gen_3552},
Delta=
{
<s>(q_gen_3554) -> q_gen_3554
<z>() -> q_gen_3554
<s, s>(q_gen_3552) -> q_gen_3552
<z, s>(q_gen_3554) -> q_gen_3552
<z, z>() -> q_gen_3552
}

Datatype: <nat, nat>
Convolution form: complete
}}}
  ;  reverse -> 
{{{
Q={q_gen_3551, q_gen_3573, q_gen_3574, q_gen_3575},
Q_f={q_gen_3551},
Delta=
{
<cons, cons>(q_gen_3575, q_gen_3574, q_gen_3573, q_gen_3551) -> q_gen_3551
<nil, nil>() -> q_gen_3551
<nil, a>() -> q_gen_3573
<nil, b>() -> q_gen_3573
<a, nil>() -> q_gen_3574
<b, nil>() -> q_gen_3574
<a, a>() -> q_gen_3575
<b, b>() -> q_gen_3575
}

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

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

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([_wda, cons(h1, nil), _xda]) /\ reverse([t1, _wda])) -> reverse([cons(h1, t1), _xda]) -> 9  ;  (append([t1, l2, _rda])) -> append([cons(h1, t1), l2, cons(h1, _rda)]) -> 7  ;  (length([_gea, _hea]) /\ length([l1, _fea]) /\ reverse([l1, _gea])) -> leq([_fea, _hea]) -> 7  ;  (length([_iea, _jea]) /\ length([l1, _kea]) /\ reverse([l1, _iea])) -> leq([_jea, _kea]) -> 7  ;  (length([ll, _bea])) -> length([cons(x, ll), s(_bea)]) -> 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(b, cons(b, nil))
})

-------------------------------------------
Step 15, which took 0.006181 s (model generation: 0.005655,  model checking: 0.000526):

Model:
|_
{
append -> 
{{{
Q={q_gen_3556, q_gen_3561, q_gen_3562, q_gen_3563, q_gen_3564, q_gen_3582, q_gen_3583},
Q_f={q_gen_3556},
Delta=
{
<nil>() -> q_gen_3582
<a>() -> q_gen_3583
<b>() -> q_gen_3583
<cons, cons>(q_gen_3564, q_gen_3563, q_gen_3562, q_gen_3561) -> q_gen_3561
<nil, nil>() -> q_gen_3561
<cons, b>(q_gen_3583, q_gen_3582) -> q_gen_3562
<nil, a>() -> q_gen_3562
<nil, b>() -> q_gen_3562
<a, nil>() -> q_gen_3563
<b, cons>(q_gen_3583, q_gen_3582) -> q_gen_3563
<b, nil>() -> q_gen_3563
<a, a>() -> q_gen_3564
<b, b>() -> q_gen_3564
<cons, nil, cons>(q_gen_3564, q_gen_3563, q_gen_3562, q_gen_3561) -> q_gen_3556
<nil, cons, cons>(q_gen_3564, q_gen_3563, q_gen_3562, q_gen_3561) -> q_gen_3556
<nil, nil, nil>() -> q_gen_3556
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_3555, q_gen_3559},
Q_f={q_gen_3555},
Delta=
{
<cons, s>(q_gen_3559, q_gen_3555) -> q_gen_3555
<nil, z>() -> q_gen_3555
<a, z>() -> q_gen_3559
<b, z>() -> q_gen_3559
}

Datatype: <eltlist, nat>
Convolution form: complete
}}}
  ;  leq -> 
{{{
Q={q_gen_3552, q_gen_3554},
Q_f={q_gen_3552},
Delta=
{
<s>(q_gen_3554) -> q_gen_3554
<z>() -> q_gen_3554
<s, s>(q_gen_3552) -> q_gen_3552
<z, s>(q_gen_3554) -> q_gen_3552
<z, z>() -> q_gen_3552
}

Datatype: <nat, nat>
Convolution form: complete
}}}
  ;  reverse -> 
{{{
Q={q_gen_3551, q_gen_3573, q_gen_3574, q_gen_3575},
Q_f={q_gen_3551},
Delta=
{
<cons, cons>(q_gen_3575, q_gen_3574, q_gen_3573, q_gen_3551) -> q_gen_3551
<nil, nil>() -> q_gen_3551
<nil, a>() -> q_gen_3573
<nil, b>() -> q_gen_3573
<a, nil>() -> q_gen_3574
<b, nil>() -> q_gen_3574
<a, a>() -> q_gen_3575
<b, b>() -> q_gen_3575
}

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

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

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([_wda, cons(h1, nil), _xda]) /\ reverse([t1, _wda])) -> reverse([cons(h1, t1), _xda]) -> 9  ;  (append([t1, l2, _rda])) -> append([cons(h1, t1), l2, cons(h1, _rda)]) -> 7  ;  (length([_gea, _hea]) /\ length([l1, _fea]) /\ reverse([l1, _gea])) -> leq([_fea, _hea]) -> 7  ;  (length([_iea, _jea]) /\ length([l1, _kea]) /\ reverse([l1, _iea])) -> leq([_jea, _kea]) -> 7  ;  (length([ll, _bea])) -> length([cons(x, ll), s(_bea)]) -> 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, _bea])) -> length([cons(x, ll), s(_bea)]), {
_bea -> s(z)  ;  ll -> cons(a, nil)  ;  x -> b
})

-------------------------------------------
Step 16, which took 0.016935 s (model generation: 0.007698,  model checking: 0.009237):

Model:
|_
{
append -> 
{{{
Q={q_gen_3556, q_gen_3561, q_gen_3562, q_gen_3563, q_gen_3564, q_gen_3582, q_gen_3583},
Q_f={q_gen_3556},
Delta=
{
<nil>() -> q_gen_3582
<a>() -> q_gen_3583
<b>() -> q_gen_3583
<cons, cons>(q_gen_3564, q_gen_3563, q_gen_3562, q_gen_3561) -> q_gen_3561
<nil, nil>() -> q_gen_3561
<cons, b>(q_gen_3583, q_gen_3582) -> q_gen_3562
<nil, a>() -> q_gen_3562
<nil, b>() -> q_gen_3562
<a, nil>() -> q_gen_3563
<b, cons>(q_gen_3583, q_gen_3582) -> q_gen_3563
<b, nil>() -> q_gen_3563
<a, a>() -> q_gen_3564
<b, b>() -> q_gen_3564
<cons, nil, cons>(q_gen_3564, q_gen_3563, q_gen_3562, q_gen_3561) -> q_gen_3556
<nil, cons, cons>(q_gen_3564, q_gen_3563, q_gen_3562, q_gen_3561) -> q_gen_3556
<nil, nil, nil>() -> q_gen_3556
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_3555, q_gen_3559, q_gen_3596},
Q_f={q_gen_3555},
Delta=
{
<z>() -> q_gen_3596
<cons, s>(q_gen_3559, q_gen_3555) -> q_gen_3555
<nil, z>() -> q_gen_3555
<a, z>() -> q_gen_3559
<b, s>(q_gen_3596) -> q_gen_3559
<b, z>() -> q_gen_3559
}

Datatype: <eltlist, nat>
Convolution form: complete
}}}
  ;  leq -> 
{{{
Q={q_gen_3552, q_gen_3554},
Q_f={q_gen_3552},
Delta=
{
<s>(q_gen_3554) -> q_gen_3554
<z>() -> q_gen_3554
<s, s>(q_gen_3552) -> q_gen_3552
<z, s>(q_gen_3554) -> q_gen_3552
<z, z>() -> q_gen_3552
}

Datatype: <nat, nat>
Convolution form: complete
}}}
  ;  reverse -> 
{{{
Q={q_gen_3551, q_gen_3573, q_gen_3574, q_gen_3575},
Q_f={q_gen_3551},
Delta=
{
<cons, cons>(q_gen_3575, q_gen_3574, q_gen_3573, q_gen_3551) -> q_gen_3551
<nil, nil>() -> q_gen_3551
<nil, a>() -> q_gen_3573
<nil, b>() -> q_gen_3573
<a, nil>() -> q_gen_3574
<b, nil>() -> q_gen_3574
<a, a>() -> q_gen_3575
<b, b>() -> q_gen_3575
}

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

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

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([_wda, cons(h1, nil), _xda]) /\ reverse([t1, _wda])) -> reverse([cons(h1, t1), _xda]) -> 9  ;  (append([t1, l2, _rda])) -> append([cons(h1, t1), l2, cons(h1, _rda)]) -> 10  ;  (length([_gea, _hea]) /\ length([l1, _fea]) /\ reverse([l1, _gea])) -> leq([_fea, _hea]) -> 8  ;  (length([_iea, _jea]) /\ length([l1, _kea]) /\ reverse([l1, _iea])) -> leq([_jea, _kea]) -> 8  ;  (length([ll, _bea])) -> length([cons(x, ll), s(_bea)]) -> 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, _rda])) -> append([cons(h1, t1), l2, cons(h1, _rda)]), {
_rda -> cons(b, nil)  ;  h1 -> a  ;  l2 -> nil  ;  t1 -> cons(b, nil)
})

-------------------------------------------
Step 17, which took 0.018333 s (model generation: 0.007136,  model checking: 0.011197):

Model:
|_
{
append -> 
{{{
Q={q_gen_3556, q_gen_3561, q_gen_3562, q_gen_3563, q_gen_3564, q_gen_3582, q_gen_3583},
Q_f={q_gen_3556},
Delta=
{
<nil>() -> q_gen_3582
<a>() -> q_gen_3583
<b>() -> q_gen_3583
<cons, cons>(q_gen_3564, q_gen_3563, q_gen_3562, q_gen_3561) -> q_gen_3561
<nil, nil>() -> q_gen_3561
<cons, a>(q_gen_3583, q_gen_3582) -> q_gen_3562
<cons, b>(q_gen_3583, q_gen_3582) -> q_gen_3562
<nil, a>() -> q_gen_3562
<nil, b>() -> q_gen_3562
<a, cons>(q_gen_3583, q_gen_3582) -> q_gen_3563
<a, nil>() -> q_gen_3563
<b, cons>(q_gen_3583, q_gen_3582) -> q_gen_3563
<b, nil>() -> q_gen_3563
<a, a>() -> q_gen_3564
<b, b>() -> q_gen_3564
<cons, nil, cons>(q_gen_3564, q_gen_3563, q_gen_3562, q_gen_3561) -> q_gen_3556
<nil, cons, cons>(q_gen_3564, q_gen_3563, q_gen_3562, q_gen_3561) -> q_gen_3556
<nil, nil, nil>() -> q_gen_3556
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_3555, q_gen_3559, q_gen_3596},
Q_f={q_gen_3555},
Delta=
{
<z>() -> q_gen_3596
<cons, s>(q_gen_3559, q_gen_3555) -> q_gen_3555
<nil, z>() -> q_gen_3555
<a, z>() -> q_gen_3559
<b, s>(q_gen_3596) -> q_gen_3559
<b, z>() -> q_gen_3559
}

Datatype: <eltlist, nat>
Convolution form: complete
}}}
  ;  leq -> 
{{{
Q={q_gen_3552, q_gen_3554},
Q_f={q_gen_3552},
Delta=
{
<s>(q_gen_3554) -> q_gen_3554
<z>() -> q_gen_3554
<s, s>(q_gen_3552) -> q_gen_3552
<z, s>(q_gen_3554) -> q_gen_3552
<z, z>() -> q_gen_3552
}

Datatype: <nat, nat>
Convolution form: complete
}}}
  ;  reverse -> 
{{{
Q={q_gen_3551, q_gen_3573, q_gen_3574, q_gen_3575},
Q_f={q_gen_3551},
Delta=
{
<cons, cons>(q_gen_3575, q_gen_3574, q_gen_3573, q_gen_3551) -> q_gen_3551
<nil, nil>() -> q_gen_3551
<nil, a>() -> q_gen_3573
<nil, b>() -> q_gen_3573
<a, nil>() -> q_gen_3574
<b, nil>() -> q_gen_3574
<a, a>() -> q_gen_3575
<b, b>() -> q_gen_3575
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 12  ;  () -> length([nil, z]) -> 8  ;  () -> leq([z, s(nn2)]) -> 8  ;  () -> leq([z, z]) -> 8  ;  () -> reverse([nil, nil]) -> 8  ;  (append([_wda, cons(h1, nil), _xda]) /\ reverse([t1, _wda])) -> reverse([cons(h1, t1), _xda]) -> 10  ;  (append([t1, l2, _rda])) -> append([cons(h1, t1), l2, cons(h1, _rda)]) -> 10  ;  (length([_gea, _hea]) /\ length([l1, _fea]) /\ reverse([l1, _gea])) -> leq([_fea, _hea]) -> 9  ;  (length([_iea, _jea]) /\ length([l1, _kea]) /\ reverse([l1, _iea])) -> leq([_jea, _kea]) -> 9  ;  (length([ll, _bea])) -> length([cons(x, ll), s(_bea)]) -> 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([nil, l2, l2]), {
l2 -> cons(b, cons(a, cons(b, nil)))
})

-------------------------------------------
Step 18, which took 0.007561 s (model generation: 0.006844,  model checking: 0.000717):

Model:
|_
{
append -> 
{{{
Q={q_gen_3556, q_gen_3561, q_gen_3562, q_gen_3563, q_gen_3564, q_gen_3582, q_gen_3583},
Q_f={q_gen_3556},
Delta=
{
<cons>(q_gen_3583, q_gen_3582) -> q_gen_3582
<nil>() -> q_gen_3582
<a>() -> q_gen_3583
<b>() -> q_gen_3583
<cons, cons>(q_gen_3564, q_gen_3563, q_gen_3562, q_gen_3561) -> q_gen_3561
<nil, nil>() -> q_gen_3561
<cons, a>(q_gen_3583, q_gen_3582) -> q_gen_3562
<cons, b>(q_gen_3583, q_gen_3582) -> q_gen_3562
<nil, a>() -> q_gen_3562
<nil, b>() -> q_gen_3562
<a, cons>(q_gen_3583, q_gen_3582) -> q_gen_3563
<a, nil>() -> q_gen_3563
<b, cons>(q_gen_3583, q_gen_3582) -> q_gen_3563
<b, nil>() -> q_gen_3563
<a, a>() -> q_gen_3564
<b, b>() -> q_gen_3564
<cons, nil, cons>(q_gen_3564, q_gen_3563, q_gen_3562, q_gen_3561) -> q_gen_3556
<nil, cons, cons>(q_gen_3564, q_gen_3563, q_gen_3562, q_gen_3561) -> q_gen_3556
<nil, nil, nil>() -> q_gen_3556
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_3555, q_gen_3559, q_gen_3596},
Q_f={q_gen_3555},
Delta=
{
<z>() -> q_gen_3596
<cons, s>(q_gen_3559, q_gen_3555) -> q_gen_3555
<nil, z>() -> q_gen_3555
<a, z>() -> q_gen_3559
<b, s>(q_gen_3596) -> q_gen_3559
<b, z>() -> q_gen_3559
}

Datatype: <eltlist, nat>
Convolution form: complete
}}}
  ;  leq -> 
{{{
Q={q_gen_3552, q_gen_3554},
Q_f={q_gen_3552},
Delta=
{
<s>(q_gen_3554) -> q_gen_3554
<z>() -> q_gen_3554
<s, s>(q_gen_3552) -> q_gen_3552
<z, s>(q_gen_3554) -> q_gen_3552
<z, z>() -> q_gen_3552
}

Datatype: <nat, nat>
Convolution form: complete
}}}
  ;  reverse -> 
{{{
Q={q_gen_3551, q_gen_3573, q_gen_3574, q_gen_3575},
Q_f={q_gen_3551},
Delta=
{
<cons, cons>(q_gen_3575, q_gen_3574, q_gen_3573, q_gen_3551) -> q_gen_3551
<nil, nil>() -> q_gen_3551
<nil, a>() -> q_gen_3573
<nil, b>() -> q_gen_3573
<a, nil>() -> q_gen_3574
<b, nil>() -> q_gen_3574
<a, a>() -> q_gen_3575
<b, b>() -> q_gen_3575
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 12  ;  () -> length([nil, z]) -> 9  ;  () -> leq([z, s(nn2)]) -> 9  ;  () -> leq([z, z]) -> 9  ;  () -> reverse([nil, nil]) -> 9  ;  (append([_wda, cons(h1, nil), _xda]) /\ reverse([t1, _wda])) -> reverse([cons(h1, t1), _xda]) -> 10  ;  (append([t1, l2, _rda])) -> append([cons(h1, t1), l2, cons(h1, _rda)]) -> 10  ;  (length([_gea, _hea]) /\ length([l1, _fea]) /\ reverse([l1, _gea])) -> leq([_fea, _hea]) -> 10  ;  (length([_iea, _jea]) /\ length([l1, _kea]) /\ reverse([l1, _iea])) -> leq([_jea, _kea]) -> 10  ;  (length([ll, _bea])) -> length([cons(x, ll), s(_bea)]) -> 13  ;  (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: ((length([ll, _bea])) -> length([cons(x, ll), s(_bea)]), {
_bea -> s(z)  ;  ll -> cons(b, nil)  ;  x -> a
})

-------------------------------------------
Step 19, which took 0.017909 s (model generation: 0.009752,  model checking: 0.008157):

Model:
|_
{
append -> 
{{{
Q={q_gen_3556, q_gen_3561, q_gen_3562, q_gen_3563, q_gen_3564, q_gen_3582, q_gen_3583},
Q_f={q_gen_3556},
Delta=
{
<cons>(q_gen_3583, q_gen_3582) -> q_gen_3582
<nil>() -> q_gen_3582
<a>() -> q_gen_3583
<b>() -> q_gen_3583
<cons, cons>(q_gen_3564, q_gen_3563, q_gen_3562, q_gen_3561) -> q_gen_3561
<nil, nil>() -> q_gen_3561
<cons, a>(q_gen_3583, q_gen_3582) -> q_gen_3562
<cons, b>(q_gen_3583, q_gen_3582) -> q_gen_3562
<nil, a>() -> q_gen_3562
<nil, b>() -> q_gen_3562
<a, cons>(q_gen_3583, q_gen_3582) -> q_gen_3563
<a, nil>() -> q_gen_3563
<b, cons>(q_gen_3583, q_gen_3582) -> q_gen_3563
<b, nil>() -> q_gen_3563
<a, a>() -> q_gen_3564
<b, b>() -> q_gen_3564
<cons, nil, cons>(q_gen_3564, q_gen_3563, q_gen_3562, q_gen_3561) -> q_gen_3556
<nil, cons, cons>(q_gen_3564, q_gen_3563, q_gen_3562, q_gen_3561) -> q_gen_3556
<nil, nil, nil>() -> q_gen_3556
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_3555, q_gen_3559, q_gen_3596},
Q_f={q_gen_3555},
Delta=
{
<z>() -> q_gen_3596
<cons, s>(q_gen_3559, q_gen_3555) -> q_gen_3555
<nil, z>() -> q_gen_3555
<a, s>(q_gen_3596) -> q_gen_3559
<a, z>() -> q_gen_3559
<b, s>(q_gen_3596) -> q_gen_3559
<b, z>() -> q_gen_3559
}

Datatype: <eltlist, nat>
Convolution form: complete
}}}
  ;  leq -> 
{{{
Q={q_gen_3552, q_gen_3554},
Q_f={q_gen_3552},
Delta=
{
<s>(q_gen_3554) -> q_gen_3554
<z>() -> q_gen_3554
<s, s>(q_gen_3552) -> q_gen_3552
<z, s>(q_gen_3554) -> q_gen_3552
<z, z>() -> q_gen_3552
}

Datatype: <nat, nat>
Convolution form: complete
}}}
  ;  reverse -> 
{{{
Q={q_gen_3551, q_gen_3573, q_gen_3574, q_gen_3575},
Q_f={q_gen_3551},
Delta=
{
<cons, cons>(q_gen_3575, q_gen_3574, q_gen_3573, q_gen_3551) -> q_gen_3551
<nil, nil>() -> q_gen_3551
<nil, a>() -> q_gen_3573
<nil, b>() -> q_gen_3573
<a, nil>() -> q_gen_3574
<b, nil>() -> q_gen_3574
<a, a>() -> q_gen_3575
<b, b>() -> q_gen_3575
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 12  ;  () -> length([nil, z]) -> 10  ;  () -> leq([z, s(nn2)]) -> 10  ;  () -> leq([z, z]) -> 10  ;  () -> reverse([nil, nil]) -> 10  ;  (append([_wda, cons(h1, nil), _xda]) /\ reverse([t1, _wda])) -> reverse([cons(h1, t1), _xda]) -> 10  ;  (append([t1, l2, _rda])) -> append([cons(h1, t1), l2, cons(h1, _rda)]) -> 13  ;  (length([_gea, _hea]) /\ length([l1, _fea]) /\ reverse([l1, _gea])) -> leq([_fea, _hea]) -> 11  ;  (length([_iea, _jea]) /\ length([l1, _kea]) /\ reverse([l1, _iea])) -> leq([_jea, _kea]) -> 11  ;  (length([ll, _bea])) -> length([cons(x, ll), s(_bea)]) -> 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, _rda])) -> append([cons(h1, t1), l2, cons(h1, _rda)]), {
_rda -> cons(b, nil)  ;  h1 -> b  ;  l2 -> cons(b, nil)  ;  t1 -> nil
})

-------------------------------------------
Step 20, which took 0.011372 s (model generation: 0.009881,  model checking: 0.001491):

Model:
|_
{
append -> 
{{{
Q={q_gen_3556, q_gen_3561, q_gen_3562, q_gen_3563, q_gen_3564, q_gen_3582, q_gen_3583, q_gen_3609, q_gen_3610, q_gen_3611, q_gen_3612, q_gen_3613, q_gen_3614, q_gen_3615},
Q_f={q_gen_3556},
Delta=
{
<cons>(q_gen_3583, q_gen_3582) -> q_gen_3582
<nil>() -> q_gen_3582
<a>() -> q_gen_3583
<b>() -> q_gen_3583
<cons, cons>(q_gen_3564, q_gen_3563, q_gen_3562, q_gen_3561) -> q_gen_3561
<nil, nil>() -> q_gen_3561
<cons, a>(q_gen_3583, q_gen_3582) -> q_gen_3562
<cons, b>(q_gen_3583, q_gen_3582) -> q_gen_3562
<nil, a>() -> q_gen_3562
<nil, b>() -> q_gen_3562
<a, cons>(q_gen_3583, q_gen_3582) -> q_gen_3563
<a, nil>() -> q_gen_3563
<b, cons>(q_gen_3583, q_gen_3582) -> q_gen_3563
<b, nil>() -> q_gen_3563
<a, a>() -> q_gen_3564
<b, b>() -> q_gen_3564
<cons, cons, cons>(q_gen_3615, q_gen_3614, q_gen_3613, q_gen_3612, q_gen_3611, q_gen_3610, q_gen_3609, q_gen_3556) -> q_gen_3556
<cons, nil, cons>(q_gen_3564, q_gen_3563, q_gen_3562, q_gen_3561) -> q_gen_3556
<nil, cons, cons>(q_gen_3564, q_gen_3563, q_gen_3562, q_gen_3561) -> q_gen_3556
<nil, nil, cons>(q_gen_3583, q_gen_3582) -> q_gen_3556
<nil, nil, nil>() -> q_gen_3556
<nil, nil, b>() -> q_gen_3609
<nil, b, cons>(q_gen_3583, q_gen_3582) -> q_gen_3610
<nil, b, b>() -> q_gen_3611
<b, nil, cons>(q_gen_3583, q_gen_3582) -> q_gen_3612
<b, nil, b>() -> q_gen_3613
<b, b, cons>(q_gen_3583, q_gen_3582) -> q_gen_3614
<b, b, b>() -> q_gen_3615
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_3555, q_gen_3559, q_gen_3596},
Q_f={q_gen_3555},
Delta=
{
<z>() -> q_gen_3596
<cons, s>(q_gen_3559, q_gen_3555) -> q_gen_3555
<nil, z>() -> q_gen_3555
<a, s>(q_gen_3596) -> q_gen_3559
<a, z>() -> q_gen_3559
<b, s>(q_gen_3596) -> q_gen_3559
<b, z>() -> q_gen_3559
}

Datatype: <eltlist, nat>
Convolution form: complete
}}}
  ;  leq -> 
{{{
Q={q_gen_3552, q_gen_3554},
Q_f={q_gen_3552},
Delta=
{
<s>(q_gen_3554) -> q_gen_3554
<z>() -> q_gen_3554
<s, s>(q_gen_3552) -> q_gen_3552
<z, s>(q_gen_3554) -> q_gen_3552
<z, z>() -> q_gen_3552
}

Datatype: <nat, nat>
Convolution form: complete
}}}
  ;  reverse -> 
{{{
Q={q_gen_3551, q_gen_3573, q_gen_3574, q_gen_3575},
Q_f={q_gen_3551},
Delta=
{
<cons, cons>(q_gen_3575, q_gen_3574, q_gen_3573, q_gen_3551) -> q_gen_3551
<nil, nil>() -> q_gen_3551
<nil, a>() -> q_gen_3573
<nil, b>() -> q_gen_3573
<a, nil>() -> q_gen_3574
<b, nil>() -> q_gen_3574
<a, a>() -> q_gen_3575
<b, b>() -> q_gen_3575
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 12  ;  () -> length([nil, z]) -> 10  ;  () -> leq([z, s(nn2)]) -> 10  ;  () -> leq([z, z]) -> 10  ;  () -> reverse([nil, nil]) -> 10  ;  (append([_wda, cons(h1, nil), _xda]) /\ reverse([t1, _wda])) -> reverse([cons(h1, t1), _xda]) -> 13  ;  (append([t1, l2, _rda])) -> append([cons(h1, t1), l2, cons(h1, _rda)]) -> 13  ;  (length([_gea, _hea]) /\ length([l1, _fea]) /\ reverse([l1, _gea])) -> leq([_fea, _hea]) -> 11  ;  (length([_iea, _jea]) /\ length([l1, _kea]) /\ reverse([l1, _iea])) -> leq([_jea, _kea]) -> 11  ;  (length([ll, _bea])) -> length([cons(x, ll), s(_bea)]) -> 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([_wda, cons(h1, nil), _xda]) /\ reverse([t1, _wda])) -> reverse([cons(h1, t1), _xda]), {
_wda -> cons(b, nil)  ;  _xda -> cons(b, cons(b, nil))  ;  h1 -> b  ;  t1 -> cons(b, nil)
})

