Solving ../../benchmarks/true/isaplanner_prop54.smt2...

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


Learning problem is:

env: {
nat -> {s, z}
}
definition:
{
(minus, F:
{() -> minus([s(u), z, s(u)])
() -> minus([z, y, z])
(minus([u, x2, _ec])) -> minus([s(u), s(x2), _ec])}
(minus([_fc, _gc, _hc]) /\ minus([_fc, _gc, _ic])) -> eq_nat([_hc, _ic])
)
(plus, F:
{() -> plus([n, z, n])
(plus([n, mm, _jc])) -> plus([n, s(mm), s(_jc)])}
(plus([_kc, _lc, _mc]) /\ plus([_kc, _lc, _nc])) -> eq_nat([_mc, _nc])
)
}

properties:
{(minus([_oc, n, _pc]) /\ plus([m, n, _oc])) -> eq_nat([_pc, m])}


over-approximation: {minus, plus}
under-approximation: {}

Clause system for inference is:

{
() -> minus([s(u), z, s(u)]) -> 0  ;  () -> minus([z, y, z]) -> 0  ;  () -> plus([n, z, n]) -> 0  ;  (minus([_oc, n, _pc]) /\ plus([m, n, _oc])) -> eq_nat([_pc, m]) -> 0  ;  (minus([u, x2, _ec])) -> minus([s(u), s(x2), _ec]) -> 0  ;  (plus([n, mm, _jc])) -> plus([n, s(mm), s(_jc)]) -> 0
}


Solving took 30.568983 seconds.
DontKnow. Stopped because: timeout
Working model:
|_
{
minus -> 
{{{
Q={q_gen_2599, q_gen_2600, q_gen_2601, q_gen_2604, q_gen_2606, q_gen_2607, q_gen_2608, q_gen_2609, q_gen_2613, q_gen_2614, q_gen_2618, q_gen_2619, q_gen_2623, q_gen_2624, q_gen_2625, q_gen_2630, q_gen_2631, q_gen_2632, q_gen_2635, q_gen_2636, q_gen_2640, q_gen_2641, q_gen_2642, q_gen_2643, q_gen_2644, q_gen_2646, q_gen_2647, q_gen_2652, q_gen_2657, q_gen_2658, q_gen_2659, q_gen_2663, q_gen_2664, q_gen_2665, q_gen_2666, q_gen_2667, q_gen_2668, q_gen_2672, q_gen_2674, q_gen_2679, q_gen_2680, q_gen_2681, q_gen_2682, q_gen_2683, q_gen_2684, q_gen_2685, q_gen_2686, q_gen_2687, q_gen_2690, q_gen_2693, q_gen_2694, q_gen_2695, q_gen_2696, q_gen_2697, q_gen_2698, q_gen_2703, q_gen_2704, q_gen_2705, q_gen_2708, q_gen_2709, q_gen_2710, q_gen_2711, q_gen_2712, q_gen_2713, q_gen_2715, q_gen_2716, q_gen_2717, q_gen_2718, q_gen_2719, q_gen_2720, q_gen_2730, q_gen_2735, q_gen_2736, q_gen_2744},
Q_f={},
Delta=
{
<z>() -> q_gen_2607
<s>(q_gen_2607) -> q_gen_2619
<s>(q_gen_2619) -> q_gen_2659
<z, z>() -> q_gen_2601
<s, s>(q_gen_2601) -> q_gen_2609
<z, s>(q_gen_2607) -> q_gen_2624
<z, s>(q_gen_2619) -> q_gen_2642
<s, z>(q_gen_2607) -> q_gen_2647
<s, s>(q_gen_2609) -> q_gen_2664
<s, s>(q_gen_2624) -> q_gen_2666
<s, z>(q_gen_2619) -> q_gen_2680
<z, s>(q_gen_2659) -> q_gen_2696
<s, s>(q_gen_2647) -> q_gen_2705
<s, s>(q_gen_2680) -> q_gen_2709
<s, z>(q_gen_2659) -> q_gen_2712
<z, z, z>() -> q_gen_2599
<s, z, s>(q_gen_2601) -> q_gen_2600
<s, s, z>(q_gen_2601) -> q_gen_2604
<z, s, z>(q_gen_2607) -> q_gen_2606
<s, z, s>(q_gen_2609) -> q_gen_2608
<s, s, s>(q_gen_2614) -> q_gen_2613
<s, z, z>(q_gen_2607) -> q_gen_2614
<z, s, z>(q_gen_2619) -> q_gen_2618
<s, s, z>(q_gen_2624) -> q_gen_2623
<s, s, s>(q_gen_2599) -> q_gen_2625
<s, z, s>(q_gen_2624) -> q_gen_2630
<s, s, s>(q_gen_2600) -> q_gen_2631
<s, s, s>(q_gen_2604) -> q_gen_2632
<s, s, s>(q_gen_2606) -> q_gen_2635
<s, s, s>(q_gen_2623) -> q_gen_2636
<s, s, s>(q_gen_2641) -> q_gen_2640
<s, z, s>(q_gen_2642) -> q_gen_2641
<s, s, s>(q_gen_2644) -> q_gen_2643
<s, s, s>(q_gen_2630) -> q_gen_2644
<s, s, z>(q_gen_2647) -> q_gen_2646
<s, s, s>(q_gen_2613) -> q_gen_2652
<s, s, s>(q_gen_2646) -> q_gen_2657
<z, s, z>(q_gen_2659) -> q_gen_2658
<s, z, s>(q_gen_2664) -> q_gen_2663
<s, s, z>(q_gen_2666) -> q_gen_2665
<s, s, s>(q_gen_2668) -> q_gen_2667
<s, z, z>(q_gen_2619) -> q_gen_2668
<s, s, z>(q_gen_2642) -> q_gen_2672
<s, s, z>(q_gen_2609) -> q_gen_2674
<s, s, z>(q_gen_2680) -> q_gen_2679
<s, s, s>(q_gen_2682) -> q_gen_2681
<s, z, s>(q_gen_2680) -> q_gen_2682
<s, s, s>(q_gen_2684) -> q_gen_2683
<s, s, s>(q_gen_2685) -> q_gen_2684
<s, z, z>(q_gen_2659) -> q_gen_2685
<s, s, s>(q_gen_2687) -> q_gen_2686
<s, z, s>(q_gen_2647) -> q_gen_2687
<s, s, s>(q_gen_2667) -> q_gen_2690
<s, z, s>(q_gen_2666) -> q_gen_2693
<s, s, s>(q_gen_2608) -> q_gen_2694
<s, z, s>(q_gen_2696) -> q_gen_2695
<s, s, s>(q_gen_2698) -> q_gen_2697
<s, s, s>(q_gen_2631) -> q_gen_2698
<s, s, s>(q_gen_2704) -> q_gen_2703
<s, s, z>(q_gen_2705) -> q_gen_2704
<s, z, s>(q_gen_2709) -> q_gen_2708
<s, s, s>(q_gen_2711) -> q_gen_2710
<s, z, s>(q_gen_2712) -> q_gen_2711
<s, s, z>(q_gen_2709) -> q_gen_2713
<s, s, s>(q_gen_2716) -> q_gen_2715
<s, z, s>(q_gen_2705) -> q_gen_2716
<s, s, s>(q_gen_2681) -> q_gen_2717
<s, s, s>(q_gen_2635) -> q_gen_2718
<s, s, s>(q_gen_2636) -> q_gen_2719
<s, s, s>(q_gen_2652) -> q_gen_2720
<s, s, s>(q_gen_2683) -> q_gen_2730
<s, s, s>(q_gen_2736) -> q_gen_2735
<s, s, s>(q_gen_2679) -> q_gen_2736
<s, s, z>(q_gen_2664) -> q_gen_2744
}

Datatype: <nat, nat, nat>
Convolution form: complete
}}}
  ;  plus -> 
{{{
Q={q_gen_2598, q_gen_2602, q_gen_2603, q_gen_2605, q_gen_2610, q_gen_2611, q_gen_2612, q_gen_2615, q_gen_2616, q_gen_2617, q_gen_2620, q_gen_2621, q_gen_2622, q_gen_2626, q_gen_2627, q_gen_2628, q_gen_2629, q_gen_2633, q_gen_2634, q_gen_2637, q_gen_2638, q_gen_2639, q_gen_2645, q_gen_2648, q_gen_2649, q_gen_2650, q_gen_2651, q_gen_2653, q_gen_2654, q_gen_2655, q_gen_2656, q_gen_2660, q_gen_2661, q_gen_2662, q_gen_2669, q_gen_2670, q_gen_2671, q_gen_2673, q_gen_2675, q_gen_2676, q_gen_2677, q_gen_2678, q_gen_2688, q_gen_2689, q_gen_2691, q_gen_2692, q_gen_2699, q_gen_2700, q_gen_2701, q_gen_2702, q_gen_2706, q_gen_2707, q_gen_2714, q_gen_2721, q_gen_2722, q_gen_2723, q_gen_2724, q_gen_2725, q_gen_2726, q_gen_2727, q_gen_2728, q_gen_2729, q_gen_2731, q_gen_2732, q_gen_2733, q_gen_2734, q_gen_2737, q_gen_2738, q_gen_2739, q_gen_2740, q_gen_2741, q_gen_2742, q_gen_2743, q_gen_2745, q_gen_2746},
Q_f={},
Delta=
{
<z>() -> q_gen_2612
<s>(q_gen_2612) -> q_gen_2629
<s>(q_gen_2629) -> q_gen_2678
<s>(q_gen_2678) -> q_gen_2734
<z, z>() -> q_gen_2603
<s, s>(q_gen_2603) -> q_gen_2617
<z, s>(q_gen_2612) -> q_gen_2622
<z, s>(q_gen_2629) -> q_gen_2649
<s, s>(q_gen_2617) -> q_gen_2651
<s, s>(q_gen_2622) -> q_gen_2671
<z, s>(q_gen_2678) -> q_gen_2729
<s, s>(q_gen_2671) -> q_gen_2739
<s, s>(q_gen_2649) -> q_gen_2743
<s, s>(q_gen_2651) -> q_gen_2746
<z, z, z>() -> q_gen_2598
<z, s, s>(q_gen_2603) -> q_gen_2602
<s, z, s>(q_gen_2603) -> q_gen_2605
<s, s, s>(q_gen_2611) -> q_gen_2610
<z, z, s>(q_gen_2612) -> q_gen_2611
<s, s, s>(q_gen_2598) -> q_gen_2615
<s, z, s>(q_gen_2617) -> q_gen_2616
<s, s, s>(q_gen_2621) -> q_gen_2620
<z, s, s>(q_gen_2622) -> q_gen_2621
<s, z, s>(q_gen_2622) -> q_gen_2626
<s, s, s>(q_gen_2628) -> q_gen_2627
<z, z, s>(q_gen_2629) -> q_gen_2628
<z, s, s>(q_gen_2617) -> q_gen_2633
<s, s, s>(q_gen_2626) -> q_gen_2634
<s, s, s>(q_gen_2615) -> q_gen_2637
<s, s, s>(q_gen_2639) -> q_gen_2638
<s, s, s>(q_gen_2602) -> q_gen_2639
<s, s, s>(q_gen_2627) -> q_gen_2645
<z, s, s>(q_gen_2649) -> q_gen_2648
<s, z, s>(q_gen_2651) -> q_gen_2650
<s, s, s>(q_gen_2654) -> q_gen_2653
<s, s, s>(q_gen_2605) -> q_gen_2654
<s, s, s>(q_gen_2656) -> q_gen_2655
<s, s, s>(q_gen_2610) -> q_gen_2656
<s, s, s>(q_gen_2633) -> q_gen_2660
<s, s, s>(q_gen_2662) -> q_gen_2661
<z, s, s>(q_gen_2651) -> q_gen_2662
<s, s, s>(q_gen_2670) -> q_gen_2669
<s, z, s>(q_gen_2671) -> q_gen_2670
<z, s, s>(q_gen_2671) -> q_gen_2673
<s, z, s>(q_gen_2649) -> q_gen_2675
<s, s, s>(q_gen_2677) -> q_gen_2676
<z, z, s>(q_gen_2678) -> q_gen_2677
<s, s, s>(q_gen_2634) -> q_gen_2688
<s, s, s>(q_gen_2645) -> q_gen_2689
<s, s, s>(q_gen_2692) -> q_gen_2691
<s, s, s>(q_gen_2675) -> q_gen_2692
<s, s, s>(q_gen_2637) -> q_gen_2699
<s, s, s>(q_gen_2638) -> q_gen_2700
<s, s, s>(q_gen_2702) -> q_gen_2701
<s, s, s>(q_gen_2676) -> q_gen_2702
<s, s, s>(q_gen_2653) -> q_gen_2706
<s, s, s>(q_gen_2655) -> q_gen_2707
<s, s, s>(q_gen_2648) -> q_gen_2714
<s, s, s>(q_gen_2722) -> q_gen_2721
<s, s, s>(q_gen_2723) -> q_gen_2722
<s, s, s>(q_gen_2616) -> q_gen_2723
<s, s, s>(q_gen_2725) -> q_gen_2724
<s, s, s>(q_gen_2688) -> q_gen_2725
<s, s, s>(q_gen_2727) -> q_gen_2726
<s, s, s>(q_gen_2714) -> q_gen_2727
<z, s, s>(q_gen_2729) -> q_gen_2728
<s, z, s>(q_gen_2729) -> q_gen_2731
<s, s, s>(q_gen_2733) -> q_gen_2732
<z, z, s>(q_gen_2734) -> q_gen_2733
<s, s, s>(q_gen_2738) -> q_gen_2737
<s, z, s>(q_gen_2739) -> q_gen_2738
<s, s, s>(q_gen_2741) -> q_gen_2740
<s, s, s>(q_gen_2742) -> q_gen_2741
<s, z, s>(q_gen_2743) -> q_gen_2742
<s, z, s>(q_gen_2746) -> q_gen_2745
}

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

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

-------------------
STEPS:
-------------------------------------------
Step 0, which took 0.004041 s (model generation: 0.003914,  model checking: 0.000127):

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

}

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

}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 0  ;  () -> minus([z, y, z]) -> 0  ;  () -> plus([n, z, n]) -> 3  ;  (minus([_oc, n, _pc]) /\ plus([m, n, _oc])) -> eq_nat([_pc, m]) -> 1  ;  (minus([u, x2, _ec])) -> minus([s(u), s(x2), _ec]) -> 1  ;  (plus([n, mm, _jc])) -> plus([n, s(mm), s(_jc)]) -> 1
}
Sat witness: Yes: (() -> plus([n, z, n]), {
n -> z
})

-------------------------------------------
Step 1, which took 0.004235 s (model generation: 0.003486,  model checking: 0.000749):

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

}

Datatype: <nat, nat, nat>
Convolution form: complete
}}}
  ;  plus -> 
{{{
Q={q_gen_2598},
Q_f={q_gen_2598},
Delta=
{
<z, z, z>() -> q_gen_2598
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 0  ;  () -> minus([z, y, z]) -> 3  ;  () -> plus([n, z, n]) -> 3  ;  (minus([_oc, n, _pc]) /\ plus([m, n, _oc])) -> eq_nat([_pc, m]) -> 1  ;  (minus([u, x2, _ec])) -> minus([s(u), s(x2), _ec]) -> 1  ;  (plus([n, mm, _jc])) -> plus([n, s(mm), s(_jc)]) -> 1
}
Sat witness: Yes: (() -> minus([z, y, z]), {
y -> z
})

-------------------------------------------
Step 2, which took 0.003538 s (model generation: 0.003475,  model checking: 0.000063):

Model:
|_
{
minus -> 
{{{
Q={q_gen_2599},
Q_f={q_gen_2599},
Delta=
{
<z, z, z>() -> q_gen_2599
}

Datatype: <nat, nat, nat>
Convolution form: complete
}}}
  ;  plus -> 
{{{
Q={q_gen_2598},
Q_f={q_gen_2598},
Delta=
{
<z, z, z>() -> q_gen_2598
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 3  ;  () -> minus([z, y, z]) -> 3  ;  () -> plus([n, z, n]) -> 3  ;  (minus([_oc, n, _pc]) /\ plus([m, n, _oc])) -> eq_nat([_pc, m]) -> 1  ;  (minus([u, x2, _ec])) -> minus([s(u), s(x2), _ec]) -> 1  ;  (plus([n, mm, _jc])) -> plus([n, s(mm), s(_jc)]) -> 1
}
Sat witness: Yes: (() -> minus([s(u), z, s(u)]), {
u -> z
})

-------------------------------------------
Step 3, which took 0.003572 s (model generation: 0.003511,  model checking: 0.000061):

Model:
|_
{
minus -> 
{{{
Q={q_gen_2599, q_gen_2601},
Q_f={q_gen_2599},
Delta=
{
<z, z>() -> q_gen_2601
<s, z, s>(q_gen_2601) -> q_gen_2599
<z, z, z>() -> q_gen_2599
}

Datatype: <nat, nat, nat>
Convolution form: complete
}}}
  ;  plus -> 
{{{
Q={q_gen_2598},
Q_f={q_gen_2598},
Delta=
{
<z, z, z>() -> q_gen_2598
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 3  ;  () -> minus([z, y, z]) -> 3  ;  () -> plus([n, z, n]) -> 3  ;  (minus([_oc, n, _pc]) /\ plus([m, n, _oc])) -> eq_nat([_pc, m]) -> 1  ;  (minus([u, x2, _ec])) -> minus([s(u), s(x2), _ec]) -> 1  ;  (plus([n, mm, _jc])) -> plus([n, s(mm), s(_jc)]) -> 4
}
Sat witness: Yes: ((plus([n, mm, _jc])) -> plus([n, s(mm), s(_jc)]), {
_jc -> z  ;  mm -> z  ;  n -> z
})

-------------------------------------------
Step 4, which took 0.003571 s (model generation: 0.003441,  model checking: 0.000130):

Model:
|_
{
minus -> 
{{{
Q={q_gen_2599, q_gen_2601},
Q_f={q_gen_2599},
Delta=
{
<z, z>() -> q_gen_2601
<s, z, s>(q_gen_2601) -> q_gen_2599
<z, z, z>() -> q_gen_2599
}

Datatype: <nat, nat, nat>
Convolution form: complete
}}}
  ;  plus -> 
{{{
Q={q_gen_2598, q_gen_2603},
Q_f={q_gen_2598},
Delta=
{
<z, z>() -> q_gen_2603
<z, s, s>(q_gen_2603) -> q_gen_2598
<z, z, z>() -> q_gen_2598
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 3  ;  () -> minus([z, y, z]) -> 3  ;  () -> plus([n, z, n]) -> 3  ;  (minus([_oc, n, _pc]) /\ plus([m, n, _oc])) -> eq_nat([_pc, m]) -> 1  ;  (minus([u, x2, _ec])) -> minus([s(u), s(x2), _ec]) -> 4  ;  (plus([n, mm, _jc])) -> plus([n, s(mm), s(_jc)]) -> 4
}
Sat witness: Yes: ((minus([u, x2, _ec])) -> minus([s(u), s(x2), _ec]), {
_ec -> z  ;  u -> z  ;  x2 -> z
})

-------------------------------------------
Step 5, which took 0.004853 s (model generation: 0.004703,  model checking: 0.000150):

Model:
|_
{
minus -> 
{{{
Q={q_gen_2599, q_gen_2601},
Q_f={q_gen_2599},
Delta=
{
<z, z>() -> q_gen_2601
<s, s, z>(q_gen_2601) -> q_gen_2599
<s, z, s>(q_gen_2601) -> q_gen_2599
<z, z, z>() -> q_gen_2599
}

Datatype: <nat, nat, nat>
Convolution form: complete
}}}
  ;  plus -> 
{{{
Q={q_gen_2598, q_gen_2603},
Q_f={q_gen_2598},
Delta=
{
<z, z>() -> q_gen_2603
<z, s, s>(q_gen_2603) -> q_gen_2598
<z, z, z>() -> q_gen_2598
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 3  ;  () -> minus([z, y, z]) -> 3  ;  () -> plus([n, z, n]) -> 6  ;  (minus([_oc, n, _pc]) /\ plus([m, n, _oc])) -> eq_nat([_pc, m]) -> 2  ;  (minus([u, x2, _ec])) -> minus([s(u), s(x2), _ec]) -> 4  ;  (plus([n, mm, _jc])) -> plus([n, s(mm), s(_jc)]) -> 4
}
Sat witness: Yes: (() -> plus([n, z, n]), {
n -> s(z)
})

-------------------------------------------
Step 6, which took 0.011109 s (model generation: 0.007459,  model checking: 0.003650):

Model:
|_
{
minus -> 
{{{
Q={q_gen_2599, q_gen_2601},
Q_f={q_gen_2599},
Delta=
{
<z, z>() -> q_gen_2601
<s, s, z>(q_gen_2601) -> q_gen_2599
<s, z, s>(q_gen_2601) -> q_gen_2599
<z, z, z>() -> q_gen_2599
}

Datatype: <nat, nat, nat>
Convolution form: complete
}}}
  ;  plus -> 
{{{
Q={q_gen_2598, q_gen_2603},
Q_f={q_gen_2598},
Delta=
{
<z, z>() -> q_gen_2603
<s, z, s>(q_gen_2603) -> q_gen_2598
<z, s, s>(q_gen_2603) -> q_gen_2598
<z, z, z>() -> q_gen_2598
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 3  ;  () -> minus([z, y, z]) -> 6  ;  () -> plus([n, z, n]) -> 6  ;  (minus([_oc, n, _pc]) /\ plus([m, n, _oc])) -> eq_nat([_pc, m]) -> 3  ;  (minus([u, x2, _ec])) -> minus([s(u), s(x2), _ec]) -> 4  ;  (plus([n, mm, _jc])) -> plus([n, s(mm), s(_jc)]) -> 4
}
Sat witness: Yes: (() -> minus([z, y, z]), {
y -> s(z)
})

-------------------------------------------
Step 7, which took 0.009979 s (model generation: 0.009854,  model checking: 0.000125):

Model:
|_
{
minus -> 
{{{
Q={q_gen_2599, q_gen_2601, q_gen_2607},
Q_f={q_gen_2599},
Delta=
{
<z>() -> q_gen_2607
<z, z>() -> q_gen_2601
<s, s, z>(q_gen_2601) -> q_gen_2599
<s, z, s>(q_gen_2601) -> q_gen_2599
<z, s, z>(q_gen_2607) -> q_gen_2599
<z, z, z>() -> q_gen_2599
}

Datatype: <nat, nat, nat>
Convolution form: complete
}}}
  ;  plus -> 
{{{
Q={q_gen_2598, q_gen_2603},
Q_f={q_gen_2598},
Delta=
{
<z, z>() -> q_gen_2603
<s, z, s>(q_gen_2603) -> q_gen_2598
<z, s, s>(q_gen_2603) -> q_gen_2598
<z, z, z>() -> q_gen_2598
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 6  ;  () -> minus([z, y, z]) -> 6  ;  () -> plus([n, z, n]) -> 6  ;  (minus([_oc, n, _pc]) /\ plus([m, n, _oc])) -> eq_nat([_pc, m]) -> 4  ;  (minus([u, x2, _ec])) -> minus([s(u), s(x2), _ec]) -> 4  ;  (plus([n, mm, _jc])) -> plus([n, s(mm), s(_jc)]) -> 4
}
Sat witness: Yes: (() -> minus([s(u), z, s(u)]), {
u -> s(z)
})

-------------------------------------------
Step 8, which took 0.009434 s (model generation: 0.009337,  model checking: 0.000097):

Model:
|_
{
minus -> 
{{{
Q={q_gen_2599, q_gen_2601, q_gen_2607},
Q_f={q_gen_2599},
Delta=
{
<z>() -> q_gen_2607
<s, s>(q_gen_2601) -> q_gen_2601
<z, z>() -> q_gen_2601
<s, s, z>(q_gen_2601) -> q_gen_2599
<s, z, s>(q_gen_2601) -> q_gen_2599
<z, s, z>(q_gen_2607) -> q_gen_2599
<z, z, z>() -> q_gen_2599
}

Datatype: <nat, nat, nat>
Convolution form: complete
}}}
  ;  plus -> 
{{{
Q={q_gen_2598, q_gen_2603},
Q_f={q_gen_2598},
Delta=
{
<z, z>() -> q_gen_2603
<s, z, s>(q_gen_2603) -> q_gen_2598
<z, s, s>(q_gen_2603) -> q_gen_2598
<z, z, z>() -> q_gen_2598
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 6  ;  () -> minus([z, y, z]) -> 6  ;  () -> plus([n, z, n]) -> 6  ;  (minus([_oc, n, _pc]) /\ plus([m, n, _oc])) -> eq_nat([_pc, m]) -> 4  ;  (minus([u, x2, _ec])) -> minus([s(u), s(x2), _ec]) -> 4  ;  (plus([n, mm, _jc])) -> plus([n, s(mm), s(_jc)]) -> 7
}
Sat witness: Yes: ((plus([n, mm, _jc])) -> plus([n, s(mm), s(_jc)]), {
_jc -> s(z)  ;  mm -> z  ;  n -> s(z)
})

-------------------------------------------
Step 9, which took 0.008000 s (model generation: 0.007068,  model checking: 0.000932):

Model:
|_
{
minus -> 
{{{
Q={q_gen_2599, q_gen_2601, q_gen_2607},
Q_f={q_gen_2599},
Delta=
{
<z>() -> q_gen_2607
<s, s>(q_gen_2601) -> q_gen_2601
<z, z>() -> q_gen_2601
<s, s, z>(q_gen_2601) -> q_gen_2599
<s, z, s>(q_gen_2601) -> q_gen_2599
<z, s, z>(q_gen_2607) -> q_gen_2599
<z, z, z>() -> q_gen_2599
}

Datatype: <nat, nat, nat>
Convolution form: complete
}}}
  ;  plus -> 
{{{
Q={q_gen_2598, q_gen_2603, q_gen_2612},
Q_f={q_gen_2598},
Delta=
{
<z>() -> q_gen_2612
<z, z>() -> q_gen_2603
<s, s, s>(q_gen_2598) -> q_gen_2598
<s, z, s>(q_gen_2603) -> q_gen_2598
<z, s, s>(q_gen_2603) -> q_gen_2598
<z, z, s>(q_gen_2612) -> q_gen_2598
<z, z, z>() -> q_gen_2598
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 6  ;  () -> minus([z, y, z]) -> 6  ;  () -> plus([n, z, n]) -> 6  ;  (minus([_oc, n, _pc]) /\ plus([m, n, _oc])) -> eq_nat([_pc, m]) -> 4  ;  (minus([u, x2, _ec])) -> minus([s(u), s(x2), _ec]) -> 7  ;  (plus([n, mm, _jc])) -> plus([n, s(mm), s(_jc)]) -> 7
}
Sat witness: Yes: ((minus([u, x2, _ec])) -> minus([s(u), s(x2), _ec]), {
_ec -> s(z)  ;  u -> s(z)  ;  x2 -> z
})

-------------------------------------------
Step 10, which took 0.008008 s (model generation: 0.007611,  model checking: 0.000397):

Model:
|_
{
minus -> 
{{{
Q={q_gen_2599, q_gen_2601, q_gen_2607},
Q_f={q_gen_2599},
Delta=
{
<z>() -> q_gen_2607
<s, s>(q_gen_2601) -> q_gen_2601
<z, z>() -> q_gen_2601
<s, s, s>(q_gen_2599) -> q_gen_2599
<s, s, z>(q_gen_2601) -> q_gen_2599
<s, z, s>(q_gen_2601) -> q_gen_2599
<s, z, z>(q_gen_2607) -> q_gen_2599
<z, s, z>(q_gen_2607) -> q_gen_2599
<z, z, z>() -> q_gen_2599
}

Datatype: <nat, nat, nat>
Convolution form: complete
}}}
  ;  plus -> 
{{{
Q={q_gen_2598, q_gen_2603, q_gen_2612},
Q_f={q_gen_2598},
Delta=
{
<z>() -> q_gen_2612
<z, z>() -> q_gen_2603
<s, s, s>(q_gen_2598) -> q_gen_2598
<s, z, s>(q_gen_2603) -> q_gen_2598
<z, s, s>(q_gen_2603) -> q_gen_2598
<z, z, s>(q_gen_2612) -> q_gen_2598
<z, z, z>() -> q_gen_2598
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 6  ;  () -> minus([z, y, z]) -> 6  ;  () -> plus([n, z, n]) -> 6  ;  (minus([_oc, n, _pc]) /\ plus([m, n, _oc])) -> eq_nat([_pc, m]) -> 7  ;  (minus([u, x2, _ec])) -> minus([s(u), s(x2), _ec]) -> 7  ;  (plus([n, mm, _jc])) -> plus([n, s(mm), s(_jc)]) -> 7
}
Sat witness: Yes: ((minus([_oc, n, _pc]) /\ plus([m, n, _oc])) -> eq_nat([_pc, m]), {
_oc -> s(z)  ;  _pc -> z  ;  m -> s(z)  ;  n -> s(z)
})

-------------------------------------------
Step 11, which took 0.008933 s (model generation: 0.008846,  model checking: 0.000087):

Model:
|_
{
minus -> 
{{{
Q={q_gen_2599, q_gen_2601, q_gen_2607},
Q_f={q_gen_2599},
Delta=
{
<z>() -> q_gen_2607
<s, s>(q_gen_2601) -> q_gen_2601
<z, z>() -> q_gen_2601
<s, s, s>(q_gen_2599) -> q_gen_2599
<s, s, z>(q_gen_2601) -> q_gen_2599
<s, z, s>(q_gen_2601) -> q_gen_2599
<s, z, z>(q_gen_2607) -> q_gen_2599
<z, s, z>(q_gen_2607) -> q_gen_2599
<z, z, z>() -> q_gen_2599
}

Datatype: <nat, nat, nat>
Convolution form: complete
}}}
  ;  plus -> 
{{{
Q={q_gen_2598, q_gen_2603, q_gen_2611, q_gen_2612},
Q_f={q_gen_2598},
Delta=
{
<z>() -> q_gen_2612
<z, z>() -> q_gen_2603
<s, s, s>(q_gen_2611) -> q_gen_2598
<s, z, s>(q_gen_2603) -> q_gen_2598
<z, s, s>(q_gen_2603) -> q_gen_2598
<z, z, z>() -> q_gen_2598
<s, s, s>(q_gen_2598) -> q_gen_2611
<z, z, s>(q_gen_2612) -> q_gen_2611
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 6  ;  () -> minus([z, y, z]) -> 6  ;  () -> plus([n, z, n]) -> 9  ;  (minus([_oc, n, _pc]) /\ plus([m, n, _oc])) -> eq_nat([_pc, m]) -> 7  ;  (minus([u, x2, _ec])) -> minus([s(u), s(x2), _ec]) -> 7  ;  (plus([n, mm, _jc])) -> plus([n, s(mm), s(_jc)]) -> 7
}
Sat witness: Yes: (() -> plus([n, z, n]), {
n -> s(s(z))
})

-------------------------------------------
Step 12, which took 0.009143 s (model generation: 0.008877,  model checking: 0.000266):

Model:
|_
{
minus -> 
{{{
Q={q_gen_2599, q_gen_2601, q_gen_2607},
Q_f={q_gen_2599},
Delta=
{
<z>() -> q_gen_2607
<s, s>(q_gen_2601) -> q_gen_2601
<z, z>() -> q_gen_2601
<s, s, s>(q_gen_2599) -> q_gen_2599
<s, s, z>(q_gen_2601) -> q_gen_2599
<s, z, s>(q_gen_2601) -> q_gen_2599
<s, z, z>(q_gen_2607) -> q_gen_2599
<z, s, z>(q_gen_2607) -> q_gen_2599
<z, z, z>() -> q_gen_2599
}

Datatype: <nat, nat, nat>
Convolution form: complete
}}}
  ;  plus -> 
{{{
Q={q_gen_2598, q_gen_2603, q_gen_2611, q_gen_2612},
Q_f={q_gen_2598},
Delta=
{
<z>() -> q_gen_2612
<s, s>(q_gen_2603) -> q_gen_2603
<z, z>() -> q_gen_2603
<s, s, s>(q_gen_2611) -> q_gen_2598
<s, z, s>(q_gen_2603) -> q_gen_2598
<z, s, s>(q_gen_2603) -> q_gen_2598
<z, z, z>() -> q_gen_2598
<s, s, s>(q_gen_2598) -> q_gen_2611
<z, z, s>(q_gen_2612) -> q_gen_2611
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 6  ;  () -> minus([z, y, z]) -> 9  ;  () -> plus([n, z, n]) -> 9  ;  (minus([_oc, n, _pc]) /\ plus([m, n, _oc])) -> eq_nat([_pc, m]) -> 7  ;  (minus([u, x2, _ec])) -> minus([s(u), s(x2), _ec]) -> 7  ;  (plus([n, mm, _jc])) -> plus([n, s(mm), s(_jc)]) -> 7
}
Sat witness: Yes: (() -> minus([z, y, z]), {
y -> s(s(z))
})

-------------------------------------------
Step 13, which took 0.012639 s (model generation: 0.011868,  model checking: 0.000771):

Model:
|_
{
minus -> 
{{{
Q={q_gen_2599, q_gen_2601, q_gen_2607},
Q_f={q_gen_2599},
Delta=
{
<s>(q_gen_2607) -> q_gen_2607
<z>() -> q_gen_2607
<s, s>(q_gen_2601) -> q_gen_2601
<z, z>() -> q_gen_2601
<s, s, s>(q_gen_2599) -> q_gen_2599
<s, s, z>(q_gen_2601) -> q_gen_2599
<s, z, s>(q_gen_2601) -> q_gen_2599
<s, z, z>(q_gen_2607) -> q_gen_2599
<z, s, z>(q_gen_2607) -> q_gen_2599
<z, z, z>() -> q_gen_2599
}

Datatype: <nat, nat, nat>
Convolution form: complete
}}}
  ;  plus -> 
{{{
Q={q_gen_2598, q_gen_2603, q_gen_2611, q_gen_2612},
Q_f={q_gen_2598},
Delta=
{
<z>() -> q_gen_2612
<s, s>(q_gen_2603) -> q_gen_2603
<z, z>() -> q_gen_2603
<s, s, s>(q_gen_2611) -> q_gen_2598
<s, z, s>(q_gen_2603) -> q_gen_2598
<z, s, s>(q_gen_2603) -> q_gen_2598
<z, z, z>() -> q_gen_2598
<s, s, s>(q_gen_2598) -> q_gen_2611
<z, z, s>(q_gen_2612) -> q_gen_2611
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 7  ;  () -> minus([z, y, z]) -> 9  ;  () -> plus([n, z, n]) -> 9  ;  (minus([_oc, n, _pc]) /\ plus([m, n, _oc])) -> eq_nat([_pc, m]) -> 7  ;  (minus([u, x2, _ec])) -> minus([s(u), s(x2), _ec]) -> 7  ;  (plus([n, mm, _jc])) -> plus([n, s(mm), s(_jc)]) -> 10
}
Sat witness: Yes: ((plus([n, mm, _jc])) -> plus([n, s(mm), s(_jc)]), {
_jc -> s(s(z))  ;  mm -> s(z)  ;  n -> s(z)
})

-------------------------------------------
Step 14, which took 0.015695 s (model generation: 0.015263,  model checking: 0.000432):

Model:
|_
{
minus -> 
{{{
Q={q_gen_2599, q_gen_2601, q_gen_2607},
Q_f={q_gen_2599},
Delta=
{
<s>(q_gen_2607) -> q_gen_2607
<z>() -> q_gen_2607
<s, s>(q_gen_2601) -> q_gen_2601
<z, z>() -> q_gen_2601
<s, s, s>(q_gen_2599) -> q_gen_2599
<s, s, z>(q_gen_2601) -> q_gen_2599
<s, z, s>(q_gen_2601) -> q_gen_2599
<s, z, z>(q_gen_2607) -> q_gen_2599
<z, s, z>(q_gen_2607) -> q_gen_2599
<z, z, z>() -> q_gen_2599
}

Datatype: <nat, nat, nat>
Convolution form: complete
}}}
  ;  plus -> 
{{{
Q={q_gen_2598, q_gen_2602, q_gen_2603, q_gen_2612, q_gen_2615},
Q_f={q_gen_2598, q_gen_2602},
Delta=
{
<z>() -> q_gen_2612
<s, s>(q_gen_2603) -> q_gen_2603
<z, s>(q_gen_2612) -> q_gen_2603
<z, z>() -> q_gen_2603
<z, z, z>() -> q_gen_2598
<s, s, s>(q_gen_2602) -> q_gen_2602
<s, z, s>(q_gen_2603) -> q_gen_2602
<z, s, s>(q_gen_2603) -> q_gen_2602
<z, z, s>(q_gen_2612) -> q_gen_2602
<s, s, s>(q_gen_2598) -> q_gen_2615
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 7  ;  () -> minus([z, y, z]) -> 9  ;  () -> plus([n, z, n]) -> 9  ;  (minus([_oc, n, _pc]) /\ plus([m, n, _oc])) -> eq_nat([_pc, m]) -> 7  ;  (minus([u, x2, _ec])) -> minus([s(u), s(x2), _ec]) -> 10  ;  (plus([n, mm, _jc])) -> plus([n, s(mm), s(_jc)]) -> 10
}
Sat witness: Yes: ((minus([u, x2, _ec])) -> minus([s(u), s(x2), _ec]), {
_ec -> z  ;  u -> z  ;  x2 -> s(z)
})

-------------------------------------------
Step 15, which took 0.018599 s (model generation: 0.016672,  model checking: 0.001927):

Model:
|_
{
minus -> 
{{{
Q={q_gen_2599, q_gen_2601, q_gen_2607},
Q_f={q_gen_2599},
Delta=
{
<s>(q_gen_2607) -> q_gen_2607
<z>() -> q_gen_2607
<s, s>(q_gen_2601) -> q_gen_2601
<z, s>(q_gen_2607) -> q_gen_2601
<z, z>() -> q_gen_2601
<s, s, s>(q_gen_2599) -> q_gen_2599
<s, s, z>(q_gen_2601) -> q_gen_2599
<s, z, s>(q_gen_2601) -> q_gen_2599
<s, z, z>(q_gen_2607) -> q_gen_2599
<z, s, z>(q_gen_2607) -> q_gen_2599
<z, z, z>() -> q_gen_2599
}

Datatype: <nat, nat, nat>
Convolution form: complete
}}}
  ;  plus -> 
{{{
Q={q_gen_2598, q_gen_2603, q_gen_2611, q_gen_2612, q_gen_2622},
Q_f={q_gen_2598},
Delta=
{
<z>() -> q_gen_2612
<s, s>(q_gen_2603) -> q_gen_2603
<z, z>() -> q_gen_2603
<z, s>(q_gen_2612) -> q_gen_2622
<s, s, s>(q_gen_2611) -> q_gen_2598
<s, z, s>(q_gen_2603) -> q_gen_2598
<z, s, s>(q_gen_2603) -> q_gen_2598
<z, z, z>() -> q_gen_2598
<s, s, s>(q_gen_2598) -> q_gen_2611
<z, s, s>(q_gen_2622) -> q_gen_2611
<z, z, s>(q_gen_2612) -> q_gen_2611
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 7  ;  () -> minus([z, y, z]) -> 9  ;  () -> plus([n, z, n]) -> 9  ;  (minus([_oc, n, _pc]) /\ plus([m, n, _oc])) -> eq_nat([_pc, m]) -> 10  ;  (minus([u, x2, _ec])) -> minus([s(u), s(x2), _ec]) -> 10  ;  (plus([n, mm, _jc])) -> plus([n, s(mm), s(_jc)]) -> 10
}
Sat witness: Yes: ((minus([_oc, n, _pc]) /\ plus([m, n, _oc])) -> eq_nat([_pc, m]), {
_oc -> s(z)  ;  _pc -> s(z)  ;  m -> z  ;  n -> s(z)
})

-------------------------------------------
Step 16, which took 0.019145 s (model generation: 0.017380,  model checking: 0.001765):

Model:
|_
{
minus -> 
{{{
Q={q_gen_2599, q_gen_2601, q_gen_2607, q_gen_2614},
Q_f={q_gen_2599},
Delta=
{
<s>(q_gen_2607) -> q_gen_2607
<z>() -> q_gen_2607
<s, s>(q_gen_2601) -> q_gen_2601
<z, s>(q_gen_2607) -> q_gen_2601
<z, z>() -> q_gen_2601
<s, s, s>(q_gen_2614) -> q_gen_2599
<s, s, z>(q_gen_2601) -> q_gen_2599
<s, z, s>(q_gen_2601) -> q_gen_2599
<z, s, z>(q_gen_2607) -> q_gen_2599
<z, z, z>() -> q_gen_2599
<s, s, s>(q_gen_2599) -> q_gen_2614
<s, z, z>(q_gen_2607) -> q_gen_2614
}

