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


Learning problem is:

env: {
nat -> {s, z}  ;  nattsil -> {nil, snoc}
}
definition:
{
(le, P:
{() -> le([z, s(nn2)])
(le([nn1, nn2])) -> le([s(nn1), s(nn2)])
(le([s(nn1), s(nn2)])) -> le([nn1, nn2])
(le([s(nn1), z])) -> BOT
(le([z, z])) -> BOT}
)
(length, F:
{() -> length([nil, z])
(length([ll, _by])) -> length([snoc(ll, x), s(_by)])}
(length([_cy, _dy]) /\ length([_cy, _ey])) -> eq_nat([_dy, _ey])
)
}

properties:
{(length([l, _fy]) /\ length([snoc(l, x), _gy])) -> le([_fy, _gy])}


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

Clause system for inference is:

{
() -> le([z, s(nn2)]) -> 0
() -> length([nil, z]) -> 0
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 0
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 0
(le([s(nn1), z])) -> BOT -> 0
(le([z, z])) -> BOT -> 0
(length([l, _fy]) /\ length([snoc(l, x), _gy])) -> le([_fy, _gy]) -> 0
(length([ll, _by])) -> length([snoc(ll, x), s(_by)]) -> 0
}


Solving took 63.638603 seconds.
DontKnow. Stopped because: timeout
Working model:
|_
{
le -> 
{{{
Q={q_gen_4468, q_gen_4469, q_gen_4473, q_gen_4474, q_gen_4475, q_gen_4486, q_gen_4487, q_gen_4492, q_gen_4498, q_gen_4499, q_gen_4500, q_gen_4509, q_gen_4516, q_gen_4521, q_gen_4522, q_gen_4523, q_gen_4525, q_gen_4526, q_gen_4529, q_gen_4545, q_gen_4547, q_gen_4552, q_gen_4553, q_gen_4554, q_gen_4560, q_gen_4561, q_gen_4562, q_gen_4566, q_gen_4580, q_gen_4581, q_gen_4588, q_gen_4589, q_gen_4590, q_gen_4591, q_gen_4605, q_gen_4618},
Q_f={},
Delta=
{
<z>() -> q_gen_4469
<s>(q_gen_4469) -> q_gen_4475
<s>(q_gen_4475) -> q_gen_4526
<s>(q_gen_4526) -> q_gen_4562
<s>(q_gen_4562) -> q_gen_4591
<z, s>(q_gen_4469) -> q_gen_4468
<s, s>(q_gen_4468) -> q_gen_4473
<z, s>(q_gen_4475) -> q_gen_4474
<s, s>(q_gen_4487) -> q_gen_4486
<z, z>() -> q_gen_4487
<s, s>(q_gen_4486) -> q_gen_4492
<s, s>(q_gen_4499) -> q_gen_4498
<s, s>(q_gen_4500) -> q_gen_4499
<s, z>(q_gen_4469) -> q_gen_4500
<s, s>(q_gen_4492) -> q_gen_4509
<s, s>(q_gen_4498) -> q_gen_4516
<s, s>(q_gen_4522) -> q_gen_4521
<s, s>(q_gen_4523) -> q_gen_4522
<s, z>(q_gen_4475) -> q_gen_4523
<z, s>(q_gen_4526) -> q_gen_4525
<s, s>(q_gen_4521) -> q_gen_4529
<s, s>(q_gen_4516) -> q_gen_4545
<s, s>(q_gen_4509) -> q_gen_4547
<s, s>(q_gen_4553) -> q_gen_4552
<s, s>(q_gen_4554) -> q_gen_4553
<s, z>(q_gen_4526) -> q_gen_4554
<s, s>(q_gen_4529) -> q_gen_4560
<z, s>(q_gen_4562) -> q_gen_4561
<s, s>(q_gen_4552) -> q_gen_4566
<s, s>(q_gen_4581) -> q_gen_4580
<s, z>(q_gen_4562) -> q_gen_4581
<s, s>(q_gen_4589) -> q_gen_4588
<s, s>(q_gen_4590) -> q_gen_4589
<s, z>(q_gen_4591) -> q_gen_4590
<s, s>(q_gen_4545) -> q_gen_4605
<s, s>(q_gen_4580) -> q_gen_4618
}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_4467, q_gen_4470, q_gen_4471, q_gen_4472, q_gen_4476, q_gen_4477, q_gen_4478, q_gen_4479, q_gen_4480, q_gen_4481, q_gen_4482, q_gen_4483, q_gen_4484, q_gen_4485, q_gen_4488, q_gen_4489, q_gen_4490, q_gen_4491, q_gen_4493, q_gen_4494, q_gen_4495, q_gen_4496, q_gen_4497, q_gen_4501, q_gen_4502, q_gen_4503, q_gen_4504, q_gen_4505, q_gen_4506, q_gen_4507, q_gen_4508, q_gen_4510, q_gen_4511, q_gen_4512, q_gen_4513, q_gen_4514, q_gen_4515, q_gen_4517, q_gen_4518, q_gen_4519, q_gen_4520, q_gen_4524, q_gen_4527, q_gen_4528, q_gen_4530, q_gen_4531, q_gen_4532, q_gen_4533, q_gen_4534, q_gen_4535, q_gen_4536, q_gen_4537, q_gen_4538, q_gen_4539, q_gen_4540, q_gen_4541, q_gen_4542, q_gen_4543, q_gen_4544, q_gen_4546, q_gen_4548, q_gen_4549, q_gen_4550, q_gen_4551, q_gen_4555, q_gen_4556, q_gen_4557, q_gen_4558, q_gen_4559, q_gen_4563, q_gen_4564, q_gen_4565, q_gen_4567, q_gen_4568, q_gen_4569, q_gen_4570, q_gen_4571, q_gen_4572, q_gen_4573, q_gen_4574, q_gen_4575, q_gen_4576, q_gen_4577, q_gen_4578, q_gen_4579, q_gen_4582, q_gen_4583, q_gen_4584, q_gen_4585, q_gen_4586, q_gen_4587, q_gen_4592, q_gen_4593, q_gen_4594, q_gen_4595, q_gen_4596, q_gen_4597, q_gen_4598, q_gen_4599, q_gen_4600, q_gen_4601, q_gen_4602, q_gen_4603, q_gen_4604, q_gen_4606, q_gen_4607, q_gen_4608, q_gen_4609, q_gen_4610, q_gen_4611, q_gen_4612, q_gen_4613, q_gen_4614, q_gen_4615, q_gen_4616, q_gen_4617, q_gen_4619, q_gen_4620, q_gen_4621, q_gen_4622, q_gen_4623, q_gen_4624, q_gen_4625, q_gen_4626, q_gen_4627, q_gen_4628, q_gen_4629, q_gen_4630, q_gen_4631, q_gen_4632, q_gen_4633, q_gen_4634, q_gen_4635, q_gen_4636, q_gen_4637, q_gen_4638, q_gen_4639, q_gen_4640, q_gen_4641, q_gen_4642, q_gen_4643, q_gen_4644, q_gen_4645, q_gen_4646, q_gen_4647, q_gen_4648, q_gen_4649, q_gen_4650, q_gen_4651, q_gen_4652, q_gen_4653, q_gen_4654, q_gen_4655, q_gen_4656, q_gen_4657, q_gen_4658, q_gen_4659, q_gen_4660, q_gen_4661, q_gen_4662, q_gen_4663, q_gen_4664, q_gen_4665, q_gen_4666, q_gen_4667, q_gen_4668, q_gen_4669, q_gen_4670, q_gen_4671, q_gen_4672, q_gen_4673, q_gen_4674, q_gen_4675, q_gen_4676, q_gen_4677, q_gen_4678, q_gen_4679, q_gen_4680, q_gen_4681, q_gen_4682, q_gen_4683, q_gen_4684, q_gen_4685, q_gen_4686, q_gen_4687, q_gen_4688, q_gen_4689, q_gen_4690, q_gen_4691, q_gen_4692, q_gen_4693, q_gen_4694, q_gen_4695, q_gen_4696, q_gen_4697, q_gen_4698, q_gen_4699, q_gen_4700, q_gen_4701, q_gen_4702, q_gen_4703, q_gen_4704, q_gen_4705, q_gen_4706, q_gen_4707, q_gen_4708, q_gen_4709, q_gen_4710, q_gen_4711, q_gen_4712, q_gen_4713, q_gen_4714, q_gen_4715, q_gen_4716, q_gen_4717, q_gen_4718, q_gen_4719, q_gen_4720, q_gen_4721, q_gen_4722, q_gen_4723, q_gen_4724, q_gen_4725, q_gen_4726, q_gen_4727, q_gen_4728, q_gen_4729, q_gen_4730, q_gen_4731, q_gen_4732},
Q_f={},
Delta=
{
<nil>() -> q_gen_4472
<z>() -> q_gen_4478
<s>(q_gen_4478) -> q_gen_4481
<snoc>(q_gen_4472, q_gen_4478) -> q_gen_4484
<snoc>(q_gen_4484, q_gen_4478) -> q_gen_4490
<s>(q_gen_4481) -> q_gen_4496
<snoc>(q_gen_4490, q_gen_4478) -> q_gen_4505
<snoc>(q_gen_4505, q_gen_4478) -> q_gen_4508
<s>(q_gen_4496) -> q_gen_4519
<snoc>(q_gen_4490, q_gen_4481) -> q_gen_4541
<s>(q_gen_4519) -> q_gen_4550
<snoc>(q_gen_4541, q_gen_4478) -> q_gen_4557
<snoc>(q_gen_4490, q_gen_4496) -> q_gen_4564
<snoc>(q_gen_4490, q_gen_4572) -> q_gen_4571
<s>(q_gen_4550) -> q_gen_4572
<snoc>(q_gen_4472, q_gen_4519) -> q_gen_4574
<snoc>(q_gen_4564, q_gen_4478) -> q_gen_4577
<snoc>(q_gen_4594, q_gen_4481) -> q_gen_4593
<snoc>(q_gen_4574, q_gen_4478) -> q_gen_4594
<snoc>(q_gen_4593, q_gen_4478) -> q_gen_4599
<snoc>(q_gen_4490, q_gen_4519) -> q_gen_4602
<snoc>(q_gen_4602, q_gen_4478) -> q_gen_4604
<snoc>(q_gen_4472, q_gen_4617) -> q_gen_4616
<s>(q_gen_4572) -> q_gen_4617
<snoc>(q_gen_4541, q_gen_4625) -> q_gen_4624
<s>(q_gen_4617) -> q_gen_4625
<snoc>(q_gen_4472, q_gen_4550) -> q_gen_4630
<snoc>(q_gen_4508, q_gen_4478) -> q_gen_4632
<snoc>(q_gen_4632, q_gen_4478) -> q_gen_4634
<snoc>(q_gen_4577, q_gen_4478) -> q_gen_4640
<snoc>(q_gen_4594, q_gen_4496) -> q_gen_4642
<snoc>(q_gen_4642, q_gen_4478) -> q_gen_4644
<snoc>(q_gen_4564, q_gen_4519) -> q_gen_4646
<snoc>(q_gen_4646, q_gen_4478) -> q_gen_4648
<snoc>(q_gen_4594, q_gen_4519) -> q_gen_4650
<snoc>(q_gen_4650, q_gen_4478) -> q_gen_4652
<snoc>(q_gen_4602, q_gen_4496) -> q_gen_4656
<snoc>(q_gen_4656, q_gen_4550) -> q_gen_4658
<snoc>(q_gen_4564, q_gen_4496) -> q_gen_4661
<snoc>(q_gen_4661, q_gen_4519) -> q_gen_4666
<snoc>(q_gen_4669, q_gen_4519) -> q_gen_4668
<snoc>(q_gen_4670, q_gen_4478) -> q_gen_4669
<snoc>(q_gen_4484, q_gen_4519) -> q_gen_4670
<snoc>(q_gen_4668, q_gen_4478) -> q_gen_4672
<snoc>(q_gen_4644, q_gen_4478) -> q_gen_4674
<snoc>(q_gen_4674, q_gen_4496) -> q_gen_4676
<snoc>(q_gen_4670, q_gen_4519) -> q_gen_4678
<snoc>(q_gen_4678, q_gen_4481) -> q_gen_4680
<snoc>(q_gen_4632, q_gen_4496) -> q_gen_4684
<snoc>(q_gen_4574, q_gen_4550) -> q_gen_4688
<snoc>(q_gen_4691, q_gen_4496) -> q_gen_4690
<snoc>(q_gen_4472, q_gen_4496) -> q_gen_4691
<snoc>(q_gen_4690, q_gen_4478) -> q_gen_4693
<snoc>(q_gen_4691, q_gen_4478) -> q_gen_4695
<snoc>(q_gen_4695, q_gen_4478) -> q_gen_4697
<snoc>(q_gen_4630, q_gen_4519) -> q_gen_4699
<snoc>(q_gen_4699, q_gen_4478) -> q_gen_4701
<snoc>(q_gen_4574, q_gen_4496) -> q_gen_4704
<snoc>(q_gen_4691, q_gen_4481) -> q_gen_4708
<snoc>(q_gen_4484, q_gen_4496) -> q_gen_4711
<snoc>(q_gen_4711, q_gen_4519) -> q_gen_4713
<snoc>(q_gen_4713, q_gen_4481) -> q_gen_4715
<snoc>(q_gen_4713, q_gen_4519) -> q_gen_4720
<snoc>(q_gen_4723, q_gen_4481) -> q_gen_4722
<snoc>(q_gen_4724, q_gen_4478) -> q_gen_4723
<snoc>(q_gen_4725, q_gen_4478) -> q_gen_4724
<snoc>(q_gen_4726, q_gen_4550) -> q_gen_4725
<snoc>(q_gen_4727, q_gen_4550) -> q_gen_4726
<snoc>(q_gen_4704, q_gen_4496) -> q_gen_4727
<snoc>(q_gen_4722, q_gen_4496) -> q_gen_4729
<snoc>(q_gen_4630, q_gen_4496) -> q_gen_4732
<nil, z>() -> q_gen_4467
<snoc, s>(q_gen_4472, q_gen_4471) -> q_gen_4470
<z, z>() -> q_gen_4471
<snoc, s>(q_gen_4472, q_gen_4477) -> q_gen_4476
<s, z>(q_gen_4478) -> q_gen_4477
<snoc, s>(q_gen_4472, q_gen_4480) -> q_gen_4479
<s, z>(q_gen_4481) -> q_gen_4480
<snoc, s>(q_gen_4484, q_gen_4483) -> q_gen_4482
<z, s>(q_gen_4478) -> q_gen_4483
<snoc, s>(q_gen_4484, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4489) -> q_gen_4488
<z, s>(q_gen_4481) -> q_gen_4489
<snoc, s>(q_gen_4472, q_gen_4483) -> q_gen_4491
<snoc, s>(q_gen_4490, q_gen_4483) -> q_gen_4493
<snoc, s>(q_gen_4472, q_gen_4495) -> q_gen_4494
<s, z>(q_gen_4496) -> q_gen_4495
<snoc, s>(q_gen_4472, q_gen_4489) -> q_gen_4497
<snoc, s>(q_gen_4484, q_gen_4502) -> q_gen_4501
<z, s>(q_gen_4496) -> q_gen_4502
<snoc, s>(q_gen_4490, q_gen_4471) -> q_gen_4503
<snoc, s>(q_gen_4505, q_gen_4502) -> q_gen_4504
<snoc, s>(q_gen_4505, q_gen_4489) -> q_gen_4506
<snoc, s>(q_gen_4508, q_gen_4489) -> q_gen_4507
<snoc, s>(q_gen_4490, q_gen_4511) -> q_gen_4510
<s, s>(q_gen_4483) -> q_gen_4511
<snoc, s>(q_gen_4505, q_gen_4483) -> q_gen_4512
<snoc, s>(q_gen_4484, q_gen_4489) -> q_gen_4513
<snoc, s>(q_gen_4490, q_gen_4502) -> q_gen_4514
<snoc, s>(q_gen_4505, q_gen_4511) -> q_gen_4515
<snoc, s>(q_gen_4472, q_gen_4518) -> q_gen_4517
<s, z>(q_gen_4519) -> q_gen_4518
<snoc, s>(q_gen_4472, q_gen_4502) -> q_gen_4520
<snoc, s>(q_gen_4508, q_gen_4502) -> q_gen_4524
<snoc, s>(q_gen_4484, q_gen_4528) -> q_gen_4527
<z, s>(q_gen_4519) -> q_gen_4528
<snoc, s>(q_gen_4508, q_gen_4528) -> q_gen_4530
<snoc, s>(q_gen_4490, q_gen_4532) -> q_gen_4531
<s, s>(q_gen_4533) -> q_gen_4532
<s, s>(q_gen_4471) -> q_gen_4533
<snoc, s>(q_gen_4490, q_gen_4533) -> q_gen_4534
<snoc, s>(q_gen_4505, q_gen_4536) -> q_gen_4535
<s, s>(q_gen_4511) -> q_gen_4536
<snoc, s>(q_gen_4505, q_gen_4471) -> q_gen_4537
<snoc, s>(q_gen_4490, q_gen_4539) -> q_gen_4538
<s, s>(q_gen_4489) -> q_gen_4539
<snoc, s>(q_gen_4541, q_gen_4528) -> q_gen_4540
<snoc, s>(q_gen_4541, q_gen_4483) -> q_gen_4542
<snoc, s>(q_gen_4484, q_gen_4533) -> q_gen_4543
<snoc, s>(q_gen_4490, q_gen_4528) -> q_gen_4544
<snoc, s>(q_gen_4541, q_gen_4502) -> q_gen_4546
<snoc, s>(q_gen_4472, q_gen_4549) -> q_gen_4548
<s, z>(q_gen_4550) -> q_gen_4549
<snoc, s>(q_gen_4472, q_gen_4528) -> q_gen_4551
<snoc, s>(q_gen_4557, q_gen_4556) -> q_gen_4555
<z, s>(q_gen_4550) -> q_gen_4556
<snoc, s>(q_gen_4490, q_gen_4556) -> q_gen_4558
<snoc, s>(q_gen_4505, q_gen_4539) -> q_gen_4559
<snoc, s>(q_gen_4564, q_gen_4536) -> q_gen_4563
<snoc, s>(q_gen_4484, q_gen_4556) -> q_gen_4565
<snoc, s>(q_gen_4490, q_gen_4568) -> q_gen_4567
<s, s>(q_gen_4569) -> q_gen_4568
<s, s>(q_gen_4495) -> q_gen_4569
<snoc, s>(q_gen_4571, q_gen_4502) -> q_gen_4570
<snoc, s>(q_gen_4574, q_gen_4533) -> q_gen_4573
<snoc, s>(q_gen_4564, q_gen_4502) -> q_gen_4575
<snoc, s>(q_gen_4577, q_gen_4483) -> q_gen_4576
<snoc, s>(q_gen_4564, q_gen_4528) -> q_gen_4578
<snoc, s>(q_gen_4577, q_gen_4471) -> q_gen_4579
<snoc, s>(q_gen_4508, q_gen_4583) -> q_gen_4582
<s, s>(q_gen_4539) -> q_gen_4583
<snoc, s>(q_gen_4490, q_gen_4585) -> q_gen_4584
<s, s>(q_gen_4586) -> q_gen_4585
<s, s>(q_gen_4528) -> q_gen_4586
<snoc, s>(q_gen_4564, q_gen_4533) -> q_gen_4587
<snoc, s>(q_gen_4593, q_gen_4556) -> q_gen_4592
<snoc, s>(q_gen_4599, q_gen_4596) -> q_gen_4595
<s, s>(q_gen_4597) -> q_gen_4596
<s, s>(q_gen_4598) -> q_gen_4597
<s, s>(q_gen_4502) -> q_gen_4598
<snoc, s>(q_gen_4577, q_gen_4556) -> q_gen_4600
<snoc, s>(q_gen_4602, q_gen_4556) -> q_gen_4601
<snoc, s>(q_gen_4604, q_gen_4598) -> q_gen_4603
<snoc, s>(q_gen_4594, q_gen_4586) -> q_gen_4606
<snoc, s>(q_gen_4593, q_gen_4608) -> q_gen_4607
<z, s>(q_gen_4572) -> q_gen_4608
<snoc, s>(q_gen_4472, q_gen_4610) -> q_gen_4609
<s, s>(q_gen_4611) -> q_gen_4610
<s, s>(q_gen_4612) -> q_gen_4611
<s, s>(q_gen_4613) -> q_gen_4612
<s, s>(q_gen_4614) -> q_gen_4613
<s, s>(q_gen_4477) -> q_gen_4614
<snoc, s>(q_gen_4616, q_gen_4533) -> q_gen_4615
<snoc, s>(q_gen_4541, q_gen_4620) -> q_gen_4619
<s, s>(q_gen_4621) -> q_gen_4620
<s, s>(q_gen_4622) -> q_gen_4621
<s, s>(q_gen_4518) -> q_gen_4622
<snoc, s>(q_gen_4624, q_gen_4598) -> q_gen_4623
<snoc, s>(q_gen_4472, q_gen_4627) -> q_gen_4626
<s, s>(q_gen_4628) -> q_gen_4627
<s, s>(q_gen_4532) -> q_gen_4628
<snoc, s>(q_gen_4630, q_gen_4483) -> q_gen_4629
<snoc, s>(q_gen_4632, q_gen_4502) -> q_gen_4631
<snoc, s>(q_gen_4634, q_gen_4598) -> q_gen_4633
<snoc, s>(q_gen_4490, q_gen_4598) -> q_gen_4635
<snoc, s>(q_gen_4574, q_gen_4528) -> q_gen_4636
<snoc, s>(q_gen_4594, q_gen_4597) -> q_gen_4637
<snoc, s>(q_gen_4577, q_gen_4528) -> q_gen_4638
<snoc, s>(q_gen_4640, q_gen_4483) -> q_gen_4639
<snoc, s>(q_gen_4642, q_gen_4528) -> q_gen_4641
<snoc, s>(q_gen_4644, q_gen_4597) -> q_gen_4643
<snoc, s>(q_gen_4646, q_gen_4528) -> q_gen_4645
<snoc, s>(q_gen_4648, q_gen_4489) -> q_gen_4647
<snoc, s>(q_gen_4650, q_gen_4502) -> q_gen_4649
<snoc, s>(q_gen_4652, q_gen_4598) -> q_gen_4651
<snoc, s>(q_gen_4656, q_gen_4654) -> q_gen_4653
<s, s>(q_gen_4655) -> q_gen_4654
<s, s>(q_gen_4480) -> q_gen_4655
<snoc, s>(q_gen_4658, q_gen_4483) -> q_gen_4657
<snoc, s>(q_gen_4661, q_gen_4660) -> q_gen_4659
<s, s>(q_gen_4585) -> q_gen_4660
<snoc, s>(q_gen_4666, q_gen_4663) -> q_gen_4662
<s, s>(q_gen_4664) -> q_gen_4663
<s, s>(q_gen_4665) -> q_gen_4664
<s, s>(q_gen_4556) -> q_gen_4665
<snoc, s>(q_gen_4668, q_gen_4528) -> q_gen_4667
<snoc, s>(q_gen_4672, q_gen_4471) -> q_gen_4671
<snoc, s>(q_gen_4674, q_gen_4532) -> q_gen_4673
<snoc, s>(q_gen_4676, q_gen_4536) -> q_gen_4675
<snoc, s>(q_gen_4678, q_gen_4511) -> q_gen_4677
<snoc, s>(q_gen_4680, q_gen_4532) -> q_gen_4679
<snoc, s>(q_gen_4632, q_gen_4585) -> q_gen_4681
<snoc, s>(q_gen_4684, q_gen_4683) -> q_gen_4682
<z, s>(q_gen_4617) -> q_gen_4683
<snoc, s>(q_gen_4571, q_gen_4489) -> q_gen_4685
<snoc, s>(q_gen_4574, q_gen_4569) -> q_gen_4686
<snoc, s>(q_gen_4688, q_gen_4511) -> q_gen_4687
<snoc, s>(q_gen_4690, q_gen_4489) -> q_gen_4689
<snoc, s>(q_gen_4693, q_gen_4471) -> q_gen_4692
<snoc, s>(q_gen_4695, q_gen_4556) -> q_gen_4694
<snoc, s>(q_gen_4697, q_gen_4665) -> q_gen_4696
<snoc, s>(q_gen_4699, q_gen_4489) -> q_gen_4698
<snoc, s>(q_gen_4701, q_gen_4471) -> q_gen_4700
<snoc, s>(q_gen_4574, q_gen_4597) -> q_gen_4702
<snoc, s>(q_gen_4704, q_gen_4665) -> q_gen_4703
<snoc, s>(q_gen_4691, q_gen_4471) -> q_gen_4705
<snoc, s>(q_gen_4691, q_gen_4539) -> q_gen_4706
<snoc, s>(q_gen_4708, q_gen_4528) -> q_gen_4707
<snoc, s>(q_gen_4484, q_gen_4614) -> q_gen_4709
<snoc, s>(q_gen_4711, q_gen_4483) -> q_gen_4710
<snoc, s>(q_gen_4713, q_gen_4586) -> q_gen_4712
<snoc, s>(q_gen_4715, q_gen_4665) -> q_gen_4714
<snoc, s>(q_gen_4711, q_gen_4471) -> q_gen_4716
<snoc, s>(q_gen_4713, q_gen_4718) -> q_gen_4717
<s, s>(q_gen_4536) -> q_gen_4718
<snoc, s>(q_gen_4720, q_gen_4597) -> q_gen_4719
<snoc, s>(q_gen_4722, q_gen_4536) -> q_gen_4721
<snoc, s>(q_gen_4729, q_gen_4483) -> q_gen_4728
<snoc, s>(q_gen_4630, q_gen_4614) -> q_gen_4730
<snoc, s>(q_gen_4732, q_gen_4532) -> q_gen_4731
}

Datatype: <nattsil, nat>
Convolution form: right
}}}

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

-------------------
STEPS:
-------------------------------------------
Step 0, which took 0.010533 s (model generation: 0.010210,  model checking: 0.000323):

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

}

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

}

Datatype: <nattsil, nat>
Convolution form: right
}}}

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 0
() -> length([nil, z]) -> 3
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 1
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 1
(le([s(nn1), z])) -> BOT -> 1
(le([z, z])) -> BOT -> 1
(length([l, _fy]) /\ length([snoc(l, x), _gy])) -> le([_fy, _gy]) -> 1
(length([ll, _by])) -> length([snoc(ll, x), s(_by)]) -> 1
}
Sat witness: Found: (() -> length([nil, z]), {

})

-------------------------------------------
Step 1, which took 0.010923 s (model generation: 0.010727,  model checking: 0.000196):

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

}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_4467},
Q_f={q_gen_4467},
Delta=
{
<nil, z>() -> q_gen_4467
}

Datatype: <nattsil, nat>
Convolution form: right
}}}

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 3
() -> length([nil, z]) -> 3
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 1
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 1
(le([s(nn1), z])) -> BOT -> 1
(le([z, z])) -> BOT -> 1
(length([l, _fy]) /\ length([snoc(l, x), _gy])) -> le([_fy, _gy]) -> 1
(length([ll, _by])) -> length([snoc(ll, x), s(_by)]) -> 1
}
Sat witness: Found: (() -> le([z, s(nn2)]), {
nn2 -> z
})

-------------------------------------------
Step 2, which took 0.011134 s (model generation: 0.010921,  model checking: 0.000213):

Model:
|_
{
le -> 
{{{
Q={q_gen_4468, q_gen_4469},
Q_f={q_gen_4468},
Delta=
{
<z>() -> q_gen_4469
<z, s>(q_gen_4469) -> q_gen_4468
}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_4467},
Q_f={q_gen_4467},
Delta=
{
<nil, z>() -> q_gen_4467
}

Datatype: <nattsil, nat>
Convolution form: right
}}}

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 3
() -> length([nil, z]) -> 3
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 1
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 1
(le([s(nn1), z])) -> BOT -> 1
(le([z, z])) -> BOT -> 1
(length([l, _fy]) /\ length([snoc(l, x), _gy])) -> le([_fy, _gy]) -> 1
(length([ll, _by])) -> length([snoc(ll, x), s(_by)]) -> 4
}
Sat witness: Found: ((length([ll, _by])) -> length([snoc(ll, x), s(_by)]), {
_by -> z  ;  ll -> nil  ;  x -> z
})

-------------------------------------------
Step 3, which took 0.010960 s (model generation: 0.010535,  model checking: 0.000425):

Model:
|_
{
le -> 
{{{
Q={q_gen_4468, q_gen_4469},
Q_f={q_gen_4468},
Delta=
{
<z>() -> q_gen_4469
<z, s>(q_gen_4469) -> q_gen_4468
}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_4467, q_gen_4471, q_gen_4472},
Q_f={q_gen_4467},
Delta=
{
<nil>() -> q_gen_4472
<nil, z>() -> q_gen_4467
<snoc, s>(q_gen_4472, q_gen_4471) -> q_gen_4467
<z, z>() -> q_gen_4471
}

Datatype: <nattsil, nat>
Convolution form: right
}}}

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 3
() -> length([nil, z]) -> 3
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 4
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 2
(le([s(nn1), z])) -> BOT -> 2
(le([z, z])) -> BOT -> 2
(length([l, _fy]) /\ length([snoc(l, x), _gy])) -> le([_fy, _gy]) -> 2
(length([ll, _by])) -> length([snoc(ll, x), s(_by)]) -> 4
}
Sat witness: Found: ((le([nn1, nn2])) -> le([s(nn1), s(nn2)]), {
nn1 -> z  ;  nn2 -> s(z)
})

-------------------------------------------
Step 4, which took 0.015010 s (model generation: 0.014405,  model checking: 0.000605):

Model:
|_
{
le -> 
{{{
Q={q_gen_4468, q_gen_4469},
Q_f={q_gen_4468},
Delta=
{
<z>() -> q_gen_4469
<s, s>(q_gen_4468) -> q_gen_4468
<z, s>(q_gen_4469) -> q_gen_4468
}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_4467, q_gen_4471, q_gen_4472},
Q_f={q_gen_4467},
Delta=
{
<nil>() -> q_gen_4472
<nil, z>() -> q_gen_4467
<snoc, s>(q_gen_4472, q_gen_4471) -> q_gen_4467
<z, z>() -> q_gen_4471
}

Datatype: <nattsil, nat>
Convolution form: right
}}}

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 6
() -> length([nil, z]) -> 4
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 4
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 3
(le([s(nn1), z])) -> BOT -> 3
(le([z, z])) -> BOT -> 3
(length([l, _fy]) /\ length([snoc(l, x), _gy])) -> le([_fy, _gy]) -> 3
(length([ll, _by])) -> length([snoc(ll, x), s(_by)]) -> 4
}
Sat witness: Found: (() -> le([z, s(nn2)]), {
nn2 -> s(z)
})

-------------------------------------------
Step 5, which took 0.011817 s (model generation: 0.011226,  model checking: 0.000591):

Model:
|_
{
le -> 
{{{
Q={q_gen_4468, q_gen_4469},
Q_f={q_gen_4468},
Delta=
{
<s>(q_gen_4469) -> q_gen_4469
<z>() -> q_gen_4469
<s, s>(q_gen_4468) -> q_gen_4468
<z, s>(q_gen_4469) -> q_gen_4468
}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_4467, q_gen_4471, q_gen_4472},
Q_f={q_gen_4467},
Delta=
{
<nil>() -> q_gen_4472
<nil, z>() -> q_gen_4467
<snoc, s>(q_gen_4472, q_gen_4471) -> q_gen_4467
<z, z>() -> q_gen_4471
}

Datatype: <nattsil, nat>
Convolution form: right
}}}

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 6
() -> length([nil, z]) -> 4
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 4
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 4
(le([s(nn1), z])) -> BOT -> 4
(le([z, z])) -> BOT -> 4
(length([l, _fy]) /\ length([snoc(l, x), _gy])) -> le([_fy, _gy]) -> 4
(length([ll, _by])) -> length([snoc(ll, x), s(_by)]) -> 7
}
Sat witness: Found: ((length([ll, _by])) -> length([snoc(ll, x), s(_by)]), {
_by -> z  ;  ll -> nil  ;  x -> s(z)
})

-------------------------------------------
Step 6, which took 0.014934 s (model generation: 0.013940,  model checking: 0.000994):

Model:
|_
{
le -> 
{{{
Q={q_gen_4468, q_gen_4469},
Q_f={q_gen_4468},
Delta=
{
<s>(q_gen_4469) -> q_gen_4469
<z>() -> q_gen_4469
<s, s>(q_gen_4468) -> q_gen_4468
<z, s>(q_gen_4469) -> q_gen_4468
}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_4467, q_gen_4471, q_gen_4472, q_gen_4478},
Q_f={q_gen_4467},
Delta=
{
<nil>() -> q_gen_4472
<z>() -> q_gen_4478
<nil, z>() -> q_gen_4467
<snoc, s>(q_gen_4472, q_gen_4471) -> q_gen_4467
<s, z>(q_gen_4478) -> q_gen_4471
<z, z>() -> q_gen_4471
}

Datatype: <nattsil, nat>
Convolution form: right
}}}

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 7
() -> length([nil, z]) -> 5
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 5
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 5
(le([s(nn1), z])) -> BOT -> 5
(le([z, z])) -> BOT -> 5
(length([l, _fy]) /\ length([snoc(l, x), _gy])) -> le([_fy, _gy]) -> 5
(length([ll, _by])) -> length([snoc(ll, x), s(_by)]) -> 10
}
Sat witness: Found: ((length([ll, _by])) -> length([snoc(ll, x), s(_by)]), {
_by -> z  ;  ll -> nil  ;  x -> s(s(z))
})

-------------------------------------------
Step 7, which took 0.014481 s (model generation: 0.012486,  model checking: 0.001995):

Model:
|_
{
le -> 
{{{
Q={q_gen_4468, q_gen_4469},
Q_f={q_gen_4468},
Delta=
{
<s>(q_gen_4469) -> q_gen_4469
<z>() -> q_gen_4469
<s, s>(q_gen_4468) -> q_gen_4468
<z, s>(q_gen_4469) -> q_gen_4468
}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_4467, q_gen_4471, q_gen_4472, q_gen_4478},
Q_f={q_gen_4467},
Delta=
{
<nil>() -> q_gen_4472
<s>(q_gen_4478) -> q_gen_4478
<z>() -> q_gen_4478
<nil, z>() -> q_gen_4467
<snoc, s>(q_gen_4472, q_gen_4471) -> q_gen_4467
<s, z>(q_gen_4478) -> q_gen_4471
<z, z>() -> q_gen_4471
}

Datatype: <nattsil, nat>
Convolution form: right
}}}

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 8
() -> length([nil, z]) -> 6
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 6
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 6
(le([s(nn1), z])) -> BOT -> 6
(le([z, z])) -> BOT -> 6
(length([l, _fy]) /\ length([snoc(l, x), _gy])) -> le([_fy, _gy]) -> 6
(length([ll, _by])) -> length([snoc(ll, x), s(_by)]) -> 13
}
Sat witness: Found: ((length([ll, _by])) -> length([snoc(ll, x), s(_by)]), {
_by -> s(z)  ;  ll -> snoc(nil, z)  ;  x -> z
})

-------------------------------------------
Step 8, which took 0.014995 s (model generation: 0.013494,  model checking: 0.001501):

Model:
|_
{
le -> 
{{{
Q={q_gen_4468, q_gen_4469},
Q_f={q_gen_4468},
Delta=
{
<s>(q_gen_4469) -> q_gen_4469
<z>() -> q_gen_4469
<s, s>(q_gen_4468) -> q_gen_4468
<z, s>(q_gen_4469) -> q_gen_4468
}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_4467, q_gen_4471, q_gen_4472, q_gen_4478},
Q_f={q_gen_4467},
Delta=
{
<nil>() -> q_gen_4472
<snoc>(q_gen_4472, q_gen_4478) -> q_gen_4472
<s>(q_gen_4478) -> q_gen_4478
<z>() -> q_gen_4478
<nil, z>() -> q_gen_4467
<snoc, s>(q_gen_4472, q_gen_4471) -> q_gen_4467
<s, z>(q_gen_4478) -> q_gen_4471
<z, s>(q_gen_4478) -> q_gen_4471
<z, z>() -> q_gen_4471
}

Datatype: <nattsil, nat>
Convolution form: right
}}}

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 8
() -> length([nil, z]) -> 6
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 6
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 6
(le([s(nn1), z])) -> BOT -> 6
(le([z, z])) -> BOT -> 6
(length([l, _fy]) /\ length([snoc(l, x), _gy])) -> le([_fy, _gy]) -> 9
(length([ll, _by])) -> length([snoc(ll, x), s(_by)]) -> 13
}
Sat witness: Found: ((length([l, _fy]) /\ length([snoc(l, x), _gy])) -> le([_fy, _gy]), {
_fy -> s(z)  ;  _gy -> s(z)  ;  l -> snoc(nil, z)  ;  x -> z
})

-------------------------------------------
Step 9, which took 0.010987 s (model generation: 0.010962,  model checking: 0.000025):

Model:
|_
{
le -> 
{{{
Q={q_gen_4468, q_gen_4469},
Q_f={q_gen_4468},
Delta=
{
<s>(q_gen_4469) -> q_gen_4469
<z>() -> q_gen_4469
<s, s>(q_gen_4468) -> q_gen_4468
<z, s>(q_gen_4469) -> q_gen_4468
<z, z>() -> q_gen_4468
}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_4467, q_gen_4471, q_gen_4472, q_gen_4478},
Q_f={q_gen_4467},
Delta=
{
<nil>() -> q_gen_4472
<snoc>(q_gen_4472, q_gen_4478) -> q_gen_4472
<s>(q_gen_4478) -> q_gen_4478
<z>() -> q_gen_4478
<nil, z>() -> q_gen_4467
<snoc, s>(q_gen_4472, q_gen_4471) -> q_gen_4467
<s, z>(q_gen_4478) -> q_gen_4471
<z, s>(q_gen_4478) -> q_gen_4471
<z, z>() -> q_gen_4471
}

Datatype: <nattsil, nat>
Convolution form: right
}}}

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 8
() -> length([nil, z]) -> 6
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 6
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 6
(le([s(nn1), z])) -> BOT -> 6
(le([z, z])) -> BOT -> 9
(length([l, _fy]) /\ length([snoc(l, x), _gy])) -> le([_fy, _gy]) -> 9
(length([ll, _by])) -> length([snoc(ll, x), s(_by)]) -> 13
}
Sat witness: Found: ((le([z, z])) -> BOT, {

})

-------------------------------------------
Step 10, which took 0.005738 s (model generation: 0.005651,  model checking: 0.000087):

Model:
|_
{
le -> 
{{{
Q={q_gen_4468, q_gen_4469, q_gen_4487},
Q_f={q_gen_4468},
Delta=
{
<s>(q_gen_4469) -> q_gen_4469
<z>() -> q_gen_4469
<s, s>(q_gen_4468) -> q_gen_4468
<s, s>(q_gen_4487) -> q_gen_4468
<z, s>(q_gen_4469) -> q_gen_4468
<z, z>() -> q_gen_4487
}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_4467, q_gen_4471, q_gen_4472, q_gen_4478},
Q_f={q_gen_4467},
Delta=
{
<nil>() -> q_gen_4472
<snoc>(q_gen_4472, q_gen_4478) -> q_gen_4472
<s>(q_gen_4478) -> q_gen_4478
<z>() -> q_gen_4478
<nil, z>() -> q_gen_4467
<snoc, s>(q_gen_4472, q_gen_4471) -> q_gen_4467
<s, z>(q_gen_4478) -> q_gen_4471
<z, s>(q_gen_4478) -> q_gen_4471
<z, z>() -> q_gen_4471
}

Datatype: <nattsil, nat>
Convolution form: right
}}}

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 8
() -> length([nil, z]) -> 6
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 6
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 9
(le([s(nn1), z])) -> BOT -> 7
(le([z, z])) -> BOT -> 9
(length([l, _fy]) /\ length([snoc(l, x), _gy])) -> le([_fy, _gy]) -> 9
(length([ll, _by])) -> length([snoc(ll, x), s(_by)]) -> 13
}
Sat witness: Found: ((le([s(nn1), s(nn2)])) -> le([nn1, nn2]), {
nn1 -> z  ;  nn2 -> z
})

-------------------------------------------
Step 11, which took 0.008478 s (model generation: 0.007671,  model checking: 0.000807):

Model:
|_
{
le -> 
{{{
Q={q_gen_4468, q_gen_4469, q_gen_4486},
Q_f={q_gen_4468},
Delta=
{
<s>(q_gen_4469) -> q_gen_4469
<z>() -> q_gen_4469
<s, s>(q_gen_4468) -> q_gen_4468
<z, s>(q_gen_4469) -> q_gen_4468
<s, s>(q_gen_4486) -> q_gen_4486
<z, z>() -> q_gen_4486
}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_4467, q_gen_4471, q_gen_4472, q_gen_4478, q_gen_4483, q_gen_4484, q_gen_4485},
Q_f={q_gen_4467},
Delta=
{
<nil>() -> q_gen_4472
<s>(q_gen_4478) -> q_gen_4478
<z>() -> q_gen_4478
<snoc>(q_gen_4472, q_gen_4478) -> q_gen_4484
<nil, z>() -> q_gen_4467
<snoc, s>(q_gen_4472, q_gen_4471) -> q_gen_4467
<snoc, s>(q_gen_4484, q_gen_4483) -> q_gen_4467
<s, z>(q_gen_4478) -> q_gen_4471
<z, z>() -> q_gen_4471
<z, s>(q_gen_4478) -> q_gen_4483
<snoc, s>(q_gen_4484, q_gen_4471) -> q_gen_4485
}

Datatype: <nattsil, nat>
Convolution form: right
}}}

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 9
() -> length([nil, z]) -> 7
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 7
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 10
(le([s(nn1), z])) -> BOT -> 8
(le([z, z])) -> BOT -> 10
(length([l, _fy]) /\ length([snoc(l, x), _gy])) -> le([_fy, _gy]) -> 10
(length([ll, _by])) -> length([snoc(ll, x), s(_by)]) -> 16
}
Sat witness: Found: ((length([ll, _by])) -> length([snoc(ll, x), s(_by)]), {
_by -> s(s(z))  ;  ll -> snoc(snoc(nil, z), z)  ;  x -> z
})

-------------------------------------------
Step 12, which took 0.006665 s (model generation: 0.005620,  model checking: 0.001045):

Model:
|_
{
le -> 
{{{
Q={q_gen_4468, q_gen_4469, q_gen_4486},
Q_f={q_gen_4468},
Delta=
{
<s>(q_gen_4469) -> q_gen_4469
<z>() -> q_gen_4469
<s, s>(q_gen_4468) -> q_gen_4468
<z, s>(q_gen_4469) -> q_gen_4468
<s, s>(q_gen_4486) -> q_gen_4486
<z, z>() -> q_gen_4486
}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_4467, q_gen_4471, q_gen_4472, q_gen_4478, q_gen_4483, q_gen_4484, q_gen_4485},
Q_f={q_gen_4467},
Delta=
{
<nil>() -> q_gen_4472
<snoc>(q_gen_4484, q_gen_4478) -> q_gen_4472
<s>(q_gen_4478) -> q_gen_4478
<z>() -> q_gen_4478
<snoc>(q_gen_4472, q_gen_4478) -> q_gen_4484
<nil, z>() -> q_gen_4467
<snoc, s>(q_gen_4472, q_gen_4471) -> q_gen_4467
<snoc, s>(q_gen_4472, q_gen_4483) -> q_gen_4467
<snoc, s>(q_gen_4484, q_gen_4483) -> q_gen_4467
<s, z>(q_gen_4478) -> q_gen_4471
<z, z>() -> q_gen_4471
<z, s>(q_gen_4478) -> q_gen_4483
<snoc, s>(q_gen_4484, q_gen_4471) -> q_gen_4485
}

Datatype: <nattsil, nat>
Convolution form: right
}}}

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 10
() -> length([nil, z]) -> 8
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 8
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 10
(le([s(nn1), z])) -> BOT -> 9
(le([z, z])) -> BOT -> 10
(length([l, _fy]) /\ length([snoc(l, x), _gy])) -> le([_fy, _gy]) -> 13
(length([ll, _by])) -> length([snoc(ll, x), s(_by)]) -> 16
}
Sat witness: Found: ((length([l, _fy]) /\ length([snoc(l, x), _gy])) -> le([_fy, _gy]), {
_fy -> s(s(z))  ;  _gy -> s(s(z))  ;  l -> snoc(nil, z)  ;  x -> z
})

-------------------------------------------
Step 13, which took 0.010793 s (model generation: 0.008283,  model checking: 0.002510):

Model:
|_
{
le -> 
{{{
Q={q_gen_4468, q_gen_4469, q_gen_4486},
Q_f={q_gen_4468},
Delta=
{
<s>(q_gen_4469) -> q_gen_4469
<z>() -> q_gen_4469
<s, s>(q_gen_4468) -> q_gen_4468
<z, s>(q_gen_4469) -> q_gen_4468
<s, s>(q_gen_4486) -> q_gen_4486
<z, z>() -> q_gen_4486
}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_4467, q_gen_4471, q_gen_4472, q_gen_4478, q_gen_4483, q_gen_4484, q_gen_4485},
Q_f={q_gen_4467},
Delta=
{
<nil>() -> q_gen_4472
<s>(q_gen_4478) -> q_gen_4478
<z>() -> q_gen_4478
<snoc>(q_gen_4472, q_gen_4478) -> q_gen_4484
<snoc>(q_gen_4484, q_gen_4478) -> q_gen_4484
<nil, z>() -> q_gen_4467
<snoc, s>(q_gen_4472, q_gen_4471) -> q_gen_4467
<snoc, s>(q_gen_4484, q_gen_4483) -> q_gen_4467
<s, z>(q_gen_4478) -> q_gen_4471
<z, z>() -> q_gen_4471
<z, s>(q_gen_4478) -> q_gen_4483
<snoc, s>(q_gen_4472, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4471) -> q_gen_4485
}

Datatype: <nattsil, nat>
Convolution form: right
}}}

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 11
() -> length([nil, z]) -> 9
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 9
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 11
(le([s(nn1), z])) -> BOT -> 10
(le([z, z])) -> BOT -> 11
(length([l, _fy]) /\ length([snoc(l, x), _gy])) -> le([_fy, _gy]) -> 16
(length([ll, _by])) -> length([snoc(ll, x), s(_by)]) -> 16
}
Sat witness: Found: ((length([l, _fy]) /\ length([snoc(l, x), _gy])) -> le([_fy, _gy]), {
_fy -> s(s(z))  ;  _gy -> s(s(z))  ;  l -> snoc(snoc(nil, z), z)  ;  x -> z
})