-------------------------------------------
Step 21, which took 0.025711 s (model generation: 0.018582,  model checking: 0.007129):

Model:
|_
{
append -> 
{{{
Q={q_gen_3556, q_gen_3561, q_gen_3562, q_gen_3563, q_gen_3564, q_gen_3582, q_gen_3583, q_gen_3609, q_gen_3610, q_gen_3611, q_gen_3612, q_gen_3613, q_gen_3614, q_gen_3615},
Q_f={q_gen_3556},
Delta=
{
<cons>(q_gen_3583, q_gen_3582) -> q_gen_3582
<nil>() -> q_gen_3582
<a>() -> q_gen_3583
<b>() -> q_gen_3583
<cons, cons>(q_gen_3564, q_gen_3563, q_gen_3562, q_gen_3561) -> q_gen_3561
<nil, nil>() -> q_gen_3561
<cons, a>(q_gen_3583, q_gen_3582) -> q_gen_3562
<cons, b>(q_gen_3583, q_gen_3582) -> q_gen_3562
<nil, a>() -> q_gen_3562
<nil, b>() -> q_gen_3562
<a, cons>(q_gen_3583, q_gen_3582) -> q_gen_3563
<a, nil>() -> q_gen_3563
<b, cons>(q_gen_3583, q_gen_3582) -> q_gen_3563
<b, nil>() -> q_gen_3563
<a, a>() -> q_gen_3564
<b, b>() -> q_gen_3564
<cons, cons, cons>(q_gen_3615, q_gen_3614, q_gen_3613, q_gen_3612, q_gen_3611, q_gen_3610, q_gen_3609, q_gen_3556) -> q_gen_3556
<cons, nil, cons>(q_gen_3564, q_gen_3563, q_gen_3562, q_gen_3561) -> q_gen_3556
<nil, cons, cons>(q_gen_3564, q_gen_3563, q_gen_3562, q_gen_3561) -> q_gen_3556
<nil, nil, cons>(q_gen_3583, q_gen_3582) -> q_gen_3556
<nil, nil, nil>() -> q_gen_3556
<nil, nil, b>() -> q_gen_3609
<nil, b, cons>(q_gen_3583, q_gen_3582) -> q_gen_3610
<nil, b, b>() -> q_gen_3611
<b, nil, cons>(q_gen_3583, q_gen_3582) -> q_gen_3612
<b, nil, b>() -> q_gen_3613
<b, b, cons>(q_gen_3583, q_gen_3582) -> q_gen_3614
<b, b, b>() -> q_gen_3615
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_3555, q_gen_3559, q_gen_3596},
Q_f={q_gen_3555},
Delta=
{
<z>() -> q_gen_3596
<cons, s>(q_gen_3559, q_gen_3555) -> q_gen_3555
<nil, z>() -> q_gen_3555
<a, s>(q_gen_3596) -> q_gen_3559
<a, z>() -> q_gen_3559
<b, s>(q_gen_3596) -> q_gen_3559
<b, z>() -> q_gen_3559
}

Datatype: <eltlist, nat>
Convolution form: complete
}}}
  ;  leq -> 
{{{
Q={q_gen_3552, q_gen_3554},
Q_f={q_gen_3552},
Delta=
{
<s>(q_gen_3554) -> q_gen_3554
<z>() -> q_gen_3554
<s, s>(q_gen_3552) -> q_gen_3552
<z, s>(q_gen_3554) -> q_gen_3552
<z, z>() -> q_gen_3552
}

Datatype: <nat, nat>
Convolution form: complete
}}}
  ;  reverse -> 
{{{
Q={q_gen_3551, q_gen_3573, q_gen_3574, q_gen_3575, q_gen_3618, q_gen_3619},
Q_f={q_gen_3551},
Delta=
{
<nil>() -> q_gen_3618
<b>() -> q_gen_3619
<cons, cons>(q_gen_3575, q_gen_3574, q_gen_3573, q_gen_3551) -> q_gen_3551
<nil, nil>() -> q_gen_3551
<cons, b>(q_gen_3619, q_gen_3618) -> q_gen_3573
<nil, a>() -> q_gen_3573
<nil, b>() -> q_gen_3573
<a, nil>() -> q_gen_3574
<b, cons>(q_gen_3619, q_gen_3618) -> q_gen_3574
<b, nil>() -> q_gen_3574
<a, a>() -> q_gen_3575
<b, b>() -> q_gen_3575
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 13  ;  () -> length([nil, z]) -> 11  ;  () -> leq([z, s(nn2)]) -> 11  ;  () -> leq([z, z]) -> 11  ;  () -> reverse([nil, nil]) -> 11  ;  (append([_wda, cons(h1, nil), _xda]) /\ reverse([t1, _wda])) -> reverse([cons(h1, t1), _xda]) -> 13  ;  (append([t1, l2, _rda])) -> append([cons(h1, t1), l2, cons(h1, _rda)]) -> 13  ;  (length([_gea, _hea]) /\ length([l1, _fea]) /\ reverse([l1, _gea])) -> leq([_fea, _hea]) -> 12  ;  (length([_iea, _jea]) /\ length([l1, _kea]) /\ reverse([l1, _iea])) -> leq([_jea, _kea]) -> 12  ;  (length([ll, _bea])) -> length([cons(x, ll), s(_bea)]) -> 16  ;  (leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 12  ;  (leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 12  ;  (leq([s(nn1), z])) -> BOT -> 12
}
Sat witness: Yes: ((length([ll, _bea])) -> length([cons(x, ll), s(_bea)]), {
_bea -> s(s(z))  ;  ll -> cons(b, cons(b, nil))  ;  x -> b
})

-------------------------------------------
Step 22, which took 0.108289 s (model generation: 0.024555,  model checking: 0.083734):

Model:
|_
{
append -> 
{{{
Q={q_gen_3556, q_gen_3561, q_gen_3562, q_gen_3563, q_gen_3564, q_gen_3582, q_gen_3583, q_gen_3609, q_gen_3610, q_gen_3611, q_gen_3612, q_gen_3613, q_gen_3614, q_gen_3615},
Q_f={q_gen_3556},
Delta=
{
<cons>(q_gen_3583, q_gen_3582) -> q_gen_3582
<nil>() -> q_gen_3582
<a>() -> q_gen_3583
<b>() -> q_gen_3583
<cons, cons>(q_gen_3564, q_gen_3563, q_gen_3562, q_gen_3561) -> q_gen_3561
<nil, nil>() -> q_gen_3561
<cons, a>(q_gen_3583, q_gen_3582) -> q_gen_3562
<cons, b>(q_gen_3583, q_gen_3582) -> q_gen_3562
<nil, a>() -> q_gen_3562
<nil, b>() -> q_gen_3562
<a, cons>(q_gen_3583, q_gen_3582) -> q_gen_3563
<a, nil>() -> q_gen_3563
<b, cons>(q_gen_3583, q_gen_3582) -> q_gen_3563
<b, nil>() -> q_gen_3563
<a, a>() -> q_gen_3564
<b, b>() -> q_gen_3564
<cons, cons, cons>(q_gen_3615, q_gen_3614, q_gen_3613, q_gen_3612, q_gen_3611, q_gen_3610, q_gen_3609, q_gen_3556) -> q_gen_3556
<cons, nil, cons>(q_gen_3564, q_gen_3563, q_gen_3562, q_gen_3561) -> q_gen_3556
<nil, cons, cons>(q_gen_3564, q_gen_3563, q_gen_3562, q_gen_3561) -> q_gen_3556
<nil, nil, cons>(q_gen_3583, q_gen_3582) -> q_gen_3556
<nil, nil, nil>() -> q_gen_3556
<nil, nil, b>() -> q_gen_3609
<nil, b, cons>(q_gen_3583, q_gen_3582) -> q_gen_3610
<nil, b, b>() -> q_gen_3611
<b, nil, cons>(q_gen_3583, q_gen_3582) -> q_gen_3612
<b, nil, b>() -> q_gen_3613
<b, b, cons>(q_gen_3583, q_gen_3582) -> q_gen_3614
<b, b, b>() -> q_gen_3615
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_3555, q_gen_3559, q_gen_3596},
Q_f={q_gen_3555},
Delta=
{
<s>(q_gen_3596) -> q_gen_3596
<z>() -> q_gen_3596
<cons, s>(q_gen_3559, q_gen_3555) -> q_gen_3555
<nil, z>() -> q_gen_3555
<a, s>(q_gen_3596) -> q_gen_3559
<a, z>() -> q_gen_3559
<b, s>(q_gen_3596) -> q_gen_3559
<b, z>() -> q_gen_3559
}

Datatype: <eltlist, nat>
Convolution form: complete
}}}
  ;  leq -> 
{{{
Q={q_gen_3552, q_gen_3554},
Q_f={q_gen_3552},
Delta=
{
<s>(q_gen_3554) -> q_gen_3554
<z>() -> q_gen_3554
<s, s>(q_gen_3552) -> q_gen_3552
<z, s>(q_gen_3554) -> q_gen_3552
<z, z>() -> q_gen_3552
}

Datatype: <nat, nat>
Convolution form: complete
}}}
  ;  reverse -> 
{{{
Q={q_gen_3551, q_gen_3573, q_gen_3574, q_gen_3575, q_gen_3618, q_gen_3619},
Q_f={q_gen_3551},
Delta=
{
<nil>() -> q_gen_3618
<b>() -> q_gen_3619
<cons, cons>(q_gen_3575, q_gen_3574, q_gen_3573, q_gen_3551) -> q_gen_3551
<nil, nil>() -> q_gen_3551
<cons, b>(q_gen_3619, q_gen_3618) -> q_gen_3573
<nil, a>() -> q_gen_3573
<nil, b>() -> q_gen_3573
<a, nil>() -> q_gen_3574
<b, cons>(q_gen_3619, q_gen_3618) -> q_gen_3574
<b, nil>() -> q_gen_3574
<a, a>() -> q_gen_3575
<b, b>() -> q_gen_3575
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 13  ;  () -> length([nil, z]) -> 12  ;  () -> leq([z, s(nn2)]) -> 12  ;  () -> leq([z, z]) -> 12  ;  () -> reverse([nil, nil]) -> 12  ;  (append([_wda, cons(h1, nil), _xda]) /\ reverse([t1, _wda])) -> reverse([cons(h1, t1), _xda]) -> 13  ;  (append([t1, l2, _rda])) -> append([cons(h1, t1), l2, cons(h1, _rda)]) -> 16  ;  (length([_gea, _hea]) /\ length([l1, _fea]) /\ reverse([l1, _gea])) -> leq([_fea, _hea]) -> 13  ;  (length([_iea, _jea]) /\ length([l1, _kea]) /\ reverse([l1, _iea])) -> leq([_jea, _kea]) -> 13  ;  (length([ll, _bea])) -> length([cons(x, ll), s(_bea)]) -> 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: ((append([t1, l2, _rda])) -> append([cons(h1, t1), l2, cons(h1, _rda)]), {
_rda -> cons(a, nil)  ;  h1 -> b  ;  l2 -> nil  ;  t1 -> nil
})

-------------------------------------------
Step 23, which took 0.012974 s (model generation: 0.010722,  model checking: 0.002252):

Model:
|_
{
append -> 
{{{
Q={q_gen_3556, q_gen_3561, q_gen_3562, q_gen_3563, q_gen_3564, q_gen_3582, q_gen_3583, q_gen_3609, q_gen_3610, q_gen_3611, q_gen_3612, q_gen_3613, q_gen_3614, q_gen_3615},
Q_f={q_gen_3556},
Delta=
{
<cons>(q_gen_3583, q_gen_3582) -> q_gen_3582
<nil>() -> q_gen_3582
<a>() -> q_gen_3583
<b>() -> q_gen_3583
<cons, cons>(q_gen_3564, q_gen_3563, q_gen_3562, q_gen_3561) -> q_gen_3561
<nil, cons>(q_gen_3583, q_gen_3582) -> q_gen_3561
<nil, nil>() -> q_gen_3561
<cons, a>(q_gen_3583, q_gen_3582) -> q_gen_3562
<cons, b>(q_gen_3583, q_gen_3582) -> q_gen_3562
<nil, a>() -> q_gen_3562
<nil, b>() -> q_gen_3562
<a, cons>(q_gen_3583, q_gen_3582) -> q_gen_3563
<a, nil>() -> q_gen_3563
<b, cons>(q_gen_3583, q_gen_3582) -> q_gen_3563
<b, nil>() -> q_gen_3563
<a, a>() -> q_gen_3564
<b, b>() -> q_gen_3564
<cons, cons, cons>(q_gen_3615, q_gen_3614, q_gen_3613, q_gen_3612, q_gen_3611, q_gen_3610, q_gen_3609, q_gen_3556) -> q_gen_3556
<cons, nil, cons>(q_gen_3564, q_gen_3563, q_gen_3562, q_gen_3561) -> q_gen_3556
<nil, cons, cons>(q_gen_3564, q_gen_3563, q_gen_3562, q_gen_3561) -> q_gen_3556
<nil, nil, cons>(q_gen_3583, q_gen_3582) -> q_gen_3556
<nil, nil, nil>() -> q_gen_3556
<nil, nil, b>() -> q_gen_3609
<nil, b, cons>(q_gen_3583, q_gen_3582) -> q_gen_3610
<nil, b, b>() -> q_gen_3611
<b, nil, cons>(q_gen_3583, q_gen_3582) -> q_gen_3612
<b, nil, b>() -> q_gen_3613
<b, b, cons>(q_gen_3583, q_gen_3582) -> q_gen_3614
<b, b, b>() -> q_gen_3615
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_3555, q_gen_3559, q_gen_3596},
Q_f={q_gen_3555},
Delta=
{
<s>(q_gen_3596) -> q_gen_3596
<z>() -> q_gen_3596
<cons, s>(q_gen_3559, q_gen_3555) -> q_gen_3555
<nil, z>() -> q_gen_3555
<a, s>(q_gen_3596) -> q_gen_3559
<a, z>() -> q_gen_3559
<b, s>(q_gen_3596) -> q_gen_3559
<b, z>() -> q_gen_3559
}

Datatype: <eltlist, nat>
Convolution form: complete
}}}
  ;  leq -> 
{{{
Q={q_gen_3552, q_gen_3554},
Q_f={q_gen_3552},
Delta=
{
<s>(q_gen_3554) -> q_gen_3554
<z>() -> q_gen_3554
<s, s>(q_gen_3552) -> q_gen_3552
<z, s>(q_gen_3554) -> q_gen_3552
<z, z>() -> q_gen_3552
}

Datatype: <nat, nat>
Convolution form: complete
}}}
  ;  reverse -> 
{{{
Q={q_gen_3551, q_gen_3573, q_gen_3574, q_gen_3575, q_gen_3618, q_gen_3619},
Q_f={q_gen_3551},
Delta=
{
<nil>() -> q_gen_3618
<b>() -> q_gen_3619
<cons, cons>(q_gen_3575, q_gen_3574, q_gen_3573, q_gen_3551) -> q_gen_3551
<nil, nil>() -> q_gen_3551
<cons, b>(q_gen_3619, q_gen_3618) -> q_gen_3573
<nil, a>() -> q_gen_3573
<nil, b>() -> q_gen_3573
<a, nil>() -> q_gen_3574
<b, cons>(q_gen_3619, q_gen_3618) -> q_gen_3574
<b, nil>() -> q_gen_3574
<a, a>() -> q_gen_3575
<b, b>() -> q_gen_3575
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 13  ;  () -> length([nil, z]) -> 13  ;  () -> leq([z, s(nn2)]) -> 13  ;  () -> leq([z, z]) -> 13  ;  () -> reverse([nil, nil]) -> 13  ;  (append([_wda, cons(h1, nil), _xda]) /\ reverse([t1, _wda])) -> reverse([cons(h1, t1), _xda]) -> 16  ;  (append([t1, l2, _rda])) -> append([cons(h1, t1), l2, cons(h1, _rda)]) -> 16  ;  (length([_gea, _hea]) /\ length([l1, _fea]) /\ reverse([l1, _gea])) -> leq([_fea, _hea]) -> 14  ;  (length([_iea, _jea]) /\ length([l1, _kea]) /\ reverse([l1, _iea])) -> leq([_jea, _kea]) -> 14  ;  (length([ll, _bea])) -> length([cons(x, ll), s(_bea)]) -> 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([_wda, cons(h1, nil), _xda]) /\ reverse([t1, _wda])) -> reverse([cons(h1, t1), _xda]), {
_wda -> nil  ;  _xda -> cons(b, cons(a, nil))  ;  h1 -> b  ;  t1 -> nil
})

-------------------------------------------
Step 24, which took 0.014047 s (model generation: 0.010741,  model checking: 0.003306):

Model:
|_
{
append -> 
{{{
Q={q_gen_3556, q_gen_3561, q_gen_3562, q_gen_3563, q_gen_3564, q_gen_3582, q_gen_3583, q_gen_3609, q_gen_3610, q_gen_3611, q_gen_3612, q_gen_3613, q_gen_3614, q_gen_3615},
Q_f={q_gen_3556},
Delta=
{
<cons>(q_gen_3583, q_gen_3582) -> q_gen_3582
<nil>() -> q_gen_3582
<a>() -> q_gen_3583
<b>() -> q_gen_3583
<cons, cons>(q_gen_3564, q_gen_3563, q_gen_3562, q_gen_3561) -> q_gen_3561
<nil, cons>(q_gen_3583, q_gen_3582) -> q_gen_3561
<nil, nil>() -> q_gen_3561
<cons, a>(q_gen_3583, q_gen_3582) -> q_gen_3562
<cons, b>(q_gen_3583, q_gen_3582) -> q_gen_3562
<nil, a>() -> q_gen_3562
<nil, b>() -> q_gen_3562
<a, cons>(q_gen_3583, q_gen_3582) -> q_gen_3563
<a, nil>() -> q_gen_3563
<b, cons>(q_gen_3583, q_gen_3582) -> q_gen_3563
<b, nil>() -> q_gen_3563
<a, a>() -> q_gen_3564
<b, b>() -> q_gen_3564
<cons, cons, cons>(q_gen_3615, q_gen_3614, q_gen_3613, q_gen_3612, q_gen_3611, q_gen_3610, q_gen_3609, q_gen_3556) -> q_gen_3556
<cons, nil, cons>(q_gen_3564, q_gen_3563, q_gen_3562, q_gen_3561) -> q_gen_3556
<nil, cons, cons>(q_gen_3564, q_gen_3563, q_gen_3562, q_gen_3561) -> q_gen_3556
<nil, nil, cons>(q_gen_3583, q_gen_3582) -> q_gen_3556
<nil, nil, nil>() -> q_gen_3556
<nil, nil, b>() -> q_gen_3609
<nil, b, cons>(q_gen_3583, q_gen_3582) -> q_gen_3610
<nil, b, b>() -> q_gen_3611
<b, nil, cons>(q_gen_3583, q_gen_3582) -> q_gen_3612
<b, nil, b>() -> q_gen_3613
<b, b, cons>(q_gen_3583, q_gen_3582) -> q_gen_3614
<b, b, b>() -> q_gen_3615
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_3555, q_gen_3559, q_gen_3596},
Q_f={q_gen_3555},
Delta=
{
<s>(q_gen_3596) -> q_gen_3596
<z>() -> q_gen_3596
<cons, s>(q_gen_3559, q_gen_3555) -> q_gen_3555
<nil, z>() -> q_gen_3555
<a, s>(q_gen_3596) -> q_gen_3559
<a, z>() -> q_gen_3559
<b, s>(q_gen_3596) -> q_gen_3559
<b, z>() -> q_gen_3559
}

Datatype: <eltlist, nat>
Convolution form: complete
}}}
  ;  leq -> 
{{{
Q={q_gen_3552, q_gen_3554},
Q_f={q_gen_3552},
Delta=
{
<s>(q_gen_3554) -> q_gen_3554
<z>() -> q_gen_3554
<s, s>(q_gen_3552) -> q_gen_3552
<z, s>(q_gen_3554) -> q_gen_3552
<z, z>() -> q_gen_3552
}

Datatype: <nat, nat>
Convolution form: complete
}}}
  ;  reverse -> 
{{{
Q={q_gen_3551, q_gen_3573, q_gen_3574, q_gen_3575, q_gen_3618, q_gen_3619},
Q_f={q_gen_3551},
Delta=
{
<nil>() -> q_gen_3618
<a>() -> q_gen_3619
<b>() -> q_gen_3619
<cons, cons>(q_gen_3575, q_gen_3574, q_gen_3573, q_gen_3551) -> q_gen_3551
<nil, cons>(q_gen_3619, q_gen_3618) -> q_gen_3551
<nil, nil>() -> q_gen_3551
<cons, b>(q_gen_3619, q_gen_3618) -> q_gen_3573
<nil, a>() -> q_gen_3573
<nil, b>() -> q_gen_3573
<a, nil>() -> q_gen_3574
<b, cons>(q_gen_3619, q_gen_3618) -> q_gen_3574
<b, nil>() -> q_gen_3574
<a, a>() -> q_gen_3575
<b, b>() -> q_gen_3575
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 14  ;  () -> length([nil, z]) -> 14  ;  () -> leq([z, s(nn2)]) -> 14  ;  () -> leq([z, z]) -> 14  ;  () -> reverse([nil, nil]) -> 14  ;  (append([_wda, cons(h1, nil), _xda]) /\ reverse([t1, _wda])) -> reverse([cons(h1, t1), _xda]) -> 16  ;  (append([t1, l2, _rda])) -> append([cons(h1, t1), l2, cons(h1, _rda)]) -> 16  ;  (length([_gea, _hea]) /\ length([l1, _fea]) /\ reverse([l1, _gea])) -> leq([_fea, _hea]) -> 14  ;  (length([_iea, _jea]) /\ length([l1, _kea]) /\ reverse([l1, _iea])) -> leq([_jea, _kea]) -> 17  ;  (length([ll, _bea])) -> length([cons(x, ll), s(_bea)]) -> 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: ((length([_iea, _jea]) /\ length([l1, _kea]) /\ reverse([l1, _iea])) -> leq([_jea, _kea]), {
_iea -> cons(b, nil)  ;  _jea -> s(z)  ;  _kea -> z  ;  l1 -> nil
})

-------------------------------------------
Step 25, which took 0.019793 s (model generation: 0.015008,  model checking: 0.004785):

Model:
|_
{
append -> 
{{{
Q={q_gen_3556, q_gen_3561, q_gen_3562, q_gen_3563, q_gen_3564, q_gen_3582, q_gen_3583, q_gen_3609, q_gen_3610, q_gen_3611, q_gen_3612, q_gen_3613, q_gen_3614, q_gen_3615},
Q_f={q_gen_3556},
Delta=
{
<cons>(q_gen_3583, q_gen_3582) -> q_gen_3582
<nil>() -> q_gen_3582
<a>() -> q_gen_3583
<b>() -> q_gen_3583
<cons, cons>(q_gen_3564, q_gen_3563, q_gen_3562, q_gen_3561) -> q_gen_3561
<nil, cons>(q_gen_3583, q_gen_3582) -> q_gen_3561
<nil, nil>() -> q_gen_3561
<cons, a>(q_gen_3583, q_gen_3582) -> q_gen_3562
<cons, b>(q_gen_3583, q_gen_3582) -> q_gen_3562
<nil, a>() -> q_gen_3562
<nil, b>() -> q_gen_3562
<a, cons>(q_gen_3583, q_gen_3582) -> q_gen_3563
<a, nil>() -> q_gen_3563
<b, cons>(q_gen_3583, q_gen_3582) -> q_gen_3563
<b, nil>() -> q_gen_3563
<a, a>() -> q_gen_3564
<b, b>() -> q_gen_3564
<cons, cons, cons>(q_gen_3615, q_gen_3614, q_gen_3613, q_gen_3612, q_gen_3611, q_gen_3610, q_gen_3609, q_gen_3556) -> q_gen_3556
<cons, nil, cons>(q_gen_3564, q_gen_3563, q_gen_3562, q_gen_3561) -> q_gen_3556
<nil, cons, cons>(q_gen_3564, q_gen_3563, q_gen_3562, q_gen_3561) -> q_gen_3556
<nil, nil, cons>(q_gen_3583, q_gen_3582) -> q_gen_3556
<nil, nil, nil>() -> q_gen_3556
<nil, nil, b>() -> q_gen_3609
<nil, b, cons>(q_gen_3583, q_gen_3582) -> q_gen_3610
<nil, b, b>() -> q_gen_3611
<b, nil, cons>(q_gen_3583, q_gen_3582) -> q_gen_3612
<b, nil, b>() -> q_gen_3613
<b, b, cons>(q_gen_3583, q_gen_3582) -> q_gen_3614
<b, b, b>() -> q_gen_3615
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_3555, q_gen_3559, q_gen_3596},
Q_f={q_gen_3555},
Delta=
{
<s>(q_gen_3596) -> q_gen_3596
<z>() -> q_gen_3596
<cons, s>(q_gen_3559, q_gen_3555) -> q_gen_3555
<nil, z>() -> q_gen_3555
<a, s>(q_gen_3596) -> q_gen_3559
<a, z>() -> q_gen_3559
<b, s>(q_gen_3596) -> q_gen_3559
<b, z>() -> q_gen_3559
}

Datatype: <eltlist, nat>
Convolution form: complete
}}}
  ;  leq -> 
{{{
Q={q_gen_3552, q_gen_3554},
Q_f={q_gen_3552},
Delta=
{
<s>(q_gen_3554) -> q_gen_3554
<z>() -> q_gen_3554
<s, s>(q_gen_3552) -> q_gen_3552
<s, z>(q_gen_3554) -> q_gen_3552
<z, s>(q_gen_3554) -> q_gen_3552
<z, z>() -> q_gen_3552
}

