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


Learning problem is:

env: {
elt -> {a, b}  ;  eltlist -> {cons, nil}  ;  nat -> {s, z}
}
definition:
{
(leq, P:
{() -> leq([a, y])
() -> leq([b, b])
(leq([b, a])) -> BOT}
)
(insert, F:
{() -> insert([x, nil, cons(x, nil)])
(insert([x, z, _zi]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _zi)])
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))])}
(insert([_aj, _bj, _cj]) /\ insert([_aj, _bj, _dj])) -> eq_eltlist([_cj, _dj])
)
(length, F:
{() -> length([nil, z])
(length([ll, _ej])) -> length([cons(x, ll), s(_ej)])}
(length([_fj, _gj]) /\ length([_fj, _hj])) -> eq_nat([_gj, _hj])
)
(leqnat, P:
{() -> leqnat([z, s(nn2)])
() -> leqnat([z, z])
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)])
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2])
(leqnat([s(nn1), z])) -> BOT}
)
}

properties:
{(insert([x, l, _jj]) /\ length([_jj, _kj]) /\ length([l, _ij])) -> leqnat([_ij, _kj])}


over-approximation: {insert, length}
under-approximation: {leq, leqnat}

Clause system for inference is:

{
() -> insert([x, nil, cons(x, nil)]) -> 0
() -> length([nil, z]) -> 0
() -> leq([a, y]) -> 0
() -> leq([b, b]) -> 0
() -> leqnat([z, s(nn2)]) -> 0
() -> leqnat([z, z]) -> 0
(insert([x, l, _jj]) /\ length([_jj, _kj]) /\ length([l, _ij])) -> leqnat([_ij, _kj]) -> 0
(insert([x, z, _zi]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _zi)]) -> 0
(length([ll, _ej])) -> length([cons(x, ll), s(_ej)]) -> 0
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 0
(leq([b, a])) -> BOT -> 0
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 0
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 0
(leqnat([s(nn1), z])) -> BOT -> 0
}


Solving took 63.090572 seconds.
DontKnow. Stopped because: timeout
Working model:
|_
{
insert -> 
{{{
Q={q_gen_2250, q_gen_2251, q_gen_2252, q_gen_2254, q_gen_2255, q_gen_2256, q_gen_2261, q_gen_2262, q_gen_2266, q_gen_2267, q_gen_2268, q_gen_2269, q_gen_2272, q_gen_2273, q_gen_2274, q_gen_2275, q_gen_2276, q_gen_2277, q_gen_2278, q_gen_2284, q_gen_2299, q_gen_2300, q_gen_2305, q_gen_2307, q_gen_2308, q_gen_2309, q_gen_2310, q_gen_2311, q_gen_2312, q_gen_2317, q_gen_2324, q_gen_2325, q_gen_2328, q_gen_2330, q_gen_2341, q_gen_2343, q_gen_2347, q_gen_2357, q_gen_2358, q_gen_2361, q_gen_2370, q_gen_2376, q_gen_2377, q_gen_2378, q_gen_2379, q_gen_2380, q_gen_2381, q_gen_2382, q_gen_2383, q_gen_2384, q_gen_2385, q_gen_2386, q_gen_2387, q_gen_2405, q_gen_2406, q_gen_2407, q_gen_2408, q_gen_2409, q_gen_2410, q_gen_2411, q_gen_2420, q_gen_2421, q_gen_2422, q_gen_2431},
Q_f={},
Delta=
{
<nil>() -> q_gen_2251
<b>() -> q_gen_2252
<a>() -> q_gen_2267
<nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2255
<b, b>() -> q_gen_2256
<a, a>() -> q_gen_2262
<b, a>() -> q_gen_2269
<nil, cons>(q_gen_2267, q_gen_2251) -> q_gen_2273
<cons, cons>(q_gen_2262, q_gen_2273) -> q_gen_2275
<cons, cons>(q_gen_2278, q_gen_2273) -> q_gen_2277
<a, b>() -> q_gen_2278
<cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2300
<cons, cons>(q_gen_2278, q_gen_2255) -> q_gen_2308
<cons, cons>(q_gen_2269, q_gen_2308) -> q_gen_2310
<cons, cons>(q_gen_2256, q_gen_2300) -> q_gen_2325
<cons, cons>(q_gen_2256, q_gen_2325) -> q_gen_2358
<cons, cons>(q_gen_2262, q_gen_2255) -> q_gen_2377
<cons, cons>(q_gen_2262, q_gen_2377) -> q_gen_2379
<cons, cons>(q_gen_2256, q_gen_2273) -> q_gen_2381
<cons, cons>(q_gen_2256, q_gen_2381) -> q_gen_2383
<cons, cons>(q_gen_2256, q_gen_2277) -> q_gen_2385
<cons, cons>(q_gen_2262, q_gen_2300) -> q_gen_2387
<cons, cons>(q_gen_2278, q_gen_2407) -> q_gen_2406
<cons, cons>(q_gen_2269, q_gen_2408) -> q_gen_2407
<cons, cons>(q_gen_2256, q_gen_2409) -> q_gen_2408
<cons, cons>(q_gen_2256, q_gen_2410) -> q_gen_2409
<cons, cons>(q_gen_2256, q_gen_2411) -> q_gen_2410
<cons, cons>(q_gen_2269, q_gen_2255) -> q_gen_2411
<cons, cons>(q_gen_2256, q_gen_2422) -> q_gen_2421
<cons, cons>(q_gen_2256, q_gen_2308) -> q_gen_2422
<b, nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2250
<b, cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2254
<b, cons, cons>(q_gen_2262, q_gen_2255) -> q_gen_2261
<a, nil, cons>(q_gen_2267, q_gen_2251) -> q_gen_2266
<a, cons, cons>(q_gen_2269, q_gen_2255) -> q_gen_2268
<b, cons, cons>(q_gen_2262, q_gen_2273) -> q_gen_2272
<b, cons, cons>(q_gen_2262, q_gen_2275) -> q_gen_2274
<b, cons, cons>(q_gen_2256, q_gen_2277) -> q_gen_2276
<b, cons, cons>(q_gen_2269, q_gen_2255) -> q_gen_2284
<a, cons, cons>(q_gen_2256, q_gen_2300) -> q_gen_2299
<b, cons, cons>(q_gen_2256, q_gen_2300) -> q_gen_2305
<b, cons, cons>(q_gen_2269, q_gen_2308) -> q_gen_2307
<b, cons, cons>(q_gen_2262, q_gen_2310) -> q_gen_2309
<a, cons, cons>(q_gen_2262, q_gen_2273) -> q_gen_2311
<a, cons, cons>(q_gen_2262, q_gen_2275) -> q_gen_2312
<a, cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2317
<a, cons, cons>(q_gen_2256, q_gen_2325) -> q_gen_2324
<b, cons, cons>(q_gen_2262, q_gen_2300) -> q_gen_2328
<b, cons, cons>(q_gen_2269, q_gen_2325) -> q_gen_2330
<b, cons, cons>(q_gen_2256, q_gen_2325) -> q_gen_2341
<a, cons, cons>(q_gen_2269, q_gen_2300) -> q_gen_2343
<a, cons, cons>(q_gen_2278, q_gen_2325) -> q_gen_2347
<a, cons, cons>(q_gen_2256, q_gen_2358) -> q_gen_2357
<b, cons, cons>(q_gen_2256, q_gen_2358) -> q_gen_2361
<a, cons, cons>(q_gen_2269, q_gen_2325) -> q_gen_2370
<b, cons, cons>(q_gen_2262, q_gen_2377) -> q_gen_2376
<b, cons, cons>(q_gen_2262, q_gen_2379) -> q_gen_2378
<b, cons, cons>(q_gen_2256, q_gen_2381) -> q_gen_2380
<b, cons, cons>(q_gen_2262, q_gen_2383) -> q_gen_2382
<b, cons, cons>(q_gen_2256, q_gen_2385) -> q_gen_2384
<b, cons, cons>(q_gen_2262, q_gen_2387) -> q_gen_2386
<a, cons, cons>(q_gen_2256, q_gen_2406) -> q_gen_2405
<a, cons, cons>(q_gen_2256, q_gen_2421) -> q_gen_2420
<a, cons, cons>(q_gen_2269, q_gen_2358) -> q_gen_2431
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_2249, q_gen_2257, q_gen_2258, q_gen_2259, q_gen_2270, q_gen_2271, q_gen_2279, q_gen_2280, q_gen_2281, q_gen_2282, q_gen_2283, q_gen_2285, q_gen_2286, q_gen_2289, q_gen_2290, q_gen_2291, q_gen_2292, q_gen_2293, q_gen_2294, q_gen_2295, q_gen_2297, q_gen_2298, q_gen_2301, q_gen_2302, q_gen_2303, q_gen_2304, q_gen_2306, q_gen_2313, q_gen_2314, q_gen_2315, q_gen_2316, q_gen_2318, q_gen_2322, q_gen_2323, q_gen_2326, q_gen_2327, q_gen_2329, q_gen_2331, q_gen_2332, q_gen_2334, q_gen_2335, q_gen_2338, q_gen_2339, q_gen_2340, q_gen_2342, q_gen_2344, q_gen_2345, q_gen_2346, q_gen_2348, q_gen_2349, q_gen_2350, q_gen_2351, q_gen_2352, q_gen_2353, q_gen_2354, q_gen_2355, q_gen_2356, q_gen_2359, q_gen_2360, q_gen_2362, q_gen_2363, q_gen_2365, q_gen_2366, q_gen_2367, q_gen_2368, q_gen_2369, q_gen_2371, q_gen_2373, q_gen_2374, q_gen_2375, q_gen_2388, q_gen_2389, q_gen_2390, q_gen_2394, q_gen_2395, q_gen_2396, q_gen_2397, q_gen_2398, q_gen_2399, q_gen_2400, q_gen_2401, q_gen_2402, q_gen_2403, q_gen_2404, q_gen_2412, q_gen_2413, q_gen_2414, q_gen_2415, q_gen_2416, q_gen_2417, q_gen_2418, q_gen_2419, q_gen_2423, q_gen_2424, q_gen_2425, q_gen_2426, q_gen_2427, q_gen_2428, q_gen_2429, q_gen_2430, q_gen_2432},
Q_f={},
Delta=
{
<nil>() -> q_gen_2258
<cons>(q_gen_2281, q_gen_2258) -> q_gen_2280
<b>() -> q_gen_2281
<z>() -> q_gen_2283
<s>(q_gen_2283) -> q_gen_2294
<cons>(q_gen_2281, q_gen_2280) -> q_gen_2298
<cons>(q_gen_2304, q_gen_2280) -> q_gen_2303
<a>() -> q_gen_2304
<cons>(q_gen_2281, q_gen_2303) -> q_gen_2314
<s>(q_gen_2294) -> q_gen_2316
<cons>(q_gen_2281, q_gen_2298) -> q_gen_2327
<cons>(q_gen_2304, q_gen_2303) -> q_gen_2351
<s>(q_gen_2316) -> q_gen_2353
<cons>(q_gen_2281, q_gen_2314) -> q_gen_2355
<cons>(q_gen_2281, q_gen_2327) -> q_gen_2360
<cons>(q_gen_2304, q_gen_2258) -> q_gen_2367
<cons>(q_gen_2304, q_gen_2367) -> q_gen_2402
<cons>(q_gen_2304, q_gen_2414) -> q_gen_2413
<cons>(q_gen_2281, q_gen_2360) -> q_gen_2414
<cons>(q_gen_2281, q_gen_2417) -> q_gen_2416
<cons>(q_gen_2304, q_gen_2418) -> q_gen_2417
<cons>(q_gen_2281, q_gen_2355) -> q_gen_2418
<cons>(q_gen_2281, q_gen_2425) -> q_gen_2424
<cons>(q_gen_2281, q_gen_2367) -> q_gen_2425
<cons>(q_gen_2281, q_gen_2424) -> q_gen_2428
<nil, z>() -> q_gen_2249
<cons, s>(q_gen_2259, q_gen_2258) -> q_gen_2257
<b, z>() -> q_gen_2259
<cons, s>(q_gen_2271, q_gen_2258) -> q_gen_2270
<a, z>() -> q_gen_2271
<cons, s>(q_gen_2282, q_gen_2280) -> q_gen_2279
<b, s>(q_gen_2283) -> q_gen_2282
<cons, s>(q_gen_2271, q_gen_2280) -> q_gen_2285
<cons, s>(q_gen_2282, q_gen_2258) -> q_gen_2286
<cons, s>(q_gen_2259, q_gen_2280) -> q_gen_2289
<cons, s>(q_gen_2291, q_gen_2280) -> q_gen_2290
<a, s>(q_gen_2283) -> q_gen_2291
<cons, s>(q_gen_2293, q_gen_2280) -> q_gen_2292
<b, s>(q_gen_2294) -> q_gen_2293
<cons, s>(q_gen_2293, q_gen_2258) -> q_gen_2295
<cons, s>(q_gen_2293, q_gen_2298) -> q_gen_2297
<cons, s>(q_gen_2282, q_gen_2298) -> q_gen_2301
<cons, s>(q_gen_2293, q_gen_2303) -> q_gen_2302
<cons, s>(q_gen_2259, q_gen_2298) -> q_gen_2306
<cons, s>(q_gen_2315, q_gen_2314) -> q_gen_2313
<b, s>(q_gen_2316) -> q_gen_2315
<cons, s>(q_gen_2315, q_gen_2258) -> q_gen_2318
<cons, s>(q_gen_2323, q_gen_2314) -> q_gen_2322
<a, s>(q_gen_2316) -> q_gen_2323
<cons, s>(q_gen_2282, q_gen_2327) -> q_gen_2326
<cons, s>(q_gen_2291, q_gen_2298) -> q_gen_2329
<cons, s>(q_gen_2291, q_gen_2327) -> q_gen_2331
<cons, s>(q_gen_2315, q_gen_2280) -> q_gen_2332
<cons, s>(q_gen_2293, q_gen_2327) -> q_gen_2334
<cons, s>(q_gen_2315, q_gen_2298) -> q_gen_2335
<cons, s>(q_gen_2339, q_gen_2327) -> q_gen_2338
<a, s>(q_gen_2294) -> q_gen_2339
<cons, s>(q_gen_2315, q_gen_2327) -> q_gen_2340
<cons, s>(q_gen_2339, q_gen_2298) -> q_gen_2342
<cons, s>(q_gen_2259, q_gen_2327) -> q_gen_2344
<cons, s>(q_gen_2282, q_gen_2303) -> q_gen_2345
<cons, s>(q_gen_2293, q_gen_2314) -> q_gen_2346
<cons, s>(q_gen_2323, q_gen_2298) -> q_gen_2348
<cons, s>(q_gen_2323, q_gen_2303) -> q_gen_2349
<cons, s>(q_gen_2352, q_gen_2351) -> q_gen_2350
<b, s>(q_gen_2353) -> q_gen_2352
<cons, s>(q_gen_2356, q_gen_2355) -> q_gen_2354
<a, s>(q_gen_2353) -> q_gen_2356
<cons, s>(q_gen_2282, q_gen_2360) -> q_gen_2359
<cons, s>(q_gen_2293, q_gen_2360) -> q_gen_2362
<cons, s>(q_gen_2352, q_gen_2327) -> q_gen_2363
<cons, s>(q_gen_2323, q_gen_2258) -> q_gen_2365
<cons, s>(q_gen_2352, q_gen_2367) -> q_gen_2366
<cons, s>(q_gen_2259, q_gen_2314) -> q_gen_2368
<cons, s>(q_gen_2282, q_gen_2355) -> q_gen_2369
<cons, s>(q_gen_2352, q_gen_2298) -> q_gen_2371
<cons, s>(q_gen_2315, q_gen_2360) -> q_gen_2373
<cons, s>(q_gen_2291, q_gen_2258) -> q_gen_2374
<cons, s>(q_gen_2293, q_gen_2367) -> q_gen_2375
<cons, s>(q_gen_2352, q_gen_2355) -> q_gen_2388
<cons, s>(q_gen_2323, q_gen_2355) -> q_gen_2389
<cons, s>(q_gen_2352, q_gen_2258) -> q_gen_2390
<cons, s>(q_gen_2259, q_gen_2360) -> q_gen_2394
<cons, s>(q_gen_2282, q_gen_2367) -> q_gen_2395
<cons, s>(q_gen_2315, q_gen_2303) -> q_gen_2396
<cons, s>(q_gen_2352, q_gen_2314) -> q_gen_2397
<cons, s>(q_gen_2352, q_gen_2280) -> q_gen_2398
<cons, s>(q_gen_2356, q_gen_2298) -> q_gen_2399
<cons, s>(q_gen_2291, q_gen_2367) -> q_gen_2400
<cons, s>(q_gen_2293, q_gen_2402) -> q_gen_2401
<cons, s>(q_gen_2339, q_gen_2367) -> q_gen_2403
<cons, s>(q_gen_2323, q_gen_2402) -> q_gen_2404
<cons, s>(q_gen_2282, q_gen_2413) -> q_gen_2412
<cons, s>(q_gen_2259, q_gen_2416) -> q_gen_2415
<cons, s>(q_gen_2323, q_gen_2327) -> q_gen_2419
<cons, s>(q_gen_2282, q_gen_2424) -> q_gen_2423
<cons, s>(q_gen_2315, q_gen_2424) -> q_gen_2426
<cons, s>(q_gen_2352, q_gen_2428) -> q_gen_2427
<cons, s>(q_gen_2259, q_gen_2425) -> q_gen_2429
<cons, s>(q_gen_2352, q_gen_2360) -> q_gen_2430
<cons, s>(q_gen_2291, q_gen_2360) -> q_gen_2432
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_2247, q_gen_2248, q_gen_2260, q_gen_2265},
Q_f={},
Delta=
{
<b, b>() -> q_gen_2247
<a, b>() -> q_gen_2248
<b, a>() -> q_gen_2260
<a, a>() -> q_gen_2265
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  leqnat -> 
{{{
Q={q_gen_2244, q_gen_2245, q_gen_2246, q_gen_2253, q_gen_2263, q_gen_2264, q_gen_2287, q_gen_2288, q_gen_2296, q_gen_2319, q_gen_2320, q_gen_2321, q_gen_2333, q_gen_2336, q_gen_2337, q_gen_2364, q_gen_2372, q_gen_2391, q_gen_2392, q_gen_2393},
Q_f={},
Delta=
{
<z>() -> q_gen_2246
<s>(q_gen_2246) -> q_gen_2264
<s>(q_gen_2264) -> q_gen_2337
<z, z>() -> q_gen_2244
<z, s>(q_gen_2246) -> q_gen_2245
<s, s>(q_gen_2244) -> q_gen_2253
<z, s>(q_gen_2264) -> q_gen_2263
<s, s>(q_gen_2288) -> q_gen_2287
<s, z>(q_gen_2246) -> q_gen_2288
<s, s>(q_gen_2287) -> q_gen_2296
<s, s>(q_gen_2320) -> q_gen_2319
<s, s>(q_gen_2321) -> q_gen_2320
<s, z>(q_gen_2264) -> q_gen_2321
<s, s>(q_gen_2296) -> q_gen_2333
<z, s>(q_gen_2337) -> q_gen_2336
<s, s>(q_gen_2319) -> q_gen_2364
<s, s>(q_gen_2333) -> q_gen_2372
<s, s>(q_gen_2392) -> q_gen_2391
<s, s>(q_gen_2393) -> q_gen_2392
<s, z>(q_gen_2337) -> q_gen_2393
}

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

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

-------------------
STEPS:
-------------------------------------------
Step 0, which took 0.008775 s (model generation: 0.008484,  model checking: 0.000291):

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

}

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

}

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

}

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

}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 0
() -> length([nil, z]) -> 0
() -> leq([a, y]) -> 0
() -> leq([b, b]) -> 0
() -> leqnat([z, s(nn2)]) -> 0
() -> leqnat([z, z]) -> 3
(insert([x, l, _jj]) /\ length([_jj, _kj]) /\ length([l, _ij])) -> leqnat([_ij, _kj]) -> 1
(insert([x, z, _zi]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _zi)]) -> 1
(length([ll, _ej])) -> length([cons(x, ll), s(_ej)]) -> 1
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 1
(leq([b, a])) -> BOT -> 1
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 1
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 1
(leqnat([s(nn1), z])) -> BOT -> 1
}
Sat witness: Found: (() -> leqnat([z, z]), {

})

-------------------------------------------
Step 1, which took 0.008914 s (model generation: 0.008807,  model checking: 0.000107):

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

}

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

}

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

}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  leqnat -> 
{{{
Q={q_gen_2244},
Q_f={q_gen_2244},
Delta=
{
<z, z>() -> q_gen_2244
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 0
() -> length([nil, z]) -> 0
() -> leq([a, y]) -> 0
() -> leq([b, b]) -> 0
() -> leqnat([z, s(nn2)]) -> 3
() -> leqnat([z, z]) -> 3
(insert([x, l, _jj]) /\ length([_jj, _kj]) /\ length([l, _ij])) -> leqnat([_ij, _kj]) -> 1
(insert([x, z, _zi]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _zi)]) -> 1
(length([ll, _ej])) -> length([cons(x, ll), s(_ej)]) -> 1
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 1
(leq([b, a])) -> BOT -> 1
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 1
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 1
(leqnat([s(nn1), z])) -> BOT -> 1
}
Sat witness: Found: (() -> leqnat([z, s(nn2)]), {
nn2 -> z
})

-------------------------------------------
Step 2, which took 0.008995 s (model generation: 0.008957,  model checking: 0.000038):

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

}

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

}

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

}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  leqnat -> 
{{{
Q={q_gen_2244, q_gen_2246},
Q_f={q_gen_2244},
Delta=
{
<z>() -> q_gen_2246
<z, s>(q_gen_2246) -> q_gen_2244
<z, z>() -> q_gen_2244
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 0
() -> length([nil, z]) -> 0
() -> leq([a, y]) -> 0
() -> leq([b, b]) -> 3
() -> leqnat([z, s(nn2)]) -> 3
() -> leqnat([z, z]) -> 3
(insert([x, l, _jj]) /\ length([_jj, _kj]) /\ length([l, _ij])) -> leqnat([_ij, _kj]) -> 1
(insert([x, z, _zi]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _zi)]) -> 1
(length([ll, _ej])) -> length([cons(x, ll), s(_ej)]) -> 1
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 1
(leq([b, a])) -> BOT -> 1
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 1
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 1
(leqnat([s(nn1), z])) -> BOT -> 1
}
Sat witness: Found: (() -> leq([b, b]), {

})

-------------------------------------------
Step 3, which took 0.007977 s (model generation: 0.007934,  model checking: 0.000043):

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

}

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

}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_2247},
Q_f={q_gen_2247},
Delta=
{
<b, b>() -> q_gen_2247
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  leqnat -> 
{{{
Q={q_gen_2244, q_gen_2246},
Q_f={q_gen_2244},
Delta=
{
<z>() -> q_gen_2246
<z, s>(q_gen_2246) -> q_gen_2244
<z, z>() -> q_gen_2244
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 0
() -> length([nil, z]) -> 0
() -> leq([a, y]) -> 3
() -> leq([b, b]) -> 3
() -> leqnat([z, s(nn2)]) -> 3
() -> leqnat([z, z]) -> 3
(insert([x, l, _jj]) /\ length([_jj, _kj]) /\ length([l, _ij])) -> leqnat([_ij, _kj]) -> 1
(insert([x, z, _zi]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _zi)]) -> 1
(length([ll, _ej])) -> length([cons(x, ll), s(_ej)]) -> 1
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 1
(leq([b, a])) -> BOT -> 1
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 1
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 1
(leqnat([s(nn1), z])) -> BOT -> 1
}
Sat witness: Found: (() -> leq([a, y]), {
y -> b
})

-------------------------------------------
Step 4, which took 0.008759 s (model generation: 0.008687,  model checking: 0.000072):

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

}

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

}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_2247},
Q_f={q_gen_2247},
Delta=
{
<a, b>() -> q_gen_2247
<b, b>() -> q_gen_2247
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  leqnat -> 
{{{
Q={q_gen_2244, q_gen_2246},
Q_f={q_gen_2244},
Delta=
{
<z>() -> q_gen_2246
<z, s>(q_gen_2246) -> q_gen_2244
<z, z>() -> q_gen_2244
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 0
() -> length([nil, z]) -> 3
() -> leq([a, y]) -> 3
() -> leq([b, b]) -> 3
() -> leqnat([z, s(nn2)]) -> 3
() -> leqnat([z, z]) -> 3
(insert([x, l, _jj]) /\ length([_jj, _kj]) /\ length([l, _ij])) -> leqnat([_ij, _kj]) -> 1
(insert([x, z, _zi]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _zi)]) -> 1
(length([ll, _ej])) -> length([cons(x, ll), s(_ej)]) -> 1
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 1
(leq([b, a])) -> BOT -> 1
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 1
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 1
(leqnat([s(nn1), z])) -> BOT -> 1
}
Sat witness: Found: (() -> length([nil, z]), {

})

-------------------------------------------
Step 5, which took 0.009833 s (model generation: 0.009700,  model checking: 0.000133):

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

}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_2249},
Q_f={q_gen_2249},
Delta=
{
<nil, z>() -> q_gen_2249
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_2247},
Q_f={q_gen_2247},
Delta=
{
<a, b>() -> q_gen_2247
<b, b>() -> q_gen_2247
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  leqnat -> 
{{{
Q={q_gen_2244, q_gen_2246},
Q_f={q_gen_2244},
Delta=
{
<z>() -> q_gen_2246
<z, s>(q_gen_2246) -> q_gen_2244
<z, z>() -> q_gen_2244
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 3
() -> length([nil, z]) -> 3
() -> leq([a, y]) -> 3
() -> leq([b, b]) -> 3
() -> leqnat([z, s(nn2)]) -> 3
() -> leqnat([z, z]) -> 3
(insert([x, l, _jj]) /\ length([_jj, _kj]) /\ length([l, _ij])) -> leqnat([_ij, _kj]) -> 1
(insert([x, z, _zi]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _zi)]) -> 1
(length([ll, _ej])) -> length([cons(x, ll), s(_ej)]) -> 1
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 1
(leq([b, a])) -> BOT -> 1
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 1
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 1
(leqnat([s(nn1), z])) -> BOT -> 1
}
Sat witness: Found: (() -> insert([x, nil, cons(x, nil)]), {
x -> b
})

-------------------------------------------
Step 6, which took 0.009881 s (model generation: 0.009685,  model checking: 0.000196):

Model:
|_
{
insert -> 
{{{
Q={q_gen_2250, q_gen_2251, q_gen_2252},
Q_f={q_gen_2250},
Delta=
{
<nil>() -> q_gen_2251
<b>() -> q_gen_2252
<b, nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2250
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_2249},
Q_f={q_gen_2249},
Delta=
{
<nil, z>() -> q_gen_2249
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_2247},
Q_f={q_gen_2247},
Delta=
{
<a, b>() -> q_gen_2247
<b, b>() -> q_gen_2247
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  leqnat -> 
{{{
Q={q_gen_2244, q_gen_2246},
Q_f={q_gen_2244},
Delta=
{
<z>() -> q_gen_2246
<z, s>(q_gen_2246) -> q_gen_2244
<z, z>() -> q_gen_2244
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 3
() -> length([nil, z]) -> 3
() -> leq([a, y]) -> 3
() -> leq([b, b]) -> 3
() -> leqnat([z, s(nn2)]) -> 3
() -> leqnat([z, z]) -> 3
(insert([x, l, _jj]) /\ length([_jj, _kj]) /\ length([l, _ij])) -> leqnat([_ij, _kj]) -> 1
(insert([x, z, _zi]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _zi)]) -> 1
(length([ll, _ej])) -> length([cons(x, ll), s(_ej)]) -> 1
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 1
(leq([b, a])) -> BOT -> 1
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 4
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 2
(leqnat([s(nn1), z])) -> BOT -> 2
}
Sat witness: Found: ((leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]), {
nn1 -> z  ;  nn2 -> z
})

-------------------------------------------
Step 7, which took 0.009291 s (model generation: 0.009047,  model checking: 0.000244):

Model:
|_
{
insert -> 
{{{
Q={q_gen_2250, q_gen_2251, q_gen_2252},
Q_f={q_gen_2250},
Delta=
{
<nil>() -> q_gen_2251
<b>() -> q_gen_2252
<b, nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2250
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_2249},
Q_f={q_gen_2249},
Delta=
{
<nil, z>() -> q_gen_2249
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_2247},
Q_f={q_gen_2247},
Delta=
{
<a, b>() -> q_gen_2247
<b, b>() -> q_gen_2247
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  leqnat -> 
{{{
Q={q_gen_2244, q_gen_2246},
Q_f={q_gen_2244},
Delta=
{
<z>() -> q_gen_2246
<s, s>(q_gen_2244) -> q_gen_2244
<z, s>(q_gen_2246) -> q_gen_2244
<z, z>() -> q_gen_2244
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 3
() -> length([nil, z]) -> 3
() -> leq([a, y]) -> 3
() -> leq([b, b]) -> 3
() -> leqnat([z, s(nn2)]) -> 3
() -> leqnat([z, z]) -> 3
(insert([x, l, _jj]) /\ length([_jj, _kj]) /\ length([l, _ij])) -> leqnat([_ij, _kj]) -> 1
(insert([x, z, _zi]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _zi)]) -> 1
(length([ll, _ej])) -> length([cons(x, ll), s(_ej)]) -> 1
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 4
(leq([b, a])) -> BOT -> 2
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 4
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 2
(leqnat([s(nn1), z])) -> BOT -> 2
}
Sat witness: Found: ((leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]), {
x -> b  ;  y -> b  ;  z -> nil
})

-------------------------------------------
Step 8, which took 0.009096 s (model generation: 0.008996,  model checking: 0.000100):

Model:
|_
{
insert -> 
{{{
Q={q_gen_2250, q_gen_2251, q_gen_2252, q_gen_2255, q_gen_2256},
Q_f={q_gen_2250},
Delta=
{
<nil>() -> q_gen_2251
<b>() -> q_gen_2252
<nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2255
<b, b>() -> q_gen_2256
<b, cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2250
<b, nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2250
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_2249},
Q_f={q_gen_2249},
Delta=
{
<nil, z>() -> q_gen_2249
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_2247},
Q_f={q_gen_2247},
Delta=
{
<a, b>() -> q_gen_2247
<b, b>() -> q_gen_2247
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  leqnat -> 
{{{
Q={q_gen_2244, q_gen_2246},
Q_f={q_gen_2244},
Delta=
{
<z>() -> q_gen_2246
<s, s>(q_gen_2244) -> q_gen_2244
<z, s>(q_gen_2246) -> q_gen_2244
<z, z>() -> q_gen_2244
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 3
() -> length([nil, z]) -> 3
() -> leq([a, y]) -> 3
() -> leq([b, b]) -> 3
() -> leqnat([z, s(nn2)]) -> 3
() -> leqnat([z, z]) -> 3
(insert([x, l, _jj]) /\ length([_jj, _kj]) /\ length([l, _ij])) -> leqnat([_ij, _kj]) -> 1
(insert([x, z, _zi]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _zi)]) -> 1
(length([ll, _ej])) -> length([cons(x, ll), s(_ej)]) -> 4
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 4
(leq([b, a])) -> BOT -> 2
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 4
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 2
(leqnat([s(nn1), z])) -> BOT -> 2
}
Sat witness: Found: ((length([ll, _ej])) -> length([cons(x, ll), s(_ej)]), {
_ej -> z  ;  ll -> nil  ;  x -> b
})

-------------------------------------------
Step 9, which took 0.008779 s (model generation: 0.008389,  model checking: 0.000390):

Model:
|_
{
insert -> 
{{{
Q={q_gen_2250, q_gen_2251, q_gen_2252, q_gen_2255, q_gen_2256},
Q_f={q_gen_2250},
Delta=
{
<nil>() -> q_gen_2251
<b>() -> q_gen_2252
<nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2255
<b, b>() -> q_gen_2256
<b, cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2250
<b, nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2250
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_2249, q_gen_2258, q_gen_2259},
Q_f={q_gen_2249},
Delta=
{
<nil>() -> q_gen_2258
<cons, s>(q_gen_2259, q_gen_2258) -> q_gen_2249
<nil, z>() -> q_gen_2249
<b, z>() -> q_gen_2259
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_2247},
Q_f={q_gen_2247},
Delta=
{
<a, b>() -> q_gen_2247
<b, b>() -> q_gen_2247
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  leqnat -> 
{{{
Q={q_gen_2244, q_gen_2246},
Q_f={q_gen_2244},
Delta=
{
<z>() -> q_gen_2246
<s, s>(q_gen_2244) -> q_gen_2244
<z, s>(q_gen_2246) -> q_gen_2244
<z, z>() -> q_gen_2244
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 3
() -> length([nil, z]) -> 3
() -> leq([a, y]) -> 3
() -> leq([b, b]) -> 3
() -> leqnat([z, s(nn2)]) -> 3
() -> leqnat([z, z]) -> 3
(insert([x, l, _jj]) /\ length([_jj, _kj]) /\ length([l, _ij])) -> leqnat([_ij, _kj]) -> 1
(insert([x, z, _zi]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _zi)]) -> 4
(length([ll, _ej])) -> length([cons(x, ll), s(_ej)]) -> 4
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 4
(leq([b, a])) -> BOT -> 2
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 4
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 2
(leqnat([s(nn1), z])) -> BOT -> 2
}
Sat witness: Found: ((insert([x, z, _zi]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _zi)]), {
_zi -> cons(b, nil)  ;  x -> b  ;  y -> a  ;  z -> nil
})

-------------------------------------------
Step 10, which took 0.011053 s (model generation: 0.010634,  model checking: 0.000419):

Model:
|_
{
insert -> 
{{{
Q={q_gen_2250, q_gen_2251, q_gen_2252, q_gen_2255, q_gen_2256},
Q_f={q_gen_2250},
Delta=
{
<nil>() -> q_gen_2251
<b>() -> q_gen_2252
<nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2255
<a, a>() -> q_gen_2256
<b, b>() -> q_gen_2256
<b, cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2250
<b, nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2250
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_2249, q_gen_2258, q_gen_2259},
Q_f={q_gen_2249},
Delta=
{
<nil>() -> q_gen_2258
<cons, s>(q_gen_2259, q_gen_2258) -> q_gen_2249
<nil, z>() -> q_gen_2249
<b, z>() -> q_gen_2259
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_2247},
Q_f={q_gen_2247},
Delta=
{
<a, b>() -> q_gen_2247
<b, a>() -> q_gen_2247
<b, b>() -> q_gen_2247
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  leqnat -> 
{{{
Q={q_gen_2244, q_gen_2246},
Q_f={q_gen_2244},
Delta=
{
<z>() -> q_gen_2246
<s, s>(q_gen_2244) -> q_gen_2244
<z, s>(q_gen_2246) -> q_gen_2244
<z, z>() -> q_gen_2244
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 3
() -> length([nil, z]) -> 3
() -> leq([a, y]) -> 3
() -> leq([b, b]) -> 3
() -> leqnat([z, s(nn2)]) -> 3
() -> leqnat([z, z]) -> 3
(insert([x, l, _jj]) /\ length([_jj, _kj]) /\ length([l, _ij])) -> leqnat([_ij, _kj]) -> 2
(insert([x, z, _zi]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _zi)]) -> 4
(length([ll, _ej])) -> length([cons(x, ll), s(_ej)]) -> 4
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 4
(leq([b, a])) -> BOT -> 5
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 4
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 3
(leqnat([s(nn1), z])) -> BOT -> 3
}
Sat witness: Found: ((leq([b, a])) -> BOT, {

})

-------------------------------------------
Step 11, which took 0.015635 s (model generation: 0.015202,  model checking: 0.000433):

Model:
|_
{
insert -> 
{{{
Q={q_gen_2250, q_gen_2251, q_gen_2252, q_gen_2255, q_gen_2256},
Q_f={q_gen_2250},
Delta=
{
<nil>() -> q_gen_2251
<b>() -> q_gen_2252
<nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2255
<a, a>() -> q_gen_2256
<b, b>() -> q_gen_2256
<b, cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2250
<b, nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2250
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_2249, q_gen_2258, q_gen_2259},
Q_f={q_gen_2249},
Delta=
{
<nil>() -> q_gen_2258
<cons, s>(q_gen_2259, q_gen_2258) -> q_gen_2249
<nil, z>() -> q_gen_2249
<b, z>() -> q_gen_2259
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_2247, q_gen_2260},
Q_f={q_gen_2247},
Delta=
{
<a, b>() -> q_gen_2247
<b, b>() -> q_gen_2247
<b, a>() -> q_gen_2260
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  leqnat -> 
{{{
Q={q_gen_2244, q_gen_2246},
Q_f={q_gen_2244},
Delta=
{
<z>() -> q_gen_2246
<s, s>(q_gen_2244) -> q_gen_2244
<z, s>(q_gen_2246) -> q_gen_2244
<z, z>() -> q_gen_2244
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 3
() -> length([nil, z]) -> 3
() -> leq([a, y]) -> 3
() -> leq([b, b]) -> 3
() -> leqnat([z, s(nn2)]) -> 6
() -> leqnat([z, z]) -> 4
(insert([x, l, _jj]) /\ length([_jj, _kj]) /\ length([l, _ij])) -> leqnat([_ij, _kj]) -> 3
(insert([x, z, _zi]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _zi)]) -> 4
(length([ll, _ej])) -> length([cons(x, ll), s(_ej)]) -> 4
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 4
(leq([b, a])) -> BOT -> 5
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 4
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 4
(leqnat([s(nn1), z])) -> BOT -> 4
}
Sat witness: Found: (() -> leqnat([z, s(nn2)]), {
nn2 -> s(z)
})

-------------------------------------------
Step 12, which took 0.012572 s (model generation: 0.012281,  model checking: 0.000291):

Model:
|_
{
insert -> 
{{{
Q={q_gen_2250, q_gen_2251, q_gen_2252, q_gen_2255, q_gen_2256},
Q_f={q_gen_2250},
Delta=
{
<nil>() -> q_gen_2251
<b>() -> q_gen_2252
<nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2255
<a, a>() -> q_gen_2256
<b, b>() -> q_gen_2256
<b, cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2250
<b, nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2250
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_2249, q_gen_2258, q_gen_2259},
Q_f={q_gen_2249},
Delta=
{
<nil>() -> q_gen_2258
<cons, s>(q_gen_2259, q_gen_2258) -> q_gen_2249
<nil, z>() -> q_gen_2249
<b, z>() -> q_gen_2259
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_2247, q_gen_2260},
Q_f={q_gen_2247},
Delta=
{
<a, b>() -> q_gen_2247
<b, b>() -> q_gen_2247
<b, a>() -> q_gen_2260
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  leqnat -> 
{{{
Q={q_gen_2244, q_gen_2246},
Q_f={q_gen_2244},
Delta=
{
<s>(q_gen_2246) -> q_gen_2246
<z>() -> q_gen_2246
<s, s>(q_gen_2244) -> q_gen_2244
<z, s>(q_gen_2246) -> q_gen_2244
<z, z>() -> q_gen_2244
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 3
() -> length([nil, z]) -> 3
() -> leq([a, y]) -> 6
() -> leq([b, b]) -> 4
() -> leqnat([z, s(nn2)]) -> 6
() -> leqnat([z, z]) -> 4
(insert([x, l, _jj]) /\ length([_jj, _kj]) /\ length([l, _ij])) -> leqnat([_ij, _kj]) -> 4
(insert([x, z, _zi]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _zi)]) -> 4
(length([ll, _ej])) -> length([cons(x, ll), s(_ej)]) -> 4
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 4
(leq([b, a])) -> BOT -> 5
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 4
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 4
(leqnat([s(nn1), z])) -> BOT -> 4
}
Sat witness: Found: (() -> leq([a, y]), {
y -> a
})

-------------------------------------------
Step 13, which took 0.011155 s (model generation: 0.010791,  model checking: 0.000364):

Model:
|_
{
insert -> 
{{{
Q={q_gen_2250, q_gen_2251, q_gen_2252, q_gen_2255, q_gen_2256},
Q_f={q_gen_2250},
Delta=
{
<nil>() -> q_gen_2251
<b>() -> q_gen_2252
<nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2255
<a, a>() -> q_gen_2256
<b, b>() -> q_gen_2256
<b, cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2250
<b, nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2250
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_2249, q_gen_2258, q_gen_2259},
Q_f={q_gen_2249},
Delta=
{
<nil>() -> q_gen_2258
<cons, s>(q_gen_2259, q_gen_2258) -> q_gen_2249
<nil, z>() -> q_gen_2249
<b, z>() -> q_gen_2259
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_2247, q_gen_2260},
Q_f={q_gen_2247},
Delta=
{
<a, a>() -> q_gen_2247
<a, b>() -> q_gen_2247
<b, b>() -> q_gen_2247
<b, a>() -> q_gen_2260
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  leqnat -> 
{{{
Q={q_gen_2244, q_gen_2246},
Q_f={q_gen_2244},
Delta=
{
<s>(q_gen_2246) -> q_gen_2246
<z>() -> q_gen_2246
<s, s>(q_gen_2244) -> q_gen_2244
<z, s>(q_gen_2246) -> q_gen_2244
<z, z>() -> q_gen_2244
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 6
() -> length([nil, z]) -> 4
() -> leq([a, y]) -> 6
() -> leq([b, b]) -> 4
() -> leqnat([z, s(nn2)]) -> 6
() -> leqnat([z, z]) -> 4
(insert([x, l, _jj]) /\ length([_jj, _kj]) /\ length([l, _ij])) -> leqnat([_ij, _kj]) -> 4
(insert([x, z, _zi]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _zi)]) -> 4
(length([ll, _ej])) -> length([cons(x, ll), s(_ej)]) -> 4
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 4
(leq([b, a])) -> BOT -> 5
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 4
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 4
(leqnat([s(nn1), z])) -> BOT -> 4
}
Sat witness: Found: (() -> insert([x, nil, cons(x, nil)]), {
x -> a
})

-------------------------------------------
Step 14, which took 0.015156 s (model generation: 0.014259,  model checking: 0.000897):

Model:
|_
{
insert -> 
{{{
Q={q_gen_2250, q_gen_2251, q_gen_2252, q_gen_2255, q_gen_2256},
Q_f={q_gen_2250},
Delta=
{
<nil>() -> q_gen_2251
<a>() -> q_gen_2252
<b>() -> q_gen_2252
<nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2255
<a, a>() -> q_gen_2256
<b, b>() -> q_gen_2256
<a, nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2250
<b, cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2250
<b, nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2250
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_2249, q_gen_2258, q_gen_2259},
Q_f={q_gen_2249},
Delta=
{
<nil>() -> q_gen_2258
<cons, s>(q_gen_2259, q_gen_2258) -> q_gen_2249
<nil, z>() -> q_gen_2249
<b, z>() -> q_gen_2259
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_2247, q_gen_2260},
Q_f={q_gen_2247},
Delta=
{
<a, a>() -> q_gen_2247
<a, b>() -> q_gen_2247
<b, b>() -> q_gen_2247
<b, a>() -> q_gen_2260
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  leqnat -> 
{{{
Q={q_gen_2244, q_gen_2246},
Q_f={q_gen_2244},
Delta=
{
<s>(q_gen_2246) -> q_gen_2246
<z>() -> q_gen_2246
<s, s>(q_gen_2244) -> q_gen_2244
<z, s>(q_gen_2246) -> q_gen_2244
<z, z>() -> q_gen_2244
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 6
() -> length([nil, z]) -> 4
() -> leq([a, y]) -> 6
() -> leq([b, b]) -> 4
() -> leqnat([z, s(nn2)]) -> 6
() -> leqnat([z, z]) -> 4
(insert([x, l, _jj]) /\ length([_jj, _kj]) /\ length([l, _ij])) -> leqnat([_ij, _kj]) -> 4
(insert([x, z, _zi]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _zi)]) -> 4
(length([ll, _ej])) -> length([cons(x, ll), s(_ej)]) -> 4
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 7
(leq([b, a])) -> BOT -> 5
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 5
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 5
(leqnat([s(nn1), z])) -> BOT -> 5
}
Sat witness: Found: ((leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]), {
x -> a  ;  y -> b  ;  z -> nil
})

-------------------------------------------
Step 15, which took 0.014001 s (model generation: 0.013824,  model checking: 0.000177):

Model:
|_
{
insert -> 
{{{
Q={q_gen_2250, q_gen_2251, q_gen_2252, q_gen_2255, q_gen_2256},
Q_f={q_gen_2250},
Delta=
{
<nil>() -> q_gen_2251
<a>() -> q_gen_2252
<b>() -> q_gen_2252
<nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2255
<a, a>() -> q_gen_2256
<b, a>() -> q_gen_2256
<b, b>() -> q_gen_2256
<a, cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2250
<a, nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2250
<b, cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2250
<b, nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2250
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_2249, q_gen_2258, q_gen_2259},
Q_f={q_gen_2249},
Delta=
{
<nil>() -> q_gen_2258
<cons, s>(q_gen_2259, q_gen_2258) -> q_gen_2249
<nil, z>() -> q_gen_2249
<b, z>() -> q_gen_2259
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_2247, q_gen_2260},
Q_f={q_gen_2247},
Delta=
{
<a, a>() -> q_gen_2247
<a, b>() -> q_gen_2247
<b, b>() -> q_gen_2247
<b, a>() -> q_gen_2260
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  leqnat -> 
{{{
Q={q_gen_2244, q_gen_2246},
Q_f={q_gen_2244},
Delta=
{
<s>(q_gen_2246) -> q_gen_2246
<z>() -> q_gen_2246
<s, s>(q_gen_2244) -> q_gen_2244
<z, s>(q_gen_2246) -> q_gen_2244
<z, z>() -> q_gen_2244
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 6
() -> length([nil, z]) -> 4
() -> leq([a, y]) -> 6
() -> leq([b, b]) -> 4
() -> leqnat([z, s(nn2)]) -> 6
() -> leqnat([z, z]) -> 4
(insert([x, l, _jj]) /\ length([_jj, _kj]) /\ length([l, _ij])) -> leqnat([_ij, _kj]) -> 4
(insert([x, z, _zi]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _zi)]) -> 4
(length([ll, _ej])) -> length([cons(x, ll), s(_ej)]) -> 7
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 7
(leq([b, a])) -> BOT -> 5
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 5
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 5
(leqnat([s(nn1), z])) -> BOT -> 5
}
Sat witness: Found: ((length([ll, _ej])) -> length([cons(x, ll), s(_ej)]), {
_ej -> z  ;  ll -> nil  ;  x -> a
})

-------------------------------------------
Step 16, which took 0.013300 s (model generation: 0.012776,  model checking: 0.000524):

Model:
|_
{
insert -> 
{{{
Q={q_gen_2250, q_gen_2251, q_gen_2252, q_gen_2255, q_gen_2256},
Q_f={q_gen_2250},
Delta=
{
<nil>() -> q_gen_2251
<a>() -> q_gen_2252
<b>() -> q_gen_2252
<nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2255
<a, a>() -> q_gen_2256
<b, a>() -> q_gen_2256
<b, b>() -> q_gen_2256
<a, cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2250
<a, nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2250
<b, cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2250
<b, nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2250
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_2249, q_gen_2258, q_gen_2259},
Q_f={q_gen_2249},
Delta=
{
<nil>() -> q_gen_2258
<cons, s>(q_gen_2259, q_gen_2258) -> q_gen_2249
<nil, z>() -> q_gen_2249
<a, z>() -> q_gen_2259
<b, z>() -> q_gen_2259
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_2247, q_gen_2260},
Q_f={q_gen_2247},
Delta=
{
<a, a>() -> q_gen_2247
<a, b>() -> q_gen_2247
<b, b>() -> q_gen_2247
<b, a>() -> q_gen_2260
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  leqnat -> 
{{{
Q={q_gen_2244, q_gen_2246},
Q_f={q_gen_2244},
Delta=
{
<s>(q_gen_2246) -> q_gen_2246
<z>() -> q_gen_2246
<s, s>(q_gen_2244) -> q_gen_2244
<z, s>(q_gen_2246) -> q_gen_2244
<z, z>() -> q_gen_2244
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 6
() -> length([nil, z]) -> 4
() -> leq([a, y]) -> 6
() -> leq([b, b]) -> 4
() -> leqnat([z, s(nn2)]) -> 6
() -> leqnat([z, z]) -> 4
(insert([x, l, _jj]) /\ length([_jj, _kj]) /\ length([l, _ij])) -> leqnat([_ij, _kj]) -> 4
(insert([x, z, _zi]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _zi)]) -> 7
(length([ll, _ej])) -> length([cons(x, ll), s(_ej)]) -> 7
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 7
(leq([b, a])) -> BOT -> 5
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 5
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 5
(leqnat([s(nn1), z])) -> BOT -> 5
}
Sat witness: Found: ((insert([x, z, _zi]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _zi)]), {
_zi -> cons(a, cons(a, nil))  ;  x -> b  ;  y -> a  ;  z -> cons(a, nil)
})

-------------------------------------------
Step 17, which took 0.013264 s (model generation: 0.012278,  model checking: 0.000986):

Model:
|_
{
insert -> 
{{{
Q={q_gen_2250, q_gen_2251, q_gen_2252, q_gen_2255, q_gen_2256},
Q_f={q_gen_2250},
Delta=
{
<nil>() -> q_gen_2251
<a>() -> q_gen_2252
<b>() -> q_gen_2252
<cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2255
<nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2255
<a, a>() -> q_gen_2256
<b, a>() -> q_gen_2256
<b, b>() -> q_gen_2256
<a, cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2250
<a, nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2250
<b, cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2250
<b, nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2250
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_2249, q_gen_2258, q_gen_2259},
Q_f={q_gen_2249},
Delta=
{
<nil>() -> q_gen_2258
<cons, s>(q_gen_2259, q_gen_2258) -> q_gen_2249
<nil, z>() -> q_gen_2249
<a, z>() -> q_gen_2259
<b, z>() -> q_gen_2259
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_2247, q_gen_2260},
Q_f={q_gen_2247},
Delta=
{
<a, a>() -> q_gen_2247
<a, b>() -> q_gen_2247
<b, b>() -> q_gen_2247
<b, a>() -> q_gen_2260
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  leqnat -> 
{{{
Q={q_gen_2244, q_gen_2246},
Q_f={q_gen_2244},
Delta=
{
<s>(q_gen_2246) -> q_gen_2246
<z>() -> q_gen_2246
<s, s>(q_gen_2244) -> q_gen_2244
<z, s>(q_gen_2246) -> q_gen_2244
<z, z>() -> q_gen_2244
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 7
() -> length([nil, z]) -> 5
() -> leq([a, y]) -> 7
() -> leq([b, b]) -> 5
() -> leqnat([z, s(nn2)]) -> 7
() -> leqnat([z, z]) -> 5
(insert([x, l, _jj]) /\ length([_jj, _kj]) /\ length([l, _ij])) -> leqnat([_ij, _kj]) -> 5
(insert([x, z, _zi]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _zi)]) -> 7
(length([ll, _ej])) -> length([cons(x, ll), s(_ej)]) -> 7
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 10
(leq([b, a])) -> BOT -> 6
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 6
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 6
(leqnat([s(nn1), z])) -> BOT -> 6
}
Sat witness: Found: ((leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]), {
x -> b  ;  y -> b  ;  z -> cons(a, nil)
})

-------------------------------------------
Step 18, which took 0.013079 s (model generation: 0.012386,  model checking: 0.000693):

Model:
|_
{
insert -> 
{{{
Q={q_gen_2250, q_gen_2251, q_gen_2252, q_gen_2255, q_gen_2256},
Q_f={q_gen_2250},
Delta=
{
<nil>() -> q_gen_2251
<a>() -> q_gen_2252
<b>() -> q_gen_2252
<cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2255
<nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2255
<a, a>() -> q_gen_2256
<a, b>() -> q_gen_2256
<b, a>() -> q_gen_2256
<b, b>() -> q_gen_2256
<a, cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2250
<a, nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2250
<b, cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2250
<b, nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2250
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_2249, q_gen_2258, q_gen_2259},
Q_f={q_gen_2249},
Delta=
{
<nil>() -> q_gen_2258
<cons, s>(q_gen_2259, q_gen_2258) -> q_gen_2249
<nil, z>() -> q_gen_2249
<a, z>() -> q_gen_2259
<b, z>() -> q_gen_2259
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_2247, q_gen_2260},
Q_f={q_gen_2247},
Delta=
{
<a, a>() -> q_gen_2247
<a, b>() -> q_gen_2247
<b, b>() -> q_gen_2247
<b, a>() -> q_gen_2260
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  leqnat -> 
{{{
Q={q_gen_2244, q_gen_2246},
Q_f={q_gen_2244},
Delta=
{
<s>(q_gen_2246) -> q_gen_2246
<z>() -> q_gen_2246
<s, s>(q_gen_2244) -> q_gen_2244
<z, s>(q_gen_2246) -> q_gen_2244
<z, z>() -> q_gen_2244
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 7
() -> length([nil, z]) -> 6
() -> leq([a, y]) -> 7
() -> leq([b, b]) -> 6
() -> leqnat([z, s(nn2)]) -> 7
() -> leqnat([z, z]) -> 6
(insert([x, l, _jj]) /\ length([_jj, _kj]) /\ length([l, _ij])) -> leqnat([_ij, _kj]) -> 6
(insert([x, z, _zi]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _zi)]) -> 7
(length([ll, _ej])) -> length([cons(x, ll), s(_ej)]) -> 10
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 10
(leq([b, a])) -> BOT -> 7
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 7
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 7
(leqnat([s(nn1), z])) -> BOT -> 7
}
Sat witness: Found: ((length([ll, _ej])) -> length([cons(x, ll), s(_ej)]), {
_ej -> s(z)  ;  ll -> cons(b, nil)  ;  x -> b
})

-------------------------------------------
Step 19, which took 0.014728 s (model generation: 0.014499,  model checking: 0.000229):