-------------------------------------------
Step 14, which took 0.021931 s (model generation: 0.018573,  model checking: 0.003358):

Model:
|_
{
le -> 
{{{
Q={q_gen_4468, q_gen_4469, q_gen_4486},
Q_f={q_gen_4468},
Delta=
{
<s>(q_gen_4469) -> q_gen_4469
<z>() -> q_gen_4469
<s, s>(q_gen_4468) -> q_gen_4468
<z, s>(q_gen_4469) -> q_gen_4468
<s, s>(q_gen_4486) -> q_gen_4486
<z, z>() -> q_gen_4486
}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_4467, q_gen_4471, q_gen_4472, q_gen_4478, q_gen_4481, q_gen_4483, q_gen_4484, q_gen_4485},
Q_f={q_gen_4467},
Delta=
{
<nil>() -> q_gen_4472
<snoc>(q_gen_4484, q_gen_4478) -> q_gen_4472
<z>() -> q_gen_4478
<s>(q_gen_4478) -> q_gen_4481
<snoc>(q_gen_4472, q_gen_4478) -> q_gen_4484
<nil, z>() -> q_gen_4467
<snoc, s>(q_gen_4472, q_gen_4471) -> q_gen_4467
<snoc, s>(q_gen_4484, q_gen_4483) -> q_gen_4467
<s, z>(q_gen_4478) -> q_gen_4471
<s, z>(q_gen_4481) -> q_gen_4471
<z, s>(q_gen_4481) -> q_gen_4471
<z, z>() -> q_gen_4471
<z, s>(q_gen_4478) -> q_gen_4483
<snoc, s>(q_gen_4472, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4471) -> q_gen_4485
}

Datatype: <nattsil, nat>
Convolution form: right
}}}

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 12
() -> length([nil, z]) -> 10
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 10
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 12
(le([s(nn1), z])) -> BOT -> 11
(le([z, z])) -> BOT -> 12
(length([l, _fy]) /\ length([snoc(l, x), _gy])) -> le([_fy, _gy]) -> 16
(length([ll, _by])) -> length([snoc(ll, x), s(_by)]) -> 19
}
Sat witness: Found: ((length([ll, _by])) -> length([snoc(ll, x), s(_by)]), {
_by -> z  ;  ll -> nil  ;  x -> s(s(s(z)))
})

-------------------------------------------
Step 15, which took 0.021974 s (model generation: 0.020501,  model checking: 0.001473):

Model:
|_
{
le -> 
{{{
Q={q_gen_4468, q_gen_4469, q_gen_4486, q_gen_4487},
Q_f={q_gen_4468},
Delta=
{
<s>(q_gen_4469) -> q_gen_4469
<z>() -> q_gen_4469
<s, s>(q_gen_4468) -> q_gen_4468
<s, s>(q_gen_4486) -> q_gen_4468
<z, s>(q_gen_4469) -> q_gen_4468
<s, s>(q_gen_4487) -> q_gen_4486
<z, z>() -> q_gen_4487
}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_4467, q_gen_4471, q_gen_4472, q_gen_4477, q_gen_4478, q_gen_4484, q_gen_4485},
Q_f={q_gen_4467},
Delta=
{
<nil>() -> q_gen_4472
<s>(q_gen_4478) -> q_gen_4478
<z>() -> q_gen_4478
<snoc>(q_gen_4472, q_gen_4478) -> q_gen_4484
<snoc>(q_gen_4484, q_gen_4478) -> q_gen_4484
<nil, z>() -> q_gen_4467
<snoc, s>(q_gen_4472, q_gen_4471) -> q_gen_4467
<snoc, s>(q_gen_4472, q_gen_4477) -> q_gen_4467
<snoc, s>(q_gen_4484, q_gen_4477) -> q_gen_4467
<z, z>() -> q_gen_4471
<s, z>(q_gen_4478) -> q_gen_4477
<z, s>(q_gen_4478) -> q_gen_4477
<snoc, s>(q_gen_4484, q_gen_4471) -> q_gen_4485
}

Datatype: <nattsil, nat>
Convolution form: right
}}}

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 12
() -> length([nil, z]) -> 11
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 11
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 15
(le([s(nn1), z])) -> BOT -> 12
(le([z, z])) -> BOT -> 13
(length([l, _fy]) /\ length([snoc(l, x), _gy])) -> le([_fy, _gy]) -> 16
(length([ll, _by])) -> length([snoc(ll, x), s(_by)]) -> 19
}
Sat witness: Found: ((le([s(nn1), s(nn2)])) -> le([nn1, nn2]), {
nn1 -> s(z)  ;  nn2 -> s(z)
})

-------------------------------------------
Step 16, which took 0.024315 s (model generation: 0.020110,  model checking: 0.004205):

Model:
|_
{
le -> 
{{{
Q={q_gen_4468, q_gen_4469, q_gen_4486},
Q_f={q_gen_4468},
Delta=
{
<s>(q_gen_4469) -> q_gen_4469
<z>() -> q_gen_4469
<s, s>(q_gen_4468) -> q_gen_4468
<z, s>(q_gen_4469) -> q_gen_4468
<s, s>(q_gen_4486) -> q_gen_4486
<z, z>() -> q_gen_4486
}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_4467, q_gen_4471, q_gen_4472, q_gen_4478, q_gen_4481, q_gen_4483, q_gen_4484, q_gen_4485},
Q_f={q_gen_4467},
Delta=
{
<nil>() -> q_gen_4472
<snoc>(q_gen_4484, q_gen_4478) -> q_gen_4472
<s>(q_gen_4481) -> q_gen_4478
<z>() -> q_gen_4478
<s>(q_gen_4478) -> q_gen_4481
<snoc>(q_gen_4472, q_gen_4478) -> q_gen_4484
<nil, z>() -> q_gen_4467
<snoc, s>(q_gen_4472, q_gen_4471) -> q_gen_4467
<snoc, s>(q_gen_4484, q_gen_4483) -> q_gen_4467
<s, z>(q_gen_4478) -> q_gen_4471
<s, z>(q_gen_4481) -> q_gen_4471
<z, s>(q_gen_4481) -> q_gen_4471
<z, z>() -> q_gen_4471
<z, s>(q_gen_4478) -> q_gen_4483
<snoc, s>(q_gen_4472, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4471) -> q_gen_4485
}

Datatype: <nattsil, nat>
Convolution form: right
}}}

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 13
() -> length([nil, z]) -> 12
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 12
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 16
(le([s(nn1), z])) -> BOT -> 13
(le([z, z])) -> BOT -> 14
(length([l, _fy]) /\ length([snoc(l, x), _gy])) -> le([_fy, _gy]) -> 19
(length([ll, _by])) -> length([snoc(ll, x), s(_by)]) -> 19
}
Sat witness: Found: ((length([l, _fy]) /\ length([snoc(l, x), _gy])) -> le([_fy, _gy]), {
_fy -> s(s(s(z)))  ;  _gy -> s(s(z))  ;  l -> snoc(nil, z)  ;  x -> z
})

-------------------------------------------
Step 17, which took 0.026361 s (model generation: 0.025894,  model checking: 0.000467):

Model:
|_
{
le -> 
{{{
Q={q_gen_4468, q_gen_4469, q_gen_4486},
Q_f={q_gen_4468},
Delta=
{
<s>(q_gen_4469) -> q_gen_4469
<z>() -> q_gen_4469
<s, s>(q_gen_4468) -> q_gen_4468
<s, z>(q_gen_4469) -> q_gen_4468
<z, s>(q_gen_4469) -> q_gen_4468
<s, s>(q_gen_4486) -> q_gen_4486
<z, z>() -> q_gen_4486
}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_4467, q_gen_4471, q_gen_4472, q_gen_4478, q_gen_4481, q_gen_4483, q_gen_4484, q_gen_4485},
Q_f={q_gen_4467},
Delta=
{
<nil>() -> q_gen_4472
<snoc>(q_gen_4484, q_gen_4478) -> q_gen_4472
<z>() -> q_gen_4478
<s>(q_gen_4478) -> q_gen_4481
<s>(q_gen_4481) -> q_gen_4481
<snoc>(q_gen_4472, q_gen_4478) -> q_gen_4484
<nil, z>() -> q_gen_4467
<snoc, s>(q_gen_4472, q_gen_4471) -> q_gen_4467
<snoc, s>(q_gen_4484, q_gen_4483) -> q_gen_4467
<s, z>(q_gen_4478) -> q_gen_4471
<s, z>(q_gen_4481) -> q_gen_4471
<z, s>(q_gen_4481) -> q_gen_4471
<z, z>() -> q_gen_4471
<z, s>(q_gen_4478) -> q_gen_4483
<snoc, s>(q_gen_4472, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4471) -> q_gen_4485
}

Datatype: <nattsil, nat>
Convolution form: right
}}}

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 13
() -> length([nil, z]) -> 13
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 13
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 16
(le([s(nn1), z])) -> BOT -> 16
(le([z, z])) -> BOT -> 14
(length([l, _fy]) /\ length([snoc(l, x), _gy])) -> le([_fy, _gy]) -> 19
(length([ll, _by])) -> length([snoc(ll, x), s(_by)]) -> 19
}
Sat witness: Found: ((le([s(nn1), z])) -> BOT, {
nn1 -> z
})

-------------------------------------------
Step 18, which took 0.025642 s (model generation: 0.024993,  model checking: 0.000649):

Model:
|_
{
le -> 
{{{
Q={q_gen_4468, q_gen_4469, q_gen_4486, q_gen_4500},
Q_f={q_gen_4468},
Delta=
{
<s>(q_gen_4469) -> q_gen_4469
<z>() -> q_gen_4469
<s, s>(q_gen_4468) -> q_gen_4468
<s, s>(q_gen_4500) -> q_gen_4468
<z, s>(q_gen_4469) -> q_gen_4468
<s, s>(q_gen_4486) -> q_gen_4486
<z, z>() -> q_gen_4486
<s, z>(q_gen_4469) -> q_gen_4500
}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_4467, q_gen_4471, q_gen_4472, q_gen_4478, q_gen_4481, q_gen_4483, q_gen_4484, q_gen_4485},
Q_f={q_gen_4467},
Delta=
{
<nil>() -> q_gen_4472
<snoc>(q_gen_4484, q_gen_4478) -> q_gen_4472
<z>() -> q_gen_4478
<s>(q_gen_4478) -> q_gen_4481
<s>(q_gen_4481) -> q_gen_4481
<snoc>(q_gen_4472, q_gen_4478) -> q_gen_4484
<nil, z>() -> q_gen_4467
<snoc, s>(q_gen_4472, q_gen_4471) -> q_gen_4467
<snoc, s>(q_gen_4484, q_gen_4483) -> q_gen_4467
<s, z>(q_gen_4478) -> q_gen_4471
<s, z>(q_gen_4481) -> q_gen_4471
<z, s>(q_gen_4481) -> q_gen_4471
<z, z>() -> q_gen_4471
<z, s>(q_gen_4478) -> q_gen_4483
<snoc, s>(q_gen_4472, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4471) -> q_gen_4485
}

Datatype: <nattsil, nat>
Convolution form: right
}}}

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 14
() -> length([nil, z]) -> 14
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 14
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 19
(le([s(nn1), z])) -> BOT -> 17
(le([z, z])) -> BOT -> 15
(length([l, _fy]) /\ length([snoc(l, x), _gy])) -> le([_fy, _gy]) -> 19
(length([ll, _by])) -> length([snoc(ll, x), s(_by)]) -> 19
}
Sat witness: Found: ((le([s(nn1), s(nn2)])) -> le([nn1, nn2]), {
nn1 -> s(z)  ;  nn2 -> z
})

-------------------------------------------
Step 19, which took 0.026296 s (model generation: 0.023596,  model checking: 0.002700):

Model:
|_
{
le -> 
{{{
Q={q_gen_4468, q_gen_4469, q_gen_4486, q_gen_4499, q_gen_4500},
Q_f={q_gen_4468},
Delta=
{
<s>(q_gen_4469) -> q_gen_4469
<z>() -> q_gen_4469
<s, s>(q_gen_4468) -> q_gen_4468
<s, s>(q_gen_4499) -> q_gen_4468
<z, s>(q_gen_4469) -> q_gen_4468
<s, s>(q_gen_4486) -> q_gen_4486
<z, z>() -> q_gen_4486
<s, s>(q_gen_4500) -> q_gen_4499
<s, z>(q_gen_4469) -> q_gen_4500
}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_4467, q_gen_4471, q_gen_4472, q_gen_4478, q_gen_4481, q_gen_4483, q_gen_4484, q_gen_4485},
Q_f={q_gen_4467},
Delta=
{
<nil>() -> q_gen_4472
<snoc>(q_gen_4484, q_gen_4478) -> q_gen_4472
<z>() -> q_gen_4478
<s>(q_gen_4478) -> q_gen_4481
<s>(q_gen_4481) -> q_gen_4481
<snoc>(q_gen_4472, q_gen_4478) -> q_gen_4484
<nil, z>() -> q_gen_4467
<snoc, s>(q_gen_4472, q_gen_4471) -> q_gen_4467
<snoc, s>(q_gen_4484, q_gen_4483) -> q_gen_4467
<s, z>(q_gen_4478) -> q_gen_4471
<s, z>(q_gen_4481) -> q_gen_4471
<z, s>(q_gen_4481) -> q_gen_4471
<z, z>() -> q_gen_4471
<z, s>(q_gen_4478) -> q_gen_4483
<snoc, s>(q_gen_4472, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4471) -> q_gen_4485
}

Datatype: <nattsil, nat>
Convolution form: right
}}}

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 15
() -> length([nil, z]) -> 15
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 15
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 19
(le([s(nn1), z])) -> BOT -> 18
(le([z, z])) -> BOT -> 16
(length([l, _fy]) /\ length([snoc(l, x), _gy])) -> le([_fy, _gy]) -> 19
(length([ll, _by])) -> length([snoc(ll, x), s(_by)]) -> 22
}
Sat witness: Found: ((length([ll, _by])) -> length([snoc(ll, x), s(_by)]), {
_by -> s(s(s(z)))  ;  ll -> snoc(nil, z)  ;  x -> z
})

-------------------------------------------
Step 20, which took 0.027896 s (model generation: 0.026260,  model checking: 0.001636):

Model:
|_
{
le -> 
{{{
Q={q_gen_4468, q_gen_4469, q_gen_4486, q_gen_4499, q_gen_4500},
Q_f={q_gen_4468},
Delta=
{
<s>(q_gen_4469) -> q_gen_4469
<z>() -> q_gen_4469
<s, s>(q_gen_4468) -> q_gen_4468
<s, s>(q_gen_4499) -> q_gen_4468
<z, s>(q_gen_4469) -> q_gen_4468
<s, s>(q_gen_4486) -> q_gen_4486
<z, z>() -> q_gen_4486
<s, s>(q_gen_4500) -> q_gen_4499
<s, z>(q_gen_4469) -> q_gen_4500
}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_4467, q_gen_4471, q_gen_4472, q_gen_4478, q_gen_4481, q_gen_4483, q_gen_4484, q_gen_4485},
Q_f={q_gen_4467},
Delta=
{
<nil>() -> q_gen_4472
<snoc>(q_gen_4484, q_gen_4478) -> q_gen_4472
<s>(q_gen_4481) -> q_gen_4478
<z>() -> q_gen_4478
<s>(q_gen_4478) -> q_gen_4481
<snoc>(q_gen_4472, q_gen_4478) -> q_gen_4484
<nil, z>() -> q_gen_4467
<snoc, s>(q_gen_4472, q_gen_4471) -> q_gen_4467
<snoc, s>(q_gen_4484, q_gen_4483) -> q_gen_4467
<s, z>(q_gen_4478) -> q_gen_4471
<s, z>(q_gen_4481) -> q_gen_4471
<z, s>(q_gen_4481) -> q_gen_4471
<z, z>() -> q_gen_4471
<z, s>(q_gen_4478) -> q_gen_4483
<snoc, s>(q_gen_4472, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4471) -> q_gen_4485
}

Datatype: <nattsil, nat>
Convolution form: right
}}}

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 16
() -> length([nil, z]) -> 16
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 16
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 19
(le([s(nn1), z])) -> BOT -> 19
(le([z, z])) -> BOT -> 17
(length([l, _fy]) /\ length([snoc(l, x), _gy])) -> le([_fy, _gy]) -> 22
(length([ll, _by])) -> length([snoc(ll, x), s(_by)]) -> 22
}
Sat witness: Found: ((length([l, _fy]) /\ length([snoc(l, x), _gy])) -> le([_fy, _gy]), {
_fy -> s(s(z))  ;  _gy -> s(z)  ;  l -> snoc(snoc(nil, z), z)  ;  x -> z
})

-------------------------------------------
Step 21, which took 0.031918 s (model generation: 0.026939,  model checking: 0.004979):

Model:
|_
{
le -> 
{{{
Q={q_gen_4468, q_gen_4469, q_gen_4486},
Q_f={q_gen_4468},
Delta=
{
<s>(q_gen_4469) -> q_gen_4469
<z>() -> q_gen_4469
<s, s>(q_gen_4468) -> q_gen_4468
<z, s>(q_gen_4469) -> q_gen_4468
<s, s>(q_gen_4486) -> q_gen_4486
<s, z>(q_gen_4469) -> q_gen_4486
<z, z>() -> q_gen_4486
}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_4467, q_gen_4471, q_gen_4472, q_gen_4478, q_gen_4481, q_gen_4483, q_gen_4484, q_gen_4485, q_gen_4489, q_gen_4490},
Q_f={q_gen_4467},
Delta=
{
<nil>() -> q_gen_4472
<z>() -> q_gen_4478
<s>(q_gen_4478) -> q_gen_4481
<s>(q_gen_4481) -> q_gen_4481
<snoc>(q_gen_4472, q_gen_4478) -> q_gen_4484
<snoc>(q_gen_4484, q_gen_4478) -> q_gen_4490
<nil, z>() -> q_gen_4467
<snoc, s>(q_gen_4472, q_gen_4471) -> q_gen_4467
<snoc, s>(q_gen_4484, q_gen_4483) -> q_gen_4467
<snoc, s>(q_gen_4490, q_gen_4489) -> q_gen_4467
<s, z>(q_gen_4478) -> q_gen_4471
<s, z>(q_gen_4481) -> q_gen_4471
<z, z>() -> q_gen_4471
<z, s>(q_gen_4478) -> q_gen_4483
<snoc, s>(q_gen_4472, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4472, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4483) -> q_gen_4485
<z, s>(q_gen_4481) -> q_gen_4489
}

Datatype: <nattsil, nat>
Convolution form: right
}}}

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 17
() -> length([nil, z]) -> 17
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 17
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 20
(le([s(nn1), z])) -> BOT -> 20
(le([z, z])) -> BOT -> 18
(length([l, _fy]) /\ length([snoc(l, x), _gy])) -> le([_fy, _gy]) -> 22
(length([ll, _by])) -> length([snoc(ll, x), s(_by)]) -> 25
}
Sat witness: Found: ((length([ll, _by])) -> length([snoc(ll, x), s(_by)]), {
_by -> s(s(s(z)))  ;  ll -> snoc(snoc(snoc(nil, z), z), z)  ;  x -> z
})

-------------------------------------------
Step 22, which took 0.033640 s (model generation: 0.030360,  model checking: 0.003280):

Model:
|_
{
le -> 
{{{
Q={q_gen_4468, q_gen_4469, q_gen_4486},
Q_f={q_gen_4468},
Delta=
{
<s>(q_gen_4469) -> q_gen_4469
<z>() -> q_gen_4469
<s, s>(q_gen_4468) -> q_gen_4468
<z, s>(q_gen_4469) -> q_gen_4468
<s, s>(q_gen_4486) -> q_gen_4486
<s, z>(q_gen_4469) -> q_gen_4486
<z, z>() -> q_gen_4486
}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_4467, q_gen_4471, q_gen_4472, q_gen_4478, q_gen_4481, q_gen_4483, q_gen_4484, q_gen_4485, q_gen_4489, q_gen_4490},
Q_f={q_gen_4467},
Delta=
{
<nil>() -> q_gen_4472
<z>() -> q_gen_4478
<s>(q_gen_4478) -> q_gen_4481
<s>(q_gen_4481) -> q_gen_4481
<snoc>(q_gen_4472, q_gen_4478) -> q_gen_4484
<snoc>(q_gen_4484, q_gen_4478) -> q_gen_4490
<snoc>(q_gen_4490, q_gen_4478) -> q_gen_4490
<nil, z>() -> q_gen_4467
<snoc, s>(q_gen_4472, q_gen_4471) -> q_gen_4467
<snoc, s>(q_gen_4484, q_gen_4483) -> q_gen_4467
<snoc, s>(q_gen_4490, q_gen_4489) -> q_gen_4467
<s, z>(q_gen_4478) -> q_gen_4471
<s, z>(q_gen_4481) -> q_gen_4471
<z, z>() -> q_gen_4471
<z, s>(q_gen_4478) -> q_gen_4483
<snoc, s>(q_gen_4472, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4472, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4483) -> q_gen_4485
<z, s>(q_gen_4481) -> q_gen_4489
}

Datatype: <nattsil, nat>
Convolution form: right
}}}

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 18
() -> length([nil, z]) -> 18
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 18
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 21
(le([s(nn1), z])) -> BOT -> 21
(le([z, z])) -> BOT -> 19
(length([l, _fy]) /\ length([snoc(l, x), _gy])) -> le([_fy, _gy]) -> 25
(length([ll, _by])) -> length([snoc(ll, x), s(_by)]) -> 25
}
Sat witness: Found: ((length([l, _fy]) /\ length([snoc(l, x), _gy])) -> le([_fy, _gy]), {
_fy -> s(s(s(z)))  ;  _gy -> s(s(s(z)))  ;  l -> snoc(snoc(snoc(snoc(nil, z), z), z), z)  ;  x -> z
})

-------------------------------------------
Step 23, which took 0.045128 s (model generation: 0.035556,  model checking: 0.009572):

Model:
|_
{
le -> 
{{{
Q={q_gen_4468, q_gen_4469, q_gen_4486},
Q_f={q_gen_4468},
Delta=
{
<s>(q_gen_4469) -> q_gen_4469
<z>() -> q_gen_4469
<s, s>(q_gen_4468) -> q_gen_4468
<z, s>(q_gen_4469) -> q_gen_4468
<s, s>(q_gen_4486) -> q_gen_4486
<s, z>(q_gen_4469) -> q_gen_4486
<z, z>() -> q_gen_4486
}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_4467, q_gen_4471, q_gen_4472, q_gen_4478, q_gen_4481, q_gen_4483, q_gen_4484, q_gen_4485, q_gen_4489, q_gen_4490},
Q_f={q_gen_4467},
Delta=
{
<nil>() -> q_gen_4472
<s>(q_gen_4481) -> q_gen_4478
<z>() -> q_gen_4478
<s>(q_gen_4478) -> q_gen_4481
<snoc>(q_gen_4472, q_gen_4478) -> q_gen_4484
<snoc>(q_gen_4490, q_gen_4478) -> q_gen_4484
<snoc>(q_gen_4484, q_gen_4478) -> q_gen_4490
<nil, z>() -> q_gen_4467
<snoc, s>(q_gen_4472, q_gen_4471) -> q_gen_4467
<snoc, s>(q_gen_4484, q_gen_4483) -> q_gen_4467
<snoc, s>(q_gen_4490, q_gen_4489) -> q_gen_4467
<s, z>(q_gen_4478) -> q_gen_4471
<s, z>(q_gen_4481) -> q_gen_4471
<z, z>() -> q_gen_4471
<z, s>(q_gen_4478) -> q_gen_4483
<snoc, s>(q_gen_4472, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4472, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4483) -> q_gen_4485
<z, s>(q_gen_4481) -> q_gen_4489
}

Datatype: <nattsil, nat>
Convolution form: right
}}}

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 19
() -> length([nil, z]) -> 19
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 19
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 22
(le([s(nn1), z])) -> BOT -> 22
(le([z, z])) -> BOT -> 20
(length([l, _fy]) /\ length([snoc(l, x), _gy])) -> le([_fy, _gy]) -> 25
(length([ll, _by])) -> length([snoc(ll, x), s(_by)]) -> 28
}
Sat witness: Found: ((length([ll, _by])) -> length([snoc(ll, x), s(_by)]), {
_by -> s(s(z))  ;  ll -> snoc(snoc(nil, z), z)  ;  x -> s(z)
})

-------------------------------------------
Step 24, which took 0.041656 s (model generation: 0.037940,  model checking: 0.003716):

Model:
|_
{
le -> 
{{{
Q={q_gen_4468, q_gen_4469, q_gen_4486},
Q_f={q_gen_4468},
Delta=
{
<s>(q_gen_4469) -> q_gen_4469
<z>() -> q_gen_4469
<s, s>(q_gen_4468) -> q_gen_4468
<z, s>(q_gen_4469) -> q_gen_4468
<s, s>(q_gen_4486) -> q_gen_4486
<s, z>(q_gen_4469) -> q_gen_4486
<z, z>() -> q_gen_4486
}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_4467, q_gen_4471, q_gen_4472, q_gen_4478, q_gen_4481, q_gen_4483, q_gen_4484, q_gen_4485, q_gen_4489, q_gen_4490},
Q_f={q_gen_4467},
Delta=
{
<nil>() -> q_gen_4472
<s>(q_gen_4481) -> q_gen_4478
<z>() -> q_gen_4478
<s>(q_gen_4478) -> q_gen_4481
<snoc>(q_gen_4472, q_gen_4478) -> q_gen_4484
<snoc>(q_gen_4490, q_gen_4478) -> q_gen_4484
<snoc>(q_gen_4484, q_gen_4478) -> q_gen_4490
<nil, z>() -> q_gen_4467
<snoc, s>(q_gen_4472, q_gen_4471) -> q_gen_4467
<snoc, s>(q_gen_4484, q_gen_4483) -> q_gen_4467
<snoc, s>(q_gen_4490, q_gen_4489) -> q_gen_4467
<s, z>(q_gen_4478) -> q_gen_4471
<s, z>(q_gen_4481) -> q_gen_4471
<z, z>() -> q_gen_4471
<z, s>(q_gen_4478) -> q_gen_4483
<snoc, s>(q_gen_4472, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4472, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4483) -> q_gen_4485
<s, s>(q_gen_4483) -> q_gen_4489
<z, s>(q_gen_4481) -> q_gen_4489
}

Datatype: <nattsil, nat>
Convolution form: right
}}}

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 20
() -> length([nil, z]) -> 20
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 20
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 23
(le([s(nn1), z])) -> BOT -> 23
(le([z, z])) -> BOT -> 21
(length([l, _fy]) /\ length([snoc(l, x), _gy])) -> le([_fy, _gy]) -> 28
(length([ll, _by])) -> length([snoc(ll, x), s(_by)]) -> 28
}
Sat witness: Found: ((length([l, _fy]) /\ length([snoc(l, x), _gy])) -> le([_fy, _gy]), {
_fy -> s(s(s(z)))  ;  _gy -> s(s(z))  ;  l -> snoc(snoc(snoc(nil, z), z), z)  ;  x -> z
})

-------------------------------------------
Step 25, which took 0.045391 s (model generation: 0.041054,  model checking: 0.004337):

Model:
|_
{
le -> 
{{{
Q={q_gen_4468, q_gen_4469, q_gen_4486},
Q_f={q_gen_4468},
Delta=
{
<s>(q_gen_4469) -> q_gen_4469
<z>() -> q_gen_4469
<s, s>(q_gen_4468) -> q_gen_4468
<z, s>(q_gen_4469) -> q_gen_4468
<s, s>(q_gen_4486) -> q_gen_4486
<s, z>(q_gen_4469) -> q_gen_4486
<z, z>() -> q_gen_4486
}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_4467, q_gen_4471, q_gen_4472, q_gen_4478, q_gen_4481, q_gen_4483, q_gen_4484, q_gen_4485, q_gen_4489, q_gen_4490, q_gen_4496},
Q_f={q_gen_4467},
Delta=
{
<nil>() -> q_gen_4472
<snoc>(q_gen_4490, q_gen_4478) -> q_gen_4472
<z>() -> q_gen_4478
<s>(q_gen_4478) -> q_gen_4481
<snoc>(q_gen_4472, q_gen_4478) -> q_gen_4484
<snoc>(q_gen_4484, q_gen_4478) -> q_gen_4490
<s>(q_gen_4481) -> q_gen_4496
<nil, z>() -> q_gen_4467
<snoc, s>(q_gen_4472, q_gen_4471) -> q_gen_4467
<snoc, s>(q_gen_4484, q_gen_4483) -> q_gen_4467
<snoc, s>(q_gen_4484, q_gen_4489) -> q_gen_4467
<snoc, s>(q_gen_4490, q_gen_4489) -> q_gen_4467
<s, z>(q_gen_4478) -> q_gen_4471
<s, z>(q_gen_4481) -> q_gen_4471
<s, z>(q_gen_4496) -> q_gen_4471
<z, s>(q_gen_4496) -> q_gen_4471
<z, z>() -> q_gen_4471
<z, s>(q_gen_4478) -> q_gen_4483
<snoc, s>(q_gen_4472, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4472, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4483) -> q_gen_4485
<s, s>(q_gen_4483) -> q_gen_4489
<z, s>(q_gen_4481) -> q_gen_4489
}

Datatype: <nattsil, nat>
Convolution form: right
}}}

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 21
() -> length([nil, z]) -> 21
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 21
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 24
(le([s(nn1), z])) -> BOT -> 24
(le([z, z])) -> BOT -> 22
(length([l, _fy]) /\ length([snoc(l, x), _gy])) -> le([_fy, _gy]) -> 28
(length([ll, _by])) -> length([snoc(ll, x), s(_by)]) -> 31
}
Sat witness: Found: ((length([ll, _by])) -> length([snoc(ll, x), s(_by)]), {
_by -> s(s(s(z)))  ;  ll -> snoc(snoc(nil, z), z)  ;  x -> z
})

-------------------------------------------
Step 26, which took 0.050473 s (model generation: 0.045234,  model checking: 0.005239):

Model:
|_
{
le -> 
{{{
Q={q_gen_4468, q_gen_4469, q_gen_4486},
Q_f={q_gen_4468},
Delta=
{
<s>(q_gen_4469) -> q_gen_4469
<z>() -> q_gen_4469
<s, s>(q_gen_4468) -> q_gen_4468
<z, s>(q_gen_4469) -> q_gen_4468
<s, s>(q_gen_4486) -> q_gen_4486
<s, z>(q_gen_4469) -> q_gen_4486
<z, z>() -> q_gen_4486
}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_4467, q_gen_4471, q_gen_4472, q_gen_4478, q_gen_4481, q_gen_4483, q_gen_4484, q_gen_4485, q_gen_4489, q_gen_4490, q_gen_4505},
Q_f={q_gen_4467},
Delta=
{
<nil>() -> q_gen_4472
<z>() -> q_gen_4478
<s>(q_gen_4478) -> q_gen_4481
<s>(q_gen_4481) -> q_gen_4481
<snoc>(q_gen_4472, q_gen_4478) -> q_gen_4484
<snoc>(q_gen_4505, q_gen_4478) -> q_gen_4484
<snoc>(q_gen_4484, q_gen_4478) -> q_gen_4490
<snoc>(q_gen_4490, q_gen_4478) -> q_gen_4505
<nil, z>() -> q_gen_4467
<snoc, s>(q_gen_4472, q_gen_4471) -> q_gen_4467
<snoc, s>(q_gen_4484, q_gen_4483) -> q_gen_4467
<snoc, s>(q_gen_4490, q_gen_4489) -> q_gen_4467
<snoc, s>(q_gen_4505, q_gen_4489) -> q_gen_4467
<s, z>(q_gen_4478) -> q_gen_4471
<s, z>(q_gen_4481) -> q_gen_4471
<z, z>() -> q_gen_4471
<z, s>(q_gen_4478) -> q_gen_4483
<snoc, s>(q_gen_4472, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4472, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4483) -> q_gen_4485
<s, s>(q_gen_4483) -> q_gen_4489
<z, s>(q_gen_4481) -> q_gen_4489
}

Datatype: <nattsil, nat>
Convolution form: right
}}}

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 22
() -> length([nil, z]) -> 22
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 22
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 25
(le([s(nn1), z])) -> BOT -> 25
(le([z, z])) -> BOT -> 23
(length([l, _fy]) /\ length([snoc(l, x), _gy])) -> le([_fy, _gy]) -> 31
(length([ll, _by])) -> length([snoc(ll, x), s(_by)]) -> 31
}
Sat witness: Found: ((length([l, _fy]) /\ length([snoc(l, x), _gy])) -> le([_fy, _gy]), {
_fy -> s(s(s(s(z))))  ;  _gy -> s(s(s(z)))  ;  l -> snoc(snoc(snoc(nil, z), z), z)  ;  x -> s(z)
})

-------------------------------------------
Step 27, which took 0.062043 s (model generation: 0.051623,  model checking: 0.010420):

Model:
|_
{
le -> 
{{{
Q={q_gen_4468, q_gen_4469, q_gen_4486},
Q_f={q_gen_4468},
Delta=
{
<s>(q_gen_4469) -> q_gen_4469
<z>() -> q_gen_4469
<s, s>(q_gen_4468) -> q_gen_4468
<z, s>(q_gen_4469) -> q_gen_4468
<s, s>(q_gen_4486) -> q_gen_4486
<s, z>(q_gen_4469) -> q_gen_4486
<z, z>() -> q_gen_4486
}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_4467, q_gen_4471, q_gen_4472, q_gen_4478, q_gen_4481, q_gen_4483, q_gen_4484, q_gen_4485, q_gen_4489, q_gen_4490, q_gen_4496},
Q_f={q_gen_4467},
Delta=
{
<nil>() -> q_gen_4472
<snoc>(q_gen_4490, q_gen_4478) -> q_gen_4472
<z>() -> q_gen_4478
<s>(q_gen_4478) -> q_gen_4481
<snoc>(q_gen_4472, q_gen_4478) -> q_gen_4484
<snoc>(q_gen_4484, q_gen_4478) -> q_gen_4490
<s>(q_gen_4481) -> q_gen_4496
<nil, z>() -> q_gen_4467
<snoc, s>(q_gen_4472, q_gen_4471) -> q_gen_4467
<snoc, s>(q_gen_4484, q_gen_4483) -> q_gen_4467
<snoc, s>(q_gen_4490, q_gen_4489) -> q_gen_4467
<s, z>(q_gen_4478) -> q_gen_4471
<s, z>(q_gen_4481) -> q_gen_4471
<s, z>(q_gen_4496) -> q_gen_4471
<z, s>(q_gen_4496) -> q_gen_4471
<z, z>() -> q_gen_4471
<z, s>(q_gen_4478) -> q_gen_4483
<snoc, s>(q_gen_4472, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4472, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4483) -> q_gen_4485
<s, s>(q_gen_4483) -> q_gen_4489
<z, s>(q_gen_4481) -> q_gen_4489
}

Datatype: <nattsil, nat>
Convolution form: right
}}}

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 23
() -> length([nil, z]) -> 23
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 23
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 26
(le([s(nn1), z])) -> BOT -> 26
(le([z, z])) -> BOT -> 24
(length([l, _fy]) /\ length([snoc(l, x), _gy])) -> le([_fy, _gy]) -> 31
(length([ll, _by])) -> length([snoc(ll, x), s(_by)]) -> 34
}
Sat witness: Found: ((length([ll, _by])) -> length([snoc(ll, x), s(_by)]), {
_by -> z  ;  ll -> nil  ;  x -> s(s(s(s(z))))
})

-------------------------------------------
Step 28, which took 0.064027 s (model generation: 0.059359,  model checking: 0.004668):

Model:
|_
{
le -> 
{{{
Q={q_gen_4468, q_gen_4469, q_gen_4486},
Q_f={q_gen_4468},
Delta=
{
<s>(q_gen_4469) -> q_gen_4469
<z>() -> q_gen_4469
<s, s>(q_gen_4468) -> q_gen_4468
<z, s>(q_gen_4469) -> q_gen_4468
<s, s>(q_gen_4486) -> q_gen_4486
<s, z>(q_gen_4469) -> q_gen_4486
<z, z>() -> q_gen_4486
}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_4467, q_gen_4471, q_gen_4472, q_gen_4478, q_gen_4481, q_gen_4483, q_gen_4484, q_gen_4485, q_gen_4489, q_gen_4490, q_gen_4496},
Q_f={q_gen_4467},
Delta=
{
<nil>() -> q_gen_4472
<snoc>(q_gen_4490, q_gen_4478) -> q_gen_4472
<z>() -> q_gen_4478
<s>(q_gen_4478) -> q_gen_4481
<s>(q_gen_4496) -> q_gen_4481
<snoc>(q_gen_4472, q_gen_4478) -> q_gen_4484
<snoc>(q_gen_4484, q_gen_4478) -> q_gen_4490
<s>(q_gen_4481) -> q_gen_4496
<nil, z>() -> q_gen_4467
<snoc, s>(q_gen_4472, q_gen_4471) -> q_gen_4467
<snoc, s>(q_gen_4484, q_gen_4483) -> q_gen_4467
<snoc, s>(q_gen_4490, q_gen_4489) -> q_gen_4467
<s, z>(q_gen_4478) -> q_gen_4471
<s, z>(q_gen_4481) -> q_gen_4471
<s, z>(q_gen_4496) -> q_gen_4471
<z, s>(q_gen_4496) -> q_gen_4471
<z, z>() -> q_gen_4471
<z, s>(q_gen_4478) -> q_gen_4483
<snoc, s>(q_gen_4472, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4472, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4483) -> q_gen_4485
<s, s>(q_gen_4483) -> q_gen_4489
<z, s>(q_gen_4481) -> q_gen_4489
}

Datatype: <nattsil, nat>
Convolution form: right
}}}

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 24
() -> length([nil, z]) -> 24
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 24
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 27
(le([s(nn1), z])) -> BOT -> 27
(le([z, z])) -> BOT -> 25
(length([l, _fy]) /\ length([snoc(l, x), _gy])) -> le([_fy, _gy]) -> 34
(length([ll, _by])) -> length([snoc(ll, x), s(_by)]) -> 34
}
Sat witness: Found: ((length([l, _fy]) /\ length([snoc(l, x), _gy])) -> le([_fy, _gy]), {
_fy -> s(s(s(s(z))))  ;  _gy -> s(s(z))  ;  l -> snoc(nil, z)  ;  x -> z
})

-------------------------------------------
Step 29, which took 0.067609 s (model generation: 0.066005,  model checking: 0.001604):

Model:
|_
{
le -> 
{{{
Q={q_gen_4468, q_gen_4469, q_gen_4486, q_gen_4487, q_gen_4492},
Q_f={q_gen_4468},
Delta=
{
<s>(q_gen_4469) -> q_gen_4469
<z>() -> q_gen_4469
<s, s>(q_gen_4468) -> q_gen_4468
<s, s>(q_gen_4492) -> q_gen_4468
<z, s>(q_gen_4469) -> q_gen_4468
<s, s>(q_gen_4487) -> q_gen_4486
<s, z>(q_gen_4469) -> q_gen_4486
<z, z>() -> q_gen_4487
<s, s>(q_gen_4486) -> q_gen_4492
}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_4467, q_gen_4471, q_gen_4472, q_gen_4478, q_gen_4480, q_gen_4481, q_gen_4483, q_gen_4484, q_gen_4485, q_gen_4490},
Q_f={q_gen_4467},
Delta=
{
<nil>() -> q_gen_4472
<z>() -> q_gen_4478
<s>(q_gen_4478) -> q_gen_4481
<s>(q_gen_4481) -> q_gen_4481
<snoc>(q_gen_4472, q_gen_4478) -> q_gen_4484
<snoc>(q_gen_4490, q_gen_4478) -> q_gen_4484
<snoc>(q_gen_4484, q_gen_4478) -> q_gen_4490
<nil, z>() -> q_gen_4467
<snoc, s>(q_gen_4472, q_gen_4471) -> q_gen_4467
<snoc, s>(q_gen_4472, q_gen_4480) -> q_gen_4467
<snoc, s>(q_gen_4484, q_gen_4480) -> q_gen_4467
<snoc, s>(q_gen_4484, q_gen_4483) -> q_gen_4467
<snoc, s>(q_gen_4490, q_gen_4480) -> q_gen_4467
<s, z>(q_gen_4478) -> q_gen_4471
<z, z>() -> q_gen_4471
<s, s>(q_gen_4483) -> q_gen_4480
<s, z>(q_gen_4481) -> q_gen_4480
<z, s>(q_gen_4481) -> q_gen_4480
<z, s>(q_gen_4478) -> q_gen_4483
<snoc, s>(q_gen_4472, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4483) -> q_gen_4485
}

Datatype: <nattsil, nat>
Convolution form: right
}}}

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 25
() -> length([nil, z]) -> 25
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 25
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 30
(le([s(nn1), z])) -> BOT -> 28
(le([z, z])) -> BOT -> 26
(length([l, _fy]) /\ length([snoc(l, x), _gy])) -> le([_fy, _gy]) -> 34
(length([ll, _by])) -> length([snoc(ll, x), s(_by)]) -> 34
}
Sat witness: Found: ((le([s(nn1), s(nn2)])) -> le([nn1, nn2]), {
nn1 -> s(s(z))  ;  nn2 -> s(z)
})

-------------------------------------------
Step 30, which took 0.056392 s (model generation: 0.055599,  model checking: 0.000793):

Model:
|_
{
le -> 
{{{
Q={q_gen_4468, q_gen_4469, q_gen_4486, q_gen_4487, q_gen_4492},
Q_f={q_gen_4468},
Delta=
{
<s>(q_gen_4469) -> q_gen_4469
<z>() -> q_gen_4469
<s, s>(q_gen_4468) -> q_gen_4468
<s, s>(q_gen_4492) -> q_gen_4468
<z, s>(q_gen_4469) -> q_gen_4468
<s, s>(q_gen_4487) -> q_gen_4486
<s, z>(q_gen_4469) -> q_gen_4487
<z, z>() -> q_gen_4487
<s, s>(q_gen_4486) -> q_gen_4492
}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_4467, q_gen_4471, q_gen_4472, q_gen_4478, q_gen_4481, q_gen_4483, q_gen_4484, q_gen_4485, q_gen_4489, q_gen_4490},
Q_f={q_gen_4467},
Delta=
{
<nil>() -> q_gen_4472
<z>() -> q_gen_4478
<s>(q_gen_4478) -> q_gen_4481
<s>(q_gen_4481) -> q_gen_4481
<snoc>(q_gen_4472, q_gen_4478) -> q_gen_4484
<snoc>(q_gen_4484, q_gen_4478) -> q_gen_4490
<snoc>(q_gen_4490, q_gen_4478) -> q_gen_4490
<nil, z>() -> q_gen_4467
<snoc, s>(q_gen_4472, q_gen_4471) -> q_gen_4467
<snoc, s>(q_gen_4484, q_gen_4483) -> q_gen_4467
<snoc, s>(q_gen_4490, q_gen_4489) -> q_gen_4467
<s, z>(q_gen_4478) -> q_gen_4471
<s, z>(q_gen_4481) -> q_gen_4471
<z, z>() -> q_gen_4471
<z, s>(q_gen_4478) -> q_gen_4483
<snoc, s>(q_gen_4472, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4472, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4483) -> q_gen_4485
<s, s>(q_gen_4483) -> q_gen_4489
<z, s>(q_gen_4481) -> q_gen_4489
}

Datatype: <nattsil, nat>
Convolution form: right
}}}

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 26
() -> length([nil, z]) -> 26
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 26
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 33
(le([s(nn1), z])) -> BOT -> 29
(le([z, z])) -> BOT -> 27
(length([l, _fy]) /\ length([snoc(l, x), _gy])) -> le([_fy, _gy]) -> 34
(length([ll, _by])) -> length([snoc(ll, x), s(_by)]) -> 34
}
Sat witness: Found: ((le([s(nn1), s(nn2)])) -> le([nn1, nn2]), {
nn1 -> s(s(z))  ;  nn2 -> s(s(z))
})

-------------------------------------------
Step 31, which took 0.056260 s (model generation: 0.047295,  model checking: 0.008965):

Model:
|_
{
le -> 
{{{
Q={q_gen_4468, q_gen_4469, q_gen_4486},
Q_f={q_gen_4468},
Delta=
{
<s>(q_gen_4469) -> q_gen_4469
<z>() -> q_gen_4469
<s, s>(q_gen_4468) -> q_gen_4468
<z, s>(q_gen_4469) -> q_gen_4468
<s, s>(q_gen_4486) -> q_gen_4486
<s, z>(q_gen_4469) -> q_gen_4486
<z, z>() -> q_gen_4486
}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_4467, q_gen_4471, q_gen_4472, q_gen_4478, q_gen_4481, q_gen_4483, q_gen_4484, q_gen_4485, q_gen_4489, q_gen_4490, q_gen_4505, q_gen_4511},
Q_f={q_gen_4467},
Delta=
{
<nil>() -> q_gen_4472
<snoc>(q_gen_4505, q_gen_4478) -> q_gen_4472
<z>() -> q_gen_4478
<s>(q_gen_4478) -> q_gen_4481
<s>(q_gen_4481) -> q_gen_4481
<snoc>(q_gen_4472, q_gen_4478) -> q_gen_4484
<snoc>(q_gen_4484, q_gen_4478) -> q_gen_4490
<snoc>(q_gen_4490, q_gen_4478) -> q_gen_4505
<nil, z>() -> q_gen_4467
<snoc, s>(q_gen_4472, q_gen_4471) -> q_gen_4467
<snoc, s>(q_gen_4484, q_gen_4483) -> q_gen_4467
<snoc, s>(q_gen_4484, q_gen_4489) -> q_gen_4467
<snoc, s>(q_gen_4490, q_gen_4489) -> q_gen_4467
<snoc, s>(q_gen_4490, q_gen_4511) -> q_gen_4467
<snoc, s>(q_gen_4505, q_gen_4489) -> q_gen_4467
<s, z>(q_gen_4478) -> q_gen_4471
<s, z>(q_gen_4481) -> q_gen_4471
<z, z>() -> q_gen_4471
<z, s>(q_gen_4478) -> q_gen_4483
<snoc, s>(q_gen_4472, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4472, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4511) -> q_gen_4485
<z, s>(q_gen_4481) -> q_gen_4489
<s, s>(q_gen_4483) -> q_gen_4511
}

Datatype: <nattsil, nat>
Convolution form: right
}}}

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 27
() -> length([nil, z]) -> 27
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 27
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 34
(le([s(nn1), z])) -> BOT -> 30
(le([z, z])) -> BOT -> 28
(length([l, _fy]) /\ length([snoc(l, x), _gy])) -> le([_fy, _gy]) -> 34
(length([ll, _by])) -> length([snoc(ll, x), s(_by)]) -> 37
}
Sat witness: Found: ((length([ll, _by])) -> length([snoc(ll, x), s(_by)]), {
_by -> s(s(s(z)))  ;  ll -> snoc(snoc(snoc(snoc(nil, z), z), z), z)  ;  x -> z
})

