Inference procedure has parameters:
Ice fuel: 200
Timeout: 60s
Convolution: left


Learning problem is:

env: {
elt -> {a, b}  ;  eltlist -> {cons, nil}  ;  nat -> {s, z}
}
definition:
{
(le, P:
{() -> le([z, s(nn2)])
(le([nn1, nn2])) -> le([s(nn1), s(nn2)])
(le([s(nn1), s(nn2)])) -> le([nn1, nn2])
(le([s(nn1), z])) -> BOT
(le([z, z])) -> BOT}
)
(length, F:
{() -> length([nil, z])
(length([ll, _kk])) -> length([cons(x, ll), s(_kk)])}
(length([_lk, _mk]) /\ length([_lk, _nk])) -> eq_nat([_mk, _nk])
)
(fcons, F:
{() -> fcons([x, l, cons(x, l)])}
(fcons([_ok, _pk, _qk]) /\ fcons([_ok, _pk, _rk])) -> eq_eltlist([_qk, _rk])
)
}

properties:
{(fcons([x, l, _tk]) /\ length([_tk, _uk]) /\ length([l, _sk])) -> le([_sk, _uk])}


over-approximation: {fcons, length}
under-approximation: {le}

Clause system for inference is:

{
() -> fcons([x, l, cons(x, l)]) -> 0
() -> le([z, s(nn2)]) -> 0
() -> length([nil, z]) -> 0
(fcons([x, l, _tk]) /\ length([_tk, _uk]) /\ length([l, _sk])) -> le([_sk, _uk]) -> 0
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 0
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 0
(le([s(nn1), z])) -> BOT -> 0
(le([z, z])) -> BOT -> 0
(length([ll, _kk])) -> length([cons(x, ll), s(_kk)]) -> 0
}


Solving took 64.136993 seconds.
DontKnow. Stopped because: timeout
Working model:
|_
{
fcons -> 
{{{
Q={q_gen_2661, q_gen_2662, q_gen_2663, q_gen_2670, q_gen_2671, q_gen_2674, q_gen_2675, q_gen_2676, q_gen_2685, q_gen_2686, q_gen_2690, q_gen_2691, q_gen_2692, q_gen_2699, q_gen_2700, q_gen_2703, q_gen_2704, q_gen_2705, q_gen_2706, q_gen_2717, q_gen_2718, q_gen_2721, q_gen_2722, q_gen_2723, q_gen_2733, q_gen_2738, q_gen_2739, q_gen_2740, q_gen_2741, q_gen_2747, q_gen_2748, q_gen_2751, q_gen_2752, q_gen_2755, q_gen_2760, q_gen_2767, q_gen_2775, q_gen_2776, q_gen_2780, q_gen_2785, q_gen_2796, q_gen_2797, q_gen_2798, q_gen_2801, q_gen_2802, q_gen_2804, q_gen_2808, q_gen_2815, q_gen_2816, q_gen_2819, q_gen_2820, q_gen_2821, q_gen_2824, q_gen_2834, q_gen_2835, q_gen_2839, q_gen_2841},
Q_f={},
Delta=
{
<nil>() -> q_gen_2662
<b>() -> q_gen_2663
<a>() -> q_gen_2671
<nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2675
<b, a>() -> q_gen_2676
<b, b>() -> q_gen_2686
<nil, cons>(q_gen_2671, q_gen_2662) -> q_gen_2691
<a, b>() -> q_gen_2692
<a, a>() -> q_gen_2700
<cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2704
<cons, cons>(q_gen_2686, q_gen_2675) -> q_gen_2706
<cons, cons>(q_gen_2686, q_gen_2706) -> q_gen_2718
<cons, cons>(q_gen_2692, q_gen_2691) -> q_gen_2722
<cons, cons>(q_gen_2700, q_gen_2691) -> q_gen_2739
<cons, cons>(q_gen_2676, q_gen_2704) -> q_gen_2748
<cons, cons>(q_gen_2692, q_gen_2739) -> q_gen_2752
<cons, cons>(q_gen_2686, q_gen_2718) -> q_gen_2776
<cons, cons>(q_gen_2700, q_gen_2704) -> q_gen_2797
<cons, cons>(q_gen_2676, q_gen_2748) -> q_gen_2816
<cons, cons>(q_gen_2692, q_gen_2704) -> q_gen_2820
<cons, cons>(q_gen_2692, q_gen_2706) -> q_gen_2835
<b, nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2661
<a, nil, cons>(q_gen_2671, q_gen_2662) -> q_gen_2670
<a, cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2674
<b, cons, cons>(q_gen_2686, q_gen_2675) -> q_gen_2685
<b, cons, cons>(q_gen_2692, q_gen_2691) -> q_gen_2690
<a, cons, cons>(q_gen_2700, q_gen_2691) -> q_gen_2699
<a, cons, cons>(q_gen_2700, q_gen_2704) -> q_gen_2703
<a, cons, cons>(q_gen_2700, q_gen_2706) -> q_gen_2705
<b, cons, cons>(q_gen_2686, q_gen_2718) -> q_gen_2717
<a, cons, cons>(q_gen_2676, q_gen_2722) -> q_gen_2721
<a, cons, cons>(q_gen_2676, q_gen_2704) -> q_gen_2723
<a, cons, cons>(q_gen_2686, q_gen_2718) -> q_gen_2733
<a, cons, cons>(q_gen_2700, q_gen_2739) -> q_gen_2738
<b, cons, cons>(q_gen_2686, q_gen_2706) -> q_gen_2740
<a, cons, cons>(q_gen_2686, q_gen_2675) -> q_gen_2741
<a, cons, cons>(q_gen_2676, q_gen_2748) -> q_gen_2747
<a, cons, cons>(q_gen_2676, q_gen_2752) -> q_gen_2751
<a, cons, cons>(q_gen_2700, q_gen_2675) -> q_gen_2755
<a, cons, cons>(q_gen_2676, q_gen_2706) -> q_gen_2760
<b, cons, cons>(q_gen_2686, q_gen_2748) -> q_gen_2767
<a, cons, cons>(q_gen_2686, q_gen_2776) -> q_gen_2775
<a, cons, cons>(q_gen_2676, q_gen_2718) -> q_gen_2780
<b, cons, cons>(q_gen_2686, q_gen_2776) -> q_gen_2785
<a, cons, cons>(q_gen_2700, q_gen_2797) -> q_gen_2796
<b, cons, cons>(q_gen_2692, q_gen_2748) -> q_gen_2798
<b, cons, cons>(q_gen_2692, q_gen_2704) -> q_gen_2801
<b, cons, cons>(q_gen_2686, q_gen_2722) -> q_gen_2802
<a, cons, cons>(q_gen_2686, q_gen_2706) -> q_gen_2804
<b, cons, cons>(q_gen_2692, q_gen_2739) -> q_gen_2808
<a, cons, cons>(q_gen_2676, q_gen_2816) -> q_gen_2815
<a, cons, cons>(q_gen_2676, q_gen_2820) -> q_gen_2819
<b, cons, cons>(q_gen_2700, q_gen_2816) -> q_gen_2821
<b, cons, cons>(q_gen_2692, q_gen_2797) -> q_gen_2824
<a, cons, cons>(q_gen_2686, q_gen_2835) -> q_gen_2834
<b, cons, cons>(q_gen_2700, q_gen_2718) -> q_gen_2839
<b, cons, cons>(q_gen_2692, q_gen_2816) -> q_gen_2841
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  le -> 
{{{
Q={q_gen_2659, q_gen_2660, q_gen_2667, q_gen_2668, q_gen_2669, q_gen_2683, q_gen_2684, q_gen_2698, q_gen_2713, q_gen_2714, q_gen_2715, q_gen_2735, q_gen_2743, q_gen_2744, q_gen_2745, q_gen_2753, q_gen_2754, q_gen_2779, q_gen_2787, q_gen_2794, q_gen_2795, q_gen_2806, q_gen_2814},
Q_f={},
Delta=
{
<z>() -> q_gen_2660
<s>(q_gen_2660) -> q_gen_2669
<s>(q_gen_2669) -> q_gen_2754
<z, s>(q_gen_2660) -> q_gen_2659
<s, s>(q_gen_2659) -> q_gen_2667
<z, s>(q_gen_2669) -> q_gen_2668
<s, s>(q_gen_2684) -> q_gen_2683
<z, z>() -> q_gen_2684
<s, s>(q_gen_2683) -> q_gen_2698
<s, s>(q_gen_2714) -> q_gen_2713
<s, s>(q_gen_2715) -> q_gen_2714
<s, z>(q_gen_2660) -> q_gen_2715
<s, s>(q_gen_2698) -> q_gen_2735
<s, s>(q_gen_2744) -> q_gen_2743
<s, s>(q_gen_2745) -> q_gen_2744
<s, z>(q_gen_2669) -> q_gen_2745
<z, s>(q_gen_2754) -> q_gen_2753
<s, s>(q_gen_2713) -> q_gen_2779
<s, s>(q_gen_2735) -> q_gen_2787
<s, s>(q_gen_2795) -> q_gen_2794
<s, z>(q_gen_2754) -> q_gen_2795
<s, s>(q_gen_2743) -> q_gen_2806
<s, s>(q_gen_2806) -> q_gen_2814
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_2658, q_gen_2664, q_gen_2665, q_gen_2666, q_gen_2672, q_gen_2673, q_gen_2677, q_gen_2678, q_gen_2679, q_gen_2680, q_gen_2681, q_gen_2682, q_gen_2687, q_gen_2688, q_gen_2689, q_gen_2693, q_gen_2694, q_gen_2695, q_gen_2696, q_gen_2697, q_gen_2701, q_gen_2702, q_gen_2707, q_gen_2708, q_gen_2709, q_gen_2710, q_gen_2711, q_gen_2712, q_gen_2716, q_gen_2719, q_gen_2720, q_gen_2724, q_gen_2725, q_gen_2726, q_gen_2727, q_gen_2728, q_gen_2729, q_gen_2730, q_gen_2731, q_gen_2732, q_gen_2734, q_gen_2736, q_gen_2737, q_gen_2742, q_gen_2746, q_gen_2749, q_gen_2750, q_gen_2756, q_gen_2757, q_gen_2758, q_gen_2759, q_gen_2761, q_gen_2762, q_gen_2763, q_gen_2764, q_gen_2765, q_gen_2766, q_gen_2768, q_gen_2769, q_gen_2770, q_gen_2771, q_gen_2772, q_gen_2773, q_gen_2774, q_gen_2777, q_gen_2778, q_gen_2781, q_gen_2782, q_gen_2783, q_gen_2784, q_gen_2786, q_gen_2788, q_gen_2789, q_gen_2790, q_gen_2791, q_gen_2792, q_gen_2793, q_gen_2799, q_gen_2800, q_gen_2803, q_gen_2805, q_gen_2807, q_gen_2809, q_gen_2810, q_gen_2811, q_gen_2812, q_gen_2813, q_gen_2817, q_gen_2818, q_gen_2822, q_gen_2823, q_gen_2825, q_gen_2826, q_gen_2827, q_gen_2828, q_gen_2829, q_gen_2830, q_gen_2831, q_gen_2832, q_gen_2833, q_gen_2836, q_gen_2837, q_gen_2838, q_gen_2840, q_gen_2842},
Q_f={},
Delta=
{
<nil>() -> q_gen_2665
<cons>(q_gen_2679, q_gen_2665) -> q_gen_2678
<b>() -> q_gen_2679
<z>() -> q_gen_2681
<cons>(q_gen_2689, q_gen_2665) -> q_gen_2688
<a>() -> q_gen_2689
<cons>(q_gen_2679, q_gen_2678) -> q_gen_2694
<s>(q_gen_2681) -> q_gen_2696
<cons>(q_gen_2679, q_gen_2694) -> q_gen_2709
<s>(q_gen_2696) -> q_gen_2711
<cons>(q_gen_2689, q_gen_2678) -> q_gen_2725
<cons>(q_gen_2679, q_gen_2725) -> q_gen_2728
<cons>(q_gen_2689, q_gen_2725) -> q_gen_2750
<s>(q_gen_2711) -> q_gen_2759
<cons>(q_gen_2679, q_gen_2688) -> q_gen_2763
<cons>(q_gen_2689, q_gen_2763) -> q_gen_2765
<cons>(q_gen_2679, q_gen_2728) -> q_gen_2773
<cons>(q_gen_2679, q_gen_2709) -> q_gen_2778
<cons>(q_gen_2689, q_gen_2778) -> q_gen_2784
<s>(q_gen_2759) -> q_gen_2813
<cons>(q_gen_2689, q_gen_2750) -> q_gen_2818
<cons>(q_gen_2689, q_gen_2827) -> q_gen_2826
<cons>(q_gen_2689, q_gen_2688) -> q_gen_2827
<cons>(q_gen_2689, q_gen_2826) -> q_gen_2829
<nil, z>() -> q_gen_2658
<cons, s>(q_gen_2666, q_gen_2665) -> q_gen_2664
<b, z>() -> q_gen_2666
<cons, s>(q_gen_2673, q_gen_2665) -> q_gen_2672
<a, z>() -> q_gen_2673
<cons, s>(q_gen_2680, q_gen_2678) -> q_gen_2677
<b, s>(q_gen_2681) -> q_gen_2680
<cons, s>(q_gen_2673, q_gen_2678) -> q_gen_2682
<cons, s>(q_gen_2680, q_gen_2688) -> q_gen_2687
<cons, s>(q_gen_2695, q_gen_2694) -> q_gen_2693
<b, s>(q_gen_2696) -> q_gen_2695
<cons, s>(q_gen_2680, q_gen_2665) -> q_gen_2697
<cons, s>(q_gen_2702, q_gen_2678) -> q_gen_2701
<a, s>(q_gen_2681) -> q_gen_2702
<cons, s>(q_gen_2702, q_gen_2694) -> q_gen_2707
<cons, s>(q_gen_2710, q_gen_2709) -> q_gen_2708
<b, s>(q_gen_2711) -> q_gen_2710
<cons, s>(q_gen_2695, q_gen_2665) -> q_gen_2712
<cons, s>(q_gen_2666, q_gen_2678) -> q_gen_2716
<cons, s>(q_gen_2680, q_gen_2709) -> q_gen_2719
<cons, s>(q_gen_2680, q_gen_2694) -> q_gen_2720
<cons, s>(q_gen_2702, q_gen_2725) -> q_gen_2724
<cons, s>(q_gen_2695, q_gen_2725) -> q_gen_2726
<cons, s>(q_gen_2729, q_gen_2728) -> q_gen_2727
<a, s>(q_gen_2711) -> q_gen_2729
<cons, s>(q_gen_2731, q_gen_2665) -> q_gen_2730
<a, s>(q_gen_2696) -> q_gen_2731
<cons, s>(q_gen_2729, q_gen_2688) -> q_gen_2732
<cons, s>(q_gen_2695, q_gen_2709) -> q_gen_2734
<cons, s>(q_gen_2680, q_gen_2725) -> q_gen_2736
<cons, s>(q_gen_2695, q_gen_2728) -> q_gen_2737
<cons, s>(q_gen_2710, q_gen_2665) -> q_gen_2742
<cons, s>(q_gen_2731, q_gen_2725) -> q_gen_2746
<cons, s>(q_gen_2702, q_gen_2750) -> q_gen_2749
<cons, s>(q_gen_2729, q_gen_2665) -> q_gen_2756
<cons, s>(q_gen_2758, q_gen_2688) -> q_gen_2757
<b, s>(q_gen_2759) -> q_gen_2758
<cons, s>(q_gen_2666, q_gen_2709) -> q_gen_2761
<cons, s>(q_gen_2731, q_gen_2763) -> q_gen_2762
<cons, s>(q_gen_2710, q_gen_2765) -> q_gen_2764
<cons, s>(q_gen_2695, q_gen_2678) -> q_gen_2766
<cons, s>(q_gen_2666, q_gen_2750) -> q_gen_2768
<cons, s>(q_gen_2729, q_gen_2725) -> q_gen_2769
<cons, s>(q_gen_2758, q_gen_2750) -> q_gen_2770
<cons, s>(q_gen_2710, q_gen_2728) -> q_gen_2771
<cons, s>(q_gen_2774, q_gen_2773) -> q_gen_2772
<a, s>(q_gen_2759) -> q_gen_2774
<cons, s>(q_gen_2695, q_gen_2778) -> q_gen_2777
<cons, s>(q_gen_2731, q_gen_2709) -> q_gen_2781
<cons, s>(q_gen_2729, q_gen_2778) -> q_gen_2782
<cons, s>(q_gen_2774, q_gen_2784) -> q_gen_2783
<cons, s>(q_gen_2710, q_gen_2778) -> q_gen_2786
<cons, s>(q_gen_2680, q_gen_2778) -> q_gen_2788
<cons, s>(q_gen_2702, q_gen_2665) -> q_gen_2789
<cons, s>(q_gen_2695, q_gen_2688) -> q_gen_2790
<cons, s>(q_gen_2729, q_gen_2678) -> q_gen_2791
<cons, s>(q_gen_2774, q_gen_2725) -> q_gen_2792
<cons, s>(q_gen_2666, q_gen_2778) -> q_gen_2793
<cons, s>(q_gen_2731, q_gen_2694) -> q_gen_2799
<cons, s>(q_gen_2680, q_gen_2750) -> q_gen_2800
<cons, s>(q_gen_2710, q_gen_2750) -> q_gen_2803
<cons, s>(q_gen_2758, q_gen_2678) -> q_gen_2805
<cons, s>(q_gen_2758, q_gen_2773) -> q_gen_2807
<cons, s>(q_gen_2710, q_gen_2678) -> q_gen_2809
<cons, s>(q_gen_2729, q_gen_2750) -> q_gen_2810
<cons, s>(q_gen_2812, q_gen_2694) -> q_gen_2811
<b, s>(q_gen_2813) -> q_gen_2812
<cons, s>(q_gen_2731, q_gen_2818) -> q_gen_2817
<cons, s>(q_gen_2702, q_gen_2818) -> q_gen_2822
<cons, s>(q_gen_2729, q_gen_2709) -> q_gen_2823
<cons, s>(q_gen_2729, q_gen_2826) -> q_gen_2825
<cons, s>(q_gen_2774, q_gen_2829) -> q_gen_2828
<cons, s>(q_gen_2729, q_gen_2765) -> q_gen_2830
<cons, s>(q_gen_2758, q_gen_2665) -> q_gen_2831
<cons, s>(q_gen_2833, q_gen_2678) -> q_gen_2832
<a, s>(q_gen_2813) -> q_gen_2833
<cons, s>(q_gen_2710, q_gen_2725) -> q_gen_2836
<cons, s>(q_gen_2702, q_gen_2688) -> q_gen_2837
<cons, s>(q_gen_2695, q_gen_2827) -> q_gen_2838
<cons, s>(q_gen_2729, q_gen_2694) -> q_gen_2840
<cons, s>(q_gen_2666, q_gen_2818) -> q_gen_2842
}

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

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

-------------------
STEPS:
-------------------------------------------
Step 0, which took 0.013606 s (model generation: 0.013302,  model checking: 0.000304):

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

}

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

}

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

}

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

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

Teacher's answer:
New clause system:
{
() -> fcons([x, l, cons(x, l)]) -> 0
() -> le([z, s(nn2)]) -> 0
() -> length([nil, z]) -> 3
(fcons([x, l, _tk]) /\ length([_tk, _uk]) /\ length([l, _sk])) -> le([_sk, _uk]) -> 1
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 1
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 1
(le([s(nn1), z])) -> BOT -> 1
(le([z, z])) -> BOT -> 1
(length([ll, _kk])) -> length([cons(x, ll), s(_kk)]) -> 1
}
Sat witness: Found: (() -> length([nil, z]), {

})

-------------------------------------------
Step 1, which took 0.010389 s (model generation: 0.010318,  model checking: 0.000071):

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

}

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

}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_2658},
Q_f={q_gen_2658},
Delta=
{
<nil, z>() -> q_gen_2658
}

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

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

Teacher's answer:
New clause system:
{
() -> fcons([x, l, cons(x, l)]) -> 0
() -> le([z, s(nn2)]) -> 3
() -> length([nil, z]) -> 3
(fcons([x, l, _tk]) /\ length([_tk, _uk]) /\ length([l, _sk])) -> le([_sk, _uk]) -> 1
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 1
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 1
(le([s(nn1), z])) -> BOT -> 1
(le([z, z])) -> BOT -> 1
(length([ll, _kk])) -> length([cons(x, ll), s(_kk)]) -> 1
}
Sat witness: Found: (() -> le([z, s(nn2)]), {
nn2 -> z
})

-------------------------------------------
Step 2, which took 0.009712 s (model generation: 0.009568,  model checking: 0.000144):

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

}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  le -> 
{{{
Q={q_gen_2659, q_gen_2660},
Q_f={q_gen_2659},
Delta=
{
<z>() -> q_gen_2660
<z, s>(q_gen_2660) -> q_gen_2659
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_2658},
Q_f={q_gen_2658},
Delta=
{
<nil, z>() -> q_gen_2658
}

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

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

Teacher's answer:
New clause system:
{
() -> fcons([x, l, cons(x, l)]) -> 3
() -> le([z, s(nn2)]) -> 3
() -> length([nil, z]) -> 3
(fcons([x, l, _tk]) /\ length([_tk, _uk]) /\ length([l, _sk])) -> le([_sk, _uk]) -> 1
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 1
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 1
(le([s(nn1), z])) -> BOT -> 1
(le([z, z])) -> BOT -> 1
(length([ll, _kk])) -> length([cons(x, ll), s(_kk)]) -> 1
}
Sat witness: Found: (() -> fcons([x, l, cons(x, l)]), {
l -> nil  ;  x -> b
})

-------------------------------------------
Step 3, which took 0.010713 s (model generation: 0.009187,  model checking: 0.001526):

Model:
|_
{
fcons -> 
{{{
Q={q_gen_2661, q_gen_2662, q_gen_2663},
Q_f={q_gen_2661},
Delta=
{
<nil>() -> q_gen_2662
<b>() -> q_gen_2663
<b, nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2661
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  le -> 
{{{
Q={q_gen_2659, q_gen_2660},
Q_f={q_gen_2659},
Delta=
{
<z>() -> q_gen_2660
<z, s>(q_gen_2660) -> q_gen_2659
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_2658},
Q_f={q_gen_2658},
Delta=
{
<nil, z>() -> q_gen_2658
}

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

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

Teacher's answer:
New clause system:
{
() -> fcons([x, l, cons(x, l)]) -> 3
() -> le([z, s(nn2)]) -> 3
() -> length([nil, z]) -> 3
(fcons([x, l, _tk]) /\ length([_tk, _uk]) /\ length([l, _sk])) -> le([_sk, _uk]) -> 1
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 1
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 1
(le([s(nn1), z])) -> BOT -> 1
(le([z, z])) -> BOT -> 1
(length([ll, _kk])) -> length([cons(x, ll), s(_kk)]) -> 4
}
Sat witness: Found: ((length([ll, _kk])) -> length([cons(x, ll), s(_kk)]), {
_kk -> z  ;  ll -> nil  ;  x -> b
})

-------------------------------------------
Step 4, which took 0.008537 s (model generation: 0.008418,  model checking: 0.000119):

Model:
|_
{
fcons -> 
{{{
Q={q_gen_2661, q_gen_2662, q_gen_2663},
Q_f={q_gen_2661},
Delta=
{
<nil>() -> q_gen_2662
<b>() -> q_gen_2663
<b, nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2661
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  le -> 
{{{
Q={q_gen_2659, q_gen_2660},
Q_f={q_gen_2659},
Delta=
{
<z>() -> q_gen_2660
<z, s>(q_gen_2660) -> q_gen_2659
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_2658, q_gen_2665, q_gen_2666},
Q_f={q_gen_2658},
Delta=
{
<nil>() -> q_gen_2665
<cons, s>(q_gen_2666, q_gen_2665) -> q_gen_2658
<nil, z>() -> q_gen_2658
<b, z>() -> q_gen_2666
}

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

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

Teacher's answer:
New clause system:
{
() -> fcons([x, l, cons(x, l)]) -> 3
() -> le([z, s(nn2)]) -> 3
() -> length([nil, z]) -> 3
(fcons([x, l, _tk]) /\ length([_tk, _uk]) /\ length([l, _sk])) -> le([_sk, _uk]) -> 1
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 4
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 2
(le([s(nn1), z])) -> BOT -> 2
(le([z, z])) -> BOT -> 2
(length([ll, _kk])) -> length([cons(x, ll), s(_kk)]) -> 4
}
Sat witness: Found: ((le([nn1, nn2])) -> le([s(nn1), s(nn2)]), {
nn1 -> z  ;  nn2 -> s(z)
})

-------------------------------------------
Step 5, which took 0.008767 s (model generation: 0.008413,  model checking: 0.000354):

Model:
|_
{
fcons -> 
{{{
Q={q_gen_2661, q_gen_2662, q_gen_2663},
Q_f={q_gen_2661},
Delta=
{
<nil>() -> q_gen_2662
<b>() -> q_gen_2663
<b, nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2661
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  le -> 
{{{
Q={q_gen_2659, q_gen_2660},
Q_f={q_gen_2659},
Delta=
{
<z>() -> q_gen_2660
<s, s>(q_gen_2659) -> q_gen_2659
<z, s>(q_gen_2660) -> q_gen_2659
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_2658, q_gen_2665, q_gen_2666},
Q_f={q_gen_2658},
Delta=
{
<nil>() -> q_gen_2665
<cons, s>(q_gen_2666, q_gen_2665) -> q_gen_2658
<nil, z>() -> q_gen_2658
<b, z>() -> q_gen_2666
}

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

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

Teacher's answer:
New clause system:
{
() -> fcons([x, l, cons(x, l)]) -> 3
() -> le([z, s(nn2)]) -> 6
() -> length([nil, z]) -> 4
(fcons([x, l, _tk]) /\ length([_tk, _uk]) /\ length([l, _sk])) -> le([_sk, _uk]) -> 2
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 4
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 3
(le([s(nn1), z])) -> BOT -> 3
(le([z, z])) -> BOT -> 3
(length([ll, _kk])) -> length([cons(x, ll), s(_kk)]) -> 4
}
Sat witness: Found: (() -> le([z, s(nn2)]), {
nn2 -> s(z)
})

-------------------------------------------
Step 6, which took 0.011911 s (model generation: 0.010581,  model checking: 0.001330):

Model:
|_
{
fcons -> 
{{{
Q={q_gen_2661, q_gen_2662, q_gen_2663},
Q_f={q_gen_2661},
Delta=
{
<nil>() -> q_gen_2662
<b>() -> q_gen_2663
<b, nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2661
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  le -> 
{{{
Q={q_gen_2659, q_gen_2660},
Q_f={q_gen_2659},
Delta=
{
<s>(q_gen_2660) -> q_gen_2660
<z>() -> q_gen_2660
<s, s>(q_gen_2659) -> q_gen_2659
<z, s>(q_gen_2660) -> q_gen_2659
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_2658, q_gen_2665, q_gen_2666},
Q_f={q_gen_2658},
Delta=
{
<nil>() -> q_gen_2665
<cons, s>(q_gen_2666, q_gen_2665) -> q_gen_2658
<nil, z>() -> q_gen_2658
<b, z>() -> q_gen_2666
}

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

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

Teacher's answer:
New clause system:
{
() -> fcons([x, l, cons(x, l)]) -> 6
() -> le([z, s(nn2)]) -> 6
() -> length([nil, z]) -> 4
(fcons([x, l, _tk]) /\ length([_tk, _uk]) /\ length([l, _sk])) -> le([_sk, _uk]) -> 3
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 4
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 4
(le([s(nn1), z])) -> BOT -> 4
(le([z, z])) -> BOT -> 4
(length([ll, _kk])) -> length([cons(x, ll), s(_kk)]) -> 4
}
Sat witness: Found: (() -> fcons([x, l, cons(x, l)]), {
l -> nil  ;  x -> a
})

-------------------------------------------
Step 7, which took 0.010872 s (model generation: 0.010610,  model checking: 0.000262):

Model:
|_
{
fcons -> 
{{{
Q={q_gen_2661, q_gen_2662, q_gen_2663},
Q_f={q_gen_2661},
Delta=
{
<nil>() -> q_gen_2662
<a>() -> q_gen_2663
<b>() -> q_gen_2663
<a, nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2661
<b, nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2661
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  le -> 
{{{
Q={q_gen_2659, q_gen_2660},
Q_f={q_gen_2659},
Delta=
{
<s>(q_gen_2660) -> q_gen_2660
<z>() -> q_gen_2660
<s, s>(q_gen_2659) -> q_gen_2659
<z, s>(q_gen_2660) -> q_gen_2659
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_2658, q_gen_2665, q_gen_2666},
Q_f={q_gen_2658},
Delta=
{
<nil>() -> q_gen_2665
<cons, s>(q_gen_2666, q_gen_2665) -> q_gen_2658
<nil, z>() -> q_gen_2658
<b, z>() -> q_gen_2666
}

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

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

Teacher's answer:
New clause system:
{
() -> fcons([x, l, cons(x, l)]) -> 6
() -> le([z, s(nn2)]) -> 6
() -> length([nil, z]) -> 4
(fcons([x, l, _tk]) /\ length([_tk, _uk]) /\ length([l, _sk])) -> le([_sk, _uk]) -> 4
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 4
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 4
(le([s(nn1), z])) -> BOT -> 4
(le([z, z])) -> BOT -> 4
(length([ll, _kk])) -> length([cons(x, ll), s(_kk)]) -> 7
}
Sat witness: Found: ((length([ll, _kk])) -> length([cons(x, ll), s(_kk)]), {
_kk -> z  ;  ll -> nil  ;  x -> a
})

-------------------------------------------
Step 8, which took 0.010783 s (model generation: 0.009653,  model checking: 0.001130):

Model:
|_
{
fcons -> 
{{{
Q={q_gen_2661, q_gen_2662, q_gen_2663},
Q_f={q_gen_2661},
Delta=
{
<nil>() -> q_gen_2662
<a>() -> q_gen_2663
<b>() -> q_gen_2663
<a, nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2661
<b, nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2661
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  le -> 
{{{
Q={q_gen_2659, q_gen_2660},
Q_f={q_gen_2659},
Delta=
{
<s>(q_gen_2660) -> q_gen_2660
<z>() -> q_gen_2660
<s, s>(q_gen_2659) -> q_gen_2659
<z, s>(q_gen_2660) -> q_gen_2659
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_2658, q_gen_2665, q_gen_2666},
Q_f={q_gen_2658},
Delta=
{
<nil>() -> q_gen_2665
<cons, s>(q_gen_2666, q_gen_2665) -> q_gen_2658
<nil, z>() -> q_gen_2658
<a, z>() -> q_gen_2666
<b, z>() -> q_gen_2666
}

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

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

Teacher's answer:
New clause system:
{
() -> fcons([x, l, cons(x, l)]) -> 9
() -> le([z, s(nn2)]) -> 7
() -> length([nil, z]) -> 5
(fcons([x, l, _tk]) /\ length([_tk, _uk]) /\ length([l, _sk])) -> le([_sk, _uk]) -> 5
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 5
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 5
(le([s(nn1), z])) -> BOT -> 5
(le([z, z])) -> BOT -> 5
(length([ll, _kk])) -> length([cons(x, ll), s(_kk)]) -> 7
}
Sat witness: Found: (() -> fcons([x, l, cons(x, l)]), {
l -> cons(b, nil)  ;  x -> a
})

-------------------------------------------
Step 9, which took 0.011953 s (model generation: 0.011009,  model checking: 0.000944):

Model:
|_
{
fcons -> 
{{{
Q={q_gen_2661, q_gen_2662, q_gen_2663, q_gen_2675, q_gen_2676},
Q_f={q_gen_2661},
Delta=
{
<nil>() -> q_gen_2662
<a>() -> q_gen_2663
<b>() -> q_gen_2663
<nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2675
<b, a>() -> q_gen_2676
<a, cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2661
<a, nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2661
<b, nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2661
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  le -> 
{{{
Q={q_gen_2659, q_gen_2660},
Q_f={q_gen_2659},
Delta=
{
<s>(q_gen_2660) -> q_gen_2660
<z>() -> q_gen_2660
<s, s>(q_gen_2659) -> q_gen_2659
<z, s>(q_gen_2660) -> q_gen_2659
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_2658, q_gen_2665, q_gen_2666},
Q_f={q_gen_2658},
Delta=
{
<nil>() -> q_gen_2665
<cons, s>(q_gen_2666, q_gen_2665) -> q_gen_2658
<nil, z>() -> q_gen_2658
<a, z>() -> q_gen_2666
<b, z>() -> q_gen_2666
}

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

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

Teacher's answer:
New clause system:
{
() -> fcons([x, l, cons(x, l)]) -> 9
() -> le([z, s(nn2)]) -> 7
() -> length([nil, z]) -> 6
(fcons([x, l, _tk]) /\ length([_tk, _uk]) /\ length([l, _sk])) -> le([_sk, _uk]) -> 6
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 6
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 6
(le([s(nn1), z])) -> BOT -> 6
(le([z, z])) -> BOT -> 6
(length([ll, _kk])) -> length([cons(x, ll), s(_kk)]) -> 10
}
Sat witness: Found: ((length([ll, _kk])) -> length([cons(x, ll), s(_kk)]), {
_kk -> s(z)  ;  ll -> cons(b, nil)  ;  x -> b
})

-------------------------------------------
Step 10, which took 0.010802 s (model generation: 0.010577,  model checking: 0.000225):

Model:
|_
{
fcons -> 
{{{
Q={q_gen_2661, q_gen_2662, q_gen_2663, q_gen_2675, q_gen_2676},
Q_f={q_gen_2661},
Delta=
{
<nil>() -> q_gen_2662
<a>() -> q_gen_2663
<b>() -> q_gen_2663
<nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2675
<b, a>() -> q_gen_2676
<a, cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2661
<a, nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2661
<b, nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2661
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  le -> 
{{{
Q={q_gen_2659, q_gen_2660},
Q_f={q_gen_2659},
Delta=
{
<s>(q_gen_2660) -> q_gen_2660
<z>() -> q_gen_2660
<s, s>(q_gen_2659) -> q_gen_2659
<z, s>(q_gen_2660) -> q_gen_2659
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_2658, q_gen_2665, q_gen_2666, q_gen_2679, q_gen_2681},
Q_f={q_gen_2658},
Delta=
{
<cons>(q_gen_2679, q_gen_2665) -> q_gen_2665
<nil>() -> q_gen_2665
<b>() -> q_gen_2679
<z>() -> q_gen_2681
<cons, s>(q_gen_2666, q_gen_2665) -> q_gen_2658
<nil, z>() -> q_gen_2658
<a, z>() -> q_gen_2666
<b, s>(q_gen_2681) -> q_gen_2666
<b, z>() -> q_gen_2666
}

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

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

Teacher's answer:
New clause system:
{
() -> fcons([x, l, cons(x, l)]) -> 9
() -> le([z, s(nn2)]) -> 7
() -> length([nil, z]) -> 6
(fcons([x, l, _tk]) /\ length([_tk, _uk]) /\ length([l, _sk])) -> le([_sk, _uk]) -> 9
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 7
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 7
(le([s(nn1), z])) -> BOT -> 7
(le([z, z])) -> BOT -> 7
(length([ll, _kk])) -> length([cons(x, ll), s(_kk)]) -> 10
}
Sat witness: Found: ((fcons([x, l, _tk]) /\ length([_tk, _uk]) /\ length([l, _sk])) -> le([_sk, _uk]), {
_sk -> s(z)  ;  _tk -> cons(a, cons(b, nil))  ;  _uk -> s(z)  ;  l -> cons(b, nil)  ;  x -> a
})

-------------------------------------------
Step 11, which took 0.011291 s (model generation: 0.011175,  model checking: 0.000116):

Model:
|_
{
fcons -> 
{{{
Q={q_gen_2661, q_gen_2662, q_gen_2663, q_gen_2675, q_gen_2676},
Q_f={q_gen_2661},
Delta=
{
<nil>() -> q_gen_2662
<a>() -> q_gen_2663
<b>() -> q_gen_2663
<nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2675
<b, a>() -> q_gen_2676
<a, cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2661
<a, nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2661
<b, nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2661
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  le -> 
{{{
Q={q_gen_2659, q_gen_2660},
Q_f={q_gen_2659},
Delta=
{
<s>(q_gen_2660) -> q_gen_2660
<z>() -> q_gen_2660
<s, s>(q_gen_2659) -> q_gen_2659
<z, s>(q_gen_2660) -> q_gen_2659
<z, z>() -> q_gen_2659
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_2658, q_gen_2665, q_gen_2666, q_gen_2679, q_gen_2681},
Q_f={q_gen_2658},
Delta=
{
<cons>(q_gen_2679, q_gen_2665) -> q_gen_2665
<nil>() -> q_gen_2665
<b>() -> q_gen_2679
<z>() -> q_gen_2681
<cons, s>(q_gen_2666, q_gen_2665) -> q_gen_2658
<nil, z>() -> q_gen_2658
<a, z>() -> q_gen_2666
<b, s>(q_gen_2681) -> q_gen_2666
<b, z>() -> q_gen_2666
}

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

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

Teacher's answer:
New clause system:
{
() -> fcons([x, l, cons(x, l)]) -> 9
() -> le([z, s(nn2)]) -> 7
() -> length([nil, z]) -> 7
(fcons([x, l, _tk]) /\ length([_tk, _uk]) /\ length([l, _sk])) -> le([_sk, _uk]) -> 9
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 7
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 7
(le([s(nn1), z])) -> BOT -> 7
(le([z, z])) -> BOT -> 10
(length([ll, _kk])) -> length([cons(x, ll), s(_kk)]) -> 10
}
Sat witness: Found: ((le([z, z])) -> BOT, {

})

-------------------------------------------
Step 12, which took 0.010643 s (model generation: 0.010538,  model checking: 0.000105):

Model:
|_
{
fcons -> 
{{{
Q={q_gen_2661, q_gen_2662, q_gen_2663, q_gen_2675, q_gen_2676},
Q_f={q_gen_2661},
Delta=
{
<nil>() -> q_gen_2662
<a>() -> q_gen_2663
<b>() -> q_gen_2663
<nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2675
<b, a>() -> q_gen_2676
<a, cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2661
<a, nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2661
<b, nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2661
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  le -> 
{{{
Q={q_gen_2659, q_gen_2660, q_gen_2684},
Q_f={q_gen_2659},
Delta=
{
<s>(q_gen_2660) -> q_gen_2660
<z>() -> q_gen_2660
<s, s>(q_gen_2659) -> q_gen_2659
<s, s>(q_gen_2684) -> q_gen_2659
<z, s>(q_gen_2660) -> q_gen_2659
<z, z>() -> q_gen_2684
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_2658, q_gen_2665, q_gen_2666, q_gen_2679, q_gen_2681},
Q_f={q_gen_2658},
Delta=
{
<cons>(q_gen_2679, q_gen_2665) -> q_gen_2665
<nil>() -> q_gen_2665
<b>() -> q_gen_2679
<z>() -> q_gen_2681
<cons, s>(q_gen_2666, q_gen_2665) -> q_gen_2658
<nil, z>() -> q_gen_2658
<a, z>() -> q_gen_2666
<b, s>(q_gen_2681) -> q_gen_2666
<b, z>() -> q_gen_2666
}

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

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

Teacher's answer:
New clause system:
{
() -> fcons([x, l, cons(x, l)]) -> 9
() -> le([z, s(nn2)]) -> 7
() -> length([nil, z]) -> 7
(fcons([x, l, _tk]) /\ length([_tk, _uk]) /\ length([l, _sk])) -> le([_sk, _uk]) -> 9
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 7
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 10
(le([s(nn1), z])) -> BOT -> 8
(le([z, z])) -> BOT -> 10
(length([ll, _kk])) -> length([cons(x, ll), s(_kk)]) -> 10
}
Sat witness: Found: ((le([s(nn1), s(nn2)])) -> le([nn1, nn2]), {
nn1 -> z  ;  nn2 -> z
})

-------------------------------------------
Step 13, which took 0.012989 s (model generation: 0.010519,  model checking: 0.002470):

Model:
|_
{
fcons -> 
{{{
Q={q_gen_2661, q_gen_2662, q_gen_2663, q_gen_2675, q_gen_2676},
Q_f={q_gen_2661},
Delta=
{
<nil>() -> q_gen_2662
<a>() -> q_gen_2663
<b>() -> q_gen_2663
<nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2675
<b, a>() -> q_gen_2676
<a, cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2661
<a, nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2661
<b, nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2661
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  le -> 
{{{
Q={q_gen_2659, q_gen_2660, q_gen_2683},
Q_f={q_gen_2659},
Delta=
{
<s>(q_gen_2660) -> q_gen_2660
<z>() -> q_gen_2660
<s, s>(q_gen_2659) -> q_gen_2659
<z, s>(q_gen_2660) -> q_gen_2659
<s, s>(q_gen_2683) -> q_gen_2683
<z, z>() -> q_gen_2683
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_2658, q_gen_2665, q_gen_2666, q_gen_2673, q_gen_2678, q_gen_2679, q_gen_2681, q_gen_2682},
Q_f={q_gen_2658},
Delta=
{
<nil>() -> q_gen_2665
<cons>(q_gen_2679, q_gen_2665) -> q_gen_2678
<b>() -> q_gen_2679
<z>() -> q_gen_2681
<cons, s>(q_gen_2666, q_gen_2665) -> q_gen_2658
<cons, s>(q_gen_2666, q_gen_2678) -> q_gen_2658
<cons, s>(q_gen_2673, q_gen_2665) -> q_gen_2658
<nil, z>() -> q_gen_2658
<b, s>(q_gen_2681) -> q_gen_2666
<b, z>() -> q_gen_2666
<a, z>() -> q_gen_2673
<cons, s>(q_gen_2673, q_gen_2678) -> q_gen_2682
}

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

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

Teacher's answer:
New clause system:
{
() -> fcons([x, l, cons(x, l)]) -> 12
() -> le([z, s(nn2)]) -> 8
() -> length([nil, z]) -> 8
(fcons([x, l, _tk]) /\ length([_tk, _uk]) /\ length([l, _sk])) -> le([_sk, _uk]) -> 10
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 8
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 10
(le([s(nn1), z])) -> BOT -> 9
(le([z, z])) -> BOT -> 10
(length([ll, _kk])) -> length([cons(x, ll), s(_kk)]) -> 10
}
Sat witness: Found: (() -> fcons([x, l, cons(x, l)]), {
l -> cons(b, nil)  ;  x -> b
})

-------------------------------------------
Step 14, which took 0.012144 s (model generation: 0.010705,  model checking: 0.001439):

Model:
|_
{
fcons -> 
{{{
Q={q_gen_2661, q_gen_2662, q_gen_2663, q_gen_2675, q_gen_2676},
Q_f={q_gen_2661},
Delta=
{
<nil>() -> q_gen_2662
<a>() -> q_gen_2663
<b>() -> q_gen_2663
<nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2675
<b, a>() -> q_gen_2676
<b, b>() -> q_gen_2676
<a, cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2661
<a, nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2661
<b, cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2661
<b, nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2661
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  le -> 
{{{
Q={q_gen_2659, q_gen_2660, q_gen_2683},
Q_f={q_gen_2659},
Delta=
{
<s>(q_gen_2660) -> q_gen_2660
<z>() -> q_gen_2660
<s, s>(q_gen_2659) -> q_gen_2659
<z, s>(q_gen_2660) -> q_gen_2659
<s, s>(q_gen_2683) -> q_gen_2683
<z, z>() -> q_gen_2683
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_2658, q_gen_2665, q_gen_2666, q_gen_2678, q_gen_2679, q_gen_2680, q_gen_2681, q_gen_2682},
Q_f={q_gen_2658},
Delta=
{
<nil>() -> q_gen_2665
<cons>(q_gen_2679, q_gen_2665) -> q_gen_2678
<b>() -> q_gen_2679
<z>() -> q_gen_2681
<cons, s>(q_gen_2666, q_gen_2665) -> q_gen_2658
<cons, s>(q_gen_2680, q_gen_2678) -> q_gen_2658
<nil, z>() -> q_gen_2658
<a, z>() -> q_gen_2666
<b, z>() -> q_gen_2666
<b, s>(q_gen_2681) -> q_gen_2680
<cons, s>(q_gen_2666, q_gen_2678) -> q_gen_2682
}

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

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

Teacher's answer:
New clause system:
{
() -> fcons([x, l, cons(x, l)]) -> 12
() -> le([z, s(nn2)]) -> 9
() -> length([nil, z]) -> 9
(fcons([x, l, _tk]) /\ length([_tk, _uk]) /\ length([l, _sk])) -> le([_sk, _uk]) -> 10
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 9
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 10
(le([s(nn1), z])) -> BOT -> 10
(le([z, z])) -> BOT -> 10
(length([ll, _kk])) -> length([cons(x, ll), s(_kk)]) -> 13
}
Sat witness: Found: ((length([ll, _kk])) -> length([cons(x, ll), s(_kk)]), {
_kk -> s(z)  ;  ll -> cons(a, nil)  ;  x -> b
})

-------------------------------------------
Step 15, which took 0.014155 s (model generation: 0.012603,  model checking: 0.001552):

Model:
|_
{
fcons -> 
{{{
Q={q_gen_2661, q_gen_2662, q_gen_2663, q_gen_2675, q_gen_2676},
Q_f={q_gen_2661},
Delta=
{
<nil>() -> q_gen_2662
<a>() -> q_gen_2663
<b>() -> q_gen_2663
<nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2675
<b, a>() -> q_gen_2676
<b, b>() -> q_gen_2676
<a, cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2661
<a, nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2661
<b, cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2661
<b, nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2661
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  le -> 
{{{
Q={q_gen_2659, q_gen_2660, q_gen_2683},
Q_f={q_gen_2659},
Delta=
{
<s>(q_gen_2660) -> q_gen_2660
<z>() -> q_gen_2660
<s, s>(q_gen_2659) -> q_gen_2659
<z, s>(q_gen_2660) -> q_gen_2659
<s, s>(q_gen_2683) -> q_gen_2683
<z, z>() -> q_gen_2683
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_2658, q_gen_2665, q_gen_2666, q_gen_2678, q_gen_2679, q_gen_2680, q_gen_2681, q_gen_2682},
Q_f={q_gen_2658},
Delta=
{
<nil>() -> q_gen_2665
<cons>(q_gen_2679, q_gen_2665) -> q_gen_2678
<a>() -> q_gen_2679
<b>() -> q_gen_2679
<z>() -> q_gen_2681
<cons, s>(q_gen_2666, q_gen_2665) -> q_gen_2658
<cons, s>(q_gen_2680, q_gen_2678) -> q_gen_2658
<nil, z>() -> q_gen_2658
<a, z>() -> q_gen_2666
<b, z>() -> q_gen_2666
<b, s>(q_gen_2681) -> q_gen_2680
<cons, s>(q_gen_2666, q_gen_2678) -> q_gen_2682
}

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

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

Teacher's answer:
New clause system:
{
() -> fcons([x, l, cons(x, l)]) -> 15
() -> le([z, s(nn2)]) -> 10
() -> length([nil, z]) -> 10
(fcons([x, l, _tk]) /\ length([_tk, _uk]) /\ length([l, _sk])) -> le([_sk, _uk]) -> 11
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 10
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 11
(le([s(nn1), z])) -> BOT -> 11
(le([z, z])) -> BOT -> 11
(length([ll, _kk])) -> length([cons(x, ll), s(_kk)]) -> 13
}
Sat witness: Found: (() -> fcons([x, l, cons(x, l)]), {
l -> cons(a, nil)  ;  x -> b
})

