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:
{
(append, F:
{() -> append([nil, l2, l2])
(append([t1, l2, _ix])) -> append([cons(h1, t1), l2, cons(h1, _ix)])}
(append([_jx, _kx, _lx]) /\ append([_jx, _kx, _mx])) -> eq_eltlist([_lx, _mx])
)
(length, F:
{() -> length([nil, z])
(length([ll, _nx])) -> length([cons(x, ll), s(_nx)])}
(length([_ox, _px]) /\ length([_ox, _qx])) -> eq_nat([_px, _qx])
)
}

properties:
{(append([l1, l2, _rx]) /\ append([l2, l1, _tx]) /\ length([_rx, _sx]) /\ length([_tx, _ux])) -> eq_nat([_sx, _ux])}


over-approximation: {append, length}
under-approximation: {}

Clause system for inference is:

{
() -> append([nil, l2, l2]) -> 0
() -> length([nil, z]) -> 0
(append([l1, l2, _rx]) /\ append([l2, l1, _tx]) /\ length([_rx, _sx]) /\ length([_tx, _ux])) -> eq_nat([_sx, _ux]) -> 0
(append([t1, l2, _ix])) -> append([cons(h1, t1), l2, cons(h1, _ix)]) -> 0
(length([ll, _nx])) -> length([cons(x, ll), s(_nx)]) -> 0
}


Solving took 73.946814 seconds.
DontKnow. Stopped because: timeout
Working model:
|_
{
append -> 
{{{
Q={q_gen_6178, q_gen_6182, q_gen_6183, q_gen_6184, q_gen_6185, q_gen_6186, q_gen_6187, q_gen_6190, q_gen_6191, q_gen_6192, q_gen_6193, q_gen_6194, q_gen_6195, q_gen_6201, q_gen_6202, q_gen_6203, q_gen_6204, q_gen_6209, q_gen_6210, q_gen_6211, q_gen_6212, q_gen_6213, q_gen_6214, q_gen_6219, q_gen_6220, q_gen_6221, q_gen_6222, q_gen_6223, q_gen_6224, q_gen_6229, q_gen_6230, q_gen_6231, q_gen_6232, q_gen_6233, q_gen_6240, q_gen_6241, q_gen_6242, q_gen_6243, q_gen_6244, q_gen_6245, q_gen_6246, q_gen_6249, q_gen_6250, q_gen_6251, q_gen_6256, q_gen_6257, q_gen_6258, q_gen_6259, q_gen_6260, q_gen_6261, q_gen_6262, q_gen_6263, q_gen_6265, q_gen_6266, q_gen_6267, q_gen_6268, q_gen_6269, q_gen_6270, q_gen_6271, q_gen_6272, q_gen_6273, q_gen_6274, q_gen_6275, q_gen_6276, q_gen_6277, q_gen_6278, q_gen_6279, q_gen_6281, q_gen_6282, q_gen_6283, q_gen_6284, q_gen_6285, q_gen_6286, q_gen_6287, q_gen_6289, q_gen_6290, q_gen_6293, q_gen_6294, q_gen_6295, q_gen_6296, q_gen_6299, q_gen_6300, q_gen_6301, q_gen_6302, q_gen_6303, q_gen_6304, q_gen_6305, q_gen_6306, q_gen_6307, q_gen_6319, q_gen_6320, q_gen_6321, q_gen_6322, q_gen_6323, q_gen_6324, q_gen_6325, q_gen_6330, q_gen_6331, q_gen_6332, q_gen_6333, q_gen_6334, q_gen_6335, q_gen_6336, q_gen_6337, q_gen_6339, q_gen_6340, q_gen_6341, q_gen_6342, q_gen_6343, q_gen_6344, q_gen_6345, q_gen_6346, q_gen_6347, q_gen_6348, q_gen_6349, q_gen_6351, q_gen_6352, q_gen_6353, q_gen_6354, q_gen_6355, q_gen_6356, q_gen_6357},
Q_f={},
Delta=
{
<nil>() -> q_gen_6193
<b>() -> q_gen_6194
<a>() -> q_gen_6212
<cons>(q_gen_6194, q_gen_6193) -> q_gen_6232
<cons>(q_gen_6194, q_gen_6232) -> q_gen_6323
<nil, nil>() -> q_gen_6183
<b, b>() -> q_gen_6184
<cons, cons>(q_gen_6187, q_gen_6183) -> q_gen_6186
<a, a>() -> q_gen_6187
<nil, cons>(q_gen_6194, q_gen_6193) -> q_gen_6203
<nil, cons>(q_gen_6212, q_gen_6193) -> q_gen_6221
<cons, cons>(q_gen_6184, q_gen_6261) -> q_gen_6260
<cons, cons>(q_gen_6184, q_gen_6183) -> q_gen_6261
<cons, cons>(q_gen_6184, q_gen_6203) -> q_gen_6271
<a, b>() -> q_gen_6275
<b, a>() -> q_gen_6284
<nil, cons>(q_gen_6194, q_gen_6232) -> q_gen_6286
<cons, cons>(q_gen_6275, q_gen_6286) -> q_gen_6331
<nil, cons>(q_gen_6194, q_gen_6323) -> q_gen_6334
<cons, cons>(q_gen_6184, q_gen_6286) -> q_gen_6336
<cons, cons>(q_gen_6184, q_gen_6186) -> q_gen_6357
<nil, nil, nil>() -> q_gen_6178
<cons, nil, cons>(q_gen_6184, q_gen_6183) -> q_gen_6182
<nil, cons, cons>(q_gen_6187, q_gen_6186) -> q_gen_6185
<nil, cons, cons>(q_gen_6184, q_gen_6183) -> q_gen_6190
<cons, cons, cons>(q_gen_6195, q_gen_6192) -> q_gen_6191
<nil, nil, cons>(q_gen_6194, q_gen_6193) -> q_gen_6192
<b, b, b>() -> q_gen_6195
<cons, cons, cons>(q_gen_6204, q_gen_6202) -> q_gen_6201
<cons, nil, cons>(q_gen_6184, q_gen_6203) -> q_gen_6202
<a, b, a>() -> q_gen_6204
<nil, cons, cons>(q_gen_6187, q_gen_6183) -> q_gen_6209
<cons, cons, cons>(q_gen_6213, q_gen_6211) -> q_gen_6210
<nil, nil, cons>(q_gen_6212, q_gen_6193) -> q_gen_6211
<b, a, b>() -> q_gen_6213
<cons, cons, cons>(q_gen_6195, q_gen_6178) -> q_gen_6214
<cons, cons, cons>(q_gen_6222, q_gen_6220) -> q_gen_6219
<cons, nil, cons>(q_gen_6184, q_gen_6221) -> q_gen_6220
<a, a, a>() -> q_gen_6222
<cons, cons, cons>(q_gen_6204, q_gen_6192) -> q_gen_6223
<cons, cons, cons>(q_gen_6213, q_gen_6192) -> q_gen_6224
<nil, cons, cons>(q_gen_6184, q_gen_6203) -> q_gen_6229
<cons, cons, cons>(q_gen_6204, q_gen_6231) -> q_gen_6230
<nil, nil, cons>(q_gen_6194, q_gen_6232) -> q_gen_6231
<cons, cons, cons>(q_gen_6195, q_gen_6231) -> q_gen_6233
<cons, cons, cons>(q_gen_6204, q_gen_6241) -> q_gen_6240
<cons, cons, cons>(q_gen_6204, q_gen_6178) -> q_gen_6241
<cons, cons, cons>(q_gen_6204, q_gen_6243) -> q_gen_6242
<cons, cons, cons>(q_gen_6204, q_gen_6244) -> q_gen_6243
<cons, nil, cons>(q_gen_6187, q_gen_6183) -> q_gen_6244
<cons, cons, cons>(q_gen_6204, q_gen_6191) -> q_gen_6245
<cons, cons, cons>(q_gen_6213, q_gen_6233) -> q_gen_6246
<cons, cons, cons>(q_gen_6204, q_gen_6229) -> q_gen_6249
<cons, cons, cons>(q_gen_6204, q_gen_6230) -> q_gen_6250
<nil, nil, cons>(q_gen_6212, q_gen_6232) -> q_gen_6251
<cons, cons, cons>(q_gen_6222, q_gen_6257) -> q_gen_6256
<nil, cons, cons>(q_gen_6187, q_gen_6221) -> q_gen_6257
<cons, cons, cons>(q_gen_6195, q_gen_6244) -> q_gen_6258
<nil, cons, cons>(q_gen_6184, q_gen_6260) -> q_gen_6259
<cons, cons, cons>(q_gen_6222, q_gen_6233) -> q_gen_6262
<cons, cons, cons>(q_gen_6222, q_gen_6191) -> q_gen_6263
<cons, cons, cons>(q_gen_6195, q_gen_6266) -> q_gen_6265
<cons, nil, cons>(q_gen_6187, q_gen_6186) -> q_gen_6266
<cons, cons, cons>(q_gen_6213, q_gen_6231) -> q_gen_6267
<cons, cons, cons>(q_gen_6213, q_gen_6202) -> q_gen_6268
<cons, cons, cons>(q_gen_6222, q_gen_6270) -> q_gen_6269
<cons, nil, cons>(q_gen_6184, q_gen_6271) -> q_gen_6270
<nil, cons, cons>(q_gen_6184, q_gen_6186) -> q_gen_6272
<cons, cons, cons>(q_gen_6204, q_gen_6274) -> q_gen_6273
<nil, cons, cons>(q_gen_6275, q_gen_6221) -> q_gen_6274
<cons, cons, cons>(q_gen_6222, q_gen_6192) -> q_gen_6276
<cons, cons, cons>(q_gen_6204, q_gen_6209) -> q_gen_6277
<cons, cons, cons>(q_gen_6195, q_gen_6279) -> q_gen_6278
<cons, cons, cons>(q_gen_6222, q_gen_6211) -> q_gen_6279
<nil, cons, cons>(q_gen_6187, q_gen_6261) -> q_gen_6281
<cons, cons, cons>(q_gen_6222, q_gen_6283) -> q_gen_6282
<nil, cons, cons>(q_gen_6284, q_gen_6203) -> q_gen_6283
<cons, nil, cons>(q_gen_6187, q_gen_6286) -> q_gen_6285
<nil, cons, cons>(q_gen_6187, q_gen_6203) -> q_gen_6287
<cons, cons, cons>(q_gen_6204, q_gen_6182) -> q_gen_6289
<cons, cons, cons>(q_gen_6213, q_gen_6190) -> q_gen_6290
<cons, nil, cons>(q_gen_6184, q_gen_6261) -> q_gen_6293
<nil, cons, cons>(q_gen_6284, q_gen_6271) -> q_gen_6294
<cons, nil, cons>(q_gen_6184, q_gen_6186) -> q_gen_6295
<cons, cons, cons>(q_gen_6222, q_gen_6231) -> q_gen_6296
<cons, cons, cons>(q_gen_6204, q_gen_6300) -> q_gen_6299
<cons, cons, cons>(q_gen_6195, q_gen_6190) -> q_gen_6300
<cons, cons, cons>(q_gen_6213, q_gen_6302) -> q_gen_6301
<cons, cons, cons>(q_gen_6195, q_gen_6202) -> q_gen_6302
<cons, cons, cons>(q_gen_6222, q_gen_6304) -> q_gen_6303
<cons, nil, cons>(q_gen_6187, q_gen_6221) -> q_gen_6304
<cons, cons, cons>(q_gen_6213, q_gen_6283) -> q_gen_6305
<cons, cons, cons>(q_gen_6213, q_gen_6307) -> q_gen_6306
<cons, cons, cons>(q_gen_6195, q_gen_6251) -> q_gen_6307
<cons, cons, cons>(q_gen_6222, q_gen_6320) -> q_gen_6319
<cons, cons, cons>(q_gen_6195, q_gen_6321) -> q_gen_6320
<cons, cons, cons>(q_gen_6195, q_gen_6322) -> q_gen_6321
<nil, nil, cons>(q_gen_6194, q_gen_6323) -> q_gen_6322
<cons, cons, cons>(q_gen_6222, q_gen_6325) -> q_gen_6324
<cons, cons, cons>(q_gen_6195, q_gen_6233) -> q_gen_6325
<nil, cons, cons>(q_gen_6284, q_gen_6331) -> q_gen_6330
<cons, cons, cons>(q_gen_6195, q_gen_6333) -> q_gen_6332
<nil, cons, cons>(q_gen_6187, q_gen_6334) -> q_gen_6333
<cons, nil, cons>(q_gen_6184, q_gen_6336) -> q_gen_6335
<nil, cons, cons>(q_gen_6284, q_gen_6261) -> q_gen_6337
<cons, cons, cons>(q_gen_6222, q_gen_6340) -> q_gen_6339
<cons, cons, cons>(q_gen_6195, q_gen_6341) -> q_gen_6340
<cons, nil, cons>(q_gen_6184, q_gen_6286) -> q_gen_6341
<cons, nil, cons>(q_gen_6275, q_gen_6183) -> q_gen_6342
<nil, cons, cons>(q_gen_6187, q_gen_6286) -> q_gen_6343
<cons, cons, cons>(q_gen_6213, q_gen_6345) -> q_gen_6344
<cons, cons, cons>(q_gen_6204, q_gen_6346) -> q_gen_6345
<nil, cons, cons>(q_gen_6284, q_gen_6183) -> q_gen_6346
<cons, cons, cons>(q_gen_6222, q_gen_6348) -> q_gen_6347
<cons, cons, cons>(q_gen_6195, q_gen_6349) -> q_gen_6348
<cons, cons, cons>(q_gen_6204, q_gen_6211) -> q_gen_6349
<cons, cons, cons>(q_gen_6213, q_gen_6352) -> q_gen_6351
<cons, cons, cons>(q_gen_6222, q_gen_6349) -> q_gen_6352
<cons, cons, cons>(q_gen_6222, q_gen_6354) -> q_gen_6353
<cons, cons, cons>(q_gen_6213, q_gen_6355) -> q_gen_6354
<cons, cons, cons>(q_gen_6204, q_gen_6304) -> q_gen_6355
<nil, cons, cons>(q_gen_6187, q_gen_6357) -> q_gen_6356
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_6177, q_gen_6179, q_gen_6180, q_gen_6181, q_gen_6188, q_gen_6189, q_gen_6196, q_gen_6197, q_gen_6198, q_gen_6199, q_gen_6200, q_gen_6205, q_gen_6206, q_gen_6207, q_gen_6208, q_gen_6215, q_gen_6216, q_gen_6217, q_gen_6218, q_gen_6225, q_gen_6226, q_gen_6227, q_gen_6228, q_gen_6234, q_gen_6235, q_gen_6236, q_gen_6237, q_gen_6238, q_gen_6239, q_gen_6247, q_gen_6248, q_gen_6252, q_gen_6253, q_gen_6254, q_gen_6255, q_gen_6264, q_gen_6280, q_gen_6288, q_gen_6291, q_gen_6292, q_gen_6297, q_gen_6298, q_gen_6308, q_gen_6309, q_gen_6310, q_gen_6311, q_gen_6312, q_gen_6313, q_gen_6314, q_gen_6315, q_gen_6316, q_gen_6317, q_gen_6318, q_gen_6326, q_gen_6327, q_gen_6328, q_gen_6329, q_gen_6338, q_gen_6350},
Q_f={},
Delta=
{
<nil>() -> q_gen_6180
<cons>(q_gen_6198, q_gen_6180) -> q_gen_6197
<b>() -> q_gen_6198
<z>() -> q_gen_6200
<cons>(q_gen_6208, q_gen_6180) -> q_gen_6207
<a>() -> q_gen_6208
<cons>(q_gen_6198, q_gen_6197) -> q_gen_6216
<s>(q_gen_6200) -> q_gen_6218
<cons>(q_gen_6198, q_gen_6216) -> q_gen_6237
<s>(q_gen_6218) -> q_gen_6239
<s>(q_gen_6239) -> q_gen_6310
<cons>(q_gen_6208, q_gen_6197) -> q_gen_6313
<cons>(q_gen_6208, q_gen_6313) -> q_gen_6318
<cons>(q_gen_6198, q_gen_6328) -> q_gen_6327
<cons>(q_gen_6198, q_gen_6237) -> q_gen_6328
<nil, z>() -> q_gen_6177
<cons, s>(q_gen_6181, q_gen_6180) -> q_gen_6179
<b, z>() -> q_gen_6181
<cons, s>(q_gen_6189, q_gen_6180) -> q_gen_6188
<a, z>() -> q_gen_6189
<cons, s>(q_gen_6199, q_gen_6197) -> q_gen_6196
<b, s>(q_gen_6200) -> q_gen_6199
<cons, s>(q_gen_6181, q_gen_6197) -> q_gen_6205
<cons, s>(q_gen_6199, q_gen_6207) -> q_gen_6206
<cons, s>(q_gen_6217, q_gen_6216) -> q_gen_6215
<b, s>(q_gen_6218) -> q_gen_6217
<cons, s>(q_gen_6189, q_gen_6197) -> q_gen_6225
<cons, s>(q_gen_6199, q_gen_6180) -> q_gen_6226
<cons, s>(q_gen_6228, q_gen_6197) -> q_gen_6227
<a, s>(q_gen_6218) -> q_gen_6228
<cons, s>(q_gen_6199, q_gen_6216) -> q_gen_6234
<cons, s>(q_gen_6217, q_gen_6197) -> q_gen_6235
<cons, s>(q_gen_6238, q_gen_6237) -> q_gen_6236
<b, s>(q_gen_6239) -> q_gen_6238
<cons, s>(q_gen_6189, q_gen_6216) -> q_gen_6247
<cons, s>(q_gen_6199, q_gen_6237) -> q_gen_6248
<cons, s>(q_gen_6253, q_gen_6197) -> q_gen_6252
<a, s>(q_gen_6200) -> q_gen_6253
<cons, s>(q_gen_6253, q_gen_6180) -> q_gen_6254
<cons, s>(q_gen_6217, q_gen_6207) -> q_gen_6255
<cons, s>(q_gen_6253, q_gen_6237) -> q_gen_6264
<cons, s>(q_gen_6228, q_gen_6180) -> q_gen_6280
<cons, s>(q_gen_6228, q_gen_6216) -> q_gen_6288
<cons, s>(q_gen_6238, q_gen_6197) -> q_gen_6291
<cons, s>(q_gen_6217, q_gen_6180) -> q_gen_6292
<cons, s>(q_gen_6298, q_gen_6216) -> q_gen_6297
<a, s>(q_gen_6239) -> q_gen_6298
<cons, s>(q_gen_6309, q_gen_6216) -> q_gen_6308
<a, s>(q_gen_6310) -> q_gen_6309
<cons, s>(q_gen_6298, q_gen_6197) -> q_gen_6311
<cons, s>(q_gen_6314, q_gen_6313) -> q_gen_6312
<b, s>(q_gen_6310) -> q_gen_6314
<cons, s>(q_gen_6228, q_gen_6237) -> q_gen_6315
<cons, s>(q_gen_6228, q_gen_6313) -> q_gen_6316
<cons, s>(q_gen_6298, q_gen_6318) -> q_gen_6317
<cons, s>(q_gen_6228, q_gen_6327) -> q_gen_6326
<cons, s>(q_gen_6253, q_gen_6328) -> q_gen_6329
<cons, s>(q_gen_6217, q_gen_6237) -> q_gen_6338
<cons, s>(q_gen_6181, q_gen_6237) -> q_gen_6350
}

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

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

-------------------
STEPS:
-------------------------------------------
Step 0, which took 0.021219 s (model generation: 0.021003,  model checking: 0.000216):

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

}

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

}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 0
() -> length([nil, z]) -> 3
(append([l1, l2, _rx]) /\ append([l2, l1, _tx]) /\ length([_rx, _sx]) /\ length([_tx, _ux])) -> eq_nat([_sx, _ux]) -> 1
(append([t1, l2, _ix])) -> append([cons(h1, t1), l2, cons(h1, _ix)]) -> 1
(length([ll, _nx])) -> length([cons(x, ll), s(_nx)]) -> 1
}
Sat witness: Found: (() -> length([nil, z]), {

})

-------------------------------------------
Step 1, which took 0.010689 s (model generation: 0.009873,  model checking: 0.000816):

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

}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_6177},
Q_f={q_gen_6177},
Delta=
{
<nil, z>() -> q_gen_6177
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 3
() -> length([nil, z]) -> 3
(append([l1, l2, _rx]) /\ append([l2, l1, _tx]) /\ length([_rx, _sx]) /\ length([_tx, _ux])) -> eq_nat([_sx, _ux]) -> 1
(append([t1, l2, _ix])) -> append([cons(h1, t1), l2, cons(h1, _ix)]) -> 1
(length([ll, _nx])) -> length([cons(x, ll), s(_nx)]) -> 1
}
Sat witness: Found: (() -> append([nil, l2, l2]), {
l2 -> nil
})

-------------------------------------------
Step 2, which took 0.008640 s (model generation: 0.008541,  model checking: 0.000099):

Model:
|_
{
append -> 
{{{
Q={q_gen_6178},
Q_f={q_gen_6178},
Delta=
{
<nil, nil, nil>() -> q_gen_6178
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_6177},
Q_f={q_gen_6177},
Delta=
{
<nil, z>() -> q_gen_6177
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 3
() -> length([nil, z]) -> 3
(append([l1, l2, _rx]) /\ append([l2, l1, _tx]) /\ length([_rx, _sx]) /\ length([_tx, _ux])) -> eq_nat([_sx, _ux]) -> 1
(append([t1, l2, _ix])) -> append([cons(h1, t1), l2, cons(h1, _ix)]) -> 1
(length([ll, _nx])) -> length([cons(x, ll), s(_nx)]) -> 4
}
Sat witness: Found: ((length([ll, _nx])) -> length([cons(x, ll), s(_nx)]), {
_nx -> z  ;  ll -> nil  ;  x -> b
})

-------------------------------------------
Step 3, which took 0.009634 s (model generation: 0.009466,  model checking: 0.000168):

Model:
|_
{
append -> 
{{{
Q={q_gen_6178},
Q_f={q_gen_6178},
Delta=
{
<nil, nil, nil>() -> q_gen_6178
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_6177, q_gen_6180, q_gen_6181},
Q_f={q_gen_6177},
Delta=
{
<nil>() -> q_gen_6180
<cons, s>(q_gen_6181, q_gen_6180) -> q_gen_6177
<nil, z>() -> q_gen_6177
<b, z>() -> q_gen_6181
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 3
() -> length([nil, z]) -> 3
(append([l1, l2, _rx]) /\ append([l2, l1, _tx]) /\ length([_rx, _sx]) /\ length([_tx, _ux])) -> eq_nat([_sx, _ux]) -> 1
(append([t1, l2, _ix])) -> append([cons(h1, t1), l2, cons(h1, _ix)]) -> 4
(length([ll, _nx])) -> length([cons(x, ll), s(_nx)]) -> 4
}
Sat witness: Found: ((append([t1, l2, _ix])) -> append([cons(h1, t1), l2, cons(h1, _ix)]), {
_ix -> nil  ;  h1 -> b  ;  l2 -> nil  ;  t1 -> nil
})

-------------------------------------------
Step 4, which took 0.009643 s (model generation: 0.009238,  model checking: 0.000405):

Model:
|_
{
append -> 
{{{
Q={q_gen_6178, q_gen_6183, q_gen_6184},
Q_f={q_gen_6178},
Delta=
{
<nil, nil>() -> q_gen_6183
<b, b>() -> q_gen_6184
<cons, nil, cons>(q_gen_6184, q_gen_6183) -> q_gen_6178
<nil, nil, nil>() -> q_gen_6178
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_6177, q_gen_6180, q_gen_6181},
Q_f={q_gen_6177},
Delta=
{
<nil>() -> q_gen_6180
<cons, s>(q_gen_6181, q_gen_6180) -> q_gen_6177
<nil, z>() -> q_gen_6177
<b, z>() -> q_gen_6181
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 6
() -> length([nil, z]) -> 4
(append([l1, l2, _rx]) /\ append([l2, l1, _tx]) /\ length([_rx, _sx]) /\ length([_tx, _ux])) -> eq_nat([_sx, _ux]) -> 2
(append([t1, l2, _ix])) -> append([cons(h1, t1), l2, cons(h1, _ix)]) -> 4
(length([ll, _nx])) -> length([cons(x, ll), s(_nx)]) -> 4
}
Sat witness: Found: (() -> append([nil, l2, l2]), {
l2 -> cons(a, cons(a, nil))
})

-------------------------------------------
Step 5, which took 0.017556 s (model generation: 0.017223,  model checking: 0.000333):

Model:
|_
{
append -> 
{{{
Q={q_gen_6178, q_gen_6183, q_gen_6184},
Q_f={q_gen_6178},
Delta=
{
<cons, cons>(q_gen_6184, q_gen_6183) -> q_gen_6183
<nil, nil>() -> q_gen_6183
<a, a>() -> q_gen_6184
<b, b>() -> q_gen_6184
<cons, nil, cons>(q_gen_6184, q_gen_6183) -> q_gen_6178
<nil, cons, cons>(q_gen_6184, q_gen_6183) -> q_gen_6178
<nil, nil, nil>() -> q_gen_6178
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_6177, q_gen_6180, q_gen_6181},
Q_f={q_gen_6177},
Delta=
{
<nil>() -> q_gen_6180
<cons, s>(q_gen_6181, q_gen_6180) -> q_gen_6177
<nil, z>() -> q_gen_6177
<b, z>() -> q_gen_6181
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 6
() -> length([nil, z]) -> 4
(append([l1, l2, _rx]) /\ append([l2, l1, _tx]) /\ length([_rx, _sx]) /\ length([_tx, _ux])) -> eq_nat([_sx, _ux]) -> 3
(append([t1, l2, _ix])) -> append([cons(h1, t1), l2, cons(h1, _ix)]) -> 4
(length([ll, _nx])) -> length([cons(x, ll), s(_nx)]) -> 7
}
Sat witness: Found: ((length([ll, _nx])) -> length([cons(x, ll), s(_nx)]), {
_nx -> z  ;  ll -> nil  ;  x -> a
})

-------------------------------------------
Step 6, which took 0.015716 s (model generation: 0.013717,  model checking: 0.001999):

Model:
|_
{
append -> 
{{{
Q={q_gen_6178, q_gen_6183, q_gen_6184},
Q_f={q_gen_6178},
Delta=
{
<cons, cons>(q_gen_6184, q_gen_6183) -> q_gen_6183
<nil, nil>() -> q_gen_6183
<a, a>() -> q_gen_6184
<b, b>() -> q_gen_6184
<cons, nil, cons>(q_gen_6184, q_gen_6183) -> q_gen_6178
<nil, cons, cons>(q_gen_6184, q_gen_6183) -> q_gen_6178
<nil, nil, nil>() -> q_gen_6178
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_6177, q_gen_6180, q_gen_6181},
Q_f={q_gen_6177},
Delta=
{
<nil>() -> q_gen_6180
<cons, s>(q_gen_6181, q_gen_6180) -> q_gen_6177
<nil, z>() -> q_gen_6177
<a, z>() -> q_gen_6181
<b, z>() -> q_gen_6181
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 6
() -> length([nil, z]) -> 4
(append([l1, l2, _rx]) /\ append([l2, l1, _tx]) /\ length([_rx, _sx]) /\ length([_tx, _ux])) -> eq_nat([_sx, _ux]) -> 4
(append([t1, l2, _ix])) -> append([cons(h1, t1), l2, cons(h1, _ix)]) -> 7
(length([ll, _nx])) -> length([cons(x, ll), s(_nx)]) -> 7
}
Sat witness: Found: ((append([t1, l2, _ix])) -> append([cons(h1, t1), l2, cons(h1, _ix)]), {
_ix -> cons(b, nil)  ;  h1 -> b  ;  l2 -> cons(b, nil)  ;  t1 -> nil
})

-------------------------------------------
Step 7, which took 0.013971 s (model generation: 0.013406,  model checking: 0.000565):

Model:
|_
{
append -> 
{{{
Q={q_gen_6178, q_gen_6183, q_gen_6184, q_gen_6193, q_gen_6194, q_gen_6195},
Q_f={q_gen_6178},
Delta=
{
<nil>() -> q_gen_6193
<b>() -> q_gen_6194
<cons, cons>(q_gen_6184, q_gen_6183) -> q_gen_6183
<nil, nil>() -> q_gen_6183
<a, a>() -> q_gen_6184
<b, b>() -> q_gen_6184
<cons, cons, cons>(q_gen_6195, q_gen_6178) -> q_gen_6178
<cons, nil, cons>(q_gen_6184, q_gen_6183) -> q_gen_6178
<nil, cons, cons>(q_gen_6184, q_gen_6183) -> q_gen_6178
<nil, nil, cons>(q_gen_6194, q_gen_6193) -> q_gen_6178
<nil, nil, nil>() -> q_gen_6178
<b, b, b>() -> q_gen_6195
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_6177, q_gen_6180, q_gen_6181},
Q_f={q_gen_6177},
Delta=
{
<nil>() -> q_gen_6180
<cons, s>(q_gen_6181, q_gen_6180) -> q_gen_6177
<nil, z>() -> q_gen_6177
<a, z>() -> q_gen_6181
<b, z>() -> q_gen_6181
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 6
() -> length([nil, z]) -> 4
(append([l1, l2, _rx]) /\ append([l2, l1, _tx]) /\ length([_rx, _sx]) /\ length([_tx, _ux])) -> eq_nat([_sx, _ux]) -> 7
(append([t1, l2, _ix])) -> append([cons(h1, t1), l2, cons(h1, _ix)]) -> 7
(length([ll, _nx])) -> length([cons(x, ll), s(_nx)]) -> 7
}
Sat witness: Found: ((append([l1, l2, _rx]) /\ append([l2, l1, _tx]) /\ length([_rx, _sx]) /\ length([_tx, _ux])) -> eq_nat([_sx, _ux]), {
_rx -> nil  ;  _sx -> z  ;  _tx -> cons(b, nil)  ;  _ux -> s(z)  ;  l1 -> nil  ;  l2 -> nil
})

-------------------------------------------
Step 8, which took 0.012672 s (model generation: 0.011731,  model checking: 0.000941):

Model:
|_
{
append -> 
{{{
Q={q_gen_6178, q_gen_6183, q_gen_6184, q_gen_6192, q_gen_6193, q_gen_6194, q_gen_6195},
Q_f={q_gen_6178},
Delta=
{
<nil>() -> q_gen_6193
<b>() -> q_gen_6194
<cons, cons>(q_gen_6184, q_gen_6183) -> q_gen_6183
<nil, nil>() -> q_gen_6183
<a, a>() -> q_gen_6184
<b, b>() -> q_gen_6184
<cons, cons, cons>(q_gen_6195, q_gen_6192) -> q_gen_6178
<cons, nil, cons>(q_gen_6184, q_gen_6183) -> q_gen_6178
<nil, cons, cons>(q_gen_6184, q_gen_6183) -> q_gen_6178
<nil, nil, nil>() -> q_gen_6178
<nil, nil, cons>(q_gen_6194, q_gen_6193) -> q_gen_6192
<b, b, b>() -> q_gen_6195
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_6177, q_gen_6180, q_gen_6181},
Q_f={q_gen_6177},
Delta=
{
<nil>() -> q_gen_6180
<cons, s>(q_gen_6181, q_gen_6180) -> q_gen_6177
<nil, z>() -> q_gen_6177
<a, z>() -> q_gen_6181
<b, z>() -> q_gen_6181
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 7
() -> length([nil, z]) -> 5
(append([l1, l2, _rx]) /\ append([l2, l1, _tx]) /\ length([_rx, _sx]) /\ length([_tx, _ux])) -> eq_nat([_sx, _ux]) -> 7
(append([t1, l2, _ix])) -> append([cons(h1, t1), l2, cons(h1, _ix)]) -> 7
(length([ll, _nx])) -> length([cons(x, ll), s(_nx)]) -> 10
}
Sat witness: Found: ((length([ll, _nx])) -> length([cons(x, ll), s(_nx)]), {
_nx -> s(z)  ;  ll -> cons(b, nil)  ;  x -> b
})

-------------------------------------------
Step 9, which took 0.012709 s (model generation: 0.011247,  model checking: 0.001462):

Model:
|_
{
append -> 
{{{
Q={q_gen_6178, q_gen_6183, q_gen_6184, q_gen_6192, q_gen_6193, q_gen_6194, q_gen_6195},
Q_f={q_gen_6178},
Delta=
{
<nil>() -> q_gen_6193
<b>() -> q_gen_6194
<cons, cons>(q_gen_6184, q_gen_6183) -> q_gen_6183
<nil, nil>() -> q_gen_6183
<a, a>() -> q_gen_6184
<b, b>() -> q_gen_6184
<cons, cons, cons>(q_gen_6195, q_gen_6192) -> q_gen_6178
<cons, nil, cons>(q_gen_6184, q_gen_6183) -> q_gen_6178
<nil, cons, cons>(q_gen_6184, q_gen_6183) -> q_gen_6178
<nil, nil, nil>() -> q_gen_6178
<nil, nil, cons>(q_gen_6194, q_gen_6193) -> q_gen_6192
<b, b, b>() -> q_gen_6195
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_6177, q_gen_6180, q_gen_6181, q_gen_6198, q_gen_6200},
Q_f={q_gen_6177},
Delta=
{
<cons>(q_gen_6198, q_gen_6180) -> q_gen_6180
<nil>() -> q_gen_6180
<b>() -> q_gen_6198
<z>() -> q_gen_6200
<cons, s>(q_gen_6181, q_gen_6180) -> q_gen_6177
<nil, z>() -> q_gen_6177
<a, z>() -> q_gen_6181
<b, s>(q_gen_6200) -> q_gen_6181
<b, z>() -> q_gen_6181
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 7
() -> length([nil, z]) -> 6
(append([l1, l2, _rx]) /\ append([l2, l1, _tx]) /\ length([_rx, _sx]) /\ length([_tx, _ux])) -> eq_nat([_sx, _ux]) -> 7
(append([t1, l2, _ix])) -> append([cons(h1, t1), l2, cons(h1, _ix)]) -> 10
(length([ll, _nx])) -> length([cons(x, ll), s(_nx)]) -> 10
}
Sat witness: Found: ((append([t1, l2, _ix])) -> append([cons(h1, t1), l2, cons(h1, _ix)]), {
_ix -> cons(b, cons(b, nil))  ;  h1 -> a  ;  l2 -> cons(b, nil)  ;  t1 -> cons(b, nil)
})

-------------------------------------------
Step 10, which took 0.014308 s (model generation: 0.013158,  model checking: 0.001150):

Model:
|_
{
append -> 
{{{
Q={q_gen_6178, q_gen_6183, q_gen_6184, q_gen_6192, q_gen_6193, q_gen_6194, q_gen_6195},
Q_f={q_gen_6178},
Delta=
{
<nil>() -> q_gen_6193
<b>() -> q_gen_6194
<cons, cons>(q_gen_6184, q_gen_6183) -> q_gen_6183
<nil, cons>(q_gen_6194, q_gen_6193) -> q_gen_6183
<nil, nil>() -> q_gen_6183
<a, a>() -> q_gen_6184
<b, b>() -> q_gen_6184
<cons, cons, cons>(q_gen_6195, q_gen_6178) -> q_gen_6178
<cons, cons, cons>(q_gen_6195, q_gen_6192) -> q_gen_6178
<cons, nil, cons>(q_gen_6184, q_gen_6183) -> q_gen_6178
<nil, cons, cons>(q_gen_6184, q_gen_6183) -> q_gen_6178
<nil, nil, nil>() -> q_gen_6178
<nil, nil, cons>(q_gen_6194, q_gen_6193) -> q_gen_6192
<a, b, a>() -> q_gen_6195
<b, b, b>() -> q_gen_6195
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_6177, q_gen_6180, q_gen_6181, q_gen_6198, q_gen_6200},
Q_f={q_gen_6177},
Delta=
{
<cons>(q_gen_6198, q_gen_6180) -> q_gen_6180
<nil>() -> q_gen_6180
<b>() -> q_gen_6198
<z>() -> q_gen_6200
<cons, s>(q_gen_6181, q_gen_6180) -> q_gen_6177
<nil, z>() -> q_gen_6177
<a, z>() -> q_gen_6181
<b, s>(q_gen_6200) -> q_gen_6181
<b, z>() -> q_gen_6181
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 7
() -> length([nil, z]) -> 7
(append([l1, l2, _rx]) /\ append([l2, l1, _tx]) /\ length([_rx, _sx]) /\ length([_tx, _ux])) -> eq_nat([_sx, _ux]) -> 10
(append([t1, l2, _ix])) -> append([cons(h1, t1), l2, cons(h1, _ix)]) -> 10
(length([ll, _nx])) -> length([cons(x, ll), s(_nx)]) -> 10
}
Sat witness: Found: ((append([l1, l2, _rx]) /\ append([l2, l1, _tx]) /\ length([_rx, _sx]) /\ length([_tx, _ux])) -> eq_nat([_sx, _ux]), {
_rx -> cons(b, cons(b, nil))  ;  _sx -> s(z)  ;  _tx -> cons(b, cons(b, nil))  ;  _ux -> s(s(z))  ;  l1 -> cons(b, nil)  ;  l2 -> cons(b, nil)
})