-------------------------------------------
Step 32, which took 0.061995 s (model generation: 0.061041,  model checking: 0.000954):

Model:
|_
{
le -> 
{{{
Q={q_gen_4468, q_gen_4469, q_gen_4475, q_gen_4486},
Q_f={q_gen_4468},
Delta=
{
<z>() -> q_gen_4469
<s>(q_gen_4469) -> q_gen_4475
<s, s>(q_gen_4468) -> q_gen_4468
<s, z>(q_gen_4475) -> q_gen_4468
<z, s>(q_gen_4469) -> q_gen_4468
<z, s>(q_gen_4475) -> q_gen_4468
<s, s>(q_gen_4486) -> q_gen_4486
<s, z>(q_gen_4469) -> q_gen_4486
<z, z>() -> q_gen_4486
}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_4467, q_gen_4471, q_gen_4472, q_gen_4478, q_gen_4481, q_gen_4483, q_gen_4484, q_gen_4485, q_gen_4489, q_gen_4490, q_gen_4496},
Q_f={q_gen_4467},
Delta=
{
<nil>() -> q_gen_4472
<snoc>(q_gen_4490, q_gen_4478) -> q_gen_4472
<s>(q_gen_4496) -> q_gen_4478
<z>() -> q_gen_4478
<s>(q_gen_4478) -> q_gen_4481
<snoc>(q_gen_4472, q_gen_4478) -> q_gen_4484
<snoc>(q_gen_4484, q_gen_4478) -> q_gen_4490
<s>(q_gen_4481) -> q_gen_4496
<nil, z>() -> q_gen_4467
<snoc, s>(q_gen_4472, q_gen_4471) -> q_gen_4467
<snoc, s>(q_gen_4484, q_gen_4483) -> q_gen_4467
<snoc, s>(q_gen_4490, q_gen_4489) -> q_gen_4467
<s, z>(q_gen_4478) -> q_gen_4471
<s, z>(q_gen_4481) -> q_gen_4471
<s, z>(q_gen_4496) -> q_gen_4471
<z, s>(q_gen_4496) -> q_gen_4471
<z, z>() -> q_gen_4471
<z, s>(q_gen_4478) -> q_gen_4483
<snoc, s>(q_gen_4472, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4472, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4483) -> q_gen_4485
<s, s>(q_gen_4483) -> q_gen_4489
<z, s>(q_gen_4481) -> q_gen_4489
}

Datatype: <nattsil, nat>
Convolution form: right
}}}

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 30
() -> length([nil, z]) -> 28
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 28
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 34
(le([s(nn1), z])) -> BOT -> 30
(le([z, z])) -> BOT -> 28
(length([l, _fy]) /\ length([snoc(l, x), _gy])) -> le([_fy, _gy]) -> 34
(length([ll, _by])) -> length([snoc(ll, x), s(_by)]) -> 37
}
Sat witness: Found: (() -> le([z, s(nn2)]), {
nn2 -> s(s(z))
})

-------------------------------------------
Step 33, which took 0.064134 s (model generation: 0.062661,  model checking: 0.001473):

Model:
|_
{
le -> 
{{{
Q={q_gen_4468, q_gen_4469, q_gen_4475, q_gen_4486},
Q_f={q_gen_4468},
Delta=
{
<z>() -> q_gen_4469
<s>(q_gen_4469) -> q_gen_4475
<s>(q_gen_4475) -> q_gen_4475
<s, s>(q_gen_4468) -> q_gen_4468
<s, z>(q_gen_4475) -> q_gen_4468
<z, s>(q_gen_4469) -> q_gen_4468
<z, s>(q_gen_4475) -> q_gen_4468
<s, s>(q_gen_4486) -> q_gen_4486
<s, z>(q_gen_4469) -> q_gen_4486
<z, z>() -> q_gen_4486
}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_4467, q_gen_4471, q_gen_4472, q_gen_4478, q_gen_4481, q_gen_4483, q_gen_4484, q_gen_4485, q_gen_4489, q_gen_4490, q_gen_4496},
Q_f={q_gen_4467},
Delta=
{
<nil>() -> q_gen_4472
<snoc>(q_gen_4490, q_gen_4478) -> q_gen_4472
<s>(q_gen_4496) -> q_gen_4478
<z>() -> q_gen_4478
<s>(q_gen_4478) -> q_gen_4481
<snoc>(q_gen_4472, q_gen_4478) -> q_gen_4484
<snoc>(q_gen_4484, q_gen_4478) -> q_gen_4490
<s>(q_gen_4481) -> q_gen_4496
<nil, z>() -> q_gen_4467
<snoc, s>(q_gen_4472, q_gen_4471) -> q_gen_4467
<snoc, s>(q_gen_4484, q_gen_4483) -> q_gen_4467
<snoc, s>(q_gen_4490, q_gen_4489) -> q_gen_4467
<s, z>(q_gen_4478) -> q_gen_4471
<s, z>(q_gen_4481) -> q_gen_4471
<s, z>(q_gen_4496) -> q_gen_4471
<z, s>(q_gen_4496) -> q_gen_4471
<z, z>() -> q_gen_4471
<z, s>(q_gen_4478) -> q_gen_4483
<snoc, s>(q_gen_4472, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4472, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4483) -> q_gen_4485
<s, s>(q_gen_4483) -> q_gen_4489
<z, s>(q_gen_4481) -> q_gen_4489
}

Datatype: <nattsil, nat>
Convolution form: right
}}}

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 30
() -> length([nil, z]) -> 29
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 29
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 34
(le([s(nn1), z])) -> BOT -> 33
(le([z, z])) -> BOT -> 29
(length([l, _fy]) /\ length([snoc(l, x), _gy])) -> le([_fy, _gy]) -> 34
(length([ll, _by])) -> length([snoc(ll, x), s(_by)]) -> 37
}
Sat witness: Found: ((le([s(nn1), z])) -> BOT, {
nn1 -> s(z)
})

-------------------------------------------
Step 34, which took 0.059278 s (model generation: 0.055461,  model checking: 0.003817):

Model:
|_
{
le -> 
{{{
Q={q_gen_4468, q_gen_4469, q_gen_4475, q_gen_4486, q_gen_4523},
Q_f={q_gen_4468},
Delta=
{
<z>() -> q_gen_4469
<s>(q_gen_4469) -> q_gen_4475
<s>(q_gen_4475) -> q_gen_4475
<s, s>(q_gen_4468) -> q_gen_4468
<s, s>(q_gen_4523) -> q_gen_4468
<z, s>(q_gen_4469) -> q_gen_4468
<z, s>(q_gen_4475) -> q_gen_4468
<s, s>(q_gen_4486) -> q_gen_4486
<s, z>(q_gen_4469) -> q_gen_4486
<z, z>() -> q_gen_4486
<s, z>(q_gen_4475) -> q_gen_4523
}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_4467, q_gen_4471, q_gen_4472, q_gen_4478, q_gen_4481, q_gen_4483, q_gen_4484, q_gen_4485, q_gen_4489, q_gen_4490, q_gen_4496},
Q_f={q_gen_4467},
Delta=
{
<nil>() -> q_gen_4472
<snoc>(q_gen_4490, q_gen_4478) -> q_gen_4472
<s>(q_gen_4496) -> q_gen_4478
<z>() -> q_gen_4478
<s>(q_gen_4478) -> q_gen_4481
<snoc>(q_gen_4472, q_gen_4478) -> q_gen_4484
<snoc>(q_gen_4484, q_gen_4478) -> q_gen_4490
<s>(q_gen_4481) -> q_gen_4496
<nil, z>() -> q_gen_4467
<snoc, s>(q_gen_4472, q_gen_4471) -> q_gen_4467
<snoc, s>(q_gen_4484, q_gen_4483) -> q_gen_4467
<snoc, s>(q_gen_4490, q_gen_4489) -> q_gen_4467
<s, z>(q_gen_4478) -> q_gen_4471
<s, z>(q_gen_4481) -> q_gen_4471
<s, z>(q_gen_4496) -> q_gen_4471
<z, s>(q_gen_4496) -> q_gen_4471
<z, z>() -> q_gen_4471
<z, s>(q_gen_4478) -> q_gen_4483
<snoc, s>(q_gen_4472, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4472, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4483) -> q_gen_4485
<s, s>(q_gen_4483) -> q_gen_4489
<z, s>(q_gen_4481) -> q_gen_4489
}

Datatype: <nattsil, nat>
Convolution form: right
}}}

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 31
() -> length([nil, z]) -> 30
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 30
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 37
(le([s(nn1), z])) -> BOT -> 34
(le([z, z])) -> BOT -> 30
(length([l, _fy]) /\ length([snoc(l, x), _gy])) -> le([_fy, _gy]) -> 35
(length([ll, _by])) -> length([snoc(ll, x), s(_by)]) -> 37
}
Sat witness: Found: ((le([s(nn1), s(nn2)])) -> le([nn1, nn2]), {
nn1 -> s(s(z))  ;  nn2 -> z
})

-------------------------------------------
Step 35, which took 0.068624 s (model generation: 0.063447,  model checking: 0.005177):

Model:
|_
{
le -> 
{{{
Q={q_gen_4468, q_gen_4469, q_gen_4486},
Q_f={q_gen_4468},
Delta=
{
<s>(q_gen_4469) -> q_gen_4469
<z>() -> q_gen_4469
<s, s>(q_gen_4468) -> q_gen_4468
<z, s>(q_gen_4469) -> q_gen_4468
<s, s>(q_gen_4486) -> q_gen_4486
<s, z>(q_gen_4469) -> q_gen_4486
<z, z>() -> q_gen_4486
}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_4467, q_gen_4471, q_gen_4472, q_gen_4478, q_gen_4481, q_gen_4483, q_gen_4484, q_gen_4485, q_gen_4489, q_gen_4490, q_gen_4496, q_gen_4502, q_gen_4505},
Q_f={q_gen_4467},
Delta=
{
<nil>() -> q_gen_4472
<s>(q_gen_4496) -> q_gen_4478
<z>() -> q_gen_4478
<s>(q_gen_4478) -> q_gen_4481
<snoc>(q_gen_4472, q_gen_4478) -> q_gen_4484
<snoc>(q_gen_4484, q_gen_4478) -> q_gen_4490
<snoc>(q_gen_4505, q_gen_4478) -> q_gen_4490
<s>(q_gen_4481) -> q_gen_4496
<snoc>(q_gen_4490, q_gen_4478) -> q_gen_4505
<nil, z>() -> q_gen_4467
<snoc, s>(q_gen_4472, q_gen_4471) -> q_gen_4467
<snoc, s>(q_gen_4484, q_gen_4483) -> q_gen_4467
<snoc, s>(q_gen_4484, q_gen_4502) -> q_gen_4467
<snoc, s>(q_gen_4490, q_gen_4489) -> q_gen_4467
<snoc, s>(q_gen_4490, q_gen_4502) -> q_gen_4467
<snoc, s>(q_gen_4505, q_gen_4502) -> q_gen_4467
<s, z>(q_gen_4478) -> q_gen_4471
<s, z>(q_gen_4481) -> q_gen_4471
<s, z>(q_gen_4496) -> q_gen_4471
<z, z>() -> q_gen_4471
<z, s>(q_gen_4478) -> q_gen_4483
<snoc, s>(q_gen_4472, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4472, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4472, q_gen_4502) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4489) -> q_gen_4485
<s, s>(q_gen_4483) -> q_gen_4489
<z, s>(q_gen_4481) -> q_gen_4489
<z, s>(q_gen_4496) -> q_gen_4502
}

Datatype: <nattsil, nat>
Convolution form: right
}}}

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 32
() -> length([nil, z]) -> 31
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 31
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 37
(le([s(nn1), z])) -> BOT -> 35
(le([z, z])) -> BOT -> 31
(length([l, _fy]) /\ length([snoc(l, x), _gy])) -> le([_fy, _gy]) -> 38
(length([ll, _by])) -> length([snoc(ll, x), s(_by)]) -> 37
}
Sat witness: Found: ((length([l, _fy]) /\ length([snoc(l, x), _gy])) -> le([_fy, _gy]), {
_fy -> s(s(s(s(s(z)))))  ;  _gy -> s(s(s(z)))  ;  l -> snoc(snoc(nil, z), z)  ;  x -> z
})

-------------------------------------------
Step 36, which took 0.084448 s (model generation: 0.076437,  model checking: 0.008011):

Model:
|_
{
le -> 
{{{
Q={q_gen_4468, q_gen_4469, q_gen_4486},
Q_f={q_gen_4468},
Delta=
{
<s>(q_gen_4469) -> q_gen_4469
<z>() -> q_gen_4469
<s, s>(q_gen_4468) -> q_gen_4468
<z, s>(q_gen_4469) -> q_gen_4468
<s, s>(q_gen_4486) -> q_gen_4486
<s, z>(q_gen_4469) -> q_gen_4486
<z, z>() -> q_gen_4486
}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_4467, q_gen_4471, q_gen_4472, q_gen_4478, q_gen_4481, q_gen_4483, q_gen_4484, q_gen_4485, q_gen_4489, q_gen_4490, q_gen_4496, q_gen_4502, q_gen_4505},
Q_f={q_gen_4467},
Delta=
{
<nil>() -> q_gen_4472
<z>() -> q_gen_4478
<s>(q_gen_4478) -> q_gen_4481
<s>(q_gen_4496) -> q_gen_4481
<snoc>(q_gen_4472, q_gen_4478) -> q_gen_4484
<snoc>(q_gen_4505, q_gen_4478) -> q_gen_4484
<snoc>(q_gen_4484, q_gen_4478) -> q_gen_4490
<s>(q_gen_4481) -> q_gen_4496
<snoc>(q_gen_4490, q_gen_4478) -> q_gen_4505
<nil, z>() -> q_gen_4467
<snoc, s>(q_gen_4472, q_gen_4471) -> q_gen_4467
<snoc, s>(q_gen_4484, q_gen_4483) -> q_gen_4467
<snoc, s>(q_gen_4490, q_gen_4489) -> q_gen_4467
<snoc, s>(q_gen_4505, q_gen_4502) -> q_gen_4467
<s, z>(q_gen_4478) -> q_gen_4471
<s, z>(q_gen_4481) -> q_gen_4471
<s, z>(q_gen_4496) -> q_gen_4471
<z, z>() -> q_gen_4471
<z, s>(q_gen_4478) -> q_gen_4483
<snoc, s>(q_gen_4472, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4472, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4472, q_gen_4502) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4502) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4502) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4489) -> q_gen_4485
<s, s>(q_gen_4483) -> q_gen_4489
<z, s>(q_gen_4481) -> q_gen_4489
<z, s>(q_gen_4496) -> q_gen_4502
}

Datatype: <nattsil, nat>
Convolution form: right
}}}

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 33
() -> length([nil, z]) -> 32
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 32
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 37
(le([s(nn1), z])) -> BOT -> 36
(le([z, z])) -> BOT -> 32
(length([l, _fy]) /\ length([snoc(l, x), _gy])) -> le([_fy, _gy]) -> 38
(length([ll, _by])) -> length([snoc(ll, x), s(_by)]) -> 40
}
Sat witness: Found: ((length([ll, _by])) -> length([snoc(ll, x), s(_by)]), {
_by -> s(s(s(s(z))))  ;  ll -> snoc(snoc(snoc(snoc(nil, z), z), z), z)  ;  x -> z
})

-------------------------------------------
Step 37, which took 0.084473 s (model generation: 0.078818,  model checking: 0.005655):

Model:
|_
{
le -> 
{{{
Q={q_gen_4468, q_gen_4469, q_gen_4486},
Q_f={q_gen_4468},
Delta=
{
<s>(q_gen_4469) -> q_gen_4469
<z>() -> q_gen_4469
<s, s>(q_gen_4468) -> q_gen_4468
<z, s>(q_gen_4469) -> q_gen_4468
<s, s>(q_gen_4486) -> q_gen_4486
<s, z>(q_gen_4469) -> q_gen_4486
<z, z>() -> q_gen_4486
}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_4467, q_gen_4471, q_gen_4472, q_gen_4478, q_gen_4481, q_gen_4483, q_gen_4484, q_gen_4485, q_gen_4489, q_gen_4490, q_gen_4496, q_gen_4502, q_gen_4505},
Q_f={q_gen_4467},
Delta=
{
<nil>() -> q_gen_4472
<z>() -> q_gen_4478
<s>(q_gen_4478) -> q_gen_4481
<snoc>(q_gen_4472, q_gen_4478) -> q_gen_4484
<snoc>(q_gen_4484, q_gen_4478) -> q_gen_4490
<s>(q_gen_4481) -> q_gen_4496
<s>(q_gen_4496) -> q_gen_4496
<snoc>(q_gen_4490, q_gen_4478) -> q_gen_4505
<snoc>(q_gen_4505, q_gen_4478) -> q_gen_4505
<nil, z>() -> q_gen_4467
<snoc, s>(q_gen_4472, q_gen_4471) -> q_gen_4467
<snoc, s>(q_gen_4484, q_gen_4483) -> q_gen_4467
<snoc, s>(q_gen_4484, q_gen_4489) -> q_gen_4467
<snoc, s>(q_gen_4490, q_gen_4489) -> q_gen_4467
<snoc, s>(q_gen_4490, q_gen_4502) -> q_gen_4467
<snoc, s>(q_gen_4505, q_gen_4502) -> q_gen_4467
<s, z>(q_gen_4478) -> q_gen_4471
<s, z>(q_gen_4481) -> q_gen_4471
<s, z>(q_gen_4496) -> q_gen_4471
<z, z>() -> q_gen_4471
<z, s>(q_gen_4478) -> q_gen_4483
<snoc, s>(q_gen_4472, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4472, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4472, q_gen_4502) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4502) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4489) -> q_gen_4485
<s, s>(q_gen_4483) -> q_gen_4489
<z, s>(q_gen_4481) -> q_gen_4489
<z, s>(q_gen_4496) -> q_gen_4502
}

Datatype: <nattsil, nat>
Convolution form: right
}}}

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 34
() -> length([nil, z]) -> 33
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 33
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 38
(le([s(nn1), z])) -> BOT -> 37
(le([z, z])) -> BOT -> 33
(length([l, _fy]) /\ length([snoc(l, x), _gy])) -> le([_fy, _gy]) -> 41
(length([ll, _by])) -> length([snoc(ll, x), s(_by)]) -> 40
}
Sat witness: Found: ((length([l, _fy]) /\ length([snoc(l, x), _gy])) -> le([_fy, _gy]), {
_fy -> s(s(s(z)))  ;  _gy -> s(s(s(z)))  ;  l -> snoc(snoc(nil, z), z)  ;  x -> z
})

-------------------------------------------
Step 38, which took 0.105847 s (model generation: 0.079686,  model checking: 0.026161):

Model:
|_
{
le -> 
{{{
Q={q_gen_4468, q_gen_4469, q_gen_4486},
Q_f={q_gen_4468},
Delta=
{
<s>(q_gen_4469) -> q_gen_4469
<z>() -> q_gen_4469
<s, s>(q_gen_4468) -> q_gen_4468
<z, s>(q_gen_4469) -> q_gen_4468
<s, s>(q_gen_4486) -> q_gen_4486
<s, z>(q_gen_4469) -> q_gen_4486
<z, z>() -> q_gen_4486
}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_4467, q_gen_4471, q_gen_4472, q_gen_4478, q_gen_4481, q_gen_4483, q_gen_4484, q_gen_4485, q_gen_4489, q_gen_4490, q_gen_4496, q_gen_4502, q_gen_4505},
Q_f={q_gen_4467},
Delta=
{
<nil>() -> q_gen_4472
<z>() -> q_gen_4478
<s>(q_gen_4478) -> q_gen_4481
<snoc>(q_gen_4472, q_gen_4478) -> q_gen_4484
<snoc>(q_gen_4484, q_gen_4478) -> q_gen_4490
<snoc>(q_gen_4505, q_gen_4478) -> q_gen_4490
<s>(q_gen_4481) -> q_gen_4496
<s>(q_gen_4496) -> q_gen_4496
<snoc>(q_gen_4490, q_gen_4478) -> q_gen_4505
<nil, z>() -> q_gen_4467
<snoc, s>(q_gen_4472, q_gen_4471) -> q_gen_4467
<snoc, s>(q_gen_4484, q_gen_4483) -> q_gen_4467
<snoc, s>(q_gen_4490, q_gen_4489) -> q_gen_4467
<snoc, s>(q_gen_4490, q_gen_4502) -> q_gen_4467
<snoc, s>(q_gen_4505, q_gen_4502) -> q_gen_4467
<s, z>(q_gen_4478) -> q_gen_4471
<s, z>(q_gen_4481) -> q_gen_4471
<s, z>(q_gen_4496) -> q_gen_4471
<z, z>() -> q_gen_4471
<z, s>(q_gen_4478) -> q_gen_4483
<snoc, s>(q_gen_4472, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4472, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4472, q_gen_4502) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4502) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4489) -> q_gen_4485
<s, s>(q_gen_4483) -> q_gen_4489
<z, s>(q_gen_4481) -> q_gen_4489
<z, s>(q_gen_4496) -> q_gen_4502
}

Datatype: <nattsil, nat>
Convolution form: right
}}}

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 35
() -> length([nil, z]) -> 34
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 34
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 39
(le([s(nn1), z])) -> BOT -> 38
(le([z, z])) -> BOT -> 34
(length([l, _fy]) /\ length([snoc(l, x), _gy])) -> le([_fy, _gy]) -> 41
(length([ll, _by])) -> length([snoc(ll, x), s(_by)]) -> 43
}
Sat witness: Found: ((length([ll, _by])) -> length([snoc(ll, x), s(_by)]), {
_by -> s(s(z))  ;  ll -> snoc(snoc(nil, z), z)  ;  x -> s(s(z))
})

-------------------------------------------
Step 39, which took 0.090860 s (model generation: 0.088552,  model checking: 0.002308):

Model:
|_
{
le -> 
{{{
Q={q_gen_4468, q_gen_4469, q_gen_4486},
Q_f={q_gen_4468},
Delta=
{
<s>(q_gen_4469) -> q_gen_4469
<z>() -> q_gen_4469
<s, s>(q_gen_4468) -> q_gen_4468
<z, s>(q_gen_4469) -> q_gen_4468
<s, s>(q_gen_4486) -> q_gen_4486
<s, z>(q_gen_4469) -> q_gen_4486
<z, z>() -> q_gen_4486
}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_4467, q_gen_4471, q_gen_4472, q_gen_4478, q_gen_4481, q_gen_4483, q_gen_4484, q_gen_4485, q_gen_4489, q_gen_4490, q_gen_4496, q_gen_4502, q_gen_4505},
Q_f={q_gen_4467},
Delta=
{
<nil>() -> q_gen_4472
<z>() -> q_gen_4478
<s>(q_gen_4478) -> q_gen_4481
<snoc>(q_gen_4472, q_gen_4478) -> q_gen_4484
<snoc>(q_gen_4484, q_gen_4478) -> q_gen_4490
<s>(q_gen_4481) -> q_gen_4496
<s>(q_gen_4496) -> q_gen_4496
<snoc>(q_gen_4490, q_gen_4478) -> q_gen_4505
<snoc>(q_gen_4505, q_gen_4478) -> q_gen_4505
<nil, z>() -> q_gen_4467
<snoc, s>(q_gen_4472, q_gen_4471) -> q_gen_4467
<snoc, s>(q_gen_4484, q_gen_4483) -> q_gen_4467
<snoc, s>(q_gen_4490, q_gen_4489) -> q_gen_4467
<snoc, s>(q_gen_4490, q_gen_4502) -> q_gen_4467
<snoc, s>(q_gen_4505, q_gen_4502) -> q_gen_4467
<s, z>(q_gen_4478) -> q_gen_4471
<s, z>(q_gen_4481) -> q_gen_4471
<s, z>(q_gen_4496) -> q_gen_4471
<z, z>() -> q_gen_4471
<z, s>(q_gen_4478) -> q_gen_4483
<snoc, s>(q_gen_4472, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4472, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4472, q_gen_4502) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4502) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4489) -> q_gen_4485
<s, s>(q_gen_4471) -> q_gen_4489
<s, s>(q_gen_4483) -> q_gen_4489
<z, s>(q_gen_4481) -> q_gen_4489
<s, s>(q_gen_4489) -> q_gen_4502
<z, s>(q_gen_4496) -> q_gen_4502
}

Datatype: <nattsil, nat>
Convolution form: right
}}}

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 36
() -> length([nil, z]) -> 35
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 35
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 40
(le([s(nn1), z])) -> BOT -> 39
(le([z, z])) -> BOT -> 35
(length([l, _fy]) /\ length([snoc(l, x), _gy])) -> le([_fy, _gy]) -> 44
(length([ll, _by])) -> length([snoc(ll, x), s(_by)]) -> 43
}
Sat witness: Found: ((length([l, _fy]) /\ length([snoc(l, x), _gy])) -> le([_fy, _gy]), {
_fy -> s(s(z))  ;  _gy -> s(s(z))  ;  l -> snoc(snoc(nil, z), z)  ;  x -> s(z)
})

-------------------------------------------
Step 40, which took 0.099058 s (model generation: 0.081814,  model checking: 0.017244):

Model:
|_
{
le -> 
{{{
Q={q_gen_4468, q_gen_4469, q_gen_4486},
Q_f={q_gen_4468},
Delta=
{
<s>(q_gen_4469) -> q_gen_4469
<z>() -> q_gen_4469
<s, s>(q_gen_4468) -> q_gen_4468
<z, s>(q_gen_4469) -> q_gen_4468
<s, s>(q_gen_4486) -> q_gen_4486
<s, z>(q_gen_4469) -> q_gen_4486
<z, z>() -> q_gen_4486
}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_4467, q_gen_4471, q_gen_4472, q_gen_4478, q_gen_4481, q_gen_4483, q_gen_4484, q_gen_4485, q_gen_4489, q_gen_4490, q_gen_4496, q_gen_4502, q_gen_4505},
Q_f={q_gen_4467},
Delta=
{
<nil>() -> q_gen_4472
<z>() -> q_gen_4478
<s>(q_gen_4478) -> q_gen_4481
<snoc>(q_gen_4472, q_gen_4478) -> q_gen_4484
<snoc>(q_gen_4484, q_gen_4478) -> q_gen_4490
<snoc>(q_gen_4505, q_gen_4478) -> q_gen_4490
<s>(q_gen_4481) -> q_gen_4496
<s>(q_gen_4496) -> q_gen_4496
<snoc>(q_gen_4490, q_gen_4478) -> q_gen_4505
<nil, z>() -> q_gen_4467
<snoc, s>(q_gen_4472, q_gen_4471) -> q_gen_4467
<snoc, s>(q_gen_4484, q_gen_4483) -> q_gen_4467
<snoc, s>(q_gen_4490, q_gen_4489) -> q_gen_4467
<snoc, s>(q_gen_4490, q_gen_4502) -> q_gen_4467
<snoc, s>(q_gen_4505, q_gen_4502) -> q_gen_4467
<s, z>(q_gen_4478) -> q_gen_4471
<s, z>(q_gen_4481) -> q_gen_4471
<s, z>(q_gen_4496) -> q_gen_4471
<z, z>() -> q_gen_4471
<s, s>(q_gen_4471) -> q_gen_4483
<z, s>(q_gen_4478) -> q_gen_4483
<snoc, s>(q_gen_4472, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4472, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4472, q_gen_4502) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4502) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4489) -> q_gen_4485
<s, s>(q_gen_4483) -> q_gen_4489
<z, s>(q_gen_4481) -> q_gen_4489
<z, s>(q_gen_4496) -> q_gen_4502
}

Datatype: <nattsil, nat>
Convolution form: right
}}}

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 37
() -> length([nil, z]) -> 36
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 36
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 41
(le([s(nn1), z])) -> BOT -> 40
(le([z, z])) -> BOT -> 36
(length([l, _fy]) /\ length([snoc(l, x), _gy])) -> le([_fy, _gy]) -> 44
(length([ll, _by])) -> length([snoc(ll, x), s(_by)]) -> 46
}
Sat witness: Found: ((length([ll, _by])) -> length([snoc(ll, x), s(_by)]), {
_by -> s(s(s(z)))  ;  ll -> snoc(snoc(snoc(nil, z), z), z)  ;  x -> s(s(z))
})

-------------------------------------------
Step 41, which took 0.102194 s (model generation: 0.093393,  model checking: 0.008801):

Model:
|_
{
le -> 
{{{
Q={q_gen_4468, q_gen_4469, q_gen_4486},
Q_f={q_gen_4468},
Delta=
{
<s>(q_gen_4469) -> q_gen_4469
<z>() -> q_gen_4469
<s, s>(q_gen_4468) -> q_gen_4468
<z, s>(q_gen_4469) -> q_gen_4468
<s, s>(q_gen_4486) -> q_gen_4486
<s, z>(q_gen_4469) -> q_gen_4486
<z, z>() -> q_gen_4486
}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_4467, q_gen_4471, q_gen_4472, q_gen_4478, q_gen_4481, q_gen_4483, q_gen_4484, q_gen_4485, q_gen_4489, q_gen_4490, q_gen_4496, q_gen_4502, q_gen_4505},
Q_f={q_gen_4467},
Delta=
{
<nil>() -> q_gen_4472
<z>() -> q_gen_4478
<s>(q_gen_4478) -> q_gen_4481
<snoc>(q_gen_4472, q_gen_4478) -> q_gen_4484
<snoc>(q_gen_4484, q_gen_4478) -> q_gen_4490
<s>(q_gen_4481) -> q_gen_4496
<s>(q_gen_4496) -> q_gen_4496
<snoc>(q_gen_4490, q_gen_4478) -> q_gen_4505
<snoc>(q_gen_4505, q_gen_4478) -> q_gen_4505
<nil, z>() -> q_gen_4467
<snoc, s>(q_gen_4472, q_gen_4471) -> q_gen_4467
<snoc, s>(q_gen_4484, q_gen_4483) -> q_gen_4467
<snoc, s>(q_gen_4490, q_gen_4489) -> q_gen_4467
<snoc, s>(q_gen_4505, q_gen_4471) -> q_gen_4467
<snoc, s>(q_gen_4505, q_gen_4502) -> q_gen_4467
<s, s>(q_gen_4489) -> q_gen_4471
<s, z>(q_gen_4478) -> q_gen_4471
<s, z>(q_gen_4481) -> q_gen_4471
<s, z>(q_gen_4496) -> q_gen_4471
<z, z>() -> q_gen_4471
<z, s>(q_gen_4478) -> q_gen_4483
<snoc, s>(q_gen_4472, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4472, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4472, q_gen_4502) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4502) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4502) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4489) -> q_gen_4485
<s, s>(q_gen_4483) -> q_gen_4489
<s, s>(q_gen_4502) -> q_gen_4489
<z, s>(q_gen_4481) -> q_gen_4489
<s, s>(q_gen_4471) -> q_gen_4502
<z, s>(q_gen_4496) -> q_gen_4502
}

Datatype: <nattsil, nat>
Convolution form: right
}}}

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 38
() -> length([nil, z]) -> 37
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 37
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 42
(le([s(nn1), z])) -> BOT -> 41
(le([z, z])) -> BOT -> 37
(length([l, _fy]) /\ length([snoc(l, x), _gy])) -> le([_fy, _gy]) -> 47
(length([ll, _by])) -> length([snoc(ll, x), s(_by)]) -> 46
}
Sat witness: Found: ((length([l, _fy]) /\ length([snoc(l, x), _gy])) -> le([_fy, _gy]), {
_fy -> s(s(s(z)))  ;  _gy -> s(z)  ;  l -> snoc(snoc(snoc(nil, z), z), z)  ;  x -> z
})

-------------------------------------------
Step 42, which took 0.121941 s (model generation: 0.092865,  model checking: 0.029076):

Model:
|_
{
le -> 
{{{
Q={q_gen_4468, q_gen_4469, q_gen_4486},
Q_f={q_gen_4468},
Delta=
{
<s>(q_gen_4469) -> q_gen_4469
<z>() -> q_gen_4469
<s, s>(q_gen_4468) -> q_gen_4468
<z, s>(q_gen_4469) -> q_gen_4468
<s, s>(q_gen_4486) -> q_gen_4486
<s, z>(q_gen_4469) -> q_gen_4486
<z, z>() -> q_gen_4486
}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_4467, q_gen_4471, q_gen_4472, q_gen_4478, q_gen_4481, q_gen_4483, q_gen_4484, q_gen_4485, q_gen_4489, q_gen_4490, q_gen_4496, q_gen_4502, q_gen_4505},
Q_f={q_gen_4467},
Delta=
{
<nil>() -> q_gen_4472
<z>() -> q_gen_4478
<s>(q_gen_4478) -> q_gen_4481
<snoc>(q_gen_4472, q_gen_4478) -> q_gen_4484
<snoc>(q_gen_4484, q_gen_4478) -> q_gen_4490
<s>(q_gen_4481) -> q_gen_4496
<s>(q_gen_4496) -> q_gen_4496
<snoc>(q_gen_4490, q_gen_4478) -> q_gen_4505
<snoc>(q_gen_4505, q_gen_4478) -> q_gen_4505
<nil, z>() -> q_gen_4467
<snoc, s>(q_gen_4472, q_gen_4471) -> q_gen_4467
<snoc, s>(q_gen_4484, q_gen_4483) -> q_gen_4467
<snoc, s>(q_gen_4490, q_gen_4489) -> q_gen_4467
<snoc, s>(q_gen_4490, q_gen_4502) -> q_gen_4467
<snoc, s>(q_gen_4505, q_gen_4502) -> q_gen_4467
<s, z>(q_gen_4478) -> q_gen_4471
<s, z>(q_gen_4481) -> q_gen_4471
<s, z>(q_gen_4496) -> q_gen_4471
<z, z>() -> q_gen_4471
<s, s>(q_gen_4471) -> q_gen_4483
<z, s>(q_gen_4478) -> q_gen_4483
<snoc, s>(q_gen_4472, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4472, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4472, q_gen_4502) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4502) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4489) -> q_gen_4485
<s, s>(q_gen_4483) -> q_gen_4489
<z, s>(q_gen_4481) -> q_gen_4489
<s, s>(q_gen_4489) -> q_gen_4502
<z, s>(q_gen_4496) -> q_gen_4502
}

Datatype: <nattsil, nat>
Convolution form: right
}}}

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 39
() -> length([nil, z]) -> 38
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 38
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 43
(le([s(nn1), z])) -> BOT -> 42
(le([z, z])) -> BOT -> 38
(length([l, _fy]) /\ length([snoc(l, x), _gy])) -> le([_fy, _gy]) -> 47
(length([ll, _by])) -> length([snoc(ll, x), s(_by)]) -> 49
}
Sat witness: Found: ((length([ll, _by])) -> length([snoc(ll, x), s(_by)]), {
_by -> s(s(s(s(z))))  ;  ll -> snoc(snoc(snoc(nil, z), z), s(z))  ;  x -> z
})

-------------------------------------------
Step 43, which took 0.105347 s (model generation: 0.103044,  model checking: 0.002303):

Model:
|_
{
le -> 
{{{
Q={q_gen_4468, q_gen_4469, q_gen_4486},
Q_f={q_gen_4468},
Delta=
{
<s>(q_gen_4469) -> q_gen_4469
<z>() -> q_gen_4469
<s, s>(q_gen_4468) -> q_gen_4468
<z, s>(q_gen_4469) -> q_gen_4468
<s, s>(q_gen_4486) -> q_gen_4486
<s, z>(q_gen_4469) -> q_gen_4486
<z, z>() -> q_gen_4486
}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_4467, q_gen_4471, q_gen_4472, q_gen_4478, q_gen_4481, q_gen_4483, q_gen_4484, q_gen_4485, q_gen_4489, q_gen_4490, q_gen_4496, q_gen_4502, q_gen_4505},
Q_f={q_gen_4467},
Delta=
{
<nil>() -> q_gen_4472
<z>() -> q_gen_4478
<s>(q_gen_4478) -> q_gen_4481
<s>(q_gen_4496) -> q_gen_4481
<snoc>(q_gen_4472, q_gen_4478) -> q_gen_4484
<snoc>(q_gen_4490, q_gen_4481) -> q_gen_4484
<snoc>(q_gen_4484, q_gen_4478) -> q_gen_4490
<snoc>(q_gen_4505, q_gen_4478) -> q_gen_4490
<s>(q_gen_4481) -> q_gen_4496
<snoc>(q_gen_4490, q_gen_4478) -> q_gen_4505
<nil, z>() -> q_gen_4467
<snoc, s>(q_gen_4472, q_gen_4471) -> q_gen_4467
<snoc, s>(q_gen_4484, q_gen_4483) -> q_gen_4467
<snoc, s>(q_gen_4490, q_gen_4489) -> q_gen_4467
<snoc, s>(q_gen_4505, q_gen_4502) -> q_gen_4467
<s, z>(q_gen_4478) -> q_gen_4471
<s, z>(q_gen_4481) -> q_gen_4471
<s, z>(q_gen_4496) -> q_gen_4471
<z, z>() -> q_gen_4471
<z, s>(q_gen_4478) -> q_gen_4483
<snoc, s>(q_gen_4472, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4472, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4472, q_gen_4502) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4502) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4502) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4489) -> q_gen_4485
<s, s>(q_gen_4483) -> q_gen_4489
<s, s>(q_gen_4502) -> q_gen_4489
<z, s>(q_gen_4481) -> q_gen_4489
<s, s>(q_gen_4471) -> q_gen_4502
<s, s>(q_gen_4489) -> q_gen_4502
<z, s>(q_gen_4496) -> q_gen_4502
}

Datatype: <nattsil, nat>
Convolution form: right
}}}

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 40
() -> length([nil, z]) -> 39
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 39
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 44
(le([s(nn1), z])) -> BOT -> 43
(le([z, z])) -> BOT -> 39
(length([l, _fy]) /\ length([snoc(l, x), _gy])) -> le([_fy, _gy]) -> 50
(length([ll, _by])) -> length([snoc(ll, x), s(_by)]) -> 49
}
Sat witness: Found: ((length([l, _fy]) /\ length([snoc(l, x), _gy])) -> le([_fy, _gy]), {
_fy -> s(s(s(z)))  ;  _gy -> s(s(z))  ;  l -> snoc(snoc(snoc(nil, z), z), s(z))  ;  x -> z
})

-------------------------------------------
Step 44, which took 0.111187 s (model generation: 0.095197,  model checking: 0.015990):

Model:
|_
{
le -> 
{{{
Q={q_gen_4468, q_gen_4469, q_gen_4486},
Q_f={q_gen_4468},
Delta=
{
<s>(q_gen_4469) -> q_gen_4469
<z>() -> q_gen_4469
<s, s>(q_gen_4468) -> q_gen_4468
<z, s>(q_gen_4469) -> q_gen_4468
<s, s>(q_gen_4486) -> q_gen_4486
<s, z>(q_gen_4469) -> q_gen_4486
<z, z>() -> q_gen_4486
}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_4467, q_gen_4471, q_gen_4472, q_gen_4478, q_gen_4481, q_gen_4483, q_gen_4484, q_gen_4485, q_gen_4489, q_gen_4490, q_gen_4496, q_gen_4502, q_gen_4505},
Q_f={q_gen_4467},
Delta=
{
<nil>() -> q_gen_4472
<snoc>(q_gen_4490, q_gen_4481) -> q_gen_4472
<z>() -> q_gen_4478
<s>(q_gen_4478) -> q_gen_4481
<snoc>(q_gen_4472, q_gen_4478) -> q_gen_4484
<snoc>(q_gen_4484, q_gen_4478) -> q_gen_4490
<s>(q_gen_4481) -> q_gen_4496
<s>(q_gen_4496) -> q_gen_4496
<snoc>(q_gen_4490, q_gen_4478) -> q_gen_4505
<snoc>(q_gen_4505, q_gen_4478) -> q_gen_4505
<nil, z>() -> q_gen_4467
<snoc, s>(q_gen_4472, q_gen_4471) -> q_gen_4467
<snoc, s>(q_gen_4484, q_gen_4483) -> q_gen_4467
<snoc, s>(q_gen_4490, q_gen_4489) -> q_gen_4467
<snoc, s>(q_gen_4505, q_gen_4502) -> q_gen_4467
<s, z>(q_gen_4478) -> q_gen_4471
<s, z>(q_gen_4481) -> q_gen_4471
<s, z>(q_gen_4496) -> q_gen_4471
<z, z>() -> q_gen_4471
<z, s>(q_gen_4478) -> q_gen_4483
<snoc, s>(q_gen_4472, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4472, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4472, q_gen_4502) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4502) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4502) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4489) -> q_gen_4485
<s, s>(q_gen_4483) -> q_gen_4489
<s, s>(q_gen_4502) -> q_gen_4489
<z, s>(q_gen_4481) -> q_gen_4489
<s, s>(q_gen_4471) -> q_gen_4502
<s, s>(q_gen_4489) -> q_gen_4502
<z, s>(q_gen_4496) -> q_gen_4502
}

Datatype: <nattsil, nat>
Convolution form: right
}}}

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 41
() -> length([nil, z]) -> 40
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 40
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 45
(le([s(nn1), z])) -> BOT -> 44
(le([z, z])) -> BOT -> 40
(length([l, _fy]) /\ length([snoc(l, x), _gy])) -> le([_fy, _gy]) -> 50
(length([ll, _by])) -> length([snoc(ll, x), s(_by)]) -> 52
}
Sat witness: Found: ((length([ll, _by])) -> length([snoc(ll, x), s(_by)]), {
_by -> s(z)  ;  ll -> snoc(nil, z)  ;  x -> s(z)
})

-------------------------------------------
Step 45, which took 0.115910 s (model generation: 0.108849,  model checking: 0.007061):

Model:
|_
{
le -> 
{{{
Q={q_gen_4468, q_gen_4469, q_gen_4486},
Q_f={q_gen_4468},
Delta=
{
<s>(q_gen_4469) -> q_gen_4469
<z>() -> q_gen_4469
<s, s>(q_gen_4468) -> q_gen_4468
<z, s>(q_gen_4469) -> q_gen_4468
<s, s>(q_gen_4486) -> q_gen_4486
<s, z>(q_gen_4469) -> q_gen_4486
<z, z>() -> q_gen_4486
}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_4467, q_gen_4471, q_gen_4472, q_gen_4478, q_gen_4481, q_gen_4483, q_gen_4484, q_gen_4485, q_gen_4489, q_gen_4490, q_gen_4496, q_gen_4502, q_gen_4505},
Q_f={q_gen_4467},
Delta=
{
<nil>() -> q_gen_4472
<z>() -> q_gen_4478
<s>(q_gen_4478) -> q_gen_4481
<s>(q_gen_4496) -> q_gen_4481
<snoc>(q_gen_4472, q_gen_4478) -> q_gen_4484
<snoc>(q_gen_4484, q_gen_4478) -> q_gen_4490
<snoc>(q_gen_4490, q_gen_4481) -> q_gen_4490
<snoc>(q_gen_4505, q_gen_4478) -> q_gen_4490
<s>(q_gen_4481) -> q_gen_4496
<snoc>(q_gen_4490, q_gen_4478) -> q_gen_4505
<nil, z>() -> q_gen_4467
<snoc, s>(q_gen_4472, q_gen_4471) -> q_gen_4467
<snoc, s>(q_gen_4484, q_gen_4483) -> q_gen_4467
<snoc, s>(q_gen_4490, q_gen_4489) -> q_gen_4467
<snoc, s>(q_gen_4490, q_gen_4502) -> q_gen_4467
<snoc, s>(q_gen_4505, q_gen_4502) -> q_gen_4467
<s, z>(q_gen_4478) -> q_gen_4471
<s, z>(q_gen_4481) -> q_gen_4471
<s, z>(q_gen_4496) -> q_gen_4471
<z, z>() -> q_gen_4471
<s, s>(q_gen_4471) -> q_gen_4483
<z, s>(q_gen_4478) -> q_gen_4483
<snoc, s>(q_gen_4472, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4472, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4472, q_gen_4502) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4502) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4489) -> q_gen_4485
<s, s>(q_gen_4483) -> q_gen_4489
<z, s>(q_gen_4481) -> q_gen_4489
<s, s>(q_gen_4489) -> q_gen_4502
<z, s>(q_gen_4496) -> q_gen_4502
}

Datatype: <nattsil, nat>
Convolution form: right
}}}

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 42
() -> length([nil, z]) -> 41
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 41
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 46
(le([s(nn1), z])) -> BOT -> 45
(le([z, z])) -> BOT -> 41
(length([l, _fy]) /\ length([snoc(l, x), _gy])) -> le([_fy, _gy]) -> 53
(length([ll, _by])) -> length([snoc(ll, x), s(_by)]) -> 52
}
Sat witness: Found: ((length([l, _fy]) /\ length([snoc(l, x), _gy])) -> le([_fy, _gy]), {
_fy -> s(s(s(s(s(z)))))  ;  _gy -> s(s(s(s(z))))  ;  l -> snoc(snoc(snoc(nil, z), z), z)  ;  x -> s(s(z))
})

-------------------------------------------
Step 46, which took 0.112729 s (model generation: 0.104050,  model checking: 0.008679):

Model:
|_
{
le -> 
{{{
Q={q_gen_4468, q_gen_4469, q_gen_4486},
Q_f={q_gen_4468},
Delta=
{
<s>(q_gen_4469) -> q_gen_4469
<z>() -> q_gen_4469
<s, s>(q_gen_4468) -> q_gen_4468
<z, s>(q_gen_4469) -> q_gen_4468
<s, s>(q_gen_4486) -> q_gen_4486
<s, z>(q_gen_4469) -> q_gen_4486
<z, z>() -> q_gen_4486
}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_4467, q_gen_4471, q_gen_4472, q_gen_4478, q_gen_4481, q_gen_4483, q_gen_4484, q_gen_4485, q_gen_4489, q_gen_4490, q_gen_4496, q_gen_4502, q_gen_4505},
Q_f={q_gen_4467},
Delta=
{
<nil>() -> q_gen_4472
<snoc>(q_gen_4490, q_gen_4481) -> q_gen_4472
<z>() -> q_gen_4478
<s>(q_gen_4478) -> q_gen_4481
<snoc>(q_gen_4472, q_gen_4478) -> q_gen_4484
<snoc>(q_gen_4484, q_gen_4478) -> q_gen_4490
<s>(q_gen_4481) -> q_gen_4496
<s>(q_gen_4496) -> q_gen_4496
<snoc>(q_gen_4490, q_gen_4478) -> q_gen_4505
<snoc>(q_gen_4505, q_gen_4478) -> q_gen_4505
<nil, z>() -> q_gen_4467
<snoc, s>(q_gen_4472, q_gen_4471) -> q_gen_4467
<snoc, s>(q_gen_4484, q_gen_4483) -> q_gen_4467
<snoc, s>(q_gen_4490, q_gen_4489) -> q_gen_4467
<snoc, s>(q_gen_4505, q_gen_4502) -> q_gen_4467
<s, z>(q_gen_4478) -> q_gen_4471
<s, z>(q_gen_4481) -> q_gen_4471
<s, z>(q_gen_4496) -> q_gen_4471
<z, z>() -> q_gen_4471
<s, s>(q_gen_4471) -> q_gen_4483
<z, s>(q_gen_4478) -> q_gen_4483
<snoc, s>(q_gen_4472, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4472, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4472, q_gen_4502) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4502) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4502) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4489) -> q_gen_4485
<s, s>(q_gen_4483) -> q_gen_4489
<z, s>(q_gen_4481) -> q_gen_4489
<s, s>(q_gen_4489) -> q_gen_4502
<z, s>(q_gen_4496) -> q_gen_4502
}