-------------------------------------------
Step 16, which took 0.015104 s (model generation: 0.013142,  model checking: 0.001962):

Model:
|_
{
fcons -> 
{{{
Q={q_gen_2661, q_gen_2662, q_gen_2663, q_gen_2675, q_gen_2676},
Q_f={q_gen_2661},
Delta=
{
<nil>() -> q_gen_2662
<a>() -> q_gen_2663
<b>() -> q_gen_2663
<nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2675
<a, b>() -> q_gen_2676
<b, a>() -> q_gen_2676
<b, b>() -> q_gen_2676
<a, cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2661
<a, nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2661
<b, cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2661
<b, nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2661
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  le -> 
{{{
Q={q_gen_2659, q_gen_2660, q_gen_2683},
Q_f={q_gen_2659},
Delta=
{
<s>(q_gen_2660) -> q_gen_2660
<z>() -> q_gen_2660
<s, s>(q_gen_2659) -> q_gen_2659
<z, s>(q_gen_2660) -> q_gen_2659
<s, s>(q_gen_2683) -> q_gen_2683
<z, z>() -> q_gen_2683
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_2658, q_gen_2665, q_gen_2666, q_gen_2678, q_gen_2679, q_gen_2680, q_gen_2681, q_gen_2682},
Q_f={q_gen_2658},
Delta=
{
<nil>() -> q_gen_2665
<cons>(q_gen_2679, q_gen_2665) -> q_gen_2678
<a>() -> q_gen_2679
<b>() -> q_gen_2679
<z>() -> q_gen_2681
<cons, s>(q_gen_2666, q_gen_2665) -> q_gen_2658
<cons, s>(q_gen_2680, q_gen_2678) -> q_gen_2658
<nil, z>() -> q_gen_2658
<a, z>() -> q_gen_2666
<b, z>() -> q_gen_2666
<b, s>(q_gen_2681) -> q_gen_2680
<cons, s>(q_gen_2666, q_gen_2678) -> q_gen_2682
}

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

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

Teacher's answer:
New clause system:
{
() -> fcons([x, l, cons(x, l)]) -> 15
() -> le([z, s(nn2)]) -> 11
() -> length([nil, z]) -> 11
(fcons([x, l, _tk]) /\ length([_tk, _uk]) /\ length([l, _sk])) -> le([_sk, _uk]) -> 12
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 11
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 12
(le([s(nn1), z])) -> BOT -> 12
(le([z, z])) -> BOT -> 12
(length([ll, _kk])) -> length([cons(x, ll), s(_kk)]) -> 16
}
Sat witness: Found: ((length([ll, _kk])) -> length([cons(x, ll), s(_kk)]), {
_kk -> s(s(z))  ;  ll -> cons(b, cons(b, nil))  ;  x -> b
})

-------------------------------------------
Step 17, which took 0.016306 s (model generation: 0.014763,  model checking: 0.001543):

Model:
|_
{
fcons -> 
{{{
Q={q_gen_2661, q_gen_2662, q_gen_2663, q_gen_2675, q_gen_2676},
Q_f={q_gen_2661},
Delta=
{
<nil>() -> q_gen_2662
<a>() -> q_gen_2663
<b>() -> q_gen_2663
<nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2675
<a, b>() -> q_gen_2676
<b, a>() -> q_gen_2676
<b, b>() -> q_gen_2676
<a, cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2661
<a, nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2661
<b, cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2661
<b, nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2661
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  le -> 
{{{
Q={q_gen_2659, q_gen_2660, q_gen_2683},
Q_f={q_gen_2659},
Delta=
{
<s>(q_gen_2660) -> q_gen_2660
<z>() -> q_gen_2660
<s, s>(q_gen_2659) -> q_gen_2659
<z, s>(q_gen_2660) -> q_gen_2659
<s, s>(q_gen_2683) -> q_gen_2683
<z, z>() -> q_gen_2683
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_2658, q_gen_2665, q_gen_2666, q_gen_2678, q_gen_2679, q_gen_2680, q_gen_2681, q_gen_2682},
Q_f={q_gen_2658},
Delta=
{
<cons>(q_gen_2679, q_gen_2678) -> q_gen_2665
<nil>() -> q_gen_2665
<cons>(q_gen_2679, q_gen_2665) -> q_gen_2678
<a>() -> q_gen_2679
<b>() -> q_gen_2679
<s>(q_gen_2681) -> q_gen_2681
<z>() -> q_gen_2681
<cons, s>(q_gen_2666, q_gen_2665) -> q_gen_2658
<cons, s>(q_gen_2680, q_gen_2665) -> q_gen_2658
<cons, s>(q_gen_2680, q_gen_2678) -> q_gen_2658
<nil, z>() -> q_gen_2658
<a, z>() -> q_gen_2666
<b, z>() -> q_gen_2666
<b, s>(q_gen_2681) -> q_gen_2680
<cons, s>(q_gen_2666, q_gen_2678) -> q_gen_2682
}

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

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

Teacher's answer:
New clause system:
{
() -> fcons([x, l, cons(x, l)]) -> 15
() -> le([z, s(nn2)]) -> 12
() -> length([nil, z]) -> 12
(fcons([x, l, _tk]) /\ length([_tk, _uk]) /\ length([l, _sk])) -> le([_sk, _uk]) -> 15
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 12
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 13
(le([s(nn1), z])) -> BOT -> 13
(le([z, z])) -> BOT -> 13
(length([ll, _kk])) -> length([cons(x, ll), s(_kk)]) -> 16
}
Sat witness: Found: ((fcons([x, l, _tk]) /\ length([_tk, _uk]) /\ length([l, _sk])) -> le([_sk, _uk]), {
_sk -> s(s(z))  ;  _tk -> cons(b, cons(b, nil))  ;  _uk -> s(s(z))  ;  l -> cons(b, nil)  ;  x -> b
})

-------------------------------------------
Step 18, which took 0.017895 s (model generation: 0.015995,  model checking: 0.001900):

Model:
|_
{
fcons -> 
{{{
Q={q_gen_2661, q_gen_2662, q_gen_2663, q_gen_2675, q_gen_2676},
Q_f={q_gen_2661},
Delta=
{
<nil>() -> q_gen_2662
<a>() -> q_gen_2663
<b>() -> q_gen_2663
<nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2675
<a, b>() -> q_gen_2676
<b, a>() -> q_gen_2676
<b, b>() -> q_gen_2676
<a, cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2661
<a, nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2661
<b, cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2661
<b, nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2661
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  le -> 
{{{
Q={q_gen_2659, q_gen_2660, q_gen_2683},
Q_f={q_gen_2659},
Delta=
{
<s>(q_gen_2660) -> q_gen_2660
<z>() -> q_gen_2660
<s, s>(q_gen_2659) -> q_gen_2659
<z, s>(q_gen_2660) -> q_gen_2659
<s, s>(q_gen_2683) -> q_gen_2683
<z, z>() -> q_gen_2683
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_2658, q_gen_2665, q_gen_2666, q_gen_2678, q_gen_2679, q_gen_2680, q_gen_2681, q_gen_2682},
Q_f={q_gen_2658},
Delta=
{
<nil>() -> q_gen_2665
<cons>(q_gen_2679, q_gen_2665) -> q_gen_2678
<cons>(q_gen_2679, q_gen_2678) -> q_gen_2678
<a>() -> q_gen_2679
<b>() -> q_gen_2679
<s>(q_gen_2681) -> q_gen_2681
<z>() -> q_gen_2681
<cons, s>(q_gen_2666, q_gen_2665) -> q_gen_2658
<cons, s>(q_gen_2680, q_gen_2678) -> q_gen_2658
<nil, z>() -> q_gen_2658
<a, z>() -> q_gen_2666
<b, z>() -> q_gen_2666
<b, s>(q_gen_2681) -> q_gen_2680
<cons, s>(q_gen_2666, q_gen_2678) -> q_gen_2682
<cons, s>(q_gen_2680, q_gen_2665) -> q_gen_2682
}

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

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

Teacher's answer:
New clause system:
{
() -> fcons([x, l, cons(x, l)]) -> 18
() -> le([z, s(nn2)]) -> 13
() -> length([nil, z]) -> 13
(fcons([x, l, _tk]) /\ length([_tk, _uk]) /\ length([l, _sk])) -> le([_sk, _uk]) -> 16
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 13
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 14
(le([s(nn1), z])) -> BOT -> 14
(le([z, z])) -> BOT -> 14
(length([ll, _kk])) -> length([cons(x, ll), s(_kk)]) -> 16
}
Sat witness: Found: (() -> fcons([x, l, cons(x, l)]), {
l -> cons(a, nil)  ;  x -> a
})

-------------------------------------------
Step 19, which took 0.020921 s (model generation: 0.019426,  model checking: 0.001495):

Model:
|_
{
fcons -> 
{{{
Q={q_gen_2661, q_gen_2662, q_gen_2663, q_gen_2675, q_gen_2676},
Q_f={q_gen_2661},
Delta=
{
<nil>() -> q_gen_2662
<a>() -> q_gen_2663
<b>() -> q_gen_2663
<nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2675
<a, a>() -> q_gen_2676
<a, b>() -> q_gen_2676
<b, a>() -> q_gen_2676
<b, b>() -> q_gen_2676
<a, cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2661
<a, nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2661
<b, cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2661
<b, nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2661
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  le -> 
{{{
Q={q_gen_2659, q_gen_2660, q_gen_2683},
Q_f={q_gen_2659},
Delta=
{
<s>(q_gen_2660) -> q_gen_2660
<z>() -> q_gen_2660
<s, s>(q_gen_2659) -> q_gen_2659
<z, s>(q_gen_2660) -> q_gen_2659
<s, s>(q_gen_2683) -> q_gen_2683
<z, z>() -> q_gen_2683
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_2658, q_gen_2665, q_gen_2666, q_gen_2678, q_gen_2679, q_gen_2680, q_gen_2681, q_gen_2682},
Q_f={q_gen_2658},
Delta=
{
<nil>() -> q_gen_2665
<cons>(q_gen_2679, q_gen_2665) -> q_gen_2678
<cons>(q_gen_2679, q_gen_2678) -> q_gen_2678
<a>() -> q_gen_2679
<b>() -> q_gen_2679
<s>(q_gen_2681) -> q_gen_2681
<z>() -> q_gen_2681
<cons, s>(q_gen_2666, q_gen_2665) -> q_gen_2658
<cons, s>(q_gen_2680, q_gen_2678) -> q_gen_2658
<nil, z>() -> q_gen_2658
<a, z>() -> q_gen_2666
<b, z>() -> q_gen_2666
<b, s>(q_gen_2681) -> q_gen_2680
<cons, s>(q_gen_2666, q_gen_2678) -> q_gen_2682
<cons, s>(q_gen_2680, q_gen_2665) -> q_gen_2682
}

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

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

Teacher's answer:
New clause system:
{
() -> fcons([x, l, cons(x, l)]) -> 18
() -> le([z, s(nn2)]) -> 14
() -> length([nil, z]) -> 14
(fcons([x, l, _tk]) /\ length([_tk, _uk]) /\ length([l, _sk])) -> le([_sk, _uk]) -> 16
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 14
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 15
(le([s(nn1), z])) -> BOT -> 15
(le([z, z])) -> BOT -> 15
(length([ll, _kk])) -> length([cons(x, ll), s(_kk)]) -> 19
}
Sat witness: Found: ((length([ll, _kk])) -> length([cons(x, ll), s(_kk)]), {
_kk -> s(z)  ;  ll -> cons(b, nil)  ;  x -> a
})

-------------------------------------------
Step 20, which took 0.018781 s (model generation: 0.016734,  model checking: 0.002047):

Model:
|_
{
fcons -> 
{{{
Q={q_gen_2661, q_gen_2662, q_gen_2663, q_gen_2675, q_gen_2676},
Q_f={q_gen_2661},
Delta=
{
<nil>() -> q_gen_2662
<a>() -> q_gen_2663
<b>() -> q_gen_2663
<nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2675
<a, a>() -> q_gen_2676
<a, b>() -> q_gen_2676
<b, a>() -> q_gen_2676
<b, b>() -> q_gen_2676
<a, cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2661
<a, nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2661
<b, cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2661
<b, nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2661
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  le -> 
{{{
Q={q_gen_2659, q_gen_2660, q_gen_2683},
Q_f={q_gen_2659},
Delta=
{
<s>(q_gen_2660) -> q_gen_2660
<z>() -> q_gen_2660
<s, s>(q_gen_2659) -> q_gen_2659
<z, s>(q_gen_2660) -> q_gen_2659
<s, s>(q_gen_2683) -> q_gen_2683
<z, z>() -> q_gen_2683
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_2658, q_gen_2665, q_gen_2666, q_gen_2678, q_gen_2679, q_gen_2680, q_gen_2681, q_gen_2682},
Q_f={q_gen_2658},
Delta=
{
<nil>() -> q_gen_2665
<cons>(q_gen_2679, q_gen_2665) -> q_gen_2678
<cons>(q_gen_2679, q_gen_2678) -> q_gen_2678
<a>() -> q_gen_2679
<b>() -> q_gen_2679
<s>(q_gen_2681) -> q_gen_2681
<z>() -> q_gen_2681
<cons, s>(q_gen_2666, q_gen_2665) -> q_gen_2658
<cons, s>(q_gen_2680, q_gen_2678) -> q_gen_2658
<nil, z>() -> q_gen_2658
<a, z>() -> q_gen_2666
<b, z>() -> q_gen_2666
<a, s>(q_gen_2681) -> q_gen_2680
<b, s>(q_gen_2681) -> q_gen_2680
<cons, s>(q_gen_2666, q_gen_2678) -> q_gen_2682
<cons, s>(q_gen_2680, q_gen_2665) -> q_gen_2682
}

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

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

Teacher's answer:
New clause system:
{
() -> fcons([x, l, cons(x, l)]) -> 21
() -> le([z, s(nn2)]) -> 15
() -> length([nil, z]) -> 15
(fcons([x, l, _tk]) /\ length([_tk, _uk]) /\ length([l, _sk])) -> le([_sk, _uk]) -> 17
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 15
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 16
(le([s(nn1), z])) -> BOT -> 16
(le([z, z])) -> BOT -> 16
(length([ll, _kk])) -> length([cons(x, ll), s(_kk)]) -> 19
}
Sat witness: Found: (() -> fcons([x, l, cons(x, l)]), {
l -> cons(a, cons(b, nil))  ;  x -> a
})

-------------------------------------------
Step 21, which took 0.019124 s (model generation: 0.017805,  model checking: 0.001319):

Model:
|_
{
fcons -> 
{{{
Q={q_gen_2661, q_gen_2662, q_gen_2663, q_gen_2675, q_gen_2676},
Q_f={q_gen_2661},
Delta=
{
<nil>() -> q_gen_2662
<a>() -> q_gen_2663
<b>() -> q_gen_2663
<cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2675
<nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2675
<a, a>() -> q_gen_2676
<a, b>() -> q_gen_2676
<b, a>() -> q_gen_2676
<b, b>() -> q_gen_2676
<a, cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2661
<a, nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2661
<b, cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2661
<b, nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2661
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  le -> 
{{{
Q={q_gen_2659, q_gen_2660, q_gen_2683},
Q_f={q_gen_2659},
Delta=
{
<s>(q_gen_2660) -> q_gen_2660
<z>() -> q_gen_2660
<s, s>(q_gen_2659) -> q_gen_2659
<z, s>(q_gen_2660) -> q_gen_2659
<s, s>(q_gen_2683) -> q_gen_2683
<z, z>() -> q_gen_2683
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_2658, q_gen_2665, q_gen_2666, q_gen_2678, q_gen_2679, q_gen_2680, q_gen_2681, q_gen_2682},
Q_f={q_gen_2658},
Delta=
{
<nil>() -> q_gen_2665
<cons>(q_gen_2679, q_gen_2665) -> q_gen_2678
<cons>(q_gen_2679, q_gen_2678) -> q_gen_2678
<a>() -> q_gen_2679
<b>() -> q_gen_2679
<s>(q_gen_2681) -> q_gen_2681
<z>() -> q_gen_2681
<cons, s>(q_gen_2666, q_gen_2665) -> q_gen_2658
<cons, s>(q_gen_2680, q_gen_2678) -> q_gen_2658
<nil, z>() -> q_gen_2658
<a, z>() -> q_gen_2666
<b, z>() -> q_gen_2666
<a, s>(q_gen_2681) -> q_gen_2680
<b, s>(q_gen_2681) -> q_gen_2680
<cons, s>(q_gen_2666, q_gen_2678) -> q_gen_2682
<cons, s>(q_gen_2680, q_gen_2665) -> q_gen_2682
}

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

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

Teacher's answer:
New clause system:
{
() -> fcons([x, l, cons(x, l)]) -> 21
() -> le([z, s(nn2)]) -> 16
() -> length([nil, z]) -> 16
(fcons([x, l, _tk]) /\ length([_tk, _uk]) /\ length([l, _sk])) -> le([_sk, _uk]) -> 20
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 16
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 17
(le([s(nn1), z])) -> BOT -> 17
(le([z, z])) -> BOT -> 17
(length([ll, _kk])) -> length([cons(x, ll), s(_kk)]) -> 19
}
Sat witness: Found: ((fcons([x, l, _tk]) /\ length([_tk, _uk]) /\ length([l, _sk])) -> le([_sk, _uk]), {
_sk -> s(s(z))  ;  _tk -> cons(a, cons(b, cons(b, nil)))  ;  _uk -> s(s(z))  ;  l -> cons(a, cons(b, nil))  ;  x -> a
})

-------------------------------------------
Step 22, which took 0.019696 s (model generation: 0.018892,  model checking: 0.000804):

Model:
|_
{
fcons -> 
{{{
Q={q_gen_2661, q_gen_2662, q_gen_2663, q_gen_2675, q_gen_2676},
Q_f={q_gen_2661},
Delta=
{
<nil>() -> q_gen_2662
<a>() -> q_gen_2663
<b>() -> q_gen_2663
<cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2675
<nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2675
<a, a>() -> q_gen_2676
<a, b>() -> q_gen_2676
<b, a>() -> q_gen_2676
<b, b>() -> q_gen_2676
<a, cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2661
<a, nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2661
<b, cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2661
<b, nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2661
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  le -> 
{{{
Q={q_gen_2659, q_gen_2660, q_gen_2683, q_gen_2684},
Q_f={q_gen_2659},
Delta=
{
<s>(q_gen_2660) -> q_gen_2660
<z>() -> q_gen_2660
<s, s>(q_gen_2659) -> q_gen_2659
<s, s>(q_gen_2683) -> q_gen_2659
<z, s>(q_gen_2660) -> q_gen_2659
<s, s>(q_gen_2684) -> q_gen_2683
<z, z>() -> q_gen_2684
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_2658, q_gen_2665, q_gen_2666, q_gen_2673, q_gen_2678, q_gen_2679, q_gen_2681, q_gen_2682},
Q_f={q_gen_2658},
Delta=
{
<cons>(q_gen_2679, q_gen_2678) -> q_gen_2665
<nil>() -> q_gen_2665
<cons>(q_gen_2679, q_gen_2665) -> q_gen_2678
<a>() -> q_gen_2679
<b>() -> q_gen_2679
<s>(q_gen_2681) -> q_gen_2681
<z>() -> q_gen_2681
<cons, s>(q_gen_2666, q_gen_2665) -> q_gen_2658
<cons, s>(q_gen_2666, q_gen_2678) -> q_gen_2658
<cons, s>(q_gen_2673, q_gen_2665) -> q_gen_2658
<nil, z>() -> q_gen_2658
<a, s>(q_gen_2681) -> q_gen_2666
<b, s>(q_gen_2681) -> q_gen_2666
<b, z>() -> q_gen_2666
<a, z>() -> q_gen_2673
<cons, s>(q_gen_2673, q_gen_2678) -> q_gen_2682
}

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

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

Teacher's answer:
New clause system:
{
() -> fcons([x, l, cons(x, l)]) -> 21
() -> le([z, s(nn2)]) -> 17
() -> length([nil, z]) -> 17
(fcons([x, l, _tk]) /\ length([_tk, _uk]) /\ length([l, _sk])) -> le([_sk, _uk]) -> 20
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 17
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 20
(le([s(nn1), z])) -> BOT -> 18
(le([z, z])) -> BOT -> 18
(length([ll, _kk])) -> length([cons(x, ll), s(_kk)]) -> 19
}
Sat witness: Found: ((le([s(nn1), s(nn2)])) -> le([nn1, nn2]), {
nn1 -> s(z)  ;  nn2 -> s(z)
})

-------------------------------------------
Step 23, which took 0.020986 s (model generation: 0.018719,  model checking: 0.002267):

Model:
|_
{
fcons -> 
{{{
Q={q_gen_2661, q_gen_2662, q_gen_2663, q_gen_2675, q_gen_2676},
Q_f={q_gen_2661},
Delta=
{
<nil>() -> q_gen_2662
<a>() -> q_gen_2663
<b>() -> q_gen_2663
<cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2675
<nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2675
<a, a>() -> q_gen_2676
<a, b>() -> q_gen_2676
<b, a>() -> q_gen_2676
<b, b>() -> q_gen_2676
<a, cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2661
<a, nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2661
<b, cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2661
<b, nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2661
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  le -> 
{{{
Q={q_gen_2659, q_gen_2660, q_gen_2683},
Q_f={q_gen_2659},
Delta=
{
<s>(q_gen_2660) -> q_gen_2660
<z>() -> q_gen_2660
<s, s>(q_gen_2659) -> q_gen_2659
<z, s>(q_gen_2660) -> q_gen_2659
<s, s>(q_gen_2683) -> q_gen_2683
<z, z>() -> q_gen_2683
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_2658, q_gen_2665, q_gen_2666, q_gen_2678, q_gen_2679, q_gen_2680, q_gen_2681, q_gen_2682, q_gen_2696},
Q_f={q_gen_2658},
Delta=
{
<cons>(q_gen_2679, q_gen_2678) -> q_gen_2665
<nil>() -> q_gen_2665
<cons>(q_gen_2679, q_gen_2665) -> q_gen_2678
<a>() -> q_gen_2679
<b>() -> q_gen_2679
<z>() -> q_gen_2681
<s>(q_gen_2681) -> q_gen_2696
<cons, s>(q_gen_2666, q_gen_2665) -> q_gen_2658
<cons, s>(q_gen_2680, q_gen_2678) -> q_gen_2658
<nil, z>() -> q_gen_2658
<a, z>() -> q_gen_2666
<b, s>(q_gen_2696) -> q_gen_2666
<b, z>() -> q_gen_2666
<a, s>(q_gen_2681) -> q_gen_2680
<b, s>(q_gen_2681) -> q_gen_2680
<cons, s>(q_gen_2666, q_gen_2678) -> q_gen_2682
<cons, s>(q_gen_2680, q_gen_2665) -> q_gen_2682
}

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

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

Teacher's answer:
New clause system:
{
() -> fcons([x, l, cons(x, l)]) -> 21
() -> le([z, s(nn2)]) -> 18
() -> length([nil, z]) -> 18
(fcons([x, l, _tk]) /\ length([_tk, _uk]) /\ length([l, _sk])) -> le([_sk, _uk]) -> 20
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 18
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 20
(le([s(nn1), z])) -> BOT -> 19
(le([z, z])) -> BOT -> 19
(length([ll, _kk])) -> length([cons(x, ll), s(_kk)]) -> 22
}
Sat witness: Found: ((length([ll, _kk])) -> length([cons(x, ll), s(_kk)]), {
_kk -> s(s(s(z)))  ;  ll -> cons(b, cons(b, cons(b, nil)))  ;  x -> b
})

-------------------------------------------
Step 24, which took 0.022682 s (model generation: 0.020456,  model checking: 0.002226):

Model:
|_
{
fcons -> 
{{{
Q={q_gen_2661, q_gen_2662, q_gen_2663, q_gen_2675, q_gen_2676},
Q_f={q_gen_2661},
Delta=
{
<nil>() -> q_gen_2662
<a>() -> q_gen_2663
<b>() -> q_gen_2663
<cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2675
<nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2675
<a, a>() -> q_gen_2676
<a, b>() -> q_gen_2676
<b, a>() -> q_gen_2676
<b, b>() -> q_gen_2676
<a, cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2661
<a, nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2661
<b, cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2661
<b, nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2661
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  le -> 
{{{
Q={q_gen_2659, q_gen_2660, q_gen_2683},
Q_f={q_gen_2659},
Delta=
{
<s>(q_gen_2660) -> q_gen_2660
<z>() -> q_gen_2660
<s, s>(q_gen_2659) -> q_gen_2659
<z, s>(q_gen_2660) -> q_gen_2659
<s, s>(q_gen_2683) -> q_gen_2683
<z, z>() -> q_gen_2683
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_2658, q_gen_2665, q_gen_2666, q_gen_2678, q_gen_2679, q_gen_2680, q_gen_2681, q_gen_2682, q_gen_2696},
Q_f={q_gen_2658},
Delta=
{
<cons>(q_gen_2679, q_gen_2678) -> q_gen_2665
<nil>() -> q_gen_2665
<cons>(q_gen_2679, q_gen_2665) -> q_gen_2678
<a>() -> q_gen_2679
<b>() -> q_gen_2679
<s>(q_gen_2696) -> q_gen_2681
<z>() -> q_gen_2681
<s>(q_gen_2681) -> q_gen_2696
<cons, s>(q_gen_2666, q_gen_2665) -> q_gen_2658
<cons, s>(q_gen_2680, q_gen_2678) -> q_gen_2658
<nil, z>() -> q_gen_2658
<a, z>() -> q_gen_2666
<b, s>(q_gen_2696) -> q_gen_2666
<b, z>() -> q_gen_2666
<a, s>(q_gen_2681) -> q_gen_2680
<b, s>(q_gen_2681) -> q_gen_2680
<cons, s>(q_gen_2666, q_gen_2678) -> q_gen_2682
<cons, s>(q_gen_2680, q_gen_2665) -> q_gen_2682
}

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

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

Teacher's answer:
New clause system:
{
() -> fcons([x, l, cons(x, l)]) -> 21
() -> le([z, s(nn2)]) -> 19
() -> length([nil, z]) -> 19
(fcons([x, l, _tk]) /\ length([_tk, _uk]) /\ length([l, _sk])) -> le([_sk, _uk]) -> 23
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 19
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 21
(le([s(nn1), z])) -> BOT -> 20
(le([z, z])) -> BOT -> 20
(length([ll, _kk])) -> length([cons(x, ll), s(_kk)]) -> 22
}
Sat witness: Found: ((fcons([x, l, _tk]) /\ length([_tk, _uk]) /\ length([l, _sk])) -> le([_sk, _uk]), {
_sk -> s(s(s(z)))  ;  _tk -> cons(a, cons(b, nil))  ;  _uk -> s(s(z))  ;  l -> cons(b, nil)  ;  x -> a
})

-------------------------------------------
Step 25, which took 0.023955 s (model generation: 0.023248,  model checking: 0.000707):

Model:
|_
{
fcons -> 
{{{
Q={q_gen_2661, q_gen_2662, q_gen_2663, q_gen_2675, q_gen_2676},
Q_f={q_gen_2661},
Delta=
{
<nil>() -> q_gen_2662
<a>() -> q_gen_2663
<b>() -> q_gen_2663
<cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2675
<nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2675
<a, a>() -> q_gen_2676
<a, b>() -> q_gen_2676
<b, a>() -> q_gen_2676
<b, b>() -> q_gen_2676
<a, cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2661
<a, nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2661
<b, cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2661
<b, nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2661
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  le -> 
{{{
Q={q_gen_2659, q_gen_2660, q_gen_2683},
Q_f={q_gen_2659},
Delta=
{
<s>(q_gen_2660) -> q_gen_2660
<z>() -> q_gen_2660
<s, s>(q_gen_2659) -> q_gen_2659
<s, z>(q_gen_2660) -> q_gen_2659
<z, s>(q_gen_2660) -> q_gen_2659
<s, s>(q_gen_2683) -> q_gen_2683
<z, z>() -> q_gen_2683
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_2658, q_gen_2665, q_gen_2666, q_gen_2678, q_gen_2679, q_gen_2680, q_gen_2681, q_gen_2682, q_gen_2696},
Q_f={q_gen_2658},
Delta=
{
<cons>(q_gen_2679, q_gen_2678) -> q_gen_2665
<nil>() -> q_gen_2665
<cons>(q_gen_2679, q_gen_2665) -> q_gen_2678
<a>() -> q_gen_2679
<b>() -> q_gen_2679
<s>(q_gen_2696) -> q_gen_2681
<z>() -> q_gen_2681
<s>(q_gen_2681) -> q_gen_2696
<cons, s>(q_gen_2666, q_gen_2665) -> q_gen_2658
<cons, s>(q_gen_2680, q_gen_2678) -> q_gen_2658
<nil, z>() -> q_gen_2658
<a, z>() -> q_gen_2666
<b, s>(q_gen_2696) -> q_gen_2666
<b, z>() -> q_gen_2666
<a, s>(q_gen_2681) -> q_gen_2680
<b, s>(q_gen_2681) -> q_gen_2680
<cons, s>(q_gen_2666, q_gen_2678) -> q_gen_2682
<cons, s>(q_gen_2680, q_gen_2665) -> q_gen_2682
}

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

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

Teacher's answer:
New clause system:
{
() -> fcons([x, l, cons(x, l)]) -> 21
() -> le([z, s(nn2)]) -> 20
() -> length([nil, z]) -> 20
(fcons([x, l, _tk]) /\ length([_tk, _uk]) /\ length([l, _sk])) -> le([_sk, _uk]) -> 23
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 20
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 21
(le([s(nn1), z])) -> BOT -> 23
(le([z, z])) -> BOT -> 21
(length([ll, _kk])) -> length([cons(x, ll), s(_kk)]) -> 22
}
Sat witness: Found: ((le([s(nn1), z])) -> BOT, {
nn1 -> z
})

-------------------------------------------
Step 26, which took 0.024707 s (model generation: 0.024344,  model checking: 0.000363):

Model:
|_
{
fcons -> 
{{{
Q={q_gen_2661, q_gen_2662, q_gen_2663, q_gen_2675, q_gen_2676},
Q_f={q_gen_2661},
Delta=
{
<nil>() -> q_gen_2662
<a>() -> q_gen_2663
<b>() -> q_gen_2663
<cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2675
<nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2675
<a, a>() -> q_gen_2676
<a, b>() -> q_gen_2676
<b, a>() -> q_gen_2676
<b, b>() -> q_gen_2676
<a, cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2661
<a, nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2661
<b, cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2661
<b, nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2661
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  le -> 
{{{
Q={q_gen_2659, q_gen_2660, q_gen_2683, q_gen_2715},
Q_f={q_gen_2659},
Delta=
{
<s>(q_gen_2660) -> q_gen_2660
<z>() -> q_gen_2660
<s, s>(q_gen_2659) -> q_gen_2659
<s, s>(q_gen_2715) -> q_gen_2659
<z, s>(q_gen_2660) -> q_gen_2659
<s, s>(q_gen_2683) -> q_gen_2683
<z, z>() -> q_gen_2683
<s, z>(q_gen_2660) -> q_gen_2715
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_2658, q_gen_2665, q_gen_2666, q_gen_2678, q_gen_2679, q_gen_2680, q_gen_2681, q_gen_2682, q_gen_2696},
Q_f={q_gen_2658},
Delta=
{
<cons>(q_gen_2679, q_gen_2678) -> q_gen_2665
<nil>() -> q_gen_2665
<cons>(q_gen_2679, q_gen_2665) -> q_gen_2678
<a>() -> q_gen_2679
<b>() -> q_gen_2679
<s>(q_gen_2696) -> q_gen_2681
<z>() -> q_gen_2681
<s>(q_gen_2681) -> q_gen_2696
<cons, s>(q_gen_2666, q_gen_2665) -> q_gen_2658
<cons, s>(q_gen_2680, q_gen_2678) -> q_gen_2658
<nil, z>() -> q_gen_2658
<a, z>() -> q_gen_2666
<b, s>(q_gen_2696) -> q_gen_2666
<b, z>() -> q_gen_2666
<a, s>(q_gen_2681) -> q_gen_2680
<b, s>(q_gen_2681) -> q_gen_2680
<cons, s>(q_gen_2666, q_gen_2678) -> q_gen_2682
<cons, s>(q_gen_2680, q_gen_2665) -> q_gen_2682
}

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

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

Teacher's answer:
New clause system:
{
() -> fcons([x, l, cons(x, l)]) -> 21
() -> le([z, s(nn2)]) -> 21
() -> length([nil, z]) -> 21
(fcons([x, l, _tk]) /\ length([_tk, _uk]) /\ length([l, _sk])) -> le([_sk, _uk]) -> 23
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 21
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 24
(le([s(nn1), z])) -> BOT -> 23
(le([z, z])) -> BOT -> 22
(length([ll, _kk])) -> length([cons(x, ll), s(_kk)]) -> 22
}
Sat witness: Found: ((le([s(nn1), s(nn2)])) -> le([nn1, nn2]), {
nn1 -> s(z)  ;  nn2 -> z
})

-------------------------------------------
Step 27, which took 0.026161 s (model generation: 0.024473,  model checking: 0.001688):

Model:
|_
{
fcons -> 
{{{
Q={q_gen_2661, q_gen_2662, q_gen_2663, q_gen_2675, q_gen_2676},
Q_f={q_gen_2661},
Delta=
{
<nil>() -> q_gen_2662
<a>() -> q_gen_2663
<b>() -> q_gen_2663
<cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2675
<nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2675
<a, a>() -> q_gen_2676
<a, b>() -> q_gen_2676
<b, a>() -> q_gen_2676
<b, b>() -> q_gen_2676
<a, cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2661
<a, nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2661
<b, cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2661
<b, nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2661
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  le -> 
{{{
Q={q_gen_2659, q_gen_2660, q_gen_2683},
Q_f={q_gen_2659},
Delta=
{
<s>(q_gen_2660) -> q_gen_2660
<z>() -> q_gen_2660
<s, s>(q_gen_2659) -> q_gen_2659
<z, s>(q_gen_2660) -> q_gen_2659
<s, s>(q_gen_2683) -> q_gen_2683
<s, z>(q_gen_2660) -> q_gen_2683
<z, z>() -> q_gen_2683
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_2658, q_gen_2665, q_gen_2666, q_gen_2673, q_gen_2678, q_gen_2679, q_gen_2680, q_gen_2681, q_gen_2682, q_gen_2694},
Q_f={q_gen_2658},
Delta=
{
<nil>() -> q_gen_2665
<cons>(q_gen_2679, q_gen_2665) -> q_gen_2678
<a>() -> q_gen_2679
<b>() -> q_gen_2679
<s>(q_gen_2681) -> q_gen_2681
<z>() -> q_gen_2681
<cons>(q_gen_2679, q_gen_2678) -> q_gen_2694
<cons>(q_gen_2679, q_gen_2694) -> q_gen_2694
<cons, s>(q_gen_2666, q_gen_2665) -> q_gen_2658
<cons, s>(q_gen_2666, q_gen_2678) -> q_gen_2658
<cons, s>(q_gen_2673, q_gen_2665) -> q_gen_2658
<cons, s>(q_gen_2680, q_gen_2678) -> q_gen_2658
<cons, s>(q_gen_2680, q_gen_2694) -> q_gen_2658
<nil, z>() -> q_gen_2658
<a, s>(q_gen_2681) -> q_gen_2666
<b, z>() -> q_gen_2666
<a, z>() -> q_gen_2673
<b, s>(q_gen_2681) -> q_gen_2680
<cons, s>(q_gen_2666, q_gen_2694) -> q_gen_2682
<cons, s>(q_gen_2673, q_gen_2678) -> q_gen_2682
<cons, s>(q_gen_2680, q_gen_2665) -> q_gen_2682
}

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

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

Teacher's answer:
New clause system:
{
() -> fcons([x, l, cons(x, l)]) -> 22
() -> le([z, s(nn2)]) -> 22
() -> length([nil, z]) -> 22
(fcons([x, l, _tk]) /\ length([_tk, _uk]) /\ length([l, _sk])) -> le([_sk, _uk]) -> 23
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 22
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 24
(le([s(nn1), z])) -> BOT -> 23
(le([z, z])) -> BOT -> 22
(length([ll, _kk])) -> length([cons(x, ll), s(_kk)]) -> 25
}
Sat witness: Found: ((length([ll, _kk])) -> length([cons(x, ll), s(_kk)]), {
_kk -> s(z)  ;  ll -> cons(b, cons(b, nil))  ;  x -> a
})

-------------------------------------------
Step 28, which took 0.028340 s (model generation: 0.024977,  model checking: 0.003363):

Model:
|_
{
fcons -> 
{{{
Q={q_gen_2661, q_gen_2662, q_gen_2663, q_gen_2675, q_gen_2676},
Q_f={q_gen_2661},
Delta=
{
<nil>() -> q_gen_2662
<a>() -> q_gen_2663
<b>() -> q_gen_2663
<cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2675
<nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2675
<a, a>() -> q_gen_2676
<a, b>() -> q_gen_2676
<b, a>() -> q_gen_2676
<b, b>() -> q_gen_2676
<a, cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2661
<a, nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2661
<b, cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2661
<b, nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2661
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  le -> 
{{{
Q={q_gen_2659, q_gen_2660, q_gen_2683},
Q_f={q_gen_2659},
Delta=
{
<s>(q_gen_2660) -> q_gen_2660
<z>() -> q_gen_2660
<s, s>(q_gen_2659) -> q_gen_2659
<z, s>(q_gen_2660) -> q_gen_2659
<s, s>(q_gen_2683) -> q_gen_2683
<s, z>(q_gen_2660) -> q_gen_2683
<z, z>() -> q_gen_2683
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_2658, q_gen_2665, q_gen_2666, q_gen_2678, q_gen_2679, q_gen_2680, q_gen_2681, q_gen_2682, q_gen_2694, q_gen_2702},
Q_f={q_gen_2658},
Delta=
{
<nil>() -> q_gen_2665
<cons>(q_gen_2679, q_gen_2665) -> q_gen_2678
<a>() -> q_gen_2679
<b>() -> q_gen_2679
<s>(q_gen_2681) -> q_gen_2681
<z>() -> q_gen_2681
<cons>(q_gen_2679, q_gen_2678) -> q_gen_2694
<cons>(q_gen_2679, q_gen_2694) -> q_gen_2694
<cons, s>(q_gen_2666, q_gen_2665) -> q_gen_2658
<cons, s>(q_gen_2680, q_gen_2678) -> q_gen_2658
<cons, s>(q_gen_2680, q_gen_2694) -> q_gen_2658
<cons, s>(q_gen_2702, q_gen_2678) -> q_gen_2658
<nil, z>() -> q_gen_2658
<a, z>() -> q_gen_2666
<b, z>() -> q_gen_2666
<b, s>(q_gen_2681) -> q_gen_2680
<cons, s>(q_gen_2666, q_gen_2678) -> q_gen_2682
<cons, s>(q_gen_2680, q_gen_2665) -> q_gen_2682
<cons, s>(q_gen_2702, q_gen_2694) -> q_gen_2682
<a, s>(q_gen_2681) -> q_gen_2702
}

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

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

Teacher's answer:
New clause system:
{
() -> fcons([x, l, cons(x, l)]) -> 23
() -> le([z, s(nn2)]) -> 23
() -> length([nil, z]) -> 23
(fcons([x, l, _tk]) /\ length([_tk, _uk]) /\ length([l, _sk])) -> le([_sk, _uk]) -> 26
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 23
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 24
(le([s(nn1), z])) -> BOT -> 24
(le([z, z])) -> BOT -> 23
(length([ll, _kk])) -> length([cons(x, ll), s(_kk)]) -> 25
}
Sat witness: Found: ((fcons([x, l, _tk]) /\ length([_tk, _uk]) /\ length([l, _sk])) -> le([_sk, _uk]), {
_sk -> s(s(z))  ;  _tk -> cons(b, cons(b, cons(b, cons(b, nil))))  ;  _uk -> s(s(z))  ;  l -> cons(b, cons(b, cons(b, nil)))  ;  x -> b
})

-------------------------------------------
Step 29, which took 0.030471 s (model generation: 0.029108,  model checking: 0.001363):

Model:
|_
{
fcons -> 
{{{
Q={q_gen_2661, q_gen_2662, q_gen_2663, q_gen_2675, q_gen_2676},
Q_f={q_gen_2661},
Delta=
{
<nil>() -> q_gen_2662
<a>() -> q_gen_2663
<b>() -> q_gen_2663
<cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2675
<nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2675
<a, a>() -> q_gen_2676
<a, b>() -> q_gen_2676
<b, a>() -> q_gen_2676
<b, b>() -> q_gen_2676
<a, cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2661
<a, nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2661
<b, cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2661
<b, nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2661
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  le -> 
{{{
Q={q_gen_2659, q_gen_2660, q_gen_2683, q_gen_2684, q_gen_2698},
Q_f={q_gen_2659},
Delta=
{
<s>(q_gen_2660) -> q_gen_2660
<z>() -> q_gen_2660
<s, s>(q_gen_2659) -> q_gen_2659
<s, s>(q_gen_2698) -> q_gen_2659
<z, s>(q_gen_2660) -> q_gen_2659
<s, s>(q_gen_2684) -> q_gen_2683
<s, z>(q_gen_2660) -> q_gen_2683
<z, z>() -> q_gen_2684
<s, s>(q_gen_2683) -> q_gen_2698
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_2658, q_gen_2665, q_gen_2666, q_gen_2678, q_gen_2679, q_gen_2680, q_gen_2681, q_gen_2682, q_gen_2696},
Q_f={q_gen_2658},
Delta=
{
<cons>(q_gen_2679, q_gen_2678) -> q_gen_2665
<nil>() -> q_gen_2665
<cons>(q_gen_2679, q_gen_2665) -> q_gen_2678
<a>() -> q_gen_2679
<b>() -> q_gen_2679
<s>(q_gen_2696) -> q_gen_2681
<z>() -> q_gen_2681
<s>(q_gen_2681) -> q_gen_2696
<cons, s>(q_gen_2666, q_gen_2665) -> q_gen_2658
<cons, s>(q_gen_2680, q_gen_2678) -> q_gen_2658
<nil, z>() -> q_gen_2658
<a, z>() -> q_gen_2666
<b, s>(q_gen_2696) -> q_gen_2666
<b, z>() -> q_gen_2666
<a, s>(q_gen_2681) -> q_gen_2680
<b, s>(q_gen_2681) -> q_gen_2680
<cons, s>(q_gen_2666, q_gen_2678) -> q_gen_2682
<cons, s>(q_gen_2680, q_gen_2665) -> q_gen_2682
}

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

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

Teacher's answer:
New clause system:
{
() -> fcons([x, l, cons(x, l)]) -> 24
() -> le([z, s(nn2)]) -> 24
() -> length([nil, z]) -> 24
(fcons([x, l, _tk]) /\ length([_tk, _uk]) /\ length([l, _sk])) -> le([_sk, _uk]) -> 26
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 24
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 27
(le([s(nn1), z])) -> BOT -> 25
(le([z, z])) -> BOT -> 24
(length([ll, _kk])) -> length([cons(x, ll), s(_kk)]) -> 25
}
Sat witness: Found: ((le([s(nn1), s(nn2)])) -> le([nn1, nn2]), {
nn1 -> s(s(z))  ;  nn2 -> s(z)
})

-------------------------------------------
Step 30, which took 0.030819 s (model generation: 0.029755,  model checking: 0.001064):

Model:
|_
{
fcons -> 
{{{
Q={q_gen_2661, q_gen_2662, q_gen_2663, q_gen_2675, q_gen_2676, q_gen_2686, q_gen_2705, q_gen_2706},
Q_f={q_gen_2661},
Delta=
{
<nil>() -> q_gen_2662
<a>() -> q_gen_2663
<b>() -> q_gen_2663
<cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2675
<nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2675
<a, a>() -> q_gen_2676
<b, a>() -> q_gen_2676
<a, b>() -> q_gen_2686
<b, b>() -> q_gen_2686
<cons, cons>(q_gen_2686, q_gen_2675) -> q_gen_2706
<cons, cons>(q_gen_2686, q_gen_2706) -> q_gen_2706
<a, cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2661
<a, nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2661
<b, cons, cons>(q_gen_2686, q_gen_2675) -> q_gen_2661
<b, nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2661
<a, cons, cons>(q_gen_2676, q_gen_2706) -> q_gen_2705
<b, cons, cons>(q_gen_2686, q_gen_2706) -> q_gen_2705
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  le -> 
{{{
Q={q_gen_2659, q_gen_2660, q_gen_2683},
Q_f={q_gen_2659},
Delta=
{
<s>(q_gen_2660) -> q_gen_2660
<z>() -> q_gen_2660
<s, s>(q_gen_2659) -> q_gen_2659
<z, s>(q_gen_2660) -> q_gen_2659
<s, s>(q_gen_2683) -> q_gen_2683
<s, z>(q_gen_2660) -> q_gen_2683
<z, z>() -> q_gen_2683
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_2658, q_gen_2665, q_gen_2666, q_gen_2678, q_gen_2679, q_gen_2680, q_gen_2681, q_gen_2682},
Q_f={q_gen_2658},
Delta=
{
<nil>() -> q_gen_2665
<cons>(q_gen_2679, q_gen_2665) -> q_gen_2678
<cons>(q_gen_2679, q_gen_2678) -> q_gen_2678
<a>() -> q_gen_2679
<b>() -> q_gen_2679
<s>(q_gen_2681) -> q_gen_2681
<z>() -> q_gen_2681
<cons, s>(q_gen_2666, q_gen_2665) -> q_gen_2658
<cons, s>(q_gen_2680, q_gen_2678) -> q_gen_2658
<nil, z>() -> q_gen_2658
<a, z>() -> q_gen_2666
<b, z>() -> q_gen_2666
<a, s>(q_gen_2681) -> q_gen_2680
<b, s>(q_gen_2681) -> q_gen_2680
<cons, s>(q_gen_2666, q_gen_2678) -> q_gen_2682
<cons, s>(q_gen_2680, q_gen_2665) -> q_gen_2682
}

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

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

Teacher's answer:
New clause system:
{
() -> fcons([x, l, cons(x, l)]) -> 27
() -> le([z, s(nn2)]) -> 25
() -> length([nil, z]) -> 25
(fcons([x, l, _tk]) /\ length([_tk, _uk]) /\ length([l, _sk])) -> le([_sk, _uk]) -> 26
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 25
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 27
(le([s(nn1), z])) -> BOT -> 25
(le([z, z])) -> BOT -> 25
(length([ll, _kk])) -> length([cons(x, ll), s(_kk)]) -> 25
}
Sat witness: Found: (() -> fcons([x, l, cons(x, l)]), {
l -> cons(b, cons(a, nil))  ;  x -> a
})

-------------------------------------------
Step 31, which took 0.032501 s (model generation: 0.029993,  model checking: 0.002508):