-------------------------------------------
Step 11, which took 0.015364 s (model generation: 0.014947,  model checking: 0.000417):

Model:
|_
{
append -> 
{{{
Q={q_gen_6178, q_gen_6183, q_gen_6184, q_gen_6187, q_gen_6190, q_gen_6193, q_gen_6194, q_gen_6195},
Q_f={q_gen_6178},
Delta=
{
<nil>() -> q_gen_6193
<b>() -> q_gen_6194
<cons, cons>(q_gen_6187, q_gen_6183) -> q_gen_6183
<nil, cons>(q_gen_6194, q_gen_6193) -> q_gen_6183
<nil, nil>() -> q_gen_6183
<b, b>() -> q_gen_6184
<a, a>() -> q_gen_6187
<cons, nil, cons>(q_gen_6184, q_gen_6183) -> q_gen_6178
<nil, cons, cons>(q_gen_6187, q_gen_6183) -> q_gen_6178
<nil, nil, nil>() -> q_gen_6178
<cons, cons, cons>(q_gen_6195, q_gen_6178) -> q_gen_6190
<cons, cons, cons>(q_gen_6195, q_gen_6190) -> q_gen_6190
<nil, cons, cons>(q_gen_6184, q_gen_6183) -> q_gen_6190
<nil, nil, cons>(q_gen_6194, q_gen_6193) -> q_gen_6190
<a, b, a>() -> q_gen_6195
<b, b, b>() -> q_gen_6195
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_6177, q_gen_6180, q_gen_6181, q_gen_6198, q_gen_6200},
Q_f={q_gen_6177},
Delta=
{
<cons>(q_gen_6198, q_gen_6180) -> q_gen_6180
<nil>() -> q_gen_6180
<b>() -> q_gen_6198
<z>() -> q_gen_6200
<cons, s>(q_gen_6181, q_gen_6180) -> q_gen_6177
<nil, z>() -> q_gen_6177
<a, z>() -> q_gen_6181
<b, s>(q_gen_6200) -> q_gen_6181
<b, z>() -> q_gen_6181
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 10
() -> length([nil, z]) -> 8
(append([l1, l2, _rx]) /\ append([l2, l1, _tx]) /\ length([_rx, _sx]) /\ length([_tx, _ux])) -> eq_nat([_sx, _ux]) -> 10
(append([t1, l2, _ix])) -> append([cons(h1, t1), l2, cons(h1, _ix)]) -> 10
(length([ll, _nx])) -> length([cons(x, ll), s(_nx)]) -> 10
}
Sat witness: Found: (() -> append([nil, l2, l2]), {
l2 -> cons(b, nil)
})

-------------------------------------------
Step 12, which took 0.014742 s (model generation: 0.013932,  model checking: 0.000810):

Model:
|_
{
append -> 
{{{
Q={q_gen_6178, q_gen_6183, q_gen_6184, q_gen_6192, q_gen_6193, q_gen_6194, q_gen_6195},
Q_f={q_gen_6178},
Delta=
{
<nil>() -> q_gen_6193
<b>() -> q_gen_6194
<cons, cons>(q_gen_6184, q_gen_6183) -> q_gen_6183
<nil, cons>(q_gen_6194, q_gen_6193) -> q_gen_6183
<nil, nil>() -> q_gen_6183
<a, a>() -> q_gen_6184
<b, b>() -> q_gen_6184
<cons, cons, cons>(q_gen_6195, q_gen_6178) -> q_gen_6178
<cons, cons, cons>(q_gen_6195, q_gen_6192) -> q_gen_6178
<cons, nil, cons>(q_gen_6184, q_gen_6183) -> q_gen_6178
<nil, cons, cons>(q_gen_6184, q_gen_6183) -> q_gen_6178
<nil, nil, nil>() -> q_gen_6178
<nil, nil, cons>(q_gen_6194, q_gen_6193) -> q_gen_6192
<a, b, a>() -> q_gen_6195
<b, b, b>() -> q_gen_6195
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_6177, q_gen_6180, q_gen_6181, q_gen_6197, q_gen_6198, q_gen_6199, q_gen_6200, q_gen_6205},
Q_f={q_gen_6177},
Delta=
{
<nil>() -> q_gen_6180
<cons>(q_gen_6198, q_gen_6180) -> q_gen_6197
<b>() -> q_gen_6198
<z>() -> q_gen_6200
<cons, s>(q_gen_6181, q_gen_6180) -> q_gen_6177
<cons, s>(q_gen_6199, q_gen_6197) -> q_gen_6177
<nil, z>() -> q_gen_6177
<a, z>() -> q_gen_6181
<b, z>() -> q_gen_6181
<b, s>(q_gen_6200) -> q_gen_6199
<cons, s>(q_gen_6181, q_gen_6197) -> q_gen_6205
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 10
() -> length([nil, z]) -> 9
(append([l1, l2, _rx]) /\ append([l2, l1, _tx]) /\ length([_rx, _sx]) /\ length([_tx, _ux])) -> eq_nat([_sx, _ux]) -> 10
(append([t1, l2, _ix])) -> append([cons(h1, t1), l2, cons(h1, _ix)]) -> 10
(length([ll, _nx])) -> length([cons(x, ll), s(_nx)]) -> 13
}
Sat witness: Found: ((length([ll, _nx])) -> length([cons(x, ll), s(_nx)]), {
_nx -> s(z)  ;  ll -> cons(a, nil)  ;  x -> b
})

-------------------------------------------
Step 13, which took 0.017180 s (model generation: 0.015188,  model checking: 0.001992):

Model:
|_
{
append -> 
{{{
Q={q_gen_6178, q_gen_6183, q_gen_6184, q_gen_6192, q_gen_6193, q_gen_6194, q_gen_6195},
Q_f={q_gen_6178},
Delta=
{
<nil>() -> q_gen_6193
<b>() -> q_gen_6194
<cons, cons>(q_gen_6184, q_gen_6183) -> q_gen_6183
<nil, cons>(q_gen_6194, q_gen_6193) -> q_gen_6183
<nil, nil>() -> q_gen_6183
<a, a>() -> q_gen_6184
<b, b>() -> q_gen_6184
<cons, cons, cons>(q_gen_6195, q_gen_6178) -> q_gen_6178
<cons, cons, cons>(q_gen_6195, q_gen_6192) -> q_gen_6178
<cons, nil, cons>(q_gen_6184, q_gen_6183) -> q_gen_6178
<nil, cons, cons>(q_gen_6184, q_gen_6183) -> q_gen_6178
<nil, nil, nil>() -> q_gen_6178
<nil, nil, cons>(q_gen_6194, q_gen_6193) -> q_gen_6192
<a, b, a>() -> q_gen_6195
<b, b, b>() -> q_gen_6195
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_6177, q_gen_6180, q_gen_6181, q_gen_6197, q_gen_6198, q_gen_6199, q_gen_6200, q_gen_6205},
Q_f={q_gen_6177},
Delta=
{
<nil>() -> q_gen_6180
<cons>(q_gen_6198, q_gen_6180) -> q_gen_6197
<a>() -> q_gen_6198
<b>() -> q_gen_6198
<z>() -> q_gen_6200
<cons, s>(q_gen_6181, q_gen_6180) -> q_gen_6177
<cons, s>(q_gen_6199, q_gen_6197) -> q_gen_6177
<nil, z>() -> q_gen_6177
<a, z>() -> q_gen_6181
<b, z>() -> q_gen_6181
<b, s>(q_gen_6200) -> q_gen_6199
<cons, s>(q_gen_6181, q_gen_6197) -> q_gen_6205
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 10
() -> length([nil, z]) -> 10
(append([l1, l2, _rx]) /\ append([l2, l1, _tx]) /\ length([_rx, _sx]) /\ length([_tx, _ux])) -> eq_nat([_sx, _ux]) -> 10
(append([t1, l2, _ix])) -> append([cons(h1, t1), l2, cons(h1, _ix)]) -> 13
(length([ll, _nx])) -> length([cons(x, ll), s(_nx)]) -> 13
}
Sat witness: Found: ((append([t1, l2, _ix])) -> append([cons(h1, t1), l2, cons(h1, _ix)]), {
_ix -> cons(a, nil)  ;  h1 -> b  ;  l2 -> cons(a, nil)  ;  t1 -> nil
})

-------------------------------------------
Step 14, which took 0.018728 s (model generation: 0.016353,  model checking: 0.002375):

Model:
|_
{
append -> 
{{{
Q={q_gen_6178, q_gen_6183, q_gen_6184, q_gen_6192, q_gen_6193, q_gen_6194, q_gen_6195},
Q_f={q_gen_6178},
Delta=
{
<nil>() -> q_gen_6193
<a>() -> q_gen_6194
<b>() -> q_gen_6194
<cons, cons>(q_gen_6184, q_gen_6183) -> q_gen_6183
<nil, cons>(q_gen_6194, q_gen_6193) -> q_gen_6183
<nil, nil>() -> q_gen_6183
<a, a>() -> q_gen_6184
<b, b>() -> q_gen_6184
<cons, cons, cons>(q_gen_6195, q_gen_6178) -> q_gen_6178
<cons, cons, cons>(q_gen_6195, q_gen_6192) -> q_gen_6178
<cons, nil, cons>(q_gen_6184, q_gen_6183) -> q_gen_6178
<nil, cons, cons>(q_gen_6184, q_gen_6183) -> q_gen_6178
<nil, nil, nil>() -> q_gen_6178
<nil, nil, cons>(q_gen_6194, q_gen_6193) -> q_gen_6192
<a, b, a>() -> q_gen_6195
<b, a, b>() -> q_gen_6195
<b, b, b>() -> q_gen_6195
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_6177, q_gen_6180, q_gen_6181, q_gen_6197, q_gen_6198, q_gen_6199, q_gen_6200, q_gen_6205},
Q_f={q_gen_6177},
Delta=
{
<nil>() -> q_gen_6180
<cons>(q_gen_6198, q_gen_6180) -> q_gen_6197
<a>() -> q_gen_6198
<b>() -> q_gen_6198
<z>() -> q_gen_6200
<cons, s>(q_gen_6181, q_gen_6180) -> q_gen_6177
<cons, s>(q_gen_6199, q_gen_6197) -> q_gen_6177
<nil, z>() -> q_gen_6177
<a, z>() -> q_gen_6181
<b, z>() -> q_gen_6181
<b, s>(q_gen_6200) -> q_gen_6199
<cons, s>(q_gen_6181, q_gen_6197) -> q_gen_6205
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 10
() -> length([nil, z]) -> 10
(append([l1, l2, _rx]) /\ append([l2, l1, _tx]) /\ length([_rx, _sx]) /\ length([_tx, _ux])) -> eq_nat([_sx, _ux]) -> 13
(append([t1, l2, _ix])) -> append([cons(h1, t1), l2, cons(h1, _ix)]) -> 13
(length([ll, _nx])) -> length([cons(x, ll), s(_nx)]) -> 13
}
Sat witness: Found: ((append([l1, l2, _rx]) /\ append([l2, l1, _tx]) /\ length([_rx, _sx]) /\ length([_tx, _ux])) -> eq_nat([_sx, _ux]), {
_rx -> cons(b, cons(b, nil))  ;  _sx -> s(s(z))  ;  _tx -> cons(b, nil)  ;  _ux -> s(z)  ;  l1 -> cons(b, nil)  ;  l2 -> cons(b, nil)
})

-------------------------------------------
Step 15, which took 0.019631 s (model generation: 0.018108,  model checking: 0.001523):

Model:
|_
{
append -> 
{{{
Q={q_gen_6178, q_gen_6182, q_gen_6183, q_gen_6184, q_gen_6192, q_gen_6193, q_gen_6194, q_gen_6195},
Q_f={q_gen_6178, q_gen_6182},
Delta=
{
<nil>() -> q_gen_6193
<a>() -> q_gen_6194
<b>() -> q_gen_6194
<cons, cons>(q_gen_6184, q_gen_6183) -> q_gen_6183
<nil, cons>(q_gen_6194, q_gen_6193) -> q_gen_6183
<nil, nil>() -> q_gen_6183
<a, a>() -> q_gen_6184
<b, b>() -> q_gen_6184
<nil, nil, nil>() -> q_gen_6178
<cons, cons, cons>(q_gen_6195, q_gen_6182) -> q_gen_6182
<cons, cons, cons>(q_gen_6195, q_gen_6192) -> q_gen_6182
<cons, nil, cons>(q_gen_6184, q_gen_6183) -> q_gen_6182
<nil, cons, cons>(q_gen_6184, q_gen_6183) -> q_gen_6182
<cons, cons, cons>(q_gen_6195, q_gen_6178) -> q_gen_6192
<nil, nil, cons>(q_gen_6194, q_gen_6193) -> q_gen_6192
<a, b, a>() -> q_gen_6195
<b, a, b>() -> q_gen_6195
<b, b, b>() -> q_gen_6195
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_6177, q_gen_6180, q_gen_6181, q_gen_6197, q_gen_6198, q_gen_6199, q_gen_6200, q_gen_6205},
Q_f={q_gen_6177},
Delta=
{
<nil>() -> q_gen_6180
<cons>(q_gen_6198, q_gen_6180) -> q_gen_6197
<a>() -> q_gen_6198
<b>() -> q_gen_6198
<z>() -> q_gen_6200
<cons, s>(q_gen_6181, q_gen_6180) -> q_gen_6177
<cons, s>(q_gen_6199, q_gen_6197) -> q_gen_6177
<nil, z>() -> q_gen_6177
<a, z>() -> q_gen_6181
<b, z>() -> q_gen_6181
<b, s>(q_gen_6200) -> q_gen_6199
<cons, s>(q_gen_6181, q_gen_6197) -> q_gen_6205
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 11
() -> length([nil, z]) -> 11
(append([l1, l2, _rx]) /\ append([l2, l1, _tx]) /\ length([_rx, _sx]) /\ length([_tx, _ux])) -> eq_nat([_sx, _ux]) -> 13
(append([t1, l2, _ix])) -> append([cons(h1, t1), l2, cons(h1, _ix)]) -> 13
(length([ll, _nx])) -> length([cons(x, ll), s(_nx)]) -> 16
}
Sat witness: Found: ((length([ll, _nx])) -> length([cons(x, ll), s(_nx)]), {
_nx -> s(s(z))  ;  ll -> cons(b, cons(b, nil))  ;  x -> b
})

-------------------------------------------
Step 16, which took 0.021248 s (model generation: 0.019219,  model checking: 0.002029):

Model:
|_
{
append -> 
{{{
Q={q_gen_6178, q_gen_6182, q_gen_6183, q_gen_6184, q_gen_6192, q_gen_6193, q_gen_6194, q_gen_6195},
Q_f={q_gen_6178, q_gen_6182},
Delta=
{
<nil>() -> q_gen_6193
<a>() -> q_gen_6194
<b>() -> q_gen_6194
<cons, cons>(q_gen_6184, q_gen_6183) -> q_gen_6183
<nil, cons>(q_gen_6194, q_gen_6193) -> q_gen_6183
<nil, nil>() -> q_gen_6183
<a, a>() -> q_gen_6184
<b, b>() -> q_gen_6184
<nil, nil, nil>() -> q_gen_6178
<cons, cons, cons>(q_gen_6195, q_gen_6182) -> q_gen_6182
<cons, cons, cons>(q_gen_6195, q_gen_6192) -> q_gen_6182
<cons, nil, cons>(q_gen_6184, q_gen_6183) -> q_gen_6182
<nil, cons, cons>(q_gen_6184, q_gen_6183) -> q_gen_6182
<cons, cons, cons>(q_gen_6195, q_gen_6178) -> q_gen_6192
<nil, nil, cons>(q_gen_6194, q_gen_6193) -> q_gen_6192
<a, b, a>() -> q_gen_6195
<b, a, b>() -> q_gen_6195
<b, b, b>() -> q_gen_6195
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_6177, q_gen_6180, q_gen_6181, q_gen_6189, q_gen_6197, q_gen_6198, q_gen_6200, q_gen_6205},
Q_f={q_gen_6177},
Delta=
{
<nil>() -> q_gen_6180
<cons>(q_gen_6198, q_gen_6180) -> q_gen_6197
<cons>(q_gen_6198, q_gen_6197) -> q_gen_6197
<a>() -> q_gen_6198
<b>() -> q_gen_6198
<s>(q_gen_6200) -> q_gen_6200
<z>() -> q_gen_6200
<cons, s>(q_gen_6181, q_gen_6180) -> q_gen_6177
<cons, s>(q_gen_6189, q_gen_6180) -> q_gen_6177
<cons, s>(q_gen_6189, q_gen_6197) -> q_gen_6177
<nil, z>() -> q_gen_6177
<b, z>() -> q_gen_6181
<a, z>() -> q_gen_6189
<b, s>(q_gen_6200) -> q_gen_6189
<cons, s>(q_gen_6181, q_gen_6197) -> q_gen_6205
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 12
() -> length([nil, z]) -> 12
(append([l1, l2, _rx]) /\ append([l2, l1, _tx]) /\ length([_rx, _sx]) /\ length([_tx, _ux])) -> eq_nat([_sx, _ux]) -> 13
(append([t1, l2, _ix])) -> append([cons(h1, t1), l2, cons(h1, _ix)]) -> 16
(length([ll, _nx])) -> length([cons(x, ll), s(_nx)]) -> 16
}
Sat witness: Found: ((append([t1, l2, _ix])) -> append([cons(h1, t1), l2, cons(h1, _ix)]), {
_ix -> cons(b, cons(a, nil))  ;  h1 -> a  ;  l2 -> cons(a, nil)  ;  t1 -> cons(b, nil)
})

-------------------------------------------
Step 17, which took 0.027274 s (model generation: 0.024920,  model checking: 0.002354):

Model:
|_
{
append -> 
{{{
Q={q_gen_6178, q_gen_6182, q_gen_6183, q_gen_6184, q_gen_6192, q_gen_6193, q_gen_6194, q_gen_6195},
Q_f={q_gen_6178, q_gen_6182},
Delta=
{
<nil>() -> q_gen_6193
<a>() -> q_gen_6194
<b>() -> q_gen_6194
<cons, cons>(q_gen_6184, q_gen_6183) -> q_gen_6183
<nil, cons>(q_gen_6194, q_gen_6193) -> q_gen_6183
<nil, nil>() -> q_gen_6183
<a, a>() -> q_gen_6184
<b, b>() -> q_gen_6184
<cons, cons, cons>(q_gen_6195, q_gen_6182) -> q_gen_6178
<nil, nil, nil>() -> q_gen_6178
<cons, cons, cons>(q_gen_6195, q_gen_6192) -> q_gen_6182
<cons, nil, cons>(q_gen_6184, q_gen_6183) -> q_gen_6182
<nil, cons, cons>(q_gen_6184, q_gen_6183) -> q_gen_6182
<cons, cons, cons>(q_gen_6195, q_gen_6178) -> q_gen_6192
<nil, nil, cons>(q_gen_6194, q_gen_6193) -> q_gen_6192
<a, a, a>() -> q_gen_6195
<a, b, a>() -> q_gen_6195
<b, a, b>() -> q_gen_6195
<b, b, b>() -> q_gen_6195
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_6177, q_gen_6180, q_gen_6181, q_gen_6189, q_gen_6197, q_gen_6198, q_gen_6200, q_gen_6205},
Q_f={q_gen_6177},
Delta=
{
<nil>() -> q_gen_6180
<cons>(q_gen_6198, q_gen_6180) -> q_gen_6197
<cons>(q_gen_6198, q_gen_6197) -> q_gen_6197
<a>() -> q_gen_6198
<b>() -> q_gen_6198
<s>(q_gen_6200) -> q_gen_6200
<z>() -> q_gen_6200
<cons, s>(q_gen_6181, q_gen_6180) -> q_gen_6177
<cons, s>(q_gen_6189, q_gen_6180) -> q_gen_6177
<cons, s>(q_gen_6189, q_gen_6197) -> q_gen_6177
<nil, z>() -> q_gen_6177
<b, z>() -> q_gen_6181
<a, z>() -> q_gen_6189
<b, s>(q_gen_6200) -> q_gen_6189
<cons, s>(q_gen_6181, q_gen_6197) -> q_gen_6205
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 13
() -> length([nil, z]) -> 13
(append([l1, l2, _rx]) /\ append([l2, l1, _tx]) /\ length([_rx, _sx]) /\ length([_tx, _ux])) -> eq_nat([_sx, _ux]) -> 16
(append([t1, l2, _ix])) -> append([cons(h1, t1), l2, cons(h1, _ix)]) -> 16
(length([ll, _nx])) -> length([cons(x, ll), s(_nx)]) -> 16
}
Sat witness: Found: ((append([l1, l2, _rx]) /\ append([l2, l1, _tx]) /\ length([_rx, _sx]) /\ length([_tx, _ux])) -> eq_nat([_sx, _ux]), {
_rx -> cons(a, cons(b, nil))  ;  _sx -> s(z)  ;  _tx -> cons(b, cons(b, nil))  ;  _ux -> s(s(z))  ;  l1 -> cons(a, nil)  ;  l2 -> cons(b, nil)
})

-------------------------------------------
Step 18, which took 0.027621 s (model generation: 0.026399,  model checking: 0.001222):

Model:
|_
{
append -> 
{{{
Q={q_gen_6178, q_gen_6182, q_gen_6183, q_gen_6184, q_gen_6192, q_gen_6193, q_gen_6194, q_gen_6195},
Q_f={q_gen_6178, q_gen_6182},
Delta=
{
<nil>() -> q_gen_6193
<a>() -> q_gen_6194
<b>() -> q_gen_6194
<cons, cons>(q_gen_6184, q_gen_6183) -> q_gen_6183
<nil, cons>(q_gen_6194, q_gen_6193) -> q_gen_6183
<nil, nil>() -> q_gen_6183
<a, a>() -> q_gen_6184
<b, b>() -> q_gen_6184
<cons, cons, cons>(q_gen_6195, q_gen_6182) -> q_gen_6178
<nil, nil, nil>() -> q_gen_6178
<cons, cons, cons>(q_gen_6195, q_gen_6192) -> q_gen_6182
<cons, nil, cons>(q_gen_6184, q_gen_6183) -> q_gen_6182
<nil, cons, cons>(q_gen_6184, q_gen_6183) -> q_gen_6182
<cons, cons, cons>(q_gen_6195, q_gen_6178) -> q_gen_6192
<nil, nil, cons>(q_gen_6194, q_gen_6193) -> q_gen_6192
<a, a, a>() -> q_gen_6195
<a, b, a>() -> q_gen_6195
<b, a, b>() -> q_gen_6195
<b, b, b>() -> q_gen_6195
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_6177, q_gen_6180, q_gen_6181, q_gen_6197, q_gen_6198, q_gen_6199, q_gen_6200, q_gen_6205},
Q_f={q_gen_6177},
Delta=
{
<cons>(q_gen_6198, q_gen_6197) -> q_gen_6180
<nil>() -> q_gen_6180
<cons>(q_gen_6198, q_gen_6180) -> q_gen_6197
<a>() -> q_gen_6198
<b>() -> q_gen_6198
<s>(q_gen_6200) -> q_gen_6200
<z>() -> q_gen_6200
<cons, s>(q_gen_6181, q_gen_6180) -> q_gen_6177
<cons, s>(q_gen_6199, q_gen_6180) -> q_gen_6177
<cons, s>(q_gen_6199, q_gen_6197) -> q_gen_6177
<nil, z>() -> q_gen_6177
<a, z>() -> q_gen_6181
<b, z>() -> q_gen_6181
<b, s>(q_gen_6200) -> q_gen_6199
<cons, s>(q_gen_6181, q_gen_6197) -> q_gen_6205
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 14
() -> length([nil, z]) -> 14
(append([l1, l2, _rx]) /\ append([l2, l1, _tx]) /\ length([_rx, _sx]) /\ length([_tx, _ux])) -> eq_nat([_sx, _ux]) -> 16
(append([t1, l2, _ix])) -> append([cons(h1, t1), l2, cons(h1, _ix)]) -> 16
(length([ll, _nx])) -> length([cons(x, ll), s(_nx)]) -> 19
}
Sat witness: Found: ((length([ll, _nx])) -> length([cons(x, ll), s(_nx)]), {
_nx -> s(s(z))  ;  ll -> cons(b, nil)  ;  x -> a
})

-------------------------------------------
Step 19, which took 0.032101 s (model generation: 0.029444,  model checking: 0.002657):

Model:
|_
{
append -> 
{{{
Q={q_gen_6178, q_gen_6182, q_gen_6183, q_gen_6184, q_gen_6192, q_gen_6193, q_gen_6194, q_gen_6195},
Q_f={q_gen_6178, q_gen_6182},
Delta=
{
<nil>() -> q_gen_6193
<a>() -> q_gen_6194
<b>() -> q_gen_6194
<cons, cons>(q_gen_6184, q_gen_6183) -> q_gen_6183
<nil, cons>(q_gen_6194, q_gen_6193) -> q_gen_6183
<nil, nil>() -> q_gen_6183
<a, a>() -> q_gen_6184
<b, b>() -> q_gen_6184
<nil, nil, nil>() -> q_gen_6178
<cons, cons, cons>(q_gen_6195, q_gen_6182) -> q_gen_6182
<cons, cons, cons>(q_gen_6195, q_gen_6192) -> q_gen_6182
<cons, nil, cons>(q_gen_6184, q_gen_6183) -> q_gen_6182
<nil, cons, cons>(q_gen_6184, q_gen_6183) -> q_gen_6182
<cons, cons, cons>(q_gen_6195, q_gen_6178) -> q_gen_6192
<nil, nil, cons>(q_gen_6194, q_gen_6193) -> q_gen_6192
<a, a, a>() -> q_gen_6195
<a, b, a>() -> q_gen_6195
<b, a, b>() -> q_gen_6195
<b, b, b>() -> q_gen_6195
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_6177, q_gen_6180, q_gen_6181, q_gen_6197, q_gen_6198, q_gen_6199, q_gen_6200, q_gen_6205},
Q_f={q_gen_6177},
Delta=
{
<nil>() -> q_gen_6180
<cons>(q_gen_6198, q_gen_6180) -> q_gen_6197
<cons>(q_gen_6198, q_gen_6197) -> q_gen_6197
<a>() -> q_gen_6198
<b>() -> q_gen_6198
<s>(q_gen_6200) -> q_gen_6200
<z>() -> q_gen_6200
<cons, s>(q_gen_6181, q_gen_6180) -> q_gen_6177
<cons, s>(q_gen_6199, q_gen_6197) -> q_gen_6177
<nil, z>() -> q_gen_6177
<a, z>() -> q_gen_6181
<b, z>() -> q_gen_6181
<a, s>(q_gen_6200) -> q_gen_6199
<b, s>(q_gen_6200) -> q_gen_6199
<cons, s>(q_gen_6181, q_gen_6197) -> q_gen_6205
<cons, s>(q_gen_6199, q_gen_6180) -> q_gen_6205
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 15
() -> length([nil, z]) -> 15
(append([l1, l2, _rx]) /\ append([l2, l1, _tx]) /\ length([_rx, _sx]) /\ length([_tx, _ux])) -> eq_nat([_sx, _ux]) -> 16
(append([t1, l2, _ix])) -> append([cons(h1, t1), l2, cons(h1, _ix)]) -> 19
(length([ll, _nx])) -> length([cons(x, ll), s(_nx)]) -> 19
}
Sat witness: Found: ((append([t1, l2, _ix])) -> append([cons(h1, t1), l2, cons(h1, _ix)]), {
_ix -> cons(b, cons(b, nil))  ;  h1 -> a  ;  l2 -> cons(b, nil)  ;  t1 -> nil
})

-------------------------------------------
Step 20, which took 0.035282 s (model generation: 0.032293,  model checking: 0.002989):

Model:
|_
{
append -> 
{{{
Q={q_gen_6178, q_gen_6182, q_gen_6183, q_gen_6184, q_gen_6192, q_gen_6193, q_gen_6194, q_gen_6195},
Q_f={q_gen_6178, q_gen_6182},
Delta=
{
<cons>(q_gen_6194, q_gen_6193) -> q_gen_6193
<nil>() -> q_gen_6193
<a>() -> q_gen_6194
<b>() -> q_gen_6194
<cons, cons>(q_gen_6184, q_gen_6183) -> q_gen_6183
<nil, cons>(q_gen_6194, q_gen_6193) -> q_gen_6183
<nil, nil>() -> q_gen_6183
<a, a>() -> q_gen_6184
<b, b>() -> q_gen_6184
<cons, cons, cons>(q_gen_6195, q_gen_6182) -> q_gen_6178
<nil, nil, nil>() -> q_gen_6178
<cons, cons, cons>(q_gen_6195, q_gen_6192) -> q_gen_6182
<cons, nil, cons>(q_gen_6184, q_gen_6183) -> q_gen_6182
<nil, cons, cons>(q_gen_6184, q_gen_6183) -> q_gen_6182
<cons, cons, cons>(q_gen_6195, q_gen_6178) -> q_gen_6192
<nil, nil, cons>(q_gen_6194, q_gen_6193) -> q_gen_6192
<a, a, a>() -> q_gen_6195
<a, b, a>() -> q_gen_6195
<b, a, b>() -> q_gen_6195
<b, b, b>() -> q_gen_6195
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_6177, q_gen_6180, q_gen_6181, q_gen_6197, q_gen_6198, q_gen_6199, q_gen_6200, q_gen_6205},
Q_f={q_gen_6177},
Delta=
{
<nil>() -> q_gen_6180
<cons>(q_gen_6198, q_gen_6180) -> q_gen_6197
<cons>(q_gen_6198, q_gen_6197) -> q_gen_6197
<a>() -> q_gen_6198
<b>() -> q_gen_6198
<s>(q_gen_6200) -> q_gen_6200
<z>() -> q_gen_6200
<cons, s>(q_gen_6181, q_gen_6180) -> q_gen_6177
<cons, s>(q_gen_6199, q_gen_6180) -> q_gen_6177
<cons, s>(q_gen_6199, q_gen_6197) -> q_gen_6177
<nil, z>() -> q_gen_6177
<a, z>() -> q_gen_6181
<b, z>() -> q_gen_6181
<a, s>(q_gen_6200) -> q_gen_6199
<b, s>(q_gen_6200) -> q_gen_6199
<cons, s>(q_gen_6181, q_gen_6197) -> q_gen_6205
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 16
() -> length([nil, z]) -> 16
(append([l1, l2, _rx]) /\ append([l2, l1, _tx]) /\ length([_rx, _sx]) /\ length([_tx, _ux])) -> eq_nat([_sx, _ux]) -> 19
(append([t1, l2, _ix])) -> append([cons(h1, t1), l2, cons(h1, _ix)]) -> 19
(length([ll, _nx])) -> length([cons(x, ll), s(_nx)]) -> 19
}
Sat witness: Found: ((append([l1, l2, _rx]) /\ append([l2, l1, _tx]) /\ length([_rx, _sx]) /\ length([_tx, _ux])) -> eq_nat([_sx, _ux]), {
_rx -> cons(b, cons(b, cons(b, nil)))  ;  _sx -> s(s(z))  ;  _tx -> cons(b, cons(b, nil))  ;  _ux -> s(s(s(z)))  ;  l1 -> cons(b, nil)  ;  l2 -> cons(b, nil)
})

-------------------------------------------
Step 21, which took 0.043180 s (model generation: 0.040640,  model checking: 0.002540):

Model:
|_
{
append -> 
{{{
Q={q_gen_6178, q_gen_6182, q_gen_6183, q_gen_6184, q_gen_6192, q_gen_6193, q_gen_6194, q_gen_6195},
Q_f={q_gen_6178, q_gen_6182},
Delta=
{
<cons>(q_gen_6194, q_gen_6193) -> q_gen_6193
<nil>() -> q_gen_6193
<a>() -> q_gen_6194
<b>() -> q_gen_6194
<cons, cons>(q_gen_6184, q_gen_6183) -> q_gen_6183
<nil, cons>(q_gen_6194, q_gen_6193) -> q_gen_6183
<nil, nil>() -> q_gen_6183
<a, a>() -> q_gen_6184
<b, b>() -> q_gen_6184
<cons, cons, cons>(q_gen_6195, q_gen_6182) -> q_gen_6178
<nil, nil, nil>() -> q_gen_6178
<cons, cons, cons>(q_gen_6195, q_gen_6192) -> q_gen_6182
<cons, nil, cons>(q_gen_6184, q_gen_6183) -> q_gen_6182
<nil, cons, cons>(q_gen_6184, q_gen_6183) -> q_gen_6182
<cons, cons, cons>(q_gen_6195, q_gen_6178) -> q_gen_6192
<nil, nil, cons>(q_gen_6194, q_gen_6193) -> q_gen_6192
<a, a, a>() -> q_gen_6195
<a, b, a>() -> q_gen_6195
<b, a, b>() -> q_gen_6195
<b, b, b>() -> q_gen_6195
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_6177, q_gen_6180, q_gen_6181, q_gen_6197, q_gen_6198, q_gen_6199, q_gen_6200, q_gen_6205, q_gen_6218},
Q_f={q_gen_6177},
Delta=
{
<cons>(q_gen_6198, q_gen_6197) -> q_gen_6180
<nil>() -> q_gen_6180
<cons>(q_gen_6198, q_gen_6180) -> q_gen_6197
<a>() -> q_gen_6198
<b>() -> q_gen_6198
<z>() -> q_gen_6200
<s>(q_gen_6200) -> q_gen_6218
<cons, s>(q_gen_6181, q_gen_6180) -> q_gen_6177
<cons, s>(q_gen_6199, q_gen_6197) -> q_gen_6177
<nil, z>() -> q_gen_6177
<a, s>(q_gen_6218) -> q_gen_6181
<a, z>() -> q_gen_6181
<b, s>(q_gen_6218) -> q_gen_6181
<b, z>() -> q_gen_6181
<b, s>(q_gen_6200) -> q_gen_6199
<cons, s>(q_gen_6181, q_gen_6197) -> q_gen_6205
<cons, s>(q_gen_6199, q_gen_6180) -> q_gen_6205
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 17
() -> length([nil, z]) -> 17
(append([l1, l2, _rx]) /\ append([l2, l1, _tx]) /\ length([_rx, _sx]) /\ length([_tx, _ux])) -> eq_nat([_sx, _ux]) -> 19
(append([t1, l2, _ix])) -> append([cons(h1, t1), l2, cons(h1, _ix)]) -> 19
(length([ll, _nx])) -> length([cons(x, ll), s(_nx)]) -> 22
}
Sat witness: Found: ((length([ll, _nx])) -> length([cons(x, ll), s(_nx)]), {
_nx -> s(s(s(z)))  ;  ll -> cons(b, cons(b, cons(b, nil)))  ;  x -> b
})

-------------------------------------------
Step 22, which took 0.038615 s (model generation: 0.037257,  model checking: 0.001358):