Model:
|_
{
insert -> 
{{{
Q={q_gen_2250, q_gen_2251, q_gen_2252, q_gen_2255, q_gen_2256},
Q_f={q_gen_2250},
Delta=
{
<nil>() -> q_gen_2251
<a>() -> q_gen_2252
<b>() -> q_gen_2252
<cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2255
<nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2255
<a, a>() -> q_gen_2256
<a, b>() -> q_gen_2256
<b, a>() -> q_gen_2256
<b, b>() -> q_gen_2256
<a, cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2250
<a, nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2250
<b, cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2250
<b, nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2250
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_2249, q_gen_2258, q_gen_2259, q_gen_2281, q_gen_2283},
Q_f={q_gen_2249},
Delta=
{
<cons>(q_gen_2281, q_gen_2258) -> q_gen_2258
<nil>() -> q_gen_2258
<b>() -> q_gen_2281
<z>() -> q_gen_2283
<cons, s>(q_gen_2259, q_gen_2258) -> q_gen_2249
<nil, z>() -> q_gen_2249
<a, z>() -> q_gen_2259
<b, s>(q_gen_2283) -> q_gen_2259
<b, z>() -> q_gen_2259
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_2247, q_gen_2260},
Q_f={q_gen_2247},
Delta=
{
<a, a>() -> q_gen_2247
<a, b>() -> q_gen_2247
<b, b>() -> q_gen_2247
<b, a>() -> q_gen_2260
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  leqnat -> 
{{{
Q={q_gen_2244, q_gen_2246},
Q_f={q_gen_2244},
Delta=
{
<s>(q_gen_2246) -> q_gen_2246
<z>() -> q_gen_2246
<s, s>(q_gen_2244) -> q_gen_2244
<z, s>(q_gen_2246) -> q_gen_2244
<z, z>() -> q_gen_2244
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 7
() -> length([nil, z]) -> 6
() -> leq([a, y]) -> 7
() -> leq([b, b]) -> 6
() -> leqnat([z, s(nn2)]) -> 7
() -> leqnat([z, z]) -> 6
(insert([x, l, _jj]) /\ length([_jj, _kj]) /\ length([l, _ij])) -> leqnat([_ij, _kj]) -> 9
(insert([x, z, _zi]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _zi)]) -> 7
(length([ll, _ej])) -> length([cons(x, ll), s(_ej)]) -> 10
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 10
(leq([b, a])) -> BOT -> 7
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 7
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 7
(leqnat([s(nn1), z])) -> BOT -> 7
}
Sat witness: Found: ((insert([x, l, _jj]) /\ length([_jj, _kj]) /\ length([l, _ij])) -> leqnat([_ij, _kj]), {
_ij -> s(s(z))  ;  _jj -> cons(a, cons(b, nil))  ;  _kj -> s(z)  ;  l -> cons(b, nil)  ;  x -> b
})

-------------------------------------------
Step 20, which took 0.015908 s (model generation: 0.015662,  model checking: 0.000246):

Model:
|_
{
insert -> 
{{{
Q={q_gen_2250, q_gen_2251, q_gen_2252, q_gen_2255, q_gen_2256},
Q_f={q_gen_2250},
Delta=
{
<nil>() -> q_gen_2251
<a>() -> q_gen_2252
<b>() -> q_gen_2252
<cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2255
<nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2255
<a, a>() -> q_gen_2256
<a, b>() -> q_gen_2256
<b, a>() -> q_gen_2256
<b, b>() -> q_gen_2256
<a, cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2250
<a, nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2250
<b, cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2250
<b, nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2250
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_2249, q_gen_2258, q_gen_2259, q_gen_2281, q_gen_2283},
Q_f={q_gen_2249},
Delta=
{
<cons>(q_gen_2281, q_gen_2258) -> q_gen_2258
<nil>() -> q_gen_2258
<b>() -> q_gen_2281
<z>() -> q_gen_2283
<cons, s>(q_gen_2259, q_gen_2258) -> q_gen_2249
<nil, z>() -> q_gen_2249
<a, z>() -> q_gen_2259
<b, s>(q_gen_2283) -> q_gen_2259
<b, z>() -> q_gen_2259
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_2247, q_gen_2260},
Q_f={q_gen_2247},
Delta=
{
<a, a>() -> q_gen_2247
<a, b>() -> q_gen_2247
<b, b>() -> q_gen_2247
<b, a>() -> q_gen_2260
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  leqnat -> 
{{{
Q={q_gen_2244, q_gen_2246},
Q_f={q_gen_2244},
Delta=
{
<s>(q_gen_2246) -> q_gen_2246
<z>() -> q_gen_2246
<s, s>(q_gen_2244) -> q_gen_2244
<s, z>(q_gen_2246) -> q_gen_2244
<z, s>(q_gen_2246) -> q_gen_2244
<z, z>() -> q_gen_2244
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 7
() -> length([nil, z]) -> 7
() -> leq([a, y]) -> 7
() -> leq([b, b]) -> 7
() -> leqnat([z, s(nn2)]) -> 7
() -> leqnat([z, z]) -> 7
(insert([x, l, _jj]) /\ length([_jj, _kj]) /\ length([l, _ij])) -> leqnat([_ij, _kj]) -> 9
(insert([x, z, _zi]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _zi)]) -> 7
(length([ll, _ej])) -> length([cons(x, ll), s(_ej)]) -> 10
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 10
(leq([b, a])) -> BOT -> 7
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 7
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 7
(leqnat([s(nn1), z])) -> BOT -> 10
}
Sat witness: Found: ((leqnat([s(nn1), z])) -> BOT, {
nn1 -> z
})

-------------------------------------------
Step 21, which took 0.017269 s (model generation: 0.017174,  model checking: 0.000095):

Model:
|_
{
insert -> 
{{{
Q={q_gen_2250, q_gen_2251, q_gen_2252, q_gen_2255, q_gen_2256},
Q_f={q_gen_2250},
Delta=
{
<nil>() -> q_gen_2251
<a>() -> q_gen_2252
<b>() -> q_gen_2252
<cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2255
<nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2255
<a, a>() -> q_gen_2256
<a, b>() -> q_gen_2256
<b, a>() -> q_gen_2256
<b, b>() -> q_gen_2256
<a, cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2250
<a, nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2250
<b, cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2250
<b, nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2250
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_2249, q_gen_2258, q_gen_2259, q_gen_2281, q_gen_2283},
Q_f={q_gen_2249},
Delta=
{
<cons>(q_gen_2281, q_gen_2258) -> q_gen_2258
<nil>() -> q_gen_2258
<b>() -> q_gen_2281
<z>() -> q_gen_2283
<cons, s>(q_gen_2259, q_gen_2258) -> q_gen_2249
<nil, z>() -> q_gen_2249
<a, z>() -> q_gen_2259
<b, s>(q_gen_2283) -> q_gen_2259
<b, z>() -> q_gen_2259
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_2247, q_gen_2260},
Q_f={q_gen_2247},
Delta=
{
<a, a>() -> q_gen_2247
<a, b>() -> q_gen_2247
<b, b>() -> q_gen_2247
<b, a>() -> q_gen_2260
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  leqnat -> 
{{{
Q={q_gen_2244, q_gen_2246, q_gen_2288},
Q_f={q_gen_2244},
Delta=
{
<s>(q_gen_2246) -> q_gen_2246
<z>() -> q_gen_2246
<s, s>(q_gen_2244) -> q_gen_2244
<s, s>(q_gen_2288) -> q_gen_2244
<z, s>(q_gen_2246) -> q_gen_2244
<z, z>() -> q_gen_2244
<s, z>(q_gen_2246) -> q_gen_2288
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 7
() -> length([nil, z]) -> 7
() -> leq([a, y]) -> 7
() -> leq([b, b]) -> 7
() -> leqnat([z, s(nn2)]) -> 7
() -> leqnat([z, z]) -> 7
(insert([x, l, _jj]) /\ length([_jj, _kj]) /\ length([l, _ij])) -> leqnat([_ij, _kj]) -> 9
(insert([x, z, _zi]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _zi)]) -> 7
(length([ll, _ej])) -> length([cons(x, ll), s(_ej)]) -> 10
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 10
(leq([b, a])) -> BOT -> 7
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 7
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 10
(leqnat([s(nn1), z])) -> BOT -> 10
}
Sat witness: Found: ((leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]), {
nn1 -> s(z)  ;  nn2 -> z
})

-------------------------------------------
Step 22, which took 0.022480 s (model generation: 0.021025,  model checking: 0.001455):

Model:
|_
{
insert -> 
{{{
Q={q_gen_2250, q_gen_2251, q_gen_2252, q_gen_2255, q_gen_2256, q_gen_2269, q_gen_2284},
Q_f={q_gen_2250},
Delta=
{
<nil>() -> q_gen_2251
<a>() -> q_gen_2252
<b>() -> q_gen_2252
<cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2255
<cons, cons>(q_gen_2269, q_gen_2255) -> q_gen_2255
<nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2255
<a, a>() -> q_gen_2256
<b, b>() -> q_gen_2256
<a, b>() -> q_gen_2269
<b, a>() -> q_gen_2269
<a, cons, cons>(q_gen_2269, q_gen_2255) -> q_gen_2250
<a, nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2250
<b, cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2250
<b, nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2250
<b, cons, cons>(q_gen_2269, q_gen_2255) -> q_gen_2284
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_2249, q_gen_2258, q_gen_2259, q_gen_2281, q_gen_2283},
Q_f={q_gen_2249},
Delta=
{
<cons>(q_gen_2281, q_gen_2258) -> q_gen_2258
<nil>() -> q_gen_2258
<b>() -> q_gen_2281
<z>() -> q_gen_2283
<cons, s>(q_gen_2259, q_gen_2258) -> q_gen_2249
<nil, z>() -> q_gen_2249
<a, z>() -> q_gen_2259
<b, s>(q_gen_2283) -> q_gen_2259
<b, z>() -> q_gen_2259
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_2247, q_gen_2260},
Q_f={q_gen_2247},
Delta=
{
<a, a>() -> q_gen_2247
<a, b>() -> q_gen_2247
<b, b>() -> q_gen_2247
<b, a>() -> q_gen_2260
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  leqnat -> 
{{{
Q={q_gen_2244, q_gen_2246, q_gen_2287},
Q_f={q_gen_2244},
Delta=
{
<s>(q_gen_2246) -> q_gen_2246
<z>() -> q_gen_2246
<s, s>(q_gen_2244) -> q_gen_2244
<z, s>(q_gen_2246) -> q_gen_2244
<z, z>() -> q_gen_2244
<s, s>(q_gen_2287) -> q_gen_2287
<s, z>(q_gen_2246) -> q_gen_2287
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 8
() -> length([nil, z]) -> 8
() -> leq([a, y]) -> 8
() -> leq([b, b]) -> 8
() -> leqnat([z, s(nn2)]) -> 8
() -> leqnat([z, z]) -> 8
(insert([x, l, _jj]) /\ length([_jj, _kj]) /\ length([l, _ij])) -> leqnat([_ij, _kj]) -> 12
(insert([x, z, _zi]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _zi)]) -> 8
(length([ll, _ej])) -> length([cons(x, ll), s(_ej)]) -> 10
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 10
(leq([b, a])) -> BOT -> 8
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 8
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 10
(leqnat([s(nn1), z])) -> BOT -> 10
}
Sat witness: Found: ((insert([x, l, _jj]) /\ length([_jj, _kj]) /\ length([l, _ij])) -> leqnat([_ij, _kj]), {
_ij -> s(s(z))  ;  _jj -> cons(b, cons(b, nil))  ;  _kj -> s(z)  ;  l -> cons(b, nil)  ;  x -> b
})

-------------------------------------------
Step 23, which took 0.018310 s (model generation: 0.016381,  model checking: 0.001929):

Model:
|_
{
insert -> 
{{{
Q={q_gen_2250, q_gen_2251, q_gen_2252, q_gen_2255, q_gen_2256},
Q_f={q_gen_2250},
Delta=
{
<nil>() -> q_gen_2251
<a>() -> q_gen_2252
<b>() -> q_gen_2252
<cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2255
<nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2255
<a, a>() -> q_gen_2256
<a, b>() -> q_gen_2256
<b, a>() -> q_gen_2256
<b, b>() -> q_gen_2256
<a, cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2250
<a, nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2250
<b, cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2250
<b, nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2250
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_2249, q_gen_2258, q_gen_2259, q_gen_2280, q_gen_2281, q_gen_2282, q_gen_2283, q_gen_2285},
Q_f={q_gen_2249},
Delta=
{
<nil>() -> q_gen_2258
<cons>(q_gen_2281, q_gen_2258) -> q_gen_2280
<b>() -> q_gen_2281
<z>() -> q_gen_2283
<cons, s>(q_gen_2259, q_gen_2258) -> q_gen_2249
<cons, s>(q_gen_2282, q_gen_2280) -> q_gen_2249
<nil, z>() -> q_gen_2249
<a, z>() -> q_gen_2259
<b, z>() -> q_gen_2259
<b, s>(q_gen_2283) -> q_gen_2282
<cons, s>(q_gen_2259, q_gen_2280) -> q_gen_2285
<cons, s>(q_gen_2282, q_gen_2258) -> q_gen_2285
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_2247, q_gen_2260},
Q_f={q_gen_2247},
Delta=
{
<a, a>() -> q_gen_2247
<a, b>() -> q_gen_2247
<b, b>() -> q_gen_2247
<b, a>() -> q_gen_2260
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  leqnat -> 
{{{
Q={q_gen_2244, q_gen_2246, q_gen_2287},
Q_f={q_gen_2244},
Delta=
{
<s>(q_gen_2246) -> q_gen_2246
<z>() -> q_gen_2246
<s, s>(q_gen_2244) -> q_gen_2244
<z, s>(q_gen_2246) -> q_gen_2244
<z, z>() -> q_gen_2244
<s, s>(q_gen_2287) -> q_gen_2287
<s, z>(q_gen_2246) -> q_gen_2287
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 9
() -> length([nil, z]) -> 9
() -> leq([a, y]) -> 9
() -> leq([b, b]) -> 9
() -> leqnat([z, s(nn2)]) -> 9
() -> leqnat([z, z]) -> 9
(insert([x, l, _jj]) /\ length([_jj, _kj]) /\ length([l, _ij])) -> leqnat([_ij, _kj]) -> 12
(insert([x, z, _zi]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _zi)]) -> 9
(length([ll, _ej])) -> length([cons(x, ll), s(_ej)]) -> 13
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 11
(leq([b, a])) -> BOT -> 9
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 9
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 11
(leqnat([s(nn1), z])) -> BOT -> 11
}
Sat witness: Found: ((length([ll, _ej])) -> length([cons(x, ll), s(_ej)]), {
_ej -> s(z)  ;  ll -> cons(b, nil)  ;  x -> a
})

-------------------------------------------
Step 24, which took 0.020257 s (model generation: 0.017698,  model checking: 0.002559):

Model:
|_
{
insert -> 
{{{
Q={q_gen_2250, q_gen_2251, q_gen_2252, q_gen_2255, q_gen_2256},
Q_f={q_gen_2250},
Delta=
{
<nil>() -> q_gen_2251
<a>() -> q_gen_2252
<b>() -> q_gen_2252
<cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2255
<nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2255
<a, a>() -> q_gen_2256
<a, b>() -> q_gen_2256
<b, a>() -> q_gen_2256
<b, b>() -> q_gen_2256
<a, cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2250
<a, nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2250
<b, cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2250
<b, nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2250
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_2249, q_gen_2258, q_gen_2259, q_gen_2280, q_gen_2281, q_gen_2282, q_gen_2283, q_gen_2285},
Q_f={q_gen_2249},
Delta=
{
<nil>() -> q_gen_2258
<cons>(q_gen_2281, q_gen_2258) -> q_gen_2280
<b>() -> q_gen_2281
<z>() -> q_gen_2283
<cons, s>(q_gen_2259, q_gen_2258) -> q_gen_2249
<cons, s>(q_gen_2282, q_gen_2258) -> q_gen_2249
<cons, s>(q_gen_2282, q_gen_2280) -> q_gen_2249
<nil, z>() -> q_gen_2249
<a, z>() -> q_gen_2259
<b, z>() -> q_gen_2259
<a, s>(q_gen_2283) -> q_gen_2282
<b, s>(q_gen_2283) -> q_gen_2282
<cons, s>(q_gen_2259, q_gen_2280) -> q_gen_2285
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_2247, q_gen_2260},
Q_f={q_gen_2247},
Delta=
{
<a, a>() -> q_gen_2247
<a, b>() -> q_gen_2247
<b, b>() -> q_gen_2247
<b, a>() -> q_gen_2260
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  leqnat -> 
{{{
Q={q_gen_2244, q_gen_2246, q_gen_2287},
Q_f={q_gen_2244},
Delta=
{
<s>(q_gen_2246) -> q_gen_2246
<z>() -> q_gen_2246
<s, s>(q_gen_2244) -> q_gen_2244
<z, s>(q_gen_2246) -> q_gen_2244
<z, z>() -> q_gen_2244
<s, s>(q_gen_2287) -> q_gen_2287
<s, z>(q_gen_2246) -> q_gen_2287
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 10
() -> length([nil, z]) -> 10
() -> leq([a, y]) -> 10
() -> leq([b, b]) -> 10
() -> leqnat([z, s(nn2)]) -> 10
() -> leqnat([z, z]) -> 10
(insert([x, l, _jj]) /\ length([_jj, _kj]) /\ length([l, _ij])) -> leqnat([_ij, _kj]) -> 13
(insert([x, z, _zi]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _zi)]) -> 10
(length([ll, _ej])) -> length([cons(x, ll), s(_ej)]) -> 16
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 12
(leq([b, a])) -> BOT -> 10
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 10
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 12
(leqnat([s(nn1), z])) -> BOT -> 12
}
Sat witness: Found: ((length([ll, _ej])) -> length([cons(x, ll), s(_ej)]), {
_ej -> s(s(z))  ;  ll -> cons(b, nil)  ;  x -> b
})

-------------------------------------------
Step 25, which took 0.023031 s (model generation: 0.021017,  model checking: 0.002014):

Model:
|_
{
insert -> 
{{{
Q={q_gen_2250, q_gen_2251, q_gen_2252, q_gen_2255, q_gen_2256},
Q_f={q_gen_2250},
Delta=
{
<nil>() -> q_gen_2251
<a>() -> q_gen_2252
<b>() -> q_gen_2252
<cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2255
<nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2255
<a, a>() -> q_gen_2256
<a, b>() -> q_gen_2256
<b, a>() -> q_gen_2256
<b, b>() -> q_gen_2256
<a, cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2250
<a, nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2250
<b, cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2250
<b, nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2250
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_2249, q_gen_2258, q_gen_2259, q_gen_2280, q_gen_2281, q_gen_2282, q_gen_2283, q_gen_2285},
Q_f={q_gen_2249},
Delta=
{
<nil>() -> q_gen_2258
<cons>(q_gen_2281, q_gen_2258) -> q_gen_2280
<b>() -> q_gen_2281
<s>(q_gen_2283) -> q_gen_2283
<z>() -> q_gen_2283
<cons, s>(q_gen_2259, q_gen_2258) -> q_gen_2249
<cons, s>(q_gen_2282, q_gen_2258) -> q_gen_2249
<cons, s>(q_gen_2282, q_gen_2280) -> q_gen_2249
<nil, z>() -> q_gen_2249
<a, z>() -> q_gen_2259
<b, z>() -> q_gen_2259
<a, s>(q_gen_2283) -> q_gen_2282
<b, s>(q_gen_2283) -> q_gen_2282
<cons, s>(q_gen_2259, q_gen_2280) -> q_gen_2285
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_2247, q_gen_2260},
Q_f={q_gen_2247},
Delta=
{
<a, a>() -> q_gen_2247
<a, b>() -> q_gen_2247
<b, b>() -> q_gen_2247
<b, a>() -> q_gen_2260
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  leqnat -> 
{{{
Q={q_gen_2244, q_gen_2246, q_gen_2287},
Q_f={q_gen_2244},
Delta=
{
<s>(q_gen_2246) -> q_gen_2246
<z>() -> q_gen_2246
<s, s>(q_gen_2244) -> q_gen_2244
<z, s>(q_gen_2246) -> q_gen_2244
<z, z>() -> q_gen_2244
<s, s>(q_gen_2287) -> q_gen_2287
<s, z>(q_gen_2246) -> q_gen_2287
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 11
() -> length([nil, z]) -> 11
() -> leq([a, y]) -> 11
() -> leq([b, b]) -> 11
() -> leqnat([z, s(nn2)]) -> 11
() -> leqnat([z, z]) -> 11
(insert([x, l, _jj]) /\ length([_jj, _kj]) /\ length([l, _ij])) -> leqnat([_ij, _kj]) -> 16
(insert([x, z, _zi]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _zi)]) -> 11
(length([ll, _ej])) -> length([cons(x, ll), s(_ej)]) -> 16
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 13
(leq([b, a])) -> BOT -> 11
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 11
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 13
(leqnat([s(nn1), z])) -> BOT -> 13
}
Sat witness: Found: ((insert([x, l, _jj]) /\ length([_jj, _kj]) /\ length([l, _ij])) -> leqnat([_ij, _kj]), {
_ij -> s(s(s(z)))  ;  _jj -> cons(b, cons(b, nil))  ;  _kj -> s(s(z))  ;  l -> cons(b, nil)  ;  x -> b
})

-------------------------------------------
Step 26, which took 0.028367 s (model generation: 0.026593,  model checking: 0.001774):

Model:
|_
{
insert -> 
{{{
Q={q_gen_2250, q_gen_2251, q_gen_2252, q_gen_2255, q_gen_2256},
Q_f={q_gen_2250},
Delta=
{
<nil>() -> q_gen_2251
<a>() -> q_gen_2252
<b>() -> q_gen_2252
<cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2255
<nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2255
<a, a>() -> q_gen_2256
<a, b>() -> q_gen_2256
<b, a>() -> q_gen_2256
<b, b>() -> q_gen_2256
<a, cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2250
<a, nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2250
<b, cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2250
<b, nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2250
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_2249, q_gen_2258, q_gen_2259, q_gen_2280, q_gen_2281, q_gen_2282, q_gen_2283, q_gen_2286},
Q_f={q_gen_2249},
Delta=
{
<nil>() -> q_gen_2258
<cons>(q_gen_2281, q_gen_2258) -> q_gen_2280
<b>() -> q_gen_2281
<s>(q_gen_2283) -> q_gen_2283
<z>() -> q_gen_2283
<cons, s>(q_gen_2259, q_gen_2258) -> q_gen_2249
<cons, s>(q_gen_2259, q_gen_2280) -> q_gen_2249
<cons, s>(q_gen_2282, q_gen_2280) -> q_gen_2249
<nil, z>() -> q_gen_2249
<a, s>(q_gen_2283) -> q_gen_2259
<a, z>() -> q_gen_2259
<b, z>() -> q_gen_2259
<b, s>(q_gen_2283) -> q_gen_2282
<cons, s>(q_gen_2282, q_gen_2258) -> q_gen_2286
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_2247, q_gen_2260},
Q_f={q_gen_2247},
Delta=
{
<a, a>() -> q_gen_2247
<a, b>() -> q_gen_2247
<b, b>() -> q_gen_2247
<b, a>() -> q_gen_2260
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  leqnat -> 
{{{
Q={q_gen_2244, q_gen_2246, q_gen_2287},
Q_f={q_gen_2244},
Delta=
{
<s>(q_gen_2246) -> q_gen_2246
<z>() -> q_gen_2246
<s, s>(q_gen_2244) -> q_gen_2244
<z, s>(q_gen_2246) -> q_gen_2244
<z, z>() -> q_gen_2244
<s, s>(q_gen_2287) -> q_gen_2287
<s, z>(q_gen_2246) -> q_gen_2287
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 12
() -> length([nil, z]) -> 12
() -> leq([a, y]) -> 12
() -> leq([b, b]) -> 12
() -> leqnat([z, s(nn2)]) -> 12
() -> leqnat([z, z]) -> 12
(insert([x, l, _jj]) /\ length([_jj, _kj]) /\ length([l, _ij])) -> leqnat([_ij, _kj]) -> 16
(insert([x, z, _zi]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _zi)]) -> 12
(length([ll, _ej])) -> length([cons(x, ll), s(_ej)]) -> 19
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 14
(leq([b, a])) -> BOT -> 12
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 12
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 14
(leqnat([s(nn1), z])) -> BOT -> 14
}
Sat witness: Found: ((length([ll, _ej])) -> length([cons(x, ll), s(_ej)]), {
_ej -> s(s(z))  ;  ll -> cons(b, cons(b, nil))  ;  x -> b
})

-------------------------------------------
Step 27, which took 0.024520 s (model generation: 0.022708,  model checking: 0.001812):

Model:
|_
{
insert -> 
{{{
Q={q_gen_2250, q_gen_2251, q_gen_2252, q_gen_2255, q_gen_2256},
Q_f={q_gen_2250},
Delta=
{
<nil>() -> q_gen_2251
<a>() -> q_gen_2252
<b>() -> q_gen_2252
<cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2255
<nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2255
<a, a>() -> q_gen_2256
<a, b>() -> q_gen_2256
<b, a>() -> q_gen_2256
<b, b>() -> q_gen_2256
<a, cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2250
<a, nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2250
<b, cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2250
<b, nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2250
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_2249, q_gen_2258, q_gen_2259, q_gen_2280, q_gen_2281, q_gen_2282, q_gen_2283, q_gen_2285},
Q_f={q_gen_2249},
Delta=
{
<nil>() -> q_gen_2258
<cons>(q_gen_2281, q_gen_2258) -> q_gen_2280
<cons>(q_gen_2281, q_gen_2280) -> q_gen_2280
<b>() -> q_gen_2281
<s>(q_gen_2283) -> q_gen_2283
<z>() -> q_gen_2283
<cons, s>(q_gen_2259, q_gen_2258) -> q_gen_2249
<cons, s>(q_gen_2282, q_gen_2280) -> q_gen_2249
<nil, z>() -> q_gen_2249
<a, z>() -> q_gen_2259
<b, z>() -> q_gen_2259
<a, s>(q_gen_2283) -> q_gen_2282
<b, s>(q_gen_2283) -> q_gen_2282
<cons, s>(q_gen_2259, q_gen_2280) -> q_gen_2285
<cons, s>(q_gen_2282, q_gen_2258) -> q_gen_2285
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_2247, q_gen_2260},
Q_f={q_gen_2247},
Delta=
{
<a, a>() -> q_gen_2247
<a, b>() -> q_gen_2247
<b, b>() -> q_gen_2247
<b, a>() -> q_gen_2260
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  leqnat -> 
{{{
Q={q_gen_2244, q_gen_2246, q_gen_2287},
Q_f={q_gen_2244},
Delta=
{
<s>(q_gen_2246) -> q_gen_2246
<z>() -> q_gen_2246
<s, s>(q_gen_2244) -> q_gen_2244
<z, s>(q_gen_2246) -> q_gen_2244
<z, z>() -> q_gen_2244
<s, s>(q_gen_2287) -> q_gen_2287
<s, z>(q_gen_2246) -> q_gen_2287
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 13
() -> length([nil, z]) -> 13
() -> leq([a, y]) -> 13
() -> leq([b, b]) -> 13
() -> leqnat([z, s(nn2)]) -> 13
() -> leqnat([z, z]) -> 13
(insert([x, l, _jj]) /\ length([_jj, _kj]) /\ length([l, _ij])) -> leqnat([_ij, _kj]) -> 19
(insert([x, z, _zi]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _zi)]) -> 13
(length([ll, _ej])) -> length([cons(x, ll), s(_ej)]) -> 19
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 15
(leq([b, a])) -> BOT -> 13
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 13
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 15
(leqnat([s(nn1), z])) -> BOT -> 15
}
Sat witness: Found: ((insert([x, l, _jj]) /\ length([_jj, _kj]) /\ length([l, _ij])) -> leqnat([_ij, _kj]), {
_ij -> s(s(s(z)))  ;  _jj -> cons(b, cons(b, cons(b, nil)))  ;  _kj -> s(s(z))  ;  l -> cons(b, cons(b, nil))  ;  x -> a
})

-------------------------------------------
Step 28, which took 0.024821 s (model generation: 0.023738,  model checking: 0.001083):

Model:
|_
{
insert -> 
{{{
Q={q_gen_2250, q_gen_2251, q_gen_2252, q_gen_2255, q_gen_2256},
Q_f={q_gen_2250},
Delta=
{
<nil>() -> q_gen_2251
<a>() -> q_gen_2252
<b>() -> q_gen_2252
<cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2255
<nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2255
<a, a>() -> q_gen_2256
<a, b>() -> q_gen_2256
<b, a>() -> q_gen_2256
<b, b>() -> q_gen_2256
<a, cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2250
<a, nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2250
<b, cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2250
<b, nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2250
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_2249, q_gen_2258, q_gen_2259, q_gen_2280, q_gen_2281, q_gen_2282, q_gen_2283, q_gen_2286},
Q_f={q_gen_2249},
Delta=
{
<nil>() -> q_gen_2258
<cons>(q_gen_2281, q_gen_2258) -> q_gen_2280
<cons>(q_gen_2281, q_gen_2280) -> q_gen_2280
<b>() -> q_gen_2281
<s>(q_gen_2283) -> q_gen_2283
<z>() -> q_gen_2283
<cons, s>(q_gen_2259, q_gen_2258) -> q_gen_2249
<cons, s>(q_gen_2259, q_gen_2280) -> q_gen_2249
<cons, s>(q_gen_2282, q_gen_2280) -> q_gen_2249
<nil, z>() -> q_gen_2249
<a, s>(q_gen_2283) -> q_gen_2259
<a, z>() -> q_gen_2259
<b, z>() -> q_gen_2259
<b, s>(q_gen_2283) -> q_gen_2282
<cons, s>(q_gen_2282, q_gen_2258) -> q_gen_2286
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_2247, q_gen_2260},
Q_f={q_gen_2247},
Delta=
{
<a, a>() -> q_gen_2247
<a, b>() -> q_gen_2247
<b, b>() -> q_gen_2247
<b, a>() -> q_gen_2260
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  leqnat -> 
{{{
Q={q_gen_2244, q_gen_2246, q_gen_2287, q_gen_2288},
Q_f={q_gen_2244},
Delta=
{
<s>(q_gen_2246) -> q_gen_2246
<z>() -> q_gen_2246
<s, s>(q_gen_2244) -> q_gen_2244
<s, s>(q_gen_2287) -> q_gen_2244
<z, s>(q_gen_2246) -> q_gen_2244
<z, z>() -> q_gen_2244
<s, s>(q_gen_2288) -> q_gen_2287
<s, z>(q_gen_2246) -> q_gen_2288
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 14
() -> length([nil, z]) -> 14
() -> leq([a, y]) -> 14
() -> leq([b, b]) -> 14
() -> leqnat([z, s(nn2)]) -> 14
() -> leqnat([z, z]) -> 14
(insert([x, l, _jj]) /\ length([_jj, _kj]) /\ length([l, _ij])) -> leqnat([_ij, _kj]) -> 19
(insert([x, z, _zi]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _zi)]) -> 14
(length([ll, _ej])) -> length([cons(x, ll), s(_ej)]) -> 19
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 15
(leq([b, a])) -> BOT -> 14
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 14
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 18
(leqnat([s(nn1), z])) -> BOT -> 16
}
Sat witness: Found: ((leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]), {
nn1 -> s(s(z))  ;  nn2 -> s(z)
})

-------------------------------------------
Step 29, which took 0.028437 s (model generation: 0.025645,  model checking: 0.002792):

Model:
|_
{
insert -> 
{{{
Q={q_gen_2250, q_gen_2251, q_gen_2252, q_gen_2255, q_gen_2256, q_gen_2262, q_gen_2299},
Q_f={q_gen_2250},
Delta=
{
<nil>() -> q_gen_2251
<a>() -> q_gen_2252
<b>() -> q_gen_2252
<cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2255
<cons, cons>(q_gen_2262, q_gen_2255) -> q_gen_2255
<nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2255
<b, b>() -> q_gen_2256
<a, a>() -> q_gen_2262
<a, b>() -> q_gen_2262
<b, a>() -> q_gen_2262
<a, cons, cons>(q_gen_2262, q_gen_2255) -> q_gen_2250
<a, nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2250
<b, cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2250
<b, cons, cons>(q_gen_2262, q_gen_2255) -> q_gen_2250
<b, nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2250
<a, cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2299
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_2249, q_gen_2258, q_gen_2259, q_gen_2280, q_gen_2281, q_gen_2282, q_gen_2283, q_gen_2286},
Q_f={q_gen_2249},
Delta=
{
<nil>() -> q_gen_2258
<cons>(q_gen_2281, q_gen_2258) -> q_gen_2280
<cons>(q_gen_2281, q_gen_2280) -> q_gen_2280
<b>() -> q_gen_2281
<s>(q_gen_2283) -> q_gen_2283
<z>() -> q_gen_2283
<cons, s>(q_gen_2259, q_gen_2258) -> q_gen_2249
<cons, s>(q_gen_2259, q_gen_2280) -> q_gen_2249
<cons, s>(q_gen_2282, q_gen_2280) -> q_gen_2249
<nil, z>() -> q_gen_2249
<a, s>(q_gen_2283) -> q_gen_2259
<a, z>() -> q_gen_2259
<b, z>() -> q_gen_2259
<b, s>(q_gen_2283) -> q_gen_2282
<cons, s>(q_gen_2282, q_gen_2258) -> q_gen_2286
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_2247, q_gen_2260},
Q_f={q_gen_2247},
Delta=
{
<a, a>() -> q_gen_2247
<a, b>() -> q_gen_2247
<b, b>() -> q_gen_2247
<b, a>() -> q_gen_2260
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  leqnat -> 
{{{
Q={q_gen_2244, q_gen_2246, q_gen_2287},
Q_f={q_gen_2244},
Delta=
{
<s>(q_gen_2246) -> q_gen_2246
<z>() -> q_gen_2246
<s, s>(q_gen_2244) -> q_gen_2244
<z, s>(q_gen_2246) -> q_gen_2244
<z, z>() -> q_gen_2244
<s, s>(q_gen_2287) -> q_gen_2287
<s, z>(q_gen_2246) -> q_gen_2287
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 15
() -> length([nil, z]) -> 15
() -> leq([a, y]) -> 15
() -> leq([b, b]) -> 15
() -> leqnat([z, s(nn2)]) -> 15
() -> leqnat([z, z]) -> 15
(insert([x, l, _jj]) /\ length([_jj, _kj]) /\ length([l, _ij])) -> leqnat([_ij, _kj]) -> 19
(insert([x, z, _zi]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _zi)]) -> 15
(length([ll, _ej])) -> length([cons(x, ll), s(_ej)]) -> 22
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 16
(leq([b, a])) -> BOT -> 15
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 15
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 19
(leqnat([s(nn1), z])) -> BOT -> 17
}
Sat witness: Found: ((length([ll, _ej])) -> length([cons(x, ll), s(_ej)]), {
_ej -> s(s(z))  ;  ll -> cons(a, cons(b, nil))  ;  x -> b
})

-------------------------------------------
Step 30, which took 0.029824 s (model generation: 0.026931,  model checking: 0.002893):

Model:
|_
{
insert -> 
{{{
Q={q_gen_2250, q_gen_2251, q_gen_2252, q_gen_2255, q_gen_2256, q_gen_2262, q_gen_2299},
Q_f={q_gen_2250},
Delta=
{
<nil>() -> q_gen_2251
<a>() -> q_gen_2252
<b>() -> q_gen_2252
<cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2255
<cons, cons>(q_gen_2262, q_gen_2255) -> q_gen_2255
<nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2255
<b, b>() -> q_gen_2256
<a, a>() -> q_gen_2262
<a, b>() -> q_gen_2262
<b, a>() -> q_gen_2262
<a, cons, cons>(q_gen_2262, q_gen_2255) -> q_gen_2250
<a, nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2250
<b, cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2250
<b, cons, cons>(q_gen_2262, q_gen_2255) -> q_gen_2250
<b, nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2250
<a, cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2299
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_2249, q_gen_2258, q_gen_2259, q_gen_2280, q_gen_2281, q_gen_2282, q_gen_2283, q_gen_2286},
Q_f={q_gen_2249},
Delta=
{
<nil>() -> q_gen_2258
<cons>(q_gen_2281, q_gen_2258) -> q_gen_2280
<cons>(q_gen_2281, q_gen_2280) -> q_gen_2280
<a>() -> q_gen_2281
<b>() -> q_gen_2281
<s>(q_gen_2283) -> q_gen_2283
<z>() -> q_gen_2283
<cons, s>(q_gen_2259, q_gen_2258) -> q_gen_2249
<cons, s>(q_gen_2259, q_gen_2280) -> q_gen_2249
<cons, s>(q_gen_2282, q_gen_2280) -> q_gen_2249
<nil, z>() -> q_gen_2249
<a, z>() -> q_gen_2259
<b, z>() -> q_gen_2259
<a, s>(q_gen_2283) -> q_gen_2282
<b, s>(q_gen_2283) -> q_gen_2282
<cons, s>(q_gen_2282, q_gen_2258) -> q_gen_2286
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_2247, q_gen_2260},
Q_f={q_gen_2247},
Delta=
{
<a, a>() -> q_gen_2247
<a, b>() -> q_gen_2247
<b, b>() -> q_gen_2247
<b, a>() -> q_gen_2260
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  leqnat -> 
{{{
Q={q_gen_2244, q_gen_2246, q_gen_2287},
Q_f={q_gen_2244},
Delta=
{
<s>(q_gen_2246) -> q_gen_2246
<z>() -> q_gen_2246
<s, s>(q_gen_2244) -> q_gen_2244
<z, s>(q_gen_2246) -> q_gen_2244
<z, z>() -> q_gen_2244
<s, s>(q_gen_2287) -> q_gen_2287
<s, z>(q_gen_2246) -> q_gen_2287
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 16
() -> length([nil, z]) -> 16
() -> leq([a, y]) -> 16
() -> leq([b, b]) -> 16
() -> leqnat([z, s(nn2)]) -> 16
() -> leqnat([z, z]) -> 16
(insert([x, l, _jj]) /\ length([_jj, _kj]) /\ length([l, _ij])) -> leqnat([_ij, _kj]) -> 22
(insert([x, z, _zi]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _zi)]) -> 16
(length([ll, _ej])) -> length([cons(x, ll), s(_ej)]) -> 22
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 17
(leq([b, a])) -> BOT -> 16
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 16
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 20
(leqnat([s(nn1), z])) -> BOT -> 18
}
Sat witness: Found: ((insert([x, l, _jj]) /\ length([_jj, _kj]) /\ length([l, _ij])) -> leqnat([_ij, _kj]), {
_ij -> s(s(z))  ;  _jj -> cons(b, cons(b, cons(b, nil)))  ;  _kj -> s(z)  ;  l -> cons(b, cons(b, nil))  ;  x -> b
})

-------------------------------------------
Step 31, which took 0.035818 s (model generation: 0.035070,  model checking: 0.000748):

Model:
|_
{
insert -> 
{{{
Q={q_gen_2250, q_gen_2251, q_gen_2252, q_gen_2255, q_gen_2256, q_gen_2275, q_gen_2299},
Q_f={q_gen_2250},
Delta=
{
<nil>() -> q_gen_2251
<a>() -> q_gen_2252
<b>() -> q_gen_2252
<nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2255
<a, a>() -> q_gen_2256
<a, b>() -> q_gen_2256
<b, a>() -> q_gen_2256
<b, b>() -> q_gen_2256
<cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2275
<a, cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2250
<a, nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2250
<b, cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2250
<b, cons, cons>(q_gen_2256, q_gen_2275) -> q_gen_2250
<b, nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2250
<a, cons, cons>(q_gen_2256, q_gen_2275) -> q_gen_2299
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_2249, q_gen_2258, q_gen_2259, q_gen_2280, q_gen_2281, q_gen_2282, q_gen_2283, q_gen_2285},
Q_f={q_gen_2249},
Delta=
{
<nil>() -> q_gen_2258
<cons>(q_gen_2281, q_gen_2258) -> q_gen_2280
<cons>(q_gen_2281, q_gen_2280) -> q_gen_2280
<a>() -> q_gen_2281
<b>() -> q_gen_2281
<s>(q_gen_2283) -> q_gen_2283
<z>() -> q_gen_2283
<cons, s>(q_gen_2259, q_gen_2258) -> q_gen_2249
<cons, s>(q_gen_2282, q_gen_2280) -> q_gen_2249
<nil, z>() -> q_gen_2249
<a, z>() -> q_gen_2259
<b, z>() -> q_gen_2259
<a, s>(q_gen_2283) -> q_gen_2282
<b, s>(q_gen_2283) -> q_gen_2282
<cons, s>(q_gen_2259, q_gen_2280) -> q_gen_2285
<cons, s>(q_gen_2282, q_gen_2258) -> q_gen_2285
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_2247, q_gen_2260},
Q_f={q_gen_2247},
Delta=
{
<a, a>() -> q_gen_2247
<a, b>() -> q_gen_2247
<b, b>() -> q_gen_2247
<b, a>() -> q_gen_2260
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  leqnat -> 
{{{
Q={q_gen_2244, q_gen_2246, q_gen_2287},
Q_f={q_gen_2244},
Delta=
{
<s>(q_gen_2246) -> q_gen_2246
<z>() -> q_gen_2246
<s, s>(q_gen_2244) -> q_gen_2244
<z, s>(q_gen_2246) -> q_gen_2244
<z, z>() -> q_gen_2244
<s, s>(q_gen_2287) -> q_gen_2287
<s, z>(q_gen_2246) -> q_gen_2287
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 16
() -> length([nil, z]) -> 16
() -> leq([a, y]) -> 16
() -> leq([b, b]) -> 16
() -> leqnat([z, s(nn2)]) -> 16
() -> leqnat([z, z]) -> 16
(insert([x, l, _jj]) /\ length([_jj, _kj]) /\ length([l, _ij])) -> leqnat([_ij, _kj]) -> 22
(insert([x, z, _zi]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _zi)]) -> 19
(length([ll, _ej])) -> length([cons(x, ll), s(_ej)]) -> 22
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 17
(leq([b, a])) -> BOT -> 17
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 17
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 20
(leqnat([s(nn1), z])) -> BOT -> 18
}
Sat witness: Found: ((insert([x, z, _zi]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _zi)]), {
_zi -> cons(a, cons(b, cons(b, nil)))  ;  x -> b  ;  y -> a  ;  z -> cons(b, cons(a, nil))
})

-------------------------------------------
Step 32, which took 0.033165 s (model generation: 0.032328,  model checking: 0.000837):

Model:
|_
{
insert -> 
{{{
Q={q_gen_2250, q_gen_2251, q_gen_2252, q_gen_2255, q_gen_2256, q_gen_2269, q_gen_2284},
Q_f={q_gen_2250},
Delta=
{
<nil>() -> q_gen_2251
<a>() -> q_gen_2252
<b>() -> q_gen_2252
<cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2255
<cons, cons>(q_gen_2269, q_gen_2255) -> q_gen_2255
<nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2255
<a, a>() -> q_gen_2256
<b, b>() -> q_gen_2256
<a, b>() -> q_gen_2269
<b, a>() -> q_gen_2269
<a, cons, cons>(q_gen_2269, q_gen_2255) -> q_gen_2250
<a, nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2250
<b, cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2250
<b, nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2250
<a, cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2284
<b, cons, cons>(q_gen_2269, q_gen_2255) -> q_gen_2284
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_2249, q_gen_2258, q_gen_2259, q_gen_2280, q_gen_2281, q_gen_2282, q_gen_2283, q_gen_2285},
Q_f={q_gen_2249},
Delta=
{
<nil>() -> q_gen_2258
<cons>(q_gen_2281, q_gen_2258) -> q_gen_2280
<cons>(q_gen_2281, q_gen_2280) -> q_gen_2280
<a>() -> q_gen_2281
<b>() -> q_gen_2281
<s>(q_gen_2283) -> q_gen_2283
<z>() -> q_gen_2283
<cons, s>(q_gen_2259, q_gen_2258) -> q_gen_2249
<cons, s>(q_gen_2282, q_gen_2280) -> q_gen_2249
<nil, z>() -> q_gen_2249
<a, z>() -> q_gen_2259
<b, z>() -> q_gen_2259
<a, s>(q_gen_2283) -> q_gen_2282
<b, s>(q_gen_2283) -> q_gen_2282
<cons, s>(q_gen_2259, q_gen_2280) -> q_gen_2285
<cons, s>(q_gen_2282, q_gen_2258) -> q_gen_2285
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_2247, q_gen_2260},
Q_f={q_gen_2247},
Delta=
{
<a, a>() -> q_gen_2247
<a, b>() -> q_gen_2247
<b, b>() -> q_gen_2247
<b, a>() -> q_gen_2260
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  leqnat -> 
{{{
Q={q_gen_2244, q_gen_2246, q_gen_2287},
Q_f={q_gen_2244},
Delta=
{
<s>(q_gen_2246) -> q_gen_2246
<z>() -> q_gen_2246
<s, s>(q_gen_2244) -> q_gen_2244
<z, s>(q_gen_2246) -> q_gen_2244
<z, z>() -> q_gen_2244
<s, s>(q_gen_2287) -> q_gen_2287
<s, z>(q_gen_2246) -> q_gen_2287
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 17
() -> length([nil, z]) -> 17
() -> leq([a, y]) -> 17
() -> leq([b, b]) -> 17
() -> leqnat([z, s(nn2)]) -> 17
() -> leqnat([z, z]) -> 17
(insert([x, l, _jj]) /\ length([_jj, _kj]) /\ length([l, _ij])) -> leqnat([_ij, _kj]) -> 22
(insert([x, z, _zi]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _zi)]) -> 19
(length([ll, _ej])) -> length([cons(x, ll), s(_ej)]) -> 22
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 20
(leq([b, a])) -> BOT -> 18
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 18
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 20
(leqnat([s(nn1), z])) -> BOT -> 18
}
Sat witness: Found: ((leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]), {
x -> a  ;  y -> a  ;  z -> nil
})

-------------------------------------------
Step 33, which took 0.042359 s (model generation: 0.040876,  model checking: 0.001483):

Model:
|_
{
insert -> 
{{{
Q={q_gen_2250, q_gen_2251, q_gen_2252, q_gen_2255, q_gen_2256, q_gen_2275, q_gen_2299},
Q_f={q_gen_2250},
Delta=
{
<nil>() -> q_gen_2251
<a>() -> q_gen_2252
<b>() -> q_gen_2252
<nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2255
<a, a>() -> q_gen_2256
<a, b>() -> q_gen_2256
<b, a>() -> q_gen_2256
<b, b>() -> q_gen_2256
<cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2275
<cons, cons>(q_gen_2256, q_gen_2275) -> q_gen_2275
<a, cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2250
<a, nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2250
<b, cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2250
<b, cons, cons>(q_gen_2256, q_gen_2275) -> q_gen_2250
<b, nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2250
<a, cons, cons>(q_gen_2256, q_gen_2275) -> q_gen_2299
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_2249, q_gen_2258, q_gen_2259, q_gen_2280, q_gen_2281, q_gen_2282, q_gen_2283, q_gen_2285},
Q_f={q_gen_2249},
Delta=
{
<nil>() -> q_gen_2258
<cons>(q_gen_2281, q_gen_2258) -> q_gen_2280
<cons>(q_gen_2281, q_gen_2280) -> q_gen_2280
<a>() -> q_gen_2281
<b>() -> q_gen_2281
<s>(q_gen_2283) -> q_gen_2283
<z>() -> q_gen_2283
<cons, s>(q_gen_2259, q_gen_2258) -> q_gen_2249
<cons, s>(q_gen_2282, q_gen_2280) -> q_gen_2249
<nil, z>() -> q_gen_2249
<a, z>() -> q_gen_2259
<b, z>() -> q_gen_2259
<a, s>(q_gen_2283) -> q_gen_2282
<b, s>(q_gen_2283) -> q_gen_2282
<cons, s>(q_gen_2259, q_gen_2280) -> q_gen_2285
<cons, s>(q_gen_2282, q_gen_2258) -> q_gen_2285
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_2247, q_gen_2260},
Q_f={q_gen_2247},
Delta=
{
<a, a>() -> q_gen_2247
<a, b>() -> q_gen_2247
<b, b>() -> q_gen_2247
<b, a>() -> q_gen_2260
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  leqnat -> 
{{{
Q={q_gen_2244, q_gen_2246, q_gen_2287},
Q_f={q_gen_2244},
Delta=
{
<s>(q_gen_2246) -> q_gen_2246
<z>() -> q_gen_2246
<s, s>(q_gen_2244) -> q_gen_2244
<z, s>(q_gen_2246) -> q_gen_2244
<z, z>() -> q_gen_2244
<s, s>(q_gen_2287) -> q_gen_2287
<s, z>(q_gen_2246) -> q_gen_2287
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 18
() -> length([nil, z]) -> 18
() -> leq([a, y]) -> 18
() -> leq([b, b]) -> 18
() -> leqnat([z, s(nn2)]) -> 18
() -> leqnat([z, z]) -> 18
(insert([x, l, _jj]) /\ length([_jj, _kj]) /\ length([l, _ij])) -> leqnat([_ij, _kj]) -> 22
(insert([x, z, _zi]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _zi)]) -> 20
(length([ll, _ej])) -> length([cons(x, ll), s(_ej)]) -> 22
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 23
(leq([b, a])) -> BOT -> 19
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 19
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 21
(leqnat([s(nn1), z])) -> BOT -> 19
}
Sat witness: Found: ((leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]), {
x -> a  ;  y -> a  ;  z -> cons(a, nil)
})

-------------------------------------------
Step 34, which took 0.036965 s (model generation: 0.034697,  model checking: 0.002268):

Model:
|_
{
insert -> 
{{{
Q={q_gen_2250, q_gen_2251, q_gen_2252, q_gen_2255, q_gen_2256, q_gen_2262, q_gen_2299},
Q_f={q_gen_2250},
Delta=
{
<nil>() -> q_gen_2251
<a>() -> q_gen_2252
<b>() -> q_gen_2252
<cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2255
<cons, cons>(q_gen_2262, q_gen_2255) -> q_gen_2255
<nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2255
<b, b>() -> q_gen_2256
<a, a>() -> q_gen_2262
<a, b>() -> q_gen_2262
<b, a>() -> q_gen_2262
<a, cons, cons>(q_gen_2262, q_gen_2255) -> q_gen_2250
<a, nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2250
<b, cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2250
<b, cons, cons>(q_gen_2262, q_gen_2255) -> q_gen_2250
<b, nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2250
<a, cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2299
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_2249, q_gen_2258, q_gen_2259, q_gen_2280, q_gen_2281, q_gen_2282, q_gen_2283, q_gen_2285},
Q_f={q_gen_2249},
Delta=
{
<nil>() -> q_gen_2258
<cons>(q_gen_2281, q_gen_2258) -> q_gen_2280
<cons>(q_gen_2281, q_gen_2280) -> q_gen_2280
<a>() -> q_gen_2281
<b>() -> q_gen_2281
<s>(q_gen_2283) -> q_gen_2283
<z>() -> q_gen_2283
<cons, s>(q_gen_2259, q_gen_2258) -> q_gen_2249
<cons, s>(q_gen_2282, q_gen_2280) -> q_gen_2249
<nil, z>() -> q_gen_2249
<a, z>() -> q_gen_2259
<b, z>() -> q_gen_2259
<a, s>(q_gen_2283) -> q_gen_2282
<b, s>(q_gen_2283) -> q_gen_2282
<cons, s>(q_gen_2259, q_gen_2280) -> q_gen_2285
<cons, s>(q_gen_2282, q_gen_2258) -> q_gen_2285
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_2247, q_gen_2260},
Q_f={q_gen_2247},
Delta=
{
<a, a>() -> q_gen_2247
<a, b>() -> q_gen_2247
<b, b>() -> q_gen_2247
<b, a>() -> q_gen_2260
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  leqnat -> 
{{{
Q={q_gen_2244, q_gen_2246, q_gen_2287},
Q_f={q_gen_2244},
Delta=
{
<s>(q_gen_2246) -> q_gen_2246
<z>() -> q_gen_2246
<s, s>(q_gen_2244) -> q_gen_2244
<z, s>(q_gen_2246) -> q_gen_2244
<z, z>() -> q_gen_2244
<s, s>(q_gen_2287) -> q_gen_2287
<s, z>(q_gen_2246) -> q_gen_2287
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 19
() -> length([nil, z]) -> 19
() -> leq([a, y]) -> 19
() -> leq([b, b]) -> 19
() -> leqnat([z, s(nn2)]) -> 19
() -> leqnat([z, z]) -> 19
(insert([x, l, _jj]) /\ length([_jj, _kj]) /\ length([l, _ij])) -> leqnat([_ij, _kj]) -> 25
(insert([x, z, _zi]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _zi)]) -> 21
(length([ll, _ej])) -> length([cons(x, ll), s(_ej)]) -> 23
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 23
(leq([b, a])) -> BOT -> 20
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 20
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 22
(leqnat([s(nn1), z])) -> BOT -> 20
}
Sat witness: Found: ((insert([x, l, _jj]) /\ length([_jj, _kj]) /\ length([l, _ij])) -> leqnat([_ij, _kj]), {
_ij -> s(s(s(z)))  ;  _jj -> cons(b, cons(b, cons(b, nil)))  ;  _kj -> s(s(z))  ;  l -> cons(b, cons(b, nil))  ;  x -> b
})

-------------------------------------------
Step 35, which took 0.040182 s (model generation: 0.035622,  model checking: 0.004560):