Model:
|_
{
fcons -> 
{{{
Q={q_gen_2661, q_gen_2662, q_gen_2663, q_gen_2675, q_gen_2676, q_gen_2686, q_gen_2705, q_gen_2706},
Q_f={q_gen_2661},
Delta=
{
<nil>() -> q_gen_2662
<a>() -> q_gen_2663
<b>() -> q_gen_2663
<cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2675
<nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2675
<b, a>() -> q_gen_2676
<a, a>() -> q_gen_2686
<a, b>() -> q_gen_2686
<b, b>() -> q_gen_2686
<cons, cons>(q_gen_2686, q_gen_2675) -> q_gen_2706
<cons, cons>(q_gen_2686, q_gen_2706) -> q_gen_2706
<a, cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2661
<a, cons, cons>(q_gen_2676, q_gen_2706) -> q_gen_2661
<a, cons, cons>(q_gen_2686, q_gen_2675) -> q_gen_2661
<a, nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2661
<b, cons, cons>(q_gen_2686, q_gen_2675) -> q_gen_2661
<b, nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2661
<a, cons, cons>(q_gen_2686, q_gen_2706) -> q_gen_2705
<b, cons, cons>(q_gen_2686, q_gen_2706) -> q_gen_2705
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  le -> 
{{{
Q={q_gen_2659, q_gen_2660, q_gen_2683},
Q_f={q_gen_2659},
Delta=
{
<s>(q_gen_2660) -> q_gen_2660
<z>() -> q_gen_2660
<s, s>(q_gen_2659) -> q_gen_2659
<z, s>(q_gen_2660) -> q_gen_2659
<s, s>(q_gen_2683) -> q_gen_2683
<s, z>(q_gen_2660) -> q_gen_2683
<z, z>() -> q_gen_2683
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_2658, q_gen_2665, q_gen_2666, q_gen_2678, q_gen_2679, q_gen_2680, q_gen_2681, q_gen_2682},
Q_f={q_gen_2658},
Delta=
{
<nil>() -> q_gen_2665
<cons>(q_gen_2679, q_gen_2665) -> q_gen_2678
<cons>(q_gen_2679, q_gen_2678) -> q_gen_2678
<a>() -> q_gen_2679
<b>() -> q_gen_2679
<s>(q_gen_2681) -> q_gen_2681
<z>() -> q_gen_2681
<cons, s>(q_gen_2666, q_gen_2665) -> q_gen_2658
<cons, s>(q_gen_2680, q_gen_2678) -> q_gen_2658
<nil, z>() -> q_gen_2658
<a, z>() -> q_gen_2666
<b, z>() -> q_gen_2666
<a, s>(q_gen_2681) -> q_gen_2680
<b, s>(q_gen_2681) -> q_gen_2680
<cons, s>(q_gen_2666, q_gen_2678) -> q_gen_2682
<cons, s>(q_gen_2680, q_gen_2665) -> q_gen_2682
}

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

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

Teacher's answer:
New clause system:
{
() -> fcons([x, l, cons(x, l)]) -> 27
() -> le([z, s(nn2)]) -> 26
() -> length([nil, z]) -> 26
(fcons([x, l, _tk]) /\ length([_tk, _uk]) /\ length([l, _sk])) -> le([_sk, _uk]) -> 29
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 26
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 27
(le([s(nn1), z])) -> BOT -> 26
(le([z, z])) -> BOT -> 26
(length([ll, _kk])) -> length([cons(x, ll), s(_kk)]) -> 26
}
Sat witness: Found: ((fcons([x, l, _tk]) /\ length([_tk, _uk]) /\ length([l, _sk])) -> le([_sk, _uk]), {
_sk -> s(s(z))  ;  _tk -> cons(a, cons(a, cons(b, nil)))  ;  _uk -> s(s(z))  ;  l -> cons(b, cons(b, nil))  ;  x -> a
})

-------------------------------------------
Step 32, which took 0.035637 s (model generation: 0.033097,  model checking: 0.002540):

Model:
|_
{
fcons -> 
{{{
Q={q_gen_2661, q_gen_2662, q_gen_2663, q_gen_2675, q_gen_2676},
Q_f={q_gen_2661},
Delta=
{
<nil>() -> q_gen_2662
<a>() -> q_gen_2663
<b>() -> q_gen_2663
<cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2675
<nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2675
<a, a>() -> q_gen_2676
<a, b>() -> q_gen_2676
<b, a>() -> q_gen_2676
<b, b>() -> q_gen_2676
<a, cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2661
<a, nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2661
<b, cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2661
<b, nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2661
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  le -> 
{{{
Q={q_gen_2659, q_gen_2660, q_gen_2683},
Q_f={q_gen_2659},
Delta=
{
<s>(q_gen_2660) -> q_gen_2660
<z>() -> q_gen_2660
<s, s>(q_gen_2659) -> q_gen_2659
<z, s>(q_gen_2660) -> q_gen_2659
<s, s>(q_gen_2683) -> q_gen_2683
<s, z>(q_gen_2660) -> q_gen_2683
<z, z>() -> q_gen_2683
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_2658, q_gen_2665, q_gen_2666, q_gen_2678, q_gen_2679, q_gen_2680, q_gen_2681, q_gen_2682, q_gen_2694, q_gen_2695, q_gen_2696},
Q_f={q_gen_2658},
Delta=
{
<nil>() -> q_gen_2665
<cons>(q_gen_2679, q_gen_2665) -> q_gen_2678
<cons>(q_gen_2679, q_gen_2694) -> q_gen_2678
<a>() -> q_gen_2679
<b>() -> q_gen_2679
<z>() -> q_gen_2681
<cons>(q_gen_2679, q_gen_2678) -> q_gen_2694
<s>(q_gen_2681) -> q_gen_2696
<s>(q_gen_2696) -> q_gen_2696
<cons, s>(q_gen_2666, q_gen_2665) -> q_gen_2658
<cons, s>(q_gen_2680, q_gen_2678) -> q_gen_2658
<cons, s>(q_gen_2695, q_gen_2678) -> q_gen_2658
<cons, s>(q_gen_2695, q_gen_2694) -> q_gen_2658
<nil, z>() -> q_gen_2658
<a, z>() -> q_gen_2666
<b, z>() -> q_gen_2666
<a, s>(q_gen_2681) -> q_gen_2680
<b, s>(q_gen_2681) -> q_gen_2680
<cons, s>(q_gen_2666, q_gen_2678) -> q_gen_2682
<cons, s>(q_gen_2680, q_gen_2665) -> q_gen_2682
<cons, s>(q_gen_2680, q_gen_2694) -> q_gen_2682
<cons, s>(q_gen_2695, q_gen_2665) -> q_gen_2682
<b, s>(q_gen_2696) -> q_gen_2695
}

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

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

Teacher's answer:
New clause system:
{
() -> fcons([x, l, cons(x, l)]) -> 27
() -> le([z, s(nn2)]) -> 26
() -> length([nil, z]) -> 26
(fcons([x, l, _tk]) /\ length([_tk, _uk]) /\ length([l, _sk])) -> le([_sk, _uk]) -> 29
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 26
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 27
(le([s(nn1), z])) -> BOT -> 26
(le([z, z])) -> BOT -> 26
(length([ll, _kk])) -> length([cons(x, ll), s(_kk)]) -> 29
}
Sat witness: Found: ((length([ll, _kk])) -> length([cons(x, ll), s(_kk)]), {
_kk -> s(s(s(z)))  ;  ll -> cons(b, cons(a, cons(b, nil)))  ;  x -> a
})

-------------------------------------------
Step 33, which took 0.041140 s (model generation: 0.039487,  model checking: 0.001653):

Model:
|_
{
fcons -> 
{{{
Q={q_gen_2661, q_gen_2662, q_gen_2663, q_gen_2675, q_gen_2676},
Q_f={q_gen_2661},
Delta=
{
<nil>() -> q_gen_2662
<a>() -> q_gen_2663
<b>() -> q_gen_2663
<cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2675
<nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2675
<a, a>() -> q_gen_2676
<a, b>() -> q_gen_2676
<b, a>() -> q_gen_2676
<b, b>() -> q_gen_2676
<a, cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2661
<a, nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2661
<b, cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2661
<b, nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2661
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  le -> 
{{{
Q={q_gen_2659, q_gen_2660, q_gen_2683},
Q_f={q_gen_2659},
Delta=
{
<s>(q_gen_2660) -> q_gen_2660
<z>() -> q_gen_2660
<s, s>(q_gen_2659) -> q_gen_2659
<z, s>(q_gen_2660) -> q_gen_2659
<s, s>(q_gen_2683) -> q_gen_2683
<s, z>(q_gen_2660) -> q_gen_2683
<z, z>() -> q_gen_2683
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_2658, q_gen_2665, q_gen_2666, q_gen_2678, q_gen_2679, q_gen_2680, q_gen_2681, q_gen_2682, q_gen_2694, q_gen_2695, q_gen_2696},
Q_f={q_gen_2658},
Delta=
{
<nil>() -> q_gen_2665
<cons>(q_gen_2679, q_gen_2665) -> q_gen_2678
<a>() -> q_gen_2679
<b>() -> q_gen_2679
<z>() -> q_gen_2681
<cons>(q_gen_2679, q_gen_2678) -> q_gen_2694
<cons>(q_gen_2679, q_gen_2694) -> q_gen_2694
<s>(q_gen_2681) -> q_gen_2696
<s>(q_gen_2696) -> q_gen_2696
<cons, s>(q_gen_2666, q_gen_2665) -> q_gen_2658
<cons, s>(q_gen_2666, q_gen_2694) -> q_gen_2658
<cons, s>(q_gen_2680, q_gen_2678) -> q_gen_2658
<cons, s>(q_gen_2695, q_gen_2694) -> q_gen_2658
<nil, z>() -> q_gen_2658
<a, s>(q_gen_2696) -> q_gen_2666
<a, z>() -> q_gen_2666
<b, z>() -> q_gen_2666
<a, s>(q_gen_2681) -> q_gen_2680
<b, s>(q_gen_2681) -> q_gen_2680
<cons, s>(q_gen_2666, q_gen_2678) -> q_gen_2682
<cons, s>(q_gen_2680, q_gen_2665) -> q_gen_2682
<cons, s>(q_gen_2680, q_gen_2694) -> q_gen_2682
<cons, s>(q_gen_2695, q_gen_2665) -> q_gen_2682
<b, s>(q_gen_2696) -> q_gen_2695
}

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

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

Teacher's answer:
New clause system:
{
() -> fcons([x, l, cons(x, l)]) -> 28
() -> le([z, s(nn2)]) -> 27
() -> length([nil, z]) -> 27
(fcons([x, l, _tk]) /\ length([_tk, _uk]) /\ length([l, _sk])) -> le([_sk, _uk]) -> 29
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 27
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 28
(le([s(nn1), z])) -> BOT -> 27
(le([z, z])) -> BOT -> 27
(length([ll, _kk])) -> length([cons(x, ll), s(_kk)]) -> 32
}
Sat witness: Found: ((length([ll, _kk])) -> length([cons(x, ll), s(_kk)]), {
_kk -> s(s(s(z)))  ;  ll -> cons(a, nil)  ;  x -> a
})

-------------------------------------------
Step 34, which took 0.049916 s (model generation: 0.046417,  model checking: 0.003499):

Model:
|_
{
fcons -> 
{{{
Q={q_gen_2661, q_gen_2662, q_gen_2663, q_gen_2675, q_gen_2676},
Q_f={q_gen_2661},
Delta=
{
<nil>() -> q_gen_2662
<a>() -> q_gen_2663
<b>() -> q_gen_2663
<cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2675
<nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2675
<a, a>() -> q_gen_2676
<a, b>() -> q_gen_2676
<b, a>() -> q_gen_2676
<b, b>() -> q_gen_2676
<a, cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2661
<a, nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2661
<b, cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2661
<b, nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2661
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  le -> 
{{{
Q={q_gen_2659, q_gen_2660, q_gen_2683},
Q_f={q_gen_2659},
Delta=
{
<s>(q_gen_2660) -> q_gen_2660
<z>() -> q_gen_2660
<s, s>(q_gen_2659) -> q_gen_2659
<z, s>(q_gen_2660) -> q_gen_2659
<s, s>(q_gen_2683) -> q_gen_2683
<s, z>(q_gen_2660) -> q_gen_2683
<z, z>() -> q_gen_2683
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_2658, q_gen_2665, q_gen_2666, q_gen_2678, q_gen_2679, q_gen_2680, q_gen_2681, q_gen_2682, q_gen_2694, q_gen_2695, q_gen_2696},
Q_f={q_gen_2658},
Delta=
{
<nil>() -> q_gen_2665
<cons>(q_gen_2679, q_gen_2665) -> q_gen_2678
<cons>(q_gen_2679, q_gen_2694) -> q_gen_2678
<a>() -> q_gen_2679
<b>() -> q_gen_2679
<z>() -> q_gen_2681
<cons>(q_gen_2679, q_gen_2678) -> q_gen_2694
<s>(q_gen_2681) -> q_gen_2696
<s>(q_gen_2696) -> q_gen_2696
<cons, s>(q_gen_2666, q_gen_2665) -> q_gen_2658
<cons, s>(q_gen_2680, q_gen_2678) -> q_gen_2658
<cons, s>(q_gen_2695, q_gen_2678) -> q_gen_2658
<cons, s>(q_gen_2695, q_gen_2694) -> q_gen_2658
<nil, z>() -> q_gen_2658
<a, z>() -> q_gen_2666
<b, z>() -> q_gen_2666
<a, s>(q_gen_2681) -> q_gen_2680
<a, s>(q_gen_2696) -> q_gen_2680
<b, s>(q_gen_2681) -> q_gen_2680
<cons, s>(q_gen_2666, q_gen_2678) -> q_gen_2682
<cons, s>(q_gen_2680, q_gen_2665) -> q_gen_2682
<cons, s>(q_gen_2680, q_gen_2694) -> q_gen_2682
<cons, s>(q_gen_2695, q_gen_2665) -> q_gen_2682
<b, s>(q_gen_2696) -> q_gen_2695
}

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

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

Teacher's answer:
New clause system:
{
() -> fcons([x, l, cons(x, l)]) -> 29
() -> le([z, s(nn2)]) -> 28
() -> length([nil, z]) -> 28
(fcons([x, l, _tk]) /\ length([_tk, _uk]) /\ length([l, _sk])) -> le([_sk, _uk]) -> 32
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 28
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 29
(le([s(nn1), z])) -> BOT -> 28
(le([z, z])) -> BOT -> 28
(length([ll, _kk])) -> length([cons(x, ll), s(_kk)]) -> 32
}
Sat witness: Found: ((fcons([x, l, _tk]) /\ length([_tk, _uk]) /\ length([l, _sk])) -> le([_sk, _uk]), {
_sk -> s(s(s(z)))  ;  _tk -> cons(b, cons(b, cons(b, cons(b, nil))))  ;  _uk -> s(s(z))  ;  l -> cons(b, cons(b, cons(b, nil)))  ;  x -> a
})

-------------------------------------------
Step 35, which took 0.052848 s (model generation: 0.047858,  model checking: 0.004990):

Model:
|_
{
fcons -> 
{{{
Q={q_gen_2661, q_gen_2662, q_gen_2663, q_gen_2675, q_gen_2676},
Q_f={q_gen_2661},
Delta=
{
<nil>() -> q_gen_2662
<a>() -> q_gen_2663
<b>() -> q_gen_2663
<cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2675
<nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2675
<a, a>() -> q_gen_2676
<a, b>() -> q_gen_2676
<b, a>() -> q_gen_2676
<b, b>() -> q_gen_2676
<a, cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2661
<a, nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2661
<b, cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2661
<b, nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2661
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  le -> 
{{{
Q={q_gen_2659, q_gen_2660, q_gen_2683},
Q_f={q_gen_2659},
Delta=
{
<s>(q_gen_2660) -> q_gen_2660
<z>() -> q_gen_2660
<s, s>(q_gen_2659) -> q_gen_2659
<z, s>(q_gen_2660) -> q_gen_2659
<s, s>(q_gen_2683) -> q_gen_2683
<s, z>(q_gen_2660) -> q_gen_2683
<z, z>() -> q_gen_2683
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_2658, q_gen_2665, q_gen_2666, q_gen_2678, q_gen_2679, q_gen_2680, q_gen_2681, q_gen_2682, q_gen_2694, q_gen_2695, q_gen_2696},
Q_f={q_gen_2658},
Delta=
{
<nil>() -> q_gen_2665
<cons>(q_gen_2679, q_gen_2665) -> q_gen_2678
<a>() -> q_gen_2679
<b>() -> q_gen_2679
<z>() -> q_gen_2681
<cons>(q_gen_2679, q_gen_2678) -> q_gen_2694
<cons>(q_gen_2679, q_gen_2694) -> q_gen_2694
<s>(q_gen_2681) -> q_gen_2696
<s>(q_gen_2696) -> q_gen_2696
<cons, s>(q_gen_2666, q_gen_2665) -> q_gen_2658
<cons, s>(q_gen_2680, q_gen_2678) -> q_gen_2658
<cons, s>(q_gen_2695, q_gen_2694) -> q_gen_2658
<nil, z>() -> q_gen_2658
<a, z>() -> q_gen_2666
<b, z>() -> q_gen_2666
<a, s>(q_gen_2681) -> q_gen_2680
<b, s>(q_gen_2681) -> q_gen_2680
<cons, s>(q_gen_2666, q_gen_2678) -> q_gen_2682
<cons, s>(q_gen_2680, q_gen_2665) -> q_gen_2682
<cons, s>(q_gen_2680, q_gen_2694) -> q_gen_2682
<cons, s>(q_gen_2695, q_gen_2665) -> q_gen_2682
<cons, s>(q_gen_2695, q_gen_2678) -> q_gen_2682
<a, s>(q_gen_2696) -> q_gen_2695
<b, s>(q_gen_2696) -> q_gen_2695
}

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

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

Teacher's answer:
New clause system:
{
() -> fcons([x, l, cons(x, l)]) -> 30
() -> le([z, s(nn2)]) -> 29
() -> length([nil, z]) -> 29
(fcons([x, l, _tk]) /\ length([_tk, _uk]) /\ length([l, _sk])) -> le([_sk, _uk]) -> 35
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 29
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 30
(le([s(nn1), z])) -> BOT -> 29
(le([z, z])) -> BOT -> 29
(length([ll, _kk])) -> length([cons(x, ll), s(_kk)]) -> 33
}
Sat witness: Found: ((fcons([x, l, _tk]) /\ length([_tk, _uk]) /\ length([l, _sk])) -> le([_sk, _uk]), {
_sk -> s(s(s(z)))  ;  _tk -> cons(b, cons(b, cons(b, cons(b, nil))))  ;  _uk -> s(s(s(z)))  ;  l -> cons(b, cons(b, cons(b, nil)))  ;  x -> b
})

-------------------------------------------
Step 36, which took 0.057050 s (model generation: 0.051868,  model checking: 0.005182):

Model:
|_
{
fcons -> 
{{{
Q={q_gen_2661, q_gen_2662, q_gen_2663, q_gen_2675, q_gen_2676},
Q_f={q_gen_2661},
Delta=
{
<nil>() -> q_gen_2662
<a>() -> q_gen_2663
<b>() -> q_gen_2663
<cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2675
<nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2675
<a, a>() -> q_gen_2676
<a, b>() -> q_gen_2676
<b, a>() -> q_gen_2676
<b, b>() -> q_gen_2676
<a, cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2661
<a, nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2661
<b, cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2661
<b, nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2661
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  le -> 
{{{
Q={q_gen_2659, q_gen_2660, q_gen_2683},
Q_f={q_gen_2659},
Delta=
{
<s>(q_gen_2660) -> q_gen_2660
<z>() -> q_gen_2660
<s, s>(q_gen_2659) -> q_gen_2659
<z, s>(q_gen_2660) -> q_gen_2659
<s, s>(q_gen_2683) -> q_gen_2683
<s, z>(q_gen_2660) -> q_gen_2683
<z, z>() -> q_gen_2683
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_2658, q_gen_2665, q_gen_2666, q_gen_2678, q_gen_2679, q_gen_2680, q_gen_2681, q_gen_2682, q_gen_2694, q_gen_2696, q_gen_2702, q_gen_2711},
Q_f={q_gen_2658},
Delta=
{
<cons>(q_gen_2679, q_gen_2694) -> q_gen_2665
<nil>() -> q_gen_2665
<cons>(q_gen_2679, q_gen_2665) -> q_gen_2678
<a>() -> q_gen_2679
<b>() -> q_gen_2679
<z>() -> q_gen_2681
<cons>(q_gen_2679, q_gen_2678) -> q_gen_2694
<s>(q_gen_2681) -> q_gen_2696
<s>(q_gen_2696) -> q_gen_2711
<cons, s>(q_gen_2666, q_gen_2665) -> q_gen_2658
<cons, s>(q_gen_2680, q_gen_2678) -> q_gen_2658
<cons, s>(q_gen_2680, q_gen_2694) -> q_gen_2658
<cons, s>(q_gen_2702, q_gen_2665) -> q_gen_2658
<cons, s>(q_gen_2702, q_gen_2678) -> q_gen_2658
<nil, z>() -> q_gen_2658
<a, s>(q_gen_2711) -> q_gen_2666
<a, z>() -> q_gen_2666
<b, z>() -> q_gen_2666
<a, s>(q_gen_2696) -> q_gen_2680
<b, s>(q_gen_2681) -> q_gen_2680
<b, s>(q_gen_2696) -> q_gen_2680
<cons, s>(q_gen_2666, q_gen_2678) -> q_gen_2682
<cons, s>(q_gen_2680, q_gen_2665) -> q_gen_2682
<cons, s>(q_gen_2702, q_gen_2694) -> q_gen_2682
<a, s>(q_gen_2681) -> q_gen_2702
<b, s>(q_gen_2711) -> q_gen_2702
}

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

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

Teacher's answer:
New clause system:
{
() -> fcons([x, l, cons(x, l)]) -> 31
() -> le([z, s(nn2)]) -> 30
() -> length([nil, z]) -> 30
(fcons([x, l, _tk]) /\ length([_tk, _uk]) /\ length([l, _sk])) -> le([_sk, _uk]) -> 35
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 30
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 31
(le([s(nn1), z])) -> BOT -> 30
(le([z, z])) -> BOT -> 30
(length([ll, _kk])) -> length([cons(x, ll), s(_kk)]) -> 36
}
Sat witness: Found: ((length([ll, _kk])) -> length([cons(x, ll), s(_kk)]), {
_kk -> s(s(z))  ;  ll -> cons(b, cons(a, cons(b, nil)))  ;  x -> b
})

-------------------------------------------
Step 37, which took 0.057872 s (model generation: 0.056652,  model checking: 0.001220):

Model:
|_
{
fcons -> 
{{{
Q={q_gen_2661, q_gen_2662, q_gen_2663, q_gen_2675, q_gen_2676, q_gen_2686, q_gen_2704, q_gen_2705, q_gen_2706},
Q_f={q_gen_2661},
Delta=
{
<nil>() -> q_gen_2662
<a>() -> q_gen_2663
<b>() -> q_gen_2663
<nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2675
<b, a>() -> q_gen_2676
<a, a>() -> q_gen_2686
<a, b>() -> q_gen_2686
<b, b>() -> q_gen_2686
<cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2704
<cons, cons>(q_gen_2686, q_gen_2675) -> q_gen_2706
<cons, cons>(q_gen_2686, q_gen_2706) -> q_gen_2706
<a, cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2661
<a, cons, cons>(q_gen_2676, q_gen_2706) -> q_gen_2661
<a, cons, cons>(q_gen_2686, q_gen_2675) -> q_gen_2661
<a, cons, cons>(q_gen_2686, q_gen_2704) -> q_gen_2661
<a, nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2661
<b, cons, cons>(q_gen_2686, q_gen_2675) -> q_gen_2661
<b, nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2661
<a, cons, cons>(q_gen_2676, q_gen_2704) -> q_gen_2705
<a, cons, cons>(q_gen_2686, q_gen_2706) -> q_gen_2705
<b, cons, cons>(q_gen_2686, q_gen_2706) -> q_gen_2705
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  le -> 
{{{
Q={q_gen_2659, q_gen_2660, q_gen_2683},
Q_f={q_gen_2659},
Delta=
{
<s>(q_gen_2660) -> q_gen_2660
<z>() -> q_gen_2660
<s, s>(q_gen_2659) -> q_gen_2659
<z, s>(q_gen_2660) -> q_gen_2659
<s, s>(q_gen_2683) -> q_gen_2683
<s, z>(q_gen_2660) -> q_gen_2683
<z, z>() -> q_gen_2683
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_2658, q_gen_2665, q_gen_2666, q_gen_2678, q_gen_2679, q_gen_2680, q_gen_2681, q_gen_2682},
Q_f={q_gen_2658},
Delta=
{
<nil>() -> q_gen_2665
<cons>(q_gen_2679, q_gen_2665) -> q_gen_2678
<cons>(q_gen_2679, q_gen_2678) -> q_gen_2678
<a>() -> q_gen_2679
<b>() -> q_gen_2679
<s>(q_gen_2681) -> q_gen_2681
<z>() -> q_gen_2681
<cons, s>(q_gen_2666, q_gen_2665) -> q_gen_2658
<cons, s>(q_gen_2680, q_gen_2678) -> q_gen_2658
<nil, z>() -> q_gen_2658
<a, z>() -> q_gen_2666
<b, z>() -> q_gen_2666
<a, s>(q_gen_2681) -> q_gen_2680
<b, s>(q_gen_2681) -> q_gen_2680
<cons, s>(q_gen_2666, q_gen_2678) -> q_gen_2682
<cons, s>(q_gen_2680, q_gen_2665) -> q_gen_2682
}

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

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

Teacher's answer:
New clause system:
{
() -> fcons([x, l, cons(x, l)]) -> 34
() -> le([z, s(nn2)]) -> 31
() -> length([nil, z]) -> 31
(fcons([x, l, _tk]) /\ length([_tk, _uk]) /\ length([l, _sk])) -> le([_sk, _uk]) -> 35
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 31
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 32
(le([s(nn1), z])) -> BOT -> 31
(le([z, z])) -> BOT -> 31
(length([ll, _kk])) -> length([cons(x, ll), s(_kk)]) -> 36
}
Sat witness: Found: (() -> fcons([x, l, cons(x, l)]), {
l -> cons(a, cons(a, nil))  ;  x -> a
})

-------------------------------------------
Step 38, which took 0.061148 s (model generation: 0.060070,  model checking: 0.001078):

Model:
|_
{
fcons -> 
{{{
Q={q_gen_2661, q_gen_2662, q_gen_2663, q_gen_2675, q_gen_2676, q_gen_2686, q_gen_2705, q_gen_2706},
Q_f={q_gen_2661},
Delta=
{
<nil>() -> q_gen_2662
<a>() -> q_gen_2663
<b>() -> q_gen_2663
<cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2675
<nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2675
<a, a>() -> q_gen_2676
<a, b>() -> q_gen_2676
<b, a>() -> q_gen_2676
<b, b>() -> q_gen_2686
<cons, cons>(q_gen_2686, q_gen_2675) -> q_gen_2706
<cons, cons>(q_gen_2686, q_gen_2706) -> q_gen_2706
<a, cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2661
<a, nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2661
<b, cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2661
<b, cons, cons>(q_gen_2686, q_gen_2675) -> q_gen_2661
<b, nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2661
<a, cons, cons>(q_gen_2676, q_gen_2706) -> q_gen_2705
<a, cons, cons>(q_gen_2686, q_gen_2706) -> q_gen_2705
<b, cons, cons>(q_gen_2686, q_gen_2706) -> q_gen_2705
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  le -> 
{{{
Q={q_gen_2659, q_gen_2660, q_gen_2683},
Q_f={q_gen_2659},
Delta=
{
<s>(q_gen_2660) -> q_gen_2660
<z>() -> q_gen_2660
<s, s>(q_gen_2659) -> q_gen_2659
<z, s>(q_gen_2660) -> q_gen_2659
<s, s>(q_gen_2683) -> q_gen_2683
<s, z>(q_gen_2660) -> q_gen_2683
<z, z>() -> q_gen_2683
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_2658, q_gen_2665, q_gen_2666, q_gen_2678, q_gen_2679, q_gen_2680, q_gen_2681, q_gen_2682, q_gen_2689},
Q_f={q_gen_2658},
Delta=
{
<cons>(q_gen_2689, q_gen_2678) -> q_gen_2665
<nil>() -> q_gen_2665
<cons>(q_gen_2679, q_gen_2665) -> q_gen_2678
<cons>(q_gen_2679, q_gen_2678) -> q_gen_2678
<cons>(q_gen_2689, q_gen_2665) -> q_gen_2678
<b>() -> q_gen_2679
<s>(q_gen_2681) -> q_gen_2681
<z>() -> q_gen_2681
<a>() -> q_gen_2689
<cons, s>(q_gen_2666, q_gen_2665) -> q_gen_2658
<cons, s>(q_gen_2680, q_gen_2678) -> q_gen_2658
<nil, z>() -> q_gen_2658
<a, z>() -> q_gen_2666
<b, z>() -> q_gen_2666
<a, s>(q_gen_2681) -> q_gen_2680
<b, s>(q_gen_2681) -> q_gen_2680
<cons, s>(q_gen_2666, q_gen_2678) -> q_gen_2682
<cons, s>(q_gen_2680, q_gen_2665) -> q_gen_2682
}

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

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

Teacher's answer:
New clause system:
{
() -> fcons([x, l, cons(x, l)]) -> 37
() -> le([z, s(nn2)]) -> 32
() -> length([nil, z]) -> 32
(fcons([x, l, _tk]) /\ length([_tk, _uk]) /\ length([l, _sk])) -> le([_sk, _uk]) -> 35
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 32
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 33
(le([s(nn1), z])) -> BOT -> 32
(le([z, z])) -> BOT -> 32
(length([ll, _kk])) -> length([cons(x, ll), s(_kk)]) -> 36
}
Sat witness: Found: (() -> fcons([x, l, cons(x, l)]), {
l -> cons(b, cons(b, nil))  ;  x -> b
})

-------------------------------------------
Step 39, which took 0.062257 s (model generation: 0.059685,  model checking: 0.002572):

Model:
|_
{
fcons -> 
{{{
Q={q_gen_2661, q_gen_2662, q_gen_2663, q_gen_2675, q_gen_2676},
Q_f={q_gen_2661},
Delta=
{
<nil>() -> q_gen_2662
<a>() -> q_gen_2663
<b>() -> q_gen_2663
<cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2675
<nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2675
<a, a>() -> q_gen_2676
<a, b>() -> q_gen_2676
<b, a>() -> q_gen_2676
<b, b>() -> q_gen_2676
<a, cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2661
<a, nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2661
<b, cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2661
<b, nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2661
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  le -> 
{{{
Q={q_gen_2659, q_gen_2660, q_gen_2683},
Q_f={q_gen_2659},
Delta=
{
<s>(q_gen_2660) -> q_gen_2660
<z>() -> q_gen_2660
<s, s>(q_gen_2659) -> q_gen_2659
<z, s>(q_gen_2660) -> q_gen_2659
<s, s>(q_gen_2683) -> q_gen_2683
<s, z>(q_gen_2660) -> q_gen_2683
<z, z>() -> q_gen_2683
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_2658, q_gen_2665, q_gen_2666, q_gen_2678, q_gen_2679, q_gen_2680, q_gen_2681, q_gen_2682, q_gen_2694, q_gen_2695, q_gen_2696, q_gen_2711},
Q_f={q_gen_2658},
Delta=
{
<cons>(q_gen_2679, q_gen_2694) -> q_gen_2665
<nil>() -> q_gen_2665
<cons>(q_gen_2679, q_gen_2665) -> q_gen_2678
<a>() -> q_gen_2679
<b>() -> q_gen_2679
<z>() -> q_gen_2681
<cons>(q_gen_2679, q_gen_2678) -> q_gen_2694
<s>(q_gen_2681) -> q_gen_2696
<s>(q_gen_2696) -> q_gen_2711
<cons, s>(q_gen_2666, q_gen_2665) -> q_gen_2658
<cons, s>(q_gen_2680, q_gen_2678) -> q_gen_2658
<cons, s>(q_gen_2695, q_gen_2694) -> q_gen_2658
<nil, z>() -> q_gen_2658
<a, s>(q_gen_2711) -> q_gen_2666
<a, z>() -> q_gen_2666
<b, s>(q_gen_2711) -> q_gen_2666
<b, z>() -> q_gen_2666
<a, s>(q_gen_2681) -> q_gen_2680
<a, s>(q_gen_2696) -> q_gen_2680
<b, s>(q_gen_2681) -> q_gen_2680
<cons, s>(q_gen_2666, q_gen_2678) -> q_gen_2682
<cons, s>(q_gen_2680, q_gen_2665) -> q_gen_2682
<cons, s>(q_gen_2680, q_gen_2694) -> q_gen_2682
<cons, s>(q_gen_2695, q_gen_2665) -> q_gen_2682
<b, s>(q_gen_2696) -> q_gen_2695
}

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

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

Teacher's answer:
New clause system:
{
() -> fcons([x, l, cons(x, l)]) -> 37
() -> le([z, s(nn2)]) -> 33
() -> length([nil, z]) -> 33
(fcons([x, l, _tk]) /\ length([_tk, _uk]) /\ length([l, _sk])) -> le([_sk, _uk]) -> 38
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 33
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 34
(le([s(nn1), z])) -> BOT -> 33
(le([z, z])) -> BOT -> 33
(length([ll, _kk])) -> length([cons(x, ll), s(_kk)]) -> 36
}
Sat witness: Found: ((fcons([x, l, _tk]) /\ length([_tk, _uk]) /\ length([l, _sk])) -> le([_sk, _uk]), {
_sk -> s(s(s(s(z))))  ;  _tk -> cons(b, cons(b, nil))  ;  _uk -> s(s(z))  ;  l -> cons(b, nil)  ;  x -> a
})

-------------------------------------------
Step 40, which took 0.072447 s (model generation: 0.070900,  model checking: 0.001547):

Model:
|_
{
fcons -> 
{{{
Q={q_gen_2661, q_gen_2662, q_gen_2663, q_gen_2675, q_gen_2676, q_gen_2686, q_gen_2692, q_gen_2704, q_gen_2705, q_gen_2706},
Q_f={q_gen_2661},
Delta=
{
<nil>() -> q_gen_2662
<a>() -> q_gen_2663
<b>() -> q_gen_2663
<cons, cons>(q_gen_2692, q_gen_2675) -> q_gen_2675
<nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2675
<b, a>() -> q_gen_2676
<b, b>() -> q_gen_2686
<a, a>() -> q_gen_2692
<a, b>() -> q_gen_2692
<cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2704
<cons, cons>(q_gen_2686, q_gen_2706) -> q_gen_2704
<cons, cons>(q_gen_2686, q_gen_2675) -> q_gen_2706
<a, cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2661
<a, cons, cons>(q_gen_2686, q_gen_2675) -> q_gen_2661
<a, cons, cons>(q_gen_2692, q_gen_2675) -> q_gen_2661
<a, cons, cons>(q_gen_2692, q_gen_2704) -> q_gen_2661
<a, nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2661
<b, cons, cons>(q_gen_2686, q_gen_2675) -> q_gen_2661
<b, cons, cons>(q_gen_2686, q_gen_2706) -> q_gen_2661
<b, cons, cons>(q_gen_2692, q_gen_2675) -> q_gen_2661
<b, nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2661
<a, cons, cons>(q_gen_2676, q_gen_2704) -> q_gen_2705
<a, cons, cons>(q_gen_2686, q_gen_2704) -> q_gen_2705
<a, cons, cons>(q_gen_2692, q_gen_2706) -> q_gen_2705
<b, cons, cons>(q_gen_2686, q_gen_2704) -> q_gen_2705
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  le -> 
{{{
Q={q_gen_2659, q_gen_2660, q_gen_2683},
Q_f={q_gen_2659},
Delta=
{
<s>(q_gen_2660) -> q_gen_2660
<z>() -> q_gen_2660
<s, s>(q_gen_2659) -> q_gen_2659
<z, s>(q_gen_2660) -> q_gen_2659
<s, s>(q_gen_2683) -> q_gen_2683
<s, z>(q_gen_2660) -> q_gen_2683
<z, z>() -> q_gen_2683
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_2658, q_gen_2665, q_gen_2666, q_gen_2678, q_gen_2679, q_gen_2680, q_gen_2681, q_gen_2682},
Q_f={q_gen_2658},
Delta=
{
<nil>() -> q_gen_2665
<cons>(q_gen_2679, q_gen_2665) -> q_gen_2678
<cons>(q_gen_2679, q_gen_2678) -> q_gen_2678
<a>() -> q_gen_2679
<b>() -> q_gen_2679
<s>(q_gen_2681) -> q_gen_2681
<z>() -> q_gen_2681
<cons, s>(q_gen_2666, q_gen_2665) -> q_gen_2658
<cons, s>(q_gen_2680, q_gen_2678) -> q_gen_2658
<nil, z>() -> q_gen_2658
<a, z>() -> q_gen_2666
<b, z>() -> q_gen_2666
<a, s>(q_gen_2681) -> q_gen_2680
<b, s>(q_gen_2681) -> q_gen_2680
<cons, s>(q_gen_2666, q_gen_2678) -> q_gen_2682
<cons, s>(q_gen_2680, q_gen_2665) -> q_gen_2682
}

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

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

Teacher's answer:
New clause system:
{
() -> fcons([x, l, cons(x, l)]) -> 40
() -> le([z, s(nn2)]) -> 34
() -> length([nil, z]) -> 34
(fcons([x, l, _tk]) /\ length([_tk, _uk]) /\ length([l, _sk])) -> le([_sk, _uk]) -> 38
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 34
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 35
(le([s(nn1), z])) -> BOT -> 34
(le([z, z])) -> BOT -> 34
(length([ll, _kk])) -> length([cons(x, ll), s(_kk)]) -> 37
}
Sat witness: Found: (() -> fcons([x, l, cons(x, l)]), {
l -> cons(b, cons(b, cons(b, nil)))  ;  x -> b
})

-------------------------------------------
Step 41, which took 0.068686 s (model generation: 0.068648,  model checking: 0.000038):

Model:
|_
{
fcons -> 
{{{
Q={q_gen_2661, q_gen_2662, q_gen_2663, q_gen_2675, q_gen_2676},
Q_f={q_gen_2661},
Delta=
{
<nil>() -> q_gen_2662
<a>() -> q_gen_2663
<b>() -> q_gen_2663
<cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2675
<nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2675
<a, a>() -> q_gen_2676
<a, b>() -> q_gen_2676
<b, a>() -> q_gen_2676
<b, b>() -> q_gen_2676
<a, cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2661
<a, nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2661
<b, cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2661
<b, nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2661
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  le -> 
{{{
Q={q_gen_2659, q_gen_2660, q_gen_2669, q_gen_2683},
Q_f={q_gen_2659},
Delta=
{
<z>() -> q_gen_2660
<s>(q_gen_2660) -> q_gen_2669
<s, s>(q_gen_2659) -> q_gen_2659
<s, z>(q_gen_2669) -> q_gen_2659
<z, s>(q_gen_2660) -> q_gen_2659
<z, s>(q_gen_2669) -> q_gen_2659
<s, s>(q_gen_2683) -> q_gen_2683
<s, z>(q_gen_2660) -> q_gen_2683
<z, z>() -> q_gen_2683
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_2658, q_gen_2665, q_gen_2666, q_gen_2678, q_gen_2679, q_gen_2680, q_gen_2681, q_gen_2682, q_gen_2694, q_gen_2695, q_gen_2696, q_gen_2711},
Q_f={q_gen_2658},
Delta=
{
<cons>(q_gen_2679, q_gen_2694) -> q_gen_2665
<nil>() -> q_gen_2665
<cons>(q_gen_2679, q_gen_2665) -> q_gen_2678
<a>() -> q_gen_2679
<b>() -> q_gen_2679
<z>() -> q_gen_2681
<cons>(q_gen_2679, q_gen_2678) -> q_gen_2694
<s>(q_gen_2681) -> q_gen_2696
<s>(q_gen_2696) -> q_gen_2711
<cons, s>(q_gen_2666, q_gen_2665) -> q_gen_2658
<cons, s>(q_gen_2680, q_gen_2678) -> q_gen_2658
<cons, s>(q_gen_2695, q_gen_2694) -> q_gen_2658
<nil, z>() -> q_gen_2658
<a, s>(q_gen_2711) -> q_gen_2666
<a, z>() -> q_gen_2666
<b, s>(q_gen_2711) -> q_gen_2666
<b, z>() -> q_gen_2666
<a, s>(q_gen_2681) -> q_gen_2680
<b, s>(q_gen_2681) -> q_gen_2680
<cons, s>(q_gen_2666, q_gen_2678) -> q_gen_2682
<cons, s>(q_gen_2680, q_gen_2665) -> q_gen_2682
<cons, s>(q_gen_2680, q_gen_2694) -> q_gen_2682
<cons, s>(q_gen_2695, q_gen_2665) -> q_gen_2682
<a, s>(q_gen_2696) -> q_gen_2695
<b, s>(q_gen_2696) -> q_gen_2695
}

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

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

Teacher's answer:
New clause system:
{
() -> fcons([x, l, cons(x, l)]) -> 40
() -> le([z, s(nn2)]) -> 34
() -> length([nil, z]) -> 34
(fcons([x, l, _tk]) /\ length([_tk, _uk]) /\ length([l, _sk])) -> le([_sk, _uk]) -> 38
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 34
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 35
(le([s(nn1), z])) -> BOT -> 37
(le([z, z])) -> BOT -> 35
(length([ll, _kk])) -> length([cons(x, ll), s(_kk)]) -> 37
}
Sat witness: Found: ((le([s(nn1), z])) -> BOT, {
nn1 -> s(z)
})

-------------------------------------------
Step 42, which took 0.073759 s (model generation: 0.073293,  model checking: 0.000466):

Model:
|_
{
fcons -> 
{{{
Q={q_gen_2661, q_gen_2662, q_gen_2663, q_gen_2675, q_gen_2676},
Q_f={q_gen_2661},
Delta=
{
<nil>() -> q_gen_2662
<a>() -> q_gen_2663
<b>() -> q_gen_2663
<cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2675
<nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2675
<a, a>() -> q_gen_2676
<a, b>() -> q_gen_2676
<b, a>() -> q_gen_2676
<b, b>() -> q_gen_2676
<a, cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2661
<a, nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2661
<b, cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2661
<b, nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2661
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  le -> 
{{{
Q={q_gen_2659, q_gen_2660, q_gen_2683, q_gen_2684, q_gen_2698},
Q_f={q_gen_2659},
Delta=
{
<s>(q_gen_2660) -> q_gen_2660
<z>() -> q_gen_2660
<s, s>(q_gen_2659) -> q_gen_2659
<s, s>(q_gen_2698) -> q_gen_2659
<z, s>(q_gen_2660) -> q_gen_2659
<s, s>(q_gen_2684) -> q_gen_2683
<s, z>(q_gen_2660) -> q_gen_2684
<z, z>() -> q_gen_2684
<s, s>(q_gen_2683) -> q_gen_2698
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_2658, q_gen_2665, q_gen_2666, q_gen_2678, q_gen_2679, q_gen_2680, q_gen_2681, q_gen_2682, q_gen_2694, q_gen_2695, q_gen_2696},
Q_f={q_gen_2658},
Delta=
{
<nil>() -> q_gen_2665
<cons>(q_gen_2679, q_gen_2665) -> q_gen_2678
<a>() -> q_gen_2679
<b>() -> q_gen_2679
<z>() -> q_gen_2681
<cons>(q_gen_2679, q_gen_2678) -> q_gen_2694
<cons>(q_gen_2679, q_gen_2694) -> q_gen_2694
<s>(q_gen_2681) -> q_gen_2696
<s>(q_gen_2696) -> q_gen_2696
<cons, s>(q_gen_2666, q_gen_2665) -> q_gen_2658
<cons, s>(q_gen_2680, q_gen_2678) -> q_gen_2658
<cons, s>(q_gen_2695, q_gen_2694) -> q_gen_2658
<nil, z>() -> q_gen_2658
<a, z>() -> q_gen_2666
<b, z>() -> q_gen_2666
<a, s>(q_gen_2681) -> q_gen_2680
<b, s>(q_gen_2681) -> q_gen_2680
<cons, s>(q_gen_2666, q_gen_2678) -> q_gen_2682
<cons, s>(q_gen_2680, q_gen_2665) -> q_gen_2682
<cons, s>(q_gen_2680, q_gen_2694) -> q_gen_2682
<cons, s>(q_gen_2695, q_gen_2665) -> q_gen_2682
<cons, s>(q_gen_2695, q_gen_2678) -> q_gen_2682
<a, s>(q_gen_2696) -> q_gen_2695
<b, s>(q_gen_2696) -> q_gen_2695
}

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

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

Teacher's answer:
New clause system:
{
() -> fcons([x, l, cons(x, l)]) -> 40
() -> le([z, s(nn2)]) -> 35
() -> length([nil, z]) -> 35
(fcons([x, l, _tk]) /\ length([_tk, _uk]) /\ length([l, _sk])) -> le([_sk, _uk]) -> 38
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 35
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 38
(le([s(nn1), z])) -> BOT -> 37
(le([z, z])) -> BOT -> 36
(length([ll, _kk])) -> length([cons(x, ll), s(_kk)]) -> 37
}
Sat witness: Found: ((le([s(nn1), s(nn2)])) -> le([nn1, nn2]), {
nn1 -> s(s(z))  ;  nn2 -> s(s(z))
})

-------------------------------------------
Step 43, which took 0.070836 s (model generation: 0.067932,  model checking: 0.002904):

Model:
|_
{
fcons -> 
{{{
Q={q_gen_2661, q_gen_2662, q_gen_2663, q_gen_2675, q_gen_2676, q_gen_2686, q_gen_2733},
Q_f={q_gen_2661},
Delta=
{
<nil>() -> q_gen_2662
<a>() -> q_gen_2663
<b>() -> q_gen_2663
<cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2675
<cons, cons>(q_gen_2686, q_gen_2675) -> q_gen_2675
<nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2675
<a, a>() -> q_gen_2676
<b, a>() -> q_gen_2676
<a, b>() -> q_gen_2686
<b, b>() -> q_gen_2686
<a, cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2661
<a, nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2661
<b, cons, cons>(q_gen_2686, q_gen_2675) -> q_gen_2661
<b, nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2661
<a, cons, cons>(q_gen_2686, q_gen_2675) -> q_gen_2733
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  le -> 
{{{
Q={q_gen_2659, q_gen_2660, q_gen_2683},
Q_f={q_gen_2659},
Delta=
{
<s>(q_gen_2660) -> q_gen_2660
<z>() -> q_gen_2660
<s, s>(q_gen_2659) -> q_gen_2659
<z, s>(q_gen_2660) -> q_gen_2659
<s, s>(q_gen_2683) -> q_gen_2683
<s, z>(q_gen_2660) -> q_gen_2683
<z, z>() -> q_gen_2683
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_2658, q_gen_2665, q_gen_2666, q_gen_2678, q_gen_2679, q_gen_2680, q_gen_2681, q_gen_2682, q_gen_2694, q_gen_2695, q_gen_2696},
Q_f={q_gen_2658},
Delta=
{
<nil>() -> q_gen_2665
<cons>(q_gen_2679, q_gen_2665) -> q_gen_2678
<cons>(q_gen_2679, q_gen_2694) -> q_gen_2678
<a>() -> q_gen_2679
<b>() -> q_gen_2679
<s>(q_gen_2696) -> q_gen_2681
<z>() -> q_gen_2681
<cons>(q_gen_2679, q_gen_2678) -> q_gen_2694
<s>(q_gen_2681) -> q_gen_2696
<cons, s>(q_gen_2666, q_gen_2665) -> q_gen_2658
<cons, s>(q_gen_2680, q_gen_2678) -> q_gen_2658
<cons, s>(q_gen_2695, q_gen_2694) -> q_gen_2658
<nil, z>() -> q_gen_2658
<a, s>(q_gen_2696) -> q_gen_2666
<a, z>() -> q_gen_2666
<b, z>() -> q_gen_2666
<a, s>(q_gen_2681) -> q_gen_2680
<b, s>(q_gen_2681) -> q_gen_2680
<cons, s>(q_gen_2666, q_gen_2678) -> q_gen_2682
<cons, s>(q_gen_2680, q_gen_2665) -> q_gen_2682
<cons, s>(q_gen_2680, q_gen_2694) -> q_gen_2682
<cons, s>(q_gen_2695, q_gen_2665) -> q_gen_2682
<cons, s>(q_gen_2695, q_gen_2678) -> q_gen_2682
<b, s>(q_gen_2696) -> q_gen_2695
}