Model:
|_
{
append -> 
{{{
Q={q_gen_6178, q_gen_6182, q_gen_6183, q_gen_6184, q_gen_6192, q_gen_6193, q_gen_6194, q_gen_6195},
Q_f={q_gen_6178, q_gen_6182},
Delta=
{
<cons>(q_gen_6194, q_gen_6193) -> q_gen_6193
<nil>() -> q_gen_6193
<a>() -> q_gen_6194
<b>() -> q_gen_6194
<cons, cons>(q_gen_6184, q_gen_6183) -> q_gen_6183
<nil, cons>(q_gen_6194, q_gen_6193) -> q_gen_6183
<nil, nil>() -> q_gen_6183
<a, a>() -> q_gen_6184
<b, b>() -> q_gen_6184
<cons, cons, cons>(q_gen_6195, q_gen_6182) -> q_gen_6178
<nil, nil, nil>() -> q_gen_6178
<cons, cons, cons>(q_gen_6195, q_gen_6192) -> q_gen_6182
<cons, nil, cons>(q_gen_6184, q_gen_6183) -> q_gen_6182
<nil, cons, cons>(q_gen_6184, q_gen_6183) -> q_gen_6182
<cons, cons, cons>(q_gen_6195, q_gen_6178) -> q_gen_6192
<nil, nil, cons>(q_gen_6194, q_gen_6193) -> q_gen_6192
<a, a, a>() -> q_gen_6195
<a, b, a>() -> q_gen_6195
<b, a, b>() -> q_gen_6195
<b, b, b>() -> q_gen_6195
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_6177, q_gen_6180, q_gen_6181, q_gen_6197, q_gen_6198, q_gen_6199, q_gen_6200, q_gen_6205, q_gen_6218},
Q_f={q_gen_6177},
Delta=
{
<cons>(q_gen_6198, q_gen_6197) -> q_gen_6180
<nil>() -> q_gen_6180
<cons>(q_gen_6198, q_gen_6180) -> q_gen_6197
<a>() -> q_gen_6198
<b>() -> q_gen_6198
<s>(q_gen_6218) -> q_gen_6200
<z>() -> q_gen_6200
<s>(q_gen_6200) -> q_gen_6218
<cons, s>(q_gen_6181, q_gen_6180) -> q_gen_6177
<cons, s>(q_gen_6199, q_gen_6180) -> q_gen_6177
<cons, s>(q_gen_6199, q_gen_6197) -> q_gen_6177
<nil, z>() -> q_gen_6177
<a, z>() -> q_gen_6181
<b, s>(q_gen_6218) -> q_gen_6181
<b, z>() -> q_gen_6181
<a, s>(q_gen_6218) -> q_gen_6199
<b, s>(q_gen_6200) -> q_gen_6199
<cons, s>(q_gen_6181, q_gen_6197) -> q_gen_6205
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 18
() -> length([nil, z]) -> 18
(append([l1, l2, _rx]) /\ append([l2, l1, _tx]) /\ length([_rx, _sx]) /\ length([_tx, _ux])) -> eq_nat([_sx, _ux]) -> 19
(append([t1, l2, _ix])) -> append([cons(h1, t1), l2, cons(h1, _ix)]) -> 22
(length([ll, _nx])) -> length([cons(x, ll), s(_nx)]) -> 22
}
Sat witness: Found: ((append([t1, l2, _ix])) -> append([cons(h1, t1), l2, cons(h1, _ix)]), {
_ix -> cons(a, cons(a, nil))  ;  h1 -> a  ;  l2 -> cons(b, cons(b, nil))  ;  t1 -> cons(a, cons(a, nil))
})

-------------------------------------------
Step 23, which took 0.053903 s (model generation: 0.049008,  model checking: 0.004895):

Model:
|_
{
append -> 
{{{
Q={q_gen_6178, q_gen_6182, q_gen_6183, q_gen_6184, q_gen_6192, q_gen_6193, q_gen_6194, q_gen_6195},
Q_f={q_gen_6178, q_gen_6182},
Delta=
{
<cons>(q_gen_6194, q_gen_6193) -> q_gen_6193
<nil>() -> q_gen_6193
<a>() -> q_gen_6194
<b>() -> q_gen_6194
<cons, cons>(q_gen_6184, q_gen_6183) -> q_gen_6183
<nil, cons>(q_gen_6194, q_gen_6193) -> q_gen_6183
<nil, nil>() -> q_gen_6183
<a, a>() -> q_gen_6184
<b, b>() -> q_gen_6184
<nil, cons, cons>(q_gen_6184, q_gen_6183) -> q_gen_6178
<nil, nil, nil>() -> q_gen_6178
<cons, cons, cons>(q_gen_6195, q_gen_6182) -> q_gen_6182
<cons, cons, cons>(q_gen_6195, q_gen_6192) -> q_gen_6182
<cons, nil, cons>(q_gen_6184, q_gen_6183) -> q_gen_6182
<cons, cons, cons>(q_gen_6195, q_gen_6178) -> q_gen_6192
<nil, nil, cons>(q_gen_6194, q_gen_6193) -> q_gen_6192
<a, a, a>() -> q_gen_6195
<a, b, a>() -> q_gen_6195
<b, a, b>() -> q_gen_6195
<b, b, b>() -> q_gen_6195
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_6177, q_gen_6180, q_gen_6181, q_gen_6197, q_gen_6198, q_gen_6199, q_gen_6200, q_gen_6205, q_gen_6218},
Q_f={q_gen_6177},
Delta=
{
<cons>(q_gen_6198, q_gen_6197) -> q_gen_6180
<nil>() -> q_gen_6180
<cons>(q_gen_6198, q_gen_6180) -> q_gen_6197
<a>() -> q_gen_6198
<b>() -> q_gen_6198
<s>(q_gen_6218) -> q_gen_6200
<z>() -> q_gen_6200
<s>(q_gen_6200) -> q_gen_6218
<cons, s>(q_gen_6181, q_gen_6180) -> q_gen_6177
<cons, s>(q_gen_6199, q_gen_6180) -> q_gen_6177
<cons, s>(q_gen_6199, q_gen_6197) -> q_gen_6177
<nil, z>() -> q_gen_6177
<a, z>() -> q_gen_6181
<b, s>(q_gen_6218) -> q_gen_6181
<b, z>() -> q_gen_6181
<a, s>(q_gen_6218) -> q_gen_6199
<b, s>(q_gen_6200) -> q_gen_6199
<cons, s>(q_gen_6181, q_gen_6197) -> q_gen_6205
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 19
() -> length([nil, z]) -> 19
(append([l1, l2, _rx]) /\ append([l2, l1, _tx]) /\ length([_rx, _sx]) /\ length([_tx, _ux])) -> eq_nat([_sx, _ux]) -> 22
(append([t1, l2, _ix])) -> append([cons(h1, t1), l2, cons(h1, _ix)]) -> 22
(length([ll, _nx])) -> length([cons(x, ll), s(_nx)]) -> 22
}
Sat witness: Found: ((append([l1, l2, _rx]) /\ append([l2, l1, _tx]) /\ length([_rx, _sx]) /\ length([_tx, _ux])) -> eq_nat([_sx, _ux]), {
_rx -> cons(a, cons(b, cons(b, nil)))  ;  _sx -> s(z)  ;  _tx -> cons(b, cons(b, cons(b, cons(b, nil))))  ;  _ux -> s(s(z))  ;  l1 -> cons(a, cons(b, nil))  ;  l2 -> cons(b, cons(b, nil))
})

-------------------------------------------
Step 24, which took 0.059722 s (model generation: 0.058543,  model checking: 0.001179):

Model:
|_
{
append -> 
{{{
Q={q_gen_6178, q_gen_6183, q_gen_6184, q_gen_6192, q_gen_6193, q_gen_6194, q_gen_6195, q_gen_6203},
Q_f={q_gen_6178},
Delta=
{
<cons>(q_gen_6194, q_gen_6193) -> q_gen_6193
<nil>() -> q_gen_6193
<a>() -> q_gen_6194
<b>() -> q_gen_6194
<cons, cons>(q_gen_6184, q_gen_6183) -> q_gen_6183
<nil, nil>() -> q_gen_6183
<a, a>() -> q_gen_6184
<b, b>() -> q_gen_6184
<nil, cons>(q_gen_6194, q_gen_6193) -> q_gen_6203
<cons, cons, cons>(q_gen_6195, q_gen_6192) -> q_gen_6178
<cons, nil, cons>(q_gen_6184, q_gen_6183) -> q_gen_6178
<nil, cons, cons>(q_gen_6184, q_gen_6183) -> q_gen_6178
<nil, nil, nil>() -> q_gen_6178
<cons, cons, cons>(q_gen_6195, q_gen_6178) -> q_gen_6192
<cons, nil, cons>(q_gen_6184, q_gen_6203) -> q_gen_6192
<nil, cons, cons>(q_gen_6184, q_gen_6203) -> q_gen_6192
<nil, nil, cons>(q_gen_6194, q_gen_6193) -> q_gen_6192
<a, a, a>() -> q_gen_6195
<a, b, a>() -> q_gen_6195
<b, a, b>() -> q_gen_6195
<b, b, b>() -> q_gen_6195
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_6177, q_gen_6180, q_gen_6181, q_gen_6197, q_gen_6198, q_gen_6199, q_gen_6200, q_gen_6205, q_gen_6218},
Q_f={q_gen_6177},
Delta=
{
<cons>(q_gen_6198, q_gen_6197) -> q_gen_6180
<nil>() -> q_gen_6180
<cons>(q_gen_6198, q_gen_6180) -> q_gen_6197
<a>() -> q_gen_6198
<b>() -> q_gen_6198
<s>(q_gen_6218) -> q_gen_6200
<z>() -> q_gen_6200
<s>(q_gen_6200) -> q_gen_6218
<cons, s>(q_gen_6181, q_gen_6180) -> q_gen_6177
<cons, s>(q_gen_6199, q_gen_6180) -> q_gen_6177
<cons, s>(q_gen_6199, q_gen_6197) -> q_gen_6177
<nil, z>() -> q_gen_6177
<a, z>() -> q_gen_6181
<b, s>(q_gen_6218) -> q_gen_6181
<b, z>() -> q_gen_6181
<a, s>(q_gen_6218) -> q_gen_6199
<b, s>(q_gen_6200) -> q_gen_6199
<cons, s>(q_gen_6181, q_gen_6197) -> q_gen_6205
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 20
() -> length([nil, z]) -> 20
(append([l1, l2, _rx]) /\ append([l2, l1, _tx]) /\ length([_rx, _sx]) /\ length([_tx, _ux])) -> eq_nat([_sx, _ux]) -> 22
(append([t1, l2, _ix])) -> append([cons(h1, t1), l2, cons(h1, _ix)]) -> 22
(length([ll, _nx])) -> length([cons(x, ll), s(_nx)]) -> 25
}
Sat witness: Found: ((length([ll, _nx])) -> length([cons(x, ll), s(_nx)]), {
_nx -> s(s(z))  ;  ll -> cons(b, nil)  ;  x -> b
})

-------------------------------------------
Step 25, which took 0.058124 s (model generation: 0.055354,  model checking: 0.002770):

Model:
|_
{
append -> 
{{{
Q={q_gen_6178, q_gen_6183, q_gen_6184, q_gen_6192, q_gen_6193, q_gen_6194, q_gen_6195, q_gen_6203},
Q_f={q_gen_6178},
Delta=
{
<cons>(q_gen_6194, q_gen_6193) -> q_gen_6193
<nil>() -> q_gen_6193
<a>() -> q_gen_6194
<b>() -> q_gen_6194
<cons, cons>(q_gen_6184, q_gen_6183) -> q_gen_6183
<nil, nil>() -> q_gen_6183
<a, a>() -> q_gen_6184
<b, b>() -> q_gen_6184
<nil, cons>(q_gen_6194, q_gen_6193) -> q_gen_6203
<cons, cons, cons>(q_gen_6195, q_gen_6192) -> q_gen_6178
<cons, nil, cons>(q_gen_6184, q_gen_6183) -> q_gen_6178
<nil, cons, cons>(q_gen_6184, q_gen_6183) -> q_gen_6178
<nil, nil, nil>() -> q_gen_6178
<cons, cons, cons>(q_gen_6195, q_gen_6178) -> q_gen_6192
<cons, nil, cons>(q_gen_6184, q_gen_6203) -> q_gen_6192
<nil, cons, cons>(q_gen_6184, q_gen_6203) -> q_gen_6192
<nil, nil, cons>(q_gen_6194, q_gen_6193) -> q_gen_6192
<a, a, a>() -> q_gen_6195
<a, b, a>() -> q_gen_6195
<b, a, b>() -> q_gen_6195
<b, b, b>() -> q_gen_6195
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_6177, q_gen_6180, q_gen_6181, q_gen_6197, q_gen_6198, q_gen_6199, q_gen_6200, q_gen_6205, q_gen_6218},
Q_f={q_gen_6177},
Delta=
{
<cons>(q_gen_6198, q_gen_6197) -> q_gen_6180
<nil>() -> q_gen_6180
<cons>(q_gen_6198, q_gen_6180) -> q_gen_6197
<a>() -> q_gen_6198
<b>() -> q_gen_6198
<s>(q_gen_6218) -> q_gen_6200
<z>() -> q_gen_6200
<s>(q_gen_6200) -> q_gen_6218
<cons, s>(q_gen_6181, q_gen_6180) -> q_gen_6177
<cons, s>(q_gen_6199, q_gen_6197) -> q_gen_6177
<nil, z>() -> q_gen_6177
<a, s>(q_gen_6218) -> q_gen_6181
<a, z>() -> q_gen_6181
<b, s>(q_gen_6218) -> q_gen_6181
<b, z>() -> q_gen_6181
<b, s>(q_gen_6200) -> q_gen_6199
<cons, s>(q_gen_6181, q_gen_6197) -> q_gen_6205
<cons, s>(q_gen_6199, q_gen_6180) -> q_gen_6205
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 21
() -> length([nil, z]) -> 21
(append([l1, l2, _rx]) /\ append([l2, l1, _tx]) /\ length([_rx, _sx]) /\ length([_tx, _ux])) -> eq_nat([_sx, _ux]) -> 22
(append([t1, l2, _ix])) -> append([cons(h1, t1), l2, cons(h1, _ix)]) -> 25
(length([ll, _nx])) -> length([cons(x, ll), s(_nx)]) -> 25
}
Sat witness: Found: ((append([t1, l2, _ix])) -> append([cons(h1, t1), l2, cons(h1, _ix)]), {
_ix -> cons(a, cons(b, cons(b, nil)))  ;  h1 -> a  ;  l2 -> cons(b, cons(b, nil))  ;  t1 -> cons(a, nil)
})

-------------------------------------------
Step 26, which took 0.065545 s (model generation: 0.062914,  model checking: 0.002631):

Model:
|_
{
append -> 
{{{
Q={q_gen_6178, q_gen_6183, q_gen_6184, q_gen_6192, q_gen_6193, q_gen_6194, q_gen_6195, q_gen_6203, q_gen_6232},
Q_f={q_gen_6178},
Delta=
{
<nil>() -> q_gen_6193
<a>() -> q_gen_6194
<b>() -> q_gen_6194
<cons>(q_gen_6194, q_gen_6193) -> q_gen_6232
<cons, cons>(q_gen_6184, q_gen_6183) -> q_gen_6183
<nil, nil>() -> q_gen_6183
<a, a>() -> q_gen_6184
<b, b>() -> q_gen_6184
<nil, cons>(q_gen_6194, q_gen_6193) -> q_gen_6203
<cons, cons, cons>(q_gen_6195, q_gen_6192) -> q_gen_6178
<cons, nil, cons>(q_gen_6184, q_gen_6183) -> q_gen_6178
<nil, cons, cons>(q_gen_6184, q_gen_6183) -> q_gen_6178
<nil, nil, cons>(q_gen_6194, q_gen_6232) -> q_gen_6178
<nil, nil, nil>() -> q_gen_6178
<cons, cons, cons>(q_gen_6195, q_gen_6178) -> q_gen_6192
<cons, nil, cons>(q_gen_6184, q_gen_6203) -> q_gen_6192
<nil, cons, cons>(q_gen_6184, q_gen_6203) -> q_gen_6192
<nil, nil, cons>(q_gen_6194, q_gen_6193) -> q_gen_6192
<a, a, a>() -> q_gen_6195
<a, b, a>() -> q_gen_6195
<b, a, b>() -> q_gen_6195
<b, b, b>() -> q_gen_6195
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_6177, q_gen_6180, q_gen_6181, q_gen_6197, q_gen_6198, q_gen_6199, q_gen_6200, q_gen_6205},
Q_f={q_gen_6177},
Delta=
{
<cons>(q_gen_6198, q_gen_6197) -> q_gen_6180
<nil>() -> q_gen_6180
<cons>(q_gen_6198, q_gen_6180) -> q_gen_6197
<a>() -> q_gen_6198
<b>() -> q_gen_6198
<s>(q_gen_6200) -> q_gen_6200
<z>() -> q_gen_6200
<cons, s>(q_gen_6181, q_gen_6180) -> q_gen_6177
<cons, s>(q_gen_6199, q_gen_6180) -> q_gen_6177
<cons, s>(q_gen_6199, q_gen_6197) -> q_gen_6177
<nil, z>() -> q_gen_6177
<a, z>() -> q_gen_6181
<b, z>() -> q_gen_6181
<a, s>(q_gen_6200) -> q_gen_6199
<b, s>(q_gen_6200) -> q_gen_6199
<cons, s>(q_gen_6181, q_gen_6197) -> q_gen_6205
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 22
() -> length([nil, z]) -> 22
(append([l1, l2, _rx]) /\ append([l2, l1, _tx]) /\ length([_rx, _sx]) /\ length([_tx, _ux])) -> eq_nat([_sx, _ux]) -> 25
(append([t1, l2, _ix])) -> append([cons(h1, t1), l2, cons(h1, _ix)]) -> 25
(length([ll, _nx])) -> length([cons(x, ll), s(_nx)]) -> 25
}
Sat witness: Found: ((append([l1, l2, _rx]) /\ append([l2, l1, _tx]) /\ length([_rx, _sx]) /\ length([_tx, _ux])) -> eq_nat([_sx, _ux]), {
_rx -> nil  ;  _sx -> z  ;  _tx -> cons(a, cons(b, nil))  ;  _ux -> s(s(z))  ;  l1 -> nil  ;  l2 -> nil
})

-------------------------------------------
Step 27, which took 0.071319 s (model generation: 0.069632,  model checking: 0.001687):

Model:
|_
{
append -> 
{{{
Q={q_gen_6178, q_gen_6183, q_gen_6184, q_gen_6192, q_gen_6193, q_gen_6194, q_gen_6195, q_gen_6203},
Q_f={q_gen_6178},
Delta=
{
<cons>(q_gen_6194, q_gen_6193) -> q_gen_6193
<nil>() -> q_gen_6193
<a>() -> q_gen_6194
<b>() -> q_gen_6194
<cons, cons>(q_gen_6184, q_gen_6183) -> q_gen_6183
<nil, nil>() -> q_gen_6183
<a, a>() -> q_gen_6184
<b, b>() -> q_gen_6184
<nil, cons>(q_gen_6194, q_gen_6193) -> q_gen_6203
<cons, cons, cons>(q_gen_6195, q_gen_6192) -> q_gen_6178
<cons, nil, cons>(q_gen_6184, q_gen_6183) -> q_gen_6178
<nil, cons, cons>(q_gen_6184, q_gen_6183) -> q_gen_6178
<nil, cons, cons>(q_gen_6184, q_gen_6203) -> q_gen_6178
<nil, nil, nil>() -> q_gen_6178
<cons, cons, cons>(q_gen_6195, q_gen_6178) -> q_gen_6192
<cons, nil, cons>(q_gen_6184, q_gen_6203) -> q_gen_6192
<nil, nil, cons>(q_gen_6194, q_gen_6193) -> q_gen_6192
<a, a, a>() -> q_gen_6195
<a, b, a>() -> q_gen_6195
<b, a, b>() -> q_gen_6195
<b, b, b>() -> q_gen_6195
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_6177, q_gen_6180, q_gen_6181, q_gen_6197, q_gen_6198, q_gen_6199, q_gen_6200, q_gen_6205, q_gen_6218},
Q_f={q_gen_6177},
Delta=
{
<cons>(q_gen_6198, q_gen_6197) -> q_gen_6180
<nil>() -> q_gen_6180
<cons>(q_gen_6198, q_gen_6180) -> q_gen_6197
<a>() -> q_gen_6198
<b>() -> q_gen_6198
<s>(q_gen_6218) -> q_gen_6200
<z>() -> q_gen_6200
<s>(q_gen_6200) -> q_gen_6218
<cons, s>(q_gen_6181, q_gen_6180) -> q_gen_6177
<cons, s>(q_gen_6199, q_gen_6197) -> q_gen_6177
<nil, z>() -> q_gen_6177
<a, s>(q_gen_6200) -> q_gen_6181
<a, s>(q_gen_6218) -> q_gen_6181
<a, z>() -> q_gen_6181
<b, s>(q_gen_6218) -> q_gen_6181
<b, z>() -> q_gen_6181
<b, s>(q_gen_6200) -> q_gen_6199
<cons, s>(q_gen_6181, q_gen_6197) -> q_gen_6205
<cons, s>(q_gen_6199, q_gen_6180) -> q_gen_6205
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 23
() -> length([nil, z]) -> 23
(append([l1, l2, _rx]) /\ append([l2, l1, _tx]) /\ length([_rx, _sx]) /\ length([_tx, _ux])) -> eq_nat([_sx, _ux]) -> 25
(append([t1, l2, _ix])) -> append([cons(h1, t1), l2, cons(h1, _ix)]) -> 25
(length([ll, _nx])) -> length([cons(x, ll), s(_nx)]) -> 28
}
Sat witness: Found: ((length([ll, _nx])) -> length([cons(x, ll), s(_nx)]), {
_nx -> s(s(z))  ;  ll -> cons(a, nil)  ;  x -> b
})

-------------------------------------------
Step 28, which took 0.090519 s (model generation: 0.083002,  model checking: 0.007517):

Model:
|_
{
append -> 
{{{
Q={q_gen_6178, q_gen_6182, q_gen_6183, q_gen_6184, q_gen_6192, q_gen_6193, q_gen_6194, q_gen_6195},
Q_f={q_gen_6178, q_gen_6182},
Delta=
{
<cons>(q_gen_6194, q_gen_6193) -> q_gen_6193
<nil>() -> q_gen_6193
<a>() -> q_gen_6194
<b>() -> q_gen_6194
<cons, cons>(q_gen_6184, q_gen_6183) -> q_gen_6183
<nil, cons>(q_gen_6194, q_gen_6193) -> q_gen_6183
<nil, nil>() -> q_gen_6183
<a, a>() -> q_gen_6184
<b, b>() -> q_gen_6184
<cons, cons, cons>(q_gen_6195, q_gen_6192) -> q_gen_6178
<nil, cons, cons>(q_gen_6184, q_gen_6183) -> q_gen_6178
<nil, nil, nil>() -> q_gen_6178
<cons, cons, cons>(q_gen_6195, q_gen_6182) -> q_gen_6182
<cons, nil, cons>(q_gen_6184, q_gen_6183) -> q_gen_6182
<cons, cons, cons>(q_gen_6195, q_gen_6178) -> q_gen_6192
<nil, nil, cons>(q_gen_6194, q_gen_6193) -> q_gen_6192
<a, a, a>() -> q_gen_6195
<a, b, a>() -> q_gen_6195
<b, a, b>() -> q_gen_6195
<b, b, b>() -> q_gen_6195
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_6177, q_gen_6180, q_gen_6181, q_gen_6197, q_gen_6198, q_gen_6199, q_gen_6200, q_gen_6205, q_gen_6218},
Q_f={q_gen_6177},
Delta=
{
<cons>(q_gen_6198, q_gen_6197) -> q_gen_6180
<nil>() -> q_gen_6180
<cons>(q_gen_6198, q_gen_6180) -> q_gen_6197
<a>() -> q_gen_6198
<b>() -> q_gen_6198
<s>(q_gen_6218) -> q_gen_6200
<z>() -> q_gen_6200
<s>(q_gen_6200) -> q_gen_6218
<cons, s>(q_gen_6181, q_gen_6180) -> q_gen_6177
<cons, s>(q_gen_6199, q_gen_6197) -> q_gen_6177
<nil, z>() -> q_gen_6177
<a, z>() -> q_gen_6181
<b, s>(q_gen_6218) -> q_gen_6181
<b, z>() -> q_gen_6181
<a, s>(q_gen_6200) -> q_gen_6199
<a, s>(q_gen_6218) -> q_gen_6199
<b, s>(q_gen_6200) -> q_gen_6199
<cons, s>(q_gen_6181, q_gen_6197) -> q_gen_6205
<cons, s>(q_gen_6199, q_gen_6180) -> q_gen_6205
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 24
() -> length([nil, z]) -> 24
(append([l1, l2, _rx]) /\ append([l2, l1, _tx]) /\ length([_rx, _sx]) /\ length([_tx, _ux])) -> eq_nat([_sx, _ux]) -> 25
(append([t1, l2, _ix])) -> append([cons(h1, t1), l2, cons(h1, _ix)]) -> 28
(length([ll, _nx])) -> length([cons(x, ll), s(_nx)]) -> 28
}
Sat witness: Found: ((append([t1, l2, _ix])) -> append([cons(h1, t1), l2, cons(h1, _ix)]), {
_ix -> cons(a, cons(a, nil))  ;  h1 -> a  ;  l2 -> cons(a, cons(a, nil))  ;  t1 -> nil
})

-------------------------------------------
Step 29, which took 0.095826 s (model generation: 0.092097,  model checking: 0.003729):

Model:
|_
{
append -> 
{{{
Q={q_gen_6178, q_gen_6183, q_gen_6184, q_gen_6192, q_gen_6193, q_gen_6194, q_gen_6195, q_gen_6204, q_gen_6232},
Q_f={q_gen_6178},
Delta=
{
<nil>() -> q_gen_6193
<a>() -> q_gen_6194
<b>() -> q_gen_6194
<cons>(q_gen_6194, q_gen_6193) -> q_gen_6232
<cons, cons>(q_gen_6184, q_gen_6183) -> q_gen_6183
<nil, cons>(q_gen_6194, q_gen_6193) -> q_gen_6183
<nil, nil>() -> q_gen_6183
<a, a>() -> q_gen_6184
<b, b>() -> q_gen_6184
<cons, cons, cons>(q_gen_6195, q_gen_6192) -> q_gen_6178
<cons, cons, cons>(q_gen_6204, q_gen_6178) -> q_gen_6178
<cons, cons, cons>(q_gen_6204, q_gen_6192) -> q_gen_6178
<cons, nil, cons>(q_gen_6184, q_gen_6183) -> q_gen_6178
<nil, cons, cons>(q_gen_6184, q_gen_6183) -> q_gen_6178
<nil, nil, cons>(q_gen_6194, q_gen_6232) -> q_gen_6178
<nil, nil, nil>() -> q_gen_6178
<cons, cons, cons>(q_gen_6195, q_gen_6178) -> q_gen_6192
<nil, nil, cons>(q_gen_6194, q_gen_6193) -> q_gen_6192
<b, b, b>() -> q_gen_6195
<a, a, a>() -> q_gen_6204
<a, b, a>() -> q_gen_6204
<b, a, b>() -> q_gen_6204
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_6177, q_gen_6180, q_gen_6181, q_gen_6197, q_gen_6198, q_gen_6199, q_gen_6200, q_gen_6205},
Q_f={q_gen_6177},
Delta=
{
<nil>() -> q_gen_6180
<cons>(q_gen_6198, q_gen_6180) -> q_gen_6197
<cons>(q_gen_6198, q_gen_6197) -> q_gen_6197
<a>() -> q_gen_6198
<b>() -> q_gen_6198
<s>(q_gen_6200) -> q_gen_6200
<z>() -> q_gen_6200
<cons, s>(q_gen_6181, q_gen_6180) -> q_gen_6177
<cons, s>(q_gen_6199, q_gen_6197) -> q_gen_6177
<nil, z>() -> q_gen_6177
<a, s>(q_gen_6200) -> q_gen_6181
<a, z>() -> q_gen_6181
<b, z>() -> q_gen_6181
<b, s>(q_gen_6200) -> q_gen_6199
<cons, s>(q_gen_6181, q_gen_6197) -> q_gen_6205
<cons, s>(q_gen_6199, q_gen_6180) -> q_gen_6205
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 25
() -> length([nil, z]) -> 25
(append([l1, l2, _rx]) /\ append([l2, l1, _tx]) /\ length([_rx, _sx]) /\ length([_tx, _ux])) -> eq_nat([_sx, _ux]) -> 28
(append([t1, l2, _ix])) -> append([cons(h1, t1), l2, cons(h1, _ix)]) -> 28
(length([ll, _nx])) -> length([cons(x, ll), s(_nx)]) -> 28
}
Sat witness: Found: ((append([l1, l2, _rx]) /\ append([l2, l1, _tx]) /\ length([_rx, _sx]) /\ length([_tx, _ux])) -> eq_nat([_sx, _ux]), {
_rx -> nil  ;  _sx -> z  ;  _tx -> cons(b, cons(b, nil))  ;  _ux -> s(s(z))  ;  l1 -> nil  ;  l2 -> nil
})

-------------------------------------------
Step 30, which took 0.091879 s (model generation: 0.089314,  model checking: 0.002565):

Model:
|_
{
append -> 
{{{
Q={q_gen_6178, q_gen_6183, q_gen_6184, q_gen_6192, q_gen_6193, q_gen_6194, q_gen_6195, q_gen_6204},
Q_f={q_gen_6178},
Delta=
{
<cons>(q_gen_6194, q_gen_6193) -> q_gen_6193
<nil>() -> q_gen_6193
<a>() -> q_gen_6194
<b>() -> q_gen_6194
<cons, cons>(q_gen_6184, q_gen_6183) -> q_gen_6183
<nil, cons>(q_gen_6194, q_gen_6193) -> q_gen_6183
<nil, nil>() -> q_gen_6183
<a, a>() -> q_gen_6184
<b, b>() -> q_gen_6184
<cons, cons, cons>(q_gen_6195, q_gen_6192) -> q_gen_6178
<cons, cons, cons>(q_gen_6204, q_gen_6178) -> q_gen_6178
<cons, cons, cons>(q_gen_6204, q_gen_6192) -> q_gen_6178
<cons, nil, cons>(q_gen_6184, q_gen_6183) -> q_gen_6178
<nil, cons, cons>(q_gen_6184, q_gen_6183) -> q_gen_6178
<nil, nil, nil>() -> q_gen_6178
<cons, cons, cons>(q_gen_6195, q_gen_6178) -> q_gen_6192
<nil, nil, cons>(q_gen_6194, q_gen_6193) -> q_gen_6192
<b, a, b>() -> q_gen_6195
<b, b, b>() -> q_gen_6195
<a, a, a>() -> q_gen_6204
<a, b, a>() -> q_gen_6204
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_6177, q_gen_6180, q_gen_6181, q_gen_6197, q_gen_6198, q_gen_6199, q_gen_6200, q_gen_6205, q_gen_6218},
Q_f={q_gen_6177},
Delta=
{
<cons>(q_gen_6198, q_gen_6197) -> q_gen_6180
<nil>() -> q_gen_6180
<cons>(q_gen_6198, q_gen_6180) -> q_gen_6197
<a>() -> q_gen_6198
<b>() -> q_gen_6198
<s>(q_gen_6218) -> q_gen_6200
<z>() -> q_gen_6200
<s>(q_gen_6200) -> q_gen_6218
<cons, s>(q_gen_6181, q_gen_6180) -> q_gen_6177
<cons, s>(q_gen_6199, q_gen_6197) -> q_gen_6177
<nil, z>() -> q_gen_6177
<a, s>(q_gen_6218) -> q_gen_6181
<a, z>() -> q_gen_6181
<b, s>(q_gen_6218) -> q_gen_6181
<b, z>() -> q_gen_6181
<a, s>(q_gen_6200) -> q_gen_6199
<b, s>(q_gen_6200) -> q_gen_6199
<cons, s>(q_gen_6181, q_gen_6197) -> q_gen_6205
<cons, s>(q_gen_6199, q_gen_6180) -> q_gen_6205
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 26
() -> length([nil, z]) -> 26
(append([l1, l2, _rx]) /\ append([l2, l1, _tx]) /\ length([_rx, _sx]) /\ length([_tx, _ux])) -> eq_nat([_sx, _ux]) -> 28
(append([t1, l2, _ix])) -> append([cons(h1, t1), l2, cons(h1, _ix)]) -> 31
(length([ll, _nx])) -> length([cons(x, ll), s(_nx)]) -> 29
}
Sat witness: Found: ((append([t1, l2, _ix])) -> append([cons(h1, t1), l2, cons(h1, _ix)]), {
_ix -> cons(a, nil)  ;  h1 -> b  ;  l2 -> cons(b, nil)  ;  t1 -> cons(a, nil)
})

-------------------------------------------
Step 31, which took 0.096709 s (model generation: 0.096205,  model checking: 0.000504):

Model:
|_
{
append -> 
{{{
Q={q_gen_6178, q_gen_6183, q_gen_6184, q_gen_6186, q_gen_6192, q_gen_6193, q_gen_6194, q_gen_6195, q_gen_6222},
Q_f={q_gen_6178},
Delta=
{
<cons>(q_gen_6194, q_gen_6193) -> q_gen_6193
<nil>() -> q_gen_6193
<a>() -> q_gen_6194
<b>() -> q_gen_6194
<nil, nil>() -> q_gen_6183
<a, a>() -> q_gen_6184
<b, b>() -> q_gen_6184
<cons, cons>(q_gen_6184, q_gen_6183) -> q_gen_6186
<nil, cons>(q_gen_6194, q_gen_6193) -> q_gen_6186
<cons, cons, cons>(q_gen_6195, q_gen_6192) -> q_gen_6178
<cons, cons, cons>(q_gen_6222, q_gen_6178) -> q_gen_6178
<cons, cons, cons>(q_gen_6222, q_gen_6192) -> q_gen_6178
<cons, nil, cons>(q_gen_6184, q_gen_6183) -> q_gen_6178
<nil, cons, cons>(q_gen_6184, q_gen_6183) -> q_gen_6178
<nil, cons, cons>(q_gen_6184, q_gen_6186) -> q_gen_6178
<nil, nil, nil>() -> q_gen_6178
<cons, cons, cons>(q_gen_6195, q_gen_6178) -> q_gen_6192
<cons, nil, cons>(q_gen_6184, q_gen_6186) -> q_gen_6192
<nil, nil, cons>(q_gen_6194, q_gen_6193) -> q_gen_6192
<a, b, a>() -> q_gen_6195
<b, a, b>() -> q_gen_6195
<b, b, b>() -> q_gen_6195
<a, a, a>() -> q_gen_6222
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_6177, q_gen_6180, q_gen_6181, q_gen_6197, q_gen_6198, q_gen_6199, q_gen_6200, q_gen_6205, q_gen_6218},
Q_f={q_gen_6177},
Delta=
{
<cons>(q_gen_6198, q_gen_6197) -> q_gen_6180
<nil>() -> q_gen_6180
<cons>(q_gen_6198, q_gen_6180) -> q_gen_6197
<a>() -> q_gen_6198
<b>() -> q_gen_6198
<s>(q_gen_6218) -> q_gen_6200
<z>() -> q_gen_6200
<s>(q_gen_6200) -> q_gen_6218
<cons, s>(q_gen_6181, q_gen_6180) -> q_gen_6177
<cons, s>(q_gen_6199, q_gen_6197) -> q_gen_6177
<nil, z>() -> q_gen_6177
<a, s>(q_gen_6218) -> q_gen_6181
<a, z>() -> q_gen_6181
<b, s>(q_gen_6218) -> q_gen_6181
<b, z>() -> q_gen_6181
<a, s>(q_gen_6200) -> q_gen_6199
<b, s>(q_gen_6200) -> q_gen_6199
<cons, s>(q_gen_6181, q_gen_6197) -> q_gen_6205
<cons, s>(q_gen_6199, q_gen_6180) -> q_gen_6205
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 29
() -> length([nil, z]) -> 27
(append([l1, l2, _rx]) /\ append([l2, l1, _tx]) /\ length([_rx, _sx]) /\ length([_tx, _ux])) -> eq_nat([_sx, _ux]) -> 28
(append([t1, l2, _ix])) -> append([cons(h1, t1), l2, cons(h1, _ix)]) -> 31
(length([ll, _nx])) -> length([cons(x, ll), s(_nx)]) -> 29
}
Sat witness: Found: (() -> append([nil, l2, l2]), {
l2 -> cons(b, cons(b, cons(b, nil)))
})

-------------------------------------------
Step 32, which took 0.117836 s (model generation: 0.110214,  model checking: 0.007622):

