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


Learning problem is:

env: {
elt -> {a, b}  ;  elt_bin_tree -> {leaf, node}  ;  nat -> {s, z}
}
definition:
{
(leq, P:
{() -> leq([z, n2])
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)])
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2])
(leq([s(nn1), z])) -> BOT}
)
(max, F:
{(leq([n, m])) -> max([n, m, m])
(not leq([n, m])) -> max([n, m, n])}
(max([_dba, _eba, _fba]) /\ max([_dba, _eba, _gba])) -> eq_nat([_fba, _gba])
)
(plus, F:
{() -> plus([n, z, n])
(plus([n, mm, _hba])) -> plus([n, s(mm), s(_hba)])}
(plus([_iba, _jba, _kba]) /\ plus([_iba, _jba, _lba])) -> eq_nat([_kba, _lba])
)
(height, F:
{() -> height([leaf, z])
(height([t1, _mba]) /\ height([t2, _nba]) /\ max([_mba, _nba, _oba])) -> height([node(e, t1, t2), s(_oba)])}
(height([_pba, _qba]) /\ height([_pba, _rba])) -> eq_nat([_qba, _rba])
)
(numnodes, F:
{() -> numnodes([leaf, z])
(numnodes([t1, _sba]) /\ numnodes([t2, _tba]) /\ plus([_sba, _tba, _uba])) -> numnodes([node(e, t1, t2), s(_uba)])}
(numnodes([_vba, _wba]) /\ numnodes([_vba, _xba])) -> eq_nat([_wba, _xba])
)
}

properties:
{(height([t1, _yba]) /\ numnodes([t1, _zba])) -> leq([_yba, _zba])}


over-approximation: {height, max, numnodes, plus}
under-approximation: {leq}

Clause system for inference is:

{
() -> height([leaf, z]) -> 0
() -> leq([z, n2]) -> 0
() -> numnodes([leaf, z]) -> 0
() -> plus([n, z, n]) -> 0
(height([t1, _mba]) /\ height([t2, _nba]) /\ max([_mba, _nba, _oba])) -> height([node(e, t1, t2), s(_oba)]) -> 0
(height([t1, _yba]) /\ numnodes([t1, _zba])) -> leq([_yba, _zba]) -> 0
(leq([n, m])) -> max([n, m, m]) -> 0
(not leq([n, m])) -> max([n, m, n]) -> 0
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 0
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 0
(leq([s(nn1), z])) -> BOT -> 0
(numnodes([t1, _sba]) /\ numnodes([t2, _tba]) /\ plus([_sba, _tba, _uba])) -> numnodes([node(e, t1, t2), s(_uba)]) -> 0
(plus([n, mm, _hba])) -> plus([n, s(mm), s(_hba)]) -> 0
}


Solving took 63.045466 seconds.
DontKnow. Stopped because: timeout
Working model:
|_
{
height -> 
{{{
Q={q_gen_7346, q_gen_7353, q_gen_7354, q_gen_7355, q_gen_7372, q_gen_7373, q_gen_7382, q_gen_7383, q_gen_7384, q_gen_7394, q_gen_7395, q_gen_7396, q_gen_7400, q_gen_7401, q_gen_7402, q_gen_7403, q_gen_7404, q_gen_7405, q_gen_7410, q_gen_7411, q_gen_7412, q_gen_7419, q_gen_7420, q_gen_7421, q_gen_7422, q_gen_7423, q_gen_7440, q_gen_7448, q_gen_7450, q_gen_7452, q_gen_7453, q_gen_7457, q_gen_7458, q_gen_7459, q_gen_7460, q_gen_7461, q_gen_7464, q_gen_7466, q_gen_7467, q_gen_7468, q_gen_7469, q_gen_7470, q_gen_7471, q_gen_7475, q_gen_7476, q_gen_7479, q_gen_7480, q_gen_7481, q_gen_7482, q_gen_7483, q_gen_7484, q_gen_7486, q_gen_7487, q_gen_7492, q_gen_7493, q_gen_7494, q_gen_7495, q_gen_7496, q_gen_7497, q_gen_7498, q_gen_7500, q_gen_7502, q_gen_7504, q_gen_7505, q_gen_7506, q_gen_7507, q_gen_7508, q_gen_7509, q_gen_7510, q_gen_7513, q_gen_7514, q_gen_7515, q_gen_7518, q_gen_7519, q_gen_7520, q_gen_7521, q_gen_7522, q_gen_7523, q_gen_7524, q_gen_7526, q_gen_7527, q_gen_7528, q_gen_7529, q_gen_7530, q_gen_7531, q_gen_7532, q_gen_7539, q_gen_7540, q_gen_7541, q_gen_7546, q_gen_7548, q_gen_7549, q_gen_7550, q_gen_7551, q_gen_7553, q_gen_7554, q_gen_7555, q_gen_7556, q_gen_7567, q_gen_7568, q_gen_7571, q_gen_7572, q_gen_7573, q_gen_7574, q_gen_7575},
Q_f={},
Delta=
{
<leaf>() -> q_gen_7354
<node>(q_gen_7384, q_gen_7354, q_gen_7354) -> q_gen_7383
<a>() -> q_gen_7384
<node>(q_gen_7396, q_gen_7354, q_gen_7354) -> q_gen_7395
<b>() -> q_gen_7396
<node>(q_gen_7396, q_gen_7395, q_gen_7395) -> q_gen_7402
<z>() -> q_gen_7404
<node>(q_gen_7396, q_gen_7402, q_gen_7395) -> q_gen_7412
<node>(q_gen_7396, q_gen_7354, q_gen_7395) -> q_gen_7420
<node>(q_gen_7396, q_gen_7420, q_gen_7395) -> q_gen_7422
<node>(q_gen_7396, q_gen_7395, q_gen_7354) -> q_gen_7453
<node>(q_gen_7396, q_gen_7395, q_gen_7420) -> q_gen_7458
<node>(q_gen_7396, q_gen_7458, q_gen_7458) -> q_gen_7460
<node>(q_gen_7396, q_gen_7420, q_gen_7420) -> q_gen_7467
<node>(q_gen_7384, q_gen_7453, q_gen_7467) -> q_gen_7469
<s>(q_gen_7404) -> q_gen_7471
<node>(q_gen_7396, q_gen_7481, q_gen_7481) -> q_gen_7480
<node>(q_gen_7384, q_gen_7453, q_gen_7395) -> q_gen_7481
<node>(q_gen_7396, q_gen_7480, q_gen_7354) -> q_gen_7483
<node>(q_gen_7396, q_gen_7420, q_gen_7453) -> q_gen_7493
<node>(q_gen_7396, q_gen_7493, q_gen_7420) -> q_gen_7496
<node>(q_gen_7396, q_gen_7354, q_gen_7493) -> q_gen_7497
<node>(q_gen_7384, q_gen_7395, q_gen_7402) -> q_gen_7506
<node>(q_gen_7396, q_gen_7395, q_gen_7506) -> q_gen_7507
<node>(q_gen_7396, q_gen_7507, q_gen_7506) -> q_gen_7509
<node>(q_gen_7396, q_gen_7402, q_gen_7354) -> q_gen_7515
<node>(q_gen_7384, q_gen_7453, q_gen_7520) -> q_gen_7519
<node>(q_gen_7384, q_gen_7395, q_gen_7521) -> q_gen_7520
<node>(q_gen_7396, q_gen_7453, q_gen_7395) -> q_gen_7521
<node>(q_gen_7396, q_gen_7519, q_gen_7453) -> q_gen_7523
<node>(q_gen_7396, q_gen_7528, q_gen_7354) -> q_gen_7527
<node>(q_gen_7384, q_gen_7458, q_gen_7529) -> q_gen_7528
<node>(q_gen_7384, q_gen_7395, q_gen_7354) -> q_gen_7529
<node>(q_gen_7396, q_gen_7354, q_gen_7527) -> q_gen_7531
<node>(q_gen_7384, q_gen_7395, q_gen_7395) -> q_gen_7541
<node>(q_gen_7396, q_gen_7453, q_gen_7420) -> q_gen_7549
<node>(q_gen_7384, q_gen_7549, q_gen_7354) -> q_gen_7551
<node>(q_gen_7384, q_gen_7555, q_gen_7383) -> q_gen_7554
<node>(q_gen_7384, q_gen_7354, q_gen_7383) -> q_gen_7555
<node>(q_gen_7396, q_gen_7555, q_gen_7555) -> q_gen_7556
<node>(q_gen_7384, q_gen_7555, q_gen_7555) -> q_gen_7568
<node>(q_gen_7396, q_gen_7481, q_gen_7395) -> q_gen_7572
<node>(q_gen_7396, q_gen_7453, q_gen_7572) -> q_gen_7574
<leaf, z>() -> q_gen_7346
<node, s>(q_gen_7355, q_gen_7354, q_gen_7354) -> q_gen_7353
<b, z>() -> q_gen_7355
<node, s>(q_gen_7373, q_gen_7354, q_gen_7354) -> q_gen_7372
<a, z>() -> q_gen_7373
<node, s>(q_gen_7355, q_gen_7354, q_gen_7383) -> q_gen_7382
<node, s>(q_gen_7355, q_gen_7354, q_gen_7395) -> q_gen_7394
<node, s>(q_gen_7355, q_gen_7395, q_gen_7395) -> q_gen_7400
<node, s>(q_gen_7403, q_gen_7354, q_gen_7402) -> q_gen_7401
<b, s>(q_gen_7404) -> q_gen_7403
<node, s>(q_gen_7403, q_gen_7354, q_gen_7354) -> q_gen_7405
<node, s>(q_gen_7355, q_gen_7402, q_gen_7395) -> q_gen_7410
<node, s>(q_gen_7355, q_gen_7354, q_gen_7412) -> q_gen_7411
<node, s>(q_gen_7355, q_gen_7420, q_gen_7395) -> q_gen_7419
<node, s>(q_gen_7403, q_gen_7354, q_gen_7422) -> q_gen_7421
<node, s>(q_gen_7403, q_gen_7354, q_gen_7395) -> q_gen_7423
<node, s>(q_gen_7403, q_gen_7412, q_gen_7354) -> q_gen_7440
<node, s>(q_gen_7403, q_gen_7354, q_gen_7420) -> q_gen_7448
<node, s>(q_gen_7403, q_gen_7395, q_gen_7354) -> q_gen_7450
<node, s>(q_gen_7355, q_gen_7354, q_gen_7453) -> q_gen_7452
<node, s>(q_gen_7355, q_gen_7458, q_gen_7458) -> q_gen_7457
<node, s>(q_gen_7461, q_gen_7354, q_gen_7460) -> q_gen_7459
<a, s>(q_gen_7404) -> q_gen_7461
<node, s>(q_gen_7461, q_gen_7395, q_gen_7354) -> q_gen_7464
<node, s>(q_gen_7461, q_gen_7453, q_gen_7467) -> q_gen_7466
<node, s>(q_gen_7470, q_gen_7354, q_gen_7469) -> q_gen_7468
<b, s>(q_gen_7471) -> q_gen_7470
<node, s>(q_gen_7476, q_gen_7395, q_gen_7354) -> q_gen_7475
<a, s>(q_gen_7471) -> q_gen_7476
<node, s>(q_gen_7403, q_gen_7480, q_gen_7354) -> q_gen_7479
<node, s>(q_gen_7470, q_gen_7354, q_gen_7483) -> q_gen_7482
<node, s>(q_gen_7461, q_gen_7354, q_gen_7395) -> q_gen_7484
<node, s>(q_gen_7461, q_gen_7420, q_gen_7354) -> q_gen_7486
<node, s>(q_gen_7403, q_gen_7453, q_gen_7395) -> q_gen_7487
<node, s>(q_gen_7355, q_gen_7354, q_gen_7493) -> q_gen_7492
<node, s>(q_gen_7355, q_gen_7493, q_gen_7420) -> q_gen_7494
<node, s>(q_gen_7403, q_gen_7497, q_gen_7496) -> q_gen_7495
<node, s>(q_gen_7461, q_gen_7354, q_gen_7354) -> q_gen_7498
<node, s>(q_gen_7403, q_gen_7402, q_gen_7402) -> q_gen_7500
<node, s>(q_gen_7470, q_gen_7395, q_gen_7395) -> q_gen_7502
<node, s>(q_gen_7476, q_gen_7420, q_gen_7354) -> q_gen_7504
<node, s>(q_gen_7355, q_gen_7507, q_gen_7506) -> q_gen_7505
<node, s>(q_gen_7403, q_gen_7509, q_gen_7354) -> q_gen_7508
<node, s>(q_gen_7403, q_gen_7420, q_gen_7354) -> q_gen_7510
<node, s>(q_gen_7355, q_gen_7354, q_gen_7420) -> q_gen_7513
<node, s>(q_gen_7403, q_gen_7354, q_gen_7515) -> q_gen_7514
<node, s>(q_gen_7403, q_gen_7519, q_gen_7453) -> q_gen_7518
<node, s>(q_gen_7476, q_gen_7523, q_gen_7354) -> q_gen_7522
<node, s>(q_gen_7403, q_gen_7395, q_gen_7453) -> q_gen_7524
<node, s>(q_gen_7355, q_gen_7354, q_gen_7527) -> q_gen_7526
<node, s>(q_gen_7461, q_gen_7531, q_gen_7354) -> q_gen_7530
<node, s>(q_gen_7470, q_gen_7354, q_gen_7395) -> q_gen_7532
<node, s>(q_gen_7461, q_gen_7395, q_gen_7395) -> q_gen_7539
<node, s>(q_gen_7470, q_gen_7354, q_gen_7541) -> q_gen_7540
<node, s>(q_gen_7470, q_gen_7354, q_gen_7354) -> q_gen_7546
<node, s>(q_gen_7461, q_gen_7549, q_gen_7354) -> q_gen_7548
<node, s>(q_gen_7476, q_gen_7354, q_gen_7551) -> q_gen_7550
<node, s>(q_gen_7403, q_gen_7556, q_gen_7554) -> q_gen_7553
<node, s>(q_gen_7403, q_gen_7568, q_gen_7555) -> q_gen_7567
<node, s>(q_gen_7403, q_gen_7453, q_gen_7572) -> q_gen_7571
<node, s>(q_gen_7470, q_gen_7354, q_gen_7574) -> q_gen_7573
<node, s>(q_gen_7470, q_gen_7420, q_gen_7354) -> q_gen_7575
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_7342, q_gen_7352, q_gen_7356, q_gen_7357, q_gen_7362, q_gen_7363, q_gen_7374, q_gen_7385, q_gen_7406, q_gen_7426, q_gen_7427, q_gen_7478, q_gen_7547},
Q_f={},
Delta=
{
<z>() -> q_gen_7357
<s>(q_gen_7357) -> q_gen_7363
<s>(q_gen_7363) -> q_gen_7427
<z, z>() -> q_gen_7342
<s, s>(q_gen_7342) -> q_gen_7352
<z, s>(q_gen_7357) -> q_gen_7356
<z, s>(q_gen_7363) -> q_gen_7362
<s, z>(q_gen_7357) -> q_gen_7374
<s, z>(q_gen_7363) -> q_gen_7385
<s, s>(q_gen_7374) -> q_gen_7406
<z, s>(q_gen_7427) -> q_gen_7426
<s, s>(q_gen_7406) -> q_gen_7478
<s, s>(q_gen_7385) -> q_gen_7547
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  max -> 
{{{
Q={q_gen_7343, q_gen_7358, q_gen_7359, q_gen_7370, q_gen_7371, q_gen_7375, q_gen_7381, q_gen_7386, q_gen_7387, q_gen_7428, q_gen_7429, q_gen_7430, q_gen_7431, q_gen_7451},
Q_f={},
Delta=
{
<z>() -> q_gen_7359
<s>(q_gen_7430) -> q_gen_7429
<s>(q_gen_7359) -> q_gen_7430
<z, z>() -> q_gen_7371
<s, s>(q_gen_7371) -> q_gen_7387
<z, z, z>() -> q_gen_7343
<z, s, z>(q_gen_7359) -> q_gen_7358
<z, s, s>(q_gen_7371) -> q_gen_7370
<s, z, s>(q_gen_7371) -> q_gen_7375
<s, s, s>(q_gen_7343) -> q_gen_7381
<s, z, s>(q_gen_7387) -> q_gen_7386
<z, s, z>(q_gen_7429) -> q_gen_7428
<z, s, s>(q_gen_7387) -> q_gen_7431
<z, s, z>(q_gen_7430) -> q_gen_7451
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  numnodes -> 
{{{
Q={q_gen_7345, q_gen_7349, q_gen_7350, q_gen_7351, q_gen_7368, q_gen_7369, q_gen_7378, q_gen_7379, q_gen_7380, q_gen_7392, q_gen_7393, q_gen_7397, q_gen_7398, q_gen_7399, q_gen_7407, q_gen_7408, q_gen_7409, q_gen_7413, q_gen_7415, q_gen_7416, q_gen_7417, q_gen_7418, q_gen_7424, q_gen_7425, q_gen_7432, q_gen_7433, q_gen_7434, q_gen_7437, q_gen_7438, q_gen_7439, q_gen_7441, q_gen_7442, q_gen_7443, q_gen_7444, q_gen_7445, q_gen_7446, q_gen_7447, q_gen_7449, q_gen_7454, q_gen_7455, q_gen_7456, q_gen_7462, q_gen_7463, q_gen_7465, q_gen_7472, q_gen_7473, q_gen_7474, q_gen_7477, q_gen_7485, q_gen_7488, q_gen_7489, q_gen_7490, q_gen_7491, q_gen_7499, q_gen_7501, q_gen_7503, q_gen_7511, q_gen_7516, q_gen_7517, q_gen_7525, q_gen_7533, q_gen_7534, q_gen_7535, q_gen_7536, q_gen_7537, q_gen_7538, q_gen_7542, q_gen_7543, q_gen_7544, q_gen_7545, q_gen_7552, q_gen_7557, q_gen_7558, q_gen_7559, q_gen_7560, q_gen_7561, q_gen_7562, q_gen_7563, q_gen_7564, q_gen_7565, q_gen_7566, q_gen_7569, q_gen_7570},
Q_f={},
Delta=
{
<leaf>() -> q_gen_7350
<z>() -> q_gen_7380
<s>(q_gen_7380) -> q_gen_7399
<node>(q_gen_7409, q_gen_7350, q_gen_7350) -> q_gen_7408
<a>() -> q_gen_7409
<node>(q_gen_7417, q_gen_7408, q_gen_7408) -> q_gen_7416
<b>() -> q_gen_7417
<node>(q_gen_7417, q_gen_7350, q_gen_7350) -> q_gen_7425
<node>(q_gen_7417, q_gen_7425, q_gen_7425) -> q_gen_7433
<node>(q_gen_7409, q_gen_7433, q_gen_7433) -> q_gen_7438
<node>(q_gen_7409, q_gen_7350, q_gen_7433) -> q_gen_7439
<node>(q_gen_7417, q_gen_7350, q_gen_7425) -> q_gen_7443
<node>(q_gen_7409, q_gen_7350, q_gen_7425) -> q_gen_7445
<node>(q_gen_7409, q_gen_7350, q_gen_7443) -> q_gen_7446
<node>(q_gen_7409, q_gen_7443, q_gen_7443) -> q_gen_7456
<node>(q_gen_7417, q_gen_7425, q_gen_7350) -> q_gen_7474
<node>(q_gen_7417, q_gen_7474, q_gen_7474) -> q_gen_7491
<node>(q_gen_7417, q_gen_7433, q_gen_7350) -> q_gen_7517
<node>(q_gen_7409, q_gen_7536, q_gen_7536) -> q_gen_7535
<node>(q_gen_7417, q_gen_7350, q_gen_7408) -> q_gen_7536
<node>(q_gen_7417, q_gen_7408, q_gen_7535) -> q_gen_7538
<node>(q_gen_7409, q_gen_7408, q_gen_7416) -> q_gen_7543
<node>(q_gen_7417, q_gen_7408, q_gen_7543) -> q_gen_7545
<node>(q_gen_7409, q_gen_7559, q_gen_7408) -> q_gen_7558
<node>(q_gen_7409, q_gen_7350, q_gen_7408) -> q_gen_7559
<node>(q_gen_7417, q_gen_7559, q_gen_7559) -> q_gen_7560
<node>(q_gen_7409, q_gen_7564, q_gen_7563) -> q_gen_7562
<node>(q_gen_7417, q_gen_7443, q_gen_7443) -> q_gen_7563
<node>(q_gen_7417, q_gen_7425, q_gen_7563) -> q_gen_7564
<node>(q_gen_7417, q_gen_7425, q_gen_7562) -> q_gen_7566
<node>(q_gen_7409, q_gen_7559, q_gen_7559) -> q_gen_7570
<leaf, z>() -> q_gen_7345
<node, s>(q_gen_7351, q_gen_7350, q_gen_7350) -> q_gen_7349
<b, z>() -> q_gen_7351
<node, s>(q_gen_7369, q_gen_7350, q_gen_7350) -> q_gen_7368
<a, z>() -> q_gen_7369
<node, s>(q_gen_7379, q_gen_7350, q_gen_7350) -> q_gen_7378
<b, s>(q_gen_7380) -> q_gen_7379
<node, s>(q_gen_7393, q_gen_7350, q_gen_7350) -> q_gen_7392
<a, s>(q_gen_7380) -> q_gen_7393
<node, s>(q_gen_7398, q_gen_7350, q_gen_7350) -> q_gen_7397
<b, s>(q_gen_7399) -> q_gen_7398
<node, s>(q_gen_7379, q_gen_7350, q_gen_7408) -> q_gen_7407
<node, s>(q_gen_7379, q_gen_7408, q_gen_7408) -> q_gen_7413
<node, s>(q_gen_7418, q_gen_7350, q_gen_7416) -> q_gen_7415
<a, s>(q_gen_7399) -> q_gen_7418
<node, s>(q_gen_7351, q_gen_7350, q_gen_7425) -> q_gen_7424
<node, s>(q_gen_7393, q_gen_7350, q_gen_7433) -> q_gen_7432
<node, s>(q_gen_7393, q_gen_7433, q_gen_7433) -> q_gen_7434
<node, s>(q_gen_7418, q_gen_7439, q_gen_7438) -> q_gen_7437
<node, s>(q_gen_7369, q_gen_7350, q_gen_7425) -> q_gen_7441
<node, s>(q_gen_7369, q_gen_7350, q_gen_7443) -> q_gen_7442
<node, s>(q_gen_7379, q_gen_7446, q_gen_7445) -> q_gen_7444
<node, s>(q_gen_7351, q_gen_7350, q_gen_7433) -> q_gen_7447
<node, s>(q_gen_7351, q_gen_7350, q_gen_7443) -> q_gen_7449
<node, s>(q_gen_7369, q_gen_7443, q_gen_7443) -> q_gen_7454
<node, s>(q_gen_7379, q_gen_7456, q_gen_7350) -> q_gen_7455
<node, s>(q_gen_7379, q_gen_7350, q_gen_7425) -> q_gen_7462
<node, s>(q_gen_7398, q_gen_7443, q_gen_7350) -> q_gen_7463
<node, s>(q_gen_7369, q_gen_7425, q_gen_7350) -> q_gen_7465
<node, s>(q_gen_7379, q_gen_7425, q_gen_7350) -> q_gen_7472
<node, s>(q_gen_7398, q_gen_7350, q_gen_7474) -> q_gen_7473
<node, s>(q_gen_7393, q_gen_7425, q_gen_7350) -> q_gen_7477
<node, s>(q_gen_7398, q_gen_7443, q_gen_7425) -> q_gen_7485
<node, s>(q_gen_7351, q_gen_7474, q_gen_7425) -> q_gen_7488
<node, s>(q_gen_7351, q_gen_7474, q_gen_7474) -> q_gen_7489
<node, s>(q_gen_7393, q_gen_7350, q_gen_7491) -> q_gen_7490
<node, s>(q_gen_7418, q_gen_7350, q_gen_7425) -> q_gen_7499
<node, s>(q_gen_7351, q_gen_7433, q_gen_7433) -> q_gen_7501
<node, s>(q_gen_7379, q_gen_7425, q_gen_7425) -> q_gen_7503
<node, s>(q_gen_7351, q_gen_7443, q_gen_7350) -> q_gen_7511
<node, s>(q_gen_7351, q_gen_7350, q_gen_7517) -> q_gen_7516
<node, s>(q_gen_7351, q_gen_7425, q_gen_7474) -> q_gen_7525
<node, s>(q_gen_7379, q_gen_7456, q_gen_7446) -> q_gen_7533
<node, s>(q_gen_7351, q_gen_7408, q_gen_7535) -> q_gen_7534
<node, s>(q_gen_7393, q_gen_7538, q_gen_7350) -> q_gen_7537
<node, s>(q_gen_7351, q_gen_7408, q_gen_7543) -> q_gen_7542
<node, s>(q_gen_7393, q_gen_7545, q_gen_7350) -> q_gen_7544
<node, s>(q_gen_7418, q_gen_7425, q_gen_7350) -> q_gen_7552
<node, s>(q_gen_7351, q_gen_7560, q_gen_7558) -> q_gen_7557
<node, s>(q_gen_7379, q_gen_7425, q_gen_7562) -> q_gen_7561
<node, s>(q_gen_7398, q_gen_7566, q_gen_7350) -> q_gen_7565
<node, s>(q_gen_7351, q_gen_7570, q_gen_7559) -> q_gen_7569
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_7344, q_gen_7347, q_gen_7348, q_gen_7360, q_gen_7361, q_gen_7364, q_gen_7365, q_gen_7366, q_gen_7367, q_gen_7376, q_gen_7377, q_gen_7388, q_gen_7389, q_gen_7390, q_gen_7391, q_gen_7414, q_gen_7435, q_gen_7436, q_gen_7512},
Q_f={},
Delta=
{
<z>() -> q_gen_7367
<s>(q_gen_7367) -> q_gen_7391
<z, z>() -> q_gen_7348
<s, s>(q_gen_7348) -> q_gen_7361
<z, s>(q_gen_7367) -> q_gen_7377
<z, z, z>() -> q_gen_7344
<z, s, s>(q_gen_7348) -> q_gen_7347
<s, z, s>(q_gen_7361) -> q_gen_7360
<s, z, s>(q_gen_7348) -> q_gen_7364
<s, s, s>(q_gen_7366) -> q_gen_7365
<z, z, s>(q_gen_7367) -> q_gen_7366
<z, s, s>(q_gen_7377) -> q_gen_7376
<s, z, s>(q_gen_7377) -> q_gen_7388
<s, s, s>(q_gen_7390) -> q_gen_7389
<z, z, s>(q_gen_7391) -> q_gen_7390
<z, s, s>(q_gen_7361) -> q_gen_7414
<s, s, s>(q_gen_7436) -> q_gen_7435
<s, s, s>(q_gen_7344) -> q_gen_7436
<s, s, s>(q_gen_7388) -> q_gen_7512
}

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

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

-------------------
STEPS:
-------------------------------------------
Step 0, which took 0.015000 s (model generation: 0.014685,  model checking: 0.000315):

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

}

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

}

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

}

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

}

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

}

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

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

Teacher's answer:
New clause system:
{
() -> height([leaf, z]) -> 0
() -> leq([z, n2]) -> 0
() -> numnodes([leaf, z]) -> 0
() -> plus([n, z, n]) -> 0
(height([t1, _mba]) /\ height([t2, _nba]) /\ max([_mba, _nba, _oba])) -> height([node(e, t1, t2), s(_oba)]) -> 0
(height([t1, _yba]) /\ numnodes([t1, _zba])) -> leq([_yba, _zba]) -> 0
(leq([n, m])) -> max([n, m, m]) -> 0
(not leq([n, m])) -> max([n, m, n]) -> 3
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 1
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 1
(leq([s(nn1), z])) -> BOT -> 1
(numnodes([t1, _sba]) /\ numnodes([t2, _tba]) /\ plus([_sba, _tba, _uba])) -> numnodes([node(e, t1, t2), s(_uba)]) -> 1
(plus([n, mm, _hba])) -> plus([n, s(mm), s(_hba)]) -> 1
}
Sat witness: Found: ((not leq([n, m])) -> max([n, m, n]), {
m -> z  ;  n -> z
})

-------------------------------------------
Step 1, which took 0.008872 s (model generation: 0.008379,  model checking: 0.000493):

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

}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_7342},
Q_f={},
Delta=
{
<z, z>() -> q_gen_7342
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  max -> 
{{{
Q={q_gen_7343},
Q_f={q_gen_7343},
Delta=
{
<z, z, z>() -> q_gen_7343
}

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

}

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

}

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

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

Teacher's answer:
New clause system:
{
() -> height([leaf, z]) -> 0
() -> leq([z, n2]) -> 0
() -> numnodes([leaf, z]) -> 0
() -> plus([n, z, n]) -> 3
(height([t1, _mba]) /\ height([t2, _nba]) /\ max([_mba, _nba, _oba])) -> height([node(e, t1, t2), s(_oba)]) -> 1
(height([t1, _yba]) /\ numnodes([t1, _zba])) -> leq([_yba, _zba]) -> 1
(leq([n, m])) -> max([n, m, m]) -> 1
(not leq([n, m])) -> max([n, m, n]) -> 3
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 1
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 1
(leq([s(nn1), z])) -> BOT -> 1
(numnodes([t1, _sba]) /\ numnodes([t2, _tba]) /\ plus([_sba, _tba, _uba])) -> numnodes([node(e, t1, t2), s(_uba)]) -> 1
(plus([n, mm, _hba])) -> plus([n, s(mm), s(_hba)]) -> 1
}
Sat witness: Found: (() -> plus([n, z, n]), {
n -> z
})

-------------------------------------------
Step 2, which took 0.008164 s (model generation: 0.008084,  model checking: 0.000080):

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

}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_7342},
Q_f={},
Delta=
{
<z, z>() -> q_gen_7342
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  max -> 
{{{
Q={q_gen_7343},
Q_f={q_gen_7343},
Delta=
{
<z, z, z>() -> q_gen_7343
}

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

}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_7344},
Q_f={q_gen_7344},
Delta=
{
<z, z, z>() -> q_gen_7344
}

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

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

Teacher's answer:
New clause system:
{
() -> height([leaf, z]) -> 0
() -> leq([z, n2]) -> 0
() -> numnodes([leaf, z]) -> 3
() -> plus([n, z, n]) -> 3
(height([t1, _mba]) /\ height([t2, _nba]) /\ max([_mba, _nba, _oba])) -> height([node(e, t1, t2), s(_oba)]) -> 1
(height([t1, _yba]) /\ numnodes([t1, _zba])) -> leq([_yba, _zba]) -> 1
(leq([n, m])) -> max([n, m, m]) -> 1
(not leq([n, m])) -> max([n, m, n]) -> 3
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 1
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 1
(leq([s(nn1), z])) -> BOT -> 1
(numnodes([t1, _sba]) /\ numnodes([t2, _tba]) /\ plus([_sba, _tba, _uba])) -> numnodes([node(e, t1, t2), s(_uba)]) -> 1
(plus([n, mm, _hba])) -> plus([n, s(mm), s(_hba)]) -> 1
}
Sat witness: Found: (() -> numnodes([leaf, z]), {

})

-------------------------------------------
Step 3, which took 0.008004 s (model generation: 0.007950,  model checking: 0.000054):

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

}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_7342},
Q_f={},
Delta=
{
<z, z>() -> q_gen_7342
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  max -> 
{{{
Q={q_gen_7343},
Q_f={q_gen_7343},
Delta=
{
<z, z, z>() -> q_gen_7343
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  numnodes -> 
{{{
Q={q_gen_7345},
Q_f={q_gen_7345},
Delta=
{
<leaf, z>() -> q_gen_7345
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_7344},
Q_f={q_gen_7344},
Delta=
{
<z, z, z>() -> q_gen_7344
}

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

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

Teacher's answer:
New clause system:
{
() -> height([leaf, z]) -> 0
() -> leq([z, n2]) -> 3
() -> numnodes([leaf, z]) -> 3
() -> plus([n, z, n]) -> 3
(height([t1, _mba]) /\ height([t2, _nba]) /\ max([_mba, _nba, _oba])) -> height([node(e, t1, t2), s(_oba)]) -> 1
(height([t1, _yba]) /\ numnodes([t1, _zba])) -> leq([_yba, _zba]) -> 1
(leq([n, m])) -> max([n, m, m]) -> 1
(not leq([n, m])) -> max([n, m, n]) -> 3
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 1
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 1
(leq([s(nn1), z])) -> BOT -> 1
(numnodes([t1, _sba]) /\ numnodes([t2, _tba]) /\ plus([_sba, _tba, _uba])) -> numnodes([node(e, t1, t2), s(_uba)]) -> 1
(plus([n, mm, _hba])) -> plus([n, s(mm), s(_hba)]) -> 1
}
Sat witness: Found: (() -> leq([z, n2]), {
n2 -> z
})

-------------------------------------------
Step 4, which took 0.008689 s (model generation: 0.008614,  model checking: 0.000075):

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

}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_7342},
Q_f={q_gen_7342},
Delta=
{
<z, z>() -> q_gen_7342
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  max -> 
{{{
Q={q_gen_7343},
Q_f={},
Delta=
{
<z, z, z>() -> q_gen_7343
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  numnodes -> 
{{{
Q={q_gen_7345},
Q_f={q_gen_7345},
Delta=
{
<leaf, z>() -> q_gen_7345
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_7344},
Q_f={q_gen_7344},
Delta=
{
<z, z, z>() -> q_gen_7344
}

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

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

Teacher's answer:
New clause system:
{
() -> height([leaf, z]) -> 3
() -> leq([z, n2]) -> 3
() -> numnodes([leaf, z]) -> 3
() -> plus([n, z, n]) -> 3
(height([t1, _mba]) /\ height([t2, _nba]) /\ max([_mba, _nba, _oba])) -> height([node(e, t1, t2), s(_oba)]) -> 1
(height([t1, _yba]) /\ numnodes([t1, _zba])) -> leq([_yba, _zba]) -> 1
(leq([n, m])) -> max([n, m, m]) -> 1
(not leq([n, m])) -> max([n, m, n]) -> 3
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 1
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 1
(leq([s(nn1), z])) -> BOT -> 1
(numnodes([t1, _sba]) /\ numnodes([t2, _tba]) /\ plus([_sba, _tba, _uba])) -> numnodes([node(e, t1, t2), s(_uba)]) -> 1
(plus([n, mm, _hba])) -> plus([n, s(mm), s(_hba)]) -> 1
}
Sat witness: Found: (() -> height([leaf, z]), {

})

-------------------------------------------
Step 5, which took 0.009835 s (model generation: 0.009737,  model checking: 0.000098):

Model:
|_
{
height -> 
{{{
Q={q_gen_7346},
Q_f={q_gen_7346},
Delta=
{
<leaf, z>() -> q_gen_7346
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_7342},
Q_f={q_gen_7342},
Delta=
{
<z, z>() -> q_gen_7342
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  max -> 
{{{
Q={q_gen_7343},
Q_f={},
Delta=
{
<z, z, z>() -> q_gen_7343
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  numnodes -> 
{{{
Q={q_gen_7345},
Q_f={q_gen_7345},
Delta=
{
<leaf, z>() -> q_gen_7345
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_7344},
Q_f={q_gen_7344},
Delta=
{
<z, z, z>() -> q_gen_7344
}

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

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

Teacher's answer:
New clause system:
{
() -> height([leaf, z]) -> 3
() -> leq([z, n2]) -> 3
() -> numnodes([leaf, z]) -> 3
() -> plus([n, z, n]) -> 3
(height([t1, _mba]) /\ height([t2, _nba]) /\ max([_mba, _nba, _oba])) -> height([node(e, t1, t2), s(_oba)]) -> 1
(height([t1, _yba]) /\ numnodes([t1, _zba])) -> leq([_yba, _zba]) -> 1
(leq([n, m])) -> max([n, m, m]) -> 1
(not leq([n, m])) -> max([n, m, n]) -> 3
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 1
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 1
(leq([s(nn1), z])) -> BOT -> 1
(numnodes([t1, _sba]) /\ numnodes([t2, _tba]) /\ plus([_sba, _tba, _uba])) -> numnodes([node(e, t1, t2), s(_uba)]) -> 1
(plus([n, mm, _hba])) -> plus([n, s(mm), s(_hba)]) -> 4
}
Sat witness: Found: ((plus([n, mm, _hba])) -> plus([n, s(mm), s(_hba)]), {
_hba -> z  ;  mm -> z  ;  n -> z
})

-------------------------------------------
Step 6, which took 0.009994 s (model generation: 0.009882,  model checking: 0.000112):

Model:
|_
{
height -> 
{{{
Q={q_gen_7346},
Q_f={q_gen_7346},
Delta=
{
<leaf, z>() -> q_gen_7346
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_7342},
Q_f={q_gen_7342},
Delta=
{
<z, z>() -> q_gen_7342
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  max -> 
{{{
Q={q_gen_7343},
Q_f={},
Delta=
{
<z, z, z>() -> q_gen_7343
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  numnodes -> 
{{{
Q={q_gen_7345},
Q_f={q_gen_7345},
Delta=
{
<leaf, z>() -> q_gen_7345
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_7344, q_gen_7348},
Q_f={q_gen_7344},
Delta=
{
<z, z>() -> q_gen_7348
<z, s, s>(q_gen_7348) -> q_gen_7344
<z, z, z>() -> q_gen_7344
}

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

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

Teacher's answer:
New clause system:
{
() -> height([leaf, z]) -> 3
() -> leq([z, n2]) -> 3
() -> numnodes([leaf, z]) -> 3
() -> plus([n, z, n]) -> 3
(height([t1, _mba]) /\ height([t2, _nba]) /\ max([_mba, _nba, _oba])) -> height([node(e, t1, t2), s(_oba)]) -> 1
(height([t1, _yba]) /\ numnodes([t1, _zba])) -> leq([_yba, _zba]) -> 1
(leq([n, m])) -> max([n, m, m]) -> 1
(not leq([n, m])) -> max([n, m, n]) -> 3
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 1
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 1
(leq([s(nn1), z])) -> BOT -> 1
(numnodes([t1, _sba]) /\ numnodes([t2, _tba]) /\ plus([_sba, _tba, _uba])) -> numnodes([node(e, t1, t2), s(_uba)]) -> 4
(plus([n, mm, _hba])) -> plus([n, s(mm), s(_hba)]) -> 4
}
Sat witness: Found: ((numnodes([t1, _sba]) /\ numnodes([t2, _tba]) /\ plus([_sba, _tba, _uba])) -> numnodes([node(e, t1, t2), s(_uba)]), {
_sba -> z  ;  _tba -> z  ;  _uba -> z  ;  e -> b  ;  t1 -> leaf  ;  t2 -> leaf
})

-------------------------------------------
Step 7, which took 0.009356 s (model generation: 0.009264,  model checking: 0.000092):

Model:
|_
{
height -> 
{{{
Q={q_gen_7346},
Q_f={q_gen_7346},
Delta=
{
<leaf, z>() -> q_gen_7346
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_7342},
Q_f={q_gen_7342},
Delta=
{
<z, z>() -> q_gen_7342
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  max -> 
{{{
Q={q_gen_7343},
Q_f={},
Delta=
{
<z, z, z>() -> q_gen_7343
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  numnodes -> 
{{{
Q={q_gen_7345, q_gen_7350, q_gen_7351},
Q_f={q_gen_7345},
Delta=
{
<leaf>() -> q_gen_7350
<leaf, z>() -> q_gen_7345
<node, s>(q_gen_7351, q_gen_7350, q_gen_7350) -> q_gen_7345
<b, z>() -> q_gen_7351
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_7344, q_gen_7348},
Q_f={q_gen_7344},
Delta=
{
<z, z>() -> q_gen_7348
<z, s, s>(q_gen_7348) -> q_gen_7344
<z, z, z>() -> q_gen_7344
}

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

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

Teacher's answer:
New clause system:
{
() -> height([leaf, z]) -> 3
() -> leq([z, n2]) -> 3
() -> numnodes([leaf, z]) -> 3
() -> plus([n, z, n]) -> 3
(height([t1, _mba]) /\ height([t2, _nba]) /\ max([_mba, _nba, _oba])) -> height([node(e, t1, t2), s(_oba)]) -> 1
(height([t1, _yba]) /\ numnodes([t1, _zba])) -> leq([_yba, _zba]) -> 1
(leq([n, m])) -> max([n, m, m]) -> 1
(not leq([n, m])) -> max([n, m, n]) -> 3
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 4
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 2
(leq([s(nn1), z])) -> BOT -> 2
(numnodes([t1, _sba]) /\ numnodes([t2, _tba]) /\ plus([_sba, _tba, _uba])) -> numnodes([node(e, t1, t2), s(_uba)]) -> 4
(plus([n, mm, _hba])) -> plus([n, s(mm), s(_hba)]) -> 4
}
Sat witness: Found: ((leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]), {
nn1 -> z  ;  nn2 -> z
})

-------------------------------------------
Step 8, which took 0.008933 s (model generation: 0.008842,  model checking: 0.000091):

Model:
|_
{
height -> 
{{{
Q={q_gen_7346},
Q_f={q_gen_7346},
Delta=
{
<leaf, z>() -> q_gen_7346
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_7342},
Q_f={q_gen_7342},
Delta=
{
<s, s>(q_gen_7342) -> q_gen_7342
<z, z>() -> q_gen_7342
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  max -> 
{{{
Q={q_gen_7343},
Q_f={},
Delta=
{
<z, z, z>() -> q_gen_7343
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  numnodes -> 
{{{
Q={q_gen_7345, q_gen_7350, q_gen_7351},
Q_f={q_gen_7345},
Delta=
{
<leaf>() -> q_gen_7350
<leaf, z>() -> q_gen_7345
<node, s>(q_gen_7351, q_gen_7350, q_gen_7350) -> q_gen_7345
<b, z>() -> q_gen_7351
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_7344, q_gen_7348},
Q_f={q_gen_7344},
Delta=
{
<z, z>() -> q_gen_7348
<z, s, s>(q_gen_7348) -> q_gen_7344
<z, z, z>() -> q_gen_7344
}

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

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

Teacher's answer:
New clause system:
{
() -> height([leaf, z]) -> 3
() -> leq([z, n2]) -> 3
() -> numnodes([leaf, z]) -> 3
() -> plus([n, z, n]) -> 3
(height([t1, _mba]) /\ height([t2, _nba]) /\ max([_mba, _nba, _oba])) -> height([node(e, t1, t2), s(_oba)]) -> 1
(height([t1, _yba]) /\ numnodes([t1, _zba])) -> leq([_yba, _zba]) -> 1
(leq([n, m])) -> max([n, m, m]) -> 4
(not leq([n, m])) -> max([n, m, n]) -> 3
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 4
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 2
(leq([s(nn1), z])) -> BOT -> 2
(numnodes([t1, _sba]) /\ numnodes([t2, _tba]) /\ plus([_sba, _tba, _uba])) -> numnodes([node(e, t1, t2), s(_uba)]) -> 4
(plus([n, mm, _hba])) -> plus([n, s(mm), s(_hba)]) -> 4
}
Sat witness: Found: ((leq([n, m])) -> max([n, m, m]), {
m -> z  ;  n -> z
})

-------------------------------------------
Step 9, which took 0.009384 s (model generation: 0.009178,  model checking: 0.000206):

Model:
|_
{
height -> 
{{{
Q={q_gen_7346},
Q_f={q_gen_7346},
Delta=
{
<leaf, z>() -> q_gen_7346
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_7342},
Q_f={q_gen_7342},
Delta=
{
<s, s>(q_gen_7342) -> q_gen_7342
<z, z>() -> q_gen_7342
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  max -> 
{{{
Q={q_gen_7343},
Q_f={q_gen_7343},
Delta=
{
<z, z, z>() -> q_gen_7343
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  numnodes -> 
{{{
Q={q_gen_7345, q_gen_7350, q_gen_7351},
Q_f={q_gen_7345},
Delta=
{
<leaf>() -> q_gen_7350
<leaf, z>() -> q_gen_7345
<node, s>(q_gen_7351, q_gen_7350, q_gen_7350) -> q_gen_7345
<b, z>() -> q_gen_7351
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_7344, q_gen_7348},
Q_f={q_gen_7344},
Delta=
{
<z, z>() -> q_gen_7348
<z, s, s>(q_gen_7348) -> q_gen_7344
<z, z, z>() -> q_gen_7344
}

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

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

Teacher's answer:
New clause system:
{
() -> height([leaf, z]) -> 3
() -> leq([z, n2]) -> 3
() -> numnodes([leaf, z]) -> 3
() -> plus([n, z, n]) -> 3
(height([t1, _mba]) /\ height([t2, _nba]) /\ max([_mba, _nba, _oba])) -> height([node(e, t1, t2), s(_oba)]) -> 4
(height([t1, _yba]) /\ numnodes([t1, _zba])) -> leq([_yba, _zba]) -> 2
(leq([n, m])) -> max([n, m, m]) -> 4
(not leq([n, m])) -> max([n, m, n]) -> 3
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 4
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 2
(leq([s(nn1), z])) -> BOT -> 2
(numnodes([t1, _sba]) /\ numnodes([t2, _tba]) /\ plus([_sba, _tba, _uba])) -> numnodes([node(e, t1, t2), s(_uba)]) -> 4
(plus([n, mm, _hba])) -> plus([n, s(mm), s(_hba)]) -> 4
}
Sat witness: Found: ((height([t1, _mba]) /\ height([t2, _nba]) /\ max([_mba, _nba, _oba])) -> height([node(e, t1, t2), s(_oba)]), {
_mba -> z  ;  _nba -> z  ;  _oba -> z  ;  e -> b  ;  t1 -> leaf  ;  t2 -> leaf
})

-------------------------------------------
Step 10, which took 0.010823 s (model generation: 0.010333,  model checking: 0.000490):

Model:
|_
{
height -> 
{{{
Q={q_gen_7346, q_gen_7354, q_gen_7355},
Q_f={q_gen_7346},
Delta=
{
<leaf>() -> q_gen_7354
<leaf, z>() -> q_gen_7346
<node, s>(q_gen_7355, q_gen_7354, q_gen_7354) -> q_gen_7346
<b, z>() -> q_gen_7355
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_7342},
Q_f={q_gen_7342},
Delta=
{
<s, s>(q_gen_7342) -> q_gen_7342
<z, z>() -> q_gen_7342
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  max -> 
{{{
Q={q_gen_7343},
Q_f={q_gen_7343},
Delta=
{
<z, z, z>() -> q_gen_7343
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  numnodes -> 
{{{
Q={q_gen_7345, q_gen_7350, q_gen_7351},
Q_f={q_gen_7345},
Delta=
{
<leaf>() -> q_gen_7350
<leaf, z>() -> q_gen_7345
<node, s>(q_gen_7351, q_gen_7350, q_gen_7350) -> q_gen_7345
<b, z>() -> q_gen_7351
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_7344, q_gen_7348},
Q_f={q_gen_7344},
Delta=
{
<z, z>() -> q_gen_7348
<z, s, s>(q_gen_7348) -> q_gen_7344
<z, z, z>() -> q_gen_7344
}

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

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

Teacher's answer:
New clause system:
{
() -> height([leaf, z]) -> 3
() -> leq([z, n2]) -> 3
() -> numnodes([leaf, z]) -> 3
() -> plus([n, z, n]) -> 3
(height([t1, _mba]) /\ height([t2, _nba]) /\ max([_mba, _nba, _oba])) -> height([node(e, t1, t2), s(_oba)]) -> 4
(height([t1, _yba]) /\ numnodes([t1, _zba])) -> leq([_yba, _zba]) -> 3
(leq([n, m])) -> max([n, m, m]) -> 4
(not leq([n, m])) -> max([n, m, n]) -> 6
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 4
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 3
(leq([s(nn1), z])) -> BOT -> 3
(numnodes([t1, _sba]) /\ numnodes([t2, _tba]) /\ plus([_sba, _tba, _uba])) -> numnodes([node(e, t1, t2), s(_uba)]) -> 4
(plus([n, mm, _hba])) -> plus([n, s(mm), s(_hba)]) -> 4
}
Sat witness: Found: ((not leq([n, m])) -> max([n, m, n]), {
m -> s(z)  ;  n -> z
})

-------------------------------------------
Step 11, which took 0.008923 s (model generation: 0.008606,  model checking: 0.000317):

Model:
|_
{
height -> 
{{{
Q={q_gen_7346, q_gen_7354, q_gen_7355},
Q_f={q_gen_7346},
Delta=
{
<leaf>() -> q_gen_7354
<leaf, z>() -> q_gen_7346
<node, s>(q_gen_7355, q_gen_7354, q_gen_7354) -> q_gen_7346
<b, z>() -> q_gen_7355
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_7342, q_gen_7357},
Q_f={q_gen_7342},
Delta=
{
<z>() -> q_gen_7357
<s, s>(q_gen_7342) -> q_gen_7342
<z, s>(q_gen_7357) -> q_gen_7342
<z, z>() -> q_gen_7342
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  max -> 
{{{
Q={q_gen_7343, q_gen_7359},
Q_f={q_gen_7343},
Delta=
{
<z>() -> q_gen_7359
<z, s, z>(q_gen_7359) -> q_gen_7343
<z, z, z>() -> q_gen_7343
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  numnodes -> 
{{{
Q={q_gen_7345, q_gen_7350, q_gen_7351},
Q_f={q_gen_7345},
Delta=
{
<leaf>() -> q_gen_7350
<leaf, z>() -> q_gen_7345
<node, s>(q_gen_7351, q_gen_7350, q_gen_7350) -> q_gen_7345
<b, z>() -> q_gen_7351
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_7344, q_gen_7348},
Q_f={q_gen_7344},
Delta=
{
<z, z>() -> q_gen_7348
<z, s, s>(q_gen_7348) -> q_gen_7344
<z, z, z>() -> q_gen_7344
}

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

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

Teacher's answer:
New clause system:
{
() -> height([leaf, z]) -> 3
() -> leq([z, n2]) -> 3
() -> numnodes([leaf, z]) -> 3
() -> plus([n, z, n]) -> 6
(height([t1, _mba]) /\ height([t2, _nba]) /\ max([_mba, _nba, _oba])) -> height([node(e, t1, t2), s(_oba)]) -> 4
(height([t1, _yba]) /\ numnodes([t1, _zba])) -> leq([_yba, _zba]) -> 4
(leq([n, m])) -> max([n, m, m]) -> 4
(not leq([n, m])) -> max([n, m, n]) -> 6
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 4
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 4
(leq([s(nn1), z])) -> BOT -> 4
(numnodes([t1, _sba]) /\ numnodes([t2, _tba]) /\ plus([_sba, _tba, _uba])) -> numnodes([node(e, t1, t2), s(_uba)]) -> 4
(plus([n, mm, _hba])) -> plus([n, s(mm), s(_hba)]) -> 4
}
Sat witness: Found: (() -> plus([n, z, n]), {
n -> s(s(z))
})

-------------------------------------------
Step 12, which took 0.009432 s (model generation: 0.009082,  model checking: 0.000350):

Model:
|_
{
height -> 
{{{
Q={q_gen_7346, q_gen_7354, q_gen_7355},
Q_f={q_gen_7346},
Delta=
{
<leaf>() -> q_gen_7354
<leaf, z>() -> q_gen_7346
<node, s>(q_gen_7355, q_gen_7354, q_gen_7354) -> q_gen_7346
<b, z>() -> q_gen_7355
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_7342, q_gen_7357},
Q_f={q_gen_7342},
Delta=
{
<z>() -> q_gen_7357
<s, s>(q_gen_7342) -> q_gen_7342
<z, s>(q_gen_7357) -> q_gen_7342
<z, z>() -> q_gen_7342
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  max -> 
{{{
Q={q_gen_7343, q_gen_7359},
Q_f={q_gen_7343},
Delta=
{
<z>() -> q_gen_7359
<z, s, z>(q_gen_7359) -> q_gen_7343
<z, z, z>() -> q_gen_7343
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  numnodes -> 
{{{
Q={q_gen_7345, q_gen_7350, q_gen_7351},
Q_f={q_gen_7345},
Delta=
{
<leaf>() -> q_gen_7350
<leaf, z>() -> q_gen_7345
<node, s>(q_gen_7351, q_gen_7350, q_gen_7350) -> q_gen_7345
<b, z>() -> q_gen_7351
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_7344, q_gen_7348},
Q_f={q_gen_7344},
Delta=
{
<s, s>(q_gen_7348) -> q_gen_7348
<z, z>() -> q_gen_7348
<s, z, s>(q_gen_7348) -> q_gen_7344
<z, s, s>(q_gen_7348) -> q_gen_7344
<z, z, z>() -> q_gen_7344
}

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

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

Teacher's answer:
New clause system:
{
() -> height([leaf, z]) -> 3
() -> leq([z, n2]) -> 6
() -> numnodes([leaf, z]) -> 4
() -> plus([n, z, n]) -> 6
(height([t1, _mba]) /\ height([t2, _nba]) /\ max([_mba, _nba, _oba])) -> height([node(e, t1, t2), s(_oba)]) -> 4
(height([t1, _yba]) /\ numnodes([t1, _zba])) -> leq([_yba, _zba]) -> 4
(leq([n, m])) -> max([n, m, m]) -> 4
(not leq([n, m])) -> max([n, m, n]) -> 6
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 4
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 4
(leq([s(nn1), z])) -> BOT -> 4
(numnodes([t1, _sba]) /\ numnodes([t2, _tba]) /\ plus([_sba, _tba, _uba])) -> numnodes([node(e, t1, t2), s(_uba)]) -> 4
(plus([n, mm, _hba])) -> plus([n, s(mm), s(_hba)]) -> 4
}
Sat witness: Found: (() -> leq([z, n2]), {
n2 -> s(s(z))
})

-------------------------------------------
Step 13, which took 0.009904 s (model generation: 0.009608,  model checking: 0.000296):

Model:
|_
{
height -> 
{{{
Q={q_gen_7346, q_gen_7354, q_gen_7355},
Q_f={q_gen_7346},
Delta=
{
<leaf>() -> q_gen_7354
<leaf, z>() -> q_gen_7346
<node, s>(q_gen_7355, q_gen_7354, q_gen_7354) -> q_gen_7346
<b, z>() -> q_gen_7355
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_7342, q_gen_7357},
Q_f={q_gen_7342},
Delta=
{
<s>(q_gen_7357) -> q_gen_7357
<z>() -> q_gen_7357
<s, s>(q_gen_7342) -> q_gen_7342
<z, s>(q_gen_7357) -> q_gen_7342
<z, z>() -> q_gen_7342
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  max -> 
{{{
Q={q_gen_7343, q_gen_7359},
Q_f={q_gen_7343},
Delta=
{
<z>() -> q_gen_7359
<z, s, z>(q_gen_7359) -> q_gen_7343
<z, z, z>() -> q_gen_7343
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  numnodes -> 
{{{
Q={q_gen_7345, q_gen_7350, q_gen_7351},
Q_f={q_gen_7345},
Delta=
{
<leaf>() -> q_gen_7350
<leaf, z>() -> q_gen_7345
<node, s>(q_gen_7351, q_gen_7350, q_gen_7350) -> q_gen_7345
<b, z>() -> q_gen_7351
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_7344, q_gen_7348},
Q_f={q_gen_7344},
Delta=
{
<s, s>(q_gen_7348) -> q_gen_7348
<z, z>() -> q_gen_7348
<s, z, s>(q_gen_7348) -> q_gen_7344
<z, s, s>(q_gen_7348) -> q_gen_7344
<z, z, z>() -> q_gen_7344
}

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

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

Teacher's answer:
New clause system:
{
() -> height([leaf, z]) -> 4
() -> leq([z, n2]) -> 6
() -> numnodes([leaf, z]) -> 4
() -> plus([n, z, n]) -> 6
(height([t1, _mba]) /\ height([t2, _nba]) /\ max([_mba, _nba, _oba])) -> height([node(e, t1, t2), s(_oba)]) -> 4
(height([t1, _yba]) /\ numnodes([t1, _zba])) -> leq([_yba, _zba]) -> 4
(leq([n, m])) -> max([n, m, m]) -> 4
(not leq([n, m])) -> max([n, m, n]) -> 6
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 4
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 4
(leq([s(nn1), z])) -> BOT -> 4
(numnodes([t1, _sba]) /\ numnodes([t2, _tba]) /\ plus([_sba, _tba, _uba])) -> numnodes([node(e, t1, t2), s(_uba)]) -> 4
(plus([n, mm, _hba])) -> plus([n, s(mm), s(_hba)]) -> 7
}
Sat witness: Found: ((plus([n, mm, _hba])) -> plus([n, s(mm), s(_hba)]), {
_hba -> s(z)  ;  mm -> z  ;  n -> s(z)
})

-------------------------------------------
Step 14, which took 0.012041 s (model generation: 0.010911,  model checking: 0.001130):

Model:
|_
{
height -> 
{{{
Q={q_gen_7346, q_gen_7354, q_gen_7355},
Q_f={q_gen_7346},
Delta=
{
<leaf>() -> q_gen_7354
<leaf, z>() -> q_gen_7346
<node, s>(q_gen_7355, q_gen_7354, q_gen_7354) -> q_gen_7346
<b, z>() -> q_gen_7355
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_7342, q_gen_7357},
Q_f={q_gen_7342},
Delta=
{
<s>(q_gen_7357) -> q_gen_7357
<z>() -> q_gen_7357
<s, s>(q_gen_7342) -> q_gen_7342
<z, s>(q_gen_7357) -> q_gen_7342
<z, z>() -> q_gen_7342
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  max -> 
{{{
Q={q_gen_7343, q_gen_7359},
Q_f={q_gen_7343},
Delta=
{
<z>() -> q_gen_7359
<z, s, z>(q_gen_7359) -> q_gen_7343
<z, z, z>() -> q_gen_7343
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  numnodes -> 
{{{
Q={q_gen_7345, q_gen_7350, q_gen_7351},
Q_f={q_gen_7345},
Delta=
{
<leaf>() -> q_gen_7350
<leaf, z>() -> q_gen_7345
<node, s>(q_gen_7351, q_gen_7350, q_gen_7350) -> q_gen_7345
<b, z>() -> q_gen_7351
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_7344, q_gen_7348, q_gen_7367},
Q_f={q_gen_7344},
Delta=
{
<z>() -> q_gen_7367
<s, s>(q_gen_7348) -> q_gen_7348
<z, z>() -> q_gen_7348
<s, s, s>(q_gen_7344) -> q_gen_7344
<s, z, s>(q_gen_7348) -> q_gen_7344
<z, s, s>(q_gen_7348) -> q_gen_7344
<z, z, s>(q_gen_7367) -> q_gen_7344
<z, z, z>() -> q_gen_7344
}

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

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

Teacher's answer:
New clause system:
{
() -> height([leaf, z]) -> 4
() -> leq([z, n2]) -> 6
() -> numnodes([leaf, z]) -> 4
() -> plus([n, z, n]) -> 6
(height([t1, _mba]) /\ height([t2, _nba]) /\ max([_mba, _nba, _oba])) -> height([node(e, t1, t2), s(_oba)]) -> 4
(height([t1, _yba]) /\ numnodes([t1, _zba])) -> leq([_yba, _zba]) -> 4
(leq([n, m])) -> max([n, m, m]) -> 4
(not leq([n, m])) -> max([n, m, n]) -> 6
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 4
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 4
(leq([s(nn1), z])) -> BOT -> 4
(numnodes([t1, _sba]) /\ numnodes([t2, _tba]) /\ plus([_sba, _tba, _uba])) -> numnodes([node(e, t1, t2), s(_uba)]) -> 7
(plus([n, mm, _hba])) -> plus([n, s(mm), s(_hba)]) -> 7
}
Sat witness: Found: ((numnodes([t1, _sba]) /\ numnodes([t2, _tba]) /\ plus([_sba, _tba, _uba])) -> numnodes([node(e, t1, t2), s(_uba)]), {
_sba -> z  ;  _tba -> z  ;  _uba -> z  ;  e -> a  ;  t1 -> leaf  ;  t2 -> leaf
})

-------------------------------------------
Step 15, which took 0.010709 s (model generation: 0.010476,  model checking: 0.000233):

Model:
|_
{
height -> 
{{{
Q={q_gen_7346, q_gen_7354, q_gen_7355},
Q_f={q_gen_7346},
Delta=
{
<leaf>() -> q_gen_7354
<leaf, z>() -> q_gen_7346
<node, s>(q_gen_7355, q_gen_7354, q_gen_7354) -> q_gen_7346
<b, z>() -> q_gen_7355
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_7342, q_gen_7357},
Q_f={q_gen_7342},
Delta=
{
<s>(q_gen_7357) -> q_gen_7357
<z>() -> q_gen_7357
<s, s>(q_gen_7342) -> q_gen_7342
<z, s>(q_gen_7357) -> q_gen_7342
<z, z>() -> q_gen_7342
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  max -> 
{{{
Q={q_gen_7343, q_gen_7359},
Q_f={q_gen_7343},
Delta=
{
<z>() -> q_gen_7359
<z, s, z>(q_gen_7359) -> q_gen_7343
<z, z, z>() -> q_gen_7343
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  numnodes -> 
{{{
Q={q_gen_7345, q_gen_7350, q_gen_7351},
Q_f={q_gen_7345},
Delta=
{
<leaf>() -> q_gen_7350
<leaf, z>() -> q_gen_7345
<node, s>(q_gen_7351, q_gen_7350, q_gen_7350) -> q_gen_7345
<a, z>() -> q_gen_7351
<b, z>() -> q_gen_7351
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_7344, q_gen_7348, q_gen_7367},
Q_f={q_gen_7344},
Delta=
{
<z>() -> q_gen_7367
<s, s>(q_gen_7348) -> q_gen_7348
<z, z>() -> q_gen_7348
<s, s, s>(q_gen_7344) -> q_gen_7344
<s, z, s>(q_gen_7348) -> q_gen_7344
<z, s, s>(q_gen_7348) -> q_gen_7344
<z, z, s>(q_gen_7367) -> q_gen_7344
<z, z, z>() -> q_gen_7344
}

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

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

Teacher's answer:
New clause system:
{
() -> height([leaf, z]) -> 4
() -> leq([z, n2]) -> 6
() -> numnodes([leaf, z]) -> 4
() -> plus([n, z, n]) -> 6
(height([t1, _mba]) /\ height([t2, _nba]) /\ max([_mba, _nba, _oba])) -> height([node(e, t1, t2), s(_oba)]) -> 4
(height([t1, _yba]) /\ numnodes([t1, _zba])) -> leq([_yba, _zba]) -> 4
(leq([n, m])) -> max([n, m, m]) -> 7
(not leq([n, m])) -> max([n, m, n]) -> 6
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 5
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 5
(leq([s(nn1), z])) -> BOT -> 5
(numnodes([t1, _sba]) /\ numnodes([t2, _tba]) /\ plus([_sba, _tba, _uba])) -> numnodes([node(e, t1, t2), s(_uba)]) -> 7
(plus([n, mm, _hba])) -> plus([n, s(mm), s(_hba)]) -> 7
}
Sat witness: Found: ((leq([n, m])) -> max([n, m, m]), {
m -> s(z)  ;  n -> z
})

-------------------------------------------
Step 16, which took 0.014914 s (model generation: 0.014063,  model checking: 0.000851):

Model:
|_
{
height -> 
{{{
Q={q_gen_7346, q_gen_7354, q_gen_7355},
Q_f={q_gen_7346},
Delta=
{
<leaf>() -> q_gen_7354
<leaf, z>() -> q_gen_7346
<node, s>(q_gen_7355, q_gen_7354, q_gen_7354) -> q_gen_7346
<b, z>() -> q_gen_7355
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_7342, q_gen_7357},
Q_f={q_gen_7342},
Delta=
{
<s>(q_gen_7357) -> q_gen_7357
<z>() -> q_gen_7357
<s, s>(q_gen_7342) -> q_gen_7342
<z, s>(q_gen_7357) -> q_gen_7342
<z, z>() -> q_gen_7342
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  max -> 
{{{
Q={q_gen_7343, q_gen_7359, q_gen_7371},
Q_f={q_gen_7343},
Delta=
{
<z>() -> q_gen_7359
<z, z>() -> q_gen_7371
<z, s, s>(q_gen_7371) -> q_gen_7343
<z, s, z>(q_gen_7359) -> q_gen_7343
<z, z, z>() -> q_gen_7343
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  numnodes -> 
{{{
Q={q_gen_7345, q_gen_7350, q_gen_7351},
Q_f={q_gen_7345},
Delta=
{
<leaf>() -> q_gen_7350
<leaf, z>() -> q_gen_7345
<node, s>(q_gen_7351, q_gen_7350, q_gen_7350) -> q_gen_7345
<a, z>() -> q_gen_7351
<b, z>() -> q_gen_7351
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_7344, q_gen_7348, q_gen_7367},
Q_f={q_gen_7344},
Delta=
{
<z>() -> q_gen_7367
<s, s>(q_gen_7348) -> q_gen_7348
<z, z>() -> q_gen_7348
<s, s, s>(q_gen_7344) -> q_gen_7344
<s, z, s>(q_gen_7348) -> q_gen_7344
<z, s, s>(q_gen_7348) -> q_gen_7344
<z, z, s>(q_gen_7367) -> q_gen_7344
<z, z, z>() -> q_gen_7344
}