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

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

Teacher's answer:
New clause system:
{
() -> fcons([x, l, cons(x, l)]) -> 40
() -> le([z, s(nn2)]) -> 36
() -> length([nil, z]) -> 36
(fcons([x, l, _tk]) /\ length([_tk, _uk]) /\ length([l, _sk])) -> le([_sk, _uk]) -> 38
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 36
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 38
(le([s(nn1), z])) -> BOT -> 37
(le([z, z])) -> BOT -> 37
(length([ll, _kk])) -> length([cons(x, ll), s(_kk)]) -> 40
}
Sat witness: Found: ((length([ll, _kk])) -> length([cons(x, ll), s(_kk)]), {
_kk -> s(s(z))  ;  ll -> cons(a, cons(b, nil))  ;  x -> a
})

-------------------------------------------
Step 44, which took 0.075056 s (model generation: 0.072323,  model checking: 0.002733):

Model:
|_
{
fcons -> 
{{{
Q={q_gen_2661, q_gen_2662, q_gen_2663, q_gen_2675, q_gen_2676, q_gen_2686, q_gen_2733},
Q_f={q_gen_2661},
Delta=
{
<nil>() -> q_gen_2662
<a>() -> q_gen_2663
<b>() -> q_gen_2663
<cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2675
<cons, cons>(q_gen_2686, q_gen_2675) -> q_gen_2675
<nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2675
<a, a>() -> q_gen_2676
<b, a>() -> q_gen_2676
<a, b>() -> q_gen_2686
<b, b>() -> q_gen_2686
<a, cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2661
<a, nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2661
<b, cons, cons>(q_gen_2686, q_gen_2675) -> q_gen_2661
<b, nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2661
<a, cons, cons>(q_gen_2686, q_gen_2675) -> q_gen_2733
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  le -> 
{{{
Q={q_gen_2659, q_gen_2660, q_gen_2683},
Q_f={q_gen_2659},
Delta=
{
<s>(q_gen_2660) -> q_gen_2660
<z>() -> q_gen_2660
<s, s>(q_gen_2659) -> q_gen_2659
<z, s>(q_gen_2660) -> q_gen_2659
<s, s>(q_gen_2683) -> q_gen_2683
<s, z>(q_gen_2660) -> q_gen_2683
<z, z>() -> q_gen_2683
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_2658, q_gen_2665, q_gen_2666, q_gen_2678, q_gen_2679, q_gen_2680, q_gen_2681, q_gen_2682, q_gen_2694, q_gen_2695, q_gen_2696},
Q_f={q_gen_2658},
Delta=
{
<nil>() -> q_gen_2665
<cons>(q_gen_2679, q_gen_2665) -> q_gen_2678
<cons>(q_gen_2679, q_gen_2694) -> q_gen_2678
<a>() -> q_gen_2679
<b>() -> q_gen_2679
<s>(q_gen_2696) -> q_gen_2681
<z>() -> q_gen_2681
<cons>(q_gen_2679, q_gen_2678) -> q_gen_2694
<s>(q_gen_2681) -> q_gen_2696
<cons, s>(q_gen_2666, q_gen_2665) -> q_gen_2658
<cons, s>(q_gen_2666, q_gen_2694) -> q_gen_2658
<cons, s>(q_gen_2680, q_gen_2678) -> q_gen_2658
<cons, s>(q_gen_2695, q_gen_2694) -> q_gen_2658
<nil, z>() -> q_gen_2658
<a, s>(q_gen_2696) -> q_gen_2666
<a, z>() -> q_gen_2666
<b, z>() -> q_gen_2666
<a, s>(q_gen_2681) -> q_gen_2680
<b, s>(q_gen_2681) -> q_gen_2680
<cons, s>(q_gen_2666, q_gen_2678) -> q_gen_2682
<cons, s>(q_gen_2680, q_gen_2665) -> q_gen_2682
<cons, s>(q_gen_2680, q_gen_2694) -> q_gen_2682
<cons, s>(q_gen_2695, q_gen_2665) -> q_gen_2682
<cons, s>(q_gen_2695, q_gen_2678) -> q_gen_2682
<b, s>(q_gen_2696) -> q_gen_2695
}

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

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

Teacher's answer:
New clause system:
{
() -> fcons([x, l, cons(x, l)]) -> 40
() -> le([z, s(nn2)]) -> 37
() -> length([nil, z]) -> 37
(fcons([x, l, _tk]) /\ length([_tk, _uk]) /\ length([l, _sk])) -> le([_sk, _uk]) -> 41
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 37
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 39
(le([s(nn1), z])) -> BOT -> 38
(le([z, z])) -> BOT -> 38
(length([ll, _kk])) -> length([cons(x, ll), s(_kk)]) -> 40
}
Sat witness: Found: ((fcons([x, l, _tk]) /\ length([_tk, _uk]) /\ length([l, _sk])) -> le([_sk, _uk]), {
_sk -> s(s(s(z)))  ;  _tk -> cons(a, cons(a, cons(a, cons(b, nil))))  ;  _uk -> s(s(z))  ;  l -> cons(b, cons(b, cons(b, nil)))  ;  x -> a
})

-------------------------------------------
Step 45, which took 0.084772 s (model generation: 0.081336,  model checking: 0.003436):

Model:
|_
{
fcons -> 
{{{
Q={q_gen_2661, q_gen_2662, q_gen_2663, q_gen_2675, q_gen_2676, q_gen_2704, q_gen_2718, q_gen_2733},
Q_f={q_gen_2661},
Delta=
{
<nil>() -> q_gen_2662
<a>() -> q_gen_2663
<b>() -> q_gen_2663
<nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2675
<a, a>() -> q_gen_2676
<a, b>() -> q_gen_2676
<b, a>() -> q_gen_2676
<b, b>() -> q_gen_2676
<cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2704
<cons, cons>(q_gen_2676, q_gen_2704) -> q_gen_2718
<a, cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2661
<a, cons, cons>(q_gen_2676, q_gen_2704) -> q_gen_2661
<a, nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2661
<b, cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2661
<b, cons, cons>(q_gen_2676, q_gen_2704) -> q_gen_2661
<b, cons, cons>(q_gen_2676, q_gen_2718) -> q_gen_2661
<b, nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2661
<a, cons, cons>(q_gen_2676, q_gen_2718) -> q_gen_2733
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  le -> 
{{{
Q={q_gen_2659, q_gen_2660, q_gen_2683},
Q_f={q_gen_2659},
Delta=
{
<s>(q_gen_2660) -> q_gen_2660
<z>() -> q_gen_2660
<s, s>(q_gen_2659) -> q_gen_2659
<z, s>(q_gen_2660) -> q_gen_2659
<s, s>(q_gen_2683) -> q_gen_2683
<s, z>(q_gen_2660) -> q_gen_2683
<z, z>() -> q_gen_2683
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_2658, q_gen_2665, q_gen_2666, q_gen_2678, q_gen_2679, q_gen_2680, q_gen_2681, q_gen_2682, q_gen_2694, q_gen_2695, q_gen_2696},
Q_f={q_gen_2658},
Delta=
{
<nil>() -> q_gen_2665
<cons>(q_gen_2679, q_gen_2665) -> q_gen_2678
<cons>(q_gen_2679, q_gen_2694) -> q_gen_2678
<a>() -> q_gen_2679
<b>() -> q_gen_2679
<s>(q_gen_2696) -> q_gen_2681
<z>() -> q_gen_2681
<cons>(q_gen_2679, q_gen_2678) -> q_gen_2694
<s>(q_gen_2681) -> q_gen_2696
<cons, s>(q_gen_2666, q_gen_2665) -> q_gen_2658
<cons, s>(q_gen_2666, q_gen_2694) -> q_gen_2658
<cons, s>(q_gen_2680, q_gen_2678) -> q_gen_2658
<cons, s>(q_gen_2695, q_gen_2694) -> q_gen_2658
<nil, z>() -> q_gen_2658
<a, s>(q_gen_2696) -> q_gen_2666
<a, z>() -> q_gen_2666
<b, z>() -> q_gen_2666
<a, s>(q_gen_2681) -> q_gen_2680
<b, s>(q_gen_2681) -> q_gen_2680
<cons, s>(q_gen_2666, q_gen_2678) -> q_gen_2682
<cons, s>(q_gen_2680, q_gen_2665) -> q_gen_2682
<cons, s>(q_gen_2680, q_gen_2694) -> q_gen_2682
<cons, s>(q_gen_2695, q_gen_2665) -> q_gen_2682
<cons, s>(q_gen_2695, q_gen_2678) -> q_gen_2682
<b, s>(q_gen_2696) -> q_gen_2695
}

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

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

Teacher's answer:
New clause system:
{
() -> fcons([x, l, cons(x, l)]) -> 43
() -> le([z, s(nn2)]) -> 38
() -> length([nil, z]) -> 38
(fcons([x, l, _tk]) /\ length([_tk, _uk]) /\ length([l, _sk])) -> le([_sk, _uk]) -> 41
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 38
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 40
(le([s(nn1), z])) -> BOT -> 39
(le([z, z])) -> BOT -> 39
(length([ll, _kk])) -> length([cons(x, ll), s(_kk)]) -> 41
}
Sat witness: Found: (() -> fcons([x, l, cons(x, l)]), {
l -> cons(b, cons(a, cons(a, nil)))  ;  x -> a
})

-------------------------------------------
Step 46, which took 0.082267 s (model generation: 0.081428,  model checking: 0.000839):

Model:
|_
{
fcons -> 
{{{
Q={q_gen_2661, q_gen_2662, q_gen_2663, q_gen_2675, q_gen_2676},
Q_f={q_gen_2661},
Delta=
{
<nil>() -> q_gen_2662
<a>() -> q_gen_2663
<b>() -> q_gen_2663
<cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2675
<nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2675
<a, a>() -> q_gen_2676
<a, b>() -> q_gen_2676
<b, a>() -> q_gen_2676
<b, b>() -> q_gen_2676
<a, cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2661
<a, nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2661
<b, cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2661
<b, nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2661
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  le -> 
{{{
Q={q_gen_2659, q_gen_2660, q_gen_2669, q_gen_2683, q_gen_2745},
Q_f={q_gen_2659},
Delta=
{
<z>() -> q_gen_2660
<s>(q_gen_2660) -> q_gen_2669
<s, s>(q_gen_2659) -> q_gen_2659
<s, s>(q_gen_2745) -> q_gen_2659
<z, s>(q_gen_2660) -> q_gen_2659
<z, s>(q_gen_2669) -> q_gen_2659
<s, s>(q_gen_2683) -> q_gen_2683
<s, z>(q_gen_2660) -> q_gen_2683
<z, z>() -> q_gen_2683
<s, z>(q_gen_2669) -> q_gen_2745
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_2658, q_gen_2665, q_gen_2666, q_gen_2678, q_gen_2679, q_gen_2680, q_gen_2681, q_gen_2682, q_gen_2694, q_gen_2695, q_gen_2696, q_gen_2711},
Q_f={q_gen_2658},
Delta=
{
<cons>(q_gen_2679, q_gen_2694) -> q_gen_2665
<nil>() -> q_gen_2665
<cons>(q_gen_2679, q_gen_2665) -> q_gen_2678
<a>() -> q_gen_2679
<b>() -> q_gen_2679
<z>() -> q_gen_2681
<cons>(q_gen_2679, q_gen_2678) -> q_gen_2694
<s>(q_gen_2681) -> q_gen_2696
<s>(q_gen_2696) -> q_gen_2711
<cons, s>(q_gen_2666, q_gen_2665) -> q_gen_2658
<cons, s>(q_gen_2680, q_gen_2678) -> q_gen_2658
<cons, s>(q_gen_2695, q_gen_2694) -> q_gen_2658
<nil, z>() -> q_gen_2658
<a, s>(q_gen_2711) -> q_gen_2666
<a, z>() -> q_gen_2666
<b, s>(q_gen_2711) -> q_gen_2666
<b, z>() -> q_gen_2666
<a, s>(q_gen_2681) -> q_gen_2680
<b, s>(q_gen_2681) -> q_gen_2680
<cons, s>(q_gen_2666, q_gen_2678) -> q_gen_2682
<cons, s>(q_gen_2680, q_gen_2665) -> q_gen_2682
<cons, s>(q_gen_2680, q_gen_2694) -> q_gen_2682
<cons, s>(q_gen_2695, q_gen_2665) -> q_gen_2682
<a, s>(q_gen_2696) -> q_gen_2695
<b, s>(q_gen_2696) -> q_gen_2695
}

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

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

Teacher's answer:
New clause system:
{
() -> fcons([x, l, cons(x, l)]) -> 43
() -> le([z, s(nn2)]) -> 41
() -> length([nil, z]) -> 39
(fcons([x, l, _tk]) /\ length([_tk, _uk]) /\ length([l, _sk])) -> le([_sk, _uk]) -> 41
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 39
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 40
(le([s(nn1), z])) -> BOT -> 39
(le([z, z])) -> BOT -> 39
(length([ll, _kk])) -> length([cons(x, ll), s(_kk)]) -> 41
}
Sat witness: Found: (() -> le([z, s(nn2)]), {
nn2 -> s(s(z))
})

-------------------------------------------
Step 47, which took 0.096787 s (model generation: 0.086411,  model checking: 0.010376):

Model:
|_
{
fcons -> 
{{{
Q={q_gen_2661, q_gen_2662, q_gen_2663, q_gen_2675, q_gen_2676, q_gen_2692, q_gen_2704, q_gen_2723},
Q_f={q_gen_2661},
Delta=
{
<nil>() -> q_gen_2662
<a>() -> q_gen_2663
<b>() -> q_gen_2663
<cons, cons>(q_gen_2692, q_gen_2675) -> q_gen_2675
<nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2675
<b, a>() -> q_gen_2676
<b, b>() -> q_gen_2676
<a, a>() -> q_gen_2692
<a, b>() -> q_gen_2692
<cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2704
<cons, cons>(q_gen_2676, q_gen_2704) -> q_gen_2704
<a, cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2661
<a, cons, cons>(q_gen_2692, q_gen_2675) -> q_gen_2661
<a, cons, cons>(q_gen_2692, q_gen_2704) -> q_gen_2661
<a, nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2661
<b, cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2661
<b, cons, cons>(q_gen_2676, q_gen_2704) -> q_gen_2661
<b, cons, cons>(q_gen_2692, q_gen_2675) -> q_gen_2661
<b, nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2661
<a, cons, cons>(q_gen_2676, q_gen_2704) -> q_gen_2723
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  le -> 
{{{
Q={q_gen_2659, q_gen_2660, q_gen_2683},
Q_f={q_gen_2659},
Delta=
{
<s>(q_gen_2660) -> q_gen_2660
<z>() -> q_gen_2660
<s, s>(q_gen_2659) -> q_gen_2659
<z, s>(q_gen_2660) -> q_gen_2659
<s, s>(q_gen_2683) -> q_gen_2683
<s, z>(q_gen_2660) -> q_gen_2683
<z, z>() -> q_gen_2683
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_2658, q_gen_2665, q_gen_2666, q_gen_2678, q_gen_2679, q_gen_2680, q_gen_2681, q_gen_2682, q_gen_2694, q_gen_2695, q_gen_2696},
Q_f={q_gen_2658},
Delta=
{
<nil>() -> q_gen_2665
<cons>(q_gen_2679, q_gen_2665) -> q_gen_2678
<cons>(q_gen_2679, q_gen_2694) -> q_gen_2678
<a>() -> q_gen_2679
<b>() -> q_gen_2679
<s>(q_gen_2696) -> q_gen_2681
<z>() -> q_gen_2681
<cons>(q_gen_2679, q_gen_2678) -> q_gen_2694
<s>(q_gen_2681) -> q_gen_2696
<cons, s>(q_gen_2666, q_gen_2665) -> q_gen_2658
<cons, s>(q_gen_2666, q_gen_2694) -> q_gen_2658
<cons, s>(q_gen_2680, q_gen_2678) -> q_gen_2658
<cons, s>(q_gen_2695, q_gen_2694) -> q_gen_2658
<nil, z>() -> q_gen_2658
<a, s>(q_gen_2696) -> q_gen_2666
<a, z>() -> q_gen_2666
<b, z>() -> q_gen_2666
<a, s>(q_gen_2681) -> q_gen_2680
<b, s>(q_gen_2681) -> q_gen_2680
<cons, s>(q_gen_2666, q_gen_2678) -> q_gen_2682
<cons, s>(q_gen_2680, q_gen_2665) -> q_gen_2682
<cons, s>(q_gen_2680, q_gen_2694) -> q_gen_2682
<cons, s>(q_gen_2695, q_gen_2665) -> q_gen_2682
<cons, s>(q_gen_2695, q_gen_2678) -> q_gen_2682
<b, s>(q_gen_2696) -> q_gen_2695
}

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

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

Teacher's answer:
New clause system:
{
() -> fcons([x, l, cons(x, l)]) -> 43
() -> le([z, s(nn2)]) -> 41
() -> length([nil, z]) -> 40
(fcons([x, l, _tk]) /\ length([_tk, _uk]) /\ length([l, _sk])) -> le([_sk, _uk]) -> 44
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 40
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 41
(le([s(nn1), z])) -> BOT -> 40
(le([z, z])) -> BOT -> 40
(length([ll, _kk])) -> length([cons(x, ll), s(_kk)]) -> 42
}
Sat witness: Found: ((fcons([x, l, _tk]) /\ length([_tk, _uk]) /\ length([l, _sk])) -> le([_sk, _uk]), {
_sk -> s(s(s(z)))  ;  _tk -> cons(a, cons(b, nil))  ;  _uk -> s(s(z))  ;  l -> cons(a, nil)  ;  x -> a
})

-------------------------------------------
Step 48, which took 0.083471 s (model generation: 0.082944,  model checking: 0.000527):

Model:
|_
{
fcons -> 
{{{
Q={q_gen_2661, q_gen_2662, q_gen_2663, q_gen_2675, q_gen_2676},
Q_f={q_gen_2661},
Delta=
{
<nil>() -> q_gen_2662
<a>() -> q_gen_2663
<b>() -> q_gen_2663
<cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2675
<nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2675
<a, a>() -> q_gen_2676
<a, b>() -> q_gen_2676
<b, a>() -> q_gen_2676
<b, b>() -> q_gen_2676
<a, cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2661
<a, nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2661
<b, cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2661
<b, nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2661
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  le -> 
{{{
Q={q_gen_2659, q_gen_2660, q_gen_2669, q_gen_2683, q_gen_2745},
Q_f={q_gen_2659},
Delta=
{
<z>() -> q_gen_2660
<s>(q_gen_2660) -> q_gen_2669
<s>(q_gen_2669) -> q_gen_2669
<s, s>(q_gen_2659) -> q_gen_2659
<s, s>(q_gen_2745) -> q_gen_2659
<z, s>(q_gen_2660) -> q_gen_2659
<z, s>(q_gen_2669) -> q_gen_2659
<s, s>(q_gen_2683) -> q_gen_2683
<s, z>(q_gen_2660) -> q_gen_2683
<z, z>() -> q_gen_2683
<s, z>(q_gen_2669) -> q_gen_2745
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_2658, q_gen_2665, q_gen_2666, q_gen_2678, q_gen_2679, q_gen_2680, q_gen_2681, q_gen_2682, q_gen_2694, q_gen_2695, q_gen_2696, q_gen_2711},
Q_f={q_gen_2658},
Delta=
{
<cons>(q_gen_2679, q_gen_2694) -> q_gen_2665
<nil>() -> q_gen_2665
<cons>(q_gen_2679, q_gen_2665) -> q_gen_2678
<a>() -> q_gen_2679
<b>() -> q_gen_2679
<z>() -> q_gen_2681
<cons>(q_gen_2679, q_gen_2678) -> q_gen_2694
<s>(q_gen_2681) -> q_gen_2696
<s>(q_gen_2696) -> q_gen_2711
<cons, s>(q_gen_2666, q_gen_2665) -> q_gen_2658
<cons, s>(q_gen_2680, q_gen_2678) -> q_gen_2658
<cons, s>(q_gen_2695, q_gen_2694) -> q_gen_2658
<nil, z>() -> q_gen_2658
<a, s>(q_gen_2711) -> q_gen_2666
<a, z>() -> q_gen_2666
<b, s>(q_gen_2711) -> q_gen_2666
<b, z>() -> q_gen_2666
<a, s>(q_gen_2681) -> q_gen_2680
<b, s>(q_gen_2681) -> q_gen_2680
<cons, s>(q_gen_2666, q_gen_2678) -> q_gen_2682
<cons, s>(q_gen_2680, q_gen_2665) -> q_gen_2682
<cons, s>(q_gen_2680, q_gen_2694) -> q_gen_2682
<cons, s>(q_gen_2695, q_gen_2665) -> q_gen_2682
<a, s>(q_gen_2696) -> q_gen_2695
<b, s>(q_gen_2696) -> q_gen_2695
}

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

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

Teacher's answer:
New clause system:
{
() -> fcons([x, l, cons(x, l)]) -> 43
() -> le([z, s(nn2)]) -> 41
() -> length([nil, z]) -> 41
(fcons([x, l, _tk]) /\ length([_tk, _uk]) /\ length([l, _sk])) -> le([_sk, _uk]) -> 44
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 41
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 44
(le([s(nn1), z])) -> BOT -> 41
(le([z, z])) -> BOT -> 41
(length([ll, _kk])) -> length([cons(x, ll), s(_kk)]) -> 42
}
Sat witness: Found: ((le([s(nn1), s(nn2)])) -> le([nn1, nn2]), {
nn1 -> s(s(z))  ;  nn2 -> z
})

-------------------------------------------
Step 49, which took 0.086595 s (model generation: 0.081724,  model checking: 0.004871):

Model:
|_
{
fcons -> 
{{{
Q={q_gen_2661, q_gen_2662, q_gen_2663, q_gen_2675, q_gen_2676, q_gen_2686, q_gen_2733},
Q_f={q_gen_2661},
Delta=
{
<nil>() -> q_gen_2662
<a>() -> q_gen_2663
<b>() -> q_gen_2663
<cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2675
<cons, cons>(q_gen_2686, q_gen_2675) -> q_gen_2675
<nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2675
<a, a>() -> q_gen_2676
<b, a>() -> q_gen_2676
<a, b>() -> q_gen_2686
<b, b>() -> q_gen_2686
<a, cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2661
<a, nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2661
<b, cons, cons>(q_gen_2686, q_gen_2675) -> q_gen_2661
<b, nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2661
<a, cons, cons>(q_gen_2686, q_gen_2675) -> q_gen_2733
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  le -> 
{{{
Q={q_gen_2659, q_gen_2660, q_gen_2683},
Q_f={q_gen_2659},
Delta=
{
<s>(q_gen_2660) -> q_gen_2660
<z>() -> q_gen_2660
<s, s>(q_gen_2659) -> q_gen_2659
<z, s>(q_gen_2660) -> q_gen_2659
<s, s>(q_gen_2683) -> q_gen_2683
<s, z>(q_gen_2660) -> q_gen_2683
<z, z>() -> q_gen_2683
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_2658, q_gen_2665, q_gen_2666, q_gen_2678, q_gen_2679, q_gen_2680, q_gen_2681, q_gen_2682, q_gen_2694, q_gen_2695, q_gen_2696, q_gen_2711},
Q_f={q_gen_2658},
Delta=
{
<cons>(q_gen_2679, q_gen_2694) -> q_gen_2665
<nil>() -> q_gen_2665
<cons>(q_gen_2679, q_gen_2665) -> q_gen_2678
<a>() -> q_gen_2679
<b>() -> q_gen_2679
<z>() -> q_gen_2681
<cons>(q_gen_2679, q_gen_2678) -> q_gen_2694
<s>(q_gen_2681) -> q_gen_2696
<s>(q_gen_2696) -> q_gen_2711
<cons, s>(q_gen_2666, q_gen_2665) -> q_gen_2658
<cons, s>(q_gen_2680, q_gen_2678) -> q_gen_2658
<cons, s>(q_gen_2695, q_gen_2694) -> q_gen_2658
<nil, z>() -> q_gen_2658
<a, s>(q_gen_2711) -> q_gen_2666
<a, z>() -> q_gen_2666
<b, s>(q_gen_2711) -> q_gen_2666
<b, z>() -> q_gen_2666
<a, s>(q_gen_2681) -> q_gen_2680
<b, s>(q_gen_2681) -> q_gen_2680
<cons, s>(q_gen_2666, q_gen_2678) -> q_gen_2682
<cons, s>(q_gen_2680, q_gen_2665) -> q_gen_2682
<cons, s>(q_gen_2680, q_gen_2694) -> q_gen_2682
<cons, s>(q_gen_2695, q_gen_2665) -> q_gen_2682
<a, s>(q_gen_2696) -> q_gen_2695
<b, s>(q_gen_2696) -> q_gen_2695
}

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

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

Teacher's answer:
New clause system:
{
() -> fcons([x, l, cons(x, l)]) -> 43
() -> le([z, s(nn2)]) -> 42
() -> length([nil, z]) -> 42
(fcons([x, l, _tk]) /\ length([_tk, _uk]) /\ length([l, _sk])) -> le([_sk, _uk]) -> 44
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 42
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 44
(le([s(nn1), z])) -> BOT -> 42
(le([z, z])) -> BOT -> 42
(length([ll, _kk])) -> length([cons(x, ll), s(_kk)]) -> 45
}
Sat witness: Found: ((length([ll, _kk])) -> length([cons(x, ll), s(_kk)]), {
_kk -> s(s(s(s(z))))  ;  ll -> cons(a, nil)  ;  x -> b
})

-------------------------------------------
Step 50, which took 0.096790 s (model generation: 0.095835,  model checking: 0.000955):

Model:
|_
{
fcons -> 
{{{
Q={q_gen_2661, q_gen_2662, q_gen_2663, q_gen_2675, q_gen_2676, q_gen_2692, q_gen_2704, q_gen_2723},
Q_f={q_gen_2661},
Delta=
{
<nil>() -> q_gen_2662
<a>() -> q_gen_2663
<b>() -> q_gen_2663
<cons, cons>(q_gen_2692, q_gen_2675) -> q_gen_2675
<nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2675
<b, a>() -> q_gen_2676
<b, b>() -> q_gen_2676
<a, a>() -> q_gen_2692
<a, b>() -> q_gen_2692
<cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2704
<cons, cons>(q_gen_2676, q_gen_2704) -> q_gen_2704
<a, cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2661
<a, cons, cons>(q_gen_2692, q_gen_2675) -> q_gen_2661
<a, cons, cons>(q_gen_2692, q_gen_2704) -> q_gen_2661
<a, nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2661
<b, cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2661
<b, cons, cons>(q_gen_2676, q_gen_2704) -> q_gen_2661
<b, cons, cons>(q_gen_2692, q_gen_2675) -> q_gen_2661
<b, nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2661
<a, cons, cons>(q_gen_2676, q_gen_2704) -> q_gen_2723
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  le -> 
{{{
Q={q_gen_2659, q_gen_2660, q_gen_2683},
Q_f={q_gen_2659},
Delta=
{
<s>(q_gen_2660) -> q_gen_2660
<z>() -> q_gen_2660
<s, s>(q_gen_2659) -> q_gen_2659
<z, s>(q_gen_2660) -> q_gen_2659
<s, s>(q_gen_2683) -> q_gen_2683
<s, z>(q_gen_2660) -> q_gen_2683
<z, z>() -> q_gen_2683
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_2658, q_gen_2665, q_gen_2666, q_gen_2678, q_gen_2679, q_gen_2680, q_gen_2681, q_gen_2682, q_gen_2694, q_gen_2695, q_gen_2696},
Q_f={q_gen_2658},
Delta=
{
<nil>() -> q_gen_2665
<cons>(q_gen_2679, q_gen_2665) -> q_gen_2678
<cons>(q_gen_2679, q_gen_2694) -> q_gen_2678
<a>() -> q_gen_2679
<b>() -> q_gen_2679
<s>(q_gen_2696) -> q_gen_2681
<z>() -> q_gen_2681
<cons>(q_gen_2679, q_gen_2678) -> q_gen_2694
<s>(q_gen_2681) -> q_gen_2696
<cons, s>(q_gen_2666, q_gen_2665) -> q_gen_2658
<cons, s>(q_gen_2680, q_gen_2678) -> q_gen_2658
<cons, s>(q_gen_2695, q_gen_2694) -> q_gen_2658
<nil, z>() -> q_gen_2658
<a, z>() -> q_gen_2666
<b, z>() -> q_gen_2666
<a, s>(q_gen_2681) -> q_gen_2680
<b, s>(q_gen_2681) -> q_gen_2680
<cons, s>(q_gen_2666, q_gen_2678) -> q_gen_2682
<cons, s>(q_gen_2680, q_gen_2665) -> q_gen_2682
<cons, s>(q_gen_2680, q_gen_2694) -> q_gen_2682
<cons, s>(q_gen_2695, q_gen_2665) -> q_gen_2682
<cons, s>(q_gen_2695, q_gen_2678) -> q_gen_2682
<a, s>(q_gen_2696) -> q_gen_2695
<b, s>(q_gen_2696) -> q_gen_2695
}

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

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

Teacher's answer:
New clause system:
{
() -> fcons([x, l, cons(x, l)]) -> 46
() -> le([z, s(nn2)]) -> 43
() -> length([nil, z]) -> 43
(fcons([x, l, _tk]) /\ length([_tk, _uk]) /\ length([l, _sk])) -> le([_sk, _uk]) -> 44
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 43
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 44
(le([s(nn1), z])) -> BOT -> 43
(le([z, z])) -> BOT -> 43
(length([ll, _kk])) -> length([cons(x, ll), s(_kk)]) -> 45
}
Sat witness: Found: (() -> fcons([x, l, cons(x, l)]), {
l -> cons(b, cons(b, nil))  ;  x -> a
})

-------------------------------------------
Step 51, which took 0.104074 s (model generation: 0.098374,  model checking: 0.005700):

Model:
|_
{
fcons -> 
{{{
Q={q_gen_2661, q_gen_2662, q_gen_2663, q_gen_2675, q_gen_2676},
Q_f={q_gen_2661},
Delta=
{
<nil>() -> q_gen_2662
<a>() -> q_gen_2663
<b>() -> q_gen_2663
<cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2675
<nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2675
<a, a>() -> q_gen_2676
<a, b>() -> q_gen_2676
<b, a>() -> q_gen_2676
<b, b>() -> q_gen_2676
<a, cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2661
<a, nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2661
<b, cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2661
<b, nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2661
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  le -> 
{{{
Q={q_gen_2659, q_gen_2660, q_gen_2683},
Q_f={q_gen_2659},
Delta=
{
<s>(q_gen_2660) -> q_gen_2660
<z>() -> q_gen_2660
<s, s>(q_gen_2659) -> q_gen_2659
<z, s>(q_gen_2660) -> q_gen_2659
<s, s>(q_gen_2683) -> q_gen_2683
<s, z>(q_gen_2660) -> q_gen_2683
<z, z>() -> q_gen_2683
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_2658, q_gen_2665, q_gen_2666, q_gen_2678, q_gen_2679, q_gen_2680, q_gen_2681, q_gen_2682, q_gen_2694, q_gen_2695, q_gen_2696, q_gen_2709, q_gen_2710, q_gen_2711},
Q_f={q_gen_2658},
Delta=
{
<nil>() -> q_gen_2665
<cons>(q_gen_2679, q_gen_2665) -> q_gen_2678
<a>() -> q_gen_2679
<b>() -> q_gen_2679
<z>() -> q_gen_2681
<cons>(q_gen_2679, q_gen_2678) -> q_gen_2694
<s>(q_gen_2681) -> q_gen_2696
<cons>(q_gen_2679, q_gen_2694) -> q_gen_2709
<s>(q_gen_2696) -> q_gen_2711
<s>(q_gen_2711) -> q_gen_2711
<cons, s>(q_gen_2666, q_gen_2665) -> q_gen_2658
<cons, s>(q_gen_2666, q_gen_2709) -> q_gen_2658
<cons, s>(q_gen_2680, q_gen_2678) -> q_gen_2658
<cons, s>(q_gen_2695, q_gen_2694) -> q_gen_2658
<cons, s>(q_gen_2710, q_gen_2678) -> q_gen_2658
<cons, s>(q_gen_2710, q_gen_2709) -> q_gen_2658
<nil, z>() -> q_gen_2658
<a, s>(q_gen_2711) -> q_gen_2666
<a, z>() -> q_gen_2666
<b, z>() -> q_gen_2666
<a, s>(q_gen_2681) -> q_gen_2680
<b, s>(q_gen_2681) -> q_gen_2680
<cons, s>(q_gen_2666, q_gen_2678) -> q_gen_2682
<cons, s>(q_gen_2680, q_gen_2665) -> q_gen_2682
<cons, s>(q_gen_2680, q_gen_2694) -> q_gen_2682
<cons, s>(q_gen_2680, q_gen_2709) -> q_gen_2682
<cons, s>(q_gen_2695, q_gen_2665) -> q_gen_2682
<cons, s>(q_gen_2695, q_gen_2709) -> q_gen_2682
<cons, s>(q_gen_2710, q_gen_2665) -> q_gen_2682
<a, s>(q_gen_2696) -> q_gen_2695
<b, s>(q_gen_2696) -> q_gen_2695
<b, s>(q_gen_2711) -> q_gen_2710
}

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

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

Teacher's answer:
New clause system:
{
() -> fcons([x, l, cons(x, l)]) -> 46
() -> le([z, s(nn2)]) -> 44
() -> length([nil, z]) -> 44
(fcons([x, l, _tk]) /\ length([_tk, _uk]) /\ length([l, _sk])) -> le([_sk, _uk]) -> 47
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 44
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 45
(le([s(nn1), z])) -> BOT -> 44
(le([z, z])) -> BOT -> 44
(length([ll, _kk])) -> length([cons(x, ll), s(_kk)]) -> 45
}
Sat witness: Found: ((fcons([x, l, _tk]) /\ length([_tk, _uk]) /\ length([l, _sk])) -> le([_sk, _uk]), {
_sk -> s(s(s(z)))  ;  _tk -> cons(b, cons(b, cons(b, cons(b, nil))))  ;  _uk -> s(z)  ;  l -> cons(b, cons(b, cons(b, nil)))  ;  x -> a
})

-------------------------------------------
Step 52, which took 0.105551 s (model generation: 0.098544,  model checking: 0.007007):

Model:
|_
{
fcons -> 
{{{
Q={q_gen_2661, q_gen_2662, q_gen_2663, q_gen_2675, q_gen_2676, q_gen_2686, q_gen_2733},
Q_f={q_gen_2661},
Delta=
{
<nil>() -> q_gen_2662
<a>() -> q_gen_2663
<b>() -> q_gen_2663
<cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2675
<cons, cons>(q_gen_2686, q_gen_2675) -> q_gen_2675
<nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2675
<a, a>() -> q_gen_2676
<b, a>() -> q_gen_2676
<a, b>() -> q_gen_2686
<b, b>() -> q_gen_2686
<a, cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2661
<a, nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2661
<b, cons, cons>(q_gen_2686, q_gen_2675) -> q_gen_2661
<b, nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2661
<a, cons, cons>(q_gen_2686, q_gen_2675) -> q_gen_2733
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  le -> 
{{{
Q={q_gen_2659, q_gen_2660, q_gen_2683},
Q_f={q_gen_2659},
Delta=
{
<s>(q_gen_2660) -> q_gen_2660
<z>() -> q_gen_2660
<s, s>(q_gen_2659) -> q_gen_2659
<z, s>(q_gen_2660) -> q_gen_2659
<s, s>(q_gen_2683) -> q_gen_2683
<s, z>(q_gen_2660) -> q_gen_2683
<z, z>() -> q_gen_2683
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_2658, q_gen_2665, q_gen_2666, q_gen_2678, q_gen_2679, q_gen_2680, q_gen_2681, q_gen_2682, q_gen_2689, q_gen_2694, q_gen_2695, q_gen_2696},
Q_f={q_gen_2658},
Delta=
{
<cons>(q_gen_2689, q_gen_2694) -> q_gen_2665
<nil>() -> q_gen_2665
<cons>(q_gen_2679, q_gen_2665) -> q_gen_2678
<cons>(q_gen_2679, q_gen_2694) -> q_gen_2678
<cons>(q_gen_2689, q_gen_2665) -> q_gen_2678
<b>() -> q_gen_2679
<s>(q_gen_2696) -> q_gen_2681
<z>() -> q_gen_2681
<a>() -> q_gen_2689
<cons>(q_gen_2679, q_gen_2678) -> q_gen_2694
<cons>(q_gen_2689, q_gen_2678) -> q_gen_2694
<s>(q_gen_2681) -> q_gen_2696
<cons, s>(q_gen_2666, q_gen_2665) -> q_gen_2658
<cons, s>(q_gen_2680, q_gen_2678) -> q_gen_2658
<cons, s>(q_gen_2695, q_gen_2694) -> q_gen_2658
<nil, z>() -> q_gen_2658
<a, z>() -> q_gen_2666
<b, z>() -> q_gen_2666
<a, s>(q_gen_2681) -> q_gen_2680
<b, s>(q_gen_2681) -> q_gen_2680
<cons, s>(q_gen_2666, q_gen_2678) -> q_gen_2682
<cons, s>(q_gen_2680, q_gen_2665) -> q_gen_2682
<cons, s>(q_gen_2680, q_gen_2694) -> q_gen_2682
<cons, s>(q_gen_2695, q_gen_2665) -> q_gen_2682
<cons, s>(q_gen_2695, q_gen_2678) -> q_gen_2682
<a, s>(q_gen_2696) -> q_gen_2695
<b, s>(q_gen_2696) -> q_gen_2695
}

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

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

Teacher's answer:
New clause system:
{
() -> fcons([x, l, cons(x, l)]) -> 46
() -> le([z, s(nn2)]) -> 45
() -> length([nil, z]) -> 45
(fcons([x, l, _tk]) /\ length([_tk, _uk]) /\ length([l, _sk])) -> le([_sk, _uk]) -> 47
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 45
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 45
(le([s(nn1), z])) -> BOT -> 45
(le([z, z])) -> BOT -> 45
(length([ll, _kk])) -> length([cons(x, ll), s(_kk)]) -> 48
}
Sat witness: Found: ((length([ll, _kk])) -> length([cons(x, ll), s(_kk)]), {
_kk -> s(s(s(z)))  ;  ll -> cons(a, cons(b, cons(a, nil)))  ;  x -> b
})

-------------------------------------------
Step 53, which took 0.116849 s (model generation: 0.110063,  model checking: 0.006786):

Model:
|_
{
fcons -> 
{{{
Q={q_gen_2661, q_gen_2662, q_gen_2663, q_gen_2675, q_gen_2676},
Q_f={q_gen_2661},
Delta=
{
<nil>() -> q_gen_2662
<a>() -> q_gen_2663
<b>() -> q_gen_2663
<cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2675
<nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2675
<a, a>() -> q_gen_2676
<a, b>() -> q_gen_2676
<b, a>() -> q_gen_2676
<b, b>() -> q_gen_2676
<a, cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2661
<a, nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2661
<b, cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2661
<b, nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2661
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  le -> 
{{{
Q={q_gen_2659, q_gen_2660, q_gen_2683},
Q_f={q_gen_2659},
Delta=
{
<s>(q_gen_2660) -> q_gen_2660
<z>() -> q_gen_2660
<s, s>(q_gen_2659) -> q_gen_2659
<z, s>(q_gen_2660) -> q_gen_2659
<s, s>(q_gen_2683) -> q_gen_2683
<s, z>(q_gen_2660) -> q_gen_2683
<z, z>() -> q_gen_2683
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_2658, q_gen_2665, q_gen_2666, q_gen_2678, q_gen_2679, q_gen_2680, q_gen_2681, q_gen_2682, q_gen_2694, q_gen_2695, q_gen_2696, q_gen_2709, q_gen_2710, q_gen_2711},
Q_f={q_gen_2658},
Delta=
{
<nil>() -> q_gen_2665
<cons>(q_gen_2679, q_gen_2665) -> q_gen_2678
<a>() -> q_gen_2679
<b>() -> q_gen_2679
<z>() -> q_gen_2681
<cons>(q_gen_2679, q_gen_2678) -> q_gen_2694
<s>(q_gen_2681) -> q_gen_2696
<s>(q_gen_2711) -> q_gen_2696
<cons>(q_gen_2679, q_gen_2694) -> q_gen_2709
<s>(q_gen_2696) -> q_gen_2711
<cons, s>(q_gen_2666, q_gen_2665) -> q_gen_2658
<cons, s>(q_gen_2680, q_gen_2678) -> q_gen_2658
<cons, s>(q_gen_2695, q_gen_2678) -> q_gen_2658
<cons, s>(q_gen_2695, q_gen_2694) -> q_gen_2658
<cons, s>(q_gen_2710, q_gen_2678) -> q_gen_2658
<cons, s>(q_gen_2710, q_gen_2709) -> q_gen_2658
<nil, z>() -> q_gen_2658
<a, z>() -> q_gen_2666
<b, z>() -> q_gen_2666
<a, s>(q_gen_2681) -> q_gen_2680
<b, s>(q_gen_2681) -> q_gen_2680
<cons, s>(q_gen_2666, q_gen_2678) -> q_gen_2682
<cons, s>(q_gen_2666, q_gen_2709) -> q_gen_2682
<cons, s>(q_gen_2680, q_gen_2665) -> q_gen_2682
<cons, s>(q_gen_2680, q_gen_2694) -> q_gen_2682
<cons, s>(q_gen_2680, q_gen_2709) -> q_gen_2682
<cons, s>(q_gen_2695, q_gen_2665) -> q_gen_2682
<cons, s>(q_gen_2695, q_gen_2709) -> q_gen_2682
<cons, s>(q_gen_2710, q_gen_2665) -> q_gen_2682
<a, s>(q_gen_2696) -> q_gen_2695
<b, s>(q_gen_2696) -> q_gen_2695
<a, s>(q_gen_2711) -> q_gen_2710
<b, s>(q_gen_2711) -> q_gen_2710
}

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

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

Teacher's answer:
New clause system:
{
() -> fcons([x, l, cons(x, l)]) -> 47
() -> le([z, s(nn2)]) -> 46
() -> length([nil, z]) -> 46
(fcons([x, l, _tk]) /\ length([_tk, _uk]) /\ length([l, _sk])) -> le([_sk, _uk]) -> 50
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 46
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 46
(le([s(nn1), z])) -> BOT -> 46
(le([z, z])) -> BOT -> 46
(length([ll, _kk])) -> length([cons(x, ll), s(_kk)]) -> 48
}
Sat witness: Found: ((fcons([x, l, _tk]) /\ length([_tk, _uk]) /\ length([l, _sk])) -> le([_sk, _uk]), {
_sk -> s(s(s(z)))  ;  _tk -> cons(b, cons(b, cons(b, nil)))  ;  _uk -> s(s(s(z)))  ;  l -> cons(b, cons(b, nil))  ;  x -> b
})

-------------------------------------------
Step 54, which took 0.122629 s (model generation: 0.115806,  model checking: 0.006823):

Model:
|_
{
fcons -> 
{{{
Q={q_gen_2661, q_gen_2662, q_gen_2663, q_gen_2675, q_gen_2676, q_gen_2686, q_gen_2733},
Q_f={q_gen_2661},
Delta=
{
<nil>() -> q_gen_2662
<a>() -> q_gen_2663
<b>() -> q_gen_2663
<cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2675
<cons, cons>(q_gen_2686, q_gen_2675) -> q_gen_2675
<nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2675
<a, a>() -> q_gen_2676
<b, a>() -> q_gen_2676
<a, b>() -> q_gen_2686
<b, b>() -> q_gen_2686
<a, cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2661
<a, nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2661
<b, cons, cons>(q_gen_2686, q_gen_2675) -> q_gen_2661
<b, nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2661
<a, cons, cons>(q_gen_2686, q_gen_2675) -> q_gen_2733
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  le -> 
{{{
Q={q_gen_2659, q_gen_2660, q_gen_2683},
Q_f={q_gen_2659},
Delta=
{
<s>(q_gen_2660) -> q_gen_2660
<z>() -> q_gen_2660
<s, s>(q_gen_2659) -> q_gen_2659
<z, s>(q_gen_2660) -> q_gen_2659
<s, s>(q_gen_2683) -> q_gen_2683
<s, z>(q_gen_2660) -> q_gen_2683
<z, z>() -> q_gen_2683
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_2658, q_gen_2665, q_gen_2666, q_gen_2678, q_gen_2679, q_gen_2680, q_gen_2681, q_gen_2682, q_gen_2694, q_gen_2695, q_gen_2696, q_gen_2711},
Q_f={q_gen_2658},
Delta=
{
<cons>(q_gen_2679, q_gen_2694) -> q_gen_2665
<nil>() -> q_gen_2665
<cons>(q_gen_2679, q_gen_2665) -> q_gen_2678
<a>() -> q_gen_2679
<b>() -> q_gen_2679
<s>(q_gen_2711) -> q_gen_2681
<z>() -> q_gen_2681
<cons>(q_gen_2679, q_gen_2678) -> q_gen_2694
<s>(q_gen_2681) -> q_gen_2696
<s>(q_gen_2696) -> q_gen_2711
<cons, s>(q_gen_2666, q_gen_2665) -> q_gen_2658
<cons, s>(q_gen_2680, q_gen_2678) -> q_gen_2658
<cons, s>(q_gen_2695, q_gen_2694) -> q_gen_2658
<nil, z>() -> q_gen_2658
<a, s>(q_gen_2711) -> q_gen_2666
<a, z>() -> q_gen_2666
<b, s>(q_gen_2711) -> q_gen_2666
<b, z>() -> q_gen_2666
<a, s>(q_gen_2681) -> q_gen_2680
<b, s>(q_gen_2681) -> q_gen_2680
<cons, s>(q_gen_2666, q_gen_2678) -> q_gen_2682
<cons, s>(q_gen_2680, q_gen_2665) -> q_gen_2682
<cons, s>(q_gen_2680, q_gen_2694) -> q_gen_2682
<cons, s>(q_gen_2695, q_gen_2665) -> q_gen_2682
<cons, s>(q_gen_2695, q_gen_2678) -> q_gen_2682
<a, s>(q_gen_2696) -> q_gen_2695
<b, s>(q_gen_2696) -> q_gen_2695
}