Model:
|_
{
append -> 
{{{
Q={q_gen_6178, q_gen_6183, q_gen_6184, q_gen_6186, q_gen_6192, q_gen_6193, q_gen_6194, q_gen_6195, q_gen_6222},
Q_f={q_gen_6178},
Delta=
{
<cons>(q_gen_6194, q_gen_6193) -> q_gen_6193
<nil>() -> q_gen_6193
<a>() -> q_gen_6194
<b>() -> q_gen_6194
<nil, nil>() -> q_gen_6183
<a, a>() -> q_gen_6184
<b, b>() -> q_gen_6184
<cons, cons>(q_gen_6184, q_gen_6183) -> q_gen_6186
<cons, cons>(q_gen_6184, q_gen_6186) -> q_gen_6186
<nil, cons>(q_gen_6194, q_gen_6193) -> q_gen_6186
<cons, cons, cons>(q_gen_6195, q_gen_6192) -> q_gen_6178
<cons, cons, cons>(q_gen_6222, q_gen_6178) -> q_gen_6178
<cons, cons, cons>(q_gen_6222, q_gen_6192) -> q_gen_6178
<cons, nil, cons>(q_gen_6184, q_gen_6183) -> q_gen_6178
<nil, cons, cons>(q_gen_6184, q_gen_6183) -> q_gen_6178
<nil, cons, cons>(q_gen_6184, q_gen_6186) -> q_gen_6178
<nil, nil, nil>() -> q_gen_6178
<cons, cons, cons>(q_gen_6195, q_gen_6178) -> q_gen_6192
<cons, nil, cons>(q_gen_6184, q_gen_6186) -> q_gen_6192
<nil, nil, cons>(q_gen_6194, q_gen_6193) -> q_gen_6192
<a, b, a>() -> q_gen_6195
<b, a, b>() -> q_gen_6195
<b, b, b>() -> q_gen_6195
<a, a, a>() -> q_gen_6222
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_6177, q_gen_6180, q_gen_6181, q_gen_6197, q_gen_6198, q_gen_6199, q_gen_6200, q_gen_6205, q_gen_6218},
Q_f={q_gen_6177},
Delta=
{
<cons>(q_gen_6198, q_gen_6197) -> q_gen_6180
<nil>() -> q_gen_6180
<cons>(q_gen_6198, q_gen_6180) -> q_gen_6197
<a>() -> q_gen_6198
<b>() -> q_gen_6198
<s>(q_gen_6218) -> q_gen_6200
<z>() -> q_gen_6200
<s>(q_gen_6200) -> q_gen_6218
<cons, s>(q_gen_6181, q_gen_6180) -> q_gen_6177
<cons, s>(q_gen_6199, q_gen_6197) -> q_gen_6177
<nil, z>() -> q_gen_6177
<a, s>(q_gen_6218) -> q_gen_6181
<a, z>() -> q_gen_6181
<b, s>(q_gen_6218) -> q_gen_6181
<b, z>() -> q_gen_6181
<a, s>(q_gen_6200) -> q_gen_6199
<b, s>(q_gen_6200) -> q_gen_6199
<cons, s>(q_gen_6181, q_gen_6197) -> q_gen_6205
<cons, s>(q_gen_6199, q_gen_6180) -> q_gen_6205
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 29
() -> length([nil, z]) -> 28
(append([l1, l2, _rx]) /\ append([l2, l1, _tx]) /\ length([_rx, _sx]) /\ length([_tx, _ux])) -> eq_nat([_sx, _ux]) -> 31
(append([t1, l2, _ix])) -> append([cons(h1, t1), l2, cons(h1, _ix)]) -> 31
(length([ll, _nx])) -> length([cons(x, ll), s(_nx)]) -> 29
}
Sat witness: Found: ((append([l1, l2, _rx]) /\ append([l2, l1, _tx]) /\ length([_rx, _sx]) /\ length([_tx, _ux])) -> eq_nat([_sx, _ux]), {
_rx -> cons(a, cons(b, cons(b, cons(b, nil))))  ;  _sx -> s(s(z))  ;  _tx -> cons(a, cons(b, cons(b, nil)))  ;  _ux -> s(z)  ;  l1 -> cons(a, cons(b, nil))  ;  l2 -> cons(a, cons(b, nil))
})

-------------------------------------------
Step 33, which took 0.118315 s (model generation: 0.117242,  model checking: 0.001073):

Model:
|_
{
append -> 
{{{
Q={q_gen_6178, q_gen_6183, q_gen_6184, q_gen_6192, q_gen_6193, q_gen_6194, q_gen_6195, q_gen_6203, q_gen_6214, q_gen_6232},
Q_f={q_gen_6178},
Delta=
{
<nil>() -> q_gen_6193
<a>() -> q_gen_6194
<b>() -> q_gen_6194
<cons>(q_gen_6194, q_gen_6193) -> q_gen_6232
<cons, cons>(q_gen_6184, q_gen_6183) -> q_gen_6183
<nil, nil>() -> q_gen_6183
<a, a>() -> q_gen_6184
<b, b>() -> q_gen_6184
<nil, cons>(q_gen_6194, q_gen_6193) -> q_gen_6203
<cons, cons, cons>(q_gen_6195, q_gen_6192) -> q_gen_6178
<cons, nil, cons>(q_gen_6184, q_gen_6183) -> q_gen_6178
<nil, cons, cons>(q_gen_6184, q_gen_6183) -> q_gen_6178
<nil, nil, nil>() -> q_gen_6178
<cons, cons, cons>(q_gen_6195, q_gen_6214) -> q_gen_6192
<cons, nil, cons>(q_gen_6184, q_gen_6203) -> q_gen_6192
<nil, cons, cons>(q_gen_6184, q_gen_6203) -> q_gen_6192
<nil, nil, cons>(q_gen_6194, q_gen_6193) -> q_gen_6192
<a, a, a>() -> q_gen_6195
<a, b, a>() -> q_gen_6195
<b, a, b>() -> q_gen_6195
<b, b, b>() -> q_gen_6195
<cons, cons, cons>(q_gen_6195, q_gen_6178) -> q_gen_6214
<nil, nil, cons>(q_gen_6194, q_gen_6232) -> q_gen_6214
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_6177, q_gen_6180, q_gen_6181, q_gen_6197, q_gen_6198, q_gen_6199, q_gen_6200, q_gen_6205},
Q_f={q_gen_6177},
Delta=
{
<nil>() -> q_gen_6180
<cons>(q_gen_6198, q_gen_6180) -> q_gen_6197
<cons>(q_gen_6198, q_gen_6197) -> q_gen_6197
<a>() -> q_gen_6198
<b>() -> q_gen_6198
<s>(q_gen_6200) -> q_gen_6200
<z>() -> q_gen_6200
<cons, s>(q_gen_6181, q_gen_6180) -> q_gen_6177
<cons, s>(q_gen_6199, q_gen_6197) -> q_gen_6177
<nil, z>() -> q_gen_6177
<a, s>(q_gen_6200) -> q_gen_6181
<a, z>() -> q_gen_6181
<b, z>() -> q_gen_6181
<b, s>(q_gen_6200) -> q_gen_6199
<cons, s>(q_gen_6181, q_gen_6197) -> q_gen_6205
<cons, s>(q_gen_6199, q_gen_6180) -> q_gen_6205
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 29
() -> length([nil, z]) -> 29
(append([l1, l2, _rx]) /\ append([l2, l1, _tx]) /\ length([_rx, _sx]) /\ length([_tx, _ux])) -> eq_nat([_sx, _ux]) -> 31
(append([t1, l2, _ix])) -> append([cons(h1, t1), l2, cons(h1, _ix)]) -> 31
(length([ll, _nx])) -> length([cons(x, ll), s(_nx)]) -> 32
}
Sat witness: Found: ((length([ll, _nx])) -> length([cons(x, ll), s(_nx)]), {
_nx -> s(z)  ;  ll -> cons(b, nil)  ;  x -> a
})

-------------------------------------------
Step 34, which took 0.121667 s (model generation: 0.119181,  model checking: 0.002486):

Model:
|_
{
append -> 
{{{
Q={q_gen_6178, q_gen_6182, q_gen_6183, q_gen_6184, q_gen_6192, q_gen_6193, q_gen_6194, q_gen_6195, q_gen_6204},
Q_f={q_gen_6178, q_gen_6182},
Delta=
{
<cons>(q_gen_6194, q_gen_6193) -> q_gen_6193
<nil>() -> q_gen_6193
<a>() -> q_gen_6194
<b>() -> q_gen_6194
<cons, cons>(q_gen_6184, q_gen_6183) -> q_gen_6183
<nil, cons>(q_gen_6194, q_gen_6193) -> q_gen_6183
<nil, nil>() -> q_gen_6183
<a, a>() -> q_gen_6184
<b, b>() -> q_gen_6184
<cons, cons, cons>(q_gen_6195, q_gen_6192) -> q_gen_6178
<nil, nil, nil>() -> q_gen_6178
<cons, cons, cons>(q_gen_6204, q_gen_6182) -> q_gen_6182
<cons, cons, cons>(q_gen_6204, q_gen_6192) -> q_gen_6182
<cons, nil, cons>(q_gen_6184, q_gen_6183) -> q_gen_6182
<nil, cons, cons>(q_gen_6184, q_gen_6183) -> q_gen_6182
<cons, cons, cons>(q_gen_6195, q_gen_6178) -> q_gen_6192
<cons, cons, cons>(q_gen_6195, q_gen_6182) -> q_gen_6192
<cons, cons, cons>(q_gen_6204, q_gen_6178) -> q_gen_6192
<nil, nil, cons>(q_gen_6194, q_gen_6193) -> q_gen_6192
<b, b, b>() -> q_gen_6195
<a, a, a>() -> q_gen_6204
<a, b, a>() -> q_gen_6204
<b, a, b>() -> q_gen_6204
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_6177, q_gen_6180, q_gen_6181, q_gen_6197, q_gen_6198, q_gen_6199, q_gen_6200, q_gen_6205, q_gen_6218},
Q_f={q_gen_6177},
Delta=
{
<cons>(q_gen_6198, q_gen_6197) -> q_gen_6180
<nil>() -> q_gen_6180
<cons>(q_gen_6198, q_gen_6180) -> q_gen_6197
<a>() -> q_gen_6198
<b>() -> q_gen_6198
<s>(q_gen_6218) -> q_gen_6200
<z>() -> q_gen_6200
<s>(q_gen_6200) -> q_gen_6218
<cons, s>(q_gen_6181, q_gen_6180) -> q_gen_6177
<cons, s>(q_gen_6199, q_gen_6197) -> q_gen_6177
<nil, z>() -> q_gen_6177
<a, z>() -> q_gen_6181
<b, s>(q_gen_6218) -> q_gen_6181
<b, z>() -> q_gen_6181
<a, s>(q_gen_6200) -> q_gen_6199
<a, s>(q_gen_6218) -> q_gen_6199
<b, s>(q_gen_6200) -> q_gen_6199
<cons, s>(q_gen_6181, q_gen_6197) -> q_gen_6205
<cons, s>(q_gen_6199, q_gen_6180) -> q_gen_6205
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 30
() -> length([nil, z]) -> 30
(append([l1, l2, _rx]) /\ append([l2, l1, _tx]) /\ length([_rx, _sx]) /\ length([_tx, _ux])) -> eq_nat([_sx, _ux]) -> 31
(append([t1, l2, _ix])) -> append([cons(h1, t1), l2, cons(h1, _ix)]) -> 34
(length([ll, _nx])) -> length([cons(x, ll), s(_nx)]) -> 32
}
Sat witness: Found: ((append([t1, l2, _ix])) -> append([cons(h1, t1), l2, cons(h1, _ix)]), {
_ix -> cons(a, cons(a, nil))  ;  h1 -> b  ;  l2 -> cons(b, nil)  ;  t1 -> cons(a, cons(a, nil))
})

-------------------------------------------
Step 35, which took 0.159669 s (model generation: 0.150586,  model checking: 0.009083):

Model:
|_
{
append -> 
{{{
Q={q_gen_6178, q_gen_6182, q_gen_6183, q_gen_6184, q_gen_6192, q_gen_6193, q_gen_6194, q_gen_6195},
Q_f={q_gen_6178, q_gen_6182},
Delta=
{
<cons>(q_gen_6194, q_gen_6193) -> q_gen_6193
<nil>() -> q_gen_6193
<a>() -> q_gen_6194
<b>() -> q_gen_6194
<cons, cons>(q_gen_6184, q_gen_6183) -> q_gen_6183
<nil, cons>(q_gen_6194, q_gen_6193) -> q_gen_6183
<nil, nil>() -> q_gen_6183
<a, a>() -> q_gen_6184
<b, b>() -> q_gen_6184
<nil, nil, nil>() -> q_gen_6178
<cons, cons, cons>(q_gen_6195, q_gen_6182) -> q_gen_6182
<cons, cons, cons>(q_gen_6195, q_gen_6192) -> q_gen_6182
<cons, nil, cons>(q_gen_6184, q_gen_6183) -> q_gen_6182
<nil, cons, cons>(q_gen_6184, q_gen_6183) -> q_gen_6182
<cons, cons, cons>(q_gen_6195, q_gen_6178) -> q_gen_6192
<nil, nil, cons>(q_gen_6194, q_gen_6193) -> q_gen_6192
<a, a, a>() -> q_gen_6195
<a, b, a>() -> q_gen_6195
<b, a, b>() -> q_gen_6195
<b, b, b>() -> q_gen_6195
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_6177, q_gen_6180, q_gen_6181, q_gen_6197, q_gen_6198, q_gen_6199, q_gen_6200, q_gen_6205, q_gen_6216, q_gen_6218},
Q_f={q_gen_6177},
Delta=
{
<nil>() -> q_gen_6180
<cons>(q_gen_6198, q_gen_6180) -> q_gen_6197
<a>() -> q_gen_6198
<b>() -> q_gen_6198
<z>() -> q_gen_6200
<cons>(q_gen_6198, q_gen_6197) -> q_gen_6216
<cons>(q_gen_6198, q_gen_6216) -> q_gen_6216
<s>(q_gen_6200) -> q_gen_6218
<s>(q_gen_6218) -> q_gen_6218
<cons, s>(q_gen_6181, q_gen_6180) -> q_gen_6177
<cons, s>(q_gen_6181, q_gen_6216) -> q_gen_6177
<cons, s>(q_gen_6199, q_gen_6197) -> q_gen_6177
<nil, z>() -> q_gen_6177
<a, z>() -> q_gen_6181
<b, s>(q_gen_6218) -> q_gen_6181
<b, z>() -> q_gen_6181
<a, s>(q_gen_6200) -> q_gen_6199
<a, s>(q_gen_6218) -> q_gen_6199
<b, s>(q_gen_6200) -> q_gen_6199
<cons, s>(q_gen_6181, q_gen_6197) -> q_gen_6205
<cons, s>(q_gen_6199, q_gen_6180) -> q_gen_6205
<cons, s>(q_gen_6199, q_gen_6216) -> q_gen_6205
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 31
() -> length([nil, z]) -> 31
(append([l1, l2, _rx]) /\ append([l2, l1, _tx]) /\ length([_rx, _sx]) /\ length([_tx, _ux])) -> eq_nat([_sx, _ux]) -> 34
(append([t1, l2, _ix])) -> append([cons(h1, t1), l2, cons(h1, _ix)]) -> 34
(length([ll, _nx])) -> length([cons(x, ll), s(_nx)]) -> 32
}
Sat witness: Found: ((append([l1, l2, _rx]) /\ append([l2, l1, _tx]) /\ length([_rx, _sx]) /\ length([_tx, _ux])) -> eq_nat([_sx, _ux]), {
_rx -> cons(a, cons(b, cons(b, nil)))  ;  _sx -> s(z)  ;  _tx -> cons(b, cons(b, cons(b, nil)))  ;  _ux -> s(s(s(z)))  ;  l1 -> cons(a, nil)  ;  l2 -> cons(b, nil)
})

-------------------------------------------
Step 36, which took 0.186155 s (model generation: 0.172189,  model checking: 0.013966):

Model:
|_
{
append -> 
{{{
Q={q_gen_6178, q_gen_6183, q_gen_6184, q_gen_6192, q_gen_6193, q_gen_6194, q_gen_6195, q_gen_6203, q_gen_6214, q_gen_6232},
Q_f={q_gen_6178},
Delta=
{
<nil>() -> q_gen_6193
<a>() -> q_gen_6194
<b>() -> q_gen_6194
<cons>(q_gen_6194, q_gen_6193) -> q_gen_6232
<cons, cons>(q_gen_6184, q_gen_6183) -> q_gen_6183
<nil, nil>() -> q_gen_6183
<a, a>() -> q_gen_6184
<b, b>() -> q_gen_6184
<nil, cons>(q_gen_6194, q_gen_6193) -> q_gen_6203
<cons, cons, cons>(q_gen_6195, q_gen_6192) -> q_gen_6178
<cons, nil, cons>(q_gen_6184, q_gen_6183) -> q_gen_6178
<nil, cons, cons>(q_gen_6184, q_gen_6183) -> q_gen_6178
<nil, nil, nil>() -> q_gen_6178
<cons, cons, cons>(q_gen_6195, q_gen_6214) -> q_gen_6192
<cons, nil, cons>(q_gen_6184, q_gen_6203) -> q_gen_6192
<nil, cons, cons>(q_gen_6184, q_gen_6203) -> q_gen_6192
<nil, nil, cons>(q_gen_6194, q_gen_6193) -> q_gen_6192
<a, a, a>() -> q_gen_6195
<a, b, a>() -> q_gen_6195
<b, a, b>() -> q_gen_6195
<b, b, b>() -> q_gen_6195
<cons, cons, cons>(q_gen_6195, q_gen_6178) -> q_gen_6214
<nil, nil, cons>(q_gen_6194, q_gen_6232) -> q_gen_6214
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_6177, q_gen_6180, q_gen_6181, q_gen_6197, q_gen_6198, q_gen_6199, q_gen_6200, q_gen_6205},
Q_f={q_gen_6177},
Delta=
{
<cons>(q_gen_6198, q_gen_6197) -> q_gen_6180
<nil>() -> q_gen_6180
<cons>(q_gen_6198, q_gen_6180) -> q_gen_6197
<a>() -> q_gen_6198
<b>() -> q_gen_6198
<s>(q_gen_6200) -> q_gen_6200
<z>() -> q_gen_6200
<cons, s>(q_gen_6181, q_gen_6180) -> q_gen_6177
<cons, s>(q_gen_6199, q_gen_6180) -> q_gen_6177
<cons, s>(q_gen_6199, q_gen_6197) -> q_gen_6177
<nil, z>() -> q_gen_6177
<a, z>() -> q_gen_6181
<b, z>() -> q_gen_6181
<a, s>(q_gen_6200) -> q_gen_6199
<b, s>(q_gen_6200) -> q_gen_6199
<cons, s>(q_gen_6181, q_gen_6197) -> q_gen_6205
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 32
() -> length([nil, z]) -> 32
(append([l1, l2, _rx]) /\ append([l2, l1, _tx]) /\ length([_rx, _sx]) /\ length([_tx, _ux])) -> eq_nat([_sx, _ux]) -> 34
(append([t1, l2, _ix])) -> append([cons(h1, t1), l2, cons(h1, _ix)]) -> 37
(length([ll, _nx])) -> length([cons(x, ll), s(_nx)]) -> 33
}
Sat witness: Found: ((append([t1, l2, _ix])) -> append([cons(h1, t1), l2, cons(h1, _ix)]), {
_ix -> cons(b, cons(b, cons(b, nil)))  ;  h1 -> a  ;  l2 -> cons(a, nil)  ;  t1 -> cons(b, cons(b, nil))
})

-------------------------------------------
Step 37, which took 0.216413 s (model generation: 0.212900,  model checking: 0.003513):

Model:
|_
{
append -> 
{{{
Q={q_gen_6178, q_gen_6183, q_gen_6184, q_gen_6192, q_gen_6193, q_gen_6194, q_gen_6195, q_gen_6203, q_gen_6231, q_gen_6232},
Q_f={q_gen_6178},
Delta=
{
<nil>() -> q_gen_6193
<a>() -> q_gen_6194
<b>() -> q_gen_6194
<cons>(q_gen_6194, q_gen_6193) -> q_gen_6232
<cons, cons>(q_gen_6184, q_gen_6183) -> q_gen_6183
<nil, nil>() -> q_gen_6183
<a, a>() -> q_gen_6184
<b, b>() -> q_gen_6184
<cons, cons>(q_gen_6184, q_gen_6203) -> q_gen_6203
<nil, cons>(q_gen_6194, q_gen_6193) -> q_gen_6203
<cons, cons, cons>(q_gen_6195, q_gen_6192) -> q_gen_6178
<cons, nil, cons>(q_gen_6184, q_gen_6183) -> q_gen_6178
<nil, cons, cons>(q_gen_6184, q_gen_6183) -> q_gen_6178
<nil, nil, nil>() -> q_gen_6178
<cons, cons, cons>(q_gen_6195, q_gen_6178) -> q_gen_6192
<cons, cons, cons>(q_gen_6195, q_gen_6231) -> q_gen_6192
<cons, nil, cons>(q_gen_6184, q_gen_6203) -> q_gen_6192
<nil, cons, cons>(q_gen_6184, q_gen_6203) -> q_gen_6192
<nil, nil, cons>(q_gen_6194, q_gen_6193) -> q_gen_6192
<a, a, a>() -> q_gen_6195
<a, b, a>() -> q_gen_6195
<b, a, b>() -> q_gen_6195
<b, b, b>() -> q_gen_6195
<nil, nil, cons>(q_gen_6194, q_gen_6232) -> q_gen_6231
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_6177, q_gen_6180, q_gen_6181, q_gen_6197, q_gen_6198, q_gen_6199, q_gen_6200, q_gen_6205},
Q_f={q_gen_6177},
Delta=
{
<cons>(q_gen_6198, q_gen_6197) -> q_gen_6180
<nil>() -> q_gen_6180
<cons>(q_gen_6198, q_gen_6180) -> q_gen_6197
<a>() -> q_gen_6198
<b>() -> q_gen_6198
<s>(q_gen_6200) -> q_gen_6200
<z>() -> q_gen_6200
<cons, s>(q_gen_6181, q_gen_6180) -> q_gen_6177
<cons, s>(q_gen_6199, q_gen_6180) -> q_gen_6177
<cons, s>(q_gen_6199, q_gen_6197) -> q_gen_6177
<nil, z>() -> q_gen_6177
<a, z>() -> q_gen_6181
<b, z>() -> q_gen_6181
<a, s>(q_gen_6200) -> q_gen_6199
<b, s>(q_gen_6200) -> q_gen_6199
<cons, s>(q_gen_6181, q_gen_6197) -> q_gen_6205
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 33
() -> length([nil, z]) -> 33
(append([l1, l2, _rx]) /\ append([l2, l1, _tx]) /\ length([_rx, _sx]) /\ length([_tx, _ux])) -> eq_nat([_sx, _ux]) -> 37
(append([t1, l2, _ix])) -> append([cons(h1, t1), l2, cons(h1, _ix)]) -> 37
(length([ll, _nx])) -> length([cons(x, ll), s(_nx)]) -> 34
}
Sat witness: Found: ((append([l1, l2, _rx]) /\ append([l2, l1, _tx]) /\ length([_rx, _sx]) /\ length([_tx, _ux])) -> eq_nat([_sx, _ux]), {
_rx -> cons(b, nil)  ;  _sx -> s(s(z))  ;  _tx -> cons(b, nil)  ;  _ux -> s(z)  ;  l1 -> cons(b, nil)  ;  l2 -> nil
})

-------------------------------------------
Step 38, which took 0.204699 s (model generation: 0.187399,  model checking: 0.017300):

Model:
|_
{
append -> 
{{{
Q={q_gen_6178, q_gen_6183, q_gen_6184, q_gen_6192, q_gen_6193, q_gen_6194, q_gen_6195, q_gen_6203, q_gen_6214, q_gen_6232},
Q_f={q_gen_6178},
Delta=
{
<nil>() -> q_gen_6193
<a>() -> q_gen_6194
<b>() -> q_gen_6194
<cons>(q_gen_6194, q_gen_6193) -> q_gen_6232
<cons, cons>(q_gen_6184, q_gen_6183) -> q_gen_6183
<nil, nil>() -> q_gen_6183
<a, a>() -> q_gen_6184
<b, b>() -> q_gen_6184
<cons, cons>(q_gen_6184, q_gen_6203) -> q_gen_6203
<nil, cons>(q_gen_6194, q_gen_6193) -> q_gen_6203
<cons, cons, cons>(q_gen_6195, q_gen_6192) -> q_gen_6178
<cons, nil, cons>(q_gen_6184, q_gen_6183) -> q_gen_6178
<nil, cons, cons>(q_gen_6184, q_gen_6183) -> q_gen_6178
<nil, nil, nil>() -> q_gen_6178
<cons, cons, cons>(q_gen_6195, q_gen_6214) -> q_gen_6192
<cons, nil, cons>(q_gen_6184, q_gen_6203) -> q_gen_6192
<nil, cons, cons>(q_gen_6184, q_gen_6203) -> q_gen_6192
<nil, nil, cons>(q_gen_6194, q_gen_6193) -> q_gen_6192
<a, a, a>() -> q_gen_6195
<a, b, a>() -> q_gen_6195
<b, a, b>() -> q_gen_6195
<b, b, b>() -> q_gen_6195
<cons, cons, cons>(q_gen_6195, q_gen_6178) -> q_gen_6214
<nil, nil, cons>(q_gen_6194, q_gen_6232) -> q_gen_6214
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_6177, q_gen_6180, q_gen_6181, q_gen_6197, q_gen_6198, q_gen_6199, q_gen_6200, q_gen_6205},
Q_f={q_gen_6177},
Delta=
{
<nil>() -> q_gen_6180
<cons>(q_gen_6198, q_gen_6180) -> q_gen_6197
<cons>(q_gen_6198, q_gen_6197) -> q_gen_6197
<a>() -> q_gen_6198
<b>() -> q_gen_6198
<s>(q_gen_6200) -> q_gen_6200
<z>() -> q_gen_6200
<cons, s>(q_gen_6181, q_gen_6180) -> q_gen_6177
<cons, s>(q_gen_6199, q_gen_6197) -> q_gen_6177
<nil, z>() -> q_gen_6177
<a, z>() -> q_gen_6181
<b, z>() -> q_gen_6181
<a, s>(q_gen_6200) -> q_gen_6199
<b, s>(q_gen_6200) -> q_gen_6199
<cons, s>(q_gen_6181, q_gen_6197) -> q_gen_6205
<cons, s>(q_gen_6199, q_gen_6180) -> q_gen_6205
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 34
() -> length([nil, z]) -> 34
(append([l1, l2, _rx]) /\ append([l2, l1, _tx]) /\ length([_rx, _sx]) /\ length([_tx, _ux])) -> eq_nat([_sx, _ux]) -> 37
(append([t1, l2, _ix])) -> append([cons(h1, t1), l2, cons(h1, _ix)]) -> 40
(length([ll, _nx])) -> length([cons(x, ll), s(_nx)]) -> 35
}
Sat witness: Found: ((append([t1, l2, _ix])) -> append([cons(h1, t1), l2, cons(h1, _ix)]), {
_ix -> cons(b, cons(a, nil))  ;  h1 -> a  ;  l2 -> cons(b, cons(a, nil))  ;  t1 -> nil
})

-------------------------------------------
Step 39, which took 0.217609 s (model generation: 0.214761,  model checking: 0.002848):

Model:
|_
{
append -> 
{{{
Q={q_gen_6178, q_gen_6183, q_gen_6184, q_gen_6192, q_gen_6193, q_gen_6194, q_gen_6195, q_gen_6203, q_gen_6214, q_gen_6232},
Q_f={q_gen_6178},
Delta=
{
<nil>() -> q_gen_6193
<a>() -> q_gen_6194
<b>() -> q_gen_6194
<cons>(q_gen_6194, q_gen_6193) -> q_gen_6232
<cons, cons>(q_gen_6184, q_gen_6183) -> q_gen_6183
<nil, nil>() -> q_gen_6183
<a, a>() -> q_gen_6184
<a, b>() -> q_gen_6184
<b, b>() -> q_gen_6184
<cons, cons>(q_gen_6184, q_gen_6203) -> q_gen_6203
<nil, cons>(q_gen_6194, q_gen_6193) -> q_gen_6203
<cons, cons, cons>(q_gen_6195, q_gen_6192) -> q_gen_6178
<cons, nil, cons>(q_gen_6184, q_gen_6183) -> q_gen_6178
<nil, cons, cons>(q_gen_6184, q_gen_6183) -> q_gen_6178
<nil, nil, nil>() -> q_gen_6178
<cons, cons, cons>(q_gen_6195, q_gen_6214) -> q_gen_6192
<cons, nil, cons>(q_gen_6184, q_gen_6203) -> q_gen_6192
<nil, cons, cons>(q_gen_6184, q_gen_6203) -> q_gen_6192
<nil, nil, cons>(q_gen_6194, q_gen_6193) -> q_gen_6192
<a, a, a>() -> q_gen_6195
<a, b, a>() -> q_gen_6195
<b, a, b>() -> q_gen_6195
<b, b, b>() -> q_gen_6195
<cons, cons, cons>(q_gen_6195, q_gen_6178) -> q_gen_6214
<nil, nil, cons>(q_gen_6194, q_gen_6232) -> q_gen_6214
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_6177, q_gen_6180, q_gen_6181, q_gen_6197, q_gen_6198, q_gen_6199, q_gen_6200, q_gen_6205},
Q_f={q_gen_6177},
Delta=
{
<nil>() -> q_gen_6180
<cons>(q_gen_6198, q_gen_6180) -> q_gen_6197
<cons>(q_gen_6198, q_gen_6197) -> q_gen_6197
<a>() -> q_gen_6198
<b>() -> q_gen_6198
<s>(q_gen_6200) -> q_gen_6200
<z>() -> q_gen_6200
<cons, s>(q_gen_6181, q_gen_6180) -> q_gen_6177
<cons, s>(q_gen_6199, q_gen_6197) -> q_gen_6177
<nil, z>() -> q_gen_6177
<a, z>() -> q_gen_6181
<b, z>() -> q_gen_6181
<a, s>(q_gen_6200) -> q_gen_6199
<b, s>(q_gen_6200) -> q_gen_6199
<cons, s>(q_gen_6181, q_gen_6197) -> q_gen_6205
<cons, s>(q_gen_6199, q_gen_6180) -> q_gen_6205
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 35
() -> length([nil, z]) -> 35
(append([l1, l2, _rx]) /\ append([l2, l1, _tx]) /\ length([_rx, _sx]) /\ length([_tx, _ux])) -> eq_nat([_sx, _ux]) -> 40
(append([t1, l2, _ix])) -> append([cons(h1, t1), l2, cons(h1, _ix)]) -> 40
(length([ll, _nx])) -> length([cons(x, ll), s(_nx)]) -> 36
}
Sat witness: Found: ((append([l1, l2, _rx]) /\ append([l2, l1, _tx]) /\ length([_rx, _sx]) /\ length([_tx, _ux])) -> eq_nat([_sx, _ux]), {
_rx -> cons(a, cons(b, nil))  ;  _sx -> s(s(z))  ;  _tx -> cons(a, cons(b, nil))  ;  _ux -> s(s(s(z)))  ;  l1 -> cons(a, nil)  ;  l2 -> cons(a, nil)
})

-------------------------------------------
Step 40, which took 0.268168 s (model generation: 0.263275,  model checking: 0.004893):

Model:
|_
{
append -> 
{{{
Q={q_gen_6178, q_gen_6182, q_gen_6183, q_gen_6184, q_gen_6192, q_gen_6193, q_gen_6194, q_gen_6195, q_gen_6204, q_gen_6214, q_gen_6232},
Q_f={q_gen_6178, q_gen_6182},
Delta=
{
<nil>() -> q_gen_6193
<a>() -> q_gen_6194
<b>() -> q_gen_6194
<cons>(q_gen_6194, q_gen_6193) -> q_gen_6232
<cons, cons>(q_gen_6184, q_gen_6183) -> q_gen_6183
<nil, cons>(q_gen_6194, q_gen_6193) -> q_gen_6183
<nil, nil>() -> q_gen_6183
<a, a>() -> q_gen_6184
<a, b>() -> q_gen_6184
<b, b>() -> q_gen_6184
<cons, cons, cons>(q_gen_6195, q_gen_6182) -> q_gen_6178
<cons, cons, cons>(q_gen_6195, q_gen_6192) -> q_gen_6178
<nil, cons, cons>(q_gen_6184, q_gen_6183) -> q_gen_6178
<nil, nil, nil>() -> q_gen_6178
<cons, cons, cons>(q_gen_6204, q_gen_6178) -> q_gen_6182
<cons, cons, cons>(q_gen_6204, q_gen_6182) -> q_gen_6182
<cons, cons, cons>(q_gen_6204, q_gen_6214) -> q_gen_6182
<cons, nil, cons>(q_gen_6184, q_gen_6183) -> q_gen_6182
<nil, nil, cons>(q_gen_6194, q_gen_6193) -> q_gen_6192
<b, a, b>() -> q_gen_6195
<b, b, b>() -> q_gen_6195
<a, a, a>() -> q_gen_6204
<a, b, a>() -> q_gen_6204
<cons, cons, cons>(q_gen_6195, q_gen_6178) -> q_gen_6214
<cons, cons, cons>(q_gen_6195, q_gen_6214) -> q_gen_6214
<cons, cons, cons>(q_gen_6204, q_gen_6192) -> q_gen_6214
<nil, nil, cons>(q_gen_6194, q_gen_6232) -> q_gen_6214
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_6177, q_gen_6180, q_gen_6181, q_gen_6197, q_gen_6198, q_gen_6199, q_gen_6200, q_gen_6205},
Q_f={q_gen_6177},
Delta=
{
<nil>() -> q_gen_6180
<cons>(q_gen_6198, q_gen_6180) -> q_gen_6197
<cons>(q_gen_6198, q_gen_6197) -> q_gen_6197
<a>() -> q_gen_6198
<b>() -> q_gen_6198
<s>(q_gen_6200) -> q_gen_6200
<z>() -> q_gen_6200
<cons, s>(q_gen_6181, q_gen_6180) -> q_gen_6177
<cons, s>(q_gen_6199, q_gen_6197) -> q_gen_6177
<nil, z>() -> q_gen_6177
<a, z>() -> q_gen_6181
<b, z>() -> q_gen_6181
<a, s>(q_gen_6200) -> q_gen_6199
<b, s>(q_gen_6200) -> q_gen_6199
<cons, s>(q_gen_6181, q_gen_6197) -> q_gen_6205
<cons, s>(q_gen_6199, q_gen_6180) -> q_gen_6205
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 36
() -> length([nil, z]) -> 36
(append([l1, l2, _rx]) /\ append([l2, l1, _tx]) /\ length([_rx, _sx]) /\ length([_tx, _ux])) -> eq_nat([_sx, _ux]) -> 40
(append([t1, l2, _ix])) -> append([cons(h1, t1), l2, cons(h1, _ix)]) -> 43
(length([ll, _nx])) -> length([cons(x, ll), s(_nx)]) -> 37
}
Sat witness: Found: ((append([t1, l2, _ix])) -> append([cons(h1, t1), l2, cons(h1, _ix)]), {
_ix -> cons(a, cons(a, nil))  ;  h1 -> b  ;  l2 -> cons(b, cons(a, nil))  ;  t1 -> cons(a, nil)
})

-------------------------------------------
Step 41, which took 0.447134 s (model generation: 0.442511,  model checking: 0.004623):