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

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

Teacher's answer:
New clause system:
{
() -> height([leaf, z]) -> 4
() -> leq([z, n2]) -> 6
() -> numnodes([leaf, z]) -> 4
() -> plus([n, z, n]) -> 6
(height([t1, _mba]) /\ height([t2, _nba]) /\ max([_mba, _nba, _oba])) -> height([node(e, t1, t2), s(_oba)]) -> 7
(height([t1, _yba]) /\ numnodes([t1, _zba])) -> leq([_yba, _zba]) -> 5
(leq([n, m])) -> max([n, m, m]) -> 7
(not leq([n, m])) -> max([n, m, n]) -> 6
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 5
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 5
(leq([s(nn1), z])) -> BOT -> 5
(numnodes([t1, _sba]) /\ numnodes([t2, _tba]) /\ plus([_sba, _tba, _uba])) -> numnodes([node(e, t1, t2), s(_uba)]) -> 7
(plus([n, mm, _hba])) -> plus([n, s(mm), s(_hba)]) -> 7
}
Sat witness: Found: ((height([t1, _mba]) /\ height([t2, _nba]) /\ max([_mba, _nba, _oba])) -> height([node(e, t1, t2), s(_oba)]), {
_mba -> z  ;  _nba -> z  ;  _oba -> z  ;  e -> a  ;  t1 -> leaf  ;  t2 -> leaf
})

-------------------------------------------
Step 17, which took 0.014520 s (model generation: 0.013840,  model checking: 0.000680):

Model:
|_
{
height -> 
{{{
Q={q_gen_7346, q_gen_7354, q_gen_7355},
Q_f={q_gen_7346},
Delta=
{
<leaf>() -> q_gen_7354
<leaf, z>() -> q_gen_7346
<node, s>(q_gen_7355, q_gen_7354, q_gen_7354) -> q_gen_7346
<a, z>() -> q_gen_7355
<b, z>() -> q_gen_7355
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_7342, q_gen_7357},
Q_f={q_gen_7342},
Delta=
{
<s>(q_gen_7357) -> q_gen_7357
<z>() -> q_gen_7357
<s, s>(q_gen_7342) -> q_gen_7342
<z, s>(q_gen_7357) -> q_gen_7342
<z, z>() -> q_gen_7342
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  max -> 
{{{
Q={q_gen_7343, q_gen_7359, q_gen_7371},
Q_f={q_gen_7343},
Delta=
{
<z>() -> q_gen_7359
<z, z>() -> q_gen_7371
<z, s, s>(q_gen_7371) -> q_gen_7343
<z, s, z>(q_gen_7359) -> q_gen_7343
<z, z, z>() -> q_gen_7343
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  numnodes -> 
{{{
Q={q_gen_7345, q_gen_7350, q_gen_7351},
Q_f={q_gen_7345},
Delta=
{
<leaf>() -> q_gen_7350
<leaf, z>() -> q_gen_7345
<node, s>(q_gen_7351, q_gen_7350, q_gen_7350) -> q_gen_7345
<a, z>() -> q_gen_7351
<b, z>() -> q_gen_7351
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_7344, q_gen_7348, q_gen_7367},
Q_f={q_gen_7344},
Delta=
{
<z>() -> q_gen_7367
<s, s>(q_gen_7348) -> q_gen_7348
<z, z>() -> q_gen_7348
<s, s, s>(q_gen_7344) -> q_gen_7344
<s, z, s>(q_gen_7348) -> q_gen_7344
<z, s, s>(q_gen_7348) -> q_gen_7344
<z, z, s>(q_gen_7367) -> q_gen_7344
<z, z, z>() -> q_gen_7344
}

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

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

Teacher's answer:
New clause system:
{
() -> height([leaf, z]) -> 5
() -> leq([z, n2]) -> 6
() -> numnodes([leaf, z]) -> 5
() -> plus([n, z, n]) -> 6
(height([t1, _mba]) /\ height([t2, _nba]) /\ max([_mba, _nba, _oba])) -> height([node(e, t1, t2), s(_oba)]) -> 7
(height([t1, _yba]) /\ numnodes([t1, _zba])) -> leq([_yba, _zba]) -> 6
(leq([n, m])) -> max([n, m, m]) -> 7
(not leq([n, m])) -> max([n, m, n]) -> 9
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 6
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 6
(leq([s(nn1), z])) -> BOT -> 6
(numnodes([t1, _sba]) /\ numnodes([t2, _tba]) /\ plus([_sba, _tba, _uba])) -> numnodes([node(e, t1, t2), s(_uba)]) -> 7
(plus([n, mm, _hba])) -> plus([n, s(mm), s(_hba)]) -> 7
}
Sat witness: Found: ((not leq([n, m])) -> max([n, m, n]), {
m -> z  ;  n -> s(z)
})

-------------------------------------------
Step 18, which took 0.011706 s (model generation: 0.011399,  model checking: 0.000307):

Model:
|_
{
height -> 
{{{
Q={q_gen_7346, q_gen_7354, q_gen_7355},
Q_f={q_gen_7346},
Delta=
{
<leaf>() -> q_gen_7354
<leaf, z>() -> q_gen_7346
<node, s>(q_gen_7355, q_gen_7354, q_gen_7354) -> q_gen_7346
<a, z>() -> q_gen_7355
<b, z>() -> q_gen_7355
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_7342, q_gen_7357},
Q_f={q_gen_7342},
Delta=
{
<s>(q_gen_7357) -> q_gen_7357
<z>() -> q_gen_7357
<s, s>(q_gen_7342) -> q_gen_7342
<s, z>(q_gen_7357) -> q_gen_7342
<z, s>(q_gen_7357) -> q_gen_7342
<z, z>() -> q_gen_7342
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  max -> 
{{{
Q={q_gen_7343, q_gen_7359, q_gen_7371},
Q_f={q_gen_7343},
Delta=
{
<z>() -> q_gen_7359
<z, z>() -> q_gen_7371
<s, z, s>(q_gen_7371) -> q_gen_7343
<z, s, s>(q_gen_7371) -> q_gen_7343
<z, s, z>(q_gen_7359) -> q_gen_7343
<z, z, z>() -> q_gen_7343
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  numnodes -> 
{{{
Q={q_gen_7345, q_gen_7350, q_gen_7351},
Q_f={q_gen_7345},
Delta=
{
<leaf>() -> q_gen_7350
<leaf, z>() -> q_gen_7345
<node, s>(q_gen_7351, q_gen_7350, q_gen_7350) -> q_gen_7345
<a, z>() -> q_gen_7351
<b, z>() -> q_gen_7351
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_7344, q_gen_7348, q_gen_7367},
Q_f={q_gen_7344},
Delta=
{
<z>() -> q_gen_7367
<s, s>(q_gen_7348) -> q_gen_7348
<z, z>() -> q_gen_7348
<s, s, s>(q_gen_7344) -> q_gen_7344
<s, z, s>(q_gen_7348) -> q_gen_7344
<z, s, s>(q_gen_7348) -> q_gen_7344
<z, z, s>(q_gen_7367) -> q_gen_7344
<z, z, z>() -> q_gen_7344
}

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

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

Teacher's answer:
New clause system:
{
() -> height([leaf, z]) -> 6
() -> leq([z, n2]) -> 6
() -> numnodes([leaf, z]) -> 6
() -> plus([n, z, n]) -> 6
(height([t1, _mba]) /\ height([t2, _nba]) /\ max([_mba, _nba, _oba])) -> height([node(e, t1, t2), s(_oba)]) -> 7
(height([t1, _yba]) /\ numnodes([t1, _zba])) -> leq([_yba, _zba]) -> 6
(leq([n, m])) -> max([n, m, m]) -> 7
(not leq([n, m])) -> max([n, m, n]) -> 9
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 6
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 6
(leq([s(nn1), z])) -> BOT -> 9
(numnodes([t1, _sba]) /\ numnodes([t2, _tba]) /\ plus([_sba, _tba, _uba])) -> numnodes([node(e, t1, t2), s(_uba)]) -> 7
(plus([n, mm, _hba])) -> plus([n, s(mm), s(_hba)]) -> 7
}
Sat witness: Found: ((leq([s(nn1), z])) -> BOT, {
nn1 -> z
})

-------------------------------------------
Step 19, which took 0.012272 s (model generation: 0.011436,  model checking: 0.000836):

Model:
|_
{
height -> 
{{{
Q={q_gen_7346, q_gen_7354, q_gen_7355},
Q_f={q_gen_7346},
Delta=
{
<leaf>() -> q_gen_7354
<leaf, z>() -> q_gen_7346
<node, s>(q_gen_7355, q_gen_7354, q_gen_7354) -> q_gen_7346
<a, z>() -> q_gen_7355
<b, z>() -> q_gen_7355
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_7342, q_gen_7357, q_gen_7374},
Q_f={q_gen_7342},
Delta=
{
<s>(q_gen_7357) -> q_gen_7357
<z>() -> q_gen_7357
<s, s>(q_gen_7342) -> q_gen_7342
<z, s>(q_gen_7357) -> q_gen_7342
<z, z>() -> q_gen_7342
<s, z>(q_gen_7357) -> q_gen_7374
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  max -> 
{{{
Q={q_gen_7343, q_gen_7359, q_gen_7371},
Q_f={q_gen_7343},
Delta=
{
<z>() -> q_gen_7359
<z, z>() -> q_gen_7371
<s, z, s>(q_gen_7371) -> q_gen_7343
<z, s, s>(q_gen_7371) -> q_gen_7343
<z, s, z>(q_gen_7359) -> q_gen_7343
<z, z, z>() -> q_gen_7343
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  numnodes -> 
{{{
Q={q_gen_7345, q_gen_7350, q_gen_7351},
Q_f={q_gen_7345},
Delta=
{
<leaf>() -> q_gen_7350
<leaf, z>() -> q_gen_7345
<node, s>(q_gen_7351, q_gen_7350, q_gen_7350) -> q_gen_7345
<a, z>() -> q_gen_7351
<b, z>() -> q_gen_7351
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_7344, q_gen_7348, q_gen_7367},
Q_f={q_gen_7344},
Delta=
{
<z>() -> q_gen_7367
<s, s>(q_gen_7348) -> q_gen_7348
<z, z>() -> q_gen_7348
<s, s, s>(q_gen_7344) -> q_gen_7344
<s, z, s>(q_gen_7348) -> q_gen_7344
<z, s, s>(q_gen_7348) -> q_gen_7344
<z, z, s>(q_gen_7367) -> q_gen_7344
<z, z, z>() -> q_gen_7344
}

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

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

Teacher's answer:
New clause system:
{
() -> height([leaf, z]) -> 7
() -> leq([z, n2]) -> 7
() -> numnodes([leaf, z]) -> 7
() -> plus([n, z, n]) -> 7
(height([t1, _mba]) /\ height([t2, _nba]) /\ max([_mba, _nba, _oba])) -> height([node(e, t1, t2), s(_oba)]) -> 7
(height([t1, _yba]) /\ numnodes([t1, _zba])) -> leq([_yba, _zba]) -> 7
(leq([n, m])) -> max([n, m, m]) -> 7
(not leq([n, m])) -> max([n, m, n]) -> 9
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 7
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 7
(leq([s(nn1), z])) -> BOT -> 9
(numnodes([t1, _sba]) /\ numnodes([t2, _tba]) /\ plus([_sba, _tba, _uba])) -> numnodes([node(e, t1, t2), s(_uba)]) -> 7
(plus([n, mm, _hba])) -> plus([n, s(mm), s(_hba)]) -> 10
}
Sat witness: Found: ((plus([n, mm, _hba])) -> plus([n, s(mm), s(_hba)]), {
_hba -> s(z)  ;  mm -> z  ;  n -> z
})

-------------------------------------------
Step 20, which took 0.012852 s (model generation: 0.011796,  model checking: 0.001056):

Model:
|_
{
height -> 
{{{
Q={q_gen_7346, q_gen_7354, q_gen_7355},
Q_f={q_gen_7346},
Delta=
{
<leaf>() -> q_gen_7354
<leaf, z>() -> q_gen_7346
<node, s>(q_gen_7355, q_gen_7354, q_gen_7354) -> q_gen_7346
<a, z>() -> q_gen_7355
<b, z>() -> q_gen_7355
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_7342, q_gen_7357, q_gen_7374},
Q_f={q_gen_7342},
Delta=
{
<s>(q_gen_7357) -> q_gen_7357
<z>() -> q_gen_7357
<s, s>(q_gen_7342) -> q_gen_7342
<z, s>(q_gen_7357) -> q_gen_7342
<z, z>() -> q_gen_7342
<s, z>(q_gen_7357) -> q_gen_7374
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  max -> 
{{{
Q={q_gen_7343, q_gen_7359, q_gen_7371},
Q_f={q_gen_7343},
Delta=
{
<z>() -> q_gen_7359
<z, z>() -> q_gen_7371
<s, z, s>(q_gen_7371) -> q_gen_7343
<z, s, s>(q_gen_7371) -> q_gen_7343
<z, s, z>(q_gen_7359) -> q_gen_7343
<z, z, z>() -> q_gen_7343
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  numnodes -> 
{{{
Q={q_gen_7345, q_gen_7350, q_gen_7351},
Q_f={q_gen_7345},
Delta=
{
<leaf>() -> q_gen_7350
<leaf, z>() -> q_gen_7345
<node, s>(q_gen_7351, q_gen_7350, q_gen_7350) -> q_gen_7345
<a, z>() -> q_gen_7351
<b, z>() -> q_gen_7351
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_7344, q_gen_7348, q_gen_7367},
Q_f={q_gen_7344},
Delta=
{
<z>() -> q_gen_7367
<s, s>(q_gen_7348) -> q_gen_7348
<z, s>(q_gen_7367) -> q_gen_7348
<z, z>() -> q_gen_7348
<s, s, s>(q_gen_7344) -> q_gen_7344
<s, z, s>(q_gen_7348) -> q_gen_7344
<z, s, s>(q_gen_7348) -> q_gen_7344
<z, z, s>(q_gen_7367) -> q_gen_7344
<z, z, z>() -> q_gen_7344
}

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

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

Teacher's answer:
New clause system:
{
() -> height([leaf, z]) -> 7
() -> leq([z, n2]) -> 7
() -> numnodes([leaf, z]) -> 7
() -> plus([n, z, n]) -> 7
(height([t1, _mba]) /\ height([t2, _nba]) /\ max([_mba, _nba, _oba])) -> height([node(e, t1, t2), s(_oba)]) -> 7
(height([t1, _yba]) /\ numnodes([t1, _zba])) -> leq([_yba, _zba]) -> 7
(leq([n, m])) -> max([n, m, m]) -> 7
(not leq([n, m])) -> max([n, m, n]) -> 9
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 7
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 7
(leq([s(nn1), z])) -> BOT -> 9
(numnodes([t1, _sba]) /\ numnodes([t2, _tba]) /\ plus([_sba, _tba, _uba])) -> numnodes([node(e, t1, t2), s(_uba)]) -> 10
(plus([n, mm, _hba])) -> plus([n, s(mm), s(_hba)]) -> 10
}
Sat witness: Found: ((numnodes([t1, _sba]) /\ numnodes([t2, _tba]) /\ plus([_sba, _tba, _uba])) -> numnodes([node(e, t1, t2), s(_uba)]), {
_sba -> z  ;  _tba -> z  ;  _uba -> s(z)  ;  e -> b  ;  t1 -> leaf  ;  t2 -> leaf
})

-------------------------------------------
Step 21, which took 0.013044 s (model generation: 0.012699,  model checking: 0.000345):

Model:
|_
{
height -> 
{{{
Q={q_gen_7346, q_gen_7354, q_gen_7355},
Q_f={q_gen_7346},
Delta=
{
<leaf>() -> q_gen_7354
<leaf, z>() -> q_gen_7346
<node, s>(q_gen_7355, q_gen_7354, q_gen_7354) -> q_gen_7346
<a, z>() -> q_gen_7355
<b, z>() -> q_gen_7355
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_7342, q_gen_7357, q_gen_7374},
Q_f={q_gen_7342},
Delta=
{
<s>(q_gen_7357) -> q_gen_7357
<z>() -> q_gen_7357
<s, s>(q_gen_7342) -> q_gen_7342
<z, s>(q_gen_7357) -> q_gen_7342
<z, z>() -> q_gen_7342
<s, z>(q_gen_7357) -> q_gen_7374
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  max -> 
{{{
Q={q_gen_7343, q_gen_7359, q_gen_7371},
Q_f={q_gen_7343},
Delta=
{
<z>() -> q_gen_7359
<z, z>() -> q_gen_7371
<s, z, s>(q_gen_7371) -> q_gen_7343
<z, s, s>(q_gen_7371) -> q_gen_7343
<z, s, z>(q_gen_7359) -> q_gen_7343
<z, z, z>() -> q_gen_7343
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  numnodes -> 
{{{
Q={q_gen_7345, q_gen_7350, q_gen_7351, q_gen_7380},
Q_f={q_gen_7345},
Delta=
{
<leaf>() -> q_gen_7350
<z>() -> q_gen_7380
<leaf, z>() -> q_gen_7345
<node, s>(q_gen_7351, q_gen_7350, q_gen_7350) -> q_gen_7345
<a, z>() -> q_gen_7351
<b, s>(q_gen_7380) -> q_gen_7351
<b, z>() -> q_gen_7351
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_7344, q_gen_7348, q_gen_7367},
Q_f={q_gen_7344},
Delta=
{
<z>() -> q_gen_7367
<s, s>(q_gen_7348) -> q_gen_7348
<z, s>(q_gen_7367) -> q_gen_7348
<z, z>() -> q_gen_7348
<s, s, s>(q_gen_7344) -> q_gen_7344
<s, z, s>(q_gen_7348) -> q_gen_7344
<z, s, s>(q_gen_7348) -> q_gen_7344
<z, z, s>(q_gen_7367) -> q_gen_7344
<z, z, z>() -> q_gen_7344
}

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

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

Teacher's answer:
New clause system:
{
() -> height([leaf, z]) -> 7
() -> leq([z, n2]) -> 7
() -> numnodes([leaf, z]) -> 7
() -> plus([n, z, n]) -> 7
(height([t1, _mba]) /\ height([t2, _nba]) /\ max([_mba, _nba, _oba])) -> height([node(e, t1, t2), s(_oba)]) -> 7
(height([t1, _yba]) /\ numnodes([t1, _zba])) -> leq([_yba, _zba]) -> 7
(leq([n, m])) -> max([n, m, m]) -> 10
(not leq([n, m])) -> max([n, m, n]) -> 9
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 8
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 8
(leq([s(nn1), z])) -> BOT -> 9
(numnodes([t1, _sba]) /\ numnodes([t2, _tba]) /\ plus([_sba, _tba, _uba])) -> numnodes([node(e, t1, t2), s(_uba)]) -> 10
(plus([n, mm, _hba])) -> plus([n, s(mm), s(_hba)]) -> 10
}
Sat witness: Found: ((leq([n, m])) -> max([n, m, m]), {
m -> s(z)  ;  n -> s(z)
})

-------------------------------------------
Step 22, which took 0.014015 s (model generation: 0.012654,  model checking: 0.001361):

Model:
|_
{
height -> 
{{{
Q={q_gen_7346, q_gen_7354, q_gen_7355},
Q_f={q_gen_7346},
Delta=
{
<leaf>() -> q_gen_7354
<leaf, z>() -> q_gen_7346
<node, s>(q_gen_7355, q_gen_7354, q_gen_7354) -> q_gen_7346
<a, z>() -> q_gen_7355
<b, z>() -> q_gen_7355
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_7342, q_gen_7357, q_gen_7374},
Q_f={q_gen_7342},
Delta=
{
<s>(q_gen_7357) -> q_gen_7357
<z>() -> q_gen_7357
<s, s>(q_gen_7342) -> q_gen_7342
<z, s>(q_gen_7357) -> q_gen_7342
<z, z>() -> q_gen_7342
<s, z>(q_gen_7357) -> q_gen_7374
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  max -> 
{{{
Q={q_gen_7343, q_gen_7359, q_gen_7371},
Q_f={q_gen_7343},
Delta=
{
<z>() -> q_gen_7359
<z, z>() -> q_gen_7371
<s, s, s>(q_gen_7343) -> q_gen_7343
<s, z, s>(q_gen_7371) -> q_gen_7343
<z, s, s>(q_gen_7371) -> q_gen_7343
<z, s, z>(q_gen_7359) -> q_gen_7343
<z, z, z>() -> q_gen_7343
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  numnodes -> 
{{{
Q={q_gen_7345, q_gen_7350, q_gen_7351, q_gen_7380},
Q_f={q_gen_7345},
Delta=
{
<leaf>() -> q_gen_7350
<z>() -> q_gen_7380
<leaf, z>() -> q_gen_7345
<node, s>(q_gen_7351, q_gen_7350, q_gen_7350) -> q_gen_7345
<a, z>() -> q_gen_7351
<b, s>(q_gen_7380) -> q_gen_7351
<b, z>() -> q_gen_7351
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_7344, q_gen_7348, q_gen_7367},
Q_f={q_gen_7344},
Delta=
{
<z>() -> q_gen_7367
<s, s>(q_gen_7348) -> q_gen_7348
<z, s>(q_gen_7367) -> q_gen_7348
<z, z>() -> q_gen_7348
<s, s, s>(q_gen_7344) -> q_gen_7344
<s, z, s>(q_gen_7348) -> q_gen_7344
<z, s, s>(q_gen_7348) -> q_gen_7344
<z, z, s>(q_gen_7367) -> q_gen_7344
<z, z, z>() -> q_gen_7344
}

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

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

Teacher's answer:
New clause system:
{
() -> height([leaf, z]) -> 7
() -> leq([z, n2]) -> 7
() -> numnodes([leaf, z]) -> 7
() -> plus([n, z, n]) -> 7
(height([t1, _mba]) /\ height([t2, _nba]) /\ max([_mba, _nba, _oba])) -> height([node(e, t1, t2), s(_oba)]) -> 10
(height([t1, _yba]) /\ numnodes([t1, _zba])) -> leq([_yba, _zba]) -> 8
(leq([n, m])) -> max([n, m, m]) -> 10
(not leq([n, m])) -> max([n, m, n]) -> 9
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 8
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 8
(leq([s(nn1), z])) -> BOT -> 9
(numnodes([t1, _sba]) /\ numnodes([t2, _tba]) /\ plus([_sba, _tba, _uba])) -> numnodes([node(e, t1, t2), s(_uba)]) -> 10
(plus([n, mm, _hba])) -> plus([n, s(mm), s(_hba)]) -> 10
}
Sat witness: Found: ((height([t1, _mba]) /\ height([t2, _nba]) /\ max([_mba, _nba, _oba])) -> height([node(e, t1, t2), s(_oba)]), {
_mba -> z  ;  _nba -> s(z)  ;  _oba -> z  ;  e -> b  ;  t1 -> leaf  ;  t2 -> node(a, leaf, leaf)
})

-------------------------------------------
Step 23, which took 0.014212 s (model generation: 0.013352,  model checking: 0.000860):

Model:
|_
{
height -> 
{{{
Q={q_gen_7346, q_gen_7354, q_gen_7355, q_gen_7384},
Q_f={q_gen_7346},
Delta=
{
<leaf>() -> q_gen_7354
<node>(q_gen_7384, q_gen_7354, q_gen_7354) -> q_gen_7354
<a>() -> q_gen_7384
<leaf, z>() -> q_gen_7346
<node, s>(q_gen_7355, q_gen_7354, q_gen_7354) -> q_gen_7346
<a, z>() -> q_gen_7355
<b, z>() -> q_gen_7355
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_7342, q_gen_7357, q_gen_7374},
Q_f={q_gen_7342},
Delta=
{
<s>(q_gen_7357) -> q_gen_7357
<z>() -> q_gen_7357
<s, s>(q_gen_7342) -> q_gen_7342
<z, s>(q_gen_7357) -> q_gen_7342
<z, z>() -> q_gen_7342
<s, z>(q_gen_7357) -> q_gen_7374
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  max -> 
{{{
Q={q_gen_7343, q_gen_7359, q_gen_7371},
Q_f={q_gen_7343},
Delta=
{
<z>() -> q_gen_7359
<z, z>() -> q_gen_7371
<s, s, s>(q_gen_7343) -> q_gen_7343
<s, z, s>(q_gen_7371) -> q_gen_7343
<z, s, s>(q_gen_7371) -> q_gen_7343
<z, s, z>(q_gen_7359) -> q_gen_7343
<z, z, z>() -> q_gen_7343
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  numnodes -> 
{{{
Q={q_gen_7345, q_gen_7350, q_gen_7351, q_gen_7380},
Q_f={q_gen_7345},
Delta=
{
<leaf>() -> q_gen_7350
<z>() -> q_gen_7380
<leaf, z>() -> q_gen_7345
<node, s>(q_gen_7351, q_gen_7350, q_gen_7350) -> q_gen_7345
<a, z>() -> q_gen_7351
<b, s>(q_gen_7380) -> q_gen_7351
<b, z>() -> q_gen_7351
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_7344, q_gen_7348, q_gen_7367},
Q_f={q_gen_7344},
Delta=
{
<z>() -> q_gen_7367
<s, s>(q_gen_7348) -> q_gen_7348
<z, s>(q_gen_7367) -> q_gen_7348
<z, z>() -> q_gen_7348
<s, s, s>(q_gen_7344) -> q_gen_7344
<s, z, s>(q_gen_7348) -> q_gen_7344
<z, s, s>(q_gen_7348) -> q_gen_7344
<z, z, s>(q_gen_7367) -> q_gen_7344
<z, z, z>() -> q_gen_7344
}

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

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

Teacher's answer:
New clause system:
{
() -> height([leaf, z]) -> 8
() -> leq([z, n2]) -> 8
() -> numnodes([leaf, z]) -> 8
() -> plus([n, z, n]) -> 8
(height([t1, _mba]) /\ height([t2, _nba]) /\ max([_mba, _nba, _oba])) -> height([node(e, t1, t2), s(_oba)]) -> 10
(height([t1, _yba]) /\ numnodes([t1, _zba])) -> leq([_yba, _zba]) -> 9
(leq([n, m])) -> max([n, m, m]) -> 10
(not leq([n, m])) -> max([n, m, n]) -> 12
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 9
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 9
(leq([s(nn1), z])) -> BOT -> 10
(numnodes([t1, _sba]) /\ numnodes([t2, _tba]) /\ plus([_sba, _tba, _uba])) -> numnodes([node(e, t1, t2), s(_uba)]) -> 10
(plus([n, mm, _hba])) -> plus([n, s(mm), s(_hba)]) -> 10
}
Sat witness: Found: ((not leq([n, m])) -> max([n, m, n]), {
m -> z  ;  n -> s(s(z))
})

-------------------------------------------
Step 24, which took 0.015642 s (model generation: 0.014722,  model checking: 0.000920):

Model:
|_
{
height -> 
{{{
Q={q_gen_7346, q_gen_7354, q_gen_7355, q_gen_7384},
Q_f={q_gen_7346},
Delta=
{
<leaf>() -> q_gen_7354
<node>(q_gen_7384, q_gen_7354, q_gen_7354) -> q_gen_7354
<a>() -> q_gen_7384
<leaf, z>() -> q_gen_7346
<node, s>(q_gen_7355, q_gen_7354, q_gen_7354) -> q_gen_7346
<a, z>() -> q_gen_7355
<b, z>() -> q_gen_7355
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_7342, q_gen_7357, q_gen_7374},
Q_f={q_gen_7342},
Delta=
{
<s>(q_gen_7357) -> q_gen_7357
<z>() -> q_gen_7357
<s, s>(q_gen_7342) -> q_gen_7342
<z, s>(q_gen_7357) -> q_gen_7342
<z, z>() -> q_gen_7342
<s, z>(q_gen_7357) -> q_gen_7374
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  max -> 
{{{
Q={q_gen_7343, q_gen_7359, q_gen_7371},
Q_f={q_gen_7343},
Delta=
{
<z>() -> q_gen_7359
<s, s>(q_gen_7371) -> q_gen_7371
<z, z>() -> q_gen_7371
<s, s, s>(q_gen_7343) -> q_gen_7343
<s, z, s>(q_gen_7371) -> q_gen_7343
<z, s, s>(q_gen_7371) -> q_gen_7343
<z, s, z>(q_gen_7359) -> q_gen_7343
<z, z, z>() -> q_gen_7343
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  numnodes -> 
{{{
Q={q_gen_7345, q_gen_7350, q_gen_7351, q_gen_7380},
Q_f={q_gen_7345},
Delta=
{
<leaf>() -> q_gen_7350
<z>() -> q_gen_7380
<leaf, z>() -> q_gen_7345
<node, s>(q_gen_7351, q_gen_7350, q_gen_7350) -> q_gen_7345
<a, z>() -> q_gen_7351
<b, s>(q_gen_7380) -> q_gen_7351
<b, z>() -> q_gen_7351
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_7344, q_gen_7348, q_gen_7367},
Q_f={q_gen_7344},
Delta=
{
<z>() -> q_gen_7367
<s, s>(q_gen_7348) -> q_gen_7348
<z, s>(q_gen_7367) -> q_gen_7348
<z, z>() -> q_gen_7348
<s, s, s>(q_gen_7344) -> q_gen_7344
<s, z, s>(q_gen_7348) -> q_gen_7344
<z, s, s>(q_gen_7348) -> q_gen_7344
<z, z, s>(q_gen_7367) -> q_gen_7344
<z, z, z>() -> q_gen_7344
}

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

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

Teacher's answer:
New clause system:
{
() -> height([leaf, z]) -> 9
() -> leq([z, n2]) -> 9
() -> numnodes([leaf, z]) -> 9
() -> plus([n, z, n]) -> 9
(height([t1, _mba]) /\ height([t2, _nba]) /\ max([_mba, _nba, _oba])) -> height([node(e, t1, t2), s(_oba)]) -> 10
(height([t1, _yba]) /\ numnodes([t1, _zba])) -> leq([_yba, _zba]) -> 10
(leq([n, m])) -> max([n, m, m]) -> 10
(not leq([n, m])) -> max([n, m, n]) -> 12
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 10
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 10
(leq([s(nn1), z])) -> BOT -> 10
(numnodes([t1, _sba]) /\ numnodes([t2, _tba]) /\ plus([_sba, _tba, _uba])) -> numnodes([node(e, t1, t2), s(_uba)]) -> 10
(plus([n, mm, _hba])) -> plus([n, s(mm), s(_hba)]) -> 13
}
Sat witness: Found: ((plus([n, mm, _hba])) -> plus([n, s(mm), s(_hba)]), {
_hba -> s(s(z))  ;  mm -> z  ;  n -> s(z)
})

-------------------------------------------
Step 25, which took 0.016789 s (model generation: 0.015275,  model checking: 0.001514):

Model:
|_
{
height -> 
{{{
Q={q_gen_7346, q_gen_7354, q_gen_7355, q_gen_7384},
Q_f={q_gen_7346},
Delta=
{
<leaf>() -> q_gen_7354
<node>(q_gen_7384, q_gen_7354, q_gen_7354) -> q_gen_7354
<a>() -> q_gen_7384
<leaf, z>() -> q_gen_7346
<node, s>(q_gen_7355, q_gen_7354, q_gen_7354) -> q_gen_7346
<a, z>() -> q_gen_7355
<b, z>() -> q_gen_7355
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_7342, q_gen_7357, q_gen_7374},
Q_f={q_gen_7342},
Delta=
{
<s>(q_gen_7357) -> q_gen_7357
<z>() -> q_gen_7357
<s, s>(q_gen_7342) -> q_gen_7342
<z, s>(q_gen_7357) -> q_gen_7342
<z, z>() -> q_gen_7342
<s, z>(q_gen_7357) -> q_gen_7374
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  max -> 
{{{
Q={q_gen_7343, q_gen_7359, q_gen_7371},
Q_f={q_gen_7343},
Delta=
{
<z>() -> q_gen_7359
<s, s>(q_gen_7371) -> q_gen_7371
<z, z>() -> q_gen_7371
<s, s, s>(q_gen_7343) -> q_gen_7343
<s, z, s>(q_gen_7371) -> q_gen_7343
<z, s, s>(q_gen_7371) -> q_gen_7343
<z, s, z>(q_gen_7359) -> q_gen_7343
<z, z, z>() -> q_gen_7343
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  numnodes -> 
{{{
Q={q_gen_7345, q_gen_7350, q_gen_7351, q_gen_7380},
Q_f={q_gen_7345},
Delta=
{
<leaf>() -> q_gen_7350
<z>() -> q_gen_7380
<leaf, z>() -> q_gen_7345
<node, s>(q_gen_7351, q_gen_7350, q_gen_7350) -> q_gen_7345
<a, z>() -> q_gen_7351
<b, s>(q_gen_7380) -> q_gen_7351
<b, z>() -> q_gen_7351
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_7344, q_gen_7348, q_gen_7367},
Q_f={q_gen_7344},
Delta=
{
<s>(q_gen_7367) -> q_gen_7367
<z>() -> q_gen_7367
<s, s>(q_gen_7348) -> q_gen_7348
<z, s>(q_gen_7367) -> q_gen_7348
<z, z>() -> q_gen_7348
<s, s, s>(q_gen_7344) -> q_gen_7344
<s, z, s>(q_gen_7348) -> q_gen_7344
<z, s, s>(q_gen_7348) -> q_gen_7344
<z, z, s>(q_gen_7367) -> q_gen_7344
<z, z, z>() -> q_gen_7344
}

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

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

Teacher's answer:
New clause system:
{
() -> height([leaf, z]) -> 10
() -> leq([z, n2]) -> 10
() -> numnodes([leaf, z]) -> 10
() -> plus([n, z, n]) -> 10
(height([t1, _mba]) /\ height([t2, _nba]) /\ max([_mba, _nba, _oba])) -> height([node(e, t1, t2), s(_oba)]) -> 10
(height([t1, _yba]) /\ numnodes([t1, _zba])) -> leq([_yba, _zba]) -> 10
(leq([n, m])) -> max([n, m, m]) -> 10
(not leq([n, m])) -> max([n, m, n]) -> 12
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 10
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 10
(leq([s(nn1), z])) -> BOT -> 10
(numnodes([t1, _sba]) /\ numnodes([t2, _tba]) /\ plus([_sba, _tba, _uba])) -> numnodes([node(e, t1, t2), s(_uba)]) -> 13
(plus([n, mm, _hba])) -> plus([n, s(mm), s(_hba)]) -> 13
}
Sat witness: Found: ((numnodes([t1, _sba]) /\ numnodes([t2, _tba]) /\ plus([_sba, _tba, _uba])) -> numnodes([node(e, t1, t2), s(_uba)]), {
_sba -> z  ;  _tba -> z  ;  _uba -> s(z)  ;  e -> a  ;  t1 -> leaf  ;  t2 -> leaf
})

-------------------------------------------
Step 26, which took 0.018465 s (model generation: 0.016320,  model checking: 0.002145):

Model:
|_
{
height -> 
{{{
Q={q_gen_7346, q_gen_7354, q_gen_7355, q_gen_7384},
Q_f={q_gen_7346},
Delta=
{
<leaf>() -> q_gen_7354
<node>(q_gen_7384, q_gen_7354, q_gen_7354) -> q_gen_7354
<a>() -> q_gen_7384
<leaf, z>() -> q_gen_7346
<node, s>(q_gen_7355, q_gen_7354, q_gen_7354) -> q_gen_7346
<a, z>() -> q_gen_7355
<b, z>() -> q_gen_7355
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_7342, q_gen_7357, q_gen_7374},
Q_f={q_gen_7342},
Delta=
{
<s>(q_gen_7357) -> q_gen_7357
<z>() -> q_gen_7357
<s, s>(q_gen_7342) -> q_gen_7342
<z, s>(q_gen_7357) -> q_gen_7342
<z, z>() -> q_gen_7342
<s, z>(q_gen_7357) -> q_gen_7374
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  max -> 
{{{
Q={q_gen_7343, q_gen_7359, q_gen_7371},
Q_f={q_gen_7343},
Delta=
{
<z>() -> q_gen_7359
<s, s>(q_gen_7371) -> q_gen_7371
<z, z>() -> q_gen_7371
<s, s, s>(q_gen_7343) -> q_gen_7343
<s, z, s>(q_gen_7371) -> q_gen_7343
<z, s, s>(q_gen_7371) -> q_gen_7343
<z, s, z>(q_gen_7359) -> q_gen_7343
<z, z, z>() -> q_gen_7343
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  numnodes -> 
{{{
Q={q_gen_7345, q_gen_7350, q_gen_7351, q_gen_7380},
Q_f={q_gen_7345},
Delta=
{
<leaf>() -> q_gen_7350
<z>() -> q_gen_7380
<leaf, z>() -> q_gen_7345
<node, s>(q_gen_7351, q_gen_7350, q_gen_7350) -> q_gen_7345
<a, s>(q_gen_7380) -> q_gen_7351
<a, z>() -> q_gen_7351
<b, s>(q_gen_7380) -> q_gen_7351
<b, z>() -> q_gen_7351
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_7344, q_gen_7348, q_gen_7367},
Q_f={q_gen_7344},
Delta=
{
<s>(q_gen_7367) -> q_gen_7367
<z>() -> q_gen_7367
<s, s>(q_gen_7348) -> q_gen_7348
<z, s>(q_gen_7367) -> q_gen_7348
<z, z>() -> q_gen_7348
<s, s, s>(q_gen_7344) -> q_gen_7344
<s, z, s>(q_gen_7348) -> q_gen_7344
<z, s, s>(q_gen_7348) -> q_gen_7344
<z, z, s>(q_gen_7367) -> q_gen_7344
<z, z, z>() -> q_gen_7344
}

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

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

Teacher's answer:
New clause system:
{
() -> height([leaf, z]) -> 10
() -> leq([z, n2]) -> 10
() -> numnodes([leaf, z]) -> 10
() -> plus([n, z, n]) -> 10
(height([t1, _mba]) /\ height([t2, _nba]) /\ max([_mba, _nba, _oba])) -> height([node(e, t1, t2), s(_oba)]) -> 13
(height([t1, _yba]) /\ numnodes([t1, _zba])) -> leq([_yba, _zba]) -> 11
(leq([n, m])) -> max([n, m, m]) -> 11
(not leq([n, m])) -> max([n, m, n]) -> 12
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 11
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 11
(leq([s(nn1), z])) -> BOT -> 11
(numnodes([t1, _sba]) /\ numnodes([t2, _tba]) /\ plus([_sba, _tba, _uba])) -> numnodes([node(e, t1, t2), s(_uba)]) -> 13
(plus([n, mm, _hba])) -> plus([n, s(mm), s(_hba)]) -> 13
}
Sat witness: Found: ((height([t1, _mba]) /\ height([t2, _nba]) /\ max([_mba, _nba, _oba])) -> height([node(e, t1, t2), s(_oba)]), {
_mba -> z  ;  _nba -> s(z)  ;  _oba -> z  ;  e -> b  ;  t1 -> leaf  ;  t2 -> node(b, leaf, leaf)
})

-------------------------------------------
Step 27, which took 0.019382 s (model generation: 0.017262,  model checking: 0.002120):

Model:
|_
{
height -> 
{{{
Q={q_gen_7346, q_gen_7354, q_gen_7355, q_gen_7384},
Q_f={q_gen_7346},
Delta=
{
<leaf>() -> q_gen_7354
<node>(q_gen_7384, q_gen_7354, q_gen_7354) -> q_gen_7354
<a>() -> q_gen_7384
<b>() -> q_gen_7384
<leaf, z>() -> q_gen_7346
<node, s>(q_gen_7355, q_gen_7354, q_gen_7354) -> q_gen_7346
<a, z>() -> q_gen_7355
<b, z>() -> q_gen_7355
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_7342, q_gen_7357, q_gen_7374},
Q_f={q_gen_7342},
Delta=
{
<s>(q_gen_7357) -> q_gen_7357
<z>() -> q_gen_7357
<s, s>(q_gen_7342) -> q_gen_7342
<z, s>(q_gen_7357) -> q_gen_7342
<z, z>() -> q_gen_7342
<s, z>(q_gen_7357) -> q_gen_7374
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  max -> 
{{{
Q={q_gen_7343, q_gen_7359, q_gen_7371},
Q_f={q_gen_7343},
Delta=
{
<z>() -> q_gen_7359
<s, s>(q_gen_7371) -> q_gen_7371
<z, z>() -> q_gen_7371
<s, s, s>(q_gen_7343) -> q_gen_7343
<s, z, s>(q_gen_7371) -> q_gen_7343
<z, s, s>(q_gen_7371) -> q_gen_7343
<z, s, z>(q_gen_7359) -> q_gen_7343
<z, z, z>() -> q_gen_7343
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  numnodes -> 
{{{
Q={q_gen_7345, q_gen_7350, q_gen_7351, q_gen_7380},
Q_f={q_gen_7345},
Delta=
{
<leaf>() -> q_gen_7350
<z>() -> q_gen_7380
<leaf, z>() -> q_gen_7345
<node, s>(q_gen_7351, q_gen_7350, q_gen_7350) -> q_gen_7345
<a, s>(q_gen_7380) -> q_gen_7351
<a, z>() -> q_gen_7351
<b, s>(q_gen_7380) -> q_gen_7351
<b, z>() -> q_gen_7351
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_7344, q_gen_7348, q_gen_7367},
Q_f={q_gen_7344},
Delta=
{
<s>(q_gen_7367) -> q_gen_7367
<z>() -> q_gen_7367
<s, s>(q_gen_7348) -> q_gen_7348
<z, s>(q_gen_7367) -> q_gen_7348
<z, z>() -> q_gen_7348
<s, s, s>(q_gen_7344) -> q_gen_7344
<s, z, s>(q_gen_7348) -> q_gen_7344
<z, s, s>(q_gen_7348) -> q_gen_7344
<z, z, s>(q_gen_7367) -> q_gen_7344
<z, z, z>() -> q_gen_7344
}

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

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

Teacher's answer:
New clause system:
{
() -> height([leaf, z]) -> 11
() -> leq([z, n2]) -> 11
() -> numnodes([leaf, z]) -> 11
() -> plus([n, z, n]) -> 11
(height([t1, _mba]) /\ height([t2, _nba]) /\ max([_mba, _nba, _oba])) -> height([node(e, t1, t2), s(_oba)]) -> 13
(height([t1, _yba]) /\ numnodes([t1, _zba])) -> leq([_yba, _zba]) -> 12
(leq([n, m])) -> max([n, m, m]) -> 12
(not leq([n, m])) -> max([n, m, n]) -> 13
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 12
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 12
(leq([s(nn1), z])) -> BOT -> 12
(numnodes([t1, _sba]) /\ numnodes([t2, _tba]) /\ plus([_sba, _tba, _uba])) -> numnodes([node(e, t1, t2), s(_uba)]) -> 16
(plus([n, mm, _hba])) -> plus([n, s(mm), s(_hba)]) -> 14
}
Sat witness: Found: ((numnodes([t1, _sba]) /\ numnodes([t2, _tba]) /\ plus([_sba, _tba, _uba])) -> numnodes([node(e, t1, t2), s(_uba)]), {
_sba -> z  ;  _tba -> z  ;  _uba -> s(s(z))  ;  e -> b  ;  t1 -> leaf  ;  t2 -> leaf
})

-------------------------------------------
Step 28, which took 0.021194 s (model generation: 0.019355,  model checking: 0.001839):

Model:
|_
{
height -> 
{{{
Q={q_gen_7346, q_gen_7354, q_gen_7355, q_gen_7384},
Q_f={q_gen_7346},
Delta=
{
<leaf>() -> q_gen_7354
<node>(q_gen_7384, q_gen_7354, q_gen_7354) -> q_gen_7354
<a>() -> q_gen_7384
<b>() -> q_gen_7384
<leaf, z>() -> q_gen_7346
<node, s>(q_gen_7355, q_gen_7354, q_gen_7354) -> q_gen_7346
<a, z>() -> q_gen_7355
<b, z>() -> q_gen_7355
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_7342, q_gen_7357, q_gen_7374},
Q_f={q_gen_7342},
Delta=
{
<s>(q_gen_7357) -> q_gen_7357
<z>() -> q_gen_7357
<s, s>(q_gen_7342) -> q_gen_7342
<z, s>(q_gen_7357) -> q_gen_7342
<z, z>() -> q_gen_7342
<s, z>(q_gen_7357) -> q_gen_7374
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  max -> 
{{{
Q={q_gen_7343, q_gen_7359, q_gen_7371},
Q_f={q_gen_7343},
Delta=
{
<z>() -> q_gen_7359
<s, s>(q_gen_7371) -> q_gen_7371
<z, z>() -> q_gen_7371
<s, s, s>(q_gen_7343) -> q_gen_7343
<s, z, s>(q_gen_7371) -> q_gen_7343
<z, s, s>(q_gen_7371) -> q_gen_7343
<z, s, z>(q_gen_7359) -> q_gen_7343
<z, z, z>() -> q_gen_7343
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  numnodes -> 
{{{
Q={q_gen_7345, q_gen_7350, q_gen_7351, q_gen_7380},
Q_f={q_gen_7345},
Delta=
{
<leaf>() -> q_gen_7350
<s>(q_gen_7380) -> q_gen_7380
<z>() -> q_gen_7380
<leaf, z>() -> q_gen_7345
<node, s>(q_gen_7351, q_gen_7350, q_gen_7350) -> q_gen_7345
<a, s>(q_gen_7380) -> q_gen_7351
<a, z>() -> q_gen_7351
<b, s>(q_gen_7380) -> q_gen_7351
<b, z>() -> q_gen_7351
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_7344, q_gen_7348, q_gen_7367},
Q_f={q_gen_7344},
Delta=
{
<s>(q_gen_7367) -> q_gen_7367
<z>() -> q_gen_7367
<s, s>(q_gen_7348) -> q_gen_7348
<z, s>(q_gen_7367) -> q_gen_7348
<z, z>() -> q_gen_7348
<s, s, s>(q_gen_7344) -> q_gen_7344
<s, z, s>(q_gen_7348) -> q_gen_7344
<z, s, s>(q_gen_7348) -> q_gen_7344
<z, z, s>(q_gen_7367) -> q_gen_7344
<z, z, z>() -> q_gen_7344
}

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

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

Teacher's answer:
New clause system:
{
() -> height([leaf, z]) -> 12
() -> leq([z, n2]) -> 12
() -> numnodes([leaf, z]) -> 12
() -> plus([n, z, n]) -> 12
(height([t1, _mba]) /\ height([t2, _nba]) /\ max([_mba, _nba, _oba])) -> height([node(e, t1, t2), s(_oba)]) -> 16
(height([t1, _yba]) /\ numnodes([t1, _zba])) -> leq([_yba, _zba]) -> 13
(leq([n, m])) -> max([n, m, m]) -> 13
(not leq([n, m])) -> max([n, m, n]) -> 14
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 13
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 13
(leq([s(nn1), z])) -> BOT -> 13
(numnodes([t1, _sba]) /\ numnodes([t2, _tba]) /\ plus([_sba, _tba, _uba])) -> numnodes([node(e, t1, t2), s(_uba)]) -> 16
(plus([n, mm, _hba])) -> plus([n, s(mm), s(_hba)]) -> 14
}
Sat witness: Found: ((height([t1, _mba]) /\ height([t2, _nba]) /\ max([_mba, _nba, _oba])) -> height([node(e, t1, t2), s(_oba)]), {
_mba -> z  ;  _nba -> s(z)  ;  _oba -> s(z)  ;  e -> b  ;  t1 -> leaf  ;  t2 -> node(b, node(b, leaf, leaf), node(b, leaf, leaf))
})

-------------------------------------------
Step 29, which took 0.022542 s (model generation: 0.021612,  model checking: 0.000930):

Model:
|_
{
height -> 
{{{
Q={q_gen_7346, q_gen_7354, q_gen_7355, q_gen_7384, q_gen_7404},
Q_f={q_gen_7346},
Delta=
{
<leaf>() -> q_gen_7354
<node>(q_gen_7384, q_gen_7354, q_gen_7354) -> q_gen_7354
<a>() -> q_gen_7384
<b>() -> q_gen_7384
<z>() -> q_gen_7404
<leaf, z>() -> q_gen_7346
<node, s>(q_gen_7355, q_gen_7354, q_gen_7354) -> q_gen_7346
<a, z>() -> q_gen_7355
<b, s>(q_gen_7404) -> q_gen_7355
<b, z>() -> q_gen_7355
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_7342, q_gen_7357, q_gen_7374},
Q_f={q_gen_7342},
Delta=
{
<s>(q_gen_7357) -> q_gen_7357
<z>() -> q_gen_7357
<s, s>(q_gen_7342) -> q_gen_7342
<z, s>(q_gen_7357) -> q_gen_7342
<z, z>() -> q_gen_7342
<s, z>(q_gen_7357) -> q_gen_7374
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  max -> 
{{{
Q={q_gen_7343, q_gen_7359, q_gen_7371},
Q_f={q_gen_7343},
Delta=
{
<z>() -> q_gen_7359
<s, s>(q_gen_7371) -> q_gen_7371
<z, z>() -> q_gen_7371
<s, s, s>(q_gen_7343) -> q_gen_7343
<s, z, s>(q_gen_7371) -> q_gen_7343
<z, s, s>(q_gen_7371) -> q_gen_7343
<z, s, z>(q_gen_7359) -> q_gen_7343
<z, z, z>() -> q_gen_7343
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  numnodes -> 
{{{
Q={q_gen_7345, q_gen_7350, q_gen_7351, q_gen_7380},
Q_f={q_gen_7345},
Delta=
{
<leaf>() -> q_gen_7350
<s>(q_gen_7380) -> q_gen_7380
<z>() -> q_gen_7380
<leaf, z>() -> q_gen_7345
<node, s>(q_gen_7351, q_gen_7350, q_gen_7350) -> q_gen_7345
<a, s>(q_gen_7380) -> q_gen_7351
<a, z>() -> q_gen_7351
<b, s>(q_gen_7380) -> q_gen_7351
<b, z>() -> q_gen_7351
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_7344, q_gen_7348, q_gen_7367},
Q_f={q_gen_7344},
Delta=
{
<s>(q_gen_7367) -> q_gen_7367
<z>() -> q_gen_7367
<s, s>(q_gen_7348) -> q_gen_7348
<z, s>(q_gen_7367) -> q_gen_7348
<z, z>() -> q_gen_7348
<s, s, s>(q_gen_7344) -> q_gen_7344
<s, z, s>(q_gen_7348) -> q_gen_7344
<z, s, s>(q_gen_7348) -> q_gen_7344
<z, z, s>(q_gen_7367) -> q_gen_7344
<z, z, z>() -> q_gen_7344
}

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

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

Teacher's answer:
New clause system:
{
() -> height([leaf, z]) -> 13
() -> leq([z, n2]) -> 13
() -> numnodes([leaf, z]) -> 13
() -> plus([n, z, n]) -> 13
(height([t1, _mba]) /\ height([t2, _nba]) /\ max([_mba, _nba, _oba])) -> height([node(e, t1, t2), s(_oba)]) -> 16
(height([t1, _yba]) /\ numnodes([t1, _zba])) -> leq([_yba, _zba]) -> 16
(leq([n, m])) -> max([n, m, m]) -> 14
(not leq([n, m])) -> max([n, m, n]) -> 14
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 14
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 14
(leq([s(nn1), z])) -> BOT -> 14
(numnodes([t1, _sba]) /\ numnodes([t2, _tba]) /\ plus([_sba, _tba, _uba])) -> numnodes([node(e, t1, t2), s(_uba)]) -> 16
(plus([n, mm, _hba])) -> plus([n, s(mm), s(_hba)]) -> 14
}
Sat witness: Found: ((height([t1, _yba]) /\ numnodes([t1, _zba])) -> leq([_yba, _zba]), {
_yba -> s(s(z))  ;  _zba -> s(z)  ;  t1 -> node(b, leaf, leaf)
})

-------------------------------------------
Step 30, which took 0.021986 s (model generation: 0.021277,  model checking: 0.000709):

Model:
|_
{
height -> 
{{{
Q={q_gen_7346, q_gen_7354, q_gen_7355, q_gen_7384, q_gen_7404},
Q_f={q_gen_7346},
Delta=
{
<leaf>() -> q_gen_7354
<node>(q_gen_7384, q_gen_7354, q_gen_7354) -> q_gen_7354
<a>() -> q_gen_7384
<b>() -> q_gen_7384
<z>() -> q_gen_7404
<leaf, z>() -> q_gen_7346
<node, s>(q_gen_7355, q_gen_7354, q_gen_7354) -> q_gen_7346
<a, z>() -> q_gen_7355
<b, s>(q_gen_7404) -> q_gen_7355
<b, z>() -> q_gen_7355
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_7342, q_gen_7357, q_gen_7374},
Q_f={q_gen_7342},
Delta=
{
<s>(q_gen_7357) -> q_gen_7357
<z>() -> q_gen_7357
<s, s>(q_gen_7342) -> q_gen_7342
<s, s>(q_gen_7374) -> q_gen_7342
<z, s>(q_gen_7357) -> q_gen_7342
<z, z>() -> q_gen_7342
<s, z>(q_gen_7357) -> q_gen_7374
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  max -> 
{{{
Q={q_gen_7343, q_gen_7359, q_gen_7371},
Q_f={q_gen_7343},
Delta=
{
<z>() -> q_gen_7359
<s, s>(q_gen_7371) -> q_gen_7371
<z, z>() -> q_gen_7371
<s, s, s>(q_gen_7343) -> q_gen_7343
<s, z, s>(q_gen_7371) -> q_gen_7343
<z, s, s>(q_gen_7371) -> q_gen_7343
<z, s, z>(q_gen_7359) -> q_gen_7343
<z, z, z>() -> q_gen_7343
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  numnodes -> 
{{{
Q={q_gen_7345, q_gen_7350, q_gen_7351, q_gen_7380},
Q_f={q_gen_7345},
Delta=
{
<leaf>() -> q_gen_7350
<s>(q_gen_7380) -> q_gen_7380
<z>() -> q_gen_7380
<leaf, z>() -> q_gen_7345
<node, s>(q_gen_7351, q_gen_7350, q_gen_7350) -> q_gen_7345
<a, s>(q_gen_7380) -> q_gen_7351
<a, z>() -> q_gen_7351
<b, s>(q_gen_7380) -> q_gen_7351
<b, z>() -> q_gen_7351
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_7344, q_gen_7348, q_gen_7367},
Q_f={q_gen_7344},
Delta=
{
<s>(q_gen_7367) -> q_gen_7367
<z>() -> q_gen_7367
<s, s>(q_gen_7348) -> q_gen_7348
<z, s>(q_gen_7367) -> q_gen_7348
<z, z>() -> q_gen_7348
<s, s, s>(q_gen_7344) -> q_gen_7344
<s, z, s>(q_gen_7348) -> q_gen_7344
<z, s, s>(q_gen_7348) -> q_gen_7344
<z, z, s>(q_gen_7367) -> q_gen_7344
<z, z, z>() -> q_gen_7344
}

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

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

Teacher's answer:
New clause system:
{
() -> height([leaf, z]) -> 14
() -> leq([z, n2]) -> 14
() -> numnodes([leaf, z]) -> 14
() -> plus([n, z, n]) -> 14
(height([t1, _mba]) /\ height([t2, _nba]) /\ max([_mba, _nba, _oba])) -> height([node(e, t1, t2), s(_oba)]) -> 16
(height([t1, _yba]) /\ numnodes([t1, _zba])) -> leq([_yba, _zba]) -> 16
(leq([n, m])) -> max([n, m, m]) -> 14
(not leq([n, m])) -> max([n, m, n]) -> 14
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 14
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 17
(leq([s(nn1), z])) -> BOT -> 15
(numnodes([t1, _sba]) /\ numnodes([t2, _tba]) /\ plus([_sba, _tba, _uba])) -> numnodes([node(e, t1, t2), s(_uba)]) -> 16
(plus([n, mm, _hba])) -> plus([n, s(mm), s(_hba)]) -> 15
}
Sat witness: Found: ((leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]), {
nn1 -> s(z)  ;  nn2 -> z
})

-------------------------------------------
Step 31, which took 0.023649 s (model generation: 0.021362,  model checking: 0.002287):

Model:
|_
{
height -> 
{{{
Q={q_gen_7346, q_gen_7354, q_gen_7355, q_gen_7383, q_gen_7384, q_gen_7400, q_gen_7403, q_gen_7404},
Q_f={q_gen_7346},
Delta=
{
<leaf>() -> q_gen_7354
<node>(q_gen_7384, q_gen_7383, q_gen_7383) -> q_gen_7354
<node>(q_gen_7384, q_gen_7354, q_gen_7354) -> q_gen_7383
<a>() -> q_gen_7384
<b>() -> q_gen_7384
<z>() -> q_gen_7404
<leaf, z>() -> q_gen_7346
<node, s>(q_gen_7355, q_gen_7354, q_gen_7354) -> q_gen_7346
<node, s>(q_gen_7355, q_gen_7354, q_gen_7383) -> q_gen_7346
<a, z>() -> q_gen_7355
<b, z>() -> q_gen_7355
<node, s>(q_gen_7355, q_gen_7383, q_gen_7383) -> q_gen_7400
<node, s>(q_gen_7403, q_gen_7354, q_gen_7354) -> q_gen_7400
<b, s>(q_gen_7404) -> q_gen_7403
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_7342, q_gen_7357, q_gen_7374},
Q_f={q_gen_7342},
Delta=
{
<s>(q_gen_7357) -> q_gen_7357
<z>() -> q_gen_7357
<s, s>(q_gen_7342) -> q_gen_7342
<z, s>(q_gen_7357) -> q_gen_7342
<z, z>() -> q_gen_7342
<s, s>(q_gen_7374) -> q_gen_7374
<s, z>(q_gen_7357) -> q_gen_7374
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  max -> 
{{{
Q={q_gen_7343, q_gen_7359, q_gen_7371},
Q_f={q_gen_7343},
Delta=
{
<z>() -> q_gen_7359
<s, s>(q_gen_7371) -> q_gen_7371
<z, z>() -> q_gen_7371
<s, s, s>(q_gen_7343) -> q_gen_7343
<s, z, s>(q_gen_7371) -> q_gen_7343
<z, s, s>(q_gen_7371) -> q_gen_7343
<z, s, z>(q_gen_7359) -> q_gen_7343
<z, z, z>() -> q_gen_7343
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  numnodes -> 
{{{
Q={q_gen_7345, q_gen_7350, q_gen_7351, q_gen_7380},
Q_f={q_gen_7345},
Delta=
{
<leaf>() -> q_gen_7350
<s>(q_gen_7380) -> q_gen_7380
<z>() -> q_gen_7380
<leaf, z>() -> q_gen_7345
<node, s>(q_gen_7351, q_gen_7350, q_gen_7350) -> q_gen_7345
<a, s>(q_gen_7380) -> q_gen_7351
<a, z>() -> q_gen_7351
<b, s>(q_gen_7380) -> q_gen_7351
<b, z>() -> q_gen_7351
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_7344, q_gen_7348, q_gen_7367},
Q_f={q_gen_7344},
Delta=
{
<s>(q_gen_7367) -> q_gen_7367
<z>() -> q_gen_7367
<s, s>(q_gen_7348) -> q_gen_7348
<z, s>(q_gen_7367) -> q_gen_7348
<z, z>() -> q_gen_7348
<s, s, s>(q_gen_7344) -> q_gen_7344
<s, z, s>(q_gen_7348) -> q_gen_7344
<z, s, s>(q_gen_7348) -> q_gen_7344
<z, z, s>(q_gen_7367) -> q_gen_7344
<z, z, z>() -> q_gen_7344
}

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

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

Teacher's answer:
New clause system:
{
() -> height([leaf, z]) -> 15
() -> leq([z, n2]) -> 15
() -> numnodes([leaf, z]) -> 15
() -> plus([n, z, n]) -> 15
(height([t1, _mba]) /\ height([t2, _nba]) /\ max([_mba, _nba, _oba])) -> height([node(e, t1, t2), s(_oba)]) -> 16
(height([t1, _yba]) /\ numnodes([t1, _zba])) -> leq([_yba, _zba]) -> 16
(leq([n, m])) -> max([n, m, m]) -> 15
(not leq([n, m])) -> max([n, m, n]) -> 15
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 15
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 17
(leq([s(nn1), z])) -> BOT -> 16
(numnodes([t1, _sba]) /\ numnodes([t2, _tba]) /\ plus([_sba, _tba, _uba])) -> numnodes([node(e, t1, t2), s(_uba)]) -> 19
(plus([n, mm, _hba])) -> plus([n, s(mm), s(_hba)]) -> 16
}
Sat witness: Found: ((numnodes([t1, _sba]) /\ numnodes([t2, _tba]) /\ plus([_sba, _tba, _uba])) -> numnodes([node(e, t1, t2), s(_uba)]), {
_sba -> z  ;  _tba -> s(z)  ;  _uba -> s(z)  ;  e -> b  ;  t1 -> leaf  ;  t2 -> node(a, leaf, leaf)
})

-------------------------------------------
Step 32, which took 0.045780 s (model generation: 0.023951,  model checking: 0.021829):

Model:
|_
{
height -> 
{{{
Q={q_gen_7346, q_gen_7354, q_gen_7355, q_gen_7383, q_gen_7384, q_gen_7400, q_gen_7403, q_gen_7404},
Q_f={q_gen_7346},
Delta=
{
<leaf>() -> q_gen_7354
<node>(q_gen_7384, q_gen_7383, q_gen_7383) -> q_gen_7354
<node>(q_gen_7384, q_gen_7354, q_gen_7354) -> q_gen_7383
<a>() -> q_gen_7384
<b>() -> q_gen_7384
<z>() -> q_gen_7404
<leaf, z>() -> q_gen_7346
<node, s>(q_gen_7355, q_gen_7354, q_gen_7354) -> q_gen_7346
<node, s>(q_gen_7355, q_gen_7354, q_gen_7383) -> q_gen_7346
<a, z>() -> q_gen_7355
<b, z>() -> q_gen_7355
<node, s>(q_gen_7355, q_gen_7383, q_gen_7383) -> q_gen_7400
<node, s>(q_gen_7403, q_gen_7354, q_gen_7354) -> q_gen_7400
<b, s>(q_gen_7404) -> q_gen_7403
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_7342, q_gen_7357, q_gen_7374},
Q_f={q_gen_7342},
Delta=
{
<s>(q_gen_7357) -> q_gen_7357
<z>() -> q_gen_7357
<s, s>(q_gen_7342) -> q_gen_7342
<z, s>(q_gen_7357) -> q_gen_7342
<z, z>() -> q_gen_7342
<s, s>(q_gen_7374) -> q_gen_7374
<s, z>(q_gen_7357) -> q_gen_7374
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  max -> 
{{{
Q={q_gen_7343, q_gen_7359, q_gen_7371},
Q_f={q_gen_7343},
Delta=
{
<z>() -> q_gen_7359
<s, s>(q_gen_7371) -> q_gen_7371
<z, z>() -> q_gen_7371
<s, s, s>(q_gen_7343) -> q_gen_7343
<s, z, s>(q_gen_7371) -> q_gen_7343
<z, s, s>(q_gen_7371) -> q_gen_7343
<z, s, z>(q_gen_7359) -> q_gen_7343
<z, z, z>() -> q_gen_7343
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  numnodes -> 
{{{
Q={q_gen_7345, q_gen_7350, q_gen_7351, q_gen_7380, q_gen_7409},
Q_f={q_gen_7345},
Delta=
{
<leaf>() -> q_gen_7350
<node>(q_gen_7409, q_gen_7350, q_gen_7350) -> q_gen_7350
<s>(q_gen_7380) -> q_gen_7380
<z>() -> q_gen_7380
<a>() -> q_gen_7409
<leaf, z>() -> q_gen_7345
<node, s>(q_gen_7351, q_gen_7350, q_gen_7350) -> q_gen_7345
<a, s>(q_gen_7380) -> q_gen_7351
<a, z>() -> q_gen_7351
<b, s>(q_gen_7380) -> q_gen_7351
<b, z>() -> q_gen_7351
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_7344, q_gen_7348, q_gen_7367},
Q_f={q_gen_7344},
Delta=
{
<s>(q_gen_7367) -> q_gen_7367
<z>() -> q_gen_7367
<s, s>(q_gen_7348) -> q_gen_7348
<z, s>(q_gen_7367) -> q_gen_7348
<z, z>() -> q_gen_7348
<s, s, s>(q_gen_7344) -> q_gen_7344
<s, z, s>(q_gen_7348) -> q_gen_7344
<z, s, s>(q_gen_7348) -> q_gen_7344
<z, z, s>(q_gen_7367) -> q_gen_7344
<z, z, z>() -> q_gen_7344
}