Model:
|_
{
insert -> 
{{{
Q={q_gen_2250, q_gen_2251, q_gen_2252, q_gen_2255, q_gen_2256},
Q_f={q_gen_2250},
Delta=
{
<nil>() -> q_gen_2251
<a>() -> q_gen_2252
<b>() -> q_gen_2252
<cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2255
<nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2255
<a, a>() -> q_gen_2256
<a, b>() -> q_gen_2256
<b, a>() -> q_gen_2256
<b, b>() -> q_gen_2256
<a, cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2250
<a, nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2250
<b, cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2250
<b, nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2250
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_2249, q_gen_2258, q_gen_2259, q_gen_2280, q_gen_2281, q_gen_2282, q_gen_2283, q_gen_2285, q_gen_2293, q_gen_2294, q_gen_2298},
Q_f={q_gen_2249},
Delta=
{
<nil>() -> q_gen_2258
<cons>(q_gen_2281, q_gen_2258) -> q_gen_2280
<a>() -> q_gen_2281
<b>() -> q_gen_2281
<z>() -> q_gen_2283
<s>(q_gen_2283) -> q_gen_2294
<cons>(q_gen_2281, q_gen_2280) -> q_gen_2298
<cons, s>(q_gen_2259, q_gen_2258) -> q_gen_2249
<cons, s>(q_gen_2282, q_gen_2280) -> q_gen_2249
<cons, s>(q_gen_2282, q_gen_2298) -> q_gen_2249
<cons, s>(q_gen_2293, q_gen_2298) -> q_gen_2249
<nil, z>() -> q_gen_2249
<a, z>() -> q_gen_2259
<b, z>() -> q_gen_2259
<a, s>(q_gen_2283) -> q_gen_2282
<b, s>(q_gen_2283) -> q_gen_2282
<cons, s>(q_gen_2259, q_gen_2280) -> q_gen_2285
<cons, s>(q_gen_2259, q_gen_2298) -> q_gen_2285
<cons, s>(q_gen_2282, q_gen_2258) -> q_gen_2285
<cons, s>(q_gen_2293, q_gen_2258) -> q_gen_2285
<cons, s>(q_gen_2293, q_gen_2280) -> q_gen_2285
<b, s>(q_gen_2294) -> q_gen_2293
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_2247, q_gen_2260},
Q_f={q_gen_2247},
Delta=
{
<a, a>() -> q_gen_2247
<a, b>() -> q_gen_2247
<b, b>() -> q_gen_2247
<b, a>() -> q_gen_2260
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  leqnat -> 
{{{
Q={q_gen_2244, q_gen_2246, q_gen_2287},
Q_f={q_gen_2244},
Delta=
{
<s>(q_gen_2246) -> q_gen_2246
<z>() -> q_gen_2246
<s, s>(q_gen_2244) -> q_gen_2244
<z, s>(q_gen_2246) -> q_gen_2244
<z, z>() -> q_gen_2244
<s, s>(q_gen_2287) -> q_gen_2287
<s, z>(q_gen_2246) -> q_gen_2287
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 20
() -> length([nil, z]) -> 20
() -> leq([a, y]) -> 20
() -> leq([b, b]) -> 20
() -> leqnat([z, s(nn2)]) -> 20
() -> leqnat([z, z]) -> 20
(insert([x, l, _jj]) /\ length([_jj, _kj]) /\ length([l, _ij])) -> leqnat([_ij, _kj]) -> 25
(insert([x, z, _zi]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _zi)]) -> 22
(length([ll, _ej])) -> length([cons(x, ll), s(_ej)]) -> 26
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 24
(leq([b, a])) -> BOT -> 21
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 21
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 23
(leqnat([s(nn1), z])) -> BOT -> 21
}
Sat witness: Found: ((length([ll, _ej])) -> length([cons(x, ll), s(_ej)]), {
_ej -> s(s(s(z)))  ;  ll -> cons(b, cons(a, cons(b, nil)))  ;  x -> b
})

-------------------------------------------
Step 36, which took 0.046901 s (model generation: 0.043321,  model checking: 0.003580):

Model:
|_
{
insert -> 
{{{
Q={q_gen_2250, q_gen_2251, q_gen_2252, q_gen_2255, q_gen_2256},
Q_f={q_gen_2250},
Delta=
{
<nil>() -> q_gen_2251
<a>() -> q_gen_2252
<b>() -> q_gen_2252
<cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2255
<nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2255
<a, a>() -> q_gen_2256
<a, b>() -> q_gen_2256
<b, a>() -> q_gen_2256
<b, b>() -> q_gen_2256
<a, cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2250
<a, nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2250
<b, cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2250
<b, nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2250
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_2249, q_gen_2258, q_gen_2259, q_gen_2280, q_gen_2281, q_gen_2282, q_gen_2283, q_gen_2285, q_gen_2291, q_gen_2294, q_gen_2298},
Q_f={q_gen_2249},
Delta=
{
<nil>() -> q_gen_2258
<cons>(q_gen_2281, q_gen_2258) -> q_gen_2280
<cons>(q_gen_2281, q_gen_2298) -> q_gen_2280
<a>() -> q_gen_2281
<b>() -> q_gen_2281
<s>(q_gen_2294) -> q_gen_2283
<z>() -> q_gen_2283
<s>(q_gen_2283) -> q_gen_2294
<cons>(q_gen_2281, q_gen_2280) -> q_gen_2298
<cons, s>(q_gen_2259, q_gen_2258) -> q_gen_2249
<cons, s>(q_gen_2282, q_gen_2258) -> q_gen_2249
<cons, s>(q_gen_2282, q_gen_2280) -> q_gen_2249
<cons, s>(q_gen_2291, q_gen_2280) -> q_gen_2249
<cons, s>(q_gen_2291, q_gen_2298) -> q_gen_2249
<nil, z>() -> q_gen_2249
<a, z>() -> q_gen_2259
<b, z>() -> q_gen_2259
<b, s>(q_gen_2283) -> q_gen_2282
<cons, s>(q_gen_2259, q_gen_2280) -> q_gen_2285
<cons, s>(q_gen_2259, q_gen_2298) -> q_gen_2285
<cons, s>(q_gen_2282, q_gen_2298) -> q_gen_2285
<cons, s>(q_gen_2291, q_gen_2258) -> q_gen_2285
<a, s>(q_gen_2283) -> q_gen_2291
<b, s>(q_gen_2294) -> q_gen_2291
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_2247, q_gen_2260},
Q_f={q_gen_2247},
Delta=
{
<a, a>() -> q_gen_2247
<a, b>() -> q_gen_2247
<b, b>() -> q_gen_2247
<b, a>() -> q_gen_2260
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  leqnat -> 
{{{
Q={q_gen_2244, q_gen_2246, q_gen_2287},
Q_f={q_gen_2244},
Delta=
{
<s>(q_gen_2246) -> q_gen_2246
<z>() -> q_gen_2246
<s, s>(q_gen_2244) -> q_gen_2244
<z, s>(q_gen_2246) -> q_gen_2244
<z, z>() -> q_gen_2244
<s, s>(q_gen_2287) -> q_gen_2287
<s, z>(q_gen_2246) -> q_gen_2287
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 21
() -> length([nil, z]) -> 21
() -> leq([a, y]) -> 21
() -> leq([b, b]) -> 21
() -> leqnat([z, s(nn2)]) -> 21
() -> leqnat([z, z]) -> 21
(insert([x, l, _jj]) /\ length([_jj, _kj]) /\ length([l, _ij])) -> leqnat([_ij, _kj]) -> 28
(insert([x, z, _zi]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _zi)]) -> 23
(length([ll, _ej])) -> length([cons(x, ll), s(_ej)]) -> 26
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 25
(leq([b, a])) -> BOT -> 22
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 22
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 24
(leqnat([s(nn1), z])) -> BOT -> 22
}
Sat witness: Found: ((insert([x, l, _jj]) /\ length([_jj, _kj]) /\ length([l, _ij])) -> leqnat([_ij, _kj]), {
_ij -> s(s(s(s(z))))  ;  _jj -> cons(b, cons(b, nil))  ;  _kj -> s(s(z))  ;  l -> cons(b, nil)  ;  x -> a
})

-------------------------------------------
Step 37, which took 0.047663 s (model generation: 0.044071,  model checking: 0.003592):

Model:
|_
{
insert -> 
{{{
Q={q_gen_2250, q_gen_2251, q_gen_2252, q_gen_2255, q_gen_2256},
Q_f={q_gen_2250},
Delta=
{
<nil>() -> q_gen_2251
<a>() -> q_gen_2252
<b>() -> q_gen_2252
<cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2255
<nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2255
<a, a>() -> q_gen_2256
<a, b>() -> q_gen_2256
<b, a>() -> q_gen_2256
<b, b>() -> q_gen_2256
<a, cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2250
<a, nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2250
<b, cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2250
<b, nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2250
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_2249, q_gen_2258, q_gen_2259, q_gen_2280, q_gen_2281, q_gen_2282, q_gen_2283, q_gen_2285, q_gen_2291, q_gen_2294, q_gen_2298},
Q_f={q_gen_2249},
Delta=
{
<nil>() -> q_gen_2258
<cons>(q_gen_2281, q_gen_2258) -> q_gen_2280
<a>() -> q_gen_2281
<b>() -> q_gen_2281
<z>() -> q_gen_2283
<s>(q_gen_2283) -> q_gen_2294
<s>(q_gen_2294) -> q_gen_2294
<cons>(q_gen_2281, q_gen_2280) -> q_gen_2298
<cons>(q_gen_2281, q_gen_2298) -> q_gen_2298
<cons, s>(q_gen_2259, q_gen_2258) -> q_gen_2249
<cons, s>(q_gen_2282, q_gen_2258) -> q_gen_2249
<cons, s>(q_gen_2282, q_gen_2280) -> q_gen_2249
<cons, s>(q_gen_2291, q_gen_2280) -> q_gen_2249
<cons, s>(q_gen_2291, q_gen_2298) -> q_gen_2249
<nil, z>() -> q_gen_2249
<a, z>() -> q_gen_2259
<b, z>() -> q_gen_2259
<b, s>(q_gen_2283) -> q_gen_2282
<cons, s>(q_gen_2259, q_gen_2280) -> q_gen_2285
<cons, s>(q_gen_2259, q_gen_2298) -> q_gen_2285
<cons, s>(q_gen_2282, q_gen_2298) -> q_gen_2285
<cons, s>(q_gen_2291, q_gen_2258) -> q_gen_2285
<a, s>(q_gen_2283) -> q_gen_2291
<b, s>(q_gen_2294) -> q_gen_2291
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_2247, q_gen_2260},
Q_f={q_gen_2247},
Delta=
{
<a, a>() -> q_gen_2247
<a, b>() -> q_gen_2247
<b, b>() -> q_gen_2247
<b, a>() -> q_gen_2260
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  leqnat -> 
{{{
Q={q_gen_2244, q_gen_2246, q_gen_2287},
Q_f={q_gen_2244},
Delta=
{
<s>(q_gen_2246) -> q_gen_2246
<z>() -> q_gen_2246
<s, s>(q_gen_2244) -> q_gen_2244
<z, s>(q_gen_2246) -> q_gen_2244
<z, z>() -> q_gen_2244
<s, s>(q_gen_2287) -> q_gen_2287
<s, z>(q_gen_2246) -> q_gen_2287
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 22
() -> length([nil, z]) -> 22
() -> leq([a, y]) -> 22
() -> leq([b, b]) -> 22
() -> leqnat([z, s(nn2)]) -> 22
() -> leqnat([z, z]) -> 22
(insert([x, l, _jj]) /\ length([_jj, _kj]) /\ length([l, _ij])) -> leqnat([_ij, _kj]) -> 28
(insert([x, z, _zi]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _zi)]) -> 24
(length([ll, _ej])) -> length([cons(x, ll), s(_ej)]) -> 29
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 26
(leq([b, a])) -> BOT -> 23
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 23
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 25
(leqnat([s(nn1), z])) -> BOT -> 23
}
Sat witness: Found: ((length([ll, _ej])) -> length([cons(x, ll), s(_ej)]), {
_ej -> s(s(s(z)))  ;  ll -> cons(b, cons(a, cons(b, nil)))  ;  x -> a
})

-------------------------------------------
Step 38, which took 0.048725 s (model generation: 0.046130,  model checking: 0.002595):

Model:
|_
{
insert -> 
{{{
Q={q_gen_2250, q_gen_2251, q_gen_2252, q_gen_2255, q_gen_2256},
Q_f={q_gen_2250},
Delta=
{
<nil>() -> q_gen_2251
<a>() -> q_gen_2252
<b>() -> q_gen_2252
<cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2255
<nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2255
<a, a>() -> q_gen_2256
<a, b>() -> q_gen_2256
<b, a>() -> q_gen_2256
<b, b>() -> q_gen_2256
<a, cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2250
<a, nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2250
<b, cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2250
<b, nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2250
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_2249, q_gen_2258, q_gen_2259, q_gen_2280, q_gen_2281, q_gen_2282, q_gen_2283, q_gen_2285, q_gen_2293, q_gen_2294, q_gen_2298},
Q_f={q_gen_2249},
Delta=
{
<nil>() -> q_gen_2258
<cons>(q_gen_2281, q_gen_2258) -> q_gen_2280
<cons>(q_gen_2281, q_gen_2298) -> q_gen_2280
<a>() -> q_gen_2281
<b>() -> q_gen_2281
<s>(q_gen_2294) -> q_gen_2283
<z>() -> q_gen_2283
<s>(q_gen_2283) -> q_gen_2294
<cons>(q_gen_2281, q_gen_2280) -> q_gen_2298
<cons, s>(q_gen_2259, q_gen_2258) -> q_gen_2249
<cons, s>(q_gen_2282, q_gen_2280) -> q_gen_2249
<cons, s>(q_gen_2293, q_gen_2298) -> q_gen_2249
<nil, z>() -> q_gen_2249
<a, z>() -> q_gen_2259
<b, z>() -> q_gen_2259
<a, s>(q_gen_2283) -> q_gen_2282
<b, s>(q_gen_2283) -> q_gen_2282
<cons, s>(q_gen_2259, q_gen_2280) -> q_gen_2285
<cons, s>(q_gen_2259, q_gen_2298) -> q_gen_2285
<cons, s>(q_gen_2282, q_gen_2258) -> q_gen_2285
<cons, s>(q_gen_2282, q_gen_2298) -> q_gen_2285
<cons, s>(q_gen_2293, q_gen_2258) -> q_gen_2285
<cons, s>(q_gen_2293, q_gen_2280) -> q_gen_2285
<b, s>(q_gen_2294) -> q_gen_2293
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_2247, q_gen_2260},
Q_f={q_gen_2247},
Delta=
{
<a, a>() -> q_gen_2247
<a, b>() -> q_gen_2247
<b, b>() -> q_gen_2247
<b, a>() -> q_gen_2260
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  leqnat -> 
{{{
Q={q_gen_2244, q_gen_2246, q_gen_2287},
Q_f={q_gen_2244},
Delta=
{
<s>(q_gen_2246) -> q_gen_2246
<z>() -> q_gen_2246
<s, s>(q_gen_2244) -> q_gen_2244
<z, s>(q_gen_2246) -> q_gen_2244
<z, z>() -> q_gen_2244
<s, s>(q_gen_2287) -> q_gen_2287
<s, z>(q_gen_2246) -> q_gen_2287
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 23
() -> length([nil, z]) -> 23
() -> leq([a, y]) -> 23
() -> leq([b, b]) -> 23
() -> leqnat([z, s(nn2)]) -> 23
() -> leqnat([z, z]) -> 23
(insert([x, l, _jj]) /\ length([_jj, _kj]) /\ length([l, _ij])) -> leqnat([_ij, _kj]) -> 31
(insert([x, z, _zi]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _zi)]) -> 25
(length([ll, _ej])) -> length([cons(x, ll), s(_ej)]) -> 29
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 27
(leq([b, a])) -> BOT -> 24
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 24
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 26
(leqnat([s(nn1), z])) -> BOT -> 24
}
Sat witness: Found: ((insert([x, l, _jj]) /\ length([_jj, _kj]) /\ length([l, _ij])) -> leqnat([_ij, _kj]), {
_ij -> s(s(s(z)))  ;  _jj -> cons(b, cons(b, cons(b, cons(b, nil))))  ;  _kj -> s(s(z))  ;  l -> cons(b, cons(b, cons(b, nil)))  ;  x -> a
})

-------------------------------------------
Step 39, which took 0.052004 s (model generation: 0.049751,  model checking: 0.002253):

Model:
|_
{
insert -> 
{{{
Q={q_gen_2250, q_gen_2251, q_gen_2252, q_gen_2255, q_gen_2256, q_gen_2262, q_gen_2299, q_gen_2300},
Q_f={q_gen_2250},
Delta=
{
<nil>() -> q_gen_2251
<a>() -> q_gen_2252
<b>() -> q_gen_2252
<cons, cons>(q_gen_2256, q_gen_2300) -> q_gen_2255
<cons, cons>(q_gen_2262, q_gen_2255) -> q_gen_2255
<nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2255
<b, b>() -> q_gen_2256
<a, a>() -> q_gen_2262
<a, b>() -> q_gen_2262
<b, a>() -> q_gen_2262
<cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2300
<a, cons, cons>(q_gen_2262, q_gen_2255) -> q_gen_2250
<a, nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2250
<b, cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2250
<b, cons, cons>(q_gen_2262, q_gen_2255) -> q_gen_2250
<b, nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2250
<a, cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2299
<a, cons, cons>(q_gen_2256, q_gen_2300) -> q_gen_2299
<b, cons, cons>(q_gen_2256, q_gen_2300) -> q_gen_2299
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_2249, q_gen_2258, q_gen_2259, q_gen_2280, q_gen_2281, q_gen_2282, q_gen_2283, q_gen_2285},
Q_f={q_gen_2249},
Delta=
{
<nil>() -> q_gen_2258
<cons>(q_gen_2281, q_gen_2258) -> q_gen_2280
<cons>(q_gen_2281, q_gen_2280) -> q_gen_2280
<a>() -> q_gen_2281
<b>() -> q_gen_2281
<s>(q_gen_2283) -> q_gen_2283
<z>() -> q_gen_2283
<cons, s>(q_gen_2259, q_gen_2258) -> q_gen_2249
<cons, s>(q_gen_2282, q_gen_2280) -> q_gen_2249
<nil, z>() -> q_gen_2249
<a, z>() -> q_gen_2259
<b, z>() -> q_gen_2259
<a, s>(q_gen_2283) -> q_gen_2282
<b, s>(q_gen_2283) -> q_gen_2282
<cons, s>(q_gen_2259, q_gen_2280) -> q_gen_2285
<cons, s>(q_gen_2282, q_gen_2258) -> q_gen_2285
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_2247, q_gen_2260},
Q_f={q_gen_2247},
Delta=
{
<a, a>() -> q_gen_2247
<a, b>() -> q_gen_2247
<b, b>() -> q_gen_2247
<b, a>() -> q_gen_2260
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  leqnat -> 
{{{
Q={q_gen_2244, q_gen_2246, q_gen_2287},
Q_f={q_gen_2244},
Delta=
{
<s>(q_gen_2246) -> q_gen_2246
<z>() -> q_gen_2246
<s, s>(q_gen_2244) -> q_gen_2244
<z, s>(q_gen_2246) -> q_gen_2244
<z, z>() -> q_gen_2244
<s, s>(q_gen_2287) -> q_gen_2287
<s, z>(q_gen_2246) -> q_gen_2287
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 24
() -> length([nil, z]) -> 24
() -> leq([a, y]) -> 24
() -> leq([b, b]) -> 24
() -> leqnat([z, s(nn2)]) -> 24
() -> leqnat([z, z]) -> 24
(insert([x, l, _jj]) /\ length([_jj, _kj]) /\ length([l, _ij])) -> leqnat([_ij, _kj]) -> 31
(insert([x, z, _zi]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _zi)]) -> 28
(length([ll, _ej])) -> length([cons(x, ll), s(_ej)]) -> 29
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 27
(leq([b, a])) -> BOT -> 25
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 25
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 26
(leqnat([s(nn1), z])) -> BOT -> 25
}
Sat witness: Found: ((insert([x, z, _zi]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _zi)]), {
_zi -> cons(b, cons(b, nil))  ;  x -> b  ;  y -> a  ;  z -> cons(b, nil)
})

-------------------------------------------
Step 40, which took 0.057088 s (model generation: 0.053758,  model checking: 0.003330):

Model:
|_
{
insert -> 
{{{
Q={q_gen_2250, q_gen_2251, q_gen_2252, q_gen_2255, q_gen_2256},
Q_f={q_gen_2250},
Delta=
{
<nil>() -> q_gen_2251
<a>() -> q_gen_2252
<b>() -> q_gen_2252
<cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2255
<nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2255
<a, a>() -> q_gen_2256
<a, b>() -> q_gen_2256
<b, a>() -> q_gen_2256
<b, b>() -> q_gen_2256
<a, cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2250
<a, nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2250
<b, cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2250
<b, nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2250
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_2249, q_gen_2258, q_gen_2259, q_gen_2280, q_gen_2281, q_gen_2282, q_gen_2283, q_gen_2286, q_gen_2293, q_gen_2294, q_gen_2298},
Q_f={q_gen_2249},
Delta=
{
<nil>() -> q_gen_2258
<cons>(q_gen_2281, q_gen_2258) -> q_gen_2280
<a>() -> q_gen_2281
<b>() -> q_gen_2281
<z>() -> q_gen_2283
<s>(q_gen_2283) -> q_gen_2294
<s>(q_gen_2294) -> q_gen_2294
<cons>(q_gen_2281, q_gen_2280) -> q_gen_2298
<cons>(q_gen_2281, q_gen_2298) -> q_gen_2298
<cons, s>(q_gen_2259, q_gen_2258) -> q_gen_2249
<cons, s>(q_gen_2259, q_gen_2280) -> q_gen_2249
<cons, s>(q_gen_2282, q_gen_2280) -> q_gen_2249
<cons, s>(q_gen_2293, q_gen_2298) -> q_gen_2249
<nil, z>() -> q_gen_2249
<a, z>() -> q_gen_2259
<b, z>() -> q_gen_2259
<a, s>(q_gen_2283) -> q_gen_2282
<b, s>(q_gen_2283) -> q_gen_2282
<cons, s>(q_gen_2259, q_gen_2298) -> q_gen_2286
<cons, s>(q_gen_2282, q_gen_2258) -> q_gen_2286
<cons, s>(q_gen_2282, q_gen_2298) -> q_gen_2286
<cons, s>(q_gen_2293, q_gen_2258) -> q_gen_2286
<cons, s>(q_gen_2293, q_gen_2280) -> q_gen_2286
<a, s>(q_gen_2294) -> q_gen_2293
<b, s>(q_gen_2294) -> q_gen_2293
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_2247, q_gen_2260},
Q_f={q_gen_2247},
Delta=
{
<a, a>() -> q_gen_2247
<a, b>() -> q_gen_2247
<b, b>() -> q_gen_2247
<b, a>() -> q_gen_2260
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  leqnat -> 
{{{
Q={q_gen_2244, q_gen_2246, q_gen_2287},
Q_f={q_gen_2244},
Delta=
{
<s>(q_gen_2246) -> q_gen_2246
<z>() -> q_gen_2246
<s, s>(q_gen_2244) -> q_gen_2244
<z, s>(q_gen_2246) -> q_gen_2244
<z, z>() -> q_gen_2244
<s, s>(q_gen_2287) -> q_gen_2287
<s, z>(q_gen_2246) -> q_gen_2287
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 25
() -> length([nil, z]) -> 25
() -> leq([a, y]) -> 25
() -> leq([b, b]) -> 25
() -> leqnat([z, s(nn2)]) -> 25
() -> leqnat([z, z]) -> 25
(insert([x, l, _jj]) /\ length([_jj, _kj]) /\ length([l, _ij])) -> leqnat([_ij, _kj]) -> 31
(insert([x, z, _zi]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _zi)]) -> 29
(length([ll, _ej])) -> length([cons(x, ll), s(_ej)]) -> 32
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 28
(leq([b, a])) -> BOT -> 26
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 26
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 27
(leqnat([s(nn1), z])) -> BOT -> 26
}
Sat witness: Found: ((length([ll, _ej])) -> length([cons(x, ll), s(_ej)]), {
_ej -> s(z)  ;  ll -> cons(b, cons(b, nil))  ;  x -> a
})

-------------------------------------------
Step 41, which took 0.059358 s (model generation: 0.058196,  model checking: 0.001162):

Model:
|_
{
insert -> 
{{{
Q={q_gen_2250, q_gen_2251, q_gen_2252, q_gen_2255, q_gen_2256, q_gen_2262, q_gen_2299, q_gen_2300},
Q_f={q_gen_2250},
Delta=
{
<nil>() -> q_gen_2251
<a>() -> q_gen_2252
<b>() -> q_gen_2252
<cons, cons>(q_gen_2262, q_gen_2255) -> q_gen_2255
<nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2255
<b, b>() -> q_gen_2256
<a, a>() -> q_gen_2262
<a, b>() -> q_gen_2262
<b, a>() -> q_gen_2262
<cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2300
<cons, cons>(q_gen_2256, q_gen_2300) -> q_gen_2300
<a, cons, cons>(q_gen_2262, q_gen_2255) -> q_gen_2250
<a, nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2250
<b, cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2250
<b, cons, cons>(q_gen_2262, q_gen_2255) -> q_gen_2250
<b, cons, cons>(q_gen_2262, q_gen_2300) -> q_gen_2250
<b, nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2250
<a, cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2299
<a, cons, cons>(q_gen_2256, q_gen_2300) -> q_gen_2299
<b, cons, cons>(q_gen_2256, q_gen_2300) -> q_gen_2299
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_2249, q_gen_2258, q_gen_2259, q_gen_2280, q_gen_2281, q_gen_2282, q_gen_2283, q_gen_2286},
Q_f={q_gen_2249},
Delta=
{
<nil>() -> q_gen_2258
<cons>(q_gen_2281, q_gen_2258) -> q_gen_2280
<cons>(q_gen_2281, q_gen_2280) -> q_gen_2280
<a>() -> q_gen_2281
<b>() -> q_gen_2281
<s>(q_gen_2283) -> q_gen_2283
<z>() -> q_gen_2283
<cons, s>(q_gen_2259, q_gen_2258) -> q_gen_2249
<cons, s>(q_gen_2259, q_gen_2280) -> q_gen_2249
<cons, s>(q_gen_2282, q_gen_2280) -> q_gen_2249
<nil, z>() -> q_gen_2249
<a, z>() -> q_gen_2259
<b, z>() -> q_gen_2259
<a, s>(q_gen_2283) -> q_gen_2282
<b, s>(q_gen_2283) -> q_gen_2282
<cons, s>(q_gen_2282, q_gen_2258) -> q_gen_2286
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_2247, q_gen_2260},
Q_f={q_gen_2247},
Delta=
{
<a, a>() -> q_gen_2247
<a, b>() -> q_gen_2247
<b, b>() -> q_gen_2247
<b, a>() -> q_gen_2260
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  leqnat -> 
{{{
Q={q_gen_2244, q_gen_2246, q_gen_2287},
Q_f={q_gen_2244},
Delta=
{
<s>(q_gen_2246) -> q_gen_2246
<z>() -> q_gen_2246
<s, s>(q_gen_2244) -> q_gen_2244
<z, s>(q_gen_2246) -> q_gen_2244
<z, z>() -> q_gen_2244
<s, s>(q_gen_2287) -> q_gen_2287
<s, z>(q_gen_2246) -> q_gen_2287
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 26
() -> length([nil, z]) -> 26
() -> leq([a, y]) -> 26
() -> leq([b, b]) -> 26
() -> leqnat([z, s(nn2)]) -> 26
() -> leqnat([z, z]) -> 26
(insert([x, l, _jj]) /\ length([_jj, _kj]) /\ length([l, _ij])) -> leqnat([_ij, _kj]) -> 31
(insert([x, z, _zi]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _zi)]) -> 29
(length([ll, _ej])) -> length([cons(x, ll), s(_ej)]) -> 32
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 31
(leq([b, a])) -> BOT -> 27
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 27
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 28
(leqnat([s(nn1), z])) -> BOT -> 27
}
Sat witness: Found: ((leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]), {
x -> b  ;  y -> b  ;  z -> cons(b, nil)
})

-------------------------------------------
Step 42, which took 0.056877 s (model generation: 0.052934,  model checking: 0.003943):

Model:
|_
{
insert -> 
{{{
Q={q_gen_2250, q_gen_2251, q_gen_2252, q_gen_2255, q_gen_2256},
Q_f={q_gen_2250},
Delta=
{
<nil>() -> q_gen_2251
<a>() -> q_gen_2252
<b>() -> q_gen_2252
<cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2255
<nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2255
<a, a>() -> q_gen_2256
<a, b>() -> q_gen_2256
<b, a>() -> q_gen_2256
<b, b>() -> q_gen_2256
<a, cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2250
<a, nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2250
<b, cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2250
<b, nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2250
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_2249, q_gen_2258, q_gen_2259, q_gen_2280, q_gen_2281, q_gen_2282, q_gen_2283, q_gen_2285, q_gen_2291, q_gen_2294, q_gen_2298},
Q_f={q_gen_2249},
Delta=
{
<nil>() -> q_gen_2258
<cons>(q_gen_2281, q_gen_2258) -> q_gen_2280
<a>() -> q_gen_2281
<b>() -> q_gen_2281
<z>() -> q_gen_2283
<s>(q_gen_2283) -> q_gen_2294
<s>(q_gen_2294) -> q_gen_2294
<cons>(q_gen_2281, q_gen_2280) -> q_gen_2298
<cons>(q_gen_2281, q_gen_2298) -> q_gen_2298
<cons, s>(q_gen_2259, q_gen_2258) -> q_gen_2249
<cons, s>(q_gen_2282, q_gen_2258) -> q_gen_2249
<cons, s>(q_gen_2282, q_gen_2280) -> q_gen_2249
<cons, s>(q_gen_2291, q_gen_2280) -> q_gen_2249
<cons, s>(q_gen_2291, q_gen_2298) -> q_gen_2249
<nil, z>() -> q_gen_2249
<a, z>() -> q_gen_2259
<b, z>() -> q_gen_2259
<b, s>(q_gen_2283) -> q_gen_2282
<cons, s>(q_gen_2259, q_gen_2280) -> q_gen_2285
<cons, s>(q_gen_2259, q_gen_2298) -> q_gen_2285
<cons, s>(q_gen_2282, q_gen_2298) -> q_gen_2285
<cons, s>(q_gen_2291, q_gen_2258) -> q_gen_2285
<a, s>(q_gen_2283) -> q_gen_2291
<a, s>(q_gen_2294) -> q_gen_2291
<b, s>(q_gen_2294) -> q_gen_2291
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_2247, q_gen_2260},
Q_f={q_gen_2247},
Delta=
{
<a, a>() -> q_gen_2247
<a, b>() -> q_gen_2247
<b, b>() -> q_gen_2247
<b, a>() -> q_gen_2260
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  leqnat -> 
{{{
Q={q_gen_2244, q_gen_2246, q_gen_2287},
Q_f={q_gen_2244},
Delta=
{
<s>(q_gen_2246) -> q_gen_2246
<z>() -> q_gen_2246
<s, s>(q_gen_2244) -> q_gen_2244
<z, s>(q_gen_2246) -> q_gen_2244
<z, z>() -> q_gen_2244
<s, s>(q_gen_2287) -> q_gen_2287
<s, z>(q_gen_2246) -> q_gen_2287
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 27
() -> length([nil, z]) -> 27
() -> leq([a, y]) -> 27
() -> leq([b, b]) -> 27
() -> leqnat([z, s(nn2)]) -> 27
() -> leqnat([z, z]) -> 27
(insert([x, l, _jj]) /\ length([_jj, _kj]) /\ length([l, _ij])) -> leqnat([_ij, _kj]) -> 34
(insert([x, z, _zi]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _zi)]) -> 30
(length([ll, _ej])) -> length([cons(x, ll), s(_ej)]) -> 32
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 32
(leq([b, a])) -> BOT -> 28
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 28
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 29
(leqnat([s(nn1), z])) -> BOT -> 28
}
Sat witness: Found: ((insert([x, l, _jj]) /\ length([_jj, _kj]) /\ length([l, _ij])) -> leqnat([_ij, _kj]), {
_ij -> s(s(s(z)))  ;  _jj -> cons(a, cons(b, cons(b, cons(b, nil))))  ;  _kj -> s(s(z))  ;  l -> cons(b, cons(b, cons(b, nil)))  ;  x -> b
})

-------------------------------------------
Step 43, which took 0.067221 s (model generation: 0.061630,  model checking: 0.005591):

Model:
|_
{
insert -> 
{{{
Q={q_gen_2250, q_gen_2251, q_gen_2252, q_gen_2255, q_gen_2256},
Q_f={q_gen_2250},
Delta=
{
<nil>() -> q_gen_2251
<a>() -> q_gen_2252
<b>() -> q_gen_2252
<cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2255
<nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2255
<a, a>() -> q_gen_2256
<a, b>() -> q_gen_2256
<b, a>() -> q_gen_2256
<b, b>() -> q_gen_2256
<a, cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2250
<a, nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2250
<b, cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2250
<b, nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2250
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_2249, q_gen_2258, q_gen_2259, q_gen_2280, q_gen_2281, q_gen_2282, q_gen_2283, q_gen_2285, q_gen_2293, q_gen_2294, q_gen_2298},
Q_f={q_gen_2249},
Delta=
{
<nil>() -> q_gen_2258
<cons>(q_gen_2281, q_gen_2258) -> q_gen_2280
<a>() -> q_gen_2281
<b>() -> q_gen_2281
<z>() -> q_gen_2283
<s>(q_gen_2283) -> q_gen_2294
<s>(q_gen_2294) -> q_gen_2294
<cons>(q_gen_2281, q_gen_2280) -> q_gen_2298
<cons>(q_gen_2281, q_gen_2298) -> q_gen_2298
<cons, s>(q_gen_2259, q_gen_2258) -> q_gen_2249
<cons, s>(q_gen_2282, q_gen_2258) -> q_gen_2249
<cons, s>(q_gen_2282, q_gen_2280) -> q_gen_2249
<cons, s>(q_gen_2293, q_gen_2280) -> q_gen_2249
<cons, s>(q_gen_2293, q_gen_2298) -> q_gen_2249
<nil, z>() -> q_gen_2249
<a, z>() -> q_gen_2259
<b, z>() -> q_gen_2259
<a, s>(q_gen_2283) -> q_gen_2282
<b, s>(q_gen_2283) -> q_gen_2282
<cons, s>(q_gen_2259, q_gen_2280) -> q_gen_2285
<cons, s>(q_gen_2259, q_gen_2298) -> q_gen_2285
<cons, s>(q_gen_2282, q_gen_2298) -> q_gen_2285
<cons, s>(q_gen_2293, q_gen_2258) -> q_gen_2285
<a, s>(q_gen_2294) -> q_gen_2293
<b, s>(q_gen_2294) -> q_gen_2293
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_2247, q_gen_2260},
Q_f={q_gen_2247},
Delta=
{
<a, a>() -> q_gen_2247
<a, b>() -> q_gen_2247
<b, b>() -> q_gen_2247
<b, a>() -> q_gen_2260
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  leqnat -> 
{{{
Q={q_gen_2244, q_gen_2246, q_gen_2287},
Q_f={q_gen_2244},
Delta=
{
<s>(q_gen_2246) -> q_gen_2246
<z>() -> q_gen_2246
<s, s>(q_gen_2244) -> q_gen_2244
<z, s>(q_gen_2246) -> q_gen_2244
<z, z>() -> q_gen_2244
<s, s>(q_gen_2287) -> q_gen_2287
<s, z>(q_gen_2246) -> q_gen_2287
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 28
() -> length([nil, z]) -> 28
() -> leq([a, y]) -> 28
() -> leq([b, b]) -> 28
() -> leqnat([z, s(nn2)]) -> 28
() -> leqnat([z, z]) -> 28
(insert([x, l, _jj]) /\ length([_jj, _kj]) /\ length([l, _ij])) -> leqnat([_ij, _kj]) -> 37
(insert([x, z, _zi]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _zi)]) -> 31
(length([ll, _ej])) -> length([cons(x, ll), s(_ej)]) -> 33
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 33
(leq([b, a])) -> BOT -> 29
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 29
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 30
(leqnat([s(nn1), z])) -> BOT -> 29
}
Sat witness: Found: ((insert([x, l, _jj]) /\ length([_jj, _kj]) /\ length([l, _ij])) -> leqnat([_ij, _kj]), {
_ij -> s(s(s(s(z))))  ;  _jj -> cons(b, cons(b, cons(b, nil)))  ;  _kj -> s(s(s(z)))  ;  l -> cons(b, cons(b, nil))  ;  x -> a
})

-------------------------------------------
Step 44, which took 0.082594 s (model generation: 0.077572,  model checking: 0.005022):

Model:
|_
{
insert -> 
{{{
Q={q_gen_2250, q_gen_2251, q_gen_2252, q_gen_2255, q_gen_2256},
Q_f={q_gen_2250},
Delta=
{
<nil>() -> q_gen_2251
<a>() -> q_gen_2252
<b>() -> q_gen_2252
<cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2255
<nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2255
<a, a>() -> q_gen_2256
<a, b>() -> q_gen_2256
<b, a>() -> q_gen_2256
<b, b>() -> q_gen_2256
<a, cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2250
<a, nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2250
<b, cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2250
<b, nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2250
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_2249, q_gen_2258, q_gen_2259, q_gen_2280, q_gen_2281, q_gen_2282, q_gen_2283, q_gen_2285, q_gen_2293, q_gen_2294, q_gen_2298},
Q_f={q_gen_2249},
Delta=
{
<nil>() -> q_gen_2258
<cons>(q_gen_2281, q_gen_2258) -> q_gen_2280
<a>() -> q_gen_2281
<b>() -> q_gen_2281
<z>() -> q_gen_2283
<s>(q_gen_2283) -> q_gen_2294
<s>(q_gen_2294) -> q_gen_2294
<cons>(q_gen_2281, q_gen_2280) -> q_gen_2298
<cons>(q_gen_2281, q_gen_2298) -> q_gen_2298
<cons, s>(q_gen_2259, q_gen_2258) -> q_gen_2249
<cons, s>(q_gen_2282, q_gen_2280) -> q_gen_2249
<cons, s>(q_gen_2293, q_gen_2298) -> q_gen_2249
<nil, z>() -> q_gen_2249
<a, z>() -> q_gen_2259
<b, z>() -> q_gen_2259
<a, s>(q_gen_2283) -> q_gen_2282
<b, s>(q_gen_2283) -> q_gen_2282
<cons, s>(q_gen_2259, q_gen_2280) -> q_gen_2285
<cons, s>(q_gen_2259, q_gen_2298) -> q_gen_2285
<cons, s>(q_gen_2282, q_gen_2258) -> q_gen_2285
<cons, s>(q_gen_2282, q_gen_2298) -> q_gen_2285
<cons, s>(q_gen_2293, q_gen_2258) -> q_gen_2285
<cons, s>(q_gen_2293, q_gen_2280) -> q_gen_2285
<a, s>(q_gen_2294) -> q_gen_2293
<b, s>(q_gen_2294) -> q_gen_2293
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_2247, q_gen_2260},
Q_f={q_gen_2247},
Delta=
{
<a, a>() -> q_gen_2247
<a, b>() -> q_gen_2247
<b, b>() -> q_gen_2247
<b, a>() -> q_gen_2260
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  leqnat -> 
{{{
Q={q_gen_2244, q_gen_2246, q_gen_2287},
Q_f={q_gen_2244},
Delta=
{
<s>(q_gen_2246) -> q_gen_2246
<z>() -> q_gen_2246
<s, s>(q_gen_2244) -> q_gen_2244
<z, s>(q_gen_2246) -> q_gen_2244
<z, z>() -> q_gen_2244
<s, s>(q_gen_2287) -> q_gen_2287
<s, z>(q_gen_2246) -> q_gen_2287
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 29
() -> length([nil, z]) -> 29
() -> leq([a, y]) -> 29
() -> leq([b, b]) -> 29
() -> leqnat([z, s(nn2)]) -> 29
() -> leqnat([z, z]) -> 29
(insert([x, l, _jj]) /\ length([_jj, _kj]) /\ length([l, _ij])) -> leqnat([_ij, _kj]) -> 40
(insert([x, z, _zi]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _zi)]) -> 32
(length([ll, _ej])) -> length([cons(x, ll), s(_ej)]) -> 34
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 34
(leq([b, a])) -> BOT -> 30
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 30
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 31
(leqnat([s(nn1), z])) -> BOT -> 30
}
Sat witness: Found: ((insert([x, l, _jj]) /\ length([_jj, _kj]) /\ length([l, _ij])) -> leqnat([_ij, _kj]), {
_ij -> s(s(s(s(z))))  ;  _jj -> cons(b, cons(b, cons(b, cons(b, nil))))  ;  _kj -> s(s(s(z)))  ;  l -> cons(b, cons(b, cons(b, nil)))  ;  x -> a
})

-------------------------------------------
Step 45, which took 0.081188 s (model generation: 0.080783,  model checking: 0.000405):

Model:
|_
{
insert -> 
{{{
Q={q_gen_2250, q_gen_2251, q_gen_2252, q_gen_2255, q_gen_2256},
Q_f={q_gen_2250},
Delta=
{
<nil>() -> q_gen_2251
<a>() -> q_gen_2252
<b>() -> q_gen_2252
<cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2255
<nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2255
<a, a>() -> q_gen_2256
<a, b>() -> q_gen_2256
<b, a>() -> q_gen_2256
<b, b>() -> q_gen_2256
<a, cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2250
<a, nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2250
<b, cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2250
<b, nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2250
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_2249, q_gen_2258, q_gen_2259, q_gen_2280, q_gen_2281, q_gen_2282, q_gen_2283, q_gen_2285, q_gen_2293, q_gen_2294, q_gen_2298, q_gen_2316},
Q_f={q_gen_2249},
Delta=
{
<cons>(q_gen_2281, q_gen_2298) -> q_gen_2258
<nil>() -> q_gen_2258
<cons>(q_gen_2281, q_gen_2258) -> q_gen_2280
<a>() -> q_gen_2281
<b>() -> q_gen_2281
<z>() -> q_gen_2283
<s>(q_gen_2283) -> q_gen_2294
<cons>(q_gen_2281, q_gen_2280) -> q_gen_2298
<s>(q_gen_2294) -> q_gen_2316
<cons, s>(q_gen_2259, q_gen_2258) -> q_gen_2249
<cons, s>(q_gen_2282, q_gen_2280) -> q_gen_2249
<cons, s>(q_gen_2282, q_gen_2298) -> q_gen_2249
<cons, s>(q_gen_2293, q_gen_2298) -> q_gen_2249
<nil, z>() -> q_gen_2249
<a, s>(q_gen_2316) -> q_gen_2259
<a, z>() -> q_gen_2259
<b, s>(q_gen_2316) -> q_gen_2259
<b, z>() -> q_gen_2259
<a, s>(q_gen_2283) -> q_gen_2282
<b, s>(q_gen_2283) -> q_gen_2282
<cons, s>(q_gen_2259, q_gen_2280) -> q_gen_2285
<cons, s>(q_gen_2259, q_gen_2298) -> q_gen_2285
<cons, s>(q_gen_2282, q_gen_2258) -> q_gen_2285
<cons, s>(q_gen_2293, q_gen_2258) -> q_gen_2285
<cons, s>(q_gen_2293, q_gen_2280) -> q_gen_2285
<b, s>(q_gen_2294) -> q_gen_2293
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_2247, q_gen_2260},
Q_f={q_gen_2247},
Delta=
{
<a, a>() -> q_gen_2247
<a, b>() -> q_gen_2247
<b, b>() -> q_gen_2247
<b, a>() -> q_gen_2260
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  leqnat -> 
{{{
Q={q_gen_2244, q_gen_2246, q_gen_2264, q_gen_2287},
Q_f={q_gen_2244},
Delta=
{
<z>() -> q_gen_2246
<s>(q_gen_2246) -> q_gen_2264
<s, s>(q_gen_2244) -> q_gen_2244
<s, z>(q_gen_2264) -> q_gen_2244
<z, s>(q_gen_2246) -> q_gen_2244
<z, s>(q_gen_2264) -> q_gen_2244
<z, z>() -> q_gen_2244
<s, s>(q_gen_2287) -> q_gen_2287
<s, z>(q_gen_2246) -> q_gen_2287
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 29
() -> length([nil, z]) -> 29
() -> leq([a, y]) -> 29
() -> leq([b, b]) -> 29
() -> leqnat([z, s(nn2)]) -> 32
() -> leqnat([z, z]) -> 30
(insert([x, l, _jj]) /\ length([_jj, _kj]) /\ length([l, _ij])) -> leqnat([_ij, _kj]) -> 40
(insert([x, z, _zi]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _zi)]) -> 32
(length([ll, _ej])) -> length([cons(x, ll), s(_ej)]) -> 34
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 34
(leq([b, a])) -> BOT -> 30
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 30
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 31
(leqnat([s(nn1), z])) -> BOT -> 30
}
Sat witness: Found: (() -> leqnat([z, s(nn2)]), {
nn2 -> s(s(z))
})

-------------------------------------------
Step 46, which took 0.090874 s (model generation: 0.085912,  model checking: 0.004962):

Model:
|_
{
insert -> 
{{{
Q={q_gen_2250, q_gen_2251, q_gen_2252, q_gen_2255, q_gen_2256},
Q_f={q_gen_2250},
Delta=
{
<nil>() -> q_gen_2251
<a>() -> q_gen_2252
<b>() -> q_gen_2252
<cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2255
<nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2255
<a, a>() -> q_gen_2256
<a, b>() -> q_gen_2256
<b, a>() -> q_gen_2256
<b, b>() -> q_gen_2256
<a, cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2250
<a, nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2250
<b, cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2250
<b, nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2250
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_2249, q_gen_2258, q_gen_2259, q_gen_2280, q_gen_2281, q_gen_2282, q_gen_2283, q_gen_2286, q_gen_2293, q_gen_2294, q_gen_2298, q_gen_2303, q_gen_2304},
Q_f={q_gen_2249},
Delta=
{
<cons>(q_gen_2281, q_gen_2298) -> q_gen_2258
<nil>() -> q_gen_2258
<cons>(q_gen_2281, q_gen_2258) -> q_gen_2280
<b>() -> q_gen_2281
<z>() -> q_gen_2283
<s>(q_gen_2283) -> q_gen_2294
<s>(q_gen_2294) -> q_gen_2294
<cons>(q_gen_2281, q_gen_2280) -> q_gen_2298
<cons>(q_gen_2281, q_gen_2303) -> q_gen_2298
<cons>(q_gen_2304, q_gen_2280) -> q_gen_2303
<a>() -> q_gen_2304
<cons, s>(q_gen_2259, q_gen_2258) -> q_gen_2249
<cons, s>(q_gen_2259, q_gen_2280) -> q_gen_2249
<cons, s>(q_gen_2282, q_gen_2280) -> q_gen_2249
<cons, s>(q_gen_2282, q_gen_2298) -> q_gen_2249
<cons, s>(q_gen_2293, q_gen_2298) -> q_gen_2249
<cons, s>(q_gen_2293, q_gen_2303) -> q_gen_2249
<nil, z>() -> q_gen_2249
<a, z>() -> q_gen_2259
<b, z>() -> q_gen_2259
<a, s>(q_gen_2283) -> q_gen_2282
<b, s>(q_gen_2283) -> q_gen_2282
<cons, s>(q_gen_2259, q_gen_2298) -> q_gen_2286
<cons, s>(q_gen_2282, q_gen_2258) -> q_gen_2286
<cons, s>(q_gen_2293, q_gen_2258) -> q_gen_2286
<cons, s>(q_gen_2293, q_gen_2280) -> q_gen_2286
<a, s>(q_gen_2294) -> q_gen_2293
<b, s>(q_gen_2294) -> q_gen_2293
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_2247, q_gen_2260},
Q_f={q_gen_2247},
Delta=
{
<a, a>() -> q_gen_2247
<a, b>() -> q_gen_2247
<b, b>() -> q_gen_2247
<b, a>() -> q_gen_2260
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  leqnat -> 
{{{
Q={q_gen_2244, q_gen_2246, q_gen_2287},
Q_f={q_gen_2244},
Delta=
{
<s>(q_gen_2246) -> q_gen_2246
<z>() -> q_gen_2246
<s, s>(q_gen_2244) -> q_gen_2244
<z, s>(q_gen_2246) -> q_gen_2244
<z, z>() -> q_gen_2244
<s, s>(q_gen_2287) -> q_gen_2287
<s, z>(q_gen_2246) -> q_gen_2287
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 30
() -> length([nil, z]) -> 30
() -> leq([a, y]) -> 30
() -> leq([b, b]) -> 30
() -> leqnat([z, s(nn2)]) -> 33
() -> leqnat([z, z]) -> 31
(insert([x, l, _jj]) /\ length([_jj, _kj]) /\ length([l, _ij])) -> leqnat([_ij, _kj]) -> 40
(insert([x, z, _zi]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _zi)]) -> 33
(length([ll, _ej])) -> length([cons(x, ll), s(_ej)]) -> 37
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 35
(leq([b, a])) -> BOT -> 31
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 31
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 32
(leqnat([s(nn1), z])) -> BOT -> 31
}
Sat witness: Found: ((length([ll, _ej])) -> length([cons(x, ll), s(_ej)]), {
_ej -> s(s(z))  ;  ll -> cons(b, cons(b, cons(b, nil)))  ;  x -> a
})

-------------------------------------------
Step 47, which took 0.093299 s (model generation: 0.090268,  model checking: 0.003031):

Model:
|_
{
insert -> 
{{{
Q={q_gen_2250, q_gen_2251, q_gen_2252, q_gen_2255, q_gen_2256},
Q_f={q_gen_2250},
Delta=
{
<nil>() -> q_gen_2251
<a>() -> q_gen_2252
<b>() -> q_gen_2252
<cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2255
<nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2255
<a, a>() -> q_gen_2256
<a, b>() -> q_gen_2256
<b, a>() -> q_gen_2256
<b, b>() -> q_gen_2256
<a, cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2250
<a, nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2250
<b, cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2250
<b, nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2250
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_2249, q_gen_2258, q_gen_2259, q_gen_2280, q_gen_2281, q_gen_2282, q_gen_2283, q_gen_2286, q_gen_2293, q_gen_2294, q_gen_2298, q_gen_2303, q_gen_2304},
Q_f={q_gen_2249},
Delta=
{
<cons>(q_gen_2281, q_gen_2298) -> q_gen_2258
<nil>() -> q_gen_2258
<cons>(q_gen_2281, q_gen_2258) -> q_gen_2280
<b>() -> q_gen_2281
<z>() -> q_gen_2283
<s>(q_gen_2283) -> q_gen_2294
<s>(q_gen_2294) -> q_gen_2294
<cons>(q_gen_2281, q_gen_2280) -> q_gen_2298
<cons>(q_gen_2281, q_gen_2303) -> q_gen_2303
<cons>(q_gen_2304, q_gen_2280) -> q_gen_2303
<a>() -> q_gen_2304
<cons, s>(q_gen_2259, q_gen_2258) -> q_gen_2249
<cons, s>(q_gen_2259, q_gen_2280) -> q_gen_2249
<cons, s>(q_gen_2259, q_gen_2303) -> q_gen_2249
<cons, s>(q_gen_2282, q_gen_2280) -> q_gen_2249
<cons, s>(q_gen_2282, q_gen_2298) -> q_gen_2249
<cons, s>(q_gen_2293, q_gen_2298) -> q_gen_2249
<cons, s>(q_gen_2293, q_gen_2303) -> q_gen_2249
<nil, z>() -> q_gen_2249
<a, s>(q_gen_2294) -> q_gen_2259
<a, z>() -> q_gen_2259
<b, z>() -> q_gen_2259
<a, s>(q_gen_2283) -> q_gen_2282
<b, s>(q_gen_2283) -> q_gen_2282
<cons, s>(q_gen_2259, q_gen_2298) -> q_gen_2286
<cons, s>(q_gen_2282, q_gen_2258) -> q_gen_2286
<cons, s>(q_gen_2293, q_gen_2258) -> q_gen_2286
<cons, s>(q_gen_2293, q_gen_2280) -> q_gen_2286
<b, s>(q_gen_2294) -> q_gen_2293
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_2247, q_gen_2260},
Q_f={q_gen_2247},
Delta=
{
<a, a>() -> q_gen_2247
<a, b>() -> q_gen_2247
<b, b>() -> q_gen_2247
<b, a>() -> q_gen_2260
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  leqnat -> 
{{{
Q={q_gen_2244, q_gen_2246, q_gen_2287},
Q_f={q_gen_2244},
Delta=
{
<s>(q_gen_2246) -> q_gen_2246
<z>() -> q_gen_2246
<s, s>(q_gen_2244) -> q_gen_2244
<z, s>(q_gen_2246) -> q_gen_2244
<z, z>() -> q_gen_2244
<s, s>(q_gen_2287) -> q_gen_2287
<s, z>(q_gen_2246) -> q_gen_2287
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 31
() -> length([nil, z]) -> 31
() -> leq([a, y]) -> 31
() -> leq([b, b]) -> 31
() -> leqnat([z, s(nn2)]) -> 34
() -> leqnat([z, z]) -> 32
(insert([x, l, _jj]) /\ length([_jj, _kj]) /\ length([l, _ij])) -> leqnat([_ij, _kj]) -> 40
(insert([x, z, _zi]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _zi)]) -> 34
(length([ll, _ej])) -> length([cons(x, ll), s(_ej)]) -> 40
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 36
(leq([b, a])) -> BOT -> 32
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 32
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 33
(leqnat([s(nn1), z])) -> BOT -> 32
}
Sat witness: Found: ((length([ll, _ej])) -> length([cons(x, ll), s(_ej)]), {
_ej -> s(s(s(z)))  ;  ll -> cons(b, cons(b, cons(b, nil)))  ;  x -> b
})