Datatype: <nattsil, nat>
Convolution form: right
}}}

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 43
() -> length([nil, z]) -> 42
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 42
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 47
(le([s(nn1), z])) -> BOT -> 46
(le([z, z])) -> BOT -> 42
(length([l, _fy]) /\ length([snoc(l, x), _gy])) -> le([_fy, _gy]) -> 53
(length([ll, _by])) -> length([snoc(ll, x), s(_by)]) -> 55
}
Sat witness: Found: ((length([ll, _by])) -> length([snoc(ll, x), s(_by)]), {
_by -> s(s(s(z)))  ;  ll -> snoc(snoc(snoc(nil, z), z), s(z))  ;  x -> z
})

-------------------------------------------
Step 47, which took 0.111785 s (model generation: 0.107582,  model checking: 0.004203):

Model:
|_
{
le -> 
{{{
Q={q_gen_4468, q_gen_4469, q_gen_4486},
Q_f={q_gen_4468},
Delta=
{
<s>(q_gen_4469) -> q_gen_4469
<z>() -> q_gen_4469
<s, s>(q_gen_4468) -> q_gen_4468
<z, s>(q_gen_4469) -> q_gen_4468
<s, s>(q_gen_4486) -> q_gen_4486
<s, z>(q_gen_4469) -> q_gen_4486
<z, z>() -> q_gen_4486
}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_4467, q_gen_4471, q_gen_4472, q_gen_4478, q_gen_4481, q_gen_4483, q_gen_4484, q_gen_4485, q_gen_4489, q_gen_4490, q_gen_4496, q_gen_4502, q_gen_4505},
Q_f={q_gen_4467},
Delta=
{
<nil>() -> q_gen_4472
<z>() -> q_gen_4478
<s>(q_gen_4478) -> q_gen_4481
<snoc>(q_gen_4472, q_gen_4478) -> q_gen_4484
<snoc>(q_gen_4484, q_gen_4478) -> q_gen_4490
<s>(q_gen_4481) -> q_gen_4496
<s>(q_gen_4496) -> q_gen_4496
<snoc>(q_gen_4490, q_gen_4478) -> q_gen_4505
<snoc>(q_gen_4490, q_gen_4481) -> q_gen_4505
<snoc>(q_gen_4505, q_gen_4478) -> q_gen_4505
<nil, z>() -> q_gen_4467
<snoc, s>(q_gen_4472, q_gen_4471) -> q_gen_4467
<snoc, s>(q_gen_4484, q_gen_4483) -> q_gen_4467
<snoc, s>(q_gen_4490, q_gen_4489) -> q_gen_4467
<snoc, s>(q_gen_4505, q_gen_4502) -> q_gen_4467
<s, z>(q_gen_4478) -> q_gen_4471
<s, z>(q_gen_4481) -> q_gen_4471
<s, z>(q_gen_4496) -> q_gen_4471
<z, z>() -> q_gen_4471
<s, s>(q_gen_4471) -> q_gen_4483
<z, s>(q_gen_4478) -> q_gen_4483
<snoc, s>(q_gen_4472, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4472, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4472, q_gen_4502) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4502) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4502) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4489) -> q_gen_4485
<s, s>(q_gen_4483) -> q_gen_4489
<z, s>(q_gen_4481) -> q_gen_4489
<s, s>(q_gen_4489) -> q_gen_4502
<z, s>(q_gen_4496) -> q_gen_4502
}

Datatype: <nattsil, nat>
Convolution form: right
}}}

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 44
() -> length([nil, z]) -> 43
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 43
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 48
(le([s(nn1), z])) -> BOT -> 47
(le([z, z])) -> BOT -> 43
(length([l, _fy]) /\ length([snoc(l, x), _gy])) -> le([_fy, _gy]) -> 56
(length([ll, _by])) -> length([snoc(ll, x), s(_by)]) -> 55
}
Sat witness: Found: ((length([l, _fy]) /\ length([snoc(l, x), _gy])) -> le([_fy, _gy]), {
_fy -> s(s(s(s(z))))  ;  _gy -> s(s(s(s(z))))  ;  l -> snoc(snoc(snoc(snoc(nil, z), z), z), z)  ;  x -> z
})

-------------------------------------------
Step 48, which took 0.118099 s (model generation: 0.102248,  model checking: 0.015851):

Model:
|_
{
le -> 
{{{
Q={q_gen_4468, q_gen_4469, q_gen_4486},
Q_f={q_gen_4468},
Delta=
{
<s>(q_gen_4469) -> q_gen_4469
<z>() -> q_gen_4469
<s, s>(q_gen_4468) -> q_gen_4468
<z, s>(q_gen_4469) -> q_gen_4468
<s, s>(q_gen_4486) -> q_gen_4486
<s, z>(q_gen_4469) -> q_gen_4486
<z, z>() -> q_gen_4486
}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_4467, q_gen_4471, q_gen_4472, q_gen_4478, q_gen_4481, q_gen_4483, q_gen_4484, q_gen_4485, q_gen_4489, q_gen_4490, q_gen_4496, q_gen_4502, q_gen_4505, q_gen_4519},
Q_f={q_gen_4467},
Delta=
{
<nil>() -> q_gen_4472
<snoc>(q_gen_4505, q_gen_4478) -> q_gen_4472
<z>() -> q_gen_4478
<s>(q_gen_4478) -> q_gen_4481
<snoc>(q_gen_4472, q_gen_4478) -> q_gen_4484
<snoc>(q_gen_4484, q_gen_4478) -> q_gen_4490
<s>(q_gen_4481) -> q_gen_4496
<snoc>(q_gen_4490, q_gen_4478) -> q_gen_4505
<snoc>(q_gen_4490, q_gen_4481) -> q_gen_4505
<s>(q_gen_4496) -> q_gen_4519
<nil, z>() -> q_gen_4467
<snoc, s>(q_gen_4472, q_gen_4471) -> q_gen_4467
<snoc, s>(q_gen_4484, q_gen_4483) -> q_gen_4467
<snoc, s>(q_gen_4490, q_gen_4489) -> q_gen_4467
<snoc, s>(q_gen_4505, q_gen_4502) -> q_gen_4467
<s, z>(q_gen_4478) -> q_gen_4471
<s, z>(q_gen_4481) -> q_gen_4471
<s, z>(q_gen_4496) -> q_gen_4471
<s, z>(q_gen_4519) -> q_gen_4471
<z, s>(q_gen_4519) -> q_gen_4471
<z, z>() -> q_gen_4471
<s, s>(q_gen_4471) -> q_gen_4483
<z, s>(q_gen_4478) -> q_gen_4483
<snoc, s>(q_gen_4472, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4472, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4472, q_gen_4502) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4502) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4502) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4489) -> q_gen_4485
<s, s>(q_gen_4483) -> q_gen_4489
<z, s>(q_gen_4481) -> q_gen_4489
<s, s>(q_gen_4489) -> q_gen_4502
<z, s>(q_gen_4496) -> q_gen_4502
}

Datatype: <nattsil, nat>
Convolution form: right
}}}

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 45
() -> length([nil, z]) -> 44
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 44
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 49
(le([s(nn1), z])) -> BOT -> 48
(le([z, z])) -> BOT -> 44
(length([l, _fy]) /\ length([snoc(l, x), _gy])) -> le([_fy, _gy]) -> 56
(length([ll, _by])) -> length([snoc(ll, x), s(_by)]) -> 58
}
Sat witness: Found: ((length([ll, _by])) -> length([snoc(ll, x), s(_by)]), {
_by -> z  ;  ll -> nil  ;  x -> s(s(s(s(s(z)))))
})

-------------------------------------------
Step 49, which took 0.119578 s (model generation: 0.116156,  model checking: 0.003422):

Model:
|_
{
le -> 
{{{
Q={q_gen_4468, q_gen_4469, q_gen_4486},
Q_f={q_gen_4468},
Delta=
{
<s>(q_gen_4469) -> q_gen_4469
<z>() -> q_gen_4469
<s, s>(q_gen_4468) -> q_gen_4468
<z, s>(q_gen_4469) -> q_gen_4468
<s, s>(q_gen_4486) -> q_gen_4486
<s, z>(q_gen_4469) -> q_gen_4486
<z, z>() -> q_gen_4486
}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_4467, q_gen_4471, q_gen_4472, q_gen_4478, q_gen_4481, q_gen_4483, q_gen_4484, q_gen_4485, q_gen_4489, q_gen_4490, q_gen_4496, q_gen_4502, q_gen_4505, q_gen_4519},
Q_f={q_gen_4467},
Delta=
{
<nil>() -> q_gen_4472
<snoc>(q_gen_4505, q_gen_4478) -> q_gen_4472
<z>() -> q_gen_4478
<s>(q_gen_4478) -> q_gen_4481
<s>(q_gen_4519) -> q_gen_4481
<snoc>(q_gen_4472, q_gen_4478) -> q_gen_4484
<snoc>(q_gen_4484, q_gen_4478) -> q_gen_4490
<s>(q_gen_4481) -> q_gen_4496
<snoc>(q_gen_4490, q_gen_4478) -> q_gen_4505
<snoc>(q_gen_4490, q_gen_4481) -> q_gen_4505
<s>(q_gen_4496) -> q_gen_4519
<nil, z>() -> q_gen_4467
<snoc, s>(q_gen_4472, q_gen_4471) -> q_gen_4467
<snoc, s>(q_gen_4484, q_gen_4483) -> q_gen_4467
<snoc, s>(q_gen_4490, q_gen_4489) -> q_gen_4467
<snoc, s>(q_gen_4505, q_gen_4502) -> q_gen_4467
<s, z>(q_gen_4478) -> q_gen_4471
<s, z>(q_gen_4481) -> q_gen_4471
<s, z>(q_gen_4496) -> q_gen_4471
<s, z>(q_gen_4519) -> q_gen_4471
<z, s>(q_gen_4519) -> q_gen_4471
<z, z>() -> q_gen_4471
<s, s>(q_gen_4471) -> q_gen_4483
<z, s>(q_gen_4478) -> q_gen_4483
<snoc, s>(q_gen_4472, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4472, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4472, q_gen_4502) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4502) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4502) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4489) -> q_gen_4485
<s, s>(q_gen_4483) -> q_gen_4489
<z, s>(q_gen_4481) -> q_gen_4489
<s, s>(q_gen_4489) -> q_gen_4502
<z, s>(q_gen_4496) -> q_gen_4502
}

Datatype: <nattsil, nat>
Convolution form: right
}}}

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 46
() -> length([nil, z]) -> 45
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 45
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 50
(le([s(nn1), z])) -> BOT -> 49
(le([z, z])) -> BOT -> 45
(length([l, _fy]) /\ length([snoc(l, x), _gy])) -> le([_fy, _gy]) -> 59
(length([ll, _by])) -> length([snoc(ll, x), s(_by)]) -> 58
}
Sat witness: Found: ((length([l, _fy]) /\ length([snoc(l, x), _gy])) -> le([_fy, _gy]), {
_fy -> s(s(s(s(s(z)))))  ;  _gy -> s(s(z))  ;  l -> snoc(nil, z)  ;  x -> s(z)
})

-------------------------------------------
Step 50, which took 0.131290 s (model generation: 0.130760,  model checking: 0.000530):

Model:
|_
{
le -> 
{{{
Q={q_gen_4468, q_gen_4469, q_gen_4475, q_gen_4486, q_gen_4522, q_gen_4523},
Q_f={q_gen_4468},
Delta=
{
<z>() -> q_gen_4469
<s>(q_gen_4469) -> q_gen_4475
<s>(q_gen_4475) -> q_gen_4475
<s, s>(q_gen_4468) -> q_gen_4468
<s, s>(q_gen_4522) -> q_gen_4468
<z, s>(q_gen_4469) -> q_gen_4468
<z, s>(q_gen_4475) -> q_gen_4468
<s, s>(q_gen_4486) -> q_gen_4486
<s, z>(q_gen_4469) -> q_gen_4486
<z, z>() -> q_gen_4486
<s, s>(q_gen_4523) -> q_gen_4522
<s, z>(q_gen_4475) -> q_gen_4523
}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_4467, q_gen_4471, q_gen_4472, q_gen_4477, q_gen_4478, q_gen_4481, q_gen_4483, q_gen_4484, q_gen_4485, q_gen_4489, q_gen_4490, q_gen_4496, q_gen_4505},
Q_f={q_gen_4467},
Delta=
{
<nil>() -> q_gen_4472
<s>(q_gen_4496) -> q_gen_4478
<z>() -> q_gen_4478
<s>(q_gen_4478) -> q_gen_4481
<snoc>(q_gen_4472, q_gen_4478) -> q_gen_4484
<snoc>(q_gen_4505, q_gen_4478) -> q_gen_4484
<snoc>(q_gen_4484, q_gen_4478) -> q_gen_4490
<s>(q_gen_4481) -> q_gen_4496
<snoc>(q_gen_4490, q_gen_4478) -> q_gen_4505
<snoc>(q_gen_4490, q_gen_4481) -> q_gen_4505
<nil, z>() -> q_gen_4467
<snoc, s>(q_gen_4472, q_gen_4471) -> q_gen_4467
<snoc, s>(q_gen_4472, q_gen_4477) -> q_gen_4467
<snoc, s>(q_gen_4484, q_gen_4483) -> q_gen_4467
<snoc, s>(q_gen_4490, q_gen_4489) -> q_gen_4467
<snoc, s>(q_gen_4505, q_gen_4477) -> q_gen_4467
<s, z>(q_gen_4481) -> q_gen_4471
<s, z>(q_gen_4496) -> q_gen_4471
<z, z>() -> q_gen_4471
<s, s>(q_gen_4489) -> q_gen_4477
<s, z>(q_gen_4478) -> q_gen_4477
<z, s>(q_gen_4496) -> q_gen_4477
<s, s>(q_gen_4471) -> q_gen_4483
<z, s>(q_gen_4478) -> q_gen_4483
<snoc, s>(q_gen_4472, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4472, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4477) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4477) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4489) -> q_gen_4485
<s, s>(q_gen_4483) -> q_gen_4489
<z, s>(q_gen_4481) -> q_gen_4489
}

Datatype: <nattsil, nat>
Convolution form: right
}}}

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 47
() -> length([nil, z]) -> 46
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 46
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 53
(le([s(nn1), z])) -> BOT -> 50
(le([z, z])) -> BOT -> 46
(length([l, _fy]) /\ length([snoc(l, x), _gy])) -> le([_fy, _gy]) -> 59
(length([ll, _by])) -> length([snoc(ll, x), s(_by)]) -> 58
}
Sat witness: Found: ((le([s(nn1), s(nn2)])) -> le([nn1, nn2]), {
nn1 -> s(s(s(z)))  ;  nn2 -> s(z)
})

-------------------------------------------
Step 51, which took 0.124410 s (model generation: 0.123479,  model checking: 0.000931):

Model:
|_
{
le -> 
{{{
Q={q_gen_4468, q_gen_4469, q_gen_4486, q_gen_4498, q_gen_4499, q_gen_4500},
Q_f={q_gen_4468},
Delta=
{
<s>(q_gen_4469) -> q_gen_4469
<z>() -> q_gen_4469
<s, s>(q_gen_4468) -> q_gen_4468
<s, s>(q_gen_4498) -> q_gen_4468
<z, s>(q_gen_4469) -> q_gen_4468
<s, s>(q_gen_4486) -> q_gen_4486
<z, z>() -> q_gen_4486
<s, s>(q_gen_4499) -> q_gen_4498
<s, s>(q_gen_4500) -> q_gen_4499
<s, z>(q_gen_4469) -> q_gen_4500
}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_4467, q_gen_4471, q_gen_4472, q_gen_4478, q_gen_4481, q_gen_4483, q_gen_4484, q_gen_4485, q_gen_4489, q_gen_4490, q_gen_4496, q_gen_4502, q_gen_4505},
Q_f={q_gen_4467},
Delta=
{
<nil>() -> q_gen_4472
<s>(q_gen_4496) -> q_gen_4478
<z>() -> q_gen_4478
<s>(q_gen_4478) -> q_gen_4481
<snoc>(q_gen_4472, q_gen_4478) -> q_gen_4484
<snoc>(q_gen_4505, q_gen_4478) -> q_gen_4484
<snoc>(q_gen_4484, q_gen_4478) -> q_gen_4490
<s>(q_gen_4481) -> q_gen_4496
<snoc>(q_gen_4490, q_gen_4478) -> q_gen_4505
<snoc>(q_gen_4490, q_gen_4481) -> q_gen_4505
<nil, z>() -> q_gen_4467
<snoc, s>(q_gen_4472, q_gen_4471) -> q_gen_4467
<snoc, s>(q_gen_4484, q_gen_4483) -> q_gen_4467
<snoc, s>(q_gen_4490, q_gen_4489) -> q_gen_4467
<snoc, s>(q_gen_4505, q_gen_4502) -> q_gen_4467
<s, z>(q_gen_4478) -> q_gen_4471
<s, z>(q_gen_4481) -> q_gen_4471
<s, z>(q_gen_4496) -> q_gen_4471
<z, z>() -> q_gen_4471
<s, s>(q_gen_4471) -> q_gen_4483
<z, s>(q_gen_4478) -> q_gen_4483
<snoc, s>(q_gen_4472, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4472, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4472, q_gen_4502) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4502) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4502) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4489) -> q_gen_4485
<s, s>(q_gen_4483) -> q_gen_4489
<z, s>(q_gen_4481) -> q_gen_4489
<s, s>(q_gen_4489) -> q_gen_4502
<z, s>(q_gen_4496) -> q_gen_4502
}

Datatype: <nattsil, nat>
Convolution form: right
}}}

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 48
() -> length([nil, z]) -> 47
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 47
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 56
(le([s(nn1), z])) -> BOT -> 51
(le([z, z])) -> BOT -> 47
(length([l, _fy]) /\ length([snoc(l, x), _gy])) -> le([_fy, _gy]) -> 59
(length([ll, _by])) -> length([snoc(ll, x), s(_by)]) -> 58
}
Sat witness: Found: ((le([s(nn1), s(nn2)])) -> le([nn1, nn2]), {
nn1 -> s(s(s(z)))  ;  nn2 -> s(s(z))
})

-------------------------------------------
Step 52, which took 0.132601 s (model generation: 0.119818,  model checking: 0.012783):

Model:
|_
{
le -> 
{{{
Q={q_gen_4468, q_gen_4469, q_gen_4486},
Q_f={q_gen_4468},
Delta=
{
<s>(q_gen_4469) -> q_gen_4469
<z>() -> q_gen_4469
<s, s>(q_gen_4468) -> q_gen_4468
<z, s>(q_gen_4469) -> q_gen_4468
<s, s>(q_gen_4486) -> q_gen_4486
<s, z>(q_gen_4469) -> q_gen_4486
<z, z>() -> q_gen_4486
}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_4467, q_gen_4471, q_gen_4472, q_gen_4478, q_gen_4481, q_gen_4483, q_gen_4484, q_gen_4485, q_gen_4489, q_gen_4490, q_gen_4496, q_gen_4502, q_gen_4505, q_gen_4508, q_gen_4519, q_gen_4528},
Q_f={q_gen_4467},
Delta=
{
<nil>() -> q_gen_4472
<z>() -> q_gen_4478
<s>(q_gen_4478) -> q_gen_4481
<s>(q_gen_4519) -> q_gen_4481
<snoc>(q_gen_4472, q_gen_4478) -> q_gen_4484
<snoc>(q_gen_4484, q_gen_4478) -> q_gen_4490
<s>(q_gen_4481) -> q_gen_4496
<snoc>(q_gen_4490, q_gen_4478) -> q_gen_4505
<snoc>(q_gen_4490, q_gen_4481) -> q_gen_4505
<snoc>(q_gen_4505, q_gen_4478) -> q_gen_4508
<s>(q_gen_4496) -> q_gen_4519
<nil, z>() -> q_gen_4467
<snoc, s>(q_gen_4472, q_gen_4471) -> q_gen_4467
<snoc, s>(q_gen_4484, q_gen_4483) -> q_gen_4467
<snoc, s>(q_gen_4490, q_gen_4489) -> q_gen_4467
<snoc, s>(q_gen_4505, q_gen_4502) -> q_gen_4467
<snoc, s>(q_gen_4505, q_gen_4528) -> q_gen_4467
<snoc, s>(q_gen_4508, q_gen_4528) -> q_gen_4467
<s, z>(q_gen_4478) -> q_gen_4471
<s, z>(q_gen_4481) -> q_gen_4471
<s, z>(q_gen_4496) -> q_gen_4471
<s, z>(q_gen_4519) -> q_gen_4471
<z, z>() -> q_gen_4471
<s, s>(q_gen_4471) -> q_gen_4483
<z, s>(q_gen_4478) -> q_gen_4483
<snoc, s>(q_gen_4472, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4472, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4472, q_gen_4502) -> q_gen_4485
<snoc, s>(q_gen_4472, q_gen_4528) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4502) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4528) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4502) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4528) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4508, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4508, q_gen_4502) -> q_gen_4485
<s, s>(q_gen_4483) -> q_gen_4489
<z, s>(q_gen_4481) -> q_gen_4489
<z, s>(q_gen_4496) -> q_gen_4502
<s, s>(q_gen_4489) -> q_gen_4528
<z, s>(q_gen_4519) -> q_gen_4528
}

Datatype: <nattsil, nat>
Convolution form: right
}}}

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 49
() -> length([nil, z]) -> 48
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 48
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 57
(le([s(nn1), z])) -> BOT -> 52
(le([z, z])) -> BOT -> 48
(length([l, _fy]) /\ length([snoc(l, x), _gy])) -> le([_fy, _gy]) -> 59
(length([ll, _by])) -> length([snoc(ll, x), s(_by)]) -> 61
}
Sat witness: Found: ((length([ll, _by])) -> length([snoc(ll, x), s(_by)]), {
_by -> s(s(s(s(s(z)))))  ;  ll -> snoc(snoc(snoc(snoc(nil, z), z), s(z)), z)  ;  x -> z
})

-------------------------------------------
Step 53, which took 0.143468 s (model generation: 0.139949,  model checking: 0.003519):

Model:
|_
{
le -> 
{{{
Q={q_gen_4468, q_gen_4469, q_gen_4486},
Q_f={q_gen_4468},
Delta=
{
<s>(q_gen_4469) -> q_gen_4469
<z>() -> q_gen_4469
<s, s>(q_gen_4468) -> q_gen_4468
<z, s>(q_gen_4469) -> q_gen_4468
<s, s>(q_gen_4486) -> q_gen_4486
<s, z>(q_gen_4469) -> q_gen_4486
<z, z>() -> q_gen_4486
}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_4467, q_gen_4471, q_gen_4472, q_gen_4478, q_gen_4481, q_gen_4483, q_gen_4484, q_gen_4485, q_gen_4489, q_gen_4490, q_gen_4496, q_gen_4502, q_gen_4505, q_gen_4508, q_gen_4519, q_gen_4528},
Q_f={q_gen_4467},
Delta=
{
<nil>() -> q_gen_4472
<z>() -> q_gen_4478
<s>(q_gen_4478) -> q_gen_4481
<s>(q_gen_4519) -> q_gen_4481
<snoc>(q_gen_4472, q_gen_4478) -> q_gen_4484
<snoc>(q_gen_4484, q_gen_4478) -> q_gen_4490
<s>(q_gen_4481) -> q_gen_4496
<snoc>(q_gen_4490, q_gen_4478) -> q_gen_4505
<snoc>(q_gen_4490, q_gen_4481) -> q_gen_4505
<snoc>(q_gen_4505, q_gen_4478) -> q_gen_4508
<s>(q_gen_4496) -> q_gen_4519
<nil, z>() -> q_gen_4467
<snoc, s>(q_gen_4472, q_gen_4471) -> q_gen_4467
<snoc, s>(q_gen_4484, q_gen_4483) -> q_gen_4467
<snoc, s>(q_gen_4490, q_gen_4489) -> q_gen_4467
<snoc, s>(q_gen_4505, q_gen_4502) -> q_gen_4467
<snoc, s>(q_gen_4508, q_gen_4528) -> q_gen_4467
<s, z>(q_gen_4478) -> q_gen_4471
<s, z>(q_gen_4481) -> q_gen_4471
<s, z>(q_gen_4496) -> q_gen_4471
<s, z>(q_gen_4519) -> q_gen_4471
<z, z>() -> q_gen_4471
<s, s>(q_gen_4471) -> q_gen_4483
<z, s>(q_gen_4478) -> q_gen_4483
<snoc, s>(q_gen_4472, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4472, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4472, q_gen_4502) -> q_gen_4485
<snoc, s>(q_gen_4472, q_gen_4528) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4502) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4528) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4502) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4528) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4528) -> q_gen_4485
<snoc, s>(q_gen_4508, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4508, q_gen_4502) -> q_gen_4485
<s, s>(q_gen_4483) -> q_gen_4489
<z, s>(q_gen_4481) -> q_gen_4489
<s, s>(q_gen_4489) -> q_gen_4502
<z, s>(q_gen_4496) -> q_gen_4502
<z, s>(q_gen_4519) -> q_gen_4528
}

Datatype: <nattsil, nat>
Convolution form: right
}}}

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 50
() -> length([nil, z]) -> 49
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 49
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 58
(le([s(nn1), z])) -> BOT -> 53
(le([z, z])) -> BOT -> 49
(length([l, _fy]) /\ length([snoc(l, x), _gy])) -> le([_fy, _gy]) -> 62
(length([ll, _by])) -> length([snoc(ll, x), s(_by)]) -> 61
}
Sat witness: Found: ((length([l, _fy]) /\ length([snoc(l, x), _gy])) -> le([_fy, _gy]), {
_fy -> s(s(s(s(s(s(z))))))  ;  _gy -> s(s(s(s(z))))  ;  l -> snoc(snoc(snoc(nil, z), z), z)  ;  x -> s(z)
})

-------------------------------------------
Step 54, which took 0.126080 s (model generation: 0.125093,  model checking: 0.000987):

Model:
|_
{
le -> 
{{{
Q={q_gen_4468, q_gen_4469, q_gen_4475, q_gen_4486, q_gen_4526},
Q_f={q_gen_4468},
Delta=
{
<z>() -> q_gen_4469
<s>(q_gen_4469) -> q_gen_4475
<s>(q_gen_4475) -> q_gen_4526
<s, s>(q_gen_4468) -> q_gen_4468
<s, z>(q_gen_4526) -> q_gen_4468
<z, s>(q_gen_4469) -> q_gen_4468
<z, s>(q_gen_4475) -> q_gen_4468
<z, s>(q_gen_4526) -> q_gen_4468
<s, s>(q_gen_4486) -> q_gen_4486
<s, z>(q_gen_4469) -> q_gen_4486
<s, z>(q_gen_4475) -> q_gen_4486
<z, z>() -> q_gen_4486
}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_4467, q_gen_4471, q_gen_4472, q_gen_4478, q_gen_4481, q_gen_4483, q_gen_4484, q_gen_4485, q_gen_4489, q_gen_4490, q_gen_4496, q_gen_4502, q_gen_4505, q_gen_4519},
Q_f={q_gen_4467},
Delta=
{
<nil>() -> q_gen_4472
<snoc>(q_gen_4505, q_gen_4478) -> q_gen_4472
<z>() -> q_gen_4478
<s>(q_gen_4478) -> q_gen_4481
<snoc>(q_gen_4472, q_gen_4478) -> q_gen_4484
<snoc>(q_gen_4484, q_gen_4478) -> q_gen_4490
<s>(q_gen_4481) -> q_gen_4496
<s>(q_gen_4519) -> q_gen_4496
<snoc>(q_gen_4490, q_gen_4478) -> q_gen_4505
<snoc>(q_gen_4490, q_gen_4481) -> q_gen_4505
<s>(q_gen_4496) -> q_gen_4519
<nil, z>() -> q_gen_4467
<snoc, s>(q_gen_4472, q_gen_4471) -> q_gen_4467
<snoc, s>(q_gen_4484, q_gen_4483) -> q_gen_4467
<snoc, s>(q_gen_4490, q_gen_4489) -> q_gen_4467
<snoc, s>(q_gen_4505, q_gen_4502) -> q_gen_4467
<s, z>(q_gen_4478) -> q_gen_4471
<s, z>(q_gen_4481) -> q_gen_4471
<s, z>(q_gen_4496) -> q_gen_4471
<s, z>(q_gen_4519) -> q_gen_4471
<z, s>(q_gen_4519) -> q_gen_4471
<z, z>() -> q_gen_4471
<s, s>(q_gen_4471) -> q_gen_4483
<z, s>(q_gen_4478) -> q_gen_4483
<snoc, s>(q_gen_4472, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4472, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4472, q_gen_4502) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4502) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4502) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4489) -> q_gen_4485
<s, s>(q_gen_4483) -> q_gen_4489
<z, s>(q_gen_4481) -> q_gen_4489
<s, s>(q_gen_4489) -> q_gen_4502
<z, s>(q_gen_4496) -> q_gen_4502
}

Datatype: <nattsil, nat>
Convolution form: right
}}}

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 53
() -> length([nil, z]) -> 50
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 50
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 58
(le([s(nn1), z])) -> BOT -> 53
(le([z, z])) -> BOT -> 50
(length([l, _fy]) /\ length([snoc(l, x), _gy])) -> le([_fy, _gy]) -> 62
(length([ll, _by])) -> length([snoc(ll, x), s(_by)]) -> 61
}
Sat witness: Found: (() -> le([z, s(nn2)]), {
nn2 -> s(s(s(z)))
})

-------------------------------------------
Step 55, which took 0.148573 s (model generation: 0.126100,  model checking: 0.022473):

Model:
|_
{
le -> 
{{{
Q={q_gen_4468, q_gen_4469, q_gen_4486},
Q_f={q_gen_4468},
Delta=
{
<s>(q_gen_4469) -> q_gen_4469
<z>() -> q_gen_4469
<s, s>(q_gen_4468) -> q_gen_4468
<z, s>(q_gen_4469) -> q_gen_4468
<s, s>(q_gen_4486) -> q_gen_4486
<s, z>(q_gen_4469) -> q_gen_4486
<z, z>() -> q_gen_4486
}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_4467, q_gen_4471, q_gen_4472, q_gen_4478, q_gen_4481, q_gen_4483, q_gen_4484, q_gen_4485, q_gen_4489, q_gen_4490, q_gen_4496, q_gen_4502, q_gen_4505, q_gen_4508, q_gen_4519, q_gen_4528},
Q_f={q_gen_4467},
Delta=
{
<nil>() -> q_gen_4472
<z>() -> q_gen_4478
<s>(q_gen_4478) -> q_gen_4481
<snoc>(q_gen_4472, q_gen_4478) -> q_gen_4484
<snoc>(q_gen_4484, q_gen_4478) -> q_gen_4490
<s>(q_gen_4481) -> q_gen_4496
<snoc>(q_gen_4490, q_gen_4478) -> q_gen_4505
<snoc>(q_gen_4490, q_gen_4481) -> q_gen_4505
<snoc>(q_gen_4505, q_gen_4478) -> q_gen_4508
<s>(q_gen_4496) -> q_gen_4519
<s>(q_gen_4519) -> q_gen_4519
<nil, z>() -> q_gen_4467
<snoc, s>(q_gen_4472, q_gen_4471) -> q_gen_4467
<snoc, s>(q_gen_4484, q_gen_4483) -> q_gen_4467
<snoc, s>(q_gen_4490, q_gen_4489) -> q_gen_4467
<snoc, s>(q_gen_4505, q_gen_4502) -> q_gen_4467
<snoc, s>(q_gen_4508, q_gen_4528) -> q_gen_4467
<s, z>(q_gen_4478) -> q_gen_4471
<s, z>(q_gen_4481) -> q_gen_4471
<s, z>(q_gen_4496) -> q_gen_4471
<s, z>(q_gen_4519) -> q_gen_4471
<z, z>() -> q_gen_4471
<s, s>(q_gen_4471) -> q_gen_4483
<z, s>(q_gen_4478) -> q_gen_4483
<snoc, s>(q_gen_4472, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4472, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4472, q_gen_4502) -> q_gen_4485
<snoc, s>(q_gen_4472, q_gen_4528) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4502) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4528) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4502) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4528) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4528) -> q_gen_4485
<snoc, s>(q_gen_4508, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4508, q_gen_4502) -> q_gen_4485
<s, s>(q_gen_4483) -> q_gen_4489
<z, s>(q_gen_4481) -> q_gen_4489
<s, s>(q_gen_4489) -> q_gen_4502
<z, s>(q_gen_4496) -> q_gen_4502
<z, s>(q_gen_4519) -> q_gen_4528
}

Datatype: <nattsil, nat>
Convolution form: right
}}}

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 54
() -> length([nil, z]) -> 51
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 51
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 59
(le([s(nn1), z])) -> BOT -> 54
(le([z, z])) -> BOT -> 51
(length([l, _fy]) /\ length([snoc(l, x), _gy])) -> le([_fy, _gy]) -> 62
(length([ll, _by])) -> length([snoc(ll, x), s(_by)]) -> 64
}
Sat witness: Found: ((length([ll, _by])) -> length([snoc(ll, x), s(_by)]), {
_by -> s(s(s(z)))  ;  ll -> snoc(snoc(snoc(nil, z), z), s(s(z)))  ;  x -> s(s(z))
})

-------------------------------------------
Step 56, which took 0.164707 s (model generation: 0.161532,  model checking: 0.003175):

Model:
|_
{
le -> 
{{{
Q={q_gen_4468, q_gen_4469, q_gen_4486},
Q_f={q_gen_4468},
Delta=
{
<s>(q_gen_4469) -> q_gen_4469
<z>() -> q_gen_4469
<s, s>(q_gen_4468) -> q_gen_4468
<z, s>(q_gen_4469) -> q_gen_4468
<s, s>(q_gen_4486) -> q_gen_4486
<s, z>(q_gen_4469) -> q_gen_4486
<z, z>() -> q_gen_4486
}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_4467, q_gen_4471, q_gen_4472, q_gen_4478, q_gen_4481, q_gen_4483, q_gen_4484, q_gen_4485, q_gen_4489, q_gen_4490, q_gen_4496, q_gen_4502, q_gen_4505, q_gen_4508, q_gen_4519, q_gen_4528},
Q_f={q_gen_4467},
Delta=
{
<nil>() -> q_gen_4472
<s>(q_gen_4519) -> q_gen_4478
<z>() -> q_gen_4478
<s>(q_gen_4478) -> q_gen_4481
<snoc>(q_gen_4472, q_gen_4478) -> q_gen_4484
<snoc>(q_gen_4484, q_gen_4478) -> q_gen_4490
<s>(q_gen_4481) -> q_gen_4496
<snoc>(q_gen_4490, q_gen_4478) -> q_gen_4505
<snoc>(q_gen_4490, q_gen_4481) -> q_gen_4505
<snoc>(q_gen_4490, q_gen_4496) -> q_gen_4505
<snoc>(q_gen_4505, q_gen_4478) -> q_gen_4508
<s>(q_gen_4496) -> q_gen_4519
<nil, z>() -> q_gen_4467
<snoc, s>(q_gen_4472, q_gen_4471) -> q_gen_4467
<snoc, s>(q_gen_4484, q_gen_4483) -> q_gen_4467
<snoc, s>(q_gen_4490, q_gen_4489) -> q_gen_4467
<snoc, s>(q_gen_4505, q_gen_4502) -> q_gen_4467
<snoc, s>(q_gen_4508, q_gen_4528) -> q_gen_4467
<s, z>(q_gen_4478) -> q_gen_4471
<s, z>(q_gen_4481) -> q_gen_4471
<s, z>(q_gen_4496) -> q_gen_4471
<s, z>(q_gen_4519) -> q_gen_4471
<z, z>() -> q_gen_4471
<s, s>(q_gen_4471) -> q_gen_4483
<z, s>(q_gen_4478) -> q_gen_4483
<snoc, s>(q_gen_4472, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4472, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4472, q_gen_4502) -> q_gen_4485
<snoc, s>(q_gen_4472, q_gen_4528) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4502) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4528) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4502) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4528) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4528) -> q_gen_4485
<snoc, s>(q_gen_4508, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4508, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4508, q_gen_4502) -> q_gen_4485
<s, s>(q_gen_4483) -> q_gen_4489
<z, s>(q_gen_4481) -> q_gen_4489
<s, s>(q_gen_4489) -> q_gen_4502
<z, s>(q_gen_4496) -> q_gen_4502
<z, s>(q_gen_4519) -> q_gen_4528
}

Datatype: <nattsil, nat>
Convolution form: right
}}}

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 55
() -> length([nil, z]) -> 52
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 52
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 60
(le([s(nn1), z])) -> BOT -> 55
(le([z, z])) -> BOT -> 52
(length([l, _fy]) /\ length([snoc(l, x), _gy])) -> le([_fy, _gy]) -> 65
(length([ll, _by])) -> length([snoc(ll, x), s(_by)]) -> 64
}
Sat witness: Found: ((length([l, _fy]) /\ length([snoc(l, x), _gy])) -> le([_fy, _gy]), {
_fy -> s(s(s(s(s(s(z))))))  ;  _gy -> s(s(s(z)))  ;  l -> snoc(snoc(nil, z), z)  ;  x -> s(s(z))
})

-------------------------------------------
Step 57, which took 0.145422 s (model generation: 0.144436,  model checking: 0.000986):

Model:
|_
{
le -> 
{{{
Q={q_gen_4468, q_gen_4469, q_gen_4475, q_gen_4486, q_gen_4526},
Q_f={q_gen_4468},
Delta=
{
<z>() -> q_gen_4469
<s>(q_gen_4469) -> q_gen_4475
<s>(q_gen_4526) -> q_gen_4475
<s>(q_gen_4475) -> q_gen_4526
<s, s>(q_gen_4468) -> q_gen_4468
<s, z>(q_gen_4526) -> q_gen_4468
<z, s>(q_gen_4469) -> q_gen_4468
<z, s>(q_gen_4475) -> q_gen_4468
<z, s>(q_gen_4526) -> q_gen_4468
<s, s>(q_gen_4486) -> q_gen_4486
<s, z>(q_gen_4469) -> q_gen_4486
<s, z>(q_gen_4475) -> q_gen_4486
<z, z>() -> q_gen_4486
}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_4467, q_gen_4471, q_gen_4472, q_gen_4478, q_gen_4481, q_gen_4483, q_gen_4484, q_gen_4485, q_gen_4489, q_gen_4490, q_gen_4496, q_gen_4502, q_gen_4505, q_gen_4519},
Q_f={q_gen_4467},
Delta=
{
<nil>() -> q_gen_4472
<snoc>(q_gen_4505, q_gen_4478) -> q_gen_4472
<z>() -> q_gen_4478
<s>(q_gen_4478) -> q_gen_4481
<snoc>(q_gen_4472, q_gen_4478) -> q_gen_4484
<snoc>(q_gen_4484, q_gen_4478) -> q_gen_4490
<s>(q_gen_4481) -> q_gen_4496
<snoc>(q_gen_4490, q_gen_4478) -> q_gen_4505
<snoc>(q_gen_4490, q_gen_4481) -> q_gen_4505
<snoc>(q_gen_4490, q_gen_4496) -> q_gen_4505
<s>(q_gen_4496) -> q_gen_4519
<s>(q_gen_4519) -> q_gen_4519
<nil, z>() -> q_gen_4467
<snoc, s>(q_gen_4472, q_gen_4471) -> q_gen_4467
<snoc, s>(q_gen_4484, q_gen_4483) -> q_gen_4467
<snoc, s>(q_gen_4490, q_gen_4489) -> q_gen_4467
<snoc, s>(q_gen_4505, q_gen_4502) -> q_gen_4467
<s, z>(q_gen_4478) -> q_gen_4471
<s, z>(q_gen_4481) -> q_gen_4471
<s, z>(q_gen_4496) -> q_gen_4471
<s, z>(q_gen_4519) -> q_gen_4471
<z, s>(q_gen_4519) -> q_gen_4471
<z, z>() -> q_gen_4471
<s, s>(q_gen_4471) -> q_gen_4483
<z, s>(q_gen_4478) -> q_gen_4483
<snoc, s>(q_gen_4472, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4472, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4472, q_gen_4502) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4502) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4502) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4489) -> q_gen_4485
<s, s>(q_gen_4483) -> q_gen_4489
<z, s>(q_gen_4481) -> q_gen_4489
<s, s>(q_gen_4489) -> q_gen_4502
<z, s>(q_gen_4496) -> q_gen_4502
}

Datatype: <nattsil, nat>
Convolution form: right
}}}

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 55
() -> length([nil, z]) -> 53
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 53
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 60
(le([s(nn1), z])) -> BOT -> 58
(le([z, z])) -> BOT -> 53
(length([l, _fy]) /\ length([snoc(l, x), _gy])) -> le([_fy, _gy]) -> 65
(length([ll, _by])) -> length([snoc(ll, x), s(_by)]) -> 64
}
Sat witness: Found: ((le([s(nn1), z])) -> BOT, {
nn1 -> s(s(z))
})

-------------------------------------------
Step 58, which took 0.164047 s (model generation: 0.128842,  model checking: 0.035205):

Model:
|_
{
le -> 
{{{
Q={q_gen_4468, q_gen_4469, q_gen_4486},
Q_f={q_gen_4468},
Delta=
{
<s>(q_gen_4469) -> q_gen_4469
<z>() -> q_gen_4469
<s, s>(q_gen_4468) -> q_gen_4468
<z, s>(q_gen_4469) -> q_gen_4468
<s, s>(q_gen_4486) -> q_gen_4486
<s, z>(q_gen_4469) -> q_gen_4486
<z, z>() -> q_gen_4486
}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_4467, q_gen_4471, q_gen_4472, q_gen_4478, q_gen_4481, q_gen_4483, q_gen_4484, q_gen_4485, q_gen_4489, q_gen_4490, q_gen_4496, q_gen_4502, q_gen_4505, q_gen_4508, q_gen_4519, q_gen_4528},
Q_f={q_gen_4467},
Delta=
{
<nil>() -> q_gen_4472
<z>() -> q_gen_4478
<s>(q_gen_4478) -> q_gen_4481
<snoc>(q_gen_4472, q_gen_4478) -> q_gen_4484
<snoc>(q_gen_4484, q_gen_4478) -> q_gen_4490
<s>(q_gen_4481) -> q_gen_4496
<s>(q_gen_4519) -> q_gen_4496
<snoc>(q_gen_4490, q_gen_4478) -> q_gen_4505
<snoc>(q_gen_4490, q_gen_4481) -> q_gen_4505
<snoc>(q_gen_4490, q_gen_4496) -> q_gen_4505
<snoc>(q_gen_4505, q_gen_4478) -> q_gen_4508
<s>(q_gen_4496) -> q_gen_4519
<nil, z>() -> q_gen_4467
<snoc, s>(q_gen_4472, q_gen_4471) -> q_gen_4467
<snoc, s>(q_gen_4484, q_gen_4483) -> q_gen_4467
<snoc, s>(q_gen_4490, q_gen_4489) -> q_gen_4467
<snoc, s>(q_gen_4505, q_gen_4502) -> q_gen_4467
<snoc, s>(q_gen_4508, q_gen_4528) -> q_gen_4467
<s, z>(q_gen_4478) -> q_gen_4471
<s, z>(q_gen_4481) -> q_gen_4471
<s, z>(q_gen_4496) -> q_gen_4471
<s, z>(q_gen_4519) -> q_gen_4471
<z, z>() -> q_gen_4471
<s, s>(q_gen_4471) -> q_gen_4483
<z, s>(q_gen_4478) -> q_gen_4483
<snoc, s>(q_gen_4472, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4472, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4472, q_gen_4502) -> q_gen_4485
<snoc, s>(q_gen_4472, q_gen_4528) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4502) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4528) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4502) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4528) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4528) -> q_gen_4485
<snoc, s>(q_gen_4508, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4508, q_gen_4502) -> q_gen_4485
<s, s>(q_gen_4483) -> q_gen_4489
<z, s>(q_gen_4481) -> q_gen_4489
<s, s>(q_gen_4489) -> q_gen_4502
<z, s>(q_gen_4496) -> q_gen_4502
<z, s>(q_gen_4519) -> q_gen_4528
}

Datatype: <nattsil, nat>
Convolution form: right
}}}

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 56
() -> length([nil, z]) -> 54
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 54
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 61
(le([s(nn1), z])) -> BOT -> 59
(le([z, z])) -> BOT -> 54
(length([l, _fy]) /\ length([snoc(l, x), _gy])) -> le([_fy, _gy]) -> 65
(length([ll, _by])) -> length([snoc(ll, x), s(_by)]) -> 67
}
Sat witness: Found: ((length([ll, _by])) -> length([snoc(ll, x), s(_by)]), {
_by -> s(s(s(z)))  ;  ll -> snoc(snoc(snoc(nil, z), z), s(s(s(s(s(z))))))  ;  x -> z
})

-------------------------------------------
Step 59, which took 0.258267 s (model generation: 0.180517,  model checking: 0.077750):