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

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

Teacher's answer:
New clause system:
{
() -> height([leaf, z]) -> 16
() -> leq([z, n2]) -> 16
() -> numnodes([leaf, z]) -> 16
() -> plus([n, z, n]) -> 16
(height([t1, _mba]) /\ height([t2, _nba]) /\ max([_mba, _nba, _oba])) -> height([node(e, t1, t2), s(_oba)]) -> 19
(height([t1, _yba]) /\ numnodes([t1, _zba])) -> leq([_yba, _zba]) -> 17
(leq([n, m])) -> max([n, m, m]) -> 16
(not leq([n, m])) -> max([n, m, n]) -> 16
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 16
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 17
(leq([s(nn1), z])) -> BOT -> 17
(numnodes([t1, _sba]) /\ numnodes([t2, _tba]) /\ plus([_sba, _tba, _uba])) -> numnodes([node(e, t1, t2), s(_uba)]) -> 19
(plus([n, mm, _hba])) -> plus([n, s(mm), s(_hba)]) -> 17
}
Sat witness: Found: ((height([t1, _mba]) /\ height([t2, _nba]) /\ max([_mba, _nba, _oba])) -> height([node(e, t1, t2), s(_oba)]), {
_mba -> z  ;  _nba -> s(z)  ;  _oba -> z  ;  e -> b  ;  t1 -> leaf  ;  t2 -> node(b, node(b, node(b, leaf, leaf), node(b, leaf, leaf)), node(b, leaf, leaf))
})

-------------------------------------------
Step 33, which took 0.047534 s (model generation: 0.034515,  model checking: 0.013019):

Model:
|_
{
height -> 
{{{
Q={q_gen_7346, q_gen_7354, q_gen_7355, q_gen_7383, q_gen_7384, q_gen_7400, q_gen_7403, q_gen_7404},
Q_f={q_gen_7346},
Delta=
{
<leaf>() -> q_gen_7354
<node>(q_gen_7384, q_gen_7354, q_gen_7383) -> q_gen_7354
<node>(q_gen_7384, q_gen_7383, q_gen_7383) -> q_gen_7354
<node>(q_gen_7384, q_gen_7354, q_gen_7354) -> q_gen_7383
<a>() -> q_gen_7384
<b>() -> q_gen_7384
<z>() -> q_gen_7404
<leaf, z>() -> q_gen_7346
<node, s>(q_gen_7355, q_gen_7354, q_gen_7354) -> q_gen_7346
<node, s>(q_gen_7355, q_gen_7354, q_gen_7383) -> q_gen_7346
<a, z>() -> q_gen_7355
<b, z>() -> q_gen_7355
<node, s>(q_gen_7355, q_gen_7383, q_gen_7383) -> q_gen_7400
<node, s>(q_gen_7403, q_gen_7354, q_gen_7354) -> q_gen_7400
<b, s>(q_gen_7404) -> q_gen_7403
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_7342, q_gen_7357, q_gen_7374},
Q_f={q_gen_7342},
Delta=
{
<s>(q_gen_7357) -> q_gen_7357
<z>() -> q_gen_7357
<s, s>(q_gen_7342) -> q_gen_7342
<z, s>(q_gen_7357) -> q_gen_7342
<z, z>() -> q_gen_7342
<s, s>(q_gen_7374) -> q_gen_7374
<s, z>(q_gen_7357) -> q_gen_7374
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  max -> 
{{{
Q={q_gen_7343, q_gen_7359, q_gen_7371},
Q_f={q_gen_7343},
Delta=
{
<z>() -> q_gen_7359
<s, s>(q_gen_7371) -> q_gen_7371
<z, z>() -> q_gen_7371
<s, s, s>(q_gen_7343) -> q_gen_7343
<s, z, s>(q_gen_7371) -> q_gen_7343
<z, s, s>(q_gen_7371) -> q_gen_7343
<z, s, z>(q_gen_7359) -> q_gen_7343
<z, z, z>() -> q_gen_7343
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  numnodes -> 
{{{
Q={q_gen_7345, q_gen_7350, q_gen_7351, q_gen_7380, q_gen_7409},
Q_f={q_gen_7345},
Delta=
{
<leaf>() -> q_gen_7350
<node>(q_gen_7409, q_gen_7350, q_gen_7350) -> q_gen_7350
<s>(q_gen_7380) -> q_gen_7380
<z>() -> q_gen_7380
<a>() -> q_gen_7409
<leaf, z>() -> q_gen_7345
<node, s>(q_gen_7351, q_gen_7350, q_gen_7350) -> q_gen_7345
<a, s>(q_gen_7380) -> q_gen_7351
<a, z>() -> q_gen_7351
<b, s>(q_gen_7380) -> q_gen_7351
<b, z>() -> q_gen_7351
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_7344, q_gen_7348, q_gen_7367},
Q_f={q_gen_7344},
Delta=
{
<s>(q_gen_7367) -> q_gen_7367
<z>() -> q_gen_7367
<s, s>(q_gen_7348) -> q_gen_7348
<z, s>(q_gen_7367) -> q_gen_7348
<z, z>() -> q_gen_7348
<s, s, s>(q_gen_7344) -> q_gen_7344
<s, z, s>(q_gen_7348) -> q_gen_7344
<z, s, s>(q_gen_7348) -> q_gen_7344
<z, z, s>(q_gen_7367) -> q_gen_7344
<z, z, z>() -> q_gen_7344
}

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

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

Teacher's answer:
New clause system:
{
() -> height([leaf, z]) -> 17
() -> leq([z, n2]) -> 17
() -> numnodes([leaf, z]) -> 17
() -> plus([n, z, n]) -> 17
(height([t1, _mba]) /\ height([t2, _nba]) /\ max([_mba, _nba, _oba])) -> height([node(e, t1, t2), s(_oba)]) -> 19
(height([t1, _yba]) /\ numnodes([t1, _zba])) -> leq([_yba, _zba]) -> 18
(leq([n, m])) -> max([n, m, m]) -> 17
(not leq([n, m])) -> max([n, m, n]) -> 17
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 17
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 18
(leq([s(nn1), z])) -> BOT -> 18
(numnodes([t1, _sba]) /\ numnodes([t2, _tba]) /\ plus([_sba, _tba, _uba])) -> numnodes([node(e, t1, t2), s(_uba)]) -> 22
(plus([n, mm, _hba])) -> plus([n, s(mm), s(_hba)]) -> 18
}
Sat witness: Found: ((numnodes([t1, _sba]) /\ numnodes([t2, _tba]) /\ plus([_sba, _tba, _uba])) -> numnodes([node(e, t1, t2), s(_uba)]), {
_sba -> z  ;  _tba -> s(s(z))  ;  _uba -> s(s(z))  ;  e -> a  ;  t1 -> leaf  ;  t2 -> node(b, node(a, leaf, leaf), node(a, leaf, leaf))
})

-------------------------------------------
Step 34, which took 0.037829 s (model generation: 0.031617,  model checking: 0.006212):

Model:
|_
{
height -> 
{{{
Q={q_gen_7346, q_gen_7354, q_gen_7355, q_gen_7383, q_gen_7384, q_gen_7400, q_gen_7403, q_gen_7404},
Q_f={q_gen_7346},
Delta=
{
<leaf>() -> q_gen_7354
<node>(q_gen_7384, q_gen_7354, q_gen_7383) -> q_gen_7354
<node>(q_gen_7384, q_gen_7383, q_gen_7383) -> q_gen_7354
<node>(q_gen_7384, q_gen_7354, q_gen_7354) -> q_gen_7383
<a>() -> q_gen_7384
<b>() -> q_gen_7384
<z>() -> q_gen_7404
<leaf, z>() -> q_gen_7346
<node, s>(q_gen_7355, q_gen_7354, q_gen_7354) -> q_gen_7346
<node, s>(q_gen_7355, q_gen_7354, q_gen_7383) -> q_gen_7346
<a, z>() -> q_gen_7355
<b, z>() -> q_gen_7355
<node, s>(q_gen_7355, q_gen_7383, q_gen_7383) -> q_gen_7400
<node, s>(q_gen_7403, q_gen_7354, q_gen_7354) -> q_gen_7400
<b, s>(q_gen_7404) -> q_gen_7403
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_7342, q_gen_7357, q_gen_7374},
Q_f={q_gen_7342},
Delta=
{
<s>(q_gen_7357) -> q_gen_7357
<z>() -> q_gen_7357
<s, s>(q_gen_7342) -> q_gen_7342
<z, s>(q_gen_7357) -> q_gen_7342
<z, z>() -> q_gen_7342
<s, s>(q_gen_7374) -> q_gen_7374
<s, z>(q_gen_7357) -> q_gen_7374
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  max -> 
{{{
Q={q_gen_7343, q_gen_7359, q_gen_7371},
Q_f={q_gen_7343},
Delta=
{
<z>() -> q_gen_7359
<s, s>(q_gen_7371) -> q_gen_7371
<z, z>() -> q_gen_7371
<s, s, s>(q_gen_7343) -> q_gen_7343
<s, z, s>(q_gen_7371) -> q_gen_7343
<z, s, s>(q_gen_7371) -> q_gen_7343
<z, s, z>(q_gen_7359) -> q_gen_7343
<z, z, z>() -> q_gen_7343
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  numnodes -> 
{{{
Q={q_gen_7345, q_gen_7350, q_gen_7351, q_gen_7380, q_gen_7409},
Q_f={q_gen_7345},
Delta=
{
<leaf>() -> q_gen_7350
<node>(q_gen_7409, q_gen_7350, q_gen_7350) -> q_gen_7350
<s>(q_gen_7380) -> q_gen_7380
<z>() -> q_gen_7380
<a>() -> q_gen_7409
<b>() -> q_gen_7409
<leaf, z>() -> q_gen_7345
<node, s>(q_gen_7351, q_gen_7350, q_gen_7350) -> q_gen_7345
<a, s>(q_gen_7380) -> q_gen_7351
<a, z>() -> q_gen_7351
<b, s>(q_gen_7380) -> q_gen_7351
<b, z>() -> q_gen_7351
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_7344, q_gen_7348, q_gen_7367},
Q_f={q_gen_7344},
Delta=
{
<s>(q_gen_7367) -> q_gen_7367
<z>() -> q_gen_7367
<s, s>(q_gen_7348) -> q_gen_7348
<z, s>(q_gen_7367) -> q_gen_7348
<z, z>() -> q_gen_7348
<s, s, s>(q_gen_7344) -> q_gen_7344
<s, z, s>(q_gen_7348) -> q_gen_7344
<z, s, s>(q_gen_7348) -> q_gen_7344
<z, z, s>(q_gen_7367) -> q_gen_7344
<z, z, z>() -> q_gen_7344
}

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

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

Teacher's answer:
New clause system:
{
() -> height([leaf, z]) -> 18
() -> leq([z, n2]) -> 18
() -> numnodes([leaf, z]) -> 18
() -> plus([n, z, n]) -> 18
(height([t1, _mba]) /\ height([t2, _nba]) /\ max([_mba, _nba, _oba])) -> height([node(e, t1, t2), s(_oba)]) -> 22
(height([t1, _yba]) /\ numnodes([t1, _zba])) -> leq([_yba, _zba]) -> 19
(leq([n, m])) -> max([n, m, m]) -> 18
(not leq([n, m])) -> max([n, m, n]) -> 18
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 18
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 19
(leq([s(nn1), z])) -> BOT -> 19
(numnodes([t1, _sba]) /\ numnodes([t2, _tba]) /\ plus([_sba, _tba, _uba])) -> numnodes([node(e, t1, t2), s(_uba)]) -> 22
(plus([n, mm, _hba])) -> plus([n, s(mm), s(_hba)]) -> 19
}
Sat witness: Found: ((height([t1, _mba]) /\ height([t2, _nba]) /\ max([_mba, _nba, _oba])) -> height([node(e, t1, t2), s(_oba)]), {
_mba -> z  ;  _nba -> s(z)  ;  _oba -> s(z)  ;  e -> b  ;  t1 -> leaf  ;  t2 -> node(b, node(b, leaf, node(b, leaf, leaf)), node(b, leaf, leaf))
})

-------------------------------------------
Step 35, which took 0.039979 s (model generation: 0.034627,  model checking: 0.005352):

Model:
|_
{
height -> 
{{{
Q={q_gen_7346, q_gen_7354, q_gen_7355, q_gen_7383, q_gen_7384, q_gen_7400, q_gen_7403, q_gen_7404},
Q_f={q_gen_7346},
Delta=
{
<leaf>() -> q_gen_7354
<node>(q_gen_7384, q_gen_7354, q_gen_7354) -> q_gen_7383
<node>(q_gen_7384, q_gen_7354, q_gen_7383) -> q_gen_7383
<node>(q_gen_7384, q_gen_7383, q_gen_7383) -> q_gen_7383
<a>() -> q_gen_7384
<b>() -> q_gen_7384
<z>() -> q_gen_7404
<leaf, z>() -> q_gen_7346
<node, s>(q_gen_7355, q_gen_7354, q_gen_7354) -> q_gen_7346
<node, s>(q_gen_7355, q_gen_7354, q_gen_7383) -> q_gen_7346
<a, z>() -> q_gen_7355
<b, z>() -> q_gen_7355
<node, s>(q_gen_7355, q_gen_7383, q_gen_7383) -> q_gen_7400
<node, s>(q_gen_7403, q_gen_7354, q_gen_7354) -> q_gen_7400
<node, s>(q_gen_7403, q_gen_7354, q_gen_7383) -> q_gen_7400
<b, s>(q_gen_7404) -> q_gen_7403
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_7342, q_gen_7357, q_gen_7374},
Q_f={q_gen_7342},
Delta=
{
<s>(q_gen_7357) -> q_gen_7357
<z>() -> q_gen_7357
<s, s>(q_gen_7342) -> q_gen_7342
<z, s>(q_gen_7357) -> q_gen_7342
<z, z>() -> q_gen_7342
<s, s>(q_gen_7374) -> q_gen_7374
<s, z>(q_gen_7357) -> q_gen_7374
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  max -> 
{{{
Q={q_gen_7343, q_gen_7359, q_gen_7371},
Q_f={q_gen_7343},
Delta=
{
<z>() -> q_gen_7359
<s, s>(q_gen_7371) -> q_gen_7371
<z, z>() -> q_gen_7371
<s, s, s>(q_gen_7343) -> q_gen_7343
<s, z, s>(q_gen_7371) -> q_gen_7343
<z, s, s>(q_gen_7371) -> q_gen_7343
<z, s, z>(q_gen_7359) -> q_gen_7343
<z, z, z>() -> q_gen_7343
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  numnodes -> 
{{{
Q={q_gen_7345, q_gen_7350, q_gen_7351, q_gen_7380, q_gen_7409},
Q_f={q_gen_7345},
Delta=
{
<leaf>() -> q_gen_7350
<node>(q_gen_7409, q_gen_7350, q_gen_7350) -> q_gen_7350
<s>(q_gen_7380) -> q_gen_7380
<z>() -> q_gen_7380
<a>() -> q_gen_7409
<b>() -> q_gen_7409
<leaf, z>() -> q_gen_7345
<node, s>(q_gen_7351, q_gen_7350, q_gen_7350) -> q_gen_7345
<a, s>(q_gen_7380) -> q_gen_7351
<a, z>() -> q_gen_7351
<b, s>(q_gen_7380) -> q_gen_7351
<b, z>() -> q_gen_7351
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_7344, q_gen_7348, q_gen_7367},
Q_f={q_gen_7344},
Delta=
{
<s>(q_gen_7367) -> q_gen_7367
<z>() -> q_gen_7367
<s, s>(q_gen_7348) -> q_gen_7348
<z, s>(q_gen_7367) -> q_gen_7348
<z, z>() -> q_gen_7348
<s, s, s>(q_gen_7344) -> q_gen_7344
<s, z, s>(q_gen_7348) -> q_gen_7344
<z, s, s>(q_gen_7348) -> q_gen_7344
<z, z, s>(q_gen_7367) -> q_gen_7344
<z, z, z>() -> q_gen_7344
}

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

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

Teacher's answer:
New clause system:
{
() -> height([leaf, z]) -> 19
() -> leq([z, n2]) -> 19
() -> numnodes([leaf, z]) -> 19
() -> plus([n, z, n]) -> 19
(height([t1, _mba]) /\ height([t2, _nba]) /\ max([_mba, _nba, _oba])) -> height([node(e, t1, t2), s(_oba)]) -> 25
(height([t1, _yba]) /\ numnodes([t1, _zba])) -> leq([_yba, _zba]) -> 20
(leq([n, m])) -> max([n, m, m]) -> 19
(not leq([n, m])) -> max([n, m, n]) -> 19
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 19
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 20
(leq([s(nn1), z])) -> BOT -> 20
(numnodes([t1, _sba]) /\ numnodes([t2, _tba]) /\ plus([_sba, _tba, _uba])) -> numnodes([node(e, t1, t2), s(_uba)]) -> 23
(plus([n, mm, _hba])) -> plus([n, s(mm), s(_hba)]) -> 20
}
Sat witness: Found: ((height([t1, _mba]) /\ height([t2, _nba]) /\ max([_mba, _nba, _oba])) -> height([node(e, t1, t2), s(_oba)]), {
_mba -> z  ;  _nba -> s(z)  ;  _oba -> s(z)  ;  e -> b  ;  t1 -> leaf  ;  t2 -> node(b, leaf, leaf)
})

-------------------------------------------
Step 36, which took 0.040845 s (model generation: 0.037456,  model checking: 0.003389):

Model:
|_
{
height -> 
{{{
Q={q_gen_7346, q_gen_7354, q_gen_7355, q_gen_7383, q_gen_7384, q_gen_7400, q_gen_7403, q_gen_7404},
Q_f={q_gen_7346},
Delta=
{
<leaf>() -> q_gen_7354
<node>(q_gen_7384, q_gen_7354, q_gen_7354) -> q_gen_7383
<node>(q_gen_7384, q_gen_7354, q_gen_7383) -> q_gen_7383
<node>(q_gen_7384, q_gen_7383, q_gen_7383) -> q_gen_7383
<a>() -> q_gen_7384
<b>() -> q_gen_7384
<z>() -> q_gen_7404
<leaf, z>() -> q_gen_7346
<node, s>(q_gen_7355, q_gen_7354, q_gen_7354) -> q_gen_7346
<node, s>(q_gen_7355, q_gen_7354, q_gen_7383) -> q_gen_7346
<node, s>(q_gen_7403, q_gen_7354, q_gen_7383) -> q_gen_7346
<a, z>() -> q_gen_7355
<b, z>() -> q_gen_7355
<node, s>(q_gen_7355, q_gen_7383, q_gen_7383) -> q_gen_7400
<node, s>(q_gen_7403, q_gen_7354, q_gen_7354) -> q_gen_7400
<b, s>(q_gen_7404) -> q_gen_7403
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_7342, q_gen_7357, q_gen_7374},
Q_f={q_gen_7342},
Delta=
{
<s>(q_gen_7357) -> q_gen_7357
<z>() -> q_gen_7357
<s, s>(q_gen_7342) -> q_gen_7342
<z, s>(q_gen_7357) -> q_gen_7342
<z, z>() -> q_gen_7342
<s, s>(q_gen_7374) -> q_gen_7374
<s, z>(q_gen_7357) -> q_gen_7374
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  max -> 
{{{
Q={q_gen_7343, q_gen_7359, q_gen_7371},
Q_f={q_gen_7343},
Delta=
{
<z>() -> q_gen_7359
<s, s>(q_gen_7371) -> q_gen_7371
<z, z>() -> q_gen_7371
<s, s, s>(q_gen_7343) -> q_gen_7343
<s, z, s>(q_gen_7371) -> q_gen_7343
<z, s, s>(q_gen_7371) -> q_gen_7343
<z, s, z>(q_gen_7359) -> q_gen_7343
<z, z, z>() -> q_gen_7343
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  numnodes -> 
{{{
Q={q_gen_7345, q_gen_7350, q_gen_7351, q_gen_7380, q_gen_7409},
Q_f={q_gen_7345},
Delta=
{
<leaf>() -> q_gen_7350
<node>(q_gen_7409, q_gen_7350, q_gen_7350) -> q_gen_7350
<s>(q_gen_7380) -> q_gen_7380
<z>() -> q_gen_7380
<a>() -> q_gen_7409
<b>() -> q_gen_7409
<leaf, z>() -> q_gen_7345
<node, s>(q_gen_7351, q_gen_7350, q_gen_7350) -> q_gen_7345
<a, s>(q_gen_7380) -> q_gen_7351
<a, z>() -> q_gen_7351
<b, s>(q_gen_7380) -> q_gen_7351
<b, z>() -> q_gen_7351
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_7344, q_gen_7348, q_gen_7367},
Q_f={q_gen_7344},
Delta=
{
<s>(q_gen_7367) -> q_gen_7367
<z>() -> q_gen_7367
<s, s>(q_gen_7348) -> q_gen_7348
<z, s>(q_gen_7367) -> q_gen_7348
<z, z>() -> q_gen_7348
<s, s, s>(q_gen_7344) -> q_gen_7344
<s, z, s>(q_gen_7348) -> q_gen_7344
<z, s, s>(q_gen_7348) -> q_gen_7344
<z, z, s>(q_gen_7367) -> q_gen_7344
<z, z, z>() -> q_gen_7344
}

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

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

Teacher's answer:
New clause system:
{
() -> height([leaf, z]) -> 20
() -> leq([z, n2]) -> 20
() -> numnodes([leaf, z]) -> 20
() -> plus([n, z, n]) -> 20
(height([t1, _mba]) /\ height([t2, _nba]) /\ max([_mba, _nba, _oba])) -> height([node(e, t1, t2), s(_oba)]) -> 25
(height([t1, _yba]) /\ numnodes([t1, _zba])) -> leq([_yba, _zba]) -> 23
(leq([n, m])) -> max([n, m, m]) -> 20
(not leq([n, m])) -> max([n, m, n]) -> 20
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 20
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 21
(leq([s(nn1), z])) -> BOT -> 21
(numnodes([t1, _sba]) /\ numnodes([t2, _tba]) /\ plus([_sba, _tba, _uba])) -> numnodes([node(e, t1, t2), s(_uba)]) -> 23
(plus([n, mm, _hba])) -> plus([n, s(mm), s(_hba)]) -> 21
}
Sat witness: Found: ((height([t1, _yba]) /\ numnodes([t1, _zba])) -> leq([_yba, _zba]), {
_yba -> s(s(z))  ;  _zba -> s(z)  ;  t1 -> node(b, leaf, node(b, leaf, leaf))
})

-------------------------------------------
Step 37, which took 0.042351 s (model generation: 0.041857,  model checking: 0.000494):

Model:
|_
{
height -> 
{{{
Q={q_gen_7346, q_gen_7354, q_gen_7355, q_gen_7384, q_gen_7401, q_gen_7403, q_gen_7404},
Q_f={q_gen_7346},
Delta=
{
<leaf>() -> q_gen_7354
<node>(q_gen_7384, q_gen_7354, q_gen_7354) -> q_gen_7354
<a>() -> q_gen_7384
<b>() -> q_gen_7384
<z>() -> q_gen_7404
<leaf, z>() -> q_gen_7346
<node, s>(q_gen_7355, q_gen_7354, q_gen_7354) -> q_gen_7346
<a, z>() -> q_gen_7355
<b, z>() -> q_gen_7355
<node, s>(q_gen_7403, q_gen_7354, q_gen_7354) -> q_gen_7401
<b, s>(q_gen_7404) -> q_gen_7403
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_7342, q_gen_7356, q_gen_7357, q_gen_7363},
Q_f={q_gen_7342},
Delta=
{
<z>() -> q_gen_7357
<s>(q_gen_7357) -> q_gen_7363
<s, s>(q_gen_7342) -> q_gen_7342
<z, s>(q_gen_7363) -> q_gen_7342
<z, z>() -> q_gen_7342
<s, s>(q_gen_7356) -> q_gen_7356
<s, z>(q_gen_7357) -> q_gen_7356
<s, z>(q_gen_7363) -> q_gen_7356
<z, s>(q_gen_7357) -> q_gen_7356
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  max -> 
{{{
Q={q_gen_7343, q_gen_7359, q_gen_7370, q_gen_7371},
Q_f={q_gen_7343},
Delta=
{
<z>() -> q_gen_7359
<s, s>(q_gen_7371) -> q_gen_7371
<z, z>() -> q_gen_7371
<s, s, s>(q_gen_7343) -> q_gen_7343
<s, z, s>(q_gen_7371) -> q_gen_7343
<z, s, z>(q_gen_7359) -> q_gen_7343
<z, z, z>() -> q_gen_7343
<z, s, s>(q_gen_7371) -> q_gen_7370
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  numnodes -> 
{{{
Q={q_gen_7345, q_gen_7350, q_gen_7351, q_gen_7380, q_gen_7409},
Q_f={q_gen_7345},
Delta=
{
<leaf>() -> q_gen_7350
<node>(q_gen_7409, q_gen_7350, q_gen_7350) -> q_gen_7350
<s>(q_gen_7380) -> q_gen_7380
<z>() -> q_gen_7380
<a>() -> q_gen_7409
<b>() -> q_gen_7409
<leaf, z>() -> q_gen_7345
<node, s>(q_gen_7351, q_gen_7350, q_gen_7350) -> q_gen_7345
<a, s>(q_gen_7380) -> q_gen_7351
<a, z>() -> q_gen_7351
<b, s>(q_gen_7380) -> q_gen_7351
<b, z>() -> q_gen_7351
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_7344, q_gen_7348, q_gen_7367},
Q_f={q_gen_7344},
Delta=
{
<s>(q_gen_7367) -> q_gen_7367
<z>() -> q_gen_7367
<s, s>(q_gen_7348) -> q_gen_7348
<z, s>(q_gen_7367) -> q_gen_7348
<z, z>() -> q_gen_7348
<s, s, s>(q_gen_7344) -> q_gen_7344
<s, z, s>(q_gen_7348) -> q_gen_7344
<z, s, s>(q_gen_7348) -> q_gen_7344
<z, z, s>(q_gen_7367) -> q_gen_7344
<z, z, z>() -> q_gen_7344
}

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

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

Teacher's answer:
New clause system:
{
() -> height([leaf, z]) -> 20
() -> leq([z, n2]) -> 20
() -> numnodes([leaf, z]) -> 20
() -> plus([n, z, n]) -> 20
(height([t1, _mba]) /\ height([t2, _nba]) /\ max([_mba, _nba, _oba])) -> height([node(e, t1, t2), s(_oba)]) -> 25
(height([t1, _yba]) /\ numnodes([t1, _zba])) -> leq([_yba, _zba]) -> 23
(leq([n, m])) -> max([n, m, m]) -> 20
(not leq([n, m])) -> max([n, m, n]) -> 23
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 21
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 21
(leq([s(nn1), z])) -> BOT -> 21
(numnodes([t1, _sba]) /\ numnodes([t2, _tba]) /\ plus([_sba, _tba, _uba])) -> numnodes([node(e, t1, t2), s(_uba)]) -> 23
(plus([n, mm, _hba])) -> plus([n, s(mm), s(_hba)]) -> 21
}
Sat witness: Found: ((not leq([n, m])) -> max([n, m, n]), {
m -> s(s(s(z)))  ;  n -> z
})

-------------------------------------------
Step 38, which took 0.040013 s (model generation: 0.039874,  model checking: 0.000139):

Model:
|_
{
height -> 
{{{
Q={q_gen_7346, q_gen_7354, q_gen_7355, q_gen_7384, q_gen_7401, q_gen_7403, q_gen_7404},
Q_f={q_gen_7346},
Delta=
{
<leaf>() -> q_gen_7354
<node>(q_gen_7384, q_gen_7354, q_gen_7354) -> q_gen_7354
<a>() -> q_gen_7384
<b>() -> q_gen_7384
<z>() -> q_gen_7404
<leaf, z>() -> q_gen_7346
<node, s>(q_gen_7355, q_gen_7354, q_gen_7354) -> q_gen_7346
<a, z>() -> q_gen_7355
<b, z>() -> q_gen_7355
<node, s>(q_gen_7403, q_gen_7354, q_gen_7354) -> q_gen_7401
<b, s>(q_gen_7404) -> q_gen_7403
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_7342, q_gen_7356, q_gen_7357, q_gen_7363},
Q_f={q_gen_7342},
Delta=
{
<z>() -> q_gen_7357
<s>(q_gen_7357) -> q_gen_7363
<s>(q_gen_7363) -> q_gen_7363
<s, s>(q_gen_7342) -> q_gen_7342
<z, s>(q_gen_7363) -> q_gen_7342
<z, z>() -> q_gen_7342
<s, s>(q_gen_7356) -> q_gen_7356
<s, z>(q_gen_7357) -> q_gen_7356
<s, z>(q_gen_7363) -> q_gen_7356
<z, s>(q_gen_7357) -> q_gen_7356
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  max -> 
{{{
Q={q_gen_7343, q_gen_7359, q_gen_7370, q_gen_7371},
Q_f={q_gen_7343},
Delta=
{
<s>(q_gen_7359) -> q_gen_7359
<z>() -> q_gen_7359
<s, s>(q_gen_7371) -> q_gen_7371
<z, z>() -> q_gen_7371
<s, s, s>(q_gen_7343) -> q_gen_7343
<s, z, s>(q_gen_7371) -> q_gen_7343
<z, s, z>(q_gen_7359) -> q_gen_7343
<z, z, z>() -> q_gen_7343
<z, s, s>(q_gen_7371) -> q_gen_7370
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  numnodes -> 
{{{
Q={q_gen_7345, q_gen_7350, q_gen_7351, q_gen_7380, q_gen_7409},
Q_f={q_gen_7345},
Delta=
{
<leaf>() -> q_gen_7350
<node>(q_gen_7409, q_gen_7350, q_gen_7350) -> q_gen_7350
<s>(q_gen_7380) -> q_gen_7380
<z>() -> q_gen_7380
<a>() -> q_gen_7409
<b>() -> q_gen_7409
<leaf, z>() -> q_gen_7345
<node, s>(q_gen_7351, q_gen_7350, q_gen_7350) -> q_gen_7345
<a, s>(q_gen_7380) -> q_gen_7351
<a, z>() -> q_gen_7351
<b, s>(q_gen_7380) -> q_gen_7351
<b, z>() -> q_gen_7351
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_7344, q_gen_7348, q_gen_7367},
Q_f={q_gen_7344},
Delta=
{
<s>(q_gen_7367) -> q_gen_7367
<z>() -> q_gen_7367
<s, s>(q_gen_7348) -> q_gen_7348
<z, s>(q_gen_7367) -> q_gen_7348
<z, z>() -> q_gen_7348
<s, s, s>(q_gen_7344) -> q_gen_7344
<s, z, s>(q_gen_7348) -> q_gen_7344
<z, s, s>(q_gen_7348) -> q_gen_7344
<z, z, s>(q_gen_7367) -> q_gen_7344
<z, z, z>() -> q_gen_7344
}

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

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

Teacher's answer:
New clause system:
{
() -> height([leaf, z]) -> 20
() -> leq([z, n2]) -> 20
() -> numnodes([leaf, z]) -> 20
() -> plus([n, z, n]) -> 20
(height([t1, _mba]) /\ height([t2, _nba]) /\ max([_mba, _nba, _oba])) -> height([node(e, t1, t2), s(_oba)]) -> 25
(height([t1, _yba]) /\ numnodes([t1, _zba])) -> leq([_yba, _zba]) -> 23
(leq([n, m])) -> max([n, m, m]) -> 23
(not leq([n, m])) -> max([n, m, n]) -> 23
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 21
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 21
(leq([s(nn1), z])) -> BOT -> 21
(numnodes([t1, _sba]) /\ numnodes([t2, _tba]) /\ plus([_sba, _tba, _uba])) -> numnodes([node(e, t1, t2), s(_uba)]) -> 23
(plus([n, mm, _hba])) -> plus([n, s(mm), s(_hba)]) -> 21
}
Sat witness: Found: ((leq([n, m])) -> max([n, m, m]), {
m -> s(s(z))  ;  n -> z
})

-------------------------------------------
Step 39, which took 0.042955 s (model generation: 0.042556,  model checking: 0.000399):

Model:
|_
{
height -> 
{{{
Q={q_gen_7346, q_gen_7354, q_gen_7355, q_gen_7384, q_gen_7401, q_gen_7403, q_gen_7404},
Q_f={q_gen_7346},
Delta=
{
<leaf>() -> q_gen_7354
<node>(q_gen_7384, q_gen_7354, q_gen_7354) -> q_gen_7354
<a>() -> q_gen_7384
<b>() -> q_gen_7384
<z>() -> q_gen_7404
<leaf, z>() -> q_gen_7346
<node, s>(q_gen_7355, q_gen_7354, q_gen_7354) -> q_gen_7346
<a, z>() -> q_gen_7355
<b, z>() -> q_gen_7355
<node, s>(q_gen_7403, q_gen_7354, q_gen_7354) -> q_gen_7401
<b, s>(q_gen_7404) -> q_gen_7403
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_7342, q_gen_7356, q_gen_7357, q_gen_7363},
Q_f={q_gen_7342},
Delta=
{
<z>() -> q_gen_7357
<s>(q_gen_7357) -> q_gen_7363
<s>(q_gen_7363) -> q_gen_7363
<s, s>(q_gen_7342) -> q_gen_7342
<s, z>(q_gen_7363) -> q_gen_7342
<z, s>(q_gen_7363) -> q_gen_7342
<z, z>() -> q_gen_7342
<s, s>(q_gen_7356) -> q_gen_7356
<s, z>(q_gen_7357) -> q_gen_7356
<z, s>(q_gen_7357) -> q_gen_7356
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  max -> 
{{{
Q={q_gen_7343, q_gen_7359, q_gen_7370, q_gen_7371, q_gen_7387},
Q_f={q_gen_7343},
Delta=
{
<s>(q_gen_7359) -> q_gen_7359
<z>() -> q_gen_7359
<z, z>() -> q_gen_7371
<s, s>(q_gen_7371) -> q_gen_7387
<s, s, s>(q_gen_7343) -> q_gen_7343
<s, z, s>(q_gen_7371) -> q_gen_7343
<z, s, s>(q_gen_7387) -> q_gen_7343
<z, s, z>(q_gen_7359) -> q_gen_7343
<z, z, z>() -> q_gen_7343
<s, z, s>(q_gen_7387) -> q_gen_7370
<z, s, s>(q_gen_7371) -> q_gen_7370
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  numnodes -> 
{{{
Q={q_gen_7345, q_gen_7350, q_gen_7351, q_gen_7380, q_gen_7409},
Q_f={q_gen_7345},
Delta=
{
<leaf>() -> q_gen_7350
<node>(q_gen_7409, q_gen_7350, q_gen_7350) -> q_gen_7350
<s>(q_gen_7380) -> q_gen_7380
<z>() -> q_gen_7380
<a>() -> q_gen_7409
<b>() -> q_gen_7409
<leaf, z>() -> q_gen_7345
<node, s>(q_gen_7351, q_gen_7350, q_gen_7350) -> q_gen_7345
<a, s>(q_gen_7380) -> q_gen_7351
<a, z>() -> q_gen_7351
<b, s>(q_gen_7380) -> q_gen_7351
<b, z>() -> q_gen_7351
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_7344, q_gen_7348, q_gen_7367},
Q_f={q_gen_7344},
Delta=
{
<s>(q_gen_7367) -> q_gen_7367
<z>() -> q_gen_7367
<s, s>(q_gen_7348) -> q_gen_7348
<z, s>(q_gen_7367) -> q_gen_7348
<z, z>() -> q_gen_7348
<s, s, s>(q_gen_7344) -> q_gen_7344
<s, z, s>(q_gen_7348) -> q_gen_7344
<z, s, s>(q_gen_7348) -> q_gen_7344
<z, z, s>(q_gen_7367) -> q_gen_7344
<z, z, z>() -> q_gen_7344
}

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

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

Teacher's answer:
New clause system:
{
() -> height([leaf, z]) -> 20
() -> leq([z, n2]) -> 23
() -> numnodes([leaf, z]) -> 21
() -> plus([n, z, n]) -> 21
(height([t1, _mba]) /\ height([t2, _nba]) /\ max([_mba, _nba, _oba])) -> height([node(e, t1, t2), s(_oba)]) -> 25
(height([t1, _yba]) /\ numnodes([t1, _zba])) -> leq([_yba, _zba]) -> 23
(leq([n, m])) -> max([n, m, m]) -> 23
(not leq([n, m])) -> max([n, m, n]) -> 23
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 21
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 21
(leq([s(nn1), z])) -> BOT -> 21
(numnodes([t1, _sba]) /\ numnodes([t2, _tba]) /\ plus([_sba, _tba, _uba])) -> numnodes([node(e, t1, t2), s(_uba)]) -> 23
(plus([n, mm, _hba])) -> plus([n, s(mm), s(_hba)]) -> 21
}
Sat witness: Found: (() -> leq([z, n2]), {
n2 -> s(z)
})

-------------------------------------------
Step 40, which took 0.065709 s (model generation: 0.038758,  model checking: 0.026951):

Model:
|_
{
height -> 
{{{
Q={q_gen_7346, q_gen_7354, q_gen_7355, q_gen_7383, q_gen_7384, q_gen_7400, q_gen_7403, q_gen_7404},
Q_f={q_gen_7346},
Delta=
{
<leaf>() -> q_gen_7354
<node>(q_gen_7384, q_gen_7383, q_gen_7383) -> q_gen_7354
<node>(q_gen_7384, q_gen_7354, q_gen_7354) -> q_gen_7383
<node>(q_gen_7384, q_gen_7354, q_gen_7383) -> q_gen_7383
<a>() -> q_gen_7384
<b>() -> q_gen_7384
<z>() -> q_gen_7404
<leaf, z>() -> q_gen_7346
<node, s>(q_gen_7355, q_gen_7354, q_gen_7354) -> q_gen_7346
<node, s>(q_gen_7355, q_gen_7354, q_gen_7383) -> q_gen_7346
<node, s>(q_gen_7403, q_gen_7354, q_gen_7383) -> q_gen_7346
<a, z>() -> q_gen_7355
<b, z>() -> q_gen_7355
<node, s>(q_gen_7355, q_gen_7383, q_gen_7383) -> q_gen_7400
<node, s>(q_gen_7403, q_gen_7354, q_gen_7354) -> q_gen_7400
<b, s>(q_gen_7404) -> q_gen_7403
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_7342, q_gen_7357, q_gen_7374},
Q_f={q_gen_7342},
Delta=
{
<s>(q_gen_7357) -> q_gen_7357
<z>() -> q_gen_7357
<s, s>(q_gen_7342) -> q_gen_7342
<z, s>(q_gen_7357) -> q_gen_7342
<z, z>() -> q_gen_7342
<s, s>(q_gen_7374) -> q_gen_7374
<s, z>(q_gen_7357) -> q_gen_7374
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  max -> 
{{{
Q={q_gen_7343, q_gen_7359, q_gen_7371},
Q_f={q_gen_7343},
Delta=
{
<s>(q_gen_7359) -> q_gen_7359
<z>() -> q_gen_7359
<s, s>(q_gen_7371) -> q_gen_7371
<z, z>() -> q_gen_7371
<s, s, s>(q_gen_7343) -> q_gen_7343
<s, z, s>(q_gen_7371) -> q_gen_7343
<z, s, s>(q_gen_7371) -> q_gen_7343
<z, s, z>(q_gen_7359) -> q_gen_7343
<z, z, z>() -> q_gen_7343
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  numnodes -> 
{{{
Q={q_gen_7345, q_gen_7350, q_gen_7351, q_gen_7379, q_gen_7380, q_gen_7408, q_gen_7409, q_gen_7413},
Q_f={q_gen_7345},
Delta=
{
<leaf>() -> q_gen_7350
<node>(q_gen_7409, q_gen_7408, q_gen_7408) -> q_gen_7350
<s>(q_gen_7380) -> q_gen_7380
<z>() -> q_gen_7380
<node>(q_gen_7409, q_gen_7350, q_gen_7350) -> q_gen_7408
<a>() -> q_gen_7409
<b>() -> q_gen_7409
<leaf, z>() -> q_gen_7345
<node, s>(q_gen_7351, q_gen_7350, q_gen_7350) -> q_gen_7345
<node, s>(q_gen_7379, q_gen_7350, q_gen_7350) -> q_gen_7345
<node, s>(q_gen_7379, q_gen_7350, q_gen_7408) -> q_gen_7345
<a, z>() -> q_gen_7351
<b, z>() -> q_gen_7351
<a, s>(q_gen_7380) -> q_gen_7379
<b, s>(q_gen_7380) -> q_gen_7379
<node, s>(q_gen_7351, q_gen_7350, q_gen_7408) -> q_gen_7413
<node, s>(q_gen_7379, q_gen_7408, q_gen_7408) -> q_gen_7413
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_7344, q_gen_7348, q_gen_7367},
Q_f={q_gen_7344},
Delta=
{
<s>(q_gen_7367) -> q_gen_7367
<z>() -> q_gen_7367
<s, s>(q_gen_7348) -> q_gen_7348
<z, s>(q_gen_7367) -> q_gen_7348
<z, z>() -> q_gen_7348
<s, s, s>(q_gen_7344) -> q_gen_7344
<s, z, s>(q_gen_7348) -> q_gen_7344
<z, s, s>(q_gen_7348) -> q_gen_7344
<z, z, s>(q_gen_7367) -> q_gen_7344
<z, z, z>() -> q_gen_7344
}

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

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

Teacher's answer:
New clause system:
{
() -> height([leaf, z]) -> 21
() -> leq([z, n2]) -> 23
() -> numnodes([leaf, z]) -> 22
() -> plus([n, z, n]) -> 22
(height([t1, _mba]) /\ height([t2, _nba]) /\ max([_mba, _nba, _oba])) -> height([node(e, t1, t2), s(_oba)]) -> 25
(height([t1, _yba]) /\ numnodes([t1, _zba])) -> leq([_yba, _zba]) -> 23
(leq([n, m])) -> max([n, m, m]) -> 23
(not leq([n, m])) -> max([n, m, n]) -> 23
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 22
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 22
(leq([s(nn1), z])) -> BOT -> 22
(numnodes([t1, _sba]) /\ numnodes([t2, _tba]) /\ plus([_sba, _tba, _uba])) -> numnodes([node(e, t1, t2), s(_uba)]) -> 26
(plus([n, mm, _hba])) -> plus([n, s(mm), s(_hba)]) -> 22
}
Sat witness: Found: ((numnodes([t1, _sba]) /\ numnodes([t2, _tba]) /\ plus([_sba, _tba, _uba])) -> numnodes([node(e, t1, t2), s(_uba)]), {
_sba -> s(s(z))  ;  _tba -> s(s(z))  ;  _uba -> s(s(z))  ;  e -> a  ;  t1 -> node(a, leaf, node(b, node(b, leaf, leaf), node(b, leaf, leaf)))  ;  t2 -> node(a, node(b, node(b, leaf, leaf), node(b, leaf, leaf)), node(b, node(b, leaf, leaf), node(b, leaf, leaf)))
})

-------------------------------------------
Step 41, which took 0.109276 s (model generation: 0.049098,  model checking: 0.060178):

Model:
|_
{
height -> 
{{{
Q={q_gen_7346, q_gen_7354, q_gen_7355, q_gen_7383, q_gen_7384, q_gen_7400, q_gen_7403, q_gen_7404},
Q_f={q_gen_7346},
Delta=
{
<leaf>() -> q_gen_7354
<node>(q_gen_7384, q_gen_7383, q_gen_7383) -> q_gen_7354
<node>(q_gen_7384, q_gen_7354, q_gen_7354) -> q_gen_7383
<node>(q_gen_7384, q_gen_7354, q_gen_7383) -> q_gen_7383
<a>() -> q_gen_7384
<b>() -> q_gen_7384
<z>() -> q_gen_7404
<leaf, z>() -> q_gen_7346
<node, s>(q_gen_7355, q_gen_7354, q_gen_7354) -> q_gen_7346
<node, s>(q_gen_7355, q_gen_7354, q_gen_7383) -> q_gen_7346
<node, s>(q_gen_7403, q_gen_7354, q_gen_7383) -> q_gen_7346
<a, z>() -> q_gen_7355
<b, z>() -> q_gen_7355
<node, s>(q_gen_7355, q_gen_7383, q_gen_7383) -> q_gen_7400
<node, s>(q_gen_7403, q_gen_7354, q_gen_7354) -> q_gen_7400
<b, s>(q_gen_7404) -> q_gen_7403
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_7342, q_gen_7357, q_gen_7374},
Q_f={q_gen_7342},
Delta=
{
<s>(q_gen_7357) -> q_gen_7357
<z>() -> q_gen_7357
<s, s>(q_gen_7342) -> q_gen_7342
<z, s>(q_gen_7357) -> q_gen_7342
<z, z>() -> q_gen_7342
<s, s>(q_gen_7374) -> q_gen_7374
<s, z>(q_gen_7357) -> q_gen_7374
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  max -> 
{{{
Q={q_gen_7343, q_gen_7359, q_gen_7371},
Q_f={q_gen_7343},
Delta=
{
<s>(q_gen_7359) -> q_gen_7359
<z>() -> q_gen_7359
<s, s>(q_gen_7371) -> q_gen_7371
<z, z>() -> q_gen_7371
<s, s, s>(q_gen_7343) -> q_gen_7343
<s, z, s>(q_gen_7371) -> q_gen_7343
<z, s, s>(q_gen_7371) -> q_gen_7343
<z, s, z>(q_gen_7359) -> q_gen_7343
<z, z, z>() -> q_gen_7343
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  numnodes -> 
{{{
Q={q_gen_7345, q_gen_7350, q_gen_7351, q_gen_7369, q_gen_7380, q_gen_7408, q_gen_7409, q_gen_7413},
Q_f={q_gen_7345},
Delta=
{
<leaf>() -> q_gen_7350
<s>(q_gen_7380) -> q_gen_7380
<z>() -> q_gen_7380
<node>(q_gen_7409, q_gen_7350, q_gen_7350) -> q_gen_7408
<node>(q_gen_7409, q_gen_7350, q_gen_7408) -> q_gen_7408
<node>(q_gen_7409, q_gen_7408, q_gen_7408) -> q_gen_7408
<a>() -> q_gen_7409
<b>() -> q_gen_7409
<leaf, z>() -> q_gen_7345
<node, s>(q_gen_7351, q_gen_7350, q_gen_7350) -> q_gen_7345
<node, s>(q_gen_7369, q_gen_7350, q_gen_7350) -> q_gen_7345
<node, s>(q_gen_7369, q_gen_7350, q_gen_7408) -> q_gen_7345
<b, z>() -> q_gen_7351
<a, s>(q_gen_7380) -> q_gen_7369
<a, z>() -> q_gen_7369
<b, s>(q_gen_7380) -> q_gen_7369
<node, s>(q_gen_7351, q_gen_7350, q_gen_7408) -> q_gen_7413
<node, s>(q_gen_7369, q_gen_7408, q_gen_7408) -> q_gen_7413
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_7344, q_gen_7348, q_gen_7367},
Q_f={q_gen_7344},
Delta=
{
<s>(q_gen_7367) -> q_gen_7367
<z>() -> q_gen_7367
<s, s>(q_gen_7348) -> q_gen_7348
<z, s>(q_gen_7367) -> q_gen_7348
<z, z>() -> q_gen_7348
<s, s, s>(q_gen_7344) -> q_gen_7344
<s, z, s>(q_gen_7348) -> q_gen_7344
<z, s, s>(q_gen_7348) -> q_gen_7344
<z, z, s>(q_gen_7367) -> q_gen_7344
<z, z, z>() -> q_gen_7344
}

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

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

Teacher's answer:
New clause system:
{
() -> height([leaf, z]) -> 22
() -> leq([z, n2]) -> 24
() -> numnodes([leaf, z]) -> 23
() -> plus([n, z, n]) -> 23
(height([t1, _mba]) /\ height([t2, _nba]) /\ max([_mba, _nba, _oba])) -> height([node(e, t1, t2), s(_oba)]) -> 28
(height([t1, _yba]) /\ numnodes([t1, _zba])) -> leq([_yba, _zba]) -> 24
(leq([n, m])) -> max([n, m, m]) -> 24
(not leq([n, m])) -> max([n, m, n]) -> 24
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 23
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 23
(leq([s(nn1), z])) -> BOT -> 23
(numnodes([t1, _sba]) /\ numnodes([t2, _tba]) /\ plus([_sba, _tba, _uba])) -> numnodes([node(e, t1, t2), s(_uba)]) -> 26
(plus([n, mm, _hba])) -> plus([n, s(mm), s(_hba)]) -> 23
}
Sat witness: Found: ((height([t1, _mba]) /\ height([t2, _nba]) /\ max([_mba, _nba, _oba])) -> height([node(e, t1, t2), s(_oba)]), {
_mba -> s(z)  ;  _nba -> z  ;  _oba -> s(z)  ;  e -> b  ;  t1 -> node(b, node(b, node(b, leaf, leaf), node(b, leaf, leaf)), node(b, leaf, leaf))  ;  t2 -> leaf
})

-------------------------------------------
Step 42, which took 0.172919 s (model generation: 0.051232,  model checking: 0.121687):

Model:
|_
{
height -> 
{{{
Q={q_gen_7346, q_gen_7354, q_gen_7355, q_gen_7383, q_gen_7384, q_gen_7400, q_gen_7403, q_gen_7404},
Q_f={q_gen_7346},
Delta=
{
<leaf>() -> q_gen_7354
<node>(q_gen_7384, q_gen_7383, q_gen_7383) -> q_gen_7354
<node>(q_gen_7384, q_gen_7354, q_gen_7354) -> q_gen_7383
<node>(q_gen_7384, q_gen_7354, q_gen_7383) -> q_gen_7383
<a>() -> q_gen_7384
<b>() -> q_gen_7384
<z>() -> q_gen_7404
<leaf, z>() -> q_gen_7346
<node, s>(q_gen_7355, q_gen_7354, q_gen_7354) -> q_gen_7346
<node, s>(q_gen_7355, q_gen_7354, q_gen_7383) -> q_gen_7346
<node, s>(q_gen_7403, q_gen_7354, q_gen_7383) -> q_gen_7346
<node, s>(q_gen_7403, q_gen_7383, q_gen_7354) -> q_gen_7346
<a, z>() -> q_gen_7355
<b, z>() -> q_gen_7355
<node, s>(q_gen_7355, q_gen_7383, q_gen_7383) -> q_gen_7400
<node, s>(q_gen_7403, q_gen_7354, q_gen_7354) -> q_gen_7400
<b, s>(q_gen_7404) -> q_gen_7403
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_7342, q_gen_7357, q_gen_7374},
Q_f={q_gen_7342},
Delta=
{
<s>(q_gen_7357) -> q_gen_7357
<z>() -> q_gen_7357
<s, s>(q_gen_7342) -> q_gen_7342
<z, s>(q_gen_7357) -> q_gen_7342
<z, z>() -> q_gen_7342
<s, s>(q_gen_7374) -> q_gen_7374
<s, z>(q_gen_7357) -> q_gen_7374
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  max -> 
{{{
Q={q_gen_7343, q_gen_7359, q_gen_7371},
Q_f={q_gen_7343},
Delta=
{
<s>(q_gen_7359) -> q_gen_7359
<z>() -> q_gen_7359
<s, s>(q_gen_7371) -> q_gen_7371
<z, z>() -> q_gen_7371
<s, s, s>(q_gen_7343) -> q_gen_7343
<s, z, s>(q_gen_7371) -> q_gen_7343
<z, s, s>(q_gen_7371) -> q_gen_7343
<z, s, z>(q_gen_7359) -> q_gen_7343
<z, z, z>() -> q_gen_7343
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  numnodes -> 
{{{
Q={q_gen_7345, q_gen_7350, q_gen_7351, q_gen_7369, q_gen_7380, q_gen_7408, q_gen_7409, q_gen_7413},
Q_f={q_gen_7345},
Delta=
{
<leaf>() -> q_gen_7350
<s>(q_gen_7380) -> q_gen_7380
<z>() -> q_gen_7380
<node>(q_gen_7409, q_gen_7350, q_gen_7350) -> q_gen_7408
<node>(q_gen_7409, q_gen_7350, q_gen_7408) -> q_gen_7408
<node>(q_gen_7409, q_gen_7408, q_gen_7408) -> q_gen_7408
<a>() -> q_gen_7409
<b>() -> q_gen_7409
<leaf, z>() -> q_gen_7345
<node, s>(q_gen_7351, q_gen_7350, q_gen_7350) -> q_gen_7345
<node, s>(q_gen_7369, q_gen_7350, q_gen_7350) -> q_gen_7345
<node, s>(q_gen_7369, q_gen_7350, q_gen_7408) -> q_gen_7345
<b, z>() -> q_gen_7351
<a, s>(q_gen_7380) -> q_gen_7369
<a, z>() -> q_gen_7369
<b, s>(q_gen_7380) -> q_gen_7369
<node, s>(q_gen_7351, q_gen_7350, q_gen_7408) -> q_gen_7413
<node, s>(q_gen_7369, q_gen_7408, q_gen_7408) -> q_gen_7413
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_7344, q_gen_7348, q_gen_7367},
Q_f={q_gen_7344},
Delta=
{
<s>(q_gen_7367) -> q_gen_7367
<z>() -> q_gen_7367
<s, s>(q_gen_7348) -> q_gen_7348
<z, s>(q_gen_7367) -> q_gen_7348
<z, z>() -> q_gen_7348
<s, s, s>(q_gen_7344) -> q_gen_7344
<s, z, s>(q_gen_7348) -> q_gen_7344
<z, s, s>(q_gen_7348) -> q_gen_7344
<z, z, s>(q_gen_7367) -> q_gen_7344
<z, z, z>() -> q_gen_7344
}

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

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

Teacher's answer:
New clause system:
{
() -> height([leaf, z]) -> 23
() -> leq([z, n2]) -> 25
() -> numnodes([leaf, z]) -> 24
() -> plus([n, z, n]) -> 24
(height([t1, _mba]) /\ height([t2, _nba]) /\ max([_mba, _nba, _oba])) -> height([node(e, t1, t2), s(_oba)]) -> 28
(height([t1, _yba]) /\ numnodes([t1, _zba])) -> leq([_yba, _zba]) -> 25
(leq([n, m])) -> max([n, m, m]) -> 25
(not leq([n, m])) -> max([n, m, n]) -> 25
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 24
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 24
(leq([s(nn1), z])) -> BOT -> 24
(numnodes([t1, _sba]) /\ numnodes([t2, _tba]) /\ plus([_sba, _tba, _uba])) -> numnodes([node(e, t1, t2), s(_uba)]) -> 29
(plus([n, mm, _hba])) -> plus([n, s(mm), s(_hba)]) -> 24
}
Sat witness: Found: ((numnodes([t1, _sba]) /\ numnodes([t2, _tba]) /\ plus([_sba, _tba, _uba])) -> numnodes([node(e, t1, t2), s(_uba)]), {
_sba -> s(z)  ;  _tba -> s(z)  ;  _uba -> s(z)  ;  e -> b  ;  t1 -> node(a, leaf, node(b, leaf, node(b, leaf, leaf)))  ;  t2 -> node(a, leaf, node(b, leaf, leaf))
})

-------------------------------------------
Step 43, which took 0.065166 s (model generation: 0.063067,  model checking: 0.002099):

Model:
|_
{
height -> 
{{{
Q={q_gen_7346, q_gen_7354, q_gen_7355, q_gen_7383, q_gen_7384, q_gen_7403, q_gen_7404, q_gen_7405},
Q_f={q_gen_7346},
Delta=
{
<leaf>() -> q_gen_7354
<node>(q_gen_7384, q_gen_7354, q_gen_7354) -> q_gen_7383
<node>(q_gen_7384, q_gen_7354, q_gen_7383) -> q_gen_7383
<node>(q_gen_7384, q_gen_7383, q_gen_7383) -> q_gen_7383
<a>() -> q_gen_7384
<b>() -> q_gen_7384
<z>() -> q_gen_7404
<leaf, z>() -> q_gen_7346
<node, s>(q_gen_7355, q_gen_7354, q_gen_7354) -> q_gen_7346
<node, s>(q_gen_7355, q_gen_7354, q_gen_7383) -> q_gen_7346
<node, s>(q_gen_7355, q_gen_7383, q_gen_7383) -> q_gen_7346
<node, s>(q_gen_7403, q_gen_7354, q_gen_7383) -> q_gen_7346
<node, s>(q_gen_7403, q_gen_7383, q_gen_7354) -> q_gen_7346
<a, z>() -> q_gen_7355
<b, z>() -> q_gen_7355
<b, s>(q_gen_7404) -> q_gen_7403
<node, s>(q_gen_7403, q_gen_7354, q_gen_7354) -> q_gen_7405
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_7342, q_gen_7357, q_gen_7374},
Q_f={q_gen_7342},
Delta=
{
<s>(q_gen_7357) -> q_gen_7357
<z>() -> q_gen_7357
<s, s>(q_gen_7342) -> q_gen_7342
<z, s>(q_gen_7357) -> q_gen_7342
<z, z>() -> q_gen_7342
<s, s>(q_gen_7374) -> q_gen_7374
<s, z>(q_gen_7357) -> q_gen_7374
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  max -> 
{{{
Q={q_gen_7343, q_gen_7359, q_gen_7371},
Q_f={q_gen_7343},
Delta=
{
<s>(q_gen_7359) -> q_gen_7359
<z>() -> q_gen_7359
<s, s>(q_gen_7371) -> q_gen_7371
<z, z>() -> q_gen_7371
<s, s, s>(q_gen_7343) -> q_gen_7343
<s, z, s>(q_gen_7371) -> q_gen_7343
<z, s, s>(q_gen_7371) -> q_gen_7343
<z, s, z>(q_gen_7359) -> q_gen_7343
<z, z, z>() -> q_gen_7343
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  numnodes -> 
{{{
Q={q_gen_7345, q_gen_7350, q_gen_7351, q_gen_7369, q_gen_7380, q_gen_7408, q_gen_7409, q_gen_7413},
Q_f={q_gen_7345},
Delta=
{
<leaf>() -> q_gen_7350
<node>(q_gen_7409, q_gen_7350, q_gen_7408) -> q_gen_7350
<node>(q_gen_7409, q_gen_7408, q_gen_7408) -> q_gen_7350
<s>(q_gen_7380) -> q_gen_7380
<z>() -> q_gen_7380
<node>(q_gen_7409, q_gen_7350, q_gen_7350) -> q_gen_7408
<a>() -> q_gen_7409
<b>() -> q_gen_7409
<leaf, z>() -> q_gen_7345
<node, s>(q_gen_7351, q_gen_7350, q_gen_7350) -> q_gen_7345
<node, s>(q_gen_7351, q_gen_7408, q_gen_7408) -> q_gen_7345
<node, s>(q_gen_7369, q_gen_7350, q_gen_7350) -> q_gen_7345
<node, s>(q_gen_7369, q_gen_7350, q_gen_7408) -> q_gen_7345
<node, s>(q_gen_7369, q_gen_7408, q_gen_7350) -> q_gen_7345
<a, s>(q_gen_7380) -> q_gen_7351
<b, z>() -> q_gen_7351
<a, z>() -> q_gen_7369
<b, s>(q_gen_7380) -> q_gen_7369
<node, s>(q_gen_7351, q_gen_7350, q_gen_7408) -> q_gen_7413
<node, s>(q_gen_7369, q_gen_7408, q_gen_7408) -> q_gen_7413
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_7344, q_gen_7348, q_gen_7367},
Q_f={q_gen_7344},
Delta=
{
<s>(q_gen_7367) -> q_gen_7367
<z>() -> q_gen_7367
<s, s>(q_gen_7348) -> q_gen_7348
<z, s>(q_gen_7367) -> q_gen_7348
<z, z>() -> q_gen_7348
<s, s, s>(q_gen_7344) -> q_gen_7344
<s, z, s>(q_gen_7348) -> q_gen_7344
<z, s, s>(q_gen_7348) -> q_gen_7344
<z, z, s>(q_gen_7367) -> q_gen_7344
<z, z, z>() -> q_gen_7344
}

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

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

Teacher's answer:
New clause system:
{
() -> height([leaf, z]) -> 24
() -> leq([z, n2]) -> 25
() -> numnodes([leaf, z]) -> 25
() -> plus([n, z, n]) -> 25
(height([t1, _mba]) /\ height([t2, _nba]) /\ max([_mba, _nba, _oba])) -> height([node(e, t1, t2), s(_oba)]) -> 28
(height([t1, _yba]) /\ numnodes([t1, _zba])) -> leq([_yba, _zba]) -> 28
(leq([n, m])) -> max([n, m, m]) -> 26
(not leq([n, m])) -> max([n, m, n]) -> 26
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 25
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 25
(leq([s(nn1), z])) -> BOT -> 25
(numnodes([t1, _sba]) /\ numnodes([t2, _tba]) /\ plus([_sba, _tba, _uba])) -> numnodes([node(e, t1, t2), s(_uba)]) -> 29
(plus([n, mm, _hba])) -> plus([n, s(mm), s(_hba)]) -> 25
}
Sat witness: Found: ((height([t1, _yba]) /\ numnodes([t1, _zba])) -> leq([_yba, _zba]), {
_yba -> s(s(z))  ;  _zba -> s(z)  ;  t1 -> node(b, leaf, node(b, node(b, leaf, leaf), node(b, leaf, leaf)))
})

-------------------------------------------
Step 44, which took 0.067098 s (model generation: 0.064978,  model checking: 0.002120):

Model:
|_
{
height -> 
{{{
Q={q_gen_7346, q_gen_7354, q_gen_7355, q_gen_7383, q_gen_7384, q_gen_7403, q_gen_7404, q_gen_7405},
Q_f={q_gen_7346},
Delta=
{
<leaf>() -> q_gen_7354
<node>(q_gen_7384, q_gen_7354, q_gen_7354) -> q_gen_7383
<node>(q_gen_7384, q_gen_7354, q_gen_7383) -> q_gen_7383
<node>(q_gen_7384, q_gen_7383, q_gen_7383) -> q_gen_7383
<a>() -> q_gen_7384
<b>() -> q_gen_7384
<z>() -> q_gen_7404
<leaf, z>() -> q_gen_7346
<node, s>(q_gen_7355, q_gen_7354, q_gen_7354) -> q_gen_7346
<node, s>(q_gen_7355, q_gen_7354, q_gen_7383) -> q_gen_7346
<node, s>(q_gen_7355, q_gen_7383, q_gen_7383) -> q_gen_7346
<node, s>(q_gen_7403, q_gen_7354, q_gen_7383) -> q_gen_7346
<node, s>(q_gen_7403, q_gen_7383, q_gen_7354) -> q_gen_7346
<a, z>() -> q_gen_7355
<b, z>() -> q_gen_7355
<b, s>(q_gen_7404) -> q_gen_7403
<node, s>(q_gen_7403, q_gen_7354, q_gen_7354) -> q_gen_7405
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_7342, q_gen_7357, q_gen_7374},
Q_f={q_gen_7342},
Delta=
{
<s>(q_gen_7357) -> q_gen_7357
<z>() -> q_gen_7357
<s, s>(q_gen_7342) -> q_gen_7342
<z, s>(q_gen_7357) -> q_gen_7342
<z, z>() -> q_gen_7342
<s, s>(q_gen_7374) -> q_gen_7374
<s, z>(q_gen_7357) -> q_gen_7374
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  max -> 
{{{
Q={q_gen_7343, q_gen_7359, q_gen_7371},
Q_f={q_gen_7343},
Delta=
{
<s>(q_gen_7359) -> q_gen_7359
<z>() -> q_gen_7359
<s, s>(q_gen_7371) -> q_gen_7371
<z, z>() -> q_gen_7371
<s, s, s>(q_gen_7343) -> q_gen_7343
<s, z, s>(q_gen_7371) -> q_gen_7343
<z, s, s>(q_gen_7371) -> q_gen_7343
<z, s, z>(q_gen_7359) -> q_gen_7343
<z, z, z>() -> q_gen_7343
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  numnodes -> 
{{{
Q={q_gen_7345, q_gen_7350, q_gen_7351, q_gen_7369, q_gen_7380, q_gen_7408, q_gen_7409, q_gen_7413},
Q_f={q_gen_7345},
Delta=
{
<leaf>() -> q_gen_7350
<node>(q_gen_7409, q_gen_7350, q_gen_7408) -> q_gen_7350
<s>(q_gen_7380) -> q_gen_7380
<z>() -> q_gen_7380
<node>(q_gen_7409, q_gen_7350, q_gen_7350) -> q_gen_7408
<node>(q_gen_7409, q_gen_7408, q_gen_7408) -> q_gen_7408
<a>() -> q_gen_7409
<b>() -> q_gen_7409
<leaf, z>() -> q_gen_7345
<node, s>(q_gen_7351, q_gen_7350, q_gen_7350) -> q_gen_7345
<node, s>(q_gen_7369, q_gen_7350, q_gen_7350) -> q_gen_7345
<node, s>(q_gen_7369, q_gen_7350, q_gen_7408) -> q_gen_7345
<node, s>(q_gen_7369, q_gen_7408, q_gen_7350) -> q_gen_7345
<a, s>(q_gen_7380) -> q_gen_7351
<b, z>() -> q_gen_7351
<a, z>() -> q_gen_7369
<b, s>(q_gen_7380) -> q_gen_7369
<node, s>(q_gen_7351, q_gen_7350, q_gen_7408) -> q_gen_7413
<node, s>(q_gen_7351, q_gen_7408, q_gen_7408) -> q_gen_7413
<node, s>(q_gen_7369, q_gen_7408, q_gen_7408) -> q_gen_7413
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_7344, q_gen_7348, q_gen_7367},
Q_f={q_gen_7344},
Delta=
{
<s>(q_gen_7367) -> q_gen_7367
<z>() -> q_gen_7367
<s, s>(q_gen_7348) -> q_gen_7348
<z, s>(q_gen_7367) -> q_gen_7348
<z, z>() -> q_gen_7348
<s, s, s>(q_gen_7344) -> q_gen_7344
<s, z, s>(q_gen_7348) -> q_gen_7344
<z, s, s>(q_gen_7348) -> q_gen_7344
<z, z, s>(q_gen_7367) -> q_gen_7344
<z, z, z>() -> q_gen_7344
}