-------------------------------------------
Step 48, which took 0.092887 s (model generation: 0.092106,  model checking: 0.000781):

Model:
|_
{
insert -> 
{{{
Q={q_gen_2250, q_gen_2251, q_gen_2252, q_gen_2255, q_gen_2256},
Q_f={q_gen_2250},
Delta=
{
<nil>() -> q_gen_2251
<a>() -> q_gen_2252
<b>() -> q_gen_2252
<cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2255
<nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2255
<a, a>() -> q_gen_2256
<a, b>() -> q_gen_2256
<b, a>() -> q_gen_2256
<b, b>() -> q_gen_2256
<a, cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2250
<a, nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2250
<b, cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2250
<b, nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2250
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_2249, q_gen_2258, q_gen_2259, q_gen_2280, q_gen_2281, q_gen_2282, q_gen_2283, q_gen_2285, q_gen_2293, q_gen_2294, q_gen_2298},
Q_f={q_gen_2249},
Delta=
{
<nil>() -> q_gen_2258
<cons>(q_gen_2281, q_gen_2258) -> q_gen_2280
<a>() -> q_gen_2281
<b>() -> q_gen_2281
<z>() -> q_gen_2283
<s>(q_gen_2283) -> q_gen_2294
<s>(q_gen_2294) -> q_gen_2294
<cons>(q_gen_2281, q_gen_2280) -> q_gen_2298
<cons>(q_gen_2281, q_gen_2298) -> q_gen_2298
<cons, s>(q_gen_2259, q_gen_2258) -> q_gen_2249
<cons, s>(q_gen_2282, q_gen_2258) -> q_gen_2249
<cons, s>(q_gen_2282, q_gen_2280) -> q_gen_2249
<cons, s>(q_gen_2293, q_gen_2280) -> q_gen_2249
<cons, s>(q_gen_2293, q_gen_2298) -> q_gen_2249
<nil, z>() -> q_gen_2249
<a, z>() -> q_gen_2259
<b, z>() -> q_gen_2259
<a, s>(q_gen_2283) -> q_gen_2282
<b, s>(q_gen_2283) -> q_gen_2282
<cons, s>(q_gen_2259, q_gen_2280) -> q_gen_2285
<cons, s>(q_gen_2259, q_gen_2298) -> q_gen_2285
<cons, s>(q_gen_2282, q_gen_2298) -> q_gen_2285
<cons, s>(q_gen_2293, q_gen_2258) -> q_gen_2285
<a, s>(q_gen_2294) -> q_gen_2293
<b, s>(q_gen_2294) -> q_gen_2293
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_2247, q_gen_2260},
Q_f={q_gen_2247},
Delta=
{
<a, a>() -> q_gen_2247
<a, b>() -> q_gen_2247
<b, b>() -> q_gen_2247
<b, a>() -> q_gen_2260
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  leqnat -> 
{{{
Q={q_gen_2244, q_gen_2246, q_gen_2287, q_gen_2288, q_gen_2296},
Q_f={q_gen_2244},
Delta=
{
<s>(q_gen_2246) -> q_gen_2246
<z>() -> q_gen_2246
<s, s>(q_gen_2244) -> q_gen_2244
<s, s>(q_gen_2296) -> q_gen_2244
<z, s>(q_gen_2246) -> q_gen_2244
<z, z>() -> q_gen_2244
<s, s>(q_gen_2288) -> q_gen_2287
<s, z>(q_gen_2246) -> q_gen_2288
<s, s>(q_gen_2287) -> q_gen_2296
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 32
() -> length([nil, z]) -> 32
() -> leq([a, y]) -> 32
() -> leq([b, b]) -> 32
() -> leqnat([z, s(nn2)]) -> 34
() -> leqnat([z, z]) -> 33
(insert([x, l, _jj]) /\ length([_jj, _kj]) /\ length([l, _ij])) -> leqnat([_ij, _kj]) -> 40
(insert([x, z, _zi]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _zi)]) -> 34
(length([ll, _ej])) -> length([cons(x, ll), s(_ej)]) -> 40
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 36
(leq([b, a])) -> BOT -> 33
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 33
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 36
(leqnat([s(nn1), z])) -> BOT -> 33
}
Sat witness: Found: ((leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]), {
nn1 -> s(s(s(z)))  ;  nn2 -> s(s(z))
})

-------------------------------------------
Step 49, which took 0.091561 s (model generation: 0.090862,  model checking: 0.000699):

Model:
|_
{
insert -> 
{{{
Q={q_gen_2250, q_gen_2251, q_gen_2252, q_gen_2255, q_gen_2256},
Q_f={q_gen_2250},
Delta=
{
<nil>() -> q_gen_2251
<a>() -> q_gen_2252
<b>() -> q_gen_2252
<cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2255
<nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2255
<a, a>() -> q_gen_2256
<a, b>() -> q_gen_2256
<b, a>() -> q_gen_2256
<b, b>() -> q_gen_2256
<a, cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2250
<a, nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2250
<b, cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2250
<b, nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2250
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_2249, q_gen_2258, q_gen_2259, q_gen_2280, q_gen_2281, q_gen_2282, q_gen_2283, q_gen_2285, q_gen_2291, q_gen_2294, q_gen_2298, q_gen_2316},
Q_f={q_gen_2249},
Delta=
{
<cons>(q_gen_2281, q_gen_2298) -> q_gen_2258
<nil>() -> q_gen_2258
<cons>(q_gen_2281, q_gen_2258) -> q_gen_2280
<a>() -> q_gen_2281
<b>() -> q_gen_2281
<z>() -> q_gen_2283
<s>(q_gen_2283) -> q_gen_2294
<cons>(q_gen_2281, q_gen_2280) -> q_gen_2298
<s>(q_gen_2294) -> q_gen_2316
<cons, s>(q_gen_2259, q_gen_2258) -> q_gen_2249
<cons, s>(q_gen_2282, q_gen_2280) -> q_gen_2249
<cons, s>(q_gen_2291, q_gen_2280) -> q_gen_2249
<cons, s>(q_gen_2291, q_gen_2298) -> q_gen_2249
<nil, z>() -> q_gen_2249
<a, s>(q_gen_2294) -> q_gen_2259
<a, s>(q_gen_2316) -> q_gen_2259
<a, z>() -> q_gen_2259
<b, s>(q_gen_2316) -> q_gen_2259
<b, z>() -> q_gen_2259
<b, s>(q_gen_2283) -> q_gen_2282
<cons, s>(q_gen_2259, q_gen_2280) -> q_gen_2285
<cons, s>(q_gen_2259, q_gen_2298) -> q_gen_2285
<cons, s>(q_gen_2282, q_gen_2258) -> q_gen_2285
<cons, s>(q_gen_2282, q_gen_2298) -> q_gen_2285
<cons, s>(q_gen_2291, q_gen_2258) -> q_gen_2285
<a, s>(q_gen_2283) -> q_gen_2291
<b, s>(q_gen_2294) -> q_gen_2291
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_2247, q_gen_2260},
Q_f={q_gen_2247},
Delta=
{
<a, a>() -> q_gen_2247
<a, b>() -> q_gen_2247
<b, b>() -> q_gen_2247
<b, a>() -> q_gen_2260
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  leqnat -> 
{{{
Q={q_gen_2244, q_gen_2246, q_gen_2264, q_gen_2287},
Q_f={q_gen_2244},
Delta=
{
<z>() -> q_gen_2246
<s>(q_gen_2246) -> q_gen_2264
<s>(q_gen_2264) -> q_gen_2264
<s, s>(q_gen_2244) -> q_gen_2244
<s, z>(q_gen_2264) -> q_gen_2244
<z, s>(q_gen_2246) -> q_gen_2244
<z, s>(q_gen_2264) -> q_gen_2244
<z, z>() -> q_gen_2244
<s, s>(q_gen_2287) -> q_gen_2287
<s, z>(q_gen_2246) -> q_gen_2287
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 33
() -> length([nil, z]) -> 33
() -> leq([a, y]) -> 33
() -> leq([b, b]) -> 33
() -> leqnat([z, s(nn2)]) -> 34
() -> leqnat([z, z]) -> 33
(insert([x, l, _jj]) /\ length([_jj, _kj]) /\ length([l, _ij])) -> leqnat([_ij, _kj]) -> 40
(insert([x, z, _zi]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _zi)]) -> 34
(length([ll, _ej])) -> length([cons(x, ll), s(_ej)]) -> 40
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 36
(leq([b, a])) -> BOT -> 33
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 33
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 36
(leqnat([s(nn1), z])) -> BOT -> 36
}
Sat witness: Found: ((leqnat([s(nn1), z])) -> BOT, {
nn1 -> s(z)
})

-------------------------------------------
Step 50, which took 0.101842 s (model generation: 0.095559,  model checking: 0.006283):

Model:
|_
{
insert -> 
{{{
Q={q_gen_2250, q_gen_2251, q_gen_2252, q_gen_2255, q_gen_2256, q_gen_2262, q_gen_2299},
Q_f={q_gen_2250},
Delta=
{
<nil>() -> q_gen_2251
<a>() -> q_gen_2252
<b>() -> q_gen_2252
<cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2255
<cons, cons>(q_gen_2262, q_gen_2255) -> q_gen_2255
<nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2255
<a, b>() -> q_gen_2256
<b, b>() -> q_gen_2256
<a, a>() -> q_gen_2262
<b, a>() -> q_gen_2262
<a, cons, cons>(q_gen_2262, q_gen_2255) -> q_gen_2250
<a, nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2250
<b, cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2250
<b, cons, cons>(q_gen_2262, q_gen_2255) -> q_gen_2250
<b, nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2250
<a, cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2299
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_2249, q_gen_2258, q_gen_2259, q_gen_2280, q_gen_2281, q_gen_2282, q_gen_2283, q_gen_2285, q_gen_2293, q_gen_2294, q_gen_2298},
Q_f={q_gen_2249},
Delta=
{
<nil>() -> q_gen_2258
<cons>(q_gen_2281, q_gen_2258) -> q_gen_2280
<a>() -> q_gen_2281
<b>() -> q_gen_2281
<z>() -> q_gen_2283
<s>(q_gen_2283) -> q_gen_2294
<s>(q_gen_2294) -> q_gen_2294
<cons>(q_gen_2281, q_gen_2280) -> q_gen_2298
<cons>(q_gen_2281, q_gen_2298) -> q_gen_2298
<cons, s>(q_gen_2259, q_gen_2258) -> q_gen_2249
<cons, s>(q_gen_2282, q_gen_2280) -> q_gen_2249
<cons, s>(q_gen_2293, q_gen_2280) -> q_gen_2249
<cons, s>(q_gen_2293, q_gen_2298) -> q_gen_2249
<nil, z>() -> q_gen_2249
<a, z>() -> q_gen_2259
<b, z>() -> q_gen_2259
<a, s>(q_gen_2283) -> q_gen_2282
<b, s>(q_gen_2283) -> q_gen_2282
<cons, s>(q_gen_2259, q_gen_2280) -> q_gen_2285
<cons, s>(q_gen_2259, q_gen_2298) -> q_gen_2285
<cons, s>(q_gen_2282, q_gen_2258) -> q_gen_2285
<cons, s>(q_gen_2282, q_gen_2298) -> q_gen_2285
<cons, s>(q_gen_2293, q_gen_2258) -> q_gen_2285
<a, s>(q_gen_2294) -> q_gen_2293
<b, s>(q_gen_2294) -> q_gen_2293
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_2247, q_gen_2260},
Q_f={q_gen_2247},
Delta=
{
<a, a>() -> q_gen_2247
<a, b>() -> q_gen_2247
<b, b>() -> q_gen_2247
<b, a>() -> q_gen_2260
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  leqnat -> 
{{{
Q={q_gen_2244, q_gen_2246, q_gen_2287},
Q_f={q_gen_2244},
Delta=
{
<s>(q_gen_2246) -> q_gen_2246
<z>() -> q_gen_2246
<s, s>(q_gen_2244) -> q_gen_2244
<z, s>(q_gen_2246) -> q_gen_2244
<z, z>() -> q_gen_2244
<s, s>(q_gen_2287) -> q_gen_2287
<s, z>(q_gen_2246) -> q_gen_2287
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 34
() -> length([nil, z]) -> 34
() -> leq([a, y]) -> 34
() -> leq([b, b]) -> 34
() -> leqnat([z, s(nn2)]) -> 35
() -> leqnat([z, z]) -> 34
(insert([x, l, _jj]) /\ length([_jj, _kj]) /\ length([l, _ij])) -> leqnat([_ij, _kj]) -> 43
(insert([x, z, _zi]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _zi)]) -> 35
(length([ll, _ej])) -> length([cons(x, ll), s(_ej)]) -> 41
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 37
(leq([b, a])) -> BOT -> 34
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 34
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 37
(leqnat([s(nn1), z])) -> BOT -> 37
}
Sat witness: Found: ((insert([x, l, _jj]) /\ length([_jj, _kj]) /\ length([l, _ij])) -> leqnat([_ij, _kj]), {
_ij -> s(s(s(s(z))))  ;  _jj -> cons(b, cons(b, cons(b, cons(b, nil))))  ;  _kj -> s(s(s(z)))  ;  l -> cons(b, cons(b, cons(b, nil)))  ;  x -> b
})

-------------------------------------------
Step 51, which took 0.111266 s (model generation: 0.106680,  model checking: 0.004586):

Model:
|_
{
insert -> 
{{{
Q={q_gen_2250, q_gen_2251, q_gen_2252, q_gen_2255, q_gen_2256, q_gen_2262, q_gen_2269, q_gen_2284},
Q_f={q_gen_2250},
Delta=
{
<nil>() -> q_gen_2251
<a>() -> q_gen_2252
<b>() -> q_gen_2252
<cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2255
<cons, cons>(q_gen_2262, q_gen_2255) -> q_gen_2255
<cons, cons>(q_gen_2269, q_gen_2255) -> q_gen_2255
<nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2255
<b, b>() -> q_gen_2256
<a, a>() -> q_gen_2262
<a, b>() -> q_gen_2269
<b, a>() -> q_gen_2269
<a, cons, cons>(q_gen_2262, q_gen_2255) -> q_gen_2250
<a, cons, cons>(q_gen_2269, q_gen_2255) -> q_gen_2250
<a, nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2250
<b, cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2250
<b, cons, cons>(q_gen_2262, q_gen_2255) -> q_gen_2250
<b, nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2250
<a, cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2284
<b, cons, cons>(q_gen_2269, q_gen_2255) -> q_gen_2284
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_2249, q_gen_2258, q_gen_2259, q_gen_2271, q_gen_2280, q_gen_2281, q_gen_2283, q_gen_2289, q_gen_2291, q_gen_2294, q_gen_2298},
Q_f={q_gen_2249},
Delta=
{
<nil>() -> q_gen_2258
<cons>(q_gen_2281, q_gen_2258) -> q_gen_2280
<cons>(q_gen_2281, q_gen_2298) -> q_gen_2280
<a>() -> q_gen_2281
<b>() -> q_gen_2281
<s>(q_gen_2294) -> q_gen_2283
<z>() -> q_gen_2283
<s>(q_gen_2283) -> q_gen_2294
<cons>(q_gen_2281, q_gen_2280) -> q_gen_2298
<cons, s>(q_gen_2259, q_gen_2258) -> q_gen_2249
<cons, s>(q_gen_2271, q_gen_2258) -> q_gen_2249
<cons, s>(q_gen_2271, q_gen_2280) -> q_gen_2249
<cons, s>(q_gen_2291, q_gen_2280) -> q_gen_2249
<cons, s>(q_gen_2291, q_gen_2298) -> q_gen_2249
<nil, z>() -> q_gen_2249
<a, s>(q_gen_2294) -> q_gen_2259
<b, z>() -> q_gen_2259
<a, z>() -> q_gen_2271
<b, s>(q_gen_2283) -> q_gen_2271
<cons, s>(q_gen_2259, q_gen_2280) -> q_gen_2289
<cons, s>(q_gen_2259, q_gen_2298) -> q_gen_2289
<cons, s>(q_gen_2271, q_gen_2298) -> q_gen_2289
<cons, s>(q_gen_2291, q_gen_2258) -> q_gen_2289
<a, s>(q_gen_2283) -> q_gen_2291
<b, s>(q_gen_2294) -> q_gen_2291
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_2247, q_gen_2260},
Q_f={q_gen_2247},
Delta=
{
<a, a>() -> q_gen_2247
<a, b>() -> q_gen_2247
<b, b>() -> q_gen_2247
<b, a>() -> q_gen_2260
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  leqnat -> 
{{{
Q={q_gen_2244, q_gen_2246, q_gen_2287},
Q_f={q_gen_2244},
Delta=
{
<s>(q_gen_2246) -> q_gen_2246
<z>() -> q_gen_2246
<s, s>(q_gen_2244) -> q_gen_2244
<z, s>(q_gen_2246) -> q_gen_2244
<z, z>() -> q_gen_2244
<s, s>(q_gen_2287) -> q_gen_2287
<s, z>(q_gen_2246) -> q_gen_2287
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 35
() -> length([nil, z]) -> 35
() -> leq([a, y]) -> 35
() -> leq([b, b]) -> 35
() -> leqnat([z, s(nn2)]) -> 36
() -> leqnat([z, z]) -> 35
(insert([x, l, _jj]) /\ length([_jj, _kj]) /\ length([l, _ij])) -> leqnat([_ij, _kj]) -> 43
(insert([x, z, _zi]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _zi)]) -> 36
(length([ll, _ej])) -> length([cons(x, ll), s(_ej)]) -> 44
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 38
(leq([b, a])) -> BOT -> 35
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 35
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 38
(leqnat([s(nn1), z])) -> BOT -> 38
}
Sat witness: Found: ((length([ll, _ej])) -> length([cons(x, ll), s(_ej)]), {
_ej -> s(s(z))  ;  ll -> cons(b, cons(b, nil))  ;  x -> a
})

-------------------------------------------
Step 52, which took 0.188307 s (model generation: 0.180819,  model checking: 0.007488):

Model:
|_
{
insert -> 
{{{
Q={q_gen_2250, q_gen_2251, q_gen_2252, q_gen_2255, q_gen_2256},
Q_f={q_gen_2250},
Delta=
{
<nil>() -> q_gen_2251
<a>() -> q_gen_2252
<b>() -> q_gen_2252
<cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2255
<nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2255
<a, a>() -> q_gen_2256
<a, b>() -> q_gen_2256
<b, a>() -> q_gen_2256
<b, b>() -> q_gen_2256
<a, cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2250
<a, nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2250
<b, cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2250
<b, nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2250
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_2249, q_gen_2258, q_gen_2259, q_gen_2280, q_gen_2281, q_gen_2282, q_gen_2283, q_gen_2286, q_gen_2291, q_gen_2294, q_gen_2298, q_gen_2314, q_gen_2315, q_gen_2316},
Q_f={q_gen_2249},
Delta=
{
<nil>() -> q_gen_2258
<cons>(q_gen_2281, q_gen_2258) -> q_gen_2280
<a>() -> q_gen_2281
<b>() -> q_gen_2281
<z>() -> q_gen_2283
<s>(q_gen_2283) -> q_gen_2294
<cons>(q_gen_2281, q_gen_2280) -> q_gen_2298
<cons>(q_gen_2281, q_gen_2298) -> q_gen_2314
<s>(q_gen_2294) -> q_gen_2316
<cons, s>(q_gen_2259, q_gen_2258) -> q_gen_2249
<cons, s>(q_gen_2259, q_gen_2280) -> q_gen_2249
<cons, s>(q_gen_2282, q_gen_2280) -> q_gen_2249
<cons, s>(q_gen_2291, q_gen_2280) -> q_gen_2249
<cons, s>(q_gen_2291, q_gen_2298) -> q_gen_2249
<cons, s>(q_gen_2315, q_gen_2298) -> q_gen_2249
<cons, s>(q_gen_2315, q_gen_2314) -> q_gen_2249
<nil, z>() -> q_gen_2249
<a, z>() -> q_gen_2259
<b, z>() -> q_gen_2259
<b, s>(q_gen_2283) -> q_gen_2282
<cons, s>(q_gen_2259, q_gen_2298) -> q_gen_2286
<cons, s>(q_gen_2282, q_gen_2258) -> q_gen_2286
<cons, s>(q_gen_2282, q_gen_2298) -> q_gen_2286
<cons, s>(q_gen_2282, q_gen_2314) -> q_gen_2286
<cons, s>(q_gen_2291, q_gen_2258) -> q_gen_2286
<cons, s>(q_gen_2291, q_gen_2314) -> q_gen_2286
<cons, s>(q_gen_2315, q_gen_2258) -> q_gen_2286
<cons, s>(q_gen_2315, q_gen_2280) -> q_gen_2286
<a, s>(q_gen_2283) -> q_gen_2291
<a, s>(q_gen_2294) -> q_gen_2291
<b, s>(q_gen_2294) -> q_gen_2291
<a, s>(q_gen_2316) -> q_gen_2315
<b, s>(q_gen_2316) -> q_gen_2315
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_2247, q_gen_2260},
Q_f={q_gen_2247},
Delta=
{
<a, a>() -> q_gen_2247
<a, b>() -> q_gen_2247
<b, b>() -> q_gen_2247
<b, a>() -> q_gen_2260
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  leqnat -> 
{{{
Q={q_gen_2244, q_gen_2246, q_gen_2287},
Q_f={q_gen_2244},
Delta=
{
<s>(q_gen_2246) -> q_gen_2246
<z>() -> q_gen_2246
<s, s>(q_gen_2244) -> q_gen_2244
<z, s>(q_gen_2246) -> q_gen_2244
<z, z>() -> q_gen_2244
<s, s>(q_gen_2287) -> q_gen_2287
<s, z>(q_gen_2246) -> q_gen_2287
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 36
() -> length([nil, z]) -> 36
() -> leq([a, y]) -> 36
() -> leq([b, b]) -> 36
() -> leqnat([z, s(nn2)]) -> 37
() -> leqnat([z, z]) -> 36
(insert([x, l, _jj]) /\ length([_jj, _kj]) /\ length([l, _ij])) -> leqnat([_ij, _kj]) -> 46
(insert([x, z, _zi]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _zi)]) -> 37
(length([ll, _ej])) -> length([cons(x, ll), s(_ej)]) -> 44
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 39
(leq([b, a])) -> BOT -> 36
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 36
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 39
(leqnat([s(nn1), z])) -> BOT -> 39
}
Sat witness: Found: ((insert([x, l, _jj]) /\ length([_jj, _kj]) /\ length([l, _ij])) -> leqnat([_ij, _kj]), {
_ij -> s(s(s(z)))  ;  _jj -> cons(a, cons(b, cons(b, nil)))  ;  _kj -> s(s(z))  ;  l -> cons(b, cons(b, nil))  ;  x -> a
})

-------------------------------------------
Step 53, which took 0.187775 s (model generation: 0.184484,  model checking: 0.003291):

Model:
|_
{
insert -> 
{{{
Q={q_gen_2250, q_gen_2251, q_gen_2252, q_gen_2255, q_gen_2256, q_gen_2262, q_gen_2299},
Q_f={q_gen_2250},
Delta=
{
<nil>() -> q_gen_2251
<a>() -> q_gen_2252
<b>() -> q_gen_2252
<cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2255
<cons, cons>(q_gen_2262, q_gen_2255) -> q_gen_2255
<nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2255
<a, b>() -> q_gen_2256
<b, b>() -> q_gen_2256
<a, a>() -> q_gen_2262
<b, a>() -> q_gen_2262
<a, cons, cons>(q_gen_2262, q_gen_2255) -> q_gen_2250
<a, nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2250
<b, cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2250
<b, cons, cons>(q_gen_2262, q_gen_2255) -> q_gen_2250
<b, nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2250
<a, cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2299
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_2249, q_gen_2258, q_gen_2259, q_gen_2280, q_gen_2281, q_gen_2282, q_gen_2283, q_gen_2285, q_gen_2293, q_gen_2294, q_gen_2298, q_gen_2316},
Q_f={q_gen_2249},
Delta=
{
<cons>(q_gen_2281, q_gen_2298) -> q_gen_2258
<nil>() -> q_gen_2258
<cons>(q_gen_2281, q_gen_2258) -> q_gen_2280
<a>() -> q_gen_2281
<b>() -> q_gen_2281
<z>() -> q_gen_2283
<s>(q_gen_2283) -> q_gen_2294
<cons>(q_gen_2281, q_gen_2280) -> q_gen_2298
<s>(q_gen_2294) -> q_gen_2316
<cons, s>(q_gen_2259, q_gen_2258) -> q_gen_2249
<cons, s>(q_gen_2282, q_gen_2280) -> q_gen_2249
<cons, s>(q_gen_2293, q_gen_2280) -> q_gen_2249
<cons, s>(q_gen_2293, q_gen_2298) -> q_gen_2249
<nil, z>() -> q_gen_2249
<a, s>(q_gen_2316) -> q_gen_2259
<a, z>() -> q_gen_2259
<b, s>(q_gen_2316) -> q_gen_2259
<b, z>() -> q_gen_2259
<a, s>(q_gen_2283) -> q_gen_2282
<b, s>(q_gen_2283) -> q_gen_2282
<cons, s>(q_gen_2259, q_gen_2280) -> q_gen_2285
<cons, s>(q_gen_2259, q_gen_2298) -> q_gen_2285
<cons, s>(q_gen_2282, q_gen_2258) -> q_gen_2285
<cons, s>(q_gen_2282, q_gen_2298) -> q_gen_2285
<cons, s>(q_gen_2293, q_gen_2258) -> q_gen_2285
<a, s>(q_gen_2294) -> q_gen_2293
<b, s>(q_gen_2294) -> q_gen_2293
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_2247, q_gen_2260},
Q_f={q_gen_2247},
Delta=
{
<a, a>() -> q_gen_2247
<a, b>() -> q_gen_2247
<b, b>() -> q_gen_2247
<b, a>() -> q_gen_2260
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  leqnat -> 
{{{
Q={q_gen_2244, q_gen_2246, q_gen_2287},
Q_f={q_gen_2244},
Delta=
{
<s>(q_gen_2246) -> q_gen_2246
<z>() -> q_gen_2246
<s, s>(q_gen_2244) -> q_gen_2244
<z, s>(q_gen_2246) -> q_gen_2244
<z, z>() -> q_gen_2244
<s, s>(q_gen_2287) -> q_gen_2287
<s, z>(q_gen_2246) -> q_gen_2287
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 37
() -> length([nil, z]) -> 37
() -> leq([a, y]) -> 37
() -> leq([b, b]) -> 37
() -> leqnat([z, s(nn2)]) -> 38
() -> leqnat([z, z]) -> 37
(insert([x, l, _jj]) /\ length([_jj, _kj]) /\ length([l, _ij])) -> leqnat([_ij, _kj]) -> 46
(insert([x, z, _zi]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _zi)]) -> 38
(length([ll, _ej])) -> length([cons(x, ll), s(_ej)]) -> 47
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 40
(leq([b, a])) -> BOT -> 37
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 37
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 40
(leqnat([s(nn1), z])) -> BOT -> 40
}
Sat witness: Found: ((length([ll, _ej])) -> length([cons(x, ll), s(_ej)]), {
_ej -> s(s(s(z)))  ;  ll -> cons(b, cons(b, nil))  ;  x -> b
})

-------------------------------------------
Step 54, which took 0.205713 s (model generation: 0.198198,  model checking: 0.007515):

Model:
|_
{
insert -> 
{{{
Q={q_gen_2250, q_gen_2251, q_gen_2252, q_gen_2255, q_gen_2256, q_gen_2262, q_gen_2269, q_gen_2284},
Q_f={q_gen_2250},
Delta=
{
<nil>() -> q_gen_2251
<a>() -> q_gen_2252
<b>() -> q_gen_2252
<cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2255
<cons, cons>(q_gen_2262, q_gen_2255) -> q_gen_2255
<cons, cons>(q_gen_2269, q_gen_2255) -> q_gen_2255
<nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2255
<b, b>() -> q_gen_2256
<a, a>() -> q_gen_2262
<a, b>() -> q_gen_2269
<b, a>() -> q_gen_2269
<a, cons, cons>(q_gen_2262, q_gen_2255) -> q_gen_2250
<a, cons, cons>(q_gen_2269, q_gen_2255) -> q_gen_2250
<a, nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2250
<b, cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2250
<b, cons, cons>(q_gen_2262, q_gen_2255) -> q_gen_2250
<b, nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2250
<a, cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2284
<b, cons, cons>(q_gen_2269, q_gen_2255) -> q_gen_2284
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_2249, q_gen_2258, q_gen_2259, q_gen_2280, q_gen_2281, q_gen_2282, q_gen_2283, q_gen_2286, q_gen_2293, q_gen_2294, q_gen_2298},
Q_f={q_gen_2249},
Delta=
{
<nil>() -> q_gen_2258
<cons>(q_gen_2281, q_gen_2258) -> q_gen_2280
<cons>(q_gen_2281, q_gen_2298) -> q_gen_2280
<a>() -> q_gen_2281
<b>() -> q_gen_2281
<s>(q_gen_2294) -> q_gen_2283
<z>() -> q_gen_2283
<s>(q_gen_2283) -> q_gen_2294
<cons>(q_gen_2281, q_gen_2280) -> q_gen_2298
<cons, s>(q_gen_2259, q_gen_2258) -> q_gen_2249
<cons, s>(q_gen_2259, q_gen_2280) -> q_gen_2249
<cons, s>(q_gen_2282, q_gen_2280) -> q_gen_2249
<cons, s>(q_gen_2282, q_gen_2298) -> q_gen_2249
<cons, s>(q_gen_2293, q_gen_2298) -> q_gen_2249
<nil, z>() -> q_gen_2249
<a, z>() -> q_gen_2259
<b, z>() -> q_gen_2259
<a, s>(q_gen_2283) -> q_gen_2282
<a, s>(q_gen_2294) -> q_gen_2282
<b, s>(q_gen_2283) -> q_gen_2282
<cons, s>(q_gen_2259, q_gen_2298) -> q_gen_2286
<cons, s>(q_gen_2282, q_gen_2258) -> q_gen_2286
<cons, s>(q_gen_2293, q_gen_2258) -> q_gen_2286
<cons, s>(q_gen_2293, q_gen_2280) -> q_gen_2286
<b, s>(q_gen_2294) -> q_gen_2293
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_2247, q_gen_2260},
Q_f={q_gen_2247},
Delta=
{
<a, a>() -> q_gen_2247
<a, b>() -> q_gen_2247
<b, b>() -> q_gen_2247
<b, a>() -> q_gen_2260
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  leqnat -> 
{{{
Q={q_gen_2244, q_gen_2246, q_gen_2287},
Q_f={q_gen_2244},
Delta=
{
<s>(q_gen_2246) -> q_gen_2246
<z>() -> q_gen_2246
<s, s>(q_gen_2244) -> q_gen_2244
<z, s>(q_gen_2246) -> q_gen_2244
<z, z>() -> q_gen_2244
<s, s>(q_gen_2287) -> q_gen_2287
<s, z>(q_gen_2246) -> q_gen_2287
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 38
() -> length([nil, z]) -> 38
() -> leq([a, y]) -> 38
() -> leq([b, b]) -> 38
() -> leqnat([z, s(nn2)]) -> 39
() -> leqnat([z, z]) -> 38
(insert([x, l, _jj]) /\ length([_jj, _kj]) /\ length([l, _ij])) -> leqnat([_ij, _kj]) -> 49
(insert([x, z, _zi]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _zi)]) -> 39
(length([ll, _ej])) -> length([cons(x, ll), s(_ej)]) -> 47
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 41
(leq([b, a])) -> BOT -> 38
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 38
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 41
(leqnat([s(nn1), z])) -> BOT -> 41
}
Sat witness: Found: ((insert([x, l, _jj]) /\ length([_jj, _kj]) /\ length([l, _ij])) -> leqnat([_ij, _kj]), {
_ij -> s(s(z))  ;  _jj -> cons(b, cons(b, cons(b, cons(b, nil))))  ;  _kj -> s(z)  ;  l -> cons(b, cons(b, cons(b, nil)))  ;  x -> b
})

-------------------------------------------
Step 55, which took 0.174517 s (model generation: 0.169603,  model checking: 0.004914):

Model:
|_
{
insert -> 
{{{
Q={q_gen_2250, q_gen_2251, q_gen_2252, q_gen_2255, q_gen_2256, q_gen_2262, q_gen_2269, q_gen_2284},
Q_f={q_gen_2250},
Delta=
{
<nil>() -> q_gen_2251
<a>() -> q_gen_2252
<b>() -> q_gen_2252
<cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2255
<cons, cons>(q_gen_2262, q_gen_2255) -> q_gen_2255
<cons, cons>(q_gen_2269, q_gen_2255) -> q_gen_2255
<nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2255
<b, b>() -> q_gen_2256
<a, a>() -> q_gen_2262
<a, b>() -> q_gen_2262
<b, a>() -> q_gen_2269
<a, cons, cons>(q_gen_2262, q_gen_2255) -> q_gen_2250
<a, cons, cons>(q_gen_2269, q_gen_2255) -> q_gen_2250
<a, nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2250
<b, cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2250
<b, cons, cons>(q_gen_2262, q_gen_2255) -> q_gen_2250
<b, nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2250
<a, cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2284
<b, cons, cons>(q_gen_2269, q_gen_2255) -> q_gen_2284
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_2249, q_gen_2258, q_gen_2259, q_gen_2280, q_gen_2281, q_gen_2282, q_gen_2283, q_gen_2285, q_gen_2293, q_gen_2294, q_gen_2298},
Q_f={q_gen_2249},
Delta=
{
<nil>() -> q_gen_2258
<cons>(q_gen_2281, q_gen_2258) -> q_gen_2280
<cons>(q_gen_2281, q_gen_2298) -> q_gen_2280
<a>() -> q_gen_2281
<b>() -> q_gen_2281
<s>(q_gen_2294) -> q_gen_2283
<z>() -> q_gen_2283
<s>(q_gen_2283) -> q_gen_2294
<cons>(q_gen_2281, q_gen_2280) -> q_gen_2298
<cons, s>(q_gen_2259, q_gen_2258) -> q_gen_2249
<cons, s>(q_gen_2282, q_gen_2280) -> q_gen_2249
<cons, s>(q_gen_2282, q_gen_2298) -> q_gen_2249
<cons, s>(q_gen_2293, q_gen_2298) -> q_gen_2249
<nil, z>() -> q_gen_2249
<a, z>() -> q_gen_2259
<b, z>() -> q_gen_2259
<a, s>(q_gen_2283) -> q_gen_2282
<a, s>(q_gen_2294) -> q_gen_2282
<b, s>(q_gen_2283) -> q_gen_2282
<cons, s>(q_gen_2259, q_gen_2280) -> q_gen_2285
<cons, s>(q_gen_2259, q_gen_2298) -> q_gen_2285
<cons, s>(q_gen_2282, q_gen_2258) -> q_gen_2285
<cons, s>(q_gen_2293, q_gen_2258) -> q_gen_2285
<cons, s>(q_gen_2293, q_gen_2280) -> q_gen_2285
<b, s>(q_gen_2294) -> q_gen_2293
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_2247, q_gen_2260},
Q_f={q_gen_2247},
Delta=
{
<a, a>() -> q_gen_2247
<a, b>() -> q_gen_2247
<b, b>() -> q_gen_2247
<b, a>() -> q_gen_2260
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  leqnat -> 
{{{
Q={q_gen_2244, q_gen_2246, q_gen_2287},
Q_f={q_gen_2244},
Delta=
{
<s>(q_gen_2246) -> q_gen_2246
<z>() -> q_gen_2246
<s, s>(q_gen_2244) -> q_gen_2244
<z, s>(q_gen_2246) -> q_gen_2244
<z, z>() -> q_gen_2244
<s, s>(q_gen_2287) -> q_gen_2287
<s, z>(q_gen_2246) -> q_gen_2287
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 39
() -> length([nil, z]) -> 39
() -> leq([a, y]) -> 39
() -> leq([b, b]) -> 39
() -> leqnat([z, s(nn2)]) -> 40
() -> leqnat([z, z]) -> 39
(insert([x, l, _jj]) /\ length([_jj, _kj]) /\ length([l, _ij])) -> leqnat([_ij, _kj]) -> 49
(insert([x, z, _zi]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _zi)]) -> 40
(length([ll, _ej])) -> length([cons(x, ll), s(_ej)]) -> 50
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 42
(leq([b, a])) -> BOT -> 39
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 39
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 42
(leqnat([s(nn1), z])) -> BOT -> 42
}
Sat witness: Found: ((length([ll, _ej])) -> length([cons(x, ll), s(_ej)]), {
_ej -> s(s(z))  ;  ll -> cons(b, cons(a, cons(b, nil)))  ;  x -> b
})

-------------------------------------------
Step 56, which took 0.252474 s (model generation: 0.244527,  model checking: 0.007947):

Model:
|_
{
insert -> 
{{{
Q={q_gen_2250, q_gen_2251, q_gen_2252, q_gen_2255, q_gen_2256},
Q_f={q_gen_2250},
Delta=
{
<nil>() -> q_gen_2251
<a>() -> q_gen_2252
<b>() -> q_gen_2252
<cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2255
<nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2255
<a, a>() -> q_gen_2256
<a, b>() -> q_gen_2256
<b, a>() -> q_gen_2256
<b, b>() -> q_gen_2256
<a, cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2250
<a, nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2250
<b, cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2250
<b, nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2250
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_2249, q_gen_2258, q_gen_2259, q_gen_2280, q_gen_2281, q_gen_2282, q_gen_2283, q_gen_2286, q_gen_2293, q_gen_2294, q_gen_2298, q_gen_2314, q_gen_2315, q_gen_2316},
Q_f={q_gen_2249},
Delta=
{
<nil>() -> q_gen_2258
<cons>(q_gen_2281, q_gen_2258) -> q_gen_2280
<a>() -> q_gen_2281
<b>() -> q_gen_2281
<z>() -> q_gen_2283
<s>(q_gen_2283) -> q_gen_2294
<cons>(q_gen_2281, q_gen_2280) -> q_gen_2298
<cons>(q_gen_2281, q_gen_2298) -> q_gen_2314
<s>(q_gen_2294) -> q_gen_2316
<cons, s>(q_gen_2259, q_gen_2258) -> q_gen_2249
<cons, s>(q_gen_2259, q_gen_2280) -> q_gen_2249
<cons, s>(q_gen_2282, q_gen_2280) -> q_gen_2249
<cons, s>(q_gen_2282, q_gen_2298) -> q_gen_2249
<cons, s>(q_gen_2293, q_gen_2298) -> q_gen_2249
<cons, s>(q_gen_2293, q_gen_2314) -> q_gen_2249
<cons, s>(q_gen_2315, q_gen_2314) -> q_gen_2249
<nil, z>() -> q_gen_2249
<a, z>() -> q_gen_2259
<b, z>() -> q_gen_2259
<a, s>(q_gen_2283) -> q_gen_2282
<b, s>(q_gen_2283) -> q_gen_2282
<cons, s>(q_gen_2259, q_gen_2298) -> q_gen_2286
<cons, s>(q_gen_2259, q_gen_2314) -> q_gen_2286
<cons, s>(q_gen_2282, q_gen_2258) -> q_gen_2286
<cons, s>(q_gen_2282, q_gen_2314) -> q_gen_2286
<cons, s>(q_gen_2293, q_gen_2258) -> q_gen_2286
<cons, s>(q_gen_2293, q_gen_2280) -> q_gen_2286
<cons, s>(q_gen_2315, q_gen_2258) -> q_gen_2286
<cons, s>(q_gen_2315, q_gen_2280) -> q_gen_2286
<cons, s>(q_gen_2315, q_gen_2298) -> q_gen_2286
<a, s>(q_gen_2294) -> q_gen_2293
<a, s>(q_gen_2316) -> q_gen_2293
<b, s>(q_gen_2294) -> q_gen_2293
<b, s>(q_gen_2316) -> q_gen_2315
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_2247, q_gen_2260},
Q_f={q_gen_2247},
Delta=
{
<a, a>() -> q_gen_2247
<a, b>() -> q_gen_2247
<b, b>() -> q_gen_2247
<b, a>() -> q_gen_2260
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  leqnat -> 
{{{
Q={q_gen_2244, q_gen_2246, q_gen_2287},
Q_f={q_gen_2244},
Delta=
{
<s>(q_gen_2246) -> q_gen_2246
<z>() -> q_gen_2246
<s, s>(q_gen_2244) -> q_gen_2244
<z, s>(q_gen_2246) -> q_gen_2244
<z, z>() -> q_gen_2244
<s, s>(q_gen_2287) -> q_gen_2287
<s, z>(q_gen_2246) -> q_gen_2287
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 40
() -> length([nil, z]) -> 40
() -> leq([a, y]) -> 40
() -> leq([b, b]) -> 40
() -> leqnat([z, s(nn2)]) -> 41
() -> leqnat([z, z]) -> 40
(insert([x, l, _jj]) /\ length([_jj, _kj]) /\ length([l, _ij])) -> leqnat([_ij, _kj]) -> 52
(insert([x, z, _zi]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _zi)]) -> 41
(length([ll, _ej])) -> length([cons(x, ll), s(_ej)]) -> 50
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 43
(leq([b, a])) -> BOT -> 40
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 40
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 43
(leqnat([s(nn1), z])) -> BOT -> 43
}
Sat witness: Found: ((insert([x, l, _jj]) /\ length([_jj, _kj]) /\ length([l, _ij])) -> leqnat([_ij, _kj]), {
_ij -> s(s(s(s(z))))  ;  _jj -> cons(b, cons(b, cons(b, cons(b, nil))))  ;  _kj -> s(s(s(z)))  ;  l -> cons(a, cons(b, cons(b, nil)))  ;  x -> a
})

-------------------------------------------
Step 57, which took 0.231086 s (model generation: 0.223938,  model checking: 0.007148):

Model:
|_
{
insert -> 
{{{
Q={q_gen_2250, q_gen_2251, q_gen_2252, q_gen_2255, q_gen_2256, q_gen_2262, q_gen_2269, q_gen_2284},
Q_f={q_gen_2250},
Delta=
{
<nil>() -> q_gen_2251
<a>() -> q_gen_2252
<b>() -> q_gen_2252
<cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2255
<cons, cons>(q_gen_2262, q_gen_2255) -> q_gen_2255
<cons, cons>(q_gen_2269, q_gen_2255) -> q_gen_2255
<nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2255
<b, b>() -> q_gen_2256
<a, a>() -> q_gen_2262
<a, b>() -> q_gen_2269
<b, a>() -> q_gen_2269
<a, cons, cons>(q_gen_2262, q_gen_2255) -> q_gen_2250
<a, cons, cons>(q_gen_2269, q_gen_2255) -> q_gen_2250
<a, nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2250
<b, cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2250
<b, cons, cons>(q_gen_2262, q_gen_2255) -> q_gen_2250
<b, nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2250
<a, cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2284
<b, cons, cons>(q_gen_2269, q_gen_2255) -> q_gen_2284
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_2249, q_gen_2258, q_gen_2259, q_gen_2280, q_gen_2281, q_gen_2282, q_gen_2283, q_gen_2285, q_gen_2293, q_gen_2294, q_gen_2298},
Q_f={q_gen_2249},
Delta=
{
<nil>() -> q_gen_2258
<cons>(q_gen_2281, q_gen_2258) -> q_gen_2280
<cons>(q_gen_2281, q_gen_2298) -> q_gen_2280
<a>() -> q_gen_2281
<b>() -> q_gen_2281
<s>(q_gen_2294) -> q_gen_2283
<z>() -> q_gen_2283
<s>(q_gen_2283) -> q_gen_2294
<cons>(q_gen_2281, q_gen_2280) -> q_gen_2298
<cons, s>(q_gen_2259, q_gen_2258) -> q_gen_2249
<cons, s>(q_gen_2282, q_gen_2280) -> q_gen_2249
<cons, s>(q_gen_2293, q_gen_2298) -> q_gen_2249
<nil, z>() -> q_gen_2249
<a, z>() -> q_gen_2259
<b, z>() -> q_gen_2259
<a, s>(q_gen_2283) -> q_gen_2282
<b, s>(q_gen_2283) -> q_gen_2282
<cons, s>(q_gen_2259, q_gen_2280) -> q_gen_2285
<cons, s>(q_gen_2259, q_gen_2298) -> q_gen_2285
<cons, s>(q_gen_2282, q_gen_2258) -> q_gen_2285
<cons, s>(q_gen_2282, q_gen_2298) -> q_gen_2285
<cons, s>(q_gen_2293, q_gen_2258) -> q_gen_2285
<cons, s>(q_gen_2293, q_gen_2280) -> q_gen_2285
<a, s>(q_gen_2294) -> q_gen_2293
<b, s>(q_gen_2294) -> q_gen_2293
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_2247, q_gen_2260},
Q_f={q_gen_2247},
Delta=
{
<a, a>() -> q_gen_2247
<a, b>() -> q_gen_2247
<b, b>() -> q_gen_2247
<b, a>() -> q_gen_2260
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  leqnat -> 
{{{
Q={q_gen_2244, q_gen_2246, q_gen_2287},
Q_f={q_gen_2244},
Delta=
{
<s>(q_gen_2246) -> q_gen_2246
<z>() -> q_gen_2246
<s, s>(q_gen_2244) -> q_gen_2244
<z, s>(q_gen_2246) -> q_gen_2244
<z, z>() -> q_gen_2244
<s, s>(q_gen_2287) -> q_gen_2287
<s, z>(q_gen_2246) -> q_gen_2287
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 41
() -> length([nil, z]) -> 41
() -> leq([a, y]) -> 41
() -> leq([b, b]) -> 41
() -> leqnat([z, s(nn2)]) -> 42
() -> leqnat([z, z]) -> 41
(insert([x, l, _jj]) /\ length([_jj, _kj]) /\ length([l, _ij])) -> leqnat([_ij, _kj]) -> 55
(insert([x, z, _zi]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _zi)]) -> 42
(length([ll, _ej])) -> length([cons(x, ll), s(_ej)]) -> 51
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 44
(leq([b, a])) -> BOT -> 41
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 41
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 44
(leqnat([s(nn1), z])) -> BOT -> 44
}
Sat witness: Found: ((insert([x, l, _jj]) /\ length([_jj, _kj]) /\ length([l, _ij])) -> leqnat([_ij, _kj]), {
_ij -> s(s(s(z)))  ;  _jj -> cons(b, cons(b, cons(b, cons(b, nil))))  ;  _kj -> s(s(z))  ;  l -> cons(b, cons(b, cons(b, nil)))  ;  x -> b
})

-------------------------------------------
Step 58, which took 0.176046 s (model generation: 0.164603,  model checking: 0.011443):

Model:
|_
{
insert -> 
{{{
Q={q_gen_2250, q_gen_2251, q_gen_2252, q_gen_2255, q_gen_2256},
Q_f={q_gen_2250},
Delta=
{
<nil>() -> q_gen_2251
<a>() -> q_gen_2252
<b>() -> q_gen_2252
<cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2255
<nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2255
<a, a>() -> q_gen_2256
<a, b>() -> q_gen_2256
<b, a>() -> q_gen_2256
<b, b>() -> q_gen_2256
<a, cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2250
<a, nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2250
<b, cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2250
<b, nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2250
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_2249, q_gen_2258, q_gen_2259, q_gen_2280, q_gen_2281, q_gen_2282, q_gen_2283, q_gen_2285, q_gen_2293, q_gen_2294, q_gen_2298, q_gen_2314, q_gen_2315, q_gen_2316},
Q_f={q_gen_2249},
Delta=
{
<nil>() -> q_gen_2258
<cons>(q_gen_2281, q_gen_2258) -> q_gen_2280
<a>() -> q_gen_2281
<b>() -> q_gen_2281
<z>() -> q_gen_2283
<s>(q_gen_2283) -> q_gen_2294
<cons>(q_gen_2281, q_gen_2280) -> q_gen_2298
<cons>(q_gen_2281, q_gen_2298) -> q_gen_2314
<s>(q_gen_2294) -> q_gen_2316
<cons, s>(q_gen_2259, q_gen_2258) -> q_gen_2249
<cons, s>(q_gen_2282, q_gen_2258) -> q_gen_2249
<cons, s>(q_gen_2282, q_gen_2280) -> q_gen_2249
<cons, s>(q_gen_2293, q_gen_2280) -> q_gen_2249
<cons, s>(q_gen_2293, q_gen_2298) -> q_gen_2249
<cons, s>(q_gen_2315, q_gen_2298) -> q_gen_2249
<cons, s>(q_gen_2315, q_gen_2314) -> q_gen_2249
<nil, z>() -> q_gen_2249
<a, z>() -> q_gen_2259
<b, z>() -> q_gen_2259
<a, s>(q_gen_2283) -> q_gen_2282
<b, s>(q_gen_2283) -> q_gen_2282
<cons, s>(q_gen_2259, q_gen_2280) -> q_gen_2285
<cons, s>(q_gen_2259, q_gen_2298) -> q_gen_2285
<cons, s>(q_gen_2259, q_gen_2314) -> q_gen_2285
<cons, s>(q_gen_2282, q_gen_2298) -> q_gen_2285
<cons, s>(q_gen_2282, q_gen_2314) -> q_gen_2285
<cons, s>(q_gen_2293, q_gen_2258) -> q_gen_2285
<cons, s>(q_gen_2293, q_gen_2314) -> q_gen_2285
<cons, s>(q_gen_2315, q_gen_2258) -> q_gen_2285
<cons, s>(q_gen_2315, q_gen_2280) -> q_gen_2285
<a, s>(q_gen_2294) -> q_gen_2293
<b, s>(q_gen_2294) -> q_gen_2293
<a, s>(q_gen_2316) -> q_gen_2315
<b, s>(q_gen_2316) -> q_gen_2315
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_2247, q_gen_2260},
Q_f={q_gen_2247},
Delta=
{
<a, a>() -> q_gen_2247
<a, b>() -> q_gen_2247
<b, b>() -> q_gen_2247
<b, a>() -> q_gen_2260
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  leqnat -> 
{{{
Q={q_gen_2244, q_gen_2246, q_gen_2287},
Q_f={q_gen_2244},
Delta=
{
<s>(q_gen_2246) -> q_gen_2246
<z>() -> q_gen_2246
<s, s>(q_gen_2244) -> q_gen_2244
<z, s>(q_gen_2246) -> q_gen_2244
<z, z>() -> q_gen_2244
<s, s>(q_gen_2287) -> q_gen_2287
<s, z>(q_gen_2246) -> q_gen_2287
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 42
() -> length([nil, z]) -> 42
() -> leq([a, y]) -> 42
() -> leq([b, b]) -> 42
() -> leqnat([z, s(nn2)]) -> 43
() -> leqnat([z, z]) -> 42
(insert([x, l, _jj]) /\ length([_jj, _kj]) /\ length([l, _ij])) -> leqnat([_ij, _kj]) -> 55
(insert([x, z, _zi]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _zi)]) -> 43
(length([ll, _ej])) -> length([cons(x, ll), s(_ej)]) -> 54
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 45
(leq([b, a])) -> BOT -> 42
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 42
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 45
(leqnat([s(nn1), z])) -> BOT -> 45
}
Sat witness: Found: ((length([ll, _ej])) -> length([cons(x, ll), s(_ej)]), {
_ej -> s(s(s(s(z))))  ;  ll -> cons(a, cons(a, cons(b, nil)))  ;  x -> b
})

-------------------------------------------
Step 59, which took 0.208992 s (model generation: 0.200748,  model checking: 0.008244):

Model:
|_
{
insert -> 
{{{
Q={q_gen_2250, q_gen_2251, q_gen_2252, q_gen_2255, q_gen_2256},
Q_f={q_gen_2250},
Delta=
{
<nil>() -> q_gen_2251
<a>() -> q_gen_2252
<b>() -> q_gen_2252
<cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2255
<nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2255
<a, a>() -> q_gen_2256
<a, b>() -> q_gen_2256
<b, a>() -> q_gen_2256
<b, b>() -> q_gen_2256
<a, cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2250
<a, nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2250
<b, cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2250
<b, nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2250
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_2249, q_gen_2258, q_gen_2259, q_gen_2280, q_gen_2281, q_gen_2282, q_gen_2283, q_gen_2286, q_gen_2293, q_gen_2294, q_gen_2298, q_gen_2314, q_gen_2315, q_gen_2316},
Q_f={q_gen_2249},
Delta=
{
<nil>() -> q_gen_2258
<cons>(q_gen_2281, q_gen_2258) -> q_gen_2280
<a>() -> q_gen_2281
<b>() -> q_gen_2281
<z>() -> q_gen_2283
<s>(q_gen_2283) -> q_gen_2294
<s>(q_gen_2316) -> q_gen_2294
<cons>(q_gen_2281, q_gen_2280) -> q_gen_2298
<cons>(q_gen_2281, q_gen_2298) -> q_gen_2314
<s>(q_gen_2294) -> q_gen_2316
<cons, s>(q_gen_2259, q_gen_2258) -> q_gen_2249
<cons, s>(q_gen_2259, q_gen_2280) -> q_gen_2249
<cons, s>(q_gen_2282, q_gen_2280) -> q_gen_2249
<cons, s>(q_gen_2282, q_gen_2298) -> q_gen_2249
<cons, s>(q_gen_2293, q_gen_2298) -> q_gen_2249
<cons, s>(q_gen_2293, q_gen_2314) -> q_gen_2249
<cons, s>(q_gen_2315, q_gen_2314) -> q_gen_2249
<nil, z>() -> q_gen_2249
<a, z>() -> q_gen_2259
<b, z>() -> q_gen_2259
<a, s>(q_gen_2283) -> q_gen_2282
<b, s>(q_gen_2283) -> q_gen_2282
<cons, s>(q_gen_2259, q_gen_2298) -> q_gen_2286
<cons, s>(q_gen_2259, q_gen_2314) -> q_gen_2286
<cons, s>(q_gen_2282, q_gen_2258) -> q_gen_2286
<cons, s>(q_gen_2282, q_gen_2314) -> q_gen_2286
<cons, s>(q_gen_2293, q_gen_2258) -> q_gen_2286
<cons, s>(q_gen_2293, q_gen_2280) -> q_gen_2286
<cons, s>(q_gen_2315, q_gen_2258) -> q_gen_2286
<cons, s>(q_gen_2315, q_gen_2280) -> q_gen_2286
<cons, s>(q_gen_2315, q_gen_2298) -> q_gen_2286
<a, s>(q_gen_2294) -> q_gen_2293
<b, s>(q_gen_2294) -> q_gen_2293
<a, s>(q_gen_2316) -> q_gen_2315
<b, s>(q_gen_2316) -> q_gen_2315
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_2247, q_gen_2260},
Q_f={q_gen_2247},
Delta=
{
<a, a>() -> q_gen_2247
<a, b>() -> q_gen_2247
<b, b>() -> q_gen_2247
<b, a>() -> q_gen_2260
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  leqnat -> 
{{{
Q={q_gen_2244, q_gen_2246, q_gen_2287},
Q_f={q_gen_2244},
Delta=
{
<s>(q_gen_2246) -> q_gen_2246
<z>() -> q_gen_2246
<s, s>(q_gen_2244) -> q_gen_2244
<z, s>(q_gen_2246) -> q_gen_2244
<z, z>() -> q_gen_2244
<s, s>(q_gen_2287) -> q_gen_2287
<s, z>(q_gen_2246) -> q_gen_2287
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 43
() -> length([nil, z]) -> 43
() -> leq([a, y]) -> 43
() -> leq([b, b]) -> 43
() -> leqnat([z, s(nn2)]) -> 44
() -> leqnat([z, z]) -> 43
(insert([x, l, _jj]) /\ length([_jj, _kj]) /\ length([l, _ij])) -> leqnat([_ij, _kj]) -> 55
(insert([x, z, _zi]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _zi)]) -> 44
(length([ll, _ej])) -> length([cons(x, ll), s(_ej)]) -> 57
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 46
(leq([b, a])) -> BOT -> 43
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 43
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 46
(leqnat([s(nn1), z])) -> BOT -> 46
}
Sat witness: Found: ((length([ll, _ej])) -> length([cons(x, ll), s(_ej)]), {
_ej -> s(s(s(s(z))))  ;  ll -> cons(b, cons(b, cons(a, cons(b, nil))))  ;  x -> a
})