Datatype: <nat, nat, nat>
Convolution form: complete
}}}
  ;  plus -> 
{{{
Q={q_gen_2598, q_gen_2602, q_gen_2603, q_gen_2612, q_gen_2615},
Q_f={q_gen_2598, q_gen_2602},
Delta=
{
<z>() -> q_gen_2612
<s, s>(q_gen_2603) -> q_gen_2603
<z, s>(q_gen_2612) -> q_gen_2603
<z, z>() -> q_gen_2603
<z, z, z>() -> q_gen_2598
<s, s, s>(q_gen_2602) -> q_gen_2602
<s, z, s>(q_gen_2603) -> q_gen_2602
<z, s, s>(q_gen_2603) -> q_gen_2602
<z, z, s>(q_gen_2612) -> q_gen_2602
<s, s, s>(q_gen_2598) -> q_gen_2615
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 8  ;  () -> minus([z, y, z]) -> 10  ;  () -> plus([n, z, n]) -> 10  ;  (minus([_oc, n, _pc]) /\ plus([m, n, _oc])) -> eq_nat([_pc, m]) -> 10  ;  (minus([u, x2, _ec])) -> minus([s(u), s(x2), _ec]) -> 10  ;  (plus([n, mm, _jc])) -> plus([n, s(mm), s(_jc)]) -> 13
}
Sat witness: Yes: ((plus([n, mm, _jc])) -> plus([n, s(mm), s(_jc)]), {
_jc -> s(s(z))  ;  mm -> z  ;  n -> s(z)
})

-------------------------------------------
Step 17, which took 0.019847 s (model generation: 0.019468,  model checking: 0.000379):

Model:
|_
{
minus -> 
{{{
Q={q_gen_2599, q_gen_2601, q_gen_2607, q_gen_2614},
Q_f={q_gen_2599},
Delta=
{
<s>(q_gen_2607) -> q_gen_2607
<z>() -> q_gen_2607
<s, s>(q_gen_2601) -> q_gen_2601
<z, s>(q_gen_2607) -> q_gen_2601
<z, z>() -> q_gen_2601
<s, s, s>(q_gen_2614) -> q_gen_2599
<s, s, z>(q_gen_2601) -> q_gen_2599
<s, z, s>(q_gen_2601) -> q_gen_2599
<z, s, z>(q_gen_2607) -> q_gen_2599
<z, z, z>() -> q_gen_2599
<s, s, s>(q_gen_2599) -> q_gen_2614
<s, z, z>(q_gen_2607) -> q_gen_2614
}

Datatype: <nat, nat, nat>
Convolution form: complete
}}}
  ;  plus -> 
{{{
Q={q_gen_2598, q_gen_2602, q_gen_2603, q_gen_2612, q_gen_2615},
Q_f={q_gen_2598, q_gen_2602},
Delta=
{
<s>(q_gen_2612) -> q_gen_2612
<z>() -> q_gen_2612
<s, s>(q_gen_2603) -> q_gen_2603
<z, s>(q_gen_2612) -> q_gen_2603
<z, z>() -> q_gen_2603
<s, z, s>(q_gen_2603) -> q_gen_2598
<z, z, z>() -> q_gen_2598
<s, s, s>(q_gen_2602) -> q_gen_2602
<z, s, s>(q_gen_2603) -> q_gen_2602
<z, z, s>(q_gen_2612) -> q_gen_2602
<s, s, s>(q_gen_2598) -> q_gen_2615
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 9  ;  () -> minus([z, y, z]) -> 10  ;  () -> plus([n, z, n]) -> 10  ;  (minus([_oc, n, _pc]) /\ plus([m, n, _oc])) -> eq_nat([_pc, m]) -> 10  ;  (minus([u, x2, _ec])) -> minus([s(u), s(x2), _ec]) -> 13  ;  (plus([n, mm, _jc])) -> plus([n, s(mm), s(_jc)]) -> 13
}
Sat witness: Yes: ((minus([u, x2, _ec])) -> minus([s(u), s(x2), _ec]), {
_ec -> s(s(z))  ;  u -> s(z)  ;  x2 -> z
})

-------------------------------------------
Step 18, which took 0.016340 s (model generation: 0.016070,  model checking: 0.000270):

Model:
|_
{
minus -> 
{{{
Q={q_gen_2599, q_gen_2600, q_gen_2601, q_gen_2607, q_gen_2625},
Q_f={q_gen_2599, q_gen_2600},
Delta=
{
<s>(q_gen_2607) -> q_gen_2607
<z>() -> q_gen_2607
<s, s>(q_gen_2601) -> q_gen_2601
<z, s>(q_gen_2607) -> q_gen_2601
<z, z>() -> q_gen_2601
<z, z, z>() -> q_gen_2599
<s, s, s>(q_gen_2600) -> q_gen_2600
<s, s, z>(q_gen_2601) -> q_gen_2600
<s, z, s>(q_gen_2601) -> q_gen_2600
<s, z, z>(q_gen_2607) -> q_gen_2600
<z, s, z>(q_gen_2607) -> q_gen_2600
<s, s, s>(q_gen_2599) -> q_gen_2625
}

Datatype: <nat, nat, nat>
Convolution form: complete
}}}
  ;  plus -> 
{{{
Q={q_gen_2598, q_gen_2602, q_gen_2603, q_gen_2612, q_gen_2615},
Q_f={q_gen_2598, q_gen_2602},
Delta=
{
<s>(q_gen_2612) -> q_gen_2612
<z>() -> q_gen_2612
<s, s>(q_gen_2603) -> q_gen_2603
<z, s>(q_gen_2612) -> q_gen_2603
<z, z>() -> q_gen_2603
<s, z, s>(q_gen_2603) -> q_gen_2598
<z, z, z>() -> q_gen_2598
<s, s, s>(q_gen_2602) -> q_gen_2602
<z, s, s>(q_gen_2603) -> q_gen_2602
<z, z, s>(q_gen_2612) -> q_gen_2602
<s, s, s>(q_gen_2598) -> q_gen_2615
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 10  ;  () -> minus([z, y, z]) -> 10  ;  () -> plus([n, z, n]) -> 10  ;  (minus([_oc, n, _pc]) /\ plus([m, n, _oc])) -> eq_nat([_pc, m]) -> 13  ;  (minus([u, x2, _ec])) -> minus([s(u), s(x2), _ec]) -> 13  ;  (plus([n, mm, _jc])) -> plus([n, s(mm), s(_jc)]) -> 13
}
Sat witness: Yes: ((minus([_oc, n, _pc]) /\ plus([m, n, _oc])) -> eq_nat([_pc, m]), {
_oc -> s(s(z))  ;  _pc -> s(z)  ;  m -> z  ;  n -> s(s(z))
})

-------------------------------------------
Step 19, which took 0.016436 s (model generation: 0.015425,  model checking: 0.001011):

Model:
|_
{
minus -> 
{{{
Q={q_gen_2599, q_gen_2600, q_gen_2601, q_gen_2607, q_gen_2625},
Q_f={q_gen_2599, q_gen_2600},
Delta=
{
<s>(q_gen_2607) -> q_gen_2607
<z>() -> q_gen_2607
<s, s>(q_gen_2601) -> q_gen_2601
<z, s>(q_gen_2607) -> q_gen_2601
<z, z>() -> q_gen_2601
<s, s, z>(q_gen_2601) -> q_gen_2599
<z, z, z>() -> q_gen_2599
<s, s, s>(q_gen_2600) -> q_gen_2600
<s, z, s>(q_gen_2601) -> q_gen_2600
<s, z, z>(q_gen_2607) -> q_gen_2600
<z, s, z>(q_gen_2607) -> q_gen_2600
<s, s, s>(q_gen_2599) -> q_gen_2625
}

Datatype: <nat, nat, nat>
Convolution form: complete
}}}
  ;  plus -> 
{{{
Q={q_gen_2598, q_gen_2602, q_gen_2603, q_gen_2612, q_gen_2615},
Q_f={q_gen_2598, q_gen_2602},
Delta=
{
<s>(q_gen_2612) -> q_gen_2612
<z>() -> q_gen_2612
<s, s>(q_gen_2603) -> q_gen_2603
<z, s>(q_gen_2612) -> q_gen_2603
<z, z>() -> q_gen_2603
<s, z, s>(q_gen_2603) -> q_gen_2598
<z, z, z>() -> q_gen_2598
<s, s, s>(q_gen_2602) -> q_gen_2602
<z, s, s>(q_gen_2603) -> q_gen_2602
<z, z, s>(q_gen_2612) -> q_gen_2602
<s, s, s>(q_gen_2598) -> q_gen_2615
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 11  ;  () -> minus([z, y, z]) -> 11  ;  () -> plus([n, z, n]) -> 11  ;  (minus([_oc, n, _pc]) /\ plus([m, n, _oc])) -> eq_nat([_pc, m]) -> 13  ;  (minus([u, x2, _ec])) -> minus([s(u), s(x2), _ec]) -> 13  ;  (plus([n, mm, _jc])) -> plus([n, s(mm), s(_jc)]) -> 16
}
Sat witness: Yes: ((plus([n, mm, _jc])) -> plus([n, s(mm), s(_jc)]), {
_jc -> s(s(z))  ;  mm -> z  ;  n -> s(s(z))
})

-------------------------------------------
Step 20, which took 0.024150 s (model generation: 0.022971,  model checking: 0.001179):

Model:
|_
{
minus -> 
{{{
Q={q_gen_2599, q_gen_2600, q_gen_2601, q_gen_2607, q_gen_2625},
Q_f={q_gen_2599, q_gen_2600},
Delta=
{
<s>(q_gen_2607) -> q_gen_2607
<z>() -> q_gen_2607
<s, s>(q_gen_2601) -> q_gen_2601
<z, s>(q_gen_2607) -> q_gen_2601
<z, z>() -> q_gen_2601
<s, s, z>(q_gen_2601) -> q_gen_2599
<z, z, z>() -> q_gen_2599
<s, s, s>(q_gen_2600) -> q_gen_2600
<s, z, s>(q_gen_2601) -> q_gen_2600
<s, z, z>(q_gen_2607) -> q_gen_2600
<z, s, z>(q_gen_2607) -> q_gen_2600
<s, s, s>(q_gen_2599) -> q_gen_2625
}

Datatype: <nat, nat, nat>
Convolution form: complete
}}}
  ;  plus -> 
{{{
Q={q_gen_2598, q_gen_2602, q_gen_2603, q_gen_2612, q_gen_2615},
Q_f={q_gen_2598, q_gen_2602},
Delta=
{
<s>(q_gen_2612) -> q_gen_2612
<z>() -> q_gen_2612
<s, s>(q_gen_2603) -> q_gen_2603
<z, s>(q_gen_2612) -> q_gen_2603
<z, z>() -> q_gen_2603
<z, z, z>() -> q_gen_2598
<s, s, s>(q_gen_2602) -> q_gen_2602
<s, z, s>(q_gen_2603) -> q_gen_2602
<z, s, s>(q_gen_2603) -> q_gen_2602
<z, z, s>(q_gen_2612) -> q_gen_2602
<s, s, s>(q_gen_2598) -> q_gen_2615
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 12  ;  () -> minus([z, y, z]) -> 12  ;  () -> plus([n, z, n]) -> 12  ;  (minus([_oc, n, _pc]) /\ plus([m, n, _oc])) -> eq_nat([_pc, m]) -> 13  ;  (minus([u, x2, _ec])) -> minus([s(u), s(x2), _ec]) -> 16  ;  (plus([n, mm, _jc])) -> plus([n, s(mm), s(_jc)]) -> 16
}
Sat witness: Yes: ((minus([u, x2, _ec])) -> minus([s(u), s(x2), _ec]), {
_ec -> s(z)  ;  u -> s(z)  ;  x2 -> s(s(z))
})

-------------------------------------------
Step 21, which took 0.023806 s (model generation: 0.022962,  model checking: 0.000844):

Model:
|_
{
minus -> 
{{{
Q={q_gen_2599, q_gen_2600, q_gen_2601, q_gen_2607, q_gen_2614},
Q_f={q_gen_2599, q_gen_2600},
Delta=
{
<s>(q_gen_2607) -> q_gen_2607
<z>() -> q_gen_2607
<s, s>(q_gen_2601) -> q_gen_2601
<z, s>(q_gen_2607) -> q_gen_2601
<z, z>() -> q_gen_2601
<s, s, s>(q_gen_2600) -> q_gen_2599
<s, s, z>(q_gen_2601) -> q_gen_2599
<z, s, z>(q_gen_2607) -> q_gen_2599
<z, z, z>() -> q_gen_2599
<s, s, s>(q_gen_2614) -> q_gen_2600
<s, z, s>(q_gen_2601) -> q_gen_2600
<s, s, s>(q_gen_2599) -> q_gen_2614
<s, z, z>(q_gen_2607) -> q_gen_2614
}

Datatype: <nat, nat, nat>
Convolution form: complete
}}}
  ;  plus -> 
{{{
Q={q_gen_2598, q_gen_2602, q_gen_2603, q_gen_2612, q_gen_2615},
Q_f={q_gen_2598, q_gen_2602},
Delta=
{
<s>(q_gen_2612) -> q_gen_2612
<z>() -> q_gen_2612
<s, s>(q_gen_2603) -> q_gen_2603
<z, s>(q_gen_2612) -> q_gen_2603
<z, z>() -> q_gen_2603
<z, z, z>() -> q_gen_2598
<s, s, s>(q_gen_2602) -> q_gen_2602
<s, z, s>(q_gen_2603) -> q_gen_2602
<z, s, s>(q_gen_2603) -> q_gen_2602
<z, z, s>(q_gen_2612) -> q_gen_2602
<s, s, s>(q_gen_2598) -> q_gen_2615
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 13  ;  () -> minus([z, y, z]) -> 13  ;  () -> plus([n, z, n]) -> 13  ;  (minus([_oc, n, _pc]) /\ plus([m, n, _oc])) -> eq_nat([_pc, m]) -> 16  ;  (minus([u, x2, _ec])) -> minus([s(u), s(x2), _ec]) -> 16  ;  (plus([n, mm, _jc])) -> plus([n, s(mm), s(_jc)]) -> 16
}
Sat witness: Yes: ((minus([_oc, n, _pc]) /\ plus([m, n, _oc])) -> eq_nat([_pc, m]), {
_oc -> s(z)  ;  _pc -> s(z)  ;  m -> z  ;  n -> z
})

-------------------------------------------
Step 22, which took 0.021456 s (model generation: 0.020451,  model checking: 0.001005):

Model:
|_
{
minus -> 
{{{
Q={q_gen_2599, q_gen_2600, q_gen_2601, q_gen_2607, q_gen_2614},
Q_f={q_gen_2599, q_gen_2600},
Delta=
{
<s>(q_gen_2607) -> q_gen_2607
<z>() -> q_gen_2607
<s, s>(q_gen_2601) -> q_gen_2601
<z, s>(q_gen_2607) -> q_gen_2601
<z, z>() -> q_gen_2601
<s, s, s>(q_gen_2600) -> q_gen_2599
<s, s, z>(q_gen_2601) -> q_gen_2599
<z, s, z>(q_gen_2607) -> q_gen_2599
<z, z, z>() -> q_gen_2599
<s, s, s>(q_gen_2614) -> q_gen_2600
<s, z, s>(q_gen_2601) -> q_gen_2600
<s, s, s>(q_gen_2599) -> q_gen_2614
<s, z, z>(q_gen_2607) -> q_gen_2614
}

Datatype: <nat, nat, nat>
Convolution form: complete
}}}
  ;  plus -> 
{{{
Q={q_gen_2598, q_gen_2602, q_gen_2603, q_gen_2611, q_gen_2612},
Q_f={q_gen_2598, q_gen_2602},
Delta=
{
<s>(q_gen_2612) -> q_gen_2612
<z>() -> q_gen_2612
<s, s>(q_gen_2603) -> q_gen_2603
<z, s>(q_gen_2612) -> q_gen_2603
<z, z>() -> q_gen_2603
<s, s, s>(q_gen_2602) -> q_gen_2598
<z, z, z>() -> q_gen_2598
<s, s, s>(q_gen_2611) -> q_gen_2602
<s, z, s>(q_gen_2603) -> q_gen_2602
<z, s, s>(q_gen_2603) -> q_gen_2602
<s, s, s>(q_gen_2598) -> q_gen_2611
<z, z, s>(q_gen_2612) -> q_gen_2611
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 14  ;  () -> minus([z, y, z]) -> 14  ;  () -> plus([n, z, n]) -> 14  ;  (minus([_oc, n, _pc]) /\ plus([m, n, _oc])) -> eq_nat([_pc, m]) -> 16  ;  (minus([u, x2, _ec])) -> minus([s(u), s(x2), _ec]) -> 16  ;  (plus([n, mm, _jc])) -> plus([n, s(mm), s(_jc)]) -> 19
}
Sat witness: Yes: ((plus([n, mm, _jc])) -> plus([n, s(mm), s(_jc)]), {
_jc -> s(s(z))  ;  mm -> s(s(z))  ;  n -> s(s(z))
})

-------------------------------------------
Step 23, which took 0.020761 s (model generation: 0.019946,  model checking: 0.000815):

Model:
|_
{
minus -> 
{{{
Q={q_gen_2599, q_gen_2601, q_gen_2607, q_gen_2614, q_gen_2624},
Q_f={q_gen_2599},
Delta=
{
<s>(q_gen_2607) -> q_gen_2607
<z>() -> q_gen_2607
<s, s>(q_gen_2601) -> q_gen_2601
<z, z>() -> q_gen_2601
<z, s>(q_gen_2607) -> q_gen_2624
<s, s, s>(q_gen_2614) -> q_gen_2599
<s, s, z>(q_gen_2601) -> q_gen_2599
<s, s, z>(q_gen_2624) -> q_gen_2599
<s, z, s>(q_gen_2601) -> q_gen_2599
<z, s, z>(q_gen_2607) -> q_gen_2599
<z, z, z>() -> q_gen_2599
<s, s, s>(q_gen_2599) -> q_gen_2614
<s, z, s>(q_gen_2624) -> q_gen_2614
<s, z, z>(q_gen_2607) -> q_gen_2614
}

Datatype: <nat, nat, nat>
Convolution form: complete
}}}
  ;  plus -> 
{{{
Q={q_gen_2598, q_gen_2603, q_gen_2611, q_gen_2612, q_gen_2622},
Q_f={q_gen_2598},
Delta=
{
<s>(q_gen_2612) -> q_gen_2612
<z>() -> q_gen_2612
<s, s>(q_gen_2603) -> q_gen_2603
<z, z>() -> q_gen_2603
<z, s>(q_gen_2612) -> q_gen_2622
<s, s, s>(q_gen_2611) -> q_gen_2598
<s, z, s>(q_gen_2603) -> q_gen_2598
<z, s, s>(q_gen_2603) -> q_gen_2598
<z, z, z>() -> q_gen_2598
<s, s, s>(q_gen_2598) -> q_gen_2611
<s, z, s>(q_gen_2622) -> q_gen_2611
<z, s, s>(q_gen_2622) -> q_gen_2611
<z, z, s>(q_gen_2612) -> q_gen_2611
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 15  ;  () -> minus([z, y, z]) -> 15  ;  () -> plus([n, z, n]) -> 15  ;  (minus([_oc, n, _pc]) /\ plus([m, n, _oc])) -> eq_nat([_pc, m]) -> 16  ;  (minus([u, x2, _ec])) -> minus([s(u), s(x2), _ec]) -> 19  ;  (plus([n, mm, _jc])) -> plus([n, s(mm), s(_jc)]) -> 19
}
Sat witness: Yes: ((minus([u, x2, _ec])) -> minus([s(u), s(x2), _ec]), {
_ec -> s(s(s(s(z))))  ;  u -> s(s(z))  ;  x2 -> s(z)
})

-------------------------------------------
Step 24, which took 0.020309 s (model generation: 0.019789,  model checking: 0.000520):

Model:
|_
{
minus -> 
{{{
Q={q_gen_2599, q_gen_2600, q_gen_2601, q_gen_2607, q_gen_2625},
Q_f={q_gen_2599, q_gen_2600},
Delta=
{
<s>(q_gen_2607) -> q_gen_2607
<z>() -> q_gen_2607
<s, s>(q_gen_2601) -> q_gen_2601
<z, s>(q_gen_2607) -> q_gen_2601
<z, z>() -> q_gen_2601
<s, s, z>(q_gen_2601) -> q_gen_2599
<z, s, z>(q_gen_2607) -> q_gen_2599
<z, z, z>() -> q_gen_2599
<s, s, s>(q_gen_2600) -> q_gen_2600
<s, z, s>(q_gen_2601) -> q_gen_2600
<s, z, z>(q_gen_2607) -> q_gen_2600
<s, s, s>(q_gen_2599) -> q_gen_2625
}

Datatype: <nat, nat, nat>
Convolution form: complete
}}}
  ;  plus -> 
{{{
Q={q_gen_2598, q_gen_2602, q_gen_2603, q_gen_2611, q_gen_2612},
Q_f={q_gen_2598, q_gen_2602},
Delta=
{
<s>(q_gen_2612) -> q_gen_2612
<z>() -> q_gen_2612
<s, s>(q_gen_2603) -> q_gen_2603
<z, s>(q_gen_2612) -> q_gen_2603
<z, z>() -> q_gen_2603
<s, s, s>(q_gen_2611) -> q_gen_2598
<z, z, z>() -> q_gen_2598
<s, s, s>(q_gen_2602) -> q_gen_2602
<s, z, s>(q_gen_2603) -> q_gen_2602
<z, s, s>(q_gen_2603) -> q_gen_2602
<s, s, s>(q_gen_2598) -> q_gen_2611
<z, z, s>(q_gen_2612) -> q_gen_2611
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 16  ;  () -> minus([z, y, z]) -> 16  ;  () -> plus([n, z, n]) -> 16  ;  (minus([_oc, n, _pc]) /\ plus([m, n, _oc])) -> eq_nat([_pc, m]) -> 19  ;  (minus([u, x2, _ec])) -> minus([s(u), s(x2), _ec]) -> 19  ;  (plus([n, mm, _jc])) -> plus([n, s(mm), s(_jc)]) -> 19
}
Sat witness: Yes: ((minus([_oc, n, _pc]) /\ plus([m, n, _oc])) -> eq_nat([_pc, m]), {
_oc -> s(s(z))  ;  _pc -> s(z)  ;  m -> z  ;  n -> s(z)
})

-------------------------------------------
Step 25, which took 0.019348 s (model generation: 0.018505,  model checking: 0.000843):

Model:
|_
{
minus -> 
{{{
Q={q_gen_2599, q_gen_2600, q_gen_2601, q_gen_2607, q_gen_2625},
Q_f={q_gen_2599, q_gen_2600},
Delta=
{
<s>(q_gen_2607) -> q_gen_2607
<z>() -> q_gen_2607
<s, s>(q_gen_2601) -> q_gen_2601
<z, s>(q_gen_2607) -> q_gen_2601
<z, z>() -> q_gen_2601
<s, s, z>(q_gen_2601) -> q_gen_2599
<z, s, z>(q_gen_2607) -> q_gen_2599
<z, z, z>() -> q_gen_2599
<s, s, s>(q_gen_2600) -> q_gen_2600
<s, z, s>(q_gen_2601) -> q_gen_2600
<s, z, z>(q_gen_2607) -> q_gen_2600
<s, s, s>(q_gen_2599) -> q_gen_2625
}

Datatype: <nat, nat, nat>
Convolution form: complete
}}}
  ;  plus -> 
{{{
Q={q_gen_2598, q_gen_2603, q_gen_2611, q_gen_2612, q_gen_2622},
Q_f={q_gen_2598},
Delta=
{
<s>(q_gen_2612) -> q_gen_2612
<z>() -> q_gen_2612
<s, s>(q_gen_2603) -> q_gen_2603
<z, z>() -> q_gen_2603
<z, s>(q_gen_2612) -> q_gen_2622
<s, s, s>(q_gen_2611) -> q_gen_2598
<s, z, s>(q_gen_2603) -> q_gen_2598
<z, s, s>(q_gen_2603) -> q_gen_2598
<z, z, z>() -> q_gen_2598
<s, s, s>(q_gen_2598) -> q_gen_2611
<s, z, s>(q_gen_2622) -> q_gen_2611
<z, s, s>(q_gen_2622) -> q_gen_2611
<z, z, s>(q_gen_2612) -> q_gen_2611
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 17  ;  () -> minus([z, y, z]) -> 17  ;  () -> plus([n, z, n]) -> 17  ;  (minus([_oc, n, _pc]) /\ plus([m, n, _oc])) -> eq_nat([_pc, m]) -> 19  ;  (minus([u, x2, _ec])) -> minus([s(u), s(x2), _ec]) -> 19  ;  (plus([n, mm, _jc])) -> plus([n, s(mm), s(_jc)]) -> 22
}
Sat witness: Yes: ((plus([n, mm, _jc])) -> plus([n, s(mm), s(_jc)]), {
_jc -> s(s(s(z)))  ;  mm -> s(z)  ;  n -> s(s(z))
})

-------------------------------------------
Step 26, which took 0.024737 s (model generation: 0.023982,  model checking: 0.000755):

Model:
|_
{
minus -> 
{{{
Q={q_gen_2599, q_gen_2600, q_gen_2601, q_gen_2607, q_gen_2625},
Q_f={q_gen_2599, q_gen_2600},
Delta=
{
<s>(q_gen_2607) -> q_gen_2607
<z>() -> q_gen_2607
<s, s>(q_gen_2601) -> q_gen_2601
<z, s>(q_gen_2607) -> q_gen_2601
<z, z>() -> q_gen_2601
<s, s, z>(q_gen_2601) -> q_gen_2599
<z, s, z>(q_gen_2607) -> q_gen_2599
<z, z, z>() -> q_gen_2599
<s, s, s>(q_gen_2600) -> q_gen_2600
<s, z, s>(q_gen_2601) -> q_gen_2600
<s, z, z>(q_gen_2607) -> q_gen_2600
<s, s, s>(q_gen_2599) -> q_gen_2625
}

Datatype: <nat, nat, nat>
Convolution form: complete
}}}
  ;  plus -> 
{{{
Q={q_gen_2598, q_gen_2602, q_gen_2603, q_gen_2611, q_gen_2612, q_gen_2622},
Q_f={q_gen_2598, q_gen_2602},
Delta=
{
<s>(q_gen_2612) -> q_gen_2612
<z>() -> q_gen_2612
<s, s>(q_gen_2603) -> q_gen_2603
<z, z>() -> q_gen_2603
<z, s>(q_gen_2612) -> q_gen_2622
<z, z, z>() -> q_gen_2598
<s, s, s>(q_gen_2602) -> q_gen_2602
<s, s, s>(q_gen_2611) -> q_gen_2602
<s, z, s>(q_gen_2603) -> q_gen_2602
<z, s, s>(q_gen_2603) -> q_gen_2602
<s, s, s>(q_gen_2598) -> q_gen_2611
<s, z, s>(q_gen_2622) -> q_gen_2611
<z, s, s>(q_gen_2622) -> q_gen_2611
<z, z, s>(q_gen_2612) -> q_gen_2611
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 18  ;  () -> minus([z, y, z]) -> 18  ;  () -> plus([n, z, n]) -> 18  ;  (minus([_oc, n, _pc]) /\ plus([m, n, _oc])) -> eq_nat([_pc, m]) -> 19  ;  (minus([u, x2, _ec])) -> minus([s(u), s(x2), _ec]) -> 22  ;  (plus([n, mm, _jc])) -> plus([n, s(mm), s(_jc)]) -> 22
}
Sat witness: Yes: ((minus([u, x2, _ec])) -> minus([s(u), s(x2), _ec]), {
_ec -> z  ;  u -> s(z)  ;  x2 -> z
})

-------------------------------------------
Step 27, which took 0.019172 s (model generation: 0.018884,  model checking: 0.000288):

Model:
|_
{
minus -> 
{{{
Q={q_gen_2599, q_gen_2600, q_gen_2601, q_gen_2607, q_gen_2625},
Q_f={q_gen_2599, q_gen_2600},
Delta=
{
<s>(q_gen_2607) -> q_gen_2607
<z>() -> q_gen_2607
<s, s>(q_gen_2601) -> q_gen_2601
<s, z>(q_gen_2607) -> q_gen_2601
<z, s>(q_gen_2607) -> q_gen_2601
<z, z>() -> q_gen_2601
<s, s, z>(q_gen_2601) -> q_gen_2599
<z, s, z>(q_gen_2607) -> q_gen_2599
<z, z, z>() -> q_gen_2599
<s, s, s>(q_gen_2600) -> q_gen_2600
<s, z, s>(q_gen_2601) -> q_gen_2600
<s, z, z>(q_gen_2607) -> q_gen_2600
<s, s, s>(q_gen_2599) -> q_gen_2625
}

Datatype: <nat, nat, nat>
Convolution form: complete
}}}
  ;  plus -> 
{{{
Q={q_gen_2598, q_gen_2602, q_gen_2603, q_gen_2611, q_gen_2612, q_gen_2622},
Q_f={q_gen_2598, q_gen_2602},
Delta=
{
<s>(q_gen_2612) -> q_gen_2612
<z>() -> q_gen_2612
<s, s>(q_gen_2603) -> q_gen_2603
<z, z>() -> q_gen_2603
<z, s>(q_gen_2612) -> q_gen_2622
<z, z, z>() -> q_gen_2598
<s, s, s>(q_gen_2602) -> q_gen_2602
<s, s, s>(q_gen_2611) -> q_gen_2602
<s, z, s>(q_gen_2603) -> q_gen_2602
<z, s, s>(q_gen_2603) -> q_gen_2602
<s, s, s>(q_gen_2598) -> q_gen_2611
<s, z, s>(q_gen_2622) -> q_gen_2611
<z, s, s>(q_gen_2622) -> q_gen_2611
<z, z, s>(q_gen_2612) -> q_gen_2611
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 19  ;  () -> minus([z, y, z]) -> 19  ;  () -> plus([n, z, n]) -> 19  ;  (minus([_oc, n, _pc]) /\ plus([m, n, _oc])) -> eq_nat([_pc, m]) -> 22  ;  (minus([u, x2, _ec])) -> minus([s(u), s(x2), _ec]) -> 22  ;  (plus([n, mm, _jc])) -> plus([n, s(mm), s(_jc)]) -> 22
}
Sat witness: Yes: ((minus([_oc, n, _pc]) /\ plus([m, n, _oc])) -> eq_nat([_pc, m]), {
_oc -> s(z)  ;  _pc -> z  ;  m -> s(z)  ;  n -> z
})

-------------------------------------------
Step 28, which took 0.020663 s (model generation: 0.019566,  model checking: 0.001097):

Model:
|_
{
minus -> 
{{{
Q={q_gen_2599, q_gen_2600, q_gen_2601, q_gen_2607, q_gen_2614},
Q_f={q_gen_2599, q_gen_2600},
Delta=
{
<s>(q_gen_2607) -> q_gen_2607
<z>() -> q_gen_2607
<s, s>(q_gen_2601) -> q_gen_2601
<s, z>(q_gen_2607) -> q_gen_2601
<z, s>(q_gen_2607) -> q_gen_2601
<z, z>() -> q_gen_2601
<s, s, z>(q_gen_2601) -> q_gen_2599
<z, s, z>(q_gen_2607) -> q_gen_2599
<z, z, z>() -> q_gen_2599
<s, s, s>(q_gen_2600) -> q_gen_2600
<s, s, s>(q_gen_2614) -> q_gen_2600
<s, z, s>(q_gen_2601) -> q_gen_2600
<s, s, s>(q_gen_2599) -> q_gen_2614
<s, z, z>(q_gen_2607) -> q_gen_2614
}

Datatype: <nat, nat, nat>
Convolution form: complete
}}}
  ;  plus -> 
{{{
Q={q_gen_2598, q_gen_2603, q_gen_2611, q_gen_2612, q_gen_2622, q_gen_2629},
Q_f={q_gen_2598},
Delta=
{
<z>() -> q_gen_2612
<s>(q_gen_2612) -> q_gen_2629
<s, s>(q_gen_2603) -> q_gen_2603
<z, z>() -> q_gen_2603
<z, s>(q_gen_2612) -> q_gen_2622
<s, s, s>(q_gen_2611) -> q_gen_2598
<s, z, s>(q_gen_2603) -> q_gen_2598
<z, s, s>(q_gen_2603) -> q_gen_2598
<z, z, s>(q_gen_2629) -> q_gen_2598
<z, z, z>() -> q_gen_2598
<s, s, s>(q_gen_2598) -> q_gen_2611
<s, z, s>(q_gen_2622) -> q_gen_2611
<z, s, s>(q_gen_2622) -> q_gen_2611
<z, z, s>(q_gen_2612) -> q_gen_2611
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 20  ;  () -> minus([z, y, z]) -> 20  ;  () -> plus([n, z, n]) -> 20  ;  (minus([_oc, n, _pc]) /\ plus([m, n, _oc])) -> eq_nat([_pc, m]) -> 22  ;  (minus([u, x2, _ec])) -> minus([s(u), s(x2), _ec]) -> 22  ;  (plus([n, mm, _jc])) -> plus([n, s(mm), s(_jc)]) -> 25
}
Sat witness: Yes: ((plus([n, mm, _jc])) -> plus([n, s(mm), s(_jc)]), {
_jc -> s(s(z))  ;  mm -> z  ;  n -> z
})

-------------------------------------------
Step 29, which took 0.024634 s (model generation: 0.024522,  model checking: 0.000112):

Model:
|_
{
minus -> 
{{{
Q={q_gen_2599, q_gen_2600, q_gen_2601, q_gen_2607, q_gen_2614},
Q_f={q_gen_2599, q_gen_2600},
Delta=
{
<s>(q_gen_2607) -> q_gen_2607
<z>() -> q_gen_2607
<s, s>(q_gen_2601) -> q_gen_2601
<s, z>(q_gen_2607) -> q_gen_2601
<z, s>(q_gen_2607) -> q_gen_2601
<z, z>() -> q_gen_2601
<s, s, z>(q_gen_2601) -> q_gen_2599
<z, s, z>(q_gen_2607) -> q_gen_2599
<z, z, z>() -> q_gen_2599
<s, s, s>(q_gen_2600) -> q_gen_2600
<s, s, s>(q_gen_2614) -> q_gen_2600
<s, z, s>(q_gen_2601) -> q_gen_2600
<s, s, s>(q_gen_2599) -> q_gen_2614
<s, z, z>(q_gen_2607) -> q_gen_2614
}

Datatype: <nat, nat, nat>
Convolution form: complete
}}}
  ;  plus -> 
{{{
Q={q_gen_2598, q_gen_2602, q_gen_2603, q_gen_2611, q_gen_2612, q_gen_2617},
Q_f={q_gen_2598, q_gen_2602},
Delta=
{
<s>(q_gen_2612) -> q_gen_2612
<z>() -> q_gen_2612
<z, z>() -> q_gen_2603
<s, s>(q_gen_2603) -> q_gen_2617
<z, s>(q_gen_2612) -> q_gen_2617
<z, z, z>() -> q_gen_2598
<s, s, s>(q_gen_2602) -> q_gen_2602
<s, s, s>(q_gen_2611) -> q_gen_2602
<s, z, s>(q_gen_2603) -> q_gen_2602
<s, z, s>(q_gen_2617) -> q_gen_2602
<z, s, s>(q_gen_2603) -> q_gen_2602
<s, s, s>(q_gen_2598) -> q_gen_2611
<z, s, s>(q_gen_2617) -> q_gen_2611
<z, z, s>(q_gen_2612) -> q_gen_2611
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 20  ;  () -> minus([z, y, z]) -> 20  ;  () -> plus([n, z, n]) -> 23  ;  (minus([_oc, n, _pc]) /\ plus([m, n, _oc])) -> eq_nat([_pc, m]) -> 22  ;  (minus([u, x2, _ec])) -> minus([s(u), s(x2), _ec]) -> 22  ;  (plus([n, mm, _jc])) -> plus([n, s(mm), s(_jc)]) -> 25
}
Sat witness: Yes: (() -> plus([n, z, n]), {
n -> s(s(s(z)))
})

-------------------------------------------
Step 30, which took 0.021223 s (model generation: 0.020723,  model checking: 0.000500):

Model:
|_
{
minus -> 
{{{
Q={q_gen_2599, q_gen_2600, q_gen_2601, q_gen_2607, q_gen_2614},
Q_f={q_gen_2599, q_gen_2600},
Delta=
{
<s>(q_gen_2607) -> q_gen_2607
<z>() -> q_gen_2607
<s, s>(q_gen_2601) -> q_gen_2601
<s, z>(q_gen_2607) -> q_gen_2601
<z, s>(q_gen_2607) -> q_gen_2601
<z, z>() -> q_gen_2601
<s, s, s>(q_gen_2614) -> q_gen_2599
<s, s, z>(q_gen_2601) -> q_gen_2599
<z, s, z>(q_gen_2607) -> q_gen_2599
<z, z, z>() -> q_gen_2599
<s, s, s>(q_gen_2600) -> q_gen_2600
<s, z, s>(q_gen_2601) -> q_gen_2600
<s, s, s>(q_gen_2599) -> q_gen_2614
<s, z, z>(q_gen_2607) -> q_gen_2614
}

Datatype: <nat, nat, nat>
Convolution form: complete
}}}
  ;  plus -> 
{{{
Q={q_gen_2598, q_gen_2603, q_gen_2605, q_gen_2611, q_gen_2612, q_gen_2622},
Q_f={q_gen_2598, q_gen_2605},
Delta=
{
<s>(q_gen_2612) -> q_gen_2612
<z>() -> q_gen_2612
<s, s>(q_gen_2603) -> q_gen_2603
<z, z>() -> q_gen_2603
<z, s>(q_gen_2612) -> q_gen_2622
<s, s, s>(q_gen_2605) -> q_gen_2598
<z, s, s>(q_gen_2603) -> q_gen_2598
<z, z, z>() -> q_gen_2598
<s, s, s>(q_gen_2611) -> q_gen_2605
<s, z, s>(q_gen_2603) -> q_gen_2605
<s, s, s>(q_gen_2598) -> q_gen_2611
<s, z, s>(q_gen_2622) -> q_gen_2611
<z, s, s>(q_gen_2622) -> q_gen_2611
<z, z, s>(q_gen_2612) -> q_gen_2611
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 21  ;  () -> minus([z, y, z]) -> 21  ;  () -> plus([n, z, n]) -> 23  ;  (minus([_oc, n, _pc]) /\ plus([m, n, _oc])) -> eq_nat([_pc, m]) -> 22  ;  (minus([u, x2, _ec])) -> minus([s(u), s(x2), _ec]) -> 25  ;  (plus([n, mm, _jc])) -> plus([n, s(mm), s(_jc)]) -> 25
}
Sat witness: Yes: ((minus([u, x2, _ec])) -> minus([s(u), s(x2), _ec]), {
_ec -> s(s(z))  ;  u -> s(s(z))  ;  x2 -> s(z)
})

-------------------------------------------
Step 31, which took 0.021313 s (model generation: 0.021000,  model checking: 0.000313):

Model:
|_
{
minus -> 
{{{
Q={q_gen_2599, q_gen_2600, q_gen_2601, q_gen_2607, q_gen_2614},
Q_f={q_gen_2599, q_gen_2600},
Delta=
{
<s>(q_gen_2607) -> q_gen_2607
<z>() -> q_gen_2607
<s, s>(q_gen_2601) -> q_gen_2601
<s, z>(q_gen_2607) -> q_gen_2601
<z, s>(q_gen_2607) -> q_gen_2601
<z, z>() -> q_gen_2601
<s, s, z>(q_gen_2601) -> q_gen_2599
<z, s, z>(q_gen_2607) -> q_gen_2599
<z, z, z>() -> q_gen_2599
<s, s, s>(q_gen_2600) -> q_gen_2600
<s, s, s>(q_gen_2614) -> q_gen_2600
<s, z, s>(q_gen_2601) -> q_gen_2600
<s, s, s>(q_gen_2599) -> q_gen_2614
<s, z, z>(q_gen_2607) -> q_gen_2614
}

Datatype: <nat, nat, nat>
Convolution form: complete
}}}
  ;  plus -> 
{{{
Q={q_gen_2598, q_gen_2602, q_gen_2603, q_gen_2611, q_gen_2612, q_gen_2617},
Q_f={q_gen_2598, q_gen_2602},
Delta=
{
<s>(q_gen_2612) -> q_gen_2612
<z>() -> q_gen_2612
<z, z>() -> q_gen_2603
<s, s>(q_gen_2603) -> q_gen_2617
<s, s>(q_gen_2617) -> q_gen_2617
<z, s>(q_gen_2612) -> q_gen_2617
<z, z, z>() -> q_gen_2598
<s, s, s>(q_gen_2602) -> q_gen_2602
<s, s, s>(q_gen_2611) -> q_gen_2602
<s, z, s>(q_gen_2603) -> q_gen_2602
<s, z, s>(q_gen_2617) -> q_gen_2602
<z, s, s>(q_gen_2603) -> q_gen_2602
<s, s, s>(q_gen_2598) -> q_gen_2611
<z, s, s>(q_gen_2617) -> q_gen_2611
<z, z, s>(q_gen_2612) -> q_gen_2611
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 22  ;  () -> minus([z, y, z]) -> 22  ;  () -> plus([n, z, n]) -> 23  ;  (minus([_oc, n, _pc]) /\ plus([m, n, _oc])) -> eq_nat([_pc, m]) -> 25  ;  (minus([u, x2, _ec])) -> minus([s(u), s(x2), _ec]) -> 25  ;  (plus([n, mm, _jc])) -> plus([n, s(mm), s(_jc)]) -> 25
}
Sat witness: Yes: ((minus([_oc, n, _pc]) /\ plus([m, n, _oc])) -> eq_nat([_pc, m]), {
_oc -> s(z)  ;  _pc -> s(s(z))  ;  m -> s(z)  ;  n -> z
})