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

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

Teacher's answer:
New clause system:
{
() -> height([leaf, z]) -> 25
() -> leq([z, n2]) -> 26
() -> numnodes([leaf, z]) -> 26
() -> plus([n, z, n]) -> 26
(height([t1, _mba]) /\ height([t2, _nba]) /\ max([_mba, _nba, _oba])) -> height([node(e, t1, t2), s(_oba)]) -> 28
(height([t1, _yba]) /\ numnodes([t1, _zba])) -> leq([_yba, _zba]) -> 31
(leq([n, m])) -> max([n, m, m]) -> 27
(not leq([n, m])) -> max([n, m, n]) -> 27
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 26
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 26
(leq([s(nn1), z])) -> BOT -> 26
(numnodes([t1, _sba]) /\ numnodes([t2, _tba]) /\ plus([_sba, _tba, _uba])) -> numnodes([node(e, t1, t2), s(_uba)]) -> 29
(plus([n, mm, _hba])) -> plus([n, s(mm), s(_hba)]) -> 26
}
Sat witness: Found: ((height([t1, _yba]) /\ numnodes([t1, _zba])) -> leq([_yba, _zba]), {
_yba -> s(s(z))  ;  _zba -> s(z)  ;  t1 -> node(b, leaf, node(b, leaf, node(b, leaf, leaf)))
})

-------------------------------------------
Step 45, which took 0.133471 s (model generation: 0.070181,  model checking: 0.063290):

Model:
|_
{
height -> 
{{{
Q={q_gen_7346, q_gen_7354, q_gen_7355, q_gen_7383, q_gen_7384, q_gen_7403, q_gen_7404, q_gen_7405},
Q_f={q_gen_7346},
Delta=
{
<leaf>() -> q_gen_7354
<node>(q_gen_7384, q_gen_7354, q_gen_7354) -> q_gen_7383
<node>(q_gen_7384, q_gen_7354, q_gen_7383) -> q_gen_7383
<node>(q_gen_7384, q_gen_7383, q_gen_7383) -> q_gen_7383
<a>() -> q_gen_7384
<b>() -> q_gen_7384
<z>() -> q_gen_7404
<leaf, z>() -> q_gen_7346
<node, s>(q_gen_7355, q_gen_7354, q_gen_7354) -> q_gen_7346
<node, s>(q_gen_7355, q_gen_7354, q_gen_7383) -> q_gen_7346
<node, s>(q_gen_7355, q_gen_7383, q_gen_7383) -> q_gen_7346
<node, s>(q_gen_7403, q_gen_7354, q_gen_7383) -> q_gen_7346
<node, s>(q_gen_7403, q_gen_7383, q_gen_7354) -> q_gen_7346
<a, z>() -> q_gen_7355
<b, z>() -> q_gen_7355
<b, s>(q_gen_7404) -> q_gen_7403
<node, s>(q_gen_7403, q_gen_7354, q_gen_7354) -> q_gen_7405
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_7342, q_gen_7357, q_gen_7374},
Q_f={q_gen_7342},
Delta=
{
<s>(q_gen_7357) -> q_gen_7357
<z>() -> q_gen_7357
<s, s>(q_gen_7342) -> q_gen_7342
<z, s>(q_gen_7357) -> q_gen_7342
<z, z>() -> q_gen_7342
<s, s>(q_gen_7374) -> q_gen_7374
<s, z>(q_gen_7357) -> q_gen_7374
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  max -> 
{{{
Q={q_gen_7343, q_gen_7359, q_gen_7371},
Q_f={q_gen_7343},
Delta=
{
<s>(q_gen_7359) -> q_gen_7359
<z>() -> q_gen_7359
<s, s>(q_gen_7371) -> q_gen_7371
<z, z>() -> q_gen_7371
<s, s, s>(q_gen_7343) -> q_gen_7343
<s, z, s>(q_gen_7371) -> q_gen_7343
<z, s, s>(q_gen_7371) -> q_gen_7343
<z, s, z>(q_gen_7359) -> q_gen_7343
<z, z, z>() -> q_gen_7343
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  numnodes -> 
{{{
Q={q_gen_7345, q_gen_7350, q_gen_7351, q_gen_7379, q_gen_7380, q_gen_7408, q_gen_7409, q_gen_7413},
Q_f={q_gen_7345},
Delta=
{
<leaf>() -> q_gen_7350
<s>(q_gen_7380) -> q_gen_7380
<z>() -> q_gen_7380
<node>(q_gen_7409, q_gen_7350, q_gen_7350) -> q_gen_7408
<node>(q_gen_7409, q_gen_7350, q_gen_7408) -> q_gen_7408
<node>(q_gen_7409, q_gen_7408, q_gen_7408) -> q_gen_7408
<a>() -> q_gen_7409
<b>() -> q_gen_7409
<leaf, z>() -> q_gen_7345
<node, s>(q_gen_7351, q_gen_7350, q_gen_7350) -> q_gen_7345
<node, s>(q_gen_7379, q_gen_7350, q_gen_7350) -> q_gen_7345
<node, s>(q_gen_7379, q_gen_7350, q_gen_7408) -> q_gen_7345
<a, s>(q_gen_7380) -> q_gen_7351
<a, z>() -> q_gen_7351
<b, z>() -> q_gen_7351
<b, s>(q_gen_7380) -> q_gen_7379
<node, s>(q_gen_7351, q_gen_7350, q_gen_7408) -> q_gen_7413
<node, s>(q_gen_7351, q_gen_7408, q_gen_7408) -> q_gen_7413
<node, s>(q_gen_7379, q_gen_7408, q_gen_7408) -> q_gen_7413
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_7344, q_gen_7348, q_gen_7367},
Q_f={q_gen_7344},
Delta=
{
<s>(q_gen_7367) -> q_gen_7367
<z>() -> q_gen_7367
<s, s>(q_gen_7348) -> q_gen_7348
<z, s>(q_gen_7367) -> q_gen_7348
<z, z>() -> q_gen_7348
<s, s, s>(q_gen_7344) -> q_gen_7344
<s, z, s>(q_gen_7348) -> q_gen_7344
<z, s, s>(q_gen_7348) -> q_gen_7344
<z, z, s>(q_gen_7367) -> q_gen_7344
<z, z, z>() -> q_gen_7344
}

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

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

Teacher's answer:
New clause system:
{
() -> height([leaf, z]) -> 26
() -> leq([z, n2]) -> 27
() -> numnodes([leaf, z]) -> 27
() -> plus([n, z, n]) -> 27
(height([t1, _mba]) /\ height([t2, _nba]) /\ max([_mba, _nba, _oba])) -> height([node(e, t1, t2), s(_oba)]) -> 31
(height([t1, _yba]) /\ numnodes([t1, _zba])) -> leq([_yba, _zba]) -> 31
(leq([n, m])) -> max([n, m, m]) -> 28
(not leq([n, m])) -> max([n, m, n]) -> 28
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 27
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 27
(leq([s(nn1), z])) -> BOT -> 27
(numnodes([t1, _sba]) /\ numnodes([t2, _tba]) /\ plus([_sba, _tba, _uba])) -> numnodes([node(e, t1, t2), s(_uba)]) -> 29
(plus([n, mm, _hba])) -> plus([n, s(mm), s(_hba)]) -> 27
}
Sat witness: Found: ((height([t1, _mba]) /\ height([t2, _nba]) /\ max([_mba, _nba, _oba])) -> height([node(e, t1, t2), s(_oba)]), {
_mba -> z  ;  _nba -> s(s(z))  ;  _oba -> z  ;  e -> b  ;  t1 -> leaf  ;  t2 -> node(b, node(b, leaf, leaf), leaf)
})

-------------------------------------------
Step 46, which took 0.138794 s (model generation: 0.083558,  model checking: 0.055236):

Model:
|_
{
height -> 
{{{
Q={q_gen_7346, q_gen_7354, q_gen_7355, q_gen_7383, q_gen_7384, q_gen_7403, q_gen_7404, q_gen_7405},
Q_f={q_gen_7346},
Delta=
{
<leaf>() -> q_gen_7354
<node>(q_gen_7384, q_gen_7383, q_gen_7354) -> q_gen_7354
<node>(q_gen_7384, q_gen_7354, q_gen_7354) -> q_gen_7383
<node>(q_gen_7384, q_gen_7354, q_gen_7383) -> q_gen_7383
<node>(q_gen_7384, q_gen_7383, q_gen_7383) -> q_gen_7383
<a>() -> q_gen_7384
<b>() -> q_gen_7384
<z>() -> q_gen_7404
<leaf, z>() -> q_gen_7346
<node, s>(q_gen_7355, q_gen_7354, q_gen_7354) -> q_gen_7346
<node, s>(q_gen_7355, q_gen_7354, q_gen_7383) -> q_gen_7346
<node, s>(q_gen_7355, q_gen_7383, q_gen_7383) -> q_gen_7346
<node, s>(q_gen_7403, q_gen_7354, q_gen_7383) -> q_gen_7346
<node, s>(q_gen_7403, q_gen_7383, q_gen_7354) -> q_gen_7346
<a, z>() -> q_gen_7355
<b, z>() -> q_gen_7355
<b, s>(q_gen_7404) -> q_gen_7403
<node, s>(q_gen_7403, q_gen_7354, q_gen_7354) -> q_gen_7405
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_7342, q_gen_7357, q_gen_7374},
Q_f={q_gen_7342},
Delta=
{
<s>(q_gen_7357) -> q_gen_7357
<z>() -> q_gen_7357
<s, s>(q_gen_7342) -> q_gen_7342
<z, s>(q_gen_7357) -> q_gen_7342
<z, z>() -> q_gen_7342
<s, s>(q_gen_7374) -> q_gen_7374
<s, z>(q_gen_7357) -> q_gen_7374
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  max -> 
{{{
Q={q_gen_7343, q_gen_7359, q_gen_7371},
Q_f={q_gen_7343},
Delta=
{
<s>(q_gen_7359) -> q_gen_7359
<z>() -> q_gen_7359
<s, s>(q_gen_7371) -> q_gen_7371
<z, z>() -> q_gen_7371
<s, s, s>(q_gen_7343) -> q_gen_7343
<s, z, s>(q_gen_7371) -> q_gen_7343
<z, s, s>(q_gen_7371) -> q_gen_7343
<z, s, z>(q_gen_7359) -> q_gen_7343
<z, z, z>() -> q_gen_7343
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  numnodes -> 
{{{
Q={q_gen_7345, q_gen_7350, q_gen_7351, q_gen_7369, q_gen_7380, q_gen_7408, q_gen_7409, q_gen_7424},
Q_f={q_gen_7345},
Delta=
{
<leaf>() -> q_gen_7350
<s>(q_gen_7380) -> q_gen_7380
<z>() -> q_gen_7380
<node>(q_gen_7409, q_gen_7350, q_gen_7350) -> q_gen_7408
<node>(q_gen_7409, q_gen_7350, q_gen_7408) -> q_gen_7408
<node>(q_gen_7409, q_gen_7408, q_gen_7408) -> q_gen_7408
<a>() -> q_gen_7409
<b>() -> q_gen_7409
<leaf, z>() -> q_gen_7345
<node, s>(q_gen_7351, q_gen_7350, q_gen_7350) -> q_gen_7345
<node, s>(q_gen_7369, q_gen_7350, q_gen_7350) -> q_gen_7345
<node, s>(q_gen_7369, q_gen_7350, q_gen_7408) -> q_gen_7345
<node, s>(q_gen_7369, q_gen_7408, q_gen_7408) -> q_gen_7345
<b, z>() -> q_gen_7351
<a, s>(q_gen_7380) -> q_gen_7369
<a, z>() -> q_gen_7369
<b, s>(q_gen_7380) -> q_gen_7369
<node, s>(q_gen_7351, q_gen_7350, q_gen_7408) -> q_gen_7424
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_7344, q_gen_7348, q_gen_7367},
Q_f={q_gen_7344},
Delta=
{
<s>(q_gen_7367) -> q_gen_7367
<z>() -> q_gen_7367
<s, s>(q_gen_7348) -> q_gen_7348
<z, s>(q_gen_7367) -> q_gen_7348
<z, z>() -> q_gen_7348
<s, s, s>(q_gen_7344) -> q_gen_7344
<s, z, s>(q_gen_7348) -> q_gen_7344
<z, s, s>(q_gen_7348) -> q_gen_7344
<z, z, s>(q_gen_7367) -> q_gen_7344
<z, z, z>() -> q_gen_7344
}

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

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

Teacher's answer:
New clause system:
{
() -> height([leaf, z]) -> 27
() -> leq([z, n2]) -> 28
() -> numnodes([leaf, z]) -> 28
() -> plus([n, z, n]) -> 28
(height([t1, _mba]) /\ height([t2, _nba]) /\ max([_mba, _nba, _oba])) -> height([node(e, t1, t2), s(_oba)]) -> 31
(height([t1, _yba]) /\ numnodes([t1, _zba])) -> leq([_yba, _zba]) -> 31
(leq([n, m])) -> max([n, m, m]) -> 29
(not leq([n, m])) -> max([n, m, n]) -> 29
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 28
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 28
(leq([s(nn1), z])) -> BOT -> 28
(numnodes([t1, _sba]) /\ numnodes([t2, _tba]) /\ plus([_sba, _tba, _uba])) -> numnodes([node(e, t1, t2), s(_uba)]) -> 32
(plus([n, mm, _hba])) -> plus([n, s(mm), s(_hba)]) -> 28
}
Sat witness: Found: ((numnodes([t1, _sba]) /\ numnodes([t2, _tba]) /\ plus([_sba, _tba, _uba])) -> numnodes([node(e, t1, t2), s(_uba)]), {
_sba -> s(z)  ;  _tba -> z  ;  _uba -> s(z)  ;  e -> b  ;  t1 -> node(a, node(b, leaf, node(b, leaf, leaf)), node(b, leaf, node(b, leaf, leaf)))  ;  t2 -> leaf
})

-------------------------------------------
Step 47, which took 0.367956 s (model generation: 0.092468,  model checking: 0.275488):

Model:
|_
{
height -> 
{{{
Q={q_gen_7346, q_gen_7354, q_gen_7355, q_gen_7383, q_gen_7384, q_gen_7403, q_gen_7404, q_gen_7405},
Q_f={q_gen_7346},
Delta=
{
<leaf>() -> q_gen_7354
<node>(q_gen_7384, q_gen_7383, q_gen_7354) -> q_gen_7354
<node>(q_gen_7384, q_gen_7354, q_gen_7354) -> q_gen_7383
<node>(q_gen_7384, q_gen_7354, q_gen_7383) -> q_gen_7383
<node>(q_gen_7384, q_gen_7383, q_gen_7383) -> q_gen_7383
<a>() -> q_gen_7384
<b>() -> q_gen_7384
<z>() -> q_gen_7404
<leaf, z>() -> q_gen_7346
<node, s>(q_gen_7355, q_gen_7354, q_gen_7354) -> q_gen_7346
<node, s>(q_gen_7355, q_gen_7354, q_gen_7383) -> q_gen_7346
<node, s>(q_gen_7355, q_gen_7383, q_gen_7383) -> q_gen_7346
<node, s>(q_gen_7403, q_gen_7354, q_gen_7383) -> q_gen_7346
<node, s>(q_gen_7403, q_gen_7383, q_gen_7354) -> q_gen_7346
<a, z>() -> q_gen_7355
<b, z>() -> q_gen_7355
<b, s>(q_gen_7404) -> q_gen_7403
<node, s>(q_gen_7403, q_gen_7354, q_gen_7354) -> q_gen_7405
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_7342, q_gen_7357, q_gen_7374},
Q_f={q_gen_7342},
Delta=
{
<s>(q_gen_7357) -> q_gen_7357
<z>() -> q_gen_7357
<s, s>(q_gen_7342) -> q_gen_7342
<z, s>(q_gen_7357) -> q_gen_7342
<z, z>() -> q_gen_7342
<s, s>(q_gen_7374) -> q_gen_7374
<s, z>(q_gen_7357) -> q_gen_7374
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  max -> 
{{{
Q={q_gen_7343, q_gen_7359, q_gen_7371},
Q_f={q_gen_7343},
Delta=
{
<s>(q_gen_7359) -> q_gen_7359
<z>() -> q_gen_7359
<s, s>(q_gen_7371) -> q_gen_7371
<z, z>() -> q_gen_7371
<s, s, s>(q_gen_7343) -> q_gen_7343
<s, z, s>(q_gen_7371) -> q_gen_7343
<z, s, s>(q_gen_7371) -> q_gen_7343
<z, s, z>(q_gen_7359) -> q_gen_7343
<z, z, z>() -> q_gen_7343
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  numnodes -> 
{{{
Q={q_gen_7345, q_gen_7350, q_gen_7351, q_gen_7369, q_gen_7380, q_gen_7408, q_gen_7409, q_gen_7424},
Q_f={q_gen_7345},
Delta=
{
<leaf>() -> q_gen_7350
<s>(q_gen_7380) -> q_gen_7380
<z>() -> q_gen_7380
<node>(q_gen_7409, q_gen_7350, q_gen_7350) -> q_gen_7408
<node>(q_gen_7409, q_gen_7350, q_gen_7408) -> q_gen_7408
<node>(q_gen_7409, q_gen_7408, q_gen_7408) -> q_gen_7408
<a>() -> q_gen_7409
<b>() -> q_gen_7409
<leaf, z>() -> q_gen_7345
<node, s>(q_gen_7351, q_gen_7350, q_gen_7350) -> q_gen_7345
<node, s>(q_gen_7369, q_gen_7350, q_gen_7350) -> q_gen_7345
<node, s>(q_gen_7369, q_gen_7350, q_gen_7408) -> q_gen_7345
<node, s>(q_gen_7369, q_gen_7408, q_gen_7350) -> q_gen_7345
<node, s>(q_gen_7369, q_gen_7408, q_gen_7408) -> q_gen_7345
<b, z>() -> q_gen_7351
<a, s>(q_gen_7380) -> q_gen_7369
<a, z>() -> q_gen_7369
<b, s>(q_gen_7380) -> q_gen_7369
<node, s>(q_gen_7351, q_gen_7350, q_gen_7408) -> q_gen_7424
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_7344, q_gen_7348, q_gen_7367},
Q_f={q_gen_7344},
Delta=
{
<s>(q_gen_7367) -> q_gen_7367
<z>() -> q_gen_7367
<s, s>(q_gen_7348) -> q_gen_7348
<z, s>(q_gen_7367) -> q_gen_7348
<z, z>() -> q_gen_7348
<s, s, s>(q_gen_7344) -> q_gen_7344
<s, z, s>(q_gen_7348) -> q_gen_7344
<z, s, s>(q_gen_7348) -> q_gen_7344
<z, z, s>(q_gen_7367) -> q_gen_7344
<z, z, z>() -> q_gen_7344
}

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

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

Teacher's answer:
New clause system:
{
() -> height([leaf, z]) -> 28
() -> leq([z, n2]) -> 29
() -> numnodes([leaf, z]) -> 29
() -> plus([n, z, n]) -> 29
(height([t1, _mba]) /\ height([t2, _nba]) /\ max([_mba, _nba, _oba])) -> height([node(e, t1, t2), s(_oba)]) -> 34
(height([t1, _yba]) /\ numnodes([t1, _zba])) -> leq([_yba, _zba]) -> 32
(leq([n, m])) -> max([n, m, m]) -> 30
(not leq([n, m])) -> max([n, m, n]) -> 30
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 29
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 29
(leq([s(nn1), z])) -> BOT -> 29
(numnodes([t1, _sba]) /\ numnodes([t2, _tba]) /\ plus([_sba, _tba, _uba])) -> numnodes([node(e, t1, t2), s(_uba)]) -> 32
(plus([n, mm, _hba])) -> plus([n, s(mm), s(_hba)]) -> 29
}
Sat witness: Found: ((height([t1, _mba]) /\ height([t2, _nba]) /\ max([_mba, _nba, _oba])) -> height([node(e, t1, t2), s(_oba)]), {
_mba -> z  ;  _nba -> s(z)  ;  _oba -> s(z)  ;  e -> a  ;  t1 -> leaf  ;  t2 -> node(b, node(b, node(b, leaf, leaf), node(b, leaf, node(b, leaf, leaf))), node(b, node(b, leaf, leaf), node(b, leaf, node(b, leaf, leaf))))
})

-------------------------------------------
Step 48, which took 0.106823 s (model generation: 0.100696,  model checking: 0.006127):

Model:
|_
{
height -> 
{{{
Q={q_gen_7346, q_gen_7354, q_gen_7355, q_gen_7383, q_gen_7384, q_gen_7400, q_gen_7403, q_gen_7404},
Q_f={q_gen_7346},
Delta=
{
<leaf>() -> q_gen_7354
<node>(q_gen_7384, q_gen_7383, q_gen_7354) -> q_gen_7354
<node>(q_gen_7384, q_gen_7383, q_gen_7383) -> q_gen_7354
<node>(q_gen_7384, q_gen_7354, q_gen_7354) -> q_gen_7383
<node>(q_gen_7384, q_gen_7354, q_gen_7383) -> q_gen_7383
<a>() -> q_gen_7384
<b>() -> q_gen_7384
<z>() -> q_gen_7404
<leaf, z>() -> q_gen_7346
<node, s>(q_gen_7355, q_gen_7354, q_gen_7354) -> q_gen_7346
<node, s>(q_gen_7355, q_gen_7354, q_gen_7383) -> q_gen_7346
<node, s>(q_gen_7403, q_gen_7354, q_gen_7383) -> q_gen_7346
<node, s>(q_gen_7403, q_gen_7383, q_gen_7354) -> q_gen_7346
<a, z>() -> q_gen_7355
<b, z>() -> q_gen_7355
<node, s>(q_gen_7355, q_gen_7383, q_gen_7383) -> q_gen_7400
<node, s>(q_gen_7403, q_gen_7354, q_gen_7354) -> q_gen_7400
<a, s>(q_gen_7404) -> q_gen_7403
<b, s>(q_gen_7404) -> q_gen_7403
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_7342, q_gen_7357, q_gen_7374},
Q_f={q_gen_7342},
Delta=
{
<s>(q_gen_7357) -> q_gen_7357
<z>() -> q_gen_7357
<s, s>(q_gen_7342) -> q_gen_7342
<z, s>(q_gen_7357) -> q_gen_7342
<z, z>() -> q_gen_7342
<s, s>(q_gen_7374) -> q_gen_7374
<s, z>(q_gen_7357) -> q_gen_7374
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  max -> 
{{{
Q={q_gen_7343, q_gen_7359, q_gen_7371},
Q_f={q_gen_7343},
Delta=
{
<s>(q_gen_7359) -> q_gen_7359
<z>() -> q_gen_7359
<s, s>(q_gen_7371) -> q_gen_7371
<z, z>() -> q_gen_7371
<s, s, s>(q_gen_7343) -> q_gen_7343
<s, z, s>(q_gen_7371) -> q_gen_7343
<z, s, s>(q_gen_7371) -> q_gen_7343
<z, s, z>(q_gen_7359) -> q_gen_7343
<z, z, z>() -> q_gen_7343
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  numnodes -> 
{{{
Q={q_gen_7345, q_gen_7350, q_gen_7351, q_gen_7379, q_gen_7380, q_gen_7408, q_gen_7409, q_gen_7413},
Q_f={q_gen_7345},
Delta=
{
<leaf>() -> q_gen_7350
<s>(q_gen_7380) -> q_gen_7380
<z>() -> q_gen_7380
<node>(q_gen_7409, q_gen_7350, q_gen_7350) -> q_gen_7408
<node>(q_gen_7409, q_gen_7350, q_gen_7408) -> q_gen_7408
<node>(q_gen_7409, q_gen_7408, q_gen_7408) -> q_gen_7408
<a>() -> q_gen_7409
<b>() -> q_gen_7409
<leaf, z>() -> q_gen_7345
<node, s>(q_gen_7351, q_gen_7350, q_gen_7350) -> q_gen_7345
<node, s>(q_gen_7379, q_gen_7350, q_gen_7350) -> q_gen_7345
<node, s>(q_gen_7379, q_gen_7350, q_gen_7408) -> q_gen_7345
<a, s>(q_gen_7380) -> q_gen_7351
<a, z>() -> q_gen_7351
<b, z>() -> q_gen_7351
<b, s>(q_gen_7380) -> q_gen_7379
<node, s>(q_gen_7351, q_gen_7350, q_gen_7408) -> q_gen_7413
<node, s>(q_gen_7351, q_gen_7408, q_gen_7408) -> q_gen_7413
<node, s>(q_gen_7379, q_gen_7408, q_gen_7350) -> q_gen_7413
<node, s>(q_gen_7379, q_gen_7408, q_gen_7408) -> q_gen_7413
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_7344, q_gen_7348, q_gen_7367},
Q_f={q_gen_7344},
Delta=
{
<s>(q_gen_7367) -> q_gen_7367
<z>() -> q_gen_7367
<s, s>(q_gen_7348) -> q_gen_7348
<z, s>(q_gen_7367) -> q_gen_7348
<z, z>() -> q_gen_7348
<s, s, s>(q_gen_7344) -> q_gen_7344
<s, z, s>(q_gen_7348) -> q_gen_7344
<z, s, s>(q_gen_7348) -> q_gen_7344
<z, z, s>(q_gen_7367) -> q_gen_7344
<z, z, z>() -> q_gen_7344
}

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

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

Teacher's answer:
New clause system:
{
() -> height([leaf, z]) -> 29
() -> leq([z, n2]) -> 30
() -> numnodes([leaf, z]) -> 30
() -> plus([n, z, n]) -> 30
(height([t1, _mba]) /\ height([t2, _nba]) /\ max([_mba, _nba, _oba])) -> height([node(e, t1, t2), s(_oba)]) -> 34
(height([t1, _yba]) /\ numnodes([t1, _zba])) -> leq([_yba, _zba]) -> 32
(leq([n, m])) -> max([n, m, m]) -> 31
(not leq([n, m])) -> max([n, m, n]) -> 31
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 30
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 30
(leq([s(nn1), z])) -> BOT -> 30
(numnodes([t1, _sba]) /\ numnodes([t2, _tba]) /\ plus([_sba, _tba, _uba])) -> numnodes([node(e, t1, t2), s(_uba)]) -> 35
(plus([n, mm, _hba])) -> plus([n, s(mm), s(_hba)]) -> 30
}
Sat witness: Found: ((numnodes([t1, _sba]) /\ numnodes([t2, _tba]) /\ plus([_sba, _tba, _uba])) -> numnodes([node(e, t1, t2), s(_uba)]), {
_sba -> s(s(z))  ;  _tba -> z  ;  _uba -> s(s(z))  ;  e -> b  ;  t1 -> node(b, leaf, node(b, leaf, leaf))  ;  t2 -> leaf
})

-------------------------------------------
Step 49, which took 0.100523 s (model generation: 0.098540,  model checking: 0.001983):

Model:
|_
{
height -> 
{{{
Q={q_gen_7346, q_gen_7354, q_gen_7355, q_gen_7383, q_gen_7384, q_gen_7400, q_gen_7403, q_gen_7404},
Q_f={q_gen_7346},
Delta=
{
<leaf>() -> q_gen_7354
<node>(q_gen_7384, q_gen_7383, q_gen_7354) -> q_gen_7354
<node>(q_gen_7384, q_gen_7383, q_gen_7383) -> q_gen_7354
<node>(q_gen_7384, q_gen_7354, q_gen_7354) -> q_gen_7383
<node>(q_gen_7384, q_gen_7354, q_gen_7383) -> q_gen_7383
<a>() -> q_gen_7384
<b>() -> q_gen_7384
<z>() -> q_gen_7404
<leaf, z>() -> q_gen_7346
<node, s>(q_gen_7355, q_gen_7354, q_gen_7354) -> q_gen_7346
<node, s>(q_gen_7355, q_gen_7354, q_gen_7383) -> q_gen_7346
<node, s>(q_gen_7403, q_gen_7354, q_gen_7383) -> q_gen_7346
<node, s>(q_gen_7403, q_gen_7383, q_gen_7354) -> q_gen_7346
<a, z>() -> q_gen_7355
<b, z>() -> q_gen_7355
<node, s>(q_gen_7355, q_gen_7383, q_gen_7383) -> q_gen_7400
<node, s>(q_gen_7403, q_gen_7354, q_gen_7354) -> q_gen_7400
<a, s>(q_gen_7404) -> q_gen_7403
<b, s>(q_gen_7404) -> q_gen_7403
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_7342, q_gen_7357, q_gen_7374},
Q_f={q_gen_7342},
Delta=
{
<s>(q_gen_7357) -> q_gen_7357
<z>() -> q_gen_7357
<s, s>(q_gen_7342) -> q_gen_7342
<z, s>(q_gen_7357) -> q_gen_7342
<z, z>() -> q_gen_7342
<s, s>(q_gen_7374) -> q_gen_7374
<s, z>(q_gen_7357) -> q_gen_7374
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  max -> 
{{{
Q={q_gen_7343, q_gen_7359, q_gen_7371},
Q_f={q_gen_7343},
Delta=
{
<s>(q_gen_7359) -> q_gen_7359
<z>() -> q_gen_7359
<s, s>(q_gen_7371) -> q_gen_7371
<z, z>() -> q_gen_7371
<s, s, s>(q_gen_7343) -> q_gen_7343
<s, z, s>(q_gen_7371) -> q_gen_7343
<z, s, s>(q_gen_7371) -> q_gen_7343
<z, s, z>(q_gen_7359) -> q_gen_7343
<z, z, z>() -> q_gen_7343
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  numnodes -> 
{{{
Q={q_gen_7345, q_gen_7350, q_gen_7351, q_gen_7369, q_gen_7380, q_gen_7408, q_gen_7409, q_gen_7424},
Q_f={q_gen_7345},
Delta=
{
<leaf>() -> q_gen_7350
<s>(q_gen_7380) -> q_gen_7380
<z>() -> q_gen_7380
<node>(q_gen_7409, q_gen_7350, q_gen_7350) -> q_gen_7408
<node>(q_gen_7409, q_gen_7350, q_gen_7408) -> q_gen_7408
<node>(q_gen_7409, q_gen_7408, q_gen_7408) -> q_gen_7408
<a>() -> q_gen_7409
<b>() -> q_gen_7409
<leaf, z>() -> q_gen_7345
<node, s>(q_gen_7351, q_gen_7350, q_gen_7350) -> q_gen_7345
<node, s>(q_gen_7369, q_gen_7350, q_gen_7350) -> q_gen_7345
<node, s>(q_gen_7369, q_gen_7350, q_gen_7408) -> q_gen_7345
<node, s>(q_gen_7369, q_gen_7408, q_gen_7350) -> q_gen_7345
<node, s>(q_gen_7369, q_gen_7408, q_gen_7408) -> q_gen_7345
<b, z>() -> q_gen_7351
<a, s>(q_gen_7380) -> q_gen_7369
<a, z>() -> q_gen_7369
<b, s>(q_gen_7380) -> q_gen_7369
<node, s>(q_gen_7351, q_gen_7350, q_gen_7408) -> q_gen_7424
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_7344, q_gen_7348, q_gen_7367},
Q_f={q_gen_7344},
Delta=
{
<s>(q_gen_7367) -> q_gen_7367
<z>() -> q_gen_7367
<s, s>(q_gen_7348) -> q_gen_7348
<z, s>(q_gen_7367) -> q_gen_7348
<z, z>() -> q_gen_7348
<s, s, s>(q_gen_7344) -> q_gen_7344
<s, z, s>(q_gen_7348) -> q_gen_7344
<z, s, s>(q_gen_7348) -> q_gen_7344
<z, z, s>(q_gen_7367) -> q_gen_7344
<z, z, z>() -> q_gen_7344
}

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

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

Teacher's answer:
New clause system:
{
() -> height([leaf, z]) -> 30
() -> leq([z, n2]) -> 31
() -> numnodes([leaf, z]) -> 31
() -> plus([n, z, n]) -> 31
(height([t1, _mba]) /\ height([t2, _nba]) /\ max([_mba, _nba, _oba])) -> height([node(e, t1, t2), s(_oba)]) -> 34
(height([t1, _yba]) /\ numnodes([t1, _zba])) -> leq([_yba, _zba]) -> 35
(leq([n, m])) -> max([n, m, m]) -> 32
(not leq([n, m])) -> max([n, m, n]) -> 32
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 31
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 31
(leq([s(nn1), z])) -> BOT -> 31
(numnodes([t1, _sba]) /\ numnodes([t2, _tba]) /\ plus([_sba, _tba, _uba])) -> numnodes([node(e, t1, t2), s(_uba)]) -> 35
(plus([n, mm, _hba])) -> plus([n, s(mm), s(_hba)]) -> 31
}
Sat witness: Found: ((height([t1, _yba]) /\ numnodes([t1, _zba])) -> leq([_yba, _zba]), {
_yba -> s(s(z))  ;  _zba -> s(z)  ;  t1 -> node(a, node(b, leaf, leaf), leaf)
})

-------------------------------------------
Step 50, which took 0.477521 s (model generation: 0.104274,  model checking: 0.373247):

Model:
|_
{
height -> 
{{{
Q={q_gen_7346, q_gen_7354, q_gen_7355, q_gen_7383, q_gen_7384, q_gen_7400, q_gen_7403, q_gen_7404},
Q_f={q_gen_7346},
Delta=
{
<leaf>() -> q_gen_7354
<node>(q_gen_7384, q_gen_7383, q_gen_7354) -> q_gen_7354
<node>(q_gen_7384, q_gen_7354, q_gen_7354) -> q_gen_7383
<node>(q_gen_7384, q_gen_7354, q_gen_7383) -> q_gen_7383
<node>(q_gen_7384, q_gen_7383, q_gen_7383) -> q_gen_7383
<a>() -> q_gen_7384
<b>() -> q_gen_7384
<z>() -> q_gen_7404
<leaf, z>() -> q_gen_7346
<node, s>(q_gen_7355, q_gen_7354, q_gen_7354) -> q_gen_7346
<node, s>(q_gen_7355, q_gen_7354, q_gen_7383) -> q_gen_7346
<node, s>(q_gen_7403, q_gen_7354, q_gen_7383) -> q_gen_7346
<node, s>(q_gen_7403, q_gen_7383, q_gen_7354) -> q_gen_7346
<a, z>() -> q_gen_7355
<b, z>() -> q_gen_7355
<node, s>(q_gen_7355, q_gen_7383, q_gen_7383) -> q_gen_7400
<node, s>(q_gen_7403, q_gen_7354, q_gen_7354) -> q_gen_7400
<a, s>(q_gen_7404) -> q_gen_7403
<b, s>(q_gen_7404) -> q_gen_7403
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_7342, q_gen_7357, q_gen_7374},
Q_f={q_gen_7342},
Delta=
{
<s>(q_gen_7357) -> q_gen_7357
<z>() -> q_gen_7357
<s, s>(q_gen_7342) -> q_gen_7342
<z, s>(q_gen_7357) -> q_gen_7342
<z, z>() -> q_gen_7342
<s, s>(q_gen_7374) -> q_gen_7374
<s, z>(q_gen_7357) -> q_gen_7374
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  max -> 
{{{
Q={q_gen_7343, q_gen_7359, q_gen_7371},
Q_f={q_gen_7343},
Delta=
{
<s>(q_gen_7359) -> q_gen_7359
<z>() -> q_gen_7359
<s, s>(q_gen_7371) -> q_gen_7371
<z, z>() -> q_gen_7371
<s, s, s>(q_gen_7343) -> q_gen_7343
<s, z, s>(q_gen_7371) -> q_gen_7343
<z, s, s>(q_gen_7371) -> q_gen_7343
<z, s, z>(q_gen_7359) -> q_gen_7343
<z, z, z>() -> q_gen_7343
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  numnodes -> 
{{{
Q={q_gen_7345, q_gen_7350, q_gen_7351, q_gen_7379, q_gen_7380, q_gen_7408, q_gen_7409, q_gen_7424},
Q_f={q_gen_7345},
Delta=
{
<leaf>() -> q_gen_7350
<s>(q_gen_7380) -> q_gen_7380
<z>() -> q_gen_7380
<node>(q_gen_7409, q_gen_7350, q_gen_7350) -> q_gen_7408
<node>(q_gen_7409, q_gen_7350, q_gen_7408) -> q_gen_7408
<node>(q_gen_7409, q_gen_7408, q_gen_7408) -> q_gen_7408
<a>() -> q_gen_7409
<b>() -> q_gen_7409
<leaf, z>() -> q_gen_7345
<node, s>(q_gen_7351, q_gen_7350, q_gen_7350) -> q_gen_7345
<node, s>(q_gen_7379, q_gen_7350, q_gen_7350) -> q_gen_7345
<node, s>(q_gen_7379, q_gen_7350, q_gen_7408) -> q_gen_7345
<node, s>(q_gen_7379, q_gen_7408, q_gen_7350) -> q_gen_7345
<node, s>(q_gen_7379, q_gen_7408, q_gen_7408) -> q_gen_7345
<a, z>() -> q_gen_7351
<b, z>() -> q_gen_7351
<a, s>(q_gen_7380) -> q_gen_7379
<b, s>(q_gen_7380) -> q_gen_7379
<node, s>(q_gen_7351, q_gen_7350, q_gen_7408) -> q_gen_7424
<node, s>(q_gen_7351, q_gen_7408, q_gen_7350) -> q_gen_7424
<node, s>(q_gen_7351, q_gen_7408, q_gen_7408) -> q_gen_7424
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_7344, q_gen_7348, q_gen_7367},
Q_f={q_gen_7344},
Delta=
{
<s>(q_gen_7367) -> q_gen_7367
<z>() -> q_gen_7367
<s, s>(q_gen_7348) -> q_gen_7348
<z, s>(q_gen_7367) -> q_gen_7348
<z, z>() -> q_gen_7348
<s, s, s>(q_gen_7344) -> q_gen_7344
<s, z, s>(q_gen_7348) -> q_gen_7344
<z, s, s>(q_gen_7348) -> q_gen_7344
<z, z, s>(q_gen_7367) -> q_gen_7344
<z, z, z>() -> q_gen_7344
}

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

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

Teacher's answer:
New clause system:
{
() -> height([leaf, z]) -> 31
() -> leq([z, n2]) -> 32
() -> numnodes([leaf, z]) -> 32
() -> plus([n, z, n]) -> 32
(height([t1, _mba]) /\ height([t2, _nba]) /\ max([_mba, _nba, _oba])) -> height([node(e, t1, t2), s(_oba)]) -> 37
(height([t1, _yba]) /\ numnodes([t1, _zba])) -> leq([_yba, _zba]) -> 35
(leq([n, m])) -> max([n, m, m]) -> 33
(not leq([n, m])) -> max([n, m, n]) -> 33
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 32
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 32
(leq([s(nn1), z])) -> BOT -> 32
(numnodes([t1, _sba]) /\ numnodes([t2, _tba]) /\ plus([_sba, _tba, _uba])) -> numnodes([node(e, t1, t2), s(_uba)]) -> 35
(plus([n, mm, _hba])) -> plus([n, s(mm), s(_hba)]) -> 32
}
Sat witness: Found: ((height([t1, _mba]) /\ height([t2, _nba]) /\ max([_mba, _nba, _oba])) -> height([node(e, t1, t2), s(_oba)]), {
_mba -> z  ;  _nba -> s(s(z))  ;  _oba -> s(s(z))  ;  e -> b  ;  t1 -> leaf  ;  t2 -> node(a, node(b, node(b, leaf, leaf), leaf), node(b, node(b, leaf, node(b, leaf, leaf)), node(b, leaf, node(b, leaf, leaf))))
})

-------------------------------------------
Step 51, which took 0.160718 s (model generation: 0.120627,  model checking: 0.040091):

Model:
|_
{
height -> 
{{{
Q={q_gen_7346, q_gen_7354, q_gen_7355, q_gen_7383, q_gen_7384, q_gen_7400, q_gen_7403, q_gen_7404},
Q_f={q_gen_7346},
Delta=
{
<leaf>() -> q_gen_7354
<node>(q_gen_7384, q_gen_7383, q_gen_7383) -> q_gen_7354
<node>(q_gen_7384, q_gen_7354, q_gen_7354) -> q_gen_7383
<node>(q_gen_7384, q_gen_7354, q_gen_7383) -> q_gen_7383
<node>(q_gen_7384, q_gen_7383, q_gen_7354) -> q_gen_7383
<a>() -> q_gen_7384
<b>() -> q_gen_7384
<s>(q_gen_7404) -> q_gen_7404
<z>() -> q_gen_7404
<leaf, z>() -> q_gen_7346
<node, s>(q_gen_7355, q_gen_7354, q_gen_7354) -> q_gen_7346
<node, s>(q_gen_7355, q_gen_7354, q_gen_7383) -> q_gen_7346
<node, s>(q_gen_7403, q_gen_7354, q_gen_7383) -> q_gen_7346
<node, s>(q_gen_7403, q_gen_7383, q_gen_7354) -> q_gen_7346
<a, s>(q_gen_7404) -> q_gen_7355
<a, z>() -> q_gen_7355
<b, z>() -> q_gen_7355
<node, s>(q_gen_7355, q_gen_7383, q_gen_7354) -> q_gen_7400
<node, s>(q_gen_7355, q_gen_7383, q_gen_7383) -> q_gen_7400
<node, s>(q_gen_7403, q_gen_7354, q_gen_7354) -> q_gen_7400
<b, s>(q_gen_7404) -> q_gen_7403
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_7342, q_gen_7357, q_gen_7374},
Q_f={q_gen_7342},
Delta=
{
<s>(q_gen_7357) -> q_gen_7357
<z>() -> q_gen_7357
<s, s>(q_gen_7342) -> q_gen_7342
<z, s>(q_gen_7357) -> q_gen_7342
<z, z>() -> q_gen_7342
<s, s>(q_gen_7374) -> q_gen_7374
<s, z>(q_gen_7357) -> q_gen_7374
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  max -> 
{{{
Q={q_gen_7343, q_gen_7359, q_gen_7371},
Q_f={q_gen_7343},
Delta=
{
<s>(q_gen_7359) -> q_gen_7359
<z>() -> q_gen_7359
<s, s>(q_gen_7371) -> q_gen_7371
<z, z>() -> q_gen_7371
<s, s, s>(q_gen_7343) -> q_gen_7343
<s, z, s>(q_gen_7371) -> q_gen_7343
<z, s, s>(q_gen_7371) -> q_gen_7343
<z, s, z>(q_gen_7359) -> q_gen_7343
<z, z, z>() -> q_gen_7343
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  numnodes -> 
{{{
Q={q_gen_7345, q_gen_7350, q_gen_7351, q_gen_7369, q_gen_7380, q_gen_7408, q_gen_7409, q_gen_7424},
Q_f={q_gen_7345},
Delta=
{
<leaf>() -> q_gen_7350
<node>(q_gen_7409, q_gen_7408, q_gen_7408) -> q_gen_7350
<s>(q_gen_7380) -> q_gen_7380
<z>() -> q_gen_7380
<node>(q_gen_7409, q_gen_7350, q_gen_7350) -> q_gen_7408
<node>(q_gen_7409, q_gen_7350, q_gen_7408) -> q_gen_7408
<a>() -> q_gen_7409
<b>() -> q_gen_7409
<leaf, z>() -> q_gen_7345
<node, s>(q_gen_7351, q_gen_7350, q_gen_7350) -> q_gen_7345
<node, s>(q_gen_7369, q_gen_7350, q_gen_7350) -> q_gen_7345
<node, s>(q_gen_7369, q_gen_7350, q_gen_7408) -> q_gen_7345
<node, s>(q_gen_7369, q_gen_7408, q_gen_7350) -> q_gen_7345
<node, s>(q_gen_7369, q_gen_7408, q_gen_7408) -> q_gen_7345
<b, z>() -> q_gen_7351
<a, s>(q_gen_7380) -> q_gen_7369
<a, z>() -> q_gen_7369
<b, s>(q_gen_7380) -> q_gen_7369
<node, s>(q_gen_7351, q_gen_7350, q_gen_7408) -> q_gen_7424
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_7344, q_gen_7348, q_gen_7367},
Q_f={q_gen_7344},
Delta=
{
<s>(q_gen_7367) -> q_gen_7367
<z>() -> q_gen_7367
<s, s>(q_gen_7348) -> q_gen_7348
<z, s>(q_gen_7367) -> q_gen_7348
<z, z>() -> q_gen_7348
<s, s, s>(q_gen_7344) -> q_gen_7344
<s, z, s>(q_gen_7348) -> q_gen_7344
<z, s, s>(q_gen_7348) -> q_gen_7344
<z, z, s>(q_gen_7367) -> q_gen_7344
<z, z, z>() -> q_gen_7344
}

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

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

Teacher's answer:
New clause system:
{
() -> height([leaf, z]) -> 32
() -> leq([z, n2]) -> 33
() -> numnodes([leaf, z]) -> 33
() -> plus([n, z, n]) -> 33
(height([t1, _mba]) /\ height([t2, _nba]) /\ max([_mba, _nba, _oba])) -> height([node(e, t1, t2), s(_oba)]) -> 37
(height([t1, _yba]) /\ numnodes([t1, _zba])) -> leq([_yba, _zba]) -> 35
(leq([n, m])) -> max([n, m, m]) -> 34
(not leq([n, m])) -> max([n, m, n]) -> 34
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 33
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 33
(leq([s(nn1), z])) -> BOT -> 33
(numnodes([t1, _sba]) /\ numnodes([t2, _tba]) /\ plus([_sba, _tba, _uba])) -> numnodes([node(e, t1, t2), s(_uba)]) -> 38
(plus([n, mm, _hba])) -> plus([n, s(mm), s(_hba)]) -> 33
}
Sat witness: Found: ((numnodes([t1, _sba]) /\ numnodes([t2, _tba]) /\ plus([_sba, _tba, _uba])) -> numnodes([node(e, t1, t2), s(_uba)]), {
_sba -> z  ;  _tba -> s(s(z))  ;  _uba -> s(s(z))  ;  e -> b  ;  t1 -> leaf  ;  t2 -> node(b, node(b, leaf, leaf), leaf)
})

-------------------------------------------
Step 52, which took 0.242251 s (model generation: 0.240345,  model checking: 0.001906):

Model:
|_
{
height -> 
{{{
Q={q_gen_7346, q_gen_7354, q_gen_7355, q_gen_7383, q_gen_7384, q_gen_7403, q_gen_7404, q_gen_7405},
Q_f={q_gen_7346},
Delta=
{
<leaf>() -> q_gen_7354
<node>(q_gen_7384, q_gen_7354, q_gen_7354) -> q_gen_7383
<node>(q_gen_7384, q_gen_7354, q_gen_7383) -> q_gen_7383
<node>(q_gen_7384, q_gen_7383, q_gen_7354) -> q_gen_7383
<node>(q_gen_7384, q_gen_7383, q_gen_7383) -> q_gen_7383
<a>() -> q_gen_7384
<b>() -> q_gen_7384
<s>(q_gen_7404) -> q_gen_7404
<z>() -> q_gen_7404
<leaf, z>() -> q_gen_7346
<node, s>(q_gen_7355, q_gen_7354, q_gen_7354) -> q_gen_7346
<node, s>(q_gen_7355, q_gen_7354, q_gen_7383) -> q_gen_7346
<node, s>(q_gen_7355, q_gen_7383, q_gen_7383) -> q_gen_7346
<node, s>(q_gen_7403, q_gen_7354, q_gen_7383) -> q_gen_7346
<node, s>(q_gen_7403, q_gen_7383, q_gen_7354) -> q_gen_7346
<a, z>() -> q_gen_7355
<b, z>() -> q_gen_7355
<a, s>(q_gen_7404) -> q_gen_7403
<b, s>(q_gen_7404) -> q_gen_7403
<node, s>(q_gen_7403, q_gen_7354, q_gen_7354) -> q_gen_7405
<node, s>(q_gen_7403, q_gen_7383, q_gen_7383) -> q_gen_7405
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_7342, q_gen_7357, q_gen_7374},
Q_f={q_gen_7342},
Delta=
{
<s>(q_gen_7357) -> q_gen_7357
<z>() -> q_gen_7357
<s, s>(q_gen_7342) -> q_gen_7342
<z, s>(q_gen_7357) -> q_gen_7342
<z, z>() -> q_gen_7342
<s, s>(q_gen_7374) -> q_gen_7374
<s, z>(q_gen_7357) -> q_gen_7374
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  max -> 
{{{
Q={q_gen_7343, q_gen_7359, q_gen_7371},
Q_f={q_gen_7343},
Delta=
{
<s>(q_gen_7359) -> q_gen_7359
<z>() -> q_gen_7359
<s, s>(q_gen_7371) -> q_gen_7371
<z, z>() -> q_gen_7371
<s, s, s>(q_gen_7343) -> q_gen_7343
<s, z, s>(q_gen_7371) -> q_gen_7343
<z, s, s>(q_gen_7371) -> q_gen_7343
<z, s, z>(q_gen_7359) -> q_gen_7343
<z, z, z>() -> q_gen_7343
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  numnodes -> 
{{{
Q={q_gen_7345, q_gen_7350, q_gen_7351, q_gen_7379, q_gen_7380, q_gen_7408, q_gen_7409, q_gen_7424},
Q_f={q_gen_7345},
Delta=
{
<leaf>() -> q_gen_7350
<s>(q_gen_7380) -> q_gen_7380
<z>() -> q_gen_7380
<node>(q_gen_7409, q_gen_7350, q_gen_7350) -> q_gen_7408
<node>(q_gen_7409, q_gen_7350, q_gen_7408) -> q_gen_7408
<node>(q_gen_7409, q_gen_7408, q_gen_7350) -> q_gen_7408
<node>(q_gen_7409, q_gen_7408, q_gen_7408) -> q_gen_7408
<a>() -> q_gen_7409
<b>() -> q_gen_7409
<leaf, z>() -> q_gen_7345
<node, s>(q_gen_7351, q_gen_7350, q_gen_7350) -> q_gen_7345
<node, s>(q_gen_7379, q_gen_7350, q_gen_7350) -> q_gen_7345
<node, s>(q_gen_7379, q_gen_7350, q_gen_7408) -> q_gen_7345
<node, s>(q_gen_7379, q_gen_7408, q_gen_7350) -> q_gen_7345
<node, s>(q_gen_7379, q_gen_7408, q_gen_7408) -> q_gen_7345
<a, z>() -> q_gen_7351
<b, z>() -> q_gen_7351
<a, s>(q_gen_7380) -> q_gen_7379
<b, s>(q_gen_7380) -> q_gen_7379
<node, s>(q_gen_7351, q_gen_7350, q_gen_7408) -> q_gen_7424
<node, s>(q_gen_7351, q_gen_7408, q_gen_7350) -> q_gen_7424
<node, s>(q_gen_7351, q_gen_7408, q_gen_7408) -> q_gen_7424
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_7344, q_gen_7348, q_gen_7367},
Q_f={q_gen_7344},
Delta=
{
<s>(q_gen_7367) -> q_gen_7367
<z>() -> q_gen_7367
<s, s>(q_gen_7348) -> q_gen_7348
<z, s>(q_gen_7367) -> q_gen_7348
<z, z>() -> q_gen_7348
<s, s, s>(q_gen_7344) -> q_gen_7344
<s, z, s>(q_gen_7348) -> q_gen_7344
<z, s, s>(q_gen_7348) -> q_gen_7344
<z, z, s>(q_gen_7367) -> q_gen_7344
<z, z, z>() -> q_gen_7344
}

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

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

Teacher's answer:
New clause system:
{
() -> height([leaf, z]) -> 33
() -> leq([z, n2]) -> 34
() -> numnodes([leaf, z]) -> 34
() -> plus([n, z, n]) -> 34
(height([t1, _mba]) /\ height([t2, _nba]) /\ max([_mba, _nba, _oba])) -> height([node(e, t1, t2), s(_oba)]) -> 37
(height([t1, _yba]) /\ numnodes([t1, _zba])) -> leq([_yba, _zba]) -> 38
(leq([n, m])) -> max([n, m, m]) -> 35
(not leq([n, m])) -> max([n, m, n]) -> 35
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 34
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 34
(leq([s(nn1), z])) -> BOT -> 34
(numnodes([t1, _sba]) /\ numnodes([t2, _tba]) /\ plus([_sba, _tba, _uba])) -> numnodes([node(e, t1, t2), s(_uba)]) -> 38
(plus([n, mm, _hba])) -> plus([n, s(mm), s(_hba)]) -> 34
}
Sat witness: Found: ((height([t1, _yba]) /\ numnodes([t1, _zba])) -> leq([_yba, _zba]), {
_yba -> s(s(s(z)))  ;  _zba -> s(s(z))  ;  t1 -> node(a, node(b, leaf, leaf), leaf)
})

-------------------------------------------
Step 53, which took 0.193438 s (model generation: 0.179543,  model checking: 0.013895):

Model:
|_
{
height -> 
{{{
Q={q_gen_7346, q_gen_7354, q_gen_7355, q_gen_7383, q_gen_7384, q_gen_7403, q_gen_7404, q_gen_7405},
Q_f={q_gen_7346},
Delta=
{
<leaf>() -> q_gen_7354
<node>(q_gen_7384, q_gen_7383, q_gen_7354) -> q_gen_7354
<node>(q_gen_7384, q_gen_7354, q_gen_7354) -> q_gen_7383
<node>(q_gen_7384, q_gen_7354, q_gen_7383) -> q_gen_7383
<node>(q_gen_7384, q_gen_7383, q_gen_7383) -> q_gen_7383
<a>() -> q_gen_7384
<b>() -> q_gen_7384
<s>(q_gen_7404) -> q_gen_7404
<z>() -> q_gen_7404
<leaf, z>() -> q_gen_7346
<node, s>(q_gen_7355, q_gen_7354, q_gen_7354) -> q_gen_7346
<node, s>(q_gen_7355, q_gen_7354, q_gen_7383) -> q_gen_7346
<node, s>(q_gen_7355, q_gen_7383, q_gen_7383) -> q_gen_7346
<node, s>(q_gen_7403, q_gen_7354, q_gen_7383) -> q_gen_7346
<node, s>(q_gen_7403, q_gen_7383, q_gen_7354) -> q_gen_7346
<a, z>() -> q_gen_7355
<b, z>() -> q_gen_7355
<a, s>(q_gen_7404) -> q_gen_7403
<b, s>(q_gen_7404) -> q_gen_7403
<node, s>(q_gen_7403, q_gen_7354, q_gen_7354) -> q_gen_7405
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_7342, q_gen_7357, q_gen_7374},
Q_f={q_gen_7342},
Delta=
{
<s>(q_gen_7357) -> q_gen_7357
<z>() -> q_gen_7357
<s, s>(q_gen_7342) -> q_gen_7342
<z, s>(q_gen_7357) -> q_gen_7342
<z, z>() -> q_gen_7342
<s, s>(q_gen_7374) -> q_gen_7374
<s, z>(q_gen_7357) -> q_gen_7374
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  max -> 
{{{
Q={q_gen_7343, q_gen_7359, q_gen_7371},
Q_f={q_gen_7343},
Delta=
{
<s>(q_gen_7359) -> q_gen_7359
<z>() -> q_gen_7359
<s, s>(q_gen_7371) -> q_gen_7371
<z, z>() -> q_gen_7371
<s, s, s>(q_gen_7343) -> q_gen_7343
<s, z, s>(q_gen_7371) -> q_gen_7343
<z, s, s>(q_gen_7371) -> q_gen_7343
<z, s, z>(q_gen_7359) -> q_gen_7343
<z, z, z>() -> q_gen_7343
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  numnodes -> 
{{{
Q={q_gen_7345, q_gen_7350, q_gen_7351, q_gen_7379, q_gen_7380, q_gen_7408, q_gen_7409, q_gen_7413},
Q_f={q_gen_7345},
Delta=
{
<leaf>() -> q_gen_7350
<s>(q_gen_7380) -> q_gen_7380
<z>() -> q_gen_7380
<node>(q_gen_7409, q_gen_7350, q_gen_7350) -> q_gen_7408
<node>(q_gen_7409, q_gen_7350, q_gen_7408) -> q_gen_7408
<node>(q_gen_7409, q_gen_7408, q_gen_7350) -> q_gen_7408
<node>(q_gen_7409, q_gen_7408, q_gen_7408) -> q_gen_7408
<a>() -> q_gen_7409
<b>() -> q_gen_7409
<leaf, z>() -> q_gen_7345
<node, s>(q_gen_7351, q_gen_7350, q_gen_7350) -> q_gen_7345
<node, s>(q_gen_7379, q_gen_7350, q_gen_7350) -> q_gen_7345
<node, s>(q_gen_7379, q_gen_7350, q_gen_7408) -> q_gen_7345
<node, s>(q_gen_7379, q_gen_7408, q_gen_7350) -> q_gen_7345
<a, s>(q_gen_7380) -> q_gen_7351
<a, z>() -> q_gen_7351
<b, z>() -> q_gen_7351
<b, s>(q_gen_7380) -> q_gen_7379
<node, s>(q_gen_7351, q_gen_7350, q_gen_7408) -> q_gen_7413
<node, s>(q_gen_7351, q_gen_7408, q_gen_7350) -> q_gen_7413
<node, s>(q_gen_7351, q_gen_7408, q_gen_7408) -> q_gen_7413
<node, s>(q_gen_7379, q_gen_7408, q_gen_7408) -> q_gen_7413
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_7344, q_gen_7348, q_gen_7367},
Q_f={q_gen_7344},
Delta=
{
<s>(q_gen_7367) -> q_gen_7367
<z>() -> q_gen_7367
<s, s>(q_gen_7348) -> q_gen_7348
<z, s>(q_gen_7367) -> q_gen_7348
<z, z>() -> q_gen_7348
<s, s, s>(q_gen_7344) -> q_gen_7344
<s, z, s>(q_gen_7348) -> q_gen_7344
<z, s, s>(q_gen_7348) -> q_gen_7344
<z, z, s>(q_gen_7367) -> q_gen_7344
<z, z, z>() -> q_gen_7344
}

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

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

Teacher's answer:
New clause system:
{
() -> height([leaf, z]) -> 34
() -> leq([z, n2]) -> 35
() -> numnodes([leaf, z]) -> 35
() -> plus([n, z, n]) -> 35
(height([t1, _mba]) /\ height([t2, _nba]) /\ max([_mba, _nba, _oba])) -> height([node(e, t1, t2), s(_oba)]) -> 40
(height([t1, _yba]) /\ numnodes([t1, _zba])) -> leq([_yba, _zba]) -> 38
(leq([n, m])) -> max([n, m, m]) -> 36
(not leq([n, m])) -> max([n, m, n]) -> 36
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 35
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 35
(leq([s(nn1), z])) -> BOT -> 35
(numnodes([t1, _sba]) /\ numnodes([t2, _tba]) /\ plus([_sba, _tba, _uba])) -> numnodes([node(e, t1, t2), s(_uba)]) -> 38
(plus([n, mm, _hba])) -> plus([n, s(mm), s(_hba)]) -> 35
}
Sat witness: Found: ((height([t1, _mba]) /\ height([t2, _nba]) /\ max([_mba, _nba, _oba])) -> height([node(e, t1, t2), s(_oba)]), {
_mba -> z  ;  _nba -> s(s(z))  ;  _oba -> s(s(z))  ;  e -> b  ;  t1 -> leaf  ;  t2 -> node(b, node(b, node(a, node(b, node(b, leaf, leaf), leaf), node(b, leaf, leaf)), node(a, node(b, node(b, leaf, leaf), leaf), node(b, leaf, leaf))), leaf)
})

-------------------------------------------
Step 54, which took 1.131747 s (model generation: 0.195925,  model checking: 0.935822):

Model:
|_
{
height -> 
{{{
Q={q_gen_7346, q_gen_7354, q_gen_7355, q_gen_7383, q_gen_7384, q_gen_7403, q_gen_7404, q_gen_7405},
Q_f={q_gen_7346},
Delta=
{
<leaf>() -> q_gen_7354
<node>(q_gen_7384, q_gen_7354, q_gen_7354) -> q_gen_7383
<node>(q_gen_7384, q_gen_7354, q_gen_7383) -> q_gen_7383
<node>(q_gen_7384, q_gen_7383, q_gen_7354) -> q_gen_7383
<node>(q_gen_7384, q_gen_7383, q_gen_7383) -> q_gen_7383
<a>() -> q_gen_7384
<b>() -> q_gen_7384
<s>(q_gen_7404) -> q_gen_7404
<z>() -> q_gen_7404
<leaf, z>() -> q_gen_7346
<node, s>(q_gen_7355, q_gen_7354, q_gen_7354) -> q_gen_7346
<node, s>(q_gen_7355, q_gen_7354, q_gen_7383) -> q_gen_7346
<node, s>(q_gen_7355, q_gen_7383, q_gen_7383) -> q_gen_7346
<node, s>(q_gen_7403, q_gen_7354, q_gen_7383) -> q_gen_7346
<node, s>(q_gen_7403, q_gen_7383, q_gen_7354) -> q_gen_7346
<a, s>(q_gen_7404) -> q_gen_7355
<a, z>() -> q_gen_7355
<b, z>() -> q_gen_7355
<b, s>(q_gen_7404) -> q_gen_7403
<node, s>(q_gen_7355, q_gen_7383, q_gen_7354) -> q_gen_7405
<node, s>(q_gen_7403, q_gen_7354, q_gen_7354) -> q_gen_7405
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_7342, q_gen_7357, q_gen_7374},
Q_f={q_gen_7342},
Delta=
{
<s>(q_gen_7357) -> q_gen_7357
<z>() -> q_gen_7357
<s, s>(q_gen_7342) -> q_gen_7342
<z, s>(q_gen_7357) -> q_gen_7342
<z, z>() -> q_gen_7342
<s, s>(q_gen_7374) -> q_gen_7374
<s, z>(q_gen_7357) -> q_gen_7374
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  max -> 
{{{
Q={q_gen_7343, q_gen_7359, q_gen_7371},
Q_f={q_gen_7343},
Delta=
{
<s>(q_gen_7359) -> q_gen_7359
<z>() -> q_gen_7359
<s, s>(q_gen_7371) -> q_gen_7371
<z, z>() -> q_gen_7371
<s, s, s>(q_gen_7343) -> q_gen_7343
<s, z, s>(q_gen_7371) -> q_gen_7343
<z, s, s>(q_gen_7371) -> q_gen_7343
<z, s, z>(q_gen_7359) -> q_gen_7343
<z, z, z>() -> q_gen_7343
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  numnodes -> 
{{{
Q={q_gen_7345, q_gen_7350, q_gen_7351, q_gen_7369, q_gen_7380, q_gen_7408, q_gen_7409, q_gen_7424},
Q_f={q_gen_7345},
Delta=
{
<leaf>() -> q_gen_7350
<s>(q_gen_7380) -> q_gen_7380
<z>() -> q_gen_7380
<node>(q_gen_7409, q_gen_7350, q_gen_7350) -> q_gen_7408
<node>(q_gen_7409, q_gen_7350, q_gen_7408) -> q_gen_7408
<node>(q_gen_7409, q_gen_7408, q_gen_7350) -> q_gen_7408
<node>(q_gen_7409, q_gen_7408, q_gen_7408) -> q_gen_7408
<a>() -> q_gen_7409
<b>() -> q_gen_7409
<leaf, z>() -> q_gen_7345
<node, s>(q_gen_7351, q_gen_7350, q_gen_7350) -> q_gen_7345
<node, s>(q_gen_7369, q_gen_7350, q_gen_7350) -> q_gen_7345
<node, s>(q_gen_7369, q_gen_7350, q_gen_7408) -> q_gen_7345
<node, s>(q_gen_7369, q_gen_7408, q_gen_7350) -> q_gen_7345
<node, s>(q_gen_7369, q_gen_7408, q_gen_7408) -> q_gen_7345
<b, z>() -> q_gen_7351
<a, s>(q_gen_7380) -> q_gen_7369
<a, z>() -> q_gen_7369
<b, s>(q_gen_7380) -> q_gen_7369
<node, s>(q_gen_7351, q_gen_7350, q_gen_7408) -> q_gen_7424
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_7344, q_gen_7348, q_gen_7367},
Q_f={q_gen_7344},
Delta=
{
<s>(q_gen_7367) -> q_gen_7367
<z>() -> q_gen_7367
<s, s>(q_gen_7348) -> q_gen_7348
<z, s>(q_gen_7367) -> q_gen_7348
<z, z>() -> q_gen_7348
<s, s, s>(q_gen_7344) -> q_gen_7344
<s, z, s>(q_gen_7348) -> q_gen_7344
<z, s, s>(q_gen_7348) -> q_gen_7344
<z, z, s>(q_gen_7367) -> q_gen_7344
<z, z, z>() -> q_gen_7344
}