-------------------------------------------
Step 60, which took 0.291306 s (model generation: 0.290083,  model checking: 0.001223):

Model:
|_
{
insert -> 
{{{
Q={q_gen_2250, q_gen_2251, q_gen_2252, q_gen_2255, q_gen_2256},
Q_f={q_gen_2250},
Delta=
{
<nil>() -> q_gen_2251
<a>() -> q_gen_2252
<b>() -> q_gen_2252
<cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2255
<nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2255
<a, a>() -> q_gen_2256
<a, b>() -> q_gen_2256
<b, a>() -> q_gen_2256
<b, b>() -> q_gen_2256
<a, cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2250
<a, nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2250
<b, cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2250
<b, nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2250
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_2249, q_gen_2258, q_gen_2259, q_gen_2280, q_gen_2281, q_gen_2282, q_gen_2283, q_gen_2285, q_gen_2293, q_gen_2294, q_gen_2298, q_gen_2316},
Q_f={q_gen_2249},
Delta=
{
<cons>(q_gen_2281, q_gen_2298) -> q_gen_2258
<nil>() -> q_gen_2258
<cons>(q_gen_2281, q_gen_2258) -> q_gen_2280
<a>() -> q_gen_2281
<b>() -> q_gen_2281
<s>(q_gen_2316) -> q_gen_2283
<z>() -> q_gen_2283
<s>(q_gen_2283) -> q_gen_2294
<cons>(q_gen_2281, q_gen_2280) -> q_gen_2298
<s>(q_gen_2294) -> q_gen_2316
<cons, s>(q_gen_2259, q_gen_2258) -> q_gen_2249
<cons, s>(q_gen_2282, q_gen_2280) -> q_gen_2249
<cons, s>(q_gen_2293, q_gen_2298) -> q_gen_2249
<nil, z>() -> q_gen_2249
<a, s>(q_gen_2316) -> q_gen_2259
<a, z>() -> q_gen_2259
<b, s>(q_gen_2316) -> q_gen_2259
<b, z>() -> q_gen_2259
<a, s>(q_gen_2283) -> q_gen_2282
<b, s>(q_gen_2283) -> q_gen_2282
<cons, s>(q_gen_2259, q_gen_2280) -> q_gen_2285
<cons, s>(q_gen_2259, q_gen_2298) -> q_gen_2285
<cons, s>(q_gen_2282, q_gen_2258) -> q_gen_2285
<cons, s>(q_gen_2282, q_gen_2298) -> q_gen_2285
<cons, s>(q_gen_2293, q_gen_2258) -> q_gen_2285
<cons, s>(q_gen_2293, q_gen_2280) -> q_gen_2285
<a, s>(q_gen_2294) -> q_gen_2293
<b, s>(q_gen_2294) -> q_gen_2293
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_2247, q_gen_2260},
Q_f={q_gen_2247},
Delta=
{
<a, a>() -> q_gen_2247
<a, b>() -> q_gen_2247
<b, b>() -> q_gen_2247
<b, a>() -> q_gen_2260
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  leqnat -> 
{{{
Q={q_gen_2244, q_gen_2246, q_gen_2264, q_gen_2287, q_gen_2321},
Q_f={q_gen_2244},
Delta=
{
<z>() -> q_gen_2246
<s>(q_gen_2246) -> q_gen_2264
<s>(q_gen_2264) -> q_gen_2264
<s, s>(q_gen_2244) -> q_gen_2244
<s, s>(q_gen_2321) -> q_gen_2244
<z, s>(q_gen_2246) -> q_gen_2244
<z, s>(q_gen_2264) -> q_gen_2244
<z, z>() -> q_gen_2244
<s, s>(q_gen_2287) -> q_gen_2287
<s, z>(q_gen_2246) -> q_gen_2287
<s, z>(q_gen_2264) -> q_gen_2321
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 44
() -> length([nil, z]) -> 44
() -> leq([a, y]) -> 44
() -> leq([b, b]) -> 44
() -> leqnat([z, s(nn2)]) -> 45
() -> leqnat([z, z]) -> 44
(insert([x, l, _jj]) /\ length([_jj, _kj]) /\ length([l, _ij])) -> leqnat([_ij, _kj]) -> 55
(insert([x, z, _zi]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _zi)]) -> 45
(length([ll, _ej])) -> length([cons(x, ll), s(_ej)]) -> 57
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 46
(leq([b, a])) -> BOT -> 44
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 44
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 49
(leqnat([s(nn1), z])) -> BOT -> 47
}
Sat witness: Found: ((leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]), {
nn1 -> s(s(z))  ;  nn2 -> z
})

-------------------------------------------
Step 61, which took 0.218219 s (model generation: 0.210237,  model checking: 0.007982):

Model:
|_
{
insert -> 
{{{
Q={q_gen_2250, q_gen_2251, q_gen_2252, q_gen_2255, q_gen_2256},
Q_f={q_gen_2250},
Delta=
{
<nil>() -> q_gen_2251
<a>() -> q_gen_2252
<b>() -> q_gen_2252
<cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2255
<nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2255
<a, a>() -> q_gen_2256
<a, b>() -> q_gen_2256
<b, a>() -> q_gen_2256
<b, b>() -> q_gen_2256
<a, cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2250
<a, nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2250
<b, cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2250
<b, nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2250
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_2249, q_gen_2258, q_gen_2259, q_gen_2280, q_gen_2281, q_gen_2282, q_gen_2283, q_gen_2286, q_gen_2293, q_gen_2294, q_gen_2298, q_gen_2314, q_gen_2315, q_gen_2316},
Q_f={q_gen_2249},
Delta=
{
<nil>() -> q_gen_2258
<cons>(q_gen_2281, q_gen_2258) -> q_gen_2280
<a>() -> q_gen_2281
<b>() -> q_gen_2281
<z>() -> q_gen_2283
<s>(q_gen_2283) -> q_gen_2294
<s>(q_gen_2316) -> q_gen_2294
<cons>(q_gen_2281, q_gen_2280) -> q_gen_2298
<cons>(q_gen_2281, q_gen_2314) -> q_gen_2298
<cons>(q_gen_2281, q_gen_2298) -> q_gen_2314
<s>(q_gen_2294) -> q_gen_2316
<cons, s>(q_gen_2259, q_gen_2258) -> q_gen_2249
<cons, s>(q_gen_2259, q_gen_2280) -> q_gen_2249
<cons, s>(q_gen_2282, q_gen_2280) -> q_gen_2249
<cons, s>(q_gen_2282, q_gen_2298) -> q_gen_2249
<cons, s>(q_gen_2293, q_gen_2298) -> q_gen_2249
<cons, s>(q_gen_2293, q_gen_2314) -> q_gen_2249
<cons, s>(q_gen_2315, q_gen_2314) -> q_gen_2249
<nil, z>() -> q_gen_2249
<a, z>() -> q_gen_2259
<b, z>() -> q_gen_2259
<a, s>(q_gen_2283) -> q_gen_2282
<b, s>(q_gen_2283) -> q_gen_2282
<cons, s>(q_gen_2259, q_gen_2298) -> q_gen_2286
<cons, s>(q_gen_2259, q_gen_2314) -> q_gen_2286
<cons, s>(q_gen_2282, q_gen_2258) -> q_gen_2286
<cons, s>(q_gen_2282, q_gen_2314) -> q_gen_2286
<cons, s>(q_gen_2293, q_gen_2258) -> q_gen_2286
<cons, s>(q_gen_2293, q_gen_2280) -> q_gen_2286
<cons, s>(q_gen_2315, q_gen_2258) -> q_gen_2286
<cons, s>(q_gen_2315, q_gen_2280) -> q_gen_2286
<cons, s>(q_gen_2315, q_gen_2298) -> q_gen_2286
<a, s>(q_gen_2294) -> q_gen_2293
<b, s>(q_gen_2294) -> q_gen_2293
<a, s>(q_gen_2316) -> q_gen_2315
<b, s>(q_gen_2316) -> q_gen_2315
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_2247, q_gen_2260},
Q_f={q_gen_2247},
Delta=
{
<a, a>() -> q_gen_2247
<a, b>() -> q_gen_2247
<b, b>() -> q_gen_2247
<b, a>() -> q_gen_2260
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  leqnat -> 
{{{
Q={q_gen_2244, q_gen_2246, q_gen_2287},
Q_f={q_gen_2244},
Delta=
{
<s>(q_gen_2246) -> q_gen_2246
<z>() -> q_gen_2246
<s, s>(q_gen_2244) -> q_gen_2244
<z, s>(q_gen_2246) -> q_gen_2244
<z, z>() -> q_gen_2244
<s, s>(q_gen_2287) -> q_gen_2287
<s, z>(q_gen_2246) -> q_gen_2287
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 45
() -> length([nil, z]) -> 45
() -> leq([a, y]) -> 45
() -> leq([b, b]) -> 45
() -> leqnat([z, s(nn2)]) -> 46
() -> leqnat([z, z]) -> 45
(insert([x, l, _jj]) /\ length([_jj, _kj]) /\ length([l, _ij])) -> leqnat([_ij, _kj]) -> 58
(insert([x, z, _zi]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _zi)]) -> 46
(length([ll, _ej])) -> length([cons(x, ll), s(_ej)]) -> 57
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 47
(leq([b, a])) -> BOT -> 45
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 45
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 50
(leqnat([s(nn1), z])) -> BOT -> 48
}
Sat witness: Found: ((insert([x, l, _jj]) /\ length([_jj, _kj]) /\ length([l, _ij])) -> leqnat([_ij, _kj]), {
_ij -> s(s(s(z)))  ;  _jj -> cons(b, cons(b, cons(b, cons(b, cons(b, nil)))))  ;  _kj -> s(s(z))  ;  l -> cons(b, cons(b, cons(b, cons(b, nil))))  ;  x -> a
})

-------------------------------------------
Step 62, which took 0.282221 s (model generation: 0.266168,  model checking: 0.016053):

Model:
|_
{
insert -> 
{{{
Q={q_gen_2250, q_gen_2251, q_gen_2252, q_gen_2255, q_gen_2256},
Q_f={q_gen_2250},
Delta=
{
<nil>() -> q_gen_2251
<a>() -> q_gen_2252
<b>() -> q_gen_2252
<cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2255
<nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2255
<a, a>() -> q_gen_2256
<a, b>() -> q_gen_2256
<b, a>() -> q_gen_2256
<b, b>() -> q_gen_2256
<a, cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2250
<a, nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2250
<b, cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2250
<b, nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2250
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_2249, q_gen_2258, q_gen_2259, q_gen_2280, q_gen_2281, q_gen_2282, q_gen_2283, q_gen_2286, q_gen_2293, q_gen_2294, q_gen_2298, q_gen_2314, q_gen_2315, q_gen_2316},
Q_f={q_gen_2249},
Delta=
{
<nil>() -> q_gen_2258
<cons>(q_gen_2281, q_gen_2258) -> q_gen_2280
<a>() -> q_gen_2281
<b>() -> q_gen_2281
<z>() -> q_gen_2283
<s>(q_gen_2283) -> q_gen_2294
<s>(q_gen_2316) -> q_gen_2294
<cons>(q_gen_2281, q_gen_2280) -> q_gen_2298
<cons>(q_gen_2281, q_gen_2298) -> q_gen_2314
<cons>(q_gen_2281, q_gen_2314) -> q_gen_2314
<s>(q_gen_2294) -> q_gen_2316
<cons, s>(q_gen_2259, q_gen_2258) -> q_gen_2249
<cons, s>(q_gen_2259, q_gen_2280) -> q_gen_2249
<cons, s>(q_gen_2282, q_gen_2280) -> q_gen_2249
<cons, s>(q_gen_2282, q_gen_2298) -> q_gen_2249
<cons, s>(q_gen_2293, q_gen_2298) -> q_gen_2249
<cons, s>(q_gen_2293, q_gen_2314) -> q_gen_2249
<cons, s>(q_gen_2315, q_gen_2314) -> q_gen_2249
<nil, z>() -> q_gen_2249
<a, z>() -> q_gen_2259
<b, z>() -> q_gen_2259
<a, s>(q_gen_2283) -> q_gen_2282
<b, s>(q_gen_2283) -> q_gen_2282
<cons, s>(q_gen_2259, q_gen_2298) -> q_gen_2286
<cons, s>(q_gen_2259, q_gen_2314) -> q_gen_2286
<cons, s>(q_gen_2282, q_gen_2258) -> q_gen_2286
<cons, s>(q_gen_2282, q_gen_2314) -> q_gen_2286
<cons, s>(q_gen_2293, q_gen_2258) -> q_gen_2286
<cons, s>(q_gen_2293, q_gen_2280) -> q_gen_2286
<cons, s>(q_gen_2315, q_gen_2258) -> q_gen_2286
<cons, s>(q_gen_2315, q_gen_2280) -> q_gen_2286
<cons, s>(q_gen_2315, q_gen_2298) -> q_gen_2286
<a, s>(q_gen_2294) -> q_gen_2293
<b, s>(q_gen_2294) -> q_gen_2293
<a, s>(q_gen_2316) -> q_gen_2315
<b, s>(q_gen_2316) -> q_gen_2315
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_2247, q_gen_2260},
Q_f={q_gen_2247},
Delta=
{
<a, a>() -> q_gen_2247
<a, b>() -> q_gen_2247
<b, b>() -> q_gen_2247
<b, a>() -> q_gen_2260
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  leqnat -> 
{{{
Q={q_gen_2244, q_gen_2246, q_gen_2287},
Q_f={q_gen_2244},
Delta=
{
<s>(q_gen_2246) -> q_gen_2246
<z>() -> q_gen_2246
<s, s>(q_gen_2244) -> q_gen_2244
<z, s>(q_gen_2246) -> q_gen_2244
<z, z>() -> q_gen_2244
<s, s>(q_gen_2287) -> q_gen_2287
<s, z>(q_gen_2246) -> q_gen_2287
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 46
() -> length([nil, z]) -> 46
() -> leq([a, y]) -> 46
() -> leq([b, b]) -> 46
() -> leqnat([z, s(nn2)]) -> 47
() -> leqnat([z, z]) -> 46
(insert([x, l, _jj]) /\ length([_jj, _kj]) /\ length([l, _ij])) -> leqnat([_ij, _kj]) -> 61
(insert([x, z, _zi]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _zi)]) -> 47
(length([ll, _ej])) -> length([cons(x, ll), s(_ej)]) -> 58
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 48
(leq([b, a])) -> BOT -> 46
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 46
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 51
(leqnat([s(nn1), z])) -> BOT -> 49
}
Sat witness: Found: ((insert([x, l, _jj]) /\ length([_jj, _kj]) /\ length([l, _ij])) -> leqnat([_ij, _kj]), {
_ij -> s(s(s(s(s(z)))))  ;  _jj -> cons(b, cons(b, cons(b, cons(b, cons(b, nil)))))  ;  _kj -> s(s(s(z)))  ;  l -> cons(b, cons(b, cons(b, cons(b, nil))))  ;  x -> b
})

-------------------------------------------
Step 63, which took 0.415600 s (model generation: 0.404705,  model checking: 0.010895):

Model:
|_
{
insert -> 
{{{
Q={q_gen_2250, q_gen_2251, q_gen_2252, q_gen_2255, q_gen_2256},
Q_f={q_gen_2250},
Delta=
{
<nil>() -> q_gen_2251
<a>() -> q_gen_2252
<b>() -> q_gen_2252
<cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2255
<nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2255
<a, a>() -> q_gen_2256
<a, b>() -> q_gen_2256
<b, a>() -> q_gen_2256
<b, b>() -> q_gen_2256
<a, cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2250
<a, nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2250
<b, cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2250
<b, nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2250
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_2249, q_gen_2258, q_gen_2259, q_gen_2280, q_gen_2281, q_gen_2282, q_gen_2283, q_gen_2285, q_gen_2293, q_gen_2294, q_gen_2298, q_gen_2314, q_gen_2315, q_gen_2316},
Q_f={q_gen_2249},
Delta=
{
<nil>() -> q_gen_2258
<cons>(q_gen_2281, q_gen_2258) -> q_gen_2280
<a>() -> q_gen_2281
<b>() -> q_gen_2281
<z>() -> q_gen_2283
<s>(q_gen_2283) -> q_gen_2294
<s>(q_gen_2316) -> q_gen_2294
<cons>(q_gen_2281, q_gen_2280) -> q_gen_2298
<cons>(q_gen_2281, q_gen_2314) -> q_gen_2298
<cons>(q_gen_2281, q_gen_2298) -> q_gen_2314
<s>(q_gen_2294) -> q_gen_2316
<cons, s>(q_gen_2259, q_gen_2258) -> q_gen_2249
<cons, s>(q_gen_2282, q_gen_2280) -> q_gen_2249
<cons, s>(q_gen_2293, q_gen_2298) -> q_gen_2249
<cons, s>(q_gen_2315, q_gen_2314) -> q_gen_2249
<nil, z>() -> q_gen_2249
<a, z>() -> q_gen_2259
<b, z>() -> q_gen_2259
<a, s>(q_gen_2283) -> q_gen_2282
<b, s>(q_gen_2283) -> q_gen_2282
<cons, s>(q_gen_2259, q_gen_2280) -> q_gen_2285
<cons, s>(q_gen_2259, q_gen_2298) -> q_gen_2285
<cons, s>(q_gen_2259, q_gen_2314) -> q_gen_2285
<cons, s>(q_gen_2282, q_gen_2258) -> q_gen_2285
<cons, s>(q_gen_2282, q_gen_2298) -> q_gen_2285
<cons, s>(q_gen_2282, q_gen_2314) -> q_gen_2285
<cons, s>(q_gen_2293, q_gen_2258) -> q_gen_2285
<cons, s>(q_gen_2293, q_gen_2280) -> q_gen_2285
<cons, s>(q_gen_2293, q_gen_2314) -> q_gen_2285
<cons, s>(q_gen_2315, q_gen_2258) -> q_gen_2285
<cons, s>(q_gen_2315, q_gen_2280) -> q_gen_2285
<cons, s>(q_gen_2315, q_gen_2298) -> q_gen_2285
<a, s>(q_gen_2294) -> q_gen_2293
<b, s>(q_gen_2294) -> q_gen_2293
<a, s>(q_gen_2316) -> q_gen_2315
<b, s>(q_gen_2316) -> q_gen_2315
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_2247, q_gen_2260},
Q_f={q_gen_2247},
Delta=
{
<a, a>() -> q_gen_2247
<a, b>() -> q_gen_2247
<b, b>() -> q_gen_2247
<b, a>() -> q_gen_2260
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  leqnat -> 
{{{
Q={q_gen_2244, q_gen_2246, q_gen_2287},
Q_f={q_gen_2244},
Delta=
{
<s>(q_gen_2246) -> q_gen_2246
<z>() -> q_gen_2246
<s, s>(q_gen_2244) -> q_gen_2244
<z, s>(q_gen_2246) -> q_gen_2244
<z, z>() -> q_gen_2244
<s, s>(q_gen_2287) -> q_gen_2287
<s, z>(q_gen_2246) -> q_gen_2287
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 47
() -> length([nil, z]) -> 47
() -> leq([a, y]) -> 47
() -> leq([b, b]) -> 47
() -> leqnat([z, s(nn2)]) -> 48
() -> leqnat([z, z]) -> 47
(insert([x, l, _jj]) /\ length([_jj, _kj]) /\ length([l, _ij])) -> leqnat([_ij, _kj]) -> 64
(insert([x, z, _zi]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _zi)]) -> 48
(length([ll, _ej])) -> length([cons(x, ll), s(_ej)]) -> 59
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 49
(leq([b, a])) -> BOT -> 47
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 47
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 52
(leqnat([s(nn1), z])) -> BOT -> 50
}
Sat witness: Found: ((insert([x, l, _jj]) /\ length([_jj, _kj]) /\ length([l, _ij])) -> leqnat([_ij, _kj]), {
_ij -> s(s(s(s(z))))  ;  _jj -> cons(b, cons(b, cons(b, cons(b, cons(b, nil)))))  ;  _kj -> s(s(s(z)))  ;  l -> cons(b, cons(b, cons(b, cons(b, nil))))  ;  x -> a
})

-------------------------------------------
Step 64, which took 0.425544 s (model generation: 0.418411,  model checking: 0.007133):

Model:
|_
{
insert -> 
{{{
Q={q_gen_2250, q_gen_2251, q_gen_2252, q_gen_2255, q_gen_2256, q_gen_2262, q_gen_2299},
Q_f={q_gen_2250},
Delta=
{
<nil>() -> q_gen_2251
<a>() -> q_gen_2252
<b>() -> q_gen_2252
<cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2255
<cons, cons>(q_gen_2262, q_gen_2255) -> q_gen_2255
<nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2255
<a, b>() -> q_gen_2256
<b, b>() -> q_gen_2256
<a, a>() -> q_gen_2262
<b, a>() -> q_gen_2262
<a, cons, cons>(q_gen_2262, q_gen_2255) -> q_gen_2250
<a, nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2250
<b, cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2250
<b, cons, cons>(q_gen_2262, q_gen_2255) -> q_gen_2250
<b, nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2250
<a, cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2299
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_2249, q_gen_2258, q_gen_2259, q_gen_2280, q_gen_2281, q_gen_2282, q_gen_2283, q_gen_2285, q_gen_2293, q_gen_2294, q_gen_2298, q_gen_2316},
Q_f={q_gen_2249},
Delta=
{
<cons>(q_gen_2281, q_gen_2298) -> q_gen_2258
<nil>() -> q_gen_2258
<cons>(q_gen_2281, q_gen_2258) -> q_gen_2280
<a>() -> q_gen_2281
<b>() -> q_gen_2281
<s>(q_gen_2316) -> q_gen_2283
<z>() -> q_gen_2283
<s>(q_gen_2283) -> q_gen_2294
<cons>(q_gen_2281, q_gen_2280) -> q_gen_2298
<s>(q_gen_2294) -> q_gen_2316
<cons, s>(q_gen_2259, q_gen_2258) -> q_gen_2249
<cons, s>(q_gen_2282, q_gen_2280) -> q_gen_2249
<cons, s>(q_gen_2293, q_gen_2298) -> q_gen_2249
<nil, z>() -> q_gen_2249
<a, s>(q_gen_2316) -> q_gen_2259
<a, z>() -> q_gen_2259
<b, s>(q_gen_2316) -> q_gen_2259
<b, z>() -> q_gen_2259
<a, s>(q_gen_2283) -> q_gen_2282
<b, s>(q_gen_2283) -> q_gen_2282
<cons, s>(q_gen_2259, q_gen_2280) -> q_gen_2285
<cons, s>(q_gen_2259, q_gen_2298) -> q_gen_2285
<cons, s>(q_gen_2282, q_gen_2258) -> q_gen_2285
<cons, s>(q_gen_2282, q_gen_2298) -> q_gen_2285
<cons, s>(q_gen_2293, q_gen_2258) -> q_gen_2285
<cons, s>(q_gen_2293, q_gen_2280) -> q_gen_2285
<a, s>(q_gen_2294) -> q_gen_2293
<b, s>(q_gen_2294) -> q_gen_2293
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_2247, q_gen_2260},
Q_f={q_gen_2247},
Delta=
{
<a, a>() -> q_gen_2247
<a, b>() -> q_gen_2247
<b, b>() -> q_gen_2247
<b, a>() -> q_gen_2260
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  leqnat -> 
{{{
Q={q_gen_2244, q_gen_2246, q_gen_2287},
Q_f={q_gen_2244},
Delta=
{
<s>(q_gen_2246) -> q_gen_2246
<z>() -> q_gen_2246
<s, s>(q_gen_2244) -> q_gen_2244
<z, s>(q_gen_2246) -> q_gen_2244
<z, z>() -> q_gen_2244
<s, s>(q_gen_2287) -> q_gen_2287
<s, z>(q_gen_2246) -> q_gen_2287
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 48
() -> length([nil, z]) -> 48
() -> leq([a, y]) -> 48
() -> leq([b, b]) -> 48
() -> leqnat([z, s(nn2)]) -> 49
() -> leqnat([z, z]) -> 48
(insert([x, l, _jj]) /\ length([_jj, _kj]) /\ length([l, _ij])) -> leqnat([_ij, _kj]) -> 67
(insert([x, z, _zi]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _zi)]) -> 49
(length([ll, _ej])) -> length([cons(x, ll), s(_ej)]) -> 60
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 50
(leq([b, a])) -> BOT -> 48
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 48
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 53
(leqnat([s(nn1), z])) -> BOT -> 51
}
Sat witness: Found: ((insert([x, l, _jj]) /\ length([_jj, _kj]) /\ length([l, _ij])) -> leqnat([_ij, _kj]), {
_ij -> s(s(s(s(z))))  ;  _jj -> cons(b, cons(b, nil))  ;  _kj -> s(s(z))  ;  l -> cons(b, nil)  ;  x -> b
})

-------------------------------------------
Step 65, which took 0.428534 s (model generation: 0.424887,  model checking: 0.003647):

Model:
|_
{
insert -> 
{{{
Q={q_gen_2250, q_gen_2251, q_gen_2252, q_gen_2255, q_gen_2256},
Q_f={q_gen_2250},
Delta=
{
<nil>() -> q_gen_2251
<a>() -> q_gen_2252
<b>() -> q_gen_2252
<cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2255
<nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2255
<a, a>() -> q_gen_2256
<a, b>() -> q_gen_2256
<b, a>() -> q_gen_2256
<b, b>() -> q_gen_2256
<a, cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2250
<a, nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2250
<b, cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2250
<b, nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2250
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_2249, q_gen_2258, q_gen_2259, q_gen_2280, q_gen_2281, q_gen_2282, q_gen_2283, q_gen_2285, q_gen_2293, q_gen_2294, q_gen_2298, q_gen_2314, q_gen_2315, q_gen_2316},
Q_f={q_gen_2249},
Delta=
{
<cons>(q_gen_2281, q_gen_2314) -> q_gen_2258
<nil>() -> q_gen_2258
<cons>(q_gen_2281, q_gen_2258) -> q_gen_2280
<a>() -> q_gen_2281
<b>() -> q_gen_2281
<z>() -> q_gen_2283
<s>(q_gen_2283) -> q_gen_2294
<cons>(q_gen_2281, q_gen_2280) -> q_gen_2298
<cons>(q_gen_2281, q_gen_2298) -> q_gen_2314
<s>(q_gen_2294) -> q_gen_2316
<s>(q_gen_2316) -> q_gen_2316
<cons, s>(q_gen_2259, q_gen_2258) -> q_gen_2249
<cons, s>(q_gen_2259, q_gen_2314) -> q_gen_2249
<cons, s>(q_gen_2282, q_gen_2280) -> q_gen_2249
<cons, s>(q_gen_2293, q_gen_2298) -> q_gen_2249
<cons, s>(q_gen_2293, q_gen_2314) -> q_gen_2249
<cons, s>(q_gen_2315, q_gen_2314) -> q_gen_2249
<nil, z>() -> q_gen_2249
<a, s>(q_gen_2316) -> q_gen_2259
<a, z>() -> q_gen_2259
<b, z>() -> q_gen_2259
<a, s>(q_gen_2283) -> q_gen_2282
<b, s>(q_gen_2283) -> q_gen_2282
<cons, s>(q_gen_2259, q_gen_2280) -> q_gen_2285
<cons, s>(q_gen_2259, q_gen_2298) -> q_gen_2285
<cons, s>(q_gen_2282, q_gen_2258) -> q_gen_2285
<cons, s>(q_gen_2282, q_gen_2298) -> q_gen_2285
<cons, s>(q_gen_2282, q_gen_2314) -> q_gen_2285
<cons, s>(q_gen_2293, q_gen_2258) -> q_gen_2285
<cons, s>(q_gen_2293, q_gen_2280) -> q_gen_2285
<cons, s>(q_gen_2315, q_gen_2258) -> q_gen_2285
<cons, s>(q_gen_2315, q_gen_2280) -> q_gen_2285
<cons, s>(q_gen_2315, q_gen_2298) -> q_gen_2285
<a, s>(q_gen_2294) -> q_gen_2293
<b, s>(q_gen_2294) -> q_gen_2293
<b, s>(q_gen_2316) -> q_gen_2315
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_2247, q_gen_2260},
Q_f={q_gen_2247},
Delta=
{
<a, a>() -> q_gen_2247
<a, b>() -> q_gen_2247
<b, b>() -> q_gen_2247
<b, a>() -> q_gen_2260
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  leqnat -> 
{{{
Q={q_gen_2244, q_gen_2246, q_gen_2287},
Q_f={q_gen_2244},
Delta=
{
<s>(q_gen_2246) -> q_gen_2246
<z>() -> q_gen_2246
<s, s>(q_gen_2244) -> q_gen_2244
<z, s>(q_gen_2246) -> q_gen_2244
<z, z>() -> q_gen_2244
<s, s>(q_gen_2287) -> q_gen_2287
<s, z>(q_gen_2246) -> q_gen_2287
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 49
() -> length([nil, z]) -> 49
() -> leq([a, y]) -> 49
() -> leq([b, b]) -> 49
() -> leqnat([z, s(nn2)]) -> 50
() -> leqnat([z, z]) -> 49
(insert([x, l, _jj]) /\ length([_jj, _kj]) /\ length([l, _ij])) -> leqnat([_ij, _kj]) -> 67
(insert([x, z, _zi]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _zi)]) -> 50
(length([ll, _ej])) -> length([cons(x, ll), s(_ej)]) -> 63
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 51
(leq([b, a])) -> BOT -> 49
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 49
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 54
(leqnat([s(nn1), z])) -> BOT -> 52
}
Sat witness: Found: ((length([ll, _ej])) -> length([cons(x, ll), s(_ej)]), {
_ej -> s(s(s(s(z))))  ;  ll -> cons(a, nil)  ;  x -> b
})

-------------------------------------------
Step 66, which took 0.491613 s (model generation: 0.482614,  model checking: 0.008999):

Model:
|_
{
insert -> 
{{{
Q={q_gen_2250, q_gen_2251, q_gen_2252, q_gen_2255, q_gen_2256},
Q_f={q_gen_2250},
Delta=
{
<nil>() -> q_gen_2251
<a>() -> q_gen_2252
<b>() -> q_gen_2252
<cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2255
<nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2255
<a, a>() -> q_gen_2256
<a, b>() -> q_gen_2256
<b, a>() -> q_gen_2256
<b, b>() -> q_gen_2256
<a, cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2250
<a, nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2250
<b, cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2250
<b, nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2250
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_2249, q_gen_2258, q_gen_2259, q_gen_2280, q_gen_2281, q_gen_2282, q_gen_2283, q_gen_2285, q_gen_2293, q_gen_2294, q_gen_2298, q_gen_2314, q_gen_2315, q_gen_2316},
Q_f={q_gen_2249},
Delta=
{
<nil>() -> q_gen_2258
<cons>(q_gen_2281, q_gen_2258) -> q_gen_2280
<a>() -> q_gen_2281
<b>() -> q_gen_2281
<z>() -> q_gen_2283
<s>(q_gen_2283) -> q_gen_2294
<cons>(q_gen_2281, q_gen_2280) -> q_gen_2298
<cons>(q_gen_2281, q_gen_2298) -> q_gen_2314
<cons>(q_gen_2281, q_gen_2314) -> q_gen_2314
<s>(q_gen_2294) -> q_gen_2316
<s>(q_gen_2316) -> q_gen_2316
<cons, s>(q_gen_2259, q_gen_2258) -> q_gen_2249
<cons, s>(q_gen_2259, q_gen_2314) -> q_gen_2249
<cons, s>(q_gen_2282, q_gen_2258) -> q_gen_2249
<cons, s>(q_gen_2282, q_gen_2280) -> q_gen_2249
<cons, s>(q_gen_2293, q_gen_2280) -> q_gen_2249
<cons, s>(q_gen_2293, q_gen_2298) -> q_gen_2249
<cons, s>(q_gen_2315, q_gen_2298) -> q_gen_2249
<cons, s>(q_gen_2315, q_gen_2314) -> q_gen_2249
<nil, z>() -> q_gen_2249
<a, z>() -> q_gen_2259
<b, z>() -> q_gen_2259
<a, s>(q_gen_2283) -> q_gen_2282
<b, s>(q_gen_2283) -> q_gen_2282
<cons, s>(q_gen_2259, q_gen_2280) -> q_gen_2285
<cons, s>(q_gen_2259, q_gen_2298) -> q_gen_2285
<cons, s>(q_gen_2282, q_gen_2298) -> q_gen_2285
<cons, s>(q_gen_2282, q_gen_2314) -> q_gen_2285
<cons, s>(q_gen_2293, q_gen_2258) -> q_gen_2285
<cons, s>(q_gen_2293, q_gen_2314) -> q_gen_2285
<cons, s>(q_gen_2315, q_gen_2258) -> q_gen_2285
<cons, s>(q_gen_2315, q_gen_2280) -> q_gen_2285
<a, s>(q_gen_2294) -> q_gen_2293
<b, s>(q_gen_2294) -> q_gen_2293
<a, s>(q_gen_2316) -> q_gen_2315
<b, s>(q_gen_2316) -> q_gen_2315
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_2247, q_gen_2260},
Q_f={q_gen_2247},
Delta=
{
<a, a>() -> q_gen_2247
<a, b>() -> q_gen_2247
<b, b>() -> q_gen_2247
<b, a>() -> q_gen_2260
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  leqnat -> 
{{{
Q={q_gen_2244, q_gen_2246, q_gen_2287},
Q_f={q_gen_2244},
Delta=
{
<s>(q_gen_2246) -> q_gen_2246
<z>() -> q_gen_2246
<s, s>(q_gen_2244) -> q_gen_2244
<z, s>(q_gen_2246) -> q_gen_2244
<z, z>() -> q_gen_2244
<s, s>(q_gen_2287) -> q_gen_2287
<s, z>(q_gen_2246) -> q_gen_2287
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 50
() -> length([nil, z]) -> 50
() -> leq([a, y]) -> 50
() -> leq([b, b]) -> 50
() -> leqnat([z, s(nn2)]) -> 51
() -> leqnat([z, z]) -> 50
(insert([x, l, _jj]) /\ length([_jj, _kj]) /\ length([l, _ij])) -> leqnat([_ij, _kj]) -> 67
(insert([x, z, _zi]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _zi)]) -> 51
(length([ll, _ej])) -> length([cons(x, ll), s(_ej)]) -> 66
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 52
(leq([b, a])) -> BOT -> 50
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 50
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 55
(leqnat([s(nn1), z])) -> BOT -> 53
}
Sat witness: Found: ((length([ll, _ej])) -> length([cons(x, ll), s(_ej)]), {
_ej -> s(z)  ;  ll -> cons(b, cons(b, cons(a, cons(b, nil))))  ;  x -> b
})

-------------------------------------------
Step 67, which took 0.478742 s (model generation: 0.475833,  model checking: 0.002909):

Model:
|_
{
insert -> 
{{{
Q={q_gen_2250, q_gen_2251, q_gen_2252, q_gen_2255, q_gen_2256},
Q_f={q_gen_2250},
Delta=
{
<nil>() -> q_gen_2251
<a>() -> q_gen_2252
<b>() -> q_gen_2252
<cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2255
<nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2255
<a, a>() -> q_gen_2256
<a, b>() -> q_gen_2256
<b, a>() -> q_gen_2256
<b, b>() -> q_gen_2256
<a, cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2250
<a, nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2250
<b, cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2250
<b, nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2250
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_2249, q_gen_2258, q_gen_2259, q_gen_2280, q_gen_2281, q_gen_2282, q_gen_2283, q_gen_2285, q_gen_2293, q_gen_2294, q_gen_2298, q_gen_2314, q_gen_2315, q_gen_2316},
Q_f={q_gen_2249},
Delta=
{
<cons>(q_gen_2281, q_gen_2314) -> q_gen_2258
<nil>() -> q_gen_2258
<cons>(q_gen_2281, q_gen_2258) -> q_gen_2280
<a>() -> q_gen_2281
<b>() -> q_gen_2281
<s>(q_gen_2316) -> q_gen_2283
<z>() -> q_gen_2283
<s>(q_gen_2283) -> q_gen_2294
<cons>(q_gen_2281, q_gen_2280) -> q_gen_2298
<cons>(q_gen_2281, q_gen_2298) -> q_gen_2314
<s>(q_gen_2294) -> q_gen_2316
<cons, s>(q_gen_2259, q_gen_2258) -> q_gen_2249
<cons, s>(q_gen_2259, q_gen_2314) -> q_gen_2249
<cons, s>(q_gen_2282, q_gen_2258) -> q_gen_2249
<cons, s>(q_gen_2282, q_gen_2280) -> q_gen_2249
<cons, s>(q_gen_2293, q_gen_2280) -> q_gen_2249
<cons, s>(q_gen_2293, q_gen_2298) -> q_gen_2249
<cons, s>(q_gen_2315, q_gen_2298) -> q_gen_2249
<cons, s>(q_gen_2315, q_gen_2314) -> q_gen_2249
<nil, z>() -> q_gen_2249
<a, s>(q_gen_2316) -> q_gen_2259
<a, z>() -> q_gen_2259
<b, z>() -> q_gen_2259
<a, s>(q_gen_2283) -> q_gen_2282
<b, s>(q_gen_2283) -> q_gen_2282
<cons, s>(q_gen_2259, q_gen_2280) -> q_gen_2285
<cons, s>(q_gen_2259, q_gen_2298) -> q_gen_2285
<cons, s>(q_gen_2282, q_gen_2298) -> q_gen_2285
<cons, s>(q_gen_2282, q_gen_2314) -> q_gen_2285
<cons, s>(q_gen_2293, q_gen_2258) -> q_gen_2285
<cons, s>(q_gen_2293, q_gen_2314) -> q_gen_2285
<cons, s>(q_gen_2315, q_gen_2258) -> q_gen_2285
<cons, s>(q_gen_2315, q_gen_2280) -> q_gen_2285
<b, s>(q_gen_2294) -> q_gen_2293
<a, s>(q_gen_2294) -> q_gen_2315
<b, s>(q_gen_2316) -> q_gen_2315
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_2247, q_gen_2260},
Q_f={q_gen_2247},
Delta=
{
<a, a>() -> q_gen_2247
<a, b>() -> q_gen_2247
<b, b>() -> q_gen_2247
<b, a>() -> q_gen_2260
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  leqnat -> 
{{{
Q={q_gen_2244, q_gen_2246, q_gen_2287},
Q_f={q_gen_2244},
Delta=
{
<s>(q_gen_2246) -> q_gen_2246
<z>() -> q_gen_2246
<s, s>(q_gen_2244) -> q_gen_2244
<z, s>(q_gen_2246) -> q_gen_2244
<z, z>() -> q_gen_2244
<s, s>(q_gen_2287) -> q_gen_2287
<s, z>(q_gen_2246) -> q_gen_2287
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 51
() -> length([nil, z]) -> 51
() -> leq([a, y]) -> 51
() -> leq([b, b]) -> 51
() -> leqnat([z, s(nn2)]) -> 52
() -> leqnat([z, z]) -> 51
(insert([x, l, _jj]) /\ length([_jj, _kj]) /\ length([l, _ij])) -> leqnat([_ij, _kj]) -> 67
(insert([x, z, _zi]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _zi)]) -> 52
(length([ll, _ej])) -> length([cons(x, ll), s(_ej)]) -> 69
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 53
(leq([b, a])) -> BOT -> 51
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 51
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 56
(leqnat([s(nn1), z])) -> BOT -> 54
}
Sat witness: Found: ((length([ll, _ej])) -> length([cons(x, ll), s(_ej)]), {
_ej -> s(s(s(z)))  ;  ll -> cons(b, cons(b, nil))  ;  x -> a
})

-------------------------------------------
Step 68, which took 0.519449 s (model generation: 0.515642,  model checking: 0.003807):

Model:
|_
{
insert -> 
{{{
Q={q_gen_2250, q_gen_2251, q_gen_2252, q_gen_2255, q_gen_2256},
Q_f={q_gen_2250},
Delta=
{
<nil>() -> q_gen_2251
<a>() -> q_gen_2252
<b>() -> q_gen_2252
<cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2255
<nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2255
<a, a>() -> q_gen_2256
<a, b>() -> q_gen_2256
<b, a>() -> q_gen_2256
<b, b>() -> q_gen_2256
<a, cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2250
<a, nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2250
<b, cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2250
<b, nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2250
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_2249, q_gen_2258, q_gen_2259, q_gen_2280, q_gen_2281, q_gen_2282, q_gen_2283, q_gen_2285, q_gen_2293, q_gen_2294, q_gen_2298, q_gen_2314, q_gen_2315, q_gen_2316},
Q_f={q_gen_2249},
Delta=
{
<nil>() -> q_gen_2258
<cons>(q_gen_2281, q_gen_2258) -> q_gen_2280
<cons>(q_gen_2281, q_gen_2314) -> q_gen_2280
<a>() -> q_gen_2281
<b>() -> q_gen_2281
<s>(q_gen_2316) -> q_gen_2283
<z>() -> q_gen_2283
<s>(q_gen_2283) -> q_gen_2294
<cons>(q_gen_2281, q_gen_2280) -> q_gen_2298
<cons>(q_gen_2281, q_gen_2298) -> q_gen_2314
<s>(q_gen_2294) -> q_gen_2316
<cons, s>(q_gen_2259, q_gen_2258) -> q_gen_2249
<cons, s>(q_gen_2282, q_gen_2280) -> q_gen_2249
<cons, s>(q_gen_2293, q_gen_2298) -> q_gen_2249
<cons, s>(q_gen_2315, q_gen_2314) -> q_gen_2249
<nil, z>() -> q_gen_2249
<a, z>() -> q_gen_2259
<b, z>() -> q_gen_2259
<a, s>(q_gen_2283) -> q_gen_2282
<b, s>(q_gen_2283) -> q_gen_2282
<cons, s>(q_gen_2259, q_gen_2280) -> q_gen_2285
<cons, s>(q_gen_2259, q_gen_2298) -> q_gen_2285
<cons, s>(q_gen_2259, q_gen_2314) -> q_gen_2285
<cons, s>(q_gen_2282, q_gen_2258) -> q_gen_2285
<cons, s>(q_gen_2282, q_gen_2298) -> q_gen_2285
<cons, s>(q_gen_2282, q_gen_2314) -> q_gen_2285
<cons, s>(q_gen_2293, q_gen_2258) -> q_gen_2285
<cons, s>(q_gen_2293, q_gen_2280) -> q_gen_2285
<cons, s>(q_gen_2293, q_gen_2314) -> q_gen_2285
<cons, s>(q_gen_2315, q_gen_2258) -> q_gen_2285
<cons, s>(q_gen_2315, q_gen_2280) -> q_gen_2285
<cons, s>(q_gen_2315, q_gen_2298) -> q_gen_2285
<a, s>(q_gen_2294) -> q_gen_2293
<b, s>(q_gen_2294) -> q_gen_2293
<a, s>(q_gen_2316) -> q_gen_2315
<b, s>(q_gen_2316) -> q_gen_2315
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_2247, q_gen_2260},
Q_f={q_gen_2247},
Delta=
{
<a, a>() -> q_gen_2247
<a, b>() -> q_gen_2247
<b, b>() -> q_gen_2247
<b, a>() -> q_gen_2260
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  leqnat -> 
{{{
Q={q_gen_2244, q_gen_2246, q_gen_2287},
Q_f={q_gen_2244},
Delta=
{
<s>(q_gen_2246) -> q_gen_2246
<z>() -> q_gen_2246
<s, s>(q_gen_2244) -> q_gen_2244
<z, s>(q_gen_2246) -> q_gen_2244
<z, z>() -> q_gen_2244
<s, s>(q_gen_2287) -> q_gen_2287
<s, z>(q_gen_2246) -> q_gen_2287
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 52
() -> length([nil, z]) -> 52
() -> leq([a, y]) -> 52
() -> leq([b, b]) -> 52
() -> leqnat([z, s(nn2)]) -> 53
() -> leqnat([z, z]) -> 52
(insert([x, l, _jj]) /\ length([_jj, _kj]) /\ length([l, _ij])) -> leqnat([_ij, _kj]) -> 70
(insert([x, z, _zi]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _zi)]) -> 53
(length([ll, _ej])) -> length([cons(x, ll), s(_ej)]) -> 69
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 54
(leq([b, a])) -> BOT -> 52
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 52
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 57
(leqnat([s(nn1), z])) -> BOT -> 55
}
Sat witness: Found: ((insert([x, l, _jj]) /\ length([_jj, _kj]) /\ length([l, _ij])) -> leqnat([_ij, _kj]), {
_ij -> s(s(s(s(z))))  ;  _jj -> cons(b, cons(b, cons(b, cons(b, cons(b, nil)))))  ;  _kj -> s(s(z))  ;  l -> cons(b, cons(b, cons(b, cons(b, nil))))  ;  x -> a
})

-------------------------------------------
Step 69, which took 0.479275 s (model generation: 0.465380,  model checking: 0.013895):

Model:
|_
{
insert -> 
{{{
Q={q_gen_2250, q_gen_2251, q_gen_2252, q_gen_2255, q_gen_2256},
Q_f={q_gen_2250},
Delta=
{
<nil>() -> q_gen_2251
<a>() -> q_gen_2252
<b>() -> q_gen_2252
<cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2255
<nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2255
<a, a>() -> q_gen_2256
<a, b>() -> q_gen_2256
<b, a>() -> q_gen_2256
<b, b>() -> q_gen_2256
<a, cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2250
<a, nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2250
<b, cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2250
<b, nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2250
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_2249, q_gen_2258, q_gen_2259, q_gen_2280, q_gen_2281, q_gen_2282, q_gen_2283, q_gen_2285, q_gen_2293, q_gen_2294, q_gen_2298, q_gen_2314, q_gen_2315, q_gen_2316},
Q_f={q_gen_2249},
Delta=
{
<nil>() -> q_gen_2258
<cons>(q_gen_2281, q_gen_2258) -> q_gen_2280
<a>() -> q_gen_2281
<b>() -> q_gen_2281
<z>() -> q_gen_2283
<s>(q_gen_2283) -> q_gen_2294
<cons>(q_gen_2281, q_gen_2280) -> q_gen_2298
<cons>(q_gen_2281, q_gen_2298) -> q_gen_2314
<cons>(q_gen_2281, q_gen_2314) -> q_gen_2314
<s>(q_gen_2294) -> q_gen_2316
<s>(q_gen_2316) -> q_gen_2316
<cons, s>(q_gen_2259, q_gen_2258) -> q_gen_2249
<cons, s>(q_gen_2282, q_gen_2280) -> q_gen_2249
<cons, s>(q_gen_2293, q_gen_2280) -> q_gen_2249
<cons, s>(q_gen_2293, q_gen_2298) -> q_gen_2249
<cons, s>(q_gen_2315, q_gen_2298) -> q_gen_2249
<cons, s>(q_gen_2315, q_gen_2314) -> q_gen_2249
<nil, z>() -> q_gen_2249
<a, z>() -> q_gen_2259
<b, z>() -> q_gen_2259
<a, s>(q_gen_2283) -> q_gen_2282
<b, s>(q_gen_2283) -> q_gen_2282
<cons, s>(q_gen_2259, q_gen_2280) -> q_gen_2285
<cons, s>(q_gen_2259, q_gen_2298) -> q_gen_2285
<cons, s>(q_gen_2259, q_gen_2314) -> q_gen_2285
<cons, s>(q_gen_2282, q_gen_2258) -> q_gen_2285
<cons, s>(q_gen_2282, q_gen_2298) -> q_gen_2285
<cons, s>(q_gen_2282, q_gen_2314) -> q_gen_2285
<cons, s>(q_gen_2293, q_gen_2258) -> q_gen_2285
<cons, s>(q_gen_2293, q_gen_2314) -> q_gen_2285
<cons, s>(q_gen_2315, q_gen_2258) -> q_gen_2285
<cons, s>(q_gen_2315, q_gen_2280) -> q_gen_2285
<b, s>(q_gen_2294) -> q_gen_2293
<a, s>(q_gen_2294) -> q_gen_2315
<a, s>(q_gen_2316) -> q_gen_2315
<b, s>(q_gen_2316) -> q_gen_2315
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_2247, q_gen_2260},
Q_f={q_gen_2247},
Delta=
{
<a, a>() -> q_gen_2247
<a, b>() -> q_gen_2247
<b, b>() -> q_gen_2247
<b, a>() -> q_gen_2260
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  leqnat -> 
{{{
Q={q_gen_2244, q_gen_2246, q_gen_2287},
Q_f={q_gen_2244},
Delta=
{
<s>(q_gen_2246) -> q_gen_2246
<z>() -> q_gen_2246
<s, s>(q_gen_2244) -> q_gen_2244
<z, s>(q_gen_2246) -> q_gen_2244
<z, z>() -> q_gen_2244
<s, s>(q_gen_2287) -> q_gen_2287
<s, z>(q_gen_2246) -> q_gen_2287
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 53
() -> length([nil, z]) -> 53
() -> leq([a, y]) -> 53
() -> leq([b, b]) -> 53
() -> leqnat([z, s(nn2)]) -> 54
() -> leqnat([z, z]) -> 53
(insert([x, l, _jj]) /\ length([_jj, _kj]) /\ length([l, _ij])) -> leqnat([_ij, _kj]) -> 73
(insert([x, z, _zi]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _zi)]) -> 54
(length([ll, _ej])) -> length([cons(x, ll), s(_ej)]) -> 70
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 55
(leq([b, a])) -> BOT -> 53
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 53
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 58
(leqnat([s(nn1), z])) -> BOT -> 56
}
Sat witness: Found: ((insert([x, l, _jj]) /\ length([_jj, _kj]) /\ length([l, _ij])) -> leqnat([_ij, _kj]), {
_ij -> s(s(s(s(z))))  ;  _jj -> cons(a, cons(b, cons(b, cons(b, nil))))  ;  _kj -> s(s(s(z)))  ;  l -> cons(b, cons(b, cons(b, nil)))  ;  x -> a
})

-------------------------------------------
Step 70, which took 0.574392 s (model generation: 0.558462,  model checking: 0.015930):