Model:
|_
{
append -> 
{{{
Q={q_gen_6178, q_gen_6182, q_gen_6183, q_gen_6184, q_gen_6192, q_gen_6193, q_gen_6194, q_gen_6195, q_gen_6204, q_gen_6214, q_gen_6232},
Q_f={q_gen_6178, q_gen_6182},
Delta=
{
<nil>() -> q_gen_6193
<a>() -> q_gen_6194
<b>() -> q_gen_6194
<cons>(q_gen_6194, q_gen_6193) -> q_gen_6232
<cons, cons>(q_gen_6184, q_gen_6183) -> q_gen_6183
<nil, cons>(q_gen_6194, q_gen_6193) -> q_gen_6183
<nil, nil>() -> q_gen_6183
<a, a>() -> q_gen_6184
<a, b>() -> q_gen_6184
<b, b>() -> q_gen_6184
<cons, cons, cons>(q_gen_6195, q_gen_6182) -> q_gen_6178
<cons, cons, cons>(q_gen_6204, q_gen_6178) -> q_gen_6178
<cons, cons, cons>(q_gen_6204, q_gen_6214) -> q_gen_6178
<nil, cons, cons>(q_gen_6184, q_gen_6183) -> q_gen_6178
<nil, nil, nil>() -> q_gen_6178
<cons, cons, cons>(q_gen_6195, q_gen_6192) -> q_gen_6182
<cons, cons, cons>(q_gen_6204, q_gen_6182) -> q_gen_6182
<cons, nil, cons>(q_gen_6184, q_gen_6183) -> q_gen_6182
<cons, cons, cons>(q_gen_6195, q_gen_6214) -> q_gen_6192
<cons, cons, cons>(q_gen_6204, q_gen_6192) -> q_gen_6192
<nil, nil, cons>(q_gen_6194, q_gen_6193) -> q_gen_6192
<b, a, b>() -> q_gen_6195
<b, b, b>() -> q_gen_6195
<a, a, a>() -> q_gen_6204
<a, b, a>() -> q_gen_6204
<cons, cons, cons>(q_gen_6195, q_gen_6178) -> q_gen_6214
<nil, nil, cons>(q_gen_6194, q_gen_6232) -> q_gen_6214
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_6177, q_gen_6180, q_gen_6181, q_gen_6197, q_gen_6198, q_gen_6199, q_gen_6200, q_gen_6205},
Q_f={q_gen_6177},
Delta=
{
<nil>() -> q_gen_6180
<cons>(q_gen_6198, q_gen_6180) -> q_gen_6197
<cons>(q_gen_6198, q_gen_6197) -> q_gen_6197
<a>() -> q_gen_6198
<b>() -> q_gen_6198
<s>(q_gen_6200) -> q_gen_6200
<z>() -> q_gen_6200
<cons, s>(q_gen_6181, q_gen_6180) -> q_gen_6177
<cons, s>(q_gen_6199, q_gen_6197) -> q_gen_6177
<nil, z>() -> q_gen_6177
<a, z>() -> q_gen_6181
<b, z>() -> q_gen_6181
<a, s>(q_gen_6200) -> q_gen_6199
<b, s>(q_gen_6200) -> q_gen_6199
<cons, s>(q_gen_6181, q_gen_6197) -> q_gen_6205
<cons, s>(q_gen_6199, q_gen_6180) -> q_gen_6205
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 37
() -> length([nil, z]) -> 37
(append([l1, l2, _rx]) /\ append([l2, l1, _tx]) /\ length([_rx, _sx]) /\ length([_tx, _ux])) -> eq_nat([_sx, _ux]) -> 43
(append([t1, l2, _ix])) -> append([cons(h1, t1), l2, cons(h1, _ix)]) -> 43
(length([ll, _nx])) -> length([cons(x, ll), s(_nx)]) -> 38
}
Sat witness: Found: ((append([l1, l2, _rx]) /\ append([l2, l1, _tx]) /\ length([_rx, _sx]) /\ length([_tx, _ux])) -> eq_nat([_sx, _ux]), {
_rx -> cons(b, cons(b, nil))  ;  _sx -> s(s(z))  ;  _tx -> cons(b, cons(b, nil))  ;  _ux -> s(s(s(z)))  ;  l1 -> cons(b, nil)  ;  l2 -> cons(b, nil)
})

-------------------------------------------
Step 42, which took 0.242163 s (model generation: 0.239858,  model checking: 0.002305):

Model:
|_
{
append -> 
{{{
Q={q_gen_6178, q_gen_6183, q_gen_6184, q_gen_6192, q_gen_6193, q_gen_6194, q_gen_6195, q_gen_6202, q_gen_6203, q_gen_6204},
Q_f={q_gen_6178},
Delta=
{
<cons>(q_gen_6194, q_gen_6193) -> q_gen_6193
<nil>() -> q_gen_6193
<a>() -> q_gen_6194
<b>() -> q_gen_6194
<cons, cons>(q_gen_6184, q_gen_6183) -> q_gen_6183
<nil, nil>() -> q_gen_6183
<a, a>() -> q_gen_6184
<a, b>() -> q_gen_6184
<b, b>() -> q_gen_6184
<cons, cons>(q_gen_6184, q_gen_6203) -> q_gen_6203
<nil, cons>(q_gen_6194, q_gen_6193) -> q_gen_6203
<cons, cons, cons>(q_gen_6195, q_gen_6192) -> q_gen_6178
<cons, cons, cons>(q_gen_6195, q_gen_6202) -> q_gen_6178
<cons, cons, cons>(q_gen_6204, q_gen_6202) -> q_gen_6178
<cons, nil, cons>(q_gen_6184, q_gen_6183) -> q_gen_6178
<nil, cons, cons>(q_gen_6184, q_gen_6183) -> q_gen_6178
<nil, nil, nil>() -> q_gen_6178
<cons, cons, cons>(q_gen_6195, q_gen_6178) -> q_gen_6192
<cons, cons, cons>(q_gen_6204, q_gen_6178) -> q_gen_6192
<nil, nil, cons>(q_gen_6194, q_gen_6193) -> q_gen_6192
<a, a, a>() -> q_gen_6195
<b, a, b>() -> q_gen_6195
<b, b, b>() -> q_gen_6195
<cons, cons, cons>(q_gen_6204, q_gen_6192) -> q_gen_6202
<cons, nil, cons>(q_gen_6184, q_gen_6203) -> q_gen_6202
<nil, cons, cons>(q_gen_6184, q_gen_6203) -> q_gen_6202
<a, b, a>() -> q_gen_6204
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_6177, q_gen_6180, q_gen_6181, q_gen_6197, q_gen_6198, q_gen_6199, q_gen_6200, q_gen_6205, q_gen_6218},
Q_f={q_gen_6177},
Delta=
{
<cons>(q_gen_6198, q_gen_6197) -> q_gen_6180
<nil>() -> q_gen_6180
<cons>(q_gen_6198, q_gen_6180) -> q_gen_6197
<a>() -> q_gen_6198
<b>() -> q_gen_6198
<s>(q_gen_6218) -> q_gen_6200
<z>() -> q_gen_6200
<s>(q_gen_6200) -> q_gen_6218
<cons, s>(q_gen_6181, q_gen_6180) -> q_gen_6177
<cons, s>(q_gen_6199, q_gen_6197) -> q_gen_6177
<nil, z>() -> q_gen_6177
<a, s>(q_gen_6218) -> q_gen_6181
<a, z>() -> q_gen_6181
<b, s>(q_gen_6218) -> q_gen_6181
<b, z>() -> q_gen_6181
<a, s>(q_gen_6200) -> q_gen_6199
<b, s>(q_gen_6200) -> q_gen_6199
<cons, s>(q_gen_6181, q_gen_6197) -> q_gen_6205
<cons, s>(q_gen_6199, q_gen_6180) -> q_gen_6205
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 38
() -> length([nil, z]) -> 38
(append([l1, l2, _rx]) /\ append([l2, l1, _tx]) /\ length([_rx, _sx]) /\ length([_tx, _ux])) -> eq_nat([_sx, _ux]) -> 43
(append([t1, l2, _ix])) -> append([cons(h1, t1), l2, cons(h1, _ix)]) -> 46
(length([ll, _nx])) -> length([cons(x, ll), s(_nx)]) -> 39
}
Sat witness: Found: ((append([t1, l2, _ix])) -> append([cons(h1, t1), l2, cons(h1, _ix)]), {
_ix -> cons(b, nil)  ;  h1 -> a  ;  l2 -> cons(b, nil)  ;  t1 -> nil
})

-------------------------------------------
Step 43, which took 0.240170 s (model generation: 0.236472,  model checking: 0.003698):

Model:
|_
{
append -> 
{{{
Q={q_gen_6178, q_gen_6183, q_gen_6184, q_gen_6192, q_gen_6193, q_gen_6194, q_gen_6195, q_gen_6203, q_gen_6214, q_gen_6232},
Q_f={q_gen_6178},
Delta=
{
<nil>() -> q_gen_6193
<a>() -> q_gen_6194
<b>() -> q_gen_6194
<cons>(q_gen_6194, q_gen_6193) -> q_gen_6232
<cons, cons>(q_gen_6184, q_gen_6183) -> q_gen_6183
<nil, nil>() -> q_gen_6183
<a, a>() -> q_gen_6184
<a, b>() -> q_gen_6184
<b, b>() -> q_gen_6184
<cons, cons>(q_gen_6184, q_gen_6203) -> q_gen_6203
<nil, cons>(q_gen_6194, q_gen_6193) -> q_gen_6203
<cons, cons, cons>(q_gen_6195, q_gen_6192) -> q_gen_6178
<cons, nil, cons>(q_gen_6184, q_gen_6183) -> q_gen_6178
<nil, cons, cons>(q_gen_6184, q_gen_6183) -> q_gen_6178
<nil, nil, nil>() -> q_gen_6178
<cons, cons, cons>(q_gen_6195, q_gen_6214) -> q_gen_6192
<cons, nil, cons>(q_gen_6184, q_gen_6203) -> q_gen_6192
<nil, cons, cons>(q_gen_6184, q_gen_6203) -> q_gen_6192
<nil, nil, cons>(q_gen_6194, q_gen_6193) -> q_gen_6192
<a, a, a>() -> q_gen_6195
<a, b, a>() -> q_gen_6195
<b, a, b>() -> q_gen_6195
<b, b, b>() -> q_gen_6195
<cons, cons, cons>(q_gen_6195, q_gen_6178) -> q_gen_6214
<nil, nil, cons>(q_gen_6194, q_gen_6232) -> q_gen_6214
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_6177, q_gen_6180, q_gen_6181, q_gen_6197, q_gen_6198, q_gen_6199, q_gen_6200, q_gen_6205, q_gen_6218},
Q_f={q_gen_6177},
Delta=
{
<cons>(q_gen_6198, q_gen_6197) -> q_gen_6180
<nil>() -> q_gen_6180
<cons>(q_gen_6198, q_gen_6180) -> q_gen_6197
<a>() -> q_gen_6198
<b>() -> q_gen_6198
<s>(q_gen_6218) -> q_gen_6200
<z>() -> q_gen_6200
<s>(q_gen_6200) -> q_gen_6218
<cons, s>(q_gen_6181, q_gen_6180) -> q_gen_6177
<cons, s>(q_gen_6199, q_gen_6197) -> q_gen_6177
<nil, z>() -> q_gen_6177
<a, s>(q_gen_6218) -> q_gen_6181
<a, z>() -> q_gen_6181
<b, s>(q_gen_6218) -> q_gen_6181
<b, z>() -> q_gen_6181
<a, s>(q_gen_6200) -> q_gen_6199
<b, s>(q_gen_6200) -> q_gen_6199
<cons, s>(q_gen_6181, q_gen_6197) -> q_gen_6205
<cons, s>(q_gen_6199, q_gen_6180) -> q_gen_6205
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 39
() -> length([nil, z]) -> 39
(append([l1, l2, _rx]) /\ append([l2, l1, _tx]) /\ length([_rx, _sx]) /\ length([_tx, _ux])) -> eq_nat([_sx, _ux]) -> 46
(append([t1, l2, _ix])) -> append([cons(h1, t1), l2, cons(h1, _ix)]) -> 46
(length([ll, _nx])) -> length([cons(x, ll), s(_nx)]) -> 40
}
Sat witness: Found: ((append([l1, l2, _rx]) /\ append([l2, l1, _tx]) /\ length([_rx, _sx]) /\ length([_tx, _ux])) -> eq_nat([_sx, _ux]), {
_rx -> cons(a, nil)  ;  _sx -> s(z)  ;  _tx -> cons(a, nil)  ;  _ux -> s(s(s(z)))  ;  l1 -> cons(a, nil)  ;  l2 -> nil
})

-------------------------------------------
Step 44, which took 0.358811 s (model generation: 0.347464,  model checking: 0.011347):

Model:
|_
{
append -> 
{{{
Q={q_gen_6178, q_gen_6182, q_gen_6183, q_gen_6184, q_gen_6192, q_gen_6193, q_gen_6194, q_gen_6195},
Q_f={q_gen_6178, q_gen_6182},
Delta=
{
<cons>(q_gen_6194, q_gen_6193) -> q_gen_6193
<nil>() -> q_gen_6193
<a>() -> q_gen_6194
<b>() -> q_gen_6194
<cons, cons>(q_gen_6184, q_gen_6183) -> q_gen_6183
<nil, cons>(q_gen_6194, q_gen_6193) -> q_gen_6183
<nil, nil>() -> q_gen_6183
<a, a>() -> q_gen_6184
<a, b>() -> q_gen_6184
<b, b>() -> q_gen_6184
<nil, nil, nil>() -> q_gen_6178
<cons, cons, cons>(q_gen_6195, q_gen_6182) -> q_gen_6182
<cons, cons, cons>(q_gen_6195, q_gen_6192) -> q_gen_6182
<cons, nil, cons>(q_gen_6184, q_gen_6183) -> q_gen_6182
<nil, cons, cons>(q_gen_6184, q_gen_6183) -> q_gen_6182
<cons, cons, cons>(q_gen_6195, q_gen_6178) -> q_gen_6192
<nil, nil, cons>(q_gen_6194, q_gen_6193) -> q_gen_6192
<a, a, a>() -> q_gen_6195
<a, b, a>() -> q_gen_6195
<b, a, b>() -> q_gen_6195
<b, b, b>() -> q_gen_6195
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_6177, q_gen_6180, q_gen_6181, q_gen_6197, q_gen_6198, q_gen_6199, q_gen_6200, q_gen_6205, q_gen_6216, q_gen_6217, q_gen_6218},
Q_f={q_gen_6177},
Delta=
{
<nil>() -> q_gen_6180
<cons>(q_gen_6198, q_gen_6180) -> q_gen_6197
<cons>(q_gen_6198, q_gen_6216) -> q_gen_6197
<a>() -> q_gen_6198
<b>() -> q_gen_6198
<s>(q_gen_6218) -> q_gen_6200
<z>() -> q_gen_6200
<cons>(q_gen_6198, q_gen_6197) -> q_gen_6216
<s>(q_gen_6200) -> q_gen_6218
<cons, s>(q_gen_6181, q_gen_6180) -> q_gen_6177
<cons, s>(q_gen_6199, q_gen_6197) -> q_gen_6177
<cons, s>(q_gen_6217, q_gen_6216) -> q_gen_6177
<nil, z>() -> q_gen_6177
<a, z>() -> q_gen_6181
<b, z>() -> q_gen_6181
<a, s>(q_gen_6200) -> q_gen_6199
<b, s>(q_gen_6200) -> q_gen_6199
<cons, s>(q_gen_6181, q_gen_6197) -> q_gen_6205
<cons, s>(q_gen_6181, q_gen_6216) -> q_gen_6205
<cons, s>(q_gen_6199, q_gen_6180) -> q_gen_6205
<cons, s>(q_gen_6199, q_gen_6216) -> q_gen_6205
<cons, s>(q_gen_6217, q_gen_6180) -> q_gen_6205
<cons, s>(q_gen_6217, q_gen_6197) -> q_gen_6205
<a, s>(q_gen_6218) -> q_gen_6217
<b, s>(q_gen_6218) -> q_gen_6217
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 40
() -> length([nil, z]) -> 40
(append([l1, l2, _rx]) /\ append([l2, l1, _tx]) /\ length([_rx, _sx]) /\ length([_tx, _ux])) -> eq_nat([_sx, _ux]) -> 46
(append([t1, l2, _ix])) -> append([cons(h1, t1), l2, cons(h1, _ix)]) -> 49
(length([ll, _nx])) -> length([cons(x, ll), s(_nx)]) -> 41
}
Sat witness: Found: ((append([t1, l2, _ix])) -> append([cons(h1, t1), l2, cons(h1, _ix)]), {
_ix -> cons(a, cons(b, nil))  ;  h1 -> a  ;  l2 -> cons(a, cons(b, nil))  ;  t1 -> nil
})

-------------------------------------------
Step 45, which took 0.286101 s (model generation: 0.274493,  model checking: 0.011608):

Model:
|_
{
append -> 
{{{
Q={q_gen_6178, q_gen_6182, q_gen_6183, q_gen_6184, q_gen_6192, q_gen_6193, q_gen_6194, q_gen_6195},
Q_f={q_gen_6178, q_gen_6182},
Delta=
{
<cons>(q_gen_6194, q_gen_6193) -> q_gen_6193
<nil>() -> q_gen_6193
<a>() -> q_gen_6194
<b>() -> q_gen_6194
<cons, cons>(q_gen_6184, q_gen_6183) -> q_gen_6183
<nil, cons>(q_gen_6194, q_gen_6193) -> q_gen_6183
<nil, nil>() -> q_gen_6183
<a, a>() -> q_gen_6184
<a, b>() -> q_gen_6184
<b, a>() -> q_gen_6184
<b, b>() -> q_gen_6184
<nil, nil, nil>() -> q_gen_6178
<cons, cons, cons>(q_gen_6195, q_gen_6182) -> q_gen_6182
<cons, cons, cons>(q_gen_6195, q_gen_6192) -> q_gen_6182
<cons, nil, cons>(q_gen_6184, q_gen_6183) -> q_gen_6182
<nil, cons, cons>(q_gen_6184, q_gen_6183) -> q_gen_6182
<cons, cons, cons>(q_gen_6195, q_gen_6178) -> q_gen_6192
<nil, nil, cons>(q_gen_6194, q_gen_6193) -> q_gen_6192
<a, a, a>() -> q_gen_6195
<a, b, a>() -> q_gen_6195
<b, a, b>() -> q_gen_6195
<b, b, b>() -> q_gen_6195
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_6177, q_gen_6180, q_gen_6181, q_gen_6197, q_gen_6198, q_gen_6199, q_gen_6200, q_gen_6205, q_gen_6216, q_gen_6217, q_gen_6218},
Q_f={q_gen_6177},
Delta=
{
<nil>() -> q_gen_6180
<cons>(q_gen_6198, q_gen_6180) -> q_gen_6197
<cons>(q_gen_6198, q_gen_6216) -> q_gen_6197
<a>() -> q_gen_6198
<b>() -> q_gen_6198
<s>(q_gen_6218) -> q_gen_6200
<z>() -> q_gen_6200
<cons>(q_gen_6198, q_gen_6197) -> q_gen_6216
<s>(q_gen_6200) -> q_gen_6218
<cons, s>(q_gen_6181, q_gen_6180) -> q_gen_6177
<cons, s>(q_gen_6199, q_gen_6197) -> q_gen_6177
<cons, s>(q_gen_6217, q_gen_6216) -> q_gen_6177
<nil, z>() -> q_gen_6177
<a, z>() -> q_gen_6181
<b, z>() -> q_gen_6181
<a, s>(q_gen_6200) -> q_gen_6199
<b, s>(q_gen_6200) -> q_gen_6199
<cons, s>(q_gen_6181, q_gen_6197) -> q_gen_6205
<cons, s>(q_gen_6181, q_gen_6216) -> q_gen_6205
<cons, s>(q_gen_6199, q_gen_6180) -> q_gen_6205
<cons, s>(q_gen_6199, q_gen_6216) -> q_gen_6205
<cons, s>(q_gen_6217, q_gen_6180) -> q_gen_6205
<cons, s>(q_gen_6217, q_gen_6197) -> q_gen_6205
<a, s>(q_gen_6218) -> q_gen_6217
<b, s>(q_gen_6218) -> q_gen_6217
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 41
() -> length([nil, z]) -> 41
(append([l1, l2, _rx]) /\ append([l2, l1, _tx]) /\ length([_rx, _sx]) /\ length([_tx, _ux])) -> eq_nat([_sx, _ux]) -> 49
(append([t1, l2, _ix])) -> append([cons(h1, t1), l2, cons(h1, _ix)]) -> 49
(length([ll, _nx])) -> length([cons(x, ll), s(_nx)]) -> 42
}
Sat witness: Found: ((append([l1, l2, _rx]) /\ append([l2, l1, _tx]) /\ length([_rx, _sx]) /\ length([_tx, _ux])) -> eq_nat([_sx, _ux]), {
_rx -> cons(a, cons(b, cons(b, nil)))  ;  _sx -> s(s(s(z)))  ;  _tx -> cons(a, cons(b, nil))  ;  _ux -> s(s(z))  ;  l1 -> cons(a, nil)  ;  l2 -> nil
})

-------------------------------------------
Step 46, which took 0.417833 s (model generation: 0.415830,  model checking: 0.002003):

Model:
|_
{
append -> 
{{{
Q={q_gen_6178, q_gen_6183, q_gen_6184, q_gen_6187, q_gen_6192, q_gen_6193, q_gen_6194, q_gen_6195, q_gen_6203, q_gen_6231, q_gen_6232},
Q_f={q_gen_6178},
Delta=
{
<nil>() -> q_gen_6193
<a>() -> q_gen_6194
<b>() -> q_gen_6194
<cons>(q_gen_6194, q_gen_6193) -> q_gen_6232
<cons, cons>(q_gen_6184, q_gen_6183) -> q_gen_6183
<cons, cons>(q_gen_6187, q_gen_6183) -> q_gen_6183
<nil, nil>() -> q_gen_6183
<a, b>() -> q_gen_6184
<b, a>() -> q_gen_6184
<b, b>() -> q_gen_6184
<a, a>() -> q_gen_6187
<cons, cons>(q_gen_6184, q_gen_6203) -> q_gen_6203
<nil, cons>(q_gen_6194, q_gen_6193) -> q_gen_6203
<nil, cons>(q_gen_6194, q_gen_6232) -> q_gen_6203
<cons, cons, cons>(q_gen_6195, q_gen_6192) -> q_gen_6178
<cons, nil, cons>(q_gen_6184, q_gen_6183) -> q_gen_6178
<nil, cons, cons>(q_gen_6184, q_gen_6183) -> q_gen_6178
<nil, cons, cons>(q_gen_6187, q_gen_6183) -> q_gen_6178
<nil, nil, nil>() -> q_gen_6178
<cons, cons, cons>(q_gen_6195, q_gen_6178) -> q_gen_6192
<cons, cons, cons>(q_gen_6195, q_gen_6231) -> q_gen_6192
<cons, nil, cons>(q_gen_6184, q_gen_6203) -> q_gen_6192
<cons, nil, cons>(q_gen_6187, q_gen_6203) -> q_gen_6192
<nil, cons, cons>(q_gen_6184, q_gen_6203) -> q_gen_6192
<nil, cons, cons>(q_gen_6187, q_gen_6203) -> q_gen_6192
<nil, nil, cons>(q_gen_6194, q_gen_6193) -> q_gen_6192
<a, a, a>() -> q_gen_6195
<a, b, a>() -> q_gen_6195
<b, a, b>() -> q_gen_6195
<b, b, b>() -> q_gen_6195
<cons, nil, cons>(q_gen_6187, q_gen_6183) -> q_gen_6231
<nil, nil, cons>(q_gen_6194, q_gen_6232) -> q_gen_6231
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_6177, q_gen_6180, q_gen_6181, q_gen_6197, q_gen_6198, q_gen_6199, q_gen_6200, q_gen_6205, q_gen_6218},
Q_f={q_gen_6177},
Delta=
{
<cons>(q_gen_6198, q_gen_6197) -> q_gen_6180
<nil>() -> q_gen_6180
<cons>(q_gen_6198, q_gen_6180) -> q_gen_6197
<a>() -> q_gen_6198
<b>() -> q_gen_6198
<s>(q_gen_6218) -> q_gen_6200
<z>() -> q_gen_6200
<s>(q_gen_6200) -> q_gen_6218
<cons, s>(q_gen_6181, q_gen_6180) -> q_gen_6177
<cons, s>(q_gen_6199, q_gen_6197) -> q_gen_6177
<nil, z>() -> q_gen_6177
<a, s>(q_gen_6218) -> q_gen_6181
<a, z>() -> q_gen_6181
<b, s>(q_gen_6218) -> q_gen_6181
<b, z>() -> q_gen_6181
<a, s>(q_gen_6200) -> q_gen_6199
<b, s>(q_gen_6200) -> q_gen_6199
<cons, s>(q_gen_6181, q_gen_6197) -> q_gen_6205
<cons, s>(q_gen_6199, q_gen_6180) -> q_gen_6205
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 42
() -> length([nil, z]) -> 42
(append([l1, l2, _rx]) /\ append([l2, l1, _tx]) /\ length([_rx, _sx]) /\ length([_tx, _ux])) -> eq_nat([_sx, _ux]) -> 49
(append([t1, l2, _ix])) -> append([cons(h1, t1), l2, cons(h1, _ix)]) -> 52
(length([ll, _nx])) -> length([cons(x, ll), s(_nx)]) -> 43
}
Sat witness: Found: ((append([t1, l2, _ix])) -> append([cons(h1, t1), l2, cons(h1, _ix)]), {
_ix -> nil  ;  h1 -> a  ;  l2 -> nil  ;  t1 -> nil
})

-------------------------------------------
Step 47, which took 0.377554 s (model generation: 0.377005,  model checking: 0.000549):

Model:
|_
{
append -> 
{{{
Q={q_gen_6178, q_gen_6182, q_gen_6183, q_gen_6184, q_gen_6186, q_gen_6187, q_gen_6192, q_gen_6193, q_gen_6194, q_gen_6195, q_gen_6213},
Q_f={q_gen_6178, q_gen_6182},
Delta=
{
<cons>(q_gen_6194, q_gen_6193) -> q_gen_6193
<nil>() -> q_gen_6193
<a>() -> q_gen_6194
<b>() -> q_gen_6194
<cons, cons>(q_gen_6184, q_gen_6183) -> q_gen_6183
<nil, nil>() -> q_gen_6183
<a, b>() -> q_gen_6184
<b, a>() -> q_gen_6184
<b, b>() -> q_gen_6184
<cons, cons>(q_gen_6184, q_gen_6186) -> q_gen_6186
<cons, cons>(q_gen_6187, q_gen_6183) -> q_gen_6186
<nil, cons>(q_gen_6194, q_gen_6193) -> q_gen_6186
<a, a>() -> q_gen_6187
<cons, cons, cons>(q_gen_6195, q_gen_6182) -> q_gen_6178
<cons, nil, cons>(q_gen_6187, q_gen_6183) -> q_gen_6178
<nil, cons, cons>(q_gen_6187, q_gen_6186) -> q_gen_6178
<nil, nil, nil>() -> q_gen_6178
<cons, cons, cons>(q_gen_6195, q_gen_6192) -> q_gen_6182
<cons, cons, cons>(q_gen_6213, q_gen_6178) -> q_gen_6182
<cons, nil, cons>(q_gen_6184, q_gen_6183) -> q_gen_6182
<nil, cons, cons>(q_gen_6184, q_gen_6183) -> q_gen_6182
<cons, cons, cons>(q_gen_6195, q_gen_6178) -> q_gen_6192
<cons, cons, cons>(q_gen_6213, q_gen_6182) -> q_gen_6192
<cons, cons, cons>(q_gen_6213, q_gen_6192) -> q_gen_6192
<cons, nil, cons>(q_gen_6184, q_gen_6186) -> q_gen_6192
<cons, nil, cons>(q_gen_6187, q_gen_6186) -> q_gen_6192
<nil, cons, cons>(q_gen_6184, q_gen_6186) -> q_gen_6192
<nil, cons, cons>(q_gen_6187, q_gen_6183) -> q_gen_6192
<nil, nil, cons>(q_gen_6194, q_gen_6193) -> q_gen_6192
<a, b, a>() -> q_gen_6195
<b, b, b>() -> q_gen_6195
<a, a, a>() -> q_gen_6213
<b, a, b>() -> q_gen_6213
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_6177, q_gen_6180, q_gen_6181, q_gen_6197, q_gen_6198, q_gen_6199, q_gen_6200, q_gen_6205, q_gen_6218},
Q_f={q_gen_6177},
Delta=
{
<cons>(q_gen_6198, q_gen_6197) -> q_gen_6180
<nil>() -> q_gen_6180
<cons>(q_gen_6198, q_gen_6180) -> q_gen_6197
<a>() -> q_gen_6198
<b>() -> q_gen_6198
<s>(q_gen_6218) -> q_gen_6200
<z>() -> q_gen_6200
<s>(q_gen_6200) -> q_gen_6218
<cons, s>(q_gen_6181, q_gen_6180) -> q_gen_6177
<cons, s>(q_gen_6199, q_gen_6197) -> q_gen_6177
<nil, z>() -> q_gen_6177
<a, s>(q_gen_6218) -> q_gen_6181
<a, z>() -> q_gen_6181
<b, s>(q_gen_6218) -> q_gen_6181
<b, z>() -> q_gen_6181
<a, s>(q_gen_6200) -> q_gen_6199
<b, s>(q_gen_6200) -> q_gen_6199
<cons, s>(q_gen_6181, q_gen_6197) -> q_gen_6205
<cons, s>(q_gen_6199, q_gen_6180) -> q_gen_6205
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 45
() -> length([nil, z]) -> 43
(append([l1, l2, _rx]) /\ append([l2, l1, _tx]) /\ length([_rx, _sx]) /\ length([_tx, _ux])) -> eq_nat([_sx, _ux]) -> 49
(append([t1, l2, _ix])) -> append([cons(h1, t1), l2, cons(h1, _ix)]) -> 52
(length([ll, _nx])) -> length([cons(x, ll), s(_nx)]) -> 43
}
Sat witness: Found: (() -> append([nil, l2, l2]), {
l2 -> cons(b, cons(a, nil))
})

-------------------------------------------
Step 48, which took 0.390321 s (model generation: 0.388362,  model checking: 0.001959):

Model:
|_
{
append -> 
{{{
Q={q_gen_6178, q_gen_6182, q_gen_6183, q_gen_6184, q_gen_6186, q_gen_6187, q_gen_6192, q_gen_6193, q_gen_6194, q_gen_6195, q_gen_6213},
Q_f={q_gen_6178, q_gen_6182},
Delta=
{
<cons>(q_gen_6194, q_gen_6193) -> q_gen_6193
<nil>() -> q_gen_6193
<a>() -> q_gen_6194
<b>() -> q_gen_6194
<cons, cons>(q_gen_6184, q_gen_6183) -> q_gen_6183
<nil, nil>() -> q_gen_6183
<a, b>() -> q_gen_6184
<b, a>() -> q_gen_6184
<b, b>() -> q_gen_6184
<cons, cons>(q_gen_6184, q_gen_6186) -> q_gen_6186
<cons, cons>(q_gen_6187, q_gen_6183) -> q_gen_6186
<nil, cons>(q_gen_6194, q_gen_6193) -> q_gen_6186
<a, a>() -> q_gen_6187
<cons, cons, cons>(q_gen_6195, q_gen_6182) -> q_gen_6178
<cons, nil, cons>(q_gen_6187, q_gen_6183) -> q_gen_6178
<nil, cons, cons>(q_gen_6184, q_gen_6183) -> q_gen_6178
<nil, cons, cons>(q_gen_6187, q_gen_6186) -> q_gen_6178
<nil, nil, nil>() -> q_gen_6178
<cons, cons, cons>(q_gen_6195, q_gen_6192) -> q_gen_6182
<cons, cons, cons>(q_gen_6213, q_gen_6178) -> q_gen_6182
<cons, nil, cons>(q_gen_6184, q_gen_6183) -> q_gen_6182
<nil, cons, cons>(q_gen_6184, q_gen_6186) -> q_gen_6182
<cons, cons, cons>(q_gen_6195, q_gen_6178) -> q_gen_6192
<cons, cons, cons>(q_gen_6213, q_gen_6182) -> q_gen_6192
<cons, cons, cons>(q_gen_6213, q_gen_6192) -> q_gen_6192
<cons, nil, cons>(q_gen_6184, q_gen_6186) -> q_gen_6192
<cons, nil, cons>(q_gen_6187, q_gen_6186) -> q_gen_6192
<nil, cons, cons>(q_gen_6187, q_gen_6183) -> q_gen_6192
<nil, nil, cons>(q_gen_6194, q_gen_6193) -> q_gen_6192
<a, b, a>() -> q_gen_6195
<b, b, b>() -> q_gen_6195
<a, a, a>() -> q_gen_6213
<b, a, b>() -> q_gen_6213
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_6177, q_gen_6180, q_gen_6181, q_gen_6197, q_gen_6198, q_gen_6199, q_gen_6200, q_gen_6205, q_gen_6218},
Q_f={q_gen_6177},
Delta=
{
<cons>(q_gen_6198, q_gen_6197) -> q_gen_6180
<nil>() -> q_gen_6180
<cons>(q_gen_6198, q_gen_6180) -> q_gen_6197
<a>() -> q_gen_6198
<b>() -> q_gen_6198
<s>(q_gen_6218) -> q_gen_6200
<z>() -> q_gen_6200
<s>(q_gen_6200) -> q_gen_6218
<cons, s>(q_gen_6181, q_gen_6180) -> q_gen_6177
<cons, s>(q_gen_6199, q_gen_6197) -> q_gen_6177
<nil, z>() -> q_gen_6177
<a, s>(q_gen_6218) -> q_gen_6181
<a, z>() -> q_gen_6181
<b, s>(q_gen_6218) -> q_gen_6181
<b, z>() -> q_gen_6181
<a, s>(q_gen_6200) -> q_gen_6199
<b, s>(q_gen_6200) -> q_gen_6199
<cons, s>(q_gen_6181, q_gen_6197) -> q_gen_6205
<cons, s>(q_gen_6199, q_gen_6180) -> q_gen_6205
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 48
() -> length([nil, z]) -> 44
(append([l1, l2, _rx]) /\ append([l2, l1, _tx]) /\ length([_rx, _sx]) /\ length([_tx, _ux])) -> eq_nat([_sx, _ux]) -> 49
(append([t1, l2, _ix])) -> append([cons(h1, t1), l2, cons(h1, _ix)]) -> 52
(length([ll, _nx])) -> length([cons(x, ll), s(_nx)]) -> 44
}
Sat witness: Found: (() -> append([nil, l2, l2]), {
l2 -> cons(a, nil)
})

-------------------------------------------
Step 49, which took 0.388411 s (model generation: 0.375828,  model checking: 0.012583):

Model:
|_
{
append -> 
{{{
Q={q_gen_6178, q_gen_6182, q_gen_6183, q_gen_6184, q_gen_6192, q_gen_6193, q_gen_6194, q_gen_6195, q_gen_6203},
Q_f={q_gen_6178, q_gen_6182},
Delta=
{
<cons>(q_gen_6194, q_gen_6193) -> q_gen_6193
<nil>() -> q_gen_6193
<a>() -> q_gen_6194
<b>() -> q_gen_6194
<cons, cons>(q_gen_6184, q_gen_6183) -> q_gen_6183
<nil, nil>() -> q_gen_6183
<a, a>() -> q_gen_6184
<a, b>() -> q_gen_6184
<b, a>() -> q_gen_6184
<b, b>() -> q_gen_6184
<cons, cons>(q_gen_6184, q_gen_6203) -> q_gen_6203
<nil, cons>(q_gen_6194, q_gen_6193) -> q_gen_6203
<nil, nil, nil>() -> q_gen_6178
<cons, cons, cons>(q_gen_6195, q_gen_6182) -> q_gen_6182
<cons, cons, cons>(q_gen_6195, q_gen_6192) -> q_gen_6182
<cons, nil, cons>(q_gen_6184, q_gen_6183) -> q_gen_6182
<nil, cons, cons>(q_gen_6184, q_gen_6183) -> q_gen_6182
<cons, cons, cons>(q_gen_6195, q_gen_6178) -> q_gen_6192
<cons, nil, cons>(q_gen_6184, q_gen_6203) -> q_gen_6192
<nil, cons, cons>(q_gen_6184, q_gen_6203) -> q_gen_6192
<nil, nil, cons>(q_gen_6194, q_gen_6193) -> q_gen_6192
<a, a, a>() -> q_gen_6195
<a, b, a>() -> q_gen_6195
<b, a, b>() -> q_gen_6195
<b, b, b>() -> q_gen_6195
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_6177, q_gen_6180, q_gen_6181, q_gen_6197, q_gen_6198, q_gen_6199, q_gen_6200, q_gen_6205, q_gen_6216, q_gen_6217, q_gen_6218},
Q_f={q_gen_6177},
Delta=
{
<nil>() -> q_gen_6180
<cons>(q_gen_6198, q_gen_6180) -> q_gen_6197
<cons>(q_gen_6198, q_gen_6216) -> q_gen_6197
<a>() -> q_gen_6198
<b>() -> q_gen_6198
<s>(q_gen_6218) -> q_gen_6200
<z>() -> q_gen_6200
<cons>(q_gen_6198, q_gen_6197) -> q_gen_6216
<s>(q_gen_6200) -> q_gen_6218
<cons, s>(q_gen_6181, q_gen_6180) -> q_gen_6177
<cons, s>(q_gen_6199, q_gen_6197) -> q_gen_6177
<cons, s>(q_gen_6217, q_gen_6216) -> q_gen_6177
<nil, z>() -> q_gen_6177
<a, z>() -> q_gen_6181
<b, z>() -> q_gen_6181
<a, s>(q_gen_6200) -> q_gen_6199
<b, s>(q_gen_6200) -> q_gen_6199
<cons, s>(q_gen_6181, q_gen_6197) -> q_gen_6205
<cons, s>(q_gen_6181, q_gen_6216) -> q_gen_6205
<cons, s>(q_gen_6199, q_gen_6180) -> q_gen_6205
<cons, s>(q_gen_6199, q_gen_6216) -> q_gen_6205
<cons, s>(q_gen_6217, q_gen_6180) -> q_gen_6205
<cons, s>(q_gen_6217, q_gen_6197) -> q_gen_6205
<a, s>(q_gen_6218) -> q_gen_6217
<b, s>(q_gen_6218) -> q_gen_6217
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 49
() -> length([nil, z]) -> 45
(append([l1, l2, _rx]) /\ append([l2, l1, _tx]) /\ length([_rx, _sx]) /\ length([_tx, _ux])) -> eq_nat([_sx, _ux]) -> 52
(append([t1, l2, _ix])) -> append([cons(h1, t1), l2, cons(h1, _ix)]) -> 52
(length([ll, _nx])) -> length([cons(x, ll), s(_nx)]) -> 45
}
Sat witness: Found: ((append([l1, l2, _rx]) /\ append([l2, l1, _tx]) /\ length([_rx, _sx]) /\ length([_tx, _ux])) -> eq_nat([_sx, _ux]), {
_rx -> cons(a, cons(b, nil))  ;  _sx -> s(s(z))  ;  _tx -> cons(b, cons(b, nil))  ;  _ux -> s(s(s(s(z))))  ;  l1 -> cons(a, cons(b, nil))  ;  l2 -> cons(b, nil)
})