Datatype: <nat, nat>
Convolution form: complete
}}}
  ;  reverse -> 
{{{
Q={q_gen_3551, q_gen_3573, q_gen_3574, q_gen_3575, q_gen_3618, q_gen_3619},
Q_f={q_gen_3551},
Delta=
{
<nil>() -> q_gen_3618
<a>() -> q_gen_3619
<b>() -> q_gen_3619
<cons, cons>(q_gen_3575, q_gen_3574, q_gen_3573, q_gen_3551) -> q_gen_3551
<nil, cons>(q_gen_3619, q_gen_3618) -> q_gen_3551
<nil, nil>() -> q_gen_3551
<cons, b>(q_gen_3619, q_gen_3618) -> q_gen_3573
<nil, a>() -> q_gen_3573
<nil, b>() -> q_gen_3573
<a, nil>() -> q_gen_3574
<b, cons>(q_gen_3619, q_gen_3618) -> q_gen_3574
<b, nil>() -> q_gen_3574
<a, a>() -> q_gen_3575
<b, b>() -> q_gen_3575
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 15  ;  () -> length([nil, z]) -> 15  ;  () -> leq([z, s(nn2)]) -> 15  ;  () -> leq([z, z]) -> 15  ;  () -> reverse([nil, nil]) -> 15  ;  (append([_wda, cons(h1, nil), _xda]) /\ reverse([t1, _wda])) -> reverse([cons(h1, t1), _xda]) -> 16  ;  (append([t1, l2, _rda])) -> append([cons(h1, t1), l2, cons(h1, _rda)]) -> 16  ;  (length([_gea, _hea]) /\ length([l1, _fea]) /\ reverse([l1, _gea])) -> leq([_fea, _hea]) -> 15  ;  (length([_iea, _jea]) /\ length([l1, _kea]) /\ reverse([l1, _iea])) -> leq([_jea, _kea]) -> 17  ;  (length([ll, _bea])) -> length([cons(x, ll), s(_bea)]) -> 16  ;  (leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 15  ;  (leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 15  ;  (leq([s(nn1), z])) -> BOT -> 18
}
Sat witness: Yes: ((leq([s(nn1), z])) -> BOT, {
nn1 -> z
})

-------------------------------------------
Step 26, which took 0.093111 s (model generation: 0.022473,  model checking: 0.070638):

Model:
|_
{
append -> 
{{{
Q={q_gen_3556, q_gen_3561, q_gen_3562, q_gen_3563, q_gen_3564, q_gen_3582, q_gen_3583, q_gen_3609, q_gen_3610, q_gen_3611, q_gen_3612, q_gen_3613, q_gen_3614, q_gen_3615},
Q_f={q_gen_3556},
Delta=
{
<cons>(q_gen_3583, q_gen_3582) -> q_gen_3582
<nil>() -> q_gen_3582
<a>() -> q_gen_3583
<b>() -> q_gen_3583
<cons, cons>(q_gen_3564, q_gen_3563, q_gen_3562, q_gen_3561) -> q_gen_3561
<nil, cons>(q_gen_3583, q_gen_3582) -> q_gen_3561
<nil, nil>() -> q_gen_3561
<cons, a>(q_gen_3583, q_gen_3582) -> q_gen_3562
<cons, b>(q_gen_3583, q_gen_3582) -> q_gen_3562
<nil, a>() -> q_gen_3562
<nil, b>() -> q_gen_3562
<a, cons>(q_gen_3583, q_gen_3582) -> q_gen_3563
<a, nil>() -> q_gen_3563
<b, cons>(q_gen_3583, q_gen_3582) -> q_gen_3563
<b, nil>() -> q_gen_3563
<a, a>() -> q_gen_3564
<b, b>() -> q_gen_3564
<cons, cons, cons>(q_gen_3615, q_gen_3614, q_gen_3613, q_gen_3612, q_gen_3611, q_gen_3610, q_gen_3609, q_gen_3556) -> q_gen_3556
<cons, nil, cons>(q_gen_3564, q_gen_3563, q_gen_3562, q_gen_3561) -> q_gen_3556
<nil, cons, cons>(q_gen_3564, q_gen_3563, q_gen_3562, q_gen_3561) -> q_gen_3556
<nil, nil, cons>(q_gen_3583, q_gen_3582) -> q_gen_3556
<nil, nil, nil>() -> q_gen_3556
<nil, nil, b>() -> q_gen_3609
<nil, b, cons>(q_gen_3583, q_gen_3582) -> q_gen_3610
<nil, b, b>() -> q_gen_3611
<b, nil, cons>(q_gen_3583, q_gen_3582) -> q_gen_3612
<b, nil, b>() -> q_gen_3613
<b, b, cons>(q_gen_3583, q_gen_3582) -> q_gen_3614
<b, b, b>() -> q_gen_3615
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_3555, q_gen_3559, q_gen_3596},
Q_f={q_gen_3555},
Delta=
{
<s>(q_gen_3596) -> q_gen_3596
<z>() -> q_gen_3596
<cons, s>(q_gen_3559, q_gen_3555) -> q_gen_3555
<nil, z>() -> q_gen_3555
<a, s>(q_gen_3596) -> q_gen_3559
<a, z>() -> q_gen_3559
<b, s>(q_gen_3596) -> q_gen_3559
<b, z>() -> q_gen_3559
}

Datatype: <eltlist, nat>
Convolution form: complete
}}}
  ;  leq -> 
{{{
Q={q_gen_3552, q_gen_3554, q_gen_3634},
Q_f={q_gen_3552},
Delta=
{
<s>(q_gen_3554) -> q_gen_3554
<z>() -> q_gen_3554
<s, s>(q_gen_3552) -> q_gen_3552
<z, s>(q_gen_3554) -> q_gen_3552
<z, z>() -> q_gen_3552
<s, z>(q_gen_3554) -> q_gen_3634
}

Datatype: <nat, nat>
Convolution form: complete
}}}
  ;  reverse -> 
{{{
Q={q_gen_3551, q_gen_3573, q_gen_3574, q_gen_3575, q_gen_3618, q_gen_3619, q_gen_3630},
Q_f={q_gen_3551},
Delta=
{
<nil>() -> q_gen_3618
<a>() -> q_gen_3619
<b>() -> q_gen_3619
<cons, cons>(q_gen_3575, q_gen_3574, q_gen_3573, q_gen_3551) -> q_gen_3551
<cons, cons>(q_gen_3575, q_gen_3574, q_gen_3573, q_gen_3630) -> q_gen_3551
<nil, nil>() -> q_gen_3551
<cons, b>(q_gen_3619, q_gen_3618) -> q_gen_3573
<nil, a>() -> q_gen_3573
<nil, b>() -> q_gen_3573
<a, nil>() -> q_gen_3574
<b, cons>(q_gen_3619, q_gen_3618) -> q_gen_3574
<b, nil>() -> q_gen_3574
<a, a>() -> q_gen_3575
<b, b>() -> q_gen_3575
<nil, cons>(q_gen_3619, q_gen_3618) -> q_gen_3630
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 16  ;  () -> length([nil, z]) -> 16  ;  () -> leq([z, s(nn2)]) -> 16  ;  () -> leq([z, z]) -> 16  ;  () -> reverse([nil, nil]) -> 16  ;  (append([_wda, cons(h1, nil), _xda]) /\ reverse([t1, _wda])) -> reverse([cons(h1, t1), _xda]) -> 16  ;  (append([t1, l2, _rda])) -> append([cons(h1, t1), l2, cons(h1, _rda)]) -> 19  ;  (length([_gea, _hea]) /\ length([l1, _fea]) /\ reverse([l1, _gea])) -> leq([_fea, _hea]) -> 16  ;  (length([_iea, _jea]) /\ length([l1, _kea]) /\ reverse([l1, _iea])) -> leq([_jea, _kea]) -> 17  ;  (length([ll, _bea])) -> length([cons(x, ll), s(_bea)]) -> 17  ;  (leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 16  ;  (leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 16  ;  (leq([s(nn1), z])) -> BOT -> 18
}
Sat witness: Yes: ((append([t1, l2, _rda])) -> append([cons(h1, t1), l2, cons(h1, _rda)]), {
_rda -> cons(a, nil)  ;  h1 -> b  ;  l2 -> cons(a, nil)  ;  t1 -> nil
})

-------------------------------------------
Step 27, which took 0.017707 s (model generation: 0.014247,  model checking: 0.003460):

Model:
|_
{
append -> 
{{{
Q={q_gen_3556, q_gen_3561, q_gen_3562, q_gen_3563, q_gen_3564, q_gen_3582, q_gen_3583, q_gen_3609, q_gen_3610, q_gen_3611, q_gen_3612, q_gen_3613, q_gen_3614, q_gen_3615},
Q_f={q_gen_3556},
Delta=
{
<cons>(q_gen_3583, q_gen_3582) -> q_gen_3582
<nil>() -> q_gen_3582
<a>() -> q_gen_3583
<b>() -> q_gen_3583
<cons, cons>(q_gen_3564, q_gen_3563, q_gen_3562, q_gen_3561) -> q_gen_3561
<nil, cons>(q_gen_3583, q_gen_3582) -> q_gen_3561
<nil, nil>() -> q_gen_3561
<cons, a>(q_gen_3583, q_gen_3582) -> q_gen_3562
<cons, b>(q_gen_3583, q_gen_3582) -> q_gen_3562
<nil, a>() -> q_gen_3562
<nil, b>() -> q_gen_3562
<a, cons>(q_gen_3583, q_gen_3582) -> q_gen_3563
<a, nil>() -> q_gen_3563
<b, cons>(q_gen_3583, q_gen_3582) -> q_gen_3563
<b, nil>() -> q_gen_3563
<a, a>() -> q_gen_3564
<b, b>() -> q_gen_3564
<cons, cons, cons>(q_gen_3615, q_gen_3614, q_gen_3613, q_gen_3612, q_gen_3611, q_gen_3610, q_gen_3609, q_gen_3556) -> q_gen_3556
<cons, nil, cons>(q_gen_3564, q_gen_3563, q_gen_3562, q_gen_3561) -> q_gen_3556
<nil, cons, cons>(q_gen_3564, q_gen_3563, q_gen_3562, q_gen_3561) -> q_gen_3556
<nil, nil, cons>(q_gen_3583, q_gen_3582) -> q_gen_3556
<nil, nil, nil>() -> q_gen_3556
<nil, nil, b>() -> q_gen_3609
<nil, a, cons>(q_gen_3583, q_gen_3582) -> q_gen_3610
<nil, b, cons>(q_gen_3583, q_gen_3582) -> q_gen_3610
<nil, a, b>() -> q_gen_3611
<nil, b, b>() -> q_gen_3611
<b, nil, cons>(q_gen_3583, q_gen_3582) -> q_gen_3612
<b, nil, b>() -> q_gen_3613
<b, a, cons>(q_gen_3583, q_gen_3582) -> q_gen_3614
<b, b, cons>(q_gen_3583, q_gen_3582) -> q_gen_3614
<b, a, b>() -> q_gen_3615
<b, b, b>() -> q_gen_3615
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_3555, q_gen_3559, q_gen_3596},
Q_f={q_gen_3555},
Delta=
{
<s>(q_gen_3596) -> q_gen_3596
<z>() -> q_gen_3596
<cons, s>(q_gen_3559, q_gen_3555) -> q_gen_3555
<nil, z>() -> q_gen_3555
<a, s>(q_gen_3596) -> q_gen_3559
<a, z>() -> q_gen_3559
<b, s>(q_gen_3596) -> q_gen_3559
<b, z>() -> q_gen_3559
}

Datatype: <eltlist, nat>
Convolution form: complete
}}}
  ;  leq -> 
{{{
Q={q_gen_3552, q_gen_3554, q_gen_3634},
Q_f={q_gen_3552},
Delta=
{
<s>(q_gen_3554) -> q_gen_3554
<z>() -> q_gen_3554
<s, s>(q_gen_3552) -> q_gen_3552
<z, s>(q_gen_3554) -> q_gen_3552
<z, z>() -> q_gen_3552
<s, z>(q_gen_3554) -> q_gen_3634
}

Datatype: <nat, nat>
Convolution form: complete
}}}
  ;  reverse -> 
{{{
Q={q_gen_3551, q_gen_3573, q_gen_3574, q_gen_3575, q_gen_3618, q_gen_3619, q_gen_3630},
Q_f={q_gen_3551},
Delta=
{
<nil>() -> q_gen_3618
<a>() -> q_gen_3619
<b>() -> q_gen_3619
<cons, cons>(q_gen_3575, q_gen_3574, q_gen_3573, q_gen_3551) -> q_gen_3551
<cons, cons>(q_gen_3575, q_gen_3574, q_gen_3573, q_gen_3630) -> q_gen_3551
<nil, nil>() -> q_gen_3551
<cons, b>(q_gen_3619, q_gen_3618) -> q_gen_3573
<nil, a>() -> q_gen_3573
<nil, b>() -> q_gen_3573
<a, nil>() -> q_gen_3574
<b, cons>(q_gen_3619, q_gen_3618) -> q_gen_3574
<b, nil>() -> q_gen_3574
<a, a>() -> q_gen_3575
<b, b>() -> q_gen_3575
<nil, cons>(q_gen_3619, q_gen_3618) -> q_gen_3630
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 16  ;  () -> length([nil, z]) -> 16  ;  () -> leq([z, s(nn2)]) -> 16  ;  () -> leq([z, z]) -> 16  ;  () -> reverse([nil, nil]) -> 16  ;  (append([_wda, cons(h1, nil), _xda]) /\ reverse([t1, _wda])) -> reverse([cons(h1, t1), _xda]) -> 19  ;  (append([t1, l2, _rda])) -> append([cons(h1, t1), l2, cons(h1, _rda)]) -> 19  ;  (length([_gea, _hea]) /\ length([l1, _fea]) /\ reverse([l1, _gea])) -> leq([_fea, _hea]) -> 17  ;  (length([_iea, _jea]) /\ length([l1, _kea]) /\ reverse([l1, _iea])) -> leq([_jea, _kea]) -> 17  ;  (length([ll, _bea])) -> length([cons(x, ll), s(_bea)]) -> 17  ;  (leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 17  ;  (leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 17  ;  (leq([s(nn1), z])) -> BOT -> 18
}
Sat witness: Yes: ((append([_wda, cons(h1, nil), _xda]) /\ reverse([t1, _wda])) -> reverse([cons(h1, t1), _xda]), {
_wda -> nil  ;  _xda -> cons(b, cons(b, cons(b, nil)))  ;  h1 -> b  ;  t1 -> nil
})

-------------------------------------------
Step 28, which took 0.017060 s (model generation: 0.014150,  model checking: 0.002910):

Model:
|_
{
append -> 
{{{
Q={q_gen_3556, q_gen_3561, q_gen_3562, q_gen_3563, q_gen_3564, q_gen_3582, q_gen_3583, q_gen_3609, q_gen_3610, q_gen_3611, q_gen_3612, q_gen_3613, q_gen_3614, q_gen_3615},
Q_f={q_gen_3556},
Delta=
{
<cons>(q_gen_3583, q_gen_3582) -> q_gen_3582
<nil>() -> q_gen_3582
<a>() -> q_gen_3583
<b>() -> q_gen_3583
<cons, cons>(q_gen_3564, q_gen_3563, q_gen_3562, q_gen_3561) -> q_gen_3561
<nil, cons>(q_gen_3583, q_gen_3582) -> q_gen_3561
<nil, nil>() -> q_gen_3561
<cons, a>(q_gen_3583, q_gen_3582) -> q_gen_3562
<cons, b>(q_gen_3583, q_gen_3582) -> q_gen_3562
<nil, a>() -> q_gen_3562
<nil, b>() -> q_gen_3562
<a, cons>(q_gen_3583, q_gen_3582) -> q_gen_3563
<a, nil>() -> q_gen_3563
<b, cons>(q_gen_3583, q_gen_3582) -> q_gen_3563
<b, nil>() -> q_gen_3563
<a, a>() -> q_gen_3564
<b, b>() -> q_gen_3564
<cons, cons, cons>(q_gen_3615, q_gen_3614, q_gen_3613, q_gen_3612, q_gen_3611, q_gen_3610, q_gen_3609, q_gen_3556) -> q_gen_3556
<cons, nil, cons>(q_gen_3564, q_gen_3563, q_gen_3562, q_gen_3561) -> q_gen_3556
<nil, cons, cons>(q_gen_3564, q_gen_3563, q_gen_3562, q_gen_3561) -> q_gen_3556
<nil, nil, cons>(q_gen_3583, q_gen_3582) -> q_gen_3556
<nil, nil, nil>() -> q_gen_3556
<nil, nil, b>() -> q_gen_3609
<nil, a, cons>(q_gen_3583, q_gen_3582) -> q_gen_3610
<nil, b, cons>(q_gen_3583, q_gen_3582) -> q_gen_3610
<nil, a, b>() -> q_gen_3611
<nil, b, b>() -> q_gen_3611
<b, nil, cons>(q_gen_3583, q_gen_3582) -> q_gen_3612
<b, nil, b>() -> q_gen_3613
<b, a, cons>(q_gen_3583, q_gen_3582) -> q_gen_3614
<b, b, cons>(q_gen_3583, q_gen_3582) -> q_gen_3614
<b, a, b>() -> q_gen_3615
<b, b, b>() -> q_gen_3615
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_3555, q_gen_3559, q_gen_3596},
Q_f={q_gen_3555},
Delta=
{
<s>(q_gen_3596) -> q_gen_3596
<z>() -> q_gen_3596
<cons, s>(q_gen_3559, q_gen_3555) -> q_gen_3555
<nil, z>() -> q_gen_3555
<a, s>(q_gen_3596) -> q_gen_3559
<a, z>() -> q_gen_3559
<b, s>(q_gen_3596) -> q_gen_3559
<b, z>() -> q_gen_3559
}

Datatype: <eltlist, nat>
Convolution form: complete
}}}
  ;  leq -> 
{{{
Q={q_gen_3552, q_gen_3554, q_gen_3634},
Q_f={q_gen_3552},
Delta=
{
<s>(q_gen_3554) -> q_gen_3554
<z>() -> q_gen_3554
<s, s>(q_gen_3552) -> q_gen_3552
<z, s>(q_gen_3554) -> q_gen_3552
<z, z>() -> q_gen_3552
<s, z>(q_gen_3554) -> q_gen_3634
}

Datatype: <nat, nat>
Convolution form: complete
}}}
  ;  reverse -> 
{{{
Q={q_gen_3551, q_gen_3573, q_gen_3574, q_gen_3575, q_gen_3618, q_gen_3619, q_gen_3630},
Q_f={q_gen_3551},
Delta=
{
<cons>(q_gen_3619, q_gen_3618) -> q_gen_3618
<nil>() -> q_gen_3618
<a>() -> q_gen_3619
<b>() -> q_gen_3619
<cons, cons>(q_gen_3575, q_gen_3574, q_gen_3573, q_gen_3551) -> q_gen_3551
<cons, cons>(q_gen_3575, q_gen_3574, q_gen_3573, q_gen_3630) -> q_gen_3551
<nil, nil>() -> q_gen_3551
<cons, b>(q_gen_3619, q_gen_3618) -> q_gen_3573
<nil, a>() -> q_gen_3573
<nil, b>() -> q_gen_3573
<a, nil>() -> q_gen_3574
<b, cons>(q_gen_3619, q_gen_3618) -> q_gen_3574
<b, nil>() -> q_gen_3574
<a, a>() -> q_gen_3575
<b, b>() -> q_gen_3575
<nil, cons>(q_gen_3619, q_gen_3618) -> q_gen_3630
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 17  ;  () -> length([nil, z]) -> 17  ;  () -> leq([z, s(nn2)]) -> 17  ;  () -> leq([z, z]) -> 17  ;  () -> reverse([nil, nil]) -> 17  ;  (append([_wda, cons(h1, nil), _xda]) /\ reverse([t1, _wda])) -> reverse([cons(h1, t1), _xda]) -> 19  ;  (append([t1, l2, _rda])) -> append([cons(h1, t1), l2, cons(h1, _rda)]) -> 19  ;  (length([_gea, _hea]) /\ length([l1, _fea]) /\ reverse([l1, _gea])) -> leq([_fea, _hea]) -> 17  ;  (length([_iea, _jea]) /\ length([l1, _kea]) /\ reverse([l1, _iea])) -> leq([_jea, _kea]) -> 20  ;  (length([ll, _bea])) -> length([cons(x, ll), s(_bea)]) -> 18  ;  (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: ((length([_iea, _jea]) /\ length([l1, _kea]) /\ reverse([l1, _iea])) -> leq([_jea, _kea]), {
_iea -> cons(b, cons(b, nil))  ;  _jea -> s(s(z))  ;  _kea -> s(z)  ;  l1 -> cons(b, nil)
})

-------------------------------------------
Step 29, which took 0.018291 s (model generation: 0.015661,  model checking: 0.002630):

Model:
|_
{
append -> 
{{{
Q={q_gen_3556, q_gen_3561, q_gen_3562, q_gen_3563, q_gen_3564, q_gen_3582, q_gen_3583, q_gen_3609, q_gen_3610, q_gen_3611, q_gen_3612, q_gen_3613, q_gen_3614, q_gen_3615},
Q_f={q_gen_3556},
Delta=
{
<cons>(q_gen_3583, q_gen_3582) -> q_gen_3582
<nil>() -> q_gen_3582
<a>() -> q_gen_3583
<b>() -> q_gen_3583
<cons, cons>(q_gen_3564, q_gen_3563, q_gen_3562, q_gen_3561) -> q_gen_3561
<nil, cons>(q_gen_3583, q_gen_3582) -> q_gen_3561
<nil, nil>() -> q_gen_3561
<cons, a>(q_gen_3583, q_gen_3582) -> q_gen_3562
<cons, b>(q_gen_3583, q_gen_3582) -> q_gen_3562
<nil, a>() -> q_gen_3562
<nil, b>() -> q_gen_3562
<a, cons>(q_gen_3583, q_gen_3582) -> q_gen_3563
<a, nil>() -> q_gen_3563
<b, cons>(q_gen_3583, q_gen_3582) -> q_gen_3563
<b, nil>() -> q_gen_3563
<a, a>() -> q_gen_3564
<b, b>() -> q_gen_3564
<cons, cons, cons>(q_gen_3615, q_gen_3614, q_gen_3613, q_gen_3612, q_gen_3611, q_gen_3610, q_gen_3609, q_gen_3556) -> q_gen_3556
<cons, nil, cons>(q_gen_3564, q_gen_3563, q_gen_3562, q_gen_3561) -> q_gen_3556
<nil, cons, cons>(q_gen_3564, q_gen_3563, q_gen_3562, q_gen_3561) -> q_gen_3556
<nil, nil, cons>(q_gen_3583, q_gen_3582) -> q_gen_3556
<nil, nil, nil>() -> q_gen_3556
<nil, nil, b>() -> q_gen_3609
<nil, a, cons>(q_gen_3583, q_gen_3582) -> q_gen_3610
<nil, b, cons>(q_gen_3583, q_gen_3582) -> q_gen_3610
<nil, a, b>() -> q_gen_3611
<nil, b, b>() -> q_gen_3611
<b, nil, cons>(q_gen_3583, q_gen_3582) -> q_gen_3612
<b, nil, b>() -> q_gen_3613
<b, a, cons>(q_gen_3583, q_gen_3582) -> q_gen_3614
<b, b, cons>(q_gen_3583, q_gen_3582) -> q_gen_3614
<b, a, b>() -> q_gen_3615
<b, b, b>() -> q_gen_3615
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_3555, q_gen_3559, q_gen_3596},
Q_f={q_gen_3555},
Delta=
{
<s>(q_gen_3596) -> q_gen_3596
<z>() -> q_gen_3596
<cons, s>(q_gen_3559, q_gen_3555) -> q_gen_3555
<nil, z>() -> q_gen_3555
<a, s>(q_gen_3596) -> q_gen_3559
<a, z>() -> q_gen_3559
<b, s>(q_gen_3596) -> q_gen_3559
<b, z>() -> q_gen_3559
}

Datatype: <eltlist, nat>
Convolution form: complete
}}}
  ;  leq -> 
{{{
Q={q_gen_3552, q_gen_3554, q_gen_3634},
Q_f={q_gen_3552},
Delta=
{
<s>(q_gen_3554) -> q_gen_3554
<z>() -> q_gen_3554
<s, s>(q_gen_3552) -> q_gen_3552
<s, s>(q_gen_3634) -> q_gen_3552
<z, s>(q_gen_3554) -> q_gen_3552
<z, z>() -> q_gen_3552
<s, z>(q_gen_3554) -> q_gen_3634
}

Datatype: <nat, nat>
Convolution form: complete
}}}
  ;  reverse -> 
{{{
Q={q_gen_3551, q_gen_3573, q_gen_3574, q_gen_3575, q_gen_3618, q_gen_3619, q_gen_3630},
Q_f={q_gen_3551},
Delta=
{
<cons>(q_gen_3619, q_gen_3618) -> q_gen_3618
<nil>() -> q_gen_3618
<a>() -> q_gen_3619
<b>() -> q_gen_3619
<cons, cons>(q_gen_3575, q_gen_3574, q_gen_3573, q_gen_3551) -> q_gen_3551
<cons, cons>(q_gen_3575, q_gen_3574, q_gen_3573, q_gen_3630) -> q_gen_3551
<nil, nil>() -> q_gen_3551
<cons, b>(q_gen_3619, q_gen_3618) -> q_gen_3573
<nil, a>() -> q_gen_3573
<nil, b>() -> q_gen_3573
<a, nil>() -> q_gen_3574
<b, cons>(q_gen_3619, q_gen_3618) -> q_gen_3574
<b, nil>() -> q_gen_3574
<a, a>() -> q_gen_3575
<b, b>() -> q_gen_3575
<nil, cons>(q_gen_3619, q_gen_3618) -> q_gen_3630
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 18  ;  () -> length([nil, z]) -> 18  ;  () -> leq([z, s(nn2)]) -> 18  ;  () -> leq([z, z]) -> 18  ;  () -> reverse([nil, nil]) -> 18  ;  (append([_wda, cons(h1, nil), _xda]) /\ reverse([t1, _wda])) -> reverse([cons(h1, t1), _xda]) -> 19  ;  (append([t1, l2, _rda])) -> append([cons(h1, t1), l2, cons(h1, _rda)]) -> 19  ;  (length([_gea, _hea]) /\ length([l1, _fea]) /\ reverse([l1, _gea])) -> leq([_fea, _hea]) -> 18  ;  (length([_iea, _jea]) /\ length([l1, _kea]) /\ reverse([l1, _iea])) -> leq([_jea, _kea]) -> 20  ;  (length([ll, _bea])) -> length([cons(x, ll), s(_bea)]) -> 18  ;  (leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 18  ;  (leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 21  ;  (leq([s(nn1), z])) -> BOT -> 19
}
Sat witness: Yes: ((leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]), {
nn1 -> s(z)  ;  nn2 -> z
})