Model:
|_
{
insert -> 
{{{
Q={q_gen_2250, q_gen_2251, q_gen_2252, q_gen_2255, q_gen_2256},
Q_f={q_gen_2250},
Delta=
{
<nil>() -> q_gen_2251
<a>() -> q_gen_2252
<b>() -> q_gen_2252
<cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2255
<nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2255
<a, a>() -> q_gen_2256
<a, b>() -> q_gen_2256
<b, a>() -> q_gen_2256
<b, b>() -> q_gen_2256
<a, cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2250
<a, nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2250
<b, cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2250
<b, nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2250
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_2249, q_gen_2258, q_gen_2259, q_gen_2280, q_gen_2281, q_gen_2282, q_gen_2283, q_gen_2285, q_gen_2293, q_gen_2294, q_gen_2298, q_gen_2314, q_gen_2315, q_gen_2316},
Q_f={q_gen_2249},
Delta=
{
<nil>() -> q_gen_2258
<cons>(q_gen_2281, q_gen_2258) -> q_gen_2280
<a>() -> q_gen_2281
<b>() -> q_gen_2281
<z>() -> q_gen_2283
<s>(q_gen_2283) -> q_gen_2294
<cons>(q_gen_2281, q_gen_2280) -> q_gen_2298
<cons>(q_gen_2281, q_gen_2298) -> q_gen_2314
<cons>(q_gen_2281, q_gen_2314) -> q_gen_2314
<s>(q_gen_2294) -> q_gen_2316
<s>(q_gen_2316) -> q_gen_2316
<cons, s>(q_gen_2259, q_gen_2258) -> q_gen_2249
<cons, s>(q_gen_2282, q_gen_2258) -> q_gen_2249
<cons, s>(q_gen_2282, q_gen_2280) -> q_gen_2249
<cons, s>(q_gen_2293, q_gen_2280) -> q_gen_2249
<cons, s>(q_gen_2293, q_gen_2298) -> q_gen_2249
<cons, s>(q_gen_2315, q_gen_2298) -> q_gen_2249
<cons, s>(q_gen_2315, q_gen_2314) -> q_gen_2249
<nil, z>() -> q_gen_2249
<a, z>() -> q_gen_2259
<b, z>() -> q_gen_2259
<a, s>(q_gen_2283) -> q_gen_2282
<b, s>(q_gen_2283) -> q_gen_2282
<cons, s>(q_gen_2259, q_gen_2280) -> q_gen_2285
<cons, s>(q_gen_2259, q_gen_2298) -> q_gen_2285
<cons, s>(q_gen_2259, q_gen_2314) -> q_gen_2285
<cons, s>(q_gen_2282, q_gen_2298) -> q_gen_2285
<cons, s>(q_gen_2282, q_gen_2314) -> q_gen_2285
<cons, s>(q_gen_2293, q_gen_2258) -> q_gen_2285
<cons, s>(q_gen_2293, q_gen_2314) -> q_gen_2285
<cons, s>(q_gen_2315, q_gen_2258) -> q_gen_2285
<cons, s>(q_gen_2315, q_gen_2280) -> q_gen_2285
<a, s>(q_gen_2294) -> q_gen_2293
<b, s>(q_gen_2294) -> q_gen_2293
<a, s>(q_gen_2316) -> q_gen_2315
<b, s>(q_gen_2316) -> q_gen_2315
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_2247, q_gen_2260},
Q_f={q_gen_2247},
Delta=
{
<a, a>() -> q_gen_2247
<a, b>() -> q_gen_2247
<b, b>() -> q_gen_2247
<b, a>() -> q_gen_2260
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  leqnat -> 
{{{
Q={q_gen_2244, q_gen_2246, q_gen_2287},
Q_f={q_gen_2244},
Delta=
{
<s>(q_gen_2246) -> q_gen_2246
<z>() -> q_gen_2246
<s, s>(q_gen_2244) -> q_gen_2244
<z, s>(q_gen_2246) -> q_gen_2244
<z, z>() -> q_gen_2244
<s, s>(q_gen_2287) -> q_gen_2287
<s, z>(q_gen_2246) -> q_gen_2287
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 54
() -> length([nil, z]) -> 54
() -> leq([a, y]) -> 54
() -> leq([b, b]) -> 54
() -> leqnat([z, s(nn2)]) -> 55
() -> leqnat([z, z]) -> 54
(insert([x, l, _jj]) /\ length([_jj, _kj]) /\ length([l, _ij])) -> leqnat([_ij, _kj]) -> 76
(insert([x, z, _zi]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _zi)]) -> 55
(length([ll, _ej])) -> length([cons(x, ll), s(_ej)]) -> 71
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 56
(leq([b, a])) -> BOT -> 54
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 54
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 59
(leqnat([s(nn1), z])) -> BOT -> 57
}
Sat witness: Found: ((insert([x, l, _jj]) /\ length([_jj, _kj]) /\ length([l, _ij])) -> leqnat([_ij, _kj]), {
_ij -> s(s(s(s(s(z)))))  ;  _jj -> cons(b, cons(b, cons(b, cons(b, nil))))  ;  _kj -> s(s(s(s(z))))  ;  l -> cons(b, cons(b, cons(b, nil)))  ;  x -> a
})

-------------------------------------------
Step 71, which took 0.485193 s (model generation: 0.473128,  model checking: 0.012065):

Model:
|_
{
insert -> 
{{{
Q={q_gen_2250, q_gen_2251, q_gen_2252, q_gen_2255, q_gen_2256},
Q_f={q_gen_2250},
Delta=
{
<nil>() -> q_gen_2251
<a>() -> q_gen_2252
<b>() -> q_gen_2252
<cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2255
<nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2255
<a, a>() -> q_gen_2256
<a, b>() -> q_gen_2256
<b, a>() -> q_gen_2256
<b, b>() -> q_gen_2256
<a, cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2250
<a, nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2250
<b, cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2250
<b, nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2250
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_2249, q_gen_2258, q_gen_2259, q_gen_2280, q_gen_2281, q_gen_2282, q_gen_2283, q_gen_2285, q_gen_2293, q_gen_2294, q_gen_2298, q_gen_2314, q_gen_2315, q_gen_2316},
Q_f={q_gen_2249},
Delta=
{
<nil>() -> q_gen_2258
<cons>(q_gen_2281, q_gen_2258) -> q_gen_2280
<a>() -> q_gen_2281
<b>() -> q_gen_2281
<z>() -> q_gen_2283
<s>(q_gen_2283) -> q_gen_2294
<cons>(q_gen_2281, q_gen_2280) -> q_gen_2298
<cons>(q_gen_2281, q_gen_2298) -> q_gen_2314
<cons>(q_gen_2281, q_gen_2314) -> q_gen_2314
<s>(q_gen_2294) -> q_gen_2316
<s>(q_gen_2316) -> q_gen_2316
<cons, s>(q_gen_2259, q_gen_2258) -> q_gen_2249
<cons, s>(q_gen_2282, q_gen_2280) -> q_gen_2249
<cons, s>(q_gen_2293, q_gen_2298) -> q_gen_2249
<cons, s>(q_gen_2315, q_gen_2314) -> q_gen_2249
<nil, z>() -> q_gen_2249
<a, z>() -> q_gen_2259
<b, z>() -> q_gen_2259
<a, s>(q_gen_2283) -> q_gen_2282
<b, s>(q_gen_2283) -> q_gen_2282
<cons, s>(q_gen_2259, q_gen_2280) -> q_gen_2285
<cons, s>(q_gen_2259, q_gen_2298) -> q_gen_2285
<cons, s>(q_gen_2259, q_gen_2314) -> q_gen_2285
<cons, s>(q_gen_2282, q_gen_2258) -> q_gen_2285
<cons, s>(q_gen_2282, q_gen_2298) -> q_gen_2285
<cons, s>(q_gen_2282, q_gen_2314) -> q_gen_2285
<cons, s>(q_gen_2293, q_gen_2258) -> q_gen_2285
<cons, s>(q_gen_2293, q_gen_2280) -> q_gen_2285
<cons, s>(q_gen_2293, q_gen_2314) -> q_gen_2285
<cons, s>(q_gen_2315, q_gen_2258) -> q_gen_2285
<cons, s>(q_gen_2315, q_gen_2280) -> q_gen_2285
<cons, s>(q_gen_2315, q_gen_2298) -> q_gen_2285
<a, s>(q_gen_2294) -> q_gen_2293
<b, s>(q_gen_2294) -> q_gen_2293
<a, s>(q_gen_2316) -> q_gen_2315
<b, s>(q_gen_2316) -> q_gen_2315
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_2247, q_gen_2260},
Q_f={q_gen_2247},
Delta=
{
<a, a>() -> q_gen_2247
<a, b>() -> q_gen_2247
<b, b>() -> q_gen_2247
<b, a>() -> q_gen_2260
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  leqnat -> 
{{{
Q={q_gen_2244, q_gen_2246, q_gen_2287},
Q_f={q_gen_2244},
Delta=
{
<s>(q_gen_2246) -> q_gen_2246
<z>() -> q_gen_2246
<s, s>(q_gen_2244) -> q_gen_2244
<z, s>(q_gen_2246) -> q_gen_2244
<z, z>() -> q_gen_2244
<s, s>(q_gen_2287) -> q_gen_2287
<s, z>(q_gen_2246) -> q_gen_2287
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 55
() -> length([nil, z]) -> 55
() -> leq([a, y]) -> 55
() -> leq([b, b]) -> 55
() -> leqnat([z, s(nn2)]) -> 56
() -> leqnat([z, z]) -> 55
(insert([x, l, _jj]) /\ length([_jj, _kj]) /\ length([l, _ij])) -> leqnat([_ij, _kj]) -> 79
(insert([x, z, _zi]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _zi)]) -> 56
(length([ll, _ej])) -> length([cons(x, ll), s(_ej)]) -> 72
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 57
(leq([b, a])) -> BOT -> 55
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 55
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 60
(leqnat([s(nn1), z])) -> BOT -> 58
}
Sat witness: Found: ((insert([x, l, _jj]) /\ length([_jj, _kj]) /\ length([l, _ij])) -> leqnat([_ij, _kj]), {
_ij -> s(s(s(s(s(z)))))  ;  _jj -> cons(b, cons(b, cons(b, cons(b, cons(b, nil)))))  ;  _kj -> s(s(s(s(z))))  ;  l -> cons(b, cons(b, cons(b, cons(b, nil))))  ;  x -> b
})

-------------------------------------------
Step 72, which took 0.776317 s (model generation: 0.771100,  model checking: 0.005217):

Model:
|_
{
insert -> 
{{{
Q={q_gen_2250, q_gen_2251, q_gen_2252, q_gen_2255, q_gen_2256},
Q_f={q_gen_2250},
Delta=
{
<nil>() -> q_gen_2251
<a>() -> q_gen_2252
<b>() -> q_gen_2252
<cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2255
<nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2255
<a, a>() -> q_gen_2256
<a, b>() -> q_gen_2256
<b, a>() -> q_gen_2256
<b, b>() -> q_gen_2256
<a, cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2250
<a, nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2250
<b, cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2250
<b, nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2250
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_2249, q_gen_2258, q_gen_2259, q_gen_2280, q_gen_2281, q_gen_2282, q_gen_2283, q_gen_2286, q_gen_2291, q_gen_2293, q_gen_2294, q_gen_2298, q_gen_2314, q_gen_2315, q_gen_2316},
Q_f={q_gen_2249},
Delta=
{
<cons>(q_gen_2281, q_gen_2314) -> q_gen_2258
<nil>() -> q_gen_2258
<cons>(q_gen_2281, q_gen_2258) -> q_gen_2280
<a>() -> q_gen_2281
<b>() -> q_gen_2281
<s>(q_gen_2316) -> q_gen_2283
<z>() -> q_gen_2283
<s>(q_gen_2283) -> q_gen_2294
<cons>(q_gen_2281, q_gen_2280) -> q_gen_2298
<cons>(q_gen_2281, q_gen_2298) -> q_gen_2314
<s>(q_gen_2294) -> q_gen_2316
<cons, s>(q_gen_2259, q_gen_2258) -> q_gen_2249
<cons, s>(q_gen_2259, q_gen_2280) -> q_gen_2249
<cons, s>(q_gen_2282, q_gen_2280) -> q_gen_2249
<cons, s>(q_gen_2291, q_gen_2258) -> q_gen_2249
<cons, s>(q_gen_2291, q_gen_2280) -> q_gen_2249
<cons, s>(q_gen_2291, q_gen_2298) -> q_gen_2249
<cons, s>(q_gen_2293, q_gen_2298) -> q_gen_2249
<cons, s>(q_gen_2315, q_gen_2314) -> q_gen_2249
<nil, z>() -> q_gen_2249
<a, z>() -> q_gen_2259
<b, z>() -> q_gen_2259
<b, s>(q_gen_2283) -> q_gen_2282
<cons, s>(q_gen_2259, q_gen_2298) -> q_gen_2286
<cons, s>(q_gen_2259, q_gen_2314) -> q_gen_2286
<cons, s>(q_gen_2282, q_gen_2258) -> q_gen_2286
<cons, s>(q_gen_2282, q_gen_2298) -> q_gen_2286
<cons, s>(q_gen_2282, q_gen_2314) -> q_gen_2286
<cons, s>(q_gen_2291, q_gen_2314) -> q_gen_2286
<cons, s>(q_gen_2293, q_gen_2258) -> q_gen_2286
<cons, s>(q_gen_2293, q_gen_2280) -> q_gen_2286
<cons, s>(q_gen_2293, q_gen_2314) -> q_gen_2286
<cons, s>(q_gen_2315, q_gen_2258) -> q_gen_2286
<cons, s>(q_gen_2315, q_gen_2280) -> q_gen_2286
<cons, s>(q_gen_2315, q_gen_2298) -> q_gen_2286
<a, s>(q_gen_2283) -> q_gen_2291
<a, s>(q_gen_2294) -> q_gen_2291
<b, s>(q_gen_2294) -> q_gen_2293
<a, s>(q_gen_2316) -> q_gen_2315
<b, s>(q_gen_2316) -> q_gen_2315
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_2247, q_gen_2260},
Q_f={q_gen_2247},
Delta=
{
<a, a>() -> q_gen_2247
<a, b>() -> q_gen_2247
<b, b>() -> q_gen_2247
<b, a>() -> q_gen_2260
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  leqnat -> 
{{{
Q={q_gen_2244, q_gen_2246, q_gen_2287},
Q_f={q_gen_2244},
Delta=
{
<s>(q_gen_2246) -> q_gen_2246
<z>() -> q_gen_2246
<s, s>(q_gen_2244) -> q_gen_2244
<z, s>(q_gen_2246) -> q_gen_2244
<z, z>() -> q_gen_2244
<s, s>(q_gen_2287) -> q_gen_2287
<s, z>(q_gen_2246) -> q_gen_2287
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 56
() -> length([nil, z]) -> 56
() -> leq([a, y]) -> 56
() -> leq([b, b]) -> 56
() -> leqnat([z, s(nn2)]) -> 57
() -> leqnat([z, z]) -> 56
(insert([x, l, _jj]) /\ length([_jj, _kj]) /\ length([l, _ij])) -> leqnat([_ij, _kj]) -> 79
(insert([x, z, _zi]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _zi)]) -> 57
(length([ll, _ej])) -> length([cons(x, ll), s(_ej)]) -> 75
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 58
(leq([b, a])) -> BOT -> 56
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 56
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 61
(leqnat([s(nn1), z])) -> BOT -> 59
}
Sat witness: Found: ((length([ll, _ej])) -> length([cons(x, ll), s(_ej)]), {
_ej -> s(s(z))  ;  ll -> cons(a, nil)  ;  x -> b
})

-------------------------------------------
Step 73, which took 0.811928 s (model generation: 0.807567,  model checking: 0.004361):

Model:
|_
{
insert -> 
{{{
Q={q_gen_2250, q_gen_2251, q_gen_2252, q_gen_2255, q_gen_2256, q_gen_2262, q_gen_2275, q_gen_2277, q_gen_2324},
Q_f={q_gen_2250},
Delta=
{
<nil>() -> q_gen_2251
<a>() -> q_gen_2252
<b>() -> q_gen_2252
<nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2255
<a, b>() -> q_gen_2256
<b, a>() -> q_gen_2256
<b, b>() -> q_gen_2256
<a, a>() -> q_gen_2262
<cons, cons>(q_gen_2256, q_gen_2275) -> q_gen_2275
<cons, cons>(q_gen_2256, q_gen_2277) -> q_gen_2275
<cons, cons>(q_gen_2262, q_gen_2255) -> q_gen_2275
<cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2277
<a, cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2250
<a, cons, cons>(q_gen_2256, q_gen_2277) -> q_gen_2250
<a, cons, cons>(q_gen_2262, q_gen_2255) -> q_gen_2250
<a, cons, cons>(q_gen_2262, q_gen_2275) -> q_gen_2250
<a, nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2250
<b, cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2250
<b, cons, cons>(q_gen_2256, q_gen_2277) -> q_gen_2250
<b, cons, cons>(q_gen_2262, q_gen_2255) -> q_gen_2250
<b, cons, cons>(q_gen_2262, q_gen_2275) -> q_gen_2250
<b, cons, cons>(q_gen_2262, q_gen_2277) -> q_gen_2250
<b, nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2250
<a, cons, cons>(q_gen_2256, q_gen_2275) -> q_gen_2324
<b, cons, cons>(q_gen_2256, q_gen_2275) -> q_gen_2324
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_2249, q_gen_2258, q_gen_2259, q_gen_2280, q_gen_2281, q_gen_2282, q_gen_2283, q_gen_2285, q_gen_2293, q_gen_2294, q_gen_2298},
Q_f={q_gen_2249},
Delta=
{
<nil>() -> q_gen_2258
<cons>(q_gen_2281, q_gen_2258) -> q_gen_2280
<a>() -> q_gen_2281
<b>() -> q_gen_2281
<z>() -> q_gen_2283
<s>(q_gen_2283) -> q_gen_2294
<s>(q_gen_2294) -> q_gen_2294
<cons>(q_gen_2281, q_gen_2280) -> q_gen_2298
<cons>(q_gen_2281, q_gen_2298) -> q_gen_2298
<cons, s>(q_gen_2259, q_gen_2258) -> q_gen_2249
<cons, s>(q_gen_2282, q_gen_2280) -> q_gen_2249
<cons, s>(q_gen_2293, q_gen_2298) -> q_gen_2249
<nil, z>() -> q_gen_2249
<a, z>() -> q_gen_2259
<b, z>() -> q_gen_2259
<a, s>(q_gen_2283) -> q_gen_2282
<b, s>(q_gen_2283) -> q_gen_2282
<cons, s>(q_gen_2259, q_gen_2280) -> q_gen_2285
<cons, s>(q_gen_2259, q_gen_2298) -> q_gen_2285
<cons, s>(q_gen_2282, q_gen_2258) -> q_gen_2285
<cons, s>(q_gen_2282, q_gen_2298) -> q_gen_2285
<cons, s>(q_gen_2293, q_gen_2258) -> q_gen_2285
<cons, s>(q_gen_2293, q_gen_2280) -> q_gen_2285
<a, s>(q_gen_2294) -> q_gen_2293
<b, s>(q_gen_2294) -> q_gen_2293
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_2247, q_gen_2260},
Q_f={q_gen_2247},
Delta=
{
<a, a>() -> q_gen_2247
<a, b>() -> q_gen_2247
<b, b>() -> q_gen_2247
<b, a>() -> q_gen_2260
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  leqnat -> 
{{{
Q={q_gen_2244, q_gen_2246, q_gen_2287},
Q_f={q_gen_2244},
Delta=
{
<s>(q_gen_2246) -> q_gen_2246
<z>() -> q_gen_2246
<s, s>(q_gen_2244) -> q_gen_2244
<z, s>(q_gen_2246) -> q_gen_2244
<z, z>() -> q_gen_2244
<s, s>(q_gen_2287) -> q_gen_2287
<s, z>(q_gen_2246) -> q_gen_2287
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 57
() -> length([nil, z]) -> 57
() -> leq([a, y]) -> 57
() -> leq([b, b]) -> 57
() -> leqnat([z, s(nn2)]) -> 57
() -> leqnat([z, z]) -> 57
(insert([x, l, _jj]) /\ length([_jj, _kj]) /\ length([l, _ij])) -> leqnat([_ij, _kj]) -> 79
(insert([x, z, _zi]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _zi)]) -> 60
(length([ll, _ej])) -> length([cons(x, ll), s(_ej)]) -> 75
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 58
(leq([b, a])) -> BOT -> 57
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 57
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 61
(leqnat([s(nn1), z])) -> BOT -> 59
}
Sat witness: Found: ((insert([x, z, _zi]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _zi)]), {
_zi -> cons(a, cons(a, cons(b, nil)))  ;  x -> b  ;  y -> a  ;  z -> cons(a, cons(a, nil))
})

-------------------------------------------
Step 74, which took 0.938162 s (model generation: 0.937019,  model checking: 0.001143):

Model:
|_
{
insert -> 
{{{
Q={q_gen_2250, q_gen_2251, q_gen_2252, q_gen_2255, q_gen_2256, q_gen_2262, q_gen_2275, q_gen_2299, q_gen_2310},
Q_f={q_gen_2250},
Delta=
{
<nil>() -> q_gen_2251
<a>() -> q_gen_2252
<b>() -> q_gen_2252
<nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2255
<b, a>() -> q_gen_2256
<b, b>() -> q_gen_2256
<a, a>() -> q_gen_2262
<a, b>() -> q_gen_2262
<cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2275
<cons, cons>(q_gen_2262, q_gen_2255) -> q_gen_2275
<cons, cons>(q_gen_2262, q_gen_2275) -> q_gen_2275
<cons, cons>(q_gen_2256, q_gen_2275) -> q_gen_2310
<cons, cons>(q_gen_2256, q_gen_2310) -> q_gen_2310
<a, cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2250
<a, cons, cons>(q_gen_2262, q_gen_2255) -> q_gen_2250
<a, cons, cons>(q_gen_2262, q_gen_2275) -> q_gen_2250
<a, nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2250
<b, cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2250
<b, cons, cons>(q_gen_2256, q_gen_2275) -> q_gen_2250
<b, cons, cons>(q_gen_2262, q_gen_2255) -> q_gen_2250
<b, cons, cons>(q_gen_2262, q_gen_2275) -> q_gen_2250
<b, cons, cons>(q_gen_2262, q_gen_2310) -> q_gen_2250
<b, nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2250
<a, cons, cons>(q_gen_2256, q_gen_2275) -> q_gen_2299
<a, cons, cons>(q_gen_2256, q_gen_2310) -> q_gen_2299
<a, cons, cons>(q_gen_2262, q_gen_2310) -> q_gen_2299
<b, cons, cons>(q_gen_2256, q_gen_2310) -> q_gen_2299
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_2249, q_gen_2258, q_gen_2259, q_gen_2280, q_gen_2281, q_gen_2282, q_gen_2283, q_gen_2286, q_gen_2291, q_gen_2294, q_gen_2298},
Q_f={q_gen_2249},
Delta=
{
<nil>() -> q_gen_2258
<cons>(q_gen_2281, q_gen_2258) -> q_gen_2280
<a>() -> q_gen_2281
<b>() -> q_gen_2281
<z>() -> q_gen_2283
<s>(q_gen_2283) -> q_gen_2294
<s>(q_gen_2294) -> q_gen_2294
<cons>(q_gen_2281, q_gen_2280) -> q_gen_2298
<cons>(q_gen_2281, q_gen_2298) -> q_gen_2298
<cons, s>(q_gen_2259, q_gen_2258) -> q_gen_2249
<cons, s>(q_gen_2259, q_gen_2280) -> q_gen_2249
<cons, s>(q_gen_2282, q_gen_2280) -> q_gen_2249
<cons, s>(q_gen_2291, q_gen_2280) -> q_gen_2249
<cons, s>(q_gen_2291, q_gen_2298) -> q_gen_2249
<nil, z>() -> q_gen_2249
<a, z>() -> q_gen_2259
<b, z>() -> q_gen_2259
<b, s>(q_gen_2283) -> q_gen_2282
<cons, s>(q_gen_2259, q_gen_2298) -> q_gen_2286
<cons, s>(q_gen_2282, q_gen_2258) -> q_gen_2286
<cons, s>(q_gen_2282, q_gen_2298) -> q_gen_2286
<cons, s>(q_gen_2291, q_gen_2258) -> q_gen_2286
<a, s>(q_gen_2283) -> q_gen_2291
<a, s>(q_gen_2294) -> q_gen_2291
<b, s>(q_gen_2294) -> q_gen_2291
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_2247, q_gen_2260},
Q_f={q_gen_2247},
Delta=
{
<a, a>() -> q_gen_2247
<a, b>() -> q_gen_2247
<b, b>() -> q_gen_2247
<b, a>() -> q_gen_2260
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  leqnat -> 
{{{
Q={q_gen_2244, q_gen_2246, q_gen_2287},
Q_f={q_gen_2244},
Delta=
{
<s>(q_gen_2246) -> q_gen_2246
<z>() -> q_gen_2246
<s, s>(q_gen_2244) -> q_gen_2244
<z, s>(q_gen_2246) -> q_gen_2244
<z, z>() -> q_gen_2244
<s, s>(q_gen_2287) -> q_gen_2287
<s, z>(q_gen_2246) -> q_gen_2287
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 58
() -> length([nil, z]) -> 58
() -> leq([a, y]) -> 58
() -> leq([b, b]) -> 58
() -> leqnat([z, s(nn2)]) -> 58
() -> leqnat([z, z]) -> 58
(insert([x, l, _jj]) /\ length([_jj, _kj]) /\ length([l, _ij])) -> leqnat([_ij, _kj]) -> 79
(insert([x, z, _zi]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _zi)]) -> 60
(length([ll, _ej])) -> length([cons(x, ll), s(_ej)]) -> 75
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 61
(leq([b, a])) -> BOT -> 58
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 58
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 61
(leqnat([s(nn1), z])) -> BOT -> 59
}
Sat witness: Found: ((leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]), {
x -> a  ;  y -> b  ;  z -> cons(b, nil)
})

-------------------------------------------
Step 75, which took 0.735910 s (model generation: 0.732837,  model checking: 0.003073):

Model:
|_
{
insert -> 
{{{
Q={q_gen_2250, q_gen_2251, q_gen_2252, q_gen_2255, q_gen_2256, q_gen_2262, q_gen_2275, q_gen_2317, q_gen_2325},
Q_f={q_gen_2250},
Delta=
{
<nil>() -> q_gen_2251
<a>() -> q_gen_2252
<b>() -> q_gen_2252
<cons, cons>(q_gen_2262, q_gen_2275) -> q_gen_2255
<nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2255
<b, b>() -> q_gen_2256
<a, a>() -> q_gen_2262
<a, b>() -> q_gen_2262
<b, a>() -> q_gen_2262
<cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2275
<cons, cons>(q_gen_2262, q_gen_2255) -> q_gen_2275
<cons, cons>(q_gen_2256, q_gen_2275) -> q_gen_2325
<cons, cons>(q_gen_2256, q_gen_2325) -> q_gen_2325
<a, cons, cons>(q_gen_2256, q_gen_2275) -> q_gen_2250
<a, cons, cons>(q_gen_2262, q_gen_2255) -> q_gen_2250
<a, cons, cons>(q_gen_2262, q_gen_2275) -> q_gen_2250
<a, nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2250
<b, cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2250
<b, cons, cons>(q_gen_2256, q_gen_2275) -> q_gen_2250
<b, cons, cons>(q_gen_2262, q_gen_2255) -> q_gen_2250
<b, cons, cons>(q_gen_2262, q_gen_2275) -> q_gen_2250
<b, nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2250
<a, cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2317
<a, cons, cons>(q_gen_2256, q_gen_2325) -> q_gen_2317
<a, cons, cons>(q_gen_2262, q_gen_2325) -> q_gen_2317
<b, cons, cons>(q_gen_2256, q_gen_2325) -> q_gen_2317
<b, cons, cons>(q_gen_2262, q_gen_2325) -> q_gen_2317
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_2249, q_gen_2258, q_gen_2259, q_gen_2280, q_gen_2281, q_gen_2282, q_gen_2283, q_gen_2286, q_gen_2293, q_gen_2294, q_gen_2298},
Q_f={q_gen_2249},
Delta=
{
<nil>() -> q_gen_2258
<cons>(q_gen_2281, q_gen_2258) -> q_gen_2280
<a>() -> q_gen_2281
<b>() -> q_gen_2281
<z>() -> q_gen_2283
<s>(q_gen_2283) -> q_gen_2294
<s>(q_gen_2294) -> q_gen_2294
<cons>(q_gen_2281, q_gen_2280) -> q_gen_2298
<cons>(q_gen_2281, q_gen_2298) -> q_gen_2298
<cons, s>(q_gen_2259, q_gen_2258) -> q_gen_2249
<cons, s>(q_gen_2259, q_gen_2280) -> q_gen_2249
<cons, s>(q_gen_2282, q_gen_2280) -> q_gen_2249
<cons, s>(q_gen_2282, q_gen_2298) -> q_gen_2249
<cons, s>(q_gen_2293, q_gen_2298) -> q_gen_2249
<nil, z>() -> q_gen_2249
<a, z>() -> q_gen_2259
<b, z>() -> q_gen_2259
<a, s>(q_gen_2283) -> q_gen_2282
<b, s>(q_gen_2283) -> q_gen_2282
<cons, s>(q_gen_2259, q_gen_2298) -> q_gen_2286
<cons, s>(q_gen_2282, q_gen_2258) -> q_gen_2286
<cons, s>(q_gen_2293, q_gen_2258) -> q_gen_2286
<cons, s>(q_gen_2293, q_gen_2280) -> q_gen_2286
<a, s>(q_gen_2294) -> q_gen_2293
<b, s>(q_gen_2294) -> q_gen_2293
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_2247, q_gen_2260},
Q_f={q_gen_2247},
Delta=
{
<a, a>() -> q_gen_2247
<a, b>() -> q_gen_2247
<b, b>() -> q_gen_2247
<b, a>() -> q_gen_2260
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  leqnat -> 
{{{
Q={q_gen_2244, q_gen_2246, q_gen_2287},
Q_f={q_gen_2244},
Delta=
{
<s>(q_gen_2246) -> q_gen_2246
<z>() -> q_gen_2246
<s, s>(q_gen_2244) -> q_gen_2244
<z, s>(q_gen_2246) -> q_gen_2244
<z, z>() -> q_gen_2244
<s, s>(q_gen_2287) -> q_gen_2287
<s, z>(q_gen_2246) -> q_gen_2287
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 59
() -> length([nil, z]) -> 59
() -> leq([a, y]) -> 59
() -> leq([b, b]) -> 59
() -> leqnat([z, s(nn2)]) -> 59
() -> leqnat([z, z]) -> 59
(insert([x, l, _jj]) /\ length([_jj, _kj]) /\ length([l, _ij])) -> leqnat([_ij, _kj]) -> 79
(insert([x, z, _zi]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _zi)]) -> 63
(length([ll, _ej])) -> length([cons(x, ll), s(_ej)]) -> 75
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 61
(leq([b, a])) -> BOT -> 59
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 59
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 61
(leqnat([s(nn1), z])) -> BOT -> 60
}
Sat witness: Found: ((insert([x, z, _zi]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _zi)]), {
_zi -> cons(b, cons(b, cons(a, nil)))  ;  x -> b  ;  y -> a  ;  z -> cons(b, cons(b, nil))
})

-------------------------------------------
Step 76, which took 1.849450 s (model generation: 1.848097,  model checking: 0.001353):

Model:
|_
{
insert -> 
{{{
Q={q_gen_2250, q_gen_2251, q_gen_2252, q_gen_2255, q_gen_2256, q_gen_2262, q_gen_2275, q_gen_2310, q_gen_2324},
Q_f={q_gen_2250},
Delta=
{
<nil>() -> q_gen_2251
<a>() -> q_gen_2252
<b>() -> q_gen_2252
<nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2255
<a, b>() -> q_gen_2256
<b, a>() -> q_gen_2256
<b, b>() -> q_gen_2256
<a, a>() -> q_gen_2262
<cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2275
<cons, cons>(q_gen_2262, q_gen_2255) -> q_gen_2275
<cons, cons>(q_gen_2256, q_gen_2275) -> q_gen_2310
<cons, cons>(q_gen_2256, q_gen_2310) -> q_gen_2310
<cons, cons>(q_gen_2262, q_gen_2275) -> q_gen_2310
<a, cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2250
<a, cons, cons>(q_gen_2256, q_gen_2275) -> q_gen_2250
<a, cons, cons>(q_gen_2262, q_gen_2255) -> q_gen_2250
<a, cons, cons>(q_gen_2262, q_gen_2275) -> q_gen_2250
<a, nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2250
<b, cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2250
<b, cons, cons>(q_gen_2256, q_gen_2275) -> q_gen_2250
<b, cons, cons>(q_gen_2262, q_gen_2255) -> q_gen_2250
<b, cons, cons>(q_gen_2262, q_gen_2275) -> q_gen_2250
<b, cons, cons>(q_gen_2262, q_gen_2310) -> q_gen_2250
<b, nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2250
<a, cons, cons>(q_gen_2256, q_gen_2310) -> q_gen_2324
<b, cons, cons>(q_gen_2256, q_gen_2310) -> q_gen_2324
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_2249, q_gen_2258, q_gen_2259, q_gen_2280, q_gen_2281, q_gen_2282, q_gen_2283, q_gen_2286, q_gen_2293, q_gen_2294, q_gen_2298},
Q_f={q_gen_2249},
Delta=
{
<nil>() -> q_gen_2258
<cons>(q_gen_2281, q_gen_2258) -> q_gen_2280
<a>() -> q_gen_2281
<b>() -> q_gen_2281
<z>() -> q_gen_2283
<s>(q_gen_2283) -> q_gen_2294
<s>(q_gen_2294) -> q_gen_2294
<cons>(q_gen_2281, q_gen_2280) -> q_gen_2298
<cons>(q_gen_2281, q_gen_2298) -> q_gen_2298
<cons, s>(q_gen_2259, q_gen_2258) -> q_gen_2249
<cons, s>(q_gen_2259, q_gen_2280) -> q_gen_2249
<cons, s>(q_gen_2282, q_gen_2280) -> q_gen_2249
<cons, s>(q_gen_2282, q_gen_2298) -> q_gen_2249
<cons, s>(q_gen_2293, q_gen_2298) -> q_gen_2249
<nil, z>() -> q_gen_2249
<a, z>() -> q_gen_2259
<b, z>() -> q_gen_2259
<a, s>(q_gen_2283) -> q_gen_2282
<b, s>(q_gen_2283) -> q_gen_2282
<cons, s>(q_gen_2259, q_gen_2298) -> q_gen_2286
<cons, s>(q_gen_2282, q_gen_2258) -> q_gen_2286
<cons, s>(q_gen_2293, q_gen_2258) -> q_gen_2286
<cons, s>(q_gen_2293, q_gen_2280) -> q_gen_2286
<a, s>(q_gen_2294) -> q_gen_2293
<b, s>(q_gen_2294) -> q_gen_2293
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_2247, q_gen_2260},
Q_f={q_gen_2247},
Delta=
{
<a, a>() -> q_gen_2247
<a, b>() -> q_gen_2247
<b, b>() -> q_gen_2247
<b, a>() -> q_gen_2260
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  leqnat -> 
{{{
Q={q_gen_2244, q_gen_2246, q_gen_2287},
Q_f={q_gen_2244},
Delta=
{
<s>(q_gen_2246) -> q_gen_2246
<z>() -> q_gen_2246
<s, s>(q_gen_2244) -> q_gen_2244
<z, s>(q_gen_2246) -> q_gen_2244
<z, z>() -> q_gen_2244
<s, s>(q_gen_2287) -> q_gen_2287
<s, z>(q_gen_2246) -> q_gen_2287
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 60
() -> length([nil, z]) -> 60
() -> leq([a, y]) -> 60
() -> leq([b, b]) -> 60
() -> leqnat([z, s(nn2)]) -> 60
() -> leqnat([z, z]) -> 60
(insert([x, l, _jj]) /\ length([_jj, _kj]) /\ length([l, _ij])) -> leqnat([_ij, _kj]) -> 79
(insert([x, z, _zi]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _zi)]) -> 63
(length([ll, _ej])) -> length([cons(x, ll), s(_ej)]) -> 75
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 64
(leq([b, a])) -> BOT -> 60
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 60
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 62
(leqnat([s(nn1), z])) -> BOT -> 61
}
Sat witness: Found: ((leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]), {
x -> b  ;  y -> b  ;  z -> cons(b, cons(a, nil))
})

-------------------------------------------
Step 77, which took 1.804048 s (model generation: 1.800180,  model checking: 0.003868):

Model:
|_
{
insert -> 
{{{
Q={q_gen_2250, q_gen_2251, q_gen_2252, q_gen_2255, q_gen_2256, q_gen_2262, q_gen_2300, q_gen_2324, q_gen_2325},
Q_f={q_gen_2250},
Delta=
{
<nil>() -> q_gen_2251
<a>() -> q_gen_2252
<b>() -> q_gen_2252
<cons, cons>(q_gen_2262, q_gen_2255) -> q_gen_2255
<nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2255
<b, a>() -> q_gen_2256
<b, b>() -> q_gen_2256
<a, a>() -> q_gen_2262
<a, b>() -> q_gen_2262
<cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2300
<cons, cons>(q_gen_2256, q_gen_2300) -> q_gen_2325
<cons, cons>(q_gen_2256, q_gen_2325) -> q_gen_2325
<a, cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2250
<a, cons, cons>(q_gen_2256, q_gen_2300) -> q_gen_2250
<a, cons, cons>(q_gen_2262, q_gen_2255) -> q_gen_2250
<a, nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2250
<b, cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2250
<b, cons, cons>(q_gen_2256, q_gen_2300) -> q_gen_2250
<b, cons, cons>(q_gen_2262, q_gen_2255) -> q_gen_2250
<b, cons, cons>(q_gen_2262, q_gen_2300) -> q_gen_2250
<b, cons, cons>(q_gen_2262, q_gen_2325) -> q_gen_2250
<b, nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2250
<a, cons, cons>(q_gen_2256, q_gen_2325) -> q_gen_2324
<a, cons, cons>(q_gen_2262, q_gen_2325) -> q_gen_2324
<b, cons, cons>(q_gen_2256, q_gen_2325) -> q_gen_2324
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_2249, q_gen_2258, q_gen_2259, q_gen_2280, q_gen_2281, q_gen_2282, q_gen_2283, q_gen_2286, q_gen_2293, q_gen_2294, q_gen_2298},
Q_f={q_gen_2249},
Delta=
{
<nil>() -> q_gen_2258
<cons>(q_gen_2281, q_gen_2258) -> q_gen_2280
<a>() -> q_gen_2281
<b>() -> q_gen_2281
<z>() -> q_gen_2283
<s>(q_gen_2283) -> q_gen_2294
<s>(q_gen_2294) -> q_gen_2294
<cons>(q_gen_2281, q_gen_2280) -> q_gen_2298
<cons>(q_gen_2281, q_gen_2298) -> q_gen_2298
<cons, s>(q_gen_2259, q_gen_2258) -> q_gen_2249
<cons, s>(q_gen_2259, q_gen_2280) -> q_gen_2249
<cons, s>(q_gen_2282, q_gen_2280) -> q_gen_2249
<cons, s>(q_gen_2282, q_gen_2298) -> q_gen_2249
<cons, s>(q_gen_2293, q_gen_2298) -> q_gen_2249
<nil, z>() -> q_gen_2249
<a, z>() -> q_gen_2259
<b, z>() -> q_gen_2259
<a, s>(q_gen_2283) -> q_gen_2282
<a, s>(q_gen_2294) -> q_gen_2282
<b, s>(q_gen_2283) -> q_gen_2282
<cons, s>(q_gen_2259, q_gen_2298) -> q_gen_2286
<cons, s>(q_gen_2282, q_gen_2258) -> q_gen_2286
<cons, s>(q_gen_2293, q_gen_2258) -> q_gen_2286
<cons, s>(q_gen_2293, q_gen_2280) -> q_gen_2286
<b, s>(q_gen_2294) -> q_gen_2293
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_2247, q_gen_2260},
Q_f={q_gen_2247},
Delta=
{
<a, a>() -> q_gen_2247
<a, b>() -> q_gen_2247
<b, b>() -> q_gen_2247
<b, a>() -> q_gen_2260
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  leqnat -> 
{{{
Q={q_gen_2244, q_gen_2246, q_gen_2287},
Q_f={q_gen_2244},
Delta=
{
<s>(q_gen_2246) -> q_gen_2246
<z>() -> q_gen_2246
<s, s>(q_gen_2244) -> q_gen_2244
<z, s>(q_gen_2246) -> q_gen_2244
<z, z>() -> q_gen_2244
<s, s>(q_gen_2287) -> q_gen_2287
<s, z>(q_gen_2246) -> q_gen_2287
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 61
() -> length([nil, z]) -> 61
() -> leq([a, y]) -> 61
() -> leq([b, b]) -> 61
() -> leqnat([z, s(nn2)]) -> 61
() -> leqnat([z, z]) -> 61
(insert([x, l, _jj]) /\ length([_jj, _kj]) /\ length([l, _ij])) -> leqnat([_ij, _kj]) -> 79
(insert([x, z, _zi]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _zi)]) -> 66
(length([ll, _ej])) -> length([cons(x, ll), s(_ej)]) -> 75
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 64
(leq([b, a])) -> BOT -> 61
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 61
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 63
(leqnat([s(nn1), z])) -> BOT -> 62
}
Sat witness: Found: ((insert([x, z, _zi]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _zi)]), {
_zi -> cons(a, cons(b, cons(b, nil)))  ;  x -> b  ;  y -> a  ;  z -> cons(a, cons(b, nil))
})

-------------------------------------------
Step 78, which took 1.156445 s (model generation: 1.147964,  model checking: 0.008481):

Model:
|_
{
insert -> 
{{{
Q={q_gen_2250, q_gen_2251, q_gen_2252, q_gen_2255, q_gen_2256},
Q_f={q_gen_2250},
Delta=
{
<nil>() -> q_gen_2251
<a>() -> q_gen_2252
<b>() -> q_gen_2252
<cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2255
<nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2255
<a, a>() -> q_gen_2256
<a, b>() -> q_gen_2256
<b, a>() -> q_gen_2256
<b, b>() -> q_gen_2256
<a, cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2250
<a, nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2250
<b, cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2250
<b, nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2250
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_2249, q_gen_2258, q_gen_2259, q_gen_2280, q_gen_2281, q_gen_2282, q_gen_2283, q_gen_2286, q_gen_2293, q_gen_2294, q_gen_2298, q_gen_2314, q_gen_2315, q_gen_2316, q_gen_2353},
Q_f={q_gen_2249},
Delta=
{
<cons>(q_gen_2281, q_gen_2314) -> q_gen_2258
<nil>() -> q_gen_2258
<cons>(q_gen_2281, q_gen_2258) -> q_gen_2280
<a>() -> q_gen_2281
<b>() -> q_gen_2281
<z>() -> q_gen_2283
<s>(q_gen_2283) -> q_gen_2294
<cons>(q_gen_2281, q_gen_2280) -> q_gen_2298
<cons>(q_gen_2281, q_gen_2298) -> q_gen_2314
<s>(q_gen_2294) -> q_gen_2316
<s>(q_gen_2316) -> q_gen_2353
<cons, s>(q_gen_2259, q_gen_2258) -> q_gen_2249
<cons, s>(q_gen_2259, q_gen_2280) -> q_gen_2249
<cons, s>(q_gen_2282, q_gen_2280) -> q_gen_2249
<cons, s>(q_gen_2282, q_gen_2298) -> q_gen_2249
<cons, s>(q_gen_2293, q_gen_2298) -> q_gen_2249
<cons, s>(q_gen_2293, q_gen_2314) -> q_gen_2249
<cons, s>(q_gen_2315, q_gen_2314) -> q_gen_2249
<nil, z>() -> q_gen_2249
<a, s>(q_gen_2353) -> q_gen_2259
<a, z>() -> q_gen_2259
<b, z>() -> q_gen_2259
<a, s>(q_gen_2283) -> q_gen_2282
<b, s>(q_gen_2283) -> q_gen_2282
<cons, s>(q_gen_2259, q_gen_2298) -> q_gen_2286
<cons, s>(q_gen_2259, q_gen_2314) -> q_gen_2286
<cons, s>(q_gen_2282, q_gen_2258) -> q_gen_2286
<cons, s>(q_gen_2282, q_gen_2314) -> q_gen_2286
<cons, s>(q_gen_2293, q_gen_2258) -> q_gen_2286
<cons, s>(q_gen_2293, q_gen_2280) -> q_gen_2286
<cons, s>(q_gen_2315, q_gen_2258) -> q_gen_2286
<cons, s>(q_gen_2315, q_gen_2280) -> q_gen_2286
<cons, s>(q_gen_2315, q_gen_2298) -> q_gen_2286
<a, s>(q_gen_2294) -> q_gen_2293
<b, s>(q_gen_2294) -> q_gen_2293
<a, s>(q_gen_2316) -> q_gen_2315
<b, s>(q_gen_2316) -> q_gen_2315
<b, s>(q_gen_2353) -> q_gen_2315
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_2247, q_gen_2260},
Q_f={q_gen_2247},
Delta=
{
<a, a>() -> q_gen_2247
<a, b>() -> q_gen_2247
<b, b>() -> q_gen_2247
<b, a>() -> q_gen_2260
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  leqnat -> 
{{{
Q={q_gen_2244, q_gen_2246, q_gen_2287},
Q_f={q_gen_2244},
Delta=
{
<s>(q_gen_2246) -> q_gen_2246
<z>() -> q_gen_2246
<s, s>(q_gen_2244) -> q_gen_2244
<z, s>(q_gen_2246) -> q_gen_2244
<z, z>() -> q_gen_2244
<s, s>(q_gen_2287) -> q_gen_2287
<s, z>(q_gen_2246) -> q_gen_2287
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 62
() -> length([nil, z]) -> 62
() -> leq([a, y]) -> 62
() -> leq([b, b]) -> 62
() -> leqnat([z, s(nn2)]) -> 62
() -> leqnat([z, z]) -> 62
(insert([x, l, _jj]) /\ length([_jj, _kj]) /\ length([l, _ij])) -> leqnat([_ij, _kj]) -> 79
(insert([x, z, _zi]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _zi)]) -> 67
(length([ll, _ej])) -> length([cons(x, ll), s(_ej)]) -> 78
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 65
(leq([b, a])) -> BOT -> 62
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 62
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 64
(leqnat([s(nn1), z])) -> BOT -> 63
}
Sat witness: Found: ((length([ll, _ej])) -> length([cons(x, ll), s(_ej)]), {
_ej -> s(s(s(s(z))))  ;  ll -> cons(b, cons(b, cons(a, cons(b, nil))))  ;  x -> b
})

-------------------------------------------
Step 79, which took 1.064031 s (model generation: 1.050878,  model checking: 0.013153):

Model:
|_
{
insert -> 
{{{
Q={q_gen_2250, q_gen_2251, q_gen_2252, q_gen_2255, q_gen_2256, q_gen_2262, q_gen_2300, q_gen_2324, q_gen_2325},
Q_f={q_gen_2250},
Delta=
{
<nil>() -> q_gen_2251
<a>() -> q_gen_2252
<b>() -> q_gen_2252
<cons, cons>(q_gen_2262, q_gen_2255) -> q_gen_2255
<nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2255
<b, a>() -> q_gen_2256
<b, b>() -> q_gen_2256
<a, a>() -> q_gen_2262
<a, b>() -> q_gen_2262
<cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2300
<cons, cons>(q_gen_2262, q_gen_2300) -> q_gen_2300
<cons, cons>(q_gen_2256, q_gen_2300) -> q_gen_2325
<cons, cons>(q_gen_2256, q_gen_2325) -> q_gen_2325
<a, cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2250
<a, cons, cons>(q_gen_2256, q_gen_2300) -> q_gen_2250
<a, cons, cons>(q_gen_2262, q_gen_2255) -> q_gen_2250
<a, nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2250
<b, cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2250
<b, cons, cons>(q_gen_2256, q_gen_2300) -> q_gen_2250
<b, cons, cons>(q_gen_2262, q_gen_2255) -> q_gen_2250
<b, cons, cons>(q_gen_2262, q_gen_2300) -> q_gen_2250
<b, cons, cons>(q_gen_2262, q_gen_2325) -> q_gen_2250
<b, nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2250
<a, cons, cons>(q_gen_2256, q_gen_2325) -> q_gen_2324
<a, cons, cons>(q_gen_2262, q_gen_2325) -> q_gen_2324
<b, cons, cons>(q_gen_2256, q_gen_2325) -> q_gen_2324
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_2249, q_gen_2258, q_gen_2259, q_gen_2280, q_gen_2281, q_gen_2282, q_gen_2283, q_gen_2286, q_gen_2293, q_gen_2294, q_gen_2298},
Q_f={q_gen_2249},
Delta=
{
<nil>() -> q_gen_2258
<cons>(q_gen_2281, q_gen_2258) -> q_gen_2280
<a>() -> q_gen_2281
<b>() -> q_gen_2281
<z>() -> q_gen_2283
<s>(q_gen_2283) -> q_gen_2294
<s>(q_gen_2294) -> q_gen_2294
<cons>(q_gen_2281, q_gen_2280) -> q_gen_2298
<cons>(q_gen_2281, q_gen_2298) -> q_gen_2298
<cons, s>(q_gen_2259, q_gen_2258) -> q_gen_2249
<cons, s>(q_gen_2259, q_gen_2280) -> q_gen_2249
<cons, s>(q_gen_2282, q_gen_2280) -> q_gen_2249
<cons, s>(q_gen_2282, q_gen_2298) -> q_gen_2249
<cons, s>(q_gen_2293, q_gen_2298) -> q_gen_2249
<nil, z>() -> q_gen_2249
<a, z>() -> q_gen_2259
<b, z>() -> q_gen_2259
<a, s>(q_gen_2283) -> q_gen_2282
<b, s>(q_gen_2283) -> q_gen_2282
<cons, s>(q_gen_2259, q_gen_2298) -> q_gen_2286
<cons, s>(q_gen_2282, q_gen_2258) -> q_gen_2286
<cons, s>(q_gen_2293, q_gen_2258) -> q_gen_2286
<cons, s>(q_gen_2293, q_gen_2280) -> q_gen_2286
<a, s>(q_gen_2294) -> q_gen_2293
<b, s>(q_gen_2294) -> q_gen_2293
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_2247, q_gen_2260},
Q_f={q_gen_2247},
Delta=
{
<a, a>() -> q_gen_2247
<a, b>() -> q_gen_2247
<b, b>() -> q_gen_2247
<b, a>() -> q_gen_2260
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  leqnat -> 
{{{
Q={q_gen_2244, q_gen_2246, q_gen_2287},
Q_f={q_gen_2244},
Delta=
{
<s>(q_gen_2246) -> q_gen_2246
<z>() -> q_gen_2246
<s, s>(q_gen_2244) -> q_gen_2244
<z, s>(q_gen_2246) -> q_gen_2244
<z, z>() -> q_gen_2244
<s, s>(q_gen_2287) -> q_gen_2287
<s, z>(q_gen_2246) -> q_gen_2287
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 63
() -> length([nil, z]) -> 63
() -> leq([a, y]) -> 63
() -> leq([b, b]) -> 63
() -> leqnat([z, s(nn2)]) -> 63
() -> leqnat([z, z]) -> 63
(insert([x, l, _jj]) /\ length([_jj, _kj]) /\ length([l, _ij])) -> leqnat([_ij, _kj]) -> 79
(insert([x, z, _zi]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _zi)]) -> 67
(length([ll, _ej])) -> length([cons(x, ll), s(_ej)]) -> 78
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 68
(leq([b, a])) -> BOT -> 63
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 63
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 65
(leqnat([s(nn1), z])) -> BOT -> 64
}
Sat witness: Found: ((leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]), {
x -> b  ;  y -> b  ;  z -> cons(b, cons(b, nil))
})

-------------------------------------------
Step 80, which took 0.824742 s (model generation: 0.808467,  model checking: 0.016275):

Model:
|_
{
insert -> 
{{{
Q={q_gen_2250, q_gen_2251, q_gen_2252, q_gen_2255, q_gen_2256},
Q_f={q_gen_2250},
Delta=
{
<nil>() -> q_gen_2251
<a>() -> q_gen_2252
<b>() -> q_gen_2252
<cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2255
<nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2255
<a, a>() -> q_gen_2256
<a, b>() -> q_gen_2256
<b, a>() -> q_gen_2256
<b, b>() -> q_gen_2256
<a, cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2250
<a, nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2250
<b, cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2250
<b, nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2250
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_2249, q_gen_2258, q_gen_2259, q_gen_2280, q_gen_2281, q_gen_2282, q_gen_2283, q_gen_2286, q_gen_2293, q_gen_2294, q_gen_2298, q_gen_2314, q_gen_2315, q_gen_2316, q_gen_2353},
Q_f={q_gen_2249},
Delta=
{
<cons>(q_gen_2281, q_gen_2314) -> q_gen_2258
<nil>() -> q_gen_2258
<cons>(q_gen_2281, q_gen_2258) -> q_gen_2280
<a>() -> q_gen_2281
<b>() -> q_gen_2281
<z>() -> q_gen_2283
<s>(q_gen_2283) -> q_gen_2294
<cons>(q_gen_2281, q_gen_2280) -> q_gen_2298
<cons>(q_gen_2281, q_gen_2298) -> q_gen_2314
<s>(q_gen_2294) -> q_gen_2316
<s>(q_gen_2316) -> q_gen_2353
<cons, s>(q_gen_2259, q_gen_2258) -> q_gen_2249
<cons, s>(q_gen_2259, q_gen_2280) -> q_gen_2249
<cons, s>(q_gen_2282, q_gen_2280) -> q_gen_2249
<cons, s>(q_gen_2282, q_gen_2298) -> q_gen_2249
<cons, s>(q_gen_2293, q_gen_2298) -> q_gen_2249
<cons, s>(q_gen_2293, q_gen_2314) -> q_gen_2249
<cons, s>(q_gen_2315, q_gen_2314) -> q_gen_2249
<nil, z>() -> q_gen_2249
<a, s>(q_gen_2353) -> q_gen_2259
<a, z>() -> q_gen_2259
<b, s>(q_gen_2353) -> q_gen_2259
<b, z>() -> q_gen_2259
<a, s>(q_gen_2283) -> q_gen_2282
<b, s>(q_gen_2283) -> q_gen_2282
<cons, s>(q_gen_2259, q_gen_2298) -> q_gen_2286
<cons, s>(q_gen_2259, q_gen_2314) -> q_gen_2286
<cons, s>(q_gen_2282, q_gen_2258) -> q_gen_2286
<cons, s>(q_gen_2282, q_gen_2314) -> q_gen_2286
<cons, s>(q_gen_2293, q_gen_2258) -> q_gen_2286
<cons, s>(q_gen_2293, q_gen_2280) -> q_gen_2286
<cons, s>(q_gen_2315, q_gen_2258) -> q_gen_2286
<cons, s>(q_gen_2315, q_gen_2280) -> q_gen_2286
<cons, s>(q_gen_2315, q_gen_2298) -> q_gen_2286
<a, s>(q_gen_2294) -> q_gen_2293
<b, s>(q_gen_2294) -> q_gen_2293
<a, s>(q_gen_2316) -> q_gen_2315
<b, s>(q_gen_2316) -> q_gen_2315
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_2247, q_gen_2260},
Q_f={q_gen_2247},
Delta=
{
<a, a>() -> q_gen_2247
<a, b>() -> q_gen_2247
<b, b>() -> q_gen_2247
<b, a>() -> q_gen_2260
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  leqnat -> 
{{{
Q={q_gen_2244, q_gen_2246, q_gen_2287},
Q_f={q_gen_2244},
Delta=
{
<s>(q_gen_2246) -> q_gen_2246
<z>() -> q_gen_2246
<s, s>(q_gen_2244) -> q_gen_2244
<z, s>(q_gen_2246) -> q_gen_2244
<z, z>() -> q_gen_2244
<s, s>(q_gen_2287) -> q_gen_2287
<s, z>(q_gen_2246) -> q_gen_2287
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 64
() -> length([nil, z]) -> 64
() -> leq([a, y]) -> 64
() -> leq([b, b]) -> 64
() -> leqnat([z, s(nn2)]) -> 64
() -> leqnat([z, z]) -> 64
(insert([x, l, _jj]) /\ length([_jj, _kj]) /\ length([l, _ij])) -> leqnat([_ij, _kj]) -> 79
(insert([x, z, _zi]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _zi)]) -> 68
(length([ll, _ej])) -> length([cons(x, ll), s(_ej)]) -> 81
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 69
(leq([b, a])) -> BOT -> 64
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 64
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 66
(leqnat([s(nn1), z])) -> BOT -> 65
}
Sat witness: Found: ((length([ll, _ej])) -> length([cons(x, ll), s(_ej)]), {
_ej -> s(s(s(z)))  ;  ll -> cons(b, cons(b, cons(a, cons(b, nil))))  ;  x -> a
})