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

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

Teacher's answer:
New clause system:
{
() -> fcons([x, l, cons(x, l)]) -> 48
() -> le([z, s(nn2)]) -> 47
() -> length([nil, z]) -> 47
(fcons([x, l, _tk]) /\ length([_tk, _uk]) /\ length([l, _sk])) -> le([_sk, _uk]) -> 53
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 47
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 47
(le([s(nn1), z])) -> BOT -> 47
(le([z, z])) -> BOT -> 47
(length([ll, _kk])) -> length([cons(x, ll), s(_kk)]) -> 49
}
Sat witness: Found: ((fcons([x, l, _tk]) /\ length([_tk, _uk]) /\ length([l, _sk])) -> le([_sk, _uk]), {
_sk -> s(s(s(z)))  ;  _tk -> cons(b, cons(a, cons(a, cons(b, nil))))  ;  _uk -> s(z)  ;  l -> cons(b, cons(b, cons(b, nil)))  ;  x -> b
})

-------------------------------------------
Step 55, which took 0.124926 s (model generation: 0.118535,  model checking: 0.006391):

Model:
|_
{
fcons -> 
{{{
Q={q_gen_2661, q_gen_2662, q_gen_2663, q_gen_2675, q_gen_2676},
Q_f={q_gen_2661},
Delta=
{
<nil>() -> q_gen_2662
<a>() -> q_gen_2663
<b>() -> q_gen_2663
<cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2675
<nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2675
<a, a>() -> q_gen_2676
<a, b>() -> q_gen_2676
<b, a>() -> q_gen_2676
<b, b>() -> q_gen_2676
<a, cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2661
<a, nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2661
<b, cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2661
<b, nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2661
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  le -> 
{{{
Q={q_gen_2659, q_gen_2660, q_gen_2683},
Q_f={q_gen_2659},
Delta=
{
<s>(q_gen_2660) -> q_gen_2660
<z>() -> q_gen_2660
<s, s>(q_gen_2659) -> q_gen_2659
<z, s>(q_gen_2660) -> q_gen_2659
<s, s>(q_gen_2683) -> q_gen_2683
<s, z>(q_gen_2660) -> q_gen_2683
<z, z>() -> q_gen_2683
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_2658, q_gen_2665, q_gen_2666, q_gen_2678, q_gen_2679, q_gen_2680, q_gen_2681, q_gen_2682, q_gen_2694, q_gen_2695, q_gen_2696, q_gen_2709, q_gen_2710, q_gen_2711},
Q_f={q_gen_2658},
Delta=
{
<nil>() -> q_gen_2665
<cons>(q_gen_2679, q_gen_2665) -> q_gen_2678
<a>() -> q_gen_2679
<b>() -> q_gen_2679
<z>() -> q_gen_2681
<cons>(q_gen_2679, q_gen_2678) -> q_gen_2694
<s>(q_gen_2681) -> q_gen_2696
<s>(q_gen_2711) -> q_gen_2696
<cons>(q_gen_2679, q_gen_2694) -> q_gen_2709
<s>(q_gen_2696) -> q_gen_2711
<cons, s>(q_gen_2666, q_gen_2665) -> q_gen_2658
<cons, s>(q_gen_2680, q_gen_2678) -> q_gen_2658
<cons, s>(q_gen_2695, q_gen_2694) -> q_gen_2658
<cons, s>(q_gen_2710, q_gen_2678) -> q_gen_2658
<cons, s>(q_gen_2710, q_gen_2694) -> q_gen_2658
<cons, s>(q_gen_2710, q_gen_2709) -> q_gen_2658
<nil, z>() -> q_gen_2658
<a, z>() -> q_gen_2666
<b, z>() -> q_gen_2666
<a, s>(q_gen_2681) -> q_gen_2680
<b, s>(q_gen_2681) -> q_gen_2680
<cons, s>(q_gen_2666, q_gen_2678) -> q_gen_2682
<cons, s>(q_gen_2666, q_gen_2709) -> q_gen_2682
<cons, s>(q_gen_2680, q_gen_2665) -> q_gen_2682
<cons, s>(q_gen_2680, q_gen_2694) -> q_gen_2682
<cons, s>(q_gen_2680, q_gen_2709) -> q_gen_2682
<cons, s>(q_gen_2695, q_gen_2665) -> q_gen_2682
<cons, s>(q_gen_2695, q_gen_2678) -> q_gen_2682
<cons, s>(q_gen_2695, q_gen_2709) -> q_gen_2682
<cons, s>(q_gen_2710, q_gen_2665) -> q_gen_2682
<b, s>(q_gen_2696) -> q_gen_2695
<a, s>(q_gen_2696) -> q_gen_2710
<a, s>(q_gen_2711) -> q_gen_2710
<b, s>(q_gen_2711) -> q_gen_2710
}

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

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

Teacher's answer:
New clause system:
{
() -> fcons([x, l, cons(x, l)]) -> 49
() -> le([z, s(nn2)]) -> 48
() -> length([nil, z]) -> 48
(fcons([x, l, _tk]) /\ length([_tk, _uk]) /\ length([l, _sk])) -> le([_sk, _uk]) -> 53
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 48
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 48
(le([s(nn1), z])) -> BOT -> 48
(le([z, z])) -> BOT -> 48
(length([ll, _kk])) -> length([cons(x, ll), s(_kk)]) -> 52
}
Sat witness: Found: ((length([ll, _kk])) -> length([cons(x, ll), s(_kk)]), {
_kk -> s(s(s(s(z))))  ;  ll -> cons(a, cons(a, cons(b, nil)))  ;  x -> b
})

-------------------------------------------
Step 56, which took 0.195021 s (model generation: 0.187089,  model checking: 0.007932):

Model:
|_
{
fcons -> 
{{{
Q={q_gen_2661, q_gen_2662, q_gen_2663, q_gen_2675, q_gen_2676},
Q_f={q_gen_2661},
Delta=
{
<nil>() -> q_gen_2662
<a>() -> q_gen_2663
<b>() -> q_gen_2663
<cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2675
<nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2675
<a, a>() -> q_gen_2676
<a, b>() -> q_gen_2676
<b, a>() -> q_gen_2676
<b, b>() -> q_gen_2676
<a, cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2661
<a, nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2661
<b, cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2661
<b, nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2661
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  le -> 
{{{
Q={q_gen_2659, q_gen_2660, q_gen_2683},
Q_f={q_gen_2659},
Delta=
{
<s>(q_gen_2660) -> q_gen_2660
<z>() -> q_gen_2660
<s, s>(q_gen_2659) -> q_gen_2659
<z, s>(q_gen_2660) -> q_gen_2659
<s, s>(q_gen_2683) -> q_gen_2683
<s, z>(q_gen_2660) -> q_gen_2683
<z, z>() -> q_gen_2683
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_2658, q_gen_2665, q_gen_2666, q_gen_2678, q_gen_2679, q_gen_2680, q_gen_2681, q_gen_2682, q_gen_2694, q_gen_2695, q_gen_2696, q_gen_2709, q_gen_2710, q_gen_2711},
Q_f={q_gen_2658},
Delta=
{
<nil>() -> q_gen_2665
<cons>(q_gen_2679, q_gen_2665) -> q_gen_2678
<a>() -> q_gen_2679
<b>() -> q_gen_2679
<z>() -> q_gen_2681
<cons>(q_gen_2679, q_gen_2678) -> q_gen_2694
<s>(q_gen_2681) -> q_gen_2696
<cons>(q_gen_2679, q_gen_2694) -> q_gen_2709
<s>(q_gen_2696) -> q_gen_2711
<s>(q_gen_2711) -> q_gen_2711
<cons, s>(q_gen_2666, q_gen_2665) -> q_gen_2658
<cons, s>(q_gen_2680, q_gen_2678) -> q_gen_2658
<cons, s>(q_gen_2695, q_gen_2694) -> q_gen_2658
<cons, s>(q_gen_2710, q_gen_2694) -> q_gen_2658
<cons, s>(q_gen_2710, q_gen_2709) -> q_gen_2658
<nil, z>() -> q_gen_2658
<a, z>() -> q_gen_2666
<b, z>() -> q_gen_2666
<a, s>(q_gen_2681) -> q_gen_2680
<b, s>(q_gen_2681) -> q_gen_2680
<cons, s>(q_gen_2666, q_gen_2678) -> q_gen_2682
<cons, s>(q_gen_2666, q_gen_2709) -> q_gen_2682
<cons, s>(q_gen_2680, q_gen_2665) -> q_gen_2682
<cons, s>(q_gen_2680, q_gen_2694) -> q_gen_2682
<cons, s>(q_gen_2680, q_gen_2709) -> q_gen_2682
<cons, s>(q_gen_2695, q_gen_2665) -> q_gen_2682
<cons, s>(q_gen_2695, q_gen_2678) -> q_gen_2682
<cons, s>(q_gen_2695, q_gen_2709) -> q_gen_2682
<cons, s>(q_gen_2710, q_gen_2665) -> q_gen_2682
<cons, s>(q_gen_2710, q_gen_2678) -> q_gen_2682
<b, s>(q_gen_2696) -> q_gen_2695
<a, s>(q_gen_2696) -> q_gen_2710
<a, s>(q_gen_2711) -> q_gen_2710
<b, s>(q_gen_2711) -> q_gen_2710
}

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

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

Teacher's answer:
New clause system:
{
() -> fcons([x, l, cons(x, l)]) -> 50
() -> le([z, s(nn2)]) -> 49
() -> length([nil, z]) -> 49
(fcons([x, l, _tk]) /\ length([_tk, _uk]) /\ length([l, _sk])) -> le([_sk, _uk]) -> 53
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 49
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 49
(le([s(nn1), z])) -> BOT -> 49
(le([z, z])) -> BOT -> 49
(length([ll, _kk])) -> length([cons(x, ll), s(_kk)]) -> 55
}
Sat witness: Found: ((length([ll, _kk])) -> length([cons(x, ll), s(_kk)]), {
_kk -> s(s(s(s(z))))  ;  ll -> cons(b, cons(b, cons(a, cons(b, nil))))  ;  x -> a
})

-------------------------------------------
Step 57, which took 0.221562 s (model generation: 0.217394,  model checking: 0.004168):

Model:
|_
{
fcons -> 
{{{
Q={q_gen_2661, q_gen_2662, q_gen_2663, q_gen_2675, q_gen_2676},
Q_f={q_gen_2661},
Delta=
{
<nil>() -> q_gen_2662
<a>() -> q_gen_2663
<b>() -> q_gen_2663
<cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2675
<nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2675
<a, a>() -> q_gen_2676
<a, b>() -> q_gen_2676
<b, a>() -> q_gen_2676
<b, b>() -> q_gen_2676
<a, cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2661
<a, nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2661
<b, cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2661
<b, nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2661
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  le -> 
{{{
Q={q_gen_2659, q_gen_2660, q_gen_2683},
Q_f={q_gen_2659},
Delta=
{
<s>(q_gen_2660) -> q_gen_2660
<z>() -> q_gen_2660
<s, s>(q_gen_2659) -> q_gen_2659
<z, s>(q_gen_2660) -> q_gen_2659
<s, s>(q_gen_2683) -> q_gen_2683
<s, z>(q_gen_2660) -> q_gen_2683
<z, z>() -> q_gen_2683
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_2658, q_gen_2665, q_gen_2666, q_gen_2678, q_gen_2679, q_gen_2680, q_gen_2681, q_gen_2682, q_gen_2694, q_gen_2695, q_gen_2696, q_gen_2709, q_gen_2710, q_gen_2711},
Q_f={q_gen_2658},
Delta=
{
<nil>() -> q_gen_2665
<cons>(q_gen_2679, q_gen_2665) -> q_gen_2678
<a>() -> q_gen_2679
<b>() -> q_gen_2679
<z>() -> q_gen_2681
<cons>(q_gen_2679, q_gen_2678) -> q_gen_2694
<cons>(q_gen_2679, q_gen_2709) -> q_gen_2694
<s>(q_gen_2681) -> q_gen_2696
<s>(q_gen_2711) -> q_gen_2696
<cons>(q_gen_2679, q_gen_2694) -> q_gen_2709
<s>(q_gen_2696) -> q_gen_2711
<cons, s>(q_gen_2666, q_gen_2665) -> q_gen_2658
<cons, s>(q_gen_2680, q_gen_2678) -> q_gen_2658
<cons, s>(q_gen_2695, q_gen_2694) -> q_gen_2658
<cons, s>(q_gen_2710, q_gen_2709) -> q_gen_2658
<nil, z>() -> q_gen_2658
<a, z>() -> q_gen_2666
<b, z>() -> q_gen_2666
<a, s>(q_gen_2681) -> q_gen_2680
<b, s>(q_gen_2681) -> q_gen_2680
<cons, s>(q_gen_2666, q_gen_2678) -> q_gen_2682
<cons, s>(q_gen_2666, q_gen_2709) -> q_gen_2682
<cons, s>(q_gen_2680, q_gen_2665) -> q_gen_2682
<cons, s>(q_gen_2680, q_gen_2694) -> q_gen_2682
<cons, s>(q_gen_2680, q_gen_2709) -> q_gen_2682
<cons, s>(q_gen_2695, q_gen_2665) -> q_gen_2682
<cons, s>(q_gen_2695, q_gen_2678) -> q_gen_2682
<cons, s>(q_gen_2695, q_gen_2709) -> q_gen_2682
<cons, s>(q_gen_2710, q_gen_2665) -> q_gen_2682
<cons, s>(q_gen_2710, q_gen_2678) -> q_gen_2682
<cons, s>(q_gen_2710, q_gen_2694) -> q_gen_2682
<a, s>(q_gen_2696) -> q_gen_2695
<b, s>(q_gen_2696) -> q_gen_2695
<a, s>(q_gen_2711) -> q_gen_2710
<b, s>(q_gen_2711) -> q_gen_2710
}

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

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

Teacher's answer:
New clause system:
{
() -> fcons([x, l, cons(x, l)]) -> 51
() -> le([z, s(nn2)]) -> 50
() -> length([nil, z]) -> 50
(fcons([x, l, _tk]) /\ length([_tk, _uk]) /\ length([l, _sk])) -> le([_sk, _uk]) -> 56
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 50
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 50
(le([s(nn1), z])) -> BOT -> 50
(le([z, z])) -> BOT -> 50
(length([ll, _kk])) -> length([cons(x, ll), s(_kk)]) -> 55
}
Sat witness: Found: ((fcons([x, l, _tk]) /\ length([_tk, _uk]) /\ length([l, _sk])) -> le([_sk, _uk]), {
_sk -> s(s(s(s(z))))  ;  _tk -> cons(b, cons(b, cons(b, cons(b, cons(b, nil)))))  ;  _uk -> s(s(s(z)))  ;  l -> cons(b, cons(b, cons(b, cons(b, nil))))  ;  x -> a
})

-------------------------------------------
Step 58, which took 0.378589 s (model generation: 0.364899,  model checking: 0.013690):

Model:
|_
{
fcons -> 
{{{
Q={q_gen_2661, q_gen_2662, q_gen_2663, q_gen_2675, q_gen_2676},
Q_f={q_gen_2661},
Delta=
{
<nil>() -> q_gen_2662
<a>() -> q_gen_2663
<b>() -> q_gen_2663
<cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2675
<nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2675
<a, a>() -> q_gen_2676
<a, b>() -> q_gen_2676
<b, a>() -> q_gen_2676
<b, b>() -> q_gen_2676
<a, cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2661
<a, nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2661
<b, cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2661
<b, nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2661
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  le -> 
{{{
Q={q_gen_2659, q_gen_2660, q_gen_2683},
Q_f={q_gen_2659},
Delta=
{
<s>(q_gen_2660) -> q_gen_2660
<z>() -> q_gen_2660
<s, s>(q_gen_2659) -> q_gen_2659
<z, s>(q_gen_2660) -> q_gen_2659
<s, s>(q_gen_2683) -> q_gen_2683
<s, z>(q_gen_2660) -> q_gen_2683
<z, z>() -> q_gen_2683
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_2658, q_gen_2665, q_gen_2666, q_gen_2678, q_gen_2679, q_gen_2680, q_gen_2681, q_gen_2682, q_gen_2694, q_gen_2695, q_gen_2696, q_gen_2709, q_gen_2710, q_gen_2711},
Q_f={q_gen_2658},
Delta=
{
<nil>() -> q_gen_2665
<cons>(q_gen_2679, q_gen_2665) -> q_gen_2678
<a>() -> q_gen_2679
<b>() -> q_gen_2679
<z>() -> q_gen_2681
<cons>(q_gen_2679, q_gen_2678) -> q_gen_2694
<s>(q_gen_2681) -> q_gen_2696
<cons>(q_gen_2679, q_gen_2694) -> q_gen_2709
<cons>(q_gen_2679, q_gen_2709) -> q_gen_2709
<s>(q_gen_2696) -> q_gen_2711
<s>(q_gen_2711) -> q_gen_2711
<cons, s>(q_gen_2666, q_gen_2665) -> q_gen_2658
<cons, s>(q_gen_2680, q_gen_2678) -> q_gen_2658
<cons, s>(q_gen_2695, q_gen_2694) -> q_gen_2658
<cons, s>(q_gen_2710, q_gen_2694) -> q_gen_2658
<cons, s>(q_gen_2710, q_gen_2709) -> q_gen_2658
<nil, z>() -> q_gen_2658
<a, z>() -> q_gen_2666
<b, z>() -> q_gen_2666
<a, s>(q_gen_2681) -> q_gen_2680
<b, s>(q_gen_2681) -> q_gen_2680
<cons, s>(q_gen_2666, q_gen_2678) -> q_gen_2682
<cons, s>(q_gen_2666, q_gen_2709) -> q_gen_2682
<cons, s>(q_gen_2680, q_gen_2665) -> q_gen_2682
<cons, s>(q_gen_2680, q_gen_2694) -> q_gen_2682
<cons, s>(q_gen_2680, q_gen_2709) -> q_gen_2682
<cons, s>(q_gen_2695, q_gen_2665) -> q_gen_2682
<cons, s>(q_gen_2695, q_gen_2678) -> q_gen_2682
<cons, s>(q_gen_2695, q_gen_2709) -> q_gen_2682
<cons, s>(q_gen_2710, q_gen_2665) -> q_gen_2682
<cons, s>(q_gen_2710, q_gen_2678) -> q_gen_2682
<b, s>(q_gen_2696) -> q_gen_2695
<a, s>(q_gen_2696) -> q_gen_2710
<a, s>(q_gen_2711) -> q_gen_2710
<b, s>(q_gen_2711) -> q_gen_2710
}

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

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

Teacher's answer:
New clause system:
{
() -> fcons([x, l, cons(x, l)]) -> 52
() -> le([z, s(nn2)]) -> 51
() -> length([nil, z]) -> 51
(fcons([x, l, _tk]) /\ length([_tk, _uk]) /\ length([l, _sk])) -> le([_sk, _uk]) -> 59
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 51
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 51
(le([s(nn1), z])) -> BOT -> 51
(le([z, z])) -> BOT -> 51
(length([ll, _kk])) -> length([cons(x, ll), s(_kk)]) -> 56
}
Sat witness: Found: ((fcons([x, l, _tk]) /\ length([_tk, _uk]) /\ length([l, _sk])) -> le([_sk, _uk]), {
_sk -> s(s(s(z)))  ;  _tk -> cons(a, cons(b, cons(b, cons(b, nil))))  ;  _uk -> s(s(s(z)))  ;  l -> cons(b, cons(b, cons(b, nil)))  ;  x -> a
})

-------------------------------------------
Step 59, which took 0.232465 s (model generation: 0.224496,  model checking: 0.007969):

Model:
|_
{
fcons -> 
{{{
Q={q_gen_2661, q_gen_2662, q_gen_2663, q_gen_2675, q_gen_2676},
Q_f={q_gen_2661},
Delta=
{
<nil>() -> q_gen_2662
<a>() -> q_gen_2663
<b>() -> q_gen_2663
<cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2675
<nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2675
<a, a>() -> q_gen_2676
<a, b>() -> q_gen_2676
<b, a>() -> q_gen_2676
<b, b>() -> q_gen_2676
<a, cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2661
<a, nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2661
<b, cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2661
<b, nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2661
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  le -> 
{{{
Q={q_gen_2659, q_gen_2660, q_gen_2683},
Q_f={q_gen_2659},
Delta=
{
<s>(q_gen_2660) -> q_gen_2660
<z>() -> q_gen_2660
<s, s>(q_gen_2659) -> q_gen_2659
<z, s>(q_gen_2660) -> q_gen_2659
<s, s>(q_gen_2683) -> q_gen_2683
<s, z>(q_gen_2660) -> q_gen_2683
<z, z>() -> q_gen_2683
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_2658, q_gen_2665, q_gen_2666, q_gen_2678, q_gen_2679, q_gen_2680, q_gen_2681, q_gen_2682, q_gen_2694, q_gen_2695, q_gen_2696, q_gen_2709, q_gen_2710, q_gen_2711},
Q_f={q_gen_2658},
Delta=
{
<nil>() -> q_gen_2665
<cons>(q_gen_2679, q_gen_2665) -> q_gen_2678
<cons>(q_gen_2679, q_gen_2709) -> q_gen_2678
<a>() -> q_gen_2679
<b>() -> q_gen_2679
<z>() -> q_gen_2681
<cons>(q_gen_2679, q_gen_2678) -> q_gen_2694
<s>(q_gen_2681) -> q_gen_2696
<cons>(q_gen_2679, q_gen_2694) -> q_gen_2709
<s>(q_gen_2696) -> q_gen_2711
<s>(q_gen_2711) -> q_gen_2711
<cons, s>(q_gen_2666, q_gen_2665) -> q_gen_2658
<cons, s>(q_gen_2680, q_gen_2678) -> q_gen_2658
<cons, s>(q_gen_2695, q_gen_2694) -> q_gen_2658
<cons, s>(q_gen_2710, q_gen_2678) -> q_gen_2658
<cons, s>(q_gen_2710, q_gen_2709) -> q_gen_2658
<nil, z>() -> q_gen_2658
<a, z>() -> q_gen_2666
<b, z>() -> q_gen_2666
<a, s>(q_gen_2681) -> q_gen_2680
<b, s>(q_gen_2681) -> q_gen_2680
<cons, s>(q_gen_2666, q_gen_2678) -> q_gen_2682
<cons, s>(q_gen_2666, q_gen_2709) -> q_gen_2682
<cons, s>(q_gen_2680, q_gen_2665) -> q_gen_2682
<cons, s>(q_gen_2680, q_gen_2694) -> q_gen_2682
<cons, s>(q_gen_2680, q_gen_2709) -> q_gen_2682
<cons, s>(q_gen_2695, q_gen_2665) -> q_gen_2682
<cons, s>(q_gen_2695, q_gen_2678) -> q_gen_2682
<cons, s>(q_gen_2695, q_gen_2709) -> q_gen_2682
<cons, s>(q_gen_2710, q_gen_2665) -> q_gen_2682
<cons, s>(q_gen_2710, q_gen_2694) -> q_gen_2682
<a, s>(q_gen_2696) -> q_gen_2695
<b, s>(q_gen_2696) -> q_gen_2695
<a, s>(q_gen_2711) -> q_gen_2710
<b, s>(q_gen_2711) -> q_gen_2710
}

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

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

Teacher's answer:
New clause system:
{
() -> fcons([x, l, cons(x, l)]) -> 53
() -> le([z, s(nn2)]) -> 52
() -> length([nil, z]) -> 52
(fcons([x, l, _tk]) /\ length([_tk, _uk]) /\ length([l, _sk])) -> le([_sk, _uk]) -> 59
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 52
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 52
(le([s(nn1), z])) -> BOT -> 52
(le([z, z])) -> BOT -> 52
(length([ll, _kk])) -> length([cons(x, ll), s(_kk)]) -> 59
}
Sat witness: Found: ((length([ll, _kk])) -> length([cons(x, ll), s(_kk)]), {
_kk -> s(s(s(s(z))))  ;  ll -> cons(a, cons(b, cons(b, cons(b, cons(b, nil)))))  ;  x -> a
})

-------------------------------------------
Step 60, which took 0.314086 s (model generation: 0.295892,  model checking: 0.018194):

Model:
|_
{
fcons -> 
{{{
Q={q_gen_2661, q_gen_2662, q_gen_2663, q_gen_2675, q_gen_2676},
Q_f={q_gen_2661},
Delta=
{
<nil>() -> q_gen_2662
<a>() -> q_gen_2663
<b>() -> q_gen_2663
<cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2675
<nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2675
<a, a>() -> q_gen_2676
<a, b>() -> q_gen_2676
<b, a>() -> q_gen_2676
<b, b>() -> q_gen_2676
<a, cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2661
<a, nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2661
<b, cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2661
<b, nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2661
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  le -> 
{{{
Q={q_gen_2659, q_gen_2660, q_gen_2683},
Q_f={q_gen_2659},
Delta=
{
<s>(q_gen_2660) -> q_gen_2660
<z>() -> q_gen_2660
<s, s>(q_gen_2659) -> q_gen_2659
<z, s>(q_gen_2660) -> q_gen_2659
<s, s>(q_gen_2683) -> q_gen_2683
<s, z>(q_gen_2660) -> q_gen_2683
<z, z>() -> q_gen_2683
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_2658, q_gen_2665, q_gen_2666, q_gen_2678, q_gen_2679, q_gen_2680, q_gen_2681, q_gen_2682, q_gen_2694, q_gen_2695, q_gen_2696, q_gen_2709, q_gen_2710, q_gen_2711},
Q_f={q_gen_2658},
Delta=
{
<nil>() -> q_gen_2665
<cons>(q_gen_2679, q_gen_2665) -> q_gen_2678
<a>() -> q_gen_2679
<b>() -> q_gen_2679
<z>() -> q_gen_2681
<cons>(q_gen_2679, q_gen_2678) -> q_gen_2694
<s>(q_gen_2681) -> q_gen_2696
<cons>(q_gen_2679, q_gen_2694) -> q_gen_2709
<cons>(q_gen_2679, q_gen_2709) -> q_gen_2709
<s>(q_gen_2696) -> q_gen_2711
<s>(q_gen_2711) -> q_gen_2711
<cons, s>(q_gen_2666, q_gen_2665) -> q_gen_2658
<cons, s>(q_gen_2680, q_gen_2678) -> q_gen_2658
<cons, s>(q_gen_2695, q_gen_2694) -> q_gen_2658
<cons, s>(q_gen_2710, q_gen_2709) -> q_gen_2658
<nil, z>() -> q_gen_2658
<a, z>() -> q_gen_2666
<b, z>() -> q_gen_2666
<a, s>(q_gen_2681) -> q_gen_2680
<b, s>(q_gen_2681) -> q_gen_2680
<cons, s>(q_gen_2666, q_gen_2678) -> q_gen_2682
<cons, s>(q_gen_2666, q_gen_2709) -> q_gen_2682
<cons, s>(q_gen_2680, q_gen_2665) -> q_gen_2682
<cons, s>(q_gen_2680, q_gen_2694) -> q_gen_2682
<cons, s>(q_gen_2680, q_gen_2709) -> q_gen_2682
<cons, s>(q_gen_2695, q_gen_2665) -> q_gen_2682
<cons, s>(q_gen_2695, q_gen_2678) -> q_gen_2682
<cons, s>(q_gen_2695, q_gen_2709) -> q_gen_2682
<cons, s>(q_gen_2710, q_gen_2665) -> q_gen_2682
<cons, s>(q_gen_2710, q_gen_2678) -> q_gen_2682
<cons, s>(q_gen_2710, q_gen_2694) -> q_gen_2682
<a, s>(q_gen_2696) -> q_gen_2695
<b, s>(q_gen_2696) -> q_gen_2695
<a, s>(q_gen_2711) -> q_gen_2710
<b, s>(q_gen_2711) -> q_gen_2710
}

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

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

Teacher's answer:
New clause system:
{
() -> fcons([x, l, cons(x, l)]) -> 54
() -> le([z, s(nn2)]) -> 53
() -> length([nil, z]) -> 53
(fcons([x, l, _tk]) /\ length([_tk, _uk]) /\ length([l, _sk])) -> le([_sk, _uk]) -> 62
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 53
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 53
(le([s(nn1), z])) -> BOT -> 53
(le([z, z])) -> BOT -> 53
(length([ll, _kk])) -> length([cons(x, ll), s(_kk)]) -> 60
}
Sat witness: Found: ((fcons([x, l, _tk]) /\ length([_tk, _uk]) /\ length([l, _sk])) -> le([_sk, _uk]), {
_sk -> s(s(s(s(z))))  ;  _tk -> cons(b, cons(b, cons(b, cons(b, cons(b, nil)))))  ;  _uk -> s(s(s(s(z))))  ;  l -> cons(b, cons(b, cons(b, cons(b, nil))))  ;  x -> b
})

-------------------------------------------
Step 61, which took 0.507228 s (model generation: 0.494106,  model checking: 0.013122):

Model:
|_
{
fcons -> 
{{{
Q={q_gen_2661, q_gen_2662, q_gen_2663, q_gen_2675, q_gen_2676},
Q_f={q_gen_2661},
Delta=
{
<nil>() -> q_gen_2662
<a>() -> q_gen_2663
<b>() -> q_gen_2663
<cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2675
<nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2675
<a, a>() -> q_gen_2676
<a, b>() -> q_gen_2676
<b, a>() -> q_gen_2676
<b, b>() -> q_gen_2676
<a, cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2661
<a, nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2661
<b, cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2661
<b, nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2661
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  le -> 
{{{
Q={q_gen_2659, q_gen_2660, q_gen_2683},
Q_f={q_gen_2659},
Delta=
{
<s>(q_gen_2660) -> q_gen_2660
<z>() -> q_gen_2660
<s, s>(q_gen_2659) -> q_gen_2659
<z, s>(q_gen_2660) -> q_gen_2659
<s, s>(q_gen_2683) -> q_gen_2683
<s, z>(q_gen_2660) -> q_gen_2683
<z, z>() -> q_gen_2683
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_2658, q_gen_2665, q_gen_2666, q_gen_2678, q_gen_2679, q_gen_2680, q_gen_2681, q_gen_2682, q_gen_2694, q_gen_2695, q_gen_2696, q_gen_2709, q_gen_2710, q_gen_2711},
Q_f={q_gen_2658},
Delta=
{
<nil>() -> q_gen_2665
<cons>(q_gen_2679, q_gen_2665) -> q_gen_2678
<cons>(q_gen_2679, q_gen_2709) -> q_gen_2678
<a>() -> q_gen_2679
<b>() -> q_gen_2679
<s>(q_gen_2711) -> q_gen_2681
<z>() -> q_gen_2681
<cons>(q_gen_2679, q_gen_2678) -> q_gen_2694
<s>(q_gen_2681) -> q_gen_2696
<cons>(q_gen_2679, q_gen_2694) -> q_gen_2709
<s>(q_gen_2696) -> q_gen_2711
<cons, s>(q_gen_2666, q_gen_2665) -> q_gen_2658
<cons, s>(q_gen_2680, q_gen_2678) -> q_gen_2658
<cons, s>(q_gen_2695, q_gen_2694) -> q_gen_2658
<cons, s>(q_gen_2710, q_gen_2709) -> q_gen_2658
<nil, z>() -> q_gen_2658
<a, z>() -> q_gen_2666
<b, z>() -> q_gen_2666
<a, s>(q_gen_2681) -> q_gen_2680
<b, s>(q_gen_2681) -> q_gen_2680
<cons, s>(q_gen_2666, q_gen_2678) -> q_gen_2682
<cons, s>(q_gen_2666, q_gen_2709) -> q_gen_2682
<cons, s>(q_gen_2680, q_gen_2665) -> q_gen_2682
<cons, s>(q_gen_2680, q_gen_2694) -> q_gen_2682
<cons, s>(q_gen_2680, q_gen_2709) -> q_gen_2682
<cons, s>(q_gen_2695, q_gen_2665) -> q_gen_2682
<cons, s>(q_gen_2695, q_gen_2678) -> q_gen_2682
<cons, s>(q_gen_2695, q_gen_2709) -> q_gen_2682
<cons, s>(q_gen_2710, q_gen_2665) -> q_gen_2682
<cons, s>(q_gen_2710, q_gen_2678) -> q_gen_2682
<cons, s>(q_gen_2710, q_gen_2694) -> q_gen_2682
<a, s>(q_gen_2696) -> q_gen_2695
<b, s>(q_gen_2696) -> q_gen_2695
<a, s>(q_gen_2711) -> q_gen_2710
<b, s>(q_gen_2711) -> q_gen_2710
}

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

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

Teacher's answer:
New clause system:
{
() -> fcons([x, l, cons(x, l)]) -> 55
() -> le([z, s(nn2)]) -> 54
() -> length([nil, z]) -> 54
(fcons([x, l, _tk]) /\ length([_tk, _uk]) /\ length([l, _sk])) -> le([_sk, _uk]) -> 65
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 54
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 54
(le([s(nn1), z])) -> BOT -> 54
(le([z, z])) -> BOT -> 54
(length([ll, _kk])) -> length([cons(x, ll), s(_kk)]) -> 61
}
Sat witness: Found: ((fcons([x, l, _tk]) /\ length([_tk, _uk]) /\ length([l, _sk])) -> le([_sk, _uk]), {
_sk -> s(s(s(s(z))))  ;  _tk -> cons(b, cons(b, cons(b, cons(b, cons(b, nil)))))  ;  _uk -> s(s(z))  ;  l -> cons(b, cons(b, cons(b, cons(b, nil))))  ;  x -> a
})

-------------------------------------------
Step 62, which took 0.581160 s (model generation: 0.493841,  model checking: 0.087319):

Model:
|_
{
fcons -> 
{{{
Q={q_gen_2661, q_gen_2662, q_gen_2663, q_gen_2675, q_gen_2676},
Q_f={q_gen_2661},
Delta=
{
<nil>() -> q_gen_2662
<a>() -> q_gen_2663
<b>() -> q_gen_2663
<cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2675
<nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2675
<a, a>() -> q_gen_2676
<a, b>() -> q_gen_2676
<b, a>() -> q_gen_2676
<b, b>() -> q_gen_2676
<a, cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2661
<a, nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2661
<b, cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2661
<b, nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2661
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  le -> 
{{{
Q={q_gen_2659, q_gen_2660, q_gen_2683},
Q_f={q_gen_2659},
Delta=
{
<s>(q_gen_2660) -> q_gen_2660
<z>() -> q_gen_2660
<s, s>(q_gen_2659) -> q_gen_2659
<z, s>(q_gen_2660) -> q_gen_2659
<s, s>(q_gen_2683) -> q_gen_2683
<s, z>(q_gen_2660) -> q_gen_2683
<z, z>() -> q_gen_2683
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_2658, q_gen_2665, q_gen_2666, q_gen_2678, q_gen_2679, q_gen_2680, q_gen_2681, q_gen_2682, q_gen_2694, q_gen_2695, q_gen_2696, q_gen_2702, q_gen_2709, q_gen_2710, q_gen_2711},
Q_f={q_gen_2658},
Delta=
{
<cons>(q_gen_2679, q_gen_2709) -> q_gen_2665
<nil>() -> q_gen_2665
<cons>(q_gen_2679, q_gen_2665) -> q_gen_2678
<a>() -> q_gen_2679
<b>() -> q_gen_2679
<s>(q_gen_2711) -> q_gen_2681
<z>() -> q_gen_2681
<cons>(q_gen_2679, q_gen_2678) -> q_gen_2694
<s>(q_gen_2681) -> q_gen_2696
<cons>(q_gen_2679, q_gen_2694) -> q_gen_2709
<s>(q_gen_2696) -> q_gen_2711
<cons, s>(q_gen_2666, q_gen_2665) -> q_gen_2658
<cons, s>(q_gen_2680, q_gen_2678) -> q_gen_2658
<cons, s>(q_gen_2695, q_gen_2694) -> q_gen_2658
<cons, s>(q_gen_2702, q_gen_2665) -> q_gen_2658
<cons, s>(q_gen_2702, q_gen_2678) -> q_gen_2658
<cons, s>(q_gen_2710, q_gen_2678) -> q_gen_2658
<cons, s>(q_gen_2710, q_gen_2709) -> q_gen_2658
<nil, z>() -> q_gen_2658
<a, z>() -> q_gen_2666
<b, z>() -> q_gen_2666
<b, s>(q_gen_2681) -> q_gen_2680
<cons, s>(q_gen_2666, q_gen_2678) -> q_gen_2682
<cons, s>(q_gen_2666, q_gen_2709) -> q_gen_2682
<cons, s>(q_gen_2680, q_gen_2665) -> q_gen_2682
<cons, s>(q_gen_2680, q_gen_2694) -> q_gen_2682
<cons, s>(q_gen_2680, q_gen_2709) -> q_gen_2682
<cons, s>(q_gen_2695, q_gen_2665) -> q_gen_2682
<cons, s>(q_gen_2695, q_gen_2678) -> q_gen_2682
<cons, s>(q_gen_2695, q_gen_2709) -> q_gen_2682
<cons, s>(q_gen_2702, q_gen_2694) -> q_gen_2682
<cons, s>(q_gen_2702, q_gen_2709) -> q_gen_2682
<cons, s>(q_gen_2710, q_gen_2665) -> q_gen_2682
<cons, s>(q_gen_2710, q_gen_2694) -> q_gen_2682
<a, s>(q_gen_2696) -> q_gen_2695
<b, s>(q_gen_2696) -> q_gen_2695
<a, s>(q_gen_2681) -> q_gen_2702
<a, s>(q_gen_2711) -> q_gen_2710
<b, s>(q_gen_2711) -> q_gen_2710
}

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

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

Teacher's answer:
New clause system:
{
() -> fcons([x, l, cons(x, l)]) -> 56
() -> le([z, s(nn2)]) -> 55
() -> length([nil, z]) -> 55
(fcons([x, l, _tk]) /\ length([_tk, _uk]) /\ length([l, _sk])) -> le([_sk, _uk]) -> 65
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 55
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 55
(le([s(nn1), z])) -> BOT -> 55
(le([z, z])) -> BOT -> 55
(length([ll, _kk])) -> length([cons(x, ll), s(_kk)]) -> 64
}
Sat witness: Found: ((length([ll, _kk])) -> length([cons(x, ll), s(_kk)]), {
_kk -> s(s(z))  ;  ll -> cons(a, nil)  ;  x -> b
})

-------------------------------------------
Step 63, which took 0.445194 s (model generation: 0.443875,  model checking: 0.001319):

Model:
|_
{
fcons -> 
{{{
Q={q_gen_2661, q_gen_2662, q_gen_2663, q_gen_2675, q_gen_2676, q_gen_2700, q_gen_2704, q_gen_2718, q_gen_2733},
Q_f={q_gen_2661},
Delta=
{
<nil>() -> q_gen_2662
<a>() -> q_gen_2663
<b>() -> q_gen_2663
<cons, cons>(q_gen_2700, q_gen_2675) -> q_gen_2675
<nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2675
<a, b>() -> q_gen_2676
<b, a>() -> q_gen_2676
<b, b>() -> q_gen_2676
<a, a>() -> q_gen_2700
<cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2704
<cons, cons>(q_gen_2676, q_gen_2704) -> q_gen_2718
<cons, cons>(q_gen_2676, q_gen_2718) -> q_gen_2718
<a, cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2661
<a, cons, cons>(q_gen_2676, q_gen_2704) -> q_gen_2661
<a, cons, cons>(q_gen_2700, q_gen_2675) -> q_gen_2661
<a, cons, cons>(q_gen_2700, q_gen_2704) -> q_gen_2661
<a, nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2661
<b, cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2661
<b, cons, cons>(q_gen_2676, q_gen_2704) -> q_gen_2661
<b, cons, cons>(q_gen_2676, q_gen_2718) -> q_gen_2661
<b, nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2661
<a, cons, cons>(q_gen_2676, q_gen_2718) -> q_gen_2733
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  le -> 
{{{
Q={q_gen_2659, q_gen_2660, q_gen_2683},
Q_f={q_gen_2659},
Delta=
{
<s>(q_gen_2660) -> q_gen_2660
<z>() -> q_gen_2660
<s, s>(q_gen_2659) -> q_gen_2659
<z, s>(q_gen_2660) -> q_gen_2659
<s, s>(q_gen_2683) -> q_gen_2683
<s, z>(q_gen_2660) -> q_gen_2683
<z, z>() -> q_gen_2683
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_2658, q_gen_2665, q_gen_2666, q_gen_2678, q_gen_2679, q_gen_2680, q_gen_2681, q_gen_2682, q_gen_2694, q_gen_2695, q_gen_2696},
Q_f={q_gen_2658},
Delta=
{
<nil>() -> q_gen_2665
<cons>(q_gen_2679, q_gen_2665) -> q_gen_2678
<cons>(q_gen_2679, q_gen_2694) -> q_gen_2678
<a>() -> q_gen_2679
<b>() -> q_gen_2679
<s>(q_gen_2696) -> q_gen_2681
<z>() -> q_gen_2681
<cons>(q_gen_2679, q_gen_2678) -> q_gen_2694
<s>(q_gen_2681) -> q_gen_2696
<cons, s>(q_gen_2666, q_gen_2665) -> q_gen_2658
<cons, s>(q_gen_2680, q_gen_2678) -> q_gen_2658
<cons, s>(q_gen_2695, q_gen_2694) -> q_gen_2658
<nil, z>() -> q_gen_2658
<a, z>() -> q_gen_2666
<b, z>() -> q_gen_2666
<a, s>(q_gen_2681) -> q_gen_2680
<b, s>(q_gen_2681) -> q_gen_2680
<cons, s>(q_gen_2666, q_gen_2678) -> q_gen_2682
<cons, s>(q_gen_2680, q_gen_2665) -> q_gen_2682
<cons, s>(q_gen_2680, q_gen_2694) -> q_gen_2682
<cons, s>(q_gen_2695, q_gen_2665) -> q_gen_2682
<cons, s>(q_gen_2695, q_gen_2678) -> q_gen_2682
<a, s>(q_gen_2696) -> q_gen_2695
<b, s>(q_gen_2696) -> q_gen_2695
}

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

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

Teacher's answer:
New clause system:
{
() -> fcons([x, l, cons(x, l)]) -> 59
() -> le([z, s(nn2)]) -> 56
() -> length([nil, z]) -> 56
(fcons([x, l, _tk]) /\ length([_tk, _uk]) /\ length([l, _sk])) -> le([_sk, _uk]) -> 65
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 56
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 56
(le([s(nn1), z])) -> BOT -> 56
(le([z, z])) -> BOT -> 56
(length([ll, _kk])) -> length([cons(x, ll), s(_kk)]) -> 64
}
Sat witness: Found: (() -> fcons([x, l, cons(x, l)]), {
l -> cons(b, cons(b, cons(b, nil)))  ;  x -> a
})

-------------------------------------------
Step 64, which took 0.500109 s (model generation: 0.492495,  model checking: 0.007614):

Model:
|_
{
fcons -> 
{{{
Q={q_gen_2661, q_gen_2662, q_gen_2663, q_gen_2675, q_gen_2676},
Q_f={q_gen_2661},
Delta=
{
<nil>() -> q_gen_2662
<a>() -> q_gen_2663
<b>() -> q_gen_2663
<cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2675
<nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2675
<a, a>() -> q_gen_2676
<a, b>() -> q_gen_2676
<b, a>() -> q_gen_2676
<b, b>() -> q_gen_2676
<a, cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2661
<a, nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2661
<b, cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2661
<b, nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2661
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  le -> 
{{{
Q={q_gen_2659, q_gen_2660, q_gen_2683},
Q_f={q_gen_2659},
Delta=
{
<s>(q_gen_2660) -> q_gen_2660
<z>() -> q_gen_2660
<s, s>(q_gen_2659) -> q_gen_2659
<z, s>(q_gen_2660) -> q_gen_2659
<s, s>(q_gen_2683) -> q_gen_2683
<s, z>(q_gen_2660) -> q_gen_2683
<z, z>() -> q_gen_2683
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_2658, q_gen_2665, q_gen_2666, q_gen_2678, q_gen_2679, q_gen_2680, q_gen_2681, q_gen_2682, q_gen_2694, q_gen_2695, q_gen_2696, q_gen_2709, q_gen_2710, q_gen_2711, q_gen_2729},
Q_f={q_gen_2658},
Delta=
{
<cons>(q_gen_2679, q_gen_2709) -> q_gen_2665
<nil>() -> q_gen_2665
<cons>(q_gen_2679, q_gen_2665) -> q_gen_2678
<a>() -> q_gen_2679
<b>() -> q_gen_2679
<z>() -> q_gen_2681
<cons>(q_gen_2679, q_gen_2678) -> q_gen_2694
<s>(q_gen_2681) -> q_gen_2696
<cons>(q_gen_2679, q_gen_2694) -> q_gen_2709
<s>(q_gen_2696) -> q_gen_2711
<s>(q_gen_2711) -> q_gen_2711
<cons, s>(q_gen_2666, q_gen_2665) -> q_gen_2658
<cons, s>(q_gen_2680, q_gen_2678) -> q_gen_2658
<cons, s>(q_gen_2695, q_gen_2694) -> q_gen_2658
<cons, s>(q_gen_2710, q_gen_2678) -> q_gen_2658
<cons, s>(q_gen_2710, q_gen_2709) -> q_gen_2658
<cons, s>(q_gen_2729, q_gen_2665) -> q_gen_2658
<cons, s>(q_gen_2729, q_gen_2678) -> q_gen_2658
<cons, s>(q_gen_2729, q_gen_2709) -> q_gen_2658
<nil, z>() -> q_gen_2658
<a, z>() -> q_gen_2666
<b, z>() -> q_gen_2666
<a, s>(q_gen_2681) -> q_gen_2680
<b, s>(q_gen_2681) -> q_gen_2680
<cons, s>(q_gen_2666, q_gen_2678) -> q_gen_2682
<cons, s>(q_gen_2666, q_gen_2709) -> q_gen_2682
<cons, s>(q_gen_2680, q_gen_2665) -> q_gen_2682
<cons, s>(q_gen_2680, q_gen_2694) -> q_gen_2682
<cons, s>(q_gen_2680, q_gen_2709) -> q_gen_2682
<cons, s>(q_gen_2695, q_gen_2665) -> q_gen_2682
<cons, s>(q_gen_2695, q_gen_2678) -> q_gen_2682
<cons, s>(q_gen_2695, q_gen_2709) -> q_gen_2682
<cons, s>(q_gen_2710, q_gen_2665) -> q_gen_2682
<cons, s>(q_gen_2729, q_gen_2694) -> q_gen_2682
<a, s>(q_gen_2696) -> q_gen_2695
<b, s>(q_gen_2696) -> q_gen_2695
<b, s>(q_gen_2711) -> q_gen_2710
<a, s>(q_gen_2711) -> q_gen_2729
}

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

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

Teacher's answer:
New clause system:
{
() -> fcons([x, l, cons(x, l)]) -> 60
() -> le([z, s(nn2)]) -> 57
() -> length([nil, z]) -> 57
(fcons([x, l, _tk]) /\ length([_tk, _uk]) /\ length([l, _sk])) -> le([_sk, _uk]) -> 65
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 57
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 57
(le([s(nn1), z])) -> BOT -> 57
(le([z, z])) -> BOT -> 57
(length([ll, _kk])) -> length([cons(x, ll), s(_kk)]) -> 67
}
Sat witness: Found: ((length([ll, _kk])) -> length([cons(x, ll), s(_kk)]), {
_kk -> s(s(s(s(z))))  ;  ll -> cons(a, cons(b, nil))  ;  x -> a
})

-------------------------------------------
Step 65, which took 0.464593 s (model generation: 0.461788,  model checking: 0.002805):