-------------------------------------------
Step 30, which took 0.325598 s (model generation: 0.016668,  model checking: 0.308930):

Model:
|_
{
append -> 
{{{
Q={q_gen_3556, q_gen_3561, q_gen_3562, q_gen_3563, q_gen_3564, q_gen_3582, q_gen_3583, q_gen_3608, q_gen_3609, q_gen_3610, q_gen_3611, q_gen_3612, q_gen_3613, q_gen_3614, q_gen_3615, q_gen_3627},
Q_f={q_gen_3556},
Delta=
{
<cons>(q_gen_3583, q_gen_3582) -> q_gen_3582
<nil>() -> q_gen_3582
<a>() -> q_gen_3583
<b>() -> q_gen_3583
<cons, cons>(q_gen_3564, q_gen_3563, q_gen_3562, q_gen_3561) -> q_gen_3561
<nil, nil>() -> q_gen_3561
<cons, a>(q_gen_3583, q_gen_3582) -> q_gen_3562
<cons, b>(q_gen_3583, q_gen_3582) -> q_gen_3562
<nil, a>() -> q_gen_3562
<nil, b>() -> q_gen_3562
<a, cons>(q_gen_3583, q_gen_3582) -> q_gen_3563
<a, nil>() -> q_gen_3563
<b, cons>(q_gen_3583, q_gen_3582) -> q_gen_3563
<b, nil>() -> q_gen_3563
<a, a>() -> q_gen_3564
<b, b>() -> q_gen_3564
<nil, cons>(q_gen_3583, q_gen_3582) -> q_gen_3627
<cons, cons, cons>(q_gen_3615, q_gen_3614, q_gen_3613, q_gen_3612, q_gen_3611, q_gen_3610, q_gen_3609, q_gen_3608) -> q_gen_3556
<cons, nil, cons>(q_gen_3564, q_gen_3563, q_gen_3562, q_gen_3561) -> q_gen_3556
<nil, cons, cons>(q_gen_3564, q_gen_3563, q_gen_3562, q_gen_3561) -> q_gen_3556
<nil, nil, nil>() -> q_gen_3556
<cons, nil, cons>(q_gen_3564, q_gen_3563, q_gen_3562, q_gen_3627) -> q_gen_3608
<nil, cons, cons>(q_gen_3564, q_gen_3563, q_gen_3562, q_gen_3627) -> q_gen_3608
<nil, nil, cons>(q_gen_3583, q_gen_3582) -> q_gen_3608
<nil, nil, b>() -> q_gen_3609
<nil, a, cons>(q_gen_3583, q_gen_3582) -> q_gen_3610
<nil, b, cons>(q_gen_3583, q_gen_3582) -> q_gen_3610
<nil, a, b>() -> q_gen_3611
<nil, b, b>() -> q_gen_3611
<b, nil, cons>(q_gen_3583, q_gen_3582) -> q_gen_3612
<b, nil, b>() -> q_gen_3613
<b, a, cons>(q_gen_3583, q_gen_3582) -> q_gen_3614
<b, b, cons>(q_gen_3583, q_gen_3582) -> q_gen_3614
<b, a, b>() -> q_gen_3615
<b, b, b>() -> q_gen_3615
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_3555, q_gen_3559, q_gen_3596},
Q_f={q_gen_3555},
Delta=
{
<s>(q_gen_3596) -> q_gen_3596
<z>() -> q_gen_3596
<cons, s>(q_gen_3559, q_gen_3555) -> q_gen_3555
<nil, z>() -> q_gen_3555
<a, s>(q_gen_3596) -> q_gen_3559
<a, z>() -> q_gen_3559
<b, s>(q_gen_3596) -> q_gen_3559
<b, z>() -> q_gen_3559
}

Datatype: <eltlist, nat>
Convolution form: complete
}}}
  ;  leq -> 
{{{
Q={q_gen_3552, q_gen_3554, q_gen_3634},
Q_f={q_gen_3552},
Delta=
{
<s>(q_gen_3554) -> q_gen_3554
<z>() -> q_gen_3554
<s, s>(q_gen_3552) -> q_gen_3552
<z, s>(q_gen_3554) -> q_gen_3552
<z, z>() -> q_gen_3552
<s, s>(q_gen_3634) -> q_gen_3634
<s, z>(q_gen_3554) -> q_gen_3634
}

Datatype: <nat, nat>
Convolution form: complete
}}}
  ;  reverse -> 
{{{
Q={q_gen_3551, q_gen_3573, q_gen_3574, q_gen_3575, q_gen_3618, q_gen_3619, q_gen_3629},
Q_f={q_gen_3551},
Delta=
{
<cons>(q_gen_3619, q_gen_3618) -> q_gen_3618
<nil>() -> q_gen_3618
<a>() -> q_gen_3619
<b>() -> q_gen_3619
<cons, cons>(q_gen_3575, q_gen_3574, q_gen_3573, q_gen_3551) -> q_gen_3551
<nil, nil>() -> q_gen_3551
<cons, b>(q_gen_3619, q_gen_3618) -> q_gen_3573
<nil, a>() -> q_gen_3573
<nil, b>() -> q_gen_3573
<a, nil>() -> q_gen_3574
<b, cons>(q_gen_3619, q_gen_3618) -> q_gen_3574
<b, nil>() -> q_gen_3574
<a, a>() -> q_gen_3575
<b, b>() -> q_gen_3575
<cons, cons>(q_gen_3575, q_gen_3574, q_gen_3573, q_gen_3629) -> q_gen_3629
<nil, cons>(q_gen_3619, q_gen_3618) -> q_gen_3629
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 19  ;  () -> length([nil, z]) -> 19  ;  () -> leq([z, s(nn2)]) -> 19  ;  () -> leq([z, z]) -> 19  ;  () -> reverse([nil, nil]) -> 19  ;  (append([_wda, cons(h1, nil), _xda]) /\ reverse([t1, _wda])) -> reverse([cons(h1, t1), _xda]) -> 19  ;  (append([t1, l2, _rda])) -> append([cons(h1, t1), l2, cons(h1, _rda)]) -> 22  ;  (length([_gea, _hea]) /\ length([l1, _fea]) /\ reverse([l1, _gea])) -> leq([_fea, _hea]) -> 19  ;  (length([_iea, _jea]) /\ length([l1, _kea]) /\ reverse([l1, _iea])) -> leq([_jea, _kea]) -> 20  ;  (length([ll, _bea])) -> length([cons(x, ll), s(_bea)]) -> 19  ;  (leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 19  ;  (leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 21  ;  (leq([s(nn1), z])) -> BOT -> 20
}
Sat witness: Yes: ((append([t1, l2, _rda])) -> append([cons(h1, t1), l2, cons(h1, _rda)]), {
_rda -> cons(b, nil)  ;  h1 -> a  ;  l2 -> cons(b, nil)  ;  t1 -> nil
})

-------------------------------------------
Step 31, which took 0.020744 s (model generation: 0.020184,  model checking: 0.000560):

Model:
|_
{
append -> 
{{{
Q={q_gen_3556, q_gen_3561, q_gen_3562, q_gen_3563, q_gen_3564, q_gen_3582, q_gen_3583, q_gen_3609, q_gen_3610, q_gen_3611, q_gen_3612, q_gen_3613, q_gen_3614, q_gen_3615, q_gen_3627, q_gen_3628},
Q_f={q_gen_3556},
Delta=
{
<cons>(q_gen_3583, q_gen_3582) -> q_gen_3582
<nil>() -> q_gen_3582
<a>() -> q_gen_3583
<b>() -> q_gen_3583
<cons, cons>(q_gen_3564, q_gen_3563, q_gen_3562, q_gen_3561) -> q_gen_3561
<nil, nil>() -> q_gen_3561
<cons, a>(q_gen_3583, q_gen_3582) -> q_gen_3562
<cons, b>(q_gen_3583, q_gen_3582) -> q_gen_3562
<nil, a>() -> q_gen_3562
<nil, b>() -> q_gen_3562
<a, cons>(q_gen_3583, q_gen_3582) -> q_gen_3563
<a, nil>() -> q_gen_3563
<b, cons>(q_gen_3583, q_gen_3582) -> q_gen_3563
<b, nil>() -> q_gen_3563
<a, a>() -> q_gen_3564
<b, b>() -> q_gen_3564
<nil, cons>(q_gen_3583, q_gen_3582) -> q_gen_3627
<cons, cons, cons>(q_gen_3615, q_gen_3614, q_gen_3613, q_gen_3612, q_gen_3611, q_gen_3610, q_gen_3609, q_gen_3556) -> q_gen_3556
<cons, nil, cons>(q_gen_3564, q_gen_3563, q_gen_3562, q_gen_3561) -> q_gen_3556
<cons, nil, cons>(q_gen_3564, q_gen_3563, q_gen_3562, q_gen_3627) -> q_gen_3556
<nil, cons, cons>(q_gen_3564, q_gen_3563, q_gen_3562, q_gen_3561) -> q_gen_3556
<nil, nil, cons>(q_gen_3583, q_gen_3582) -> q_gen_3556
<nil, nil, nil>() -> q_gen_3556
<nil, nil, a>() -> q_gen_3609
<nil, nil, b>() -> q_gen_3609
<nil, a, cons>(q_gen_3583, q_gen_3582) -> q_gen_3610
<nil, b, cons>(q_gen_3583, q_gen_3582) -> q_gen_3610
<nil, a, b>() -> q_gen_3611
<nil, b, a>() -> q_gen_3611
<nil, b, b>() -> q_gen_3611
<a, nil, cons>(q_gen_3583, q_gen_3582) -> q_gen_3612
<b, nil, cons>(q_gen_3583, q_gen_3582) -> q_gen_3612
<a, nil, a>() -> q_gen_3613
<b, nil, b>() -> q_gen_3613
<a, b, cons>(q_gen_3583, q_gen_3582) -> q_gen_3614
<b, a, cons>(q_gen_3583, q_gen_3582) -> q_gen_3614
<b, b, cons>(q_gen_3583, q_gen_3582) -> q_gen_3614
<a, b, a>() -> q_gen_3615
<b, a, b>() -> q_gen_3615
<b, b, b>() -> q_gen_3615
<nil, cons, cons>(q_gen_3564, q_gen_3563, q_gen_3562, q_gen_3627) -> q_gen_3628
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_3555, q_gen_3559, q_gen_3596},
Q_f={q_gen_3555},
Delta=
{
<s>(q_gen_3596) -> q_gen_3596
<z>() -> q_gen_3596
<cons, s>(q_gen_3559, q_gen_3555) -> q_gen_3555
<nil, z>() -> q_gen_3555
<a, s>(q_gen_3596) -> q_gen_3559
<a, z>() -> q_gen_3559
<b, s>(q_gen_3596) -> q_gen_3559
<b, z>() -> q_gen_3559
}

Datatype: <eltlist, nat>
Convolution form: complete
}}}
  ;  leq -> 
{{{
Q={q_gen_3552, q_gen_3554, q_gen_3634},
Q_f={q_gen_3552},
Delta=
{
<s>(q_gen_3554) -> q_gen_3554
<z>() -> q_gen_3554
<s, s>(q_gen_3552) -> q_gen_3552
<z, s>(q_gen_3554) -> q_gen_3552
<z, z>() -> q_gen_3552
<s, s>(q_gen_3634) -> q_gen_3634
<s, z>(q_gen_3554) -> q_gen_3634
}

Datatype: <nat, nat>
Convolution form: complete
}}}
  ;  reverse -> 
{{{
Q={q_gen_3551, q_gen_3573, q_gen_3574, q_gen_3575, q_gen_3618, q_gen_3619, q_gen_3629},
Q_f={q_gen_3551},
Delta=
{
<cons>(q_gen_3619, q_gen_3618) -> q_gen_3618
<nil>() -> q_gen_3618
<a>() -> q_gen_3619
<b>() -> q_gen_3619
<cons, cons>(q_gen_3575, q_gen_3574, q_gen_3573, q_gen_3551) -> q_gen_3551
<nil, nil>() -> q_gen_3551
<cons, b>(q_gen_3619, q_gen_3618) -> q_gen_3573
<nil, a>() -> q_gen_3573
<nil, b>() -> q_gen_3573
<a, nil>() -> q_gen_3574
<b, cons>(q_gen_3619, q_gen_3618) -> q_gen_3574
<b, nil>() -> q_gen_3574
<a, a>() -> q_gen_3575
<b, b>() -> q_gen_3575
<cons, cons>(q_gen_3575, q_gen_3574, q_gen_3573, q_gen_3629) -> q_gen_3629
<nil, cons>(q_gen_3619, q_gen_3618) -> q_gen_3629
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 19  ;  () -> length([nil, z]) -> 19  ;  () -> leq([z, s(nn2)]) -> 19  ;  () -> leq([z, z]) -> 19  ;  () -> reverse([nil, nil]) -> 19  ;  (append([_wda, cons(h1, nil), _xda]) /\ reverse([t1, _wda])) -> reverse([cons(h1, t1), _xda]) -> 22  ;  (append([t1, l2, _rda])) -> append([cons(h1, t1), l2, cons(h1, _rda)]) -> 22  ;  (length([_gea, _hea]) /\ length([l1, _fea]) /\ reverse([l1, _gea])) -> leq([_fea, _hea]) -> 20  ;  (length([_iea, _jea]) /\ length([l1, _kea]) /\ reverse([l1, _iea])) -> leq([_jea, _kea]) -> 20  ;  (length([ll, _bea])) -> length([cons(x, ll), s(_bea)]) -> 20  ;  (leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 20  ;  (leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 21  ;  (leq([s(nn1), z])) -> BOT -> 20
}
Sat witness: Yes: ((append([_wda, cons(h1, nil), _xda]) /\ reverse([t1, _wda])) -> reverse([cons(h1, t1), _xda]), {
_wda -> cons(b, nil)  ;  _xda -> cons(b, cons(b, cons(b, nil)))  ;  h1 -> b  ;  t1 -> cons(b, nil)
})

-------------------------------------------
Step 32, which took 0.023591 s (model generation: 0.020846,  model checking: 0.002745):

Model:
|_
{
append -> 
{{{
Q={q_gen_3556, q_gen_3561, q_gen_3562, q_gen_3563, q_gen_3564, q_gen_3582, q_gen_3583, q_gen_3609, q_gen_3610, q_gen_3611, q_gen_3612, q_gen_3613, q_gen_3614, q_gen_3615},
Q_f={q_gen_3556},
Delta=
{
<cons>(q_gen_3583, q_gen_3582) -> q_gen_3582
<nil>() -> q_gen_3582
<a>() -> q_gen_3583
<b>() -> q_gen_3583
<cons, cons>(q_gen_3564, q_gen_3563, q_gen_3562, q_gen_3561) -> q_gen_3561
<nil, cons>(q_gen_3583, q_gen_3582) -> q_gen_3561
<nil, nil>() -> q_gen_3561
<cons, a>(q_gen_3583, q_gen_3582) -> q_gen_3562
<cons, b>(q_gen_3583, q_gen_3582) -> q_gen_3562
<nil, a>() -> q_gen_3562
<nil, b>() -> q_gen_3562
<a, cons>(q_gen_3583, q_gen_3582) -> q_gen_3563
<a, nil>() -> q_gen_3563
<b, cons>(q_gen_3583, q_gen_3582) -> q_gen_3563
<b, nil>() -> q_gen_3563
<a, a>() -> q_gen_3564
<b, b>() -> q_gen_3564
<cons, cons, cons>(q_gen_3615, q_gen_3614, q_gen_3613, q_gen_3612, q_gen_3611, q_gen_3610, q_gen_3609, q_gen_3556) -> q_gen_3556
<cons, nil, cons>(q_gen_3564, q_gen_3563, q_gen_3562, q_gen_3561) -> q_gen_3556
<nil, cons, cons>(q_gen_3564, q_gen_3563, q_gen_3562, q_gen_3561) -> q_gen_3556
<nil, nil, cons>(q_gen_3583, q_gen_3582) -> q_gen_3556
<nil, nil, nil>() -> q_gen_3556
<nil, nil, a>() -> q_gen_3609
<nil, nil, b>() -> q_gen_3609
<nil, a, cons>(q_gen_3583, q_gen_3582) -> q_gen_3610
<nil, b, cons>(q_gen_3583, q_gen_3582) -> q_gen_3610
<nil, a, b>() -> q_gen_3611
<nil, b, a>() -> q_gen_3611
<nil, b, b>() -> q_gen_3611
<a, nil, cons>(q_gen_3583, q_gen_3582) -> q_gen_3612
<b, nil, cons>(q_gen_3583, q_gen_3582) -> q_gen_3612
<a, nil, a>() -> q_gen_3613
<b, nil, b>() -> q_gen_3613
<a, b, cons>(q_gen_3583, q_gen_3582) -> q_gen_3614
<b, a, cons>(q_gen_3583, q_gen_3582) -> q_gen_3614
<b, b, cons>(q_gen_3583, q_gen_3582) -> q_gen_3614
<a, b, a>() -> q_gen_3615
<b, a, b>() -> q_gen_3615
<b, b, b>() -> q_gen_3615
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_3555, q_gen_3559, q_gen_3596},
Q_f={q_gen_3555},
Delta=
{
<s>(q_gen_3596) -> q_gen_3596
<z>() -> q_gen_3596
<cons, s>(q_gen_3559, q_gen_3555) -> q_gen_3555
<nil, z>() -> q_gen_3555
<a, s>(q_gen_3596) -> q_gen_3559
<a, z>() -> q_gen_3559
<b, s>(q_gen_3596) -> q_gen_3559
<b, z>() -> q_gen_3559
}

Datatype: <eltlist, nat>
Convolution form: complete
}}}
  ;  leq -> 
{{{
Q={q_gen_3552, q_gen_3554, q_gen_3634},
Q_f={q_gen_3552},
Delta=
{
<s>(q_gen_3554) -> q_gen_3554
<z>() -> q_gen_3554
<s, s>(q_gen_3552) -> q_gen_3552
<z, s>(q_gen_3554) -> q_gen_3552
<z, z>() -> q_gen_3552
<s, s>(q_gen_3634) -> q_gen_3634
<s, z>(q_gen_3554) -> q_gen_3634
}

Datatype: <nat, nat>
Convolution form: complete
}}}
  ;  reverse -> 
{{{
Q={q_gen_3551, q_gen_3573, q_gen_3574, q_gen_3575, q_gen_3618, q_gen_3619, q_gen_3620, q_gen_3631, q_gen_3633, q_gen_3646},
Q_f={q_gen_3551},
Delta=
{
<nil>() -> q_gen_3618
<b>() -> q_gen_3619
<a>() -> q_gen_3631
<cons>(q_gen_3619, q_gen_3618) -> q_gen_3646
<cons, cons>(q_gen_3575, q_gen_3574, q_gen_3573, q_gen_3551) -> q_gen_3551
<cons, cons>(q_gen_3575, q_gen_3574, q_gen_3573, q_gen_3633) -> q_gen_3551
<cons, cons>(q_gen_3575, q_gen_3620, q_gen_3573, q_gen_3551) -> q_gen_3551
<nil, cons>(q_gen_3619, q_gen_3646) -> q_gen_3551
<nil, cons>(q_gen_3631, q_gen_3618) -> q_gen_3551
<nil, nil>() -> q_gen_3551
<cons, b>(q_gen_3619, q_gen_3618) -> q_gen_3573
<nil, a>() -> q_gen_3573
<nil, b>() -> q_gen_3573
<a, nil>() -> q_gen_3574
<b, cons>(q_gen_3619, q_gen_3646) -> q_gen_3574
<b, nil>() -> q_gen_3574
<a, a>() -> q_gen_3575
<b, b>() -> q_gen_3575
<b, cons>(q_gen_3619, q_gen_3618) -> q_gen_3620
<b, cons>(q_gen_3631, q_gen_3618) -> q_gen_3620
<cons, cons>(q_gen_3575, q_gen_3620, q_gen_3573, q_gen_3633) -> q_gen_3633
<nil, cons>(q_gen_3619, q_gen_3618) -> q_gen_3633
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 20  ;  () -> length([nil, z]) -> 20  ;  () -> leq([z, s(nn2)]) -> 20  ;  () -> leq([z, z]) -> 20  ;  () -> reverse([nil, nil]) -> 20  ;  (append([_wda, cons(h1, nil), _xda]) /\ reverse([t1, _wda])) -> reverse([cons(h1, t1), _xda]) -> 22  ;  (append([t1, l2, _rda])) -> append([cons(h1, t1), l2, cons(h1, _rda)]) -> 22  ;  (length([_gea, _hea]) /\ length([l1, _fea]) /\ reverse([l1, _gea])) -> leq([_fea, _hea]) -> 20  ;  (length([_iea, _jea]) /\ length([l1, _kea]) /\ reverse([l1, _iea])) -> leq([_jea, _kea]) -> 23  ;  (length([ll, _bea])) -> length([cons(x, ll), s(_bea)]) -> 21  ;  (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: ((length([_iea, _jea]) /\ length([l1, _kea]) /\ reverse([l1, _iea])) -> leq([_jea, _kea]), {
_iea -> cons(a, nil)  ;  _jea -> s(z)  ;  _kea -> z  ;  l1 -> nil
})

-------------------------------------------
Step 33, which took 0.028937 s (model generation: 0.025449,  model checking: 0.003488):

Model:
|_
{
append -> 
{{{
Q={q_gen_3556, q_gen_3561, q_gen_3562, q_gen_3563, q_gen_3564, q_gen_3582, q_gen_3583, q_gen_3609, q_gen_3610, q_gen_3611, q_gen_3612, q_gen_3613, q_gen_3614, q_gen_3615},
Q_f={q_gen_3556},
Delta=
{
<cons>(q_gen_3583, q_gen_3582) -> q_gen_3582
<nil>() -> q_gen_3582
<a>() -> q_gen_3583
<b>() -> q_gen_3583
<cons, cons>(q_gen_3564, q_gen_3563, q_gen_3562, q_gen_3561) -> q_gen_3561
<nil, cons>(q_gen_3583, q_gen_3582) -> q_gen_3561
<nil, nil>() -> q_gen_3561
<cons, a>(q_gen_3583, q_gen_3582) -> q_gen_3562
<cons, b>(q_gen_3583, q_gen_3582) -> q_gen_3562
<nil, a>() -> q_gen_3562
<nil, b>() -> q_gen_3562
<a, cons>(q_gen_3583, q_gen_3582) -> q_gen_3563
<a, nil>() -> q_gen_3563
<b, cons>(q_gen_3583, q_gen_3582) -> q_gen_3563
<b, nil>() -> q_gen_3563
<a, a>() -> q_gen_3564
<b, b>() -> q_gen_3564
<cons, cons, cons>(q_gen_3615, q_gen_3614, q_gen_3613, q_gen_3612, q_gen_3611, q_gen_3610, q_gen_3609, q_gen_3556) -> q_gen_3556
<cons, nil, cons>(q_gen_3564, q_gen_3563, q_gen_3562, q_gen_3561) -> q_gen_3556
<nil, cons, cons>(q_gen_3564, q_gen_3563, q_gen_3562, q_gen_3561) -> q_gen_3556
<nil, nil, cons>(q_gen_3583, q_gen_3582) -> q_gen_3556
<nil, nil, nil>() -> q_gen_3556
<nil, nil, a>() -> q_gen_3609
<nil, nil, b>() -> q_gen_3609
<nil, a, cons>(q_gen_3583, q_gen_3582) -> q_gen_3610
<nil, b, cons>(q_gen_3583, q_gen_3582) -> q_gen_3610
<nil, a, b>() -> q_gen_3611
<nil, b, a>() -> q_gen_3611
<nil, b, b>() -> q_gen_3611
<a, nil, cons>(q_gen_3583, q_gen_3582) -> q_gen_3612
<b, nil, cons>(q_gen_3583, q_gen_3582) -> q_gen_3612
<a, nil, a>() -> q_gen_3613
<b, nil, b>() -> q_gen_3613
<a, b, cons>(q_gen_3583, q_gen_3582) -> q_gen_3614
<b, a, cons>(q_gen_3583, q_gen_3582) -> q_gen_3614
<b, b, cons>(q_gen_3583, q_gen_3582) -> q_gen_3614
<a, b, a>() -> q_gen_3615
<b, a, b>() -> q_gen_3615
<b, b, b>() -> q_gen_3615
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_3555, q_gen_3558, q_gen_3559, q_gen_3577, q_gen_3596, q_gen_3621},
Q_f={q_gen_3555, q_gen_3558},
Delta=
{
<s>(q_gen_3596) -> q_gen_3596
<z>() -> q_gen_3596
<cons, s>(q_gen_3559, q_gen_3558) -> q_gen_3555
<cons, s>(q_gen_3577, q_gen_3555) -> q_gen_3555
<nil, z>() -> q_gen_3555
<cons, s>(q_gen_3559, q_gen_3555) -> q_gen_3558
<a, s>(q_gen_3596) -> q_gen_3559
<b, z>() -> q_gen_3559
<a, z>() -> q_gen_3577
<b, s>(q_gen_3596) -> q_gen_3577
<cons, s>(q_gen_3577, q_gen_3558) -> q_gen_3621
<cons, s>(q_gen_3577, q_gen_3621) -> q_gen_3621
}

Datatype: <eltlist, nat>
Convolution form: complete
}}}
  ;  leq -> 
{{{
Q={q_gen_3552, q_gen_3554, q_gen_3634},
Q_f={q_gen_3552},
Delta=
{
<s>(q_gen_3554) -> q_gen_3554
<z>() -> q_gen_3554
<s, s>(q_gen_3552) -> q_gen_3552
<z, s>(q_gen_3554) -> q_gen_3552
<z, z>() -> q_gen_3552
<s, s>(q_gen_3634) -> q_gen_3634
<s, z>(q_gen_3554) -> q_gen_3634
}