Model:
|_
{
le -> 
{{{
Q={q_gen_4468, q_gen_4469, q_gen_4486},
Q_f={q_gen_4468},
Delta=
{
<s>(q_gen_4469) -> q_gen_4469
<z>() -> q_gen_4469
<s, s>(q_gen_4468) -> q_gen_4468
<z, s>(q_gen_4469) -> q_gen_4468
<s, s>(q_gen_4486) -> q_gen_4486
<s, z>(q_gen_4469) -> q_gen_4486
<z, z>() -> q_gen_4486
}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_4467, q_gen_4471, q_gen_4472, q_gen_4478, q_gen_4481, q_gen_4483, q_gen_4484, q_gen_4485, q_gen_4489, q_gen_4490, q_gen_4496, q_gen_4502, q_gen_4505, q_gen_4508, q_gen_4519, q_gen_4528},
Q_f={q_gen_4467},
Delta=
{
<nil>() -> q_gen_4472
<z>() -> q_gen_4478
<s>(q_gen_4478) -> q_gen_4481
<snoc>(q_gen_4472, q_gen_4478) -> q_gen_4484
<snoc>(q_gen_4484, q_gen_4478) -> q_gen_4490
<s>(q_gen_4481) -> q_gen_4496
<snoc>(q_gen_4490, q_gen_4478) -> q_gen_4505
<snoc>(q_gen_4490, q_gen_4481) -> q_gen_4505
<snoc>(q_gen_4490, q_gen_4496) -> q_gen_4505
<snoc>(q_gen_4490, q_gen_4519) -> q_gen_4505
<snoc>(q_gen_4505, q_gen_4478) -> q_gen_4508
<s>(q_gen_4496) -> q_gen_4519
<s>(q_gen_4519) -> q_gen_4519
<nil, z>() -> q_gen_4467
<snoc, s>(q_gen_4472, q_gen_4471) -> q_gen_4467
<snoc, s>(q_gen_4484, q_gen_4483) -> q_gen_4467
<snoc, s>(q_gen_4490, q_gen_4489) -> q_gen_4467
<snoc, s>(q_gen_4505, q_gen_4502) -> q_gen_4467
<snoc, s>(q_gen_4508, q_gen_4528) -> q_gen_4467
<s, z>(q_gen_4478) -> q_gen_4471
<s, z>(q_gen_4481) -> q_gen_4471
<s, z>(q_gen_4496) -> q_gen_4471
<s, z>(q_gen_4519) -> q_gen_4471
<z, z>() -> q_gen_4471
<s, s>(q_gen_4471) -> q_gen_4483
<z, s>(q_gen_4478) -> q_gen_4483
<snoc, s>(q_gen_4472, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4472, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4472, q_gen_4502) -> q_gen_4485
<snoc, s>(q_gen_4472, q_gen_4528) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4502) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4528) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4502) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4528) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4528) -> q_gen_4485
<snoc, s>(q_gen_4508, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4508, q_gen_4502) -> q_gen_4485
<s, s>(q_gen_4483) -> q_gen_4489
<z, s>(q_gen_4481) -> q_gen_4489
<s, s>(q_gen_4489) -> q_gen_4502
<z, s>(q_gen_4496) -> q_gen_4502
<z, s>(q_gen_4519) -> q_gen_4528
}

Datatype: <nattsil, nat>
Convolution form: right
}}}

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 57
() -> length([nil, z]) -> 55
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 55
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 62
(le([s(nn1), z])) -> BOT -> 60
(le([z, z])) -> BOT -> 55
(length([l, _fy]) /\ length([snoc(l, x), _gy])) -> le([_fy, _gy]) -> 66
(length([ll, _by])) -> length([snoc(ll, x), s(_by)]) -> 70
}
Sat witness: Found: ((length([ll, _by])) -> length([snoc(ll, x), s(_by)]), {
_by -> s(z)  ;  ll -> snoc(nil, s(s(s(z))))  ;  x -> s(z)
})

-------------------------------------------
Step 60, which took 0.182360 s (model generation: 0.175226,  model checking: 0.007134):

Model:
|_
{
le -> 
{{{
Q={q_gen_4468, q_gen_4469, q_gen_4486},
Q_f={q_gen_4468},
Delta=
{
<s>(q_gen_4469) -> q_gen_4469
<z>() -> q_gen_4469
<s, s>(q_gen_4468) -> q_gen_4468
<z, s>(q_gen_4469) -> q_gen_4468
<s, s>(q_gen_4486) -> q_gen_4486
<s, z>(q_gen_4469) -> q_gen_4486
<z, z>() -> q_gen_4486
}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_4467, q_gen_4471, q_gen_4472, q_gen_4478, q_gen_4481, q_gen_4483, q_gen_4484, q_gen_4485, q_gen_4489, q_gen_4490, q_gen_4496, q_gen_4502, q_gen_4505, q_gen_4508, q_gen_4519, q_gen_4528},
Q_f={q_gen_4467},
Delta=
{
<nil>() -> q_gen_4472
<z>() -> q_gen_4478
<s>(q_gen_4478) -> q_gen_4481
<snoc>(q_gen_4472, q_gen_4478) -> q_gen_4484
<snoc>(q_gen_4484, q_gen_4478) -> q_gen_4490
<s>(q_gen_4481) -> q_gen_4496
<snoc>(q_gen_4490, q_gen_4478) -> q_gen_4505
<snoc>(q_gen_4490, q_gen_4481) -> q_gen_4505
<snoc>(q_gen_4490, q_gen_4496) -> q_gen_4505
<snoc>(q_gen_4490, q_gen_4519) -> q_gen_4505
<snoc>(q_gen_4472, q_gen_4519) -> q_gen_4508
<snoc>(q_gen_4505, q_gen_4478) -> q_gen_4508
<s>(q_gen_4496) -> q_gen_4519
<s>(q_gen_4519) -> q_gen_4519
<nil, z>() -> q_gen_4467
<snoc, s>(q_gen_4472, q_gen_4471) -> q_gen_4467
<snoc, s>(q_gen_4484, q_gen_4483) -> q_gen_4467
<snoc, s>(q_gen_4490, q_gen_4489) -> q_gen_4467
<snoc, s>(q_gen_4505, q_gen_4502) -> q_gen_4467
<snoc, s>(q_gen_4508, q_gen_4483) -> q_gen_4467
<snoc, s>(q_gen_4508, q_gen_4528) -> q_gen_4467
<s, z>(q_gen_4478) -> q_gen_4471
<s, z>(q_gen_4481) -> q_gen_4471
<s, z>(q_gen_4496) -> q_gen_4471
<s, z>(q_gen_4519) -> q_gen_4471
<z, z>() -> q_gen_4471
<s, s>(q_gen_4471) -> q_gen_4483
<z, s>(q_gen_4478) -> q_gen_4483
<snoc, s>(q_gen_4472, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4472, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4472, q_gen_4502) -> q_gen_4485
<snoc, s>(q_gen_4472, q_gen_4528) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4502) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4528) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4502) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4528) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4528) -> q_gen_4485
<snoc, s>(q_gen_4508, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4508, q_gen_4502) -> q_gen_4485
<s, s>(q_gen_4483) -> q_gen_4489
<z, s>(q_gen_4481) -> q_gen_4489
<s, s>(q_gen_4489) -> q_gen_4502
<z, s>(q_gen_4496) -> q_gen_4502
<z, s>(q_gen_4519) -> q_gen_4528
}

Datatype: <nattsil, nat>
Convolution form: right
}}}

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 58
() -> length([nil, z]) -> 56
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 56
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 63
(le([s(nn1), z])) -> BOT -> 61
(le([z, z])) -> BOT -> 56
(length([l, _fy]) /\ length([snoc(l, x), _gy])) -> le([_fy, _gy]) -> 69
(length([ll, _by])) -> length([snoc(ll, x), s(_by)]) -> 70
}
Sat witness: Found: ((length([l, _fy]) /\ length([snoc(l, x), _gy])) -> le([_fy, _gy]), {
_fy -> s(s(s(s(z))))  ;  _gy -> s(s(z))  ;  l -> snoc(snoc(snoc(snoc(nil, z), z), s(s(z))), z)  ;  x -> z
})

-------------------------------------------
Step 61, which took 0.229093 s (model generation: 0.222867,  model checking: 0.006226):

Model:
|_
{
le -> 
{{{
Q={q_gen_4468, q_gen_4469, q_gen_4486},
Q_f={q_gen_4468},
Delta=
{
<s>(q_gen_4469) -> q_gen_4469
<z>() -> q_gen_4469
<s, s>(q_gen_4468) -> q_gen_4468
<z, s>(q_gen_4469) -> q_gen_4468
<s, s>(q_gen_4486) -> q_gen_4486
<s, z>(q_gen_4469) -> q_gen_4486
<z, z>() -> q_gen_4486
}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_4467, q_gen_4471, q_gen_4472, q_gen_4478, q_gen_4481, q_gen_4483, q_gen_4484, q_gen_4485, q_gen_4489, q_gen_4490, q_gen_4496, q_gen_4502, q_gen_4505, q_gen_4508, q_gen_4519, q_gen_4528},
Q_f={q_gen_4467},
Delta=
{
<nil>() -> q_gen_4472
<snoc>(q_gen_4508, q_gen_4478) -> q_gen_4472
<z>() -> q_gen_4478
<s>(q_gen_4478) -> q_gen_4481
<snoc>(q_gen_4472, q_gen_4478) -> q_gen_4484
<snoc>(q_gen_4472, q_gen_4519) -> q_gen_4484
<snoc>(q_gen_4484, q_gen_4478) -> q_gen_4490
<s>(q_gen_4481) -> q_gen_4496
<snoc>(q_gen_4490, q_gen_4478) -> q_gen_4505
<snoc>(q_gen_4490, q_gen_4481) -> q_gen_4505
<snoc>(q_gen_4490, q_gen_4519) -> q_gen_4505
<snoc>(q_gen_4490, q_gen_4496) -> q_gen_4508
<snoc>(q_gen_4505, q_gen_4478) -> q_gen_4508
<s>(q_gen_4496) -> q_gen_4519
<s>(q_gen_4519) -> q_gen_4519
<nil, z>() -> q_gen_4467
<snoc, s>(q_gen_4472, q_gen_4471) -> q_gen_4467
<snoc, s>(q_gen_4484, q_gen_4483) -> q_gen_4467
<snoc, s>(q_gen_4490, q_gen_4489) -> q_gen_4467
<snoc, s>(q_gen_4505, q_gen_4502) -> q_gen_4467
<snoc, s>(q_gen_4505, q_gen_4528) -> q_gen_4467
<snoc, s>(q_gen_4508, q_gen_4528) -> q_gen_4467
<s, z>(q_gen_4478) -> q_gen_4471
<s, z>(q_gen_4481) -> q_gen_4471
<s, z>(q_gen_4496) -> q_gen_4471
<s, z>(q_gen_4519) -> q_gen_4471
<z, z>() -> q_gen_4471
<s, s>(q_gen_4471) -> q_gen_4483
<z, s>(q_gen_4478) -> q_gen_4483
<snoc, s>(q_gen_4472, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4472, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4472, q_gen_4502) -> q_gen_4485
<snoc, s>(q_gen_4472, q_gen_4528) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4502) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4528) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4502) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4528) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4508, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4508, q_gen_4502) -> q_gen_4485
<s, s>(q_gen_4483) -> q_gen_4489
<z, s>(q_gen_4481) -> q_gen_4489
<z, s>(q_gen_4496) -> q_gen_4502
<s, s>(q_gen_4489) -> q_gen_4528
<z, s>(q_gen_4519) -> q_gen_4528
}

Datatype: <nattsil, nat>
Convolution form: right
}}}

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 59
() -> length([nil, z]) -> 57
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 57
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 64
(le([s(nn1), z])) -> BOT -> 62
(le([z, z])) -> BOT -> 57
(length([l, _fy]) /\ length([snoc(l, x), _gy])) -> le([_fy, _gy]) -> 72
(length([ll, _by])) -> length([snoc(ll, x), s(_by)]) -> 70
}
Sat witness: Found: ((length([l, _fy]) /\ length([snoc(l, x), _gy])) -> le([_fy, _gy]), {
_fy -> s(s(s(s(s(z)))))  ;  _gy -> s(z)  ;  l -> snoc(snoc(snoc(snoc(nil, z), z), s(s(z))), z)  ;  x -> z
})

-------------------------------------------
Step 62, which took 0.272593 s (model generation: 0.205480,  model checking: 0.067113):

Model:
|_
{
le -> 
{{{
Q={q_gen_4468, q_gen_4469, q_gen_4486},
Q_f={q_gen_4468},
Delta=
{
<s>(q_gen_4469) -> q_gen_4469
<z>() -> q_gen_4469
<s, s>(q_gen_4468) -> q_gen_4468
<z, s>(q_gen_4469) -> q_gen_4468
<s, s>(q_gen_4486) -> q_gen_4486
<s, z>(q_gen_4469) -> q_gen_4486
<z, z>() -> q_gen_4486
}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_4467, q_gen_4471, q_gen_4472, q_gen_4478, q_gen_4481, q_gen_4483, q_gen_4484, q_gen_4485, q_gen_4489, q_gen_4490, q_gen_4496, q_gen_4502, q_gen_4505, q_gen_4508, q_gen_4519, q_gen_4528},
Q_f={q_gen_4467},
Delta=
{
<nil>() -> q_gen_4472
<z>() -> q_gen_4478
<s>(q_gen_4478) -> q_gen_4481
<snoc>(q_gen_4472, q_gen_4478) -> q_gen_4484
<snoc>(q_gen_4472, q_gen_4519) -> q_gen_4484
<snoc>(q_gen_4484, q_gen_4478) -> q_gen_4490
<s>(q_gen_4481) -> q_gen_4496
<s>(q_gen_4519) -> q_gen_4496
<snoc>(q_gen_4490, q_gen_4478) -> q_gen_4505
<snoc>(q_gen_4490, q_gen_4481) -> q_gen_4505
<snoc>(q_gen_4490, q_gen_4496) -> q_gen_4505
<snoc>(q_gen_4490, q_gen_4519) -> q_gen_4505
<snoc>(q_gen_4505, q_gen_4478) -> q_gen_4508
<s>(q_gen_4496) -> q_gen_4519
<nil, z>() -> q_gen_4467
<snoc, s>(q_gen_4472, q_gen_4471) -> q_gen_4467
<snoc, s>(q_gen_4484, q_gen_4483) -> q_gen_4467
<snoc, s>(q_gen_4490, q_gen_4489) -> q_gen_4467
<snoc, s>(q_gen_4505, q_gen_4502) -> q_gen_4467
<snoc, s>(q_gen_4508, q_gen_4528) -> q_gen_4467
<s, z>(q_gen_4478) -> q_gen_4471
<s, z>(q_gen_4481) -> q_gen_4471
<s, z>(q_gen_4496) -> q_gen_4471
<s, z>(q_gen_4519) -> q_gen_4471
<z, z>() -> q_gen_4471
<s, s>(q_gen_4471) -> q_gen_4483
<z, s>(q_gen_4478) -> q_gen_4483
<snoc, s>(q_gen_4472, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4472, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4472, q_gen_4502) -> q_gen_4485
<snoc, s>(q_gen_4472, q_gen_4528) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4502) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4528) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4502) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4528) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4528) -> q_gen_4485
<snoc, s>(q_gen_4508, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4508, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4508, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4508, q_gen_4502) -> q_gen_4485
<s, s>(q_gen_4483) -> q_gen_4489
<z, s>(q_gen_4481) -> q_gen_4489
<s, s>(q_gen_4489) -> q_gen_4502
<z, s>(q_gen_4496) -> q_gen_4502
<z, s>(q_gen_4519) -> q_gen_4528
}

Datatype: <nattsil, nat>
Convolution form: right
}}}

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 60
() -> length([nil, z]) -> 58
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 58
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 65
(le([s(nn1), z])) -> BOT -> 63
(le([z, z])) -> BOT -> 58
(length([l, _fy]) /\ length([snoc(l, x), _gy])) -> le([_fy, _gy]) -> 72
(length([ll, _by])) -> length([snoc(ll, x), s(_by)]) -> 73
}
Sat witness: Found: ((length([ll, _by])) -> length([snoc(ll, x), s(_by)]), {
_by -> s(s(s(s(z))))  ;  ll -> snoc(snoc(snoc(snoc(nil, z), z), z), z)  ;  x -> s(s(z))
})

-------------------------------------------
Step 63, which took 0.269885 s (model generation: 0.247452,  model checking: 0.022433):

Model:
|_
{
le -> 
{{{
Q={q_gen_4468, q_gen_4469, q_gen_4486},
Q_f={q_gen_4468},
Delta=
{
<s>(q_gen_4469) -> q_gen_4469
<z>() -> q_gen_4469
<s, s>(q_gen_4468) -> q_gen_4468
<z, s>(q_gen_4469) -> q_gen_4468
<s, s>(q_gen_4486) -> q_gen_4486
<s, z>(q_gen_4469) -> q_gen_4486
<z, z>() -> q_gen_4486
}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_4467, q_gen_4471, q_gen_4472, q_gen_4478, q_gen_4481, q_gen_4483, q_gen_4484, q_gen_4485, q_gen_4489, q_gen_4490, q_gen_4496, q_gen_4502, q_gen_4505, q_gen_4508, q_gen_4519, q_gen_4528},
Q_f={q_gen_4467},
Delta=
{
<nil>() -> q_gen_4472
<z>() -> q_gen_4478
<s>(q_gen_4478) -> q_gen_4481
<snoc>(q_gen_4472, q_gen_4478) -> q_gen_4484
<snoc>(q_gen_4472, q_gen_4519) -> q_gen_4484
<snoc>(q_gen_4484, q_gen_4478) -> q_gen_4490
<snoc>(q_gen_4508, q_gen_4478) -> q_gen_4490
<s>(q_gen_4481) -> q_gen_4496
<snoc>(q_gen_4490, q_gen_4478) -> q_gen_4505
<snoc>(q_gen_4490, q_gen_4481) -> q_gen_4505
<snoc>(q_gen_4490, q_gen_4519) -> q_gen_4505
<snoc>(q_gen_4490, q_gen_4496) -> q_gen_4508
<snoc>(q_gen_4505, q_gen_4478) -> q_gen_4508
<s>(q_gen_4496) -> q_gen_4519
<s>(q_gen_4519) -> q_gen_4519
<nil, z>() -> q_gen_4467
<snoc, s>(q_gen_4472, q_gen_4471) -> q_gen_4467
<snoc, s>(q_gen_4484, q_gen_4483) -> q_gen_4467
<snoc, s>(q_gen_4490, q_gen_4489) -> q_gen_4467
<snoc, s>(q_gen_4505, q_gen_4502) -> q_gen_4467
<snoc, s>(q_gen_4505, q_gen_4528) -> q_gen_4467
<snoc, s>(q_gen_4508, q_gen_4483) -> q_gen_4467
<snoc, s>(q_gen_4508, q_gen_4528) -> q_gen_4467
<s, z>(q_gen_4478) -> q_gen_4471
<s, z>(q_gen_4481) -> q_gen_4471
<s, z>(q_gen_4496) -> q_gen_4471
<s, z>(q_gen_4519) -> q_gen_4471
<z, z>() -> q_gen_4471
<s, s>(q_gen_4471) -> q_gen_4483
<s, s>(q_gen_4528) -> q_gen_4483
<z, s>(q_gen_4478) -> q_gen_4483
<snoc, s>(q_gen_4472, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4472, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4472, q_gen_4502) -> q_gen_4485
<snoc, s>(q_gen_4472, q_gen_4528) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4502) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4528) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4502) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4528) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4508, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4508, q_gen_4502) -> q_gen_4485
<s, s>(q_gen_4483) -> q_gen_4489
<z, s>(q_gen_4481) -> q_gen_4489
<z, s>(q_gen_4496) -> q_gen_4502
<s, s>(q_gen_4489) -> q_gen_4528
<z, s>(q_gen_4519) -> q_gen_4528
}

Datatype: <nattsil, nat>
Convolution form: right
}}}

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 61
() -> length([nil, z]) -> 59
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 59
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 66
(le([s(nn1), z])) -> BOT -> 64
(le([z, z])) -> BOT -> 59
(length([l, _fy]) /\ length([snoc(l, x), _gy])) -> le([_fy, _gy]) -> 75
(length([ll, _by])) -> length([snoc(ll, x), s(_by)]) -> 73
}
Sat witness: Found: ((length([l, _fy]) /\ length([snoc(l, x), _gy])) -> le([_fy, _gy]), {
_fy -> s(s(s(s(s(s(s(z)))))))  ;  _gy -> s(s(z))  ;  l -> snoc(snoc(snoc(nil, z), z), s(s(z)))  ;  x -> s(z)
})

-------------------------------------------
Step 64, which took 0.316017 s (model generation: 0.291490,  model checking: 0.024527):

Model:
|_
{
le -> 
{{{
Q={q_gen_4468, q_gen_4469, q_gen_4486},
Q_f={q_gen_4468},
Delta=
{
<s>(q_gen_4469) -> q_gen_4469
<z>() -> q_gen_4469
<s, s>(q_gen_4468) -> q_gen_4468
<z, s>(q_gen_4469) -> q_gen_4468
<s, s>(q_gen_4486) -> q_gen_4486
<s, z>(q_gen_4469) -> q_gen_4486
<z, z>() -> q_gen_4486
}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_4467, q_gen_4471, q_gen_4472, q_gen_4478, q_gen_4481, q_gen_4483, q_gen_4484, q_gen_4485, q_gen_4489, q_gen_4490, q_gen_4496, q_gen_4502, q_gen_4505, q_gen_4508, q_gen_4519, q_gen_4528},
Q_f={q_gen_4467},
Delta=
{
<nil>() -> q_gen_4472
<z>() -> q_gen_4478
<s>(q_gen_4478) -> q_gen_4481
<snoc>(q_gen_4472, q_gen_4478) -> q_gen_4484
<snoc>(q_gen_4472, q_gen_4519) -> q_gen_4484
<snoc>(q_gen_4484, q_gen_4478) -> q_gen_4490
<s>(q_gen_4481) -> q_gen_4496
<s>(q_gen_4519) -> q_gen_4496
<snoc>(q_gen_4490, q_gen_4478) -> q_gen_4505
<snoc>(q_gen_4490, q_gen_4481) -> q_gen_4505
<snoc>(q_gen_4490, q_gen_4496) -> q_gen_4505
<snoc>(q_gen_4490, q_gen_4519) -> q_gen_4505
<snoc>(q_gen_4505, q_gen_4478) -> q_gen_4508
<s>(q_gen_4496) -> q_gen_4519
<nil, z>() -> q_gen_4467
<snoc, s>(q_gen_4472, q_gen_4471) -> q_gen_4467
<snoc, s>(q_gen_4484, q_gen_4483) -> q_gen_4467
<snoc, s>(q_gen_4490, q_gen_4489) -> q_gen_4467
<snoc, s>(q_gen_4505, q_gen_4502) -> q_gen_4467
<snoc, s>(q_gen_4508, q_gen_4528) -> q_gen_4467
<s, z>(q_gen_4478) -> q_gen_4471
<s, z>(q_gen_4481) -> q_gen_4471
<s, z>(q_gen_4496) -> q_gen_4471
<s, z>(q_gen_4519) -> q_gen_4471
<z, z>() -> q_gen_4471
<s, s>(q_gen_4471) -> q_gen_4483
<s, s>(q_gen_4528) -> q_gen_4483
<z, s>(q_gen_4478) -> q_gen_4483
<snoc, s>(q_gen_4472, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4472, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4472, q_gen_4502) -> q_gen_4485
<snoc, s>(q_gen_4472, q_gen_4528) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4502) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4528) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4502) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4528) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4528) -> q_gen_4485
<snoc, s>(q_gen_4508, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4508, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4508, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4508, q_gen_4502) -> q_gen_4485
<s, s>(q_gen_4483) -> q_gen_4489
<z, s>(q_gen_4481) -> q_gen_4489
<s, s>(q_gen_4489) -> q_gen_4502
<z, s>(q_gen_4496) -> q_gen_4502
<s, s>(q_gen_4502) -> q_gen_4528
<z, s>(q_gen_4519) -> q_gen_4528
}

Datatype: <nattsil, nat>
Convolution form: right
}}}

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 62
() -> length([nil, z]) -> 60
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 60
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 67
(le([s(nn1), z])) -> BOT -> 65
(le([z, z])) -> BOT -> 60
(length([l, _fy]) /\ length([snoc(l, x), _gy])) -> le([_fy, _gy]) -> 75
(length([ll, _by])) -> length([snoc(ll, x), s(_by)]) -> 76
}
Sat witness: Found: ((length([ll, _by])) -> length([snoc(ll, x), s(_by)]), {
_by -> s(s(s(s(s(s(z))))))  ;  ll -> snoc(snoc(snoc(snoc(nil, s(s(s(z)))), z), s(z)), z)  ;  x -> s(s(s(z)))
})

-------------------------------------------
Step 65, which took 0.385354 s (model generation: 0.378376,  model checking: 0.006978):

Model:
|_
{
le -> 
{{{
Q={q_gen_4468, q_gen_4469, q_gen_4486},
Q_f={q_gen_4468},
Delta=
{
<s>(q_gen_4469) -> q_gen_4469
<z>() -> q_gen_4469
<s, s>(q_gen_4468) -> q_gen_4468
<z, s>(q_gen_4469) -> q_gen_4468
<s, s>(q_gen_4486) -> q_gen_4486
<s, z>(q_gen_4469) -> q_gen_4486
<z, z>() -> q_gen_4486
}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_4467, q_gen_4471, q_gen_4472, q_gen_4478, q_gen_4481, q_gen_4483, q_gen_4484, q_gen_4485, q_gen_4489, q_gen_4490, q_gen_4496, q_gen_4502, q_gen_4505, q_gen_4508, q_gen_4519, q_gen_4528},
Q_f={q_gen_4467},
Delta=
{
<nil>() -> q_gen_4472
<z>() -> q_gen_4478
<s>(q_gen_4478) -> q_gen_4481
<snoc>(q_gen_4472, q_gen_4478) -> q_gen_4484
<snoc>(q_gen_4508, q_gen_4481) -> q_gen_4484
<snoc>(q_gen_4484, q_gen_4478) -> q_gen_4490
<s>(q_gen_4481) -> q_gen_4496
<snoc>(q_gen_4472, q_gen_4519) -> q_gen_4505
<snoc>(q_gen_4490, q_gen_4478) -> q_gen_4505
<snoc>(q_gen_4490, q_gen_4481) -> q_gen_4505
<snoc>(q_gen_4490, q_gen_4496) -> q_gen_4505
<snoc>(q_gen_4490, q_gen_4519) -> q_gen_4505
<snoc>(q_gen_4505, q_gen_4478) -> q_gen_4508
<s>(q_gen_4496) -> q_gen_4519
<s>(q_gen_4519) -> q_gen_4519
<nil, z>() -> q_gen_4467
<snoc, s>(q_gen_4472, q_gen_4471) -> q_gen_4467
<snoc, s>(q_gen_4484, q_gen_4483) -> q_gen_4467
<snoc, s>(q_gen_4484, q_gen_4502) -> q_gen_4467
<snoc, s>(q_gen_4490, q_gen_4489) -> q_gen_4467
<snoc, s>(q_gen_4505, q_gen_4502) -> q_gen_4467
<snoc, s>(q_gen_4505, q_gen_4528) -> q_gen_4467
<snoc, s>(q_gen_4508, q_gen_4528) -> q_gen_4467
<s, z>(q_gen_4478) -> q_gen_4471
<s, z>(q_gen_4481) -> q_gen_4471
<s, z>(q_gen_4496) -> q_gen_4471
<s, z>(q_gen_4519) -> q_gen_4471
<z, z>() -> q_gen_4471
<z, s>(q_gen_4478) -> q_gen_4483
<snoc, s>(q_gen_4472, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4472, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4472, q_gen_4502) -> q_gen_4485
<snoc, s>(q_gen_4472, q_gen_4528) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4528) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4502) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4528) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4508, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4508, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4508, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4508, q_gen_4502) -> q_gen_4485
<s, s>(q_gen_4483) -> q_gen_4489
<s, s>(q_gen_4502) -> q_gen_4489
<z, s>(q_gen_4481) -> q_gen_4489
<s, s>(q_gen_4471) -> q_gen_4502
<z, s>(q_gen_4496) -> q_gen_4502
<s, s>(q_gen_4489) -> q_gen_4528
<s, s>(q_gen_4528) -> q_gen_4528
<z, s>(q_gen_4519) -> q_gen_4528
}

Datatype: <nattsil, nat>
Convolution form: right
}}}

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 63
() -> length([nil, z]) -> 61
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 61
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 68
(le([s(nn1), z])) -> BOT -> 66
(le([z, z])) -> BOT -> 61
(length([l, _fy]) /\ length([snoc(l, x), _gy])) -> le([_fy, _gy]) -> 78
(length([ll, _by])) -> length([snoc(ll, x), s(_by)]) -> 76
}
Sat witness: Found: ((length([l, _fy]) /\ length([snoc(l, x), _gy])) -> le([_fy, _gy]), {
_fy -> s(s(s(s(z))))  ;  _gy -> s(s(s(z)))  ;  l -> snoc(snoc(nil, z), z)  ;  x -> z
})

-------------------------------------------
Step 66, which took 0.314827 s (model generation: 0.291960,  model checking: 0.022867):

Model:
|_
{
le -> 
{{{
Q={q_gen_4468, q_gen_4469, q_gen_4486},
Q_f={q_gen_4468},
Delta=
{
<s>(q_gen_4469) -> q_gen_4469
<z>() -> q_gen_4469
<s, s>(q_gen_4468) -> q_gen_4468
<z, s>(q_gen_4469) -> q_gen_4468
<s, s>(q_gen_4486) -> q_gen_4486
<s, z>(q_gen_4469) -> q_gen_4486
<z, z>() -> q_gen_4486
}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_4467, q_gen_4471, q_gen_4472, q_gen_4478, q_gen_4481, q_gen_4483, q_gen_4484, q_gen_4485, q_gen_4489, q_gen_4490, q_gen_4496, q_gen_4502, q_gen_4505, q_gen_4508, q_gen_4519, q_gen_4528},
Q_f={q_gen_4467},
Delta=
{
<nil>() -> q_gen_4472
<z>() -> q_gen_4478
<s>(q_gen_4478) -> q_gen_4481
<snoc>(q_gen_4472, q_gen_4478) -> q_gen_4484
<snoc>(q_gen_4472, q_gen_4519) -> q_gen_4484
<snoc>(q_gen_4484, q_gen_4478) -> q_gen_4490
<snoc>(q_gen_4508, q_gen_4478) -> q_gen_4490
<s>(q_gen_4481) -> q_gen_4496
<snoc>(q_gen_4490, q_gen_4478) -> q_gen_4505
<snoc>(q_gen_4490, q_gen_4481) -> q_gen_4505
<snoc>(q_gen_4490, q_gen_4519) -> q_gen_4505
<snoc>(q_gen_4490, q_gen_4496) -> q_gen_4508
<snoc>(q_gen_4505, q_gen_4478) -> q_gen_4508
<s>(q_gen_4496) -> q_gen_4519
<s>(q_gen_4519) -> q_gen_4519
<nil, z>() -> q_gen_4467
<snoc, s>(q_gen_4472, q_gen_4471) -> q_gen_4467
<snoc, s>(q_gen_4484, q_gen_4483) -> q_gen_4467
<snoc, s>(q_gen_4490, q_gen_4489) -> q_gen_4467
<snoc, s>(q_gen_4505, q_gen_4502) -> q_gen_4467
<snoc, s>(q_gen_4505, q_gen_4528) -> q_gen_4467
<snoc, s>(q_gen_4508, q_gen_4528) -> q_gen_4467
<s, z>(q_gen_4478) -> q_gen_4471
<s, z>(q_gen_4481) -> q_gen_4471
<s, z>(q_gen_4496) -> q_gen_4471
<s, z>(q_gen_4519) -> q_gen_4471
<z, z>() -> q_gen_4471
<s, s>(q_gen_4471) -> q_gen_4483
<z, s>(q_gen_4478) -> q_gen_4483
<snoc, s>(q_gen_4472, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4472, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4472, q_gen_4502) -> q_gen_4485
<snoc, s>(q_gen_4472, q_gen_4528) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4502) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4528) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4502) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4528) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4508, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4508, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4508, q_gen_4502) -> q_gen_4485
<s, s>(q_gen_4483) -> q_gen_4489
<s, s>(q_gen_4502) -> q_gen_4489
<z, s>(q_gen_4481) -> q_gen_4489
<z, s>(q_gen_4496) -> q_gen_4502
<s, s>(q_gen_4489) -> q_gen_4528
<s, s>(q_gen_4528) -> q_gen_4528
<z, s>(q_gen_4519) -> q_gen_4528
}

Datatype: <nattsil, nat>
Convolution form: right
}}}

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 64
() -> length([nil, z]) -> 62
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 62
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 69
(le([s(nn1), z])) -> BOT -> 67
(le([z, z])) -> BOT -> 62
(length([l, _fy]) /\ length([snoc(l, x), _gy])) -> le([_fy, _gy]) -> 78
(length([ll, _by])) -> length([snoc(ll, x), s(_by)]) -> 79
}
Sat witness: Found: ((length([ll, _by])) -> length([snoc(ll, x), s(_by)]), {
_by -> s(s(s(s(s(z)))))  ;  ll -> snoc(snoc(snoc(snoc(nil, z), z), s(s(z))), z)  ;  x -> z
})

-------------------------------------------
Step 67, which took 0.363023 s (model generation: 0.348340,  model checking: 0.014683):

Model:
|_
{
le -> 
{{{
Q={q_gen_4468, q_gen_4469, q_gen_4486},
Q_f={q_gen_4468},
Delta=
{
<s>(q_gen_4469) -> q_gen_4469
<z>() -> q_gen_4469
<s, s>(q_gen_4468) -> q_gen_4468
<z, s>(q_gen_4469) -> q_gen_4468
<s, s>(q_gen_4486) -> q_gen_4486
<s, z>(q_gen_4469) -> q_gen_4486
<z, z>() -> q_gen_4486
}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_4467, q_gen_4471, q_gen_4472, q_gen_4478, q_gen_4481, q_gen_4483, q_gen_4484, q_gen_4485, q_gen_4489, q_gen_4490, q_gen_4496, q_gen_4502, q_gen_4505, q_gen_4508, q_gen_4519, q_gen_4528},
Q_f={q_gen_4467},
Delta=
{
<nil>() -> q_gen_4472
<z>() -> q_gen_4478
<s>(q_gen_4478) -> q_gen_4481
<snoc>(q_gen_4472, q_gen_4478) -> q_gen_4484
<snoc>(q_gen_4472, q_gen_4519) -> q_gen_4484
<snoc>(q_gen_4484, q_gen_4478) -> q_gen_4490
<s>(q_gen_4481) -> q_gen_4496
<s>(q_gen_4519) -> q_gen_4496
<snoc>(q_gen_4490, q_gen_4478) -> q_gen_4505
<snoc>(q_gen_4490, q_gen_4481) -> q_gen_4505
<snoc>(q_gen_4490, q_gen_4496) -> q_gen_4505
<snoc>(q_gen_4490, q_gen_4519) -> q_gen_4505
<snoc>(q_gen_4505, q_gen_4478) -> q_gen_4508
<s>(q_gen_4496) -> q_gen_4519
<nil, z>() -> q_gen_4467
<snoc, s>(q_gen_4472, q_gen_4471) -> q_gen_4467
<snoc, s>(q_gen_4484, q_gen_4483) -> q_gen_4467
<snoc, s>(q_gen_4490, q_gen_4489) -> q_gen_4467
<snoc, s>(q_gen_4505, q_gen_4502) -> q_gen_4467
<snoc, s>(q_gen_4508, q_gen_4528) -> q_gen_4467
<s, z>(q_gen_4478) -> q_gen_4471
<s, z>(q_gen_4481) -> q_gen_4471
<s, z>(q_gen_4496) -> q_gen_4471
<s, z>(q_gen_4519) -> q_gen_4471
<z, z>() -> q_gen_4471
<s, s>(q_gen_4471) -> q_gen_4483
<z, s>(q_gen_4478) -> q_gen_4483
<snoc, s>(q_gen_4472, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4472, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4472, q_gen_4502) -> q_gen_4485
<snoc, s>(q_gen_4472, q_gen_4528) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4502) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4528) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4502) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4528) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4528) -> q_gen_4485
<snoc, s>(q_gen_4508, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4508, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4508, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4508, q_gen_4502) -> q_gen_4485
<s, s>(q_gen_4483) -> q_gen_4489
<z, s>(q_gen_4481) -> q_gen_4489
<s, s>(q_gen_4489) -> q_gen_4502
<s, s>(q_gen_4528) -> q_gen_4502
<z, s>(q_gen_4496) -> q_gen_4502
<s, s>(q_gen_4502) -> q_gen_4528
<z, s>(q_gen_4519) -> q_gen_4528
}

Datatype: <nattsil, nat>
Convolution form: right
}}}

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 65
() -> length([nil, z]) -> 63
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 63
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 70
(le([s(nn1), z])) -> BOT -> 68
(le([z, z])) -> BOT -> 63
(length([l, _fy]) /\ length([snoc(l, x), _gy])) -> le([_fy, _gy]) -> 81
(length([ll, _by])) -> length([snoc(ll, x), s(_by)]) -> 79
}
Sat witness: Found: ((length([l, _fy]) /\ length([snoc(l, x), _gy])) -> le([_fy, _gy]), {
_fy -> s(s(s(s(s(s(z))))))  ;  _gy -> s(s(s(s(s(z)))))  ;  l -> snoc(snoc(snoc(snoc(nil, z), z), s(s(s(z)))), z)  ;  x -> s(z)
})

-------------------------------------------
Step 68, which took 0.411802 s (model generation: 0.394860,  model checking: 0.016942):

Model:
|_
{
le -> 
{{{
Q={q_gen_4468, q_gen_4469, q_gen_4486},
Q_f={q_gen_4468},
Delta=
{
<s>(q_gen_4469) -> q_gen_4469
<z>() -> q_gen_4469
<s, s>(q_gen_4468) -> q_gen_4468
<z, s>(q_gen_4469) -> q_gen_4468
<s, s>(q_gen_4486) -> q_gen_4486
<s, z>(q_gen_4469) -> q_gen_4486
<z, z>() -> q_gen_4486
}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_4467, q_gen_4471, q_gen_4472, q_gen_4478, q_gen_4481, q_gen_4483, q_gen_4484, q_gen_4485, q_gen_4489, q_gen_4490, q_gen_4496, q_gen_4502, q_gen_4505, q_gen_4508, q_gen_4519, q_gen_4528},
Q_f={q_gen_4467},
Delta=
{
<nil>() -> q_gen_4472
<z>() -> q_gen_4478
<s>(q_gen_4478) -> q_gen_4481
<snoc>(q_gen_4472, q_gen_4478) -> q_gen_4484
<snoc>(q_gen_4472, q_gen_4519) -> q_gen_4484
<snoc>(q_gen_4484, q_gen_4478) -> q_gen_4490
<s>(q_gen_4481) -> q_gen_4496
<snoc>(q_gen_4490, q_gen_4478) -> q_gen_4505
<snoc>(q_gen_4490, q_gen_4481) -> q_gen_4505
<snoc>(q_gen_4490, q_gen_4496) -> q_gen_4505
<snoc>(q_gen_4490, q_gen_4519) -> q_gen_4505
<snoc>(q_gen_4505, q_gen_4478) -> q_gen_4508
<s>(q_gen_4496) -> q_gen_4519
<s>(q_gen_4519) -> q_gen_4519
<nil, z>() -> q_gen_4467
<snoc, s>(q_gen_4472, q_gen_4471) -> q_gen_4467
<snoc, s>(q_gen_4484, q_gen_4483) -> q_gen_4467
<snoc, s>(q_gen_4490, q_gen_4489) -> q_gen_4467
<snoc, s>(q_gen_4505, q_gen_4502) -> q_gen_4467
<snoc, s>(q_gen_4508, q_gen_4471) -> q_gen_4467
<snoc, s>(q_gen_4508, q_gen_4528) -> q_gen_4467
<s, s>(q_gen_4502) -> q_gen_4471
<s, z>(q_gen_4478) -> q_gen_4471
<s, z>(q_gen_4481) -> q_gen_4471
<s, z>(q_gen_4496) -> q_gen_4471
<s, z>(q_gen_4519) -> q_gen_4471
<z, z>() -> q_gen_4471
<s, s>(q_gen_4471) -> q_gen_4483
<z, s>(q_gen_4478) -> q_gen_4483
<snoc, s>(q_gen_4472, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4472, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4472, q_gen_4502) -> q_gen_4485
<snoc, s>(q_gen_4472, q_gen_4528) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4502) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4528) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4502) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4528) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4528) -> q_gen_4485
<snoc, s>(q_gen_4508, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4508, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4508, q_gen_4502) -> q_gen_4485
<s, s>(q_gen_4483) -> q_gen_4489
<s, s>(q_gen_4528) -> q_gen_4489
<z, s>(q_gen_4481) -> q_gen_4489
<s, s>(q_gen_4489) -> q_gen_4502
<z, s>(q_gen_4496) -> q_gen_4502
<z, s>(q_gen_4519) -> q_gen_4528
}

Datatype: <nattsil, nat>
Convolution form: right
}}}

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 66
() -> length([nil, z]) -> 64
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 64
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 71
(le([s(nn1), z])) -> BOT -> 69
(le([z, z])) -> BOT -> 64
(length([l, _fy]) /\ length([snoc(l, x), _gy])) -> le([_fy, _gy]) -> 81
(length([ll, _by])) -> length([snoc(ll, x), s(_by)]) -> 82
}
Sat witness: Found: ((length([ll, _by])) -> length([snoc(ll, x), s(_by)]), {
_by -> s(s(s(s(s(s(z))))))  ;  ll -> snoc(snoc(snoc(nil, s(s(s(z)))), z), s(z))  ;  x -> z
})

-------------------------------------------
Step 69, which took 0.413819 s (model generation: 0.399448,  model checking: 0.014371):

Model:
|_
{
le -> 
{{{
Q={q_gen_4468, q_gen_4469, q_gen_4486},
Q_f={q_gen_4468},
Delta=
{
<s>(q_gen_4469) -> q_gen_4469
<z>() -> q_gen_4469
<s, s>(q_gen_4468) -> q_gen_4468
<z, s>(q_gen_4469) -> q_gen_4468
<s, s>(q_gen_4486) -> q_gen_4486
<s, z>(q_gen_4469) -> q_gen_4486
<z, z>() -> q_gen_4486
}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_4467, q_gen_4471, q_gen_4472, q_gen_4478, q_gen_4481, q_gen_4483, q_gen_4484, q_gen_4485, q_gen_4489, q_gen_4490, q_gen_4496, q_gen_4502, q_gen_4505, q_gen_4508, q_gen_4519, q_gen_4528},
Q_f={q_gen_4467},
Delta=
{
<nil>() -> q_gen_4472
<z>() -> q_gen_4478
<s>(q_gen_4478) -> q_gen_4481
<snoc>(q_gen_4472, q_gen_4478) -> q_gen_4484
<snoc>(q_gen_4472, q_gen_4519) -> q_gen_4484
<snoc>(q_gen_4484, q_gen_4478) -> q_gen_4490
<s>(q_gen_4481) -> q_gen_4496
<snoc>(q_gen_4490, q_gen_4478) -> q_gen_4505
<snoc>(q_gen_4490, q_gen_4481) -> q_gen_4505
<snoc>(q_gen_4490, q_gen_4496) -> q_gen_4505
<snoc>(q_gen_4490, q_gen_4519) -> q_gen_4505
<snoc>(q_gen_4505, q_gen_4478) -> q_gen_4508
<s>(q_gen_4496) -> q_gen_4519
<s>(q_gen_4519) -> q_gen_4519
<nil, z>() -> q_gen_4467
<snoc, s>(q_gen_4472, q_gen_4471) -> q_gen_4467
<snoc, s>(q_gen_4484, q_gen_4483) -> q_gen_4467
<snoc, s>(q_gen_4490, q_gen_4489) -> q_gen_4467
<snoc, s>(q_gen_4505, q_gen_4502) -> q_gen_4467
<snoc, s>(q_gen_4508, q_gen_4528) -> q_gen_4467
<s, s>(q_gen_4528) -> q_gen_4471
<s, z>(q_gen_4478) -> q_gen_4471
<s, z>(q_gen_4481) -> q_gen_4471
<s, z>(q_gen_4496) -> q_gen_4471
<s, z>(q_gen_4519) -> q_gen_4471
<z, z>() -> q_gen_4471
<s, s>(q_gen_4471) -> q_gen_4483
<z, s>(q_gen_4478) -> q_gen_4483
<snoc, s>(q_gen_4472, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4472, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4472, q_gen_4502) -> q_gen_4485
<snoc, s>(q_gen_4472, q_gen_4528) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4502) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4528) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4502) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4528) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4528) -> q_gen_4485
<snoc, s>(q_gen_4508, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4508, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4508, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4508, q_gen_4502) -> q_gen_4485
<s, s>(q_gen_4483) -> q_gen_4489
<z, s>(q_gen_4481) -> q_gen_4489
<s, s>(q_gen_4489) -> q_gen_4502
<z, s>(q_gen_4496) -> q_gen_4502
<s, s>(q_gen_4502) -> q_gen_4528
<z, s>(q_gen_4519) -> q_gen_4528
}

Datatype: <nattsil, nat>
Convolution form: right
}}}

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 67
() -> length([nil, z]) -> 65
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 65
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 72
(le([s(nn1), z])) -> BOT -> 70
(le([z, z])) -> BOT -> 65
(length([l, _fy]) /\ length([snoc(l, x), _gy])) -> le([_fy, _gy]) -> 84
(length([ll, _by])) -> length([snoc(ll, x), s(_by)]) -> 82
}
Sat witness: Found: ((length([l, _fy]) /\ length([snoc(l, x), _gy])) -> le([_fy, _gy]), {
_fy -> s(s(s(s(s(s(z))))))  ;  _gy -> s(s(z))  ;  l -> snoc(nil, s(s(s(s(s(s(z)))))))  ;  x -> s(z)
})

-------------------------------------------
Step 70, which took 0.629464 s (model generation: 0.544600,  model checking: 0.084864):