-------------------------------------------
Step 50, which took 0.410895 s (model generation: 0.409656,  model checking: 0.001239):

Model:
|_
{
append -> 
{{{
Q={q_gen_6178, q_gen_6182, q_gen_6183, q_gen_6184, q_gen_6192, q_gen_6193, q_gen_6194, q_gen_6195, q_gen_6222},
Q_f={q_gen_6178, q_gen_6182},
Delta=
{
<cons>(q_gen_6194, q_gen_6193) -> q_gen_6193
<nil>() -> q_gen_6193
<a>() -> q_gen_6194
<b>() -> q_gen_6194
<cons, cons>(q_gen_6184, q_gen_6183) -> q_gen_6183
<nil, cons>(q_gen_6194, q_gen_6193) -> q_gen_6183
<nil, nil>() -> q_gen_6183
<a, a>() -> q_gen_6184
<a, b>() -> q_gen_6184
<b, a>() -> q_gen_6184
<b, b>() -> q_gen_6184
<cons, cons, cons>(q_gen_6222, q_gen_6182) -> q_gen_6178
<nil, nil, nil>() -> q_gen_6178
<cons, cons, cons>(q_gen_6195, q_gen_6182) -> q_gen_6182
<cons, cons, cons>(q_gen_6195, q_gen_6192) -> q_gen_6182
<cons, nil, cons>(q_gen_6184, q_gen_6183) -> q_gen_6182
<nil, cons, cons>(q_gen_6184, q_gen_6183) -> q_gen_6182
<cons, cons, cons>(q_gen_6195, q_gen_6178) -> q_gen_6192
<cons, cons, cons>(q_gen_6222, q_gen_6192) -> q_gen_6192
<nil, nil, cons>(q_gen_6194, q_gen_6193) -> q_gen_6192
<a, b, a>() -> q_gen_6195
<b, a, b>() -> q_gen_6195
<b, b, b>() -> q_gen_6195
<a, a, a>() -> q_gen_6222
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_6177, q_gen_6180, q_gen_6181, q_gen_6189, q_gen_6197, q_gen_6198, q_gen_6199, q_gen_6200, q_gen_6205, q_gen_6216, q_gen_6218},
Q_f={q_gen_6177},
Delta=
{
<cons>(q_gen_6198, q_gen_6216) -> q_gen_6180
<nil>() -> q_gen_6180
<cons>(q_gen_6198, q_gen_6180) -> q_gen_6197
<a>() -> q_gen_6198
<b>() -> q_gen_6198
<z>() -> q_gen_6200
<cons>(q_gen_6198, q_gen_6197) -> q_gen_6216
<s>(q_gen_6200) -> q_gen_6218
<s>(q_gen_6218) -> q_gen_6218
<cons, s>(q_gen_6181, q_gen_6180) -> q_gen_6177
<cons, s>(q_gen_6181, q_gen_6216) -> q_gen_6177
<cons, s>(q_gen_6189, q_gen_6180) -> q_gen_6177
<cons, s>(q_gen_6199, q_gen_6197) -> q_gen_6177
<nil, z>() -> q_gen_6177
<b, s>(q_gen_6218) -> q_gen_6181
<b, z>() -> q_gen_6181
<a, z>() -> q_gen_6189
<a, s>(q_gen_6200) -> q_gen_6199
<a, s>(q_gen_6218) -> q_gen_6199
<b, s>(q_gen_6200) -> q_gen_6199
<cons, s>(q_gen_6181, q_gen_6197) -> q_gen_6205
<cons, s>(q_gen_6189, q_gen_6197) -> q_gen_6205
<cons, s>(q_gen_6189, q_gen_6216) -> q_gen_6205
<cons, s>(q_gen_6199, q_gen_6180) -> q_gen_6205
<cons, s>(q_gen_6199, q_gen_6216) -> q_gen_6205
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 49
() -> length([nil, z]) -> 45
(append([l1, l2, _rx]) /\ append([l2, l1, _tx]) /\ length([_rx, _sx]) /\ length([_tx, _ux])) -> eq_nat([_sx, _ux]) -> 52
(append([t1, l2, _ix])) -> append([cons(h1, t1), l2, cons(h1, _ix)]) -> 52
(length([ll, _nx])) -> length([cons(x, ll), s(_nx)]) -> 48
}
Sat witness: Found: ((length([ll, _nx])) -> length([cons(x, ll), s(_nx)]), {
_nx -> s(s(s(z)))  ;  ll -> cons(b, nil)  ;  x -> b
})

-------------------------------------------
Step 51, which took 0.376532 s (model generation: 0.329851,  model checking: 0.046681):

Model:
|_
{
append -> 
{{{
Q={q_gen_6178, q_gen_6182, q_gen_6183, q_gen_6184, q_gen_6192, q_gen_6193, q_gen_6194, q_gen_6195, q_gen_6203},
Q_f={q_gen_6178, q_gen_6182},
Delta=
{
<cons>(q_gen_6194, q_gen_6193) -> q_gen_6193
<nil>() -> q_gen_6193
<a>() -> q_gen_6194
<b>() -> q_gen_6194
<cons, cons>(q_gen_6184, q_gen_6183) -> q_gen_6183
<nil, nil>() -> q_gen_6183
<a, a>() -> q_gen_6184
<a, b>() -> q_gen_6184
<b, a>() -> q_gen_6184
<b, b>() -> q_gen_6184
<cons, cons>(q_gen_6184, q_gen_6203) -> q_gen_6203
<nil, cons>(q_gen_6194, q_gen_6193) -> q_gen_6203
<nil, nil, nil>() -> q_gen_6178
<cons, cons, cons>(q_gen_6195, q_gen_6182) -> q_gen_6182
<cons, cons, cons>(q_gen_6195, q_gen_6192) -> q_gen_6182
<cons, nil, cons>(q_gen_6184, q_gen_6183) -> q_gen_6182
<nil, cons, cons>(q_gen_6184, q_gen_6183) -> q_gen_6182
<nil, cons, cons>(q_gen_6184, q_gen_6203) -> q_gen_6182
<cons, cons, cons>(q_gen_6195, q_gen_6178) -> q_gen_6192
<cons, nil, cons>(q_gen_6184, q_gen_6203) -> q_gen_6192
<nil, nil, cons>(q_gen_6194, q_gen_6193) -> q_gen_6192
<a, a, a>() -> q_gen_6195
<a, b, a>() -> q_gen_6195
<b, a, b>() -> q_gen_6195
<b, b, b>() -> q_gen_6195
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_6177, q_gen_6180, q_gen_6181, q_gen_6197, q_gen_6198, q_gen_6199, q_gen_6200, q_gen_6205, q_gen_6216, q_gen_6217, q_gen_6218},
Q_f={q_gen_6177},
Delta=
{
<nil>() -> q_gen_6180
<cons>(q_gen_6198, q_gen_6180) -> q_gen_6197
<a>() -> q_gen_6198
<b>() -> q_gen_6198
<z>() -> q_gen_6200
<cons>(q_gen_6198, q_gen_6197) -> q_gen_6216
<cons>(q_gen_6198, q_gen_6216) -> q_gen_6216
<s>(q_gen_6200) -> q_gen_6218
<s>(q_gen_6218) -> q_gen_6218
<cons, s>(q_gen_6181, q_gen_6180) -> q_gen_6177
<cons, s>(q_gen_6199, q_gen_6197) -> q_gen_6177
<cons, s>(q_gen_6217, q_gen_6216) -> q_gen_6177
<nil, z>() -> q_gen_6177
<a, z>() -> q_gen_6181
<b, z>() -> q_gen_6181
<a, s>(q_gen_6200) -> q_gen_6199
<b, s>(q_gen_6200) -> q_gen_6199
<cons, s>(q_gen_6181, q_gen_6197) -> q_gen_6205
<cons, s>(q_gen_6181, q_gen_6216) -> q_gen_6205
<cons, s>(q_gen_6199, q_gen_6180) -> q_gen_6205
<cons, s>(q_gen_6199, q_gen_6216) -> q_gen_6205
<cons, s>(q_gen_6217, q_gen_6180) -> q_gen_6205
<cons, s>(q_gen_6217, q_gen_6197) -> q_gen_6205
<a, s>(q_gen_6218) -> q_gen_6217
<b, s>(q_gen_6218) -> q_gen_6217
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 50
() -> length([nil, z]) -> 46
(append([l1, l2, _rx]) /\ append([l2, l1, _tx]) /\ length([_rx, _sx]) /\ length([_tx, _ux])) -> eq_nat([_sx, _ux]) -> 55
(append([t1, l2, _ix])) -> append([cons(h1, t1), l2, cons(h1, _ix)]) -> 53
(length([ll, _nx])) -> length([cons(x, ll), s(_nx)]) -> 49
}
Sat witness: Found: ((append([l1, l2, _rx]) /\ append([l2, l1, _tx]) /\ length([_rx, _sx]) /\ length([_tx, _ux])) -> eq_nat([_sx, _ux]), {
_rx -> cons(a, cons(b, cons(b, nil)))  ;  _sx -> s(s(s(z)))  ;  _tx -> cons(b, cons(b, nil))  ;  _ux -> s(s(z))  ;  l1 -> nil  ;  l2 -> cons(b, cons(b, nil))
})

-------------------------------------------
Step 52, which took 0.418617 s (model generation: 0.415605,  model checking: 0.003012):

Model:
|_
{
append -> 
{{{
Q={q_gen_6178, q_gen_6182, q_gen_6183, q_gen_6184, q_gen_6186, q_gen_6192, q_gen_6193, q_gen_6194, q_gen_6195},
Q_f={q_gen_6178, q_gen_6182},
Delta=
{
<cons>(q_gen_6194, q_gen_6193) -> q_gen_6193
<nil>() -> q_gen_6193
<a>() -> q_gen_6194
<b>() -> q_gen_6194
<nil, nil>() -> q_gen_6183
<a, a>() -> q_gen_6184
<a, b>() -> q_gen_6184
<b, a>() -> q_gen_6184
<b, b>() -> q_gen_6184
<cons, cons>(q_gen_6184, q_gen_6183) -> q_gen_6186
<cons, cons>(q_gen_6184, q_gen_6186) -> q_gen_6186
<nil, cons>(q_gen_6194, q_gen_6193) -> q_gen_6186
<nil, cons, cons>(q_gen_6184, q_gen_6183) -> q_gen_6178
<nil, nil, nil>() -> q_gen_6178
<cons, cons, cons>(q_gen_6195, q_gen_6182) -> q_gen_6182
<cons, cons, cons>(q_gen_6195, q_gen_6192) -> q_gen_6182
<cons, nil, cons>(q_gen_6184, q_gen_6183) -> q_gen_6182
<nil, cons, cons>(q_gen_6184, q_gen_6186) -> q_gen_6182
<cons, cons, cons>(q_gen_6195, q_gen_6178) -> q_gen_6192
<cons, nil, cons>(q_gen_6184, q_gen_6186) -> q_gen_6192
<nil, nil, cons>(q_gen_6194, q_gen_6193) -> q_gen_6192
<a, a, a>() -> q_gen_6195
<a, b, a>() -> q_gen_6195
<b, a, b>() -> q_gen_6195
<b, b, b>() -> q_gen_6195
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_6177, q_gen_6180, q_gen_6181, q_gen_6197, q_gen_6198, q_gen_6199, q_gen_6200, q_gen_6205, q_gen_6216, q_gen_6217, q_gen_6218},
Q_f={q_gen_6177},
Delta=
{
<nil>() -> q_gen_6180
<cons>(q_gen_6198, q_gen_6180) -> q_gen_6197
<cons>(q_gen_6198, q_gen_6216) -> q_gen_6197
<a>() -> q_gen_6198
<b>() -> q_gen_6198
<s>(q_gen_6218) -> q_gen_6200
<z>() -> q_gen_6200
<cons>(q_gen_6198, q_gen_6197) -> q_gen_6216
<s>(q_gen_6200) -> q_gen_6218
<cons, s>(q_gen_6181, q_gen_6180) -> q_gen_6177
<cons, s>(q_gen_6199, q_gen_6197) -> q_gen_6177
<cons, s>(q_gen_6217, q_gen_6216) -> q_gen_6177
<nil, z>() -> q_gen_6177
<a, z>() -> q_gen_6181
<b, z>() -> q_gen_6181
<a, s>(q_gen_6200) -> q_gen_6199
<b, s>(q_gen_6200) -> q_gen_6199
<cons, s>(q_gen_6181, q_gen_6197) -> q_gen_6205
<cons, s>(q_gen_6181, q_gen_6216) -> q_gen_6205
<cons, s>(q_gen_6199, q_gen_6180) -> q_gen_6205
<cons, s>(q_gen_6199, q_gen_6216) -> q_gen_6205
<cons, s>(q_gen_6217, q_gen_6180) -> q_gen_6205
<cons, s>(q_gen_6217, q_gen_6197) -> q_gen_6205
<a, s>(q_gen_6218) -> q_gen_6217
<b, s>(q_gen_6218) -> q_gen_6217
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 51
() -> length([nil, z]) -> 47
(append([l1, l2, _rx]) /\ append([l2, l1, _tx]) /\ length([_rx, _sx]) /\ length([_tx, _ux])) -> eq_nat([_sx, _ux]) -> 55
(append([t1, l2, _ix])) -> append([cons(h1, t1), l2, cons(h1, _ix)]) -> 56
(length([ll, _nx])) -> length([cons(x, ll), s(_nx)]) -> 50
}
Sat witness: Found: ((append([t1, l2, _ix])) -> append([cons(h1, t1), l2, cons(h1, _ix)]), {
_ix -> cons(a, nil)  ;  h1 -> b  ;  l2 -> nil  ;  t1 -> cons(a, nil)
})

-------------------------------------------
Step 53, which took 0.548238 s (model generation: 0.544523,  model checking: 0.003715):

Model:
|_
{
append -> 
{{{
Q={q_gen_6178, q_gen_6182, q_gen_6183, q_gen_6184, q_gen_6192, q_gen_6193, q_gen_6194, q_gen_6195, q_gen_6222},
Q_f={q_gen_6178, q_gen_6182},
Delta=
{
<cons>(q_gen_6194, q_gen_6193) -> q_gen_6193
<nil>() -> q_gen_6193
<a>() -> q_gen_6194
<b>() -> q_gen_6194
<cons, cons>(q_gen_6184, q_gen_6183) -> q_gen_6183
<nil, cons>(q_gen_6194, q_gen_6193) -> q_gen_6183
<nil, nil>() -> q_gen_6183
<a, a>() -> q_gen_6184
<a, b>() -> q_gen_6184
<b, a>() -> q_gen_6184
<b, b>() -> q_gen_6184
<cons, cons, cons>(q_gen_6222, q_gen_6182) -> q_gen_6178
<nil, nil, nil>() -> q_gen_6178
<cons, cons, cons>(q_gen_6195, q_gen_6182) -> q_gen_6182
<cons, cons, cons>(q_gen_6195, q_gen_6192) -> q_gen_6182
<cons, nil, cons>(q_gen_6184, q_gen_6183) -> q_gen_6182
<nil, cons, cons>(q_gen_6184, q_gen_6183) -> q_gen_6182
<cons, cons, cons>(q_gen_6195, q_gen_6178) -> q_gen_6192
<cons, cons, cons>(q_gen_6222, q_gen_6192) -> q_gen_6192
<nil, nil, cons>(q_gen_6194, q_gen_6193) -> q_gen_6192
<a, b, a>() -> q_gen_6195
<b, a, b>() -> q_gen_6195
<b, b, b>() -> q_gen_6195
<a, a, a>() -> q_gen_6222
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_6177, q_gen_6180, q_gen_6181, q_gen_6197, q_gen_6198, q_gen_6199, q_gen_6200, q_gen_6205, q_gen_6216, q_gen_6217, q_gen_6218},
Q_f={q_gen_6177},
Delta=
{
<nil>() -> q_gen_6180
<cons>(q_gen_6198, q_gen_6180) -> q_gen_6197
<a>() -> q_gen_6198
<b>() -> q_gen_6198
<z>() -> q_gen_6200
<cons>(q_gen_6198, q_gen_6197) -> q_gen_6216
<cons>(q_gen_6198, q_gen_6216) -> q_gen_6216
<s>(q_gen_6200) -> q_gen_6218
<s>(q_gen_6218) -> q_gen_6218
<cons, s>(q_gen_6181, q_gen_6180) -> q_gen_6177
<cons, s>(q_gen_6199, q_gen_6197) -> q_gen_6177
<cons, s>(q_gen_6217, q_gen_6216) -> q_gen_6177
<nil, z>() -> q_gen_6177
<a, z>() -> q_gen_6181
<b, z>() -> q_gen_6181
<a, s>(q_gen_6200) -> q_gen_6199
<a, s>(q_gen_6218) -> q_gen_6199
<b, s>(q_gen_6200) -> q_gen_6199
<cons, s>(q_gen_6181, q_gen_6197) -> q_gen_6205
<cons, s>(q_gen_6181, q_gen_6216) -> q_gen_6205
<cons, s>(q_gen_6199, q_gen_6180) -> q_gen_6205
<cons, s>(q_gen_6199, q_gen_6216) -> q_gen_6205
<cons, s>(q_gen_6217, q_gen_6180) -> q_gen_6205
<cons, s>(q_gen_6217, q_gen_6197) -> q_gen_6205
<b, s>(q_gen_6218) -> q_gen_6217
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 51
() -> length([nil, z]) -> 48
(append([l1, l2, _rx]) /\ append([l2, l1, _tx]) /\ length([_rx, _sx]) /\ length([_tx, _ux])) -> eq_nat([_sx, _ux]) -> 55
(append([t1, l2, _ix])) -> append([cons(h1, t1), l2, cons(h1, _ix)]) -> 56
(length([ll, _nx])) -> length([cons(x, ll), s(_nx)]) -> 53
}
Sat witness: Found: ((length([ll, _nx])) -> length([cons(x, ll), s(_nx)]), {
_nx -> s(s(z))  ;  ll -> cons(b, cons(b, nil))  ;  x -> a
})

-------------------------------------------
Step 54, which took 0.432799 s (model generation: 0.419516,  model checking: 0.013283):

Model:
|_
{
append -> 
{{{
Q={q_gen_6178, q_gen_6182, q_gen_6183, q_gen_6184, q_gen_6192, q_gen_6193, q_gen_6194, q_gen_6195, q_gen_6203},
Q_f={q_gen_6178, q_gen_6182},
Delta=
{
<cons>(q_gen_6194, q_gen_6193) -> q_gen_6193
<nil>() -> q_gen_6193
<a>() -> q_gen_6194
<b>() -> q_gen_6194
<cons, cons>(q_gen_6184, q_gen_6183) -> q_gen_6183
<nil, nil>() -> q_gen_6183
<a, a>() -> q_gen_6184
<a, b>() -> q_gen_6184
<b, a>() -> q_gen_6184
<b, b>() -> q_gen_6184
<cons, cons>(q_gen_6184, q_gen_6203) -> q_gen_6203
<nil, cons>(q_gen_6194, q_gen_6193) -> q_gen_6203
<nil, nil, nil>() -> q_gen_6178
<cons, cons, cons>(q_gen_6195, q_gen_6182) -> q_gen_6182
<cons, cons, cons>(q_gen_6195, q_gen_6192) -> q_gen_6182
<cons, nil, cons>(q_gen_6184, q_gen_6183) -> q_gen_6182
<nil, cons, cons>(q_gen_6184, q_gen_6183) -> q_gen_6182
<cons, cons, cons>(q_gen_6195, q_gen_6178) -> q_gen_6192
<cons, nil, cons>(q_gen_6184, q_gen_6203) -> q_gen_6192
<nil, cons, cons>(q_gen_6184, q_gen_6203) -> q_gen_6192
<nil, nil, cons>(q_gen_6194, q_gen_6193) -> q_gen_6192
<a, a, a>() -> q_gen_6195
<a, b, a>() -> q_gen_6195
<b, a, b>() -> q_gen_6195
<b, b, b>() -> q_gen_6195
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_6177, q_gen_6180, q_gen_6181, q_gen_6197, q_gen_6198, q_gen_6199, q_gen_6200, q_gen_6205, q_gen_6216, q_gen_6217, q_gen_6218},
Q_f={q_gen_6177},
Delta=
{
<nil>() -> q_gen_6180
<cons>(q_gen_6198, q_gen_6180) -> q_gen_6197
<a>() -> q_gen_6198
<b>() -> q_gen_6198
<z>() -> q_gen_6200
<cons>(q_gen_6198, q_gen_6197) -> q_gen_6216
<cons>(q_gen_6198, q_gen_6216) -> q_gen_6216
<s>(q_gen_6200) -> q_gen_6218
<s>(q_gen_6218) -> q_gen_6218
<cons, s>(q_gen_6181, q_gen_6180) -> q_gen_6177
<cons, s>(q_gen_6199, q_gen_6197) -> q_gen_6177
<cons, s>(q_gen_6217, q_gen_6216) -> q_gen_6177
<nil, z>() -> q_gen_6177
<a, z>() -> q_gen_6181
<b, z>() -> q_gen_6181
<a, s>(q_gen_6200) -> q_gen_6199
<b, s>(q_gen_6200) -> q_gen_6199
<cons, s>(q_gen_6181, q_gen_6197) -> q_gen_6205
<cons, s>(q_gen_6181, q_gen_6216) -> q_gen_6205
<cons, s>(q_gen_6199, q_gen_6180) -> q_gen_6205
<cons, s>(q_gen_6199, q_gen_6216) -> q_gen_6205
<cons, s>(q_gen_6217, q_gen_6180) -> q_gen_6205
<cons, s>(q_gen_6217, q_gen_6197) -> q_gen_6205
<a, s>(q_gen_6218) -> q_gen_6217
<b, s>(q_gen_6218) -> q_gen_6217
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 52
() -> length([nil, z]) -> 49
(append([l1, l2, _rx]) /\ append([l2, l1, _tx]) /\ length([_rx, _sx]) /\ length([_tx, _ux])) -> eq_nat([_sx, _ux]) -> 58
(append([t1, l2, _ix])) -> append([cons(h1, t1), l2, cons(h1, _ix)]) -> 56
(length([ll, _nx])) -> length([cons(x, ll), s(_nx)]) -> 54
}
Sat witness: Found: ((append([l1, l2, _rx]) /\ append([l2, l1, _tx]) /\ length([_rx, _sx]) /\ length([_tx, _ux])) -> eq_nat([_sx, _ux]), {
_rx -> cons(a, cons(b, cons(b, nil)))  ;  _sx -> s(s(s(z)))  ;  _tx -> cons(a, cons(b, cons(b, nil)))  ;  _ux -> s(s(s(s(z))))  ;  l1 -> cons(a, nil)  ;  l2 -> cons(a, nil)
})

-------------------------------------------
Step 55, which took 0.660939 s (model generation: 0.612430,  model checking: 0.048509):

Model:
|_
{
append -> 
{{{
Q={q_gen_6178, q_gen_6182, q_gen_6183, q_gen_6184, q_gen_6192, q_gen_6193, q_gen_6194, q_gen_6195, q_gen_6203},
Q_f={q_gen_6178, q_gen_6182},
Delta=
{
<cons>(q_gen_6194, q_gen_6193) -> q_gen_6193
<nil>() -> q_gen_6193
<a>() -> q_gen_6194
<b>() -> q_gen_6194
<cons, cons>(q_gen_6184, q_gen_6183) -> q_gen_6183
<nil, nil>() -> q_gen_6183
<a, a>() -> q_gen_6184
<a, b>() -> q_gen_6184
<b, a>() -> q_gen_6184
<b, b>() -> q_gen_6184
<cons, cons>(q_gen_6184, q_gen_6203) -> q_gen_6203
<nil, cons>(q_gen_6194, q_gen_6193) -> q_gen_6203
<nil, cons, cons>(q_gen_6184, q_gen_6183) -> q_gen_6178
<nil, nil, nil>() -> q_gen_6178
<cons, cons, cons>(q_gen_6195, q_gen_6182) -> q_gen_6182
<cons, cons, cons>(q_gen_6195, q_gen_6192) -> q_gen_6182
<cons, nil, cons>(q_gen_6184, q_gen_6183) -> q_gen_6182
<cons, cons, cons>(q_gen_6195, q_gen_6178) -> q_gen_6192
<cons, nil, cons>(q_gen_6184, q_gen_6203) -> q_gen_6192
<nil, cons, cons>(q_gen_6184, q_gen_6203) -> q_gen_6192
<nil, nil, cons>(q_gen_6194, q_gen_6193) -> q_gen_6192
<a, a, a>() -> q_gen_6195
<a, b, a>() -> q_gen_6195
<b, a, b>() -> q_gen_6195
<b, b, b>() -> q_gen_6195
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_6177, q_gen_6180, q_gen_6181, q_gen_6197, q_gen_6198, q_gen_6199, q_gen_6200, q_gen_6205, q_gen_6216, q_gen_6217, q_gen_6218},
Q_f={q_gen_6177},
Delta=
{
<nil>() -> q_gen_6180
<cons>(q_gen_6198, q_gen_6180) -> q_gen_6197
<cons>(q_gen_6198, q_gen_6216) -> q_gen_6197
<a>() -> q_gen_6198
<b>() -> q_gen_6198
<s>(q_gen_6218) -> q_gen_6200
<z>() -> q_gen_6200
<cons>(q_gen_6198, q_gen_6197) -> q_gen_6216
<s>(q_gen_6200) -> q_gen_6218
<cons, s>(q_gen_6181, q_gen_6180) -> q_gen_6177
<cons, s>(q_gen_6199, q_gen_6197) -> q_gen_6177
<cons, s>(q_gen_6217, q_gen_6216) -> q_gen_6177
<nil, z>() -> q_gen_6177
<a, z>() -> q_gen_6181
<b, z>() -> q_gen_6181
<a, s>(q_gen_6200) -> q_gen_6199
<b, s>(q_gen_6200) -> q_gen_6199
<cons, s>(q_gen_6181, q_gen_6197) -> q_gen_6205
<cons, s>(q_gen_6181, q_gen_6216) -> q_gen_6205
<cons, s>(q_gen_6199, q_gen_6180) -> q_gen_6205
<cons, s>(q_gen_6199, q_gen_6216) -> q_gen_6205
<cons, s>(q_gen_6217, q_gen_6180) -> q_gen_6205
<cons, s>(q_gen_6217, q_gen_6197) -> q_gen_6205
<a, s>(q_gen_6218) -> q_gen_6217
<b, s>(q_gen_6218) -> q_gen_6217
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 53
() -> length([nil, z]) -> 50
(append([l1, l2, _rx]) /\ append([l2, l1, _tx]) /\ length([_rx, _sx]) /\ length([_tx, _ux])) -> eq_nat([_sx, _ux]) -> 61
(append([t1, l2, _ix])) -> append([cons(h1, t1), l2, cons(h1, _ix)]) -> 57
(length([ll, _nx])) -> length([cons(x, ll), s(_nx)]) -> 55
}
Sat witness: Found: ((append([l1, l2, _rx]) /\ append([l2, l1, _tx]) /\ length([_rx, _sx]) /\ length([_tx, _ux])) -> eq_nat([_sx, _ux]), {
_rx -> cons(a, cons(b, cons(b, nil)))  ;  _sx -> s(s(s(z)))  ;  _tx -> cons(b, cons(b, cons(b, cons(b, nil))))  ;  _ux -> s(s(z))  ;  l1 -> cons(a, cons(b, nil))  ;  l2 -> cons(b, cons(b, cons(b, nil)))
})

-------------------------------------------
Step 56, which took 0.571825 s (model generation: 0.571327,  model checking: 0.000498):

Model:
|_
{
append -> 
{{{
Q={q_gen_6178, q_gen_6183, q_gen_6184, q_gen_6187, q_gen_6192, q_gen_6193, q_gen_6194, q_gen_6195, q_gen_6203},
Q_f={q_gen_6178},
Delta=
{
<cons>(q_gen_6194, q_gen_6193) -> q_gen_6193
<nil>() -> q_gen_6193
<a>() -> q_gen_6194
<b>() -> q_gen_6194
<cons, cons>(q_gen_6187, q_gen_6183) -> q_gen_6183
<nil, nil>() -> q_gen_6183
<b, a>() -> q_gen_6184
<b, b>() -> q_gen_6184
<a, a>() -> q_gen_6187
<a, b>() -> q_gen_6187
<cons, cons>(q_gen_6184, q_gen_6183) -> q_gen_6203
<cons, cons>(q_gen_6184, q_gen_6203) -> q_gen_6203
<nil, cons>(q_gen_6194, q_gen_6193) -> q_gen_6203
<cons, cons, cons>(q_gen_6195, q_gen_6192) -> q_gen_6178
<cons, nil, cons>(q_gen_6184, q_gen_6183) -> q_gen_6178
<cons, nil, cons>(q_gen_6187, q_gen_6183) -> q_gen_6178
<nil, cons, cons>(q_gen_6184, q_gen_6183) -> q_gen_6178
<nil, cons, cons>(q_gen_6184, q_gen_6203) -> q_gen_6178
<nil, cons, cons>(q_gen_6187, q_gen_6183) -> q_gen_6178
<nil, nil, nil>() -> q_gen_6178
<cons, cons, cons>(q_gen_6195, q_gen_6178) -> q_gen_6192
<cons, nil, cons>(q_gen_6184, q_gen_6203) -> q_gen_6192
<cons, nil, cons>(q_gen_6187, q_gen_6203) -> q_gen_6192
<nil, cons, cons>(q_gen_6187, q_gen_6203) -> q_gen_6192
<nil, nil, cons>(q_gen_6194, q_gen_6193) -> q_gen_6192
<a, a, a>() -> q_gen_6195
<a, b, a>() -> q_gen_6195
<b, a, b>() -> q_gen_6195
<b, b, b>() -> q_gen_6195
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_6177, q_gen_6180, q_gen_6181, q_gen_6197, q_gen_6198, q_gen_6199, q_gen_6200, q_gen_6205, q_gen_6216, q_gen_6217, q_gen_6218},
Q_f={q_gen_6177},
Delta=
{
<nil>() -> q_gen_6180
<cons>(q_gen_6198, q_gen_6180) -> q_gen_6197
<cons>(q_gen_6198, q_gen_6216) -> q_gen_6197
<a>() -> q_gen_6198
<b>() -> q_gen_6198
<s>(q_gen_6218) -> q_gen_6200
<z>() -> q_gen_6200
<cons>(q_gen_6198, q_gen_6197) -> q_gen_6216
<s>(q_gen_6200) -> q_gen_6218
<cons, s>(q_gen_6181, q_gen_6180) -> q_gen_6177
<cons, s>(q_gen_6199, q_gen_6197) -> q_gen_6177
<cons, s>(q_gen_6217, q_gen_6216) -> q_gen_6177
<nil, z>() -> q_gen_6177
<a, z>() -> q_gen_6181
<b, z>() -> q_gen_6181
<a, s>(q_gen_6200) -> q_gen_6199
<b, s>(q_gen_6200) -> q_gen_6199
<cons, s>(q_gen_6181, q_gen_6197) -> q_gen_6205
<cons, s>(q_gen_6181, q_gen_6216) -> q_gen_6205
<cons, s>(q_gen_6199, q_gen_6180) -> q_gen_6205
<cons, s>(q_gen_6199, q_gen_6216) -> q_gen_6205
<cons, s>(q_gen_6217, q_gen_6180) -> q_gen_6205
<cons, s>(q_gen_6217, q_gen_6197) -> q_gen_6205
<a, s>(q_gen_6218) -> q_gen_6217
<b, s>(q_gen_6218) -> q_gen_6217
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 56
() -> length([nil, z]) -> 51
(append([l1, l2, _rx]) /\ append([l2, l1, _tx]) /\ length([_rx, _sx]) /\ length([_tx, _ux])) -> eq_nat([_sx, _ux]) -> 61
(append([t1, l2, _ix])) -> append([cons(h1, t1), l2, cons(h1, _ix)]) -> 57
(length([ll, _nx])) -> length([cons(x, ll), s(_nx)]) -> 55
}
Sat witness: Found: (() -> append([nil, l2, l2]), {
l2 -> cons(a, cons(b, nil))
})

-------------------------------------------
Step 57, which took 0.678166 s (model generation: 0.672159,  model checking: 0.006007):

Model:
|_
{
append -> 
{{{
Q={q_gen_6178, q_gen_6183, q_gen_6184, q_gen_6187, q_gen_6192, q_gen_6193, q_gen_6194, q_gen_6195, q_gen_6203},
Q_f={q_gen_6178},
Delta=
{
<cons>(q_gen_6194, q_gen_6193) -> q_gen_6193
<nil>() -> q_gen_6193
<a>() -> q_gen_6194
<b>() -> q_gen_6194
<cons, cons>(q_gen_6184, q_gen_6183) -> q_gen_6183
<cons, cons>(q_gen_6187, q_gen_6183) -> q_gen_6183
<nil, nil>() -> q_gen_6183
<b, b>() -> q_gen_6184
<a, a>() -> q_gen_6187
<a, b>() -> q_gen_6187
<b, a>() -> q_gen_6187
<cons, cons>(q_gen_6184, q_gen_6203) -> q_gen_6203
<nil, cons>(q_gen_6194, q_gen_6193) -> q_gen_6203
<cons, cons, cons>(q_gen_6195, q_gen_6192) -> q_gen_6178
<cons, nil, cons>(q_gen_6184, q_gen_6183) -> q_gen_6178
<cons, nil, cons>(q_gen_6187, q_gen_6183) -> q_gen_6178
<cons, nil, cons>(q_gen_6187, q_gen_6203) -> q_gen_6178
<nil, cons, cons>(q_gen_6184, q_gen_6183) -> q_gen_6178
<nil, cons, cons>(q_gen_6184, q_gen_6203) -> q_gen_6178
<nil, cons, cons>(q_gen_6187, q_gen_6183) -> q_gen_6178
<nil, nil, nil>() -> q_gen_6178
<cons, cons, cons>(q_gen_6195, q_gen_6178) -> q_gen_6192
<cons, nil, cons>(q_gen_6184, q_gen_6203) -> q_gen_6192
<nil, cons, cons>(q_gen_6187, q_gen_6203) -> q_gen_6192
<nil, nil, cons>(q_gen_6194, q_gen_6193) -> q_gen_6192
<a, a, a>() -> q_gen_6195
<a, b, a>() -> q_gen_6195
<b, a, b>() -> q_gen_6195
<b, b, b>() -> q_gen_6195
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_6177, q_gen_6180, q_gen_6181, q_gen_6197, q_gen_6198, q_gen_6199, q_gen_6200, q_gen_6205, q_gen_6216, q_gen_6217, q_gen_6218},
Q_f={q_gen_6177},
Delta=
{
<nil>() -> q_gen_6180
<cons>(q_gen_6198, q_gen_6180) -> q_gen_6197
<cons>(q_gen_6198, q_gen_6216) -> q_gen_6197
<a>() -> q_gen_6198
<b>() -> q_gen_6198
<s>(q_gen_6218) -> q_gen_6200
<z>() -> q_gen_6200
<cons>(q_gen_6198, q_gen_6197) -> q_gen_6216
<s>(q_gen_6200) -> q_gen_6218
<cons, s>(q_gen_6181, q_gen_6180) -> q_gen_6177
<cons, s>(q_gen_6199, q_gen_6197) -> q_gen_6177
<cons, s>(q_gen_6217, q_gen_6216) -> q_gen_6177
<nil, z>() -> q_gen_6177
<a, z>() -> q_gen_6181
<b, z>() -> q_gen_6181
<a, s>(q_gen_6200) -> q_gen_6199
<b, s>(q_gen_6200) -> q_gen_6199
<cons, s>(q_gen_6181, q_gen_6197) -> q_gen_6205
<cons, s>(q_gen_6181, q_gen_6216) -> q_gen_6205
<cons, s>(q_gen_6199, q_gen_6180) -> q_gen_6205
<cons, s>(q_gen_6199, q_gen_6216) -> q_gen_6205
<cons, s>(q_gen_6217, q_gen_6180) -> q_gen_6205
<cons, s>(q_gen_6217, q_gen_6197) -> q_gen_6205
<a, s>(q_gen_6218) -> q_gen_6217
<b, s>(q_gen_6218) -> q_gen_6217
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 57
() -> length([nil, z]) -> 52
(append([l1, l2, _rx]) /\ append([l2, l1, _tx]) /\ length([_rx, _sx]) /\ length([_tx, _ux])) -> eq_nat([_sx, _ux]) -> 61
(append([t1, l2, _ix])) -> append([cons(h1, t1), l2, cons(h1, _ix)]) -> 60
(length([ll, _nx])) -> length([cons(x, ll), s(_nx)]) -> 56
}
Sat witness: Found: ((append([t1, l2, _ix])) -> append([cons(h1, t1), l2, cons(h1, _ix)]), {
_ix -> cons(a, cons(a, nil))  ;  h1 -> a  ;  l2 -> cons(a, nil)  ;  t1 -> cons(a, nil)
})