-------------------------------------------
Step 32, which took 0.022327 s (model generation: 0.021692,  model checking: 0.000635):

Model:
|_
{
minus -> 
{{{
Q={q_gen_2599, q_gen_2601, q_gen_2607, q_gen_2613, q_gen_2614, q_gen_2624},
Q_f={q_gen_2599, q_gen_2613},
Delta=
{
<s>(q_gen_2607) -> q_gen_2607
<z>() -> q_gen_2607
<s, s>(q_gen_2601) -> q_gen_2601
<s, z>(q_gen_2607) -> q_gen_2601
<z, z>() -> q_gen_2601
<z, s>(q_gen_2607) -> q_gen_2624
<s, s, s>(q_gen_2613) -> q_gen_2599
<s, s, z>(q_gen_2601) -> q_gen_2599
<s, s, z>(q_gen_2624) -> q_gen_2599
<s, z, s>(q_gen_2601) -> q_gen_2599
<z, s, z>(q_gen_2607) -> q_gen_2599
<z, z, z>() -> q_gen_2599
<s, s, s>(q_gen_2614) -> q_gen_2613
<s, s, s>(q_gen_2599) -> q_gen_2614
<s, z, s>(q_gen_2624) -> q_gen_2614
<s, z, z>(q_gen_2607) -> q_gen_2614
}

Datatype: <nat, nat, nat>
Convolution form: complete
}}}
  ;  plus -> 
{{{
Q={q_gen_2598, q_gen_2603, q_gen_2610, q_gen_2611, q_gen_2612, q_gen_2617},
Q_f={q_gen_2598, q_gen_2610},
Delta=
{
<s>(q_gen_2612) -> q_gen_2612
<z>() -> q_gen_2612
<z, z>() -> q_gen_2603
<s, s>(q_gen_2603) -> q_gen_2617
<s, s>(q_gen_2617) -> q_gen_2617
<z, s>(q_gen_2612) -> q_gen_2617
<s, s, s>(q_gen_2610) -> q_gen_2598
<s, z, s>(q_gen_2603) -> q_gen_2598
<z, s, s>(q_gen_2603) -> q_gen_2598
<z, z, z>() -> q_gen_2598
<s, s, s>(q_gen_2611) -> q_gen_2610
<s, z, s>(q_gen_2617) -> q_gen_2610
<s, s, s>(q_gen_2598) -> q_gen_2611
<z, s, s>(q_gen_2617) -> q_gen_2611
<z, z, s>(q_gen_2612) -> q_gen_2611
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 23  ;  () -> minus([z, y, z]) -> 23  ;  () -> plus([n, z, n]) -> 24  ;  (minus([_oc, n, _pc]) /\ plus([m, n, _oc])) -> eq_nat([_pc, m]) -> 25  ;  (minus([u, x2, _ec])) -> minus([s(u), s(x2), _ec]) -> 25  ;  (plus([n, mm, _jc])) -> plus([n, s(mm), s(_jc)]) -> 28
}
Sat witness: Yes: ((plus([n, mm, _jc])) -> plus([n, s(mm), s(_jc)]), {
_jc -> s(s(s(z)))  ;  mm -> s(s(z))  ;  n -> s(s(s(z)))
})

-------------------------------------------
Step 33, which took 0.023289 s (model generation: 0.022645,  model checking: 0.000644):

Model:
|_
{
minus -> 
{{{
Q={q_gen_2599, q_gen_2601, q_gen_2607, q_gen_2613, q_gen_2614, q_gen_2624},
Q_f={q_gen_2599, q_gen_2613},
Delta=
{
<s>(q_gen_2607) -> q_gen_2607
<z>() -> q_gen_2607
<s, s>(q_gen_2601) -> q_gen_2601
<s, z>(q_gen_2607) -> q_gen_2601
<z, z>() -> q_gen_2601
<z, s>(q_gen_2607) -> q_gen_2624
<s, s, s>(q_gen_2613) -> q_gen_2599
<s, s, z>(q_gen_2601) -> q_gen_2599
<s, s, z>(q_gen_2624) -> q_gen_2599
<s, z, s>(q_gen_2601) -> q_gen_2599
<z, s, z>(q_gen_2607) -> q_gen_2599
<z, z, z>() -> q_gen_2599
<s, s, s>(q_gen_2614) -> q_gen_2613
<s, s, s>(q_gen_2599) -> q_gen_2614
<s, z, s>(q_gen_2624) -> q_gen_2614
<s, z, z>(q_gen_2607) -> q_gen_2614
}

Datatype: <nat, nat, nat>
Convolution form: complete
}}}
  ;  plus -> 
{{{
Q={q_gen_2598, q_gen_2603, q_gen_2605, q_gen_2611, q_gen_2612, q_gen_2622},
Q_f={q_gen_2598, q_gen_2605},
Delta=
{
<s>(q_gen_2612) -> q_gen_2612
<z>() -> q_gen_2612
<s, s>(q_gen_2603) -> q_gen_2603
<z, z>() -> q_gen_2603
<z, s>(q_gen_2612) -> q_gen_2622
<s, s, s>(q_gen_2605) -> q_gen_2598
<z, s, s>(q_gen_2603) -> q_gen_2598
<z, z, z>() -> q_gen_2598
<s, s, s>(q_gen_2611) -> q_gen_2605
<s, z, s>(q_gen_2603) -> q_gen_2605
<s, s, s>(q_gen_2598) -> q_gen_2611
<s, z, s>(q_gen_2622) -> q_gen_2611
<z, s, s>(q_gen_2622) -> q_gen_2611
<z, z, s>(q_gen_2612) -> q_gen_2611
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 24  ;  () -> minus([z, y, z]) -> 24  ;  () -> plus([n, z, n]) -> 25  ;  (minus([_oc, n, _pc]) /\ plus([m, n, _oc])) -> eq_nat([_pc, m]) -> 25  ;  (minus([u, x2, _ec])) -> minus([s(u), s(x2), _ec]) -> 28  ;  (plus([n, mm, _jc])) -> plus([n, s(mm), s(_jc)]) -> 28
}
Sat witness: Yes: ((minus([u, x2, _ec])) -> minus([s(u), s(x2), _ec]), {
_ec -> s(z)  ;  u -> s(s(z))  ;  x2 -> s(z)
})

-------------------------------------------
Step 34, which took 0.021297 s (model generation: 0.020788,  model checking: 0.000509):

Model:
|_
{
minus -> 
{{{
Q={q_gen_2599, q_gen_2601, q_gen_2606, q_gen_2607, q_gen_2614, q_gen_2624},
Q_f={q_gen_2599, q_gen_2606},
Delta=
{
<s>(q_gen_2607) -> q_gen_2607
<z>() -> q_gen_2607
<s, s>(q_gen_2601) -> q_gen_2601
<z, z>() -> q_gen_2601
<s, z>(q_gen_2607) -> q_gen_2624
<z, s>(q_gen_2607) -> q_gen_2624
<s, s, z>(q_gen_2601) -> q_gen_2599
<s, z, s>(q_gen_2601) -> q_gen_2599
<z, z, z>() -> q_gen_2599
<s, s, s>(q_gen_2606) -> q_gen_2606
<s, s, s>(q_gen_2614) -> q_gen_2606
<s, s, z>(q_gen_2624) -> q_gen_2606
<z, s, z>(q_gen_2607) -> q_gen_2606
<s, s, s>(q_gen_2599) -> q_gen_2614
<s, z, s>(q_gen_2624) -> q_gen_2614
<s, z, z>(q_gen_2607) -> q_gen_2614
}

Datatype: <nat, nat, nat>
Convolution form: complete
}}}
  ;  plus -> 
{{{
Q={q_gen_2598, q_gen_2603, q_gen_2605, q_gen_2611, q_gen_2612, q_gen_2622},
Q_f={q_gen_2598, q_gen_2605},
Delta=
{
<s>(q_gen_2612) -> q_gen_2612
<z>() -> q_gen_2612
<s, s>(q_gen_2603) -> q_gen_2603
<z, z>() -> q_gen_2603
<z, s>(q_gen_2612) -> q_gen_2622
<s, s, s>(q_gen_2605) -> q_gen_2598
<z, s, s>(q_gen_2603) -> q_gen_2598
<z, z, z>() -> q_gen_2598
<s, s, s>(q_gen_2611) -> q_gen_2605
<s, z, s>(q_gen_2603) -> q_gen_2605
<s, s, s>(q_gen_2598) -> q_gen_2611
<s, z, s>(q_gen_2622) -> q_gen_2611
<z, s, s>(q_gen_2622) -> q_gen_2611
<z, z, s>(q_gen_2612) -> q_gen_2611
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 25  ;  () -> minus([z, y, z]) -> 25  ;  () -> plus([n, z, n]) -> 25  ;  (minus([_oc, n, _pc]) /\ plus([m, n, _oc])) -> eq_nat([_pc, m]) -> 28  ;  (minus([u, x2, _ec])) -> minus([s(u), s(x2), _ec]) -> 28  ;  (plus([n, mm, _jc])) -> plus([n, s(mm), s(_jc)]) -> 28
}
Sat witness: Yes: ((minus([_oc, n, _pc]) /\ plus([m, n, _oc])) -> eq_nat([_pc, m]), {
_oc -> s(s(z))  ;  _pc -> z  ;  m -> s(z)  ;  n -> s(z)
})

-------------------------------------------
Step 35, which took 0.021482 s (model generation: 0.021010,  model checking: 0.000472):

Model:
|_
{
minus -> 
{{{
Q={q_gen_2599, q_gen_2601, q_gen_2607, q_gen_2614, q_gen_2619, q_gen_2624, q_gen_2642},
Q_f={q_gen_2599},
Delta=
{
<z>() -> q_gen_2607
<s>(q_gen_2607) -> q_gen_2619
<s, s>(q_gen_2601) -> q_gen_2601
<z, z>() -> q_gen_2601
<z, s>(q_gen_2607) -> q_gen_2624
<s, z>(q_gen_2607) -> q_gen_2642
<z, s>(q_gen_2619) -> q_gen_2642
<s, s, s>(q_gen_2614) -> q_gen_2599
<s, s, z>(q_gen_2601) -> q_gen_2599
<s, s, z>(q_gen_2624) -> q_gen_2599
<s, z, s>(q_gen_2601) -> q_gen_2599
<s, z, s>(q_gen_2642) -> q_gen_2599
<z, s, z>(q_gen_2607) -> q_gen_2599
<z, s, z>(q_gen_2619) -> q_gen_2599
<z, z, z>() -> q_gen_2599
<s, s, s>(q_gen_2599) -> q_gen_2614
<s, s, z>(q_gen_2642) -> q_gen_2614
<s, z, s>(q_gen_2624) -> q_gen_2614
<s, z, z>(q_gen_2607) -> q_gen_2614
}

Datatype: <nat, nat, nat>
Convolution form: complete
}}}
  ;  plus -> 
{{{
Q={q_gen_2598, q_gen_2603, q_gen_2605, q_gen_2611, q_gen_2612, q_gen_2617},
Q_f={q_gen_2598, q_gen_2605},
Delta=
{
<s>(q_gen_2612) -> q_gen_2612
<z>() -> q_gen_2612
<z, z>() -> q_gen_2603
<s, s>(q_gen_2603) -> q_gen_2617
<s, s>(q_gen_2617) -> q_gen_2617
<z, s>(q_gen_2612) -> q_gen_2617
<s, s, s>(q_gen_2605) -> q_gen_2598
<z, s, s>(q_gen_2603) -> q_gen_2598
<z, z, z>() -> q_gen_2598
<s, s, s>(q_gen_2611) -> q_gen_2605
<s, z, s>(q_gen_2603) -> q_gen_2605
<s, z, s>(q_gen_2617) -> q_gen_2605
<s, s, s>(q_gen_2598) -> q_gen_2611
<z, s, s>(q_gen_2617) -> q_gen_2611
<z, z, s>(q_gen_2612) -> q_gen_2611
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 25  ;  () -> minus([z, y, z]) -> 28  ;  () -> plus([n, z, n]) -> 26  ;  (minus([_oc, n, _pc]) /\ plus([m, n, _oc])) -> eq_nat([_pc, m]) -> 28  ;  (minus([u, x2, _ec])) -> minus([s(u), s(x2), _ec]) -> 28  ;  (plus([n, mm, _jc])) -> plus([n, s(mm), s(_jc)]) -> 28
}
Sat witness: Yes: (() -> minus([z, y, z]), {
y -> s(s(s(z)))
})

-------------------------------------------
Step 36, which took 0.023837 s (model generation: 0.023197,  model checking: 0.000640):

Model:
|_
{
minus -> 
{{{
Q={q_gen_2599, q_gen_2601, q_gen_2607, q_gen_2614, q_gen_2624, q_gen_2625, q_gen_2647},
Q_f={q_gen_2599},
Delta=
{
<s>(q_gen_2607) -> q_gen_2607
<z>() -> q_gen_2607
<s, s>(q_gen_2601) -> q_gen_2601
<z, z>() -> q_gen_2601
<z, s>(q_gen_2607) -> q_gen_2624
<s, z>(q_gen_2607) -> q_gen_2647
<s, s, s>(q_gen_2614) -> q_gen_2599
<s, s, z>(q_gen_2601) -> q_gen_2599
<s, s, z>(q_gen_2624) -> q_gen_2599
<s, z, s>(q_gen_2601) -> q_gen_2599
<z, s, z>(q_gen_2607) -> q_gen_2599
<z, z, z>() -> q_gen_2599
<s, s, s>(q_gen_2625) -> q_gen_2614
<s, s, z>(q_gen_2647) -> q_gen_2614
<s, z, z>(q_gen_2607) -> q_gen_2614
<s, s, s>(q_gen_2599) -> q_gen_2625
<s, z, s>(q_gen_2624) -> q_gen_2625
}

Datatype: <nat, nat, nat>
Convolution form: complete
}}}
  ;  plus -> 
{{{
Q={q_gen_2598, q_gen_2603, q_gen_2610, q_gen_2611, q_gen_2612, q_gen_2617},
Q_f={q_gen_2598, q_gen_2610},
Delta=
{
<s>(q_gen_2612) -> q_gen_2612
<z>() -> q_gen_2612
<s, s>(q_gen_2617) -> q_gen_2603
<z, z>() -> q_gen_2603
<s, s>(q_gen_2603) -> q_gen_2617
<z, s>(q_gen_2612) -> q_gen_2617
<s, z, s>(q_gen_2603) -> q_gen_2598
<z, s, s>(q_gen_2603) -> q_gen_2598
<z, z, z>() -> q_gen_2598
<s, s, s>(q_gen_2610) -> q_gen_2610
<s, s, s>(q_gen_2611) -> q_gen_2610
<s, z, s>(q_gen_2617) -> q_gen_2610
<s, s, s>(q_gen_2598) -> q_gen_2611
<z, s, s>(q_gen_2617) -> q_gen_2611
<z, z, s>(q_gen_2612) -> q_gen_2611
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 26  ;  () -> minus([z, y, z]) -> 28  ;  () -> plus([n, z, n]) -> 27  ;  (minus([_oc, n, _pc]) /\ plus([m, n, _oc])) -> eq_nat([_pc, m]) -> 28  ;  (minus([u, x2, _ec])) -> minus([s(u), s(x2), _ec]) -> 28  ;  (plus([n, mm, _jc])) -> plus([n, s(mm), s(_jc)]) -> 31
}
Sat witness: Yes: ((plus([n, mm, _jc])) -> plus([n, s(mm), s(_jc)]), {
_jc -> s(s(s(z)))  ;  mm -> s(s(s(z)))  ;  n -> s(z)
})

-------------------------------------------
Step 37, which took 0.026335 s (model generation: 0.026223,  model checking: 0.000112):

Model:
|_
{
minus -> 
{{{
Q={q_gen_2599, q_gen_2601, q_gen_2607, q_gen_2609, q_gen_2613, q_gen_2614, q_gen_2624},
Q_f={q_gen_2599, q_gen_2613},
Delta=
{
<s>(q_gen_2607) -> q_gen_2607
<z>() -> q_gen_2607
<z, z>() -> q_gen_2601
<s, s>(q_gen_2601) -> q_gen_2609
<s, z>(q_gen_2607) -> q_gen_2609
<z, s>(q_gen_2607) -> q_gen_2624
<s, s, z>(q_gen_2601) -> q_gen_2599
<s, s, z>(q_gen_2624) -> q_gen_2599
<s, z, s>(q_gen_2601) -> q_gen_2599
<s, z, s>(q_gen_2609) -> q_gen_2599
<z, s, z>(q_gen_2607) -> q_gen_2599
<z, z, z>() -> q_gen_2599
<s, s, s>(q_gen_2613) -> q_gen_2613
<s, s, s>(q_gen_2614) -> q_gen_2613
<s, s, s>(q_gen_2599) -> q_gen_2614
<s, s, z>(q_gen_2609) -> q_gen_2614
<s, z, s>(q_gen_2624) -> q_gen_2614
<s, z, z>(q_gen_2607) -> q_gen_2614
}

Datatype: <nat, nat, nat>
Convolution form: complete
}}}
  ;  plus -> 
{{{
Q={q_gen_2598, q_gen_2603, q_gen_2605, q_gen_2611, q_gen_2612, q_gen_2622},
Q_f={q_gen_2598, q_gen_2605},
Delta=
{
<s>(q_gen_2612) -> q_gen_2612
<z>() -> q_gen_2612
<s, s>(q_gen_2603) -> q_gen_2603
<z, z>() -> q_gen_2603
<z, s>(q_gen_2612) -> q_gen_2622
<s, s, s>(q_gen_2605) -> q_gen_2598
<z, s, s>(q_gen_2603) -> q_gen_2598
<z, z, z>() -> q_gen_2598
<s, s, s>(q_gen_2611) -> q_gen_2605
<s, z, s>(q_gen_2603) -> q_gen_2605
<s, s, s>(q_gen_2598) -> q_gen_2611
<s, z, s>(q_gen_2622) -> q_gen_2611
<z, s, s>(q_gen_2622) -> q_gen_2611
<z, z, s>(q_gen_2612) -> q_gen_2611
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 29  ;  () -> minus([z, y, z]) -> 28  ;  () -> plus([n, z, n]) -> 27  ;  (minus([_oc, n, _pc]) /\ plus([m, n, _oc])) -> eq_nat([_pc, m]) -> 28  ;  (minus([u, x2, _ec])) -> minus([s(u), s(x2), _ec]) -> 28  ;  (plus([n, mm, _jc])) -> plus([n, s(mm), s(_jc)]) -> 31
}
Sat witness: Yes: (() -> minus([s(u), z, s(u)]), {
u -> s(s(z))
})

-------------------------------------------
Step 38, which took 0.026326 s (model generation: 0.025964,  model checking: 0.000362):

Model:
|_
{
minus -> 
{{{
Q={q_gen_2599, q_gen_2601, q_gen_2606, q_gen_2607, q_gen_2614, q_gen_2624, q_gen_2647},
Q_f={q_gen_2599, q_gen_2606},
Delta=
{
<s>(q_gen_2607) -> q_gen_2607
<z>() -> q_gen_2607
<s, s>(q_gen_2601) -> q_gen_2601
<z, z>() -> q_gen_2601
<z, s>(q_gen_2607) -> q_gen_2624
<s, z>(q_gen_2607) -> q_gen_2647
<s, s, z>(q_gen_2601) -> q_gen_2599
<s, z, s>(q_gen_2601) -> q_gen_2599
<z, z, z>() -> q_gen_2599
<s, s, s>(q_gen_2606) -> q_gen_2606
<s, s, s>(q_gen_2614) -> q_gen_2606
<s, s, z>(q_gen_2624) -> q_gen_2606
<z, s, z>(q_gen_2607) -> q_gen_2606
<s, s, s>(q_gen_2599) -> q_gen_2614
<s, s, z>(q_gen_2647) -> q_gen_2614
<s, z, s>(q_gen_2624) -> q_gen_2614
<s, z, z>(q_gen_2607) -> q_gen_2614
}

Datatype: <nat, nat, nat>
Convolution form: complete
}}}
  ;  plus -> 
{{{
Q={q_gen_2598, q_gen_2603, q_gen_2605, q_gen_2611, q_gen_2612, q_gen_2622},
Q_f={q_gen_2598, q_gen_2605},
Delta=
{
<s>(q_gen_2612) -> q_gen_2612
<z>() -> q_gen_2612
<s, s>(q_gen_2603) -> q_gen_2603
<z, z>() -> q_gen_2603
<z, s>(q_gen_2612) -> q_gen_2622
<s, s, s>(q_gen_2605) -> q_gen_2598
<z, s, s>(q_gen_2603) -> q_gen_2598
<z, z, z>() -> q_gen_2598
<s, s, s>(q_gen_2611) -> q_gen_2605
<s, z, s>(q_gen_2603) -> q_gen_2605
<s, s, s>(q_gen_2598) -> q_gen_2611
<s, z, s>(q_gen_2622) -> q_gen_2611
<z, s, s>(q_gen_2622) -> q_gen_2611
<z, z, s>(q_gen_2612) -> q_gen_2611
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 29  ;  () -> minus([z, y, z]) -> 28  ;  () -> plus([n, z, n]) -> 28  ;  (minus([_oc, n, _pc]) /\ plus([m, n, _oc])) -> eq_nat([_pc, m]) -> 28  ;  (minus([u, x2, _ec])) -> minus([s(u), s(x2), _ec]) -> 31  ;  (plus([n, mm, _jc])) -> plus([n, s(mm), s(_jc)]) -> 31
}
Sat witness: Yes: ((minus([u, x2, _ec])) -> minus([s(u), s(x2), _ec]), {
_ec -> z  ;  u -> s(z)  ;  x2 -> s(s(z))
})

-------------------------------------------
Step 39, which took 0.026505 s (model generation: 0.026311,  model checking: 0.000194):

Model:
|_
{
minus -> 
{{{
Q={q_gen_2599, q_gen_2601, q_gen_2607, q_gen_2613, q_gen_2614, q_gen_2624, q_gen_2647},
Q_f={q_gen_2599, q_gen_2613},
Delta=
{
<s>(q_gen_2607) -> q_gen_2607
<z>() -> q_gen_2607
<s, s>(q_gen_2601) -> q_gen_2601
<z, z>() -> q_gen_2601
<s, s>(q_gen_2624) -> q_gen_2624
<z, s>(q_gen_2607) -> q_gen_2624
<s, z>(q_gen_2607) -> q_gen_2647
<s, s, z>(q_gen_2601) -> q_gen_2599
<s, s, z>(q_gen_2624) -> q_gen_2599
<s, z, s>(q_gen_2601) -> q_gen_2599
<z, s, z>(q_gen_2607) -> q_gen_2599
<z, z, z>() -> q_gen_2599
<s, s, s>(q_gen_2613) -> q_gen_2613
<s, s, s>(q_gen_2614) -> q_gen_2613
<s, s, s>(q_gen_2599) -> q_gen_2614
<s, s, z>(q_gen_2647) -> q_gen_2614
<s, z, s>(q_gen_2624) -> q_gen_2614
<s, z, z>(q_gen_2607) -> q_gen_2614
}

Datatype: <nat, nat, nat>
Convolution form: complete
}}}
  ;  plus -> 
{{{
Q={q_gen_2598, q_gen_2603, q_gen_2605, q_gen_2611, q_gen_2612, q_gen_2622},
Q_f={q_gen_2598, q_gen_2605},
Delta=
{
<s>(q_gen_2612) -> q_gen_2612
<z>() -> q_gen_2612
<s, s>(q_gen_2603) -> q_gen_2603
<z, z>() -> q_gen_2603
<z, s>(q_gen_2612) -> q_gen_2622
<s, s, s>(q_gen_2605) -> q_gen_2598
<z, s, s>(q_gen_2603) -> q_gen_2598
<z, z, z>() -> q_gen_2598
<s, s, s>(q_gen_2611) -> q_gen_2605
<s, z, s>(q_gen_2603) -> q_gen_2605
<s, s, s>(q_gen_2598) -> q_gen_2611
<s, z, s>(q_gen_2622) -> q_gen_2611
<z, s, s>(q_gen_2622) -> q_gen_2611
<z, z, s>(q_gen_2612) -> q_gen_2611
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 29  ;  () -> minus([z, y, z]) -> 28  ;  () -> plus([n, z, n]) -> 28  ;  (minus([_oc, n, _pc]) /\ plus([m, n, _oc])) -> eq_nat([_pc, m]) -> 31  ;  (minus([u, x2, _ec])) -> minus([s(u), s(x2), _ec]) -> 31  ;  (plus([n, mm, _jc])) -> plus([n, s(mm), s(_jc)]) -> 31
}
Sat witness: Yes: ((minus([_oc, n, _pc]) /\ plus([m, n, _oc])) -> eq_nat([_pc, m]), {
_oc -> s(s(s(z)))  ;  _pc -> s(z)  ;  m -> s(s(z))  ;  n -> s(z)
})

-------------------------------------------
Step 40, which took 0.026164 s (model generation: 0.025363,  model checking: 0.000801):

Model:
|_
{
minus -> 
{{{
Q={q_gen_2599, q_gen_2601, q_gen_2607, q_gen_2614, q_gen_2619, q_gen_2624, q_gen_2647},
Q_f={q_gen_2599},
Delta=
{
<s>(q_gen_2619) -> q_gen_2607
<z>() -> q_gen_2607
<s>(q_gen_2607) -> q_gen_2619
<s, s>(q_gen_2601) -> q_gen_2601
<z, s>(q_gen_2619) -> q_gen_2601
<z, z>() -> q_gen_2601
<s, s>(q_gen_2624) -> q_gen_2624
<z, s>(q_gen_2607) -> q_gen_2624
<s, z>(q_gen_2607) -> q_gen_2647
<s, s, s>(q_gen_2614) -> q_gen_2599
<s, s, z>(q_gen_2601) -> q_gen_2599
<s, s, z>(q_gen_2624) -> q_gen_2599
<s, z, s>(q_gen_2601) -> q_gen_2599
<s, z, z>(q_gen_2619) -> q_gen_2599
<z, s, z>(q_gen_2607) -> q_gen_2599
<z, s, z>(q_gen_2619) -> q_gen_2599
<z, z, z>() -> q_gen_2599
<s, s, s>(q_gen_2599) -> q_gen_2614
<s, s, z>(q_gen_2647) -> q_gen_2614
<s, z, s>(q_gen_2624) -> q_gen_2614
<s, z, z>(q_gen_2607) -> q_gen_2614
}

Datatype: <nat, nat, nat>
Convolution form: complete
}}}
  ;  plus -> 
{{{
Q={q_gen_2598, q_gen_2603, q_gen_2605, q_gen_2611, q_gen_2612, q_gen_2622},
Q_f={q_gen_2598, q_gen_2605},
Delta=
{
<s>(q_gen_2612) -> q_gen_2612
<z>() -> q_gen_2612
<s, s>(q_gen_2603) -> q_gen_2603
<z, z>() -> q_gen_2603
<z, s>(q_gen_2612) -> q_gen_2622
<s, s, s>(q_gen_2605) -> q_gen_2598
<z, s, s>(q_gen_2603) -> q_gen_2598
<z, z, z>() -> q_gen_2598
<s, s, s>(q_gen_2611) -> q_gen_2605
<s, z, s>(q_gen_2603) -> q_gen_2605
<s, s, s>(q_gen_2598) -> q_gen_2611
<s, z, s>(q_gen_2622) -> q_gen_2611
<z, s, s>(q_gen_2622) -> q_gen_2611
<z, z, s>(q_gen_2612) -> q_gen_2611
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 30  ;  () -> minus([z, y, z]) -> 29  ;  () -> plus([n, z, n]) -> 29  ;  (minus([_oc, n, _pc]) /\ plus([m, n, _oc])) -> eq_nat([_pc, m]) -> 31  ;  (minus([u, x2, _ec])) -> minus([s(u), s(x2), _ec]) -> 31  ;  (plus([n, mm, _jc])) -> plus([n, s(mm), s(_jc)]) -> 34
}
Sat witness: Yes: ((plus([n, mm, _jc])) -> plus([n, s(mm), s(_jc)]), {
_jc -> s(s(s(z)))  ;  mm -> z  ;  n -> s(s(s(z)))
})

-------------------------------------------
Step 41, which took 0.037394 s (model generation: 0.036842,  model checking: 0.000552):

Model:
|_
{
minus -> 
{{{
Q={q_gen_2599, q_gen_2601, q_gen_2607, q_gen_2614, q_gen_2619, q_gen_2624, q_gen_2642},
Q_f={q_gen_2599},
Delta=
{
<s>(q_gen_2619) -> q_gen_2607
<z>() -> q_gen_2607
<s>(q_gen_2607) -> q_gen_2619
<s, s>(q_gen_2601) -> q_gen_2601
<z, z>() -> q_gen_2601
<s, s>(q_gen_2624) -> q_gen_2624
<z, s>(q_gen_2607) -> q_gen_2624
<s, z>(q_gen_2607) -> q_gen_2642
<z, s>(q_gen_2619) -> q_gen_2642
<s, s, s>(q_gen_2614) -> q_gen_2599
<s, s, z>(q_gen_2601) -> q_gen_2599
<s, s, z>(q_gen_2624) -> q_gen_2599
<s, z, s>(q_gen_2601) -> q_gen_2599
<s, z, s>(q_gen_2642) -> q_gen_2599
<s, z, z>(q_gen_2619) -> q_gen_2599
<z, s, z>(q_gen_2607) -> q_gen_2599
<z, s, z>(q_gen_2619) -> q_gen_2599
<z, z, z>() -> q_gen_2599
<s, s, s>(q_gen_2599) -> q_gen_2614
<s, s, z>(q_gen_2642) -> q_gen_2614
<s, z, s>(q_gen_2624) -> q_gen_2614
<s, z, z>(q_gen_2607) -> q_gen_2614
}

Datatype: <nat, nat, nat>
Convolution form: complete
}}}
  ;  plus -> 
{{{
Q={q_gen_2598, q_gen_2602, q_gen_2603, q_gen_2611, q_gen_2612, q_gen_2622},
Q_f={q_gen_2598, q_gen_2602},
Delta=
{
<s>(q_gen_2612) -> q_gen_2612
<z>() -> q_gen_2612
<s, s>(q_gen_2603) -> q_gen_2603
<z, z>() -> q_gen_2603
<s, s>(q_gen_2622) -> q_gen_2622
<z, s>(q_gen_2612) -> q_gen_2622
<z, z, z>() -> q_gen_2598
<s, s, s>(q_gen_2602) -> q_gen_2602
<s, s, s>(q_gen_2611) -> q_gen_2602
<s, z, s>(q_gen_2603) -> q_gen_2602
<z, s, s>(q_gen_2603) -> q_gen_2602
<s, s, s>(q_gen_2598) -> q_gen_2611
<s, z, s>(q_gen_2622) -> q_gen_2611
<z, s, s>(q_gen_2622) -> q_gen_2611
<z, z, s>(q_gen_2612) -> q_gen_2611
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 31  ;  () -> minus([z, y, z]) -> 30  ;  () -> plus([n, z, n]) -> 30  ;  (minus([_oc, n, _pc]) /\ plus([m, n, _oc])) -> eq_nat([_pc, m]) -> 31  ;  (minus([u, x2, _ec])) -> minus([s(u), s(x2), _ec]) -> 34  ;  (plus([n, mm, _jc])) -> plus([n, s(mm), s(_jc)]) -> 34
}
Sat witness: Yes: ((minus([u, x2, _ec])) -> minus([s(u), s(x2), _ec]), {
_ec -> z  ;  u -> z  ;  x2 -> s(s(z))
})

-------------------------------------------
Step 42, which took 0.037010 s (model generation: 0.036593,  model checking: 0.000417):

Model:
|_
{
minus -> 
{{{
Q={q_gen_2599, q_gen_2601, q_gen_2607, q_gen_2609, q_gen_2614, q_gen_2619, q_gen_2624},
Q_f={q_gen_2599},
Delta=
{
<s>(q_gen_2619) -> q_gen_2607
<z>() -> q_gen_2607
<s>(q_gen_2607) -> q_gen_2619
<z, s>(q_gen_2619) -> q_gen_2601
<z, z>() -> q_gen_2601
<s, s>(q_gen_2601) -> q_gen_2609
<s, s>(q_gen_2609) -> q_gen_2609
<s, z>(q_gen_2607) -> q_gen_2609
<s, s>(q_gen_2624) -> q_gen_2624
<z, s>(q_gen_2607) -> q_gen_2624
<s, s, s>(q_gen_2614) -> q_gen_2599
<s, s, z>(q_gen_2601) -> q_gen_2599
<s, s, z>(q_gen_2624) -> q_gen_2599
<s, z, s>(q_gen_2601) -> q_gen_2599
<s, z, s>(q_gen_2609) -> q_gen_2599
<s, z, z>(q_gen_2619) -> q_gen_2599
<z, s, z>(q_gen_2607) -> q_gen_2599
<z, s, z>(q_gen_2619) -> q_gen_2599
<z, z, z>() -> q_gen_2599
<s, s, s>(q_gen_2599) -> q_gen_2614
<s, s, z>(q_gen_2609) -> q_gen_2614
<s, z, s>(q_gen_2624) -> q_gen_2614
<s, z, z>(q_gen_2607) -> q_gen_2614
}

Datatype: <nat, nat, nat>
Convolution form: complete
}}}
  ;  plus -> 
{{{
Q={q_gen_2598, q_gen_2602, q_gen_2603, q_gen_2611, q_gen_2612, q_gen_2617},
Q_f={q_gen_2598, q_gen_2602},
Delta=
{
<s>(q_gen_2612) -> q_gen_2612
<z>() -> q_gen_2612
<s, s>(q_gen_2617) -> q_gen_2603
<z, z>() -> q_gen_2603
<s, s>(q_gen_2603) -> q_gen_2617
<z, s>(q_gen_2612) -> q_gen_2617
<z, z, z>() -> q_gen_2598
<s, s, s>(q_gen_2602) -> q_gen_2602
<s, s, s>(q_gen_2611) -> q_gen_2602
<s, z, s>(q_gen_2603) -> q_gen_2602
<s, z, s>(q_gen_2617) -> q_gen_2602
<z, s, s>(q_gen_2603) -> q_gen_2602
<s, s, s>(q_gen_2598) -> q_gen_2611
<z, s, s>(q_gen_2617) -> q_gen_2611
<z, z, s>(q_gen_2612) -> q_gen_2611
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 31  ;  () -> minus([z, y, z]) -> 31  ;  () -> plus([n, z, n]) -> 31  ;  (minus([_oc, n, _pc]) /\ plus([m, n, _oc])) -> eq_nat([_pc, m]) -> 34  ;  (minus([u, x2, _ec])) -> minus([s(u), s(x2), _ec]) -> 34  ;  (plus([n, mm, _jc])) -> plus([n, s(mm), s(_jc)]) -> 34
}
Sat witness: Yes: ((minus([_oc, n, _pc]) /\ plus([m, n, _oc])) -> eq_nat([_pc, m]), {
_oc -> s(s(s(z)))  ;  _pc -> s(z)  ;  m -> z  ;  n -> s(s(z))
})

-------------------------------------------
Step 43, which took 0.039362 s (model generation: 0.038309,  model checking: 0.001053):

Model:
|_
{
minus -> 
{{{
Q={q_gen_2599, q_gen_2601, q_gen_2607, q_gen_2609, q_gen_2614, q_gen_2619, q_gen_2624},
Q_f={q_gen_2599},
Delta=
{
<s>(q_gen_2619) -> q_gen_2607
<z>() -> q_gen_2607
<s>(q_gen_2607) -> q_gen_2619
<z, s>(q_gen_2619) -> q_gen_2601
<z, z>() -> q_gen_2601
<s, s>(q_gen_2601) -> q_gen_2609
<s, s>(q_gen_2609) -> q_gen_2609
<s, z>(q_gen_2607) -> q_gen_2609
<s, s>(q_gen_2624) -> q_gen_2624
<z, s>(q_gen_2607) -> q_gen_2624
<s, s, s>(q_gen_2614) -> q_gen_2599
<s, s, z>(q_gen_2601) -> q_gen_2599
<s, s, z>(q_gen_2624) -> q_gen_2599
<s, z, s>(q_gen_2601) -> q_gen_2599
<s, z, s>(q_gen_2609) -> q_gen_2599
<s, z, z>(q_gen_2619) -> q_gen_2599
<z, s, z>(q_gen_2607) -> q_gen_2599
<z, s, z>(q_gen_2619) -> q_gen_2599
<z, z, z>() -> q_gen_2599
<s, s, s>(q_gen_2599) -> q_gen_2614
<s, s, z>(q_gen_2609) -> q_gen_2614
<s, z, s>(q_gen_2624) -> q_gen_2614
<s, z, z>(q_gen_2607) -> q_gen_2614
}

Datatype: <nat, nat, nat>
Convolution form: complete
}}}
  ;  plus -> 
{{{
Q={q_gen_2598, q_gen_2602, q_gen_2603, q_gen_2611, q_gen_2612, q_gen_2622},
Q_f={q_gen_2598, q_gen_2602},
Delta=
{
<s>(q_gen_2612) -> q_gen_2612
<z>() -> q_gen_2612
<s, s>(q_gen_2603) -> q_gen_2603
<z, z>() -> q_gen_2603
<s, s>(q_gen_2622) -> q_gen_2622
<z, s>(q_gen_2612) -> q_gen_2622
<z, z, z>() -> q_gen_2598
<s, s, s>(q_gen_2602) -> q_gen_2602
<s, s, s>(q_gen_2611) -> q_gen_2602
<s, z, s>(q_gen_2603) -> q_gen_2602
<z, s, s>(q_gen_2603) -> q_gen_2602
<s, s, s>(q_gen_2598) -> q_gen_2611
<s, z, s>(q_gen_2622) -> q_gen_2611
<z, s, s>(q_gen_2622) -> q_gen_2611
<z, z, s>(q_gen_2612) -> q_gen_2611
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 32  ;  () -> minus([z, y, z]) -> 32  ;  () -> plus([n, z, n]) -> 32  ;  (minus([_oc, n, _pc]) /\ plus([m, n, _oc])) -> eq_nat([_pc, m]) -> 34  ;  (minus([u, x2, _ec])) -> minus([s(u), s(x2), _ec]) -> 37  ;  (plus([n, mm, _jc])) -> plus([n, s(mm), s(_jc)]) -> 35
}
Sat witness: Yes: ((minus([u, x2, _ec])) -> minus([s(u), s(x2), _ec]), {
_ec -> z  ;  u -> s(z)  ;  x2 -> s(z)
})

-------------------------------------------
Step 44, which took 0.038616 s (model generation: 0.038206,  model checking: 0.000410):

Model:
|_
{
minus -> 
{{{
Q={q_gen_2599, q_gen_2601, q_gen_2607, q_gen_2614, q_gen_2619, q_gen_2624, q_gen_2647},
Q_f={q_gen_2599},
Delta=
{
<s>(q_gen_2619) -> q_gen_2607
<z>() -> q_gen_2607
<s>(q_gen_2607) -> q_gen_2619
<s, s>(q_gen_2601) -> q_gen_2601
<z, s>(q_gen_2619) -> q_gen_2601
<z, z>() -> q_gen_2601
<s, s>(q_gen_2624) -> q_gen_2624
<z, s>(q_gen_2607) -> q_gen_2624
<s, z>(q_gen_2607) -> q_gen_2647
<s, s, s>(q_gen_2614) -> q_gen_2599
<s, s, z>(q_gen_2601) -> q_gen_2599
<s, s, z>(q_gen_2624) -> q_gen_2599
<s, z, s>(q_gen_2601) -> q_gen_2599
<s, z, z>(q_gen_2619) -> q_gen_2599
<z, s, z>(q_gen_2607) -> q_gen_2599
<z, s, z>(q_gen_2619) -> q_gen_2599
<z, z, z>() -> q_gen_2599
<s, s, s>(q_gen_2599) -> q_gen_2614
<s, s, z>(q_gen_2647) -> q_gen_2614
<s, z, s>(q_gen_2624) -> q_gen_2614
<s, z, z>(q_gen_2607) -> q_gen_2614
}