Model:
|_
{
le -> 
{{{
Q={q_gen_4468, q_gen_4469, q_gen_4486},
Q_f={q_gen_4468},
Delta=
{
<s>(q_gen_4469) -> q_gen_4469
<z>() -> q_gen_4469
<s, s>(q_gen_4468) -> q_gen_4468
<z, s>(q_gen_4469) -> q_gen_4468
<s, s>(q_gen_4486) -> q_gen_4486
<s, z>(q_gen_4469) -> q_gen_4486
<z, z>() -> q_gen_4486
}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_4467, q_gen_4471, q_gen_4472, q_gen_4478, q_gen_4481, q_gen_4483, q_gen_4484, q_gen_4485, q_gen_4489, q_gen_4490, q_gen_4496, q_gen_4502, q_gen_4505, q_gen_4508, q_gen_4519, q_gen_4528},
Q_f={q_gen_4467},
Delta=
{
<nil>() -> q_gen_4472
<z>() -> q_gen_4478
<s>(q_gen_4478) -> q_gen_4481
<snoc>(q_gen_4472, q_gen_4478) -> q_gen_4484
<snoc>(q_gen_4472, q_gen_4519) -> q_gen_4484
<snoc>(q_gen_4484, q_gen_4478) -> q_gen_4490
<s>(q_gen_4481) -> q_gen_4496
<snoc>(q_gen_4490, q_gen_4478) -> q_gen_4505
<snoc>(q_gen_4490, q_gen_4481) -> q_gen_4505
<snoc>(q_gen_4490, q_gen_4496) -> q_gen_4505
<snoc>(q_gen_4490, q_gen_4519) -> q_gen_4505
<snoc>(q_gen_4505, q_gen_4478) -> q_gen_4508
<s>(q_gen_4496) -> q_gen_4519
<s>(q_gen_4519) -> q_gen_4519
<nil, z>() -> q_gen_4467
<snoc, s>(q_gen_4472, q_gen_4471) -> q_gen_4467
<snoc, s>(q_gen_4484, q_gen_4483) -> q_gen_4467
<snoc, s>(q_gen_4490, q_gen_4489) -> q_gen_4467
<snoc, s>(q_gen_4505, q_gen_4502) -> q_gen_4467
<snoc, s>(q_gen_4508, q_gen_4528) -> q_gen_4467
<s, z>(q_gen_4478) -> q_gen_4471
<s, z>(q_gen_4481) -> q_gen_4471
<s, z>(q_gen_4496) -> q_gen_4471
<s, z>(q_gen_4519) -> q_gen_4471
<z, z>() -> q_gen_4471
<s, s>(q_gen_4471) -> q_gen_4483
<z, s>(q_gen_4478) -> q_gen_4483
<snoc, s>(q_gen_4472, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4472, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4472, q_gen_4502) -> q_gen_4485
<snoc, s>(q_gen_4472, q_gen_4528) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4502) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4528) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4502) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4528) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4528) -> q_gen_4485
<snoc, s>(q_gen_4508, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4508, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4508, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4508, q_gen_4502) -> q_gen_4485
<s, s>(q_gen_4483) -> q_gen_4489
<z, s>(q_gen_4481) -> q_gen_4489
<s, s>(q_gen_4489) -> q_gen_4502
<z, s>(q_gen_4496) -> q_gen_4502
<s, s>(q_gen_4502) -> q_gen_4528
<s, s>(q_gen_4528) -> q_gen_4528
<z, s>(q_gen_4519) -> q_gen_4528
}

Datatype: <nattsil, nat>
Convolution form: right
}}}

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 68
() -> length([nil, z]) -> 66
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 66
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 73
(le([s(nn1), z])) -> BOT -> 71
(le([z, z])) -> BOT -> 66
(length([l, _fy]) /\ length([snoc(l, x), _gy])) -> le([_fy, _gy]) -> 84
(length([ll, _by])) -> length([snoc(ll, x), s(_by)]) -> 85
}
Sat witness: Found: ((length([ll, _by])) -> length([snoc(ll, x), s(_by)]), {
_by -> s(s(s(s(z))))  ;  ll -> snoc(snoc(snoc(snoc(nil, z), z), s(z)), s(s(s(s(s(s(s(z))))))))  ;  x -> s(z)
})

-------------------------------------------
Step 71, which took 0.553209 s (model generation: 0.540482,  model checking: 0.012727):

Model:
|_
{
le -> 
{{{
Q={q_gen_4468, q_gen_4469, q_gen_4486},
Q_f={q_gen_4468},
Delta=
{
<s>(q_gen_4469) -> q_gen_4469
<z>() -> q_gen_4469
<s, s>(q_gen_4468) -> q_gen_4468
<z, s>(q_gen_4469) -> q_gen_4468
<s, s>(q_gen_4486) -> q_gen_4486
<s, z>(q_gen_4469) -> q_gen_4486
<z, z>() -> q_gen_4486
}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_4467, q_gen_4471, q_gen_4472, q_gen_4478, q_gen_4481, q_gen_4483, q_gen_4484, q_gen_4485, q_gen_4489, q_gen_4490, q_gen_4496, q_gen_4502, q_gen_4505, q_gen_4508, q_gen_4519, q_gen_4528},
Q_f={q_gen_4467},
Delta=
{
<nil>() -> q_gen_4472
<z>() -> q_gen_4478
<s>(q_gen_4478) -> q_gen_4481
<snoc>(q_gen_4472, q_gen_4478) -> q_gen_4484
<snoc>(q_gen_4472, q_gen_4519) -> q_gen_4484
<snoc>(q_gen_4484, q_gen_4478) -> q_gen_4490
<snoc>(q_gen_4490, q_gen_4481) -> q_gen_4490
<s>(q_gen_4481) -> q_gen_4496
<snoc>(q_gen_4490, q_gen_4478) -> q_gen_4505
<snoc>(q_gen_4490, q_gen_4519) -> q_gen_4505
<snoc>(q_gen_4508, q_gen_4478) -> q_gen_4505
<snoc>(q_gen_4490, q_gen_4496) -> q_gen_4508
<snoc>(q_gen_4505, q_gen_4478) -> q_gen_4508
<s>(q_gen_4496) -> q_gen_4519
<s>(q_gen_4519) -> q_gen_4519
<nil, z>() -> q_gen_4467
<snoc, s>(q_gen_4472, q_gen_4471) -> q_gen_4467
<snoc, s>(q_gen_4484, q_gen_4483) -> q_gen_4467
<snoc, s>(q_gen_4490, q_gen_4489) -> q_gen_4467
<snoc, s>(q_gen_4490, q_gen_4502) -> q_gen_4467
<snoc, s>(q_gen_4505, q_gen_4502) -> q_gen_4467
<snoc, s>(q_gen_4505, q_gen_4528) -> q_gen_4467
<snoc, s>(q_gen_4508, q_gen_4471) -> q_gen_4467
<snoc, s>(q_gen_4508, q_gen_4528) -> q_gen_4467
<s, s>(q_gen_4528) -> q_gen_4471
<s, z>(q_gen_4478) -> q_gen_4471
<s, z>(q_gen_4481) -> q_gen_4471
<s, z>(q_gen_4496) -> q_gen_4471
<s, z>(q_gen_4519) -> q_gen_4471
<z, z>() -> q_gen_4471
<s, s>(q_gen_4471) -> q_gen_4483
<z, s>(q_gen_4478) -> q_gen_4483
<snoc, s>(q_gen_4472, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4472, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4472, q_gen_4502) -> q_gen_4485
<snoc, s>(q_gen_4472, q_gen_4528) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4502) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4528) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4528) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4508, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4508, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4508, q_gen_4502) -> q_gen_4485
<s, s>(q_gen_4483) -> q_gen_4489
<z, s>(q_gen_4481) -> q_gen_4489
<s, s>(q_gen_4502) -> q_gen_4502
<z, s>(q_gen_4496) -> q_gen_4502
<s, s>(q_gen_4489) -> q_gen_4528
<z, s>(q_gen_4519) -> q_gen_4528
}

Datatype: <nattsil, nat>
Convolution form: right
}}}

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 69
() -> length([nil, z]) -> 67
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 67
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 74
(le([s(nn1), z])) -> BOT -> 72
(le([z, z])) -> BOT -> 67
(length([l, _fy]) /\ length([snoc(l, x), _gy])) -> le([_fy, _gy]) -> 87
(length([ll, _by])) -> length([snoc(ll, x), s(_by)]) -> 85
}
Sat witness: Found: ((length([l, _fy]) /\ length([snoc(l, x), _gy])) -> le([_fy, _gy]), {
_fy -> s(s(s(s(s(z)))))  ;  _gy -> s(s(z))  ;  l -> snoc(nil, s(s(s(s(z)))))  ;  x -> z
})

-------------------------------------------
Step 72, which took 0.472424 s (model generation: 0.451198,  model checking: 0.021226):

Model:
|_
{
le -> 
{{{
Q={q_gen_4468, q_gen_4469, q_gen_4486},
Q_f={q_gen_4468},
Delta=
{
<s>(q_gen_4469) -> q_gen_4469
<z>() -> q_gen_4469
<s, s>(q_gen_4468) -> q_gen_4468
<z, s>(q_gen_4469) -> q_gen_4468
<s, s>(q_gen_4486) -> q_gen_4486
<s, z>(q_gen_4469) -> q_gen_4486
<z, z>() -> q_gen_4486
}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_4467, q_gen_4471, q_gen_4472, q_gen_4478, q_gen_4481, q_gen_4483, q_gen_4484, q_gen_4485, q_gen_4489, q_gen_4490, q_gen_4496, q_gen_4502, q_gen_4505, q_gen_4508, q_gen_4519, q_gen_4528},
Q_f={q_gen_4467},
Delta=
{
<nil>() -> q_gen_4472
<z>() -> q_gen_4478
<s>(q_gen_4478) -> q_gen_4481
<snoc>(q_gen_4472, q_gen_4478) -> q_gen_4484
<snoc>(q_gen_4472, q_gen_4519) -> q_gen_4484
<snoc>(q_gen_4505, q_gen_4519) -> q_gen_4484
<snoc>(q_gen_4484, q_gen_4478) -> q_gen_4490
<snoc>(q_gen_4490, q_gen_4519) -> q_gen_4490
<s>(q_gen_4481) -> q_gen_4496
<snoc>(q_gen_4490, q_gen_4478) -> q_gen_4505
<snoc>(q_gen_4490, q_gen_4481) -> q_gen_4505
<snoc>(q_gen_4508, q_gen_4478) -> q_gen_4505
<snoc>(q_gen_4490, q_gen_4496) -> q_gen_4508
<snoc>(q_gen_4505, q_gen_4478) -> q_gen_4508
<s>(q_gen_4496) -> q_gen_4519
<s>(q_gen_4519) -> q_gen_4519
<nil, z>() -> q_gen_4467
<snoc, s>(q_gen_4472, q_gen_4471) -> q_gen_4467
<snoc, s>(q_gen_4484, q_gen_4483) -> q_gen_4467
<snoc, s>(q_gen_4490, q_gen_4489) -> q_gen_4467
<snoc, s>(q_gen_4490, q_gen_4502) -> q_gen_4467
<snoc, s>(q_gen_4505, q_gen_4502) -> q_gen_4467
<snoc, s>(q_gen_4505, q_gen_4528) -> q_gen_4467
<snoc, s>(q_gen_4508, q_gen_4528) -> q_gen_4467
<s, z>(q_gen_4478) -> q_gen_4471
<s, z>(q_gen_4481) -> q_gen_4471
<s, z>(q_gen_4496) -> q_gen_4471
<s, z>(q_gen_4519) -> q_gen_4471
<z, z>() -> q_gen_4471
<s, s>(q_gen_4471) -> q_gen_4483
<s, s>(q_gen_4502) -> q_gen_4483
<z, s>(q_gen_4478) -> q_gen_4483
<snoc, s>(q_gen_4472, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4472, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4472, q_gen_4502) -> q_gen_4485
<snoc, s>(q_gen_4472, q_gen_4528) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4502) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4528) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4528) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4508, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4508, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4508, q_gen_4502) -> q_gen_4485
<s, s>(q_gen_4483) -> q_gen_4489
<z, s>(q_gen_4481) -> q_gen_4489
<z, s>(q_gen_4496) -> q_gen_4502
<s, s>(q_gen_4489) -> q_gen_4528
<s, s>(q_gen_4528) -> q_gen_4528
<z, s>(q_gen_4519) -> q_gen_4528
}

Datatype: <nattsil, nat>
Convolution form: right
}}}

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 70
() -> length([nil, z]) -> 68
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 68
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 75
(le([s(nn1), z])) -> BOT -> 73
(le([z, z])) -> BOT -> 68
(length([l, _fy]) /\ length([snoc(l, x), _gy])) -> le([_fy, _gy]) -> 87
(length([ll, _by])) -> length([snoc(ll, x), s(_by)]) -> 88
}
Sat witness: Found: ((length([ll, _by])) -> length([snoc(ll, x), s(_by)]), {
_by -> s(s(s(s(z))))  ;  ll -> snoc(snoc(snoc(snoc(snoc(snoc(nil, z), z), z), z), z), z)  ;  x -> s(z)
})

-------------------------------------------
Step 73, which took 0.653382 s (model generation: 0.639850,  model checking: 0.013532):

Model:
|_
{
le -> 
{{{
Q={q_gen_4468, q_gen_4469, q_gen_4486},
Q_f={q_gen_4468},
Delta=
{
<s>(q_gen_4469) -> q_gen_4469
<z>() -> q_gen_4469
<s, s>(q_gen_4468) -> q_gen_4468
<z, s>(q_gen_4469) -> q_gen_4468
<s, s>(q_gen_4486) -> q_gen_4486
<s, z>(q_gen_4469) -> q_gen_4486
<z, z>() -> q_gen_4486
}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_4467, q_gen_4471, q_gen_4472, q_gen_4478, q_gen_4481, q_gen_4483, q_gen_4484, q_gen_4485, q_gen_4489, q_gen_4490, q_gen_4496, q_gen_4502, q_gen_4505, q_gen_4508, q_gen_4519, q_gen_4528},
Q_f={q_gen_4467},
Delta=
{
<nil>() -> q_gen_4472
<z>() -> q_gen_4478
<s>(q_gen_4478) -> q_gen_4481
<snoc>(q_gen_4472, q_gen_4478) -> q_gen_4484
<snoc>(q_gen_4472, q_gen_4519) -> q_gen_4484
<snoc>(q_gen_4484, q_gen_4478) -> q_gen_4490
<s>(q_gen_4481) -> q_gen_4496
<snoc>(q_gen_4490, q_gen_4478) -> q_gen_4505
<snoc>(q_gen_4490, q_gen_4481) -> q_gen_4505
<snoc>(q_gen_4490, q_gen_4496) -> q_gen_4505
<snoc>(q_gen_4490, q_gen_4519) -> q_gen_4505
<snoc>(q_gen_4508, q_gen_4478) -> q_gen_4505
<snoc>(q_gen_4505, q_gen_4478) -> q_gen_4508
<snoc>(q_gen_4505, q_gen_4519) -> q_gen_4508
<s>(q_gen_4496) -> q_gen_4519
<s>(q_gen_4519) -> q_gen_4519
<nil, z>() -> q_gen_4467
<snoc, s>(q_gen_4472, q_gen_4471) -> q_gen_4467
<snoc, s>(q_gen_4484, q_gen_4483) -> q_gen_4467
<snoc, s>(q_gen_4490, q_gen_4489) -> q_gen_4467
<snoc, s>(q_gen_4505, q_gen_4502) -> q_gen_4467
<snoc, s>(q_gen_4508, q_gen_4489) -> q_gen_4467
<snoc, s>(q_gen_4508, q_gen_4528) -> q_gen_4467
<s, z>(q_gen_4478) -> q_gen_4471
<s, z>(q_gen_4481) -> q_gen_4471
<s, z>(q_gen_4496) -> q_gen_4471
<s, z>(q_gen_4519) -> q_gen_4471
<z, z>() -> q_gen_4471
<s, s>(q_gen_4471) -> q_gen_4483
<z, s>(q_gen_4478) -> q_gen_4483
<snoc, s>(q_gen_4472, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4472, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4472, q_gen_4502) -> q_gen_4485
<snoc, s>(q_gen_4472, q_gen_4528) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4502) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4528) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4502) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4528) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4528) -> q_gen_4485
<snoc, s>(q_gen_4508, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4508, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4508, q_gen_4502) -> q_gen_4485
<s, s>(q_gen_4483) -> q_gen_4489
<s, s>(q_gen_4502) -> q_gen_4489
<z, s>(q_gen_4481) -> q_gen_4489
<s, s>(q_gen_4489) -> q_gen_4502
<z, s>(q_gen_4496) -> q_gen_4502
<s, s>(q_gen_4528) -> q_gen_4528
<z, s>(q_gen_4519) -> q_gen_4528
}

Datatype: <nattsil, nat>
Convolution form: right
}}}

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 71
() -> length([nil, z]) -> 69
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 69
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 76
(le([s(nn1), z])) -> BOT -> 74
(le([z, z])) -> BOT -> 69
(length([l, _fy]) /\ length([snoc(l, x), _gy])) -> le([_fy, _gy]) -> 90
(length([ll, _by])) -> length([snoc(ll, x), s(_by)]) -> 88
}
Sat witness: Found: ((length([l, _fy]) /\ length([snoc(l, x), _gy])) -> le([_fy, _gy]), {
_fy -> s(s(s(s(s(z)))))  ;  _gy -> s(s(s(s(z))))  ;  l -> snoc(snoc(snoc(nil, z), z), s(z))  ;  x -> z
})

-------------------------------------------
Step 74, which took 0.619209 s (model generation: 0.607364,  model checking: 0.011845):

Model:
|_
{
le -> 
{{{
Q={q_gen_4468, q_gen_4469, q_gen_4486},
Q_f={q_gen_4468},
Delta=
{
<s>(q_gen_4469) -> q_gen_4469
<z>() -> q_gen_4469
<s, s>(q_gen_4468) -> q_gen_4468
<z, s>(q_gen_4469) -> q_gen_4468
<s, s>(q_gen_4486) -> q_gen_4486
<s, z>(q_gen_4469) -> q_gen_4486
<z, z>() -> q_gen_4486
}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_4467, q_gen_4471, q_gen_4472, q_gen_4478, q_gen_4481, q_gen_4483, q_gen_4484, q_gen_4485, q_gen_4489, q_gen_4490, q_gen_4496, q_gen_4502, q_gen_4505, q_gen_4508, q_gen_4519, q_gen_4528},
Q_f={q_gen_4467},
Delta=
{
<nil>() -> q_gen_4472
<snoc>(q_gen_4508, q_gen_4478) -> q_gen_4472
<z>() -> q_gen_4478
<s>(q_gen_4478) -> q_gen_4481
<snoc>(q_gen_4472, q_gen_4478) -> q_gen_4484
<snoc>(q_gen_4472, q_gen_4481) -> q_gen_4484
<snoc>(q_gen_4484, q_gen_4478) -> q_gen_4490
<snoc>(q_gen_4490, q_gen_4496) -> q_gen_4490
<snoc>(q_gen_4490, q_gen_4519) -> q_gen_4490
<s>(q_gen_4481) -> q_gen_4496
<snoc>(q_gen_4490, q_gen_4478) -> q_gen_4505
<snoc>(q_gen_4490, q_gen_4481) -> q_gen_4505
<snoc>(q_gen_4472, q_gen_4519) -> q_gen_4508
<snoc>(q_gen_4505, q_gen_4478) -> q_gen_4508
<snoc>(q_gen_4505, q_gen_4519) -> q_gen_4508
<s>(q_gen_4496) -> q_gen_4519
<s>(q_gen_4519) -> q_gen_4519
<nil, z>() -> q_gen_4467
<snoc, s>(q_gen_4472, q_gen_4471) -> q_gen_4467
<snoc, s>(q_gen_4484, q_gen_4483) -> q_gen_4467
<snoc, s>(q_gen_4490, q_gen_4489) -> q_gen_4467
<snoc, s>(q_gen_4490, q_gen_4502) -> q_gen_4467
<snoc, s>(q_gen_4505, q_gen_4502) -> q_gen_4467
<snoc, s>(q_gen_4505, q_gen_4528) -> q_gen_4467
<snoc, s>(q_gen_4508, q_gen_4483) -> q_gen_4467
<snoc, s>(q_gen_4508, q_gen_4528) -> q_gen_4467
<s, z>(q_gen_4478) -> q_gen_4471
<s, z>(q_gen_4481) -> q_gen_4471
<s, z>(q_gen_4496) -> q_gen_4471
<s, z>(q_gen_4519) -> q_gen_4471
<z, z>() -> q_gen_4471
<s, s>(q_gen_4471) -> q_gen_4483
<z, s>(q_gen_4478) -> q_gen_4483
<snoc, s>(q_gen_4472, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4472, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4472, q_gen_4502) -> q_gen_4485
<snoc, s>(q_gen_4472, q_gen_4528) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4502) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4528) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4528) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4508, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4508, q_gen_4502) -> q_gen_4485
<s, s>(q_gen_4483) -> q_gen_4489
<z, s>(q_gen_4481) -> q_gen_4489
<s, s>(q_gen_4489) -> q_gen_4502
<s, s>(q_gen_4528) -> q_gen_4502
<z, s>(q_gen_4496) -> q_gen_4502
<s, s>(q_gen_4502) -> q_gen_4528
<z, s>(q_gen_4519) -> q_gen_4528
}

Datatype: <nattsil, nat>
Convolution form: right
}}}

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 72
() -> length([nil, z]) -> 70
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 70
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 77
(le([s(nn1), z])) -> BOT -> 75
(le([z, z])) -> BOT -> 70
(length([l, _fy]) /\ length([snoc(l, x), _gy])) -> le([_fy, _gy]) -> 90
(length([ll, _by])) -> length([snoc(ll, x), s(_by)]) -> 91
}
Sat witness: Found: ((length([ll, _by])) -> length([snoc(ll, x), s(_by)]), {
_by -> s(s(s(s(s(z)))))  ;  ll -> snoc(snoc(nil, s(s(s(z)))), z)  ;  x -> s(s(z))
})

-------------------------------------------
Step 75, which took 0.661388 s (model generation: 0.643555,  model checking: 0.017833):

Model:
|_
{
le -> 
{{{
Q={q_gen_4468, q_gen_4469, q_gen_4486},
Q_f={q_gen_4468},
Delta=
{
<s>(q_gen_4469) -> q_gen_4469
<z>() -> q_gen_4469
<s, s>(q_gen_4468) -> q_gen_4468
<z, s>(q_gen_4469) -> q_gen_4468
<s, s>(q_gen_4486) -> q_gen_4486
<s, z>(q_gen_4469) -> q_gen_4486
<z, z>() -> q_gen_4486
}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_4467, q_gen_4471, q_gen_4472, q_gen_4478, q_gen_4481, q_gen_4483, q_gen_4484, q_gen_4485, q_gen_4489, q_gen_4490, q_gen_4496, q_gen_4502, q_gen_4505, q_gen_4508, q_gen_4519, q_gen_4528},
Q_f={q_gen_4467},
Delta=
{
<nil>() -> q_gen_4472
<z>() -> q_gen_4478
<s>(q_gen_4478) -> q_gen_4481
<snoc>(q_gen_4472, q_gen_4478) -> q_gen_4484
<snoc>(q_gen_4472, q_gen_4519) -> q_gen_4484
<snoc>(q_gen_4508, q_gen_4478) -> q_gen_4484
<snoc>(q_gen_4484, q_gen_4478) -> q_gen_4490
<s>(q_gen_4481) -> q_gen_4496
<snoc>(q_gen_4490, q_gen_4478) -> q_gen_4505
<snoc>(q_gen_4490, q_gen_4481) -> q_gen_4505
<snoc>(q_gen_4490, q_gen_4496) -> q_gen_4505
<snoc>(q_gen_4490, q_gen_4519) -> q_gen_4505
<snoc>(q_gen_4505, q_gen_4478) -> q_gen_4508
<snoc>(q_gen_4505, q_gen_4519) -> q_gen_4508
<s>(q_gen_4496) -> q_gen_4519
<s>(q_gen_4519) -> q_gen_4519
<nil, z>() -> q_gen_4467
<snoc, s>(q_gen_4472, q_gen_4471) -> q_gen_4467
<snoc, s>(q_gen_4484, q_gen_4483) -> q_gen_4467
<snoc, s>(q_gen_4490, q_gen_4489) -> q_gen_4467
<snoc, s>(q_gen_4505, q_gen_4502) -> q_gen_4467
<snoc, s>(q_gen_4508, q_gen_4528) -> q_gen_4467
<s, z>(q_gen_4478) -> q_gen_4471
<s, z>(q_gen_4481) -> q_gen_4471
<s, z>(q_gen_4496) -> q_gen_4471
<s, z>(q_gen_4519) -> q_gen_4471
<z, z>() -> q_gen_4471
<s, s>(q_gen_4471) -> q_gen_4483
<s, s>(q_gen_4528) -> q_gen_4483
<z, s>(q_gen_4478) -> q_gen_4483
<snoc, s>(q_gen_4472, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4472, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4472, q_gen_4502) -> q_gen_4485
<snoc, s>(q_gen_4472, q_gen_4528) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4502) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4528) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4502) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4528) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4528) -> q_gen_4485
<snoc, s>(q_gen_4508, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4508, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4508, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4508, q_gen_4502) -> q_gen_4485
<s, s>(q_gen_4483) -> q_gen_4489
<z, s>(q_gen_4481) -> q_gen_4489
<s, s>(q_gen_4489) -> q_gen_4502
<z, s>(q_gen_4496) -> q_gen_4502
<s, s>(q_gen_4502) -> q_gen_4528
<z, s>(q_gen_4519) -> q_gen_4528
}

Datatype: <nattsil, nat>
Convolution form: right
}}}

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 73
() -> length([nil, z]) -> 71
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 71
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 78
(le([s(nn1), z])) -> BOT -> 76
(le([z, z])) -> BOT -> 71
(length([l, _fy]) /\ length([snoc(l, x), _gy])) -> le([_fy, _gy]) -> 93
(length([ll, _by])) -> length([snoc(ll, x), s(_by)]) -> 91
}
Sat witness: Found: ((length([l, _fy]) /\ length([snoc(l, x), _gy])) -> le([_fy, _gy]), {
_fy -> s(s(s(s(s(z)))))  ;  _gy -> s(s(z))  ;  l -> snoc(snoc(snoc(snoc(snoc(nil, z), z), s(s(z))), z), z)  ;  x -> z
})

-------------------------------------------
Step 76, which took 0.755112 s (model generation: 0.741837,  model checking: 0.013275):

Model:
|_
{
le -> 
{{{
Q={q_gen_4468, q_gen_4469, q_gen_4486},
Q_f={q_gen_4468},
Delta=
{
<s>(q_gen_4469) -> q_gen_4469
<z>() -> q_gen_4469
<s, s>(q_gen_4468) -> q_gen_4468
<z, s>(q_gen_4469) -> q_gen_4468
<s, s>(q_gen_4486) -> q_gen_4486
<s, z>(q_gen_4469) -> q_gen_4486
<z, z>() -> q_gen_4486
}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_4467, q_gen_4471, q_gen_4472, q_gen_4478, q_gen_4481, q_gen_4483, q_gen_4484, q_gen_4485, q_gen_4489, q_gen_4490, q_gen_4496, q_gen_4502, q_gen_4505, q_gen_4508, q_gen_4519, q_gen_4528},
Q_f={q_gen_4467},
Delta=
{
<nil>() -> q_gen_4472
<snoc>(q_gen_4508, q_gen_4478) -> q_gen_4472
<z>() -> q_gen_4478
<s>(q_gen_4478) -> q_gen_4481
<snoc>(q_gen_4472, q_gen_4478) -> q_gen_4484
<snoc>(q_gen_4472, q_gen_4519) -> q_gen_4484
<snoc>(q_gen_4484, q_gen_4478) -> q_gen_4490
<snoc>(q_gen_4490, q_gen_4481) -> q_gen_4490
<snoc>(q_gen_4490, q_gen_4519) -> q_gen_4490
<s>(q_gen_4481) -> q_gen_4496
<snoc>(q_gen_4490, q_gen_4478) -> q_gen_4505
<snoc>(q_gen_4490, q_gen_4496) -> q_gen_4505
<snoc>(q_gen_4505, q_gen_4478) -> q_gen_4508
<s>(q_gen_4496) -> q_gen_4519
<s>(q_gen_4519) -> q_gen_4519
<nil, z>() -> q_gen_4467
<snoc, s>(q_gen_4472, q_gen_4471) -> q_gen_4467
<snoc, s>(q_gen_4484, q_gen_4483) -> q_gen_4467
<snoc, s>(q_gen_4490, q_gen_4489) -> q_gen_4467
<snoc, s>(q_gen_4490, q_gen_4502) -> q_gen_4467
<snoc, s>(q_gen_4505, q_gen_4502) -> q_gen_4467
<snoc, s>(q_gen_4505, q_gen_4528) -> q_gen_4467
<snoc, s>(q_gen_4508, q_gen_4528) -> q_gen_4467
<s, s>(q_gen_4502) -> q_gen_4471
<s, z>(q_gen_4478) -> q_gen_4471
<s, z>(q_gen_4481) -> q_gen_4471
<s, z>(q_gen_4496) -> q_gen_4471
<s, z>(q_gen_4519) -> q_gen_4471
<z, z>() -> q_gen_4471
<s, s>(q_gen_4471) -> q_gen_4483
<z, s>(q_gen_4478) -> q_gen_4483
<snoc, s>(q_gen_4472, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4472, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4472, q_gen_4502) -> q_gen_4485
<snoc, s>(q_gen_4472, q_gen_4528) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4502) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4528) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4528) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4508, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4508, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4508, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4508, q_gen_4502) -> q_gen_4485
<s, s>(q_gen_4483) -> q_gen_4489
<z, s>(q_gen_4481) -> q_gen_4489
<z, s>(q_gen_4496) -> q_gen_4502
<s, s>(q_gen_4489) -> q_gen_4528
<s, s>(q_gen_4528) -> q_gen_4528
<z, s>(q_gen_4519) -> q_gen_4528
}

Datatype: <nattsil, nat>
Convolution form: right
}}}

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 74
() -> length([nil, z]) -> 72
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 72
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 79
(le([s(nn1), z])) -> BOT -> 77
(le([z, z])) -> BOT -> 72
(length([l, _fy]) /\ length([snoc(l, x), _gy])) -> le([_fy, _gy]) -> 93
(length([ll, _by])) -> length([snoc(ll, x), s(_by)]) -> 94
}
Sat witness: Found: ((length([ll, _by])) -> length([snoc(ll, x), s(_by)]), {
_by -> s(s(s(s(s(z)))))  ;  ll -> snoc(snoc(snoc(snoc(nil, s(s(s(z)))), z), s(s(z))), z)  ;  x -> s(s(z))
})

-------------------------------------------
Step 77, which took 0.718486 s (model generation: 0.700318,  model checking: 0.018168):

Model:
|_
{
le -> 
{{{
Q={q_gen_4468, q_gen_4469, q_gen_4486},
Q_f={q_gen_4468},
Delta=
{
<s>(q_gen_4469) -> q_gen_4469
<z>() -> q_gen_4469
<s, s>(q_gen_4468) -> q_gen_4468
<z, s>(q_gen_4469) -> q_gen_4468
<s, s>(q_gen_4486) -> q_gen_4486
<s, z>(q_gen_4469) -> q_gen_4486
<z, z>() -> q_gen_4486
}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_4467, q_gen_4471, q_gen_4472, q_gen_4478, q_gen_4481, q_gen_4483, q_gen_4484, q_gen_4485, q_gen_4489, q_gen_4490, q_gen_4496, q_gen_4502, q_gen_4505, q_gen_4508, q_gen_4519, q_gen_4528},
Q_f={q_gen_4467},
Delta=
{
<nil>() -> q_gen_4472
<z>() -> q_gen_4478
<s>(q_gen_4478) -> q_gen_4481
<snoc>(q_gen_4472, q_gen_4478) -> q_gen_4484
<snoc>(q_gen_4472, q_gen_4519) -> q_gen_4484
<snoc>(q_gen_4484, q_gen_4478) -> q_gen_4490
<snoc>(q_gen_4508, q_gen_4478) -> q_gen_4490
<s>(q_gen_4481) -> q_gen_4496
<snoc>(q_gen_4490, q_gen_4478) -> q_gen_4505
<snoc>(q_gen_4490, q_gen_4481) -> q_gen_4505
<snoc>(q_gen_4490, q_gen_4496) -> q_gen_4505
<snoc>(q_gen_4490, q_gen_4519) -> q_gen_4505
<snoc>(q_gen_4505, q_gen_4478) -> q_gen_4508
<snoc>(q_gen_4505, q_gen_4519) -> q_gen_4508
<s>(q_gen_4496) -> q_gen_4519
<s>(q_gen_4519) -> q_gen_4519
<nil, z>() -> q_gen_4467
<snoc, s>(q_gen_4472, q_gen_4471) -> q_gen_4467
<snoc, s>(q_gen_4484, q_gen_4483) -> q_gen_4467
<snoc, s>(q_gen_4490, q_gen_4489) -> q_gen_4467
<snoc, s>(q_gen_4505, q_gen_4502) -> q_gen_4467
<snoc, s>(q_gen_4508, q_gen_4528) -> q_gen_4467
<s, z>(q_gen_4478) -> q_gen_4471
<s, z>(q_gen_4481) -> q_gen_4471
<s, z>(q_gen_4496) -> q_gen_4471
<s, z>(q_gen_4519) -> q_gen_4471
<z, z>() -> q_gen_4471
<s, s>(q_gen_4471) -> q_gen_4483
<s, s>(q_gen_4528) -> q_gen_4483
<z, s>(q_gen_4478) -> q_gen_4483
<snoc, s>(q_gen_4472, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4472, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4472, q_gen_4502) -> q_gen_4485
<snoc, s>(q_gen_4472, q_gen_4528) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4502) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4528) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4502) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4528) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4528) -> q_gen_4485
<snoc, s>(q_gen_4508, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4508, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4508, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4508, q_gen_4502) -> q_gen_4485
<s, s>(q_gen_4483) -> q_gen_4489
<z, s>(q_gen_4481) -> q_gen_4489
<s, s>(q_gen_4489) -> q_gen_4502
<z, s>(q_gen_4496) -> q_gen_4502
<s, s>(q_gen_4502) -> q_gen_4528
<z, s>(q_gen_4519) -> q_gen_4528
}

Datatype: <nattsil, nat>
Convolution form: right
}}}

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 75
() -> length([nil, z]) -> 73
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 73
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 80
(le([s(nn1), z])) -> BOT -> 78
(le([z, z])) -> BOT -> 73
(length([l, _fy]) /\ length([snoc(l, x), _gy])) -> le([_fy, _gy]) -> 96
(length([ll, _by])) -> length([snoc(ll, x), s(_by)]) -> 94
}
Sat witness: Found: ((length([l, _fy]) /\ length([snoc(l, x), _gy])) -> le([_fy, _gy]), {
_fy -> s(s(s(s(s(z)))))  ;  _gy -> s(s(s(z)))  ;  l -> snoc(snoc(snoc(snoc(snoc(nil, z), z), s(s(z))), s(s(s(z)))), z)  ;  x -> z
})

-------------------------------------------
Step 78, which took 0.921904 s (model generation: 0.835525,  model checking: 0.086379):

Model:
|_
{
le -> 
{{{
Q={q_gen_4468, q_gen_4469, q_gen_4486},
Q_f={q_gen_4468},
Delta=
{
<s>(q_gen_4469) -> q_gen_4469
<z>() -> q_gen_4469
<s, s>(q_gen_4468) -> q_gen_4468
<z, s>(q_gen_4469) -> q_gen_4468
<s, s>(q_gen_4486) -> q_gen_4486
<s, z>(q_gen_4469) -> q_gen_4486
<z, z>() -> q_gen_4486
}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_4467, q_gen_4471, q_gen_4472, q_gen_4478, q_gen_4481, q_gen_4483, q_gen_4484, q_gen_4485, q_gen_4489, q_gen_4490, q_gen_4496, q_gen_4502, q_gen_4505, q_gen_4508, q_gen_4519, q_gen_4528},
Q_f={q_gen_4467},
Delta=
{
<nil>() -> q_gen_4472
<z>() -> q_gen_4478
<s>(q_gen_4478) -> q_gen_4481
<snoc>(q_gen_4472, q_gen_4478) -> q_gen_4484
<snoc>(q_gen_4472, q_gen_4519) -> q_gen_4484
<snoc>(q_gen_4505, q_gen_4519) -> q_gen_4484
<snoc>(q_gen_4484, q_gen_4478) -> q_gen_4490
<snoc>(q_gen_4508, q_gen_4519) -> q_gen_4490
<s>(q_gen_4481) -> q_gen_4496
<snoc>(q_gen_4490, q_gen_4478) -> q_gen_4505
<snoc>(q_gen_4490, q_gen_4481) -> q_gen_4505
<snoc>(q_gen_4490, q_gen_4519) -> q_gen_4505
<snoc>(q_gen_4490, q_gen_4496) -> q_gen_4508
<snoc>(q_gen_4505, q_gen_4478) -> q_gen_4508
<snoc>(q_gen_4508, q_gen_4478) -> q_gen_4508
<s>(q_gen_4496) -> q_gen_4519
<s>(q_gen_4519) -> q_gen_4519
<nil, z>() -> q_gen_4467
<snoc, s>(q_gen_4472, q_gen_4471) -> q_gen_4467
<snoc, s>(q_gen_4484, q_gen_4483) -> q_gen_4467
<snoc, s>(q_gen_4490, q_gen_4489) -> q_gen_4467
<snoc, s>(q_gen_4505, q_gen_4502) -> q_gen_4467
<snoc, s>(q_gen_4505, q_gen_4528) -> q_gen_4467
<snoc, s>(q_gen_4508, q_gen_4489) -> q_gen_4467
<snoc, s>(q_gen_4508, q_gen_4528) -> q_gen_4467
<s, z>(q_gen_4478) -> q_gen_4471
<s, z>(q_gen_4481) -> q_gen_4471
<s, z>(q_gen_4496) -> q_gen_4471
<s, z>(q_gen_4519) -> q_gen_4471
<z, z>() -> q_gen_4471
<s, s>(q_gen_4471) -> q_gen_4483
<s, s>(q_gen_4502) -> q_gen_4483
<z, s>(q_gen_4478) -> q_gen_4483
<snoc, s>(q_gen_4472, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4472, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4472, q_gen_4502) -> q_gen_4485
<snoc, s>(q_gen_4472, q_gen_4528) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4502) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4528) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4502) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4528) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4508, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4508, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4508, q_gen_4502) -> q_gen_4485
<s, s>(q_gen_4483) -> q_gen_4489
<z, s>(q_gen_4481) -> q_gen_4489
<z, s>(q_gen_4496) -> q_gen_4502
<s, s>(q_gen_4489) -> q_gen_4528
<s, s>(q_gen_4528) -> q_gen_4528
<z, s>(q_gen_4519) -> q_gen_4528
}

Datatype: <nattsil, nat>
Convolution form: right
}}}

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 76
() -> length([nil, z]) -> 74
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 74
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 81
(le([s(nn1), z])) -> BOT -> 79
(le([z, z])) -> BOT -> 74
(length([l, _fy]) /\ length([snoc(l, x), _gy])) -> le([_fy, _gy]) -> 96
(length([ll, _by])) -> length([snoc(ll, x), s(_by)]) -> 97
}
Sat witness: Found: ((length([ll, _by])) -> length([snoc(ll, x), s(_by)]), {
_by -> s(s(s(s(z))))  ;  ll -> snoc(snoc(snoc(snoc(nil, s(s(s(z)))), z), s(s(s(z)))), z)  ;  x -> s(z)
})

-------------------------------------------
Step 79, which took 1.040734 s (model generation: 1.017973,  model checking: 0.022761):

Model:
|_
{
le -> 
{{{
Q={q_gen_4468, q_gen_4469, q_gen_4486},
Q_f={q_gen_4468},
Delta=
{
<s>(q_gen_4469) -> q_gen_4469
<z>() -> q_gen_4469
<s, s>(q_gen_4468) -> q_gen_4468
<z, s>(q_gen_4469) -> q_gen_4468
<s, s>(q_gen_4486) -> q_gen_4486
<s, z>(q_gen_4469) -> q_gen_4486
<z, z>() -> q_gen_4486
}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_4467, q_gen_4471, q_gen_4472, q_gen_4478, q_gen_4481, q_gen_4483, q_gen_4484, q_gen_4485, q_gen_4489, q_gen_4490, q_gen_4496, q_gen_4502, q_gen_4505, q_gen_4508, q_gen_4519, q_gen_4528},
Q_f={q_gen_4467},
Delta=
{
<nil>() -> q_gen_4472
<z>() -> q_gen_4478
<s>(q_gen_4478) -> q_gen_4481
<snoc>(q_gen_4472, q_gen_4478) -> q_gen_4484
<snoc>(q_gen_4472, q_gen_4519) -> q_gen_4484
<snoc>(q_gen_4508, q_gen_4519) -> q_gen_4484
<snoc>(q_gen_4484, q_gen_4478) -> q_gen_4490
<snoc>(q_gen_4490, q_gen_4519) -> q_gen_4490
<s>(q_gen_4481) -> q_gen_4496
<snoc>(q_gen_4490, q_gen_4478) -> q_gen_4505
<snoc>(q_gen_4490, q_gen_4481) -> q_gen_4505
<snoc>(q_gen_4505, q_gen_4519) -> q_gen_4505
<snoc>(q_gen_4508, q_gen_4478) -> q_gen_4505
<snoc>(q_gen_4490, q_gen_4496) -> q_gen_4508
<snoc>(q_gen_4505, q_gen_4478) -> q_gen_4508
<s>(q_gen_4496) -> q_gen_4519
<s>(q_gen_4519) -> q_gen_4519
<nil, z>() -> q_gen_4467
<snoc, s>(q_gen_4472, q_gen_4471) -> q_gen_4467
<snoc, s>(q_gen_4484, q_gen_4483) -> q_gen_4467
<snoc, s>(q_gen_4490, q_gen_4489) -> q_gen_4467
<snoc, s>(q_gen_4490, q_gen_4502) -> q_gen_4467
<snoc, s>(q_gen_4505, q_gen_4502) -> q_gen_4467
<snoc, s>(q_gen_4505, q_gen_4528) -> q_gen_4467
<snoc, s>(q_gen_4508, q_gen_4489) -> q_gen_4467
<snoc, s>(q_gen_4508, q_gen_4528) -> q_gen_4467
<s, z>(q_gen_4478) -> q_gen_4471
<s, z>(q_gen_4481) -> q_gen_4471
<s, z>(q_gen_4496) -> q_gen_4471
<s, z>(q_gen_4519) -> q_gen_4471
<z, z>() -> q_gen_4471
<s, s>(q_gen_4471) -> q_gen_4483
<z, s>(q_gen_4478) -> q_gen_4483
<snoc, s>(q_gen_4472, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4472, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4472, q_gen_4502) -> q_gen_4485
<snoc, s>(q_gen_4472, q_gen_4528) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4502) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4528) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4528) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4508, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4508, q_gen_4502) -> q_gen_4485
<s, s>(q_gen_4483) -> q_gen_4489
<z, s>(q_gen_4481) -> q_gen_4489
<z, s>(q_gen_4496) -> q_gen_4502
<s, s>(q_gen_4489) -> q_gen_4528
<s, s>(q_gen_4502) -> q_gen_4528
<s, s>(q_gen_4528) -> q_gen_4528
<z, s>(q_gen_4519) -> q_gen_4528
}

Datatype: <nattsil, nat>
Convolution form: right
}}}

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 77
() -> length([nil, z]) -> 75
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 75
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 82
(le([s(nn1), z])) -> BOT -> 80
(le([z, z])) -> BOT -> 75
(length([l, _fy]) /\ length([snoc(l, x), _gy])) -> le([_fy, _gy]) -> 99
(length([ll, _by])) -> length([snoc(ll, x), s(_by)]) -> 97
}
Sat witness: Found: ((length([l, _fy]) /\ length([snoc(l, x), _gy])) -> le([_fy, _gy]), {
_fy -> s(s(s(z)))  ;  _gy -> s(s(z))  ;  l -> snoc(snoc(snoc(snoc(snoc(nil, z), z), s(s(s(z)))), s(s(z))), s(s(s(s(z)))))  ;  x -> z
})

-------------------------------------------
Step 80, which took 1.256653 s (model generation: 1.157869,  model checking: 0.098784):

Model:
|_
{
le -> 
{{{
Q={q_gen_4468, q_gen_4469, q_gen_4486},
Q_f={q_gen_4468},
Delta=
{
<s>(q_gen_4469) -> q_gen_4469
<z>() -> q_gen_4469
<s, s>(q_gen_4468) -> q_gen_4468
<z, s>(q_gen_4469) -> q_gen_4468
<s, s>(q_gen_4486) -> q_gen_4486
<s, z>(q_gen_4469) -> q_gen_4486
<z, z>() -> q_gen_4486
}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_4467, q_gen_4471, q_gen_4472, q_gen_4478, q_gen_4481, q_gen_4483, q_gen_4484, q_gen_4485, q_gen_4489, q_gen_4490, q_gen_4496, q_gen_4502, q_gen_4505, q_gen_4508, q_gen_4519, q_gen_4528},
Q_f={q_gen_4467},
Delta=
{
<nil>() -> q_gen_4472
<z>() -> q_gen_4478
<s>(q_gen_4478) -> q_gen_4481
<snoc>(q_gen_4472, q_gen_4478) -> q_gen_4484
<snoc>(q_gen_4472, q_gen_4519) -> q_gen_4484
<snoc>(q_gen_4508, q_gen_4519) -> q_gen_4484
<snoc>(q_gen_4484, q_gen_4478) -> q_gen_4490
<s>(q_gen_4481) -> q_gen_4496
<snoc>(q_gen_4490, q_gen_4478) -> q_gen_4505
<snoc>(q_gen_4490, q_gen_4481) -> q_gen_4505
<snoc>(q_gen_4490, q_gen_4496) -> q_gen_4505
<snoc>(q_gen_4490, q_gen_4519) -> q_gen_4505
<snoc>(q_gen_4505, q_gen_4478) -> q_gen_4508
<snoc>(q_gen_4505, q_gen_4496) -> q_gen_4508
<snoc>(q_gen_4505, q_gen_4519) -> q_gen_4508
<snoc>(q_gen_4508, q_gen_4478) -> q_gen_4508
<s>(q_gen_4496) -> q_gen_4519
<s>(q_gen_4519) -> q_gen_4519
<nil, z>() -> q_gen_4467
<snoc, s>(q_gen_4472, q_gen_4471) -> q_gen_4467
<snoc, s>(q_gen_4484, q_gen_4483) -> q_gen_4467
<snoc, s>(q_gen_4490, q_gen_4489) -> q_gen_4467
<snoc, s>(q_gen_4505, q_gen_4502) -> q_gen_4467
<snoc, s>(q_gen_4508, q_gen_4528) -> q_gen_4467
<s, z>(q_gen_4478) -> q_gen_4471
<s, z>(q_gen_4481) -> q_gen_4471
<s, z>(q_gen_4496) -> q_gen_4471
<s, z>(q_gen_4519) -> q_gen_4471
<z, z>() -> q_gen_4471
<s, s>(q_gen_4471) -> q_gen_4483
<z, s>(q_gen_4478) -> q_gen_4483
<snoc, s>(q_gen_4472, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4472, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4472, q_gen_4502) -> q_gen_4485
<snoc, s>(q_gen_4472, q_gen_4528) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4502) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4528) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4502) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4528) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4528) -> q_gen_4485
<snoc, s>(q_gen_4508, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4508, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4508, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4508, q_gen_4502) -> q_gen_4485
<s, s>(q_gen_4483) -> q_gen_4489
<z, s>(q_gen_4481) -> q_gen_4489
<s, s>(q_gen_4489) -> q_gen_4502
<z, s>(q_gen_4496) -> q_gen_4502
<s, s>(q_gen_4502) -> q_gen_4528
<s, s>(q_gen_4528) -> q_gen_4528
<z, s>(q_gen_4519) -> q_gen_4528
}