Model:
|_
{
fcons -> 
{{{
Q={q_gen_2661, q_gen_2662, q_gen_2663, q_gen_2675, q_gen_2676},
Q_f={q_gen_2661},
Delta=
{
<nil>() -> q_gen_2662
<a>() -> q_gen_2663
<b>() -> q_gen_2663
<cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2675
<nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2675
<a, a>() -> q_gen_2676
<a, b>() -> q_gen_2676
<b, a>() -> q_gen_2676
<b, b>() -> q_gen_2676
<a, cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2661
<a, nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2661
<b, cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2661
<b, nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2661
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  le -> 
{{{
Q={q_gen_2659, q_gen_2660, q_gen_2683},
Q_f={q_gen_2659},
Delta=
{
<s>(q_gen_2660) -> q_gen_2660
<z>() -> q_gen_2660
<s, s>(q_gen_2659) -> q_gen_2659
<z, s>(q_gen_2660) -> q_gen_2659
<s, s>(q_gen_2683) -> q_gen_2683
<s, z>(q_gen_2660) -> q_gen_2683
<z, z>() -> q_gen_2683
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_2658, q_gen_2665, q_gen_2666, q_gen_2678, q_gen_2679, q_gen_2680, q_gen_2681, q_gen_2682, q_gen_2694, q_gen_2695, q_gen_2696, q_gen_2709, q_gen_2710, q_gen_2711, q_gen_2759},
Q_f={q_gen_2658},
Delta=
{
<cons>(q_gen_2679, q_gen_2709) -> q_gen_2665
<nil>() -> q_gen_2665
<cons>(q_gen_2679, q_gen_2665) -> q_gen_2678
<a>() -> q_gen_2679
<b>() -> q_gen_2679
<z>() -> q_gen_2681
<cons>(q_gen_2679, q_gen_2678) -> q_gen_2694
<s>(q_gen_2681) -> q_gen_2696
<cons>(q_gen_2679, q_gen_2694) -> q_gen_2709
<s>(q_gen_2696) -> q_gen_2711
<s>(q_gen_2711) -> q_gen_2759
<cons, s>(q_gen_2666, q_gen_2665) -> q_gen_2658
<cons, s>(q_gen_2680, q_gen_2678) -> q_gen_2658
<cons, s>(q_gen_2695, q_gen_2694) -> q_gen_2658
<cons, s>(q_gen_2710, q_gen_2709) -> q_gen_2658
<nil, z>() -> q_gen_2658
<a, s>(q_gen_2759) -> q_gen_2666
<a, z>() -> q_gen_2666
<b, z>() -> q_gen_2666
<a, s>(q_gen_2681) -> q_gen_2680
<b, s>(q_gen_2681) -> q_gen_2680
<cons, s>(q_gen_2666, q_gen_2678) -> q_gen_2682
<cons, s>(q_gen_2666, q_gen_2694) -> q_gen_2682
<cons, s>(q_gen_2666, q_gen_2709) -> q_gen_2682
<cons, s>(q_gen_2680, q_gen_2665) -> q_gen_2682
<cons, s>(q_gen_2680, q_gen_2694) -> q_gen_2682
<cons, s>(q_gen_2680, q_gen_2709) -> q_gen_2682
<cons, s>(q_gen_2695, q_gen_2665) -> q_gen_2682
<cons, s>(q_gen_2695, q_gen_2678) -> q_gen_2682
<cons, s>(q_gen_2695, q_gen_2709) -> q_gen_2682
<cons, s>(q_gen_2710, q_gen_2665) -> q_gen_2682
<cons, s>(q_gen_2710, q_gen_2678) -> q_gen_2682
<cons, s>(q_gen_2710, q_gen_2694) -> q_gen_2682
<a, s>(q_gen_2696) -> q_gen_2695
<b, s>(q_gen_2696) -> q_gen_2695
<b, s>(q_gen_2759) -> q_gen_2695
<a, s>(q_gen_2711) -> q_gen_2710
<b, s>(q_gen_2711) -> q_gen_2710
}

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

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

Teacher's answer:
New clause system:
{
() -> fcons([x, l, cons(x, l)]) -> 61
() -> le([z, s(nn2)]) -> 58
() -> length([nil, z]) -> 58
(fcons([x, l, _tk]) /\ length([_tk, _uk]) /\ length([l, _sk])) -> le([_sk, _uk]) -> 68
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 58
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 58
(le([s(nn1), z])) -> BOT -> 58
(le([z, z])) -> BOT -> 58
(length([ll, _kk])) -> length([cons(x, ll), s(_kk)]) -> 67
}
Sat witness: Found: ((fcons([x, l, _tk]) /\ length([_tk, _uk]) /\ length([l, _sk])) -> le([_sk, _uk]), {
_sk -> s(s(s(s(z))))  ;  _tk -> cons(b, cons(b, cons(b, cons(b, cons(b, nil)))))  ;  _uk -> s(z)  ;  l -> cons(b, cons(b, cons(b, cons(b, nil))))  ;  x -> a
})

-------------------------------------------
Step 66, which took 0.820680 s (model generation: 0.817483,  model checking: 0.003197):

Model:
|_
{
fcons -> 
{{{
Q={q_gen_2661, q_gen_2662, q_gen_2663, q_gen_2675, q_gen_2676, q_gen_2686, q_gen_2733},
Q_f={q_gen_2661},
Delta=
{
<nil>() -> q_gen_2662
<a>() -> q_gen_2663
<b>() -> q_gen_2663
<cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2675
<cons, cons>(q_gen_2686, q_gen_2675) -> q_gen_2675
<nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2675
<a, a>() -> q_gen_2676
<a, b>() -> q_gen_2676
<b, a>() -> q_gen_2676
<b, b>() -> q_gen_2686
<a, cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2661
<a, nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2661
<b, cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2661
<b, cons, cons>(q_gen_2686, q_gen_2675) -> q_gen_2661
<b, nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2661
<a, cons, cons>(q_gen_2686, q_gen_2675) -> q_gen_2733
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  le -> 
{{{
Q={q_gen_2659, q_gen_2660, q_gen_2683},
Q_f={q_gen_2659},
Delta=
{
<s>(q_gen_2660) -> q_gen_2660
<z>() -> q_gen_2660
<s, s>(q_gen_2659) -> q_gen_2659
<z, s>(q_gen_2660) -> q_gen_2659
<s, s>(q_gen_2683) -> q_gen_2683
<s, z>(q_gen_2660) -> q_gen_2683
<z, z>() -> q_gen_2683
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_2658, q_gen_2665, q_gen_2666, q_gen_2678, q_gen_2679, q_gen_2680, q_gen_2681, q_gen_2682, q_gen_2688, q_gen_2689, q_gen_2694, q_gen_2695, q_gen_2696},
Q_f={q_gen_2658},
Delta=
{
<cons>(q_gen_2679, q_gen_2688) -> q_gen_2665
<nil>() -> q_gen_2665
<cons>(q_gen_2679, q_gen_2665) -> q_gen_2678
<cons>(q_gen_2679, q_gen_2694) -> q_gen_2678
<b>() -> q_gen_2679
<s>(q_gen_2696) -> q_gen_2681
<z>() -> q_gen_2681
<cons>(q_gen_2689, q_gen_2665) -> q_gen_2688
<a>() -> q_gen_2689
<cons>(q_gen_2679, q_gen_2678) -> q_gen_2694
<cons>(q_gen_2689, q_gen_2678) -> q_gen_2694
<cons>(q_gen_2689, q_gen_2694) -> q_gen_2694
<s>(q_gen_2681) -> q_gen_2696
<cons, s>(q_gen_2666, q_gen_2665) -> q_gen_2658
<cons, s>(q_gen_2680, q_gen_2678) -> q_gen_2658
<cons, s>(q_gen_2680, q_gen_2688) -> q_gen_2658
<cons, s>(q_gen_2695, q_gen_2694) -> q_gen_2658
<nil, z>() -> q_gen_2658
<a, z>() -> q_gen_2666
<b, z>() -> q_gen_2666
<a, s>(q_gen_2681) -> q_gen_2680
<b, s>(q_gen_2681) -> q_gen_2680
<cons, s>(q_gen_2666, q_gen_2678) -> q_gen_2682
<cons, s>(q_gen_2666, q_gen_2694) -> q_gen_2682
<cons, s>(q_gen_2680, q_gen_2665) -> q_gen_2682
<cons, s>(q_gen_2680, q_gen_2694) -> q_gen_2682
<cons, s>(q_gen_2695, q_gen_2665) -> q_gen_2682
<cons, s>(q_gen_2695, q_gen_2678) -> q_gen_2682
<cons, s>(q_gen_2695, q_gen_2688) -> q_gen_2682
<a, s>(q_gen_2696) -> q_gen_2695
<b, s>(q_gen_2696) -> q_gen_2695
}

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

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

Teacher's answer:
New clause system:
{
() -> fcons([x, l, cons(x, l)]) -> 62
() -> le([z, s(nn2)]) -> 59
() -> length([nil, z]) -> 59
(fcons([x, l, _tk]) /\ length([_tk, _uk]) /\ length([l, _sk])) -> le([_sk, _uk]) -> 68
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 59
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 59
(le([s(nn1), z])) -> BOT -> 59
(le([z, z])) -> BOT -> 59
(length([ll, _kk])) -> length([cons(x, ll), s(_kk)]) -> 70
}
Sat witness: Found: ((length([ll, _kk])) -> length([cons(x, ll), s(_kk)]), {
_kk -> s(s(z))  ;  ll -> cons(b, cons(a, nil))  ;  x -> a
})

-------------------------------------------
Step 67, which took 0.507351 s (model generation: 0.505828,  model checking: 0.001523):

Model:
|_
{
fcons -> 
{{{
Q={q_gen_2661, q_gen_2662, q_gen_2663, q_gen_2675, q_gen_2676, q_gen_2686, q_gen_2700, q_gen_2704, q_gen_2723},
Q_f={q_gen_2661},
Delta=
{
<nil>() -> q_gen_2662
<a>() -> q_gen_2663
<b>() -> q_gen_2663
<cons, cons>(q_gen_2686, q_gen_2675) -> q_gen_2675
<cons, cons>(q_gen_2686, q_gen_2704) -> q_gen_2675
<nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2675
<b, a>() -> q_gen_2676
<a, b>() -> q_gen_2686
<b, b>() -> q_gen_2686
<a, a>() -> q_gen_2700
<cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2704
<cons, cons>(q_gen_2676, q_gen_2704) -> q_gen_2704
<cons, cons>(q_gen_2700, q_gen_2675) -> q_gen_2704
<a, cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2661
<a, cons, cons>(q_gen_2700, q_gen_2675) -> q_gen_2661
<a, cons, cons>(q_gen_2700, q_gen_2704) -> q_gen_2661
<a, nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2661
<b, cons, cons>(q_gen_2686, q_gen_2675) -> q_gen_2661
<b, cons, cons>(q_gen_2686, q_gen_2704) -> q_gen_2661
<b, nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2661
<a, cons, cons>(q_gen_2676, q_gen_2704) -> q_gen_2723
<a, cons, cons>(q_gen_2686, q_gen_2675) -> q_gen_2723
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  le -> 
{{{
Q={q_gen_2659, q_gen_2660, q_gen_2683},
Q_f={q_gen_2659},
Delta=
{
<s>(q_gen_2660) -> q_gen_2660
<z>() -> q_gen_2660
<s, s>(q_gen_2659) -> q_gen_2659
<z, s>(q_gen_2660) -> q_gen_2659
<s, s>(q_gen_2683) -> q_gen_2683
<s, z>(q_gen_2660) -> q_gen_2683
<z, z>() -> q_gen_2683
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_2658, q_gen_2665, q_gen_2666, q_gen_2678, q_gen_2679, q_gen_2680, q_gen_2681, q_gen_2682, q_gen_2694, q_gen_2695, q_gen_2696},
Q_f={q_gen_2658},
Delta=
{
<nil>() -> q_gen_2665
<cons>(q_gen_2679, q_gen_2665) -> q_gen_2678
<cons>(q_gen_2679, q_gen_2694) -> q_gen_2678
<a>() -> q_gen_2679
<b>() -> q_gen_2679
<s>(q_gen_2696) -> q_gen_2681
<z>() -> q_gen_2681
<cons>(q_gen_2679, q_gen_2678) -> q_gen_2694
<s>(q_gen_2681) -> q_gen_2696
<cons, s>(q_gen_2666, q_gen_2665) -> q_gen_2658
<cons, s>(q_gen_2680, q_gen_2678) -> q_gen_2658
<cons, s>(q_gen_2695, q_gen_2694) -> q_gen_2658
<nil, z>() -> q_gen_2658
<a, z>() -> q_gen_2666
<b, z>() -> q_gen_2666
<a, s>(q_gen_2681) -> q_gen_2680
<b, s>(q_gen_2681) -> q_gen_2680
<cons, s>(q_gen_2666, q_gen_2678) -> q_gen_2682
<cons, s>(q_gen_2666, q_gen_2694) -> q_gen_2682
<cons, s>(q_gen_2680, q_gen_2665) -> q_gen_2682
<cons, s>(q_gen_2680, q_gen_2694) -> q_gen_2682
<cons, s>(q_gen_2695, q_gen_2665) -> q_gen_2682
<cons, s>(q_gen_2695, q_gen_2678) -> q_gen_2682
<a, s>(q_gen_2696) -> q_gen_2695
<b, s>(q_gen_2696) -> q_gen_2695
}

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

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

Teacher's answer:
New clause system:
{
() -> fcons([x, l, cons(x, l)]) -> 65
() -> le([z, s(nn2)]) -> 60
() -> length([nil, z]) -> 60
(fcons([x, l, _tk]) /\ length([_tk, _uk]) /\ length([l, _sk])) -> le([_sk, _uk]) -> 68
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 60
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 60
(le([s(nn1), z])) -> BOT -> 60
(le([z, z])) -> BOT -> 60
(length([ll, _kk])) -> length([cons(x, ll), s(_kk)]) -> 70
}
Sat witness: Found: (() -> fcons([x, l, cons(x, l)]), {
l -> cons(a, cons(a, cons(b, nil)))  ;  x -> a
})

-------------------------------------------
Step 68, which took 0.638334 s (model generation: 0.634489,  model checking: 0.003845):

Model:
|_
{
fcons -> 
{{{
Q={q_gen_2661, q_gen_2662, q_gen_2663, q_gen_2675, q_gen_2676, q_gen_2686, q_gen_2700, q_gen_2704, q_gen_2723},
Q_f={q_gen_2661},
Delta=
{
<nil>() -> q_gen_2662
<a>() -> q_gen_2663
<b>() -> q_gen_2663
<cons, cons>(q_gen_2686, q_gen_2675) -> q_gen_2675
<cons, cons>(q_gen_2686, q_gen_2704) -> q_gen_2675
<cons, cons>(q_gen_2700, q_gen_2704) -> q_gen_2675
<nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2675
<b, a>() -> q_gen_2676
<a, b>() -> q_gen_2686
<b, b>() -> q_gen_2686
<a, a>() -> q_gen_2700
<cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2704
<cons, cons>(q_gen_2676, q_gen_2704) -> q_gen_2704
<cons, cons>(q_gen_2700, q_gen_2675) -> q_gen_2704
<a, cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2661
<a, cons, cons>(q_gen_2700, q_gen_2675) -> q_gen_2661
<a, cons, cons>(q_gen_2700, q_gen_2704) -> q_gen_2661
<a, nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2661
<b, cons, cons>(q_gen_2686, q_gen_2675) -> q_gen_2661
<b, cons, cons>(q_gen_2686, q_gen_2704) -> q_gen_2661
<b, nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2661
<a, cons, cons>(q_gen_2676, q_gen_2704) -> q_gen_2723
<a, cons, cons>(q_gen_2686, q_gen_2675) -> q_gen_2723
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  le -> 
{{{
Q={q_gen_2659, q_gen_2660, q_gen_2683},
Q_f={q_gen_2659},
Delta=
{
<s>(q_gen_2660) -> q_gen_2660
<z>() -> q_gen_2660
<s, s>(q_gen_2659) -> q_gen_2659
<z, s>(q_gen_2660) -> q_gen_2659
<s, s>(q_gen_2683) -> q_gen_2683
<s, z>(q_gen_2660) -> q_gen_2683
<z, z>() -> q_gen_2683
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_2658, q_gen_2665, q_gen_2666, q_gen_2678, q_gen_2679, q_gen_2680, q_gen_2681, q_gen_2682, q_gen_2694, q_gen_2695, q_gen_2696},
Q_f={q_gen_2658},
Delta=
{
<nil>() -> q_gen_2665
<cons>(q_gen_2679, q_gen_2665) -> q_gen_2678
<cons>(q_gen_2679, q_gen_2694) -> q_gen_2678
<a>() -> q_gen_2679
<b>() -> q_gen_2679
<s>(q_gen_2696) -> q_gen_2681
<z>() -> q_gen_2681
<cons>(q_gen_2679, q_gen_2678) -> q_gen_2694
<s>(q_gen_2681) -> q_gen_2696
<cons, s>(q_gen_2666, q_gen_2665) -> q_gen_2658
<cons, s>(q_gen_2680, q_gen_2678) -> q_gen_2658
<cons, s>(q_gen_2695, q_gen_2694) -> q_gen_2658
<nil, z>() -> q_gen_2658
<a, z>() -> q_gen_2666
<b, z>() -> q_gen_2666
<a, s>(q_gen_2681) -> q_gen_2680
<b, s>(q_gen_2681) -> q_gen_2680
<cons, s>(q_gen_2666, q_gen_2678) -> q_gen_2682
<cons, s>(q_gen_2666, q_gen_2694) -> q_gen_2682
<cons, s>(q_gen_2680, q_gen_2665) -> q_gen_2682
<cons, s>(q_gen_2680, q_gen_2694) -> q_gen_2682
<cons, s>(q_gen_2695, q_gen_2665) -> q_gen_2682
<cons, s>(q_gen_2695, q_gen_2678) -> q_gen_2682
<a, s>(q_gen_2696) -> q_gen_2695
<b, s>(q_gen_2696) -> q_gen_2695
}

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

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

Teacher's answer:
New clause system:
{
() -> fcons([x, l, cons(x, l)]) -> 66
() -> le([z, s(nn2)]) -> 61
() -> length([nil, z]) -> 61
(fcons([x, l, _tk]) /\ length([_tk, _uk]) /\ length([l, _sk])) -> le([_sk, _uk]) -> 71
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 61
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 61
(le([s(nn1), z])) -> BOT -> 61
(le([z, z])) -> BOT -> 61
(length([ll, _kk])) -> length([cons(x, ll), s(_kk)]) -> 70
}
Sat witness: Found: ((fcons([x, l, _tk]) /\ length([_tk, _uk]) /\ length([l, _sk])) -> le([_sk, _uk]), {
_sk -> s(s(s(z)))  ;  _tk -> cons(b, cons(a, cons(a, cons(b, nil))))  ;  _uk -> s(s(z))  ;  l -> cons(a, cons(b, cons(b, nil)))  ;  x -> b
})

-------------------------------------------
Step 69, which took 0.693461 s (model generation: 0.692181,  model checking: 0.001280):

Model:
|_
{
fcons -> 
{{{
Q={q_gen_2661, q_gen_2662, q_gen_2663, q_gen_2675, q_gen_2676, q_gen_2686, q_gen_2700, q_gen_2704, q_gen_2723},
Q_f={q_gen_2661},
Delta=
{
<nil>() -> q_gen_2662
<a>() -> q_gen_2663
<b>() -> q_gen_2663
<cons, cons>(q_gen_2686, q_gen_2675) -> q_gen_2675
<cons, cons>(q_gen_2700, q_gen_2675) -> q_gen_2675
<nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2675
<b, a>() -> q_gen_2676
<a, b>() -> q_gen_2686
<b, b>() -> q_gen_2686
<a, a>() -> q_gen_2700
<cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2704
<cons, cons>(q_gen_2676, q_gen_2704) -> q_gen_2704
<cons, cons>(q_gen_2700, q_gen_2704) -> q_gen_2704
<a, cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2661
<a, cons, cons>(q_gen_2700, q_gen_2675) -> q_gen_2661
<a, cons, cons>(q_gen_2700, q_gen_2704) -> q_gen_2661
<a, nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2661
<b, cons, cons>(q_gen_2686, q_gen_2675) -> q_gen_2661
<b, nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2661
<a, cons, cons>(q_gen_2676, q_gen_2704) -> q_gen_2723
<a, cons, cons>(q_gen_2686, q_gen_2675) -> q_gen_2723
<b, cons, cons>(q_gen_2686, q_gen_2704) -> q_gen_2723
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  le -> 
{{{
Q={q_gen_2659, q_gen_2660, q_gen_2683},
Q_f={q_gen_2659},
Delta=
{
<s>(q_gen_2660) -> q_gen_2660
<z>() -> q_gen_2660
<s, s>(q_gen_2659) -> q_gen_2659
<z, s>(q_gen_2660) -> q_gen_2659
<s, s>(q_gen_2683) -> q_gen_2683
<s, z>(q_gen_2660) -> q_gen_2683
<z, z>() -> q_gen_2683
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_2658, q_gen_2665, q_gen_2666, q_gen_2678, q_gen_2679, q_gen_2680, q_gen_2681, q_gen_2682, q_gen_2694, q_gen_2695, q_gen_2696},
Q_f={q_gen_2658},
Delta=
{
<nil>() -> q_gen_2665
<cons>(q_gen_2679, q_gen_2665) -> q_gen_2678
<cons>(q_gen_2679, q_gen_2694) -> q_gen_2678
<a>() -> q_gen_2679
<b>() -> q_gen_2679
<s>(q_gen_2696) -> q_gen_2681
<z>() -> q_gen_2681
<cons>(q_gen_2679, q_gen_2678) -> q_gen_2694
<s>(q_gen_2681) -> q_gen_2696
<cons, s>(q_gen_2666, q_gen_2665) -> q_gen_2658
<cons, s>(q_gen_2680, q_gen_2678) -> q_gen_2658
<cons, s>(q_gen_2695, q_gen_2694) -> q_gen_2658
<nil, z>() -> q_gen_2658
<a, z>() -> q_gen_2666
<b, z>() -> q_gen_2666
<a, s>(q_gen_2681) -> q_gen_2680
<b, s>(q_gen_2681) -> q_gen_2680
<cons, s>(q_gen_2666, q_gen_2678) -> q_gen_2682
<cons, s>(q_gen_2666, q_gen_2694) -> q_gen_2682
<cons, s>(q_gen_2680, q_gen_2665) -> q_gen_2682
<cons, s>(q_gen_2680, q_gen_2694) -> q_gen_2682
<cons, s>(q_gen_2695, q_gen_2665) -> q_gen_2682
<cons, s>(q_gen_2695, q_gen_2678) -> q_gen_2682
<a, s>(q_gen_2696) -> q_gen_2695
<b, s>(q_gen_2696) -> q_gen_2695
}

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

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

Teacher's answer:
New clause system:
{
() -> fcons([x, l, cons(x, l)]) -> 69
() -> le([z, s(nn2)]) -> 62
() -> length([nil, z]) -> 62
(fcons([x, l, _tk]) /\ length([_tk, _uk]) /\ length([l, _sk])) -> le([_sk, _uk]) -> 71
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 62
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 62
(le([s(nn1), z])) -> BOT -> 62
(le([z, z])) -> BOT -> 62
(length([ll, _kk])) -> length([cons(x, ll), s(_kk)]) -> 70
}
Sat witness: Found: (() -> fcons([x, l, cons(x, l)]), {
l -> cons(a, cons(b, nil))  ;  x -> b
})

-------------------------------------------
Step 70, which took 1.099235 s (model generation: 1.098563,  model checking: 0.000672):

Model:
|_
{
fcons -> 
{{{
Q={q_gen_2661, q_gen_2662, q_gen_2663, q_gen_2675, q_gen_2676, q_gen_2686, q_gen_2704, q_gen_2733},
Q_f={q_gen_2661},
Delta=
{
<nil>() -> q_gen_2662
<a>() -> q_gen_2663
<b>() -> q_gen_2663
<cons, cons>(q_gen_2686, q_gen_2675) -> q_gen_2675
<nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2675
<a, a>() -> q_gen_2676
<a, b>() -> q_gen_2676
<b, a>() -> q_gen_2676
<b, b>() -> q_gen_2686
<cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2704
<cons, cons>(q_gen_2676, q_gen_2704) -> q_gen_2704
<a, cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2661
<a, cons, cons>(q_gen_2676, q_gen_2704) -> q_gen_2661
<a, nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2661
<b, cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2661
<b, cons, cons>(q_gen_2676, q_gen_2704) -> q_gen_2661
<b, cons, cons>(q_gen_2686, q_gen_2675) -> q_gen_2661
<b, nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2661
<a, cons, cons>(q_gen_2686, q_gen_2675) -> q_gen_2733
<b, cons, cons>(q_gen_2686, q_gen_2704) -> q_gen_2733
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  le -> 
{{{
Q={q_gen_2659, q_gen_2660, q_gen_2683},
Q_f={q_gen_2659},
Delta=
{
<s>(q_gen_2660) -> q_gen_2660
<z>() -> q_gen_2660
<s, s>(q_gen_2659) -> q_gen_2659
<z, s>(q_gen_2660) -> q_gen_2659
<s, s>(q_gen_2683) -> q_gen_2683
<s, z>(q_gen_2660) -> q_gen_2683
<z, z>() -> q_gen_2683
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_2658, q_gen_2665, q_gen_2666, q_gen_2678, q_gen_2679, q_gen_2680, q_gen_2681, q_gen_2682, q_gen_2694, q_gen_2695, q_gen_2696, q_gen_2711},
Q_f={q_gen_2658},
Delta=
{
<cons>(q_gen_2679, q_gen_2694) -> q_gen_2665
<nil>() -> q_gen_2665
<cons>(q_gen_2679, q_gen_2665) -> q_gen_2678
<a>() -> q_gen_2679
<b>() -> q_gen_2679
<s>(q_gen_2711) -> q_gen_2681
<z>() -> q_gen_2681
<cons>(q_gen_2679, q_gen_2678) -> q_gen_2694
<s>(q_gen_2681) -> q_gen_2696
<s>(q_gen_2696) -> q_gen_2711
<cons, s>(q_gen_2666, q_gen_2665) -> q_gen_2658
<cons, s>(q_gen_2680, q_gen_2678) -> q_gen_2658
<cons, s>(q_gen_2695, q_gen_2694) -> q_gen_2658
<nil, z>() -> q_gen_2658
<a, s>(q_gen_2711) -> q_gen_2666
<a, z>() -> q_gen_2666
<b, s>(q_gen_2711) -> q_gen_2666
<b, z>() -> q_gen_2666
<a, s>(q_gen_2681) -> q_gen_2680
<b, s>(q_gen_2681) -> q_gen_2680
<cons, s>(q_gen_2666, q_gen_2678) -> q_gen_2682
<cons, s>(q_gen_2666, q_gen_2694) -> q_gen_2682
<cons, s>(q_gen_2680, q_gen_2665) -> q_gen_2682
<cons, s>(q_gen_2680, q_gen_2694) -> q_gen_2682
<cons, s>(q_gen_2695, q_gen_2665) -> q_gen_2682
<cons, s>(q_gen_2695, q_gen_2678) -> q_gen_2682
<a, s>(q_gen_2696) -> q_gen_2695
<b, s>(q_gen_2696) -> q_gen_2695
}

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

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

Teacher's answer:
New clause system:
{
() -> fcons([x, l, cons(x, l)]) -> 72
() -> le([z, s(nn2)]) -> 63
() -> length([nil, z]) -> 63
(fcons([x, l, _tk]) /\ length([_tk, _uk]) /\ length([l, _sk])) -> le([_sk, _uk]) -> 71
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 63
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 63
(le([s(nn1), z])) -> BOT -> 63
(le([z, z])) -> BOT -> 63
(length([ll, _kk])) -> length([cons(x, ll), s(_kk)]) -> 70
}
Sat witness: Found: (() -> fcons([x, l, cons(x, l)]), {
l -> cons(b, cons(a, nil))  ;  x -> b
})

-------------------------------------------
Step 71, which took 1.342985 s (model generation: 1.337923,  model checking: 0.005062):

Model:
|_
{
fcons -> 
{{{
Q={q_gen_2661, q_gen_2662, q_gen_2663, q_gen_2675, q_gen_2676, q_gen_2686, q_gen_2733},
Q_f={q_gen_2661},
Delta=
{
<nil>() -> q_gen_2662
<a>() -> q_gen_2663
<b>() -> q_gen_2663
<cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2675
<cons, cons>(q_gen_2686, q_gen_2675) -> q_gen_2675
<nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2675
<a, a>() -> q_gen_2676
<a, b>() -> q_gen_2676
<b, a>() -> q_gen_2676
<b, b>() -> q_gen_2686
<a, cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2661
<a, nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2661
<b, cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2661
<b, cons, cons>(q_gen_2686, q_gen_2675) -> q_gen_2661
<b, nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2661
<a, cons, cons>(q_gen_2686, q_gen_2675) -> q_gen_2733
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  le -> 
{{{
Q={q_gen_2659, q_gen_2660, q_gen_2683},
Q_f={q_gen_2659},
Delta=
{
<s>(q_gen_2660) -> q_gen_2660
<z>() -> q_gen_2660
<s, s>(q_gen_2659) -> q_gen_2659
<z, s>(q_gen_2660) -> q_gen_2659
<s, s>(q_gen_2683) -> q_gen_2683
<s, z>(q_gen_2660) -> q_gen_2683
<z, z>() -> q_gen_2683
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_2658, q_gen_2665, q_gen_2666, q_gen_2678, q_gen_2679, q_gen_2680, q_gen_2681, q_gen_2682, q_gen_2688, q_gen_2689, q_gen_2694, q_gen_2695, q_gen_2696},
Q_f={q_gen_2658},
Delta=
{
<nil>() -> q_gen_2665
<cons>(q_gen_2679, q_gen_2665) -> q_gen_2678
<cons>(q_gen_2679, q_gen_2694) -> q_gen_2678
<b>() -> q_gen_2679
<s>(q_gen_2696) -> q_gen_2681
<z>() -> q_gen_2681
<cons>(q_gen_2679, q_gen_2688) -> q_gen_2688
<cons>(q_gen_2689, q_gen_2665) -> q_gen_2688
<cons>(q_gen_2689, q_gen_2688) -> q_gen_2688
<a>() -> q_gen_2689
<cons>(q_gen_2679, q_gen_2678) -> q_gen_2694
<cons>(q_gen_2689, q_gen_2678) -> q_gen_2694
<cons>(q_gen_2689, q_gen_2694) -> q_gen_2694
<s>(q_gen_2681) -> q_gen_2696
<cons, s>(q_gen_2666, q_gen_2665) -> q_gen_2658
<cons, s>(q_gen_2680, q_gen_2678) -> q_gen_2658
<cons, s>(q_gen_2680, q_gen_2688) -> q_gen_2658
<cons, s>(q_gen_2695, q_gen_2688) -> q_gen_2658
<cons, s>(q_gen_2695, q_gen_2694) -> q_gen_2658
<nil, z>() -> q_gen_2658
<a, z>() -> q_gen_2666
<b, z>() -> q_gen_2666
<a, s>(q_gen_2681) -> q_gen_2680
<b, s>(q_gen_2681) -> q_gen_2680
<cons, s>(q_gen_2666, q_gen_2678) -> q_gen_2682
<cons, s>(q_gen_2666, q_gen_2694) -> q_gen_2682
<cons, s>(q_gen_2680, q_gen_2665) -> q_gen_2682
<cons, s>(q_gen_2680, q_gen_2694) -> q_gen_2682
<cons, s>(q_gen_2695, q_gen_2665) -> q_gen_2682
<cons, s>(q_gen_2695, q_gen_2678) -> q_gen_2682
<a, s>(q_gen_2696) -> q_gen_2695
<b, s>(q_gen_2696) -> q_gen_2695
}

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

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

Teacher's answer:
New clause system:
{
() -> fcons([x, l, cons(x, l)]) -> 72
() -> le([z, s(nn2)]) -> 64
() -> length([nil, z]) -> 64
(fcons([x, l, _tk]) /\ length([_tk, _uk]) /\ length([l, _sk])) -> le([_sk, _uk]) -> 71
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 64
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 64
(le([s(nn1), z])) -> BOT -> 64
(le([z, z])) -> BOT -> 64
(length([ll, _kk])) -> length([cons(x, ll), s(_kk)]) -> 73
}
Sat witness: Found: ((length([ll, _kk])) -> length([cons(x, ll), s(_kk)]), {
_kk -> s(s(s(z)))  ;  ll -> cons(a, cons(a, cons(b, nil)))  ;  x -> b
})

-------------------------------------------
Step 72, which took 1.259726 s (model generation: 1.254519,  model checking: 0.005207):

Model:
|_
{
fcons -> 
{{{
Q={q_gen_2661, q_gen_2662, q_gen_2663, q_gen_2675, q_gen_2676},
Q_f={q_gen_2661},
Delta=
{
<nil>() -> q_gen_2662
<a>() -> q_gen_2663
<b>() -> q_gen_2663
<cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2675
<nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2675
<a, a>() -> q_gen_2676
<a, b>() -> q_gen_2676
<b, a>() -> q_gen_2676
<b, b>() -> q_gen_2676
<a, cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2661
<a, nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2661
<b, cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2661
<b, nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2661
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  le -> 
{{{
Q={q_gen_2659, q_gen_2660, q_gen_2683},
Q_f={q_gen_2659},
Delta=
{
<s>(q_gen_2660) -> q_gen_2660
<z>() -> q_gen_2660
<s, s>(q_gen_2659) -> q_gen_2659
<z, s>(q_gen_2660) -> q_gen_2659
<s, s>(q_gen_2683) -> q_gen_2683
<s, z>(q_gen_2660) -> q_gen_2683
<z, z>() -> q_gen_2683
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_2658, q_gen_2665, q_gen_2666, q_gen_2678, q_gen_2679, q_gen_2680, q_gen_2681, q_gen_2682, q_gen_2694, q_gen_2695, q_gen_2696, q_gen_2702, q_gen_2709, q_gen_2710, q_gen_2711, q_gen_2773},
Q_f={q_gen_2658},
Delta=
{
<nil>() -> q_gen_2665
<cons>(q_gen_2679, q_gen_2665) -> q_gen_2678
<a>() -> q_gen_2679
<b>() -> q_gen_2679
<s>(q_gen_2711) -> q_gen_2681
<z>() -> q_gen_2681
<cons>(q_gen_2679, q_gen_2678) -> q_gen_2694
<cons>(q_gen_2679, q_gen_2773) -> q_gen_2694
<s>(q_gen_2681) -> q_gen_2696
<cons>(q_gen_2679, q_gen_2694) -> q_gen_2709
<s>(q_gen_2696) -> q_gen_2711
<cons>(q_gen_2679, q_gen_2709) -> q_gen_2773
<cons, s>(q_gen_2666, q_gen_2665) -> q_gen_2658
<cons, s>(q_gen_2680, q_gen_2678) -> q_gen_2658
<cons, s>(q_gen_2695, q_gen_2694) -> q_gen_2658
<cons, s>(q_gen_2702, q_gen_2678) -> q_gen_2658
<cons, s>(q_gen_2702, q_gen_2773) -> q_gen_2658
<cons, s>(q_gen_2710, q_gen_2709) -> q_gen_2658
<nil, z>() -> q_gen_2658
<a, z>() -> q_gen_2666
<b, z>() -> q_gen_2666
<b, s>(q_gen_2681) -> q_gen_2680
<cons, s>(q_gen_2666, q_gen_2678) -> q_gen_2682
<cons, s>(q_gen_2666, q_gen_2709) -> q_gen_2682
<cons, s>(q_gen_2666, q_gen_2773) -> q_gen_2682
<cons, s>(q_gen_2680, q_gen_2665) -> q_gen_2682
<cons, s>(q_gen_2680, q_gen_2694) -> q_gen_2682
<cons, s>(q_gen_2680, q_gen_2709) -> q_gen_2682
<cons, s>(q_gen_2680, q_gen_2773) -> q_gen_2682
<cons, s>(q_gen_2695, q_gen_2665) -> q_gen_2682
<cons, s>(q_gen_2695, q_gen_2678) -> q_gen_2682
<cons, s>(q_gen_2695, q_gen_2709) -> q_gen_2682
<cons, s>(q_gen_2695, q_gen_2773) -> q_gen_2682
<cons, s>(q_gen_2702, q_gen_2665) -> q_gen_2682
<cons, s>(q_gen_2702, q_gen_2694) -> q_gen_2682
<cons, s>(q_gen_2702, q_gen_2709) -> q_gen_2682
<cons, s>(q_gen_2710, q_gen_2665) -> q_gen_2682
<cons, s>(q_gen_2710, q_gen_2678) -> q_gen_2682
<cons, s>(q_gen_2710, q_gen_2694) -> q_gen_2682
<cons, s>(q_gen_2710, q_gen_2773) -> q_gen_2682
<a, s>(q_gen_2696) -> q_gen_2695
<b, s>(q_gen_2696) -> q_gen_2695
<a, s>(q_gen_2681) -> q_gen_2702
<a, s>(q_gen_2711) -> q_gen_2710
<b, s>(q_gen_2711) -> q_gen_2710
}

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

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

Teacher's answer:
New clause system:
{
() -> fcons([x, l, cons(x, l)]) -> 72
() -> le([z, s(nn2)]) -> 65
() -> length([nil, z]) -> 65
(fcons([x, l, _tk]) /\ length([_tk, _uk]) /\ length([l, _sk])) -> le([_sk, _uk]) -> 74
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 65
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 65
(le([s(nn1), z])) -> BOT -> 65
(le([z, z])) -> BOT -> 65
(length([ll, _kk])) -> length([cons(x, ll), s(_kk)]) -> 73
}
Sat witness: Found: ((fcons([x, l, _tk]) /\ length([_tk, _uk]) /\ length([l, _sk])) -> le([_sk, _uk]), {
_sk -> s(s(s(s(s(z)))))  ;  _tk -> cons(b, cons(b, cons(b, nil)))  ;  _uk -> s(s(s(z)))  ;  l -> cons(b, cons(b, nil))  ;  x -> a
})

-------------------------------------------
Step 73, which took 2.578166 s (model generation: 2.563875,  model checking: 0.014291):

Model:
|_
{
fcons -> 
{{{
Q={q_gen_2661, q_gen_2662, q_gen_2663, q_gen_2675, q_gen_2676},
Q_f={q_gen_2661},
Delta=
{
<nil>() -> q_gen_2662
<a>() -> q_gen_2663
<b>() -> q_gen_2663
<cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2675
<nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2675
<a, a>() -> q_gen_2676
<a, b>() -> q_gen_2676
<b, a>() -> q_gen_2676
<b, b>() -> q_gen_2676
<a, cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2661
<a, nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2661
<b, cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2661
<b, nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2661
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  le -> 
{{{
Q={q_gen_2659, q_gen_2660, q_gen_2683},
Q_f={q_gen_2659},
Delta=
{
<s>(q_gen_2660) -> q_gen_2660
<z>() -> q_gen_2660
<s, s>(q_gen_2659) -> q_gen_2659
<z, s>(q_gen_2660) -> q_gen_2659
<s, s>(q_gen_2683) -> q_gen_2683
<s, z>(q_gen_2660) -> q_gen_2683
<z, z>() -> q_gen_2683
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_2658, q_gen_2665, q_gen_2666, q_gen_2678, q_gen_2679, q_gen_2680, q_gen_2681, q_gen_2682, q_gen_2694, q_gen_2695, q_gen_2696, q_gen_2709, q_gen_2710, q_gen_2711, q_gen_2729, q_gen_2773},
Q_f={q_gen_2658},
Delta=
{
<nil>() -> q_gen_2665
<cons>(q_gen_2679, q_gen_2665) -> q_gen_2678
<a>() -> q_gen_2679
<b>() -> q_gen_2679
<z>() -> q_gen_2681
<cons>(q_gen_2679, q_gen_2678) -> q_gen_2694
<s>(q_gen_2681) -> q_gen_2696
<cons>(q_gen_2679, q_gen_2694) -> q_gen_2709
<cons>(q_gen_2679, q_gen_2773) -> q_gen_2709
<s>(q_gen_2696) -> q_gen_2711
<s>(q_gen_2711) -> q_gen_2711
<cons>(q_gen_2679, q_gen_2709) -> q_gen_2773
<cons, s>(q_gen_2666, q_gen_2665) -> q_gen_2658
<cons, s>(q_gen_2680, q_gen_2678) -> q_gen_2658
<cons, s>(q_gen_2695, q_gen_2694) -> q_gen_2658
<cons, s>(q_gen_2710, q_gen_2709) -> q_gen_2658
<cons, s>(q_gen_2729, q_gen_2709) -> q_gen_2658
<cons, s>(q_gen_2729, q_gen_2773) -> q_gen_2658
<nil, z>() -> q_gen_2658
<a, z>() -> q_gen_2666
<b, z>() -> q_gen_2666
<a, s>(q_gen_2681) -> q_gen_2680
<b, s>(q_gen_2681) -> q_gen_2680
<cons, s>(q_gen_2666, q_gen_2678) -> q_gen_2682
<cons, s>(q_gen_2666, q_gen_2709) -> q_gen_2682
<cons, s>(q_gen_2666, q_gen_2773) -> q_gen_2682
<cons, s>(q_gen_2680, q_gen_2665) -> q_gen_2682
<cons, s>(q_gen_2680, q_gen_2694) -> q_gen_2682
<cons, s>(q_gen_2680, q_gen_2709) -> q_gen_2682
<cons, s>(q_gen_2680, q_gen_2773) -> q_gen_2682
<cons, s>(q_gen_2695, q_gen_2665) -> q_gen_2682
<cons, s>(q_gen_2695, q_gen_2678) -> q_gen_2682
<cons, s>(q_gen_2695, q_gen_2709) -> q_gen_2682
<cons, s>(q_gen_2695, q_gen_2773) -> q_gen_2682
<cons, s>(q_gen_2710, q_gen_2665) -> q_gen_2682
<cons, s>(q_gen_2710, q_gen_2678) -> q_gen_2682
<cons, s>(q_gen_2710, q_gen_2773) -> q_gen_2682
<cons, s>(q_gen_2729, q_gen_2665) -> q_gen_2682
<cons, s>(q_gen_2729, q_gen_2678) -> q_gen_2682
<cons, s>(q_gen_2729, q_gen_2694) -> q_gen_2682
<a, s>(q_gen_2696) -> q_gen_2695
<b, s>(q_gen_2696) -> q_gen_2695
<b, s>(q_gen_2711) -> q_gen_2710
<a, s>(q_gen_2711) -> q_gen_2729
}

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

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

Teacher's answer:
New clause system:
{
() -> fcons([x, l, cons(x, l)]) -> 73
() -> le([z, s(nn2)]) -> 66
() -> length([nil, z]) -> 66
(fcons([x, l, _tk]) /\ length([_tk, _uk]) /\ length([l, _sk])) -> le([_sk, _uk]) -> 74
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 66
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 66
(le([s(nn1), z])) -> BOT -> 66
(le([z, z])) -> BOT -> 66
(length([ll, _kk])) -> length([cons(x, ll), s(_kk)]) -> 76
}
Sat witness: Found: ((length([ll, _kk])) -> length([cons(x, ll), s(_kk)]), {
_kk -> s(s(s(s(z))))  ;  ll -> cons(b, cons(b, cons(a, cons(b, nil))))  ;  x -> b
})

-------------------------------------------
Step 74, which took 2.294237 s (model generation: 2.291525,  model checking: 0.002712):

Model:
|_
{
fcons -> 
{{{
Q={q_gen_2661, q_gen_2662, q_gen_2663, q_gen_2675, q_gen_2676, q_gen_2686, q_gen_2700, q_gen_2704, q_gen_2723, q_gen_2739},
Q_f={q_gen_2661},
Delta=
{
<nil>() -> q_gen_2662
<a>() -> q_gen_2663
<b>() -> q_gen_2663
<cons, cons>(q_gen_2686, q_gen_2675) -> q_gen_2675
<cons, cons>(q_gen_2686, q_gen_2739) -> q_gen_2675
<cons, cons>(q_gen_2700, q_gen_2704) -> q_gen_2675
<nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2675
<b, a>() -> q_gen_2676
<a, b>() -> q_gen_2686
<b, b>() -> q_gen_2686
<a, a>() -> q_gen_2700
<cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2704
<cons, cons>(q_gen_2676, q_gen_2704) -> q_gen_2739
<cons, cons>(q_gen_2700, q_gen_2675) -> q_gen_2739
<a, cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2661
<a, cons, cons>(q_gen_2700, q_gen_2675) -> q_gen_2661
<a, cons, cons>(q_gen_2700, q_gen_2704) -> q_gen_2661
<a, cons, cons>(q_gen_2700, q_gen_2739) -> q_gen_2661
<a, nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2661
<b, cons, cons>(q_gen_2686, q_gen_2675) -> q_gen_2661
<b, cons, cons>(q_gen_2686, q_gen_2704) -> q_gen_2661
<b, nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2661
<a, cons, cons>(q_gen_2676, q_gen_2704) -> q_gen_2723
<a, cons, cons>(q_gen_2676, q_gen_2739) -> q_gen_2723
<a, cons, cons>(q_gen_2686, q_gen_2675) -> q_gen_2723
<b, cons, cons>(q_gen_2686, q_gen_2739) -> q_gen_2723
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  le -> 
{{{
Q={q_gen_2659, q_gen_2660, q_gen_2683},
Q_f={q_gen_2659},
Delta=
{
<s>(q_gen_2660) -> q_gen_2660
<z>() -> q_gen_2660
<s, s>(q_gen_2659) -> q_gen_2659
<z, s>(q_gen_2660) -> q_gen_2659
<s, s>(q_gen_2683) -> q_gen_2683
<s, z>(q_gen_2660) -> q_gen_2683
<z, z>() -> q_gen_2683
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_2658, q_gen_2665, q_gen_2666, q_gen_2678, q_gen_2679, q_gen_2680, q_gen_2681, q_gen_2682, q_gen_2694, q_gen_2695, q_gen_2696},
Q_f={q_gen_2658},
Delta=
{
<nil>() -> q_gen_2665
<cons>(q_gen_2679, q_gen_2665) -> q_gen_2678
<cons>(q_gen_2679, q_gen_2694) -> q_gen_2678
<a>() -> q_gen_2679
<b>() -> q_gen_2679
<s>(q_gen_2696) -> q_gen_2681
<z>() -> q_gen_2681
<cons>(q_gen_2679, q_gen_2678) -> q_gen_2694
<s>(q_gen_2681) -> q_gen_2696
<cons, s>(q_gen_2666, q_gen_2665) -> q_gen_2658
<cons, s>(q_gen_2680, q_gen_2678) -> q_gen_2658
<cons, s>(q_gen_2695, q_gen_2694) -> q_gen_2658
<nil, z>() -> q_gen_2658
<a, z>() -> q_gen_2666
<b, z>() -> q_gen_2666
<a, s>(q_gen_2681) -> q_gen_2680
<b, s>(q_gen_2681) -> q_gen_2680
<cons, s>(q_gen_2666, q_gen_2678) -> q_gen_2682
<cons, s>(q_gen_2666, q_gen_2694) -> q_gen_2682
<cons, s>(q_gen_2680, q_gen_2665) -> q_gen_2682
<cons, s>(q_gen_2680, q_gen_2694) -> q_gen_2682
<cons, s>(q_gen_2695, q_gen_2665) -> q_gen_2682
<cons, s>(q_gen_2695, q_gen_2678) -> q_gen_2682
<a, s>(q_gen_2696) -> q_gen_2695
<b, s>(q_gen_2696) -> q_gen_2695
}