Datatype: <nat, nat, nat>
Convolution form: complete
}}}
  ;  plus -> 
{{{
Q={q_gen_2598, q_gen_2602, q_gen_2603, q_gen_2611, q_gen_2612, q_gen_2617},
Q_f={q_gen_2598, q_gen_2602},
Delta=
{
<s>(q_gen_2612) -> q_gen_2612
<z>() -> q_gen_2612
<z, z>() -> q_gen_2603
<s, s>(q_gen_2603) -> q_gen_2617
<s, s>(q_gen_2617) -> q_gen_2617
<z, s>(q_gen_2612) -> q_gen_2617
<z, z, z>() -> q_gen_2598
<s, s, s>(q_gen_2602) -> q_gen_2602
<s, s, s>(q_gen_2611) -> q_gen_2602
<s, z, s>(q_gen_2603) -> q_gen_2602
<s, z, s>(q_gen_2617) -> q_gen_2602
<z, s, s>(q_gen_2603) -> q_gen_2602
<s, s, s>(q_gen_2598) -> q_gen_2611
<z, s, s>(q_gen_2617) -> q_gen_2611
<z, z, s>(q_gen_2612) -> q_gen_2611
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 33  ;  () -> minus([z, y, z]) -> 33  ;  () -> plus([n, z, n]) -> 33  ;  (minus([_oc, n, _pc]) /\ plus([m, n, _oc])) -> eq_nat([_pc, m]) -> 37  ;  (minus([u, x2, _ec])) -> minus([s(u), s(x2), _ec]) -> 37  ;  (plus([n, mm, _jc])) -> plus([n, s(mm), s(_jc)]) -> 35
}
Sat witness: Yes: ((minus([_oc, n, _pc]) /\ plus([m, n, _oc])) -> eq_nat([_pc, m]), {
_oc -> s(s(z))  ;  _pc -> z  ;  m -> s(z)  ;  n -> s(s(z))
})

-------------------------------------------
Step 45, which took 0.039311 s (model generation: 0.038299,  model checking: 0.001012):

Model:
|_
{
minus -> 
{{{
Q={q_gen_2599, q_gen_2601, q_gen_2607, q_gen_2614, q_gen_2619, q_gen_2624, q_gen_2647},
Q_f={q_gen_2599},
Delta=
{
<s>(q_gen_2619) -> q_gen_2607
<z>() -> q_gen_2607
<s>(q_gen_2607) -> q_gen_2619
<s, s>(q_gen_2601) -> q_gen_2601
<z, s>(q_gen_2619) -> q_gen_2601
<z, z>() -> q_gen_2601
<s, s>(q_gen_2624) -> q_gen_2624
<z, s>(q_gen_2607) -> q_gen_2624
<s, z>(q_gen_2607) -> q_gen_2647
<s, s, s>(q_gen_2614) -> q_gen_2599
<s, s, z>(q_gen_2601) -> q_gen_2599
<s, s, z>(q_gen_2624) -> q_gen_2599
<s, z, s>(q_gen_2601) -> q_gen_2599
<s, z, z>(q_gen_2619) -> q_gen_2599
<z, s, z>(q_gen_2607) -> q_gen_2599
<z, s, z>(q_gen_2619) -> q_gen_2599
<z, z, z>() -> q_gen_2599
<s, s, s>(q_gen_2599) -> q_gen_2614
<s, s, z>(q_gen_2647) -> q_gen_2614
<s, z, s>(q_gen_2624) -> q_gen_2614
<s, z, z>(q_gen_2607) -> q_gen_2614
}

Datatype: <nat, nat, nat>
Convolution form: complete
}}}
  ;  plus -> 
{{{
Q={q_gen_2598, q_gen_2603, q_gen_2611, q_gen_2612, q_gen_2622, q_gen_2629},
Q_f={q_gen_2598},
Delta=
{
<z>() -> q_gen_2612
<s>(q_gen_2612) -> q_gen_2629
<s, s>(q_gen_2603) -> q_gen_2603
<z, s>(q_gen_2629) -> q_gen_2603
<z, z>() -> q_gen_2603
<s, s>(q_gen_2622) -> q_gen_2622
<z, s>(q_gen_2612) -> q_gen_2622
<s, s, s>(q_gen_2611) -> q_gen_2598
<s, z, s>(q_gen_2603) -> q_gen_2598
<z, s, s>(q_gen_2603) -> q_gen_2598
<z, z, s>(q_gen_2629) -> q_gen_2598
<z, z, z>() -> q_gen_2598
<s, s, s>(q_gen_2598) -> q_gen_2611
<s, z, s>(q_gen_2622) -> q_gen_2611
<z, s, s>(q_gen_2622) -> q_gen_2611
<z, z, s>(q_gen_2612) -> q_gen_2611
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 34  ;  () -> minus([z, y, z]) -> 34  ;  () -> plus([n, z, n]) -> 34  ;  (minus([_oc, n, _pc]) /\ plus([m, n, _oc])) -> eq_nat([_pc, m]) -> 37  ;  (minus([u, x2, _ec])) -> minus([s(u), s(x2), _ec]) -> 37  ;  (plus([n, mm, _jc])) -> plus([n, s(mm), s(_jc)]) -> 38
}
Sat witness: Yes: ((plus([n, mm, _jc])) -> plus([n, s(mm), s(_jc)]), {
_jc -> s(s(s(z)))  ;  mm -> z  ;  n -> s(z)
})

-------------------------------------------
Step 46, which took 0.048391 s (model generation: 0.047590,  model checking: 0.000801):

Model:
|_
{
minus -> 
{{{
Q={q_gen_2599, q_gen_2601, q_gen_2607, q_gen_2614, q_gen_2619, q_gen_2624, q_gen_2647},
Q_f={q_gen_2599},
Delta=
{
<s>(q_gen_2619) -> q_gen_2607
<z>() -> q_gen_2607
<s>(q_gen_2607) -> q_gen_2619
<s, s>(q_gen_2601) -> q_gen_2601
<z, s>(q_gen_2619) -> q_gen_2601
<z, z>() -> q_gen_2601
<s, s>(q_gen_2624) -> q_gen_2624
<z, s>(q_gen_2607) -> q_gen_2624
<s, z>(q_gen_2607) -> q_gen_2647
<s, s, s>(q_gen_2614) -> q_gen_2599
<s, s, z>(q_gen_2601) -> q_gen_2599
<s, s, z>(q_gen_2624) -> q_gen_2599
<s, z, s>(q_gen_2601) -> q_gen_2599
<s, z, z>(q_gen_2619) -> q_gen_2599
<z, s, z>(q_gen_2607) -> q_gen_2599
<z, s, z>(q_gen_2619) -> q_gen_2599
<z, z, z>() -> q_gen_2599
<s, s, s>(q_gen_2599) -> q_gen_2614
<s, s, z>(q_gen_2647) -> q_gen_2614
<s, z, s>(q_gen_2624) -> q_gen_2614
<s, z, z>(q_gen_2607) -> q_gen_2614
}

Datatype: <nat, nat, nat>
Convolution form: complete
}}}
  ;  plus -> 
{{{
Q={q_gen_2598, q_gen_2603, q_gen_2611, q_gen_2612, q_gen_2622, q_gen_2629},
Q_f={q_gen_2598},
Delta=
{
<s>(q_gen_2629) -> q_gen_2612
<z>() -> q_gen_2612
<s>(q_gen_2612) -> q_gen_2629
<s, s>(q_gen_2603) -> q_gen_2603
<z, s>(q_gen_2629) -> q_gen_2603
<z, z>() -> q_gen_2603
<s, s>(q_gen_2622) -> q_gen_2622
<z, s>(q_gen_2612) -> q_gen_2622
<s, s, s>(q_gen_2611) -> q_gen_2598
<s, z, s>(q_gen_2603) -> q_gen_2598
<z, s, s>(q_gen_2603) -> q_gen_2598
<z, z, s>(q_gen_2629) -> q_gen_2598
<z, z, z>() -> q_gen_2598
<s, s, s>(q_gen_2598) -> q_gen_2611
<s, z, s>(q_gen_2622) -> q_gen_2611
<z, s, s>(q_gen_2622) -> q_gen_2611
<z, z, s>(q_gen_2612) -> q_gen_2611
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 35  ;  () -> minus([z, y, z]) -> 35  ;  () -> plus([n, z, n]) -> 35  ;  (minus([_oc, n, _pc]) /\ plus([m, n, _oc])) -> eq_nat([_pc, m]) -> 37  ;  (minus([u, x2, _ec])) -> minus([s(u), s(x2), _ec]) -> 40  ;  (plus([n, mm, _jc])) -> plus([n, s(mm), s(_jc)]) -> 38
}
Sat witness: Yes: ((minus([u, x2, _ec])) -> minus([s(u), s(x2), _ec]), {
_ec -> z  ;  u -> s(s(z))  ;  x2 -> z
})

-------------------------------------------
Step 47, which took 0.058975 s (model generation: 0.058204,  model checking: 0.000771):

Model:
|_
{
minus -> 
{{{
Q={q_gen_2599, q_gen_2601, q_gen_2607, q_gen_2614, q_gen_2619, q_gen_2624, q_gen_2647},
Q_f={q_gen_2599},
Delta=
{
<s>(q_gen_2619) -> q_gen_2607
<z>() -> q_gen_2607
<s>(q_gen_2607) -> q_gen_2619
<s, s>(q_gen_2601) -> q_gen_2601
<z, s>(q_gen_2619) -> q_gen_2601
<z, z>() -> q_gen_2601
<s, s>(q_gen_2624) -> q_gen_2624
<s, z>(q_gen_2619) -> q_gen_2624
<z, s>(q_gen_2607) -> q_gen_2624
<s, z>(q_gen_2607) -> q_gen_2647
<s, s, s>(q_gen_2614) -> q_gen_2599
<s, s, z>(q_gen_2601) -> q_gen_2599
<s, s, z>(q_gen_2624) -> q_gen_2599
<s, z, s>(q_gen_2601) -> q_gen_2599
<s, z, z>(q_gen_2619) -> q_gen_2599
<z, s, z>(q_gen_2607) -> q_gen_2599
<z, s, z>(q_gen_2619) -> q_gen_2599
<z, z, z>() -> q_gen_2599
<s, s, s>(q_gen_2599) -> q_gen_2614
<s, s, z>(q_gen_2647) -> q_gen_2614
<s, z, s>(q_gen_2624) -> q_gen_2614
<s, z, z>(q_gen_2607) -> q_gen_2614
}

Datatype: <nat, nat, nat>
Convolution form: complete
}}}
  ;  plus -> 
{{{
Q={q_gen_2598, q_gen_2603, q_gen_2610, q_gen_2611, q_gen_2612, q_gen_2617},
Q_f={q_gen_2598, q_gen_2610},
Delta=
{
<s>(q_gen_2612) -> q_gen_2612
<z>() -> q_gen_2612
<z, z>() -> q_gen_2603
<s, s>(q_gen_2603) -> q_gen_2617
<s, s>(q_gen_2617) -> q_gen_2617
<z, s>(q_gen_2612) -> q_gen_2617
<s, z, s>(q_gen_2603) -> q_gen_2598
<z, s, s>(q_gen_2603) -> q_gen_2598
<z, z, z>() -> q_gen_2598
<s, s, s>(q_gen_2610) -> q_gen_2610
<s, s, s>(q_gen_2611) -> q_gen_2610
<s, z, s>(q_gen_2617) -> q_gen_2610
<s, s, s>(q_gen_2598) -> q_gen_2611
<z, s, s>(q_gen_2617) -> q_gen_2611
<z, z, s>(q_gen_2612) -> q_gen_2611
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 36  ;  () -> minus([z, y, z]) -> 36  ;  () -> plus([n, z, n]) -> 36  ;  (minus([_oc, n, _pc]) /\ plus([m, n, _oc])) -> eq_nat([_pc, m]) -> 40  ;  (minus([u, x2, _ec])) -> minus([s(u), s(x2), _ec]) -> 40  ;  (plus([n, mm, _jc])) -> plus([n, s(mm), s(_jc)]) -> 38
}
Sat witness: Yes: ((minus([_oc, n, _pc]) /\ plus([m, n, _oc])) -> eq_nat([_pc, m]), {
_oc -> s(s(z))  ;  _pc -> z  ;  m -> s(z)  ;  n -> z
})

-------------------------------------------
Step 48, which took 0.059275 s (model generation: 0.057989,  model checking: 0.001286):

Model:
|_
{
minus -> 
{{{
Q={q_gen_2599, q_gen_2601, q_gen_2607, q_gen_2614, q_gen_2619, q_gen_2624, q_gen_2647},
Q_f={q_gen_2599},
Delta=
{
<s>(q_gen_2619) -> q_gen_2607
<z>() -> q_gen_2607
<s>(q_gen_2607) -> q_gen_2619
<s, s>(q_gen_2601) -> q_gen_2601
<z, s>(q_gen_2619) -> q_gen_2601
<z, z>() -> q_gen_2601
<s, s>(q_gen_2624) -> q_gen_2624
<s, z>(q_gen_2619) -> q_gen_2624
<z, s>(q_gen_2607) -> q_gen_2624
<s, z>(q_gen_2607) -> q_gen_2647
<s, s, s>(q_gen_2614) -> q_gen_2599
<s, s, z>(q_gen_2601) -> q_gen_2599
<s, s, z>(q_gen_2624) -> q_gen_2599
<s, z, s>(q_gen_2601) -> q_gen_2599
<s, z, z>(q_gen_2619) -> q_gen_2599
<z, s, z>(q_gen_2607) -> q_gen_2599
<z, s, z>(q_gen_2619) -> q_gen_2599
<z, z, z>() -> q_gen_2599
<s, s, s>(q_gen_2599) -> q_gen_2614
<s, s, z>(q_gen_2647) -> q_gen_2614
<s, z, s>(q_gen_2624) -> q_gen_2614
<s, z, z>(q_gen_2607) -> q_gen_2614
}

Datatype: <nat, nat, nat>
Convolution form: complete
}}}
  ;  plus -> 
{{{
Q={q_gen_2598, q_gen_2603, q_gen_2611, q_gen_2612, q_gen_2622, q_gen_2629},
Q_f={q_gen_2598},
Delta=
{
<s>(q_gen_2629) -> q_gen_2612
<z>() -> q_gen_2612
<s>(q_gen_2612) -> q_gen_2629
<s, s>(q_gen_2603) -> q_gen_2603
<z, s>(q_gen_2629) -> q_gen_2603
<z, z>() -> q_gen_2603
<s, s>(q_gen_2622) -> q_gen_2622
<z, s>(q_gen_2612) -> q_gen_2622
<s, s, s>(q_gen_2611) -> q_gen_2598
<s, z, s>(q_gen_2603) -> q_gen_2598
<z, s, s>(q_gen_2603) -> q_gen_2598
<z, z, s>(q_gen_2629) -> q_gen_2598
<z, z, z>() -> q_gen_2598
<s, s, s>(q_gen_2598) -> q_gen_2611
<s, z, s>(q_gen_2622) -> q_gen_2611
<z, s, s>(q_gen_2622) -> q_gen_2611
<z, z, s>(q_gen_2612) -> q_gen_2611
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 37  ;  () -> minus([z, y, z]) -> 37  ;  () -> plus([n, z, n]) -> 37  ;  (minus([_oc, n, _pc]) /\ plus([m, n, _oc])) -> eq_nat([_pc, m]) -> 40  ;  (minus([u, x2, _ec])) -> minus([s(u), s(x2), _ec]) -> 43  ;  (plus([n, mm, _jc])) -> plus([n, s(mm), s(_jc)]) -> 39
}
Sat witness: Yes: ((minus([u, x2, _ec])) -> minus([s(u), s(x2), _ec]), {
_ec -> s(s(z))  ;  u -> s(s(s(s(z))))  ;  x2 -> s(z)
})

-------------------------------------------
Step 49, which took 0.074189 s (model generation: 0.072944,  model checking: 0.001245):

Model:
|_
{
minus -> 
{{{
Q={q_gen_2599, q_gen_2601, q_gen_2607, q_gen_2614, q_gen_2619, q_gen_2624, q_gen_2647},
Q_f={q_gen_2599},
Delta=
{
<s>(q_gen_2619) -> q_gen_2607
<z>() -> q_gen_2607
<s>(q_gen_2607) -> q_gen_2619
<s, s>(q_gen_2601) -> q_gen_2601
<s, z>(q_gen_2619) -> q_gen_2601
<z, s>(q_gen_2619) -> q_gen_2601
<z, z>() -> q_gen_2601
<s, s>(q_gen_2624) -> q_gen_2624
<z, s>(q_gen_2607) -> q_gen_2624
<s, z>(q_gen_2607) -> q_gen_2647
<s, s, s>(q_gen_2614) -> q_gen_2599
<s, s, z>(q_gen_2601) -> q_gen_2599
<s, s, z>(q_gen_2624) -> q_gen_2599
<s, z, s>(q_gen_2601) -> q_gen_2599
<s, z, z>(q_gen_2619) -> q_gen_2599
<z, s, z>(q_gen_2607) -> q_gen_2599
<z, s, z>(q_gen_2619) -> q_gen_2599
<z, z, z>() -> q_gen_2599
<s, s, s>(q_gen_2599) -> q_gen_2614
<s, s, z>(q_gen_2647) -> q_gen_2614
<s, z, s>(q_gen_2624) -> q_gen_2614
<s, z, z>(q_gen_2607) -> q_gen_2614
}

Datatype: <nat, nat, nat>
Convolution form: complete
}}}
  ;  plus -> 
{{{
Q={q_gen_2598, q_gen_2603, q_gen_2611, q_gen_2612, q_gen_2622, q_gen_2629},
Q_f={q_gen_2598},
Delta=
{
<s>(q_gen_2629) -> q_gen_2612
<z>() -> q_gen_2612
<s>(q_gen_2612) -> q_gen_2629
<s, s>(q_gen_2603) -> q_gen_2603
<z, s>(q_gen_2629) -> q_gen_2603
<z, z>() -> q_gen_2603
<s, s>(q_gen_2622) -> q_gen_2622
<z, s>(q_gen_2612) -> q_gen_2622
<s, s, s>(q_gen_2611) -> q_gen_2598
<s, z, s>(q_gen_2603) -> q_gen_2598
<z, s, s>(q_gen_2603) -> q_gen_2598
<z, z, s>(q_gen_2629) -> q_gen_2598
<z, z, z>() -> q_gen_2598
<s, s, s>(q_gen_2598) -> q_gen_2611
<s, z, s>(q_gen_2622) -> q_gen_2611
<z, s, s>(q_gen_2622) -> q_gen_2611
<z, z, s>(q_gen_2612) -> q_gen_2611
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 38  ;  () -> minus([z, y, z]) -> 38  ;  () -> plus([n, z, n]) -> 38  ;  (minus([_oc, n, _pc]) /\ plus([m, n, _oc])) -> eq_nat([_pc, m]) -> 43  ;  (minus([u, x2, _ec])) -> minus([s(u), s(x2), _ec]) -> 43  ;  (plus([n, mm, _jc])) -> plus([n, s(mm), s(_jc)]) -> 40
}
Sat witness: Yes: ((minus([_oc, n, _pc]) /\ plus([m, n, _oc])) -> eq_nat([_pc, m]), {
_oc -> s(s(z))  ;  _pc -> z  ;  m -> s(s(z))  ;  n -> z
})

-------------------------------------------
Step 50, which took 0.070643 s (model generation: 0.069263,  model checking: 0.001380):

Model:
|_
{
minus -> 
{{{
Q={q_gen_2599, q_gen_2601, q_gen_2607, q_gen_2614, q_gen_2619, q_gen_2624, q_gen_2647, q_gen_2667},
Q_f={q_gen_2599},
Delta=
{
<s>(q_gen_2619) -> q_gen_2607
<z>() -> q_gen_2607
<s>(q_gen_2607) -> q_gen_2619
<s, s>(q_gen_2601) -> q_gen_2601
<s, z>(q_gen_2619) -> q_gen_2601
<z, s>(q_gen_2619) -> q_gen_2601
<z, z>() -> q_gen_2601
<s, s>(q_gen_2624) -> q_gen_2624
<z, s>(q_gen_2607) -> q_gen_2624
<s, z>(q_gen_2607) -> q_gen_2647
<s, s, s>(q_gen_2614) -> q_gen_2599
<s, s, z>(q_gen_2601) -> q_gen_2599
<s, s, z>(q_gen_2624) -> q_gen_2599
<s, z, s>(q_gen_2601) -> q_gen_2599
<z, s, z>(q_gen_2607) -> q_gen_2599
<z, s, z>(q_gen_2619) -> q_gen_2599
<z, z, z>() -> q_gen_2599
<s, s, s>(q_gen_2599) -> q_gen_2614
<s, s, z>(q_gen_2647) -> q_gen_2614
<s, z, s>(q_gen_2624) -> q_gen_2614
<s, z, z>(q_gen_2607) -> q_gen_2614
<s, s, s>(q_gen_2667) -> q_gen_2667
<s, z, z>(q_gen_2619) -> q_gen_2667
}

Datatype: <nat, nat, nat>
Convolution form: complete
}}}
  ;  plus -> 
{{{
Q={q_gen_2598, q_gen_2603, q_gen_2611, q_gen_2612, q_gen_2622, q_gen_2629},
Q_f={q_gen_2598},
Delta=
{
<s>(q_gen_2629) -> q_gen_2612
<z>() -> q_gen_2612
<s>(q_gen_2612) -> q_gen_2629
<s, s>(q_gen_2603) -> q_gen_2603
<z, s>(q_gen_2629) -> q_gen_2603
<z, z>() -> q_gen_2603
<s, s>(q_gen_2622) -> q_gen_2622
<z, s>(q_gen_2612) -> q_gen_2622
<s, s, s>(q_gen_2611) -> q_gen_2598
<s, z, s>(q_gen_2603) -> q_gen_2598
<z, s, s>(q_gen_2603) -> q_gen_2598
<z, z, s>(q_gen_2629) -> q_gen_2598
<z, z, z>() -> q_gen_2598
<s, s, s>(q_gen_2598) -> q_gen_2611
<s, z, s>(q_gen_2622) -> q_gen_2611
<z, s, s>(q_gen_2622) -> q_gen_2611
<z, z, s>(q_gen_2612) -> q_gen_2611
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 39  ;  () -> minus([z, y, z]) -> 39  ;  () -> plus([n, z, n]) -> 39  ;  (minus([_oc, n, _pc]) /\ plus([m, n, _oc])) -> eq_nat([_pc, m]) -> 43  ;  (minus([u, x2, _ec])) -> minus([s(u), s(x2), _ec]) -> 46  ;  (plus([n, mm, _jc])) -> plus([n, s(mm), s(_jc)]) -> 41
}
Sat witness: Yes: ((minus([u, x2, _ec])) -> minus([s(u), s(x2), _ec]), {
_ec -> s(s(z))  ;  u -> s(s(z))  ;  x2 -> z
})

-------------------------------------------
Step 51, which took 0.082248 s (model generation: 0.081148,  model checking: 0.001100):

Model:
|_
{
minus -> 
{{{
Q={q_gen_2599, q_gen_2601, q_gen_2607, q_gen_2614, q_gen_2619, q_gen_2624, q_gen_2630, q_gen_2647},
Q_f={q_gen_2599},
Delta=
{
<z>() -> q_gen_2607
<s>(q_gen_2607) -> q_gen_2619
<s>(q_gen_2619) -> q_gen_2619
<s, s>(q_gen_2601) -> q_gen_2601
<s, s>(q_gen_2624) -> q_gen_2601
<z, z>() -> q_gen_2601
<z, s>(q_gen_2607) -> q_gen_2624
<z, s>(q_gen_2619) -> q_gen_2624
<s, z>(q_gen_2607) -> q_gen_2647
<s, z>(q_gen_2619) -> q_gen_2647
<s, s, s>(q_gen_2614) -> q_gen_2599
<s, s, z>(q_gen_2601) -> q_gen_2599
<s, s, z>(q_gen_2624) -> q_gen_2599
<s, z, s>(q_gen_2601) -> q_gen_2599
<z, s, z>(q_gen_2607) -> q_gen_2599
<z, s, z>(q_gen_2619) -> q_gen_2599
<z, z, z>() -> q_gen_2599
<s, s, s>(q_gen_2599) -> q_gen_2614
<s, s, s>(q_gen_2630) -> q_gen_2614
<s, s, z>(q_gen_2647) -> q_gen_2614
<s, z, s>(q_gen_2647) -> q_gen_2614
<s, z, z>(q_gen_2607) -> q_gen_2614
<s, z, s>(q_gen_2624) -> q_gen_2630
<s, z, z>(q_gen_2619) -> q_gen_2630
}

Datatype: <nat, nat, nat>
Convolution form: complete
}}}
  ;  plus -> 
{{{
Q={q_gen_2598, q_gen_2603, q_gen_2611, q_gen_2612, q_gen_2622, q_gen_2629},
Q_f={q_gen_2598},
Delta=
{
<s>(q_gen_2629) -> q_gen_2612
<z>() -> q_gen_2612
<s>(q_gen_2612) -> q_gen_2629
<s, s>(q_gen_2603) -> q_gen_2603
<z, s>(q_gen_2629) -> q_gen_2603
<z, z>() -> q_gen_2603
<s, s>(q_gen_2622) -> q_gen_2622
<z, s>(q_gen_2612) -> q_gen_2622
<s, s, s>(q_gen_2611) -> q_gen_2598
<s, z, s>(q_gen_2603) -> q_gen_2598
<z, s, s>(q_gen_2603) -> q_gen_2598
<z, z, s>(q_gen_2629) -> q_gen_2598
<z, z, z>() -> q_gen_2598
<s, s, s>(q_gen_2598) -> q_gen_2611
<s, z, s>(q_gen_2622) -> q_gen_2611
<z, s, s>(q_gen_2622) -> q_gen_2611
<z, z, s>(q_gen_2612) -> q_gen_2611
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 40  ;  () -> minus([z, y, z]) -> 40  ;  () -> plus([n, z, n]) -> 40  ;  (minus([_oc, n, _pc]) /\ plus([m, n, _oc])) -> eq_nat([_pc, m]) -> 46  ;  (minus([u, x2, _ec])) -> minus([s(u), s(x2), _ec]) -> 46  ;  (plus([n, mm, _jc])) -> plus([n, s(mm), s(_jc)]) -> 42
}
Sat witness: Yes: ((minus([_oc, n, _pc]) /\ plus([m, n, _oc])) -> eq_nat([_pc, m]), {
_oc -> s(s(z))  ;  _pc -> s(s(z))  ;  m -> z  ;  n -> z
})

-------------------------------------------
Step 52, which took 0.089743 s (model generation: 0.088841,  model checking: 0.000902):

Model:
|_
{
minus -> 
{{{
Q={q_gen_2599, q_gen_2601, q_gen_2607, q_gen_2614, q_gen_2619, q_gen_2624, q_gen_2647, q_gen_2667},
Q_f={q_gen_2599},
Delta=
{
<z>() -> q_gen_2607
<s>(q_gen_2607) -> q_gen_2619
<s>(q_gen_2619) -> q_gen_2619
<s, s>(q_gen_2601) -> q_gen_2601
<s, s>(q_gen_2624) -> q_gen_2601
<s, z>(q_gen_2619) -> q_gen_2601
<z, s>(q_gen_2619) -> q_gen_2601
<z, z>() -> q_gen_2601
<z, s>(q_gen_2607) -> q_gen_2624
<s, z>(q_gen_2607) -> q_gen_2647
<s, s, s>(q_gen_2614) -> q_gen_2599
<s, s, z>(q_gen_2601) -> q_gen_2599
<s, s, z>(q_gen_2624) -> q_gen_2599
<s, z, s>(q_gen_2601) -> q_gen_2599
<z, s, z>(q_gen_2607) -> q_gen_2599
<z, s, z>(q_gen_2619) -> q_gen_2599
<z, z, z>() -> q_gen_2599
<s, s, s>(q_gen_2599) -> q_gen_2614
<s, s, z>(q_gen_2647) -> q_gen_2614
<s, z, s>(q_gen_2624) -> q_gen_2614
<s, z, s>(q_gen_2647) -> q_gen_2614
<s, z, z>(q_gen_2607) -> q_gen_2614
<s, s, s>(q_gen_2667) -> q_gen_2667
<s, z, z>(q_gen_2619) -> q_gen_2667
}

Datatype: <nat, nat, nat>
Convolution form: complete
}}}
  ;  plus -> 
{{{
Q={q_gen_2598, q_gen_2603, q_gen_2605, q_gen_2611, q_gen_2612, q_gen_2622},
Q_f={q_gen_2598, q_gen_2605},
Delta=
{
<s>(q_gen_2612) -> q_gen_2612
<z>() -> q_gen_2612
<s, s>(q_gen_2603) -> q_gen_2603
<z, z>() -> q_gen_2603
<s, s>(q_gen_2622) -> q_gen_2622
<z, s>(q_gen_2612) -> q_gen_2622
<s, s, s>(q_gen_2605) -> q_gen_2598
<z, s, s>(q_gen_2603) -> q_gen_2598
<z, z, z>() -> q_gen_2598
<s, s, s>(q_gen_2611) -> q_gen_2605
<s, z, s>(q_gen_2603) -> q_gen_2605
<s, s, s>(q_gen_2598) -> q_gen_2611
<s, z, s>(q_gen_2622) -> q_gen_2611
<z, s, s>(q_gen_2622) -> q_gen_2611
<z, z, s>(q_gen_2612) -> q_gen_2611
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 41  ;  () -> minus([z, y, z]) -> 41  ;  () -> plus([n, z, n]) -> 41  ;  (minus([_oc, n, _pc]) /\ plus([m, n, _oc])) -> eq_nat([_pc, m]) -> 46  ;  (minus([u, x2, _ec])) -> minus([s(u), s(x2), _ec]) -> 46  ;  (plus([n, mm, _jc])) -> plus([n, s(mm), s(_jc)]) -> 45
}
Sat witness: Yes: ((plus([n, mm, _jc])) -> plus([n, s(mm), s(_jc)]), {
_jc -> s(s(s(s(z))))  ;  mm -> s(s(z))  ;  n -> s(s(s(z)))
})

-------------------------------------------
Step 53, which took 0.136121 s (model generation: 0.135220,  model checking: 0.000901):

Model:
|_
{
minus -> 
{{{
Q={q_gen_2599, q_gen_2601, q_gen_2607, q_gen_2614, q_gen_2619, q_gen_2624, q_gen_2630, q_gen_2647},
Q_f={q_gen_2599},
Delta=
{
<z>() -> q_gen_2607
<s>(q_gen_2607) -> q_gen_2619
<s>(q_gen_2619) -> q_gen_2619
<s, s>(q_gen_2601) -> q_gen_2601
<s, s>(q_gen_2624) -> q_gen_2601
<z, z>() -> q_gen_2601
<z, s>(q_gen_2607) -> q_gen_2624
<z, s>(q_gen_2619) -> q_gen_2624
<s, z>(q_gen_2607) -> q_gen_2647
<s, z>(q_gen_2619) -> q_gen_2647
<s, s, s>(q_gen_2614) -> q_gen_2599
<s, s, z>(q_gen_2601) -> q_gen_2599
<s, s, z>(q_gen_2624) -> q_gen_2599
<s, z, s>(q_gen_2601) -> q_gen_2599
<z, s, z>(q_gen_2607) -> q_gen_2599
<z, s, z>(q_gen_2619) -> q_gen_2599
<z, z, z>() -> q_gen_2599
<s, s, s>(q_gen_2599) -> q_gen_2614
<s, s, s>(q_gen_2630) -> q_gen_2614
<s, s, z>(q_gen_2647) -> q_gen_2614
<s, z, s>(q_gen_2647) -> q_gen_2614
<s, z, z>(q_gen_2607) -> q_gen_2614
<s, z, s>(q_gen_2624) -> q_gen_2630
<s, z, z>(q_gen_2619) -> q_gen_2630
}

Datatype: <nat, nat, nat>
Convolution form: complete
}}}
  ;  plus -> 
{{{
Q={q_gen_2598, q_gen_2603, q_gen_2610, q_gen_2611, q_gen_2612, q_gen_2617},
Q_f={q_gen_2598, q_gen_2610},
Delta=
{
<s>(q_gen_2612) -> q_gen_2612
<z>() -> q_gen_2612
<z, z>() -> q_gen_2603
<s, s>(q_gen_2603) -> q_gen_2617
<s, s>(q_gen_2617) -> q_gen_2617
<z, s>(q_gen_2612) -> q_gen_2617
<s, z, s>(q_gen_2603) -> q_gen_2598
<z, s, s>(q_gen_2603) -> q_gen_2598
<z, z, z>() -> q_gen_2598
<s, s, s>(q_gen_2610) -> q_gen_2610
<s, s, s>(q_gen_2611) -> q_gen_2610
<s, z, s>(q_gen_2617) -> q_gen_2610
<s, s, s>(q_gen_2598) -> q_gen_2611
<z, s, s>(q_gen_2617) -> q_gen_2611
<z, z, s>(q_gen_2612) -> q_gen_2611
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 42  ;  () -> minus([z, y, z]) -> 42  ;  () -> plus([n, z, n]) -> 42  ;  (minus([_oc, n, _pc]) /\ plus([m, n, _oc])) -> eq_nat([_pc, m]) -> 46  ;  (minus([u, x2, _ec])) -> minus([s(u), s(x2), _ec]) -> 46  ;  (plus([n, mm, _jc])) -> plus([n, s(mm), s(_jc)]) -> 48
}
Sat witness: Yes: ((plus([n, mm, _jc])) -> plus([n, s(mm), s(_jc)]), {
_jc -> s(z)  ;  mm -> s(z)  ;  n -> z
})

-------------------------------------------
Step 54, which took 0.089738 s (model generation: 0.089255,  model checking: 0.000483):

Model:
|_
{
minus -> 
{{{
Q={q_gen_2599, q_gen_2601, q_gen_2607, q_gen_2614, q_gen_2619, q_gen_2624, q_gen_2630, q_gen_2647},
Q_f={q_gen_2599},
Delta=
{
<s>(q_gen_2619) -> q_gen_2607
<z>() -> q_gen_2607
<s>(q_gen_2607) -> q_gen_2619
<s, s>(q_gen_2601) -> q_gen_2601
<s, s>(q_gen_2624) -> q_gen_2601
<z, s>(q_gen_2619) -> q_gen_2601
<z, z>() -> q_gen_2601
<s, z>(q_gen_2619) -> q_gen_2624
<z, s>(q_gen_2607) -> q_gen_2624
<s, z>(q_gen_2607) -> q_gen_2647
<s, s, s>(q_gen_2614) -> q_gen_2599
<s, s, z>(q_gen_2601) -> q_gen_2599
<s, s, z>(q_gen_2624) -> q_gen_2599
<s, z, s>(q_gen_2601) -> q_gen_2599
<z, s, z>(q_gen_2607) -> q_gen_2599
<z, s, z>(q_gen_2619) -> q_gen_2599
<z, z, z>() -> q_gen_2599
<s, s, s>(q_gen_2599) -> q_gen_2614
<s, s, z>(q_gen_2647) -> q_gen_2614
<s, z, s>(q_gen_2647) -> q_gen_2614
<s, z, z>(q_gen_2607) -> q_gen_2614
<s, s, s>(q_gen_2630) -> q_gen_2630
<s, z, s>(q_gen_2624) -> q_gen_2630
<s, z, z>(q_gen_2619) -> q_gen_2630
}

Datatype: <nat, nat, nat>
Convolution form: complete
}}}
  ;  plus -> 
{{{
Q={q_gen_2598, q_gen_2603, q_gen_2610, q_gen_2611, q_gen_2612, q_gen_2622},
Q_f={q_gen_2598, q_gen_2610},
Delta=
{
<s>(q_gen_2612) -> q_gen_2612
<z>() -> q_gen_2612
<s, s>(q_gen_2603) -> q_gen_2603
<z, z>() -> q_gen_2603
<s, s>(q_gen_2622) -> q_gen_2622
<z, s>(q_gen_2612) -> q_gen_2622
<s, z, s>(q_gen_2603) -> q_gen_2598
<z, s, s>(q_gen_2603) -> q_gen_2598
<z, z, z>() -> q_gen_2598
<s, s, s>(q_gen_2610) -> q_gen_2610
<s, s, s>(q_gen_2611) -> q_gen_2610
<s, z, s>(q_gen_2622) -> q_gen_2610
<s, s, s>(q_gen_2598) -> q_gen_2611
<z, s, s>(q_gen_2622) -> q_gen_2611
<z, z, s>(q_gen_2612) -> q_gen_2611
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 43  ;  () -> minus([z, y, z]) -> 43  ;  () -> plus([n, z, n]) -> 43  ;  (minus([_oc, n, _pc]) /\ plus([m, n, _oc])) -> eq_nat([_pc, m]) -> 46  ;  (minus([u, x2, _ec])) -> minus([s(u), s(x2), _ec]) -> 49  ;  (plus([n, mm, _jc])) -> plus([n, s(mm), s(_jc)]) -> 48
}
Sat witness: Yes: ((minus([u, x2, _ec])) -> minus([s(u), s(x2), _ec]), {
_ec -> s(s(z))  ;  u -> s(s(s(z)))  ;  x2 -> s(z)
})

-------------------------------------------
Step 55, which took 0.100651 s (model generation: 0.099823,  model checking: 0.000828):

Model:
|_
{
minus -> 
{{{
Q={q_gen_2599, q_gen_2601, q_gen_2607, q_gen_2614, q_gen_2619, q_gen_2624, q_gen_2630, q_gen_2647},
Q_f={q_gen_2599},
Delta=
{
<z>() -> q_gen_2607
<s>(q_gen_2607) -> q_gen_2619
<s>(q_gen_2619) -> q_gen_2619
<s, s>(q_gen_2601) -> q_gen_2601
<z, s>(q_gen_2619) -> q_gen_2601
<z, z>() -> q_gen_2601
<s, s>(q_gen_2624) -> q_gen_2624
<z, s>(q_gen_2607) -> q_gen_2624
<s, z>(q_gen_2607) -> q_gen_2647
<s, z>(q_gen_2619) -> q_gen_2647
<s, s, s>(q_gen_2614) -> q_gen_2599
<s, s, z>(q_gen_2601) -> q_gen_2599
<s, s, z>(q_gen_2624) -> q_gen_2599
<s, z, s>(q_gen_2601) -> q_gen_2599
<z, s, z>(q_gen_2607) -> q_gen_2599
<z, s, z>(q_gen_2619) -> q_gen_2599
<z, z, z>() -> q_gen_2599
<s, s, s>(q_gen_2599) -> q_gen_2614
<s, s, s>(q_gen_2630) -> q_gen_2614
<s, s, z>(q_gen_2647) -> q_gen_2614
<s, z, s>(q_gen_2647) -> q_gen_2614
<s, z, z>(q_gen_2607) -> q_gen_2614
<s, z, s>(q_gen_2624) -> q_gen_2630
<s, z, z>(q_gen_2619) -> q_gen_2630
}

Datatype: <nat, nat, nat>
Convolution form: complete
}}}
  ;  plus -> 
{{{
Q={q_gen_2598, q_gen_2603, q_gen_2605, q_gen_2611, q_gen_2612, q_gen_2622},
Q_f={q_gen_2598, q_gen_2605},
Delta=
{
<s>(q_gen_2612) -> q_gen_2612
<z>() -> q_gen_2612
<s, s>(q_gen_2603) -> q_gen_2603
<z, z>() -> q_gen_2603
<s, s>(q_gen_2622) -> q_gen_2622
<z, s>(q_gen_2612) -> q_gen_2622
<s, s, s>(q_gen_2605) -> q_gen_2598
<z, s, s>(q_gen_2603) -> q_gen_2598
<z, z, z>() -> q_gen_2598
<s, s, s>(q_gen_2611) -> q_gen_2605
<s, z, s>(q_gen_2603) -> q_gen_2605
<s, z, s>(q_gen_2622) -> q_gen_2605
<s, s, s>(q_gen_2598) -> q_gen_2611
<z, s, s>(q_gen_2622) -> q_gen_2611
<z, z, s>(q_gen_2612) -> q_gen_2611
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 44  ;  () -> minus([z, y, z]) -> 44  ;  () -> plus([n, z, n]) -> 44  ;  (minus([_oc, n, _pc]) /\ plus([m, n, _oc])) -> eq_nat([_pc, m]) -> 49  ;  (minus([u, x2, _ec])) -> minus([s(u), s(x2), _ec]) -> 49  ;  (plus([n, mm, _jc])) -> plus([n, s(mm), s(_jc)]) -> 48
}
Sat witness: Yes: ((minus([_oc, n, _pc]) /\ plus([m, n, _oc])) -> eq_nat([_pc, m]), {
_oc -> s(s(z))  ;  _pc -> z  ;  m -> s(s(z))  ;  n -> s(s(z))
})

-------------------------------------------
Step 56, which took 0.094840 s (model generation: 0.094261,  model checking: 0.000579):