Datatype: <nattsil, nat>
Convolution form: right
}}}

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 78
() -> length([nil, z]) -> 76
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 76
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 83
(le([s(nn1), z])) -> BOT -> 81
(le([z, z])) -> BOT -> 76
(length([l, _fy]) /\ length([snoc(l, x), _gy])) -> le([_fy, _gy]) -> 99
(length([ll, _by])) -> length([snoc(ll, x), s(_by)]) -> 100
}
Sat witness: Found: ((length([ll, _by])) -> length([snoc(ll, x), s(_by)]), {
_by -> s(s(s(s(s(s(s(s(z))))))))  ;  ll -> snoc(snoc(snoc(snoc(snoc(nil, z), z), s(s(z))), s(s(z))), s(s(s(z))))  ;  x -> s(s(s(z)))
})

-------------------------------------------
Step 81, which took 1.120066 s (model generation: 1.089877,  model checking: 0.030189):

Model:
|_
{
le -> 
{{{
Q={q_gen_4468, q_gen_4469, q_gen_4486},
Q_f={q_gen_4468},
Delta=
{
<s>(q_gen_4469) -> q_gen_4469
<z>() -> q_gen_4469
<s, s>(q_gen_4468) -> q_gen_4468
<z, s>(q_gen_4469) -> q_gen_4468
<s, s>(q_gen_4486) -> q_gen_4486
<s, z>(q_gen_4469) -> q_gen_4486
<z, z>() -> q_gen_4486
}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_4467, q_gen_4471, q_gen_4472, q_gen_4478, q_gen_4481, q_gen_4483, q_gen_4484, q_gen_4485, q_gen_4489, q_gen_4490, q_gen_4496, q_gen_4502, q_gen_4505, q_gen_4508, q_gen_4519, q_gen_4528},
Q_f={q_gen_4467},
Delta=
{
<nil>() -> q_gen_4472
<snoc>(q_gen_4508, q_gen_4478) -> q_gen_4472
<z>() -> q_gen_4478
<s>(q_gen_4478) -> q_gen_4481
<snoc>(q_gen_4472, q_gen_4478) -> q_gen_4484
<snoc>(q_gen_4472, q_gen_4519) -> q_gen_4484
<snoc>(q_gen_4505, q_gen_4496) -> q_gen_4484
<snoc>(q_gen_4484, q_gen_4478) -> q_gen_4490
<snoc>(q_gen_4484, q_gen_4519) -> q_gen_4490
<snoc>(q_gen_4490, q_gen_4519) -> q_gen_4490
<s>(q_gen_4481) -> q_gen_4496
<snoc>(q_gen_4490, q_gen_4478) -> q_gen_4505
<snoc>(q_gen_4490, q_gen_4481) -> q_gen_4505
<snoc>(q_gen_4490, q_gen_4496) -> q_gen_4505
<snoc>(q_gen_4505, q_gen_4478) -> q_gen_4508
<snoc>(q_gen_4505, q_gen_4519) -> q_gen_4508
<s>(q_gen_4496) -> q_gen_4519
<s>(q_gen_4519) -> q_gen_4519
<nil, z>() -> q_gen_4467
<snoc, s>(q_gen_4472, q_gen_4471) -> q_gen_4467
<snoc, s>(q_gen_4484, q_gen_4483) -> q_gen_4467
<snoc, s>(q_gen_4490, q_gen_4489) -> q_gen_4467
<snoc, s>(q_gen_4490, q_gen_4502) -> q_gen_4467
<snoc, s>(q_gen_4505, q_gen_4502) -> q_gen_4467
<snoc, s>(q_gen_4505, q_gen_4528) -> q_gen_4467
<snoc, s>(q_gen_4508, q_gen_4489) -> q_gen_4467
<snoc, s>(q_gen_4508, q_gen_4528) -> q_gen_4467
<s, z>(q_gen_4478) -> q_gen_4471
<s, z>(q_gen_4481) -> q_gen_4471
<s, z>(q_gen_4496) -> q_gen_4471
<s, z>(q_gen_4519) -> q_gen_4471
<z, z>() -> q_gen_4471
<s, s>(q_gen_4471) -> q_gen_4483
<z, s>(q_gen_4478) -> q_gen_4483
<snoc, s>(q_gen_4472, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4472, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4472, q_gen_4502) -> q_gen_4485
<snoc, s>(q_gen_4472, q_gen_4528) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4502) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4528) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4528) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4508, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4508, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4508, q_gen_4502) -> q_gen_4485
<s, s>(q_gen_4483) -> q_gen_4489
<s, s>(q_gen_4528) -> q_gen_4489
<z, s>(q_gen_4481) -> q_gen_4489
<z, s>(q_gen_4496) -> q_gen_4502
<s, s>(q_gen_4489) -> q_gen_4528
<s, s>(q_gen_4502) -> q_gen_4528
<z, s>(q_gen_4519) -> q_gen_4528
}

Datatype: <nattsil, nat>
Convolution form: right
}}}

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 79
() -> length([nil, z]) -> 77
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 77
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 84
(le([s(nn1), z])) -> BOT -> 82
(le([z, z])) -> BOT -> 77
(length([l, _fy]) /\ length([snoc(l, x), _gy])) -> le([_fy, _gy]) -> 102
(length([ll, _by])) -> length([snoc(ll, x), s(_by)]) -> 100
}
Sat witness: Found: ((length([l, _fy]) /\ length([snoc(l, x), _gy])) -> le([_fy, _gy]), {
_fy -> s(s(s(s(s(z)))))  ;  _gy -> s(z)  ;  l -> snoc(snoc(snoc(snoc(snoc(nil, z), s(s(s(z)))), z), s(s(s(z)))), z)  ;  x -> z
})

-------------------------------------------
Step 82, which took 1.526610 s (model generation: 1.526017,  model checking: 0.000593):

Model:
|_
{
le -> 
{{{
Q={q_gen_4468, q_gen_4469, q_gen_4486, q_gen_4487, q_gen_4492, q_gen_4509},
Q_f={q_gen_4468},
Delta=
{
<s>(q_gen_4469) -> q_gen_4469
<z>() -> q_gen_4469
<s, s>(q_gen_4468) -> q_gen_4468
<s, s>(q_gen_4509) -> q_gen_4468
<z, s>(q_gen_4469) -> q_gen_4468
<s, s>(q_gen_4487) -> q_gen_4486
<s, z>(q_gen_4469) -> q_gen_4487
<z, z>() -> q_gen_4487
<s, s>(q_gen_4486) -> q_gen_4492
<s, s>(q_gen_4492) -> q_gen_4509
}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_4467, q_gen_4471, q_gen_4472, q_gen_4478, q_gen_4481, q_gen_4483, q_gen_4484, q_gen_4485, q_gen_4489, q_gen_4490, q_gen_4496, q_gen_4502, q_gen_4505},
Q_f={q_gen_4467},
Delta=
{
<nil>() -> q_gen_4472
<z>() -> q_gen_4478
<s>(q_gen_4478) -> q_gen_4481
<snoc>(q_gen_4472, q_gen_4478) -> q_gen_4484
<snoc>(q_gen_4472, q_gen_4496) -> q_gen_4484
<snoc>(q_gen_4484, q_gen_4496) -> q_gen_4484
<snoc>(q_gen_4484, q_gen_4478) -> q_gen_4490
<s>(q_gen_4481) -> q_gen_4496
<s>(q_gen_4496) -> q_gen_4496
<snoc>(q_gen_4490, q_gen_4478) -> q_gen_4505
<snoc>(q_gen_4490, q_gen_4481) -> q_gen_4505
<snoc>(q_gen_4490, q_gen_4496) -> q_gen_4505
<snoc>(q_gen_4505, q_gen_4478) -> q_gen_4505
<snoc>(q_gen_4505, q_gen_4496) -> q_gen_4505
<nil, z>() -> q_gen_4467
<snoc, s>(q_gen_4472, q_gen_4471) -> q_gen_4467
<snoc, s>(q_gen_4484, q_gen_4483) -> q_gen_4467
<snoc, s>(q_gen_4490, q_gen_4489) -> q_gen_4467
<snoc, s>(q_gen_4505, q_gen_4502) -> q_gen_4467
<s, z>(q_gen_4478) -> q_gen_4471
<s, z>(q_gen_4481) -> q_gen_4471
<s, z>(q_gen_4496) -> q_gen_4471
<z, z>() -> q_gen_4471
<s, s>(q_gen_4471) -> q_gen_4483
<z, s>(q_gen_4478) -> q_gen_4483
<snoc, s>(q_gen_4472, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4472, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4472, q_gen_4502) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4502) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4502) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4489) -> q_gen_4485
<s, s>(q_gen_4483) -> q_gen_4489
<z, s>(q_gen_4481) -> q_gen_4489
<s, s>(q_gen_4489) -> q_gen_4502
<s, s>(q_gen_4502) -> q_gen_4502
<z, s>(q_gen_4496) -> q_gen_4502
}

Datatype: <nattsil, nat>
Convolution form: right
}}}

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 80
() -> length([nil, z]) -> 78
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 78
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 87
(le([s(nn1), z])) -> BOT -> 83
(le([z, z])) -> BOT -> 78
(length([l, _fy]) /\ length([snoc(l, x), _gy])) -> le([_fy, _gy]) -> 102
(length([ll, _by])) -> length([snoc(ll, x), s(_by)]) -> 100
}
Sat witness: Found: ((le([s(nn1), s(nn2)])) -> le([nn1, nn2]), {
nn1 -> s(s(s(z)))  ;  nn2 -> s(s(s(z)))
})

-------------------------------------------
Step 83, which took 1.294808 s (model generation: 1.219355,  model checking: 0.075453):

Model:
|_
{
le -> 
{{{
Q={q_gen_4468, q_gen_4469, q_gen_4486},
Q_f={q_gen_4468},
Delta=
{
<s>(q_gen_4469) -> q_gen_4469
<z>() -> q_gen_4469
<s, s>(q_gen_4468) -> q_gen_4468
<z, s>(q_gen_4469) -> q_gen_4468
<s, s>(q_gen_4486) -> q_gen_4486
<s, z>(q_gen_4469) -> q_gen_4486
<z, z>() -> q_gen_4486
}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_4467, q_gen_4471, q_gen_4472, q_gen_4478, q_gen_4481, q_gen_4483, q_gen_4484, q_gen_4485, q_gen_4489, q_gen_4490, q_gen_4496, q_gen_4502, q_gen_4505, q_gen_4508, q_gen_4519, q_gen_4528},
Q_f={q_gen_4467},
Delta=
{
<nil>() -> q_gen_4472
<snoc>(q_gen_4508, q_gen_4496) -> q_gen_4472
<z>() -> q_gen_4478
<s>(q_gen_4478) -> q_gen_4481
<snoc>(q_gen_4472, q_gen_4478) -> q_gen_4484
<snoc>(q_gen_4472, q_gen_4519) -> q_gen_4484
<snoc>(q_gen_4484, q_gen_4478) -> q_gen_4490
<snoc>(q_gen_4484, q_gen_4519) -> q_gen_4490
<snoc>(q_gen_4490, q_gen_4519) -> q_gen_4490
<snoc>(q_gen_4508, q_gen_4519) -> q_gen_4490
<s>(q_gen_4481) -> q_gen_4496
<snoc>(q_gen_4490, q_gen_4478) -> q_gen_4505
<snoc>(q_gen_4490, q_gen_4481) -> q_gen_4505
<snoc>(q_gen_4505, q_gen_4519) -> q_gen_4505
<snoc>(q_gen_4508, q_gen_4478) -> q_gen_4505
<snoc>(q_gen_4490, q_gen_4496) -> q_gen_4508
<snoc>(q_gen_4505, q_gen_4478) -> q_gen_4508
<s>(q_gen_4496) -> q_gen_4519
<s>(q_gen_4519) -> q_gen_4519
<nil, z>() -> q_gen_4467
<snoc, s>(q_gen_4472, q_gen_4471) -> q_gen_4467
<snoc, s>(q_gen_4484, q_gen_4483) -> q_gen_4467
<snoc, s>(q_gen_4490, q_gen_4489) -> q_gen_4467
<snoc, s>(q_gen_4490, q_gen_4502) -> q_gen_4467
<snoc, s>(q_gen_4505, q_gen_4502) -> q_gen_4467
<snoc, s>(q_gen_4505, q_gen_4528) -> q_gen_4467
<snoc, s>(q_gen_4508, q_gen_4489) -> q_gen_4467
<snoc, s>(q_gen_4508, q_gen_4528) -> q_gen_4467
<s, z>(q_gen_4478) -> q_gen_4471
<s, z>(q_gen_4481) -> q_gen_4471
<s, z>(q_gen_4496) -> q_gen_4471
<s, z>(q_gen_4519) -> q_gen_4471
<z, z>() -> q_gen_4471
<s, s>(q_gen_4471) -> q_gen_4483
<z, s>(q_gen_4478) -> q_gen_4483
<snoc, s>(q_gen_4472, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4472, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4472, q_gen_4502) -> q_gen_4485
<snoc, s>(q_gen_4472, q_gen_4528) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4502) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4528) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4528) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4508, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4508, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4508, q_gen_4502) -> q_gen_4485
<s, s>(q_gen_4483) -> q_gen_4489
<z, s>(q_gen_4481) -> q_gen_4489
<z, s>(q_gen_4496) -> q_gen_4502
<s, s>(q_gen_4489) -> q_gen_4528
<s, s>(q_gen_4502) -> q_gen_4528
<s, s>(q_gen_4528) -> q_gen_4528
<z, s>(q_gen_4519) -> q_gen_4528
}

Datatype: <nattsil, nat>
Convolution form: right
}}}

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 81
() -> length([nil, z]) -> 79
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 79
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 88
(le([s(nn1), z])) -> BOT -> 84
(le([z, z])) -> BOT -> 79
(length([l, _fy]) /\ length([snoc(l, x), _gy])) -> le([_fy, _gy]) -> 102
(length([ll, _by])) -> length([snoc(ll, x), s(_by)]) -> 103
}
Sat witness: Found: ((length([ll, _by])) -> length([snoc(ll, x), s(_by)]), {
_by -> s(s(s(z)))  ;  ll -> snoc(snoc(snoc(snoc(snoc(snoc(nil, s(s(s(z)))), z), s(s(z))), z), z), s(s(z)))  ;  x -> s(s(z))
})

-------------------------------------------
Step 84, which took 1.313411 s (model generation: 1.268741,  model checking: 0.044670):

Model:
|_
{
le -> 
{{{
Q={q_gen_4468, q_gen_4469, q_gen_4486},
Q_f={q_gen_4468},
Delta=
{
<s>(q_gen_4469) -> q_gen_4469
<z>() -> q_gen_4469
<s, s>(q_gen_4468) -> q_gen_4468
<z, s>(q_gen_4469) -> q_gen_4468
<s, s>(q_gen_4486) -> q_gen_4486
<s, z>(q_gen_4469) -> q_gen_4486
<z, z>() -> q_gen_4486
}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_4467, q_gen_4471, q_gen_4472, q_gen_4478, q_gen_4481, q_gen_4483, q_gen_4484, q_gen_4485, q_gen_4489, q_gen_4490, q_gen_4496, q_gen_4502, q_gen_4505, q_gen_4508, q_gen_4519, q_gen_4528},
Q_f={q_gen_4467},
Delta=
{
<nil>() -> q_gen_4472
<z>() -> q_gen_4478
<s>(q_gen_4478) -> q_gen_4481
<snoc>(q_gen_4472, q_gen_4478) -> q_gen_4484
<snoc>(q_gen_4472, q_gen_4519) -> q_gen_4484
<snoc>(q_gen_4484, q_gen_4478) -> q_gen_4490
<snoc>(q_gen_4484, q_gen_4519) -> q_gen_4490
<snoc>(q_gen_4490, q_gen_4481) -> q_gen_4490
<snoc>(q_gen_4490, q_gen_4519) -> q_gen_4490
<s>(q_gen_4481) -> q_gen_4496
<snoc>(q_gen_4490, q_gen_4478) -> q_gen_4505
<snoc>(q_gen_4505, q_gen_4519) -> q_gen_4505
<snoc>(q_gen_4508, q_gen_4478) -> q_gen_4505
<snoc>(q_gen_4490, q_gen_4496) -> q_gen_4508
<snoc>(q_gen_4505, q_gen_4478) -> q_gen_4508
<snoc>(q_gen_4508, q_gen_4496) -> q_gen_4508
<snoc>(q_gen_4508, q_gen_4519) -> q_gen_4508
<s>(q_gen_4496) -> q_gen_4519
<s>(q_gen_4519) -> q_gen_4519
<nil, z>() -> q_gen_4467
<snoc, s>(q_gen_4472, q_gen_4471) -> q_gen_4467
<snoc, s>(q_gen_4484, q_gen_4483) -> q_gen_4467
<snoc, s>(q_gen_4490, q_gen_4489) -> q_gen_4467
<snoc, s>(q_gen_4490, q_gen_4502) -> q_gen_4467
<snoc, s>(q_gen_4505, q_gen_4502) -> q_gen_4467
<snoc, s>(q_gen_4505, q_gen_4528) -> q_gen_4467
<snoc, s>(q_gen_4508, q_gen_4489) -> q_gen_4467
<snoc, s>(q_gen_4508, q_gen_4528) -> q_gen_4467
<s, z>(q_gen_4478) -> q_gen_4471
<s, z>(q_gen_4481) -> q_gen_4471
<s, z>(q_gen_4496) -> q_gen_4471
<s, z>(q_gen_4519) -> q_gen_4471
<z, z>() -> q_gen_4471
<s, s>(q_gen_4471) -> q_gen_4483
<z, s>(q_gen_4478) -> q_gen_4483
<snoc, s>(q_gen_4472, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4472, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4472, q_gen_4502) -> q_gen_4485
<snoc, s>(q_gen_4472, q_gen_4528) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4502) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4528) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4528) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4508, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4508, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4508, q_gen_4502) -> q_gen_4485
<s, s>(q_gen_4483) -> q_gen_4489
<z, s>(q_gen_4481) -> q_gen_4489
<z, s>(q_gen_4496) -> q_gen_4502
<s, s>(q_gen_4489) -> q_gen_4528
<s, s>(q_gen_4502) -> q_gen_4528
<s, s>(q_gen_4528) -> q_gen_4528
<z, s>(q_gen_4519) -> q_gen_4528
}

Datatype: <nattsil, nat>
Convolution form: right
}}}

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 82
() -> length([nil, z]) -> 80
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 80
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 89
(le([s(nn1), z])) -> BOT -> 85
(le([z, z])) -> BOT -> 80
(length([l, _fy]) /\ length([snoc(l, x), _gy])) -> le([_fy, _gy]) -> 105
(length([ll, _by])) -> length([snoc(ll, x), s(_by)]) -> 103
}
Sat witness: Found: ((length([l, _fy]) /\ length([snoc(l, x), _gy])) -> le([_fy, _gy]), {
_fy -> s(s(s(z)))  ;  _gy -> s(s(s(z)))  ;  l -> snoc(snoc(snoc(snoc(nil, z), s(s(s(z)))), s(s(s(z)))), s(z))  ;  x -> s(s(z))
})

-------------------------------------------
Step 85, which took 1.430097 s (model generation: 1.393431,  model checking: 0.036666):

Model:
|_
{
le -> 
{{{
Q={q_gen_4468, q_gen_4469, q_gen_4486},
Q_f={q_gen_4468},
Delta=
{
<s>(q_gen_4469) -> q_gen_4469
<z>() -> q_gen_4469
<s, s>(q_gen_4468) -> q_gen_4468
<z, s>(q_gen_4469) -> q_gen_4468
<s, s>(q_gen_4486) -> q_gen_4486
<s, z>(q_gen_4469) -> q_gen_4486
<z, z>() -> q_gen_4486
}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_4467, q_gen_4471, q_gen_4472, q_gen_4478, q_gen_4481, q_gen_4483, q_gen_4484, q_gen_4485, q_gen_4489, q_gen_4490, q_gen_4496, q_gen_4502, q_gen_4505, q_gen_4508, q_gen_4519, q_gen_4528},
Q_f={q_gen_4467},
Delta=
{
<nil>() -> q_gen_4472
<snoc>(q_gen_4508, q_gen_4496) -> q_gen_4472
<z>() -> q_gen_4478
<s>(q_gen_4478) -> q_gen_4481
<snoc>(q_gen_4472, q_gen_4478) -> q_gen_4484
<snoc>(q_gen_4472, q_gen_4519) -> q_gen_4484
<snoc>(q_gen_4505, q_gen_4496) -> q_gen_4484
<snoc>(q_gen_4484, q_gen_4478) -> q_gen_4490
<s>(q_gen_4481) -> q_gen_4496
<snoc>(q_gen_4484, q_gen_4519) -> q_gen_4505
<snoc>(q_gen_4490, q_gen_4478) -> q_gen_4505
<snoc>(q_gen_4490, q_gen_4481) -> q_gen_4505
<snoc>(q_gen_4490, q_gen_4496) -> q_gen_4505
<snoc>(q_gen_4490, q_gen_4519) -> q_gen_4505
<snoc>(q_gen_4508, q_gen_4481) -> q_gen_4505
<snoc>(q_gen_4508, q_gen_4519) -> q_gen_4505
<snoc>(q_gen_4505, q_gen_4478) -> q_gen_4508
<snoc>(q_gen_4505, q_gen_4519) -> q_gen_4508
<snoc>(q_gen_4508, q_gen_4478) -> q_gen_4508
<s>(q_gen_4496) -> q_gen_4519
<s>(q_gen_4519) -> q_gen_4519
<nil, z>() -> q_gen_4467
<snoc, s>(q_gen_4472, q_gen_4471) -> q_gen_4467
<snoc, s>(q_gen_4484, q_gen_4483) -> q_gen_4467
<snoc, s>(q_gen_4490, q_gen_4489) -> q_gen_4467
<snoc, s>(q_gen_4505, q_gen_4502) -> q_gen_4467
<snoc, s>(q_gen_4508, q_gen_4528) -> q_gen_4467
<s, z>(q_gen_4478) -> q_gen_4471
<s, z>(q_gen_4481) -> q_gen_4471
<s, z>(q_gen_4496) -> q_gen_4471
<s, z>(q_gen_4519) -> q_gen_4471
<z, z>() -> q_gen_4471
<s, s>(q_gen_4471) -> q_gen_4483
<z, s>(q_gen_4478) -> q_gen_4483
<snoc, s>(q_gen_4472, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4472, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4472, q_gen_4502) -> q_gen_4485
<snoc, s>(q_gen_4472, q_gen_4528) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4502) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4528) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4502) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4528) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4528) -> q_gen_4485
<snoc, s>(q_gen_4508, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4508, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4508, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4508, q_gen_4502) -> q_gen_4485
<s, s>(q_gen_4483) -> q_gen_4489
<z, s>(q_gen_4481) -> q_gen_4489
<s, s>(q_gen_4489) -> q_gen_4502
<s, s>(q_gen_4528) -> q_gen_4502
<z, s>(q_gen_4496) -> q_gen_4502
<s, s>(q_gen_4502) -> q_gen_4528
<z, s>(q_gen_4519) -> q_gen_4528
}

Datatype: <nattsil, nat>
Convolution form: right
}}}

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 83
() -> length([nil, z]) -> 81
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 81
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 90
(le([s(nn1), z])) -> BOT -> 86
(le([z, z])) -> BOT -> 81
(length([l, _fy]) /\ length([snoc(l, x), _gy])) -> le([_fy, _gy]) -> 105
(length([ll, _by])) -> length([snoc(ll, x), s(_by)]) -> 106
}
Sat witness: Found: ((length([ll, _by])) -> length([snoc(ll, x), s(_by)]), {
_by -> s(s(s(s(s(s(s(z)))))))  ;  ll -> snoc(snoc(snoc(snoc(snoc(snoc(nil, z), z), z), z), z), s(s(z)))  ;  x -> z
})

-------------------------------------------
Step 86, which took 1.749611 s (model generation: 1.676110,  model checking: 0.073501):

Model:
|_
{
le -> 
{{{
Q={q_gen_4468, q_gen_4469, q_gen_4486},
Q_f={q_gen_4468},
Delta=
{
<s>(q_gen_4469) -> q_gen_4469
<z>() -> q_gen_4469
<s, s>(q_gen_4468) -> q_gen_4468
<z, s>(q_gen_4469) -> q_gen_4468
<s, s>(q_gen_4486) -> q_gen_4486
<s, z>(q_gen_4469) -> q_gen_4486
<z, z>() -> q_gen_4486
}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_4467, q_gen_4471, q_gen_4472, q_gen_4478, q_gen_4481, q_gen_4483, q_gen_4484, q_gen_4485, q_gen_4489, q_gen_4490, q_gen_4496, q_gen_4502, q_gen_4505, q_gen_4508, q_gen_4519, q_gen_4528},
Q_f={q_gen_4467},
Delta=
{
<nil>() -> q_gen_4472
<z>() -> q_gen_4478
<s>(q_gen_4478) -> q_gen_4481
<snoc>(q_gen_4472, q_gen_4478) -> q_gen_4484
<snoc>(q_gen_4472, q_gen_4519) -> q_gen_4484
<snoc>(q_gen_4505, q_gen_4519) -> q_gen_4484
<snoc>(q_gen_4484, q_gen_4478) -> q_gen_4490
<snoc>(q_gen_4490, q_gen_4481) -> q_gen_4490
<snoc>(q_gen_4490, q_gen_4519) -> q_gen_4490
<s>(q_gen_4481) -> q_gen_4496
<snoc>(q_gen_4484, q_gen_4481) -> q_gen_4505
<snoc>(q_gen_4484, q_gen_4519) -> q_gen_4505
<snoc>(q_gen_4490, q_gen_4478) -> q_gen_4505
<snoc>(q_gen_4508, q_gen_4478) -> q_gen_4505
<snoc>(q_gen_4490, q_gen_4496) -> q_gen_4508
<snoc>(q_gen_4505, q_gen_4478) -> q_gen_4508
<snoc>(q_gen_4505, q_gen_4496) -> q_gen_4508
<snoc>(q_gen_4508, q_gen_4496) -> q_gen_4508
<snoc>(q_gen_4508, q_gen_4519) -> q_gen_4508
<s>(q_gen_4496) -> q_gen_4519
<s>(q_gen_4519) -> q_gen_4519
<nil, z>() -> q_gen_4467
<snoc, s>(q_gen_4472, q_gen_4471) -> q_gen_4467
<snoc, s>(q_gen_4484, q_gen_4483) -> q_gen_4467
<snoc, s>(q_gen_4490, q_gen_4489) -> q_gen_4467
<snoc, s>(q_gen_4490, q_gen_4502) -> q_gen_4467
<snoc, s>(q_gen_4505, q_gen_4502) -> q_gen_4467
<snoc, s>(q_gen_4505, q_gen_4528) -> q_gen_4467
<snoc, s>(q_gen_4508, q_gen_4489) -> q_gen_4467
<snoc, s>(q_gen_4508, q_gen_4528) -> q_gen_4467
<s, z>(q_gen_4478) -> q_gen_4471
<s, z>(q_gen_4481) -> q_gen_4471
<s, z>(q_gen_4496) -> q_gen_4471
<s, z>(q_gen_4519) -> q_gen_4471
<z, z>() -> q_gen_4471
<s, s>(q_gen_4471) -> q_gen_4483
<z, s>(q_gen_4478) -> q_gen_4483
<snoc, s>(q_gen_4472, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4472, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4472, q_gen_4502) -> q_gen_4485
<snoc, s>(q_gen_4472, q_gen_4528) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4502) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4528) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4528) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4508, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4508, q_gen_4502) -> q_gen_4485
<s, s>(q_gen_4483) -> q_gen_4489
<z, s>(q_gen_4481) -> q_gen_4489
<z, s>(q_gen_4496) -> q_gen_4502
<s, s>(q_gen_4489) -> q_gen_4528
<s, s>(q_gen_4502) -> q_gen_4528
<s, s>(q_gen_4528) -> q_gen_4528
<z, s>(q_gen_4519) -> q_gen_4528
}

Datatype: <nattsil, nat>
Convolution form: right
}}}

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 84
() -> length([nil, z]) -> 82
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 82
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 91
(le([s(nn1), z])) -> BOT -> 87
(le([z, z])) -> BOT -> 82
(length([l, _fy]) /\ length([snoc(l, x), _gy])) -> le([_fy, _gy]) -> 108
(length([ll, _by])) -> length([snoc(ll, x), s(_by)]) -> 106
}
Sat witness: Found: ((length([l, _fy]) /\ length([snoc(l, x), _gy])) -> le([_fy, _gy]), {
_fy -> s(s(s(z)))  ;  _gy -> s(s(s(z)))  ;  l -> snoc(snoc(snoc(nil, z), z), s(s(s(s(s(z))))))  ;  x -> z
})

-------------------------------------------
Step 87, which took 1.467521 s (model generation: 1.433614,  model checking: 0.033907):

Model:
|_
{
le -> 
{{{
Q={q_gen_4468, q_gen_4469, q_gen_4486},
Q_f={q_gen_4468},
Delta=
{
<s>(q_gen_4469) -> q_gen_4469
<z>() -> q_gen_4469
<s, s>(q_gen_4468) -> q_gen_4468
<z, s>(q_gen_4469) -> q_gen_4468
<s, s>(q_gen_4486) -> q_gen_4486
<s, z>(q_gen_4469) -> q_gen_4486
<z, z>() -> q_gen_4486
}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_4467, q_gen_4471, q_gen_4472, q_gen_4478, q_gen_4481, q_gen_4483, q_gen_4484, q_gen_4485, q_gen_4489, q_gen_4490, q_gen_4496, q_gen_4502, q_gen_4505, q_gen_4508, q_gen_4519, q_gen_4528},
Q_f={q_gen_4467},
Delta=
{
<nil>() -> q_gen_4472
<z>() -> q_gen_4478
<s>(q_gen_4478) -> q_gen_4481
<snoc>(q_gen_4472, q_gen_4478) -> q_gen_4484
<snoc>(q_gen_4472, q_gen_4519) -> q_gen_4484
<snoc>(q_gen_4484, q_gen_4478) -> q_gen_4490
<snoc>(q_gen_4508, q_gen_4519) -> q_gen_4490
<s>(q_gen_4481) -> q_gen_4496
<snoc>(q_gen_4490, q_gen_4478) -> q_gen_4505
<snoc>(q_gen_4490, q_gen_4481) -> q_gen_4505
<snoc>(q_gen_4490, q_gen_4496) -> q_gen_4505
<snoc>(q_gen_4490, q_gen_4519) -> q_gen_4505
<snoc>(q_gen_4505, q_gen_4496) -> q_gen_4505
<snoc>(q_gen_4508, q_gen_4478) -> q_gen_4505
<snoc>(q_gen_4484, q_gen_4519) -> q_gen_4508
<snoc>(q_gen_4505, q_gen_4478) -> q_gen_4508
<snoc>(q_gen_4505, q_gen_4519) -> q_gen_4508
<s>(q_gen_4496) -> q_gen_4519
<s>(q_gen_4519) -> q_gen_4519
<nil, z>() -> q_gen_4467
<snoc, s>(q_gen_4472, q_gen_4471) -> q_gen_4467
<snoc, s>(q_gen_4484, q_gen_4483) -> q_gen_4467
<snoc, s>(q_gen_4490, q_gen_4489) -> q_gen_4467
<snoc, s>(q_gen_4505, q_gen_4502) -> q_gen_4467
<snoc, s>(q_gen_4508, q_gen_4471) -> q_gen_4467
<snoc, s>(q_gen_4508, q_gen_4528) -> q_gen_4467
<s, z>(q_gen_4478) -> q_gen_4471
<s, z>(q_gen_4481) -> q_gen_4471
<s, z>(q_gen_4496) -> q_gen_4471
<s, z>(q_gen_4519) -> q_gen_4471
<z, z>() -> q_gen_4471
<s, s>(q_gen_4471) -> q_gen_4483
<z, s>(q_gen_4478) -> q_gen_4483
<snoc, s>(q_gen_4472, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4472, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4472, q_gen_4502) -> q_gen_4485
<snoc, s>(q_gen_4472, q_gen_4528) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4502) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4528) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4502) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4528) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4528) -> q_gen_4485
<snoc, s>(q_gen_4508, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4508, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4508, q_gen_4502) -> q_gen_4485
<s, s>(q_gen_4483) -> q_gen_4489
<z, s>(q_gen_4481) -> q_gen_4489
<s, s>(q_gen_4489) -> q_gen_4502
<z, s>(q_gen_4496) -> q_gen_4502
<s, s>(q_gen_4502) -> q_gen_4528
<s, s>(q_gen_4528) -> q_gen_4528
<z, s>(q_gen_4519) -> q_gen_4528
}

Datatype: <nattsil, nat>
Convolution form: right
}}}

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 85
() -> length([nil, z]) -> 83
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 83
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 92
(le([s(nn1), z])) -> BOT -> 88
(le([z, z])) -> BOT -> 83
(length([l, _fy]) /\ length([snoc(l, x), _gy])) -> le([_fy, _gy]) -> 108
(length([ll, _by])) -> length([snoc(ll, x), s(_by)]) -> 109
}
Sat witness: Found: ((length([ll, _by])) -> length([snoc(ll, x), s(_by)]), {
_by -> s(s(z))  ;  ll -> snoc(snoc(nil, s(s(s(z)))), s(s(s(s(z)))))  ;  x -> s(z)
})

-------------------------------------------
Step 88, which took 1.895313 s (model generation: 1.885180,  model checking: 0.010133):

Model:
|_
{
le -> 
{{{
Q={q_gen_4468, q_gen_4469, q_gen_4486},
Q_f={q_gen_4468},
Delta=
{
<s>(q_gen_4469) -> q_gen_4469
<z>() -> q_gen_4469
<s, s>(q_gen_4468) -> q_gen_4468
<z, s>(q_gen_4469) -> q_gen_4468
<s, s>(q_gen_4486) -> q_gen_4486
<s, z>(q_gen_4469) -> q_gen_4486
<z, z>() -> q_gen_4486
}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_4467, q_gen_4471, q_gen_4472, q_gen_4478, q_gen_4481, q_gen_4483, q_gen_4484, q_gen_4485, q_gen_4489, q_gen_4490, q_gen_4496, q_gen_4502, q_gen_4505, q_gen_4508, q_gen_4519, q_gen_4528},
Q_f={q_gen_4467},
Delta=
{
<nil>() -> q_gen_4472
<snoc>(q_gen_4508, q_gen_4478) -> q_gen_4472
<z>() -> q_gen_4478
<s>(q_gen_4478) -> q_gen_4481
<snoc>(q_gen_4472, q_gen_4478) -> q_gen_4484
<snoc>(q_gen_4472, q_gen_4519) -> q_gen_4484
<snoc>(q_gen_4484, q_gen_4478) -> q_gen_4490
<snoc>(q_gen_4505, q_gen_4481) -> q_gen_4490
<s>(q_gen_4481) -> q_gen_4496
<snoc>(q_gen_4472, q_gen_4496) -> q_gen_4505
<snoc>(q_gen_4490, q_gen_4478) -> q_gen_4505
<snoc>(q_gen_4490, q_gen_4481) -> q_gen_4505
<snoc>(q_gen_4490, q_gen_4496) -> q_gen_4505
<snoc>(q_gen_4490, q_gen_4519) -> q_gen_4505
<snoc>(q_gen_4508, q_gen_4519) -> q_gen_4505
<snoc>(q_gen_4484, q_gen_4519) -> q_gen_4508
<snoc>(q_gen_4505, q_gen_4478) -> q_gen_4508
<snoc>(q_gen_4505, q_gen_4496) -> q_gen_4508
<snoc>(q_gen_4505, q_gen_4519) -> q_gen_4508
<s>(q_gen_4496) -> q_gen_4519
<s>(q_gen_4519) -> q_gen_4519
<nil, z>() -> q_gen_4467
<snoc, s>(q_gen_4472, q_gen_4471) -> q_gen_4467
<snoc, s>(q_gen_4484, q_gen_4483) -> q_gen_4467
<snoc, s>(q_gen_4490, q_gen_4489) -> q_gen_4467
<snoc, s>(q_gen_4505, q_gen_4502) -> q_gen_4467
<snoc, s>(q_gen_4508, q_gen_4489) -> q_gen_4467
<snoc, s>(q_gen_4508, q_gen_4528) -> q_gen_4467
<s, z>(q_gen_4478) -> q_gen_4471
<s, z>(q_gen_4481) -> q_gen_4471
<s, z>(q_gen_4496) -> q_gen_4471
<s, z>(q_gen_4519) -> q_gen_4471
<z, z>() -> q_gen_4471
<s, s>(q_gen_4471) -> q_gen_4483
<z, s>(q_gen_4478) -> q_gen_4483
<snoc, s>(q_gen_4472, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4472, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4472, q_gen_4502) -> q_gen_4485
<snoc, s>(q_gen_4472, q_gen_4528) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4502) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4528) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4502) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4528) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4528) -> q_gen_4485
<snoc, s>(q_gen_4508, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4508, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4508, q_gen_4502) -> q_gen_4485
<s, s>(q_gen_4483) -> q_gen_4489
<z, s>(q_gen_4481) -> q_gen_4489
<s, s>(q_gen_4489) -> q_gen_4502
<s, s>(q_gen_4528) -> q_gen_4502
<z, s>(q_gen_4496) -> q_gen_4502
<s, s>(q_gen_4502) -> q_gen_4528
<z, s>(q_gen_4519) -> q_gen_4528
}

Datatype: <nattsil, nat>
Convolution form: right
}}}

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 86
() -> length([nil, z]) -> 84
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 84
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 93
(le([s(nn1), z])) -> BOT -> 89
(le([z, z])) -> BOT -> 84
(length([l, _fy]) /\ length([snoc(l, x), _gy])) -> le([_fy, _gy]) -> 111
(length([ll, _by])) -> length([snoc(ll, x), s(_by)]) -> 109
}
Sat witness: Found: ((length([l, _fy]) /\ length([snoc(l, x), _gy])) -> le([_fy, _gy]), {
_fy -> s(s(s(z)))  ;  _gy -> s(z)  ;  l -> snoc(snoc(snoc(nil, s(s(z))), s(s(z))), z)  ;  x -> z
})

-------------------------------------------
Step 89, which took 1.686564 s (model generation: 1.660153,  model checking: 0.026411):

Model:
|_
{
le -> 
{{{
Q={q_gen_4468, q_gen_4469, q_gen_4486},
Q_f={q_gen_4468},
Delta=
{
<s>(q_gen_4469) -> q_gen_4469
<z>() -> q_gen_4469
<s, s>(q_gen_4468) -> q_gen_4468
<z, s>(q_gen_4469) -> q_gen_4468
<s, s>(q_gen_4486) -> q_gen_4486
<s, z>(q_gen_4469) -> q_gen_4486
<z, z>() -> q_gen_4486
}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_4467, q_gen_4471, q_gen_4472, q_gen_4478, q_gen_4481, q_gen_4483, q_gen_4484, q_gen_4485, q_gen_4489, q_gen_4490, q_gen_4496, q_gen_4502, q_gen_4505, q_gen_4508, q_gen_4519, q_gen_4528},
Q_f={q_gen_4467},
Delta=
{
<nil>() -> q_gen_4472
<z>() -> q_gen_4478
<s>(q_gen_4478) -> q_gen_4481
<snoc>(q_gen_4472, q_gen_4478) -> q_gen_4484
<snoc>(q_gen_4472, q_gen_4519) -> q_gen_4484
<snoc>(q_gen_4505, q_gen_4481) -> q_gen_4484
<snoc>(q_gen_4484, q_gen_4478) -> q_gen_4490
<snoc>(q_gen_4484, q_gen_4519) -> q_gen_4490
<snoc>(q_gen_4505, q_gen_4496) -> q_gen_4490
<s>(q_gen_4481) -> q_gen_4496
<snoc>(q_gen_4472, q_gen_4496) -> q_gen_4505
<snoc>(q_gen_4490, q_gen_4478) -> q_gen_4505
<snoc>(q_gen_4490, q_gen_4481) -> q_gen_4505
<snoc>(q_gen_4490, q_gen_4496) -> q_gen_4505
<snoc>(q_gen_4490, q_gen_4519) -> q_gen_4505
<snoc>(q_gen_4508, q_gen_4478) -> q_gen_4505
<snoc>(q_gen_4505, q_gen_4478) -> q_gen_4508
<snoc>(q_gen_4505, q_gen_4519) -> q_gen_4508
<s>(q_gen_4496) -> q_gen_4519
<s>(q_gen_4519) -> q_gen_4519
<nil, z>() -> q_gen_4467
<snoc, s>(q_gen_4472, q_gen_4471) -> q_gen_4467
<snoc, s>(q_gen_4484, q_gen_4483) -> q_gen_4467
<snoc, s>(q_gen_4490, q_gen_4489) -> q_gen_4467
<snoc, s>(q_gen_4505, q_gen_4502) -> q_gen_4467
<snoc, s>(q_gen_4508, q_gen_4489) -> q_gen_4467
<snoc, s>(q_gen_4508, q_gen_4528) -> q_gen_4467
<s, z>(q_gen_4478) -> q_gen_4471
<s, z>(q_gen_4481) -> q_gen_4471
<s, z>(q_gen_4496) -> q_gen_4471
<s, z>(q_gen_4519) -> q_gen_4471
<z, z>() -> q_gen_4471
<s, s>(q_gen_4471) -> q_gen_4483
<s, s>(q_gen_4528) -> q_gen_4483
<z, s>(q_gen_4478) -> q_gen_4483
<snoc, s>(q_gen_4472, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4472, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4472, q_gen_4502) -> q_gen_4485
<snoc, s>(q_gen_4472, q_gen_4528) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4502) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4528) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4502) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4528) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4528) -> q_gen_4485
<snoc, s>(q_gen_4508, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4508, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4508, q_gen_4502) -> q_gen_4485
<s, s>(q_gen_4483) -> q_gen_4489
<z, s>(q_gen_4481) -> q_gen_4489
<s, s>(q_gen_4489) -> q_gen_4502
<z, s>(q_gen_4496) -> q_gen_4502
<s, s>(q_gen_4502) -> q_gen_4528
<z, s>(q_gen_4519) -> q_gen_4528
}

Datatype: <nattsil, nat>
Convolution form: right
}}}

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 87
() -> length([nil, z]) -> 85
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 85
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 94
(le([s(nn1), z])) -> BOT -> 90
(le([z, z])) -> BOT -> 85
(length([l, _fy]) /\ length([snoc(l, x), _gy])) -> le([_fy, _gy]) -> 111
(length([ll, _by])) -> length([snoc(ll, x), s(_by)]) -> 112
}
Sat witness: Found: ((length([ll, _by])) -> length([snoc(ll, x), s(_by)]), {
_by -> s(s(s(s(s(s(z))))))  ;  ll -> snoc(snoc(snoc(nil, s(s(z))), z), z)  ;  x -> s(z)
})

-------------------------------------------
Step 90, which took 2.815033 s (model generation: 2.806577,  model checking: 0.008456):

Model:
|_
{
le -> 
{{{
Q={q_gen_4468, q_gen_4469, q_gen_4486},
Q_f={q_gen_4468},
Delta=
{
<s>(q_gen_4469) -> q_gen_4469
<z>() -> q_gen_4469
<s, s>(q_gen_4468) -> q_gen_4468
<z, s>(q_gen_4469) -> q_gen_4468
<s, s>(q_gen_4486) -> q_gen_4486
<s, z>(q_gen_4469) -> q_gen_4486
<z, z>() -> q_gen_4486
}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_4467, q_gen_4471, q_gen_4472, q_gen_4478, q_gen_4481, q_gen_4483, q_gen_4484, q_gen_4485, q_gen_4489, q_gen_4490, q_gen_4496, q_gen_4502, q_gen_4505, q_gen_4508, q_gen_4519, q_gen_4528},
Q_f={q_gen_4467},
Delta=
{
<nil>() -> q_gen_4472
<snoc>(q_gen_4508, q_gen_4478) -> q_gen_4472
<z>() -> q_gen_4478
<s>(q_gen_4478) -> q_gen_4481
<snoc>(q_gen_4472, q_gen_4478) -> q_gen_4484
<snoc>(q_gen_4472, q_gen_4519) -> q_gen_4484
<snoc>(q_gen_4484, q_gen_4481) -> q_gen_4484
<snoc>(q_gen_4508, q_gen_4519) -> q_gen_4484
<snoc>(q_gen_4472, q_gen_4496) -> q_gen_4490
<snoc>(q_gen_4484, q_gen_4478) -> q_gen_4490
<snoc>(q_gen_4505, q_gen_4496) -> q_gen_4490
<s>(q_gen_4481) -> q_gen_4496
<snoc>(q_gen_4490, q_gen_4478) -> q_gen_4505
<snoc>(q_gen_4490, q_gen_4481) -> q_gen_4505
<snoc>(q_gen_4490, q_gen_4496) -> q_gen_4505
<snoc>(q_gen_4490, q_gen_4519) -> q_gen_4505
<snoc>(q_gen_4484, q_gen_4519) -> q_gen_4508
<snoc>(q_gen_4505, q_gen_4478) -> q_gen_4508
<snoc>(q_gen_4505, q_gen_4519) -> q_gen_4508
<s>(q_gen_4496) -> q_gen_4519
<s>(q_gen_4519) -> q_gen_4519
<nil, z>() -> q_gen_4467
<snoc, s>(q_gen_4472, q_gen_4471) -> q_gen_4467
<snoc, s>(q_gen_4484, q_gen_4483) -> q_gen_4467
<snoc, s>(q_gen_4490, q_gen_4489) -> q_gen_4467
<snoc, s>(q_gen_4505, q_gen_4502) -> q_gen_4467
<snoc, s>(q_gen_4508, q_gen_4489) -> q_gen_4467
<snoc, s>(q_gen_4508, q_gen_4528) -> q_gen_4467
<s, z>(q_gen_4478) -> q_gen_4471
<s, z>(q_gen_4481) -> q_gen_4471
<s, z>(q_gen_4496) -> q_gen_4471
<s, z>(q_gen_4519) -> q_gen_4471
<z, z>() -> q_gen_4471
<s, s>(q_gen_4471) -> q_gen_4483
<s, s>(q_gen_4528) -> q_gen_4483
<z, s>(q_gen_4478) -> q_gen_4483
<snoc, s>(q_gen_4472, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4472, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4472, q_gen_4502) -> q_gen_4485
<snoc, s>(q_gen_4472, q_gen_4528) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4502) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4528) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4502) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4528) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4528) -> q_gen_4485
<snoc, s>(q_gen_4508, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4508, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4508, q_gen_4502) -> q_gen_4485
<s, s>(q_gen_4483) -> q_gen_4489
<z, s>(q_gen_4481) -> q_gen_4489
<s, s>(q_gen_4489) -> q_gen_4502
<z, s>(q_gen_4496) -> q_gen_4502
<s, s>(q_gen_4502) -> q_gen_4528
<z, s>(q_gen_4519) -> q_gen_4528
}