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

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

Teacher's answer:
New clause system:
{
() -> fcons([x, l, cons(x, l)]) -> 76
() -> le([z, s(nn2)]) -> 67
() -> length([nil, z]) -> 67
(fcons([x, l, _tk]) /\ length([_tk, _uk]) /\ length([l, _sk])) -> le([_sk, _uk]) -> 74
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 67
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 67
(le([s(nn1), z])) -> BOT -> 67
(le([z, z])) -> BOT -> 67
(length([ll, _kk])) -> length([cons(x, ll), s(_kk)]) -> 76
}
Sat witness: Found: (() -> fcons([x, l, cons(x, l)]), {
l -> cons(a, cons(a, nil))  ;  x -> b
})

-------------------------------------------
Step 75, which took 1.330316 s (model generation: 1.326815,  model checking: 0.003501):

Model:
|_
{
fcons -> 
{{{
Q={q_gen_2661, q_gen_2662, q_gen_2663, q_gen_2671, q_gen_2675, q_gen_2676, q_gen_2686, q_gen_2691, q_gen_2705, q_gen_2748},
Q_f={q_gen_2661},
Delta=
{
<nil>() -> q_gen_2662
<b>() -> q_gen_2663
<a>() -> q_gen_2671
<cons, cons>(q_gen_2686, q_gen_2675) -> q_gen_2675
<nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2675
<b, a>() -> q_gen_2676
<a, a>() -> q_gen_2686
<a, b>() -> q_gen_2686
<b, b>() -> q_gen_2686
<cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2691
<cons, cons>(q_gen_2686, q_gen_2691) -> q_gen_2691
<nil, cons>(q_gen_2671, q_gen_2662) -> q_gen_2691
<cons, cons>(q_gen_2676, q_gen_2691) -> q_gen_2748
<a, cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2661
<a, cons, cons>(q_gen_2676, q_gen_2691) -> q_gen_2661
<a, cons, cons>(q_gen_2686, q_gen_2691) -> q_gen_2661
<a, nil, cons>(q_gen_2671, q_gen_2662) -> q_gen_2661
<b, cons, cons>(q_gen_2686, q_gen_2675) -> q_gen_2661
<b, cons, cons>(q_gen_2686, q_gen_2691) -> q_gen_2661
<b, nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2661
<a, cons, cons>(q_gen_2676, q_gen_2748) -> q_gen_2705
<a, cons, cons>(q_gen_2686, q_gen_2675) -> q_gen_2705
<b, cons, cons>(q_gen_2686, q_gen_2748) -> q_gen_2705
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  le -> 
{{{
Q={q_gen_2659, q_gen_2660, q_gen_2683},
Q_f={q_gen_2659},
Delta=
{
<s>(q_gen_2660) -> q_gen_2660
<z>() -> q_gen_2660
<s, s>(q_gen_2659) -> q_gen_2659
<z, s>(q_gen_2660) -> q_gen_2659
<s, s>(q_gen_2683) -> q_gen_2683
<s, z>(q_gen_2660) -> q_gen_2683
<z, z>() -> q_gen_2683
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_2658, q_gen_2665, q_gen_2666, q_gen_2678, q_gen_2679, q_gen_2680, q_gen_2681, q_gen_2682, q_gen_2694, q_gen_2695, q_gen_2696},
Q_f={q_gen_2658},
Delta=
{
<nil>() -> q_gen_2665
<cons>(q_gen_2679, q_gen_2665) -> q_gen_2678
<cons>(q_gen_2679, q_gen_2694) -> q_gen_2678
<a>() -> q_gen_2679
<b>() -> q_gen_2679
<s>(q_gen_2696) -> q_gen_2681
<z>() -> q_gen_2681
<cons>(q_gen_2679, q_gen_2678) -> q_gen_2694
<s>(q_gen_2681) -> q_gen_2696
<cons, s>(q_gen_2666, q_gen_2665) -> q_gen_2658
<cons, s>(q_gen_2680, q_gen_2678) -> q_gen_2658
<cons, s>(q_gen_2695, q_gen_2694) -> q_gen_2658
<nil, z>() -> q_gen_2658
<a, z>() -> q_gen_2666
<b, z>() -> q_gen_2666
<a, s>(q_gen_2681) -> q_gen_2680
<b, s>(q_gen_2681) -> q_gen_2680
<cons, s>(q_gen_2666, q_gen_2678) -> q_gen_2682
<cons, s>(q_gen_2666, q_gen_2694) -> q_gen_2682
<cons, s>(q_gen_2680, q_gen_2665) -> q_gen_2682
<cons, s>(q_gen_2680, q_gen_2694) -> q_gen_2682
<cons, s>(q_gen_2695, q_gen_2665) -> q_gen_2682
<cons, s>(q_gen_2695, q_gen_2678) -> q_gen_2682
<a, s>(q_gen_2696) -> q_gen_2695
<b, s>(q_gen_2696) -> q_gen_2695
}

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

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

Teacher's answer:
New clause system:
{
() -> fcons([x, l, cons(x, l)]) -> 76
() -> le([z, s(nn2)]) -> 68
() -> length([nil, z]) -> 68
(fcons([x, l, _tk]) /\ length([_tk, _uk]) /\ length([l, _sk])) -> le([_sk, _uk]) -> 77
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 68
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 68
(le([s(nn1), z])) -> BOT -> 68
(le([z, z])) -> BOT -> 68
(length([ll, _kk])) -> length([cons(x, ll), s(_kk)]) -> 76
}
Sat witness: Found: ((fcons([x, l, _tk]) /\ length([_tk, _uk]) /\ length([l, _sk])) -> le([_sk, _uk]), {
_sk -> s(s(s(s(z))))  ;  _tk -> cons(a, cons(a, cons(b, nil)))  ;  _uk -> s(s(s(z)))  ;  l -> cons(b, cons(b, nil))  ;  x -> a
})

-------------------------------------------
Step 76, which took 1.777019 s (model generation: 1.766580,  model checking: 0.010439):

Model:
|_
{
fcons -> 
{{{
Q={q_gen_2661, q_gen_2662, q_gen_2663, q_gen_2675, q_gen_2676, q_gen_2686, q_gen_2733},
Q_f={q_gen_2661},
Delta=
{
<nil>() -> q_gen_2662
<a>() -> q_gen_2663
<b>() -> q_gen_2663
<cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2675
<cons, cons>(q_gen_2686, q_gen_2675) -> q_gen_2675
<nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2675
<a, a>() -> q_gen_2676
<a, b>() -> q_gen_2676
<b, a>() -> q_gen_2676
<b, b>() -> q_gen_2686
<a, cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2661
<a, nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2661
<b, cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2661
<b, cons, cons>(q_gen_2686, q_gen_2675) -> q_gen_2661
<b, nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2661
<a, cons, cons>(q_gen_2686, q_gen_2675) -> q_gen_2733
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  le -> 
{{{
Q={q_gen_2659, q_gen_2660, q_gen_2683},
Q_f={q_gen_2659},
Delta=
{
<s>(q_gen_2660) -> q_gen_2660
<z>() -> q_gen_2660
<s, s>(q_gen_2659) -> q_gen_2659
<z, s>(q_gen_2660) -> q_gen_2659
<s, s>(q_gen_2683) -> q_gen_2683
<s, z>(q_gen_2660) -> q_gen_2683
<z, z>() -> q_gen_2683
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_2658, q_gen_2665, q_gen_2666, q_gen_2678, q_gen_2679, q_gen_2680, q_gen_2681, q_gen_2682, q_gen_2694, q_gen_2695, q_gen_2696, q_gen_2709, q_gen_2710, q_gen_2711},
Q_f={q_gen_2658},
Delta=
{
<nil>() -> q_gen_2665
<cons>(q_gen_2679, q_gen_2665) -> q_gen_2678
<cons>(q_gen_2679, q_gen_2709) -> q_gen_2678
<a>() -> q_gen_2679
<b>() -> q_gen_2679
<s>(q_gen_2711) -> q_gen_2681
<z>() -> q_gen_2681
<cons>(q_gen_2679, q_gen_2678) -> q_gen_2694
<s>(q_gen_2681) -> q_gen_2696
<cons>(q_gen_2679, q_gen_2694) -> q_gen_2709
<s>(q_gen_2696) -> q_gen_2711
<cons, s>(q_gen_2666, q_gen_2665) -> q_gen_2658
<cons, s>(q_gen_2680, q_gen_2678) -> q_gen_2658
<cons, s>(q_gen_2695, q_gen_2694) -> q_gen_2658
<cons, s>(q_gen_2710, q_gen_2709) -> q_gen_2658
<nil, z>() -> q_gen_2658
<a, z>() -> q_gen_2666
<b, z>() -> q_gen_2666
<a, s>(q_gen_2681) -> q_gen_2680
<b, s>(q_gen_2681) -> q_gen_2680
<cons, s>(q_gen_2666, q_gen_2678) -> q_gen_2682
<cons, s>(q_gen_2666, q_gen_2709) -> q_gen_2682
<cons, s>(q_gen_2680, q_gen_2665) -> q_gen_2682
<cons, s>(q_gen_2680, q_gen_2694) -> q_gen_2682
<cons, s>(q_gen_2680, q_gen_2709) -> q_gen_2682
<cons, s>(q_gen_2695, q_gen_2665) -> q_gen_2682
<cons, s>(q_gen_2695, q_gen_2678) -> q_gen_2682
<cons, s>(q_gen_2695, q_gen_2709) -> q_gen_2682
<cons, s>(q_gen_2710, q_gen_2665) -> q_gen_2682
<cons, s>(q_gen_2710, q_gen_2678) -> q_gen_2682
<cons, s>(q_gen_2710, q_gen_2694) -> q_gen_2682
<a, s>(q_gen_2696) -> q_gen_2695
<b, s>(q_gen_2696) -> q_gen_2695
<a, s>(q_gen_2711) -> q_gen_2710
<b, s>(q_gen_2711) -> q_gen_2710
}

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

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

Teacher's answer:
New clause system:
{
() -> fcons([x, l, cons(x, l)]) -> 77
() -> le([z, s(nn2)]) -> 69
() -> length([nil, z]) -> 69
(fcons([x, l, _tk]) /\ length([_tk, _uk]) /\ length([l, _sk])) -> le([_sk, _uk]) -> 80
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 69
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 69
(le([s(nn1), z])) -> BOT -> 69
(le([z, z])) -> BOT -> 69
(length([ll, _kk])) -> length([cons(x, ll), s(_kk)]) -> 77
}
Sat witness: Found: ((fcons([x, l, _tk]) /\ length([_tk, _uk]) /\ length([l, _sk])) -> le([_sk, _uk]), {
_sk -> s(s(s(s(s(s(z))))))  ;  _tk -> cons(a, cons(a, cons(a, cons(b, nil))))  ;  _uk -> s(s(s(s(z))))  ;  l -> cons(b, cons(b, cons(b, nil)))  ;  x -> a
})

-------------------------------------------
Step 77, which took 2.128868 s (model generation: 2.118587,  model checking: 0.010281):

Model:
|_
{
fcons -> 
{{{
Q={q_gen_2661, q_gen_2662, q_gen_2663, q_gen_2675, q_gen_2676, q_gen_2686, q_gen_2733},
Q_f={q_gen_2661},
Delta=
{
<nil>() -> q_gen_2662
<a>() -> q_gen_2663
<b>() -> q_gen_2663
<cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2675
<cons, cons>(q_gen_2686, q_gen_2675) -> q_gen_2675
<nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2675
<a, a>() -> q_gen_2676
<a, b>() -> q_gen_2676
<b, a>() -> q_gen_2676
<b, b>() -> q_gen_2686
<a, cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2661
<a, nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2661
<b, cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2661
<b, cons, cons>(q_gen_2686, q_gen_2675) -> q_gen_2661
<b, nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2661
<a, cons, cons>(q_gen_2686, q_gen_2675) -> q_gen_2733
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  le -> 
{{{
Q={q_gen_2659, q_gen_2660, q_gen_2683},
Q_f={q_gen_2659},
Delta=
{
<s>(q_gen_2660) -> q_gen_2660
<z>() -> q_gen_2660
<s, s>(q_gen_2659) -> q_gen_2659
<z, s>(q_gen_2660) -> q_gen_2659
<s, s>(q_gen_2683) -> q_gen_2683
<s, z>(q_gen_2660) -> q_gen_2683
<z, z>() -> q_gen_2683
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_2658, q_gen_2665, q_gen_2666, q_gen_2678, q_gen_2679, q_gen_2680, q_gen_2681, q_gen_2682, q_gen_2694, q_gen_2695, q_gen_2696, q_gen_2709, q_gen_2710, q_gen_2711},
Q_f={q_gen_2658},
Delta=
{
<nil>() -> q_gen_2665
<cons>(q_gen_2679, q_gen_2665) -> q_gen_2678
<a>() -> q_gen_2679
<b>() -> q_gen_2679
<z>() -> q_gen_2681
<cons>(q_gen_2679, q_gen_2678) -> q_gen_2694
<cons>(q_gen_2679, q_gen_2709) -> q_gen_2694
<s>(q_gen_2681) -> q_gen_2696
<s>(q_gen_2711) -> q_gen_2696
<cons>(q_gen_2679, q_gen_2694) -> q_gen_2709
<s>(q_gen_2696) -> q_gen_2711
<cons, s>(q_gen_2666, q_gen_2665) -> q_gen_2658
<cons, s>(q_gen_2680, q_gen_2678) -> q_gen_2658
<cons, s>(q_gen_2695, q_gen_2694) -> q_gen_2658
<cons, s>(q_gen_2710, q_gen_2709) -> q_gen_2658
<nil, z>() -> q_gen_2658
<a, z>() -> q_gen_2666
<b, z>() -> q_gen_2666
<a, s>(q_gen_2681) -> q_gen_2680
<b, s>(q_gen_2681) -> q_gen_2680
<cons, s>(q_gen_2666, q_gen_2678) -> q_gen_2682
<cons, s>(q_gen_2666, q_gen_2694) -> q_gen_2682
<cons, s>(q_gen_2666, q_gen_2709) -> q_gen_2682
<cons, s>(q_gen_2680, q_gen_2665) -> q_gen_2682
<cons, s>(q_gen_2680, q_gen_2694) -> q_gen_2682
<cons, s>(q_gen_2680, q_gen_2709) -> q_gen_2682
<cons, s>(q_gen_2695, q_gen_2665) -> q_gen_2682
<cons, s>(q_gen_2695, q_gen_2678) -> q_gen_2682
<cons, s>(q_gen_2695, q_gen_2709) -> q_gen_2682
<cons, s>(q_gen_2710, q_gen_2665) -> q_gen_2682
<cons, s>(q_gen_2710, q_gen_2678) -> q_gen_2682
<cons, s>(q_gen_2710, q_gen_2694) -> q_gen_2682
<a, s>(q_gen_2696) -> q_gen_2695
<b, s>(q_gen_2696) -> q_gen_2695
<a, s>(q_gen_2711) -> q_gen_2710
<b, s>(q_gen_2711) -> q_gen_2710
}

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

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

Teacher's answer:
New clause system:
{
() -> fcons([x, l, cons(x, l)]) -> 78
() -> le([z, s(nn2)]) -> 70
() -> length([nil, z]) -> 70
(fcons([x, l, _tk]) /\ length([_tk, _uk]) /\ length([l, _sk])) -> le([_sk, _uk]) -> 83
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 70
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 70
(le([s(nn1), z])) -> BOT -> 70
(le([z, z])) -> BOT -> 70
(length([ll, _kk])) -> length([cons(x, ll), s(_kk)]) -> 78
}
Sat witness: Found: ((fcons([x, l, _tk]) /\ length([_tk, _uk]) /\ length([l, _sk])) -> le([_sk, _uk]), {
_sk -> s(s(s(s(z))))  ;  _tk -> cons(a, cons(a, cons(a, cons(a, cons(b, nil)))))  ;  _uk -> s(s(s(z)))  ;  l -> cons(b, cons(b, cons(b, cons(b, nil))))  ;  x -> a
})

-------------------------------------------
Step 78, which took 1.938714 s (model generation: 1.932600,  model checking: 0.006114):

Model:
|_
{
fcons -> 
{{{
Q={q_gen_2661, q_gen_2662, q_gen_2663, q_gen_2675, q_gen_2676, q_gen_2686, q_gen_2700, q_gen_2704, q_gen_2723, q_gen_2748},
Q_f={q_gen_2661},
Delta=
{
<nil>() -> q_gen_2662
<a>() -> q_gen_2663
<b>() -> q_gen_2663
<cons, cons>(q_gen_2686, q_gen_2675) -> q_gen_2675
<cons, cons>(q_gen_2686, q_gen_2704) -> q_gen_2675
<nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2675
<b, a>() -> q_gen_2676
<a, b>() -> q_gen_2686
<b, b>() -> q_gen_2686
<a, a>() -> q_gen_2700
<cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2704
<cons, cons>(q_gen_2676, q_gen_2748) -> q_gen_2704
<cons, cons>(q_gen_2700, q_gen_2675) -> q_gen_2704
<cons, cons>(q_gen_2700, q_gen_2704) -> q_gen_2704
<cons, cons>(q_gen_2676, q_gen_2704) -> q_gen_2748
<a, cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2661
<a, cons, cons>(q_gen_2700, q_gen_2675) -> q_gen_2661
<a, cons, cons>(q_gen_2700, q_gen_2704) -> q_gen_2661
<a, nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2661
<b, cons, cons>(q_gen_2686, q_gen_2675) -> q_gen_2661
<b, cons, cons>(q_gen_2686, q_gen_2704) -> q_gen_2661
<b, nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2661
<a, cons, cons>(q_gen_2676, q_gen_2704) -> q_gen_2723
<a, cons, cons>(q_gen_2676, q_gen_2748) -> q_gen_2723
<a, cons, cons>(q_gen_2686, q_gen_2675) -> q_gen_2723
<b, cons, cons>(q_gen_2686, q_gen_2748) -> q_gen_2723
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  le -> 
{{{
Q={q_gen_2659, q_gen_2660, q_gen_2683},
Q_f={q_gen_2659},
Delta=
{
<s>(q_gen_2660) -> q_gen_2660
<z>() -> q_gen_2660
<s, s>(q_gen_2659) -> q_gen_2659
<z, s>(q_gen_2660) -> q_gen_2659
<s, s>(q_gen_2683) -> q_gen_2683
<s, z>(q_gen_2660) -> q_gen_2683
<z, z>() -> q_gen_2683
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_2658, q_gen_2665, q_gen_2666, q_gen_2678, q_gen_2679, q_gen_2680, q_gen_2681, q_gen_2682, q_gen_2694, q_gen_2695, q_gen_2696},
Q_f={q_gen_2658},
Delta=
{
<nil>() -> q_gen_2665
<cons>(q_gen_2679, q_gen_2665) -> q_gen_2678
<cons>(q_gen_2679, q_gen_2694) -> q_gen_2678
<a>() -> q_gen_2679
<b>() -> q_gen_2679
<s>(q_gen_2696) -> q_gen_2681
<z>() -> q_gen_2681
<cons>(q_gen_2679, q_gen_2678) -> q_gen_2694
<s>(q_gen_2681) -> q_gen_2696
<cons, s>(q_gen_2666, q_gen_2665) -> q_gen_2658
<cons, s>(q_gen_2680, q_gen_2678) -> q_gen_2658
<cons, s>(q_gen_2695, q_gen_2694) -> q_gen_2658
<nil, z>() -> q_gen_2658
<a, z>() -> q_gen_2666
<b, z>() -> q_gen_2666
<a, s>(q_gen_2681) -> q_gen_2680
<b, s>(q_gen_2681) -> q_gen_2680
<cons, s>(q_gen_2666, q_gen_2678) -> q_gen_2682
<cons, s>(q_gen_2666, q_gen_2694) -> q_gen_2682
<cons, s>(q_gen_2680, q_gen_2665) -> q_gen_2682
<cons, s>(q_gen_2680, q_gen_2694) -> q_gen_2682
<cons, s>(q_gen_2695, q_gen_2665) -> q_gen_2682
<cons, s>(q_gen_2695, q_gen_2678) -> q_gen_2682
<a, s>(q_gen_2696) -> q_gen_2695
<b, s>(q_gen_2696) -> q_gen_2695
}

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

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

Teacher's answer:
New clause system:
{
() -> fcons([x, l, cons(x, l)]) -> 79
() -> le([z, s(nn2)]) -> 71
() -> length([nil, z]) -> 71
(fcons([x, l, _tk]) /\ length([_tk, _uk]) /\ length([l, _sk])) -> le([_sk, _uk]) -> 86
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 71
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 71
(le([s(nn1), z])) -> BOT -> 71
(le([z, z])) -> BOT -> 71
(length([ll, _kk])) -> length([cons(x, ll), s(_kk)]) -> 79
}
Sat witness: Found: ((fcons([x, l, _tk]) /\ length([_tk, _uk]) /\ length([l, _sk])) -> le([_sk, _uk]), {
_sk -> s(s(s(s(z))))  ;  _tk -> cons(a, cons(a, cons(b, nil)))  ;  _uk -> s(s(s(z)))  ;  l -> cons(a, cons(b, nil))  ;  x -> a
})

-------------------------------------------
Step 79, which took 1.935622 s (model generation: 1.931137,  model checking: 0.004485):

Model:
|_
{
fcons -> 
{{{
Q={q_gen_2661, q_gen_2662, q_gen_2663, q_gen_2675, q_gen_2676, q_gen_2686, q_gen_2692, q_gen_2704, q_gen_2723},
Q_f={q_gen_2661},
Delta=
{
<nil>() -> q_gen_2662
<a>() -> q_gen_2663
<b>() -> q_gen_2663
<cons, cons>(q_gen_2686, q_gen_2675) -> q_gen_2675
<cons, cons>(q_gen_2692, q_gen_2675) -> q_gen_2675
<nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2675
<b, a>() -> q_gen_2676
<b, b>() -> q_gen_2686
<a, a>() -> q_gen_2692
<a, b>() -> q_gen_2692
<cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2704
<cons, cons>(q_gen_2676, q_gen_2704) -> q_gen_2704
<cons, cons>(q_gen_2692, q_gen_2704) -> q_gen_2704
<a, cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2661
<a, cons, cons>(q_gen_2692, q_gen_2675) -> q_gen_2661
<a, cons, cons>(q_gen_2692, q_gen_2704) -> q_gen_2661
<a, nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2661
<b, cons, cons>(q_gen_2686, q_gen_2675) -> q_gen_2661
<b, cons, cons>(q_gen_2692, q_gen_2675) -> q_gen_2661
<b, cons, cons>(q_gen_2692, q_gen_2704) -> q_gen_2661
<b, nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2661
<a, cons, cons>(q_gen_2676, q_gen_2704) -> q_gen_2723
<a, cons, cons>(q_gen_2686, q_gen_2675) -> q_gen_2723
<b, cons, cons>(q_gen_2686, q_gen_2704) -> q_gen_2723
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  le -> 
{{{
Q={q_gen_2659, q_gen_2660, q_gen_2683},
Q_f={q_gen_2659},
Delta=
{
<s>(q_gen_2660) -> q_gen_2660
<z>() -> q_gen_2660
<s, s>(q_gen_2659) -> q_gen_2659
<z, s>(q_gen_2660) -> q_gen_2659
<s, s>(q_gen_2683) -> q_gen_2683
<s, z>(q_gen_2660) -> q_gen_2683
<z, z>() -> q_gen_2683
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_2658, q_gen_2665, q_gen_2666, q_gen_2678, q_gen_2679, q_gen_2680, q_gen_2681, q_gen_2682, q_gen_2694, q_gen_2695, q_gen_2696, q_gen_2711},
Q_f={q_gen_2658},
Delta=
{
<cons>(q_gen_2679, q_gen_2694) -> q_gen_2665
<nil>() -> q_gen_2665
<cons>(q_gen_2679, q_gen_2665) -> q_gen_2678
<a>() -> q_gen_2679
<b>() -> q_gen_2679
<s>(q_gen_2711) -> q_gen_2681
<z>() -> q_gen_2681
<cons>(q_gen_2679, q_gen_2678) -> q_gen_2694
<s>(q_gen_2681) -> q_gen_2696
<s>(q_gen_2696) -> q_gen_2711
<cons, s>(q_gen_2666, q_gen_2665) -> q_gen_2658
<cons, s>(q_gen_2680, q_gen_2678) -> q_gen_2658
<cons, s>(q_gen_2695, q_gen_2694) -> q_gen_2658
<nil, z>() -> q_gen_2658
<a, s>(q_gen_2711) -> q_gen_2666
<a, z>() -> q_gen_2666
<b, s>(q_gen_2711) -> q_gen_2666
<b, z>() -> q_gen_2666
<a, s>(q_gen_2681) -> q_gen_2680
<b, s>(q_gen_2681) -> q_gen_2680
<cons, s>(q_gen_2666, q_gen_2678) -> q_gen_2682
<cons, s>(q_gen_2666, q_gen_2694) -> q_gen_2682
<cons, s>(q_gen_2680, q_gen_2665) -> q_gen_2682
<cons, s>(q_gen_2680, q_gen_2694) -> q_gen_2682
<cons, s>(q_gen_2695, q_gen_2665) -> q_gen_2682
<cons, s>(q_gen_2695, q_gen_2678) -> q_gen_2682
<a, s>(q_gen_2696) -> q_gen_2695
<b, s>(q_gen_2696) -> q_gen_2695
}

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

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

Teacher's answer:
New clause system:
{
() -> fcons([x, l, cons(x, l)]) -> 82
() -> le([z, s(nn2)]) -> 72
() -> length([nil, z]) -> 72
(fcons([x, l, _tk]) /\ length([_tk, _uk]) /\ length([l, _sk])) -> le([_sk, _uk]) -> 86
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 72
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 72
(le([s(nn1), z])) -> BOT -> 72
(le([z, z])) -> BOT -> 72
(length([ll, _kk])) -> length([cons(x, ll), s(_kk)]) -> 80
}
Sat witness: Found: (() -> fcons([x, l, cons(x, l)]), {
l -> cons(b, cons(a, cons(b, nil)))  ;  x -> a
})

-------------------------------------------
Step 80, which took 2.850361 s (model generation: 2.841625,  model checking: 0.008736):

Model:
|_
{
fcons -> 
{{{
Q={q_gen_2661, q_gen_2662, q_gen_2663, q_gen_2675, q_gen_2676, q_gen_2686, q_gen_2692, q_gen_2704, q_gen_2723},
Q_f={q_gen_2661},
Delta=
{
<nil>() -> q_gen_2662
<a>() -> q_gen_2663
<b>() -> q_gen_2663
<cons, cons>(q_gen_2686, q_gen_2675) -> q_gen_2675
<cons, cons>(q_gen_2692, q_gen_2675) -> q_gen_2675
<cons, cons>(q_gen_2692, q_gen_2704) -> q_gen_2675
<nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2675
<b, a>() -> q_gen_2676
<b, b>() -> q_gen_2686
<a, a>() -> q_gen_2692
<a, b>() -> q_gen_2692
<cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2704
<cons, cons>(q_gen_2676, q_gen_2704) -> q_gen_2704
<a, cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2661
<a, cons, cons>(q_gen_2692, q_gen_2675) -> q_gen_2661
<a, cons, cons>(q_gen_2692, q_gen_2704) -> q_gen_2661
<a, nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2661
<b, cons, cons>(q_gen_2686, q_gen_2675) -> q_gen_2661
<b, cons, cons>(q_gen_2692, q_gen_2675) -> q_gen_2661
<b, cons, cons>(q_gen_2692, q_gen_2704) -> q_gen_2661
<b, nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2661
<a, cons, cons>(q_gen_2676, q_gen_2704) -> q_gen_2723
<a, cons, cons>(q_gen_2686, q_gen_2675) -> q_gen_2723
<b, cons, cons>(q_gen_2686, q_gen_2704) -> q_gen_2723
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  le -> 
{{{
Q={q_gen_2659, q_gen_2660, q_gen_2683},
Q_f={q_gen_2659},
Delta=
{
<s>(q_gen_2660) -> q_gen_2660
<z>() -> q_gen_2660
<s, s>(q_gen_2659) -> q_gen_2659
<z, s>(q_gen_2660) -> q_gen_2659
<s, s>(q_gen_2683) -> q_gen_2683
<s, z>(q_gen_2660) -> q_gen_2683
<z, z>() -> q_gen_2683
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_2658, q_gen_2665, q_gen_2666, q_gen_2678, q_gen_2679, q_gen_2680, q_gen_2681, q_gen_2682, q_gen_2694, q_gen_2695, q_gen_2696, q_gen_2711},
Q_f={q_gen_2658},
Delta=
{
<cons>(q_gen_2679, q_gen_2694) -> q_gen_2665
<nil>() -> q_gen_2665
<cons>(q_gen_2679, q_gen_2665) -> q_gen_2678
<a>() -> q_gen_2679
<b>() -> q_gen_2679
<s>(q_gen_2711) -> q_gen_2681
<z>() -> q_gen_2681
<cons>(q_gen_2679, q_gen_2678) -> q_gen_2694
<s>(q_gen_2681) -> q_gen_2696
<s>(q_gen_2696) -> q_gen_2711
<cons, s>(q_gen_2666, q_gen_2665) -> q_gen_2658
<cons, s>(q_gen_2680, q_gen_2678) -> q_gen_2658
<cons, s>(q_gen_2695, q_gen_2694) -> q_gen_2658
<nil, z>() -> q_gen_2658
<a, s>(q_gen_2711) -> q_gen_2666
<a, z>() -> q_gen_2666
<b, s>(q_gen_2711) -> q_gen_2666
<b, z>() -> q_gen_2666
<a, s>(q_gen_2681) -> q_gen_2680
<b, s>(q_gen_2681) -> q_gen_2680
<cons, s>(q_gen_2666, q_gen_2678) -> q_gen_2682
<cons, s>(q_gen_2666, q_gen_2694) -> q_gen_2682
<cons, s>(q_gen_2680, q_gen_2665) -> q_gen_2682
<cons, s>(q_gen_2680, q_gen_2694) -> q_gen_2682
<cons, s>(q_gen_2695, q_gen_2665) -> q_gen_2682
<cons, s>(q_gen_2695, q_gen_2678) -> q_gen_2682
<a, s>(q_gen_2696) -> q_gen_2695
<b, s>(q_gen_2696) -> q_gen_2695
}

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

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

Teacher's answer:
New clause system:
{
() -> fcons([x, l, cons(x, l)]) -> 83
() -> le([z, s(nn2)]) -> 73
() -> length([nil, z]) -> 73
(fcons([x, l, _tk]) /\ length([_tk, _uk]) /\ length([l, _sk])) -> le([_sk, _uk]) -> 89
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 73
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 73
(le([s(nn1), z])) -> BOT -> 73
(le([z, z])) -> BOT -> 73
(length([ll, _kk])) -> length([cons(x, ll), s(_kk)]) -> 81
}
Sat witness: Found: ((fcons([x, l, _tk]) /\ length([_tk, _uk]) /\ length([l, _sk])) -> le([_sk, _uk]), {
_sk -> s(s(s(s(z))))  ;  _tk -> cons(a, cons(a, cons(a, cons(a, cons(b, nil)))))  ;  _uk -> s(s(z))  ;  l -> cons(a, cons(b, cons(b, cons(b, nil))))  ;  x -> b
})

-------------------------------------------
Step 81, which took 4.112762 s (model generation: 4.107841,  model checking: 0.004921):

Model:
|_
{
fcons -> 
{{{
Q={q_gen_2661, q_gen_2662, q_gen_2663, q_gen_2675, q_gen_2676, q_gen_2686, q_gen_2700, q_gen_2704, q_gen_2723, q_gen_2748},
Q_f={q_gen_2661},
Delta=
{
<nil>() -> q_gen_2662
<a>() -> q_gen_2663
<b>() -> q_gen_2663
<cons, cons>(q_gen_2686, q_gen_2675) -> q_gen_2675
<cons, cons>(q_gen_2686, q_gen_2704) -> q_gen_2675
<cons, cons>(q_gen_2700, q_gen_2675) -> q_gen_2675
<nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2675
<b, a>() -> q_gen_2676
<a, b>() -> q_gen_2686
<b, b>() -> q_gen_2686
<a, a>() -> q_gen_2700
<cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2704
<cons, cons>(q_gen_2676, q_gen_2704) -> q_gen_2748
<cons, cons>(q_gen_2676, q_gen_2748) -> q_gen_2748
<cons, cons>(q_gen_2700, q_gen_2704) -> q_gen_2748
<a, cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2661
<a, cons, cons>(q_gen_2700, q_gen_2675) -> q_gen_2661
<a, cons, cons>(q_gen_2700, q_gen_2704) -> q_gen_2661
<a, cons, cons>(q_gen_2700, q_gen_2748) -> q_gen_2661
<a, nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2661
<b, cons, cons>(q_gen_2686, q_gen_2675) -> q_gen_2661
<b, cons, cons>(q_gen_2686, q_gen_2704) -> q_gen_2661
<b, nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2661
<a, cons, cons>(q_gen_2676, q_gen_2704) -> q_gen_2723
<a, cons, cons>(q_gen_2676, q_gen_2748) -> q_gen_2723
<a, cons, cons>(q_gen_2686, q_gen_2675) -> q_gen_2723
<b, cons, cons>(q_gen_2686, q_gen_2748) -> q_gen_2723
<b, cons, cons>(q_gen_2700, q_gen_2748) -> q_gen_2723
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  le -> 
{{{
Q={q_gen_2659, q_gen_2660, q_gen_2683},
Q_f={q_gen_2659},
Delta=
{
<s>(q_gen_2660) -> q_gen_2660
<z>() -> q_gen_2660
<s, s>(q_gen_2659) -> q_gen_2659
<z, s>(q_gen_2660) -> q_gen_2659
<s, s>(q_gen_2683) -> q_gen_2683
<s, z>(q_gen_2660) -> q_gen_2683
<z, z>() -> q_gen_2683
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_2658, q_gen_2665, q_gen_2666, q_gen_2678, q_gen_2679, q_gen_2680, q_gen_2681, q_gen_2682, q_gen_2694, q_gen_2695, q_gen_2696, q_gen_2711},
Q_f={q_gen_2658},
Delta=
{
<cons>(q_gen_2679, q_gen_2694) -> q_gen_2665
<nil>() -> q_gen_2665
<cons>(q_gen_2679, q_gen_2665) -> q_gen_2678
<a>() -> q_gen_2679
<b>() -> q_gen_2679
<s>(q_gen_2711) -> q_gen_2681
<z>() -> q_gen_2681
<cons>(q_gen_2679, q_gen_2678) -> q_gen_2694
<s>(q_gen_2681) -> q_gen_2696
<s>(q_gen_2696) -> q_gen_2711
<cons, s>(q_gen_2666, q_gen_2665) -> q_gen_2658
<cons, s>(q_gen_2680, q_gen_2678) -> q_gen_2658
<cons, s>(q_gen_2695, q_gen_2694) -> q_gen_2658
<nil, z>() -> q_gen_2658
<a, s>(q_gen_2711) -> q_gen_2666
<a, z>() -> q_gen_2666
<b, s>(q_gen_2711) -> q_gen_2666
<b, z>() -> q_gen_2666
<a, s>(q_gen_2681) -> q_gen_2680
<b, s>(q_gen_2681) -> q_gen_2680
<cons, s>(q_gen_2666, q_gen_2678) -> q_gen_2682
<cons, s>(q_gen_2666, q_gen_2694) -> q_gen_2682
<cons, s>(q_gen_2680, q_gen_2665) -> q_gen_2682
<cons, s>(q_gen_2680, q_gen_2694) -> q_gen_2682
<cons, s>(q_gen_2695, q_gen_2665) -> q_gen_2682
<cons, s>(q_gen_2695, q_gen_2678) -> q_gen_2682
<a, s>(q_gen_2696) -> q_gen_2695
<b, s>(q_gen_2696) -> q_gen_2695
}

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

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

Teacher's answer:
New clause system:
{
() -> fcons([x, l, cons(x, l)]) -> 86
() -> le([z, s(nn2)]) -> 74
() -> length([nil, z]) -> 74
(fcons([x, l, _tk]) /\ length([_tk, _uk]) /\ length([l, _sk])) -> le([_sk, _uk]) -> 89
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 74
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 74
(le([s(nn1), z])) -> BOT -> 74
(le([z, z])) -> BOT -> 74
(length([ll, _kk])) -> length([cons(x, ll), s(_kk)]) -> 82
}
Sat witness: Found: (() -> fcons([x, l, cons(x, l)]), {
l -> cons(a, cons(a, cons(b, nil)))  ;  x -> b
})

-------------------------------------------
Step 82, which took 1.644263 s (model generation: 1.631563,  model checking: 0.012700):

Model:
|_
{
fcons -> 
{{{
Q={q_gen_2661, q_gen_2662, q_gen_2663, q_gen_2675, q_gen_2676},
Q_f={q_gen_2661},
Delta=
{
<nil>() -> q_gen_2662
<a>() -> q_gen_2663
<b>() -> q_gen_2663
<cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2675
<nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2675
<a, a>() -> q_gen_2676
<a, b>() -> q_gen_2676
<b, a>() -> q_gen_2676
<b, b>() -> q_gen_2676
<a, cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2661
<a, nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2661
<b, cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2661
<b, nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2661
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  le -> 
{{{
Q={q_gen_2659, q_gen_2660, q_gen_2683},
Q_f={q_gen_2659},
Delta=
{
<s>(q_gen_2660) -> q_gen_2660
<z>() -> q_gen_2660
<s, s>(q_gen_2659) -> q_gen_2659
<z, s>(q_gen_2660) -> q_gen_2659
<s, s>(q_gen_2683) -> q_gen_2683
<s, z>(q_gen_2660) -> q_gen_2683
<z, z>() -> q_gen_2683
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_2658, q_gen_2665, q_gen_2666, q_gen_2678, q_gen_2679, q_gen_2680, q_gen_2681, q_gen_2682, q_gen_2689, q_gen_2694, q_gen_2695, q_gen_2696, q_gen_2709, q_gen_2710, q_gen_2711, q_gen_2725, q_gen_2731},
Q_f={q_gen_2658},
Delta=
{
<cons>(q_gen_2689, q_gen_2709) -> q_gen_2665
<nil>() -> q_gen_2665
<cons>(q_gen_2679, q_gen_2665) -> q_gen_2678
<cons>(q_gen_2679, q_gen_2725) -> q_gen_2678
<cons>(q_gen_2689, q_gen_2665) -> q_gen_2678
<b>() -> q_gen_2679
<z>() -> q_gen_2681
<a>() -> q_gen_2689
<cons>(q_gen_2679, q_gen_2678) -> q_gen_2694
<s>(q_gen_2681) -> q_gen_2696
<s>(q_gen_2711) -> q_gen_2696
<cons>(q_gen_2679, q_gen_2694) -> q_gen_2709
<cons>(q_gen_2689, q_gen_2694) -> q_gen_2709
<cons>(q_gen_2689, q_gen_2725) -> q_gen_2709
<s>(q_gen_2696) -> q_gen_2711
<cons>(q_gen_2679, q_gen_2709) -> q_gen_2725
<cons>(q_gen_2689, q_gen_2678) -> q_gen_2725
<cons, s>(q_gen_2666, q_gen_2665) -> q_gen_2658
<cons, s>(q_gen_2680, q_gen_2678) -> q_gen_2658
<cons, s>(q_gen_2695, q_gen_2694) -> q_gen_2658
<cons, s>(q_gen_2710, q_gen_2709) -> q_gen_2658
<cons, s>(q_gen_2731, q_gen_2694) -> q_gen_2658
<cons, s>(q_gen_2731, q_gen_2725) -> q_gen_2658
<nil, z>() -> q_gen_2658
<a, z>() -> q_gen_2666
<b, z>() -> q_gen_2666
<a, s>(q_gen_2681) -> q_gen_2680
<b, s>(q_gen_2681) -> q_gen_2680
<cons, s>(q_gen_2666, q_gen_2678) -> q_gen_2682
<cons, s>(q_gen_2666, q_gen_2709) -> q_gen_2682
<cons, s>(q_gen_2666, q_gen_2725) -> q_gen_2682
<cons, s>(q_gen_2680, q_gen_2665) -> q_gen_2682
<cons, s>(q_gen_2680, q_gen_2694) -> q_gen_2682
<cons, s>(q_gen_2680, q_gen_2709) -> q_gen_2682
<cons, s>(q_gen_2680, q_gen_2725) -> q_gen_2682
<cons, s>(q_gen_2695, q_gen_2665) -> q_gen_2682
<cons, s>(q_gen_2695, q_gen_2678) -> q_gen_2682
<cons, s>(q_gen_2695, q_gen_2709) -> q_gen_2682
<cons, s>(q_gen_2695, q_gen_2725) -> q_gen_2682
<cons, s>(q_gen_2710, q_gen_2665) -> q_gen_2682
<cons, s>(q_gen_2710, q_gen_2678) -> q_gen_2682
<cons, s>(q_gen_2710, q_gen_2694) -> q_gen_2682
<cons, s>(q_gen_2710, q_gen_2725) -> q_gen_2682
<cons, s>(q_gen_2731, q_gen_2665) -> q_gen_2682
<cons, s>(q_gen_2731, q_gen_2709) -> q_gen_2682
<b, s>(q_gen_2696) -> q_gen_2695
<a, s>(q_gen_2711) -> q_gen_2710
<b, s>(q_gen_2711) -> q_gen_2710
<a, s>(q_gen_2696) -> q_gen_2731
}

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

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

Teacher's answer:
New clause system:
{
() -> fcons([x, l, cons(x, l)]) -> 86
() -> le([z, s(nn2)]) -> 75
() -> length([nil, z]) -> 75
(fcons([x, l, _tk]) /\ length([_tk, _uk]) /\ length([l, _sk])) -> le([_sk, _uk]) -> 89
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 75
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 75
(le([s(nn1), z])) -> BOT -> 75
(le([z, z])) -> BOT -> 75
(length([ll, _kk])) -> length([cons(x, ll), s(_kk)]) -> 85
}
Sat witness: Found: ((length([ll, _kk])) -> length([cons(x, ll), s(_kk)]), {
_kk -> s(s(s(s(z))))  ;  ll -> cons(a, cons(a, cons(a, cons(a, nil))))  ;  x -> a
})

-------------------------------------------
Step 83, which took 1.740087 s (model generation: 1.738255,  model checking: 0.001832):

Model:
|_
{
fcons -> 
{{{
Q={q_gen_2661, q_gen_2662, q_gen_2663, q_gen_2675, q_gen_2676, q_gen_2686, q_gen_2692, q_gen_2704, q_gen_2733},
Q_f={q_gen_2661},
Delta=
{
<nil>() -> q_gen_2662
<a>() -> q_gen_2663
<b>() -> q_gen_2663
<cons, cons>(q_gen_2686, q_gen_2675) -> q_gen_2675
<cons, cons>(q_gen_2692, q_gen_2675) -> q_gen_2675
<cons, cons>(q_gen_2692, q_gen_2704) -> q_gen_2675
<nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2675
<a, a>() -> q_gen_2676
<b, a>() -> q_gen_2676
<b, b>() -> q_gen_2686
<a, b>() -> q_gen_2692
<cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2704
<cons, cons>(q_gen_2676, q_gen_2704) -> q_gen_2704
<a, cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2661
<a, cons, cons>(q_gen_2676, q_gen_2704) -> q_gen_2661
<a, nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2661
<b, cons, cons>(q_gen_2686, q_gen_2675) -> q_gen_2661
<b, cons, cons>(q_gen_2692, q_gen_2675) -> q_gen_2661
<b, cons, cons>(q_gen_2692, q_gen_2704) -> q_gen_2661
<b, nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2661
<a, cons, cons>(q_gen_2686, q_gen_2675) -> q_gen_2733
<b, cons, cons>(q_gen_2676, q_gen_2704) -> q_gen_2733
<b, cons, cons>(q_gen_2686, q_gen_2704) -> q_gen_2733
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  le -> 
{{{
Q={q_gen_2659, q_gen_2660, q_gen_2683},
Q_f={q_gen_2659},
Delta=
{
<s>(q_gen_2660) -> q_gen_2660
<z>() -> q_gen_2660
<s, s>(q_gen_2659) -> q_gen_2659
<z, s>(q_gen_2660) -> q_gen_2659
<s, s>(q_gen_2683) -> q_gen_2683
<s, z>(q_gen_2660) -> q_gen_2683
<z, z>() -> q_gen_2683
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_2658, q_gen_2665, q_gen_2666, q_gen_2678, q_gen_2679, q_gen_2680, q_gen_2681, q_gen_2682, q_gen_2694, q_gen_2695, q_gen_2696, q_gen_2711, q_gen_2759},
Q_f={q_gen_2658},
Delta=
{
<cons>(q_gen_2679, q_gen_2694) -> q_gen_2665
<nil>() -> q_gen_2665
<cons>(q_gen_2679, q_gen_2665) -> q_gen_2678
<a>() -> q_gen_2679
<b>() -> q_gen_2679
<z>() -> q_gen_2681
<cons>(q_gen_2679, q_gen_2678) -> q_gen_2694
<s>(q_gen_2681) -> q_gen_2696
<s>(q_gen_2696) -> q_gen_2711
<s>(q_gen_2759) -> q_gen_2711
<s>(q_gen_2711) -> q_gen_2759
<cons, s>(q_gen_2666, q_gen_2665) -> q_gen_2658
<cons, s>(q_gen_2680, q_gen_2678) -> q_gen_2658
<cons, s>(q_gen_2695, q_gen_2694) -> q_gen_2658
<nil, z>() -> q_gen_2658
<a, s>(q_gen_2711) -> q_gen_2666
<a, z>() -> q_gen_2666
<b, s>(q_gen_2711) -> q_gen_2666
<b, z>() -> q_gen_2666
<a, s>(q_gen_2681) -> q_gen_2680
<a, s>(q_gen_2759) -> q_gen_2680
<b, s>(q_gen_2681) -> q_gen_2680
<b, s>(q_gen_2759) -> q_gen_2680
<cons, s>(q_gen_2666, q_gen_2678) -> q_gen_2682
<cons, s>(q_gen_2666, q_gen_2694) -> q_gen_2682
<cons, s>(q_gen_2680, q_gen_2665) -> q_gen_2682
<cons, s>(q_gen_2680, q_gen_2694) -> q_gen_2682
<cons, s>(q_gen_2695, q_gen_2665) -> q_gen_2682
<cons, s>(q_gen_2695, q_gen_2678) -> q_gen_2682
<a, s>(q_gen_2696) -> q_gen_2695
<b, s>(q_gen_2696) -> q_gen_2695
}

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

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

Teacher's answer:
New clause system:
{
() -> fcons([x, l, cons(x, l)]) -> 86
() -> le([z, s(nn2)]) -> 76
() -> length([nil, z]) -> 76
(fcons([x, l, _tk]) /\ length([_tk, _uk]) /\ length([l, _sk])) -> le([_sk, _uk]) -> 89
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 76
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 76
(le([s(nn1), z])) -> BOT -> 76
(le([z, z])) -> BOT -> 76
(length([ll, _kk])) -> length([cons(x, ll), s(_kk)]) -> 88
}
Sat witness: Found: ((length([ll, _kk])) -> length([cons(x, ll), s(_kk)]), {
_kk -> s(s(s(s(s(z)))))  ;  ll -> cons(b, cons(b, nil))  ;  x -> b
})

-------------------------------------------
Step 84, which took 2.974334 s (model generation: 2.974057,  model checking: 0.000277):