Model:
|_
{
minus -> 
{{{
Q={q_gen_2599, q_gen_2601, q_gen_2607, q_gen_2614, q_gen_2619, q_gen_2624, q_gen_2630, q_gen_2647},
Q_f={q_gen_2599},
Delta=
{
<s>(q_gen_2619) -> q_gen_2607
<z>() -> q_gen_2607
<s>(q_gen_2607) -> q_gen_2619
<s, s>(q_gen_2601) -> q_gen_2601
<s, s>(q_gen_2624) -> q_gen_2601
<s, z>(q_gen_2619) -> q_gen_2601
<z, s>(q_gen_2619) -> q_gen_2601
<z, z>() -> q_gen_2601
<z, s>(q_gen_2607) -> q_gen_2624
<s, z>(q_gen_2607) -> q_gen_2647
<s, s, s>(q_gen_2614) -> q_gen_2599
<s, s, z>(q_gen_2601) -> q_gen_2599
<s, s, z>(q_gen_2624) -> q_gen_2599
<s, z, s>(q_gen_2601) -> q_gen_2599
<z, s, z>(q_gen_2607) -> q_gen_2599
<z, s, z>(q_gen_2619) -> q_gen_2599
<z, z, z>() -> q_gen_2599
<s, s, s>(q_gen_2599) -> q_gen_2614
<s, s, s>(q_gen_2630) -> q_gen_2614
<s, s, z>(q_gen_2647) -> q_gen_2614
<s, z, s>(q_gen_2647) -> q_gen_2614
<s, z, z>(q_gen_2607) -> q_gen_2614
<s, z, s>(q_gen_2624) -> q_gen_2630
<s, z, z>(q_gen_2619) -> q_gen_2630
}

Datatype: <nat, nat, nat>
Convolution form: complete
}}}
  ;  plus -> 
{{{
Q={q_gen_2598, q_gen_2603, q_gen_2611, q_gen_2612, q_gen_2615, q_gen_2622, q_gen_2629},
Q_f={q_gen_2598},
Delta=
{
<z>() -> q_gen_2612
<s>(q_gen_2612) -> q_gen_2629
<s>(q_gen_2629) -> q_gen_2629
<s, s>(q_gen_2603) -> q_gen_2603
<z, z>() -> q_gen_2603
<s, s>(q_gen_2622) -> q_gen_2622
<z, s>(q_gen_2612) -> q_gen_2622
<z, s>(q_gen_2629) -> q_gen_2622
<s, s, s>(q_gen_2611) -> q_gen_2598
<s, z, s>(q_gen_2603) -> q_gen_2598
<z, s, s>(q_gen_2603) -> q_gen_2598
<z, z, z>() -> q_gen_2598
<s, s, s>(q_gen_2615) -> q_gen_2611
<s, z, s>(q_gen_2622) -> q_gen_2611
<z, s, s>(q_gen_2622) -> q_gen_2611
<z, z, s>(q_gen_2612) -> q_gen_2611
<s, s, s>(q_gen_2598) -> q_gen_2615
<z, z, s>(q_gen_2629) -> q_gen_2615
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 45  ;  () -> minus([z, y, z]) -> 45  ;  () -> plus([n, z, n]) -> 45  ;  (minus([_oc, n, _pc]) /\ plus([m, n, _oc])) -> eq_nat([_pc, m]) -> 49  ;  (minus([u, x2, _ec])) -> minus([s(u), s(x2), _ec]) -> 49  ;  (plus([n, mm, _jc])) -> plus([n, s(mm), s(_jc)]) -> 51
}
Sat witness: Yes: ((plus([n, mm, _jc])) -> plus([n, s(mm), s(_jc)]), {
_jc -> s(s(s(s(z))))  ;  mm -> s(z)  ;  n -> s(s(s(z)))
})

-------------------------------------------
Step 57, which took 0.123430 s (model generation: 0.122680,  model checking: 0.000750):

Model:
|_
{
minus -> 
{{{
Q={q_gen_2599, q_gen_2601, q_gen_2607, q_gen_2614, q_gen_2619, q_gen_2624, q_gen_2630, q_gen_2647},
Q_f={q_gen_2599},
Delta=
{
<s>(q_gen_2619) -> q_gen_2607
<z>() -> q_gen_2607
<s>(q_gen_2607) -> q_gen_2619
<s, s>(q_gen_2601) -> q_gen_2601
<s, s>(q_gen_2624) -> q_gen_2601
<z, s>(q_gen_2619) -> q_gen_2601
<z, z>() -> q_gen_2601
<s, z>(q_gen_2619) -> q_gen_2624
<z, s>(q_gen_2607) -> q_gen_2624
<s, z>(q_gen_2607) -> q_gen_2647
<s, s, s>(q_gen_2614) -> q_gen_2599
<s, s, z>(q_gen_2601) -> q_gen_2599
<s, s, z>(q_gen_2624) -> q_gen_2599
<s, z, s>(q_gen_2601) -> q_gen_2599
<z, s, z>(q_gen_2607) -> q_gen_2599
<z, s, z>(q_gen_2619) -> q_gen_2599
<z, z, z>() -> q_gen_2599
<s, s, s>(q_gen_2599) -> q_gen_2614
<s, s, s>(q_gen_2630) -> q_gen_2614
<s, s, z>(q_gen_2647) -> q_gen_2614
<s, z, s>(q_gen_2647) -> q_gen_2614
<s, z, z>(q_gen_2607) -> q_gen_2614
<s, z, s>(q_gen_2624) -> q_gen_2630
<s, z, z>(q_gen_2619) -> q_gen_2630
}

Datatype: <nat, nat, nat>
Convolution form: complete
}}}
  ;  plus -> 
{{{
Q={q_gen_2598, q_gen_2603, q_gen_2610, q_gen_2611, q_gen_2612, q_gen_2615, q_gen_2622},
Q_f={q_gen_2598, q_gen_2610},
Delta=
{
<s>(q_gen_2612) -> q_gen_2612
<z>() -> q_gen_2612
<s, s>(q_gen_2603) -> q_gen_2603
<z, z>() -> q_gen_2603
<s, s>(q_gen_2622) -> q_gen_2622
<z, s>(q_gen_2612) -> q_gen_2622
<s, z, s>(q_gen_2603) -> q_gen_2598
<z, s, s>(q_gen_2603) -> q_gen_2598
<z, z, z>() -> q_gen_2598
<s, s, s>(q_gen_2610) -> q_gen_2610
<s, s, s>(q_gen_2611) -> q_gen_2610
<s, s, s>(q_gen_2615) -> q_gen_2611
<s, z, s>(q_gen_2622) -> q_gen_2611
<z, s, s>(q_gen_2622) -> q_gen_2611
<z, z, s>(q_gen_2612) -> q_gen_2611
<s, s, s>(q_gen_2598) -> q_gen_2615
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 46  ;  () -> minus([z, y, z]) -> 46  ;  () -> plus([n, z, n]) -> 46  ;  (minus([_oc, n, _pc]) /\ plus([m, n, _oc])) -> eq_nat([_pc, m]) -> 49  ;  (minus([u, x2, _ec])) -> minus([s(u), s(x2), _ec]) -> 52  ;  (plus([n, mm, _jc])) -> plus([n, s(mm), s(_jc)]) -> 51
}
Sat witness: Yes: ((minus([u, x2, _ec])) -> minus([s(u), s(x2), _ec]), {
_ec -> s(s(s(z)))  ;  u -> s(s(z))  ;  x2 -> z
})

-------------------------------------------
Step 58, which took 0.112204 s (model generation: 0.111307,  model checking: 0.000897):

Model:
|_
{
minus -> 
{{{
Q={q_gen_2599, q_gen_2601, q_gen_2607, q_gen_2614, q_gen_2619, q_gen_2624, q_gen_2630, q_gen_2647},
Q_f={q_gen_2599},
Delta=
{
<z>() -> q_gen_2607
<s>(q_gen_2607) -> q_gen_2619
<s>(q_gen_2619) -> q_gen_2619
<s, s>(q_gen_2601) -> q_gen_2601
<z, s>(q_gen_2619) -> q_gen_2601
<z, z>() -> q_gen_2601
<s, s>(q_gen_2624) -> q_gen_2624
<s, z>(q_gen_2619) -> q_gen_2624
<z, s>(q_gen_2607) -> q_gen_2624
<s, z>(q_gen_2607) -> q_gen_2647
<s, s, s>(q_gen_2614) -> q_gen_2599
<s, s, z>(q_gen_2601) -> q_gen_2599
<s, s, z>(q_gen_2624) -> q_gen_2599
<s, z, s>(q_gen_2601) -> q_gen_2599
<z, s, z>(q_gen_2607) -> q_gen_2599
<z, s, z>(q_gen_2619) -> q_gen_2599
<z, z, z>() -> q_gen_2599
<s, s, s>(q_gen_2599) -> q_gen_2614
<s, s, s>(q_gen_2630) -> q_gen_2614
<s, s, z>(q_gen_2647) -> q_gen_2614
<s, z, s>(q_gen_2647) -> q_gen_2614
<s, z, z>(q_gen_2607) -> q_gen_2614
<s, z, s>(q_gen_2624) -> q_gen_2630
<s, z, z>(q_gen_2619) -> q_gen_2630
}

Datatype: <nat, nat, nat>
Convolution form: complete
}}}
  ;  plus -> 
{{{
Q={q_gen_2598, q_gen_2603, q_gen_2610, q_gen_2611, q_gen_2612, q_gen_2615, q_gen_2622},
Q_f={q_gen_2598, q_gen_2610},
Delta=
{
<s>(q_gen_2612) -> q_gen_2612
<z>() -> q_gen_2612
<s, s>(q_gen_2603) -> q_gen_2603
<z, z>() -> q_gen_2603
<s, s>(q_gen_2622) -> q_gen_2622
<z, s>(q_gen_2612) -> q_gen_2622
<s, z, s>(q_gen_2603) -> q_gen_2598
<z, s, s>(q_gen_2603) -> q_gen_2598
<z, z, z>() -> q_gen_2598
<s, s, s>(q_gen_2610) -> q_gen_2610
<s, s, s>(q_gen_2611) -> q_gen_2610
<s, z, s>(q_gen_2622) -> q_gen_2611
<z, s, s>(q_gen_2622) -> q_gen_2611
<z, z, s>(q_gen_2612) -> q_gen_2611
<s, s, s>(q_gen_2598) -> q_gen_2615
<s, s, s>(q_gen_2615) -> q_gen_2615
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 47  ;  () -> minus([z, y, z]) -> 47  ;  () -> plus([n, z, n]) -> 47  ;  (minus([_oc, n, _pc]) /\ plus([m, n, _oc])) -> eq_nat([_pc, m]) -> 52  ;  (minus([u, x2, _ec])) -> minus([s(u), s(x2), _ec]) -> 52  ;  (plus([n, mm, _jc])) -> plus([n, s(mm), s(_jc)]) -> 51
}
Sat witness: Yes: ((minus([_oc, n, _pc]) /\ plus([m, n, _oc])) -> eq_nat([_pc, m]), {
_oc -> s(s(s(z)))  ;  _pc -> z  ;  m -> s(z)  ;  n -> s(z)
})

-------------------------------------------
Step 59, which took 0.116087 s (model generation: 0.114594,  model checking: 0.001493):

Model:
|_
{
minus -> 
{{{
Q={q_gen_2599, q_gen_2601, q_gen_2607, q_gen_2614, q_gen_2619, q_gen_2624, q_gen_2647, q_gen_2668},
Q_f={q_gen_2599},
Delta=
{
<z>() -> q_gen_2607
<s>(q_gen_2607) -> q_gen_2619
<s>(q_gen_2619) -> q_gen_2619
<s, s>(q_gen_2601) -> q_gen_2601
<z, s>(q_gen_2619) -> q_gen_2601
<z, z>() -> q_gen_2601
<s, s>(q_gen_2624) -> q_gen_2624
<z, s>(q_gen_2607) -> q_gen_2624
<s, z>(q_gen_2607) -> q_gen_2647
<s, z>(q_gen_2619) -> q_gen_2647
<s, s, s>(q_gen_2614) -> q_gen_2599
<s, s, z>(q_gen_2601) -> q_gen_2599
<s, s, z>(q_gen_2624) -> q_gen_2599
<s, z, s>(q_gen_2601) -> q_gen_2599
<z, s, z>(q_gen_2607) -> q_gen_2599
<z, s, z>(q_gen_2619) -> q_gen_2599
<z, z, z>() -> q_gen_2599
<s, s, s>(q_gen_2599) -> q_gen_2614
<s, s, s>(q_gen_2668) -> q_gen_2614
<s, s, z>(q_gen_2647) -> q_gen_2614
<s, z, s>(q_gen_2624) -> q_gen_2614
<s, z, s>(q_gen_2647) -> q_gen_2614
<s, z, z>(q_gen_2607) -> q_gen_2614
<s, z, z>(q_gen_2619) -> q_gen_2668
}

Datatype: <nat, nat, nat>
Convolution form: complete
}}}
  ;  plus -> 
{{{
Q={q_gen_2598, q_gen_2603, q_gen_2610, q_gen_2611, q_gen_2612, q_gen_2615, q_gen_2622},
Q_f={q_gen_2598, q_gen_2610},
Delta=
{
<s>(q_gen_2612) -> q_gen_2612
<z>() -> q_gen_2612
<s, s>(q_gen_2603) -> q_gen_2603
<z, z>() -> q_gen_2603
<s, s>(q_gen_2622) -> q_gen_2622
<z, s>(q_gen_2612) -> q_gen_2622
<s, z, s>(q_gen_2603) -> q_gen_2598
<z, s, s>(q_gen_2603) -> q_gen_2598
<z, z, z>() -> q_gen_2598
<s, s, s>(q_gen_2610) -> q_gen_2610
<s, s, s>(q_gen_2611) -> q_gen_2610
<s, z, s>(q_gen_2622) -> q_gen_2611
<z, s, s>(q_gen_2622) -> q_gen_2611
<z, z, s>(q_gen_2612) -> q_gen_2611
<s, s, s>(q_gen_2598) -> q_gen_2615
<s, s, s>(q_gen_2615) -> q_gen_2615
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 48  ;  () -> minus([z, y, z]) -> 48  ;  () -> plus([n, z, n]) -> 48  ;  (minus([_oc, n, _pc]) /\ plus([m, n, _oc])) -> eq_nat([_pc, m]) -> 52  ;  (minus([u, x2, _ec])) -> minus([s(u), s(x2), _ec]) -> 55  ;  (plus([n, mm, _jc])) -> plus([n, s(mm), s(_jc)]) -> 52
}
Sat witness: Yes: ((minus([u, x2, _ec])) -> minus([s(u), s(x2), _ec]), {
_ec -> s(s(s(s(z))))  ;  u -> s(z)  ;  x2 -> z
})

-------------------------------------------
Step 60, which took 0.122720 s (model generation: 0.121448,  model checking: 0.001272):

Model:
|_
{
minus -> 
{{{
Q={q_gen_2599, q_gen_2601, q_gen_2607, q_gen_2614, q_gen_2619, q_gen_2624, q_gen_2630, q_gen_2647},
Q_f={q_gen_2599},
Delta=
{
<z>() -> q_gen_2607
<s>(q_gen_2607) -> q_gen_2619
<s>(q_gen_2619) -> q_gen_2619
<s, s>(q_gen_2601) -> q_gen_2601
<z, z>() -> q_gen_2601
<s, s>(q_gen_2624) -> q_gen_2624
<z, s>(q_gen_2607) -> q_gen_2624
<z, s>(q_gen_2619) -> q_gen_2624
<s, z>(q_gen_2607) -> q_gen_2647
<s, z>(q_gen_2619) -> q_gen_2647
<s, s, s>(q_gen_2614) -> q_gen_2599
<s, s, z>(q_gen_2601) -> q_gen_2599
<s, s, z>(q_gen_2624) -> q_gen_2599
<s, z, s>(q_gen_2601) -> q_gen_2599
<z, s, z>(q_gen_2607) -> q_gen_2599
<z, s, z>(q_gen_2619) -> q_gen_2599
<z, z, z>() -> q_gen_2599
<s, s, s>(q_gen_2599) -> q_gen_2614
<s, s, s>(q_gen_2630) -> q_gen_2614
<s, s, z>(q_gen_2647) -> q_gen_2614
<s, z, s>(q_gen_2647) -> q_gen_2614
<s, z, z>(q_gen_2607) -> q_gen_2614
<s, z, s>(q_gen_2624) -> q_gen_2630
<s, z, z>(q_gen_2619) -> q_gen_2630
}

Datatype: <nat, nat, nat>
Convolution form: complete
}}}
  ;  plus -> 
{{{
Q={q_gen_2598, q_gen_2603, q_gen_2605, q_gen_2611, q_gen_2612, q_gen_2615, q_gen_2622},
Q_f={q_gen_2598, q_gen_2605},
Delta=
{
<s>(q_gen_2612) -> q_gen_2612
<z>() -> q_gen_2612
<s, s>(q_gen_2603) -> q_gen_2603
<z, z>() -> q_gen_2603
<s, s>(q_gen_2622) -> q_gen_2622
<z, s>(q_gen_2612) -> q_gen_2622
<z, s, s>(q_gen_2603) -> q_gen_2598
<z, z, z>() -> q_gen_2598
<s, s, s>(q_gen_2605) -> q_gen_2605
<s, s, s>(q_gen_2611) -> q_gen_2605
<s, z, s>(q_gen_2603) -> q_gen_2605
<s, z, s>(q_gen_2622) -> q_gen_2611
<z, s, s>(q_gen_2622) -> q_gen_2611
<z, z, s>(q_gen_2612) -> q_gen_2611
<s, s, s>(q_gen_2598) -> q_gen_2615
<s, s, s>(q_gen_2615) -> q_gen_2615
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 49  ;  () -> minus([z, y, z]) -> 49  ;  () -> plus([n, z, n]) -> 49  ;  (minus([_oc, n, _pc]) /\ plus([m, n, _oc])) -> eq_nat([_pc, m]) -> 55  ;  (minus([u, x2, _ec])) -> minus([s(u), s(x2), _ec]) -> 55  ;  (plus([n, mm, _jc])) -> plus([n, s(mm), s(_jc)]) -> 53
}
Sat witness: Yes: ((minus([_oc, n, _pc]) /\ plus([m, n, _oc])) -> eq_nat([_pc, m]), {
_oc -> s(s(z))  ;  _pc -> s(z)  ;  m -> s(s(z))  ;  n -> s(z)
})

-------------------------------------------
Step 61, which took 0.130458 s (model generation: 0.129443,  model checking: 0.001015):

Model:
|_
{
minus -> 
{{{
Q={q_gen_2599, q_gen_2601, q_gen_2607, q_gen_2614, q_gen_2619, q_gen_2624, q_gen_2630, q_gen_2647},
Q_f={q_gen_2599},
Delta=
{
<z>() -> q_gen_2607
<s>(q_gen_2607) -> q_gen_2619
<s>(q_gen_2619) -> q_gen_2619
<s, s>(q_gen_2601) -> q_gen_2601
<z, z>() -> q_gen_2601
<s, s>(q_gen_2624) -> q_gen_2624
<z, s>(q_gen_2607) -> q_gen_2624
<z, s>(q_gen_2619) -> q_gen_2624
<s, z>(q_gen_2607) -> q_gen_2647
<s, z>(q_gen_2619) -> q_gen_2647
<s, s, s>(q_gen_2614) -> q_gen_2599
<s, s, z>(q_gen_2601) -> q_gen_2599
<s, s, z>(q_gen_2624) -> q_gen_2599
<s, z, s>(q_gen_2601) -> q_gen_2599
<z, s, z>(q_gen_2607) -> q_gen_2599
<z, s, z>(q_gen_2619) -> q_gen_2599
<z, z, z>() -> q_gen_2599
<s, s, s>(q_gen_2599) -> q_gen_2614
<s, s, s>(q_gen_2630) -> q_gen_2614
<s, s, z>(q_gen_2647) -> q_gen_2614
<s, z, s>(q_gen_2647) -> q_gen_2614
<s, z, z>(q_gen_2607) -> q_gen_2614
<s, z, s>(q_gen_2624) -> q_gen_2630
<s, z, z>(q_gen_2619) -> q_gen_2630
}

Datatype: <nat, nat, nat>
Convolution form: complete
}}}
  ;  plus -> 
{{{
Q={q_gen_2598, q_gen_2603, q_gen_2610, q_gen_2611, q_gen_2612, q_gen_2615, q_gen_2622},
Q_f={q_gen_2598, q_gen_2610},
Delta=
{
<s>(q_gen_2612) -> q_gen_2612
<z>() -> q_gen_2612
<s, s>(q_gen_2603) -> q_gen_2603
<z, z>() -> q_gen_2603
<s, s>(q_gen_2622) -> q_gen_2622
<z, s>(q_gen_2612) -> q_gen_2622
<s, z, s>(q_gen_2603) -> q_gen_2598
<z, s, s>(q_gen_2603) -> q_gen_2598
<z, z, z>() -> q_gen_2598
<s, s, s>(q_gen_2610) -> q_gen_2610
<s, s, s>(q_gen_2611) -> q_gen_2610
<s, z, s>(q_gen_2622) -> q_gen_2611
<z, s, s>(q_gen_2622) -> q_gen_2611
<z, z, s>(q_gen_2612) -> q_gen_2611
<s, s, s>(q_gen_2598) -> q_gen_2615
<s, s, s>(q_gen_2615) -> q_gen_2615
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 50  ;  () -> minus([z, y, z]) -> 50  ;  () -> plus([n, z, n]) -> 50  ;  (minus([_oc, n, _pc]) /\ plus([m, n, _oc])) -> eq_nat([_pc, m]) -> 55  ;  (minus([u, x2, _ec])) -> minus([s(u), s(x2), _ec]) -> 58  ;  (plus([n, mm, _jc])) -> plus([n, s(mm), s(_jc)]) -> 54
}
Sat witness: Yes: ((minus([u, x2, _ec])) -> minus([s(u), s(x2), _ec]), {
_ec -> s(s(s(s(z))))  ;  u -> s(s(s(z)))  ;  x2 -> s(s(z))
})

-------------------------------------------
Step 62, which took 0.132982 s (model generation: 0.131855,  model checking: 0.001127):

Model:
|_
{
minus -> 
{{{
Q={q_gen_2599, q_gen_2601, q_gen_2607, q_gen_2614, q_gen_2619, q_gen_2624, q_gen_2625, q_gen_2647},
Q_f={q_gen_2599},
Delta=
{
<z>() -> q_gen_2607
<s>(q_gen_2607) -> q_gen_2619
<s>(q_gen_2619) -> q_gen_2619
<s, s>(q_gen_2601) -> q_gen_2601
<z, z>() -> q_gen_2601
<s, s>(q_gen_2624) -> q_gen_2624
<z, s>(q_gen_2607) -> q_gen_2624
<z, s>(q_gen_2619) -> q_gen_2624
<s, z>(q_gen_2607) -> q_gen_2647
<s, z>(q_gen_2619) -> q_gen_2647
<s, s, s>(q_gen_2614) -> q_gen_2599
<s, s, z>(q_gen_2601) -> q_gen_2599
<s, s, z>(q_gen_2624) -> q_gen_2599
<s, z, s>(q_gen_2601) -> q_gen_2599
<z, s, z>(q_gen_2607) -> q_gen_2599
<z, s, z>(q_gen_2619) -> q_gen_2599
<z, z, z>() -> q_gen_2599
<s, s, s>(q_gen_2625) -> q_gen_2614
<s, s, z>(q_gen_2647) -> q_gen_2614
<s, z, s>(q_gen_2647) -> q_gen_2614
<s, z, z>(q_gen_2607) -> q_gen_2614
<s, s, s>(q_gen_2599) -> q_gen_2625
<s, z, s>(q_gen_2624) -> q_gen_2625
<s, z, z>(q_gen_2619) -> q_gen_2625
}

Datatype: <nat, nat, nat>
Convolution form: complete
}}}
  ;  plus -> 
{{{
Q={q_gen_2598, q_gen_2603, q_gen_2610, q_gen_2611, q_gen_2612, q_gen_2615, q_gen_2622},
Q_f={q_gen_2598, q_gen_2610},
Delta=
{
<s>(q_gen_2612) -> q_gen_2612
<z>() -> q_gen_2612
<s, s>(q_gen_2603) -> q_gen_2603
<z, z>() -> q_gen_2603
<s, s>(q_gen_2622) -> q_gen_2622
<z, s>(q_gen_2612) -> q_gen_2622
<s, z, s>(q_gen_2603) -> q_gen_2598
<z, s, s>(q_gen_2603) -> q_gen_2598
<z, z, z>() -> q_gen_2598
<s, s, s>(q_gen_2610) -> q_gen_2610
<s, s, s>(q_gen_2611) -> q_gen_2610
<s, z, s>(q_gen_2622) -> q_gen_2611
<z, s, s>(q_gen_2622) -> q_gen_2611
<z, z, s>(q_gen_2612) -> q_gen_2611
<s, s, s>(q_gen_2598) -> q_gen_2615
<s, s, s>(q_gen_2615) -> q_gen_2615
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 51  ;  () -> minus([z, y, z]) -> 51  ;  () -> plus([n, z, n]) -> 51  ;  (minus([_oc, n, _pc]) /\ plus([m, n, _oc])) -> eq_nat([_pc, m]) -> 58  ;  (minus([u, x2, _ec])) -> minus([s(u), s(x2), _ec]) -> 58  ;  (plus([n, mm, _jc])) -> plus([n, s(mm), s(_jc)]) -> 55
}
Sat witness: Yes: ((minus([_oc, n, _pc]) /\ plus([m, n, _oc])) -> eq_nat([_pc, m]), {
_oc -> s(s(s(z)))  ;  _pc -> s(s(z))  ;  m -> s(z)  ;  n -> s(z)
})

-------------------------------------------
Step 63, which took 0.112338 s (model generation: 0.111489,  model checking: 0.000849):

Model:
|_
{
minus -> 
{{{
Q={q_gen_2599, q_gen_2601, q_gen_2607, q_gen_2614, q_gen_2619, q_gen_2624, q_gen_2647, q_gen_2668},
Q_f={q_gen_2599},
Delta=
{
<s>(q_gen_2619) -> q_gen_2607
<z>() -> q_gen_2607
<s>(q_gen_2607) -> q_gen_2619
<s, s>(q_gen_2601) -> q_gen_2601
<s, z>(q_gen_2619) -> q_gen_2601
<z, s>(q_gen_2619) -> q_gen_2601
<z, z>() -> q_gen_2601
<s, s>(q_gen_2624) -> q_gen_2624
<z, s>(q_gen_2607) -> q_gen_2624
<s, z>(q_gen_2607) -> q_gen_2647
<s, s, s>(q_gen_2614) -> q_gen_2599
<s, s, z>(q_gen_2601) -> q_gen_2599
<s, s, z>(q_gen_2624) -> q_gen_2599
<s, z, s>(q_gen_2601) -> q_gen_2599
<z, s, z>(q_gen_2607) -> q_gen_2599
<z, s, z>(q_gen_2619) -> q_gen_2599
<z, z, z>() -> q_gen_2599
<s, s, s>(q_gen_2599) -> q_gen_2614
<s, s, s>(q_gen_2668) -> q_gen_2614
<s, s, z>(q_gen_2647) -> q_gen_2614
<s, z, s>(q_gen_2624) -> q_gen_2614
<s, z, s>(q_gen_2647) -> q_gen_2614
<s, z, z>(q_gen_2607) -> q_gen_2614
<s, z, z>(q_gen_2619) -> q_gen_2668
}

Datatype: <nat, nat, nat>
Convolution form: complete
}}}
  ;  plus -> 
{{{
Q={q_gen_2598, q_gen_2602, q_gen_2603, q_gen_2611, q_gen_2612, q_gen_2615, q_gen_2622, q_gen_2629},
Q_f={q_gen_2598, q_gen_2602},
Delta=
{
<s>(q_gen_2629) -> q_gen_2612
<z>() -> q_gen_2612
<s>(q_gen_2612) -> q_gen_2629
<s, s>(q_gen_2603) -> q_gen_2603
<z, s>(q_gen_2629) -> q_gen_2603
<z, z>() -> q_gen_2603
<s, s>(q_gen_2622) -> q_gen_2622
<z, s>(q_gen_2612) -> q_gen_2622
<z, z, z>() -> q_gen_2598
<s, s, s>(q_gen_2611) -> q_gen_2602
<s, z, s>(q_gen_2603) -> q_gen_2602
<z, s, s>(q_gen_2603) -> q_gen_2602
<s, s, s>(q_gen_2602) -> q_gen_2611
<s, s, s>(q_gen_2615) -> q_gen_2611
<s, z, s>(q_gen_2622) -> q_gen_2611
<z, s, s>(q_gen_2622) -> q_gen_2611
<z, z, s>(q_gen_2612) -> q_gen_2611
<s, s, s>(q_gen_2598) -> q_gen_2615
<z, z, s>(q_gen_2629) -> q_gen_2615
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 52  ;  () -> minus([z, y, z]) -> 52  ;  () -> plus([n, z, n]) -> 52  ;  (minus([_oc, n, _pc]) /\ plus([m, n, _oc])) -> eq_nat([_pc, m]) -> 58  ;  (minus([u, x2, _ec])) -> minus([s(u), s(x2), _ec]) -> 58  ;  (plus([n, mm, _jc])) -> plus([n, s(mm), s(_jc)]) -> 58
}
Sat witness: Yes: ((plus([n, mm, _jc])) -> plus([n, s(mm), s(_jc)]), {
_jc -> s(s(s(z)))  ;  mm -> s(s(s(z)))  ;  n -> s(s(s(z)))
})

-------------------------------------------
Step 64, which took 0.164079 s (model generation: 0.163155,  model checking: 0.000924):

Model:
|_
{
minus -> 
{{{
Q={q_gen_2599, q_gen_2601, q_gen_2607, q_gen_2614, q_gen_2619, q_gen_2624, q_gen_2647, q_gen_2668},
Q_f={q_gen_2599},
Delta=
{
<s>(q_gen_2619) -> q_gen_2607
<z>() -> q_gen_2607
<s>(q_gen_2607) -> q_gen_2619
<s, s>(q_gen_2601) -> q_gen_2601
<s, z>(q_gen_2619) -> q_gen_2601
<z, s>(q_gen_2619) -> q_gen_2601
<z, z>() -> q_gen_2601
<s, s>(q_gen_2624) -> q_gen_2624
<z, s>(q_gen_2607) -> q_gen_2624
<s, z>(q_gen_2607) -> q_gen_2647
<s, s, s>(q_gen_2614) -> q_gen_2599
<s, s, z>(q_gen_2601) -> q_gen_2599
<s, s, z>(q_gen_2624) -> q_gen_2599
<s, z, s>(q_gen_2601) -> q_gen_2599
<z, s, z>(q_gen_2607) -> q_gen_2599
<z, s, z>(q_gen_2619) -> q_gen_2599
<z, z, z>() -> q_gen_2599
<s, s, s>(q_gen_2599) -> q_gen_2614
<s, s, s>(q_gen_2668) -> q_gen_2614
<s, s, z>(q_gen_2647) -> q_gen_2614
<s, z, s>(q_gen_2624) -> q_gen_2614
<s, z, s>(q_gen_2647) -> q_gen_2614
<s, z, z>(q_gen_2607) -> q_gen_2614
<s, z, z>(q_gen_2619) -> q_gen_2668
}

Datatype: <nat, nat, nat>
Convolution form: complete
}}}
  ;  plus -> 
{{{
Q={q_gen_2598, q_gen_2603, q_gen_2611, q_gen_2612, q_gen_2615, q_gen_2622, q_gen_2629, q_gen_2649},
Q_f={q_gen_2598},
Delta=
{
<z>() -> q_gen_2612
<s>(q_gen_2612) -> q_gen_2629
<s>(q_gen_2629) -> q_gen_2629
<s, s>(q_gen_2603) -> q_gen_2603
<z, z>() -> q_gen_2603
<s, s>(q_gen_2622) -> q_gen_2622
<z, s>(q_gen_2612) -> q_gen_2622
<z, s>(q_gen_2629) -> q_gen_2649
<s, s, s>(q_gen_2611) -> q_gen_2598
<s, z, s>(q_gen_2603) -> q_gen_2598
<z, s, s>(q_gen_2603) -> q_gen_2598
<z, z, z>() -> q_gen_2598
<s, s, s>(q_gen_2615) -> q_gen_2611
<s, z, s>(q_gen_2622) -> q_gen_2611
<z, s, s>(q_gen_2622) -> q_gen_2611
<z, z, s>(q_gen_2612) -> q_gen_2611
<s, s, s>(q_gen_2598) -> q_gen_2615
<s, z, s>(q_gen_2649) -> q_gen_2615
<z, s, s>(q_gen_2649) -> q_gen_2615
<z, z, s>(q_gen_2629) -> q_gen_2615
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 53  ;  () -> minus([z, y, z]) -> 53  ;  () -> plus([n, z, n]) -> 53  ;  (minus([_oc, n, _pc]) /\ plus([m, n, _oc])) -> eq_nat([_pc, m]) -> 58  ;  (minus([u, x2, _ec])) -> minus([s(u), s(x2), _ec]) -> 58  ;  (plus([n, mm, _jc])) -> plus([n, s(mm), s(_jc)]) -> 61
}
Sat witness: Yes: ((plus([n, mm, _jc])) -> plus([n, s(mm), s(_jc)]), {
_jc -> s(s(s(s(s(z)))))  ;  mm -> s(s(z))  ;  n -> s(s(s(z)))
})

-------------------------------------------
Step 65, which took 0.173169 s (model generation: 0.171931,  model checking: 0.001238):

Model:
|_
{
minus -> 
{{{
Q={q_gen_2599, q_gen_2601, q_gen_2607, q_gen_2614, q_gen_2619, q_gen_2624, q_gen_2647, q_gen_2668},
Q_f={q_gen_2599},
Delta=
{
<s>(q_gen_2619) -> q_gen_2607
<z>() -> q_gen_2607
<s>(q_gen_2607) -> q_gen_2619
<s, s>(q_gen_2601) -> q_gen_2601
<s, z>(q_gen_2619) -> q_gen_2601
<z, s>(q_gen_2619) -> q_gen_2601
<z, z>() -> q_gen_2601
<s, s>(q_gen_2624) -> q_gen_2624
<z, s>(q_gen_2607) -> q_gen_2624
<s, z>(q_gen_2607) -> q_gen_2647
<s, s, s>(q_gen_2614) -> q_gen_2599
<s, s, z>(q_gen_2601) -> q_gen_2599
<s, s, z>(q_gen_2624) -> q_gen_2599
<s, z, s>(q_gen_2601) -> q_gen_2599
<z, s, z>(q_gen_2607) -> q_gen_2599
<z, s, z>(q_gen_2619) -> q_gen_2599
<z, z, z>() -> q_gen_2599
<s, s, s>(q_gen_2599) -> q_gen_2614
<s, s, s>(q_gen_2668) -> q_gen_2614
<s, s, z>(q_gen_2647) -> q_gen_2614
<s, z, s>(q_gen_2624) -> q_gen_2614
<s, z, s>(q_gen_2647) -> q_gen_2614
<s, z, z>(q_gen_2607) -> q_gen_2614
<s, z, z>(q_gen_2619) -> q_gen_2668
}

Datatype: <nat, nat, nat>
Convolution form: complete
}}}
  ;  plus -> 
{{{
Q={q_gen_2598, q_gen_2603, q_gen_2605, q_gen_2611, q_gen_2612, q_gen_2615, q_gen_2622, q_gen_2629},
Q_f={q_gen_2598, q_gen_2605},
Delta=
{
<s>(q_gen_2629) -> q_gen_2612
<z>() -> q_gen_2612
<s>(q_gen_2612) -> q_gen_2629
<s, s>(q_gen_2603) -> q_gen_2603
<z, s>(q_gen_2629) -> q_gen_2603
<z, z>() -> q_gen_2603
<s, s>(q_gen_2622) -> q_gen_2622
<z, s>(q_gen_2612) -> q_gen_2622
<z, s, s>(q_gen_2603) -> q_gen_2598
<z, z, z>() -> q_gen_2598
<s, s, s>(q_gen_2611) -> q_gen_2605
<s, z, s>(q_gen_2603) -> q_gen_2605
<s, s, s>(q_gen_2605) -> q_gen_2611
<s, s, s>(q_gen_2615) -> q_gen_2611
<s, z, s>(q_gen_2622) -> q_gen_2611
<z, s, s>(q_gen_2622) -> q_gen_2611
<z, z, s>(q_gen_2612) -> q_gen_2611
<s, s, s>(q_gen_2598) -> q_gen_2615
<z, z, s>(q_gen_2629) -> q_gen_2615
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 54  ;  () -> minus([z, y, z]) -> 54  ;  () -> plus([n, z, n]) -> 54  ;  (minus([_oc, n, _pc]) /\ plus([m, n, _oc])) -> eq_nat([_pc, m]) -> 58  ;  (minus([u, x2, _ec])) -> minus([s(u), s(x2), _ec]) -> 61  ;  (plus([n, mm, _jc])) -> plus([n, s(mm), s(_jc)]) -> 61
}
Sat witness: Yes: ((minus([u, x2, _ec])) -> minus([s(u), s(x2), _ec]), {
_ec -> s(z)  ;  u -> s(s(s(z)))  ;  x2 -> s(s(z))
})

-------------------------------------------
Step 66, which took 0.160273 s (model generation: 0.159349,  model checking: 0.000924):

Model:
|_
{
minus -> 
{{{
Q={q_gen_2599, q_gen_2601, q_gen_2607, q_gen_2614, q_gen_2619, q_gen_2624, q_gen_2647, q_gen_2668},
Q_f={q_gen_2599},
Delta=
{
<s>(q_gen_2619) -> q_gen_2607
<z>() -> q_gen_2607
<s>(q_gen_2607) -> q_gen_2619
<s, s>(q_gen_2601) -> q_gen_2601
<s, z>(q_gen_2619) -> q_gen_2601
<z, s>(q_gen_2619) -> q_gen_2601
<z, z>() -> q_gen_2601
<s, s>(q_gen_2624) -> q_gen_2624
<z, s>(q_gen_2607) -> q_gen_2624
<s, s>(q_gen_2647) -> q_gen_2647
<s, z>(q_gen_2607) -> q_gen_2647
<s, s, s>(q_gen_2614) -> q_gen_2599
<s, s, z>(q_gen_2601) -> q_gen_2599
<s, s, z>(q_gen_2624) -> q_gen_2599
<s, z, s>(q_gen_2601) -> q_gen_2599
<z, s, z>(q_gen_2607) -> q_gen_2599
<z, s, z>(q_gen_2619) -> q_gen_2599
<z, z, z>() -> q_gen_2599
<s, s, s>(q_gen_2599) -> q_gen_2614
<s, s, s>(q_gen_2668) -> q_gen_2614
<s, s, z>(q_gen_2647) -> q_gen_2614
<s, z, s>(q_gen_2624) -> q_gen_2614
<s, z, s>(q_gen_2647) -> q_gen_2614
<s, z, z>(q_gen_2607) -> q_gen_2614
<s, z, z>(q_gen_2619) -> q_gen_2668
}

Datatype: <nat, nat, nat>
Convolution form: complete
}}}
  ;  plus -> 
{{{
Q={q_gen_2598, q_gen_2603, q_gen_2605, q_gen_2611, q_gen_2612, q_gen_2615, q_gen_2622, q_gen_2629},
Q_f={q_gen_2598, q_gen_2605},
Delta=
{
<s>(q_gen_2629) -> q_gen_2612
<z>() -> q_gen_2612
<s>(q_gen_2612) -> q_gen_2629
<s, s>(q_gen_2603) -> q_gen_2603
<z, s>(q_gen_2629) -> q_gen_2603
<z, z>() -> q_gen_2603
<s, s>(q_gen_2622) -> q_gen_2622
<z, s>(q_gen_2612) -> q_gen_2622
<z, s, s>(q_gen_2603) -> q_gen_2598
<z, z, z>() -> q_gen_2598
<s, s, s>(q_gen_2611) -> q_gen_2605
<s, z, s>(q_gen_2603) -> q_gen_2605
<s, s, s>(q_gen_2605) -> q_gen_2611
<s, s, s>(q_gen_2615) -> q_gen_2611
<s, z, s>(q_gen_2622) -> q_gen_2611
<z, s, s>(q_gen_2622) -> q_gen_2611
<z, z, s>(q_gen_2612) -> q_gen_2611
<s, s, s>(q_gen_2598) -> q_gen_2615
<z, z, s>(q_gen_2629) -> q_gen_2615
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 55  ;  () -> minus([z, y, z]) -> 55  ;  () -> plus([n, z, n]) -> 55  ;  (minus([_oc, n, _pc]) /\ plus([m, n, _oc])) -> eq_nat([_pc, m]) -> 61  ;  (minus([u, x2, _ec])) -> minus([s(u), s(x2), _ec]) -> 61  ;  (plus([n, mm, _jc])) -> plus([n, s(mm), s(_jc)]) -> 61
}
Sat witness: Yes: ((minus([_oc, n, _pc]) /\ plus([m, n, _oc])) -> eq_nat([_pc, m]), {
_oc -> s(z)  ;  _pc -> s(s(s(z)))  ;  m -> s(z)  ;  n -> z
})