Datatype: <nattsil, nat>
Convolution form: right
}}}

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 88
() -> length([nil, z]) -> 86
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 86
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 95
(le([s(nn1), z])) -> BOT -> 91
(le([z, z])) -> BOT -> 86
(length([l, _fy]) /\ length([snoc(l, x), _gy])) -> le([_fy, _gy]) -> 114
(length([ll, _by])) -> length([snoc(ll, x), s(_by)]) -> 112
}
Sat witness: Found: ((length([l, _fy]) /\ length([snoc(l, x), _gy])) -> le([_fy, _gy]), {
_fy -> s(s(s(z)))  ;  _gy -> s(z)  ;  l -> snoc(snoc(snoc(nil, s(s(s(s(z))))), s(s(s(z)))), z)  ;  x -> z
})

-------------------------------------------
Step 91, which took 2.120711 s (model generation: 2.063332,  model checking: 0.057379):

Model:
|_
{
le -> 
{{{
Q={q_gen_4468, q_gen_4469, q_gen_4486},
Q_f={q_gen_4468},
Delta=
{
<s>(q_gen_4469) -> q_gen_4469
<z>() -> q_gen_4469
<s, s>(q_gen_4468) -> q_gen_4468
<z, s>(q_gen_4469) -> q_gen_4468
<s, s>(q_gen_4486) -> q_gen_4486
<s, z>(q_gen_4469) -> q_gen_4486
<z, z>() -> q_gen_4486
}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_4467, q_gen_4471, q_gen_4472, q_gen_4478, q_gen_4481, q_gen_4483, q_gen_4484, q_gen_4485, q_gen_4489, q_gen_4490, q_gen_4496, q_gen_4502, q_gen_4505, q_gen_4508, q_gen_4519, q_gen_4528},
Q_f={q_gen_4467},
Delta=
{
<nil>() -> q_gen_4472
<z>() -> q_gen_4478
<s>(q_gen_4478) -> q_gen_4481
<snoc>(q_gen_4472, q_gen_4478) -> q_gen_4484
<snoc>(q_gen_4472, q_gen_4496) -> q_gen_4484
<snoc>(q_gen_4472, q_gen_4519) -> q_gen_4484
<snoc>(q_gen_4505, q_gen_4481) -> q_gen_4484
<snoc>(q_gen_4484, q_gen_4478) -> q_gen_4490
<snoc>(q_gen_4484, q_gen_4496) -> q_gen_4490
<snoc>(q_gen_4484, q_gen_4519) -> q_gen_4490
<snoc>(q_gen_4508, q_gen_4519) -> q_gen_4490
<s>(q_gen_4481) -> q_gen_4496
<snoc>(q_gen_4490, q_gen_4478) -> q_gen_4505
<snoc>(q_gen_4490, q_gen_4481) -> q_gen_4505
<snoc>(q_gen_4490, q_gen_4496) -> q_gen_4505
<snoc>(q_gen_4490, q_gen_4519) -> q_gen_4505
<snoc>(q_gen_4508, q_gen_4478) -> q_gen_4505
<snoc>(q_gen_4505, q_gen_4478) -> q_gen_4508
<snoc>(q_gen_4505, q_gen_4496) -> q_gen_4508
<snoc>(q_gen_4505, q_gen_4519) -> q_gen_4508
<s>(q_gen_4496) -> q_gen_4519
<s>(q_gen_4519) -> q_gen_4519
<nil, z>() -> q_gen_4467
<snoc, s>(q_gen_4472, q_gen_4471) -> q_gen_4467
<snoc, s>(q_gen_4484, q_gen_4483) -> q_gen_4467
<snoc, s>(q_gen_4490, q_gen_4489) -> q_gen_4467
<snoc, s>(q_gen_4505, q_gen_4502) -> q_gen_4467
<snoc, s>(q_gen_4508, q_gen_4471) -> q_gen_4467
<snoc, s>(q_gen_4508, q_gen_4489) -> q_gen_4467
<snoc, s>(q_gen_4508, q_gen_4528) -> q_gen_4467
<s, z>(q_gen_4478) -> q_gen_4471
<s, z>(q_gen_4481) -> q_gen_4471
<s, z>(q_gen_4496) -> q_gen_4471
<s, z>(q_gen_4519) -> q_gen_4471
<z, z>() -> q_gen_4471
<s, s>(q_gen_4471) -> q_gen_4483
<s, s>(q_gen_4528) -> q_gen_4483
<z, s>(q_gen_4478) -> q_gen_4483
<snoc, s>(q_gen_4472, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4472, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4472, q_gen_4502) -> q_gen_4485
<snoc, s>(q_gen_4472, q_gen_4528) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4502) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4528) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4502) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4528) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4528) -> q_gen_4485
<snoc, s>(q_gen_4508, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4508, q_gen_4502) -> q_gen_4485
<s, s>(q_gen_4483) -> q_gen_4489
<z, s>(q_gen_4481) -> q_gen_4489
<s, s>(q_gen_4489) -> q_gen_4502
<z, s>(q_gen_4496) -> q_gen_4502
<s, s>(q_gen_4502) -> q_gen_4528
<z, s>(q_gen_4519) -> q_gen_4528
}

Datatype: <nattsil, nat>
Convolution form: right
}}}

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 89
() -> length([nil, z]) -> 87
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 87
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 96
(le([s(nn1), z])) -> BOT -> 92
(le([z, z])) -> BOT -> 87
(length([l, _fy]) /\ length([snoc(l, x), _gy])) -> le([_fy, _gy]) -> 114
(length([ll, _by])) -> length([snoc(ll, x), s(_by)]) -> 115
}
Sat witness: Found: ((length([ll, _by])) -> length([snoc(ll, x), s(_by)]), {
_by -> s(s(s(s(s(s(z))))))  ;  ll -> snoc(snoc(nil, s(s(s(z)))), s(s(z)))  ;  x -> s(z)
})

-------------------------------------------
Step 92, which took 2.515332 s (model generation: 2.512289,  model checking: 0.003043):

Model:
|_
{
le -> 
{{{
Q={q_gen_4468, q_gen_4469, q_gen_4486},
Q_f={q_gen_4468},
Delta=
{
<s>(q_gen_4469) -> q_gen_4469
<z>() -> q_gen_4469
<s, s>(q_gen_4468) -> q_gen_4468
<z, s>(q_gen_4469) -> q_gen_4468
<s, s>(q_gen_4486) -> q_gen_4486
<s, z>(q_gen_4469) -> q_gen_4486
<z, z>() -> q_gen_4486
}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_4467, q_gen_4471, q_gen_4472, q_gen_4478, q_gen_4481, q_gen_4483, q_gen_4484, q_gen_4485, q_gen_4489, q_gen_4490, q_gen_4496, q_gen_4502, q_gen_4505, q_gen_4508, q_gen_4519, q_gen_4528},
Q_f={q_gen_4467},
Delta=
{
<nil>() -> q_gen_4472
<snoc>(q_gen_4472, q_gen_4496) -> q_gen_4472
<snoc>(q_gen_4484, q_gen_4481) -> q_gen_4472
<z>() -> q_gen_4478
<s>(q_gen_4478) -> q_gen_4481
<snoc>(q_gen_4472, q_gen_4478) -> q_gen_4484
<snoc>(q_gen_4472, q_gen_4519) -> q_gen_4484
<snoc>(q_gen_4508, q_gen_4519) -> q_gen_4484
<snoc>(q_gen_4484, q_gen_4478) -> q_gen_4490
<s>(q_gen_4481) -> q_gen_4496
<snoc>(q_gen_4490, q_gen_4478) -> q_gen_4505
<snoc>(q_gen_4490, q_gen_4481) -> q_gen_4505
<snoc>(q_gen_4490, q_gen_4496) -> q_gen_4505
<snoc>(q_gen_4490, q_gen_4519) -> q_gen_4505
<snoc>(q_gen_4505, q_gen_4496) -> q_gen_4505
<snoc>(q_gen_4508, q_gen_4478) -> q_gen_4505
<snoc>(q_gen_4484, q_gen_4496) -> q_gen_4508
<snoc>(q_gen_4484, q_gen_4519) -> q_gen_4508
<snoc>(q_gen_4505, q_gen_4478) -> q_gen_4508
<snoc>(q_gen_4505, q_gen_4519) -> q_gen_4508
<s>(q_gen_4496) -> q_gen_4519
<s>(q_gen_4519) -> q_gen_4519
<nil, z>() -> q_gen_4467
<snoc, s>(q_gen_4472, q_gen_4471) -> q_gen_4467
<snoc, s>(q_gen_4484, q_gen_4483) -> q_gen_4467
<snoc, s>(q_gen_4490, q_gen_4489) -> q_gen_4467
<snoc, s>(q_gen_4505, q_gen_4502) -> q_gen_4467
<snoc, s>(q_gen_4508, q_gen_4489) -> q_gen_4467
<snoc, s>(q_gen_4508, q_gen_4528) -> q_gen_4467
<s, z>(q_gen_4478) -> q_gen_4471
<s, z>(q_gen_4481) -> q_gen_4471
<s, z>(q_gen_4496) -> q_gen_4471
<s, z>(q_gen_4519) -> q_gen_4471
<z, z>() -> q_gen_4471
<s, s>(q_gen_4471) -> q_gen_4483
<z, s>(q_gen_4478) -> q_gen_4483
<snoc, s>(q_gen_4472, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4472, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4472, q_gen_4502) -> q_gen_4485
<snoc, s>(q_gen_4472, q_gen_4528) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4502) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4528) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4502) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4528) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4528) -> q_gen_4485
<snoc, s>(q_gen_4508, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4508, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4508, q_gen_4502) -> q_gen_4485
<s, s>(q_gen_4483) -> q_gen_4489
<z, s>(q_gen_4481) -> q_gen_4489
<s, s>(q_gen_4489) -> q_gen_4502
<z, s>(q_gen_4496) -> q_gen_4502
<s, s>(q_gen_4502) -> q_gen_4528
<s, s>(q_gen_4528) -> q_gen_4528
<z, s>(q_gen_4519) -> q_gen_4528
}

Datatype: <nattsil, nat>
Convolution form: right
}}}

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 90
() -> length([nil, z]) -> 88
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 88
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 97
(le([s(nn1), z])) -> BOT -> 93
(le([z, z])) -> BOT -> 88
(length([l, _fy]) /\ length([snoc(l, x), _gy])) -> le([_fy, _gy]) -> 117
(length([ll, _by])) -> length([snoc(ll, x), s(_by)]) -> 115
}
Sat witness: Found: ((length([l, _fy]) /\ length([snoc(l, x), _gy])) -> le([_fy, _gy]), {
_fy -> s(z)  ;  _gy -> s(z)  ;  l -> snoc(nil, s(s(z)))  ;  x -> z
})

-------------------------------------------
Step 93, which took 2.505059 s (model generation: 2.493896,  model checking: 0.011163):

Model:
|_
{
le -> 
{{{
Q={q_gen_4468, q_gen_4469, q_gen_4486},
Q_f={q_gen_4468},
Delta=
{
<s>(q_gen_4469) -> q_gen_4469
<z>() -> q_gen_4469
<s, s>(q_gen_4468) -> q_gen_4468
<z, s>(q_gen_4469) -> q_gen_4468
<s, s>(q_gen_4486) -> q_gen_4486
<s, z>(q_gen_4469) -> q_gen_4486
<z, z>() -> q_gen_4486
}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_4467, q_gen_4471, q_gen_4472, q_gen_4478, q_gen_4481, q_gen_4483, q_gen_4484, q_gen_4485, q_gen_4489, q_gen_4490, q_gen_4496, q_gen_4502, q_gen_4505, q_gen_4508, q_gen_4519, q_gen_4528},
Q_f={q_gen_4467},
Delta=
{
<nil>() -> q_gen_4472
<snoc>(q_gen_4505, q_gen_4481) -> q_gen_4472
<z>() -> q_gen_4478
<s>(q_gen_4478) -> q_gen_4481
<snoc>(q_gen_4472, q_gen_4478) -> q_gen_4484
<snoc>(q_gen_4472, q_gen_4519) -> q_gen_4484
<snoc>(q_gen_4484, q_gen_4496) -> q_gen_4484
<snoc>(q_gen_4484, q_gen_4478) -> q_gen_4490
<snoc>(q_gen_4484, q_gen_4519) -> q_gen_4490
<s>(q_gen_4481) -> q_gen_4496
<snoc>(q_gen_4472, q_gen_4496) -> q_gen_4505
<snoc>(q_gen_4490, q_gen_4478) -> q_gen_4505
<snoc>(q_gen_4490, q_gen_4481) -> q_gen_4505
<snoc>(q_gen_4490, q_gen_4496) -> q_gen_4505
<snoc>(q_gen_4490, q_gen_4519) -> q_gen_4505
<snoc>(q_gen_4505, q_gen_4496) -> q_gen_4505
<snoc>(q_gen_4505, q_gen_4478) -> q_gen_4508
<snoc>(q_gen_4505, q_gen_4519) -> q_gen_4508
<snoc>(q_gen_4508, q_gen_4478) -> q_gen_4508
<snoc>(q_gen_4508, q_gen_4496) -> q_gen_4508
<s>(q_gen_4496) -> q_gen_4519
<s>(q_gen_4519) -> q_gen_4519
<nil, z>() -> q_gen_4467
<snoc, s>(q_gen_4472, q_gen_4471) -> q_gen_4467
<snoc, s>(q_gen_4484, q_gen_4483) -> q_gen_4467
<snoc, s>(q_gen_4490, q_gen_4489) -> q_gen_4467
<snoc, s>(q_gen_4505, q_gen_4502) -> q_gen_4467
<snoc, s>(q_gen_4508, q_gen_4528) -> q_gen_4467
<s, z>(q_gen_4478) -> q_gen_4471
<s, z>(q_gen_4481) -> q_gen_4471
<s, z>(q_gen_4496) -> q_gen_4471
<s, z>(q_gen_4519) -> q_gen_4471
<z, z>() -> q_gen_4471
<s, s>(q_gen_4471) -> q_gen_4483
<z, s>(q_gen_4478) -> q_gen_4483
<snoc, s>(q_gen_4472, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4472, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4472, q_gen_4502) -> q_gen_4485
<snoc, s>(q_gen_4472, q_gen_4528) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4502) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4528) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4502) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4528) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4528) -> q_gen_4485
<snoc, s>(q_gen_4508, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4508, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4508, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4508, q_gen_4502) -> q_gen_4485
<s, s>(q_gen_4483) -> q_gen_4489
<z, s>(q_gen_4481) -> q_gen_4489
<s, s>(q_gen_4489) -> q_gen_4502
<z, s>(q_gen_4496) -> q_gen_4502
<s, s>(q_gen_4502) -> q_gen_4528
<s, s>(q_gen_4528) -> q_gen_4528
<z, s>(q_gen_4519) -> q_gen_4528
}

Datatype: <nattsil, nat>
Convolution form: right
}}}

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 91
() -> length([nil, z]) -> 89
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 89
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 98
(le([s(nn1), z])) -> BOT -> 94
(le([z, z])) -> BOT -> 89
(length([l, _fy]) /\ length([snoc(l, x), _gy])) -> le([_fy, _gy]) -> 117
(length([ll, _by])) -> length([snoc(ll, x), s(_by)]) -> 118
}
Sat witness: Found: ((length([ll, _by])) -> length([snoc(ll, x), s(_by)]), {
_by -> s(s(s(s(z))))  ;  ll -> snoc(snoc(nil, s(s(z))), s(z))  ;  x -> z
})

-------------------------------------------
Step 94, which took 2.777435 s (model generation: 2.773841,  model checking: 0.003594):

Model:
|_
{
le -> 
{{{
Q={q_gen_4468, q_gen_4469, q_gen_4486},
Q_f={q_gen_4468},
Delta=
{
<s>(q_gen_4469) -> q_gen_4469
<z>() -> q_gen_4469
<s, s>(q_gen_4468) -> q_gen_4468
<z, s>(q_gen_4469) -> q_gen_4468
<s, s>(q_gen_4486) -> q_gen_4486
<s, z>(q_gen_4469) -> q_gen_4486
<z, z>() -> q_gen_4486
}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_4467, q_gen_4471, q_gen_4472, q_gen_4478, q_gen_4481, q_gen_4483, q_gen_4484, q_gen_4485, q_gen_4489, q_gen_4490, q_gen_4496, q_gen_4502, q_gen_4505, q_gen_4508, q_gen_4519, q_gen_4528},
Q_f={q_gen_4467},
Delta=
{
<nil>() -> q_gen_4472
<z>() -> q_gen_4478
<s>(q_gen_4478) -> q_gen_4481
<snoc>(q_gen_4472, q_gen_4478) -> q_gen_4484
<snoc>(q_gen_4472, q_gen_4519) -> q_gen_4484
<snoc>(q_gen_4484, q_gen_4496) -> q_gen_4484
<snoc>(q_gen_4472, q_gen_4496) -> q_gen_4490
<snoc>(q_gen_4484, q_gen_4478) -> q_gen_4490
<snoc>(q_gen_4484, q_gen_4519) -> q_gen_4490
<snoc>(q_gen_4505, q_gen_4481) -> q_gen_4490
<s>(q_gen_4481) -> q_gen_4496
<snoc>(q_gen_4490, q_gen_4478) -> q_gen_4505
<snoc>(q_gen_4490, q_gen_4481) -> q_gen_4505
<snoc>(q_gen_4490, q_gen_4496) -> q_gen_4505
<snoc>(q_gen_4490, q_gen_4519) -> q_gen_4505
<snoc>(q_gen_4508, q_gen_4496) -> q_gen_4505
<snoc>(q_gen_4508, q_gen_4519) -> q_gen_4505
<snoc>(q_gen_4505, q_gen_4478) -> q_gen_4508
<snoc>(q_gen_4505, q_gen_4496) -> q_gen_4508
<snoc>(q_gen_4505, q_gen_4519) -> q_gen_4508
<snoc>(q_gen_4508, q_gen_4478) -> q_gen_4508
<s>(q_gen_4496) -> q_gen_4519
<s>(q_gen_4519) -> q_gen_4519
<nil, z>() -> q_gen_4467
<snoc, s>(q_gen_4472, q_gen_4471) -> q_gen_4467
<snoc, s>(q_gen_4484, q_gen_4483) -> q_gen_4467
<snoc, s>(q_gen_4490, q_gen_4489) -> q_gen_4467
<snoc, s>(q_gen_4505, q_gen_4502) -> q_gen_4467
<snoc, s>(q_gen_4508, q_gen_4528) -> q_gen_4467
<s, z>(q_gen_4478) -> q_gen_4471
<s, z>(q_gen_4481) -> q_gen_4471
<s, z>(q_gen_4496) -> q_gen_4471
<s, z>(q_gen_4519) -> q_gen_4471
<z, z>() -> q_gen_4471
<s, s>(q_gen_4471) -> q_gen_4483
<s, s>(q_gen_4528) -> q_gen_4483
<z, s>(q_gen_4478) -> q_gen_4483
<snoc, s>(q_gen_4472, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4472, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4472, q_gen_4502) -> q_gen_4485
<snoc, s>(q_gen_4472, q_gen_4528) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4502) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4528) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4502) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4528) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4528) -> q_gen_4485
<snoc, s>(q_gen_4508, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4508, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4508, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4508, q_gen_4502) -> q_gen_4485
<s, s>(q_gen_4483) -> q_gen_4489
<z, s>(q_gen_4481) -> q_gen_4489
<s, s>(q_gen_4489) -> q_gen_4502
<z, s>(q_gen_4496) -> q_gen_4502
<s, s>(q_gen_4502) -> q_gen_4528
<z, s>(q_gen_4519) -> q_gen_4528
}

Datatype: <nattsil, nat>
Convolution form: right
}}}

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 92
() -> length([nil, z]) -> 90
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 90
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 99
(le([s(nn1), z])) -> BOT -> 95
(le([z, z])) -> BOT -> 90
(length([l, _fy]) /\ length([snoc(l, x), _gy])) -> le([_fy, _gy]) -> 120
(length([ll, _by])) -> length([snoc(ll, x), s(_by)]) -> 118
}
Sat witness: Found: ((length([l, _fy]) /\ length([snoc(l, x), _gy])) -> le([_fy, _gy]), {
_fy -> s(s(z))  ;  _gy -> s(s(z))  ;  l -> snoc(snoc(nil, z), s(s(z)))  ;  x -> z
})

-------------------------------------------
Step 95, which took 2.705006 s (model generation: 2.639770,  model checking: 0.065236):

Model:
|_
{
le -> 
{{{
Q={q_gen_4468, q_gen_4469, q_gen_4486},
Q_f={q_gen_4468},
Delta=
{
<s>(q_gen_4469) -> q_gen_4469
<z>() -> q_gen_4469
<s, s>(q_gen_4468) -> q_gen_4468
<z, s>(q_gen_4469) -> q_gen_4468
<s, s>(q_gen_4486) -> q_gen_4486
<s, z>(q_gen_4469) -> q_gen_4486
<z, z>() -> q_gen_4486
}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_4467, q_gen_4471, q_gen_4472, q_gen_4478, q_gen_4481, q_gen_4483, q_gen_4484, q_gen_4485, q_gen_4489, q_gen_4490, q_gen_4496, q_gen_4502, q_gen_4505, q_gen_4508, q_gen_4519, q_gen_4528},
Q_f={q_gen_4467},
Delta=
{
<nil>() -> q_gen_4472
<snoc>(q_gen_4484, q_gen_4481) -> q_gen_4472
<snoc>(q_gen_4508, q_gen_4481) -> q_gen_4472
<z>() -> q_gen_4478
<s>(q_gen_4478) -> q_gen_4481
<snoc>(q_gen_4472, q_gen_4478) -> q_gen_4484
<snoc>(q_gen_4472, q_gen_4496) -> q_gen_4484
<snoc>(q_gen_4472, q_gen_4519) -> q_gen_4484
<snoc>(q_gen_4484, q_gen_4478) -> q_gen_4490
<s>(q_gen_4481) -> q_gen_4496
<snoc>(q_gen_4490, q_gen_4478) -> q_gen_4505
<snoc>(q_gen_4490, q_gen_4481) -> q_gen_4505
<snoc>(q_gen_4490, q_gen_4496) -> q_gen_4505
<snoc>(q_gen_4490, q_gen_4519) -> q_gen_4505
<snoc>(q_gen_4508, q_gen_4478) -> q_gen_4505
<snoc>(q_gen_4484, q_gen_4496) -> q_gen_4508
<snoc>(q_gen_4484, q_gen_4519) -> q_gen_4508
<snoc>(q_gen_4505, q_gen_4478) -> q_gen_4508
<snoc>(q_gen_4505, q_gen_4496) -> q_gen_4508
<snoc>(q_gen_4505, q_gen_4519) -> q_gen_4508
<snoc>(q_gen_4508, q_gen_4519) -> q_gen_4508
<s>(q_gen_4496) -> q_gen_4519
<s>(q_gen_4519) -> q_gen_4519
<nil, z>() -> q_gen_4467
<snoc, s>(q_gen_4472, q_gen_4471) -> q_gen_4467
<snoc, s>(q_gen_4484, q_gen_4483) -> q_gen_4467
<snoc, s>(q_gen_4490, q_gen_4489) -> q_gen_4467
<snoc, s>(q_gen_4505, q_gen_4502) -> q_gen_4467
<snoc, s>(q_gen_4508, q_gen_4471) -> q_gen_4467
<snoc, s>(q_gen_4508, q_gen_4489) -> q_gen_4467
<snoc, s>(q_gen_4508, q_gen_4528) -> q_gen_4467
<s, z>(q_gen_4478) -> q_gen_4471
<s, z>(q_gen_4481) -> q_gen_4471
<s, z>(q_gen_4496) -> q_gen_4471
<s, z>(q_gen_4519) -> q_gen_4471
<z, z>() -> q_gen_4471
<s, s>(q_gen_4471) -> q_gen_4483
<z, s>(q_gen_4478) -> q_gen_4483
<snoc, s>(q_gen_4472, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4472, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4472, q_gen_4502) -> q_gen_4485
<snoc, s>(q_gen_4472, q_gen_4528) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4502) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4528) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4502) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4528) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4528) -> q_gen_4485
<snoc, s>(q_gen_4508, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4508, q_gen_4502) -> q_gen_4485
<s, s>(q_gen_4483) -> q_gen_4489
<z, s>(q_gen_4481) -> q_gen_4489
<s, s>(q_gen_4489) -> q_gen_4502
<z, s>(q_gen_4496) -> q_gen_4502
<s, s>(q_gen_4502) -> q_gen_4528
<s, s>(q_gen_4528) -> q_gen_4528
<z, s>(q_gen_4519) -> q_gen_4528
}

Datatype: <nattsil, nat>
Convolution form: right
}}}

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 93
() -> length([nil, z]) -> 91
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 91
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 100
(le([s(nn1), z])) -> BOT -> 96
(le([z, z])) -> BOT -> 91
(length([l, _fy]) /\ length([snoc(l, x), _gy])) -> le([_fy, _gy]) -> 120
(length([ll, _by])) -> length([snoc(ll, x), s(_by)]) -> 121
}
Sat witness: Found: ((length([ll, _by])) -> length([snoc(ll, x), s(_by)]), {
_by -> s(s(s(s(s(s(z))))))  ;  ll -> snoc(snoc(snoc(snoc(nil, z), s(s(z))), s(s(s(z)))), s(z))  ;  x -> s(z)
})

-------------------------------------------
Step 96, which took 3.368089 s (model generation: 3.363817,  model checking: 0.004272):

Model:
|_
{
le -> 
{{{
Q={q_gen_4468, q_gen_4469, q_gen_4486},
Q_f={q_gen_4468},
Delta=
{
<s>(q_gen_4469) -> q_gen_4469
<z>() -> q_gen_4469
<s, s>(q_gen_4468) -> q_gen_4468
<z, s>(q_gen_4469) -> q_gen_4468
<s, s>(q_gen_4486) -> q_gen_4486
<s, z>(q_gen_4469) -> q_gen_4486
<z, z>() -> q_gen_4486
}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_4467, q_gen_4471, q_gen_4472, q_gen_4478, q_gen_4481, q_gen_4483, q_gen_4484, q_gen_4485, q_gen_4489, q_gen_4490, q_gen_4496, q_gen_4502, q_gen_4505, q_gen_4508, q_gen_4519, q_gen_4528},
Q_f={q_gen_4467},
Delta=
{
<nil>() -> q_gen_4472
<snoc>(q_gen_4484, q_gen_4496) -> q_gen_4472
<z>() -> q_gen_4478
<s>(q_gen_4478) -> q_gen_4481
<snoc>(q_gen_4472, q_gen_4478) -> q_gen_4484
<snoc>(q_gen_4472, q_gen_4496) -> q_gen_4484
<snoc>(q_gen_4472, q_gen_4519) -> q_gen_4484
<snoc>(q_gen_4484, q_gen_4481) -> q_gen_4484
<snoc>(q_gen_4505, q_gen_4481) -> q_gen_4484
<snoc>(q_gen_4505, q_gen_4496) -> q_gen_4484
<snoc>(q_gen_4484, q_gen_4478) -> q_gen_4490
<snoc>(q_gen_4484, q_gen_4519) -> q_gen_4490
<s>(q_gen_4481) -> q_gen_4496
<snoc>(q_gen_4490, q_gen_4478) -> q_gen_4505
<snoc>(q_gen_4490, q_gen_4481) -> q_gen_4505
<snoc>(q_gen_4490, q_gen_4496) -> q_gen_4505
<snoc>(q_gen_4490, q_gen_4519) -> q_gen_4505
<snoc>(q_gen_4505, q_gen_4478) -> q_gen_4508
<snoc>(q_gen_4505, q_gen_4519) -> q_gen_4508
<snoc>(q_gen_4508, q_gen_4478) -> q_gen_4508
<snoc>(q_gen_4508, q_gen_4496) -> q_gen_4508
<s>(q_gen_4496) -> q_gen_4519
<s>(q_gen_4519) -> q_gen_4519
<nil, z>() -> q_gen_4467
<snoc, s>(q_gen_4472, q_gen_4471) -> q_gen_4467
<snoc, s>(q_gen_4484, q_gen_4483) -> q_gen_4467
<snoc, s>(q_gen_4490, q_gen_4489) -> q_gen_4467
<snoc, s>(q_gen_4505, q_gen_4502) -> q_gen_4467
<snoc, s>(q_gen_4508, q_gen_4528) -> q_gen_4467
<s, z>(q_gen_4478) -> q_gen_4471
<s, z>(q_gen_4481) -> q_gen_4471
<s, z>(q_gen_4496) -> q_gen_4471
<s, z>(q_gen_4519) -> q_gen_4471
<z, z>() -> q_gen_4471
<s, s>(q_gen_4471) -> q_gen_4483
<z, s>(q_gen_4478) -> q_gen_4483
<snoc, s>(q_gen_4472, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4472, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4472, q_gen_4502) -> q_gen_4485
<snoc, s>(q_gen_4472, q_gen_4528) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4502) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4528) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4502) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4528) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4528) -> q_gen_4485
<snoc, s>(q_gen_4508, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4508, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4508, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4508, q_gen_4502) -> q_gen_4485
<s, s>(q_gen_4483) -> q_gen_4489
<z, s>(q_gen_4481) -> q_gen_4489
<s, s>(q_gen_4489) -> q_gen_4502
<s, s>(q_gen_4528) -> q_gen_4502
<z, s>(q_gen_4496) -> q_gen_4502
<s, s>(q_gen_4502) -> q_gen_4528
<z, s>(q_gen_4519) -> q_gen_4528
}

Datatype: <nattsil, nat>
Convolution form: right
}}}

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 94
() -> length([nil, z]) -> 92
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 92
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 101
(le([s(nn1), z])) -> BOT -> 97
(le([z, z])) -> BOT -> 92
(length([l, _fy]) /\ length([snoc(l, x), _gy])) -> le([_fy, _gy]) -> 123
(length([ll, _by])) -> length([snoc(ll, x), s(_by)]) -> 121
}
Sat witness: Found: ((length([l, _fy]) /\ length([snoc(l, x), _gy])) -> le([_fy, _gy]), {
_fy -> s(s(z))  ;  _gy -> s(z)  ;  l -> snoc(snoc(nil, z), s(s(z)))  ;  x -> z
})

-------------------------------------------
Step 97, which took 3.558459 s (model generation: 3.470876,  model checking: 0.087583):

Model:
|_
{
le -> 
{{{
Q={q_gen_4468, q_gen_4469, q_gen_4486},
Q_f={q_gen_4468},
Delta=
{
<s>(q_gen_4469) -> q_gen_4469
<z>() -> q_gen_4469
<s, s>(q_gen_4468) -> q_gen_4468
<z, s>(q_gen_4469) -> q_gen_4468
<s, s>(q_gen_4486) -> q_gen_4486
<s, z>(q_gen_4469) -> q_gen_4486
<z, z>() -> q_gen_4486
}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_4467, q_gen_4471, q_gen_4472, q_gen_4478, q_gen_4481, q_gen_4483, q_gen_4484, q_gen_4485, q_gen_4489, q_gen_4490, q_gen_4496, q_gen_4502, q_gen_4505, q_gen_4508, q_gen_4519, q_gen_4528},
Q_f={q_gen_4467},
Delta=
{
<nil>() -> q_gen_4472
<snoc>(q_gen_4484, q_gen_4481) -> q_gen_4472
<snoc>(q_gen_4508, q_gen_4519) -> q_gen_4472
<z>() -> q_gen_4478
<s>(q_gen_4478) -> q_gen_4481
<snoc>(q_gen_4472, q_gen_4478) -> q_gen_4484
<snoc>(q_gen_4472, q_gen_4481) -> q_gen_4484
<snoc>(q_gen_4472, q_gen_4496) -> q_gen_4484
<snoc>(q_gen_4472, q_gen_4519) -> q_gen_4484
<snoc>(q_gen_4484, q_gen_4478) -> q_gen_4490
<s>(q_gen_4481) -> q_gen_4496
<snoc>(q_gen_4484, q_gen_4496) -> q_gen_4505
<snoc>(q_gen_4490, q_gen_4478) -> q_gen_4505
<snoc>(q_gen_4490, q_gen_4481) -> q_gen_4505
<snoc>(q_gen_4490, q_gen_4496) -> q_gen_4505
<snoc>(q_gen_4490, q_gen_4519) -> q_gen_4505
<snoc>(q_gen_4505, q_gen_4496) -> q_gen_4505
<snoc>(q_gen_4508, q_gen_4478) -> q_gen_4505
<snoc>(q_gen_4484, q_gen_4519) -> q_gen_4508
<snoc>(q_gen_4505, q_gen_4478) -> q_gen_4508
<snoc>(q_gen_4505, q_gen_4519) -> q_gen_4508
<snoc>(q_gen_4508, q_gen_4481) -> q_gen_4508
<s>(q_gen_4496) -> q_gen_4519
<s>(q_gen_4519) -> q_gen_4519
<nil, z>() -> q_gen_4467
<snoc, s>(q_gen_4472, q_gen_4471) -> q_gen_4467
<snoc, s>(q_gen_4484, q_gen_4483) -> q_gen_4467
<snoc, s>(q_gen_4490, q_gen_4489) -> q_gen_4467
<snoc, s>(q_gen_4505, q_gen_4502) -> q_gen_4467
<snoc, s>(q_gen_4508, q_gen_4489) -> q_gen_4467
<snoc, s>(q_gen_4508, q_gen_4528) -> q_gen_4467
<s, z>(q_gen_4478) -> q_gen_4471
<s, z>(q_gen_4481) -> q_gen_4471
<s, z>(q_gen_4496) -> q_gen_4471
<s, z>(q_gen_4519) -> q_gen_4471
<z, z>() -> q_gen_4471
<s, s>(q_gen_4471) -> q_gen_4483
<z, s>(q_gen_4478) -> q_gen_4483
<snoc, s>(q_gen_4472, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4472, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4472, q_gen_4502) -> q_gen_4485
<snoc, s>(q_gen_4472, q_gen_4528) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4502) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4528) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4502) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4528) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4528) -> q_gen_4485
<snoc, s>(q_gen_4508, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4508, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4508, q_gen_4502) -> q_gen_4485
<s, s>(q_gen_4483) -> q_gen_4489
<z, s>(q_gen_4481) -> q_gen_4489
<s, s>(q_gen_4489) -> q_gen_4502
<z, s>(q_gen_4496) -> q_gen_4502
<s, s>(q_gen_4502) -> q_gen_4528
<s, s>(q_gen_4528) -> q_gen_4528
<z, s>(q_gen_4519) -> q_gen_4528
}

Datatype: <nattsil, nat>
Convolution form: right
}}}

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 95
() -> length([nil, z]) -> 93
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 93
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 102
(le([s(nn1), z])) -> BOT -> 98
(le([z, z])) -> BOT -> 93
(length([l, _fy]) /\ length([snoc(l, x), _gy])) -> le([_fy, _gy]) -> 123
(length([ll, _by])) -> length([snoc(ll, x), s(_by)]) -> 124
}
Sat witness: Found: ((length([ll, _by])) -> length([snoc(ll, x), s(_by)]), {
_by -> s(s(s(s(s(z)))))  ;  ll -> snoc(snoc(snoc(snoc(nil, z), s(s(z))), s(s(s(z)))), s(s(s(z))))  ;  x -> s(s(z))
})

-------------------------------------------
Step 98, which took 4.358400 s (model generation: 4.302542,  model checking: 0.055858):

Model:
|_
{
le -> 
{{{
Q={q_gen_4468, q_gen_4469, q_gen_4486},
Q_f={q_gen_4468},
Delta=
{
<s>(q_gen_4469) -> q_gen_4469
<z>() -> q_gen_4469
<s, s>(q_gen_4468) -> q_gen_4468
<z, s>(q_gen_4469) -> q_gen_4468
<s, s>(q_gen_4486) -> q_gen_4486
<s, z>(q_gen_4469) -> q_gen_4486
<z, z>() -> q_gen_4486
}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_4467, q_gen_4471, q_gen_4472, q_gen_4478, q_gen_4481, q_gen_4483, q_gen_4484, q_gen_4485, q_gen_4489, q_gen_4490, q_gen_4496, q_gen_4502, q_gen_4505, q_gen_4508, q_gen_4519, q_gen_4528},
Q_f={q_gen_4467},
Delta=
{
<nil>() -> q_gen_4472
<z>() -> q_gen_4478
<s>(q_gen_4478) -> q_gen_4481
<snoc>(q_gen_4472, q_gen_4478) -> q_gen_4484
<snoc>(q_gen_4472, q_gen_4519) -> q_gen_4484
<snoc>(q_gen_4505, q_gen_4496) -> q_gen_4484
<snoc>(q_gen_4472, q_gen_4496) -> q_gen_4490
<snoc>(q_gen_4484, q_gen_4478) -> q_gen_4490
<snoc>(q_gen_4484, q_gen_4519) -> q_gen_4490
<snoc>(q_gen_4505, q_gen_4481) -> q_gen_4490
<s>(q_gen_4481) -> q_gen_4496
<snoc>(q_gen_4484, q_gen_4496) -> q_gen_4505
<snoc>(q_gen_4490, q_gen_4478) -> q_gen_4505
<snoc>(q_gen_4490, q_gen_4481) -> q_gen_4505
<snoc>(q_gen_4490, q_gen_4496) -> q_gen_4505
<snoc>(q_gen_4490, q_gen_4519) -> q_gen_4505
<snoc>(q_gen_4508, q_gen_4481) -> q_gen_4505
<snoc>(q_gen_4508, q_gen_4519) -> q_gen_4505
<snoc>(q_gen_4505, q_gen_4478) -> q_gen_4508
<snoc>(q_gen_4505, q_gen_4519) -> q_gen_4508
<snoc>(q_gen_4508, q_gen_4478) -> q_gen_4508
<snoc>(q_gen_4508, q_gen_4496) -> q_gen_4508
<s>(q_gen_4496) -> q_gen_4519
<s>(q_gen_4519) -> q_gen_4519
<nil, z>() -> q_gen_4467
<snoc, s>(q_gen_4472, q_gen_4471) -> q_gen_4467
<snoc, s>(q_gen_4484, q_gen_4483) -> q_gen_4467
<snoc, s>(q_gen_4490, q_gen_4489) -> q_gen_4467
<snoc, s>(q_gen_4505, q_gen_4502) -> q_gen_4467
<snoc, s>(q_gen_4508, q_gen_4528) -> q_gen_4467
<s, z>(q_gen_4478) -> q_gen_4471
<s, z>(q_gen_4481) -> q_gen_4471
<s, z>(q_gen_4496) -> q_gen_4471
<s, z>(q_gen_4519) -> q_gen_4471
<z, z>() -> q_gen_4471
<s, s>(q_gen_4471) -> q_gen_4483
<z, s>(q_gen_4478) -> q_gen_4483
<snoc, s>(q_gen_4472, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4472, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4472, q_gen_4502) -> q_gen_4485
<snoc, s>(q_gen_4472, q_gen_4528) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4502) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4528) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4502) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4528) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4528) -> q_gen_4485
<snoc, s>(q_gen_4508, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4508, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4508, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4508, q_gen_4502) -> q_gen_4485
<s, s>(q_gen_4483) -> q_gen_4489
<z, s>(q_gen_4481) -> q_gen_4489
<s, s>(q_gen_4489) -> q_gen_4502
<s, s>(q_gen_4528) -> q_gen_4502
<z, s>(q_gen_4496) -> q_gen_4502
<s, s>(q_gen_4502) -> q_gen_4528
<z, s>(q_gen_4519) -> q_gen_4528
}

Datatype: <nattsil, nat>
Convolution form: right
}}}

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 96
() -> length([nil, z]) -> 94
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 94
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 103
(le([s(nn1), z])) -> BOT -> 99
(le([z, z])) -> BOT -> 94
(length([l, _fy]) /\ length([snoc(l, x), _gy])) -> le([_fy, _gy]) -> 126
(length([ll, _by])) -> length([snoc(ll, x), s(_by)]) -> 124
}
Sat witness: Found: ((length([l, _fy]) /\ length([snoc(l, x), _gy])) -> le([_fy, _gy]), {
_fy -> s(s(s(s(z))))  ;  _gy -> s(s(z))  ;  l -> snoc(snoc(snoc(snoc(snoc(snoc(snoc(snoc(snoc(nil, s(s(s(z)))), s(s(z))), s(s(z))), s(s(s(s(z))))), s(s(s(s(z))))), z), z), s(z)), s(s(z)))  ;  x -> z
})

-------------------------------------------
Step 99, which took 3.586681 s (model generation: 3.495812,  model checking: 0.090869):

Model:
|_
{
le -> 
{{{
Q={q_gen_4468, q_gen_4469, q_gen_4486},
Q_f={q_gen_4468},
Delta=
{
<s>(q_gen_4469) -> q_gen_4469
<z>() -> q_gen_4469
<s, s>(q_gen_4468) -> q_gen_4468
<z, s>(q_gen_4469) -> q_gen_4468
<s, s>(q_gen_4486) -> q_gen_4486
<s, z>(q_gen_4469) -> q_gen_4486
<z, z>() -> q_gen_4486
}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_4467, q_gen_4471, q_gen_4472, q_gen_4478, q_gen_4481, q_gen_4483, q_gen_4484, q_gen_4485, q_gen_4489, q_gen_4490, q_gen_4496, q_gen_4502, q_gen_4505, q_gen_4508, q_gen_4519, q_gen_4528},
Q_f={q_gen_4467},
Delta=
{
<nil>() -> q_gen_4472
<snoc>(q_gen_4505, q_gen_4496) -> q_gen_4472
<z>() -> q_gen_4478
<s>(q_gen_4478) -> q_gen_4481
<snoc>(q_gen_4472, q_gen_4478) -> q_gen_4484
<snoc>(q_gen_4472, q_gen_4519) -> q_gen_4484
<snoc>(q_gen_4484, q_gen_4478) -> q_gen_4490
<snoc>(q_gen_4484, q_gen_4519) -> q_gen_4490
<s>(q_gen_4481) -> q_gen_4496
<snoc>(q_gen_4472, q_gen_4496) -> q_gen_4505
<snoc>(q_gen_4484, q_gen_4496) -> q_gen_4505
<snoc>(q_gen_4490, q_gen_4478) -> q_gen_4505
<snoc>(q_gen_4490, q_gen_4481) -> q_gen_4505
<snoc>(q_gen_4490, q_gen_4496) -> q_gen_4505
<snoc>(q_gen_4490, q_gen_4519) -> q_gen_4505
<snoc>(q_gen_4505, q_gen_4478) -> q_gen_4508
<snoc>(q_gen_4505, q_gen_4481) -> q_gen_4508
<snoc>(q_gen_4505, q_gen_4519) -> q_gen_4508
<snoc>(q_gen_4508, q_gen_4478) -> q_gen_4508
<snoc>(q_gen_4508, q_gen_4481) -> q_gen_4508
<snoc>(q_gen_4508, q_gen_4496) -> q_gen_4508
<snoc>(q_gen_4508, q_gen_4519) -> q_gen_4508
<s>(q_gen_4496) -> q_gen_4519
<s>(q_gen_4519) -> q_gen_4519
<nil, z>() -> q_gen_4467
<snoc, s>(q_gen_4472, q_gen_4471) -> q_gen_4467
<snoc, s>(q_gen_4484, q_gen_4483) -> q_gen_4467
<snoc, s>(q_gen_4490, q_gen_4489) -> q_gen_4467
<snoc, s>(q_gen_4505, q_gen_4502) -> q_gen_4467
<snoc, s>(q_gen_4508, q_gen_4528) -> q_gen_4467
<s, z>(q_gen_4478) -> q_gen_4471
<s, z>(q_gen_4481) -> q_gen_4471
<s, z>(q_gen_4496) -> q_gen_4471
<s, z>(q_gen_4519) -> q_gen_4471
<z, z>() -> q_gen_4471
<s, s>(q_gen_4471) -> q_gen_4483
<z, s>(q_gen_4478) -> q_gen_4483
<snoc, s>(q_gen_4472, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4472, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4472, q_gen_4502) -> q_gen_4485
<snoc, s>(q_gen_4472, q_gen_4528) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4502) -> q_gen_4485
<snoc, s>(q_gen_4484, q_gen_4528) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4502) -> q_gen_4485
<snoc, s>(q_gen_4490, q_gen_4528) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4505, q_gen_4528) -> q_gen_4485
<snoc, s>(q_gen_4508, q_gen_4471) -> q_gen_4485
<snoc, s>(q_gen_4508, q_gen_4483) -> q_gen_4485
<snoc, s>(q_gen_4508, q_gen_4489) -> q_gen_4485
<snoc, s>(q_gen_4508, q_gen_4502) -> q_gen_4485
<s, s>(q_gen_4483) -> q_gen_4489
<z, s>(q_gen_4481) -> q_gen_4489
<s, s>(q_gen_4489) -> q_gen_4502
<z, s>(q_gen_4496) -> q_gen_4502
<s, s>(q_gen_4502) -> q_gen_4528
<s, s>(q_gen_4528) -> q_gen_4528
<z, s>(q_gen_4519) -> q_gen_4528
}

Datatype: <nattsil, nat>
Convolution form: right
}}}

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 97
() -> length([nil, z]) -> 95
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 95
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 104
(le([s(nn1), z])) -> BOT -> 100
(le([z, z])) -> BOT -> 95
(length([l, _fy]) /\ length([snoc(l, x), _gy])) -> le([_fy, _gy]) -> 126
(length([ll, _by])) -> length([snoc(ll, x), s(_by)]) -> 127
}
Sat witness: Found: ((length([ll, _by])) -> length([snoc(ll, x), s(_by)]), {
_by -> s(s(z))  ;  ll -> snoc(snoc(nil, s(s(s(s(z))))), s(s(z)))  ;  x -> s(s(z))
})

Total time: 63.638603
Reason for stopping: DontKnow. Stopped because: timeout