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

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

Teacher's answer:
New clause system:
{
() -> height([leaf, z]) -> 35
() -> leq([z, n2]) -> 36
() -> numnodes([leaf, z]) -> 36
() -> plus([n, z, n]) -> 36
(height([t1, _mba]) /\ height([t2, _nba]) /\ max([_mba, _nba, _oba])) -> height([node(e, t1, t2), s(_oba)]) -> 40
(height([t1, _yba]) /\ numnodes([t1, _zba])) -> leq([_yba, _zba]) -> 41
(leq([n, m])) -> max([n, m, m]) -> 37
(not leq([n, m])) -> max([n, m, n]) -> 37
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 36
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 36
(leq([s(nn1), z])) -> BOT -> 36
(numnodes([t1, _sba]) /\ numnodes([t2, _tba]) /\ plus([_sba, _tba, _uba])) -> numnodes([node(e, t1, t2), s(_uba)]) -> 39
(plus([n, mm, _hba])) -> plus([n, s(mm), s(_hba)]) -> 36
}
Sat witness: Found: ((height([t1, _yba]) /\ numnodes([t1, _zba])) -> leq([_yba, _zba]), {
_yba -> s(s(z))  ;  _zba -> s(z)  ;  t1 -> node(a, leaf, node(b, leaf, leaf))
})

-------------------------------------------
Step 55, which took 0.327154 s (model generation: 0.290816,  model checking: 0.036338):

Model:
|_
{
height -> 
{{{
Q={q_gen_7346, q_gen_7354, q_gen_7355, q_gen_7383, q_gen_7384, q_gen_7403, q_gen_7404, q_gen_7405},
Q_f={q_gen_7346},
Delta=
{
<leaf>() -> q_gen_7354
<node>(q_gen_7384, q_gen_7354, q_gen_7354) -> q_gen_7383
<node>(q_gen_7384, q_gen_7354, q_gen_7383) -> q_gen_7383
<node>(q_gen_7384, q_gen_7383, q_gen_7354) -> q_gen_7383
<node>(q_gen_7384, q_gen_7383, q_gen_7383) -> q_gen_7383
<a>() -> q_gen_7384
<b>() -> q_gen_7384
<s>(q_gen_7404) -> q_gen_7404
<z>() -> q_gen_7404
<leaf, z>() -> q_gen_7346
<node, s>(q_gen_7355, q_gen_7354, q_gen_7354) -> q_gen_7346
<node, s>(q_gen_7355, q_gen_7354, q_gen_7383) -> q_gen_7346
<node, s>(q_gen_7355, q_gen_7383, q_gen_7383) -> q_gen_7346
<node, s>(q_gen_7403, q_gen_7354, q_gen_7383) -> q_gen_7346
<node, s>(q_gen_7403, q_gen_7383, q_gen_7354) -> q_gen_7346
<a, s>(q_gen_7404) -> q_gen_7355
<a, z>() -> q_gen_7355
<b, z>() -> q_gen_7355
<b, s>(q_gen_7404) -> q_gen_7403
<node, s>(q_gen_7355, q_gen_7383, q_gen_7354) -> q_gen_7405
<node, s>(q_gen_7403, q_gen_7354, q_gen_7354) -> q_gen_7405
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_7342, q_gen_7357, q_gen_7374},
Q_f={q_gen_7342},
Delta=
{
<s>(q_gen_7357) -> q_gen_7357
<z>() -> q_gen_7357
<s, s>(q_gen_7342) -> q_gen_7342
<z, s>(q_gen_7357) -> q_gen_7342
<z, z>() -> q_gen_7342
<s, s>(q_gen_7374) -> q_gen_7374
<s, z>(q_gen_7357) -> q_gen_7374
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  max -> 
{{{
Q={q_gen_7343, q_gen_7359, q_gen_7371},
Q_f={q_gen_7343},
Delta=
{
<s>(q_gen_7359) -> q_gen_7359
<z>() -> q_gen_7359
<s, s>(q_gen_7371) -> q_gen_7371
<z, z>() -> q_gen_7371
<s, s, s>(q_gen_7343) -> q_gen_7343
<s, z, s>(q_gen_7371) -> q_gen_7343
<z, s, s>(q_gen_7371) -> q_gen_7343
<z, s, z>(q_gen_7359) -> q_gen_7343
<z, z, z>() -> q_gen_7343
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  numnodes -> 
{{{
Q={q_gen_7345, q_gen_7350, q_gen_7351, q_gen_7379, q_gen_7380, q_gen_7408, q_gen_7409, q_gen_7413},
Q_f={q_gen_7345},
Delta=
{
<leaf>() -> q_gen_7350
<s>(q_gen_7380) -> q_gen_7380
<z>() -> q_gen_7380
<node>(q_gen_7409, q_gen_7350, q_gen_7350) -> q_gen_7408
<node>(q_gen_7409, q_gen_7350, q_gen_7408) -> q_gen_7408
<node>(q_gen_7409, q_gen_7408, q_gen_7350) -> q_gen_7408
<node>(q_gen_7409, q_gen_7408, q_gen_7408) -> q_gen_7408
<a>() -> q_gen_7409
<b>() -> q_gen_7409
<leaf, z>() -> q_gen_7345
<node, s>(q_gen_7351, q_gen_7350, q_gen_7350) -> q_gen_7345
<node, s>(q_gen_7379, q_gen_7350, q_gen_7350) -> q_gen_7345
<node, s>(q_gen_7379, q_gen_7350, q_gen_7408) -> q_gen_7345
<node, s>(q_gen_7379, q_gen_7408, q_gen_7350) -> q_gen_7345
<a, z>() -> q_gen_7351
<b, z>() -> q_gen_7351
<a, s>(q_gen_7380) -> q_gen_7379
<b, s>(q_gen_7380) -> q_gen_7379
<node, s>(q_gen_7351, q_gen_7350, q_gen_7408) -> q_gen_7413
<node, s>(q_gen_7351, q_gen_7408, q_gen_7350) -> q_gen_7413
<node, s>(q_gen_7351, q_gen_7408, q_gen_7408) -> q_gen_7413
<node, s>(q_gen_7379, q_gen_7408, q_gen_7408) -> q_gen_7413
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_7344, q_gen_7348, q_gen_7367},
Q_f={q_gen_7344},
Delta=
{
<s>(q_gen_7367) -> q_gen_7367
<z>() -> q_gen_7367
<s, s>(q_gen_7348) -> q_gen_7348
<z, s>(q_gen_7367) -> q_gen_7348
<z, z>() -> q_gen_7348
<s, s, s>(q_gen_7344) -> q_gen_7344
<s, z, s>(q_gen_7348) -> q_gen_7344
<z, s, s>(q_gen_7348) -> q_gen_7344
<z, z, s>(q_gen_7367) -> q_gen_7344
<z, z, z>() -> q_gen_7344
}

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

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

Teacher's answer:
New clause system:
{
() -> height([leaf, z]) -> 36
() -> leq([z, n2]) -> 37
() -> numnodes([leaf, z]) -> 37
() -> plus([n, z, n]) -> 37
(height([t1, _mba]) /\ height([t2, _nba]) /\ max([_mba, _nba, _oba])) -> height([node(e, t1, t2), s(_oba)]) -> 40
(height([t1, _yba]) /\ numnodes([t1, _zba])) -> leq([_yba, _zba]) -> 41
(leq([n, m])) -> max([n, m, m]) -> 38
(not leq([n, m])) -> max([n, m, n]) -> 38
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 37
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 37
(leq([s(nn1), z])) -> BOT -> 37
(numnodes([t1, _sba]) /\ numnodes([t2, _tba]) /\ plus([_sba, _tba, _uba])) -> numnodes([node(e, t1, t2), s(_uba)]) -> 42
(plus([n, mm, _hba])) -> plus([n, s(mm), s(_hba)]) -> 37
}
Sat witness: Found: ((numnodes([t1, _sba]) /\ numnodes([t2, _tba]) /\ plus([_sba, _tba, _uba])) -> numnodes([node(e, t1, t2), s(_uba)]), {
_sba -> s(s(z))  ;  _tba -> s(s(z))  ;  _uba -> s(s(z))  ;  e -> b  ;  t1 -> node(b, leaf, node(b, leaf, leaf))  ;  t2 -> node(b, leaf, leaf)
})

-------------------------------------------
Step 56, which took 0.243600 s (model generation: 0.232947,  model checking: 0.010653):

Model:
|_
{
height -> 
{{{
Q={q_gen_7346, q_gen_7354, q_gen_7355, q_gen_7383, q_gen_7384, q_gen_7403, q_gen_7404, q_gen_7405},
Q_f={q_gen_7346},
Delta=
{
<leaf>() -> q_gen_7354
<node>(q_gen_7384, q_gen_7354, q_gen_7354) -> q_gen_7383
<node>(q_gen_7384, q_gen_7354, q_gen_7383) -> q_gen_7383
<node>(q_gen_7384, q_gen_7383, q_gen_7354) -> q_gen_7383
<node>(q_gen_7384, q_gen_7383, q_gen_7383) -> q_gen_7383
<a>() -> q_gen_7384
<b>() -> q_gen_7384
<s>(q_gen_7404) -> q_gen_7404
<z>() -> q_gen_7404
<leaf, z>() -> q_gen_7346
<node, s>(q_gen_7355, q_gen_7354, q_gen_7354) -> q_gen_7346
<node, s>(q_gen_7355, q_gen_7354, q_gen_7383) -> q_gen_7346
<node, s>(q_gen_7355, q_gen_7383, q_gen_7383) -> q_gen_7346
<node, s>(q_gen_7403, q_gen_7354, q_gen_7383) -> q_gen_7346
<node, s>(q_gen_7403, q_gen_7383, q_gen_7354) -> q_gen_7346
<a, s>(q_gen_7404) -> q_gen_7355
<a, z>() -> q_gen_7355
<b, z>() -> q_gen_7355
<b, s>(q_gen_7404) -> q_gen_7403
<node, s>(q_gen_7355, q_gen_7383, q_gen_7354) -> q_gen_7405
<node, s>(q_gen_7403, q_gen_7354, q_gen_7354) -> q_gen_7405
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_7342, q_gen_7357, q_gen_7374},
Q_f={q_gen_7342},
Delta=
{
<s>(q_gen_7357) -> q_gen_7357
<z>() -> q_gen_7357
<s, s>(q_gen_7342) -> q_gen_7342
<z, s>(q_gen_7357) -> q_gen_7342
<z, z>() -> q_gen_7342
<s, s>(q_gen_7374) -> q_gen_7374
<s, z>(q_gen_7357) -> q_gen_7374
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  max -> 
{{{
Q={q_gen_7343, q_gen_7359, q_gen_7371},
Q_f={q_gen_7343},
Delta=
{
<s>(q_gen_7359) -> q_gen_7359
<z>() -> q_gen_7359
<s, s>(q_gen_7371) -> q_gen_7371
<z, z>() -> q_gen_7371
<s, s, s>(q_gen_7343) -> q_gen_7343
<s, z, s>(q_gen_7371) -> q_gen_7343
<z, s, s>(q_gen_7371) -> q_gen_7343
<z, s, z>(q_gen_7359) -> q_gen_7343
<z, z, z>() -> q_gen_7343
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  numnodes -> 
{{{
Q={q_gen_7345, q_gen_7350, q_gen_7351, q_gen_7379, q_gen_7380, q_gen_7408, q_gen_7409, q_gen_7424},
Q_f={q_gen_7345},
Delta=
{
<leaf>() -> q_gen_7350
<node>(q_gen_7409, q_gen_7408, q_gen_7350) -> q_gen_7350
<s>(q_gen_7380) -> q_gen_7380
<z>() -> q_gen_7380
<node>(q_gen_7409, q_gen_7350, q_gen_7350) -> q_gen_7408
<node>(q_gen_7409, q_gen_7350, q_gen_7408) -> q_gen_7408
<node>(q_gen_7409, q_gen_7408, q_gen_7408) -> q_gen_7408
<a>() -> q_gen_7409
<b>() -> q_gen_7409
<leaf, z>() -> q_gen_7345
<node, s>(q_gen_7351, q_gen_7350, q_gen_7350) -> q_gen_7345
<node, s>(q_gen_7379, q_gen_7350, q_gen_7350) -> q_gen_7345
<node, s>(q_gen_7379, q_gen_7350, q_gen_7408) -> q_gen_7345
<node, s>(q_gen_7379, q_gen_7408, q_gen_7350) -> q_gen_7345
<node, s>(q_gen_7379, q_gen_7408, q_gen_7408) -> q_gen_7345
<a, z>() -> q_gen_7351
<b, z>() -> q_gen_7351
<a, s>(q_gen_7380) -> q_gen_7379
<b, s>(q_gen_7380) -> q_gen_7379
<node, s>(q_gen_7351, q_gen_7350, q_gen_7408) -> q_gen_7424
<node, s>(q_gen_7351, q_gen_7408, q_gen_7350) -> q_gen_7424
<node, s>(q_gen_7351, q_gen_7408, q_gen_7408) -> q_gen_7424
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_7344, q_gen_7348, q_gen_7367},
Q_f={q_gen_7344},
Delta=
{
<s>(q_gen_7367) -> q_gen_7367
<z>() -> q_gen_7367
<s, s>(q_gen_7348) -> q_gen_7348
<z, s>(q_gen_7367) -> q_gen_7348
<z, z>() -> q_gen_7348
<s, s, s>(q_gen_7344) -> q_gen_7344
<s, z, s>(q_gen_7348) -> q_gen_7344
<z, s, s>(q_gen_7348) -> q_gen_7344
<z, z, s>(q_gen_7367) -> q_gen_7344
<z, z, z>() -> q_gen_7344
}

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

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

Teacher's answer:
New clause system:
{
() -> height([leaf, z]) -> 37
() -> leq([z, n2]) -> 38
() -> numnodes([leaf, z]) -> 38
() -> plus([n, z, n]) -> 38
(height([t1, _mba]) /\ height([t2, _nba]) /\ max([_mba, _nba, _oba])) -> height([node(e, t1, t2), s(_oba)]) -> 43
(height([t1, _yba]) /\ numnodes([t1, _zba])) -> leq([_yba, _zba]) -> 41
(leq([n, m])) -> max([n, m, m]) -> 39
(not leq([n, m])) -> max([n, m, n]) -> 39
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 38
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 38
(leq([s(nn1), z])) -> BOT -> 38
(numnodes([t1, _sba]) /\ numnodes([t2, _tba]) /\ plus([_sba, _tba, _uba])) -> numnodes([node(e, t1, t2), s(_uba)]) -> 42
(plus([n, mm, _hba])) -> plus([n, s(mm), s(_hba)]) -> 38
}
Sat witness: Found: ((height([t1, _mba]) /\ height([t2, _nba]) /\ max([_mba, _nba, _oba])) -> height([node(e, t1, t2), s(_oba)]), {
_mba -> s(z)  ;  _nba -> z  ;  _oba -> s(z)  ;  e -> a  ;  t1 -> node(b, leaf, node(b, leaf, leaf))  ;  t2 -> leaf
})

-------------------------------------------
Step 57, which took 0.269333 s (model generation: 0.267124,  model checking: 0.002209):

Model:
|_
{
height -> 
{{{
Q={q_gen_7346, q_gen_7354, q_gen_7355, q_gen_7383, q_gen_7384, q_gen_7400, q_gen_7403, q_gen_7404},
Q_f={q_gen_7346},
Delta=
{
<leaf>() -> q_gen_7354
<node>(q_gen_7384, q_gen_7383, q_gen_7354) -> q_gen_7354
<node>(q_gen_7384, q_gen_7383, q_gen_7383) -> q_gen_7354
<node>(q_gen_7384, q_gen_7354, q_gen_7354) -> q_gen_7383
<node>(q_gen_7384, q_gen_7354, q_gen_7383) -> q_gen_7383
<a>() -> q_gen_7384
<b>() -> q_gen_7384
<s>(q_gen_7404) -> q_gen_7404
<z>() -> q_gen_7404
<leaf, z>() -> q_gen_7346
<node, s>(q_gen_7355, q_gen_7354, q_gen_7354) -> q_gen_7346
<node, s>(q_gen_7355, q_gen_7354, q_gen_7383) -> q_gen_7346
<node, s>(q_gen_7403, q_gen_7354, q_gen_7383) -> q_gen_7346
<node, s>(q_gen_7403, q_gen_7383, q_gen_7354) -> q_gen_7346
<a, z>() -> q_gen_7355
<b, z>() -> q_gen_7355
<node, s>(q_gen_7355, q_gen_7383, q_gen_7383) -> q_gen_7400
<node, s>(q_gen_7403, q_gen_7354, q_gen_7354) -> q_gen_7400
<a, s>(q_gen_7404) -> q_gen_7403
<b, s>(q_gen_7404) -> q_gen_7403
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_7342, q_gen_7357, q_gen_7374},
Q_f={q_gen_7342},
Delta=
{
<s>(q_gen_7357) -> q_gen_7357
<z>() -> q_gen_7357
<s, s>(q_gen_7342) -> q_gen_7342
<z, s>(q_gen_7357) -> q_gen_7342
<z, z>() -> q_gen_7342
<s, s>(q_gen_7374) -> q_gen_7374
<s, z>(q_gen_7357) -> q_gen_7374
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  max -> 
{{{
Q={q_gen_7343, q_gen_7359, q_gen_7371},
Q_f={q_gen_7343},
Delta=
{
<s>(q_gen_7359) -> q_gen_7359
<z>() -> q_gen_7359
<s, s>(q_gen_7371) -> q_gen_7371
<z, z>() -> q_gen_7371
<s, s, s>(q_gen_7343) -> q_gen_7343
<s, z, s>(q_gen_7371) -> q_gen_7343
<z, s, s>(q_gen_7371) -> q_gen_7343
<z, s, z>(q_gen_7359) -> q_gen_7343
<z, z, z>() -> q_gen_7343
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  numnodes -> 
{{{
Q={q_gen_7345, q_gen_7350, q_gen_7351, q_gen_7379, q_gen_7380, q_gen_7408, q_gen_7409, q_gen_7424},
Q_f={q_gen_7345},
Delta=
{
<leaf>() -> q_gen_7350
<node>(q_gen_7409, q_gen_7408, q_gen_7408) -> q_gen_7350
<s>(q_gen_7380) -> q_gen_7380
<z>() -> q_gen_7380
<node>(q_gen_7409, q_gen_7350, q_gen_7350) -> q_gen_7408
<node>(q_gen_7409, q_gen_7350, q_gen_7408) -> q_gen_7408
<node>(q_gen_7409, q_gen_7408, q_gen_7350) -> q_gen_7408
<a>() -> q_gen_7409
<b>() -> q_gen_7409
<leaf, z>() -> q_gen_7345
<node, s>(q_gen_7351, q_gen_7350, q_gen_7350) -> q_gen_7345
<node, s>(q_gen_7351, q_gen_7408, q_gen_7408) -> q_gen_7345
<node, s>(q_gen_7379, q_gen_7350, q_gen_7350) -> q_gen_7345
<node, s>(q_gen_7379, q_gen_7350, q_gen_7408) -> q_gen_7345
<node, s>(q_gen_7379, q_gen_7408, q_gen_7350) -> q_gen_7345
<node, s>(q_gen_7379, q_gen_7408, q_gen_7408) -> q_gen_7345
<a, s>(q_gen_7380) -> q_gen_7351
<a, z>() -> q_gen_7351
<b, z>() -> q_gen_7351
<b, s>(q_gen_7380) -> q_gen_7379
<node, s>(q_gen_7351, q_gen_7350, q_gen_7408) -> q_gen_7424
<node, s>(q_gen_7351, q_gen_7408, q_gen_7350) -> q_gen_7424
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_7344, q_gen_7348, q_gen_7367},
Q_f={q_gen_7344},
Delta=
{
<s>(q_gen_7367) -> q_gen_7367
<z>() -> q_gen_7367
<s, s>(q_gen_7348) -> q_gen_7348
<z, s>(q_gen_7367) -> q_gen_7348
<z, z>() -> q_gen_7348
<s, s, s>(q_gen_7344) -> q_gen_7344
<s, z, s>(q_gen_7348) -> q_gen_7344
<z, s, s>(q_gen_7348) -> q_gen_7344
<z, z, s>(q_gen_7367) -> q_gen_7344
<z, z, z>() -> q_gen_7344
}

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

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

Teacher's answer:
New clause system:
{
() -> height([leaf, z]) -> 38
() -> leq([z, n2]) -> 39
() -> numnodes([leaf, z]) -> 39
() -> plus([n, z, n]) -> 39
(height([t1, _mba]) /\ height([t2, _nba]) /\ max([_mba, _nba, _oba])) -> height([node(e, t1, t2), s(_oba)]) -> 43
(height([t1, _yba]) /\ numnodes([t1, _zba])) -> leq([_yba, _zba]) -> 44
(leq([n, m])) -> max([n, m, m]) -> 40
(not leq([n, m])) -> max([n, m, n]) -> 40
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 39
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 39
(leq([s(nn1), z])) -> BOT -> 39
(numnodes([t1, _sba]) /\ numnodes([t2, _tba]) /\ plus([_sba, _tba, _uba])) -> numnodes([node(e, t1, t2), s(_uba)]) -> 42
(plus([n, mm, _hba])) -> plus([n, s(mm), s(_hba)]) -> 39
}
Sat witness: Found: ((height([t1, _yba]) /\ numnodes([t1, _zba])) -> leq([_yba, _zba]), {
_yba -> s(s(z))  ;  _zba -> s(z)  ;  t1 -> node(b, node(b, node(b, leaf, leaf), leaf), node(b, leaf, leaf))
})

-------------------------------------------
Step 58, which took 0.284689 s (model generation: 0.268300,  model checking: 0.016389):

Model:
|_
{
height -> 
{{{
Q={q_gen_7346, q_gen_7354, q_gen_7355, q_gen_7383, q_gen_7384, q_gen_7400, q_gen_7403, q_gen_7404},
Q_f={q_gen_7346},
Delta=
{
<leaf>() -> q_gen_7354
<node>(q_gen_7384, q_gen_7383, q_gen_7383) -> q_gen_7354
<node>(q_gen_7384, q_gen_7354, q_gen_7354) -> q_gen_7383
<node>(q_gen_7384, q_gen_7354, q_gen_7383) -> q_gen_7383
<node>(q_gen_7384, q_gen_7383, q_gen_7354) -> q_gen_7383
<a>() -> q_gen_7384
<b>() -> q_gen_7384
<s>(q_gen_7404) -> q_gen_7404
<z>() -> q_gen_7404
<leaf, z>() -> q_gen_7346
<node, s>(q_gen_7355, q_gen_7354, q_gen_7354) -> q_gen_7346
<node, s>(q_gen_7355, q_gen_7354, q_gen_7383) -> q_gen_7346
<node, s>(q_gen_7355, q_gen_7383, q_gen_7354) -> q_gen_7346
<node, s>(q_gen_7403, q_gen_7354, q_gen_7383) -> q_gen_7346
<node, s>(q_gen_7403, q_gen_7383, q_gen_7354) -> q_gen_7346
<a, s>(q_gen_7404) -> q_gen_7355
<a, z>() -> q_gen_7355
<b, z>() -> q_gen_7355
<node, s>(q_gen_7355, q_gen_7383, q_gen_7383) -> q_gen_7400
<node, s>(q_gen_7403, q_gen_7354, q_gen_7354) -> q_gen_7400
<node, s>(q_gen_7403, q_gen_7383, q_gen_7383) -> q_gen_7400
<b, s>(q_gen_7404) -> q_gen_7403
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_7342, q_gen_7357, q_gen_7374},
Q_f={q_gen_7342},
Delta=
{
<s>(q_gen_7357) -> q_gen_7357
<z>() -> q_gen_7357
<s, s>(q_gen_7342) -> q_gen_7342
<z, s>(q_gen_7357) -> q_gen_7342
<z, z>() -> q_gen_7342
<s, s>(q_gen_7374) -> q_gen_7374
<s, z>(q_gen_7357) -> q_gen_7374
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  max -> 
{{{
Q={q_gen_7343, q_gen_7359, q_gen_7371},
Q_f={q_gen_7343},
Delta=
{
<s>(q_gen_7359) -> q_gen_7359
<z>() -> q_gen_7359
<s, s>(q_gen_7371) -> q_gen_7371
<z, z>() -> q_gen_7371
<s, s, s>(q_gen_7343) -> q_gen_7343
<s, z, s>(q_gen_7371) -> q_gen_7343
<z, s, s>(q_gen_7371) -> q_gen_7343
<z, s, z>(q_gen_7359) -> q_gen_7343
<z, z, z>() -> q_gen_7343
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  numnodes -> 
{{{
Q={q_gen_7345, q_gen_7350, q_gen_7351, q_gen_7379, q_gen_7380, q_gen_7408, q_gen_7409, q_gen_7424},
Q_f={q_gen_7345},
Delta=
{
<leaf>() -> q_gen_7350
<node>(q_gen_7409, q_gen_7408, q_gen_7350) -> q_gen_7350
<node>(q_gen_7409, q_gen_7408, q_gen_7408) -> q_gen_7350
<s>(q_gen_7380) -> q_gen_7380
<z>() -> q_gen_7380
<node>(q_gen_7409, q_gen_7350, q_gen_7350) -> q_gen_7408
<node>(q_gen_7409, q_gen_7350, q_gen_7408) -> q_gen_7408
<a>() -> q_gen_7409
<b>() -> q_gen_7409
<leaf, z>() -> q_gen_7345
<node, s>(q_gen_7351, q_gen_7350, q_gen_7350) -> q_gen_7345
<node, s>(q_gen_7351, q_gen_7408, q_gen_7408) -> q_gen_7345
<node, s>(q_gen_7379, q_gen_7350, q_gen_7350) -> q_gen_7345
<node, s>(q_gen_7379, q_gen_7350, q_gen_7408) -> q_gen_7345
<node, s>(q_gen_7379, q_gen_7408, q_gen_7350) -> q_gen_7345
<node, s>(q_gen_7379, q_gen_7408, q_gen_7408) -> q_gen_7345
<a, s>(q_gen_7380) -> q_gen_7351
<a, z>() -> q_gen_7351
<b, z>() -> q_gen_7351
<b, s>(q_gen_7380) -> q_gen_7379
<node, s>(q_gen_7351, q_gen_7350, q_gen_7408) -> q_gen_7424
<node, s>(q_gen_7351, q_gen_7408, q_gen_7350) -> q_gen_7424
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_7344, q_gen_7348, q_gen_7367},
Q_f={q_gen_7344},
Delta=
{
<s>(q_gen_7367) -> q_gen_7367
<z>() -> q_gen_7367
<s, s>(q_gen_7348) -> q_gen_7348
<z, s>(q_gen_7367) -> q_gen_7348
<z, z>() -> q_gen_7348
<s, s, s>(q_gen_7344) -> q_gen_7344
<s, z, s>(q_gen_7348) -> q_gen_7344
<z, s, s>(q_gen_7348) -> q_gen_7344
<z, z, s>(q_gen_7367) -> q_gen_7344
<z, z, z>() -> q_gen_7344
}

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

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

Teacher's answer:
New clause system:
{
() -> height([leaf, z]) -> 39
() -> leq([z, n2]) -> 40
() -> numnodes([leaf, z]) -> 40
() -> plus([n, z, n]) -> 40
(height([t1, _mba]) /\ height([t2, _nba]) /\ max([_mba, _nba, _oba])) -> height([node(e, t1, t2), s(_oba)]) -> 43
(height([t1, _yba]) /\ numnodes([t1, _zba])) -> leq([_yba, _zba]) -> 44
(leq([n, m])) -> max([n, m, m]) -> 41
(not leq([n, m])) -> max([n, m, n]) -> 41
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 40
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 40
(leq([s(nn1), z])) -> BOT -> 40
(numnodes([t1, _sba]) /\ numnodes([t2, _tba]) /\ plus([_sba, _tba, _uba])) -> numnodes([node(e, t1, t2), s(_uba)]) -> 45
(plus([n, mm, _hba])) -> plus([n, s(mm), s(_hba)]) -> 40
}
Sat witness: Found: ((numnodes([t1, _sba]) /\ numnodes([t2, _tba]) /\ plus([_sba, _tba, _uba])) -> numnodes([node(e, t1, t2), s(_uba)]), {
_sba -> z  ;  _tba -> s(z)  ;  _uba -> s(z)  ;  e -> a  ;  t1 -> leaf  ;  t2 -> node(b, node(b, node(b, leaf, leaf), leaf), node(b, node(b, leaf, leaf), leaf))
})

-------------------------------------------
Step 59, which took 0.498957 s (model generation: 0.311549,  model checking: 0.187408):

Model:
|_
{
height -> 
{{{
Q={q_gen_7346, q_gen_7354, q_gen_7355, q_gen_7383, q_gen_7384, q_gen_7400, q_gen_7403, q_gen_7404},
Q_f={q_gen_7346},
Delta=
{
<leaf>() -> q_gen_7354
<node>(q_gen_7384, q_gen_7383, q_gen_7383) -> q_gen_7354
<node>(q_gen_7384, q_gen_7354, q_gen_7354) -> q_gen_7383
<node>(q_gen_7384, q_gen_7354, q_gen_7383) -> q_gen_7383
<node>(q_gen_7384, q_gen_7383, q_gen_7354) -> q_gen_7383
<a>() -> q_gen_7384
<b>() -> q_gen_7384
<s>(q_gen_7404) -> q_gen_7404
<z>() -> q_gen_7404
<leaf, z>() -> q_gen_7346
<node, s>(q_gen_7355, q_gen_7354, q_gen_7354) -> q_gen_7346
<node, s>(q_gen_7355, q_gen_7354, q_gen_7383) -> q_gen_7346
<node, s>(q_gen_7355, q_gen_7383, q_gen_7354) -> q_gen_7346
<node, s>(q_gen_7403, q_gen_7354, q_gen_7383) -> q_gen_7346
<node, s>(q_gen_7403, q_gen_7383, q_gen_7354) -> q_gen_7346
<a, s>(q_gen_7404) -> q_gen_7355
<a, z>() -> q_gen_7355
<b, z>() -> q_gen_7355
<node, s>(q_gen_7355, q_gen_7383, q_gen_7383) -> q_gen_7400
<node, s>(q_gen_7403, q_gen_7354, q_gen_7354) -> q_gen_7400
<node, s>(q_gen_7403, q_gen_7383, q_gen_7383) -> q_gen_7400
<b, s>(q_gen_7404) -> q_gen_7403
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_7342, q_gen_7357, q_gen_7374},
Q_f={q_gen_7342},
Delta=
{
<s>(q_gen_7357) -> q_gen_7357
<z>() -> q_gen_7357
<s, s>(q_gen_7342) -> q_gen_7342
<z, s>(q_gen_7357) -> q_gen_7342
<z, z>() -> q_gen_7342
<s, s>(q_gen_7374) -> q_gen_7374
<s, z>(q_gen_7357) -> q_gen_7374
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  max -> 
{{{
Q={q_gen_7343, q_gen_7359, q_gen_7371},
Q_f={q_gen_7343},
Delta=
{
<s>(q_gen_7359) -> q_gen_7359
<z>() -> q_gen_7359
<s, s>(q_gen_7371) -> q_gen_7371
<z, z>() -> q_gen_7371
<s, s, s>(q_gen_7343) -> q_gen_7343
<s, z, s>(q_gen_7371) -> q_gen_7343
<z, s, s>(q_gen_7371) -> q_gen_7343
<z, s, z>(q_gen_7359) -> q_gen_7343
<z, z, z>() -> q_gen_7343
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  numnodes -> 
{{{
Q={q_gen_7345, q_gen_7350, q_gen_7351, q_gen_7379, q_gen_7380, q_gen_7408, q_gen_7409, q_gen_7424},
Q_f={q_gen_7345},
Delta=
{
<leaf>() -> q_gen_7350
<node>(q_gen_7409, q_gen_7408, q_gen_7408) -> q_gen_7350
<s>(q_gen_7380) -> q_gen_7380
<z>() -> q_gen_7380
<node>(q_gen_7409, q_gen_7350, q_gen_7350) -> q_gen_7408
<node>(q_gen_7409, q_gen_7350, q_gen_7408) -> q_gen_7408
<node>(q_gen_7409, q_gen_7408, q_gen_7350) -> q_gen_7408
<a>() -> q_gen_7409
<b>() -> q_gen_7409
<leaf, z>() -> q_gen_7345
<node, s>(q_gen_7351, q_gen_7350, q_gen_7350) -> q_gen_7345
<node, s>(q_gen_7351, q_gen_7408, q_gen_7408) -> q_gen_7345
<node, s>(q_gen_7379, q_gen_7350, q_gen_7350) -> q_gen_7345
<node, s>(q_gen_7379, q_gen_7350, q_gen_7408) -> q_gen_7345
<node, s>(q_gen_7379, q_gen_7408, q_gen_7350) -> q_gen_7345
<node, s>(q_gen_7379, q_gen_7408, q_gen_7408) -> q_gen_7345
<a, s>(q_gen_7380) -> q_gen_7351
<a, z>() -> q_gen_7351
<b, z>() -> q_gen_7351
<b, s>(q_gen_7380) -> q_gen_7379
<node, s>(q_gen_7351, q_gen_7350, q_gen_7408) -> q_gen_7424
<node, s>(q_gen_7351, q_gen_7408, q_gen_7350) -> q_gen_7424
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_7344, q_gen_7348, q_gen_7367},
Q_f={q_gen_7344},
Delta=
{
<s>(q_gen_7367) -> q_gen_7367
<z>() -> q_gen_7367
<s, s>(q_gen_7348) -> q_gen_7348
<z, s>(q_gen_7367) -> q_gen_7348
<z, z>() -> q_gen_7348
<s, s, s>(q_gen_7344) -> q_gen_7344
<s, z, s>(q_gen_7348) -> q_gen_7344
<z, s, s>(q_gen_7348) -> q_gen_7344
<z, z, s>(q_gen_7367) -> q_gen_7344
<z, z, z>() -> q_gen_7344
}

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

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

Teacher's answer:
New clause system:
{
() -> height([leaf, z]) -> 40
() -> leq([z, n2]) -> 41
() -> numnodes([leaf, z]) -> 41
() -> plus([n, z, n]) -> 41
(height([t1, _mba]) /\ height([t2, _nba]) /\ max([_mba, _nba, _oba])) -> height([node(e, t1, t2), s(_oba)]) -> 46
(height([t1, _yba]) /\ numnodes([t1, _zba])) -> leq([_yba, _zba]) -> 44
(leq([n, m])) -> max([n, m, m]) -> 42
(not leq([n, m])) -> max([n, m, n]) -> 42
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 41
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 41
(leq([s(nn1), z])) -> BOT -> 41
(numnodes([t1, _sba]) /\ numnodes([t2, _tba]) /\ plus([_sba, _tba, _uba])) -> numnodes([node(e, t1, t2), s(_uba)]) -> 45
(plus([n, mm, _hba])) -> plus([n, s(mm), s(_hba)]) -> 41
}
Sat witness: Found: ((height([t1, _mba]) /\ height([t2, _nba]) /\ max([_mba, _nba, _oba])) -> height([node(e, t1, t2), s(_oba)]), {
_mba -> s(z)  ;  _nba -> s(z)  ;  _oba -> s(z)  ;  e -> b  ;  t1 -> node(b, leaf, node(b, node(b, leaf, node(b, leaf, leaf)), node(b, node(b, leaf, leaf), leaf)))  ;  t2 -> node(b, node(b, node(b, leaf, node(b, leaf, leaf)), node(b, node(b, leaf, leaf), leaf)), node(b, leaf, node(b, leaf, leaf)))
})

-------------------------------------------
Step 60, which took 0.354693 s (model generation: 0.351510,  model checking: 0.003183):

Model:
|_
{
height -> 
{{{
Q={q_gen_7346, q_gen_7354, q_gen_7355, q_gen_7383, q_gen_7384, q_gen_7403, q_gen_7404, q_gen_7405},
Q_f={q_gen_7346},
Delta=
{
<leaf>() -> q_gen_7354
<node>(q_gen_7384, q_gen_7354, q_gen_7354) -> q_gen_7383
<node>(q_gen_7384, q_gen_7354, q_gen_7383) -> q_gen_7383
<node>(q_gen_7384, q_gen_7383, q_gen_7354) -> q_gen_7383
<node>(q_gen_7384, q_gen_7383, q_gen_7383) -> q_gen_7383
<a>() -> q_gen_7384
<b>() -> q_gen_7384
<s>(q_gen_7404) -> q_gen_7404
<z>() -> q_gen_7404
<leaf, z>() -> q_gen_7346
<node, s>(q_gen_7355, q_gen_7354, q_gen_7354) -> q_gen_7346
<node, s>(q_gen_7355, q_gen_7354, q_gen_7383) -> q_gen_7346
<node, s>(q_gen_7355, q_gen_7383, q_gen_7354) -> q_gen_7346
<node, s>(q_gen_7355, q_gen_7383, q_gen_7383) -> q_gen_7346
<node, s>(q_gen_7403, q_gen_7354, q_gen_7383) -> q_gen_7346
<node, s>(q_gen_7403, q_gen_7383, q_gen_7354) -> q_gen_7346
<node, s>(q_gen_7403, q_gen_7383, q_gen_7383) -> q_gen_7346
<a, s>(q_gen_7404) -> q_gen_7355
<a, z>() -> q_gen_7355
<b, z>() -> q_gen_7355
<b, s>(q_gen_7404) -> q_gen_7403
<node, s>(q_gen_7403, q_gen_7354, q_gen_7354) -> q_gen_7405
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_7342, q_gen_7357, q_gen_7374},
Q_f={q_gen_7342},
Delta=
{
<s>(q_gen_7357) -> q_gen_7357
<z>() -> q_gen_7357
<s, s>(q_gen_7342) -> q_gen_7342
<z, s>(q_gen_7357) -> q_gen_7342
<z, z>() -> q_gen_7342
<s, s>(q_gen_7374) -> q_gen_7374
<s, z>(q_gen_7357) -> q_gen_7374
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  max -> 
{{{
Q={q_gen_7343, q_gen_7359, q_gen_7371},
Q_f={q_gen_7343},
Delta=
{
<s>(q_gen_7359) -> q_gen_7359
<z>() -> q_gen_7359
<s, s>(q_gen_7371) -> q_gen_7371
<z, z>() -> q_gen_7371
<s, s, s>(q_gen_7343) -> q_gen_7343
<s, z, s>(q_gen_7371) -> q_gen_7343
<z, s, s>(q_gen_7371) -> q_gen_7343
<z, s, z>(q_gen_7359) -> q_gen_7343
<z, z, z>() -> q_gen_7343
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  numnodes -> 
{{{
Q={q_gen_7345, q_gen_7350, q_gen_7351, q_gen_7380, q_gen_7408, q_gen_7409, q_gen_7417, q_gen_7424, q_gen_7425},
Q_f={q_gen_7345},
Delta=
{
<leaf>() -> q_gen_7350
<node>(q_gen_7417, q_gen_7408, q_gen_7408) -> q_gen_7350
<s>(q_gen_7380) -> q_gen_7380
<z>() -> q_gen_7380
<node>(q_gen_7409, q_gen_7350, q_gen_7350) -> q_gen_7408
<node>(q_gen_7409, q_gen_7350, q_gen_7425) -> q_gen_7408
<a>() -> q_gen_7409
<b>() -> q_gen_7417
<node>(q_gen_7409, q_gen_7425, q_gen_7425) -> q_gen_7425
<node>(q_gen_7417, q_gen_7350, q_gen_7350) -> q_gen_7425
<node>(q_gen_7417, q_gen_7350, q_gen_7425) -> q_gen_7425
<node>(q_gen_7417, q_gen_7425, q_gen_7350) -> q_gen_7425
<node>(q_gen_7417, q_gen_7425, q_gen_7425) -> q_gen_7425
<leaf, z>() -> q_gen_7345
<node, s>(q_gen_7351, q_gen_7350, q_gen_7350) -> q_gen_7345
<node, s>(q_gen_7351, q_gen_7350, q_gen_7408) -> q_gen_7345
<node, s>(q_gen_7351, q_gen_7408, q_gen_7408) -> q_gen_7345
<node, s>(q_gen_7351, q_gen_7408, q_gen_7425) -> q_gen_7345
<a, s>(q_gen_7380) -> q_gen_7351
<a, z>() -> q_gen_7351
<b, s>(q_gen_7380) -> q_gen_7351
<b, z>() -> q_gen_7351
<node, s>(q_gen_7351, q_gen_7350, q_gen_7425) -> q_gen_7424
<node, s>(q_gen_7351, q_gen_7425, q_gen_7350) -> q_gen_7424
<node, s>(q_gen_7351, q_gen_7425, q_gen_7425) -> q_gen_7424
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_7344, q_gen_7348, q_gen_7367},
Q_f={q_gen_7344},
Delta=
{
<s>(q_gen_7367) -> q_gen_7367
<z>() -> q_gen_7367
<s, s>(q_gen_7348) -> q_gen_7348
<z, s>(q_gen_7367) -> q_gen_7348
<z, z>() -> q_gen_7348
<s, s, s>(q_gen_7344) -> q_gen_7344
<s, z, s>(q_gen_7348) -> q_gen_7344
<z, s, s>(q_gen_7348) -> q_gen_7344
<z, z, s>(q_gen_7367) -> q_gen_7344
<z, z, z>() -> q_gen_7344
}

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

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

Teacher's answer:
New clause system:
{
() -> height([leaf, z]) -> 41
() -> leq([z, n2]) -> 42
() -> numnodes([leaf, z]) -> 42
() -> plus([n, z, n]) -> 42
(height([t1, _mba]) /\ height([t2, _nba]) /\ max([_mba, _nba, _oba])) -> height([node(e, t1, t2), s(_oba)]) -> 46
(height([t1, _yba]) /\ numnodes([t1, _zba])) -> leq([_yba, _zba]) -> 47
(leq([n, m])) -> max([n, m, m]) -> 43
(not leq([n, m])) -> max([n, m, n]) -> 43
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 42
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 42
(leq([s(nn1), z])) -> BOT -> 42
(numnodes([t1, _sba]) /\ numnodes([t2, _tba]) /\ plus([_sba, _tba, _uba])) -> numnodes([node(e, t1, t2), s(_uba)]) -> 45
(plus([n, mm, _hba])) -> plus([n, s(mm), s(_hba)]) -> 42
}
Sat witness: Found: ((height([t1, _yba]) /\ numnodes([t1, _zba])) -> leq([_yba, _zba]), {
_yba -> s(s(z))  ;  _zba -> s(z)  ;  t1 -> node(a, leaf, leaf)
})

-------------------------------------------
Step 61, which took 0.432569 s (model generation: 0.418374,  model checking: 0.014195):

Model:
|_
{
height -> 
{{{
Q={q_gen_7346, q_gen_7354, q_gen_7355, q_gen_7383, q_gen_7384, q_gen_7400, q_gen_7403, q_gen_7404},
Q_f={q_gen_7346},
Delta=
{
<leaf>() -> q_gen_7354
<node>(q_gen_7384, q_gen_7383, q_gen_7383) -> q_gen_7354
<node>(q_gen_7384, q_gen_7354, q_gen_7354) -> q_gen_7383
<node>(q_gen_7384, q_gen_7354, q_gen_7383) -> q_gen_7383
<node>(q_gen_7384, q_gen_7383, q_gen_7354) -> q_gen_7383
<a>() -> q_gen_7384
<b>() -> q_gen_7384
<s>(q_gen_7404) -> q_gen_7404
<z>() -> q_gen_7404
<leaf, z>() -> q_gen_7346
<node, s>(q_gen_7355, q_gen_7354, q_gen_7354) -> q_gen_7346
<node, s>(q_gen_7355, q_gen_7354, q_gen_7383) -> q_gen_7346
<node, s>(q_gen_7403, q_gen_7354, q_gen_7383) -> q_gen_7346
<node, s>(q_gen_7403, q_gen_7383, q_gen_7354) -> q_gen_7346
<node, s>(q_gen_7403, q_gen_7383, q_gen_7383) -> q_gen_7346
<a, z>() -> q_gen_7355
<b, z>() -> q_gen_7355
<node, s>(q_gen_7355, q_gen_7383, q_gen_7383) -> q_gen_7400
<node, s>(q_gen_7403, q_gen_7354, q_gen_7354) -> q_gen_7400
<a, s>(q_gen_7404) -> q_gen_7403
<b, s>(q_gen_7404) -> q_gen_7403
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_7342, q_gen_7357, q_gen_7374},
Q_f={q_gen_7342},
Delta=
{
<s>(q_gen_7357) -> q_gen_7357
<z>() -> q_gen_7357
<s, s>(q_gen_7342) -> q_gen_7342
<z, s>(q_gen_7357) -> q_gen_7342
<z, z>() -> q_gen_7342
<s, s>(q_gen_7374) -> q_gen_7374
<s, z>(q_gen_7357) -> q_gen_7374
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  max -> 
{{{
Q={q_gen_7343, q_gen_7359, q_gen_7371},
Q_f={q_gen_7343},
Delta=
{
<s>(q_gen_7359) -> q_gen_7359
<z>() -> q_gen_7359
<s, s>(q_gen_7371) -> q_gen_7371
<z, z>() -> q_gen_7371
<s, s, s>(q_gen_7343) -> q_gen_7343
<s, z, s>(q_gen_7371) -> q_gen_7343
<z, s, s>(q_gen_7371) -> q_gen_7343
<z, s, z>(q_gen_7359) -> q_gen_7343
<z, z, z>() -> q_gen_7343
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  numnodes -> 
{{{
Q={q_gen_7345, q_gen_7350, q_gen_7351, q_gen_7369, q_gen_7379, q_gen_7380, q_gen_7408, q_gen_7409, q_gen_7424},
Q_f={q_gen_7345},
Delta=
{
<leaf>() -> q_gen_7350
<node>(q_gen_7409, q_gen_7408, q_gen_7408) -> q_gen_7350
<s>(q_gen_7380) -> q_gen_7380
<z>() -> q_gen_7380
<node>(q_gen_7409, q_gen_7350, q_gen_7350) -> q_gen_7408
<node>(q_gen_7409, q_gen_7350, q_gen_7408) -> q_gen_7408
<node>(q_gen_7409, q_gen_7408, q_gen_7350) -> q_gen_7408
<a>() -> q_gen_7409
<b>() -> q_gen_7409
<leaf, z>() -> q_gen_7345
<node, s>(q_gen_7351, q_gen_7350, q_gen_7350) -> q_gen_7345
<node, s>(q_gen_7369, q_gen_7350, q_gen_7350) -> q_gen_7345
<node, s>(q_gen_7369, q_gen_7408, q_gen_7408) -> q_gen_7345
<node, s>(q_gen_7379, q_gen_7350, q_gen_7350) -> q_gen_7345
<node, s>(q_gen_7379, q_gen_7350, q_gen_7408) -> q_gen_7345
<node, s>(q_gen_7379, q_gen_7408, q_gen_7350) -> q_gen_7345
<node, s>(q_gen_7379, q_gen_7408, q_gen_7408) -> q_gen_7345
<b, z>() -> q_gen_7351
<a, s>(q_gen_7380) -> q_gen_7369
<a, z>() -> q_gen_7369
<b, s>(q_gen_7380) -> q_gen_7379
<node, s>(q_gen_7351, q_gen_7350, q_gen_7408) -> q_gen_7424
<node, s>(q_gen_7351, q_gen_7408, q_gen_7408) -> q_gen_7424
<node, s>(q_gen_7369, q_gen_7350, q_gen_7408) -> q_gen_7424
<node, s>(q_gen_7369, q_gen_7408, q_gen_7350) -> q_gen_7424
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_7344, q_gen_7348, q_gen_7367},
Q_f={q_gen_7344},
Delta=
{
<s>(q_gen_7367) -> q_gen_7367
<z>() -> q_gen_7367
<s, s>(q_gen_7348) -> q_gen_7348
<z, s>(q_gen_7367) -> q_gen_7348
<z, z>() -> q_gen_7348
<s, s, s>(q_gen_7344) -> q_gen_7344
<s, z, s>(q_gen_7348) -> q_gen_7344
<z, s, s>(q_gen_7348) -> q_gen_7344
<z, z, s>(q_gen_7367) -> q_gen_7344
<z, z, z>() -> q_gen_7344
}

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

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

Teacher's answer:
New clause system:
{
() -> height([leaf, z]) -> 42
() -> leq([z, n2]) -> 43
() -> numnodes([leaf, z]) -> 43
() -> plus([n, z, n]) -> 43
(height([t1, _mba]) /\ height([t2, _nba]) /\ max([_mba, _nba, _oba])) -> height([node(e, t1, t2), s(_oba)]) -> 46
(height([t1, _yba]) /\ numnodes([t1, _zba])) -> leq([_yba, _zba]) -> 47
(leq([n, m])) -> max([n, m, m]) -> 44
(not leq([n, m])) -> max([n, m, n]) -> 44
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 43
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 43
(leq([s(nn1), z])) -> BOT -> 43
(numnodes([t1, _sba]) /\ numnodes([t2, _tba]) /\ plus([_sba, _tba, _uba])) -> numnodes([node(e, t1, t2), s(_uba)]) -> 48
(plus([n, mm, _hba])) -> plus([n, s(mm), s(_hba)]) -> 43
}
Sat witness: Found: ((numnodes([t1, _sba]) /\ numnodes([t2, _tba]) /\ plus([_sba, _tba, _uba])) -> numnodes([node(e, t1, t2), s(_uba)]), {
_sba -> z  ;  _tba -> s(s(z))  ;  _uba -> s(s(z))  ;  e -> a  ;  t1 -> leaf  ;  t2 -> node(b, leaf, leaf)
})

-------------------------------------------
Step 62, which took 0.647282 s (model generation: 0.463750,  model checking: 0.183532):

Model:
|_
{
height -> 
{{{
Q={q_gen_7346, q_gen_7354, q_gen_7355, q_gen_7383, q_gen_7384, q_gen_7403, q_gen_7404, q_gen_7405},
Q_f={q_gen_7346},
Delta=
{
<leaf>() -> q_gen_7354
<node>(q_gen_7384, q_gen_7354, q_gen_7354) -> q_gen_7383
<node>(q_gen_7384, q_gen_7354, q_gen_7383) -> q_gen_7383
<node>(q_gen_7384, q_gen_7383, q_gen_7354) -> q_gen_7383
<node>(q_gen_7384, q_gen_7383, q_gen_7383) -> q_gen_7383
<a>() -> q_gen_7384
<b>() -> q_gen_7384
<s>(q_gen_7404) -> q_gen_7404
<z>() -> q_gen_7404
<leaf, z>() -> q_gen_7346
<node, s>(q_gen_7355, q_gen_7354, q_gen_7354) -> q_gen_7346
<node, s>(q_gen_7355, q_gen_7354, q_gen_7383) -> q_gen_7346
<node, s>(q_gen_7355, q_gen_7383, q_gen_7383) -> q_gen_7346
<node, s>(q_gen_7403, q_gen_7354, q_gen_7383) -> q_gen_7346
<node, s>(q_gen_7403, q_gen_7383, q_gen_7354) -> q_gen_7346
<node, s>(q_gen_7403, q_gen_7383, q_gen_7383) -> q_gen_7346
<a, z>() -> q_gen_7355
<b, z>() -> q_gen_7355
<a, s>(q_gen_7404) -> q_gen_7403
<b, s>(q_gen_7404) -> q_gen_7403
<node, s>(q_gen_7403, q_gen_7354, q_gen_7354) -> q_gen_7405
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_7342, q_gen_7357, q_gen_7374},
Q_f={q_gen_7342},
Delta=
{
<s>(q_gen_7357) -> q_gen_7357
<z>() -> q_gen_7357
<s, s>(q_gen_7342) -> q_gen_7342
<z, s>(q_gen_7357) -> q_gen_7342
<z, z>() -> q_gen_7342
<s, s>(q_gen_7374) -> q_gen_7374
<s, z>(q_gen_7357) -> q_gen_7374
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  max -> 
{{{
Q={q_gen_7343, q_gen_7359, q_gen_7371},
Q_f={q_gen_7343},
Delta=
{
<s>(q_gen_7359) -> q_gen_7359
<z>() -> q_gen_7359
<s, s>(q_gen_7371) -> q_gen_7371
<z, z>() -> q_gen_7371
<s, s, s>(q_gen_7343) -> q_gen_7343
<s, z, s>(q_gen_7371) -> q_gen_7343
<z, s, s>(q_gen_7371) -> q_gen_7343
<z, s, z>(q_gen_7359) -> q_gen_7343
<z, z, z>() -> q_gen_7343
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  numnodes -> 
{{{
Q={q_gen_7345, q_gen_7350, q_gen_7351, q_gen_7379, q_gen_7380, q_gen_7408, q_gen_7409, q_gen_7416, q_gen_7424},
Q_f={q_gen_7345},
Delta=
{
<leaf>() -> q_gen_7350
<node>(q_gen_7409, q_gen_7416, q_gen_7416) -> q_gen_7350
<s>(q_gen_7380) -> q_gen_7380
<z>() -> q_gen_7380
<node>(q_gen_7409, q_gen_7350, q_gen_7350) -> q_gen_7408
<a>() -> q_gen_7409
<b>() -> q_gen_7409
<node>(q_gen_7409, q_gen_7350, q_gen_7408) -> q_gen_7416
<node>(q_gen_7409, q_gen_7350, q_gen_7416) -> q_gen_7416
<node>(q_gen_7409, q_gen_7408, q_gen_7350) -> q_gen_7416
<node>(q_gen_7409, q_gen_7408, q_gen_7408) -> q_gen_7416
<leaf, z>() -> q_gen_7345
<node, s>(q_gen_7351, q_gen_7350, q_gen_7350) -> q_gen_7345
<node, s>(q_gen_7351, q_gen_7416, q_gen_7416) -> q_gen_7345
<node, s>(q_gen_7379, q_gen_7350, q_gen_7350) -> q_gen_7345
<node, s>(q_gen_7379, q_gen_7350, q_gen_7408) -> q_gen_7345
<node, s>(q_gen_7379, q_gen_7350, q_gen_7416) -> q_gen_7345
<node, s>(q_gen_7379, q_gen_7408, q_gen_7408) -> q_gen_7345
<node, s>(q_gen_7379, q_gen_7416, q_gen_7350) -> q_gen_7345
<node, s>(q_gen_7379, q_gen_7416, q_gen_7408) -> q_gen_7345
<a, z>() -> q_gen_7351
<b, z>() -> q_gen_7351
<a, s>(q_gen_7380) -> q_gen_7379
<b, s>(q_gen_7380) -> q_gen_7379
<node, s>(q_gen_7351, q_gen_7350, q_gen_7408) -> q_gen_7424
<node, s>(q_gen_7351, q_gen_7350, q_gen_7416) -> q_gen_7424
<node, s>(q_gen_7351, q_gen_7408, q_gen_7350) -> q_gen_7424
<node, s>(q_gen_7351, q_gen_7416, q_gen_7408) -> q_gen_7424
<node, s>(q_gen_7379, q_gen_7408, q_gen_7350) -> q_gen_7424
<node, s>(q_gen_7379, q_gen_7416, q_gen_7416) -> q_gen_7424
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_7344, q_gen_7348, q_gen_7367},
Q_f={q_gen_7344},
Delta=
{
<s>(q_gen_7367) -> q_gen_7367
<z>() -> q_gen_7367
<s, s>(q_gen_7348) -> q_gen_7348
<z, s>(q_gen_7367) -> q_gen_7348
<z, z>() -> q_gen_7348
<s, s, s>(q_gen_7344) -> q_gen_7344
<s, z, s>(q_gen_7348) -> q_gen_7344
<z, s, s>(q_gen_7348) -> q_gen_7344
<z, z, s>(q_gen_7367) -> q_gen_7344
<z, z, z>() -> q_gen_7344
}

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

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

Teacher's answer:
New clause system:
{
() -> height([leaf, z]) -> 43
() -> leq([z, n2]) -> 44
() -> numnodes([leaf, z]) -> 44
() -> plus([n, z, n]) -> 44
(height([t1, _mba]) /\ height([t2, _nba]) /\ max([_mba, _nba, _oba])) -> height([node(e, t1, t2), s(_oba)]) -> 47
(height([t1, _yba]) /\ numnodes([t1, _zba])) -> leq([_yba, _zba]) -> 50
(leq([n, m])) -> max([n, m, m]) -> 45
(not leq([n, m])) -> max([n, m, n]) -> 45
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 44
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 44
(leq([s(nn1), z])) -> BOT -> 44
(numnodes([t1, _sba]) /\ numnodes([t2, _tba]) /\ plus([_sba, _tba, _uba])) -> numnodes([node(e, t1, t2), s(_uba)]) -> 48
(plus([n, mm, _hba])) -> plus([n, s(mm), s(_hba)]) -> 44
}
Sat witness: Found: ((height([t1, _yba]) /\ numnodes([t1, _zba])) -> leq([_yba, _zba]), {
_yba -> s(s(z))  ;  _zba -> s(z)  ;  t1 -> node(b, node(b, node(b, leaf, leaf), node(b, leaf, leaf)), node(b, node(b, leaf, leaf), node(b, leaf, leaf)))
})

-------------------------------------------
Step 63, which took 1.484437 s (model generation: 1.240845,  model checking: 0.243592):

Model:
|_
{
height -> 
{{{
Q={q_gen_7346, q_gen_7354, q_gen_7355, q_gen_7383, q_gen_7384, q_gen_7403, q_gen_7404, q_gen_7405},
Q_f={q_gen_7346},
Delta=
{
<leaf>() -> q_gen_7354
<node>(q_gen_7384, q_gen_7354, q_gen_7354) -> q_gen_7383
<node>(q_gen_7384, q_gen_7354, q_gen_7383) -> q_gen_7383
<node>(q_gen_7384, q_gen_7383, q_gen_7354) -> q_gen_7383
<node>(q_gen_7384, q_gen_7383, q_gen_7383) -> q_gen_7383
<a>() -> q_gen_7384
<b>() -> q_gen_7384
<s>(q_gen_7404) -> q_gen_7404
<z>() -> q_gen_7404
<leaf, z>() -> q_gen_7346
<node, s>(q_gen_7355, q_gen_7354, q_gen_7354) -> q_gen_7346
<node, s>(q_gen_7355, q_gen_7354, q_gen_7383) -> q_gen_7346
<node, s>(q_gen_7355, q_gen_7383, q_gen_7383) -> q_gen_7346
<node, s>(q_gen_7403, q_gen_7354, q_gen_7383) -> q_gen_7346
<node, s>(q_gen_7403, q_gen_7383, q_gen_7354) -> q_gen_7346
<node, s>(q_gen_7403, q_gen_7383, q_gen_7383) -> q_gen_7346
<a, z>() -> q_gen_7355
<b, z>() -> q_gen_7355
<a, s>(q_gen_7404) -> q_gen_7403
<b, s>(q_gen_7404) -> q_gen_7403
<node, s>(q_gen_7403, q_gen_7354, q_gen_7354) -> q_gen_7405
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_7342, q_gen_7357, q_gen_7374},
Q_f={q_gen_7342},
Delta=
{
<s>(q_gen_7357) -> q_gen_7357
<z>() -> q_gen_7357
<s, s>(q_gen_7342) -> q_gen_7342
<z, s>(q_gen_7357) -> q_gen_7342
<z, z>() -> q_gen_7342
<s, s>(q_gen_7374) -> q_gen_7374
<s, z>(q_gen_7357) -> q_gen_7374
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  max -> 
{{{
Q={q_gen_7343, q_gen_7359, q_gen_7371},
Q_f={q_gen_7343},
Delta=
{
<s>(q_gen_7359) -> q_gen_7359
<z>() -> q_gen_7359
<s, s>(q_gen_7371) -> q_gen_7371
<z, z>() -> q_gen_7371
<s, s, s>(q_gen_7343) -> q_gen_7343
<s, z, s>(q_gen_7371) -> q_gen_7343
<z, s, s>(q_gen_7371) -> q_gen_7343
<z, s, z>(q_gen_7359) -> q_gen_7343
<z, z, z>() -> q_gen_7343
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  numnodes -> 
{{{
Q={q_gen_7345, q_gen_7350, q_gen_7351, q_gen_7379, q_gen_7380, q_gen_7408, q_gen_7409, q_gen_7416, q_gen_7424},
Q_f={q_gen_7345},
Delta=
{
<leaf>() -> q_gen_7350
<s>(q_gen_7380) -> q_gen_7380
<z>() -> q_gen_7380
<node>(q_gen_7409, q_gen_7350, q_gen_7350) -> q_gen_7408
<node>(q_gen_7409, q_gen_7350, q_gen_7416) -> q_gen_7408
<a>() -> q_gen_7409
<b>() -> q_gen_7409
<node>(q_gen_7409, q_gen_7350, q_gen_7408) -> q_gen_7416
<node>(q_gen_7409, q_gen_7408, q_gen_7350) -> q_gen_7416
<node>(q_gen_7409, q_gen_7408, q_gen_7408) -> q_gen_7416
<node>(q_gen_7409, q_gen_7416, q_gen_7416) -> q_gen_7416
<leaf, z>() -> q_gen_7345
<node, s>(q_gen_7351, q_gen_7350, q_gen_7350) -> q_gen_7345
<node, s>(q_gen_7379, q_gen_7350, q_gen_7350) -> q_gen_7345
<node, s>(q_gen_7379, q_gen_7350, q_gen_7408) -> q_gen_7345
<node, s>(q_gen_7379, q_gen_7350, q_gen_7416) -> q_gen_7345
<node, s>(q_gen_7379, q_gen_7408, q_gen_7408) -> q_gen_7345
<node, s>(q_gen_7379, q_gen_7416, q_gen_7350) -> q_gen_7345
<node, s>(q_gen_7379, q_gen_7416, q_gen_7408) -> q_gen_7345
<a, z>() -> q_gen_7351
<b, z>() -> q_gen_7351
<a, s>(q_gen_7380) -> q_gen_7379
<b, s>(q_gen_7380) -> q_gen_7379
<node, s>(q_gen_7351, q_gen_7350, q_gen_7408) -> q_gen_7424
<node, s>(q_gen_7351, q_gen_7350, q_gen_7416) -> q_gen_7424
<node, s>(q_gen_7351, q_gen_7408, q_gen_7350) -> q_gen_7424
<node, s>(q_gen_7351, q_gen_7416, q_gen_7408) -> q_gen_7424
<node, s>(q_gen_7351, q_gen_7416, q_gen_7416) -> q_gen_7424
<node, s>(q_gen_7379, q_gen_7408, q_gen_7350) -> q_gen_7424
<node, s>(q_gen_7379, q_gen_7408, q_gen_7416) -> q_gen_7424
<node, s>(q_gen_7379, q_gen_7416, q_gen_7416) -> q_gen_7424
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_7344, q_gen_7348, q_gen_7367},
Q_f={q_gen_7344},
Delta=
{
<s>(q_gen_7367) -> q_gen_7367
<z>() -> q_gen_7367
<s, s>(q_gen_7348) -> q_gen_7348
<z, s>(q_gen_7367) -> q_gen_7348
<z, z>() -> q_gen_7348
<s, s, s>(q_gen_7344) -> q_gen_7344
<s, z, s>(q_gen_7348) -> q_gen_7344
<z, s, s>(q_gen_7348) -> q_gen_7344
<z, z, s>(q_gen_7367) -> q_gen_7344
<z, z, z>() -> q_gen_7344
}

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

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

Teacher's answer:
New clause system:
{
() -> height([leaf, z]) -> 44
() -> leq([z, n2]) -> 45
() -> numnodes([leaf, z]) -> 45
() -> plus([n, z, n]) -> 45
(height([t1, _mba]) /\ height([t2, _nba]) /\ max([_mba, _nba, _oba])) -> height([node(e, t1, t2), s(_oba)]) -> 48
(height([t1, _yba]) /\ numnodes([t1, _zba])) -> leq([_yba, _zba]) -> 50
(leq([n, m])) -> max([n, m, m]) -> 46
(not leq([n, m])) -> max([n, m, n]) -> 46
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 45
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 45
(leq([s(nn1), z])) -> BOT -> 45
(numnodes([t1, _sba]) /\ numnodes([t2, _tba]) /\ plus([_sba, _tba, _uba])) -> numnodes([node(e, t1, t2), s(_uba)]) -> 51
(plus([n, mm, _hba])) -> plus([n, s(mm), s(_hba)]) -> 45
}
Sat witness: Found: ((numnodes([t1, _sba]) /\ numnodes([t2, _tba]) /\ plus([_sba, _tba, _uba])) -> numnodes([node(e, t1, t2), s(_uba)]), {
_sba -> s(z)  ;  _tba -> z  ;  _uba -> s(z)  ;  e -> b  ;  t1 -> node(b, leaf, leaf)  ;  t2 -> leaf
})

-------------------------------------------
Step 64, which took 1.855203 s (model generation: 1.653303,  model checking: 0.201900):