Model:
|_
{
fcons -> 
{{{
Q={q_gen_2661, q_gen_2662, q_gen_2663, q_gen_2675, q_gen_2676},
Q_f={q_gen_2661},
Delta=
{
<nil>() -> q_gen_2662
<a>() -> q_gen_2663
<b>() -> q_gen_2663
<cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2675
<nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2675
<a, a>() -> q_gen_2676
<a, b>() -> q_gen_2676
<b, a>() -> q_gen_2676
<b, b>() -> q_gen_2676
<a, cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2661
<a, nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2661
<b, cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2661
<b, nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2661
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  le -> 
{{{
Q={q_gen_2659, q_gen_2660, q_gen_2683, q_gen_2684, q_gen_2698, q_gen_2713},
Q_f={q_gen_2659},
Delta=
{
<s>(q_gen_2660) -> q_gen_2660
<z>() -> q_gen_2660
<s, s>(q_gen_2659) -> q_gen_2659
<s, s>(q_gen_2713) -> q_gen_2659
<z, s>(q_gen_2660) -> q_gen_2659
<s, s>(q_gen_2684) -> q_gen_2683
<s, z>(q_gen_2660) -> q_gen_2683
<z, z>() -> q_gen_2684
<s, s>(q_gen_2683) -> q_gen_2698
<s, s>(q_gen_2698) -> q_gen_2713
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_2658, q_gen_2665, q_gen_2666, q_gen_2678, q_gen_2679, q_gen_2680, q_gen_2681, q_gen_2682, q_gen_2694, q_gen_2695, q_gen_2696, q_gen_2709, q_gen_2710, q_gen_2711},
Q_f={q_gen_2658},
Delta=
{
<nil>() -> q_gen_2665
<cons>(q_gen_2679, q_gen_2665) -> q_gen_2678
<a>() -> q_gen_2679
<b>() -> q_gen_2679
<z>() -> q_gen_2681
<cons>(q_gen_2679, q_gen_2678) -> q_gen_2694
<s>(q_gen_2681) -> q_gen_2696
<cons>(q_gen_2679, q_gen_2694) -> q_gen_2709
<cons>(q_gen_2679, q_gen_2709) -> q_gen_2709
<s>(q_gen_2696) -> q_gen_2711
<s>(q_gen_2711) -> q_gen_2711
<cons, s>(q_gen_2666, q_gen_2665) -> q_gen_2658
<cons, s>(q_gen_2680, q_gen_2678) -> q_gen_2658
<cons, s>(q_gen_2695, q_gen_2694) -> q_gen_2658
<cons, s>(q_gen_2710, q_gen_2709) -> q_gen_2658
<nil, z>() -> q_gen_2658
<a, z>() -> q_gen_2666
<b, z>() -> q_gen_2666
<a, s>(q_gen_2681) -> q_gen_2680
<b, s>(q_gen_2681) -> q_gen_2680
<cons, s>(q_gen_2666, q_gen_2678) -> q_gen_2682
<cons, s>(q_gen_2666, q_gen_2709) -> q_gen_2682
<cons, s>(q_gen_2680, q_gen_2665) -> q_gen_2682
<cons, s>(q_gen_2680, q_gen_2694) -> q_gen_2682
<cons, s>(q_gen_2680, q_gen_2709) -> q_gen_2682
<cons, s>(q_gen_2695, q_gen_2665) -> q_gen_2682
<cons, s>(q_gen_2695, q_gen_2678) -> q_gen_2682
<cons, s>(q_gen_2695, q_gen_2709) -> q_gen_2682
<cons, s>(q_gen_2710, q_gen_2665) -> q_gen_2682
<cons, s>(q_gen_2710, q_gen_2678) -> q_gen_2682
<cons, s>(q_gen_2710, q_gen_2694) -> q_gen_2682
<a, s>(q_gen_2696) -> q_gen_2695
<b, s>(q_gen_2696) -> q_gen_2695
<a, s>(q_gen_2711) -> q_gen_2710
<b, s>(q_gen_2711) -> q_gen_2710
}

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

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

Teacher's answer:
New clause system:
{
() -> fcons([x, l, cons(x, l)]) -> 86
() -> le([z, s(nn2)]) -> 76
() -> length([nil, z]) -> 76
(fcons([x, l, _tk]) /\ length([_tk, _uk]) /\ length([l, _sk])) -> le([_sk, _uk]) -> 89
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 76
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 79
(le([s(nn1), z])) -> BOT -> 77
(le([z, z])) -> BOT -> 77
(length([ll, _kk])) -> length([cons(x, ll), s(_kk)]) -> 88
}
Sat witness: Found: ((le([s(nn1), s(nn2)])) -> le([nn1, nn2]), {
nn1 -> s(s(s(z)))  ;  nn2 -> s(s(z))
})

-------------------------------------------
Step 85, which took 2.358149 s (model generation: 2.357028,  model checking: 0.001121):

Model:
|_
{
fcons -> 
{{{
Q={q_gen_2661, q_gen_2662, q_gen_2663, q_gen_2675, q_gen_2676},
Q_f={q_gen_2661},
Delta=
{
<nil>() -> q_gen_2662
<a>() -> q_gen_2663
<b>() -> q_gen_2663
<cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2675
<nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2675
<a, a>() -> q_gen_2676
<a, b>() -> q_gen_2676
<b, a>() -> q_gen_2676
<b, b>() -> q_gen_2676
<a, cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2661
<a, nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2661
<b, cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2661
<b, nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2661
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  le -> 
{{{
Q={q_gen_2659, q_gen_2660, q_gen_2669, q_gen_2683, q_gen_2744, q_gen_2745},
Q_f={q_gen_2659},
Delta=
{
<s>(q_gen_2669) -> q_gen_2660
<z>() -> q_gen_2660
<s>(q_gen_2660) -> q_gen_2669
<s, s>(q_gen_2659) -> q_gen_2659
<s, s>(q_gen_2744) -> q_gen_2659
<z, s>(q_gen_2660) -> q_gen_2659
<z, s>(q_gen_2669) -> q_gen_2659
<s, s>(q_gen_2683) -> q_gen_2683
<s, z>(q_gen_2660) -> q_gen_2683
<z, z>() -> q_gen_2683
<s, s>(q_gen_2745) -> q_gen_2744
<s, z>(q_gen_2669) -> q_gen_2745
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_2658, q_gen_2665, q_gen_2666, q_gen_2673, q_gen_2678, q_gen_2679, q_gen_2680, q_gen_2681, q_gen_2682, q_gen_2694, q_gen_2695, q_gen_2696, q_gen_2709, q_gen_2711},
Q_f={q_gen_2658},
Delta=
{
<nil>() -> q_gen_2665
<cons>(q_gen_2679, q_gen_2665) -> q_gen_2678
<cons>(q_gen_2679, q_gen_2709) -> q_gen_2678
<a>() -> q_gen_2679
<b>() -> q_gen_2679
<s>(q_gen_2711) -> q_gen_2681
<z>() -> q_gen_2681
<cons>(q_gen_2679, q_gen_2678) -> q_gen_2694
<s>(q_gen_2681) -> q_gen_2696
<cons>(q_gen_2679, q_gen_2694) -> q_gen_2709
<s>(q_gen_2696) -> q_gen_2711
<cons, s>(q_gen_2666, q_gen_2665) -> q_gen_2658
<cons, s>(q_gen_2673, q_gen_2665) -> q_gen_2658
<cons, s>(q_gen_2673, q_gen_2709) -> q_gen_2658
<cons, s>(q_gen_2680, q_gen_2678) -> q_gen_2658
<cons, s>(q_gen_2695, q_gen_2694) -> q_gen_2658
<nil, z>() -> q_gen_2658
<b, z>() -> q_gen_2666
<a, s>(q_gen_2711) -> q_gen_2673
<a, z>() -> q_gen_2673
<b, s>(q_gen_2711) -> q_gen_2673
<a, s>(q_gen_2681) -> q_gen_2680
<b, s>(q_gen_2681) -> q_gen_2680
<cons, s>(q_gen_2666, q_gen_2678) -> q_gen_2682
<cons, s>(q_gen_2666, q_gen_2709) -> q_gen_2682
<cons, s>(q_gen_2673, q_gen_2678) -> q_gen_2682
<cons, s>(q_gen_2673, q_gen_2694) -> q_gen_2682
<cons, s>(q_gen_2680, q_gen_2665) -> q_gen_2682
<cons, s>(q_gen_2680, q_gen_2694) -> q_gen_2682
<cons, s>(q_gen_2680, q_gen_2709) -> q_gen_2682
<cons, s>(q_gen_2695, q_gen_2665) -> q_gen_2682
<cons, s>(q_gen_2695, q_gen_2678) -> q_gen_2682
<cons, s>(q_gen_2695, q_gen_2709) -> q_gen_2682
<a, s>(q_gen_2696) -> q_gen_2695
<b, s>(q_gen_2696) -> q_gen_2695
}

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

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

Teacher's answer:
New clause system:
{
() -> fcons([x, l, cons(x, l)]) -> 86
() -> le([z, s(nn2)]) -> 77
() -> length([nil, z]) -> 77
(fcons([x, l, _tk]) /\ length([_tk, _uk]) /\ length([l, _sk])) -> le([_sk, _uk]) -> 89
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 77
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 82
(le([s(nn1), z])) -> BOT -> 78
(le([z, z])) -> BOT -> 78
(length([ll, _kk])) -> length([cons(x, ll), s(_kk)]) -> 88
}
Sat witness: Found: ((le([s(nn1), s(nn2)])) -> le([nn1, nn2]), {
nn1 -> s(s(s(z)))  ;  nn2 -> s(z)
})

-------------------------------------------
Step 86, which took 1.504728 s (model generation: 1.499648,  model checking: 0.005080):

Model:
|_
{
fcons -> 
{{{
Q={q_gen_2661, q_gen_2662, q_gen_2663, q_gen_2675, q_gen_2676, q_gen_2686, q_gen_2733},
Q_f={q_gen_2661},
Delta=
{
<nil>() -> q_gen_2662
<a>() -> q_gen_2663
<b>() -> q_gen_2663
<cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2675
<cons, cons>(q_gen_2686, q_gen_2675) -> q_gen_2675
<nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2675
<a, a>() -> q_gen_2676
<b, a>() -> q_gen_2676
<a, b>() -> q_gen_2686
<b, b>() -> q_gen_2686
<a, cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2661
<a, nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2661
<b, cons, cons>(q_gen_2686, q_gen_2675) -> q_gen_2661
<b, nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2661
<a, cons, cons>(q_gen_2686, q_gen_2675) -> q_gen_2733
<b, cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2733
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  le -> 
{{{
Q={q_gen_2659, q_gen_2660, q_gen_2683},
Q_f={q_gen_2659},
Delta=
{
<s>(q_gen_2660) -> q_gen_2660
<z>() -> q_gen_2660
<s, s>(q_gen_2659) -> q_gen_2659
<z, s>(q_gen_2660) -> q_gen_2659
<s, s>(q_gen_2683) -> q_gen_2683
<s, z>(q_gen_2660) -> q_gen_2683
<z, z>() -> q_gen_2683
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_2658, q_gen_2665, q_gen_2666, q_gen_2678, q_gen_2679, q_gen_2680, q_gen_2681, q_gen_2682, q_gen_2689, q_gen_2694, q_gen_2695, q_gen_2696, q_gen_2710, q_gen_2711, q_gen_2750},
Q_f={q_gen_2658},
Delta=
{
<cons>(q_gen_2679, q_gen_2694) -> q_gen_2665
<nil>() -> q_gen_2665
<cons>(q_gen_2679, q_gen_2665) -> q_gen_2678
<cons>(q_gen_2689, q_gen_2665) -> q_gen_2678
<cons>(q_gen_2689, q_gen_2750) -> q_gen_2678
<b>() -> q_gen_2679
<s>(q_gen_2711) -> q_gen_2681
<z>() -> q_gen_2681
<a>() -> q_gen_2689
<cons>(q_gen_2679, q_gen_2678) -> q_gen_2694
<cons>(q_gen_2689, q_gen_2678) -> q_gen_2694
<s>(q_gen_2681) -> q_gen_2696
<s>(q_gen_2696) -> q_gen_2711
<cons>(q_gen_2689, q_gen_2694) -> q_gen_2750
<cons, s>(q_gen_2666, q_gen_2665) -> q_gen_2658
<cons, s>(q_gen_2680, q_gen_2678) -> q_gen_2658
<cons, s>(q_gen_2695, q_gen_2694) -> q_gen_2658
<cons, s>(q_gen_2710, q_gen_2665) -> q_gen_2658
<cons, s>(q_gen_2710, q_gen_2750) -> q_gen_2658
<nil, z>() -> q_gen_2658
<a, s>(q_gen_2711) -> q_gen_2666
<a, z>() -> q_gen_2666
<b, z>() -> q_gen_2666
<a, s>(q_gen_2681) -> q_gen_2680
<b, s>(q_gen_2681) -> q_gen_2680
<cons, s>(q_gen_2666, q_gen_2678) -> q_gen_2682
<cons, s>(q_gen_2666, q_gen_2694) -> q_gen_2682
<cons, s>(q_gen_2666, q_gen_2750) -> q_gen_2682
<cons, s>(q_gen_2680, q_gen_2665) -> q_gen_2682
<cons, s>(q_gen_2680, q_gen_2694) -> q_gen_2682
<cons, s>(q_gen_2680, q_gen_2750) -> q_gen_2682
<cons, s>(q_gen_2695, q_gen_2665) -> q_gen_2682
<cons, s>(q_gen_2695, q_gen_2678) -> q_gen_2682
<cons, s>(q_gen_2710, q_gen_2678) -> q_gen_2682
<a, s>(q_gen_2696) -> q_gen_2695
<b, s>(q_gen_2696) -> q_gen_2695
<b, s>(q_gen_2711) -> q_gen_2710
}

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

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

Teacher's answer:
New clause system:
{
() -> fcons([x, l, cons(x, l)]) -> 87
() -> le([z, s(nn2)]) -> 78
() -> length([nil, z]) -> 78
(fcons([x, l, _tk]) /\ length([_tk, _uk]) /\ length([l, _sk])) -> le([_sk, _uk]) -> 89
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 78
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 83
(le([s(nn1), z])) -> BOT -> 79
(le([z, z])) -> BOT -> 79
(length([ll, _kk])) -> length([cons(x, ll), s(_kk)]) -> 91
}
Sat witness: Found: ((length([ll, _kk])) -> length([cons(x, ll), s(_kk)]), {
_kk -> s(s(s(z)))  ;  ll -> cons(a, cons(b, cons(a, nil)))  ;  x -> a
})

-------------------------------------------
Step 87, which took 2.200091 s (model generation: 2.194864,  model checking: 0.005227):

Model:
|_
{
fcons -> 
{{{
Q={q_gen_2661, q_gen_2662, q_gen_2663, q_gen_2671, q_gen_2675, q_gen_2676, q_gen_2686, q_gen_2691, q_gen_2692, q_gen_2705},
Q_f={q_gen_2661},
Delta=
{
<nil>() -> q_gen_2662
<b>() -> q_gen_2663
<a>() -> q_gen_2671
<cons, cons>(q_gen_2686, q_gen_2675) -> q_gen_2675
<cons, cons>(q_gen_2692, q_gen_2691) -> q_gen_2675
<nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2675
<b, a>() -> q_gen_2676
<a, a>() -> q_gen_2686
<b, b>() -> q_gen_2686
<cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2691
<cons, cons>(q_gen_2676, q_gen_2691) -> q_gen_2691
<cons, cons>(q_gen_2686, q_gen_2691) -> q_gen_2691
<nil, cons>(q_gen_2671, q_gen_2662) -> q_gen_2691
<a, b>() -> q_gen_2692
<a, cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2661
<a, cons, cons>(q_gen_2686, q_gen_2691) -> q_gen_2661
<a, nil, cons>(q_gen_2671, q_gen_2662) -> q_gen_2661
<b, cons, cons>(q_gen_2686, q_gen_2675) -> q_gen_2661
<b, cons, cons>(q_gen_2692, q_gen_2691) -> q_gen_2661
<b, nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2661
<a, cons, cons>(q_gen_2676, q_gen_2691) -> q_gen_2705
<a, cons, cons>(q_gen_2686, q_gen_2675) -> q_gen_2705
<b, cons, cons>(q_gen_2686, q_gen_2691) -> q_gen_2705
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  le -> 
{{{
Q={q_gen_2659, q_gen_2660, q_gen_2683},
Q_f={q_gen_2659},
Delta=
{
<s>(q_gen_2660) -> q_gen_2660
<z>() -> q_gen_2660
<s, s>(q_gen_2659) -> q_gen_2659
<z, s>(q_gen_2660) -> q_gen_2659
<s, s>(q_gen_2683) -> q_gen_2683
<s, z>(q_gen_2660) -> q_gen_2683
<z, z>() -> q_gen_2683
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_2658, q_gen_2665, q_gen_2666, q_gen_2678, q_gen_2679, q_gen_2680, q_gen_2681, q_gen_2682, q_gen_2694, q_gen_2695, q_gen_2696, q_gen_2711},
Q_f={q_gen_2658},
Delta=
{
<cons>(q_gen_2679, q_gen_2694) -> q_gen_2665
<nil>() -> q_gen_2665
<cons>(q_gen_2679, q_gen_2665) -> q_gen_2678
<a>() -> q_gen_2679
<b>() -> q_gen_2679
<s>(q_gen_2711) -> q_gen_2681
<z>() -> q_gen_2681
<cons>(q_gen_2679, q_gen_2678) -> q_gen_2694
<s>(q_gen_2681) -> q_gen_2696
<s>(q_gen_2696) -> q_gen_2711
<cons, s>(q_gen_2666, q_gen_2665) -> q_gen_2658
<cons, s>(q_gen_2680, q_gen_2678) -> q_gen_2658
<cons, s>(q_gen_2695, q_gen_2694) -> q_gen_2658
<nil, z>() -> q_gen_2658
<a, s>(q_gen_2711) -> q_gen_2666
<a, z>() -> q_gen_2666
<b, s>(q_gen_2711) -> q_gen_2666
<b, z>() -> q_gen_2666
<a, s>(q_gen_2681) -> q_gen_2680
<b, s>(q_gen_2681) -> q_gen_2680
<cons, s>(q_gen_2666, q_gen_2678) -> q_gen_2682
<cons, s>(q_gen_2666, q_gen_2694) -> q_gen_2682
<cons, s>(q_gen_2680, q_gen_2665) -> q_gen_2682
<cons, s>(q_gen_2680, q_gen_2694) -> q_gen_2682
<cons, s>(q_gen_2695, q_gen_2665) -> q_gen_2682
<cons, s>(q_gen_2695, q_gen_2678) -> q_gen_2682
<a, s>(q_gen_2696) -> q_gen_2695
<b, s>(q_gen_2696) -> q_gen_2695
}

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

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

Teacher's answer:
New clause system:
{
() -> fcons([x, l, cons(x, l)]) -> 88
() -> le([z, s(nn2)]) -> 79
() -> length([nil, z]) -> 79
(fcons([x, l, _tk]) /\ length([_tk, _uk]) /\ length([l, _sk])) -> le([_sk, _uk]) -> 92
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 79
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 84
(le([s(nn1), z])) -> BOT -> 80
(le([z, z])) -> BOT -> 80
(length([ll, _kk])) -> length([cons(x, ll), s(_kk)]) -> 91
}
Sat witness: Found: ((fcons([x, l, _tk]) /\ length([_tk, _uk]) /\ length([l, _sk])) -> le([_sk, _uk]), {
_sk -> s(s(s(s(z))))  ;  _tk -> cons(b, cons(a, nil))  ;  _uk -> s(s(z))  ;  l -> cons(a, nil)  ;  x -> b
})

-------------------------------------------
Step 88, which took 2.268551 s (model generation: 2.260049,  model checking: 0.008502):

Model:
|_
{
fcons -> 
{{{
Q={q_gen_2661, q_gen_2662, q_gen_2663, q_gen_2675, q_gen_2676, q_gen_2686, q_gen_2733},
Q_f={q_gen_2661},
Delta=
{
<nil>() -> q_gen_2662
<a>() -> q_gen_2663
<b>() -> q_gen_2663
<cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2675
<cons, cons>(q_gen_2686, q_gen_2675) -> q_gen_2675
<nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2675
<a, a>() -> q_gen_2676
<b, a>() -> q_gen_2676
<a, b>() -> q_gen_2686
<b, b>() -> q_gen_2686
<a, cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2661
<a, nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2661
<b, cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2661
<b, cons, cons>(q_gen_2686, q_gen_2675) -> q_gen_2661
<b, nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2661
<a, cons, cons>(q_gen_2686, q_gen_2675) -> q_gen_2733
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  le -> 
{{{
Q={q_gen_2659, q_gen_2660, q_gen_2683},
Q_f={q_gen_2659},
Delta=
{
<s>(q_gen_2660) -> q_gen_2660
<z>() -> q_gen_2660
<s, s>(q_gen_2659) -> q_gen_2659
<z, s>(q_gen_2660) -> q_gen_2659
<s, s>(q_gen_2683) -> q_gen_2683
<s, z>(q_gen_2660) -> q_gen_2683
<z, z>() -> q_gen_2683
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_2658, q_gen_2665, q_gen_2666, q_gen_2678, q_gen_2679, q_gen_2680, q_gen_2681, q_gen_2682, q_gen_2694, q_gen_2695, q_gen_2696, q_gen_2709, q_gen_2710, q_gen_2711, q_gen_2759},
Q_f={q_gen_2658},
Delta=
{
<cons>(q_gen_2679, q_gen_2709) -> q_gen_2665
<nil>() -> q_gen_2665
<cons>(q_gen_2679, q_gen_2665) -> q_gen_2678
<a>() -> q_gen_2679
<b>() -> q_gen_2679
<z>() -> q_gen_2681
<cons>(q_gen_2679, q_gen_2678) -> q_gen_2694
<s>(q_gen_2681) -> q_gen_2696
<cons>(q_gen_2679, q_gen_2694) -> q_gen_2709
<s>(q_gen_2696) -> q_gen_2711
<s>(q_gen_2759) -> q_gen_2711
<s>(q_gen_2711) -> q_gen_2759
<cons, s>(q_gen_2666, q_gen_2665) -> q_gen_2658
<cons, s>(q_gen_2666, q_gen_2694) -> q_gen_2658
<cons, s>(q_gen_2680, q_gen_2678) -> q_gen_2658
<cons, s>(q_gen_2695, q_gen_2694) -> q_gen_2658
<cons, s>(q_gen_2710, q_gen_2709) -> q_gen_2658
<nil, z>() -> q_gen_2658
<a, s>(q_gen_2759) -> q_gen_2666
<a, z>() -> q_gen_2666
<b, s>(q_gen_2759) -> q_gen_2666
<b, z>() -> q_gen_2666
<a, s>(q_gen_2681) -> q_gen_2680
<b, s>(q_gen_2681) -> q_gen_2680
<cons, s>(q_gen_2666, q_gen_2678) -> q_gen_2682
<cons, s>(q_gen_2666, q_gen_2709) -> q_gen_2682
<cons, s>(q_gen_2680, q_gen_2665) -> q_gen_2682
<cons, s>(q_gen_2680, q_gen_2694) -> q_gen_2682
<cons, s>(q_gen_2680, q_gen_2709) -> q_gen_2682
<cons, s>(q_gen_2695, q_gen_2665) -> q_gen_2682
<cons, s>(q_gen_2695, q_gen_2678) -> q_gen_2682
<cons, s>(q_gen_2695, q_gen_2709) -> q_gen_2682
<cons, s>(q_gen_2710, q_gen_2665) -> q_gen_2682
<cons, s>(q_gen_2710, q_gen_2678) -> q_gen_2682
<cons, s>(q_gen_2710, q_gen_2694) -> q_gen_2682
<a, s>(q_gen_2696) -> q_gen_2695
<b, s>(q_gen_2696) -> q_gen_2695
<a, s>(q_gen_2711) -> q_gen_2710
<b, s>(q_gen_2711) -> q_gen_2710
}

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

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

Teacher's answer:
New clause system:
{
() -> fcons([x, l, cons(x, l)]) -> 89
() -> le([z, s(nn2)]) -> 80
() -> length([nil, z]) -> 80
(fcons([x, l, _tk]) /\ length([_tk, _uk]) /\ length([l, _sk])) -> le([_sk, _uk]) -> 92
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 80
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 85
(le([s(nn1), z])) -> BOT -> 81
(le([z, z])) -> BOT -> 81
(length([ll, _kk])) -> length([cons(x, ll), s(_kk)]) -> 94
}
Sat witness: Found: ((length([ll, _kk])) -> length([cons(x, ll), s(_kk)]), {
_kk -> s(s(s(s(s(z)))))  ;  ll -> cons(b, nil)  ;  x -> a
})

-------------------------------------------
Step 89, which took 3.493000 s (model generation: 3.486213,  model checking: 0.006787):

Model:
|_
{
fcons -> 
{{{
Q={q_gen_2661, q_gen_2662, q_gen_2663, q_gen_2675, q_gen_2676},
Q_f={q_gen_2661},
Delta=
{
<nil>() -> q_gen_2662
<a>() -> q_gen_2663
<b>() -> q_gen_2663
<cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2675
<nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2675
<a, a>() -> q_gen_2676
<a, b>() -> q_gen_2676
<b, a>() -> q_gen_2676
<b, b>() -> q_gen_2676
<a, cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2661
<a, nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2661
<b, cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2661
<b, nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2661
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  le -> 
{{{
Q={q_gen_2659, q_gen_2660, q_gen_2683},
Q_f={q_gen_2659},
Delta=
{
<s>(q_gen_2660) -> q_gen_2660
<z>() -> q_gen_2660
<s, s>(q_gen_2659) -> q_gen_2659
<z, s>(q_gen_2660) -> q_gen_2659
<s, s>(q_gen_2683) -> q_gen_2683
<s, z>(q_gen_2660) -> q_gen_2683
<z, z>() -> q_gen_2683
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_2658, q_gen_2665, q_gen_2666, q_gen_2678, q_gen_2679, q_gen_2680, q_gen_2681, q_gen_2682, q_gen_2689, q_gen_2694, q_gen_2695, q_gen_2696, q_gen_2709, q_gen_2710, q_gen_2711, q_gen_2725, q_gen_2778},
Q_f={q_gen_2658},
Delta=
{
<nil>() -> q_gen_2665
<cons>(q_gen_2679, q_gen_2665) -> q_gen_2678
<cons>(q_gen_2689, q_gen_2665) -> q_gen_2678
<b>() -> q_gen_2679
<z>() -> q_gen_2681
<a>() -> q_gen_2689
<cons>(q_gen_2679, q_gen_2678) -> q_gen_2694
<s>(q_gen_2681) -> q_gen_2696
<cons>(q_gen_2679, q_gen_2694) -> q_gen_2709
<cons>(q_gen_2689, q_gen_2709) -> q_gen_2709
<cons>(q_gen_2689, q_gen_2725) -> q_gen_2709
<s>(q_gen_2696) -> q_gen_2711
<s>(q_gen_2711) -> q_gen_2711
<cons>(q_gen_2679, q_gen_2725) -> q_gen_2725
<cons>(q_gen_2689, q_gen_2678) -> q_gen_2725
<cons>(q_gen_2689, q_gen_2694) -> q_gen_2725
<cons>(q_gen_2689, q_gen_2778) -> q_gen_2725
<cons>(q_gen_2679, q_gen_2709) -> q_gen_2778
<cons, s>(q_gen_2666, q_gen_2665) -> q_gen_2658
<cons, s>(q_gen_2680, q_gen_2678) -> q_gen_2658
<cons, s>(q_gen_2695, q_gen_2694) -> q_gen_2658
<cons, s>(q_gen_2695, q_gen_2725) -> q_gen_2658
<cons, s>(q_gen_2710, q_gen_2709) -> q_gen_2658
<cons, s>(q_gen_2710, q_gen_2725) -> q_gen_2658
<nil, z>() -> q_gen_2658
<a, z>() -> q_gen_2666
<b, z>() -> q_gen_2666
<a, s>(q_gen_2681) -> q_gen_2680
<b, s>(q_gen_2681) -> q_gen_2680
<cons, s>(q_gen_2666, q_gen_2678) -> q_gen_2682
<cons, s>(q_gen_2666, q_gen_2709) -> q_gen_2682
<cons, s>(q_gen_2666, q_gen_2778) -> q_gen_2682
<cons, s>(q_gen_2680, q_gen_2665) -> q_gen_2682
<cons, s>(q_gen_2680, q_gen_2694) -> q_gen_2682
<cons, s>(q_gen_2680, q_gen_2709) -> q_gen_2682
<cons, s>(q_gen_2680, q_gen_2725) -> q_gen_2682
<cons, s>(q_gen_2680, q_gen_2778) -> q_gen_2682
<cons, s>(q_gen_2695, q_gen_2665) -> q_gen_2682
<cons, s>(q_gen_2695, q_gen_2678) -> q_gen_2682
<cons, s>(q_gen_2695, q_gen_2709) -> q_gen_2682
<cons, s>(q_gen_2695, q_gen_2778) -> q_gen_2682
<cons, s>(q_gen_2710, q_gen_2665) -> q_gen_2682
<cons, s>(q_gen_2710, q_gen_2678) -> q_gen_2682
<cons, s>(q_gen_2710, q_gen_2694) -> q_gen_2682
<cons, s>(q_gen_2710, q_gen_2778) -> q_gen_2682
<a, s>(q_gen_2696) -> q_gen_2695
<b, s>(q_gen_2696) -> q_gen_2695
<a, s>(q_gen_2711) -> q_gen_2710
<b, s>(q_gen_2711) -> q_gen_2710
}

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

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

Teacher's answer:
New clause system:
{
() -> fcons([x, l, cons(x, l)]) -> 90
() -> le([z, s(nn2)]) -> 81
() -> length([nil, z]) -> 81
(fcons([x, l, _tk]) /\ length([_tk, _uk]) /\ length([l, _sk])) -> le([_sk, _uk]) -> 95
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 81
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 86
(le([s(nn1), z])) -> BOT -> 82
(le([z, z])) -> BOT -> 82
(length([ll, _kk])) -> length([cons(x, ll), s(_kk)]) -> 94
}
Sat witness: Found: ((fcons([x, l, _tk]) /\ length([_tk, _uk]) /\ length([l, _sk])) -> le([_sk, _uk]), {
_sk -> s(s(s(s(z))))  ;  _tk -> cons(b, cons(b, cons(b, cons(b, nil))))  ;  _uk -> s(s(s(s(z))))  ;  l -> cons(b, cons(a, cons(b, nil)))  ;  x -> a
})

-------------------------------------------
Step 90, which took 2.141239 s (model generation: 2.126726,  model checking: 0.014513):

Model:
|_
{
fcons -> 
{{{
Q={q_gen_2661, q_gen_2662, q_gen_2663, q_gen_2675, q_gen_2676},
Q_f={q_gen_2661},
Delta=
{
<nil>() -> q_gen_2662
<a>() -> q_gen_2663
<b>() -> q_gen_2663
<cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2675
<nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2675
<a, a>() -> q_gen_2676
<a, b>() -> q_gen_2676
<b, a>() -> q_gen_2676
<b, b>() -> q_gen_2676
<a, cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2661
<a, nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2661
<b, cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2661
<b, nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2661
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  le -> 
{{{
Q={q_gen_2659, q_gen_2660, q_gen_2683},
Q_f={q_gen_2659},
Delta=
{
<s>(q_gen_2660) -> q_gen_2660
<z>() -> q_gen_2660
<s, s>(q_gen_2659) -> q_gen_2659
<z, s>(q_gen_2660) -> q_gen_2659
<s, s>(q_gen_2683) -> q_gen_2683
<s, z>(q_gen_2660) -> q_gen_2683
<z, z>() -> q_gen_2683
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_2658, q_gen_2665, q_gen_2666, q_gen_2678, q_gen_2679, q_gen_2680, q_gen_2681, q_gen_2682, q_gen_2689, q_gen_2694, q_gen_2695, q_gen_2696, q_gen_2709, q_gen_2710, q_gen_2711, q_gen_2725, q_gen_2731},
Q_f={q_gen_2658},
Delta=
{
<nil>() -> q_gen_2665
<cons>(q_gen_2679, q_gen_2665) -> q_gen_2678
<cons>(q_gen_2679, q_gen_2725) -> q_gen_2678
<cons>(q_gen_2689, q_gen_2665) -> q_gen_2678
<b>() -> q_gen_2679
<z>() -> q_gen_2681
<a>() -> q_gen_2689
<cons>(q_gen_2679, q_gen_2678) -> q_gen_2694
<cons>(q_gen_2689, q_gen_2694) -> q_gen_2694
<s>(q_gen_2681) -> q_gen_2696
<cons>(q_gen_2679, q_gen_2694) -> q_gen_2709
<cons>(q_gen_2689, q_gen_2709) -> q_gen_2709
<cons>(q_gen_2689, q_gen_2725) -> q_gen_2709
<s>(q_gen_2696) -> q_gen_2711
<s>(q_gen_2711) -> q_gen_2711
<cons>(q_gen_2679, q_gen_2709) -> q_gen_2725
<cons>(q_gen_2689, q_gen_2678) -> q_gen_2725
<cons, s>(q_gen_2666, q_gen_2665) -> q_gen_2658
<cons, s>(q_gen_2680, q_gen_2678) -> q_gen_2658
<cons, s>(q_gen_2695, q_gen_2694) -> q_gen_2658
<cons, s>(q_gen_2710, q_gen_2694) -> q_gen_2658
<cons, s>(q_gen_2710, q_gen_2709) -> q_gen_2658
<cons, s>(q_gen_2731, q_gen_2694) -> q_gen_2658
<cons, s>(q_gen_2731, q_gen_2725) -> q_gen_2658
<nil, z>() -> q_gen_2658
<a, z>() -> q_gen_2666
<b, z>() -> q_gen_2666
<a, s>(q_gen_2681) -> q_gen_2680
<b, s>(q_gen_2681) -> q_gen_2680
<cons, s>(q_gen_2666, q_gen_2678) -> q_gen_2682
<cons, s>(q_gen_2666, q_gen_2709) -> q_gen_2682
<cons, s>(q_gen_2666, q_gen_2725) -> q_gen_2682
<cons, s>(q_gen_2680, q_gen_2665) -> q_gen_2682
<cons, s>(q_gen_2680, q_gen_2694) -> q_gen_2682
<cons, s>(q_gen_2680, q_gen_2709) -> q_gen_2682
<cons, s>(q_gen_2680, q_gen_2725) -> q_gen_2682
<cons, s>(q_gen_2695, q_gen_2665) -> q_gen_2682
<cons, s>(q_gen_2695, q_gen_2678) -> q_gen_2682
<cons, s>(q_gen_2695, q_gen_2709) -> q_gen_2682
<cons, s>(q_gen_2695, q_gen_2725) -> q_gen_2682
<cons, s>(q_gen_2710, q_gen_2665) -> q_gen_2682
<cons, s>(q_gen_2710, q_gen_2678) -> q_gen_2682
<cons, s>(q_gen_2710, q_gen_2725) -> q_gen_2682
<cons, s>(q_gen_2731, q_gen_2665) -> q_gen_2682
<cons, s>(q_gen_2731, q_gen_2709) -> q_gen_2682
<a, s>(q_gen_2711) -> q_gen_2695
<b, s>(q_gen_2696) -> q_gen_2695
<b, s>(q_gen_2711) -> q_gen_2710
<a, s>(q_gen_2696) -> q_gen_2731
}

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

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

Teacher's answer:
New clause system:
{
() -> fcons([x, l, cons(x, l)]) -> 91
() -> le([z, s(nn2)]) -> 82
() -> length([nil, z]) -> 82
(fcons([x, l, _tk]) /\ length([_tk, _uk]) /\ length([l, _sk])) -> le([_sk, _uk]) -> 95
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 82
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 87
(le([s(nn1), z])) -> BOT -> 83
(le([z, z])) -> BOT -> 83
(length([ll, _kk])) -> length([cons(x, ll), s(_kk)]) -> 97
}
Sat witness: Found: ((length([ll, _kk])) -> length([cons(x, ll), s(_kk)]), {
_kk -> s(s(z))  ;  ll -> cons(a, cons(a, nil))  ;  x -> b
})

-------------------------------------------
Step 91, which took 2.062280 s (model generation: 2.048890,  model checking: 0.013390):

Model:
|_
{
fcons -> 
{{{
Q={q_gen_2661, q_gen_2662, q_gen_2663, q_gen_2675, q_gen_2676},
Q_f={q_gen_2661},
Delta=
{
<nil>() -> q_gen_2662
<a>() -> q_gen_2663
<b>() -> q_gen_2663
<cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2675
<nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2675
<a, a>() -> q_gen_2676
<a, b>() -> q_gen_2676
<b, a>() -> q_gen_2676
<b, b>() -> q_gen_2676
<a, cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2661
<a, nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2661
<b, cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2661
<b, nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2661
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  le -> 
{{{
Q={q_gen_2659, q_gen_2660, q_gen_2683},
Q_f={q_gen_2659},
Delta=
{
<s>(q_gen_2660) -> q_gen_2660
<z>() -> q_gen_2660
<s, s>(q_gen_2659) -> q_gen_2659
<z, s>(q_gen_2660) -> q_gen_2659
<s, s>(q_gen_2683) -> q_gen_2683
<s, z>(q_gen_2660) -> q_gen_2683
<z, z>() -> q_gen_2683
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_2658, q_gen_2665, q_gen_2666, q_gen_2678, q_gen_2679, q_gen_2680, q_gen_2681, q_gen_2682, q_gen_2694, q_gen_2695, q_gen_2696, q_gen_2709, q_gen_2710, q_gen_2711, q_gen_2729, q_gen_2759, q_gen_2773},
Q_f={q_gen_2658},
Delta=
{
<nil>() -> q_gen_2665
<cons>(q_gen_2679, q_gen_2665) -> q_gen_2678
<a>() -> q_gen_2679
<b>() -> q_gen_2679
<s>(q_gen_2759) -> q_gen_2681
<z>() -> q_gen_2681
<cons>(q_gen_2679, q_gen_2678) -> q_gen_2694
<s>(q_gen_2681) -> q_gen_2696
<cons>(q_gen_2679, q_gen_2694) -> q_gen_2709
<s>(q_gen_2696) -> q_gen_2711
<s>(q_gen_2711) -> q_gen_2759
<cons>(q_gen_2679, q_gen_2709) -> q_gen_2773
<cons>(q_gen_2679, q_gen_2773) -> q_gen_2773
<cons, s>(q_gen_2666, q_gen_2665) -> q_gen_2658
<cons, s>(q_gen_2680, q_gen_2678) -> q_gen_2658
<cons, s>(q_gen_2695, q_gen_2694) -> q_gen_2658
<cons, s>(q_gen_2710, q_gen_2709) -> q_gen_2658
<cons, s>(q_gen_2729, q_gen_2694) -> q_gen_2658
<cons, s>(q_gen_2729, q_gen_2709) -> q_gen_2658
<cons, s>(q_gen_2729, q_gen_2773) -> q_gen_2658
<nil, z>() -> q_gen_2658
<a, z>() -> q_gen_2666
<b, z>() -> q_gen_2666
<a, s>(q_gen_2681) -> q_gen_2680
<b, s>(q_gen_2681) -> q_gen_2680
<cons, s>(q_gen_2666, q_gen_2678) -> q_gen_2682
<cons, s>(q_gen_2666, q_gen_2709) -> q_gen_2682
<cons, s>(q_gen_2666, q_gen_2773) -> q_gen_2682
<cons, s>(q_gen_2680, q_gen_2665) -> q_gen_2682
<cons, s>(q_gen_2680, q_gen_2694) -> q_gen_2682
<cons, s>(q_gen_2680, q_gen_2709) -> q_gen_2682
<cons, s>(q_gen_2680, q_gen_2773) -> q_gen_2682
<cons, s>(q_gen_2695, q_gen_2665) -> q_gen_2682
<cons, s>(q_gen_2695, q_gen_2678) -> q_gen_2682
<cons, s>(q_gen_2695, q_gen_2709) -> q_gen_2682
<cons, s>(q_gen_2695, q_gen_2773) -> q_gen_2682
<cons, s>(q_gen_2710, q_gen_2665) -> q_gen_2682
<cons, s>(q_gen_2710, q_gen_2678) -> q_gen_2682
<cons, s>(q_gen_2710, q_gen_2694) -> q_gen_2682
<cons, s>(q_gen_2710, q_gen_2773) -> q_gen_2682
<cons, s>(q_gen_2729, q_gen_2665) -> q_gen_2682
<cons, s>(q_gen_2729, q_gen_2678) -> q_gen_2682
<a, s>(q_gen_2696) -> q_gen_2695
<b, s>(q_gen_2696) -> q_gen_2695
<b, s>(q_gen_2711) -> q_gen_2710
<a, s>(q_gen_2711) -> q_gen_2729
<a, s>(q_gen_2759) -> q_gen_2729
<b, s>(q_gen_2759) -> q_gen_2729
}

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

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

Teacher's answer:
New clause system:
{
() -> fcons([x, l, cons(x, l)]) -> 92
() -> le([z, s(nn2)]) -> 83
() -> length([nil, z]) -> 83
(fcons([x, l, _tk]) /\ length([_tk, _uk]) /\ length([l, _sk])) -> le([_sk, _uk]) -> 98
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 83
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 88
(le([s(nn1), z])) -> BOT -> 84
(le([z, z])) -> BOT -> 84
(length([ll, _kk])) -> length([cons(x, ll), s(_kk)]) -> 97
}
Sat witness: Found: ((fcons([x, l, _tk]) /\ length([_tk, _uk]) /\ length([l, _sk])) -> le([_sk, _uk]), {
_sk -> s(s(s(s(z))))  ;  _tk -> cons(a, cons(b, cons(b, cons(b, nil))))  ;  _uk -> s(s(s(s(z))))  ;  l -> cons(a, cons(b, cons(b, nil)))  ;  x -> b
})

-------------------------------------------
Step 92, which took 3.500399 s (model generation: 3.485526,  model checking: 0.014873):

Model:
|_
{
fcons -> 
{{{
Q={q_gen_2661, q_gen_2662, q_gen_2663, q_gen_2675, q_gen_2676, q_gen_2686, q_gen_2733},
Q_f={q_gen_2661},
Delta=
{
<nil>() -> q_gen_2662
<a>() -> q_gen_2663
<b>() -> q_gen_2663
<cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2675
<cons, cons>(q_gen_2686, q_gen_2675) -> q_gen_2675
<nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2675
<a, a>() -> q_gen_2676
<a, b>() -> q_gen_2676
<b, a>() -> q_gen_2676
<b, b>() -> q_gen_2686
<a, cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2661
<a, nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2661
<b, cons, cons>(q_gen_2676, q_gen_2675) -> q_gen_2661
<b, cons, cons>(q_gen_2686, q_gen_2675) -> q_gen_2661
<b, nil, cons>(q_gen_2663, q_gen_2662) -> q_gen_2661
<a, cons, cons>(q_gen_2686, q_gen_2675) -> q_gen_2733
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  le -> 
{{{
Q={q_gen_2659, q_gen_2660, q_gen_2683},
Q_f={q_gen_2659},
Delta=
{
<s>(q_gen_2660) -> q_gen_2660
<z>() -> q_gen_2660
<s, s>(q_gen_2659) -> q_gen_2659
<z, s>(q_gen_2660) -> q_gen_2659
<s, s>(q_gen_2683) -> q_gen_2683
<s, z>(q_gen_2660) -> q_gen_2683
<z, z>() -> q_gen_2683
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_2658, q_gen_2665, q_gen_2666, q_gen_2678, q_gen_2679, q_gen_2680, q_gen_2681, q_gen_2682, q_gen_2694, q_gen_2695, q_gen_2696, q_gen_2709, q_gen_2710, q_gen_2711, q_gen_2759},
Q_f={q_gen_2658},
Delta=
{
<cons>(q_gen_2679, q_gen_2709) -> q_gen_2665
<nil>() -> q_gen_2665
<cons>(q_gen_2679, q_gen_2665) -> q_gen_2678
<a>() -> q_gen_2679
<b>() -> q_gen_2679
<s>(q_gen_2759) -> q_gen_2681
<z>() -> q_gen_2681
<cons>(q_gen_2679, q_gen_2678) -> q_gen_2694
<s>(q_gen_2681) -> q_gen_2696
<cons>(q_gen_2679, q_gen_2694) -> q_gen_2709
<s>(q_gen_2696) -> q_gen_2711
<s>(q_gen_2711) -> q_gen_2759
<cons, s>(q_gen_2666, q_gen_2665) -> q_gen_2658
<cons, s>(q_gen_2680, q_gen_2678) -> q_gen_2658
<cons, s>(q_gen_2695, q_gen_2694) -> q_gen_2658
<cons, s>(q_gen_2710, q_gen_2709) -> q_gen_2658
<nil, z>() -> q_gen_2658
<a, s>(q_gen_2759) -> q_gen_2666
<a, z>() -> q_gen_2666
<b, s>(q_gen_2759) -> q_gen_2666
<b, z>() -> q_gen_2666
<a, s>(q_gen_2681) -> q_gen_2680
<b, s>(q_gen_2681) -> q_gen_2680
<cons, s>(q_gen_2666, q_gen_2678) -> q_gen_2682
<cons, s>(q_gen_2666, q_gen_2694) -> q_gen_2682
<cons, s>(q_gen_2666, q_gen_2709) -> q_gen_2682
<cons, s>(q_gen_2680, q_gen_2665) -> q_gen_2682
<cons, s>(q_gen_2680, q_gen_2694) -> q_gen_2682
<cons, s>(q_gen_2680, q_gen_2709) -> q_gen_2682
<cons, s>(q_gen_2695, q_gen_2665) -> q_gen_2682
<cons, s>(q_gen_2695, q_gen_2678) -> q_gen_2682
<cons, s>(q_gen_2695, q_gen_2709) -> q_gen_2682
<cons, s>(q_gen_2710, q_gen_2665) -> q_gen_2682
<cons, s>(q_gen_2710, q_gen_2678) -> q_gen_2682
<cons, s>(q_gen_2710, q_gen_2694) -> q_gen_2682
<a, s>(q_gen_2696) -> q_gen_2695
<b, s>(q_gen_2696) -> q_gen_2695
<a, s>(q_gen_2711) -> q_gen_2710
<b, s>(q_gen_2711) -> q_gen_2710
}

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

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

Teacher's answer:
New clause system:
{
() -> fcons([x, l, cons(x, l)]) -> 93
() -> le([z, s(nn2)]) -> 84
() -> length([nil, z]) -> 84
(fcons([x, l, _tk]) /\ length([_tk, _uk]) /\ length([l, _sk])) -> le([_sk, _uk]) -> 101
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 84
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 89
(le([s(nn1), z])) -> BOT -> 85
(le([z, z])) -> BOT -> 85
(length([ll, _kk])) -> length([cons(x, ll), s(_kk)]) -> 98
}
Sat witness: Found: ((fcons([x, l, _tk]) /\ length([_tk, _uk]) /\ length([l, _sk])) -> le([_sk, _uk]), {
_sk -> s(s(s(s(z))))  ;  _tk -> cons(b, cons(a, cons(a, cons(a, cons(b, nil)))))  ;  _uk -> s(z)  ;  l -> cons(a, cons(b, cons(b, cons(b, nil))))  ;  x -> b
})

Total time: 64.136993
Reason for stopping: DontKnow. Stopped because: timeout