-------------------------------------------
Step 58, which took 0.771512 s (model generation: 0.762565,  model checking: 0.008947):

Model:
|_
{
append -> 
{{{
Q={q_gen_6178, q_gen_6183, q_gen_6184, q_gen_6187, q_gen_6192, q_gen_6193, q_gen_6194, q_gen_6195, q_gen_6203},
Q_f={q_gen_6178},
Delta=
{
<cons>(q_gen_6194, q_gen_6193) -> q_gen_6193
<nil>() -> q_gen_6193
<a>() -> q_gen_6194
<b>() -> q_gen_6194
<cons, cons>(q_gen_6184, q_gen_6183) -> q_gen_6183
<cons, cons>(q_gen_6187, q_gen_6183) -> q_gen_6183
<nil, nil>() -> q_gen_6183
<b, b>() -> q_gen_6184
<a, a>() -> q_gen_6187
<a, b>() -> q_gen_6187
<b, a>() -> q_gen_6187
<cons, cons>(q_gen_6184, q_gen_6203) -> q_gen_6203
<nil, cons>(q_gen_6194, q_gen_6193) -> q_gen_6203
<cons, cons, cons>(q_gen_6195, q_gen_6192) -> q_gen_6178
<cons, nil, cons>(q_gen_6184, q_gen_6183) -> q_gen_6178
<cons, nil, cons>(q_gen_6187, q_gen_6183) -> q_gen_6178
<nil, cons, cons>(q_gen_6184, q_gen_6183) -> q_gen_6178
<nil, cons, cons>(q_gen_6184, q_gen_6203) -> q_gen_6178
<nil, cons, cons>(q_gen_6187, q_gen_6183) -> q_gen_6178
<nil, nil, nil>() -> q_gen_6178
<cons, cons, cons>(q_gen_6195, q_gen_6178) -> q_gen_6192
<cons, nil, cons>(q_gen_6184, q_gen_6203) -> q_gen_6192
<cons, nil, cons>(q_gen_6187, q_gen_6203) -> q_gen_6192
<nil, cons, cons>(q_gen_6187, q_gen_6203) -> q_gen_6192
<nil, nil, cons>(q_gen_6194, q_gen_6193) -> q_gen_6192
<a, a, a>() -> q_gen_6195
<a, b, a>() -> q_gen_6195
<b, a, b>() -> q_gen_6195
<b, b, b>() -> q_gen_6195
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_6177, q_gen_6180, q_gen_6181, q_gen_6197, q_gen_6198, q_gen_6199, q_gen_6200, q_gen_6205, q_gen_6216, q_gen_6217, q_gen_6218},
Q_f={q_gen_6177},
Delta=
{
<nil>() -> q_gen_6180
<cons>(q_gen_6198, q_gen_6180) -> q_gen_6197
<cons>(q_gen_6198, q_gen_6216) -> q_gen_6197
<a>() -> q_gen_6198
<b>() -> q_gen_6198
<s>(q_gen_6218) -> q_gen_6200
<z>() -> q_gen_6200
<cons>(q_gen_6198, q_gen_6197) -> q_gen_6216
<s>(q_gen_6200) -> q_gen_6218
<cons, s>(q_gen_6181, q_gen_6180) -> q_gen_6177
<cons, s>(q_gen_6199, q_gen_6197) -> q_gen_6177
<cons, s>(q_gen_6217, q_gen_6216) -> q_gen_6177
<nil, z>() -> q_gen_6177
<a, z>() -> q_gen_6181
<b, z>() -> q_gen_6181
<a, s>(q_gen_6200) -> q_gen_6199
<b, s>(q_gen_6200) -> q_gen_6199
<cons, s>(q_gen_6181, q_gen_6197) -> q_gen_6205
<cons, s>(q_gen_6181, q_gen_6216) -> q_gen_6205
<cons, s>(q_gen_6199, q_gen_6180) -> q_gen_6205
<cons, s>(q_gen_6199, q_gen_6216) -> q_gen_6205
<cons, s>(q_gen_6217, q_gen_6180) -> q_gen_6205
<cons, s>(q_gen_6217, q_gen_6197) -> q_gen_6205
<a, s>(q_gen_6218) -> q_gen_6217
<b, s>(q_gen_6218) -> q_gen_6217
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 58
() -> length([nil, z]) -> 53
(append([l1, l2, _rx]) /\ append([l2, l1, _tx]) /\ length([_rx, _sx]) /\ length([_tx, _ux])) -> eq_nat([_sx, _ux]) -> 61
(append([t1, l2, _ix])) -> append([cons(h1, t1), l2, cons(h1, _ix)]) -> 63
(length([ll, _nx])) -> length([cons(x, ll), s(_nx)]) -> 57
}
Sat witness: Found: ((append([t1, l2, _ix])) -> append([cons(h1, t1), l2, cons(h1, _ix)]), {
_ix -> cons(b, cons(a, cons(b, nil)))  ;  h1 -> b  ;  l2 -> cons(a, cons(b, nil))  ;  t1 -> cons(b, nil)
})

-------------------------------------------
Step 59, which took 0.804126 s (model generation: 0.799686,  model checking: 0.004440):

Model:
|_
{
append -> 
{{{
Q={q_gen_6178, q_gen_6183, q_gen_6184, q_gen_6191, q_gen_6192, q_gen_6193, q_gen_6194, q_gen_6195, q_gen_6203},
Q_f={q_gen_6178, q_gen_6191},
Delta=
{
<cons>(q_gen_6194, q_gen_6193) -> q_gen_6193
<nil>() -> q_gen_6193
<a>() -> q_gen_6194
<b>() -> q_gen_6194
<cons, cons>(q_gen_6184, q_gen_6183) -> q_gen_6183
<nil, nil>() -> q_gen_6183
<a, a>() -> q_gen_6184
<a, b>() -> q_gen_6184
<b, a>() -> q_gen_6184
<b, b>() -> q_gen_6184
<cons, cons>(q_gen_6184, q_gen_6203) -> q_gen_6203
<nil, cons>(q_gen_6194, q_gen_6193) -> q_gen_6203
<cons, cons, cons>(q_gen_6195, q_gen_6191) -> q_gen_6178
<cons, nil, cons>(q_gen_6184, q_gen_6183) -> q_gen_6178
<nil, cons, cons>(q_gen_6184, q_gen_6183) -> q_gen_6178
<nil, nil, nil>() -> q_gen_6178
<cons, cons, cons>(q_gen_6195, q_gen_6192) -> q_gen_6191
<cons, nil, cons>(q_gen_6184, q_gen_6203) -> q_gen_6191
<cons, cons, cons>(q_gen_6195, q_gen_6178) -> q_gen_6192
<nil, cons, cons>(q_gen_6184, q_gen_6203) -> q_gen_6192
<nil, nil, cons>(q_gen_6194, q_gen_6193) -> q_gen_6192
<a, a, a>() -> q_gen_6195
<a, b, a>() -> q_gen_6195
<b, a, b>() -> q_gen_6195
<b, b, b>() -> q_gen_6195
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_6177, q_gen_6180, q_gen_6181, q_gen_6197, q_gen_6198, q_gen_6199, q_gen_6200, q_gen_6205, q_gen_6216, q_gen_6217, q_gen_6218},
Q_f={q_gen_6177},
Delta=
{
<nil>() -> q_gen_6180
<cons>(q_gen_6198, q_gen_6180) -> q_gen_6197
<cons>(q_gen_6198, q_gen_6216) -> q_gen_6197
<a>() -> q_gen_6198
<b>() -> q_gen_6198
<s>(q_gen_6218) -> q_gen_6200
<z>() -> q_gen_6200
<cons>(q_gen_6198, q_gen_6197) -> q_gen_6216
<s>(q_gen_6200) -> q_gen_6218
<cons, s>(q_gen_6181, q_gen_6180) -> q_gen_6177
<cons, s>(q_gen_6199, q_gen_6197) -> q_gen_6177
<cons, s>(q_gen_6217, q_gen_6216) -> q_gen_6177
<nil, z>() -> q_gen_6177
<a, z>() -> q_gen_6181
<b, z>() -> q_gen_6181
<a, s>(q_gen_6200) -> q_gen_6199
<b, s>(q_gen_6200) -> q_gen_6199
<cons, s>(q_gen_6181, q_gen_6197) -> q_gen_6205
<cons, s>(q_gen_6181, q_gen_6216) -> q_gen_6205
<cons, s>(q_gen_6199, q_gen_6180) -> q_gen_6205
<cons, s>(q_gen_6199, q_gen_6216) -> q_gen_6205
<cons, s>(q_gen_6217, q_gen_6180) -> q_gen_6205
<cons, s>(q_gen_6217, q_gen_6197) -> q_gen_6205
<a, s>(q_gen_6218) -> q_gen_6217
<b, s>(q_gen_6218) -> q_gen_6217
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 59
() -> length([nil, z]) -> 54
(append([l1, l2, _rx]) /\ append([l2, l1, _tx]) /\ length([_rx, _sx]) /\ length([_tx, _ux])) -> eq_nat([_sx, _ux]) -> 64
(append([t1, l2, _ix])) -> append([cons(h1, t1), l2, cons(h1, _ix)]) -> 63
(length([ll, _nx])) -> length([cons(x, ll), s(_nx)]) -> 58
}
Sat witness: Found: ((append([l1, l2, _rx]) /\ append([l2, l1, _tx]) /\ length([_rx, _sx]) /\ length([_tx, _ux])) -> eq_nat([_sx, _ux]), {
_rx -> cons(a, cons(b, cons(b, nil)))  ;  _sx -> s(s(s(z)))  ;  _tx -> cons(a, cons(b, cons(b, nil)))  ;  _ux -> s(s(s(s(s(z)))))  ;  l1 -> cons(a, nil)  ;  l2 -> cons(a, nil)
})

-------------------------------------------
Step 60, which took 0.976871 s (model generation: 0.974120,  model checking: 0.002751):

Model:
|_
{
append -> 
{{{
Q={q_gen_6178, q_gen_6182, q_gen_6183, q_gen_6184, q_gen_6192, q_gen_6193, q_gen_6194, q_gen_6195, q_gen_6203},
Q_f={q_gen_6178, q_gen_6182},
Delta=
{
<cons>(q_gen_6194, q_gen_6193) -> q_gen_6193
<nil>() -> q_gen_6193
<a>() -> q_gen_6194
<b>() -> q_gen_6194
<cons, cons>(q_gen_6184, q_gen_6183) -> q_gen_6183
<nil, nil>() -> q_gen_6183
<a, a>() -> q_gen_6184
<a, b>() -> q_gen_6184
<b, a>() -> q_gen_6184
<b, b>() -> q_gen_6184
<cons, cons>(q_gen_6184, q_gen_6203) -> q_gen_6203
<nil, cons>(q_gen_6194, q_gen_6193) -> q_gen_6203
<nil, nil, nil>() -> q_gen_6178
<cons, cons, cons>(q_gen_6195, q_gen_6182) -> q_gen_6182
<cons, cons, cons>(q_gen_6195, q_gen_6192) -> q_gen_6182
<cons, nil, cons>(q_gen_6184, q_gen_6183) -> q_gen_6182
<nil, cons, cons>(q_gen_6184, q_gen_6183) -> q_gen_6182
<cons, cons, cons>(q_gen_6195, q_gen_6178) -> q_gen_6192
<cons, nil, cons>(q_gen_6184, q_gen_6203) -> q_gen_6192
<nil, cons, cons>(q_gen_6184, q_gen_6203) -> q_gen_6192
<nil, nil, cons>(q_gen_6194, q_gen_6193) -> q_gen_6192
<a, a, a>() -> q_gen_6195
<a, b, a>() -> q_gen_6195
<b, a, b>() -> q_gen_6195
<b, b, b>() -> q_gen_6195
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_6177, q_gen_6180, q_gen_6181, q_gen_6197, q_gen_6198, q_gen_6199, q_gen_6200, q_gen_6205, q_gen_6216, q_gen_6217, q_gen_6218, q_gen_6239},
Q_f={q_gen_6177},
Delta=
{
<cons>(q_gen_6198, q_gen_6216) -> q_gen_6180
<nil>() -> q_gen_6180
<cons>(q_gen_6198, q_gen_6180) -> q_gen_6197
<a>() -> q_gen_6198
<b>() -> q_gen_6198
<s>(q_gen_6239) -> q_gen_6200
<z>() -> q_gen_6200
<cons>(q_gen_6198, q_gen_6197) -> q_gen_6216
<s>(q_gen_6200) -> q_gen_6218
<s>(q_gen_6218) -> q_gen_6239
<cons, s>(q_gen_6181, q_gen_6180) -> q_gen_6177
<cons, s>(q_gen_6199, q_gen_6197) -> q_gen_6177
<cons, s>(q_gen_6217, q_gen_6216) -> q_gen_6177
<nil, z>() -> q_gen_6177
<a, z>() -> q_gen_6181
<b, s>(q_gen_6239) -> q_gen_6181
<b, z>() -> q_gen_6181
<a, s>(q_gen_6200) -> q_gen_6199
<a, s>(q_gen_6239) -> q_gen_6199
<b, s>(q_gen_6200) -> q_gen_6199
<cons, s>(q_gen_6181, q_gen_6197) -> q_gen_6205
<cons, s>(q_gen_6181, q_gen_6216) -> q_gen_6205
<cons, s>(q_gen_6199, q_gen_6180) -> q_gen_6205
<cons, s>(q_gen_6199, q_gen_6216) -> q_gen_6205
<cons, s>(q_gen_6217, q_gen_6180) -> q_gen_6205
<cons, s>(q_gen_6217, q_gen_6197) -> q_gen_6205
<a, s>(q_gen_6218) -> q_gen_6217
<b, s>(q_gen_6218) -> q_gen_6217
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 59
() -> length([nil, z]) -> 55
(append([l1, l2, _rx]) /\ append([l2, l1, _tx]) /\ length([_rx, _sx]) /\ length([_tx, _ux])) -> eq_nat([_sx, _ux]) -> 64
(append([t1, l2, _ix])) -> append([cons(h1, t1), l2, cons(h1, _ix)]) -> 63
(length([ll, _nx])) -> length([cons(x, ll), s(_nx)]) -> 61
}
Sat witness: Found: ((length([ll, _nx])) -> length([cons(x, ll), s(_nx)]), {
_nx -> s(s(s(s(z))))  ;  ll -> cons(a, cons(b, nil))  ;  x -> b
})

-------------------------------------------
Step 61, which took 1.140374 s (model generation: 1.136751,  model checking: 0.003623):

Model:
|_
{
append -> 
{{{
Q={q_gen_6178, q_gen_6183, q_gen_6184, q_gen_6192, q_gen_6193, q_gen_6194, q_gen_6195, q_gen_6203, q_gen_6214, q_gen_6232},
Q_f={q_gen_6178},
Delta=
{
<nil>() -> q_gen_6193
<a>() -> q_gen_6194
<b>() -> q_gen_6194
<cons>(q_gen_6194, q_gen_6193) -> q_gen_6232
<cons, cons>(q_gen_6184, q_gen_6183) -> q_gen_6183
<nil, cons>(q_gen_6194, q_gen_6232) -> q_gen_6183
<nil, nil>() -> q_gen_6183
<a, a>() -> q_gen_6184
<a, b>() -> q_gen_6184
<b, a>() -> q_gen_6184
<b, b>() -> q_gen_6184
<cons, cons>(q_gen_6184, q_gen_6203) -> q_gen_6203
<nil, cons>(q_gen_6194, q_gen_6193) -> q_gen_6203
<cons, cons, cons>(q_gen_6195, q_gen_6192) -> q_gen_6178
<cons, nil, cons>(q_gen_6184, q_gen_6183) -> q_gen_6178
<nil, cons, cons>(q_gen_6184, q_gen_6183) -> q_gen_6178
<nil, nil, nil>() -> q_gen_6178
<cons, cons, cons>(q_gen_6195, q_gen_6214) -> q_gen_6192
<cons, nil, cons>(q_gen_6184, q_gen_6203) -> q_gen_6192
<nil, cons, cons>(q_gen_6184, q_gen_6203) -> q_gen_6192
<nil, nil, cons>(q_gen_6194, q_gen_6193) -> q_gen_6192
<a, a, a>() -> q_gen_6195
<a, b, a>() -> q_gen_6195
<b, a, b>() -> q_gen_6195
<b, b, b>() -> q_gen_6195
<cons, cons, cons>(q_gen_6195, q_gen_6178) -> q_gen_6214
<nil, nil, cons>(q_gen_6194, q_gen_6232) -> q_gen_6214
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_6177, q_gen_6180, q_gen_6181, q_gen_6197, q_gen_6198, q_gen_6199, q_gen_6200, q_gen_6205, q_gen_6216, q_gen_6217, q_gen_6218},
Q_f={q_gen_6177},
Delta=
{
<nil>() -> q_gen_6180
<cons>(q_gen_6198, q_gen_6180) -> q_gen_6197
<cons>(q_gen_6198, q_gen_6216) -> q_gen_6197
<a>() -> q_gen_6198
<b>() -> q_gen_6198
<s>(q_gen_6218) -> q_gen_6200
<z>() -> q_gen_6200
<cons>(q_gen_6198, q_gen_6197) -> q_gen_6216
<s>(q_gen_6200) -> q_gen_6218
<cons, s>(q_gen_6181, q_gen_6180) -> q_gen_6177
<cons, s>(q_gen_6181, q_gen_6216) -> q_gen_6177
<cons, s>(q_gen_6199, q_gen_6197) -> q_gen_6177
<cons, s>(q_gen_6199, q_gen_6216) -> q_gen_6177
<cons, s>(q_gen_6217, q_gen_6216) -> q_gen_6177
<nil, z>() -> q_gen_6177
<a, z>() -> q_gen_6181
<b, z>() -> q_gen_6181
<a, s>(q_gen_6200) -> q_gen_6199
<b, s>(q_gen_6200) -> q_gen_6199
<cons, s>(q_gen_6181, q_gen_6197) -> q_gen_6205
<cons, s>(q_gen_6199, q_gen_6180) -> q_gen_6205
<cons, s>(q_gen_6217, q_gen_6180) -> q_gen_6205
<cons, s>(q_gen_6217, q_gen_6197) -> q_gen_6205
<a, s>(q_gen_6218) -> q_gen_6217
<b, s>(q_gen_6218) -> q_gen_6217
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 60
() -> length([nil, z]) -> 56
(append([l1, l2, _rx]) /\ append([l2, l1, _tx]) /\ length([_rx, _sx]) /\ length([_tx, _ux])) -> eq_nat([_sx, _ux]) -> 64
(append([t1, l2, _ix])) -> append([cons(h1, t1), l2, cons(h1, _ix)]) -> 63
(length([ll, _nx])) -> length([cons(x, ll), s(_nx)]) -> 64
}
Sat witness: Found: ((length([ll, _nx])) -> length([cons(x, ll), s(_nx)]), {
_nx -> s(s(z))  ;  ll -> cons(b, cons(b, cons(b, nil)))  ;  x -> a
})

-------------------------------------------
Step 62, which took 1.114984 s (model generation: 1.084712,  model checking: 0.030272):

Model:
|_
{
append -> 
{{{
Q={q_gen_6178, q_gen_6182, q_gen_6183, q_gen_6184, q_gen_6192, q_gen_6193, q_gen_6194, q_gen_6195, q_gen_6203},
Q_f={q_gen_6178, q_gen_6182},
Delta=
{
<cons>(q_gen_6194, q_gen_6193) -> q_gen_6193
<nil>() -> q_gen_6193
<a>() -> q_gen_6194
<b>() -> q_gen_6194
<cons, cons>(q_gen_6184, q_gen_6183) -> q_gen_6183
<nil, nil>() -> q_gen_6183
<a, a>() -> q_gen_6184
<a, b>() -> q_gen_6184
<b, a>() -> q_gen_6184
<b, b>() -> q_gen_6184
<cons, cons>(q_gen_6184, q_gen_6203) -> q_gen_6203
<nil, cons>(q_gen_6194, q_gen_6193) -> q_gen_6203
<nil, cons, cons>(q_gen_6184, q_gen_6183) -> q_gen_6178
<nil, nil, nil>() -> q_gen_6178
<cons, cons, cons>(q_gen_6195, q_gen_6182) -> q_gen_6182
<cons, cons, cons>(q_gen_6195, q_gen_6192) -> q_gen_6182
<cons, nil, cons>(q_gen_6184, q_gen_6183) -> q_gen_6182
<cons, cons, cons>(q_gen_6195, q_gen_6178) -> q_gen_6192
<cons, nil, cons>(q_gen_6184, q_gen_6203) -> q_gen_6192
<nil, cons, cons>(q_gen_6184, q_gen_6203) -> q_gen_6192
<nil, nil, cons>(q_gen_6194, q_gen_6193) -> q_gen_6192
<a, a, a>() -> q_gen_6195
<a, b, a>() -> q_gen_6195
<b, a, b>() -> q_gen_6195
<b, b, b>() -> q_gen_6195
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_6177, q_gen_6180, q_gen_6181, q_gen_6197, q_gen_6198, q_gen_6199, q_gen_6200, q_gen_6205, q_gen_6216, q_gen_6217, q_gen_6218, q_gen_6239},
Q_f={q_gen_6177},
Delta=
{
<nil>() -> q_gen_6180
<cons>(q_gen_6198, q_gen_6180) -> q_gen_6197
<a>() -> q_gen_6198
<b>() -> q_gen_6198
<s>(q_gen_6239) -> q_gen_6200
<z>() -> q_gen_6200
<cons>(q_gen_6198, q_gen_6197) -> q_gen_6216
<cons>(q_gen_6198, q_gen_6216) -> q_gen_6216
<s>(q_gen_6200) -> q_gen_6218
<s>(q_gen_6218) -> q_gen_6239
<cons, s>(q_gen_6181, q_gen_6180) -> q_gen_6177
<cons, s>(q_gen_6199, q_gen_6197) -> q_gen_6177
<cons, s>(q_gen_6217, q_gen_6216) -> q_gen_6177
<nil, z>() -> q_gen_6177
<a, s>(q_gen_6239) -> q_gen_6181
<a, z>() -> q_gen_6181
<b, z>() -> q_gen_6181
<a, s>(q_gen_6200) -> q_gen_6199
<b, s>(q_gen_6200) -> q_gen_6199
<cons, s>(q_gen_6181, q_gen_6197) -> q_gen_6205
<cons, s>(q_gen_6181, q_gen_6216) -> q_gen_6205
<cons, s>(q_gen_6199, q_gen_6180) -> q_gen_6205
<cons, s>(q_gen_6199, q_gen_6216) -> q_gen_6205
<cons, s>(q_gen_6217, q_gen_6180) -> q_gen_6205
<cons, s>(q_gen_6217, q_gen_6197) -> q_gen_6205
<a, s>(q_gen_6218) -> q_gen_6217
<b, s>(q_gen_6218) -> q_gen_6217
<b, s>(q_gen_6239) -> q_gen_6217
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 61
() -> length([nil, z]) -> 57
(append([l1, l2, _rx]) /\ append([l2, l1, _tx]) /\ length([_rx, _sx]) /\ length([_tx, _ux])) -> eq_nat([_sx, _ux]) -> 64
(append([t1, l2, _ix])) -> append([cons(h1, t1), l2, cons(h1, _ix)]) -> 64
(length([ll, _nx])) -> length([cons(x, ll), s(_nx)]) -> 67
}
Sat witness: Found: ((length([ll, _nx])) -> length([cons(x, ll), s(_nx)]), {
_nx -> s(s(s(z)))  ;  ll -> cons(a, cons(a, cons(b, nil)))  ;  x -> a
})

-------------------------------------------
Step 63, which took 0.927555 s (model generation: 0.891363,  model checking: 0.036192):

Model:
|_
{
append -> 
{{{
Q={q_gen_6178, q_gen_6182, q_gen_6183, q_gen_6184, q_gen_6192, q_gen_6193, q_gen_6194, q_gen_6195, q_gen_6203},
Q_f={q_gen_6178, q_gen_6182},
Delta=
{
<cons>(q_gen_6194, q_gen_6193) -> q_gen_6193
<nil>() -> q_gen_6193
<a>() -> q_gen_6194
<b>() -> q_gen_6194
<cons, cons>(q_gen_6184, q_gen_6183) -> q_gen_6183
<nil, nil>() -> q_gen_6183
<a, a>() -> q_gen_6184
<a, b>() -> q_gen_6184
<b, a>() -> q_gen_6184
<b, b>() -> q_gen_6184
<cons, cons>(q_gen_6184, q_gen_6203) -> q_gen_6203
<nil, cons>(q_gen_6194, q_gen_6193) -> q_gen_6203
<nil, cons, cons>(q_gen_6184, q_gen_6183) -> q_gen_6178
<nil, nil, nil>() -> q_gen_6178
<cons, cons, cons>(q_gen_6195, q_gen_6182) -> q_gen_6182
<cons, cons, cons>(q_gen_6195, q_gen_6192) -> q_gen_6182
<cons, nil, cons>(q_gen_6184, q_gen_6183) -> q_gen_6182
<cons, cons, cons>(q_gen_6195, q_gen_6178) -> q_gen_6192
<cons, nil, cons>(q_gen_6184, q_gen_6203) -> q_gen_6192
<nil, cons, cons>(q_gen_6184, q_gen_6203) -> q_gen_6192
<nil, nil, cons>(q_gen_6194, q_gen_6193) -> q_gen_6192
<a, a, a>() -> q_gen_6195
<a, b, a>() -> q_gen_6195
<b, a, b>() -> q_gen_6195
<b, b, b>() -> q_gen_6195
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_6177, q_gen_6180, q_gen_6181, q_gen_6197, q_gen_6198, q_gen_6199, q_gen_6200, q_gen_6205, q_gen_6216, q_gen_6217, q_gen_6218, q_gen_6239},
Q_f={q_gen_6177},
Delta=
{
<cons>(q_gen_6198, q_gen_6216) -> q_gen_6180
<nil>() -> q_gen_6180
<cons>(q_gen_6198, q_gen_6180) -> q_gen_6197
<a>() -> q_gen_6198
<b>() -> q_gen_6198
<z>() -> q_gen_6200
<cons>(q_gen_6198, q_gen_6197) -> q_gen_6216
<s>(q_gen_6200) -> q_gen_6218
<s>(q_gen_6218) -> q_gen_6239
<s>(q_gen_6239) -> q_gen_6239
<cons, s>(q_gen_6181, q_gen_6180) -> q_gen_6177
<cons, s>(q_gen_6199, q_gen_6197) -> q_gen_6177
<cons, s>(q_gen_6217, q_gen_6216) -> q_gen_6177
<nil, z>() -> q_gen_6177
<a, s>(q_gen_6239) -> q_gen_6181
<a, z>() -> q_gen_6181
<b, s>(q_gen_6239) -> q_gen_6181
<b, z>() -> q_gen_6181
<a, s>(q_gen_6200) -> q_gen_6199
<b, s>(q_gen_6200) -> q_gen_6199
<cons, s>(q_gen_6181, q_gen_6197) -> q_gen_6205
<cons, s>(q_gen_6181, q_gen_6216) -> q_gen_6205
<cons, s>(q_gen_6199, q_gen_6180) -> q_gen_6205
<cons, s>(q_gen_6199, q_gen_6216) -> q_gen_6205
<cons, s>(q_gen_6217, q_gen_6180) -> q_gen_6205
<cons, s>(q_gen_6217, q_gen_6197) -> q_gen_6205
<a, s>(q_gen_6218) -> q_gen_6217
<b, s>(q_gen_6218) -> q_gen_6217
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 62
() -> length([nil, z]) -> 58
(append([l1, l2, _rx]) /\ append([l2, l1, _tx]) /\ length([_rx, _sx]) /\ length([_tx, _ux])) -> eq_nat([_sx, _ux]) -> 67
(append([t1, l2, _ix])) -> append([cons(h1, t1), l2, cons(h1, _ix)]) -> 65
(length([ll, _nx])) -> length([cons(x, ll), s(_nx)]) -> 67
}
Sat witness: Found: ((append([l1, l2, _rx]) /\ append([l2, l1, _tx]) /\ length([_rx, _sx]) /\ length([_tx, _ux])) -> eq_nat([_sx, _ux]), {
_rx -> cons(a, cons(b, cons(b, cons(b, cons(b, nil)))))  ;  _sx -> s(s(z))  ;  _tx -> cons(a, cons(b, cons(b, cons(b, cons(b, cons(b, nil))))))  ;  _ux -> s(s(s(z)))  ;  l1 -> cons(a, cons(b, cons(b, nil)))  ;  l2 -> cons(a, cons(b, cons(b, nil)))
})

-------------------------------------------
Step 64, which took 1.889174 s (model generation: 1.883643,  model checking: 0.005531):

Model:
|_
{
append -> 
{{{
Q={q_gen_6178, q_gen_6183, q_gen_6184, q_gen_6192, q_gen_6193, q_gen_6194, q_gen_6195, q_gen_6203, q_gen_6231, q_gen_6232},
Q_f={q_gen_6178},
Delta=
{
<nil>() -> q_gen_6193
<a>() -> q_gen_6194
<b>() -> q_gen_6194
<cons>(q_gen_6194, q_gen_6193) -> q_gen_6232
<cons>(q_gen_6194, q_gen_6232) -> q_gen_6232
<cons, cons>(q_gen_6184, q_gen_6183) -> q_gen_6183
<nil, cons>(q_gen_6194, q_gen_6232) -> q_gen_6183
<nil, nil>() -> q_gen_6183
<a, a>() -> q_gen_6184
<a, b>() -> q_gen_6184
<b, a>() -> q_gen_6184
<b, b>() -> q_gen_6184
<cons, cons>(q_gen_6184, q_gen_6203) -> q_gen_6203
<nil, cons>(q_gen_6194, q_gen_6193) -> q_gen_6203
<cons, cons, cons>(q_gen_6195, q_gen_6192) -> q_gen_6178
<cons, nil, cons>(q_gen_6184, q_gen_6183) -> q_gen_6178
<nil, cons, cons>(q_gen_6184, q_gen_6183) -> q_gen_6178
<nil, nil, nil>() -> q_gen_6178
<cons, cons, cons>(q_gen_6195, q_gen_6178) -> q_gen_6192
<cons, cons, cons>(q_gen_6195, q_gen_6231) -> q_gen_6192
<cons, nil, cons>(q_gen_6184, q_gen_6203) -> q_gen_6192
<nil, cons, cons>(q_gen_6184, q_gen_6203) -> q_gen_6192
<nil, nil, cons>(q_gen_6194, q_gen_6193) -> q_gen_6192
<a, a, a>() -> q_gen_6195
<a, b, a>() -> q_gen_6195
<b, a, b>() -> q_gen_6195
<b, b, b>() -> q_gen_6195
<nil, nil, cons>(q_gen_6194, q_gen_6232) -> q_gen_6231
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_6177, q_gen_6180, q_gen_6181, q_gen_6197, q_gen_6198, q_gen_6199, q_gen_6200, q_gen_6205, q_gen_6216, q_gen_6217, q_gen_6218},
Q_f={q_gen_6177},
Delta=
{
<nil>() -> q_gen_6180
<cons>(q_gen_6198, q_gen_6180) -> q_gen_6197
<a>() -> q_gen_6198
<b>() -> q_gen_6198
<s>(q_gen_6218) -> q_gen_6200
<z>() -> q_gen_6200
<cons>(q_gen_6198, q_gen_6197) -> q_gen_6216
<cons>(q_gen_6198, q_gen_6216) -> q_gen_6216
<s>(q_gen_6200) -> q_gen_6218
<cons, s>(q_gen_6181, q_gen_6180) -> q_gen_6177
<cons, s>(q_gen_6199, q_gen_6197) -> q_gen_6177
<cons, s>(q_gen_6199, q_gen_6216) -> q_gen_6177
<cons, s>(q_gen_6217, q_gen_6216) -> q_gen_6177
<nil, z>() -> q_gen_6177
<a, z>() -> q_gen_6181
<b, z>() -> q_gen_6181
<a, s>(q_gen_6200) -> q_gen_6199
<b, s>(q_gen_6200) -> q_gen_6199
<cons, s>(q_gen_6181, q_gen_6197) -> q_gen_6205
<cons, s>(q_gen_6181, q_gen_6216) -> q_gen_6205
<cons, s>(q_gen_6199, q_gen_6180) -> q_gen_6205
<cons, s>(q_gen_6217, q_gen_6180) -> q_gen_6205
<cons, s>(q_gen_6217, q_gen_6197) -> q_gen_6205
<a, s>(q_gen_6218) -> q_gen_6217
<b, s>(q_gen_6218) -> q_gen_6217
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 63
() -> length([nil, z]) -> 59
(append([l1, l2, _rx]) /\ append([l2, l1, _tx]) /\ length([_rx, _sx]) /\ length([_tx, _ux])) -> eq_nat([_sx, _ux]) -> 67
(append([t1, l2, _ix])) -> append([cons(h1, t1), l2, cons(h1, _ix)]) -> 68
(length([ll, _nx])) -> length([cons(x, ll), s(_nx)]) -> 67
}
Sat witness: Found: ((append([t1, l2, _ix])) -> append([cons(h1, t1), l2, cons(h1, _ix)]), {
_ix -> cons(a, cons(b, cons(b, cons(b, nil))))  ;  h1 -> b  ;  l2 -> cons(b, cons(a, nil))  ;  t1 -> nil
})

-------------------------------------------
Step 65, which took 6.420087 s (model generation: 6.411465,  model checking: 0.008622):