Model:
|_
{
height -> 
{{{
Q={q_gen_7346, q_gen_7354, q_gen_7355, q_gen_7383, q_gen_7384, q_gen_7403, q_gen_7404, q_gen_7405},
Q_f={q_gen_7346},
Delta=
{
<leaf>() -> q_gen_7354
<node>(q_gen_7384, q_gen_7354, q_gen_7354) -> q_gen_7383
<node>(q_gen_7384, q_gen_7354, q_gen_7383) -> q_gen_7383
<node>(q_gen_7384, q_gen_7383, q_gen_7354) -> q_gen_7383
<node>(q_gen_7384, q_gen_7383, q_gen_7383) -> q_gen_7383
<a>() -> q_gen_7384
<b>() -> q_gen_7384
<s>(q_gen_7404) -> q_gen_7404
<z>() -> q_gen_7404
<leaf, z>() -> q_gen_7346
<node, s>(q_gen_7355, q_gen_7354, q_gen_7354) -> q_gen_7346
<node, s>(q_gen_7355, q_gen_7354, q_gen_7383) -> q_gen_7346
<node, s>(q_gen_7355, q_gen_7383, q_gen_7383) -> q_gen_7346
<node, s>(q_gen_7403, q_gen_7354, q_gen_7383) -> q_gen_7346
<node, s>(q_gen_7403, q_gen_7383, q_gen_7354) -> q_gen_7346
<node, s>(q_gen_7403, q_gen_7383, q_gen_7383) -> q_gen_7346
<a, z>() -> q_gen_7355
<b, z>() -> q_gen_7355
<a, s>(q_gen_7404) -> q_gen_7403
<b, s>(q_gen_7404) -> q_gen_7403
<node, s>(q_gen_7403, q_gen_7354, q_gen_7354) -> q_gen_7405
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_7342, q_gen_7357, q_gen_7374},
Q_f={q_gen_7342},
Delta=
{
<s>(q_gen_7357) -> q_gen_7357
<z>() -> q_gen_7357
<s, s>(q_gen_7342) -> q_gen_7342
<z, s>(q_gen_7357) -> q_gen_7342
<z, z>() -> q_gen_7342
<s, s>(q_gen_7374) -> q_gen_7374
<s, z>(q_gen_7357) -> q_gen_7374
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  max -> 
{{{
Q={q_gen_7343, q_gen_7359, q_gen_7371},
Q_f={q_gen_7343},
Delta=
{
<s>(q_gen_7359) -> q_gen_7359
<z>() -> q_gen_7359
<s, s>(q_gen_7371) -> q_gen_7371
<z, z>() -> q_gen_7371
<s, s, s>(q_gen_7343) -> q_gen_7343
<s, z, s>(q_gen_7371) -> q_gen_7343
<z, s, s>(q_gen_7371) -> q_gen_7343
<z, s, z>(q_gen_7359) -> q_gen_7343
<z, z, z>() -> q_gen_7343
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  numnodes -> 
{{{
Q={q_gen_7345, q_gen_7350, q_gen_7351, q_gen_7379, q_gen_7380, q_gen_7399, q_gen_7408, q_gen_7409, q_gen_7424},
Q_f={q_gen_7345},
Delta=
{
<leaf>() -> q_gen_7350
<z>() -> q_gen_7380
<s>(q_gen_7380) -> q_gen_7399
<node>(q_gen_7409, q_gen_7350, q_gen_7350) -> q_gen_7408
<node>(q_gen_7409, q_gen_7350, q_gen_7408) -> q_gen_7408
<node>(q_gen_7409, q_gen_7408, q_gen_7350) -> q_gen_7408
<node>(q_gen_7409, q_gen_7408, q_gen_7408) -> q_gen_7408
<a>() -> q_gen_7409
<b>() -> q_gen_7409
<leaf, z>() -> q_gen_7345
<node, s>(q_gen_7351, q_gen_7350, q_gen_7350) -> q_gen_7345
<node, s>(q_gen_7379, q_gen_7350, q_gen_7350) -> q_gen_7345
<node, s>(q_gen_7379, q_gen_7350, q_gen_7408) -> q_gen_7345
<node, s>(q_gen_7379, q_gen_7408, q_gen_7350) -> q_gen_7345
<node, s>(q_gen_7379, q_gen_7408, q_gen_7408) -> q_gen_7345
<a, s>(q_gen_7380) -> q_gen_7351
<a, z>() -> q_gen_7351
<b, z>() -> q_gen_7351
<a, s>(q_gen_7399) -> q_gen_7379
<b, s>(q_gen_7380) -> q_gen_7379
<b, s>(q_gen_7399) -> q_gen_7379
<node, s>(q_gen_7351, q_gen_7350, q_gen_7408) -> q_gen_7424
<node, s>(q_gen_7351, q_gen_7408, q_gen_7350) -> q_gen_7424
<node, s>(q_gen_7351, q_gen_7408, q_gen_7408) -> q_gen_7424
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_7344, q_gen_7348, q_gen_7367},
Q_f={q_gen_7344},
Delta=
{
<s>(q_gen_7367) -> q_gen_7367
<z>() -> q_gen_7367
<s, s>(q_gen_7348) -> q_gen_7348
<z, s>(q_gen_7367) -> q_gen_7348
<z, z>() -> q_gen_7348
<s, s, s>(q_gen_7344) -> q_gen_7344
<s, z, s>(q_gen_7348) -> q_gen_7344
<z, s, s>(q_gen_7348) -> q_gen_7344
<z, z, s>(q_gen_7367) -> q_gen_7344
<z, z, z>() -> q_gen_7344
}

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

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

Teacher's answer:
New clause system:
{
() -> height([leaf, z]) -> 45
() -> leq([z, n2]) -> 46
() -> numnodes([leaf, z]) -> 46
() -> plus([n, z, n]) -> 46
(height([t1, _mba]) /\ height([t2, _nba]) /\ max([_mba, _nba, _oba])) -> height([node(e, t1, t2), s(_oba)]) -> 49
(height([t1, _yba]) /\ numnodes([t1, _zba])) -> leq([_yba, _zba]) -> 53
(leq([n, m])) -> max([n, m, m]) -> 47
(not leq([n, m])) -> max([n, m, n]) -> 47
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 46
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 46
(leq([s(nn1), z])) -> BOT -> 46
(numnodes([t1, _sba]) /\ numnodes([t2, _tba]) /\ plus([_sba, _tba, _uba])) -> numnodes([node(e, t1, t2), s(_uba)]) -> 51
(plus([n, mm, _hba])) -> plus([n, s(mm), s(_hba)]) -> 46
}
Sat witness: Found: ((height([t1, _yba]) /\ numnodes([t1, _zba])) -> leq([_yba, _zba]), {
_yba -> s(s(s(z)))  ;  _zba -> s(s(z))  ;  t1 -> node(b, node(b, leaf, leaf), node(b, leaf, leaf))
})

-------------------------------------------
Step 65, which took 0.724975 s (model generation: 0.714183,  model checking: 0.010792):

Model:
|_
{
height -> 
{{{
Q={q_gen_7346, q_gen_7354, q_gen_7355, q_gen_7382, q_gen_7383, q_gen_7384, q_gen_7403, q_gen_7404},
Q_f={q_gen_7346},
Delta=
{
<leaf>() -> q_gen_7354
<node>(q_gen_7384, q_gen_7354, q_gen_7354) -> q_gen_7383
<node>(q_gen_7384, q_gen_7354, q_gen_7383) -> q_gen_7383
<node>(q_gen_7384, q_gen_7383, q_gen_7354) -> q_gen_7383
<node>(q_gen_7384, q_gen_7383, q_gen_7383) -> q_gen_7383
<a>() -> q_gen_7384
<b>() -> q_gen_7384
<s>(q_gen_7404) -> q_gen_7404
<z>() -> q_gen_7404
<leaf, z>() -> q_gen_7346
<node, s>(q_gen_7355, q_gen_7354, q_gen_7354) -> q_gen_7346
<node, s>(q_gen_7403, q_gen_7354, q_gen_7383) -> q_gen_7346
<a, z>() -> q_gen_7355
<b, z>() -> q_gen_7355
<node, s>(q_gen_7355, q_gen_7354, q_gen_7383) -> q_gen_7382
<node, s>(q_gen_7355, q_gen_7383, q_gen_7383) -> q_gen_7382
<node, s>(q_gen_7403, q_gen_7354, q_gen_7354) -> q_gen_7382
<node, s>(q_gen_7403, q_gen_7383, q_gen_7354) -> q_gen_7382
<node, s>(q_gen_7403, q_gen_7383, q_gen_7383) -> q_gen_7382
<a, s>(q_gen_7404) -> q_gen_7403
<b, s>(q_gen_7404) -> q_gen_7403
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_7342, q_gen_7357, q_gen_7374},
Q_f={q_gen_7342},
Delta=
{
<s>(q_gen_7357) -> q_gen_7357
<z>() -> q_gen_7357
<s, s>(q_gen_7342) -> q_gen_7342
<z, s>(q_gen_7357) -> q_gen_7342
<z, z>() -> q_gen_7342
<s, s>(q_gen_7374) -> q_gen_7374
<s, z>(q_gen_7357) -> q_gen_7374
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  max -> 
{{{
Q={q_gen_7343, q_gen_7358, q_gen_7359, q_gen_7371},
Q_f={q_gen_7343},
Delta=
{
<s>(q_gen_7359) -> q_gen_7359
<z>() -> q_gen_7359
<s, s>(q_gen_7371) -> q_gen_7371
<z, z>() -> q_gen_7371
<s, s, s>(q_gen_7343) -> q_gen_7343
<s, z, s>(q_gen_7371) -> q_gen_7343
<z, s, s>(q_gen_7371) -> q_gen_7343
<z, z, z>() -> q_gen_7343
<z, s, z>(q_gen_7359) -> q_gen_7358
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  numnodes -> 
{{{
Q={q_gen_7345, q_gen_7350, q_gen_7351, q_gen_7379, q_gen_7380, q_gen_7408, q_gen_7409, q_gen_7424},
Q_f={q_gen_7345},
Delta=
{
<leaf>() -> q_gen_7350
<s>(q_gen_7380) -> q_gen_7380
<z>() -> q_gen_7380
<node>(q_gen_7409, q_gen_7350, q_gen_7350) -> q_gen_7408
<node>(q_gen_7409, q_gen_7350, q_gen_7408) -> q_gen_7408
<node>(q_gen_7409, q_gen_7408, q_gen_7350) -> q_gen_7408
<node>(q_gen_7409, q_gen_7408, q_gen_7408) -> q_gen_7408
<a>() -> q_gen_7409
<b>() -> q_gen_7409
<leaf, z>() -> q_gen_7345
<node, s>(q_gen_7351, q_gen_7350, q_gen_7350) -> q_gen_7345
<node, s>(q_gen_7351, q_gen_7408, q_gen_7350) -> q_gen_7345
<node, s>(q_gen_7351, q_gen_7408, q_gen_7408) -> q_gen_7345
<node, s>(q_gen_7379, q_gen_7350, q_gen_7350) -> q_gen_7345
<node, s>(q_gen_7379, q_gen_7350, q_gen_7408) -> q_gen_7345
<node, s>(q_gen_7379, q_gen_7408, q_gen_7350) -> q_gen_7345
<node, s>(q_gen_7379, q_gen_7408, q_gen_7408) -> q_gen_7345
<a, z>() -> q_gen_7351
<b, z>() -> q_gen_7351
<a, s>(q_gen_7380) -> q_gen_7379
<b, s>(q_gen_7380) -> q_gen_7379
<node, s>(q_gen_7351, q_gen_7350, q_gen_7408) -> q_gen_7424
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_7344, q_gen_7348, q_gen_7367},
Q_f={q_gen_7344},
Delta=
{
<s>(q_gen_7367) -> q_gen_7367
<z>() -> q_gen_7367
<s, s>(q_gen_7348) -> q_gen_7348
<z, s>(q_gen_7367) -> q_gen_7348
<z, z>() -> q_gen_7348
<s, s, s>(q_gen_7344) -> q_gen_7344
<s, z, s>(q_gen_7348) -> q_gen_7344
<z, s, s>(q_gen_7348) -> q_gen_7344
<z, z, s>(q_gen_7367) -> q_gen_7344
<z, z, z>() -> q_gen_7344
}

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

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

Teacher's answer:
New clause system:
{
() -> height([leaf, z]) -> 46
() -> leq([z, n2]) -> 47
() -> numnodes([leaf, z]) -> 47
() -> plus([n, z, n]) -> 47
(height([t1, _mba]) /\ height([t2, _nba]) /\ max([_mba, _nba, _oba])) -> height([node(e, t1, t2), s(_oba)]) -> 52
(height([t1, _yba]) /\ numnodes([t1, _zba])) -> leq([_yba, _zba]) -> 53
(leq([n, m])) -> max([n, m, m]) -> 48
(not leq([n, m])) -> max([n, m, n]) -> 48
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 47
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 47
(leq([s(nn1), z])) -> BOT -> 47
(numnodes([t1, _sba]) /\ numnodes([t2, _tba]) /\ plus([_sba, _tba, _uba])) -> numnodes([node(e, t1, t2), s(_uba)]) -> 51
(plus([n, mm, _hba])) -> plus([n, s(mm), s(_hba)]) -> 47
}
Sat witness: Found: ((height([t1, _mba]) /\ height([t2, _nba]) /\ max([_mba, _nba, _oba])) -> height([node(e, t1, t2), s(_oba)]), {
_mba -> s(s(z))  ;  _nba -> z  ;  _oba -> s(s(z))  ;  e -> a  ;  t1 -> node(b, leaf, node(b, leaf, leaf))  ;  t2 -> leaf
})

-------------------------------------------
Step 66, which took 1.526768 s (model generation: 1.340697,  model checking: 0.186071):

Model:
|_
{
height -> 
{{{
Q={q_gen_7346, q_gen_7354, q_gen_7355, q_gen_7383, q_gen_7384, q_gen_7400, q_gen_7403, q_gen_7404, q_gen_7412},
Q_f={q_gen_7346},
Delta=
{
<leaf>() -> q_gen_7354
<node>(q_gen_7384, q_gen_7383, q_gen_7383) -> q_gen_7354
<node>(q_gen_7384, q_gen_7383, q_gen_7412) -> q_gen_7354
<node>(q_gen_7384, q_gen_7354, q_gen_7354) -> q_gen_7383
<node>(q_gen_7384, q_gen_7354, q_gen_7412) -> q_gen_7383
<node>(q_gen_7384, q_gen_7412, q_gen_7383) -> q_gen_7383
<a>() -> q_gen_7384
<b>() -> q_gen_7384
<s>(q_gen_7404) -> q_gen_7404
<z>() -> q_gen_7404
<node>(q_gen_7384, q_gen_7354, q_gen_7383) -> q_gen_7412
<node>(q_gen_7384, q_gen_7383, q_gen_7354) -> q_gen_7412
<node>(q_gen_7384, q_gen_7412, q_gen_7412) -> q_gen_7412
<leaf, z>() -> q_gen_7346
<node, s>(q_gen_7355, q_gen_7354, q_gen_7354) -> q_gen_7346
<node, s>(q_gen_7355, q_gen_7354, q_gen_7383) -> q_gen_7346
<node, s>(q_gen_7355, q_gen_7354, q_gen_7412) -> q_gen_7346
<node, s>(q_gen_7355, q_gen_7412, q_gen_7383) -> q_gen_7346
<node, s>(q_gen_7403, q_gen_7354, q_gen_7383) -> q_gen_7346
<node, s>(q_gen_7403, q_gen_7412, q_gen_7354) -> q_gen_7346
<a, z>() -> q_gen_7355
<b, z>() -> q_gen_7355
<node, s>(q_gen_7355, q_gen_7383, q_gen_7383) -> q_gen_7400
<node, s>(q_gen_7355, q_gen_7412, q_gen_7412) -> q_gen_7400
<node, s>(q_gen_7403, q_gen_7354, q_gen_7354) -> q_gen_7400
<node, s>(q_gen_7403, q_gen_7354, q_gen_7412) -> q_gen_7400
<node, s>(q_gen_7403, q_gen_7383, q_gen_7354) -> q_gen_7400
<node, s>(q_gen_7403, q_gen_7383, q_gen_7383) -> q_gen_7400
<node, s>(q_gen_7403, q_gen_7383, q_gen_7412) -> q_gen_7400
<node, s>(q_gen_7403, q_gen_7412, q_gen_7383) -> q_gen_7400
<node, s>(q_gen_7403, q_gen_7412, q_gen_7412) -> q_gen_7400
<a, s>(q_gen_7404) -> q_gen_7403
<b, s>(q_gen_7404) -> q_gen_7403
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_7342, q_gen_7357, q_gen_7374},
Q_f={q_gen_7342},
Delta=
{
<s>(q_gen_7357) -> q_gen_7357
<z>() -> q_gen_7357
<s, s>(q_gen_7342) -> q_gen_7342
<z, s>(q_gen_7357) -> q_gen_7342
<z, z>() -> q_gen_7342
<s, s>(q_gen_7374) -> q_gen_7374
<s, z>(q_gen_7357) -> q_gen_7374
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  max -> 
{{{
Q={q_gen_7343, q_gen_7359, q_gen_7371},
Q_f={q_gen_7343},
Delta=
{
<s>(q_gen_7359) -> q_gen_7359
<z>() -> q_gen_7359
<s, s>(q_gen_7371) -> q_gen_7371
<z, z>() -> q_gen_7371
<s, s, s>(q_gen_7343) -> q_gen_7343
<s, z, s>(q_gen_7371) -> q_gen_7343
<z, s, s>(q_gen_7371) -> q_gen_7343
<z, s, z>(q_gen_7359) -> q_gen_7343
<z, z, z>() -> q_gen_7343
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  numnodes -> 
{{{
Q={q_gen_7345, q_gen_7350, q_gen_7351, q_gen_7379, q_gen_7380, q_gen_7408, q_gen_7409, q_gen_7424},
Q_f={q_gen_7345},
Delta=
{
<leaf>() -> q_gen_7350
<node>(q_gen_7409, q_gen_7408, q_gen_7350) -> q_gen_7350
<s>(q_gen_7380) -> q_gen_7380
<z>() -> q_gen_7380
<node>(q_gen_7409, q_gen_7350, q_gen_7350) -> q_gen_7408
<node>(q_gen_7409, q_gen_7350, q_gen_7408) -> q_gen_7408
<node>(q_gen_7409, q_gen_7408, q_gen_7408) -> q_gen_7408
<a>() -> q_gen_7409
<b>() -> q_gen_7409
<leaf, z>() -> q_gen_7345
<node, s>(q_gen_7351, q_gen_7350, q_gen_7350) -> q_gen_7345
<node, s>(q_gen_7351, q_gen_7408, q_gen_7350) -> q_gen_7345
<node, s>(q_gen_7379, q_gen_7350, q_gen_7350) -> q_gen_7345
<node, s>(q_gen_7379, q_gen_7350, q_gen_7408) -> q_gen_7345
<node, s>(q_gen_7379, q_gen_7408, q_gen_7350) -> q_gen_7345
<node, s>(q_gen_7379, q_gen_7408, q_gen_7408) -> q_gen_7345
<a, z>() -> q_gen_7351
<b, z>() -> q_gen_7351
<a, s>(q_gen_7380) -> q_gen_7379
<b, s>(q_gen_7380) -> q_gen_7379
<node, s>(q_gen_7351, q_gen_7350, q_gen_7408) -> q_gen_7424
<node, s>(q_gen_7351, q_gen_7408, q_gen_7408) -> q_gen_7424
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_7344, q_gen_7348, q_gen_7367},
Q_f={q_gen_7344},
Delta=
{
<s>(q_gen_7367) -> q_gen_7367
<z>() -> q_gen_7367
<s, s>(q_gen_7348) -> q_gen_7348
<z, s>(q_gen_7367) -> q_gen_7348
<z, z>() -> q_gen_7348
<s, s, s>(q_gen_7344) -> q_gen_7344
<s, z, s>(q_gen_7348) -> q_gen_7344
<z, s, s>(q_gen_7348) -> q_gen_7344
<z, z, s>(q_gen_7367) -> q_gen_7344
<z, z, z>() -> q_gen_7344
}

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

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

Teacher's answer:
New clause system:
{
() -> height([leaf, z]) -> 47
() -> leq([z, n2]) -> 48
() -> numnodes([leaf, z]) -> 48
() -> plus([n, z, n]) -> 48
(height([t1, _mba]) /\ height([t2, _nba]) /\ max([_mba, _nba, _oba])) -> height([node(e, t1, t2), s(_oba)]) -> 55
(height([t1, _yba]) /\ numnodes([t1, _zba])) -> leq([_yba, _zba]) -> 53
(leq([n, m])) -> max([n, m, m]) -> 49
(not leq([n, m])) -> max([n, m, n]) -> 49
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 48
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 48
(leq([s(nn1), z])) -> BOT -> 48
(numnodes([t1, _sba]) /\ numnodes([t2, _tba]) /\ plus([_sba, _tba, _uba])) -> numnodes([node(e, t1, t2), s(_uba)]) -> 52
(plus([n, mm, _hba])) -> plus([n, s(mm), s(_hba)]) -> 48
}
Sat witness: Found: ((height([t1, _mba]) /\ height([t2, _nba]) /\ max([_mba, _nba, _oba])) -> height([node(e, t1, t2), s(_oba)]), {
_mba -> s(z)  ;  _nba -> z  ;  _oba -> s(z)  ;  e -> b  ;  t1 -> node(b, node(b, node(b, leaf, leaf), node(a, node(b, leaf, leaf), node(b, node(b, leaf, leaf), node(b, leaf, leaf)))), node(a, node(b, leaf, leaf), node(b, node(b, leaf, leaf), node(b, leaf, leaf))))  ;  t2 -> leaf
})

-------------------------------------------
Step 67, which took 1.093088 s (model generation: 1.002788,  model checking: 0.090300):

Model:
|_
{
height -> 
{{{
Q={q_gen_7346, q_gen_7354, q_gen_7355, q_gen_7383, q_gen_7384, q_gen_7402, q_gen_7403, q_gen_7404, q_gen_7405},
Q_f={q_gen_7346},
Delta=
{
<leaf>() -> q_gen_7354
<node>(q_gen_7384, q_gen_7402, q_gen_7383) -> q_gen_7354
<node>(q_gen_7384, q_gen_7354, q_gen_7354) -> q_gen_7383
<node>(q_gen_7384, q_gen_7354, q_gen_7402) -> q_gen_7383
<node>(q_gen_7384, q_gen_7383, q_gen_7402) -> q_gen_7383
<a>() -> q_gen_7384
<b>() -> q_gen_7384
<node>(q_gen_7384, q_gen_7354, q_gen_7383) -> q_gen_7402
<node>(q_gen_7384, q_gen_7383, q_gen_7354) -> q_gen_7402
<node>(q_gen_7384, q_gen_7383, q_gen_7383) -> q_gen_7402
<node>(q_gen_7384, q_gen_7402, q_gen_7402) -> q_gen_7402
<s>(q_gen_7404) -> q_gen_7404
<z>() -> q_gen_7404
<leaf, z>() -> q_gen_7346
<node, s>(q_gen_7355, q_gen_7354, q_gen_7354) -> q_gen_7346
<node, s>(q_gen_7355, q_gen_7354, q_gen_7383) -> q_gen_7346
<node, s>(q_gen_7355, q_gen_7383, q_gen_7383) -> q_gen_7346
<node, s>(q_gen_7403, q_gen_7354, q_gen_7383) -> q_gen_7346
<node, s>(q_gen_7403, q_gen_7354, q_gen_7402) -> q_gen_7346
<node, s>(q_gen_7403, q_gen_7402, q_gen_7354) -> q_gen_7346
<a, z>() -> q_gen_7355
<b, z>() -> q_gen_7355
<a, s>(q_gen_7404) -> q_gen_7403
<b, s>(q_gen_7404) -> q_gen_7403
<node, s>(q_gen_7355, q_gen_7354, q_gen_7402) -> q_gen_7405
<node, s>(q_gen_7355, q_gen_7402, q_gen_7383) -> q_gen_7405
<node, s>(q_gen_7355, q_gen_7402, q_gen_7402) -> q_gen_7405
<node, s>(q_gen_7403, q_gen_7354, q_gen_7354) -> q_gen_7405
<node, s>(q_gen_7403, q_gen_7383, q_gen_7354) -> q_gen_7405
<node, s>(q_gen_7403, q_gen_7383, q_gen_7383) -> q_gen_7405
<node, s>(q_gen_7403, q_gen_7383, q_gen_7402) -> q_gen_7405
<node, s>(q_gen_7403, q_gen_7402, q_gen_7383) -> q_gen_7405
<node, s>(q_gen_7403, q_gen_7402, q_gen_7402) -> q_gen_7405
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_7342, q_gen_7357, q_gen_7374},
Q_f={q_gen_7342},
Delta=
{
<s>(q_gen_7357) -> q_gen_7357
<z>() -> q_gen_7357
<s, s>(q_gen_7342) -> q_gen_7342
<z, s>(q_gen_7357) -> q_gen_7342
<z, z>() -> q_gen_7342
<s, s>(q_gen_7374) -> q_gen_7374
<s, z>(q_gen_7357) -> q_gen_7374
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  max -> 
{{{
Q={q_gen_7343, q_gen_7359, q_gen_7371},
Q_f={q_gen_7343},
Delta=
{
<s>(q_gen_7359) -> q_gen_7359
<z>() -> q_gen_7359
<s, s>(q_gen_7371) -> q_gen_7371
<z, z>() -> q_gen_7371
<s, s, s>(q_gen_7343) -> q_gen_7343
<s, z, s>(q_gen_7371) -> q_gen_7343
<z, s, s>(q_gen_7371) -> q_gen_7343
<z, s, z>(q_gen_7359) -> q_gen_7343
<z, z, z>() -> q_gen_7343
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  numnodes -> 
{{{
Q={q_gen_7345, q_gen_7350, q_gen_7351, q_gen_7379, q_gen_7380, q_gen_7408, q_gen_7409, q_gen_7424},
Q_f={q_gen_7345},
Delta=
{
<leaf>() -> q_gen_7350
<node>(q_gen_7409, q_gen_7408, q_gen_7350) -> q_gen_7350
<s>(q_gen_7380) -> q_gen_7380
<z>() -> q_gen_7380
<node>(q_gen_7409, q_gen_7350, q_gen_7350) -> q_gen_7408
<node>(q_gen_7409, q_gen_7350, q_gen_7408) -> q_gen_7408
<node>(q_gen_7409, q_gen_7408, q_gen_7408) -> q_gen_7408
<a>() -> q_gen_7409
<b>() -> q_gen_7409
<leaf, z>() -> q_gen_7345
<node, s>(q_gen_7351, q_gen_7350, q_gen_7350) -> q_gen_7345
<node, s>(q_gen_7351, q_gen_7408, q_gen_7350) -> q_gen_7345
<node, s>(q_gen_7379, q_gen_7350, q_gen_7350) -> q_gen_7345
<node, s>(q_gen_7379, q_gen_7350, q_gen_7408) -> q_gen_7345
<node, s>(q_gen_7379, q_gen_7408, q_gen_7350) -> q_gen_7345
<node, s>(q_gen_7379, q_gen_7408, q_gen_7408) -> q_gen_7345
<a, z>() -> q_gen_7351
<b, z>() -> q_gen_7351
<a, s>(q_gen_7380) -> q_gen_7379
<b, s>(q_gen_7380) -> q_gen_7379
<node, s>(q_gen_7351, q_gen_7350, q_gen_7408) -> q_gen_7424
<node, s>(q_gen_7351, q_gen_7408, q_gen_7408) -> q_gen_7424
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_7344, q_gen_7348, q_gen_7367},
Q_f={q_gen_7344},
Delta=
{
<s>(q_gen_7367) -> q_gen_7367
<z>() -> q_gen_7367
<s, s>(q_gen_7348) -> q_gen_7348
<z, s>(q_gen_7367) -> q_gen_7348
<z, z>() -> q_gen_7348
<s, s, s>(q_gen_7344) -> q_gen_7344
<s, z, s>(q_gen_7348) -> q_gen_7344
<z, s, s>(q_gen_7348) -> q_gen_7344
<z, z, s>(q_gen_7367) -> q_gen_7344
<z, z, z>() -> q_gen_7344
}

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

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

Teacher's answer:
New clause system:
{
() -> height([leaf, z]) -> 48
() -> leq([z, n2]) -> 49
() -> numnodes([leaf, z]) -> 49
() -> plus([n, z, n]) -> 49
(height([t1, _mba]) /\ height([t2, _nba]) /\ max([_mba, _nba, _oba])) -> height([node(e, t1, t2), s(_oba)]) -> 55
(height([t1, _yba]) /\ numnodes([t1, _zba])) -> leq([_yba, _zba]) -> 56
(leq([n, m])) -> max([n, m, m]) -> 50
(not leq([n, m])) -> max([n, m, n]) -> 50
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 49
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 49
(leq([s(nn1), z])) -> BOT -> 49
(numnodes([t1, _sba]) /\ numnodes([t2, _tba]) /\ plus([_sba, _tba, _uba])) -> numnodes([node(e, t1, t2), s(_uba)]) -> 53
(plus([n, mm, _hba])) -> plus([n, s(mm), s(_hba)]) -> 49
}
Sat witness: Found: ((height([t1, _yba]) /\ numnodes([t1, _zba])) -> leq([_yba, _zba]), {
_yba -> s(s(z))  ;  _zba -> s(z)  ;  t1 -> node(b, node(b, leaf, node(b, leaf, leaf)), leaf)
})

-------------------------------------------
Step 68, which took 1.480929 s (model generation: 1.480434,  model checking: 0.000495):

Model:
|_
{
height -> 
{{{
Q={q_gen_7346, q_gen_7354, q_gen_7355, q_gen_7383, q_gen_7384, q_gen_7403, q_gen_7404, q_gen_7405},
Q_f={q_gen_7346},
Delta=
{
<leaf>() -> q_gen_7354
<node>(q_gen_7384, q_gen_7354, q_gen_7354) -> q_gen_7383
<node>(q_gen_7384, q_gen_7354, q_gen_7383) -> q_gen_7383
<node>(q_gen_7384, q_gen_7383, q_gen_7354) -> q_gen_7383
<node>(q_gen_7384, q_gen_7383, q_gen_7383) -> q_gen_7383
<a>() -> q_gen_7384
<b>() -> q_gen_7384
<s>(q_gen_7404) -> q_gen_7404
<z>() -> q_gen_7404
<leaf, z>() -> q_gen_7346
<node, s>(q_gen_7355, q_gen_7354, q_gen_7354) -> q_gen_7346
<node, s>(q_gen_7355, q_gen_7354, q_gen_7383) -> q_gen_7346
<node, s>(q_gen_7355, q_gen_7383, q_gen_7383) -> q_gen_7346
<node, s>(q_gen_7403, q_gen_7354, q_gen_7383) -> q_gen_7346
<node, s>(q_gen_7403, q_gen_7383, q_gen_7354) -> q_gen_7346
<node, s>(q_gen_7403, q_gen_7383, q_gen_7383) -> q_gen_7346
<a, z>() -> q_gen_7355
<b, z>() -> q_gen_7355
<a, s>(q_gen_7404) -> q_gen_7403
<b, s>(q_gen_7404) -> q_gen_7403
<node, s>(q_gen_7403, q_gen_7354, q_gen_7354) -> q_gen_7405
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_7342, q_gen_7357, q_gen_7374},
Q_f={q_gen_7342},
Delta=
{
<s>(q_gen_7357) -> q_gen_7357
<z>() -> q_gen_7357
<s, s>(q_gen_7342) -> q_gen_7342
<z, s>(q_gen_7357) -> q_gen_7342
<z, z>() -> q_gen_7342
<s, s>(q_gen_7374) -> q_gen_7374
<s, z>(q_gen_7357) -> q_gen_7374
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  max -> 
{{{
Q={q_gen_7343, q_gen_7359, q_gen_7371},
Q_f={q_gen_7343},
Delta=
{
<s>(q_gen_7359) -> q_gen_7359
<z>() -> q_gen_7359
<s, s>(q_gen_7371) -> q_gen_7371
<z, z>() -> q_gen_7371
<s, s, s>(q_gen_7343) -> q_gen_7343
<s, z, s>(q_gen_7371) -> q_gen_7343
<z, s, s>(q_gen_7371) -> q_gen_7343
<z, s, z>(q_gen_7359) -> q_gen_7343
<z, z, z>() -> q_gen_7343
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  numnodes -> 
{{{
Q={q_gen_7345, q_gen_7350, q_gen_7351, q_gen_7378, q_gen_7379, q_gen_7380, q_gen_7408, q_gen_7409},
Q_f={q_gen_7345},
Delta=
{
<leaf>() -> q_gen_7350
<s>(q_gen_7380) -> q_gen_7380
<z>() -> q_gen_7380
<node>(q_gen_7409, q_gen_7350, q_gen_7350) -> q_gen_7408
<node>(q_gen_7409, q_gen_7350, q_gen_7408) -> q_gen_7408
<node>(q_gen_7409, q_gen_7408, q_gen_7350) -> q_gen_7408
<node>(q_gen_7409, q_gen_7408, q_gen_7408) -> q_gen_7408
<a>() -> q_gen_7409
<b>() -> q_gen_7409
<leaf, z>() -> q_gen_7345
<node, s>(q_gen_7351, q_gen_7350, q_gen_7350) -> q_gen_7345
<node, s>(q_gen_7379, q_gen_7350, q_gen_7408) -> q_gen_7345
<node, s>(q_gen_7379, q_gen_7408, q_gen_7350) -> q_gen_7345
<a, s>(q_gen_7380) -> q_gen_7351
<a, z>() -> q_gen_7351
<b, z>() -> q_gen_7351
<node, s>(q_gen_7351, q_gen_7350, q_gen_7408) -> q_gen_7378
<node, s>(q_gen_7351, q_gen_7408, q_gen_7350) -> q_gen_7378
<node, s>(q_gen_7351, q_gen_7408, q_gen_7408) -> q_gen_7378
<node, s>(q_gen_7379, q_gen_7350, q_gen_7350) -> q_gen_7378
<node, s>(q_gen_7379, q_gen_7408, q_gen_7408) -> q_gen_7378
<b, s>(q_gen_7380) -> q_gen_7379
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_7344, q_gen_7348, q_gen_7366, q_gen_7367},
Q_f={q_gen_7344},
Delta=
{
<s>(q_gen_7367) -> q_gen_7367
<z>() -> q_gen_7367
<s, s>(q_gen_7348) -> q_gen_7348
<z, s>(q_gen_7367) -> q_gen_7348
<z, z>() -> q_gen_7348
<s, s, s>(q_gen_7366) -> q_gen_7344
<s, z, s>(q_gen_7348) -> q_gen_7344
<z, s, s>(q_gen_7348) -> q_gen_7344
<z, z, z>() -> q_gen_7344
<s, s, s>(q_gen_7344) -> q_gen_7366
<z, z, s>(q_gen_7367) -> q_gen_7366
}

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

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

Teacher's answer:
New clause system:
{
() -> height([leaf, z]) -> 49
() -> leq([z, n2]) -> 49
() -> numnodes([leaf, z]) -> 49
() -> plus([n, z, n]) -> 49
(height([t1, _mba]) /\ height([t2, _nba]) /\ max([_mba, _nba, _oba])) -> height([node(e, t1, t2), s(_oba)]) -> 55
(height([t1, _yba]) /\ numnodes([t1, _zba])) -> leq([_yba, _zba]) -> 56
(leq([n, m])) -> max([n, m, m]) -> 50
(not leq([n, m])) -> max([n, m, n]) -> 50
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 49
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 49
(leq([s(nn1), z])) -> BOT -> 49
(numnodes([t1, _sba]) /\ numnodes([t2, _tba]) /\ plus([_sba, _tba, _uba])) -> numnodes([node(e, t1, t2), s(_uba)]) -> 53
(plus([n, mm, _hba])) -> plus([n, s(mm), s(_hba)]) -> 52
}
Sat witness: Found: ((plus([n, mm, _hba])) -> plus([n, s(mm), s(_hba)]), {
_hba -> s(s(z))  ;  mm -> z  ;  n -> s(s(z))
})

-------------------------------------------
Step 69, which took 0.849448 s (model generation: 0.527929,  model checking: 0.321519):

Model:
|_
{
height -> 
{{{
Q={q_gen_7346, q_gen_7354, q_gen_7355, q_gen_7383, q_gen_7384, q_gen_7402, q_gen_7403, q_gen_7404, q_gen_7405},
Q_f={q_gen_7346},
Delta=
{
<leaf>() -> q_gen_7354
<node>(q_gen_7384, q_gen_7354, q_gen_7402) -> q_gen_7354
<node>(q_gen_7384, q_gen_7354, q_gen_7354) -> q_gen_7383
<a>() -> q_gen_7384
<b>() -> q_gen_7384
<node>(q_gen_7384, q_gen_7354, q_gen_7383) -> q_gen_7402
<node>(q_gen_7384, q_gen_7383, q_gen_7354) -> q_gen_7402
<node>(q_gen_7384, q_gen_7383, q_gen_7383) -> q_gen_7402
<node>(q_gen_7384, q_gen_7383, q_gen_7402) -> q_gen_7402
<node>(q_gen_7384, q_gen_7402, q_gen_7354) -> q_gen_7402
<node>(q_gen_7384, q_gen_7402, q_gen_7383) -> q_gen_7402
<node>(q_gen_7384, q_gen_7402, q_gen_7402) -> q_gen_7402
<s>(q_gen_7404) -> q_gen_7404
<z>() -> q_gen_7404
<leaf, z>() -> q_gen_7346
<node, s>(q_gen_7355, q_gen_7354, q_gen_7354) -> q_gen_7346
<node, s>(q_gen_7355, q_gen_7354, q_gen_7383) -> q_gen_7346
<node, s>(q_gen_7355, q_gen_7383, q_gen_7383) -> q_gen_7346
<node, s>(q_gen_7403, q_gen_7354, q_gen_7383) -> q_gen_7346
<node, s>(q_gen_7403, q_gen_7354, q_gen_7402) -> q_gen_7346
<node, s>(q_gen_7403, q_gen_7402, q_gen_7354) -> q_gen_7346
<a, z>() -> q_gen_7355
<b, z>() -> q_gen_7355
<a, s>(q_gen_7404) -> q_gen_7403
<b, s>(q_gen_7404) -> q_gen_7403
<node, s>(q_gen_7355, q_gen_7354, q_gen_7402) -> q_gen_7405
<node, s>(q_gen_7355, q_gen_7402, q_gen_7383) -> q_gen_7405
<node, s>(q_gen_7355, q_gen_7402, q_gen_7402) -> q_gen_7405
<node, s>(q_gen_7403, q_gen_7354, q_gen_7354) -> q_gen_7405
<node, s>(q_gen_7403, q_gen_7383, q_gen_7354) -> q_gen_7405
<node, s>(q_gen_7403, q_gen_7383, q_gen_7383) -> q_gen_7405
<node, s>(q_gen_7403, q_gen_7402, q_gen_7383) -> q_gen_7405
<node, s>(q_gen_7403, q_gen_7402, q_gen_7402) -> q_gen_7405
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_7342, q_gen_7357, q_gen_7374},
Q_f={q_gen_7342},
Delta=
{
<s>(q_gen_7357) -> q_gen_7357
<z>() -> q_gen_7357
<s, s>(q_gen_7342) -> q_gen_7342
<z, s>(q_gen_7357) -> q_gen_7342
<z, z>() -> q_gen_7342
<s, s>(q_gen_7374) -> q_gen_7374
<s, z>(q_gen_7357) -> q_gen_7374
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  max -> 
{{{
Q={q_gen_7343, q_gen_7359, q_gen_7371},
Q_f={q_gen_7343},
Delta=
{
<s>(q_gen_7359) -> q_gen_7359
<z>() -> q_gen_7359
<s, s>(q_gen_7371) -> q_gen_7371
<z, z>() -> q_gen_7371
<s, s, s>(q_gen_7343) -> q_gen_7343
<s, z, s>(q_gen_7371) -> q_gen_7343
<z, s, s>(q_gen_7371) -> q_gen_7343
<z, s, z>(q_gen_7359) -> q_gen_7343
<z, z, z>() -> q_gen_7343
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  numnodes -> 
{{{
Q={q_gen_7345, q_gen_7350, q_gen_7351, q_gen_7379, q_gen_7380, q_gen_7408, q_gen_7409, q_gen_7424},
Q_f={q_gen_7345},
Delta=
{
<leaf>() -> q_gen_7350
<s>(q_gen_7380) -> q_gen_7380
<z>() -> q_gen_7380
<node>(q_gen_7409, q_gen_7350, q_gen_7350) -> q_gen_7408
<node>(q_gen_7409, q_gen_7350, q_gen_7408) -> q_gen_7408
<node>(q_gen_7409, q_gen_7408, q_gen_7350) -> q_gen_7408
<node>(q_gen_7409, q_gen_7408, q_gen_7408) -> q_gen_7408
<a>() -> q_gen_7409
<b>() -> q_gen_7409
<leaf, z>() -> q_gen_7345
<node, s>(q_gen_7351, q_gen_7350, q_gen_7350) -> q_gen_7345
<node, s>(q_gen_7379, q_gen_7350, q_gen_7350) -> q_gen_7345
<node, s>(q_gen_7379, q_gen_7350, q_gen_7408) -> q_gen_7345
<node, s>(q_gen_7379, q_gen_7408, q_gen_7350) -> q_gen_7345
<node, s>(q_gen_7379, q_gen_7408, q_gen_7408) -> q_gen_7345
<a, z>() -> q_gen_7351
<b, z>() -> q_gen_7351
<a, s>(q_gen_7380) -> q_gen_7379
<b, s>(q_gen_7380) -> q_gen_7379
<node, s>(q_gen_7351, q_gen_7350, q_gen_7408) -> q_gen_7424
<node, s>(q_gen_7351, q_gen_7408, q_gen_7350) -> q_gen_7424
<node, s>(q_gen_7351, q_gen_7408, q_gen_7408) -> q_gen_7424
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_7344, q_gen_7348, q_gen_7367},
Q_f={q_gen_7344},
Delta=
{
<s>(q_gen_7367) -> q_gen_7367
<z>() -> q_gen_7367
<s, s>(q_gen_7348) -> q_gen_7348
<z, s>(q_gen_7367) -> q_gen_7348
<z, z>() -> q_gen_7348
<s, s, s>(q_gen_7344) -> q_gen_7344
<s, z, s>(q_gen_7348) -> q_gen_7344
<z, s, s>(q_gen_7348) -> q_gen_7344
<z, z, s>(q_gen_7367) -> q_gen_7344
<z, z, z>() -> q_gen_7344
}

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

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

Teacher's answer:
New clause system:
{
() -> height([leaf, z]) -> 50
() -> leq([z, n2]) -> 50
() -> numnodes([leaf, z]) -> 50
() -> plus([n, z, n]) -> 50
(height([t1, _mba]) /\ height([t2, _nba]) /\ max([_mba, _nba, _oba])) -> height([node(e, t1, t2), s(_oba)]) -> 58
(height([t1, _yba]) /\ numnodes([t1, _zba])) -> leq([_yba, _zba]) -> 56
(leq([n, m])) -> max([n, m, m]) -> 51
(not leq([n, m])) -> max([n, m, n]) -> 51
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 50
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 50
(leq([s(nn1), z])) -> BOT -> 50
(numnodes([t1, _sba]) /\ numnodes([t2, _tba]) /\ plus([_sba, _tba, _uba])) -> numnodes([node(e, t1, t2), s(_uba)]) -> 54
(plus([n, mm, _hba])) -> plus([n, s(mm), s(_hba)]) -> 53
}
Sat witness: Found: ((height([t1, _mba]) /\ height([t2, _nba]) /\ max([_mba, _nba, _oba])) -> height([node(e, t1, t2), s(_oba)]), {
_mba -> z  ;  _nba -> s(z)  ;  _oba -> z  ;  e -> b  ;  t1 -> leaf  ;  t2 -> node(b, leaf, node(b, leaf, leaf))
})

-------------------------------------------
Step 70, which took 1.022618 s (model generation: 0.946711,  model checking: 0.075907):

Model:
|_
{
height -> 
{{{
Q={q_gen_7346, q_gen_7354, q_gen_7355, q_gen_7383, q_gen_7384, q_gen_7402, q_gen_7403, q_gen_7404, q_gen_7405},
Q_f={q_gen_7346},
Delta=
{
<leaf>() -> q_gen_7354
<node>(q_gen_7384, q_gen_7354, q_gen_7354) -> q_gen_7383
<node>(q_gen_7384, q_gen_7402, q_gen_7354) -> q_gen_7383
<node>(q_gen_7384, q_gen_7402, q_gen_7383) -> q_gen_7383
<node>(q_gen_7384, q_gen_7402, q_gen_7402) -> q_gen_7383
<a>() -> q_gen_7384
<b>() -> q_gen_7384
<node>(q_gen_7384, q_gen_7354, q_gen_7383) -> q_gen_7402
<node>(q_gen_7384, q_gen_7383, q_gen_7354) -> q_gen_7402
<node>(q_gen_7384, q_gen_7383, q_gen_7383) -> q_gen_7402
<node>(q_gen_7384, q_gen_7383, q_gen_7402) -> q_gen_7402
<s>(q_gen_7404) -> q_gen_7404
<z>() -> q_gen_7404
<leaf, z>() -> q_gen_7346
<node, s>(q_gen_7355, q_gen_7354, q_gen_7354) -> q_gen_7346
<node, s>(q_gen_7355, q_gen_7354, q_gen_7383) -> q_gen_7346
<node, s>(q_gen_7355, q_gen_7354, q_gen_7402) -> q_gen_7346
<node, s>(q_gen_7355, q_gen_7383, q_gen_7383) -> q_gen_7346
<node, s>(q_gen_7403, q_gen_7354, q_gen_7383) -> q_gen_7346
<node, s>(q_gen_7403, q_gen_7354, q_gen_7402) -> q_gen_7346
<node, s>(q_gen_7403, q_gen_7402, q_gen_7354) -> q_gen_7346
<a, z>() -> q_gen_7355
<b, z>() -> q_gen_7355
<a, s>(q_gen_7404) -> q_gen_7403
<b, s>(q_gen_7404) -> q_gen_7403
<node, s>(q_gen_7355, q_gen_7383, q_gen_7402) -> q_gen_7405
<node, s>(q_gen_7355, q_gen_7402, q_gen_7383) -> q_gen_7405
<node, s>(q_gen_7355, q_gen_7402, q_gen_7402) -> q_gen_7405
<node, s>(q_gen_7403, q_gen_7354, q_gen_7354) -> q_gen_7405
<node, s>(q_gen_7403, q_gen_7383, q_gen_7354) -> q_gen_7405
<node, s>(q_gen_7403, q_gen_7383, q_gen_7383) -> q_gen_7405
<node, s>(q_gen_7403, q_gen_7402, q_gen_7383) -> q_gen_7405
<node, s>(q_gen_7403, q_gen_7402, q_gen_7402) -> q_gen_7405
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_7342, q_gen_7357, q_gen_7374},
Q_f={q_gen_7342},
Delta=
{
<s>(q_gen_7357) -> q_gen_7357
<z>() -> q_gen_7357
<s, s>(q_gen_7342) -> q_gen_7342
<z, s>(q_gen_7357) -> q_gen_7342
<z, z>() -> q_gen_7342
<s, s>(q_gen_7374) -> q_gen_7374
<s, z>(q_gen_7357) -> q_gen_7374
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  max -> 
{{{
Q={q_gen_7343, q_gen_7359, q_gen_7371},
Q_f={q_gen_7343},
Delta=
{
<s>(q_gen_7359) -> q_gen_7359
<z>() -> q_gen_7359
<s, s>(q_gen_7371) -> q_gen_7371
<z, z>() -> q_gen_7371
<s, s, s>(q_gen_7343) -> q_gen_7343
<s, z, s>(q_gen_7371) -> q_gen_7343
<z, s, s>(q_gen_7371) -> q_gen_7343
<z, s, z>(q_gen_7359) -> q_gen_7343
<z, z, z>() -> q_gen_7343
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  numnodes -> 
{{{
Q={q_gen_7345, q_gen_7350, q_gen_7351, q_gen_7379, q_gen_7380, q_gen_7408, q_gen_7409, q_gen_7424},
Q_f={q_gen_7345},
Delta=
{
<leaf>() -> q_gen_7350
<node>(q_gen_7409, q_gen_7408, q_gen_7350) -> q_gen_7350
<s>(q_gen_7380) -> q_gen_7380
<z>() -> q_gen_7380
<node>(q_gen_7409, q_gen_7350, q_gen_7350) -> q_gen_7408
<node>(q_gen_7409, q_gen_7350, q_gen_7408) -> q_gen_7408
<node>(q_gen_7409, q_gen_7408, q_gen_7408) -> q_gen_7408
<a>() -> q_gen_7409
<b>() -> q_gen_7409
<leaf, z>() -> q_gen_7345
<node, s>(q_gen_7351, q_gen_7350, q_gen_7350) -> q_gen_7345
<node, s>(q_gen_7379, q_gen_7350, q_gen_7350) -> q_gen_7345
<node, s>(q_gen_7379, q_gen_7350, q_gen_7408) -> q_gen_7345
<node, s>(q_gen_7379, q_gen_7408, q_gen_7350) -> q_gen_7345
<node, s>(q_gen_7379, q_gen_7408, q_gen_7408) -> q_gen_7345
<a, z>() -> q_gen_7351
<b, z>() -> q_gen_7351
<a, s>(q_gen_7380) -> q_gen_7379
<b, s>(q_gen_7380) -> q_gen_7379
<node, s>(q_gen_7351, q_gen_7350, q_gen_7408) -> q_gen_7424
<node, s>(q_gen_7351, q_gen_7408, q_gen_7350) -> q_gen_7424
<node, s>(q_gen_7351, q_gen_7408, q_gen_7408) -> q_gen_7424
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_7344, q_gen_7348, q_gen_7367},
Q_f={q_gen_7344},
Delta=
{
<s>(q_gen_7367) -> q_gen_7367
<z>() -> q_gen_7367
<s, s>(q_gen_7348) -> q_gen_7348
<z, s>(q_gen_7367) -> q_gen_7348
<z, z>() -> q_gen_7348
<s, s, s>(q_gen_7344) -> q_gen_7344
<s, z, s>(q_gen_7348) -> q_gen_7344
<z, s, s>(q_gen_7348) -> q_gen_7344
<z, z, s>(q_gen_7367) -> q_gen_7344
<z, z, z>() -> q_gen_7344
}

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

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

Teacher's answer:
New clause system:
{
() -> height([leaf, z]) -> 51
() -> leq([z, n2]) -> 51
() -> numnodes([leaf, z]) -> 51
() -> plus([n, z, n]) -> 51
(height([t1, _mba]) /\ height([t2, _nba]) /\ max([_mba, _nba, _oba])) -> height([node(e, t1, t2), s(_oba)]) -> 58
(height([t1, _yba]) /\ numnodes([t1, _zba])) -> leq([_yba, _zba]) -> 59
(leq([n, m])) -> max([n, m, m]) -> 52
(not leq([n, m])) -> max([n, m, n]) -> 52
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 51
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 51
(leq([s(nn1), z])) -> BOT -> 51
(numnodes([t1, _sba]) /\ numnodes([t2, _tba]) /\ plus([_sba, _tba, _uba])) -> numnodes([node(e, t1, t2), s(_uba)]) -> 55
(plus([n, mm, _hba])) -> plus([n, s(mm), s(_hba)]) -> 54
}
Sat witness: Found: ((height([t1, _yba]) /\ numnodes([t1, _zba])) -> leq([_yba, _zba]), {
_yba -> s(s(z))  ;  _zba -> s(z)  ;  t1 -> node(b, leaf, node(b, node(b, node(b, leaf, leaf), node(b, leaf, leaf)), leaf))
})

-------------------------------------------
Step 71, which took 1.568858 s (model generation: 1.083616,  model checking: 0.485242):

Model:
|_
{
height -> 
{{{
Q={q_gen_7346, q_gen_7354, q_gen_7355, q_gen_7383, q_gen_7384, q_gen_7402, q_gen_7403, q_gen_7404, q_gen_7405},
Q_f={q_gen_7346},
Delta=
{
<leaf>() -> q_gen_7354
<node>(q_gen_7384, q_gen_7383, q_gen_7354) -> q_gen_7354
<node>(q_gen_7384, q_gen_7354, q_gen_7354) -> q_gen_7383
<node>(q_gen_7384, q_gen_7402, q_gen_7354) -> q_gen_7383
<a>() -> q_gen_7384
<b>() -> q_gen_7384
<node>(q_gen_7384, q_gen_7354, q_gen_7383) -> q_gen_7402
<node>(q_gen_7384, q_gen_7354, q_gen_7402) -> q_gen_7402
<node>(q_gen_7384, q_gen_7383, q_gen_7383) -> q_gen_7402
<node>(q_gen_7384, q_gen_7383, q_gen_7402) -> q_gen_7402
<node>(q_gen_7384, q_gen_7402, q_gen_7383) -> q_gen_7402
<node>(q_gen_7384, q_gen_7402, q_gen_7402) -> q_gen_7402
<s>(q_gen_7404) -> q_gen_7404
<z>() -> q_gen_7404
<leaf, z>() -> q_gen_7346
<node, s>(q_gen_7355, q_gen_7354, q_gen_7354) -> q_gen_7346
<node, s>(q_gen_7355, q_gen_7354, q_gen_7383) -> q_gen_7346
<node, s>(q_gen_7355, q_gen_7354, q_gen_7402) -> q_gen_7346
<node, s>(q_gen_7355, q_gen_7383, q_gen_7383) -> q_gen_7346
<node, s>(q_gen_7403, q_gen_7354, q_gen_7383) -> q_gen_7346
<node, s>(q_gen_7403, q_gen_7354, q_gen_7402) -> q_gen_7346
<node, s>(q_gen_7403, q_gen_7402, q_gen_7354) -> q_gen_7346
<a, z>() -> q_gen_7355
<b, z>() -> q_gen_7355
<a, s>(q_gen_7404) -> q_gen_7403
<b, s>(q_gen_7404) -> q_gen_7403
<node, s>(q_gen_7355, q_gen_7383, q_gen_7402) -> q_gen_7405
<node, s>(q_gen_7355, q_gen_7402, q_gen_7383) -> q_gen_7405
<node, s>(q_gen_7355, q_gen_7402, q_gen_7402) -> q_gen_7405
<node, s>(q_gen_7403, q_gen_7354, q_gen_7354) -> q_gen_7405
<node, s>(q_gen_7403, q_gen_7383, q_gen_7354) -> q_gen_7405
<node, s>(q_gen_7403, q_gen_7383, q_gen_7383) -> q_gen_7405
<node, s>(q_gen_7403, q_gen_7402, q_gen_7402) -> q_gen_7405
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_7342, q_gen_7357, q_gen_7374},
Q_f={q_gen_7342},
Delta=
{
<s>(q_gen_7357) -> q_gen_7357
<z>() -> q_gen_7357
<s, s>(q_gen_7342) -> q_gen_7342
<z, s>(q_gen_7357) -> q_gen_7342
<z, z>() -> q_gen_7342
<s, s>(q_gen_7374) -> q_gen_7374
<s, z>(q_gen_7357) -> q_gen_7374
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  max -> 
{{{
Q={q_gen_7343, q_gen_7359, q_gen_7371},
Q_f={q_gen_7343},
Delta=
{
<s>(q_gen_7359) -> q_gen_7359
<z>() -> q_gen_7359
<s, s>(q_gen_7371) -> q_gen_7371
<z, z>() -> q_gen_7371
<s, s, s>(q_gen_7343) -> q_gen_7343
<s, z, s>(q_gen_7371) -> q_gen_7343
<z, s, s>(q_gen_7371) -> q_gen_7343
<z, s, z>(q_gen_7359) -> q_gen_7343
<z, z, z>() -> q_gen_7343
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  numnodes -> 
{{{
Q={q_gen_7345, q_gen_7350, q_gen_7351, q_gen_7379, q_gen_7380, q_gen_7408, q_gen_7409, q_gen_7424},
Q_f={q_gen_7345},
Delta=
{
<leaf>() -> q_gen_7350
<s>(q_gen_7380) -> q_gen_7380
<z>() -> q_gen_7380
<node>(q_gen_7409, q_gen_7350, q_gen_7350) -> q_gen_7408
<node>(q_gen_7409, q_gen_7350, q_gen_7408) -> q_gen_7408
<node>(q_gen_7409, q_gen_7408, q_gen_7350) -> q_gen_7408
<node>(q_gen_7409, q_gen_7408, q_gen_7408) -> q_gen_7408
<a>() -> q_gen_7409
<b>() -> q_gen_7409
<leaf, z>() -> q_gen_7345
<node, s>(q_gen_7351, q_gen_7350, q_gen_7350) -> q_gen_7345
<node, s>(q_gen_7379, q_gen_7350, q_gen_7350) -> q_gen_7345
<node, s>(q_gen_7379, q_gen_7350, q_gen_7408) -> q_gen_7345
<node, s>(q_gen_7379, q_gen_7408, q_gen_7350) -> q_gen_7345
<node, s>(q_gen_7379, q_gen_7408, q_gen_7408) -> q_gen_7345
<a, z>() -> q_gen_7351
<b, z>() -> q_gen_7351
<a, s>(q_gen_7380) -> q_gen_7379
<b, s>(q_gen_7380) -> q_gen_7379
<node, s>(q_gen_7351, q_gen_7350, q_gen_7408) -> q_gen_7424
<node, s>(q_gen_7351, q_gen_7408, q_gen_7350) -> q_gen_7424
<node, s>(q_gen_7351, q_gen_7408, q_gen_7408) -> q_gen_7424
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_7344, q_gen_7348, q_gen_7367},
Q_f={q_gen_7344},
Delta=
{
<s>(q_gen_7367) -> q_gen_7367
<z>() -> q_gen_7367
<s, s>(q_gen_7348) -> q_gen_7348
<z, s>(q_gen_7367) -> q_gen_7348
<z, z>() -> q_gen_7348
<s, s, s>(q_gen_7344) -> q_gen_7344
<s, z, s>(q_gen_7348) -> q_gen_7344
<z, s, s>(q_gen_7348) -> q_gen_7344
<z, z, s>(q_gen_7367) -> q_gen_7344
<z, z, z>() -> q_gen_7344
}

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

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

Teacher's answer:
New clause system:
{
() -> height([leaf, z]) -> 52
() -> leq([z, n2]) -> 52
() -> numnodes([leaf, z]) -> 52
() -> plus([n, z, n]) -> 52
(height([t1, _mba]) /\ height([t2, _nba]) /\ max([_mba, _nba, _oba])) -> height([node(e, t1, t2), s(_oba)]) -> 61
(height([t1, _yba]) /\ numnodes([t1, _zba])) -> leq([_yba, _zba]) -> 59
(leq([n, m])) -> max([n, m, m]) -> 53
(not leq([n, m])) -> max([n, m, n]) -> 53
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 52
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 52
(leq([s(nn1), z])) -> BOT -> 52
(numnodes([t1, _sba]) /\ numnodes([t2, _tba]) /\ plus([_sba, _tba, _uba])) -> numnodes([node(e, t1, t2), s(_uba)]) -> 56
(plus([n, mm, _hba])) -> plus([n, s(mm), s(_hba)]) -> 55
}
Sat witness: Found: ((height([t1, _mba]) /\ height([t2, _nba]) /\ max([_mba, _nba, _oba])) -> height([node(e, t1, t2), s(_oba)]), {
_mba -> s(s(z))  ;  _nba -> z  ;  _oba -> s(s(z))  ;  e -> a  ;  t1 -> node(b, node(a, node(b, node(b, leaf, leaf), leaf), node(a, node(b, leaf, leaf), node(b, node(b, node(b, leaf, leaf), leaf), node(b, leaf, leaf)))), node(b, node(b, leaf, leaf), leaf))  ;  t2 -> leaf
})

-------------------------------------------
Step 72, which took 1.418660 s (model generation: 1.173035,  model checking: 0.245625):

Model:
|_
{
height -> 
{{{
Q={q_gen_7346, q_gen_7354, q_gen_7355, q_gen_7383, q_gen_7384, q_gen_7400, q_gen_7403, q_gen_7404, q_gen_7420},
Q_f={q_gen_7346},
Delta=
{
<leaf>() -> q_gen_7354
<node>(q_gen_7384, q_gen_7420, q_gen_7420) -> q_gen_7354
<node>(q_gen_7384, q_gen_7354, q_gen_7354) -> q_gen_7383
<node>(q_gen_7384, q_gen_7383, q_gen_7383) -> q_gen_7383
<a>() -> q_gen_7384
<b>() -> q_gen_7384
<s>(q_gen_7404) -> q_gen_7404
<z>() -> q_gen_7404
<node>(q_gen_7384, q_gen_7354, q_gen_7383) -> q_gen_7420
<node>(q_gen_7384, q_gen_7354, q_gen_7420) -> q_gen_7420
<node>(q_gen_7384, q_gen_7383, q_gen_7354) -> q_gen_7420
<node>(q_gen_7384, q_gen_7383, q_gen_7420) -> q_gen_7420
<node>(q_gen_7384, q_gen_7420, q_gen_7354) -> q_gen_7420
<node>(q_gen_7384, q_gen_7420, q_gen_7383) -> q_gen_7420
<leaf, z>() -> q_gen_7346
<node, s>(q_gen_7355, q_gen_7354, q_gen_7354) -> q_gen_7346
<node, s>(q_gen_7355, q_gen_7354, q_gen_7383) -> q_gen_7346
<node, s>(q_gen_7355, q_gen_7354, q_gen_7420) -> q_gen_7346
<node, s>(q_gen_7403, q_gen_7354, q_gen_7383) -> q_gen_7346
<node, s>(q_gen_7403, q_gen_7354, q_gen_7420) -> q_gen_7346
<node, s>(q_gen_7403, q_gen_7383, q_gen_7420) -> q_gen_7346
<node, s>(q_gen_7403, q_gen_7420, q_gen_7354) -> q_gen_7346
<a, z>() -> q_gen_7355
<b, z>() -> q_gen_7355
<node, s>(q_gen_7355, q_gen_7383, q_gen_7383) -> q_gen_7400
<node, s>(q_gen_7355, q_gen_7420, q_gen_7383) -> q_gen_7400
<node, s>(q_gen_7355, q_gen_7420, q_gen_7420) -> q_gen_7400
<node, s>(q_gen_7403, q_gen_7354, q_gen_7354) -> q_gen_7400
<node, s>(q_gen_7403, q_gen_7383, q_gen_7354) -> q_gen_7400
<node, s>(q_gen_7403, q_gen_7383, q_gen_7383) -> q_gen_7400
<node, s>(q_gen_7403, q_gen_7420, q_gen_7383) -> q_gen_7400
<a, s>(q_gen_7404) -> q_gen_7403
<b, s>(q_gen_7404) -> q_gen_7403
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_7342, q_gen_7357, q_gen_7374},
Q_f={q_gen_7342},
Delta=
{
<s>(q_gen_7357) -> q_gen_7357
<z>() -> q_gen_7357
<s, s>(q_gen_7342) -> q_gen_7342
<z, s>(q_gen_7357) -> q_gen_7342
<z, z>() -> q_gen_7342
<s, s>(q_gen_7374) -> q_gen_7374
<s, z>(q_gen_7357) -> q_gen_7374
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  max -> 
{{{
Q={q_gen_7343, q_gen_7359, q_gen_7371},
Q_f={q_gen_7343},
Delta=
{
<s>(q_gen_7359) -> q_gen_7359
<z>() -> q_gen_7359
<s, s>(q_gen_7371) -> q_gen_7371
<z, z>() -> q_gen_7371
<s, s, s>(q_gen_7343) -> q_gen_7343
<s, z, s>(q_gen_7371) -> q_gen_7343
<z, s, s>(q_gen_7371) -> q_gen_7343
<z, s, z>(q_gen_7359) -> q_gen_7343
<z, z, z>() -> q_gen_7343
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  numnodes -> 
{{{
Q={q_gen_7345, q_gen_7350, q_gen_7351, q_gen_7379, q_gen_7380, q_gen_7408, q_gen_7409, q_gen_7424},
Q_f={q_gen_7345},
Delta=
{
<leaf>() -> q_gen_7350
<s>(q_gen_7380) -> q_gen_7380
<z>() -> q_gen_7380
<node>(q_gen_7409, q_gen_7350, q_gen_7350) -> q_gen_7408
<node>(q_gen_7409, q_gen_7350, q_gen_7408) -> q_gen_7408
<node>(q_gen_7409, q_gen_7408, q_gen_7350) -> q_gen_7408
<node>(q_gen_7409, q_gen_7408, q_gen_7408) -> q_gen_7408
<a>() -> q_gen_7409
<b>() -> q_gen_7409
<leaf, z>() -> q_gen_7345
<node, s>(q_gen_7351, q_gen_7350, q_gen_7350) -> q_gen_7345
<node, s>(q_gen_7351, q_gen_7408, q_gen_7408) -> q_gen_7345
<node, s>(q_gen_7379, q_gen_7350, q_gen_7350) -> q_gen_7345
<node, s>(q_gen_7379, q_gen_7350, q_gen_7408) -> q_gen_7345
<node, s>(q_gen_7379, q_gen_7408, q_gen_7350) -> q_gen_7345
<node, s>(q_gen_7379, q_gen_7408, q_gen_7408) -> q_gen_7345
<a, z>() -> q_gen_7351
<b, z>() -> q_gen_7351
<a, s>(q_gen_7380) -> q_gen_7379
<b, s>(q_gen_7380) -> q_gen_7379
<node, s>(q_gen_7351, q_gen_7350, q_gen_7408) -> q_gen_7424
<node, s>(q_gen_7351, q_gen_7408, q_gen_7350) -> q_gen_7424
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_7344, q_gen_7348, q_gen_7367},
Q_f={q_gen_7344},
Delta=
{
<s>(q_gen_7367) -> q_gen_7367
<z>() -> q_gen_7367
<s, s>(q_gen_7348) -> q_gen_7348
<z, s>(q_gen_7367) -> q_gen_7348
<z, z>() -> q_gen_7348
<s, s, s>(q_gen_7344) -> q_gen_7344
<s, z, s>(q_gen_7348) -> q_gen_7344
<z, s, s>(q_gen_7348) -> q_gen_7344
<z, z, s>(q_gen_7367) -> q_gen_7344
<z, z, z>() -> q_gen_7344
}