-------------------------------------------
Step 81, which took 0.905463 s (model generation: 0.901271,  model checking: 0.004192):

Model:
|_
{
insert -> 
{{{
Q={q_gen_2250, q_gen_2251, q_gen_2252, q_gen_2255, q_gen_2256},
Q_f={q_gen_2250},
Delta=
{
<nil>() -> q_gen_2251
<a>() -> q_gen_2252
<b>() -> q_gen_2252
<cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2255
<nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2255
<a, a>() -> q_gen_2256
<a, b>() -> q_gen_2256
<b, a>() -> q_gen_2256
<b, b>() -> q_gen_2256
<a, cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2250
<a, nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2250
<b, cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2250
<b, nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2250
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_2249, q_gen_2258, q_gen_2259, q_gen_2280, q_gen_2281, q_gen_2282, q_gen_2283, q_gen_2285, q_gen_2293, q_gen_2294, q_gen_2298, q_gen_2314, q_gen_2315, q_gen_2316, q_gen_2353},
Q_f={q_gen_2249},
Delta=
{
<cons>(q_gen_2281, q_gen_2314) -> q_gen_2258
<nil>() -> q_gen_2258
<cons>(q_gen_2281, q_gen_2258) -> q_gen_2280
<a>() -> q_gen_2281
<b>() -> q_gen_2281
<z>() -> q_gen_2283
<s>(q_gen_2283) -> q_gen_2294
<cons>(q_gen_2281, q_gen_2280) -> q_gen_2298
<cons>(q_gen_2281, q_gen_2298) -> q_gen_2314
<s>(q_gen_2294) -> q_gen_2316
<s>(q_gen_2316) -> q_gen_2353
<cons, s>(q_gen_2259, q_gen_2258) -> q_gen_2249
<cons, s>(q_gen_2282, q_gen_2280) -> q_gen_2249
<cons, s>(q_gen_2293, q_gen_2298) -> q_gen_2249
<cons, s>(q_gen_2315, q_gen_2314) -> q_gen_2249
<nil, z>() -> q_gen_2249
<a, s>(q_gen_2353) -> q_gen_2259
<a, z>() -> q_gen_2259
<b, s>(q_gen_2353) -> q_gen_2259
<b, z>() -> q_gen_2259
<a, s>(q_gen_2283) -> q_gen_2282
<b, s>(q_gen_2283) -> q_gen_2282
<cons, s>(q_gen_2259, q_gen_2280) -> q_gen_2285
<cons, s>(q_gen_2259, q_gen_2298) -> q_gen_2285
<cons, s>(q_gen_2259, q_gen_2314) -> q_gen_2285
<cons, s>(q_gen_2282, q_gen_2258) -> q_gen_2285
<cons, s>(q_gen_2282, q_gen_2298) -> q_gen_2285
<cons, s>(q_gen_2282, q_gen_2314) -> q_gen_2285
<cons, s>(q_gen_2293, q_gen_2258) -> q_gen_2285
<cons, s>(q_gen_2293, q_gen_2280) -> q_gen_2285
<cons, s>(q_gen_2293, q_gen_2314) -> q_gen_2285
<cons, s>(q_gen_2315, q_gen_2258) -> q_gen_2285
<cons, s>(q_gen_2315, q_gen_2280) -> q_gen_2285
<cons, s>(q_gen_2315, q_gen_2298) -> q_gen_2285
<a, s>(q_gen_2294) -> q_gen_2293
<b, s>(q_gen_2294) -> q_gen_2293
<a, s>(q_gen_2316) -> q_gen_2315
<b, s>(q_gen_2316) -> q_gen_2315
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_2247, q_gen_2260},
Q_f={q_gen_2247},
Delta=
{
<a, a>() -> q_gen_2247
<a, b>() -> q_gen_2247
<b, b>() -> q_gen_2247
<b, a>() -> q_gen_2260
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  leqnat -> 
{{{
Q={q_gen_2244, q_gen_2246, q_gen_2287},
Q_f={q_gen_2244},
Delta=
{
<s>(q_gen_2246) -> q_gen_2246
<z>() -> q_gen_2246
<s, s>(q_gen_2244) -> q_gen_2244
<z, s>(q_gen_2246) -> q_gen_2244
<z, z>() -> q_gen_2244
<s, s>(q_gen_2287) -> q_gen_2287
<s, z>(q_gen_2246) -> q_gen_2287
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 65
() -> length([nil, z]) -> 65
() -> leq([a, y]) -> 65
() -> leq([b, b]) -> 65
() -> leqnat([z, s(nn2)]) -> 65
() -> leqnat([z, z]) -> 65
(insert([x, l, _jj]) /\ length([_jj, _kj]) /\ length([l, _ij])) -> leqnat([_ij, _kj]) -> 82
(insert([x, z, _zi]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _zi)]) -> 69
(length([ll, _ej])) -> length([cons(x, ll), s(_ej)]) -> 81
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 70
(leq([b, a])) -> BOT -> 65
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 65
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 67
(leqnat([s(nn1), z])) -> BOT -> 66
}
Sat witness: Found: ((insert([x, l, _jj]) /\ length([_jj, _kj]) /\ length([l, _ij])) -> leqnat([_ij, _kj]), {
_ij -> s(s(s(s(s(z)))))  ;  _jj -> cons(b, cons(b, nil))  ;  _kj -> s(s(z))  ;  l -> cons(b, nil)  ;  x -> a
})

-------------------------------------------
Step 82, which took 1.845950 s (model generation: 1.844511,  model checking: 0.001439):

Model:
|_
{
insert -> 
{{{
Q={q_gen_2250, q_gen_2251, q_gen_2252, q_gen_2255, q_gen_2256},
Q_f={q_gen_2250},
Delta=
{
<nil>() -> q_gen_2251
<a>() -> q_gen_2252
<b>() -> q_gen_2252
<cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2255
<nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2255
<a, a>() -> q_gen_2256
<a, b>() -> q_gen_2256
<b, a>() -> q_gen_2256
<b, b>() -> q_gen_2256
<a, cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2250
<a, nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2250
<b, cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2250
<b, nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2250
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_2249, q_gen_2258, q_gen_2259, q_gen_2280, q_gen_2281, q_gen_2282, q_gen_2283, q_gen_2285, q_gen_2293, q_gen_2294, q_gen_2298, q_gen_2316},
Q_f={q_gen_2249},
Delta=
{
<cons>(q_gen_2281, q_gen_2298) -> q_gen_2258
<nil>() -> q_gen_2258
<cons>(q_gen_2281, q_gen_2258) -> q_gen_2280
<a>() -> q_gen_2281
<b>() -> q_gen_2281
<s>(q_gen_2316) -> q_gen_2283
<z>() -> q_gen_2283
<s>(q_gen_2283) -> q_gen_2294
<cons>(q_gen_2281, q_gen_2280) -> q_gen_2298
<s>(q_gen_2294) -> q_gen_2316
<cons, s>(q_gen_2259, q_gen_2258) -> q_gen_2249
<cons, s>(q_gen_2282, q_gen_2280) -> q_gen_2249
<cons, s>(q_gen_2293, q_gen_2298) -> q_gen_2249
<nil, z>() -> q_gen_2249
<a, s>(q_gen_2316) -> q_gen_2259
<a, z>() -> q_gen_2259
<b, s>(q_gen_2316) -> q_gen_2259
<b, z>() -> q_gen_2259
<a, s>(q_gen_2283) -> q_gen_2282
<b, s>(q_gen_2283) -> q_gen_2282
<cons, s>(q_gen_2259, q_gen_2280) -> q_gen_2285
<cons, s>(q_gen_2259, q_gen_2298) -> q_gen_2285
<cons, s>(q_gen_2282, q_gen_2258) -> q_gen_2285
<cons, s>(q_gen_2282, q_gen_2298) -> q_gen_2285
<cons, s>(q_gen_2293, q_gen_2258) -> q_gen_2285
<cons, s>(q_gen_2293, q_gen_2280) -> q_gen_2285
<a, s>(q_gen_2294) -> q_gen_2293
<b, s>(q_gen_2294) -> q_gen_2293
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_2247, q_gen_2260},
Q_f={q_gen_2247},
Delta=
{
<a, a>() -> q_gen_2247
<a, b>() -> q_gen_2247
<b, b>() -> q_gen_2247
<b, a>() -> q_gen_2260
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  leqnat -> 
{{{
Q={q_gen_2244, q_gen_2246, q_gen_2264, q_gen_2287, q_gen_2320, q_gen_2321},
Q_f={q_gen_2244},
Delta=
{
<s>(q_gen_2264) -> q_gen_2246
<z>() -> q_gen_2246
<s>(q_gen_2246) -> q_gen_2264
<s, s>(q_gen_2244) -> q_gen_2244
<s, s>(q_gen_2320) -> q_gen_2244
<z, s>(q_gen_2246) -> q_gen_2244
<z, s>(q_gen_2264) -> q_gen_2244
<z, z>() -> q_gen_2244
<s, s>(q_gen_2287) -> q_gen_2287
<s, z>(q_gen_2246) -> q_gen_2287
<s, s>(q_gen_2321) -> q_gen_2320
<s, z>(q_gen_2264) -> q_gen_2321
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 66
() -> length([nil, z]) -> 66
() -> leq([a, y]) -> 66
() -> leq([b, b]) -> 66
() -> leqnat([z, s(nn2)]) -> 66
() -> leqnat([z, z]) -> 66
(insert([x, l, _jj]) /\ length([_jj, _kj]) /\ length([l, _ij])) -> leqnat([_ij, _kj]) -> 82
(insert([x, z, _zi]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _zi)]) -> 69
(length([ll, _ej])) -> length([cons(x, ll), s(_ej)]) -> 81
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 70
(leq([b, a])) -> BOT -> 66
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 66
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 70
(leqnat([s(nn1), z])) -> BOT -> 67
}
Sat witness: Found: ((leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]), {
nn1 -> s(s(s(z)))  ;  nn2 -> s(z)
})

-------------------------------------------
Step 83, which took 1.134235 s (model generation: 1.114367,  model checking: 0.019868):

Model:
|_
{
insert -> 
{{{
Q={q_gen_2250, q_gen_2251, q_gen_2252, q_gen_2255, q_gen_2256, q_gen_2262, q_gen_2299},
Q_f={q_gen_2250},
Delta=
{
<nil>() -> q_gen_2251
<a>() -> q_gen_2252
<b>() -> q_gen_2252
<cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2255
<cons, cons>(q_gen_2262, q_gen_2255) -> q_gen_2255
<nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2255
<b, b>() -> q_gen_2256
<a, a>() -> q_gen_2262
<a, b>() -> q_gen_2262
<b, a>() -> q_gen_2262
<a, cons, cons>(q_gen_2262, q_gen_2255) -> q_gen_2250
<a, nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2250
<b, cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2250
<b, cons, cons>(q_gen_2262, q_gen_2255) -> q_gen_2250
<b, nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2250
<a, cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2299
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_2249, q_gen_2258, q_gen_2259, q_gen_2280, q_gen_2281, q_gen_2282, q_gen_2283, q_gen_2286, q_gen_2293, q_gen_2294, q_gen_2298, q_gen_2314, q_gen_2315, q_gen_2316},
Q_f={q_gen_2249},
Delta=
{
<nil>() -> q_gen_2258
<cons>(q_gen_2281, q_gen_2258) -> q_gen_2280
<cons>(q_gen_2281, q_gen_2314) -> q_gen_2280
<a>() -> q_gen_2281
<b>() -> q_gen_2281
<s>(q_gen_2316) -> q_gen_2283
<z>() -> q_gen_2283
<s>(q_gen_2283) -> q_gen_2294
<cons>(q_gen_2281, q_gen_2280) -> q_gen_2298
<cons>(q_gen_2281, q_gen_2298) -> q_gen_2314
<s>(q_gen_2294) -> q_gen_2316
<cons, s>(q_gen_2259, q_gen_2258) -> q_gen_2249
<cons, s>(q_gen_2259, q_gen_2280) -> q_gen_2249
<cons, s>(q_gen_2282, q_gen_2280) -> q_gen_2249
<cons, s>(q_gen_2282, q_gen_2298) -> q_gen_2249
<cons, s>(q_gen_2293, q_gen_2298) -> q_gen_2249
<cons, s>(q_gen_2293, q_gen_2314) -> q_gen_2249
<cons, s>(q_gen_2315, q_gen_2280) -> q_gen_2249
<cons, s>(q_gen_2315, q_gen_2314) -> q_gen_2249
<nil, z>() -> q_gen_2249
<a, z>() -> q_gen_2259
<b, z>() -> q_gen_2259
<a, s>(q_gen_2283) -> q_gen_2282
<b, s>(q_gen_2283) -> q_gen_2282
<cons, s>(q_gen_2259, q_gen_2298) -> q_gen_2286
<cons, s>(q_gen_2259, q_gen_2314) -> q_gen_2286
<cons, s>(q_gen_2282, q_gen_2258) -> q_gen_2286
<cons, s>(q_gen_2282, q_gen_2314) -> q_gen_2286
<cons, s>(q_gen_2293, q_gen_2258) -> q_gen_2286
<cons, s>(q_gen_2293, q_gen_2280) -> q_gen_2286
<cons, s>(q_gen_2315, q_gen_2258) -> q_gen_2286
<cons, s>(q_gen_2315, q_gen_2298) -> q_gen_2286
<a, s>(q_gen_2294) -> q_gen_2293
<b, s>(q_gen_2294) -> q_gen_2293
<a, s>(q_gen_2316) -> q_gen_2315
<b, s>(q_gen_2316) -> q_gen_2315
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_2247, q_gen_2260},
Q_f={q_gen_2247},
Delta=
{
<a, a>() -> q_gen_2247
<a, b>() -> q_gen_2247
<b, b>() -> q_gen_2247
<b, a>() -> q_gen_2260
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  leqnat -> 
{{{
Q={q_gen_2244, q_gen_2246, q_gen_2287},
Q_f={q_gen_2244},
Delta=
{
<s>(q_gen_2246) -> q_gen_2246
<z>() -> q_gen_2246
<s, s>(q_gen_2244) -> q_gen_2244
<z, s>(q_gen_2246) -> q_gen_2244
<z, z>() -> q_gen_2244
<s, s>(q_gen_2287) -> q_gen_2287
<s, z>(q_gen_2246) -> q_gen_2287
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 67
() -> length([nil, z]) -> 67
() -> leq([a, y]) -> 67
() -> leq([b, b]) -> 67
() -> leqnat([z, s(nn2)]) -> 67
() -> leqnat([z, z]) -> 67
(insert([x, l, _jj]) /\ length([_jj, _kj]) /\ length([l, _ij])) -> leqnat([_ij, _kj]) -> 85
(insert([x, z, _zi]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _zi)]) -> 70
(length([ll, _ej])) -> length([cons(x, ll), s(_ej)]) -> 82
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 71
(leq([b, a])) -> BOT -> 67
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 67
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 71
(leqnat([s(nn1), z])) -> BOT -> 68
}
Sat witness: Found: ((insert([x, l, _jj]) /\ length([_jj, _kj]) /\ length([l, _ij])) -> leqnat([_ij, _kj]), {
_ij -> s(s(s(z)))  ;  _jj -> cons(b, cons(b, cons(b, cons(b, cons(b, nil)))))  ;  _kj -> s(z)  ;  l -> cons(b, cons(b, cons(b, cons(b, nil))))  ;  x -> b
})

-------------------------------------------
Step 84, which took 1.433518 s (model generation: 1.421035,  model checking: 0.012483):

Model:
|_
{
insert -> 
{{{
Q={q_gen_2250, q_gen_2251, q_gen_2252, q_gen_2255, q_gen_2256},
Q_f={q_gen_2250},
Delta=
{
<nil>() -> q_gen_2251
<a>() -> q_gen_2252
<b>() -> q_gen_2252
<cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2255
<nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2255
<a, a>() -> q_gen_2256
<a, b>() -> q_gen_2256
<b, a>() -> q_gen_2256
<b, b>() -> q_gen_2256
<a, cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2250
<a, nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2250
<b, cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2250
<b, nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2250
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_2249, q_gen_2258, q_gen_2259, q_gen_2280, q_gen_2281, q_gen_2282, q_gen_2283, q_gen_2285, q_gen_2293, q_gen_2294, q_gen_2298, q_gen_2303, q_gen_2304, q_gen_2315, q_gen_2316, q_gen_2327},
Q_f={q_gen_2249},
Delta=
{
<cons>(q_gen_2304, q_gen_2258) -> q_gen_2258
<nil>() -> q_gen_2258
<cons>(q_gen_2281, q_gen_2258) -> q_gen_2280
<cons>(q_gen_2304, q_gen_2303) -> q_gen_2280
<b>() -> q_gen_2281
<s>(q_gen_2316) -> q_gen_2283
<z>() -> q_gen_2283
<s>(q_gen_2283) -> q_gen_2294
<cons>(q_gen_2281, q_gen_2280) -> q_gen_2298
<cons>(q_gen_2281, q_gen_2303) -> q_gen_2303
<cons>(q_gen_2304, q_gen_2280) -> q_gen_2303
<a>() -> q_gen_2304
<s>(q_gen_2294) -> q_gen_2316
<cons>(q_gen_2281, q_gen_2298) -> q_gen_2327
<cons>(q_gen_2281, q_gen_2327) -> q_gen_2327
<cons, s>(q_gen_2259, q_gen_2258) -> q_gen_2249
<cons, s>(q_gen_2282, q_gen_2280) -> q_gen_2249
<cons, s>(q_gen_2282, q_gen_2303) -> q_gen_2249
<cons, s>(q_gen_2293, q_gen_2280) -> q_gen_2249
<cons, s>(q_gen_2293, q_gen_2298) -> q_gen_2249
<cons, s>(q_gen_2293, q_gen_2303) -> q_gen_2249
<cons, s>(q_gen_2315, q_gen_2298) -> q_gen_2249
<cons, s>(q_gen_2315, q_gen_2303) -> q_gen_2249
<cons, s>(q_gen_2315, q_gen_2327) -> q_gen_2249
<nil, z>() -> q_gen_2249
<a, z>() -> q_gen_2259
<b, z>() -> q_gen_2259
<a, s>(q_gen_2283) -> q_gen_2282
<b, s>(q_gen_2283) -> q_gen_2282
<cons, s>(q_gen_2259, q_gen_2280) -> q_gen_2285
<cons, s>(q_gen_2259, q_gen_2298) -> q_gen_2285
<cons, s>(q_gen_2259, q_gen_2303) -> q_gen_2285
<cons, s>(q_gen_2259, q_gen_2327) -> q_gen_2285
<cons, s>(q_gen_2282, q_gen_2258) -> q_gen_2285
<cons, s>(q_gen_2282, q_gen_2298) -> q_gen_2285
<cons, s>(q_gen_2282, q_gen_2327) -> q_gen_2285
<cons, s>(q_gen_2293, q_gen_2258) -> q_gen_2285
<cons, s>(q_gen_2293, q_gen_2327) -> q_gen_2285
<cons, s>(q_gen_2315, q_gen_2258) -> q_gen_2285
<cons, s>(q_gen_2315, q_gen_2280) -> q_gen_2285
<a, s>(q_gen_2294) -> q_gen_2293
<b, s>(q_gen_2294) -> q_gen_2293
<a, s>(q_gen_2316) -> q_gen_2315
<b, s>(q_gen_2316) -> q_gen_2315
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_2247, q_gen_2260},
Q_f={q_gen_2247},
Delta=
{
<a, a>() -> q_gen_2247
<a, b>() -> q_gen_2247
<b, b>() -> q_gen_2247
<b, a>() -> q_gen_2260
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  leqnat -> 
{{{
Q={q_gen_2244, q_gen_2246, q_gen_2287},
Q_f={q_gen_2244},
Delta=
{
<s>(q_gen_2246) -> q_gen_2246
<z>() -> q_gen_2246
<s, s>(q_gen_2244) -> q_gen_2244
<z, s>(q_gen_2246) -> q_gen_2244
<z, z>() -> q_gen_2244
<s, s>(q_gen_2287) -> q_gen_2287
<s, z>(q_gen_2246) -> q_gen_2287
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 68
() -> length([nil, z]) -> 68
() -> leq([a, y]) -> 68
() -> leq([b, b]) -> 68
() -> leqnat([z, s(nn2)]) -> 68
() -> leqnat([z, z]) -> 68
(insert([x, l, _jj]) /\ length([_jj, _kj]) /\ length([l, _ij])) -> leqnat([_ij, _kj]) -> 85
(insert([x, z, _zi]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _zi)]) -> 71
(length([ll, _ej])) -> length([cons(x, ll), s(_ej)]) -> 85
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 72
(leq([b, a])) -> BOT -> 68
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 68
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 72
(leqnat([s(nn1), z])) -> BOT -> 69
}
Sat witness: Found: ((length([ll, _ej])) -> length([cons(x, ll), s(_ej)]), {
_ej -> s(z)  ;  ll -> cons(a, nil)  ;  x -> b
})

-------------------------------------------
Step 85, which took 1.618984 s (model generation: 1.605544,  model checking: 0.013440):

Model:
|_
{
insert -> 
{{{
Q={q_gen_2250, q_gen_2251, q_gen_2252, q_gen_2255, q_gen_2256, q_gen_2262, q_gen_2299},
Q_f={q_gen_2250},
Delta=
{
<nil>() -> q_gen_2251
<a>() -> q_gen_2252
<b>() -> q_gen_2252
<cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2255
<cons, cons>(q_gen_2262, q_gen_2255) -> q_gen_2255
<nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2255
<a, b>() -> q_gen_2256
<b, b>() -> q_gen_2256
<a, a>() -> q_gen_2262
<b, a>() -> q_gen_2262
<a, cons, cons>(q_gen_2262, q_gen_2255) -> q_gen_2250
<a, nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2250
<b, cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2250
<b, cons, cons>(q_gen_2262, q_gen_2255) -> q_gen_2250
<b, nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2250
<a, cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2299
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_2249, q_gen_2258, q_gen_2259, q_gen_2280, q_gen_2281, q_gen_2282, q_gen_2283, q_gen_2285, q_gen_2293, q_gen_2294, q_gen_2298, q_gen_2314, q_gen_2315, q_gen_2316},
Q_f={q_gen_2249},
Delta=
{
<nil>() -> q_gen_2258
<cons>(q_gen_2281, q_gen_2258) -> q_gen_2280
<a>() -> q_gen_2281
<b>() -> q_gen_2281
<z>() -> q_gen_2283
<s>(q_gen_2283) -> q_gen_2294
<s>(q_gen_2316) -> q_gen_2294
<cons>(q_gen_2281, q_gen_2280) -> q_gen_2298
<cons>(q_gen_2281, q_gen_2314) -> q_gen_2298
<cons>(q_gen_2281, q_gen_2298) -> q_gen_2314
<s>(q_gen_2294) -> q_gen_2316
<cons, s>(q_gen_2259, q_gen_2258) -> q_gen_2249
<cons, s>(q_gen_2282, q_gen_2280) -> q_gen_2249
<cons, s>(q_gen_2293, q_gen_2298) -> q_gen_2249
<cons, s>(q_gen_2315, q_gen_2280) -> q_gen_2249
<cons, s>(q_gen_2315, q_gen_2314) -> q_gen_2249
<nil, z>() -> q_gen_2249
<a, z>() -> q_gen_2259
<b, z>() -> q_gen_2259
<a, s>(q_gen_2283) -> q_gen_2282
<b, s>(q_gen_2283) -> q_gen_2282
<cons, s>(q_gen_2259, q_gen_2280) -> q_gen_2285
<cons, s>(q_gen_2259, q_gen_2298) -> q_gen_2285
<cons, s>(q_gen_2259, q_gen_2314) -> q_gen_2285
<cons, s>(q_gen_2282, q_gen_2258) -> q_gen_2285
<cons, s>(q_gen_2282, q_gen_2298) -> q_gen_2285
<cons, s>(q_gen_2282, q_gen_2314) -> q_gen_2285
<cons, s>(q_gen_2293, q_gen_2258) -> q_gen_2285
<cons, s>(q_gen_2293, q_gen_2280) -> q_gen_2285
<cons, s>(q_gen_2293, q_gen_2314) -> q_gen_2285
<cons, s>(q_gen_2315, q_gen_2258) -> q_gen_2285
<cons, s>(q_gen_2315, q_gen_2298) -> q_gen_2285
<a, s>(q_gen_2294) -> q_gen_2293
<b, s>(q_gen_2294) -> q_gen_2293
<a, s>(q_gen_2316) -> q_gen_2315
<b, s>(q_gen_2316) -> q_gen_2315
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_2247, q_gen_2260},
Q_f={q_gen_2247},
Delta=
{
<a, a>() -> q_gen_2247
<a, b>() -> q_gen_2247
<b, b>() -> q_gen_2247
<b, a>() -> q_gen_2260
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  leqnat -> 
{{{
Q={q_gen_2244, q_gen_2246, q_gen_2287},
Q_f={q_gen_2244},
Delta=
{
<s>(q_gen_2246) -> q_gen_2246
<z>() -> q_gen_2246
<s, s>(q_gen_2244) -> q_gen_2244
<z, s>(q_gen_2246) -> q_gen_2244
<z, z>() -> q_gen_2244
<s, s>(q_gen_2287) -> q_gen_2287
<s, z>(q_gen_2246) -> q_gen_2287
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 69
() -> length([nil, z]) -> 69
() -> leq([a, y]) -> 69
() -> leq([b, b]) -> 69
() -> leqnat([z, s(nn2)]) -> 69
() -> leqnat([z, z]) -> 69
(insert([x, l, _jj]) /\ length([_jj, _kj]) /\ length([l, _ij])) -> leqnat([_ij, _kj]) -> 88
(insert([x, z, _zi]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _zi)]) -> 72
(length([ll, _ej])) -> length([cons(x, ll), s(_ej)]) -> 86
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 73
(leq([b, a])) -> BOT -> 69
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 69
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 73
(leqnat([s(nn1), z])) -> BOT -> 70
}
Sat witness: Found: ((insert([x, l, _jj]) /\ length([_jj, _kj]) /\ length([l, _ij])) -> leqnat([_ij, _kj]), {
_ij -> s(s(s(s(z))))  ;  _jj -> cons(b, cons(b, cons(b, cons(b, cons(b, nil)))))  ;  _kj -> s(s(s(z)))  ;  l -> cons(b, cons(b, cons(b, cons(b, nil))))  ;  x -> b
})

-------------------------------------------
Step 86, which took 1.609469 s (model generation: 1.601637,  model checking: 0.007832):

Model:
|_
{
insert -> 
{{{
Q={q_gen_2250, q_gen_2251, q_gen_2252, q_gen_2255, q_gen_2256, q_gen_2262, q_gen_2299},
Q_f={q_gen_2250},
Delta=
{
<nil>() -> q_gen_2251
<a>() -> q_gen_2252
<b>() -> q_gen_2252
<cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2255
<cons, cons>(q_gen_2262, q_gen_2255) -> q_gen_2255
<nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2255
<b, b>() -> q_gen_2256
<a, a>() -> q_gen_2262
<a, b>() -> q_gen_2262
<b, a>() -> q_gen_2262
<a, cons, cons>(q_gen_2262, q_gen_2255) -> q_gen_2250
<a, nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2250
<b, cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2250
<b, cons, cons>(q_gen_2262, q_gen_2255) -> q_gen_2250
<b, nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2250
<a, cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2299
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_2249, q_gen_2258, q_gen_2259, q_gen_2280, q_gen_2281, q_gen_2282, q_gen_2283, q_gen_2285, q_gen_2293, q_gen_2294, q_gen_2298, q_gen_2314, q_gen_2315, q_gen_2316},
Q_f={q_gen_2249},
Delta=
{
<nil>() -> q_gen_2258
<cons>(q_gen_2281, q_gen_2258) -> q_gen_2280
<cons>(q_gen_2281, q_gen_2314) -> q_gen_2280
<a>() -> q_gen_2281
<b>() -> q_gen_2281
<s>(q_gen_2316) -> q_gen_2283
<z>() -> q_gen_2283
<s>(q_gen_2283) -> q_gen_2294
<cons>(q_gen_2281, q_gen_2280) -> q_gen_2298
<cons>(q_gen_2281, q_gen_2298) -> q_gen_2314
<s>(q_gen_2294) -> q_gen_2316
<cons, s>(q_gen_2259, q_gen_2258) -> q_gen_2249
<cons, s>(q_gen_2259, q_gen_2314) -> q_gen_2249
<cons, s>(q_gen_2282, q_gen_2280) -> q_gen_2249
<cons, s>(q_gen_2293, q_gen_2298) -> q_gen_2249
<cons, s>(q_gen_2315, q_gen_2298) -> q_gen_2249
<cons, s>(q_gen_2315, q_gen_2314) -> q_gen_2249
<nil, z>() -> q_gen_2249
<a, s>(q_gen_2316) -> q_gen_2259
<a, z>() -> q_gen_2259
<b, z>() -> q_gen_2259
<a, s>(q_gen_2283) -> q_gen_2282
<b, s>(q_gen_2283) -> q_gen_2282
<cons, s>(q_gen_2259, q_gen_2280) -> q_gen_2285
<cons, s>(q_gen_2259, q_gen_2298) -> q_gen_2285
<cons, s>(q_gen_2282, q_gen_2258) -> q_gen_2285
<cons, s>(q_gen_2282, q_gen_2298) -> q_gen_2285
<cons, s>(q_gen_2282, q_gen_2314) -> q_gen_2285
<cons, s>(q_gen_2293, q_gen_2258) -> q_gen_2285
<cons, s>(q_gen_2293, q_gen_2280) -> q_gen_2285
<cons, s>(q_gen_2293, q_gen_2314) -> q_gen_2285
<cons, s>(q_gen_2315, q_gen_2258) -> q_gen_2285
<cons, s>(q_gen_2315, q_gen_2280) -> q_gen_2285
<a, s>(q_gen_2294) -> q_gen_2293
<b, s>(q_gen_2294) -> q_gen_2293
<b, s>(q_gen_2316) -> q_gen_2315
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_2247, q_gen_2260},
Q_f={q_gen_2247},
Delta=
{
<a, a>() -> q_gen_2247
<a, b>() -> q_gen_2247
<b, b>() -> q_gen_2247
<b, a>() -> q_gen_2260
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  leqnat -> 
{{{
Q={q_gen_2244, q_gen_2246, q_gen_2287},
Q_f={q_gen_2244},
Delta=
{
<s>(q_gen_2246) -> q_gen_2246
<z>() -> q_gen_2246
<s, s>(q_gen_2244) -> q_gen_2244
<z, s>(q_gen_2246) -> q_gen_2244
<z, z>() -> q_gen_2244
<s, s>(q_gen_2287) -> q_gen_2287
<s, z>(q_gen_2246) -> q_gen_2287
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 70
() -> length([nil, z]) -> 70
() -> leq([a, y]) -> 70
() -> leq([b, b]) -> 70
() -> leqnat([z, s(nn2)]) -> 70
() -> leqnat([z, z]) -> 70
(insert([x, l, _jj]) /\ length([_jj, _kj]) /\ length([l, _ij])) -> leqnat([_ij, _kj]) -> 88
(insert([x, z, _zi]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _zi)]) -> 73
(length([ll, _ej])) -> length([cons(x, ll), s(_ej)]) -> 89
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 74
(leq([b, a])) -> BOT -> 70
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 70
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 74
(leqnat([s(nn1), z])) -> BOT -> 71
}
Sat witness: Found: ((length([ll, _ej])) -> length([cons(x, ll), s(_ej)]), {
_ej -> s(s(s(s(z))))  ;  ll -> cons(b, cons(a, cons(b, nil)))  ;  x -> b
})

-------------------------------------------
Step 87, which took 1.215278 s (model generation: 1.207147,  model checking: 0.008131):

Model:
|_
{
insert -> 
{{{
Q={q_gen_2250, q_gen_2251, q_gen_2252, q_gen_2255, q_gen_2256, q_gen_2262, q_gen_2299},
Q_f={q_gen_2250},
Delta=
{
<nil>() -> q_gen_2251
<a>() -> q_gen_2252
<b>() -> q_gen_2252
<cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2255
<cons, cons>(q_gen_2262, q_gen_2255) -> q_gen_2255
<nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2255
<a, b>() -> q_gen_2256
<b, b>() -> q_gen_2256
<a, a>() -> q_gen_2262
<b, a>() -> q_gen_2262
<a, cons, cons>(q_gen_2262, q_gen_2255) -> q_gen_2250
<a, nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2250
<b, cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2250
<b, cons, cons>(q_gen_2262, q_gen_2255) -> q_gen_2250
<b, nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2250
<a, cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2299
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_2249, q_gen_2258, q_gen_2259, q_gen_2280, q_gen_2281, q_gen_2282, q_gen_2283, q_gen_2285, q_gen_2293, q_gen_2294, q_gen_2298, q_gen_2314, q_gen_2315, q_gen_2316},
Q_f={q_gen_2249},
Delta=
{
<nil>() -> q_gen_2258
<cons>(q_gen_2281, q_gen_2258) -> q_gen_2280
<cons>(q_gen_2281, q_gen_2314) -> q_gen_2280
<a>() -> q_gen_2281
<b>() -> q_gen_2281
<s>(q_gen_2316) -> q_gen_2283
<z>() -> q_gen_2283
<s>(q_gen_2283) -> q_gen_2294
<cons>(q_gen_2281, q_gen_2280) -> q_gen_2298
<cons>(q_gen_2281, q_gen_2298) -> q_gen_2314
<s>(q_gen_2294) -> q_gen_2316
<cons, s>(q_gen_2259, q_gen_2258) -> q_gen_2249
<cons, s>(q_gen_2282, q_gen_2280) -> q_gen_2249
<cons, s>(q_gen_2282, q_gen_2298) -> q_gen_2249
<cons, s>(q_gen_2293, q_gen_2298) -> q_gen_2249
<cons, s>(q_gen_2293, q_gen_2314) -> q_gen_2249
<cons, s>(q_gen_2315, q_gen_2280) -> q_gen_2249
<cons, s>(q_gen_2315, q_gen_2314) -> q_gen_2249
<nil, z>() -> q_gen_2249
<a, z>() -> q_gen_2259
<b, z>() -> q_gen_2259
<a, s>(q_gen_2283) -> q_gen_2282
<b, s>(q_gen_2283) -> q_gen_2282
<cons, s>(q_gen_2259, q_gen_2280) -> q_gen_2285
<cons, s>(q_gen_2259, q_gen_2298) -> q_gen_2285
<cons, s>(q_gen_2259, q_gen_2314) -> q_gen_2285
<cons, s>(q_gen_2282, q_gen_2258) -> q_gen_2285
<cons, s>(q_gen_2282, q_gen_2314) -> q_gen_2285
<cons, s>(q_gen_2293, q_gen_2258) -> q_gen_2285
<cons, s>(q_gen_2293, q_gen_2280) -> q_gen_2285
<cons, s>(q_gen_2315, q_gen_2258) -> q_gen_2285
<cons, s>(q_gen_2315, q_gen_2298) -> q_gen_2285
<a, s>(q_gen_2294) -> q_gen_2293
<b, s>(q_gen_2294) -> q_gen_2293
<a, s>(q_gen_2316) -> q_gen_2315
<b, s>(q_gen_2316) -> q_gen_2315
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_2247, q_gen_2260},
Q_f={q_gen_2247},
Delta=
{
<a, a>() -> q_gen_2247
<a, b>() -> q_gen_2247
<b, b>() -> q_gen_2247
<b, a>() -> q_gen_2260
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  leqnat -> 
{{{
Q={q_gen_2244, q_gen_2246, q_gen_2287},
Q_f={q_gen_2244},
Delta=
{
<s>(q_gen_2246) -> q_gen_2246
<z>() -> q_gen_2246
<s, s>(q_gen_2244) -> q_gen_2244
<z, s>(q_gen_2246) -> q_gen_2244
<z, z>() -> q_gen_2244
<s, s>(q_gen_2287) -> q_gen_2287
<s, z>(q_gen_2246) -> q_gen_2287
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 71
() -> length([nil, z]) -> 71
() -> leq([a, y]) -> 71
() -> leq([b, b]) -> 71
() -> leqnat([z, s(nn2)]) -> 71
() -> leqnat([z, z]) -> 71
(insert([x, l, _jj]) /\ length([_jj, _kj]) /\ length([l, _ij])) -> leqnat([_ij, _kj]) -> 91
(insert([x, z, _zi]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _zi)]) -> 74
(length([ll, _ej])) -> length([cons(x, ll), s(_ej)]) -> 89
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 75
(leq([b, a])) -> BOT -> 71
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 71
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 75
(leqnat([s(nn1), z])) -> BOT -> 72
}
Sat witness: Found: ((insert([x, l, _jj]) /\ length([_jj, _kj]) /\ length([l, _ij])) -> leqnat([_ij, _kj]), {
_ij -> s(s(s(s(s(z)))))  ;  _jj -> cons(b, cons(b, cons(b, nil)))  ;  _kj -> s(s(z))  ;  l -> cons(b, cons(b, nil))  ;  x -> b
})

-------------------------------------------
Step 88, which took 1.232555 s (model generation: 1.224449,  model checking: 0.008106):

Model:
|_
{
insert -> 
{{{
Q={q_gen_2250, q_gen_2251, q_gen_2252, q_gen_2255, q_gen_2256, q_gen_2262, q_gen_2299},
Q_f={q_gen_2250},
Delta=
{
<nil>() -> q_gen_2251
<a>() -> q_gen_2252
<b>() -> q_gen_2252
<cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2255
<cons, cons>(q_gen_2262, q_gen_2255) -> q_gen_2255
<nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2255
<a, b>() -> q_gen_2256
<b, b>() -> q_gen_2256
<a, a>() -> q_gen_2262
<b, a>() -> q_gen_2262
<a, cons, cons>(q_gen_2262, q_gen_2255) -> q_gen_2250
<a, nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2250
<b, cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2250
<b, cons, cons>(q_gen_2262, q_gen_2255) -> q_gen_2250
<b, nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2250
<a, cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2299
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_2249, q_gen_2258, q_gen_2259, q_gen_2280, q_gen_2281, q_gen_2282, q_gen_2283, q_gen_2285, q_gen_2293, q_gen_2294, q_gen_2298, q_gen_2314, q_gen_2315, q_gen_2316},
Q_f={q_gen_2249},
Delta=
{
<nil>() -> q_gen_2258
<cons>(q_gen_2281, q_gen_2258) -> q_gen_2280
<cons>(q_gen_2281, q_gen_2314) -> q_gen_2280
<a>() -> q_gen_2281
<b>() -> q_gen_2281
<s>(q_gen_2316) -> q_gen_2283
<z>() -> q_gen_2283
<s>(q_gen_2283) -> q_gen_2294
<cons>(q_gen_2281, q_gen_2280) -> q_gen_2298
<cons>(q_gen_2281, q_gen_2298) -> q_gen_2314
<s>(q_gen_2294) -> q_gen_2316
<cons, s>(q_gen_2259, q_gen_2258) -> q_gen_2249
<cons, s>(q_gen_2282, q_gen_2280) -> q_gen_2249
<cons, s>(q_gen_2293, q_gen_2298) -> q_gen_2249
<cons, s>(q_gen_2315, q_gen_2280) -> q_gen_2249
<cons, s>(q_gen_2315, q_gen_2314) -> q_gen_2249
<nil, z>() -> q_gen_2249
<a, z>() -> q_gen_2259
<b, z>() -> q_gen_2259
<a, s>(q_gen_2283) -> q_gen_2282
<b, s>(q_gen_2283) -> q_gen_2282
<cons, s>(q_gen_2259, q_gen_2280) -> q_gen_2285
<cons, s>(q_gen_2259, q_gen_2298) -> q_gen_2285
<cons, s>(q_gen_2259, q_gen_2314) -> q_gen_2285
<cons, s>(q_gen_2282, q_gen_2258) -> q_gen_2285
<cons, s>(q_gen_2282, q_gen_2298) -> q_gen_2285
<cons, s>(q_gen_2282, q_gen_2314) -> q_gen_2285
<cons, s>(q_gen_2293, q_gen_2258) -> q_gen_2285
<cons, s>(q_gen_2293, q_gen_2280) -> q_gen_2285
<cons, s>(q_gen_2293, q_gen_2314) -> q_gen_2285
<cons, s>(q_gen_2315, q_gen_2258) -> q_gen_2285
<cons, s>(q_gen_2315, q_gen_2298) -> q_gen_2285
<a, s>(q_gen_2294) -> q_gen_2293
<b, s>(q_gen_2294) -> q_gen_2293
<a, s>(q_gen_2316) -> q_gen_2315
<b, s>(q_gen_2316) -> q_gen_2315
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_2247, q_gen_2260},
Q_f={q_gen_2247},
Delta=
{
<a, a>() -> q_gen_2247
<a, b>() -> q_gen_2247
<b, b>() -> q_gen_2247
<b, a>() -> q_gen_2260
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  leqnat -> 
{{{
Q={q_gen_2244, q_gen_2246, q_gen_2287},
Q_f={q_gen_2244},
Delta=
{
<s>(q_gen_2246) -> q_gen_2246
<z>() -> q_gen_2246
<s, s>(q_gen_2244) -> q_gen_2244
<z, s>(q_gen_2246) -> q_gen_2244
<z, z>() -> q_gen_2244
<s, s>(q_gen_2287) -> q_gen_2287
<s, z>(q_gen_2246) -> q_gen_2287
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 72
() -> length([nil, z]) -> 72
() -> leq([a, y]) -> 72
() -> leq([b, b]) -> 72
() -> leqnat([z, s(nn2)]) -> 72
() -> leqnat([z, z]) -> 72
(insert([x, l, _jj]) /\ length([_jj, _kj]) /\ length([l, _ij])) -> leqnat([_ij, _kj]) -> 91
(insert([x, z, _zi]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _zi)]) -> 75
(length([ll, _ej])) -> length([cons(x, ll), s(_ej)]) -> 92
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 76
(leq([b, a])) -> BOT -> 72
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 72
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 76
(leqnat([s(nn1), z])) -> BOT -> 73
}
Sat witness: Found: ((length([ll, _ej])) -> length([cons(x, ll), s(_ej)]), {
_ej -> s(s(s(s(z))))  ;  ll -> cons(b, cons(b, nil))  ;  x -> a
})

-------------------------------------------
Step 89, which took 1.859876 s (model generation: 1.853520,  model checking: 0.006356):

Model:
|_
{
insert -> 
{{{
Q={q_gen_2250, q_gen_2251, q_gen_2252, q_gen_2255, q_gen_2256, q_gen_2262, q_gen_2299},
Q_f={q_gen_2250},
Delta=
{
<nil>() -> q_gen_2251
<a>() -> q_gen_2252
<b>() -> q_gen_2252
<cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2255
<cons, cons>(q_gen_2262, q_gen_2255) -> q_gen_2255
<nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2255
<a, b>() -> q_gen_2256
<b, b>() -> q_gen_2256
<a, a>() -> q_gen_2262
<b, a>() -> q_gen_2262
<a, cons, cons>(q_gen_2262, q_gen_2255) -> q_gen_2250
<a, nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2250
<b, cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2250
<b, cons, cons>(q_gen_2262, q_gen_2255) -> q_gen_2250
<b, nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2250
<a, cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2299
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_2249, q_gen_2258, q_gen_2259, q_gen_2280, q_gen_2281, q_gen_2282, q_gen_2283, q_gen_2285, q_gen_2293, q_gen_2294, q_gen_2298, q_gen_2314, q_gen_2315, q_gen_2316},
Q_f={q_gen_2249},
Delta=
{
<nil>() -> q_gen_2258
<cons>(q_gen_2281, q_gen_2258) -> q_gen_2280
<cons>(q_gen_2281, q_gen_2314) -> q_gen_2280
<a>() -> q_gen_2281
<b>() -> q_gen_2281
<s>(q_gen_2316) -> q_gen_2283
<z>() -> q_gen_2283
<s>(q_gen_2283) -> q_gen_2294
<cons>(q_gen_2281, q_gen_2280) -> q_gen_2298
<cons>(q_gen_2281, q_gen_2298) -> q_gen_2314
<s>(q_gen_2294) -> q_gen_2316
<cons, s>(q_gen_2259, q_gen_2258) -> q_gen_2249
<cons, s>(q_gen_2259, q_gen_2314) -> q_gen_2249
<cons, s>(q_gen_2282, q_gen_2280) -> q_gen_2249
<cons, s>(q_gen_2293, q_gen_2298) -> q_gen_2249
<cons, s>(q_gen_2315, q_gen_2314) -> q_gen_2249
<nil, z>() -> q_gen_2249
<a, z>() -> q_gen_2259
<b, z>() -> q_gen_2259
<a, s>(q_gen_2283) -> q_gen_2282
<b, s>(q_gen_2283) -> q_gen_2282
<cons, s>(q_gen_2259, q_gen_2280) -> q_gen_2285
<cons, s>(q_gen_2259, q_gen_2298) -> q_gen_2285
<cons, s>(q_gen_2282, q_gen_2258) -> q_gen_2285
<cons, s>(q_gen_2282, q_gen_2298) -> q_gen_2285
<cons, s>(q_gen_2282, q_gen_2314) -> q_gen_2285
<cons, s>(q_gen_2293, q_gen_2258) -> q_gen_2285
<cons, s>(q_gen_2293, q_gen_2280) -> q_gen_2285
<cons, s>(q_gen_2293, q_gen_2314) -> q_gen_2285
<cons, s>(q_gen_2315, q_gen_2258) -> q_gen_2285
<cons, s>(q_gen_2315, q_gen_2280) -> q_gen_2285
<cons, s>(q_gen_2315, q_gen_2298) -> q_gen_2285
<a, s>(q_gen_2294) -> q_gen_2293
<b, s>(q_gen_2294) -> q_gen_2293
<a, s>(q_gen_2316) -> q_gen_2315
<b, s>(q_gen_2316) -> q_gen_2315
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_2247, q_gen_2260},
Q_f={q_gen_2247},
Delta=
{
<a, a>() -> q_gen_2247
<a, b>() -> q_gen_2247
<b, b>() -> q_gen_2247
<b, a>() -> q_gen_2260
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  leqnat -> 
{{{
Q={q_gen_2244, q_gen_2246, q_gen_2287},
Q_f={q_gen_2244},
Delta=
{
<s>(q_gen_2246) -> q_gen_2246
<z>() -> q_gen_2246
<s, s>(q_gen_2244) -> q_gen_2244
<z, s>(q_gen_2246) -> q_gen_2244
<z, z>() -> q_gen_2244
<s, s>(q_gen_2287) -> q_gen_2287
<s, z>(q_gen_2246) -> q_gen_2287
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 73
() -> length([nil, z]) -> 73
() -> leq([a, y]) -> 73
() -> leq([b, b]) -> 73
() -> leqnat([z, s(nn2)]) -> 73
() -> leqnat([z, z]) -> 73
(insert([x, l, _jj]) /\ length([_jj, _kj]) /\ length([l, _ij])) -> leqnat([_ij, _kj]) -> 94
(insert([x, z, _zi]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _zi)]) -> 76
(length([ll, _ej])) -> length([cons(x, ll), s(_ej)]) -> 92
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 77
(leq([b, a])) -> BOT -> 73
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 73
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 77
(leqnat([s(nn1), z])) -> BOT -> 74
}
Sat witness: Found: ((insert([x, l, _jj]) /\ length([_jj, _kj]) /\ length([l, _ij])) -> leqnat([_ij, _kj]), {
_ij -> s(s(s(z)))  ;  _jj -> cons(b, cons(b, cons(b, cons(b, nil))))  ;  _kj -> s(z)  ;  l -> cons(b, cons(b, cons(b, nil)))  ;  x -> b
})

-------------------------------------------
Step 90, which took 1.670134 s (model generation: 1.658219,  model checking: 0.011915):

Model:
|_
{
insert -> 
{{{
Q={q_gen_2250, q_gen_2251, q_gen_2252, q_gen_2255, q_gen_2256, q_gen_2262, q_gen_2299},
Q_f={q_gen_2250},
Delta=
{
<nil>() -> q_gen_2251
<a>() -> q_gen_2252
<b>() -> q_gen_2252
<cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2255
<cons, cons>(q_gen_2262, q_gen_2255) -> q_gen_2255
<nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2255
<b, b>() -> q_gen_2256
<a, a>() -> q_gen_2262
<a, b>() -> q_gen_2262
<b, a>() -> q_gen_2262
<a, cons, cons>(q_gen_2262, q_gen_2255) -> q_gen_2250
<a, nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2250
<b, cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2250
<b, cons, cons>(q_gen_2262, q_gen_2255) -> q_gen_2250
<b, nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2250
<a, cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2299
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_2249, q_gen_2258, q_gen_2259, q_gen_2280, q_gen_2281, q_gen_2282, q_gen_2283, q_gen_2285, q_gen_2293, q_gen_2294, q_gen_2298, q_gen_2314, q_gen_2315, q_gen_2316},
Q_f={q_gen_2249},
Delta=
{
<nil>() -> q_gen_2258
<cons>(q_gen_2281, q_gen_2258) -> q_gen_2280
<cons>(q_gen_2281, q_gen_2314) -> q_gen_2280
<a>() -> q_gen_2281
<b>() -> q_gen_2281
<s>(q_gen_2316) -> q_gen_2283
<z>() -> q_gen_2283
<s>(q_gen_2283) -> q_gen_2294
<cons>(q_gen_2281, q_gen_2280) -> q_gen_2298
<cons>(q_gen_2281, q_gen_2298) -> q_gen_2314
<s>(q_gen_2294) -> q_gen_2316
<cons, s>(q_gen_2259, q_gen_2258) -> q_gen_2249
<cons, s>(q_gen_2282, q_gen_2280) -> q_gen_2249
<cons, s>(q_gen_2293, q_gen_2298) -> q_gen_2249
<cons, s>(q_gen_2315, q_gen_2314) -> q_gen_2249
<nil, z>() -> q_gen_2249
<a, z>() -> q_gen_2259
<b, z>() -> q_gen_2259
<a, s>(q_gen_2283) -> q_gen_2282
<b, s>(q_gen_2283) -> q_gen_2282
<cons, s>(q_gen_2259, q_gen_2280) -> q_gen_2285
<cons, s>(q_gen_2259, q_gen_2298) -> q_gen_2285
<cons, s>(q_gen_2259, q_gen_2314) -> q_gen_2285
<cons, s>(q_gen_2282, q_gen_2258) -> q_gen_2285
<cons, s>(q_gen_2282, q_gen_2298) -> q_gen_2285
<cons, s>(q_gen_2282, q_gen_2314) -> q_gen_2285
<cons, s>(q_gen_2293, q_gen_2258) -> q_gen_2285
<cons, s>(q_gen_2293, q_gen_2280) -> q_gen_2285
<cons, s>(q_gen_2293, q_gen_2314) -> q_gen_2285
<cons, s>(q_gen_2315, q_gen_2258) -> q_gen_2285
<cons, s>(q_gen_2315, q_gen_2280) -> q_gen_2285
<cons, s>(q_gen_2315, q_gen_2298) -> q_gen_2285
<a, s>(q_gen_2294) -> q_gen_2293
<b, s>(q_gen_2294) -> q_gen_2293
<a, s>(q_gen_2316) -> q_gen_2315
<b, s>(q_gen_2316) -> q_gen_2315
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_2247, q_gen_2260},
Q_f={q_gen_2247},
Delta=
{
<a, a>() -> q_gen_2247
<a, b>() -> q_gen_2247
<b, b>() -> q_gen_2247
<b, a>() -> q_gen_2260
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  leqnat -> 
{{{
Q={q_gen_2244, q_gen_2246, q_gen_2287},
Q_f={q_gen_2244},
Delta=
{
<s>(q_gen_2246) -> q_gen_2246
<z>() -> q_gen_2246
<s, s>(q_gen_2244) -> q_gen_2244
<z, s>(q_gen_2246) -> q_gen_2244
<z, z>() -> q_gen_2244
<s, s>(q_gen_2287) -> q_gen_2287
<s, z>(q_gen_2246) -> q_gen_2287
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 74
() -> length([nil, z]) -> 74
() -> leq([a, y]) -> 74
() -> leq([b, b]) -> 74
() -> leqnat([z, s(nn2)]) -> 74
() -> leqnat([z, z]) -> 74
(insert([x, l, _jj]) /\ length([_jj, _kj]) /\ length([l, _ij])) -> leqnat([_ij, _kj]) -> 97
(insert([x, z, _zi]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _zi)]) -> 77
(length([ll, _ej])) -> length([cons(x, ll), s(_ej)]) -> 93
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 78
(leq([b, a])) -> BOT -> 74
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 74
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 78
(leqnat([s(nn1), z])) -> BOT -> 75
}
Sat witness: Found: ((insert([x, l, _jj]) /\ length([_jj, _kj]) /\ length([l, _ij])) -> leqnat([_ij, _kj]), {
_ij -> s(s(s(s(z))))  ;  _jj -> cons(b, cons(b, cons(b, cons(b, cons(b, nil)))))  ;  _kj -> s(s(z))  ;  l -> cons(b, cons(b, cons(b, cons(b, nil))))  ;  x -> b
})