Datatype: <nat, nat>
Convolution form: complete
}}}
  ;  reverse -> 
{{{
Q={q_gen_3551, q_gen_3573, q_gen_3574, q_gen_3575, q_gen_3618, q_gen_3619, q_gen_3630},
Q_f={q_gen_3551},
Delta=
{
<cons>(q_gen_3619, q_gen_3618) -> q_gen_3618
<nil>() -> q_gen_3618
<a>() -> q_gen_3619
<b>() -> q_gen_3619
<cons, cons>(q_gen_3575, q_gen_3574, q_gen_3573, q_gen_3551) -> q_gen_3551
<cons, cons>(q_gen_3575, q_gen_3574, q_gen_3573, q_gen_3630) -> q_gen_3551
<nil, nil>() -> q_gen_3551
<cons, b>(q_gen_3619, q_gen_3618) -> q_gen_3573
<nil, a>() -> q_gen_3573
<nil, b>() -> q_gen_3573
<a, nil>() -> q_gen_3574
<b, cons>(q_gen_3619, q_gen_3618) -> q_gen_3574
<b, nil>() -> q_gen_3574
<a, a>() -> q_gen_3575
<b, b>() -> q_gen_3575
<nil, cons>(q_gen_3619, q_gen_3618) -> q_gen_3630
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 21  ;  () -> length([nil, z]) -> 21  ;  () -> leq([z, s(nn2)]) -> 21  ;  () -> leq([z, z]) -> 21  ;  () -> reverse([nil, nil]) -> 21  ;  (append([_wda, cons(h1, nil), _xda]) /\ reverse([t1, _wda])) -> reverse([cons(h1, t1), _xda]) -> 22  ;  (append([t1, l2, _rda])) -> append([cons(h1, t1), l2, cons(h1, _rda)]) -> 22  ;  (length([_gea, _hea]) /\ length([l1, _fea]) /\ reverse([l1, _gea])) -> leq([_fea, _hea]) -> 21  ;  (length([_iea, _jea]) /\ length([l1, _kea]) /\ reverse([l1, _iea])) -> leq([_jea, _kea]) -> 23  ;  (length([ll, _bea])) -> length([cons(x, ll), s(_bea)]) -> 24  ;  (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: ((length([ll, _bea])) -> length([cons(x, ll), s(_bea)]), {
_bea -> s(z)  ;  ll -> cons(b, nil)  ;  x -> b
})

-------------------------------------------
Step 34, which took 0.221836 s (model generation: 0.022916,  model checking: 0.198920):

Model:
|_
{
append -> 
{{{
Q={q_gen_3556, q_gen_3561, q_gen_3562, q_gen_3563, q_gen_3564, q_gen_3582, q_gen_3583, q_gen_3603, q_gen_3609, q_gen_3610, q_gen_3611, q_gen_3612, q_gen_3613, q_gen_3614, q_gen_3615, q_gen_3627, q_gen_3628},
Q_f={q_gen_3556},
Delta=
{
<nil>() -> q_gen_3582
<a>() -> q_gen_3583
<b>() -> q_gen_3583
<cons>(q_gen_3583, q_gen_3582) -> q_gen_3603
<cons, cons>(q_gen_3564, q_gen_3563, q_gen_3562, q_gen_3561) -> q_gen_3561
<nil, nil>() -> q_gen_3561
<cons, a>(q_gen_3583, q_gen_3582) -> q_gen_3562
<cons, b>(q_gen_3583, q_gen_3582) -> q_gen_3562
<cons, b>(q_gen_3583, q_gen_3603) -> q_gen_3562
<nil, a>() -> q_gen_3562
<nil, b>() -> q_gen_3562
<a, cons>(q_gen_3583, q_gen_3582) -> q_gen_3563
<a, nil>() -> q_gen_3563
<b, cons>(q_gen_3583, q_gen_3582) -> q_gen_3563
<b, cons>(q_gen_3583, q_gen_3603) -> q_gen_3563
<b, nil>() -> q_gen_3563
<a, a>() -> q_gen_3564
<b, b>() -> q_gen_3564
<nil, cons>(q_gen_3583, q_gen_3582) -> q_gen_3627
<nil, cons>(q_gen_3583, q_gen_3603) -> q_gen_3627
<cons, cons, cons>(q_gen_3615, q_gen_3614, q_gen_3613, q_gen_3612, q_gen_3611, q_gen_3610, q_gen_3609, q_gen_3556) -> q_gen_3556
<cons, nil, cons>(q_gen_3564, q_gen_3563, q_gen_3562, q_gen_3561) -> q_gen_3556
<cons, nil, cons>(q_gen_3564, q_gen_3563, q_gen_3562, q_gen_3627) -> q_gen_3556
<nil, cons, cons>(q_gen_3564, q_gen_3563, q_gen_3562, q_gen_3561) -> q_gen_3556
<nil, nil, cons>(q_gen_3583, q_gen_3582) -> q_gen_3556
<nil, nil, nil>() -> q_gen_3556
<nil, nil, a>() -> q_gen_3609
<nil, nil, b>() -> q_gen_3609
<nil, a, cons>(q_gen_3583, q_gen_3582) -> q_gen_3610
<nil, b, cons>(q_gen_3583, q_gen_3582) -> q_gen_3610
<nil, b, cons>(q_gen_3583, q_gen_3603) -> q_gen_3610
<nil, a, b>() -> q_gen_3611
<nil, b, a>() -> q_gen_3611
<nil, b, b>() -> q_gen_3611
<a, nil, cons>(q_gen_3583, q_gen_3582) -> q_gen_3612
<b, nil, cons>(q_gen_3583, q_gen_3582) -> q_gen_3612
<b, nil, cons>(q_gen_3583, q_gen_3603) -> q_gen_3612
<a, nil, a>() -> q_gen_3613
<b, nil, b>() -> q_gen_3613
<a, b, cons>(q_gen_3583, q_gen_3582) -> q_gen_3614
<b, a, cons>(q_gen_3583, q_gen_3582) -> q_gen_3614
<b, b, cons>(q_gen_3583, q_gen_3582) -> q_gen_3614
<b, b, cons>(q_gen_3583, q_gen_3603) -> q_gen_3614
<a, b, a>() -> q_gen_3615
<b, a, b>() -> q_gen_3615
<b, b, b>() -> q_gen_3615
<cons, cons, cons>(q_gen_3615, q_gen_3614, q_gen_3613, q_gen_3612, q_gen_3611, q_gen_3610, q_gen_3609, q_gen_3628) -> q_gen_3628
<nil, cons, cons>(q_gen_3564, q_gen_3563, q_gen_3562, q_gen_3627) -> q_gen_3628
<nil, nil, cons>(q_gen_3583, q_gen_3603) -> q_gen_3628
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_3555, q_gen_3559, q_gen_3596},
Q_f={q_gen_3555},
Delta=
{
<s>(q_gen_3596) -> q_gen_3596
<z>() -> q_gen_3596
<cons, s>(q_gen_3559, q_gen_3555) -> q_gen_3555
<nil, z>() -> q_gen_3555
<a, s>(q_gen_3596) -> q_gen_3559
<a, z>() -> q_gen_3559
<b, s>(q_gen_3596) -> q_gen_3559
<b, z>() -> q_gen_3559
}

Datatype: <eltlist, nat>
Convolution form: complete
}}}
  ;  leq -> 
{{{
Q={q_gen_3552, q_gen_3554, q_gen_3634},
Q_f={q_gen_3552},
Delta=
{
<s>(q_gen_3554) -> q_gen_3554
<z>() -> q_gen_3554
<s, s>(q_gen_3552) -> q_gen_3552
<z, s>(q_gen_3554) -> q_gen_3552
<z, z>() -> q_gen_3552
<s, s>(q_gen_3634) -> q_gen_3634
<s, z>(q_gen_3554) -> q_gen_3634
}

Datatype: <nat, nat>
Convolution form: complete
}}}
  ;  reverse -> 
{{{
Q={q_gen_3551, q_gen_3573, q_gen_3574, q_gen_3575, q_gen_3618, q_gen_3619, q_gen_3629},
Q_f={q_gen_3551},
Delta=
{
<cons>(q_gen_3619, q_gen_3618) -> q_gen_3618
<nil>() -> q_gen_3618
<a>() -> q_gen_3619
<b>() -> q_gen_3619
<cons, cons>(q_gen_3575, q_gen_3574, q_gen_3573, q_gen_3551) -> q_gen_3551
<nil, nil>() -> q_gen_3551
<cons, b>(q_gen_3619, q_gen_3618) -> q_gen_3573
<nil, a>() -> q_gen_3573
<nil, b>() -> q_gen_3573
<a, nil>() -> q_gen_3574
<b, cons>(q_gen_3619, q_gen_3618) -> q_gen_3574
<b, nil>() -> q_gen_3574
<a, a>() -> q_gen_3575
<b, b>() -> q_gen_3575
<cons, cons>(q_gen_3575, q_gen_3574, q_gen_3573, q_gen_3629) -> q_gen_3629
<nil, cons>(q_gen_3619, q_gen_3618) -> q_gen_3629
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 24  ;  () -> length([nil, z]) -> 22  ;  () -> leq([z, s(nn2)]) -> 22  ;  () -> leq([z, z]) -> 22  ;  () -> reverse([nil, nil]) -> 22  ;  (append([_wda, cons(h1, nil), _xda]) /\ reverse([t1, _wda])) -> reverse([cons(h1, t1), _xda]) -> 22  ;  (append([t1, l2, _rda])) -> append([cons(h1, t1), l2, cons(h1, _rda)]) -> 22  ;  (length([_gea, _hea]) /\ length([l1, _fea]) /\ reverse([l1, _gea])) -> leq([_fea, _hea]) -> 22  ;  (length([_iea, _jea]) /\ length([l1, _kea]) /\ reverse([l1, _iea])) -> leq([_jea, _kea]) -> 23  ;  (length([ll, _bea])) -> length([cons(x, ll), s(_bea)]) -> 24  ;  (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([nil, l2, l2]), {
l2 -> cons(b, cons(a, cons(a, cons(b, nil))))
})

-------------------------------------------
Step 35, which took 0.105003 s (model generation: 0.025210,  model checking: 0.079793):

Model:
|_
{
append -> 
{{{
Q={q_gen_3556, q_gen_3561, q_gen_3562, q_gen_3563, q_gen_3564, q_gen_3582, q_gen_3583, q_gen_3603, q_gen_3609, q_gen_3610, q_gen_3611, q_gen_3612, q_gen_3613, q_gen_3614, q_gen_3615, q_gen_3627, q_gen_3628},
Q_f={q_gen_3556},
Delta=
{
<nil>() -> q_gen_3582
<a>() -> q_gen_3583
<b>() -> q_gen_3583
<cons>(q_gen_3583, q_gen_3582) -> q_gen_3603
<cons>(q_gen_3583, q_gen_3603) -> q_gen_3603
<cons, cons>(q_gen_3564, q_gen_3563, q_gen_3562, q_gen_3561) -> q_gen_3561
<nil, nil>() -> q_gen_3561
<cons, a>(q_gen_3583, q_gen_3582) -> q_gen_3562
<cons, a>(q_gen_3583, q_gen_3603) -> q_gen_3562
<cons, b>(q_gen_3583, q_gen_3582) -> q_gen_3562
<cons, b>(q_gen_3583, q_gen_3603) -> q_gen_3562
<nil, a>() -> q_gen_3562
<nil, b>() -> q_gen_3562
<a, cons>(q_gen_3583, q_gen_3582) -> q_gen_3563
<a, cons>(q_gen_3583, q_gen_3603) -> q_gen_3563
<a, nil>() -> q_gen_3563
<b, cons>(q_gen_3583, q_gen_3582) -> q_gen_3563
<b, cons>(q_gen_3583, q_gen_3603) -> q_gen_3563
<b, nil>() -> q_gen_3563
<a, a>() -> q_gen_3564
<b, b>() -> q_gen_3564
<nil, cons>(q_gen_3583, q_gen_3582) -> q_gen_3627
<nil, cons>(q_gen_3583, q_gen_3603) -> q_gen_3627
<cons, cons, cons>(q_gen_3615, q_gen_3614, q_gen_3613, q_gen_3612, q_gen_3611, q_gen_3610, q_gen_3609, q_gen_3556) -> q_gen_3556
<cons, nil, cons>(q_gen_3564, q_gen_3563, q_gen_3562, q_gen_3561) -> q_gen_3556
<cons, nil, cons>(q_gen_3564, q_gen_3563, q_gen_3562, q_gen_3627) -> q_gen_3556
<nil, cons, cons>(q_gen_3564, q_gen_3563, q_gen_3562, q_gen_3561) -> q_gen_3556
<nil, nil, cons>(q_gen_3583, q_gen_3582) -> q_gen_3556
<nil, nil, nil>() -> q_gen_3556
<nil, nil, a>() -> q_gen_3609
<nil, nil, b>() -> q_gen_3609
<nil, a, cons>(q_gen_3583, q_gen_3582) -> q_gen_3610
<nil, b, cons>(q_gen_3583, q_gen_3582) -> q_gen_3610
<nil, b, cons>(q_gen_3583, q_gen_3603) -> q_gen_3610
<nil, a, b>() -> q_gen_3611
<nil, b, a>() -> q_gen_3611
<nil, b, b>() -> q_gen_3611
<a, nil, cons>(q_gen_3583, q_gen_3582) -> q_gen_3612
<b, nil, cons>(q_gen_3583, q_gen_3582) -> q_gen_3612
<b, nil, cons>(q_gen_3583, q_gen_3603) -> q_gen_3612
<a, nil, a>() -> q_gen_3613
<b, nil, b>() -> q_gen_3613
<a, b, cons>(q_gen_3583, q_gen_3582) -> q_gen_3614
<b, a, cons>(q_gen_3583, q_gen_3582) -> q_gen_3614
<b, b, cons>(q_gen_3583, q_gen_3582) -> q_gen_3614
<b, b, cons>(q_gen_3583, q_gen_3603) -> q_gen_3614
<a, b, a>() -> q_gen_3615
<b, a, b>() -> q_gen_3615
<b, b, b>() -> q_gen_3615
<cons, cons, cons>(q_gen_3615, q_gen_3614, q_gen_3613, q_gen_3612, q_gen_3611, q_gen_3610, q_gen_3609, q_gen_3628) -> q_gen_3628
<nil, cons, cons>(q_gen_3564, q_gen_3563, q_gen_3562, q_gen_3627) -> q_gen_3628
<nil, nil, cons>(q_gen_3583, q_gen_3603) -> q_gen_3628
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_3555, q_gen_3559, q_gen_3596},
Q_f={q_gen_3555},
Delta=
{
<s>(q_gen_3596) -> q_gen_3596
<z>() -> q_gen_3596
<cons, s>(q_gen_3559, q_gen_3555) -> q_gen_3555
<nil, z>() -> q_gen_3555
<a, s>(q_gen_3596) -> q_gen_3559
<a, z>() -> q_gen_3559
<b, s>(q_gen_3596) -> q_gen_3559
<b, z>() -> q_gen_3559
}

Datatype: <eltlist, nat>
Convolution form: complete
}}}
  ;  leq -> 
{{{
Q={q_gen_3552, q_gen_3554, q_gen_3634},
Q_f={q_gen_3552},
Delta=
{
<s>(q_gen_3554) -> q_gen_3554
<z>() -> q_gen_3554
<s, s>(q_gen_3552) -> q_gen_3552
<z, s>(q_gen_3554) -> q_gen_3552
<z, z>() -> q_gen_3552
<s, s>(q_gen_3634) -> q_gen_3634
<s, z>(q_gen_3554) -> q_gen_3634
}

Datatype: <nat, nat>
Convolution form: complete
}}}
  ;  reverse -> 
{{{
Q={q_gen_3551, q_gen_3573, q_gen_3574, q_gen_3575, q_gen_3618, q_gen_3619, q_gen_3629},
Q_f={q_gen_3551},
Delta=
{
<cons>(q_gen_3619, q_gen_3618) -> q_gen_3618
<nil>() -> q_gen_3618
<a>() -> q_gen_3619
<b>() -> q_gen_3619
<cons, cons>(q_gen_3575, q_gen_3574, q_gen_3573, q_gen_3551) -> q_gen_3551
<nil, nil>() -> q_gen_3551
<cons, b>(q_gen_3619, q_gen_3618) -> q_gen_3573
<nil, a>() -> q_gen_3573
<nil, b>() -> q_gen_3573
<a, nil>() -> q_gen_3574
<b, cons>(q_gen_3619, q_gen_3618) -> q_gen_3574
<b, nil>() -> q_gen_3574
<a, a>() -> q_gen_3575
<b, b>() -> q_gen_3575
<cons, cons>(q_gen_3575, q_gen_3574, q_gen_3573, q_gen_3629) -> q_gen_3629
<nil, cons>(q_gen_3619, q_gen_3618) -> q_gen_3629
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 24  ;  () -> length([nil, z]) -> 22  ;  () -> leq([z, s(nn2)]) -> 22  ;  () -> leq([z, z]) -> 22  ;  () -> reverse([nil, nil]) -> 22  ;  (append([_wda, cons(h1, nil), _xda]) /\ reverse([t1, _wda])) -> reverse([cons(h1, t1), _xda]) -> 22  ;  (append([t1, l2, _rda])) -> append([cons(h1, t1), l2, cons(h1, _rda)]) -> 25  ;  (length([_gea, _hea]) /\ length([l1, _fea]) /\ reverse([l1, _gea])) -> leq([_fea, _hea]) -> 23  ;  (length([_iea, _jea]) /\ length([l1, _kea]) /\ reverse([l1, _iea])) -> leq([_jea, _kea]) -> 23  ;  (length([ll, _bea])) -> length([cons(x, ll), s(_bea)]) -> 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([t1, l2, _rda])) -> append([cons(h1, t1), l2, cons(h1, _rda)]), {
_rda -> cons(a, cons(b, cons(b, nil)))  ;  h1 -> b  ;  l2 -> nil  ;  t1 -> cons(a, nil)
})

-------------------------------------------
Step 36, which took 0.045303 s (model generation: 0.028875,  model checking: 0.016428):

Model:
|_
{
append -> 
{{{
Q={q_gen_3556, q_gen_3561, q_gen_3562, q_gen_3563, q_gen_3564, q_gen_3582, q_gen_3583, q_gen_3609, q_gen_3610, q_gen_3611, q_gen_3612, q_gen_3613, q_gen_3614, q_gen_3615, q_gen_3627, q_gen_3628},
Q_f={q_gen_3556},
Delta=
{
<cons>(q_gen_3583, q_gen_3582) -> q_gen_3582
<nil>() -> q_gen_3582
<a>() -> q_gen_3583
<b>() -> q_gen_3583
<cons, cons>(q_gen_3564, q_gen_3563, q_gen_3562, q_gen_3561) -> q_gen_3561
<cons, cons>(q_gen_3564, q_gen_3563, q_gen_3562, q_gen_3627) -> q_gen_3561
<nil, nil>() -> q_gen_3561
<cons, a>(q_gen_3583, q_gen_3582) -> q_gen_3562
<cons, b>(q_gen_3583, q_gen_3582) -> q_gen_3562
<nil, a>() -> q_gen_3562
<nil, b>() -> q_gen_3562
<a, cons>(q_gen_3583, q_gen_3582) -> q_gen_3563
<a, nil>() -> q_gen_3563
<b, cons>(q_gen_3583, q_gen_3582) -> q_gen_3563
<b, nil>() -> q_gen_3563
<a, a>() -> q_gen_3564
<b, b>() -> q_gen_3564
<nil, cons>(q_gen_3583, q_gen_3582) -> q_gen_3627
<cons, cons, cons>(q_gen_3615, q_gen_3614, q_gen_3613, q_gen_3612, q_gen_3611, q_gen_3610, q_gen_3609, q_gen_3556) -> q_gen_3556
<cons, nil, cons>(q_gen_3564, q_gen_3563, q_gen_3562, q_gen_3561) -> q_gen_3556
<cons, nil, cons>(q_gen_3564, q_gen_3563, q_gen_3562, q_gen_3627) -> q_gen_3556
<nil, cons, cons>(q_gen_3564, q_gen_3563, q_gen_3562, q_gen_3561) -> q_gen_3556
<nil, nil, cons>(q_gen_3583, q_gen_3582) -> q_gen_3556
<nil, nil, nil>() -> q_gen_3556
<nil, nil, a>() -> q_gen_3609
<nil, nil, b>() -> q_gen_3609
<nil, a, cons>(q_gen_3583, q_gen_3582) -> q_gen_3610
<nil, b, cons>(q_gen_3583, q_gen_3582) -> q_gen_3610
<nil, a, b>() -> q_gen_3611
<nil, b, a>() -> q_gen_3611
<nil, b, b>() -> q_gen_3611
<a, nil, cons>(q_gen_3583, q_gen_3582) -> q_gen_3612
<b, nil, cons>(q_gen_3583, q_gen_3582) -> q_gen_3612
<a, nil, a>() -> q_gen_3613
<b, nil, b>() -> q_gen_3613
<a, b, cons>(q_gen_3583, q_gen_3582) -> q_gen_3614
<b, a, cons>(q_gen_3583, q_gen_3582) -> q_gen_3614
<b, b, cons>(q_gen_3583, q_gen_3582) -> q_gen_3614
<a, b, a>() -> q_gen_3615
<b, a, b>() -> q_gen_3615
<b, b, b>() -> q_gen_3615
<nil, cons, cons>(q_gen_3564, q_gen_3563, q_gen_3562, q_gen_3627) -> q_gen_3628
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_3555, q_gen_3559, q_gen_3596},
Q_f={q_gen_3555},
Delta=
{
<s>(q_gen_3596) -> q_gen_3596
<z>() -> q_gen_3596
<cons, s>(q_gen_3559, q_gen_3555) -> q_gen_3555
<nil, z>() -> q_gen_3555
<a, s>(q_gen_3596) -> q_gen_3559
<a, z>() -> q_gen_3559
<b, s>(q_gen_3596) -> q_gen_3559
<b, z>() -> q_gen_3559
}

Datatype: <eltlist, nat>
Convolution form: complete
}}}
  ;  leq -> 
{{{
Q={q_gen_3552, q_gen_3554, q_gen_3634},
Q_f={q_gen_3552},
Delta=
{
<s>(q_gen_3554) -> q_gen_3554
<z>() -> q_gen_3554
<s, s>(q_gen_3552) -> q_gen_3552
<z, s>(q_gen_3554) -> q_gen_3552
<z, z>() -> q_gen_3552
<s, s>(q_gen_3634) -> q_gen_3634
<s, z>(q_gen_3554) -> q_gen_3634
}

Datatype: <nat, nat>
Convolution form: complete
}}}
  ;  reverse -> 
{{{
Q={q_gen_3551, q_gen_3573, q_gen_3574, q_gen_3575, q_gen_3586, q_gen_3618, q_gen_3619, q_gen_3629},
Q_f={q_gen_3551},
Delta=
{
<cons>(q_gen_3619, q_gen_3618) -> q_gen_3618
<nil>() -> q_gen_3618
<a>() -> q_gen_3619
<b>() -> q_gen_3619
<cons, cons>(q_gen_3575, q_gen_3574, q_gen_3573, q_gen_3551) -> q_gen_3551
<cons, cons>(q_gen_3575, q_gen_3574, q_gen_3586, q_gen_3551) -> q_gen_3551
<cons, cons>(q_gen_3575, q_gen_3574, q_gen_3586, q_gen_3629) -> q_gen_3551
<nil, nil>() -> q_gen_3551
<nil, b>() -> q_gen_3573
<a, nil>() -> q_gen_3574
<b, cons>(q_gen_3619, q_gen_3618) -> q_gen_3574
<b, nil>() -> q_gen_3574
<a, a>() -> q_gen_3575
<b, b>() -> q_gen_3575
<cons, b>(q_gen_3619, q_gen_3618) -> q_gen_3586
<nil, a>() -> q_gen_3586
<cons, cons>(q_gen_3575, q_gen_3574, q_gen_3573, q_gen_3629) -> q_gen_3629
<nil, cons>(q_gen_3619, q_gen_3618) -> q_gen_3629
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 24  ;  () -> length([nil, z]) -> 22  ;  () -> leq([z, s(nn2)]) -> 22  ;  () -> leq([z, z]) -> 22  ;  () -> reverse([nil, nil]) -> 22  ;  (append([_wda, cons(h1, nil), _xda]) /\ reverse([t1, _wda])) -> reverse([cons(h1, t1), _xda]) -> 25  ;  (append([t1, l2, _rda])) -> append([cons(h1, t1), l2, cons(h1, _rda)]) -> 25  ;  (length([_gea, _hea]) /\ length([l1, _fea]) /\ reverse([l1, _gea])) -> leq([_fea, _hea]) -> 23  ;  (length([_iea, _jea]) /\ length([l1, _kea]) /\ reverse([l1, _iea])) -> leq([_jea, _kea]) -> 23  ;  (length([ll, _bea])) -> length([cons(x, ll), s(_bea)]) -> 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([_wda, cons(h1, nil), _xda]) /\ reverse([t1, _wda])) -> reverse([cons(h1, t1), _xda]), {
_wda -> cons(b, nil)  ;  _xda -> cons(b, cons(a, nil))  ;  h1 -> b  ;  t1 -> cons(b, nil)
})

-------------------------------------------
Step 37, which took 0.039152 s (model generation: 0.035167,  model checking: 0.003985):