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

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

Teacher's answer:
New clause system:
{
() -> height([leaf, z]) -> 53
() -> leq([z, n2]) -> 53
() -> numnodes([leaf, z]) -> 53
() -> plus([n, z, n]) -> 53
(height([t1, _mba]) /\ height([t2, _nba]) /\ max([_mba, _nba, _oba])) -> height([node(e, t1, t2), s(_oba)]) -> 61
(height([t1, _yba]) /\ numnodes([t1, _zba])) -> leq([_yba, _zba]) -> 62
(leq([n, m])) -> max([n, m, m]) -> 54
(not leq([n, m])) -> max([n, m, n]) -> 54
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 53
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 53
(leq([s(nn1), z])) -> BOT -> 53
(numnodes([t1, _sba]) /\ numnodes([t2, _tba]) /\ plus([_sba, _tba, _uba])) -> numnodes([node(e, t1, t2), s(_uba)]) -> 57
(plus([n, mm, _hba])) -> plus([n, s(mm), s(_hba)]) -> 56
}
Sat witness: Found: ((height([t1, _yba]) /\ numnodes([t1, _zba])) -> leq([_yba, _zba]), {
_yba -> s(s(z))  ;  _zba -> s(z)  ;  t1 -> node(b, node(b, leaf, leaf), node(b, node(b, leaf, leaf), leaf))
})

-------------------------------------------
Step 73, which took 1.837961 s (model generation: 1.378088,  model checking: 0.459873):

Model:
|_
{
height -> 
{{{
Q={q_gen_7346, q_gen_7354, q_gen_7355, q_gen_7383, q_gen_7384, q_gen_7402, q_gen_7403, q_gen_7404, q_gen_7405},
Q_f={q_gen_7346},
Delta=
{
<leaf>() -> q_gen_7354
<node>(q_gen_7384, q_gen_7383, q_gen_7402) -> q_gen_7354
<node>(q_gen_7384, q_gen_7402, q_gen_7354) -> q_gen_7354
<node>(q_gen_7384, q_gen_7354, q_gen_7354) -> q_gen_7383
<node>(q_gen_7384, q_gen_7402, q_gen_7402) -> q_gen_7383
<a>() -> q_gen_7384
<b>() -> q_gen_7384
<node>(q_gen_7384, q_gen_7354, q_gen_7383) -> q_gen_7402
<node>(q_gen_7384, q_gen_7354, q_gen_7402) -> q_gen_7402
<node>(q_gen_7384, q_gen_7383, q_gen_7354) -> q_gen_7402
<node>(q_gen_7384, q_gen_7383, q_gen_7383) -> q_gen_7402
<node>(q_gen_7384, q_gen_7402, q_gen_7383) -> q_gen_7402
<s>(q_gen_7404) -> q_gen_7404
<z>() -> q_gen_7404
<leaf, z>() -> q_gen_7346
<node, s>(q_gen_7355, q_gen_7354, q_gen_7354) -> q_gen_7346
<node, s>(q_gen_7355, q_gen_7354, q_gen_7383) -> q_gen_7346
<node, s>(q_gen_7355, q_gen_7354, q_gen_7402) -> q_gen_7346
<node, s>(q_gen_7355, q_gen_7383, q_gen_7383) -> q_gen_7346
<node, s>(q_gen_7403, q_gen_7354, q_gen_7383) -> q_gen_7346
<node, s>(q_gen_7403, q_gen_7354, q_gen_7402) -> q_gen_7346
<node, s>(q_gen_7403, q_gen_7383, q_gen_7402) -> q_gen_7346
<node, s>(q_gen_7403, q_gen_7402, q_gen_7354) -> q_gen_7346
<a, z>() -> q_gen_7355
<b, z>() -> q_gen_7355
<a, s>(q_gen_7404) -> q_gen_7403
<b, s>(q_gen_7404) -> q_gen_7403
<node, s>(q_gen_7355, q_gen_7383, q_gen_7402) -> q_gen_7405
<node, s>(q_gen_7355, q_gen_7402, q_gen_7354) -> q_gen_7405
<node, s>(q_gen_7355, q_gen_7402, q_gen_7383) -> q_gen_7405
<node, s>(q_gen_7403, q_gen_7354, q_gen_7354) -> q_gen_7405
<node, s>(q_gen_7403, q_gen_7383, q_gen_7354) -> q_gen_7405
<node, s>(q_gen_7403, q_gen_7383, q_gen_7383) -> q_gen_7405
<node, s>(q_gen_7403, q_gen_7402, q_gen_7383) -> q_gen_7405
<node, s>(q_gen_7403, q_gen_7402, q_gen_7402) -> q_gen_7405
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_7342, q_gen_7357, q_gen_7374},
Q_f={q_gen_7342},
Delta=
{
<s>(q_gen_7357) -> q_gen_7357
<z>() -> q_gen_7357
<s, s>(q_gen_7342) -> q_gen_7342
<z, s>(q_gen_7357) -> q_gen_7342
<z, z>() -> q_gen_7342
<s, s>(q_gen_7374) -> q_gen_7374
<s, z>(q_gen_7357) -> q_gen_7374
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  max -> 
{{{
Q={q_gen_7343, q_gen_7359, q_gen_7371},
Q_f={q_gen_7343},
Delta=
{
<s>(q_gen_7359) -> q_gen_7359
<z>() -> q_gen_7359
<s, s>(q_gen_7371) -> q_gen_7371
<z, z>() -> q_gen_7371
<s, s, s>(q_gen_7343) -> q_gen_7343
<s, z, s>(q_gen_7371) -> q_gen_7343
<z, s, s>(q_gen_7371) -> q_gen_7343
<z, s, z>(q_gen_7359) -> q_gen_7343
<z, z, z>() -> q_gen_7343
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  numnodes -> 
{{{
Q={q_gen_7345, q_gen_7350, q_gen_7351, q_gen_7379, q_gen_7380, q_gen_7408, q_gen_7409, q_gen_7424},
Q_f={q_gen_7345},
Delta=
{
<leaf>() -> q_gen_7350
<node>(q_gen_7409, q_gen_7408, q_gen_7350) -> q_gen_7350
<s>(q_gen_7380) -> q_gen_7380
<z>() -> q_gen_7380
<node>(q_gen_7409, q_gen_7350, q_gen_7350) -> q_gen_7408
<node>(q_gen_7409, q_gen_7350, q_gen_7408) -> q_gen_7408
<node>(q_gen_7409, q_gen_7408, q_gen_7408) -> q_gen_7408
<a>() -> q_gen_7409
<b>() -> q_gen_7409
<leaf, z>() -> q_gen_7345
<node, s>(q_gen_7351, q_gen_7350, q_gen_7350) -> q_gen_7345
<node, s>(q_gen_7379, q_gen_7350, q_gen_7350) -> q_gen_7345
<node, s>(q_gen_7379, q_gen_7350, q_gen_7408) -> q_gen_7345
<node, s>(q_gen_7379, q_gen_7408, q_gen_7350) -> q_gen_7345
<node, s>(q_gen_7379, q_gen_7408, q_gen_7408) -> q_gen_7345
<a, z>() -> q_gen_7351
<b, z>() -> q_gen_7351
<a, s>(q_gen_7380) -> q_gen_7379
<b, s>(q_gen_7380) -> q_gen_7379
<node, s>(q_gen_7351, q_gen_7350, q_gen_7408) -> q_gen_7424
<node, s>(q_gen_7351, q_gen_7408, q_gen_7350) -> q_gen_7424
<node, s>(q_gen_7351, q_gen_7408, q_gen_7408) -> q_gen_7424
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_7344, q_gen_7348, q_gen_7367},
Q_f={q_gen_7344},
Delta=
{
<s>(q_gen_7367) -> q_gen_7367
<z>() -> q_gen_7367
<s, s>(q_gen_7348) -> q_gen_7348
<z, s>(q_gen_7367) -> q_gen_7348
<z, z>() -> q_gen_7348
<s, s, s>(q_gen_7344) -> q_gen_7344
<s, z, s>(q_gen_7348) -> q_gen_7344
<z, s, s>(q_gen_7348) -> q_gen_7344
<z, z, s>(q_gen_7367) -> q_gen_7344
<z, z, z>() -> q_gen_7344
}

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

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

Teacher's answer:
New clause system:
{
() -> height([leaf, z]) -> 54
() -> leq([z, n2]) -> 54
() -> numnodes([leaf, z]) -> 54
() -> plus([n, z, n]) -> 54
(height([t1, _mba]) /\ height([t2, _nba]) /\ max([_mba, _nba, _oba])) -> height([node(e, t1, t2), s(_oba)]) -> 64
(height([t1, _yba]) /\ numnodes([t1, _zba])) -> leq([_yba, _zba]) -> 62
(leq([n, m])) -> max([n, m, m]) -> 55
(not leq([n, m])) -> max([n, m, n]) -> 55
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 54
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 54
(leq([s(nn1), z])) -> BOT -> 54
(numnodes([t1, _sba]) /\ numnodes([t2, _tba]) /\ plus([_sba, _tba, _uba])) -> numnodes([node(e, t1, t2), s(_uba)]) -> 58
(plus([n, mm, _hba])) -> plus([n, s(mm), s(_hba)]) -> 57
}
Sat witness: Found: ((height([t1, _mba]) /\ height([t2, _nba]) /\ max([_mba, _nba, _oba])) -> height([node(e, t1, t2), s(_oba)]), {
_mba -> s(z)  ;  _nba -> z  ;  _oba -> s(z)  ;  e -> a  ;  t1 -> node(b, leaf, node(b, node(a, node(b, node(b, leaf, leaf), node(b, leaf, node(b, leaf, leaf))), node(a, node(b, leaf, leaf), leaf)), leaf))  ;  t2 -> leaf
})

-------------------------------------------
Step 74, which took 1.315747 s (model generation: 1.069444,  model checking: 0.246303):

Model:
|_
{
height -> 
{{{
Q={q_gen_7346, q_gen_7354, q_gen_7355, q_gen_7383, q_gen_7384, q_gen_7400, q_gen_7403, q_gen_7404, q_gen_7420},
Q_f={q_gen_7346},
Delta=
{
<leaf>() -> q_gen_7354
<node>(q_gen_7384, q_gen_7354, q_gen_7354) -> q_gen_7383
<node>(q_gen_7384, q_gen_7383, q_gen_7383) -> q_gen_7383
<a>() -> q_gen_7384
<b>() -> q_gen_7384
<s>(q_gen_7404) -> q_gen_7404
<z>() -> q_gen_7404
<node>(q_gen_7384, q_gen_7354, q_gen_7383) -> q_gen_7420
<node>(q_gen_7384, q_gen_7354, q_gen_7420) -> q_gen_7420
<node>(q_gen_7384, q_gen_7383, q_gen_7354) -> q_gen_7420
<node>(q_gen_7384, q_gen_7383, q_gen_7420) -> q_gen_7420
<node>(q_gen_7384, q_gen_7420, q_gen_7354) -> q_gen_7420
<node>(q_gen_7384, q_gen_7420, q_gen_7383) -> q_gen_7420
<node>(q_gen_7384, q_gen_7420, q_gen_7420) -> q_gen_7420
<leaf, z>() -> q_gen_7346
<node, s>(q_gen_7355, q_gen_7354, q_gen_7354) -> q_gen_7346
<node, s>(q_gen_7355, q_gen_7354, q_gen_7383) -> q_gen_7346
<node, s>(q_gen_7355, q_gen_7354, q_gen_7420) -> q_gen_7346
<node, s>(q_gen_7403, q_gen_7354, q_gen_7383) -> q_gen_7346
<node, s>(q_gen_7403, q_gen_7354, q_gen_7420) -> q_gen_7346
<node, s>(q_gen_7403, q_gen_7420, q_gen_7354) -> q_gen_7346
<a, z>() -> q_gen_7355
<b, z>() -> q_gen_7355
<node, s>(q_gen_7355, q_gen_7383, q_gen_7383) -> q_gen_7400
<node, s>(q_gen_7355, q_gen_7420, q_gen_7383) -> q_gen_7400
<node, s>(q_gen_7355, q_gen_7420, q_gen_7420) -> q_gen_7400
<node, s>(q_gen_7403, q_gen_7354, q_gen_7354) -> q_gen_7400
<node, s>(q_gen_7403, q_gen_7383, q_gen_7354) -> q_gen_7400
<node, s>(q_gen_7403, q_gen_7383, q_gen_7383) -> q_gen_7400
<node, s>(q_gen_7403, q_gen_7383, q_gen_7420) -> q_gen_7400
<node, s>(q_gen_7403, q_gen_7420, q_gen_7383) -> q_gen_7400
<node, s>(q_gen_7403, q_gen_7420, q_gen_7420) -> q_gen_7400
<a, s>(q_gen_7404) -> q_gen_7403
<b, s>(q_gen_7404) -> q_gen_7403
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_7342, q_gen_7357, q_gen_7374},
Q_f={q_gen_7342},
Delta=
{
<s>(q_gen_7357) -> q_gen_7357
<z>() -> q_gen_7357
<s, s>(q_gen_7342) -> q_gen_7342
<z, s>(q_gen_7357) -> q_gen_7342
<z, z>() -> q_gen_7342
<s, s>(q_gen_7374) -> q_gen_7374
<s, z>(q_gen_7357) -> q_gen_7374
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  max -> 
{{{
Q={q_gen_7343, q_gen_7359, q_gen_7371},
Q_f={q_gen_7343},
Delta=
{
<s>(q_gen_7359) -> q_gen_7359
<z>() -> q_gen_7359
<s, s>(q_gen_7371) -> q_gen_7371
<z, z>() -> q_gen_7371
<s, s, s>(q_gen_7343) -> q_gen_7343
<s, z, s>(q_gen_7371) -> q_gen_7343
<z, s, s>(q_gen_7371) -> q_gen_7343
<z, s, z>(q_gen_7359) -> q_gen_7343
<z, z, z>() -> q_gen_7343
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  numnodes -> 
{{{
Q={q_gen_7345, q_gen_7350, q_gen_7351, q_gen_7379, q_gen_7380, q_gen_7408, q_gen_7409, q_gen_7424},
Q_f={q_gen_7345},
Delta=
{
<leaf>() -> q_gen_7350
<s>(q_gen_7380) -> q_gen_7380
<z>() -> q_gen_7380
<node>(q_gen_7409, q_gen_7350, q_gen_7350) -> q_gen_7408
<node>(q_gen_7409, q_gen_7350, q_gen_7408) -> q_gen_7408
<node>(q_gen_7409, q_gen_7408, q_gen_7350) -> q_gen_7408
<node>(q_gen_7409, q_gen_7408, q_gen_7408) -> q_gen_7408
<a>() -> q_gen_7409
<b>() -> q_gen_7409
<leaf, z>() -> q_gen_7345
<node, s>(q_gen_7351, q_gen_7350, q_gen_7350) -> q_gen_7345
<node, s>(q_gen_7351, q_gen_7408, q_gen_7408) -> q_gen_7345
<node, s>(q_gen_7379, q_gen_7350, q_gen_7350) -> q_gen_7345
<node, s>(q_gen_7379, q_gen_7350, q_gen_7408) -> q_gen_7345
<node, s>(q_gen_7379, q_gen_7408, q_gen_7350) -> q_gen_7345
<node, s>(q_gen_7379, q_gen_7408, q_gen_7408) -> q_gen_7345
<a, z>() -> q_gen_7351
<b, z>() -> q_gen_7351
<a, s>(q_gen_7380) -> q_gen_7379
<b, s>(q_gen_7380) -> q_gen_7379
<node, s>(q_gen_7351, q_gen_7350, q_gen_7408) -> q_gen_7424
<node, s>(q_gen_7351, q_gen_7408, q_gen_7350) -> q_gen_7424
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_7344, q_gen_7348, q_gen_7367},
Q_f={q_gen_7344},
Delta=
{
<s>(q_gen_7367) -> q_gen_7367
<z>() -> q_gen_7367
<s, s>(q_gen_7348) -> q_gen_7348
<z, s>(q_gen_7367) -> q_gen_7348
<z, z>() -> q_gen_7348
<s, s, s>(q_gen_7344) -> q_gen_7344
<s, z, s>(q_gen_7348) -> q_gen_7344
<z, s, s>(q_gen_7348) -> q_gen_7344
<z, z, s>(q_gen_7367) -> q_gen_7344
<z, z, z>() -> q_gen_7344
}

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

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

Teacher's answer:
New clause system:
{
() -> height([leaf, z]) -> 55
() -> leq([z, n2]) -> 55
() -> numnodes([leaf, z]) -> 55
() -> plus([n, z, n]) -> 55
(height([t1, _mba]) /\ height([t2, _nba]) /\ max([_mba, _nba, _oba])) -> height([node(e, t1, t2), s(_oba)]) -> 64
(height([t1, _yba]) /\ numnodes([t1, _zba])) -> leq([_yba, _zba]) -> 65
(leq([n, m])) -> max([n, m, m]) -> 56
(not leq([n, m])) -> max([n, m, n]) -> 56
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 55
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 55
(leq([s(nn1), z])) -> BOT -> 55
(numnodes([t1, _sba]) /\ numnodes([t2, _tba]) /\ plus([_sba, _tba, _uba])) -> numnodes([node(e, t1, t2), s(_uba)]) -> 59
(plus([n, mm, _hba])) -> plus([n, s(mm), s(_hba)]) -> 58
}
Sat witness: Found: ((height([t1, _yba]) /\ numnodes([t1, _zba])) -> leq([_yba, _zba]), {
_yba -> s(s(s(z)))  ;  _zba -> s(s(z))  ;  t1 -> node(b, leaf, node(b, leaf, leaf))
})

-------------------------------------------
Step 75, which took 0.973015 s (model generation: 0.971671,  model checking: 0.001344):

Model:
|_
{
height -> 
{{{
Q={q_gen_7346, q_gen_7354, q_gen_7355, q_gen_7383, q_gen_7384, q_gen_7403, q_gen_7404, q_gen_7405},
Q_f={q_gen_7346},
Delta=
{
<leaf>() -> q_gen_7354
<node>(q_gen_7384, q_gen_7354, q_gen_7354) -> q_gen_7383
<node>(q_gen_7384, q_gen_7354, q_gen_7383) -> q_gen_7383
<node>(q_gen_7384, q_gen_7383, q_gen_7354) -> q_gen_7383
<node>(q_gen_7384, q_gen_7383, q_gen_7383) -> q_gen_7383
<a>() -> q_gen_7384
<b>() -> q_gen_7384
<s>(q_gen_7404) -> q_gen_7404
<z>() -> q_gen_7404
<leaf, z>() -> q_gen_7346
<node, s>(q_gen_7355, q_gen_7354, q_gen_7354) -> q_gen_7346
<node, s>(q_gen_7355, q_gen_7354, q_gen_7383) -> q_gen_7346
<node, s>(q_gen_7355, q_gen_7383, q_gen_7383) -> q_gen_7346
<node, s>(q_gen_7403, q_gen_7354, q_gen_7383) -> q_gen_7346
<node, s>(q_gen_7403, q_gen_7383, q_gen_7354) -> q_gen_7346
<node, s>(q_gen_7403, q_gen_7383, q_gen_7383) -> q_gen_7346
<a, z>() -> q_gen_7355
<b, z>() -> q_gen_7355
<a, s>(q_gen_7404) -> q_gen_7403
<b, s>(q_gen_7404) -> q_gen_7403
<node, s>(q_gen_7403, q_gen_7354, q_gen_7354) -> q_gen_7405
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_7342, q_gen_7357, q_gen_7374, q_gen_7406},
Q_f={q_gen_7342},
Delta=
{
<s>(q_gen_7357) -> q_gen_7357
<z>() -> q_gen_7357
<s, s>(q_gen_7342) -> q_gen_7342
<s, s>(q_gen_7406) -> q_gen_7342
<z, s>(q_gen_7357) -> q_gen_7342
<z, z>() -> q_gen_7342
<s, z>(q_gen_7357) -> q_gen_7374
<s, s>(q_gen_7374) -> q_gen_7406
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  max -> 
{{{
Q={q_gen_7343, q_gen_7359, q_gen_7371},
Q_f={q_gen_7343},
Delta=
{
<s>(q_gen_7359) -> q_gen_7359
<z>() -> q_gen_7359
<s, s>(q_gen_7371) -> q_gen_7371
<z, z>() -> q_gen_7371
<s, s, s>(q_gen_7343) -> q_gen_7343
<s, z, s>(q_gen_7371) -> q_gen_7343
<z, s, s>(q_gen_7371) -> q_gen_7343
<z, s, z>(q_gen_7359) -> q_gen_7343
<z, z, z>() -> q_gen_7343
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  numnodes -> 
{{{
Q={q_gen_7345, q_gen_7350, q_gen_7351, q_gen_7379, q_gen_7380, q_gen_7408, q_gen_7409, q_gen_7424},
Q_f={q_gen_7345},
Delta=
{
<leaf>() -> q_gen_7350
<s>(q_gen_7380) -> q_gen_7380
<z>() -> q_gen_7380
<node>(q_gen_7409, q_gen_7350, q_gen_7350) -> q_gen_7408
<node>(q_gen_7409, q_gen_7350, q_gen_7408) -> q_gen_7408
<node>(q_gen_7409, q_gen_7408, q_gen_7350) -> q_gen_7408
<node>(q_gen_7409, q_gen_7408, q_gen_7408) -> q_gen_7408
<a>() -> q_gen_7409
<b>() -> q_gen_7409
<leaf, z>() -> q_gen_7345
<node, s>(q_gen_7351, q_gen_7350, q_gen_7350) -> q_gen_7345
<node, s>(q_gen_7379, q_gen_7350, q_gen_7350) -> q_gen_7345
<node, s>(q_gen_7379, q_gen_7350, q_gen_7408) -> q_gen_7345
<node, s>(q_gen_7379, q_gen_7408, q_gen_7350) -> q_gen_7345
<node, s>(q_gen_7379, q_gen_7408, q_gen_7408) -> q_gen_7345
<a, z>() -> q_gen_7351
<b, z>() -> q_gen_7351
<a, s>(q_gen_7380) -> q_gen_7379
<b, s>(q_gen_7380) -> q_gen_7379
<node, s>(q_gen_7351, q_gen_7350, q_gen_7408) -> q_gen_7424
<node, s>(q_gen_7351, q_gen_7408, q_gen_7350) -> q_gen_7424
<node, s>(q_gen_7351, q_gen_7408, q_gen_7408) -> q_gen_7424
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_7344, q_gen_7348, q_gen_7367},
Q_f={q_gen_7344},
Delta=
{
<s>(q_gen_7367) -> q_gen_7367
<z>() -> q_gen_7367
<s, s>(q_gen_7348) -> q_gen_7348
<z, s>(q_gen_7367) -> q_gen_7348
<z, z>() -> q_gen_7348
<s, s, s>(q_gen_7344) -> q_gen_7344
<s, z, s>(q_gen_7348) -> q_gen_7344
<z, s, s>(q_gen_7348) -> q_gen_7344
<z, z, s>(q_gen_7367) -> q_gen_7344
<z, z, z>() -> q_gen_7344
}

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

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

Teacher's answer:
New clause system:
{
() -> height([leaf, z]) -> 55
() -> leq([z, n2]) -> 55
() -> numnodes([leaf, z]) -> 55
() -> plus([n, z, n]) -> 55
(height([t1, _mba]) /\ height([t2, _nba]) /\ max([_mba, _nba, _oba])) -> height([node(e, t1, t2), s(_oba)]) -> 64
(height([t1, _yba]) /\ numnodes([t1, _zba])) -> leq([_yba, _zba]) -> 65
(leq([n, m])) -> max([n, m, m]) -> 56
(not leq([n, m])) -> max([n, m, n]) -> 56
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 55
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 58
(leq([s(nn1), z])) -> BOT -> 56
(numnodes([t1, _sba]) /\ numnodes([t2, _tba]) /\ plus([_sba, _tba, _uba])) -> numnodes([node(e, t1, t2), s(_uba)]) -> 59
(plus([n, mm, _hba])) -> plus([n, s(mm), s(_hba)]) -> 58
}
Sat witness: Found: ((leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]), {
nn1 -> s(s(z))  ;  nn2 -> s(z)
})

-------------------------------------------
Step 76, which took 2.461500 s (model generation: 2.461272,  model checking: 0.000228):

Model:
|_
{
height -> 
{{{
Q={q_gen_7346, q_gen_7354, q_gen_7355, q_gen_7383, q_gen_7384, q_gen_7403, q_gen_7404, q_gen_7405},
Q_f={q_gen_7346},
Delta=
{
<leaf>() -> q_gen_7354
<node>(q_gen_7384, q_gen_7354, q_gen_7354) -> q_gen_7383
<node>(q_gen_7384, q_gen_7354, q_gen_7383) -> q_gen_7383
<node>(q_gen_7384, q_gen_7383, q_gen_7354) -> q_gen_7383
<node>(q_gen_7384, q_gen_7383, q_gen_7383) -> q_gen_7383
<a>() -> q_gen_7384
<b>() -> q_gen_7384
<s>(q_gen_7404) -> q_gen_7404
<z>() -> q_gen_7404
<leaf, z>() -> q_gen_7346
<node, s>(q_gen_7355, q_gen_7354, q_gen_7354) -> q_gen_7346
<node, s>(q_gen_7355, q_gen_7354, q_gen_7383) -> q_gen_7346
<node, s>(q_gen_7355, q_gen_7383, q_gen_7383) -> q_gen_7346
<node, s>(q_gen_7403, q_gen_7354, q_gen_7383) -> q_gen_7346
<node, s>(q_gen_7403, q_gen_7383, q_gen_7354) -> q_gen_7346
<node, s>(q_gen_7403, q_gen_7383, q_gen_7383) -> q_gen_7346
<a, z>() -> q_gen_7355
<b, z>() -> q_gen_7355
<a, s>(q_gen_7404) -> q_gen_7403
<b, s>(q_gen_7404) -> q_gen_7403
<node, s>(q_gen_7403, q_gen_7354, q_gen_7354) -> q_gen_7405
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_7342, q_gen_7357, q_gen_7374},
Q_f={q_gen_7342},
Delta=
{
<s>(q_gen_7357) -> q_gen_7357
<z>() -> q_gen_7357
<s, s>(q_gen_7342) -> q_gen_7342
<z, s>(q_gen_7357) -> q_gen_7342
<z, z>() -> q_gen_7342
<s, s>(q_gen_7374) -> q_gen_7374
<s, z>(q_gen_7357) -> q_gen_7374
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  max -> 
{{{
Q={q_gen_7343, q_gen_7359, q_gen_7371},
Q_f={q_gen_7343},
Delta=
{
<s>(q_gen_7359) -> q_gen_7359
<z>() -> q_gen_7359
<s, s>(q_gen_7371) -> q_gen_7371
<z, z>() -> q_gen_7371
<s, s, s>(q_gen_7343) -> q_gen_7343
<s, z, s>(q_gen_7371) -> q_gen_7343
<z, s, s>(q_gen_7371) -> q_gen_7343
<z, s, z>(q_gen_7359) -> q_gen_7343
<z, z, z>() -> q_gen_7343
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  numnodes -> 
{{{
Q={q_gen_7345, q_gen_7350, q_gen_7351, q_gen_7380, q_gen_7409, q_gen_7415, q_gen_7416, q_gen_7417},
Q_f={q_gen_7345},
Delta=
{
<leaf>() -> q_gen_7350
<node>(q_gen_7409, q_gen_7350, q_gen_7350) -> q_gen_7350
<node>(q_gen_7409, q_gen_7350, q_gen_7416) -> q_gen_7350
<node>(q_gen_7409, q_gen_7416, q_gen_7416) -> q_gen_7350
<s>(q_gen_7380) -> q_gen_7380
<z>() -> q_gen_7380
<a>() -> q_gen_7409
<node>(q_gen_7417, q_gen_7350, q_gen_7350) -> q_gen_7416
<node>(q_gen_7417, q_gen_7350, q_gen_7416) -> q_gen_7416
<node>(q_gen_7417, q_gen_7416, q_gen_7350) -> q_gen_7416
<node>(q_gen_7417, q_gen_7416, q_gen_7416) -> q_gen_7416
<b>() -> q_gen_7417
<leaf, z>() -> q_gen_7345
<node, s>(q_gen_7351, q_gen_7350, q_gen_7350) -> q_gen_7345
<a, s>(q_gen_7380) -> q_gen_7351
<a, z>() -> q_gen_7351
<b, s>(q_gen_7380) -> q_gen_7351
<b, z>() -> q_gen_7351
<node, s>(q_gen_7351, q_gen_7350, q_gen_7416) -> q_gen_7415
<node, s>(q_gen_7351, q_gen_7416, q_gen_7350) -> q_gen_7415
<node, s>(q_gen_7351, q_gen_7416, q_gen_7416) -> q_gen_7415
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_7344, q_gen_7348, q_gen_7361, q_gen_7364, q_gen_7367},
Q_f={q_gen_7344},
Delta=
{
<s>(q_gen_7367) -> q_gen_7367
<z>() -> q_gen_7367
<z, z>() -> q_gen_7348
<s, s>(q_gen_7348) -> q_gen_7361
<z, s>(q_gen_7367) -> q_gen_7361
<s, s, s>(q_gen_7344) -> q_gen_7344
<s, s, s>(q_gen_7364) -> q_gen_7344
<s, z, s>(q_gen_7361) -> q_gen_7344
<z, s, s>(q_gen_7348) -> q_gen_7344
<z, z, z>() -> q_gen_7344
<s, z, s>(q_gen_7348) -> q_gen_7364
<z, s, s>(q_gen_7361) -> q_gen_7364
<z, z, s>(q_gen_7367) -> q_gen_7364
}

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

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

Teacher's answer:
New clause system:
{
() -> height([leaf, z]) -> 55
() -> leq([z, n2]) -> 55
() -> numnodes([leaf, z]) -> 55
() -> plus([n, z, n]) -> 58
(height([t1, _mba]) /\ height([t2, _nba]) /\ max([_mba, _nba, _oba])) -> height([node(e, t1, t2), s(_oba)]) -> 64
(height([t1, _yba]) /\ numnodes([t1, _zba])) -> leq([_yba, _zba]) -> 65
(leq([n, m])) -> max([n, m, m]) -> 56
(not leq([n, m])) -> max([n, m, n]) -> 56
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 56
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 58
(leq([s(nn1), z])) -> BOT -> 56
(numnodes([t1, _sba]) /\ numnodes([t2, _tba]) /\ plus([_sba, _tba, _uba])) -> numnodes([node(e, t1, t2), s(_uba)]) -> 59
(plus([n, mm, _hba])) -> plus([n, s(mm), s(_hba)]) -> 58
}
Sat witness: Found: (() -> plus([n, z, n]), {
n -> s(z)
})

-------------------------------------------
Step 77, which took 1.658753 s (model generation: 1.519019,  model checking: 0.139734):

Model:
|_
{
height -> 
{{{
Q={q_gen_7346, q_gen_7354, q_gen_7355, q_gen_7382, q_gen_7383, q_gen_7384, q_gen_7403, q_gen_7404, q_gen_7471},
Q_f={q_gen_7346},
Delta=
{
<leaf>() -> q_gen_7354
<node>(q_gen_7384, q_gen_7354, q_gen_7383) -> q_gen_7354
<node>(q_gen_7384, q_gen_7383, q_gen_7383) -> q_gen_7354
<node>(q_gen_7384, q_gen_7354, q_gen_7354) -> q_gen_7383
<node>(q_gen_7384, q_gen_7383, q_gen_7354) -> q_gen_7383
<a>() -> q_gen_7384
<b>() -> q_gen_7384
<z>() -> q_gen_7404
<s>(q_gen_7404) -> q_gen_7471
<leaf, z>() -> q_gen_7346
<node, s>(q_gen_7355, q_gen_7354, q_gen_7354) -> q_gen_7346
<node, s>(q_gen_7403, q_gen_7354, q_gen_7383) -> q_gen_7346
<node, s>(q_gen_7403, q_gen_7383, q_gen_7383) -> q_gen_7346
<a, s>(q_gen_7471) -> q_gen_7355
<a, z>() -> q_gen_7355
<b, s>(q_gen_7471) -> q_gen_7355
<b, z>() -> q_gen_7355
<node, s>(q_gen_7355, q_gen_7354, q_gen_7383) -> q_gen_7382
<node, s>(q_gen_7355, q_gen_7383, q_gen_7354) -> q_gen_7382
<node, s>(q_gen_7355, q_gen_7383, q_gen_7383) -> q_gen_7382
<node, s>(q_gen_7403, q_gen_7354, q_gen_7354) -> q_gen_7382
<node, s>(q_gen_7403, q_gen_7383, q_gen_7354) -> q_gen_7382
<a, s>(q_gen_7404) -> q_gen_7403
<b, s>(q_gen_7404) -> q_gen_7403
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_7342, q_gen_7357, q_gen_7374},
Q_f={q_gen_7342},
Delta=
{
<s>(q_gen_7357) -> q_gen_7357
<z>() -> q_gen_7357
<s, s>(q_gen_7342) -> q_gen_7342
<z, s>(q_gen_7357) -> q_gen_7342
<z, z>() -> q_gen_7342
<s, s>(q_gen_7374) -> q_gen_7374
<s, z>(q_gen_7357) -> q_gen_7374
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  max -> 
{{{
Q={q_gen_7343, q_gen_7358, q_gen_7359, q_gen_7371},
Q_f={q_gen_7343},
Delta=
{
<s>(q_gen_7359) -> q_gen_7359
<z>() -> q_gen_7359
<s, s>(q_gen_7371) -> q_gen_7371
<z, z>() -> q_gen_7371
<s, s, s>(q_gen_7343) -> q_gen_7343
<s, z, s>(q_gen_7371) -> q_gen_7343
<z, s, s>(q_gen_7371) -> q_gen_7343
<z, z, z>() -> q_gen_7343
<z, s, z>(q_gen_7359) -> q_gen_7358
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  numnodes -> 
{{{
Q={q_gen_7345, q_gen_7350, q_gen_7351, q_gen_7379, q_gen_7380, q_gen_7408, q_gen_7409, q_gen_7413},
Q_f={q_gen_7345},
Delta=
{
<leaf>() -> q_gen_7350
<node>(q_gen_7409, q_gen_7350, q_gen_7408) -> q_gen_7350
<s>(q_gen_7380) -> q_gen_7380
<z>() -> q_gen_7380
<node>(q_gen_7409, q_gen_7350, q_gen_7350) -> q_gen_7408
<node>(q_gen_7409, q_gen_7408, q_gen_7350) -> q_gen_7408
<node>(q_gen_7409, q_gen_7408, q_gen_7408) -> q_gen_7408
<a>() -> q_gen_7409
<b>() -> q_gen_7409
<leaf, z>() -> q_gen_7345
<node, s>(q_gen_7351, q_gen_7350, q_gen_7350) -> q_gen_7345
<node, s>(q_gen_7351, q_gen_7408, q_gen_7350) -> q_gen_7345
<node, s>(q_gen_7379, q_gen_7350, q_gen_7350) -> q_gen_7345
<node, s>(q_gen_7379, q_gen_7350, q_gen_7408) -> q_gen_7345
<node, s>(q_gen_7379, q_gen_7408, q_gen_7350) -> q_gen_7345
<a, z>() -> q_gen_7351
<b, z>() -> q_gen_7351
<a, s>(q_gen_7380) -> q_gen_7379
<b, s>(q_gen_7380) -> q_gen_7379
<node, s>(q_gen_7351, q_gen_7350, q_gen_7408) -> q_gen_7413
<node, s>(q_gen_7351, q_gen_7408, q_gen_7408) -> q_gen_7413
<node, s>(q_gen_7379, q_gen_7408, q_gen_7408) -> q_gen_7413
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_7344, q_gen_7348, q_gen_7367},
Q_f={q_gen_7344},
Delta=
{
<s>(q_gen_7367) -> q_gen_7367
<z>() -> q_gen_7367
<s, s>(q_gen_7348) -> q_gen_7348
<z, s>(q_gen_7367) -> q_gen_7348
<z, z>() -> q_gen_7348
<s, s, s>(q_gen_7344) -> q_gen_7344
<s, z, s>(q_gen_7348) -> q_gen_7344
<z, s, s>(q_gen_7348) -> q_gen_7344
<z, z, s>(q_gen_7367) -> q_gen_7344
<z, z, z>() -> q_gen_7344
}

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

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

Teacher's answer:
New clause system:
{
() -> height([leaf, z]) -> 56
() -> leq([z, n2]) -> 56
() -> numnodes([leaf, z]) -> 56
() -> plus([n, z, n]) -> 59
(height([t1, _mba]) /\ height([t2, _nba]) /\ max([_mba, _nba, _oba])) -> height([node(e, t1, t2), s(_oba)]) -> 64
(height([t1, _yba]) /\ numnodes([t1, _zba])) -> leq([_yba, _zba]) -> 65
(leq([n, m])) -> max([n, m, m]) -> 57
(not leq([n, m])) -> max([n, m, n]) -> 57
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 57
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 59
(leq([s(nn1), z])) -> BOT -> 57
(numnodes([t1, _sba]) /\ numnodes([t2, _tba]) /\ plus([_sba, _tba, _uba])) -> numnodes([node(e, t1, t2), s(_uba)]) -> 62
(plus([n, mm, _hba])) -> plus([n, s(mm), s(_hba)]) -> 59
}
Sat witness: Found: ((numnodes([t1, _sba]) /\ numnodes([t2, _tba]) /\ plus([_sba, _tba, _uba])) -> numnodes([node(e, t1, t2), s(_uba)]), {
_sba -> s(z)  ;  _tba -> s(z)  ;  _uba -> s(z)  ;  e -> b  ;  t1 -> node(a, node(b, leaf, node(b, leaf, leaf)), node(b, leaf, node(b, leaf, leaf)))  ;  t2 -> node(a, leaf, node(b, leaf, node(b, leaf, leaf)))
})

-------------------------------------------
Step 78, which took 1.326446 s (model generation: 1.237552,  model checking: 0.088894):

Model:
|_
{
height -> 
{{{
Q={q_gen_7346, q_gen_7354, q_gen_7355, q_gen_7383, q_gen_7384, q_gen_7400, q_gen_7403, q_gen_7404, q_gen_7461},
Q_f={q_gen_7346},
Delta=
{
<leaf>() -> q_gen_7354
<node>(q_gen_7384, q_gen_7383, q_gen_7354) -> q_gen_7354
<node>(q_gen_7384, q_gen_7354, q_gen_7354) -> q_gen_7383
<node>(q_gen_7384, q_gen_7354, q_gen_7383) -> q_gen_7383
<node>(q_gen_7384, q_gen_7383, q_gen_7383) -> q_gen_7383
<a>() -> q_gen_7384
<b>() -> q_gen_7384
<s>(q_gen_7404) -> q_gen_7404
<z>() -> q_gen_7404
<leaf, z>() -> q_gen_7346
<node, s>(q_gen_7355, q_gen_7354, q_gen_7354) -> q_gen_7346
<node, s>(q_gen_7355, q_gen_7354, q_gen_7383) -> q_gen_7346
<node, s>(q_gen_7403, q_gen_7354, q_gen_7383) -> q_gen_7346
<node, s>(q_gen_7403, q_gen_7383, q_gen_7383) -> q_gen_7346
<node, s>(q_gen_7461, q_gen_7383, q_gen_7354) -> q_gen_7346
<a, z>() -> q_gen_7355
<b, z>() -> q_gen_7355
<node, s>(q_gen_7355, q_gen_7383, q_gen_7383) -> q_gen_7400
<node, s>(q_gen_7403, q_gen_7354, q_gen_7354) -> q_gen_7400
<node, s>(q_gen_7403, q_gen_7383, q_gen_7354) -> q_gen_7400
<node, s>(q_gen_7461, q_gen_7354, q_gen_7354) -> q_gen_7400
<node, s>(q_gen_7461, q_gen_7354, q_gen_7383) -> q_gen_7400
<b, s>(q_gen_7404) -> q_gen_7403
<a, s>(q_gen_7404) -> q_gen_7461
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_7342, q_gen_7357, q_gen_7374},
Q_f={q_gen_7342},
Delta=
{
<s>(q_gen_7357) -> q_gen_7357
<z>() -> q_gen_7357
<s, s>(q_gen_7342) -> q_gen_7342
<z, s>(q_gen_7357) -> q_gen_7342
<z, z>() -> q_gen_7342
<s, s>(q_gen_7374) -> q_gen_7374
<s, z>(q_gen_7357) -> q_gen_7374
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  max -> 
{{{
Q={q_gen_7343, q_gen_7359, q_gen_7371},
Q_f={q_gen_7343},
Delta=
{
<s>(q_gen_7359) -> q_gen_7359
<z>() -> q_gen_7359
<s, s>(q_gen_7371) -> q_gen_7371
<z, z>() -> q_gen_7371
<s, s, s>(q_gen_7343) -> q_gen_7343
<s, z, s>(q_gen_7371) -> q_gen_7343
<z, s, s>(q_gen_7371) -> q_gen_7343
<z, s, z>(q_gen_7359) -> q_gen_7343
<z, z, z>() -> q_gen_7343
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  numnodes -> 
{{{
Q={q_gen_7345, q_gen_7350, q_gen_7351, q_gen_7369, q_gen_7380, q_gen_7409, q_gen_7416, q_gen_7417, q_gen_7424},
Q_f={q_gen_7345},
Delta=
{
<leaf>() -> q_gen_7350
<node>(q_gen_7409, q_gen_7350, q_gen_7350) -> q_gen_7350
<node>(q_gen_7409, q_gen_7350, q_gen_7416) -> q_gen_7350
<node>(q_gen_7409, q_gen_7416, q_gen_7416) -> q_gen_7350
<node>(q_gen_7417, q_gen_7416, q_gen_7350) -> q_gen_7350
<s>(q_gen_7380) -> q_gen_7380
<z>() -> q_gen_7380
<a>() -> q_gen_7409
<node>(q_gen_7417, q_gen_7350, q_gen_7350) -> q_gen_7416
<node>(q_gen_7417, q_gen_7350, q_gen_7416) -> q_gen_7416
<node>(q_gen_7417, q_gen_7416, q_gen_7416) -> q_gen_7416
<b>() -> q_gen_7417
<leaf, z>() -> q_gen_7345
<node, s>(q_gen_7351, q_gen_7350, q_gen_7350) -> q_gen_7345
<node, s>(q_gen_7351, q_gen_7416, q_gen_7350) -> q_gen_7345
<node, s>(q_gen_7369, q_gen_7350, q_gen_7350) -> q_gen_7345
<node, s>(q_gen_7369, q_gen_7350, q_gen_7416) -> q_gen_7345
<b, s>(q_gen_7380) -> q_gen_7351
<b, z>() -> q_gen_7351
<a, s>(q_gen_7380) -> q_gen_7369
<a, z>() -> q_gen_7369
<node, s>(q_gen_7351, q_gen_7350, q_gen_7416) -> q_gen_7424
<node, s>(q_gen_7351, q_gen_7416, q_gen_7416) -> q_gen_7424
<node, s>(q_gen_7369, q_gen_7416, q_gen_7350) -> q_gen_7424
<node, s>(q_gen_7369, q_gen_7416, q_gen_7416) -> q_gen_7424
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_7344, q_gen_7348, q_gen_7367},
Q_f={q_gen_7344},
Delta=
{
<s>(q_gen_7367) -> q_gen_7367
<z>() -> q_gen_7367
<s, s>(q_gen_7348) -> q_gen_7348
<z, s>(q_gen_7367) -> q_gen_7348
<z, z>() -> q_gen_7348
<s, s, s>(q_gen_7344) -> q_gen_7344
<s, z, s>(q_gen_7348) -> q_gen_7344
<z, s, s>(q_gen_7348) -> q_gen_7344
<z, z, s>(q_gen_7367) -> q_gen_7344
<z, z, z>() -> q_gen_7344
}

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

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

Teacher's answer:
New clause system:
{
() -> height([leaf, z]) -> 57
() -> leq([z, n2]) -> 57
() -> numnodes([leaf, z]) -> 57
() -> plus([n, z, n]) -> 60
(height([t1, _mba]) /\ height([t2, _nba]) /\ max([_mba, _nba, _oba])) -> height([node(e, t1, t2), s(_oba)]) -> 64
(height([t1, _yba]) /\ numnodes([t1, _zba])) -> leq([_yba, _zba]) -> 65
(leq([n, m])) -> max([n, m, m]) -> 58
(not leq([n, m])) -> max([n, m, n]) -> 58
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 58
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 60
(leq([s(nn1), z])) -> BOT -> 58
(numnodes([t1, _sba]) /\ numnodes([t2, _tba]) /\ plus([_sba, _tba, _uba])) -> numnodes([node(e, t1, t2), s(_uba)]) -> 65
(plus([n, mm, _hba])) -> plus([n, s(mm), s(_hba)]) -> 60
}
Sat witness: Found: ((numnodes([t1, _sba]) /\ numnodes([t2, _tba]) /\ plus([_sba, _tba, _uba])) -> numnodes([node(e, t1, t2), s(_uba)]), {
_sba -> s(z)  ;  _tba -> z  ;  _uba -> s(z)  ;  e -> a  ;  t1 -> node(b, node(a, leaf, leaf), node(a, node(b, leaf, node(a, leaf, leaf)), node(b, leaf, node(a, leaf, leaf))))  ;  t2 -> leaf
})

-------------------------------------------
Step 79, which took 1.718422 s (model generation: 1.711969,  model checking: 0.006453):

Model:
|_
{
height -> 
{{{
Q={q_gen_7346, q_gen_7354, q_gen_7355, q_gen_7382, q_gen_7383, q_gen_7384, q_gen_7403, q_gen_7404, q_gen_7471},
Q_f={q_gen_7346},
Delta=
{
<leaf>() -> q_gen_7354
<node>(q_gen_7384, q_gen_7354, q_gen_7383) -> q_gen_7354
<node>(q_gen_7384, q_gen_7383, q_gen_7354) -> q_gen_7354
<node>(q_gen_7384, q_gen_7354, q_gen_7354) -> q_gen_7383
<node>(q_gen_7384, q_gen_7383, q_gen_7383) -> q_gen_7383
<a>() -> q_gen_7384
<b>() -> q_gen_7384
<z>() -> q_gen_7404
<s>(q_gen_7404) -> q_gen_7471
<leaf, z>() -> q_gen_7346
<node, s>(q_gen_7355, q_gen_7354, q_gen_7354) -> q_gen_7346
<node, s>(q_gen_7403, q_gen_7354, q_gen_7383) -> q_gen_7346
<node, s>(q_gen_7403, q_gen_7383, q_gen_7354) -> q_gen_7346
<node, s>(q_gen_7403, q_gen_7383, q_gen_7383) -> q_gen_7346
<a, s>(q_gen_7471) -> q_gen_7355
<a, z>() -> q_gen_7355
<b, s>(q_gen_7471) -> q_gen_7355
<b, z>() -> q_gen_7355
<node, s>(q_gen_7355, q_gen_7354, q_gen_7383) -> q_gen_7382
<node, s>(q_gen_7355, q_gen_7383, q_gen_7354) -> q_gen_7382
<node, s>(q_gen_7355, q_gen_7383, q_gen_7383) -> q_gen_7382
<node, s>(q_gen_7403, q_gen_7354, q_gen_7354) -> q_gen_7382
<a, s>(q_gen_7404) -> q_gen_7403
<b, s>(q_gen_7404) -> q_gen_7403
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_7342, q_gen_7357, q_gen_7374},
Q_f={q_gen_7342},
Delta=
{
<s>(q_gen_7357) -> q_gen_7357
<z>() -> q_gen_7357
<s, s>(q_gen_7342) -> q_gen_7342
<z, s>(q_gen_7357) -> q_gen_7342
<z, z>() -> q_gen_7342
<s, s>(q_gen_7374) -> q_gen_7374
<s, z>(q_gen_7357) -> q_gen_7374
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  max -> 
{{{
Q={q_gen_7343, q_gen_7358, q_gen_7359, q_gen_7371},
Q_f={q_gen_7343},
Delta=
{
<s>(q_gen_7359) -> q_gen_7359
<z>() -> q_gen_7359
<s, s>(q_gen_7371) -> q_gen_7371
<z, z>() -> q_gen_7371
<s, s, s>(q_gen_7343) -> q_gen_7343
<s, z, s>(q_gen_7371) -> q_gen_7343
<z, s, s>(q_gen_7371) -> q_gen_7343
<z, z, z>() -> q_gen_7343
<z, s, z>(q_gen_7359) -> q_gen_7358
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  numnodes -> 
{{{
Q={q_gen_7345, q_gen_7350, q_gen_7351, q_gen_7379, q_gen_7380, q_gen_7408, q_gen_7409, q_gen_7424},
Q_f={q_gen_7345},
Delta=
{
<leaf>() -> q_gen_7350
<s>(q_gen_7380) -> q_gen_7380
<z>() -> q_gen_7380
<node>(q_gen_7409, q_gen_7350, q_gen_7350) -> q_gen_7408
<node>(q_gen_7409, q_gen_7350, q_gen_7408) -> q_gen_7408
<node>(q_gen_7409, q_gen_7408, q_gen_7350) -> q_gen_7408
<node>(q_gen_7409, q_gen_7408, q_gen_7408) -> q_gen_7408
<a>() -> q_gen_7409
<b>() -> q_gen_7409
<leaf, z>() -> q_gen_7345
<node, s>(q_gen_7351, q_gen_7350, q_gen_7350) -> q_gen_7345
<node, s>(q_gen_7379, q_gen_7350, q_gen_7350) -> q_gen_7345
<node, s>(q_gen_7379, q_gen_7350, q_gen_7408) -> q_gen_7345
<node, s>(q_gen_7379, q_gen_7408, q_gen_7350) -> q_gen_7345
<node, s>(q_gen_7379, q_gen_7408, q_gen_7408) -> q_gen_7345
<a, z>() -> q_gen_7351
<b, z>() -> q_gen_7351
<a, s>(q_gen_7380) -> q_gen_7379
<b, s>(q_gen_7380) -> q_gen_7379
<node, s>(q_gen_7351, q_gen_7350, q_gen_7408) -> q_gen_7424
<node, s>(q_gen_7351, q_gen_7408, q_gen_7350) -> q_gen_7424
<node, s>(q_gen_7351, q_gen_7408, q_gen_7408) -> q_gen_7424
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_7344, q_gen_7348, q_gen_7367},
Q_f={q_gen_7344},
Delta=
{
<s>(q_gen_7367) -> q_gen_7367
<z>() -> q_gen_7367
<s, s>(q_gen_7348) -> q_gen_7348
<z, s>(q_gen_7367) -> q_gen_7348
<z, z>() -> q_gen_7348
<s, s, s>(q_gen_7344) -> q_gen_7344
<s, z, s>(q_gen_7348) -> q_gen_7344
<z, s, s>(q_gen_7348) -> q_gen_7344
<z, z, s>(q_gen_7367) -> q_gen_7344
<z, z, z>() -> q_gen_7344
}

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

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

Teacher's answer:
New clause system:
{
() -> height([leaf, z]) -> 58
() -> leq([z, n2]) -> 58
() -> numnodes([leaf, z]) -> 58
() -> plus([n, z, n]) -> 61
(height([t1, _mba]) /\ height([t2, _nba]) /\ max([_mba, _nba, _oba])) -> height([node(e, t1, t2), s(_oba)]) -> 67
(height([t1, _yba]) /\ numnodes([t1, _zba])) -> leq([_yba, _zba]) -> 65
(leq([n, m])) -> max([n, m, m]) -> 59
(not leq([n, m])) -> max([n, m, n]) -> 59
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 59
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 61
(leq([s(nn1), z])) -> BOT -> 59
(numnodes([t1, _sba]) /\ numnodes([t2, _tba]) /\ plus([_sba, _tba, _uba])) -> numnodes([node(e, t1, t2), s(_uba)]) -> 65
(plus([n, mm, _hba])) -> plus([n, s(mm), s(_hba)]) -> 61
}
Sat witness: Found: ((height([t1, _mba]) /\ height([t2, _nba]) /\ max([_mba, _nba, _oba])) -> height([node(e, t1, t2), s(_oba)]), {
_mba -> z  ;  _nba -> s(s(z))  ;  _oba -> s(s(z))  ;  e -> b  ;  t1 -> leaf  ;  t2 -> node(a, node(b, leaf, leaf), node(b, leaf, leaf))
})

-------------------------------------------
Step 80, which took 1.531112 s (model generation: 1.449125,  model checking: 0.081987):

Model:
|_
{
height -> 
{{{
Q={q_gen_7346, q_gen_7354, q_gen_7355, q_gen_7383, q_gen_7384, q_gen_7400, q_gen_7403, q_gen_7404, q_gen_7461},
Q_f={q_gen_7346},
Delta=
{
<leaf>() -> q_gen_7354
<node>(q_gen_7384, q_gen_7383, q_gen_7354) -> q_gen_7354
<node>(q_gen_7384, q_gen_7354, q_gen_7354) -> q_gen_7383
<node>(q_gen_7384, q_gen_7354, q_gen_7383) -> q_gen_7383
<node>(q_gen_7384, q_gen_7383, q_gen_7383) -> q_gen_7383
<a>() -> q_gen_7384
<b>() -> q_gen_7384
<s>(q_gen_7404) -> q_gen_7404
<z>() -> q_gen_7404
<leaf, z>() -> q_gen_7346
<node, s>(q_gen_7355, q_gen_7354, q_gen_7354) -> q_gen_7346
<node, s>(q_gen_7355, q_gen_7354, q_gen_7383) -> q_gen_7346
<node, s>(q_gen_7403, q_gen_7354, q_gen_7383) -> q_gen_7346
<node, s>(q_gen_7403, q_gen_7383, q_gen_7383) -> q_gen_7346
<node, s>(q_gen_7461, q_gen_7383, q_gen_7354) -> q_gen_7346
<a, z>() -> q_gen_7355
<b, z>() -> q_gen_7355
<node, s>(q_gen_7355, q_gen_7383, q_gen_7383) -> q_gen_7400
<node, s>(q_gen_7403, q_gen_7354, q_gen_7354) -> q_gen_7400
<node, s>(q_gen_7403, q_gen_7383, q_gen_7354) -> q_gen_7400
<node, s>(q_gen_7461, q_gen_7354, q_gen_7354) -> q_gen_7400
<node, s>(q_gen_7461, q_gen_7354, q_gen_7383) -> q_gen_7400
<node, s>(q_gen_7461, q_gen_7383, q_gen_7383) -> q_gen_7400
<b, s>(q_gen_7404) -> q_gen_7403
<a, s>(q_gen_7404) -> q_gen_7461
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_7342, q_gen_7357, q_gen_7374},
Q_f={q_gen_7342},
Delta=
{
<s>(q_gen_7357) -> q_gen_7357
<z>() -> q_gen_7357
<s, s>(q_gen_7342) -> q_gen_7342
<z, s>(q_gen_7357) -> q_gen_7342
<z, z>() -> q_gen_7342
<s, s>(q_gen_7374) -> q_gen_7374
<s, z>(q_gen_7357) -> q_gen_7374
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  max -> 
{{{
Q={q_gen_7343, q_gen_7359, q_gen_7371},
Q_f={q_gen_7343},
Delta=
{
<s>(q_gen_7359) -> q_gen_7359
<z>() -> q_gen_7359
<s, s>(q_gen_7371) -> q_gen_7371
<z, z>() -> q_gen_7371
<s, s, s>(q_gen_7343) -> q_gen_7343
<s, z, s>(q_gen_7371) -> q_gen_7343
<z, s, s>(q_gen_7371) -> q_gen_7343
<z, s, z>(q_gen_7359) -> q_gen_7343
<z, z, z>() -> q_gen_7343
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  numnodes -> 
{{{
Q={q_gen_7345, q_gen_7350, q_gen_7351, q_gen_7369, q_gen_7380, q_gen_7409, q_gen_7416, q_gen_7417, q_gen_7424},
Q_f={q_gen_7345},
Delta=
{
<leaf>() -> q_gen_7350
<node>(q_gen_7409, q_gen_7350, q_gen_7350) -> q_gen_7350
<node>(q_gen_7409, q_gen_7350, q_gen_7416) -> q_gen_7350
<node>(q_gen_7417, q_gen_7416, q_gen_7350) -> q_gen_7350
<s>(q_gen_7380) -> q_gen_7380
<z>() -> q_gen_7380
<a>() -> q_gen_7409
<node>(q_gen_7409, q_gen_7416, q_gen_7416) -> q_gen_7416
<node>(q_gen_7417, q_gen_7350, q_gen_7350) -> q_gen_7416
<node>(q_gen_7417, q_gen_7350, q_gen_7416) -> q_gen_7416
<node>(q_gen_7417, q_gen_7416, q_gen_7416) -> q_gen_7416
<b>() -> q_gen_7417
<leaf, z>() -> q_gen_7345
<node, s>(q_gen_7351, q_gen_7350, q_gen_7350) -> q_gen_7345
<node, s>(q_gen_7351, q_gen_7416, q_gen_7350) -> q_gen_7345
<node, s>(q_gen_7369, q_gen_7350, q_gen_7350) -> q_gen_7345
<node, s>(q_gen_7369, q_gen_7350, q_gen_7416) -> q_gen_7345
<b, s>(q_gen_7380) -> q_gen_7351
<b, z>() -> q_gen_7351
<a, s>(q_gen_7380) -> q_gen_7369
<a, z>() -> q_gen_7369
<node, s>(q_gen_7351, q_gen_7350, q_gen_7416) -> q_gen_7424
<node, s>(q_gen_7351, q_gen_7416, q_gen_7416) -> q_gen_7424
<node, s>(q_gen_7369, q_gen_7416, q_gen_7350) -> q_gen_7424
<node, s>(q_gen_7369, q_gen_7416, q_gen_7416) -> q_gen_7424
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_7344, q_gen_7348, q_gen_7367},
Q_f={q_gen_7344},
Delta=
{
<s>(q_gen_7367) -> q_gen_7367
<z>() -> q_gen_7367
<s, s>(q_gen_7348) -> q_gen_7348
<z, s>(q_gen_7367) -> q_gen_7348
<z, z>() -> q_gen_7348
<s, s, s>(q_gen_7344) -> q_gen_7344
<s, z, s>(q_gen_7348) -> q_gen_7344
<z, s, s>(q_gen_7348) -> q_gen_7344
<z, z, s>(q_gen_7367) -> q_gen_7344
<z, z, z>() -> q_gen_7344
}

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

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

Teacher's answer:
New clause system:
{
() -> height([leaf, z]) -> 59
() -> leq([z, n2]) -> 59
() -> numnodes([leaf, z]) -> 59
() -> plus([n, z, n]) -> 62
(height([t1, _mba]) /\ height([t2, _nba]) /\ max([_mba, _nba, _oba])) -> height([node(e, t1, t2), s(_oba)]) -> 67
(height([t1, _yba]) /\ numnodes([t1, _zba])) -> leq([_yba, _zba]) -> 65
(leq([n, m])) -> max([n, m, m]) -> 60
(not leq([n, m])) -> max([n, m, n]) -> 60
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 60
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 62
(leq([s(nn1), z])) -> BOT -> 60
(numnodes([t1, _sba]) /\ numnodes([t2, _tba]) /\ plus([_sba, _tba, _uba])) -> numnodes([node(e, t1, t2), s(_uba)]) -> 68
(plus([n, mm, _hba])) -> plus([n, s(mm), s(_hba)]) -> 62
}
Sat witness: Found: ((numnodes([t1, _sba]) /\ numnodes([t2, _tba]) /\ plus([_sba, _tba, _uba])) -> numnodes([node(e, t1, t2), s(_uba)]), {
_sba -> s(z)  ;  _tba -> z  ;  _uba -> s(z)  ;  e -> a  ;  t1 -> node(b, node(a, leaf, leaf), node(a, node(a, leaf, leaf), node(b, node(a, leaf, leaf), node(a, leaf, leaf))))  ;  t2 -> leaf
})

-------------------------------------------
Step 81, which took 1.737777 s (model generation: 1.735686,  model checking: 0.002091):

Model:
|_
{
height -> 
{{{
Q={q_gen_7346, q_gen_7354, q_gen_7355, q_gen_7382, q_gen_7383, q_gen_7384, q_gen_7403, q_gen_7404, q_gen_7471},
Q_f={q_gen_7346},
Delta=
{
<leaf>() -> q_gen_7354
<node>(q_gen_7384, q_gen_7354, q_gen_7383) -> q_gen_7354
<node>(q_gen_7384, q_gen_7383, q_gen_7354) -> q_gen_7354
<node>(q_gen_7384, q_gen_7354, q_gen_7354) -> q_gen_7383
<node>(q_gen_7384, q_gen_7383, q_gen_7383) -> q_gen_7383
<a>() -> q_gen_7384
<b>() -> q_gen_7384
<z>() -> q_gen_7404
<s>(q_gen_7404) -> q_gen_7471
<leaf, z>() -> q_gen_7346
<node, s>(q_gen_7355, q_gen_7354, q_gen_7354) -> q_gen_7346
<node, s>(q_gen_7403, q_gen_7354, q_gen_7383) -> q_gen_7346
<node, s>(q_gen_7403, q_gen_7383, q_gen_7354) -> q_gen_7346
<a, s>(q_gen_7471) -> q_gen_7355
<a, z>() -> q_gen_7355
<b, s>(q_gen_7471) -> q_gen_7355
<b, z>() -> q_gen_7355
<node, s>(q_gen_7355, q_gen_7354, q_gen_7383) -> q_gen_7382
<node, s>(q_gen_7355, q_gen_7383, q_gen_7354) -> q_gen_7382
<node, s>(q_gen_7355, q_gen_7383, q_gen_7383) -> q_gen_7382
<node, s>(q_gen_7403, q_gen_7354, q_gen_7354) -> q_gen_7382
<node, s>(q_gen_7403, q_gen_7383, q_gen_7383) -> q_gen_7382
<a, s>(q_gen_7404) -> q_gen_7403
<b, s>(q_gen_7404) -> q_gen_7403
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_7342, q_gen_7357, q_gen_7374},
Q_f={q_gen_7342},
Delta=
{
<s>(q_gen_7357) -> q_gen_7357
<z>() -> q_gen_7357
<s, s>(q_gen_7342) -> q_gen_7342
<z, s>(q_gen_7357) -> q_gen_7342
<z, z>() -> q_gen_7342
<s, s>(q_gen_7374) -> q_gen_7374
<s, z>(q_gen_7357) -> q_gen_7374
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  max -> 
{{{
Q={q_gen_7343, q_gen_7358, q_gen_7359, q_gen_7371},
Q_f={q_gen_7343},
Delta=
{
<s>(q_gen_7359) -> q_gen_7359
<z>() -> q_gen_7359
<s, s>(q_gen_7371) -> q_gen_7371
<z, z>() -> q_gen_7371
<s, s, s>(q_gen_7343) -> q_gen_7343
<s, z, s>(q_gen_7371) -> q_gen_7343
<z, s, s>(q_gen_7371) -> q_gen_7343
<z, z, z>() -> q_gen_7343
<z, s, z>(q_gen_7359) -> q_gen_7358
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  numnodes -> 
{{{
Q={q_gen_7345, q_gen_7350, q_gen_7351, q_gen_7379, q_gen_7380, q_gen_7408, q_gen_7409, q_gen_7424},
Q_f={q_gen_7345},
Delta=
{
<leaf>() -> q_gen_7350
<node>(q_gen_7409, q_gen_7350, q_gen_7408) -> q_gen_7350
<node>(q_gen_7409, q_gen_7408, q_gen_7350) -> q_gen_7350
<s>(q_gen_7380) -> q_gen_7380
<z>() -> q_gen_7380
<node>(q_gen_7409, q_gen_7350, q_gen_7350) -> q_gen_7408
<node>(q_gen_7409, q_gen_7408, q_gen_7408) -> q_gen_7408
<a>() -> q_gen_7409
<b>() -> q_gen_7409
<leaf, z>() -> q_gen_7345
<node, s>(q_gen_7351, q_gen_7350, q_gen_7350) -> q_gen_7345
<node, s>(q_gen_7351, q_gen_7408, q_gen_7408) -> q_gen_7345
<node, s>(q_gen_7379, q_gen_7350, q_gen_7350) -> q_gen_7345
<node, s>(q_gen_7379, q_gen_7350, q_gen_7408) -> q_gen_7345
<node, s>(q_gen_7379, q_gen_7408, q_gen_7350) -> q_gen_7345
<node, s>(q_gen_7379, q_gen_7408, q_gen_7408) -> q_gen_7345
<a, z>() -> q_gen_7351
<b, z>() -> q_gen_7351
<a, s>(q_gen_7380) -> q_gen_7379
<b, s>(q_gen_7380) -> q_gen_7379
<node, s>(q_gen_7351, q_gen_7350, q_gen_7408) -> q_gen_7424
<node, s>(q_gen_7351, q_gen_7408, q_gen_7350) -> q_gen_7424
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_7344, q_gen_7348, q_gen_7367},
Q_f={q_gen_7344},
Delta=
{
<s>(q_gen_7367) -> q_gen_7367
<z>() -> q_gen_7367
<s, s>(q_gen_7348) -> q_gen_7348
<z, s>(q_gen_7367) -> q_gen_7348
<z, z>() -> q_gen_7348
<s, s, s>(q_gen_7344) -> q_gen_7344
<s, z, s>(q_gen_7348) -> q_gen_7344
<z, s, s>(q_gen_7348) -> q_gen_7344
<z, z, s>(q_gen_7367) -> q_gen_7344
<z, z, z>() -> q_gen_7344
}