-------------------------------------------
Step 67, which took 0.214821 s (model generation: 0.213963,  model checking: 0.000858):

Model:
|_
{
minus -> 
{{{
Q={q_gen_2599, q_gen_2601, q_gen_2607, q_gen_2614, q_gen_2619, q_gen_2624, q_gen_2625, q_gen_2647},
Q_f={q_gen_2599},
Delta=
{
<z>() -> q_gen_2607
<s>(q_gen_2607) -> q_gen_2619
<s>(q_gen_2619) -> q_gen_2619
<s, s>(q_gen_2601) -> q_gen_2601
<z, z>() -> q_gen_2601
<s, s>(q_gen_2624) -> q_gen_2624
<z, s>(q_gen_2607) -> q_gen_2624
<z, s>(q_gen_2619) -> q_gen_2624
<s, s>(q_gen_2647) -> q_gen_2647
<s, z>(q_gen_2607) -> q_gen_2647
<s, z>(q_gen_2619) -> q_gen_2647
<s, s, s>(q_gen_2614) -> q_gen_2599
<s, s, z>(q_gen_2601) -> q_gen_2599
<s, s, z>(q_gen_2624) -> q_gen_2599
<s, z, s>(q_gen_2601) -> q_gen_2599
<z, s, z>(q_gen_2607) -> q_gen_2599
<z, s, z>(q_gen_2619) -> q_gen_2599
<z, z, z>() -> q_gen_2599
<s, s, s>(q_gen_2625) -> q_gen_2614
<s, s, z>(q_gen_2647) -> q_gen_2614
<s, z, s>(q_gen_2647) -> q_gen_2614
<s, z, z>(q_gen_2607) -> q_gen_2614
<s, s, s>(q_gen_2599) -> q_gen_2625
<s, z, s>(q_gen_2624) -> q_gen_2625
<s, z, z>(q_gen_2619) -> q_gen_2625
}

Datatype: <nat, nat, nat>
Convolution form: complete
}}}
  ;  plus -> 
{{{
Q={q_gen_2598, q_gen_2603, q_gen_2610, q_gen_2611, q_gen_2612, q_gen_2615, q_gen_2622, q_gen_2629},
Q_f={q_gen_2598, q_gen_2610},
Delta=
{
<z>() -> q_gen_2612
<s>(q_gen_2612) -> q_gen_2629
<s>(q_gen_2629) -> q_gen_2629
<s, s>(q_gen_2603) -> q_gen_2603
<z, z>() -> q_gen_2603
<s, s>(q_gen_2622) -> q_gen_2622
<z, s>(q_gen_2612) -> q_gen_2622
<z, s>(q_gen_2629) -> q_gen_2622
<s, s, s>(q_gen_2610) -> q_gen_2598
<s, z, s>(q_gen_2603) -> q_gen_2598
<z, s, s>(q_gen_2603) -> q_gen_2598
<z, z, z>() -> q_gen_2598
<s, s, s>(q_gen_2611) -> q_gen_2610
<s, s, s>(q_gen_2615) -> q_gen_2611
<s, z, s>(q_gen_2622) -> q_gen_2611
<z, s, s>(q_gen_2622) -> q_gen_2611
<z, z, s>(q_gen_2612) -> q_gen_2611
<s, s, s>(q_gen_2598) -> q_gen_2615
<z, z, s>(q_gen_2629) -> q_gen_2615
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 56  ;  () -> minus([z, y, z]) -> 56  ;  () -> plus([n, z, n]) -> 56  ;  (minus([_oc, n, _pc]) /\ plus([m, n, _oc])) -> eq_nat([_pc, m]) -> 61  ;  (minus([u, x2, _ec])) -> minus([s(u), s(x2), _ec]) -> 61  ;  (plus([n, mm, _jc])) -> plus([n, s(mm), s(_jc)]) -> 64
}
Sat witness: Yes: ((plus([n, mm, _jc])) -> plus([n, s(mm), s(_jc)]), {
_jc -> s(s(s(s(z))))  ;  mm -> s(s(s(z)))  ;  n -> s(s(s(s(z))))
})

-------------------------------------------
Step 68, which took 0.261613 s (model generation: 0.260875,  model checking: 0.000738):

Model:
|_
{
minus -> 
{{{
Q={q_gen_2599, q_gen_2601, q_gen_2607, q_gen_2614, q_gen_2619, q_gen_2624, q_gen_2625, q_gen_2647},
Q_f={q_gen_2599},
Delta=
{
<z>() -> q_gen_2607
<s>(q_gen_2607) -> q_gen_2619
<s>(q_gen_2619) -> q_gen_2619
<s, s>(q_gen_2601) -> q_gen_2601
<s, z>(q_gen_2619) -> q_gen_2601
<z, z>() -> q_gen_2601
<s, s>(q_gen_2624) -> q_gen_2624
<z, s>(q_gen_2607) -> q_gen_2624
<z, s>(q_gen_2619) -> q_gen_2624
<s, s>(q_gen_2647) -> q_gen_2647
<s, z>(q_gen_2607) -> q_gen_2647
<s, s, s>(q_gen_2614) -> q_gen_2599
<s, s, z>(q_gen_2601) -> q_gen_2599
<s, s, z>(q_gen_2624) -> q_gen_2599
<s, z, s>(q_gen_2601) -> q_gen_2599
<z, s, z>(q_gen_2607) -> q_gen_2599
<z, s, z>(q_gen_2619) -> q_gen_2599
<z, z, z>() -> q_gen_2599
<s, s, s>(q_gen_2625) -> q_gen_2614
<s, s, z>(q_gen_2647) -> q_gen_2614
<s, z, s>(q_gen_2647) -> q_gen_2614
<s, z, z>(q_gen_2607) -> q_gen_2614
<s, s, s>(q_gen_2599) -> q_gen_2625
<s, z, s>(q_gen_2624) -> q_gen_2625
<s, z, z>(q_gen_2619) -> q_gen_2625
}

Datatype: <nat, nat, nat>
Convolution form: complete
}}}
  ;  plus -> 
{{{
Q={q_gen_2598, q_gen_2603, q_gen_2610, q_gen_2611, q_gen_2612, q_gen_2615, q_gen_2622, q_gen_2629},
Q_f={q_gen_2598, q_gen_2610},
Delta=
{
<z>() -> q_gen_2612
<s>(q_gen_2612) -> q_gen_2629
<s>(q_gen_2629) -> q_gen_2629
<s, s>(q_gen_2603) -> q_gen_2603
<z, z>() -> q_gen_2603
<s, s>(q_gen_2622) -> q_gen_2622
<z, s>(q_gen_2612) -> q_gen_2622
<z, s>(q_gen_2629) -> q_gen_2622
<s, z, s>(q_gen_2603) -> q_gen_2598
<z, s, s>(q_gen_2603) -> q_gen_2598
<z, z, z>() -> q_gen_2598
<s, s, s>(q_gen_2610) -> q_gen_2610
<s, s, s>(q_gen_2611) -> q_gen_2610
<s, s, s>(q_gen_2615) -> q_gen_2611
<s, z, s>(q_gen_2622) -> q_gen_2611
<z, s, s>(q_gen_2622) -> q_gen_2611
<z, z, s>(q_gen_2612) -> q_gen_2611
<s, s, s>(q_gen_2598) -> q_gen_2615
<z, z, s>(q_gen_2629) -> q_gen_2615
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 57  ;  () -> minus([z, y, z]) -> 57  ;  () -> plus([n, z, n]) -> 57  ;  (minus([_oc, n, _pc]) /\ plus([m, n, _oc])) -> eq_nat([_pc, m]) -> 61  ;  (minus([u, x2, _ec])) -> minus([s(u), s(x2), _ec]) -> 64  ;  (plus([n, mm, _jc])) -> plus([n, s(mm), s(_jc)]) -> 64
}
Sat witness: Yes: ((minus([u, x2, _ec])) -> minus([s(u), s(x2), _ec]), {
_ec -> s(s(z))  ;  u -> s(s(s(s(z))))  ;  x2 -> z
})

-------------------------------------------
Step 69, which took 0.306196 s (model generation: 0.305398,  model checking: 0.000798):

Model:
|_
{
minus -> 
{{{
Q={q_gen_2599, q_gen_2601, q_gen_2607, q_gen_2614, q_gen_2619, q_gen_2624, q_gen_2625, q_gen_2647},
Q_f={q_gen_2599},
Delta=
{
<s>(q_gen_2619) -> q_gen_2607
<z>() -> q_gen_2607
<s>(q_gen_2607) -> q_gen_2619
<s, s>(q_gen_2601) -> q_gen_2601
<s, z>(q_gen_2619) -> q_gen_2601
<z, z>() -> q_gen_2601
<s, s>(q_gen_2624) -> q_gen_2624
<z, s>(q_gen_2607) -> q_gen_2624
<z, s>(q_gen_2619) -> q_gen_2624
<s, s>(q_gen_2647) -> q_gen_2647
<s, z>(q_gen_2607) -> q_gen_2647
<s, s, s>(q_gen_2614) -> q_gen_2599
<s, s, z>(q_gen_2601) -> q_gen_2599
<s, s, z>(q_gen_2624) -> q_gen_2599
<s, z, s>(q_gen_2601) -> q_gen_2599
<z, s, z>(q_gen_2607) -> q_gen_2599
<z, s, z>(q_gen_2619) -> q_gen_2599
<z, z, z>() -> q_gen_2599
<s, s, s>(q_gen_2625) -> q_gen_2614
<s, s, z>(q_gen_2647) -> q_gen_2614
<s, z, s>(q_gen_2647) -> q_gen_2614
<s, z, z>(q_gen_2607) -> q_gen_2614
<s, s, s>(q_gen_2599) -> q_gen_2625
<s, z, s>(q_gen_2624) -> q_gen_2625
<s, z, z>(q_gen_2619) -> q_gen_2625
}

Datatype: <nat, nat, nat>
Convolution form: complete
}}}
  ;  plus -> 
{{{
Q={q_gen_2598, q_gen_2603, q_gen_2610, q_gen_2611, q_gen_2612, q_gen_2615, q_gen_2622, q_gen_2629},
Q_f={q_gen_2598, q_gen_2610},
Delta=
{
<z>() -> q_gen_2612
<s>(q_gen_2612) -> q_gen_2629
<s>(q_gen_2629) -> q_gen_2629
<s, s>(q_gen_2603) -> q_gen_2603
<z, z>() -> q_gen_2603
<s, s>(q_gen_2622) -> q_gen_2622
<z, s>(q_gen_2612) -> q_gen_2622
<z, s>(q_gen_2629) -> q_gen_2622
<s, z, s>(q_gen_2603) -> q_gen_2598
<z, s, s>(q_gen_2603) -> q_gen_2598
<z, z, z>() -> q_gen_2598
<s, s, s>(q_gen_2610) -> q_gen_2610
<s, s, s>(q_gen_2611) -> q_gen_2610
<s, s, s>(q_gen_2615) -> q_gen_2611
<s, z, s>(q_gen_2622) -> q_gen_2611
<z, s, s>(q_gen_2622) -> q_gen_2611
<z, z, s>(q_gen_2612) -> q_gen_2611
<s, s, s>(q_gen_2598) -> q_gen_2615
<z, z, s>(q_gen_2629) -> q_gen_2615
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 58  ;  () -> minus([z, y, z]) -> 58  ;  () -> plus([n, z, n]) -> 58  ;  (minus([_oc, n, _pc]) /\ plus([m, n, _oc])) -> eq_nat([_pc, m]) -> 64  ;  (minus([u, x2, _ec])) -> minus([s(u), s(x2), _ec]) -> 64  ;  (plus([n, mm, _jc])) -> plus([n, s(mm), s(_jc)]) -> 64
}
Sat witness: Yes: ((minus([_oc, n, _pc]) /\ plus([m, n, _oc])) -> eq_nat([_pc, m]), {
_oc -> s(s(s(s(z))))  ;  _pc -> z  ;  m -> s(z)  ;  n -> s(s(z))
})

-------------------------------------------
Step 70, which took 0.257271 s (model generation: 0.256190,  model checking: 0.001081):

Model:
|_
{
minus -> 
{{{
Q={q_gen_2599, q_gen_2601, q_gen_2607, q_gen_2614, q_gen_2619, q_gen_2624, q_gen_2625, q_gen_2647},
Q_f={q_gen_2599},
Delta=
{
<z>() -> q_gen_2607
<s>(q_gen_2607) -> q_gen_2619
<s>(q_gen_2619) -> q_gen_2619
<s, s>(q_gen_2601) -> q_gen_2601
<z, z>() -> q_gen_2601
<s, s>(q_gen_2624) -> q_gen_2624
<z, s>(q_gen_2607) -> q_gen_2624
<z, s>(q_gen_2619) -> q_gen_2624
<s, s>(q_gen_2647) -> q_gen_2647
<s, z>(q_gen_2607) -> q_gen_2647
<s, z>(q_gen_2619) -> q_gen_2647
<s, s, s>(q_gen_2614) -> q_gen_2599
<s, s, z>(q_gen_2601) -> q_gen_2599
<s, s, z>(q_gen_2624) -> q_gen_2599
<s, z, s>(q_gen_2601) -> q_gen_2599
<z, s, z>(q_gen_2607) -> q_gen_2599
<z, s, z>(q_gen_2619) -> q_gen_2599
<z, z, z>() -> q_gen_2599
<s, s, s>(q_gen_2625) -> q_gen_2614
<s, s, z>(q_gen_2647) -> q_gen_2614
<s, z, s>(q_gen_2647) -> q_gen_2614
<s, z, z>(q_gen_2607) -> q_gen_2614
<s, s, s>(q_gen_2599) -> q_gen_2625
<s, z, s>(q_gen_2624) -> q_gen_2625
<s, z, z>(q_gen_2619) -> q_gen_2625
}

Datatype: <nat, nat, nat>
Convolution form: complete
}}}
  ;  plus -> 
{{{
Q={q_gen_2598, q_gen_2603, q_gen_2610, q_gen_2611, q_gen_2612, q_gen_2615, q_gen_2622, q_gen_2629},
Q_f={q_gen_2598, q_gen_2610},
Delta=
{
<z>() -> q_gen_2612
<s>(q_gen_2612) -> q_gen_2629
<s>(q_gen_2629) -> q_gen_2629
<s, s>(q_gen_2603) -> q_gen_2603
<z, z>() -> q_gen_2603
<s, s>(q_gen_2622) -> q_gen_2622
<z, s>(q_gen_2612) -> q_gen_2622
<z, s>(q_gen_2629) -> q_gen_2622
<s, z, s>(q_gen_2603) -> q_gen_2598
<z, s, s>(q_gen_2603) -> q_gen_2598
<z, z, z>() -> q_gen_2598
<s, s, s>(q_gen_2610) -> q_gen_2610
<s, s, s>(q_gen_2611) -> q_gen_2610
<s, s, s>(q_gen_2615) -> q_gen_2611
<s, z, s>(q_gen_2622) -> q_gen_2611
<z, s, s>(q_gen_2622) -> q_gen_2611
<z, z, s>(q_gen_2612) -> q_gen_2611
<s, s, s>(q_gen_2598) -> q_gen_2615
<z, z, s>(q_gen_2629) -> q_gen_2615
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 59  ;  () -> minus([z, y, z]) -> 59  ;  () -> plus([n, z, n]) -> 59  ;  (minus([_oc, n, _pc]) /\ plus([m, n, _oc])) -> eq_nat([_pc, m]) -> 64  ;  (minus([u, x2, _ec])) -> minus([s(u), s(x2), _ec]) -> 67  ;  (plus([n, mm, _jc])) -> plus([n, s(mm), s(_jc)]) -> 65
}
Sat witness: Yes: ((minus([u, x2, _ec])) -> minus([s(u), s(x2), _ec]), {
_ec -> s(s(s(z)))  ;  u -> s(s(s(s(z))))  ;  x2 -> s(z)
})

-------------------------------------------
Step 71, which took 0.224674 s (model generation: 0.224103,  model checking: 0.000571):

Model:
|_
{
minus -> 
{{{
Q={q_gen_2599, q_gen_2601, q_gen_2607, q_gen_2614, q_gen_2619, q_gen_2624, q_gen_2625, q_gen_2647},
Q_f={q_gen_2599},
Delta=
{
<z>() -> q_gen_2607
<s>(q_gen_2607) -> q_gen_2619
<s>(q_gen_2619) -> q_gen_2619
<s, s>(q_gen_2601) -> q_gen_2601
<z, z>() -> q_gen_2601
<s, s>(q_gen_2624) -> q_gen_2624
<s, z>(q_gen_2619) -> q_gen_2624
<z, s>(q_gen_2607) -> q_gen_2624
<z, s>(q_gen_2619) -> q_gen_2624
<s, s>(q_gen_2647) -> q_gen_2647
<s, z>(q_gen_2607) -> q_gen_2647
<s, s, s>(q_gen_2614) -> q_gen_2599
<s, s, z>(q_gen_2601) -> q_gen_2599
<s, s, z>(q_gen_2624) -> q_gen_2599
<s, z, s>(q_gen_2601) -> q_gen_2599
<z, s, z>(q_gen_2607) -> q_gen_2599
<z, s, z>(q_gen_2619) -> q_gen_2599
<z, z, z>() -> q_gen_2599
<s, s, s>(q_gen_2625) -> q_gen_2614
<s, s, z>(q_gen_2647) -> q_gen_2614
<s, z, s>(q_gen_2647) -> q_gen_2614
<s, z, z>(q_gen_2607) -> q_gen_2614
<s, s, s>(q_gen_2599) -> q_gen_2625
<s, z, s>(q_gen_2624) -> q_gen_2625
<s, z, z>(q_gen_2619) -> q_gen_2625
}

Datatype: <nat, nat, nat>
Convolution form: complete
}}}
  ;  plus -> 
{{{
Q={q_gen_2598, q_gen_2603, q_gen_2605, q_gen_2611, q_gen_2612, q_gen_2615, q_gen_2622, q_gen_2629},
Q_f={q_gen_2598, q_gen_2605},
Delta=
{
<s>(q_gen_2629) -> q_gen_2612
<z>() -> q_gen_2612
<s>(q_gen_2612) -> q_gen_2629
<s, s>(q_gen_2603) -> q_gen_2603
<z, s>(q_gen_2629) -> q_gen_2603
<z, z>() -> q_gen_2603
<s, s>(q_gen_2622) -> q_gen_2622
<z, s>(q_gen_2612) -> q_gen_2622
<z, s, s>(q_gen_2603) -> q_gen_2598
<z, z, z>() -> q_gen_2598
<s, s, s>(q_gen_2611) -> q_gen_2605
<s, z, s>(q_gen_2603) -> q_gen_2605
<s, s, s>(q_gen_2605) -> q_gen_2611
<s, s, s>(q_gen_2615) -> q_gen_2611
<s, z, s>(q_gen_2622) -> q_gen_2611
<z, s, s>(q_gen_2622) -> q_gen_2611
<z, z, s>(q_gen_2612) -> q_gen_2611
<s, s, s>(q_gen_2598) -> q_gen_2615
<z, z, s>(q_gen_2629) -> q_gen_2615
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 60  ;  () -> minus([z, y, z]) -> 60  ;  () -> plus([n, z, n]) -> 60  ;  (minus([_oc, n, _pc]) /\ plus([m, n, _oc])) -> eq_nat([_pc, m]) -> 67  ;  (minus([u, x2, _ec])) -> minus([s(u), s(x2), _ec]) -> 67  ;  (plus([n, mm, _jc])) -> plus([n, s(mm), s(_jc)]) -> 65
}
Sat witness: Yes: ((minus([_oc, n, _pc]) /\ plus([m, n, _oc])) -> eq_nat([_pc, m]), {
_oc -> s(s(s(z)))  ;  _pc -> z  ;  m -> s(s(z))  ;  n -> s(z)
})

-------------------------------------------
Step 72, which took 0.331301 s (model generation: 0.330215,  model checking: 0.001086):

Model:
|_
{
minus -> 
{{{
Q={q_gen_2599, q_gen_2600, q_gen_2601, q_gen_2607, q_gen_2614, q_gen_2619, q_gen_2624, q_gen_2647, q_gen_2668},
Q_f={q_gen_2599, q_gen_2600},
Delta=
{
<s>(q_gen_2619) -> q_gen_2607
<z>() -> q_gen_2607
<s>(q_gen_2607) -> q_gen_2619
<s, s>(q_gen_2601) -> q_gen_2601
<z, z>() -> q_gen_2601
<s, s>(q_gen_2624) -> q_gen_2624
<z, s>(q_gen_2607) -> q_gen_2624
<z, s>(q_gen_2619) -> q_gen_2624
<s, s>(q_gen_2647) -> q_gen_2647
<s, z>(q_gen_2607) -> q_gen_2647
<s, z>(q_gen_2619) -> q_gen_2647
<s, s, s>(q_gen_2600) -> q_gen_2599
<s, s, z>(q_gen_2601) -> q_gen_2599
<z, s, z>(q_gen_2607) -> q_gen_2599
<z, s, z>(q_gen_2619) -> q_gen_2599
<z, z, z>() -> q_gen_2599
<s, s, s>(q_gen_2614) -> q_gen_2600
<s, s, z>(q_gen_2624) -> q_gen_2600
<s, z, s>(q_gen_2601) -> q_gen_2600
<s, s, s>(q_gen_2599) -> q_gen_2614
<s, s, s>(q_gen_2668) -> q_gen_2614
<s, s, z>(q_gen_2647) -> q_gen_2614
<s, z, s>(q_gen_2624) -> q_gen_2614
<s, z, s>(q_gen_2647) -> q_gen_2614
<s, z, z>(q_gen_2607) -> q_gen_2614
<s, z, z>(q_gen_2619) -> q_gen_2668
}

Datatype: <nat, nat, nat>
Convolution form: complete
}}}
  ;  plus -> 
{{{
Q={q_gen_2598, q_gen_2603, q_gen_2610, q_gen_2611, q_gen_2612, q_gen_2615, q_gen_2622, q_gen_2629},
Q_f={q_gen_2598, q_gen_2610},
Delta=
{
<z>() -> q_gen_2612
<s>(q_gen_2612) -> q_gen_2629
<s>(q_gen_2629) -> q_gen_2629
<s, s>(q_gen_2603) -> q_gen_2603
<z, z>() -> q_gen_2603
<s, s>(q_gen_2622) -> q_gen_2622
<z, s>(q_gen_2612) -> q_gen_2622
<z, s>(q_gen_2629) -> q_gen_2622
<s, z, s>(q_gen_2603) -> q_gen_2598
<z, s, s>(q_gen_2603) -> q_gen_2598
<z, z, z>() -> q_gen_2598
<s, s, s>(q_gen_2610) -> q_gen_2610
<s, s, s>(q_gen_2611) -> q_gen_2610
<s, s, s>(q_gen_2615) -> q_gen_2611
<s, z, s>(q_gen_2622) -> q_gen_2611
<z, s, s>(q_gen_2622) -> q_gen_2611
<z, z, s>(q_gen_2612) -> q_gen_2611
<s, s, s>(q_gen_2598) -> q_gen_2615
<z, z, s>(q_gen_2629) -> q_gen_2615
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 61  ;  () -> minus([z, y, z]) -> 61  ;  () -> plus([n, z, n]) -> 61  ;  (minus([_oc, n, _pc]) /\ plus([m, n, _oc])) -> eq_nat([_pc, m]) -> 67  ;  (minus([u, x2, _ec])) -> minus([s(u), s(x2), _ec]) -> 70  ;  (plus([n, mm, _jc])) -> plus([n, s(mm), s(_jc)]) -> 66
}
Sat witness: Yes: ((minus([u, x2, _ec])) -> minus([s(u), s(x2), _ec]), {
_ec -> s(s(z))  ;  u -> s(s(z))  ;  x2 -> s(s(s(z)))
})

-------------------------------------------
Step 73, which took 0.289656 s (model generation: 0.288525,  model checking: 0.001131):

Model:
|_
{
minus -> 
{{{
Q={q_gen_2599, q_gen_2601, q_gen_2607, q_gen_2614, q_gen_2619, q_gen_2623, q_gen_2624, q_gen_2625, q_gen_2647},
Q_f={q_gen_2599, q_gen_2623},
Delta=
{
<z>() -> q_gen_2607
<s>(q_gen_2607) -> q_gen_2619
<s>(q_gen_2619) -> q_gen_2619
<s, s>(q_gen_2601) -> q_gen_2601
<z, z>() -> q_gen_2601
<s, s>(q_gen_2624) -> q_gen_2624
<z, s>(q_gen_2607) -> q_gen_2624
<z, s>(q_gen_2619) -> q_gen_2624
<s, s>(q_gen_2647) -> q_gen_2647
<s, z>(q_gen_2607) -> q_gen_2647
<s, z>(q_gen_2619) -> q_gen_2647
<s, s, s>(q_gen_2614) -> q_gen_2599
<s, s, z>(q_gen_2601) -> q_gen_2599
<s, z, s>(q_gen_2601) -> q_gen_2599
<z, s, z>(q_gen_2607) -> q_gen_2599
<z, s, z>(q_gen_2619) -> q_gen_2599
<z, z, z>() -> q_gen_2599
<s, s, s>(q_gen_2625) -> q_gen_2614
<s, s, z>(q_gen_2647) -> q_gen_2614
<s, z, z>(q_gen_2607) -> q_gen_2614
<s, s, s>(q_gen_2623) -> q_gen_2623
<s, s, z>(q_gen_2624) -> q_gen_2623
<s, z, s>(q_gen_2647) -> q_gen_2623
<s, s, s>(q_gen_2599) -> q_gen_2625
<s, z, s>(q_gen_2624) -> q_gen_2625
<s, z, z>(q_gen_2619) -> q_gen_2625
}

Datatype: <nat, nat, nat>
Convolution form: complete
}}}
  ;  plus -> 
{{{
Q={q_gen_2598, q_gen_2603, q_gen_2610, q_gen_2611, q_gen_2612, q_gen_2615, q_gen_2622, q_gen_2629},
Q_f={q_gen_2598, q_gen_2610},
Delta=
{
<s>(q_gen_2629) -> q_gen_2612
<z>() -> q_gen_2612
<s>(q_gen_2612) -> q_gen_2629
<s, s>(q_gen_2603) -> q_gen_2603
<z, z>() -> q_gen_2603
<s, s>(q_gen_2622) -> q_gen_2622
<z, s>(q_gen_2612) -> q_gen_2622
<z, s>(q_gen_2629) -> q_gen_2622
<s, z, s>(q_gen_2603) -> q_gen_2598
<z, s, s>(q_gen_2603) -> q_gen_2598
<z, z, z>() -> q_gen_2598
<s, s, s>(q_gen_2610) -> q_gen_2610
<s, s, s>(q_gen_2611) -> q_gen_2610
<s, s, s>(q_gen_2615) -> q_gen_2611
<s, z, s>(q_gen_2622) -> q_gen_2611
<z, s, s>(q_gen_2622) -> q_gen_2611
<z, z, s>(q_gen_2612) -> q_gen_2611
<s, s, s>(q_gen_2598) -> q_gen_2615
<z, z, s>(q_gen_2629) -> q_gen_2615
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 62  ;  () -> minus([z, y, z]) -> 62  ;  () -> plus([n, z, n]) -> 62  ;  (minus([_oc, n, _pc]) /\ plus([m, n, _oc])) -> eq_nat([_pc, m]) -> 70  ;  (minus([u, x2, _ec])) -> minus([s(u), s(x2), _ec]) -> 70  ;  (plus([n, mm, _jc])) -> plus([n, s(mm), s(_jc)]) -> 67
}
Sat witness: Yes: ((minus([_oc, n, _pc]) /\ plus([m, n, _oc])) -> eq_nat([_pc, m]), {
_oc -> s(s(s(s(z))))  ;  _pc -> s(s(z))  ;  m -> s(z)  ;  n -> s(z)
})

-------------------------------------------
Step 74, which took 0.378585 s (model generation: 0.377556,  model checking: 0.001029):

Model:
|_
{
minus -> 
{{{
Q={q_gen_2599, q_gen_2600, q_gen_2601, q_gen_2607, q_gen_2614, q_gen_2619, q_gen_2624, q_gen_2647, q_gen_2668},
Q_f={q_gen_2599, q_gen_2600},
Delta=
{
<s>(q_gen_2619) -> q_gen_2607
<z>() -> q_gen_2607
<s>(q_gen_2607) -> q_gen_2619
<s, s>(q_gen_2601) -> q_gen_2601
<z, z>() -> q_gen_2601
<s, s>(q_gen_2624) -> q_gen_2624
<z, s>(q_gen_2607) -> q_gen_2624
<z, s>(q_gen_2619) -> q_gen_2624
<s, s>(q_gen_2647) -> q_gen_2647
<s, z>(q_gen_2607) -> q_gen_2647
<s, z>(q_gen_2619) -> q_gen_2647
<s, s, z>(q_gen_2601) -> q_gen_2599
<z, s, z>(q_gen_2619) -> q_gen_2599
<z, z, z>() -> q_gen_2599
<s, s, s>(q_gen_2600) -> q_gen_2600
<s, s, s>(q_gen_2614) -> q_gen_2600
<s, s, z>(q_gen_2624) -> q_gen_2600
<s, z, s>(q_gen_2601) -> q_gen_2600
<s, z, s>(q_gen_2647) -> q_gen_2600
<z, s, z>(q_gen_2607) -> q_gen_2600
<s, s, s>(q_gen_2599) -> q_gen_2614
<s, s, s>(q_gen_2668) -> q_gen_2614
<s, s, z>(q_gen_2647) -> q_gen_2614
<s, z, s>(q_gen_2624) -> q_gen_2614
<s, z, z>(q_gen_2607) -> q_gen_2614
<s, z, z>(q_gen_2619) -> q_gen_2668
}

Datatype: <nat, nat, nat>
Convolution form: complete
}}}
  ;  plus -> 
{{{
Q={q_gen_2598, q_gen_2603, q_gen_2610, q_gen_2611, q_gen_2612, q_gen_2615, q_gen_2622, q_gen_2629},
Q_f={q_gen_2598, q_gen_2610},
Delta=
{
<z>() -> q_gen_2612
<s>(q_gen_2612) -> q_gen_2629
<s>(q_gen_2629) -> q_gen_2629
<s, s>(q_gen_2603) -> q_gen_2603
<z, z>() -> q_gen_2603
<s, s>(q_gen_2622) -> q_gen_2622
<z, s>(q_gen_2612) -> q_gen_2622
<z, s>(q_gen_2629) -> q_gen_2622
<s, z, s>(q_gen_2603) -> q_gen_2598
<z, s, s>(q_gen_2603) -> q_gen_2598
<z, z, z>() -> q_gen_2598
<s, s, s>(q_gen_2610) -> q_gen_2610
<s, s, s>(q_gen_2611) -> q_gen_2610
<s, s, s>(q_gen_2615) -> q_gen_2611
<s, z, s>(q_gen_2622) -> q_gen_2611
<z, s, s>(q_gen_2622) -> q_gen_2611
<z, z, s>(q_gen_2612) -> q_gen_2611
<s, s, s>(q_gen_2598) -> q_gen_2615
<z, z, s>(q_gen_2629) -> q_gen_2615
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 63  ;  () -> minus([z, y, z]) -> 63  ;  () -> plus([n, z, n]) -> 63  ;  (minus([_oc, n, _pc]) /\ plus([m, n, _oc])) -> eq_nat([_pc, m]) -> 70  ;  (minus([u, x2, _ec])) -> minus([s(u), s(x2), _ec]) -> 73  ;  (plus([n, mm, _jc])) -> plus([n, s(mm), s(_jc)]) -> 68
}
Sat witness: Yes: ((minus([u, x2, _ec])) -> minus([s(u), s(x2), _ec]), {
_ec -> s(z)  ;  u -> s(s(z))  ;  x2 -> z
})

-------------------------------------------
Step 75, which took 0.380614 s (model generation: 0.379349,  model checking: 0.001265):

Model:
|_
{
minus -> 
{{{
Q={q_gen_2599, q_gen_2600, q_gen_2601, q_gen_2607, q_gen_2614, q_gen_2619, q_gen_2624, q_gen_2630, q_gen_2647},
Q_f={q_gen_2599, q_gen_2600},
Delta=
{
<s>(q_gen_2619) -> q_gen_2607
<z>() -> q_gen_2607
<s>(q_gen_2607) -> q_gen_2619
<s, s>(q_gen_2601) -> q_gen_2601
<z, z>() -> q_gen_2601
<s, s>(q_gen_2624) -> q_gen_2624
<z, s>(q_gen_2607) -> q_gen_2624
<z, s>(q_gen_2619) -> q_gen_2624
<s, s>(q_gen_2647) -> q_gen_2647
<s, z>(q_gen_2607) -> q_gen_2647
<s, z>(q_gen_2619) -> q_gen_2647
<s, s, z>(q_gen_2601) -> q_gen_2599
<z, s, z>(q_gen_2619) -> q_gen_2599
<z, z, z>() -> q_gen_2599
<s, s, s>(q_gen_2600) -> q_gen_2600
<s, s, s>(q_gen_2614) -> q_gen_2600
<s, s, z>(q_gen_2624) -> q_gen_2600
<s, z, s>(q_gen_2601) -> q_gen_2600
<z, s, z>(q_gen_2607) -> q_gen_2600
<s, s, s>(q_gen_2599) -> q_gen_2614
<s, s, s>(q_gen_2630) -> q_gen_2614
<s, s, z>(q_gen_2647) -> q_gen_2614
<s, z, s>(q_gen_2647) -> q_gen_2614
<s, z, z>(q_gen_2607) -> q_gen_2614
<s, z, s>(q_gen_2624) -> q_gen_2630
<s, z, z>(q_gen_2619) -> q_gen_2630
}

Datatype: <nat, nat, nat>
Convolution form: complete
}}}
  ;  plus -> 
{{{
Q={q_gen_2598, q_gen_2603, q_gen_2610, q_gen_2611, q_gen_2612, q_gen_2615, q_gen_2622, q_gen_2629},
Q_f={q_gen_2598, q_gen_2610},
Delta=
{
<z>() -> q_gen_2612
<s>(q_gen_2612) -> q_gen_2629
<s>(q_gen_2629) -> q_gen_2629
<s, s>(q_gen_2603) -> q_gen_2603
<z, z>() -> q_gen_2603
<s, s>(q_gen_2622) -> q_gen_2622
<z, s>(q_gen_2612) -> q_gen_2622
<z, s>(q_gen_2629) -> q_gen_2622
<s, z, s>(q_gen_2603) -> q_gen_2598
<z, s, s>(q_gen_2603) -> q_gen_2598
<z, z, z>() -> q_gen_2598
<s, s, s>(q_gen_2610) -> q_gen_2610
<s, s, s>(q_gen_2611) -> q_gen_2610
<s, s, s>(q_gen_2615) -> q_gen_2611
<s, z, s>(q_gen_2622) -> q_gen_2611
<z, s, s>(q_gen_2622) -> q_gen_2611
<z, z, s>(q_gen_2612) -> q_gen_2611
<s, s, s>(q_gen_2598) -> q_gen_2615
<z, z, s>(q_gen_2629) -> q_gen_2615
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 64  ;  () -> minus([z, y, z]) -> 64  ;  () -> plus([n, z, n]) -> 64  ;  (minus([_oc, n, _pc]) /\ plus([m, n, _oc])) -> eq_nat([_pc, m]) -> 73  ;  (minus([u, x2, _ec])) -> minus([s(u), s(x2), _ec]) -> 73  ;  (plus([n, mm, _jc])) -> plus([n, s(mm), s(_jc)]) -> 69
}
Sat witness: Yes: ((minus([_oc, n, _pc]) /\ plus([m, n, _oc])) -> eq_nat([_pc, m]), {
_oc -> s(s(z))  ;  _pc -> s(s(z))  ;  m -> s(z)  ;  n -> s(z)
})

-------------------------------------------
Step 76, which took 0.448855 s (model generation: 0.447836,  model checking: 0.001019):

Model:
|_
{
minus -> 
{{{
Q={q_gen_2599, q_gen_2601, q_gen_2607, q_gen_2613, q_gen_2614, q_gen_2619, q_gen_2624, q_gen_2630, q_gen_2647},
Q_f={q_gen_2599, q_gen_2613},
Delta=
{
<s>(q_gen_2619) -> q_gen_2607
<z>() -> q_gen_2607
<s>(q_gen_2607) -> q_gen_2619
<s, s>(q_gen_2601) -> q_gen_2601
<z, z>() -> q_gen_2601
<s, s>(q_gen_2624) -> q_gen_2624
<z, s>(q_gen_2607) -> q_gen_2624
<z, s>(q_gen_2619) -> q_gen_2624
<s, s>(q_gen_2647) -> q_gen_2647
<s, z>(q_gen_2607) -> q_gen_2647
<s, z>(q_gen_2619) -> q_gen_2647
<s, s, s>(q_gen_2613) -> q_gen_2599
<s, s, z>(q_gen_2601) -> q_gen_2599
<s, s, z>(q_gen_2624) -> q_gen_2599
<s, z, s>(q_gen_2601) -> q_gen_2599
<z, s, z>(q_gen_2607) -> q_gen_2599
<z, s, z>(q_gen_2619) -> q_gen_2599
<z, z, z>() -> q_gen_2599
<s, s, s>(q_gen_2614) -> q_gen_2613
<s, s, s>(q_gen_2599) -> q_gen_2614
<s, s, s>(q_gen_2630) -> q_gen_2614
<s, s, z>(q_gen_2647) -> q_gen_2614
<s, z, s>(q_gen_2647) -> q_gen_2614
<s, z, z>(q_gen_2607) -> q_gen_2614
<s, z, s>(q_gen_2624) -> q_gen_2630
<s, z, z>(q_gen_2619) -> q_gen_2630
}

Datatype: <nat, nat, nat>
Convolution form: complete
}}}
  ;  plus -> 
{{{
Q={q_gen_2598, q_gen_2603, q_gen_2610, q_gen_2611, q_gen_2612, q_gen_2615, q_gen_2622, q_gen_2629},
Q_f={q_gen_2598, q_gen_2610},
Delta=
{
<z>() -> q_gen_2612
<s>(q_gen_2612) -> q_gen_2629
<s>(q_gen_2629) -> q_gen_2629
<s, s>(q_gen_2603) -> q_gen_2603
<z, z>() -> q_gen_2603
<s, s>(q_gen_2622) -> q_gen_2622
<z, s>(q_gen_2612) -> q_gen_2622
<z, s>(q_gen_2629) -> q_gen_2622
<s, z, s>(q_gen_2603) -> q_gen_2598
<z, s, s>(q_gen_2603) -> q_gen_2598
<z, z, z>() -> q_gen_2598
<s, s, s>(q_gen_2610) -> q_gen_2610
<s, s, s>(q_gen_2611) -> q_gen_2610
<s, s, s>(q_gen_2615) -> q_gen_2611
<s, z, s>(q_gen_2622) -> q_gen_2611
<z, s, s>(q_gen_2622) -> q_gen_2611
<z, z, s>(q_gen_2612) -> q_gen_2611
<s, s, s>(q_gen_2598) -> q_gen_2615
<z, z, s>(q_gen_2629) -> q_gen_2615
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 65  ;  () -> minus([z, y, z]) -> 65  ;  () -> plus([n, z, n]) -> 65  ;  (minus([_oc, n, _pc]) /\ plus([m, n, _oc])) -> eq_nat([_pc, m]) -> 73  ;  (minus([u, x2, _ec])) -> minus([s(u), s(x2), _ec]) -> 76  ;  (plus([n, mm, _jc])) -> plus([n, s(mm), s(_jc)]) -> 70
}
Sat witness: Yes: ((minus([u, x2, _ec])) -> minus([s(u), s(x2), _ec]), {
_ec -> s(s(s(z)))  ;  u -> s(s(s(z)))  ;  x2 -> s(s(z))
})

-------------------------------------------
Step 77, which took 0.446788 s (model generation: 0.445596,  model checking: 0.001192):