Model:
|_
{
append -> 
{{{
Q={q_gen_6178, q_gen_6183, q_gen_6184, q_gen_6192, q_gen_6193, q_gen_6194, q_gen_6195, q_gen_6203, q_gen_6214, q_gen_6232},
Q_f={q_gen_6178},
Delta=
{
<cons>(q_gen_6194, q_gen_6232) -> q_gen_6193
<nil>() -> q_gen_6193
<a>() -> q_gen_6194
<b>() -> q_gen_6194
<cons>(q_gen_6194, q_gen_6193) -> q_gen_6232
<cons, cons>(q_gen_6184, q_gen_6183) -> q_gen_6183
<nil, cons>(q_gen_6194, q_gen_6232) -> q_gen_6183
<nil, nil>() -> q_gen_6183
<a, a>() -> q_gen_6184
<a, b>() -> q_gen_6184
<b, a>() -> q_gen_6184
<b, b>() -> q_gen_6184
<cons, cons>(q_gen_6184, q_gen_6203) -> q_gen_6203
<nil, cons>(q_gen_6194, q_gen_6193) -> q_gen_6203
<cons, cons, cons>(q_gen_6195, q_gen_6192) -> q_gen_6178
<cons, nil, cons>(q_gen_6184, q_gen_6183) -> q_gen_6178
<nil, cons, cons>(q_gen_6184, q_gen_6183) -> q_gen_6178
<nil, nil, nil>() -> q_gen_6178
<cons, cons, cons>(q_gen_6195, q_gen_6214) -> q_gen_6192
<cons, nil, cons>(q_gen_6184, q_gen_6203) -> q_gen_6192
<nil, cons, cons>(q_gen_6184, q_gen_6203) -> q_gen_6192
<nil, nil, cons>(q_gen_6194, q_gen_6193) -> q_gen_6192
<a, a, a>() -> q_gen_6195
<a, b, a>() -> q_gen_6195
<b, a, b>() -> q_gen_6195
<b, b, b>() -> q_gen_6195
<cons, cons, cons>(q_gen_6195, q_gen_6178) -> q_gen_6214
<nil, nil, cons>(q_gen_6194, q_gen_6232) -> q_gen_6214
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_6177, q_gen_6180, q_gen_6181, q_gen_6197, q_gen_6198, q_gen_6199, q_gen_6200, q_gen_6205, q_gen_6216, q_gen_6217, q_gen_6218},
Q_f={q_gen_6177},
Delta=
{
<nil>() -> q_gen_6180
<cons>(q_gen_6198, q_gen_6180) -> q_gen_6197
<a>() -> q_gen_6198
<b>() -> q_gen_6198
<s>(q_gen_6218) -> q_gen_6200
<z>() -> q_gen_6200
<cons>(q_gen_6198, q_gen_6197) -> q_gen_6216
<cons>(q_gen_6198, q_gen_6216) -> q_gen_6216
<s>(q_gen_6200) -> q_gen_6218
<cons, s>(q_gen_6181, q_gen_6180) -> q_gen_6177
<cons, s>(q_gen_6199, q_gen_6197) -> q_gen_6177
<cons, s>(q_gen_6199, q_gen_6216) -> q_gen_6177
<cons, s>(q_gen_6217, q_gen_6216) -> q_gen_6177
<nil, z>() -> q_gen_6177
<a, z>() -> q_gen_6181
<b, z>() -> q_gen_6181
<a, s>(q_gen_6200) -> q_gen_6199
<b, s>(q_gen_6200) -> q_gen_6199
<cons, s>(q_gen_6181, q_gen_6197) -> q_gen_6205
<cons, s>(q_gen_6181, q_gen_6216) -> q_gen_6205
<cons, s>(q_gen_6199, q_gen_6180) -> q_gen_6205
<cons, s>(q_gen_6217, q_gen_6180) -> q_gen_6205
<cons, s>(q_gen_6217, q_gen_6197) -> q_gen_6205
<a, s>(q_gen_6218) -> q_gen_6217
<b, s>(q_gen_6218) -> q_gen_6217
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 64
() -> length([nil, z]) -> 60
(append([l1, l2, _rx]) /\ append([l2, l1, _tx]) /\ length([_rx, _sx]) /\ length([_tx, _ux])) -> eq_nat([_sx, _ux]) -> 70
(append([t1, l2, _ix])) -> append([cons(h1, t1), l2, cons(h1, _ix)]) -> 68
(length([ll, _nx])) -> length([cons(x, ll), s(_nx)]) -> 68
}
Sat witness: Found: ((append([l1, l2, _rx]) /\ append([l2, l1, _tx]) /\ length([_rx, _sx]) /\ length([_tx, _ux])) -> eq_nat([_sx, _ux]), {
_rx -> cons(a, cons(b, nil))  ;  _sx -> s(s(z))  ;  _tx -> cons(b, cons(b, cons(b, cons(b, nil))))  ;  _ux -> s(s(s(z)))  ;  l1 -> nil  ;  l2 -> cons(b, cons(b, nil))
})

-------------------------------------------
Step 66, which took 4.388456 s (model generation: 4.380547,  model checking: 0.007909):

Model:
|_
{
append -> 
{{{
Q={q_gen_6178, q_gen_6183, q_gen_6184, q_gen_6192, q_gen_6193, q_gen_6194, q_gen_6195, q_gen_6203, q_gen_6231, q_gen_6232},
Q_f={q_gen_6178},
Delta=
{
<nil>() -> q_gen_6193
<a>() -> q_gen_6194
<b>() -> q_gen_6194
<cons>(q_gen_6194, q_gen_6193) -> q_gen_6232
<cons>(q_gen_6194, q_gen_6232) -> q_gen_6232
<cons, cons>(q_gen_6184, q_gen_6183) -> q_gen_6183
<nil, nil>() -> q_gen_6183
<a, a>() -> q_gen_6184
<a, b>() -> q_gen_6184
<b, a>() -> q_gen_6184
<b, b>() -> q_gen_6184
<cons, cons>(q_gen_6184, q_gen_6203) -> q_gen_6203
<nil, cons>(q_gen_6194, q_gen_6193) -> q_gen_6203
<nil, cons>(q_gen_6194, q_gen_6232) -> q_gen_6203
<cons, cons, cons>(q_gen_6195, q_gen_6192) -> q_gen_6178
<cons, nil, cons>(q_gen_6184, q_gen_6183) -> q_gen_6178
<nil, cons, cons>(q_gen_6184, q_gen_6183) -> q_gen_6178
<nil, nil, nil>() -> q_gen_6178
<cons, cons, cons>(q_gen_6195, q_gen_6178) -> q_gen_6192
<cons, cons, cons>(q_gen_6195, q_gen_6231) -> q_gen_6192
<cons, nil, cons>(q_gen_6184, q_gen_6203) -> q_gen_6192
<nil, cons, cons>(q_gen_6184, q_gen_6203) -> q_gen_6192
<nil, nil, cons>(q_gen_6194, q_gen_6193) -> q_gen_6192
<a, a, a>() -> q_gen_6195
<a, b, a>() -> q_gen_6195
<b, a, b>() -> q_gen_6195
<b, b, b>() -> q_gen_6195
<nil, nil, cons>(q_gen_6194, q_gen_6232) -> q_gen_6231
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_6177, q_gen_6180, q_gen_6181, q_gen_6197, q_gen_6198, q_gen_6199, q_gen_6200, q_gen_6205, q_gen_6216, q_gen_6218, q_gen_6228},
Q_f={q_gen_6177},
Delta=
{
<nil>() -> q_gen_6180
<cons>(q_gen_6198, q_gen_6180) -> q_gen_6197
<a>() -> q_gen_6198
<b>() -> q_gen_6198
<s>(q_gen_6218) -> q_gen_6200
<z>() -> q_gen_6200
<cons>(q_gen_6198, q_gen_6197) -> q_gen_6216
<cons>(q_gen_6198, q_gen_6216) -> q_gen_6216
<s>(q_gen_6200) -> q_gen_6218
<cons, s>(q_gen_6181, q_gen_6180) -> q_gen_6177
<cons, s>(q_gen_6181, q_gen_6216) -> q_gen_6177
<cons, s>(q_gen_6199, q_gen_6197) -> q_gen_6177
<cons, s>(q_gen_6199, q_gen_6216) -> q_gen_6177
<cons, s>(q_gen_6228, q_gen_6216) -> q_gen_6177
<nil, z>() -> q_gen_6177
<a, z>() -> q_gen_6181
<b, s>(q_gen_6218) -> q_gen_6181
<b, z>() -> q_gen_6181
<a, s>(q_gen_6200) -> q_gen_6199
<b, s>(q_gen_6200) -> q_gen_6199
<cons, s>(q_gen_6181, q_gen_6197) -> q_gen_6205
<cons, s>(q_gen_6199, q_gen_6180) -> q_gen_6205
<cons, s>(q_gen_6228, q_gen_6180) -> q_gen_6205
<cons, s>(q_gen_6228, q_gen_6197) -> q_gen_6205
<a, s>(q_gen_6218) -> q_gen_6228
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 65
() -> length([nil, z]) -> 61
(append([l1, l2, _rx]) /\ append([l2, l1, _tx]) /\ length([_rx, _sx]) /\ length([_tx, _ux])) -> eq_nat([_sx, _ux]) -> 70
(append([t1, l2, _ix])) -> append([cons(h1, t1), l2, cons(h1, _ix)]) -> 71
(length([ll, _nx])) -> length([cons(x, ll), s(_nx)]) -> 69
}
Sat witness: Found: ((append([t1, l2, _ix])) -> append([cons(h1, t1), l2, cons(h1, _ix)]), {
_ix -> cons(b, cons(b, cons(b, cons(b, nil))))  ;  h1 -> a  ;  l2 -> cons(a, cons(b, nil))  ;  t1 -> cons(b, cons(b, nil))
})

-------------------------------------------
Step 67, which took 5.702187 s (model generation: 5.690309,  model checking: 0.011878):

Model:
|_
{
append -> 
{{{
Q={q_gen_6178, q_gen_6183, q_gen_6184, q_gen_6192, q_gen_6193, q_gen_6194, q_gen_6195, q_gen_6203, q_gen_6231, q_gen_6232},
Q_f={q_gen_6178},
Delta=
{
<cons>(q_gen_6194, q_gen_6232) -> q_gen_6193
<nil>() -> q_gen_6193
<a>() -> q_gen_6194
<b>() -> q_gen_6194
<cons>(q_gen_6194, q_gen_6193) -> q_gen_6232
<cons, cons>(q_gen_6184, q_gen_6183) -> q_gen_6183
<nil, cons>(q_gen_6194, q_gen_6232) -> q_gen_6183
<nil, nil>() -> q_gen_6183
<a, a>() -> q_gen_6184
<a, b>() -> q_gen_6184
<b, a>() -> q_gen_6184
<b, b>() -> q_gen_6184
<cons, cons>(q_gen_6184, q_gen_6203) -> q_gen_6203
<nil, cons>(q_gen_6194, q_gen_6193) -> q_gen_6203
<cons, cons, cons>(q_gen_6195, q_gen_6192) -> q_gen_6178
<cons, nil, cons>(q_gen_6184, q_gen_6183) -> q_gen_6178
<nil, cons, cons>(q_gen_6184, q_gen_6183) -> q_gen_6178
<nil, nil, nil>() -> q_gen_6178
<cons, cons, cons>(q_gen_6195, q_gen_6178) -> q_gen_6192
<cons, cons, cons>(q_gen_6195, q_gen_6231) -> q_gen_6192
<cons, nil, cons>(q_gen_6184, q_gen_6203) -> q_gen_6192
<nil, cons, cons>(q_gen_6184, q_gen_6203) -> q_gen_6192
<nil, nil, cons>(q_gen_6194, q_gen_6193) -> q_gen_6192
<a, a, a>() -> q_gen_6195
<a, b, a>() -> q_gen_6195
<b, a, b>() -> q_gen_6195
<b, b, b>() -> q_gen_6195
<nil, nil, cons>(q_gen_6194, q_gen_6232) -> q_gen_6231
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_6177, q_gen_6180, q_gen_6181, q_gen_6197, q_gen_6198, q_gen_6199, q_gen_6200, q_gen_6205, q_gen_6216, q_gen_6217, q_gen_6218},
Q_f={q_gen_6177},
Delta=
{
<nil>() -> q_gen_6180
<cons>(q_gen_6198, q_gen_6180) -> q_gen_6197
<cons>(q_gen_6198, q_gen_6216) -> q_gen_6197
<a>() -> q_gen_6198
<b>() -> q_gen_6198
<s>(q_gen_6218) -> q_gen_6200
<z>() -> q_gen_6200
<cons>(q_gen_6198, q_gen_6197) -> q_gen_6216
<s>(q_gen_6200) -> q_gen_6218
<cons, s>(q_gen_6181, q_gen_6180) -> q_gen_6177
<cons, s>(q_gen_6199, q_gen_6197) -> q_gen_6177
<cons, s>(q_gen_6217, q_gen_6216) -> q_gen_6177
<nil, z>() -> q_gen_6177
<a, z>() -> q_gen_6181
<b, z>() -> q_gen_6181
<a, s>(q_gen_6200) -> q_gen_6199
<b, s>(q_gen_6200) -> q_gen_6199
<cons, s>(q_gen_6181, q_gen_6197) -> q_gen_6205
<cons, s>(q_gen_6181, q_gen_6216) -> q_gen_6205
<cons, s>(q_gen_6199, q_gen_6180) -> q_gen_6205
<cons, s>(q_gen_6199, q_gen_6216) -> q_gen_6205
<cons, s>(q_gen_6217, q_gen_6180) -> q_gen_6205
<cons, s>(q_gen_6217, q_gen_6197) -> q_gen_6205
<a, s>(q_gen_6218) -> q_gen_6217
<b, s>(q_gen_6218) -> q_gen_6217
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 66
() -> length([nil, z]) -> 62
(append([l1, l2, _rx]) /\ append([l2, l1, _tx]) /\ length([_rx, _sx]) /\ length([_tx, _ux])) -> eq_nat([_sx, _ux]) -> 73
(append([t1, l2, _ix])) -> append([cons(h1, t1), l2, cons(h1, _ix)]) -> 71
(length([ll, _nx])) -> length([cons(x, ll), s(_nx)]) -> 70
}
Sat witness: Found: ((append([l1, l2, _rx]) /\ append([l2, l1, _tx]) /\ length([_rx, _sx]) /\ length([_tx, _ux])) -> eq_nat([_sx, _ux]), {
_rx -> cons(a, cons(b, cons(b, nil)))  ;  _sx -> s(s(s(z)))  ;  _tx -> cons(b, nil)  ;  _ux -> s(z)  ;  l1 -> nil  ;  l2 -> cons(a, nil)
})

-------------------------------------------
Step 68, which took 3.776531 s (model generation: 3.769751,  model checking: 0.006780):

Model:
|_
{
append -> 
{{{
Q={q_gen_6178, q_gen_6183, q_gen_6184, q_gen_6191, q_gen_6192, q_gen_6193, q_gen_6194, q_gen_6195, q_gen_6203},
Q_f={q_gen_6178, q_gen_6191},
Delta=
{
<cons>(q_gen_6194, q_gen_6193) -> q_gen_6193
<nil>() -> q_gen_6193
<a>() -> q_gen_6194
<b>() -> q_gen_6194
<cons, cons>(q_gen_6184, q_gen_6183) -> q_gen_6183
<nil, nil>() -> q_gen_6183
<a, a>() -> q_gen_6184
<a, b>() -> q_gen_6184
<b, a>() -> q_gen_6184
<b, b>() -> q_gen_6184
<cons, cons>(q_gen_6184, q_gen_6203) -> q_gen_6203
<nil, cons>(q_gen_6194, q_gen_6193) -> q_gen_6203
<cons, cons, cons>(q_gen_6195, q_gen_6191) -> q_gen_6178
<cons, nil, cons>(q_gen_6184, q_gen_6183) -> q_gen_6178
<nil, cons, cons>(q_gen_6184, q_gen_6183) -> q_gen_6178
<nil, nil, nil>() -> q_gen_6178
<cons, cons, cons>(q_gen_6195, q_gen_6192) -> q_gen_6191
<cons, cons, cons>(q_gen_6195, q_gen_6178) -> q_gen_6192
<cons, nil, cons>(q_gen_6184, q_gen_6203) -> q_gen_6192
<nil, cons, cons>(q_gen_6184, q_gen_6203) -> q_gen_6192
<nil, nil, cons>(q_gen_6194, q_gen_6193) -> q_gen_6192
<a, a, a>() -> q_gen_6195
<a, b, a>() -> q_gen_6195
<b, a, b>() -> q_gen_6195
<b, b, b>() -> q_gen_6195
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_6177, q_gen_6180, q_gen_6181, q_gen_6197, q_gen_6198, q_gen_6199, q_gen_6200, q_gen_6205, q_gen_6216, q_gen_6217, q_gen_6218, q_gen_6239},
Q_f={q_gen_6177},
Delta=
{
<cons>(q_gen_6198, q_gen_6216) -> q_gen_6180
<nil>() -> q_gen_6180
<cons>(q_gen_6198, q_gen_6180) -> q_gen_6197
<a>() -> q_gen_6198
<b>() -> q_gen_6198
<s>(q_gen_6239) -> q_gen_6200
<z>() -> q_gen_6200
<cons>(q_gen_6198, q_gen_6197) -> q_gen_6216
<s>(q_gen_6200) -> q_gen_6218
<s>(q_gen_6218) -> q_gen_6239
<cons, s>(q_gen_6181, q_gen_6180) -> q_gen_6177
<cons, s>(q_gen_6199, q_gen_6197) -> q_gen_6177
<cons, s>(q_gen_6217, q_gen_6216) -> q_gen_6177
<nil, z>() -> q_gen_6177
<a, s>(q_gen_6239) -> q_gen_6181
<a, z>() -> q_gen_6181
<b, s>(q_gen_6239) -> q_gen_6181
<b, z>() -> q_gen_6181
<a, s>(q_gen_6200) -> q_gen_6199
<b, s>(q_gen_6200) -> q_gen_6199
<cons, s>(q_gen_6181, q_gen_6197) -> q_gen_6205
<cons, s>(q_gen_6181, q_gen_6216) -> q_gen_6205
<cons, s>(q_gen_6199, q_gen_6180) -> q_gen_6205
<cons, s>(q_gen_6199, q_gen_6216) -> q_gen_6205
<cons, s>(q_gen_6217, q_gen_6180) -> q_gen_6205
<cons, s>(q_gen_6217, q_gen_6197) -> q_gen_6205
<a, s>(q_gen_6218) -> q_gen_6217
<b, s>(q_gen_6218) -> q_gen_6217
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 67
() -> length([nil, z]) -> 63
(append([l1, l2, _rx]) /\ append([l2, l1, _tx]) /\ length([_rx, _sx]) /\ length([_tx, _ux])) -> eq_nat([_sx, _ux]) -> 73
(append([t1, l2, _ix])) -> append([cons(h1, t1), l2, cons(h1, _ix)]) -> 74
(length([ll, _nx])) -> length([cons(x, ll), s(_nx)]) -> 71
}
Sat witness: Found: ((append([t1, l2, _ix])) -> append([cons(h1, t1), l2, cons(h1, _ix)]), {
_ix -> cons(b, cons(a, cons(a, nil)))  ;  h1 -> a  ;  l2 -> cons(a, cons(b, cons(b, nil)))  ;  t1 -> cons(b, cons(a, nil))
})

-------------------------------------------
Step 69, which took 9.414646 s (model generation: 9.407963,  model checking: 0.006683):

Model:
|_
{
append -> 
{{{
Q={q_gen_6178, q_gen_6183, q_gen_6184, q_gen_6185, q_gen_6192, q_gen_6193, q_gen_6194, q_gen_6195, q_gen_6203},
Q_f={q_gen_6178, q_gen_6185},
Delta=
{
<cons>(q_gen_6194, q_gen_6193) -> q_gen_6193
<nil>() -> q_gen_6193
<a>() -> q_gen_6194
<b>() -> q_gen_6194
<cons, cons>(q_gen_6184, q_gen_6183) -> q_gen_6183
<nil, nil>() -> q_gen_6183
<a, a>() -> q_gen_6184
<a, b>() -> q_gen_6184
<b, a>() -> q_gen_6184
<b, b>() -> q_gen_6184
<cons, cons>(q_gen_6184, q_gen_6203) -> q_gen_6203
<nil, cons>(q_gen_6194, q_gen_6193) -> q_gen_6203
<cons, cons, cons>(q_gen_6195, q_gen_6185) -> q_gen_6178
<cons, nil, cons>(q_gen_6184, q_gen_6183) -> q_gen_6178
<nil, nil, nil>() -> q_gen_6178
<cons, cons, cons>(q_gen_6195, q_gen_6192) -> q_gen_6185
<nil, cons, cons>(q_gen_6184, q_gen_6183) -> q_gen_6185
<cons, cons, cons>(q_gen_6195, q_gen_6178) -> q_gen_6192
<cons, nil, cons>(q_gen_6184, q_gen_6203) -> q_gen_6192
<nil, cons, cons>(q_gen_6184, q_gen_6203) -> q_gen_6192
<nil, nil, cons>(q_gen_6194, q_gen_6193) -> q_gen_6192
<a, a, a>() -> q_gen_6195
<a, b, a>() -> q_gen_6195
<b, a, b>() -> q_gen_6195
<b, b, b>() -> q_gen_6195
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_6177, q_gen_6180, q_gen_6181, q_gen_6197, q_gen_6198, q_gen_6199, q_gen_6200, q_gen_6205, q_gen_6216, q_gen_6217, q_gen_6218, q_gen_6239},
Q_f={q_gen_6177},
Delta=
{
<cons>(q_gen_6198, q_gen_6216) -> q_gen_6180
<nil>() -> q_gen_6180
<cons>(q_gen_6198, q_gen_6180) -> q_gen_6197
<a>() -> q_gen_6198
<b>() -> q_gen_6198
<s>(q_gen_6239) -> q_gen_6200
<z>() -> q_gen_6200
<cons>(q_gen_6198, q_gen_6197) -> q_gen_6216
<s>(q_gen_6200) -> q_gen_6218
<s>(q_gen_6218) -> q_gen_6239
<cons, s>(q_gen_6181, q_gen_6180) -> q_gen_6177
<cons, s>(q_gen_6199, q_gen_6197) -> q_gen_6177
<cons, s>(q_gen_6217, q_gen_6216) -> q_gen_6177
<nil, z>() -> q_gen_6177
<a, s>(q_gen_6239) -> q_gen_6181
<a, z>() -> q_gen_6181
<b, s>(q_gen_6239) -> q_gen_6181
<b, z>() -> q_gen_6181
<a, s>(q_gen_6200) -> q_gen_6199
<b, s>(q_gen_6200) -> q_gen_6199
<cons, s>(q_gen_6181, q_gen_6197) -> q_gen_6205
<cons, s>(q_gen_6181, q_gen_6216) -> q_gen_6205
<cons, s>(q_gen_6199, q_gen_6180) -> q_gen_6205
<cons, s>(q_gen_6199, q_gen_6216) -> q_gen_6205
<cons, s>(q_gen_6217, q_gen_6180) -> q_gen_6205
<cons, s>(q_gen_6217, q_gen_6197) -> q_gen_6205
<a, s>(q_gen_6218) -> q_gen_6217
<b, s>(q_gen_6218) -> q_gen_6217
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 68
() -> length([nil, z]) -> 64
(append([l1, l2, _rx]) /\ append([l2, l1, _tx]) /\ length([_rx, _sx]) /\ length([_tx, _ux])) -> eq_nat([_sx, _ux]) -> 76
(append([t1, l2, _ix])) -> append([cons(h1, t1), l2, cons(h1, _ix)]) -> 74
(length([ll, _nx])) -> length([cons(x, ll), s(_nx)]) -> 72
}
Sat witness: Found: ((append([l1, l2, _rx]) /\ append([l2, l1, _tx]) /\ length([_rx, _sx]) /\ length([_tx, _ux])) -> eq_nat([_sx, _ux]), {
_rx -> cons(b, cons(b, cons(b, nil)))  ;  _sx -> s(s(s(z)))  ;  _tx -> cons(b, cons(b, cons(b, cons(b, nil))))  ;  _ux -> s(z)  ;  l1 -> cons(b, nil)  ;  l2 -> cons(b, nil)
})

-------------------------------------------
Step 70, which took 7.075748 s (model generation: 7.058732,  model checking: 0.017016):

Model:
|_
{
append -> 
{{{
Q={q_gen_6178, q_gen_6182, q_gen_6183, q_gen_6184, q_gen_6192, q_gen_6193, q_gen_6194, q_gen_6195, q_gen_6202, q_gen_6203, q_gen_6222},
Q_f={q_gen_6178, q_gen_6182},
Delta=
{
<cons>(q_gen_6194, q_gen_6193) -> q_gen_6193
<nil>() -> q_gen_6193
<a>() -> q_gen_6194
<b>() -> q_gen_6194
<cons, cons>(q_gen_6184, q_gen_6183) -> q_gen_6183
<nil, nil>() -> q_gen_6183
<a, a>() -> q_gen_6184
<a, b>() -> q_gen_6184
<b, a>() -> q_gen_6184
<b, b>() -> q_gen_6184
<cons, cons>(q_gen_6184, q_gen_6203) -> q_gen_6203
<nil, cons>(q_gen_6194, q_gen_6193) -> q_gen_6203
<cons, cons, cons>(q_gen_6195, q_gen_6202) -> q_gen_6178
<cons, cons, cons>(q_gen_6222, q_gen_6178) -> q_gen_6178
<nil, cons, cons>(q_gen_6184, q_gen_6183) -> q_gen_6178
<nil, nil, nil>() -> q_gen_6178
<cons, cons, cons>(q_gen_6195, q_gen_6182) -> q_gen_6182
<cons, cons, cons>(q_gen_6195, q_gen_6192) -> q_gen_6182
<cons, cons, cons>(q_gen_6222, q_gen_6182) -> q_gen_6182
<cons, cons, cons>(q_gen_6222, q_gen_6202) -> q_gen_6182
<cons, nil, cons>(q_gen_6184, q_gen_6183) -> q_gen_6182
<cons, cons, cons>(q_gen_6195, q_gen_6178) -> q_gen_6192
<nil, nil, cons>(q_gen_6194, q_gen_6193) -> q_gen_6192
<a, b, a>() -> q_gen_6195
<b, a, b>() -> q_gen_6195
<b, b, b>() -> q_gen_6195
<cons, cons, cons>(q_gen_6222, q_gen_6192) -> q_gen_6202
<cons, nil, cons>(q_gen_6184, q_gen_6203) -> q_gen_6202
<nil, cons, cons>(q_gen_6184, q_gen_6203) -> q_gen_6202
<a, a, a>() -> q_gen_6222
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_6177, q_gen_6180, q_gen_6181, q_gen_6197, q_gen_6198, q_gen_6199, q_gen_6200, q_gen_6205, q_gen_6216, q_gen_6217, q_gen_6218},
Q_f={q_gen_6177},
Delta=
{
<nil>() -> q_gen_6180
<cons>(q_gen_6198, q_gen_6180) -> q_gen_6197
<cons>(q_gen_6198, q_gen_6216) -> q_gen_6197
<a>() -> q_gen_6198
<b>() -> q_gen_6198
<s>(q_gen_6218) -> q_gen_6200
<z>() -> q_gen_6200
<cons>(q_gen_6198, q_gen_6197) -> q_gen_6216
<s>(q_gen_6200) -> q_gen_6218
<cons, s>(q_gen_6181, q_gen_6180) -> q_gen_6177
<cons, s>(q_gen_6199, q_gen_6197) -> q_gen_6177
<cons, s>(q_gen_6217, q_gen_6216) -> q_gen_6177
<nil, z>() -> q_gen_6177
<a, z>() -> q_gen_6181
<b, z>() -> q_gen_6181
<a, s>(q_gen_6200) -> q_gen_6199
<b, s>(q_gen_6200) -> q_gen_6199
<cons, s>(q_gen_6181, q_gen_6197) -> q_gen_6205
<cons, s>(q_gen_6181, q_gen_6216) -> q_gen_6205
<cons, s>(q_gen_6199, q_gen_6180) -> q_gen_6205
<cons, s>(q_gen_6199, q_gen_6216) -> q_gen_6205
<cons, s>(q_gen_6217, q_gen_6180) -> q_gen_6205
<cons, s>(q_gen_6217, q_gen_6197) -> q_gen_6205
<a, s>(q_gen_6218) -> q_gen_6217
<b, s>(q_gen_6218) -> q_gen_6217
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 69
() -> length([nil, z]) -> 65
(append([l1, l2, _rx]) /\ append([l2, l1, _tx]) /\ length([_rx, _sx]) /\ length([_tx, _ux])) -> eq_nat([_sx, _ux]) -> 76
(append([t1, l2, _ix])) -> append([cons(h1, t1), l2, cons(h1, _ix)]) -> 77
(length([ll, _nx])) -> length([cons(x, ll), s(_nx)]) -> 73
}
Sat witness: Found: ((append([t1, l2, _ix])) -> append([cons(h1, t1), l2, cons(h1, _ix)]), {
_ix -> cons(b, cons(a, cons(a, cons(a, nil))))  ;  h1 -> a  ;  l2 -> cons(a, cons(a, cons(b, nil)))  ;  t1 -> cons(b, cons(a, cons(a, nil)))
})

-------------------------------------------
Step 71, which took 5.045407 s (model generation: 5.042494,  model checking: 0.002913):

Model:
|_
{
append -> 
{{{
Q={q_gen_6178, q_gen_6182, q_gen_6183, q_gen_6184, q_gen_6186, q_gen_6187, q_gen_6192, q_gen_6193, q_gen_6194, q_gen_6195, q_gen_6210, q_gen_6212, q_gen_6213, q_gen_6221, q_gen_6231, q_gen_6232, q_gen_6243, q_gen_6244, q_gen_6268, q_gen_6269, q_gen_6275, q_gen_6278, q_gen_6283},
Q_f={q_gen_6178, q_gen_6182, q_gen_6210, q_gen_6244, q_gen_6268, q_gen_6269, q_gen_6278},
Delta=
{
<cons>(q_gen_6194, q_gen_6232) -> q_gen_6193
<nil>() -> q_gen_6193
<b>() -> q_gen_6194
<a>() -> q_gen_6212
<cons>(q_gen_6194, q_gen_6193) -> q_gen_6232
<cons, cons>(q_gen_6184, q_gen_6221) -> q_gen_6183
<cons, cons>(q_gen_6275, q_gen_6221) -> q_gen_6183
<nil, cons>(q_gen_6194, q_gen_6193) -> q_gen_6183
<nil, nil>() -> q_gen_6183
<b, b>() -> q_gen_6184
<cons, cons>(q_gen_6184, q_gen_6183) -> q_gen_6186
<cons, cons>(q_gen_6187, q_gen_6183) -> q_gen_6186
<a, a>() -> q_gen_6187
<cons, cons>(q_gen_6184, q_gen_6186) -> q_gen_6221
<nil, cons>(q_gen_6194, q_gen_6232) -> q_gen_6221
<nil, cons>(q_gen_6212, q_gen_6193) -> q_gen_6221
<a, b>() -> q_gen_6275
<b, a>() -> q_gen_6275
<cons, cons, cons>(q_gen_6195, q_gen_6182) -> q_gen_6178
<cons, cons, cons>(q_gen_6195, q_gen_6192) -> q_gen_6178
<cons, cons, cons>(q_gen_6195, q_gen_6231) -> q_gen_6178
<cons, cons, cons>(q_gen_6213, q_gen_6269) -> q_gen_6178
<nil, cons, cons>(q_gen_6184, q_gen_6183) -> q_gen_6178
<nil, cons, cons>(q_gen_6184, q_gen_6186) -> q_gen_6178
<nil, cons, cons>(q_gen_6187, q_gen_6183) -> q_gen_6178
<nil, nil, nil>() -> q_gen_6178
<cons, cons, cons>(q_gen_6195, q_gen_6243) -> q_gen_6182
<cons, cons, cons>(q_gen_6195, q_gen_6278) -> q_gen_6182
<cons, nil, cons>(q_gen_6184, q_gen_6183) -> q_gen_6182
<cons, nil, cons>(q_gen_6187, q_gen_6186) -> q_gen_6182
<nil, cons, cons>(q_gen_6184, q_gen_6221) -> q_gen_6182
<nil, cons, cons>(q_gen_6187, q_gen_6186) -> q_gen_6182
<cons, cons, cons>(q_gen_6195, q_gen_6178) -> q_gen_6192
<cons, cons, cons>(q_gen_6213, q_gen_6192) -> q_gen_6192
<nil, nil, cons>(q_gen_6194, q_gen_6193) -> q_gen_6192
<a, b, a>() -> q_gen_6195
<b, b, b>() -> q_gen_6195
<cons, cons, cons>(q_gen_6213, q_gen_6210) -> q_gen_6210
<cons, cons, cons>(q_gen_6213, q_gen_6243) -> q_gen_6210
<cons, nil, cons>(q_gen_6184, q_gen_6221) -> q_gen_6210
<nil, nil, cons>(q_gen_6212, q_gen_6193) -> q_gen_6210
<a, a, a>() -> q_gen_6213
<b, a, b>() -> q_gen_6213
<cons, cons, cons>(q_gen_6213, q_gen_6231) -> q_gen_6231
<nil, cons, cons>(q_gen_6275, q_gen_6221) -> q_gen_6231
<nil, nil, cons>(q_gen_6194, q_gen_6232) -> q_gen_6231
<cons, cons, cons>(q_gen_6195, q_gen_6244) -> q_gen_6243
<cons, cons, cons>(q_gen_6195, q_gen_6283) -> q_gen_6243
<cons, cons, cons>(q_gen_6213, q_gen_6178) -> q_gen_6243
<nil, cons, cons>(q_gen_6187, q_gen_6221) -> q_gen_6243
<nil, nil, cons>(q_gen_6212, q_gen_6232) -> q_gen_6243
<cons, nil, cons>(q_gen_6184, q_gen_6186) -> q_gen_6244
<cons, nil, cons>(q_gen_6187, q_gen_6183) -> q_gen_6244
<cons, cons, cons>(q_gen_6213, q_gen_6182) -> q_gen_6268
<cons, cons, cons>(q_gen_6213, q_gen_6244) -> q_gen_6269
<cons, cons, cons>(q_gen_6213, q_gen_6278) -> q_gen_6269
<cons, cons, cons>(q_gen_6195, q_gen_6210) -> q_gen_6278
<cons, cons, cons>(q_gen_6213, q_gen_6283) -> q_gen_6278
<cons, nil, cons>(q_gen_6187, q_gen_6221) -> q_gen_6283
<cons, nil, cons>(q_gen_6275, q_gen_6183) -> q_gen_6283
<nil, cons, cons>(q_gen_6275, q_gen_6183) -> q_gen_6283
<nil, cons, cons>(q_gen_6275, q_gen_6186) -> q_gen_6283
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_6177, q_gen_6180, q_gen_6181, q_gen_6197, q_gen_6198, q_gen_6199, q_gen_6200, q_gen_6205, q_gen_6216, q_gen_6218},
Q_f={q_gen_6177},
Delta=
{
<nil>() -> q_gen_6180
<cons>(q_gen_6198, q_gen_6180) -> q_gen_6197
<cons>(q_gen_6198, q_gen_6216) -> q_gen_6197
<a>() -> q_gen_6198
<b>() -> q_gen_6198
<s>(q_gen_6218) -> q_gen_6200
<z>() -> q_gen_6200
<cons>(q_gen_6198, q_gen_6197) -> q_gen_6216
<s>(q_gen_6200) -> q_gen_6218
<cons, s>(q_gen_6181, q_gen_6180) -> q_gen_6177
<cons, s>(q_gen_6181, q_gen_6216) -> q_gen_6177
<cons, s>(q_gen_6199, q_gen_6197) -> q_gen_6177
<cons, s>(q_gen_6199, q_gen_6216) -> q_gen_6177
<nil, z>() -> q_gen_6177
<a, z>() -> q_gen_6181
<b, s>(q_gen_6218) -> q_gen_6181
<b, z>() -> q_gen_6181
<a, s>(q_gen_6200) -> q_gen_6199
<a, s>(q_gen_6218) -> q_gen_6199
<b, s>(q_gen_6200) -> q_gen_6199
<cons, s>(q_gen_6181, q_gen_6197) -> q_gen_6205
<cons, s>(q_gen_6199, q_gen_6180) -> q_gen_6205
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 72
() -> length([nil, z]) -> 66
(append([l1, l2, _rx]) /\ append([l2, l1, _tx]) /\ length([_rx, _sx]) /\ length([_tx, _ux])) -> eq_nat([_sx, _ux]) -> 76
(append([t1, l2, _ix])) -> append([cons(h1, t1), l2, cons(h1, _ix)]) -> 77
(length([ll, _nx])) -> length([cons(x, ll), s(_nx)]) -> 73
}
Sat witness: Found: (() -> append([nil, l2, l2]), {
l2 -> cons(a, cons(b, cons(a, nil)))
})

Total time: 73.946814
Reason for stopping: DontKnow. Stopped because: timeout