Model:
|_
{
append -> 
{{{
Q={q_gen_3556, q_gen_3561, q_gen_3562, q_gen_3563, q_gen_3564, q_gen_3568, q_gen_3571, q_gen_3582, q_gen_3583, q_gen_3609, q_gen_3610, q_gen_3611, q_gen_3612, q_gen_3613, q_gen_3614, q_gen_3615},
Q_f={q_gen_3556},
Delta=
{
<cons>(q_gen_3583, q_gen_3582) -> q_gen_3582
<nil>() -> q_gen_3582
<a>() -> q_gen_3583
<b>() -> q_gen_3583
<cons, cons>(q_gen_3564, q_gen_3563, q_gen_3562, q_gen_3561) -> q_gen_3561
<cons, cons>(q_gen_3564, q_gen_3563, q_gen_3568, q_gen_3561) -> q_gen_3561
<nil, cons>(q_gen_3583, q_gen_3582) -> q_gen_3561
<nil, nil>() -> q_gen_3561
<cons, a>(q_gen_3583, q_gen_3582) -> q_gen_3562
<nil, b>() -> q_gen_3562
<a, cons>(q_gen_3583, q_gen_3582) -> q_gen_3563
<a, nil>() -> q_gen_3563
<b, cons>(q_gen_3583, q_gen_3582) -> q_gen_3563
<b, nil>() -> q_gen_3563
<a, a>() -> q_gen_3564
<b, b>() -> q_gen_3564
<cons, b>(q_gen_3583, q_gen_3582) -> q_gen_3568
<nil, a>() -> q_gen_3568
<cons, cons, cons>(q_gen_3615, q_gen_3614, q_gen_3613, q_gen_3612, q_gen_3611, q_gen_3610, q_gen_3609, q_gen_3556) -> q_gen_3556
<cons, nil, cons>(q_gen_3564, q_gen_3563, q_gen_3562, q_gen_3561) -> q_gen_3556
<nil, cons, cons>(q_gen_3564, q_gen_3563, q_gen_3568, q_gen_3561) -> q_gen_3556
<nil, nil, cons>(q_gen_3583, q_gen_3582) -> q_gen_3556
<nil, nil, nil>() -> q_gen_3556
<cons, nil, cons>(q_gen_3564, q_gen_3563, q_gen_3568, q_gen_3561) -> q_gen_3571
<nil, cons, cons>(q_gen_3564, q_gen_3563, q_gen_3562, q_gen_3561) -> q_gen_3571
<nil, nil, a>() -> q_gen_3609
<nil, nil, b>() -> q_gen_3609
<nil, a, cons>(q_gen_3583, q_gen_3582) -> q_gen_3610
<nil, b, cons>(q_gen_3583, q_gen_3582) -> q_gen_3610
<nil, a, b>() -> q_gen_3611
<nil, b, a>() -> q_gen_3611
<nil, b, b>() -> q_gen_3611
<a, nil, cons>(q_gen_3583, q_gen_3582) -> q_gen_3612
<b, nil, cons>(q_gen_3583, q_gen_3582) -> q_gen_3612
<a, nil, a>() -> q_gen_3613
<b, nil, b>() -> q_gen_3613
<a, b, cons>(q_gen_3583, q_gen_3582) -> q_gen_3614
<b, a, cons>(q_gen_3583, q_gen_3582) -> q_gen_3614
<b, b, cons>(q_gen_3583, q_gen_3582) -> q_gen_3614
<a, b, a>() -> q_gen_3615
<b, a, b>() -> q_gen_3615
<b, b, b>() -> q_gen_3615
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_3555, q_gen_3559, q_gen_3596},
Q_f={q_gen_3555},
Delta=
{
<s>(q_gen_3596) -> q_gen_3596
<z>() -> q_gen_3596
<cons, s>(q_gen_3559, q_gen_3555) -> q_gen_3555
<nil, z>() -> q_gen_3555
<a, s>(q_gen_3596) -> q_gen_3559
<a, z>() -> q_gen_3559
<b, s>(q_gen_3596) -> q_gen_3559
<b, z>() -> q_gen_3559
}

Datatype: <eltlist, nat>
Convolution form: complete
}}}
  ;  leq -> 
{{{
Q={q_gen_3552, q_gen_3554, q_gen_3634},
Q_f={q_gen_3552},
Delta=
{
<s>(q_gen_3554) -> q_gen_3554
<z>() -> q_gen_3554
<s, s>(q_gen_3552) -> q_gen_3552
<z, s>(q_gen_3554) -> q_gen_3552
<z, z>() -> q_gen_3552
<s, s>(q_gen_3634) -> q_gen_3634
<s, z>(q_gen_3554) -> q_gen_3634
}

Datatype: <nat, nat>
Convolution form: complete
}}}
  ;  reverse -> 
{{{
Q={q_gen_3551, q_gen_3572, q_gen_3573, q_gen_3574, q_gen_3575, q_gen_3588, q_gen_3618, q_gen_3619},
Q_f={q_gen_3551},
Delta=
{
<cons>(q_gen_3619, q_gen_3618) -> q_gen_3618
<nil>() -> q_gen_3618
<a>() -> q_gen_3619
<b>() -> q_gen_3619
<cons, cons>(q_gen_3588, q_gen_3574, q_gen_3573, q_gen_3551) -> q_gen_3551
<nil, nil>() -> q_gen_3551
<cons, cons>(q_gen_3575, q_gen_3574, q_gen_3573, q_gen_3551) -> q_gen_3572
<cons, cons>(q_gen_3575, q_gen_3574, q_gen_3573, q_gen_3572) -> q_gen_3572
<nil, cons>(q_gen_3619, q_gen_3618) -> q_gen_3572
<cons, b>(q_gen_3619, q_gen_3618) -> q_gen_3573
<nil, a>() -> q_gen_3573
<nil, b>() -> q_gen_3573
<a, nil>() -> q_gen_3574
<b, cons>(q_gen_3619, q_gen_3618) -> q_gen_3574
<b, nil>() -> q_gen_3574
<b, b>() -> q_gen_3575
<a, a>() -> q_gen_3588
<b, a>() -> q_gen_3588
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 27  ;  () -> length([nil, z]) -> 23  ;  () -> leq([z, s(nn2)]) -> 23  ;  () -> leq([z, z]) -> 23  ;  () -> reverse([nil, nil]) -> 23  ;  (append([_wda, cons(h1, nil), _xda]) /\ reverse([t1, _wda])) -> reverse([cons(h1, t1), _xda]) -> 25  ;  (append([t1, l2, _rda])) -> append([cons(h1, t1), l2, cons(h1, _rda)]) -> 25  ;  (length([_gea, _hea]) /\ length([l1, _fea]) /\ reverse([l1, _gea])) -> leq([_fea, _hea]) -> 24  ;  (length([_iea, _jea]) /\ length([l1, _kea]) /\ reverse([l1, _iea])) -> leq([_jea, _kea]) -> 24  ;  (length([ll, _bea])) -> length([cons(x, ll), s(_bea)]) -> 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([nil, l2, l2]), {
l2 -> cons(b, nil)
})

-------------------------------------------
Step 38, which took 0.031236 s (model generation: 0.030368,  model checking: 0.000868):

Model:
|_
{
append -> 
{{{
Q={q_gen_3556, q_gen_3561, q_gen_3562, q_gen_3563, q_gen_3564, q_gen_3582, q_gen_3583, q_gen_3609, q_gen_3610, q_gen_3611, q_gen_3612, q_gen_3613, q_gen_3614, q_gen_3615},
Q_f={q_gen_3556},
Delta=
{
<cons>(q_gen_3583, q_gen_3582) -> q_gen_3582
<nil>() -> q_gen_3582
<a>() -> q_gen_3583
<b>() -> q_gen_3583
<cons, cons>(q_gen_3564, q_gen_3563, q_gen_3562, q_gen_3561) -> q_gen_3561
<nil, cons>(q_gen_3583, q_gen_3582) -> q_gen_3561
<nil, nil>() -> q_gen_3561
<cons, a>(q_gen_3583, q_gen_3582) -> q_gen_3562
<cons, b>(q_gen_3583, q_gen_3582) -> q_gen_3562
<nil, a>() -> q_gen_3562
<nil, b>() -> q_gen_3562
<a, cons>(q_gen_3583, q_gen_3582) -> q_gen_3563
<a, nil>() -> q_gen_3563
<b, cons>(q_gen_3583, q_gen_3582) -> q_gen_3563
<b, nil>() -> q_gen_3563
<a, a>() -> q_gen_3564
<b, b>() -> q_gen_3564
<cons, cons, cons>(q_gen_3615, q_gen_3614, q_gen_3613, q_gen_3612, q_gen_3611, q_gen_3610, q_gen_3609, q_gen_3556) -> q_gen_3556
<cons, nil, cons>(q_gen_3564, q_gen_3563, q_gen_3562, q_gen_3561) -> q_gen_3556
<nil, cons, cons>(q_gen_3564, q_gen_3563, q_gen_3562, q_gen_3561) -> q_gen_3556
<nil, nil, cons>(q_gen_3583, q_gen_3582) -> q_gen_3556
<nil, nil, nil>() -> q_gen_3556
<nil, nil, a>() -> q_gen_3609
<nil, nil, b>() -> q_gen_3609
<nil, a, cons>(q_gen_3583, q_gen_3582) -> q_gen_3610
<nil, b, cons>(q_gen_3583, q_gen_3582) -> q_gen_3610
<nil, a, b>() -> q_gen_3611
<nil, b, a>() -> q_gen_3611
<nil, b, b>() -> q_gen_3611
<a, nil, cons>(q_gen_3583, q_gen_3582) -> q_gen_3612
<b, nil, cons>(q_gen_3583, q_gen_3582) -> q_gen_3612
<a, nil, a>() -> q_gen_3613
<b, nil, b>() -> q_gen_3613
<a, b, cons>(q_gen_3583, q_gen_3582) -> q_gen_3614
<b, a, cons>(q_gen_3583, q_gen_3582) -> q_gen_3614
<b, b, cons>(q_gen_3583, q_gen_3582) -> q_gen_3614
<a, b, a>() -> q_gen_3615
<b, a, b>() -> q_gen_3615
<b, b, b>() -> q_gen_3615
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_3555, q_gen_3559, q_gen_3596},
Q_f={q_gen_3555},
Delta=
{
<s>(q_gen_3596) -> q_gen_3596
<z>() -> q_gen_3596
<cons, s>(q_gen_3559, q_gen_3555) -> q_gen_3555
<nil, z>() -> q_gen_3555
<a, s>(q_gen_3596) -> q_gen_3559
<a, z>() -> q_gen_3559
<b, s>(q_gen_3596) -> q_gen_3559
<b, z>() -> q_gen_3559
}

Datatype: <eltlist, nat>
Convolution form: complete
}}}
  ;  leq -> 
{{{
Q={q_gen_3552, q_gen_3554, q_gen_3634},
Q_f={q_gen_3552},
Delta=
{
<s>(q_gen_3554) -> q_gen_3554
<z>() -> q_gen_3554
<s, s>(q_gen_3552) -> q_gen_3552
<z, s>(q_gen_3554) -> q_gen_3552
<z, z>() -> q_gen_3552
<s, s>(q_gen_3634) -> q_gen_3634
<s, z>(q_gen_3554) -> q_gen_3634
}

Datatype: <nat, nat>
Convolution form: complete
}}}
  ;  reverse -> 
{{{
Q={q_gen_3551, q_gen_3573, q_gen_3574, q_gen_3575, q_gen_3618, q_gen_3619, q_gen_3630, q_gen_3631, q_gen_3633, q_gen_3646},
Q_f={q_gen_3551},
Delta=
{
<nil>() -> q_gen_3618
<b>() -> q_gen_3619
<a>() -> q_gen_3631
<cons>(q_gen_3619, q_gen_3618) -> q_gen_3646
<cons, cons>(q_gen_3575, q_gen_3574, q_gen_3573, q_gen_3551) -> q_gen_3551
<cons, cons>(q_gen_3575, q_gen_3574, q_gen_3573, q_gen_3630) -> q_gen_3551
<nil, nil>() -> q_gen_3551
<cons, b>(q_gen_3619, q_gen_3618) -> q_gen_3573
<nil, a>() -> q_gen_3573
<nil, b>() -> q_gen_3573
<a, nil>() -> q_gen_3574
<b, cons>(q_gen_3619, q_gen_3618) -> q_gen_3574
<b, cons>(q_gen_3619, q_gen_3646) -> q_gen_3574
<b, cons>(q_gen_3631, q_gen_3618) -> q_gen_3574
<b, nil>() -> q_gen_3574
<a, a>() -> q_gen_3575
<b, a>() -> q_gen_3575
<b, b>() -> q_gen_3575
<cons, cons>(q_gen_3575, q_gen_3574, q_gen_3573, q_gen_3633) -> q_gen_3630
<nil, cons>(q_gen_3619, q_gen_3646) -> q_gen_3630
<nil, cons>(q_gen_3631, q_gen_3618) -> q_gen_3630
<nil, cons>(q_gen_3619, q_gen_3618) -> q_gen_3633
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 27  ;  () -> length([nil, z]) -> 24  ;  () -> leq([z, s(nn2)]) -> 24  ;  () -> leq([z, z]) -> 24  ;  () -> reverse([nil, nil]) -> 24  ;  (append([_wda, cons(h1, nil), _xda]) /\ reverse([t1, _wda])) -> reverse([cons(h1, t1), _xda]) -> 25  ;  (append([t1, l2, _rda])) -> append([cons(h1, t1), l2, cons(h1, _rda)]) -> 25  ;  (length([_gea, _hea]) /\ length([l1, _fea]) /\ reverse([l1, _gea])) -> leq([_fea, _hea]) -> 24  ;  (length([_iea, _jea]) /\ length([l1, _kea]) /\ reverse([l1, _iea])) -> leq([_jea, _kea]) -> 27  ;  (length([ll, _bea])) -> length([cons(x, ll), s(_bea)]) -> 25  ;  (leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 25  ;  (leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 25  ;  (leq([s(nn1), z])) -> BOT -> 25
}
Sat witness: Yes: ((length([_iea, _jea]) /\ length([l1, _kea]) /\ reverse([l1, _iea])) -> leq([_jea, _kea]), {
_iea -> cons(b, cons(a, nil))  ;  _jea -> s(s(z))  ;  _kea -> s(z)  ;  l1 -> cons(b, nil)
})

-------------------------------------------
Step 39, which took 0.191896 s (model generation: 0.026906,  model checking: 0.164990):

Model:
|_
{
append -> 
{{{
Q={q_gen_3556, q_gen_3561, q_gen_3562, q_gen_3563, q_gen_3564, q_gen_3582, q_gen_3583, q_gen_3608, q_gen_3609, q_gen_3610, q_gen_3611, q_gen_3612, q_gen_3613, q_gen_3614, q_gen_3615, q_gen_3627},
Q_f={q_gen_3556},
Delta=
{
<cons>(q_gen_3583, q_gen_3582) -> q_gen_3582
<nil>() -> q_gen_3582
<a>() -> q_gen_3583
<b>() -> q_gen_3583
<cons, cons>(q_gen_3564, q_gen_3563, q_gen_3562, q_gen_3561) -> q_gen_3561
<cons, cons>(q_gen_3564, q_gen_3563, q_gen_3562, q_gen_3627) -> q_gen_3561
<nil, nil>() -> q_gen_3561
<cons, a>(q_gen_3583, q_gen_3582) -> q_gen_3562
<cons, b>(q_gen_3583, q_gen_3582) -> q_gen_3562
<nil, a>() -> q_gen_3562
<nil, b>() -> q_gen_3562
<a, cons>(q_gen_3583, q_gen_3582) -> q_gen_3563
<a, nil>() -> q_gen_3563
<b, cons>(q_gen_3583, q_gen_3582) -> q_gen_3563
<b, nil>() -> q_gen_3563
<a, a>() -> q_gen_3564
<b, b>() -> q_gen_3564
<nil, cons>(q_gen_3583, q_gen_3582) -> q_gen_3627
<cons, cons, cons>(q_gen_3615, q_gen_3614, q_gen_3613, q_gen_3612, q_gen_3611, q_gen_3610, q_gen_3609, q_gen_3608) -> q_gen_3556
<cons, nil, cons>(q_gen_3564, q_gen_3563, q_gen_3562, q_gen_3561) -> q_gen_3556
<cons, nil, cons>(q_gen_3564, q_gen_3563, q_gen_3562, q_gen_3627) -> q_gen_3556
<nil, cons, cons>(q_gen_3564, q_gen_3563, q_gen_3562, q_gen_3561) -> q_gen_3556
<nil, nil, nil>() -> q_gen_3556
<nil, cons, cons>(q_gen_3564, q_gen_3563, q_gen_3562, q_gen_3627) -> q_gen_3608
<nil, nil, cons>(q_gen_3583, q_gen_3582) -> q_gen_3608
<nil, nil, a>() -> q_gen_3609
<nil, nil, b>() -> q_gen_3609
<nil, a, cons>(q_gen_3583, q_gen_3582) -> q_gen_3610
<nil, b, cons>(q_gen_3583, q_gen_3582) -> q_gen_3610
<nil, a, b>() -> q_gen_3611
<nil, b, a>() -> q_gen_3611
<nil, b, b>() -> q_gen_3611
<a, nil, cons>(q_gen_3583, q_gen_3582) -> q_gen_3612
<b, nil, cons>(q_gen_3583, q_gen_3582) -> q_gen_3612
<a, nil, a>() -> q_gen_3613
<b, nil, b>() -> q_gen_3613
<a, b, cons>(q_gen_3583, q_gen_3582) -> q_gen_3614
<b, a, cons>(q_gen_3583, q_gen_3582) -> q_gen_3614
<b, b, cons>(q_gen_3583, q_gen_3582) -> q_gen_3614
<a, b, a>() -> q_gen_3615
<b, a, b>() -> q_gen_3615
<b, b, b>() -> q_gen_3615
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_3555, q_gen_3559, q_gen_3596},
Q_f={q_gen_3555},
Delta=
{
<s>(q_gen_3596) -> q_gen_3596
<z>() -> q_gen_3596
<cons, s>(q_gen_3559, q_gen_3555) -> q_gen_3555
<nil, z>() -> q_gen_3555
<a, s>(q_gen_3596) -> q_gen_3559
<a, z>() -> q_gen_3559
<b, s>(q_gen_3596) -> q_gen_3559
<b, z>() -> q_gen_3559
}

Datatype: <eltlist, nat>
Convolution form: complete
}}}
  ;  leq -> 
{{{
Q={q_gen_3552, q_gen_3554, q_gen_3634},
Q_f={q_gen_3552},
Delta=
{
<s>(q_gen_3554) -> q_gen_3554
<z>() -> q_gen_3554
<s, s>(q_gen_3552) -> q_gen_3552
<z, s>(q_gen_3554) -> q_gen_3552
<z, z>() -> q_gen_3552
<s, s>(q_gen_3634) -> q_gen_3634
<s, z>(q_gen_3554) -> q_gen_3634
}

Datatype: <nat, nat>
Convolution form: complete
}}}
  ;  reverse -> 
{{{
Q={q_gen_3551, q_gen_3573, q_gen_3574, q_gen_3575, q_gen_3618, q_gen_3619, q_gen_3629, q_gen_3630},
Q_f={q_gen_3551},
Delta=
{
<cons>(q_gen_3619, q_gen_3618) -> q_gen_3618
<nil>() -> q_gen_3618
<a>() -> q_gen_3619
<b>() -> q_gen_3619
<cons, cons>(q_gen_3575, q_gen_3574, q_gen_3573, q_gen_3551) -> q_gen_3551
<cons, cons>(q_gen_3575, q_gen_3574, q_gen_3573, q_gen_3629) -> q_gen_3551
<nil, nil>() -> q_gen_3551
<cons, b>(q_gen_3619, q_gen_3618) -> q_gen_3573
<nil, a>() -> q_gen_3573
<nil, b>() -> q_gen_3573
<a, nil>() -> q_gen_3574
<b, cons>(q_gen_3619, q_gen_3618) -> q_gen_3574
<b, nil>() -> q_gen_3574
<a, a>() -> q_gen_3575
<b, a>() -> q_gen_3575
<b, b>() -> q_gen_3575
<cons, cons>(q_gen_3575, q_gen_3574, q_gen_3573, q_gen_3630) -> q_gen_3629
<nil, cons>(q_gen_3619, q_gen_3618) -> q_gen_3630
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 27  ;  () -> length([nil, z]) -> 25  ;  () -> leq([z, s(nn2)]) -> 25  ;  () -> leq([z, z]) -> 25  ;  () -> reverse([nil, nil]) -> 25  ;  (append([_wda, cons(h1, nil), _xda]) /\ reverse([t1, _wda])) -> reverse([cons(h1, t1), _xda]) -> 25  ;  (append([t1, l2, _rda])) -> append([cons(h1, t1), l2, cons(h1, _rda)]) -> 28  ;  (length([_gea, _hea]) /\ length([l1, _fea]) /\ reverse([l1, _gea])) -> leq([_fea, _hea]) -> 25  ;  (length([_iea, _jea]) /\ length([l1, _kea]) /\ reverse([l1, _iea])) -> leq([_jea, _kea]) -> 27  ;  (length([ll, _bea])) -> length([cons(x, ll), s(_bea)]) -> 26  ;  (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, _rda])) -> append([cons(h1, t1), l2, cons(h1, _rda)]), {
_rda -> cons(a, nil)  ;  h1 -> a  ;  l2 -> cons(a, nil)  ;  t1 -> nil
})

-------------------------------------------
Step 40, which took 0.036409 s (model generation: 0.033139,  model checking: 0.003270):

Model:
|_
{
append -> 
{{{
Q={q_gen_3556, q_gen_3561, q_gen_3562, q_gen_3563, q_gen_3564, q_gen_3582, q_gen_3583, q_gen_3603, q_gen_3608, q_gen_3609, q_gen_3610, q_gen_3611, q_gen_3612, q_gen_3613, q_gen_3614, q_gen_3615, q_gen_3627},
Q_f={q_gen_3556},
Delta=
{
<nil>() -> q_gen_3582
<a>() -> q_gen_3583
<b>() -> q_gen_3583
<cons>(q_gen_3583, q_gen_3582) -> q_gen_3603
<cons>(q_gen_3583, q_gen_3603) -> q_gen_3603
<cons, cons>(q_gen_3564, q_gen_3563, q_gen_3562, q_gen_3561) -> q_gen_3561
<cons, cons>(q_gen_3564, q_gen_3563, q_gen_3562, q_gen_3627) -> q_gen_3561
<nil, nil>() -> q_gen_3561
<cons, a>(q_gen_3583, q_gen_3582) -> q_gen_3562
<cons, a>(q_gen_3583, q_gen_3603) -> q_gen_3562
<cons, b>(q_gen_3583, q_gen_3582) -> q_gen_3562
<cons, b>(q_gen_3583, q_gen_3603) -> q_gen_3562
<nil, a>() -> q_gen_3562
<nil, b>() -> q_gen_3562
<a, cons>(q_gen_3583, q_gen_3582) -> q_gen_3563
<a, cons>(q_gen_3583, q_gen_3603) -> q_gen_3563
<a, nil>() -> q_gen_3563
<b, cons>(q_gen_3583, q_gen_3582) -> q_gen_3563
<b, cons>(q_gen_3583, q_gen_3603) -> q_gen_3563
<b, nil>() -> q_gen_3563
<a, a>() -> q_gen_3564
<b, b>() -> q_gen_3564
<nil, cons>(q_gen_3583, q_gen_3582) -> q_gen_3627
<nil, cons>(q_gen_3583, q_gen_3603) -> q_gen_3627
<cons, cons, cons>(q_gen_3615, q_gen_3614, q_gen_3613, q_gen_3612, q_gen_3611, q_gen_3610, q_gen_3609, q_gen_3608) -> q_gen_3556
<cons, nil, cons>(q_gen_3564, q_gen_3563, q_gen_3562, q_gen_3561) -> q_gen_3556
<nil, cons, cons>(q_gen_3564, q_gen_3563, q_gen_3562, q_gen_3561) -> q_gen_3556
<nil, nil, cons>(q_gen_3583, q_gen_3603) -> q_gen_3556
<nil, nil, nil>() -> q_gen_3556
<cons, cons, cons>(q_gen_3615, q_gen_3614, q_gen_3613, q_gen_3612, q_gen_3611, q_gen_3610, q_gen_3609, q_gen_3556) -> q_gen_3608
<cons, nil, cons>(q_gen_3564, q_gen_3563, q_gen_3562, q_gen_3627) -> q_gen_3608
<nil, cons, cons>(q_gen_3564, q_gen_3563, q_gen_3562, q_gen_3627) -> q_gen_3608
<nil, nil, cons>(q_gen_3583, q_gen_3582) -> q_gen_3608
<nil, nil, a>() -> q_gen_3609
<nil, nil, b>() -> q_gen_3609
<nil, a, cons>(q_gen_3583, q_gen_3582) -> q_gen_3610
<nil, b, cons>(q_gen_3583, q_gen_3582) -> q_gen_3610
<nil, b, cons>(q_gen_3583, q_gen_3603) -> q_gen_3610
<nil, a, a>() -> q_gen_3611
<nil, a, b>() -> q_gen_3611
<nil, b, a>() -> q_gen_3611
<nil, b, b>() -> q_gen_3611
<a, nil, cons>(q_gen_3583, q_gen_3582) -> q_gen_3612
<b, nil, cons>(q_gen_3583, q_gen_3582) -> q_gen_3612
<b, nil, cons>(q_gen_3583, q_gen_3603) -> q_gen_3612
<a, nil, a>() -> q_gen_3613
<b, nil, b>() -> q_gen_3613
<a, a, cons>(q_gen_3583, q_gen_3582) -> q_gen_3614
<a, b, cons>(q_gen_3583, q_gen_3582) -> q_gen_3614
<b, a, cons>(q_gen_3583, q_gen_3582) -> q_gen_3614
<b, b, cons>(q_gen_3583, q_gen_3582) -> q_gen_3614
<b, b, cons>(q_gen_3583, q_gen_3603) -> q_gen_3614
<a, a, a>() -> q_gen_3615
<a, b, a>() -> q_gen_3615
<b, a, b>() -> q_gen_3615
<b, b, b>() -> q_gen_3615
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_3555, q_gen_3559, q_gen_3596},
Q_f={q_gen_3555},
Delta=
{
<s>(q_gen_3596) -> q_gen_3596
<z>() -> q_gen_3596
<cons, s>(q_gen_3559, q_gen_3555) -> q_gen_3555
<nil, z>() -> q_gen_3555
<a, s>(q_gen_3596) -> q_gen_3559
<a, z>() -> q_gen_3559
<b, s>(q_gen_3596) -> q_gen_3559
<b, z>() -> q_gen_3559
}

Datatype: <eltlist, nat>
Convolution form: complete
}}}
  ;  leq -> 
{{{
Q={q_gen_3552, q_gen_3554, q_gen_3634},
Q_f={q_gen_3552},
Delta=
{
<s>(q_gen_3554) -> q_gen_3554
<z>() -> q_gen_3554
<s, s>(q_gen_3552) -> q_gen_3552
<z, s>(q_gen_3554) -> q_gen_3552
<z, z>() -> q_gen_3552
<s, s>(q_gen_3634) -> q_gen_3634
<s, z>(q_gen_3554) -> q_gen_3634
}