-------------------------------------------
Step 91, which took 1.877051 s (model generation: 1.861020,  model checking: 0.016031):

Model:
|_
{
insert -> 
{{{
Q={q_gen_2250, q_gen_2251, q_gen_2252, q_gen_2255, q_gen_2256},
Q_f={q_gen_2250},
Delta=
{
<nil>() -> q_gen_2251
<a>() -> q_gen_2252
<b>() -> q_gen_2252
<cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2255
<nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2255
<a, a>() -> q_gen_2256
<a, b>() -> q_gen_2256
<b, a>() -> q_gen_2256
<b, b>() -> q_gen_2256
<a, cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2250
<a, nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2250
<b, cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2250
<b, nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2250
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_2249, q_gen_2258, q_gen_2259, q_gen_2280, q_gen_2281, q_gen_2282, q_gen_2283, q_gen_2285, q_gen_2293, q_gen_2294, q_gen_2298, q_gen_2303, q_gen_2304, q_gen_2315, q_gen_2316, q_gen_2327},
Q_f={q_gen_2249},
Delta=
{
<cons>(q_gen_2281, q_gen_2327) -> q_gen_2258
<nil>() -> q_gen_2258
<cons>(q_gen_2281, q_gen_2258) -> q_gen_2280
<cons>(q_gen_2304, q_gen_2303) -> q_gen_2280
<b>() -> q_gen_2281
<s>(q_gen_2316) -> q_gen_2283
<z>() -> q_gen_2283
<s>(q_gen_2283) -> q_gen_2294
<cons>(q_gen_2281, q_gen_2280) -> q_gen_2298
<cons>(q_gen_2281, q_gen_2303) -> q_gen_2303
<cons>(q_gen_2304, q_gen_2258) -> q_gen_2303
<cons>(q_gen_2304, q_gen_2280) -> q_gen_2303
<a>() -> q_gen_2304
<s>(q_gen_2294) -> q_gen_2316
<cons>(q_gen_2281, q_gen_2298) -> q_gen_2327
<cons, s>(q_gen_2259, q_gen_2258) -> q_gen_2249
<cons, s>(q_gen_2282, q_gen_2280) -> q_gen_2249
<cons, s>(q_gen_2282, q_gen_2303) -> q_gen_2249
<cons, s>(q_gen_2293, q_gen_2298) -> q_gen_2249
<cons, s>(q_gen_2293, q_gen_2303) -> q_gen_2249
<cons, s>(q_gen_2315, q_gen_2298) -> q_gen_2249
<cons, s>(q_gen_2315, q_gen_2303) -> q_gen_2249
<cons, s>(q_gen_2315, q_gen_2327) -> q_gen_2249
<nil, z>() -> q_gen_2249
<a, z>() -> q_gen_2259
<b, z>() -> q_gen_2259
<a, s>(q_gen_2283) -> q_gen_2282
<b, s>(q_gen_2283) -> q_gen_2282
<cons, s>(q_gen_2259, q_gen_2280) -> q_gen_2285
<cons, s>(q_gen_2259, q_gen_2298) -> q_gen_2285
<cons, s>(q_gen_2259, q_gen_2303) -> q_gen_2285
<cons, s>(q_gen_2259, q_gen_2327) -> q_gen_2285
<cons, s>(q_gen_2282, q_gen_2258) -> q_gen_2285
<cons, s>(q_gen_2282, q_gen_2298) -> q_gen_2285
<cons, s>(q_gen_2282, q_gen_2327) -> q_gen_2285
<cons, s>(q_gen_2293, q_gen_2258) -> q_gen_2285
<cons, s>(q_gen_2293, q_gen_2280) -> q_gen_2285
<cons, s>(q_gen_2293, q_gen_2327) -> q_gen_2285
<cons, s>(q_gen_2315, q_gen_2258) -> q_gen_2285
<cons, s>(q_gen_2315, q_gen_2280) -> q_gen_2285
<a, s>(q_gen_2294) -> q_gen_2293
<a, s>(q_gen_2316) -> q_gen_2293
<b, s>(q_gen_2294) -> q_gen_2293
<b, s>(q_gen_2316) -> q_gen_2315
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_2247, q_gen_2260},
Q_f={q_gen_2247},
Delta=
{
<a, a>() -> q_gen_2247
<a, b>() -> q_gen_2247
<b, b>() -> q_gen_2247
<b, a>() -> q_gen_2260
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  leqnat -> 
{{{
Q={q_gen_2244, q_gen_2246, q_gen_2287},
Q_f={q_gen_2244},
Delta=
{
<s>(q_gen_2246) -> q_gen_2246
<z>() -> q_gen_2246
<s, s>(q_gen_2244) -> q_gen_2244
<z, s>(q_gen_2246) -> q_gen_2244
<z, z>() -> q_gen_2244
<s, s>(q_gen_2287) -> q_gen_2287
<s, z>(q_gen_2246) -> q_gen_2287
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 75
() -> length([nil, z]) -> 75
() -> leq([a, y]) -> 75
() -> leq([b, b]) -> 75
() -> leqnat([z, s(nn2)]) -> 75
() -> leqnat([z, z]) -> 75
(insert([x, l, _jj]) /\ length([_jj, _kj]) /\ length([l, _ij])) -> leqnat([_ij, _kj]) -> 97
(insert([x, z, _zi]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _zi)]) -> 78
(length([ll, _ej])) -> length([cons(x, ll), s(_ej)]) -> 96
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 79
(leq([b, a])) -> BOT -> 75
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 75
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 79
(leqnat([s(nn1), z])) -> BOT -> 76
}
Sat witness: Found: ((length([ll, _ej])) -> length([cons(x, ll), s(_ej)]), {
_ej -> s(s(z))  ;  ll -> cons(a, cons(a, nil))  ;  x -> b
})

-------------------------------------------
Step 92, which took 2.554249 s (model generation: 2.542099,  model checking: 0.012150):

Model:
|_
{
insert -> 
{{{
Q={q_gen_2250, q_gen_2251, q_gen_2252, q_gen_2255, q_gen_2256},
Q_f={q_gen_2250},
Delta=
{
<nil>() -> q_gen_2251
<a>() -> q_gen_2252
<b>() -> q_gen_2252
<cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2255
<nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2255
<a, a>() -> q_gen_2256
<a, b>() -> q_gen_2256
<b, a>() -> q_gen_2256
<b, b>() -> q_gen_2256
<a, cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2250
<a, nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2250
<b, cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2250
<b, nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2250
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_2249, q_gen_2258, q_gen_2259, q_gen_2280, q_gen_2281, q_gen_2282, q_gen_2283, q_gen_2285, q_gen_2293, q_gen_2294, q_gen_2298, q_gen_2303, q_gen_2304, q_gen_2315, q_gen_2316, q_gen_2327},
Q_f={q_gen_2249},
Delta=
{
<nil>() -> q_gen_2258
<cons>(q_gen_2281, q_gen_2258) -> q_gen_2280
<cons>(q_gen_2304, q_gen_2303) -> q_gen_2280
<b>() -> q_gen_2281
<s>(q_gen_2316) -> q_gen_2283
<z>() -> q_gen_2283
<s>(q_gen_2283) -> q_gen_2294
<cons>(q_gen_2281, q_gen_2280) -> q_gen_2298
<cons>(q_gen_2281, q_gen_2303) -> q_gen_2303
<cons>(q_gen_2304, q_gen_2258) -> q_gen_2303
<cons>(q_gen_2304, q_gen_2280) -> q_gen_2303
<a>() -> q_gen_2304
<s>(q_gen_2294) -> q_gen_2316
<cons>(q_gen_2281, q_gen_2298) -> q_gen_2327
<cons>(q_gen_2281, q_gen_2327) -> q_gen_2327
<cons, s>(q_gen_2259, q_gen_2258) -> q_gen_2249
<cons, s>(q_gen_2282, q_gen_2280) -> q_gen_2249
<cons, s>(q_gen_2282, q_gen_2303) -> q_gen_2249
<cons, s>(q_gen_2293, q_gen_2280) -> q_gen_2249
<cons, s>(q_gen_2293, q_gen_2298) -> q_gen_2249
<cons, s>(q_gen_2293, q_gen_2303) -> q_gen_2249
<cons, s>(q_gen_2315, q_gen_2298) -> q_gen_2249
<cons, s>(q_gen_2315, q_gen_2303) -> q_gen_2249
<cons, s>(q_gen_2315, q_gen_2327) -> q_gen_2249
<nil, z>() -> q_gen_2249
<a, z>() -> q_gen_2259
<b, z>() -> q_gen_2259
<a, s>(q_gen_2283) -> q_gen_2282
<b, s>(q_gen_2283) -> q_gen_2282
<cons, s>(q_gen_2259, q_gen_2280) -> q_gen_2285
<cons, s>(q_gen_2259, q_gen_2298) -> q_gen_2285
<cons, s>(q_gen_2259, q_gen_2303) -> q_gen_2285
<cons, s>(q_gen_2259, q_gen_2327) -> q_gen_2285
<cons, s>(q_gen_2282, q_gen_2258) -> q_gen_2285
<cons, s>(q_gen_2282, q_gen_2298) -> q_gen_2285
<cons, s>(q_gen_2282, q_gen_2327) -> q_gen_2285
<cons, s>(q_gen_2293, q_gen_2258) -> q_gen_2285
<cons, s>(q_gen_2293, q_gen_2327) -> q_gen_2285
<cons, s>(q_gen_2315, q_gen_2258) -> q_gen_2285
<cons, s>(q_gen_2315, q_gen_2280) -> q_gen_2285
<a, s>(q_gen_2294) -> q_gen_2293
<b, s>(q_gen_2294) -> q_gen_2293
<a, s>(q_gen_2316) -> q_gen_2315
<b, s>(q_gen_2316) -> q_gen_2315
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_2247, q_gen_2260},
Q_f={q_gen_2247},
Delta=
{
<a, a>() -> q_gen_2247
<a, b>() -> q_gen_2247
<b, b>() -> q_gen_2247
<b, a>() -> q_gen_2260
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  leqnat -> 
{{{
Q={q_gen_2244, q_gen_2246, q_gen_2287},
Q_f={q_gen_2244},
Delta=
{
<s>(q_gen_2246) -> q_gen_2246
<z>() -> q_gen_2246
<s, s>(q_gen_2244) -> q_gen_2244
<z, s>(q_gen_2246) -> q_gen_2244
<z, z>() -> q_gen_2244
<s, s>(q_gen_2287) -> q_gen_2287
<s, z>(q_gen_2246) -> q_gen_2287
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 76
() -> length([nil, z]) -> 76
() -> leq([a, y]) -> 76
() -> leq([b, b]) -> 76
() -> leqnat([z, s(nn2)]) -> 76
() -> leqnat([z, z]) -> 76
(insert([x, l, _jj]) /\ length([_jj, _kj]) /\ length([l, _ij])) -> leqnat([_ij, _kj]) -> 97
(insert([x, z, _zi]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _zi)]) -> 79
(length([ll, _ej])) -> length([cons(x, ll), s(_ej)]) -> 99
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 80
(leq([b, a])) -> BOT -> 76
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 76
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 80
(leqnat([s(nn1), z])) -> BOT -> 77
}
Sat witness: Found: ((length([ll, _ej])) -> length([cons(x, ll), s(_ej)]), {
_ej -> s(s(s(z)))  ;  ll -> cons(a, cons(a, nil))  ;  x -> a
})

-------------------------------------------
Step 93, which took 2.308339 s (model generation: 2.299584,  model checking: 0.008755):

Model:
|_
{
insert -> 
{{{
Q={q_gen_2250, q_gen_2251, q_gen_2252, q_gen_2255, q_gen_2256},
Q_f={q_gen_2250},
Delta=
{
<nil>() -> q_gen_2251
<a>() -> q_gen_2252
<b>() -> q_gen_2252
<cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2255
<nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2255
<a, a>() -> q_gen_2256
<a, b>() -> q_gen_2256
<b, a>() -> q_gen_2256
<b, b>() -> q_gen_2256
<a, cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2250
<a, nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2250
<b, cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2250
<b, nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2250
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_2249, q_gen_2258, q_gen_2259, q_gen_2280, q_gen_2281, q_gen_2282, q_gen_2283, q_gen_2285, q_gen_2293, q_gen_2294, q_gen_2298, q_gen_2303, q_gen_2304, q_gen_2315, q_gen_2316, q_gen_2327},
Q_f={q_gen_2249},
Delta=
{
<cons>(q_gen_2281, q_gen_2327) -> q_gen_2258
<nil>() -> q_gen_2258
<cons>(q_gen_2281, q_gen_2258) -> q_gen_2280
<cons>(q_gen_2304, q_gen_2258) -> q_gen_2280
<b>() -> q_gen_2281
<z>() -> q_gen_2283
<s>(q_gen_2283) -> q_gen_2294
<cons>(q_gen_2281, q_gen_2280) -> q_gen_2298
<cons>(q_gen_2281, q_gen_2303) -> q_gen_2303
<cons>(q_gen_2304, q_gen_2280) -> q_gen_2303
<a>() -> q_gen_2304
<s>(q_gen_2294) -> q_gen_2316
<s>(q_gen_2316) -> q_gen_2316
<cons>(q_gen_2281, q_gen_2298) -> q_gen_2327
<cons>(q_gen_2304, q_gen_2303) -> q_gen_2327
<cons, s>(q_gen_2259, q_gen_2258) -> q_gen_2249
<cons, s>(q_gen_2282, q_gen_2280) -> q_gen_2249
<cons, s>(q_gen_2282, q_gen_2303) -> q_gen_2249
<cons, s>(q_gen_2293, q_gen_2298) -> q_gen_2249
<cons, s>(q_gen_2293, q_gen_2303) -> q_gen_2249
<cons, s>(q_gen_2315, q_gen_2303) -> q_gen_2249
<cons, s>(q_gen_2315, q_gen_2327) -> q_gen_2249
<nil, z>() -> q_gen_2249
<a, z>() -> q_gen_2259
<b, z>() -> q_gen_2259
<a, s>(q_gen_2283) -> q_gen_2282
<b, s>(q_gen_2283) -> q_gen_2282
<cons, s>(q_gen_2259, q_gen_2280) -> q_gen_2285
<cons, s>(q_gen_2259, q_gen_2298) -> q_gen_2285
<cons, s>(q_gen_2259, q_gen_2303) -> q_gen_2285
<cons, s>(q_gen_2259, q_gen_2327) -> q_gen_2285
<cons, s>(q_gen_2282, q_gen_2258) -> q_gen_2285
<cons, s>(q_gen_2282, q_gen_2298) -> q_gen_2285
<cons, s>(q_gen_2282, q_gen_2327) -> q_gen_2285
<cons, s>(q_gen_2293, q_gen_2258) -> q_gen_2285
<cons, s>(q_gen_2293, q_gen_2280) -> q_gen_2285
<cons, s>(q_gen_2293, q_gen_2327) -> q_gen_2285
<cons, s>(q_gen_2315, q_gen_2258) -> q_gen_2285
<cons, s>(q_gen_2315, q_gen_2280) -> q_gen_2285
<cons, s>(q_gen_2315, q_gen_2298) -> q_gen_2285
<a, s>(q_gen_2294) -> q_gen_2293
<a, s>(q_gen_2316) -> q_gen_2293
<b, s>(q_gen_2294) -> q_gen_2293
<b, s>(q_gen_2316) -> q_gen_2315
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_2247, q_gen_2260},
Q_f={q_gen_2247},
Delta=
{
<a, a>() -> q_gen_2247
<a, b>() -> q_gen_2247
<b, b>() -> q_gen_2247
<b, a>() -> q_gen_2260
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  leqnat -> 
{{{
Q={q_gen_2244, q_gen_2246, q_gen_2287},
Q_f={q_gen_2244},
Delta=
{
<s>(q_gen_2246) -> q_gen_2246
<z>() -> q_gen_2246
<s, s>(q_gen_2244) -> q_gen_2244
<z, s>(q_gen_2246) -> q_gen_2244
<z, z>() -> q_gen_2244
<s, s>(q_gen_2287) -> q_gen_2287
<s, z>(q_gen_2246) -> q_gen_2287
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 77
() -> length([nil, z]) -> 77
() -> leq([a, y]) -> 77
() -> leq([b, b]) -> 77
() -> leqnat([z, s(nn2)]) -> 77
() -> leqnat([z, z]) -> 77
(insert([x, l, _jj]) /\ length([_jj, _kj]) /\ length([l, _ij])) -> leqnat([_ij, _kj]) -> 100
(insert([x, z, _zi]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _zi)]) -> 80
(length([ll, _ej])) -> length([cons(x, ll), s(_ej)]) -> 99
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 81
(leq([b, a])) -> BOT -> 77
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 77
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 81
(leqnat([s(nn1), z])) -> BOT -> 78
}
Sat witness: Found: ((insert([x, l, _jj]) /\ length([_jj, _kj]) /\ length([l, _ij])) -> leqnat([_ij, _kj]), {
_ij -> s(s(z))  ;  _jj -> cons(b, cons(b, cons(a, cons(b, cons(b, cons(b, cons(a, cons(b, nil))))))))  ;  _kj -> s(z)  ;  l -> cons(b, cons(a, cons(b, cons(b, cons(b, cons(b, cons(b, nil)))))))  ;  x -> a
})

-------------------------------------------
Step 94, which took 2.166368 s (model generation: 2.155442,  model checking: 0.010926):

Model:
|_
{
insert -> 
{{{
Q={q_gen_2250, q_gen_2251, q_gen_2252, q_gen_2255, q_gen_2256},
Q_f={q_gen_2250},
Delta=
{
<nil>() -> q_gen_2251
<a>() -> q_gen_2252
<b>() -> q_gen_2252
<cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2255
<nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2255
<a, a>() -> q_gen_2256
<a, b>() -> q_gen_2256
<b, a>() -> q_gen_2256
<b, b>() -> q_gen_2256
<a, cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2250
<a, nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2250
<b, cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2250
<b, nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2250
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_2249, q_gen_2258, q_gen_2259, q_gen_2280, q_gen_2281, q_gen_2282, q_gen_2283, q_gen_2285, q_gen_2293, q_gen_2294, q_gen_2298, q_gen_2303, q_gen_2304, q_gen_2315, q_gen_2316, q_gen_2327},
Q_f={q_gen_2249},
Delta=
{
<nil>() -> q_gen_2258
<cons>(q_gen_2281, q_gen_2258) -> q_gen_2280
<cons>(q_gen_2304, q_gen_2258) -> q_gen_2280
<cons>(q_gen_2304, q_gen_2303) -> q_gen_2280
<cons>(q_gen_2304, q_gen_2327) -> q_gen_2280
<b>() -> q_gen_2281
<s>(q_gen_2316) -> q_gen_2283
<z>() -> q_gen_2283
<s>(q_gen_2283) -> q_gen_2294
<cons>(q_gen_2281, q_gen_2280) -> q_gen_2298
<cons>(q_gen_2281, q_gen_2303) -> q_gen_2303
<cons>(q_gen_2304, q_gen_2280) -> q_gen_2303
<a>() -> q_gen_2304
<s>(q_gen_2294) -> q_gen_2316
<cons>(q_gen_2281, q_gen_2298) -> q_gen_2327
<cons>(q_gen_2281, q_gen_2327) -> q_gen_2327
<cons, s>(q_gen_2259, q_gen_2258) -> q_gen_2249
<cons, s>(q_gen_2259, q_gen_2303) -> q_gen_2249
<cons, s>(q_gen_2282, q_gen_2280) -> q_gen_2249
<cons, s>(q_gen_2282, q_gen_2303) -> q_gen_2249
<cons, s>(q_gen_2293, q_gen_2298) -> q_gen_2249
<cons, s>(q_gen_2293, q_gen_2303) -> q_gen_2249
<cons, s>(q_gen_2315, q_gen_2298) -> q_gen_2249
<cons, s>(q_gen_2315, q_gen_2303) -> q_gen_2249
<cons, s>(q_gen_2315, q_gen_2327) -> q_gen_2249
<nil, z>() -> q_gen_2249
<a, s>(q_gen_2316) -> q_gen_2259
<a, z>() -> q_gen_2259
<b, z>() -> q_gen_2259
<a, s>(q_gen_2283) -> q_gen_2282
<b, s>(q_gen_2283) -> q_gen_2282
<cons, s>(q_gen_2259, q_gen_2280) -> q_gen_2285
<cons, s>(q_gen_2259, q_gen_2298) -> q_gen_2285
<cons, s>(q_gen_2259, q_gen_2327) -> q_gen_2285
<cons, s>(q_gen_2282, q_gen_2258) -> q_gen_2285
<cons, s>(q_gen_2282, q_gen_2298) -> q_gen_2285
<cons, s>(q_gen_2282, q_gen_2327) -> q_gen_2285
<cons, s>(q_gen_2293, q_gen_2258) -> q_gen_2285
<cons, s>(q_gen_2293, q_gen_2280) -> q_gen_2285
<cons, s>(q_gen_2293, q_gen_2327) -> q_gen_2285
<cons, s>(q_gen_2315, q_gen_2258) -> q_gen_2285
<cons, s>(q_gen_2315, q_gen_2280) -> q_gen_2285
<a, s>(q_gen_2294) -> q_gen_2293
<b, s>(q_gen_2294) -> q_gen_2293
<b, s>(q_gen_2316) -> q_gen_2315
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_2247, q_gen_2260},
Q_f={q_gen_2247},
Delta=
{
<a, a>() -> q_gen_2247
<a, b>() -> q_gen_2247
<b, b>() -> q_gen_2247
<b, a>() -> q_gen_2260
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  leqnat -> 
{{{
Q={q_gen_2244, q_gen_2246, q_gen_2287},
Q_f={q_gen_2244},
Delta=
{
<s>(q_gen_2246) -> q_gen_2246
<z>() -> q_gen_2246
<s, s>(q_gen_2244) -> q_gen_2244
<z, s>(q_gen_2246) -> q_gen_2244
<z, z>() -> q_gen_2244
<s, s>(q_gen_2287) -> q_gen_2287
<s, z>(q_gen_2246) -> q_gen_2287
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 78
() -> length([nil, z]) -> 78
() -> leq([a, y]) -> 78
() -> leq([b, b]) -> 78
() -> leqnat([z, s(nn2)]) -> 78
() -> leqnat([z, z]) -> 78
(insert([x, l, _jj]) /\ length([_jj, _kj]) /\ length([l, _ij])) -> leqnat([_ij, _kj]) -> 100
(insert([x, z, _zi]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _zi)]) -> 81
(length([ll, _ej])) -> length([cons(x, ll), s(_ej)]) -> 102
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 82
(leq([b, a])) -> BOT -> 78
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 78
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 82
(leqnat([s(nn1), z])) -> BOT -> 79
}
Sat witness: Found: ((length([ll, _ej])) -> length([cons(x, ll), s(_ej)]), {
_ej -> s(s(s(z)))  ;  ll -> cons(b, cons(b, cons(b, nil)))  ;  x -> a
})

-------------------------------------------
Step 95, which took 3.791443 s (model generation: 3.784541,  model checking: 0.006902):

Model:
|_
{
insert -> 
{{{
Q={q_gen_2250, q_gen_2251, q_gen_2252, q_gen_2255, q_gen_2256},
Q_f={q_gen_2250},
Delta=
{
<nil>() -> q_gen_2251
<a>() -> q_gen_2252
<b>() -> q_gen_2252
<cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2255
<nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2255
<a, a>() -> q_gen_2256
<a, b>() -> q_gen_2256
<b, a>() -> q_gen_2256
<b, b>() -> q_gen_2256
<a, cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2250
<a, nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2250
<b, cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2250
<b, nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2250
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_2249, q_gen_2258, q_gen_2259, q_gen_2280, q_gen_2281, q_gen_2282, q_gen_2283, q_gen_2285, q_gen_2293, q_gen_2294, q_gen_2298, q_gen_2303, q_gen_2304, q_gen_2315, q_gen_2316, q_gen_2327},
Q_f={q_gen_2249},
Delta=
{
<cons>(q_gen_2281, q_gen_2327) -> q_gen_2258
<nil>() -> q_gen_2258
<cons>(q_gen_2281, q_gen_2258) -> q_gen_2280
<b>() -> q_gen_2281
<z>() -> q_gen_2283
<s>(q_gen_2283) -> q_gen_2294
<cons>(q_gen_2281, q_gen_2280) -> q_gen_2298
<cons>(q_gen_2281, q_gen_2303) -> q_gen_2303
<cons>(q_gen_2304, q_gen_2258) -> q_gen_2303
<cons>(q_gen_2304, q_gen_2280) -> q_gen_2303
<cons>(q_gen_2304, q_gen_2303) -> q_gen_2303
<a>() -> q_gen_2304
<s>(q_gen_2294) -> q_gen_2316
<s>(q_gen_2316) -> q_gen_2316
<cons>(q_gen_2281, q_gen_2298) -> q_gen_2327
<cons, s>(q_gen_2259, q_gen_2258) -> q_gen_2249
<cons, s>(q_gen_2282, q_gen_2280) -> q_gen_2249
<cons, s>(q_gen_2282, q_gen_2303) -> q_gen_2249
<cons, s>(q_gen_2293, q_gen_2298) -> q_gen_2249
<cons, s>(q_gen_2293, q_gen_2303) -> q_gen_2249
<cons, s>(q_gen_2315, q_gen_2303) -> q_gen_2249
<cons, s>(q_gen_2315, q_gen_2327) -> q_gen_2249
<nil, z>() -> q_gen_2249
<a, z>() -> q_gen_2259
<b, z>() -> q_gen_2259
<a, s>(q_gen_2283) -> q_gen_2282
<b, s>(q_gen_2283) -> q_gen_2282
<cons, s>(q_gen_2259, q_gen_2280) -> q_gen_2285
<cons, s>(q_gen_2259, q_gen_2298) -> q_gen_2285
<cons, s>(q_gen_2259, q_gen_2303) -> q_gen_2285
<cons, s>(q_gen_2259, q_gen_2327) -> q_gen_2285
<cons, s>(q_gen_2282, q_gen_2258) -> q_gen_2285
<cons, s>(q_gen_2282, q_gen_2298) -> q_gen_2285
<cons, s>(q_gen_2282, q_gen_2327) -> q_gen_2285
<cons, s>(q_gen_2293, q_gen_2258) -> q_gen_2285
<cons, s>(q_gen_2293, q_gen_2280) -> q_gen_2285
<cons, s>(q_gen_2293, q_gen_2327) -> q_gen_2285
<cons, s>(q_gen_2315, q_gen_2258) -> q_gen_2285
<cons, s>(q_gen_2315, q_gen_2280) -> q_gen_2285
<cons, s>(q_gen_2315, q_gen_2298) -> q_gen_2285
<a, s>(q_gen_2294) -> q_gen_2293
<b, s>(q_gen_2294) -> q_gen_2293
<a, s>(q_gen_2316) -> q_gen_2315
<b, s>(q_gen_2316) -> q_gen_2315
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_2247, q_gen_2260},
Q_f={q_gen_2247},
Delta=
{
<a, a>() -> q_gen_2247
<a, b>() -> q_gen_2247
<b, b>() -> q_gen_2247
<b, a>() -> q_gen_2260
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  leqnat -> 
{{{
Q={q_gen_2244, q_gen_2246, q_gen_2287},
Q_f={q_gen_2244},
Delta=
{
<s>(q_gen_2246) -> q_gen_2246
<z>() -> q_gen_2246
<s, s>(q_gen_2244) -> q_gen_2244
<z, s>(q_gen_2246) -> q_gen_2244
<z, z>() -> q_gen_2244
<s, s>(q_gen_2287) -> q_gen_2287
<s, z>(q_gen_2246) -> q_gen_2287
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 79
() -> length([nil, z]) -> 79
() -> leq([a, y]) -> 79
() -> leq([b, b]) -> 79
() -> leqnat([z, s(nn2)]) -> 79
() -> leqnat([z, z]) -> 79
(insert([x, l, _jj]) /\ length([_jj, _kj]) /\ length([l, _ij])) -> leqnat([_ij, _kj]) -> 103
(insert([x, z, _zi]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _zi)]) -> 82
(length([ll, _ej])) -> length([cons(x, ll), s(_ej)]) -> 102
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 83
(leq([b, a])) -> BOT -> 79
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 79
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 83
(leqnat([s(nn1), z])) -> BOT -> 80
}
Sat witness: Found: ((insert([x, l, _jj]) /\ length([_jj, _kj]) /\ length([l, _ij])) -> leqnat([_ij, _kj]), {
_ij -> s(s(z))  ;  _jj -> cons(b, cons(b, cons(b, cons(b, cons(b, nil)))))  ;  _kj -> s(z)  ;  l -> cons(b, cons(b, cons(b, cons(a, nil))))  ;  x -> a
})

-------------------------------------------
Step 96, which took 4.596551 s (model generation: 4.582279,  model checking: 0.014272):

Model:
|_
{
insert -> 
{{{
Q={q_gen_2250, q_gen_2251, q_gen_2252, q_gen_2255, q_gen_2256},
Q_f={q_gen_2250},
Delta=
{
<nil>() -> q_gen_2251
<a>() -> q_gen_2252
<b>() -> q_gen_2252
<cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2255
<nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2255
<a, a>() -> q_gen_2256
<a, b>() -> q_gen_2256
<b, a>() -> q_gen_2256
<b, b>() -> q_gen_2256
<a, cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2250
<a, nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2250
<b, cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2250
<b, nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2250
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_2249, q_gen_2258, q_gen_2259, q_gen_2280, q_gen_2281, q_gen_2282, q_gen_2283, q_gen_2285, q_gen_2293, q_gen_2294, q_gen_2298, q_gen_2303, q_gen_2304, q_gen_2315, q_gen_2316, q_gen_2327},
Q_f={q_gen_2249},
Delta=
{
<cons>(q_gen_2281, q_gen_2327) -> q_gen_2258
<nil>() -> q_gen_2258
<cons>(q_gen_2281, q_gen_2258) -> q_gen_2280
<cons>(q_gen_2304, q_gen_2258) -> q_gen_2280
<b>() -> q_gen_2281
<z>() -> q_gen_2283
<s>(q_gen_2283) -> q_gen_2294
<cons>(q_gen_2281, q_gen_2280) -> q_gen_2298
<cons>(q_gen_2281, q_gen_2303) -> q_gen_2303
<cons>(q_gen_2304, q_gen_2280) -> q_gen_2303
<a>() -> q_gen_2304
<s>(q_gen_2294) -> q_gen_2316
<s>(q_gen_2316) -> q_gen_2316
<cons>(q_gen_2281, q_gen_2298) -> q_gen_2327
<cons>(q_gen_2304, q_gen_2303) -> q_gen_2327
<cons, s>(q_gen_2259, q_gen_2258) -> q_gen_2249
<cons, s>(q_gen_2282, q_gen_2280) -> q_gen_2249
<cons, s>(q_gen_2293, q_gen_2298) -> q_gen_2249
<cons, s>(q_gen_2293, q_gen_2303) -> q_gen_2249
<cons, s>(q_gen_2315, q_gen_2303) -> q_gen_2249
<cons, s>(q_gen_2315, q_gen_2327) -> q_gen_2249
<nil, z>() -> q_gen_2249
<a, z>() -> q_gen_2259
<b, z>() -> q_gen_2259
<a, s>(q_gen_2283) -> q_gen_2282
<b, s>(q_gen_2283) -> q_gen_2282
<cons, s>(q_gen_2259, q_gen_2280) -> q_gen_2285
<cons, s>(q_gen_2259, q_gen_2298) -> q_gen_2285
<cons, s>(q_gen_2259, q_gen_2303) -> q_gen_2285
<cons, s>(q_gen_2259, q_gen_2327) -> q_gen_2285
<cons, s>(q_gen_2282, q_gen_2258) -> q_gen_2285
<cons, s>(q_gen_2282, q_gen_2298) -> q_gen_2285
<cons, s>(q_gen_2282, q_gen_2303) -> q_gen_2285
<cons, s>(q_gen_2282, q_gen_2327) -> q_gen_2285
<cons, s>(q_gen_2293, q_gen_2258) -> q_gen_2285
<cons, s>(q_gen_2293, q_gen_2280) -> q_gen_2285
<cons, s>(q_gen_2293, q_gen_2327) -> q_gen_2285
<cons, s>(q_gen_2315, q_gen_2258) -> q_gen_2285
<cons, s>(q_gen_2315, q_gen_2280) -> q_gen_2285
<cons, s>(q_gen_2315, q_gen_2298) -> q_gen_2285
<a, s>(q_gen_2294) -> q_gen_2293
<b, s>(q_gen_2294) -> q_gen_2293
<a, s>(q_gen_2316) -> q_gen_2315
<b, s>(q_gen_2316) -> q_gen_2315
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_2247, q_gen_2260},
Q_f={q_gen_2247},
Delta=
{
<a, a>() -> q_gen_2247
<a, b>() -> q_gen_2247
<b, b>() -> q_gen_2247
<b, a>() -> q_gen_2260
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  leqnat -> 
{{{
Q={q_gen_2244, q_gen_2246, q_gen_2287},
Q_f={q_gen_2244},
Delta=
{
<s>(q_gen_2246) -> q_gen_2246
<z>() -> q_gen_2246
<s, s>(q_gen_2244) -> q_gen_2244
<z, s>(q_gen_2246) -> q_gen_2244
<z, z>() -> q_gen_2244
<s, s>(q_gen_2287) -> q_gen_2287
<s, z>(q_gen_2246) -> q_gen_2287
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 80
() -> length([nil, z]) -> 80
() -> leq([a, y]) -> 80
() -> leq([b, b]) -> 80
() -> leqnat([z, s(nn2)]) -> 80
() -> leqnat([z, z]) -> 80
(insert([x, l, _jj]) /\ length([_jj, _kj]) /\ length([l, _ij])) -> leqnat([_ij, _kj]) -> 103
(insert([x, z, _zi]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _zi)]) -> 83
(length([ll, _ej])) -> length([cons(x, ll), s(_ej)]) -> 105
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 84
(leq([b, a])) -> BOT -> 80
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 80
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 84
(leqnat([s(nn1), z])) -> BOT -> 81
}
Sat witness: Found: ((length([ll, _ej])) -> length([cons(x, ll), s(_ej)]), {
_ej -> s(s(s(s(z))))  ;  ll -> cons(b, cons(b, cons(b, cons(a, nil))))  ;  x -> b
})

-------------------------------------------
Step 97, which took 3.466743 s (model generation: 3.449127,  model checking: 0.017616):

Model:
|_
{
insert -> 
{{{
Q={q_gen_2250, q_gen_2251, q_gen_2252, q_gen_2255, q_gen_2256},
Q_f={q_gen_2250},
Delta=
{
<nil>() -> q_gen_2251
<a>() -> q_gen_2252
<b>() -> q_gen_2252
<cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2255
<nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2255
<a, a>() -> q_gen_2256
<a, b>() -> q_gen_2256
<b, a>() -> q_gen_2256
<b, b>() -> q_gen_2256
<a, cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2250
<a, nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2250
<b, cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2250
<b, nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2250
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_2249, q_gen_2258, q_gen_2259, q_gen_2280, q_gen_2281, q_gen_2282, q_gen_2283, q_gen_2285, q_gen_2293, q_gen_2294, q_gen_2298, q_gen_2303, q_gen_2304, q_gen_2315, q_gen_2316, q_gen_2327},
Q_f={q_gen_2249},
Delta=
{
<nil>() -> q_gen_2258
<cons>(q_gen_2281, q_gen_2258) -> q_gen_2280
<b>() -> q_gen_2281
<s>(q_gen_2316) -> q_gen_2283
<z>() -> q_gen_2283
<s>(q_gen_2283) -> q_gen_2294
<cons>(q_gen_2281, q_gen_2280) -> q_gen_2298
<cons>(q_gen_2281, q_gen_2303) -> q_gen_2303
<cons>(q_gen_2304, q_gen_2258) -> q_gen_2303
<cons>(q_gen_2304, q_gen_2280) -> q_gen_2303
<cons>(q_gen_2304, q_gen_2303) -> q_gen_2303
<a>() -> q_gen_2304
<s>(q_gen_2294) -> q_gen_2316
<cons>(q_gen_2281, q_gen_2298) -> q_gen_2327
<cons>(q_gen_2281, q_gen_2327) -> q_gen_2327
<cons>(q_gen_2304, q_gen_2327) -> q_gen_2327
<cons, s>(q_gen_2259, q_gen_2258) -> q_gen_2249
<cons, s>(q_gen_2259, q_gen_2303) -> q_gen_2249
<cons, s>(q_gen_2282, q_gen_2280) -> q_gen_2249
<cons, s>(q_gen_2282, q_gen_2303) -> q_gen_2249
<cons, s>(q_gen_2293, q_gen_2298) -> q_gen_2249
<cons, s>(q_gen_2293, q_gen_2303) -> q_gen_2249
<cons, s>(q_gen_2315, q_gen_2298) -> q_gen_2249
<cons, s>(q_gen_2315, q_gen_2303) -> q_gen_2249
<cons, s>(q_gen_2315, q_gen_2327) -> q_gen_2249
<nil, z>() -> q_gen_2249
<a, z>() -> q_gen_2259
<b, z>() -> q_gen_2259
<a, s>(q_gen_2283) -> q_gen_2282
<b, s>(q_gen_2283) -> q_gen_2282
<cons, s>(q_gen_2259, q_gen_2280) -> q_gen_2285
<cons, s>(q_gen_2259, q_gen_2298) -> q_gen_2285
<cons, s>(q_gen_2259, q_gen_2327) -> q_gen_2285
<cons, s>(q_gen_2282, q_gen_2258) -> q_gen_2285
<cons, s>(q_gen_2282, q_gen_2298) -> q_gen_2285
<cons, s>(q_gen_2282, q_gen_2327) -> q_gen_2285
<cons, s>(q_gen_2293, q_gen_2258) -> q_gen_2285
<cons, s>(q_gen_2293, q_gen_2280) -> q_gen_2285
<cons, s>(q_gen_2293, q_gen_2327) -> q_gen_2285
<cons, s>(q_gen_2315, q_gen_2258) -> q_gen_2285
<cons, s>(q_gen_2315, q_gen_2280) -> q_gen_2285
<a, s>(q_gen_2294) -> q_gen_2293
<b, s>(q_gen_2294) -> q_gen_2293
<a, s>(q_gen_2316) -> q_gen_2315
<b, s>(q_gen_2316) -> q_gen_2315
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_2247, q_gen_2260},
Q_f={q_gen_2247},
Delta=
{
<a, a>() -> q_gen_2247
<a, b>() -> q_gen_2247
<b, b>() -> q_gen_2247
<b, a>() -> q_gen_2260
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  leqnat -> 
{{{
Q={q_gen_2244, q_gen_2246, q_gen_2287},
Q_f={q_gen_2244},
Delta=
{
<s>(q_gen_2246) -> q_gen_2246
<z>() -> q_gen_2246
<s, s>(q_gen_2244) -> q_gen_2244
<z, s>(q_gen_2246) -> q_gen_2244
<z, z>() -> q_gen_2244
<s, s>(q_gen_2287) -> q_gen_2287
<s, z>(q_gen_2246) -> q_gen_2287
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 81
() -> length([nil, z]) -> 81
() -> leq([a, y]) -> 81
() -> leq([b, b]) -> 81
() -> leqnat([z, s(nn2)]) -> 81
() -> leqnat([z, z]) -> 81
(insert([x, l, _jj]) /\ length([_jj, _kj]) /\ length([l, _ij])) -> leqnat([_ij, _kj]) -> 106
(insert([x, z, _zi]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _zi)]) -> 84
(length([ll, _ej])) -> length([cons(x, ll), s(_ej)]) -> 105
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 85
(leq([b, a])) -> BOT -> 81
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 81
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 85
(leqnat([s(nn1), z])) -> BOT -> 82
}
Sat witness: Found: ((insert([x, l, _jj]) /\ length([_jj, _kj]) /\ length([l, _ij])) -> leqnat([_ij, _kj]), {
_ij -> s(s(z))  ;  _jj -> cons(b, cons(b, cons(a, nil)))  ;  _kj -> s(z)  ;  l -> cons(b, cons(a, nil))  ;  x -> b
})

-------------------------------------------
Step 98, which took 2.935363 s (model generation: 2.919973,  model checking: 0.015390):

Model:
|_
{
insert -> 
{{{
Q={q_gen_2250, q_gen_2251, q_gen_2252, q_gen_2255, q_gen_2256},
Q_f={q_gen_2250},
Delta=
{
<nil>() -> q_gen_2251
<a>() -> q_gen_2252
<b>() -> q_gen_2252
<cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2255
<nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2255
<a, a>() -> q_gen_2256
<a, b>() -> q_gen_2256
<b, a>() -> q_gen_2256
<b, b>() -> q_gen_2256
<a, cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2250
<a, nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2250
<b, cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2250
<b, nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2250
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_2249, q_gen_2258, q_gen_2259, q_gen_2280, q_gen_2281, q_gen_2282, q_gen_2283, q_gen_2285, q_gen_2293, q_gen_2294, q_gen_2298, q_gen_2303, q_gen_2304, q_gen_2315, q_gen_2316, q_gen_2327},
Q_f={q_gen_2249},
Delta=
{
<nil>() -> q_gen_2258
<cons>(q_gen_2281, q_gen_2258) -> q_gen_2280
<b>() -> q_gen_2281
<s>(q_gen_2316) -> q_gen_2283
<z>() -> q_gen_2283
<s>(q_gen_2283) -> q_gen_2294
<cons>(q_gen_2281, q_gen_2280) -> q_gen_2298
<cons>(q_gen_2281, q_gen_2303) -> q_gen_2303
<cons>(q_gen_2304, q_gen_2258) -> q_gen_2303
<cons>(q_gen_2304, q_gen_2280) -> q_gen_2303
<cons>(q_gen_2304, q_gen_2303) -> q_gen_2303
<cons>(q_gen_2304, q_gen_2327) -> q_gen_2303
<a>() -> q_gen_2304
<s>(q_gen_2294) -> q_gen_2316
<cons>(q_gen_2281, q_gen_2298) -> q_gen_2327
<cons>(q_gen_2281, q_gen_2327) -> q_gen_2327
<cons, s>(q_gen_2259, q_gen_2258) -> q_gen_2249
<cons, s>(q_gen_2282, q_gen_2280) -> q_gen_2249
<cons, s>(q_gen_2282, q_gen_2303) -> q_gen_2249
<cons, s>(q_gen_2293, q_gen_2298) -> q_gen_2249
<cons, s>(q_gen_2293, q_gen_2303) -> q_gen_2249
<cons, s>(q_gen_2315, q_gen_2303) -> q_gen_2249
<cons, s>(q_gen_2315, q_gen_2327) -> q_gen_2249
<nil, z>() -> q_gen_2249
<a, z>() -> q_gen_2259
<b, z>() -> q_gen_2259
<a, s>(q_gen_2283) -> q_gen_2282
<b, s>(q_gen_2283) -> q_gen_2282
<cons, s>(q_gen_2259, q_gen_2280) -> q_gen_2285
<cons, s>(q_gen_2259, q_gen_2298) -> q_gen_2285
<cons, s>(q_gen_2259, q_gen_2303) -> q_gen_2285
<cons, s>(q_gen_2259, q_gen_2327) -> q_gen_2285
<cons, s>(q_gen_2282, q_gen_2258) -> q_gen_2285
<cons, s>(q_gen_2282, q_gen_2298) -> q_gen_2285
<cons, s>(q_gen_2282, q_gen_2327) -> q_gen_2285
<cons, s>(q_gen_2293, q_gen_2258) -> q_gen_2285
<cons, s>(q_gen_2293, q_gen_2280) -> q_gen_2285
<cons, s>(q_gen_2293, q_gen_2327) -> q_gen_2285
<cons, s>(q_gen_2315, q_gen_2258) -> q_gen_2285
<cons, s>(q_gen_2315, q_gen_2280) -> q_gen_2285
<cons, s>(q_gen_2315, q_gen_2298) -> q_gen_2285
<a, s>(q_gen_2294) -> q_gen_2293
<b, s>(q_gen_2294) -> q_gen_2293
<a, s>(q_gen_2316) -> q_gen_2315
<b, s>(q_gen_2316) -> q_gen_2315
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_2247, q_gen_2260},
Q_f={q_gen_2247},
Delta=
{
<a, a>() -> q_gen_2247
<a, b>() -> q_gen_2247
<b, b>() -> q_gen_2247
<b, a>() -> q_gen_2260
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  leqnat -> 
{{{
Q={q_gen_2244, q_gen_2246, q_gen_2287},
Q_f={q_gen_2244},
Delta=
{
<s>(q_gen_2246) -> q_gen_2246
<z>() -> q_gen_2246
<s, s>(q_gen_2244) -> q_gen_2244
<z, s>(q_gen_2246) -> q_gen_2244
<z, z>() -> q_gen_2244
<s, s>(q_gen_2287) -> q_gen_2287
<s, z>(q_gen_2246) -> q_gen_2287
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 82
() -> length([nil, z]) -> 82
() -> leq([a, y]) -> 82
() -> leq([b, b]) -> 82
() -> leqnat([z, s(nn2)]) -> 82
() -> leqnat([z, z]) -> 82
(insert([x, l, _jj]) /\ length([_jj, _kj]) /\ length([l, _ij])) -> leqnat([_ij, _kj]) -> 106
(insert([x, z, _zi]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _zi)]) -> 85
(length([ll, _ej])) -> length([cons(x, ll), s(_ej)]) -> 108
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 86
(leq([b, a])) -> BOT -> 82
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 82
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 86
(leqnat([s(nn1), z])) -> BOT -> 83
}
Sat witness: Found: ((length([ll, _ej])) -> length([cons(x, ll), s(_ej)]), {
_ej -> s(s(s(s(z))))  ;  ll -> cons(b, cons(b, cons(b, cons(b, nil))))  ;  x -> b
})

-------------------------------------------
Step 99, which took 2.811252 s (model generation: 2.798457,  model checking: 0.012795):

Model:
|_
{
insert -> 
{{{
Q={q_gen_2250, q_gen_2251, q_gen_2252, q_gen_2255, q_gen_2256},
Q_f={q_gen_2250},
Delta=
{
<nil>() -> q_gen_2251
<a>() -> q_gen_2252
<b>() -> q_gen_2252
<cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2255
<nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2255
<a, a>() -> q_gen_2256
<a, b>() -> q_gen_2256
<b, a>() -> q_gen_2256
<b, b>() -> q_gen_2256
<a, cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2250
<a, nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2250
<b, cons, cons>(q_gen_2256, q_gen_2255) -> q_gen_2250
<b, nil, cons>(q_gen_2252, q_gen_2251) -> q_gen_2250
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_2249, q_gen_2258, q_gen_2259, q_gen_2280, q_gen_2281, q_gen_2282, q_gen_2283, q_gen_2285, q_gen_2291, q_gen_2293, q_gen_2294, q_gen_2298, q_gen_2314, q_gen_2315, q_gen_2316, q_gen_2353, q_gen_2355},
Q_f={q_gen_2249},
Delta=
{
<nil>() -> q_gen_2258
<cons>(q_gen_2281, q_gen_2258) -> q_gen_2280
<a>() -> q_gen_2281
<b>() -> q_gen_2281
<z>() -> q_gen_2283
<s>(q_gen_2283) -> q_gen_2294
<cons>(q_gen_2281, q_gen_2280) -> q_gen_2298
<cons>(q_gen_2281, q_gen_2355) -> q_gen_2298
<cons>(q_gen_2281, q_gen_2298) -> q_gen_2314
<s>(q_gen_2294) -> q_gen_2316
<s>(q_gen_2316) -> q_gen_2353
<cons>(q_gen_2281, q_gen_2314) -> q_gen_2355
<cons, s>(q_gen_2259, q_gen_2258) -> q_gen_2249
<cons, s>(q_gen_2282, q_gen_2280) -> q_gen_2249
<cons, s>(q_gen_2291, q_gen_2280) -> q_gen_2249
<cons, s>(q_gen_2291, q_gen_2355) -> q_gen_2249
<cons, s>(q_gen_2293, q_gen_2298) -> q_gen_2249
<cons, s>(q_gen_2293, q_gen_2314) -> q_gen_2249
<cons, s>(q_gen_2315, q_gen_2314) -> q_gen_2249
<cons, s>(q_gen_2315, q_gen_2355) -> q_gen_2249
<nil, z>() -> q_gen_2249
<a, z>() -> q_gen_2259
<b, z>() -> q_gen_2259
<b, s>(q_gen_2283) -> q_gen_2282
<cons, s>(q_gen_2259, q_gen_2280) -> q_gen_2285
<cons, s>(q_gen_2259, q_gen_2298) -> q_gen_2285
<cons, s>(q_gen_2259, q_gen_2314) -> q_gen_2285
<cons, s>(q_gen_2259, q_gen_2355) -> q_gen_2285
<cons, s>(q_gen_2282, q_gen_2258) -> q_gen_2285
<cons, s>(q_gen_2282, q_gen_2298) -> q_gen_2285
<cons, s>(q_gen_2282, q_gen_2314) -> q_gen_2285
<cons, s>(q_gen_2282, q_gen_2355) -> q_gen_2285
<cons, s>(q_gen_2291, q_gen_2258) -> q_gen_2285
<cons, s>(q_gen_2291, q_gen_2298) -> q_gen_2285
<cons, s>(q_gen_2291, q_gen_2314) -> q_gen_2285
<cons, s>(q_gen_2293, q_gen_2258) -> q_gen_2285
<cons, s>(q_gen_2293, q_gen_2280) -> q_gen_2285
<cons, s>(q_gen_2293, q_gen_2355) -> q_gen_2285
<cons, s>(q_gen_2315, q_gen_2258) -> q_gen_2285
<cons, s>(q_gen_2315, q_gen_2280) -> q_gen_2285
<cons, s>(q_gen_2315, q_gen_2298) -> q_gen_2285
<a, s>(q_gen_2283) -> q_gen_2291
<a, s>(q_gen_2353) -> q_gen_2291
<b, s>(q_gen_2353) -> q_gen_2291
<a, s>(q_gen_2294) -> q_gen_2293
<b, s>(q_gen_2294) -> q_gen_2293
<a, s>(q_gen_2316) -> q_gen_2315
<b, s>(q_gen_2316) -> q_gen_2315
}

Datatype: <eltlist, nat>
Convolution form: left
}}}
  ;  leq -> 
{{{
Q={q_gen_2247, q_gen_2260},
Q_f={q_gen_2247},
Delta=
{
<a, a>() -> q_gen_2247
<a, b>() -> q_gen_2247
<b, b>() -> q_gen_2247
<b, a>() -> q_gen_2260
}

Datatype: <elt, elt>
Convolution form: left
}}}
  ;  leqnat -> 
{{{
Q={q_gen_2244, q_gen_2246, q_gen_2287},
Q_f={q_gen_2244},
Delta=
{
<s>(q_gen_2246) -> q_gen_2246
<z>() -> q_gen_2246
<s, s>(q_gen_2244) -> q_gen_2244
<z, s>(q_gen_2246) -> q_gen_2244
<z, z>() -> q_gen_2244
<s, s>(q_gen_2287) -> q_gen_2287
<s, z>(q_gen_2246) -> q_gen_2287
}

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

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

Teacher's answer:
New clause system:
{
() -> insert([x, nil, cons(x, nil)]) -> 83
() -> length([nil, z]) -> 83
() -> leq([a, y]) -> 83
() -> leq([b, b]) -> 83
() -> leqnat([z, s(nn2)]) -> 83
() -> leqnat([z, z]) -> 83
(insert([x, l, _jj]) /\ length([_jj, _kj]) /\ length([l, _ij])) -> leqnat([_ij, _kj]) -> 109
(insert([x, z, _zi]) /\ not leq([x, y])) -> insert([x, cons(y, z), cons(y, _zi)]) -> 86
(length([ll, _ej])) -> length([cons(x, ll), s(_ej)]) -> 108
(leq([x, y])) -> insert([x, cons(y, z), cons(x, cons(y, z))]) -> 87
(leq([b, a])) -> BOT -> 83
(leqnat([nn1, nn2])) -> leqnat([s(nn1), s(nn2)]) -> 83
(leqnat([s(nn1), s(nn2)])) -> leqnat([nn1, nn2]) -> 87
(leqnat([s(nn1), z])) -> BOT -> 84
}
Sat witness: Found: ((insert([x, l, _jj]) /\ length([_jj, _kj]) /\ length([l, _ij])) -> leqnat([_ij, _kj]), {
_ij -> s(s(s(z)))  ;  _jj -> cons(a, cons(b, cons(b, cons(b, cons(b, nil)))))  ;  _kj -> s(s(z))  ;  l -> cons(b, cons(b, cons(b, cons(b, nil))))  ;  x -> a
})

Total time: 63.090572
Reason for stopping: DontKnow. Stopped because: timeout