Model:
|_
{
minus -> 
{{{
Q={q_gen_2599, q_gen_2601, q_gen_2607, q_gen_2613, q_gen_2614, q_gen_2619, q_gen_2624, q_gen_2630, q_gen_2647},
Q_f={q_gen_2599, q_gen_2613},
Delta=
{
<s>(q_gen_2619) -> q_gen_2607
<z>() -> q_gen_2607
<s>(q_gen_2607) -> q_gen_2619
<s, s>(q_gen_2601) -> q_gen_2601
<z, z>() -> q_gen_2601
<s, s>(q_gen_2624) -> q_gen_2624
<z, s>(q_gen_2607) -> q_gen_2624
<z, s>(q_gen_2619) -> q_gen_2624
<s, s>(q_gen_2647) -> q_gen_2647
<s, z>(q_gen_2607) -> q_gen_2647
<s, z>(q_gen_2619) -> q_gen_2647
<s, s, z>(q_gen_2601) -> q_gen_2599
<s, s, z>(q_gen_2624) -> q_gen_2599
<s, z, s>(q_gen_2601) -> q_gen_2599
<z, s, z>(q_gen_2607) -> q_gen_2599
<z, s, z>(q_gen_2619) -> q_gen_2599
<z, z, z>() -> q_gen_2599
<s, s, s>(q_gen_2613) -> q_gen_2613
<s, s, s>(q_gen_2614) -> q_gen_2613
<s, s, s>(q_gen_2599) -> q_gen_2614
<s, s, s>(q_gen_2630) -> q_gen_2614
<s, s, z>(q_gen_2647) -> q_gen_2614
<s, z, s>(q_gen_2647) -> q_gen_2614
<s, z, z>(q_gen_2607) -> q_gen_2614
<s, z, s>(q_gen_2624) -> q_gen_2630
<s, z, z>(q_gen_2619) -> q_gen_2630
}

Datatype: <nat, nat, nat>
Convolution form: complete
}}}
  ;  plus -> 
{{{
Q={q_gen_2598, q_gen_2603, q_gen_2610, q_gen_2611, q_gen_2612, q_gen_2615, q_gen_2622, q_gen_2629},
Q_f={q_gen_2598, q_gen_2610},
Delta=
{
<z>() -> q_gen_2612
<s>(q_gen_2612) -> q_gen_2629
<s>(q_gen_2629) -> q_gen_2629
<s, s>(q_gen_2603) -> q_gen_2603
<z, z>() -> q_gen_2603
<s, s>(q_gen_2622) -> q_gen_2622
<z, s>(q_gen_2612) -> q_gen_2622
<z, s>(q_gen_2629) -> q_gen_2622
<s, z, s>(q_gen_2603) -> q_gen_2598
<z, s, s>(q_gen_2603) -> q_gen_2598
<z, z, z>() -> q_gen_2598
<s, s, s>(q_gen_2610) -> q_gen_2610
<s, s, s>(q_gen_2611) -> q_gen_2610
<s, s, s>(q_gen_2615) -> q_gen_2611
<s, z, s>(q_gen_2622) -> q_gen_2611
<z, s, s>(q_gen_2622) -> q_gen_2611
<z, z, s>(q_gen_2612) -> q_gen_2611
<s, s, s>(q_gen_2598) -> q_gen_2615
<z, z, s>(q_gen_2629) -> q_gen_2615
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 66  ;  () -> minus([z, y, z]) -> 66  ;  () -> plus([n, z, n]) -> 66  ;  (minus([_oc, n, _pc]) /\ plus([m, n, _oc])) -> eq_nat([_pc, m]) -> 76  ;  (minus([u, x2, _ec])) -> minus([s(u), s(x2), _ec]) -> 76  ;  (plus([n, mm, _jc])) -> plus([n, s(mm), s(_jc)]) -> 71
}
Sat witness: Yes: ((minus([_oc, n, _pc]) /\ plus([m, n, _oc])) -> eq_nat([_pc, m]), {
_oc -> s(s(s(s(z))))  ;  _pc -> s(z)  ;  m -> s(s(s(z)))  ;  n -> s(s(s(z)))
})

-------------------------------------------
Step 78, which took 0.733457 s (model generation: 0.732820,  model checking: 0.000637):

Model:
|_
{
minus -> 
{{{
Q={q_gen_2599, q_gen_2601, q_gen_2606, q_gen_2607, q_gen_2614, q_gen_2619, q_gen_2624, q_gen_2647, q_gen_2668},
Q_f={q_gen_2599, q_gen_2606},
Delta=
{
<z>() -> q_gen_2607
<s>(q_gen_2607) -> q_gen_2619
<s>(q_gen_2619) -> q_gen_2619
<s, s>(q_gen_2601) -> q_gen_2601
<z, z>() -> q_gen_2601
<s, s>(q_gen_2624) -> q_gen_2624
<z, s>(q_gen_2607) -> q_gen_2624
<z, s>(q_gen_2619) -> q_gen_2624
<s, s>(q_gen_2647) -> q_gen_2647
<s, z>(q_gen_2607) -> q_gen_2647
<s, z>(q_gen_2619) -> q_gen_2647
<s, s, z>(q_gen_2601) -> q_gen_2599
<s, z, s>(q_gen_2601) -> q_gen_2599
<z, s, z>(q_gen_2619) -> q_gen_2599
<z, z, z>() -> q_gen_2599
<s, s, s>(q_gen_2606) -> q_gen_2606
<s, s, s>(q_gen_2614) -> q_gen_2606
<s, s, z>(q_gen_2624) -> q_gen_2606
<z, s, z>(q_gen_2607) -> q_gen_2606
<s, s, s>(q_gen_2599) -> q_gen_2614
<s, s, s>(q_gen_2668) -> q_gen_2614
<s, s, z>(q_gen_2647) -> q_gen_2614
<s, z, s>(q_gen_2624) -> q_gen_2614
<s, z, s>(q_gen_2647) -> q_gen_2614
<s, z, z>(q_gen_2607) -> q_gen_2614
<s, z, z>(q_gen_2619) -> q_gen_2668
}

Datatype: <nat, nat, nat>
Convolution form: complete
}}}
  ;  plus -> 
{{{
Q={q_gen_2598, q_gen_2603, q_gen_2611, q_gen_2612, q_gen_2615, q_gen_2620, q_gen_2621, q_gen_2622, q_gen_2629},
Q_f={q_gen_2598, q_gen_2620},
Delta=
{
<z>() -> q_gen_2612
<s>(q_gen_2612) -> q_gen_2629
<s>(q_gen_2629) -> q_gen_2629
<s, s>(q_gen_2603) -> q_gen_2603
<z, z>() -> q_gen_2603
<s, s>(q_gen_2622) -> q_gen_2622
<z, s>(q_gen_2612) -> q_gen_2622
<z, s>(q_gen_2629) -> q_gen_2622
<s, s, s>(q_gen_2611) -> q_gen_2598
<s, s, s>(q_gen_2620) -> q_gen_2598
<s, z, s>(q_gen_2603) -> q_gen_2598
<z, s, s>(q_gen_2603) -> q_gen_2598
<z, z, z>() -> q_gen_2598
<z, z, s>(q_gen_2612) -> q_gen_2611
<s, s, s>(q_gen_2598) -> q_gen_2615
<z, z, s>(q_gen_2629) -> q_gen_2615
<s, s, s>(q_gen_2621) -> q_gen_2620
<s, s, s>(q_gen_2615) -> q_gen_2621
<s, z, s>(q_gen_2622) -> q_gen_2621
<z, s, s>(q_gen_2622) -> q_gen_2621
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 67  ;  () -> minus([z, y, z]) -> 67  ;  () -> plus([n, z, n]) -> 67  ;  (minus([_oc, n, _pc]) /\ plus([m, n, _oc])) -> eq_nat([_pc, m]) -> 76  ;  (minus([u, x2, _ec])) -> minus([s(u), s(x2), _ec]) -> 76  ;  (plus([n, mm, _jc])) -> plus([n, s(mm), s(_jc)]) -> 74
}
Sat witness: Yes: ((plus([n, mm, _jc])) -> plus([n, s(mm), s(_jc)]), {
_jc -> s(s(s(s(s(z)))))  ;  mm -> s(s(s(z)))  ;  n -> s(s(s(s(s(z)))))
})

-------------------------------------------
Step 79, which took 1.021039 s (model generation: 1.019099,  model checking: 0.001940):

Model:
|_
{
minus -> 
{{{
Q={q_gen_2599, q_gen_2601, q_gen_2606, q_gen_2607, q_gen_2614, q_gen_2619, q_gen_2624, q_gen_2630, q_gen_2647},
Q_f={q_gen_2599, q_gen_2606},
Delta=
{
<z>() -> q_gen_2607
<s>(q_gen_2607) -> q_gen_2619
<s>(q_gen_2619) -> q_gen_2619
<s, s>(q_gen_2601) -> q_gen_2601
<z, z>() -> q_gen_2601
<s, s>(q_gen_2624) -> q_gen_2624
<z, s>(q_gen_2607) -> q_gen_2624
<z, s>(q_gen_2619) -> q_gen_2624
<s, s>(q_gen_2647) -> q_gen_2647
<s, z>(q_gen_2607) -> q_gen_2647
<s, z>(q_gen_2619) -> q_gen_2647
<s, s, z>(q_gen_2601) -> q_gen_2599
<s, z, s>(q_gen_2601) -> q_gen_2599
<z, s, z>(q_gen_2619) -> q_gen_2599
<z, z, z>() -> q_gen_2599
<s, s, s>(q_gen_2606) -> q_gen_2606
<s, s, s>(q_gen_2614) -> q_gen_2606
<s, s, z>(q_gen_2624) -> q_gen_2606
<z, s, z>(q_gen_2607) -> q_gen_2606
<s, s, s>(q_gen_2599) -> q_gen_2614
<s, s, s>(q_gen_2630) -> q_gen_2614
<s, s, z>(q_gen_2647) -> q_gen_2614
<s, z, s>(q_gen_2647) -> q_gen_2614
<s, z, z>(q_gen_2607) -> q_gen_2614
<s, z, s>(q_gen_2624) -> q_gen_2630
<s, z, z>(q_gen_2619) -> q_gen_2630
}

Datatype: <nat, nat, nat>
Convolution form: complete
}}}
  ;  plus -> 
{{{
Q={q_gen_2598, q_gen_2603, q_gen_2611, q_gen_2612, q_gen_2615, q_gen_2620, q_gen_2621, q_gen_2622, q_gen_2629},
Q_f={q_gen_2598, q_gen_2620},
Delta=
{
<z>() -> q_gen_2612
<s>(q_gen_2612) -> q_gen_2629
<s>(q_gen_2629) -> q_gen_2629
<s, s>(q_gen_2603) -> q_gen_2603
<z, z>() -> q_gen_2603
<s, s>(q_gen_2622) -> q_gen_2622
<z, s>(q_gen_2612) -> q_gen_2622
<z, s>(q_gen_2629) -> q_gen_2622
<s, s, s>(q_gen_2611) -> q_gen_2598
<s, z, s>(q_gen_2603) -> q_gen_2598
<z, s, s>(q_gen_2603) -> q_gen_2598
<z, z, z>() -> q_gen_2598
<z, z, s>(q_gen_2612) -> q_gen_2611
<s, s, s>(q_gen_2598) -> q_gen_2615
<z, z, s>(q_gen_2629) -> q_gen_2615
<s, s, s>(q_gen_2620) -> q_gen_2620
<s, s, s>(q_gen_2621) -> q_gen_2620
<s, s, s>(q_gen_2615) -> q_gen_2621
<s, z, s>(q_gen_2622) -> q_gen_2621
<z, s, s>(q_gen_2622) -> q_gen_2621
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 68  ;  () -> minus([z, y, z]) -> 68  ;  () -> plus([n, z, n]) -> 68  ;  (minus([_oc, n, _pc]) /\ plus([m, n, _oc])) -> eq_nat([_pc, m]) -> 79  ;  (minus([u, x2, _ec])) -> minus([s(u), s(x2), _ec]) -> 77  ;  (plus([n, mm, _jc])) -> plus([n, s(mm), s(_jc)]) -> 75
}
Sat witness: Yes: ((minus([_oc, n, _pc]) /\ plus([m, n, _oc])) -> eq_nat([_pc, m]), {
_oc -> s(s(s(z)))  ;  _pc -> s(s(z))  ;  m -> s(z)  ;  n -> s(s(z))
})

-------------------------------------------
Step 80, which took 0.492323 s (model generation: 0.491427,  model checking: 0.000896):

Model:
|_
{
minus -> 
{{{
Q={q_gen_2599, q_gen_2601, q_gen_2607, q_gen_2614, q_gen_2619, q_gen_2624, q_gen_2625, q_gen_2647, q_gen_2680},
Q_f={q_gen_2599},
Delta=
{
<s>(q_gen_2619) -> q_gen_2607
<z>() -> q_gen_2607
<s>(q_gen_2607) -> q_gen_2619
<s, s>(q_gen_2601) -> q_gen_2601
<z, z>() -> q_gen_2601
<s, s>(q_gen_2624) -> q_gen_2624
<z, s>(q_gen_2607) -> q_gen_2624
<z, s>(q_gen_2619) -> q_gen_2624
<s, s>(q_gen_2680) -> q_gen_2647
<s, z>(q_gen_2607) -> q_gen_2647
<s, s>(q_gen_2647) -> q_gen_2680
<s, z>(q_gen_2619) -> q_gen_2680
<s, s, s>(q_gen_2614) -> q_gen_2599
<s, s, z>(q_gen_2601) -> q_gen_2599
<s, s, z>(q_gen_2624) -> q_gen_2599
<s, z, s>(q_gen_2601) -> q_gen_2599
<s, z, s>(q_gen_2680) -> q_gen_2599
<z, s, z>(q_gen_2607) -> q_gen_2599
<z, s, z>(q_gen_2619) -> q_gen_2599
<z, z, z>() -> q_gen_2599
<s, s, s>(q_gen_2625) -> q_gen_2614
<s, s, z>(q_gen_2647) -> q_gen_2614
<s, s, z>(q_gen_2680) -> q_gen_2614
<s, z, s>(q_gen_2647) -> q_gen_2614
<s, z, z>(q_gen_2607) -> q_gen_2614
<s, s, s>(q_gen_2599) -> q_gen_2625
<s, z, s>(q_gen_2624) -> q_gen_2625
<s, z, z>(q_gen_2619) -> q_gen_2625
}

Datatype: <nat, nat, nat>
Convolution form: complete
}}}
  ;  plus -> 
{{{
Q={q_gen_2598, q_gen_2603, q_gen_2610, q_gen_2611, q_gen_2612, q_gen_2615, q_gen_2622, q_gen_2628, q_gen_2629},
Q_f={q_gen_2598, q_gen_2610},
Delta=
{
<z>() -> q_gen_2612
<s>(q_gen_2612) -> q_gen_2629
<s>(q_gen_2629) -> q_gen_2629
<s, s>(q_gen_2603) -> q_gen_2603
<z, z>() -> q_gen_2603
<s, s>(q_gen_2622) -> q_gen_2622
<z, s>(q_gen_2612) -> q_gen_2622
<z, s>(q_gen_2629) -> q_gen_2622
<s, s, s>(q_gen_2610) -> q_gen_2598
<s, z, s>(q_gen_2603) -> q_gen_2598
<z, s, s>(q_gen_2603) -> q_gen_2598
<z, z, z>() -> q_gen_2598
<s, s, s>(q_gen_2611) -> q_gen_2610
<s, s, s>(q_gen_2628) -> q_gen_2611
<s, z, s>(q_gen_2622) -> q_gen_2611
<z, s, s>(q_gen_2622) -> q_gen_2611
<z, z, s>(q_gen_2612) -> q_gen_2611
<s, s, s>(q_gen_2598) -> q_gen_2615
<s, s, s>(q_gen_2615) -> q_gen_2615
<z, z, s>(q_gen_2629) -> q_gen_2628
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 69  ;  () -> minus([z, y, z]) -> 69  ;  () -> plus([n, z, n]) -> 69  ;  (minus([_oc, n, _pc]) /\ plus([m, n, _oc])) -> eq_nat([_pc, m]) -> 79  ;  (minus([u, x2, _ec])) -> minus([s(u), s(x2), _ec]) -> 77  ;  (plus([n, mm, _jc])) -> plus([n, s(mm), s(_jc)]) -> 78
}
Sat witness: Yes: ((plus([n, mm, _jc])) -> plus([n, s(mm), s(_jc)]), {
_jc -> s(s(s(s(s(z)))))  ;  mm -> s(s(s(z)))  ;  n -> s(s(s(z)))
})

-------------------------------------------
Step 81, which took 0.743488 s (model generation: 0.742743,  model checking: 0.000745):

Model:
|_
{
minus -> 
{{{
Q={q_gen_2599, q_gen_2601, q_gen_2607, q_gen_2614, q_gen_2619, q_gen_2624, q_gen_2625, q_gen_2647, q_gen_2680},
Q_f={q_gen_2599},
Delta=
{
<z>() -> q_gen_2607
<s>(q_gen_2607) -> q_gen_2619
<s>(q_gen_2619) -> q_gen_2619
<s, s>(q_gen_2601) -> q_gen_2601
<z, z>() -> q_gen_2601
<s, s>(q_gen_2624) -> q_gen_2624
<s, s>(q_gen_2680) -> q_gen_2624
<z, s>(q_gen_2607) -> q_gen_2624
<z, s>(q_gen_2619) -> q_gen_2624
<s, z>(q_gen_2607) -> q_gen_2647
<s, s>(q_gen_2647) -> q_gen_2680
<s, z>(q_gen_2619) -> q_gen_2680
<s, s, s>(q_gen_2614) -> q_gen_2599
<s, s, z>(q_gen_2601) -> q_gen_2599
<s, s, z>(q_gen_2624) -> q_gen_2599
<s, z, s>(q_gen_2601) -> q_gen_2599
<s, z, s>(q_gen_2680) -> q_gen_2599
<z, s, z>(q_gen_2607) -> q_gen_2599
<z, s, z>(q_gen_2619) -> q_gen_2599
<z, z, z>() -> q_gen_2599
<s, s, s>(q_gen_2625) -> q_gen_2614
<s, s, z>(q_gen_2647) -> q_gen_2614
<s, s, z>(q_gen_2680) -> q_gen_2614
<s, z, s>(q_gen_2647) -> q_gen_2614
<s, z, z>(q_gen_2607) -> q_gen_2614
<s, s, s>(q_gen_2599) -> q_gen_2625
<s, z, s>(q_gen_2624) -> q_gen_2625
<s, z, z>(q_gen_2619) -> q_gen_2625
}

Datatype: <nat, nat, nat>
Convolution form: complete
}}}
  ;  plus -> 
{{{
Q={q_gen_2598, q_gen_2603, q_gen_2611, q_gen_2612, q_gen_2615, q_gen_2622, q_gen_2629, q_gen_2649, q_gen_2678},
Q_f={q_gen_2598},
Delta=
{
<z>() -> q_gen_2612
<s>(q_gen_2612) -> q_gen_2629
<s>(q_gen_2629) -> q_gen_2678
<s, s>(q_gen_2603) -> q_gen_2603
<z, z>() -> q_gen_2603
<s, s>(q_gen_2622) -> q_gen_2622
<z, s>(q_gen_2612) -> q_gen_2622
<z, s>(q_gen_2629) -> q_gen_2649
<s, s, s>(q_gen_2611) -> q_gen_2598
<s, z, s>(q_gen_2603) -> q_gen_2598
<z, s, s>(q_gen_2603) -> q_gen_2598
<z, z, s>(q_gen_2678) -> q_gen_2598
<z, z, z>() -> q_gen_2598
<s, s, s>(q_gen_2615) -> q_gen_2611
<s, z, s>(q_gen_2622) -> q_gen_2611
<z, s, s>(q_gen_2622) -> q_gen_2611
<z, z, s>(q_gen_2612) -> q_gen_2611
<s, s, s>(q_gen_2598) -> q_gen_2615
<s, z, s>(q_gen_2649) -> q_gen_2615
<z, s, s>(q_gen_2649) -> q_gen_2615
<z, z, s>(q_gen_2629) -> q_gen_2615
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 70  ;  () -> minus([z, y, z]) -> 70  ;  () -> plus([n, z, n]) -> 70  ;  (minus([_oc, n, _pc]) /\ plus([m, n, _oc])) -> eq_nat([_pc, m]) -> 79  ;  (minus([u, x2, _ec])) -> minus([s(u), s(x2), _ec]) -> 80  ;  (plus([n, mm, _jc])) -> plus([n, s(mm), s(_jc)]) -> 78
}
Sat witness: Yes: ((minus([u, x2, _ec])) -> minus([s(u), s(x2), _ec]), {
_ec -> s(s(z))  ;  u -> s(s(s(z)))  ;  x2 -> z
})

-------------------------------------------
Step 82, which took 0.837158 s (model generation: 0.835372,  model checking: 0.001786):

Model:
|_
{
minus -> 
{{{
Q={q_gen_2599, q_gen_2601, q_gen_2607, q_gen_2614, q_gen_2619, q_gen_2624, q_gen_2625, q_gen_2647, q_gen_2680},
Q_f={q_gen_2599},
Delta=
{
<s>(q_gen_2619) -> q_gen_2607
<z>() -> q_gen_2607
<s>(q_gen_2607) -> q_gen_2619
<s, s>(q_gen_2601) -> q_gen_2601
<z, z>() -> q_gen_2601
<s, s>(q_gen_2624) -> q_gen_2624
<z, s>(q_gen_2607) -> q_gen_2624
<z, s>(q_gen_2619) -> q_gen_2624
<s, s>(q_gen_2680) -> q_gen_2647
<s, z>(q_gen_2607) -> q_gen_2647
<s, s>(q_gen_2647) -> q_gen_2680
<s, z>(q_gen_2619) -> q_gen_2680
<s, s, s>(q_gen_2614) -> q_gen_2599
<s, s, z>(q_gen_2601) -> q_gen_2599
<s, s, z>(q_gen_2624) -> q_gen_2599
<s, z, s>(q_gen_2601) -> q_gen_2599
<z, s, z>(q_gen_2607) -> q_gen_2599
<z, s, z>(q_gen_2619) -> q_gen_2599
<z, z, z>() -> q_gen_2599
<s, s, s>(q_gen_2625) -> q_gen_2614
<s, s, z>(q_gen_2647) -> q_gen_2614
<s, s, z>(q_gen_2680) -> q_gen_2614
<s, z, s>(q_gen_2647) -> q_gen_2614
<s, z, z>(q_gen_2607) -> q_gen_2614
<s, s, s>(q_gen_2599) -> q_gen_2625
<s, z, s>(q_gen_2624) -> q_gen_2625
<s, z, s>(q_gen_2680) -> q_gen_2625
<s, z, z>(q_gen_2619) -> q_gen_2625
}

Datatype: <nat, nat, nat>
Convolution form: complete
}}}
  ;  plus -> 
{{{
Q={q_gen_2598, q_gen_2603, q_gen_2611, q_gen_2612, q_gen_2615, q_gen_2620, q_gen_2621, q_gen_2622, q_gen_2629},
Q_f={q_gen_2598, q_gen_2620},
Delta=
{
<z>() -> q_gen_2612
<s>(q_gen_2612) -> q_gen_2629
<s>(q_gen_2629) -> q_gen_2629
<s, s>(q_gen_2603) -> q_gen_2603
<z, z>() -> q_gen_2603
<s, s>(q_gen_2622) -> q_gen_2622
<z, s>(q_gen_2612) -> q_gen_2622
<z, s>(q_gen_2629) -> q_gen_2622
<s, s, s>(q_gen_2611) -> q_gen_2598
<s, z, s>(q_gen_2603) -> q_gen_2598
<z, s, s>(q_gen_2603) -> q_gen_2598
<z, z, z>() -> q_gen_2598
<z, z, s>(q_gen_2612) -> q_gen_2611
<s, s, s>(q_gen_2598) -> q_gen_2615
<z, z, s>(q_gen_2629) -> q_gen_2615
<s, s, s>(q_gen_2620) -> q_gen_2620
<s, s, s>(q_gen_2621) -> q_gen_2620
<s, s, s>(q_gen_2615) -> q_gen_2621
<s, z, s>(q_gen_2622) -> q_gen_2621
<z, s, s>(q_gen_2622) -> q_gen_2621
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 71  ;  () -> minus([z, y, z]) -> 71  ;  () -> plus([n, z, n]) -> 71  ;  (minus([_oc, n, _pc]) /\ plus([m, n, _oc])) -> eq_nat([_pc, m]) -> 82  ;  (minus([u, x2, _ec])) -> minus([s(u), s(x2), _ec]) -> 80  ;  (plus([n, mm, _jc])) -> plus([n, s(mm), s(_jc)]) -> 79
}
Sat witness: Yes: ((minus([_oc, n, _pc]) /\ plus([m, n, _oc])) -> eq_nat([_pc, m]), {
_oc -> s(s(s(z)))  ;  _pc -> s(s(s(s(z))))  ;  m -> s(z)  ;  n -> s(s(z))
})

-------------------------------------------
Step 83, which took 0.913620 s (model generation: 0.912403,  model checking: 0.001217):

Model:
|_
{
minus -> 
{{{
Q={q_gen_2599, q_gen_2601, q_gen_2607, q_gen_2614, q_gen_2619, q_gen_2624, q_gen_2630, q_gen_2647, q_gen_2668, q_gen_2680},
Q_f={q_gen_2599},
Delta=
{
<s>(q_gen_2619) -> q_gen_2607
<z>() -> q_gen_2607
<s>(q_gen_2607) -> q_gen_2619
<s, s>(q_gen_2601) -> q_gen_2601
<z, z>() -> q_gen_2601
<s, s>(q_gen_2624) -> q_gen_2624
<z, s>(q_gen_2607) -> q_gen_2624
<z, s>(q_gen_2619) -> q_gen_2624
<s, s>(q_gen_2680) -> q_gen_2647
<s, z>(q_gen_2607) -> q_gen_2647
<s, s>(q_gen_2647) -> q_gen_2680
<s, z>(q_gen_2619) -> q_gen_2680
<s, s, s>(q_gen_2614) -> q_gen_2599
<s, s, z>(q_gen_2601) -> q_gen_2599
<s, s, z>(q_gen_2624) -> q_gen_2599
<s, z, s>(q_gen_2601) -> q_gen_2599
<z, s, z>(q_gen_2607) -> q_gen_2599
<z, s, z>(q_gen_2619) -> q_gen_2599
<z, z, z>() -> q_gen_2599
<s, s, s>(q_gen_2599) -> q_gen_2614
<s, s, s>(q_gen_2668) -> q_gen_2614
<s, s, z>(q_gen_2647) -> q_gen_2614
<s, s, z>(q_gen_2680) -> q_gen_2614
<s, z, s>(q_gen_2647) -> q_gen_2614
<s, z, z>(q_gen_2607) -> q_gen_2614
<s, s, s>(q_gen_2630) -> q_gen_2630
<s, z, s>(q_gen_2624) -> q_gen_2630
<s, z, s>(q_gen_2680) -> q_gen_2630
<s, z, z>(q_gen_2619) -> q_gen_2668
}

Datatype: <nat, nat, nat>
Convolution form: complete
}}}
  ;  plus -> 
{{{
Q={q_gen_2598, q_gen_2603, q_gen_2611, q_gen_2612, q_gen_2615, q_gen_2620, q_gen_2621, q_gen_2622, q_gen_2629},
Q_f={q_gen_2598, q_gen_2620},
Delta=
{
<z>() -> q_gen_2612
<s>(q_gen_2612) -> q_gen_2629
<s>(q_gen_2629) -> q_gen_2629
<s, s>(q_gen_2603) -> q_gen_2603
<z, z>() -> q_gen_2603
<s, s>(q_gen_2622) -> q_gen_2622
<z, s>(q_gen_2612) -> q_gen_2622
<z, s>(q_gen_2629) -> q_gen_2622
<s, s, s>(q_gen_2611) -> q_gen_2598
<s, z, s>(q_gen_2603) -> q_gen_2598
<z, s, s>(q_gen_2603) -> q_gen_2598
<z, z, z>() -> q_gen_2598
<z, z, s>(q_gen_2612) -> q_gen_2611
<s, s, s>(q_gen_2598) -> q_gen_2615
<z, z, s>(q_gen_2629) -> q_gen_2615
<s, s, s>(q_gen_2620) -> q_gen_2620
<s, s, s>(q_gen_2621) -> q_gen_2620
<s, s, s>(q_gen_2615) -> q_gen_2621
<s, z, s>(q_gen_2622) -> q_gen_2621
<z, s, s>(q_gen_2622) -> q_gen_2621
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 72  ;  () -> minus([z, y, z]) -> 72  ;  () -> plus([n, z, n]) -> 72  ;  (minus([_oc, n, _pc]) /\ plus([m, n, _oc])) -> eq_nat([_pc, m]) -> 82  ;  (minus([u, x2, _ec])) -> minus([s(u), s(x2), _ec]) -> 83  ;  (plus([n, mm, _jc])) -> plus([n, s(mm), s(_jc)]) -> 80
}
Sat witness: Yes: ((minus([u, x2, _ec])) -> minus([s(u), s(x2), _ec]), {
_ec -> s(s(s(z)))  ;  u -> s(s(s(z)))  ;  x2 -> z
})

-------------------------------------------
Step 84, which took 1.343547 s (model generation: 1.342625,  model checking: 0.000922):

Model:
|_
{
minus -> 
{{{
Q={q_gen_2599, q_gen_2601, q_gen_2607, q_gen_2614, q_gen_2619, q_gen_2624, q_gen_2630, q_gen_2647, q_gen_2668, q_gen_2680},
Q_f={q_gen_2599},
Delta=
{
<z>() -> q_gen_2607
<s>(q_gen_2607) -> q_gen_2619
<s>(q_gen_2619) -> q_gen_2619
<s, s>(q_gen_2601) -> q_gen_2601
<z, z>() -> q_gen_2601
<s, s>(q_gen_2624) -> q_gen_2624
<z, s>(q_gen_2607) -> q_gen_2624
<z, s>(q_gen_2619) -> q_gen_2624
<s, s>(q_gen_2647) -> q_gen_2647
<s, s>(q_gen_2680) -> q_gen_2647
<s, z>(q_gen_2607) -> q_gen_2647
<s, z>(q_gen_2619) -> q_gen_2680
<s, s, s>(q_gen_2614) -> q_gen_2599
<s, s, z>(q_gen_2601) -> q_gen_2599
<s, s, z>(q_gen_2624) -> q_gen_2599
<s, z, s>(q_gen_2601) -> q_gen_2599
<s, z, s>(q_gen_2680) -> q_gen_2599
<z, s, z>(q_gen_2607) -> q_gen_2599
<z, s, z>(q_gen_2619) -> q_gen_2599
<z, z, z>() -> q_gen_2599
<s, s, s>(q_gen_2599) -> q_gen_2614
<s, s, s>(q_gen_2668) -> q_gen_2614
<s, s, z>(q_gen_2647) -> q_gen_2614
<s, s, z>(q_gen_2680) -> q_gen_2614
<s, z, s>(q_gen_2647) -> q_gen_2614
<s, z, z>(q_gen_2607) -> q_gen_2614
<s, s, s>(q_gen_2630) -> q_gen_2630
<s, z, s>(q_gen_2624) -> q_gen_2630
<s, z, z>(q_gen_2619) -> q_gen_2668
}

Datatype: <nat, nat, nat>
Convolution form: complete
}}}
  ;  plus -> 
{{{
Q={q_gen_2598, q_gen_2603, q_gen_2611, q_gen_2612, q_gen_2615, q_gen_2622, q_gen_2629, q_gen_2649, q_gen_2678},
Q_f={q_gen_2598},
Delta=
{
<z>() -> q_gen_2612
<s>(q_gen_2612) -> q_gen_2629
<s>(q_gen_2629) -> q_gen_2678
<s, s>(q_gen_2603) -> q_gen_2603
<z, z>() -> q_gen_2603
<s, s>(q_gen_2622) -> q_gen_2622
<z, s>(q_gen_2612) -> q_gen_2622
<z, s>(q_gen_2629) -> q_gen_2649
<s, s, s>(q_gen_2611) -> q_gen_2598
<s, z, s>(q_gen_2603) -> q_gen_2598
<z, s, s>(q_gen_2603) -> q_gen_2598
<z, s, s>(q_gen_2649) -> q_gen_2598
<z, z, s>(q_gen_2678) -> q_gen_2598
<z, z, z>() -> q_gen_2598
<s, s, s>(q_gen_2615) -> q_gen_2611
<s, z, s>(q_gen_2622) -> q_gen_2611
<z, s, s>(q_gen_2622) -> q_gen_2611
<z, z, s>(q_gen_2612) -> q_gen_2611
<s, s, s>(q_gen_2598) -> q_gen_2615
<s, z, s>(q_gen_2649) -> q_gen_2615
<z, z, s>(q_gen_2629) -> q_gen_2615
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 73  ;  () -> minus([z, y, z]) -> 73  ;  () -> plus([n, z, n]) -> 73  ;  (minus([_oc, n, _pc]) /\ plus([m, n, _oc])) -> eq_nat([_pc, m]) -> 82  ;  (minus([u, x2, _ec])) -> minus([s(u), s(x2), _ec]) -> 83  ;  (plus([n, mm, _jc])) -> plus([n, s(mm), s(_jc)]) -> 83
}
Sat witness: Yes: ((plus([n, mm, _jc])) -> plus([n, s(mm), s(_jc)]), {
_jc -> s(s(s(s(z))))  ;  mm -> s(s(z))  ;  n -> s(s(z))
})

-------------------------------------------
Step 85, which took 0.850430 s (model generation: 0.849352,  model checking: 0.001078):

Model:
|_
{
minus -> 
{{{
Q={q_gen_2599, q_gen_2601, q_gen_2607, q_gen_2614, q_gen_2619, q_gen_2624, q_gen_2630, q_gen_2647, q_gen_2668, q_gen_2680},
Q_f={q_gen_2599},
Delta=
{
<s>(q_gen_2619) -> q_gen_2607
<z>() -> q_gen_2607
<s>(q_gen_2607) -> q_gen_2619
<s, s>(q_gen_2601) -> q_gen_2601
<s, s>(q_gen_2680) -> q_gen_2601
<z, z>() -> q_gen_2601
<s, s>(q_gen_2624) -> q_gen_2624
<z, s>(q_gen_2607) -> q_gen_2624
<z, s>(q_gen_2619) -> q_gen_2624
<s, s>(q_gen_2647) -> q_gen_2647
<s, z>(q_gen_2607) -> q_gen_2647
<s, z>(q_gen_2619) -> q_gen_2680
<s, s, s>(q_gen_2614) -> q_gen_2599
<s, s, z>(q_gen_2601) -> q_gen_2599
<s, s, z>(q_gen_2624) -> q_gen_2599
<s, z, s>(q_gen_2601) -> q_gen_2599
<s, z, s>(q_gen_2680) -> q_gen_2599
<z, s, z>(q_gen_2607) -> q_gen_2599
<z, s, z>(q_gen_2619) -> q_gen_2599
<z, z, z>() -> q_gen_2599
<s, s, s>(q_gen_2599) -> q_gen_2614
<s, s, s>(q_gen_2668) -> q_gen_2614
<s, s, z>(q_gen_2647) -> q_gen_2614
<s, z, s>(q_gen_2647) -> q_gen_2614
<s, z, z>(q_gen_2607) -> q_gen_2614
<s, s, s>(q_gen_2630) -> q_gen_2630
<s, z, s>(q_gen_2624) -> q_gen_2630
<s, s, z>(q_gen_2680) -> q_gen_2668
<s, z, z>(q_gen_2619) -> q_gen_2668
}

Datatype: <nat, nat, nat>
Convolution form: complete
}}}
  ;  plus -> 
{{{
Q={q_gen_2598, q_gen_2603, q_gen_2611, q_gen_2612, q_gen_2615, q_gen_2622, q_gen_2629, q_gen_2649, q_gen_2678},
Q_f={q_gen_2598},
Delta=
{
<z>() -> q_gen_2612
<s>(q_gen_2612) -> q_gen_2629
<s>(q_gen_2629) -> q_gen_2678
<s, s>(q_gen_2603) -> q_gen_2603
<z, z>() -> q_gen_2603
<s, s>(q_gen_2622) -> q_gen_2622
<z, s>(q_gen_2612) -> q_gen_2622
<z, s>(q_gen_2629) -> q_gen_2649
<s, s, s>(q_gen_2611) -> q_gen_2598
<s, z, s>(q_gen_2603) -> q_gen_2598
<z, s, s>(q_gen_2603) -> q_gen_2598
<z, z, s>(q_gen_2678) -> q_gen_2598
<z, z, z>() -> q_gen_2598
<s, s, s>(q_gen_2615) -> q_gen_2611
<s, z, s>(q_gen_2622) -> q_gen_2611
<z, s, s>(q_gen_2622) -> q_gen_2611
<z, z, s>(q_gen_2612) -> q_gen_2611
<s, s, s>(q_gen_2598) -> q_gen_2615
<s, z, s>(q_gen_2649) -> q_gen_2615
<z, s, s>(q_gen_2649) -> q_gen_2615
<z, z, s>(q_gen_2629) -> q_gen_2615
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 74  ;  () -> minus([z, y, z]) -> 74  ;  () -> plus([n, z, n]) -> 74  ;  (minus([_oc, n, _pc]) /\ plus([m, n, _oc])) -> eq_nat([_pc, m]) -> 85  ;  (minus([u, x2, _ec])) -> minus([s(u), s(x2), _ec]) -> 83  ;  (plus([n, mm, _jc])) -> plus([n, s(mm), s(_jc)]) -> 83
}
Sat witness: Yes: ((minus([_oc, n, _pc]) /\ plus([m, n, _oc])) -> eq_nat([_pc, m]), {
_oc -> s(s(s(s(z))))  ;  _pc -> z  ;  m -> s(s(z))  ;  n -> s(s(z))
})

-------------------------------------------
Step 86, which took 1.047290 s (model generation: 1.045940,  model checking: 0.001350):

Model:
|_
{
minus -> 
{{{
Q={q_gen_2599, q_gen_2601, q_gen_2607, q_gen_2614, q_gen_2619, q_gen_2624, q_gen_2630, q_gen_2647, q_gen_2668, q_gen_2680},
Q_f={q_gen_2599},
Delta=
{
<s>(q_gen_2619) -> q_gen_2607
<z>() -> q_gen_2607
<s>(q_gen_2607) -> q_gen_2619
<s, s>(q_gen_2601) -> q_gen_2601
<z, z>() -> q_gen_2601
<s, s>(q_gen_2624) -> q_gen_2624
<z, s>(q_gen_2607) -> q_gen_2624
<z, s>(q_gen_2619) -> q_gen_2624
<s, s>(q_gen_2647) -> q_gen_2647
<s, z>(q_gen_2607) -> q_gen_2647
<s, s>(q_gen_2680) -> q_gen_2680
<s, z>(q_gen_2619) -> q_gen_2680
<s, s, s>(q_gen_2614) -> q_gen_2599
<s, s, z>(q_gen_2601) -> q_gen_2599
<s, s, z>(q_gen_2624) -> q_gen_2599
<s, z, s>(q_gen_2601) -> q_gen_2599
<s, z, s>(q_gen_2680) -> q_gen_2599
<z, s, z>(q_gen_2607) -> q_gen_2599
<z, s, z>(q_gen_2619) -> q_gen_2599
<z, z, z>() -> q_gen_2599
<s, s, s>(q_gen_2599) -> q_gen_2614
<s, s, s>(q_gen_2668) -> q_gen_2614
<s, s, z>(q_gen_2647) -> q_gen_2614
<s, z, s>(q_gen_2647) -> q_gen_2614
<s, z, z>(q_gen_2607) -> q_gen_2614
<s, s, s>(q_gen_2630) -> q_gen_2630
<s, z, s>(q_gen_2624) -> q_gen_2630
<s, s, z>(q_gen_2680) -> q_gen_2668
<s, z, z>(q_gen_2619) -> q_gen_2668
}

Datatype: <nat, nat, nat>
Convolution form: complete
}}}
  ;  plus -> 
{{{
Q={q_gen_2598, q_gen_2603, q_gen_2611, q_gen_2612, q_gen_2615, q_gen_2622, q_gen_2629, q_gen_2649, q_gen_2678},
Q_f={q_gen_2598},
Delta=
{
<z>() -> q_gen_2612
<s>(q_gen_2612) -> q_gen_2629
<s>(q_gen_2629) -> q_gen_2678
<s, s>(q_gen_2603) -> q_gen_2603
<z, z>() -> q_gen_2603
<s, s>(q_gen_2622) -> q_gen_2622
<z, s>(q_gen_2612) -> q_gen_2622
<z, s>(q_gen_2629) -> q_gen_2649
<s, s, s>(q_gen_2611) -> q_gen_2598
<s, z, s>(q_gen_2603) -> q_gen_2598
<z, s, s>(q_gen_2603) -> q_gen_2598
<z, z, s>(q_gen_2678) -> q_gen_2598
<z, z, z>() -> q_gen_2598
<s, s, s>(q_gen_2615) -> q_gen_2611
<s, z, s>(q_gen_2622) -> q_gen_2611
<z, s, s>(q_gen_2622) -> q_gen_2611
<z, z, s>(q_gen_2612) -> q_gen_2611
<s, s, s>(q_gen_2598) -> q_gen_2615
<s, z, s>(q_gen_2649) -> q_gen_2615
<z, s, s>(q_gen_2649) -> q_gen_2615
<z, z, s>(q_gen_2629) -> q_gen_2615
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 75  ;  () -> minus([z, y, z]) -> 75  ;  () -> plus([n, z, n]) -> 75  ;  (minus([_oc, n, _pc]) /\ plus([m, n, _oc])) -> eq_nat([_pc, m]) -> 85  ;  (minus([u, x2, _ec])) -> minus([s(u), s(x2), _ec]) -> 83  ;  (plus([n, mm, _jc])) -> plus([n, s(mm), s(_jc)]) -> 86
}
Sat witness: Yes: ((plus([n, mm, _jc])) -> plus([n, s(mm), s(_jc)]), {
_jc -> s(s(s(z)))  ;  mm -> z  ;  n -> z
})