Datatype: <nat, nat>
Convolution form: complete
}}}
  ;  reverse -> 
{{{
Q={q_gen_3551, q_gen_3573, q_gen_3574, q_gen_3575, q_gen_3618, q_gen_3619, q_gen_3629},
Q_f={q_gen_3551},
Delta=
{
<cons>(q_gen_3619, q_gen_3618) -> q_gen_3618
<nil>() -> q_gen_3618
<a>() -> q_gen_3619
<b>() -> q_gen_3619
<cons, cons>(q_gen_3575, q_gen_3574, q_gen_3573, q_gen_3551) -> q_gen_3551
<nil, nil>() -> q_gen_3551
<cons, b>(q_gen_3619, q_gen_3618) -> q_gen_3573
<nil, a>() -> q_gen_3573
<nil, b>() -> q_gen_3573
<a, nil>() -> q_gen_3574
<b, cons>(q_gen_3619, q_gen_3618) -> q_gen_3574
<b, nil>() -> q_gen_3574
<a, a>() -> q_gen_3575
<b, a>() -> q_gen_3575
<b, b>() -> q_gen_3575
<cons, cons>(q_gen_3575, q_gen_3574, q_gen_3573, q_gen_3629) -> q_gen_3629
<nil, cons>(q_gen_3619, q_gen_3618) -> q_gen_3629
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 27  ;  () -> length([nil, z]) -> 25  ;  () -> leq([z, s(nn2)]) -> 25  ;  () -> leq([z, z]) -> 25  ;  () -> reverse([nil, nil]) -> 25  ;  (append([_wda, cons(h1, nil), _xda]) /\ reverse([t1, _wda])) -> reverse([cons(h1, t1), _xda]) -> 28  ;  (append([t1, l2, _rda])) -> append([cons(h1, t1), l2, cons(h1, _rda)]) -> 28  ;  (length([_gea, _hea]) /\ length([l1, _fea]) /\ reverse([l1, _gea])) -> leq([_fea, _hea]) -> 26  ;  (length([_iea, _jea]) /\ length([l1, _kea]) /\ reverse([l1, _iea])) -> leq([_jea, _kea]) -> 27  ;  (length([ll, _bea])) -> length([cons(x, ll), s(_bea)]) -> 26  ;  (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([_wda, cons(h1, nil), _xda]) /\ reverse([t1, _wda])) -> reverse([cons(h1, t1), _xda]), {
_wda -> cons(a, nil)  ;  _xda -> cons(a, cons(b, nil))  ;  h1 -> b  ;  t1 -> cons(b, nil)
})

-------------------------------------------
Step 41, which took 0.035417 s (model generation: 0.034220,  model checking: 0.001197):

Model:
|_
{
append -> 
{{{
Q={q_gen_3556, q_gen_3561, q_gen_3562, q_gen_3563, q_gen_3564, q_gen_3582, q_gen_3583, q_gen_3608, q_gen_3609, q_gen_3610, q_gen_3611, q_gen_3612, q_gen_3613, q_gen_3614, q_gen_3615, q_gen_3627},
Q_f={q_gen_3556},
Delta=
{
<cons>(q_gen_3583, q_gen_3582) -> q_gen_3582
<nil>() -> q_gen_3582
<a>() -> q_gen_3583
<b>() -> q_gen_3583
<cons, cons>(q_gen_3564, q_gen_3563, q_gen_3562, q_gen_3561) -> q_gen_3561
<cons, cons>(q_gen_3564, q_gen_3563, q_gen_3562, q_gen_3627) -> q_gen_3561
<nil, nil>() -> q_gen_3561
<cons, a>(q_gen_3583, q_gen_3582) -> q_gen_3562
<cons, b>(q_gen_3583, q_gen_3582) -> q_gen_3562
<nil, a>() -> q_gen_3562
<nil, b>() -> q_gen_3562
<a, cons>(q_gen_3583, q_gen_3582) -> q_gen_3563
<a, nil>() -> q_gen_3563
<b, cons>(q_gen_3583, q_gen_3582) -> q_gen_3563
<b, nil>() -> q_gen_3563
<a, a>() -> q_gen_3564
<b, b>() -> q_gen_3564
<nil, cons>(q_gen_3583, q_gen_3582) -> q_gen_3627
<cons, cons, cons>(q_gen_3615, q_gen_3614, q_gen_3613, q_gen_3612, q_gen_3611, q_gen_3610, q_gen_3609, q_gen_3608) -> q_gen_3556
<cons, nil, cons>(q_gen_3564, q_gen_3563, q_gen_3562, q_gen_3561) -> q_gen_3556
<nil, cons, cons>(q_gen_3564, q_gen_3563, q_gen_3562, q_gen_3561) -> q_gen_3556
<nil, nil, nil>() -> q_gen_3556
<cons, nil, cons>(q_gen_3564, q_gen_3563, q_gen_3562, q_gen_3627) -> q_gen_3608
<nil, cons, cons>(q_gen_3564, q_gen_3563, q_gen_3562, q_gen_3627) -> q_gen_3608
<nil, nil, cons>(q_gen_3583, q_gen_3582) -> q_gen_3608
<nil, nil, a>() -> q_gen_3609
<nil, nil, b>() -> q_gen_3609
<nil, a, cons>(q_gen_3583, q_gen_3582) -> q_gen_3610
<nil, b, cons>(q_gen_3583, q_gen_3582) -> q_gen_3610
<nil, a, a>() -> q_gen_3611
<nil, a, b>() -> q_gen_3611
<nil, b, a>() -> q_gen_3611
<nil, b, b>() -> q_gen_3611
<a, nil, cons>(q_gen_3583, q_gen_3582) -> q_gen_3612
<b, nil, cons>(q_gen_3583, q_gen_3582) -> q_gen_3612
<a, nil, a>() -> q_gen_3613
<b, nil, b>() -> q_gen_3613
<a, a, cons>(q_gen_3583, q_gen_3582) -> q_gen_3614
<a, b, cons>(q_gen_3583, q_gen_3582) -> q_gen_3614
<b, a, cons>(q_gen_3583, q_gen_3582) -> q_gen_3614
<b, b, cons>(q_gen_3583, q_gen_3582) -> q_gen_3614
<a, a, a>() -> q_gen_3615
<a, b, a>() -> q_gen_3615
<b, a, b>() -> q_gen_3615
<b, b, b>() -> q_gen_3615
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_3555, q_gen_3559, q_gen_3596},
Q_f={q_gen_3555},
Delta=
{
<s>(q_gen_3596) -> q_gen_3596
<z>() -> q_gen_3596
<cons, s>(q_gen_3559, q_gen_3555) -> q_gen_3555
<nil, z>() -> q_gen_3555
<a, s>(q_gen_3596) -> q_gen_3559
<a, z>() -> q_gen_3559
<b, s>(q_gen_3596) -> q_gen_3559
<b, z>() -> q_gen_3559
}

Datatype: <eltlist, nat>
Convolution form: complete
}}}
  ;  leq -> 
{{{
Q={q_gen_3552, q_gen_3554, q_gen_3634},
Q_f={q_gen_3552},
Delta=
{
<s>(q_gen_3554) -> q_gen_3554
<z>() -> q_gen_3554
<s, s>(q_gen_3552) -> q_gen_3552
<z, s>(q_gen_3554) -> q_gen_3552
<z, z>() -> q_gen_3552
<s, s>(q_gen_3634) -> q_gen_3634
<s, z>(q_gen_3554) -> q_gen_3634
}

Datatype: <nat, nat>
Convolution form: complete
}}}
  ;  reverse -> 
{{{
Q={q_gen_3551, q_gen_3573, q_gen_3574, q_gen_3575, q_gen_3617, q_gen_3618, q_gen_3619, q_gen_3629},
Q_f={q_gen_3551},
Delta=
{
<cons>(q_gen_3619, q_gen_3618) -> q_gen_3618
<nil>() -> q_gen_3618
<a>() -> q_gen_3619
<b>() -> q_gen_3619
<cons, cons>(q_gen_3575, q_gen_3574, q_gen_3573, q_gen_3551) -> q_gen_3551
<cons, cons>(q_gen_3575, q_gen_3574, q_gen_3617, q_gen_3551) -> q_gen_3551
<cons, cons>(q_gen_3575, q_gen_3574, q_gen_3617, q_gen_3629) -> q_gen_3551
<nil, nil>() -> q_gen_3551
<cons, a>(q_gen_3619, q_gen_3618) -> q_gen_3573
<nil, a>() -> q_gen_3573
<nil, b>() -> q_gen_3573
<a, nil>() -> q_gen_3574
<b, cons>(q_gen_3619, q_gen_3618) -> q_gen_3574
<b, nil>() -> q_gen_3574
<a, a>() -> q_gen_3575
<b, a>() -> q_gen_3575
<b, b>() -> q_gen_3575
<cons, b>(q_gen_3619, q_gen_3618) -> q_gen_3617
<cons, cons>(q_gen_3575, q_gen_3574, q_gen_3573, q_gen_3629) -> q_gen_3629
<nil, cons>(q_gen_3619, q_gen_3618) -> q_gen_3629
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 27  ;  () -> length([nil, z]) -> 26  ;  () -> leq([z, s(nn2)]) -> 26  ;  () -> leq([z, z]) -> 26  ;  () -> reverse([nil, nil]) -> 26  ;  (append([_wda, cons(h1, nil), _xda]) /\ reverse([t1, _wda])) -> reverse([cons(h1, t1), _xda]) -> 28  ;  (append([t1, l2, _rda])) -> append([cons(h1, t1), l2, cons(h1, _rda)]) -> 28  ;  (length([_gea, _hea]) /\ length([l1, _fea]) /\ reverse([l1, _gea])) -> leq([_fea, _hea]) -> 27  ;  (length([_iea, _jea]) /\ length([l1, _kea]) /\ reverse([l1, _iea])) -> leq([_jea, _kea]) -> 30  ;  (length([ll, _bea])) -> length([cons(x, ll), s(_bea)]) -> 27  ;  (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: ((length([_iea, _jea]) /\ length([l1, _kea]) /\ reverse([l1, _iea])) -> leq([_jea, _kea]), {
_iea -> cons(b, cons(a, cons(b, nil)))  ;  _jea -> s(s(s(z)))  ;  _kea -> s(s(z))  ;  l1 -> cons(b, cons(b, nil))
})

-------------------------------------------
Step 42, which took 0.048070 s (model generation: 0.039728,  model checking: 0.008342):

Model:
|_
{
append -> 
{{{
Q={q_gen_3556, q_gen_3561, q_gen_3562, q_gen_3563, q_gen_3564, q_gen_3582, q_gen_3583, q_gen_3603, q_gen_3608, q_gen_3609, q_gen_3610, q_gen_3611, q_gen_3612, q_gen_3613, q_gen_3614, q_gen_3615, q_gen_3627},
Q_f={q_gen_3556},
Delta=
{
<nil>() -> q_gen_3582
<a>() -> q_gen_3583
<b>() -> q_gen_3583
<cons>(q_gen_3583, q_gen_3582) -> q_gen_3603
<cons>(q_gen_3583, q_gen_3603) -> q_gen_3603
<cons, cons>(q_gen_3564, q_gen_3563, q_gen_3562, q_gen_3561) -> q_gen_3561
<cons, cons>(q_gen_3564, q_gen_3563, q_gen_3562, q_gen_3627) -> q_gen_3561
<nil, nil>() -> q_gen_3561
<cons, a>(q_gen_3583, q_gen_3582) -> q_gen_3562
<cons, a>(q_gen_3583, q_gen_3603) -> q_gen_3562
<cons, b>(q_gen_3583, q_gen_3582) -> q_gen_3562
<cons, b>(q_gen_3583, q_gen_3603) -> q_gen_3562
<nil, a>() -> q_gen_3562
<nil, b>() -> q_gen_3562
<a, cons>(q_gen_3583, q_gen_3582) -> q_gen_3563
<a, cons>(q_gen_3583, q_gen_3603) -> q_gen_3563
<a, nil>() -> q_gen_3563
<b, cons>(q_gen_3583, q_gen_3582) -> q_gen_3563
<b, cons>(q_gen_3583, q_gen_3603) -> q_gen_3563
<b, nil>() -> q_gen_3563
<a, a>() -> q_gen_3564
<b, b>() -> q_gen_3564
<nil, cons>(q_gen_3583, q_gen_3582) -> q_gen_3627
<nil, cons>(q_gen_3583, q_gen_3603) -> q_gen_3627
<cons, cons, cons>(q_gen_3615, q_gen_3614, q_gen_3613, q_gen_3612, q_gen_3611, q_gen_3610, q_gen_3609, q_gen_3608) -> q_gen_3556
<cons, nil, cons>(q_gen_3564, q_gen_3563, q_gen_3562, q_gen_3561) -> q_gen_3556
<nil, cons, cons>(q_gen_3564, q_gen_3563, q_gen_3562, q_gen_3561) -> q_gen_3556
<nil, nil, cons>(q_gen_3583, q_gen_3603) -> q_gen_3556
<nil, nil, nil>() -> q_gen_3556
<cons, cons, cons>(q_gen_3615, q_gen_3614, q_gen_3613, q_gen_3612, q_gen_3611, q_gen_3610, q_gen_3609, q_gen_3556) -> q_gen_3608
<cons, nil, cons>(q_gen_3564, q_gen_3563, q_gen_3562, q_gen_3627) -> q_gen_3608
<nil, cons, cons>(q_gen_3564, q_gen_3563, q_gen_3562, q_gen_3627) -> q_gen_3608
<nil, nil, cons>(q_gen_3583, q_gen_3582) -> q_gen_3608
<nil, nil, a>() -> q_gen_3609
<nil, nil, b>() -> q_gen_3609
<nil, a, cons>(q_gen_3583, q_gen_3582) -> q_gen_3610
<nil, b, cons>(q_gen_3583, q_gen_3582) -> q_gen_3610
<nil, b, cons>(q_gen_3583, q_gen_3603) -> q_gen_3610
<nil, a, a>() -> q_gen_3611
<nil, a, b>() -> q_gen_3611
<nil, b, a>() -> q_gen_3611
<nil, b, b>() -> q_gen_3611
<a, nil, cons>(q_gen_3583, q_gen_3582) -> q_gen_3612
<b, nil, cons>(q_gen_3583, q_gen_3582) -> q_gen_3612
<b, nil, cons>(q_gen_3583, q_gen_3603) -> q_gen_3612
<a, nil, a>() -> q_gen_3613
<b, nil, b>() -> q_gen_3613
<a, a, cons>(q_gen_3583, q_gen_3582) -> q_gen_3614
<a, b, cons>(q_gen_3583, q_gen_3582) -> q_gen_3614
<b, a, cons>(q_gen_3583, q_gen_3582) -> q_gen_3614
<b, b, cons>(q_gen_3583, q_gen_3582) -> q_gen_3614
<b, b, cons>(q_gen_3583, q_gen_3603) -> q_gen_3614
<a, a, a>() -> q_gen_3615
<a, b, a>() -> q_gen_3615
<b, a, b>() -> q_gen_3615
<b, b, b>() -> q_gen_3615
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_3555, q_gen_3559, q_gen_3596},
Q_f={q_gen_3555},
Delta=
{
<s>(q_gen_3596) -> q_gen_3596
<z>() -> q_gen_3596
<cons, s>(q_gen_3559, q_gen_3555) -> q_gen_3555
<nil, z>() -> q_gen_3555
<a, s>(q_gen_3596) -> q_gen_3559
<a, z>() -> q_gen_3559
<b, s>(q_gen_3596) -> q_gen_3559
<b, z>() -> q_gen_3559
}

Datatype: <eltlist, nat>
Convolution form: complete
}}}
  ;  leq -> 
{{{
Q={q_gen_3552, q_gen_3554, q_gen_3634},
Q_f={q_gen_3552},
Delta=
{
<s>(q_gen_3554) -> q_gen_3554
<z>() -> q_gen_3554
<s, s>(q_gen_3552) -> q_gen_3552
<z, s>(q_gen_3554) -> q_gen_3552
<z, z>() -> q_gen_3552
<s, s>(q_gen_3634) -> q_gen_3634
<s, z>(q_gen_3554) -> q_gen_3634
}

Datatype: <nat, nat>
Convolution form: complete
}}}
  ;  reverse -> 
{{{
Q={q_gen_3551, q_gen_3573, q_gen_3574, q_gen_3575, q_gen_3618, q_gen_3619, q_gen_3629},
Q_f={q_gen_3551},
Delta=
{
<cons>(q_gen_3619, q_gen_3618) -> q_gen_3618
<nil>() -> q_gen_3618
<a>() -> q_gen_3619
<b>() -> q_gen_3619
<cons, cons>(q_gen_3575, q_gen_3574, q_gen_3573, q_gen_3551) -> q_gen_3551
<nil, nil>() -> q_gen_3551
<cons, a>(q_gen_3619, q_gen_3618) -> q_gen_3573
<cons, b>(q_gen_3619, q_gen_3618) -> q_gen_3573
<nil, a>() -> q_gen_3573
<nil, b>() -> q_gen_3573
<a, nil>() -> q_gen_3574
<b, cons>(q_gen_3619, q_gen_3618) -> q_gen_3574
<b, nil>() -> q_gen_3574
<a, a>() -> q_gen_3575
<b, a>() -> q_gen_3575
<b, b>() -> q_gen_3575
<cons, cons>(q_gen_3575, q_gen_3574, q_gen_3573, q_gen_3629) -> q_gen_3629
<nil, cons>(q_gen_3619, q_gen_3618) -> q_gen_3629
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 28  ;  () -> length([nil, z]) -> 27  ;  () -> leq([z, s(nn2)]) -> 27  ;  () -> leq([z, z]) -> 27  ;  () -> reverse([nil, nil]) -> 27  ;  (append([_wda, cons(h1, nil), _xda]) /\ reverse([t1, _wda])) -> reverse([cons(h1, t1), _xda]) -> 28  ;  (append([t1, l2, _rda])) -> append([cons(h1, t1), l2, cons(h1, _rda)]) -> 31  ;  (length([_gea, _hea]) /\ length([l1, _fea]) /\ reverse([l1, _gea])) -> leq([_fea, _hea]) -> 28  ;  (length([_iea, _jea]) /\ length([l1, _kea]) /\ reverse([l1, _iea])) -> leq([_jea, _kea]) -> 30  ;  (length([ll, _bea])) -> length([cons(x, ll), s(_bea)]) -> 28  ;  (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, _rda])) -> append([cons(h1, t1), l2, cons(h1, _rda)]), {
_rda -> cons(b, cons(b, nil))  ;  h1 -> b  ;  l2 -> nil  ;  t1 -> nil
})

-------------------------------------------
Step 43, which took 0.043291 s (model generation: 0.036137,  model checking: 0.007154):

Model:
|_
{
append -> 
{{{
Q={q_gen_3556, q_gen_3561, q_gen_3562, q_gen_3563, q_gen_3564, q_gen_3582, q_gen_3583, q_gen_3603, q_gen_3608, q_gen_3609, q_gen_3610, q_gen_3611, q_gen_3612, q_gen_3613, q_gen_3614, q_gen_3615, q_gen_3627},
Q_f={q_gen_3556},
Delta=
{
<nil>() -> q_gen_3582
<a>() -> q_gen_3583
<b>() -> q_gen_3583
<cons>(q_gen_3583, q_gen_3582) -> q_gen_3603
<cons>(q_gen_3583, q_gen_3603) -> q_gen_3603
<cons, cons>(q_gen_3564, q_gen_3563, q_gen_3562, q_gen_3561) -> q_gen_3561
<cons, cons>(q_gen_3564, q_gen_3563, q_gen_3562, q_gen_3627) -> q_gen_3561
<nil, nil>() -> q_gen_3561
<cons, a>(q_gen_3583, q_gen_3582) -> q_gen_3562
<cons, a>(q_gen_3583, q_gen_3603) -> q_gen_3562
<cons, b>(q_gen_3583, q_gen_3582) -> q_gen_3562
<cons, b>(q_gen_3583, q_gen_3603) -> q_gen_3562
<nil, a>() -> q_gen_3562
<nil, b>() -> q_gen_3562
<a, cons>(q_gen_3583, q_gen_3582) -> q_gen_3563
<a, cons>(q_gen_3583, q_gen_3603) -> q_gen_3563
<a, nil>() -> q_gen_3563
<b, cons>(q_gen_3583, q_gen_3582) -> q_gen_3563
<b, cons>(q_gen_3583, q_gen_3603) -> q_gen_3563
<b, nil>() -> q_gen_3563
<a, a>() -> q_gen_3564
<b, b>() -> q_gen_3564
<nil, cons>(q_gen_3583, q_gen_3582) -> q_gen_3627
<nil, cons>(q_gen_3583, q_gen_3603) -> q_gen_3627
<cons, cons, cons>(q_gen_3615, q_gen_3614, q_gen_3613, q_gen_3612, q_gen_3611, q_gen_3610, q_gen_3609, q_gen_3608) -> q_gen_3556
<cons, nil, cons>(q_gen_3564, q_gen_3563, q_gen_3562, q_gen_3561) -> q_gen_3556
<cons, nil, cons>(q_gen_3564, q_gen_3563, q_gen_3562, q_gen_3627) -> q_gen_3556
<nil, cons, cons>(q_gen_3564, q_gen_3563, q_gen_3562, q_gen_3561) -> q_gen_3556
<nil, nil, cons>(q_gen_3583, q_gen_3603) -> q_gen_3556
<nil, nil, nil>() -> q_gen_3556
<cons, cons, cons>(q_gen_3615, q_gen_3614, q_gen_3613, q_gen_3612, q_gen_3611, q_gen_3610, q_gen_3609, q_gen_3556) -> q_gen_3608
<nil, cons, cons>(q_gen_3564, q_gen_3563, q_gen_3562, q_gen_3627) -> q_gen_3608
<nil, nil, cons>(q_gen_3583, q_gen_3582) -> q_gen_3608
<nil, nil, a>() -> q_gen_3609
<nil, nil, b>() -> q_gen_3609
<nil, a, cons>(q_gen_3583, q_gen_3582) -> q_gen_3610
<nil, b, cons>(q_gen_3583, q_gen_3582) -> q_gen_3610
<nil, b, cons>(q_gen_3583, q_gen_3603) -> q_gen_3610
<nil, a, a>() -> q_gen_3611
<nil, a, b>() -> q_gen_3611
<nil, b, a>() -> q_gen_3611
<nil, b, b>() -> q_gen_3611
<a, nil, cons>(q_gen_3583, q_gen_3582) -> q_gen_3612
<b, nil, cons>(q_gen_3583, q_gen_3582) -> q_gen_3612
<b, nil, cons>(q_gen_3583, q_gen_3603) -> q_gen_3612
<a, nil, a>() -> q_gen_3613
<b, nil, b>() -> q_gen_3613
<a, a, cons>(q_gen_3583, q_gen_3582) -> q_gen_3614
<a, b, cons>(q_gen_3583, q_gen_3582) -> q_gen_3614
<b, a, cons>(q_gen_3583, q_gen_3582) -> q_gen_3614
<b, b, cons>(q_gen_3583, q_gen_3582) -> q_gen_3614
<b, b, cons>(q_gen_3583, q_gen_3603) -> q_gen_3614
<a, a, a>() -> q_gen_3615
<a, b, a>() -> q_gen_3615
<b, a, b>() -> q_gen_3615
<b, b, b>() -> q_gen_3615
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_3555, q_gen_3559, q_gen_3596},
Q_f={q_gen_3555},
Delta=
{
<s>(q_gen_3596) -> q_gen_3596
<z>() -> q_gen_3596
<cons, s>(q_gen_3559, q_gen_3555) -> q_gen_3555
<nil, z>() -> q_gen_3555
<a, s>(q_gen_3596) -> q_gen_3559
<a, z>() -> q_gen_3559
<b, s>(q_gen_3596) -> q_gen_3559
<b, z>() -> q_gen_3559
}

Datatype: <eltlist, nat>
Convolution form: complete
}}}
  ;  leq -> 
{{{
Q={q_gen_3552, q_gen_3554, q_gen_3634},
Q_f={q_gen_3552},
Delta=
{
<s>(q_gen_3554) -> q_gen_3554
<z>() -> q_gen_3554
<s, s>(q_gen_3552) -> q_gen_3552
<z, s>(q_gen_3554) -> q_gen_3552
<z, z>() -> q_gen_3552
<s, s>(q_gen_3634) -> q_gen_3634
<s, z>(q_gen_3554) -> q_gen_3634
}

Datatype: <nat, nat>
Convolution form: complete
}}}
  ;  reverse -> 
{{{
Q={q_gen_3551, q_gen_3573, q_gen_3574, q_gen_3575, q_gen_3618, q_gen_3619, q_gen_3629},
Q_f={q_gen_3551},
Delta=
{
<cons>(q_gen_3619, q_gen_3618) -> q_gen_3618
<nil>() -> q_gen_3618
<a>() -> q_gen_3619
<b>() -> q_gen_3619
<cons, cons>(q_gen_3575, q_gen_3574, q_gen_3573, q_gen_3551) -> q_gen_3551
<nil, nil>() -> q_gen_3551
<cons, a>(q_gen_3619, q_gen_3618) -> q_gen_3573
<cons, b>(q_gen_3619, q_gen_3618) -> q_gen_3573
<nil, a>() -> q_gen_3573
<nil, b>() -> q_gen_3573
<a, nil>() -> q_gen_3574
<b, cons>(q_gen_3619, q_gen_3618) -> q_gen_3574
<b, nil>() -> q_gen_3574
<a, a>() -> q_gen_3575
<b, a>() -> q_gen_3575
<b, b>() -> q_gen_3575
<cons, cons>(q_gen_3575, q_gen_3574, q_gen_3573, q_gen_3629) -> q_gen_3629
<nil, cons>(q_gen_3619, q_gen_3618) -> q_gen_3629
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 28  ;  () -> length([nil, z]) -> 28  ;  () -> leq([z, s(nn2)]) -> 28  ;  () -> leq([z, z]) -> 28  ;  () -> reverse([nil, nil]) -> 28  ;  (append([_wda, cons(h1, nil), _xda]) /\ reverse([t1, _wda])) -> reverse([cons(h1, t1), _xda]) -> 31  ;  (append([t1, l2, _rda])) -> append([cons(h1, t1), l2, cons(h1, _rda)]) -> 31  ;  (length([_gea, _hea]) /\ length([l1, _fea]) /\ reverse([l1, _gea])) -> leq([_fea, _hea]) -> 29  ;  (length([_iea, _jea]) /\ length([l1, _kea]) /\ reverse([l1, _iea])) -> leq([_jea, _kea]) -> 30  ;  (length([ll, _bea])) -> length([cons(x, ll), s(_bea)]) -> 29  ;  (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([_wda, cons(h1, nil), _xda]) /\ reverse([t1, _wda])) -> reverse([cons(h1, t1), _xda]), {
_wda -> cons(a, nil)  ;  _xda -> cons(a, cons(b, nil))  ;  h1 -> b  ;  t1 -> cons(a, nil)
})