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

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

Teacher's answer:
New clause system:
{
() -> height([leaf, z]) -> 60
() -> leq([z, n2]) -> 60
() -> numnodes([leaf, z]) -> 60
() -> plus([n, z, n]) -> 63
(height([t1, _mba]) /\ height([t2, _nba]) /\ max([_mba, _nba, _oba])) -> height([node(e, t1, t2), s(_oba)]) -> 67
(height([t1, _yba]) /\ numnodes([t1, _zba])) -> leq([_yba, _zba]) -> 68
(leq([n, m])) -> max([n, m, m]) -> 61
(not leq([n, m])) -> max([n, m, n]) -> 61
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 61
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 63
(leq([s(nn1), z])) -> BOT -> 61
(numnodes([t1, _sba]) /\ numnodes([t2, _tba]) /\ plus([_sba, _tba, _uba])) -> numnodes([node(e, t1, t2), s(_uba)]) -> 68
(plus([n, mm, _hba])) -> plus([n, s(mm), s(_hba)]) -> 63
}
Sat witness: Found: ((height([t1, _yba]) /\ numnodes([t1, _zba])) -> leq([_yba, _zba]), {
_yba -> s(s(s(z)))  ;  _zba -> s(z)  ;  t1 -> node(b, leaf, leaf)
})

-------------------------------------------
Step 82, which took 3.040093 s (model generation: 3.011404,  model checking: 0.028689):

Model:
|_
{
height -> 
{{{
Q={q_gen_7346, q_gen_7354, q_gen_7355, q_gen_7383, q_gen_7384, q_gen_7400, q_gen_7403, q_gen_7404, q_gen_7461, q_gen_7471},
Q_f={q_gen_7346},
Delta=
{
<leaf>() -> q_gen_7354
<node>(q_gen_7384, q_gen_7354, q_gen_7354) -> q_gen_7383
<node>(q_gen_7384, q_gen_7354, q_gen_7383) -> q_gen_7383
<node>(q_gen_7384, q_gen_7383, q_gen_7354) -> q_gen_7383
<node>(q_gen_7384, q_gen_7383, q_gen_7383) -> q_gen_7383
<a>() -> q_gen_7384
<b>() -> q_gen_7384
<z>() -> q_gen_7404
<s>(q_gen_7404) -> q_gen_7471
<leaf, z>() -> q_gen_7346
<node, s>(q_gen_7355, q_gen_7354, q_gen_7354) -> q_gen_7346
<node, s>(q_gen_7355, q_gen_7354, q_gen_7383) -> q_gen_7346
<node, s>(q_gen_7403, q_gen_7354, q_gen_7383) -> q_gen_7346
<node, s>(q_gen_7461, q_gen_7383, q_gen_7354) -> q_gen_7346
<a, z>() -> q_gen_7355
<b, z>() -> q_gen_7355
<node, s>(q_gen_7355, q_gen_7383, q_gen_7383) -> q_gen_7400
<node, s>(q_gen_7403, q_gen_7354, q_gen_7354) -> q_gen_7400
<node, s>(q_gen_7403, q_gen_7383, q_gen_7354) -> q_gen_7400
<node, s>(q_gen_7403, q_gen_7383, q_gen_7383) -> q_gen_7400
<node, s>(q_gen_7461, q_gen_7354, q_gen_7354) -> q_gen_7400
<node, s>(q_gen_7461, q_gen_7354, q_gen_7383) -> q_gen_7400
<node, s>(q_gen_7461, q_gen_7383, q_gen_7383) -> q_gen_7400
<b, s>(q_gen_7404) -> q_gen_7403
<a, s>(q_gen_7404) -> q_gen_7461
<a, s>(q_gen_7471) -> q_gen_7461
<b, s>(q_gen_7471) -> q_gen_7461
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_7342, q_gen_7357, q_gen_7374},
Q_f={q_gen_7342},
Delta=
{
<s>(q_gen_7357) -> q_gen_7357
<z>() -> q_gen_7357
<s, s>(q_gen_7342) -> q_gen_7342
<z, s>(q_gen_7357) -> q_gen_7342
<z, z>() -> q_gen_7342
<s, s>(q_gen_7374) -> q_gen_7374
<s, z>(q_gen_7357) -> q_gen_7374
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  max -> 
{{{
Q={q_gen_7343, q_gen_7359, q_gen_7371},
Q_f={q_gen_7343},
Delta=
{
<s>(q_gen_7359) -> q_gen_7359
<z>() -> q_gen_7359
<s, s>(q_gen_7371) -> q_gen_7371
<z, z>() -> q_gen_7371
<s, s, s>(q_gen_7343) -> q_gen_7343
<s, z, s>(q_gen_7371) -> q_gen_7343
<z, s, s>(q_gen_7371) -> q_gen_7343
<z, s, z>(q_gen_7359) -> q_gen_7343
<z, z, z>() -> q_gen_7343
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  numnodes -> 
{{{
Q={q_gen_7345, q_gen_7350, q_gen_7351, q_gen_7379, q_gen_7380, q_gen_7399, q_gen_7408, q_gen_7409, q_gen_7424},
Q_f={q_gen_7345},
Delta=
{
<leaf>() -> q_gen_7350
<z>() -> q_gen_7380
<s>(q_gen_7380) -> q_gen_7399
<node>(q_gen_7409, q_gen_7350, q_gen_7350) -> q_gen_7408
<node>(q_gen_7409, q_gen_7350, q_gen_7408) -> q_gen_7408
<node>(q_gen_7409, q_gen_7408, q_gen_7350) -> q_gen_7408
<node>(q_gen_7409, q_gen_7408, q_gen_7408) -> q_gen_7408
<a>() -> q_gen_7409
<b>() -> q_gen_7409
<leaf, z>() -> q_gen_7345
<node, s>(q_gen_7351, q_gen_7350, q_gen_7350) -> q_gen_7345
<node, s>(q_gen_7379, q_gen_7350, q_gen_7350) -> q_gen_7345
<node, s>(q_gen_7379, q_gen_7350, q_gen_7408) -> q_gen_7345
<node, s>(q_gen_7379, q_gen_7408, q_gen_7350) -> q_gen_7345
<node, s>(q_gen_7379, q_gen_7408, q_gen_7408) -> q_gen_7345
<a, s>(q_gen_7380) -> q_gen_7351
<a, z>() -> q_gen_7351
<b, z>() -> q_gen_7351
<a, s>(q_gen_7399) -> q_gen_7379
<b, s>(q_gen_7380) -> q_gen_7379
<b, s>(q_gen_7399) -> q_gen_7379
<node, s>(q_gen_7351, q_gen_7350, q_gen_7408) -> q_gen_7424
<node, s>(q_gen_7351, q_gen_7408, q_gen_7350) -> q_gen_7424
<node, s>(q_gen_7351, q_gen_7408, q_gen_7408) -> q_gen_7424
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_7344, q_gen_7348, q_gen_7367},
Q_f={q_gen_7344},
Delta=
{
<s>(q_gen_7367) -> q_gen_7367
<z>() -> q_gen_7367
<s, s>(q_gen_7348) -> q_gen_7348
<z, s>(q_gen_7367) -> q_gen_7348
<z, z>() -> q_gen_7348
<s, s, s>(q_gen_7344) -> q_gen_7344
<s, z, s>(q_gen_7348) -> q_gen_7344
<z, s, s>(q_gen_7348) -> q_gen_7344
<z, z, s>(q_gen_7367) -> q_gen_7344
<z, z, z>() -> q_gen_7344
}

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

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

Teacher's answer:
New clause system:
{
() -> height([leaf, z]) -> 61
() -> leq([z, n2]) -> 61
() -> numnodes([leaf, z]) -> 61
() -> plus([n, z, n]) -> 64
(height([t1, _mba]) /\ height([t2, _nba]) /\ max([_mba, _nba, _oba])) -> height([node(e, t1, t2), s(_oba)]) -> 70
(height([t1, _yba]) /\ numnodes([t1, _zba])) -> leq([_yba, _zba]) -> 68
(leq([n, m])) -> max([n, m, m]) -> 62
(not leq([n, m])) -> max([n, m, n]) -> 62
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 62
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 64
(leq([s(nn1), z])) -> BOT -> 62
(numnodes([t1, _sba]) /\ numnodes([t2, _tba]) /\ plus([_sba, _tba, _uba])) -> numnodes([node(e, t1, t2), s(_uba)]) -> 68
(plus([n, mm, _hba])) -> plus([n, s(mm), s(_hba)]) -> 64
}
Sat witness: Found: ((height([t1, _mba]) /\ height([t2, _nba]) /\ max([_mba, _nba, _oba])) -> height([node(e, t1, t2), s(_oba)]), {
_mba -> z  ;  _nba -> s(s(z))  ;  _oba -> s(s(z))  ;  e -> a  ;  t1 -> leaf  ;  t2 -> node(a, node(b, node(b, node(b, leaf, leaf), leaf), node(b, leaf, node(b, leaf, leaf))), leaf)
})

-------------------------------------------
Step 83, which took 4.467384 s (model generation: 4.379538,  model checking: 0.087846):

Model:
|_
{
height -> 
{{{
Q={q_gen_7346, q_gen_7354, q_gen_7355, q_gen_7383, q_gen_7384, q_gen_7403, q_gen_7404, q_gen_7405},
Q_f={q_gen_7346},
Delta=
{
<leaf>() -> q_gen_7354
<node>(q_gen_7384, q_gen_7354, q_gen_7354) -> q_gen_7383
<node>(q_gen_7384, q_gen_7354, q_gen_7383) -> q_gen_7383
<node>(q_gen_7384, q_gen_7383, q_gen_7354) -> q_gen_7383
<node>(q_gen_7384, q_gen_7383, q_gen_7383) -> q_gen_7383
<a>() -> q_gen_7384
<b>() -> q_gen_7384
<s>(q_gen_7404) -> q_gen_7404
<z>() -> q_gen_7404
<leaf, z>() -> q_gen_7346
<node, s>(q_gen_7355, q_gen_7354, q_gen_7354) -> q_gen_7346
<node, s>(q_gen_7355, q_gen_7354, q_gen_7383) -> q_gen_7346
<node, s>(q_gen_7355, q_gen_7383, q_gen_7383) -> q_gen_7346
<node, s>(q_gen_7403, q_gen_7354, q_gen_7383) -> q_gen_7346
<node, s>(q_gen_7403, q_gen_7383, q_gen_7354) -> q_gen_7346
<node, s>(q_gen_7403, q_gen_7383, q_gen_7383) -> q_gen_7346
<a, z>() -> q_gen_7355
<b, z>() -> q_gen_7355
<a, s>(q_gen_7404) -> q_gen_7403
<b, s>(q_gen_7404) -> q_gen_7403
<node, s>(q_gen_7403, q_gen_7354, q_gen_7354) -> q_gen_7405
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_7342, q_gen_7357, q_gen_7374},
Q_f={q_gen_7342},
Delta=
{
<s>(q_gen_7357) -> q_gen_7357
<z>() -> q_gen_7357
<s, s>(q_gen_7342) -> q_gen_7342
<z, s>(q_gen_7357) -> q_gen_7342
<z, z>() -> q_gen_7342
<s, s>(q_gen_7374) -> q_gen_7374
<s, z>(q_gen_7357) -> q_gen_7374
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  max -> 
{{{
Q={q_gen_7343, q_gen_7359, q_gen_7371},
Q_f={q_gen_7343},
Delta=
{
<s>(q_gen_7359) -> q_gen_7359
<z>() -> q_gen_7359
<s, s>(q_gen_7371) -> q_gen_7371
<z, z>() -> q_gen_7371
<s, s, s>(q_gen_7343) -> q_gen_7343
<s, z, s>(q_gen_7371) -> q_gen_7343
<z, s, s>(q_gen_7371) -> q_gen_7343
<z, s, z>(q_gen_7359) -> q_gen_7343
<z, z, z>() -> q_gen_7343
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  numnodes -> 
{{{
Q={q_gen_7345, q_gen_7350, q_gen_7351, q_gen_7379, q_gen_7380, q_gen_7393, q_gen_7408, q_gen_7409, q_gen_7413, q_gen_7417, q_gen_7425},
Q_f={q_gen_7345},
Delta=
{
<leaf>() -> q_gen_7350
<node>(q_gen_7409, q_gen_7350, q_gen_7425) -> q_gen_7350
<node>(q_gen_7417, q_gen_7350, q_gen_7408) -> q_gen_7350
<node>(q_gen_7417, q_gen_7408, q_gen_7408) -> q_gen_7350
<s>(q_gen_7380) -> q_gen_7380
<z>() -> q_gen_7380
<node>(q_gen_7409, q_gen_7350, q_gen_7350) -> q_gen_7408
<node>(q_gen_7409, q_gen_7350, q_gen_7408) -> q_gen_7408
<node>(q_gen_7409, q_gen_7408, q_gen_7350) -> q_gen_7408
<node>(q_gen_7409, q_gen_7408, q_gen_7408) -> q_gen_7408
<node>(q_gen_7409, q_gen_7425, q_gen_7425) -> q_gen_7408
<node>(q_gen_7417, q_gen_7350, q_gen_7425) -> q_gen_7408
<node>(q_gen_7417, q_gen_7425, q_gen_7350) -> q_gen_7408
<a>() -> q_gen_7409
<b>() -> q_gen_7417
<node>(q_gen_7417, q_gen_7350, q_gen_7350) -> q_gen_7425
<node>(q_gen_7417, q_gen_7425, q_gen_7425) -> q_gen_7425
<leaf, z>() -> q_gen_7345
<node, s>(q_gen_7351, q_gen_7350, q_gen_7350) -> q_gen_7345
<node, s>(q_gen_7351, q_gen_7408, q_gen_7408) -> q_gen_7345
<node, s>(q_gen_7379, q_gen_7350, q_gen_7350) -> q_gen_7345
<node, s>(q_gen_7379, q_gen_7350, q_gen_7408) -> q_gen_7345
<node, s>(q_gen_7379, q_gen_7408, q_gen_7350) -> q_gen_7345
<node, s>(q_gen_7379, q_gen_7408, q_gen_7425) -> q_gen_7345
<node, s>(q_gen_7379, q_gen_7425, q_gen_7350) -> q_gen_7345
<node, s>(q_gen_7393, q_gen_7350, q_gen_7350) -> q_gen_7345
<node, s>(q_gen_7393, q_gen_7350, q_gen_7408) -> q_gen_7345
<node, s>(q_gen_7393, q_gen_7350, q_gen_7425) -> q_gen_7345
<node, s>(q_gen_7393, q_gen_7425, q_gen_7425) -> q_gen_7345
<a, z>() -> q_gen_7351
<b, z>() -> q_gen_7351
<b, s>(q_gen_7380) -> q_gen_7379
<a, s>(q_gen_7380) -> q_gen_7393
<node, s>(q_gen_7351, q_gen_7350, q_gen_7408) -> q_gen_7413
<node, s>(q_gen_7351, q_gen_7350, q_gen_7425) -> q_gen_7413
<node, s>(q_gen_7351, q_gen_7408, q_gen_7350) -> q_gen_7413
<node, s>(q_gen_7351, q_gen_7408, q_gen_7425) -> q_gen_7413
<node, s>(q_gen_7351, q_gen_7425, q_gen_7350) -> q_gen_7413
<node, s>(q_gen_7351, q_gen_7425, q_gen_7408) -> q_gen_7413
<node, s>(q_gen_7351, q_gen_7425, q_gen_7425) -> q_gen_7413
<node, s>(q_gen_7379, q_gen_7350, q_gen_7425) -> q_gen_7413
<node, s>(q_gen_7379, q_gen_7408, q_gen_7408) -> q_gen_7413
<node, s>(q_gen_7379, q_gen_7425, q_gen_7425) -> q_gen_7413
<node, s>(q_gen_7393, q_gen_7425, q_gen_7350) -> q_gen_7413
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_7344, q_gen_7348, q_gen_7367},
Q_f={q_gen_7344},
Delta=
{
<s>(q_gen_7367) -> q_gen_7367
<z>() -> q_gen_7367
<s, s>(q_gen_7348) -> q_gen_7348
<z, s>(q_gen_7367) -> q_gen_7348
<z, z>() -> q_gen_7348
<s, s, s>(q_gen_7344) -> q_gen_7344
<s, z, s>(q_gen_7348) -> q_gen_7344
<z, s, s>(q_gen_7348) -> q_gen_7344
<z, z, s>(q_gen_7367) -> q_gen_7344
<z, z, z>() -> q_gen_7344
}

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

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

Teacher's answer:
New clause system:
{
() -> height([leaf, z]) -> 62
() -> leq([z, n2]) -> 62
() -> numnodes([leaf, z]) -> 62
() -> plus([n, z, n]) -> 65
(height([t1, _mba]) /\ height([t2, _nba]) /\ max([_mba, _nba, _oba])) -> height([node(e, t1, t2), s(_oba)]) -> 70
(height([t1, _yba]) /\ numnodes([t1, _zba])) -> leq([_yba, _zba]) -> 68
(leq([n, m])) -> max([n, m, m]) -> 63
(not leq([n, m])) -> max([n, m, n]) -> 63
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 63
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 65
(leq([s(nn1), z])) -> BOT -> 63
(numnodes([t1, _sba]) /\ numnodes([t2, _tba]) /\ plus([_sba, _tba, _uba])) -> numnodes([node(e, t1, t2), s(_uba)]) -> 71
(plus([n, mm, _hba])) -> plus([n, s(mm), s(_hba)]) -> 65
}
Sat witness: Found: ((numnodes([t1, _sba]) /\ numnodes([t2, _tba]) /\ plus([_sba, _tba, _uba])) -> numnodes([node(e, t1, t2), s(_uba)]), {
_sba -> s(s(z))  ;  _tba -> z  ;  _uba -> s(s(z))  ;  e -> a  ;  t1 -> node(b, leaf, leaf)  ;  t2 -> leaf
})

-------------------------------------------
Step 84, which took 3.051117 s (model generation: 3.045529,  model checking: 0.005588):

Model:
|_
{
height -> 
{{{
Q={q_gen_7346, q_gen_7354, q_gen_7355, q_gen_7383, q_gen_7384, q_gen_7400, q_gen_7402, q_gen_7403, q_gen_7404},
Q_f={q_gen_7346},
Delta=
{
<leaf>() -> q_gen_7354
<node>(q_gen_7384, q_gen_7402, q_gen_7402) -> q_gen_7354
<node>(q_gen_7384, q_gen_7354, q_gen_7354) -> q_gen_7383
<node>(q_gen_7384, q_gen_7402, q_gen_7354) -> q_gen_7383
<node>(q_gen_7384, q_gen_7402, q_gen_7383) -> q_gen_7383
<a>() -> q_gen_7384
<b>() -> q_gen_7384
<node>(q_gen_7384, q_gen_7354, q_gen_7383) -> q_gen_7402
<node>(q_gen_7384, q_gen_7354, q_gen_7402) -> q_gen_7402
<node>(q_gen_7384, q_gen_7383, q_gen_7354) -> q_gen_7402
<node>(q_gen_7384, q_gen_7383, q_gen_7383) -> q_gen_7402
<node>(q_gen_7384, q_gen_7383, q_gen_7402) -> q_gen_7402
<s>(q_gen_7404) -> q_gen_7404
<z>() -> q_gen_7404
<leaf, z>() -> q_gen_7346
<node, s>(q_gen_7355, q_gen_7354, q_gen_7354) -> q_gen_7346
<node, s>(q_gen_7355, q_gen_7354, q_gen_7383) -> q_gen_7346
<node, s>(q_gen_7355, q_gen_7354, q_gen_7402) -> q_gen_7346
<node, s>(q_gen_7403, q_gen_7354, q_gen_7383) -> q_gen_7346
<node, s>(q_gen_7403, q_gen_7383, q_gen_7402) -> q_gen_7346
<node, s>(q_gen_7403, q_gen_7402, q_gen_7354) -> q_gen_7346
<a, z>() -> q_gen_7355
<b, z>() -> q_gen_7355
<node, s>(q_gen_7355, q_gen_7383, q_gen_7383) -> q_gen_7400
<node, s>(q_gen_7355, q_gen_7402, q_gen_7383) -> q_gen_7400
<node, s>(q_gen_7355, q_gen_7402, q_gen_7402) -> q_gen_7400
<node, s>(q_gen_7403, q_gen_7354, q_gen_7354) -> q_gen_7400
<node, s>(q_gen_7403, q_gen_7354, q_gen_7402) -> q_gen_7400
<node, s>(q_gen_7403, q_gen_7383, q_gen_7354) -> q_gen_7400
<node, s>(q_gen_7403, q_gen_7383, q_gen_7383) -> q_gen_7400
<node, s>(q_gen_7403, q_gen_7402, q_gen_7383) -> q_gen_7400
<node, s>(q_gen_7403, q_gen_7402, q_gen_7402) -> q_gen_7400
<a, s>(q_gen_7404) -> q_gen_7403
<b, s>(q_gen_7404) -> q_gen_7403
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_7342, q_gen_7357, q_gen_7374},
Q_f={q_gen_7342},
Delta=
{
<s>(q_gen_7357) -> q_gen_7357
<z>() -> q_gen_7357
<s, s>(q_gen_7342) -> q_gen_7342
<z, s>(q_gen_7357) -> q_gen_7342
<z, z>() -> q_gen_7342
<s, s>(q_gen_7374) -> q_gen_7374
<s, z>(q_gen_7357) -> q_gen_7374
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  max -> 
{{{
Q={q_gen_7343, q_gen_7359, q_gen_7371},
Q_f={q_gen_7343},
Delta=
{
<s>(q_gen_7359) -> q_gen_7359
<z>() -> q_gen_7359
<s, s>(q_gen_7371) -> q_gen_7371
<z, z>() -> q_gen_7371
<s, s, s>(q_gen_7343) -> q_gen_7343
<s, z, s>(q_gen_7371) -> q_gen_7343
<z, s, s>(q_gen_7371) -> q_gen_7343
<z, s, z>(q_gen_7359) -> q_gen_7343
<z, z, z>() -> q_gen_7343
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  numnodes -> 
{{{
Q={q_gen_7345, q_gen_7350, q_gen_7351, q_gen_7380, q_gen_7393, q_gen_7408, q_gen_7409, q_gen_7413, q_gen_7417, q_gen_7425},
Q_f={q_gen_7345},
Delta=
{
<leaf>() -> q_gen_7350
<node>(q_gen_7409, q_gen_7350, q_gen_7408) -> q_gen_7350
<node>(q_gen_7409, q_gen_7408, q_gen_7408) -> q_gen_7350
<node>(q_gen_7417, q_gen_7425, q_gen_7425) -> q_gen_7350
<s>(q_gen_7380) -> q_gen_7380
<z>() -> q_gen_7380
<node>(q_gen_7409, q_gen_7350, q_gen_7350) -> q_gen_7408
<node>(q_gen_7409, q_gen_7350, q_gen_7425) -> q_gen_7408
<node>(q_gen_7417, q_gen_7350, q_gen_7425) -> q_gen_7408
<node>(q_gen_7417, q_gen_7408, q_gen_7350) -> q_gen_7408
<node>(q_gen_7417, q_gen_7408, q_gen_7408) -> q_gen_7408
<node>(q_gen_7417, q_gen_7408, q_gen_7425) -> q_gen_7408
<node>(q_gen_7417, q_gen_7425, q_gen_7350) -> q_gen_7408
<a>() -> q_gen_7409
<b>() -> q_gen_7417
<node>(q_gen_7409, q_gen_7425, q_gen_7425) -> q_gen_7425
<node>(q_gen_7417, q_gen_7350, q_gen_7350) -> q_gen_7425
<node>(q_gen_7417, q_gen_7350, q_gen_7408) -> q_gen_7425
<leaf, z>() -> q_gen_7345
<node, s>(q_gen_7351, q_gen_7350, q_gen_7350) -> q_gen_7345
<node, s>(q_gen_7351, q_gen_7350, q_gen_7408) -> q_gen_7345
<node, s>(q_gen_7351, q_gen_7425, q_gen_7350) -> q_gen_7345
<node, s>(q_gen_7393, q_gen_7350, q_gen_7350) -> q_gen_7345
<node, s>(q_gen_7393, q_gen_7350, q_gen_7408) -> q_gen_7345
<node, s>(q_gen_7393, q_gen_7350, q_gen_7425) -> q_gen_7345
<node, s>(q_gen_7393, q_gen_7408, q_gen_7408) -> q_gen_7345
<node, s>(q_gen_7393, q_gen_7425, q_gen_7350) -> q_gen_7345
<a, z>() -> q_gen_7351
<b, s>(q_gen_7380) -> q_gen_7351
<b, z>() -> q_gen_7351
<a, s>(q_gen_7380) -> q_gen_7393
<node, s>(q_gen_7351, q_gen_7350, q_gen_7425) -> q_gen_7413
<node, s>(q_gen_7351, q_gen_7408, q_gen_7350) -> q_gen_7413
<node, s>(q_gen_7351, q_gen_7408, q_gen_7408) -> q_gen_7413
<node, s>(q_gen_7351, q_gen_7408, q_gen_7425) -> q_gen_7413
<node, s>(q_gen_7351, q_gen_7425, q_gen_7408) -> q_gen_7413
<node, s>(q_gen_7351, q_gen_7425, q_gen_7425) -> q_gen_7413
<node, s>(q_gen_7393, q_gen_7408, q_gen_7350) -> q_gen_7413
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_7344, q_gen_7348, q_gen_7367},
Q_f={q_gen_7344},
Delta=
{
<s>(q_gen_7367) -> q_gen_7367
<z>() -> q_gen_7367
<s, s>(q_gen_7348) -> q_gen_7348
<z, s>(q_gen_7367) -> q_gen_7348
<z, z>() -> q_gen_7348
<s, s, s>(q_gen_7344) -> q_gen_7344
<s, z, s>(q_gen_7348) -> q_gen_7344
<z, s, s>(q_gen_7348) -> q_gen_7344
<z, z, s>(q_gen_7367) -> q_gen_7344
<z, z, z>() -> q_gen_7344
}

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

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

Teacher's answer:
New clause system:
{
() -> height([leaf, z]) -> 63
() -> leq([z, n2]) -> 63
() -> numnodes([leaf, z]) -> 63
() -> plus([n, z, n]) -> 66
(height([t1, _mba]) /\ height([t2, _nba]) /\ max([_mba, _nba, _oba])) -> height([node(e, t1, t2), s(_oba)]) -> 70
(height([t1, _yba]) /\ numnodes([t1, _zba])) -> leq([_yba, _zba]) -> 71
(leq([n, m])) -> max([n, m, m]) -> 64
(not leq([n, m])) -> max([n, m, n]) -> 64
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 64
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 66
(leq([s(nn1), z])) -> BOT -> 64
(numnodes([t1, _sba]) /\ numnodes([t2, _tba]) /\ plus([_sba, _tba, _uba])) -> numnodes([node(e, t1, t2), s(_uba)]) -> 71
(plus([n, mm, _hba])) -> plus([n, s(mm), s(_hba)]) -> 66
}
Sat witness: Found: ((height([t1, _yba]) /\ numnodes([t1, _zba])) -> leq([_yba, _zba]), {
_yba -> s(s(z))  ;  _zba -> s(z)  ;  t1 -> node(b, node(b, node(a, leaf, node(a, leaf, leaf)), node(a, leaf, node(a, leaf, leaf))), node(a, node(a, leaf, node(a, leaf, leaf)), node(a, leaf, leaf)))
})

-------------------------------------------
Step 85, which took 3.740133 s (model generation: 3.231346,  model checking: 0.508787):

Model:
|_
{
height -> 
{{{
Q={q_gen_7346, q_gen_7354, q_gen_7355, q_gen_7383, q_gen_7384, q_gen_7403, q_gen_7404, q_gen_7405},
Q_f={q_gen_7346},
Delta=
{
<leaf>() -> q_gen_7354
<node>(q_gen_7384, q_gen_7354, q_gen_7354) -> q_gen_7383
<node>(q_gen_7384, q_gen_7354, q_gen_7383) -> q_gen_7383
<node>(q_gen_7384, q_gen_7383, q_gen_7354) -> q_gen_7383
<node>(q_gen_7384, q_gen_7383, q_gen_7383) -> q_gen_7383
<a>() -> q_gen_7384
<b>() -> q_gen_7384
<s>(q_gen_7404) -> q_gen_7404
<z>() -> q_gen_7404
<leaf, z>() -> q_gen_7346
<node, s>(q_gen_7355, q_gen_7354, q_gen_7354) -> q_gen_7346
<node, s>(q_gen_7355, q_gen_7354, q_gen_7383) -> q_gen_7346
<node, s>(q_gen_7355, q_gen_7383, q_gen_7383) -> q_gen_7346
<node, s>(q_gen_7403, q_gen_7354, q_gen_7383) -> q_gen_7346
<node, s>(q_gen_7403, q_gen_7383, q_gen_7354) -> q_gen_7346
<node, s>(q_gen_7403, q_gen_7383, q_gen_7383) -> q_gen_7346
<a, z>() -> q_gen_7355
<b, z>() -> q_gen_7355
<a, s>(q_gen_7404) -> q_gen_7403
<b, s>(q_gen_7404) -> q_gen_7403
<node, s>(q_gen_7403, q_gen_7354, q_gen_7354) -> q_gen_7405
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_7342, q_gen_7357, q_gen_7374},
Q_f={q_gen_7342},
Delta=
{
<s>(q_gen_7357) -> q_gen_7357
<z>() -> q_gen_7357
<s, s>(q_gen_7342) -> q_gen_7342
<z, s>(q_gen_7357) -> q_gen_7342
<z, z>() -> q_gen_7342
<s, s>(q_gen_7374) -> q_gen_7374
<s, z>(q_gen_7357) -> q_gen_7374
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  max -> 
{{{
Q={q_gen_7343, q_gen_7359, q_gen_7371},
Q_f={q_gen_7343},
Delta=
{
<s>(q_gen_7359) -> q_gen_7359
<z>() -> q_gen_7359
<s, s>(q_gen_7371) -> q_gen_7371
<z, z>() -> q_gen_7371
<s, s, s>(q_gen_7343) -> q_gen_7343
<s, z, s>(q_gen_7371) -> q_gen_7343
<z, s, s>(q_gen_7371) -> q_gen_7343
<z, s, z>(q_gen_7359) -> q_gen_7343
<z, z, z>() -> q_gen_7343
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  numnodes -> 
{{{
Q={q_gen_7345, q_gen_7350, q_gen_7351, q_gen_7378, q_gen_7379, q_gen_7380, q_gen_7408, q_gen_7409, q_gen_7417, q_gen_7425},
Q_f={q_gen_7345},
Delta=
{
<leaf>() -> q_gen_7350
<node>(q_gen_7409, q_gen_7350, q_gen_7425) -> q_gen_7350
<node>(q_gen_7409, q_gen_7408, q_gen_7350) -> q_gen_7350
<node>(q_gen_7409, q_gen_7425, q_gen_7425) -> q_gen_7350
<node>(q_gen_7417, q_gen_7408, q_gen_7350) -> q_gen_7350
<node>(q_gen_7417, q_gen_7408, q_gen_7408) -> q_gen_7350
<s>(q_gen_7380) -> q_gen_7380
<z>() -> q_gen_7380
<node>(q_gen_7409, q_gen_7350, q_gen_7350) -> q_gen_7408
<node>(q_gen_7409, q_gen_7350, q_gen_7408) -> q_gen_7408
<node>(q_gen_7409, q_gen_7408, q_gen_7408) -> q_gen_7408
<node>(q_gen_7417, q_gen_7350, q_gen_7408) -> q_gen_7408
<node>(q_gen_7417, q_gen_7350, q_gen_7425) -> q_gen_7408
<node>(q_gen_7417, q_gen_7425, q_gen_7350) -> q_gen_7408
<a>() -> q_gen_7409
<b>() -> q_gen_7417
<node>(q_gen_7417, q_gen_7350, q_gen_7350) -> q_gen_7425
<node>(q_gen_7417, q_gen_7425, q_gen_7425) -> q_gen_7425
<leaf, z>() -> q_gen_7345
<node, s>(q_gen_7351, q_gen_7350, q_gen_7350) -> q_gen_7345
<node, s>(q_gen_7379, q_gen_7350, q_gen_7408) -> q_gen_7345
<node, s>(q_gen_7379, q_gen_7408, q_gen_7408) -> q_gen_7345
<node, s>(q_gen_7379, q_gen_7408, q_gen_7425) -> q_gen_7345
<node, s>(q_gen_7379, q_gen_7425, q_gen_7350) -> q_gen_7345
<a, s>(q_gen_7380) -> q_gen_7351
<a, z>() -> q_gen_7351
<b, z>() -> q_gen_7351
<node, s>(q_gen_7351, q_gen_7350, q_gen_7408) -> q_gen_7378
<node, s>(q_gen_7351, q_gen_7350, q_gen_7425) -> q_gen_7378
<node, s>(q_gen_7351, q_gen_7408, q_gen_7350) -> q_gen_7378
<node, s>(q_gen_7351, q_gen_7408, q_gen_7408) -> q_gen_7378
<node, s>(q_gen_7351, q_gen_7408, q_gen_7425) -> q_gen_7378
<node, s>(q_gen_7351, q_gen_7425, q_gen_7350) -> q_gen_7378
<node, s>(q_gen_7351, q_gen_7425, q_gen_7408) -> q_gen_7378
<node, s>(q_gen_7351, q_gen_7425, q_gen_7425) -> q_gen_7378
<node, s>(q_gen_7379, q_gen_7350, q_gen_7350) -> q_gen_7378
<node, s>(q_gen_7379, q_gen_7350, q_gen_7425) -> q_gen_7378
<node, s>(q_gen_7379, q_gen_7408, q_gen_7350) -> q_gen_7378
<node, s>(q_gen_7379, q_gen_7425, q_gen_7425) -> q_gen_7378
<b, s>(q_gen_7380) -> q_gen_7379
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_7344, q_gen_7348, q_gen_7366, q_gen_7367},
Q_f={q_gen_7344},
Delta=
{
<s>(q_gen_7367) -> q_gen_7367
<z>() -> q_gen_7367
<s, s>(q_gen_7348) -> q_gen_7348
<z, s>(q_gen_7367) -> q_gen_7348
<z, z>() -> q_gen_7348
<s, s, s>(q_gen_7344) -> q_gen_7344
<s, s, s>(q_gen_7366) -> q_gen_7344
<s, z, s>(q_gen_7348) -> q_gen_7344
<z, s, s>(q_gen_7348) -> q_gen_7344
<z, z, z>() -> q_gen_7344
<z, z, s>(q_gen_7367) -> q_gen_7366
}

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

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

Teacher's answer:
New clause system:
{
() -> height([leaf, z]) -> 64
() -> leq([z, n2]) -> 64
() -> numnodes([leaf, z]) -> 64
() -> plus([n, z, n]) -> 67
(height([t1, _mba]) /\ height([t2, _nba]) /\ max([_mba, _nba, _oba])) -> height([node(e, t1, t2), s(_oba)]) -> 71
(height([t1, _yba]) /\ numnodes([t1, _zba])) -> leq([_yba, _zba]) -> 71
(leq([n, m])) -> max([n, m, m]) -> 65
(not leq([n, m])) -> max([n, m, n]) -> 65
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 65
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 67
(leq([s(nn1), z])) -> BOT -> 65
(numnodes([t1, _sba]) /\ numnodes([t2, _tba]) /\ plus([_sba, _tba, _uba])) -> numnodes([node(e, t1, t2), s(_uba)]) -> 74
(plus([n, mm, _hba])) -> plus([n, s(mm), s(_hba)]) -> 67
}
Sat witness: Found: ((numnodes([t1, _sba]) /\ numnodes([t2, _tba]) /\ plus([_sba, _tba, _uba])) -> numnodes([node(e, t1, t2), s(_uba)]), {
_sba -> s(s(z))  ;  _tba -> z  ;  _uba -> s(s(z))  ;  e -> b  ;  t1 -> node(b, node(b, leaf, leaf), node(a, node(b, node(b, leaf, leaf), node(b, node(b, leaf, node(b, leaf, leaf)), node(b, leaf, node(b, leaf, leaf)))), node(b, node(b, leaf, node(b, leaf, leaf)), node(b, leaf, node(b, leaf, leaf)))))  ;  t2 -> leaf
})

-------------------------------------------
Step 86, which took 3.467719 s (model generation: 3.462704,  model checking: 0.005015):

Model:
|_
{
height -> 
{{{
Q={q_gen_7346, q_gen_7354, q_gen_7355, q_gen_7383, q_gen_7384, q_gen_7400, q_gen_7402, q_gen_7403, q_gen_7404},
Q_f={q_gen_7346},
Delta=
{
<leaf>() -> q_gen_7354
<node>(q_gen_7384, q_gen_7383, q_gen_7402) -> q_gen_7354
<node>(q_gen_7384, q_gen_7354, q_gen_7354) -> q_gen_7383
<node>(q_gen_7384, q_gen_7383, q_gen_7354) -> q_gen_7383
<node>(q_gen_7384, q_gen_7402, q_gen_7402) -> q_gen_7383
<a>() -> q_gen_7384
<b>() -> q_gen_7384
<node>(q_gen_7384, q_gen_7354, q_gen_7383) -> q_gen_7402
<node>(q_gen_7384, q_gen_7354, q_gen_7402) -> q_gen_7402
<node>(q_gen_7384, q_gen_7383, q_gen_7383) -> q_gen_7402
<node>(q_gen_7384, q_gen_7402, q_gen_7354) -> q_gen_7402
<node>(q_gen_7384, q_gen_7402, q_gen_7383) -> q_gen_7402
<s>(q_gen_7404) -> q_gen_7404
<z>() -> q_gen_7404
<leaf, z>() -> q_gen_7346
<node, s>(q_gen_7355, q_gen_7354, q_gen_7354) -> q_gen_7346
<node, s>(q_gen_7355, q_gen_7354, q_gen_7383) -> q_gen_7346
<node, s>(q_gen_7355, q_gen_7354, q_gen_7402) -> q_gen_7346
<node, s>(q_gen_7403, q_gen_7354, q_gen_7383) -> q_gen_7346
<node, s>(q_gen_7403, q_gen_7383, q_gen_7402) -> q_gen_7346
<node, s>(q_gen_7403, q_gen_7402, q_gen_7354) -> q_gen_7346
<a, z>() -> q_gen_7355
<b, z>() -> q_gen_7355
<node, s>(q_gen_7355, q_gen_7383, q_gen_7354) -> q_gen_7400
<node, s>(q_gen_7355, q_gen_7383, q_gen_7383) -> q_gen_7400
<node, s>(q_gen_7355, q_gen_7402, q_gen_7383) -> q_gen_7400
<node, s>(q_gen_7355, q_gen_7402, q_gen_7402) -> q_gen_7400
<node, s>(q_gen_7403, q_gen_7354, q_gen_7354) -> q_gen_7400
<node, s>(q_gen_7403, q_gen_7354, q_gen_7402) -> q_gen_7400
<node, s>(q_gen_7403, q_gen_7383, q_gen_7354) -> q_gen_7400
<node, s>(q_gen_7403, q_gen_7383, q_gen_7383) -> q_gen_7400
<node, s>(q_gen_7403, q_gen_7402, q_gen_7383) -> q_gen_7400
<node, s>(q_gen_7403, q_gen_7402, q_gen_7402) -> q_gen_7400
<a, s>(q_gen_7404) -> q_gen_7403
<b, s>(q_gen_7404) -> q_gen_7403
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_7342, q_gen_7357, q_gen_7374},
Q_f={q_gen_7342},
Delta=
{
<s>(q_gen_7357) -> q_gen_7357
<z>() -> q_gen_7357
<s, s>(q_gen_7342) -> q_gen_7342
<z, s>(q_gen_7357) -> q_gen_7342
<z, z>() -> q_gen_7342
<s, s>(q_gen_7374) -> q_gen_7374
<s, z>(q_gen_7357) -> q_gen_7374
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  max -> 
{{{
Q={q_gen_7343, q_gen_7359, q_gen_7371},
Q_f={q_gen_7343},
Delta=
{
<s>(q_gen_7359) -> q_gen_7359
<z>() -> q_gen_7359
<s, s>(q_gen_7371) -> q_gen_7371
<z, z>() -> q_gen_7371
<s, s, s>(q_gen_7343) -> q_gen_7343
<s, z, s>(q_gen_7371) -> q_gen_7343
<z, s, s>(q_gen_7371) -> q_gen_7343
<z, s, z>(q_gen_7359) -> q_gen_7343
<z, z, z>() -> q_gen_7343
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  numnodes -> 
{{{
Q={q_gen_7345, q_gen_7350, q_gen_7351, q_gen_7380, q_gen_7393, q_gen_7408, q_gen_7409, q_gen_7413, q_gen_7417, q_gen_7425},
Q_f={q_gen_7345},
Delta=
{
<leaf>() -> q_gen_7350
<node>(q_gen_7409, q_gen_7408, q_gen_7408) -> q_gen_7350
<s>(q_gen_7380) -> q_gen_7380
<z>() -> q_gen_7380
<node>(q_gen_7409, q_gen_7350, q_gen_7350) -> q_gen_7408
<node>(q_gen_7409, q_gen_7350, q_gen_7408) -> q_gen_7408
<node>(q_gen_7409, q_gen_7425, q_gen_7425) -> q_gen_7408
<node>(q_gen_7417, q_gen_7350, q_gen_7408) -> q_gen_7408
<node>(q_gen_7417, q_gen_7350, q_gen_7425) -> q_gen_7408
<node>(q_gen_7417, q_gen_7408, q_gen_7408) -> q_gen_7408
<node>(q_gen_7417, q_gen_7425, q_gen_7350) -> q_gen_7408
<a>() -> q_gen_7409
<b>() -> q_gen_7417
<node>(q_gen_7409, q_gen_7350, q_gen_7425) -> q_gen_7425
<node>(q_gen_7409, q_gen_7425, q_gen_7408) -> q_gen_7425
<node>(q_gen_7417, q_gen_7350, q_gen_7350) -> q_gen_7425
<node>(q_gen_7417, q_gen_7408, q_gen_7350) -> q_gen_7425
<node>(q_gen_7417, q_gen_7425, q_gen_7408) -> q_gen_7425
<node>(q_gen_7417, q_gen_7425, q_gen_7425) -> q_gen_7425
<leaf, z>() -> q_gen_7345
<node, s>(q_gen_7351, q_gen_7350, q_gen_7350) -> q_gen_7345
<node, s>(q_gen_7351, q_gen_7350, q_gen_7408) -> q_gen_7345
<node, s>(q_gen_7351, q_gen_7425, q_gen_7350) -> q_gen_7345
<node, s>(q_gen_7351, q_gen_7425, q_gen_7425) -> q_gen_7345
<node, s>(q_gen_7393, q_gen_7350, q_gen_7350) -> q_gen_7345
<node, s>(q_gen_7393, q_gen_7350, q_gen_7425) -> q_gen_7345
<node, s>(q_gen_7393, q_gen_7425, q_gen_7350) -> q_gen_7345
<node, s>(q_gen_7393, q_gen_7425, q_gen_7408) -> q_gen_7345
<a, z>() -> q_gen_7351
<b, s>(q_gen_7380) -> q_gen_7351
<b, z>() -> q_gen_7351
<a, s>(q_gen_7380) -> q_gen_7393
<node, s>(q_gen_7351, q_gen_7350, q_gen_7425) -> q_gen_7413
<node, s>(q_gen_7351, q_gen_7408, q_gen_7350) -> q_gen_7413
<node, s>(q_gen_7351, q_gen_7408, q_gen_7408) -> q_gen_7413
<node, s>(q_gen_7351, q_gen_7408, q_gen_7425) -> q_gen_7413
<node, s>(q_gen_7351, q_gen_7425, q_gen_7408) -> q_gen_7413
<node, s>(q_gen_7393, q_gen_7350, q_gen_7408) -> q_gen_7413
<node, s>(q_gen_7393, q_gen_7425, q_gen_7425) -> q_gen_7413
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_7344, q_gen_7348, q_gen_7367},
Q_f={q_gen_7344},
Delta=
{
<s>(q_gen_7367) -> q_gen_7367
<z>() -> q_gen_7367
<s, s>(q_gen_7348) -> q_gen_7348
<z, s>(q_gen_7367) -> q_gen_7348
<z, z>() -> q_gen_7348
<s, s, s>(q_gen_7344) -> q_gen_7344
<s, z, s>(q_gen_7348) -> q_gen_7344
<z, s, s>(q_gen_7348) -> q_gen_7344
<z, z, s>(q_gen_7367) -> q_gen_7344
<z, z, z>() -> q_gen_7344
}

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

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

Teacher's answer:
New clause system:
{
() -> height([leaf, z]) -> 65
() -> leq([z, n2]) -> 65
() -> numnodes([leaf, z]) -> 65
() -> plus([n, z, n]) -> 68
(height([t1, _mba]) /\ height([t2, _nba]) /\ max([_mba, _nba, _oba])) -> height([node(e, t1, t2), s(_oba)]) -> 71
(height([t1, _yba]) /\ numnodes([t1, _zba])) -> leq([_yba, _zba]) -> 74
(leq([n, m])) -> max([n, m, m]) -> 66
(not leq([n, m])) -> max([n, m, n]) -> 66
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 66
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 68
(leq([s(nn1), z])) -> BOT -> 66
(numnodes([t1, _sba]) /\ numnodes([t2, _tba]) /\ plus([_sba, _tba, _uba])) -> numnodes([node(e, t1, t2), s(_uba)]) -> 74
(plus([n, mm, _hba])) -> plus([n, s(mm), s(_hba)]) -> 68
}
Sat witness: Found: ((height([t1, _yba]) /\ numnodes([t1, _zba])) -> leq([_yba, _zba]), {
_yba -> s(s(z))  ;  _zba -> s(z)  ;  t1 -> node(b, node(a, node(a, leaf, node(a, leaf, leaf)), node(a, leaf, node(a, leaf, leaf))), node(a, leaf, node(a, leaf, leaf)))
})

-------------------------------------------
Step 87, which took 4.728461 s (model generation: 4.689008,  model checking: 0.039453):

Model:
|_
{
height -> 
{{{
Q={q_gen_7346, q_gen_7354, q_gen_7355, q_gen_7383, q_gen_7384, q_gen_7400, q_gen_7403, q_gen_7404, q_gen_7461, q_gen_7471},
Q_f={q_gen_7346},
Delta=
{
<leaf>() -> q_gen_7354
<node>(q_gen_7384, q_gen_7383, q_gen_7354) -> q_gen_7354
<node>(q_gen_7384, q_gen_7354, q_gen_7354) -> q_gen_7383
<node>(q_gen_7384, q_gen_7354, q_gen_7383) -> q_gen_7383
<node>(q_gen_7384, q_gen_7383, q_gen_7383) -> q_gen_7383
<a>() -> q_gen_7384
<b>() -> q_gen_7384
<z>() -> q_gen_7404
<s>(q_gen_7404) -> q_gen_7471
<leaf, z>() -> q_gen_7346
<node, s>(q_gen_7355, q_gen_7354, q_gen_7354) -> q_gen_7346
<node, s>(q_gen_7355, q_gen_7354, q_gen_7383) -> q_gen_7346
<node, s>(q_gen_7355, q_gen_7383, q_gen_7354) -> q_gen_7346
<node, s>(q_gen_7403, q_gen_7354, q_gen_7383) -> q_gen_7346
<node, s>(q_gen_7403, q_gen_7383, q_gen_7383) -> q_gen_7346
<node, s>(q_gen_7461, q_gen_7383, q_gen_7354) -> q_gen_7346
<a, s>(q_gen_7471) -> q_gen_7355
<a, z>() -> q_gen_7355
<b, z>() -> q_gen_7355
<node, s>(q_gen_7355, q_gen_7383, q_gen_7383) -> q_gen_7400
<node, s>(q_gen_7403, q_gen_7354, q_gen_7354) -> q_gen_7400
<node, s>(q_gen_7403, q_gen_7383, q_gen_7354) -> q_gen_7400
<node, s>(q_gen_7461, q_gen_7354, q_gen_7354) -> q_gen_7400
<node, s>(q_gen_7461, q_gen_7354, q_gen_7383) -> q_gen_7400
<node, s>(q_gen_7461, q_gen_7383, q_gen_7383) -> q_gen_7400
<b, s>(q_gen_7404) -> q_gen_7403
<a, s>(q_gen_7404) -> q_gen_7461
<b, s>(q_gen_7471) -> q_gen_7461
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_7342, q_gen_7357, q_gen_7374},
Q_f={q_gen_7342},
Delta=
{
<s>(q_gen_7357) -> q_gen_7357
<z>() -> q_gen_7357
<s, s>(q_gen_7342) -> q_gen_7342
<z, s>(q_gen_7357) -> q_gen_7342
<z, z>() -> q_gen_7342
<s, s>(q_gen_7374) -> q_gen_7374
<s, z>(q_gen_7357) -> q_gen_7374
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  max -> 
{{{
Q={q_gen_7343, q_gen_7359, q_gen_7371},
Q_f={q_gen_7343},
Delta=
{
<s>(q_gen_7359) -> q_gen_7359
<z>() -> q_gen_7359
<s, s>(q_gen_7371) -> q_gen_7371
<z, z>() -> q_gen_7371
<s, s, s>(q_gen_7343) -> q_gen_7343
<s, z, s>(q_gen_7371) -> q_gen_7343
<z, s, s>(q_gen_7371) -> q_gen_7343
<z, s, z>(q_gen_7359) -> q_gen_7343
<z, z, z>() -> q_gen_7343
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  numnodes -> 
{{{
Q={q_gen_7345, q_gen_7350, q_gen_7351, q_gen_7378, q_gen_7379, q_gen_7380, q_gen_7408, q_gen_7409},
Q_f={q_gen_7345},
Delta=
{
<leaf>() -> q_gen_7350
<s>(q_gen_7380) -> q_gen_7380
<z>() -> q_gen_7380
<node>(q_gen_7409, q_gen_7350, q_gen_7350) -> q_gen_7408
<node>(q_gen_7409, q_gen_7350, q_gen_7408) -> q_gen_7408
<node>(q_gen_7409, q_gen_7408, q_gen_7350) -> q_gen_7408
<node>(q_gen_7409, q_gen_7408, q_gen_7408) -> q_gen_7408
<a>() -> q_gen_7409
<b>() -> q_gen_7409
<leaf, z>() -> q_gen_7345
<node, s>(q_gen_7351, q_gen_7350, q_gen_7350) -> q_gen_7345
<node, s>(q_gen_7379, q_gen_7350, q_gen_7408) -> q_gen_7345
<node, s>(q_gen_7379, q_gen_7408, q_gen_7350) -> q_gen_7345
<a, s>(q_gen_7380) -> q_gen_7351
<a, z>() -> q_gen_7351
<b, z>() -> q_gen_7351
<node, s>(q_gen_7351, q_gen_7350, q_gen_7408) -> q_gen_7378
<node, s>(q_gen_7351, q_gen_7408, q_gen_7350) -> q_gen_7378
<node, s>(q_gen_7351, q_gen_7408, q_gen_7408) -> q_gen_7378
<node, s>(q_gen_7379, q_gen_7350, q_gen_7350) -> q_gen_7378
<node, s>(q_gen_7379, q_gen_7408, q_gen_7408) -> q_gen_7378
<b, s>(q_gen_7380) -> q_gen_7379
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_7344, q_gen_7348, q_gen_7366, q_gen_7367},
Q_f={q_gen_7344},
Delta=
{
<s>(q_gen_7367) -> q_gen_7367
<z>() -> q_gen_7367
<s, s>(q_gen_7348) -> q_gen_7348
<z, s>(q_gen_7367) -> q_gen_7348
<z, z>() -> q_gen_7348
<s, s, s>(q_gen_7344) -> q_gen_7344
<s, s, s>(q_gen_7366) -> q_gen_7344
<s, z, s>(q_gen_7348) -> q_gen_7344
<z, s, s>(q_gen_7348) -> q_gen_7344
<z, z, z>() -> q_gen_7344
<z, z, s>(q_gen_7367) -> q_gen_7366
}

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

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

Teacher's answer:
New clause system:
{
() -> height([leaf, z]) -> 66
() -> leq([z, n2]) -> 66
() -> numnodes([leaf, z]) -> 66
() -> plus([n, z, n]) -> 69
(height([t1, _mba]) /\ height([t2, _nba]) /\ max([_mba, _nba, _oba])) -> height([node(e, t1, t2), s(_oba)]) -> 74
(height([t1, _yba]) /\ numnodes([t1, _zba])) -> leq([_yba, _zba]) -> 74
(leq([n, m])) -> max([n, m, m]) -> 67
(not leq([n, m])) -> max([n, m, n]) -> 67
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 67
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 69
(leq([s(nn1), z])) -> BOT -> 67
(numnodes([t1, _sba]) /\ numnodes([t2, _tba]) /\ plus([_sba, _tba, _uba])) -> numnodes([node(e, t1, t2), s(_uba)]) -> 74
(plus([n, mm, _hba])) -> plus([n, s(mm), s(_hba)]) -> 69
}
Sat witness: Found: ((height([t1, _mba]) /\ height([t2, _nba]) /\ max([_mba, _nba, _oba])) -> height([node(e, t1, t2), s(_oba)]), {
_mba -> z  ;  _nba -> s(s(z))  ;  _oba -> s(s(z))  ;  e -> b  ;  t1 -> leaf  ;  t2 -> node(b, node(b, node(b, leaf, leaf), leaf), node(b, node(a, node(b, node(b, leaf, leaf), leaf), node(b, leaf, leaf)), node(b, leaf, leaf)))
})

-------------------------------------------
Step 88, which took 2.082037 s (model generation: 2.035826,  model checking: 0.046211):

Model:
|_
{
height -> 
{{{
Q={q_gen_7346, q_gen_7354, q_gen_7355, q_gen_7383, q_gen_7384, q_gen_7401, q_gen_7402, q_gen_7403, q_gen_7404, q_gen_7405, q_gen_7410, q_gen_7411, q_gen_7412, q_gen_7419, q_gen_7421, q_gen_7440, q_gen_7452, q_gen_7457, q_gen_7459, q_gen_7461, q_gen_7464, q_gen_7468, q_gen_7471},
Q_f={q_gen_7346, q_gen_7401, q_gen_7411, q_gen_7452},
Delta=
{
<leaf>() -> q_gen_7354
<node>(q_gen_7384, q_gen_7383, q_gen_7402) -> q_gen_7354
<node>(q_gen_7384, q_gen_7402, q_gen_7354) -> q_gen_7354
<node>(q_gen_7384, q_gen_7354, q_gen_7354) -> q_gen_7383
<a>() -> q_gen_7384
<b>() -> q_gen_7384
<node>(q_gen_7384, q_gen_7383, q_gen_7354) -> q_gen_7402
<node>(q_gen_7384, q_gen_7383, q_gen_7383) -> q_gen_7402
<node>(q_gen_7384, q_gen_7402, q_gen_7402) -> q_gen_7402
<node>(q_gen_7384, q_gen_7402, q_gen_7412) -> q_gen_7402
<z>() -> q_gen_7404
<node>(q_gen_7384, q_gen_7354, q_gen_7383) -> q_gen_7412
<node>(q_gen_7384, q_gen_7354, q_gen_7412) -> q_gen_7412
<node>(q_gen_7384, q_gen_7383, q_gen_7412) -> q_gen_7412
<node>(q_gen_7384, q_gen_7402, q_gen_7383) -> q_gen_7412
<node>(q_gen_7384, q_gen_7412, q_gen_7354) -> q_gen_7412
<node>(q_gen_7384, q_gen_7412, q_gen_7383) -> q_gen_7412
<node>(q_gen_7384, q_gen_7412, q_gen_7402) -> q_gen_7412
<node>(q_gen_7384, q_gen_7412, q_gen_7412) -> q_gen_7412
<s>(q_gen_7404) -> q_gen_7471
<leaf, z>() -> q_gen_7346
<node, s>(q_gen_7355, q_gen_7354, q_gen_7354) -> q_gen_7346
<node, s>(q_gen_7355, q_gen_7354, q_gen_7383) -> q_gen_7346
<node, s>(q_gen_7355, q_gen_7383, q_gen_7383) -> q_gen_7346
<a, z>() -> q_gen_7355
<b, z>() -> q_gen_7355
<node, s>(q_gen_7403, q_gen_7354, q_gen_7383) -> q_gen_7401
<node, s>(q_gen_7403, q_gen_7354, q_gen_7402) -> q_gen_7401
<node, s>(q_gen_7461, q_gen_7412, q_gen_7354) -> q_gen_7401
<b, s>(q_gen_7404) -> q_gen_7403
<node, s>(q_gen_7403, q_gen_7354, q_gen_7354) -> q_gen_7405
<node, s>(q_gen_7461, q_gen_7354, q_gen_7354) -> q_gen_7405
<node, s>(q_gen_7355, q_gen_7402, q_gen_7383) -> q_gen_7410
<node, s>(q_gen_7355, q_gen_7354, q_gen_7412) -> q_gen_7411
<node, s>(q_gen_7355, q_gen_7412, q_gen_7383) -> q_gen_7419
<node, s>(q_gen_7403, q_gen_7354, q_gen_7412) -> q_gen_7421
<node, s>(q_gen_7461, q_gen_7354, q_gen_7383) -> q_gen_7421
<node, s>(q_gen_7403, q_gen_7383, q_gen_7354) -> q_gen_7440
<node, s>(q_gen_7403, q_gen_7412, q_gen_7354) -> q_gen_7440
<node, s>(q_gen_7355, q_gen_7354, q_gen_7402) -> q_gen_7452
<node, s>(q_gen_7355, q_gen_7412, q_gen_7412) -> q_gen_7457
<node, s>(q_gen_7461, q_gen_7354, q_gen_7412) -> q_gen_7459
<a, s>(q_gen_7404) -> q_gen_7461
<a, s>(q_gen_7471) -> q_gen_7461
<b, s>(q_gen_7471) -> q_gen_7461
<node, s>(q_gen_7403, q_gen_7402, q_gen_7402) -> q_gen_7464
<node, s>(q_gen_7403, q_gen_7402, q_gen_7412) -> q_gen_7464
<node, s>(q_gen_7403, q_gen_7412, q_gen_7412) -> q_gen_7464
<node, s>(q_gen_7461, q_gen_7383, q_gen_7354) -> q_gen_7464
<node, s>(q_gen_7461, q_gen_7402, q_gen_7354) -> q_gen_7464
<node, s>(q_gen_7461, q_gen_7402, q_gen_7412) -> q_gen_7464
<node, s>(q_gen_7355, q_gen_7402, q_gen_7354) -> q_gen_7468
<node, s>(q_gen_7403, q_gen_7383, q_gen_7402) -> q_gen_7468
<node, s>(q_gen_7403, q_gen_7402, q_gen_7383) -> q_gen_7468
<node, s>(q_gen_7461, q_gen_7354, q_gen_7402) -> q_gen_7468
<node, s>(q_gen_7461, q_gen_7383, q_gen_7383) -> q_gen_7468
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_7342, q_gen_7357, q_gen_7374},
Q_f={q_gen_7342},
Delta=
{
<s>(q_gen_7357) -> q_gen_7357
<z>() -> q_gen_7357
<s, s>(q_gen_7342) -> q_gen_7342
<z, s>(q_gen_7357) -> q_gen_7342
<z, z>() -> q_gen_7342
<s, s>(q_gen_7374) -> q_gen_7374
<s, z>(q_gen_7357) -> q_gen_7374
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  max -> 
{{{
Q={q_gen_7343, q_gen_7359, q_gen_7371},
Q_f={q_gen_7343},
Delta=
{
<s>(q_gen_7359) -> q_gen_7359
<z>() -> q_gen_7359
<s, s>(q_gen_7371) -> q_gen_7371
<z, z>() -> q_gen_7371
<s, s, s>(q_gen_7343) -> q_gen_7343
<s, z, s>(q_gen_7371) -> q_gen_7343
<z, s, s>(q_gen_7371) -> q_gen_7343
<z, s, z>(q_gen_7359) -> q_gen_7343
<z, z, z>() -> q_gen_7343
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  numnodes -> 
{{{
Q={q_gen_7345, q_gen_7349, q_gen_7350, q_gen_7351, q_gen_7369, q_gen_7380, q_gen_7408, q_gen_7409, q_gen_7424},
Q_f={q_gen_7345, q_gen_7349},
Delta=
{
<leaf>() -> q_gen_7350
<node>(q_gen_7409, q_gen_7408, q_gen_7350) -> q_gen_7350
<s>(q_gen_7380) -> q_gen_7380
<z>() -> q_gen_7380
<node>(q_gen_7409, q_gen_7350, q_gen_7350) -> q_gen_7408
<node>(q_gen_7409, q_gen_7350, q_gen_7408) -> q_gen_7408
<node>(q_gen_7409, q_gen_7408, q_gen_7408) -> q_gen_7408
<a>() -> q_gen_7409
<b>() -> q_gen_7409
<leaf, z>() -> q_gen_7345
<node, s>(q_gen_7351, q_gen_7408, q_gen_7408) -> q_gen_7345
<node, s>(q_gen_7369, q_gen_7350, q_gen_7408) -> q_gen_7345
<node, s>(q_gen_7369, q_gen_7408, q_gen_7408) -> q_gen_7345
<node, s>(q_gen_7351, q_gen_7350, q_gen_7350) -> q_gen_7349
<node, s>(q_gen_7351, q_gen_7408, q_gen_7350) -> q_gen_7349
<node, s>(q_gen_7369, q_gen_7350, q_gen_7350) -> q_gen_7349
<node, s>(q_gen_7369, q_gen_7408, q_gen_7350) -> q_gen_7349
<b, z>() -> q_gen_7351
<a, s>(q_gen_7380) -> q_gen_7369
<a, z>() -> q_gen_7369
<b, s>(q_gen_7380) -> q_gen_7369
<node, s>(q_gen_7351, q_gen_7350, q_gen_7408) -> q_gen_7424
}

Datatype: <elt_bin_tree, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_7344, q_gen_7348, q_gen_7367},
Q_f={q_gen_7344},
Delta=
{
<s>(q_gen_7367) -> q_gen_7367
<z>() -> q_gen_7367
<s, s>(q_gen_7348) -> q_gen_7348
<z, s>(q_gen_7367) -> q_gen_7348
<z, z>() -> q_gen_7348
<s, s, s>(q_gen_7344) -> q_gen_7344
<s, z, s>(q_gen_7348) -> q_gen_7344
<z, s, s>(q_gen_7348) -> q_gen_7344
<z, z, s>(q_gen_7367) -> q_gen_7344
<z, z, z>() -> q_gen_7344
}

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

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

Teacher's answer:
New clause system:
{
() -> height([leaf, z]) -> 67
() -> leq([z, n2]) -> 67
() -> numnodes([leaf, z]) -> 67
() -> plus([n, z, n]) -> 70
(height([t1, _mba]) /\ height([t2, _nba]) /\ max([_mba, _nba, _oba])) -> height([node(e, t1, t2), s(_oba)]) -> 74
(height([t1, _yba]) /\ numnodes([t1, _zba])) -> leq([_yba, _zba]) -> 77
(leq([n, m])) -> max([n, m, m]) -> 68
(not leq([n, m])) -> max([n, m, n]) -> 68
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 68
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 70
(leq([s(nn1), z])) -> BOT -> 68
(numnodes([t1, _sba]) /\ numnodes([t2, _tba]) /\ plus([_sba, _tba, _uba])) -> numnodes([node(e, t1, t2), s(_uba)]) -> 75
(plus([n, mm, _hba])) -> plus([n, s(mm), s(_hba)]) -> 70
}
Sat witness: Found: ((height([t1, _yba]) /\ numnodes([t1, _zba])) -> leq([_yba, _zba]), {
_yba -> s(s(s(z)))  ;  _zba -> s(z)  ;  t1 -> node(b, node(b, leaf, node(b, leaf, leaf)), leaf)
})

Total time: 63.045466
Reason for stopping: DontKnow. Stopped because: timeout