-------------------------------------------
Step 87, which took 1.221926 s (model generation: 1.220676,  model checking: 0.001250):

Model:
|_
{
minus -> 
{{{
Q={q_gen_2599, q_gen_2601, q_gen_2607, q_gen_2614, q_gen_2619, q_gen_2624, q_gen_2630, q_gen_2647, q_gen_2668, q_gen_2680},
Q_f={q_gen_2599},
Delta=
{
<z>() -> q_gen_2607
<s>(q_gen_2607) -> q_gen_2619
<s>(q_gen_2619) -> q_gen_2619
<s, s>(q_gen_2601) -> q_gen_2601
<z, z>() -> q_gen_2601
<s, s>(q_gen_2624) -> q_gen_2624
<z, s>(q_gen_2607) -> q_gen_2624
<z, s>(q_gen_2619) -> q_gen_2624
<s, s>(q_gen_2647) -> q_gen_2647
<s, s>(q_gen_2680) -> q_gen_2647
<s, z>(q_gen_2607) -> q_gen_2647
<s, z>(q_gen_2619) -> q_gen_2680
<s, s, s>(q_gen_2614) -> q_gen_2599
<s, s, z>(q_gen_2601) -> q_gen_2599
<s, s, z>(q_gen_2624) -> q_gen_2599
<s, z, s>(q_gen_2601) -> q_gen_2599
<s, z, s>(q_gen_2680) -> q_gen_2599
<z, s, z>(q_gen_2607) -> q_gen_2599
<z, s, z>(q_gen_2619) -> q_gen_2599
<z, z, z>() -> q_gen_2599
<s, s, s>(q_gen_2599) -> q_gen_2614
<s, s, s>(q_gen_2668) -> q_gen_2614
<s, s, z>(q_gen_2647) -> q_gen_2614
<s, z, s>(q_gen_2647) -> q_gen_2614
<s, z, z>(q_gen_2607) -> q_gen_2614
<s, s, s>(q_gen_2630) -> q_gen_2630
<s, z, s>(q_gen_2624) -> q_gen_2630
<s, s, z>(q_gen_2680) -> q_gen_2668
<s, z, z>(q_gen_2619) -> q_gen_2668
}

Datatype: <nat, nat, nat>
Convolution form: complete
}}}
  ;  plus -> 
{{{
Q={q_gen_2598, q_gen_2603, q_gen_2611, q_gen_2612, q_gen_2615, q_gen_2622, q_gen_2629, q_gen_2649, q_gen_2678},
Q_f={q_gen_2598},
Delta=
{
<z>() -> q_gen_2612
<s>(q_gen_2612) -> q_gen_2629
<s>(q_gen_2629) -> q_gen_2678
<s, s>(q_gen_2603) -> q_gen_2603
<z, s>(q_gen_2678) -> q_gen_2603
<z, z>() -> q_gen_2603
<s, s>(q_gen_2622) -> q_gen_2622
<z, s>(q_gen_2612) -> q_gen_2622
<z, s>(q_gen_2629) -> q_gen_2649
<s, s, s>(q_gen_2611) -> q_gen_2598
<s, z, s>(q_gen_2603) -> q_gen_2598
<z, s, s>(q_gen_2603) -> q_gen_2598
<z, z, s>(q_gen_2678) -> q_gen_2598
<z, z, z>() -> q_gen_2598
<s, s, s>(q_gen_2615) -> q_gen_2611
<s, z, s>(q_gen_2622) -> q_gen_2611
<z, s, s>(q_gen_2622) -> q_gen_2611
<z, z, s>(q_gen_2612) -> q_gen_2611
<s, s, s>(q_gen_2598) -> q_gen_2615
<s, z, s>(q_gen_2649) -> q_gen_2615
<z, s, s>(q_gen_2649) -> q_gen_2615
<z, z, s>(q_gen_2629) -> q_gen_2615
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 76  ;  () -> minus([z, y, z]) -> 76  ;  () -> plus([n, z, n]) -> 76  ;  (minus([_oc, n, _pc]) /\ plus([m, n, _oc])) -> eq_nat([_pc, m]) -> 85  ;  (minus([u, x2, _ec])) -> minus([s(u), s(x2), _ec]) -> 86  ;  (plus([n, mm, _jc])) -> plus([n, s(mm), s(_jc)]) -> 86
}
Sat witness: Yes: ((minus([u, x2, _ec])) -> minus([s(u), s(x2), _ec]), {
_ec -> s(z)  ;  u -> s(s(s(z)))  ;  x2 -> z
})

-------------------------------------------
Step 88, which took 1.214486 s (model generation: 1.212939,  model checking: 0.001547):

Model:
|_
{
minus -> 
{{{
Q={q_gen_2599, q_gen_2601, q_gen_2607, q_gen_2614, q_gen_2619, q_gen_2624, q_gen_2630, q_gen_2647, q_gen_2668, q_gen_2680},
Q_f={q_gen_2599},
Delta=
{
<s>(q_gen_2619) -> q_gen_2607
<z>() -> q_gen_2607
<s>(q_gen_2607) -> q_gen_2619
<s, s>(q_gen_2601) -> q_gen_2601
<z, z>() -> q_gen_2601
<s, s>(q_gen_2624) -> q_gen_2624
<z, s>(q_gen_2607) -> q_gen_2624
<z, s>(q_gen_2619) -> q_gen_2624
<s, s>(q_gen_2647) -> q_gen_2647
<s, z>(q_gen_2607) -> q_gen_2647
<s, s>(q_gen_2680) -> q_gen_2680
<s, z>(q_gen_2619) -> q_gen_2680
<s, s, s>(q_gen_2614) -> q_gen_2599
<s, s, z>(q_gen_2601) -> q_gen_2599
<s, s, z>(q_gen_2624) -> q_gen_2599
<s, z, s>(q_gen_2601) -> q_gen_2599
<s, z, s>(q_gen_2680) -> q_gen_2599
<z, s, z>(q_gen_2607) -> q_gen_2599
<z, s, z>(q_gen_2619) -> q_gen_2599
<z, z, z>() -> q_gen_2599
<s, s, s>(q_gen_2599) -> q_gen_2614
<s, s, s>(q_gen_2668) -> q_gen_2614
<s, s, z>(q_gen_2647) -> q_gen_2614
<s, z, s>(q_gen_2647) -> q_gen_2614
<s, z, z>(q_gen_2607) -> q_gen_2614
<s, s, s>(q_gen_2630) -> q_gen_2630
<s, z, s>(q_gen_2624) -> q_gen_2630
<s, s, z>(q_gen_2680) -> q_gen_2668
<s, z, z>(q_gen_2619) -> q_gen_2668
}

Datatype: <nat, nat, nat>
Convolution form: complete
}}}
  ;  plus -> 
{{{
Q={q_gen_2598, q_gen_2603, q_gen_2611, q_gen_2612, q_gen_2615, q_gen_2620, q_gen_2621, q_gen_2622, q_gen_2629},
Q_f={q_gen_2598, q_gen_2620},
Delta=
{
<z>() -> q_gen_2612
<s>(q_gen_2612) -> q_gen_2629
<s>(q_gen_2629) -> q_gen_2629
<s, s>(q_gen_2603) -> q_gen_2603
<z, z>() -> q_gen_2603
<s, s>(q_gen_2622) -> q_gen_2622
<z, s>(q_gen_2612) -> q_gen_2622
<z, s>(q_gen_2629) -> q_gen_2622
<s, s, s>(q_gen_2611) -> q_gen_2598
<s, z, s>(q_gen_2603) -> q_gen_2598
<z, s, s>(q_gen_2603) -> q_gen_2598
<z, z, z>() -> q_gen_2598
<z, z, s>(q_gen_2612) -> q_gen_2611
<s, s, s>(q_gen_2598) -> q_gen_2615
<z, z, s>(q_gen_2629) -> q_gen_2615
<s, s, s>(q_gen_2620) -> q_gen_2620
<s, s, s>(q_gen_2621) -> q_gen_2620
<s, s, s>(q_gen_2615) -> q_gen_2621
<s, z, s>(q_gen_2622) -> q_gen_2621
<z, s, s>(q_gen_2622) -> q_gen_2621
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 77  ;  () -> minus([z, y, z]) -> 77  ;  () -> plus([n, z, n]) -> 77  ;  (minus([_oc, n, _pc]) /\ plus([m, n, _oc])) -> eq_nat([_pc, m]) -> 88  ;  (minus([u, x2, _ec])) -> minus([s(u), s(x2), _ec]) -> 86  ;  (plus([n, mm, _jc])) -> plus([n, s(mm), s(_jc)]) -> 86
}
Sat witness: Yes: ((minus([_oc, n, _pc]) /\ plus([m, n, _oc])) -> eq_nat([_pc, m]), {
_oc -> s(s(s(s(z))))  ;  _pc -> s(z)  ;  m -> s(s(z))  ;  n -> s(z)
})

-------------------------------------------
Step 89, which took 1.164547 s (model generation: 1.162866,  model checking: 0.001681):

Model:
|_
{
minus -> 
{{{
Q={q_gen_2599, q_gen_2601, q_gen_2607, q_gen_2614, q_gen_2619, q_gen_2624, q_gen_2630, q_gen_2647, q_gen_2668, q_gen_2680},
Q_f={q_gen_2599},
Delta=
{
<z>() -> q_gen_2607
<s>(q_gen_2607) -> q_gen_2619
<s>(q_gen_2619) -> q_gen_2619
<s, s>(q_gen_2601) -> q_gen_2601
<z, z>() -> q_gen_2601
<s, s>(q_gen_2624) -> q_gen_2624
<z, s>(q_gen_2607) -> q_gen_2624
<z, s>(q_gen_2619) -> q_gen_2624
<s, s>(q_gen_2647) -> q_gen_2647
<s, z>(q_gen_2607) -> q_gen_2647
<s, s>(q_gen_2680) -> q_gen_2680
<s, z>(q_gen_2619) -> q_gen_2680
<s, s, s>(q_gen_2614) -> q_gen_2599
<s, s, z>(q_gen_2601) -> q_gen_2599
<s, s, z>(q_gen_2624) -> q_gen_2599
<s, z, s>(q_gen_2601) -> q_gen_2599
<z, s, z>(q_gen_2607) -> q_gen_2599
<z, s, z>(q_gen_2619) -> q_gen_2599
<z, z, z>() -> q_gen_2599
<s, s, s>(q_gen_2599) -> q_gen_2614
<s, s, s>(q_gen_2668) -> q_gen_2614
<s, s, z>(q_gen_2647) -> q_gen_2614
<s, z, s>(q_gen_2647) -> q_gen_2614
<s, z, z>(q_gen_2607) -> q_gen_2614
<s, s, s>(q_gen_2630) -> q_gen_2630
<s, z, s>(q_gen_2624) -> q_gen_2630
<s, s, z>(q_gen_2680) -> q_gen_2668
<s, z, s>(q_gen_2680) -> q_gen_2668
<s, z, z>(q_gen_2619) -> q_gen_2668
}

Datatype: <nat, nat, nat>
Convolution form: complete
}}}
  ;  plus -> 
{{{
Q={q_gen_2598, q_gen_2603, q_gen_2611, q_gen_2612, q_gen_2615, q_gen_2620, q_gen_2621, q_gen_2622, q_gen_2629},
Q_f={q_gen_2598, q_gen_2620},
Delta=
{
<z>() -> q_gen_2612
<s>(q_gen_2612) -> q_gen_2629
<s>(q_gen_2629) -> q_gen_2629
<s, s>(q_gen_2603) -> q_gen_2603
<z, z>() -> q_gen_2603
<s, s>(q_gen_2622) -> q_gen_2622
<z, s>(q_gen_2612) -> q_gen_2622
<z, s>(q_gen_2629) -> q_gen_2622
<s, s, s>(q_gen_2611) -> q_gen_2598
<s, z, s>(q_gen_2603) -> q_gen_2598
<z, s, s>(q_gen_2603) -> q_gen_2598
<z, z, z>() -> q_gen_2598
<z, z, s>(q_gen_2612) -> q_gen_2611
<s, s, s>(q_gen_2598) -> q_gen_2615
<z, z, s>(q_gen_2629) -> q_gen_2615
<s, s, s>(q_gen_2620) -> q_gen_2620
<s, s, s>(q_gen_2621) -> q_gen_2620
<s, s, s>(q_gen_2615) -> q_gen_2621
<s, z, s>(q_gen_2622) -> q_gen_2621
<z, s, s>(q_gen_2622) -> q_gen_2621
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 78  ;  () -> minus([z, y, z]) -> 78  ;  () -> plus([n, z, n]) -> 78  ;  (minus([_oc, n, _pc]) /\ plus([m, n, _oc])) -> eq_nat([_pc, m]) -> 88  ;  (minus([u, x2, _ec])) -> minus([s(u), s(x2), _ec]) -> 89  ;  (plus([n, mm, _jc])) -> plus([n, s(mm), s(_jc)]) -> 87
}
Sat witness: Yes: ((minus([u, x2, _ec])) -> minus([s(u), s(x2), _ec]), {
_ec -> s(s(s(z)))  ;  u -> s(s(s(s(s(z)))))  ;  x2 -> s(s(z))
})

-------------------------------------------
Step 90, which took 1.139603 s (model generation: 1.138233,  model checking: 0.001370):

Model:
|_
{
minus -> 
{{{
Q={q_gen_2599, q_gen_2601, q_gen_2607, q_gen_2614, q_gen_2619, q_gen_2624, q_gen_2630, q_gen_2647, q_gen_2668, q_gen_2680},
Q_f={q_gen_2599},
Delta=
{
<s>(q_gen_2619) -> q_gen_2607
<z>() -> q_gen_2607
<s>(q_gen_2607) -> q_gen_2619
<s, s>(q_gen_2601) -> q_gen_2601
<z, z>() -> q_gen_2601
<s, s>(q_gen_2624) -> q_gen_2624
<z, s>(q_gen_2607) -> q_gen_2624
<z, s>(q_gen_2619) -> q_gen_2624
<s, s>(q_gen_2647) -> q_gen_2647
<s, s>(q_gen_2680) -> q_gen_2647
<s, z>(q_gen_2607) -> q_gen_2647
<s, z>(q_gen_2619) -> q_gen_2680
<s, s, s>(q_gen_2614) -> q_gen_2599
<s, s, z>(q_gen_2601) -> q_gen_2599
<s, s, z>(q_gen_2624) -> q_gen_2599
<s, z, s>(q_gen_2601) -> q_gen_2599
<s, z, s>(q_gen_2680) -> q_gen_2599
<z, s, z>(q_gen_2607) -> q_gen_2599
<z, s, z>(q_gen_2619) -> q_gen_2599
<z, z, z>() -> q_gen_2599
<s, s, s>(q_gen_2599) -> q_gen_2614
<s, s, s>(q_gen_2668) -> q_gen_2614
<s, s, z>(q_gen_2647) -> q_gen_2614
<s, z, s>(q_gen_2647) -> q_gen_2614
<s, z, z>(q_gen_2607) -> q_gen_2614
<s, s, s>(q_gen_2630) -> q_gen_2630
<s, z, s>(q_gen_2624) -> q_gen_2630
<s, s, z>(q_gen_2680) -> q_gen_2668
<s, z, z>(q_gen_2619) -> q_gen_2668
}

Datatype: <nat, nat, nat>
Convolution form: complete
}}}
  ;  plus -> 
{{{
Q={q_gen_2598, q_gen_2603, q_gen_2611, q_gen_2612, q_gen_2615, q_gen_2622, q_gen_2629, q_gen_2649, q_gen_2678},
Q_f={q_gen_2598},
Delta=
{
<z>() -> q_gen_2612
<s>(q_gen_2612) -> q_gen_2629
<s>(q_gen_2629) -> q_gen_2678
<s, s>(q_gen_2603) -> q_gen_2603
<z, s>(q_gen_2678) -> q_gen_2603
<z, z>() -> q_gen_2603
<s, s>(q_gen_2622) -> q_gen_2622
<z, s>(q_gen_2612) -> q_gen_2622
<z, s>(q_gen_2629) -> q_gen_2649
<s, s, s>(q_gen_2611) -> q_gen_2598
<s, z, s>(q_gen_2603) -> q_gen_2598
<z, s, s>(q_gen_2603) -> q_gen_2598
<z, z, s>(q_gen_2678) -> q_gen_2598
<z, z, z>() -> q_gen_2598
<s, s, s>(q_gen_2615) -> q_gen_2611
<s, z, s>(q_gen_2622) -> q_gen_2611
<z, s, s>(q_gen_2622) -> q_gen_2611
<z, z, s>(q_gen_2612) -> q_gen_2611
<s, s, s>(q_gen_2598) -> q_gen_2615
<s, z, s>(q_gen_2649) -> q_gen_2615
<z, s, s>(q_gen_2649) -> q_gen_2615
<z, z, s>(q_gen_2629) -> q_gen_2615
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 79  ;  () -> minus([z, y, z]) -> 79  ;  () -> plus([n, z, n]) -> 79  ;  (minus([_oc, n, _pc]) /\ plus([m, n, _oc])) -> eq_nat([_pc, m]) -> 88  ;  (minus([u, x2, _ec])) -> minus([s(u), s(x2), _ec]) -> 89  ;  (plus([n, mm, _jc])) -> plus([n, s(mm), s(_jc)]) -> 90
}
Sat witness: Yes: ((plus([n, mm, _jc])) -> plus([n, s(mm), s(_jc)]), {
_jc -> s(s(s(s(z))))  ;  mm -> z  ;  n -> s(z)
})

-------------------------------------------
Step 91, which took 1.668064 s (model generation: 1.667198,  model checking: 0.000866):

Model:
|_
{
minus -> 
{{{
Q={q_gen_2599, q_gen_2601, q_gen_2607, q_gen_2614, q_gen_2619, q_gen_2624, q_gen_2630, q_gen_2647, q_gen_2668, q_gen_2680},
Q_f={q_gen_2599},
Delta=
{
<s>(q_gen_2619) -> q_gen_2607
<z>() -> q_gen_2607
<s>(q_gen_2607) -> q_gen_2619
<s, s>(q_gen_2601) -> q_gen_2601
<z, z>() -> q_gen_2601
<s, s>(q_gen_2624) -> q_gen_2624
<z, s>(q_gen_2607) -> q_gen_2624
<z, s>(q_gen_2619) -> q_gen_2624
<s, s>(q_gen_2647) -> q_gen_2647
<s, z>(q_gen_2607) -> q_gen_2647
<s, s>(q_gen_2680) -> q_gen_2680
<s, z>(q_gen_2619) -> q_gen_2680
<s, s, s>(q_gen_2614) -> q_gen_2599
<s, s, z>(q_gen_2601) -> q_gen_2599
<s, s, z>(q_gen_2624) -> q_gen_2599
<s, z, s>(q_gen_2601) -> q_gen_2599
<s, z, s>(q_gen_2680) -> q_gen_2599
<z, s, z>(q_gen_2607) -> q_gen_2599
<z, s, z>(q_gen_2619) -> q_gen_2599
<z, z, z>() -> q_gen_2599
<s, s, s>(q_gen_2599) -> q_gen_2614
<s, s, s>(q_gen_2668) -> q_gen_2614
<s, s, z>(q_gen_2647) -> q_gen_2614
<s, z, s>(q_gen_2647) -> q_gen_2614
<s, z, z>(q_gen_2607) -> q_gen_2614
<s, s, s>(q_gen_2630) -> q_gen_2630
<s, z, s>(q_gen_2624) -> q_gen_2630
<s, s, z>(q_gen_2680) -> q_gen_2668
<s, z, z>(q_gen_2619) -> q_gen_2668
}

Datatype: <nat, nat, nat>
Convolution form: complete
}}}
  ;  plus -> 
{{{
Q={q_gen_2598, q_gen_2603, q_gen_2611, q_gen_2612, q_gen_2615, q_gen_2622, q_gen_2629, q_gen_2649, q_gen_2678},
Q_f={q_gen_2598},
Delta=
{
<s>(q_gen_2678) -> q_gen_2612
<z>() -> q_gen_2612
<s>(q_gen_2612) -> q_gen_2629
<s>(q_gen_2629) -> q_gen_2678
<s, s>(q_gen_2603) -> q_gen_2603
<z, s>(q_gen_2678) -> q_gen_2603
<z, z>() -> q_gen_2603
<s, s>(q_gen_2622) -> q_gen_2622
<z, s>(q_gen_2612) -> q_gen_2622
<z, s>(q_gen_2629) -> q_gen_2649
<s, s, s>(q_gen_2611) -> q_gen_2598
<s, z, s>(q_gen_2603) -> q_gen_2598
<z, s, s>(q_gen_2603) -> q_gen_2598
<z, z, s>(q_gen_2678) -> q_gen_2598
<z, z, z>() -> q_gen_2598
<s, s, s>(q_gen_2615) -> q_gen_2611
<s, z, s>(q_gen_2622) -> q_gen_2611
<z, s, s>(q_gen_2622) -> q_gen_2611
<z, z, s>(q_gen_2612) -> q_gen_2611
<s, s, s>(q_gen_2598) -> q_gen_2615
<s, z, s>(q_gen_2649) -> q_gen_2615
<z, s, s>(q_gen_2649) -> q_gen_2615
<z, z, s>(q_gen_2629) -> q_gen_2615
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 80  ;  () -> minus([z, y, z]) -> 80  ;  () -> plus([n, z, n]) -> 80  ;  (minus([_oc, n, _pc]) /\ plus([m, n, _oc])) -> eq_nat([_pc, m]) -> 91  ;  (minus([u, x2, _ec])) -> minus([s(u), s(x2), _ec]) -> 89  ;  (plus([n, mm, _jc])) -> plus([n, s(mm), s(_jc)]) -> 90
}
Sat witness: Yes: ((minus([_oc, n, _pc]) /\ plus([m, n, _oc])) -> eq_nat([_pc, m]), {
_oc -> s(s(s(s(z))))  ;  _pc -> s(z)  ;  m -> z  ;  n -> s(z)
})

-------------------------------------------
Step 92, which took 2.587208 s (model generation: 2.586133,  model checking: 0.001075):

Model:
|_
{
minus -> 
{{{
Q={q_gen_2599, q_gen_2601, q_gen_2607, q_gen_2614, q_gen_2619, q_gen_2623, q_gen_2624, q_gen_2625, q_gen_2641, q_gen_2642, q_gen_2647},
Q_f={q_gen_2599, q_gen_2623},
Delta=
{
<z>() -> q_gen_2607
<s>(q_gen_2607) -> q_gen_2619
<s>(q_gen_2619) -> q_gen_2619
<s, s>(q_gen_2601) -> q_gen_2601
<z, z>() -> q_gen_2601
<s, s>(q_gen_2624) -> q_gen_2624
<z, s>(q_gen_2607) -> q_gen_2624
<z, s>(q_gen_2619) -> q_gen_2642
<s, s>(q_gen_2647) -> q_gen_2647
<s, z>(q_gen_2607) -> q_gen_2647
<s, z>(q_gen_2619) -> q_gen_2647
<s, s, s>(q_gen_2614) -> q_gen_2599
<s, s, z>(q_gen_2601) -> q_gen_2599
<s, s, z>(q_gen_2642) -> q_gen_2599
<s, z, s>(q_gen_2601) -> q_gen_2599
<z, s, z>(q_gen_2607) -> q_gen_2599
<z, s, z>(q_gen_2619) -> q_gen_2599
<z, z, z>() -> q_gen_2599
<s, s, z>(q_gen_2647) -> q_gen_2614
<s, z, s>(q_gen_2624) -> q_gen_2614
<s, z, z>(q_gen_2607) -> q_gen_2614
<s, s, s>(q_gen_2623) -> q_gen_2623
<s, s, s>(q_gen_2625) -> q_gen_2623
<s, s, z>(q_gen_2624) -> q_gen_2623
<s, s, s>(q_gen_2599) -> q_gen_2625
<s, s, s>(q_gen_2641) -> q_gen_2625
<s, z, s>(q_gen_2647) -> q_gen_2625
<s, z, s>(q_gen_2642) -> q_gen_2641
<s, z, z>(q_gen_2619) -> q_gen_2641
}

Datatype: <nat, nat, nat>
Convolution form: complete
}}}
  ;  plus -> 
{{{
Q={q_gen_2598, q_gen_2603, q_gen_2611, q_gen_2612, q_gen_2615, q_gen_2622, q_gen_2629, q_gen_2649, q_gen_2678},
Q_f={q_gen_2598},
Delta=
{
<s>(q_gen_2678) -> q_gen_2612
<z>() -> q_gen_2612
<s>(q_gen_2612) -> q_gen_2629
<s>(q_gen_2629) -> q_gen_2678
<s, s>(q_gen_2603) -> q_gen_2603
<z, s>(q_gen_2678) -> q_gen_2603
<z, z>() -> q_gen_2603
<s, s>(q_gen_2622) -> q_gen_2622
<z, s>(q_gen_2612) -> q_gen_2622
<z, s>(q_gen_2629) -> q_gen_2649
<s, s, s>(q_gen_2611) -> q_gen_2598
<s, z, s>(q_gen_2603) -> q_gen_2598
<z, s, s>(q_gen_2603) -> q_gen_2598
<z, z, s>(q_gen_2678) -> q_gen_2598
<z, z, z>() -> q_gen_2598
<s, s, s>(q_gen_2615) -> q_gen_2611
<s, z, s>(q_gen_2622) -> q_gen_2611
<z, s, s>(q_gen_2622) -> q_gen_2611
<z, z, s>(q_gen_2612) -> q_gen_2611
<s, s, s>(q_gen_2598) -> q_gen_2615
<s, z, s>(q_gen_2649) -> q_gen_2615
<z, s, s>(q_gen_2649) -> q_gen_2615
<z, z, s>(q_gen_2629) -> q_gen_2615
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 81  ;  () -> minus([z, y, z]) -> 81  ;  () -> plus([n, z, n]) -> 81  ;  (minus([_oc, n, _pc]) /\ plus([m, n, _oc])) -> eq_nat([_pc, m]) -> 91  ;  (minus([u, x2, _ec])) -> minus([s(u), s(x2), _ec]) -> 92  ;  (plus([n, mm, _jc])) -> plus([n, s(mm), s(_jc)]) -> 90
}
Sat witness: Yes: ((minus([u, x2, _ec])) -> minus([s(u), s(x2), _ec]), {
_ec -> s(s(z))  ;  u -> s(s(s(s(z))))  ;  x2 -> s(s(z))
})

-------------------------------------------
Step 93, which took 1.558021 s (model generation: 1.556916,  model checking: 0.001105):

Model:
|_
{
minus -> 
{{{
Q={q_gen_2599, q_gen_2601, q_gen_2607, q_gen_2614, q_gen_2619, q_gen_2624, q_gen_2630, q_gen_2647, q_gen_2668, q_gen_2680},
Q_f={q_gen_2599},
Delta=
{
<s>(q_gen_2619) -> q_gen_2607
<z>() -> q_gen_2607
<s>(q_gen_2607) -> q_gen_2619
<s, s>(q_gen_2601) -> q_gen_2601
<z, z>() -> q_gen_2601
<s, s>(q_gen_2624) -> q_gen_2624
<z, s>(q_gen_2607) -> q_gen_2624
<z, s>(q_gen_2619) -> q_gen_2624
<s, s>(q_gen_2647) -> q_gen_2647
<s, z>(q_gen_2607) -> q_gen_2647
<s, s>(q_gen_2680) -> q_gen_2680
<s, z>(q_gen_2619) -> q_gen_2680
<s, s, s>(q_gen_2614) -> q_gen_2599
<s, s, z>(q_gen_2601) -> q_gen_2599
<s, s, z>(q_gen_2624) -> q_gen_2599
<s, z, s>(q_gen_2601) -> q_gen_2599
<s, z, s>(q_gen_2680) -> q_gen_2599
<z, s, z>(q_gen_2607) -> q_gen_2599
<z, s, z>(q_gen_2619) -> q_gen_2599
<z, z, z>() -> q_gen_2599
<s, s, s>(q_gen_2599) -> q_gen_2614
<s, s, s>(q_gen_2668) -> q_gen_2614
<s, s, z>(q_gen_2647) -> q_gen_2614
<s, z, s>(q_gen_2647) -> q_gen_2614
<s, z, z>(q_gen_2607) -> q_gen_2614
<s, s, s>(q_gen_2630) -> q_gen_2630
<s, z, s>(q_gen_2624) -> q_gen_2630
<s, s, z>(q_gen_2680) -> q_gen_2668
<s, z, z>(q_gen_2619) -> q_gen_2668
}

Datatype: <nat, nat, nat>
Convolution form: complete
}}}
  ;  plus -> 
{{{
Q={q_gen_2598, q_gen_2602, q_gen_2603, q_gen_2610, q_gen_2611, q_gen_2612, q_gen_2615, q_gen_2622, q_gen_2629, q_gen_2649},
Q_f={q_gen_2598, q_gen_2602, q_gen_2610},
Delta=
{
<z>() -> q_gen_2612
<s>(q_gen_2612) -> q_gen_2629
<s>(q_gen_2629) -> q_gen_2629
<s, s>(q_gen_2603) -> q_gen_2603
<z, z>() -> q_gen_2603
<s, s>(q_gen_2622) -> q_gen_2622
<z, s>(q_gen_2612) -> q_gen_2622
<z, s>(q_gen_2629) -> q_gen_2649
<s, z, s>(q_gen_2603) -> q_gen_2598
<z, z, z>() -> q_gen_2598
<s, s, s>(q_gen_2610) -> q_gen_2602
<z, s, s>(q_gen_2603) -> q_gen_2602
<s, s, s>(q_gen_2611) -> q_gen_2610
<s, s, s>(q_gen_2602) -> q_gen_2611
<s, s, s>(q_gen_2615) -> q_gen_2611
<s, z, s>(q_gen_2622) -> q_gen_2611
<z, s, s>(q_gen_2622) -> q_gen_2611
<z, z, s>(q_gen_2612) -> q_gen_2611
<s, s, s>(q_gen_2598) -> q_gen_2615
<s, z, s>(q_gen_2649) -> q_gen_2615
<z, s, s>(q_gen_2649) -> q_gen_2615
<z, z, s>(q_gen_2629) -> q_gen_2615
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 82  ;  () -> minus([z, y, z]) -> 82  ;  () -> plus([n, z, n]) -> 82  ;  (minus([_oc, n, _pc]) /\ plus([m, n, _oc])) -> eq_nat([_pc, m]) -> 91  ;  (minus([u, x2, _ec])) -> minus([s(u), s(x2), _ec]) -> 92  ;  (plus([n, mm, _jc])) -> plus([n, s(mm), s(_jc)]) -> 93
}
Sat witness: Yes: ((plus([n, mm, _jc])) -> plus([n, s(mm), s(_jc)]), {
_jc -> s(s(s(s(s(z)))))  ;  mm -> s(z)  ;  n -> s(s(s(s(z))))
})

-------------------------------------------
Step 94, which took 2.337840 s (model generation: 2.337001,  model checking: 0.000839):

Model:
|_
{
minus -> 
{{{
Q={q_gen_2599, q_gen_2601, q_gen_2607, q_gen_2614, q_gen_2619, q_gen_2624, q_gen_2630, q_gen_2640, q_gen_2647, q_gen_2680},
Q_f={q_gen_2599},
Delta=
{
<s>(q_gen_2619) -> q_gen_2607
<z>() -> q_gen_2607
<s>(q_gen_2607) -> q_gen_2619
<s, s>(q_gen_2601) -> q_gen_2601
<z, z>() -> q_gen_2601
<s, s>(q_gen_2624) -> q_gen_2624
<z, s>(q_gen_2607) -> q_gen_2624
<z, s>(q_gen_2619) -> q_gen_2624
<s, s>(q_gen_2647) -> q_gen_2647
<s, z>(q_gen_2607) -> q_gen_2647
<s, s>(q_gen_2680) -> q_gen_2680
<s, z>(q_gen_2619) -> q_gen_2680
<s, s, s>(q_gen_2614) -> q_gen_2599
<s, s, z>(q_gen_2601) -> q_gen_2599
<s, s, z>(q_gen_2624) -> q_gen_2599
<s, z, s>(q_gen_2601) -> q_gen_2599
<s, z, s>(q_gen_2680) -> q_gen_2599
<z, s, z>(q_gen_2607) -> q_gen_2599
<z, s, z>(q_gen_2619) -> q_gen_2599
<z, z, z>() -> q_gen_2599
<s, s, s>(q_gen_2599) -> q_gen_2614
<s, s, s>(q_gen_2640) -> q_gen_2614
<s, s, z>(q_gen_2647) -> q_gen_2614
<s, z, s>(q_gen_2647) -> q_gen_2614
<s, z, z>(q_gen_2607) -> q_gen_2614
<s, z, s>(q_gen_2624) -> q_gen_2630
<s, s, s>(q_gen_2630) -> q_gen_2640
<s, s, z>(q_gen_2680) -> q_gen_2640
<s, z, z>(q_gen_2619) -> q_gen_2640
}

Datatype: <nat, nat, nat>
Convolution form: complete
}}}
  ;  plus -> 
{{{
Q={q_gen_2598, q_gen_2602, q_gen_2603, q_gen_2610, q_gen_2611, q_gen_2612, q_gen_2615, q_gen_2622, q_gen_2629, q_gen_2649},
Q_f={q_gen_2598, q_gen_2602, q_gen_2610},
Delta=
{
<z>() -> q_gen_2612
<s>(q_gen_2612) -> q_gen_2629
<s>(q_gen_2629) -> q_gen_2629
<s, s>(q_gen_2603) -> q_gen_2603
<z, z>() -> q_gen_2603
<s, s>(q_gen_2622) -> q_gen_2622
<z, s>(q_gen_2612) -> q_gen_2622
<s, s>(q_gen_2649) -> q_gen_2649
<z, s>(q_gen_2629) -> q_gen_2649
<s, z, s>(q_gen_2603) -> q_gen_2598
<z, z, z>() -> q_gen_2598
<s, s, s>(q_gen_2610) -> q_gen_2602
<z, s, s>(q_gen_2603) -> q_gen_2602
<s, s, s>(q_gen_2611) -> q_gen_2610
<s, s, s>(q_gen_2602) -> q_gen_2611
<s, s, s>(q_gen_2615) -> q_gen_2611
<s, z, s>(q_gen_2622) -> q_gen_2611
<z, s, s>(q_gen_2622) -> q_gen_2611
<z, z, s>(q_gen_2612) -> q_gen_2611
<s, s, s>(q_gen_2598) -> q_gen_2615
<s, z, s>(q_gen_2649) -> q_gen_2615
<z, s, s>(q_gen_2649) -> q_gen_2615
<z, z, s>(q_gen_2629) -> q_gen_2615
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 83  ;  () -> minus([z, y, z]) -> 83  ;  () -> plus([n, z, n]) -> 83  ;  (minus([_oc, n, _pc]) /\ plus([m, n, _oc])) -> eq_nat([_pc, m]) -> 94  ;  (minus([u, x2, _ec])) -> minus([s(u), s(x2), _ec]) -> 92  ;  (plus([n, mm, _jc])) -> plus([n, s(mm), s(_jc)]) -> 93
}
Sat witness: Yes: ((minus([_oc, n, _pc]) /\ plus([m, n, _oc])) -> eq_nat([_pc, m]), {
_oc -> s(s(s(z)))  ;  _pc -> z  ;  m -> s(s(z))  ;  n -> s(s(s(z)))
})

-------------------------------------------
Step 95, which took 2.009433 s (model generation: 2.009240,  model checking: 0.000193):

Model:
|_
{
minus -> 
{{{
Q={q_gen_2599, q_gen_2601, q_gen_2607, q_gen_2614, q_gen_2619, q_gen_2623, q_gen_2624, q_gen_2630, q_gen_2636, q_gen_2640, q_gen_2643, q_gen_2647},
Q_f={q_gen_2599, q_gen_2623, q_gen_2636},
Delta=
{
<z>() -> q_gen_2607
<s>(q_gen_2607) -> q_gen_2619
<s>(q_gen_2619) -> q_gen_2619
<s, s>(q_gen_2601) -> q_gen_2601
<z, z>() -> q_gen_2601
<s, s>(q_gen_2624) -> q_gen_2624
<z, s>(q_gen_2607) -> q_gen_2624
<z, s>(q_gen_2619) -> q_gen_2624
<s, s>(q_gen_2647) -> q_gen_2647
<s, z>(q_gen_2607) -> q_gen_2647
<s, z>(q_gen_2619) -> q_gen_2647
<s, s, s>(q_gen_2614) -> q_gen_2599
<s, s, s>(q_gen_2636) -> q_gen_2599
<s, s, z>(q_gen_2601) -> q_gen_2599
<s, z, s>(q_gen_2601) -> q_gen_2599
<z, s, z>(q_gen_2607) -> q_gen_2599
<z, s, z>(q_gen_2619) -> q_gen_2599
<z, z, z>() -> q_gen_2599
<s, s, s>(q_gen_2599) -> q_gen_2614
<s, z, z>(q_gen_2607) -> q_gen_2614
<s, s, z>(q_gen_2624) -> q_gen_2623
<s, z, s>(q_gen_2624) -> q_gen_2630
<s, s, s>(q_gen_2623) -> q_gen_2636
<s, s, s>(q_gen_2643) -> q_gen_2636
<s, s, s>(q_gen_2630) -> q_gen_2640
<s, z, z>(q_gen_2619) -> q_gen_2640
<s, s, s>(q_gen_2640) -> q_gen_2643
<s, s, z>(q_gen_2647) -> q_gen_2643
<s, z, s>(q_gen_2647) -> q_gen_2643
}

Datatype: <nat, nat, nat>
Convolution form: complete
}}}
  ;  plus -> 
{{{
Q={q_gen_2598, q_gen_2603, q_gen_2611, q_gen_2612, q_gen_2615, q_gen_2617, q_gen_2622, q_gen_2629, q_gen_2649, q_gen_2651, q_gen_2678},
Q_f={q_gen_2598},
Delta=
{
<s>(q_gen_2678) -> q_gen_2612
<z>() -> q_gen_2612
<s>(q_gen_2612) -> q_gen_2629
<s>(q_gen_2629) -> q_gen_2678
<z, z>() -> q_gen_2603
<s, s>(q_gen_2603) -> q_gen_2617
<s, s>(q_gen_2622) -> q_gen_2622
<z, s>(q_gen_2612) -> q_gen_2622
<s, s>(q_gen_2649) -> q_gen_2649
<z, s>(q_gen_2629) -> q_gen_2649
<s, s>(q_gen_2617) -> q_gen_2651
<z, s>(q_gen_2678) -> q_gen_2651
<s, s, s>(q_gen_2611) -> q_gen_2598
<s, z, s>(q_gen_2603) -> q_gen_2598
<s, z, s>(q_gen_2617) -> q_gen_2598
<s, z, s>(q_gen_2651) -> q_gen_2598
<z, s, s>(q_gen_2603) -> q_gen_2598
<z, s, s>(q_gen_2617) -> q_gen_2598
<z, s, s>(q_gen_2651) -> q_gen_2598
<z, z, s>(q_gen_2678) -> q_gen_2598
<z, z, z>() -> q_gen_2598
<s, s, s>(q_gen_2615) -> q_gen_2611
<s, z, s>(q_gen_2622) -> q_gen_2611
<z, s, s>(q_gen_2622) -> q_gen_2611
<z, z, s>(q_gen_2612) -> q_gen_2611
<s, s, s>(q_gen_2598) -> q_gen_2615
<s, z, s>(q_gen_2649) -> q_gen_2615
<z, s, s>(q_gen_2649) -> q_gen_2615
<z, z, s>(q_gen_2629) -> q_gen_2615
}

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

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

Teacher's answer:
New clause system:
{
() -> minus([s(u), z, s(u)]) -> 83  ;  () -> minus([z, y, z]) -> 83  ;  () -> plus([n, z, n]) -> 86  ;  (minus([_oc, n, _pc]) /\ plus([m, n, _oc])) -> eq_nat([_pc, m]) -> 94  ;  (minus([u, x2, _ec])) -> minus([s(u), s(x2), _ec]) -> 92  ;  (plus([n, mm, _jc])) -> plus([n, s(mm), s(_jc)]) -> 93
}
Sat witness: Yes: (() -> plus([n, z, n]), {
n -> s(s(s(s(z))))
})

Total time: 30.568983
Reason for stopping: DontKnow. Stopped because: timeout