-------------------------------------------
Step 44, which took 13.536654 s (model generation: 0.039496,  model checking: 13.497158):

Model:
|_
{
append -> 
{{{
Q={q_gen_3556, q_gen_3561, q_gen_3562, q_gen_3563, q_gen_3564, q_gen_3582, q_gen_3583, q_gen_3603, q_gen_3608, q_gen_3609, q_gen_3610, q_gen_3611, q_gen_3612, q_gen_3613, q_gen_3614, q_gen_3615, q_gen_3627},
Q_f={q_gen_3556},
Delta=
{
<nil>() -> q_gen_3582
<a>() -> q_gen_3583
<b>() -> q_gen_3583
<cons>(q_gen_3583, q_gen_3582) -> q_gen_3603
<cons>(q_gen_3583, q_gen_3603) -> q_gen_3603
<cons, cons>(q_gen_3564, q_gen_3563, q_gen_3562, q_gen_3561) -> q_gen_3561
<cons, cons>(q_gen_3564, q_gen_3563, q_gen_3562, q_gen_3627) -> q_gen_3561
<nil, nil>() -> q_gen_3561
<cons, a>(q_gen_3583, q_gen_3582) -> q_gen_3562
<cons, a>(q_gen_3583, q_gen_3603) -> q_gen_3562
<cons, b>(q_gen_3583, q_gen_3582) -> q_gen_3562
<cons, b>(q_gen_3583, q_gen_3603) -> q_gen_3562
<nil, a>() -> q_gen_3562
<nil, b>() -> q_gen_3562
<a, cons>(q_gen_3583, q_gen_3582) -> q_gen_3563
<a, cons>(q_gen_3583, q_gen_3603) -> q_gen_3563
<a, nil>() -> q_gen_3563
<b, cons>(q_gen_3583, q_gen_3582) -> q_gen_3563
<b, cons>(q_gen_3583, q_gen_3603) -> q_gen_3563
<b, nil>() -> q_gen_3563
<a, a>() -> q_gen_3564
<b, b>() -> q_gen_3564
<nil, cons>(q_gen_3583, q_gen_3582) -> q_gen_3627
<nil, cons>(q_gen_3583, q_gen_3603) -> q_gen_3627
<cons, cons, cons>(q_gen_3615, q_gen_3614, q_gen_3613, q_gen_3612, q_gen_3611, q_gen_3610, q_gen_3609, q_gen_3608) -> q_gen_3556
<cons, nil, cons>(q_gen_3564, q_gen_3563, q_gen_3562, q_gen_3561) -> q_gen_3556
<cons, nil, cons>(q_gen_3564, q_gen_3563, q_gen_3562, q_gen_3627) -> q_gen_3556
<nil, cons, cons>(q_gen_3564, q_gen_3563, q_gen_3562, q_gen_3561) -> q_gen_3556
<nil, nil, cons>(q_gen_3583, q_gen_3603) -> q_gen_3556
<nil, nil, nil>() -> q_gen_3556
<cons, cons, cons>(q_gen_3615, q_gen_3614, q_gen_3613, q_gen_3612, q_gen_3611, q_gen_3610, q_gen_3609, q_gen_3556) -> q_gen_3608
<nil, cons, cons>(q_gen_3564, q_gen_3563, q_gen_3562, q_gen_3627) -> q_gen_3608
<nil, nil, cons>(q_gen_3583, q_gen_3582) -> q_gen_3608
<nil, nil, a>() -> q_gen_3609
<nil, nil, b>() -> q_gen_3609
<nil, a, cons>(q_gen_3583, q_gen_3582) -> q_gen_3610
<nil, b, cons>(q_gen_3583, q_gen_3582) -> q_gen_3610
<nil, b, cons>(q_gen_3583, q_gen_3603) -> q_gen_3610
<nil, a, a>() -> q_gen_3611
<nil, a, b>() -> q_gen_3611
<nil, b, a>() -> q_gen_3611
<nil, b, b>() -> q_gen_3611
<a, nil, cons>(q_gen_3583, q_gen_3582) -> q_gen_3612
<b, nil, cons>(q_gen_3583, q_gen_3582) -> q_gen_3612
<b, nil, cons>(q_gen_3583, q_gen_3603) -> q_gen_3612
<a, nil, a>() -> q_gen_3613
<b, nil, b>() -> q_gen_3613
<a, a, cons>(q_gen_3583, q_gen_3582) -> q_gen_3614
<a, b, cons>(q_gen_3583, q_gen_3582) -> q_gen_3614
<b, a, cons>(q_gen_3583, q_gen_3582) -> q_gen_3614
<b, b, cons>(q_gen_3583, q_gen_3582) -> q_gen_3614
<b, b, cons>(q_gen_3583, q_gen_3603) -> q_gen_3614
<a, a, a>() -> q_gen_3615
<a, b, a>() -> q_gen_3615
<b, a, b>() -> q_gen_3615
<b, b, b>() -> q_gen_3615
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_3555, q_gen_3559, q_gen_3596},
Q_f={q_gen_3555},
Delta=
{
<s>(q_gen_3596) -> q_gen_3596
<z>() -> q_gen_3596
<cons, s>(q_gen_3559, q_gen_3555) -> q_gen_3555
<nil, z>() -> q_gen_3555
<a, s>(q_gen_3596) -> q_gen_3559
<a, z>() -> q_gen_3559
<b, s>(q_gen_3596) -> q_gen_3559
<b, z>() -> q_gen_3559
}

Datatype: <eltlist, nat>
Convolution form: complete
}}}
  ;  leq -> 
{{{
Q={q_gen_3552, q_gen_3554, q_gen_3634},
Q_f={q_gen_3552},
Delta=
{
<s>(q_gen_3554) -> q_gen_3554
<z>() -> q_gen_3554
<s, s>(q_gen_3552) -> q_gen_3552
<z, s>(q_gen_3554) -> q_gen_3552
<z, z>() -> q_gen_3552
<s, s>(q_gen_3634) -> q_gen_3634
<s, z>(q_gen_3554) -> q_gen_3634
}

Datatype: <nat, nat>
Convolution form: complete
}}}
  ;  reverse -> 
{{{
Q={q_gen_3551, q_gen_3573, q_gen_3574, q_gen_3575, q_gen_3618, q_gen_3619, q_gen_3629},
Q_f={q_gen_3551},
Delta=
{
<cons>(q_gen_3619, q_gen_3618) -> q_gen_3618
<nil>() -> q_gen_3618
<a>() -> q_gen_3619
<b>() -> q_gen_3619
<cons, cons>(q_gen_3575, q_gen_3574, q_gen_3573, q_gen_3551) -> q_gen_3551
<nil, nil>() -> q_gen_3551
<cons, a>(q_gen_3619, q_gen_3618) -> q_gen_3573
<cons, b>(q_gen_3619, q_gen_3618) -> q_gen_3573
<nil, a>() -> q_gen_3573
<nil, b>() -> q_gen_3573
<a, nil>() -> q_gen_3574
<b, cons>(q_gen_3619, q_gen_3618) -> q_gen_3574
<b, nil>() -> q_gen_3574
<a, a>() -> q_gen_3575
<a, b>() -> q_gen_3575
<b, a>() -> q_gen_3575
<b, b>() -> q_gen_3575
<cons, cons>(q_gen_3575, q_gen_3574, q_gen_3573, q_gen_3629) -> q_gen_3629
<nil, cons>(q_gen_3619, q_gen_3618) -> q_gen_3629
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 29  ;  () -> length([nil, z]) -> 29  ;  () -> leq([z, s(nn2)]) -> 29  ;  () -> leq([z, z]) -> 29  ;  () -> reverse([nil, nil]) -> 29  ;  (append([_wda, cons(h1, nil), _xda]) /\ reverse([t1, _wda])) -> reverse([cons(h1, t1), _xda]) -> 31  ;  (append([t1, l2, _rda])) -> append([cons(h1, t1), l2, cons(h1, _rda)]) -> 34  ;  (length([_gea, _hea]) /\ length([l1, _fea]) /\ reverse([l1, _gea])) -> leq([_fea, _hea]) -> 30  ;  (length([_iea, _jea]) /\ length([l1, _kea]) /\ reverse([l1, _iea])) -> leq([_jea, _kea]) -> 31  ;  (length([ll, _bea])) -> length([cons(x, ll), s(_bea)]) -> 30  ;  (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, _rda])) -> append([cons(h1, t1), l2, cons(h1, _rda)]), {
_rda -> cons(b, cons(b, nil))  ;  h1 -> a  ;  l2 -> cons(b, cons(b, nil))  ;  t1 -> nil
})

-------------------------------------------
Step 45, which took 0.057841 s (model generation: 0.047199,  model checking: 0.010642):

Model:
|_
{
append -> 
{{{
Q={q_gen_3556, q_gen_3561, q_gen_3562, q_gen_3563, q_gen_3564, q_gen_3582, q_gen_3583, q_gen_3603, q_gen_3608, q_gen_3609, q_gen_3610, q_gen_3611, q_gen_3612, q_gen_3613, q_gen_3614, q_gen_3615, q_gen_3627},
Q_f={q_gen_3556},
Delta=
{
<nil>() -> q_gen_3582
<a>() -> q_gen_3583
<b>() -> q_gen_3583
<cons>(q_gen_3583, q_gen_3582) -> q_gen_3603
<cons>(q_gen_3583, q_gen_3603) -> q_gen_3603
<cons, cons>(q_gen_3564, q_gen_3563, q_gen_3562, q_gen_3561) -> q_gen_3561
<cons, cons>(q_gen_3564, q_gen_3563, q_gen_3562, q_gen_3627) -> q_gen_3561
<nil, nil>() -> q_gen_3561
<cons, a>(q_gen_3583, q_gen_3582) -> q_gen_3562
<cons, a>(q_gen_3583, q_gen_3603) -> q_gen_3562
<cons, b>(q_gen_3583, q_gen_3582) -> q_gen_3562
<cons, b>(q_gen_3583, q_gen_3603) -> q_gen_3562
<nil, a>() -> q_gen_3562
<nil, b>() -> q_gen_3562
<a, cons>(q_gen_3583, q_gen_3582) -> q_gen_3563
<a, cons>(q_gen_3583, q_gen_3603) -> q_gen_3563
<a, nil>() -> q_gen_3563
<b, cons>(q_gen_3583, q_gen_3582) -> q_gen_3563
<b, cons>(q_gen_3583, q_gen_3603) -> q_gen_3563
<b, nil>() -> q_gen_3563
<a, a>() -> q_gen_3564
<b, b>() -> q_gen_3564
<nil, cons>(q_gen_3583, q_gen_3582) -> q_gen_3627
<nil, cons>(q_gen_3583, q_gen_3603) -> q_gen_3627
<cons, cons, cons>(q_gen_3615, q_gen_3614, q_gen_3613, q_gen_3612, q_gen_3611, q_gen_3610, q_gen_3609, q_gen_3608) -> q_gen_3556
<cons, nil, cons>(q_gen_3564, q_gen_3563, q_gen_3562, q_gen_3561) -> q_gen_3556
<cons, nil, cons>(q_gen_3564, q_gen_3563, q_gen_3562, q_gen_3627) -> q_gen_3556
<nil, cons, cons>(q_gen_3564, q_gen_3563, q_gen_3562, q_gen_3561) -> q_gen_3556
<nil, nil, cons>(q_gen_3583, q_gen_3603) -> q_gen_3556
<nil, nil, nil>() -> q_gen_3556
<cons, cons, cons>(q_gen_3615, q_gen_3614, q_gen_3613, q_gen_3612, q_gen_3611, q_gen_3610, q_gen_3609, q_gen_3556) -> q_gen_3608
<nil, cons, cons>(q_gen_3564, q_gen_3563, q_gen_3562, q_gen_3627) -> q_gen_3608
<nil, nil, cons>(q_gen_3583, q_gen_3582) -> q_gen_3608
<nil, cons, a>(q_gen_3583, q_gen_3582) -> q_gen_3609
<nil, nil, a>() -> q_gen_3609
<nil, nil, b>() -> q_gen_3609
<nil, a, cons>(q_gen_3583, q_gen_3582) -> q_gen_3610
<nil, b, cons>(q_gen_3583, q_gen_3582) -> q_gen_3610
<nil, b, cons>(q_gen_3583, q_gen_3603) -> q_gen_3610
<nil, a, a>() -> q_gen_3611
<nil, a, b>() -> q_gen_3611
<nil, b, a>() -> q_gen_3611
<nil, b, b>() -> q_gen_3611
<a, cons, cons>(q_gen_3564, q_gen_3563, q_gen_3562, q_gen_3627) -> q_gen_3612
<a, nil, cons>(q_gen_3583, q_gen_3582) -> q_gen_3612
<b, nil, cons>(q_gen_3583, q_gen_3582) -> q_gen_3612
<b, nil, cons>(q_gen_3583, q_gen_3603) -> q_gen_3612
<a, cons, a>(q_gen_3583, q_gen_3582) -> q_gen_3613
<a, nil, a>() -> q_gen_3613
<b, nil, b>() -> q_gen_3613
<a, a, cons>(q_gen_3583, q_gen_3582) -> q_gen_3614
<a, b, cons>(q_gen_3583, q_gen_3582) -> q_gen_3614
<a, b, cons>(q_gen_3583, q_gen_3603) -> q_gen_3614
<b, a, cons>(q_gen_3583, q_gen_3582) -> q_gen_3614
<b, b, cons>(q_gen_3583, q_gen_3582) -> q_gen_3614
<b, b, cons>(q_gen_3583, q_gen_3603) -> q_gen_3614
<a, a, a>() -> q_gen_3615
<a, b, a>() -> q_gen_3615
<b, a, b>() -> q_gen_3615
<b, b, b>() -> q_gen_3615
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_3555, q_gen_3559, q_gen_3596},
Q_f={q_gen_3555},
Delta=
{
<s>(q_gen_3596) -> q_gen_3596
<z>() -> q_gen_3596
<cons, s>(q_gen_3559, q_gen_3555) -> q_gen_3555
<nil, z>() -> q_gen_3555
<a, s>(q_gen_3596) -> q_gen_3559
<a, z>() -> q_gen_3559
<b, s>(q_gen_3596) -> q_gen_3559
<b, z>() -> q_gen_3559
}

Datatype: <eltlist, nat>
Convolution form: complete
}}}
  ;  leq -> 
{{{
Q={q_gen_3552, q_gen_3554, q_gen_3634},
Q_f={q_gen_3552},
Delta=
{
<s>(q_gen_3554) -> q_gen_3554
<z>() -> q_gen_3554
<s, s>(q_gen_3552) -> q_gen_3552
<z, s>(q_gen_3554) -> q_gen_3552
<z, z>() -> q_gen_3552
<s, s>(q_gen_3634) -> q_gen_3634
<s, z>(q_gen_3554) -> q_gen_3634
}

Datatype: <nat, nat>
Convolution form: complete
}}}
  ;  reverse -> 
{{{
Q={q_gen_3551, q_gen_3573, q_gen_3574, q_gen_3575, q_gen_3618, q_gen_3619, q_gen_3629},
Q_f={q_gen_3551},
Delta=
{
<cons>(q_gen_3619, q_gen_3618) -> q_gen_3618
<nil>() -> q_gen_3618
<a>() -> q_gen_3619
<b>() -> q_gen_3619
<cons, cons>(q_gen_3575, q_gen_3574, q_gen_3573, q_gen_3551) -> q_gen_3551
<nil, nil>() -> q_gen_3551
<cons, a>(q_gen_3619, q_gen_3618) -> q_gen_3573
<cons, b>(q_gen_3619, q_gen_3618) -> q_gen_3573
<nil, a>() -> q_gen_3573
<nil, b>() -> q_gen_3573
<a, nil>() -> q_gen_3574
<b, cons>(q_gen_3619, q_gen_3618) -> q_gen_3574
<b, nil>() -> q_gen_3574
<a, a>() -> q_gen_3575
<a, b>() -> q_gen_3575
<b, a>() -> q_gen_3575
<b, b>() -> q_gen_3575
<cons, cons>(q_gen_3575, q_gen_3574, q_gen_3573, q_gen_3629) -> q_gen_3629
<nil, cons>(q_gen_3619, q_gen_3618) -> q_gen_3629
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 30  ;  () -> length([nil, z]) -> 30  ;  () -> leq([z, s(nn2)]) -> 30  ;  () -> leq([z, z]) -> 30  ;  () -> reverse([nil, nil]) -> 30  ;  (append([_wda, cons(h1, nil), _xda]) /\ reverse([t1, _wda])) -> reverse([cons(h1, t1), _xda]) -> 34  ;  (append([t1, l2, _rda])) -> append([cons(h1, t1), l2, cons(h1, _rda)]) -> 34  ;  (length([_gea, _hea]) /\ length([l1, _fea]) /\ reverse([l1, _gea])) -> leq([_fea, _hea]) -> 31  ;  (length([_iea, _jea]) /\ length([l1, _kea]) /\ reverse([l1, _iea])) -> leq([_jea, _kea]) -> 32  ;  (length([ll, _bea])) -> length([cons(x, ll), s(_bea)]) -> 31  ;  (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([_wda, cons(h1, nil), _xda]) /\ reverse([t1, _wda])) -> reverse([cons(h1, t1), _xda]), {
_wda -> cons(a, nil)  ;  _xda -> cons(a, cons(b, nil))  ;  h1 -> a  ;  t1 -> cons(b, nil)
})

-------------------------------------------
Step 46, which took 3.459638 s (model generation: 0.067399,  model checking: 3.392239):

Model:
|_
{
append -> 
{{{
Q={q_gen_3556, q_gen_3561, q_gen_3562, q_gen_3563, q_gen_3564, q_gen_3582, q_gen_3583, q_gen_3603, q_gen_3608, q_gen_3609, q_gen_3610, q_gen_3611, q_gen_3612, q_gen_3613, q_gen_3614, q_gen_3615, q_gen_3627},
Q_f={q_gen_3556},
Delta=
{
<cons>(q_gen_3583, q_gen_3603) -> q_gen_3582
<nil>() -> q_gen_3582
<a>() -> q_gen_3583
<b>() -> q_gen_3583
<cons>(q_gen_3583, q_gen_3582) -> q_gen_3603
<cons, cons>(q_gen_3564, q_gen_3563, q_gen_3562, q_gen_3561) -> q_gen_3561
<nil, nil>() -> q_gen_3561
<cons, a>(q_gen_3583, q_gen_3582) -> q_gen_3562
<cons, a>(q_gen_3583, q_gen_3603) -> q_gen_3562
<cons, b>(q_gen_3583, q_gen_3582) -> q_gen_3562
<cons, b>(q_gen_3583, q_gen_3603) -> q_gen_3562
<nil, a>() -> q_gen_3562
<nil, b>() -> q_gen_3562
<a, cons>(q_gen_3583, q_gen_3582) -> q_gen_3563
<a, cons>(q_gen_3583, q_gen_3603) -> q_gen_3563
<a, nil>() -> q_gen_3563
<b, cons>(q_gen_3583, q_gen_3582) -> q_gen_3563
<b, cons>(q_gen_3583, q_gen_3603) -> q_gen_3563
<b, nil>() -> q_gen_3563
<a, a>() -> q_gen_3564
<b, b>() -> q_gen_3564
<cons, cons>(q_gen_3564, q_gen_3563, q_gen_3562, q_gen_3627) -> q_gen_3627
<nil, cons>(q_gen_3583, q_gen_3582) -> q_gen_3627
<nil, cons>(q_gen_3583, q_gen_3603) -> q_gen_3627
<cons, cons, cons>(q_gen_3615, q_gen_3614, q_gen_3613, q_gen_3612, q_gen_3611, q_gen_3610, q_gen_3609, q_gen_3608) -> q_gen_3556
<cons, nil, cons>(q_gen_3564, q_gen_3563, q_gen_3562, q_gen_3561) -> q_gen_3556
<cons, nil, cons>(q_gen_3564, q_gen_3563, q_gen_3562, q_gen_3627) -> q_gen_3556
<nil, cons, cons>(q_gen_3564, q_gen_3563, q_gen_3562, q_gen_3561) -> q_gen_3556
<nil, nil, cons>(q_gen_3583, q_gen_3603) -> q_gen_3556
<nil, nil, nil>() -> q_gen_3556
<cons, cons, cons>(q_gen_3615, q_gen_3614, q_gen_3613, q_gen_3612, q_gen_3611, q_gen_3610, q_gen_3609, q_gen_3556) -> q_gen_3608
<nil, cons, cons>(q_gen_3564, q_gen_3563, q_gen_3562, q_gen_3627) -> q_gen_3608
<nil, nil, cons>(q_gen_3583, q_gen_3582) -> q_gen_3608
<nil, cons, a>(q_gen_3583, q_gen_3582) -> q_gen_3609
<nil, nil, a>() -> q_gen_3609
<nil, nil, b>() -> q_gen_3609
<nil, a, cons>(q_gen_3583, q_gen_3582) -> q_gen_3610
<nil, b, cons>(q_gen_3583, q_gen_3582) -> q_gen_3610
<nil, b, cons>(q_gen_3583, q_gen_3603) -> q_gen_3610
<nil, a, a>() -> q_gen_3611
<nil, a, b>() -> q_gen_3611
<nil, b, a>() -> q_gen_3611
<nil, b, b>() -> q_gen_3611
<a, cons, cons>(q_gen_3564, q_gen_3563, q_gen_3562, q_gen_3627) -> q_gen_3612
<a, nil, cons>(q_gen_3583, q_gen_3582) -> q_gen_3612
<b, nil, cons>(q_gen_3583, q_gen_3582) -> q_gen_3612
<b, nil, cons>(q_gen_3583, q_gen_3603) -> q_gen_3612
<a, cons, a>(q_gen_3583, q_gen_3582) -> q_gen_3613
<a, nil, a>() -> q_gen_3613
<b, nil, b>() -> q_gen_3613
<a, a, cons>(q_gen_3583, q_gen_3582) -> q_gen_3614
<a, b, cons>(q_gen_3583, q_gen_3582) -> q_gen_3614
<a, b, cons>(q_gen_3583, q_gen_3603) -> q_gen_3614
<b, a, cons>(q_gen_3583, q_gen_3582) -> q_gen_3614
<b, b, cons>(q_gen_3583, q_gen_3582) -> q_gen_3614
<b, b, cons>(q_gen_3583, q_gen_3603) -> q_gen_3614
<a, a, a>() -> q_gen_3615
<a, b, a>() -> q_gen_3615
<b, a, b>() -> q_gen_3615
<b, b, b>() -> q_gen_3615
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_3555, q_gen_3559, q_gen_3596},
Q_f={q_gen_3555},
Delta=
{
<s>(q_gen_3596) -> q_gen_3596
<z>() -> q_gen_3596
<cons, s>(q_gen_3559, q_gen_3555) -> q_gen_3555
<nil, z>() -> q_gen_3555
<a, s>(q_gen_3596) -> q_gen_3559
<a, z>() -> q_gen_3559
<b, s>(q_gen_3596) -> q_gen_3559
<b, z>() -> q_gen_3559
}

Datatype: <eltlist, nat>
Convolution form: complete
}}}
  ;  leq -> 
{{{
Q={q_gen_3552, q_gen_3554, q_gen_3634},
Q_f={q_gen_3552},
Delta=
{
<s>(q_gen_3554) -> q_gen_3554
<z>() -> q_gen_3554
<s, s>(q_gen_3552) -> q_gen_3552
<z, s>(q_gen_3554) -> q_gen_3552
<z, z>() -> q_gen_3552
<s, s>(q_gen_3634) -> q_gen_3634
<s, z>(q_gen_3554) -> q_gen_3634
}

Datatype: <nat, nat>
Convolution form: complete
}}}
  ;  reverse -> 
{{{
Q={q_gen_3551, q_gen_3573, q_gen_3574, q_gen_3575, q_gen_3618, q_gen_3619, q_gen_3629},
Q_f={q_gen_3551},
Delta=
{
<cons>(q_gen_3619, q_gen_3618) -> q_gen_3618
<nil>() -> q_gen_3618
<a>() -> q_gen_3619
<b>() -> q_gen_3619
<cons, cons>(q_gen_3575, q_gen_3574, q_gen_3573, q_gen_3551) -> q_gen_3551
<nil, nil>() -> q_gen_3551
<cons, a>(q_gen_3619, q_gen_3618) -> q_gen_3573
<cons, b>(q_gen_3619, q_gen_3618) -> q_gen_3573
<nil, a>() -> q_gen_3573
<nil, b>() -> q_gen_3573
<a, cons>(q_gen_3619, q_gen_3618) -> q_gen_3574
<a, nil>() -> q_gen_3574
<b, cons>(q_gen_3619, q_gen_3618) -> q_gen_3574
<b, nil>() -> q_gen_3574
<a, a>() -> q_gen_3575
<a, b>() -> q_gen_3575
<b, a>() -> q_gen_3575
<b, b>() -> q_gen_3575
<cons, cons>(q_gen_3575, q_gen_3574, q_gen_3573, q_gen_3629) -> q_gen_3629
<nil, cons>(q_gen_3619, q_gen_3618) -> q_gen_3629
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 31  ;  () -> length([nil, z]) -> 31  ;  () -> leq([z, s(nn2)]) -> 31  ;  () -> leq([z, z]) -> 31  ;  () -> reverse([nil, nil]) -> 31  ;  (append([_wda, cons(h1, nil), _xda]) /\ reverse([t1, _wda])) -> reverse([cons(h1, t1), _xda]) -> 34  ;  (append([t1, l2, _rda])) -> append([cons(h1, t1), l2, cons(h1, _rda)]) -> 37  ;  (length([_gea, _hea]) /\ length([l1, _fea]) /\ reverse([l1, _gea])) -> leq([_fea, _hea]) -> 32  ;  (length([_iea, _jea]) /\ length([l1, _kea]) /\ reverse([l1, _iea])) -> leq([_jea, _kea]) -> 33  ;  (length([ll, _bea])) -> length([cons(x, ll), s(_bea)]) -> 32  ;  (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([t1, l2, _rda])) -> append([cons(h1, t1), l2, cons(h1, _rda)]), {
_rda -> cons(a, cons(a, nil))  ;  h1 -> b  ;  l2 -> cons(a, cons(a, nil))  ;  t1 -> nil
})

Total time: 30.000246
Reason for stopping: DontKnow. Stopped because: timeout